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 <map>

using namespace std;

int main(){
	int half;
	cin>>half;
	string s;
	cin>>s;

	map<string, int>m;

	for(int i=0;i<(1<<half);i++){
		string r="", b="";
		for(int j=0;j<half;j++){
			if(i & (1<<j)){
				r = r + s[j];
			}
			else
				b = b + s[j];
		}
		m[r + '.' + b]++;
	}

	long long ans=0;

	for(int i=0;i<(1<<half);i++){
		string r="", b="";
		for(int j=0;j<half;j++){
			if(i & (1<<j)){
				r = s[half + j] + r;
			}
			else
				b = s[half + j] + b;
		}
		ans += 1ll*m[b + '.' + r];
	}

	cout<<ans;
}