level=0 a=1 b=1 d=1
level=1 a=0.5,0.5 b=1 d=1
level=1 a=1 b=0.5,0.5 d=1
level=1 a=1 b=1 d=0.5,0.5
level=2 a=0.5,0.5 b=0.5,0.5 d=1
level=2 a=0.5,0.5 b=1 d=0.5,0.5
level=2 a=1 b=0.5,0.5 d=0.5,0.5