题目描述
Cosmic-Cat picked up a positive $n$-gon biscuit with side length $1$ on the road! He was very happy and decided to treasure this biscuit. But then it rained for a long time, the air became very humid, and the molds on the biscuit began to spread!
In the beginning, molds were only on the $n$ vertices of the biscuit. But over time, they began to spread continuously. However, molds from each vertex are limited in that they can only spread as far as the distance from the vertex farthest from the original vertex.
For example, the diffusion area for a regular triangle, square and regular pentagon is shown below:
When Cosmic-Cat discovered it, all the mold had spread to the furthest distance. He looked at the beautiful moldy biscuit with tears in his eyes, and now he just wants to know how large the area covered by mold is in total?
