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 dfs(string s, map<pair<string, string>, ll>& r, string a, string b) {
  int i = a.size() + b.size();
  if (i == s.size() / 2) {
    r[{a, b}]++;
    return;
  }
  dfs(s, r, a + s[i], b);
  dfs(s, r, a, b + s[i]);
}

int main() {
  int n;
  string s;
  cin >> n >> s;

  map<pair<string, string>, ll> u, v;
  dfs(s, u, "", "");
  reverse(begin(s), end(s));
  dfs(s, v, "", "");

  ll m = 0;
  for (auto e : u) {
    m += e.second * v[e.first];
  }
  cout << m << endl;
}