Bastu Bathing

Finns love bathing in a bastu. That is not so strange, really. Bastu bathing feels good, and it usually happens in pleasant company.

In company, problems often arise. The most important thing when bathing in a bastu is to set the temperature right. A Finn is very particular about the temperature of the bastu. Different Finns have different maximum temperatures they tolerate. If the temperature is too high for a certain Finn, that Finn goes home. Within the temperature interval a certain Finn can handle, the Finn is also more or less happy depending on the temperature. A Finn's happiness is given by a quadratic function (of the form $ax^2 + bx + c$).

A large company of Finns is now going to bathe in a bastu and needs your help. Can you determine the maximum sum of the Finns' happiness if the bastu temperature is set optimally? If the temperature is set higher than a Finn tolerates, that Finn does not contribute to the total happiness at all (they have gone home). The temperature is given in kelvin, with a lower bound of $0 \textrm{ K}$ and an upper bound of $100\,000 \textrm{ K}$.

The first line contains an integer $1 \le N \le 100\,000$: the number of Finns. After that follow $N$ lines, one per Finn. Each line contains four integers $a, b, c, t$ ($-10^9 \le a,b,c \le 10^9, 1 \le t \le 100\,000$), which represents that the Finn has happiness function $ax^2 + bx + c$, and only tolerates temperatures between $0\textrm{ K}$ and $t\textrm{ K}$, inclusive. The function is guaranteed to be positive everywhere between $0$ and $t$.

Print a single number: the greatest possible happiness that can be achieved if the temperature is set right. The answer will be accepted if it has a relative or absolute error of at most $10^{-5}$.