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:
//cyan piece of shit
import static java.lang.Math.max;
import static java.lang.Math.min;
import static java.lang.Math.abs;
import java.util.*;
import java.io.*;
import java.math.*;

   public class x1381A
   {
      public static void main(String hi[]) throws Exception
      {
         BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));
         StringTokenizer st = new StringTokenizer(infile.readLine());
         int T = Integer.parseInt(st.nextToken());
         StringBuilder sb = new StringBuilder();
         while(T-->0)
         {
            st = new StringTokenizer(infile.readLine());
            int N = Integer.parseInt(st.nextToken());
            String input1 = infile.readLine();
            String input2 = infile.readLine();
            int[] arr = new int[N];
            int[] brr = new int[N];
            for(int i=0; i < N; i++)
            {
               if(input1.charAt(i) == '1')
                  arr[i] = 1;
               if(input2.charAt(i) == '1')
                  brr[i] = 1;
            }
            ArrayList<Integer> moves = new ArrayList<Integer>();
            for(int i=1; i < N; i++)
               if(arr[i-1] != arr[i])
                  moves.add(i);
            if((arr[0]+moves.size())%2 == 1)
               moves.add(N);
            int curr = 0;
            for(int i=N-1; i >= 0; i--)
               if(brr[i] != curr)
               {
                  moves.add(i+1);
                  curr ^= 1;
               }
            sb.append(moves.size()+" ");
            for(int x: moves)
               sb.append(x+" ");
            sb.append("\n");
         }
         System.out.print(sb);
      }
   }