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:
//'main' method must be in a class 'Rextester'.
//openjdk version '11.0.5' 

import java.util.*;
import java.lang.*;

public class Rextester
{  
    public static void main(String args[])
    {
        Scanner s = new Scanner(System.in);
        int t =s.nextInt();
        while(t-- >0){
         
            int n =s.nextInt(); s.nextLine();
            String change = s.nextLine();
            String check = s.nextLine();
            if(check.equals(change)){
             System.out.println("0");
                continue;
            }
            int flip=0;
            int j=0;
            int left=0;
            int right=n-1;
            int fliper=n;
            int count=0;
            StringBuilder sb= new StringBuilder();
            while(j!=n){
                
                if(flip==0){
                 char use = change.charAt(left);
                 char alter = change.charAt(right);
                    
                    if(alter!=check.charAt(j)){
                     j++;
                        right=right-1;
                        fliper--;
                        continue;
                    }else{
                        if(use!=check.charAt(j)){
                             //   System.out.print("1 ");
                            sb.append("1 ");
                            count++;
                        }
                        j++;
                        flip=1;
                    int    temp=right;
                        right=left+1;
                        left=temp;
                    //    System.out.println(left+"left");
                    //    System.out.println(right+"right");
                     //   System.out.print(fliper+" ");
                        sb.append(fliper+" ");
                        count++;
                        fliper--;
                    }
                }else{
                     char use = change.charAt(left);
                 char alter = change.charAt(right);
                    
                    if(use=='1'){
                     use='0';   
                    }else{
                     use='1';   
                    }
                    
                    if(alter=='1'){
                     alter='0';   
                    }else{
                        alter='1';
                    }
                    
                     if(alter!=check.charAt(j)){
                     j++;
                        right=right+1;
                         fliper--;
                        continue;
                    }else{
                        if(use!=check.charAt(j)){
                             //   System.out.print("1 ");
                            sb.append("1 ");
                        count++;
                        }
                      //   System.out.print(fliper+" ");
                         sb.append(fliper+" ");
                        count++;
                         fliper--;
                        j++;
                        flip=0;
                      int  temp=right;
                        right=left-1;
                        left=temp;
                    //     System.out.println(left+"left");
                    //    System.out.println(right+"right");
                    }
                    
                    
                    
                }
                
                
            }
            
            System.out.print((count+1)+" ");
                sb.append(n);
                System.out.println(sb);
            
            
        }
    }
}