"Welcome to gVATTER, a Maple package for the enumeration of" "permutations avoiding generalized permutation patterns." "To see a list of available functions, type Help();" "or to learn more about a particular function type Help(function_name);" "There are ", 479, " equivalence classes of generalized patterns of lengths ", [5] "Class ", 1, " is:" {{[[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[5, 4, 3, 2, 1], [0, 0, 0, 0]]}} {[[1, 2, 3, 4, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, {[[5, 4, 3, 2, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {1, 2, 3, 4}, {}], [[1, 2, 4, 5, 3], {1, 2, 3, 4}, {}], [[1, 3, 4, 5, 2], {1, 2, 3, 4}, {}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 709, 4928, 39144, 349776, 3472811, 37928331, 451891992, 5832672456, 81074690424, 1207441809209, 19181203110129, 323753459184738, 5785975294622694, 109149016813544376, 2167402030585724571] "" "Class ", 2, " is:" {{[[1, 2, 3, 4, 5], [0, 1, 1, 0]]}, {[[5, 4, 3, 2, 1], [0, 1, 1, 0]]}} {[[1, 2, 3, 4, 5], [0, 1, 1, 0]]} "Class ", 3, " is:" {{[[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[5, 4, 3, 2, 1], [1, 0, 0, 1]]}} {[[1, 2, 3, 4, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, {[[5, 4, 3, 2, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2, 3, 4}, {[0, 0, 0, 0, 1]}], [[1, 2, 4, 3], {2, 3}, {}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 701, 4768, 36699, 314873, 2976594, 30716173, 343381013, 4132329885, 53246591294, 731247853656, 10660411248600, 164396895171652, 2673453999718142, 45720042117632633, 820188876576377955] "" "Class ", 4, " is:" {{[[1, 2, 3, 4, 5], [1, 1, 1, 1]]}, {[[5, 4, 3, 2, 1], [1, 1, 1, 1]]}} {[[1, 2, 3, 4, 5], [1, 1, 1, 1]]} "Class ", 5, " is:" {{[[1, 4, 3, 2, 5], [0, 0, 0, 0]]}, {[[5, 2, 3, 4, 1], [0, 0, 0, 0]]}} {[[1, 4, 3, 2, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 4, 3, 2, 5], [0, 0, 0, 0]]}, {[[5, 2, 3, 4, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {1, 2, 3, 4}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38982, 347869, 3449252, 37620655, 447627708, 5769915215, 80095218258, 1191261103432, 18898879914026, 318562100279543, 5685592510437500, 107112079379106657, 2124112747338010252] "" "Class ", 6, " is:" {{[[1, 4, 3, 2, 5], [0, 1, 1, 0]]}, {[[5, 2, 3, 4, 1], [0, 1, 1, 0]]}} {[[1, 4, 3, 2, 5], [0, 1, 1, 0]]} "Class ", 7, " is:" {{[[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[5, 2, 3, 4, 1], [1, 0, 0, 1]]}} {[[1, 4, 3, 2, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, {[[5, 2, 3, 4, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 2, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 701, 4768, 36699, 314873, 2976594, 30716173, 343381013, 4132329885, 53246591294, 731247853656, 10660411248600, 164396895171652, 2673453999718142, 45720042117632633, 820188876576377955] "" "Class ", 8, " is:" {{[[1, 4, 3, 2, 5], [1, 1, 1, 1]]}, {[[5, 2, 3, 4, 1], [1, 1, 1, 1]]}} {[[1, 4, 3, 2, 5], [1, 1, 1, 1]]} "Class ", 9, " is:" {{[[2, 1, 3, 5, 4], [0, 0, 0, 0]]}, {[[4, 5, 3, 1, 2], [0, 0, 0, 0]]}} {[[2, 1, 3, 5, 4], [0, 0, 0, 0]]} "For the class ", {{[[2, 1, 3, 5, 4], [0, 0, 0, 0]]}, {[[4, 5, 3, 1, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3, 5, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {1, 2, 3, 4}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {1, 2, 3}, {}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 4, 5, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38977, 347794, 3448202, 37605875, 447411544, 5766612686, 80042208149, 1190366133003, 18882991058982, 318265784348321, 5679795502722184, 106993290279989932, 2121567147336853153] "" "Class ", 10, " is:" {{[[2, 1, 3, 5, 4], [0, 1, 1, 0]]}, {[[4, 5, 3, 1, 2], [0, 1, 1, 0]]}} {[[2, 1, 3, 5, 4], [0, 1, 1, 0]]} "Class ", 11, " is:" {{[[2, 1, 3, 5, 4], [1, 0, 0, 1]]}, {[[4, 5, 3, 1, 2], [1, 0, 0, 1]]}} {[[2, 1, 3, 5, 4], [1, 0, 0, 1]]} "Class ", 12, " is:" {{[[2, 1, 3, 5, 4], [1, 1, 1, 1]]}, {[[4, 5, 3, 1, 2], [1, 1, 1, 1]]}} {[[2, 1, 3, 5, 4], [1, 1, 1, 1]]} "Class ", 13, " is:" {{[[2, 5, 3, 1, 4], [0, 0, 0, 0]]}, {[[4, 1, 3, 5, 2], [0, 0, 0, 0]]}} {[[2, 5, 3, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[2, 5, 3, 1, 4], [0, 0, 0, 0]]}, {[[4, 1, 3, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[2, 5, 3, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 1, 3], {1, 2, 3}, {}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38982, 347884, 3449552, 37625605, 447705880, 5771174672, 80116195690, 1191625115214, 18905479581944, 318687249924106, 5688074315975376, 107163510318836508, 2125225387203526220] "" "Class ", 14, " is:" {{[[2, 5, 3, 1, 4], [0, 1, 1, 0]]}, {[[4, 1, 3, 5, 2], [0, 1, 1, 0]]}} {[[2, 5, 3, 1, 4], [0, 1, 1, 0]]} "Class ", 15, " is:" {{[[2, 5, 3, 1, 4], [1, 0, 0, 1]]}, {[[4, 1, 3, 5, 2], [1, 0, 0, 1]]}} {[[2, 5, 3, 1, 4], [1, 0, 0, 1]]} "Class ", 16, " is:" {{[[2, 5, 3, 1, 4], [1, 1, 1, 1]]}, {[[4, 1, 3, 5, 2], [1, 1, 1, 1]]}} {[[2, 5, 3, 1, 4], [1, 1, 1, 1]]} "Class ", 17, " is:" {{[[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[5, 4, 3, 2, 1], [1, 0, 0, 0]]}} {[[1, 2, 3, 4, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, {[[1, 2, 3, 4, 5], [1, 0, 0, 0]]}, {[[5, 4, 3, 2, 1], [0, 0, 0, 1]]}, {[[5, 4, 3, 2, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1, 2, 3, 4}, {[0, 0, 0, 0, 1]}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 705, 4857, 38142, 336291, 3289057, 35337067, 413698248, 5241768017, 71465060725, 1043175024243, 16231998346794, 268207096127991, 4690005160446721, 86528908665043683, 1679764981327051508] "" "Class ", 18, " is:" {{[[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[5, 4, 3, 2, 1], [0, 1, 0, 0]]}} {[[1, 2, 3, 4, 5], [0, 0, 1, 0]]} {[[1, 2, 3, 4, 5], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3, 4, 5], [0, 0, 1, 0]]}, {[[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, {[[5, 4, 3, 2, 1], [0, 0, 1, 0]]}, {[[5, 4, 3, 2, 1], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 4, 5], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 2, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 3, 5, 4], {3, 4}, {}], [[1, 2, 4, 5, 3], {3, 4}, {}], [[1, 3, 4, 5, 2], {3, 4}, {}], [[2, 3, 4, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4834, 37771, 330757, 3207470, 34112273, 394713222, 4935828067, 66322824979, 952907083193, 14576684676065, 236510024091756, 4056690660787118, 73338391714695646, 1393689870381947191] "" "Class ", 19, " is:" {{[[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[1, 2, 3, 4, 5], [1, 1, 0, 0]]}, {[[5, 4, 3, 2, 1], [0, 0, 1, 1]]}, {[[5, 4, 3, 2, 1], [1, 1, 0, 0]]}} {[[1, 2, 3, 4, 5], [0, 0, 1, 1]]} {[[1, 2, 3, 4, 5], [1, 1, 0, 0]]} "Class ", 20, " is:" {{[[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[5, 4, 3, 2, 1], [1, 0, 1, 0]]}} {[[1, 2, 3, 4, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, {[[1, 2, 3, 4, 5], [1, 0, 1, 0]]}, {[[5, 4, 3, 2, 1], [0, 1, 0, 1]]}, {[[5, 4, 3, 2, 1], [1, 0, 1, 0]]}}, " the pattern set ", {[[1, 2, 3, 4, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3, 4}, {[0, 0, 0, 0, 1]}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4745, 36310, 308919, 2887980, 29392211, 323201330, 3815857732, 48116262912, 645071086840, 9158805860008, 137245734060145, 2164092026050332, 35809882818819669, 620348584920591806] "" "Class ", 21, " is:" {{[[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[1, 2, 3, 4, 5], [1, 1, 1, 0]]}, {[[5, 4, 3, 2, 1], [0, 1, 1, 1]]}, {[[5, 4, 3, 2, 1], [1, 1, 1, 0]]}} {[[1, 2, 3, 4, 5], [0, 1, 1, 1]]} {[[1, 2, 3, 4, 5], [1, 1, 1, 0]]} "Class ", 22, " is:" {{[[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[5, 4, 3, 2, 1], [1, 1, 0, 1]]}} {[[1, 2, 3, 4, 5], [1, 0, 1, 1]]} {[[1, 2, 3, 4, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3, 4, 5], [1, 0, 1, 1]]}, {[[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, {[[5, 4, 3, 2, 1], [1, 0, 1, 1]]}, {[[5, 4, 3, 2, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 4, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3, 4}, {[0, 0, 0, 0, 1]}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4, 5}, {[0, 0, 0, 0, 0, 1]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 5, 3], {1, 2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 697, 4667, 34914, 287021, 2560927, 24564432, 251402043, 2728595190, 31249318461, 376054861780, 4738323819153, 62320719361124, 853336550119565, 12136026469900249, 178898287711657242] "" "Class ", 23, " is:" {{[[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, {[[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[5, 4, 3, 1, 2], [0, 0, 0, 0]]}} {[[1, 2, 3, 5, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, {[[2, 1, 3, 4, 5], [0, 0, 0, 0]]}, {[[4, 5, 3, 2, 1], [0, 0, 0, 0]]}, {[[5, 4, 3, 1, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 5, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {1}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {1, 2, 3, 4}, {}], [[1, 3, 4, 5, 2], {1, 2, 3, 4}, {}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38976, 347765, 3447712, 37598286, 447294144, 5764747515, 80011430240, 1189835682714, 18873422539776, 318085061976105, 5676223254661760, 106919460527212950, 2119973556022047744] "" "Class ", 24, " is:" {{[[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[5, 4, 3, 1, 2], [0, 0, 0, 1]]}} {[[1, 2, 3, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3, 4, 5], [1, 0, 0, 0]]}, {[[4, 5, 3, 2, 1], [1, 0, 0, 0]]}, {[[5, 4, 3, 1, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4840, 37918, 333474, 3253240, 34865094, 407182648, 5147117981, 70016168040, 1019805996877, 15835244743270, 261126262127666, 4557371584964216, 83925642544448426, 1626312397622715570] "" "Class ", 25, " is:" {{[[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, {[[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[5, 4, 3, 1, 2], [0, 0, 1, 0]]}} {[[1, 2, 3, 5, 4], [0, 0, 1, 0]]} {[[2, 1, 3, 4, 5], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3, 5, 4], [0, 0, 1, 0]]}, {[[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, {[[4, 5, 3, 2, 1], [0, 1, 0, 0]]}, {[[5, 4, 3, 1, 2], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4, 5], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {3}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[2, 1, 3, 4, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 3, 5, 4], {3, 4}, {}], [[2, 1, 4, 5, 3], {3, 4}, {}], [[3, 1, 4, 5, 2], {2, 3, 4}, {}], [[3, 2, 4, 5, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4834, 37771, 330757, 3207470, 34112273, 394713222, 4935828067, 66322824979, 952907083193, 14576684676065, 236510024091756, 4056690660787118, 73338391714695646, 1393689870381947191] "" "Class ", 26, " is:" {{[[1, 2, 3, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 3, 4, 5], [1, 1, 0, 0]]}, {[[4, 5, 3, 2, 1], [1, 1, 0, 0]]}, {[[5, 4, 3, 1, 2], [0, 0, 1, 1]]}} {[[1, 2, 3, 5, 4], [0, 0, 1, 1]]} {[[2, 1, 3, 4, 5], [1, 1, 0, 0]]} "Class ", 27, " is:" {{[[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[2, 1, 3, 4, 5], [0, 0, 1, 0]]}, {[[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[5, 4, 3, 1, 2], [0, 1, 0, 0]]}} {[[1, 2, 3, 5, 4], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, {[[2, 1, 3, 4, 5], [0, 0, 1, 0]]}, {[[4, 5, 3, 2, 1], [0, 0, 1, 0]]}, {[[5, 4, 3, 1, 2], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 5, 4], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 2, 3, 4, 5], {3}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {3, 4}, {}], [[1, 3, 4, 5, 2], {3, 4}, {}], [[2, 3, 4, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 703, 4817, 37534, 327599, 3164891, 33519051, 386090952, 4804566545, 64226920247, 917805091675, 13960498198182, 225185003512111, 3839042851786987, 68970587034336831, 1302286587667567976] "" "Class ", 28, " is:" {{[[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[5, 4, 3, 1, 2], [0, 1, 0, 1]]}} {[[1, 2, 3, 5, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, {[[2, 1, 3, 4, 5], [1, 0, 1, 0]]}, {[[4, 5, 3, 2, 1], [1, 0, 1, 0]]}, {[[5, 4, 3, 1, 2], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 5, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 699, 4723, 35969, 304179, 2823910, 28520022, 311039615, 3640665886, 45497926429, 604390322111, 8501294894254, 126191172400559, 1970854869817747, 32300525430002906, 554192586837675141] "" "Class ", 29, " is:" {{[[1, 2, 3, 5, 4], [0, 1, 1, 0]]}, {[[2, 1, 3, 4, 5], [0, 1, 1, 0]]}, {[[4, 5, 3, 2, 1], [0, 1, 1, 0]]}, {[[5, 4, 3, 1, 2], [0, 1, 1, 0]]}} {[[1, 2, 3, 5, 4], [0, 1, 1, 0]]} {[[2, 1, 3, 4, 5], [0, 1, 1, 0]]} "Class ", 30, " is:" {{[[1, 2, 3, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3, 4, 5], [1, 1, 1, 0]]}, {[[4, 5, 3, 2, 1], [1, 1, 1, 0]]}, {[[5, 4, 3, 1, 2], [0, 1, 1, 1]]}} {[[1, 2, 3, 5, 4], [0, 1, 1, 1]]} {[[2, 1, 3, 4, 5], [1, 1, 1, 0]]} "Class ", 31, " is:" {{[[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, {[[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[5, 4, 3, 1, 2], [1, 0, 0, 0]]}} {[[1, 2, 3, 5, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, {[[2, 1, 3, 4, 5], [0, 0, 0, 1]]}, {[[4, 5, 3, 2, 1], [0, 0, 0, 1]]}, {[[5, 4, 3, 1, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 3, 5, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {2, 3}, {}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {2}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 4, 5, 3], {2, 3, 4}, {}], [[1, 3, 4, 5, 2], {2, 3, 4}, {}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37868, 332546, 3237620, 34609332, 402972008, 5076245018, 68785548072, 997655804160, 15420936790944, 253064231968336, 4394118358559280, 80486313018869424, 1550969499004966272] "" "Class ", 32, " is:" {{[[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[5, 4, 3, 1, 2], [1, 0, 0, 1]]}} {[[1, 2, 3, 5, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, {[[2, 1, 3, 4, 5], [1, 0, 0, 1]]}, {[[4, 5, 3, 2, 1], [1, 0, 0, 1]]}, {[[5, 4, 3, 1, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 5, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3], {2, 3}, {}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4746, 36350, 309879, 2906997, 29739277, 329338301, 3923804983, 50033410784, 679753984650, 9801361733063, 149476485272753, 2403745451333236, 40649117808310755, 721103112638944175] "" "Class ", 33, " is:" {{[[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[5, 4, 3, 1, 2], [1, 0, 1, 0]]}} {[[1, 2, 3, 5, 4], [1, 0, 1, 0]]} {[[2, 1, 3, 4, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 3, 5, 4], [1, 0, 1, 0]]}, {[[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, {[[4, 5, 3, 2, 1], [0, 1, 0, 1]]}, {[[5, 4, 3, 1, 2], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 4, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 0, 1]}], [[2, 1, 4, 3], {3}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4745, 36310, 308919, 2887980, 29392211, 323201330, 3815857732, 48116262912, 645071086840, 9158805860008, 137245734060145, 2164092026050332, 35809882818819669, 620348584920591806] "" "Class ", 34, " is:" {{[[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3, 4, 5], [1, 1, 0, 1]]}, {[[4, 5, 3, 2, 1], [1, 1, 0, 1]]}, {[[5, 4, 3, 1, 2], [1, 0, 1, 1]]}} {[[1, 2, 3, 5, 4], [1, 0, 1, 1]]} {[[2, 1, 3, 4, 5], [1, 1, 0, 1]]} "Class ", 35, " is:" {{[[1, 2, 3, 5, 4], [1, 1, 0, 0]]}, {[[2, 1, 3, 4, 5], [0, 0, 1, 1]]}, {[[4, 5, 3, 2, 1], [0, 0, 1, 1]]}, {[[5, 4, 3, 1, 2], [1, 1, 0, 0]]}} {[[1, 2, 3, 5, 4], [1, 1, 0, 0]]} {[[2, 1, 3, 4, 5], [0, 0, 1, 1]]} "Class ", 36, " is:" {{[[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[2, 1, 3, 4, 5], [1, 0, 1, 1]]}, {[[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[5, 4, 3, 1, 2], [1, 1, 0, 1]]}} {[[1, 2, 3, 5, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, {[[2, 1, 3, 4, 5], [1, 0, 1, 1]]}, {[[4, 5, 3, 2, 1], [1, 0, 1, 1]]}, {[[5, 4, 3, 1, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 3, 5, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 5, 3], {1, 2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 696, 4641, 34458, 280109, 2462232, 23184127, 232113130, 2456302399, 27342208324, 318864865311, 3882635726822, 49219149594445, 647949431806302, 8838904277549434, 124701134431812640] "" "Class ", 37, " is:" {{[[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[2, 1, 3, 4, 5], [0, 1, 1, 1]]}, {[[4, 5, 3, 2, 1], [0, 1, 1, 1]]}, {[[5, 4, 3, 1, 2], [1, 1, 1, 0]]}} {[[1, 2, 3, 5, 4], [1, 1, 1, 0]]} {[[2, 1, 3, 4, 5], [0, 1, 1, 1]]} "Class ", 38, " is:" {{[[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3, 4, 5], [1, 1, 1, 1]]}, {[[4, 5, 3, 2, 1], [1, 1, 1, 1]]}, {[[5, 4, 3, 1, 2], [1, 1, 1, 1]]}} {[[1, 2, 3, 5, 4], [1, 1, 1, 1]]} {[[2, 1, 3, 4, 5], [1, 1, 1, 1]]} "Class ", 39, " is:" {{[[1, 2, 4, 3, 5], [0, 0, 0, 0]]}, {[[1, 3, 2, 4, 5], [0, 0, 0, 0]]}, {[[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[5, 4, 2, 3, 1], [0, 0, 0, 0]]}} {[[1, 2, 4, 3, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3, 5], [0, 0, 0, 0]]}, {[[1, 3, 2, 4, 5], [0, 0, 0, 0]]}, {[[5, 3, 4, 2, 1], [0, 0, 0, 0]]}, {[[5, 4, 2, 3, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {1, 2, 3}, {}], [[1, 2, 5, 4, 3], {1, 2, 3, 4}, {}], [[1, 3, 5, 4, 2], {1, 2, 3, 4}, {}], [[2, 3, 5, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38977, 347779, 3447902, 37600925, 447332398, 5765327905, 80020698913, 1189991560707, 18876181370841, 318136382176708, 5677225148401090, 106939954137362482, 2120412050923152077] "" "Class ", 40, " is:" {{[[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, {[[1, 3, 2, 4, 5], [1, 0, 0, 0]]}, {[[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[5, 4, 2, 3, 1], [0, 0, 0, 1]]}} {[[1, 2, 4, 3, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, {[[1, 3, 2, 4, 5], [1, 0, 0, 0]]}, {[[5, 3, 4, 2, 1], [1, 0, 0, 0]]}, {[[5, 4, 2, 3, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37868, 332546, 3237620, 34609332, 402972008, 5076245018, 68785548072, 997655804160, 15420936790944, 253064231968336, 4394118358559280, 80486313018869424, 1550969499004966272] "" "Class ", 41, " is:" {{[[1, 2, 4, 3, 5], [0, 0, 1, 0]]}, {[[1, 3, 2, 4, 5], [0, 1, 0, 0]]}, {[[5, 3, 4, 2, 1], [0, 1, 0, 0]]}, {[[5, 4, 2, 3, 1], [0, 0, 1, 0]]}} {[[1, 2, 4, 3, 5], [0, 0, 1, 0]]} {[[1, 3, 2, 4, 5], [0, 1, 0, 0]]} "Class ", 42, " is:" {{[[1, 2, 4, 3, 5], [0, 0, 1, 1]]}, {[[1, 3, 2, 4, 5], [1, 1, 0, 0]]}, {[[5, 3, 4, 2, 1], [1, 1, 0, 0]]}, {[[5, 4, 2, 3, 1], [0, 0, 1, 1]]}} {[[1, 2, 4, 3, 5], [0, 0, 1, 1]]} {[[1, 3, 2, 4, 5], [1, 1, 0, 0]]} "Class ", 43, " is:" {{[[1, 2, 4, 3, 5], [0, 1, 0, 0]]}, {[[1, 3, 2, 4, 5], [0, 0, 1, 0]]}, {[[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[5, 4, 2, 3, 1], [0, 1, 0, 0]]}} {[[1, 2, 4, 3, 5], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 4, 3, 5], [0, 1, 0, 0]]}, {[[1, 3, 2, 4, 5], [0, 0, 1, 0]]}, {[[5, 3, 4, 2, 1], [0, 0, 1, 0]]}, {[[5, 4, 2, 3, 1], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3, 5], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {3, 4}, {}], [[1, 2, 5, 4, 3], {3}, {}], [[1, 3, 5, 4, 2], {3, 4}, {}], [[2, 3, 5, 4, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 703, 4817, 37534, 327599, 3164891, 33519051, 386090952, 4804566545, 64226920247, 917805091675, 13960498198182, 225185003512111, 3839042851786987, 68970587034336831, 1302286587667567976] "" "Class ", 44, " is:" {{[[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, {[[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[5, 4, 2, 3, 1], [0, 1, 0, 1]]}} {[[1, 2, 4, 3, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, {[[1, 3, 2, 4, 5], [1, 0, 1, 0]]}, {[[5, 3, 4, 2, 1], [1, 0, 1, 0]]}, {[[5, 4, 2, 3, 1], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4745, 36310, 308919, 2887980, 29392211, 323201330, 3815857732, 48116262912, 645071086840, 9158805860008, 137245734060145, 2164092026050332, 35809882818819669, 620348584920591806] "" "Class ", 45, " is:" {{[[1, 2, 4, 3, 5], [0, 1, 1, 0]]}, {[[1, 3, 2, 4, 5], [0, 1, 1, 0]]}, {[[5, 3, 4, 2, 1], [0, 1, 1, 0]]}, {[[5, 4, 2, 3, 1], [0, 1, 1, 0]]}} {[[1, 2, 4, 3, 5], [0, 1, 1, 0]]} {[[1, 3, 2, 4, 5], [0, 1, 1, 0]]} "Class ", 46, " is:" {{[[1, 2, 4, 3, 5], [0, 1, 1, 1]]}, {[[1, 3, 2, 4, 5], [1, 1, 1, 0]]}, {[[5, 3, 4, 2, 1], [1, 1, 1, 0]]}, {[[5, 4, 2, 3, 1], [0, 1, 1, 1]]}} {[[1, 2, 4, 3, 5], [0, 1, 1, 1]]} {[[1, 3, 2, 4, 5], [1, 1, 1, 0]]} "Class ", 47, " is:" {{[[1, 2, 4, 3, 5], [1, 0, 0, 0]]}, {[[1, 3, 2, 4, 5], [0, 0, 0, 1]]}, {[[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[5, 4, 2, 3, 1], [1, 0, 0, 0]]}} {[[1, 2, 4, 3, 5], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 4, 3, 5], [1, 0, 0, 0]]}, {[[1, 3, 2, 4, 5], [0, 0, 0, 1]]}, {[[5, 3, 4, 2, 1], [0, 0, 0, 1]]}, {[[5, 4, 2, 3, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 3, 5], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {}, {}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 3, 4], {2, 3}, {}], [[1, 2, 5, 4, 3], {2, 3, 4}, {}], [[1, 3, 5, 4, 2], {2, 3, 4}, {}], [[2, 3, 5, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4840, 37909, 333198, 3247430, 34756773, 405240252, 5112381957, 69385068297, 1008039125310, 15608836683658, 256616866094986, 4464256712904744, 81930953664017213, 1581980127397527165] "" "Class ", 48, " is:" {{[[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[1, 3, 2, 4, 5], [1, 0, 0, 1]]}, {[[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[5, 4, 2, 3, 1], [1, 0, 0, 1]]}} {[[1, 2, 4, 3, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, {[[1, 3, 2, 4, 5], [1, 0, 0, 1]]}, {[[5, 3, 4, 2, 1], [1, 0, 0, 1]]}, {[[5, 4, 2, 3, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2, 3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4747, 36368, 310075, 2908152, 29727309, 328706824, 3907096334, 49658121296, 671806789486, 9636188879148, 146040655162497, 2331441700773988, 39100039578607877, 687183928229131712] "" "Class ", 49, " is:" {{[[1, 2, 4, 3, 5], [1, 0, 1, 0]]}, {[[1, 3, 2, 4, 5], [0, 1, 0, 1]]}, {[[5, 3, 4, 2, 1], [0, 1, 0, 1]]}, {[[5, 4, 2, 3, 1], [1, 0, 1, 0]]}} {[[1, 2, 4, 3, 5], [1, 0, 1, 0]]} {[[1, 3, 2, 4, 5], [0, 1, 0, 1]]} "Class ", 50, " is:" {{[[1, 2, 4, 3, 5], [1, 0, 1, 1]]}, {[[1, 3, 2, 4, 5], [1, 1, 0, 1]]}, {[[5, 3, 4, 2, 1], [1, 1, 0, 1]]}, {[[5, 4, 2, 3, 1], [1, 0, 1, 1]]}} {[[1, 2, 4, 3, 5], [1, 0, 1, 1]]} {[[1, 3, 2, 4, 5], [1, 1, 0, 1]]} "Class ", 51, " is:" {{[[1, 2, 4, 3, 5], [1, 1, 0, 0]]}, {[[1, 3, 2, 4, 5], [0, 0, 1, 1]]}, {[[5, 3, 4, 2, 1], [0, 0, 1, 1]]}, {[[5, 4, 2, 3, 1], [1, 1, 0, 0]]}} {[[1, 2, 4, 3, 5], [1, 1, 0, 0]]} {[[1, 3, 2, 4, 5], [0, 0, 1, 1]]} "Class ", 52, " is:" {{[[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, {[[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[5, 4, 2, 3, 1], [1, 1, 0, 1]]}} {[[1, 2, 4, 3, 5], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, {[[1, 3, 2, 4, 5], [1, 0, 1, 1]]}, {[[5, 3, 4, 2, 1], [1, 0, 1, 1]]}, {[[5, 4, 2, 3, 1], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 3, 5], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 0, 1]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 697, 4667, 34914, 287021, 2560927, 24564432, 251402043, 2728595190, 31249318461, 376054861780, 4738323819153, 62320719361124, 853336550119565, 12136026469900249, 178898287711657242] "" "Class ", 53, " is:" {{[[1, 2, 4, 3, 5], [1, 1, 1, 0]]}, {[[1, 3, 2, 4, 5], [0, 1, 1, 1]]}, {[[5, 3, 4, 2, 1], [0, 1, 1, 1]]}, {[[5, 4, 2, 3, 1], [1, 1, 1, 0]]}} {[[1, 2, 4, 3, 5], [1, 1, 1, 0]]} {[[1, 3, 2, 4, 5], [0, 1, 1, 1]]} "Class ", 54, " is:" {{[[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[1, 3, 2, 4, 5], [1, 1, 1, 1]]}, {[[5, 3, 4, 2, 1], [1, 1, 1, 1]]}, {[[5, 4, 2, 3, 1], [1, 1, 1, 1]]}} {[[1, 2, 4, 3, 5], [1, 1, 1, 1]]} {[[1, 3, 2, 4, 5], [1, 1, 1, 1]]} "Class ", 55, " is:" {{[[1, 2, 4, 5, 3], [0, 0, 0, 0]]}, {[[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, {[[5, 4, 2, 1, 3], [0, 0, 0, 0]]}} {[[1, 2, 4, 5, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 4, 5, 3], [0, 0, 0, 0]]}, {[[3, 1, 2, 4, 5], [0, 0, 0, 0]]}, {[[3, 5, 4, 2, 1], [0, 0, 0, 0]]}, {[[5, 