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
/*
 ID: tommatt1
 LANG: JAVA
 TASK: 
*/
import java.util.*;
import java.io.*;
public class cf1385g{

	public static void main(String[] args)throws IOException {
		PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		BufferedReader bf=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer(bf.readLine());
		int tt=Integer.parseInt(st.nextToken());
		while(tt-->0) {
			st=new StringTokenizer(bf.readLine());
			int n=Integer.parseInt(st.nextToken());
			int[] a=new int[n];
			int[] b=new int[n];
			ArrayList<Integer>[] adj=new ArrayList[n];
			for(int i=0;i<n;i++) {
				adj[i]=new ArrayList<Integer>();
			}
			st=new StringTokenizer(bf.readLine());
			for(int i=0;i<n;i++) {
				a[i]=Integer.parseInt(st.nextToken())-1;
				adj[a[i]].add(i);
			}
			st=new StringTokenizer(bf.readLine());
			ArrayList<Integer> ans=new ArrayList<Integer>();
			for(int i=0;i<n;i++) {
				b[i]=Integer.parseInt(st.nextToken())-1;
				adj[b[i]].add(i);
			}
			boolean exit=false;
			for(int i=0;i<n;i++) {
				if(adj[i].size()!=2) {
					exit=true;
					break;
				}
			}
			if(exit) {
				out.println(-1);
				continue;
			}
			boolean[] vis=new boolean[n];
			for(int i=0;i<n;i++) {
				if(vis[i]) continue;
				if(adj[i].get(0)==adj[i].get(1)) continue;
				ArrayList<Integer> a1=new ArrayList<Integer>();
				ArrayList<Integer> b1=new ArrayList<Integer>();
				for(int j=i,x=adj[i].get(0);!vis[j];) {
					vis[j]=true;
					x=x^adj[j].get(0)^adj[j].get(1);
					if(a[x]==j) {
						a1.add(x+1);
						j=b[x];
					}
					else if(b[x]==j) {
						b1.add(x+1);
						j=a[x];
					}
				}
				if(a1.size()<b1.size()) {
					ans.addAll(a1);
				}
				else {
					ans.addAll(b1);
				}
			}
			out.println(ans.size());
			for(int i:ans) {
				out.print(i+" ");
			}
			out.println();
		}
		out.close();
	}
}
