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A Library of Mixed-Integer and Continuous Nonlinear Programming Instances

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Instance pooling_foulds4pq

PQ formulation of pooling problem. Explicitly added RLT constraints were removed from the original formulation of Alfaki and Haugland.
Formats ams gms lp mod nl osil pip py
Primal Bounds (infeas ≤ 1e-08)
-8.00000000 p1 ( gdx sol )
(infeas: 2e-15)
Other points (infeas > 1e-08)  
Dual Bounds
-8.00000001 (ANTIGONE)
-8.00000000 (BARON)
-8.00000002 (COUENNE)
-8.00000000 (GUROBI)
-8.00000000 (LINDO)
-8.00000000 (SCIP)
References Foulds, L. R., Haugland, D., and Jörnsten, K., A bilinear approach to the pooling problem, Optimization, 24:1-2, 1992, 165-180.
Alfaki, Mohammed and Haugland, Dag, Strong formulations for the pooling problem, Journal of Global Optimization, 56:3, 2013, 897-916.
Source Foulds4.gms from Standard Pooling Problem Instances
Application Pooling problem
Added to library 12 Sep 2017
Problem type QCP
#Variables 672
#Binary Variables 0
#Integer Variables 0
#Nonlinear Variables 160
#Nonlinear Binary Variables 0
#Nonlinear Integer Variables 0
Objective Sense min
Objective type linear
Objective curvature linear
#Nonzeros in Objective 486
#Nonlinear Nonzeros in Objective 0
#Constraints 571
#Linear Constraints 59
#Quadratic Constraints 512
#Polynomial Constraints 0
#Signomial Constraints 0
#General Nonlinear Constraints 0
Operands in Gen. Nonlin. Functions  
Constraints curvature indefinite
#Nonzeros in Jacobian 3588
#Nonlinear Nonzeros in Jacobian 1024
#Nonzeros in (Upper-Left) Hessian of Lagrangian 1024
#Nonzeros in Diagonal of Hessian of Lagrangian 0
#Blocks in Hessian of Lagrangian 8
Minimal blocksize in Hessian of Lagrangian 20
Maximal blocksize in Hessian of Lagrangian 20
Average blocksize in Hessian of Lagrangian 20.0
#Semicontinuities 0
#Nonlinear Semicontinuities 0
#SOS type 1 0
#SOS type 2 0
Minimal coefficient 5.0000e-02
Maximal coefficient 1.0000e+01
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
*        572      521        0       51        0        0        0        0
*  
*  Variable counts
*                   x        b        i      s1s      s2s       sc       si
*      Total     cont   binary  integer     sos1     sos2    scont     sint
*        673      673        0        0        0        0        0        0
*  FX      0
*  
*  Nonzero counts
*      Total    const       NL      DLL
*       4075     3051     1024        0
*
*  Solve m using NLP 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;

Positive Variables  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;

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;


