Problem Description

One day , Teddy and WhereIsHeroFrom want to pay a visit to their friend yifenfei who are in another city.They own a car ,but the car is so small that it can only contains two people.But both Teddy and WhereIsHeroFrom can't drive a car,so they needs a driver to help them.
Now give you the speed of Teddy and WhereIsHeroFrom , and the speed of the car ,you are asked to worked out the least time Teddy and WhereIsHeroFrom need to spend if they want to reach yifenfei's home at the same time.You may suppose if one gets off the car ,the driver can turn around to carry the other one .

Input

Each line will contain three integers A (0<A<=1000), B(0<B<=10000) and C(0<C<=10^9). A stands for the speed of Teddy and WhereIsHeroFrom ,B stands for the speed of the car,C stands for the distance between the two cities .Process to end of file.

Output

For each case, output the least needed time in one line,accurate to three decimal places.

1 2 1

0.700

Author

dandelion