Problem: 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.

Examples

Input

4
cabaacba


Output

4


Input

11
mippiisssisssiipsspiim


Output

504


Input

4
abcdefgh


Output

0


Input

18
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa


Output

9075135300

Solution (in CPP):

Solution:
#include <map>
#include <cstdio>
#include <string>
#include <iostream>
#include <algorithm>
typedef long long ll;

int n;
char s[40];
std::map<std::pair<std::string,std::string>,int> C;

int main()
{
    scanf("%d%s",&n,s);
    std::reverse(s+n,s+(n<<1));
    for(int i=0;i<(1<<n);++i)
    {
        std::string a,b;
        for(int j=0;j<n;++j)
            if(i>>j&1)a+=s[j];
            else b+=s[j];
        ++C[std::make_pair(a,b)];
    }
    ll Ans=0;
    for(int i=0;i<(1<<n);++i)
    {
        std::string a,b;
        for(int j=0;j<n;++j)
            if(i>>j&1)a+=s[n+j];
            else b+=s[n+j];
        Ans+=C[std::make_pair(a,b)];
    }
    printf("%lld\n",Ans);
    return 0;
}