A string is a valid parentheses string (denoted VPS) if it meets one of the following: It is an empty string "", or a single character not equal to "(" or ")", It can be written as AB (A concatenated with B), where A and B are VPS's, or It can be written as (A), where A is a VPS. We can similarly define the nesting depth depth(S) of any VPS S as follows: depth("") = 0 depth(C) = 0, where C is a string with a single character not equal to "(" or ")". depth(A + B) = max(depth(A), depth(B)), where A and B are VPS's. depth("(" + A + ")") = 1 + depth(A), where A is a VPS. For example, "", "()()", and "()(()())" are VPS's (with nesting depths 0, 1, and 2), and ")(" and "(()" are not VPS's. Given a VPS represented as string s, return the nesting depth of s. 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 Example 3: Input: s = "1+(2*3)/(2-1)" Output: 1 Example 4: Input: s = "1" Output: 0 Constraints: 1 <= s.length <= 100 s consists of digits 0-9 and characters '+', '-', '*', '/', '(', and ')'. It is guaranteed that parentheses expression s is a VPS.