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
import sys

def input():
	return sys.stdin.readline().strip()

def solve():
	n = int(input())
	a = list(map(int,input().split()))
	b = list(map(int,input().split()))
	pos = [[] for i in range(n+1)]
	for i in range(n):
		pos[a[i]].extend((i,0))
		pos[b[i]].extend((i,1))
		if len(pos[a[i]]) > 4 \
		or len(pos[b[i]]) > 4:
			print(-1)
			return
	was = [False]*(n+1)
	res = []
	for i in range(1, n):
		if not was[i]:
			x = i
			p = pos[i][0]
			if pos[i][1] == 1:
				one, two = [p], []
			else:
				one, two = [], [p]
			first = p
			while True:
				was[x] = True
				if pos[x][0] == p:
					p = pos[x][2]
					if p == first:
						break
					r = pos[x][3]
				else:
					p = pos[x][0]
					if p == first:
						break
					r = pos[x][1]
				if r == 0:
					one.append(p)
					x = b[p]
				else:
					two.append(p)
					x = a[p]
			if len(one) > len(two):
				one = two
			res.extend(one)
	'''for i in res:
		a[i], b[i] = b[i], a[i]
	if len(set(a)) != n:
		print(-1)
		return'''
	print(len(res))
	print(' '.join([str(i+1) for i in res]))

for i in range(int(input())):
	solve()
