Let f(x)=\log _{10}(\sin (\pi x) \cdot \sin (2 \pi x) \cdot \sin (3 \pi x) \cdots \sin (8 \pi x)). The intersection of the domain of f(x) with the interval [0,1] is a union of n disjoint open intervals. What is n ?
Answer Choices
A. 2
B. 12
C. 18
D. 22
E. 36