You are a time traveler tasked with the duty of introducing pizza to the ancient Greeks. Along your journey, you meet the mathematician Euclid. After studying the pizza you have brought, Euclid gives you a problem. He tells you to envision the pizza as a 2D plane centered at the origin. The toppings are represented as $$$N$$$ points scattered on the plane. Additionally, the "crust" of the pizza is represented by $$$M$$$ points scattered on the plane. He defines "a slice of pizza" as a valid triangle comprised of 2 crust points and the origin. Euclid asks you to count the number of topping points that are enclosed within some valid slice of pizza (including toppings on the boundary).
The first line of input contains 2 space-separated integers $$$N, M\ (0 \leq N \leq 5 \cdot 10^4, 4 \leq M \leq 5 \cdot 10^4) - $$$ the number of topping and crust points, respectively.
Note: It is guaranteed that there is at least 1 crust point in each of the 4 quadrants.
The next $$$N$$$ lines of input contain 2 space-separated integers $$$x, y\ (-10^9 \leq x, y \leq 10^9) - $$$ the $$$x$$$ and $$$y$$$ coordinates of the $$$i^{th}$$$ topping point.
The next $$$M$$$ lines of input contain 2 space-separated integers $$$x, y\ (-10^9 \leq x, y \leq 10^9) - $$$ the $$$x$$$ and $$$y$$$ coordinates of the $$$i^{th}$$$ crust point.
Note: It is guaranteed that no two points, topping or crust, have the same $$$x$$$ or $$$y$$$ values.
Please output 1 integer, the total number of topping points that are enclosed within some slice of pizza.
5 62 2-8 0-3 14 -30 48 -23 3-2 6-1 51 -1-4 -4
3
2 53 -21000000000 10000000000 01 1-2 2-3 -34 -4
0
The first sample case is drawn below (toppings represented by orange points and crusts represented by black points). Two example pizza slices are also drawn. Three out of the five toppings can be enclosed by a slice. Observe that no other topping can be enclosed by a slice.
