IMC 2007 Problem 4

Let $G$ be a finite group. For arbitrary sets $U, V, W \subset G$ , denote by $N_{UVW}$ the number of triples $(x, y, z) \in U \times V \times W$ for which $xyz$ is the unity . Suppose that $G$ is partitioned into three sets $A, B$ and $C$ (i.e. sets $A, B, C$ are pairwise disjoint and $G = A \cup B \cup C$ ). Prove that $N_{ABC}= N_{CBA}.$