neighborDict.py

neighbors = {(0, 0): {(3, 0), (8, 0), (0, 7), (2, 1), (0, 3), (4, 0), (1, 2), (5, 0), (0, 4), (2, 2), (1, 1), (6, 0), (0, 5), (1, 0), (0, 8), (0, 1), (7, 0), (0, 6), (2, 0), (0, 2)}, (0, 1): {(0, 7), (2, 1), (5, 1), (0, 3), (1, 2), (8, 1), (0, 4), (2, 2), (4, 1), (1, 1), (0, 0), (7, 1), (0, 5), (1, 0), (0, 8), (6, 1), (3, 1), (0, 6), (2, 0), (0, 2)}, (0, 2): {(0, 7), (2, 1), (6, 2), (0, 3), (7, 2), (1, 2), (2, 2), (0, 4), (1, 1), (3, 2), (0, 0), (8, 2), (0, 5), (4, 2), (1, 0), (0, 8), (0, 1), (0, 6), (2, 0), (5, 2)}, (0, 3): {(7, 3), (1, 3), (0, 2), (0, 7), (2, 5), (3, 3), (6, 3), (1, 5), (0, 4), (0, 0), (1, 4), (0, 5), (2, 3), (0, 8), (5, 3), (0, 1), (8, 3), (0, 6), (4, 3), (2, 4)}, (0, 4): {(1, 3), (0, 2), (0, 7), (0, 3), (2, 5), (4, 4), (1, 5), (6, 4), (5, 4), (0, 0), (1, 4), (0, 5), (2, 3), (0, 8), (0, 1), (7, 4), (0, 6), (3, 4), (2, 4), (8, 4)}, (0, 5): {(1, 3), (0, 7), (2, 5), (0, 3), (8, 5), (2, 4), (5, 5), (1, 5), (0, 4), (0, 0), (4, 5), (1, 4), (7, 5), (2, 3), (0, 8), (6, 5), (3, 5), (0, 1), (0, 6), (0, 2)}, (0, 6): {(6, 6), (5, 6), (2, 8), (0, 7), (1, 6), (0, 3), (7, 6), (3, 6), (0, 4), (8, 6), (0, 0), (2, 6), (0, 5), (0, 8), (0, 1), (2, 7), (4, 6), (1, 8), (1, 7), (0, 2)}, (0, 7): {(4, 7), (2, 8), (7, 7), (1, 6), (3, 7), (0, 3), (6, 7), (0, 4), (0, 0), (2, 6), (0, 5), (8, 7), (0, 8), (0, 1), (2, 7), (5, 7), (0, 6), (1, 8), (1, 7), (0, 2)}, (0, 8): {(4, 8), (2, 8), (0, 7), (1, 6), (0, 3), (5, 8), (0, 4), (0, 0), (2, 6), (0, 5), (0, 1), (2, 7), (6, 8), (3, 8), (0, 6), (1, 8), (8, 8), (1, 7), (7, 8), (0, 2)}, (1, 0): {(1, 3), (3, 0), (8, 0), (2, 1), (1, 6), (4, 0), (1, 2), (1, 5), (5, 0), (2, 2), (1, 1), (0, 0), (6, 0), (1, 4), (0, 1), (7, 0), (2, 0), (1, 8), (1, 7), (0, 2)}, (1, 1): {(1, 3), (2, 1), (1, 6), (5, 1), (1, 2), (8, 1), (1, 5), (2, 2), (4, 1), (0, 0), (7, 1), (1, 4), (1, 0), (0, 1), (6, 1), (3, 1), (2, 0), (1, 8), (1, 7), (0, 2)}, (1, 2): {(1, 3), (2, 1), (6, 2), (1, 6), (7, 2), (1, 5), (2, 2), (1, 1), (3, 2), (0, 0), (8, 2), (1, 4), (4, 2), (1, 0), (0, 1), (2, 0), (1, 8), (1, 7), (5, 2), (0, 2)}, (1, 3): {(7, 3), (1, 6), (0, 3), (2, 5), (1, 2), (3, 3), (6, 3), (1, 5), (0, 4), (1, 1), (1, 4), (2, 3), (0, 5), (1, 0), (5, 3), (8, 3), (1, 8), (4, 3), (1, 7), (2, 4)}, (1, 4): {(1, 3), (1, 6), (0, 3), (2, 5), (1, 2), (4, 4), (1, 