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>
#define MOD 1000000007
using namespace std;
map<pair<string, string>, int> stringtocnt; 
int n;
string s;
int main() {
	cin >> n;
	cin >> s;
	for (int i = 0; i < (1 << n); i++) {
		string reds = "";
		string blues = "";
		for (int j = 0; j < n; j++) {
			if ((1 << j) & i) {
				reds += s[n + j];
			}
			else {
				blues = s[n + j] + blues;
			}
		}
		stringtocnt[make_pair(reds, blues)]++;
	}
	long long int ans = 0;
	for (int i = 0; i < (1 << n); i++) {
		string reds = "";
		string blues = "";
		for (int j = 0; j < n; j++) {
			if ((1 << j) & i) {
				reds += s[j];
			}
			else {
				blues = s[j] + blues;
			}
		}
		ans += stringtocnt[make_pair(blues, reds)];
	}	
	cout << ans << '\n';
}