San Francisco to Beijing to Hong Kong

Hi, I am a US citizen with a valid passport expiring in 2020. I booked a ticket flying from San Francisco to Beijing with a stopover of about 6 days (arriving Beijing in the afternoon on 1/1 and departing for Hong Kong in the afternoon on 1/7). I will arrive Hong Kong on the same day and will stay therefore until the take the same return route back to San Francisco, i.e. Hong Kong to Beijing to San Francisco, but without the layover in Beijing as incoming trip. Do I qualify for the 144 hour free exemption for my first lag of stay in Beijing?