A13601 | Columns Swaps

You 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).

The 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 $2 \cdot 10^5$ ( $\sum n \le 2 \cdot 10^5$ ).

For 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.