Farabi is good at Geometry.

And he loves to make challenge.

He gave two triangle (ABC and CAD) where there is a common side and two side are parallel to each other.

Here you can see the following figure for better realization.

Input

You will be given angle BAC, ABC and side BC and AD . 

Here, pi = acos(-1.0)

Output

Find the area of the circle CDE. Your answer will be considered correct if the absolute difference between your and judge's solution will not differ more than 10^(-6).

Example

Input:
10 30 40 50

Output:
19311.6239189261