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Ural Championship 2006

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D. Floo Powder

Time limit: 0.5 second
Memory limit: 64 MB
Wizards and witches can move from one place to another using Floo powder. A pinch of the powder is enough to transfer a wizard from one fireplace to any other fireplace connected to the Floo Network.
There is a secret room at the Ministry of Magic where a reserve stock of Floo powder is stored, which may be needed in the event of emergency evacuation. The powder is stored in an enchanted box suspended with chains to the ceiling (to save the powder from mice). The room is well defended against burglars and the box can be opened by the Minister of Magic only.
The new Minister of Magic noticed that though the box was thoroughly protected with charms, storage conditions were not observed correctly, so the box dried up. The boards shrank, and a thin straight slit formed in the bottom of the box, through which a portion of the powder could fall and be used by mice for their own mysterious purposes.
Help the Minister to calculate whether the remaining amount of Floo powder is enough for the evacuation of all employees.
The length of the box is 1 meter, the width and height are 50 cm. The powder was poured into the box through a special small hole in the center of the lid. The powder formed inside the box a regular cone with the natural angle of repose. If the slit intersects the base of the cone, the powder pours through the slit forming slopes with the same angle of repose along it.


The first line contains an integer r that is the radius of the base of the original cone (1 ≤ r ≤ 25). The second line contains an integer d that is the distance from the center of this base to the slit (1 ≤ d ≤ 25). The third line contains an integer h that is the original height of the cone (1 ≤ h ≤ 50). All values are measured in centimeters.


Output the amount of the powder remaining in the box in cubic centimeters accurate to four decimal places.


Problem Author: Author — Anton Botov, text — Stanislav Vasilyev
Problem Source: The Xth Urals Collegiate Programing Championship, March 24-25, 2006
To submit the solution for this problem go to the Problem set: 1442. Floo Powder