Case 1, n = 5, unique stars = 1
Case 2, n = 6, unique stars = 0
Case 3, n = 7, unique stars = 2
Case 4, n = 10, unique stars = 1
Case 5, n = 63, unique stars = 17
Case 6, n = 271, unique stars = 134
Case 7, n = 500, unique stars = 99