There are three floors in a building: floor 1 at the bottom, floor 2 in the middle, and floor 3 at the top. Each floor has two flats: Flat A is to the...

There are three floors in a building: floor 1 at the bottom, floor 2 in the middle, and floor 3 at the top. Each floor has two flats: Flat A is to the west of Flat B. Each flat has an area of 576 sq ft and contains a certain number of rooms, with no two flats having the same number of rooms.

• On the even-numbered floor, one flat has rooms each measuring 64 sq ft.
• The total number of rooms on floor 3 is 7.
• The flat with rooms of 72 sq ft each is on an odd-numbered floor.
• The flat directly below the flat with 9 rooms has rooms measuring 288 sq ft each.
• There is exactly one floor between the flat with rooms of 192 sq ft each and the flat with rooms of 72 sq ft each.
• There is no flat to the west of the flat that has 6 rooms.

What is the total number of rooms on the 2nd floor?