Am i eligible for 144 free visa?

Is this eligable for 144 free visa
Us passports

Fly from usa - beijing( 2 hours -wont leave airport basically a stop over) - shanghai ( stay for 3 days
Then fly
Shanghai. - bangkok (straight flight)

Return
Fly from Bangkok - beijing (9 hour stop and planning to do a layover tour) - and back to usa from beijing

I Know im eligible for beijing lay over tour as my 3rd country is different.

Will i still be eligible for shanghai (3 days stop) if my 1st leg of tour stops at Beijing first before shanghai??

Sorry if its confusing cuz im also very confused