CGMO 2015 Problem 7

Let $x_1,x_2,\cdots,x_n \in(0,1)$ , $n\geq2$ . Prove that $$\frac{\sqrt{1-x_1}}{x_1}+\frac{\sqrt{1-x_2}}{x_2}+\cdots+\frac{\sqrt{1-x_n}}{x_n}<\frac{\sqrt{n-1}}{x_1 x_2 \cdots x_n}.$$