#include<bits/stdc++.h>
using namespace std;
int n,q[500005],front,back;
double p[500005],f[500005];
double get_x(int i){
	return p[i];
}
double get_y(int i){
	return p[i]*f[i+1]+p[i];
}
double get_k(int i,int j){
	return (get_y(i)-get_y(j))/(get_x(i)-get_x(j));
}
double culcu(int i,int j){
	return p[j]*f[j+1]+(1-p[j])*(i-1);
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%lf",&p[i]);
	f[n+1]=n;
	for(int i=n;i>=1;i--){
		while(front<back&&get_k(q[back],q[back-1])<get_k(i,q[back]))back--;
		q[++back]=i;
		while(front<back&&culcu(i,q[front])<culcu(i,q[front+1]))front++;
		f[i]=culcu(i,q[front]);
	}
	printf("%.6lf",f[1]);
}