(1,1) -> {(1,1) (2,1) (3,1) }
(1,2) -> {(1,1) (1,2) (1,3) }
(1,3) -> {(1,3) (2,3) (3,3) }
(2,1) -> {(3,1) (3,2) (3,3) }
(2,3) -> {(3,1) (3,2) (3,3) }
(3,1) -> {(1,3) (2,3) (3,3) }
(3,2) -> {(1,1) (1,2) (1,3) }
(3,3) -> {(1,1) (2,1) (3,1) }