Polarized lenses are a great feat in the field of optics and have many fascinating properties. As you are messing around with a set of polarized lenses, you notice that the region of light they block is equivalent to the XOR of the regions that each lens covers. More formally, let's consider the 2D Cartesian Plane. Each lens will take the form of a circle in the plane. A point is considered to be blocked if there is an odd number of circles that contain the point within its border or on its border.
Now you want to explore the results of several updates. In each update, a new polarized lens of radius $$$r$$$ is added into the Cartesian Plane at $$$(x, y)$$$. After each update, you want to determine the total area of the set of blocked points in the entire plane.
The first line of input will consist of a single integer $$$n$$$ ($$$1 \leq n \leq 1000$$$) — the number of polarized lenses that are being added to the plane.
The following $$$n$$$ lines will consist of three integers $$$x$$$, $$$y$$$ ($$$-10000 \leq x, y \leq 10000$$$), and $$$r$$$ ($$$1 \leq r \leq 10000$$$) — the $$$x$$$ and $$$y$$$ coordinate of the center of the lens and the radius of the lens.
After each update, output a single real number – the area of the set of blocked points. Your answer will be accepted if it has an absolute or relative error of $$$10^{-4}$$$ with the judge's solution.
3-1 1 31 -1 30 0 1
28.2743338823 32.6384059655 35.7799986191
