AT_past202209_j スプリンクラー

There is a rectangular garden that is $ H $ meters long and $ W $ meters wide. At the center of the garden is a sprinkler, which sprays water within a radius of $ D $ meters from it. Find the proportion of the area sprayed by the sprinkler in the garden.

Input is given from Standard Input in the following format: > $ H $ $ W $ $ D $

Print the answer. Your answer will be considered correct if the absolute or relative error from the true value is at most $ 10^{-6} $ .

### Sample Explanation 1 The sprinkler sprays the interior of a circle of radius $ 3 $ meters, whose area is about $ 28.3 $ square meters. The area of the garden is $ 10\times 15=150 $ square meters, so the desired proportion is $ 0.1884955592\ldots $ .  ### Sample Explanation 2 The sprinkler sprays the interior of a circle of radius $ 6 $ meters, some of which sticks out of the garden. The area of the region sprayed by the sprinkler is about $ 104.1 $ square meters, and the area of the garden is $ 10\times 15=150 $ square meters, so the desired proportion is $ 0.6939614954\ldots $ .  ### Constraints - $ 1 \leq H,W \leq 10^5 $ - $ 1 \leq D \leq 10^5 $ - All values in input are integers.