CF2033E Sakurako, Kosuke, and the Permutation

Sakurako's exams are over, and she did excellently. As a reward, she received a permutation $ p $ . Kosuke was not entirely satisfied because he failed one exam and did not receive a gift. He decided to sneak into her room (thanks to the code for her lock) and spoil the permutation so that it becomes simple. A permutation $ p $ is considered simple if for every $ i $ $ (1\le i \le n) $ one of the following conditions holds: - $ p_i=i $ - $ p_{p_i}=i $ For example, the permutations $ [1, 2, 3, 4] $ , $ [5, 2, 4, 3, 1] $ , and $ [2, 1] $ are simple, while $ [2, 3, 1] $ and $ [5, 2, 1, 4, 3] $ are not. In one operation, Kosuke can choose indices $ i,j $ $ (1\le i,j\le n) $ and swap the elements $ p_i $ and $ p_j $ . Sakurako is about to return home. Your task is to calculate the minimum number of operations that Kosuke needs to perform to make the permutation simple.

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In the first and second examples, the permutations are already simple. In the fourth example, it is sufficient to swap $ p_2 $ and $ p_4 $ . Thus, the permutation will become $ [2, 1, 4, 3] $ in $ 1 $ operation.