Description
Figure 2: A Frozen Swarm of Ants
in Flatland
Flatland needs a superhero! Recently swarms of killer ants
have been invading Flatland, and nobody in Flatland can
figure out how to stop these dastardly denizens. Fortunately,
you (as a higher dimensional being) have the opportunity
to become a superhero in the eyes of the Flatland citizens!
Your job is to “freeze” swarms of ants using parallelograms.
You will do this by writing a program that finds a minimal
area enclosing parallelogram for each swarm of ants. Once a
minimal area parallelogram is placed around the ant swarm,
they are effectively frozen in place and can no longer inflict
terror on planar inhabitants.
Flatland needs a superhero! Recently swarms of killer ants have been invading Flatland, and nobody in Flatland
can figure out how to stop these dastardly denizens. Fortunately, you (as a higher dimensionalbeing) have the
opportunity to become a superhero in the eyes of the Flatland citizens!
Your job is to “freeze” swarms of ants using parallelograms. You will do this by writing a program that finds a
minimal area enclosing parallelogram for each swarm of ants. Once a minimal area parallelogram is placed around
the ant swarm, they are effectively frozen in place and can no longer inflict terror on planar inhabitants.
 
Input
The input will consist of the following:
• A line containing a single integer, s (1<=s<=20), which denotes the number of killer ant swarms.
• Each swarm will start with a single line containing an integer, n (4<=n<=1000), which indicates the number of killer ants in the swarm.
• The next n lines contain the current location of each killer ant in the swarm.
• Each killer ant is represented by a single line containing two numbers: x (−1000<=x<=1000) and y (−1000<=y<=1000) separated by a space.
• Only one killer ant will occupy each (x, y) location in a particular swarm. Each swarm should be dealt with independently of other swarms.
• All data inputs are in fixed point decimal format with four digits after the decimal (e.g., dddd.dddd).
• There may be multiple parallelograms with the same minimum area.
 
Output
For each swarm, your algorithm should output a line that contains “Swarm i Parallelogram Area: ”, 
where i (1<=i<=s) is the swarm number, followed by the minimum area (rounded to 4 decimal
digits and using fixed point format) of an enclosing parallelogram for that swarm. All computations
should be done using 64 bit IEEE floating point numbers, and the final answers displayed in fixed
point decimal notation and rounded to four decimal digits of accuracy as shown in the sample input
and output.
 
Example
Input:
2
6
0.0000 0.0000
-0.5000 -0.5000
-1.0000 0.0000
-0.7000 -7.0000
-1.0000 -1.0000
0.0000 -1.0000
5
2.0000 2.0000
0.0000 0.0000
0.5000 2.0000
1.0000 1.0000
1.5000 0.0000

Output:
Swarm 1 Parallelogram Area: 7.0000
Swarm 2 Parallelogram Area: 3.0000