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Instance faclay75
single-row facility layout problem modeled as a quadratic linear ordering problem An instance of the single-row facility layout problem is formally defined by n one-dimensional facilities with given positive lengths and pairwise non-negative weights. The objective is to arrange the facilities so as to minimize the total weighted sum of the center-to-center distances between all pairs of facilities. This problem can be modeled as a quadratic objective over linear ordering variables.
| Formatsⓘ | ams gms lp mod nl osil pip py |
| Primal Bounds (infeas ≤ 1e-08)ⓘ | |
| Other points (infeas > 1e-08)ⓘ | |
| Dual Boundsⓘ | -11157930.00000000 (BARON) 151500.87730000 (COUENNE) -9289470.60600000 (CPLEX) 1281138.00000000 (GUROBI) 2481301.00000000 (LINDO) 174794.97770000 (SCIP) 189619.75580000 (SHOT) |
| Referencesⓘ | Anjos, Miguel F, Kennings, Andrew, and Vannelli, Anthony, A semidefinite optimization approach for the single-row layout problem with unequal dimensions, Discrete Optimization, 2:2, 2005, 113-122. |
| Sourceⓘ | POLIP instance quadratic_linear_ordering/AnKeVa_2005_75dept_set1 |
| Applicationⓘ | Layout |
| Added to libraryⓘ | 26 Feb 2014 |
| Problem typeⓘ | MBQCP |
| #Variablesⓘ | 2776 |
| #Binary Variablesⓘ | 2775 |
| #Integer Variablesⓘ | 0 |
| #Nonlinear Variablesⓘ | 2775 |
| #Nonlinear Binary Variablesⓘ | 2775 |
| #Nonlinear Integer Variablesⓘ | 0 |
| Objective Senseⓘ | min |
| Objective typeⓘ | linear |
| Objective curvatureⓘ | linear |
| #Nonzeros in Objectiveⓘ | 1 |
| #Nonlinear Nonzeros in Objectiveⓘ | 0 |
| #Constraintsⓘ | 135051 |
| #Linear Constraintsⓘ | 135050 |
| #Quadratic Constraintsⓘ | 1 |
| #Polynomial Constraintsⓘ | 0 |
| #Signomial Constraintsⓘ | 0 |
| #General Nonlinear Constraintsⓘ | 0 |
| Operands in Gen. Nonlin. Functionsⓘ | |
| Constraints curvatureⓘ | indefinite |
| #Nonzeros in Jacobianⓘ | 407926 |
| #Nonlinear Nonzeros in Jacobianⓘ | 2775 |
| #Nonzeros in (Upper-Left) Hessian of Lagrangianⓘ | 293752 |
| #Nonzeros in Diagonal of Hessian of Lagrangianⓘ | 0 |
| #Blocks in Hessian of Lagrangianⓘ | 1 |
| Minimal blocksize in Hessian of Lagrangianⓘ | 2775 |
| Maximal blocksize in Hessian of Lagrangianⓘ | 2775 |
| Average blocksize in Hessian of Lagrangianⓘ | 2775.0 |
| #Semicontinuitiesⓘ | 0 |
| #Nonlinear Semicontinuitiesⓘ | 0 |
| #SOS type 1ⓘ | 0 |
| #SOS type 2ⓘ | 0 |
| Minimal coefficientⓘ | 1.0000e+00 |
| Maximal coefficientⓘ | 3.1494e+04 |
| Infeasibility of initial pointⓘ | 3.945e+06 |
| Sparsity Jacobianⓘ |  |
| Sparsity Hessian of Lagrangianⓘ |  |
$offlisting
*
* Equation counts
* Total E G L N X C B
* 135051 0 1 135050 0 0 0 0
*
* Variable counts
* x b i s1s s2s sc si
* Total cont binary integer sos1 sos2 scont sint
* 2776 1 2775 0 0 0 0 0
* FX 0
*
* Nonzero counts
* Total const NL DLL
* 407926 405151 2775 0
*
* Solve m using MINLP minimizing objvar;
Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17,b18,b19
,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34,b35,b36
,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51,b52,b53
,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68,b69,b70
,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85,b86,b87
,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101,b102,b103
,b104,b105,b106,b107,b108,b109,b110,b111,b112,b113,b114,b115,b116
,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127,b128,b129
,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140,b141,b142
,b143,b144,b145,b146,b147,b148,b149,b150,b151,b152,b153,b154,b155
,b156,b157,b158,b159,b160,b161,b162,b163,b164,b165,b166,b167,b168
,b169,b170,b171,b172,b173,b174,b175,b176,b177,b178,b179,b180,b181
,b182,b183,b184,b185,b186,b187,b188,b189,b190,b191,b192,b193,b194
,b195,b196,b197,b198,b199,b200,b201,b202,b203,b204,b205,b206,b207
,b208,b209,b210,b211,b212,b213,b214,b215,b216,b217,b218,b219,b220
,b221,b222,b223,b224,b225,b226,b227,b228,b229,b230,b231,b232,b233
,b234,b235,b236,b237,b238,b239,b240,b241,b242,b243,b244,b245,b246
,b247,b248,b249,b250,b251,b252,b253,b254,b255,b256,b257,b258,b259
,b260,b261,b262,b263,b264,b265,b266,b267,b268,b269,b270,b271,b272
,b273,b274,b275,b276,b277,b278,b279,b280,b281,b282,b283,b284,b285
,b286,b287,b288,b289,b290,b291,b292,b293,b294,b295,b296,b297,b298
,b299,b300,b301,b302,b303,b304,b305,b306,b307,b308,b309,b310,b311
