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 long double ld;
typedef complex<ld> point;
const int maxn = 300 + 5;
const int mod = 998244353; 

map<pair<string,string>, int> mp;

int main(){
	ios_base::sync_with_stdio(false);
	int n;
	string s;
	cin >> n >> s;
	for (int mask = 0; mask < (1<<n); mask++){
		string A, B;
		for (int i = 0; i < n; i++)
			if (mask & (1 << i))
				A += s[i];
			else
				B += s[i];
		mp[{A,B}] ++;
	}
	ll answer = 0;
	for (int mask = 0; mask < (1<<n); mask++){
		string A, B;
		for (int i = 0; i < n; i++)
			if (mask & (1 << i))
				A += s[2*n-i-1];
			else
				B += s[2*n-i-1];
		answer += mp[{A,B}];
	}
	cout << answer << endl;
}