5), (0, 4), (1, 1), (6, 4), (5, 4), (0, 5), (2, 3), (1, 0), (7, 4), (1, 8), (1, 7), (3, 4), (2, 4), (8, 4)}, (1, 5): {(1, 3), (1, 6), (0, 3), (2, 5), (8, 5), (1, 2), (5, 5), (0, 4), (1, 1), (4, 5), (1, 4), (7, 5), (0, 5), (2, 3), (1, 0), (6, 5), (3, 5), (1, 8), (1, 7), (2, 4)}, (1, 6): {(1, 3), (6, 6), (5, 6), (2, 8), (0, 7), (1, 2), (7, 6), (1, 5), (3, 6), (8, 6), (1, 1), (2, 6), (1, 4), (1, 0), (0, 8), (2, 7), (4, 6), (0, 6), (1, 8), (1, 7)}, (1, 7): {(4, 7), (1, 3), (2, 8), (7, 7), (0, 7), (1, 6), (3, 7), (1, 2), (6, 7), (1, 5), (1, 1), (2, 6), (1, 4), (8, 7), (1, 0), (0, 8), (2, 7), (5, 7), (0, 6), (1, 8)}, (1, 8): {(1, 3), (4, 8), (2, 8), (0, 7), (1, 6), (5, 8), (1, 2), (1, 5), (1, 1), (2, 6), (1, 4), (1, 0), (0, 8), (2, 7), (6, 8), (3, 8), (0, 6), (8, 8), (1, 7), (7, 8)}, (2, 0): {(3, 0), (2, 8), (8, 0), (2, 1), (2, 5), (2, 4), (4, 0), (1, 2), (5, 0), (2, 2), (1, 1), (2, 6), (0, 0), (6, 0), (2, 3), (1, 0), (2, 7), (0, 1), (7, 0), (0, 2)}, (2, 1): {(2, 8), (5, 1), (2, 5), (2, 4), (1, 2), (8, 1), (2, 2), (4, 1), (1, 1), (2, 6), (0, 0), (7, 1), (2, 3), (1, 0), (2, 7), (0, 1), (6, 1), (3, 1), (2, 0), (0, 2)}, (2, 2): {(2, 8), (2, 1), (6, 2), (2, 5), (2, 4), (7, 2), (1, 2), (1, 1), (3, 2), (2, 6), (0, 0), (8, 2), (2, 3), (4, 2), (1, 0), (2, 7), (0, 1), (2, 0), (5, 2), (0, 2)}, (2, 3): {(7, 3), (1, 3), (2, 8), (2, 1), (2, 5), (0, 3), (3, 3), (6, 3), (1, 5), (0, 4), (2, 2), (2, 6), (1, 4), (0, 5), (5, 3), (2, 7), (8, 3), (2, 0), (4, 3), (2, 4)}, (2, 4): {(1, 3), (2, 8), (2, 1), (0, 3), (2, 5), (4, 4), (1, 5), (0, 4), (2, 2), (6, 4), (5, 4), (2, 6), (1, 4), (2, 3), (0, 5), (2, 7), (7, 4), (2, 0), (3, 4), (8, 4)}, (2, 5): {(1, 3), (2, 8), (2, 1), (0, 3), (8, 5), (5, 5), (1, 5), (0, 4), (2, 2), (2, 6), (4, 5), (1, 4), (7, 5), (2, 3), (0, 5), (6, 5), (3, 5), (2, 7), (2, 0), (2, 4)}, (2, 6): {(6, 6), (5, 6), (2, 8), (2, 1), (0, 7), (1, 6), (2, 5), (7, 6), (3, 6), (2, 2), (8, 6), (2, 3), (0, 8), (2, 7), (4, 6), (2, 0), (0, 6), (1, 8), (1, 7), (2, 4)}, (2, 7): {(4, 7), (2, 8), (7, 7), (2, 1), (0, 7), (1, 6), (3, 7), (2, 5), (6, 7), (2, 2), (2, 6), (2, 3), (8, 7), (0, 8), (5, 7), (2, 0), (0, 6), (1, 8), (1, 7), (2, 4)}, (2, 8): {(4, 8), (2, 1), (0, 7), (1, 6), (2, 5), (5, 8), (2, 2), (2, 6), (2, 3), (0, 8), (2, 7), (6, 8), (3, 8), (2, 0), (1, 8), (8, 8), (0, 6), (1, 