C4graphGraph forms for C4 [ 512, 624 ] = SS[512,178]

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On this page are computer-accessible forms for the graph C4[ 512, 624 ] = SS[512,178].

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {464, 465} under the group generated by the following permutations:

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

(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
C4[ 512, 624 ]
512
-1 2 3 4 5
-2 1 509 501 505
-3 506 1 510 502
-4 1 507 512 504
-5 1 508 511 503
-6 176 442 312 316
-7 319 179 443 314
-8 178 443 315 318
-9 177 442 313 317
-10 28 29 30 31
-11 24 25 26 27
-12 180 412 84 64
-13 181 413 85 65
-14 183 414 65 87
-15 182 415 64 86
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-17 66 88 184 416
-18 66 187 419 91
-19 418 67 90 186
-20 176 308 440 68
-21 441 310 179 71
-22 441 178 311 70
-23 440 177 309 69
-24 11 308 72 317
-25 11 309 73 316
-26 11 319 311 74
-27 11 310 75 318
-28 68 313 73 10
-29 69 312 72 10
-30 71 315 74 10
-31 70 314 75 10
-32 57 413 205 428
-33 429 56 412 204
-34 59 414 207 428
-35 429 58 206 415
-36 209 418 431 61
-37 419 430 60 208
-38 210 431 63 417
-39 430 211 62 416
-40 188 57 321 76
-41 77 56 320 189
-42 79 58 190 323
-43 78 322 59 191
-44 81 60 325 194
-45 80 324 61 195
-46 82 193 63 327
-47 192 83 62 326
-48 77 60 327 196
-49 61 326 76 197
-50 78 199 325 63
-51 198 79 324 62
-52 56 321 201 81
-53 320 57 200 80
-54 59 202 323 82
-55 58 322 203 83
-56 33 145 41 52
-57 144 40 53 32
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-59 34 147 43 54
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-62 47 148 39 51
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-64 121 12 122 15
-65 13 123 14 120
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-67 124 16 126 19
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-69 23 138 29 139
-70 22 143 31 141
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-72 24 29 130 131
-73 25 28 128 129
-74 133 135 26 30
-75 132 134 27 31
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-79 51 106 118 42
-80 45 113 53 109
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-82 111 46 114 54
-83 55 110 47 115
-84 12 113 105 97
-85 13 112 104 96
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-87 99 14 115 106
-88 100 17 117 109
-89 101 16 116 108
-90 110 103 19 118
-91 111 102 18 119
-92 97 141 98 142
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-94 101 103 137 139
-95 100 102 136 138
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-97 168 92 84 206
-98 92 171 204 86
-99 93 170 205 87
-100 88 95 175 208
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-102 211 91 95 172
-103 210 90 94 173
-104 77 188 85 152
-105 189 84 76 153
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-117 88 198 158 76
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-119 78 156 91 196
-120 333 160 458 65
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-125 66 166 456 336
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-130 345 72 424 173
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-135 342 170 423 74
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-140 333 71 93 161
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-145 56 168 182 328
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-150 331 61 173 185
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-163 143 122 277 271
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-165 126 138 282 274
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-167 124 136 280 272
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-170 99 265 135 147
-171 264 134 146 98
-172 102 267 151 131
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-175 100 148 129 263
-176 266 267 6 20
-177 23 9 262 263
-178 22 265 260 8
-179 264 7 261 21
-180 253 12 146 245
