MINLPLib

A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance: gabriel10

The question to answer is to find the minimum value of k such that the k-Gabriel graph of any set of points in the plane is Hamiltonian.
A known upper bound on k is 10. Infeasibility of this instance would give some indication for lower bounds on k.
Formats ams gms lp mod osil pip
Primal Bounds
226.49000000 p1 ( gdx sol )
(infeas: 4e-16)
230.32000000 p2 ( gdx sol )
(infeas: 3e-16)
Dual Bounds
239.62000000 (BARON)
8266.52000000 (LINDO)
239.48000000 (SCIP)
References Kaiser, Tomáš, Saumell, Maria, and Cleemput, Nico Van, 10-Gabriel graphs are Hamiltonian, Information Processing Letters, 115:11, 2015, 877-881.
Source QPLIB instance 690, contributed by Maria Saumell
Application Computational geometry
Added to library 18 Aug 2018
Problem type MBQCP
#Variables 16476
#Binary Variables 6428
#Integer Variables 0
#Nonlinear Variables 8688
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense max
Objective type linear
Objective curvature linear
#Nonzeros in Objective 11859
#Nonlinear Nonzeros in Objective 0
#Constraints 115600
#Linear Constraints 112400
#Quadratic Constraints 3200
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 407245
#Nonlinear Nonzeros in Jacobian 155360
#Nonzeros in (Upper-Left) Hessian of Lagrangian 109760
#Nonzeros in Diagonal of Hessian of Lagrangian 0
#Blocks in Hessian of Lagrangian 320
Minimal blocksize in Hessian of Lagrangian 11
Maximal blocksize in Hessian of Lagrangian 28
Average blocksize in Hessian of Lagrangian 27.15
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 2
Sparsity Jacobian Sparsity of Objective Gradient and Jacobian
Sparsity Hessian of Lagrangian Sparsity of Hessian of Lagrangian

$offlisting
*  
*  Equation counts
*      Total        E        G        L        N        X        C        B
*     115601     3621     6080   105900        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*      16477    10049     6428        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*     419105   263745   155360        0
*
*  Solve m using MIQCP maximizing objvar;


Variables  objvar,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17,x18
          ,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34,x35
          ,x36,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52
          ,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68,x69
          ,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85,x86
          ,x87,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101,x102
          ,x103,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114,x115
          ,x116,x117,x118,x119,x120,x121,x122,x123,x124,x125,x126,x127,x128
          ,x129,x130,x131,x132,x133,x134,x135,x136,x137,x138,x139,x140,x141
          ,x142,x143,x144,x145,x146,x147,x148,x149,x150,x151,x152,x153,x154
          ,x155,x156,x157,x158,x159,x160,x161,x162,x163,x164,x165,x166,x167
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          ,x298,x299,x300,x301,x302,x303,x304,x305,x306,x307,x308,x309,x310
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          ,x727,x728,x729,x730,x731,x732,x733,x734,x735,x736,x737,x738,x739
          ,x740,x741,x742,x743,x744,x745,x746,x747,x748,x749,x750,x751,x752
          ,x753,x754,x755,x756,x757,x758,x759,x760,x761,x762,x763,x764,x765
          ,x766,x767,x768,x769,x770,x771,x772,x773,x774,x775,x776,x777,x778
          ,x779,x780,x781,x782,x783,x784,x785,x786,x787,x788,x789,x790,x791
          ,x792,x793,x794,x795,x796,x797,x798,x799,x800,x801,x802,x803,x804
          ,x805,x806,x807,x808,x809,x810,x811,x812,x813,x814,x815,x816,x817
          ,x818,x819,x820,x821,x822,x823,x824,x825,x826,x827,x828,x829,x830
          ,x831,x832,x833,x834,x835,x836,x837,x838,x839,x840,x841,x842,x843
          ,x844,x845,x846,x847,x848,x849,x850,x851,x852,x853,x854,x855,x856
          ,x857,x858,x859,x860,x861,x862,x863,x864,x865,x866,x867,x868,x869
          ,x870,x871,x872,x873,x874,x875,x876,x877,x878,x879,x880,x881,x882
          ,x883,x884,x885,x886,x887,x888,x889,x890,x891,x892,x893,x894,x895
          ,x896,x897,x898,x899,x900,x901,x902,x903,x904,x905,x906,x907,x908
          ,x909,x910,x911,x912,x913,x914,x915,x916,x917,x918,x919,x920,x921
          ,x922,x923,x924,x925,x926,x927,x928,x929,x930,x931,x932,x933,x934
          ,x935,x936,x937,x938,x939,x940,x941,x942,x943,x944,x945,x946,x947
          ,x948,x949,x950,x951,x952,x953,x954,x955,x956,x957,x958,x959,x960
          ,x961,x962,x963,x964,x965,x966,x967,x968,x969,x970,x971,x972,x973
          ,x974,x975,x976,x977,x978,x979,x980,x981,x982,x983,x984,x985,x986
          ,x987,x988,x989,x990,x991,x992,x993,x994,x995,x996,x997,x998,x999
          ,x1000,x1001,x1002,x1003,x1004,x1005,x1006,x1007,x1008,x1009,x1010
          ,x1011,x1012,x1013,x1014,x1015,x1016,x1017,x1018,x1019,x1020,x1021
          ,x1022,x1023,x1024,x1025,x1026,x1027,x1028,x1029,x1030,x1031,x1032
          ,x1033,x1034,x1035,x1036,x1037,x1038,x1039,x1040,x1041,x1042,x1043
          ,x1044,x1045,x1046,x1047,x1048,x1049,x1050,x1051,x1052,x1053,x1054
          ,x1055,x1056,x1057,x1058,x1059,x1060,x1061,x1062,x1063,x1064,x1065
          ,x1066,x1067,x1068,x1069,x1070,x1071,x1072,x1073,x1074,x1075,x1076
          ,x1077,x1078,x1079,x1080,x1081,x1082,x1083,x1084,x1085,x1086,x1087
          ,x1088,x1089,x1090,x1091,x1092,x1093,x1094,x1095,x1096,x1097,x1098
          ,x1099,x1100,x1101,x1102,x1103,x1104,x1105,x1106,x1107,x1108,x1109
          ,x1110,x1111,x1112,x1113,x1114,x1115,x1116,x1117,x1118,x1119,x1120
          ,x1121,x1122,x1123,x1124,x1125,x1126,x1127,x1128,x1129,x1130,x1131
          ,x1132,x1133,x1134,x1135,x1136,x1137,x1138,x1139,x1140,x1141,x1142
          ,x1143,x1144,x1145,x1146,x1147,x1148,x1149,x1150,x1151,x1152,x1153
          ,x1154,x1155,x1156,x1157,x1158,x1159,x1160,x1161,x1162,x1163,x1164
          ,x1165,x1166,x1167,x1168,x1169,x1170,x1171,x1172,x1173,x1174,x1175
          ,x1176,x1177,x1178,x1179,x1180,x1181,x1182,x1183,x1184,x1185,x1186
          ,x1187,x1188,x1189,x1190,x1191,x1192,x1193,x1194,x1195,x1196,x1197
          ,x1198,x1199,x1200,x1201,x1202,x1203,x1204,x1205,x1206,x1207,x1208
          ,x1209,x1210,x1211,x1212,x1213,x1214,x1215,x1216,x1217,x1218,x1219
          ,x1220,x1221,x1222,x1223,x1224,x1225,x1226,x1227,x1228,x1229,x1230
          ,x1231,x1232,x1233,x1234,x1235,x1236,x1237,x1238,x1239,x1240,x1241
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          ,x1253,x1254,x1255,x1256,x1257,x1258,x1259,x1260,x1261,x1262,x1263
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          ,x1858,x1859,x1860,x1861,x1862,x1863,x1864,x1865,x1866,x1867,x1868
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          ,x1880,x1881,x1882,x1883,x1884,x1885,x1886,x1887,x1888,x1889,x1890
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          ,x1902,x1903,x1904,x1905,x1906,x1907,x1908,x1909,x1910,x1911,x1912
          ,x1913,x1914,x1915,x1916,x1917,x1918,x1919,x1920,x1921,x1922,x1923
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          ,x15129,x15130,x15131,x15132,x15133,x15134,x15135,x15136,x15137
          ,x15138,x15139,x15140,x15141,x15142,x15143,x15144,x15145,x15146
          ,x15147,x15148,x15149,x15150,x15151,x15152,x15153,x15154,x15155
          ,x15156,x15157,x15158,x15159,x15160,x15161,x15162,x15163,x15164
          ,x15165,x15166,x15167,x15168,x15169,x15170,x15171,x15172,x15173
          ,x15174,x15175,x15176,x15177,x15178,x15179,x15180,x15181,x15182
          ,x15183,x15184,x15185,x15186,x15187,x15188,x15189,x15190,x15191
          ,x15192,x15193,x15194,x15195,x15196,x15197,x15198,x15199,x15200
          ,x15201,x15202,x15203,x15204,x15205,x15206,x15207,x15208,x15209
          ,x15210,x15211,x15212,x15213,x15214,x15215,x15216,x15217,x15218
          ,x15219,x15220,x15221,x15222,x15223,x15224,x15225,x15226,x15227
          ,x15228,x15229,x15230,x15231,x15232,x15233,x15234,x15235,x15236
          ,x15237,x15238,x15239,x15240,x15241,x15242,x15243,x15244,x15245
          ,x15246,x15247,x15248,x15249,x15250,x15251,x15252,x15253,x15254
          ,x15255,x15256,x15257,x15258,x15259,x15260,x15261,x15262,x15263
