Measure the Deepest Parenthesis Nest

### Problem The parentheses in `s` are balanced. Other characters are digits or arithmetic operator symbols. Return the largest number of simultaneously open parentheses while reading the string. ```cpp class Solution { public: int maxDepth(string s); }; ``` ### Examples **Example 1:** ```text s = "2*((3+4)/(5-1))" Output: 2 Explanation: The groups around 3+4 and 5-1 are each nested inside the outer multiplication group. ``` **Example 2:** ```text s = "7+8/2" Output: 0 Explanation: No parentheses occur. ``` ### Constraints - `1 <= s.length <= 100`. - Permitted characters are digits `0..9` and `+`, `-`, `*`, `/`, `(`, `)`. - The parentheses form a valid balanced sequence. ### Clarifying Questions Do not evaluate the arithmetic expression. Parenthesis validity is guaranteed rather than something the function must reject. ```hint Inspect the structure How do nested groups differ from consecutive groups in the requested depth? ``` ### Reasoning checkpoints - Relate the reported nesting level to the balanced parentheses without evaluating the arithmetic expression. - Distinguish nested groups from adjacent groups and handle a string with no parentheses. ### Optional extensions What additional check would detect an invalid parenthesis sequence?