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.*;

public class CF1385G extends PrintWriter {
	CF1385G() { super(System.out); }
	Scanner sc = new Scanner(System.in);
	public static void main(String[] $) {
		CF1385G o = new CF1385G(); o.main(); o.flush();
	}

	void main() {
		int t = sc.nextInt();
out:
		while (t-- > 0) {
			int n = sc.nextInt();
			int[] aa = new int[n];
			int[] bb = new int[n];
			int[] ij = new int[n];
			int[] kk = new int[n];
			for (int i = 0; i < n; i++) {
				int a = sc.nextInt() - 1;
				aa[i] = a;
				ij[a] ^= i;
				kk[a]++;
			}
			for (int i = 0; i < n; i++) {
				int b = sc.nextInt() - 1;
				bb[i] = b;
				ij[b] ^= i;
				kk[b]++;
			}
			for (int a = 0; a < n; a++)
				if (kk[a] != 2) {
					println(-1);
					continue out;
				}
			boolean[] used = new boolean[n];
			int[] qu = new int[n]; int cnt = 0;
			for (int i = 0; i < n; i++) {
				if (used[i])
					continue;
				int a = aa[i], b = bb[i];
				int l = 1, j = i;
				used[i] = true;
				while (b != a) {
					j ^= ij[b];
					used[j] = true;
					b ^= aa[j] ^ bb[j];
					l++;
				}
				int k = 0; j = i;
				b = bb[i];
				while (b != a) {
					j ^= ij[b];
					if (b == aa[j])
						b = bb[j];
					else {
						b = aa[j];
						k++;
					}
				}
				j = i;
				if (k + k <= l) {
					a = aa[i];
					b = bb[i];
				} else {
					a = bb[i];
					b = aa[i];
					qu[cnt++] = i;
				}
				while (b != a) {
					j ^= ij[b];
					if (b == aa[j])
						b = bb[j];
					else {
						b = aa[j];
						qu[cnt++] = j;
					}
				}
			}
			println(cnt);
			for (int h = 0; h < cnt; h++)
				print(qu[h] + 1 + " ");
			println();
		}
	}
}
