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;

int n;
char s[200];
map<pair<string, string>, long long > mp;

int main(void) {
  scanf("%d", &n); 
  scanf("%s", s);
  for(int i = 0; i < (1 << n); i++) {
    string a = "", b = "";
    for(int j = 0; j < n; j++)
      ((i >> j & 1) ? a : b) += s[j];
    //cerr << a << " " << b << endl;
    mp[make_pair(a, b)]++;
  }
  long long ans = 0;
  reverse(s, s + n + n);
  for(int i = 0; i < (1 << n); i++) {
    string a = "", b = "";
    for(int j = 0; j < n; j++)
      ((i >> j & 1) ? a : b) += s[j];
    //cerr << a << " " << b << " " << mp[make_pair(a, b)] << endl;
    ans += mp[make_pair(a, b)];
  }
  cout << ans << endl;
  return 0;
}