Graph forms
for C4 [ 297, 1 ] = C_297(1,109)
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On this page are computer-accessible forms for the graph C4[ 297, 1 ] =
C_297(1,109).
(I) Following is a form readable by MAGMA:
g:=Graph<297|{ {2, 3}, {296, 297}, {294, 295}, {292, 293}, {290, 291}, {288,
289}, {286, 287}, {284, 285}, {282, 283}, {280, 281}, {278, 279}, {276, 277},
{274, 275}, {272, 273}, {270, 271}, {268, 269}, {266, 267}, {264, 265}, {262,
263}, {260, 261}, {258, 259}, {256, 257}, {254, 255}, {252, 253}, {250, 251},
{248, 249}, {246, 247}, {244, 245}, {242, 243}, {240, 241}, {238, 239}, {236,
237}, {234, 235}, {232, 233}, {230, 231}, {228, 229}, {226, 227}, {224, 225},
{222, 223}, {220, 221}, {218, 219}, {216, 217}, {214, 215}, {212, 213}, {210,
211}, {208, 209}, {206, 207}, {204, 205}, {202, 203}, {200, 201}, {198, 199},
{196, 197}, {194, 195}, {192, 193}, {190, 191}, {188, 189}, {186, 187}, {184,
185}, {182, 183}, {180, 181}, {178, 179}, {90, 91}, {88, 89}, {86, 87}, {84,
85}, {82, 83}, {80, 81}, {78, 79}, {76, 77}, {74, 75}, {72, 73}, {70, 71}, {68,
69}, {66, 67}, {64, 65}, {62, 63}, {60, 61}, {58, 59}, {56, 57}, {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},
{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}, {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}, {1, 2}, {293, 294}, {289, 290}, {285,
286}, {281, 282}, {277, 278}, {273, 274}, {269, 270}, {265, 266}, {261, 262},
{257, 258}, {253, 254}, {249, 250}, {245, 246}, {241, 242}, {237, 238}, {233,
234}, {229, 230}, {225, 226}, {221, 222}, {217, 218}, {213, 214}, {209, 210},
{205, 206}, {201, 202}, {197, 198}, {193, 194}, {189, 190}, {185, 186}, {181,
182}, {177, 178}, {89, 90}, {85, 86}, {81, 82}, {77, 78}, {73, 74}, {69, 70},
{65, 66}, {61, 62}, {57, 58}, {5, 6}, {9, 10}, {13, 14}, {17, 18}, {21, 22},
{25, 26}, {29, 30}, {33, 34}, {37, 38}, {41, 42}, {45, 46}, {49, 50}, {53, 54},
{93, 94}, {97, 98}, {101, 102}, {105, 106}, {109, 110}, {113, 114}, {117, 118},
{121, 122}, {125, 126}, {129, 130}, {133, 134}, {137, 138}, {141, 142}, {145,
146}, {149, 150}, {153, 154}, {157, 158}, {161, 162}, {165, 166}, {169, 170},
{173, 174}, {3, 4}, {291, 292}, {283, 284}, {275, 276}, {267, 268}, {259, 260},
{251, 252}, {243, 244}, {235, 236}, {227, 228}, {219, 220}, {211, 212}, {203,
204}, {195, 196}, {187, 188}, {179, 180}, {83, 84}, {75, 76}, {67, 68}, {59,
60}, {11, 12}, {19, 20}, {27, 28}, {35, 36}, {43, 44}, {51, 52}, {91, 92}, {99,
100}, {107, 108}, {115, 116}, {123, 124}, {131, 132}, {139, 140}, {147, 148},
{155, 156}, {163, 164}, {171, 172}, {7, 8}, {295, 296}, {279, 280}, {263, 264},
{247, 248}, {231, 232}, {215, 216}, {199, 200}, {183, 184}, {87, 88}, {71, 72},
{55, 56}, {23, 24}, {39, 40}, {103, 104}, {119, 120}, {135, 136}, {151, 152},
{167, 168}, {15, 16}, {271, 272}, {239, 240}, {207, 208}, {79, 80}, {47, 48},
{111, 112}, {143, 144}, {175, 176}, {31, 32}, {287, 288}, {223, 224}, {95, 96},
{159, 160}, {2, 111}, {16, 125}, {18, 127}, {128, 237}, {130, 239}, {144, 253},
