Directed Graphs and Network Flows · Superchallenge problem

A theorem of Stanley states that $|P(G,-1)|$ (the chromatic polynomial evaluated at $k=-1$) equals the number of ways to orient every edge of $G$ so that the result has NO directed cycle. Using the cycle formula $P(C_n,k)=(k-1)^n+(-1)^n(k-1)$, how many such "no directed cycle" orientations does $C_8$ have?