maximum-nesting-depth-of-the-parentheses

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.