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One face of a cube contains a circle, as shown. This cube rolls without sliding on a four by four checkerboard. The cube always begins a path on the bottom left square in the position shown and completes the path on the top right square. During each move, an edge of the cube remains in contact with the board. Each move of the cube is either to the right or up. For each path, a face of the cube contacts seven different squares on the checkerboard, including the bottom left and top right squares. The number of different squares that will not be contacted by the face with the circle on any path is

\( \textbf{(A)}\ 9\qquad \textbf{(B)}\ 11\qquad \textbf{(C)}\ 8\qquad \textbf{(D)}\ 12\qquad \textbf{(E)}\ 10\qquad\)