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.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;
public class cf658_2_3_1 {

	public static void main(String args[]){
		Scanner sc=new Scanner(System.in);
        int t=sc.nextInt();
        while(t-->0)
        {
            int n=sc.nextInt();
            String a=sc.next();
            String b=sc.next();
            List<Integer> ans=new ArrayList<>();
            List<Integer> ansb=new ArrayList<>();
            int si = 0;
            
            for(int i=1;i<n;i++)
            {
                if(a.charAt(i)!=a.charAt(i-1))
                {
                	si++;
                    ans.add(i);
                }
            }
            for(int i=1;i<n;i++)
            {
                if(b.charAt(i)!=b.charAt(i-1))
                {
                	si++;
                    ansb.add(i);
                }
            }
            if (a.charAt(a.length() - 1) != b.charAt(b.length() - 1)) {
				ans.add(b.length());
				si++;
			}
            Collections.reverse(ansb);
            StringBuilder k= new StringBuilder();
            for (int x:ans) {
                k.append(x).append(" ");
            }
            for (int x:ansb) {
                k.append(x).append(" ");
            }
            System.out.println(si + " " + k);
        }
        sc.close();
    }

}