C4graphGraph forms for C4 [ 240, 129 ] = PL(CS(PS(6,5;2)[6^10],0))

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On this page are computer-accessible forms for the graph C4[ 240, 129 ] = PL(CS(PS(6,5;2)[6^10],0)).

(I) Following is a form readable by MAGMA:

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

(II) A more general form is to represent the graph as the orbit of {112, 127} under the group generated by the following permutations:

a: (5, 6)(7, 8)(13, 14)(15, 16)(29, 32)(30, 31)(89, 92)(90, 91)(105, 106)(107, 108)(113, 114)(115, 116)(157, 163)(158, 164)(159, 165)(160, 166)(161, 167)(162, 168)
b: (2, 4)(5, 18)(6, 17)(7, 20)(8, 19)(9, 15)(10, 16)(11, 13)(12, 14)(25, 40)(26, 39)(27, 38)(28, 37)(29, 35)(30, 36)(31, 33)(32, 34)(42, 44)(45, 60)(46, 57)(47, 58)(48, 59)(49, 53)(50, 54)(51, 55)(52, 56)(62, 64)(65, 80)(66, 77)(67, 78)(68, 79)(69, 73)(70, 74)(71, 75)(72, 76)(85, 100)(86, 99)(87, 98)(88, 97)(89, 95)(90, 96)(91, 93)(92, 94)(102, 104)(105, 118)(106, 117)(107, 120)(108, 119)(109, 115)(110, 116)(111, 113)(112, 114)(121, 139)(122, 140)(123, 141)(124, 142)(125, 143)(126, 144)(127, 133)(128, 134)(129, 135)(130, 136)(131, 137)(132, 138)(145, 148)(146, 147)(149, 150)(151, 154)(152, 153)(155, 156)(157, 178)(158, 177)(159, 176)(160, 175)(161, 180)(162, 179)(163, 172)(164, 171)(165, 170)(166, 169)(167, 174)(168, 173)(181, 182)(183, 186)(184, 185)(187, 188)(189, 192)(190, 191)(193, 230)(194, 229)(195, 234)(196, 233)(197, 232)(198, 231)(199, 236)(200, 235)(201, 240)(202, 239)(203, 238)(204, 237)(205, 223)(206, 224)(207, 225)(208, 226)(209, 227)(210, 228)(211, 217)(212, 218)(213, 219)(214, 220)(215, 221)(216, 222)
c: (9, 10)(11, 12)(17, 18)(19, 20)(33, 36)(34, 35)(93, 96)(94, 95)(109, 110)(111, 112)(117, 118)(119, 120)(169, 175)(170, 176)(171, 177)(172, 178)(173, 179)(174, 180)
d: (1, 5, 10, 16, 18)(2, 8, 11, 15, 17)(3, 7, 12, 14, 20)(4, 6, 9, 13, 19)(21, 25, 32, 33, 40)(22, 26, 31, 34, 39)(23, 27, 30, 35, 38)(24, 28, 29, 36, 37)(41, 45, 51, 53, 57)(42, 46, 50, 54, 58)(43, 47, 49, 55, 59)(44, 48, 52, 56, 60)(61, 65, 71, 73, 77)(62, 66, 70, 74, 78)(63, 67, 69, 75, 79)(64, 68, 72, 76, 80)(81, 85, 92, 93, 100)(82, 86, 91, 94, 99)(83, 87, 90, 95, 98)(84, 88, 89, 96, 97)(101, 105, 110, 116, 118)(102, 108, 111, 115, 117)(103, 107, 112, 114, 120)(104, 106, 109, 113, 119)(121, 163, 169, 142, 148)(122, 164, 170, 141, 147)(123, 165, 171, 140, 146)(124, 166, 172, 139, 145)(125, 167, 173, 144, 150)(126, 168, 174, 143, 149)(127, 157, 175, 136, 154)(128, 158, 176, 135, 153)(129, 159, 177, 134, 152)(130, 160, 178, 133, 151)(131, 161, 179, 138, 156)(132, 162, 180, 137, 155)(181, 193, 206, 217, 229)(182, 194, 205, 218, 230)(183, 195, 210, 219, 231)(184, 196, 209, 220, 232)(185, 197, 208, 221, 233)(186, 198, 207, 222, 234)(187, 199, 212, 223, 235)(188, 200, 211, 224, 236)(189, 201, 216, 225, 237)(190, 202, 215, 226, 238)(191, 203, 214, 227, 239)(192, 204, 213, 228, 240)
e: (5, 8)(6, 7)(17, 20)(18, 19)(21, 23)(22, 24)(49, 52)(50, 51)(53, 56)(54, 55)(69, 72)(70, 71)(73, 76)(74, 75)(81, 83)(82, 84)(105, 108)(106, 107)(117, 120)(118, 119)(145, 151)(146, 152)(147, 153)(148, 154)(149, 155)(150, 156)(181, 187)(182, 188)(183, 189)(184, 190)(185, 191)(186, 192)
