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.util.*;
import java.io.*;
public class PrefixFlipHard {
    public static void main(String args[]) {
        Scanner in = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int t = Integer.parseInt(in.nextLine());
        for(int i = 0; i < t; i++)
        {
            int n = Integer.parseInt(in.nextLine());
            ArrayList<Integer> swaps = new ArrayList<>();
            String a = in.nextLine();
            String b = in.nextLine();
            boolean flip = false;
            int index = 0;
            for(int k = n - 1; k >= 0; k--)
            {
                if(flip ^ a.substring(index,index+ 1).equals(b.substring(k,k + 1)))
                {
                    swaps.add(1);
                }
                swaps.add(k + 1);
                if(flip)
                    index -= k;
                else
                    index += k;
                flip = !flip;
            }
            out.print(swaps.size() + " ");
            for(int k = 0; k < swaps.size(); k++)
            {
                out.print(swaps.get(k) + " ");
            }
            out.println();
        }
        out.close();
    }
}