OME 1988 Problem 2

We choose $n > 3$ points on a circle and number them $1$ to $n$ in some order. We say that two non-adjacent points $A$ and $B$ are related if, in one of the arcs $AB$ , all the points are marked with numbers less than those at $A,B$ . Show that the number of pairs of related points is exactly $n-3$ .