-181 13 244 147 252
-182 145 15 258 251
-183 144 14 259 250
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-185 256 16 248 150
-186 255 247 149 19
-187 254 246 148 18
-188 257 104 40 228
-189 256 105 41 229
-190 255 234 107 42
-191 254 235 106 43
-192 233 47 259 109
-193 232 46 258 108
-194 44 231 111 252
-195 110 253 45 230
-196 48 237 119 251
-197 49 236 118 250
-198 242 245 51 117
-199 243 244 50 116
-200 112 248 53 241
-201 113 249 52 240
-202 115 247 238 54
-203 55 114 246 239
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-205 99 242 32 230
-206 35 233 236 97
-207 34 232 237 96
-208 100 37 229 241
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-210 103 235 38 239
-211 102 234 39 238
-212 231 233 234 229
-213 232 235 228 230
-214 242 237 238 241
-215 243 236 239 240
-216 245 246 249 251
-217 244 247 248 250
-218 254 257 259 252
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-220 342 292 413 447
-221 343 412 446 293
-222 419 299 346 445
-223 418 298 445 347
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-225 447 415 296 340
-226 345 444 295 417
-227 344 444 294 416
-228 209 188 213 285
-229 189 212 284 208
-230 213 290 205 195
-231 212 291 204 194
-232 289 213 193 207
-233 288 212 192 206
-234 287 211 190 212
-235 286 210 191 213
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-237 300 214 196 207
-238 211 202 214 307
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-240 209 201 215 305
-241 200 214 304 208
-242 198 214 303 205
-243 199 302 204 215
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-245 198 289 180 216
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-247 202 217 284 186
-248 287 200 217 185
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-250 291 183 217 197
-251 290 182 216 196
-252 301 181 194 218
-253 300 180 195 219
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-255 190 304 186 219
-256 189 185 219 307
-257 188 184 218 306
-258 182 193 303 219
-259 192 302 183 218
-260 178 168 292 449
-261 179 169 293 448
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-263 177 298 454 175
-264 297 452 179 171
-265 178 453 170 296
-266 176 451 173 294
-267 176 172 295 450
-268 421 303 161 153
-269 420 302 160 152
-270 155 301 423 162
-271 154 300 422 163
-272 156 167 304 427
-273 166 157 305 426
-274 165 158 424 307
-275 159 425 306 164
-276 291 293 162 153
-277 290 292 152 163
-278 297 155 289 161
-279 154 288 160 296
-280 287 167 157 294
-281 286 166 156 295
-282 165 299 159 284
-283 298 158 164 285
-284 389 247 282 229
-285 388 246 228 283
-286 235 281 249 395
-287 234 280 248 394
-288 233 244 279 393
-289 232 245 278 392
-290 277 391 251 230
-291 231 276 390 250
-292 220 277 260 393
-293 221 276 392 261
-294 266 280 227 395
-295 267 226 281 394
-296 265 279 225 391
-297 264 278 224 390
-298 223 389 283 263
-299 222 388 282 262
-300 253 237 271 381
-301 236 270 380 252
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-303 242 386 268 258
-304 385 255 272 241
-305 254 240 273 384
-306 275 257 239 383
-307 256 238 382 274
-308 24 20 372 373
-309 374 23 375 25
-310 377 378 27 21
-311 22 376 26 379
-312 364 365 6 29
-313 366 367 28 9
-314 369 7 370 31
-315 368 8 30 371
-316 25 6 358 359
-317 24 356 357 9
-318 363 27 8 361
-319 26 7 360 362
-320 381 41 393 53
-321 380 40 392 52
-322 55 387 391 43
-323 386 390 42 54
-324 385 45 51 395
-325 44 50 394 384
-326 47 389 49 383
-327 46 388 48 382
-328 145 146 361 362
-329 363 144 147 360
-330 148 357 359 151
-331 356 149 358 150
-332 121 366 349 141
-333 367 348 140 120
-334 143 123 365 355
-335 122 364 354 142
-336 353 125 138 371
-337 352 124 139 370
-338 136 127 369 350
-339 126 137 368 351
-340 133 366 225 373
-341 132 224 367 372
-342 220 375 365 135
-343 374 221 364 134
-344 379 369 227 131
-345 378 368 226 130
-346 222 377 129 371
-347 376 223 128 370
