CMO 1974 Problem 4

Let $n$ be a fixed positive integer. To any choice of real numbers satisfying $$0\le x_{i}\le 1, i=1,2,\ldots, n,$$ there corresponds the sum $$\sum_{1\le i<j\le n}|x_{i}-x_{j}|.$$ Let $S(n)$ denote the largest possible value of this sum. Find $S(n)$ .