Beijing 72 hours Visa coming from Hong Kong and leaving to Taiwan

I am now at Taipei. If I stay in Beijing less than 72 hours free transit, I arrive from Hong Kong and leave to Taipei, It is possible to get the 72 hours free transit? In addition, if go to Taipei to Beijing in flight with a transfer in Hong Kong and leave Beijing in a flight that goes directly to Taipei, is possible to get the 72 hours free transit or should I take to independent fights ( One from Taipei to Hong Kong and an other one from Hong Kong to Beijing) Thank You. My passport if from Spain.