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