7), (7, 8), (2, 4)}, (3, 0): {(8, 0), (5, 1), (3, 7), (4, 0), (3, 3), (3, 6), (5, 0), (4, 1), (3, 2), (0, 0), (5, 2), (6, 0), (4, 2), (1, 0), (3, 5), (7, 0), (3, 1), (3, 8), (2, 0), (3, 4)}, (3, 1): {(3, 0), (2, 1), (5, 1), (3, 7), (4, 0), (3, 3), (8, 1), (3, 6), (5, 0), (4, 1), (1, 1), (3, 2), (7, 1), (5, 2), (4, 2), (3, 5), (0, 1), (6, 1), (3, 8), (3, 4)}, (3, 2): {(3, 0), (6, 2), (3, 7), (5, 1), (7, 2), (4, 0), (1, 2), (3, 3), (3, 6), (2, 2), (5, 0), (3, 4), (4, 1), (8, 2), (4, 2), (3, 5), (3, 1), (3, 8), (5, 2), (0, 2)}, (3, 3): {(7, 3), (1, 3), (3, 0), (3, 7), (0, 3), (5, 5), (4, 4), (6, 3), (3, 6), (3, 2), (5, 4), (4, 5), (2, 3), (5, 3), (3, 5), (8, 3), (3, 1), (3, 8), (4, 3), (3, 4)}, (3, 4): {(3, 0), (3, 7), (3, 3), (5, 5), (4, 4), (3, 6), (0, 4), (6, 4), (3, 2), (5, 4), (4, 5), (1, 4), (5, 3), (3, 5), (3, 1), (3, 8), (7, 4), (4, 3), (2, 4), (8, 4)}, (3, 5): {(3, 0), (3, 7), (2, 5), (8, 5), (3, 3), (5, 5), (4, 4), (1, 5), (3, 6), (3, 2), (5, 4), (4, 5), (7, 5), (0, 5), (6, 5), (5, 3), (3, 1), (3, 8), (4, 3), (3, 4)}, (3, 6): {(4, 7), (6, 6), (3, 0), (5, 6), (4, 8), (1, 6), (3, 7), (5, 8), (3, 3), (7, 6), (8, 6), (3, 2), (2, 6), (3, 5), (4, 6), (3, 1), (5, 7), (3, 8), (0, 6), (3, 4)}, (3, 7): {(4, 7), (4, 8), (3, 0), (5, 6), (7, 7), (0, 7), (5, 8), (6, 7), (3, 3), (3, 6), (3, 2), (8, 7), (3, 5), (2, 7), (4, 6), (3, 1), (5, 7), (3, 8), (1, 7), (3, 4)}, (3, 8): {(4, 7), (4, 8), (3, 0), (2, 8), (5, 6), (3, 7), (5, 8), (3, 3), (3, 6), (3, 4), (3, 2), (0, 8), (3, 5), (6, 8), (4, 6), (3, 1), (5, 7), (1, 8), (8, 8), (7, 8)}, (4, 0): {(4, 7), (4, 8), (3, 0), (8, 0), (5, 1), (4, 4), (5, 0), (4, 1), (3, 2), (0, 0), (4, 5), (6, 0), (4, 2), (1, 0), (7, 0), (4, 6), (3, 1), (2, 0), (4, 3), (5, 2)}, (4, 1): {(4, 7), (4, 8), (3, 0), (2, 1), (5, 1), (4, 0), (8, 1), (4, 4), (5, 0), (1, 1), (3, 2), (7, 1), (4, 5), (4, 2), (0, 1), (4, 6), (6, 1), (3, 1), (4, 3), (5, 2)}, (4, 2): {(4, 7), (4, 8), (3, 0), (6, 2), (5, 1), (7, 2), (4, 0), (1, 2), (4, 4), (5, 0), (2, 2), (4, 1), (3, 2), (8, 2), (4, 5), (4, 6), (3, 1), (4, 3), (5, 2), (0, 2)}, (4, 3): {(7, 3), (4, 7), (1, 3), (4, 8), (0, 3), (4, 0), (3, 3), (5, 5), (4, 4), (6, 3), (4, 1), (5, 4), (4, 5), (2, 3), (4, 2), (3, 5), (5, 3), (8, 3), (4, 6), (3, 4)}, (4, 4): {(4, 7), (4, 8), (4, 0), (3, 3), (5, 5), (0, 4), (4, 1), (6, 