4, 2, 1, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 5, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {1}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4}, {}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {1, 2, 3, 4}, {}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38976, 347775, 3447912, 37601586, 447346944, 5765604885, 80025786960, 1190085736014, 18877969022976, 318171464604945, 5677939605422880, 106955077375109430, 2120744934976978944] "" "Class ", 56, " is:" {{[[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[5, 4, 2, 1, 3], [0, 0, 0, 1]]}} {[[1, 2, 4, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2, 4, 5], [1, 0, 0, 0]]}, {[[3, 5, 4, 2, 1], [1, 0, 0, 0]]}, {[[5, 4, 2, 1, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4840, 37918, 333474, 3253240, 34865094, 407182648, 5147117981, 70016168040, 1019805996877, 15835244743270, 261126262127666, 4557371584964216, 83925642544448426, 1626312397622715570] "" "Class ", 57, " is:" {{[[1, 2, 4, 5, 3], [0, 0, 1, 0]]}, {[[3, 1, 2, 4, 5], [0, 1, 0, 0]]}, {[[3, 5, 4, 2, 1], [0, 1, 0, 0]]}, {[[5, 4, 2, 1, 3], [0, 0, 1, 0]]}} {[[1, 2, 4, 5, 3], [0, 0, 1, 0]]} {[[3, 1, 2, 4, 5], [0, 1, 0, 0]]} "Class ", 58, " is:" {{[[1, 2, 4, 5, 3], [0, 0, 1, 1]]}, {[[3, 1, 2, 4, 5], [1, 1, 0, 0]]}, {[[3, 5, 4, 2, 1], [1, 1, 0, 0]]}, {[[5, 4, 2, 1, 3], [0, 0, 1, 1]]}} {[[1, 2, 4, 5, 3], [0, 0, 1, 1]]} {[[3, 1, 2, 4, 5], [1, 1, 0, 0]]} "Class ", 59, " is:" {{[[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, {[[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[5, 4, 2, 1, 3], [0, 1, 0, 0]]}} {[[1, 2, 4, 5, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, {[[3, 1, 2, 4, 5], [0, 0, 1, 0]]}, {[[3, 5, 4, 2, 1], [0, 0, 1, 0]]}, {[[5, 4, 2, 1, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 5, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 2, 3, 4, 5], {3}, {}], [[1, 2, 3, 5, 4], {3, 4}, {}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {3, 4}, {}], [[2, 3, 4, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 703, 4817, 37534, 327599, 3164891, 33519051, 386090952, 4804566545, 64226920247, 917805091675, 13960498198182, 225185003512111, 3839042851786987, 68970587034336831, 1302286587667567976] "" "Class ", 60, " is:" {{[[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[5, 4, 2, 1, 3], [0, 1, 0, 1]]}} {[[1, 2, 4, 5, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 2, 4, 5], [1, 0, 1, 0]]}, {[[3, 5, 4, 2, 1], [1, 0, 1, 0]]}, {[[5, 4, 2, 1, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 5, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {1}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4745, 36310, 308919, 2887980, 29392211, 323201330, 3815857732, 48116262912, 645071086840, 9158805860008, 137245734060145, 2164092026050332, 35809882818819669, 620348584920591806] "" "Class ", 61, " is:" {{[[1, 2, 4, 5, 3], [0, 1, 1, 0]]}, {[[3, 1, 2, 4, 5], [0, 1, 1, 0]]}, {[[3, 5, 4, 2, 1], [0, 1, 1, 0]]}, {[[5, 4, 2, 1, 3], [0, 1, 1, 0]]}} {[[1, 2, 4, 5, 3], [0, 1, 1, 0]]} {[[3, 1, 2, 4, 5], [0, 1, 1, 0]]} "Class ", 62, " is:" {{[[1, 2, 4, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 2, 4, 5], [1, 1, 1, 0]]}, {[[3, 5, 4, 2, 1], [1, 1, 1, 0]]}, {[[5, 4, 2, 1, 3], [0, 1, 1, 1]]}} {[[1, 2, 4, 5, 3], [0, 1, 1, 1]]} {[[3, 1, 2, 4, 5], [1, 1, 1, 0]]} "Class ", 63, " is:" {{[[1, 2, 4, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, {[[5, 4, 2, 1, 3], [1, 0, 0, 0]]}} {[[1, 2, 4, 5, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 4, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 2, 4, 5], [0, 0, 0, 1]]}, {[[3, 5, 4, 2, 1], [0, 0, 0, 1]]}, {[[5, 4, 2, 1, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 4, 5, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {2, 3}, {}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {2}, {}], [[1, 2, 3, 5, 4], {2, 3, 4}, {}], [[1, 2, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 4, 5, 2], {2, 3, 4}, {}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37874, 332696, 3240416, 34657116, 403773512, 5089835936, 69021919224, 1001903928804, 15500138755224, 254598918643168, 4425046557089424, 81134570778122256, 1565095717271557536] "" "Class ", 64, " is:" {{[[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[5, 4, 2, 1, 3], [1, 0, 0, 1]]}} {[[1, 2, 4, 5, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2, 4, 5], [1, 0, 0, 1]]}, {[[3, 5, 4, 2, 1], [1, 0, 0, 1]]}, {[[5, 4, 2, 1, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 5, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {2, 3}, {}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4746, 36350, 309879, 2906997, 29739277, 329338301, 3923804983, 50033410784, 679753984650, 9801361733063, 149476485272753, 2403745451333236, 40649117808310755, 721103112638944175] "" "Class ", 65, " is:" {{[[1, 2, 4, 5, 3], [1, 0, 1, 0]]}, {[[3, 1, 2, 4, 5], [0, 1, 0, 1]]}, {[[3, 5, 4, 2, 1], [0, 1, 0, 1]]}, {[[5, 4, 2, 1, 3], [1, 0, 1, 0]]}} {[[1, 2, 4, 5, 3], [1, 0, 1, 0]]} {[[3, 1, 2, 4, 5], [0, 1, 0, 1]]} "Class ", 66, " is:" {{[[1, 2, 4, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 2, 4, 5], [1, 1, 0, 1]]}, {[[3, 5, 4, 2, 1], [1, 1, 0, 1]]}, {[[5, 4, 2, 1, 3], [1, 0, 1, 1]]}} {[[1, 2, 4, 5, 3], [1, 0, 1, 1]]} {[[3, 1, 2, 4, 5], [1, 1, 0, 1]]} "Class ", 67, " is:" {{[[1, 2, 4, 5, 3], [1, 1, 0, 0]]}, {[[3, 1, 2, 4, 5], [0, 0, 1, 1]]}, {[[3, 5, 4, 2, 1], [0, 0, 1, 1]]}, {[[5, 4, 2, 1, 3], [1, 1, 0, 0]]}} {[[1, 2, 4, 5, 3], [1, 1, 0, 0]]} {[[3, 1, 2, 4, 5], [0, 0, 1, 1]]} "Class ", 68, " is:" {{[[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[5, 4, 2, 1, 3], [1, 1, 0, 1]]}} {[[1, 2, 4, 5, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 2, 4, 5], [1, 0, 1, 1]]}, {[[3, 5, 4, 2, 1], [1, 0, 1, 1]]}, {[[5, 4, 2, 1, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 4, 5, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {2}, {[0, 0, 1, 0, 0]}], [[1, 2, 4, 3], {3}, {}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {1, 2}, {[0, 0, 0, 1, 0, 0]}], [[2, 3, 1, 5, 4], {4}, {}], [[2, 4, 1, 5, 3], {1, 2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 697, 4667, 34914, 287021, 2560927, 24564432, 251402043, 2728595190, 31249318461, 376054861780, 4738323819153, 62320719361124, 853336550119565, 12136026469900249, 178898287711657242] "" "Class ", 69, " is:" {{[[1, 2, 4, 5, 3], [1, 1, 1, 0]]}, {[[3, 1, 2, 4, 5], [0, 1, 1, 1]]}, {[[3, 5, 4, 2, 1], [0, 1, 1, 1]]}, {[[5, 4, 2, 1, 3], [1, 1, 1, 0]]}} {[[1, 2, 4, 5, 3], [1, 1, 1, 0]]} {[[3, 1, 2, 4, 5], [0, 1, 1, 1]]} "Class ", 70, " is:" {{[[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1, 4, 5], [0, 0, 0, 0]]}, {[[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, {[[5, 4, 1, 3, 2], [0, 0, 0, 0]]}} {[[1, 2, 5, 3, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1, 4, 5], [0, 0, 0, 0]]}, {[[4, 3, 5, 2, 1], [0, 0, 0, 0]]}, {[[5, 4, 1, 3, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 5, 3, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 4, 3, 5], {1, 2, 3}, {}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {1, 2, 3, 4}, {}], [[1, 3, 5, 4, 2], {1, 2, 3, 4}, {}], [[2, 3, 5, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38980, 347837, 3448792, 37614098, 447531000, 5768428803, 80071254648, 1190855183414, 18891654561628, 318427067939961, 5682946188447440, 107057773100175102, 2122947536807150960] "" "Class ", 71, " is:" {{[[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1, 4, 5], [1, 0, 0, 0]]}, {[[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, {[[5, 4, 1, 3, 2], [0, 0, 0, 1]]}} {[[1, 2, 5, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1, 4, 5], [1, 0, 0, 0]]}, {[[4, 3, 5, 2, 1], [1, 0, 0, 0]]}, {[[5, 4, 1, 3, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 5, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37868, 332546, 3237620, 34609332, 402972008, 5076245018, 68785548072, 997655804160, 15420936790944, 253064231968336, 4394118358559280, 80486313018869424, 1550969499004966272] "" "Class ", 72, " is:" {{[[1, 2, 5, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1, 4, 5], [0, 1, 0, 0]]}, {[[4, 3, 5, 2, 1], [0, 1, 0, 0]]}, {[[5, 4, 1, 3, 2], [0, 0, 1, 0]]}} {[[1, 2, 5, 3, 4], [0, 0, 1, 0]]} {[[2, 3, 1, 4, 5], [0, 1, 0, 0]]} "Class ", 73, " is:" {{[[1, 2, 5, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1, 4, 5], [1, 1, 0, 0]]}, {[[4, 3, 5, 2, 1], [1, 1, 0, 0]]}, {[[5, 4, 1, 3, 2], [0, 0, 1, 1]]}} {[[1, 2, 5, 3, 4], [0, 0, 1, 1]]} {[[2, 3, 1, 4, 5], [1, 1, 0, 0]]} "Class ", 74, " is:" {{[[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1, 4, 5], [0, 0, 1, 0]]}, {[[4, 3, 5, 2, 1], [0, 0, 1, 0]]}, {[[5, 4, 1, 3, 2], [0, 1, 0, 0]]}} {[[1, 2, 5, 3, 4], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1, 4, 5], [0, 0, 1, 0]]}, {[[4, 3, 5, 2, 1], [0, 0, 1, 0]]}, {[[5, 4, 1, 3, 2], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 5, 3, 4], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 2, 4, 3, 5], {3, 4}, {}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {3}, {}], [[1, 3, 5, 4, 2], {3, 4}, {}], [[2, 3, 5, 4, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 703, 4817, 37534, 327599, 3164891, 33519051, 386090952, 4804566545, 64226920247, 917805091675, 13960498198182, 225185003512111, 3839042851786987, 68970587034336831, 1302286587667567976] "" "Class ", 75, " is:" {{[[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1, 4, 5], [1, 0, 1, 0]]}, {[[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[5, 4, 1, 3, 2], [0, 1, 0, 1]]}} {[[1, 2, 5, 3, 4], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1, 4, 5], [1, 0, 1, 0]]}, {[[4, 3, 5, 2, 1], [1, 0, 1, 0]]}, {[[5, 4, 1, 3, 2], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 5, 3, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 1, 0]}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 699, 4723, 35969, 304179, 2823910, 28520022, 311039615, 3640665886, 45497926429, 604390322111, 8501294894254, 126191172400559, 1970854869817747, 32300525430002906, 554192586837675141] "" "Class ", 76, " is:" {{[[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1, 4, 5], [0, 1, 1, 0]]}, {[[4, 3, 5, 2, 1], [0, 1, 1, 0]]}, {[[5, 4, 1, 3, 2], [0, 1, 1, 0]]}} {[[1, 2, 5, 3, 4], [0, 1, 1, 0]]} {[[2, 3, 1, 4, 5], [0, 1, 1, 0]]} "Class ", 77, " is:" {{[[1, 2, 5, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1, 4, 5], [1, 1, 1, 0]]}, {[[4, 3, 5, 2, 1], [1, 1, 1, 0]]}, {[[5, 4, 1, 3, 2], [0, 1, 1, 1]]}} {[[1, 2, 5, 3, 4], [0, 1, 1, 1]]} {[[2, 3, 1, 4, 5], [1, 1, 1, 0]]} "Class ", 78, " is:" {{[[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, {[[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, {[[5, 4, 1, 3, 2], [1, 0, 0, 0]]}} {[[1, 2, 5, 3, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1, 4, 5], [0, 0, 0, 1]]}, {[[4, 3, 5, 2, 1], [0, 0, 0, 1]]}, {[[5, 4, 1, 3, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 5, 3, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {}, {}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 4, 3, 5], {2, 3}, {}], [[1, 2, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 2, 5, 4, 3], {2, 3, 4}, {}], [[1, 3, 5, 4, 2], {2, 3, 4}, {}], [[2, 3, 5, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4839, 37890, 332911, 3243252, 34695475, 404314543, 5097846976, 69146743589, 1003951140459, 15535452873197, 255238810253701, 4437207990186150, 81376613057795459, 1570132210422810657] "" "Class ", 79, " is:" {{[[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1, 4, 5], [1, 0, 0, 1]]}, {[[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[5, 4, 1, 3, 2], [1, 0, 0, 1]]}} {[[1, 2, 5, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1, 4, 5], [1, 0, 0, 1]]}, {[[4, 3, 5, 2, 1], [1, 0, 0, 1]]}, {[[5, 4, 1, 3, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 5, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2, 3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4747, 36368, 310075, 2908152, 29727309, 328706824, 3907096334, 49658121296, 671806789486, 9636188879148, 146040655162497, 2331441700773988, 39100039578607877, 687183928229131712] "" "Class ", 80, " is:" {{[[1, 2, 5, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1, 4, 5], [0, 1, 0, 1]]}, {[[4, 3, 5, 2, 1], [0, 1, 0, 1]]}, {[[5, 4, 1, 3, 2], [1, 0, 1, 0]]}} {[[1, 2, 5, 3, 4], [1, 0, 1, 0]]} {[[2, 3, 1, 4, 5], [0, 1, 0, 1]]} "Class ", 81, " is:" {{[[1, 2, 5, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1, 4, 5], [1, 1, 0, 1]]}, {[[4, 3, 5, 2, 1], [1, 1, 0, 1]]}, {[[5, 4, 1, 3, 2], [1, 0, 1, 1]]}} {[[1, 2, 5, 3, 4], [1, 0, 1, 1]]} {[[2, 3, 1, 4, 5], [1, 1, 0, 1]]} "Class ", 82, " is:" {{[[1, 2, 5, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1, 4, 5], [0, 0, 1, 1]]}, {[[4, 3, 5, 2, 1], [0, 0, 1, 1]]}, {[[5, 4, 1, 3, 2], [1, 1, 0, 0]]}} {[[1, 2, 5, 3, 4], [1, 1, 0, 0]]} {[[2, 3, 1, 4, 5], [0, 0, 1, 1]]} "Class ", 83, " is:" {{[[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, {[[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[5, 4, 1, 3, 2], [1, 1, 0, 1]]}} {[[1, 2, 5, 3, 4], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1, 4, 5], [1, 0, 1, 1]]}, {[[4, 3, 5, 2, 1], [1, 0, 1, 1]]}, {[[5, 4, 1, 3, 2], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 5, 3, 4], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {3}, {[0, 0, 0, 1, 0]}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {4}, {[0, 0, 0, 0, 1, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 696, 4641, 34458, 280109, 2462232, 23184127, 232113130, 2456302399, 27342208324, 318864865311, 3882635726822, 49219149594445, 647949431806302, 8838904277549434, 124701134431812640] "" "Class ", 84, " is:" {{[[1, 2, 5, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1, 4, 5], [0, 1, 1, 1]]}, {[[4, 3, 5, 2, 1], [0, 1, 1, 1]]}, {[[5, 4, 1, 3, 2], [1, 1, 1, 0]]}} {[[1, 2, 5, 3, 4], [1, 1, 1, 0]]} {[[2, 3, 1, 4, 5], [0, 1, 1, 1]]} "Class ", 85, " is:" {{[[1, 2, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, {[[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, {[[5, 4, 1, 2, 3], [0, 0, 0, 0]]}} {[[1, 2, 5, 4, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 2, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1, 4, 5], [0, 0, 0, 0]]}, {[[3, 4, 5, 2, 1], [0, 0, 0, 0]]}, {[[5, 4, 1, 2, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 5, 4, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 4, 3, 5], {1, 2, 3}, {}], [[1, 2, 5, 3, 4], {1, 2, 3}, {}], [[1, 2, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 4, 2], {1, 2, 3, 4}, {}], [[2, 3, 5, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38976, 347775, 3447912, 37601586, 447346944, 5765604885, 80025786960, 1190085736014, 18877969022976, 318171464604945, 5677939605422880, 106955077375109430, 2120744934976978944] "" "Class ", 86, " is:" {{[[1, 2, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1, 4, 5], [1, 0, 0, 0]]}, {[[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, {[[5, 4, 1, 2, 3], [0, 0, 0, 1]]}} {[[1, 2, 5, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 2, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1, 4, 5], [1, 0, 0, 0]]}, {[[3, 4, 5, 2, 1], [1, 0, 0, 0]]}, {[[5, 4, 1, 2, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 5, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37864, 332456, 3236090, 34585138, 402593652, 5070228606, 68686946674, 995979034197, 15391250508204, 252516266313184, 4383569184807315, 80274560406376557, 1546540548551811738] "" "Class ", 87, " is:" {{[[1, 2, 5, 4, 3], [0, 0, 1, 0]]}, {[[3, 2, 1, 4, 5], [0, 1, 0, 0]]}, {[[3, 4, 5, 2, 1], [0, 1, 0, 0]]}, {[[5, 4, 1, 2, 3], [0, 0, 1, 0]]}} {[[1, 2, 5, 4, 3], [0, 0, 1, 0]]} {[[3, 2, 1, 4, 5], [0, 1, 0, 0]]} "Class ", 88, " is:" {{[[1, 2, 5, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 1, 4, 5], [1, 1, 0, 0]]}, {[[3, 4, 5, 2, 1], [1, 1, 0, 0]]}, {[[5, 4, 1, 2, 3], [0, 0, 1, 1]]}} {[[1, 2, 5, 4, 3], [0, 0, 1, 1]]} {[[3, 2, 1, 4, 5], [1, 1, 0, 0]]} "Class ", 89, " is:" {{[[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {[[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, {[[5, 4, 1, 2, 3], [0, 1, 0, 0]]}} {[[1, 2, 5, 4, 3], [0, 1, 0, 0]]} "For the class ", {{[[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, {[[3, 2, 1, 4, 5], [0, 0, 1, 0]]}, {[[3, 4, 5, 2, 1], [0, 0, 1, 0]]}, {[[5, 4, 1, 2, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[1, 2, 5, 4, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {}, {}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[1, 2, 4, 3, 5], {3, 4}, {}], [[1, 2, 5, 3, 4], {3, 4}, {}], [[1, 2, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 4, 2], {3, 4}, {}], [[2, 3, 5, 4, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4834, 37771, 330757, 3207470, 34112273, 394713222, 4935828067, 66322824979, 952907083193, 14576684676065, 236510024091756, 4056690660787118, 73338391714695646, 1393689870381947191] "" "Class ", 90, " is:" {{[[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[5, 4, 1, 2, 3], [0, 1, 0, 1]]}} {[[1, 2, 5, 4, 3], [0, 1, 0, 1]]} "For the class ", {{[[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1, 4, 5], [1, 0, 1, 0]]}, {[[3, 4, 5, 2, 1], [1, 0, 1, 0]]}, {[[5, 4, 1, 2, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 5, 4, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {1, 3}, {[0, 0, 1, 0, 0]}], [[1, 3, 2, 4], {3}, {}], [[1, 3, 4, 2], {3}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {3}, {}], [[2, 3, 1, 4], {3}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[2, 4, 3, 1], {3}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4745, 36310, 308919, 2887980, 29392211, 323201330, 3815857732, 48116262912, 645071086840, 9158805860008, 137245734060145, 2164092026050332, 35809882818819669, 620348584920591806] "" "Class ", 91, " is:" {{[[1, 2, 5, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 1, 4, 5], [0, 1, 1, 0]]}, {[[3, 4, 5, 2, 1], [0, 1, 1, 0]]}, {[[5, 4, 1, 2, 3], [0, 1, 1, 0]]}} {[[1, 2, 5, 4, 3], [0, 1, 1, 0]]} {[[3, 2, 1, 4, 5], [0, 1, 1, 0]]} "Class ", 92, " is:" {{[[1, 2, 5, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 1, 4, 5], [1, 1, 1, 0]]}, {[[3, 4, 5, 2, 1], [1, 1, 1, 0]]}, {[[5, 4, 1, 2, 3], [0, 1, 1, 1]]}} {[[1, 2, 5, 4, 3], [0, 1, 1, 1]]} {[[3, 2, 1, 4, 5], [1, 1, 1, 0]]} "Class ", 93, " is:" {{[[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, {[[5, 4, 1, 2, 3], [1, 0, 0, 0]]}} {[[1, 2, 5, 4, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1, 4, 5], [0, 0, 0, 1]]}, {[[3, 4, 5, 2, 1], [0, 0, 0, 1]]}, {[[5, 4, 1, 2, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 2, 5, 4, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {}, {}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 4, 3, 5], {2, 3}, {}], [[1, 2, 5, 3, 4], {2, 3}, {}], [[1, 2, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 4, 2], {2, 3, 4}, {}], [[2, 3, 5, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37874, 332696, 3240416, 34657116, 403773512, 5089835936, 69021919224, 1001903928804, 15500138755224, 254598918643168, 4425046557089424, 81134570778122256, 1565095717271557536] "" "Class ", 94, " is:" {{[[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[5, 4, 1, 2, 3], [1, 0, 0, 1]]}} {[[1, 2, 5, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1, 4, 5], [1, 0, 0, 1]]}, {[[3, 4, 5, 2, 1], [1, 0, 0, 1]]}, {[[5, 4, 1, 2, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 2, 5, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4744, 36292, 308712, 2886402, 29393260, 323591088, 3827558510, 48390344564, 650977968568, 9282414304672, 139819244502621, 2218089634202168, 36960165887099814, 645337858836147504] "" "Class ", 95, " is:" {{[[1, 2, 5, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 1, 4, 5], [0, 1, 0, 1]]}, {[[3, 4, 5, 2, 1], [0, 1, 0, 1]]}, {[[5, 4, 1, 2, 3], [1, 0, 1, 0]]}} {[[1, 2, 5, 4, 3], [1, 0, 1, 0]]} {[[3, 2, 1, 4, 5], [0, 1, 0, 1]]} "Class ", 96, " is:" {{[[1, 2, 5, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1, 4, 5], [1, 1, 0, 1]]}, {[[3, 4, 5, 2, 1], [1, 1, 0, 1]]}, {[[5, 4, 1, 2, 3], [1, 0, 1, 1]]}} {[[1, 2, 5, 4, 3], [1, 0, 1, 1]]} {[[3, 2, 1, 4, 5], [1, 1, 0, 1]]} "Class ", 97, " is:" {{[[1, 2, 5, 4, 3], [1, 1, 0, 0]]}, {[[3, 2, 1, 4, 5], [0, 0, 1, 1]]}, {[[3, 4, 5, 2, 1], [0, 0, 1, 1]]}, {[[5, 4, 1, 2, 3], [1, 1, 0, 0]]}} {[[1, 2, 5, 4, 3], [1, 1, 0, 0]]} {[[3, 2, 1, 4, 5], [0, 0, 1, 1]]} "Class ", 98, " is:" {{[[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[5, 4, 1, 2, 3], [1, 1, 0, 1]]}} {[[1, 2, 5, 4, 3], [1, 1, 0, 1]]} "For the class ", {{[[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1, 4, 5], [1, 0, 1, 1]]}, {[[3, 4, 5, 2, 1], [1, 0, 1, 1]]}, {[[5, 4, 1, 2, 3], [1, 1, 0, 1]]}}, " the pattern set ", {[[1, 2, 5, 4, 3], [1, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {}, {}], [[1, 2, 3, 4], {3}, {}], [[1, 2, 4, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 1, 4], {}, {}], [[2, 3, 4, 1], {3}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {3}, {}], [[2, 3, 1, 4, 5], {4}, {}], [[2, 3, 1, 5, 4], {1, 2, 4}, {[0, 0, 0, 1, 0, 0]}], [[2, 4, 1, 5, 3], {1, 2, 4}, {}], [[3, 4, 1, 5, 2], {1, 2, 4}, {}], [[3, 4, 2, 5, 1], {3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 697, 4667, 34914, 287021, 2560927, 24564432, 251402043, 2728595190, 31249318461, 376054861780, 4738323819153, 62320719361124, 853336550119565, 12136026469900249, 178898287711657242] "" "Class ", 99, " is:" {{[[1, 2, 5, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1, 4, 5], [0, 1, 1, 1]]}, {[[3, 4, 5, 2, 1], [0, 1, 1, 1]]}, {[[5, 4, 1, 2, 3], [1, 1, 1, 0]]}} {[[1, 2, 5, 4, 3], [1, 1, 1, 0]]} {[[3, 2, 1, 4, 5], [0, 1, 1, 1]]} "Class ", 100, " is:" {{[[1, 2, 5, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1, 4, 5], [1, 1, 1, 1]]}, {[[3, 4, 5, 2, 1], [1, 1, 1, 1]]}, {[[5, 4, 1, 2, 3], [1, 1, 1, 1]]}} {[[1, 2, 5, 4, 3], [1, 1, 1, 1]]} {[[3, 2, 1, 4, 5], [1, 1, 1, 1]]} "Class ", 101, " is:" {{[[1, 3, 2, 5, 4], [0, 0, 0, 0]]}, {[[2, 1, 4, 3, 5], [0, 0, 0, 0]]}, {[[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[5, 3, 4, 1, 2], [0, 0, 0, 0]]}} {[[1, 3, 2, 5, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 2, 5, 4], [0, 0, 0, 0]]}, {[[2, 1, 4, 3, 5], [0, 0, 0, 0]]}, {[[4, 5, 2, 3, 1], [0, 0, 0, 0]]}, {[[5, 3, 4, 1, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 5, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3}, {}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {1, 2}, {}], [[1, 4, 3, 5, 2], {1, 2, 3, 4}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4915, 38992, 347980, 3450572, 37637545, 447857256, 5773243451, 80146549212, 1192100892680, 18913413488544, 318827489139059, 5690693361661052, 107215038571876213, 2126290615269312536] "" "Class ", 102, " is:" {{[[1, 3, 2, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 4, 3, 5], [1, 0, 0, 0]]}, {[[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[5, 3, 4, 1, 2], [0, 0, 0, 1]]}} {[[1, 3, 2, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 2, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 4, 3, 5], [1, 0, 0, 0]]}, {[[4, 5, 2, 3, 1], [1, 0, 0, 0]]}, {[[5, 3, 4, 1, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4839, 37888, 332873, 3242738, 34689337, 404248858, 5097276735, 69145058260, 1004051134836, 15539476098372, 255354244279852, 4440215626923370, 81452615929265326, 1572046216677522286] "" "Class ", 103, " is:" {{[[1, 3, 2, 5, 4], [0, 0, 1, 0]]}, {[[2, 1, 4, 3, 5], [0, 1, 0, 0]]}, {[[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[5, 3, 4, 1, 2], [0, 0, 1, 0]]}} {[[1, 3, 2, 5, 4], [0, 0, 1, 0]]} {[[2, 1, 4, 3, 5], [0, 1, 0, 0]]} "For the class ", {{[[1, 3, 2, 5, 4], [0, 0, 1, 0]]}, {[[2, 1, 4, 3, 5], [0, 1, 0, 0]]}, {[[4, 5, 2, 3, 1], [0, 1, 0, 0]]}, {[[5, 3, 4, 1, 2], [0, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 4, 3, 5], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[2, 1, 4, 3, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 3, 4], {3, 4}, {}], [[2, 1, 5, 4, 3], {3}, {}], [[3, 1, 5, 4, 2], {2, 3, 4}, {}], [[3, 2, 5, 4, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 703, 4817, 37534, 