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 C{
	private static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	private static BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
	
	public static void main (String[] args) throws IOException{
        int t = Integer.parseInt(br.readLine());
        while(t-- > 0){
            int n = Integer.parseInt(br.readLine());
            String ar = br.readLine();
            char a[] = new char[n];
            for(int i=0;i<n;i++){
                a[i] = ar.charAt(i);
            }
            String b = br.readLine();
            int moves = 0;
            ArrayList<Integer> p = new ArrayList<>();
            for(int i=n-1;i>=0;i--){
                if(b.charAt(i)==a[i]){
                    continue;
                }
                if(a[0]!=b.charAt(i)){
                    p.add(i+1);
                    moves++;
                }else{
                    p.add(1);
                    moves++;
                    if(a[0] == '1'){
                        a[0] = '0';
                    }else{
                        a[0] = '1';
                    }
                    p.add(i+1);
                    moves++;
                }
                int idx = i;
                for(int j=0;j<=i/2;j++){
                    char temp = a[j];
                    a[j] = a[idx];
                    a[idx] = temp;
                    if(a[j]=='1'){
                        a[j] = '0';
                    }else{
                        a[j] = '1';
                    }
                    if(a[idx] == '1'){
                        a[idx] = '0';
                    }else{
                        a[idx] = '1';
                    }
                    if(i%2==0 && idx == i/2){
                        if(a[idx] == '1'){
                            a[idx] = '0';
                        }else{
                            a[idx] = '1';
                        }
                    }
                    idx--;
                }
            }
            bw.write(moves + " ");
            for(int i=0;i<p.size();i++){
                bw.write(p.get(i) + " ");
            }
            bw.newLine();
        }
        bw.flush();
    }
}