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<map>
#include<cstring>
#include<cmath>
#include<iostream>
using namespace std;
typedef long long LL;

map<pair <string,string>,LL> cnt;
const int maxn = 50;
char s[maxn];

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