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<cstdio>
#include<iostream>
#include<map>
#include<string>
#include<algorithm>
using namespace std;
#define i64 long long int
char s[99];int n;
map<pair<string,string>,int> Map;
int main(){
	scanf("%d%s",&n,s);
	for(int mask=0; mask<(1<<n); mask++){
		string r = "", b = "";
		for(int i=0; i<n; i++)if(mask&(1<<i))
			r += s[i];
		else
			b += s[i];
		reverse(b.begin(), b.end());
		Map[make_pair(r,b)]++;
	}
	i64 res = 0;
	for(int mask=0; mask<(1<<n); mask++){
		string r = "", b = "";
		for(int i=0; i<n; i++)if(mask&(1<<i))
			r += s[i+n];
		else
			b += s[i+n];
		reverse(b.begin(), b.end());
		auto tmp = make_pair(b,r);
		if(Map.count(tmp))
			res += Map[tmp];
	}
	cout << res << endl;
	return 0;
}