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.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner input = new Scanner(System.in);
		int test = input.nextInt();
		while(test-->0){
		    int n = input.nextInt();
		    input.nextLine();
		    char c1[] = input.nextLine().toCharArray();
		    char c2[] = input.nextLine().toCharArray();
		    ArrayList<Integer>list = new ArrayList<>();
		    for(int i = n-1;i>=0;i--){
		        if(c1[i] != c2[i]){
		            if(c1[0] == c2[i]){
		                list.add(1);
		                c1[0] = (c1[0] == '0'?'1':'0');
		            }
		            
		            for(int j = 0;j<=i;j++){
		                c1[j] = (c1[j] == '0'?'1':'0');
		            }
		            reverse(i,c1);
		            list.add(i+1);
		        }
		    }
		    System.out.print(list.size()+" ");
		    for(int it:list)System.out.print(it+" ");
		    System.out.println();
		}
	}
	public static void reverse(int n,char c1[]){
	    int z =0;
	    char res[] = new char[n+1];
	    for(int i =n;i>=0;i--)res[z++] = c1[i];
	    for(int i =0;i<z;i++)c1[i] = res[i];
	}
}