Let \( \mathbb{C} \) be the set of all complex numbers. Let \( S_1 = \{ z \in \mathbb{C} \mid |z - 3 - 2i|^2 = 8 \} \), \( S_2 = \{ z \in \mathbb{C} \mid \operatorname{Re}(z) \ge 5 \} \) and \( S_3 = \{ z \in \mathbb{C} \mid |z - \overline{z}| \ge 8 \} \). Then the number of elements in \( S_1 \cap S_2 \cap S_3 \) is equal to:
