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 <string>
#include <map>
#include <utility>

using namespace std;
int main(){
	int i,j,n;
	long long ans = 0;
	map<pair<string,string>,long long> l;
	string s;
	cin >> n >> s;
	for(i=0;i<1<<n;i++){
		string r,b;
		for(j=0;j<n;j++){
			if(i&(1LL<<j)){
				r = s[j] + r;
			}else{
				b = s[j] + b;
			}
		}
		l[{r,b}]++;
	}
	for(i=0;i<1<<n;i++){
		string r,b;
		for(j=0;j<n;j++){
			if(i&(1LL<<j)){
				r = r + s[j+n];
			}else{
				b = b + s[j+n];
			}
		}
		ans += l[{b,r}];
	}
	cout << ans << endl;
}