Case #1: 512
Case #2: 21003948
Case #3: 396727972
Case #4: 166299874
Case #5: 849275180
Case #6: 0
Case #7: 294032380
Case #8: 796456345
Case #9: 715191229
Case #10: 242746563
Case #11: 774220861
Case #12: 510029534
Case #13: 637180403
Case #14: 901645920
Case #15: 539110298
Case #16: 731957228
Case #17: 273613783
Case #18: 123024587
Case #19: 44067557
Case #20: 122914388
Case #21: 87053117
Case #22: 905758912
Case #23: 175941257
Case #24: 705194838
Case #25: 756899956
Case #26: 668011195
Case #27: 85619190
Case #28: 427852657
Case #29: 126787535
Case #30: 792996579
Case #31: 575732908
Case #32: 909708555
Case #33: 356980127
Case #34: 330326318
Case #35: 317057027
Case #36: 531236470
Case #37: 963519448
Case #38: 476112727
Case #39: 622697334
Case #40: 419873534
Case #41: 929433169
Case #42: 899632009
Case #43: 850676519
Case #44: 823702088
Case #45: 314351226
Case #46: 157473736
Case #47: 420262624
Case #48: 781889509
Case #49: 995084196
Case #50: 188121137
Case #51: 896739134
Case #52: 815999421
Case #53: 553061310
Case #54: 626982321
Case #55: 821955127
Case #56: 130504928
Case #57: 972798062
Case #58: 679132390
Case #59: 489630481
Case #60: 550782882
Case #61: 428899533
Case #62: 312794194
Case #63: 682522958
Case #64: 323577399
Case #65: 628274590
Case #66: 665450369
Case #67: 882484874
Case #68: 690657728
Case #69: 278778174
Case #70: 223997110
Case #71: 837162234
Case #72: 782062742
Case #73: 403504250
Case #74: 132950209
Case #75: 899703070
Case #76: 104495356
Case #77: 398364871
Case #78: 408628281
Case #79: 22565581
Case #80: 675401981
Case #81: 639389470
Case #82: 859145988
Case #83: 922276869
Case #84: 932135994
Case #85: 547993542
Case #86: 567952361
Case #87: 130550172
Case #88: 75730821
Case #89: 198635873
Case #90: 953658866
Case #91: 851760825
Case #92: 262622474
Case #93: 926929194
Case #94: 893611506
Case #95: 855817242
Case #96: 460053524
Case #97: 869672197
Case #98: 707213320
Case #99: 90217302
Case #100: 676599448
Case #101: 724235412
Case #102: 792299448
Case #103: 773710199
Case #104: 137898020
Case #105: 538910223
Case #106: 324930780
Case #107: 306595544
Case #108: 720499692
Case #109: 753030073