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<algorithm>
#include <string>
#include <map>
using namespace std;

int main(){
	int n;cin>>n;
	string s;cin>>s;
	
	using P = pair<string,string>;
	map<P,int> mp;
	
	for(int i=0;i<(1<<n);i++)
	{
		string t="",rt="";
		for(int j=0;j<n;j++)
		{
			if((i>>j)&1) t+=s[j];
			else rt+=s[j];
		}

		mp[P(t,rt)]++;
	}

	reverse(s.begin(),s.end());

	
	long long ans = 0;
	
	for(int i=0;i<(1<<n);i++)
	{
		string t,rt;
		for(int j=0;j<n;j++)
		{
			if((i>>j)&1) t+=s[j];
			else rt+=s[j];
		}
		ans += mp[P(t,rt)];
	}
	
	cout << ans << endl;
	
}