US citizen going to Hong Kong, Taipei, and Shanghai

I will be arriving (from Los Angeles) into Hong Kong on Dec. 5, to Taipei on Dec. 9, and to Shanghai on Dec. 13. I return to Los Angeles on Dec. 16. Do I need any visas for this trip? If not, is the 72 hour rule exact or is it for 3 days, for example, if we arrive in the morning on Dec. 13 and leave in the evening on Dec. 16, do we need one?
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