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Instance: dtoc5

A discrete time optimal control (DTOC) problem with 50000 time periods, 1 control variable, and 1 state variable. Problem 5 in Coleman and Liao (1995)
Formats ams gms lp mod osil pip
Primal Bounds
5.38967212 p1 ( gdx sol )
(infeas: 6e-17)
Dual Bounds
0.00065522 (BARON)
0.00062677 (SCIP)
References Coleman, Thomas F. and Liao, Aiping, An efficient trust region method for unconstrained discrete-time optimal control problems, Computational Optimization and Applications, 4:1, 1995, 47-66.
Source QPLIB instance 8585, contributed by Nick Gould, CUTEr model DTOC5
Application Optimal Control
Added to library 18 Aug 2018
Problem type QCQP
#Variables 99999
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 99998
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type quadratic
Objective curvature convex
#Nonzeros in Objective 99998
#Nonlinear Nonzeros in Objective 99998
#Constraints 49999
#Linear Constraints 0
#Quadratic Constraints 49999
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 149997
#Nonlinear Nonzeros in Jacobian 49999
#Nonzeros in (Upper-Left) Hessian of Lagrangian 99998
#Nonzeros in Diagonal of Hessian of Lagrangian 99998
#Blocks in Hessian of Lagrangian 99998
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 1
Average blocksize in Hessian of Lagrangian 1.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Infeasibility of initial point 1
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
*      50000    50000        0        0        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*     100000   100000        0        0        0        0        0        0
*  FX      1
*  
*  Nonzero counts
*      Total    const       NL      DLL
*     249996    99999   149997        0
*
*  Solve m using QCP minimizing 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
          ,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,x687
          ,x688,x689,x690,x691,x692,x693,x694,x695,x696,x697,x698,x699,x700
          ,x701,x702,x703,x704,x705,x706,x707,x708,x709,x710,x711,x712,x713
          ,x714,x715,x716,x717,x718,x719,x720,x721,x722,x723,x724,x725,x726
          ,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
          ,x1242,x1243,x1244,x1245,x1246,x1247,x1248,x1249,x1250,x1251,x1252
          ,x1253,x1254,x1255,x1256,x1257,x1258,x1259,x1260,x1261,x1262,x1263
          ,x1264,x1265,x1266,x1267,x1268,x1269,x1270,x1271,x1272,x1273,x1274
          ,x1275,x1276,x1277,x1278,x1279,x1280,x1281,x1282,x1283,x1284,x1285
          ,x1286,x1287,x1288,x1289,x1290,x1291,x1292,x1293,x1294,x1295,x1296
          ,x1297,x1298,x1299,x1300,x1301,x1302,x1303,x1304,x1305,x1306,x1307
          ,x1308,x1309,x1310,x1311,x1312,x1313,x1314,x1315,x1316,x1317,x1318
          ,x1319,x1320,x1321,x1322,x1323,x1324,x1325,x1326,x1327,x1328,x1329
          ,x1330,x1331,x1332,x1333,x1334,x1335,x1336,x1337,x1338,x1339,x1340
          ,x1341,x1342,x1343,x1344,x1345,x1346,x1347,x1348,x1349,x1350,x1351
