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