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 Main {
    public static void main(String args[])
    {
        FastReader input=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        int T=input.nextInt();
        while(T-->0)
        {
            int n=input.nextInt();
            String a=input.next();
            String b=input.next();
            int c=0;
            int x=0;
            int y=n-1;
            int f=0;
            ArrayList<Integer> list=new ArrayList<>();
            for(int i=n-1;i>=0;i--)
            {
                char ch='0';
                if(f==0)
                {
                    ch=a.charAt(x);
                    if(c%2!=0)
                    {
                        if(ch=='1')
                        {
                            ch='0';
                        }
                        else
                        {
                            ch='1';
                        }
                    }
                    if(ch==b.charAt(i))
                    {
                        list.add(1);
                        list.add(i+1);
                        c++;
                        x++;
                        f=1;
                    }
                    else
                    {
                        list.add(i+1);
                        c++;
                        x++;
                        f=1;
                    }
                }
                else
                {
                    ch=a.charAt(y);
                    if(c%2!=0)
                    {
                        if(ch=='1')
                        {
                            ch='0';
                        }
                        else
                        {
                            ch='1';
                        }
                    }
                    if(ch==b.charAt(i))
                    {
                        list.add(1);
                        list.add(i+1);
                        c++;
                        y--;
                        f=0;
                    }
                    else
                    {
                        list.add(i+1);
                        c++;
                        y--;
                        f=0;
                    }
                }
            }
            out.print(list.size()+" ");
            for(int i=0;i<list.size();i++)
            {
                out.print(list.get(i)+" ");
            }
            out.println();
        }
        out.close();
    }
    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;
        }
    }
}