C. Chasing the Treasure
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Tiagodfs, a legendary competitive programmer, decided to hide his most valuable solutions in a rectangular field of dimensions $$$b \times h$$$.

The hiding spot was chosen completely at random: every point inside the field has the same probability of containing the treasure.

After a long investigation, the team Chappell Roan, vc tá jurada aqui em São Sebastião finally discovered the existence of this hiding spot. To recover the secret codes, they decided to use a special excavation machine capable of digging a region in the shape of a regular hexagon with side length $$$l$$$. The excavated region will be positioned so that it is entirely contained within the field.

Determine the probability that the team Chappell Roan, vc tá jurada aqui em São Sebastião finds the treasure with this kind of excavation.

Input

The input contains three integers $$$b$$$, $$$h$$$, and $$$l$$$ ($$$1 \leq b, h, l \leq 10^3$$$).

It is guaranteed that some regular hexagon of side length $$$l$$$ fits entirely inside the rectangle.

Output

Print the probability that the treasure lies inside the excavated region.

Your answer will be considered correct if the absolute or relative error does not exceed $$$10^{-4}$$$.

Examples
Input
10 10 5
Output
0.6495190528
Input
29 23 11
Output
0.4713151748