,b312,b313,b314,b315,b316,b317,b318,b319,b320,b321,b322,b323,b324
,b325,b326,b327,b328,b329,b330,b331,b332,b333,b334,b335,b336,b337
,b338,b339,b340,b341,b342,b343,b344,b345,b346,b347,b348,b349,b350
,b351,b352,b353,b354,b355,b356,b357,b358,b359,b360,b361,b362,b363
,b364,b365,b366,b367,b368,b369,b370,b371,b372,b373,b374,b375,b376
,b377,b378,b379,b380,b381,b382,b383,b384,b385,b386,b387,b388,b389
,b390,b391,b392,b393,b394,b395,b396,b397,b398,b399,b400,b401,b402
,b403,b404,b405,b406,b407,b408,b409,b410,b411,b412,b413,b414,b415
,b416,b417,b418,b419,b420,b421,b422,b423,b424,b425,b426,b427,b428
,b429,b430,b431,b432,b433,b434,b435,b436,b437,b438,b439,b440,b441
,b442,b443,b444,b445,b446,b447,b448,b449,b450,b451,b452,b453,b454
,b455,b456,b457,b458,b459,b460,b461,b462,b463,b464,b465,b466,b467
,b468,b469,b470,b471,b472,b473,b474,b475,b476,b477,b478,b479,b480
,b481,b482,b483,b484,b485,b486,b487,b488,b489,b490,b491,b492,b493
,b494,b495,b496,b497,b498,b499,b500,b501,b502,b503,b504,b505,b506
,b507,b508,b509,b510,b511,b512,b513,b514,b515,b516,b517,b518,b519
,b520,b521,b522,b523,b524,b525,b526,b527,b528,b529,b530,b531,b532
,b533,b534,b535,b536,b537,b538,b539,b540,b541,b542,b543,b544,b545
,b546,b547,b548,b549,b550,b551,b552,b553,b554,b555,b556,b557,b558
,b559,b560,b561,b562,b563,b564,b565,b566,b567,b568,b569,b570,b571
,b572,b573,b574,b575,b576,b577,b578,b579,b580,b581,b582,b583,b584
,b585,b586,b587,b588,b589,b590,b591,b592,b593,b594,b595,b596,b597
,b598,b599,b600,b601,b602,b603,b604,b605,b606,b607,b608,b609,b610
,b611,b612,b613,b614,b615,b616,b617,b618,b619,b620,b621,b622,b623
,b624,b625,b626,b627,b628,b629,b630,b631,b632,b633,b634,b635,b636
,b637,b638,b639,b640,b641,b642,b643,b644,b645,b646,b647,b648,b649
,b650,b651,b652,b653,b654,b655,b656,b657,b658,b659,b660,b661,b662
,b663,b664,b665,b666,b667,b668,b669,b670,b671,b672,b673,b674,b675
,b676,b677,b678,b679,b680,b681,b682,b683,b684,b685,b686,b687,b688
,b689,b690,b691,b692,b693,b694,b695,b696,b697,b698,b699,b700,b701
,b702,b703,b704,b705,b706,b707,b708,b709,b710,b711,b712,b713,b714
,b715,b716,b717,b718,b719,b720,b721,b722,b723,b724,b725,b726,b727
,b728,b729,b730,b731,b732,b733,b734,b735,b736,b737,b738,b739,b740
,b741,b742,b743,b744,b745,b746,b747,b748,b749,b750,b751,b752,b753
,b754,b755,b756,b757,b758,b759,b760,b761,b762,b763,b764,b765,b766
,b767,b768,b769,b770,b771,b772,b773,b774,b775,b776,b777,b778,b779
,b780,b781,b782,b783,b784,b785,b786,b787,b788,b789,b790,b791,b792
,b793,b794,b795,b796,b797,b798,b799,b800,b801,b802,b803,b804,b805
,b806,b807,b808,b809,b810,b811,b812,b813,b814,b815,b816,b817,b818
,b819,b820,b821,b822,b823,b824,b825,b826,b827,b828,b829,b830,b831
,b832,b833,b834,b835,b836,b837,b838,b839,b840,b841,b842,b843,b844
,b845,b846,b847,b848,b849,b850,b851,b852,b853,b854,b855,b856,b857
,b858,b859,b860,b861,b862,b863,b864,b865,b866,b867,b868,b869,b870
,b871,b872,b873,b874,b875,b876,b877,b878,b879,b880,b881,b882,b883
,b884,b885,b886,b887,b888,b889,b890,b891,b892,b893,b894,b895,b896
,b897,b898,b899,b900,b901,b902,b903,b904,b905,b906,b907,b908,b909
,b910,b911,b912,b913,b914,b915,b916,b917,b918,b919,b920,b921,b922
,b923,b924,b925,b926,b927,b928,b929,b930,b931,b932,b933,b934,b935
,b936,b937,b938,b939,b940,b941,b942,b943,b944,b945,b946,b947,b948
,b949,b950,b951,b952,b953,b954,b955,b956,b957,b958,b959,b960,b961
,b962,b963,b964,b965,b966,b967,b968,b969,b970,b971,b972,b973,b974
,b975,b976,b977,b978,b979,b980,b981,b982,b983,b984,b985,b986,b987
,b988,b989,b990,b991,b992,b993,b994,b995,b996,b997,b998,b999,b1000
,b1001,b1002,b1003,b1004,b1005,b1006,b1007,b1008,b1009,b1010,b1011
,b1012,b1013,b1014,b1015,b1016,b1017,b1018,b1019,b1020,b1021,b1022
,b1023,b1024,b1025,b1026,b1027,b1028,b1029,b1030,b1031,b1032,b1033
,b1034,b1035,b1036,b1037,b1038,b1039,b1040,b1041,b1042,b1043,b1044
,b1045,b1046,b1047,b1048,b1049,b1050,b1051,b1052,b1053,b1054,b1055
,b1056,b1057,b1058,b1059,b1060,b1061,b1062,b1063,b1064,b1065,b1066
,b1067,b1068,b1069,b1070,b1071,b1072,b1073,b1074,b1075,b1076,b1077
,b1078,b1079,b1080,b1081,b1082,b1083,b1084,b1085,b1086,b1087,b1088
,b1089,b1090,b1091,b1092,b1093,b1094,b1095,b1096,b1097,b1098,b1099
,b1100,b1101,b1102,b1103,b1104,b1105,b1106,b1107,b1108,b1109,b1110
,b1111,b1112,b1113,b1114,b1115,b1116,b1117,b1118,b1119,b1120,b1121
,b1122,b1123,b1124,b1125,b1126,b1127,b1128,b1129,b1130,b1131,b1132
