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;

public class Ques1 {
    public static void main(String[] args) throws Exception {
        BufferedReader z = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(z.readLine());
        while (t-- > 0) {
            int n = Integer.parseInt(z.readLine()), i, j;
            String a = z.readLine(), b = z.readLine();
            StringBuilder e;
            ArrayList<Integer> l = new ArrayList<>();
            char c, d;
            for (i = n - 1; i >= 0; i--) {
                c = a.charAt(i);
                d = b.charAt(i);
                if (c == d) {
                    continue;
                }
                if (i == 0) {
                    l.add(1);
                    continue;
                }
                d = a.charAt(0);
                if (d != c) {
                    a = d + a.substring(1);
                    l.add(1);
                }
                e = new StringBuilder();
                for (j = 0; j <= i; j++) {
                    e.append(a.charAt(j) == '0' ? '1' : '0');
                }
                a = e.reverse().toString();
                l.add(i + 1);
            }
            System.out.print(l.size());
            for (Integer y : l) {
                System.out.print(" " + y);
            }
            System.out.println();
        }
    }
}