Free Time Finder

You are given a list of events, each represented by a pair of integers [start, end] indicating that an event starts at time start and ends at time end. The times are expressed as integers corresponding to hours in a day (from 0 to 24), where 0 represents midnight at the start of the day and 24 represents midnight at the end of the day.

Your task is to write a function that takes this list of events and returns a list of time intervals during which no events are scheduled. Each free time interval should also be represented as a pair [start, end].

Please note the following:

• The list of events may be unsorted.
• Some events may overlap or touch each other. When events overlap or are contiguous, they should be merged together.
• The day starts at time 0 and ends at time 24. Consider these as the boundaries for free time.
• Return the free time intervals in increasing order by start time.

Example 1:

Input: [[1, 3], [5, 6], [2, 4]]

After merging overlapping events: [[1, 4], [5, 6]]

Output: [[0, 1], [4, 5], [6, 24]]

Example 2:

Input: [[0, 8], [10, 12], [12, 18]]

After merging adjacent events: [[0, 8], [10, 18]]

Output: [[8, 10], [18, 24]]

Write clean, efficient, and well-documented code to solve this problem.