          ,x1352,x1353,x1354,x1355,x1356,x1357,x1358,x1359,x1360,x1361,x1362
          ,x1363,x1364,x1365,x1366,x1367,x1368,x1369,x1370,x1371,x1372,x1373
          ,x1374,x1375,x1376,x1377,x1378,x1379,x1380,x1381,x1382,x1383,x1384
          ,x1385,x1386,x1387,x1388,x1389,x1390,x1391,x1392,x1393,x1394,x1395
          ,x1396,x1397,x1398,x1399,x1400,x1401,x1402,x1403,x1404,x1405,x1406
          ,x1407,x1408,x1409,x1410,x1411,x1412,x1413,x1414,x1415,x1416,x1417
          ,x1418,x1419,x1420,x1421,x1422,x1423,x1424,x1425,x1426,x1427,x1428
          ,x1429,x1430,x1431,x1432,x1433,x1434,x1435,x1436,x1437,x1438,x1439
          ,x1440,x1441,x1442,x1443,x1444,x1445,x1446,x1447,x1448,x1449,x1450
          ,x1451,x1452,x1453,x1454,x1455,x1456,x1457,x1458,x1459,x1460,x1461
          ,x1462,x1463,x1464,x1465,x1466,x1467,x1468,x1469,x1470,x1471,x1472
          ,x1473,x1474,x1475,x1476,x1477,x1478,x1479,x1480,x1481,x1482,x1483
          ,x1484,x1485,x1486,x1487,x1488,x1489,x1490,x1491,x1492,x1493,x1494
          ,x1495,x1496,x1497,x1498,x1499,x1500,x1501,x1502,x1503,x1504,x1505
          ,x1506,x1507,x1508,x1509,x1510,x1511,x1512,x1513,x1514,x1515,x1516
          ,x1517,x1518,x1519,x1520,x1521,x1522,x1523,x1524,x1525,x1526,x1527
          ,x1528,x1529,x1530,x1531,x1532,x1533,x1534,x1535,x1536,x1537,x1538
          ,x1539,x1540,x1541,x1542,x1543,x1544,x1545,x1546,x1547,x1548,x1549
          ,x1550,x1551,x1552,x1553,x1554,x1555,x1556,x1557,x1558,x1559,x1560
          ,x1561,x1562,x1563,x1564,x1565,x1566,x1567,x1568,x1569,x1570,x1571
          ,x1572,x1573,x1574,x1575,x1576,x1577,x1578,x1579,x1580,x1581,x1582
          ,x1583,x1584,x1585,x1586,x1587,x1588,x1589,x1590,x1591,x1592,x1593
          ,x1594,x1595,x1596,x1597,x1598,x1599,x1600,x1601,x1602,x1603,x1604
          ,x1605,x1606,x1607,x1608,x1609,x1610,x1611,x1612,x1613,x1614,x1615
          ,x1616,x1617,x1618,x1619,x1620,x1621,x1622,x1623,x1624,x1625,x1626
          ,x1627,x1628,x1629,x1630,x1631,x1632,x1633,x1634,x1635,x1636,x1637
          ,x1638,x1639,x1640,x1641,x1642,x1643,x1644,x1645,x1646,x1647,x1648
          ,x1649,x1650,x1651,x1652,x1653,x1654,x1655,x1656,x1657,x1658,x1659
          ,x1660,x1661,x1662,x1663,x1664,x1665,x1666,x1667,x1668,x1669,x1670
          ,x1671,x1672,x1673,x1674,x1675,x1676,x1677,x1678,x1679,x1680,x1681
          ,x1682,x1683,x1684,x1685,x1686,x1687,x1688,x1689,x1690,x1691,x1692
          ,x1693,x1694,x1695,x1696,x1697,x1698,x1699,x1700,x1701,x1702,x1703
          ,x1704,x1705,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,x1862,x1863,x1864,x1865,x1866,x1867,x1868
          ,x1869,x1870,x1871,x1872,x1873,x1874,x1875,x1876,x1877,x1878,x1879
          ,x1880,x1881,x1882,x1883,x1884,x1885,x1886,x1887,x1888,x1889,x1890
          ,x1891,x1892,x1893,x1894,x1895,x1896,x1897,x1898,x1899,x1900,x1901
          ,x1902,x1903,x1904,x1905,x1906,x1907,x1908,x1909,x1910,x1911,x1912
          ,x1913,x1914,x1915,x1916,x1917,x1918,x1919,x1920,x1921,x1922,x1923
          ,x1924,x1925,x1926,x1927,x1928,x1929,x1930,x1931,x1932,x1933,x1934
