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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class G {
	
	static int[][] nums, locations;

	public static void main(String[] args) throws NumberFormatException, IOException {
		BufferedReader file = new BufferedReader(new InputStreamReader(System.in));
		int inputs = Integer.parseInt(file.readLine());
		while(inputs-->0) {
			int n = Integer.parseInt(file.readLine());
			int[] count = new int[n+1];
			nums = new int[n][2];
			locations = new int[n+1][2];
			for(int[] i : locations) {
				Arrays.fill(i, -1);
			}
			StringTokenizer st = new StringTokenizer(file.readLine());
			for(int i = 0; i < n; i++) {
				nums[i][0] = Integer.parseInt(st.nextToken());
				count[nums[i][0]]++;
				if(locations[nums[i][0]][0] == -1) {
					locations[nums[i][0]][0] = i;
				}
				else {
					locations[nums[i][0]][1] = i;
				}
			}
			st = new StringTokenizer(file.readLine());
			for(int i = 0; i < n; i++) {
				nums[i][1] = Integer.parseInt(st.nextToken());
				count[nums[i][1]]++;
				if(locations[nums[i][1]][0] == -1) {
					locations[nums[i][1]][0] = i;
				}
				else {
					locations[nums[i][1]][1] = i;
				}
			}
//			for(int[] i : nums)
//				System.out.println(Arrays.toString(i));
//			for(int[] i : locations)
//				System.out.println(Arrays.toString(i));
			boolean pos = true;
			for(int i = 1; i <= n; i++) {
				if(count[i] != 2) {
					pos = false;
					break;
				}
			}
			if(!pos) {
				System.out.println(-1);
			}
			else {
				int[] state = new int[n];
				int[] id = new int[n];
				Arrays.fill(id, -1);
				int currId = 0;
				for(int i = 0; i < n; i++) {
					if(id[i] == -1) {
						solveCycle(i, nums[i][1], 0, 0, 0, currId, id, state);
						currId += 2;
					}
				}
				int moves = 0;
				StringBuilder ans = new StringBuilder();
				for(int i = 0; i < n; i++) {
					if(state[id[i]/2] == id[i]) {
						moves++;
						ans.append((i+1) + " ");
					}
				}
//				System.out.println(Arrays.toString(id));
//				System.out.println(Arrays.toString(state));
				System.out.println(moves);
				System.out.println(ans);
			}
		}

	}
	
	public static int solveCycle(int currPos, int prevNum, int prevLoc, int len, int swapped, int currId, int[] id, int[] state) {
//		System.out.println(currPos);
		if(id[currPos] != -1) {
//			System.out.println("currId " + currId);
			if(swapped < len-swapped) {
				state[currId/2] = currId+1;
				return swapped;
			}
			else {
				state[currId/2] = currId;
				return len-swapped;
			}
		}
		
		int currLoc = -1;
		if(nums[currPos][0] == prevNum)
			currLoc = 0;
		else
			currLoc = 1;
		if(currLoc == prevLoc) {
			id[currPos] = currId+1;
			swapped++;
		}
		else {
			id[currPos] = currId;
			currLoc = 1-currLoc;
		}
		
		int nextNum = nums[currPos][0]+nums[currPos][1]-prevNum;
		int nextPos = locations[nextNum][0]+locations[nextNum][1]-currPos;
//		System.out.println(prevNum + " " + nextNum + " " + nextPos + " " + currLoc);
		return solveCycle(nextPos, nextNum, currLoc, len+1, swapped, currId, id, state);
	}

}
