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 PrefixFlip {

	// https://codeforces.com/contest/1382/problem/C1
	
	public static void main(String[] args) throws IOException, FileNotFoundException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		//BufferedReader in = new BufferedReader(new FileReader("PrefixFlip"));

		int t = Integer.parseInt(in.readLine());
		while (t -->0 ) {
			int n = Integer.parseInt(in.readLine());
			int pointer = n-1;
			String a = in.readLine();
			String b = in.readLine();
			
			ArrayList<Integer> moves = new ArrayList<>();
			while (pointer >= 0) {
				while (pointer >= 0 && a.charAt(pointer) == b.charAt(pointer)) {
					pointer--;
				}
				if (pointer<0) break;
				if (a.charAt(0) == b.charAt(pointer)) {
					moves.add(0);
					if (a.charAt(0) == '0') {
						a = '1' + a.substring(1);
					}
					else {
						a = '0' + a.substring(1);
					}
				}
				moves.add(pointer);
				String cur="";
				for (int i=pointer; i>=0; i--) {
					if (a.charAt(i) == '0') {
						cur += '1';
					}
					else {
						cur += '0';
					}
				}
				a = cur + a.substring(pointer+1);
			}
			System.out.print(moves.size() + " ");
			for (int i=0; i<moves.size(); i++) {
				System.out.print(moves.get(i)+1 + " ");
			}
			System.out.println();
		}
	}
}