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.io.*;

public class Question3b {

	static FastReader sc = new FastReader();
	static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
	public static void main(String[] args) throws IOException{
		int t = sc.nextInt();
		while(t-->0) {
			solve();
		}
		bw.flush();
		bw.close();
		
	}
	
	public static void solve() throws IOException{
		int n = sc.nextInt();
		char[] arr = sc.next().toCharArray();
		char[] brr = sc.next().toCharArray();
		char ch = arr[0];
		
		int i = 0;
		ArrayList<Integer> list1 = new ArrayList<Integer>();
		ArrayList<Integer> list2 = new ArrayList<Integer>();
		
		while(i < n) {
			if(arr[i] == ch)i++;
			else {
				list1.add(i);
				
				ch = ch == '0' ? '1' : '0';
				i++;
			}
			
		}
		if(ch == '1')list1.add(n);
		
		//System.out.println(list);
		
		ch = brr[0];
		i = 0;
		while(i < n) {
			if(brr[i] == ch)i++;
			else {
				list2.add(i);
				ch = ch == '0' ? '1' : '0';
				i++;
			}
		}
		
		if(ch == '1')list2.add(n);
		
		bw.write(String.valueOf(list1.size() + list2.size()) + " ");
		for(int j = 0;j < list1.size();j++)bw.write(String.valueOf(list1.get(j) + " "));
		for(int j = list2.size() - 1;j >= 0;j--)bw.write(String.valueOf(list2.get(j)) + " ");
		bw.write("\n");
	}
	
	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; 
        } 
    } 
}