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.
4
2 1 4 3
3 4 2 1
4
2 1 3 4
-1
5
2 3 4 5 1
4 5 1 2 3