Max Points on a Line

You are given an array points where points[i] = [xi, yi] represents the coordinates of the i-th point on a 2D plane.

Find the largest number of these points that all lie on some single straight line, and return that count.

Rules to keep in mind:

A line is determined by any two distinct points, and you need to consider every possible line formed by pairs of the given points.
All points are guaranteed to be distinct — no two entries in points are identical.
A line can be vertical (undefined slope), so don't assume you can always compute a slope as dy / dx without handling that case separately.
Watch out for floating point precision issues when comparing slopes; consider using integer-based comparisons (e.g., cross products or reduced fraction ratios) instead of dividing.

Examples

Example 1:

Input: points = [[1,1],[3,3],[2,2],[5,1],[8,1]]

Output: 3

Explanation:

The points (1,1), (2,2), and (3,3) all satisfy y = x, so they are collinear, giving a line with 3 points.
The points (1,1), (5,1), and (8,1) all lie on y = 1, which is also a line with 3 points.
No line passes through 4 or more of the given points, so the answer is 3.

Example 2:

Input: points = [[0,0],[0,4],[0,-2],[3,5]]

Output: 3

Explanation:

(0,0), (0,4), and (0,-2) all share x = 0, forming a vertical line containing 3 points.
(3,5) does not lie on that vertical line and does not align with any pair of the other points to form a larger group.
The maximum is therefore 3.