{146, 255}, {1, 110}, {17, 126}, {129, 238}, {145, 254}, {3, 112}, {7, 116},
{11, 120}, {15, 124}, {131, 240}, {135, 244}, {139, 248}, {143, 252}, {4, 113},
{6, 115}, {12, 121}, {14, 123}, {132, 241}, {134, 243}, {140, 249}, {142, 251},
{5, 114}, {13, 122}, {133, 242}, {141, 250}, {8, 117}, {10, 119}, {136, 245},
{138, 247}, {9, 118}, {191, 192}, {63, 64}, {137, 246}, {19, 128}, {87, 196},
{83, 192}, {63, 172}, {59, 168}, {55, 164}, {23, 132}, {27, 136}, {31, 140},
{51, 160}, {91, 200}, {95, 204}, {115, 224}, {119, 228}, {123, 232}, {127, 236},
{20, 129}, {86, 195}, {84, 193}, {62, 171}, {60, 169}, {54, 163}, {22, 131},
{28, 137}, {30, 139}, {52, 161}, {92, 201}, {94, 203}, {116, 225}, {118, 227},
{124, 233}, {126, 235}, {21, 130}, {85, 194}, {61, 170}, {29, 138}, {53, 162},
{93, 202}, {117, 226}, {125, 234}, {24, 133}, {90, 199}, {88, 197}, {58, 167},
{56, 165}, {26, 135}, {120, 229}, {122, 231}, {25, 134}, {89, 198}, {57, 166},
{121, 230}, {32, 141}, {34, 143}, {48, 157}, {50, 159}, {96, 205}, {98, 207},
{112, 221}, {114, 223}, {33, 142}, {49, 158}, {97, 206}, {113, 222}, {35, 144},
{39, 148}, {43, 152}, {47, 156}, {99, 208}, {103, 212}, {107, 216}, {111, 220},
{36, 145}, {38, 147}, {44, 153}, {46, 155}, {100, 209}, {102, 211}, {108, 217},
{110, 219}, {37, 146}, {45, 154}, {101, 210}, {109, 218}, {1, 189}, {67, 255},
{66, 254}, {65, 253}, {64, 252}, {2, 190}, {3, 191}, {40, 149}, {42, 151}, {104,
213}, {106, 215}, {41, 150}, {105, 214}, {4, 192}, {63, 251}, {62, 250}, {61,
249}, {60, 248}, {55, 243}, {54, 242}, {5, 193}, {6, 194}, {7, 195}, {12, 200},
{13, 201}, {14, 202}, {15, 203}, {20, 208}, {21, 209}, {22, 210}, {23, 211},
{28, 216}, {29, 217}, {30, 218}, {31, 219}, {36, 224}, {37, 225}, {38, 226},
{39, 227}, {44, 232}, {45, 233}, {46, 234}, {47, 235}, {52, 240}, {53, 241}, {8,
196}, {59, 247}, {58, 246}, {57, 245}, {56, 244}, {9, 197}, {10, 198}, {11,
199}, {24, 212}, {25, 213}, {26, 214}, {27, 215}, {40, 228}, {41, 229}, {42,
230}, {43, 231}, {16, 204}, {17, 205}, {18, 206}, {19, 207}, {48, 236}, {49,
237}, {50, 238}, {51, 239}, {64, 173}, {82, 191}, {80, 189}, {66, 175}, {65,
174}, {81, 190}, {67, 176}, {79, 188}, {75, 184}, {71, 180}, {68, 177}, {78,
187}, {76, 185}, {70, 179}, {69, 178}, {77, 186}, {32, 220}, {33, 221}, {34,
222}, {35, 223}, {72, 181}, {74, 183}, {73, 182}, {127, 128}, {1, 297}, {68,
256}, {87, 275}, {86, 274}, {85, 273}, {84, 272}, {79, 267}, {78, 266}, {77,
265}, {76, 264}, {71, 259}, {70, 258}, {69, 257}, {92, 280}, {93, 281}, {94,
282}, {95, 283}, {100, 288}, {101, 289}, {102, 290}, {103, 291}, {108, 296},
{109, 297}, {72, 260}, {90, 278}, {89, 277}, {88, 276}, {75, 263}, {74, 262},
{73, 261}, {91, 279}, {104, 292}, {105, 293}, {106, 294}, {107, 295}, {80, 268},
{83, 271}, {82, 270}, {81, 269}, {96, 284}, {97, 285}, {98, 286}, {99, 287},
{147, 256}, {187, 296}, {183, 292}, {179, 288}, {151, 260}, {155, 264}, {159,
268}, {148, 257}, {188, 297}, {182, 291}, {180, 289}, {150, 259}, {156, 265},
{158, 267}, {149, 258}, {181, 290}, {157, 266}, {152, 261}, {186, 295}, {184,
