The reaction is all about the *migration* part, isn't it? The amine has one less carbon because the alkyl group attached to the carbonyl carbon migrates and gets kicked out entirely, so you lose that original carbon from the chain. Honestly, the only migration I understand is my uncle's family moving to Surat last month for a factory job. Now my aunt sends city-bought dresses for my sister, and the only thing with one less carbon here is my own business.
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