Case 1: maximum height = 40
Case 2: maximum height = 21
Case 3: maximum height = 28
Case 4: maximum height = 342
Case 5: maximum height = 104
Case 6: maximum height = 282
Case 7: maximum height = 248
Case 8: maximum height = 224
Case 9: maximum height = 252
Case 10: maximum height = 390
Case 11: maximum height = 270
Case 12: maximum height = 479
Case 13: maximum height = 371
Case 14: maximum height = 502
Case 15: maximum height = 507
Case 16: maximum height = 577
Case 17: maximum height = 633
Case 18: maximum height = 756
Case 19: maximum height = 656
Case 20: maximum height = 636
Case 21: maximum height = 825
Case 22: maximum height = 668
Case 23: maximum height = 730
Case 24: maximum height = 767
Case 25: maximum height = 744
Case 26: maximum height = 851
Case 27: maximum height = 1017
Case 28: maximum height = 1139
Case 29: maximum height = 947
Case 30: maximum height = 950
Case 31: maximum height = 1191
Case 32: maximum height = 883
Case 33: maximum height = 940
Case 34: maximum height = 1310