Graph forms
for C4 [ 512, 87 ] = UG(ATD[512,83])
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On this page are computer-accessible forms for the graph C4[ 512, 87 ] =
UG(ATD[512,83]).
(I) Following is a form readable by MAGMA:
g:=Graph<512|{ {16, 17}, {368, 377}, {1, 17}, {352, 368}, {4, 20}, {485, 503},
{487, 501}, {331, 344}, {360, 379}, {329, 348}, {486, 499}, {361, 380}, {332,
345}, {331, 349}, {365, 379}, {364, 378}, {5, 18}, {488, 511}, {332, 340}, {485,
509}, {356, 380}, {353, 377}, {488, 497}, {8, 19}, {330, 337}, {329, 341}, {487,
507}, {416, 444}, {9, 20}, {12, 18}, {13, 19}, {357, 378}, {486, 505}, {1, 33},
{471, 503}, {469, 501}, {409, 441}, {128, 160}, {4, 36}, {267, 298}, {473, 504},
{268, 302}, {408, 442}, {338, 368}, {320, 355}, {268, 296}, {266, 300}, {384,
422}, {2, 37}, {465, 502}, {413, 442}, {412, 443}, {320, 361}, {479, 502}, {330,
352}, {477, 503}, {3, 40}, {467, 504}, {384, 427}, {265, 290}, {266, 294}, {4,
41}, {404, 441}, {401, 444}, {2, 44}, {475, 501}, {405, 443}, {3, 45}, {267,
292}, {1, 49}, {463, 511}, {462, 510}, {1, 48}, {64, 113}, {348, 367}, {350,
365}, {7, 51}, {346, 366}, {344, 365}, {3, 52}, {458, 509}, {5, 50}, {11, 50},
{455, 510}, {342, 367}, {265, 304}, {340, 366}, {9, 52}, {450, 511}, {13, 51},
{451, 509}, {15, 49}, {17, 81}, {271, 335}, {52, 116}, {49, 113}, {33, 97},
{144, 208}, {284, 349}, {140, 207}, {270, 333}, {141, 206}, {23, 83}, {269,
329}, {137, 205}, {48, 116}, {39, 99}, {282, 351}, {136, 206}, {19, 84}, {53,
114}, {37, 98}, {35, 100}, {21, 82}, {27, 82}, {270, 327}, {132, 205}, {48,
121}, {43, 98}, {133, 207}, {56, 115}, {278, 349}, {276, 351}, {274, 350}, {25,
84}, {57, 116}, {41, 100}, {29, 83}, {271, 321}, {269, 323}, {61, 115}, {60,
114}, {47, 97}, {45, 99}, {31, 81}, {17, 65}, {391, 471}, {389, 469}, {20, 68},
{129, 208}, {393, 472}, {46, 124}, {319, 365}, {317, 367}, {47, 125}, {166,
245}, {442, 489}, {288, 371}, {162, 246}, {447, 491}, {446, 490}, {163, 247},
{272, 325}, {318, 363}, {174, 248}, {21, 66}, {443, 492}, {385, 470}, {47, 120},
{319, 359}, {175, 246}, {434, 491}, {399, 470}, {288, 377}, {397, 471}, {438,
492}, {435, 489}, {24, 67}, {387, 472}, {318, 357}, {272, 331}, {46, 117}, {45,
113}, {317, 353}, {25, 68}, {439, 490}, {170, 247}, {28, 66}, {395, 469}, {29,
67}, {171, 245}, {167, 248}, {389, 485}, {391, 487}, {32, 65}, {392, 489}, {171,
202}, {136, 234}, {287, 381}, {285, 383}, {172, 206}, {138, 233}, {142, 234},
{172, 200}, {33, 68}, {286, 379}, {36, 65}, {35, 69}, {170, 204}, {176, 214},
{140, 235}, {390, 481}, {33, 73}, {287, 375}, {390, 495}, {34, 72}, {391, 493},
{169, 194}, {392, 483}, {286, 373}, {170, 198}, {285, 369}, {132, 233}, {134,
235}, {130, 236}, {389, 491}, {34, 77}, {35, 76}, {171, 196}, {168, 216}, {299,
347}, {298, 346}, {128, 241}, {138, 248}, {137, 250}, {300, 351}, {164, 215},
{166, 213}, {36, 80}, {138, 254}, {162, 214}, {174, 216}, {139, 252}, {297,
350}, {280, 352}, {169, 208}, {298, 339}, {172, 213}, {144, 236}, {137, 244},
{299, 342}, {139, 246}, {170, 215}, {140, 242}, {300, 338}, {297, 343}, {288,
350}, {286, 352}, {94, 222}, {96, 224}, {34, 161}, {127, 252}, {126, 253}, {95,
220}, {38, 162}, {125, 249}, {94, 216}, {126, 248}, {36, 163}, {279, 400}, {272,
407}, {93, 218}, {42, 163}, {125, 244}, {95, 214}, {93, 212}, {46, 164}, {127,
245}, {40, 164}, {44, 162}, {73, 217}, {97, 241}, {84, 196}, {81, 193}, {48,
161}, {288, 433}, {74, 216}, {278, 388}, {260, 406}, {314, 425}, {103, 243},
{315, 431}, {313, 429}, {280, 396}, {268, 408}, {257, 407}, {374, 480}, {279,
385}, {74, 221}, {316, 427}, {101, 242}, {99, 244}, {85, 194}, {75, 220}, {269,
405}, {277, 397}, {107, 242}, {316, 421}, {314, 419}, {315, 417}, {88, 195},
{379, 480}, {73, 212}, {280, 389}, {277, 392}, {264, 405}, {261, 408}, {105,
244}, {89, 196}, {76, 209}, {75, 213}, {313, 423}, {111, 241}, {109, 243}, {93,
195}, {92, 194}, {265, 406}, {278, 393}, {273, 433}, {383, 479}, {382, 478},
{276, 436}, {96, 193}, {315, 410}, {112, 209}, {106, 203}, {256, 418}, {303,
397}, {108, 201}, {313, 412}, {299, 398}, {298, 399}, {105, 207}, {319, 409},
{317, 411}, {107, 205}, {277, 434}, {378, 477}, {105, 193}, {305, 409}, {294,
398}, {375, 478}, {280, 435}, {76, 224}, {311, 411}, {291, 399}, {107, 199},
{45, 128}, {370, 479}, {281, 436}, {284, 434}, {371, 477}, {285, 435}, {106,
197}, {309, 410}, {307, 412}, {290, 397}, {108, 195}, {49, 129}, {256, 432},
{100, 212}, {97, 209}, {81, 225}, {96, 210}, {55, 131}, {87, 227}, {51, 132},
{295, 400}, {101, 210}, {85, 226}, {83, 228}, {53, 130}, {59, 130}, {91, 226},
{104, 211}, {57, 132}, {105, 212}, {89, 228}, {61, 131}, {302, 400}, {109, 211},
{108, 210}, {95, 225}, {93, 227}, {63, 129}, {257, 449}, {123, 186}, {14, 204},
{341, 407}, {15, 205}, {330, 393}, {344, 411}, {263, 451}, {335, 395}, {334,
394}, {121, 188}, {342, 403}, {125, 187}, {343, 401}, {127, 185}, {15, 200},
{331, 396}, {261, 450}, {259, 452}, {113, 185}, {343, 415}, {341, 413}, {267,
450}, {322, 395}, {323, 393}, {326, 396}, {14, 197}, {13, 193}, {119, 187},
{265, 452}, {344, 405}, {327, 394}, {269, 451}, {271, 449}, {115, 188}, {342,
409}, {117, 186}, {65, 145}, {383, 431}, {114, 160}, {381, 430}, {16, 196},
{382, 426}, {71, 147}, {67, 148}, {69, 146}, {16, 201}, {75, 146}, {381, 423},
{13, 208}, {383, 418}, {382, 419}, {73, 148}, {77, 147}, {79, 145}, {126, 158},
{261, 485}, {264, 489}, {124, 159}, {80, 180}, {120, 158}, {310, 464}, {122,
157}, {262, 481}, {116, 157}, {261, 492}, {118, 159}, {263, 493}, {315, 464},
{264, 484}, {263, 488}, {319, 463}, {347, 426}, {349, 428}, {345, 427}, {318,
461}, {314, 462}, {68, 177}, {70, 179}, {66, 180}, {351, 425}, {262, 496}, {337,
425}, {339, 427}, {72, 178}, {311, 461}, {74, 177}, {343, 428}, {78, 178}, {306,
463}, {307, 462}, {76, 179}, {341, 426}, {64, 322}, {88, 346}, {2, 257}, {90,
345}, {192, 451}, {218, 473}, {6, 258}, {94, 346}, {32, 292}, {160, 420}, {222,
474}, {223, 475}, {20, 273}, {22, 275}, {176, 437}, {18, 276}, {4, 259}, {92,
