Find largest connected group of overlapping intervals

You are given `n` people, where person `i` works during an inclusive time interval `[start_i, end_i]`. Define a communication graph: - Each person is a node. - Two people have an (undirected) edge if their work intervals **overlap**, i.e.: \[ \max(start_a, start_b) \le \min(end_a, end_b) \] A **work group** is any set of people whose induced subgraph is **connected** (it does not need to be a clique; connectivity through a chain is enough). For example, if A overlaps B and B overlaps C, then `{A,B,C}` is a valid group even if A does not overlap C. Task: Return the maximum possible size of such a work group (i.e., the size of the largest connected component in this overlap graph). Constraints (typical interview setting): - `n` up to `2e5`. - Times are integers; `start_i <= end_i`. - Your solution should be around `O(n log n)`.