Let $A$ be a finite set with $n\geq 4$ elements
and let $\rho$ be an equivalence relation on $A$.
Suppose that there are exactly 4 equivalence
classes, $C\_1,C\_2, C\_3,C\_4$.
Moreover we know that $\lvert C\_1\rvert=\lvert C\_2\rvert=1$.
Let $a\in A$ be an element that we know is in $C\_3$.

What is the *maximum* number of ordered pairs of $(x,y)\in\rho$
in which $a$ can occur (meaning $a=x$ or $a=y$ or $a=x=y$)?