1385_G. Columns Swaps
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
```python
for t in range(int(input())):
    n = int(input())
    aa = [
        [int(s)-1 for s in input().split(' ')]
        for _ in [0, 1]
    ]
    maxv = max(max(aa[0]), max(aa[1]))
    minv = min(min(aa[0]), min(aa[1]))
    if minv != 0 or maxv != n - 1:
        print(-1)
        continue
    counts = [0] * n
    index = [[] for _ in range(n)]
    for row in aa:
        for x, a in enumerate(row):
            counts[a] += 1
            index[a] += [x]
    if not min(counts) == 2 == max(counts):
        print(-1)
        continue

    proc = [False] * n
    ans = []
    for i in range(n):
        if proc[i]:
            continue

        swapped = set()
        used = set()

        curcol = i
        curval = aa[0][i]
        while True:
            proc[curcol] = True
            used.add(curcol)
            if aa[0][curcol] == curval:
                nexval = aa[1][curcol]
            else:
                nexval = aa[0][curcol]
                swapped.add(curcol)

            nexcol = index[nexval][1] if index[nexval][0] == curcol else index[nexval][0]

            curcol = nexcol
            curval = nexval

            if curcol == i:
                break
            
        part = swapped if 2 * len(swapped) <= len(used) else used.difference(swapped)
        ans += part

    print(len(ans))
    print(' '.join(str(v + 1) for v in ans))

```