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 = q2 = [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 q2 = p. If there are several such q find any of them. The first line contains integer n (1 ≤ n ≤ 106) -- the number of elements in permutation p. The second line contains n distinct integers p1, p2, ..., pn (1 ≤ pi ≤ n) -- the elements of permutation p. If there is no permutation q such that q2 = p print the number "-1". If the answer exists print it. The only line should contain n different integers qi (1 ≤ qi ≤ n) -- the elements of the permutation q. If there are several solutions print any of them.