Graph forms
for C4 [ 512, 53 ] = PL(BC_128({0,64},{1,31})
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On this page are computer-accessible forms for the graph C4[ 512, 53 ] =
PL(BC_128({0,64},{1,31}).
(I) Following is a form readable by MAGMA:
g:=Graph<512|{ {117, 125}, {118, 126}, {244, 253}, {244, 254}, {117, 126}, {118,
125}, {243, 254}, {243, 253}, {405, 437}, {404, 437}, {259, 299}, {391, 431},
{390, 430}, {260, 300}, {390, 431}, {391, 430}, {411, 433}, {410, 433}, {269,
289}, {404, 440}, {286, 306}, {285, 305}, {270, 290}, {405, 440}, {410, 436},
{259, 300}, {411, 436}, {286, 305}, {285, 306}, {270, 289}, {269, 290}, {260,
299}, {256, 310}, {256, 311}, {261, 324}, {262, 324}, {276, 343}, {275, 343},
{262, 323}, {261, 323}, {416, 486}, {280, 351}, {416, 487}, {279, 351}, {284,
341}, {284, 342}, {180, 255}, {275, 344}, {179, 255}, {276, 344}, {283, 342},
{283, 341}, {265, 345}, {266, 346}, {288, 369}, {288, 370}, {265, 346}, {266,
345}, {403, 453}, {402, 453}, {388, 476}, {396, 468}, {395, 467}, {389, 476},
{402, 456}, {403, 456}, {389, 473}, {388, 473}, {395, 468}, {396, 467}, {399,
494}, {399, 493}, {258, 363}, {386, 491}, {257, 363}, {385, 491}, {404, 511},
{403, 511}, {257, 364}, {385, 492}, {287, 370}, {271, 354}, {258, 364}, {386,
492}, {287, 369}, {271, 353}, {272, 353}, {272, 354}, {397, 505}, {398, 506},
{387, 501}, {279, 352}, {398, 505}, {397, 506}, {386, 501}, {280, 352}, {386,
504}, {387, 504}, {400, 493}, {400, 494}, {68, 197}, {109, 236}, {84, 213}, {68,
198}, {319, 445}, {110, 236}, {100, 230}, {84, 214}, {11, 136}, {318, 445},
{263, 388}, {100, 231}, {12, 136}, {353, 485}, {263, 387}, {72, 204}, {67, 198},
{352, 485}, {274, 407}, {110, 235}, {83, 214}, {72, 205}, {67, 197}, {273, 407},
{109, 235}, {97, 231}, {83, 213}, {97, 230}, {69, 205}, {352, 488}, {299, 419},
{298, 418}, {114, 250}, {115, 251}, {69, 204}, {353, 488}, {299, 418}, {298,
419}, {278, 415}, {273, 408}, {114, 251}, {115, 250}, {274, 408}, {277, 415},
{12, 135}, {264, 387}, {11, 135}, {366, 482}, {365, 481}, {282, 406}, {281,
405}, {264, 388}, {18, 156}, {27, 149}, {26, 148}, {19, 157}, {18, 157}, {366,
481}, {365, 482}, {282, 405}, {281, 406}, {27, 148}, {26, 149}, {19, 156}, {73,
217}, {74, 218}, {267, 410}, {310, 423}, {267, 409}, {309, 423}, {73, 218}, {74,
217}, {338, 454}, {339, 455}, {268, 409}, {339, 454}, {338, 455}, {268, 410},
{92, 196}, {308, 428}, {5, 156}, {362, 499}, {331, 466}, {309, 428}, {293, 444},
{92, 197}, {57, 160}, {122, 227}, {6, 156}, {378, 480}, {361, 499}, {331, 465},
{294, 444}, {58, 160}, {121, 227}, {379, 480}, {89, 197}, {309, 425}, {6, 155},
{361, 500}, {332, 465}, {309, 424}, {308, 425}, {294, 443}, {89, 196}, {121,
228}, {5, 155}, {362, 500}, {332, 466}, {325, 475}, {324, 474}, {310, 424},
{293, 443}, {122, 228}, {324, 475}, {325, 474}, {335, 495}, {336, 496}, {40,
137}, {53, 148}, {42, 139}, {40, 138}, {77, 239}, {54, 148}, {41, 139}, {77,
238}, {61, 153}, {41, 140}, {104, 205}, {61, 152}, {58, 159}, {54, 147}, {42,