          ,x15264,x15265,x15266,x15267,x15268,x15269,x15270,x15271,x15272
          ,x15273,x15274,x15275,x15276,x15277,x15278,x15279,x15280,x15281
          ,x15282,x15283,x15284,x15285,x15286,x15287,x15288,x15289,x15290
          ,x15291,x15292,x15293,x15294,x15295,x15296,x15297,x15298,x15299
          ,x15300,x15301,x15302,x15303,x15304,x15305,x15306,x15307,x15308
          ,x15309,x15310,x15311,x15312,x15313,x15314,x15315,x15316,x15317
          ,x15318,x15319,x15320,x15321,x15322,x15323,x15324,x15325,x15326
          ,x15327,x15328,x15329,x15330,x15331,x15332,x15333,x15334,x15335
          ,x15336,x15337,x15338,x15339,x15340,x15341,x15342,x15343,x15344
          ,x15345,x15346,x15347,x15348,x15349,x15350,x15351,x15352,x15353
          ,x15354,x15355,x15356,x15357,x15358,x15359,x15360,x15361,x15362
          ,x15363,x15364,x15365,x15366,x15367,x15368,x15369,x15370,x15371
          ,x15372,x15373,x15374,x15375,x15376,x15377,x15378,x15379,x15380
          ,x15381,x15382,x15383,x15384,x15385,x15386,x15387,x15388,x15389
          ,x15390,x15391,x15392,x15393,x15394,x15395,x15396,x15397,x15398
          ,x15399,x15400,x15401,x15402,x15403,x15404,x15405,x15406,x15407
          ,x15408,x15409,x15410,x15411,x15412,x15413,x15414,x15415,x15416
          ,x15417,x15418,x15419,x15420,x15421,x15422,x15423,x15424,x15425
          ,x15426,x15427,x15428,x15429,x15430,x15431,x15432,x15433,x15434
          ,x15435,x15436,x15437,x15438,x15439,x15440,x15441,x15442,x15443
          ,x15444,x15445,x15446,x15447,x15448,x15449,x15450,x15451,x15452
          ,x15453,x15454,x15455,x15456,x15457,x15458,x15459,x15460,x15461
          ,x15462,x15463,x15464,x15465,x15466,x15467,x15468,x15469,x15470
          ,x15471,x15472,x15473,x15474,x15475,x15476,x15477,x15478,x15479
          ,x15480,x15481,x15482,x15483,x15484,x15485,x15486,x15487,x15488
          ,x15489,x15490,x15491,x15492,x15493,x15494,x15495,x15496,x15497
          ,x15498,x15499,x15500,x15501,x15502,x15503,x15504,x15505,x15506
          ,x15507,x15508,x15509,x15510,x15511,x15512,x15513,x15514,x15515
          ,x15516,x15517,x15518,x15519,x15520,x15521,x15522,x15523,x15524
          ,x15525,x15526,x15527,x15528,x15529,x15530,x15531,x15532,x15533
          ,x15534,x15535,x15536,x15537,x15538,x15539,x15540,x15541,x15542
          ,x15543,x15544,x15545,x15546,x15547,x15548,x15549,x15550,x15551
          ,x15552,x15553,x15554,x15555,x15556,x15557,x15558,x15559,x15560
          ,x15561,x15562,x15563,x15564,x15565,x15566,x15567,x15568,x15569
          ,x15570,x15571,x15572,x15573,x15574,x15575,x15576,x15577,x15578
          ,x15579,x15580,x15581,x15582,x15583,x15584,x15585,x15586,x15587
          ,x15588,x15589,x15590,x15591,x15592,x15593,x15594,x15595,x15596
          ,x15597,x15598,x15599,x15600,x15601,x15602,x15603,x15604,x15605
          ,x15606,x15607,x15608,x15609,x15610,x15611,x15612,x15613,x15614
          ,x15615,x15616,x15617,x15618,x15619,x15620,x15621,x15622,x15623
          ,x15624,x15625,x15626,x15627,x15628,x15629,x15630,x15631,x15632
          ,x15633,x15634,x15635,x15636,x15637,x15638,x15639,x15640,x15641
          ,x15642,x15643,x15644,x15645,x15646,x15647,x15648,x15649,x15650
          ,x15651,x15652,x15653,x15654,x15655,x15656,x15657,x15658,x15659
          ,x15660,x15661,x15662,x15663,x15664,x15665,x15666,x15667,x15668
          ,x15669,x15670,x15671,x15672,x15673,x15674,x15675,x15676,x15677
          ,x15678,x15679,x15680,x15681,x15682,x15683,x15684,x15685,x15686
          ,x15687,x15688,x15689,x15690,x15691,x15692,x15693,x15694,x15695
          ,x15696,x15697,x15698,x15699,x15700,x15701,x15702,x15703,x15704
          ,x15705,x15706,x15707,x15708,x15709,x15710,x15711,x15712,x15713
          ,x15714,x15715,x15716,x15717,x15718,x15719,x15720,x15721,x15722
          ,x15723,x15724,x15725,x15726,x15727,x15728,x15729,x15730,x15731
          ,x15732,x15733,x15734,x15735,x15736,x15737,x15738,x15739,x15740
          ,x15741,x15742,x15743,x15744,x15745,x15746,x15747,x15748,x15749
          ,x15750,x15751,x15752,x15753,x15754,x15755,x15756,x15757,x15758
          ,x15759,x15760,x15761,x15762,x15763,x15764,x15765,x15766,x15767
          ,x15768,x15769,x15770,x15771,x15772,x15773,x15774,x15775,x15776
          ,x15777,x15778,x15779,x15780,x15781,x15782,x15783,x15784,x15785
          ,x15786,x15787,x15788,x15789,x15790,x15791,x15792,x15793,x15794
          ,x15795,x15796,x15797,x15798,x15799,x15800,x15801,x15802,x15803
          ,x15804,x15805,x15806,x15807,x15808,x15809,x15810,x15811,x15812
          ,x15813,x15814,x15815,x15816,x15817,x15818,x15819,x15820,x15821
          ,x15822,x15823,x15824,x15825,x15826,x15827,x15828,x15829,x15830
          ,x15831,x15832,x15833,x15834,x15835,x15836,x15837,x15838,x15839
          ,x15840,x15841,x15842,x15843,x15844,x15845,x15846,x15847,x15848
          ,x15849,x15850,x15851,x15852,x15853,x15854,x15855,x15856,x15857
          ,x15858,x15859,x15860,x15861,x15862,x15863,x15864,x15865,x15866
          ,x15867,x15868,x15869,x15870,x15871,x15872,x15873,x15874,x15875
          ,x15876,x15877,x15878,x15879,x15880,x15881,x15882,x15883,x15884
          ,x15885,x15886,x15887,x15888,x15889,x15890,x15891,x15892,x15893
          ,x15894,x15895,x15896,x15897,x15898,x15899,x15900,x15901,x15902
          ,x15903,x15904,x15905,x15906,x15907,x15908,x15909,x15910,x15911
          ,x15912,x15913,x15914,x15915,x15916,x15917,x15918,x15919,x15920
          ,x15921,x15922,x15923,x15924,x15925,x15926,x15927,x15928,x15929
          ,x15930,x15931,x15932,x15933,x15934,x15935,x15936,x15937,x15938
          ,x15939,x15940,x15941,x15942,x15943,x15944,x15945,x15946,x15947
          ,x15948,x15949,x15950,x15951,x15952,x15953,x15954,x15955,x15956
          ,x15957,x15958,x15959,x15960,x15961,x15962,x15963,x15964,x15965
          ,x15966,x15967,x15968,x15969,x15970,x15971,x15972,x15973,x15974
          ,x15975,x15976,x15977,x15978,x15979,x15980,x15981,x15982,x15983
          ,x15984,x15985,x15986,x15987,x15988,x15989,x15990,x15991,x15992
          ,x15993,x15994,x15995,x15996,x15997,x15998,x15999,x16000,x16001
          ,x16002,x16003,x16004,x16005,x16006,x16007,x16008,x16009,x16010
          ,x16011,x16012,x16013,x16014,x16015,x16016,x16017,x16018,x16019
          ,x16020,x16021,x16022,x16023,x16024,x16025,x16026,x16027,x16028
          ,x16029,x16030,x16031,x16032,x16033,x16034,x16035,x16036,x16037
          ,x16038,x16039,x16040,x16041,x16042,x16043,x16044,x16045,x16046
          ,x16047,x16048,x16049,x16050,x16051,x16052,x16053,x16054,x16055
          ,x16056,x16057,x16058,x16059,x16060,x16061,x16062,x16063,x16064
          ,x16065,x16066,x16067,x16068,x16069,x16070,x16071,x16072,x16073
          ,x16074,x16075,x16076,x16077,x16078,x16079,x16080,x16081,x16082
          ,x16083,x16084,x16085,x16086,x16087,x16088,x16089,x16090,x16091
          ,x16092,x16093,x16094,x16095,x16096,x16097,x16098,x16099,x16100
          ,x16101,x16102,x16103,x16104,x16105,x16106,x16107,x16108,x16109
          ,x16110,x16111,x16112,x16113,x16114,x16115,x16116,x16117,x16118
          ,x16119,x16120,x16121,x16122,x16123,x16124,x16125,x16126,x16127
          ,x16128,x16129,x16130,x16131,x16132,x16133,x16134,x16135,x16136
          ,x16137,x16138,x16139,x16140,x16141,x16142,x16143,x16144,x16145
          ,x16146,x16147,x16148,x16149,x16150,x16151,x16152,x16153,x16154
          ,x16155,x16156,x16157,x16158,x16159,x16160,x16161,x16162,x16163
          ,x16164,x16165,x16166,x16167,x16168,x16169,x16170,x16171,x16172
          ,x16173,x16174,x16175,x16176,x16177,x16178,x16179,x16180,x16181
          ,x16182,x16183,x16184,x16185,x16186,x16187,x16188,x16189,x16190
          ,x16191,x16192,x16193,x16194,x16195,x16196,x16197,x16198,x16199
          ,x16200,x16201,x16202,x16203,x16204,x16205,x16206,x16207,x16208
          ,x16209,x16210,x16211,x16212,x16213,x16214,x16215,x16216,x16217
          ,x16218,x16219,x16220,x16221,x16222,x16223,x16224,x16225,x16226
          ,x16227,x16228,x16229,x16230,x16231,x16232,x16233,x16234,x16235
          ,x16236,x16237,x16238,x16239,x16240,x16241,x16242,x16243,x16244
          ,x16245,x16246,x16247,x16248,x16249,x16250,x16251,x16252,x16253
          ,x16254,x16255,x16256,x16257,x16258,x16259,x16260,x16261,x16262
