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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances
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Instance acopf_caseactivsg25k_qcqp
AC Optimal Power Flow: Given an undirected network, where at every node electric power is generated or demanded and edges model transmission lines, the goal is to minimize the cost of power generation subject to network demand, the nonlinear physics of power flows, and operational constraints. Synthetic US power system model
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | 3129447.11300000 (BARON) 3129447.11300000 (GUROBI) 3129447.10800000 (SCIP) |
| Referencesⓘ | Bienstock, Daniel and Villagra, Matias, Accurate and Warm-Startable Linear Cutting-Plane Relaxations for ACOPF, Tech. Rep., 2024. Hua Wei, H. Sasaki, J. Kubokawa, R. Yokoyama, An interior point nonlinear programming for optimal power flow problems with a novel data structure. In Proceedings of the 20th International Conference on Power Industry Computer Applications, 1997, 134-141. Carpentier, J. L., Contribution a l'Etude du Dispatching Economique, Bulletin de la Societe Francoise des Electriciens, 8, 1962, 431-447. Birchfield, Adam B., Xu, Ti, Gegner, Kathleen M., Shetye, Komal S., and Overbye, Thomas J., Grid Structural Characteristics as Validation Criteria for Synthetic Networks, IEEE Transactions on Power Systems, 32:4, 2017, 3258-3265. Birchfield, Adam B., Xu, Ti, and Overbye, Thomas J., Power Flow Convergence and Reactive Power Planning in the Creation of Large Synthetic Grids, IEEE Transactions on Power Systems, 33:6, 2018, 6667-6674. |
| Applicationⓘ | Electricity Networks |
| Added to libraryⓘ | 04 Mar 2024 |
| Problem typeⓘ | QCQP |
| #Variablesⓘ | 328043 |
| #Binary Variablesⓘ | 0 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 146129 |
| #Nonlinear Binary Variablesⓘ | 0 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | quadratic |
| Objective curvatureⓘ | convex |
| #Nonzeros in Objectiveⓘ | 2858 |
| #Nonlinear Nonzeros in Objectiveⓘ | 2809 |
| #Constraintsⓘ | 365034 |
| #Linear Constraintsⓘ | 228916 |
| #Quadratic Constraintsⓘ | 136118 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 1245593 |
| #Nonlinear Nonzeros in Jacobianⓘ | 401152 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 387009 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 146129 |
| #Blocks in Hessian of Lagrangianⓘ | 96130 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 1 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 50000 |
| Average blocksize in Hessian of Lagrangianⓘ | 1.520119 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.1323e-03 |
| Maximal coefficientⓘ | 1.5103e+06 |
| Infeasibility of initial pointⓘ | 5.062e+04 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 365035 318375 0 46660 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 328044 328044 0 0 0 0 0 0
* FX 47398
*
* Nonzero counts
* Total const NL
* 1248452 844491 403961
* Solve m using RMIQCP minimizing objvar;
Variables
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x40,x41,x42,x43,x44,x45,x46,x47,x48,x49,x50,x51,x52,x53,x54,x55,x56,x57,x58,
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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,
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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,
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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,x1242,x1243,x1244,x1245,x1246,x1247,x1248,x1249,
x1250,x1251,x1252,x1253,x1254,x1255,x1256,x1257,x1258,x1259,x1260,x1261,
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x1394,x1395,x1396,x1397,x1398,x1399,x1400,x1401,x1402,x1403,x1404,x1405,
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x1418,x1419,x1420,x1421,x1422,x1423,x1424,x1425,x1426,x1427,x1428,x1429,
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x1538,x1539,x1540,x1541,x1542,x1543,x1544,x1545,x1546,x1547,x1548,x1549,
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x1706,x1707,x1708,x1709,x1710,x1711,x1712,x1713,x1714,x1715,x1716,x1717,
x1718,x1719,x1720,x1721,x1722,x1723,x1724,x1725,x1726,x1727,x1728,x1729,
x1730,x1731,x1732,x1733,x1734,x1735,x1736,x1737,x1738,x1739,x1740,x1741,
x1742,x1743,x1744,x1745,x1746,x1747,x1748,x1749,x1750,x1751,x1752,x1753,
x1754,x1755,x1756,x1757,x1758,x1759,x1760,x1761,x1762,x1763,x1764,x1765,
x1766,x1767,x1768,x1769,x1770,x1771,x1772,x1773,x1774,x1775,x1776,x1777,
x1778,x1779,x1780,x1781,x1782,x1783,x1784,x1785,x1786,x1787,x1788,x1789,
x1790,x1791,x1792,x1793,x1794,x1795,x1796,x1797,x1798,x1799,x1800,x1801,
x1802,x1803,x1804,x1805,x1806,x1807,x1808,x1809,x1810,x1811,x1812,x1813,
x1814,x1815,x1816,x1817,x1818,x1819,x1820,x1821,x1822,x1823,x1824,x1825,
x1826,x1827,x1828,x1829,x1830,x1831,x1832,x1833,x1834,x1835,x1836,x1837,
x1838,x1839,x1840,x1841,x1842,x1843,x1844,x1845,x1846,x1847,x1848,x1849,
x1850,x1851,x1852,x1853,x1854,x1855,x1856,x1857,x1858,x1859,x1860,x1861,
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x25459,x25460,x25461,x25462,x25463,x25464,x25465,x25466,x25467,x25468,
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x25479,x25480,x25481,x25482,x25483,x25484,x25485,x25486,x25487,x25488,
x25489,x25490,x25491,x25492,x25493,x25494,x25495,x25496,x25497,x25498,
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x25559,x25560,x25561,x25562,x25563,x25564,x25565,x25566,x25567,x25568,
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x25679,x25680,x25681,x25682,x25683,x25684,x25685,x25686,x25687,x25688,
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x25789,x25790,x25791,x25792,x25793,x25794,x25795,x25796,x25797,x25798,
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x127422,x127423,x127424,x127425,x127426,x127427,x127428,x127429,x127430,
x127431,x127432,x127433,x127434,x127435,x127436,x127437,x127438,x127439,
x127440,x127441,x127442,x127443,x127444,x127445,x127446,x127447,x127448,
x127449,x127450,x127451,x127452,x127453,x127454,x127455,x127456,x127457,
x127458,x127459,x127460,x127461,x127462,x127463,x127464,x127465,x127466,
x127467,x127468,x127469,x127470,x127471,x127472,x127473,x127474,x127475,
x127476,x127477,x127478,x127479,x127480,x127481,x127482,x127483,x127484,
x127485,x127486,x127487,x127488,x127489,x127490,x127491,x127492,x127493,
x127494,x127495,x127496,x127497,x127498,x127499,x127500,x127501,x127502,
x127503,x127504,x127505,x127506,x127507,x127508,x127509,x127510,x127511,
x127512,x127513,x127514,x127515,x127516,x127517,x127518,x127519,x127520,
x127521,x127522,x127523,x127524,x127525,x127526,x127527,x127528,x127529,
x127530,x127531,x127532,x127533,x127534,x127535,x127536,x127537,x127538,
x127539,x127540,x127541,x127542,x127543,x127544,x127545,x127546,x127547,
x127548,x127549,x127550,x127551,x127552,x127553,x127554,x127555,x127556,
x127557,x127558,x127559,x127560,x127561,x127562,x127563,x127564,x127565,
x127566,x127567,x127568,x127569,x127570,x127571,x127572,x127573,x127574,
x127575,x127576,x127577,x127578,x127579,x127580,x127581,x127582,x127583,
x127584,x127585,x127586,x127587,x127588,x127589,x127590,x127591,x127592,
x127593,x127594,x127595,x127596,x127597,x127598,x127599,x127600,x127601,
x127602,x127603,x127604,x127605,x127606,x127607,x127608,x127609,x127610,
x127611,x127612,x127613,x127614,x127615,x127616,x127617,x127618,x127619,
x127620,x127621,x127622,x127623,x127624,x127625,x127626,x127627,x127628,
x127629,x127630,x127631,x127632,x127633,x127634,x127635,x127636,x127637,
x127638,x127639,x127640,x127641,x127642,x127643,x127644,x127645,x127646,
x127647,x127648,x127649,x127650,x127651,x127652,x127653,x127654,x127655,
x127656,x127657,x127658,x127659,x127660,x127661,x127662,x127663,x127664,
x127665,x127666,x127667,x127668,x127669,x127670,x127671,x127672,x127673,
x127674,x127675,x127676,x127677,x127678,x127679,x127680,x127681,x127682,
x127683,x127684,x127685,x127686,x127687,x127688,x127689,x127690,x127691,
x127692,x127693,x127694,x127695,x127696,x127697,x127698,x127699,x127700,
x127701,x127702,x127703,x127704,x127705,x127706,x127707,x127708,x127709,
x127710,x127711,x127712,x127713,x127714,x127715,x127716,x127717,x127718,
x127719,x127720,x127721,x127722,x127723,x127724,x127725,x127726,x127727,
x127728,x127729,x127730,x127731,x127732,x127733,x127734,x127735,x127736,
x127737,x127738,x127739,x127740,x127741,x127742,x127743,x127744,x127745,
x127746,x127747,x127748,x127749,x127750,x127751,x127752,x127753,x127754,
x127755,x127756,x127757,x127758,x127759,x127760,x127761,x127762,x127763,
x127764,x127765,x127766,x127767,x127768,x127769,x127770,x127771,x127772,
x127773,x127774,x127775,x127776,x127777,x127778,x127779,x127780,x127781,
x127782,x127783,x127784,x127785,x127786,x127787,x127788,x127789,x127790,
x127791,x127792,x127793,x127794,x127795,x127796,x127797,x127798,x127799,
x127800,x127801,x127802,x127803,x127804,x127805,x127806,x127807,x127808,
x127809,x127810,x127811,x127812,x127813,x127814,x127815,x127816,x127817,
x127818,x127819,x127820,x127821,x127822,x127823,x127824,x127825,x127826,
x127827,x127828,x127829,x127830,x127831,x127832,x127833,x127834,x127835,
x127836,x127837,x127838,x127839,x127840,x127841,x127842,x127843,x127844,
x127845,x127846,x127847,x127848,x127849,x127850,x127851,x127852,x127853,
x127854,x127855,x127856,x127857,x127858,x127859,x127860,x127861,x127862,
x127863,x127864,x127865,x127866,x127867,x127868,x127869,x127870,x127871,
