Graph forms
for C4 [ 512, 542 ] = SS[512,75]
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On this page are computer-accessible forms for the graph C4[ 512, 542 ] =
SS[512,75].
(I) Following is a form readable by MAGMA:
g:=Graph<512|{ {1, 3}, {1, 2}, {500, 503}, {464, 467}, {1, 5}, {498, 502}, {497,
501}, {464, 468}, {96, 100}, {211, 215}, {1, 4}, {464, 469}, {64, 69}, {64, 70},
{464, 470}, {98, 101}, {97, 104}, {211, 218}, {81, 91}, {214, 220}, {36, 47},
{499, 504}, {213, 222}, {214, 221}, {35, 46}, {82, 95}, {81, 92}, {212, 217},
{213, 216}, {35, 45}, {496, 510}, {80, 94}, {81, 94}, {82, 93}, {212, 219}, {68,
84}, {495, 511}, {493, 509}, {492, 508}, {487, 503}, {366, 382}, {365, 381},
{71, 87}, {70, 86}, {10, 27}, {490, 507}, {66, 83}, {11, 26}, {11, 25}, {491,
505}, {484, 502}, {456, 474}, {363, 377}, {73, 91}, {72, 90}, {35, 49}, {11,
24}, {489, 506}, {456, 475}, {448, 467}, {360, 379}, {76, 95}, {36, 48}, {481,
501}, {457, 477}, {449, 469}, {361, 380}, {483, 502}, {458, 479}, {450, 471},
{10, 28}, {364, 378}, {75, 93}, {74, 92}, {67, 85}, {36, 50}, {33, 55}, {32,
54}, {193, 215}, {10, 29}, {482, 501}, {463, 472}, {457, 478}, {36, 51}, {35,
52}, {12, 20}, {463, 471}, {359, 383}, {352, 376}, {194, 218}, {198, 222}, {12,
21}, {65, 88}, {32, 58}, {355, 377}, {34, 56}, {33, 59}, {358, 381}, {455, 476},
{10, 22}, {69, 89}, {11, 23}, {34, 63}, {485, 504}, {463, 466}, {362, 375},
{192, 221}, {196, 217}, {12, 18}, {486, 504}, {463, 465}, {455, 473}, {354,
380}, {34, 60}, {32, 62}, {197, 219}, {12, 19}, {488, 503}, {480, 511}, {359,
376}, {357, 378}, {356, 379}, {353, 382}, {195, 220}, {30, 62}, {478, 510},
{477, 509}, {476, 508}, {475, 507}, {474, 506}, {473, 505}, {197, 229}, {209,
241}, {30, 63}, {198, 231}, {31, 61}, {207, 237}, {210, 240}, {30, 61}, {207,
236}, {209, 242}, {192, 228}, {194, 230}, {461, 488}, {31, 57}, {472, 511},
{351, 375}, {470, 510}, {469, 509}, {468, 508}, {459, 483}, {454, 494}, {453,
493}, {452, 492}, {451, 490}, {466, 507}, {462, 487}, {460, 485}, {454, 495},
{31, 53}, {467, 505}, {462, 484}, {459, 481}, {458, 480}, {451, 489}, {193,
234}, {465, 506}, {461, 486}, {195, 232}, {78, 98}, {77, 96}, {196, 233}, {79,
97}, {460, 482}, {452, 491}, {82, 98}, {88, 104}, {85, 101}, {83, 99}, {81, 96},
{329, 376}, {86, 103}, {331, 377}, {82, 97}, {334, 381}, {205, 249}, {330, 382},
{206, 250}, {95, 106}, {453, 496}, {200, 253}, {202, 255}, {206, 248}, {333,
379}, {332, 378}, {94, 105}, {201, 254}, {91, 99}, {203, 243}, {205, 245}, {210,
235}, {92, 102}, {93, 103}, {204, 246}, {199, 252}, {327, 380}, {204, 247},
{199, 251}, {84, 105}, {87, 106}, {90, 100}, {208, 238}, {89, 102}, {328, 375},
{203, 244}, {208, 239}, {319, 383}, {179, 240}, {177, 244}, {152, 223}, {181,
242}, {182, 241}, {149, 223}, {176, 250}, {178, 248}, {307, 383}, {431, 480},
{185, 232}, {418, 499}, {187, 234}, {169, 251}, {416, 498}, {179, 224}, {183,
228}, {180, 225}, {417, 500}, {188, 233}, {175, 249}, {181, 226}, {439, 480},
{171, 243}, {180, 237}, {172, 246}, {173, 247}, {180, 238}, {181, 239}, {164,
255}, {166, 253}, {165, 254}, {174, 245}, {189, 230}, {191, 227}, {182, 235},
{184, 229}, {186, 231}, {190, 227}, {30, 64}, {163, 252}, {179, 236}, {44, 76},
{404, 500}, {402, 498}, {388, 484}, {139, 235}, {33, 64}, {400, 497}, {145,
240}, {140, 237}, {142, 236}, {440, 474}, {394, 488}, {384, 482}, {41, 74},
{401, 498}, {390, 485}, {43, 79}, {391, 483}, {389, 481}, {387, 487}, {406,
499}, {23, 113}, {446, 472}, {441, 479}, {405, 499}, {54, 80}, {40, 78}, {42,
77}, {442, 477}, {403, 500}, {385, 486}, {191, 216}, {26, 114}, {438, 478},
{397, 485}, {47, 71}, {176, 216}, {25, 112}, {437, 476}, {45, 68}, {28, 117},
{182, 223}, {386, 488}, {443, 465}, {435, 473}, {392, 482}, {24, 115}, {447,
468}, {445, 470}, {433, 474}, {396, 487}, {46, 69}, {29, 118}, {177, 218}, {39,
75}, {412, 496}, {145, 253}, {178, 222}, {432, 477}, {434, 479}, {144, 254},
