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 \le n \le 106) - the number of elements in permutation p.

The second line contains n distinct integers p1,p2,...,pn (1 \le pi \le 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 \le qi \le n) - the elements of the permutation q. If there are several solutions print any of them.