Let $D = \{1, 2, 3, 4\}$ be a domain. Consider the first-order sentence $\phi = \forall x \forall y (d(x,y) \implies \neg d(y,x))$, where $d(x,y)$ is a binary relation on $D$. How many distinct models (interpretations of $d$) over the domain $D$ satisfy $\phi$?