327599, 3164891, 33519051, 386090952, 4804566545, 64226920247, 917805091675, 13960498198182, 225185003512111, 3839042851786987, 68970587034336831, 1302286587667567976] "" "Class ", 104, " is:" {{[[1, 3, 2, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 4, 3, 5], [1, 1, 0, 0]]}, {[[4, 5, 2, 3, 1], [1, 1, 0, 0]]}, {[[5, 3, 4, 1, 2], [0, 0, 1, 1]]}} {[[1, 3, 2, 5, 4], [0, 0, 1, 1]]} {[[2, 1, 4, 3, 5], [1, 1, 0, 0]]} "Class ", 105, " is:" {{[[1, 3, 2, 5, 4], [0, 1, 0, 0]]}, {[[2, 1, 4, 3, 5], [0, 0, 1, 0]]}, {[[4, 5, 2, 3, 1], [0, 0, 1, 0]]}, {[[5, 3, 4, 1, 2], [0, 1, 0, 0]]}} {[[1, 3, 2, 5, 4], [0, 1, 0, 0]]} {[[2, 1, 4, 3, 5], [0, 0, 1, 0]]} "Class ", 106, " is:" {{[[1, 3, 2, 5, 4], [0, 1, 0, 1]]}, {[[2, 1, 4, 3, 5], [1, 0, 1, 0]]}, {[[4, 5, 2, 3, 1], [1, 0, 1, 0]]}, {[[5, 3, 4, 1, 2], [0, 1, 0, 1]]}} {[[1, 3, 2, 5, 4], [0, 1, 0, 1]]} {[[2, 1, 4, 3, 5], [1, 0, 1, 0]]} "Class ", 107, " is:" {{[[1, 3, 2, 5, 4], [0, 1, 1, 0]]}, {[[2, 1, 4, 3, 5], [0, 1, 1, 0]]}, {[[4, 5, 2, 3, 1], [0, 1, 1, 0]]}, {[[5, 3, 4, 1, 2], [0, 1, 1, 0]]}} {[[1, 3, 2, 5, 4], [0, 1, 1, 0]]} {[[2, 1, 4, 3, 5], [0, 1, 1, 0]]} "Class ", 108, " is:" {{[[1, 3, 2, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 4, 3, 5], [1, 1, 1, 0]]}, {[[4, 5, 2, 3, 1], [1, 1, 1, 0]]}, {[[5, 3, 4, 1, 2], [0, 1, 1, 1]]}} {[[1, 3, 2, 5, 4], [0, 1, 1, 1]]} {[[2, 1, 4, 3, 5], [1, 1, 1, 0]]} "Class ", 109, " is:" {{[[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, {[[2, 1, 4, 3, 5], [0, 0, 0, 1]]}, {[[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[5, 3, 4, 1, 2], [1, 0, 0, 0]]}} {[[1, 3, 2, 5, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, {[[2, 1, 4, 3, 5], [0, 0, 0, 1]]}, {[[4, 5, 2, 3, 1], [0, 0, 0, 1]]}, {[[5, 3, 4, 1, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 2, 5, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {2, 3, 4}, {}], [[1, 3, 2, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4839, 37895, 333036, 3245568, 34734865, 404972789, 5108976367, 69339875102, 1007416328328, 15599977305688, 256487971024811, 4462366668225250, 81903744063787789, 1581616945528988403] "" "Class ", 110, " is:" {{[[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, {[[2, 1, 4, 3, 5], [1, 0, 0, 1]]}, {[[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[5, 3, 4, 1, 2], [1, 0, 0, 1]]}} {[[1, 3, 2, 5, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, {[[2, 1, 4, 3, 5], [1, 0, 0, 1]]}, {[[4, 5, 2, 3, 1], [1, 0, 0, 1]]}, {[[5, 3, 4, 1, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 2, 5, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 0, 1, 0]}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4745, 36316, 309125, 2892742, 29487053, 324975992, 3848338570, 48710309440, 656061287952, 9365988775080, 141243339052717, 2243255588816608, 37421405085853269, 654102896643897068] "" "Class ", 111, " is:" {{[[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[5, 3, 4, 1, 2], [1, 0, 1, 0]]}} {[[1, 3, 2, 5, 4], [1, 0, 1, 0]]} {[[2, 1, 4, 3, 5], [0, 1, 0, 1]]} "For the class ", {{[[1, 3, 2, 5, 4], [1, 0, 1, 0]]}, {[[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, {[[4, 5, 2, 3, 1], [0, 1, 0, 1]]}, {[[5, 3, 4, 1, 2], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 4, 3, 5], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 0, 1]}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4745, 36310, 308919, 2887980, 29392211, 323201330, 3815857732, 48116262912, 645071086840, 9158805860008, 137245734060145, 2164092026050332, 35809882818819669, 620348584920591806] "" "Class ", 112, " is:" {{[[1, 3, 2, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 4, 3, 5], [1, 1, 0, 1]]}, {[[4, 5, 2, 3, 1], [1, 1, 0, 1]]}, {[[5, 3, 4, 1, 2], [1, 0, 1, 1]]}} {[[1, 3, 2, 5, 4], [1, 0, 1, 1]]} {[[2, 1, 4, 3, 5], [1, 1, 0, 1]]} "Class ", 113, " is:" {{[[1, 3, 2, 5, 4], [1, 1, 0, 0]]}, {[[2, 1, 4, 3, 5], [0, 0, 1, 1]]}, {[[4, 5, 2, 3, 1], [0, 0, 1, 1]]}, {[[5, 3, 4, 1, 2], [1, 1, 0, 0]]}} {[[1, 3, 2, 5, 4], [1, 1, 0, 0]]} {[[2, 1, 4, 3, 5], [0, 0, 1, 1]]} "Class ", 114, " is:" {{[[1, 3, 2, 5, 4], [1, 1, 0, 1]]}, {[[2, 1, 4, 3, 5], [1, 0, 1, 1]]}, {[[4, 5, 2, 3, 1], [1, 0, 1, 1]]}, {[[5, 3, 4, 1, 2], [1, 1, 0, 1]]}} {[[1, 3, 2, 5, 4], [1, 1, 0, 1]]} {[[2, 1, 4, 3, 5], [1, 0, 1, 1]]} "Class ", 115, " is:" {{[[1, 3, 2, 5, 4], [1, 1, 1, 0]]}, {[[2, 1, 4, 3, 5], [0, 1, 1, 1]]}, {[[4, 5, 2, 3, 1], [0, 1, 1, 1]]}, {[[5, 3, 4, 1, 2], [1, 1, 1, 0]]}} {[[1, 3, 2, 5, 4], [1, 1, 1, 0]]} {[[2, 1, 4, 3, 5], [0, 1, 1, 1]]} "Class ", 116, " is:" {{[[1, 3, 2, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 4, 3, 5], [1, 1, 1, 1]]}, {[[4, 5, 2, 3, 1], [1, 1, 1, 1]]}, {[[5, 3, 4, 1, 2], [1, 1, 1, 1]]}} {[[1, 3, 2, 5, 4], [1, 1, 1, 1]]} {[[2, 1, 4, 3, 5], [1, 1, 1, 1]]} "Class ", 117, " is:" {{[[1, 3, 4, 2, 5], [0, 0, 0, 0]]}, {[[1, 4, 2, 3, 5], [0, 0, 0, 0]]}, {[[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, {[[5, 3, 2, 4, 1], [0, 0, 0, 0]]}} {[[1, 3, 4, 2, 5], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2, 5], [0, 0, 0, 0]]}, {[[1, 4, 2, 3, 5], [0, 0, 0, 0]]}, {[[5, 2, 4, 3, 1], [0, 0, 0, 0]]}, {[[5, 3, 2, 4, 1], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2, 5], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {1, 2, 3}, {}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {1, 2, 3, 4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38979, 347815, 3448442, 37608834, 447450930, 5767170785, 80050654711, 1190502148797, 18885313699983, 318307710883720, 5680593325882836, 107009253612595865, 2121902210596869336] "" "Class ", 118, " is:" {{[[1, 3, 4, 2, 5], [0, 0, 0, 1]]}, {[[1, 4, 2, 3, 5], [1, 0, 0, 0]]}, {[[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, {[[5, 3, 2, 4, 1], [0, 0, 0, 1]]}} {[[1, 3, 4, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2, 5], [0, 0, 0, 1]]}, {[[1, 4, 2, 3, 5], [1, 0, 0, 0]]}, {[[5, 2, 4, 3, 1], [1, 0, 0, 0]]}, {[[5, 3, 2, 4, 1], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37874, 332696, 3240416, 34657116, 403773512, 5089835936, 69021919224, 1001903928804, 15500138755224, 254598918643168, 4425046557089424, 81134570778122256, 1565095717271557536] "" "Class ", 119, " is:" {{[[1, 3, 4, 2, 5], [0, 0, 1, 0]]}, {[[1, 4, 2, 3, 5], [0, 1, 0, 0]]}, {[[5, 2, 4, 3, 1], [0, 1, 0, 0]]}, {[[5, 3, 2, 4, 1], [0, 0, 1, 0]]}} {[[1, 3, 4, 2, 5], [0, 0, 1, 0]]} {[[1, 4, 2, 3, 5], [0, 1, 0, 0]]} "Class ", 120, " is:" {{[[1, 3, 4, 2, 5], [0, 0, 1, 1]]}, {[[1, 4, 2, 3, 5], [1, 1, 0, 0]]}, {[[5, 2, 4, 3, 1], [1, 1, 0, 0]]}, {[[5, 3, 2, 4, 1], [0, 0, 1, 1]]}} {[[1, 3, 4, 2, 5], [0, 0, 1, 1]]} {[[1, 4, 2, 3, 5], [1, 1, 0, 0]]} "Class ", 121, " is:" {{[[1, 3, 4, 2, 5], [0, 1, 0, 0]]}, {[[1, 4, 2, 3, 5], [0, 0, 1, 0]]}, {[[5, 2, 4, 3, 1], [0, 0, 1, 0]]}, {[[5, 3, 2, 4, 1], [0, 1, 0, 0]]}} {[[1, 3, 4, 2, 5], [0, 1, 0, 0]]} {[[1, 4, 2, 3, 5], [0, 0, 1, 0]]} "Class ", 122, " is:" {{[[1, 3, 4, 2, 5], [0, 1, 0, 1]]}, {[[1, 4, 2, 3, 5], [1, 0, 1, 0]]}, {[[5, 2, 4, 3, 1], [1, 0, 1, 0]]}, {[[5, 3, 2, 4, 1], [0, 1, 0, 1]]}} {[[1, 3, 4, 2, 5], [0, 1, 0, 1]]} {[[1, 4, 2, 3, 5], [1, 0, 1, 0]]} "Class ", 123, " is:" {{[[1, 3, 4, 2, 5], [0, 1, 1, 0]]}, {[[1, 4, 2, 3, 5], [0, 1, 1, 0]]}, {[[5, 2, 4, 3, 1], [0, 1, 1, 0]]}, {[[5, 3, 2, 4, 1], [0, 1, 1, 0]]}} {[[1, 3, 4, 2, 5], [0, 1, 1, 0]]} {[[1, 4, 2, 3, 5], [0, 1, 1, 0]]} "Class ", 124, " is:" {{[[1, 3, 4, 2, 5], [0, 1, 1, 1]]}, {[[1, 4, 2, 3, 5], [1, 1, 1, 0]]}, {[[5, 2, 4, 3, 1], [1, 1, 1, 0]]}, {[[5, 3, 2, 4, 1], [0, 1, 1, 1]]}} {[[1, 3, 4, 2, 5], [0, 1, 1, 1]]} {[[1, 4, 2, 3, 5], [1, 1, 1, 0]]} "Class ", 125, " is:" {{[[1, 3, 4, 2, 5], [1, 0, 0, 0]]}, {[[1, 4, 2, 3, 5], [0, 0, 0, 1]]}, {[[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[5, 3, 2, 4, 1], [1, 0, 0, 0]]}} {[[1, 3, 4, 2, 5], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 4, 2, 5], [1, 0, 0, 0]]}, {[[1, 4, 2, 3, 5], [0, 0, 0, 1]]}, {[[5, 2, 4, 3, 1], [0, 0, 0, 1]]}, {[[5, 3, 2, 4, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 2, 5], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2, 3}, {}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {2, 3, 4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4839, 37890, 332911, 3243252, 34695475, 404314543, 5097846976, 69146743589, 1003951140459, 15535452873197, 255238810253701, 4437207990186150, 81376613057795459, 1570132210422810657] "" "Class ", 126, " is:" {{[[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, {[[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[5, 3, 2, 4, 1], [1, 0, 0, 1]]}} {[[1, 3, 4, 2, 5], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, {[[1, 4, 2, 3, 5], [1, 0, 0, 1]]}, {[[5, 2, 4, 3, 1], [1, 0, 0, 1]]}, {[[5, 3, 2, 4, 1], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 2, 5], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2, 3}, {}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 0, 1]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4747, 36368, 310075, 2908152, 29727309, 328706824, 3907096334, 49658121296, 671806789486, 9636188879148, 146040655162497, 2331441700773988, 39100039578607877, 687183928229131712] "" "Class ", 127, " is:" {{[[1, 3, 4, 2, 5], [1, 0, 1, 0]]}, {[[1, 4, 2, 3, 5], [0, 1, 0, 1]]}, {[[5, 2, 4, 3, 1], [0, 1, 0, 1]]}, {[[5, 3, 2, 4, 1], [1, 0, 1, 0]]}} {[[1, 3, 4, 2, 5], [1, 0, 1, 0]]} {[[1, 4, 2, 3, 5], [0, 1, 0, 1]]} "Class ", 128, " is:" {{[[1, 3, 4, 2, 5], [1, 0, 1, 1]]}, {[[1, 4, 2, 3, 5], [1, 1, 0, 1]]}, {[[5, 2, 4, 3, 1], [1, 1, 0, 1]]}, {[[5, 3, 2, 4, 1], [1, 0, 1, 1]]}} {[[1, 3, 4, 2, 5], [1, 0, 1, 1]]} {[[1, 4, 2, 3, 5], [1, 1, 0, 1]]} "Class ", 129, " is:" {{[[1, 3, 4, 2, 5], [1, 1, 0, 0]]}, {[[1, 4, 2, 3, 5], [0, 0, 1, 1]]}, {[[5, 2, 4, 3, 1], [0, 0, 1, 1]]}, {[[5, 3, 2, 4, 1], [1, 1, 0, 0]]}} {[[1, 3, 4, 2, 5], [1, 1, 0, 0]]} {[[1, 4, 2, 3, 5], [0, 0, 1, 1]]} "Class ", 130, " is:" {{[[1, 3, 4, 2, 5], [1, 1, 0, 1]]}, {[[1, 4, 2, 3, 5], [1, 0, 1, 1]]}, {[[5, 2, 4, 3, 1], [1, 0, 1, 1]]}, {[[5, 3, 2, 4, 1], [1, 1, 0, 1]]}} {[[1, 3, 4, 2, 5], [1, 1, 0, 1]]} {[[1, 4, 2, 3, 5], [1, 0, 1, 1]]} "Class ", 131, " is:" {{[[1, 3, 4, 2, 5], [1, 1, 1, 0]]}, {[[1, 4, 2, 3, 5], [0, 1, 1, 1]]}, {[[5, 2, 4, 3, 1], [0, 1, 1, 1]]}, {[[5, 3, 2, 4, 1], [1, 1, 1, 0]]}} {[[1, 3, 4, 2, 5], [1, 1, 1, 0]]} {[[1, 4, 2, 3, 5], [0, 1, 1, 1]]} "Class ", 132, " is:" {{[[1, 3, 4, 2, 5], [1, 1, 1, 1]]}, {[[1, 4, 2, 3, 5], [1, 1, 1, 1]]}, {[[5, 2, 4, 3, 1], [1, 1, 1, 1]]}, {[[5, 3, 2, 4, 1], [1, 1, 1, 1]]}} {[[1, 3, 4, 2, 5], [1, 1, 1, 1]]} {[[1, 4, 2, 3, 5], [1, 1, 1, 1]]} "Class ", 133, " is:" {{[[1, 3, 4, 5, 2], [0, 0, 0, 0]]}, {[[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, {[[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[5, 3, 2, 1, 4], [0, 0, 0, 0]]}} {[[1, 3, 4, 5, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 4, 5, 2], [0, 0, 0, 0]]}, {[[2, 5, 4, 3, 1], [0, 0, 0, 0]]}, {[[4, 1, 2, 3, 5], [0, 0, 0, 0]]}, {[[5, 3, 2, 1, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 5, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {1}, {}], [[1, 2, 3, 5, 4], {1, 2, 3, 4}, {}], [[1, 2, 4, 5, 3], {1, 2, 3, 4}, {}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38976, 347795, 3448312, 37608186, 447452544, 5767315785, 80054392880, 1190583423414, 18887010379776, 318343175603145, 5681348801115680, 107025793890636390, 2122275973981599744] "" "Class ", 134, " is:" {{[[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, {[[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[5, 3, 2, 1, 4], [0, 0, 0, 1]]}} {[[1, 3, 4, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, {[[2, 5, 4, 3, 1], [1, 0, 0, 0]]}, {[[4, 1, 2, 3, 5], [1, 0, 0, 0]]}, {[[5, 3, 2, 1, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4840, 37918, 333474, 3253240, 34865094, 407182648, 5147117981, 70016168040, 1019805996877, 15835244743270, 261126262127666, 4557371584964216, 83925642544448426, 1626312397622715570] "" "Class ", 135, " is:" {{[[1, 3, 4, 5, 2], [0, 0, 1, 0]]}, {[[2, 5, 4, 3, 1], [0, 1, 0, 0]]}, {[[4, 1, 2, 3, 5], [0, 1, 0, 0]]}, {[[5, 3, 2, 1, 4], [0, 0, 1, 0]]}} {[[1, 3, 4, 5, 2], [0, 0, 1, 0]]} {[[2, 5, 4, 3, 1], [0, 1, 0, 0]]} "Class ", 136, " is:" {{[[1, 3, 4, 5, 2], [0, 0, 1, 1]]}, {[[2, 5, 4, 3, 1], [1, 1, 0, 0]]}, {[[4, 1, 2, 3, 5], [1, 1, 0, 0]]}, {[[5, 3, 2, 1, 4], [0, 0, 1, 1]]}} {[[1, 3, 4, 5, 2], [0, 0, 1, 1]]} {[[2, 5, 4, 3, 1], [1, 1, 0, 0]]} "Class ", 137, " is:" {{[[1, 3, 4, 5, 2], [0, 1, 0, 0]]}, {[[2, 5, 4, 3, 1], [0, 0, 1, 0]]}, {[[4, 1, 2, 3, 5], [0, 0, 1, 0]]}, {[[5, 3, 2, 1, 4], [0, 1, 0, 0]]}} {[[1, 3, 4, 5, 2], [0, 1, 0, 0]]} {[[2, 5, 4, 3, 1], [0, 0, 1, 0]]} "Class ", 138, " is:" {{[[1, 3, 4, 5, 2], [0, 1, 0, 1]]}, {[[2, 5, 4, 3, 1], [1, 0, 1, 0]]}, {[[4, 1, 2, 3, 5], [1, 0, 1, 0]]}, {[[5, 3, 2, 1, 4], [0, 1, 0, 1]]}} {[[1, 3, 4, 5, 2], [0, 1, 0, 1]]} {[[2, 5, 4, 3, 1], [1, 0, 1, 0]]} "Class ", 139, " is:" {{[[1, 3, 4, 5, 2], [0, 1, 1, 0]]}, {[[2, 5, 4, 3, 1], [0, 1, 1, 0]]}, {[[4, 1, 2, 3, 5], [0, 1, 1, 0]]}, {[[5, 3, 2, 1, 4], [0, 1, 1, 0]]}} {[[1, 3, 4, 5, 2], [0, 1, 1, 0]]} {[[2, 5, 4, 3, 1], [0, 1, 1, 0]]} "Class ", 140, " is:" {{[[1, 3, 4, 5, 2], [0, 1, 1, 1]]}, {[[2, 5, 4, 3, 1], [1, 1, 1, 0]]}, {[[4, 1, 2, 3, 5], [1, 1, 1, 0]]}, {[[5, 3, 2, 1, 4], [0, 1, 1, 1]]}} {[[1, 3, 4, 5, 2], [0, 1, 1, 1]]} {[[2, 5, 4, 3, 1], [1, 1, 1, 0]]} "Class ", 141, " is:" {{[[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, {[[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[5, 3, 2, 1, 4], [1, 0, 0, 0]]}} {[[1, 3, 4, 5, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, {[[2, 5, 4, 3, 1], [0, 0, 0, 1]]}, {[[4, 1, 2, 3, 5], [0, 0, 0, 1]]}, {[[5, 3, 2, 1, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 4, 5, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {}, {}], [[1, 2, 4, 3], {2, 3}, {}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 3, 4, 5], {2}, {}], [[1, 2, 3, 5, 4], {2, 3, 4}, {}], [[1, 2, 4, 5, 3], {2, 3, 4}, {}], [[1, 3, 4, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 4, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37874, 332696, 3240416, 34657116, 403773512, 5089835936, 69021919224, 1001903928804, 15500138755224, 254598918643168, 4425046557089424, 81134570778122256, 1565095717271557536] "" "Class ", 142, " is:" {{[[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[5, 3, 2, 1, 4], [1, 0, 0, 1]]}} {[[1, 3, 4, 5, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, {[[2, 5, 4, 3, 1], [1, 0, 0, 1]]}, {[[4, 1, 2, 3, 5], [1, 0, 0, 1]]}, {[[5, 3, 2, 1, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 4, 5, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {[0, 1, 0, 0, 0]}], [[1, 2, 4, 3], {2, 3}, {}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 701, 4768, 36699, 314873, 2976594, 30716173, 343381013, 4132329885, 53246591294, 731247853656, 10660411248600, 164396895171652, 2673453999718142, 45720042117632633, 820188876576377955] "" "Class ", 143, " is:" {{[[1, 3, 4, 5, 2], [1, 0, 1, 0]]}, {[[2, 5, 4, 3, 1], [0, 1, 0, 1]]}, {[[4, 1, 2, 3, 5], [0, 1, 0, 1]]}, {[[5, 3, 2, 1, 4], [1, 0, 1, 0]]}} {[[1, 3, 4, 5, 2], [1, 0, 1, 0]]} {[[2, 5, 4, 3, 1], [0, 1, 0, 1]]} "Class ", 144, " is:" {{[[1, 3, 4, 5, 2], [1, 0, 1, 1]]}, {[[2, 5, 4, 3, 1], [1, 1, 0, 1]]}, {[[4, 1, 2, 3, 5], [1, 1, 0, 1]]}, {[[5, 3, 2, 1, 4], [1, 0, 1, 1]]}} {[[1, 3, 4, 5, 2], [1, 0, 1, 1]]} {[[2, 5, 4, 3, 1], [1, 1, 0, 1]]} "Class ", 145, " is:" {{[[1, 3, 4, 5, 2], [1, 1, 0, 0]]}, {[[2, 5, 4, 3, 1], [0, 0, 1, 1]]}, {[[4, 1, 2, 3, 5], [0, 0, 1, 1]]}, {[[5, 3, 2, 1, 4], [1, 1, 0, 0]]}} {[[1, 3, 4, 5, 2], [1, 1, 0, 0]]} {[[2, 5, 4, 3, 1], [0, 0, 1, 1]]} "Class ", 146, " is:" {{[[1, 3, 4, 5, 2], [1, 1, 0, 1]]}, {[[2, 5, 4, 3, 1], [1, 0, 1, 1]]}, {[[4, 1, 2, 3, 5], [1, 0, 1, 1]]}, {[[5, 3, 2, 1, 4], [1, 1, 0, 1]]}} {[[1, 3, 4, 5, 2], [1, 1, 0, 1]]} {[[2, 5, 4, 3, 1], [1, 0, 1, 1]]} "Class ", 147, " is:" {{[[1, 3, 4, 5, 2], [1, 1, 1, 0]]}, {[[2, 5, 4, 3, 1], [0, 1, 1, 1]]}, {[[4, 1, 2, 3, 5], [0, 1, 1, 1]]}, {[[5, 3, 2, 1, 4], [1, 1, 1, 0]]}} {[[1, 3, 4, 5, 2], [1, 1, 1, 0]]} {[[2, 5, 4, 3, 1], [0, 1, 1, 1]]} "Class ", 148, " is:" {{[[1, 3, 5, 2, 4], [0, 0, 0, 0]]}, {[[2, 4, 1, 3, 5], [0, 0, 0, 0]]}, {[[4, 2, 5, 3, 1], [0, 0, 0, 0]]}, {[[5, 3, 1, 4, 2], [0, 0, 0, 0]]}} {[[1, 3, 5, 2, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 5, 2, 4], [0, 0, 0, 0]]}, {[[2, 4, 1, 3, 5], [0, 0, 0, 0]]}, {[[4, 2, 5, 3, 1], [0, 0, 0, 0]]}, {[[5, 3, 1, 4, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 5, 2, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3}, {}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {1, 2, 3, 4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38982, 347873, 3449332, 37621965, 447648482, 5770250935, 80100822074, 1191358479790, 18900647287550, 318595643201902, 5686258136269396, 107125880782919395, 2124411456922993308] "" "Class ", 149, " is:" {{[[1, 3, 5, 2, 4], [0, 0, 0, 1]]}, {[[2, 4, 1, 3, 5], [1, 0, 0, 0]]}, {[[4, 2, 5, 3, 1], [1, 0, 0, 0]]}, {[[5, 3, 1, 4, 2], [0, 0, 0, 1]]}} {[[1, 3, 5, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 5, 2, 4], [0, 0, 0, 1]]}, {[[2, 4, 1, 3, 5], [1, 0, 0, 0]]}, {[[4, 2, 5, 3, 1], [1, 0, 0, 0]]}, {[[5, 3, 1, 4, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 5, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37874, 332696, 3240416, 34657116, 403773512, 5089835936, 69021919224, 1001903928804, 15500138755224, 254598918643168, 4425046557089424, 81134570778122256, 1565095717271557536] "" "Class ", 150, " is:" {{[[1, 3, 5, 2, 4], [0, 0, 1, 0]]}, {[[2, 4, 1, 3, 5], [0, 1, 0, 0]]}, {[[4, 2, 5, 3, 1], [0, 1, 0, 0]]}, {[[5, 3, 1, 4, 2], [0, 0, 1, 0]]}} {[[1, 3, 5, 2, 4], [0, 0, 1, 0]]} {[[2, 4, 1, 3, 5], [0, 1, 0, 0]]} "Class ", 151, " is:" {{[[1, 3, 5, 2, 4], [0, 0, 1, 1]]}, {[[2, 4, 1, 3, 5], [1, 1, 0, 0]]}, {[[4, 2, 5, 3, 1], [1, 1, 0, 0]]}, {[[5, 3, 1, 4, 2], [0, 0, 1, 1]]}} {[[1, 3, 5, 2, 4], [0, 0, 1, 1]]} {[[2, 4, 1, 3, 5], [1, 1, 0, 0]]} "Class ", 152, " is:" {{[[1, 3, 5, 2, 4], [0, 1, 0, 0]]}, {[[2, 4, 1, 3, 5], [0, 0, 1, 0]]}, {[[4, 2, 5, 3, 1], [0, 0, 1, 0]]}, {[[5, 3, 1, 4, 2], [0, 1, 0, 0]]}} {[[1, 3, 5, 2, 4], [0, 1, 0, 0]]} {[[2, 4, 1, 3, 5], [0, 0, 1, 0]]} "Class ", 153, " is:" {{[[1, 3, 5, 2, 4], [0, 1, 0, 1]]}, {[[2, 4, 1, 3, 5], [1, 0, 1, 0]]}, {[[4, 2, 5, 3, 1], [1, 0, 1, 0]]}, {[[5, 3, 1, 4, 2], [0, 1, 0, 1]]}} {[[1, 3, 5, 2, 4], [0, 1, 0, 1]]} {[[2, 4, 1, 3, 5], [1, 0, 1, 0]]} "Class ", 154, " is:" {{[[1, 3, 5, 2, 4], [0, 1, 1, 0]]}, {[[2, 4, 1, 3, 5], [0, 1, 1, 0]]}, {[[4, 2, 5, 3, 1], [0, 1, 1, 0]]}, {[[5, 3, 1, 4, 2], [0, 1, 1, 0]]}} {[[1, 3, 5, 2, 4], [0, 1, 1, 0]]} {[[2, 4, 1, 3, 5], [0, 1, 1, 0]]} "Class ", 155, " is:" {{[[1, 3, 5, 2, 4], [0, 1, 1, 1]]}, {[[2, 4, 1, 3, 5], [1, 1, 1, 0]]}, {[[4, 2, 5, 3, 1], [1, 1, 1, 0]]}, {[[5, 3, 1, 4, 2], [0, 1, 1, 1]]}} {[[1, 3, 5, 2, 4], [0, 1, 1, 1]]} {[[2, 4, 1, 3, 5], [1, 1, 1, 0]]} "Class ", 156, " is:" {{[[1, 3, 5, 2, 4], [1, 0, 0, 0]]}, {[[2, 4, 1, 3, 5], [0, 0, 0, 1]]}, {[[4, 2, 5, 3, 1], [0, 0, 0, 1]]}, {[[5, 3, 1, 4, 2], [1, 0, 0, 0]]}} {[[1, 3, 5, 2, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 5, 2, 4], [1, 0, 0, 0]]}, {[[2, 4, 1, 3, 5], [0, 0, 0, 1]]}, {[[4, 2, 5, 3, 1], [0, 0, 0, 1]]}, {[[5, 3, 1, 4, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 5, 2, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2, 3}, {}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {2, 3, 4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4840, 37917, 333398, 3251054, 34817364, 406240436, 5129138453, 69673817902, 1013191590724, 15704362165226, 258459713943091, 4501267003500612, 82704604695806956, 1598803929052608790] "" "Class ", 157, " is:" {{[[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, {[[2, 4, 1, 3, 5], [1, 0, 0, 1]]}, {[[4, 2, 5, 3, 1], [1, 0, 0, 1]]}, {[[5, 3, 1, 4, 2], [1, 0, 0, 1]]}} {[[1, 3, 5, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, {[[2, 4, 1, 3, 5], [1, 0, 0, 1]]}, {[[4, 2, 5, 3, 1], [1, 0, 0, 1]]}, {[[5, 3, 1, 4, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 5, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2, 3}, {}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 0, 1, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4747, 36368, 310075, 2908152, 29727309, 328706824, 3907096334, 49658121296, 671806789486, 9636188879148, 146040655162497, 2331441700773988, 39100039578607877, 687183928229131712] "" "Class ", 158, " is:" {{[[1, 3, 5, 2, 4], [1, 0, 1, 0]]}, {[[2, 4, 1, 3, 5], [0, 1, 0, 1]]}, {[[4, 2, 5, 3, 1], [0, 1, 0, 1]]}, {[[5, 3, 1, 4, 2], [1, 0, 1, 0]]}} {[[1, 3, 5, 2, 4], [1, 0, 1, 0]]} {[[2, 4, 1, 3, 5], [0, 1, 0, 1]]} "Class ", 159, " is:" {{[[1, 3, 5, 2, 4], [1, 0, 1, 1]]}, {[[2, 4, 1, 3, 5], [1, 1, 0, 1]]}, {[[4, 2, 5, 3, 1], [1, 1, 0, 1]]}, {[[5, 3, 1, 4, 2], [1, 0, 1, 1]]}} {[[1, 3, 5, 2, 4], [1, 0, 1, 1]]} {[[2, 4, 1, 3, 5], [1, 1, 0, 1]]} "Class ", 160, " is:" {{[[1, 3, 5, 2, 4], [1, 1, 0, 0]]}, {[[2, 4, 1, 3, 5], [0, 0, 1, 1]]}, {[[4, 2, 5, 3, 1], [0, 0, 1, 1]]}, {[[5, 3, 1, 4, 2], [1, 1, 0, 0]]}} {[[1, 3, 5, 2, 4], [1, 1, 0, 0]]} {[[2, 4, 1, 3, 5], [0, 0, 1, 1]]} "Class ", 161, " is:" {{[[1, 3, 5, 2, 4], [1, 1, 0, 1]]}, {[[2, 4, 1, 3, 5], [1, 0, 1, 1]]}, {[[4, 2, 5, 3, 1], [1, 0, 1, 1]]}, {[[5, 3, 1, 4, 2], [1, 1, 0, 1]]}} {[[1, 3, 5, 2, 4], [1, 1, 0, 1]]} {[[2, 4, 1, 3, 5], [1, 0, 1, 1]]} "Class ", 162, " is:" {{[[1, 3, 5, 2, 4], [1, 1, 1, 0]]}, {[[2, 4, 1, 3, 5], [0, 1, 1, 1]]}, {[[4, 2, 5, 3, 1], [0, 1, 1, 1]]}, {[[5, 3, 1, 4, 2], [1, 1, 1, 0]]}} {[[1, 3, 5, 2, 4], [1, 1, 1, 0]]} {[[2, 4, 1, 3, 5], [0, 1, 1, 1]]} "Class ", 163, " is:" {{[[1, 3, 5, 4, 2], [0, 0, 0, 0]]}, {[[2, 4, 5, 3, 1], [0, 0, 0, 0]]}, {[[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, {[[5, 3, 1, 2, 4], [0, 0, 0, 0]]}} {[[1, 3, 5, 4, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 3, 5, 4, 2], [0, 0, 0, 0]]}, {[[2, 4, 5, 3, 1], [0, 0, 0, 0]]}, {[[4, 2, 1, 3, 5], [0, 0, 0, 0]]}, {[[5, 3, 1, 2, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 5, 4, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 4, 3, 5], {1, 2, 3}, {}], [[1, 2, 5, 3, 4], {1, 2, 3}, {}], [[1, 2, 5, 4, 3], {1, 2, 3, 4}, {}], [[1, 3, 5, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38976, 347795, 3448312, 37608186, 447452544, 5767315785, 80054392880, 1190583423414, 18887010379776, 318343175603145, 5681348801115680, 107025793890636390, 2122275973981599744] "" "Class ", 164, " is:" {{[[1, 3, 5, 4, 2], [0, 0, 0, 1]]}, {[[2, 4, 5, 3, 1], [1, 0, 0, 0]]}, {[[4, 2, 1, 3, 5], [1, 0, 0, 0]]}, {[[5, 3, 1, 2, 4], [0, 0, 0, 1]]}} {[[1, 3, 5, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 3, 5, 4, 2], [0, 0, 0, 1]]}, {[[2, 4, 5, 3, 1], [1, 0, 0, 0]]}, {[[4, 2, 1, 3, 5], [1, 0, 0, 0]]}, {[[5, 3, 1, 2, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 5, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37864, 332456, 3236090, 34585138, 402593652, 5070228606, 68686946674, 995979034197, 15391250508204, 252516266313184, 4383569184807315, 80274560406376557, 1546540548551811738] "" "Class ", 165, " is:" {{[[1, 3, 5, 4, 2], [0, 0, 1, 0]]}, {[[2, 4, 5, 3, 1], [0, 1, 0, 0]]}, {[[4, 2, 1, 3, 5], [0, 1, 0, 0]]}, {[[5, 3, 1, 2, 4], [0, 0, 1, 0]]}} {[[1, 3, 5, 4, 2], [0, 0, 1, 0]]} {[[2, 4, 5, 3, 1], [0, 1, 0, 0]]} "Class ", 166, " is:" {{[[1, 3, 5, 4, 2], [0, 0, 1, 1]]}, {[[2, 4, 5, 3, 1], [1, 1, 0, 0]]}, {[[4, 2, 1, 3, 5], [1, 1, 0, 0]]}, {[[5, 3, 1, 2, 4], [0, 0, 1, 1]]}} {[[1, 3, 5, 4, 2], [0, 0, 1, 1]]} {[[2, 4, 5, 3, 1], [1, 1, 0, 0]]} "Class ", 167, " is:" {{[[1, 3, 5, 4, 2], [0, 1, 0, 0]]}, {[[2, 4, 5, 3, 1], [0, 0, 1, 0]]}, {[[4, 2, 1, 3, 5], [0, 0, 1, 0]]}, {[[5, 3, 1, 2, 4], [0, 1, 0, 0]]}} {[[1, 3, 5, 4, 2], [0, 1, 0, 0]]} {[[2, 4, 5, 3, 1], [0, 0, 1, 0]]} "Class ", 168, " is:" {{[[1, 3, 5, 4, 2], [0, 1, 0, 1]]}, {[[2, 4, 5, 3, 1], [1, 0, 1, 0]]}, {[[4, 2, 1, 3, 5], [1, 0, 1, 0]]}, {[[5, 3, 1, 2, 4], [0, 1, 0, 1]]}} {[[1, 3, 5, 4, 2], [0, 1, 0, 1]]} {[[2, 4, 5, 3, 1], [1, 0, 1, 0]]} "Class ", 169, " is:" {{[[1, 3, 5, 4, 2], [0, 1, 1, 0]]}, {[[2, 4, 5, 3, 1], [0, 1, 1, 0]]}, {[[4, 2, 1, 3, 5], [0, 1, 1, 0]]}, {[[5, 3, 1, 2, 4], [0, 1, 1, 0]]}} {[[1, 3, 5, 4, 2], [0, 1, 1, 0]]} {[[2, 4, 5, 3, 1], [0, 1, 1, 0]]} "Class ", 