Find the Number of Ways to Place People I

Medium

You receive 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 ), except for the points A and B .

Produce the count.

Example 1

Original illustrative diagram 1 for Find the Number of Ways to Place People I

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

Output: 0

Explanation: There is no way to choose A and B such that A is on the upper left side of B .

Example 2

Original illustrative diagram 2 for Find the Number of Ways to Place People I

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

Original illustrative diagram 3 for Find the Number of Ways to Place People I

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