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> pss;

ll n, ans;
string s;
map<pss, int> cnt;

int main() {
	cin >> n >> s;
	for (int i = 0; i < (1 << n); i++) {
		string a = "", b = "";
		for (int j = 0; j < n; j++)
			if(i & (1 << j))
				a.push_back(s[j]);
		for (int j = n - 1; j >= 0; j--)
			if((i & (1 << j)) == 0)
				b.push_back(s[j]);
		cnt[pss(a, b)]++;
	}
	
	for (int i = 0; i < (1 << n); i++) {
		string a = "", b = "";
		for (int j = 0; j < n; j++)
			if(i & (1 << j))
				a.push_back(s[n + j]);
		for (int j = n - 1; j >= 0; j--)
			if((i & (1 << j)) == 0)
				b.push_back(s[j + n]);
		ans += cnt[pss(b, a)];
	}
	cout << ans;
	return 0;
}