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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.BigInteger; 

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
     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;
		}
	}
    
	
     
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		FastReader reader = new FastReader();
		int t = reader.nextInt();
		while(t-->0){
		    ArrayList<Integer> list = new ArrayList<Integer>(30);
		  int n = reader.nextInt();
		  String a = reader.next();
		   String b = reader.next();
	//	   System.out.println(n + " " + a + " " + b);
		  char a1[] = a.toCharArray();
		  char b1[] = b.toCharArray();
		  int count=0;
		  for(int i=1; i<n; i++){
		       if(a1[i]!=a1[i-1])
		       list.add(i);
		  }
		  if(a1[n-1]!=b1[n-1])
		  list.add(n);
		  for(int i=n-1; i>0; i--){
		       if(b1[i]!=b1[i-1]){
		          list.add(i);
		       }
		  }
		  System.out.print(list.size() + " ");
		  for(int i=0; i<list.size(); i++){
		       System.out.print(list.get(i) + " ");
		  }
		  System.out.println();
		}
	}
}