140}, {379, 477}, {104, 206}, {57, 159}, {53, 147}, {378, 477}, {321, 489},
{322, 490}, {103, 206}, {340, 509}, {48, 154}, {340, 510}, {103, 205}, {48,
155}, {322, 489}, {321, 490}, {1, 173}, {2, 174}, {39, 138}, {339, 510}, {13,
163}, {339, 509}, {39, 137}, {23, 185}, {22, 184}, {1, 174}, {23, 184}, {22,
185}, {13, 162}, {2, 173}, {49, 129}, {377, 457}, {49, 128}, {376, 457}, {333,
508}, {16, 162}, {381, 463}, {380, 462}, {371, 449}, {334, 508}, {16, 163},
{381, 462}, {380, 463}, {370, 449}, {34, 150}, {376, 460}, {323, 503}, {322,
502}, {86, 226}, {85, 225}, {52, 128}, {35, 151}, {34, 151}, {377, 460}, {334,
507}, {323, 502}, {322, 503}, {277, 416}, {52, 129}, {35, 150}, {45, 155}, {370,
452}, {333, 507}, {278, 416}, {45, 154}, {371, 452}, {86, 225}, {85, 226}, {29,
165}, {30, 166}, {94, 228}, {365, 471}, {364, 470}, {107, 209}, {106, 208}, {95,
229}, {29, 166}, {365, 470}, {364, 471}, {107, 208}, {106, 209}, {95, 228}, {94,
229}, {30, 165}, {80, 238}, {80, 239}, {336, 495}, {335, 496}, {382, 446}, {383,
447}, {9, 200}, {383, 446}, {382, 447}, {10, 200}, {111, 172}, {65, 133}, {111,
171}, {99, 167}, {98, 166}, {96, 164}, {82, 150}, {81, 149}, {66, 134}, {32,
229}, {99, 166}, {98, 167}, {96, 165}, {120, 189}, {32, 230}, {289, 487}, {120,
190}, {65, 134}, {289, 486}, {82, 149}, {81, 150}, {66, 133}, {20, 220}, {28,
212}, {20, 221}, {301, 484}, {28, 213}, {119, 190}, {70, 140}, {363, 417}, {302,
484}, {113, 187}, {71, 141}, {119, 189}, {70, 141}, {362, 417}, {113, 186}, {71,
140}, {17, 221}, {25, 213}, {10, 199}, {302, 483}, {25, 212}, {17, 220}, {9,
199}, {362, 420}, {301, 483}, {116, 186}, {116, 187}, {363, 420}, {373, 421},
{374, 422}, {75, 154}, {75, 153}, {8, 219}, {374, 421}, {373, 422}, {8, 220},
{76, 153}, {76, 154}, {64, 152}, {298, 498}, {297, 497}, {123, 163}, {124, 164},
{64, 153}, {7, 220}, {298, 497}, {297, 498}, {112, 171}, {59, 224}, {7, 219},
{358, 442}, {357, 441}, {112, 172}, {60, 224}, {90, 132}, {373, 427}, {372,
426}, {91, 133}, {90, 133}, {373, 426}, {372, 427}, {358, 441}, {357, 442}, {91,
132}, {123, 164}, {124, 163}, {24, 248}, {79, 175}, {78, 174}, {44, 204}, {43,
203}, {24, 249}, {79, 174}, {78, 175}, {340, 438}, {341, 439}, {55, 212}, {341,
438}, {340, 439}, {60, 223}, {55, 211}, {315, 479}, {314, 478}, {59, 223}, {314,
479}, {315, 478}, {62, 216}, {63, 217}, {43, 204}, {63, 216}, {62, 217}, {44,
203}, {101, 141}, {347, 435}, {346, 434}, {102, 142}, {4, 237}, {347, 434},
{346, 435}, {4, 238}, {327, 429}, {56, 211}, {326, 429}, {102, 141}, {101, 142},
{14, 226}, {316, 464}, {56, 212}, {38, 202}, {37, 201}, {21, 249}, {15, 227},
{3, 238}, {317, 464}, {21, 248}, {15, 226}, {14, 227}, {3, 237}, {37, 202}, {38,
201}, {306, 450}, {317, 461}, {307, 451}, {306, 451}, {316, 461}, {307, 450},
{36, 214}, {313, 459}, {312, 458}, {51, 193}, {50, 192}, {36, 215}, {313, 458},
{312, 459}, {51, 192}, {50, 193}, {46, 218}, {300, 472}, {47, 219}, {46, 219},
