Heat (Easy)#4791
The heat was unbearable... The prudent boatswain, along with the jibs, handed out neat handkerchiefs to the sailors in the form of triangles with two equal sides, made from the material left over from sewing the jibs.
Alex decided to cover the porthole in his cabin with this sturdy fabric to let in less sun. At the same time, the curious sailor was interested in the question: What is the maximum area of the porthole that can be covered in this way?
Help Alex solve this simple problem, as he cannot solve it on his own yet.
The single line of the input file contains three natural numbers: , , and (0 < r \leq 100, 0 < a, c \leq 200), where is the radius of the porthole, is the length of one of the equal sides of the handkerchief, and is the length of its third side. It is guaranteed that the handkerchief has a non-zero area.
Output a single number — the maximum area of the covered part of the porthole with a precision of at least decimal places.
Example 1