CZ-SK-MO 2023 Problem 2

Let $n$ be a positive integer, where $n \geq 3$ and let $a_1, a_2, ..., a_n$ be the lengths of sides of some $n$ -gon. Prove that $$a_1 + a_2 + ... + a_n \geq \sqrt{2 \cdot (a_1^2 + a_2^2 + ... + a_n^2)}$$