{301, 472}, {87, 162}, {47, 218}, {33, 215}, {326, 432}, {87, 161}, {33, 214},
{327, 432}, {93, 165}, {301, 469}, {105, 145}, {31, 230}, {300, 469}, {105,
144}, {93, 164}, {88, 161}, {31, 229}, {88, 162}, {108, 144}, {108, 145}, {318,
448}, {319, 448}, {110, 366}, {111, 367}, {110, 367}, {111, 366}, {236, 494},
{237, 495}, {63, 316}, {237, 494}, {236, 495}, {188, 447}, {63, 315}, {187,
447}, {167, 418}, {167, 417}, {65, 329}, {81, 345}, {65, 328}, {81, 344}, {168,
417}, {207, 454}, {168, 418}, {207, 453}, {68, 328}, {241, 509}, {84, 344}, {48,
317}, {240, 509}, {84, 345}, {68, 329}, {48, 318}, {51, 291}, {235, 507}, {234,
506}, {52, 292}, {47, 318}, {235, 506}, {234, 507}, {47, 317}, {208, 453}, {74,
348}, {75, 349}, {208, 454}, {51, 292}, {247, 480}, {95, 328}, {75, 348}, {74,
349}, {52, 291}, {33, 313}, {248, 480}, {95, 327}, {59, 291}, {58, 290}, {34,
314}, {193, 473}, {194, 474}, {58, 291}, {106, 371}, {59, 290}, {178, 427},
{105, 371}, {177, 427}, {33, 314}, {34, 313}, {193, 474}, {194, 473}, {77, 337},
{78, 338}, {122, 358}, {123, 359}, {105, 372}, {122, 359}, {123, 358}, {177,
428}, {106, 372}, {178, 428}, {77, 338}, {78, 337}, {25, 312}, {26, 312}, {151,
436}, {151, 435}, {146, 439}, {145, 439}, {72, 367}, {248, 479}, {96, 327}, {71,
367}, {247, 479}, {98, 330}, {97, 329}, {96, 328}, {202, 482}, {203, 483}, {116,
349}, {132, 429}, {145, 440}, {202, 483}, {203, 482}, {116, 350}, {132, 430},
{146, 440}, {97, 330}, {239, 452}, {98, 329}, {152, 435}, {152, 436}, {239,
451}, {18, 319}, {26, 311}, {115, 350}, {131, 430}, {17, 319}, {25, 311}, {115,
349}, {131, 429}, {2, 304}, {222, 492}, {87, 357}, {86, 356}, {3, 305}, {198,
500}, {2, 305}, {240, 451}, {223, 492}, {91, 360}, {87, 356}, {86, 357}, {3,
304}, {199, 500}, {92, 360}, {250, 462}, {249, 461}, {240, 452}, {101, 337},
{117, 321}, {101, 336}, {221, 488}, {117, 320}, {192, 501}, {30, 296}, {223,
489}, {222, 488}, {31, 297}, {147, 421}, {192, 502}, {199, 497}, {30, 297},
{250, 461}, {249, 462}, {222, 489}, {71, 368}, {31, 296}, {146, 421}, {198,
497}, {72, 368}, {233, 465}, {104, 336}, {120, 320}, {104, 337}, {245, 460},
{232, 465}, {222, 487}, {120, 321}, {131, 441}, {246, 460}, {221, 487}, {146,
424}, {92, 359}, {130, 441}, {147, 424}, {91, 359}, {234, 470}, {233, 469},
{232, 468}, {233, 468}, {246, 459}, {130, 444}, {245, 459}, {131, 444}, {234,
469}, {233, 470}, {10, 330}, {11, 331}, {173, 493}, {10, 331}, {252, 445}, {61,
380}, {11, 330}, {172, 493}, {62, 380}, {252, 446}, {109, 303}, {109, 302},
{231, 420}, {231, 419}, {62, 379}, {251, 446}, {61, 379}, {251, 445}, {143,
456}, {32, 360}, {143, 455}, {15, 326}, {32, 361}, {21, 348}, {191, 502}, {15,
325}, {22, 348}, {191, 501}, {232, 419}, {232, 420}, {22, 347}, {21, 347}, {176,
510}, {177, 511}, {176, 511}, {177, 510}, {45, 381}, {46, 382}, {17, 320}, {50,
355}, {18, 320}, {49, 355}, {171, 505}, {45, 382}, {46, 381}, {170, 505}, {16,
325}, {49, 356}, {8, 350}, {50, 356}, {16, 326}, {170, 508}, {8, 351}, {144,
