<s>[INST] A box of $n$ balls, in which each ball is painted one of $c$ possible colors, is called special if for every integer $k \ge 0$ such that $2k \le n$, there is at least one ball such that exactly $2k$ of the balls in the box have the same color as this ball. We are given that $c=10$ and $n=100$, and we want to find the minimum number of balls of each color that in total form a special box.[/INST]