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:

import java.util.Collections;

import com.sun.org.apache.bcel.internal.generic.SWAP;

import java.util.*;
import java.lang.*;
import java.io.*;
import java.util.Arrays;

public class CodeChef {
	 StringBuilder sb=new StringBuilder();
	public static void rever(char[] sr,int l,int r)
		{
		for(int i=0;i<=r;i++)
		{
			if(sr[i]=='0')
				sr[i]='1';
			else
				sr[i]='0';
		}
	 for(int i=0;i<((r-l+1)/2);i++)
	 {
		 char temp=sr[i];
		 sr[i]=sr[r-i];
		 sr[r-i]=temp;
	 }
	  
		
	}
    public static void main(String args[] ) throws Exception {
 

        
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
       
            int t=Integer.parseInt(br.readLine());
            		while(t-->0)
            		{
            		
       int n=Integer.parseInt(br.readLine());
       
       ArrayList<Integer> list=new ArrayList();
       
      String st=br.readLine();
      String su=br.readLine();
      if(st.equals(su))
    	  System.out.println("0");
      else {
      char[] sr=st.toCharArray();
      char[] ss=su.toCharArray();
      
       
     for(int i=n-1;i>=0;i--)
     {
    	 if(sr[i]==ss[i])
    		 continue;
    	 else {
    		 
    		 if(ss[i]==sr[0])
    		 {
    			 list.add(1);
    			 
    			 if(sr[0]=='1')
    				 sr[0]='0';
    			 else
    				 sr[0]='1';
    			list.add(i+1);
    			 rever(sr,0,i);
    				 
    		 }
    		 else
    		 {list.add(i+1);
    			 rever(sr,0,i);
    		 }
    	 }
    	 
    	 
     }
       
            	



	System.out.print(list.size()+" ");
	for(int i=0;i<list.size();i++)
	{
		System.out.print(list.get(i)+" ");
	}
	System.out.println("");
}
            		}

    } 
}