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Ural Championship 2007

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I. Dean's Pyramid 3

Time limit: 1.0 second
Memory limit: 64 MB
Not long ago, at the world's finals in Tokyo, Bill Poucher asked Dean of the Department of Mathematics and Mechanics of the Ural State University:
“How are Ural students getting on? Aren't tired of rolling over your pyramid?” Poucher was referring to problems Dean's Pyramid and Dean's Pyramid 2.
“Then won't get tired, the pyramid is very light,” Dean answered.
“It isn't light, it has some liquid inside,” Denis, who was translating, retorted.
“And what is the volume of your pyramid?” asked Poucher.
Today you will answer Poucher's question.
Note that the pyramid is in fact a pen holder with a cylindrical hole going through it. If the pyramid is put on its base, then the axis of the hole is strictly vertical.


The first line contains numbers H and W, which are the height of the pyramid and the length of a side of the base (as you remember, Dean's pyramid is a regular quadrangular pyramid). The second line contains numbers X and Y, which are the coordinates of the center of the hole (we assume that the axes are parallel to the sides of the base and the origin is at the center of the base). The third line contains the radius of the hole R. It is known that the hole does not intersect the edges of the pyramid (0 < HW < 104, |X| < W/2, |Y| < W/2, 0 < R < W/2).


Output the volume of the pyramid accurate to 10–3.


3.0 3.0
-1.00 -0.70
Problem Author: Evgeniy Krokhalev
Problem Source: The 11th Urals Collegiate Programing Championship, Ekaterinburg, April 21, 2007
To submit the solution for this problem go to the Problem set: 1550. Dean's Pyramid 3