#include <bits/stdc++.h>
#define st first
#define nd second
using lint = long long;
constexpr int mod = 998244353;
constexpr int inf = 0x3f3f3f3f;
constexpr lint linf = 0x3f3f3f3f3f3f3f3f;
using namespace std;

struct Line { ///start-hash
	mutable double k, m, p;
	bool operator<(const Line& o) const { return k < o.k; }
	bool operator<(double x) const { return p < x; }
}; ///end-hash
struct LineContainer : multiset<Line, less<>> {
	const double inf = 1/.0; //for doubles 1/.0
	double div(double a, double b) { //for doubles a/b
		return a / b; }
	bool isect(iterator x, iterator y) { ///start-hash
		if (y == end()) { x->p = inf; return false; }
		if (x->k == y->k) x->p = x->m > y->m ? inf : -inf;
		else x->p = div(y->m - x->m, x->k - y->k);
		return x->p >= y->p;
	} ///end-hash
	void add(double k, double m) { ///start-hash
		auto z = insert({k, m, 0}), y = z++, x = y;
		while (isect(y, z)) z = erase(z);
		if (x != begin() && isect(--x, y)) isect(x, y = erase(y));
		while ((y = x) != begin() && (--x)->p >= y->p) 
			isect(x, erase(y));
	}///end-hash
	double query(double x) { ///start-hash
		assert(!empty()); auto l = *lower_bound(x);
		return l.k * x + l.m;
	}///end-hash
};

int main(){
    cin.tie(nullptr)->sync_with_stdio(false);
    int n;
    cin>>n;
    vector<double>p(n);
    for(int i=0;i<n;i++) cin>>p[i];
    vector<double>dp(n+1);
    dp[n] = n;
    LineContainer g;
    for(int i=n-1;i>=0;i--){
        g.add(1 - p[i], p[i] * dp[i+1]);
        dp[i] = g.query(i);
    }
    cout<<fixed<<setprecision(8);
    cout<<dp[0]<<"\n";
    
    return 0;
}