A scanning code consists of a grid of squares with some of its squares colored black and the rest colored white. There must be at least one square of each color in this grid of squares. A scanning code is called symmetric if its look does not change when the entire square is rotated by a multiple of counterclockwise around its center, nor when it is reflected across a line joining opposite corners or a line joining midpoints of opposite sides. What is the total number of possible symmetric scanning codes?
30
32
62
64
126