347}, {219, 476}, {10, 259}, {32, 297}, {192, 457}, {210, 475}, {14, 260}, {24,
274}, {211, 473}, {214, 476}, {26, 273}, {176, 443}, {8, 260}, {30, 274}, {84,
345}, {86, 347}, {215, 474}, {12, 258}, {82, 348}, {28, 275}, {64, 336}, {175,
447}, {184, 424}, {16, 257}, {58, 299}, {102, 373}, {174, 445}, {180, 423},
{182, 421}, {98, 374}, {99, 375}, {173, 441}, {178, 422}, {60, 297}, {57, 303},
{110, 376}, {59, 301}, {190, 424}, {57, 289}, {111, 374}, {174, 439}, {188,
421}, {59, 295}, {106, 375}, {186, 423}, {107, 373}, {173, 435}, {175, 433},
{58, 293}, {103, 376}, {60, 291}, {80, 369}, {90, 376}, {207, 493}, {89, 378},
{90, 382}, {202, 495}, {203, 494}, {91, 380}, {198, 494}, {195, 495}, {29, 304},
{91, 374}, {89, 372}, {92, 370}, {194, 493}, {250, 458}, {143, 446}, {30, 300},
{31, 301}, {78, 381}, {79, 380}, {32, 276}, {255, 459}, {77, 377}, {138, 447},
{148, 417}, {150, 419}, {78, 376}, {139, 445}, {146, 420}, {31, 296}, {254,
457}, {251, 460}, {199, 496}, {77, 372}, {243, 458}, {242, 459}, {79, 373},
{246, 460}, {152, 418}, {30, 293}, {134, 445}, {154, 417}, {29, 289}, {131,
447}, {130, 446}, {124, 320}, {96, 348}, {158, 418}, {206, 496}, {247, 457},
{156, 419}, {121, 313}, {122, 312}, {239, 429}, {237, 431}, {149, 470}, {150,
466}, {151, 467}, {235, 430}, {112, 310}, {152, 478}, {122, 317}, {135, 448},
{123, 316}, {231, 431}, {150, 479}, {229, 430}, {28, 336}, {156, 464}, {225,
429}, {121, 308}, {124, 305}, {151, 474}, {123, 309}, {238, 416}, {142, 448},
{149, 475}, {152, 471}, {25, 329}, {254, 430}, {104, 312}, {167, 502}, {203,
410}, {26, 328}, {154, 456}, {165, 503}, {201, 411}, {204, 414}, {100, 311},
{255, 428}, {243, 416}, {102, 309}, {153, 458}, {227, 432}, {98, 310}, {154,
462}, {166, 499}, {202, 415}, {110, 312}, {254, 424}, {26, 333}, {253, 426},
{27, 332}, {155, 460}, {168, 511}, {183, 480}, {202, 402}, {203, 403}, {108,
309}, {255, 422}, {253, 420}, {249, 416}, {233, 432}, {168, 498}, {165, 510},
{204, 407}, {166, 506}, {167, 507}, {25, 324}, {106, 311}, {28, 321}, {153,
452}, {155, 454}, {27, 325}, {156, 450}, {201, 406}, {182, 468}, {255, 413},
{253, 415}, {184, 476}, {251, 414}, {118, 272}, {183, 465}, {192, 422}, {181,
477}, {247, 415}, {240, 408}, {245, 414}, {220, 432}, {241, 413}, {181, 472},
{184, 469}, {240, 414}, {182, 473}, {62, 334}, {120, 264}, {217, 425}, {237,
412}, {189, 463}, {191, 461}, {218, 424}, {63, 332}, {119, 260}, {117, 262},
{118, 258}, {190, 459}, {239, 410}, {62, 328}, {120, 270}, {61, 330}, {218,
429}, {219, 428}, {191, 455}, {61, 324}, {117, 268}, {63, 326}, {190, 453},
{239, 404}, {237, 406}, {189, 449}, {238, 402}, {119, 266}, {217, 420}, {220,
417}, {219, 421}, {3, 387}, {128, 256}, {160, 289}, {176, 305}, {192, 321},
{232, 362}, {2, 385}, {133, 262}, {122, 505}, {7, 388}, {234, 361}, {6, 386},
{238, 362}, {135, 259}, {134, 258}, {127, 507}, {126, 506}, {136, 270}, {123,
508}, {236, 363}, {224, 359}, {10, 387}, {134, 271}, {114, 507}, {11, 386}, {14,
