Ahmad is passionate about physics, and recently he learned something new.
He learned that to keep an object from falling off the table, the center of mass of that object must be positioned on the table, even if the rest of this object is outside the table.
Ahmad was thrilled to learn this new concept, so he went to Ismail to share this idea.
Unfortunately, Ismail loves geometry and is a quick learner and quickly understood Ahmad's new idea and gave him a good problem.
The problem involves a circular table with radius $$$R$$$ and a dish with a regular polygon shape of $$$N$$$ sides, each side of length $$$L$$$.
There are an unlimited number of dishes; The dishes can be placed anywhere on the table as long as they don't fall off the table and at least one side of them is parallel to the x-axis.
The task is to find the maximum possible area that can be covered using the dishes.
$$$ $$$
In the above example$$$R = 4, N = 4, L = 2$$$. The purple shape is the maximum area the dishes can cover. $$$ $$$
As a good friend of Ahmad, you want to help him solve this problem.
The first line contains one integer number $$$T$$$ the number of testcases ($$$1 \le T \le 10^6 $$$)
The following $$$T$$$ lines contain 3 integers $$$R, N, L$$$ ($$$1 \le R,L \le 10^3$$$ , $$$3 \le N \le 100$$$)
For each test case, print a single value of the answer for the problem. Your answers must have a relative or absolute error of at most $$$10^{-6}$$$.
14 4 2
86.265482457437
14 5 2
97.147392059793
