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On this page are computer-accessible forms for the graph C4[ 324, 24 ] =
UG(ATD[324,1]).
(I) Following is a form readable by MAGMA:
g:=Graph<324|{ {48, 49}, {50, 51}, {58, 59}, {90, 91}, {105, 107}, {1, 2}, {16,
19}, {1, 4}, {3, 6}, {72, 78}, {129, 135}, {2, 5}, {313, 318}, {153, 158}, {27,
28}, {34, 37}, {225, 230}, {256, 263}, {2, 10}, {149, 157}, {116, 124}, {3, 11},
{4, 12}, {5, 13}, {6, 14}, {7, 15}, {52, 60}, {224, 232}, {259, 266}, {38, 44},
{150, 156}, {39, 45}, {71, 77}, {83, 89}, {53, 62}, {291, 296}, {66, 73}, {226,
233}, {19, 31}, {293, 297}, {290, 302}, {147, 159}, {118, 122}, {85, 89}, {260,
264}, {32, 46}, {113, 127}, {261, 267}, {82, 93}, {304, 319}, {119, 120}, {65,
81}, {302, 318}, {70, 87}, {108, 125}, {106, 123}, {258, 272}, {43, 56}, {8,
28}, {290, 310}, {9, 29}, {10, 30}, {11, 31}, {106, 126}, {298, 319}, {33, 55},
{289, 311}, {8, 16}, {166, 190}, {9, 17}, {64, 88}, {96, 122}, {291, 313}, {15,
20}, {67, 88}, {4, 24}, {294, 314}, {292, 312}, {110, 114}, {5, 25}, {6, 26},
{7, 27}, {259, 286}, {288, 317}, {103, 121}, {109, 115}, {107, 117}, {258, 284},
{47, 48}, {256, 287}, {12, 44}, {153, 185}, {140, 172}, {31, 63}, {78, 110},
{207, 239}, {223, 255}, {274, 306}, {11, 42}, {154, 187}, {143, 174}, {68, 101},
{221, 252}, {277, 308}, {138, 168}, {151, 181}, {266, 296}, {267, 297}, {270,
300}, {271, 301}, {279, 309}, {196, 231}, {200, 235}, {222, 253}, {262, 293},
{280, 315}, {287, 316}, {212, 240}, {260, 288}, {274, 310}, {275, 311}, {28,
57}, {147, 182}, {145, 180}, {136, 173}, {130, 167}, {128, 165}, {69, 96}, {76,
105}, {91, 126}, {193, 228}, {195, 230}, {201, 236}, {203, 238}, {210, 247},
{215, 242}, {272, 309}, {278, 307}, {281, 316}, {24, 62}, {25, 63}, {65, 103},
{208, 246}, {216, 254}, {268, 298}, {269, 299}, {129, 166}, {141, 170}, {194,
229}, {202, 237}, {214, 241}, {220, 251}, {257, 294}, {261, 290}, {264, 303},
{282, 317}, {284, 315}, {16, 56}, {148, 188}, {17, 57}, {18, 58}, {209, 249},
{21, 60}, {150, 191}, {24, 49}, {86, 127}, {281, 304}, {23, 61}, {144, 186},
{133, 175}, {66, 104}, {75, 97}, {80, 122}, {81, 123}, {84, 126}, {211, 248},
{282, 305}, {12, 32}, {13, 33}, {14, 34}, {67, 111}, {132, 169}, {149, 184},
{134, 171}, {197, 232}, {199, 234}, {277, 312}, {279, 314}, {82, 124}, {83,
125}, {89, 119}, {265, 295}, {20, 59}, {152, 183}, {146, 189}, {25, 54}, {192,
239}, {198, 233}, {208, 255}, {213, 250}, {278, 313}, {30, 46}, {151, 167},
{148, 164}, {143, 191}, {142, 190}, {141, 189}, {140, 188}, {139, 187}, {138,
186}, {137, 185}, {136, 184}, {135, 183}, {134, 182}, {133, 181}, {132, 180},
{220, 236}, {130, 179}, {146, 163}, {193, 240}, {195, 242}, {197, 244}, {199,
246}, {201, 248}, {203, 250}, {205, 252}, {207, 254}, {218, 235}, {223, 238},
{283, 298}, {284, 301}, {20, 38}, {144, 162}, {128, 178}, {21, 39}, {77, 127},