388}, {250, 368}, {118, 508}, {115, 505}, {140, 256}, {119, 506}, {135, 266},
{228, 361}, {230, 363}, {15, 385}, {133, 267}, {224, 366}, {226, 364}, {136,
263}, {161, 305}, {164, 308}, {251, 362}, {102, 500}, {252, 366}, {183, 293},
{187, 296}, {104, 508}, {252, 360}, {178, 295}, {249, 364}, {179, 294}, {103,
497}, {165, 306}, {101, 509}, {250, 354}, {191, 295}, {168, 307}, {190, 293},
{186, 294}, {240, 364}, {101, 504}, {104, 501}, {169, 308}, {172, 306}, {173,
307}, {182, 296}, {102, 505}, {251, 356}, {249, 358}, {239, 334}, {144, 306},
{52, 401}, {54, 403}, {234, 335}, {50, 404}, {235, 333}, {56, 402}, {58, 401},
{230, 333}, {62, 402}, {226, 334}, {227, 335}, {60, 403}, {9, 441}, {142, 318},
{112, 448}, {67, 499}, {145, 289}, {148, 292}, {222, 367}, {10, 440}, {66, 497},
{71, 500}, {143, 316}, {70, 498}, {223, 362}, {142, 312}, {221, 363}, {10, 445},
{141, 314}, {11, 444}, {149, 290}, {231, 336}, {74, 499}, {143, 310}, {141,
308}, {75, 498}, {78, 500}, {152, 291}, {221, 358}, {222, 354}, {223, 355}, {9,
436}, {12, 433}, {153, 292}, {11, 437}, {238, 336}, {79, 497}, {156, 290}, {157,
291}, {19, 467}, {240, 304}, {72, 392}, {35, 483}, {219, 282}, {112, 434}, {18,
465}, {237, 302}, {71, 388}, {69, 390}, {39, 484}, {34, 481}, {23, 468}, {236,
303}, {22, 466}, {70, 386}, {38, 482}, {233, 301}, {217, 284}, {72, 398}, {221,
283}, {223, 281}, {232, 302}, {39, 480}, {209, 281}, {26, 467}, {69, 396}, {43,
482}, {42, 483}, {27, 466}, {228, 301}, {30, 468}, {46, 484}, {229, 303}, {12,
448}, {215, 283}, {71, 394}, {31, 465}, {47, 481}, {211, 284}, {213, 282}, {80,
384}, {129, 337}, {110, 446}, {144, 320}, {161, 369}, {225, 304}, {151, 325},
{183, 357}, {197, 279}, {53, 486}, {111, 444}, {85, 390}, {155, 328}, {187,
360}, {200, 283}, {54, 482}, {135, 339}, {87, 387}, {86, 386}, {64, 404}, {55,
483}, {167, 371}, {146, 327}, {147, 326}, {179, 358}, {198, 275}, {199, 274},
{56, 494}, {110, 440}, {88, 398}, {70, 400}, {177, 359}, {109, 442}, {133, 338},
{131, 340}, {163, 372}, {165, 370}, {159, 327}, {189, 357}, {191, 359}, {199,
287}, {54, 495}, {139, 338}, {111, 438}, {109, 436}, {86, 399}, {171, 370},
{158, 325}, {197, 286}, {92, 384}, {154, 326}, {198, 282}, {55, 490}, {137,
340}, {87, 394}, {169, 372}, {181, 360}, {53, 491}, {141, 339}, {85, 395}, {143,
337}, {150, 328}, {173, 371}, {175, 369}, {200, 278}, {56, 487}, {88, 391},
{185, 358}, {87, 437}, {43, 456}, {91, 440}, {44, 457}, {83, 438}, {82, 439},
{22, 496}, {43, 461}, {42, 460}, {41, 449}, {95, 439}, {44, 452}, {94, 437},
{90, 438}, {86, 440}, {42, 453}, {24, 488}, {145, 353}, {177, 321}, {180, 324},
{6, 500}, {38, 468}, {229, 279}, {21, 486}, {54, 453}, {23, 484}, {232, 283},
{8, 508}, {51, 455}, {50, 454}, {40, 476}, {22, 482}, {151, 355}, {7, 498}, {39,
466}, {230, 275}, {24, 494}, {62, 456}, {231, 273}, {147, 356}, {149, 354},
{181, 322}, {229, 285}, {231, 287}, {21, 492}, {63, 454}, {41, 464}, {155, 354},
{5, 510}, {37, 478}, {184, 323}, {6, 506}, {38, 474}, {5, 504}, {58, 455}, {37,
