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.


def maxDepth(s: str) -> int:
    depth, max_depth = 0, 0
    for ch in s:
        if ch == '(':
            depth += 1
        elif ch == ')':
            depth -= 1
        max_depth = max(max_depth, depth)
    return max_depth
