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<stdio.h>
#include<string>
#include<map>
#include<algorithm>
using namespace std;
typedef long long ll;
string a,b;
map<pair<string,string>,int>m;
char s[40];
int main(){
	int n,i,j;
	ll ans;
	scanf("%d%s",&n,s);
	reverse(s+n,s+n*2);
	for(i=0;i<1<<n;i++){
		a=b="";
		for(j=0;j<n;j++)(i>>j&1?a:b).append(1,s[j]);
		m[make_pair(a,b)]++;
	}
	ans=0;
	for(i=0;i<1<<n;i++){
		a=b="";
		for(j=0;j<n;j++)(i>>j&1?a:b).append(1,s[j+n]);
		ans+=m[make_pair(a,b)];
	}
	printf("%lld",ans);
}