x127872,x127873,x127874,x127875,x127876,x127877,x127878,x127879,x127880,
x127881,x127882,x127883,x127884,x127885,x127886,x127887,x127888,x127889,
x127890,x127891,x127892,x127893,x127894,x127895,x127896,x127897,x127898,
x127899,x127900,x127901,x127902,x127903,x127904,x127905,x127906,x127907,
x127908,x127909,x127910,x127911,x127912,x127913,x127914,x127915,x127916,
x127917,x127918,x127919,x127920,x127921,x127922,x127923,x127924,x127925,
x127926,x127927,x127928,x127929,x127930,x127931,x127932,x127933,x127934,
x127935,x127936,x127937,x127938,x127939,x127940,x127941,x127942,x127943,
x127944,x127945,x127946,x127947,x127948,x127949,x127950,x127951,x127952,
x127953,x127954,x127955,x127956,x127957,x127958,x127959,x127960,x127961,
x127962,x127963,x127964,x127965,x127966,x127967,x127968,x127969,x127970,
x127971,x127972,x127973,x127974,x127975,x127976,x127977,x127978,x127979,
x127980,x127981,x127982,x127983,x127984,x127985,x127986,x127987,x127988,
x127989,x127990,x127991,x127992,x127993,x127994,x127995,x127996,x127997,
x127998,x127999,x128000,x128001,x128002,x128003,x128004,x128005,x128006,
x128007,x128008,x128009,x128010,x128011,x128012,x128013,x128014,x128015,
x128016,x128017,x128018,x128019,x128020,x128021,x128022,x128023,x128024,
x128025,x128026,x128027,x128028,x128029,x128030,x128031,x128032,x128033,
x128034,x128035,x128036,x128037,x128038,x128039,x128040,x128041,x128042,
x128043,x128044,x128045,x128046,x128047,x128048,x128049,x128050,x128051,
x128052,x128053,x128054,x128055,x128056,x128057,x128058,x128059,x128060,
x128061,x128062,x128063,x128064,x128065,x128066,x128067,x128068,x128069,
x128070,x128071,x128072,x128073,x128074,x128075,x128076,x128077,x128078,
x128079,x128080,x128081,x128082,x128083,x128084,x128085,x128086,x128087,
x128088,x128089,x128090,x128091,x128092,x128093,x128094,x128095,x128096,
x128097,x128098,x128099,x128100,x128101,x128102,x128103,x128104,x128105,
x128106,x128107,x128108,x128109,x128110,x128111,x128112,x128113,x128114,
x128115,x128116,x128117,x128118,x128119,x128120,x128121,x128122,x128123,
x128124,x128125,x128126,x128127,x128128,x128129,x128130,x128131,x128132,
x128133,x128134,x128135,x128136,x128137,x128138,x128139,x128140,x128141,
x128142,x128143,x128144,x128145,x128146,x128147,x128148,x128149,x128150,
x128151,x128152,x128153,x128154,x128155,x128156,x128157,x128158,x128159,
x128160,x128161,x128162,x128163,x128164,x128165,x128166,x128167,x128168,
x128169,x128170,x128171,x128172,x128173,x128174,x128175,x128176,x128177,
x128178,x128179,x128180,x128181,x128182,x128183,x128184,x128185,x128186,
x128187,x128188,x128189,x128190,x128191,x128192,x128193,x128194,x128195,
x128196,x128197,x128198,x128199,x128200,x128201,x128202,x128203,x128204,
x128205,x128206,x128207,x128208,x128209,x128210,x128211,x128212,x128213,
x128214,x128215,x128216,x128217,x128218,x128219,x128220,x128221,x128222,
x128223,x128224,x128225,x128226,x128227,x128228,x128229,x128230,x128231,
x128232,x128233,x128234,x128235,x128236,x128237,x128238,x128239,x128240,
x128241,x128242,x128243,x128244,x128245,x128246,x128247,x128248,x128249,
x128250,x128251,x128252,x128253,x128254,x128255,x128256,x128257,x128258,
x128259,x128260,x128261,x128262,x128263,x128264,x128265,x128266,x128267,
x128268,x128269,x128270,x128271,x128272,x128273,x128274,x128275,x128276,
x128277,x128278,x128279,x128280,x128281,x128282,x128283,x128284,x128285,
x128286,x128287,x128288,x128289,x128290,x128291,x128292,x128293,x128294,
x128295,x128296,x128297,x128298,x128299,x128300,x128301,x128302,x128303,
x128304,x128305,x128306,x128307,x128308,x128309,x128310,x128311,x128312,
x128313,x128314,x128315,x128316,x128317,x128318,x128319,x128320,x128321,
x128322,x128323,x128324,x128325,x128326,x128327,x128328,x128329,x128330,
x128331,x128332,x128333,x128334,x128335,x128336,x128337,x128338,x128339,
x128340,x128341,x128342,x128343,x128344,x128345,x128346,x128347,x128348,
x128349,x128350,x128351,x128352,x128353,x128354,x128355,x128356,x128357,
x128358,x128359,x128360,x128361,x128362,x128363,x128364,x128365,x128366,
x128367,x128368,x128369,x128370,x128371,x128372,x128373,x128374,x128375,
x128376,x128377,x128378,x128379,x128380,x128381,x128382,x128383,x128384,
x128385,x128386,x128387,x128388,x128389,x128390,x128391,x128392,x128393,
x128394,x128395,x128396,x128397,x128398,x128399,x128400,x128401,x128402,
x128403,x128404,x128405,x128406,x128407,x128408,x128409,x128410,x128411,
x128412,x128413,x128414,x128415,x128416,x128417,x128418,x128419,x128420,
x128421,x128422,x128423,x128424,x128425,x128426,x128427,x128428,x128429,
x128430,x128431,x128432,x128433,x128434,x128435,x128436,x128437,x128438,
x128439,x128440,x128441,x128442,x128443,x128444,x128445,x128446,x128447,
x128448,x128449,x128450,x128451,x128452,x128453,x128454,x128455,x128456,
