Arriving at Malpensa Airport on May 24th. Need to book train from there to Genoa. Will be using trains as main transportation around Italy. From Genoa to Cinque Terre, Pisa, Rome, Florence and then Venice. Thinking that a train pass is the way to go. Would like advice. If I buy a months pass that I will only use for 8-9 days will it include the fast trains and the intercity ones as well?