Vaqt limiti: 1 sekund
Xotira limiti: 64 MB
Once upon a time the world famous heroDroopy decided
to relax in the village. He has a garden of the triangular shape with
sides a, b and c in his country site. The hero often
released his sheep to walk there: unlike characters of some programming problems,
the sheep of Droopy was perfectly trained and didn't touch the grass and the
vegetables in the garden.
Everything was changed when the new experiment of the
hero transmuted the sheep into the black hole which had the shape of circle
with a fixed radius r. Unlike the sheep, the black hole was absorbing all
the plants it touched while moving along the garden. Fortunately, Droopy has
immediately figured out to set the innovative energy barriers along the
perimeter of the garden. These barriers were designed so that no point of the
black hole can cross them.
You are to calculate Droopy's losses. Find what part
of the garden could be absorbed by the black hole in the worst case.
Input: The only line contains 4
integers a, b, c and r (1 ≤ a, b, c, r ≤ 104) —
the lengths of the garden's sides and the radius of the black hole. It is
guaranteed that there exists a no degenerate triangle with
sides a, b and c, and that the black hole can actually fit
in the garden.
Output: Output a single real number — the biggest part of
the garden that could be absorbed by the black hole. Round
this number to 4 places
after the decimal point.
№ |
Sample input |
Sample output |
1 |
3 4 5 1 |
0.5236 |
2 |
6 8 10 1 |
0.8809 |