472}, {23, 490}, {153, 356}, {185, 324}, {232, 277}, {8, 502}, {59, 453}, {40,
470}, {157, 355}, {159, 353}, {188, 322}, {189, 323}, {55, 456}, {230, 281}, {7,
512}, {103, 512}, {454, 512}, {459, 512} }>;
(II) A more general form is to represent the graph as the orbit of {16, 17}
under the group generated by the following permutations:
a: (1, 5)(2, 6)(3, 7)(4, 8)(9, 13)(10, 14)(11, 15)(12, 16)(17, 18)(19, 20)(21,
22)(23, 24)(25, 26)(27, 28)(29, 30)(31, 32)(33, 504)(34, 503)(35, 501)(36,
502)(37, 500)(38, 499)(39, 497)(40, 498)(41, 508)(42, 507)(43, 505)(44, 506)(45,
512)(46, 511)(47, 509)(48, 510)(49, 50)(51, 52)(53, 54)(55, 56)(57, 58)(59,
60)(61, 62)(63, 64)(65, 465)(66, 466)(67, 468)(68, 467)(69, 469)(70, 470)(71,
472)(72, 471)(73, 473)(74, 474)(75, 476)(76, 475)(77, 477)(78, 478)(79, 480)(80,
479)(81, 276)(82, 275)(83, 274)(84, 273)(85, 280)(86, 279)(87, 278)(88, 277)(89,
288)(90, 287)(91, 286)(92, 285)(93, 284)(94, 283)(95, 282)(96, 281)(97, 101)(98,
102)(99, 103)(100, 104)(105, 109)(106, 110)(107, 111)(108, 112)(113, 454)(114,
453)(115, 456)(116, 455)(117, 450)(118, 449)(119, 452)(120, 451)(121, 462)(122,
461)(123, 464)(124, 463)(125, 458)(126, 457)(127, 460)(128, 459)(129, 404)(130,
403)(131, 402)(132, 401)(133, 408)(134, 407)(135, 406)(136, 405)(137, 416)(138,
415)(139, 414)(140, 413)(141, 412)(142, 411)(143, 410)(144, 409)(145, 183)(146,
184)(147, 181)(148, 182)(149, 179)(150, 180)(151, 177)(152, 178)(153, 187)(154,
188)(155, 185)(156, 186)(157, 191)(158, 192)(159, 189)(160, 190)(161, 165)(162,
166)(163, 167)(164, 168)(169, 173)(170, 174)(171, 175)(172, 176)(193, 436)(194,
435)(195, 434)(196, 433)(197, 440)(198, 439)(199, 438)(200, 437)(201, 448)(202,
447)(203, 446)(204, 445)(205, 444)(206, 443)(207, 442)(208, 441)(209, 210)(211,
212)(213, 214)(215, 216)(217, 218)(219, 220)(221, 222)(223, 224)(225, 351)(226,
352)(227, 349)(228, 350)(229, 347)(230, 348)(231, 345)(232, 346)(233, 343)(234,
344)(235, 341)(236, 342)(237, 339)(238, 340)(239, 337)(240, 338)(241, 242)(243,
244)(245, 246)(247, 248)(249, 250)(251, 252)(253, 254)(255, 256)(257, 258)(259,
260)(261, 262)(263, 264)(265, 266)(267, 268)(269, 270)(271, 272)(289, 293)(290,
294)(291, 295)(292, 296)(297, 301)(298, 302)(299, 303)(300, 304)(305, 306)(307,
308)(309, 310)(311, 312)(313, 314)(315, 316)(317, 318)(319, 320)(321, 325)(322,
326)(323, 327)(324, 328)(329, 333)(330, 334)(331, 335)(332, 336)(353, 357)(354,
358)(355, 359)(356, 360)(361, 365)(362, 366)(363, 367)(364, 368)(369, 370)(371,
372)(373, 374)(375, 376)(377, 378)(379, 380)(381, 382)(383, 384)(385, 386)(387,
388)(389, 390)(391, 392)(393, 394)(395, 396)(397, 398)(399, 400)(417, 421)(418,
422)(419, 423)(420, 424)(425, 429)(426, 430)(427, 431)(428, 432)(481, 485)(482,
486)(483, 487)(484, 488)(489, 493)(490, 494)(491, 495)(492, 496) (III) Last is Groups&Graphs. Copy everything between (not including)
the lines of asterisks into a plain text file and save it as "graph.txt". Then
launch G&G (Groups&Graphs) and select Read Text from the File menu.
