Steven the troll submits problems using silly names instead of his own. On day $1$, he gives no name at all. Every subsequent day, he alternates between adding $2$ words and $4$ words to his name. For example, on day $4$, he submits an $8\text{-word}$ name. On day $n$, he submits a $44\text{-word}$ name: "Steven the AJ Dennis the DJ Menace the Prince of Tennis the Merchant of Venice the Hygienist the Evil Dentist the Major Premise the AJ Lettuce the Novel’s Preface the Core Essence the Young and the Reckless the Many Tenants the Deep, Dark Crevice". Compute $n$.

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