144/ 72 free entry Chinise visa

We have US passport and we are planning to travel from US to Bangkok for 5 days, then going to Hong kong for 3 and Beijing for 3 days, then returninh to US. Can we qualified for the 144 free visa entry? As it mentoned that you need to leave Beijing to a third country but US is our residence. I'm not clear the meaning for third country. Please clarify it.