x128457,x128458,x128459,x128460,x128461,x128462,x128463,x128464,x128465,
x128466,x128467,x128468,x128469,x128470,x128471,x128472,x128473,x128474,
x128475,x128476,x128477,x128478,x128479,x128480,x128481,x128482,x128483,
x128484,x128485,x128486,x128487,x128488,x128489,x128490,x128491,x128492,
x128493,x128494,x128495,x128496,x128497,x128498,x128499,x128500,x128501,
x128502,x128503,x128504,x128505,x128506,x128507,x128508,x128509,x128510,
x128511,x128512,x128513,x128514,x128515,x128516,x128517,x128518,x128519,
x128520,x128521,x128522,x128523,x128524,x128525,x128526,x128527,x128528,
x128529,x128530,x128531,x128532,x128533,x128534,x128535,x128536,x128537,
x128538,x128539,x128540,x128541,x128542,x128543,x128544,x128545,x128546,
x128547,x128548,x128549,x128550,x128551,x128552,x128553,x128554,x128555,
x128556,x128557,x128558,x128559,x128560,x128561,x128562,x128563,x128564,
x128565,x128566,x128567,x128568,x128569,x128570,x128571,x128572,x128573,
x128574,x128575,x128576,x128577,x128578,x128579,x128580,x128581,x128582,
x128583,x128584,x128585,x128586,x128587,x128588,x128589,x128590,x128591,
x128592,x128593,x128594,x128595,x128596,x128597,x128598,x128599,x128600,
x128601,x128602,x128603,x128604,x128605,x128606,x128607,x128608,x128609,
x128610,x128611,x128612,x128613,x128614,x128615,x128616,x128617,x128618,
x128619,x128620,x128621,x128622,x128623,x128624,x128625,x128626,x128627,
x128628,x128629,x128630,x128631,x128632,x128633,x128634,x128635,x128636,
x128637,x128638,x128639,x128640,x128641,x128642,x128643,x128644,x128645,
x128646,x128647,x128648,x128649,x128650,x128651,x128652,x128653,x128654,
x128655,x128656,x128657,x128658,x128659,x128660,x128661,x128662,x128663,
x128664,x128665,x128666,x128667,x128668,x128669,x128670,x128671,x128672,
x128673,x128674,x128675,x128676,x128677,x128678,x128679,x128680,x128681,
x128682,x128683,x128684,x128685,x128686,x128687,x128688,x128689,x128690,
x128691,x128692,x128693,x128694,x128695,x128696,x128697,x128698,x128699,
x128700,x128701,x128702,x128703,x128704,x128705,x128706,x128707,x128708,
x128709,x128710,x128711,x128712,x128713,x128714,x128715,x128716,x128717,
x128718,x128719,x128720,x128721,x128722,x128723,x128724,x128725,x128726,
x128727,x128728,x128729,x128730,x128731,x128732,x128733,x128734,x128735,
x128736,x128737,x128738,x128739,x128740,x128741,x128742,x128743,x128744,
x128745,x128746,x128747,x128748,x128749,x128750,x128751,x128752,x128753,
x128754,x128755,x128756,x128757,x128758,x128759,x128760,x128761,x128762,
x128763,x128764,x128765,x128766,x128767,x128768,x128769,x128770,x128771,
x128772,x128773,x128774,x128775,x128776,x128777,x128778,x128779,x128780,
x128781,x128782,x128783,x128784,x128785,x128786,x128787,x128788,x128789,
x128790,x128791,x128792,x128793,x128794,x128795,x128796,x128797,x128798,
x128799,x128800,x128801,x128802,x128803,x128804,x128805,x128806,x128807,
x128808,x128809,x128810,x128811,x128812,x128813,x128814,x128815,x128816,
x128817,x128818,x128819,x128820,x128821,x128822,x128823,x128824,x128825,
x128826,x128827,x128828,x128829,x128830,x128831,x128832,x128833,x128834,
x128835,x128836,x128837,x128838,x128839,x128840,x128841,x128842,x128843,
x128844,x128845,x128846,x128847,x128848,x128849,x128850,x128851,x128852,
x128853,x128854,x128855,x128856,x128857,x128858,x128859,x128860,x128861,
x128862,x128863,x128864,x128865,x128866,x128867,x128868,x128869,x128870,
x128871,x128872,x128873,x128874,x128875,x128876,x128877,x128878,x128879,
x128880,x128881,x128882,x128883,x128884,x128885,x128886,x128887,x128888,
x128889,x128890,x128891,x128892,x128893,x128894,x128895,x128896,x128897,
x128898,x128899,x128900,x128901,x128902,x128903,x128904,x128905,x128906,
x128907,x128908,x128909,x128910,x128911,x128912,x128913,x128914,x128915,
x128916,x128917,x128918,x128919,x128920,x128921,x128922,x128923,x128924,
x128925,x128926,x128927,x128928,x128929,x128930,x128931,x128932,x128933,
x128934,x128935,x128936,x128937,x128938,x128939,x128940,x128941,x128942,
x128943,x128944,x128945,x128946,x128947,x128948,x128949,x128950,x128951,
x128952,x128953,x128954,x128955,x128956,x128957,x128958,x128959,x128960,
x128961,x128962,x128963,x128964,x128965,x128966,x128967,x128968,x128969,
x128970,x128971,x128972,x128973,x128974,x128975,x128976,x128977,x128978,
x128979,x128980,x128981,x128982,x128983,x128984,x128985,x128986,x128987,
x128988,x128989,x128990,x128991,x128992,x128993,x128994,x128995,x128996,
x128997,x128998,x128999,x129000,x129001,x129002,x129003,x129004,x129005,
x129006,x129007,x129008,x129009,x129010,x129011,x129012,x129013,x129014,
x129015,x129016,x129017,x129018,x129019,x129020,x129021,x129022,x129023,
x129024,x129025,x129026,x129027,x129028,x129029,x129030,x129031,x129032,
