Let $$P = \{z \in \mathbb{C} : |z + 2 - 3i| \leq 1\}$$ and $$Q = \{z \in \mathbb{C} : z(1+i) + \bar{z}(1-i) \leq -8\}$$. Let in $$P \cap Q$$, $$|z - 3 + 2i|$$ be maximum and minimum at $$z_1$$ and $$z_2$$ respectively. If $$|z_1|^2 + 2|z_2|^2 = \alpha + \beta\sqrt{2}$$, where $$\alpha, \beta$$ are integers, then $$\alpha + \beta$$ equals: