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
t = int(input())
Maxn = 210000
while t > 0:
	t -= 1
	n = int(input())
	a = input().split()
	b = input().split()
	a1 = [-1] * (n + 1)
	a2 = [-1] * (n + 1)
	b1 = [-1] * (n + 1)
	b2 = [-1] * (n + 1)
	for i in range(0, n):
		now = int(a[i])
		if a1[now] == -1:
			a1[now] = i
			b1[now] = 1
		else:
			a2[now] = i
			b2[now] = 1
		now = int(b[i])
		if a1[now] == -1:
			a1[now] = i
			b1[now] = 2
		else:
			a2[now] = i
			b2[now] = 2
	flag = 0
	for i in range(1, n + 1):
		if a2[i] == -1:
			print("-1")
			flag = 1
			break
	if flag:
		continue
	to = []
	nxt = []
	w = []
	que = []
	first = [-1] * (n + 1)
	col = [-1] * (n + 1)
	
	
	def add(u, v, wi):
		to.append(v)
		nxt.append(first[u])
		w.append(wi)
		first[u] = len(to) - 1
		to.append(u)
		nxt.append(first[v])
		first[v] = len(to) - 1
		w.append(wi)
	
	
	for i in range(1, n + 1):
		if a1[i] == a2[i]:
			continue
		elif b1[i] == b2[i]:
			add(a1[i], a2[i], 1)
		else:
			add(a1[i], a2[i], 0)
	ans = []
	for i in range(0, n):
		if first[i] != -1 and col[i] == -1:
			col[i] = 0
			que.append(i)
			q = [[i], []]
			while len(que):
				now = que.pop()
				cur = first[now]
				while cur != -1:
					if col[to[cur]] == -1:
						if w[cur] == 0:
							col[to[cur]] = col[now]
						else:
							col[to[cur]] = (col[now] + 1) % 2
						q[col[to[cur]]].append(to[cur])
						que.append(to[cur])
					cur = nxt[cur]
			if len(q[0]) < len(q[1]):
				while len(q[0]):
					ans.append(q[0].pop() + 1)
			else:
				while len(q[1]):
					ans.append(q[1].pop() + 1)
	print(len(ans))
	for i in ans:
		print(i, end=' ')
	print('')
