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 Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
	   // Scanner sc=new Scanner(System.in);
		FastReader sc=new FastReader(); 
		Writer w=new PrintWriter(System.out);
		int t=sc.nextInt();
		while(t-->0){
		  //  HashMap<Integer,Integer> map=new HashMap<>();
		    int n=sc.nextInt();
		    String a=sc.next();String b=sc.next();
		    ArrayList<Integer> al=new ArrayList<Integer>();
		    char[] c=a.toCharArray();char[] d=b.toCharArray();
		    for(int i=n-1;i>=0;i--){
		        if(c[i]==d[i])continue;
		        else if(c[i]!=d[i]){
		            if(c[0]==c[i]){
		                al.add(i+1);
		                f(i,c);
		            }
		            else{
		                f(0,c);
		                al.add(1);al.add(i+1);
		                f(i,c);
		            }
		        }
		    }
		    System.out.print(al.size()+" ");
		    for(int i=0;i<al.size();i++){
		        System.out.print(al.get(i)+" ");
		    }
		    System.out.println();
		}
		w.flush();
		w.close();
	}
	public static void f(int j,char[] c){
	    for(int i=0;i<=j;i++){
	        if(c[i]=='0')c[i]='1';
	        else c[i]='0';
	    }
	    int n=c.length;
	    for(int i=0;i<=j/2;i++){
	        char temp=c[i];
	        c[i]=c[j-i];
	        c[j-i]=temp;
	    }
	}
}
class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }