Case #1: 0
Case #2: 1
Case #3: 0
Case #4: 36
Case #5: 146
Case #6: 0
Case #7: 2
Case #8: 0
Case #9: 32
Case #10: 188
Case #11: 0
Case #12: 0
Case #13: 0
Case #14: 165
Case #15: 165
Case #16: 834058048
Case #17: 735866676
Case #18: 148472118
Case #19: 553484346
Case #20: 0
Case #21: 0
Case #22: 0
Case #23: 0
Case #24: 0
Case #25: 0
Case #26: 0
Case #27: 0
Case #28: 1390
Case #29: 64753838
Case #30: 0
Case #31: 0
Case #32: 5747095
Case #33: 1626785
Case #34: 1615237
Case #35: 207097
Case #36: 107906
Case #37: 56032428
Case #38: 17236422
Case #39: 154206
Case #40: 220988
Case #41: 29639004
Case #42: 330330
Case #43: 14613562
Case #44: 437384
Case #45: 729879
Case #46: 1871972
Case #47: 44802909
Case #48: 960469
Case #49: 2486902
Case #50: 52510928
Case #51: 17078071
Case #52: 50657009
Case #53: 33315064
Case #54: 1223607
Case #55: 1109920
Case #56: 671796
Case #57: 24358475
Case #58: 12450431
Case #59: 10269141
Case #60: 19820558
Case #61: 3391455
Case #62: 3086380
Case #63: 4589254
Case #64: 6801215
Case #65: 27529065
Case #66: 907592
Case #67: 12521059
Case #68: 36776368
Case #69: 18137497
Case #70: 16770582
Case #71: 25461827
Case #72: 10254945
Case #73: 944403
Case #74: 39100184
Case #75: 8831706
Case #76: 1036408
Case #77: 6142681
Case #78: 10133048
Case #79: 41898492
Case #80: 11639385
Case #81: 4156428
Case #82: 20074945
Case #83: 32833
Case #84: 58222271
Case #85: 7280734
Case #86: 230182
Case #87: 3018037
Case #88: 6963374
Case #89: 1542116
Case #90: 2042265
Case #91: 56100830
Case #92: 3409902
Case #93: 3280
Case #94: 778303
Case #95: 18002252
Case #96: 54221446
Case #97: 2311248
Case #98: 8240529
Case #99: 274610
Case #100: 8808845
Case #101: 42545057
Case #102: 15457955
Case #103: 10890701
Case #104: 2110139
Case #105: 24581824
Case #106: 1645320
Case #107: 132748
Case #108: 316631
Case #109: 3227509
Case #110: 17228709
Case #111: 2286510
Case #112: 59108176
Case #113: 31104515
Case #114: 697327
Case #115: 16016
Case #116: 9898960