Consider functions f that satisfy |f(x)-f(y)| \leq \dfrac{1}{2}|x-y| for all real numbers x and y. Of all such functions that also satisfy the equation f(300)=f(900), what is the greatest possible value of

f(f(800))-f(f(400)) ?

**Answer Choices**

A. 25

B. 50

C. 100

D. 150

E. 200