solutions = (
(0, 2, 3, 7, 13, 15, 4, 11),
(0, 2, 3, 8, 12, 15, 4, 11),
(0, 2, 3, 12, 13, 15, 4, 11),
(0, 2, 7, 8, 12, 15, 4, 11),
(0, 2, 7, 12, 13, 15, 4, 11),
(0, 2, 8, 10, 7, 9, 11, 12),
(0, 2, 8, 10, 7, 12, 11, 15),
(0, 2, 8, 12, 11, 15, 9, 13),
(0, 2, 8, 15, 7, 12, 9, 11),
(0, 3, 4, 7, 12, 15, 8, 11),
(0, 3, 4, 8, 9, 14, 7, 12),
(0, 3, 4, 8, 12, 15, 7, 11),
(0, 3, 4, 11, 12, 15, 7, 8),
(0, 3, 4, 15, 9, 14, 7, 11),
(0, 3, 4, 15, 9, 14, 8, 11),
(0, 3, 4, 15, 12, 14, 7, 8),
(0, 3, 7, 8, 12, 15, 4, 11),
(0, 3, 7, 11, 10, 13, 4, 15),
(0, 3, 7, 11, 12, 15, 4, 8),
(0, 3, 7, 12, 10, 13, 4, 8),
(0, 3, 7, 12, 10, 13, 8, 11),
(0, 3, 7, 12, 13, 15, 4, 11),
(0, 3, 8, 11, 9, 14, 4, 7),
(0, 3, 8, 11, 9, 14, 7, 12),
(0, 3, 8, 11, 10, 13, 4, 7),
(0, 3, 8, 11, 10, 13, 4, 15),
(0, 3, 8, 11, 12, 15, 4, 7),
(0, 3, 8, 12, 9, 14, 4, 7),
(0, 3, 8, 12, 13, 15, 2, 11),
(0, 3, 11, 15, 10, 13, 4, 7),
(0, 3, 11, 15, 12, 14, 1, 8),
(0, 3, 12, 15, 9, 14, 7, 11),
(0, 3, 12, 15, 9, 14, 8, 11),
(0, 3, 12, 15, 10, 13, 4, 8),
(0, 3, 12, 15, 10, 13, 8, 11),
(0, 7, 3, 8, 12, 13, 4, 11),
(0, 7, 3, 15, 12, 14, 1, 8),
(0, 7, 8, 15, 12, 13, 4, 11),
(0, 8, 2, 3, 14, 15, 6, 7),
(0, 8, 2, 10, 3, 13, 14, 15),
(0, 8, 2, 10, 6, 13, 3, 14),
(0, 8, 2, 12, 3, 15, 1, 14),
(0, 8, 2, 13, 3, 15, 1, 14),
(0, 8, 2, 15, 3, 13, 6, 14),
(0, 8, 3, 12, 7, 15, 1, 14),
(0, 8, 3, 13, 7, 15, 1, 14),
(0, 8, 12, 13, 7, 15, 1, 14),
(0, 12, 1, 2, 3, 15, 13, 14),
(0, 12, 1, 2, 6, 11, 3, 13),
(0, 12, 1, 13, 3, 15, 2, 14),
(0, 12, 1, 14, 3, 15, 2, 13),
(0, 12, 1, 15, 3, 11, 2, 13),
(0, 12, 1, 15, 6, 11, 2, 14),
(0, 12, 1, 15, 6, 11, 13, 14),
(0, 12, 2, 3, 6, 11, 1, 13),
(0, 12, 2, 3, 7, 15, 8, 14),
(0, 12, 2, 13, 3, 15, 1, 14),
(0, 12, 2, 14, 3, 15, 1, 13),
(0, 12, 2, 14, 6, 11, 1, 13),
(0, 12, 2, 14, 6, 11, 3, 13),
(0, 12, 2, 14, 7, 10, 1, 13),
(0, 12, 2, 14, 7, 10, 1, 15),
(0, 12, 3, 13, 7, 10, 1, 2),
(0, 12, 3, 13, 7, 10, 2, 14),
(0, 12, 3, 13, 7, 15, 1, 14),
