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