f: (21, 22)(23, 24)(49, 52)(50, 51)(53, 56)(54, 55)(69, 72)(70, 71)(73, 76)(74, 75)(81, 82)(83, 84)(181, 187)(182, 188)(183, 189)(184, 190)(185, 191)(186, 192)
g: (25, 26)(27, 28)(53, 54)(55, 56)(57, 60)(58, 59)(73, 74)(75, 76)(77, 80)(78, 79)(85, 86)(87, 88)(193, 199)(194, 200)(195, 201)(196, 202)(197, 203)(198, 204)
h: (29, 30)(31, 32)(33, 34)(35, 36)(41, 43)(42, 44)(45, 48)(46, 47)(57, 58)(59, 60)(61, 63)(62, 64)(65, 68)(66, 67)(77, 78)(79, 80)(89, 90)(91, 92)(93, 94)(95, 96)(205, 211)(206, 212)(207, 213)(208, 214)(209, 215)(210, 216)(217, 223)(218, 224)(219, 225)(220, 226)(221, 227)(222, 228)
m: (1, 21)(2, 24)(3, 23)(4, 22)(5, 115)(6, 116)(7, 113)(8, 114)(9, 71, 10, 72)(11, 69, 12, 70)(13, 107)(14, 108)(15, 105)(16, 106)(17, 39, 18, 40)(19, 37, 20, 38)(25, 56)(26, 55)(27, 54)(28, 53)(29, 92)(30, 91)(31, 90)(32, 89)(33, 48, 36, 47)(34, 45, 35, 46)(41, 61)(42, 62)(43, 63)(44, 64)(49, 112, 50, 111)(51, 110, 52, 109)(57, 77)(58, 78)(59, 79)(60, 80)(65, 95, 66, 94)(67, 93, 68, 96)(73, 88)(74, 87)(75, 86)(76, 85)(81, 101)(82, 104)(83, 103)(84, 102)(97, 120, 98, 119)(99, 118, 100, 117)(121, 188)(122, 187)(123, 192)(124, 191)(125, 190)(126, 189)(127, 182)(128, 181)(129, 186)(130, 185)(131, 184)(132, 183)(133, 152)(134, 153)(135, 154)(136, 155)(137, 156)(138, 151)(139, 146)(140, 147)(141, 148)(142, 149)(143, 150)(144, 145)(157, 163)(158, 168)(159, 167)(160, 166)(161, 165)(162, 164)(169, 238, 175, 232)(170, 237, 176, 231)(171, 236, 177, 230)(172, 235, 178, 229)(173, 240, 179, 234)(174, 239, 180, 233)(193, 195)(196, 198)(199, 201)(202, 204)(205, 208)(206, 209)(207, 210)(211, 214)(212, 215)(213, 216)(218, 222)(219, 221)(224, 228)(225, 227)
n1: (5, 48)(6, 47)(7, 46)(8, 45)(13, 97)(14, 98)(15, 99)(16, 100)(17, 96)(18, 93)(19, 94)(20, 95)(21, 61)(22, 64)(23, 63)(24, 62)(29, 70)(30, 71)(31, 72)(32, 69)(33, 118)(34, 119)(35, 120)(36, 117)(37, 113)(38, 114)(39, 115)(40, 116)(41, 81)(42, 84)(43, 83)(44, 82)(49, 92)(50, 89)(51, 90)(52, 91)(53, 60)(54, 57)(55, 58)(56, 59)(65, 108)(66, 107)(67, 106)(68, 105)(73, 80)(74, 77)(75, 78)(76, 79)(133, 134)(135, 138)(136, 137)(139, 140)(141, 144)(142, 143)(145, 223)(146, 228)(147, 227)(148, 226)(149, 225)(150, 224)(151, 217)(152, 222)(153, 221)(154, 220)(155, 219)(156, 218)(157, 230)(158, 231)(159, 232)(160, 233)(161, 234)(162, 229)(163, 236)(164, 237)(165, 238)(166, 239)(167, 240)(168, 235)(169, 170)(171, 174)(172, 173)(175, 176)(177, 180)(178, 179)(181, 216)(182, 215)(183, 214)(184, 213)(185, 212)(186, 211)(187, 210)(188, 209)(189, 208)(190, 207)(191, 206)(192, 205)(193, 194)(195, 198)(196, 197)(199, 200)(201, 204)(202, 203)
a1: (33, 34)(35, 36)(41, 42)(43, 44)(45, 48)(46, 47)(61, 62)(63, 64)(65, 68)(66, 67)(93, 94)(95, 96)(217, 223)(218, 224)(219, 225)(220, 226)(221, 227)(222, 228)
b1: (1, 2)(3, 4)(5, 6)(7, 8)(13, 15)(14, 16)(29, 32)(30, 31)(37, 40)(38, 39)(89, 92)(90, 91)(97, 100)(98, 99)(101, 102)(103, 104)(105, 106)(107, 108)(113, 115)(114, 116)(133, 139)(134, 140)(135, 141)(136, 142)(137, 143)(138, 144)(157, 163)(158, 164)(159, 165)(160, 166)(161, 167)(162, 168)
c1: (37, 38)(39, 40)(45, 46)(47, 48)(49, 50)(51, 52)(65, 66)(67, 68)(69, 70)(71, 72)(97, 98)(99, 100)(229, 235)(230, 236)(231, 237)(232, 238)(233, 239)(234, 240)

