Will be arriving Rome mid-Oct for five nights, then heading to Florence by train for 4 nights, then to Bologna for one night, flying home the next morning. Is it advisable or recommended that we purchase our train tickets from Rome-Florence and Florence-Bologna as soon as possible upon arrival in Italy? Or, should there be sufficient seats available if we choose to wait until the dates of departure? Also, do ticket prices go up the longer you wait to purchase? Thanks!