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 int ll;
map < pair< string,string >,ll > x; 
int n;
string s;
ll ans;
void rec1(int ind,string r,string b,int cnt)
{
	
	if(cnt==n)
	{
	reverse(b.begin(),b.end());
	x[make_pair(r,b)]++;
	return;
	}
	rec1(ind+1,r+s[ind],b,cnt+1);
	rec1(ind+1,r,b+s[ind],cnt+1);
}
void rec2(int ind,string r,string b,int cnt)
{
	if(cnt==n)
	{
	    reverse(b.begin(),b.end());
	    ans+=x[make_pair(b,r)];
	    return;
	}
	rec2(ind+1,r+s[ind],b,cnt+1);
	rec2(ind+1,r,b+s[ind],cnt+1);
}
int main()
{
	cin>>n;
	cin>>s;
	rec1(0,"","",0);
	rec2(n,"","",0);
	cout<<ans<<endl;
}