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