Problem:
Score : 600 points

Problem Statement

You are given a string S of length 2N consisting of lowercase English letters.

There are 2^{2N} ways to color each character in S red or blue. Among these ways, how many satisfy the following condition?

The string obtained by reading the characters painted red from left to right is equal to the string obtained by reading the characters painted blue from right to left.

Constraints

1 \leq N \leq 18

The length of S is 2N.

S consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

N
S

Output

Print the number of ways to paint the string that satisfy the condition.

Sample Input 1

4
cabaacba

Sample Output 1

4

There are four ways to paint the string, as follows:

cabaacba

cabaacba

cabaacba

cabaacba

Sample Input 2

11
mippiisssisssiipsspiim

Sample Output 2

504

Sample Input 3

4
abcdefgh

Sample Output 3

0

Sample Input 4

18
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Sample Output 4

9075135300

The answer may not be representable as a 32-bit integer.

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using System.Globalization;
using System.Diagnostics;
using System.Threading.Tasks;



class Myon
{
    public Myon() { }
    public static int Main()
    {
        new Myon().calc();
        return 0;
    }
    

    Scanner cin;

    void calc()
    {
        cin = new Scanner();
        int N = cin.nextInt();
        string S = cin.next();
        string S1 = S.Substring(0, N);

        Dictionary<string, int> dic = new Dictionary<string, int>();
        for (int i = 0; i < (1 << N); i++)
        {
            StringBuilder sa = new StringBuilder();
            StringBuilder sb = new StringBuilder();
            for (int j = 0; j < N; j++)
            {
                if (((i >> j) & 1) == 0) sa.Append(S1[j]);
                else sb.Append(S1[j]);
            }
            string SS = sa.ToString() + "-" + sb.ToString();
            if (!dic.ContainsKey(SS)) dic[SS] = 0;
            dic[SS]++;
        }

        long ans = 0;

        for (int i = 0; i < (1 << N); i++)
        {
            StringBuilder sa = new StringBuilder();
            StringBuilder sb = new StringBuilder();
            for (int j = 0; j < N; j++)
            {
                if (((i >> j) & 1) == 0) sa.Append(S[2 * N - j - 1]);
                else sb.Append(S[2 * N - j - 1]);
            }
            string SS = sa.ToString() + "-" + sb.ToString();
            if (dic.ContainsKey(SS)) ans += dic[SS];
        }

        Console.WriteLine(ans);
    }

}




class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string next()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return next();
        i = 0;
        return s[i++];
    }

    public int nextInt()
    {
        return int.Parse(next());
    }
    public int[] ArrayInt(int N, int add = 0)
    {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextInt() + add;
        }
        return Array;
    }

    public long nextLong()
    {
        return long.Parse(next());
    }

    public long[] ArrayLong(int N, long add = 0)
    {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextLong() + add;
        }
        return Array;
    }

    public double nextDouble()
    {
        return double.Parse(next());
    }


    public double[] ArrayDouble(int N, double add = 0)
    {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextDouble() + add;
        }
        return Array;
    }
}