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 pair<string,string> pss;
#define size(x) ((int) x.size())

map <pss, int> mp; 

string s, s1, s2;

long long n, mid, sz;

long long ans;

int main() {
	ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
	cin >> n >> s;
	sz = (1 << n);
	for (int mask = 0; mask < sz; mask++) {
		s1 = s2 = "";
		for (int i = 0; i < n; i++) {
			if ((mask >> i) & 1)
				s1 += s[i];
			else 
				s2 += s[i];
		} 
		mp[{s1, s2}]++;
	}
	for (int mask = 0; mask < sz; mask++) {
		s1 = s2 = "";
		for (int i = (2 * n) - 1; i >= n; i--) {
			if (mask >> (i - n) & 1) {
				s1 += s[i];
			}
			else
				s2 += s[i];
		}
		ans += mp[{s1, s2}];
	}
	cout << ans << endl;
	return 0;
}