Ant Entrapment

Your friend Oscar bought an ant farm. He let the ants loose on his floor by accident, and now they are crawling everywhere. You want to fence them in with one continuous rectangle so they stop wandering off. Because of how the fence pieces are built, the sides of the rectangle must be parallel to the X and Y axes. The figure below shows a fence around a group of ants. The small gap between the fence and the outermost ants is drawn only to keep the picture readable.

Find the area and the perimeter of the smallest fence that contains every ant.

The first line contains the number of test cases $T$ ($1 \le T \le 100$).

Each test case begins with a line containing the number of ants $N$ ($1 \le N \le 100$). Each of the next $N$ lines contains the position of one ant as two real numbers $X$ and $Y$ ($-1000.0 \le X, Y \le 1000.0$) separated by a space. Coordinates are given with at most three digits after the decimal point. An ant is a single point and has no area.

For each test case print one line in the form Case x: Area A, Perimeter P, where $x$ is the test case number starting from 1, $A$ is the area of the fence and $P$ is its perimeter.

Print both $A$ and $P$ with exactly six digits after the decimal point. Every input coordinate has at most three decimal digits, so six digits write both values exactly.