Downtime Calculator

You are given a list of time intervals during which a system is active. Each interval is represented by a pair of times in 24-hour format (HH:MM) indicating the start and end times of activity. You are also provided with a full day period (from 00:00 to 24:00).

Your task is as follows:

1. Merge all overlapping or contiguous active intervals.
2. Calculate the total amount of downtime (in minutes) during the day when the system was not active.
3. Return the total downtime.

Assume the following:

• The input is a list of intervals. Each interval is a tuple or list of two strings [start, end] (e.g., ["09:00", "11:30"]).
• Intervals may not be in sorted order and could be overlapping or touching (i.e., the end time of one interval could be the same as the start time of another).
• The day always starts at "00:00" and ends at "24:00".

Write a function that implements the above requirements.

Example:

Given the intervals:

[ ["08:00", "10:00"], ["09:30", "12:00"], ["13:00", "15:00"], ["14:30", "16:00"] ]

After merging, the intervals become:

[ ["08:00", "12:00"], ["13:00", "16:00"] ]

The downtime is calculated as the sum of the following periods:

• From 00:00 to 08:00
• From 12:00 to 13:00
• From 16:00 to 24:00

Your function should compute and return the total downtime in minutes.