e1..    objvar + 10*x162 + 9.5*x163 + 9*x164 + 8.5*x165 + 8*x166 + 7.5*x167
      + 7*x168 + 6.5*x169 + 6*x170 + 5.5*x171 + 5*x172 + 4.5*x173 + 4*x174
      + 3.5*x175 + 3*x176 + 2.5*x177 + 9*x178 + 8.5*x179 + 8*x180 + 7.5*x181
      + 7*x182 + 6.5*x183 + 6*x184 + 5.5*x185 + 5*x186 + 4.5*x187 + 4*x188
      + 3.5*x189 + 3*x190 + 2.5*x191 + 2*x192 + 1.5*x193 + 9*x194 + 8.5*x195
      + 8*x196 + 7.5*x197 + 7*x198 + 6.5*x199 + 6*x200 + 5.5*x201 + 5*x202
      + 4.5*x203 + 4*x204 + 3.5*x205 + 3*x206 + 2.5*x207 + 2*x208 + 1.5*x209
      + 8*x210 + 7.5*x211 + 7*x212 + 6.5*x213 + 6*x214 + 5.5*x215 + 5*x216
      + 4.5*x217 + 4*x218 + 3.5*x219 + 3*x220 + 2.5*x221 + 2*x222 + 1.5*x223
      + x224 + 0.5*x225 + 8*x226 + 7.5*x227 + 7*x228 + 6.5*x229 + 6*x230
      + 5.5*x231 + 5*x232 + 4.5*x233 + 4*x234 + 3.5*x235 + 3*x236 + 2.5*x237
      + 2*x238 + 1.5*x239 + x240 + 0.5*x241 + 8*x242 + 7.5*x243 + 7*x244
      + 6.5*x245 + 6*x246 + 5.5*x247 + 5*x248 + 4.5*x249 + 4*x250 + 3.5*x251
      + 3*x252 + 2.5*x253 + 2*x254 + 1.5*x255 + x256 + 0.5*x257 + 7*x258
      + 6.5*x259 + 6*x260 + 5.5*x261 + 5*x262 + 4.5*x263 + 4*x264 + 3.5*x265
      + 3*x266 + 2.5*x267 + 2*x268 + 1.5*x269 + x270 + 0.5*x271 - 0.5*x273
      + 7*x274 + 6.5*x275 + 6*x276 + 5.5*x277 + 5*x278 + 4.5*x279 + 4*x280
      + 3.5*x281 + 3*x282 + 2.5*x283 + 2*x284 + 1.5*x285 + x286 + 0.5*x287
      - 0.5*x289 + 7*x290 + 6.5*x291 + 6*x292 + 5.5*x293 + 5*x294 + 4.5*x295
      + 4*x296 + 3.5*x297 + 3*x298 + 2.5*x299 + 2*x300 + 1.5*x301 + x302
      + 0.5*x303 - 0.5*x305 + 7*x306 + 6.5*x307 + 6*x308 + 5.5*x309 + 5*x310
      + 4.5*x311 + 4*x312 + 3.5*x313 + 3*x314 + 2.5*x315 + 2*x316 + 1.5*x317
      + x318 + 0.5*x319 - 0.5*x321 + 6*x322 + 5.5*x323 + 5*x324 + 4.5*x325
      + 4*x326 + 3.5*x327 + 3*x328 + 2.5*x329 + 2*x330 + 1.5*x331 + x332
      + 0.5*x333 - 0.5*x335 - x336 - 1.5*x337 + 6*x338 + 5.5*x339 + 5*x340
      + 4.5*x341 + 4*x342 + 3.5*x343 + 3*x344 + 2.5*x345 + 2*x346 + 1.5*x347
      + x348 + 0.5*x349 - 0.5*x351 - x352 - 1.5*x353 + 6*x354 + 5.5*x355
      + 5*x356 + 4.5*x357 + 4*x358 + 3.5*x359 + 3*x360 + 2.5*x361 + 2*x362
      + 1.5*x363 + x364 + 0.5*x365 - 0.5*x367 - x368 - 1.5*x369 + 6*x370
      + 5.5*x371 + 5*x372 + 4.5*x373 + 4*x374 + 3.5*x375 + 3*x376 + 2.5*x377
      + 2*x378 + 1.5*x379 + x380 + 0.5*x381 - 0.5*x383 - x384 - 1.5*x385
      + 5*x386 + 4.5*x387 + 4*x388 + 3.5*x389 + 3*x390 + 2.5*x391 + 2*x392
      + 1.5*x393 + x394 + 0.5*x395 - 0.5*x397 - x398 - 1.5*x399 - 2*x400
      - 2.5*x401 + 5*x402 + 4.5*x403 + 4*x404 + 3.5*x405 + 3*x406 + 2.5*x407
      + 2*x408 + 1.5*x409 + x410 + 0.5*x411 - 0.5*x413 - x414 - 1.5*x415
      - 2*x416 - 2.5*x417 + 5*x418 + 4.5*x419 + 4*x420 + 3.5*x421 + 3*x422
      + 2.5*x423 + 2*x424 + 1.5*x425 + x426 + 0.5*x427 - 0.5*x429 - x430
      - 1.5*x431 - 2*x432 - 2.5*x433 + 5*x434 + 4.5*x435 + 4*x436 + 3.5*x437
      + 3*x438 + 2.5*x439 + 2*x440 + 1.5*x441 + x442 + 0.5*x443 - 0.5*x445
      - x446 - 1.5*x447 - 2*x448 - 2.5*x449 + 4*x450 + 3.5*x451 + 3*x452
      + 2.5*x453 + 2*x454 + 1.5*x455 + x456 + 0.5*x457 - 0.5*x459 - x460
      - 1.5*x461 - 2*x462 - 2.5*x463 - 3*x464 - 3.5*x465 + 4*x466 + 3.5*x467
      + 3*x468 + 2.5*x469 + 2*x470 + 1.5*x471 + x472 + 0.5*x473 - 0.5*x475
      - x476 - 1.5*x477 - 2*x478 - 2.5*x479 - 3*x480 - 3.5*x481 + 4*x482
      + 3.5*x483 + 3*x484 + 2.5*x485 + 2*x486 + 1.5*x487 + x488 + 0.5*x489
      - 0.5*x491 - x492 - 1.5*x493 - 2*x494 - 2.5*x495 - 3*x496 - 3.5*x497
      + 4*x498 + 3.5*x499 + 3*x500 + 2.5*x501 + 2*x502 + 1.5*x503 + x504
      + 0.5*x505 - 0.5*x507 - x508 - 1.5*x509 - 2*x510 - 2.5*x511 - 3*x512
      - 3.5*x513 + 3*x514 + 2.5*x515 + 2*x516 + 1.5*x517 + x518 + 0.5*x519
      - 0.5*x521 - x522 - 1.5*x523 - 2*x524 - 2.5*x525 - 3*x526 - 3.5*x527
      - 4*x528 - 4.5*x529 + 3*x530 + 2.5*x531 + 2*x532 + 1.5*x533 + x534
      + 0.5*x535 - 0.5*x537 - x538 - 1.5*x539 - 2*x540 - 2.5*x541 - 3*x542
      - 3.5*x543 - 4*x544 - 4.5*x545 + 3*x546 + 2.5*x547 + 2*x548 + 1.5*x549
      + x550 + 0.5*x551 - 0.5*x553 - x554 - 1.5*x555 - 2*x556 - 2.5*x557
      - 3*x558 - 3.5*x559 - 4*x560 - 4.5*x561 + 3*x562 + 2.5*x563 + 2*x564
      + 1.5*x565 + x566 + 0.5*x567 - 0.5*x569 - x570 - 1.5*x571 - 2*x572
      - 2.5*x573 - 3*x574 - 3.5*x575 - 4*x576 - 4.5*x577 + 2*x578 + 1.5*x579
      + x580 + 0.5*x581 - 0.5*x583 - x584 - 1.5*x585 - 2*x586 - 2.5*x587
      - 3*x588 - 3.5*x589 - 4*x590 - 4.5*x591 - 5*x592 - 5.5*x593 + 2*x594
      + 1.5*x595 + x596 + 0.5*x597 - 0.5*x599 - x600 - 1.5*x601 - 2*x602
      - 2.5*x603 - 3*x604 - 3.5*x605 - 4*x606 - 4.5*x607 - 5*x608 - 5.5*x609
      + 2*x610 + 1.5*x611 + x612 + 0.5*x613 - 0.5*x615 - x616 - 1.5*x617
      - 2*x618 - 2.5*x619 - 3*x620 - 3.5*x621 - 4*x622 - 4.5*x623 - 5*x624
      - 5.5*x625 + x626 + 0.5*x627 - 0.5*x629 - x630 - 1.5*x631 - 2*x632
      - 2.5*x633 - 3*x634 - 3.5*x635 - 4*x636 - 4.5*x637 - 5*x638 - 5.5*x639
      - 6*x640 - 6.5*x641 + x642 + 0.5*x643 - 0.5*x645 - x646 - 1.5*x647
      - 2*x648 - 2.5*x649 - 3*x650 - 3.5*x651 - 4*x652 - 4.5*x653 - 5*x654
      - 5.5*x655 - 6*x656 - 6.5*x657 - 0.5*x659 - x660 - 1.5*x661 - 2*x662
      - 2.5*x663 - 3*x664 - 3.5*x665 - 4*x666 - 4.5*x667 - 5*x668 - 5.5*x669
      - 6*x670 - 6.5*x671 - 7*x672 - 7.5*x673 =E= 0;

e2..    x162 + x163 + x164 + x165 + x166 + x167 + x168 + x169 + x170 + x171
      + x172 + x173 + x174 + x175 + x176 + x177 =L= 16;

e3..    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 =L= 16;

e4..    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 =L= 16;

e5..    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 =L= 16;

e6..    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 =L= 16;

e7..    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 =L= 16;

e8..    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 =L= 16;

e9..    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 =L= 16;

