Maximum Nesting Depth of the Parentheses

You are given a valid parentheses string s, return the nesting depth of s. The nesting depth is the maximum number of nested parentheses.

Example 1:

Input: s = "(1+(2*3)+((8)/4))+1"

Output: 3

Explanation: Digit 8 is inside of 3 nested parentheses in the string.

Example 2:

Input: s = "(1)+((2))+(((3)))"

Output: 3

Explanation: Digit 3 is inside of 3 nested parentheses in the string.

Example 3:

Input: s = "()(())((()()))"

Output: 3

Constraints:

• 1 <= s.length <= 100
• s consists of digits 0-9 and characters '+', '-', '*', '/', '(', and ')'.
• It is guaranteed that parentheses expression s is a VPS.

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