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, ..., p_n (1 ≤ p_i ≤ 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 q_i (1 ≤ q_i ≤ n) — the elements of the permutation q. If there are several solutions print any of them.