96. Cow and House

I'm a slow walker, but I never walk backwards.

Task Description

Write a program to determine how much grass a cow can eat. A cow is attached to a rope of length $c$, and the other end of the rope is attached to a corner of a rectangular house of width $a$ and depth $b$. Please determine the area the cow can browse.

p96.pngp96.png

Input

The input has three double precision number $a$, $b$, and $c$.

Output

The output has a double precision number (in %f) format.

Bounds

  • We assume that $\pi = 3.1415926$.
  • $0 \lt a, \; b \le 1000$
  • $c \le a+b$

Sample input

10.0 10.0 5.0

Sample output

58.904861

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