{216, 234}, {16, 35}, {194, 241}, {198, 245}, {202, 249}, {206, 253}, {287,
300}, {68, 112}, {145, 165}, {69, 113}, {70, 114}, {71, 115}, {76, 120}, {86,
98}, {217, 237}, {17, 36}, {79, 121}, {285, 299}, {18, 37}, {135, 176}, {196,
243}, {204, 251}, {13, 53}, {152, 160}, {137, 177}, {14, 54}, {15, 55}, {221,
229}, {139, 178}, {205, 244}, {265, 304}, {286, 295}, {222, 228}, {270, 308},
{22, 45}, {154, 161}, {87, 108}, {206, 245}, {266, 305}, {64, 124}, {72, 116},
{73, 117}, {74, 118}, {75, 119}, {219, 231}, {142, 179}, {155, 166}, {10, 52},
{22, 40}, {23, 41}, {268, 306}, {269, 307}, {272, 302}, {273, 303}, {200, 247},
{204, 243}, {37, 96}, {39, 98}, {38, 97}, {30, 87}, {41, 99}, {46, 100}, {29,
80}, {27, 84}, {159, 208}, {176, 224}, {177, 225}, {178, 226}, {179, 227}, {60,
109}, {158, 207}, {156, 205}, {53, 103}, {56, 106}, {57, 107}, {63, 109}, {61,
110}, {157, 206}, {181, 225}, {48, 101}, {51, 102}, {57, 111}, {59, 108}, {155,
204}, {59, 99}, {26, 64}, {184, 226}, {185, 227}, {61, 102}, {159, 196}, {155,
192}, {31, 67}, {56, 100}, {28, 65}, {158, 195}, {156, 193}, {26, 68}, {54,
104}, {55, 105}, {29, 66}, {157, 194}, {191, 224}, {50, 82}, {51, 83}, {60, 92},
{46, 79}, {48, 81}, {173, 204}, {187, 218}, {178, 208}, {179, 209}, {40, 75},
{188, 223}, {189, 222}, {32, 68}, {33, 69}, {34, 70}, {35, 71}, {41, 76}, {162,
199}, {160, 197}, {43, 78}, {190, 219}, {168, 206}, {169, 207}, {186, 220}, {42,
77}, {161, 198}, {176, 215}, {54, 95}, {62, 87}, {180, 221}, {40, 67}, {163,
200}, {53, 94}, {36, 72}, {167, 203}, {39, 74}, {301, 320}, {164, 201}, {44,
65}, {52, 89}, {182, 216}, {183, 217}, {38, 73}, {302, 321}, {165, 202}, {45,
66}, {63, 79}, {308, 324}, {167, 215}, {168, 216}, {169, 217}, {170, 218}, {171,
219}, {172, 220}, {173, 221}, {174, 222}, {175, 223}, {187, 203}, {160, 209},
{306, 323}, {305, 320}, {164, 213}, {162, 211}, {184, 201}, {304, 322}, {161,
210}, {165, 214}, {180, 199}, {183, 196}, {308, 321}, {35, 85}, {163, 212}, {42,
82}, {315, 323}, {190, 198}, {170, 211}, {317, 324}, {188, 197}, {36, 95}, {313,
322}, {174, 213}, {175, 212}, {185, 194}, {186, 193}, {177, 205}, {33, 92}, {35,
94}, {41, 84}, {171, 214}, {172, 210}, {182, 200}, {189, 195}, {34, 93}, {47,
80}, {49, 78}, {181, 202}, {191, 192}, {58, 131}, {1, 192}, {69, 132}, {71,
134}, {73, 136}, {70, 133}, {74, 137}, {79, 139}, {76, 138}, {74, 131}, {123,
176}, {92, 144}, {125, 177}, {93, 145}, {94, 146}, {95, 147}, {107, 166}, {72,
135}, {80, 129}, {91, 143}, {92, 136}, {93, 137}, {94, 138}, {88, 142}, {121,
175}, {120, 174}, {118, 160}, {88, 128}, {123, 163}, {91, 130}, {125, 164},
{120, 161}, {117, 172}, {115, 170}, {113, 168}, {90, 129}, {121, 162}, {118,
173}, {114, 169}, {95, 132}, {81, 140}, {83, 141}, {116, 171}, {101, 133}, {7,
230}, {1, 227}, {119, 149}, {112, 148}, {127, 153}, {3, 228}, {104, 128}, {100,