4), (5, 4), (4, 5), (1, 4), (4, 2), (3, 5), (5, 3), (4, 6), (7, 4), (4, 3), (3, 4), (2, 4), (8, 4)}, (4, 5): {(4, 7), (4, 8), (2, 5), (8, 5), (4, 0), (5, 5), (3, 3), (4, 4), (1, 5), (4, 1), (5, 4), (7, 5), (0, 5), (4, 2), (6, 5), (3, 5), (5, 3), (4, 6), (4, 3), (3, 4)}, (4, 6): {(4, 7), (4, 8), (5, 6), (6, 6), (1, 6), (3, 7), (5, 8), (4, 0), (7, 6), (4, 4), (3, 6), (8, 6), (4, 1), (2, 6), (4, 5), (4, 2), (5, 7), (3, 8), (0, 6), (4, 3)}, (4, 7): {(4, 8), (5, 6), (7, 7), (0, 7), (3, 7), (5, 8), (4, 0), (6, 7), (4, 4), (3, 6), (4, 1), (4, 5), (8, 7), (4, 2), (2, 7), (4, 6), (5, 7), (3, 8), (4, 3), (1, 7)}, (4, 8): {(4, 7), (5, 6), (2, 8), (3, 7), (5, 8), (4, 0), (4, 4), (3, 6), (4, 1), (4, 5), (4, 2), (0, 8), (4, 6), (6, 8), (5, 7), (3, 8), (1, 8), (8, 8), (4, 3), (7, 8)}, (5, 0): {(5, 6), (3, 0), (8, 0), (5, 1), (5, 8), (4, 0), (5, 5), (4, 1), (5, 4), (0, 0), (3, 2), (6, 0), (4, 2), (1, 0), (5, 3), (7, 0), (5, 7), (3, 1), (2, 0), (5, 2)}, (5, 1): {(5, 6), (3, 0), (2, 1), (5, 8), (4, 0), (5, 5), (8, 1), (5, 0), (4, 1), (1, 1), (5, 4), (3, 2), (7, 1), (4, 2), (5, 3), (0, 1), (6, 1), (5, 7), (3, 1), (5, 2)}, (5, 2): {(5, 6), (3, 0), (6, 2), (5, 1), (7, 2), (4, 0), (1, 2), (5, 8), (5, 5), (5, 0), (2, 2), (4, 1), (5, 4), (3, 2), (8, 2), (4, 2), (5, 3), (5, 7), (3, 1), (0, 2)}, (5, 3): {(7, 3), (1, 3), (5, 6), (5, 1), (0, 3), (5, 8), (5, 5), (3, 3), (4, 4), (6, 3), (5, 0), (5, 4), (4, 5), (5, 2), (2, 3), (3, 5), (8, 3), (5, 7), (4, 3), (3, 4)}, (5, 4): {(5, 6), (5, 1), (5, 8), (5, 5), (3, 3), (4, 4), (5, 0), (0, 4), (6, 4), (4, 5), (5, 2), (1, 4), (3, 5), (5, 3), (5, 7), (7, 4), (4, 3), (3, 4), (2, 4), (8, 4)}, (5, 5): {(5, 6), (5, 1), (2, 5), (8, 5), (5, 8), (3, 3), (4, 4), (1, 5), (5, 0), (5, 4), (4, 5), (5, 2), (7, 5), (0, 5), (6, 5), (3, 5), (5, 3), (5, 7), (4, 3), (3, 4)}, (5, 6): {(4, 7), (6, 6), (4, 8), (1, 6), (3, 7), (5, 1), (5, 8), (5, 5), (7, 6), (5, 0), (3, 6), (8, 6), (5, 4), (2, 6), (5, 3), (4, 6), (5, 7), (3, 8), (0, 6), (5, 2)}, (5, 7): {(4, 7), (4, 8), (5, 6), (7, 7), (0, 7), (3, 7), (5, 1), (5, 8), (6, 7), (5, 5), (5, 0), (3, 6), (5, 4), (8, 7), (5, 3), (2, 7), (4, 6), (3, 8), (1, 7), (5, 2)}, (5, 8): {(4, 7), (4, 8), (5, 6), (2, 8), (3, 7), (5, 1), (5, 5), (5, 0), (3, 6), (5, 4), (5, 2), (0, 8), (5, 3), (6, 8), (4, 6), (5, 7), (3, 8), (1, 8), (8, 