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 <map>
#include <algorithm>
#include <iostream>
#include <string>
using namespace std;

map<pair<string, string> , long long> mp;
long long ans;
string tmp;
int n;

int main() {
	cin >> n >> tmp;
	for (int i = 0; i < (1 << n); i++) {
		string r1, r2;
		for (int j = 0; j < n; j++)
			if ((i & (1 << j)) != 0)
				r1.push_back(tmp[n + j]);
			else
				r2.push_back(tmp[n + j]);
		reverse(r2.begin(), r2.end());
		mp[{r1, r2}]++;
	}
	for (int i = 0; i < (1 << n); i++) {
		string r1, r2;
		for (int j = 0; j < n; j++)
			if ((i & (1 << j)) != 0)
				r1.push_back(tmp[j]);
			else
				r2.push_back(tmp[j]);
		reverse(r2.begin(), r2.end());
		ans += mp[{r2, r1}];
	}
	cout << ans;
}