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.*;
import java.io.*;
public class MyClass {
static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }
    
    static String flip(String str)
    {
        char ch[]=str.toCharArray();
        for(int i=0;i<ch.length;i++)
        {
            if(ch[i]=='0')
            ch[i]='1';
            else
            ch[i]='0';
        }
        return String.valueOf(ch);
    }
    
    static String fliprev(String str,int m)
    {
        String s1=str.substring(0,m);
        String s2=str.substring(m,str.length());
        s1=flip(s1);
        StringBuffer sb=new StringBuffer(s1);
        sb.reverse();
        String new1=sb.toString();
        new1+=s2;
        return new1;
        
    }
    public static void main(String args[]) 
{
	FastReader s=new FastReader();int t=0,n=0,m=0;String str1="",str2="";
     //Scanner in=new Scanner(System.in);
     //if(in.hasNext())
     t=s.nextInt();
     for(int j=0;j<t;j++)
     {
      //   if(in.hasNext())
         n=s.nextInt();
         str1=s.next();
         str2=s.next();
         m=n-1;
         ArrayList<Integer> ans=new ArrayList<>();
         while(m>=0 || str2.charAt(m)!=str1.charAt(m))
         {
             if(str2.charAt(m)!=str1.charAt(m))
             {
                 if(str2.charAt(m)=='1')
                 {
                     if(str1.charAt(0)=='1')
                     {
                         char ch[]=str1.toCharArray();
                         ch[0]='0';
                         ans.add(1);
                         str1=String.valueOf(ch);
                     }
                     ans.add(m+1);
                     str1=fliprev(str1,m+1);
                 }
                 else
                 {
                     if(str1.charAt(0)=='0')
                     {
                         char ch[]=str1.toCharArray();
                         ch[0]='1';
                         ans.add(1);
                         str1=String.valueOf(ch);
                     }
                     ans.add(m+1);
                     str1=fliprev(str1,m+1);
                 }
                 m--;
             }
             else
             m--;
             //System.out.println("str1="+str1+" str2="+str2);
             //System.out.println("m="+m);
             if(m<0)
             break;
         }
         System.out.print(ans.size()+" ");
         for(int i=0;i<ans.size();i++)
         System.out.print(ans.get(i)+" ");
         System.out.println();
     }
    }
}