,b1133,b1134,b1135,b1136,b1137,b1138,b1139,b1140,b1141,b1142,b1143
,b1144,b1145,b1146,b1147,b1148,b1149,b1150,b1151,b1152,b1153,b1154
,b1155,b1156,b1157,b1158,b1159,b1160,b1161,b1162,b1163,b1164,b1165
,b1166,b1167,b1168,b1169,b1170,b1171,b1172,b1173,b1174,b1175,b1176
,b1177,b1178,b1179,b1180,b1181,b1182,b1183,b1184,b1185,b1186,b1187
,b1188,b1189,b1190,b1191,b1192,b1193,b1194,b1195,b1196,b1197,b1198
,b1199,b1200,b1201,b1202,b1203,b1204,b1205,b1206,b1207,b1208,b1209
,b1210,b1211,b1212,b1213,b1214,b1215,b1216,b1217,b1218,b1219,b1220
,b1221,b1222,b1223,b1224,b1225,b1226,b1227,b1228,b1229,b1230,b1231
,b1232,b1233,b1234,b1235,b1236,b1237,b1238,b1239,b1240,b1241,b1242
,b1243,b1244,b1245,b1246,b1247,b1248,b1249,b1250,b1251,b1252,b1253
,b1254,b1255,b1256,b1257,b1258,b1259,b1260,b1261,b1262,b1263,b1264
,b1265,b1266,b1267,b1268,b1269,b1270,b1271,b1272,b1273,b1274,b1275
,b1276,b1277,b1278,b1279,b1280,b1281,b1282,b1283,b1284,b1285,b1286
,b1287,b1288,b1289,b1290,b1291,b1292,b1293,b1294,b1295,b1296,b1297
,b1298,b1299,b1300,b1301,b1302,b1303,b1304,b1305,b1306,b1307,b1308
,b1309,b1310,b1311,b1312,b1313,b1314,b1315,b1316,b1317,b1318,b1319
,b1320,b1321,b1322,b1323,b1324,b1325,b1326,b1327,b1328,b1329,b1330
,b1331,b1332,b1333,b1334,b1335,b1336,b1337,b1338,b1339,b1340,b1341
,b1342,b1343,b1344,b1345,b1346,b1347,b1348,b1349,b1350,b1351,b1352
,b1353,b1354,b1355,b1356,b1357,b1358,b1359,b1360,b1361,b1362,b1363
,b1364,b1365,b1366,b1367,b1368,b1369,b1370,b1371,b1372,b1373,b1374
,b1375,b1376,b1377,b1378,b1379,b1380,b1381,b1382,b1383,b1384,b1385
,b1386,b1387,b1388,b1389,b1390,b1391,b1392,b1393,b1394,b1395,b1396
,b1397,b1398,b1399,b1400,b1401,b1402,b1403,b1404,b1405,b1406,b1407
,b1408,b1409,b1410,b1411,b1412,b1413,b1414,b1415,b1416,b1417,b1418
,b1419,b1420,b1421,b1422,b1423,b1424,b1425,b1426,b1427,b1428,b1429
,b1430,b1431,b1432,b1433,b1434,b1435,b1436,b1437,b1438,b1439,b1440
,b1441,b1442,b1443,b1444,b1445,b1446,b1447,b1448,b1449,b1450,b1451
,b1452,b1453,b1454,b1455,b1456,b1457,b1458,b1459,b1460,b1461,b1462
,b1463,b1464,b1465,b1466,b1467,b1468,b1469,b1470,b1471,b1472,b1473
,b1474,b1475,b1476,b1477,b1478,b1479,b1480,b1481,b1482,b1483,b1484
,b1485,b1486,b1487,b1488,b1489,b1490,b1491,b1492,b1493,b1494,b1495
,b1496,b1497,b1498,b1499,b1500,b1501,b1502,b1503,b1504,b1505,b1506
,b1507,b1508,b1509,b1510,b1511,b1512,b1513,b1514,b1515,b1516,b1517
,b1518,b1519,b1520,b1521,b1522,b1523,b1524,b1525,b1526,b1527,b1528
,b1529,b1530,b1531,b1532,b1533,b1534,b1535,b1536,b1537,b1538,b1539
,b1540,b1541,b1542,b1543,b1544,b1545,b1546,b1547,b1548,b1549,b1550
,b1551,b1552,b1553,b1554,b1555,b1556,b1557,b1558,b1559,b1560,b1561
,b1562,b1563,b1564,b1565,b1566,b1567,b1568,b1569,b1570,b1571,b1572
,b1573,b1574,b1575,b1576,b1577,b1578,b1579,b1580,b1581,b1582,b1583
,b1584,b1585,b1586,b1587,b1588,b1589,b1590,b1591,b1592,b1593,b1594
,b1595,b1596,b1597,b1598,b1599,b1600,b1601,b1602,b1603,b1604,b1605
,b1606,b1607,b1608,b1609,b1610,b1611,b1612,b1613,b1614,b1615,b1616
,b1617,b1618,b1619,b1620,b1621,b1622,b1623,b1624,b1625,b1626,b1627
,b1628,b1629,b1630,b1631,b1632,b1633,b1634,b1635,b1636,b1637,b1638
,b1639,b1640,b1641,b1642,b1643,b1644,b1645,b1646,b1647,b1648,b1649
,b1650,b1651,b1652,b1653,b1654,b1655,b1656,b1657,b1658,b1659,b1660
,b1661,b1662,b1663,b1664,b1665,b1666,b1667,b1668,b1669,b1670,b1671
,b1672,b1673,b1674,b1675,b1676,b1677,b1678,b1679,b1680,b1681,b1682
,b1683,b1684,b1685,b1686,b1687,b1688,b1689,b1690,b1691,b1692,b1693
,b1694,b1695,b1696,b1697,b1698,b1699,b1700,b1701,b1702,b1703,b1704
,b1705,b1706,b1707,b1708,b1709,b1710,b1711,b1712,b1713,b1714,b1715
,b1716,b1717,b1718,b1719,b1720,b1721,b1722,b1723,b1724,b1725,b1726
,b1727,b1728,b1729,b1730,b1731,b1732,b1733,b1734,b1735,b1736,b1737
,b1738,b1739,b1740,b1741,b1742,b1743,b1744,b1745,b1746,b1747,b1748
,b1749,b1750,b1751,b1752,b1753,b1754,b1755,b1756,b1757,b1758,b1759
,b1760,b1761,b1762,b1763,b1764,b1765,b1766,b1767,b1768,b1769,b1770
,b1771,b1772,b1773,b1774,b1775,b1776,b1777,b1778,b1779,b1780,b1781
,b1782,b1783,b1784,b1785,b1786,b1787,b1788,b1789,b1790,b1791,b1792
,b1793,b1794,b1795,b1796,b1797,b1798,b1799,b1800,b1801,b1802,b1803
,b1804,b1805,b1806,b1807,b1808,b1809,b1810,b1811,b1812,b1813,b1814
,b1815,b1816,b1817,b1818,b1819,b1820,b1821,b1822,b1823,b1824,b1825
,b1826,b1827,b1828,b1829,b1830,b1831,b1832,b1833,b1834,b1835,b1836
