Selling Cells#1382
Competition is intense among cellphone providers in the town of Eastern WestField. Several companies are advertising, each claiming to provide more coverage to the town than their competitors.
AetherTech Telecommunications suspects that they actually cover a larger portion of the town than their rivals. They want to calculate their actual coverage to advertise the true amount.
The metropolitan area of Eastern WestField will be modeled as a circle around the town center. The area covered by each cell tower is also modeled as a circle, centered at the tower's location, indicating the area where the tower provides sufficient signal strength for a phone to connect (for example, one bar on a typical phone's signal meter).
All towers to be considered have their centers within the metropolitan area, though their coverage area may extend beyond its border. The coverage areas of different towers can overlap, but for economic reasons, no two towers are constructed so close that the center of one is within the coverage area of another.
Determine what fraction of the metropolitan area is covered by at least one tower.
The input consists of several data sets. Each data set begins with a line containing a single integer , where 1 \leq N \leq 25. This line is followed by lines, each with three floating point numbers , , . These are the coordinates of the circle's center and the radius of that circle.
The first circle in the list describes the metropolitan area of Eastern WestField. The remaining N-1 circles describe cell towers.
The final data set is followed by a line containing zero.
For each data set, compute the fraction of the metropolitan area covered by the cell towers (as a number in the range ) and print a line containing that fraction as a real number with precision to decimal points.
Example 1