Meeting Overlap Counter

Problem Statement:

You are given an array of meeting intervals. Each meeting interval is represented as an object or a tuple with two properties: start and end, where start denotes the beginning time of a meeting and end denotes the ending time. Note that the meeting time is inclusive of the start time and exclusive of the end time.

Your task is to implement a function that computes and returns the maximum number of meetings that are overlapping at any given time.

Example:

Given the meeting intervals:

• {start: 1, end: 4}
• {start: 2, end: 5}
• {start: 7, end: 9}

The maximum overlap is 2, which occurs between time 2 and time 4 where the first two meetings overlap.

Constraints:

• If the input array is empty, return 0.
• The input intervals may not be sorted.
• Consider efficiency for large inputs.

Implement your solution in your preferred programming language.