Permutation Rounds

There is a sorted array [1,2,\dots,n] and a permutation p_1,p_2,\dots,p_n. On each round, all elements move according to the permutation: the element at position i moves to position p_i. After how many rounds is the array sorted again for the first time? Input The first line has an integer n. The next line contains n integers p_1,p_2,\dots,p_n. Output Print the number of rounds modulo 10^9+7