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 java.util.*;
import java.io.*;

public class Swaps {
	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));

		int t = Integer.parseInt(br.readLine());

		while (--t >= 0) {
			int n = Integer.parseInt(br.readLine());

			int[][] a = new int[n][2];
			int[][] indices = new int[n][2];
			for (int[] row: indices) {
				Arrays.fill(row, -1);
			}
			boolean possible = true;

			for (int j = 0; j < 2; ++j) {
				String[] line = br.readLine().split(" ");
				for (int i = 0; i < n ; ++i) {
					a[i][j] = Integer.parseInt(line[i]) - 1;
					if (indices[a[i][j]][0] == -1) {
						indices[a[i][j]][0] = i;
					} else if (indices[a[i][j]][1] == -1) {
						indices[a[i][j]][1] = i;
					} else if (possible) {
						possible = false;
					}
				}
			}

			if (possible) {
				Deque<Integer> dif = new ArrayDeque<>();
				boolean[] visited = new boolean[n];

				for (int i = 0; i < n; ++i) {
					if (visited[i] || a[i][0] == a[i][1]) {
						continue;
					}
					Deque<Integer> group = new ArrayDeque<>();
					Set<Integer> swapped = new HashSet<>();
					int val = a[i][0];
					int index = indices[val][0] == i ? indices[val][1] : indices[val][0];
					group.add(i);
					visited[i] = true;

					while (!visited[index]) {
						visited[index] = true;
						group.add(index);
						if (a[index][1] == val) {
							val = a[index][0];
						} else {
							val = a[index][1];
							swapped.add(index);
						}
						index = indices[val][0] == index ? indices[val][1] : indices[val][0];
					}

					val = a[i][1];
					index = indices[val][0] == i ? indices[val][1] : indices[val][0];

					while (!visited[index]) {
						visited[index] = true;
						group.add(index);
						if (a[index][0] == val) {
							val = a[index][0];
						} else {
							val = a[index][1];
							swapped.add(index);
						}
						index = indices[val][0] == index ? indices[val][1] : indices[val][0];
					}

					boolean inv = swapped.size() >= group.size() - swapped.size();

					for (int place: group) {
						if (swapped.contains(place) ^ inv) {
							dif.add(place);
						}
					}
				}

				bw.write(Integer.toString(dif.size()));
				bw.newLine();
				for (int i: dif) {
					bw.write(Integer.toString(i + 1));
					bw.write(' ');
				}
				bw.newLine();
			} else {
				bw.write("-1\n");
			}
		}

		br.close();
		bw.close();
	}
}