Hologram Advertisements#1635
In the 31st century, the Planet Express delivery company has launched a new advertising campaign in New New York. They installed circular hologram projectors at various locations around the city. Each projector displays a circular hologram advertisement with radius units. All projectors are positioned along one street (on a straight line).
The marketing manager wants to know the total advertising coverage area. Some holograms may overlap, so it's important to calculate the area correctly.
Write a program to calculate the total area covered by the holograms.
The first line of the input contains two integers and (1 \leq n \leq 1000, 1 \leq r \leq 100) — the number of hologram projectors and their radius, respectively. The next line contains space-separated integers a_1, a_2, \ldots, a_n (0 \leq a_i \leq 5000) — the positions of the projectors' centers relative to some origin point. All positions are guaranteed to be distinct.
Output a single real number — the total area covered by the holograms. Your answer must be truncated to five decimal places.
Example 1