170, " is:" {{[[1, 3, 5, 4, 2], [0, 1, 1, 1]]}, {[[2, 4, 5, 3, 1], [1, 1, 1, 0]]}, {[[4, 2, 1, 3, 5], [1, 1, 1, 0]]}, {[[5, 3, 1, 2, 4], [0, 1, 1, 1]]}} {[[1, 3, 5, 4, 2], [0, 1, 1, 1]]} {[[2, 4, 5, 3, 1], [1, 1, 1, 0]]} "Class ", 171, " is:" {{[[1, 3, 5, 4, 2], [1, 0, 0, 0]]}, {[[2, 4, 5, 3, 1], [0, 0, 0, 1]]}, {[[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[5, 3, 1, 2, 4], [1, 0, 0, 0]]}} {[[1, 3, 5, 4, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 3, 5, 4, 2], [1, 0, 0, 0]]}, {[[2, 4, 5, 3, 1], [0, 0, 0, 1]]}, {[[4, 2, 1, 3, 5], [0, 0, 0, 1]]}, {[[5, 3, 1, 2, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 3, 5, 4, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {}, {}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 2, 4, 3, 5], {2, 3}, {}], [[1, 2, 5, 3, 4], {2, 3}, {}], [[1, 2, 5, 4, 3], {2, 3, 4}, {}], [[1, 3, 5, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 3, 5, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37874, 332696, 3240416, 34657116, 403773512, 5089835936, 69021919224, 1001903928804, 15500138755224, 254598918643168, 4425046557089424, 81134570778122256, 1565095717271557536] "" "Class ", 172, " is:" {{[[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, {[[2, 4, 5, 3, 1], [1, 0, 0, 1]]}, {[[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[5, 3, 1, 2, 4], [1, 0, 0, 1]]}} {[[1, 3, 5, 4, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, {[[2, 4, 5, 3, 1], [1, 0, 0, 1]]}, {[[4, 2, 1, 3, 5], [1, 0, 0, 1]]}, {[[5, 3, 1, 2, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 3, 5, 4, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {1, 3}, {[0, 1, 0, 0, 0]}], [[1, 3, 4, 2], {2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4747, 36368, 310075, 2908152, 29727309, 328706824, 3907096334, 49658121296, 671806789486, 9636188879148, 146040655162497, 2331441700773988, 39100039578607877, 687183928229131712] "" "Class ", 173, " is:" {{[[1, 3, 5, 4, 2], [1, 0, 1, 0]]}, {[[2, 4, 5, 3, 1], [0, 1, 0, 1]]}, {[[4, 2, 1, 3, 5], [0, 1, 0, 1]]}, {[[5, 3, 1, 2, 4], [1, 0, 1, 0]]}} {[[1, 3, 5, 4, 2], [1, 0, 1, 0]]} {[[2, 4, 5, 3, 1], [0, 1, 0, 1]]} "Class ", 174, " is:" {{[[1, 3, 5, 4, 2], [1, 0, 1, 1]]}, {[[2, 4, 5, 3, 1], [1, 1, 0, 1]]}, {[[4, 2, 1, 3, 5], [1, 1, 0, 1]]}, {[[5, 3, 1, 2, 4], [1, 0, 1, 1]]}} {[[1, 3, 5, 4, 2], [1, 0, 1, 1]]} {[[2, 4, 5, 3, 1], [1, 1, 0, 1]]} "Class ", 175, " is:" {{[[1, 3, 5, 4, 2], [1, 1, 0, 0]]}, {[[2, 4, 5, 3, 1], [0, 0, 1, 1]]}, {[[4, 2, 1, 3, 5], [0, 0, 1, 1]]}, {[[5, 3, 1, 2, 4], [1, 1, 0, 0]]}} {[[1, 3, 5, 4, 2], [1, 1, 0, 0]]} {[[2, 4, 5, 3, 1], [0, 0, 1, 1]]} "Class ", 176, " is:" {{[[1, 3, 5, 4, 2], [1, 1, 0, 1]]}, {[[2, 4, 5, 3, 1], [1, 0, 1, 1]]}, {[[4, 2, 1, 3, 5], [1, 0, 1, 1]]}, {[[5, 3, 1, 2, 4], [1, 1, 0, 1]]}} {[[1, 3, 5, 4, 2], [1, 1, 0, 1]]} {[[2, 4, 5, 3, 1], [1, 0, 1, 1]]} "Class ", 177, " is:" {{[[1, 3, 5, 4, 2], [1, 1, 1, 0]]}, {[[2, 4, 5, 3, 1], [0, 1, 1, 1]]}, {[[4, 2, 1, 3, 5], [0, 1, 1, 1]]}, {[[5, 3, 1, 2, 4], [1, 1, 1, 0]]}} {[[1, 3, 5, 4, 2], [1, 1, 1, 0]]} {[[2, 4, 5, 3, 1], [0, 1, 1, 1]]} "Class ", 178, " is:" {{[[1, 4, 2, 5, 3], [0, 0, 0, 0]]}, {[[3, 1, 4, 2, 5], [0, 0, 0, 0]]}, {[[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, {[[5, 2, 4, 1, 3], [0, 0, 0, 0]]}} {[[1, 4, 2, 5, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 4, 2, 5, 3], [0, 0, 0, 0]]}, {[[3, 1, 4, 2, 5], [0, 0, 0, 0]]}, {[[3, 5, 2, 4, 1], [0, 0, 0, 0]]}, {[[5, 2, 4, 1, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 5, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3}, {}], [[1, 3, 2, 5, 4], {1, 2}, {}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {1, 2, 3, 4}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4916, 39008, 348202, 3453572, 37679044, 448455648, 5782307134, 80291122976, 1194530208634, 18956382485568, 319626461800751, 5706286536509228, 107533930423507736, 2133112981295131824] "" "Class ", 179, " is:" {{[[1, 4, 2, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 4, 2, 5], [1, 0, 0, 0]]}, {[[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, {[[5, 2, 4, 1, 3], [0, 0, 0, 1]]}} {[[1, 4, 2, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 4, 2, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 4, 2, 5], [1, 0, 0, 0]]}, {[[3, 5, 2, 4, 1], [1, 0, 0, 0]]}, {[[5, 2, 4, 1, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4840, 37908, 333175, 3247036, 34750496, 405141356, 5110798362, 69358940652, 1007591939582, 15600870466520, 256468946976323, 4461392769354994, 81873149644166974, 1580764698238996508] "" "Class ", 180, " is:" {{[[1, 4, 2, 5, 3], [0, 0, 1, 0]]}, {[[3, 1, 4, 2, 5], [0, 1, 0, 0]]}, {[[3, 5, 2, 4, 1], [0, 1, 0, 0]]}, {[[5, 2, 4, 1, 3], [0, 0, 1, 0]]}} {[[1, 4, 2, 5, 3], [0, 0, 1, 0]]} {[[3, 1, 4, 2, 5], [0, 1, 0, 0]]} "Class ", 181, " is:" {{[[1, 4, 2, 5, 3], [0, 0, 1, 1]]}, {[[3, 1, 4, 2, 5], [1, 1, 0, 0]]}, {[[3, 5, 2, 4, 1], [1, 1, 0, 0]]}, {[[5, 2, 4, 1, 3], [0, 0, 1, 1]]}} {[[1, 4, 2, 5, 3], [0, 0, 1, 1]]} {[[3, 1, 4, 2, 5], [1, 1, 0, 0]]} "Class ", 182, " is:" {{[[1, 4, 2, 5, 3], [0, 1, 0, 0]]}, {[[3, 1, 4, 2, 5], [0, 0, 1, 0]]}, {[[3, 5, 2, 4, 1], [0, 0, 1, 0]]}, {[[5, 2, 4, 1, 3], [0, 1, 0, 0]]}} {[[1, 4, 2, 5, 3], [0, 1, 0, 0]]} {[[3, 1, 4, 2, 5], [0, 0, 1, 0]]} "Class ", 183, " is:" {{[[1, 4, 2, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 4, 2, 5], [1, 0, 1, 0]]}, {[[3, 5, 2, 4, 1], [1, 0, 1, 0]]}, {[[5, 2, 4, 1, 3], [0, 1, 0, 1]]}} {[[1, 4, 2, 5, 3], [0, 1, 0, 1]]} {[[3, 1, 4, 2, 5], [1, 0, 1, 0]]} "Class ", 184, " is:" {{[[1, 4, 2, 5, 3], [0, 1, 1, 0]]}, {[[3, 1, 4, 2, 5], [0, 1, 1, 0]]}, {[[3, 5, 2, 4, 1], [0, 1, 1, 0]]}, {[[5, 2, 4, 1, 3], [0, 1, 1, 0]]}} {[[1, 4, 2, 5, 3], [0, 1, 1, 0]]} {[[3, 1, 4, 2, 5], [0, 1, 1, 0]]} "Class ", 185, " is:" {{[[1, 4, 2, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 4, 2, 5], [1, 1, 1, 0]]}, {[[3, 5, 2, 4, 1], [1, 1, 1, 0]]}, {[[5, 2, 4, 1, 3], [0, 1, 1, 1]]}} {[[1, 4, 2, 5, 3], [0, 1, 1, 1]]} {[[3, 1, 4, 2, 5], [1, 1, 1, 0]]} "Class ", 186, " is:" {{[[1, 4, 2, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 4, 2, 5], [0, 0, 0, 1]]}, {[[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, {[[5, 2, 4, 1, 3], [1, 0, 0, 0]]}} {[[1, 4, 2, 5, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 4, 2, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 4, 2, 5], [0, 0, 0, 1]]}, {[[3, 5, 2, 4, 1], [0, 0, 0, 1]]}, {[[5, 2, 4, 1, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 4, 2, 5, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {2, 3, 4}, {}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 3, 5, 2], {2, 3}, {}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4840, 37917, 333398, 3251054, 34817364, 406240436, 5129138453, 69673817902, 1013191590724, 15704362165226, 258459713943091, 4501267003500612, 82704604695806956, 1598803929052608790] "" "Class ", 187, " is:" {{[[1, 4, 2, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 4, 2, 5], [1, 0, 0, 1]]}, {[[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[5, 2, 4, 1, 3], [1, 0, 0, 1]]}} {[[1, 4, 2, 5, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 4, 2, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 4, 2, 5], [1, 0, 0, 1]]}, {[[3, 5, 2, 4, 1], [1, 0, 0, 1]]}, {[[5, 2, 4, 1, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 4, 2, 5, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4747, 36368, 310075, 2908152, 29727309, 328706824, 3907096334, 49658121296, 671806789486, 9636188879148, 146040655162497, 2331441700773988, 39100039578607877, 687183928229131712] "" "Class ", 188, " is:" {{[[1, 4, 2, 5, 3], [1, 0, 1, 0]]}, {[[3, 1, 4, 2, 5], [0, 1, 0, 1]]}, {[[3, 5, 2, 4, 1], [0, 1, 0, 1]]}, {[[5, 2, 4, 1, 3], [1, 0, 1, 0]]}} {[[1, 4, 2, 5, 3], [1, 0, 1, 0]]} {[[3, 1, 4, 2, 5], [0, 1, 0, 1]]} "Class ", 189, " is:" {{[[1, 4, 2, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 4, 2, 5], [1, 1, 0, 1]]}, {[[3, 5, 2, 4, 1], [1, 1, 0, 1]]}, {[[5, 2, 4, 1, 3], [1, 0, 1, 1]]}} {[[1, 4, 2, 5, 3], [1, 0, 1, 1]]} {[[3, 1, 4, 2, 5], [1, 1, 0, 1]]} "Class ", 190, " is:" {{[[1, 4, 2, 5, 3], [1, 1, 0, 0]]}, {[[3, 1, 4, 2, 5], [0, 0, 1, 1]]}, {[[3, 5, 2, 4, 1], [0, 0, 1, 1]]}, {[[5, 2, 4, 1, 3], [1, 1, 0, 0]]}} {[[1, 4, 2, 5, 3], [1, 1, 0, 0]]} {[[3, 1, 4, 2, 5], [0, 0, 1, 1]]} "Class ", 191, " is:" {{[[1, 4, 2, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 4, 2, 5], [1, 0, 1, 1]]}, {[[3, 5, 2, 4, 1], [1, 0, 1, 1]]}, {[[5, 2, 4, 1, 3], [1, 1, 0, 1]]}} {[[1, 4, 2, 5, 3], [1, 1, 0, 1]]} {[[3, 1, 4, 2, 5], [1, 0, 1, 1]]} "Class ", 192, " is:" {{[[1, 4, 2, 5, 3], [1, 1, 1, 0]]}, {[[3, 1, 4, 2, 5], [0, 1, 1, 1]]}, {[[3, 5, 2, 4, 1], [0, 1, 1, 1]]}, {[[5, 2, 4, 1, 3], [1, 1, 1, 0]]}} {[[1, 4, 2, 5, 3], [1, 1, 1, 0]]} {[[3, 1, 4, 2, 5], [0, 1, 1, 1]]} "Class ", 193, " is:" {{[[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, {[[1, 4, 3, 2, 5], [1, 0, 0, 0]]}, {[[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[5, 2, 3, 4, 1], [1, 0, 0, 0]]}} {[[1, 4, 3, 2, 5], [0, 0, 0, 1]]} "For the class ", {{[[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, {[[1, 4, 3, 2, 5], [1, 0, 0, 0]]}, {[[5, 2, 3, 4, 1], [0, 0, 0, 1]]}, {[[5, 2, 3, 4, 1], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 2, 5], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 0, 1]}], [[2, 4, 3, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37874, 332696, 3240416, 34657116, 403773512, 5089835936, 69021919224, 1001903928804, 15500138755224, 254598918643168, 4425046557089424, 81134570778122256, 1565095717271557536] "" "Class ", 194, " is:" {{[[1, 4, 3, 2, 5], [0, 0, 1, 0]]}, {[[1, 4, 3, 2, 5], [0, 1, 0, 0]]}, {[[5, 2, 3, 4, 1], [0, 0, 1, 0]]}, {[[5, 2, 3, 4, 1], [0, 1, 0, 0]]}} {[[1, 4, 3, 2, 5], [0, 0, 1, 0]]} {[[1, 4, 3, 2, 5], [0, 1, 0, 0]]} "Class ", 195, " is:" {{[[1, 4, 3, 2, 5], [0, 0, 1, 1]]}, {[[1, 4, 3, 2, 5], [1, 1, 0, 0]]}, {[[5, 2, 3, 4, 1], [0, 0, 1, 1]]}, {[[5, 2, 3, 4, 1], [1, 1, 0, 0]]}} {[[1, 4, 3, 2, 5], [0, 0, 1, 1]]} {[[1, 4, 3, 2, 5], [1, 1, 0, 0]]} "Class ", 196, " is:" {{[[1, 4, 3, 2, 5], [0, 1, 0, 1]]}, {[[1, 4, 3, 2, 5], [1, 0, 1, 0]]}, {[[5, 2, 3, 4, 1], [0, 1, 0, 1]]}, {[[5, 2, 3, 4, 1], [1, 0, 1, 0]]}} {[[1, 4, 3, 2, 5], [0, 1, 0, 1]]} {[[1, 4, 3, 2, 5], [1, 0, 1, 0]]} "Class ", 197, " is:" {{[[1, 4, 3, 2, 5], [0, 1, 1, 1]]}, {[[1, 4, 3, 2, 5], [1, 1, 1, 0]]}, {[[5, 2, 3, 4, 1], [0, 1, 1, 1]]}, {[[5, 2, 3, 4, 1], [1, 1, 1, 0]]}} {[[1, 4, 3, 2, 5], [0, 1, 1, 1]]} {[[1, 4, 3, 2, 5], [1, 1, 1, 0]]} "Class ", 198, " is:" {{[[1, 4, 3, 2, 5], [1, 0, 1, 1]]}, {[[1, 4, 3, 2, 5], [1, 1, 0, 1]]}, {[[5, 2, 3, 4, 1], [1, 0, 1, 1]]}, {[[5, 2, 3, 4, 1], [1, 1, 0, 1]]}} {[[1, 4, 3, 2, 5], [1, 0, 1, 1]]} {[[1, 4, 3, 2, 5], [1, 1, 0, 1]]} "Class ", 199, " is:" {{[[1, 4, 3, 5, 2], [0, 0, 0, 0]]}, {[[2, 5, 3, 4, 1], [0, 0, 0, 0]]}, {[[4, 1, 3, 2, 5], [0, 0, 0, 0]]}, {[[5, 2, 3, 1, 4], [0, 0, 0, 0]]}} {[[1, 4, 3, 5, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 4, 3, 5, 2], [0, 0, 0, 0]]}, {[[2, 5, 3, 4, 1], [0, 0, 0, 0]]}, {[[4, 1, 3, 2, 5], [0, 0, 0, 0]]}, {[[5, 2, 3, 1, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 5, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {1, 2, 3}, {}], [[1, 3, 2, 5, 4], {1, 2}, {}], [[1, 4, 2, 5, 3], {1, 2}, {}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38976, 347795, 3448312, 37608186, 447452544, 5767315785, 80054392880, 1190583423414, 18887010379776, 318343175603145, 5681348801115680, 107025793890636390, 2122275973981599744] "" "Class ", 200, " is:" {{[[1, 4, 3, 5, 2], [0, 0, 0, 1]]}, {[[2, 5, 3, 4, 1], [1, 0, 0, 0]]}, {[[4, 1, 3, 2, 5], [1, 0, 0, 0]]}, {[[5, 2, 3, 1, 4], [0, 0, 0, 1]]}} {[[1, 4, 3, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 4, 3, 5, 2], [0, 0, 0, 1]]}, {[[2, 5, 3, 4, 1], [1, 0, 0, 0]]}, {[[4, 1, 3, 2, 5], [1, 0, 0, 0]]}, {[[5, 2, 3, 1, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37870, 332622, 3239412, 34645000, 403639152, 5088526637, 69013347428, 1001967763197, 15504837990938, 254749318431831, 4429130902826452, 81239785911603649, 1567770683268449858] "" "Class ", 201, " is:" {{[[1, 4, 3, 5, 2], [0, 0, 1, 0]]}, {[[2, 5, 3, 4, 1], [0, 1, 0, 0]]}, {[[4, 1, 3, 2, 5], [0, 1, 0, 0]]}, {[[5, 2, 3, 1, 4], [0, 0, 1, 0]]}} {[[1, 4, 3, 5, 2], [0, 0, 1, 0]]} {[[2, 5, 3, 4, 1], [0, 1, 0, 0]]} "Class ", 202, " is:" {{[[1, 4, 3, 5, 2], [0, 0, 1, 1]]}, {[[2, 5, 3, 4, 1], [1, 1, 0, 0]]}, {[[4, 1, 3, 2, 5], [1, 1, 0, 0]]}, {[[5, 2, 3, 1, 4], [0, 0, 1, 1]]}} {[[1, 4, 3, 5, 2], [0, 0, 1, 1]]} {[[2, 5, 3, 4, 1], [1, 1, 0, 0]]} "Class ", 203, " is:" {{[[1, 4, 3, 5, 2], [0, 1, 0, 0]]}, {[[2, 5, 3, 4, 1], [0, 0, 1, 0]]}, {[[4, 1, 3, 2, 5], [0, 0, 1, 0]]}, {[[5, 2, 3, 1, 4], [0, 1, 0, 0]]}} {[[1, 4, 3, 5, 2], [0, 1, 0, 0]]} {[[2, 5, 3, 4, 1], [0, 0, 1, 0]]} "Class ", 204, " is:" {{[[1, 4, 3, 5, 2], [0, 1, 0, 1]]}, {[[2, 5, 3, 4, 1], [1, 0, 1, 0]]}, {[[4, 1, 3, 2, 5], [1, 0, 1, 0]]}, {[[5, 2, 3, 1, 4], [0, 1, 0, 1]]}} {[[1, 4, 3, 5, 2], [0, 1, 0, 1]]} {[[2, 5, 3, 4, 1], [1, 0, 1, 0]]} "Class ", 205, " is:" {{[[1, 4, 3, 5, 2], [0, 1, 1, 0]]}, {[[2, 5, 3, 4, 1], [0, 1, 1, 0]]}, {[[4, 1, 3, 2, 5], [0, 1, 1, 0]]}, {[[5, 2, 3, 1, 4], [0, 1, 1, 0]]}} {[[1, 4, 3, 5, 2], [0, 1, 1, 0]]} {[[2, 5, 3, 4, 1], [0, 1, 1, 0]]} "Class ", 206, " is:" {{[[1, 4, 3, 5, 2], [0, 1, 1, 1]]}, {[[2, 5, 3, 4, 1], [1, 1, 1, 0]]}, {[[4, 1, 3, 2, 5], [1, 1, 1, 0]]}, {[[5, 2, 3, 1, 4], [0, 1, 1, 1]]}} {[[1, 4, 3, 5, 2], [0, 1, 1, 1]]} {[[2, 5, 3, 4, 1], [1, 1, 1, 0]]} "Class ", 207, " is:" {{[[1, 4, 3, 5, 2], [1, 0, 0, 0]]}, {[[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, {[[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, {[[5, 2, 3, 1, 4], [1, 0, 0, 0]]}} {[[1, 4, 3, 5, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 4, 3, 5, 2], [1, 0, 0, 0]]}, {[[2, 5, 3, 4, 1], [0, 0, 0, 1]]}, {[[4, 1, 3, 2, 5], [0, 0, 0, 1]]}, {[[5, 2, 3, 1, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 4, 3, 5, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 3, 2, 4, 5], {2, 3, 4}, {}], [[1, 3, 2, 5, 4], {2, 3}, {}], [[1, 4, 2, 5, 3], {2, 3}, {}], [[1, 4, 3, 5, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 3, 5, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4839, 37890, 332911, 3243252, 34695475, 404314543, 5097846976, 69146743589, 1003951140459, 15535452873197, 255238810253701, 4437207990186150, 81376613057795459, 1570132210422810657] "" "Class ", 208, " is:" {{[[1, 4, 3, 5, 2], [1, 0, 0, 1]]}, {[[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[4, 1, 3, 2, 5], [1, 0, 0, 1]]}, {[[5, 2, 3, 1, 4], [1, 0, 0, 1]]}} {[[1, 4, 3, 5, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 4, 3, 5, 2], [1, 0, 0, 1]]}, {[[2, 5, 3, 4, 1], [1, 0, 0, 1]]}, {[[4, 1, 3, 2, 5], [1, 0, 0, 1]]}, {[[5, 2, 3, 1, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 4, 3, 5, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4747, 36368, 310075, 2908152, 29727309, 328706824, 3907096334, 49658121296, 671806789486, 9636188879148, 146040655162497, 2331441700773988, 39100039578607877, 687183928229131712] "" "Class ", 209, " is:" {{[[1, 4, 3, 5, 2], [1, 0, 1, 0]]}, {[[2, 5, 3, 4, 1], [0, 1, 0, 1]]}, {[[4, 1, 3, 2, 5], [0, 1, 0, 1]]}, {[[5, 2, 3, 1, 4], [1, 0, 1, 0]]}} {[[1, 4, 3, 5, 2], [1, 0, 1, 0]]} {[[2, 5, 3, 4, 1], [0, 1, 0, 1]]} "Class ", 210, " is:" {{[[1, 4, 3, 5, 2], [1, 0, 1, 1]]}, {[[2, 5, 3, 4, 1], [1, 1, 0, 1]]}, {[[4, 1, 3, 2, 5], [1, 1, 0, 1]]}, {[[5, 2, 3, 1, 4], [1, 0, 1, 1]]}} {[[1, 4, 3, 5, 2], [1, 0, 1, 1]]} {[[2, 5, 3, 4, 1], [1, 1, 0, 1]]} "Class ", 211, " is:" {{[[1, 4, 3, 5, 2], [1, 1, 0, 0]]}, {[[2, 5, 3, 4, 1], [0, 0, 1, 1]]}, {[[4, 1, 3, 2, 5], [0, 0, 1, 1]]}, {[[5, 2, 3, 1, 4], [1, 1, 0, 0]]}} {[[1, 4, 3, 5, 2], [1, 1, 0, 0]]} {[[2, 5, 3, 4, 1], [0, 0, 1, 1]]} "Class ", 212, " is:" {{[[1, 4, 3, 5, 2], [1, 1, 0, 1]]}, {[[2, 5, 3, 4, 1], [1, 0, 1, 1]]}, {[[4, 1, 3, 2, 5], [1, 0, 1, 1]]}, {[[5, 2, 3, 1, 4], [1, 1, 0, 1]]}} {[[1, 4, 3, 5, 2], [1, 1, 0, 1]]} {[[2, 5, 3, 4, 1], [1, 0, 1, 1]]} "Class ", 213, " is:" {{[[1, 4, 3, 5, 2], [1, 1, 1, 0]]}, {[[2, 5, 3, 4, 1], [0, 1, 1, 1]]}, {[[4, 1, 3, 2, 5], [0, 1, 1, 1]]}, {[[5, 2, 3, 1, 4], [1, 1, 1, 0]]}} {[[1, 4, 3, 5, 2], [1, 1, 1, 0]]} {[[2, 5, 3, 4, 1], [0, 1, 1, 1]]} "Class ", 214, " is:" {{[[1, 4, 5, 2, 3], [0, 0, 0, 0]]}, {[[3, 2, 5, 4, 1], [0, 0, 0, 0]]}, {[[3, 4, 1, 2, 5], [0, 0, 0, 0]]}, {[[5, 2, 1, 4, 3], [0, 0, 0, 0]]}} {[[1, 4, 5, 2, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 4, 5, 2, 3], [0, 0, 0, 0]]}, {[[3, 2, 5, 4, 1], [0, 0, 0, 0]]}, {[[3, 4, 1, 2, 5], [0, 0, 0, 0]]}, {[[5, 2, 1, 4, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 4, 5, 2, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3}, {}], [[1, 3, 5, 2, 4], {1, 2, 3}, {}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {1, 2, 3, 4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38979, 347829, 3448722, 37613451, 447524466, 5768361795, 80070563433, 1190848464594, 18891604332045, 318427172178204, 5682965018856093, 107058447534630429, 2122967250258006555] "" "Class ", 215, " is:" {{[[1, 4, 5, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 5, 4, 1], [1, 0, 0, 0]]}, {[[3, 4, 1, 2, 5], [1, 0, 0, 0]]}, {[[5, 2, 1, 4, 3], [0, 0, 0, 1]]}} {[[1, 4, 5, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 4, 5, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 5, 4, 1], [1, 0, 0, 0]]}, {[[3, 4, 1, 2, 5], [1, 0, 0, 0]]}, {[[5, 2, 1, 4, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 4, 5, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37874, 332696, 3240416, 34657116, 403773512, 5089835936, 69021919224, 1001903928804, 15500138755224, 254598918643168, 4425046557089424, 81134570778122256, 1565095717271557536] "" "Class ", 216, " is:" {{[[1, 4, 5, 2, 3], [0, 0, 1, 0]]}, {[[3, 2, 5, 4, 1], [0, 1, 0, 0]]}, {[[3, 4, 1, 2, 5], [0, 1, 0, 0]]}, {[[5, 2, 1, 4, 3], [0, 0, 1, 0]]}} {[[1, 4, 5, 2, 3], [0, 0, 1, 0]]} {[[3, 2, 5, 4, 1], [0, 1, 0, 0]]} "Class ", 217, " is:" {{[[1, 4, 5, 2, 3], [0, 0, 1, 1]]}, {[[3, 2, 5, 4, 1], [1, 1, 0, 0]]}, {[[3, 4, 1, 2, 5], [1, 1, 0, 0]]}, {[[5, 2, 1, 4, 3], [0, 0, 1, 1]]}} {[[1, 4, 5, 2, 3], [0, 0, 1, 1]]} {[[3, 2, 5, 4, 1], [1, 1, 0, 0]]} "Class ", 218, " is:" {{[[1, 4, 5, 2, 3], [0, 1, 0, 0]]}, {[[3, 2, 5, 4, 1], [0, 0, 1, 0]]}, {[[3, 4, 1, 2, 5], [0, 0, 1, 0]]}, {[[5, 2, 1, 4, 3], [0, 1, 0, 0]]}} {[[1, 4, 5, 2, 3], [0, 1, 0, 0]]} {[[3, 2, 5, 4, 1], [0, 0, 1, 0]]} "Class ", 219, " is:" {{[[1, 4, 5, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 5, 4, 1], [1, 0, 1, 0]]}, {[[3, 4, 1, 2, 5], [1, 0, 1, 0]]}, {[[5, 2, 1, 4, 3], [0, 1, 0, 1]]}} {[[1, 4, 5, 2, 3], [0, 1, 0, 1]]} {[[3, 2, 5, 4, 1], [1, 0, 1, 0]]} "Class ", 220, " is:" {{[[1, 4, 5, 2, 3], [0, 1, 1, 0]]}, {[[3, 2, 5, 4, 1], [0, 1, 1, 0]]}, {[[3, 4, 1, 2, 5], [0, 1, 1, 0]]}, {[[5, 2, 1, 4, 3], [0, 1, 1, 0]]}} {[[1, 4, 5, 2, 3], [0, 1, 1, 0]]} {[[3, 2, 5, 4, 1], [0, 1, 1, 0]]} "Class ", 221, " is:" {{[[1, 4, 5, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 5, 4, 1], [1, 1, 1, 0]]}, {[[3, 4, 1, 2, 5], [1, 1, 1, 0]]}, {[[5, 2, 1, 4, 3], [0, 1, 1, 1]]}} {[[1, 4, 5, 2, 3], [0, 1, 1, 1]]} {[[3, 2, 5, 4, 1], [1, 1, 1, 0]]} "Class ", 222, " is:" {{[[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 5, 4, 1], [0, 0, 0, 1]]}, {[[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, {[[5, 2, 1, 4, 3], [1, 0, 0, 0]]}} {[[1, 4, 5, 2, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 5, 4, 1], [0, 0, 0, 1]]}, {[[3, 4, 1, 2, 5], [0, 0, 0, 1]]}, {[[5, 2, 1, 4, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 4, 5, 2, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2, 3}, {}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 4, 5, 3, 2], {2, 3, 4}, {}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4839, 37895, 333036, 3245568, 34734865, 404972789, 5108976367, 69339875102, 1007416328328, 15599977305688, 256487971024811, 4462366668225250, 81903744063787789, 1581616945528988403] "" "Class ", 223, " is:" {{[[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 5, 4, 1], [1, 0, 0, 1]]}, {[[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[5, 2, 1, 4, 3], [1, 0, 0, 1]]}} {[[1, 4, 5, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 5, 4, 1], [1, 0, 0, 1]]}, {[[3, 4, 1, 2, 5], [1, 0, 0, 1]]}, {[[5, 2, 1, 4, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 4, 5, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2, 3}, {}], [[1, 3, 4, 2], {2, 3}, {[0, 0, 1, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4745, 36316, 309125, 2892742, 29487053, 324975992, 3848338570, 48710309440, 656061287952, 9365988775080, 141243339052717, 2243255588816608, 37421405085853269, 654102896643897068] "" "Class ", 224, " is:" {{[[1, 4, 5, 2, 3], [1, 0, 1, 0]]}, {[[3, 2, 5, 4, 1], [0, 1, 0, 1]]}, {[[3, 4, 1, 2, 5], [0, 1, 0, 1]]}, {[[5, 2, 1, 4, 3], [1, 0, 1, 0]]}} {[[1, 4, 5, 2, 3], [1, 0, 1, 0]]} {[[3, 2, 5, 4, 1], [0, 1, 0, 1]]} "Class ", 225, " is:" {{[[1, 4, 5, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 5, 4, 1], [1, 1, 0, 1]]}, {[[3, 4, 1, 2, 5], [1, 1, 0, 1]]}, {[[5, 2, 1, 4, 3], [1, 0, 1, 1]]}} {[[1, 4, 5, 2, 3], [1, 0, 1, 1]]} {[[3, 2, 5, 4, 1], [1, 1, 0, 1]]} "Class ", 226, " is:" {{[[1, 4, 5, 2, 3], [1, 1, 0, 0]]}, {[[3, 2, 5, 4, 1], [0, 0, 1, 1]]}, {[[3, 4, 1, 2, 5], [0, 0, 1, 1]]}, {[[5, 2, 1, 4, 3], [1, 1, 0, 0]]}} {[[1, 4, 5, 2, 3], [1, 1, 0, 0]]} {[[3, 2, 5, 4, 1], [0, 0, 1, 1]]} "Class ", 227, " is:" {{[[1, 4, 5, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 5, 4, 1], [1, 0, 1, 1]]}, {[[3, 4, 1, 2, 5], [1, 0, 1, 1]]}, {[[5, 2, 1, 4, 3], [1, 1, 0, 1]]}} {[[1, 4, 5, 2, 3], [1, 1, 0, 1]]} {[[3, 2, 5, 4, 1], [1, 0, 1, 1]]} "Class ", 228, " is:" {{[[1, 4, 5, 2, 3], [1, 1, 1, 0]]}, {[[3, 2, 5, 4, 1], [0, 1, 1, 1]]}, {[[3, 4, 1, 2, 5], [0, 1, 1, 1]]}, {[[5, 2, 1, 4, 3], [1, 1, 1, 0]]}} {[[1, 4, 5, 2, 3], [1, 1, 1, 0]]} {[[3, 2, 5, 4, 1], [0, 1, 1, 1]]} "Class ", 229, " is:" {{[[1, 4, 5, 2, 3], [1, 1, 1, 1]]}, {[[3, 2, 5, 4, 1], [1, 1, 1, 1]]}, {[[3, 4, 1, 2, 5], [1, 1, 1, 1]]}, {[[5, 2, 1, 4, 3], [1, 1, 1, 1]]}} {[[1, 4, 5, 2, 3], [1, 1, 1, 1]]} {[[3, 2, 5, 4, 1], [1, 1, 1, 1]]} "Class ", 230, " is:" {{[[1, 4, 5, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 5, 4, 1], [0, 0, 0, 0]]}, {[[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, {[[5, 2, 1, 3, 4], [0, 0, 0, 0]]}} {[[1, 4, 5, 3, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 4, 5, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 5, 4, 1], [0, 0, 0, 0]]}, {[[4, 3, 1, 2, 5], [0, 0, 0, 0]]}, {[[5, 2, 1, 3, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 4, 5, 3, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {1, 2, 3}, {}], [[1, 3, 5, 2, 4], {1, 2, 3}, {}], [[1, 4, 5, 2, 3], {1, 2, 3}, {}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38976, 347795, 3448312, 37608186, 447452544, 5767315785, 80054392880, 1190583423414, 18887010379776, 318343175603145, 5681348801115680, 107025793890636390, 2122275973981599744] "" "Class ", 231, " is:" {{[[1, 4, 5, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 5, 4, 1], [1, 0, 0, 0]]}, {[[4, 3, 1, 2, 5], [1, 0, 0, 0]]}, {[[5, 2, 1, 3, 4], [0, 0, 0, 1]]}} {[[1, 4, 5, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 4, 5, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 5, 4, 1], [1, 0, 0, 0]]}, {[[4, 3, 1, 2, 5], [1, 0, 0, 0]]}, {[[5, 2, 1, 3, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 4, 5, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37864, 332476, 3236740, 34599992, 402894232, 5076048610, 68798725120, 998148956009, 15434279713400, 253393186307010, 4402000665397314, 80674887543929046, 1555534563807643908] "" "Class ", 232, " is:" {{[[1, 4, 5, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 5, 4, 1], [0, 1, 0, 0]]}, {[[4, 3, 1, 2, 5], [0, 1, 0, 0]]}, {[[5, 2, 1, 3, 4], [0, 0, 1, 0]]}} {[[1, 4, 5, 3, 2], [0, 0, 1, 0]]} {[[2, 3, 5, 4, 1], [0, 1, 0, 0]]} "Class ", 233, " is:" {{[[1, 4, 5, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 5, 4, 1], [1, 1, 0, 0]]}, {[[4, 3, 1, 2, 5], [1, 1, 0, 0]]}, {[[5, 2, 1, 3, 4], [0, 0, 1, 1]]}} {[[1, 4, 5, 3, 2], [0, 0, 1, 1]]} {[[2, 3, 5, 4, 1], [1, 1, 0, 0]]} "Class ", 234, " is:" {{[[1, 4, 5, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 5, 4, 1], [0, 0, 1, 0]]}, {[[4, 3, 1, 2, 5], [0, 0, 1, 0]]}, {[[5, 2, 1, 3, 4], [0, 1, 0, 0]]}} {[[1, 4, 5, 3, 2], [0, 1, 0, 0]]} {[[2, 3, 5, 4, 1], [0, 0, 1, 0]]} "Class ", 235, " is:" {{[[1, 4, 5, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 5, 4, 1], [1, 0, 1, 0]]}, {[[4, 3, 1, 2, 5], [1, 0, 1, 0]]}, {[[5, 2, 1, 3, 4], [0, 1, 0, 1]]}} {[[1, 4, 5, 3, 2], [0, 1, 0, 1]]} {[[2, 3, 5, 4, 1], [1, 0, 1, 0]]} "Class ", 236, " is:" {{[[1, 4, 5, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 5, 4, 1], [0, 1, 1, 0]]}, {[[4, 3, 1, 2, 5], [0, 1, 1, 0]]}, {[[5, 2, 1, 3, 4], [0, 1, 1, 0]]}} {[[1, 4, 5, 3, 2], [0, 1, 1, 0]]} {[[2, 3, 5, 4, 1], [0, 1, 1, 0]]} "Class ", 237, " is:" {{[[1, 4, 5, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 5, 4, 1], [1, 1, 1, 0]]}, {[[4, 3, 1, 2, 5], [1, 1, 1, 0]]}, {[[5, 2, 1, 3, 4], [0, 1, 1, 1]]}} {[[1, 4, 5, 3, 2], [0, 1, 1, 1]]} {[[2, 3, 5, 4, 1], [1, 1, 1, 0]]} "Class ", 238, " is:" {{[[1, 4, 5, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 5, 4, 1], [0, 0, 0, 1]]}, {[[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[5, 2, 1, 3, 4], [1, 0, 0, 0]]}} {[[1, 4, 5, 3, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 4, 5, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 5, 4, 1], [0, 0, 0, 1]]}, {[[4, 3, 1, 2, 5], [0, 0, 0, 1]]}, {[[5, 2, 1, 3, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 4, 5, 3, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2, 3}, {}], [[1, 3, 4, 2], {}, {}], [[2, 3, 4, 1], {1, 2, 3}, {}], [[1, 3, 4, 2, 5], {2, 3}, {}], [[1, 3, 5, 2, 4], {2, 3}, {}], [[1, 4, 5, 2, 3], {2, 3}, {}], [[1, 4, 5, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37868, 332546, 3237620, 34609332, 402972008, 5076245018, 68785548072, 997655804160, 15420936790944, 253064231968336, 4394118358559280, 80486313018869424, 1550969499004966272] "" "Class ", 239, " is:" {{[[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 5, 4, 1], [1, 0, 0, 1]]}, {[[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[5, 2, 1, 3, 4], [1, 0, 0, 1]]}} {[[1, 4, 5, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 5, 4, 1], [1, 0, 0, 1]]}, {[[4, 3, 1, 2, 5], [1, 0, 0, 1]]}, {[[5, 2, 1, 3, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 4, 5, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {2}, {}], [[1, 2, 4, 3], {2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[2, 3, 4, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4747, 36368, 310075, 2908152, 29727309, 328706824, 3907096334, 49658121296, 671806789486, 9636188879148, 146040655162497, 2331441700773988, 39100039578607877, 687183928229131712] "" "Class ", 240, " is:" {{[[1, 4, 5, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 5, 4, 1], [0, 1, 0, 1]]}, {[[4, 3, 1, 2, 5], [0, 1, 0, 1]]}, {[[5, 2, 1, 3, 4], [1, 0, 1, 0]]}} {[[1, 4, 5, 3, 2], [1, 0, 1, 0]]} {[[2, 3, 5, 4, 1], [0, 1, 0, 1]]} "Class ", 241, " is:" {{[[1, 4, 5, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 5, 4, 1], [1, 1, 0, 1]]}, {[[4, 3, 1, 2, 5], [1, 1, 0, 1]]}, {[[5, 2, 1, 3, 4], [1, 0, 1, 1]]}} {[[1, 4, 5, 3, 2], [1, 0, 1, 1]]} {[[2, 3, 5, 4, 1], [1, 1, 0, 1]]} "Class ", 242, " is:" {{[[1, 4, 5, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 5, 4, 1], [0, 0, 1, 1]]}, {[[4, 3, 1, 2, 5], [0, 0, 1, 1]]}, {[[5, 2, 1, 3, 4], [1, 1, 0, 0]]}} {[[1, 4, 5, 3, 2], [1, 1, 0, 0]]} {[[2, 3, 5, 4, 1], [0, 0, 1, 1]]} "Class ", 243, " is:" {{[[1, 4, 5, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 5, 4, 1], [1, 0, 1, 1]]}, {[[4, 3, 1, 2, 5], [1, 0, 1, 1]]}, {[[5, 2, 1, 3, 4], [1, 1, 0, 1]]}} {[[1, 4, 5, 3, 2], [1, 1, 0, 1]]} {[[2, 3, 5, 4, 1], [1, 0, 1, 1]]} "Class ", 244, " is:" {{[[1, 4, 5, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 5, 4, 1], [0, 1, 1, 1]]}, {[[4, 3, 1, 2, 5], [0, 1, 1, 1]]}, {[[5, 2, 1, 3, 4], [1, 1, 1, 0]]}} {[[1, 4, 5, 3, 2], [1, 1, 1, 0]]} {[[2, 3, 5, 4, 1], [0, 1, 1, 1]]} "Class ", 245, " is:" {{[[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 4, 1, 5], [0, 0, 0, 0]]}, {[[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, {[[5, 1, 4, 3, 2], [0, 0, 0, 0]]}} {[[1, 5, 2, 3, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 4, 1, 5], [0, 0, 0, 0]]}, {[[4, 3, 2, 5, 1], [0, 0, 0, 0]]}, {[[5, 1, 4, 3, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 5, 2, 3, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 2, 3, 5], {1, 2, 3}, {}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {1, 2}, {}], [[1, 5, 3, 4, 2], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38977, 347783, 3447982, 37602245, 447353497, 5765670515, 80026435959, 1190091483826, 18877998176267, 318170909582504, 5677911026433716, 106954187252974515, 2120720309936327198] "" "Class ", 246, " is:" {{[[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 4, 1, 5], [1, 0, 0, 0]]}, {[[4, 3, 2, 5, 1], [1, 0, 0, 0]]}, {[[5, 1, 4, 3, 2], [0, 0, 0, 1]]}} {[[1, 5, 2, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 4, 1, 5], [1, 0, 0, 0]]}, {[[4, 3, 2, 5, 1], [1, 0, 0, 0]]}, {[[5, 1, 4, 3, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 5, 2, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37870, 332606, 3238886, 34633106, 403401630, 5083984545, 68927088254, 1000309842601, 15472249815968, 254090342105070, 4415376035398424, 80942881312997816, 1561137287018363462] "" "Class ", 247, " is:" {{[[1, 5, 2, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 4, 1, 5], [0, 1, 0, 0]]}, {[[4, 3, 2, 5, 1], [0, 1, 0, 0]]}, {[[5, 1, 4, 3, 2], [0, 0, 1, 0]]}} {[[1, 5, 2, 3, 4], [0, 0, 1, 0]]} {[[2, 3, 4, 1, 5], [0, 1, 0, 0]]} "Class ", 248, " is:" {{[[1, 5, 2, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 4, 1, 5], [1, 1, 0, 0]]}, {[[4, 3, 2, 5, 1], [1, 1, 0, 0]]}, {[[5, 1, 4, 3, 2], [0, 0, 1, 1]]}} {[[1, 5, 2, 3, 4], [0, 0, 1, 1]]} {[[2, 3, 4, 1, 5], [1, 1, 0, 0]]} "Class ", 249, " is:" {{[[1, 5, 2, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 4, 1, 5], [0, 0, 1, 0]]}, {[[4, 3, 2, 5, 1], [0, 0, 1, 0]]}, {[[5, 1, 4, 3, 2], [0, 1, 0, 0]]}} {[[1, 5, 2, 3, 4], [0, 1, 0, 0]]} {[[2, 3, 4, 1, 5], [0, 0, 1, 0]]} "Class ", 250, " is:" {{[[1, 5, 2, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 4, 1, 5], [1, 0, 1, 0]]}, {[[4, 3, 2, 5, 1], [1, 0, 1, 0]]}, {[[5, 1, 4, 3, 2], [0, 1, 0, 1]]}} {[[1, 5, 2, 3, 4], [0, 1, 0, 1]]} {[[2, 3, 4, 1, 5], [1, 0, 1, 0]]} "Class ", 251, " is:" {{[[1, 5, 2, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 4, 1, 5], [0, 1, 1, 0]]}, {[[4, 3, 2, 5, 1], [0, 1, 1, 0]]}, {[[5, 1, 4, 3, 2], [0, 1, 1, 0]]}} {[[1, 5, 2, 3, 4], [0, 1, 1, 0]]} {[[2, 3, 4, 1, 5], [0, 1, 1, 0]]} "Class ", 252, " is:" {{[[1, 5, 2, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 4, 1, 5], [1, 1, 1, 0]]}, {[[4, 3, 2, 5, 1], [1, 1, 1, 0]]}, {[[5, 1, 4, 3, 2], [0, 1, 1, 1]]}} {[[1, 5, 2, 3, 4], [0, 1, 1, 1]]} {[[2, 3, 4, 1, 5], [1, 1, 1, 0]]} "Class ", 253, " is:" {{[[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 4, 1, 5], [0, 0, 0, 1]]}, {[[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[5, 1, 4, 3, 2], [1, 0, 0, 0]]}} {[[1, 5, 2, 3, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 4, 1, 5], [0, 0, 0, 1]]}, {[[4, 3, 2, 5, 1], [0, 0, 0, 1]]}, {[[5, 1, 4, 3, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 5, 2, 3, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 2, 3, 5], {2, 3, 4}, {}], [[1, 5, 2, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37874, 332696, 3240416, 34657116, 403773512, 5089835936, 69021919224, 1001903928804, 15500138755224, 254598918643168, 4425046557089424, 81134570778122256, 1565095717271557536] "" "Class ", 254, " is:" {{[[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 4, 1, 5], [1, 0, 0, 1]]}, {[[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {[[5, 1, 4, 3, 2], [1, 0, 0, 1]]}} {[[1, 5, 2, 3, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 4, 1, 5], [1, 0, 0, 1]]}, {[[4, 3, 2, 5, 1], [1, 0, 0, 1]]}, {[[5, 1, 4, 3, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 5, 2, 3, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 0, 1, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4744, 36292, 308712, 2886402, 29393260, 323591088, 3827558510, 48390344564, 650977968568, 9282414304672, 139819244502621, 2218089634202168, 36960165887099814, 645337858836147504] "" "Class ", 255, " is:" {{[[1, 5, 2, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 4, 1, 5], [0, 1, 0, 1]]}, {[[4, 3, 2, 5, 1], [0, 1, 0, 1]]}, {[[5, 1, 4, 3, 2], [1, 0, 1, 0]]}} {[[1, 5, 2, 3, 4], [1, 0, 1, 0]]} {[[2, 3, 4, 1, 5], [0, 1, 0, 1]]} "Class ", 256, " is:" {{[[1, 5, 2, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 4, 1, 5], [1, 1, 0, 1]]}, {[[4, 3, 2, 5, 1], [1, 1, 0, 1]]}, {[[5, 1, 4, 3, 2], [1, 0, 1, 1]]}} {[[1, 5, 2, 3, 4], [1, 0, 1, 1]]} {[[2, 3, 4, 1, 5], [1, 1, 0, 1]]} "Class ", 257, " is:" {{[[1, 5, 2, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 4, 1, 5], [0, 0, 1, 1]]}, {[[4, 3, 2, 5, 1], [0, 0, 1, 1]]}, {[[5, 1, 4, 3, 2], [1, 1, 0, 0]]}} {[[1, 5, 2, 3, 4], [1, 1, 0, 0]]} {[[2, 3, 4, 1, 5], [0, 0, 1, 1]]} "Class ", 258, " is:" {{[[1, 5, 2, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 4, 1, 5], [1, 0, 1, 1]]}, {[[4, 3, 2, 5, 1], [1, 0, 1, 1]]}, {[[5, 1, 4, 3, 2], [1, 1, 0, 1]]}} {[[1, 5, 2, 3, 4], [1, 1, 0, 1]]} {[[2, 3, 4, 1, 5], [1, 0, 1, 1]]} "Class ", 259, " is:" {{[[1, 5, 2, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 4, 1, 5], [0, 1, 1, 1]]}, {[[4, 3, 2, 5, 1], [0, 1, 1, 1]]}, {[[5, 1, 4, 3, 2], [1, 1, 1, 0]]}} {[[1, 5, 2, 3, 4], [1, 1, 1, 0]]} {[[2, 3, 4, 1, 5], [0, 1, 1, 1]]} "Class ", 260, " is:" {{[[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 4, 1, 5], [0, 0, 0, 0]]}, {[[3, 4, 2, 5, 1], [0, 0, 0, 0]]}, {[[5, 1, 4, 2, 3], [0, 0, 0, 0]]}} {[[1, 5, 2, 4, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 4, 1, 5], [0, 0, 0, 0]]}, {[[3, 4, 2, 5, 1], [0, 0, 0, 0]]}, {[[5, 1, 4, 2, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 5, 2, 4, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 2, 3, 5], {1, 2, 3}, {}], [[1, 5, 2, 3, 4], {1, 2, 3}, {}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {1, 2, 3, 4}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4915, 38992, 347990, 3450772, 37640794, 447908832, 5774077131, 80160465380, 1192342710241, 18917802834912, 318910800658728, 5692346715440768, 107249322475436984, 2127032690422975168] "" "Class ", 261, " is:" {{[[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 4, 1, 5], [1, 0, 0, 0]]}, {[[3, 4, 2, 5, 1], [1, 0, 0, 0]]}, {[[5, 1, 4, 2, 3], [0, 0, 0, 1]]}} {[[1, 5, 2, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 4, 1, 5], [1, 0, 0, 0]]}, {[[3, 4, 2, 5, 1], [1, 0, 0, 0]]}, {[[5, 1, 4, 2, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 5, 2, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4839, 37886, 332821, 3241738, 34671733, 403945564, 5092008273, 69051414157, 1002334684941, 15506897401976, 254712591446974, 4427089839643551, 81173687783179707, 1565890305970612128] "" "Class ", 262, " is:" {{[[1, 5, 2, 4, 3], [0, 0, 1, 0]]}, {[[3, 2, 4, 1, 5], [0, 1, 0, 0]]}, {[[3, 4, 2, 5, 1], [0, 1, 0, 0]]}, {[[5, 1, 4, 2, 3], [0, 0, 1, 0]]}} {[[1, 5, 2, 4, 3], [0, 0, 1, 0]]} {[[3, 2, 4, 1, 5], [0, 1, 0, 0]]} "Class ", 263, " is:" {{[[1, 5, 2, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 4, 1, 5], [1, 1, 0, 0]]}, {[[3, 4, 2, 5, 1], [1, 1, 0, 0]]}, {[[5, 1, 4, 2, 3], [0, 0, 1, 1]]}} {[[1, 5, 2, 4, 3], [0, 0, 1, 1]]} {[[3, 2, 4, 1, 5], [1, 1, 0, 0]]} "Class ", 264, " is:" {{[[1, 5, 2, 4, 3], [0, 1, 0, 0]]}, {[[3, 2, 4, 1, 5], [0, 0, 1, 0]]}, {[[3, 4, 2, 5, 1], [0, 0, 1, 0]]}, {[[5, 1, 4, 2, 3], [0, 1, 0, 0]]}} {[[1, 5, 2, 4, 3], [0, 1, 0, 0]]} {[[3, 2, 4, 1, 5], [0, 0, 1, 0]]} "Class ", 265, " is:" {{[[1, 5, 2, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 4, 1, 5], [1, 0, 1, 0]]}, {[[3, 4, 2, 5, 1], [1, 0, 1, 0]]}, {[[5, 1, 4, 2, 3], [0, 1, 0, 1]]}} {[[1, 5, 2, 4, 3], [0, 1, 0, 1]]} {[[3, 2, 4, 1, 5], [1, 0, 1, 0]]} "Class ", 266, " is:" {{[[1, 5, 2, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 4, 1, 5], [0, 1, 1, 0]]}, {[[3, 4, 2, 5, 1], [0, 1, 1, 0]]}, {[[5, 1, 4, 2, 3], [0, 1, 1, 0]]}} {[[1, 5, 2, 4, 3], [0, 1, 1, 0]]} {[[3, 2, 4, 1, 5], [0, 1, 1, 0]]} "Class ", 267, " is:" {{[[1, 5, 2, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 4, 1, 5], [1, 1, 1, 0]]}, {[[3, 4, 2, 5, 1], [1, 1, 1, 0]]}, {[[5, 1, 4, 2, 3], [0, 1, 1, 1]]}} {[[1, 5, 2, 4, 3], [0, 1, 1, 1]]} {[[3, 2, 4, 1, 5], [1, 1, 1, 0]]} "Class ", 268, " is:" {{[[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 4, 1, 5], [0, 0, 0, 1]]}, {[[3, 4, 2, 5, 1], [0, 0, 0, 1]]}, {[[5, 1, 4, 2, 3], [1, 0, 0, 0]]}} {[[1, 5, 2, 4, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 4, 1, 5], [0, 0, 0, 1]]}, {[[3, 4, 2, 5, 1], [0, 0, 0, 1]]}, {[[5, 1, 4, 2, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 5, 2, 4, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 2, 3, 5], {2, 3, 4}, {}], [[1, 5, 2, 3, 4], {2, 3, 4}, {}], [[1, 5, 2, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 3, 4, 2], {2, 3}, {}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4839, 37890, 332911, 3243252, 34695475, 404314543, 5097846976, 69146743589, 1003951140459, 15535452873197, 255238810253701, 4437207990186150, 81376613057795459, 1570132210422810657] "" "Class ", 269, " is:" {{[[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 4, 1, 5], [1, 0, 0, 1]]}, {[[3, 4, 2, 5, 1], [1, 0, 0, 1]]}, {[[5, 1, 4, 2, 3], [1, 0, 0, 1]]}} {[[1, 5, 2, 4, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 4, 1, 5], [1, 0, 0, 1]]}, {[[3, 4, 2, 5, 1], [1, 0, 0, 1]]}, {[[5, 1, 4, 2, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 5, 2, 4, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {[0, 0, 1, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4747, 36368, 310075, 2908152, 29727309, 328706824, 3907096334, 49658121296, 671806789486, 9636188879148, 146040655162497, 2331441700773988, 39100039578607877, 687183928229131712] "" "Class ", 270, " is:" {{[[1, 5, 2, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 4, 1, 5], [0, 1, 0, 1]]}, {[[3, 4, 2, 5, 1], [0, 1, 0, 1]]}, {[[5, 1, 4, 2, 3], [1, 0, 1, 0]]}} {[[1, 5, 2, 4, 3], [1, 0, 1, 0]]} {[[3, 2, 4, 1, 5], [0, 1, 0, 1]]} "Class ", 271, " is:" {{[[1, 5, 2, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 4, 1, 5], [1, 1, 0, 1]]}, {[[3, 4, 2, 5, 1], [1, 1, 0, 1]]}, {[[5, 1, 4, 2, 3], [1, 0, 1, 1]]}} {[[1, 5, 2, 4, 3], [1, 0, 1, 1]]} {[[3, 2, 4, 1, 5], [1, 1, 0, 1]]} "Class ", 272, " is:" {{[[1, 5, 2, 4, 3], [1, 1, 0, 0]]}, {[[3, 2, 4, 1, 5], [0, 0, 1, 1]]}, {[[3, 4, 2, 5, 1], [0, 0, 1, 1]]}, {[[5, 1, 4, 2, 3], [1, 1, 0, 0]]}} {[[1, 5, 2, 4, 3], [1, 1, 0, 0]]} {[[3, 2, 4, 1, 5], [0, 0, 1, 1]]} "Class ", 273, " is:" {{[[1, 5, 2, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 4, 1, 5], [1, 0, 1, 1]]}, {[[3, 4, 2, 5, 1], [1, 0, 1, 1]]}, {[[5, 1, 4, 2, 3], [1, 1, 0, 1]]}} {[[1, 5, 2, 4, 3], [1, 1, 0, 1]]} {[[3, 2, 4, 1, 5], [1, 0, 1, 1]]} "Class ", 274, " is:" {{[[1, 5, 2, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 4, 1, 5], [0, 1, 1, 1]]}, {[[3, 4, 2, 5, 1], [0, 1, 1, 1]]}, {[[5, 1, 4, 2, 3], [1, 1, 1, 0]]}} {[[1, 5, 2, 4, 3], [1, 1, 1, 0]]} {[[3, 2, 4, 1, 5], [0, 1, 1, 1]]} "Class ", 275, " is:" {{[[1, 5, 3, 2, 4], [0, 0, 0, 0]]}, {[[2, 4, 3, 1, 5], [0, 0, 0, 0]]}, {[[4, 2, 3, 5, 1], [0, 0, 0, 0]]}, {[[5, 1, 3, 4, 2], [0, 0, 0, 0]]}} {[[1, 5, 3, 2, 4], [0, 0, 0, 0]]} "For the class ", {{[[1, 5, 3, 2, 4], [0, 0, 0, 0]]}, {[[2, 4, 3, 1, 5], [0, 0, 0, 0]]}, {[[4, 2, 3, 5, 1], [0, 0, 0, 0]]}, {[[5, 1, 3, 4, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 5, 3, 2, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {1, 2, 3, 4}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38980, 347837, 3448792, 37614098, 447530960, 5768427763, 80071232808, 1190854748337, 18891645882204, 318426891675529, 5682942507677216, 107057693682517823, 2122945762085834896] "" "Class ", 276, " is:" {{[[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, {[[2, 4, 3, 1, 5], [1, 0, 0, 0]]}, {[[4, 2, 3, 5, 1], [1, 0, 0, 0]]}, {[[5, 1, 3, 4, 2], [0, 0, 0, 1]]}} {[[1, 5, 3, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, {[[2, 4, 3, 1, 5], [1, 0, 0, 0]]}, {[[4, 2, 3, 5, 1], [1, 0, 0, 0]]}, {[[5, 1, 3, 4, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 5, 3, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37874, 332696, 3240416, 34657116, 403773512, 5089835936, 69021919224, 1001903928804, 15500138755224, 254598918643168, 4425046557089424, 81134570778122256, 1565095717271557536] "" "Class ", 277, " is:" {{[[1, 5, 3, 2, 4], [0, 0, 1, 0]]}, {[[2, 4, 3, 1, 5], [0, 1, 0, 0]]}, {[[4, 2, 3, 5, 1], [0, 1, 0, 0]]}, {[[5, 1, 3, 4, 2], [0, 0, 1, 0]]}} {[[1, 5, 3, 2, 4], [0, 0, 1, 0]]} {[[2, 4, 3, 1, 5], [0, 1, 0, 0]]} "Class ", 278, " is:" {{[[1, 5, 3, 2, 4], [0, 0, 1, 1]]}, {[[2, 4, 3, 1, 5], [1, 1, 0, 0]]}, {[[4, 2, 3, 5, 1], [1, 1, 0, 0]]}, {[[5, 1, 3, 4, 2], [0, 0, 1, 1]]}} {[[1, 5, 3, 2, 4], [0, 0, 1, 1]]} {[[2, 4, 3, 1, 5], [1, 1, 0, 0]]} "Class ", 279, " is:" {{[[1, 5, 3, 2, 4], [0, 1, 0, 0]]}, {[[2, 4, 3, 1, 5], [0, 0, 1, 0]]}, {[[4, 2, 3, 5, 1], [0, 0, 1, 0]]}, {[[5, 1, 3, 4, 2], [0, 1, 0, 0]]}} {[[1, 5, 3, 2, 4], [0, 1, 0, 0]]} {[[2, 4, 3, 1, 5], [0, 0, 1, 0]]} "Class ", 280, " is:" {{[[1, 5, 3, 2, 4], [0, 1, 0, 1]]}, {[[2, 4, 3, 1, 5], [1, 0, 1, 0]]}, {[[4, 2, 3, 5, 1], [1, 0, 1, 0]]}, {[[5, 1, 3, 4, 2], [0, 1, 0, 1]]}} {[[1, 5, 3, 2, 4], [0, 1, 0, 1]]} {[[2, 4, 3, 1, 5], [1, 0, 1, 0]]} "Class ", 281, " is:" {{[[1, 5, 3, 2, 4], [0, 1, 1, 0]]}, {[[2, 4, 3, 1, 5], [0, 1, 1, 0]]}, {[[4, 2, 3, 5, 1], [0, 1, 1, 0]]}, {[[5, 1, 3, 4, 2], [0, 1, 1, 0]]}} {[[1, 5, 3, 2, 4], [0, 1, 1, 0]]} {[[2, 4, 3, 1, 5], [0, 1, 1, 0]]} "Class ", 282, " is:" {{[[1, 5, 3, 2, 4], [0, 1, 1, 1]]}, {[[2, 4, 3, 1, 5], [1, 1, 1, 0]]}, {[[4, 2, 3, 5, 1], [1, 1, 1, 0]]}, {[[5, 1, 3, 4, 2], [0, 1, 1, 1]]}} {[[1, 5, 3, 2, 4], [0, 1, 1, 1]]} {[[2, 4, 3, 1, 5], [1, 1, 1, 0]]} "Class ", 283, " is:" {{[[1, 5, 3, 2, 4], [1, 0, 0, 0]]}, {[[2, 4, 3, 1, 5], [0, 0, 0, 1]]}, {[[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, {[[5, 1, 3, 4, 2], [1, 0, 0, 0]]}} {[[1, 5, 3, 2, 4], [1, 0, 0, 0]]} "For the class ", {{[[1, 5, 3, 2, 4], [1, 0, 0, 0]]}, {[[2, 4, 3, 1, 5], [0, 0, 0, 1]]}, {[[4, 2, 3, 5, 1], [0, 0, 0, 1]]}, {[[5, 1, 3, 4, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 5, 3, 2, 4], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 3, 2, 5], {2, 3, 4}, {}], [[1, 5, 3, 2, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 2, 3], {2, 3, 4}, {}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37874, 332696, 3240416, 34657116, 403773512, 5089835936, 69021919224, 1001903928804, 15500138755224, 254598918643168, 4425046557089424, 81134570778122256, 1565095717271557536] "" "Class ", 284, " is:" {{[[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, {[[2, 4, 3, 1, 5], [1, 0, 0, 1]]}, {[[4, 2, 3, 5, 1], [1, 0, 0, 1]]}, {[[5, 1, 3, 4, 2], [1, 0, 0, 1]]}} {[[1, 5, 3, 2, 4], [1, 0, 0, 1]]} "For the class ", {{[[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, {[[2, 4, 3, 1, 5], [1, 0, 0, 1]]}, {[[4, 2, 3, 5, 1], [1, 0, 0, 1]]}, {[[5, 1, 3, 4, 2], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 5, 3, 2, 4], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 0, 1, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4746, 36350, 309879, 2906997, 29739277, 329338301, 3923804983, 50033410784, 679753984650, 9801361733063, 149476485272753, 2403745451333236, 40649117808310755, 721103112638944175] "" "Class ", 285, " is:" {{[[1, 5, 3, 2, 4], [1, 0, 1, 0]]}, {[[2, 4, 3, 1, 5], [0, 1, 0, 1]]}, {[[4, 2, 3, 5, 1], [0, 1, 0, 1]]}, {[[5, 1, 3, 4, 2], [1, 0, 1, 0]]}} {[[1, 5, 3, 2, 4], [1, 0, 1, 0]]} {[[2, 4, 3, 1, 5], [0, 1, 0, 1]]} "Class ", 286, " is:" {{[[1, 5, 3, 2, 4], [1, 0, 1, 1]]}, {[[2, 4, 3, 1, 5], [1, 1, 0, 1]]}, {[[4, 2, 3, 5, 1], [1, 1, 0, 1]]}, {[[5, 1, 3, 4, 2], [1, 0, 1, 1]]}} {[[1, 5, 3, 2, 4], [1, 0, 1, 1]]} {[[2, 4, 3, 1, 5], [1, 1, 0, 1]]} "Class ", 287, " is:" {{[[1, 5, 3, 2, 4], [1, 1, 0, 0]]}, {[[2, 4, 3, 1, 5], [0, 0, 1, 1]]}, {[[4, 2, 3, 5, 1], [0, 0, 1, 1]]}, {[[5, 1, 3, 4, 2], [1, 1, 0, 0]]}} {[[1, 5, 3, 2, 4], [1, 1, 0, 0]]} {[[2, 4, 3, 1, 5], [0, 0, 1, 1]]} "Class ", 288, " is:" {{[[1, 5, 3, 2, 4], [1, 1, 0, 1]]}, {[[2, 4, 3, 1, 5], [1, 0, 1, 1]]}, {[[4, 2, 3, 5, 1], [1, 0, 1, 1]]}, {[[5, 1, 3, 4, 2], [1, 1, 0, 1]]}} {[[1, 5, 3, 2, 4], [1, 1, 0, 1]]} {[[2, 4, 3, 1, 5], [1, 0, 1, 1]]} "Class ", 289, " is:" {{[[1, 5, 3, 2, 4], [1, 1, 1, 0]]}, {[[2, 4, 3, 1, 5], [0, 1, 1, 1]]}, {[[4, 2, 3, 5, 1], [0, 1, 1, 1]]}, {[[5, 1, 3, 4, 2], [1, 1, 1, 0]]}} {[[1, 5, 3, 2, 4], [1, 1, 1, 0]]} {[[2, 4, 3, 1, 5], [0, 1, 1, 1]]} "Class ", 290, " is:" {{[[1, 5, 3, 4, 2], [0, 0, 0, 0]]}, {[[2, 4, 3, 5, 1], [0, 0, 0, 0]]}, {[[4, 2, 3, 1, 5], [0, 0, 0, 0]]}, {[[5, 1, 3, 2, 4], [0, 0, 0, 0]]}} {[[1, 5, 3, 4, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 5, 3, 4, 2], [0, 0, 0, 0]]}, {[[2, 4, 3, 5, 1], [0, 0, 0, 0]]}, {[[4, 2, 3, 1, 5], [0, 0, 0, 0]]}, {[[5, 1, 3, 2, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 5, 3, 4, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 2, 3, 5], {1, 2, 3}, {}], [[1, 5, 2, 3, 4], {1, 2, 3}, {}], [[1, 5, 2, 4, 3], {1, 2}, {}], [[1, 5, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38976, 347795, 3448312, 37608186, 447452544, 5767315785, 80054392880, 1190583423414, 18887010379776, 318343175603145, 5681348801115680, 107025793890636390, 2122275973981599744] "" "Class ", 291, " is:" {{[[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, {[[2, 4, 3, 5, 1], [1, 0, 0, 0]]}, {[[4, 2, 3, 1, 5], [1, 0, 0, 0]]}, {[[5, 1, 3, 2, 4], [0, 0, 0, 1]]}} {[[1, 5, 3, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, {[[2, 4, 3, 5, 1], [1, 0, 0, 0]]}, {[[4, 2, 3, 1, 5], [1, 0, 0, 0]]}, {[[5, 1, 3, 2, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 5, 3, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37866, 332516, 3237362, 34609120, 403028262, 5078073309, 68830593950, 998674699334, 15443390757396, 253559100810872, 4405173166762731, 80738502391478788, 1556870160310072869] "" "Class ", 292, " is:" {{[[1, 5, 3, 4, 2], [0, 0, 1, 0]]}, {[[2, 4, 3, 5, 1], [0, 1, 0, 0]]}, {[[4, 2, 3, 1, 5], [0, 1, 0, 0]]}, {[[5, 1, 3, 2, 4], [0, 0, 1, 0]]}} {[[1, 5, 3, 4, 2], [0, 0, 1, 0]]} {[[2, 4, 3, 5, 1], [0, 1, 0, 0]]} "Class ", 293, " is:" {{[[1, 5, 3, 4, 2], [0, 0, 1, 1]]}, {[[2, 4, 3, 5, 1], [1, 1, 0, 0]]}, {[[4, 2, 3, 1, 5], [1, 1, 0, 0]]}, {[[5, 1, 3, 2, 4], [0, 0, 1, 1]]}} {[[1, 5, 3, 4, 2], [0, 0, 1, 1]]} {[[2, 4, 3, 5, 1], [1, 1, 0, 0]]} "Class ", 294, " is:" {{[[1, 5, 3, 4, 2], [0, 1, 0, 0]]}, {[[2, 4, 3, 5, 1], [0, 0, 1, 0]]}, {[[4, 2, 3, 1, 5], [0, 0, 1, 0]]}, {[[5, 1, 3, 2, 4], [0, 1, 0, 0]]}} {[[1, 5, 3, 4, 2], [0, 1, 0, 0]]} {[[2, 4, 3, 5, 1], [0, 0, 1, 0]]} "Class ", 295, " is:" {{[[1, 5, 3, 4, 2], [0, 1, 0, 1]]}, {[[2, 4, 3, 5, 1], [1, 0, 1, 0]]}, {[[4, 2, 3, 1, 5], [1, 0, 1, 0]]}, {[[5, 1, 3, 2, 4], [0, 1, 0, 1]]}} {[[1, 5, 3, 4, 2], [0, 1, 0, 1]]} {[[2, 4, 3, 5, 1], [1, 0, 1, 0]]} "Class ", 296, " is:" {{[[1, 5, 3, 4, 2], [0, 1, 1, 0]]}, {[[2, 4, 3, 5, 1], [0, 1, 1, 0]]}, {[[4, 2, 3, 1, 5], [0, 1, 1, 0]]}, {[[5, 1, 3, 2, 4], [0, 1, 1, 0]]}} {[[1, 5, 3, 4, 2], [0, 1, 1, 0]]} {[[2, 4, 3, 5, 1], [0, 1, 1, 0]]} "Class ", 297, " is:" {{[[1, 5, 3, 4, 2], [0, 1, 1, 1]]}, {[[2, 4, 3, 5, 1], [1, 1, 1, 0]]}, {[[4, 2, 3, 1, 5], [1, 1, 1, 0]]}, {[[5, 1, 3, 2, 4], [0, 1, 1, 1]]}} {[[1, 5, 3, 4, 2], [0, 1, 1, 1]]} {[[2, 4, 3, 5, 1], [1, 1, 1, 0]]} "Class ", 298, " is:" {{[[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 4, 3, 5, 1], [0, 0, 0, 1]]}, {[[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, {[[5, 1, 3, 2, 4], [1, 0, 0, 0]]}} {[[1, 5, 3, 4, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, {[[2, 4, 3, 5, 1], [0, 0, 0, 1]]}, {[[4, 2, 3, 1, 5], [0, 0, 0, 1]]}, {[[5, 1, 3, 2, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 5, 3, 4, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {}, {}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 2, 3, 5], {2, 3, 4}, {}], [[1, 5, 2, 