141}, {111, 134}, {102, 143}, {97, 139}, {117, 159}, {116, 158}, {113, 155},
{124, 151}, {98, 142}, {122, 150}, {114, 156}, {115, 157}, {99, 140}, {104,
152}, {106, 154}, {4, 245}, {112, 130}, {100, 151}, {112, 131}, {103, 147}, {97,
148}, {111, 154}, {99, 150}, {7, 241}, {98, 149}, {108, 144}, {110, 146}, {109,
145}, {101, 152}, {102, 153}, {9, 264}, {18, 275}, {3, 257}, {42, 296}, {55,
309}, {44, 303}, {64, 323}, {2, 262}, {47, 299}, {40, 301}, {50, 311}, {19,
276}, {22, 273}, {43, 300}, {19, 283}, {22, 286}, {49, 312}, {77, 324}, {32,
298}, {8, 263}, {12, 285}, {58, 299}, {11, 280}, {52, 295}, {27, 271}, {86,
320}, {62, 297}, {18, 267}, {43, 306}, {47, 310}, {90, 323}, {10, 276}, {45,
307}, {50, 300}, {24, 263}, {37, 314}, {96, 321}, {5, 294}, {6, 289}, {8, 288},
{29, 309}, {26, 307}, {30, 311}, {105, 320}, {15, 293}, {17, 315}, {23, 316},
{9, 292}, {21, 314}, {13, 317}, {20, 295}, {14, 312}, {25, 303}, {21, 296}, {23,
297}, {126, 319}, {36, 324}, {84, 310}, {85, 305}, {90, 318}, {86, 318}, {85,
316}, {51, 322}, {75, 319}, {61, 321}, {131, 322}, {209, 256}, {211, 258}, {213,
260}, {215, 262}, {210, 257}, {214, 261}, {244, 288}, {245, 289}, {246, 290},
{247, 291}, {212, 259}, {253, 292}, {217, 259}, {251, 289}, {248, 292}, {249,
293}, {250, 294}, {255, 291}, {219, 262}, {218, 261}, {224, 257}, {226, 256},
{229, 263}, {232, 266}, {233, 267}, {236, 270}, {237, 271}, {225, 258}, {249,
282}, {254, 285}, {247, 275}, {242, 279}, {234, 268}, {235, 269}, {240, 278},
{227, 260}, {243, 276}, {252, 283}, {248, 274}, {240, 284}, {241, 285}, {242,
286}, {243, 287}, {244, 280}, {230, 264}, {231, 265}, {246, 281}, {250, 277},
{253, 269}, {255, 270}, {252, 271}, {231, 275}, {236, 280}, {237, 281}, {238,
282}, {239, 283}, {228, 273}, {229, 274}, {251, 268}, {254, 265}, {232, 276},
{233, 277}, {234, 278}, {235, 279}, {238, 272}, {239, 273} }>;
(II) A more general form is to represent the graph as the orbit of {48, 49}
under the group generated by the following permutations:
a: (2, 4)(3, 7)(5, 12)(6, 15)(8, 19)(9, 22)(10, 24)(11, 27)(13, 32)(14, 20)(17,
40)(21, 47)(23, 50)(25, 44)(26, 55)(28, 31)(29, 45)(30, 62)(33, 68)(34, 59)(35,
56)(36, 75)(37, 58)(38, 54)(39, 80)(41, 82)(42, 84)(43, 85)(46, 53)(48, 60)(49,
52)(51, 61)(57, 67)(63, 65)(64, 105)(69, 112)(70, 108)(71, 106)(72, 119)(73,
104)(74, 122)(76, 124)(77, 126)(78, 89)(79, 103)(81, 109)(83, 110)(86, 90)(88,
107)(91, 127)(92, 101)(93, 99)(94, 100)(95, 97)(96, 131)(98, 129)(113, 130)(114,
125)(115, 123)(116, 120)(117, 128)(132, 148)(133, 144)(134, 154)(135, 149)(136,
152)(137, 150)(138, 151)(139, 147)(140, 145)(141, 146)(142, 166)(143, 153)(155,
179)(156, 177)(157, 176)(158, 174)(159, 178)(160, 173)(161, 171)(162, 175)(163,
170)(164, 169)(165, 172)(167, 168)(180, 188)(181, 186)(182, 187)(183, 184)(185,