          ,x16263,x16264,x16265,x16266,x16267,x16268,x16269,x16270,x16271
          ,x16272,x16273,x16274,x16275,x16276,x16277,x16278,x16279,x16280
          ,x16281,x16282,x16283,x16284,x16285,x16286,x16287,x16288,x16289
          ,x16290,x16291,x16292,x16293,x16294,x16295,x16296,x16297,x16298
          ,x16299,x16300,x16301,x16302,x16303,x16304,x16305,x16306,x16307
          ,x16308,x16309,x16310,x16311,x16312,x16313,x16314,x16315,x16316
          ,x16317,x16318,x16319,x16320,x16321,x16322,x16323,x16324,x16325
          ,x16326,x16327,x16328,x16329,x16330,x16331,x16332,x16333,x16334
          ,x16335,x16336,x16337,x16338,x16339,x16340,x16341,x16342,x16343
          ,x16344,x16345,x16346,x16347,x16348,x16349,x16350,x16351,x16352
          ,x16353,x16354,x16355,x16356,x16357,x16358,x16359,x16360,x16361
          ,x16362,x16363,x16364,x16365,x16366,x16367,x16368,x16369,x16370
          ,x16371,x16372,x16373,x16374,x16375,x16376,x16377,x16378,x16379
          ,x16380,x16381,x16382,x16383,x16384,x16385,x16386,x16387,x16388
          ,x16389,x16390,x16391,x16392,x16393,x16394,x16395,x16396,x16397
          ,x16398,x16399,x16400,x16401,x16402,x16403,x16404,x16405,x16406
          ,x16407,x16408,x16409,x16410,x16411,x16412,x16413,x16414,x16415
          ,x16416,x16417,x16418,x16419,x16420,x16421,x16422,x16423,x16424
          ,x16425,x16426,x16427,x16428,x16429,x16430,x16431,x16432,x16433
          ,x16434,x16435,x16436,x16437,x16438,x16439,x16440,x16441,x16442
          ,x16443,x16444,x16445,x16446,x16447,x16448,x16449,x16450,x16451
          ,x16452,x16453,x16454,x16455,x16456,x16457,x16458,x16459,x16460
          ,x16461,x16462,x16463,x16464,x16465,x16466,x16467,x16468,x16469
          ,x16470,x16471,x16472,x16473,x16474,x16475,x16476,x16477;

Positive Variables  x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16,x17
          ,x18,x19,x20,x21,x22,x23,x24,x25,x26,x27,x28,x29,x30,x31,x32,x33,x34
          ,x35,x36,x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51
          ,x52,x53,x54,x55,x56,x57,x58,x59,x60,x61,x62,x63,x64,x65,x66,x67,x68
          ,x69,x70,x71,x72,x73,x74,x75,x76,x77,x78,x79,x80,x81,x82,x83,x84,x85
          ,x86,x87,x88,x89,x90,x91,x92,x93,x94,x95,x96,x97,x98,x99,x100,x101
          ,x102,x103,x104,x105,x106,x107,x108,x109,x110,x111,x112,x113,x114
          ,x115,x116,x117,x118,x119,x120,x121,x122,x123,x124,x125,x126,x127
          ,x128,x129,x130,x131,x132,x133,x134,x135,x136,x137,x138,x139,x140
          ,x141,x142,x143,x144,x145,x146,x147,x148,x149,x150,x151,x152,x153
          ,x154,x155,x156,x157,x158,x159,x160,x161,x162,x163,x164,x165,x166
          ,x167,x168,x169,x170,x171,x172,x173,x174,x175,x176,x177,x178,x179
          ,x180,x181,x182,x183,x184,x185,x186,x187,x188,x189,x190,x191,x192
          ,x193,x194,x195,x196,x197,x198,x199,x200,x201,x202,x203,x204,x205
          ,x206,x207,x208,x209,x210,x211,x212,x213,x214,x215,x216,x217,x218
          ,x219,x220,x221,x222,x223,x224,x225,x226,x227,x228,x229,x230,x231
          ,x232,x233,x234,x235,x236,x237,x238,x239,x240,x241,x242,x243,x244
          ,x245,x246,x247,x248,x249,x250,x251,x252,x253,x254,x255,x256,x257
          ,x258,x259,x260,x261,x262,x263,x264,x265,x266,x267,x268,x269,x270
          ,x271,x272,x273,x274,x275,x276,x277,x278,x279,x280,x281,x282,x283
          ,x284,x285,x286,x287,x288,x289,x290,x291,x292,x293,x294,x295,x296
          ,x297,x298,x299,x300,x301,x302,x303,x304,x305,x306,x307,x308,x309
          ,x310,x311,x312,x313,x314,x315,x316,x317,x318,x319,x320,x321,x322
          ,x323,x324,x325,x326,x327,x328,x329,x330,x331,x332,x333,x334,x335
          ,x336,x337,x338,x339,x340,x341,x342,x343,x344,x345,x346,x347,x348
          ,x349,x350,x351,x352,x353,x354,x355,x356,x357,x358,x359,x360,x361
          ,x362,x363,x364,x365,x366,x367,x368,x369,x370,x371,x372,x373,x374
          ,x375,x376,x377,x378,x379,x380,x381,x382,x383,x384,x385,x386,x387
          ,x388,x389,x390,x391,x392,x393,x394,x395,x396,x397,x398,x399,x400
          ,x401,x402,x403,x404,x405,x406,x407,x408,x409,x410,x411,x412,x413
          ,x414,x415,x416,x417,x418,x419,x420,x421,x422,x423,x424,x425,x426
          ,x427,x428,x429,x430,x431,x432,x433,x434,x435,x436,x437,x438,x439
          ,x440,x441,x442,x443,x444,x445,x446,x447,x448,x449,x450,x451,x452
          ,x453,x454,x455,x456,x457,x458,x459,x460,x461,x462,x463,x464,x465
          ,x466,x467,x468,x469,x470,x471,x472,x473,x474,x475,x476,x477,x478
          ,x479,x480,x481,x482,x483,x484,x485,x486,x487,x488,x489,x490,x491
          ,x492,x493,x494,x495,x496,x497,x498,x499,x500,x501,x502,x503,x504
          ,x505,x506,x507,x508,x509,x510,x511,x512,x513,x514,x515,x516,x517
          ,x518,x519,x520,x521,x522,x523,x524,x525,x526,x527,x528,x529,x530
          ,x531,x532,x533,x534,x535,x536,x537,x538,x539,x540,x541,x542,x543
          ,x544,x545,x546,x547,x548,x549,x550,x551,x552,x553,x554,x555,x556
          ,x557,x558,x559,x560,x561,x562,x563,x564,x565,x566,x567,x568,x569
          ,x570,x571,x572,x573,x574,x575,x576,x577,x578,x579,x580,x581,x582
          ,x583,x584,x585,x586,x587,x588,x589,x590,x591,x592,x593,x594,x595
          ,x596,x597,x598,x599,x600,x601,x602,x603,x604,x605,x606,x607,x608
          ,x609,x610,x611,x612,x613,x614,x615,x616,x617,x618,x619,x620,x621
          ,x622,x623,x624,x625,x626,x627,x628,x629,x630,x631,x632,x633,x634
          ,x635,x636,x637,x638,x639,x640,x641,x642,x643,x644,x645,x646,x647
          ,x648,x649,x650,x651,x652,x653,x654,x655,x656,x657,x658,x659,x660
          ,x661,x662,x663,x664,x665,x666,x667,x668,x669,x670,x671,x672,x673
          ,x674,x675,x676,x677,x678,x679,x680,x681,x682,x683,x684,x685,x686
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          ,x14794,x14795,x14796,x14797,x14798,x14799,x14800,x14801,x14802
          ,x14803,x14804,x14805,x14806,x14807,x14808,x14809,x14810,x14811
          ,x14812,x14813,x14814,x14815,x14816,x14817,x14818,x14819,x14820
          ,x14821,x14822,x14823,x14824,x14825,x14826,x14827,x14828,x14829
          ,x14830,x14831,x14832,x14833,x14834,x14835,x14836,x14837,x14838
          ,x14839,x14840,x14841,x14842,x14843,x14844,x14845,x14846,x14847
          ,x14848,x14849,x14850,x14851,x14852,x14853,x14854,x14855,x14856
          ,x14857,x14858,x14859,x14860,x14861,x14862,x14863,x14864,x14865
          ,x14866,x14867,x14868,x14869,x14870,x14871,x14872,x14873,x14874
          ,x14875,x14876,x14877,x14878,x14879,x14880,x14881,x14882,x14883
          ,x14884,x14885,x14886,x14887,x14888,x14889,x14890,x14891,x14892
          ,x14893,x14894,x14895,x14896,x14897,x14898,x14899,x14900,x14901
          ,x14902,x14903,x14904,x14905,x14906,x14907,x14908,x14909,x14910
          ,x14911,x14912,x14913,x14914,x14915,x14916,x14917,x14918,x14919
          ,x14920,x14921,x14922,x14923,x14924,x14925,x14926,x14927,x14928
          ,x14929,x14930,x14931,x14932,x14933,x14934,x14935,x14936,x14937
          ,x14938,x14939,x14940,x14941,x14942,x14943,x14944,x14945,x14946
          ,x14947,x14948,x14949,x14950,x14951,x14952,x14953,x14954,x14955
          ,x14956,x14957,x14958,x14959,x14960,x14961,x14962,x14963,x14964
          ,x14965,x14966,x14967,x14968,x14969,x14970,x14971,x14972,x14973
          ,x14974,x14975,x14976,x14977,x14978,x14979,x14980,x14981,x14982
          ,x14983,x14984,x14985,x14986,x14987,x14988,x14989,x14990,x14991
          ,x14992,x14993,x14994,x14995,x14996,x14997,x14998,x14999,x15000
          ,x15001,x15002,x15003,x15004,x15005,x15006,x15007,x15008,x15009
          ,x15010,x15011,x15012,x15013,x15014,x15015,x15016,x15017,x15018
          ,x15019,x15020,x15021,x15022,x15023,x15024,x15025,x15026,x15027
          ,x15028,x15029,x15030,x15031,x15032,x15033,x15034,x15035,x15036
          ,x15037,x15038,x15039,x15040,x15041,x15042,x15043,x15044,x15045
          ,x15046,x15047,x15048,x15049,x15050,x15051,x15052,x15053,x15054
          ,x15055,x15056,x15057,x15058,x15059,x15060,x15061,x15062,x15063
          ,x15064,x15065,x15066,x15067,x15068,x15069,x15070,x15071,x15072
          ,x15073,x15074,x15075,x15076,x15077,x15078,x15079,x15080,x15081
          ,x15082,x15083,x15084,x15085,x15086,x15087,x15088,x15089,x15090