3, 4], {2, 3, 4}, {}], [[1, 5, 2, 4, 3], {2, 3}, {}], [[1, 5, 3, 4, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 3, 4, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4840, 37909, 333198, 3247430, 34756773, 405240252, 5112381957, 69385068297, 1008039125310, 15608836683658, 256616866094986, 4464256712904744, 81930953664017213, 1581980127397527165] "" "Class ", 299, " is:" {{[[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, {[[2, 4, 3, 5, 1], [1, 0, 0, 1]]}, {[[4, 2, 3, 1, 5], [1, 0, 0, 1]]}, {[[5, 1, 3, 2, 4], [1, 0, 0, 1]]}} {[[1, 5, 3, 4, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, {[[2, 4, 3, 5, 1], [1, 0, 0, 1]]}, {[[4, 2, 3, 1, 5], [1, 0, 0, 1]]}, {[[5, 1, 3, 2, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 5, 3, 4, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[1, 4, 3, 2], {2}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4747, 36368, 310075, 2908152, 29727309, 328706824, 3907096334, 49658121296, 671806789486, 9636188879148, 146040655162497, 2331441700773988, 39100039578607877, 687183928229131712] "" "Class ", 300, " is:" {{[[1, 5, 3, 4, 2], [1, 0, 1, 0]]}, {[[2, 4, 3, 5, 1], [0, 1, 0, 1]]}, {[[4, 2, 3, 1, 5], [0, 1, 0, 1]]}, {[[5, 1, 3, 2, 4], [1, 0, 1, 0]]}} {[[1, 5, 3, 4, 2], [1, 0, 1, 0]]} {[[2, 4, 3, 5, 1], [0, 1, 0, 1]]} "Class ", 301, " is:" {{[[1, 5, 3, 4, 2], [1, 0, 1, 1]]}, {[[2, 4, 3, 5, 1], [1, 1, 0, 1]]}, {[[4, 2, 3, 1, 5], [1, 1, 0, 1]]}, {[[5, 1, 3, 2, 4], [1, 0, 1, 1]]}} {[[1, 5, 3, 4, 2], [1, 0, 1, 1]]} {[[2, 4, 3, 5, 1], [1, 1, 0, 1]]} "Class ", 302, " is:" {{[[1, 5, 3, 4, 2], [1, 1, 0, 0]]}, {[[2, 4, 3, 5, 1], [0, 0, 1, 1]]}, {[[4, 2, 3, 1, 5], [0, 0, 1, 1]]}, {[[5, 1, 3, 2, 4], [1, 1, 0, 0]]}} {[[1, 5, 3, 4, 2], [1, 1, 0, 0]]} {[[2, 4, 3, 5, 1], [0, 0, 1, 1]]} "Class ", 303, " is:" {{[[1, 5, 3, 4, 2], [1, 1, 0, 1]]}, {[[2, 4, 3, 5, 1], [1, 0, 1, 1]]}, {[[4, 2, 3, 1, 5], [1, 0, 1, 1]]}, {[[5, 1, 3, 2, 4], [1, 1, 0, 1]]}} {[[1, 5, 3, 4, 2], [1, 1, 0, 1]]} {[[2, 4, 3, 5, 1], [1, 0, 1, 1]]} "Class ", 304, " is:" {{[[1, 5, 3, 4, 2], [1, 1, 1, 0]]}, {[[2, 4, 3, 5, 1], [0, 1, 1, 1]]}, {[[4, 2, 3, 1, 5], [0, 1, 1, 1]]}, {[[5, 1, 3, 2, 4], [1, 1, 1, 0]]}} {[[1, 5, 3, 4, 2], [1, 1, 1, 0]]} {[[2, 4, 3, 5, 1], [0, 1, 1, 1]]} "Class ", 305, " is:" {{[[1, 5, 3, 4, 2], [1, 1, 1, 1]]}, {[[2, 4, 3, 5, 1], [1, 1, 1, 1]]}, {[[4, 2, 3, 1, 5], [1, 1, 1, 1]]}, {[[5, 1, 3, 2, 4], [1, 1, 1, 1]]}} {[[1, 5, 3, 4, 2], [1, 1, 1, 1]]} {[[2, 4, 3, 5, 1], [1, 1, 1, 1]]} "Class ", 306, " is:" {{[[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 2, 4, 5, 1], [0, 0, 0, 0]]}, {[[3, 4, 2, 1, 5], [0, 0, 0, 0]]}, {[[5, 1, 2, 4, 3], [0, 0, 0, 0]]}} {[[1, 5, 4, 2, 3], [0, 0, 0, 0]]} "For the class ", {{[[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, {[[3, 2, 4, 5, 1], [0, 0, 0, 0]]}, {[[3, 4, 2, 1, 5], [0, 0, 0, 0]]}, {[[5, 1, 2, 4, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 5, 4, 2, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {1, 2, 3, 4}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38977, 347793, 3448182, 37605545, 447406214, 5766525727, 80040747361, 1190340631290, 18882526564227, 318256944873984, 5679619717431613, 106989639176572571, 2121488012937187849] "" "Class ", 307, " is:" {{[[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 4, 5, 1], [1, 0, 0, 0]]}, {[[3, 4, 2, 1, 5], [1, 0, 0, 0]]}, {[[5, 1, 2, 4, 3], [0, 0, 0, 1]]}} {[[1, 5, 4, 2, 3], [0, 0, 0, 1]]} "For the class ", {{[[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, {[[3, 2, 4, 5, 1], [1, 0, 0, 0]]}, {[[3, 4, 2, 1, 5], [1, 0, 0, 0]]}, {[[5, 1, 2, 4, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 5, 4, 2, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37874, 332696, 3240416, 34657116, 403773512, 5089835936, 69021919224, 1001903928804, 15500138755224, 254598918643168, 4425046557089424, 81134570778122256, 1565095717271557536] "" "Class ", 308, " is:" {{[[1, 5, 4, 2, 3], [0, 0, 1, 0]]}, {[[3, 2, 4, 5, 1], [0, 1, 0, 0]]}, {[[3, 4, 2, 1, 5], [0, 1, 0, 0]]}, {[[5, 1, 2, 4, 3], [0, 0, 1, 0]]}} {[[1, 5, 4, 2, 3], [0, 0, 1, 0]]} {[[3, 2, 4, 5, 1], [0, 1, 0, 0]]} "Class ", 309, " is:" {{[[1, 5, 4, 2, 3], [0, 0, 1, 1]]}, {[[3, 2, 4, 5, 1], [1, 1, 0, 0]]}, {[[3, 4, 2, 1, 5], [1, 1, 0, 0]]}, {[[5, 1, 2, 4, 3], [0, 0, 1, 1]]}} {[[1, 5, 4, 2, 3], [0, 0, 1, 1]]} {[[3, 2, 4, 5, 1], [1, 1, 0, 0]]} "Class ", 310, " is:" {{[[1, 5, 4, 2, 3], [0, 1, 0, 0]]}, {[[3, 2, 4, 5, 1], [0, 0, 1, 0]]}, {[[3, 4, 2, 1, 5], [0, 0, 1, 0]]}, {[[5, 1, 2, 4, 3], [0, 1, 0, 0]]}} {[[1, 5, 4, 2, 3], [0, 1, 0, 0]]} {[[3, 2, 4, 5, 1], [0, 0, 1, 0]]} "Class ", 311, " is:" {{[[1, 5, 4, 2, 3], [0, 1, 0, 1]]}, {[[3, 2, 4, 5, 1], [1, 0, 1, 0]]}, {[[3, 4, 2, 1, 5], [1, 0, 1, 0]]}, {[[5, 1, 2, 4, 3], [0, 1, 0, 1]]}} {[[1, 5, 4, 2, 3], [0, 1, 0, 1]]} {[[3, 2, 4, 5, 1], [1, 0, 1, 0]]} "Class ", 312, " is:" {{[[1, 5, 4, 2, 3], [0, 1, 1, 0]]}, {[[3, 2, 4, 5, 1], [0, 1, 1, 0]]}, {[[3, 4, 2, 1, 5], [0, 1, 1, 0]]}, {[[5, 1, 2, 4, 3], [0, 1, 1, 0]]}} {[[1, 5, 4, 2, 3], [0, 1, 1, 0]]} {[[3, 2, 4, 5, 1], [0, 1, 1, 0]]} "Class ", 313, " is:" {{[[1, 5, 4, 2, 3], [0, 1, 1, 1]]}, {[[3, 2, 4, 5, 1], [1, 1, 1, 0]]}, {[[3, 4, 2, 1, 5], [1, 1, 1, 0]]}, {[[5, 1, 2, 4, 3], [0, 1, 1, 1]]}} {[[1, 5, 4, 2, 3], [0, 1, 1, 1]]} {[[3, 2, 4, 5, 1], [1, 1, 1, 0]]} "Class ", 314, " is:" {{[[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 4, 5, 1], [0, 0, 0, 1]]}, {[[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, {[[5, 1, 2, 4, 3], [1, 0, 0, 0]]}} {[[1, 5, 4, 2, 3], [1, 0, 0, 0]]} "For the class ", {{[[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, {[[3, 2, 4, 5, 1], [0, 0, 0, 1]]}, {[[3, 4, 2, 1, 5], [0, 0, 0, 1]]}, {[[5, 1, 2, 4, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 5, 4, 2, 3], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 3, 2, 5], {2, 3, 4}, {}], [[1, 5, 3, 2, 4], {2, 3, 4}, {}], [[1, 5, 4, 2, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[1, 5, 4, 3, 2], {2}, {}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37868, 332546, 3237620, 34609332, 402972008, 5076245018, 68785548072, 997655804160, 15420936790944, 253064231968336, 4394118358559280, 80486313018869424, 1550969499004966272] "" "Class ", 315, " is:" {{[[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 4, 5, 1], [1, 0, 0, 1]]}, {[[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[5, 1, 2, 4, 3], [1, 0, 0, 1]]}} {[[1, 5, 4, 2, 3], [1, 0, 0, 1]]} "For the class ", {{[[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, {[[3, 2, 4, 5, 1], [1, 0, 0, 1]]}, {[[3, 4, 2, 1, 5], [1, 0, 0, 1]]}, {[[5, 1, 2, 4, 3], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 5, 4, 2, 3], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {2}, {[0, 0, 1, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4746, 36350, 309879, 2906997, 29739277, 329338301, 3923804983, 50033410784, 679753984650, 9801361733063, 149476485272753, 2403745451333236, 40649117808310755, 721103112638944175] "" "Class ", 316, " is:" {{[[1, 5, 4, 2, 3], [1, 0, 1, 0]]}, {[[3, 2, 4, 5, 1], [0, 1, 0, 1]]}, {[[3, 4, 2, 1, 5], [0, 1, 0, 1]]}, {[[5, 1, 2, 4, 3], [1, 0, 1, 0]]}} {[[1, 5, 4, 2, 3], [1, 0, 1, 0]]} {[[3, 2, 4, 5, 1], [0, 1, 0, 1]]} "Class ", 317, " is:" {{[[1, 5, 4, 2, 3], [1, 0, 1, 1]]}, {[[3, 2, 4, 5, 1], [1, 1, 0, 1]]}, {[[3, 4, 2, 1, 5], [1, 1, 0, 1]]}, {[[5, 1, 2, 4, 3], [1, 0, 1, 1]]}} {[[1, 5, 4, 2, 3], [1, 0, 1, 1]]} {[[3, 2, 4, 5, 1], [1, 1, 0, 1]]} "Class ", 318, " is:" {{[[1, 5, 4, 2, 3], [1, 1, 0, 0]]}, {[[3, 2, 4, 5, 1], [0, 0, 1, 1]]}, {[[3, 4, 2, 1, 5], [0, 0, 1, 1]]}, {[[5, 1, 2, 4, 3], [1, 1, 0, 0]]}} {[[1, 5, 4, 2, 3], [1, 1, 0, 0]]} {[[3, 2, 4, 5, 1], [0, 0, 1, 1]]} "Class ", 319, " is:" {{[[1, 5, 4, 2, 3], [1, 1, 0, 1]]}, {[[3, 2, 4, 5, 1], [1, 0, 1, 1]]}, {[[3, 4, 2, 1, 5], [1, 0, 1, 1]]}, {[[5, 1, 2, 4, 3], [1, 1, 0, 1]]}} {[[1, 5, 4, 2, 3], [1, 1, 0, 1]]} {[[3, 2, 4, 5, 1], [1, 0, 1, 1]]} "Class ", 320, " is:" {{[[1, 5, 4, 2, 3], [1, 1, 1, 0]]}, {[[3, 2, 4, 5, 1], [0, 1, 1, 1]]}, {[[3, 4, 2, 1, 5], [0, 1, 1, 1]]}, {[[5, 1, 2, 4, 3], [1, 1, 1, 0]]}} {[[1, 5, 4, 2, 3], [1, 1, 1, 0]]} {[[3, 2, 4, 5, 1], [0, 1, 1, 1]]} "Class ", 321, " is:" {{[[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[5, 1, 2, 3, 4], [0, 0, 0, 0]]}} {[[1, 5, 4, 3, 2], [0, 0, 0, 0]]} "For the class ", {{[[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, {[[2, 3, 4, 5, 1], [0, 0, 0, 0]]}, {[[4, 3, 2, 1, 5], [0, 0, 0, 0]]}, {[[5, 1, 2, 3, 4], [0, 0, 0, 0]]}}, " the pattern set ", {[[1, 5, 4, 3, 2], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 3, 2, 5], {1, 2, 3}, {}], [[1, 5, 3, 2, 4], {1, 2, 3}, {}], [[1, 5, 4, 2, 3], {1, 2, 3}, {}], [[1, 5, 4, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38976, 347795, 3448312, 37608186, 447452544, 5767315785, 80054392880, 1190583423414, 18887010379776, 318343175603145, 5681348801115680, 107025793890636390, 2122275973981599744] "" "Class ", 322, " is:" {{[[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[5, 1, 2, 3, 4], [0, 0, 0, 1]]}} {[[1, 5, 4, 3, 2], [0, 0, 0, 1]]} "For the class ", {{[[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, {[[2, 3, 4, 5, 1], [1, 0, 0, 0]]}, {[[4, 3, 2, 1, 5], [1, 0, 0, 0]]}, {[[5, 1, 2, 3, 4], [0, 0, 0, 1]]}}, " the pattern set ", {[[1, 5, 4, 3, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37864, 332476, 3236740, 34599992, 402894232, 5076048610, 68798725120, 998148956009, 15434279713400, 253393186307010, 4402000665397314, 80674887543929046, 1555534563807643908] "" "Class ", 323, " is:" {{[[1, 5, 4, 3, 2], [0, 0, 1, 0]]}, {[[2, 3, 4, 5, 1], [0, 1, 0, 0]]}, {[[4, 3, 2, 1, 5], [0, 1, 0, 0]]}, {[[5, 1, 2, 3, 4], [0, 0, 1, 0]]}} {[[1, 5, 4, 3, 2], [0, 0, 1, 0]]} {[[2, 3, 4, 5, 1], [0, 1, 0, 0]]} "Class ", 324, " is:" {{[[1, 5, 4, 3, 2], [0, 0, 1, 1]]}, {[[2, 3, 4, 5, 1], [1, 1, 0, 0]]}, {[[4, 3, 2, 1, 5], [1, 1, 0, 0]]}, {[[5, 1, 2, 3, 4], [0, 0, 1, 1]]}} {[[1, 5, 4, 3, 2], [0, 0, 1, 1]]} {[[2, 3, 4, 5, 1], [1, 1, 0, 0]]} "Class ", 325, " is:" {{[[1, 5, 4, 3, 2], [0, 1, 0, 0]]}, {[[2, 3, 4, 5, 1], [0, 0, 1, 0]]}, {[[4, 3, 2, 1, 5], [0, 0, 1, 0]]}, {[[5, 1, 2, 3, 4], [0, 1, 0, 0]]}} {[[1, 5, 4, 3, 2], [0, 1, 0, 0]]} {[[2, 3, 4, 5, 1], [0, 0, 1, 0]]} "Class ", 326, " is:" {{[[1, 5, 4, 3, 2], [0, 1, 0, 1]]}, {[[2, 3, 4, 5, 1], [1, 0, 1, 0]]}, {[[4, 3, 2, 1, 5], [1, 0, 1, 0]]}, {[[5, 1, 2, 3, 4], [0, 1, 0, 1]]}} {[[1, 5, 4, 3, 2], [0, 1, 0, 1]]} {[[2, 3, 4, 5, 1], [1, 0, 1, 0]]} "Class ", 327, " is:" {{[[1, 5, 4, 3, 2], [0, 1, 1, 0]]}, {[[2, 3, 4, 5, 1], [0, 1, 1, 0]]}, {[[4, 3, 2, 1, 5], [0, 1, 1, 0]]}, {[[5, 1, 2, 3, 4], [0, 1, 1, 0]]}} {[[1, 5, 4, 3, 2], [0, 1, 1, 0]]} {[[2, 3, 4, 5, 1], [0, 1, 1, 0]]} "Class ", 328, " is:" {{[[1, 5, 4, 3, 2], [0, 1, 1, 1]]}, {[[2, 3, 4, 5, 1], [1, 1, 1, 0]]}, {[[4, 3, 2, 1, 5], [1, 1, 1, 0]]}, {[[5, 1, 2, 3, 4], [0, 1, 1, 1]]}} {[[1, 5, 4, 3, 2], [0, 1, 1, 1]]} {[[2, 3, 4, 5, 1], [1, 1, 1, 0]]} "Class ", 329, " is:" {{[[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[5, 1, 2, 3, 4], [1, 0, 0, 0]]}} {[[1, 5, 4, 3, 2], [1, 0, 0, 0]]} "For the class ", {{[[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, {[[2, 3, 4, 5, 1], [0, 0, 0, 1]]}, {[[4, 3, 2, 1, 5], [0, 0, 0, 1]]}, {[[5, 1, 2, 3, 4], [1, 0, 0, 0]]}}, " the pattern set ", {[[1, 5, 4, 3, 2], [1, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {}, {}], [[2, 4, 3, 1], {1, 2, 3}, {}], [[1, 4, 3, 2, 5], {2, 3, 4}, {}], [[1, 5, 3, 2, 4], {2, 3, 4}, {}], [[1, 5, 4, 2, 3], {2, 3, 4}, {}], [[1, 5, 4, 3, 2], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 5, 4, 3, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 705, 4857, 38142, 336291, 3289057, 35337067, 413698248, 5241768017, 71465060725, 1043175024243, 16231998346794, 268207096127991, 4690005160446721, 86528908665043683, 1679764981327051508] "" "Class ", 330, " is:" {{[[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[5, 1, 2, 3, 4], [1, 0, 0, 1]]}} {[[1, 5, 4, 3, 2], [1, 0, 0, 1]]} "For the class ", {{[[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, {[[2, 3, 4, 5, 1], [1, 0, 0, 1]]}, {[[4, 3, 2, 1, 5], [1, 0, 0, 1]]}, {[[5, 1, 2, 3, 4], [1, 0, 0, 1]]}}, " the pattern set ", {[[1, 5, 4, 3, 2], [1, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {2}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {2, 3}, {}], [[1, 4, 2, 3], {2, 3}, {}], [[1, 4, 3, 2], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[2, 4, 3, 1], {1, 2, 3}, {}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 701, 4768, 36699, 314873, 2976594, 30716173, 343381013, 4132329885, 53246591294, 731247853656, 10660411248600, 164396895171652, 2673453999718142, 45720042117632633, 820188876576377955] "" "Class ", 331, " is:" {{[[1, 5, 4, 3, 2], [1, 0, 1, 0]]}, {[[2, 3, 4, 5, 1], [0, 1, 0, 1]]}, {[[4, 3, 2, 1, 5], [0, 1, 0, 1]]}, {[[5, 1, 2, 3, 4], [1, 0, 1, 0]]}} {[[1, 5, 4, 3, 2], [1, 0, 1, 0]]} {[[2, 3, 4, 5, 1], [0, 1, 0, 1]]} "Class ", 332, " is:" {{[[1, 5, 4, 3, 2], [1, 0, 1, 1]]}, {[[2, 3, 4, 5, 1], [1, 1, 0, 1]]}, {[[4, 3, 2, 1, 5], [1, 1, 0, 1]]}, {[[5, 1, 2, 3, 4], [1, 0, 1, 1]]}} {[[1, 5, 4, 3, 2], [1, 0, 1, 1]]} {[[2, 3, 4, 5, 1], [1, 1, 0, 1]]} "Class ", 333, " is:" {{[[1, 5, 4, 3, 2], [1, 1, 0, 0]]}, {[[2, 3, 4, 5, 1], [0, 0, 1, 1]]}, {[[4, 3, 2, 1, 5], [0, 0, 1, 1]]}, {[[5, 1, 2, 3, 4], [1, 1, 0, 0]]}} {[[1, 5, 4, 3, 2], [1, 1, 0, 0]]} {[[2, 3, 4, 5, 1], [0, 0, 1, 1]]} "Class ", 334, " is:" {{[[1, 5, 4, 3, 2], [1, 1, 0, 1]]}, {[[2, 3, 4, 5, 1], [1, 0, 1, 1]]}, {[[4, 3, 2, 1, 5], [1, 0, 1, 1]]}, {[[5, 1, 2, 3, 4], [1, 1, 0, 1]]}} {[[1, 5, 4, 3, 2], [1, 1, 0, 1]]} {[[2, 3, 4, 5, 1], [1, 0, 1, 1]]} "Class ", 335, " is:" {{[[1, 5, 4, 3, 2], [1, 1, 1, 0]]}, {[[2, 3, 4, 5, 1], [0, 1, 1, 1]]}, {[[4, 3, 2, 1, 5], [0, 1, 1, 1]]}, {[[5, 1, 2, 3, 4], [1, 1, 1, 0]]}} {[[1, 5, 4, 3, 2], [1, 1, 1, 0]]} {[[2, 3, 4, 5, 1], [0, 1, 1, 1]]} "Class ", 336, " is:" {{[[1, 5, 4, 3, 2], [1, 1, 1, 1]]}, {[[2, 3, 4, 5, 1], [1, 1, 1, 1]]}, {[[4, 3, 2, 1, 5], [1, 1, 1, 1]]}, {[[5, 1, 2, 3, 4], [1, 1, 1, 1]]}} {[[1, 5, 4, 3, 2], [1, 1, 1, 1]]} {[[2, 3, 4, 5, 1], [1, 1, 1, 1]]} "Class ", 337, " is:" {{[[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3, 5, 4], [1, 0, 0, 0]]}, {[[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[4, 5, 3, 1, 2], [1, 0, 0, 0]]}} {[[2, 1, 3, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, {[[2, 1, 3, 5, 4], [1, 0, 0, 0]]}, {[[4, 5, 3, 1, 2], [0, 0, 0, 1]]}, {[[4, 5, 3, 1, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 3, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37865, 332477, 3236426, 34590177, 402668738, 5071370729, 68704912881, 996273162495, 15396276858765, 252606030208648, 4385244619452210, 80307227773966998, 1547205357376714365] "" "Class ", 338, " is:" {{[[2, 1, 3, 5, 4], [0, 0, 1, 0]]}, {[[2, 1, 3, 5, 4], [0, 1, 0, 0]]}, {[[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[4, 5, 3, 1, 2], [0, 1, 0, 0]]}} {[[2, 1, 3, 5, 4], [0, 0, 1, 0]]} {[[2, 1, 3, 5, 4], [0, 1, 0, 0]]} "For the class ", {{[[2, 1, 3, 5, 4], [0, 0, 1, 0]]}, {[[2, 1, 3, 5, 4], [0, 1, 0, 0]]}, {[[4, 5, 3, 1, 2], [0, 0, 1, 0]]}, {[[4, 5, 3, 1, 2], [0, 1, 0, 0]]}}, " the pattern set ", {[[2, 1, 3, 5, 4], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {3}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 4, 5, 3], {3, 4}, {}], [[3, 1, 4, 5, 2], {2, 3, 4}, {}], [[3, 2, 4, 5, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 703, 4817, 37534, 327599, 3164891, 33519051, 386090952, 4804566545, 64226920247, 917805091675, 13960498198182, 225185003512111, 3839042851786987, 68970587034336831, 1302286587667567976] "" "Class ", 339, " is:" {{[[2, 1, 3, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 3, 5, 4], [1, 1, 0, 0]]}, {[[4, 5, 3, 1, 2], [0, 0, 1, 1]]}, {[[4, 5, 3, 1, 2], [1, 1, 0, 0]]}} {[[2, 1, 3, 5, 4], [0, 0, 1, 1]]} {[[2, 1, 3, 5, 4], [1, 1, 0, 0]]} "Class ", 340, " is:" {{[[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[2, 1, 3, 5, 4], [1, 0, 1, 0]]}, {[[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[4, 5, 3, 1, 2], [1, 0, 1, 0]]}} {[[2, 1, 3, 5, 4], [0, 1, 0, 1]]} "For the class ", {{[[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, {[[2, 1, 3, 5, 4], [1, 0, 1, 0]]}, {[[4, 5, 3, 1, 2], [0, 1, 0, 1]]}, {[[4, 5, 3, 1, 2], [1, 0, 1, 0]]}}, " the pattern set ", {[[2, 1, 3, 5, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 0, 1, 0]}], [[2, 1, 4, 3], {3}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 699, 4723, 35969, 304179, 2823910, 28520022, 311039615, 3640665886, 45497926429, 604390322111, 8501294894254, 126191172400559, 1970854869817747, 32300525430002906, 554192586837675141] "" "Class ", 341, " is:" {{[[2, 1, 3, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3, 5, 4], [1, 1, 1, 0]]}, {[[4, 5, 3, 1, 2], [0, 1, 1, 1]]}, {[[4, 5, 3, 1, 2], [1, 1, 1, 0]]}} {[[2, 1, 3, 5, 4], [0, 1, 1, 1]]} {[[2, 1, 3, 5, 4], [1, 1, 1, 0]]} "Class ", 342, " is:" {{[[2, 1, 3, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3, 5, 4], [1, 1, 0, 1]]}, {[[4, 5, 3, 1, 2], [1, 0, 1, 1]]}, {[[4, 5, 3, 1, 2], [1, 1, 0, 1]]}} {[[2, 1, 3, 5, 4], [1, 0, 1, 1]]} {[[2, 1, 3, 5, 4], [1, 1, 0, 1]]} "Class ", 343, " is:" {{[[2, 1, 4, 5, 3], [0, 0, 0, 0]]}, {[[3, 1, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, {[[4, 5, 2, 1, 3], [0, 0, 0, 0]]}} {[[2, 1, 4, 5, 3], [0, 0, 0, 0]]} "For the class ", {{[[2, 1, 4, 5, 3], [0, 0, 0, 0]]}, {[[3, 1, 2, 5, 4], [0, 0, 0, 0]]}, {[[3, 5, 4, 1, 2], [0, 0, 0, 0]]}, {[[4, 5, 2, 1, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 5, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}], [[2, 1, 3, 4, 5], {1, 2, 3, 4}, {}], [[2, 1, 3, 5, 4], {1, 2, 3}, {}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {1, 2, 3}, {}], [[3, 2, 4, 5, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38977, 347808, 3448482, 37610495, 447485376, 5767807974, 80062182733, 1190713519497, 18889300119942, 318385578137273, 5682173514985293, 107042610409389945, 2122634830121877061] "" "Class ", 344, " is:" {{[[2, 1, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[4, 5, 2, 1, 3], [0, 0, 0, 1]]}} {[[2, 1, 4, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[2, 1, 4, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 2, 5, 4], [1, 0, 0, 0]]}, {[[3, 5, 4, 1, 2], [1, 0, 0, 0]]}, {[[4, 5, 2, 1, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 4, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37865, 332477, 3236426, 34590177, 402668738, 5071370729, 68704912881, 996273162495, 15396276858765, 252606030208648, 4385244619452210, 80307227773966998, 1547205357376714365] "" "Class ", 345, " is:" {{[[2, 1, 4, 5, 3], [0, 0, 1, 0]]}, {[[3, 1, 2, 5, 4], [0, 1, 0, 0]]}, {[[3, 5, 4, 1, 2], [0, 1, 0, 0]]}, {[[4, 5, 2, 1, 3], [0, 0, 1, 0]]}} {[[2, 1, 4, 5, 3], [0, 0, 1, 0]]} {[[3, 1, 2, 5, 4], [0, 1, 0, 0]]} "Class ", 346, " is:" {{[[2, 1, 4, 5, 3], [0, 0, 1, 1]]}, {[[3, 1, 2, 5, 4], [1, 1, 0, 0]]}, {[[3, 5, 4, 1, 2], [1, 1, 0, 0]]}, {[[4, 5, 2, 1, 3], [0, 0, 1, 1]]}} {[[2, 1, 4, 5, 3], [0, 0, 1, 1]]} {[[3, 1, 2, 5, 4], [1, 1, 0, 0]]} "Class ", 347, " is:" {{[[2, 1, 4, 5, 3], [0, 1, 0, 0]]}, {[[3, 1, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[4, 5, 2, 1, 3], [0, 1, 0, 0]]}} {[[2, 1, 4, 5, 3], [0, 1, 0, 0]]} "For the class ", {{[[2, 1, 4, 5, 3], [0, 1, 0, 0]]}, {[[3, 1, 2, 5, 4], [0, 0, 1, 0]]}, {[[3, 5, 4, 1, 2], [0, 0, 1, 0]]}, {[[4, 5, 2, 1, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[2, 1, 4, 5, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {}, {}], [[2, 1, 4, 3], {3}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[2, 1, 3, 4, 5], {3}, {}], [[2, 1, 3, 5, 4], {3, 4}, {}], [[2, 1, 4, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 4, 5, 2], {2, 3, 4}, {}], [[3, 2, 4, 5, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 703, 4817, 37534, 327599, 3164891, 33519051, 386090952, 4804566545, 64226920247, 917805091675, 13960498198182, 225185003512111, 3839042851786987, 68970587034336831, 1302286587667567976] "" "Class ", 348, " is:" {{[[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[4, 5, 2, 1, 3], [0, 1, 0, 1]]}} {[[2, 1, 4, 5, 3], [0, 1, 0, 1]]} "For the class ", {{[[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 2, 5, 4], [1, 0, 1, 0]]}, {[[3, 5, 4, 1, 2], [1, 0, 1, 0]]}, {[[4, 5, 2, 1, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[2, 1, 4, 5, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {[0, 0, 1, 0, 0]}], [[2, 1, 4, 3], {3}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4745, 36310, 308919, 2887980, 29392211, 323201330, 3815857732, 48116262912, 645071086840, 9158805860008, 137245734060145, 2164092026050332, 35809882818819669, 620348584920591806] "" "Class ", 349, " is:" {{[[2, 1, 4, 5, 3], [0, 1, 1, 0]]}, {[[3, 1, 2, 5, 4], [0, 1, 1, 0]]}, {[[3, 5, 4, 1, 2], [0, 1, 1, 0]]}, {[[4, 5, 2, 1, 3], [0, 1, 1, 0]]}} {[[2, 1, 4, 5, 3], [0, 1, 1, 0]]} {[[3, 1, 2, 5, 4], [0, 1, 1, 0]]} "Class ", 350, " is:" {{[[2, 1, 4, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 2, 5, 4], [1, 1, 1, 0]]}, {[[3, 5, 4, 1, 2], [1, 1, 1, 0]]}, {[[4, 5, 2, 1, 3], [0, 1, 1, 1]]}} {[[2, 1, 4, 5, 3], [0, 1, 1, 1]]} {[[3, 1, 2, 5, 4], [1, 1, 1, 0]]} "Class ", 351, " is:" {{[[2, 1, 4, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, {[[4, 5, 2, 1, 3], [1, 0, 0, 0]]}} {[[2, 1, 4, 5, 3], [1, 0, 0, 0]]} {[[3, 1, 2, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[2, 1, 4, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 2, 5, 4], [0, 0, 0, 1]]}, {[[3, 5, 4, 1, 2], [0, 0, 0, 1]]}, {[[4, 5, 2, 1, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[3, 1, 2, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {}], [[3, 1, 2], {}, {}], [[3, 2, 1], {1}, {}], [[3, 1, 2, 4], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[4, 1, 2, 3], {1, 2, 3}, {}], [[4, 1, 3, 2], {1, 2}, {}], [[4, 2, 3, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37868, 332558, 3238028, 34618998, 403173236, 5080235750, 68863804944, 999203154888, 15452127899940, 253709339041360, 4407859543644456, 80788408031974320, 1557832095119647872] "" "Class ", 352, " is:" {{[[2, 1, 4, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 2, 5, 4], [1, 0, 0, 1]]}, {[[3, 5, 4, 1, 2], [1, 0, 0, 1]]}, {[[4, 5, 2, 1, 3], [1, 0, 0, 1]]}} {[[2, 1, 4, 5, 3], [1, 0, 0, 1]]} {[[3, 1, 2, 5, 4], [1, 0, 0, 1]]} "Class ", 353, " is:" {{[[2, 1, 4, 5, 3], [1, 0, 1, 0]]}, {[[3, 1, 2, 5, 4], [0, 1, 0, 1]]}, {[[3, 5, 4, 1, 2], [0, 1, 0, 1]]}, {[[4, 5, 2, 1, 3], [1, 0, 1, 0]]}} {[[2, 1, 4, 5, 3], [1, 0, 1, 0]]} {[[3, 1, 2, 5, 4], [0, 1, 0, 1]]} "Class ", 354, " is:" {{[[2, 1, 4, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 2, 5, 4], [1, 1, 0, 1]]}, {[[3, 5, 4, 1, 2], [1, 1, 0, 1]]}, {[[4, 5, 2, 1, 3], [1, 0, 1, 1]]}} {[[2, 1, 4, 5, 3], [1, 0, 1, 1]]} {[[3, 1, 2, 5, 4], [1, 1, 0, 1]]} "Class ", 355, " is:" {{[[2, 1, 4, 5, 3], [1, 1, 0, 0]]}, {[[3, 1, 2, 5, 4], [0, 0, 1, 1]]}, {[[3, 5, 4, 1, 2], [0, 0, 1, 1]]}, {[[4, 5, 2, 1, 3], [1, 1, 0, 0]]}} {[[2, 1, 4, 5, 3], [1, 1, 0, 0]]} {[[3, 1, 2, 5, 4], [0, 0, 1, 1]]} "Class ", 356, " is:" {{[[2, 1, 4, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 2, 5, 4], [1, 0, 1, 1]]}, {[[3, 5, 4, 1, 2], [1, 0, 1, 1]]}, {[[4, 5, 2, 1, 3], [1, 1, 0, 1]]}} {[[2, 1, 4, 5, 3], [1, 1, 0, 1]]} {[[3, 1, 2, 5, 4], [1, 0, 1, 1]]} "Class ", 357, " is:" {{[[2, 1, 4, 5, 3], [1, 1, 1, 0]]}, {[[3, 1, 2, 5, 4], [0, 1, 1, 1]]}, {[[3, 5, 4, 1, 2], [0, 1, 1, 1]]}, {[[4, 5, 2, 1, 3], [1, 1, 1, 0]]}} {[[2, 1, 4, 5, 3], [1, 1, 1, 0]]} {[[3, 1, 2, 5, 4], [0, 1, 1, 1]]} "Class ", 358, " is:" {{[[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1, 5, 4], [0, 0, 0, 0]]}, {[[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, {[[4, 5, 1, 3, 2], [0, 0, 0, 0]]}} {[[2, 1, 5, 3, 4], [0, 0, 0, 0]]} "For the class ", {{[[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, {[[2, 3, 1, 5, 4], [0, 0, 0, 0]]}, {[[4, 3, 5, 1, 2], [0, 0, 0, 0]]}, {[[4, 5, 1, 3, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 5, 3, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {}], [[2, 1, 4, 3], {}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {1, 2}, {}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {1, 