{444, 466}, {415, 497}, {27, 116}, {436, 475}, {398, 481}, {395, 484}, {393,
486}, {38, 73}, {59, 75}, {430, 478}, {414, 494}, {138, 250}, {136, 248}, {60,
76}, {141, 252}, {429, 476}, {423, 470}, {173, 220}, {172, 221}, {51, 65}, {427,
473}, {422, 468}, {419, 465}, {413, 495}, {409, 491}, {408, 490}, {147, 225},
{48, 67}, {140, 255}, {50, 70}, {143, 251}, {135, 243}, {58, 78}, {175, 219},
{37, 80}, {56, 77}, {52, 66}, {420, 466}, {411, 493}, {410, 492}, {151, 225},
{150, 224}, {148, 226}, {57, 79}, {63, 72}, {428, 475}, {174, 217}, {63, 71},
{22, 111}, {426, 467}, {49, 72}, {62, 68}, {154, 224}, {153, 226}, {53, 73},
{425, 469}, {171, 215}, {138, 246}, {61, 65}, {55, 74}, {421, 472}, {146, 239},
{137, 244}, {136, 245}, {62, 67}, {135, 249}, {407, 489}, {399, 497}, {144,
238}, {143, 241}, {137, 247}, {61, 66}, {424, 471}, {141, 242}, {290, 419},
{314, 443}, {39, 165}, {43, 168}, {108, 232}, {110, 234}, {109, 233}, {45, 170},
{19, 155}, {107, 227}, {47, 167}, {300, 420}, {302, 422}, {303, 423}, {310,
446}, {311, 447}, {21, 156}, {42, 163}, {288, 425}, {308, 445}, {20, 158}, {109,
231}, {108, 230}, {46, 164}, {20, 159}, {110, 229}, {44, 167}, {27, 144}, {289,
426}, {29, 145}, {380, 496}, {41, 164}, {28, 146}, {40, 166}, {299, 421}, {301,
419}, {18, 157}, {107, 228}, {45, 162}, {38, 169}, {37, 170}, {307, 444}, {39,
183}, {382, 494}, {86, 198}, {279, 391}, {49, 160}, {84, 197}, {280, 393}, {281,
392}, {49, 163}, {381, 495}, {377, 491}, {376, 490}, {43, 184}, {319, 428}, {50,
161}, {296, 443}, {26, 142}, {316, 424}, {40, 188}, {25, 140}, {44, 185}, {48,
166}, {379, 493}, {378, 492}, {87, 193}, {24, 143}, {318, 425}, {317, 426}, {83,
196}, {50, 165}, {42, 189}, {41, 190}, {282, 397}, {278, 398}, {304, 424}, {275,
394}, {277, 396}, {292, 445}, {294, 447}, {23, 141}, {318, 420}, {90, 192}, {89,
195}, {88, 194}, {51, 168}, {316, 423}, {293, 446}, {305, 426}, {306, 425},
{383, 483}, {22, 139}, {315, 422}, {52, 169}, {38, 187}, {315, 421}, {375, 489},
{317, 419}, {37, 186}, {276, 395}, {291, 444}, {21, 181}, {57, 153}, {270, 430},
{273, 433}, {18, 179}, {59, 154}, {20, 182}, {271, 429}, {53, 150}, {55, 148},
{19, 180}, {267, 428}, {58, 147}, {60, 149}, {27, 176}, {52, 159}, {28, 177},
{51, 158}, {48, 157}, {54, 152}, {29, 178}, {56, 151}, {18, 162}, {259, 435},
{260, 437}, {264, 441}, {309, 388}, {311, 390}, {19, 161}, {261, 439}, {47,
156}, {263, 436}, {265, 442}, {26, 174}, {21, 160}, {46, 155}, {25, 172}, {258,
436}, {286, 424}, {24, 175}, {308, 387}, {310, 385}, {257, 441}, {312, 384},
{274, 427}, {23, 173}, {256, 442}, {284, 422}, {285, 423}, {287, 420}, {313,
386}, {266, 438}, {268, 432}, {22, 171}, {262, 440}, {283, 421}, {269, 434},
{272, 431}, {314, 389}, {322, 386}, {348, 412}, {341, 405}, {335, 399}, {328,
392}, {326, 390}, {342, 407}, {347, 410}, {323, 385}, {374, 436}, {348, 414},
{329, 395}, {334, 397}, {339, 400}, {337, 402}, {320, 388}, {371, 439}, {349,
409}, {324, 384}, {321, 389}, {331, 398}, {368, 437}, {350, 411}, {342, 403},
{340, 401}, {332, 393}, {325, 387}, {350, 408}, {347, 413}, {338, 404}, {336,
406}, {330, 396}, {369, 438}, {333, 391}, {370, 440}, {349, 407}, {336, 411},
{338, 409}, {98, 174}, {373, 441}, {337, 413}, {327, 394}, {341, 408}, {97,
175}, {372, 442}, {340, 410}, {339, 412}, {367, 416}, {351, 399}, {370, 418},
{96, 177}, {368, 417}, {344, 393}, {335, 414}, {344, 395}, {369, 418}, {345,
396}, {373, 416}, {345, 398}, {374, 417}, {346, 397}, {367, 435}, {343, 394},
{346, 391}, {343, 392}, {295, 448}, {85, 191}, {364, 390}, {361, 387}, {297,
450}, {372, 415}, {363, 384}, {326, 429}, {325, 430}, {298, 449}, {92, 176},
{371, 415}, {366, 386}, {365, 385}, {360, 388}, {323, 431}, {94, 178}, {324,
427}, {362, 389}, {91, 171}, {322, 434}, {321, 433}, {320, 432}, {93, 172}, {95,
173}, {353, 403}, {352, 402}, {355, 400}, {358, 405}, {357, 406}, {309, 449},
{356, 401}, {354, 404}, {312, 448}, {313, 450}, {124, 372}, {120, 369}, {123,
