I have US passport, I will be flying Alitalia in early June from JFK to Rome, landing on a Wednesday at 8:40 am in Terminal 3. On the same booking reservation code/ ticket, I will be departing from Rome to Naples at 9:45 am from Terminal 1. I booked this flight on the Alitalia website, same reservation code. I will only have Carry on luggage, NO CHECKED Bags. Since I booked this on the official Alitalia website, I thought I'd have sufficient time (1 hour 5 minutes) since Alitalia had this as a flight combination on their website. Now I'm not so sure. Will I? And do I have to go through customs when I land in Rome to get to the flight to Naples?