Ali defines a pronunciation of any sequence of English letters to be a partition of those letters into substrings such that each substring contains at least one vowel. For example, $\text{A } | \text{ THEN } | \text{ A}$, $\text{ATH } | \text{ E } | \text{ NA}$, $\text{ATHENA}$, and $\text{AT } | \text{ HEN } | \text{ A}$ are all pronunciations of the sequence $\text{ATHENA}$. How many distinct pronunciations does $\text{YALEMATHCOMP}$ have? (Y is not a vowel.)

Let's think step by step and output the final answer within \boxed{}.
user