370}, {122, 371}, {121, 368}, {125, 374}, {126, 373}, {99, 367}, {100, 368},
{103, 370}, {101, 371}, {102, 369}, {71, 351}, {119, 367}, {106, 374}, {220,
448}, {221, 449}, {222, 450}, {104, 373}, {105, 372}, {78, 366}, {69, 356},
{117, 340}, {67, 353}, {79, 365}, {74, 360}, {114, 337}, {113, 341}, {73, 364},
{16, 310}, {118, 336}, {112, 342}, {77, 363}, {76, 362}, {70, 352}, {68, 354},
{17, 311}, {65, 358}, {116, 339}, {66, 357}, {16, 313}, {17, 312}, {72, 355},
{127, 340}, {75, 359}, {13, 317}, {110, 350}, {109, 349}, {108, 348}, {107,
347}, {13, 316}, {13, 318}, {14, 314}, {108, 344}, {9, 319}, {13, 315}, {109,
346}, {127, 328}, {110, 345}, {80, 361}, {15, 309}, {15, 308}, {107, 343}, {115,
335}, {14, 307}, {111, 338}, {119, 310}, {224, 417}, {225, 416}, {121, 314},
{232, 427}, {31, 347}, {124, 313}, {125, 312}, {234, 431}, {104, 302}, {254,
440}, {233, 430}, {8, 320}, {99, 299}, {9, 321}, {229, 429}, {251, 435}, {100,
301}, {126, 311}, {252, 437}, {255, 438}, {9, 323}, {102, 300}, {101, 303},
{253, 439}, {9, 322}, {120, 307}, {8, 324}, {8, 325}, {8, 326}, {123, 309},
{122, 308}, {227, 428}, {15, 351}, {113, 289}, {112, 288}, {123, 297}, {119,
292}, {121, 298}, {228, 432}, {103, 306}, {231, 434}, {126, 296}, {117, 290},
{230, 433}, {125, 293}, {105, 304}, {122, 291}, {124, 294}, {106, 305}, {127,
292}, {120, 295}, {7, 359}, {218, 443}, {244, 405}, {116, 278}, {117, 279},
{245, 406}, {216, 444}, {217, 445}, {219, 447}, {112, 277}, {114, 276}, {246,
400}, {247, 401}, {118, 286}, {241, 409}, {242, 410}, {7, 366}, {15, 358}, {215,
446}, {250, 403}, {6, 364}, {120, 274}, {115, 281}, {7, 365}, {248, 402}, {14,
357}, {116, 287}, {113, 282}, {14, 354}, {6, 363}, {125, 272}, {7, 362}, {240,
413}, {249, 404}, {6, 360}, {118, 280}, {6, 361}, {126, 273}, {115, 284}, {114,
285}, {17, 353}, {17, 352}, {122, 267}, {237, 412}, {16, 355}, {124, 271}, {16,
356}, {111, 283}, {121, 268}, {235, 414}, {123, 269}, {127, 264}, {236, 411},
{239, 408}, {119, 270}, {238, 407}, {32, 348}, {111, 275}, {243, 399}, {223,
418}, {226, 415}, {33, 350}, {34, 349}, {130, 259}, {134, 260}, {132, 263},
{129, 261}, {154, 286}, {152, 284}, {157, 280}, {128, 262}, {159, 281}, {183,
304}, {131, 266}, {139, 257}, {150, 285}, {156, 279}, {133, 265}, {147, 287},
{158, 275}, {142, 256}, {156, 274}, {155, 277}, {149, 283}, {159, 272}, {189,
306}, {190, 305}, {146, 258}, {155, 267}, {188, 300}, {158, 271}, {185, 299},
{157, 270}, {89, 461}, {186, 302}, {187, 303}, {184, 301}, {88, 462}, {90, 461},
{83, 459}, {85, 460}, {87, 462}, {86, 460}, {191, 292}, {84, 459}, {170, 264},
{134, 293}, {164, 263}, {167, 259}, {163, 262}, {167, 258}, {133, 291}, {128,
295}, {129, 294}, {168, 257}, {130, 296}, {170, 256}, {131, 297}, {165, 265},
{169, 261}, {168, 260}, {166, 266}, {161, 268}, {132, 298}, {162, 269}, {160,
273}, {187, 266}, {140, 319}, {136, 316}, {138, 318}, {137, 317}, {189, 265},
{148, 289}, {162, 276}, {151, 288}, {161, 278}, {160, 282}, {153, 290}, {188,
263}, {135, 315}, {185, 261}, {190, 259}, {184, 262}, {186, 260}, {183, 264},
{203, 267}, {205, 268}, {204, 270}, {212, 278}, {204, 271}, {212, 279}, {130,
327}, {214, 275}, {203, 269}, {211, 277}, {211, 276}, {129, 329}, {131, 331},
{133, 332}, {200, 257}, {128, 330}, {133, 335}, {132, 334}, {202, 256}, {134,
333}, {201, 258}, {141, 321}, {143, 323}, {142, 322}, {213, 281}, {139, 326},
{214, 280}, {213, 282}, {128, 336}, {144, 320}, {136, 344}, {135, 343}, {134,
342}, {202, 283}, {129, 339}, {152, 330}, {130, 337}, {138, 345}, {137, 346},
{145, 325}, {147, 327}, {201, 285}, {153, 332}, {201, 284}, {131, 341}, {146,
324}, {132, 338}, {154, 333}, {150, 334}, {199, 287}, {199, 286}, {148, 329},
{149, 331}, {206, 272}, {151, 328}, {205, 274}, {206, 273}, {195, 291}, {210,
306}, {196, 293}, {209, 304}, {207, 301}, {39, 452}, {210, 305}, {194, 294},
{207, 299}, {38, 451}, {37, 451}, {193, 295}, {192, 296}, {200, 288}, {202,
