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.*;
public class file{
    public static void main(String[] args){
    	Scanner scn=new Scanner(System.in);
        int test=scn.nextInt();
        while(test-->0) {
        	int n=scn.nextInt();
        	 scn.nextLine();
             String a=scn.nextLine();
             String bb=scn.nextLine();
             StringBuilder tem=new StringBuilder();
        
             for(int i=n-1;i>=0;i--){
                 if(bb.charAt(i)=='0')
                 tem.append('1');
                 else
                 tem.append('0');
             }
             String b=tem.toString();
             StringBuilder ans=new StringBuilder();
             int c=0;
             for(int i=0;i<n;i++){
                 if(i==0){
                     if(a.charAt(i)!=b.charAt(i)){
                         c+=1;
                         ans.append(i+1+" ");
                     }
                     
                     
                 }else{
                     if(a.charAt(i) != b.charAt(i)){
                         c+=3;
                         ans.append(i+1+" ");
                         ans.append(1+" ");
                         ans.append(i+1+" ");
                     }
                 }
             }
             
             c++;
             ans.append(n);
             System.out.println(c+" "+ans);
        	
        }
       
    }
}