(0, 12, 3, 15, 6, 11, 2, 14),
(0, 12, 3, 15, 6, 11, 13, 14),
(0, 12, 3, 15, 7, 10, 1, 2),
(0, 12, 3, 15, 7, 10, 2, 14),
(0, 12, 13, 14, 3, 15, 1, 2),
(0, 12, 13, 14, 7, 10, 1, 15),
(0, 12, 14, 15, 3, 11, 2, 4),
(0, 12, 14, 15, 7, 10, 1, 13),
(0, 13, 2, 12, 3, 7, 1, 14),
(0, 13, 2, 15, 3, 7, 1, 14),
(0, 13, 12, 15, 3, 11, 2, 4),
(0, 15, 2, 7, 5, 10, 3, 12),
(0, 15, 2, 8, 5, 10, 3, 12),
(0, 15, 2, 13, 5, 10, 3, 12),
(0, 15, 7, 8, 5, 10, 3, 12),
(0, 15, 7, 13, 5, 10, 3, 12),
(0, 15, 8, 13, 5, 10, 3, 12),
(1, 3, 0, 4, 12, 14, 7, 8),
(1, 3, 0, 11, 12, 15, 7, 8),
(1, 3, 0, 15, 12, 14, 7, 8),
(1, 3, 4, 11, 12, 15, 7, 8),
(1, 3, 4, 15, 12, 14, 7, 8),
(1, 3, 9, 11, 4, 10, 8, 15),
(1, 3, 9, 11, 4, 15, 8, 12),
(1, 3, 11, 12, 4, 15, 8, 10),
(1, 3, 11, 15, 8, 12, 10, 14),
(1, 7, 3, 4, 12, 14, 0, 8),
(1, 7, 3, 4, 12, 14, 8, 15),
(1, 7, 3, 11, 12, 14, 0, 8),
(1, 7, 3, 11, 12, 14, 8, 15),
(1, 7, 4, 11, 12, 14, 0, 8),
(1, 7, 4, 11, 12, 14, 8, 15),
(1, 8, 0, 2, 7, 15, 3, 14),
(1, 8, 0, 2, 7, 15, 12, 14),
(1, 8, 0, 13, 7, 15, 3, 14),
(1, 8, 0, 13, 7, 15, 12, 14),
(1, 8, 2, 13, 7, 15, 3, 14),
(1, 8, 2, 13, 7, 15, 12, 14),
(1, 12, 0, 3, 7, 15, 8, 14),
(1, 12, 0, 14, 11, 15, 2, 13),
(1, 12, 3, 14, 11, 15, 2, 13),
(1, 14, 3, 12, 4, 11, 2, 13),
(2, 4, 0, 7, 13, 15, 3, 11),
(2, 4, 0, 7, 13, 15, 11, 12),
(2, 4, 0, 8, 13, 15, 3, 11),
(2, 4, 0, 8, 13, 15, 11, 12),
(2, 4, 7, 8, 13, 15, 3, 11),
(2, 4, 7, 8, 13, 15, 11, 12),
(2, 11, 1, 3, 4, 12, 0, 13),
(2, 11, 1, 3, 4, 12, 13, 15),
(2, 11, 1, 14, 4, 12, 0, 13),
(2, 11, 1, 14, 4, 12, 13, 15),
(2, 11, 3, 14, 4, 12, 0, 13),
(2, 11, 3, 14, 4, 12, 13, 15),
(2, 13, 0, 15, 7, 8, 1, 14),
(2, 15, 0, 3, 4, 12, 11, 13),
(2, 15, 0, 13, 8, 12, 1, 14),
(2, 15, 3, 13, 8, 12, 1, 14),
(3, 4, 0, 11, 14, 15, 7, 8),
(3, 4, 0, 12, 13, 15, 2, 11),
(3, 4, 11, 12, 14, 15, 7, 8),
(3, 11, 0, 1, 12, 13, 4, 5),
(3, 11, 0, 14, 4, 12, 2, 13),
(3, 11, 0, 15, 4, 12, 2, 13),
(3, 11, 1, 9, 0, 14, 12, 13),
(3, 11, 1, 9, 5, 14, 0, 13),
