USA Citizen Flying into Beijing from Taiwan then to US

I am a US Citizen. I will be traveling to a few countries in Asia. I will be in Taiwan. From Tawain, I will be flying to Beijing. I will be there for a day and a half. From Beijing, I will be traveling back to the US. I already purchased my flight tickets for both of my flights into and out of Beijing. Do I qualify for the 72 hour Visa?
Thanks.