x129033,x129034,x129035,x129036,x129037,x129038,x129039,x129040,x129041,
x129042,x129043,x129044,x129045,x129046,x129047,x129048,x129049,x129050,
x129051,x129052,x129053,x129054,x129055,x129056,x129057,x129058,x129059,
x129060,x129061,x129062,x129063,x129064,x129065,x129066,x129067,x129068,
x129069,x129070,x129071,x129072,x129073,x129074,x129075,x129076,x129077,
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x170622,x170623,x170624,x170625,x170626,x170627,x170628,x170629,x170630,
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x170649,x170650,x170651,x170652,x170653,x170654,x170655,x170656,x170657,
x170658,x170659,x170660,x170661,x170662,x170663,x170664,x170665,x170666,
x170667,x170668,x170669,x170670,x170671,x170672,x170673,x170674,x170675,
x170676,x170677,x170678,x170679,x170680,x170681,x170682,x170683,x170684,
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x239247,x239248,x239249,x239250,x239251,x239252,x239253,x239254,x239255,
x239256,x239257,x239258,x239259,x239260,x239261,x239262,x239263,x239264,
x239265,x239266,x239267,x239268,x239269,x239270,x239271,x239272,x239273,
x239274,x239275,x239276,x239277,x239278,x239279,x239280,x239281,x239282,
x239283,x239284,x239285,x239286,x239287,x239288,x239289,x239290,x239291,
x239292,x239293,x239294,x239295,x239296,x239297,x239298,x239299,x239300,
x239301,x239302,x239303,x239304,x239305,x239306,x239307,x239308,x239309,
x239310,x239311,x239312,x239313,x239314,x239315,x239316,x239317,x239318,
x239319,x239320,x239321,x239322,x239323,x239324,x239325,x239326,x239327,
x239328,x239329,x239330,x239331,x239332,x239333,x239334,x239335,x239336,
x239337,x239338,x239339,x239340,x239341,x239342,x239343,x239344,x239345,
x239346,x239347,x239348,x239349,x239350,x239351,x239352,x239353,x239354,
x239355,x239356,x239357,x239358,x239359,x239360,x239361,x239362,x239363,
x239364,x239365,x239366,x239367,x239368,x239369,x239370,x239371,x239372,
x239373,x239374,x239375,x239376,x239377,x239378,x239379,x239380,x239381,
x239382,x239383,x239384,x239385,x239386,x239387,x239388,x239389,x239390,
x239391,x239392,x239393,x239394,x239395,x239396,x239397,x239398,x239399,
x239400,x239401,x239402,x239403,x239404,x239405,x239406,x239407,x239408,
x239409,x239410,x239411,x239412,x239413,x239414,x239415,x239416,x239417,
x239418,x239419,x239420,x239421,x239422,x239423,x239424,x239425,x239426,
x239427,x239428,x239429,x239430,x239431,x239432,x239433,x239434,x239435,
x239436,x239437,x239438,x239439,x239440,x239441,x239442,x239443,x239444,
x239445,x239446,x239447,x239448,x239449,x239450,x239451,x239452,x239453,
x239454,x239455,x239456,x239457,x239458,x239459,x239460,x239461,x239462,
x239463,x239464,x239465,x239466,x239467,x239468,x239469,x239470,x239471,
x239472,x239473,x239474,x239475,x239476,x239477,x239478,x239479,x239480,
x239481,x239482,x239483,x239484,x239485,x239486,x239487,x239488,x239489,
x239490,x239491,x239492,x239493,x239494,x239495,x239496,x239497,x239498,
x239499,x239500,x239501,x239502,x239503,x239504,x239505,x239506,x239507,
x239508,x239509,x239510,x239511,x239512,x239513,x239514,x239515,x239516,
x239517,x239518,x239519,x239520,x239521,x239522,x239523,x239524,x239525,
x239526,x239527,x239528,x239529,x239530,x239531,x239532,x239533,x239534,
x239535,x239536,x239537,x239538,x239539,x239540,x239541,x239542,x239543,
x239544,x239545,x239546,x239547,x239548,x239549,x239550,x239551,x239552,
x239553,x239554,x239555,x239556,x239557,x239558,x239559,x239560,x239561,
x239562,x239563,x239564,x239565,x239566,x239567,x239568,x239569,x239570,
x239571,x239572,x239573,x239574,x239575,x239576,x239577,x239578,x239579,
x239580,x239581,x239582,x239583,x239584,x239585,x239586,x239587,x239588,
x239589,x239590,x239591,x239592,x239593,x239594,x239595,x239596,x239597,
x239598,x239599,x239600,x239601,x239602,x239603,x239604,x239605,x239606,
x239607,x239608,x239609,x239610,x239611,x239612,x239613,x239614,x239615,
x239616,x239617,x239618,x239619,x239620,x239621,x239622,x239623,x239624,
x239625,x239626,x239627,x239628,x239629,x239630,x239631,x239632,x239633,
x239634,x239635,x239636,x239637,x239638,x239639,x239640,x239641,x239642,
x239643,x239644,x239645,x239646,x239647,x239648,x239649,x239650,x239651,
x239652,x239653,x239654,x239655,x239656,x239657,x239658,x239659,x239660,
x239661,x239662,x239663,x239664,x239665,x239666,x239667,x239668,x239669,
x239670,x239671,x239672,x239673,x239674,x239675,x239676,x239677,x239678,
x239679,x239680,x239681,x239682,x239683,x239684,x239685,x239686,x239687,
x239688,x239689,x239690,x239691,x239692,x239693,x239694,x239695,x239696,
x239697,x239698,x239699,x239700,x239701,x239702,x239703,x239704,x239705,
x239706,x239707,x239708,x239709,x239710,x239711,x239712,x239713,x239714,
x239715,x239716,x239717,x239718,x239719,x239720,x239721,x239722,x239723,
