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