290}, {44, 453}, {200, 289}, {40, 452}, {42, 454}, {197, 297}, {198, 298}, {43,
453}, {41, 454}, {57, 457}, {5, 503}, {56, 458}, {3, 502}, {60, 457}, {2, 501},
{2, 506}, {4, 508}, {3, 507}, {2, 505}, {5, 510}, {4, 511}, {4, 504}, {59, 455},
{53, 456}, {58, 455}, {55, 458}, {209, 300}, {3, 509}, {54, 456}, {208, 302},
{208, 303}, {5, 512}, {471, 512}, {479, 512}, {494, 512} }>;
(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, 65, 450, 193, 415, 196, 115, 383, 12, 420, 167, 183, 417, 189, 379,
139)(2, 61, 222, 295, 226, 233, 284, 359, 18, 318, 44, 264, 500, 230, 356,
22)(3, 51, 471, 87, 372, 293, 335, 483, 20, 466, 47, 304, 374, 265, 333, 235)(4,
358, 297, 234, 371, 217, 24, 319, 19, 287, 259, 228, 368, 42, 360, 326)(5, 88,
313, 215, 497, 83, 281, 307, 21, 300, 258, 39, 224, 306, 493, 257)(6, 390, 504,
405, 131, 187, 101, 174, 11, 140, 180, 147, 130, 192, 100, 77)(7, 162, 138, 185,
127, 404, 433, 69, 10, 505, 31, 198, 128, 148, 430, 422)(8, 508, 381, 123, 110,
439, 445, 175, 9, 155, 116, 435, 107, 121, 163, 74)(13, 76, 170, 403, 108, 401,
111, 506, 30, 178, 448, 153, 109, 152, 376, 157)(14, 160, 102, 146, 452, 150,
103, 411, 200, 510, 104, 386, 211, 400, 99, 392)(15, 197, 431, 122, 212, 143,
428, 161, 199, 190, 432, 437, 454, 388, 429, 511)(16, 171, 501, 66, 213, 120,
181, 188, 201, 75, 179, 425, 453, 441, 503, 194)(17, 393, 137, 149, 451, 67,
136, 173, 202, 407, 32, 402, 214, 419, 34, 80)(23, 255, 238, 58, 337, 221, 301,
56, 361, 311, 486, 244, 331, 38, 85, 245)(25, 237, 225, 327, 296, 90, 96, 363,
364, 485, 499, 341, 266, 303, 98, 26)(27, 473, 347, 298, 262, 55, 325, 468, 365,
269, 345, 261, 292, 249, 321, 46)(28, 491, 53, 86, 336, 289, 478, 302, 366, 276,
246, 299, 328, 354, 273, 89)(29, 467, 57, 231, 330, 329, 270, 315, 362, 45, 250,
232, 340, 338, 474, 64)(33, 145, 464, 79, 434, 396, 129, 119, 135, 389, 35, 176,
427, 410, 132, 440)(36, 424, 106, 442, 134, 414, 502, 158, 463, 71, 105, 125,
133, 391, 182, 507)(37, 353, 344, 247, 283, 489, 62, 248, 220, 290, 349, 54,
352, 280, 317, 60)(40, 285, 93, 236, 288, 496, 373, 488, 218, 355, 91, 482, 357,
282, 369, 239)(41, 320, 476, 495, 309, 229, 480, 308, 219, 323, 267, 278, 251,
227, 268, 252)(43, 479, 487, 294, 310, 243, 481, 52, 216, 274, 242, 263, 254,
59, 240, 469)(48, 316, 95, 256, 342, 348, 498, 275, 465, 63, 94, 312, 332, 346,
223, 490)(49, 92, 324, 492, 334, 370, 350, 253, 470, 97, 322, 277, 339, 367,
343, 314)(50, 286, 305, 477, 260, 494, 484, 271, 472, 351, 84, 272, 291, 279,
241, 475)(68, 206, 195, 117, 409, 456, 70, 118, 426, 457, 186, 382, 395, 204,
421, 375)(72, 81, 384, 378, 397, 418, 408, 166, 423, 82, 142, 112, 412, 416,
394, 443)(73, 460, 406, 113, 438, 208, 78, 114, 172, 207, 151, 380, 126, 461,
177, 377)(124, 446, 399, 459, 159, 444, 156, 209, 436, 165, 154, 210, 509, 168,
512, 462)(141, 164, 144, 455, 413, 449, 184, 458, 387, 447, 385, 203, 398, 169,
191, 205) (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)(6, 7)(8, 9)(10, 11)(14, 15, 16, 17)(18, 20, 21, 19)(22, 23, 27,
26)(24, 28, 25, 29)(31, 34, 33, 32)(35, 36)(37, 43, 42, 39)(38, 44, 41, 40)(45,
51, 49, 50)(46, 48, 52, 47)(53, 60, 55, 58)(54, 57, 56, 59)(61, 63, 64, 62)(65,
72, 70, 68)(66, 71, 69, 67)(73, 76, 74, 78)(75, 80, 79, 77)(81, 82)(83, 87, 89,
85)(84, 88, 90, 86)(91, 95, 92, 98)(93, 94, 97, 96)(99, 106, 102, 101)(100, 103,
105, 104)(107, 109, 110, 108)(111, 113, 116, 114)(112, 118, 115, 117)(119, 125,
120, 122)(121, 123, 124, 126)(127, 134, 128, 133)(129, 130, 132, 131)(135, 137,
138, 136)(139, 141, 144, 142)(140, 145, 143, 146)(147, 150, 149, 148)(151, 154,
152, 153)(155, 157, 159, 156)(158, 160, 161, 162)(163, 165, 170, 168)(164, 166,
169, 167)(171, 173, 176, 174)(172, 178, 175, 177)(179, 182, 181, 180)(183, 186,
184, 189)(185, 190, 188, 187)(191, 196, 193, 195)(192, 198, 197, 194)(199, 201,
202, 200)(203, 204, 206, 205)(207, 210, 209, 208)(211, 214, 213, 212)(215, 220,
216, 217)(218, 221, 222, 219)(223, 226, 225, 224)(227, 233, 234, 232)(228, 231,
229, 230)(235, 242, 238, 236)(237, 240, 241, 239)(243, 247, 250, 245)(244, 246,
248, 249)(251, 258, 255, 253)(252, 254, 256, 257)(259, 263, 266, 261)(260, 262,
265, 264)(267, 270, 272, 274)(268, 269, 271, 273)(275, 282, 278, 276)(277, 280,
281, 279)(283, 289, 287, 285)(284, 290, 288, 286)(291, 292, 293, 295)(294, 296,
298, 297)(299, 305, 300, 303)(301, 306, 304, 302)(307, 308, 310, 312)(309, 313,
311, 314)(315, 317, 318, 316)(319, 325, 323, 324)(320, 322, 326, 321)(327, 334,
331, 329)(328, 333, 330, 332)(335, 340, 342, 336)(337, 338, 341, 339)(343, 346,
345, 344)(347, 349, 350, 348)(351, 356, 353, 357)(352, 354, 358, 355)(359, 361,
365, 363)(360, 366, 364, 362)(367, 374, 369, 371)(368, 370, 372, 373)(375, 379,
382, 378)(376, 380, 381, 377)(383, 387, 385, 384)(386, 390, 389, 388)(391, 396,
393, 392)(394, 397, 398, 395)(399, 401, 403, 406)(400, 402, 404, 405)(407, 411,
414, 410)(408, 412, 413, 409)(415, 416, 417, 418)(419, 425, 424, 422)(420, 423,
421, 426)(427, 428, 430, 431)(429, 433, 432, 434)(435, 436, 438, 439)(437, 440,
442, 441)(443, 449, 450, 447)(444, 445, 446, 448)(451, 453, 454, 452)(455, 456,
457, 458)(459, 462, 461, 460)(463, 464)(465, 469, 471, 468)(466, 470, 472,
467)(473, 475, 478, 480)(474, 477, 479, 476)(481, 484, 488, 485)(482, 483, 487,
486)(489, 493, 494, 492)(490, 496, 495, 491)(497, 498, 500, 499)(501, 502, 503,
504)(505, 507, 510, 511)(506, 509, 512, 508)
c: (1, 8, 12, 9)(2, 326, 18, 319)(3, 324, 20, 322)(4, 325, 19, 321)(5, 320, 21,
323)(6, 36, 11, 463)(7, 464, 10, 35)(13, 81, 30, 82)(14, 452, 200, 211)(15, 212,
199, 454)(16, 453, 201, 213)(17, 214, 202, 451)(22, 45, 359, 467)(23, 472, 361,
50)(24, 471, 360, 47)(25, 465, 364, 48)(26, 466, 363, 51)(27, 49, 365, 470)(28,
52, 366, 469)(29, 46, 362, 468)(31, 101, 138, 100)(32, 103, 137, 99)(33, 106,
135, 105)(34, 104, 136, 102)(37, 352, 220, 283)(38, 353, 221, 290)(39, 289, 215,
354)(40, 288, 218, 357)(41, 351, 219, 286)(42, 358, 217, 287)(43, 285, 216,
355)(44, 284, 222, 356)(53, 85, 246, 301)(54, 86, 247, 299)(55, 87, 249,
304)(56, 88, 245, 300)(57, 303, 250, 90)(58, 306, 244, 83)(59, 305, 243, 84)(60,
302, 248, 89)(61, 98, 318, 96)(62, 93, 317, 91)(63, 97, 316, 92)(64, 95, 315,
94)(65, 174, 420, 77)(66, 78, 425, 177)(67, 172, 419, 73)(68, 75, 426, 171)(69,
76, 422, 178)(70, 173, 421, 80)(71, 175, 424, 74)(72, 79, 423, 176)(107, 415,
110, 417)(108, 418, 109, 416)(111, 170, 376, 448)(112, 443, 378, 166)(113, 446,
380, 165)(114, 444, 377, 168)(115, 450, 379, 167)(116, 163, 381, 445)(117, 169,
382, 449)(118, 164, 375, 447)(119, 412, 440, 397)(120, 409, 441, 395)(121, 410,
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442, 408)(126, 393, 438, 407)(127, 129, 128, 132)(130, 133, 131, 134)(139, 162,
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405, 196)(148, 193, 404, 183)(149, 186, 402, 195)(150, 191, 400, 184)(151, 194,
406, 188)(152, 198, 401, 185)(153, 187, 403, 192)(154, 190, 399, 197)(179, 428,
501, 429)(180, 433, 504, 430)(181, 431, 503, 432)(182, 434, 502, 427)(203, 459,
455, 210)(204, 207, 456, 460)(205, 209, 458, 462)(206, 461, 457, 208)(223, 231,
498, 232)(224, 227, 497, 229)(225, 230, 499, 233)(226, 234, 500, 228)(235, 269,
483, 473)(236, 475, 482, 271)(237, 474, 485, 270)(238, 273, 486, 478)(239, 272,
488, 477)(240, 267, 481, 476)(241, 479, 484, 274)(242, 480, 487, 268)(251, 494,
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297, 333)(260, 337, 291, 331)(261, 330, 298, 340)(262, 334, 292, 339)(263, 328,
294, 336)(264, 329, 295, 338)(265, 341, 293, 327)(266, 342, 296, 332)(343, 372,
350, 374)(344, 369, 349, 373)(345, 368, 347, 371)(346, 367, 348, 370)
d: (2, 5)(6, 7)(8, 9)(10, 11)(14, 15)(16, 17)(18, 21)(22, 24)(23, 29)(25,
27)(26, 28)(32, 34)(35, 36)(37, 44)(38, 43)(39, 41)(40, 42)(45, 47)(46, 50)(48,
49)(51, 52)(53, 57)(54, 60)(55, 59)(56, 58)(62, 63)(65, 66)(67, 72)(68, 71)(69,
