Bob loves ice cream. In fact, he loves ice cream so much that he often dreams about it! In a recent dream, Bob was standing at the origin of a two-dimensional plane made of ice cream, as one would typically do. However, this wasn't an ordinary two-dimensional universe, since there were $N$ sprinkles scattered around the plane ($1 \leq N \leq 2*10^5$). These sprinkles come in two colors: red and blue. Bob loves the color red and despises the color blue, so he will do anything in order to not eat a blue sprinkle. The sprinkles are also magical, so they cannot move under any condition. He also has the capability to construct an ice cream cone of infinite size, but he is too lazy to move from the origin, so the vertex of the ice cream cone must be located at the origin. In Bob's two-dimensional world, ice cream cones are equivalent to geometric sectors. They can be defined by their radius, along with two angles, as seen in the image below:

Each sprinkle is located at integer coordinates $(x_i, y_i), (|x_i| \leq 10^9, 1 \leq y_i \leq 10^9)$. Note that all $y_i$ must be positive. Every sprinkle is either red or blue. Sprinkles have negligible width, and no two sprinkles have the same position. A sprinkle is considered to be inside a cone if it is inside or on the boundary of the sector representing the cone. Also, negative y coordinates typically have many blue sprinkles, so Bob will not make a cone which covers any point below the x-axis.

Bob wants to capture as many red sprinkles as he can inside of a single ice cream cone, without capturing any blue sprinkles. Help Bob determine the maximum number of red sprinkles he can collect!