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.lang.String;
import java.io.*;
import java.util.*;
import java.util.StringTokenizer;
//class Main    //AtCoder
//class Solution // Codechef
public class Solution2 //Codeforces
{
    public final static int d = 256;
    static int MOD = 1000000007;
    static int V = 0;
    static final float EPSILON = (float)0.01;
    static final double PI = Math.PI;
    private static BufferedReader in = new BufferedReader (new InputStreamReader (System.in));
    private static PrintWriter out = new PrintWriter (new OutputStreamWriter (System.out));
    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;
        }
    }
    static void sop(Object o){System.out.print(o);}
    static void sopln(Object o){System.out.println(o);}
    public static void main(String args[])
    {
        try {
            FastReader sc = new FastReader();
            int TT = sc.nextInt();
            for (int hehe = 1 ; hehe <= TT ; hehe++) {
                int N = sc.nextInt();
                String st1 = sc.nextLine();
                String st2 = sc.nextLine();
                Vector<Integer> vec = new Vector<>();
                for(int i = 0 ; i < st1.length() ; i++)
                {
                    if(st1.charAt(i) != st2.charAt(i))
                    {
                        vec.add(i+1);
                        vec.add(1);
                        vec.add(i+1);
                    }
                }
                sop(vec.size()+" ");
                for(int I : vec)
                {
                    sop(I+" ");
                }
                sopln("");
            }
            out.flush();
        }catch (Exception e) {
            sopln("HEHE" + e.toString());
        }
    }
}