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>
#define rep(i,l,r) for (int i=l;i<=r;i++)
using namespace std;
typedef unsigned long long ull;
map<pair<ull,ull>,int > mp;
int n;
char s[55];
ull ans;
int main(){
	scanf("%d%s",&n,s);
	rep(i,0,(1<<n)-1){
		ull a=0,b=0;
		rep(j,0,n-1) if (i&(1<<j)) a=a*233+s[j];
		for (int j=n-1;j>=0;j--) if ((i&(1<<j))==0) b=b*233+s[j];
		mp[make_pair(a,b)]++;
	}
	rep(i,0,(1<<n)-1){
		ull a=0,b=0;
		rep(j,0,n-1) if (i&(1<<j)) a=a*233+s[j+n];
		for (int j=n-1;j>=0;j--) if ((i&(1<<j))==0) b=b*233+s[j+n];
		ans+=mp[make_pair(b,a)];	
	}
	cout<<ans<<endl;
	return 0;
}