191)(192, 227)(193, 225)(194, 224)(195, 222)(196, 226)(197, 221)(198, 219)(199,
223)(200, 218)(201, 217)(202, 220)(203, 216)(204, 209)(206, 215)(207, 213)(210,
214)(211, 212)(228, 230)(229, 232)(231, 233)(234, 238)(236, 237)(239, 260)(240,
258)(241, 257)(242, 253)(243, 256)(244, 252)(245, 262)(246, 255)(247, 261)(248,
259)(249, 251)(250, 254)(263, 276)(264, 273)(265, 277)(266, 274)(267, 275)(268,
282)(269, 279)(270, 281)(271, 280)(272, 278)(283, 288)(285, 294)(286, 292)(289,
293)(290, 291)(295, 312)(296, 310)(297, 311)(298, 317)(299, 314)(300, 316)(301,
315)(302, 313)(304, 308)(305, 306)(307, 309)(319, 324)(320, 323)(321, 322) (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, 5, 13, 33, 69, 113, 155, 192)(3, 8, 20, 34, 71, 117, 156, 194, 231)(4,
10, 25, 53, 92, 132, 168, 204, 239)(6, 16, 38, 70, 115, 159, 193, 229, 265)(7,
18, 42, 57, 99, 137, 171, 210, 244)(9, 23, 39, 72, 120, 160, 195, 233, 266)(11,
28, 59, 93, 134, 172, 205, 241, 275)(12, 30, 63, 103, 144, 180, 216, 251,
283)(14, 35, 73, 114, 157, 196, 228, 263, 295)(15, 37, 77, 107, 150, 185, 219,
257, 288)(17, 41, 74, 116, 161, 197, 230, 267, 296)(19, 44, 87, 109, 147, 186,
221, 254, 289)(21, 36, 76, 118, 158, 198, 232, 264, 297)(22, 49, 89, 104, 146,
184, 217, 253, 287)(24, 52, 54, 94, 136, 169, 206, 243, 273)(26, 56, 97, 133,
170, 208, 240, 274, 304)(27, 58, 82, 111, 140, 177, 214, 247, 280)(29, 61, 98,
135, 174, 209, 242, 277, 305)(31, 65, 108, 145, 182, 220, 252, 285, 311)(32, 46,
79, 121, 162, 199, 234, 268, 298)(40, 48, 83, 128, 163, 201, 237, 269, 300)(43,
75, 101, 141, 178, 212, 248, 281, 307)(45, 78, 119, 152, 189, 226, 259, 292,
316)(47, 51, 88, 123, 164, 202, 235, 270, 301)(50, 67, 81, 125, 165, 200, 236,
271, 299)(55, 96, 127, 166, 191, 227, 262, 294, 317)(60, 95, 138, 173, 207, 245,
276, 303, 62)(64, 106, 148, 181, 218, 255, 284, 310, 322)(66, 110, 149, 183,
222, 256, 286, 312, 85)(68, 100, 139, 175, 211, 246, 278, 306, 319)(80, 102,
142, 176, 213, 249, 279, 308, 320)(84, 131, 124, 154, 188, 225, 261, 291,
315)(86, 129, 143, 179, 215, 250, 282, 309, 321)(90, 91, 130, 167, 203, 238,
272, 302, 318)(105, 122, 153, 190, 224, 260, 293, 314, 324)(112, 151, 187, 223,
258, 290, 313, 323, 126)
C4[ 324, 24 ]
324
-1 2 4 192 227
-2 1 5 262 10
-3 11 257 6 228
-4 1 12 24 245
-5 2 13 25 294
-6 3 14 289 26
-7 15 27 230 241
-8 288 16 28 263
-9 264 17 292 29
-10 276 2 30 52
-11 3 280 31 42
-12 44 4 32 285
-13 33 5 53 317
-14 34 312 6 54
-15 55 7 293 20
-16 56 35 8 19
-17 57 36 315 9
-18 275 58 267 37
-19 276 16 283 31
-20 15 59 38 295
-21 60 39 314 296
-22 286 45 40 273
-23 297 61 41 316
-24 4 49 62 263
-25 5 303 63 54
-26 68 6 64 307
-27 28 7 84 271
-28 57 27 8 65
-29 66 309 80 9
-30 46 311 10 87
-31 11 67 19 63
-32 12 298 46 68
-33 55 13 69 92
-34 14 37 70 93
-35 16 71 94 85
-36 324 17 72 95
-37 34 314 18 96
-38 44 73 20 97