455}, {171, 508}, {107, 307}, {242, 426}, {241, 425}, {108, 308}, {144, 456},
{35, 378}, {130, 475}, {5, 351}, {57, 355}, {35, 377}, {124, 294}, {129, 475},
{5, 350}, {242, 425}, {241, 426}, {57, 354}, {124, 295}, {172, 496}, {36, 377},
{129, 476}, {173, 496}, {36, 378}, {112, 302}, {60, 354}, {121, 295}, {130,
476}, {60, 355}, {112, 303}, {108, 307}, {107, 308}, {121, 294}, {44, 334}, {53,
343}, {27, 376}, {53, 342}, {44, 335}, {28, 376}, {209, 437}, {210, 438}, {184,
477}, {215, 434}, {41, 335}, {215, 433}, {184, 478}, {41, 334}, {209, 438},
{210, 437}, {70, 303}, {216, 433}, {183, 478}, {185, 464}, {38, 332}, {216,
434}, {69, 303}, {39, 333}, {125, 279}, {139, 481}, {183, 477}, {186, 464}, {20,
383}, {39, 332}, {38, 333}, {28, 375}, {125, 278}, {138, 481}, {196, 431}, {19,
383}, {27, 375}, {195, 431}, {175, 450}, {56, 342}, {138, 484}, {175, 449}, {56,
343}, {139, 484}, {1, 369}, {85, 293}, {126, 270}, {127, 271}, {1, 368}, {89,
296}, {85, 292}, {126, 271}, {127, 270}, {169, 472}, {176, 449}, {90, 296},
{170, 472}, {176, 450}, {195, 432}, {4, 368}, {211, 423}, {29, 361}, {134, 498},
{135, 499}, {158, 490}, {159, 491}, {196, 432}, {210, 422}, {4, 369}, {211,
422}, {69, 304}, {29, 360}, {134, 499}, {135, 498}, {158, 491}, {159, 490},
{186, 463}, {210, 423}, {70, 304}, {185, 463}, {128, 503}, {128, 504}, {157,
485}, {158, 486}, {194, 442}, {195, 443}, {194, 443}, {195, 442}, {168, 466},
{169, 467}, {64, 315}, {157, 486}, {158, 485}, {168, 467}, {169, 466}, {187,
448}, {64, 316}, {88, 292}, {181, 457}, {182, 458}, {188, 448}, {88, 293}, {90,
295}, {170, 471}, {89, 295}, {169, 471}, {181, 458}, {182, 457}, {9, 395}, {9,
394}, {24, 411}, {24, 412}, {12, 394}, {12, 395}, {127, 504}, {13, 389}, {255,
375}, {254, 374}, {14, 390}, {127, 503}, {137, 257}, {136, 257}, {255, 374},
{254, 375}, {13, 390}, {23, 412}, {14, 389}, {23, 411}, {136, 260}, {137, 260},
{142, 286}, {143, 287}, {142, 287}, {143, 286}, {19, 384}, {20, 384}, {6, 414},
{7, 415}, {6, 415}, {7, 414}, {54, 406}, {55, 407}, {180, 276}, {54, 407}, {55,
406}, {181, 276}, {40, 396}, {43, 399}, {42, 398}, {181, 273}, {188, 280}, {40,
397}, {43, 398}, {42, 399}, {180, 273}, {189, 280}, {160, 262}, {161, 263},
{160, 263}, {161, 262}, {37, 397}, {189, 277}, {37, 396}, {188, 277}, {179,
281}, {178, 281}, {178, 284}, {190, 272}, {179, 284}, {191, 272}, {191, 269},
{179, 256}, {190, 269}, {180, 256}, {182, 266}, {183, 267}, {182, 267}, {183,
266}, {80, 401}, {80, 402}, {66, 392}, {253, 311}, {83, 409}, {82, 408}, {67,
393}, {200, 258}, {201, 259}, {66, 393}, {253, 310}, {83, 408}, {82, 409}, {67,
392}, {200, 259}, {201, 258}, {76, 412}, {76, 413}, {207, 285}, {206, 285}, {73,
413}, {73, 412}, {93, 392}, {94, 392}, {94, 391}, {93, 391}, {79, 402}, {79,
401}, {225, 261}, {224, 261}, {244, 274}, {245, 275}, {244, 275}, {245, 274},
{224, 264}, {243, 283}, {242, 282}, {99, 394}, {243, 282}, {242, 283}, {225,
264}, {99, 393}, {252, 278}, {252, 279}, {113, 413}, {114, 414}, {100, 393},
