Given an elliptical ranch with dimensions $2^{**}R$ units horizontally and $1$ unit vertically, a goat is tied to the fence inside the ranch using a leash of length $r$ units. The angle formed between the point of tying and the horizontal axis is $.$

To determine the area of grass the goat can graze, the following inputs are provided as shown in the image below:

$R$ half of the horizontal dimension of the ranch,

$r$ the length of the leash, and

$$ the angle formed by the point of tying and the horizontal axis.

Write a program that takes these three inputs as floating$-$point numbers on separate lines and prints the total area of grass the goat can graze, rounded to three decimal points.

Example:

Input:

$\mathrm{.}75$

$8.25$

$310$

Output:

$8\mathrm{.}091$