Amber is making a scratching post for her cat. The scratching post is composed of two rectangular prisms with the dimensions shown. A square prism is stacked vertically and centered on a rectangular prism. The base of the square prism has side lengths of three inches. The height of the square prism is twenty-three and a half inches. The rectangular prism has a length of sixteen inches, width of fourteen inches, and height of one and one-fourth inches.
Amber plans to cover all exposed faces, except for the bottom face, with carpet. How many square inches of carpet does she need?

Enter the correct answer in the box.