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