,b1837,b1838,b1839,b1840,b1841,b1842,b1843,b1844,b1845,b1846,b1847
,b1848,b1849,b1850,b1851,b1852,b1853,b1854,b1855,b1856,b1857,b1858
,b1859,b1860,b1861,b1862,b1863,b1864,b1865,b1866,b1867,b1868,b1869
,b1870,b1871,b1872,b1873,b1874,b1875,b1876,b1877,b1878,b1879,b1880
,b1881,b1882,b1883,b1884,b1885,b1886,b1887,b1888,b1889,b1890,b1891
,b1892,b1893,b1894,b1895,b1896,b1897,b1898,b1899,b1900,b1901,b1902
,b1903,b1904,b1905,b1906,b1907,b1908,b1909,b1910,b1911,b1912,b1913
,b1914,b1915,b1916,b1917,b1918,b1919,b1920,b1921,b1922,b1923,b1924
,b1925,b1926,b1927,b1928,b1929,b1930,b1931,b1932,b1933,b1934,b1935
,b1936,b1937,b1938,b1939,b1940,b1941,b1942,b1943,b1944,b1945,b1946
,b1947,b1948,b1949,b1950,b1951,b1952,b1953,b1954,b1955,b1956,b1957
,b1958,b1959,b1960,b1961,b1962,b1963,b1964,b1965,b1966,b1967,b1968
,b1969,b1970,b1971,b1972,b1973,b1974,b1975,b1976,b1977,b1978,b1979
,b1980,b1981,b1982,b1983,b1984,b1985,b1986,b1987,b1988,b1989,b1990
,b1991,b1992,b1993,b1994,b1995,b1996,b1997,b1998,b1999,b2000,b2001
,b2002,b2003,b2004,b2005,b2006,b2007,b2008,b2009,b2010,b2011,b2012
,b2013,b2014,b2015,b2016,b2017,b2018,b2019,b2020,b2021,b2022,b2023
,b2024,b2025,b2026,b2027,b2028,b2029,b2030,b2031,b2032,b2033,b2034
,b2035,b2036,b2037,b2038,b2039,b2040,b2041,b2042,b2043,b2044,b2045
,b2046,b2047,b2048,b2049,b2050,b2051,b2052,b2053,b2054,b2055,b2056
,b2057,b2058,b2059,b2060,b2061,b2062,b2063,b2064,b2065,b2066,b2067
,b2068,b2069,b2070,b2071,b2072,b2073,b2074,b2075,b2076,b2077,b2078
,b2079,b2080,b2081,b2082,b2083,b2084,b2085,b2086,b2087,b2088,b2089
,b2090,b2091,b2092,b2093,b2094,b2095,b2096,b2097,b2098,b2099,b2100
,b2101,b2102,b2103,b2104,b2105,b2106,b2107,b2108,b2109,b2110,b2111
,b2112,b2113,b2114,b2115,b2116,b2117,b2118,b2119,b2120,b2121,b2122
,b2123,b2124,b2125,b2126,b2127,b2128,b2129,b2130,b2131,b2132,b2133
,b2134,b2135,b2136,b2137,b2138,b2139,b2140,b2141,b2142,b2143,b2144
,b2145,b2146,b2147,b2148,b2149,b2150,b2151,b2152,b2153,b2154,b2155
,b2156,b2157,b2158,b2159,b2160,b2161,b2162,b2163,b2164,b2165,b2166
,b2167,b2168,b2169,b2170,b2171,b2172,b2173,b2174,b2175,b2176,b2177
,b2178,b2179,b2180,b2181,b2182,b2183,b2184,b2185,b2186,b2187,b2188
,b2189,b2190,b2191,b2192,b2193,b2194,b2195,b2196,b2197,b2198,b2199
,b2200,b2201,b2202,b2203,b2204,b2205,b2206,b2207,b2208,b2209,b2210
,b2211,b2212,b2213,b2214,b2215,b2216,b2217,b2218,b2219,b2220,b2221
,b2222,b2223,b2224,b2225,b2226,b2227,b2228,b2229,b2230,b2231,b2232
,b2233,b2234,b2235,b2236,b2237,b2238,b2239,b2240,b2241,b2242,b2243
,b2244,b2245,b2246,b2247,b2248,b2249,b2250,b2251,b2252,b2253,b2254
,b2255,b2256,b2257,b2258,b2259,b2260,b2261,b2262,b2263,b2264,b2265
,b2266,b2267,b2268,b2269,b2270,b2271,b2272,b2273,b2274,b2275,b2276
,b2277,b2278,b2279,b2280,b2281,b2282,b2283,b2284,b2285,b2286,b2287
,b2288,b2289,b2290,b2291,b2292,b2293,b2294,b2295,b2296,b2297,b2298
,b2299,b2300,b2301,b2302,b2303,b2304,b2305,b2306,b2307,b2308,b2309
,b2310,b2311,b2312,b2313,b2314,b2315,b2316,b2317,b2318,b2319,b2320
,b2321,b2322,b2323,b2324,b2325,b2326,b2327,b2328,b2329,b2330,b2331
,b2332,b2333,b2334,b2335,b2336,b2337,b2338,b2339,b2340,b2341,b2342
,b2343,b2344,b2345,b2346,b2347,b2348,b2349,b2350,b2351,b2352,b2353
,b2354,b2355,b2356,b2357,b2358,b2359,b2360,b2361,b2362,b2363,b2364
,b2365,b2366,b2367,b2368,b2369,b2370,b2371,b2372,b2373,b2374,b2375
,b2376,b2377,b2378,b2379,b2380,b2381,b2382,b2383,b2384,b2385,b2386
,b2387,b2388,b2389,b2390,b2391,b2392,b2393,b2394,b2395,b2396,b2397
,b2398,b2399,b2400,b2401,b2402,b2403,b2404,b2405,b2406,b2407,b2408
,b2409,b2410,b2411,b2412,b2413,b2414,b2415,b2416,b2417,b2418,b2419
,b2420,b2421,b2422,b2423,b2424,b2425,b2426,b2427,b2428,b2429,b2430
,b2431,b2432,b2433,b2434,b2435,b2436,b2437,b2438,b2439,b2440,b2441
,b2442,b2443,b2444,b2445,b2446,b2447,b2448,b2449,b2450,b2451,b2452
,b2453,b2454,b2455,b2456,b2457,b2458,b2459,b2460,b2461,b2462,b2463
,b2464,b2465,b2466,b2467,b2468,b2469,b2470,b2471,b2472,b2473,b2474
,b2475,b2476,b2477,b2478,b2479,b2480,b2481,b2482,b2483,b2484,b2485
,b2486,b2487,b2488,b2489,b2490,b2491,b2492,b2493,b2494,b2495,b2496
,b2497,b2498,b2499,b2500,b2501,b2502,b2503,b2504,b2505,b2506,b2507
,b2508,b2509,b2510,b2511,b2512,b2513,b2514,b2515,b2516,b2517,b2518
,b2519,b2520,b2521,b2522,b2523,b2524,b2525,b2526,b2527,b2528,b2529
,b2530,b2531,b2532,b2533,b2534,b2535,b2536,b2537,b2538,b2539,b2540
,b2541,b2542,b2543,b2544,b2545,b2546,b2547,b2548,b2549,b2550,b2551
