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G. Columns Swaps

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard 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).

Input

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

Output

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.

Example

Input

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

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