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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class ColumnSwaps {

	public static void solve(IO io) {
		int n = io.getInt();
		int[] val1 = new int[n];
		int[] val2 = new int[n];
		int[] count1 = new int[n];
		int[] count2 = new int[n];
		for (int i = 0; i < n; i++) {
			val1[i] = io.getInt() - 1;
			count1[val1[i]]++;
		}
		for (int i = 0; i < n; i++) {
			val2[i] = io.getInt() - 1;
			count2[val2[i]]++;
		}
		for (int i = 0; i < n; i++) {
			if (count1[i] + count2[i] != 2) {
				io.println(-1);
				return;
			}
		}
		int[] neigh1 = new int[n];
		int[] neigh2 = new int[n];
		int[] neigh1Index = new int[n];
		int[] neigh2Index = new int[n];
		for (int i = 0; i < n; i++) {
			neigh1[i] = -1;
			neigh2[i] = -1;
			neigh1Index[i] = -1;
			neigh2Index[i] = -1;
		}

		for (int i = 0; i < n; i++) {
			if (neigh1[val1[i]] == -1) {
				neigh1[val1[i]] = val2[i];
				neigh1Index[val1[i]] = i;
			} else {
				neigh2[val1[i]] = val2[i];
				neigh2Index[val1[i]] = i;
			}

			if (neigh1[val2[i]] == -1) {
				neigh1[val2[i]] = val1[i];
				neigh1Index[val2[i]] = i;
			} else {
				neigh2[val2[i]] = val1[i];
				neigh2Index[val2[i]] = i;
			}
		}

		boolean[] visited = new boolean[n];
		int totalCount = 0;
		
		ArrayList<Integer> pos = new ArrayList<>();
		
		for (int i = 0; i < n; i++) {
			if (visited[i])
				continue;

			int curr = i;
			visited[curr] = true;

			boolean counting = false;
			int count = 0;
			int cycle = 0;

			ArrayList<Pair> smol = new ArrayList<>();
			while(true) {
				if (count1[curr] == 2 || count2[curr] == 2) {
					counting = !counting;
				}
				if (counting) {
					count++;
				}
				
				cycle++;
				
				if (!visited[neigh1[curr]]) {
					smol.add(new Pair(neigh1Index[curr],counting));
					curr = neigh1[curr];
				} else if (!visited[neigh2[curr]]) {
					smol.add(new Pair(neigh2Index[curr],counting));
					curr = neigh2[curr];
				} else {
					if (neigh1[curr] == i) {
						smol.add(new Pair(neigh1Index[curr],counting));
					} else if (neigh2[curr] == i) {
						smol.add(new Pair(neigh2Index[curr],counting));
					}
					break;
				}
				visited[curr] = true;
			}
			
			boolean check = false;
			if (count < cycle - count) {
				check = true;
				totalCount += count;
			} else {
				totalCount += cycle - count;
			}
			for (Pair pair:smol) {
				if (check == pair.b) {
					pos.add(pair.index);
				}
			}
			
			

		}
		io.println(totalCount);
		for (int a : pos) {
			io.print(a + 1 + " ");
		}
		io.println();

	}
	
	static class Pair {
		
		int index;
		boolean b;
		
		public Pair(int i, boolean bo) {
			index = i;
			b = bo;
		}
	}
	

	public static void main(String[] args) {
		IO io = new IO();
		int t = io.getInt();
		for (int testIndex = 0; testIndex < t; testIndex++) {
			solve(io);
		}
		io.close();
	}

	static class IO extends PrintWriter {

		public IO() {
			super(new BufferedOutputStream(System.out));
			r = new BufferedReader(new InputStreamReader(System.in));
		}

		public IO(InputStream i) {
			super(new BufferedOutputStream(System.out));
			r = new BufferedReader(new InputStreamReader(i));
		}

		public IO(InputStream i, OutputStream o) {
			super(new BufferedOutputStream(o));
			r = new BufferedReader(new InputStreamReader(i));
		}

		public boolean hasMoreTokens() {
			return peekToken() != null;
		}

		public int getInt() {
			return Integer.parseInt(nextToken());
		}

		public double getDouble() {
			return Double.parseDouble(nextToken());
		}

		public long getLong() {
			return Long.parseLong(nextToken());
		}

		public String getWord() {
			return nextToken();
		}

		private BufferedReader r;
		private String line;
		private StringTokenizer st;
		private String token;

		private String peekToken() {
			if (token == null)
				try {
					while (st == null || !st.hasMoreTokens()) {
						line = r.readLine();
						if (line == null)
							return null;
						st = new StringTokenizer(line);
					}
					token = st.nextToken();
				} catch (IOException e) {
				}
			return token;
		}

		private String nextToken() {
			String ans = peekToken();
			token = null;
			return ans;
		}
	}

}