,b2552,b2553,b2554,b2555,b2556,b2557,b2558,b2559,b2560,b2561,b2562
,b2563,b2564,b2565,b2566,b2567,b2568,b2569,b2570,b2571,b2572,b2573
,b2574,b2575,b2576,b2577,b2578,b2579,b2580,b2581,b2582,b2583,b2584
,b2585,b2586,b2587,b2588,b2589,b2590,b2591,b2592,b2593,b2594,b2595
,b2596,b2597,b2598,b2599,b2600,b2601,b2602,b2603,b2604,b2605,b2606
,b2607,b2608,b2609,b2610,b2611,b2612,b2613,b2614,b2615,b2616,b2617
,b2618,b2619,b2620,b2621,b2622,b2623,b2624,b2625,b2626,b2627,b2628
,b2629,b2630,b2631,b2632,b2633,b2634,b2635,b2636,b2637,b2638,b2639
,b2640,b2641,b2642,b2643,b2644,b2645,b2646,b2647,b2648,b2649,b2650
,b2651,b2652,b2653,b2654,b2655,b2656,b2657,b2658,b2659,b2660,b2661
,b2662,b2663,b2664,b2665,b2666,b2667,b2668,b2669,b2670,b2671,b2672
,b2673,b2674,b2675,b2676,b2677,b2678,b2679,b2680,b2681,b2682,b2683
,b2684,b2685,b2686,b2687,b2688,b2689,b2690,b2691,b2692,b2693,b2694
,b2695,b2696,b2697,b2698,b2699,b2700,b2701,b2702,b2703,b2704,b2705
,b2706,b2707,b2708,b2709,b2710,b2711,b2712,b2713,b2714,b2715,b2716
,b2717,b2718,b2719,b2720,b2721,b2722,b2723,b2724,b2725,b2726,b2727
,b2728,b2729,b2730,b2731,b2732,b2733,b2734,b2735,b2736,b2737,b2738
,b2739,b2740,b2741,b2742,b2743,b2744,b2745,b2746,b2747,b2748,b2749
,b2750,b2751,b2752,b2753,b2754,b2755,b2756,b2757,b2758,b2759,b2760
,b2761,b2762,b2763,b2764,b2765,b2766,b2767,b2768,b2769,b2770,b2771
,b2772,b2773,b2774,b2775,objvar;
Binary Variables b1,b2,b3,b4,b5,b6,b7,b8,b9,b10,b11,b12,b13,b14,b15,b16,b17
,b18,b19,b20,b21,b22,b23,b24,b25,b26,b27,b28,b29,b30,b31,b32,b33,b34
,b35,b36,b37,b38,b39,b40,b41,b42,b43,b44,b45,b46,b47,b48,b49,b50,b51
,b52,b53,b54,b55,b56,b57,b58,b59,b60,b61,b62,b63,b64,b65,b66,b67,b68
,b69,b70,b71,b72,b73,b74,b75,b76,b77,b78,b79,b80,b81,b82,b83,b84,b85
,b86,b87,b88,b89,b90,b91,b92,b93,b94,b95,b96,b97,b98,b99,b100,b101
,b102,b103,b104,b105,b106,b107,b108,b109,b110,b111,b112,b113,b114
,b115,b116,b117,b118,b119,b120,b121,b122,b123,b124,b125,b126,b127
,b128,b129,b130,b131,b132,b133,b134,b135,b136,b137,b138,b139,b140
,b141,b142,b143,b144,b145,b146,b147,b148,b149,b150,b151,b152,b153
,b154,b155,b156,b157,b158,b159,b160,b161,b162,b163,b164,b165,b166
,b167,b168,b169,b170,b171,b172,b173,b174,b175,b176,b177,b178,b179
,b180,b181,b182,b183,b184,b185,b186,b187,b188,b189,b190,b191,b192
,b193,b194,b195,b196,b197,b198,b199,b200,b201,b202,b203,b204,b205
,b206,b207,b208,b209,b210,b211,b212,b213,b214,b215,b216,b217,b218
,b219,b220,b221,b222,b223,b224,b225,b226,b227,b228,b229,b230,b231
,b232,b233,b234,b235,b236,b237,b238,b239,b240,b241,b242,b243,b244
,b245,b246,b247,b248,b249,b250,b251,b252,b253,b254,b255,b256,b257
,b258,b259,b260,b261,b262,b263,b264,b265,b266,b267,b268,b269,b270
,b271,b272,b273,b274,b275,b276,b277,b278,b279,b280,b281,b282,b283
,b284,b285,b286,b287,b288,b289,b290,b291,b292,b293,b294,b295,b296
,b297,b298,b299,b300,b301,b302,b303,b304,b305,b306,b307,b308,b309
,b310,b311,b312,b313,b314,b315,b316,b317,b318,b319,b320,b321,b322
,b323,b324,b325,b326,b327,b328,b329,b330,b331,b332,b333,b334,b335
,b336,b337,b338,b339,b340,b341,b342,b343,b344,b345,b346,b347,b348
,b349,b350,b351,b352,b353,b354,b355,b356,b357,b358,b359,b360,b361
,b362,b363,b364,b365,b366,b367,b368,b369,b370,b371,b372,b373,b374
,b375,b376,b377,b378,b379,b380,b381,b382,b383,b384,b385,b386,b387
,b388,b389,b390,b391,b392,b393,b394,b395,b396,b397,b398,b399,b400
,b401,b402,b403,b404,b405,b406,b407,b408,b409,b410,b411,b412,b413
,b414,b415,b416,b417,b418,b419,b420,b421,b422,b423,b424,b425,b426
,b427,b428,b429,b430,b431,b432,b433,b434,b435,b436,b437,b438,b439
,b440,b441,b442,b443,b444,b445,b446,b447,b448,b449,b450,b451,b452
,b453,b454,b455,b456,b457,b458,b459,b460,b461,b462,b463,b464,b465
,b466,b467,b468,b469,b470,b471,b472,b473,b474,b475,b476,b477,b478
,b479,b480,b481,b482,b483,b484,b485,b486,b487,b488,b489,b490,b491
,b492,b493,b494,b495,b496,b497,b498,b499,b500,b501,b502,b503,b504
,b505,b506,b507,b508,b509,b510,b511,b512,b513,b514,b515,b516,b517
,b518,b519,b520,b521,b522,b523,b524,b525,b526,b527,b528,b529,b530
,b531,b532,b533,b534,b535,b536,b537,b538,b539,b540,b541,b542,b543
,b544,b545,b546,b547,b548,b549,b550,b551,b552,b553,b554,b555,b556
,b557,b558,b559,b560,b561,b562,b563,b564,b565,b566,b567,b568,b569
,b570,b571,b572,b573,b574,b575,b576,b577,b578,b579,b580,b581,b582
,b583,b584,b585,b586,b587,b588,b589,b590,b591,b592,b593,b594,b595
