#include <bits/stdc++.h>
#define N 500011
#define dubble long double
#define s1 first
#define s2 second
using namespace std;
int n;
dubble p[N],f[N];
int main()
{
	scanf("%d",&n);
	p[0]=1;
	for(int i=1;i<=n;++i)scanf("%Lf",p+i);
	f[n]=n;
	deque<pair<dubble,dubble> > vp;
	vp.push_back({p[n],p[n]*f[n]});
	for(int i=n-1;~i;--i)
	{
		// for(int j=i+1;j<=n;++j)f[i]=max(f[i],p[j]*f[j]+(1-p[j])*i);
		// printf("vp:");for(auto x:vp)printf("(%Lf,%Lf) ",x.s1,x.s2);putchar(10);
		int L=0,R=(int)vp.size()-1;
		f[i]=i;
		while(L+1<=R)
		{
			int M=L+R>>1;
			dubble v1=vp[M].s2-vp[M].s1*i+i;
			dubble v2=vp[M+1].s2-vp[M+1].s1*i+i;
			f[i]=max({f[i],v1,v2});
			if(v1>v2)R=M-1;else L=M+2;
		}
		for(int _=L;_<=R;++_)f[i]=max(f[i],vp[_].s2-vp[_].s1*i+i);
		dubble nx=p[i],ny=p[i]*f[i];
		while(vp.size()>1&&(ny-vp.end()[-1].s2)/(nx-vp.end()[-1].s1)>=(vp.end()[-1].s2-vp.end()[-2].s2)/(vp.end()[-1].s1-vp.end()[-2].s1))vp.pop_back();
		vp.push_back({p[i],f[i]*p[i]});
	}
	printf("%.20Lf\n",f[0]);
	fclose(stdin);fclose(stdout);return 0;
}