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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)
6017830.61200000 p1 ( gdx sol )
(infeas: 1e-09)
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.
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 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
*    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
    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,
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    x1886,x1887,x1888,x1889,x1890,x1891,x1892,x1893,x1894,x1895,x1896,x1897,
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    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,
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    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,
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    x128898,x128899,x128900,x128901,x128902,x128903,x128904,x128905,x128906,
    x128907,x128908,x128909,x128910,x128911,x128912,x128913,x128914,x128915,
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    x128925,x128926,x128927,x128928,x128929,x128930,x128931,x128932,x128933,
    x128934,x128935,x128936,x128937,x128938,x128939,x128940,x128941,x128942,
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    x129627,x129628,x129629,x129630,x129631,x129632,x129633,x129634,x129635,
    x129636,x129637,x129638,x129639,x129640,x129641,x129642,x129643,x129644,
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