Square Root of Permutation

题意翻译

给定一个$n$的排列$p_i$，求一个排列$q_i$，使得对于任意$1\leq i\leq n$，$q_{q_i}=p_i$。无解输出$-1$。 $1\leq n\leq10^6$。

题目描述

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=q^{2}=[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 $ q^{2}=p $ . If there are several such $ q $ find any of them.

输入输出格式

输入格式

The first line contains integer $ n $ ( $ 1<=n<=10^{6} $ ) — the number of elements in permutation $ p $ . The second line contains $ n $ distinct integers $ p_{1},p_{2},...,p_{n} $ ( $ 1<=p_{i}<=n $ ) — the elements of permutation $ p $ .

输出格式

If there is no permutation $ q $ such that $ q^{2}=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.

输入输出样例

输入样例 #1

4
2 1 4 3

输出样例 #1

3 4 2 1

输入样例 #2

4
2 1 3 4

输出样例 #2

-1

输入样例 #3

5
2 3 4 5 1

输出样例 #3

4 5 1 2 3