Estimated Difficulty: 40 (% not solved)

Problem:
	Fit regular polygons to a set of sample points and find
	the number of corners that leads to the optimal score.
	
Solution:
	For every point, the radius of the k-gon that the point lies
	on is given by the following formula, which can be derived
	using some trigonometry:
		
		r * cos((alpha mod (2*pi/k)) - pi/k) / cos(pi/k)
	
	where (r,alpha) are the polar coordinates of the point.
	Note that the "modulo" above is taken in the real numbers.
	
	Finding the optimal score is then straightforward and
	somewhat simplified by the fact that some constants
	cancel out when computing the ratio.

	Alternatively, the inner and outer radius can be found by
	binary search, combined with running a point-in-polygon
	test on all sample points.

Time complexity:
	O(n) for the trig solution, O(n*precision) for the binary search.
