IL-GILLIS 1995 Problem 5

Let $n$ be an odd positive integer and let $x_1,x_2,...,x_n$ be n distinct real numbers that satisfy $|x_i -x_j| \le 1$ for $1 \le i < j \le n$ . Prove that $$\sum_{i<j} |x_i -x_j| \le \left[\frac{n}{2} \right] \left(\left[\frac{n}{2} \right]-1 \right)$$