-39 45 74 21 98
-40 22 67 301 75
-41 99 23 84 76
-42 11 77 82 296
-43 56 78 300 306
-44 12 38 303 65
-45 22 66 39 307
-46 100 79 30 32
-47 299 310 80 48
-48 101 47 81 49
-49 78 24 48 312
-50 300 311 82 51
-51 102 322 50 83
-52 89 60 295 10
-53 13 103 94 62
-54 14 25 104 95
-55 33 309 15 105
-56 100 16 106 43
-57 111 17 28 107
-58 299 59 18 131
-59 99 58 20 108
-60 92 52 21 109
-61 110 23 321 102
-62 297 24 53 87
-63 79 25 31 109
-64 88 124 26 323
-65 44 81 103 28
-66 45 104 29 73
-67 88 111 40 31
-68 101 112 26 32
-69 33 132 113 96
-70 34 133 114 87
-71 77 35 134 115
-72 78 36 135 116
-73 66 136 38 117
-74 137 39 118 131
-75 319 40 97 119
-76 105 138 41 120
-77 71 324 127 42
-78 110 49 72 43
-79 121 46 139 63
-80 122 47 29 129
-81 123 48 140 65
-82 124 93 50 42
-83 89 125 51 141
-84 310 27 126 41
-85 89 35 305 316
-86 320 127 98 318
-87 70 62 30 108
-88 67 128 64 142
-89 83 52 85 119
-90 91 323 129 318
-91 143 90 126 130
-92 33 144 136 60
-93 34 145 82 137
-94 35 146 138 53
-95 132 36 147 54
-96 122 321 69 37
-97 38 148 139 75
-98 39 149 86 142
-99 59 150 41 140
-100 56 46 151 141
-101 133 68 48 152
-102 143 61 51 153
-103 121 147 53 65
-104 66 128 152 54
-105 55 320 107 76
-106 154 56 123 126
-107 166 57 105 117
-108 144 59 125 87
-109 145 60 115 63
-110 78 146 114 61
-111 154 67 57 134
-112 68 148 130 131
-113 155 69 168 127
-114 110 156 70 169
-115 157 71 170 109
-116 124 158 72 171
-117 159 73 172 107
-118 122 160 74 173
-119 89 149 75 120
-120 161 119 174 76
-121 79 103 162 175
-122 80 150 96 118
-123 176 81 106 163
-124 82 116 151 64
-125 177 83 108 164
-126 319 91 84 106
-127 77 113 86 153
-128 88 165 178 104
-129 166 90 80 135
-130 112 167 91 179
-131 112 58 322 74
-132 69 169 180 95
-133 101 70 181 175
-134 111 71 171 182
-135 176 72 183 129
-136 92 73 173 184
-137 177 93 74 185
-138 168 94 76 186
-139 187 79 178 97
-140 99 188 81 172
-141 100 189 170 83
-142 88 179 190 98
-143 91 102 191 174
-144 92 162 108 186
-145 165 180 93 109
-146 110 189 94 163
-147 103 159 182 95
-148 188 112 97 164
-149 157 184 119 98
-150 99 122 156 191
-151 100 167 124 181
-152 101 104 160 183
-153 102 158 127 185
-154 187 111 106 161
-155 166 113 192 204
-156 114 193 150 205
-157 115 149 194 206
-158 116 195 207 153
-159 147 117 196 208
-160 209 118 152 197
-161 154 198 210 120
-162 121 144 199 211
-163 123 200 146 212
-164 201 125 213 148
-165 145 202 214 128
-166 155 190 107 129
-167 203 215 151 130
-168 113 138 216 206
-169 132 114 217 207
-170 211 115 141 218
-171 134 214 116 219
-172 220 210 117 140
-173 221 136 204 118
-174 143 222 213 120
-175 121 133 212 223
-176 123 135 224 215
-177 125 137 225 205
-178 226 128 139 208
-179 209 227 130 142
-180 132 199 221 145
-181 133 202 225 151
-182 134 200 147 216
-183 135 217 152 196
-184 201 136 149 226
-185 137 194 227 153
-186 220 144 138 193
