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<bits/stdc++.h>

#define mx 100005
#define md 1000000007

using namespace std;

map<string, int> mp;
string s;
long long n, ans;

int main(){
  cin >> n >> s;
  for(int i = 0; i < 2; i++){
    for(int j = 0; j < (1<<n); j++){
      int l = 0, r = n;
      char t[20]; t[n+1] = '\0';
      for(int k = 0; k < n; k++){
        if((j>>k)&1) t[l++] = s[i ? 2*n-1-k : k];
        else t[r--] = s[i ? 2*n-1-k : k];
      }
      t[l] = 'A';
      if(i) ans += mp[(string)t];
      else mp[(string)t]++;
    }
  }
  printf("%lld\n", ans);
}