          ,x15091,x15092,x15093,x15094,x15095,x15096,x15097,x15098,x15099
          ,x15100,x15101,x15102,x15103,x15104,x15105,x15106,x15107,x15108
          ,x15109,x15110,x15111,x15112,x15113,x15114,x15115,x15116,x15117
          ,x15118,x15119,x15120,x15121,x15122,x15123,x15124,x15125,x15126
          ,x15127,x15128,x15129,x15130,x15131,x15132,x15133,x15134,x15135
          ,x15136,x15137,x15138,x15139,x15140,x15141,x15142,x15143,x15144
          ,x15145,x15146,x15147,x15148,x15149,x15150,x15151,x15152,x15153
          ,x15154,x15155,x15156,x15157,x15158,x15159,x15160,x15161,x15162
          ,x15163,x15164,x15165,x15166,x15167,x15168,x15169,x15170,x15171
          ,x15172,x15173,x15174,x15175,x15176,x15177,x15178,x15179,x15180
          ,x15181,x15182,x15183,x15184,x15185,x15186,x15187,x15188,x15189
          ,x15190,x15191,x15192,x15193,x15194,x15195,x15196,x15197,x15198
          ,x15199,x15200,x15201,x15202,x15203,x15204,x15205,x15206,x15207
          ,x15208,x15209,x15210,x15211,x15212,x15213,x15214,x15215,x15216
          ,x15217,x15218,x15219,x15220,x15221,x15222,x15223,x15224,x15225
          ,x15226,x15227,x15228,x15229,x15230,x15231,x15232,x15233,x15234
          ,x15235,x15236,x15237,x15238,x15239,x15240,x15241,x15242,x15243
          ,x15244,x15245,x15246,x15247,x15248,x15249,x15250,x15251,x15252
          ,x15253,x15254,x15255,x15256,x15257,x15258,x15259,x15260,x15261
          ,x15262,x15263,x15264,x15265,x15266,x15267,x15268,x15269,x15270
          ,x15271,x15272,x15273,x15274,x15275,x15276,x15277,x15278,x15279
          ,x15280,x15281,x15282,x15283,x15284,x15285,x15286,x15287,x15288
          ,x15289,x15290,x15291,x15292,x15293,x15294,x15295,x15296,x15297
          ,x15298,x15299,x15300,x15301,x15302,x15303,x15304,x15305,x15306
          ,x15307,x15308,x15309,x15310,x15311,x15312,x15313,x15314,x15315
          ,x15316,x15317,x15318,x15319,x15320,x15321,x15322,x15323,x15324
          ,x15325,x15326,x15327,x15328,x15329,x15330,x15331,x15332,x15333
          ,x15334,x15335,x15336,x15337,x15338,x15339,x15340,x15341,x15342
          ,x15343,x15344,x15345,x15346,x15347,x15348,x15349,x15350,x15351
          ,x15352,x15353,x15354,x15355,x15356,x15357,x15358,x15359,x15360
          ,x15361,x15362,x15363,x15364,x15365,x15366,x15367,x15368,x15369
          ,x15370,x15371,x15372,x15373,x15374,x15375,x15376,x15377,x15378
          ,x15379,x15380,x15381,x15382,x15383,x15384,x15385,x15386,x15387
          ,x15388,x15389,x15390,x15391,x15392,x15393,x15394,x15395,x15396
          ,x15397,x15398,x15399,x15400,x15401,x15402,x15403,x15404,x15405
          ,x15406,x15407,x15408,x15409,x15410,x15411,x15412,x15413,x15414
          ,x15415,x15416,x15417,x15418,x15419,x15420,x15421,x15422,x15423
          ,x15424,x15425,x15426,x15427,x15428,x15429,x15430,x15431,x15432
          ,x15433,x15434,x15435,x15436,x15437,x15438,x15439,x15440,x15441
          ,x15442,x15443,x15444,x15445,x15446,x15447,x15448,x15449,x15450
          ,x15451,x15452,x15453,x15454,x15455,x15456,x15457,x15458,x15459
          ,x15460,x15461,x15462,x15463,x15464,x15465,x15466,x15467,x15468
          ,x15469,x15470,x15471,x15472,x15473,x15474,x15475,x15476,x15477
          ,x15478,x15479,x15480,x15481,x15482,x15483,x15484,x15485,x15486
          ,x15487,x15488,x15489,x15490,x15491,x15492,x15493,x15494,x15495
          ,x15496,x15497,x15498,x15499,x15500,x15501,x15502,x15503,x15504
          ,x15505,x15506,x15507,x15508,x15509,x15510,x15511,x15512,x15513
          ,x15514,x15515,x15516,x15517,x15518,x15519,x15520,x15521,x15522
          ,x15523,x15524,x15525,x15526,x15527,x15528,x15529,x15530,x15531
          ,x15532,x15533,x15534,x15535,x15536,x15537,x15538,x15539,x15540
          ,x15541,x15542,x15543,x15544,x15545,x15546,x15547,x15548,x15549
          ,x15550,x15551,x15552,x15553,x15554,x15555,x15556,x15557,x15558
          ,x15559,x15560,x15561,x15562,x15563,x15564,x15565,x16174,x16175
          ,x16176,x16177,x16178,x16179,x16180,x16181,x16182,x16183,x16184
          ,x16185,x16186,x16187,x16188,x16189,x16190,x16191,x16192,x16193
          ,x16194,x16195,x16196,x16197,x16198,x16199,x16200,x16201,x16202
          ,x16203,x16204,x16205,x16206,x16207,x16208,x16209,x16210,x16211
          ,x16212,x16213,x16214,x16215,x16216,x16217,x16218,x16219,x16220
          ,x16221,x16222,x16223,x16224,x16225,x16226,x16227,x16228,x16229
          ,x16230,x16231,x16232,x16233,x16234,x16235,x16236,x16237,x16238
          ,x16239,x16240,x16241,x16242,x16243,x16244,x16245,x16246,x16247
          ,x16248,x16249,x16250,x16251,x16252,x16253,x16254,x16255,x16256
          ,x16257,x16258,x16259,x16260,x16261,x16262,x16263,x16264,x16265
          ,x16266,x16267,x16268,x16269,x16270,x16271,x16272,x16273,x16274
          ,x16275,x16276,x16277,x16278,x16279,x16280,x16281,x16282,x16283
          ,x16284,x16285,x16286,x16287,x16288,x16289,x16290,x16291,x16292
          ,x16293,x16294,x16295,x16296,x16297,x16298,x16299,x16300,x16301
          ,x16302,x16303,x16304,x16305,x16306,x16307,x16308,x16309,x16310
          ,x16311,x16312,x16313,x16314,x16315,x16316,x16317,x16318,x16319
          ,x16320,x16321,x16322,x16323,x16324,x16325,x16326,x16327,x16328
          ,x16329,x16330,x16331,x16332,x16333,x16334,x16335,x16336,x16337
          ,x16338,x16339,x16340,x16341,x16342,x16343,x16344,x16345,x16346
          ,x16347,x16348,x16349,x16350,x16351,x16352,x16353,x16354,x16355
          ,x16356,x16357,x16358,x16359,x16360,x16361,x16362,x16363,x16364
          ,x16365,x16366,x16367,x16368,x16369,x16370,x16371,x16372,x16373
          ,x16374,x16375,x16376,x16377,x16378,x16379,x16380,x16381,x16382
          ,x16383,x16384,x16385,x16386,x16387,x16388,x16389,x16390,x16391
          ,x16392,x16393,x16394,x16395,x16396,x16397,x16398,x16399,x16400
          ,x16401,x16402,x16403,x16404,x16405,x16406,x16407,x16408,x16409
          ,x16410,x16411,x16412,x16413,x16414,x16415,x16416,x16417,x16418
          ,x16419,x16420,x16421,x16422,x16423,x16424,x16425,x16426,x16427
          ,x16428,x16429,x16430,x16431,x16432,x16433,x16434,x16435,x16436
          ,x16437,x16438,x16439,x16440,x16441,x16442,x16443,x16444,x16445
          ,x16446,x16447,x16448,x16449,x16450,x16451,x16452,x16453,x16454
          ,x16455,x16456,x16457,x16458,x16459,x16460,x16461,x16462,x16463
          ,x16464,x16465,x16466,x16467,x16468,x16469,x16470,x16471,x16472
          ,x16473,x16474,x16475,x16476,x16477;

Binary Variables  b6230,b6231,b6232,b6233,b6234,b6235,b6236,b6237,b6238,b6239
          ,b6240,b6241,b6242,b6243,b6244,b6245,b6246,b6247,b6248,b6249,b6250
          ,b6251,b6252,b6253,b6254,b6255,b6256,b6257,b6258,b6259,b6260,b6261
          ,b6262,b6263,b6264,b6265,b6266,b6267,b6268,b6269,b6270,b6271,b6272
          ,b6273,b6274,b6275,b6276,b6277,b6278,b6279,b6280,b6281,b6282,b6283
          ,b6284,b6285,b6286,b6287,b6288,b6289,b6290,b6291,b6292,b6293,b6294
          ,b6295,b6296,b6297,b6298,b6299,b6300,b6301,b6302,b6303,b6304,b6305
          ,b6306,b6307,b6308,b6309,b6310,b6311,b6312,b6313,b6314,b6315,b6316
          ,b6317,b6318,b6319,b6320,b6321,b6322,b6323,b6324,b6325,b6326,b6327
          ,b6328,b6329,b6330,b6331,b6332,b6333,b6334,b6335,b6336,b6337,b6338
          ,b6339,b6340,b6341,b6342,b6343,b6344,b6345,b6346,b6347,b6348,b6349
          ,b6350,b6351,b6352,b6353,b6354,b6355,b6356,b6357,b6358,b6359,b6360
          ,b6361,b6362,b6363,b6364,b6365,b6366,b6367,b6368,b6369,b6370,b6371
          ,b6372,b6373,b6374,b6375,b6376,b6377,b6378,b6379,b6380,b6381,b6382
          ,b6383,b6384,b6385,b6386,b6387,b6388,b6389,b6390,b6391,b6392,b6393
          ,b6394,b6395,b6396,b6397,b6398,b6399,b6400,b6401,b6402,b6403,b6404
          ,b6405,b6406,b6407,b6408,b6409,b6410,b6411,b6412,b6413,b6414,b6415
          ,b6416,b6417,b6418,b6419,b6420,b6421,b6422,b6423,b6424,b6425,b6426
          ,b6427,b6428,b6429,b6430,b6431,b6432,b6433,b6434,b6435,b6436,b6437
          ,b6438,b6439,b6440,b6441,b6442,b6443,b6444,b6445,b6446,b6447,b6448
          ,b6449,b6450,b6451,b6452,b6453,b6454,b6455,b6456,b6457,b6458,b6459
          ,b6460,b6461,b6462,b6463,b6464,b6465,b6466,b6467,b6468,b6469,b6470
          ,b6471,b6472,b6473,b6474,b6475,b6476,b6477,b6478,b6479,b6480,b6481
