Count distinct passwords from one substring reversal

A security team scores a password by its variability. Variability is the number of distinct strings you can get by reversing exactly one contiguous substring of the password.

Reversing a single character, or any palindromic substring, leaves the password unchanged. So the original password always counts once.

Implement:

def count_distinct_passwords(password: str) -> int

Return the variability of password.

Constraints

• 1 <= len(password) <= 10^5
• password has only lowercase English letters.
• The answer can be larger than 2^31 - 1.

Example 1

Input: password = "xyz"

Output: 4

The reachable strings are "xyz" (unchanged), "yxz", "xzy", and "zyx".

Example 2

Input: password = "ppq"

Output: 3

The reachable strings are "ppq", "pqp", and "qpp". Reversing "pp" gives back the original.