"At the Frying Pan" near the Polytechnic
"On the Pan" is the name of the student magazine at AltGTU. Why is it called that, you ask? It's simple—the circular area in front of the main building of the polytechnic is known as the pan. This is where meetings are held, student initiations occur, and generally, all major student events take place.
Everyone knows that the pan in front of the polytechnic is a circular area with a monument to Polzunov at its center. At night, the monument feels lonely and rotates around its axis, observing the world around it, though it never leaves its pedestal. Unfortunately, the trees surrounding the pan block the monument's view, so it can only see clearly up to a distance of R, where R is the radius of the pan. Additionally, since the monument cannot see behind itself, it can only observe events within a semicircle of radius R. The monument can also clearly see points on the boundary of this semicircle.
Naturally, the monument wants to observe as many people on the pan as possible. Your task is to write a program that calculates the maximum number of people the monument can observe. Examples are illustrated in the figures. Figures 1 and 2 demonstrate different orientations of the monument (and thus, different segments of the pan that the monument can observe). Pay attention to the optimal orientation of the monument that allows it to see the maximum number of people.
Input
The first line of the input file contains three numbers:
Two integers representing the coordinates of the Polzunov monument.
One real number representing the radius of the pan R.
The second line contains an integer N—the number of people on the pan. Following this, N lines list the coordinates of the points where people are located.
All coordinates are integers that do not exceed 1000 in absolute value. The viewing radius R is a positive real number. At night, there aren't many people on the pan, so you can assume there are 1 ≤ N ≤ 150 points where people are located on the pan.
Output
Output a single number—the solution to the problem.