177. Maximum Nesting Depth of Parentheses

Given a valid parentheses string s (which may include letters, digits, and other characters), return the maximum depth of nested parentheses.

Depth increases by 1 each time a '(' is encountered and decreases by 1 at each ')'.

Input: A string s (valid parentheses, may contain other characters).

Output: An integer — the maximum nesting depth.

Examples

Input: (1+(2*3)+((8)/4))+1
Output: 3
Explanation: The deepest nesting is (( )) inside — depth 3.

Input: (1)+((2))+(((3)))
Output: 3
Explanation: (((3))) has depth 3.

Input: 1+(2*3)/(2-1)
Output: 1
Explanation: Single level of parentheses.

Constraints

• 1 <= s.length <= 100
• s consists of digits, operators, parentheses
• s is a valid VPS (valid parentheses string)

Asked by