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.io.*;
import java.util.*;
public class PrefixFlipE
{
    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 class OutputWriter 
    {
        private final PrintWriter writer;
        
        public OutputWriter(OutputStream outputStream) 
        {
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
        }
        
        public OutputWriter(Writer writer) 
        {
            this.writer = new PrintWriter(writer);
        }
        
        public void print(Object...objects) 
        {
            for (int i = 0; i < objects.length; i++) 
            {
                if (i != 0)
                    writer.print(' ');
                writer.print(objects[i]);
            }
        }
        
        public void printLine(Object...objects) 
        {
            print(objects);
            writer.println();
        }
        
        public void close() 
        {
            writer.close();
        }
        
        public void flush() {
            writer.flush();
        }
    }
    public static void main(String args[])
    {
        FastReader sc=new FastReader();
        OutputWriter out=new OutputWriter(System.out);
        int t=sc.nextInt();
        while(t-->0)
        {
            int n=sc.nextInt();
            String s1=sc.next();
            String s2=sc.next();
            int count=0;
            List<Integer> list=new ArrayList();
            for(int i=0;i<n;i++)
            {
                if(s1.charAt(i)!=s2.charAt(i))
                {
                    String r=s1.substring(0,i+1);
                    String q="";
                    for(int j=0;j<r.length();j++)
                    {
                        if(r.charAt(j)=='0')
                            q="1"+q;
                        else
                            q="0"+q;
                    }
                    list.add(i+1);
                    if(q.charAt(0)=='0')
                        q="1"+q.substring(1);
                    else
                        q="0"+q.substring(1);
                    r="";
                    list.add(1);
                    for(int j=0;j<q.length();j++)
                    {
                        if(q.charAt(j)=='1')
                            r="0"+r;
                        else
                            r="1"+r;
                    }
                    s1=r+s1.substring(i+1);
                    list.add(i+1);
                    count+=3;
                }
            }
            Integer a[]=new Integer[list.size()];
            a=list.toArray(a);
            out.print(count+" ");
            for(int j=0;j<a.length;j++)
                out.print(a[j]+" ");
            out.printLine();
            out.flush();
        }
    }
}