Given is a positive integer $n \geq 2$ and three pairwise disjoint sets $A, B, C$, each of $n$ distinct real numbers. Denote by $a$ the number of triples $(x, y, z) \in A \times B \times C$ satisfying $x<y<z$ and let $b$ denote the number of triples $(x, y, z) \in A \times B \times C$ such that $x>y>z$. Prove that $n$ divides $a-b$.