2, 3}, {}], [[3, 1, 5, 4, 2], {1, 2, 3}, {}], [[3, 2, 5, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38976, 347776, 3447932, 37601916, 447352224, 5765690544, 80027220448, 1190110692204, 18878422622976, 318180082610048, 5678110761876224, 106958628519952128, 2120821833862388544] "" "Class ", 359, " is:" {{[[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1, 5, 4], [1, 0, 0, 0]]}, {[[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[4, 5, 1, 3, 2], [0, 0, 0, 1]]}} {[[2, 1, 5, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, {[[2, 3, 1, 5, 4], [1, 0, 0, 0]]}, {[[4, 3, 5, 1, 2], [1, 0, 0, 0]]}, {[[4, 5, 1, 3, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 5, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37875, 332731, 3241219, 34672985, 404070204, 5095311600, 69123884873, 1003842966405, 15538053602481, 255364198147398, 4441025751738867, 81480097195041104, 1572836249593499556] "" "Class ", 360, " is:" {{[[2, 1, 5, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1, 5, 4], [0, 1, 0, 0]]}, {[[4, 3, 5, 1, 2], [0, 1, 0, 0]]}, {[[4, 5, 1, 3, 2], [0, 0, 1, 0]]}} {[[2, 1, 5, 3, 4], [0, 0, 1, 0]]} {[[2, 3, 1, 5, 4], [0, 1, 0, 0]]} "Class ", 361, " is:" {{[[2, 1, 5, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1, 5, 4], [1, 1, 0, 0]]}, {[[4, 3, 5, 1, 2], [1, 1, 0, 0]]}, {[[4, 5, 1, 3, 2], [0, 0, 1, 1]]}} {[[2, 1, 5, 3, 4], [0, 0, 1, 1]]} {[[2, 3, 1, 5, 4], [1, 1, 0, 0]]} "Class ", 362, " is:" {{[[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1, 5, 4], [0, 0, 1, 0]]}, {[[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[4, 5, 1, 3, 2], [0, 1, 0, 0]]}} {[[2, 1, 5, 3, 4], [0, 1, 0, 0]]} "For the class ", {{[[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, {[[2, 3, 1, 5, 4], [0, 0, 1, 0]]}, {[[4, 3, 5, 1, 2], [0, 0, 1, 0]]}, {[[4, 5, 1, 3, 2], [0, 1, 0, 0]]}}, " the pattern set ", {[[2, 1, 5, 3, 4], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[2, 1, 4, 3, 5], {3, 4}, {}], [[2, 1, 5, 3, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 1, 5, 4, 3], {3}, {}], [[3, 1, 5, 4, 2], {2, 3, 4}, {}], [[3, 2, 5, 4, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 703, 4817, 37534, 327599, 3164891, 33519051, 386090952, 4804566545, 64226920247, 917805091675, 13960498198182, 225185003512111, 3839042851786987, 68970587034336831, 1302286587667567976] "" "Class ", 363, " is:" {{[[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1, 5, 4], [1, 0, 1, 0]]}, {[[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[4, 5, 1, 3, 2], [0, 1, 0, 1]]}} {[[2, 1, 5, 3, 4], [0, 1, 0, 1]]} "For the class ", {{[[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, {[[2, 3, 1, 5, 4], [1, 0, 1, 0]]}, {[[4, 3, 5, 1, 2], [1, 0, 1, 0]]}, {[[4, 5, 1, 3, 2], [0, 1, 0, 1]]}}, " the pattern set ", {[[2, 1, 5, 3, 4], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {3}, {[0, 0, 0, 1, 0]}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 699, 4723, 35969, 304179, 2823910, 28520022, 311039615, 3640665886, 45497926429, 604390322111, 8501294894254, 126191172400559, 1970854869817747, 32300525430002906, 554192586837675141] "" "Class ", 364, " is:" {{[[2, 1, 5, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1, 5, 4], [0, 1, 1, 0]]}, {[[4, 3, 5, 1, 2], [0, 1, 1, 0]]}, {[[4, 5, 1, 3, 2], [0, 1, 1, 0]]}} {[[2, 1, 5, 3, 4], [0, 1, 1, 0]]} {[[2, 3, 1, 5, 4], [0, 1, 1, 0]]} "Class ", 365, " is:" {{[[2, 1, 5, 3, 4], [0, 1, 1, 1]]}, {[[2, 3, 1, 5, 4], [1, 1, 1, 0]]}, {[[4, 3, 5, 1, 2], [1, 1, 1, 0]]}, {[[4, 5, 1, 3, 2], [0, 1, 1, 1]]}} {[[2, 1, 5, 3, 4], [0, 1, 1, 1]]} {[[2, 3, 1, 5, 4], [1, 1, 1, 0]]} "Class ", 366, " is:" {{[[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1, 5, 4], [0, 0, 0, 1]]}, {[[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, {[[4, 5, 1, 3, 2], [1, 0, 0, 0]]}} {[[2, 1, 5, 3, 4], [1, 0, 0, 0]]} {[[2, 3, 1, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[2, 1, 5, 3, 4], [1, 0, 0, 0]]}, {[[2, 3, 1, 5, 4], [0, 0, 0, 1]]}, {[[4, 3, 5, 1, 2], [0, 0, 0, 1]]}, {[[4, 5, 1, 3, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 3, 1, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 0, 1, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37867, 332537, 3237698, 34614147, 403102922, 5079204904, 68848332547, 998964163292, 15448323010438, 253646958004644, 4406809345062872, 80770342909388468, 1557517079236173915] "" "Class ", 367, " is:" {{[[2, 1, 5, 3, 4], [1, 0, 0, 1]]}, {[[2, 3, 1, 5, 4], [1, 0, 0, 1]]}, {[[4, 3, 5, 1, 2], [1, 0, 0, 1]]}, {[[4, 5, 1, 3, 2], [1, 0, 0, 1]]}} {[[2, 1, 5, 3, 4], [1, 0, 0, 1]]} {[[2, 3, 1, 5, 4], [1, 0, 0, 1]]} "Class ", 368, " is:" {{[[2, 1, 5, 3, 4], [1, 0, 1, 0]]}, {[[2, 3, 1, 5, 4], [0, 1, 0, 1]]}, {[[4, 3, 5, 1, 2], [0, 1, 0, 1]]}, {[[4, 5, 1, 3, 2], [1, 0, 1, 0]]}} {[[2, 1, 5, 3, 4], [1, 0, 1, 0]]} {[[2, 3, 1, 5, 4], [0, 1, 0, 1]]} "Class ", 369, " is:" {{[[2, 1, 5, 3, 4], [1, 0, 1, 1]]}, {[[2, 3, 1, 5, 4], [1, 1, 0, 1]]}, {[[4, 3, 5, 1, 2], [1, 1, 0, 1]]}, {[[4, 5, 1, 3, 2], [1, 0, 1, 1]]}} {[[2, 1, 5, 3, 4], [1, 0, 1, 1]]} {[[2, 3, 1, 5, 4], [1, 1, 0, 1]]} "Class ", 370, " is:" {{[[2, 1, 5, 3, 4], [1, 1, 0, 0]]}, {[[2, 3, 1, 5, 4], [0, 0, 1, 1]]}, {[[4, 3, 5, 1, 2], [0, 0, 1, 1]]}, {[[4, 5, 1, 3, 2], [1, 1, 0, 0]]}} {[[2, 1, 5, 3, 4], [1, 1, 0, 0]]} {[[2, 3, 1, 5, 4], [0, 0, 1, 1]]} "Class ", 371, " is:" {{[[2, 1, 5, 3, 4], [1, 1, 0, 1]]}, {[[2, 3, 1, 5, 4], [1, 0, 1, 1]]}, {[[4, 3, 5, 1, 2], [1, 0, 1, 1]]}, {[[4, 5, 1, 3, 2], [1, 1, 0, 1]]}} {[[2, 1, 5, 3, 4], [1, 1, 0, 1]]} {[[2, 3, 1, 5, 4], [1, 0, 1, 1]]} "Class ", 372, " is:" {{[[2, 1, 5, 3, 4], [1, 1, 1, 0]]}, {[[2, 3, 1, 5, 4], [0, 1, 1, 1]]}, {[[4, 3, 5, 1, 2], [0, 1, 1, 1]]}, {[[4, 5, 1, 3, 2], [1, 1, 1, 0]]}} {[[2, 1, 5, 3, 4], [1, 1, 1, 0]]} {[[2, 3, 1, 5, 4], [0, 1, 1, 1]]} "Class ", 373, " is:" {{[[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[4, 5, 1, 2, 3], [0, 0, 0, 0]]}} {[[2, 1, 5, 4, 3], [0, 0, 0, 0]]} "For the class ", {{[[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 1, 5, 4], [0, 0, 0, 0]]}, {[[3, 4, 5, 1, 2], [0, 0, 0, 0]]}, {[[4, 5, 1, 2, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[2, 1, 5, 4, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {}], [[2, 1, 4, 3], {}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}], [[2, 1, 4, 3, 5], {1, 2}, {}], [[2, 1, 5, 3, 4], {1, 2, 3, 4}, {}], [[2, 1, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {1, 2, 3}, {}], [[3, 2, 5, 4, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38980, 347862, 3449292, 37622348, 447662376, 5770553184, 80106726784, 1191471740436, 18902847341664, 318639524995160, 5687162644422552, 107145206713313556, 2124840033683212648] "" "Class ", 374, " is:" {{[[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[4, 5, 1, 2, 3], [0, 0, 0, 1]]}} {[[2, 1, 5, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 1, 5, 4], [1, 0, 0, 0]]}, {[[3, 4, 5, 1, 2], [1, 0, 0, 0]]}, {[[4, 5, 1, 2, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[2, 1, 5, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {}], [[2, 1, 4, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37870, 332620, 3239356, 34644052, 403625548, 5088352285, 69011438254, 1001954572981, 15504987212642, 254759724594139, 4429487400388256, 81250218528540854, 1568059833769977450] "" "Class ", 375, " is:" {{[[2, 1, 5, 4, 3], [0, 0, 1, 0]]}, {[[3, 2, 1, 5, 4], [0, 1, 0, 0]]}, {[[3, 4, 5, 1, 2], [0, 1, 0, 0]]}, {[[4, 5, 1, 2, 3], [0, 0, 1, 0]]}} {[[2, 1, 5, 4, 3], [0, 0, 1, 0]]} {[[3, 2, 1, 5, 4], [0, 1, 0, 0]]} "Class ", 376, " is:" {{[[2, 1, 5, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 1, 5, 4], [1, 1, 0, 0]]}, {[[3, 4, 5, 1, 2], [1, 1, 0, 0]]}, {[[4, 5, 1, 2, 3], [0, 0, 1, 1]]}} {[[2, 1, 5, 4, 3], [0, 0, 1, 1]]} {[[3, 2, 1, 5, 4], [1, 1, 0, 0]]} "Class ", 377, " is:" {{[[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[4, 5, 1, 2, 3], [0, 1, 0, 0]]}} {[[2, 1, 5, 4, 3], [0, 1, 0, 0]]} "For the class ", {{[[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, {[[3, 2, 1, 5, 4], [0, 0, 1, 0]]}, {[[3, 4, 5, 1, 2], [0, 0, 1, 0]]}, {[[4, 5, 1, 2, 3], [0, 1, 0, 0]]}}, " the pattern set ", {[[2, 1, 5, 4, 3], [0, 1, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {}, {}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}], [[2, 1, 4, 3, 5], {3, 4}, {}], [[2, 1, 5, 3, 4], {3, 4}, {}], [[2, 1, 5, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 1, 5, 4, 2], {2, 3, 4}, {}], [[3, 2, 5, 4, 1], {2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4834, 37771, 330757, 3207470, 34112273, 394713222, 4935828067, 66322824979, 952907083193, 14576684676065, 236510024091756, 4056690660787118, 73338391714695646, 1393689870381947191] "" "Class ", 378, " is:" {{[[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[4, 5, 1, 2, 3], [0, 1, 0, 1]]}} {[[2, 1, 5, 4, 3], [0, 1, 0, 1]]} "For the class ", {{[[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 1, 5, 4], [1, 0, 1, 0]]}, {[[3, 4, 5, 1, 2], [1, 0, 1, 0]]}, {[[4, 5, 1, 2, 3], [0, 1, 0, 1]]}}, " the pattern set ", {[[2, 1, 5, 4, 3], [0, 1, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {3}, {}], [[2, 1, 4, 3], {3}, {[0, 0, 1, 0, 0]}], [[3, 1, 4, 2], {2, 3}, {}], [[3, 2, 4, 1], {2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 700, 4745, 36310, 308919, 2887980, 29392211, 323201330, 3815857732, 48116262912, 645071086840, 9158805860008, 137245734060145, 2164092026050332, 35809882818819669, 620348584920591806] "" "Class ", 379, " is:" {{[[2, 1, 5, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 1, 5, 4], [0, 1, 1, 0]]}, {[[3, 4, 5, 1, 2], [0, 1, 1, 0]]}, {[[4, 5, 1, 2, 3], [0, 1, 1, 0]]}} {[[2, 1, 5, 4, 3], [0, 1, 1, 0]]} {[[3, 2, 1, 5, 4], [0, 1, 1, 0]]} "Class ", 380, " is:" {{[[2, 1, 5, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 1, 5, 4], [1, 1, 1, 0]]}, {[[3, 4, 5, 1, 2], [1, 1, 1, 0]]}, {[[4, 5, 1, 2, 3], [0, 1, 1, 1]]}} {[[2, 1, 5, 4, 3], [0, 1, 1, 1]]} {[[3, 2, 1, 5, 4], [1, 1, 1, 0]]} "Class ", 381, " is:" {{[[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, {[[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[4, 5, 1, 2, 3], [1, 0, 0, 0]]}} {[[2, 1, 5, 4, 3], [1, 0, 0, 0]]} {[[3, 2, 1, 5, 4], [0, 0, 0, 1]]} "For the class ", {{[[2, 1, 5, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, {[[3, 4, 5, 1, 2], [0, 0, 0, 1]]}, {[[4, 5, 1, 2, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[3, 2, 1, 5, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {1, 2}, {}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {}, {}], [[3, 2, 1, 4], {1, 2, 3}, {[0, 0, 0, 1, 0]}], [[4, 2, 1, 3], {1, 2, 3}, {}], [[4, 3, 1, 2], {1, 2, 3}, {}], [[4, 3, 2, 1], {1}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37868, 332558, 3238028, 34618998, 403173236, 5080235750, 68863804944, 999203154888, 15452127899940, 253709339041360, 4407859543644456, 80788408031974320, 1557832095119647872] "" "Class ", 382, " is:" {{[[2, 1, 5, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 1, 5, 4], [1, 0, 0, 1]]}, {[[3, 4, 5, 1, 2], [1, 0, 0, 1]]}, {[[4, 5, 1, 2, 3], [1, 0, 0, 1]]}} {[[2, 1, 5, 4, 3], [1, 0, 0, 1]]} {[[3, 2, 1, 5, 4], [1, 0, 0, 1]]} "Class ", 383, " is:" {{[[2, 1, 5, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 1, 5, 4], [0, 1, 0, 1]]}, {[[3, 4, 5, 1, 2], [0, 1, 0, 1]]}, {[[4, 5, 1, 2, 3], [1, 0, 1, 0]]}} {[[2, 1, 5, 4, 3], [1, 0, 1, 0]]} {[[3, 2, 1, 5, 4], [0, 1, 0, 1]]} "Class ", 384, " is:" {{[[2, 1, 5, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 1, 5, 4], [1, 1, 0, 1]]}, {[[3, 4, 5, 1, 2], [1, 1, 0, 1]]}, {[[4, 5, 1, 2, 3], [1, 0, 1, 1]]}} {[[2, 1, 5, 4, 3], [1, 0, 1, 1]]} {[[3, 2, 1, 5, 4], [1, 1, 0, 1]]} "Class ", 385, " is:" {{[[2, 1, 5, 4, 3], [1, 1, 0, 0]]}, {[[3, 2, 1, 5, 4], [0, 0, 1, 1]]}, {[[3, 4, 5, 1, 2], [0, 0, 1, 1]]}, {[[4, 5, 1, 2, 3], [1, 1, 0, 0]]}} {[[2, 1, 5, 4, 3], [1, 1, 0, 0]]} {[[3, 2, 1, 5, 4], [0, 0, 1, 1]]} "Class ", 386, " is:" {{[[2, 1, 5, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 1, 5, 4], [1, 0, 1, 1]]}, {[[3, 4, 5, 1, 2], [1, 0, 1, 1]]}, {[[4, 5, 1, 2, 3], [1, 1, 0, 1]]}} {[[2, 1, 5, 4, 3], [1, 1, 0, 1]]} {[[3, 2, 1, 5, 4], [1, 0, 1, 1]]} "Class ", 387, " is:" {{[[2, 1, 5, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 1, 5, 4], [0, 1, 1, 1]]}, {[[3, 4, 5, 1, 2], [0, 1, 1, 1]]}, {[[4, 5, 1, 2, 3], [1, 1, 1, 0]]}} {[[2, 1, 5, 4, 3], [1, 1, 1, 0]]} {[[3, 2, 1, 5, 4], [0, 1, 1, 1]]} "Class ", 388, " is:" {{[[2, 1, 5, 4, 3], [1, 1, 1, 1]]}, {[[3, 2, 1, 5, 4], [1, 1, 1, 1]]}, {[[3, 4, 5, 1, 2], [1, 1, 1, 1]]}, {[[4, 5, 1, 2, 3], [1, 1, 1, 1]]}} {[[2, 1, 5, 4, 3], [1, 1, 1, 1]]} {[[3, 2, 1, 5, 4], [1, 1, 1, 1]]} "Class ", 389, " is:" {{[[2, 3, 5, 1, 4], [0, 0, 0, 0]]}, {[[2, 5, 1, 3, 4], [0, 0, 0, 0]]}, {[[4, 1, 5, 3, 2], [0, 0, 0, 0]]}, {[[4, 3, 1, 5, 2], [0, 0, 0, 0]]}} {[[2, 3, 5, 1, 4], [0, 0, 0, 0]]} "For the class ", {{[[2, 3, 5, 1, 4], [0, 0, 0, 0]]}, {[[2, 5, 1, 3, 4], [0, 0, 0, 0]]}, {[[4, 1, 5, 3, 2], [0, 0, 0, 0]]}, {[[4, 3, 1, 5, 2], [0, 0, 0, 0]]}}, " the pattern set ", {[[2, 3, 5, 1, 4], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 3, 4, 1, 5], {1, 2, 3}, {}], [[2, 3, 5, 1, 4], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[2, 4, 5, 1, 3], {1, 2, 3}, {}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38979, 347830, 3448742, 37613781, 447529736, 5768447194, 80071991461, 1190873311644, 18892055757622, 318435746208625, 5683135262448470, 107061979121943224, 2123043715555546099] "" "Class ", 390, " is:" {{[[2, 3, 5, 1, 4], [0, 0, 0, 1]]}, {[[2, 5, 1, 3, 4], [1, 0, 0, 0]]}, {[[4, 1, 5, 3, 2], [1, 0, 0, 0]]}, {[[4, 3, 1, 5, 2], [0, 0, 0, 1]]}} {[[2, 3, 5, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[2, 3, 5, 1, 4], [0, 0, 0, 1]]}, {[[2, 5, 1, 3, 4], [1, 0, 0, 0]]}, {[[4, 1, 5, 3, 2], [1, 0, 0, 0]]}, {[[4, 3, 1, 5, 2], [0, 0, 0, 1]]}}, " the pattern set ", {[[2, 3, 5, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37874, 332696, 3240416, 34657116, 403773512, 5089835936, 69021919224, 1001903928804, 15500138755224, 254598918643168, 4425046557089424, 81134570778122256, 1565095717271557536] "" "Class ", 391, " is:" {{[[2, 3, 5, 1, 4], [0, 0, 1, 0]]}, {[[2, 5, 1, 3, 4], [0, 1, 0, 0]]}, {[[4, 1, 5, 3, 2], [0, 1, 0, 0]]}, {[[4, 3, 1, 5, 2], [0, 0, 1, 0]]}} {[[2, 3, 5, 1, 4], [0, 0, 1, 0]]} {[[2, 5, 1, 3, 4], [0, 1, 0, 0]]} "Class ", 392, " is:" {{[[2, 3, 5, 1, 4], [0, 0, 1, 1]]}, {[[2, 5, 1, 3, 4], [1, 1, 0, 0]]}, {[[4, 1, 5, 3, 2], [1, 1, 0, 0]]}, {[[4, 3, 1, 5, 2], [0, 0, 1, 1]]}} {[[2, 3, 5, 1, 4], [0, 0, 1, 1]]} {[[2, 5, 1, 3, 4], [1, 1, 0, 0]]} "Class ", 393, " is:" {{[[2, 3, 5, 1, 4], [0, 1, 0, 0]]}, {[[2, 5, 1, 3, 4], [0, 0, 1, 0]]}, {[[4, 1, 5, 3, 2], [0, 0, 1, 0]]}, {[[4, 3, 1, 5, 2], [0, 1, 0, 0]]}} {[[2, 3, 5, 1, 4], [0, 1, 0, 0]]} {[[2, 5, 1, 3, 4], [0, 0, 1, 0]]} "Class ", 394, " is:" {{[[2, 3, 5, 1, 4], [0, 1, 0, 1]]}, {[[2, 5, 1, 3, 4], [1, 0, 1, 0]]}, {[[4, 1, 5, 3, 2], [1, 0, 1, 0]]}, {[[4, 3, 1, 5, 2], [0, 1, 0, 1]]}} {[[2, 3, 5, 1, 4], [0, 1, 0, 1]]} {[[2, 5, 1, 3, 4], [1, 0, 1, 0]]} "Class ", 395, " is:" {{[[2, 3, 5, 1, 4], [0, 1, 1, 0]]}, {[[2, 5, 1, 3, 4], [0, 1, 1, 0]]}, {[[4, 1, 5, 3, 2], [0, 1, 1, 0]]}, {[[4, 3, 1, 5, 2], [0, 1, 1, 0]]}} {[[2, 3, 5, 1, 4], [0, 1, 1, 0]]} {[[2, 5, 1, 3, 4], [0, 1, 1, 0]]} "Class ", 396, " is:" {{[[2, 3, 5, 1, 4], [0, 1, 1, 1]]}, {[[2, 5, 1, 3, 4], [1, 1, 1, 0]]}, {[[4, 1, 5, 3, 2], [1, 1, 1, 0]]}, {[[4, 3, 1, 5, 2], [0, 1, 1, 1]]}} {[[2, 3, 5, 1, 4], [0, 1, 1, 1]]} {[[2, 5, 1, 3, 4], [1, 1, 1, 0]]} "Class ", 397, " is:" {{[[2, 3, 5, 1, 4], [1, 0, 0, 0]]}, {[[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, {[[4, 1, 5, 3, 2], [0, 0, 0, 1]]}, {[[4, 3, 1, 5, 2], [1, 0, 0, 0]]}} {[[2, 3, 5, 1, 4], [1, 0, 0, 0]]} {[[2, 5, 1, 3, 4], [0, 0, 0, 1]]} "For the class ", {{[[2, 3, 5, 1, 4], [1, 0, 0, 0]]}, {[[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, {[[4, 1, 5, 3, 2], [0, 0, 0, 1]]}, {[[4, 3, 1, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 5, 1, 3, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37879, 332845, 3243505, 34713895, 404778030, 5107582033, 69340812315, 1007790793888, 15612385696687, 256816003288705, 4470475620573666, 82100771671098180, 1586425252805278598] "" "Class ", 398, " is:" {{[[2, 3, 5, 1, 4], [1, 0, 0, 1]]}, {[[2, 5, 1, 3, 4], [1, 0, 0, 1]]}, {[[4, 1, 5, 3, 2], [1, 0, 0, 1]]}, {[[4, 3, 1, 5, 2], [1, 0, 0, 1]]}} {[[2, 3, 5, 1, 4], [1, 0, 0, 1]]} {[[2, 5, 1, 3, 4], [1, 0, 0, 1]]} "Class ", 399, " is:" {{[[2, 3, 5, 1, 4], [1, 0, 1, 0]]}, {[[2, 5, 1, 3, 4], [0, 1, 0, 1]]}, {[[4, 1, 5, 3, 2], [0, 1, 0, 1]]}, {[[4, 3, 1, 5, 2], [1, 0, 1, 0]]}} {[[2, 3, 5, 1, 4], [1, 0, 1, 0]]} {[[2, 5, 1, 3, 4], [0, 1, 0, 1]]} "Class ", 400, " is:" {{[[2, 3, 5, 1, 4], [1, 0, 1, 1]]}, {[[2, 5, 1, 3, 4], [1, 1, 0, 1]]}, {[[4, 1, 5, 3, 2], [1, 1, 0, 1]]}, {[[4, 3, 1, 5, 2], [1, 0, 1, 1]]}} {[[2, 3, 5, 1, 4], [1, 0, 1, 1]]} {[[2, 5, 1, 3, 4], [1, 1, 0, 1]]} "Class ", 401, " is:" {{[[2, 3, 5, 1, 4], [1, 1, 0, 0]]}, {[[2, 5, 1, 3, 4], [0, 0, 1, 1]]}, {[[4, 1, 5, 3, 2], [0, 0, 1, 1]]}, {[[4, 3, 1, 5, 2], [1, 1, 0, 0]]}} {[[2, 3, 5, 1, 4], [1, 1, 0, 0]]} {[[2, 5, 1, 3, 4], [0, 0, 1, 1]]} "Class ", 402, " is:" {{[[2, 3, 5, 1, 4], [1, 1, 0, 1]]}, {[[2, 5, 1, 3, 4], [1, 0, 1, 1]]}, {[[4, 1, 5, 3, 2], [1, 0, 1, 1]]}, {[[4, 3, 1, 5, 2], [1, 1, 0, 1]]}} {[[2, 3, 5, 1, 4], [1, 1, 0, 1]]} {[[2, 5, 1, 3, 4], [1, 0, 1, 1]]} "Class ", 403, " is:" {{[[2, 3, 5, 1, 4], [1, 1, 1, 0]]}, {[[2, 5, 1, 3, 4], [0, 1, 1, 1]]}, {[[4, 1, 5, 3, 2], [0, 1, 1, 1]]}, {[[4, 3, 1, 5, 2], [1, 1, 1, 0]]}} {[[2, 3, 5, 1, 4], [1, 1, 1, 0]]} {[[2, 5, 1, 3, 4], [0, 1, 1, 1]]} "Class ", 404, " is:" {{[[2, 4, 1, 5, 3], [0, 0, 0, 0]]}, {[[3, 1, 5, 2, 4], [0, 0, 0, 0]]}, {[[3, 5, 1, 4, 2], [0, 0, 0, 0]]}, {[[4, 2, 5, 1, 3], [0, 0, 0, 0]]}} {[[2, 4, 1, 5, 3], [0, 0, 0, 0]]} "For the class ", {{[[2, 4, 1, 5, 3], [0, 0, 0, 0]]}, {[[3, 1, 5, 2, 4], [0, 0, 0, 0]]}, {[[3, 5, 1, 4, 2], [0, 0, 0, 0]]}, {[[4, 2, 5, 1, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[2, 4, 1, 5, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {}, {}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 3, 1, 4, 5], {1, 2, 3}, {}], [[2, 3, 1, 5, 4], {1, 2, 3, 4}, {}], [[2, 4, 1, 5, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 1, 5, 2], {1, 2, 3, 4}, {}], [[3, 4, 2, 5, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38976, 347790, 3448212, 37606536, 447426144, 5766888120, 80047243080, 1190459039364, 18884750846976, 318300264871440, 5680496863401840, 107008122578788800, 2121893387875882944] "" "Class ", 405, " is:" {{[[2, 4, 1, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 5, 2, 4], [1, 0, 0, 0]]}, {[[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[4, 2, 5, 1, 3], [0, 0, 0, 1]]}} {[[2, 4, 1, 5, 3], [0, 0, 0, 1]]} "For the class ", {{[[2, 4, 1, 5, 3], [0, 0, 0, 1]]}, {[[3, 1, 5, 2, 4], [1, 0, 0, 0]]}, {[[3, 5, 1, 4, 2], [1, 0, 0, 0]]}, {[[4, 2, 5, 1, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[2, 4, 1, 5, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {[0, 0, 1, 0, 0]}], [[2, 4, 1, 3], {1, 2}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4839, 37887, 332842, 3242069, 34676639, 404018039, 5093103260, 69068549977, 1002614111740, 15511658118280, 254797417217505, 4428670404927331, 81204467190253592, 1566516153549352731] "" "Class ", 406, " is:" {{[[2, 4, 1, 5, 3], [0, 0, 1, 0]]}, {[[3, 1, 5, 2, 4], [0, 1, 0, 0]]}, {[[3, 5, 1, 4, 2], [0, 1, 0, 0]]}, {[[4, 2, 5, 1, 3], [0, 0, 1, 0]]}} {[[2, 4, 1, 5, 3], [0, 0, 1, 0]]} {[[3, 1, 5, 2, 4], [0, 1, 0, 0]]} "Class ", 407, " is:" {{[[2, 4, 1, 5, 3], [0, 0, 1, 1]]}, {[[3, 1, 5, 2, 4], [1, 1, 0, 0]]}, {[[3, 5, 1, 4, 2], [1, 1, 0, 0]]}, {[[4, 2, 5, 1, 3], [0, 0, 1, 1]]}} {[[2, 4, 1, 5, 3], [0, 0, 1, 1]]} {[[3, 1, 5, 2, 4], [1, 1, 0, 0]]} "Class ", 408, " is:" {{[[2, 4, 1, 5, 3], [0, 1, 0, 0]]}, {[[3, 1, 5, 2, 4], [0, 0, 1, 0]]}, {[[3, 5, 1, 4, 2], [0, 0, 1, 0]]}, {[[4, 2, 5, 1, 3], [0, 1, 0, 0]]}} {[[2, 4, 1, 5, 3], [0, 1, 0, 0]]} {[[3, 1, 5, 2, 4], [0, 0, 1, 0]]} "Class ", 409, " is:" {{[[2, 4, 1, 5, 3], [0, 1, 0, 1]]}, {[[3, 1, 5, 2, 4], [1, 0, 1, 0]]}, {[[3, 5, 1, 4, 2], [1, 0, 1, 0]]}, {[[4, 2, 5, 1, 3], [0, 1, 0, 1]]}} {[[2, 4, 1, 5, 3], [0, 1, 0, 1]]} {[[3, 1, 5, 2, 4], [1, 0, 1, 0]]} "Class ", 410, " is:" {{[[2, 4, 1, 5, 3], [0, 1, 1, 0]]}, {[[3, 1, 5, 2, 4], [0, 1, 1, 0]]}, {[[3, 5, 1, 4, 2], [0, 1, 1, 0]]}, {[[4, 2, 5, 1, 3], [0, 1, 1, 0]]}} {[[2, 4, 1, 5, 3], [0, 1, 1, 0]]} {[[3, 1, 5, 2, 4], [0, 1, 1, 0]]} "Class ", 411, " is:" {{[[2, 4, 1, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 5, 2, 4], [1, 1, 1, 0]]}, {[[3, 5, 1, 4, 2], [1, 1, 1, 0]]}, {[[4, 2, 5, 1, 3], [0, 1, 1, 1]]}} {[[2, 4, 1, 5, 3], [0, 1, 1, 1]]} {[[3, 1, 5, 2, 4], [1, 1, 1, 0]]} "Class ", 412, " is:" {{[[2, 4, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 5, 2, 4], [0, 0, 0, 1]]}, {[[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[4, 2, 5, 1, 3], [1, 0, 0, 0]]}} {[[2, 4, 1, 5, 3], [1, 0, 0, 0]]} {[[3, 1, 5, 2, 4], [0, 0, 0, 1]]} "For the class ", {{[[2, 4, 1, 5, 3], [1, 0, 0, 0]]}, {[[3, 1, 5, 2, 4], [0, 0, 0, 1]]}, {[[3, 5, 1, 4, 2], [0, 0, 0, 1]]}, {[[4, 2, 5, 1, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[3, 1, 5, 2, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {[0, 0, 0, 1, 0]}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4839, 37897, 333096, 3246798, 34757387, 405371816, 5116056935, 69467859749, 1009794339229, 15645623200503, 257395553298207, 4481083813847145, 82304310068651058, 1590512557397146922] "" "Class ", 413, " is:" {{[[2, 4, 1, 5, 3], [1, 0, 0, 1]]}, {[[3, 1, 5, 2, 4], [1, 0, 0, 1]]}, {[[3, 5, 1, 4, 2], [1, 0, 0, 1]]}, {[[4, 2, 5, 1, 3], [1, 0, 0, 1]]}} {[[2, 4, 1, 5, 3], [1, 0, 0, 1]]} {[[3, 1, 5, 2, 4], [1, 0, 0, 1]]} "Class ", 414, " is:" {{[[2, 4, 1, 5, 3], [1, 0, 1, 0]]}, {[[3, 1, 5, 2, 4], [0, 1, 0, 1]]}, {[[3, 5, 1, 4, 2], [0, 1, 0, 1]]}, {[[4, 2, 5, 1, 3], [1, 0, 1, 0]]}} {[[2, 4, 1, 5, 3], [1, 0, 1, 0]]} {[[3, 1, 5, 2, 4], [0, 1, 0, 1]]} "Class ", 415, " is:" {{[[2, 4, 1, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 5, 2, 4], [1, 1, 0, 1]]}, {[[3, 5, 1, 4, 2], [1, 1, 0, 1]]}, {[[4, 2, 5, 1, 3], [1, 0, 1, 1]]}} {[[2, 4, 1, 5, 3], [1, 0, 1, 1]]} {[[3, 1, 5, 2, 4], [1, 1, 0, 1]]} "Class ", 416, " is:" {{[[2, 4, 1, 5, 3], [1, 1, 0, 0]]}, {[[3, 1, 5, 2, 4], [0, 0, 1, 1]]}, {[[3, 5, 1, 4, 2], [0, 0, 1, 1]]}, {[[4, 2, 5, 1, 3], [1, 1, 0, 0]]}} {[[2, 4, 1, 5, 3], [1, 1, 0, 0]]} {[[3, 1, 5, 2, 4], [0, 0, 1, 1]]} "Class ", 417, " is:" {{[[2, 4, 1, 5, 3], [1, 1, 0, 1]]}, {[[3, 1, 5, 2, 4], [1, 0, 1, 1]]}, {[[3, 5, 1, 4, 2], [1, 0, 1, 1]]}, {[[4, 2, 5, 1, 3], [1, 1, 0, 1]]}} {[[2, 4, 1, 5, 3], [1, 1, 0, 1]]} {[[3, 1, 5, 2, 4], [1, 0, 1, 1]]} "Class ", 418, " is:" {{[[2, 4, 1, 5, 3], [1, 1, 1, 0]]}, {[[3, 1, 5, 2, 4], [0, 1, 1, 1]]}, {[[3, 5, 1, 4, 2], [0, 1, 1, 1]]}, {[[4, 2, 5, 1, 3], [1, 1, 1, 0]]}} {[[2, 4, 1, 5, 3], [1, 1, 1, 0]]} {[[3, 1, 5, 2, 4], [0, 1, 1, 1]]} "Class ", 419, " is:" {{[[2, 4, 1, 5, 3], [1, 1, 1, 1]]}, {[[3, 1, 5, 2, 4], [1, 1, 1, 1]]}, {[[3, 5, 1, 4, 2], [1, 1, 1, 1]]}, {[[4, 2, 5, 1, 3], [1, 1, 1, 1]]}} {[[2, 4, 1, 5, 3], [1, 1, 1, 1]]} {[[3, 1, 5, 2, 4], [1, 1, 1, 1]]} "Class ", 420, " is:" {{[[2, 4, 5, 1, 3], [0, 0, 0, 0]]}, {[[3, 1, 5, 4, 2], [0, 0, 0, 0]]}, {[[3, 5, 1, 2, 4], [0, 0, 0, 0]]}, {[[4, 2, 1, 5, 3], [0, 0, 0, 0]]}} {[[2, 4, 5, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[2, 4, 5, 1, 3], [0, 0, 0, 0]]}, {[[3, 1, 5, 4, 2], [0, 0, 0, 0]]}, {[[3, 5, 1, 2, 4], [0, 0, 0, 0]]}, {[[4, 2, 1, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[2, 4, 5, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {}, {}], [[2, 3, 4, 1, 5], {1, 2, 3}, {}], [[2, 3, 5, 1, 4], {1, 2, 3}, {}], [[2, 4, 5, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 4, 5, 1, 2], {1, 2, 3}, {}], [[3, 4, 5, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38982, 347898, 3449832, 37630215, 447778848, 5772349056, 80135742750, 1191964110777, 18911623686552, 318803730114225, 5690383738630956, 107211361385886516, 2126260453008788598] "" "Class ", 421, " is:" {{[[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, {[[3, 1, 5, 4, 2], [1, 0, 0, 