Problem E: Texas Trip
After a day trip with his friend Dick, Harry noticed a strange
pattern of tiny holes in the door of his SUV. The local American
Tire store sells fiberglass patching material only in square sheets.
What is the smallest patch that Harry needs to fix his door?
Assume that the holes are points on the integer lattice in the plane. Your job is
to find the area of the smallest square that will cover all
the holes.
Input
The first line of input contains a single integer T expressed in decimal
with no leading zeroes, denoting the number of test cases to follow. The
subsequent lines of input describe the test cases.
Each test case begins with a single line, containing a single integer n
expressed in decimal with no leading zeroes, the number of points to
follow; each of the following n lines contains two integers x and y, both
expressed in decimal with no leading zeroes, giving the coordinates of one
of your points.
You are guaranteed that T <= 30 and that no data set contains more than 30
points. All points in each data set will be no more than 500 units away
from (0,0).
Output
Print, on a single line with two decimal places of precision, the area of
the smallest square containing all of your points. An answer will be
accepted if it lies within 0.1 of the correct answer.
Sample Input
2
4
-1 -1
1 -1
1 1
-1 1
4
10 1
10 -1
-10 1
-10 -1
Sample Output
4.00
242.00
Tor Myklebust and Gordon V. Cormack