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.*;
public class Codeforces{
 
    static int gcd(Integer a,Integer b)
    {
        if(b==0)
            return a;
        else
            return gcd(b,a%b);
    }
 
    public static void main(String args[])
    {
        Scanner sc=new Scanner(System.in);
        int t=sc.nextInt();
        for(int q=0;q<t;q++)
        {
            int n=sc.nextInt();
            sc.nextLine();
            String a=sc.next();
            String b=sc.next();
            ArrayList<Integer> arr=new ArrayList<Integer>();
            int count=0;
            for(int i=0;i<n;i++)
            {
                if(a.charAt(i)!=b.charAt(i))
                {
                    count+=3;
                    arr.add(i);
                    arr.add(0);
                    arr.add(i);
                }
            }
            System.out.print(count+" ");
            for(int i=0;i<arr.size();i++)
            {
                System.out.print((arr.get(i)+1)+" ");
            } 
            System.out.println();
        }
        sc.close();
    }
}