Appleby Contest '19 P4 - Rectangles

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Points: 7 (partial)
Time limit: 0.5s
Memory limit: 64M
Python 256M
Author:
Plasmatic
Problem types

King Brian is looking at rectangles!

He has a list of N points (x_1, y_1), (x_2, y_2), \dots, (x_N, y_N) and can select any four at random. If the four points form the four corners of an axis aligned rectangle, he writes down the area.

What is the largest possible area he can get from selecting four random points?

Note: axis aligned means that the four lines that form the rectangle are all either horizontal or vertical (aligning with the x and y axes respectively).

Constraints

For all subtasks:

4 \le N \le 2 \times 10^3

1 \le |x_i|, |y_i| \le 2 \times 10^4

No two points will be the same.

Subtask 1 [15%]

1 \le N \le 50

Subtask 2 [70%]

1 \le N \le 500

Subtask 3 [15%]

No additional constraints.

Input Specification

The first line will contain the integer N.

The next N lines will each contain two space separated integers: x_i, y_i.

Output Specification

Output one line, the maximum possible area of an axis aligned rectangle King Brian can get from selecting four random points. If no rectangles can be formed, print 0.

Sample Input

9
1 1
5 5
7 7
5 7
7 5
10 10
5 10
10 5
20 20

Sample Output

25

Sample Explanation

There are two possible rectangles that can be constructed with the 9 points:

  • From (5, 5) to (7, 7) with an area of 4
  • From (5, 5) to (10, 10) with an area of 25

Thus the answer is 25.

Comments


  • 1
    Humanthe2nd  commented on Nov. 17, 2024, 2:31 a.m.

    Negative coordinates are possible. I'm dumb and missed that in the constraints.


  • 1
    thunder200911133  commented on Feb. 12, 2024, 7:08 p.m.

    from (1,1) to (20,20) with an area of 361 what?


    • 1
      thunder200911133  commented on March 20, 2024, 2:58 p.m.

      guys, nvm, I get it, we have to have all 4 points in the points list, python3 is a bit hard


      • 0
        Sam629566  commented on Sept. 12, 2024, 1:43 a.m. ← edited

        your code works in pypy3 (erm oops didn't know u solved it)