**************
&Graph **************
b: (3, 4)(7, 8)(11, 12)(15, 16)(17, 49)(18, 50)(19, 51)(20, 52)(21, 53)(22,
54)(23, 55)(24, 56)(25, 57)(26, 58)(27, 59)(28, 60)(29, 61)(30, 62)(31, 63)(32,
64)(33, 48)(34, 47)(35, 46)(36, 45)(37, 44)(38, 43)(39, 42)(40, 41)(65, 113)(66,
114)(67, 115)(68, 116)(69, 117)(70, 118)(71, 119)(72, 120)(73, 121)(74, 122)(75,
123)(76, 124)(77, 125)(78, 126)(79, 127)(80, 128)(81, 129)(82, 130)(83, 131)(84,
132)(85, 133)(86, 134)(87, 135)(88, 136)(89, 137)(90, 138)(91, 139)(92, 140)(93,
141)(94, 142)(95, 143)(96, 144)(97, 161)(98, 162)(99, 163)(100, 164)(101,
165)(102, 166)(103, 167)(104, 168)(105, 169)(106, 170)(107, 171)(108, 172)(109,
173)(110, 174)(111, 175)(112, 176)(145, 185)(146, 186)(147, 187)(148, 188)(149,
189)(150, 190)(151, 191)(152, 192)(153, 181)(154, 182)(155, 183)(156, 184)(157,
177)(158, 178)(159, 179)(160, 180)(193, 208)(194, 207)(195, 206)(196, 205)(197,
204)(198, 203)(199, 202)(200, 201)(209, 305)(210, 306)(211, 307)(212, 308)(213,
309)(214, 310)(215, 311)(216, 312)(217, 313)(218, 314)(219, 315)(220, 316)(221,
317)(222, 318)(223, 319)(224, 320)(225, 337)(226, 338)(227, 339)(228, 340)(229,
341)(230, 342)(231, 343)(232, 344)(233, 345)(234, 346)(235, 347)(236, 348)(237,
349)(238, 350)(239, 351)(240, 352)(241, 369)(242, 370)(243, 371)(244, 372)(245,
373)(246, 374)(247, 375)(248, 376)(249, 377)(250, 378)(251, 379)(252, 380)(253,
381)(254, 382)(255, 383)(256, 384)(257, 385)(258, 386)(259, 387)(260, 388)(261,
389)(262, 390)(263, 391)(264, 392)(265, 393)(266, 394)(267, 395)(268, 396)(269,
397)(270, 398)(271, 399)(272, 400)(273, 401)(274, 402)(275, 403)(276, 404)(277,
405)(278, 406)(279, 407)(280, 408)(281, 409)(282, 410)(283, 411)(284, 412)(285,
413)(286, 414)(287, 415)(288, 416)(289, 324)(290, 323)(291, 321)(292, 322)(293,
328)(294, 327)(295, 325)(296, 326)(297, 336)(298, 335)(299, 333)(300, 334)(301,
332)(302, 331)(303, 329)(304, 330)(353, 358)(354, 357)(355, 359)(356, 360)(361,
366)(362, 365)(363, 367)(364, 368)(417, 421)(418, 422)(419, 424)(420, 423)(425,
429)(426, 430)(427, 432)(428, 431)(433, 444)(434, 443)(435, 442)(436, 441)(437,
448)(438, 447)(439, 446)(440, 445)(449, 470)(450, 469)(451, 471)(452, 472)(453,
466)(454, 465)(455, 467)(456, 468)(457, 478)(458, 477)(459, 479)(460, 480)(461,
474)(462, 473)(463, 475)(464, 476)(483, 484)(487, 488)(491, 492)(495, 496)(497,
507)(498, 508)(499, 505)(500, 506)(501, 511)(502, 512)(503, 509)(504, 510)
c: (1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 14)(15, 16)(17, 385)(18, 386)(19,
388)(20, 387)(21, 389)(22, 390)(23, 392)(24, 391)(25, 393)(26, 394)(27, 396)(28,
395)(29, 397)(30, 398)(31, 400)(32, 399)(33, 37)(34, 38)(35, 39)(36, 40)(41,
45)(42, 46)(43, 47)(44, 48)(49, 257)(50, 258)(51, 260)(52, 259)(53, 261)(54,
262)(55, 264)(56, 263)(57, 265)(58, 266)(59, 268)(60, 267)(61, 269)(62, 270)(63,
272)(64, 271)(65, 470)(66, 469)(67, 471)(68, 472)(69, 466)(70, 465)(71, 467)(72,
468)(73, 478)(74, 477)(75, 479)(76, 480)(77, 474)(78, 473)(79, 475)(80, 476)(81,
279)(82, 280)(83, 277)(84, 278)(85, 275)(86, 276)(87, 273)(88, 274)(89, 283)(90,
284)(91, 281)(92, 282)(93, 287)(94, 288)(95, 285)(96, 286)(97, 98)(99, 100)(101,
102)(103, 104)(105, 106)(107, 108)(109, 110)(111, 112)(113, 449)(114, 450)(115,
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151)(148, 152)(153, 157)(154, 158)(155, 159)(156, 160)(161, 162)(163, 164)(165,
