CWMO 2015 Problem 3

Let the integer $n \ge 2$ , and $x_1,x_2,\cdots,x_n$ be positive real numbers such that $\sum_{i=1}^nx_i=1$ .Prove that $$\left(\sum_{i=1}^n\frac{1}{1-x_i}\right)\left(\sum_{1\le i<j\le n} x_ix_j\right)\le \frac{n}{2}.$$