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 \( \alpha,\beta \) integers, then \( \alpha+\beta \) equals ______.
