Predicting product of a Hofmann elimination with a cyclic amine What is the final product of this reaction?



Here's what I have:



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



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