You are given two strings `a` and `b` that consist of lowercase letters. In one operation, you can change any character in `a` or `b` to any lowercase letter.

Your goal is to satisfy one of the following three conditions:

- Every letter in `a` is strictly less than every letter in `b` in the alphabet.
- Every letter in `b` is strictly less than every letter in `a` in the alphabet.
- Both `a` and `b` consist of only one distinct letter.

Return the minimum number of operations needed to achieve your goal.

Example 1:

    Input: a = "aba", b = "caa"
    Output: 2
    Explanation: Consider the best way to make each condition true:
    1) Change b to "ccc" in 2 operations, then every letter in a is less than every letter in b.
    2) Change a to "bbb" and b to "aaa" in 3 operations, then every letter in b is less than every letter in a.
    3) Change a to "aaa" and b to "aaa" in 2 operations, then a and b consist of one distinct letter.
    The best way was done in 2 operations (either condition 1 or condition 3).

Example 2:

    Input: a = "dabadd", b = "cda"
    Output: 3
    Explanation: The best way is to make condition 1 true by changing b to "eee".

Constraints:

- `1 <= a.length, b.length <= 105`
- `a` and `b` consist only of lowercase letters.