#include <bits/stdc++.h>
using namespace std;

int n;
long long ans;
string a,z;
map<pair<string,string>,int> M;

void dfs(int i,int j,string x,string y)
{
	if(i>j)
	{
		z="";
		for(int i=x.size()-1;i>=0;i--)z+=x[i];
		x=z,z="";
		for(int i=y.size()-1;i>=0;i--)z+=y[i];
		y=z;
		M[make_pair(x,y)]++;
		return ;
	}
	dfs(i+1,j,x+a[i],y);
	dfs(i+1,j,x,y+a[i]);
}

void dfs2(int i,int j,string x,string y)
{
	if(i>j)
	{
		ans+=M[make_pair(x,y)];
		return ;
	}
	dfs2(i+1,j,x+a[i],y);
	dfs2(i+1,j,x,y+a[i]);
}

int main()
{
	cin>>n>>a;
	dfs(0,n-1,"","");
	dfs2(n,n*2-1,"","");
	cout<<ans;
	return 0;
}

### Prompt

In CPP, your task is to solve the following 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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

int n;
long long ans;
string a,z;
map<pair<string,string>,int> M;

void dfs(int i,int j,string x,string y)
{
	if(i>j)
	{
		z="";
		for(int i=x.size()-1;i>=0;i--)z+=x[i];
		x=z,z="";
		for(int i=y.size()-1;i>=0;i--)z+=y[i];
		y=z;
		M[make_pair(x,y)]++;
		return ;
	}
	dfs(i+1,j,x+a[i],y);
	dfs(i+1,j,x,y+a[i]);
}

void dfs2(int i,int j,string x,string y)
{
	if(i>j)
	{
		ans+=M[make_pair(x,y)];
		return ;
	}
	dfs2(i+1,j,x+a[i],y);
	dfs2(i+1,j,x,y+a[i]);
}

int main()
{
	cin>>n>>a;
	dfs(0,n-1,"","");
	dfs2(n,n*2-1,"","");
	cout<<ans;
	return 0;
}

```