          ,x1935,x1936,x1937,x1938,x1939,x1940,x1941,x1942,x1943,x1944,x1945
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          ,x99297,x99298,x99299,x99300,x99301,x99302,x99303,x99304,x99305
          ,x99306,x99307,x99308,x99309,x99310,x99311,x99312,x99313,x99314
          ,x99315,x99316,x99317,x99318,x99319,x99320,x99321,x99322,x99323
          ,x99324,x99325,x99326,x99327,x99328,x99329,x99330,x99331,x99332
          ,x99333,x99334,x99335,x99336,x99337,x99338,x99339,x99340,x99341
          ,x99342,x99343,x99344,x99345,x99346,x99347,x99348,x99349,x99350
          ,x99351,x99352,x99353,x99354,x99355,x99356,x99357,x99358,x99359
          ,x99360,x99361,x99362,x99363,x99364,x99365,x99366,x99367,x99368
          ,x99369,x99370,x99371,x99372,x99373,x99374,x99375,x99376,x99377
          ,x99378,x99379,x99380,x99381,x99382,x99383,x99384,x99385,x99386
          ,x99387,x99388,x99389,x99390,x99391,x99392,x99393,x99394,x99395
          ,x99396,x99397,x99398,x99399,x99400,x99401,x99402,x99403,x99404
          ,x99405,x99406,x99407,x99408,x99409,x99410,x99411,x99412,x99413
          ,x99414,x99415,x99416,x99417,x99418,x99419,x99420,x99421,x99422
          ,x99423,x99424,x99425,x99426,x99427,x99428,x99429,x99430,x99431
          ,x99432,x99433,x99434,x99435,x99436,x99437,x99438,x99439,x99440
          ,x99441,x99442,x99443,x99444,x99445,x99446,x99447,x99448,x99449
          ,x99450,x99451,x99452,x99453,x99454,x99455,x99456,x99457,x99458
          ,x99459,x99460,x99461,x99462,x99463,x99464,x99465,x99466,x99467
          ,x99468,x99469,x99470,x99471,x99472,x99473,x99474,x99475,x99476
          ,x99477,x99478,x99479,x99480,x99481,x99482,x99483,x99484,x99485
          ,x99486,x99487,x99488,x99489,x99490,x99491,x99492,x99493,x99494
          ,x99495,x99496,x99497,x99498,x99499,x99500,x99501,x99502,x99503
          ,x99504,x99505,x99506,x99507,x99508,x99509,x99510,x99511,x99512
          ,x99513,x99514,x99515,x99516,x99517,x99518,x99519,x99520,x99521
          ,x99522,x99523,x99524,x99525,x99526,x99527,x99528,x99529,x99530
          ,x99531,x99532,x99533,x99534,x99535,x99536,x99537,x99538,x99539
          ,x99540,x99541,x99542,x99543,x99544,x99545,x99546,x99547,x99548
          ,x99549,x99550,x99551,x99552,x99553,x99554,x99555,x99556,x99557
          ,x99558,x99559,x99560,x99561,x99562,x99563,x99564,x99565,x99566
          ,x99567,x99568,x99569,x99570,x99571,x99572,x99573,x99574,x99575
          ,x99576,x99577,x99578,x99579,x99580,x99581,x99582,x99583,x99584
          ,x99585,x99586,x99587,x99588,x99589,x99590,x99591,x99592,x99593
          ,x99594,x99595,x99596,x99597,x99598,x99599,x99600,x99601,x99602
          ,x99603,x99604,x99605,x99606,x99607,x99608,x99609,x99610,x99611
          ,x99612,x99613,x99614,x99615,x99616,x99617,x99618,x99619,x99620
          ,x99621,x99622,x99623,x99624,x99625,x99626,x99627,x99628,x99629
          ,x99630,x99631,x99632,x99633,x99634,x99635,x99636,x99637,x99638
          ,x99639,x99640,x99641,x99642,x99643,x99644,x99645,x99646,x99647