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199)(196, 200)(201, 205)(202, 206)(203, 207)(204, 208)(209, 374)(210, 373)(211,
376)(212, 375)(213, 370)(214, 369)(215, 372)(216, 371)(217, 382)(218, 381)(219,
384)(220, 383)(221, 378)(222, 377)(223, 380)(224, 379)(225, 229)(226, 230)(227,
231)(228, 232)(233, 237)(234, 238)(235, 239)(236, 240)(241, 310)(242, 309)(243,
312)(244, 311)(245, 306)(246, 305)(247, 308)(248, 307)(249, 318)(250, 317)(251,
320)(252, 319)(253, 314)(254, 313)(255, 316)(256, 315)(289, 290)(291, 292)(293,
294)(295, 296)(297, 298)(299, 300)(301, 302)(303, 304)(321, 322)(323, 324)(325,
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358)(359, 360)(361, 362)(363, 364)(365, 366)(367, 368)(417, 418)(419, 420)(421,
422)(423, 424)(425, 426)(427, 428)(429, 430)(431, 432)(433, 437)(434, 438)(435,
439)(436, 440)(441, 445)(442, 446)(443, 447)(444, 448)(481, 482)(483, 484)(485,
486)(487, 488)(489, 490)(491, 492)(493, 494)(495, 496)(497, 501)(498, 502)(499,
503)(500, 504)(505, 509)(506, 510)(507, 511)(508, 512)
d: (1, 17, 65, 36, 4, 20, 68, 33)(2, 18, 66, 35, 3, 19, 67, 34)(5, 21, 69, 40,
8, 24, 72, 37)(6, 22, 70, 39, 7, 23, 71, 38)(9, 25, 73, 48, 16, 32, 80, 41)(10,
26, 74, 47, 15, 31, 79, 42)(11, 27, 75, 46, 14, 30, 78, 43)(12, 28, 76, 45, 13,
29, 77, 44)(49, 81, 145, 163, 259, 273, 177, 97)(50, 82, 146, 164, 260, 274,
178, 98)(51, 83, 147, 162, 258, 275, 179, 99)(52, 84, 148, 161, 257, 276, 180,
100)(53, 85, 149, 167, 263, 277, 181, 101)(54, 86, 150, 168, 264, 278, 182,
102)(55, 87, 151, 166, 262, 279, 183, 103)(56, 88, 152, 165, 261, 280, 184,
104)(57, 89, 153, 175, 271, 281, 185, 105)(58, 90, 154, 176, 272, 282, 186,
106)(59, 91, 155, 174, 270, 283, 187, 107)(60, 92, 156, 173, 269, 284, 188,
108)(61, 93, 157, 171, 267, 285, 189, 109)(62, 94, 158, 172, 268, 286, 190,
110)(63, 95, 159, 170, 266, 287, 191, 111)(64, 96, 160, 169, 265, 288, 192,
112)(113, 193, 289, 372, 452, 433, 321, 209)(114, 194, 290, 371, 451, 434, 322,
210)(115, 195, 291, 370, 450, 435, 323, 211)(116, 196, 292, 369, 449, 436, 324,
212)(117, 197, 293, 376, 456, 437, 325, 213)(118, 198, 294, 375, 455, 438, 326,
214)(119, 199, 295, 374, 454, 439, 327, 215)(120, 200, 296, 373, 453, 440, 328,
216)(121, 201, 297, 384, 464, 441, 329, 217)(122, 202, 298, 383, 463, 442, 330,
218)(123, 203, 299, 382, 462, 443, 331, 219)(124, 204, 300, 381, 461, 444, 332,
220)(125, 205, 301, 380, 460, 445, 333, 221)(126, 206, 302, 379, 459, 446, 334,
222)(127, 207, 303, 378, 458, 447, 335, 223)(128, 208, 304, 377, 457, 448, 336,
224)(129, 225, 353, 247, 135, 231, 359, 241)(130, 226, 354, 248, 136, 232, 360,
242)(131, 227, 355, 245, 133, 229, 357, 243)(132, 228, 356, 246, 134, 230, 358,
244)(137, 233, 361, 251, 139, 235, 363, 249)(138, 234, 362, 252, 140, 236, 364,
250)(141, 237, 365, 255, 143, 239, 367, 253)(142, 238, 366, 256, 144, 240, 368,
254)(305, 407, 351, 423, 311, 401, 345, 417)(306, 408, 352, 424, 312, 402, 346,
418)(307, 405, 349, 421, 309, 403, 347, 419)(308, 406, 350, 422, 310, 404, 348,
420)(313, 411, 343, 427, 315, 409, 341, 425)(314, 412, 344, 428, 316, 410, 342,
426)(317, 415, 339, 431, 319, 413, 337, 429)(318, 416, 340, 432, 320, 414, 338,
430)(385, 465, 497, 483, 387, 467, 499, 481)(386, 466, 498, 484, 388, 468, 500,
482)(389, 469, 501, 487, 391, 471, 503, 485)(390, 470, 502, 488, 392, 472, 504,
486)(393, 473, 505, 495, 399, 479, 511, 489)(394, 474, 506, 496, 400, 480, 512,