e10..    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 =L= 16;

e11..    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 =L= 16;

e12..    x658 + x659 + x660 + x661 + x662 + x663 + x664 + x665 + x666 + x667
       + x668 + x669 + x670 + x671 + x672 + x673 =L= 16;

e13..    x178 + x179 + x180 + x181 + x182 + x183 + x184 + x185 + x186 + x187
       + x188 + x189 + x190 + x191 + x192 + x193 + x322 + x323 + x324 + x325
       + x326 + x327 + x328 + x329 + x330 + x331 + x332 + x333 + x334 + x335
       + x336 + x337 + x514 + x515 + x516 + x517 + x518 + x519 + x520 + x521
       + x522 + x523 + x524 + x525 + x526 + x527 + x528 + x529 + x658 + x659
       + x660 + x661 + x662 + x663 + x664 + x665 + x666 + x667 + x668 + x669
       + x670 + x671 + x672 + x673 =L= 16;

e14..    x162 + x163 + x164 + x165 + x166 + x167 + x168 + x169 + x170 + x171
       + x172 + x173 + x174 + x175 + x176 + x177 + x258 + x259 + x260 + x261
       + x262 + x263 + x264 + x265 + x266 + x267 + x268 + x269 + x270 + x271
       + x272 + x273 + x450 + x451 + x452 + x453 + x454 + x455 + x456 + x457
       + x458 + x459 + x460 + x461 + x462 + x463 + x464 + x465 + x626 + x627
       + x628 + x629 + x630 + x631 + x632 + x633 + x634 + x635 + x636 + x637
       + x638 + x639 + x640 + x641 =L= 16;

e15..    x386 + x387 + x388 + x389 + x390 + x391 + x392 + x393 + x394 + x395
       + x396 + x397 + x398 + x399 + x400 + x401 + x466 + x467 + x468 + x469
       + x470 + x471 + x472 + x473 + x474 + x475 + x476 + x477 + x478 + x479
       + x480 + x481 + x578 + x579 + x580 + x581 + x582 + x583 + x584 + x585
       + x586 + x587 + x588 + x589 + x590 + x591 + x592 + x593 + x642 + x643
       + x644 + x645 + x646 + x647 + x648 + x649 + x650 + x651 + x652 + x653
       + x654 + x655 + x656 + x657 =L= 16;

e16..    x338 + x339 + x340 + x341 + x342 + x343 + x344 + x345 + x346 + x347
       + x348 + x349 + x350 + x351 + x352 + x353 + x402 + x403 + x404 + x405
       + x406 + x407 + x408 + x409 + x410 + x411 + x412 + x413 + x414 + x415
       + x416 + x417 + x530 + x531 + x532 + x533 + x534 + x535 + x536 + x537
       + x538 + x539 + x540 + x541 + x542 + x543 + x544 + x545 + x594 + x595
       + x596 + x597 + x598 + x599 + x600 + x601 + x602 + x603 + x604 + x605
       + x606 + x607 + x608 + x609 =L= 16;

e17..    x274 + x275 + x276 + x277 + x278 + x279 + x280 + x281 + x282 + x283
       + x284 + x285 + x286 + x287 + x288 + x289 + x418 + x419 + x420 + x421
       + x422 + x423 + x424 + x425 + x426 + x427 + x428 + x429 + x430 + x431
       + x432 + x433 + x482 + x483 + x484 + x485 + x486 + x487 + x488 + x489
       + x490 + x491 + x492 + x493 + x494 + x495 + x496 + x497 + x610 + x611
       + x612 + x613 + x614 + x615 + x616 + x617 + x618 + x619 + x620 + x621
       + x622 + x623 + x624 + x625 =L= 16;

e18..    x210 + x211 + x212 + x213 + x214 + x215 + x216 + x217 + x218 + x219
       + x220 + x221 + x222 + x223 + x224 + x225 + x354 + x355 + x356 + x357
       + x358 + x359 + x360 + x361 + x362 + x363 + x364 + x365 + x366 + x367
       + x368 + x369 + x434 + x435 + x436 + x437 + x438 + x439 + x440 + x441
       + x442 + x443 + x444 + x445 + x446 + x447 + x448 + x449 + x546 + x547
       + x548 + x549 + x550 + x551 + x552 + x553 + x554 + x555 + x556 + x557
       + x558 + x559 + x560 + x561 =L= 16;

e19..    x226 + x227 + x228 + x229 + x230 + x231 + x232 + x233 + x234 + x235
       + x236 + x237 + x238 + x239 + x240 + x241 + x290 + x291 + x292 + x293
       + x294 + x295 + x296 + x297 + x298 + x299 + x300 + x301 + x302 + x303
       + x304 + x305 + x370 + x371 + x372 + x373 + x374 + x375 + x376 + x377
       + x378 + x379 + x380 + x381 + x382 + x383 + x384 + x385 + x562 + x563
       + x564 + x565 + x566 + x567 + x568 + x569 + x570 + x571 + x572 + x573
       + x574 + x575 + x576 + x577 =L= 16;

e20..    x194 + x195 + x196 + x197 + x198 + x199 + x200 + x201 + x202 + x203
       + x204 + x205 + x206 + x207 + x208 + x209 + x242 + x243 + x244 + x245
       + x246 + x247 + x248 + x249 + x250 + x251 + x252 + x253 + x254 + x255
       + x256 + x257 + x306 + x307 + x308 + x309 + x310 + x311 + x312 + x313
       + x314 + x315 + x316 + x317 + x318 + x319 + x320 + x321 + x498 + x499
       + x500 + x501 + x502 + x503 + x504 + x505 + x506 + x507 + x508 + x509
       + x510 + x511 + x512 + x513 =L= 16;

e21..    x162 + x178 + x194 + x210 + x226 + x242 + x258 + x274 + x290 + x306
       + x322 + x338 + x354 + x370 + x386 + x402 + x418 + x434 + x450 + x466
       + x482 + x498 + x514 + x530 + x546 + x562 + x578 + x594 + x610 + x626
       + x642 + x658 =L= 1;

e22..    x163 + x179 + x195 + x211 + x227 + x243 + x259 + x275 + x291 + x307
       + x323 + x339 + x355 + x371 + x387 + x403 + x419 + x435 + x451 + x467
       + x483 + x499 + x515 + x531 + x547 + x563 + x579 + x595 + x611 + x627
       + x643 + x659 =L= 1;