{100, 394}, {206, 288}, {113, 414}, {114, 413}, {207, 288}, {102, 400}, {103,
401}, {118, 384}, {119, 385}, {102, 401}, {103, 400}, {118, 385}, {119, 384},
{246, 268}, {247, 268}, {247, 265}, {246, 265}, {240, 512}, {241, 512}, {403,
512}, {404, 512} }>;
(II) A more general form is to represent the graph as the orbit of {117, 125}
under the group generated by the following permutations:
a: (1, 13, 436, 70, 475, 265, 110, 264, 83, 483, 502, 276, 471, 491, 54, 260,
117, 283, 420, 20, 437, 497, 448, 510, 29, 45, 456, 90, 461, 77, 122, 62, 103,
443, 478, 496, 87, 35, 42, 52, 459, 507, 60, 28, 37, 269, 256, 466, 485, 421,
12, 278, 425, 97, 8, 106, 67, 113, 450, 96, 75, 287, 430, 24, 3, 15, 434, 72,
473, 267, 112, 262, 81, 481, 504, 274, 469, 489, 56, 258, 119, 281, 418, 18,
439, 499, 446, 512, 31, 47, 454, 92, 463, 79, 124, 64, 101, 441, 480, 494, 85,
33, 44, 50, 457, 505, 58, 26, 39, 271, 254, 468, 487, 423, 10, 280, 427, 99, 6,
108, 65, 115, 452, 94, 73, 285, 432, 22)(2, 16, 435, 71, 476, 268, 109, 261, 84,
482, 501, 273, 472, 490, 53, 257, 118, 282, 419, 17, 438, 500, 447, 511, 30, 48,
455, 91, 462, 80, 121, 63, 104, 442, 477, 493, 88, 34, 41, 49, 460, 506, 59, 25,
38, 272, 255, 467, 486, 424, 11, 279, 426, 100, 7, 107, 68, 116, 449, 93, 76,
286, 429, 21, 4, 14, 433, 69, 474, 266, 111, 263, 82, 484, 503, 275, 470, 492,
55, 259, 120, 284, 417, 19, 440, 498, 445, 509, 32, 46, 453, 89, 464, 78, 123,
61, 102, 444, 479, 495, 86, 36, 43, 51, 458, 508, 57, 27, 40, 270, 253, 465,
488, 422, 9, 277, 428, 98, 5, 105, 66, 114, 451, 95, 74, 288, 431, 23)(125, 242,
231, 220, 209, 198, 187, 176, 165, 154, 143, 132, 249, 238, 227, 216, 205, 194,
183, 172, 161, 150, 139, 128, 245, 234, 223, 212, 201, 190, 179, 168, 157, 146,
135, 252, 241, 230, 219, 208, 197, 186, 175, 164, 153, 142, 131, 248, 237, 226,
215, 204, 193, 182, 171, 160, 149, 138, 127, 244, 233, 222, 211, 200, 189, 178,
167, 156, 145, 134, 251, 240, 229, 218, 207, 196, 185, 174, 163, 152, 141, 130,
247, 236, 225, 214, 203, 192, 181, 170, 159, 148, 137, 126, 243, 232, 221, 210,
199, 188, 177, 166, 155, 144, 133, 250, 239, 228, 217, 206, 195, 184, 173, 162,
151, 140, 129, 246, 235, 224, 213, 202, 191, 180, 169, 158, 147, 136)(289, 310,
331, 352, 373, 394, 415, 308, 329, 350, 371, 392, 413, 306, 327, 348, 369, 390,
411, 304, 325, 346, 367, 388, 409, 302, 323, 344, 365, 386, 407, 300, 321, 342,
363, 384, 405, 298, 319, 340, 361, 382, 403, 296, 317, 338, 359, 380, 401, 294,
315, 336, 357, 378, 399, 292, 313, 334, 355, 376, 397, 290, 311, 332, 353, 374,
395, 416, 309, 330, 351, 372, 393, 414, 307, 328, 349, 370, 391, 412, 305, 326,
347, 368, 389, 410, 303, 324, 345, 366, 387, 408, 301, 322, 343, 364, 385, 406,
299, 320, 341, 362, 383, 404, 297, 318, 339, 360, 381, 402, 295, 316, 337, 358,
379, 400, 293, 314, 335, 356, 377, 398, 291, 312, 333, 354, 375, 396) (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, 4)(5, 501)(6, 504)(7, 503)(8, 502)(9, 53)(10, 56)(11, 55)(12, 54)(13,
