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 <iostream>
#include <map>
using namespace std;
string s;
int n;
map <pair <string,string>,long long> ml,mr;
int main()
{
	cin>>n>>s;
	string l=s.substr(0,n),r=s.substr(n,n);
	for (int i=0;i<1<<n;i++)
	{
		string lr="",lb="",rr="",rb="";
		for (int j=0;j<n;j++)
		{
			if (i&(1<<j))
			{
				lr+=l[j];
				rr+=r[n-1-j];
			}
			else
			{
				lb+=l[j];
				rb+=r[n-1-j];
			}
		}
		ml[make_pair(lr,lb)]++;
		mr[make_pair(rr,rb)]++;
	}
	long long ans=0;
	for (auto x:ml) ans+=x.second*mr[x.first];
	cout<<ans<<endl;
	return 0;
}