Rabbits and Polygons. HARD
N rabbits are positioned at the vertices of a regular N-gon with side length a. They all start moving simultaneously at a constant speed v. The first rabbit moves towards the second, the second towards the third, the third towards the fourth, and so on, with the Nth rabbit moving towards the first. After a certain time t, all N rabbits will converge at a single point. Each rabbit wants to know the distance it will travel before this meeting occurs. Help them determine this distance.
Input
Each test case consists of 3 numbers: a natural number N (1 ≤ N < 2^20), a real number a (0 < a < 2^20), and a real number v (0 ≤ v < 2^20).
Output
Output the distance one rabbit will travel until the meeting, with an absolute error of 10^{-9}, or output -1 if the rabbits will never meet.