490)(395, 475, 507, 493, 397, 477, 509, 491)(396, 476, 508, 494, 398, 478, 510,
492)
e: (1, 9, 5, 13)(2, 10, 6, 14)(3, 11, 7, 15)(4, 12, 8, 16)(17, 20, 18, 19)(21,
24, 22, 23)(25, 32, 26, 31)(27, 29, 28, 30)(33, 436, 504, 193)(34, 435, 503,
194)(35, 434, 501, 195)(36, 433, 502, 196)(37, 440, 500, 197)(38, 439, 499,
198)(39, 438, 497, 199)(40, 437, 498, 200)(41, 448, 508, 201)(42, 447, 507,
202)(43, 446, 505, 203)(44, 445, 506, 204)(45, 444, 512, 205)(46, 443, 511,
206)(47, 442, 509, 207)(48, 441, 510, 208)(49, 52, 50, 51)(53, 56, 54, 55)(57,
64, 58, 63)(59, 61, 60, 62)(65, 273, 465, 84)(66, 274, 466, 83)(67, 275, 468,
82)(68, 276, 467, 81)(69, 277, 469, 88)(70, 278, 470, 87)(71, 279, 472, 86)(72,
280, 471, 85)(73, 281, 473, 96)(74, 282, 474, 95)(75, 283, 476, 94)(76, 284,
475, 93)(77, 285, 477, 92)(78, 286, 478, 91)(79, 287, 480, 90)(80, 288, 479,
89)(97, 109, 101, 105)(98, 110, 102, 106)(99, 111, 103, 107)(100, 112, 104,
108)(113, 401, 454, 132)(114, 402, 453, 131)(115, 403, 456, 130)(116, 404, 455,
129)(117, 405, 450, 136)(118, 406, 449, 135)(119, 407, 452, 134)(120, 408, 451,
133)(121, 409, 462, 144)(122, 410, 461, 143)(123, 411, 464, 142)(124, 412, 463,
141)(125, 413, 458, 140)(126, 414, 457, 139)(127, 415, 460, 138)(128, 416, 459,
137)(145, 231, 183, 345)(146, 232, 184, 346)(147, 229, 181, 347)(148, 230, 182,
348)(149, 227, 179, 349)(150, 228, 180, 350)(151, 225, 177, 351)(152, 226, 178,
352)(153, 235, 187, 341)(154, 236, 188, 342)(155, 233, 185, 343)(156, 234, 186,
344)(157, 239, 191, 337)(158, 240, 192, 338)(159, 237, 189, 339)(160, 238, 190,
340)(161, 173, 165, 169)(162, 174, 166, 170)(163, 175, 167, 171)(164, 176, 168,
172)(209, 211, 210, 212)(213, 215, 214, 216)(217, 223, 218, 224)(219, 222, 220,
221)(241, 243, 242, 244)(245, 247, 246, 248)(249, 255, 250, 256)(251, 254, 252,
253)(257, 259, 258, 260)(261, 263, 262, 264)(265, 271, 266, 272)(267, 270, 268,
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381)(385, 387, 386, 388)(389, 391, 390, 392)(393, 399, 394, 400)(395, 398, 396,
397)(481, 489, 485, 493)(482, 490, 486, 494)(483, 491, 487, 495)(484, 492, 488,
496)
f: (1, 3)(2, 4)(5, 7)(6, 8)(9, 15)(10, 16)(11, 13)(12, 14)(17, 387)(18, 388)(19,
386)(20, 385)(21, 391)(22, 392)(23, 390)(24, 389)(25, 399)(26, 400)(27, 398)(28,
397)(29, 395)(30, 396)(31, 394)(32, 393)(33, 40)(34, 39)(35, 38)(36, 37)(41,
44)(42, 43)(45, 48)(46, 47)(49, 52)(50, 51)(53, 56)(54, 55)(57, 64)(58, 63)(59,
62)(60, 61)(65, 472)(66, 471)(67, 469)(68, 470)(69, 468)(70, 467)(71, 465)(72,
466)(73, 476)(74, 475)(75, 473)(76, 474)(77, 480)(78, 479)(79, 477)(80, 478)(81,
87)(82, 88)(83, 85)(84, 86)(89, 91)(90, 92)(93, 95)(94, 96)(97, 164)(98,
163)(99, 161)(100, 162)(101, 168)(102, 167)(103, 165)(104, 166)(105, 176)(106,
175)(107, 173)(108, 174)(109, 172)(110, 171)(111, 169)(112, 170)(113, 116)(114,
115)(117, 120)(118, 119)(121, 128)(122, 127)(123, 126)(124, 125)(129, 401)(130,
402)(131, 403)(132, 404)(133, 405)(134, 406)(135, 407)(136, 408)(137, 409)(138,
410)(139, 411)(140, 412)(141, 413)(142, 414)(143, 415)(144, 416)(145, 181)(146,
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483)(485, 488)(486, 487)(489, 496)(490, 495)(491, 494)(492, 493)(497, 503)(498,
504)(499, 501)(500, 502)(505, 507)(506, 508)(509, 511)(510, 512)
C4[ 512, 87 ]
512
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0