Let D(n) denote the number of ways of writing the positive integer n as a product

n=f_{1} \cdot f_{2} \cdots f_{k}

where k \geq 1, the f_{i} are integers strictly greater than 1 , and the order in which the factors are listed matters (that is, two representations that differ only in the order of the factors are counted as distinct). For example, the number 6 can be written as 6,2 \cdot 3, and 3 \cdot 2, so D(6)=3. What is D(96) ?

**Answer Choices**

A. 112

B. 128

C. 144

D. 172

E. 134