level=0 a=1 b=1
level=1 a=0.5,0.5 b=1
level=1 a=1 b=0.5,0.5
level=2 a=0.75,0.25 b=1
level=2 a=1 b=0.75,0.25
level=3 a=0.5,0.5 b=0.5,0.5
level=4 a=0.75,0.25 b=0.5,0.5
level=4 a=0.5,0.5 b=0.75,0.25
level=4 a=0.75,0.25 b=0.75,0.25