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<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=40;
int n,S;
char str[N];
ll sum;
map<pair<string,string>,int>dd;
int main(){
	int i;
	scanf("%d",&n);
	scanf("%s",str+1);
	for(S=0;S<1<<n;S++){
		string R="",B="";
		for(i=0;i<n;i++)((S>>i&1)?R:B)+=str[i+1];
		++dd[make_pair(R,B)];
	}
	for(S=0;S<1<<n;S++){
		string R="",B="";
		for(i=0;i<n;i++)((S>>i&1)?R:B)+=str[2*n-i];
		sum+=dd[make_pair(R,B)];
	}
	printf("%lld\n",sum);
}