          ,b6482,b6483,b6484,b6485,b6486,b6487,b6488,b6489,b6490,b6491,b6492
          ,b6493,b6494,b6495,b6496,b6497,b6498,b6499,b6500,b6501,b6502,b6503
          ,b6504,b6505,b6506,b6507,b6508,b6509,b6510,b6511,b6512,b6513,b6514
          ,b6515,b6516,b6517,b6518,b6519,b6520,b6521,b6522,b6523,b6524,b6525
          ,b6526,b6527,b6528,b6529,b6530,b6531,b6532,b6533,b6534,b6535,b6536
          ,b6537,b6538,b6539,b6540,b6541,b6542,b6543,b6544,b6545,b6546,b6547
          ,b6548,b6549,b6550,b6551,b6552,b6553,b6554,b6555,b6556,b6557,b6558
          ,b6559,b6560,b6561,b6562,b6563,b6564,b6565,b6566,b6567,b6568,b6569
          ,b6570,b6571,b6572,b6573,b6574,b6575,b6576,b6577,b6578,b6579,b6580
          ,b6581,b6582,b6583,b6584,b6585,b6586,b6587,b6588,b6589,b6590,b6591
          ,b6592,b6593,b6594,b6595,b6596,b6597,b6598,b6599,b6600,b6601,b6602
          ,b6603,b6604,b6605,b6606,b6607,b6608,b6609,b6610,b6611,b6612,b6613
          ,b6614,b6615,b6616,b6617,b6618,b6619,b6620,b6621,b6622,b6623,b6624
          ,b6625,b6626,b6627,b6628,b6629,b6630,b6631,b6632,b6633,b6634,b6635
          ,b6636,b6637,b6638,b6639,b6640,b6641,b6642,b6643,b6644,b6645,b6646
          ,b6647,b6648,b6649,b6650,b6651,b6652,b6653,b6654,b6655,b6656,b6657
          ,b6658,b6659,b6660,b6661,b6662,b6663,b6664,b6665,b6666,b6667,b6668
          ,b6669,b6670,b6671,b6672,b6673,b6674,b6675,b6676,b6677,b6678,b6679
          ,b6680,b6681,b6682,b6683,b6684,b6685,b6686,b6687,b6688,b6689,b6690
          ,b6691,b6692,b6693,b6694,b6695,b6696,b6697,b6698,b6699,b6700,b6701
          ,b6702,b6703,b6704,b6705,b6706,b6707,b6708,b6709,b6710,b6711,b6712
          ,b6713,b6714,b6715,b6716,b6717,b6718,b6719,b6720,b6721,b6722,b6723
          ,b6724,b6725,b6726,b6727,b6728,b6729,b6730,b6731,b6732,b6733,b6734
          ,b6735,b6736,b6737,b6738,b6739,b6740,b6741,b6742,b6743,b6744,b6745
          ,b6746,b6747,b6748,b6749,b6750,b6751,b6752,b6753,b6754,b6755,b6756
          ,b6757,b6758,b6759,b6760,b6761,b6762,b6763,b6764,b6765,b6766,b6767
          ,b6768,b6769,b6770,b6771,b6772,b6773,b6774,b6775,b6776,b6777,b6778
          ,b6779,b6780,b6781,b6782,b6783,b6784,b6785,b6786,b6787,b6788,b6789
          ,b6790,b6791,b6792,b6793,b6794,b6795,b6796,b6797,b6798,b6799,b6800
          ,b6801,b6802,b6803,b6804,b6805,b6806,b6807,b6808,b6809,b6810,b6811
          ,b6812,b6813,b6814,b6815,b6816,b6817,b6818,b6819,b6820,b6821,b6822
          ,b6823,b6824,b6825,b6826,b6827,b6828,b6829,b6830,b6831,b6832,b6833
          ,b6834,b6835,b6836,b6837,b6838,b6839,b6840,b6841,b6842,b6843,b6844
          ,b6845,b6846,b6847,b6848,b6849,b6850,b6851,b6852,b6853,b6854,b6855
          ,b6856,b6857,b6858,b6859,b6860,b6861,b6862,b6863,b6864,b6865,b6866
          ,b6867,b6868,b6869,b6870,b6871,b6872,b6873,b6874,b6875,b6876,b6877
          ,b6878,b6879,b6880,b6881,b6882,b6883,b6884,b6885,b6886,b6887,b6888
          ,b6889,b6890,b6891,b6892,b6893,b6894,b6895,b6896,b6897,b6898,b6899
          ,b6900,b6901,b6902,b6903,b6904,b6905,b6906,b6907,b6908,b6909,b6910
          ,b6911,b6912,b6913,b6914,b6915,b6916,b6917,b6918,b6919,b6920,b6921
          ,b6922,b6923,b6924,b6925,b6926,b6927,b6928,b6929,b6930,b6931,b6932
          ,b6933,b6934,b6935,b6936,b6937,b6938,b6939,b6940,b6941,b6942,b6943
          ,b6944,b6945,b6946,b6947,b6948,b6949,b6950,b6951,b6952,b6953,b6954
          ,b6955,b6956,b6957,b6958,b6959,b6960,b6961,b6962,b6963,b6964,b6965
          ,b6966,b6967,b6968,b6969,b6970,b6971,b6972,b6973,b6974,b6975,b6976
          ,b6977,b6978,b6979,b6980,b6981,b6982,b6983,b6984,b6985,b6986,b6987
          ,b6988,b6989,b6990,b6991,b6992,b6993,b6994,b6995,b6996,b6997,b6998
          ,b6999,b7000,b7001,b7002,b7003,b7004,b7005,b7006,b7007,b7008,b7009
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          ,b10794,b10795,b10796,b10797,b10798,b10799,b10800,b10801,b10802
          ,b10803,b10804,b10805,b10806,b10807,b10808,b10809,b10810,b10811
          ,b10812,b10813,b10814,b10815,b10816,b10817,b10818,b10819,b10820
          ,b10821,b10822,b10823,b10824,b10825,b10826,b10827,b10828,b10829
          ,b10830,b10831,b10832,b10833,b10834,b10835,b10836,b10837,b10838
          ,b10839,b10840,b10841,b10842,b10843,b10844,b10845,b10846,b10847
          ,b10848,b10849,b10850,b10851,b10852,b10853,b10854,b10855,b10856
          ,b10857,b10858,b10859,b10860,b10861,b10862,b10863,b10864,b10865
          ,b10866,b10867,b10868,b10869,b10870,b10871,b10872,b10873,b10874
          ,b10875,b10876,b10877,b10878,b10879,b10880,b10881,b10882,b10883
          ,b10884,b10885,b10886,b10887,b10888,b10889,b10890,b10891,b10892
          ,b10893,b10894,b10895,b10896,b10897,b10898,b10899,b10900,b10901
          ,b10902,b10903,b10904,b10905,b10906,b10907,b10908,b10909,b10910
          ,b10911,b10912,b10913,b10914,b10915,b10916,b10917,b10918,b10919
          ,b10920,b10921,b10922,b10923,b10924,b10925,b10926,b10927,b10928
          ,b10929,b10930,b10931,b10932,b10933,b10934,b10935,b10936,b10937
          ,b10938,b10939,b10940,b10941,b10942,b10943,b10944,b10945,b10946
          ,b10947,b10948,b10949,b10950,b10951,b10952,b10953,b10954,b10955
          ,b10956,b10957,b10958,b10959,b10960,b10961,b10962,b10963,b10964
          ,b10965,b10966,b10967,b10968,b10969,b10970,b10971,b10972,b10973
          ,b10974,b10975,b10976,b10977,b10978,b10979,b10980,b10981,b10982
          ,b10983,b10984,b10985,b10986,b10987,b10988,b10989,b10990,b10991
          ,b10992,b10993,b10994,b10995,b10996,b10997,b10998,b10999,b11000
          ,b11001,b11002,b11003,b11004,b11005,b11006,b11007,b11008,b11009
          ,b11010,b11011,b11012,b11013,b11014,b11015,b11016,b11017,b11018
          ,b11019,b11020,b11021,b11022,b11023,b11024,b11025,b11026,b11027
          ,b11028,b11029,b11030,b11031,b11032,b11033,b11034,b11035,b11036
          ,b11037,b11038,b11039,b11040,b11041,b11042,b11043,b11044,b11045
          ,b11046,b11047,b11048,b11049,b11050,b11051,b11052,b11053,b11054
          ,b11055,b11056,b11057,b11058,b11059,b11060,b11061,b11062,b11063
          ,b11064,b11065,b11066,b11067,b11068,b11069,b11070,b11071,b11072
          ,b11073,b11074,b11075,b11076,b11077,b11078,b11079,b11080,b11081
          ,b11082,b11083,b11084,b11085,b11086,b11087,b11088,b11089,b11090
          ,b11091,b11092,b11093,b11094,b11095,b11096,b11097,b11098,b11099
          ,b11100,b11101,b11102,b11103,b11104,b11105,b11106,b11107,b11108
          ,b11109,b11110,b11111,b11112,b11113,b11114,b11115,b11116,b11117
          ,b11118,b11119,b11120,b11121,b11122,b11123,b11124,b11125,b11126
          ,b11127,b11128,b11129,b11130,b11131,b11132,b11133,b11134,b11135
          ,b11136,b11137,b11138,b11139,b11140,b11141,b11142,b11143,b11144
          ,b11145,b11146,b11147,b11148,b11149,b11150,b11151,b11152,b11153
          ,b11154,b11155,b11156,b11157,b11158,b11159,b11160,b11161,b11162
          ,b11163,b11164,b11165,b11166,b11167,b11168,b11169,b11170,b11171
          ,b11172,b11173,b11174,b11175,b11176,b11177,b11178,b11179,b11180
          ,b11181,b11182,b11183,b11184,b11185,b11186,b11187,b11188,b11189
          ,b11190,b11191,b11192,b11193,b11194,b11195,b11196,b11197,b11198
          ,b11199,b11200,b11201,b11202,b11203,b11204,b11205,b11206,b11207
          ,b11208,b11209,b11210,b11211,b11212,b11213,b11214,b11215,b11216
          ,b11217,b11218,b11219,b11220,b11221,b11222,b11223,b11224,b11225
          ,b11226,b11227,b11228,b11229,b11230,b11231,b11232,b11233,b11234
          ,b11235,b11236,b11237,b11238,b11239,b11240,b11241,b11242,b11243
          ,b11244,b11245,b11246,b11247,b11248,b11249,b11250,b11251,b11252
          ,b11253,b11254,b11255,b11256,b11257,b11258,b11259,b11260,b11261
          ,b11262,b11263,b11264,b11265,b11266,b11267,b11268,b11269,b11270
          ,b11271,b11272,b11273,b11274,b11275,b11276,b11277,b11278,b11279
          ,b11280,b11281,b11282,b11283,b11284,b11285,b11286,b11287,b11288
          ,b11289,b11290,b11291,b11292,b11293,b11294,b11295,b11296,b11297
          ,b11298,b11299,b11300,b11301,b11302,b11303,b11304,b11305,b11306
          ,b11307,b11308,b11309,b11310,b11311,b11312,b11313,b11314,b11315
          ,b11316,b11317,b11318,b11319,b11320,b11321,b11322,b11323,b11324
          ,b11325,b11326,b11327,b11328,b11329,b11330,b11331,b11332,b11333
