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.util.Scanner;

public class Main {
	
	public static void main(String[] args)
	{
		Scanner s=new Scanner(System.in);
		
		StringBuilder sb=new StringBuilder();
		
		int t=s.nextInt();
		
		for(int i=0;i<t;i++)
		{
			int count=0;
			StringBuilder ans=new StringBuilder();
			
			int n=s.nextInt();
			
			char[] str1=s.next().toCharArray();
			char[] str2=s.next().toCharArray();
			
			for(int j=n-1;j>0;j--)
			{
				if(str1[j]!=str2[j])
				{
					if(str1[j]=='0')
					{
						if(str1[0]=='0')
						{
							count++;
							ans.append((j+1)+" ");
							
							StringBuilder temp=new StringBuilder();
							
							for(int k=0;k<=j;k++)
							{
								if(str1[k]=='0')
								{
									temp.append('1');
								}
								else
								{
									temp.append('0');
								}
							}
							
							temp.reverse();
							
							for(int k=0;k<=j;k++)
							{
								str1[k]=temp.charAt(k);
							}
							
						}
						else
						{
							count++;
							ans.append(1+" ");
							
							count++;
							ans.append(j+1+" ");
							
							str1[0]='0';
							
							StringBuilder temp=new StringBuilder();
							
							for(int k=0;k<=j;k++)
							{
								if(str1[k]=='0')
								{
									temp.append('1');
								}
								else
								{
									temp.append('0');
								}
							}
							
							temp.reverse();
							
							for(int k=0;k<=j;k++)
							{
								str1[k]=temp.charAt(k);
							}
							
						}
					}
					else
					{
						if(str1[0]=='1')
						{
							count++;
							ans.append(j+1+" ");
							
							StringBuilder temp=new StringBuilder();
							
							for(int k=0;k<=j;k++)
							{
								if(str1[k]=='0')
								{
									temp.append('1');
								}
								else
								{
									temp.append('0');
								}
							}
							
							temp.reverse();
							
							for(int k=0;k<=j;k++)
							{
								str1[k]=temp.charAt(k);
							}
							
						}
						else
						{
							count++;
							ans.append(1+" ");
							
							count++;
							ans.append(j+1+" ");
							
							str1[0]='1';
							
							StringBuilder temp=new StringBuilder();
							
							for(int k=0;k<=j;k++)
							{
								if(str1[k]=='0')
								{
									temp.append('1');
								}
								else
								{
									temp.append('0');
								}
							}
							
							temp.reverse();
							
							for(int k=0;k<=j;k++)
							{
								str1[k]=temp.charAt(k);
							}
							
						}
					}
				}
				
			}
			
			if(str1[0]!=str2[0])
			{
				count++;
				ans.append(1+" ");
			}
			
			sb.append(count+" ");
			sb.append(ans);
			sb.append("\n");
			
		}
		
		System.out.println(sb);
		
	}
	
}