Caitlin is an overworked clerk in a store that is open 6 days a week, 16 hours a day, with clerks working 8-hour shifts. Caitlin gets exactly 2 days off (that is, 2 days where the store is open, but Caitlin isn't working) each week, but they are not necessarily 2 days in a row. On workdays, Caitlin always works the earlier shift, but sometimes has to work a double shift (work the whole 16 hours). Next week, Caitlin has to work 3 double shifts. How many different schedules could Caitlin have next week?