Can you enter China twice within a short period, using the 72 hour rule each time.

I would like to visit both Shanghai and Japan. Can I use the 72 hr. rule (or is it even 144 hrs for Shanghai?) to avoid getting a Chinese visa if I do the following:
Fly from USA to Shanghai on a round trip ticket, stay 72 hrs or less (or 144??) in Shanghai.
Fly from Shanghai to Japan on a separate round trip ticket on China Eastern or whatever, spend let's say 3-4 days in Japan and then return to Shanghai.
Spend another 72 hours (or 144?) in Shanghai.
Return to USA on the return portion of my USA-Shanghai ticket.

Will this work? If so, I could get a total of 72 + 72 hours in Shanghai without a visa (or if the rule for Shanghai is actually a more generous 144 hours, I could get 144 +144 hrs= 288 hours there, essentially 12 days) Thank you for your help!!