(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.

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&Graph
C4[ 240, 129 ]
240
-1 121 122 139 140
-2 121 122 133 134
-3 133 134 127 128
-4 127 128 139 140
-5 145 146 163 164
-6 145 146 157 158
-7 157 158 151 152
-8 151 152 163 164
-9 176 123 124 175
-10 123 124 169 170
-11 169 170 129 130
-12 176 129 130 175
-13 165 166 135 136
-14 135 136 159 160
-15 159 160 141 142
-16 165 166 141 142
-17 177 178 147 148
-18 147 148 171 172
-19 154 171 172 153
-20 154 177 178 153
-21 187 188 146 147
-22 146 147 181 182
-23 181 182 152 153
-24 187 188 152 153
-25 122 199 123 200
-26 122 123 193 194
-27 193 128 194 129
-28 199 200 128 129
-29 211 212 158 159
-30 158 159 205 206
-31 165 205 206 164
-32 165 211 212 164
-33 223 224 170 171
-34 170 171 217 218
-35 176 177 217 218
-36 176 177 223 224
-37 134 135 235 236
-38 134 135 229 230
-39 140 141 229 230
-40 235 236 140 141
-41 224 225 206 207
-42 206 207 218 219
-43 212 213 218 219
-44 212 213 224 225
-45 222 236 237 217
-46 231 222 217 230
-47 231 223 228 230
-48 223 236 237 228
-49 235 182 183 240
-50 234 182 183 229
-51 188 189 234 229
-52 188 189 235 240
-53 200 201 181 186
-54 181 194 195 186
-55 187 192 194 195
-56 187 200 201 192
-57 198 211 193 216
-58 198 210 193 205
-59 199 210 204 205
-60 199 211 204 216
-61 209 210 227 228
-62 209 210 221 222
-63 221 222 215 216
-64 215 216 227 228
-65 220 239 240 219
-66 220 233 234 219
-67 233 234 225 226
-68 225 226 239 240
-69 237 238 185 186
-70 231 232 185 186
-71 231 232 191 192
-72 191 192 237 238
-73 203 204 183 184
-74 198 183 184 197
-75 198 189 190 197
-76 189 190 203 204
-77 213 214 195 196
-78 195 196 207 208
-79 201 202 207 208
-80 201 202 213 214
-81 190 191 149 150
-82 149 150 184 185
-83 155 156 184 185
-84 155 156 190 191
-85 125 202 126 203
-86 125 126 196 197
-87 132 196 131 197
-88 132 202 203 131
-89 214 215 161 162
-90 209 161 162 208
-91 209 167 168 208
-92 167 168 214 215
-93 226 227 173 174
-94 220 221 173 174
-95 220 221 179 180
-96 179 180 226 227
-97 137 138 238 239
-98 232 233 137 138
-99 143 144 232 233
-100 143 144 238 239
-101 143 124 125 142
-102 124 125 136 137
-103 136 137 130 131
-104 143 130 131 142
-105 166 167 148 149
-106 148 149 160 161
-107 154 155 160 161
-108 154 155 166 167
-109 121 178 179 126
-110 121 126 172 173
