Tomosynthesis is a medical imaging modality in which a 3D
dataset is obtained algorithmically from a set of Xray images
taken in different directions within a limited range of angles.
A larger range of angles normally gives a better
reconstruction, but is more difficult to acquire. Arvid is
working on a reconstruction algorithm for obtaining the 3D
image, but so far it doesn’t seem to work when there are
overlapping structures in any of the input images. The sample
he will first reconstruct is a test object consisting of
parallel equallength cylinders of varying diameters that will
be rotated around the axis of the cylinders.
Disregarding the fact that his algorithm will not work in
practice, Arvid asks you for help. What is the largest range of
angles in which the test object can be imaged without any
cylinders overlapping in any of the images? An image is a plane
projection of the structure perpendicular to the axes of the
cylinders.
Input
The first line of input contains a single integer
$2\leq N\leq 100$ denoting
the number of cylinders that constitute the test object. This
is followed by $N$ rows,
each containing three floating point numbers $x$, $y$ and $r$, denoting the $x$ and $y$coordinate of the center of a
cylinder, and the radius of that cylinder, respectively. The
coordinates are in the range $1\, 000\leq x,y \leq 1\, 000$ and
the radius $0<r\leq 1\,
000$. None of the cylinders touch or overlap.
Output
Output a single number, the size in radians of the largest
continuous range of projection directions over which no
cylinders overlap. If no such angle exists output 0.
Your answer should have an absolute error of at most
$10^{8}$.
Sample Input 1 
Sample Output 1 
3
1 1 0.5
1 1 0.25
1 1 1

0.511268019

Sample Input 2 
Sample Output 2 
2
0 0 1
2 2 1

1.570796327
