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<iostream>
#include<map>
#include<algorithm>
using namespace std;
map<pair<string,string>,long>M;
int n;string s;
int main()
{
  cin>>n>>s;
  for(int i=0;i<1<<n;i++)
  {
    string a="",b="";
    for(int j=0;j<n;j++)
    {
      if(i&1<<j)a+=s[j];
      else b+=s[j];
    }
    M[make_pair(a,b)]++;
  }
  long ans=0;
  for(int i=0;i<1<<n;i++)
  {
    string a="",b="";
    for(int j=0;j<n;j++)
    {
      if(i&1<<j)a+=s[n+j];
      else b+=s[n+j];
    }
    reverse(a.begin(),a.end());
    reverse(b.begin(),b.end());
    ans+=M[make_pair(b,a)];
  }
  cout<<ans<<endl;
}