find-the-number-of-ways-to-place-people-i

You are given a 2D array points of size n x 2 representing integer coordinates of some points on a 2D plane, where points[i] = [xi, yi].

Count the number of pairs of points (A, B), where

• A is on the upper left side of B, and


• there are no other points in the rectangle (or line) they make (including the border).

Return the count.

Example 1:

Input: points = [[1,1],[2,2],[3,3]]

Output: 0

Explanation:

There is no way to choose A and B so A is on the upper left side of B.

Example 2:

Input: points = [[6,2],[4,4],[2,6]]

Output: 2

Explanation:

• The left one is the pair (points[1], points[0]), where points[1] is on the upper left side of points[0] and the rectangle is empty.


• The middle one is the pair (points[2], points[1]), same as the left one it is a valid pair.


• The right one is the pair (points[2], points[0]), where points[2] is on the upper left side of points[0], but points[1] is inside the rectangle so it's not a valid pair.

Example 3:

Input: points = [[3,1],[1,3],[1,1]]

Output: 2

Explanation:

• The left one is the pair (points[2], points[0]), where points[2] is on the upper left side of points[0] and there are no other points on the line they form. Note that it is a valid state when the two points form a line.


• The middle one is the pair (points[1], points[2]), it is a valid pair same as the left one.


• The right one is the pair (points[1], points[0]), it is not a valid pair as points[2] is on the border of the rectangle.

Constraints:

• 2 <= n <= 50


• points[i].length == 2


• 0 <= points[i][0], points[i][1] <= 50


• All points[i] are distinct.