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<map>
#include<cstring>
#include<iomanip>
#include<iostream>
#include<algorithm>
#define MAXN 56
using namespace std;
int n;
long long ans;
char a[MAXN];
map<pair<unsigned long long,unsigned long long>,long long> ma;
int main()
{
	scanf("%d",&n);
	scanf("%s",a);
	int Max=1<<n;
	for(int s=0;s<Max;s++)
	{
		unsigned long long p=0,q=0;
		for(int i=0;i<n;i++)
		{
			if(s&(1<<i)) p=p*131+a[i];
			else q=q*131+a[i];
		}
		ma[make_pair(p,q)]++;
	}
	for(int s=0;s<Max;s++)
	{
		unsigned long long p=0,q=0;
		for(int i=n*2-1;i>=n;i--)
		{
			if(s&(1<<(i-n))) p=p*131+a[i];
			else q=q*131+a[i];
		}
		ans+=ma[make_pair(q,p)];
	}
	printf("%lld",ans);
}