e23..    x164 + x180 + x196 + x212 + x228 + x244 + x260 + x276 + x292 + x308
       + x324 + x340 + x356 + x372 + x388 + x404 + x420 + x436 + x452 + x468
       + x484 + x500 + x516 + x532 + x548 + x564 + x580 + x596 + x612 + x628
       + x644 + x660 =L= 1;

e24..    x165 + x181 + x197 + x213 + x229 + x245 + x261 + x277 + x293 + x309
       + x325 + x341 + x357 + x373 + x389 + x405 + x421 + x437 + x453 + x469
       + x485 + x501 + x517 + x533 + x549 + x565 + x581 + x597 + x613 + x629
       + x645 + x661 =L= 1;

e25..    x166 + x182 + x198 + x214 + x230 + x246 + x262 + x278 + x294 + x310
       + x326 + x342 + x358 + x374 + x390 + x406 + x422 + x438 + x454 + x470
       + x486 + x502 + x518 + x534 + x550 + x566 + x582 + x598 + x614 + x630
       + x646 + x662 =L= 1;

e26..    x167 + x183 + x199 + x215 + x231 + x247 + x263 + x279 + x295 + x311
       + x327 + x343 + x359 + x375 + x391 + x407 + x423 + x439 + x455 + x471
       + x487 + x503 + x519 + x535 + x551 + x567 + x583 + x599 + x615 + x631
       + x647 + x663 =L= 1;

e27..    x168 + x184 + x200 + x216 + x232 + x248 + x264 + x280 + x296 + x312
       + x328 + x344 + x360 + x376 + x392 + x408 + x424 + x440 + x456 + x472
       + x488 + x504 + x520 + x536 + x552 + x568 + x584 + x600 + x616 + x632
       + x648 + x664 =L= 1;

e28..    x169 + x185 + x201 + x217 + x233 + x249 + x265 + x281 + x297 + x313
       + x329 + x345 + x361 + x377 + x393 + x409 + x425 + x441 + x457 + x473
       + x489 + x505 + x521 + x537 + x553 + x569 + x585 + x601 + x617 + x633
       + x649 + x665 =L= 1;

e29..    x170 + x186 + x202 + x218 + x234 + x250 + x266 + x282 + x298 + x314
       + x330 + x346 + x362 + x378 + x394 + x410 + x426 + x442 + x458 + x474
       + x490 + x506 + x522 + x538 + x554 + x570 + x586 + x602 + x618 + x634
       + x650 + x666 =L= 1;

e30..    x171 + x187 + x203 + x219 + x235 + x251 + x267 + x283 + x299 + x315
       + x331 + x347 + x363 + x379 + x395 + x411 + x427 + x443 + x459 + x475
       + x491 + x507 + x523 + x539 + x555 + x571 + x587 + x603 + x619 + x635
       + x651 + x667 =L= 1;

e31..    x172 + x188 + x204 + x220 + x236 + x252 + x268 + x284 + x300 + x316
       + x332 + x348 + x364 + x380 + x396 + x412 + x428 + x444 + x460 + x476
       + x492 + x508 + x524 + x540 + x556 + x572 + x588 + x604 + x620 + x636
       + x652 + x668 =L= 1;

e32..    x173 + x189 + x205 + x221 + x237 + x253 + x269 + x285 + x301 + x317
       + x333 + x349 + x365 + x381 + x397 + x413 + x429 + x445 + x461 + x477
       + x493 + x509 + x525 + x541 + x557 + x573 + x589 + x605 + x621 + x637
       + x653 + x669 =L= 1;

e33..    x174 + x190 + x206 + x222 + x238 + x254 + x270 + x286 + x302 + x318
       + x334 + x350 + x366 + x382 + x398 + x414 + x430 + x446 + x462 + x478
       + x494 + x510 + x526 + x542 + x558 + x574 + x590 + x606 + x622 + x638
       + x654 + x670 =L= 1;

e34..    x175 + x191 + x207 + x223 + x239 + x255 + x271 + x287 + x303 + x319
       + x335 + x351 + x367 + x383 + x399 + x415 + x431 + x447 + x463 + x479
       + x495 + x511 + x527 + x543 + x559 + x575 + x591 + x607 + x623 + x639
       + x655 + x671 =L= 1;

e35..    x176 + x192 + x208 + x224 + x240 + x256 + x272 + x288 + x304 + x320
       + x336 + x352 + x368 + x384 + x400 + x416 + x432 + x448 + x464 + x480
       + x496 + x512 + x528 + x544 + x560 + x576 + x592 + x608 + x624 + x640
       + x656 + x672 =L= 1;

e36..    x177 + x193 + x209 + x225 + x241 + x257 + x273 + x289 + x305 + x321
       + x337 + x353 + x369 + x385 + x401 + x417 + x433 + x449 + x465 + x481
       + x497 + x513 + x529 + x545 + x561 + x577 + x593 + x609 + x625 + x641
       + x657 + x673 =L= 1;

e37..    0.95*x162 + 0.85*x178 + 0.85*x194 + 0.75*x210 + 0.75*x226 + 0.75*x242
       + 0.65*x258 + 0.65*x274 + 0.65*x290 + 0.65*x306 + 0.55*x322 + 0.55*x338
       + 0.55*x354 + 0.55*x370 + 0.45*x386 + 0.45*x402 + 0.45*x418 + 0.45*x434
       + 0.35*x450 + 0.35*x466 + 0.35*x482 + 0.35*x498 + 0.25*x514 + 0.25*x530
       + 0.25*x546 + 0.25*x562 + 0.15*x578 + 0.15*x594 + 0.15*x610 + 0.05*x626
       + 0.05*x642 - 0.05*x658 =L= 0;

e38..    0.9*x163 + 0.8*x179 + 0.8*x195 + 0.7*x211 + 0.7*x227 + 0.7*x243
       + 0.6*x259 + 0.6*x275 + 0.6*x291 + 0.6*x307 + 0.5*x323 + 0.5*x339
       + 0.5*x355 + 0.5*x371 + 0.4*x387 + 0.4*x403 + 0.4*x419 + 0.4*x435
       + 0.3*x451 + 0.3*x467 + 0.3*x483 + 0.3*x499 + 0.2*x515 + 0.2*x531
       + 0.2*x547 + 0.2*x563 + 0.0999999999999999*x579
       + 0.0999999999999999*x595 + 0.0999999999999999*x611 - 0.1*x659 =L= 0;

