CF82E Corridor

Consider a house plan. Let the house be represented by an infinite horizontal strip defined by the inequality $ -h

The first line of the input file contains three integers $ n $ , $ h $ and $ f $ ( $ 1

Print the single real number — the area of the illuminated part of the floor with an absolute or relative error of no more than $ 10^{-4} $ .

The second sample test is shown on the figure. Green area is the desired area of the illuminated part of the floor. Violet segments indicate windows.