Hello. 2 of us will be arriving from Florence to Termini at 23:35. Our flight the next morning leaves at 7:05 from Terminal 3. If I'm correct, we would need to arrive at the airport at least by 5 a.m., which leaves us a little over 5 hours. If we take a taxi to Termini that late at night, will we be able to get through security to rest near our gate, or does security close at a certain time? Thank you.