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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.util.regex.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
    public static void main (String[] args) throws java.lang.Exception
	{
	    Scanner sc= new Scanner(System.in);
	    int t=sc.nextInt();//String a; char c; int l,k,count;
	    while(t>0){
	        int n= sc.nextInt();
	        String a1= sc.next();
	        char a[]=a1.toCharArray();
	        String b1= sc.next();
	        char b[]=b1.toCharArray();
	        ArrayList<Integer> arr= new ArrayList<>();
	        for(int i=n-1;i>=0;i--){
	            if(b[i]!=a[i]){
	                if(a[0]!=b[i]){
	                    arr.add(i+1);
	                    for(int j=0;j<=i;j++){
	                        if(a[j]=='1'){
	                        a[j]='0';
	                    }
	                    else{
	                        a[j]='1';
	                    }
	                    }
	                    for(int j=0;j<=i/2;j++){
	                        char k=a[j];
	                        a[j]=a[i-j];
	                        a[i-j]=k;
	                    }
	               //     for(int k=0;k<n;k++){
	               //         System.out.print(a[k]);
	               //     }
	                }
	                else{
	                    arr.add(1);
	                    if(a[0]=='1'){
	                        a[0]='0';
	                    }
	                    else{
	                        a[0]='1';
	                    }
	                   // for(int k=0;k<n;k++){
	                   //     System.out.print(a[k]);
	                   // }
	                   // System.out.println();
	                    arr.add(i+1);
	                    for(int j=0;j<=i;j++){
	                        if(a[j]=='1'){
	                            a[j]='0';
	                        }
	                        else{
	                            a[j]='1';
	                        }
	                    }
	                   // for(int k=0;k<n;k++){
	                   //     System.out.print(a[k]);
	                   // }
	                    //System.out.println(i);
	                    for(int j=0;j<=i/2;j++){
	                        char k=a[j];
	                        a[j]=a[i-j];
	                        a[i-j]=k;
	                    }
	                   // for(int k=0;k<n;k++){
	                   //     System.out.print(a[k]);
	                   // }
	                   // System.out.println("ok");
	                }
	            }
	        }
	       // for(int i=0;i<n;i++){
	       //     System.out.print(a[i]);
	       // }
	        System.out.print(arr.size()+" ");
	        for(int i=0;i<arr.size();i++){
	            System.out.print(arr.get(i)+" ");
	        }
	        System.out.println();
	        t--;
	    }
	   
	    }
	    	// your code goes here
	}