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 <cstdio>
#include <algorithm>
#include <map>
using namespace std;
typedef long long ll;

ll n, ans;
string s;
map<pair<string, string>, ll> mp;

void f(int p) {
	ll i, j;
	for(i=0; i<1<<n; i++) {
		string r, b;
		for(j=0; j<n; j++) {
			if(i & 1<<j) r.push_back(s[j]);
			else b.push_back(s[j]);
		}
		p<1 ? mp[{r,b}]++ : ans += mp[{r,b}];
	}
}

int main() {
	cin >> n >> s;
	f(0);
	reverse(s.begin(), s.end());
	f(1);
	cout << ans;
	return 0;
}