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-349 396 452 332 460
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-351 462 455 402 339
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-354 399 335 449 461
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-356 331 410 317 439
-357 330 411 317 438
-358 331 408 316 437
-359 330 409 436 316
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-361 434 328 405 318
-362 319 433 328 406
-363 407 432 318 329
-364 343 312 400 335
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-366 332 313 403 340
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-368 397 345 315 339
-369 396 344 314 338
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-371 399 346 336 315
-372 308 341 396 435
-373 308 397 434 340
-374 309 343 398 433
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-376 311 347 403 439
-377 310 346 402 438
-378 310 345 400 437
-379 311 344 401 436
-380 321 421 301 404
-381 320 420 300 405
-382 410 425 327 307
-383 411 424 326 306
-384 409 325 305 427
-385 408 324 304 426
-386 323 423 303 406
-387 407 322 422 302
-388 299 411 327 285
-389 298 410 326 284
-390 297 323 291 404
-391 322 290 405 296
-392 321 289 293 406
-393 407 320 288 292
-394 287 408 325 295
-395 286 409 324 294
-396 369 479 349 372
-397 368 348 480 373
-398 374 484 355 370
-399 375 354 371 483
-400 353 364 378 478
-401 352 365 477 379
-402 377 367 482 351
-403 376 366 481 350
-404 488 390 380 360
-405 487 391 381 361
-406 386 392 492 362
-407 363 387 491 393
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-409 485 359 384 395
-410 356 389 490 382
-411 388 357 489 383
-412 33 12 221 498
-413 220 13 497 32
-414 34 14 224 500
-415 35 15 499 225
-416 17 39 227 494
-417 16 38 226 493
-418 496 36 223 19
-419 495 222 37 18
-420 132 498 269 381
-421 133 497 268 380
-422 134 387 500 271
-423 386 135 499 270
-424 130 383 274 494
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-426 385 496 129 273
-427 495 128 272 384
-428 34 487 492 32
-429 33 35 488 491
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-431 485 36 38 489
-432 363 375 478 492
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-434 488 361 482 373
-435 487 360 481 372
-436 484 379 490 359
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-438 486 377 357 480
-439 485 376 356 479
-440 23 475 476 20
-441 22 473 474 21
-442 6 9 471 472
-443 7 469 8 470
-444 474 226 227 470
-445 473 222 223 469
-446 221 476 224 472
-447 220 475 225 471
-448 355 478 500 261
-449 354 477 499 260
-450 353 267 480 494
-451 352 266 479 493
-452 264 498 349 482
-453 265 497 348 481
-454 484 495 350 263
-455 496 262 351 483
-456 124 125 466 470
-457 121 123 467 472
-458 122 468 471 120
-459 465 126 127 469
-460 474 465 348 349
-461 473 354 355 466
-462 353 476 468 351
-463 352 475 467 350
-464 465 466 467 468
-465 464 509 459 460
-466 464 510 456 461
-467 463 464 457 512
-468 462 464 511 458
-469 443 445 502 459
-470 443 444 456 501
-471 442 447 458 504
-472 442 446 457 503
-473 441 445 461 505
-474 506 441 444 460
-475 440 463 508 447
-476 440 462 507 446
-477 433 401 501 449
-478 432 400 501 448
-479 396 451 503 439
-480 397 438 504 450
-481 453 435 403 502
-482 452 434 402 502
-483 399 455 437 504
-484 398 454 436 503
-485 506 409 431 439
-486 506 408 430 438
-487 508 435 405 428
-488 429 507 434 404
-489 431 411 437 505
-490 430 410 436 505
-491 407 429 508 433
-492 507 432 406 428
-493 451 509 425 417
-494 509 424 416 450
-495 419 454 510 427
-496 418 455 510 426
-497 453 421 413 512
-498 452 420 412 511
-499 423 512 415 449
-500 422 511 414 448
-501 2 477 478 470
-502 3 469 481 482
-503 484 5 479 472
-504 4 480 471 483
-505 473 2 489 490
-506 474 485 486 3
-507 476 4 488 492
-508 475 487 5 491
-509 2 465 493 494
-510 495 496 3 466
-511 498 5 500 468
-512 497 4 499 467
0

**************