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

int N; string S; map<pair<string, string>, int>M;
long long ret = 0;

int main() {
	cin >> N >> S;
	for (int i = 0; i < (1 << N); i++) {
		string T1 = "", T2 = "";
		for (int j = 0; j < N; j++) {
			if ((i / (1 << j)) % 2 == 0) T1 += S[N + j];
			else T2 += S[N + j];
		}
		M[make_pair(T1, T2)]++;
	}
	for (int i = 0; i < (1 << N); i++) {
		string T1 = "", T2 = "";
		for (int j = 0; j < N; j++) {
			if ((i / (1 << j)) % 2 == 0) T1 += S[j];
			else T2 += S[j];
		}
		reverse(T1.begin(), T1.end());
		reverse(T2.begin(), T2.end());
		ret += M[make_pair(T2, T1)];
	}
	cout << ret << endl;
	return 0;
}