Complex Number Region Intersection

Let P={z∈C:|z+2−3i|≤1} and Q={z∈C:z(1+i)+z(1−i)≤−8}. Let in P∩Q,|z−3+2i| be maximum and minimum at z1 and z2 respectively. If |z1|2+2z|2=α+β√2, where α,β are integers, then α+β equals______