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.IOException;
import java.io.InputStreamReader;
import java.util.LinkedList;
import java.util.Queue;

public class demo_C2 {
    public static char reverse(char c) {
        if (c == '1')
            return '0';
        return '1';
    }

    public static void main(String[] args) throws IOException {
        BufferedReader rd = new BufferedReader(new InputStreamReader(System.in));
        StringBuilder print = new StringBuilder();
        int t = Integer.parseInt(rd.readLine());
        while (t-- != 0) {
            int n = Integer.parseInt(rd.readLine());
            String a = rd.readLine(), b = rd.readLine();
            Queue<Integer> q = new LinkedList<>();
            for (int i = 1; i < n; i++) {
                if (a.charAt(i) != a.charAt(i - 1)) {
                    q.add(i);
                }
            }
            char c = a.charAt(n - 1);
            for (int i = n - 1; i >= 0; i--) {
                if (b.charAt(i) != c) {
                    q.add(i + 1);
                    c = reverse(c);
                }
            }
            int size = q.size();
            print.append(size + " ");
            for (int i = 0; i < size; i++) {
                print.append(q.poll() + " ");
            }
            print.append('\n');
        }
        System.out.println(print);
    }
}