Given a string s representing a valid parentheses string expression, return the maximum nesting depth of parentheses in s.

The nesting depth at any position is the number of currently open parentheses that have not yet been closed. The answer is the largest such value over the entire string.

Note: It is guaranteed that s is a valid parentheses string, meaning every opening parenthesis in s is properly matched and closed in the correct order.

Constraints:

• $1 \leq$ s.length $\leq 100$

• s consists of digits $0$ to $9$ and the characters '+', '-', '*', '/', '(', and ')'

• s is guaranteed to be a VPS

Input: s = "7+8"-str
Output: 0-int
Explanation: There are no parentheses, so the nesting depth never exceeds 0.

Input: s = "((1+2)*3)"-str
Output: 2-int
Explanation: The deepest point occurs after the second (, where two parentheses are open at once.

Input: s = "1+(2*(3+(4/5)))"-str
Output: 3-int
Explanation: The maximum number of simultaneously open parentheses is 3 (at the start of (4/5)).

Input: s = "()(())(())"-str
Output: 2-int
Explanation: The deepest nesting happens in the (()) groups, where the depth reaches 2.

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