-111 132 127 172 173
-112 132 178 179 127
-113 133 168 138 163
-114 133 157 138 162
-115 144 157 139 162
-116 144 168 139 163
-117 145 180 150 175
-118 145 169 150 174
-119 156 169 151 174
-120 156 180 151 175
-121 110 1 2 109
-122 1 2 25 26
-123 25 26 9 10
-124 101 102 9 10
-125 101 102 85 86
-126 110 85 86 109
-127 111 112 3 4
-128 3 4 27 28
-129 11 12 27 28
-130 11 12 103 104
-131 88 103 104 87
-132 88 111 112 87
-133 2 3 113 114
-134 2 3 37 38
-135 13 14 37 38
-136 13 14 102 103
-137 102 103 97 98
-138 113 114 97 98
-139 1 4 115 116
-140 1 4 39 40
-141 15 16 39 40
-142 101 15 16 104
-143 99 100 101 104
-144 99 100 115 116
-145 5 6 117 118
-146 22 5 6 21
-147 22 17 18 21
-148 17 105 18 106
-149 81 82 105 106
-150 81 82 117 118
-151 7 8 119 120
-152 23 24 7 8
-153 23 24 19 20
-154 19 107 20 108
-155 83 84 107 108
-156 83 84 119 120
-157 114 115 6 7
-158 6 7 29 30
-159 14 15 29 30
-160 14 15 106 107
-161 89 90 106 107
-162 89 90 114 115
-163 113 5 116 8
-164 5 8 31 32
-165 13 16 31 32
-166 13 16 105 108
-167 91 92 105 108
-168 91 113 92 116
-169 11 118 119 10
-170 11 33 34 10
-171 33 34 18 19
-172 110 111 18 19
-173 110 111 93 94
-174 93 94 118 119
-175 12 117 9 120
-176 12 35 36 9
-177 35 36 17 20
-178 112 17 20 109
-179 112 95 96 109
-180 95 117 96 120
-181 22 23 53 54
-182 22 23 49 50
-183 49 50 73 74
-184 82 83 73 74
-185 69 70 82 83
-186 69 70 53 54
-187 55 56 24 21
-188 24 51 52 21
-189 51 52 75 76
-190 81 84 75 76
-191 81 71 72 84
-192 55 56 71 72
-193 57 58 26 27
-194 55 26 27 54
-195 55 77 78 54
-196 77 78 86 87
-197 74 75 86 87
-198 57 58 74 75
-199 25 59 60 28
-200 56 25 28 53
-201 56 79 80 53
-202 88 79 80 85
-203 88 73 85 76
-204 59 60 73 76
-205 58 59 30 31
-206 30 41 31 42
-207 78 79 41 42
-208 78 79 90 91
-209 90 91 61 62
-210 58 59 61 62
-211 57 60 29 32
-212 44 29 32 43
-213 44 77 80 43
-214 77 89 80 92
-215 89 92 63 64
-216 57 60 63 64
-217 34 45 35 46
-218 34 35 42 43
-219 66 42 43 65
-220 66 94 95 65
-221 94 62 95 63
-222 45 46 62 63
-223 33 36 47 48
-224 33 44 36 41
-225 44 67 68 41
-226 67 68 93 96
-227 93 61 96 64
-228 47 48 61 64
-229 38 39 50 51
-230 46 47 38 39
-231 46 47 70 71
-232 99 70 71 98
-233 66 99 67 98
-234 66 67 50 51
-235 37 49 40 52
-236 45 37 48 40
-237 45 69 48 72
-238 100 69 72 97
-239 100 68 97 65
-240 68 49 52 65
0

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