US - Seoul - Shanghai - Seoul - US

I'm planning to go to Korea end of May to early June and was hoping that if I could travel to China during the time I stay in Korea. Would 144 hours visa free work for this schedule? So, it would be that I will arrive in Korea and after about a week staying there, I will go to China and visit there for 3 days and go back to Korea. Stay in korea about one more week and come back to US. Would this work??