Recently, Goni read a book by Plato. Inspired by Plato's life, he decided to invent a theorem related to geometry. While attempting to prove his own theorem, he encountered a problem and needs help to solve it.

Here the center of this circle is O (0, 0), OA lies on X axis. And CB || OA. You have to find the area of ABCO.

Input

The first line contains two integers x, y, denoting the coordinate of C(x, y).

The next line contain one integer r, denoting the radius of this circle.

Output

Print the area of ABCO. The value calculated must be presented with 3 digits after the decimal point.

Example

Input:
1 1
2

Output:
1.047

Input:
3 8
25

Output:
101.790