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