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.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;

public class PreflixFlip {
	public static void main(String args[]) {
		try {
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

			int t = Integer.parseInt(br.readLine());

			while (t-- > 0) {
				int n = Integer.parseInt(br.readLine());
				char[] a = br.readLine().toCharArray();
				char[] b = br.readLine().toCharArray();
				
				ArrayList<Integer> op = new ArrayList<>();
				
				char[] a2;
				for (int i = n-1; i > 0; i--) {
					if (a[i] == b[i]) {
						continue;
					}
					a2 = Arrays.copyOf(a, i+1);					
					if (a[0] == b[i]) {						
						op.add(1);
						a2[0] = (a2[0] == '1') ? '0' : '1';						
					}
					op.add(i+1);				
					for (int j = 0; j <= i; j++) {
						a[i-j] = (a2[j] == '0') ? '1' : '0';						
					}					
				}
				if (a[0] != b[0]) {
					op.add(1);
				}				
				
				// print
				System.out.print(op.size() + " ");
				for (int i: op) {
					System.out.print(i + " ");
				}
				System.out.println();
			}

		} catch (Exception e) {
			return;
		}
	}
}