CC sum

You are provided with an array $z1, z2, ...., zn$ of $n$ elements. The task is to find for each integer $i$ $(0 \leq i \lt n)$ number of ways to consequently choose one of the integers from the array $n$ times, so that the CC sum of these integers is equal to $i$. Before that, let's define CC sum of number '$p$' having digits $p1, …, pk$ and number '$q$' having digits $q1, …, qk$ (to equate the n