#include <bits/stdc++.h>

#define int int64_t
using namespace std;

using ll = long double;
struct Line { // tested with $N,Q\leq 2\cdot 10^5$ (296 ms)
  mutable ll k, m, p;
  bool operator<(const Line& o) const { return k < o.k; }
  bool operator<(ll x) const { return p < x; }
};
struct LineContainer : multiset<Line, less<>> {
  // (for doubles, use inf = 1/.0, div(a,b) = a/b)
  static constexpr ll inf = numeric_limits<ll>::infinity();
  ll div(ll a, ll b) {
	return a/b;
  }
  bool isect(iterator x, iterator y) {
    if (y == end()) return x->p = inf, 0;
    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;
  }
  void add(ll k, ll m) {
    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));
  }
  ll query(ll x) {
    assert(!empty());
    auto l = *lower_bound(x);
    return l.k * x + l.m;
  }
};

signed main() {
	cin.tie(0);
	ios_base::sync_with_stdio(0);
	int n;
	cin>>n;
	vector<ll> p(n+1,0);
	p[0]=1;
	for(int i=1; i<=n; ++i) cin>>p[i];
	LineContainer cht;
	cht.add(1,0);
	for(int i=n; i>=1; --i) {
		// i * (1-p[j]) + dp[j] * p[j]
		// (1-p[j]), dp[j]*p[j]
		ll dp = cht.query((ll)i);
		cht.add(ll(1)-p[i], dp*p[i]);
	}
	cout<<setprecision(18)<<cht.query(0)<<endl;

	return 0;
}