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What is the final product of this reaction?

reaction

Here's what I have:

my solution

Does this look correct? I'm concerned because I'm used to seeing the nitrogen removed from the product (in the cases of primary amines).

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With excess of methylamine, I wouldn't exclude additional methylation, yielding a trimethylanilinium iodide.

alkylation of dimethylaniline

However, the reaction should stop there since a further hydrogen abstraction from a $\beta$-position isn't possible.

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