Roger, having figured out how to reason in two dimensions, has crafted a tricky puzzle for Victor to crack.
Roger has highlighted several lattice points in the -plane and wants Victor to find the rectangle with maximum area inside that has vertices among the highlighted points!
Victor takes a look at this task and scoffs. It's just a line sweep problem, what's so tricky about that?
However, Roger points out to Victor that the rectangle need not be axis-aligned. The rectangles, much like Roger, can be tilted.
Is Victor tilt-proof?
For at most 20% of full credit, .
All are distinct.
The first line will contain a single integer, .
Each of the next lines will contain two space-separated integers and , indicating that Roger has highlighted point .
Print, on a single line, the maximum area of a rectangle with lattice points among the highlighted points. It is guaranteed that a non-degenerate rectangle exists.
8 -2 3 -2 -1 0 3 0 -1 1 -1 2 1 -3 1 -2 1