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 Round_658;

import java.io.*;
import java.math.*;
import java.util.*;

public class Problem_C1 {  
    public static void main(String[] args) {
        FastReader in = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        
        int numTrials = in.nextInt();
        while(numTrials --> 0) {
            int len = in.nextInt();
            StringBuffer startStr = new StringBuffer(in.next());
            StringBuffer endStr = new StringBuffer(in.next());
            
            int[] index = new int[len];
            for(int i = 0; i < len; i++) {
            	index[i] = i;
            }
            
            int non1Moves = 0;
            ArrayList<Integer> moves = new ArrayList<Integer>();
            for(int i = startStr.length() - 1; i >= 1; i--) {
            	int startC = (Integer.parseInt(startStr.substring(index[i], index[i] + 1)) + non1Moves) % 2;
            	int endC = Integer.parseInt(endStr.substring(i, i + 1));
            	
            	if(startC != endC) {
            		int first = (Integer.parseInt(startStr.substring(0, 1)) + moves.size()) % 2;
            		
            		if(startC != first) {
            			moves.add(1);
            		}
            		
            		moves.add(i + 1);
            		non1Moves++;
            		
            		for(int j = 1; j < (i + 1) / 2; j++) {
            			int temp = index[j];
            			index[j] = index[i - j];
            			index[i - j] = temp;
            		}
            	}
            }
            
            int firstVal = (Integer.parseInt(startStr.substring(0, 1)) + moves.size()) % 2;
            if(firstVal != Integer.parseInt(endStr.substring(0, 1))) {
            	moves.add(1);
            }
            
            StringBuilder s = new StringBuilder();
            s.append(moves.size() + " ");
            for(int i = 0; i < moves.size(); i++) {
            	s.append(moves.get(i) + " ");
            }
            
            out.println(s.toString().trim());
        }
        
        out.flush();
    }
    
    static 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; 
        } 
    } 
}