Round trip to Beijing Capital Airport with a 3rd point stopover (HKG)

Hi! I want to buy a round trip ticket from Taipei to BJ. The first leg of the flight is with an overnight stopover in Hong Kong, then the next day to BJ, then after 2 days in BJ a direct flight to Taipei. Will that qualify as a "different point of origin" for the 72-hour visa? Please advise. Thank you