Maratona de Programação da SBC Brazil
A factory wants to produce a toboggan of marbles toy (marble run) as shown in the following figure, consisting of two vertical rods of wood, which support small rigid flaps connected to the rods. The flaps are connected to the left and right rods in an alternate fashion. A small marble ball is dropped on the highest flap of the marble run, and under the effect of gravity the marble slides by the flaps, eventually
leaving the toy.
The design of the toy, containing the specifications of its size, position and tilt of each flap, was made by the factory owner. Thousands of units are already being made in China, and the factory manager has been asked to buy the marbles. Before placing the order for thousands of marbles, however, he wants to know the maximum diameter of the marble so it does not get stuck in the middle of the toy.
Figure 1: Two examples: (a) the marble reaches the end, and (b) the marble gets stuck in the middle of the toy.
The factory manager wants you to write a program that, given the toy specifications, determines the maximum diameter of the marble so that it does not get stuck in the middle of the toy.
The input contains several test cases. The first line of a test case contains an integer N (1 ≤ N ≤ 103) indicating the number of flaps of the toy. The second line contains two integers L (1 ≤ L ≤ 103) and H (1 ≤ H ≤ 103), indicating respectively the distance between the rods and the height of the rods. The left rod is at position 0 of the coordinate axis X, so that the right rod is at position L of the X axis.
Consider that the flaps are very thin, so that its thickness can be neglected.
For each test case print a line containing a single number, with exactly two decimal places, indicating the largest diameter of a marble so it that it can reach the end of the toy.
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