level=0 a=1 c=1
level=1 a=0.5,0.5 c=1
level=1 a=1 c=0.5,0.5
level=2 a=0.5,0.5 c=0.5,0.5
level=3 a=0.75,0.25 c=1
level=3 a=1 c=0.75,0.25