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