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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.StringTokenizer;

public class PrefixFlip {
    public static void main(String[] args) {

        FastReader input=new FastReader();
        int t=input.nextInt();
        for(int i=0;i<t;i++)
        {
            int n = input.nextInt();
            String sa = input.next();
            String sb = input.next();
            char a[]=sa.toCharArray();
            char b[]=sb.toCharArray();
            ArrayList<Integer> flips=new ArrayList<>();
            for(int j=n-1;j>=0;j--)
            {
                if(a[j]!=b[j])
                {
                    if(a[0]!=b[j])
                    {
                        a=flip(a,j);
                        flips.add(j+1);
                    }
                    else
                    {
                        a=flip(a,0);
                        flips.add(1);
                        a=flip(a,j);
                        flips.add(j+1);
                    }
                }
            }
            System.out.print(flips.size()+" ");
            for(int j=0;j<flips.size();j++)
            {
                System.out.print(flips.get(j)+" ");
            }
            System.out.println();
        }



    }
    static char[] flip(char a[],int h)
    {
        for(int i=0;i<=h;i++)
        {
            if(a[i]=='1')
            {
                a[i]='0';
            }
            else
            {
                a[i]='1';
            }
        }
        char dup[]=new char[a.length];
        for(int i=0;i<=h;i++)
        {
            dup[i]=a[h-i];
        }
        for(int i=h+1;i<a.length;i++)
        {
            dup[i]=a[i];
        }
        return dup;
    }

    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;
        }
    }
}