dpI - Coins

using namespace std;
const int NMAX = 3e3 + 11;
int n;
double p[NMAX], dp[NMAX][NMAX];
double solve(void)
{
    dp[0][0] = 1;
    for (int i = 1; i <= n; ++i)
        dp[0][i] = 0;
    for (int i = 1; i <= n; ++i)
    {
        for (int j = 0; j <= n; ++j)
        {
            dp[i][j] = (1 - p[i]) * dp[i - 1][j];
            if (j != 0)
                dp[i][j] += p[i] * dp[i - 1][j - 1];
        }
    }
    return accumulate(dp[n] + n / 2 + 1, dp[n] + n + 1, 0.0);
}
int main(void)
{
    cin >> n;
    for (int i = 1; i <= n; ++i)
        cin >> p[i];
    cout << setprecision(10) << solve() << endl;
    return 0;
}