293}, {154, 263}, {153, 262}, {185, 294}, {160, 269}, {178, 287}, {176, 285},
{162, 271}, {161, 270}, {177, 286}, {163, 272}, {167, 276}, {171, 280}, {175,
284}, {164, 273}, {166, 275}, {172, 281}, {174, 283}, {165, 274}, {173, 282},
{168, 277}, {170, 279}, {169, 278}, {255, 256} }>;
(II) A more general form is to represent the graph as the orbit of {2, 3}
under the group generated by the following permutations:
a: (2, 110)(3, 219)(4, 31)(5, 140)(6, 249)(7, 61)(8, 170)(9, 279)(10, 91)(11,
200)(13, 121)(14, 230)(15, 42)(16, 151)(17, 260)(18, 72)(19, 181)(20, 290)(21,
102)(22, 211)(24, 132)(25, 241)(26, 53)(27, 162)(28, 271)(29, 83)(30, 192)(32,
113)(33, 222)(35, 143)(36, 252)(37, 64)(38, 173)(39, 282)(40, 94)(41, 203)(43,
124)(44, 233)(46, 154)(47, 263)(48, 75)(49, 184)(50, 293)(51, 105)(52, 214)(54,
135)(55, 244)(57, 165)(58, 274)(59, 86)(60, 195)(62, 116)(63, 225)(65, 146)(66,
255)(68, 176)(69, 285)(70, 97)(71, 206)(73, 127)(74, 236)(76, 157)(77, 266)(79,
187)(80, 296)(81, 108)(82, 217)(84, 138)(85, 247)(87, 168)(88, 277)(90, 198)(92,
119)(93, 228)(95, 149)(96, 258)(98, 179)(99, 288)(101, 209)(103, 130)(104,
239)(106, 160)(107, 269)(109, 190)(112, 220)(114, 141)(115, 250)(117, 171)(118,
280)(120, 201)(123, 231)(125, 152)(126, 261)(128, 182)(129, 291)(131, 212)(134,
242)(136, 163)(137, 272)(139, 193)(142, 223)(145, 253)(147, 174)(148, 283)(150,
204)(153, 234)(156, 264)(158, 185)(159, 294)(161, 215)(164, 245)(167, 275)(169,
196)(172, 226)(175, 256)(178, 286)(180, 207)(183, 237)(186, 267)(189, 297)(191,
218)(194, 248)(197, 278)(202, 229)(205, 259)(208, 289)(213, 240)(216, 270)(224,
251)(227, 281)(235, 262)(238, 292)(246, 273)(257, 284)(268, 295) (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, 58, 59, 60, 61,
62, 63, 64, 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, 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, 194, 195, 196,
197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212,
213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 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)
c: (2, 189)(3, 80)(4, 268)(5, 159)(6, 50)(7, 238)(8, 129)(9, 20)(10, 208)(11,
99)(12, 287)(13, 178)(14, 69)(15, 257)(16, 148)(17, 39)(18, 227)(19, 118)(21,
197)(22, 88)(23, 276)(24, 167)(25, 58)(26, 246)(27, 137)(29, 216)(30, 107)(31,
295)(32, 186)(33, 77)(34, 265)(35, 156)(36, 47)(37, 235)(38, 126)(40, 205)(41,
96)(42, 284)(43, 175)(44, 66)(45, 254)(46, 145)(48, 224)(49, 115)(51, 194)(52,
85)(53, 273)(54, 164)(56, 243)(57, 134)(59, 213)(60, 104)(61, 292)(62, 183)(63,
74)(64, 262)(65, 153)(67, 232)(68, 123)(70, 202)(71, 93)(72, 281)(73, 172)(75,
251)(76, 142)(78, 221)(79, 112)(81, 191)(83, 270)(84, 161)(86, 240)(87, 131)(89,
210)(90, 101)(91, 289)(92, 180)(94, 259)(95, 150)(97, 229)(98, 120)(100,
199)(102, 278)(103, 169)(105, 248)(106, 139)(108, 218)(110, 297)(111, 188)(113,
267)(114, 158)(116, 237)(117, 128)(119, 207)(121, 286)(122, 177)(124, 256)(125,
147)(127, 226)(130, 196)(132, 275)(133, 166)(135, 245)(138, 215)(140, 294)(141,
