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.io.PrintWriter;
import java.util.*;

public class Problem658A {
    public static void main(String[] args) throws Exception {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter writer = new PrintWriter(System.out);

        int testCases = Integer.parseInt(reader.readLine());
        for (int tt = 0; tt < testCases; tt++) {
            StringTokenizer info = new StringTokenizer(reader.readLine());
            int n = Integer.parseInt(info.nextToken());
            String a = reader.readLine();
            String b = reader.readLine();
            int left = 0;
            int right = n - 1;
            boolean reversed = false;
            List<Integer> answer = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                if (reversed) {
                    // reversed
                    // look at rightmost
                    if (a.charAt(right) != b.charAt(n - i - 1)) {
                        // also means it's flipped
                        answer.add(1);
                    }
                    answer.add(right - left + 1);
                    right--;
                } else {
                    // forward
                    // look at leftmost
                    if (a.charAt(left) == b.charAt(n - i - 1)) {
                        // flip one letter
                        answer.add(1);
                    }
                    // flip the entire thing
                    answer.add(right - left + 1);
                    left++;
                }
                reversed = !reversed;
            }
            writer.print(answer.size());
            for (int i = 0; i < answer.size(); i++) {
                writer.print(' ');
                writer.print(answer.get(i));
            }
            writer.println();
        }

        reader.close();
        writer.close();
    }
}