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;

const int N = 18 + 1;

typedef pair<string, string> pss;

map<pss, int> mp;
string s, t;
long long ans, n;

int main() {
	ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0);
	cin >> n >> s;
	for (int mask = 0; mask < (1 << n); mask++) {
		string a, b;
		a = b = "";
		for (int i = 2 * n - 1; i >= n; i--) {
			if (mask >> (i - n) & 1)
				a += s[i];
			else
				b += s[i];
		}
		mp[{a, b}]++;
	}
	for (int mask = 0; mask < (1 << n); mask++) {
		string a, b;
		a = b = "";
		for (int i = 0; i < n; i++) {
			if ((mask >> i) & 1)
				a += s[i];
			else
				b += s[i];
		}
		ans += mp[{a, b}];
	}
	return cout << ans, 0;
}