MathNet 2012 Question 64

Fill an $8\times8$ chessboard with letters $A,B,C,D$ so that any two squares sharing a side or a vertex have different letters. Require also the following property for $A$ and $B$: whenever an $A$ or $B$ has a letter $X$ horizontally or vertically adjacent ($X$ may be $A,B,C,D$), the square on the opposite side contains another $X$, unless that side is beyond the board's edge. In how many ways can the board be filled?
(A) 136 (B) 144 (C) 168 (D) 328 (E) 360.