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.*;
import java.util.*;
import java.math.*;

public class A2 {
	public static void main(String[] args) throws IOException {

		/**/
		Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		/*/
		Scanner sc = new Scanner(new BufferedReader(new InputStreamReader(new FileInputStream("src/a.in"))));
		/**/
		
		int t = sc.nextInt();
		for (int z = 0; z < t; ++z) {
			int n = sc.nextInt();
			String a = sc.next();
			String b = sc.next();
			int ac = 0;
			ArrayDeque<Character> ad = new ArrayDeque<>();
			for (char c : a.toCharArray()) {
				ad.add(c);
			}
			boolean parity = false;
			StringBuilder ans = new StringBuilder();
			for (int i = n-1; i >= 0; --i) {
				char cc = b.charAt(i);
				char nc = ad.peekLast();
				if (parity) {
					nc = (char)(ad.peekFirst()^1);
				}
				if (nc==cc) {
					if (parity) {
						ad.removeFirst();
					} else {
						ad.removeLast();
					}
					continue;
				} else {
					if (parity) {
						nc = ad.removeLast();
					} else {
						nc = (char)(ad.removeFirst()^1);
					}
					if (nc!=cc) {
						++ac;
						ans.append(" 1");
					}
					++ac;
					ans.append(" "+(i+1));
					parity=!parity;
				}
			}
			System.out.print(ac);
			System.out.println(ans.toString());
		}
    }
}