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<map>
#include<cstdio>
#include<algorithm>
#include<string>
using namespace std;
int n;
long long ans;
char s[10005];
map<pair<string,string>,int>f;
int main(){
	scanf("%d%s",&n,s);
	for(int i=0;i<1<<n;i++){
		string a,b;
		for(int j=0;j<n;j++){
			if((i>>j)&1)a+=s[j];
			else b+=s[j];
		}
		f[{a,b}]++;
	}
	for(int i=0;i<1<<n;i++){
		string a,b;
		for(int j=0;j<n;j++){
		    if((i>>j)&1)a+=s[2*n-1-j];
			else b+=s[2*n-1-j]; 
		}
		ans+=f[{a,b}]; 
	}
	printf("%lld",ans);
}