do I qualify for the 144 hour visa free transit? I have stops in Shanghai and Beijing

I am a UK traveler and I am looking at flying from Manchester to Shanghai, and then after spending 5 days in Shanghai getting a flight from Shanghai to Bangkok. My question is associated to my outbound flight. My flight from Manchester to Shanghai has a stop of 2 hours in Beijing.
I read that the 144 hour free transit only permits you to stay in selected administrative regions in Shanghai and two other areas. Because my outbound plane isn't direct to Shanghai and stops in Beijing will this affect my eligibility?