Crossword Puzzle Design

A Japanese-style crossword puzzle grid is a rectangular grid of white and black-shaded squares that follow these design rules:

• All white cells must be orthogonally contiguous (that is, connected in one mass through shared sides, to form a single polyomino).
• There must be at least one shaded cell. Shaded cells may not share a side (i.e. they may not be orthogonally contiguous).
• The grid should have $180^\circ$ rotational (also known as "radial") symmetry so that its pattern appears the same if the paper is turned upside down.
• The four corner squares must be white.

How many different $5 \times 5$ Japanese-style crossword puzzle grids are there?

Note: A grid that is obtained from another grid by rotation, reflection, or a combination of both is considered the same as the initial grid.