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;
typedef long long ll;

void f(int n, string s, vector<map<string, int>>& r, string a, string b) {
  int i = a.size() + b.size();
  if (i == n) {
    reverse(begin(b), end(b));
    string c = a + b;
    r[a.size()][c]++;
    return;
  }
  a.push_back(s[i]);
  f(n, s, r, a, b);
  a.pop_back();
  b.push_back(s[i]);
  f(n, s, r, a, b);
}

int main() {
  int n;
  string s;
  cin >> n >> s;
  vector<map<string, int>> u(n + 1), v(n + 1);
  f(n, s, u, "", "");
  reverse(begin(s), end(s));
  f(n, s, v, "", "");
  ll m = 0;
  for (int i = 0; i < n + 1; i++) {
    for (auto e : u[i]) {
      m += (ll)e.second * v[i][e.first];
    }
  }
  cout << m << endl;
  return 0;
}