e39..    0.85*x164 + 0.75*x180 + 0.75*x196 + 0.65*x212 + 0.65*x228 + 0.65*x244
       + 0.55*x260 + 0.55*x276 + 0.55*x292 + 0.55*x308 + 0.45*x324 + 0.45*x340
       + 0.45*x356 + 0.45*x372 + 0.35*x388 + 0.35*x404 + 0.35*x420 + 0.35*x436
       + 0.25*x452 + 0.25*x468 + 0.25*x484 + 0.25*x500 + 0.15*x516 + 0.15*x532
       + 0.15*x548 + 0.15*x564 + 0.05*x580 + 0.05*x596 + 0.05*x612
       - 0.0499999999999998*x628 - 0.0499999999999998*x644 - 0.15*x660 =L= 0;

e40..    0.8*x165 + 0.7*x181 + 0.7*x197 + 0.6*x213 + 0.6*x229 + 0.6*x245
       + 0.5*x261 + 0.5*x277 + 0.5*x293 + 0.5*x309 + 0.4*x325 + 0.4*x341
       + 0.4*x357 + 0.4*x373 + 0.3*x389 + 0.3*x405 + 0.3*x421 + 0.3*x437
       + 0.2*x453 + 0.2*x469 + 0.2*x485 + 0.2*x501 + 0.1*x517 + 0.1*x533
       + 0.1*x549 + 0.1*x565 - 0.0999999999999999*x629
       - 0.0999999999999999*x645 - 0.2*x661 =L= 0;

e41..    0.75*x166 + 0.65*x182 + 0.65*x198 + 0.55*x214 + 0.55*x230 + 0.55*x246
       + 0.45*x262 + 0.45*x278 + 0.45*x294 + 0.45*x310 + 0.35*x326 + 0.35*x342
       + 0.35*x358 + 0.35*x374 + 0.25*x390 + 0.25*x406 + 0.25*x422 + 0.25*x438
       + 0.15*x454 + 0.15*x470 + 0.15*x486 + 0.15*x502 + 0.05*x518 + 0.05*x534
       + 0.05*x550 + 0.05*x566 - 0.05*x582 - 0.05*x598 - 0.05*x614 - 0.15*x630
       - 0.15*x646 - 0.25*x662 =L= 0;

e42..    0.7*x167 + 0.6*x183 + 0.6*x199 + 0.5*x215 + 0.5*x231 + 0.5*x247
       + 0.4*x263 + 0.4*x279 + 0.4*x295 + 0.4*x311 + 0.3*x327 + 0.3*x343
       + 0.3*x359 + 0.3*x375 + 0.2*x391 + 0.2*x407 + 0.2*x423 + 0.2*x439
       + 0.0999999999999999*x455 + 0.0999999999999999*x471
       + 0.0999999999999999*x487 + 0.0999999999999999*x503 - 0.1*x583
       - 0.1*x599 - 0.1*x615 - 0.2*x631 - 0.2*x647 - 0.3*x663 =L= 0;

e43..    0.65*x168 + 0.55*x184 + 0.55*x200 + 0.45*x216 + 0.45*x232 + 0.45*x248
       + 0.35*x264 + 0.35*x280 + 0.35*x296 + 0.35*x312 + 0.25*x328 + 0.25*x344
       + 0.25*x360 + 0.25*x376 + 0.15*x392 + 0.15*x408 + 0.15*x424 + 0.15*x440
       + 0.0499999999999998*x456 + 0.0499999999999998*x472
       + 0.0499999999999998*x488 + 0.0499999999999998*x504 - 0.05*x520
       - 0.05*x536 - 0.05*x552 - 0.05*x568 - 0.15*x584 - 0.15*x600 - 0.15*x616
       - 0.25*x632 - 0.25*x648 - 0.35*x664 =L= 0;

e44..    0.6*x169 + 0.5*x185 + 0.5*x201 + 0.4*x217 + 0.4*x233 + 0.4*x249
       + 0.3*x265 + 0.3*x281 + 0.3*x297 + 0.3*x313 + 0.2*x329 + 0.2*x345
       + 0.2*x361 + 0.2*x377 + 0.1*x393 + 0.1*x409 + 0.1*x425 + 0.1*x441
       - 0.0999999999999999*x521 - 0.0999999999999999*x537
       - 0.0999999999999999*x553 - 0.0999999999999999*x569 - 0.2*x585
       - 0.2*x601 - 0.2*x617 - 0.3*x633 - 0.3*x649 - 0.4*x665 =L= 0;

e45..    0.55*x170 + 0.45*x186 + 0.45*x202 + 0.35*x218 + 0.35*x234 + 0.35*x250
       + 0.25*x266 + 0.25*x282 + 0.25*x298 + 0.25*x314 + 0.15*x330 + 0.15*x346
       + 0.15*x362 + 0.15*x378 + 0.05*x394 + 0.05*x410 + 0.05*x426 + 0.05*x442
       - 0.05*x458 - 0.05*x474 - 0.05*x490 - 0.05*x506 - 0.15*x522 - 0.15*x538
       - 0.15*x554 - 0.15*x570 - 0.25*x586 - 0.25*x602 - 0.25*x618 - 0.35*x634
       - 0.35*x650 - 0.45*x666 =L= 0;

e46..    0.5*x171 + 0.4*x187 + 0.4*x203 + 0.3*x219 + 0.3*x235 + 0.3*x251
       + 0.2*x267 + 0.2*x283 + 0.2*x299 + 0.2*x315 + 0.1*x331 + 0.1*x347
       + 0.1*x363 + 0.1*x379 - 0.1*x459 - 0.1*x475 - 0.1*x491 - 0.1*x507
       - 0.2*x523 - 0.2*x539 - 0.2*x555 - 0.2*x571 - 0.3*x587 - 0.3*x603
       - 0.3*x619 - 0.4*x635 - 0.4*x651 - 0.5*x667 =L= 0;

e47..    0.45*x172 + 0.35*x188 + 0.35*x204 + 0.25*x220 + 0.25*x236 + 0.25*x252
       + 0.15*x268 + 0.15*x284 + 0.15*x300 + 0.15*x316 + 0.05*x332 + 0.05*x348
       + 0.05*x364 + 0.05*x380 - 0.05*x396 - 0.05*x412 - 0.05*x428 - 0.05*x444
       - 0.15*x460 - 0.15*x476 - 0.15*x492 - 0.15*x508 - 0.25*x524 - 0.25*x540
       - 0.25*x556 - 0.25*x572 - 0.35*x588 - 0.35*x604 - 0.35*x620 - 0.45*x636
       - 0.45*x652 - 0.55*x668 =L= 0;