61)(14, 64)(15, 63)(16, 62)(17, 489)(18, 492)(19, 491)(20, 490)(21, 443)(22,
442)(23, 441)(24, 444)(25, 97)(26, 100)(27, 99)(28, 98)(29, 457)(30, 460)(31,
459)(32, 458)(33, 95)(34, 94)(35, 93)(36, 96)(37, 439)(38, 438)(39, 437)(40,
440)(41, 453)(42, 456)(43, 455)(44, 454)(45, 263)(46, 262)(47, 261)(48, 264)(49,
113)(50, 116)(51, 115)(52, 114)(57, 447)(58, 446)(59, 445)(60, 448)(65, 83)(66,
82)(67, 81)(68, 84)(69, 77)(70, 80)(71, 79)(72, 78)(73, 475)(74, 474)(75,
473)(76, 476)(85, 461)(86, 464)(87, 463)(88, 462)(89, 265)(90, 268)(91, 267)(92,
266)(101, 103)(105, 505)(106, 508)(107, 507)(108, 506)(109, 451)(110, 450)(111,
449)(112, 452)(117, 487)(118, 486)(119, 485)(120, 488)(121, 479)(122, 478)(123,
477)(124, 480)(125, 289)(126, 416)(127, 415)(128, 414)(129, 413)(130, 412)(131,
411)(132, 410)(133, 409)(134, 408)(135, 407)(136, 406)(137, 405)(138, 404)(139,
403)(140, 402)(141, 401)(142, 400)(143, 399)(144, 398)(145, 397)(146, 396)(147,
395)(148, 394)(149, 393)(150, 392)(151, 391)(152, 390)(153, 389)(154, 388)(155,
387)(156, 386)(157, 385)(158, 384)(159, 383)(160, 382)(161, 381)(162, 380)(163,
379)(164, 378)(165, 377)(166, 376)(167, 375)(168, 374)(169, 373)(170, 372)(171,
371)(172, 370)(173, 369)(174, 368)(175, 367)(176, 366)(177, 365)(178, 364)(179,
363)(180, 362)(181, 361)(182, 360)(183, 359)(184, 358)(185, 357)(186, 356)(187,
355)(188, 354)(189, 353)(190, 352)(191, 351)(192, 350)(193, 349)(194, 348)(195,
347)(196, 346)(197, 345)(198, 344)(199, 343)(200, 342)(201, 341)(202, 340)(203,
339)(204, 338)(205, 337)(206, 336)(207, 335)(208, 334)(209, 333)(210, 332)(211,
331)(212, 330)(213, 329)(214, 328)(215, 327)(216, 326)(217, 325)(218, 324)(219,
323)(220, 322)(221, 321)(222, 320)(223, 319)(224, 318)(225, 317)(226, 316)(227,
315)(228, 314)(229, 313)(230, 312)(231, 311)(232, 310)(233, 309)(234, 308)(235,
307)(236, 306)(237, 305)(238, 304)(239, 303)(240, 302)(241, 301)(242, 300)(243,
299)(244, 298)(245, 297)(246, 296)(247, 295)(248, 294)(249, 293)(250, 292)(251,
291)(252, 290)(253, 419)(254, 418)(255, 417)(256, 420)(257, 281)(258, 284)(259,
283)(260, 282)(269, 279)(270, 278)(271, 277)(272, 280)(273, 499)(274, 498)(275,
497)(276, 500)(285, 495)(286, 494)(287, 493)(288, 496)(421, 467)(422, 466)(423,
465)(424, 468)(425, 469)(426, 472)(427, 471)(428, 470)(429, 433)(430, 436)(431,
435)(432, 434)(481, 511)(482, 510)(483, 509)(484, 512)
c: (2, 4)(6, 8)(10, 12)(13, 442)(14, 443)(15, 444)(16, 441)(17, 278)(18,
279)(19, 280)(20, 277)(21, 64)(22, 61)(23, 62)(24, 63)(25, 274)(26, 275)(27,
276)(28, 273)(30, 32)(33, 268)(34, 265)(35, 266)(36, 267)(38, 40)(42, 44)(45,
116)(46, 113)(47, 114)(48, 115)(49, 262)(50, 263)(51, 264)(52, 261)(54, 56)(58,
60)(66, 68)(69, 494)(70, 495)(71, 496)(72, 493)(74, 76)(77, 286)(78, 287)(79,
288)(80, 285)(82, 84)(86, 88)(89, 94)(90, 95)(91, 96)(92, 93)(97, 498)(98,
499)(99, 500)(100, 497)(102, 104)(105, 510)(106, 511)(107, 512)(108, 509)(110,
