IMO Shortlist 1966 problem 13

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

Izvor: Međunarodna matematička olimpijada, shortlist 1966

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IMO Shortlist 1966 problem 13