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