,b596,b597,b598,b599,b600,b601,b602,b603,b604,b605,b606,b607,b608
,b609,b610,b611,b612,b613,b614,b615,b616,b617,b618,b619,b620,b621
,b622,b623,b624,b625,b626,b627,b628,b629,b630,b631,b632,b633,b634
,b635,b636,b637,b638,b639,b640,b641,b642,b643,b644,b645,b646,b647
,b648,b649,b650,b651,b652,b653,b654,b655,b656,b657,b658,b659,b660
,b661,b662,b663,b664,b665,b666,b667,b668,b669,b670,b671,b672,b673
,b674,b675,b676,b677,b678,b679,b680,b681,b682,b683,b684,b685,b686
,b687,b688,b689,b690,b691,b692,b693,b694,b695,b696,b697,b698,b699
,b700,b701,b702,b703,b704,b705,b706,b707,b708,b709,b710,b711,b712
,b713,b714,b715,b716,b717,b718,b719,b720,b721,b722,b723,b724,b725
,b726,b727,b728,b729,b730,b731,b732,b733,b734,b735,b736,b737,b738
,b739,b740,b741,b742,b743,b744,b745,b746,b747,b748,b749,b750,b751
,b752,b753,b754,b755,b756,b757,b758,b759,b760,b761,b762,b763,b764
,b765,b766,b767,b768,b769,b770,b771,b772,b773,b774,b775,b776,b777
,b778,b779,b780,b781,b782,b783,b784,b785,b786,b787,b788,b789,b790
,b791,b792,b793,b794,b795,b796,b797,b798,b799,b800,b801,b802,b803
,b804,b805,b806,b807,b808,b809,b810,b811,b812,b813,b814,b815,b816
,b817,b818,b819,b820,b821,b822,b823,b824,b825,b826,b827,b828,b829
,b830,b831,b832,b833,b834,b835,b836,b837,b838,b839,b840,b841,b842
,b843,b844,b845,b846,b847,b848,b849,b850,b851,b852,b853,b854,b855
,b856,b857,b858,b859,b860,b861,b862,b863,b864,b865,b866,b867,b868
,b869,b870,b871,b872,b873,b874,b875,b876,b877,b878,b879,b880,b881
,b882,b883,b884,b885,b886,b887,b888,b889,b890,b891,b892,b893,b894
,b895,b896,b897,b898,b899,b900,b901,b902,b903,b904,b905,b906,b907
,b908,b909,b910,b911,b912,b913,b914,b915,b916,b917,b918,b919,b920
,b921,b922,b923,b924,b925,b926,b927,b928,b929,b930,b931,b932,b933
,b934,b935,b936,b937,b938,b939,b940,b941,b942,b943,b944,b945,b946
,b947,b948,b949,b950,b951,b952,b953,b954,b955,b956,b957,b958,b959
,b960,b961,b962,b963,b964,b965,b966,b967,b968,b969,b970,b971,b972
,b973,b974,b975,b976,b977,b978,b979,b980,b981,b982,b983,b984,b985
,b986,b987,b988,b989,b990,b991,b992,b993,b994,b995,b996,b997,b998
,b999,b1000,b1001,b1002,b1003,b1004,b1005,b1006,b1007,b1008,b1009
,b1010,b1011,b1012,b1013,b1014,b1015,b1016,b1017,b1018,b1019,b1020
,b1021,b1022,b1023,b1024,b1025,b1026,b1027,b1028,b1029,b1030,b1031
,b1032,b1033,b1034,b1035,b1036,b1037,b1038,b1039,b1040,b1041,b1042
,b1043,b1044,b1045,b1046,b1047,b1048,b1049,b1050,b1051,b1052,b1053
,b1054,b1055,b1056,b1057,b1058,b1059,b1060,b1061,b1062,b1063,b1064
,b1065,b1066,b1067,b1068,b1069,b1070,b1071,b1072,b1073,b1074,b1075
,b1076,b1077,b1078,b1079,b1080,b1081,b1082,b1083,b1084,b1085,b1086
,b1087,b1088,b1089,b1090,b1091,b1092,b1093,b1094,b1095,b1096,b1097
,b1098,b1099,b1100,b1101,b1102,b1103,b1104,b1105,b1106,b1107,b1108
,b1109,b1110,b1111,b1112,b1113,b1114,b1115,b1116,b1117,b1118,b1119
,b1120,b1121,b1122,b1123,b1124,b1125,b1126,b1127,b1128,b1129,b1130
,b1131,b1132,b1133,b1134,b1135,b1136,b1137,b1138,b1139,b1140,b1141
,b1142,b1143,b1144,b1145,b1146,b1147,b1148,b1149,b1150,b1151,b1152
,b1153,b1154,b1155,b1156,b1157,b1158,b1159,b1160,b1161,b1162,b1163
,b1164,b1165,b1166,b1167,b1168,b1169,b1170,b1171,b1172,b1173,b1174
,b1175,b1176,b1177,b1178,b1179,b1180,b1181,b1182,b1183,b1184,b1185
,b1186,b1187,b1188,b1189,b1190,b1191,b1192,b1193,b1194,b1195,b1196
,b1197,b1198,b1199,b1200,b1201,b1202,b1203,b1204,b1205,b1206,b1207
,b1208,b1209,b1210,b1211,b1212,b1213,b1214,b1215,b1216,b1217,b1218
,b1219,b1220,b1221,b1222,b1223,b1224,b1225,b1226,b1227,b1228,b1229
,b1230,b1231,b1232,b1233,b1234,b1235,b1236,b1237,b1238,b1239,b1240
,b1241,b1242,b1243,b1244,b1245,b1246,b1247,b1248,b1249,b1250,b1251
,b1252,b1253,b1254,b1255,b1256,b1257,b1258,b1259,b1260,b1261,b1262
,b1263,b1264,b1265,b1266,b1267,b1268,b1269,b1270,b1271,b1272,b1273
,b1274,b1275,b1276,b1277,b1278,b1279,b1280,b1281,b1282,b1283,b1284
,b1285,b1286,b1287,b1288,b1289,b1290,b1291,b1292,b1293,b1294,b1295
,b1296,b1297,b1298,b1299,b1300,b1301,b1302,b1303,b1304,b1305,b1306
,b1307,b1308,b1309,b1310,b1311,b1312,b1313,b1314,b1315,b1316,b1317
,b1318,b1319,b1320,b1321,b1322,b1323,b1324,b1325,b1326,b1327,b1328
,b1329,b1330,b1331,b1332,b1333,b1334,b1335,b1336,b1337,b1338,b1339
,b1340,b1341,b1342,b1343,b1344,b1345,b1346,b1347,b1348,b1349,b1350
,b1351,b1352,b1353,b1354,b1355,b1356,b1357,b1358,b1359,b1360,b1361
,b1362,b1363,b1364,b1365,b1366,b1367,b1368,b1369,b1370,b1371,b1372