70)(73, 79)(74, 75)(76, 80)(77, 78)(81, 82)(83, 88)(84, 87)(85, 90)(86, 89)(91,
97)(92, 93)(94, 95)(96, 98)(99, 104)(100, 101)(102, 103)(105, 106)(108,
109)(111, 115)(112, 116)(113, 118)(114, 117)(119, 126)(120, 123)(121, 122)(124,
125)(127, 130)(128, 131)(129, 134)(132, 133)(136, 137)(139, 143)(140, 144)(141,
145)(142, 146)(147, 151)(148, 154)(149, 152)(150, 153)(155, 161)(156, 162)(157,
160)(158, 159)(163, 166)(164, 165)(167, 170)(168, 169)(171, 175)(172, 176)(173,
178)(174, 177)(179, 181)(183, 190)(184, 187)(185, 186)(188, 189)(191, 192)(193,
197)(194, 196)(195, 198)(199, 200)(201, 202)(203, 205)(204, 206)(207, 208)(209,
210)(211, 212)(213, 214)(215, 219)(216, 221)(217, 218)(220, 222)(224, 226)(227,
228)(229, 234)(230, 233)(231, 232)(235, 241)(236, 239)(237, 238)(240, 242)(243,
249)(244, 245)(246, 250)(247, 248)(251, 257)(252, 253)(254, 255)(256, 258)(259,
264)(260, 261)(262, 266)(263, 265)(267, 268)(269, 274)(270, 273)(271, 272)(275,
281)(276, 279)(277, 278)(280, 282)(283, 284)(285, 290)(286, 289)(287, 288)(291,
298)(292, 296)(293, 294)(295, 297)(299, 302)(300, 306)(301, 303)(304, 305)(307,
309)(308, 314)(310, 311)(312, 313)(316, 317)(319, 320)(321, 325)(322, 324)(323,
326)(327, 328)(329, 333)(330, 331)(332, 334)(335, 338)(336, 341)(337, 340)(339,
342)(344, 346)(348, 349)(351, 354)(352, 356)(353, 355)(357, 358)(359, 360)(361,
362)(363, 366)(364, 365)(367, 373)(368, 371)(369, 370)(372, 374)(375, 380)(376,
379)(377, 382)(378, 381)(383, 388)(384, 386)(385, 390)(387, 389)(391, 395)(392,
394)(393, 397)(396, 398)(399, 404)(400, 403)(401, 402)(405, 406)(407, 412)(408,
411)(409, 414)(410, 413)(415, 417)(419, 423)(420, 425)(421, 422)(424, 426)(427,
434)(428, 432)(429, 431)(430, 433)(435, 441)(436, 442)(437, 439)(438, 440)(443,
445)(444, 449)(446, 447)(448, 450)(451, 453)(452, 454)(455, 458)(456, 457)(459,
462)(460, 461)(463, 464)(465, 470)(466, 469)(467, 471)(468, 472)(473, 479)(474,
478)(475, 477)(476, 480)(481, 487)(482, 488)(483, 484)(485, 486)(489, 496)(490,
493)(491, 494)(492, 495)(497, 500)(501, 503)(505, 512)(506, 510)(507, 509)(508,
511)
e: (1, 14, 108, 17)(2, 307, 344, 311)(3, 357, 230, 312)(4, 314, 232, 352)(5,
354, 348, 353)(6, 456, 128, 462)(7, 461, 130, 455)(8, 451, 418, 211)(9, 214,
416, 452)(10, 208, 131, 203)(11, 204, 127, 209)(12, 200, 109, 202)(13, 212, 415,
213)(15, 81, 201, 110)(16, 107, 199, 82)(18, 257, 349, 255)(19, 253, 231,
283)(20, 288, 233, 256)(21, 289, 346, 290)(22, 238, 266, 269)(23, 247, 340,
242)(24, 246, 292, 304)(25, 270, 264, 241)(26, 271, 328, 300)(27, 303, 297,
243)(28, 239, 341, 244)(29, 302, 331, 267)(30, 454, 417, 453)(31, 163, 106,
379)(32, 382, 503, 380)(33, 381, 100, 167)(34, 164, 179, 168)(35, 210, 134,
457)(36, 458, 132, 207)(37, 223, 277, 325)(38, 370, 215, 320)(39, 323, 221,
367)(40, 322, 275, 225)(41, 224, 43, 63)(42, 374, 493, 61)(44, 64, 495, 368)(45,
235, 342, 478)(46, 240, 260, 60)(47, 55, 334, 301)(48, 479, 338, 237)(49, 305,
333, 57)(50, 480, 298, 299)(51, 56, 263, 236)(52, 306, 293, 477)(53, 262, 87,
360)(54, 330, 487, 361)(58, 366, 488, 327)(59, 365, 90, 259)(62, 494, 500,
496)(65, 77, 436, 411)(66, 189, 125, 509)(67, 512, 404, 412)(68, 414, 403,
510)(69, 413, 437, 76)(70, 511, 121, 185)(71, 74, 150, 184)(72, 190, 154,
79)(73, 440, 193, 388)(75, 385, 192, 435)(78, 386, 394, 147)(80, 152, 396,
387)(83, 265, 272, 469)(84, 335, 250, 470)(85, 471, 249, 339)(86, 472, 268,
261)(88, 363, 475, 336)(89, 337, 476, 362)(91, 254, 234, 309)(92, 285, 229,
351)(93, 310, 228, 251)(94, 284, 345, 308)(95, 356, 347, 252)(96, 258, 350,
358)(97, 355, 227, 286)(98, 313, 343, 287)(99, 165, 431, 449)(101, 450, 135,
116)(102, 114, 429, 375)(103, 446, 432, 169)(104, 377, 428, 118)(105, 115, 138,
445)(111, 180, 166, 434)(112, 430, 170, 182)(113, 137, 117, 181)(119, 183, 143,
172)(120, 395, 390, 506)(122, 178, 422, 398)(123, 171, 144, 187)(124, 392, 420,