          ,b11334,b11335,b11336,b11337,b11338,b11339,b11340,b11341,b11342
          ,b11343,b11344,b11345,b11346,b11347,b11348,b11349,b11350,b11351
          ,b11352,b11353,b11354,b11355,b11356,b11357,b11358,b11359,b11360
          ,b11361,b11362,b11363,b11364,b11365,b11366,b11367,b11368,b11369
          ,b11370,b11371,b11372,b11373,b11374,b11375,b11376,b11377,b11378
          ,b11379,b11380,b11381,b11382,b11383,b11384,b11385,b11386,b11387
          ,b11388,b11389,b11390,b11391,b11392,b11393,b11394,b11395,b11396
          ,b11397,b11398,b11399,b11400,b11401,b11402,b11403,b11404,b11405
          ,b11406,b11407,b11408,b11409,b11410,b11411,b11412,b11413,b11414
          ,b11415,b11416,b11417,b11418,b11419,b11420,b11421,b11422,b11423
          ,b11424,b11425,b11426,b11427,b11428,b11429,b11430,b11431,b11432
          ,b11433,b11434,b11435,b11436,b11437,b11438,b11439,b11440,b11441
          ,b11442,b11443,b11444,b11445,b11446,b11447,b11448,b11449,b11450
          ,b11451,b11452,b11453,b11454,b11455,b11456,b11457,b11458,b11459
          ,b11460,b11461,b11462,b11463,b11464,b11465,b11466,b11467,b11468
          ,b11469,b11470,b11471,b11472,b11473,b11474,b11475,b11476,b11477
          ,b11478,b11479,b11480,b11481,b11482,b11483,b11484,b11485,b11486
          ,b11487,b11488,b11489,b11490,b11491,b11492,b11493,b11494,b11495
          ,b11496,b11497,b11498,b11499,b11500,b11501,b11502,b11503,b11504
          ,b11505,b11506,b11507,b11508,b11509,b11510,b11511,b11512,b11513
          ,b11514,b11515,b11516,b11517,b11518,b11519,b11520,b11521,b11522
          ,b11523,b11524,b11525,b11526,b11527,b11528,b11529,b11530,b11531
          ,b11532,b11533,b11534,b11535,b11536,b11537,b11538,b11539,b11540
          ,b11541,b11542,b11543,b11544,b11545,b11546,b11547,b11548,b11549
          ,b11550,b11551,b11552,b11553,b11554,b11555,b11556,b11557,b11558
          ,b11559,b11560,b11561,b11562,b11563,b11564,b11565,b11566,b11567
          ,b11568,b11569,b11570,b11571,b11572,b11573,b11574,b11575,b11576
          ,b11577,b11578,b11579,b11580,b11581,b11582,b11583,b11584,b11585
          ,b11586,b11587,b11588,b11589,b11590,b11591,b11592,b11593,b11594
          ,b11595,b11596,b11597,b11598,b11599,b11600,b11601,b11602,b11603
          ,b11604,b11605,b11606,b11607,b11608,b11609,b11610,b11611,b11612
          ,b11613,b11614,b11615,b11616,b11617,b11618,b11619,b11620,b11621
          ,b11622,b11623,b11624,b11625,b11626,b11627,b11628,b11629,b11630
          ,b11631,b11632,b11633,b11634,b11635,b11636,b11637,b11638,b11639
          ,b11640,b11641,b11642,b11643,b11644,b11645,b11646,b11647,b11648
          ,b11649,b11650,b11651,b11652,b11653,b11654,b11655,b11656,b11657
          ,b11658,b11659,b11660,b11661,b11662,b11663,b11664,b11665,b11666
          ,b11667,b11668,b11669,b11670,b11671,b11672,b11673,b11674,b11675
          ,b11676,b11677,b11678,b11679,b11680,b11681,b11682,b11683,b11684
          ,b11685,b11686,b11687,b11688,b11689,b11690,b11691,b11692,b11693
          ,b11694,b11695,b11696,b11697,b11698,b11699,b11700,b11701,b11702
          ,b11703,b11704,b11705,b11706,b11707,b11708,b11709,b11710,b11711
          ,b11712,b11713,b11714,b11715,b11716,b11717,b11718,b11719,b11720
          ,b11721,b11722,b11723,b11724,b11725,b11726,b11727,b11728,b11729
          ,b11730,b11731,b11732,b11733,b11734,b11735,b11736,b11737,b11738
          ,b11739,b11740,b11741,b11742,b11743,b11744,b11745,b11746,b11747
          ,b11748,b11749,b11750,b11751,b11752,b11753,b11754,b11755,b11756
          ,b11757,b11758,b11759,b11760,b11761,b11762,b11763,b11764,b11765
          ,b11766,b11767,b11768,b11769,b11770,b11771,b11772,b11773,b11774
          ,b11775,b11776,b11777,b11778,b11779,b11780,b11781,b11782,b11783
          ,b11784,b11785,b11786,b11787,b11788,b11789,b11790,b11791,b11792
          ,b11793,b11794,b11795,b11796,b11797,b11798,b11799,b11800,b11801
          ,b11802,b11803,b11804,b11805,b11806,b11807,b11808,b11809,b11810
          ,b11811,b11812,b11813,b11814,b11815,b11816,b11817,b11818,b11819
          ,b11820,b11821,b11822,b11823,b11824,b11825,b11826,b11827,b11828
          ,b11829,b11830,b11831,b11832,b11833,b11834,b11835,b11836,b11837
          ,b11838,b11839,b11840,b11841,b11842,b11843,b11844,b11845,b11846
          ,b11847,b11848,b11849,b11850,b11851,b11852,b11853,b11854,b11855
          ,b11856,b11857,b11858,b11859,b11860,b11861,b11862,b11863,b11864
          ,b11865,b11866,b11867,b11868,b11869,b11870,b11871,b11872,b11873
          ,b11874,b11875,b11876,b11877,b11878,b11879,b11880,b11881,b11882
          ,b11883,b11884,b11885,b11886,b11887,b11888,b11889,b11890,b11891
          ,b11892,b11893,b11894,b11895,b11896,b11897,b11898,b11899,b11900
          ,b11901,b11902,b11903,b11904,b11905,b11906,b11907,b11908,b11909
          ,b11910,b11911,b11912,b11913,b11914,b11915,b11916,b11917,b11918
          ,b11919,b11920,b11921,b11922,b11923,b11924,b11925,b11926,b11927
          ,b11928,b11929,b11930,b11931,b11932,b11933,b11934,b11935,b11936
          ,b11937,b11938,b11939,b11940,b11941,b11942,b11943,b11944,b11945
          ,b11946,b11947,b11948,b11949,b11950,b11951,b11952,b11953,b11954
          ,b11955,b11956,b11957,b11958,b11959,b11960,b11961,b11962,b11963
          ,b11964,b11965,b11966,b11967,b11968,b11969,b11970,b11971,b11972
          ,b11973,b11974,b11975,b11976,b11977,b11978,b11979,b11980,b11981
          ,b11982,b11983,b11984,b11985,b11986,b11987,b11988,b11989,b11990
          ,b11991,b11992,b11993,b11994,b11995,b11996,b11997,b11998,b11999
          ,b12000,b12001,b12002,b12003,b12004,b12005,b12006,b12007,b12008
          ,b12009,b12010,b12011,b12012,b12013,b12014,b12015,b12016,b12017
          ,b12018,b12019,b12020,b12801,b12802,b12803,b12804,b12805,b12806
          ,b12807,b12808,b12809,b12810,b12811,b12812,b12813,b12814,b12815
          ,b12816,b12817,b12818,b12819,b12820,b12821,b12822,b12823,b12824
          ,b12825,b12826,b12827,b12828,b12829,b12830,b12831,b12832,b12833
          ,b12834,b12835,b12836,b12837,b12838,b12839,b12840,b12841,b12842
          ,b12843,b12844,b12845,b12846,b12847,b12848,b12849,b12850,b12851
          ,b12852,b12853,b12854,b12855,b12856,b12857,b12858,b12859,b12860
          ,b12861,b12862,b12863,b12864,b12865,b12866,b12867,b12868,b12869
          ,b12870,b12871,b12872,b12873,b12874,b12875,b12876,b12877,b12878
          ,b12879,b12880,b12881,b12882,b12883,b12884,b12885,b12886,b12887
          ,b12888,b12889,b12890,b12891,b12892,b12893,b12894,b12895,b12896
          ,b12897,b12898,b12899,b12900,b12901,b12902,b12903,b12904,b12905
          ,b12906,b12907,b12908,b12909,b12910,b12911,b12912,b12913,b12914
          ,b12915,b12916,b12917,b12918,b12919,b12920,b12921,b12922,b12923
          ,b12924,b12925,b12926,b12927,b12928,b12929,b12930,b12931,b12932
          ,b12933,b12934,b12935,b12936,b12937,b12938,b12939,b12940,b12941
          ,b12942,b12943,b12944,b12945,b12946,b12947,b12948,b12949,b12950
          ,b12951,b12952,b12953,b12954,b12955,b12956,b12957,b12958,b12959
          ,b12960,b12961,b12962,b12963,b12964,b12965,b12966,b12967,b12968
          ,b12969,b12970,b12971,b12972,b12973,b12974,b12975,b12976,b12977
          ,b12978,b12979,b12980,b12981,b12982,b12983,b12984,b12985,b12986
          ,b12987,b12988,b12989,b12990,b12991,b12992,b12993,b12994,b12995
          ,b12996,b12997,b12998,b12999,b13000,b13001,b13002,b13003,b13004
          ,b13005,b13006,b13007,b13008,b13009,b13010,b13011,b13012,b13013
          ,b13014,b13015,b13016,b13017,b13018,b13019,b13020,b13021,b13022
          ,b13023,b13024,b13025,b13026,b13027,b13028,b13029,b13030,b13031
          ,b13032,b13033,b13034,b13035,b13036,b13037,b13038,b13039,b13040
          ,b13041,b13042,b13043,b13044,b13045,b13046,b13047,b13048,b13049
          ,b13050,b13051,b13052,b13053,b13054,b13055,b13056,b13057,b13058
          ,b13059,b13060,b13061,b13062,b13063,b13064,b13065,b13066,b13067
          ,b13068,b13069,b13070,b13071,b13072,b13073,b13074,b13075,b13076
          ,b13077,b13078,b13079,b13080,b13081,b13082,b13083,b13084,b13085
          ,b13086,b13087,b13088,b13089,b13090,b13091,b13092,b13093,b13094
          ,b13095,b13096,b13097,b13098,b13099,b13100,b13101,b13102,b13103
          ,b13104,b13105,b13106,b13107,b13108,b13109,b13110,b13111,b13112
