2 - Sums divisible by 3

Let's consider some multiset $A$ consisting of $0$s, $1$s, and $2$s. Define $S(A)$ to be the sum of the elements in $A$. It is guaranteed that $S(A)$ is divisible by $3$. You need to partition $A$ into some number of nonempty multisets $A_1, A_2, \ldots, A_k$ such that: - $A_1 \cup A_2 \cup \ldots \cup A_k = A$ - for all $1 \leq i \leq k$, $S(A_i)$ is divisible by $3$ You are given $s_0$