<gh_stars>1-10
"""
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.


"""

"""
The basic idea here is to get the maximum size of the stack after parsing the string
"""


class Solution:
    def maxDepth(self, s: str) -> int:
        s = "".join(c for c in s if c in "()")
        if not s:
            return 0
        s = [c for c in s]

        stack = []
        mx = 0

        for c in s:
            if c in "(":
                stack.append(c)
                mx = max(mx, len(stack))
            else:
                stack.pop()
        return mx

"""
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.


"""

"""
The basic idea here is to get the maximum size of the stack after parsing the string
"""


class Solution:
    def maxDepth(self, s: str) -> int:
        s = "".join(c for c in s if c in "()")
        if not s:
            return 0
        s = [c for c in s]

        stack = []
        mx = 0

        for c in s:
            if c in "(":
                stack.append(c)
                mx = max(mx, len(stack))
            else:
                stack.pop()
        return mx
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. The basic idea here is to get the maximum size of the stack after parsing the string