Merge overlapping 2D line segments

You are given a list of 2D line segments. Each segment is represented as a **list of 2D points** `[(x1,y1), (x2,y2), ...]` that all lie on the same straight line. ### Definitions - Within a segment, the points are already **sorted along the segment** (from one end to the other). - Different segments are **not** sorted relative to each other. - Two segments should be **merged** if: 1. They are **collinear** (lie on the same infinite line; i.e., same slope and offset), and 2. Their **geometric segments intersect** (they share at least one point in common, including touching at endpoints). When merging multiple segments, the result for that merged group should contain **all distinct points that appear in any of the original segments in the group**, sorted along the line. ### Task Return a list of merged segments (each as a sorted list of points). The order of merged segments in the output does not matter. ### Example **Input** ``` [ [(1, 1), (2, 2), (4, 4)], [(2, 1), (4, 2)], [(3, 3), (6, 6)], [(7, 7), (8, 8)] ] ``` **Output (one valid ordering)** ``` [ [(1, 1), (2, 2), (3, 3), (4, 4), (6, 6)], [(7, 7), (8, 8)], [(2, 1), (4, 2)] ] ``` ### Notes / Assumptions - Coordinates are integers. - Each input segment contains at least 2 points. - You should remove duplicate points within a merged segment.