0]]}, {[[3, 5, 1, 2, 4], [1, 0, 0, 0]]}, {[[4, 2, 1, 5, 3], [0, 0, 0, 1]]}} {[[2, 4, 5, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, {[[3, 1, 5, 4, 2], [1, 0, 0, 0]]}, {[[3, 5, 1, 2, 4], [1, 0, 0, 0]]}, {[[4, 2, 1, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[2, 4, 5, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 2, 3, 4], {1}, {}], [[1, 2, 4, 3], {1, 2, 3}, {}], [[1, 3, 4, 2], {1, 2, 3}, {}], [[2, 3, 4, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37874, 332696, 3240416, 34657116, 403773512, 5089835936, 69021919224, 1001903928804, 15500138755224, 254598918643168, 4425046557089424, 81134570778122256, 1565095717271557536] "" "Class ", 422, " is:" {{[[2, 4, 5, 1, 3], [0, 0, 1, 0]]}, {[[3, 1, 5, 4, 2], [0, 1, 0, 0]]}, {[[3, 5, 1, 2, 4], [0, 1, 0, 0]]}, {[[4, 2, 1, 5, 3], [0, 0, 1, 0]]}} {[[2, 4, 5, 1, 3], [0, 0, 1, 0]]} {[[3, 1, 5, 4, 2], [0, 1, 0, 0]]} "Class ", 423, " is:" {{[[2, 4, 5, 1, 3], [0, 0, 1, 1]]}, {[[3, 1, 5, 4, 2], [1, 1, 0, 0]]}, {[[3, 5, 1, 2, 4], [1, 1, 0, 0]]}, {[[4, 2, 1, 5, 3], [0, 0, 1, 1]]}} {[[2, 4, 5, 1, 3], [0, 0, 1, 1]]} {[[3, 1, 5, 4, 2], [1, 1, 0, 0]]} "Class ", 424, " is:" {{[[2, 4, 5, 1, 3], [0, 1, 0, 0]]}, {[[3, 1, 5, 4, 2], [0, 0, 1, 0]]}, {[[3, 5, 1, 2, 4], [0, 0, 1, 0]]}, {[[4, 2, 1, 5, 3], [0, 1, 0, 0]]}} {[[2, 4, 5, 1, 3], [0, 1, 0, 0]]} {[[3, 1, 5, 4, 2], [0, 0, 1, 0]]} "Class ", 425, " is:" {{[[2, 4, 5, 1, 3], [0, 1, 0, 1]]}, {[[3, 1, 5, 4, 2], [1, 0, 1, 0]]}, {[[3, 5, 1, 2, 4], [1, 0, 1, 0]]}, {[[4, 2, 1, 5, 3], [0, 1, 0, 1]]}} {[[2, 4, 5, 1, 3], [0, 1, 0, 1]]} {[[3, 1, 5, 4, 2], [1, 0, 1, 0]]} "Class ", 426, " is:" {{[[2, 4, 5, 1, 3], [0, 1, 1, 0]]}, {[[3, 1, 5, 4, 2], [0, 1, 1, 0]]}, {[[3, 5, 1, 2, 4], [0, 1, 1, 0]]}, {[[4, 2, 1, 5, 3], [0, 1, 1, 0]]}} {[[2, 4, 5, 1, 3], [0, 1, 1, 0]]} {[[3, 1, 5, 4, 2], [0, 1, 1, 0]]} "Class ", 427, " is:" {{[[2, 4, 5, 1, 3], [0, 1, 1, 1]]}, {[[3, 1, 5, 4, 2], [1, 1, 1, 0]]}, {[[3, 5, 1, 2, 4], [1, 1, 1, 0]]}, {[[4, 2, 1, 5, 3], [0, 1, 1, 1]]}} {[[2, 4, 5, 1, 3], [0, 1, 1, 1]]} {[[3, 1, 5, 4, 2], [1, 1, 1, 0]]} "Class ", 428, " is:" {{[[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, {[[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, {[[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, {[[4, 2, 1, 5, 3], [1, 0, 0, 0]]}} {[[2, 4, 5, 1, 3], [1, 0, 0, 0]]} {[[3, 1, 5, 4, 2], [0, 0, 0, 1]]} "For the class ", {{[[2, 4, 5, 1, 3], [1, 0, 0, 0]]}, {[[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, {[[3, 5, 1, 2, 4], [0, 0, 0, 1]]}, {[[4, 2, 1, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[3, 1, 5, 4, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {}], [[2, 1, 4, 3], {1, 2}, {[0, 1, 0, 0, 0]}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37875, 332731, 3241219, 34672985, 404070204, 5095311600, 69123884873, 1003842966405, 15538053602481, 255364198147398, 4441025751738867, 81480097195041104, 1572836249593499556] "" "Class ", 429, " is:" {{[[2, 4, 5, 1, 3], [1, 0, 0, 1]]}, {[[3, 1, 5, 4, 2], [1, 0, 0, 1]]}, {[[3, 5, 1, 2, 4], [1, 0, 0, 1]]}, {[[4, 2, 1, 5, 3], [1, 0, 0, 1]]}} {[[2, 4, 5, 1, 3], [1, 0, 0, 1]]} {[[3, 1, 5, 4, 2], [1, 0, 0, 1]]} "Class ", 430, " is:" {{[[2, 4, 5, 1, 3], [1, 0, 1, 0]]}, {[[3, 1, 5, 4, 2], [0, 1, 0, 1]]}, {[[3, 5, 1, 2, 4], [0, 1, 0, 1]]}, {[[4, 2, 1, 5, 3], [1, 0, 1, 0]]}} {[[2, 4, 5, 1, 3], [1, 0, 1, 0]]} {[[3, 1, 5, 4, 2], [0, 1, 0, 1]]} "Class ", 431, " is:" {{[[2, 4, 5, 1, 3], [1, 0, 1, 1]]}, {[[3, 1, 5, 4, 2], [1, 1, 0, 1]]}, {[[3, 5, 1, 2, 4], [1, 1, 0, 1]]}, {[[4, 2, 1, 5, 3], [1, 0, 1, 1]]}} {[[2, 4, 5, 1, 3], [1, 0, 1, 1]]} {[[3, 1, 5, 4, 2], [1, 1, 0, 1]]} "Class ", 432, " is:" {{[[2, 4, 5, 1, 3], [1, 1, 0, 0]]}, {[[3, 1, 5, 4, 2], [0, 0, 1, 1]]}, {[[3, 5, 1, 2, 4], [0, 0, 1, 1]]}, {[[4, 2, 1, 5, 3], [1, 1, 0, 0]]}} {[[2, 4, 5, 1, 3], [1, 1, 0, 0]]} {[[3, 1, 5, 4, 2], [0, 0, 1, 1]]} "Class ", 433, " is:" {{[[2, 4, 5, 1, 3], [1, 1, 0, 1]]}, {[[3, 1, 5, 4, 2], [1, 0, 1, 1]]}, {[[3, 5, 1, 2, 4], [1, 0, 1, 1]]}, {[[4, 2, 1, 5, 3], [1, 1, 0, 1]]}} {[[2, 4, 5, 1, 3], [1, 1, 0, 1]]} {[[3, 1, 5, 4, 2], [1, 0, 1, 1]]} "Class ", 434, " is:" {{[[2, 4, 5, 1, 3], [1, 1, 1, 0]]}, {[[3, 1, 5, 4, 2], [0, 1, 1, 1]]}, {[[3, 5, 1, 2, 4], [0, 1, 1, 1]]}, {[[4, 2, 1, 5, 3], [1, 1, 1, 0]]}} {[[2, 4, 5, 1, 3], [1, 1, 1, 0]]} {[[3, 1, 5, 4, 2], [0, 1, 1, 1]]} "Class ", 435, " is:" {{[[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 5, 1, 4], [0, 0, 0, 0]]}, {[[3, 4, 1, 5, 2], [0, 0, 0, 0]]}, {[[4, 1, 5, 2, 3], [0, 0, 0, 0]]}} {[[2, 5, 1, 4, 3], [0, 0, 0, 0]]} "For the class ", {{[[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, {[[3, 2, 5, 1, 4], [0, 0, 0, 0]]}, {[[3, 4, 1, 5, 2], [0, 0, 0, 0]]}, {[[4, 1, 5, 2, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[2, 5, 1, 4, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {}, {}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}], [[2, 4, 1, 3, 5], {1, 2, 3}, {}], [[2, 5, 1, 3, 4], {1, 2, 3}, {}], [[2, 5, 1, 4, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 1, 4, 2], {1, 2, 3, 4}, {}], [[3, 5, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38976, 347790, 3448212, 37606536, 447426144, 5766888120, 80047243080, 1190459039364, 18884750846976, 318300264871440, 5680496863401840, 107008122578788800, 2121893387875882944] "" "Class ", 436, " is:" {{[[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 5, 1, 4], [1, 0, 0, 0]]}, {[[3, 4, 1, 5, 2], [1, 0, 0, 0]]}, {[[4, 1, 5, 2, 3], [0, 0, 0, 1]]}} {[[2, 5, 1, 4, 3], [0, 0, 0, 1]]} "For the class ", {{[[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, {[[3, 2, 5, 1, 4], [1, 0, 0, 0]]}, {[[3, 4, 1, 5, 2], [1, 0, 0, 0]]}, {[[4, 1, 5, 2, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[2, 5, 1, 4, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {1, 2}, {}], [[2, 3, 1], {}, {}], [[2, 3, 1, 4], {1, 2}, {}], [[2, 4, 1, 3], {1, 2}, {[0, 0, 1, 0, 0]}], [[3, 4, 1, 2], {1, 2}, {}], [[3, 4, 2, 1], {1, 2, 3}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4840, 37912, 333287, 3249227, 34789373, 405813975, 5122497215, 69566797954, 1011396522137, 15672937965136, 257885035979971, 4490288235377664, 82485624078635407, 1594247741652501112] "" "Class ", 437, " is:" {{[[2, 5, 1, 4, 3], [0, 0, 1, 0]]}, {[[3, 2, 5, 1, 4], [0, 1, 0, 0]]}, {[[3, 4, 1, 5, 2], [0, 1, 0, 0]]}, {[[4, 1, 5, 2, 3], [0, 0, 1, 0]]}} {[[2, 5, 1, 4, 3], [0, 0, 1, 0]]} {[[3, 2, 5, 1, 4], [0, 1, 0, 0]]} "Class ", 438, " is:" {{[[2, 5, 1, 4, 3], [0, 0, 1, 1]]}, {[[3, 2, 5, 1, 4], [1, 1, 0, 0]]}, {[[3, 4, 1, 5, 2], [1, 1, 0, 0]]}, {[[4, 1, 5, 2, 3], [0, 0, 1, 1]]}} {[[2, 5, 1, 4, 3], [0, 0, 1, 1]]} {[[3, 2, 5, 1, 4], [1, 1, 0, 0]]} "Class ", 439, " is:" {{[[2, 5, 1, 4, 3], [0, 1, 0, 0]]}, {[[3, 2, 5, 1, 4], [0, 0, 1, 0]]}, {[[3, 4, 1, 5, 2], [0, 0, 1, 0]]}, {[[4, 1, 5, 2, 3], [0, 1, 0, 0]]}} {[[2, 5, 1, 4, 3], [0, 1, 0, 0]]} {[[3, 2, 5, 1, 4], [0, 0, 1, 0]]} "Class ", 440, " is:" {{[[2, 5, 1, 4, 3], [0, 1, 0, 1]]}, {[[3, 2, 5, 1, 4], [1, 0, 1, 0]]}, {[[3, 4, 1, 5, 2], [1, 0, 1, 0]]}, {[[4, 1, 5, 2, 3], [0, 1, 0, 1]]}} {[[2, 5, 1, 4, 3], [0, 1, 0, 1]]} {[[3, 2, 5, 1, 4], [1, 0, 1, 0]]} "Class ", 441, " is:" {{[[2, 5, 1, 4, 3], [0, 1, 1, 0]]}, {[[3, 2, 5, 1, 4], [0, 1, 1, 0]]}, {[[3, 4, 1, 5, 2], [0, 1, 1, 0]]}, {[[4, 1, 5, 2, 3], [0, 1, 1, 0]]}} {[[2, 5, 1, 4, 3], [0, 1, 1, 0]]} {[[3, 2, 5, 1, 4], [0, 1, 1, 0]]} "Class ", 442, " is:" {{[[2, 5, 1, 4, 3], [0, 1, 1, 1]]}, {[[3, 2, 5, 1, 4], [1, 1, 1, 0]]}, {[[3, 4, 1, 5, 2], [1, 1, 1, 0]]}, {[[4, 1, 5, 2, 3], [0, 1, 1, 1]]}} {[[2, 5, 1, 4, 3], [0, 1, 1, 1]]} {[[3, 2, 5, 1, 4], [1, 1, 1, 0]]} "Class ", 443, " is:" {{[[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 5, 1, 4], [0, 0, 0, 1]]}, {[[3, 4, 1, 5, 2], [0, 0, 0, 1]]}, {[[4, 1, 5, 2, 3], [1, 0, 0, 0]]}} {[[2, 5, 1, 4, 3], [1, 0, 0, 0]]} {[[3, 2, 5, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[2, 5, 1, 4, 3], [1, 0, 0, 0]]}, {[[3, 2, 5, 1, 4], [0, 0, 0, 1]]}, {[[3, 4, 1, 5, 2], [0, 0, 0, 1]]}, {[[4, 1, 5, 2, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[3, 2, 5, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {[0, 0, 0, 1, 0]}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37870, 332606, 3238891, 34633233, 403404044, 5084026843, 68927816094, 1000322503967, 15472475705201, 254094506017353, 4415455643795340, 80944462778100425, 1561169952929670587] "" "Class ", 444, " is:" {{[[2, 5, 1, 4, 3], [1, 0, 0, 1]]}, {[[3, 2, 5, 1, 4], [1, 0, 0, 1]]}, {[[3, 4, 1, 5, 2], [1, 0, 0, 1]]}, {[[4, 1, 5, 2, 3], [1, 0, 0, 1]]}} {[[2, 5, 1, 4, 3], [1, 0, 0, 1]]} {[[3, 2, 5, 1, 4], [1, 0, 0, 1]]} "Class ", 445, " is:" {{[[2, 5, 1, 4, 3], [1, 0, 1, 0]]}, {[[3, 2, 5, 1, 4], [0, 1, 0, 1]]}, {[[3, 4, 1, 5, 2], [0, 1, 0, 1]]}, {[[4, 1, 5, 2, 3], [1, 0, 1, 0]]}} {[[2, 5, 1, 4, 3], [1, 0, 1, 0]]} {[[3, 2, 5, 1, 4], [0, 1, 0, 1]]} "Class ", 446, " is:" {{[[2, 5, 1, 4, 3], [1, 0, 1, 1]]}, {[[3, 2, 5, 1, 4], [1, 1, 0, 1]]}, {[[3, 4, 1, 5, 2], [1, 1, 0, 1]]}, {[[4, 1, 5, 2, 3], [1, 0, 1, 1]]}} {[[2, 5, 1, 4, 3], [1, 0, 1, 1]]} {[[3, 2, 5, 1, 4], [1, 1, 0, 1]]} "Class ", 447, " is:" {{[[2, 5, 1, 4, 3], [1, 1, 0, 0]]}, {[[3, 2, 5, 1, 4], [0, 0, 1, 1]]}, {[[3, 4, 1, 5, 2], [0, 0, 1, 1]]}, {[[4, 1, 5, 2, 3], [1, 1, 0, 0]]}} {[[2, 5, 1, 4, 3], [1, 1, 0, 0]]} {[[3, 2, 5, 1, 4], [0, 0, 1, 1]]} "Class ", 448, " is:" {{[[2, 5, 1, 4, 3], [1, 1, 0, 1]]}, {[[3, 2, 5, 1, 4], [1, 0, 1, 1]]}, {[[3, 4, 1, 5, 2], [1, 0, 1, 1]]}, {[[4, 1, 5, 2, 3], [1, 1, 0, 1]]}} {[[2, 5, 1, 4, 3], [1, 1, 0, 1]]} {[[3, 2, 5, 1, 4], [1, 0, 1, 1]]} "Class ", 449, " is:" {{[[2, 5, 1, 4, 3], [1, 1, 1, 0]]}, {[[3, 2, 5, 1, 4], [0, 1, 1, 1]]}, {[[3, 4, 1, 5, 2], [0, 1, 1, 1]]}, {[[4, 1, 5, 2, 3], [1, 1, 1, 0]]}} {[[2, 5, 1, 4, 3], [1, 1, 1, 0]]} {[[3, 2, 5, 1, 4], [0, 1, 1, 1]]} "Class ", 450, " is:" {{[[2, 5, 3, 1, 4], [0, 0, 0, 1]]}, {[[2, 5, 3, 1, 4], [1, 0, 0, 0]]}, {[[4, 1, 3, 5, 2], [0, 0, 0, 1]]}, {[[4, 1, 3, 5, 2], [1, 0, 0, 0]]}} {[[2, 5, 3, 1, 4], [0, 0, 0, 1]]} "For the class ", {{[[2, 5, 3, 1, 4], [0, 0, 0, 1]]}, {[[2, 5, 3, 1, 4], [1, 0, 0, 0]]}, {[[4, 1, 3, 5, 2], [0, 0, 0, 1]]}, {[[4, 1, 3, 5, 2], [1, 0, 0, 0]]}}, " the pattern set ", {[[2, 5, 3, 1, 4], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 0, 1, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37874, 332696, 3240416, 34657116, 403773512, 5089835936, 69021919224, 1001903928804, 15500138755224, 254598918643168, 4425046557089424, 81134570778122256, 1565095717271557536] "" "Class ", 451, " is:" {{[[2, 5, 3, 1, 4], [0, 0, 1, 0]]}, {[[2, 5, 3, 1, 4], [0, 1, 0, 0]]}, {[[4, 1, 3, 5, 2], [0, 0, 1, 0]]}, {[[4, 1, 3, 5, 2], [0, 1, 0, 0]]}} {[[2, 5, 3, 1, 4], [0, 0, 1, 0]]} {[[2, 5, 3, 1, 4], [0, 1, 0, 0]]} "Class ", 452, " is:" {{[[2, 5, 3, 1, 4], [0, 0, 1, 1]]}, {[[2, 5, 3, 1, 4], [1, 1, 0, 0]]}, {[[4, 1, 3, 5, 2], [0, 0, 1, 1]]}, {[[4, 1, 3, 5, 2], [1, 1, 0, 0]]}} {[[2, 5, 3, 1, 4], [0, 0, 1, 1]]} {[[2, 5, 3, 1, 4], [1, 1, 0, 0]]} "Class ", 453, " is:" {{[[2, 5, 3, 1, 4], [0, 1, 0, 1]]}, {[[2, 5, 3, 1, 4], [1, 0, 1, 0]]}, {[[4, 1, 3, 5, 2], [0, 1, 0, 1]]}, {[[4, 1, 3, 5, 2], [1, 0, 1, 0]]}} {[[2, 5, 3, 1, 4], [0, 1, 0, 1]]} {[[2, 5, 3, 1, 4], [1, 0, 1, 0]]} "Class ", 454, " is:" {{[[2, 5, 3, 1, 4], [0, 1, 1, 1]]}, {[[2, 5, 3, 1, 4], [1, 1, 1, 0]]}, {[[4, 1, 3, 5, 2], [0, 1, 1, 1]]}, {[[4, 1, 3, 5, 2], [1, 1, 1, 0]]}} {[[2, 5, 3, 1, 4], [0, 1, 1, 1]]} {[[2, 5, 3, 1, 4], [1, 1, 1, 0]]} "Class ", 455, " is:" {{[[2, 5, 3, 1, 4], [1, 0, 1, 1]]}, {[[2, 5, 3, 1, 4], [1, 1, 0, 1]]}, {[[4, 1, 3, 5, 2], [1, 0, 1, 1]]}, {[[4, 1, 3, 5, 2], [1, 1, 0, 1]]}} {[[2, 5, 3, 1, 4], [1, 0, 1, 1]]} {[[2, 5, 3, 1, 4], [1, 1, 0, 1]]} "Class ", 456, " is:" {{[[2, 5, 4, 1, 3], [0, 0, 0, 0]]}, {[[3, 1, 4, 5, 2], [0, 0, 0, 0]]}, {[[3, 5, 2, 1, 4], [0, 0, 0, 0]]}, {[[4, 1, 2, 5, 3], [0, 0, 0, 0]]}} {[[2, 5, 4, 1, 3], [0, 0, 0, 0]]} "For the class ", {{[[2, 5, 4, 1, 3], [0, 0, 0, 0]]}, {[[3, 1, 4, 5, 2], [0, 0, 0, 0]]}, {[[3, 5, 2, 1, 4], [0, 0, 0, 0]]}, {[[4, 1, 2, 5, 3], [0, 0, 0, 0]]}}, " the pattern set ", {[[2, 5, 4, 1, 3], [0, 0, 0, 0]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {}, {}], [[2, 4, 3, 1, 5], {1, 2, 3}, {}], [[2, 5, 3, 1, 4], {1, 2, 3}, {}], [[2, 5, 4, 1, 3], {1, 2, 3, 4, 5}, {[0, 0, 0, 0, 0, 0]}], [[3, 5, 4, 1, 2], {1, 2, 3}, {}], [[3, 5, 4, 2, 1], {1, 2, 3, 4}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 708, 4914, 38979, 347844, 3449022, 37618404, 447603154, 5769631250, 80091726847, 1191215895231, 18898269051750, 318553597247225, 5685472764793353, 107110426612465623, 2124091932221770696] "" "Class ", 457, " is:" {{[[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, {[[3, 1, 4, 5, 2], [1, 0, 0, 0]]}, {[[3, 5, 2, 1, 4], [1, 0, 0, 0]]}, {[[4, 1, 2, 5, 3], [0, 0, 0, 1]]}} {[[2, 5, 4, 1, 3], [0, 0, 0, 1]]} "For the class ", {{[[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, {[[3, 1, 4, 5, 2], [1, 0, 0, 0]]}, {[[3, 5, 2, 1, 4], [1, 0, 0, 0]]}, {[[4, 1, 2, 5, 3], [0, 0, 0, 1]]}}, " the pattern set ", {[[2, 5, 4, 1, 3], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {}, {}], [[2, 1], {1}, {}], [[1, 2, 3], {1}, {}], [[1, 3, 2], {}, {}], [[2, 3, 1], {1, 2}, {}], [[1, 3, 2, 4], {1, 2}, {}], [[1, 4, 2, 3], {1, 2}, {}], [[1, 4, 3, 2], {1, 2, 3}, {}], [[2, 4, 3, 1], {1, 2, 3}, {[0, 0, 1, 0, 0]}] } "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37874, 332696, 3240416, 34657116, 403773512, 5089835936, 69021919224, 1001903928804, 15500138755224, 254598918643168, 4425046557089424, 81134570778122256, 1565095717271557536] "" "Class ", 458, " is:" {{[[2, 5, 4, 1, 3], [0, 0, 1, 0]]}, {[[3, 1, 4, 5, 2], [0, 1, 0, 0]]}, {[[3, 5, 2, 1, 4], [0, 1, 0, 0]]}, {[[4, 1, 2, 5, 3], [0, 0, 1, 0]]}} {[[2, 5, 4, 1, 3], [0, 0, 1, 0]]} {[[3, 1, 4, 5, 2], [0, 1, 0, 0]]} "Class ", 459, " is:" {{[[2, 5, 4, 1, 3], [0, 0, 1, 1]]}, {[[3, 1, 4, 5, 2], [1, 1, 0, 0]]}, {[[3, 5, 2, 1, 4], [1, 1, 0, 0]]}, {[[4, 1, 2, 5, 3], [0, 0, 1, 1]]}} {[[2, 5, 4, 1, 3], [0, 0, 1, 1]]} {[[3, 1, 4, 5, 2], [1, 1, 0, 0]]} "Class ", 460, " is:" {{[[2, 5, 4, 1, 3], [0, 1, 0, 0]]}, {[[3, 1, 4, 5, 2], [0, 0, 1, 0]]}, {[[3, 5, 2, 1, 4], [0, 0, 1, 0]]}, {[[4, 1, 2, 5, 3], [0, 1, 0, 0]]}} {[[2, 5, 4, 1, 3], [0, 1, 0, 0]]} {[[3, 1, 4, 5, 2], [0, 0, 1, 0]]} "Class ", 461, " is:" {{[[2, 5, 4, 1, 3], [0, 1, 0, 1]]}, {[[3, 1, 4, 5, 2], [1, 0, 1, 0]]}, {[[3, 5, 2, 1, 4], [1, 0, 1, 0]]}, {[[4, 1, 2, 5, 3], [0, 1, 0, 1]]}} {[[2, 5, 4, 1, 3], [0, 1, 0, 1]]} {[[3, 1, 4, 5, 2], [1, 0, 1, 0]]} "Class ", 462, " is:" {{[[2, 5, 4, 1, 3], [0, 1, 1, 0]]}, {[[3, 1, 4, 5, 2], [0, 1, 1, 0]]}, {[[3, 5, 2, 1, 4], [0, 1, 1, 0]]}, {[[4, 1, 2, 5, 3], [0, 1, 1, 0]]}} {[[2, 5, 4, 1, 3], [0, 1, 1, 0]]} {[[3, 1, 4, 5, 2], [0, 1, 1, 0]]} "Class ", 463, " is:" {{[[2, 5, 4, 1, 3], [0, 1, 1, 1]]}, {[[3, 1, 4, 5, 2], [1, 1, 1, 0]]}, {[[3, 5, 2, 1, 4], [1, 1, 1, 0]]}, {[[4, 1, 2, 5, 3], [0, 1, 1, 1]]}} {[[2, 5, 4, 1, 3], [0, 1, 1, 1]]} {[[3, 1, 4, 5, 2], [1, 1, 1, 0]]} "Class ", 464, " is:" {{[[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, {[[3, 1, 4, 5, 2], [0, 0, 0, 1]]}, {[[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, {[[4, 1, 2, 5, 3], [1, 0, 0, 0]]}} {[[2, 5, 4, 1, 3], [1, 0, 0, 0]]} {[[3, 1, 4, 5, 2], [0, 0, 0, 1]]} "For the class ", {{[[2, 5, 4, 1, 3], [1, 0, 0, 0]]}, {[[3, 1, 4, 5, 2], [0, 0, 0, 1]]}, {[[3, 5, 2, 1, 4], [0, 0, 0, 1]]}, {[[4, 1, 2, 5, 3], [1, 0, 0, 0]]}}, " the pattern set ", {[[3, 1, 4, 5, 2], [0, 0, 0, 1]]}, " has scheme:" {[[], {}, {}], [[1], {}, {}], [[1, 2], {1}, {}], [[2, 1], {}, {}], [[2, 1, 3], {}, {}], [[3, 1, 2], {1, 2}, {}], [[3, 2, 1], {1}, {}], [[2, 1, 3, 4], {1, 2, 3}, {[0, 1, 0, 0, 0]}], [[2, 1, 4, 3], {1, 2}, {}], [[3, 1, 4, 2], {1, 2}, {}], [[3, 2, 4, 1], {1, 2}, {}]} "The first ", 20, " terms of the counting sequence are:" [1, 2, 6, 24, 119, 704, 4838, 37868, 332546, 3237620, 34609332, 402972008, 5076245018, 68785548072, 997655804160, 15420936790944, 253064231968336, 4394118358559280, 80486313018869424, 1550969499004966272] "" "Class ", 465, " is:" {{[[2, 5, 4, 1, 3], [1, 0, 0, 1]]}, {[[3, 1, 4, 5, 2], [1, 0, 0, 1]]}, {[[3, 5, 2, 1, 4], [1, 0, 0, 1]]}, {[[4, 1, 2, 5, 3], [1, 0, 0, 1]]}} {[[2, 5, 4, 1, 3], [1, 0, 0, 1]]} {[[3, 1, 4, 5, 2], [1, 0, 0, 1]]} "Class ", 466, " is:" {{[[2, 5, 4, 1, 3], [1, 0, 1, 0]]}, {[[3, 1, 4, 5, 2], [0, 1, 0, 1]]}, {[[3, 5, 2, 1, 4], [0, 1, 0, 1]]}, {[[4, 1, 2, 5, 3], [1, 0, 1, 0]]}} {[[2, 5, 4, 1, 3], [1, 0, 1, 0]]} {[[3, 1, 4, 5, 2], [0, 1, 0, 1]]} "Class ", 467, " is:" {{[[2, 5, 4, 1, 3], [1, 0, 1, 1]]}, {[[3, 1, 4, 5, 2], [1, 1, 0, 1]]}, {[[3, 5, 2, 1, 4], [1, 1, 0, 1]]}, {[[4, 1, 2, 5, 3], [1, 0, 1, 1]]}} {[[2, 5, 4, 1, 3], [1, 0, 1, 1]]} {[[3, 1, 4, 5, 2], [1, 1, 0, 1]]} "Class ", 468, " is:" {{[[2, 5, 4, 1, 3], [1, 1, 0, 0]]}, {[[3, 1, 4, 5, 2], [0, 0, 1, 1]]}, {[[3, 5, 2, 1, 4], [0, 0, 1, 1]]}, {[[4, 1, 2, 5, 3], [1, 1, 0, 0]]}} {[[2, 5, 4, 1, 3], [1, 1, 0, 0]]} {[[3, 1, 4, 5, 2], [0, 0, 1, 1]]} "Class ", 469, " is:" {{[[2, 5, 4, 1, 3], [1, 1, 0, 1]]}, {[[3, 1, 4, 5, 2], [1, 0, 1, 1]]}, {[[3, 5, 2, 1, 4], [1, 0, 1, 1]]}, {[[4, 1, 2, 5, 3], [1, 1, 0, 1]]}} {[[2, 5, 4, 1, 3], [1, 1, 0, 1]]} {[[3, 1, 4, 5, 2], [1, 0, 1, 1]]} "Class ", 470, " is:" {{[[2, 5, 4, 1, 3], [1, 1, 1, 0]]}, {[[3, 1, 4, 5, 2], [0, 1, 1, 1]]}, {[[3, 5, 2, 1, 4], [0, 1, 1, 1]]}, {[[4, 1, 2, 5, 3], [1, 1, 1, 0]]}} {[[2, 5, 4, 1, 3], [1, 1, 1, 0]]} {[[3, 1, 4, 5, 2], [0, 1, 1, 1]]} "Class ", 471, " is:" {{[[1, 2, 4, 5, 3], [1, 1, 1, 1]]}, {[[1, 2, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1, 4, 5], [1, 1, 1, 1]]}, {[[3, 1, 2, 4, 5], [1, 1, 1, 1]]}, {[[3, 5, 4, 2, 1], [1, 1, 1, 1]]}, {[[4, 3, 5, 2, 1], [1, 1, 1, 1]]}, {[[5, 4, 1, 3, 2], [1, 1, 1, 1]]}, {[[5, 4, 2, 1, 3], [1, 1, 1, 1]]}} {[[1, 2, 4, 5, 3], [1, 1, 1, 1]]} {[[1, 2, 5, 3, 4], [1, 1, 1, 1]]} {[[2, 3, 1, 4, 5], [1, 1, 1, 1]]} {[[3, 1, 2, 4, 5], [1, 1, 1, 1]]} "Class ", 472, " is:" {{[[1, 3, 4, 5, 2], [1, 1, 1, 1]]}, {[[1, 5, 2, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 4, 1, 5], [1, 1, 1, 1]]}, {[[2, 5, 4, 3, 1], [1, 1, 1, 1]]}, {[[4, 1, 2, 3, 5], [1, 1, 1, 1]]}, {[[4, 3, 2, 5, 1], [1, 1, 1, 1]]}, {[[5, 1, 4, 3, 2], [1, 1, 1, 1]]}, {[[5, 3, 2, 1, 4], [1, 1, 1, 1]]}} {[[1, 3, 4, 5, 2], [1, 1, 1, 1]]} {[[1, 5, 2, 3, 4], [1, 1, 1, 1]]} {[[2, 3, 4, 1, 5], [1, 1, 1, 1]]} {[[2, 5, 4, 3, 1], [1, 1, 1, 1]]} "Class ", 473, " is:" {{[[1, 3, 5, 2, 4], [1, 1, 1, 1]]}, {[[1, 4, 2, 5, 3], [1, 1, 1, 1]]}, {[[2, 4, 1, 3, 5], [1, 1, 1, 1]]}, {[[3, 1, 4, 2, 5], [1, 1, 1, 1]]}, {[[3, 5, 2, 4, 1], [1, 1, 1, 1]]}, {[[4, 2, 5, 3, 1], [1, 1, 1, 1]]}, {[[5, 2, 4, 1, 3], [1, 1, 1, 1]]}, {[[5, 3, 1, 4, 2], [1, 1, 1, 1]]}} {[[1, 3, 5, 2, 4], [1, 1, 1, 1]]} {[[1, 4, 2, 5, 3], [1, 1, 1, 1]]} {[[2, 4, 1, 3, 5], [1, 1, 1, 1]]} {[[3, 1, 4, 2, 5], [1, 1, 1, 1]]} "Class ", 474, " is:" {{[[1, 3, 5, 4, 2], [1, 1, 1, 1]]}, {[[1, 5, 2, 4, 3], [1, 1, 1, 1]]}, {[[2, 4, 5, 3, 1], [1, 1, 1, 1]]}, {[[3, 2, 4, 1, 5], [1, 1, 1, 1]]}, {[[3, 4, 2, 5, 1], [1, 1, 1, 1]]}, {[[4, 2, 1, 3, 5], [1, 1, 1, 1]]}, {[[5, 1, 4, 2, 3], [1, 1, 1, 1]]}, {[[5, 3, 1, 2, 4], [1, 1, 1, 1]]}} {[[1, 3, 5, 4, 2], [1, 1, 1, 1]]} {[[1, 5, 2, 4, 3], [1, 1, 1, 1]]} {[[2, 4, 5, 3, 1], [1, 1, 1, 1]]} {[[3, 2, 4, 1, 5], [1, 1, 1, 1]]} "Class ", 475, " is:" {{[[1, 4, 3, 5, 2], [1, 1, 1, 1]]}, {[[1, 5, 3, 2, 4], [1, 1, 1, 1]]}, {[[2, 4, 3, 1, 5], [1, 1, 1, 1]]}, {[[2, 5, 3, 4, 1], [1, 1, 1, 1]]}, {[[4, 1, 3, 2, 5], [1, 1, 1, 1]]}, {[[4, 2, 3, 5, 1], [1, 1, 1, 1]]}, {[[5, 1, 3, 4, 2], [1, 1, 1, 1]]}, {[[5, 2, 3, 1, 4], [1, 1, 1, 1]]}} {[[1, 4, 3, 5, 2], [1, 1, 1, 1]]} {[[1, 5, 3, 2, 4], [1, 1, 1, 1]]} {[[2, 4, 3, 1, 5], [1, 1, 1, 1]]} {[[2, 5, 3, 4, 1], [1, 1, 1, 1]]} "Class ", 476, " is:" {{[[1, 4, 5, 3, 2], [1, 1, 1, 1]]}, {[[1, 5, 4, 2, 3], [1, 1, 1, 1]]}, {[[2, 3, 5, 4, 1], [1, 1, 1, 1]]}, {[[3, 2, 4, 5, 1], [1, 1, 1, 1]]}, {[[3, 4, 2, 1, 5], [1, 1, 1, 1]]}, {[[4, 3, 1, 2, 5], [1, 1, 1, 1]]}, {[[5, 1, 2, 4, 3], [1, 1, 1, 1]]}, {[[5, 2, 1, 3, 4], [1, 1, 1, 1]]}} {[[1, 4, 5, 3, 2], [1, 1, 1, 1]]} {[[1, 5, 4, 2, 3], [1, 1, 1, 1]]} {[[2, 3, 5, 4, 1], [1, 1, 1, 1]]} {[[3, 2, 4, 5, 1], [1, 1, 1, 1]]} "Class ", 477, " is:" {{[[2, 1, 4, 5, 3], [1, 1, 1, 1]]}, {[[2, 1, 5, 3, 4], [1, 1, 1, 1]]}, {[[2, 3, 1, 5, 4], [1, 1, 1, 1]]}, {[[3, 1, 2, 5, 4], [1, 1, 1, 1]]}, {[[3, 5, 4, 1, 2], [1, 1, 1, 1]]}, {[[4, 3, 5, 1, 2], [1, 1, 1, 1]]}, {[[4, 5, 1, 3, 2], [1, 1, 1, 1]]}, {[[4, 5, 2, 1, 3], [1, 1, 1, 1]]}} {[[2, 1, 4, 5, 3], [1, 1, 1, 1]]} {[[2, 1, 5, 3, 4], [1, 1, 1, 1]]} {[[2, 3, 1, 5, 4], [1, 1, 1, 1]]} {[[3, 1, 2, 5, 4], [1, 1, 1, 1]]} "Class ", 478, " is:" {{[[2, 3, 5, 1, 4], [1, 1, 1, 1]]}, {[[2, 5, 1, 3, 4], [1, 1, 1, 1]]}, {[[2, 5, 4, 1, 3], [1, 1, 1, 1]]}, {[[3, 1, 4, 5, 2], [1, 1, 1, 1]]}, {[[3, 5, 2, 1, 4], [1, 1, 1, 1]]}, {[[4, 1, 2, 5, 3], [1, 1, 1, 1]]}, {[[4, 1, 5, 3, 2], [1, 1, 1, 1]]}, {[[4, 3, 1, 5, 2], [1, 1, 1, 1]]}} {[[2, 3, 5, 1, 4], [1, 1, 1, 1]]} {[[2, 5, 1, 3, 4], [1, 1, 1, 1]]} {[[2, 5, 4, 1, 3], [1, 1, 1, 1]]} {[[3, 1, 4, 5, 2], [1, 1, 1, 1]]} "Class ", 479, " is:" {{[[2, 4, 5, 1, 3], [1, 1, 1, 1]]}, {[[2, 5, 1, 4, 3], [1, 1, 1, 1]]}, {[[3, 1, 5, 4, 2], [1, 1, 1, 1]]}, {[[3, 2, 5, 1, 4], [1, 1, 1, 1]]}, {[[3, 4, 1, 5, 2], [1, 1, 1, 1]]}, {[[3, 5, 1, 2, 4], [1, 1, 1, 1]]}, {[[4, 1, 5, 2, 3], [1, 1, 1, 1]]}, {[[4, 2, 1, 5, 3], [1, 1, 1, 1]]}} {[[2, 4, 5, 1, 3], [1, 1, 1, 1]]} {[[2, 5, 1, 4, 3], [1, 1, 1, 1]]} {[[3, 1, 5, 4, 2], [1, 1, 1, 1]]} {[[3, 2, 5, 1, 4], [1, 1, 1, 1]]} "Out of the ", 479, " equivalence classes ", 144, "(or ", 30.06263048, " %) classes have enumeration schemes." 335, "(or ", 69.93736952, " %) classes do not have enumeration schemes of depth <=", 5, ", with gap vectors of weight <=", 2 "The classes that failed are: " {{{[[1, 2, 3, 4, 5], [0, 1, 1, 0]]}}, {{[[1, 2, 3, 4, 5], [1, 1, 1, 1]]}}, {{[[1, 4, 3, 2, 5], [0, 1, 1, 0]]}}, {{[[1, 4, 3, 2, 5], [1, 1, 1, 1]]}}, {{[[2, 1, 3, 5, 4], [0, 1, 1, 0]]}}, {{[[2, 1, 3, 5, 4], [1, 0, 0, 1]]}}, {{[[2, 1, 3, 5, 4], [1, 1, 1, 1]]}}, {{[[2, 5, 3, 1, 4], [0, 1, 1, 0]]}}, {{[[2, 5, 3, 1, 4], [1, 0, 0, 1]]}}, {{[[2, 5, 3, 1, 4], [1, 1, 1, 1]]}}, {{[[1, 2, 3, 4, 5], [0, 0, 1, 1]]}, {[[1, 2, 3, 4, 5], [1, 1, 0, 0]]}}, {{[[1, 2, 3, 4, 5], [0, 1, 1, 1]]}, {[[1, 2, 3, 4, 5], [1, 1, 1, 0]]}}, {{[[1, 2, 3, 5, 4], [0, 0, 1, 1]]}, {[[2, 1, 3, 4, 5], [1, 1, 0, 0]]}}, {{[[1, 2, 3, 5, 4], [0, 1, 1, 0]]}, {[[2, 1, 3, 4, 5], [0, 1, 1, 0]]}}, {{[[1, 2, 3, 5, 4], [0, 1, 1, 1]]}, {[[2, 1, 3, 4, 5], [1, 1, 1, 0]]}}, {{[[1, 2, 3, 5, 4], [1, 0, 1, 1]]}, {[[2, 1, 3, 4, 5], [1, 1, 0, 1]]}}, {{[[1, 2, 3, 5, 4], [1, 1, 0, 0]]}, {[[2, 1, 3, 4, 5], [0, 0, 1, 1]]}}, {{[[1, 2, 3, 5, 4], [1, 1, 1, 0]]}, {[[2, 1, 3, 4, 5], [0, 1, 1, 1]]}}, {{[[1, 2, 3, 5, 4], [1, 1, 1, 1]]}, {[[2, 1, 3, 4, 5], [1, 1, 1, 1]]}}, {{[[1, 2, 4, 3, 5], [0, 0, 1, 0]]}, {[[1, 3, 2, 4, 5], [0, 1, 0, 0]]}}, {{[[1, 2, 4, 3, 5], [0, 0, 1, 1]]}, {[[1, 3, 2, 4, 5], [1, 1, 0, 0]]}}, {{[[1, 2, 4, 3, 5], [0, 1, 1, 0]]}, {[[1, 3, 2, 4, 5], [0, 1, 1, 0]]}}, {{[[1, 2, 4, 3, 5], [0, 1, 1, 1]]}, {[[1, 3, 2, 4, 5], [1, 1, 1, 0]]}}, {{[[1, 2, 4, 3, 5], [1, 0, 1, 0]]}, {[[1, 3, 2, 4, 5], [0, 1, 0, 1]]}}, {{[[1, 2, 4, 3, 5], [1, 0, 1, 1]]}, {[[1, 3, 2, 4, 5], [1, 1, 0, 1]]}}, {{[[1, 2, 4, 3, 5], [1, 1, 0, 0]]}, {[[1, 3, 2, 4, 5], [0, 0, 1, 1]]}}, {{[[1, 2, 4, 3, 5], [1, 1, 1, 0]]}, {[[1, 3, 2, 4, 5], [0, 1, 1, 1]]}}, {{[[1, 2, 4, 3, 5], [1, 1, 1, 1]]}, {[[1, 3, 2, 4, 5], [1, 1, 1, 1]]}}, {{[[1, 2, 4, 5, 3], [0, 0, 1, 0]]}, {[[3, 1, 2, 4, 5], [0, 1, 0, 0]]}}, {{[[1, 2, 4, 5, 3], [0, 0, 1, 1]]}, {[[3, 1, 2, 4, 5], [1, 1, 0, 0]]}}, {{[[1, 2, 4, 5, 3], [0, 1, 1, 0]]}, {[[3, 1, 2, 4, 5], [0, 1, 1, 0]]}}, {{[[1, 2, 4, 5, 3], [0, 1, 1, 1]]}, {[[3, 1, 2, 4, 5], [1, 1, 1, 0]]}}, {{[[1, 2, 4, 5, 3], [1, 0, 1, 0]]}, {[[3, 1, 2, 4, 5], [0, 1, 0, 1]]}}, {{[[1, 2, 4, 5, 3], [1, 0, 1, 1]]}, {[[3, 1, 2, 4, 5], [1, 1, 0, 1]]}}, {{[[1, 2, 4, 5, 3], [1, 1, 0, 0]]}, {[[3, 1, 2, 4, 5], [0, 0, 1, 1]]}}, {{[[1, 2, 4, 5, 3], [1, 1, 1, 0]]}, {[[3, 1, 2, 4, 5], [0, 1, 1, 1]]}}, {{[[1, 2, 5, 3, 4], [0, 0, 1, 0]]}, {[[2, 3, 1, 4, 5], [0, 1, 0, 0]]}}, {{[[1, 2, 5, 3, 4], [0, 0, 1, 1]]}, {[[2, 3, 1, 4, 5], [1, 1, 0, 0]]}}, {{[[1, 2, 5, 3, 4], [0, 1, 1, 0]]}, {[[2, 3, 1, 4, 5], [0, 1, 1, 0]]}}, 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