Longest Balanced Substring in a String of Parentheses

Reported from a Meta software engineering coding round. You are given a string `s` that contains only the characters `(` and `)`. A string is **balanced** if it can be built with these rules: - the empty string is balanced; - if `A` is balanced, then `(A)` is balanced; - if `A` and `B` are balanced, then their concatenation `AB` is balanced. Return the length of the longest non-empty contiguous substring of `s` that is balanced. If `s` has no such substring, return `0`. ### Function Signature ```python def longest_balanced_substring(s: str) -> int: ``` ### Rules - Only contiguous substrings count; characters may not be skipped. - The result is a single integer (a length), so it is unique even when several substrings share the maximum length. ### Constraints - `0 <= len(s) <= 3 * 10^4` - Every character of `s` is `(` or `)`. - The answer is at most `len(s)`, well inside the 32-bit signed integer range. ### Examples **Example 1** - Input: `s = ")(())()"` - Output: `6` - Explanation: the substring `"(())()"` starting at index 1 is balanced. The leading `)` cannot belong to any balanced substring. **Example 2** - Input: `s = "()(()"` - Output: `2` - Explanation: `"()"` at indices 0-1 and `"()"` at indices 3-4 are balanced, but the unmatched `(` at index 2 sits between them, so nothing longer is balanced. **Example 3** - Input: `s = "))(("` - Output: `0` - Explanation: no non-empty substring is balanced.