,b1373,b1374,b1375,b1376,b1377,b1378,b1379,b1380,b1381,b1382,b1383
,b1384,b1385,b1386,b1387,b1388,b1389,b1390,b1391,b1392,b1393,b1394
,b1395,b1396,b1397,b1398,b1399,b1400,b1401,b1402,b1403,b1404,b1405
,b1406,b1407,b1408,b1409,b1410,b1411,b1412,b1413,b1414,b1415,b1416
,b1417,b1418,b1419,b1420,b1421,b1422,b1423,b1424,b1425,b1426,b1427
,b1428,b1429,b1430,b1431,b1432,b1433,b1434,b1435,b1436,b1437,b1438
,b1439,b1440,b1441,b1442,b1443,b1444,b1445,b1446,b1447,b1448,b1449
,b1450,b1451,b1452,b1453,b1454,b1455,b1456,b1457,b1458,b1459,b1460
,b1461,b1462,b1463,b1464,b1465,b1466,b1467,b1468,b1469,b1470,b1471
,b1472,b1473,b1474,b1475,b1476,b1477,b1478,b1479,b1480,b1481,b1482
,b1483,b1484,b1485,b1486,b1487,b1488,b1489,b1490,b1491,b1492,b1493
,b1494,b1495,b1496,b1497,b1498,b1499,b1500,b1501,b1502,b1503,b1504
,b1505,b1506,b1507,b1508,b1509,b1510,b1511,b1512,b1513,b1514,b1515
,b1516,b1517,b1518,b1519,b1520,b1521,b1522,b1523,b1524,b1525,b1526
,b1527,b1528,b1529,b1530,b1531,b1532,b1533,b1534,b1535,b1536,b1537
,b1538,b1539,b1540,b1541,b1542,b1543,b1544,b1545,b1546,b1547,b1548
,b1549,b1550,b1551,b1552,b1553,b1554,b1555,b1556,b1557,b1558,b1559
,b1560,b1561,b1562,b1563,b1564,b1565,b1566,b1567,b1568,b1569,b1570
,b1571,b1572,b1573,b1574,b1575,b1576,b1577,b1578,b1579,b1580,b1581
,b1582,b1583,b1584,b1585,b1586,b1587,b1588,b1589,b1590,b1591,b1592
,b1593,b1594,b1595,b1596,b1597,b1598,b1599,b1600,b1601,b1602,b1603
,b1604,b1605,b1606,b1607,b1608,b1609,b1610,b1611,b1612,b1613,b1614
,b1615,b1616,b1617,b1618,b1619,b1620,b1621,b1622,b1623,b1624,b1625
,b1626,b1627,b1628,b1629,b1630,b1631,b1632,b1633,b1634,b1635,b1636
,b1637,b1638,b1639,b1640,b1641,b1642,b1643,b1644,b1645,b1646,b1647
,b1648,b1649,b1650,b1651,b1652,b1653,b1654,b1655,b1656,b1657,b1658
,b1659,b1660,b1661,b1662,b1663,b1664,b1665,b1666,b1667,b1668,b1669
,b1670,b1671,b1672,b1673,b1674,b1675,b1676,b1677,b1678,b1679,b1680
,b1681,b1682,b1683,b1684,b1685,b1686,b1687,b1688,b1689,b1690,b1691
,b1692,b1693,b1694,b1695,b1696,b1697,b1698,b1699,b1700,b1701,b1702
,b1703,b1704,b1705,b1706,b1707,b1708,b1709,b1710,b1711,b1712,b1713
,b1714,b1715,b1716,b1717,b1718,b1719,b1720,b1721,b1722,b1723,b1724
,b1725,b1726,b1727,b1728,b1729,b1730,b1731,b1732,b1733,b1734,b1735
,b1736,b1737,b1738,b1739,b1740,b1741,b1742,b1743,b1744,b1745,b1746
,b1747,b1748,b1749,b1750,b1751,b1752,b1753,b1754,b1755,b1756,b1757
,b1758,b1759,b1760,b1761,b1762,b1763,b1764,b1765,b1766,b1767,b1768
,b1769,b1770,b1771,b1772,b1773,b1774,b1775,b1776,b1777,b1778,b1779
,b1780,b1781,b1782,b1783,b1784,b1785,b1786,b1787,b1788,b1789,b1790
,b1791,b1792,b1793,b1794,b1795,b1796,b1797,b1798,b1799,b1800,b1801
,b1802,b1803,b1804,b1805,b1806,b1807,b1808,b1809,b1810,b1811,b1812
,b1813,b1814,b1815,b1816,b1817,b1818,b1819,b1820,b1821,b1822,b1823
,b1824,b1825,b1826,b1827,b1828,b1829,b1830,b1831,b1832,b1833,b1834
,b1835,b1836,b1837,b1838,b1839,b1840,b1841,b1842,b1843,b1844,b1845
,b1846,b1847,b1848,b1849,b1850,b1851,b1852,b1853,b1854,b1855,b1856
,b1857,b1858,b1859,b1860,b1861,b1862,b1863,b1864,b1865,b1866,b1867
,b1868,b1869,b1870,b1871,b1872,b1873,b1874,b1875,b1876,b1877,b1878
,b1879,b1880,b1881,b1882,b1883,b1884,b1885,b1886,b1887,b1888,b1889
,b1890,b1891,b1892,b1893,b1894,b1895,b1896,b1897,b1898,b1899,b1900
,b1901,b1902,b1903,b1904,b1905,b1906,b1907,b1908,b1909,b1910,b1911
,b1912,b1913,b1914,b1915,b1916,b1917,b1918,b1919,b1920,b1921,b1922
,b1923,b1924,b1925,b1926,b1927,b1928,b1929,b1930,b1931,b1932,b1933
,b1934,b1935,b1936,b1937,b1938,b1939,b1940,b1941,b1942,b1943,b1944
,b1945,b1946,b1947,b1948,b1949,b1950,b1951,b1952,b1953,b1954,b1955
,b1956,b1957,b1958,b1959,b1960,b1961,b1962,b1963,b1964,b1965,b1966
,b1967,b1968,b1969,b1970,b1971,b1972,b1973,b1974,b1975,b1976,b1977
,b1978,b1979,b1980,b1981,b1982,b1983,b1984,b1985,b1986,b1987,b1988
,b1989,b1990,b1991,b1992,b1993,b1994,b1995,b1996,b1997,b1998,b1999
,b2000,b2001,b2002,b2003,b2004,b2005,b2006,b2007,b2008,b2009,b2010
,b2011,b2012,b2013,b2014,b2015,b2016,b2017,b2018,b2019,b2020,b2021
,b2022,b2023,b2024,b2025,b2026,b2027,b2028,b2029,b2030,b2031,b2032
,b2033,b2034,b2035,b2036,b2037,b2038,b2039,b2040,b2041,b2042,b2043
,b2044,b2045,b2046,b2047,b2048,b2049,b2050,b2051,b2052,b2053,b2054
,b2055,b2056,b2057,b2058,b2059,b2060,b2061,b2062,b2063,b2064,b2065
,b2066,b2067,b2068,b2069,b2070,b2071,b2072,b2073,b2074,b2075,b2076
,b2077,b2078,b2079,b2080,b2081,b2082,b2083,b2084,b2085,b2086,b2087
