You think you can count

You are given the vertices of a $N$ sided convex polygon on a 2D cartesian plane. You have to answer $Q$ queries. Each query consists of four space separated integers $x1, y1, x2, y2$ where the point $(x1, y1)$ lies on any one side of the given polygon and the point $(x2, y2)$ lies on any other side of the polygon. Upon joining these two points, the polygon is divided into two smaller polygons le