Trip to Taipei and Jakarta with two layovers in Shanghai

I have a round trip ticket form USA (Spokane, WA via Seattle) to Shanghai arriving in Shanghai (PVG) on December 9, 6:05 pm and returning to to the USA on December 22 at 1:10 PM. However, my main two destinations are Taipei, Taiwan and Jakarta, Indonesia and I have round trip tickets from Shanghai to Taipei (Leave Dec 12 return Dec 15) and Shanghai to Jakarta (leave Dec 15 and return Dec 21). Thus, I will have three separate layovers in Shanghai (PVG), none of which individually exceed 72 hours, although all three layovers together exceed 72 hours. The longest layover is 62 hours, the other two are both less than 24 hours. Can I still use the 72 hour visa free transit or do I need to apply for a visa?