112)(118, 120)(122, 124)(125, 320)(126, 321)(127, 322)(128, 323)(129, 324)(130,
325)(131, 326)(132, 327)(133, 328)(134, 329)(135, 330)(136, 331)(137, 332)(138,
333)(139, 334)(140, 335)(141, 336)(142, 337)(143, 338)(144, 339)(145, 340)(146,
341)(147, 342)(148, 343)(149, 344)(150, 345)(151, 346)(152, 347)(153, 348)(154,
349)(155, 350)(156, 351)(157, 352)(158, 353)(159, 354)(160, 355)(161, 356)(162,
357)(163, 358)(164, 359)(165, 360)(166, 361)(167, 362)(168, 363)(169, 364)(170,
365)(171, 366)(172, 367)(173, 368)(174, 369)(175, 370)(176, 371)(177, 372)(178,
373)(179, 374)(180, 375)(181, 376)(182, 377)(183, 378)(184, 379)(185, 380)(186,
381)(187, 382)(188, 383)(189, 384)(190, 385)(191, 386)(192, 387)(193, 388)(194,
389)(195, 390)(196, 391)(197, 392)(198, 393)(199, 394)(200, 395)(201, 396)(202,
397)(203, 398)(204, 399)(205, 400)(206, 401)(207, 402)(208, 403)(209, 404)(210,
405)(211, 406)(212, 407)(213, 408)(214, 409)(215, 410)(216, 411)(217, 412)(218,
413)(219, 414)(220, 415)(221, 416)(222, 289)(223, 290)(224, 291)(225, 292)(226,
293)(227, 294)(228, 295)(229, 296)(230, 297)(231, 298)(232, 299)(233, 300)(234,
301)(235, 302)(236, 303)(237, 304)(238, 305)(239, 306)(240, 307)(241, 308)(242,
309)(243, 310)(244, 311)(245, 312)(246, 313)(247, 314)(248, 315)(249, 316)(250,
317)(251, 318)(252, 319)(254, 256)(257, 466)(258, 467)(259, 468)(260, 465)(269,
492)(270, 489)(271, 490)(272, 491)(281, 422)(282, 423)(283, 424)(284, 421)(418,
420)(426, 428)(430, 432)(434, 436)(438, 440)(446, 448)(450, 452)(454, 456)(458,
460)(462, 464)(470, 472)(474, 476)(478, 480)(481, 508)(482, 505)(483, 506)(484,
507)(486, 488)(502, 504)
d: (1, 5)(2, 8)(3, 7)(4, 6)(9, 475)(10, 474)(11, 473)(12, 476)(13, 499)(14,
498)(15, 497)(16, 500)(17, 69)(18, 72)(19, 71)(20, 70)(21, 511)(22, 510)(23,
509)(24, 512)(26, 28)(29, 123)(30, 122)(31, 121)(32, 124)(33, 423)(34, 422)(35,
421)(36, 424)(37, 503)(38, 502)(39, 501)(40, 504)(41, 119)(42, 118)(43, 117)(44,
120)(45, 287)(46, 286)(47, 285)(48, 288)(49, 467)(50, 466)(51, 465)(52, 468)(53,
457)(54, 460)(55, 459)(56, 458)(57, 471)(58, 470)(59, 469)(60, 472)(61, 105)(62,
108)(63, 107)(64, 106)(65, 431)(66, 430)(67, 429)(68, 432)(73, 451)(74, 450)(75,
449)(76, 452)(77, 113)(78, 116)(79, 115)(80, 114)(81, 255)(82, 254)(83, 253)(84,
256)(85, 419)(86, 418)(87, 417)(88, 420)(89, 95)(90, 94)(91, 93)(92, 96)(97,
443)(98, 442)(99, 441)(100, 444)(101, 447)(102, 446)(103, 445)(104, 448)(109,
487)(110, 486)(111, 485)(112, 488)(125, 399)(126, 398)(127, 397)(128, 396)(129,
395)(130, 394)(131, 393)(132, 392)(133, 391)(134, 390)(135, 389)(136, 388)(137,
387)(138, 386)(139, 385)(140, 384)(141, 383)(142, 382)(143, 381)(144, 380)(145,
379)(146, 378)(147, 377)(148, 376)(149, 375)(150, 374)(151, 373)(152, 372)(153,
371)(154, 370)(155, 369)(156, 368)(157, 367)(158, 366)(159, 365)(160, 364)(161,
363)(162, 362)(163, 361)(164, 360)(165, 359)(166, 358)(167, 357)(168, 356)(169,
355)(170, 354)(171, 353)(172, 352)(173, 351)(174, 350)(175, 349)(176, 348)(177,
