Write detail mechanism for the following rearrangements:

i) Wagner-Meerwein rearrangement

ii) Beckmann rearrangement

i) Wagner-Meerwein Rearrangement:  
The Wagner-Meerwein rearrangement is a type of carbocation rearrangement, often occurring in the presence of a strong acid. It involves the migration of an alkyl or aryl group from one carbon atom to an adjacent carbon atom in a molecule, resulting in the formation of a new carbocation.

The mechanism starts with the protonation of a suitable substrate, typically a tertiary alcohol, which leads to the formation of a carbocation at the tertiary carbon. The formed carbocation _____ _____ ________ ___ ____ _____ ____ _______ __________ ____.
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