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 <string>
#include <map>

using namespace std;

int n;
string s;

int main() {
  cin >> n >> s;
  long long int ans = 0;
  map<string, int> mp;
  for (int t = 0; t < (1 << n); t++) {
    string a = "", b = "";
    for (int i = 0; i < n; i++) {
      if (t & (1 << i)) a += s[i];
      else b += s[i];
    }
    string c = a + "." + string(b.rbegin(), b.rend());
    mp[c]++;
  }
  
  for (int t = 0; t < (1 << n); t++) {
    string a = "", b = "";
    for (int i = 0; i < n; i++) {
      if (t & (1 << i)) a += s[i + n];
      else b += s[i + n];
    }
    string c = string(a.rbegin(), a.rend()) + "." + b;
    ans += mp[c];
  }
  cout << ans;
}