Galactic Confederation

The Galactic Confederation reorganized its administration to spread the resources of its fleet more evenly. It started by cutting all of space into regions. A set of infinite planes was fixed first, and every piece those planes cut space into is one region. Some regions are unbounded, and bounded regions can appear too.

The planes were chosen so that no plane meets the orbit of any planet. Each planet therefore stays inside a single region for its whole orbit. A planet inside a region never crosses a plane into another region.

Given the equations of the planes and the positions of the planets, find how many planets lie in the region that holds the most planets.

The first line has two integers $M$ and $N$, the number of planes and the number of planets. ($1 \le M \le 500$, $1 \le N \le 10000$)

Each of the next $M$ lines has four integers $A$, $B$, $C$, $D$, the coefficients and the constant term of the equation $Ax + By + Cz = D$ of one plane. ($-10000 \le A, B, C, D \le 10000$)

Each of the following $N$ lines has three integers $X$, $Y$, $Z$, the position $(X, Y, Z)$ of one planet. ($-10000 \le X, Y, Z \le 10000$)

Print one line with a single integer, the number of planets in the region that contains the most planets.