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 <cstdio>
#include <algorithm>
#include <cmath>
#include <cstring>
#include <map>
#include <iostream>

using namespace std;
map <pair <string, string> , int> cnt;

long long res;
int n;
char s[40];
int main() 
{
	scanf("%d%s", &n, s);
	for (int i = 0; i < (1 << n); i++) {
		string s1 = "", s2 = "";
		for (int j = 0; j < n; j++) {
			if(i & (1 << j)) s1 += s[j];
			else s2 += s[j];
		}
		cnt[make_pair(s1, s2)]++;
	}
	for (int i = 0; i < (1 << n); i++) {
		string s1 = "", s2 = "";
		for (int j = n - 1; j >= 0; j--) {
			if(i & (1 << j)) s1 += s[j + n];
			else s2 += s[j + n];
		}
		res += cnt[make_pair(s2, s1)];
	}
	printf("%lld\n", res);
	return 0;
}