Sorted tuples in logical order 1, 2, 1, 1, 3, 1, 2, 2, 2, 1, 1, 1, 4, 1, 3, 2, 3, 3, 3, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 5, 1, 4, 2, 4, 3, 4, 4, 4, 1, 1, 3, 1, 2, 3, 2, 2, 3, 1, 3, 3, 2, 3, 3, 3, 3, 3, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 6, 1, 5, 2, 5, 3, 5, 4, 5, 5, 5, 1, 1, 4, 1, 2, 4, 2, 2, 4, 1, 3, 4, 2, 3, 4, 3, 3, 4, 1, 4, 4, 2, 4, 4, 3, 4, 4, 4, 4, 4, 1, 1, 1, 3, 1, 1, 2, 3, 1, 2, 2, 3, 2, 2, 2, 3, 1, 1, 3, 3, 1, 2, 3, 3, 2, 2, 3, 3, 1, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 7, 1, 6, 2, 6, 3, 6, 4, 6, 5, 6, 6, 6, 1, 1, 5, 1, 2, 5, 2, 2, 5, 1, 3, 5, 2, 3, 5, 3, 3, 5, 1, 4, 5, 2, 4, 5, 3, 4, 5, 4, 4, 5, 1, 5, 5, 2, 5, 5, 3, 5, 5, 4, 5, 5, 5, 5, 5, 1, 1, 1, 4, 1, 1, 2, 4, 1, 2, 2, 4, 2, 2, 2, 4, 1, 1, 3, 4, 1, 2, 3, 4, 2, 2, 3, 4, 1, 3, 3, 4, 2, 3, 3, 4, 3, 3, 3, 4, 1, 1, 4, 4, 1, 2, 4, 4, 2, 2, 4, 4, 1, 3, 4, 4, 2, 3, 4, 4, 3, 3, 4, 4, 1, 4, 4, 4, 2, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 3, 1, 1, 1, 2, 3, 1, 1, 2, 2, 3, 1, 2, 2, 2, 3, 2, 2, 2, 2, 3, 1, 1, 1, 3, 3, 1, 1, 2, 3, 3, 1, 2, 2, 3, 3, 2, 2, 2, 3, 3, 1, 1, 3, 3, 3, 1, 2, 3, 3, 3, 2, 2, 3, 3, 3, 1, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 8, 1, 7, 2, 7, 3, 7, 4, 7, 5, 7, 6, 7, 7, 7, 1, 1, 6, 1, 2, 6, 2, 2, 6, 1, 3, 6, 2, 3, 6, 3, 3, 6, 1, 4, 6, 2, 4, 6, 3, 4, 6, 4, 4, 6, 1, 5, 6, 2, 5, 6, 3, 5, 6, 4, 5, 6, 5, 5, 6, 1, 6, 6, 2, 6, 6, 3, 6, 6, 4, 6, 6, 5, 6, 6, 6, 6, 6, 1, 1, 1, 5, 1, 1, 2, 5, 1, 2, 2, 5, 2, 2, 2, 5, 1, 1, 3, 5, 1, 2, 3, 5, 2, 2, 3, 5, 1, 3, 3, 5, 2, 3, 3, 5, 3, 3, 3, 5, 1, 1, 4, 5, 1, 2, 4, 5, 2, 2, 4, 5, 1, 3, 4, 5, 2, 3, 4, 5, 3, 3, 4, 5, 1, 4, 4, 5, 2, 4, 4, 5, 3, 4, 4, 5, 4, 4, 4, 5, 1, 1, 5, 5, 1, 2, 5, 5, 2, 2, 5, 5, 1, 3, 5, 5, 2, 3, 5, 5, 3, 3, 5, 5, 1, 4, 5, 5, 2, 4, 5, 5, 3, 4, 5, 5, 4, 4, 5, 5, 1, 5, 5, 5, 2, 5, 5, 5, 3, 5, 5, 5, 4, 5, 5, 5, 5, 5, 5, 5, 1, 1, 1, 1, 4, 1, 1, 1, 2, 4, 1, 1, 2, 2, 4, 1, 2, 2, 2, 4, 2, 2, 2, 2, 4, 1, 1, 1, 3, 4, 1, 1, 2, 3, 4, 1, 2, 2, 3, 4, 2, 2, 2, 3, 4, 1, 1, 3, 3, 4, 1, 2, 3, 3, 4, 2, 2, 3, 3, 4, 1, 3, 3, 3, 4, 2, 3, 3, 3, 4, 3, 3, 3, 3, 4, 1, 1, 1, 4, 4, 1, 1, 2, 4, 4, 1, 2, 2, 4, 4, 2, 2, 2, 4, 4, 1, 1, 3, 4, 4, 1, 2, 3, 4, 4, 2, 2, 3, 4, 4, 1, 3, 3, 4, 4, 2, 3, 3, 4, 4, 3, 3, 3, 4, 4, 1, 1, 4, 4, 4, 1, 2, 4, 4, 4, 2, 2, 4, 4, 4, 1, 3, 4, 4, 4, 2, 3, 4, 4, 4, 3, 3, 4, 4, 4, 1, 4, 4, 4, 4, 2, 4, 4, 4, 4, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 2, 3, 1, 1, 1, 2, 2, 3, 1, 1, 2, 2, 2, 3, 1, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 1, 1, 1, 1, 3, 3, 1, 1, 1, 2, 3, 3, 1, 1, 2, 2, 3, 3, 1, 2, 2, 2, 3, 3, 2, 2, 2, 2, 3, 3, 1, 1, 1, 3, 3, 3, 1, 1, 2, 3, 3, 3, 1, 2, 2, 3, 3, 3, 2, 2, 2, 3, 3, 3, 1, 1, 3, 3, 3, 3, 1, 2, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3, 1, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 9