Nested Boxes

A box in a box in a box… how deep does the wrapping go? 📦

You get a balanced string of ( and ) where each ( opens a box and ) closes one. Print the deepest nesting level (an empty string is depth 0).

Example:

Input: boxes = "(())()" Output: 2

The depth climbs to 1, then 2, inside the first group before descending back to 0, then rises to 1 in the second group — the deepest point ever reached is 2.