185)(143, 264)(144, 155)(146, 234)(149, 204)(151, 283)(152, 174)(154, 253)(157,
223)(160, 193)(162, 272)(165, 242)(168, 212)(170, 291)(171, 182)(173, 261)(176,
231)(179, 201)(181, 280)(184, 250)(187, 220)(192, 269)(195, 239)(198, 209)(200,
288)(203, 258)(206, 228)(211, 277)(214, 247)(219, 296)(222, 266)(225, 236)(230,
285)(233, 255)(241, 274)(249, 293)(252, 263)(260, 282)(279, 290)
C4[ 297, 1 ]
297
-1 110 297 2 189
-2 1 111 3 190
-3 2 112 4 191
-4 3 113 5 192
-5 4 114 6 193
-6 5 115 7 194
-7 6 116 8 195
-8 7 117 9 196
-9 8 118 10 197
-10 11 198 9 119
-11 12 199 10 120
-12 11 121 13 200
-13 12 122 14 201
-14 13 123 15 202
-15 14 124 16 203
-16 15 125 17 204
-17 16 126 18 205
-18 17 127 19 206
-19 18 128 20 207
-20 19 129 21 208
-21 22 209 20 130
-22 23 210 21 131
-23 22 132 24 211
-24 23 133 25 212
-25 24 134 26 213
-26 25 135 27 214
-27 26 136 28 215
-28 27 137 29 216
-29 28 138 30 217
-30 29 139 31 218
-31 30 140 32 219
-32 33 220 31 141
-33 34 221 32 142
-34 33 143 35 222
-35 34 144 36 223
-36 35 145 37 224
-37 36 146 38 225
-38 37 147 39 226
-39 38 148 40 227
-40 39 149 41 228
-41 40 150 42 229
-42 41 151 43 230
-43 44 231 42 152
-44 45 232 43 153
-45 44 154 46 233
-46 45 155 47 234
-47 46 156 48 235
-48 47 157 49 236
-49 48 158 50 237
-50 49 159 51 238
-51 50 160 52 239
-52 51 161 53 240
-53 52 162 54 241
-54 55 242 53 163
-55 56 243 54 164
-56 55 165 57 244
-57 56 166 58 245
-58 57 167 59 246
-59 58 168 60 247
-60 59 169 61 248
-61 60 170 62 249
-62 61 171 63 250
-63 62 172 64 251
-64 63 173 65 252
-65 66 253 64 174
-66 67 254 65 175
-67 66 176 68 255
-68 67 177 69 256
-69 68 178 70 257
-70 69 179 71 258
-71 70 180 72 259
-72 71 181 73 260
-73 72 182 74 261
-74 73 183 75 262
-75 74 184 76 263
-76 77 264 75 185
-77 78 265 76 186
-78 77 187 79 266
-79 78 188 80 267
-80 79 189 81 268
-81 80 190 82 269
-82 81 191 83 270
-83 82 192 84 271
-84 83 193 85 272
-85 84 194 86 273
-86 85 195 87 274
-87 88 275 86 196
-88 89 276 87 197
-89 88 198 90 277
-90 89 199 91 278
-91 90 200 92 279
-92 91 201 93 280
-93 92 202 94 281
-94 93 203 95 282
-95 94 204 96 283
-96 95 205 97 284
-97 96 206 98 285
-98 99 286 97 207
-99 100 287 98 208
-100 99 209 101 288
-101 100 210 102 289
-102 101 211 103 290
-103 102 212 104 291
-104 103 213 105 292
-105 104 214 106 293
-106 105 215 107 294
-107 106 216 108 295
-108 107 217 109 296
-109 110 297 108 218
-110 1 111 109 219
-111 110 220 2 112
-112 111 221 3 113
-113 112 222 4 114
-114 113 223 5 115
-115 114 224 6 116
-116 115 225 7 117
-117 116 226 8 118
-118 117 227 9 119
-119 118 228 10 120
-120 11 121 119 229
-121 12 122 120 230
-122 121 231 13 123
-123 122 232 14 124
-124 123 233 15 125
-125 124 234 16 126
-126 125 235 17 127
-127 126 236 18 128
-128 127 237 19 129
-129 128 238 20 130
-130 129 239 21 131
-131 22 132 130 240
-132 23 133 131 241
-133 132 242 24 134
-134 133 243 25 135
-135 134 244 26 136
-136 135 245 27 137
-137 136 246 28 138
-138 137 247 29 139
-139 138 248 30 140
-140 139 249 31 141
-141 140 250 32 142
-142 33 143 141 251
-143 34 144 142 252
-144 143 253 35 145
