G. Columns Swapstime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given a table a of size 2 \times n (i.e. two rows and n columns) consisting of integers from 1 to n.In one move, you can choose some column j (1 \le j \le n) and swap values a_{1, j} and a_{2, j} in it. Each column can be chosen no more than once.Your task is to find the minimum number of moves required to obtain permutations of size n in both first and second rows of the table or determine if it is impossible to do that.You have to answer t independent test cases.Recall that the permutation of size n is such an array of size n that contains each integer from 1 to n exactly once (the order of elements doesn't matter).InputThe first line of the input contains one integer t (1 \le t \le 2 \cdot 10^4) — the number of test cases. Then t test cases follow.The first line of the test case contains one integer n (1 \le n \le 2 \cdot 10^5) — the number of columns in the table. The second line of the test case contains n integers a_{1, 1}, a_{1, 2}, \dots, a_{1, n} (1 \le a_{1, i} \le n), where a_{1, i} is the i-th element of the first row of the table. The third line of the test case contains n integers a_{2, 1}, a_{2, 2}, \dots, a_{2, n} (1 \le a_{2, i} \le n), where a_{2, i} is the i-th element of the second row of the table.It is guaranteed that the sum of n does not exceed 2 \cdot 10^5 (\sum n \le 2 \cdot 10^5).OutputFor each test case print the answer: -1 if it is impossible to obtain permutation of size n in both first and the second rows of the table, or one integer k in the first line, where k is the minimum number of moves required to obtain permutations in both rows, and k distinct integers pos_1, pos_2, \dots, pos_k in the second line (1 \le pos_i \le n) in any order — indices of columns in which you need to swap values to obtain permutations in both rows. If there are several answers, you can print any.ExampleInput
6
4
1 2 3 4
2 3 1 4
5
5 3 5 1 4
1 2 3 2 4
3
1 2 1
3 3 2
4
1 2 2 1
3 4 3 4
4
4 3 1 4
3 2 2 1
3
1 1 2
3 2 2
Output
0

2
2 3 
1
1 
2
3 4 
2
3 4 
-1

6
4
1 2 3 4
2 3 1 4
5
5 3 5 1 4
1 2 3 2 4
3
1 2 1
3 3 2
4
1 2 2 1
3 4 3 4
4
4 3 1 4
3 2 2 1
3
1 1 2
3 2 2

0  2 2 3  1 1  2 3 4  2 3 4  -1 
['2-sat', 'dfs and similar', 'dsu', 'graphs', 'implementation', '*2300']