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Recently, your friend Oscar purchased an ant farm. He accidentally let the ants loose on his floor and now they’re crawling everywhere! You want to fence them off with a single continuous rectangle so that they’re not running amok. However, due to technical limitations your fence pieces must be aligned with the X and Y axes. The figure below shows an example of a fence around a set of ants (slight offsets from the border are just for visual effect).
What is the perimeter and area of the smallest fence that contains all of the ants?
The first line of input is the number of test cases that follow. Each test case starts with an integer N (1 ≤ N ≤ 100) on a line by itself representing the number of ants. The following N lines of input contain two floating-point values X and Y (−1000.0 ≤ X, Y ≤ 1000.0) representing the position of an ant. You can assume that ants are single points–they have no area.
For each case output the line “Case x:” where x is the case number, on a single line, followed by the string “Area” and the area of the fence as a floating-point value and then a comma, followed by a space and then “Perimeter” and the perimeter of the fence as a floating-point value. Floating-point value will be considered correct if it is within an absolute or relative error of 10-9 of the correct answer.
2 3 -1.000 0.000 5.000 11.500 3.200 -4.250 2 2.125 0.500 6.875 9.100
Case 1: Area 94.5, Perimeter 43.5 Case 2: Area 40.85, Perimeter 26.7