International Mathematical Olympiad 2003 Problem 5

Given $n > 2$ and reals $x_1 \leq x_2 \leq \cdots \leq x_n$, show that $(\sum_{i,j} |x_i - x_j|)^2 \leq \frac{2}{3}(n^2 - 1)\sum_{i,j}(x_i - x_j)^2$. Show that we have equality iff the sequence is an arithmetic progression.