#include<bits/stdc++.h>
using namespace std;
#define ld long double
#define ll long long 
#define MP make_pair
mt19937 rnd(time(0));
const int MAXN=5e5+5;
ld f[MAXN],a[MAXN];int n;
ld z(int j,int i){return a[j]*f[j]+(1-a[j])*i;}
struct info { int l,r,x; } g[MAXN];
int main(){
	// freopen("Otomachi_Una.in","r",stdin);
	// freopen("Otomachi_Una.out","w",stdout);
	ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
	cin>>n;
	for(int i=1;i<=n;i++) cin>>a[i];
	int tp=0,hd=1;
	g[++tp]={1,n,n},f[n]=n;
	for(int i=n-1;i>=0;--i) {
		while(hd<tp&&i<g[hd].l) ++hd;
		f[i]=z(g[hd].x,i);
		if(!i) break;
		while(tp&&z(g[tp].x,g[tp].r)<z(i,g[tp].r)) --tp;
		if(!tp) g[++tp]={0,i-1,i};
		else {
			int l=g[tp].l,r=g[tp].r-1,k=g[tp].r;
			while(l<=r) {
				int mid=(l+r)>>1;
				if(z(g[tp].x,mid)>z(i,mid)) k=mid,r=mid-1;
				else l=mid+1;
			}
			g[tp].l=k;
			if(k>1) g[++tp]={0,k-1,i};
		}
	}
	cout<<fixed<<setprecision(20)<<f[0]<<'\n';
	return 0;
}