Ghost Busters

The Ghost Busters team has upgraded their Ecto-1 with a powerful proton gun and an automatic targeting system, and you have been hired to write a prototype for the targeting software.

Each ghost is detected as a floating sphere, given by the coordinates of its center and its radius. The proton gun fires from the origin $(0, 0, 0)$ in any direction inside the octant $X \ge 0,\ Y \ge 0,\ Z \ge 0$. It emits a single ray that travels in a straight line from the origin; even a graze from this ray destroys a ghost, and one ray can destroy an unlimited number of ghosts lying along its path.

Determine the maximum number of ghosts that can be destroyed with a single shot fired from the origin.

The first line contains the number of detected ghosts $N$ ($0 \le N \le 100$).

Each of the next $N$ lines describes one ghost with four integers $X_i$, $Y_i$, $Z_i$, $R_i$ separated by spaces, where $(X_i, Y_i, Z_i)$ is the center and $R_i$ is the radius. It is guaranteed that $1 \le X_i, Y_i, Z_i \le 10000$ and $1 \le R_i \le \min(X_i, Y_i, Z_i)$.

Ghosts may overlap, be contained in one another, or coincide.

Print a single integer: the maximum number of ghosts that can be destroyed with one shot.