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
Inputs = "(1+(2*3)+((8)/4))+1"
Output3
Digit 8 is inside of 3 nested parentheses in the string.
Example 2
Inputs = "(1)+((2))+(((3)))"
Output3
Digit 3 is inside of 3 nested parentheses in the string.

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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