174)(126, 505, 383, 393)(129, 460, 463, 205)(133, 206, 464, 459)(136, 447, 501,
444)(139, 407, 438, 162)(140, 157, 441, 409)(141, 173, 401, 410)(142, 158, 151,
188)(145, 186, 149, 155)(146, 408, 405, 177)(148, 397, 419, 156)(153, 160, 426,
391)(159, 425, 196, 442)(161, 439, 198, 421)(175, 400, 191, 424)(176, 423, 197,
399)(194, 384, 507, 406)(195, 402, 508, 389)(216, 316, 219, 497)(217, 372, 281,
318)(218, 324, 490, 499)(220, 498, 492, 321)(222, 315, 278, 371)(226, 282, 317,
279)(245, 294, 482, 466)(248, 468, 481, 291)(273, 467, 483, 332)(274, 329, 485,
465)(276, 326, 489, 369)(280, 373, 491, 319)(295, 484, 364, 474)(296, 473, 359,
486)(376, 504, 443, 427)(378, 433, 448, 502)
f: (1, 6, 30, 7)(2, 364, 62, 359)(3, 363, 61, 366)(4, 361, 64, 362)(5, 360, 63,
365)(8, 35, 82, 463)(9, 464, 81, 36)(10, 12, 11, 13)(14, 455, 451, 460)(15, 461,
453, 458)(16, 457, 454, 462)(17, 459, 452, 456)(18, 25, 317, 22)(19, 23, 315,
29)(20, 26, 318, 28)(21, 24, 316, 27)(31, 382, 502, 377)(32, 376, 501, 378)(33,
375, 504, 380)(34, 381, 503, 379)(37, 86, 314, 476)(38, 85, 307, 473)(39, 474,
311, 84)(40, 475, 312, 83)(41, 87, 310, 478)(42, 88, 313, 477)(43, 479, 309,
90)(44, 480, 308, 89)(45, 93, 465, 326)(46, 95, 472, 325)(47, 323, 470, 92)(48,
319, 467, 91)(49, 97, 471, 320)(50, 321, 468, 94)(51, 322, 469, 96)(52, 98, 466,
324)(53, 353, 483, 491)(54, 352, 481, 492)(55, 351, 486, 496)(56, 358, 488,
493)(57, 494, 484, 355)(58, 490, 482, 357)(59, 489, 485, 354)(60, 495, 487,
356)(65, 386, 509, 77)(66, 78, 507, 384)(67, 383, 505, 73)(68, 75, 506, 390)(69,
76, 511, 387)(70, 389, 508, 80)(71, 385, 510, 74)(72, 79, 512, 388)(99, 166,
428, 448)(100, 168, 434, 449)(101, 444, 427, 169)(102, 167, 431, 445)(103, 443,
429, 170)(104, 450, 432, 163)(105, 165, 433, 447)(106, 446, 430, 164)(107, 128,
416, 131)(108, 129, 415, 133)(109, 132, 417, 134)(110, 127, 418, 130)(111, 179,
112, 137)(113, 135, 118, 180)(114, 138, 117, 182)(115, 136, 116, 181)(119, 438,
190, 193)(120, 435, 187, 191)(121, 437, 186, 198)(122, 195, 185, 439)(123, 192,
184, 441)(124, 442, 189, 194)(125, 196, 188, 436)(126, 197, 183, 440)(139, 162,
172, 419)(140, 426, 171, 157)(141, 422, 178, 161)(142, 425, 177, 158)(143, 423,
176, 156)(144, 160, 175, 424)(145, 155, 173, 421)(146, 159, 174, 420)(147, 408,
392, 406)(148, 399, 393, 412)(149, 413, 396, 401)(150, 403, 391, 409)(151, 405,
394, 411)(152, 402, 398, 410)(153, 414, 395, 400)(154, 407, 397, 404)(199, 208,
213, 205)(200, 203, 214, 207)(201, 206, 212, 209)(202, 210, 211, 204)(215, 270,
255, 305)(216, 274, 251, 303)(217, 300, 258, 272)(218, 271, 256, 306)(219, 304,
254, 273)(220, 299, 253, 267)(221, 301, 257, 269)(222, 268, 252, 302)(223, 337,
345, 340)(224, 342, 346, 338)(225, 341, 343, 336)(226, 335, 344, 339)(227, 295,
367, 266)(228, 262, 373, 297)(229, 264, 370, 296)(230, 294, 372, 265)(231, 298,
368, 260)(232, 261, 371, 291)(233, 263, 374, 293)(234, 292, 369, 259)(235, 276,
246, 290)(236, 288, 244, 275)(237, 289, 243, 280)(238, 282, 249, 286)(239, 281,
245, 287)(240, 277, 247, 283)(241, 285, 250, 279)(242, 284, 248, 278)(327, 350,
328, 499)(329, 497, 332, 348)(330, 498, 331, 347)(333, 349, 334, 500)
g: (1, 31, 207, 136)(2, 61, 237, 248)(3, 53, 299, 344)(4, 57, 236, 316)(5, 347,
301, 245)(6, 167, 211, 444)(7, 170, 199, 447)(8, 106, 203, 102)(9, 105, 455,
104)(10, 448, 15, 164)(11, 450, 452, 168)(12, 138, 460, 34)(13, 504, 457,
179)(14, 380, 130, 443)(16, 165, 134, 115)(17, 375, 35, 116)(18, 318, 485,
60)(19, 250, 482, 63)(20, 246, 86, 349)(21, 345, 85, 56)(22, 220, 309, 263)(23,
297, 40, 257)(24, 313, 39, 260)(25, 222, 491, 51)(26, 471, 492, 43)(27, 312,
351, 46)(28, 295, 308, 41)(29, 467, 358, 255)(30, 180, 206, 501)(32, 416, 433,
459)(33, 208, 431, 415)(36, 112, 213, 377)(37, 251, 294, 359)(38, 261, 329,
490)(42, 279, 330, 292)(44, 276, 466, 364)(45, 287, 311, 362)(47, 277, 216,
363)(48, 288, 282, 331)(49, 278, 353, 328)(50, 342, 281, 355)(52, 339, 352,
