Roof#1165
Little Orysia loves 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, Orysia noticed several pipes on the roof, each also circular and adorned with a beautiful pattern. All pipes have a radius and are positioned precisely along the edge of the roof, forming circles. Naturally, these pipes partially block her view of the pattern. Determine the area of the roof—that is, the pattern—that Orysia can see.
The first line of the input contains three integers , , and (1 \leq R \leq 30000, 1 \leq k \leq 100, 1 \leq r \leq 1000)—the radius of the roof, the number of pipes on it, and the radius of each pipe. The center of the roof coincides with the origin. The following lines describe the pipes. Each description consists of two integers x_i, y_i (1 \leq i \leq k)—the coordinates of the center of the pipe.
It is guaranteed that the circles representing the pipes are entirely within the circle representing the roof, touch its boundary, and do not intersect with each other. Also, the center of the roof does not lie inside or on the boundary of any pipe.
Output a single number—the area of the roof that Orysia can see. Your answer must differ from the correct one by no more than 10^{-6} (absolute or relative error).
Example 1