E. Square Root of Permutationtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputA 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.InputThe 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.OutputIf 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.ExamplesInput42 1 4 3Output3 4 2 1Input42 1 3 4Output-1Input52 3 4 5 1Output4 5 1 2 3
Input42 1 4 3
Output3 4 2 1
['combinatorics', 'constructive algorithms', 'dfs and similar', 'graphs', 'math', '*2200']