Let $Z$ be the set of all integers, $A = \left\{ (x,y) \in Z \times Z:(x - 2)^{2} + y^{2} \leq 4 \right\}$ $B = \left\{ (x,y) \in Z \times Z:x^{2} + y^{2} \leq 4 \right\}$ and\\ $C = \left\{ (x,y) \in Z \times Z:(x - 2)^{2} + (y - 2)^{2} \leq 4 \right\}$ If the total number of relations from $A \cap B$ to $A \cap C$ is $2^{p}$, then the value of $p$ is