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 Main {

    /**
     * @param args the command line arguments
     */
    static BufferedReader input = new BufferedReader(new InputStreamReader(System.in));
    static StringTokenizer st;
    static PrintWriter pr = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    public static void main(String[] args) throws IOException{
        int t = readInt();
        for(int z = 0; z<t; z++){
            int n = readInt();
            ArrayList<Integer>arr = new ArrayList<>();
            String a = readLine(), b = readLine();
            for(int i = 0; i<n; i++){
                if(a.charAt(i)!=b.charAt(i)){
                    a = flip(a, i+1);
                    a = flip(a, 1);
                    a = flip(a, i+1);
                    arr.add(i+1);
                    arr.add(1);
                    arr.add(i+1);
                }
            }
            System.out.print(arr.size()+" ");
            for(int i = 0; i<arr.size(); i++){
                if(i==arr.size()-1)System.out.print(arr.get(i));
                else System.out.print(arr.get(i)+" ");
            }
            System.out.println();
        }
    }
    static String flip(String s, int cur){
        String ans = "";
        for(int i = 0; i<cur; i++){
            if(s.charAt(i)=='1')ans+='0';
            else ans+='1';
        }
        ans = new StringBuilder(ans).reverse().toString();
        ans+=s.substring(cur);
        return ans;
    }
    static String next () throws IOException {
        while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(input.readLine().trim());
        return st.nextToken();
    }
    static long readLong () throws IOException {
        return Long.parseLong(next());
    }
    static int readInt () throws IOException {
        return Integer.parseInt(next());
    }
    static double readDouble () throws IOException {
        return Double.parseDouble(next());
    }
    static char readChar () throws IOException {
        return next().charAt(0);
    }
    static String readLine () throws IOException {
        return input.readLine().trim();
    }
}