In a city,no two persons have an identical set of teeth,and there is no person without a tooth. Also,no person has more than $32$ teeth. If we disregard the shape and size of the teeth and consider only the presence or absence of a tooth at each of the $32$ positions,then the maximum population of the city is:
- A$2^{32}$
- B$(32)^2 - 1$
- C$2^{32} - 1$
- D$2^{32 - 1}$
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