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> P;
const ll MOD = 1000000007LL;

int main() {
	int N;
	cin >> N;
	string S;
	cin >> S;
	map<P, int> cnt;
	for (int bit = 0; bit < (1 << N); bit++) {
		string a = "", b = "";
		for (int i = 0; i < N; i++) {
			if (bit&(1 << i)) a.push_back(S[i]);
			else b.push_back(S[i]);
		}
		cnt[P(a, b)]++;
	}
	ll ans = 0;
	for (int bit = 0; bit < (1 << N); bit++) {
		string a = "", b = "";
		for (int i = 0; i < N; i++) {
			if (bit&(1 << i)) b.push_back(S[i + N]);
			else a.push_back(S[i + N]);
		}
		reverse(a.begin(), a.end());
		reverse(b.begin(), b.end());
		ans += cnt[P(a, b)];
	}
	cout << ans << endl;
}