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