489)(54, 367, 230, 483)(55, 239, 234, 371)(58, 373, 321, 84)(59, 302, 323,
372)(62, 225, 273, 481)(64, 238, 272, 497)(65, 140, 178, 505)(66, 412, 402,
506)(67, 151, 160, 398)(68, 147, 126, 389)(69, 144, 125, 399)(70, 407, 159,
400)(71, 155, 176, 384)(72, 161, 403, 392)(73, 185, 395, 507)(74, 146, 193,
122)(75, 186, 143, 124)(76, 162, 420, 390)(77, 156, 396, 191)(78, 441, 141,
197)(79, 142, 424, 508)(80, 435, 194, 383)(81, 427, 462, 428)(82, 434, 209,
429)(83, 348, 498, 474)(87, 267, 92, 324)(88, 319, 94, 473)(89, 320, 374,
243)(90, 268, 500, 343)(91, 232, 484, 475)(93, 231, 241, 271)(95, 269, 300,
326)(96, 274, 487, 227)(97, 322, 304, 476)(98, 479, 242, 229)(99, 108, 502,
456)(100, 205, 503, 107)(101, 458, 181, 110)(103, 109, 182, 204)(111, 214, 449,
132)(113, 131, 166, 200)(114, 463, 378, 453)(117, 128, 445, 454)(118, 464, 381,
202)(119, 189, 391, 152)(120, 387, 190, 177)(121, 404, 394, 192)(123, 188, 139,
173)(127, 163, 212, 382)(129, 376, 451, 169)(133, 379, 201, 446)(135, 461, 432,
417)(137, 418, 430, 210)(145, 426, 405, 438)(148, 408, 187, 439)(149, 157, 425,
397)(150, 421, 393, 509)(153, 411, 423, 511)(154, 422, 385, 442)(158, 172, 198,
409)(171, 195, 388, 436)(174, 512, 410, 184)(175, 386, 183, 437)(196, 414, 401,
440)(215, 291, 360, 258)(217, 494, 340, 262)(218, 307, 361, 259)(219, 366, 264,
252)(221, 298, 338, 275)(223, 270, 306, 346)(224, 315, 486, 477)(226, 350, 303,
480)(228, 368, 249, 488)(233, 235, 247, 370)(240, 317, 499, 478)(244, 369, 325,
305)(253, 289, 341, 266)(254, 293, 335, 356)(256, 286, 468, 365)(265, 333, 284,
310)(280, 469, 334, 283)(285, 472, 332, 493)(290, 336, 470, 495)(296, 314, 354,
327)(337, 465, 357, 496)(406, 510, 413, 419)
C4[ 512, 542 ]
512
-1 2 3 4 5
-2 506 1 501 505
-3 1 507 509 502
-4 1 508 511 504
-5 1 510 512 503
-6 363 364 360 361
-7 365 366 359 362
-8 320 324 325 326
-9 319 321 322 323
-10 22 27 28 29
-11 23 24 25 26
-12 18 19 20 21
-13 315 316 317 318
-14 354 357 314 307
-15 308 309 358 351
-16 310 355 356 313
-17 352 353 311 312
-18 12 157 179 162
-19 12 155 180 161
-20 12 158 159 182
-21 12 156 181 160
-22 111 171 139 10
-23 11 113 173 141
-24 11 143 115 175
-25 11 112 172 140
-26 11 114 174 142
-27 176 144 116 10
-28 177 146 117 10
-29 145 178 118 10
-30 61 62 63 64
-31 57 61 347 53
-32 58 62 348 54
-33 55 59 64 350
-34 56 60 63 349
-35 45 46 49 52
-36 47 48 50 51
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-38 187 451 169 73
-39 165 452 183 75
-40 188 78 452 166
-41 190 454 74 164
-42 77 189 454 163
-43 79 453 168 184
-44 167 453 185 76
-45 35 68 170 162
-46 155 35 69 164
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-48 67 166 36 157
-49 35 72 160 163
-50 165 36 70 161
-51 36 168 158 65
-52 66 35 169 159
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-54 80 456 152 32
-55 33 148 458 74
-56 77 34 458 151
-57 79 457 31 153
-58 78 147 455 32
-59 33 154 455 75
-60 34 149 457 76
-61 66 30 31 65
-62 67 68 30 32
-63 34 71 72 30
-64 33 69 70 30
-65 88 61 358 51
-66 357 61 83 52
-67 353 48 62 85
-68 45 354 62 84
-69 89 46 356 64
-70 352 50 64 86
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-80 37 94 361 54
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-82 93 95 97 98
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-221 192 214 172 449
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-226 148 181 415 153
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-317 419 13 137 426
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-349 407 34 409 109
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-356 69 16 379 401
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-363 77 377 6 384
-364 378 390 6 73
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-378 364 332 357 492
-379 333 356 360 493
-380 496 354 327 361
-381 495 365 334 358
-382 330 353 366 494
-383 319 359 307 483
-384 363 312 324 482
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