Dynamic Interval Query

You are tasked with designing and implementing a data structure to manage a collection of time intervals (events) that can dynamically change over time. Each event is represented by a start time and an end time (both inclusive). Your data structure must efficiently support the following operations:

• addEvent(start, end): Add a new event defined by the interval [start, end]. You can assume that start ≤ end.
• removeEvent(start, end): Remove an existing event defined by the interval [start, end]. If multiple identical events exist, remove just one instance.
• query(time): Given a specific time, return the count of events whose intervals include that time.

Your solution should consider that the number of events can be large and that the operations (especially query) may be called frequently. Aim to optimize the time complexity of each operation and provide justifications for your design choices when documenting your code.

Implement your solution in the programming language of your choice. Make sure your code is well-structured, commented, and covers edge cases.