Concurrent Event Overlap

You are given an array of events, where each event is represented as an object or a tuple with a start time and an end time (both integers). The times indicate when an event begins and ends. Your task is to write a function that calculates the maximum number of events that overlap at any given time and returns:

1. The maximum count of overlapping events.
2. A list (or array) of time interval(s) during which this maximum overlap occurs.

For example, given the following events:

• Event 1: (1, 4)
• Event 2: (2, 5)
• Event 3: (7, 9)

The maximum overlap is 2 between time 2 and 4.

You may assume that the events are not guaranteed to be in any particular order. Consider edge cases such as events that share a boundary time (for instance, one event ending exactly when another starts). Design and implement an efficient solution.

Write code in the programming language of your choice.