#include <iostream>
#include <vector>
#include <array>
#include <string>
#include <algorithm>
#include <iomanip>
#include <map>
#include <deque>

using namespace std;
#define ld long double
const ld INF = 1e18;

struct Line {
    ld k, b;
};

ld inter(Line a, Line b) {
    return (a.b - b.b) / (b.k - a.k);
}

struct Part {
    Line ln;
    ld x;
};

struct CHT {
    vector <Part> st;

    void add(Line a) {
        while (st.size() > 1 && inter(st[st.size() - 2].ln, a) <= st[st.size() - 2].x) {
            st.pop_back();
        }
        if (!st.empty()) st.back().x = inter(st.back().ln, a);
        st.push_back({a, INF});
    }

    inline ld get_val(ld x) {
        if (st.empty()) return -INF;
        int l = -1;
        int r = st.size() - 1;

        while (r - l > 1) {
            int m = (l + r) / 2;
            if (st[m].x >= x) r = m;
            else l = m;
        }

        return st[r].ln.k * x + st[r].ln.b;
    }
};

void solve() {
    int n;
    cin >> n;
    vector <ld> p(n + 1);
    p[0] = 1;
    for (int i = 1; i <= n; ++i) cin >> p[i];

    vector <ld> dp(n + 1);
    dp[n] = n;
    CHT now;

    now.add({p[n], p[n] * dp[n]});

    for (int i = n - 1; i >= 0; --i) {
        dp[i] = now.get_val(-i) + i;
        now.add({p[i], p[i] * dp[i]});
    }

    cout << fixed << setprecision(10) << dp[0];
}

signed main() {
    if (1) {
        ios_base::sync_with_stdio(false);
        cin.tie(nullptr);
    }
    int t = 1;
//    cin >> t;
    while (t--) {
        solve();
    }
    return 0;
}

/*
5
0.9 0.85 0.6 0.456000 0.000000017
 */