#include <bits/stdc++.h>
#define fi first
#define se second
#define pb push_back
using namespace std;

using pdd = pair<double, double>;
const int N = 500010, SZ = (1 << 18) + 5;
static char buf[SZ], *bgn = buf, *til = buf;
char getc() {
    if(bgn == til)  bgn = buf, til = buf + fread(buf, 1, SZ, stdin);
    return bgn == til ? EOF : *bgn++;
}
template<typename T>
void read(T &x) {
    char ch = getc();  T fh = 0;   x = 0;
    while(ch < '0' || ch > '9')    fh |= (ch == '-'), ch = getc();
    while(ch >= '0' && ch <= '9')   x = x * 10 + ch - '0', ch = getc();
    x = fh ? -x : x;
}
template<typename Type, typename... argc>
void read(Type &x, argc &...args)   {read(x), read(args...);}
template<typename T>
void print(T x) {
    if(x < 0)  putchar('-'), x = -x;
    if(x / 10)  print(x / 10);
    putchar(x % 10 + '0');
}
int n, que[N], hh = 1, tt;
double p[N], f[N];
double slope(const pdd &x, const pdd &y)    {return (y.se - x.se) / (y.fi - x.fi);}
pdd get(int x)  {return {p[x], p[x] * f[x]};}
int main() {
    #ifdef Kelly
        freopen("in.txt", "r", stdin);
        freopen("out.txt", "w", stdout);
        freopen("err.txt", "w", stderr);
    #endif
    ios::sync_with_stdio(false), cin.tie(nullptr);
    cin >> n;
    for(int i = 1; i <= n; ++i) cin >> p[i];
    f[n] = n, que[++tt] = n;
    for(int i = n - 1; i >= 0; --i) {
        while(hh < tt && slope(get(que[hh]), get(que[hh + 1])) > i) ++hh;
        f[i] = get(que[hh]).se + (1 - p[que[hh]]) * i;
        if(i == 0)  break;
        while(hh < tt && slope(get(que[tt - 1]), get(que[tt])) <= slope(get(que[tt]), get(i)))  --tt;
        que[++tt] = i;
    }
    cout << fixed << setprecision(12) << f[0];
    return 0;
}