e48..    0.4*x173 + 0.3*x189 + 0.3*x205 + 0.2*x221 + 0.2*x237 + 0.2*x253
       + 0.0999999999999999*x269 + 0.0999999999999999*x285
       + 0.0999999999999999*x301 + 0.0999999999999999*x317 - 0.1*x397
       - 0.1*x413 - 0.1*x429 - 0.1*x445 - 0.2*x461 - 0.2*x477 - 0.2*x493
       - 0.2*x509 - 0.3*x525 - 0.3*x541 - 0.3*x557 - 0.3*x573 - 0.4*x589
       - 0.4*x605 - 0.4*x621 - 0.5*x637 - 0.5*x653 - 0.6*x669 =L= 0;

e49..    0.35*x174 + 0.25*x190 + 0.25*x206 + 0.15*x222 + 0.15*x238 + 0.15*x254
       + 0.05*x270 + 0.05*x286 + 0.05*x302 + 0.05*x318
       - 0.0499999999999998*x334 - 0.0499999999999998*x350
       - 0.0499999999999998*x366 - 0.0499999999999998*x382 - 0.15*x398
       - 0.15*x414 - 0.15*x430 - 0.15*x446 - 0.25*x462 - 0.25*x478 - 0.25*x494
       - 0.25*x510 - 0.35*x526 - 0.35*x542 - 0.35*x558 - 0.35*x574 - 0.45*x590
       - 0.45*x606 - 0.45*x622 - 0.55*x638 - 0.55*x654 - 0.65*x670 =L= 0;

e50..    0.3*x175 + 0.2*x191 + 0.2*x207 + 0.1*x223 + 0.1*x239 + 0.1*x255
       - 0.0999999999999999*x335 - 0.0999999999999999*x351
       - 0.0999999999999999*x367 - 0.0999999999999999*x383 - 0.2*x399
       - 0.2*x415 - 0.2*x431 - 0.2*x447 - 0.3*x463 - 0.3*x479 - 0.3*x495
       - 0.3*x511 - 0.4*x527 - 0.4*x543 - 0.4*x559 - 0.4*x575 - 0.5*x591
       - 0.5*x607 - 0.5*x623 - 0.6*x639 - 0.6*x655 - 0.7*x671 =L= 0;

e51..    0.25*x176 + 0.15*x192 + 0.15*x208 + 0.05*x224 + 0.05*x240 + 0.05*x256
       - 0.05*x272 - 0.05*x288 - 0.05*x304 - 0.05*x320 - 0.15*x336 - 0.15*x352
       - 0.15*x368 - 0.15*x384 - 0.25*x400 - 0.25*x416 - 0.25*x432 - 0.25*x448
       - 0.35*x464 - 0.35*x480 - 0.35*x496 - 0.35*x512 - 0.45*x528 - 0.45*x544
       - 0.45*x560 - 0.45*x576 - 0.55*x592 - 0.55*x608 - 0.55*x624 - 0.65*x640
       - 0.65*x656 - 0.75*x672 =L= 0;

e52..    0.2*x177 + 0.0999999999999999*x193 + 0.0999999999999999*x209
       - 0.1*x273 - 0.1*x289 - 0.1*x305 - 0.1*x321 - 0.2*x337 - 0.2*x353
       - 0.2*x369 - 0.2*x385 - 0.3*x401 - 0.3*x417 - 0.3*x433 - 0.3*x449
       - 0.4*x465 - 0.4*x481 - 0.4*x497 - 0.4*x513 - 0.5*x529 - 0.5*x545
       - 0.5*x561 - 0.5*x577 - 0.6*x593 - 0.6*x609 - 0.6*x625 - 0.7*x641
       - 0.7*x657 - 0.8*x673 =L= 0;

e53..    x3 + x12 + x24 + x33 =E= 1;

e54..    x2 + x8 + x20 + x31 =E= 1;

e55..    x16 + x21 + x28 + x32 =E= 1;

e56..    x13 + x17 + x25 + x29 =E= 1;

e57..    x9 + x18 + x22 + x30 =E= 1;

e58..    x5 + x14 + x19 + x26 =E= 1;

e59..    x6 + x10 + x15 + x27 =E= 1;

e60..    x4 + x7 + x11 + x23 =E= 1;

e61.. -x2*x50 + x162 =E= 0;

e62.. -x2*x51 + x163 =E= 0;

e63.. -x2*x52 + x164 =E= 0;

e64.. -x2*x53 + x165 =E= 0;

e65.. -x2*x54 + x166 =E= 0;

e66.. -x2*x55 + x167 =E= 0;

e67.. -x2*x56 + x168 =E= 0;

e68.. -x2*x57 + x169 =E= 0;

e69.. -x2*x58 + x170 =E= 0;

e70.. -x2*x59 + x171 =E= 0;

e71.. -x2*x60 + x172 =E= 0;

e72.. -x2*x61 + x173 =E= 0;

e73.. -x2*x62 + x174 =E= 0;

e74.. -x2*x63 + x175 =E= 0;

e75.. -x2*x64 + x176 =E= 0;

e76.. -x2*x65 + x177 =E= 0;

e77.. -x3*x34 + x178 =E= 0;

e78.. -x3*x35 + x179 =E= 0;

e79.. -x3*x36 + x180 =E= 0;

e80.. -x3*x37 + x181 =E= 0;

e81.. -x3*x38 + x182 =E= 0;

e82.. -x3*x39 + x183 =E= 0;

e83.. -x3*x40 + x184 =E= 0;

e84.. -x3*x41 + x185 =E= 0;

e85.. -x3*x42 + x186 =E= 0;

e86.. -x3*x43 + x187 =E= 0;

e87.. -x3*x44 + x188 =E= 0;

e88.. -x3*x45 + x189 =E= 0;

e89.. -x3*x46 + x190 =E= 0;

e90.. -x3*x47 + x191 =E= 0;

e91.. -x3*x48 + x192 =E= 0;

e92.. -x3*x49 + x193 =E= 0;

e93.. -x4*x146 + x194 =E= 0;

e94.. -x4*x147 + x195 =E= 0;

e95.. -x4*x148 + x196 =E= 0;

e96.. -x4*x149 + x197 =E= 0;

e97.. -x4*x150 + x198 =E= 0;