-145 144 254 36 146
-146 145 255 37 147
-147 146 256 38 148
-148 147 257 39 149
-149 148 258 40 150
-150 149 259 41 151
-151 150 260 42 152
-152 151 261 43 153
-153 44 154 152 262
-154 45 155 153 263
-155 154 264 46 156
-156 155 265 47 157
-157 156 266 48 158
-158 157 267 49 159
-159 158 268 50 160
-160 159 269 51 161
-161 160 270 52 162
-162 161 271 53 163
-163 162 272 54 164
-164 55 165 163 273
-165 56 166 164 274
-166 165 275 57 167
-167 166 276 58 168
-168 167 277 59 169
-169 168 278 60 170
-170 169 279 61 171
-171 170 280 62 172
-172 171 281 63 173
-173 172 282 64 174
-174 173 283 65 175
-175 66 176 174 284
-176 67 177 175 285
-177 176 286 68 178
-178 177 287 69 179
-179 178 288 70 180
-180 179 289 71 181
-181 180 290 72 182
-182 181 291 73 183
-183 182 292 74 184
-184 183 293 75 185
-185 184 294 76 186
-186 77 187 185 295
-187 78 188 186 296
-188 187 297 79 189
-189 1 188 80 190
-190 2 189 81 191
-191 3 190 82 192
-192 4 191 83 193
-193 5 192 84 194
-194 6 193 85 195
-195 7 194 86 196
-196 8 195 87 197
-197 88 198 9 196
-198 89 199 10 197
-199 11 198 90 200
-200 12 199 91 201
-201 13 200 92 202
-202 14 201 93 203
-203 15 202 94 204
-204 16 203 95 205
-205 17 204 96 206
-206 18 205 97 207
-207 19 206 98 208
-208 99 209 20 207
-209 100 210 21 208
-210 22 209 101 211
-211 23 210 102 212
-212 24 211 103 213
-213 25 212 104 214
-214 26 213 105 215
-215 27 214 106 216
-216 28 215 107 217
-217 29 216 108 218
-218 30 217 109 219
-219 110 220 31 218
-220 111 221 32 219
-221 33 220 112 222
-222 34 221 113 223
-223 35 222 114 224
-224 36 223 115 225
-225 37 224 116 226
-226 38 225 117 227
-227 39 226 118 228
-228 40 227 119 229
-229 41 228 120 230
-230 121 231 42 229
-231 122 232 43 230
-232 44 231 123 233
-233 45 232 124 234
-234 46 233 125 235
-235 47 234 126 236
-236 48 235 127 237
-237 49 236 128 238
-238 50 237 129 239
-239 51 238 130 240
-240 52 239 131 241
-241 132 242 53 240
-242 133 243 54 241
-243 55 242 134 244
-244 56 243 135 245
-245 57 244 136 246
-246 58 245 137 247
-247 59 246 138 248
-248 60 247 139 249
-249 61 248 140 250
-250 62 249 141 251
-251 63 250 142 252
-252 143 253 64 251
-253 144 254 65 252
-254 66 253 145 255
-255 67 254 146 256
-256 68 255 147 257
-257 69 256 148 258
-258 70 257 149 259
-259 71 258 150 260
-260 72 259 151 261
-261 73 260 152 262
-262 74 261 153 263
-263 154 264 75 262
-264 155 265 76 263
-265 77 264 156 266
-266 78 265 157 267
-267 79 266 158 268
-268 80 267 159 269
-269 81 268 160 270
-270 82 269 161 271
-271 83 270 162 272
-272 84 271 163 273
-273 85 272 164 274
-274 165 275 86 273
-275 166 276 87 274
-276 88 275 167 277
-277 89 276 168 278
-278 90 277 169 279
-279 91 278 170 280
-280 92 279 171 281
-281 93 280 172 282
-282 94 281 173 283
-283 95 282 174 284
-284 96 283 175 285
-285 176 286 97 284
-286 177 287 98 285
-287 99 286 178 288
-288 100 287 179 289
-289 101 288 180 290
-290 102 289 181 291
-291 103 290 182 292
-292 104 291 183 293
-293 105 292 184 294
-294 106 293 185 295
-295 107 294 186 296
-296 187 297 108 295
-297 1 188 109 296
0