8), (7, 8)}, (6, 0): {(6, 6), (3, 0), (8, 0), (6, 2), (7, 2), (4, 0), (6, 7), (8, 1), (6, 3), (5, 0), (6, 4), (0, 0), (8, 2), (7, 1), (1, 0), (6, 5), (7, 0), (6, 8), (6, 1), (2, 0)}, (6, 1): {(6, 6), (8, 0), (2, 1), (6, 2), (5, 1), (7, 2), (6, 7), (8, 1), (6, 3), (4, 1), (1, 1), (6, 4), (8, 2), (7, 1), (6, 0), (6, 5), (0, 1), (7, 0), (6, 8), (3, 1)}, (6, 2): {(6, 6), (8, 0), (7, 2), (1, 2), (6, 7), (8, 1), (6, 3), (2, 2), (6, 4), (3, 2), (8, 2), (7, 1), (6, 0), (4, 2), (6, 5), (7, 0), (6, 8), (6, 1), (5, 2), (0, 2)}, (6, 3): {(7, 3), (1, 3), (6, 6), (6, 2), (0, 3), (8, 5), (6, 7), (3, 3), (6, 4), (6, 0), (7, 5), (2, 3), (6, 5), (5, 3), (8, 3), (6, 8), (6, 1), (7, 4), (4, 3), (8, 4)}, (6, 4): {(7, 3), (6, 6), (6, 2), (8, 5), (6, 7), (4, 4), (6, 3), (0, 4), (5, 4), (6, 0), (1, 4), (7, 5), (6, 5), (8, 3), (6, 8), (6, 1), (7, 4), (3, 4), (2, 4), (8, 4)}, (6, 5): {(7, 3), (6, 6), (6, 2), (2, 5), (8, 5), (6, 7), (5, 5), (6, 3), (1, 5), (6, 4), (4, 5), (6, 0), (7, 5), (0, 5), (3, 5), (8, 3), (6, 8), (6, 1), (7, 4), (8, 4)}, (6, 6): {(5, 6), (7, 7), (6, 2), (1, 6), (6, 7), (7, 6), (6, 3), (3, 6), (8, 6), (6, 4), (2, 6), (6, 0), (8, 7), (6, 5), (6, 8), (4, 6), (6, 1), (0, 6), (8, 8), (7, 8)}, (6, 7): {(4, 7), (6, 6), (7, 7), (0, 7), (6, 2), (3, 7), (7, 6), (6, 3), (8, 6), (6, 4), (6, 0), (8, 7), (6, 5), (2, 7), (6, 8), (6, 1), (5, 7), (8, 8), (1, 7), (7, 8)}, (6, 8): {(6, 6), (4, 8), (2, 8), (7, 7), (6, 2), (5, 8), (6, 7), (7, 6), (6, 3), (8, 6), (6, 4), (6, 0), (8, 7), (0, 8), (6, 5), (6, 1), (3, 8), (1, 8), (8, 8), (7, 8)}, (7, 0): {(7, 3), (3, 0), (8, 0), (7, 7), (6, 2), (7, 2), (4, 0), (8, 1), (7, 6), (5, 0), (0, 0), (8, 2), (7, 1), (6, 0), (7, 5), (1, 0), (6, 1), (7, 4), (2, 0), (7, 8)}, (7, 1): {(7, 3), (8, 0), (7, 7), (2, 1), (6, 2), (5, 1), (7, 2), (8, 1), (7, 6), (4, 1), (1, 1), (8, 2), (6, 0), (7, 5), (0, 1), (7, 0), (6, 1), (3, 1), (7, 4), (7, 8)}, (7, 2): {(7, 3), (8, 0), (7, 7), (6, 2), (1, 2), (8, 1), (7, 6), (2, 2), (3, 2), (8, 2), (7, 1), (6, 0), (7, 5), (4, 2), (7, 8), (7, 0), (6, 1), (7, 4), (5, 2), (0, 2)}, (7, 3): {(1, 3), (7, 7), (0, 3), (8, 5), (7, 2), (3, 3), (7, 6), (6, 3), (6, 4), (7, 1), (7, 5), (2, 3), (6, 5), (5, 3), (8, 3), (7, 0), (7, 4), (4, 3), (7, 8), (8, 4)}, (7, 4): {(7, 3), (7, 7), (8, 5), (7, 2), (7, 6), (4, 4), (6, 3), (0, 4), (6, 