ISL 1995 A6

Let $n$ be an integer, $n \geq 3.$ Let $x_1, x_2, \ldots, x_n$ be real numbers such that $x_i < x_{i+1}$ for $1 \leq i \leq n - 1$ . Prove that

$$\frac{n(n-1)}{2} \sum_{i < j} x_ix_j > \left(\sum^{n-1}_{i=1} (n-i)\cdot x_i \right) \cdot \left(\sum^{n}_{j=2} (j-1) \cdot x_j \right)$$