          ,b13113,b13114,b13115,b13116,b13117,b13118,b13119,b13120,b13121
          ,b13122,b13123,b13124,b13125,b13126,b13127,b13128,b13129,b13130
          ,b13131,b13132,b13133,b13134,b13135,b13136,b13137,b13138,b13139
          ,b13140,b13141,b13142,b13143,b13144,b13145,b13146,b13147,b13148
          ,b13149,b13150,b13151,b13152,b13153,b13154,b13155,b13156,b13157
          ,b13158,b13159,b13160,b13161,b13162,b13163,b13164,b13165,b13166
          ,b13167,b13168,b13169,b13170,b13171,b13172,b13173,b13174,b13175
          ,b13176,b13177,b13178,b13179,b13180,b13181,b13182,b13183,b13184
          ,b13185,b13186,b13187,b13188,b13189,b13190,b13191,b13192,b13193
          ,b13194,b13195,b13196,b13197,b13198,b13199,b13200,b13201,b13202
          ,b13203,b13204,b13205,b13206,b13207,b13208,b13209,b13210,b13211
          ,b13212,b13213,b13214,b13215,b13216,b13217,b13218,b13219,b13220
          ,b13221,b13222,b13223,b13224,b13225,b13226,b13227,b13228,b13229
          ,b13230,b13231,b13232,b13233,b13234,b13235,b13236,b13237,b13238
          ,b13239,b13240,b13241,b13242,b13243,b13244,b13245,b13246,b13247
          ,b13248,b13249,b13250,b13251,b13252,b13253,b13254,b13255,b13256
          ,b13257,b13258,b13259,b13260,b13261,b13262,b13263,b13264,b13265
          ,b13266,b13267,b13268,b13269,b13270,b13271,b13272,b13273,b13274
          ,b13275,b13276,b13277,b13278,b13279,b13280,b13281,b13282,b13283
          ,b13284,b13285,b13286,b13287,b13288,b13289,b13290,b13291,b13292
          ,b13293,b13294,b13295,b13296,b13297,b13298,b13299,b13300,b13301
          ,b13302,b13303,b13304,b13305,b13306,b13307,b13308,b13309,b13310
          ,b13311,b13312,b13313,b13314,b13315,b13316,b13317,b13318,b13319
          ,b13320,b13321,b13322,b13323,b13324,b13325,b13326,b13327,b13328
          ,b13329,b13330,b13331,b13332,b13333,b13334,b13335,b13336,b13337
          ,b13338,b13339,b13340,b13341,b13342,b13343,b13344,b13345,b13346
          ,b13347,b13348,b13349,b13350,b13351,b13352,b13353,b13354,b13355
          ,b13356,b13357,b13358,b13359,b13360,b13361,b13362,b13363,b13364
          ,b13365,b13366,b13367,b13368,b13369,b13370,b13371,b13372,b13373
          ,b13374,b13375,b13376,b13377,b13378,b13379,b13380,b13381,b13382
          ,b13383,b13384,b13385,b13386,b13387,b13388,b13389,b13390,b13391
          ,b13392,b13393,b13394,b13395,b13396,b13397,b13398,b13399,b13400
          ,b13401,b13402,b13403,b13404,b13405,b13406,b13407,b13408,b13409
          ,b13410,b13411,b13412,b13413,b13414,b13415,b13416,b13417,b13418
          ,b13419,b13420,b13421,b13422,b13423,b13424,b13425,b13426,b13427
          ,b13428,b13429,b13430,b13431,b13432,b13433,b13434,b13435,b13436
          ,b13437;

Equations  e1,e2,e3,e4,e5,e6,e7,e8,e9,e10,e11,e12,e13,e14,e15,e16,e17,e18,e19
          ,e20,e21,e22,e23,e24,e25,e26,e27,e28,e29,e30,e31,e32,e33,e34,e35,e36
          ,e37,e38,e39,e40,e41,e42,e43,e44,e45,e46,e47,e48,e49,e50,e51,e52,e53
          ,e54,e55,e56,e57,e58,e59,e60,e61,e62,e63,e64,e65,e66,e67,e68,e69,e70
          ,e71,e72,e73,e74,e75,e76,e77,e78,e79,e80,e81,e82,e83,e84,e85,e86,e87
          ,e88,e89,e90,e91,e92,e93,e94,e95,e96,e97,e98,e99,e100,e101,e102,e103
          ,e104,e105,e106,e107,e108,e109,e110,e111,e112,e113,e114,e115,e116
          ,e117,e118,e119,e120,e121,e122,e123,e124,e125,e126,e127,e128,e129
          ,e130,e131,e132,e133,e134,e135,e136,e137,e138,e139,e140,e141,e142
          ,e143,e144,e145,e146,e147,e148,e149,e150,e151,e152,e153,e154,e155
          ,e156,e157,e158,e159,e160,e161,e162,e163,e164,e165,e166,e167,e168
          ,e169,e170,e171,e172,e173,e174,e175,e176,e177,e178,e179,e180,e181
          ,e182,e183,e184,e185,e186,e187,e188,e189,e190,e191,e192,e193,e194
          ,e195,e196,e197,e198,e199,e200,e201,e202,e203,e204,e205,e206,e207
          ,e208,e209,e210,e211,e212,e213,e214,e215,e216,e217,e218,e219,e220
          ,e221,e222,e223,e224,e225,e226,e227,e228,e229,e230,e231,e232,e233
          ,e234,e235,e236,e237,e238,e239,e240,e241,e242,e243,e244,e245,e246
          ,e247,e248,e249,e250,e251,e252,e253,e254,e255,e256,e257,e258,e259
          ,e260,e261,e262,e263,e264,e265,e266,e267,e268,e269,e270,e271,e272
          ,e273,e274,e275,e276,e277,e278,e279,e280,e281,e282,e283,e284,e285
          ,e286,e287,e288,e289,e290,e291,e292,e293,e294,e295,e296,e297,e298
          ,e299,e300,e301,e302,e303,e304,e305,e306,e307,e308,e309,e310,e311
          ,e312,e313,e314,e315,e316,e317,e318,e319,e320,e321,e322,e323,e324
          ,e325,e326,e327,e328,e329,e330,e331,e332,e333,e334,e335,e336,e337
          ,e338,e339,e340,e341,e342,e343,e344,e345,e346,e347,e348,e349,e350
          ,e351,e352,e353,e354,e355,e356,e357,e358,e359,e360,e361,e362,e363
          ,e364,e365,e366,e367,e368,e369,e370,e371,e372,e373,e374,e375,e376
          ,e377,e378,e379,e380,e381,e382,e383,e384,e385,e386,e387,e388,e389
          ,e390,e391,e392,e393,e394,e395,e396,e397,e398,e399,e400,e401,e402
          ,e403,e404,e405,e406,e407,e408,e409,e410,e411,e412,e413,e414,e415
          ,e416,e417,e418,e419,e420,e421,e422,e423,e424,e425,e426,e427,e428
          ,e429,e430,e431,e432,e433,e434,e435,e436,e437,e438,e439,e440,e441
          ,e442,e443,e444,e445,e446,e447,e448,e449,e450,e451,e452,e453,e454
          ,e455,e456,e457,e458,e459,e460,e461,e462,e463,e464,e465,e466,e467
          ,e468,e469,e470,e471,e472,e473,e474,e475,e476,e477,e478,e479,e480
          ,e481,e482,e483,e484,e485,e486,e487,e488,e489,e490,e491,e492,e493
          ,e494,e495,e496,e497,e498,e499,e500,e501,e502,e503,e504,e505,e506
          ,e507,e508,e509,e510,e511,e512,e513,e514,e515,e516,e517,e518,e519
          ,e520,e521,e522,e523,e524,e525,e526,e527,e528,e529,e530,e531,e532
          ,e533,e534,e535,e536,e537,e538,e539,e540,e541,e542,e543,e544,e545
          ,e546,e547,e548,e549,e550,e551,e552,e553,e554,e555,e556,e557,e558
          ,e559,e560,e561,e562,e563,e564,e565,e566,e567,e568,e569,e570,e571
          ,e572,e573,e574,e575,e576,e577,e578,e579,e580,e581,e582,e583,e584
          ,e585,e586,e587,e588,e589,e590,e591,e592,e593,e594,e595,e596,e597
          ,e598,e599,e600,e601,e602,e603,e604,e605,e606,e607,e608,e609,e610
          ,e611,e612,e613,e614,e615,e616,e617,e618,e619,e620,e621,e622,e623
          ,e624,e625,e626,e627,e628,e629,e630,e631,e632,e633,e634,e635,e636
          ,e637,e638,e639,e640,e641,e642,e643,e644,e645,e646,e647,e648,e649
          ,e650,e651,e652,e653,e654,e655,e656,e657,e658,e659,e660,e661,e662
          ,e663,e664,e665,e666,e667,e668,e669,e670,e671,e672,e673,e674,e675
          ,e676,e677,e678,e679,e680,e681,e682,e683,e684,e685,e686,e687,e688
          ,e689,e690,e691,e692,e693,e694,e695,e696,e697,e698,e699,e700,e701
          ,e702,e703,e704,e705,e706,e707,e708,e709,e710,e711,e712,e713,e714
          ,e715,e716,e717,e718,e719,e720,e721,e722,e723,e724,e725,e726,e727
          ,e728,e729,e730,e731,e732,e733,e734,e735,e736,e737,e738,e739,e740
          ,e741,e742,e743,e744,e745,e746,e747,e748,e749,e750,e751,e752,e753
          ,e754,e755,e756,e757,e758,e759,e760,e761,e762,e763,e764,e765,e766
          ,e767,e768,e769,e770,e771,e772,e773,e774,e775,e776,e777,e778,e779
          ,e780,e781,e782,e783,e784,e785,e786,e787,e788,e789,e790,e791,e792
          ,e793,e794,e795,e796,e797,e798,e799,e800,e801,e802,e803,e804,e805
          ,e806,e807,e808,e809,e810,e811,e812,e813,e814,e815,e816,e817,e818
          ,e819,e820,e821,e822,e823,e824,e825,e826,e827,e828,e829,e830,e831
          ,e832,e833,e834,e835,e836,e837,e838,e839,e840,e841,e842,e843,e844
          ,e845,e846,e847,e848,e849,e850,e851,e852,e853,e854,e855,e856,e857
          ,e858,e859,e860,e861,e862,e863,e864,e865,e866,e867,e868,e869,e870
          ,e871,e872,e873,e874,e875,e876,e877,e878,e879,e880,e881,e882,e883
          ,e884,e885,e886,e887,e888,e889,e890,e891,e892,e893,e894,e895,e896
          ,e897,e898,e899,e900,e901,e902,e903,e904,e905,e906,e907,e908,e909
          ,e910,e911,e912,e913,e914,e915,e916,e917,e918,e919,e920,e921,e922
          ,e923,e924,e925,e926,e927,e928,e929,e930,e931,e932,e933,e934,e935
          ,e936,e937,e938,e939,e940,e941,e942,e943,e944,e945,e946,e947,e948
          ,e949,e950,e951,e952,e953,e954,e955,e956,e957,e958,e959,e960,e961
