Nested Parentheses

Given a string containing only '(' and ')', determine its depth. The depth of the string is defined as the maximum number of nested parentheses. For instance, for the input '((()))', the depth is 3, and for input '()', the depth is 1. Make sure to consider different edge cases such as an empty string, no valid parentheses, etc. Write a function to return this depth. Example Input ((()))