Vera is an astronomer studying locality of nearby star
systems. The star systems can be thought of as 3D points in
space. Vera would like to place a can around the stars. In
other words, she would like to know what is the smallest volume
cylinder that encloses the stars. The cylinder can be oriented
in any direction. At least one base of the cylinder must have
at least three stars.
Input
Each input will consist of a single test case. Note that
your program may be run multiple times on different inputs. The
first line of input will contain a single integer $n$ ($4
\le n \le 1\, 000$), representing the number of
stars.
Each of the next $n$
lines will contain three integers $x$, $y$ and $z$ ($1\, 000 \le x, y, z \le 1\, 000$),
representing the position of a single star. No two stars will
be at the same position. No four stars will be coplanar.
Output
Output a floating point number representing the smallest
volume cylinder that can enclose all the stars. Your answer
must be accurate within a relative tolerance of $10^{6}$.
Sample Input 1 
Sample Output 1 
4
1 0 0
1 1 0
0 0 0
0 0 1

1.57079633

Sample Input 2 
Sample Output 2 
4
100 0 0
10 0 10
10 10 10
0 0 0

41938.65135885

Sample Input 3 
Sample Output 3 
7
10 20 30
0 0 0
100 1000 20
100 20 33
8 7 900
100 223 23
3 0 3

298192571.11934924
