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