Problem: This is the easy version of the problem. The difference between the versions is the constraint on n and the required number of operations. You can make hacks only if all versions of the problem are solved.

There are two binary strings a and b of length n (a binary string is a string consisting of symbols 0 and 1). In an operation, you select a prefix of a, and simultaneously invert the bits in the prefix (0 changes to 1 and 1 changes to 0) and reverse the order of the bits in the prefix.

For example, if a=001011 and you select the prefix of length 3, it becomes 011011. Then if you select the entire string, it becomes 001001.

Your task is to transform the string a into b in at most 3n operations. It can be proved that it is always possible.

Input

The first line contains a single integer t (1≤ t≤ 1000) — the number of test cases. Next 3t lines contain descriptions of test cases.

The first line of each test case contains a single integer n (1≤ n≤ 1000) — the length of the binary strings.

The next two lines contain two binary strings a and b of length n.

It is guaranteed that the sum of n across all test cases does not exceed 1000.

Output

For each test case, output an integer k (0≤ k≤ 3n), followed by k integers p_1,…,p_k (1≤ p_i≤ n). Here k is the number of operations you use and p_i is the length of the prefix you flip in the i-th operation.

Example

Input


5
2
01
10
5
01011
11100
2
01
01
10
0110011011
1000110100
1
0
1


Output


3 1 2 1
6 5 2 5 3 1 2
0
9 4 1 2 10 4 1 2 1 5
1 1

Note

In the first test case, we have 01→ 11→ 00→ 10.

In the second test case, we have 01011→ 00101→ 11101→ 01000→ 10100→ 00100→ 11100.

In the third test case, the strings are already the same. Another solution is to flip the prefix of length 2, which will leave a unchanged.

Solution (in JAVA):

Solution:

// template : secondThread

import java.io.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.nio.charset.IllegalCharsetNameException;
import java.util.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.util.Collections;
import java.io.InputStreamReader;
import java.util.*;
import java.util.LinkedList;
import java.util.logging.SimpleFormatter;


public   class main2 {











    public static void main(String[] args) {
        try {


            PrintWriter fop = new PrintWriter(System.out);
            FastScanner fsca = new FastScanner();

            int t = fsca.nextInt();
            while (t-- > 0) {
                int n = fsca.nextInt();
                char A[] = fsca.next().toCharArray();
                char B[] = fsca.next().toCharArray();
                StringBuilder sb = new StringBuilder() ;
                int ct = 0 ;
                for (int i = 0; i <n ; i++) {
                    if (i==0 && A[i] != B[i]){
                        ct++ ;
                        sb.append(1 + " ") ;
                        continue;
                    }
                    if (A[i] != B[i] ){
                        ct += 3 ;
                        sb.append( (i+1) + " " + (1) + " " + (i+1) + " ") ;
                    }
                }
                fop.print(ct + " "); fop.println(sb);



            }





            fop.flush();
            fop.close();
        }
        catch (Exception e){
            return;
        }



    }
    /*-----------------------------------------------------------------------------------------------------------------------------------------------*/





    static void sieve(int n){
        boolean[] flag = new boolean[n] ;

        for (int i=2 ; i*i<n ; i++){
            if (flag[i])
                continue;
            else
                for (int j= i*i ; j<=n ; j+= i){
                    flag[j] = true;
                }
        }


    }
    static int gcd(int a , int b){
        if (b > a){
            int tenp = b ;
            b = a ;
            a = tenp ;
        }
        int temp = 0 ;
        while (b != 0){
            a %= b ;
            temp = b ;
            b = a ;
            a = temp ;
        }
        return a ;
    }

    static long gcd1( long a , long b){
        if (b > a){
            long tenp = b ;
            b = a ;
            a = tenp ;
        }
        long temp = 0 ;
        while (b != 0){
            a %= b ;
            temp = b ;
            b = a ;
            a = temp ;
        }
        return a ;
    }


    static final Random random=new Random();

    static void ruffleSort(int[] a) {
        int n=a.length;//shuffle, then sort
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n), temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }




    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
        int[] readArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }
        long[] readLongArray(int n){
            long[] a = new long[n];
            for (int i=0 ; i<n ; i++)
                a[i] = nextLong() ;
            return a ;
        }
        long nextLong() {
            return Long.parseLong(next());
        }
    }






}