Sam colors each tile in a 4 by 4 grid white or black. A coloring is called rotationally symmetric if the grid can be rotated 90, 180, or 270 degrees to achieve the same pattern. Two colorings are called rotationally distinct if neither can be rotated to match the other. How many rotationally distinct ways are there for Sam to color the grid such that the colorings are not rotationally symmetric?
