#include<bits/stdc++.h>
using namespace std;
const int N=2e5+10;
double f[N][2],g[N][2],h[N][2];
char s[N];
int n;
int main(){
	scanf("%d",&n);
	scanf("%s",s);
	g[n-1][1]=1; f[n-1][1]=1;
	for (int i=n-2;i>=0;i--)if (s[i]=='.'){
		if (i+1>n-1||s[i+1]=='#'){
			h[i][0]+=1.0/3;
			h[i][1]+=1.0/3;
		}else{
			h[i][0]+=h[i+1][0]/3+h[i+1][1]/3;
			h[i][1]+=h[i+1][1]/3;
		}
		if (i+2>n-1||s[i+2]=='#'){
			h[i][0]+=1.0/3;
			h[i][1]+=1.0/3;			
		}else{
			h[i][0]+=h[i+2][0]/3+h[i+2][1]/3;
			h[i][1]+=h[i+2][1]/3;
		}
		double p=h[i][1]+1.0/3;
		double e=1.0/(1.0-p)*(h[i][0]+1.0/3)/(1.0-p);
		p=1.0/(1.0-p);
		double p1,e1;
		e1=(g[i+1][1]+g[i+1][0]+g[i+2][0]+g[i+2][1])/3;
		p1=(g[i+1][1]+g[i+2][1])/3;
		f[i][1]=p1*p;
		f[i][0]=p*e1+p1*e;
		g[i][1]=f[i][1]/3+p1;
		g[i][0]=f[i][0]/3+f[i][1]/3+e1;
	}
	printf("%.8lf\n",f[0][0]);
}