x239724,x239725,x239726,x239727,x239728,x239729,x239730,x239731,x239732,
x239733,x239734,x239735,x239736,x239737,x239738,x239739,x239740,x239741,
x239742,x239743,x239744,x239745,x239746,x239747,x239748,x239749,x239750,
x239751,x239752,x239753,x239754,x239755,x239756,x239757,x239758,x239759,
x239760,x239761,x239762,x239763,x239764,x239765,x239766,x239767,x239768,
x239769,x239770,x239771,x239772,x239773,x239774,x239775,x239776,x239777,
x239778,x239779,x239780,x239781,x239782,x239783,x239784,x239785,x239786,
x239787,x239788,x239789,x239790,x239791,x239792,x239793,x239794,x239795,
x239796,x239797,x239798,x239799,x239800,x239801,x239802,x239803,x239804,
x239805,x239806,x239807,x239808,x239809,x239810,x239811,x239812,x239813,
x239814,x239815,x239816,x239817,x239818,x239819,x239820,x239821,x239822,
x239823,x239824,x239825,x239826,x239827,x239828,x239829,x239830,x239831,
x239832,x239833,x239834,x239835,x239836,x239837,x239838,x239839,x239840,
x239841,x239842,x239843,x239844,x239845,x239846,x239847,x239848,x239849,
x239850,x239851,x239852,x239853,x239854,x239855,x239856,x239857,x239858,
x239859,x239860,x239861,x239862,x239863,x239864,x239865,x239866,x239867,
x239868,x239869,x239870,x239871,x239872,x239873,x239874,x239875,x239876,
x239877,x239878,x239879,x239880,x239881,x239882,x239883,x239884,x239885,
x239886,x239887,x239888,x239889,x239890,x239891,x239892,x239893,x239894,
x239895,x239896,x239897,x239898,x239899,x239900,x239901,x239902,x239903,
x239904,x239905,x239906,x239907,x239908,x239909,x239910,x239911,x239912,
x239913,x239914,x239915,x239916,x239917,x239918,x239919,x239920,x239921,
x239922,x239923,x239924,x239925,x239926,x239927,x239928,x239929,x239930,
x239931,x239932,x239933,x239934,x239935,x239936,x239937,x239938,x239939,
x239940,x239941,x239942,x239943,x239944,x239945,x239946,x239947,x239948,
x239949,x239950,x239951,x239952,x239953,x239954,x239955,x239956,x239957,
x239958,x239959,x239960,x239961,x239962,x239963,x239964,x239965,x239966,
x239967,x239968,x239969,x239970,x239971,x239972,x239973,x239974,x239975,
x239976,x239977,x239978,x239979,x239980,x239981,x239982,x239983,x239984,
x239985,x239986,x239987,x239988,x239989,x239990,x239991,x239992,x239993,
x239994,x239995,x239996,x239997,x239998,x239999,x240000,x240001,x240002,
x240003,x240004,x240005,x240006,x240007,x240008,x240009,x240010,x240011,
x240012,x240013,x240014,x240015,x240016,x240017,x240018,x240019,x240020,
x240021,x240022,x240023,x240024,x240025,x240026,x240027,x240028,x240029,
x240030,x240031,x240032,x240033,x240034,x240035,x240036,x240037,x240038,
x240039,x240040,x240041,x240042,x240043,x240044,x240045,x240046,x240047,
x240048,x240049,x240050,x240051,x240052,x240053,x240054,x240055,x240056,
x240057,x240058,x240059,x240060,x240061,x240062,x240063,x240064,x240065,
x240066,x240067,x240068,x240069,x240070,x240071,x240072,x240073,x240074,
x240075,x240076,x240077,x240078,x240079,x240080,x240081,x240082,x240083,
x240084,x240085,x240086,x240087,x240088,x240089,x240090,x240091,x240092,
x240093,x240094,x240095,x240096,x240097,x240098,x240099,x240100,x240101,
x240102,x240103,x240104,x240105,x240106,x240107,x240108,x240109,x240110,
x240111,x240112,x240113,x240114,x240115,x240116,x240117,x240118,x240119,
x240120,x240121,x240122,x240123,x240124,x240125,x240126,x240127,x240128,
x240129,x240130,x240131,x240132,x240133,x240134,x240135,x240136,x240137,
x240138,x240139,x240140,x240141,x240142,x240143,x240144,x240145,x240146,
x240147,x240148,x240149,x240150,x240151,x240152,x240153,x240154,x240155,
x240156,x240157,x240158,x240159,x240160,x240161,x240162,x240163,x240164,
x240165,x240166,x240167,x240168,x240169,x240170,x240171,x240172,x240173,
x240174,x240175,x240176,x240177,x240178,x240179,x240180,x240181,x240182,
x240183,x240184,x240185,x240186,x240187,x240188,x240189,x240190,x240191,
x240192,x240193,x240194,x240195,x240196,x240197,x240198,x240199,x240200,
x240201,x240202,x240203,x240204,x240205,x240206,x240207,x240208,x240209,
x240210,x240211,x240212,x240213,x240214,x240215,x240216,x240217,x240218,
x240219,x240220,x240221,x240222,x240223,x240224,x240225,x240226,x240227,
x240228,x240229,x240230,x240231,x240232,x240233,x240234,x240235,x240236,
x240237,x240238,x240239,x240240,x240241,x240242,x240243,x240244,x240245,
x240246,x240247,x240248,x240249,x240250,x240251,x240252,x240253,x240254,
x240255,x240256,x240257,x240258,x240259,x240260,x240261,x240262,x240263,
x240264,x240265,x240266,x240267,x240268,x240269,x240270,x240271,x240272,
x240273,x240274,x240275,x240276,x240277,x240278,x240279,x240280,x240281,
x240282,x240283,x240284,x240285,x240286,x240287,x240288,x240289,x240290,
x240291,x240292,x240293,x240294,x240295,x240296,x240297,x240298,x240299,
