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

public class Main {
    public static void main(String args[]) {new Main().run();}

    FastReader in = new FastReader();
    PrintWriter out = new PrintWriter(System.out);
    void run(){
        for(int q=ni();q>0;q--){
            work();
        }
        out.flush();
    }
    long mod=1000000007;
    long gcd(long a,long b) {
        return a==0?b:gcd(b%a,a);
    }
    int[] A,B;
    int n;
    ArrayList<Integer>[] rec;
    int[] count;
    int sum;
    boolean[] vis;
    ArrayList<Integer> l1;
    ArrayList<Integer> l2;
    void work() {
       n=ni();
       A=nia(n);
       B=nia(n);
       count=new int[n];
       vis=new boolean[2*n];
       l1=new ArrayList<>();
       l2=new ArrayList<>();
       rec=(ArrayList<Integer>[])new ArrayList[n];
       for(int i=0;i<n;i++)rec[i]=new ArrayList<>();
       for(int i=0;i<n;i++){
           count[A[i]]++;
           count[B[i]]++;
           if(A[i]==B[i])sum--;
           rec[A[i]].add(i);
           rec[B[i]].add(i+n);
       }
       for(int c:count){
           if(c!=2){
               out.println(-1);
               return;
           }
       }
       ArrayList<Integer> list=new ArrayList<>();
       for(int i=0;i<n;i++){
           if(!vis[i]){
               l1=new ArrayList<>();
               l2=new ArrayList<>();
               dfs(i,false);
               if(l1.size()<l2.size()){
                   list.addAll(l1);
               }else{
                   list.addAll(l2);
               }
           }
       }
       out.println(list.size());
       for(int l:list){
           out.print((l+1)+" ");
       }
       out.println();
    }

    private void dfs(int idx,boolean turn) {//turn==1反转,idx>n代表B
        if(!vis[idx%n]&&!vis[(idx%n)+n]){
            if(turn){
                l1.add(idx%n);
            }else if(A[idx%n]!=B[idx%n]){
                l2.add(idx%n);
            }
        }
        vis[idx]=true;
        int node=0;
        if(idx<n){
            node=A[idx];
        }else{
            node=B[idx%n];
        }
        for(int i:rec[node]){
            if(vis[i])continue;
            dfs(i,(idx/n==i/n)^turn);
        }
        int s=idx%n,e=(idx%n)+n;
        if(!vis[s]){
            dfs(s,turn);
        }
        if(!vis[e]){
            dfs(e,turn);
        }
    }

    //input
    private ArrayList<Integer>[] ng(int n, int m) {
        ArrayList<Integer>[] graph=(ArrayList<Integer>[])new ArrayList[n];
        for(int i=0;i<n;i++) {
            graph[i]=new ArrayList<>();
        }
        for(int i=1;i<=m;i++) {
            int s=in.nextInt()-1,e=in.nextInt()-1;
            graph[s].add(e);
            graph[e].add(s);
        }
        return graph;
    }

    private ArrayList<long[]>[] ngw(int n, int m) {
        ArrayList<long[]>[] graph=(ArrayList<long[]>[])new ArrayList[n];
        for(int i=0;i<n;i++) {
            graph[i]=new ArrayList<>();
        }
        for(int i=1;i<=m;i++) {
            long s=in.nextLong()-1,e=in.nextLong()-1,w=in.nextLong();
            graph[(int)s].add(new long[] {e,w,i});
            graph[(int)e].add(new long[] {s,w});
        }
        return graph;
    }

    private int ni() {
        return in.nextInt();
    }

    private long nl() {
        return in.nextLong();
    }

    private String ns() {
        return in.next();
    }

    private long[] na(int n) {
        long[] A=new long[n];
        for(int i=0;i<n;i++) {
            A[i]=in.nextLong();
        }
        return A;
    }
    private int[] nia(int n) {
        int[] A=new int[n];
        for(int i=0;i<n;i++) {
            A[i]=in.nextInt()-1;
        }
        return A;
    }
}

class FastReader
{
    BufferedReader br;
    StringTokenizer st;

    public FastReader()
    {
        br=new BufferedReader(new InputStreamReader(System.in));
    }


    public String next()
    {
        while(st==null || !st.hasMoreElements())//回车，空行情况
        {
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return st.nextToken();
    }

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

    public long nextLong()
    {
        return Long.parseLong(next());
    }
}