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>
#define ll long long
using namespace std;
typedef pair<string,string> P;
map<P,ll>num;

ll solution(int n,string s){
  ll ans = 0;
  string l, r;
  for(int i=0;i<(1<<n);++i){
		l="",r="";
		for(int j=0;j<n;++j){
			if(i>>j&1)l+=s[j];
			else r+=s[j];
		}
		num[P(l,r)]++;
	}
	for(int i=0;i<(1<<n);++i){
		l="",r="";
		for(int j=n-1;j>=0;--j){
			if(i>>j&1)l+=s[n+j];
			else r+=s[n+j];
		}
		ans+=num[P(r,l)];
	}
	return ans;
}

int main()
{
	int n = 2;
  cin>>n;
	string s = "abba";
  cin>>s;
	ll res = solution(n, s);
  cout<<res<<endl;
}