NO-ABEL 1995 Problem 4

Let $x_i,y_i$ be positive real numbers, $i = 1,2,...,n$ . Prove that $$\left( \sum_{i=1}^n (x_i +y_i)^2\right)\left( \sum_{i=1}^n\frac{1}{x_iy_i}\right)\ge 4n^2$$