Find the Longest Ordered Run Containing Every Vowel

### Problem `word` contains only the five lowercase vowels. Find the longest contiguous substring whose characters are nondecreasing alphabetically and which contains each of a, e, i, o, and u at least once. Return its length, or zero if none exists. ```cpp class Solution { public: int longestBeautifulSubstring(string word); }; ``` ### Examples **Example 1:** ```text word = "aaeeiioouu" Output: 10 Explanation: The whole string contains every vowel in order. ``` **Example 2:** ```text word = "uuaeioou" Output: 6 Explanation: The suffix aeioou is valid; the leading u characters cannot precede a in an ordered substring. ``` ### Constraints - `1 <= word.length <= 5*10^5`. - Every character is one of `a`, `e`, `i`, `o`, `u`. ### Clarifying Questions Order is nondecreasing, so repetitions are permitted. All five vowels must occur; a sorted run omitting one vowel is insufficient. ```hint Inspect the structure What must hold about order and vowel coverage inside a qualifying contiguous substring? ``` ### Reasoning checkpoints - Enforce contiguity, nondecreasing order, and presence of all five vowels. - Prove that no longer qualifying substring exists, including runs that skip a required vowel. ### Optional extensions How would you generalize the method to a specified ordered alphabet?