Statement

A field of tulips is represented as an axis-aligned rectangle, with irrigation sprinklers placed on its four sides. These sprinklers spray a fertilizing solution over the field. The Dutch farmer, Jakob, wants to determine how many tulips will ripen faster because they are planted in a special fertilized zone. There are N tulips planted at locations (X_i, Y_i) for i=0… N-1. A tulip is considered to be in the fertilized zone if, together with the four corners of the rectangle, it forms (1) two acute-angled triangles, and (2) two obtuse-angled triangles. Your task is to count how many tulips meet this condition.