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

@SuppressWarnings("unchecked")
public class Problem_G {
	static class Edge {
		int n, u, v;
		boolean tof;

		Edge(int n, int u, int v) {
			this.n = n;
			this.u = u;
			this.v = v;
		}
	}

	static List<Edge>[] G;
	static List<Integer> Q, W;

	public static void dfs(int x) {
		for (Edge e : G[x]) {
			if (e.tof) {
				continue;
			}
			e.tof = true;
			if (x == e.u) {
				Q.add(e.n);
				dfs(e.v);
			} else {
				W.add(e.n);
				dfs(e.u);
			}
		}
	}

	public static void main(String[] args) {
		InputReader in = new InputReader();
		StringBuilder out = new StringBuilder();

		int T = in.nextInt();
		while (T-- > 0) {
			int N = in.nextInt();
			int[][] A = new int[2][N];
			for (int i = 0; i < 2; i++) {
				for (int j = 0; j < N; j++) {
					A[i][j] = in.nextInt();
				}
			}
			int[] cnt = new int[N + 1];
			for (int i = 0; i < 2; i++) {
				for (int j = 0; j < N; j++) {
					cnt[A[i][j]]++;
				}
			}
			boolean flag = true;
			for (int i = 1; i <= N; i++) {
				if (cnt[i] == 2) {
					continue;
				}
				flag = false;
				break;
			}
			if (!flag) {
				out.append("-1\n");
				continue;
			}
			G = new List[N + 1];
			for (int i = 1; i <= N; i++) {
				G[i] = new ArrayList<>();
			}
			boolean[] chk = new boolean[N + 1];
			for (int i = 0; i < N; i++) {
				if (A[0][i] == A[1][i]) {
					chk[A[0][i]] = true;
					continue;
				}
				Edge e = new Edge(i + 1, A[0][i], A[1][i]);
				G[A[0][i]].add(e);
				G[A[1][i]].add(e);
			}
			Q = new ArrayList<>();
			W = new ArrayList<>();
			List<Integer> pos = new ArrayList<>();
			for (int i = 1; i <= N; i++) {
				if (chk[i]) {
					continue;
				}
				Q.clear();
				W.clear();
				dfs(i);
				pos.addAll(Q.size() < W.size() ? Q : W);
			}
			out.append(pos.size()).append('\n');
			for (int x : pos) {
				out.append(x).append(' ');
			}
			out.setCharAt(out.length() - 1, '\n');
			if (pos.isEmpty()) {
				out.append('\n');
			}
		}

		System.out.print(out);
	}

	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer st;

		public InputReader() {
			reader = new BufferedReader(new InputStreamReader(System.in));
		}

		public String next() {
			while (st == null || !st.hasMoreTokens()) {
				st = new StringTokenizer(nextLine());
			}
			return st.nextToken();
		}

		public String nextLine() {
			try {
				return reader.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return null;
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}
	}
}
