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 string S;
long long n,r,i,j;S s;map<pair<S,S>,long long> a;
int main() {
	cin>>n>>s;
	for(;i<1<<n;++i){
		S x,y;
		for(j=0;j<n;++j)(i>>j&1?x:y).push_back(s[j]);
		a[{x,y}]++;
	}
	while(i--){
		S x,y;
		for(j=n-1;j>=0;--j)(i>>j&1?y:x).push_back(s[n+j]);
		r+=a[{x,y}];
	}
	cout<<r;
}