You are given a table a of size 2 × 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 ≤ j ≤ 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 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow.

The first line of the test case contains one integer n (1 ≤ n ≤ 2 ⋅ 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}, ..., a_{1, n} (1 ≤ a_{1, i} ≤ 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}, ..., a_{2, n} (1 ≤ a_{2, i} ≤ 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 ⋅ 10^5 (∑ n ≤ 2 ⋅ 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, ..., pos_k in the second line (1 ≤ pos_i ≤ 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
from sys import stdin, gettrace

if gettrace():
    inputi = input
else:
    def input():
        return next(stdin)[:-1]


    def inputi():
        return stdin.buffer.readline()


def solve():
    n = int(inputi())
    aa = []
    aa.append([0] + [int(a) for a in inputi().split()])
    aa.append([0] + [int(a) for a in inputi().split()])
    ndx = [[[] for _ in range(n+1)] for _ in range(2)]
    for i in range(n+1):
        ndx[0][aa[0][i]].append(i)
        ndx[1][aa[1][i]].append(i)
    res = set()
    for i in range(1, n+1):
        if len(ndx[0][i]) + len(ndx[1][i]) != 2:
            print(-1)
            return
        for r in range(2):
            if len(ndx[r][i]) == 2:
                swaps = []
                nsc = []
                for j in range(2):
                    c = ndx[r][i][j]
                    swaps.append([c])
                    nsc.append(1)
                    v = aa[1-r][c]
                    while len(ndx[1-r][v]) == 1:
                        if len(ndx[r][v]) != 1:
                            print(-1)
                            return
                        c = ndx[r][v][0]
                        swaps[-1].append(c)
                        nsc[-1] += -1 if c in res else 1
                        v = aa[1-r][c]
                swaps = swaps[0] if nsc[0] <= nsc[1] else swaps[1]
                for c in swaps:
                    ndx[0][aa[0][c]].remove(c)
                    ndx[1][aa[1][c]].remove(c)
                    aa[0][c], aa[1][c] = aa[1][c], aa[0][c]
                    ndx[0][aa[0][c]].append(c)
                    ndx[1][aa[1][c]].append(c)
                    if c in res:
                        res.remove(c)
                    else:
                        res.add(c)
    print(len(res))
    print(' '.join(map(str, res)))









def main():
    t = int(inputi())
    for _ in range(t):
        solve()


if __name__ == "__main__":
    main()