ILL 1966 Problem 13

Let $a_1, a_2, \ldots, a_n$ be positive real numbers. Prove the inequality $$\binom n2 \sum_{i<j} \frac{1}{a_ia_j} \geq 4 \left( \sum_{i<j} \frac{1}{a_i+a_j} \right)^2$$