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.io.PrintWriter;
import java.util.ArrayList;

public class C1
{
	public static void main(String[] args) throws NumberFormatException, IOException
	{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(System.out);
		int t = Integer.parseInt(br.readLine());
		while(t-->0)
		{
			int n = Integer.parseInt(br.readLine());
			String s1 = br.readLine();
			String s2 = br.readLine();
			ArrayList<Integer> changes = new ArrayList<Integer>();
			for(int i=n-1;i>=0;i--)
			{
				if(s1.charAt(i)!=s2.charAt(i))
				{
					StringBuilder temp = new StringBuilder();
				
					if(s1.charAt(0)!=s2.charAt(i))
					{
						changes.add(i+1);
						for(int j=i;j>=0;j--)
						{
							if(s1.charAt(j)=='1')temp.append('0');
							else temp.append('1');
						}
					}
					else
					{
						changes.add(1);
						changes.add(i+1);
						for(int j=i;j>0;j--)
						{
							if(s1.charAt(j)=='1')temp.append('0');
							else temp.append('1');
						}
						temp.append(s1.charAt(0));
					}
					for(int j=i+1;j<n;j++)
						temp.append(s1.charAt(j));
					s1=temp.toString();
				}
			}
			pw.print(changes.size()+" ");
			for(int x:changes)
				pw.print(x+" ");
			pw.println();
		}
		pw.close();
		pw.flush();
	}

}