CF612E Square Root of Permutation

A permutation of length $ n $ is an array containing each integer from $ 1 $ to $ n $ exactly once. For example, $ q=[4,5,1,2,3] $ is a permutation. For the permutation $ q $ the square of permutation is the permutation $ p $ that $ p[i]=q[q[i]] $ for each $ i=1...\ n $ . For example, the square of $ q=[4,5,1,2,3] $ is $ p=q^{2}=[2,3,4,5,1] $ . This problem is about the inverse operation: given the permutation $ p $ you task is to find such permutation $ q $ that $ q^{2}=p $ . If there are several such $ q $ find any of them.

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