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>
using namespace std;
#define rep(i,n) for(int i = 0; i < (n);i++)
#define sz(x) int(x.size())
typedef long long ll;
typedef pair<int,int> P;


int main(){
  int n;
  string s;
  cin >> n >> s;
  map<pair<string,string>,ll> mp;
  ll res = 0;
  for (int bit = 0; bit < (1 << n); bit++) {
    string blue, red;
    for (int i = 0; i < n; i++) {
      if (bit & (1<<i)) blue += s[i];
      else red += s[i];
    }
    mp[{blue,red}]++;
  }
  reverse(s.begin(), s.end());
  for (int bit = 0; bit < (1 << n); bit++) {
    string blue, red;
    for (int i = 0; i < n; i++) {
      if (bit & (1<<i)) blue += s[i];
      else red += s[i];
    }
    res += mp[{red,blue}];
  }
  cout << res << endl;
  return 0;
}