Maximum Nesting Depth Sorter

You are given several strings containing lowercase letters and parentheses. Sort the strings based on their 'Maximum Nesting Depth' of parentheses (the highest number of nested open parentheses at any point). If depths are equal, sort by the total length of the string, and finally by the string's lexicographical order. Example: Input: '(a) (a(b)) ((c))' - '(a)': Depth 1 - '(a(b))': Depth 2 - '((c))': Depth 2 Output: (a) ((c)) (a(b))