CF1622F Quadratic Set

Let's call a set of positive integers $ a_1, a_2, \dots, a_k $ quadratic if the product of the factorials of its elements is a square of an integer, i. e. $ \prod\limits_{i=1}^{k} a_i! = m^2 $ , for some integer $ m $ . You are given a positive integer $ n $ . Your task is to find a quadratic subset of a set $ 1, 2, \dots, n $ of maximum size. If there are multiple answers, print any of them.

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