x240300,x240301,x240302,x240303,x240304,x240305,x240306,x240307,x240308,
x240309,x240310,x240311,x240312,x240313,x240314,x240315,x240316,x240317,
x240318,x240319,x240320,x240321,x240322,x240323,x240324,x240325,x240326,
x240327,x240328,x240329,x240330,x240331,x240332,x240333,x240334,x240335,
x240336,x240337,x240338,x240339,x240340,x240341,x240342,x240343,x240344,
x240345,x240346,x240347,x240348,x240349,x240350,x240351,x240352,x240353,
x240354,x240355,x240356,x240357,x240358,x240359,x240360,x240361,x240362,
x240363,x240364,x240365,x240366,x240367,x240368,x240369,x240370,x240371,
x240372,x240373,x240374,x240375,x240376,x240377,x240378,x240379,x240380,
x240381,x240382,x240383,x240384,x240385,x240386,x240387,x240388,x240389,
x240390,x240391,x240392,x240393,x240394,x240395,x240396,x240397,x240398,
x240399,x240400,x240401,x240402,x240403,x240404,x240405,x240406,x240407,
x240408,x240409,x240410,x240411,x240412,x240413,x240414,x240415,x240416,
x240417,x240418,x240419,x240420,x240421,x240422,x240423,x240424,x240425,
x240426,x240427,x240428,x240429,x240430,x240431,x240432,x240433,x240434,
x240435,x240436,x240437,x240438,x240439,x240440,x240441,x240442,x240443,
x240444,x240445,x240446,x240447,x240448,x240449,x240450,x240451,x240452,
x240453,x240454,x240455,x240456,x240457,x240458,x240459,x240460,x240461,
x240462,x240463,x240464,x240465,x240466,x240467,x240468,x240469,x240470,
x240471,x240472,x240473,x240474,x240475,x240476,x240477,x240478,x240479,
x240480,x240481,x240482,x240483,x240484,x240485,x240486,x240487,x240488,
x240489,x240490,x240491,x240492,x240493,x240494,x240495,x240496,x240497,
x240498,x240499,x240500,x240501,x240502,x240503,x240504,x240505,x240506,
x240507,x240508,x240509,x240510,x240511,x240512,x240513,x240514,x240515,
x240516,x240517,x240518,x240519,x240520,x240521,x240522,x240523,x240524,
x240525,x240526,x240527,x240528,x240529,x240530,x240531,x240532,x240533,
x240534,x240535,x240536,x240537,x240538,x240539,x240540,x240541,x240542,
x240543,x240544,x240545,x240546,x240547,x240548,x240549,x240550,x240551,
x240552,x240553,x240554,x240555,x240556,x240557,x240558,x240559,x240560,
x240561,x240562,x240563,x240564,x240565,x240566,x240567,x240568,x240569,
x240570,x240571,x240572,x240573,x240574,x240575,x240576,x240577,x240578,
x240579,x240580,x240581,x240582,x240583,x240584,x240585,x240586,x240587,
x240588,x240589,x240590,x240591,x240592,x240593,x240594,x240595,x240596,
x240597,x240598,x240599,x240600,x240601,x240602,x240603,x240604,x240605,
x240606,x240607,x240608,x240609,x240610,x240611,x240612,x240613,x240614,
x240615,x240616,x240617,x240618,x240619,x240620,x240621,x240622,x240623,
x240624,x240625,x240626,x240627,x240628,x240629,x240630,x240631,x240632,
x240633,x240634,x240635,x240636,x240637,x240638,x240639,x240640,x240641,
x240642,x240643,x240644,x240645,x240646,x240647,x240648,x240649,x240650,
x240651,x240652,x240653,x240654,x240655,x240656,x240657,x240658,x240659,
x240660,x240661,x240662,x240663,x240664,x240665,x240666,x240667,x240668,
x240669,x240670,x240671,x240672,x240673,x240674,x240675,x240676,x240677,
x240678,x240679,x240680,x240681,x240682,x240683,x240684,x240685,x240686,
x240687,x240688,x240689,x240690,x240691,x240692,x240693,x240694,x240695,
x240696,x240697,x240698,x240699,x240700,x240701,x240702,x240703,x240704,
x240705,x240706,x240707,x240708,x240709,x240710,x240711,x240712,x240713,
x240714,x240715,x240716,x240717,x240718,x240719,x240720,x240721,x240722,
x240723,x240724,x240725,x240726,x240727,x240728,x240729,x240730,x240731,
x240732,x240733,x240734,x240735,x240736,x240737,x240738,x240739,x240740,
x240741,x240742,x240743,x240744,x240745,x240746,x240747,x240748,x240749,
x240750,x240751,x240752,x240753,x240754,x240755,x240756,x240757,x240758,
x240759,x240760,x240761,x240762,x240763,x240764,x240765,x240766,x240767,
x240768,x240769,x240770,x240771,x240772,x240773,x240774,x240775,x240776,
x240777,x240778,x240779,x240780,x240781,x240782,x240783,x240784,x240785,
x240786,x240787,x240788,x240789,x240790,x240791,x240792,x240793,x240794,
x240795,x240796,x240797,x240798,x240799,x240800,x240801,x240802,x240803,
x240804,x240805,x240806,x240807,x240808,x240809,x240810,x240811,x240812,
x240813,x240814,x240815,x240816,x240817,x240818,x240819,x240820,x240821,
x240822,x240823,x240824,x240825,x240826,x240827,x240828,x240829,x240830,
x240831,x240832,x240833,x240834,x240835,x240836,x240837,x240838,x240839,
x240840,x240841,x240842,x240843,x240844,x240845,x240846,x240847,x240848,
x240849,x240850,x240851,x240852,x240853,x240854,x240855,x240856,x240857,
x240858,x240859,x240860,x240861,x240862,x240863,x240864,x240865,x240866,
x240867,x240868,x240869,x240870,x240871,x240872,x240873,x240874,x240875,