-187 154 203 139 218
-188 223 148 140 197
-189 222 146 195 141
-190 198 166 142 219
-191 143 224 192 150
-192 1 155 191 239
-193 156 228 240 186
-194 157 185 229 241
-195 242 189 158 230
-196 231 243 159 183
-197 188 232 244 160
-198 233 190 245 161
-199 234 180 246 162
-200 235 247 182 163
-201 236 248 184 164
-202 165 181 237 249
-203 187 167 238 250
-204 155 243 173 251
-205 177 156 244 252
-206 253 157 168 245
-207 254 158 169 239
-208 178 255 246 159
-209 179 256 160 249
-210 257 247 161 172
-211 170 258 248 162
-212 259 163 240 175
-213 260 250 174 164
-214 165 171 261 241
-215 176 242 167 262
-216 254 168 234 182
-217 169 237 259 183
-218 187 235 170 261
-219 231 190 171 262
-220 236 172 251 186
-221 180 173 229 252
-222 253 189 228 174
-223 188 255 238 175
-224 176 232 191 257
-225 177 181 258 230
-226 178 233 256 184
-227 1 179 260 185
-228 222 3 193 273
-229 221 194 263 274
-230 264 225 7 195
-231 275 265 196 219
-232 276 266 224 197
-233 198 277 267 226
-234 199 278 268 216
-235 200 279 269 218
-236 220 201 280 270
-237 202 281 271 217
-238 223 203 282 272
-239 192 283 207 273
-240 212 278 193 284
-241 214 7 194 285
-242 286 279 215 195
-243 276 287 204 196
-244 288 280 205 197
-245 198 289 4 206
-246 199 290 281 208
-247 275 210 200 291
-248 211 201 292 274
-249 209 202 282 293
-250 277 213 203 294
-251 220 289 268 204
-252 221 205 271 283
-253 222 269 292 206
-254 265 216 207 285
-255 223 291 270 208
-256 209 287 226 263
-257 210 3 224 294
-258 211 225 272 284
-259 286 266 212 217
-260 264 288 213 227
-261 267 290 214 218
-262 2 215 293 219
-263 24 256 8 229
-264 303 260 9 230
-265 231 254 304 295
-266 232 259 305 296
-267 297 233 18 261
-268 298 234 251 306
-269 253 299 235 307
-270 308 255 300 236
-271 301 27 237 252
-272 309 258 302 238
-273 22 303 228 239
-274 310 248 229 306
-275 231 311 247 18
-276 232 243 19 10
-277 308 233 312 250
-278 234 313 240 307
-279 242 309 235 314
-280 11 244 236 315
-281 246 237 304 316
-282 238 249 305 317
-283 298 19 239 252
-284 301 258 315 240
-285 12 254 299 241
-286 22 242 259 295
-287 243 256 300 316
-288 244 260 8 317
-289 245 311 6 251
-290 310 246 302 261
-291 255 247 313 296
-292 253 312 248 9
-293 297 15 249 262
-294 257 5 314 250
-295 286 265 52 20
-296 266 291 42 21
-297 23 267 62 293
-298 319 268 283 32
-299 47 58 269 285
-300 287 50 270 43
-301 320 40 271 284
-302 321 290 272 318
-303 44 264 25 273
-304 319 265 322 281
-305 320 266 282 85
-306 268 323 43 274
-307 45 278 26 269
-308 277 321 324 270
-309 55 279 29 272
-310 47 290 84 274
-311 275 289 50 30
-312 277 14 49 292
-313 278 322 291 318
-314 37 279 294 21
-315 323 280 17 284
-316 23 287 281 85
-317 13 288 324 282
-318 90 302 313 86
-319 298 126 304 75
-320 301 105 305 86
-321 308 302 61 96
-322 313 51 304 131
-323 90 315 64 306
-324 77 308 36 317
0