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.*;
import java.io.*;

public class a {

	public static void main(String[] args) throws Exception {
	
		BufferedReader stdin = new BufferedReader(new InputStreamReader(System.in));
		int nC = Integer.parseInt(stdin.readLine());
		
		for (int loop=0; loop<nC; loop++) {
			
			int n = Integer.parseInt(stdin.readLine());
			char[] s1 = stdin.readLine().toCharArray();
			char[] s2 = stdin.readLine().toCharArray();
			
			ArrayList<Integer> moves = new ArrayList<Integer>();
			
			int s = 0, e = n-1;
			int s1Dir = -1;
			boolean flip = false;
			
			for (int i=n-1; i>=0; i--) {
				
				int s1Idx = s1Dir == -1 ? e : s;
				char c = !flip ? s1[s1Idx] : flip(s1[s1Idx]);
				//System.out.println(moves);
				
				//System.out.println("in loop "+i+" "+s1Idx+" c is "+c+" "+s2[i]);
				if (c == s2[i]) { 
					s1Idx += s1Dir; 
					if (s1Dir == -1) e--;
					else s++;
					continue; 
				}
				
				
				if (s1[0] != c) {
					moves.add(1);
				}
				else {
					s1[0] = flip(s1[0]);
				}
				//s1[0] = flip(s1[0]);
				
				moves.add(i+1);
				
				s1Dir = -s1Dir;
				flip = !flip;
				
				if (s1Dir == -1) e--;
				else s++;
				
			}
			
			System.out.print(moves.size());
			for (int i=0; i<moves.size(); i++)
				System.out.print(" "+moves.get(i));
			System.out.println();
			
		}
	
	}
	
	public static char flip(char c) {
		if (c == '0') return '1';
		return '0';
	}

}