144 hours visa exemption - would like to have your confirmation

I plan to go to Beijing in August and have a question in relation to the 144 hours visa exemption. The following is my itinerary.

1 August 2018: Sydney-Beijing (transit in Taipei and arrive in Beijing at 18:50 on 2 August 2018)
8 August 2018: Beijing-Hong Kong
9 August 2018: Hong Kong-Taipei
12 August 2018: Taipei-Sydney

I am not so sure with this itinerary I am qualified for the 144 hours visa exemption in Beijing. Thanks a lot for the assistance.