Problem: Find Largest Connected Group of Overlapping Intervals

You are given n people, where each person i works during an inclusive time interval [start_i, end_i].

We define a communication graph as follows:

• Each person is a node in the graph.
• An undirected edge exists between two people, a and b, if their work intervals overlap. Two intervals [start_a, end_a] and [start_b, end_b] overlap if max(start_a, start_b) <= min(end_a, end_b).

A work group is defined as any set of people whose induced subgraph is connected. It is important to note that this does not require the subgraph to be a clique; connectivity through a chain of overlaps is sufficient. For example, if person A overlaps with person B, and person B overlaps with person C, then {A, B, C} forms a valid work group, even if person A does not directly overlap with person C.

Task: Return the maximum possible size of such a work group. This is equivalent to finding the size of the largest connected component in the defined overlap graph.

Constraints:

• n can be up to 2e5 (200,000).
• All times (start_i, end_i) are integers.
• For all intervals, start_i <= end_i.
• Your solution should achieve a time complexity of approximately O(n log n).