(3, 11, 1, 12, 0, 14, 5, 13),
(3, 11, 1, 14, 0, 12, 2, 13),
(3, 11, 1, 15, 0, 12, 2, 13),
(3, 11, 14, 15, 4, 12, 2, 13),
(3, 12, 1, 4, 6, 9, 0, 15),
(3, 12, 1, 11, 6, 9, 0, 15),
(3, 12, 1, 14, 6, 9, 0, 15),
(3, 12, 4, 11, 6, 9, 0, 15),
(3, 12, 4, 14, 6, 9, 0, 15),
(3, 12, 11, 14, 6, 9, 0, 15),
(3, 14, 1, 12, 0, 4, 2, 13),
(3, 14, 1, 15, 0, 4, 2, 13),
(3, 14, 12, 15, 0, 8, 1, 7),
(3, 15, 0, 1, 4, 12, 11, 13),
(3, 15, 0, 1, 5, 8, 2, 14),
(3, 15, 0, 12, 4, 9, 1, 2),
(3, 15, 0, 12, 4, 9, 1, 13),
(3, 15, 0, 12, 5, 8, 1, 13),
(3, 15, 0, 12, 5, 8, 13, 14),
(3, 15, 0, 14, 4, 9, 1, 2),
(3, 15, 0, 14, 4, 9, 1, 13),
(3, 15, 0, 14, 4, 12, 2, 13),
(3, 15, 1, 2, 0, 12, 13, 14),
(3, 15, 1, 2, 5, 8, 0, 14),
(3, 15, 1, 13, 0, 12, 2, 14),
(3, 15, 1, 13, 4, 9, 2, 12),
(3, 15, 1, 13, 4, 9, 2, 14),
(3, 15, 1, 13, 5, 8, 0, 14),
(3, 15, 1, 13, 5, 8, 2, 14),
(3, 15, 1, 14, 0, 12, 2, 13),
(3, 15, 2, 12, 0, 8, 1, 14),
(3, 15, 2, 12, 5, 8, 1, 13),
(3, 15, 2, 12, 5, 8, 13, 14),
(3, 15, 2, 13, 0, 12, 1, 14),
(3, 15, 2, 14, 0, 12, 1, 13),
(3, 15, 12, 13, 0, 8, 1, 7),
(3, 15, 12, 13, 4, 9, 2, 14),
(3, 15, 13, 14, 0, 12, 1, 2),
(3, 15, 13, 14, 4, 9, 2, 12),
(4, 11, 3, 12, 1, 14, 7, 8),
(4, 12, 0, 1, 3, 11, 2, 13),
(4, 12, 0, 14, 3, 15, 2, 13),
(4, 12, 0, 15, 3, 11, 2, 13),
(4, 12, 1, 14, 3, 15, 2, 13),
(4, 12, 1, 15, 3, 11, 2, 13),
(4, 12, 3, 14, 1, 15, 2, 10),
(4, 12, 6, 14, 1, 10, 2, 15),
(4, 12, 6, 14, 1, 15, 2, 3),
(4, 12, 14, 15, 2, 3, 10, 11),
(4, 13, 1, 12, 3, 11, 0, 2),
(4, 13, 1, 12, 3, 11, 2, 15),
(4, 13, 1, 14, 3, 11, 0, 2),
(4, 13, 1, 14, 3, 11, 2, 15),
(4, 13, 12, 14, 3, 11, 0, 2),
(4, 13, 12, 14, 3, 11, 2, 15),
(7, 8, 0, 15, 2, 13, 4, 11),
(7, 14, 2, 13, 0, 8, 1, 3),
(7, 14, 2, 13, 0, 8, 1, 12),
(7, 14, 2, 15, 0, 8, 1, 3),
(7, 14, 2, 15, 0, 8, 1, 12),
(7, 14, 13, 15, 0, 8, 1, 3),
(7, 14, 13, 15, 0, 8, 1, 12),
(7, 15, 0, 13, 2, 12, 1, 9),
(7, 15, 2, 3, 0, 8, 1, 14),
(7, 15, 2, 12, 0, 8, 1, 14),
(7, 15, 2, 13, 0, 12, 1, 14),
