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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance acopf_case6515rte_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. French system
Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
109802.22060000 p1 ( gdx sol )
(infeas: 6e-12)
Other points (infeas > 1e-08)  
Dual Bounds  
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.
Josz, Cédric, Fliscounakis, Stéphane, Maeght, Jean, and Panciatici, Patrick, AC Power Flow Data in MATPOWER and QCQP Format: iTesla, RTE Snapshots, and PEGASE, Tech. Rep., 2016.
Application Electricity Networks
Added to library 04 Mar 2024
Problem type QCP
#Variables 89575
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 25554
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 1389
#Nonlinear Nonzeros in Objective 0
#Constraints 93059
#Linear Constraints 62208
#Quadratic Constraints 30851
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 330541
#Nonlinear Nonzeros in Jacobian 97850
#Nonzeros in (Upper-Left) Hessian of Lagrangian 90386
#Nonzeros in Diagonal of Hessian of Lagrangian 25554
#Blocks in Hessian of Lagrangian 12525
Minimal blocksize in Hessian of Lagrangian 1
Maximal blocksize in Hessian of Lagrangian 13030
Average blocksize in Hessian of Lagrangian 2.04024
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 1.0940e-03
Maximal coefficient 9.9751e+03
Infeasibility of initial point 1.078e+04
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
*     93060    86798        0     6262        0        0        0        0
*
* Variable counts
*                  x        b        i      s1s      s2s       sc       si
*     Total     cont   binary  integer     sos1     sos2    scont     sint
*     89576    89576        0        0        0        0        0        0
* FX  13471
*
* Nonzero counts
*     Total    const       NL
*    331931   234081    97850

* Solve m using RMIQCP 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,
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    x1910,x1911,x1912,x1913,x1914,x1915,x1916,x1917,x1918,x1919,x1920,x1921,
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    x89289,x89290,x89291,x89292,x89293,x89294,x89295,x89296,x89297,x89298,
    x89299,x89300,x89301,x89302,x89303,x89304,x89305,x89306,x89307,x89308,
    x89309,x89310,x89311,x89312,x89313,x89314,x89315,x89316,x89317,x89318,
    x89319,x89320,x89321,x89322,x89323,x89324,x89325,x89326,x89327,x89328,
    x89329,x89330,x89331,x89332,x89333,x89334,x89335,x89336,x89337,x89338,
    x89339,x89340,x89341,x89342,x89343,x89344,x89345,x89346,x89347,x89348,
    x89349,x89350,x89351,x89352,x89353,x89354,x89355,x89356,x89357,x89358,
    x89359,x89360,x89361,x89362,x89363,x89364,x89365,x89366,x89367,x89368,
    x89369,x89370,x89371,x89372,x89373,x89374,x89375,x89376,x89377,x89378,
    x89379,x89380,x89381,x89382,x89383,x89384,x89385,x89386,x89387,x89388,
    x89389,x89390,x89391,x89392,x89393,x89394,x89395,x89396,x89397,x89398,
    x89399,x89400,x89401,x89402,x89403,x89404,x89405,x89406,x89407,x89408,
    x89409,x89410,x89411,x89412,x89413,x89414,x89415,x89416,x89417,x89418,
    x89419,x89420,x89421,x89422,x89423,x89424,x89425,x89426,x89427,x89428,
    x89429,x89430,x89431,x89432,x89433,x89434,x89435,x89436,x89437,x89438,
    x89439,x89440,x89441,x89442,x89443,x89444,x89445,x89446,x89447,x89448,
    x89449,x89450,x89451,x89452,x89453,x89454,x89455,x89456,x89457,x89458,
    x89459,x89460,x89461,x89462,x89463,x89464,x89465,x89466,x89467,x89468,
    x89469,x89470,x89471,x89472,x89473,x89474,x89475,x89476,x89477,x89478,
    x89479,x89480,x89481,x89482,x89483,x89484,x89485,x89486,x89487,x89488,
    x89489,x89490,x89491,x89492,x89493,x89494,x89495,x89496,x89497,x89498,
    x89499,x89500,x89501,x89502,x89503,x89504,x89505,x89506,x89507,x89508,
    x89509,x89510,x89511,x89512,x89513,x89514,x89515,x89516,x89517,x89518,
    x89519,x89520,x89521,x89522,x89523,x89524,x89525,x89526,x89527,x89528,
    x89529,x89530,x89531,x89532,x89533,x89534,x89535,x89536,x89537,x89538,
    x89539,x89540,x89541,x89542,x89543,x89544,x89545,x89546,x89547,x89548,
    x89549,x89550,x89551,x89552,x89553,x89554,x89555,x89556,x89557,x89558,
    x89559,x89560,x89561,x89562,x89563,x89564,x89565,x89566,x89567,x89568,
    x89569,x89570,x89571,x89572,x89573,x89574,x89575,x89576;

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,
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