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 <cstdio>
#include <cstring>
using namespace std;
int n,x,y,c[100];
long long f[20][20],ans;
char a[100],d[100],e[100];
void dfs(int t)
{
		if (t>n)
		{
				x=y=0;
				for (int i=1;i<=n;++i)
						if (c[i]==0)
								d[++x]=a[i];
						else	e[++y]=a[i];
				memset(f,0,sizeof(f));
				f[0][0]=1;
				for (int i=1;i<=n;++i)
						for (int j=0;j<=min(i,x);++j)
						{
								if (j && a[n+n-i+1]==d[j])
										f[i][j]+=f[i-1][j-1];
								if (i>j && i-j<=y && a[n+n-i+1]==e[i-j])
										f[i][j]+=f[i-1][j];
						}
				ans+=f[n][x];
				return;
		}
		c[t]=0;	dfs(t+1);
		c[t]=1;	dfs(t+1);
}
int main()
{
		scanf("%d",&n);
		scanf("%s",a+1);
		dfs(1);
		printf("%lld\n",ans);
		return 0;
}