e98.. -x4*x151 + x199 =E= 0;

e99.. -x4*x152 + x200 =E= 0;

e100.. -x4*x153 + x201 =E= 0;

e101.. -x4*x154 + x202 =E= 0;

e102.. -x4*x155 + x203 =E= 0;

e103.. -x4*x156 + x204 =E= 0;

e104.. -x4*x157 + x205 =E= 0;

e105.. -x4*x158 + x206 =E= 0;

e106.. -x4*x159 + x207 =E= 0;

e107.. -x4*x160 + x208 =E= 0;

e108.. -x4*x161 + x209 =E= 0;

e109.. -x5*x114 + x210 =E= 0;

e110.. -x5*x115 + x211 =E= 0;

e111.. -x5*x116 + x212 =E= 0;

e112.. -x5*x117 + x213 =E= 0;

e113.. -x5*x118 + x214 =E= 0;

e114.. -x5*x119 + x215 =E= 0;

e115.. -x5*x120 + x216 =E= 0;

e116.. -x5*x121 + x217 =E= 0;

e117.. -x5*x122 + x218 =E= 0;

e118.. -x5*x123 + x219 =E= 0;

e119.. -x5*x124 + x220 =E= 0;

e120.. -x5*x125 + x221 =E= 0;

e121.. -x5*x126 + x222 =E= 0;

e122.. -x5*x127 + x223 =E= 0;

e123.. -x5*x128 + x224 =E= 0;

e124.. -x5*x129 + x225 =E= 0;

e125.. -x6*x130 + x226 =E= 0;

e126.. -x6*x131 + x227 =E= 0;

e127.. -x6*x132 + x228 =E= 0;

e128.. -x6*x133 + x229 =E= 0;

e129.. -x6*x134 + x230 =E= 0;

e130.. -x6*x135 + x231 =E= 0;

e131.. -x6*x136 + x232 =E= 0;

e132.. -x6*x137 + x233 =E= 0;

e133.. -x6*x138 + x234 =E= 0;

e134.. -x6*x139 + x235 =E= 0;

e135.. -x6*x140 + x236 =E= 0;

e136.. -x6*x141 + x237 =E= 0;

e137.. -x6*x142 + x238 =E= 0;

e138.. -x6*x143 + x239 =E= 0;

e139.. -x6*x144 + x240 =E= 0;

e140.. -x6*x145 + x241 =E= 0;

e141.. -x7*x146 + x242 =E= 0;

e142.. -x7*x147 + x243 =E= 0;

e143.. -x7*x148 + x244 =E= 0;

e144.. -x7*x149 + x245 =E= 0;

e145.. -x7*x150 + x246 =E= 0;

e146.. -x7*x151 + x247 =E= 0;

e147.. -x7*x152 + x248 =E= 0;

e148.. -x7*x153 + x249 =E= 0;

e149.. -x7*x154 + x250 =E= 0;

e150.. -x7*x155 + x251 =E= 0;

e151.. -x7*x156 + x252 =E= 0;

e152.. -x7*x157 + x253 =E= 0;

e153.. -x7*x158 + x254 =E= 0;

e154.. -x7*x159 + x255 =E= 0;

e155.. -x7*x160 + x256 =E= 0;

e156.. -x7*x161 + x257 =E= 0;

e157.. -x8*x50 + x258 =E= 0;

e158.. -x8*x51 + x259 =E= 0;

e159.. -x8*x52 + x260 =E= 0;

e160.. -x8*x53 + x261 =E= 0;

e161.. -x8*x54 + x262 =E= 0;

e162.. -x8*x55 + x263 =E= 0;

e163.. -x8*x56 + x264 =E= 0;

e164.. -x8*x57 + x265 =E= 0;

e165.. -x8*x58 + x266 =E= 0;

e166.. -x8*x59 + x267 =E= 0;

e167.. -x8*x60 + x268 =E= 0;

e168.. -x8*x61 + x269 =E= 0;

e169.. -x8*x62 + x270 =E= 0;

e170.. -x8*x63 + x271 =E= 0;

e171.. -x8*x64 + x272 =E= 0;

e172.. -x8*x65 + x273 =E= 0;

e173.. -x9*x98 + x274 =E= 0;

e174.. -x9*x99 + x275 =E= 0;

e175.. -x9*x100 + x276 =E= 0;

e176.. -x9*x101 + x277 =E= 0;

e177.. -x9*x102 + x278 =E= 0;

e178.. -x9*x103 + x279 =E= 0;

e179.. -x9*x104 + x280 =E= 0;

e180.. -x9*x105 + x281 =E= 0;

e181.. -x9*x106 + x282 =E= 0;

e182.. -x9*x107 + x283 =E= 0;

e183.. -x9*x108 + x284 =E= 0;

e184.. -x9*x109 + x285 =E= 0;

e185.. -x9*x110 + x286 =E= 0;

e186.. -x9*x111 + x287 =E= 0;

e187.. -x9*x112 + x288 =E= 0;

e188.. -x9*x113 + x289 =E= 0;

e189.. -x10*x130 + x290 =E= 0;

e190.. -x10*x131 + x291 =E= 0;

e191.. -x10*x132 + x292 =E= 0;

e192.. -x10*x133 + x293 =E= 0;

e193.. -x10*x134 + x294 =E= 0;

e194.. -x10*x135 + x295 =E= 0;

e195.. -x10*x136 + x296 =E= 0;

e196.. -x10*x137 + x297 =E= 0;

e197.. -x10*x138 + x298 =E= 0;

e198.. -x10*x139 + x299 =E= 0;

e199.. -x10*x140 + x300 =E= 0;

e200.. -x10*x141 + x301 =E= 0;

e201.. -x10*x142 + x302 =E= 0;

e202.. -x10*x143 + x303 =E= 0;

e203.. -x10*x144 + x304 =E= 0;

e204.. -x10*x145 + x305 =E= 0;

e205.. -x11*x146 + x306 =E= 0;

e206.. -x11*x147 + x307 =E= 0;

e207.. -x11*x148 + x308 =E= 0;

e208.. -x11*x149 + x309 =E= 0;

e209.. -x11*x150 + x310 =E= 0;

e210.. -x11*x151 + x311 =E= 0;

e211.. -x11*x152 + x312 =E= 0;

e212.. -x11*x153 + x313 =E= 0;

e213.. -x11*x154 + x314 =E= 0;

e214.. -x11*x155 + x315 =E= 0;