,b2088,b2089,b2090,b2091,b2092,b2093,b2094,b2095,b2096,b2097,b2098
,b2099,b2100,b2101,b2102,b2103,b2104,b2105,b2106,b2107,b2108,b2109
,b2110,b2111,b2112,b2113,b2114,b2115,b2116,b2117,b2118,b2119,b2120
,b2121,b2122,b2123,b2124,b2125,b2126,b2127,b2128,b2129,b2130,b2131
,b2132,b2133,b2134,b2135,b2136,b2137,b2138,b2139,b2140,b2141,b2142
,b2143,b2144,b2145,b2146,b2147,b2148,b2149,b2150,b2151,b2152,b2153
,b2154,b2155,b2156,b2157,b2158,b2159,b2160,b2161,b2162,b2163,b2164
,b2165,b2166,b2167,b2168,b2169,b2170,b2171,b2172,b2173,b2174,b2175
,b2176,b2177,b2178,b2179,b2180,b2181,b2182,b2183,b2184,b2185,b2186
,b2187,b2188,b2189,b2190,b2191,b2192,b2193,b2194,b2195,b2196,b2197
,b2198,b2199,b2200,b2201,b2202,b2203,b2204,b2205,b2206,b2207,b2208
,b2209,b2210,b2211,b2212,b2213,b2214,b2215,b2216,b2217,b2218,b2219
,b2220,b2221,b2222,b2223,b2224,b2225,b2226,b2227,b2228,b2229,b2230
,b2231,b2232,b2233,b2234,b2235,b2236,b2237,b2238,b2239,b2240,b2241
,b2242,b2243,b2244,b2245,b2246,b2247,b2248,b2249,b2250,b2251,b2252
,b2253,b2254,b2255,b2256,b2257,b2258,b2259,b2260,b2261,b2262,b2263
,b2264,b2265,b2266,b2267,b2268,b2269,b2270,b2271,b2272,b2273,b2274
,b2275,b2276,b2277,b2278,b2279,b2280,b2281,b2282,b2283,b2284,b2285
,b2286,b2287,b2288,b2289,b2290,b2291,b2292,b2293,b2294,b2295,b2296
,b2297,b2298,b2299,b2300,b2301,b2302,b2303,b2304,b2305,b2306,b2307
,b2308,b2309,b2310,b2311,b2312,b2313,b2314,b2315,b2316,b2317,b2318
,b2319,b2320,b2321,b2322,b2323,b2324,b2325,b2326,b2327,b2328,b2329
,b2330,b2331,b2332,b2333,b2334,b2335,b2336,b2337,b2338,b2339,b2340
,b2341,b2342,b2343,b2344,b2345,b2346,b2347,b2348,b2349,b2350,b2351
,b2352,b2353,b2354,b2355,b2356,b2357,b2358,b2359,b2360,b2361,b2362
,b2363,b2364,b2365,b2366,b2367,b2368,b2369,b2370,b2371,b2372,b2373
,b2374,b2375,b2376,b2377,b2378,b2379,b2380,b2381,b2382,b2383,b2384
,b2385,b2386,b2387,b2388,b2389,b2390,b2391,b2392,b2393,b2394,b2395
,b2396,b2397,b2398,b2399,b2400,b2401,b2402,b2403,b2404,b2405,b2406
,b2407,b2408,b2409,b2410,b2411,b2412,b2413,b2414,b2415,b2416,b2417
,b2418,b2419,b2420,b2421,b2422,b2423,b2424,b2425,b2426,b2427,b2428
,b2429,b2430,b2431,b2432,b2433,b2434,b2435,b2436,b2437,b2438,b2439
,b2440,b2441,b2442,b2443,b2444,b2445,b2446,b2447,b2448,b2449,b2450
,b2451,b2452,b2453,b2454,b2455,b2456,b2457,b2458,b2459,b2460,b2461
,b2462,b2463,b2464,b2465,b2466,b2467,b2468,b2469,b2470,b2471,b2472
,b2473,b2474,b2475,b2476,b2477,b2478,b2479,b2480,b2481,b2482,b2483
,b2484,b2485,b2486,b2487,b2488,b2489,b2490,b2491,b2492,b2493,b2494
,b2495,b2496,b2497,b2498,b2499,b2500,b2501,b2502,b2503,b2504,b2505
,b2506,b2507,b2508,b2509,b2510,b2511,b2512,b2513,b2514,b2515,b2516
,b2517,b2518,b2519,b2520,b2521,b2522,b2523,b2524,b2525,b2526,b2527
,b2528,b2529,b2530,b2531,b2532,b2533,b2534,b2535,b2536,b2537,b2538
,b2539,b2540,b2541,b2542,b2543,b2544,b2545,b2546,b2547,b2548,b2549
,b2550,b2551,b2552,b2553,b2554,b2555,b2556,b2557,b2558,b2559,b2560
,b2561,b2562,b2563,b2564,b2565,b2566,b2567,b2568,b2569,b2570,b2571
,b2572,b2573,b2574,b2575,b2576,b2577,b2578,b2579,b2580,b2581,b2582
,b2583,b2584,b2585,b2586,b2587,b2588,b2589,b2590,b2591,b2592,b2593
,b2594,b2595,b2596,b2597,b2598,b2599,b2600,b2601,b2602,b2603,b2604
,b2605,b2606,b2607,b2608,b2609,b2610,b2611,b2612,b2613,b2614,b2615
,b2616,b2617,b2618,b2619,b2620,b2621,b2622,b2623,b2624,b2625,b2626
,b2627,b2628,b2629,b2630,b2631,b2632,b2633,b2634,b2635,b2636,b2637
,b2638,b2639,b2640,b2641,b2642,b2643,b2644,b2645,b2646,b2647,b2648
,b2649,b2650,b2651,b2652,b2653,b2654,b2655,b2656,b2657,b2658,b2659
,b2660,b2661,b2662,b2663,b2664,b2665,b2666,b2667,b2668,b2669,b2670
,b2671,b2672,b2673,b2674,b2675,b2676,b2677,b2678,b2679,b2680,b2681
,b2682,b2683,b2684,b2685,b2686,b2687,b2688,b2689,b2690,b2691,b2692
,b2693,b2694,b2695,b2696,b2697,b2698,b2699,b2700,b2701,b2702,b2703
,b2704,b2705,b2706,b2707,b2708,b2709,b2710,b2711,b2712,b2713,b2714
,b2715,b2716,b2717,b2718,b2719,b2720,b2721,b2722,b2723,b2724,b2725
,b2726,b2727,b2728,b2729,b2730,b2731,b2732,b2733,b2734,b2735,b2736
,b2737,b2738,b2739,b2740,b2741,b2742,b2743,b2744,b2745,b2746,b2747
,b2748,b2749,b2750,b2751,b2752,b2753,b2754,b2755,b2756,b2757,b2758
,b2759,b2760,b2761,b2762,b2763,b2764,b2765,b2766,b2767,b2768,b2769
,b2770,b2771,b2772,b2773,b2774,b2775;
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
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