Count letters whose lowercase copies all come before uppercase

Given a string s of English letters (it may also contain other characters, which you ignore), count the distinct letters, compared case-insensitively, that satisfy this rule:

Every lowercase occurrence of the letter appears before every uppercase occurrence of the same letter.

A letter that appears only in lowercase, or only in uppercase, satisfies the rule.

Implement:

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

Constraints

• 0 <= len(s) <= 10^5
• Aim for O(n) time.

Example 1

Input:  s = "xxXyYyz"
Output: 2

x: both lowercase copies come before X, so it counts. y: a lowercase y follows Y, so it does not. z: lowercase only, so it counts.

Example 2

Input:  s = "Hello hELLO"
Output: 3

e, l and o count. h does not, because a lowercase h follows H.