Roof
Masha approaches the edge of the roof...
"Song about Crazy Masha"
Little Masha has a fascination with rooftops. Today, she climbed onto the roof of a building that is circular in shape. The stairs from the attic lead directly to the center of this roof. As she looked around, Masha noticed several pipes on the roof, each also circular and adorned with a beautiful pattern. These pipes have a radius of r and are positioned precisely along the edge of the roof, forming circles. Naturally, these pipes partially block her view of the pattern. Your task is to calculate the area of the roof—and thus the pattern—that Masha can see.
Input
The first line of the input contains three integers R, k, and r (1 ≤ R ≤ 30000, 1 ≤ k ≤ 100, 1 ≤ r ≤ 1000)—representing the radius of the roof, the number of pipes on it, and the radius of each pipe. The center of the roof is at the origin of the coordinate system. The next k lines provide the details of the pipes. Each line contains two integers x_i, y_i (1 ≤ i ≤ k)—the coordinates of the center of each pipe.
It is guaranteed that the circles representing the pipes are entirely within the circle representing the roof, touching its boundary, and do not intersect with each other. Additionally, the center of the roof is neither inside nor on the boundary of any pipe.
Output
Output a single number—the area of the roof that Masha can see. Your answer should have an absolute or relative error of no more than 10^{-6}.