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.Collections;
import java.util.List;
import java.util.Scanner;

/**
 * CF1381A2 Prefix Flip (Hard Version)
 */
public class Main {

    public static void main(String[] args) {
        Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        Integer t = Integer.valueOf(in.nextLine());
        while (t-- > 0) {
            int n = Integer.valueOf(in.nextLine());
            String a = in.nextLine();
            String b = in.nextLine();
            char[] chars1 = a.toCharArray();
            char[] chars2 = b.toCharArray();
            List<String> la = new ArrayList<>();
            List<String> lb = new ArrayList<>();
            for (int i = 1; i < n; i++) {
                if (chars1[i] != chars1[i - 1]) la.add(String.valueOf(i));
                if (chars2[i] != chars2[i - 1]) lb.add(String.valueOf(i));
            }
            if (chars1[n - 1] == '1') la.add(String.valueOf(n));
            if (chars2[n - 1] == '1') lb.add(String.valueOf(n));
            Collections.reverse(lb);
            System.out.println((la.size() + lb.size()) + " " + String.join(" ", la) + " " + String.join(" ", lb));
        }
    }
}