(7, 15, 3, 12, 0, 8, 1, 14),
(7, 15, 3, 13, 0, 12, 1, 14),
(7, 15, 5, 13, 2, 9, 1, 12),
(7, 15, 5, 13, 2, 12, 0, 1),
(7, 15, 12, 13, 0, 1, 8, 9),
(8, 14, 4, 11, 1, 3, 0, 7),
(8, 14, 4, 11, 1, 3, 7, 15),
(8, 14, 4, 12, 1, 3, 0, 7),
(8, 14, 4, 12, 1, 3, 7, 15),
(8, 14, 11, 12, 1, 3, 0, 7),
(8, 14, 11, 12, 1, 3, 7, 15),
(8, 15, 0, 7, 2, 3, 4, 11),
(8, 15, 0, 12, 1, 3, 7, 14),
(8, 15, 7, 12, 2, 3, 4, 11),
(11, 12, 3, 4, 0, 1, 7, 8),
(11, 12, 3, 15, 0, 2, 4, 13),
(11, 12, 4, 15, 0, 1, 7, 8),
(11, 13, 7, 8, 0, 2, 3, 4),
(11, 13, 7, 8, 0, 2, 4, 12),
(11, 13, 7, 15, 0, 2, 3, 4),
(11, 13, 7, 15, 0, 2, 4, 12),
(11, 13, 8, 15, 0, 2, 3, 4),
(11, 13, 8, 15, 0, 2, 4, 12),
(12, 14, 0, 4, 3, 7, 1, 5),
(12, 14, 0, 11, 1, 3, 7, 8),
(12, 14, 0, 15, 1, 3, 7, 8),
(12, 14, 3, 4, 0, 11, 5, 7),
(12, 14, 4, 6, 0, 11, 3, 7),
(12, 14, 4, 6, 5, 11, 0, 7),
(12, 14, 4, 11, 0, 3, 7, 8),
(12, 14, 4, 15, 0, 3, 7, 8),
(12, 14, 11, 15, 1, 3, 7, 8),
(12, 15, 0, 3, 1, 6, 4, 7),
(12, 15, 0, 3, 1, 6, 4, 8),
(12, 15, 0, 3, 2, 5, 4, 7),
(12, 15, 0, 3, 2, 5, 7, 11),
(12, 15, 0, 4, 1, 3, 7, 14),
(12, 15, 0, 4, 2, 5, 8, 11),
(12, 15, 0, 11, 1, 3, 7, 8),
(12, 15, 0, 11, 1, 6, 4, 7),
(12, 15, 0, 11, 1, 6, 4, 8),
(12, 15, 3, 7, 0, 2, 4, 13),
(12, 15, 3, 7, 1, 6, 8, 11),
(12, 15, 3, 8, 0, 2, 4, 11),
(12, 15, 3, 8, 2, 5, 4, 7),
(12, 15, 3, 8, 2, 5, 7, 11),
(12, 15, 4, 7, 0, 3, 8, 11),
(12, 15, 4, 7, 1, 6, 3, 8),
(12, 15, 4, 7, 1, 6, 8, 11),
(12, 15, 4, 7, 2, 5, 0, 11),
(12, 15, 4, 7, 2, 5, 8, 11),
(12, 15, 4, 8, 0, 3, 7, 11),
(12, 15, 4, 8, 2, 5, 0, 11),
(12, 15, 4, 11, 0, 3, 7, 8),
(12, 15, 7, 8, 0, 3, 4, 11),
(12, 15, 7, 11, 0, 3, 4, 8),
(12, 15, 7, 11, 1, 6, 3, 8),
(12, 15, 8, 11, 0, 3, 4, 7),
(13, 15, 0, 7, 3, 8, 4, 6),
(13, 15, 3, 7, 0, 4, 2, 6),
(13, 15, 3, 8, 0, 2, 4, 11),
(13, 15, 3, 12, 0, 2, 4, 11),
(13, 15, 5, 7, 3, 8, 0, 4),
(13, 15, 5, 7, 6, 8, 3, 4),
(13, 15, 7, 8, 0, 3, 4, 11),
(13, 15, 7, 12, 0, 3, 4, 11),
(13, 15, 8, 12, 0, 2, 4, 11),
)