4), (5, 4), (7, 1), (1, 4), (7, 5), (6, 5), (7, 8), (8, 3), (7, 0), (3, 4), (2, 4), (8, 4)}, (7, 5): {(7, 3), (7, 7), (2, 5), (8, 5), (7, 2), (5, 5), (7, 6), (6, 3), (1, 5), (6, 4), (7, 1), (4, 5), (0, 5), (6, 5), (3, 5), (8, 3), (7, 0), (7, 4), (7, 8), (8, 4)}, (7, 6): {(7, 3), (6, 6), (5, 6), (7, 7), (1, 6), (7, 2), (6, 7), (3, 6), (8, 6), (2, 6), (7, 1), (7, 5), (8, 7), (7, 0), (4, 6), (6, 8), (7, 4), (0, 6), (8, 8), (7, 8)}, (7, 7): {(7, 3), (4, 7), (6, 6), (0, 7), (3, 7), (7, 2), (6, 7), (7, 6), (8, 6), (7, 1), (7, 5), (8, 7), (2, 7), (7, 0), (6, 8), (5, 7), (7, 4), (8, 8), (1, 7), (7, 8)}, (7, 8): {(7, 3), (4, 8), (6, 6), (2, 8), (7, 7), (5, 8), (7, 2), (6, 7), (7, 6), (8, 6), (7, 1), (7, 5), (8, 7), (0, 8), (7, 0), (6, 8), (7, 4), (3, 8), (1, 8), (8, 8)}, (8, 0): {(3, 0), (6, 2), (8, 5), (7, 2), (4, 0), (8, 1), (5, 0), (8, 6), (0, 0), (8, 2), (7, 1), (6, 0), (8, 7), (1, 0), (8, 3), (7, 0), (6, 1), (2, 0), (8, 8), (8, 4)}, (8, 1): {(8, 0), (2, 1), (6, 2), (5, 1), (8, 5), (7, 2), (8, 6), (4, 1), (1, 1), (8, 2), (7, 1), (6, 0), (8, 7), (0, 1), (8, 3), (7, 0), (6, 1), (3, 1), (8, 8), (8, 4)}, (8, 2): {(8, 0), (6, 2), (8, 5), (7, 2), (1, 2), (8, 1), (2, 2), (8, 6), (3, 2), (7, 1), (6, 0), (8, 7), (4, 2), (8, 3), (7, 0), (6, 1), (8, 8), (5, 2), (0, 2), (8, 4)}, (8, 3): {(7, 3), (1, 3), (8, 0), (0, 3), (8, 5), (3, 3), (8, 1), (6, 3), (8, 6), (6, 4), (8, 2), (7, 5), (2, 3), (8, 7), (6, 5), (5, 3), (7, 4), (8, 8), (4, 3), (8, 4)}, (8, 4): {(7, 3), (8, 0), (8, 5), (8, 1), (4, 4), (6, 3), (0, 4), (8, 6), (6, 4), (5, 4), (8, 2), (1, 4), (7, 5), (8, 7), (6, 5), (8, 3), (7, 4), (8, 8), (3, 4), (2, 4)}, (8, 5): {(7, 3), (8, 0), (2, 5), (5, 5), (8, 1), (6, 3), (1, 5), (8, 6), (6, 4), (8, 2), (4, 5), (7, 5), (0, 5), (8, 7), (6, 5), (3, 5), (8, 3), (7, 4), (8, 8), (8, 4)}, (8, 6): {(6, 6), (5, 6), (8, 0), (7, 7), (1, 6), (8, 5), (6, 7), (8, 1), (7, 6), (3, 6), (2, 6), (8, 2), (8, 7), (8, 3), (4, 6), (6, 8), (0, 6), (8, 8), (7, 8), (8, 4)}, (8, 7): {(4, 7), (6, 6), (8, 0), (7, 7), (0, 7), (3, 7), (8, 5), (6, 7), (8, 1), (7, 6), (8, 6), (8, 2), (2, 7), (8, 3), (6, 8), (5, 7), (8, 8), (1, 7), (7, 8), (8, 4)}, (8, 8): {(4, 8), (6, 6), (2, 8), (8, 0), (7, 7), (8, 5), (5, 8), (6, 7), (8, 1), (7, 6), (8, 6), (8, 2), (8, 7), (0, 8), (8, 3), (6, 8), (3, 8), (1, 8), (7, 8), (8, 4)}}