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