Camera Time

Camera Time
Gogol is rolling out its new camera on wheels for its program called Gogol Road View. It can take pictures
at a surprising 5e5 megapixel. However, each photo takes a lot of energy so Gogol needs help determining
the smallest number of pictures to take such that each object can be in view of at least one of the taken
photos. Each time a picture is taken every object with a direct line of sight of the Gogol Camera Vehicle
(GCV) is captured by the GCV and is thus in the corresponding photo.
For the current situation the GCV will be moving in a straight line parallel to an infinitely long wall called
the Great Occluder. Unfortunately for Gogol, some objects that Gogol wants to take a picture of is on the
opposite side of the wall from GCV’s path. There does exist a single stretch in the wall (the Glass Partition)
that allows for photons to pass, such that photos can be taken of objects on the opposite side. In general
if the only part of the wall directly between the object and the camera is the Glass Partition, then a photo
taken at that point will contain the object.
For simplicity we will give the description of the objects such that the GCV is traveling along the x-axis.
You are given the distance of the GCV’s path from the Great Occluder in meters, which means that the
wall lies on the line y = d, where d is the distance from the path in meters. You are also given the starting
and ending point of the Glass Partition. Using the combined information the glass partition lies on the line
segment (b, d) and (e, d), where the partition begins at b meters from the y-axis and ends at e meters
from the y-axis. You will be given a list of objects that need their picture taken. No object will be on the
Great Occluder. Additionally you can assume that no object will block the vision of any other object; all
objects can be consider points for the sake of width. Lastly the wall’s thickness will be negligible.
Input
The first line of input begins with two positive integers, n and d (n < 100,000; d < 100,000), which
represents the number of objects and the distance (in meters) in the positive y direction the Great
Occluder is from the path of the GCV. The next line contains two positive integers, b and e (b < e <
100,000), which represent the beginning and ending index of the Glass Partition in meters from the y-axis.
The remaining n lines contain two positive integers, xi and yi (xi, yi < 100,000), where the i-th pair (xi, yi)
represent the Cartesian coordinate of the i-th object in meters from the origin.
Output
Output a single integer the minimum number of pictures needed to be taken to photograph each object
at least once.
Samples
Input Output
2 2
3 5
2 3
6 3
2
2 1
3 5
2 2
6 2
1
1 4
1 10
1 1
1
4 1
9 10
1 2
20 2
9 100
9 2
3