x240876,x240877,x240878,x240879,x240880,x240881,x240882,x240883,x240884,
x240885,x240886,x240887,x240888,x240889,x240890,x240891,x240892,x240893,
x240894,x240895,x240896,x240897,x240898,x240899,x240900,x240901,x240902,
x240903,x240904,x240905,x240906,x240907,x240908,x240909,x240910,x240911,
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x250776,x250777,x250778,x250779,x250780,x250781,x250782,x250783,x250784,
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x250794,x250795,x250796,x250797,x250798,x250799,x250800,x250801,x250802,
x250803,x250804,x250805,x250806,x250807,x250808,x250809,x250810,x250811,
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x250857,x250858,x250859,x250860,x250861,x250862,x250863,x250864,x250865,
x250866,x250867,x250868,x250869,x250870,x250871,x250872,x250873,x250874,
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x327915,x327916,x327917,x327918,x327919,x327920,x327921,x327922,x327923,
x327924,x327925,x327926,x327927,x327928,x327929,x327930,x327931,x327932,
x327933,x327934,x327935,x327936,x327937,x327938,x327939,x327940,x327941,
x327942,x327943,x327944,x327945,x327946,x327947,x327948,x327949,x327950,
x327951,x327952,x327953,x327954,x327955,x327956,x327957,x327958,x327959,
x327960,x327961,x327962,x327963,x327964,x327965,x327966,x327967,x327968,
x327969,x327970,x327971,x327972,x327973,x327974,x327975,x327976,x327977,
x327978,x327979,x327980,x327981,x327982,x327983,x327984,x327985,x327986,
x327987,x327988,x327989,x327990,x327991,x327992,x327993,x327994,x327995,
x327996,x327997,x327998,x327999,x328000,x328001,x328002,x328003,x328004,
x328005,x328006,x328007,x328008,x328009,x328010,x328011,x328012,x328013,
x328014,x328015,x328016,x328017,x328018,x328019,x328020,x328021,x328022,
x328023,x328024,x328025,x328026,x328027,x328028,x328029,x328030,x328031,
x328032,x328033,x328034,x328035,x328036,x328037,x328038,x328039,x328040,
x328041,x328042,x328043,x328044;
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,
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e98900,e98901,e98902,e98903,e98904,e98905,e98906,e98907,e98908,e98909,
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e98930,e98931,e98932,e98933,e98934,e98935,e98936,e98937,e98938,e98939,
e98940,e98941,e98942,e98943,e98944,e98945,e98946,e98947,e98948,e98949,
e98950,e98951,e98952,e98953,e98954,e98955,e98956,e98957,e98958,e98959,
e98960,e98961,e98962,e98963,e98964,e98965,e98966,e98967,e98968,e98969,
e98970,e98971,e98972,e98973,e98974,e98975,e98976,e98977,e98978,e98979,
e98980,e98981,e98982,e98983,e98984,e98985,e98986,e98987,e98988,e98989,
e98990,e98991,e98992,e98993,e98994,e98995,e98996,e98997,e98998,e98999,
e99000,e99001,e99002,e99003,e99004,e99005,e99006,e99007,e99008,e99009,
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e99710,e99711,e99712,e99713,e99714,e99715,e99716,e99717,e99718,e99719,
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e99770,e99771,e99772,e99773,e99774,e99775,e99776,e99777,e99778,e99779,
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e99790,e99791,e99792,e99793,e99794,e99795,e99796,e99797,e99798,e99799,
e99800,e99801,e99802,e99803,e99804,e99805,e99806,e99807,e99808,e99809,
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e99890,e99891,e99892,e99893,e99894,e99895,e99896,e99897,e99898,e99899,
e99900,e99901,e99902,e99903,e99904,e99905,e99906,e99907,e99908,e99909,
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e99960,e99961,e99962,e99963,e99964,e99965,e99966,e99967,e99968,e99969,
e99970,e99971,e99972,e99973,e99974,e99975,e99976,e99977,e99978,e99979,
e99980,e99981,e99982,e99983,e99984,e99985,e99986,e99987,e99988,e99989,
e99990,e99991,e99992,e99993,e99994,e99995,e99996,e99997,e99998,e99999,
e100000,e100001,e100002,e100003,e100004,e100005,e100006,e100007,e100008,
e100009,e100010,e100011,e100012,e100013,e100014,e100015,e100016,e100017,
e100018,e100019,e100020,e100021,e100022,e100023,e100024,e100025,e100026,
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e100090,e100091,e100092,e100093,e100094,e100095,e100096,e100097,e100098,
e100099,e100100,e100101,e100102,e100103,e100104,e100105,e100106,e100107,
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e100243,e100244,e100245,e100246,e100247,e100248,e100249,e100250,e100251,
e100252,e100253,e100254,e100255,e100256,e100257,e100258,e100259,e100260,
e100261,e100262,e100263,e100264,e100265,e100266,e100267,e100268,e100269,
e100270,e100271,e100272,e100273,e100274,e100275,e100276,e100277,e100278,
e100279,e100280,e100281,e100282,e100283,e100284,e100285,e100286,e100287,
e100288,e100289,e100290,e100291,e100292,e100293,e100294,e100295,e100296,
e100297,e100298,e100299,e100300,e100301,e100302,e100303,e100304,e100305,
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e31