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<unordered_map>
#include<algorithm>

using namespace std;

long long n, sol;
string s;
unordered_map <string, int> mp;

void f (string t, int flg) {
	string a, b;
	for (int mask=0; mask<(1<<n); mask++) {
		a = "", b = "";
		for (int i=0; i<n; i++) {
			if (mask & (1 << i)) {
				a += t[i];
			} else {
				b += t[i];
			}
		}
		if (flg) mp[a+'.'+b]++; else sol += mp[a+'.'+b];
	}
}

int main () {
	cin >> n >> s;
	f(s.substr(0, n), 1);
	s = s.substr(n, n);
	reverse(s.begin(), s.end());
	f(s, 0);
	cout << sol;
	return 0;
}