Count the Maximum Number of Collinear Points

Given points in a two-dimensional plane, return the largest number of input points that lie on one straight line. ### Function Contract Implement `maximum_collinear_points(points) -> int`, where every element of `points` is an integer pair `[x, y]`. ### Constraints and Clarifications The following bounds and repeated-point convention are explicit practice assumptions: - `0 <= len(points) <= 300`. - Coordinates are integers between `-1000000` and `1000000`, inclusive. - Repeated coordinates represent distinct input points and each counts toward the result. - Horizontal and vertical lines are allowed. - Return `0` for no points and `1` for a single point. - Collinearity is exact; do not use a floating-point tolerance that can merge different slopes. - Aim for `O(n^2)` pair processing, apart from integer-normalization costs. ### Examples ```text points = [[0, 0], [1, 1], [2, 2], [2, 0]] Output: 3 ``` Three points lie on the line `y = x`. ```text points = [[1, 1], [1, 1], [2, 2], [3, 4]] Output: 3 ``` The two occurrences of `(1, 1)` and the point `(2, 2)` lie on one line. ```hint Compare directions from one point Lines through a fixed point can be grouped by direction. Decide how to represent equal directions exactly and how coincident points should affect every possible line through that point. ```