Count substrings that use only vowels and contain all five

Given a string s of lowercase English letters, return the number of contiguous substrings that satisfy both rules:

1. Every character of the substring is a vowel (a, e, i, o, u).
2. The substring contains each of the five vowels at least once.

Substrings are counted by position: two equal substrings that start at different indices both count.

Implement:

def count_vowel_substrings(s: str) -> int: ...

Constraints

• 0 <= len(s) <= 10^5
• s contains only lowercase English letters.
• The answer can exceed 32 bits.

Start with a working solution, then aim for linear time.

Example 1

Input:  s = "aaeiou"
Output: 2

The valid substrings are "aaeiou" and "aeiou".

Example 2

Input:  s = "aeioxuaei"
Output: 0

The x splits the vowels into "aeio" and "uaei", and neither part contains all five vowels.