Valid date from three integers in any order

You are given three integers a, b and c. Their order is unknown: any one of them may be the year, the month or the day. This covers formats such as yyyy-MM-dd, MM-dd-yyyy and dd-MM-yyyy.

Implement:

def can_form_date(a: int, b: int, c: int) -> bool: ...
def all_valid_dates(a: int, b: int, c: int) -> list[tuple[int, int, int]]: ...

• can_form_date returns True if at least one assignment of the three numbers to (year, month, day) is a real calendar date.
• all_valid_dates returns every distinct valid (year, month, day), sorted chronologically.

A date is valid when:

• 1 <= year <= 9999
• 1 <= month <= 12
• 1 <= day <= the number of days in that month of that year. February has 29 days in a leap year and 28 otherwise.
• A leap year is divisible by 4, except century years, which must also be divisible by 400 (2000 is a leap year, 1900 is not).

Inputs may be zero, negative or larger than 9999. Such values are never valid in any role.

Example 1

Input:  a = 30, b = 1987, c = 7
can_form_date   -> True
all_valid_dates -> [(1987, 7, 30)]

Only year 1987, month 7, day 30 works. 30 and 1987 can't be months.

Example 2

Input:  a = 2, b = 1900, c = 29
can_form_date   -> False

February 29, 1900 does not exist, because 1900 is not a leap year. No other assignment has a month between 1 and 12 with a valid day and year.

Example 3

Input:  a = 6, b = 6, c = 2021
all_valid_dates -> [(2021, 6, 6)]

Two permutations give the same date, and it is listed once.