There are $5$ boxes on the table. From left to right, each of them has $8,$ $4,$ $2,$ $1,$ and $5$ balls of the same size, respectively. Every time, Judy can take one ball each from the other four boxes, and then put them into the box with the smallest number of balls. She follows the rules and operates $2023$ times. Now how many balls are there in the first box counting from the left? 
Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem
Without operation: $$8$$, $$4$$, $$2$$, $$1$$, $$5$$  After the first operation: $$7$$, $$3$$, $$1$$, $$5$$, $$4$$  After the second operation: $$6$$, $$2$$, $$5$$, $$4$$, $$3$$  After the third operation: $$5$$, $$6$$, $$4$$, $$3$$, $$2$$  After the fourth operation: $$4$$, $$5$$, $$3$$, $$2$$, $$6$$  After the fifth operation: $$3$$, $$4$$, $$2$$, $$6$$, $$5$$  After the sixth operation: $$2$$, $$3$$, $$6$$, $$5$$, $$4$$  After the seventh operation: $$6$$, $$2$$, $$5$$, $$4$$, $$3$$  We can find that $6-2-5-4-3$ is repeating starting from the second operation.  $$（2023-1）\div5$$R$$2$$  Thus, after the $2023$\textsuperscript{rd}~operation, the result will be the same as the third one, which means there are $5$ balls in the first box. 