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<iostream>
#include<cstdio>
#include<cstring>
#include<map> 
using namespace std;
typedef long long ll;
int n;
char s[45];
typedef pair<string,string> P;
map<P,ll>num;
ll ans;
string l,r;//l从左到右 r从右到左 
int main()
{
	scanf("%d",&n);
	scanf("%s",s);
	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)];
	}
	printf("%lld\n",ans);
}