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.lang.*;
import java.io.*;
public class Codechef
{
	public static void main (String[] args) throws java.lang.Exception
	{
	   // Scanner sc=new Scanner(System.in);
	    BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	   // int t=1;
	    //t=sc.nextInt();
	    int t=Integer.parseInt(br.readLine());
	    while(--t>=0){
	        //int n=sc.nextInt();
	              int n=Integer.parseInt(br.readLine());
	          //     int k=sc.nextInt();
	              String s=br.readLine();
	              String r=br.readLine();
	         //     StringTokenizer st=new StringTokenizer(br.readLine());
	         //      int n=Integer.parseInt(st.nextToken());
	       // for(int i=0;i<n;i++)a[i]=sc.nextInt();
	       ArrayList<Integer> arr=new ArrayList<>();
	       int k=n;
	       int temp=0;
	         for(int i=0;i<n;i++){
	             if(i%2==0){
	             if(s.charAt(temp)==r.charAt(n-1-i)){
	             arr.add(1);
	             arr.add(k);
	             }
	             else
	                 arr.add(k);
	             }
	             else{
	                if(s.charAt(n-1-temp)!=r.charAt(n-1-i)){
	             arr.add(1);
	             arr.add(k);
	             }
	             else
	                 arr.add(k);
	              temp++;
	                 
	             }
	             k--;
	         }
	       System.out.print(arr.size()+" ");
	       for(int i=0;i<arr.size();i++){
	           System.out.print(arr.get(i)+" ");
	       }
	       System.out.println();
	       
	       
	      //  for(int i=0;i<n;i++)
	      //  System.out.print(arr[i]+" ");
	        
	     
	        
	    }
	    
	}
}