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;

long long n, res = 0;
string s, s1, s2;
map<pair<string, string>, long long> a;
int main() {
	cin >> n >> s;
	s1 = s.substr(0, n), s2 = s.substr(n);
	reverse(s2.begin(), s2.end());
	for (int bit = 0; bit < 1<<n; bit++)
	{
		string x, y;
		for (int i = 0; i < n; i++)
		{
			(bit>>i & 1 ? x : y).push_back(s1[i]);
		}
		a[{x, y}]++;
	}
	for (int bit = 0; bit < 1<<n; bit++)
	{
		string x, y;
		for (int i = 0; i < n; i++)
		{
			(bit>>i & 1 ? x : y).push_back(s2[i]);
		}
		res += a[{x, y}];
	}
	cout << res << endl;
	return 0;
}