Yes, you can. I had happened same situation. My flight was at 7:05a.m and I stayed at the airport from 1:00 a.m. to the departure time. Some uncomfortable on the chair. But I had a little bit slept on that night. But IF you wish close to the Terminal A you can go to the Marriot hotel (around $100.00)
Almost all airports at 24/7. Especially an International Airport like this
I think the airport is open 24 hours
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