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;
typedef long long ll;
typedef pair<string, string> pii;

int n;
string s;
map<pii, ll> m;
ll ans = 0;

int main() {
	cin >> n;
	cin >> s;
	for (int i = 0; i < (1<<n); ++i) {
		string a, b;
		for (int j = 0; j < n; ++j) {
			if ((i&(1<<j)) == 0)
				a += s[j];
			else
				b += s[j];
		}
		m[pii(a, b)]++;
	}

	for (int i = 0; i < (1<<n); ++i) {
		string a, b;
		for (int j = 0; j < n; ++j) {
			if ((i&(1<<j)) == 0)
				a += s[2*n-1-j];
			else
				b += s[2*n-1-j];
		}
		ans += m[pii(b, a)];
	}
	cout << ans << endl;
}