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