Mock CCO '18 Contest 2 Problem 4 - Victor's Rectangles

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Points: 20 (partial)
Time limit: 0.6s
Memory limit: 64M

Problem type

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 xy-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?


4 \le N \le 1500

For at most 20% of full credit, N \le 500.

\left|x_i\right| \le 10^8

\left|y_i\right| \le 10^8

All (x_i, y_i) are distinct.

Input Specification

The first line will contain a single integer, N.

Each of the next N lines will contain two space-separated integers x_i and y_i, indicating that Roger has highlighted point (x_i, y_i).

Output Specification

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.

Sample Input

-2 3
-2 -1
0 3
0 -1
1 -1
2 1
-3 1
-2 1

Sample Output



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