Changing minds

Suppose you have created a machine that allows you to change minds with whomever you desire, but an exchange between a particular pair of minds is only allowed once. Suppose now that a set of 17 people have switched minds once. What is the least number of new bodies necessary for everyone to switch back to their original bodies?

OBS: This question is easy because it is only a tribute to an episode of Futurama.

Image credit: 20th century Fox, Futurama
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