A - 3 Partition

You are given $3 \cdot N$ numbers $A_1, A_2, \ldots, A_{3N}$ ($1 \le A_i \le 3$). You need to partition these $3N$ integers into $N$ triplets, each of size $3$. Each of the triplets must have the same sum. Formally, let $B_i = [C_{(i, 1)}, C_{(i, 2)}, C_{(i, 3)}]$ be the $i$-th triplet, then $C_{(i, 1)} + C_{(i, 2)} + C_{(i, 3)} = C_{(j, 1)} + C_{(j, 2)} + C_{(j, 3)}$ for all $1 \le i, j \le N$