Let Z be the set of all integers, A ={(x, y) ∈ Z × Z:(x-2)^2+y^2 ≤ 4}, B ={(x, y) ∈ Z × Z: x^2+y^2 ≤ 4} and C ={(x, y) ∈ Z × Z:(x-2)^2+(y-2)^2 ≤ 4}…

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