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;
typedef pair<string,string> p;

int main(){
  int N,i,j,bi;
  cin>>N;
  map<p,ll> cnt;
  string s;
  cin>>s;
  ll ans=0;
  for(bi=0;bi<(1<<N);bi++){
	string a="", b="";
	for(i=0;i<N;i++){
		if((bi>>i)&1) a+=s[i];
		else b+=s[i];
	}
	cnt[p(a,b)]++;
  }
  for(bi=0;bi<(1<<N);bi++){
	string a="", b="";
	for(i=0;i<N;i++){
		if((bi>>i)&1) a+=s[i+N];
		else b+=s[i+N];
	}
	reverse(a.begin(),a.end());
	reverse(b.begin(),b.end());
	ans+=cnt[p(a,b)];
  }
  cout<<ans<<endl;
  return 0;
}