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I am trying to come up with a logical mechanism for the following transformation, where 2-methylenecyclobutan-1-ol is converted to cyclopentanone under acidic conditions:

Acid-catalysed rearrangement of 2-methylenecyclobutan-1-ol to cyclopentanone

What I have tried to do was contract the ring to a methylcyclopropyl carbocation as it is exceptionally stable. I also tried to expand the ring but got an unsaturated primary alcohol instead. Can somebody suggest a proper mechanism for the reaction?

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