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.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.Collections;
import java.util.HashMap;
import java.util.Scanner;

/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 *
 * @author anmol
 */
public class fghef {
    public static void main(String []args){
        Scanner s = new Scanner(System.in);
        int t = s.nextInt();
        outer:
        while(t-->0){
               //int n = s.nextInt();
               int n = s.nextInt();
               String s1 = s.next();
               String s2  =s.next();
               char c1 = s1.charAt(0);
               char c2  =s2.charAt(0);
               ArrayList list1 = new ArrayList();
               ArrayList list2 = new ArrayList();
               for(int i=1;i<n;i++){
                   if(c1!=s1.charAt(i)) {
                   list1.add(i);
                   if(c1=='0') c1='1';
                   else c1='0';
                   }
                }
               for(int i=1;i<n;i++){
                   if(c2!=s2.charAt(i)) {
                   list2.add(i);
                   if(c2=='0') c2='1';
                   else c2='0';
                   }
                }
               if(c1 == c2){
                   for(int i=list2.size()-1;i>=0;i--) list1.add(list2.get(i));
               }else{
                   list2.add(s2.length());
                   for(int i=list2.size()-1;i>=0;i--) list1.add(list2.get(i));
               }
               
               
               System.out.print(list1.size()+" ");
               for(int i=0;i<list1.size();i++){
                   System.out.print(list1.get(i)+ " ");
               }
               System.out.println();

        }
    }



    
}