347)(178, 346)(179, 345)(180, 344)(181, 343)(182, 342)(183, 341)(184, 340)(185,
339)(186, 338)(187, 337)(188, 336)(189, 335)(190, 334)(191, 333)(192, 332)(193,
331)(194, 330)(195, 329)(196, 328)(197, 327)(198, 326)(199, 325)(200, 324)(201,
323)(202, 322)(203, 321)(204, 320)(205, 319)(206, 318)(207, 317)(208, 316)(209,
315)(210, 314)(211, 313)(212, 312)(213, 311)(214, 310)(215, 309)(216, 308)(217,
307)(218, 306)(219, 305)(220, 304)(221, 303)(222, 302)(223, 301)(224, 300)(225,
299)(226, 298)(227, 297)(228, 296)(229, 295)(230, 294)(231, 293)(232, 292)(233,
291)(234, 290)(235, 289)(236, 416)(237, 415)(238, 414)(239, 413)(240, 412)(241,
411)(242, 410)(243, 409)(244, 408)(245, 407)(246, 406)(247, 405)(248, 404)(249,
403)(250, 402)(251, 401)(252, 400)(257, 263)(258, 262)(259, 261)(260, 264)(265,
281)(266, 284)(267, 283)(268, 282)(269, 507)(270, 506)(271, 505)(272, 508)(273,
275)(277, 495)(278, 494)(279, 493)(280, 496)(425, 433)(426, 436)(427, 435)(428,
434)(437, 479)(438, 478)(439, 477)(440, 480)(453, 461)(454, 464)(455, 463)(456,
462)(481, 491)(482, 490)(483, 489)(484, 492)
e: (1, 2)(3, 4)(5, 6)(7, 8)(9, 10)(11, 12)(13, 16)(14, 15)(17, 20)(18, 19)(21,
24)(22, 23)(25, 28)(26, 27)(29, 30)(31, 32)(33, 36)(34, 35)(37, 38)(39, 40)(41,
42)(43, 44)(45, 48)(46, 47)(49, 52)(50, 51)(53, 54)(55, 56)(57, 58)(59, 60)(61,
64)(62, 63)(65, 66)(67, 68)(69, 72)(70, 71)(73, 74)(75, 76)(77, 80)(78, 79)(81,
82)(83, 84)(85, 86)(87, 88)(89, 92)(90, 91)(93, 96)(94, 95)(97, 100)(98,
99)(101, 102)(103, 104)(105, 108)(106, 107)(109, 110)(111, 112)(113, 116)(114,
115)(117, 118)(119, 120)(121, 122)(123, 124)(253, 254)(255, 256)(257, 260)(258,
259)(261, 264)(262, 263)(265, 268)(266, 267)(269, 272)(270, 271)(273, 276)(274,
275)(277, 280)(278, 279)(281, 284)(282, 283)(285, 288)(286, 287)(289, 353)(290,
354)(291, 355)(292, 356)(293, 357)(294, 358)(295, 359)(296, 360)(297, 361)(298,
362)(299, 363)(300, 364)(301, 365)(302, 366)(303, 367)(304, 368)(305, 369)(306,
370)(307, 371)(308, 372)(309, 373)(310, 374)(311, 375)(312, 376)(313, 377)(314,
378)(315, 379)(316, 380)(317, 381)(318, 382)(319, 383)(320, 384)(321, 385)(322,
386)(323, 387)(324, 388)(325, 389)(326, 390)(327, 391)(328, 392)(329, 393)(330,
394)(331, 395)(332, 396)(333, 397)(334, 398)(335, 399)(336, 400)(337, 401)(338,
402)(339, 403)(340, 404)(341, 405)(342, 406)(343, 407)(344, 408)(345, 409)(346,
410)(347, 411)(348, 412)(349, 413)(350, 414)(351, 415)(352, 416)(417, 418)(419,
420)(421, 424)(422, 423)(425, 426)(427, 428)(429, 430)(431, 432)(433, 434)(435,
436)(437, 438)(439, 440)(441, 444)(442, 443)(445, 446)(447, 448)(449, 450)(451,
452)(453, 454)(455, 456)(457, 458)(459, 460)(461, 462)(463, 464)(465, 468)(466,
467)(469, 470)(471, 472)(473, 474)(475, 476)(477, 478)(479, 480)(481, 484)(482,
483)(485, 486)(487, 488)(489, 492)(490, 491)(493, 496)(494, 495)(497, 500)(498,
499)(501, 502)(503, 504)(505, 508)(506, 507)(509, 512)(510, 511)
C4[ 512, 53 ]
512
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0