          ,x99648,x99649,x99650,x99651,x99652,x99653,x99654,x99655,x99656
          ,x99657,x99658,x99659,x99660,x99661,x99662,x99663,x99664,x99665
          ,x99666,x99667,x99668,x99669,x99670,x99671,x99672,x99673,x99674
          ,x99675,x99676,x99677,x99678,x99679,x99680,x99681,x99682,x99683
          ,x99684,x99685,x99686,x99687,x99688,x99689,x99690,x99691,x99692
          ,x99693,x99694,x99695,x99696,x99697,x99698,x99699,x99700,x99701
          ,x99702,x99703,x99704,x99705,x99706,x99707,x99708,x99709,x99710
          ,x99711,x99712,x99713,x99714,x99715,x99716,x99717,x99718,x99719
          ,x99720,x99721,x99722,x99723,x99724,x99725,x99726,x99727,x99728
          ,x99729,x99730,x99731,x99732,x99733,x99734,x99735,x99736,x99737
          ,x99738,x99739,x99740,x99741,x99742,x99743,x99744,x99745,x99746
          ,x99747,x99748,x99749,x99750,x99751,x99752,x99753,x99754,x99755
          ,x99756,x99757,x99758,x99759,x99760,x99761,x99762,x99763,x99764
          ,x99765,x99766,x99767,x99768,x99769,x99770,x99771,x99772,x99773
          ,x99774,x99775,x99776,x99777,x99778,x99779,x99780,x99781,x99782
          ,x99783,x99784,x99785,x99786,x99787,x99788,x99789,x99790,x99791
          ,x99792,x99793,x99794,x99795,x99796,x99797,x99798,x99799,x99800
          ,x99801,x99802,x99803,x99804,x99805,x99806,x99807,x99808,x99809
          ,x99810,x99811,x99812,x99813,x99814,x99815,x99816,x99817,x99818
          ,x99819,x99820,x99821,x99822,x99823,x99824,x99825,x99826,x99827
          ,x99828,x99829,x99830,x99831,x99832,x99833,x99834,x99835,x99836
          ,x99837,x99838,x99839,x99840,x99841,x99842,x99843,x99844,x99845
          ,x99846,x99847,x99848,x99849,x99850,x99851,x99852,x99853,x99854
          ,x99855,x99856,x99857,x99858,x99859,x99860,x99861,x99862,x99863
          ,x99864,x99865,x99866,x99867,x99868,x99869,x99870,x99871,x99872
          ,x99873,x99874,x99875,x99876,x99877,x99878,x99879,x99880,x99881
          ,x99882,x99883,x99884,x99885,x99886,x99887,x99888,x99889,x99890
          ,x99891,x99892,x99893,x99894,x99895,x99896,x99897,x99898,x99899
          ,x99900,x99901,x99902,x99903,x99904,x99905,x99906,x99907,x99908
          ,x99909,x99910,x99911,x99912,x99913,x99914,x99915,x99916,x99917
          ,x99918,x99919,x99920,x99921,x99922,x99923,x99924,x99925,x99926
          ,x99927,x99928,x99929,x99930,x99931,x99932,x99933,x99934,x99935
          ,x99936,x99937,x99938,x99939,x99940,x99941,x99942,x99943,x99944
          ,x99945,x99946,x99947,x99948,x99949,x99950,x99951,x99952,x99953
          ,x99954,x99955,x99956,x99957,x99958,x99959,x99960,x99961,x99962
          ,x99963,x99964,x99965,x99966,x99967,x99968,x99969,x99970,x99971
          ,x99972,x99973,x99974,x99975,x99976,x99977,x99978,x99979,x99980
          ,x99981,x99982,x99983,x99984,x99985,x99986,x99987,x99988,x99989
          ,x99990,x99991,x99992,x99993,x99994,x99995,x99996,x99997,x99998
          ,x99999,x100000;

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
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