          ,e962,e963,e964,e965,e966,e967,e968,e969,e970,e971,e972,e973,e974
          ,e975,e976,e977,e978,e979,e980,e981,e982,e983,e984,e985,e986,e987
          ,e988,e989,e990,e991,e992,e993,e994,e995,e996,e997,e998,e999,e1000
          ,e1001,e1002,e1003,e1004,e1005,e1006,e1007,e1008,e1009,e1010,e1011
          ,e1012,e1013,e1014,e1015,e1016,e1017,e1018,e1019,e1020,e1021,e1022
          ,e1023,e1024,e1025,e1026,e1027,e1028,e1029,e1030,e1031,e1032,e1033
          ,e1034,e1035,e1036,e1037,e1038,e1039,e1040,e1041,e1042,e1043,e1044
          ,e1045,e1046,e1047,e1048,e1049,e1050,e1051,e1052,e1053,e1054,e1055
          ,e1056,e1057,e1058,e1059,e1060,e1061,e1062,e1063,e1064,e1065,e1066
          ,e1067,e1068,e1069,e1070,e1071,e1072,e1073,e1074,e1075,e1076,e1077
          ,e1078,e1079,e1080,e1081,e1082,e1083,e1084,e1085,e1086,e1087,e1088
          ,e1089,e1090,e1091,e1092,e1093,e1094,e1095,e1096,e1097,e1098,e1099
          ,e1100,e1101,e1102,e1103,e1104,e1105,e1106,e1107,e1108,e1109,e1110
          ,e1111,e1112,e1113,e1114,e1115,e1116,e1117,e1118,e1119,e1120,e1121
          ,e1122,e1123,e1124,e1125,e1126,e1127,e1128,e1129,e1130,e1131,e1132
          ,e1133,e1134,e1135,e1136,e1137,e1138,e1139,e1140,e1141,e1142,e1143
          ,e1144,e1145,e1146,e1147,e1148,e1149,e1150,e1151,e1152,e1153,e1154
          ,e1155,e1156,e1157,e1158,e1159,e1160,e1161,e1162,e1163,e1164,e1165
          ,e1166,e1167,e1168,e1169,e1170,e1171,e1172,e1173,e1174,e1175,e1176
          ,e1177,e1178,e1179,e1180,e1181,e1182,e1183,e1184,e1185,e1186,e1187
          ,e1188,e1189,e1190,e1191,e1192,e1193,e1194,e1195,e1196,e1197,e1198
          ,e1199,e1200,e1201,e1202,e1203,e1204,e1205,e1206,e1207,e1208,e1209
          ,e1210,e1211,e1212,e1213,e1214,e1215,e1216,e1217,e1218,e1219,e1220
          ,e1221,e1222,e1223,e1224,e1225,e1226,e1227,e1228,e1229,e1230,e1231
          ,e1232,e1233,e1234,e1235,e1236,e1237,e1238,e1239,e1240,e1241,e1242
          ,e1243,e1244,e1245,e1246,e1247,e1248,e1249,e1250,e1251,e1252,e1253
          ,e1254,e1255,e1256,e1257,e1258,e1259,e1260,e1261,e1262,e1263,e1264
          ,e1265,e1266,e1267,e1268,e1269,e1270,e1271,e1272,e1273,e1274,e1275
          ,e1276,e1277,e1278,e1279,e1280,e1281,e1282,e1283,e1284,e1285,e1286
          ,e1287,e1288,e1289,e1290,e1291,e1292,e1293,e1294,e1295,e1296,e1297
          ,e1298,e1299,e1300,e1301,e1302,e1303,e1304,e1305,e1306,e1307,e1308
          ,e1309,e1310,e1311,e1312,e1313,e1314,e1315,e1316,e1317,e1318,e1319
          ,e1320,e1321,e1322,e1323,e1324,e1325,e1326,e1327,e1328,e1329,e1330
          ,e1331,e1332,e1333,e1334,e1335,e1336,e1337,e1338,e1339,e1340,e1341
          ,e1342,e1343,e1344,e1345,e1346,e1347,e1348,e1349,e1350,e1351,e1352
          ,e1353,e1354,e1355,e1356,e1357,e1358,e1359,e1360,e1361,e1362,e1363
          ,e1364,e1365,e1366,e1367,e1368,e1369,e1370,e1371,e1372,e1373,e1374
          ,e1375,e1376,e1377,e1378,e1379,e1380,e1381,e1382,e1383,e1384,e1385
          ,e1386,e1387,e1388,e1389,e1390,e1391,e1392,e1393,e1394,e1395,e1396
          ,e1397,e1398,e1399,e1400,e1401,e1402,e1403,e1404,e1405,e1406,e1407
          ,e1408,e1409,e1410,e1411,e1412,e1413,e1414,e1415,e1416,e1417,e1418
          ,e1419,e1420,e1421,e1422,e1423,e1424,e1425,e1426,e1427,e1428,e1429
          ,e1430,e1431,e1432,e1433,e1434,e1435,e1436,e1437,e1438,e1439,e1440
          ,e1441,e1442,e1443,e1444,e1445,e1446,e1447,e1448,e1449,e1450,e1451
          ,e1452,e1453,e1454,e1455,e1456,e1457,e1458,e1459,e1460,e1461,e1462
          ,e1463,e1464,e1465,e1466,e1467,e1468,e1469,e1470,e1471,e1472,e1473
          ,e1474,e1475,e1476,e1477,e1478,e1479,e1480,e1481,e1482,e1483,e1484
          ,e1485,e1486,e1487,e1488,e1489,e1490,e1491,e1492,e1493,e1494,e1495
          ,e1496,e1497,e1498,e1499,e1500,e1501,e1502,e1503,e1504,e1505,e1506
          ,e1507,e1508,e1509,e1510,e1511,e1512,e1513,e1514,e1515,e1516,e1517
          ,e1518,e1519,e1520,e1521,e1522,e1523,e1524,e1525,e1526,e1527,e1528
          ,e1529,e1530,e1531,e1532,e1533,e1534,e1535,e1536,e1537,e1538,e1539
          ,e1540,e1541,e1542,e1543,e1544,e1545,e1546,e1547,e1548,e1549,e1550
          ,e1551,e1552,e1553,e1554,e1555,e1556,e1557,e1558,e1559,e1560,e1561
          ,e1562,e1563,e1564,e1565,e1566,e1567,e1568,e1569,e1570,e1571,e1572
          ,e1573,e1574,e1575,e1576,e1577,e1578,e1579,e1580,e1581,e1582,e1583
          ,e1584,e1585,e1586,e1587,e1588,e1589,e1590,e1591,e1592,e1593,e1594
          ,e1595,e1596,e1597,e1598,e1599,e1600,e1601,e1602,e1603,e1604,e1605
          ,e1606,e1607,e1608,e1609,e1610,e1611,e1612,e1613,e1614,e1615,e1616
          ,e1617,e1618,e1619,e1620,e1621,e1622,e1623,e1624,e1625,e1626,e1627
          ,e1628,e1629,e1630,e1631,e1632,e1633,e1634,e1635,e1636,e1637,e1638
          ,e1639,e1640,e1641,e1642,e1643,e1644,e1645,e1646,e1647,e1648,e1649
          ,e1650,e1651,e1652,e1653,e1654,e1655,e1656,e1657,e1658,e1659,e1660
          ,e1661,e1662,e1663,e1664,e1665,e1666,e1667,e1668,e1669,e1670,e1671
          ,e1672,e1673,e1674,e1675,e1676,e1677,e1678,e1679,e1680,e1681,e1682
          ,e1683,e1684,e1685,e1686,e1687,e1688,e1689,e1690,e1691,e1692,e1693
          ,e1694,e1695,e1696,e1697,e1698,e1699,e1700,e1701,e1702,e1703,e1704
          ,e1705,e1706,e1707,e1708,e1709,e1710,e1711,e1712,e1713,e1714,e1715
          ,e1716,e1717,e1718,e1719,e1720,e1721,e1722,e1723,e1724,e1725,e1726
          ,e1727,e1728,e1729,e1730,e1731,e1732,e1733,e1734,e1735,e1736,e1737
          ,e1738,e1739,e1740,e1741,e1742,e1743,e1744,e1745,e1746,e1747,e1748
          ,e1749,e1750,e1751,e1752,e1753,e1754,e1755,e1756,e1757,e1758,e1759
          ,e1760,e1761,e1762,e1763,e1764,e1765,e1766,e1767,e1768,e1769,e1770
          ,e1771,e1772,e1773,e1774,e1775,e1776,e1777,e1778,e1779,e1780,e1781
          ,e1782,e1783,e1784,e1785,e1786,e1787,e1788,e1789,e1790,e1791,e1792
          ,e1793,e1794,e1795,e1796,e1797,e1798,e1799,e1800,e1801,e1802,e1803
          ,e1804,e1805,e1806,e1807,e1808,e1809,e1810,e1811,e1812,e1813,e1814
          ,e1815,e1816,e1817,e1818,e1819,e1820,e1821,e1822,e1823,e1824,e1825
          ,e1826,e1827,e1828,e1829,e1830,e1831,e1832,e1833,e1834,e1835,e1836
          ,e1837,e1838,e1839,e1840,e1841,e1842,e1843,e1844,e1845,e1846,e1847
          ,e1848,e1849,e1850,e1851,e1852,e1853,e1854,e1855,e1856,e1857,e1858
          ,e1859,e1860,e1861,e1862,e1863,e1864,e1865,e1866,e1867,e1868,e1869
          ,e1870,e1871,e1872,e1873,e1874,e1875,e1876,e1877,e1878,e1879,e1880
          ,e1881,e1882,e1883,e1884,e1885,e1886,e1887,e1888,e1889,e1890,e1891
          ,e1892,e1893,e1894,e1895,e1896,e1897,e1898,e1899,e1900,e1901,e1902
          ,e1903,e1904,e1905,e1906,e1907,e1908,e1909,e1910,e1911,e1912,e1913
          ,e1914,e1915,e1916,e1917,e1918,e1919,e1920,e1921,e1922,e1923,e1924
          ,e1925,e1926,e1927,e1928,e1929,e1930,e1931,e1932,e1933,e1934,e1935
          ,e1936,e1937,e1938,e1939,e1940,e1941,e1942,e1943,e1944,e1945,e1946
          ,e1947,e1948,e1949,e1950,e1951,e1952,e1953,e1954,e1955,e1956,e1957
          ,e1958,e1959,e1960,e1961,e1962,e1963,e1964,e1965,e1966,e1967,e1968
          ,e1969,e1970,e1971,e1972,e1973,e1974,e1975,e1976,e1977,e1978,e1979
          ,e1980,e1981,e1982,e1983,e1984,e1985,e1986,e1987,e1988,e1989,e1990
          ,e1991,e1992,e1993,e1994,e1995,e1996,e1997,e1998,e1999,e2000,e2001
          ,e2002,e2003,e2004,e2005,e2006,e2007,e2008,e2009,e2010,e2011,e2012
          ,e2013,e2014,e2015,e2016,e2017,e2018,e2019,e2020,e2021,e2022,e2023
          ,e2024,e2025,e2026,e2027,e2028,e2029,e2030,e2031,e2032,e2033,e2034
          ,e2035,e2036,e2037,e2038,e2039,e2040,e2041,e2042,e2043,e2044,e2045
          ,e2046,e2047,e2048,e2049,e2050,e2051,e2052,e2053,e2054,e2055,e2056
          ,e2057,e2058,e2059,e2060,e2061,e2062,e2063,e2064,e2065,e2066,e2067
          ,e2068,e2069,e2070,e2071,e2072,e2073,e2074,e2075,e2076,e2077,e2078
          ,e2079,e2080,e2081,e2082,e2083,e2084,e2085,e2086,e2087,e2088,e2089
          ,e2090,e2091,e2092,e2093,e2094,e2095,e2096,e2097,e2098,e2099,e2100
          ,e2101,e2102,e2103,e2104,e2105,e2106,e2107,e2108,e2109,e2110,e2111
          ,e2112,e2113,e2114,e2115,e2116,e2117,e2118,e2119,e2120,e2121,e2122
          ,e2123,e2124,e2125,e2126,e2127,e2128,e2129,e2130,e2131,e2132,e2133
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