Strong password checker

Observations:

• When len(password) < 6, inserts are required
• When len(password) > 20, removals are required
• Inserts and replacements can be used to meet lower/upper/digit constraints
• When eliminating repeating groups, replacements are more valuable than inserts
• When 6 <= len(password) <= 20, replacements are most valuable
• Repeating groups should be eliminated as effectively as possible while inserting / removing characters

The observation that replacements are more effective comes from the fact that "aaaaa" can be fixed with a single replacement, whereas it would require two inserts. Replacements can reduce the repeat count by 3, inserts by 2, removals by 1:

Repeats	Replacements	Inserts	Removals
3	1	1	1
4	1	1	2
5	1	2	3
6	2	2	4
7	2	3	5
8	2	3	6

Since replacements are more effective than inserts and removals, inserts or removals should only be used when necessary, i.e. when len(password) < 6 or > 20. And when insert or removal is required, the goal is to unlock efficient use of replacements afterwards. Basically, insert/remove should "land on" 5, 8, 11, ... counts[i]%3 == 2.

This gives the following prioritization for removal of characters while n > 20

1. Remove once in groups of 6, 9, 12, ..., i.e. counts[i]%3 == 0
2. (n>21) Remove twice in groups of 7, 10, 13, ..., i.e. counts[i]%3 == 1
3. Repeated removal from group until <= 2
4. Remove without reducing repeated group

And for inserts, i.e. n < 6:

1. Insert once in groups of 7, 10, 13, i.e. counts[i]%3 == 1
2. Insert in any group
3. Insert without reducing repeated group

Once 6 <= n <= 20, use replacements to fix any repeating groups.

Finally, count number of inserts/replacements to determine if more replacements are needed to match constraints.