e215.. -x11*x156 + x316 =E= 0;

e216.. -x11*x157 + x317 =E= 0;

e217.. -x11*x158 + x318 =E= 0;

e218.. -x11*x159 + x319 =E= 0;

e219.. -x11*x160 + x320 =E= 0;

e220.. -x11*x161 + x321 =E= 0;

e221.. -x12*x34 + x322 =E= 0;

e222.. -x12*x35 + x323 =E= 0;

e223.. -x12*x36 + x324 =E= 0;

e224.. -x12*x37 + x325 =E= 0;

e225.. -x12*x38 + x326 =E= 0;

e226.. -x12*x39 + x327 =E= 0;

e227.. -x12*x40 + x328 =E= 0;

e228.. -x12*x41 + x329 =E= 0;

e229.. -x12*x42 + x330 =E= 0;

e230.. -x12*x43 + x331 =E= 0;

e231.. -x12*x44 + x332 =E= 0;

e232.. -x12*x45 + x333 =E= 0;

e233.. -x12*x46 + x334 =E= 0;

e234.. -x12*x47 + x335 =E= 0;

e235.. -x12*x48 + x336 =E= 0;

e236.. -x12*x49 + x337 =E= 0;

e237.. -x13*x82 + x338 =E= 0;

e238.. -x13*x83 + x339 =E= 0;

e239.. -x13*x84 + x340 =E= 0;

e240.. -x13*x85 + x341 =E= 0;

e241.. -x13*x86 + x342 =E= 0;

e242.. -x13*x87 + x343 =E= 0;

e243.. -x13*x88 + x344 =E= 0;

e244.. -x13*x89 + x345 =E= 0;

e245.. -x13*x90 + x346 =E= 0;

e246.. -x13*x91 + x347 =E= 0;

e247.. -x13*x92 + x348 =E= 0;

e248.. -x13*x93 + x349 =E= 0;

e249.. -x13*x94 + x350 =E= 0;

e250.. -x13*x95 + x351 =E= 0;

e251.. -x13*x96 + x352 =E= 0;

e252.. -x13*x97 + x353 =E= 0;

e253.. -x14*x114 + x354 =E= 0;

e254.. -x14*x115 + x355 =E= 0;

e255.. -x14*x116 + x356 =E= 0;

e256.. -x14*x117 + x357 =E= 0;

e257.. -x14*x118 + x358 =E= 0;

e258.. -x14*x119 + x359 =E= 0;

e259.. -x14*x120 + x360 =E= 0;

e260.. -x14*x121 + x361 =E= 0;

e261.. -x14*x122 + x362 =E= 0;

e262.. -x14*x123 + x363 =E= 0;

e263.. -x14*x124 + x364 =E= 0;

e264.. -x14*x125 + x365 =E= 0;

e265.. -x14*x126 + x366 =E= 0;

e266.. -x14*x127 + x367 =E= 0;

e267.. -x14*x128 + x368 =E= 0;

e268.. -x14*x129 + x369 =E= 0;

e269.. -x15*x130 + x370 =E= 0;

e270.. -x15*x131 + x371 =E= 0;

e271.. -x15*x132 + x372 =E= 0;

e272.. -x15*x133 + x373 =E= 0;

e273.. -x15*x134 + x374 =E= 0;

e274.. -x15*x135 + x375 =E= 0;

e275.. -x15*x136 + x376 =E= 0;

e276.. -x15*x137 + x377 =E= 0;

e277.. -x15*x138 + x378 =E= 0;

e278.. -x15*x139 + x379 =E= 0;

e279.. -x15*x140 + x380 =E= 0;

e280.. -x15*x141 + x381 =E= 0;

e281.. -x15*x142 + x382 =E= 0;

e282.. -x15*x143 + x383 =E= 0;

e283.. -x15*x144 + x384 =E= 0;

e284.. -x15*x145 + x385 =E= 0;

e285.. -x16*x66 + x386 =E= 0;

e286.. -x16*x67 + x387 =E= 0;

e287.. -x16*x68 + x388 =E= 0;

e288.. -x16*x69 + x389 =E= 0;

e289.. -x16*x70 + x390 =E= 0;

e290.. -x16*x71 + x391 =E= 0;

e291.. -x16*x72 + x392 =E= 0;

e292.. -x16*x73 + x393 =E= 0;

e293.. -x16*x74 + x394 =E= 0;

e294.. -x16*x75 + x395 =E= 0;

e295.. -x16*x76 + x396 =E= 0;

e296.. -x16*x77 + x397 =E= 0;

e297.. -x16*x78 + x398 =E= 0;

e298.. -x16*x79 + x399 =E= 0;

e299.. -x16*x80 + x400 =E= 0;

e300.. -x16*x81 + x401 =E= 0;

e301.. -x17*x82 + x402 =E= 0;

e302.. -x17*x83 + x403 =E= 0;

e303.. -x17*x84 + x404 =E= 0;

e304.. -x17*x85 + x405 =E= 0;

e305.. -x17*x86 + x406 =E= 0;

e306.. -x17*x87 + x407 =E= 0;

e307.. -x17*x88 + x408 =E= 0;

e308.. -x17*x89 + x409 =E= 0;

e309.. -x17*x90 + x410 =E= 0;

e310.. -x17*x91 + x411 =E= 0;

e311.. -x17*x92 + x412 =E= 0;

e312.. -x17*x93 + x413 =E= 0;

e313.. -x17*x94 + x414 =E= 0;

e314.. -x17*x95 + x415 =E= 0;

e315.. -x17*x96 + x416 =E= 0;

e316.. -x17*x97 + x417 =E= 0;

e317.. -x18*x98 + x418 =E= 0;

e318.. -x18*x99 + x419 =E= 0;

e319.. -x18*x100 + x420 =E= 0;

e320.. -x18*x101 + x421 =E= 0;

e321.. -x18*x102 + x422 =E= 0;

e322.. -x18*x103 + x423 =E= 0;

e323.. -x18*x104 + x424 =E= 0;

e324.. -x18*x105 + x425 =E= 0;

e325.. -x18*x106 + x426 =E= 0;

e326.. -x18*x107 + x427 =E= 0;

e327.. -x18*x108 + x428 =E= 0;

e328.. -x18*x109 + x429 =E= 0;

e329.. -x18*x110 + x430 =E= 0;

e330.. -x18*x111 + x431 =E= 0;

e331.. -x18*x112 + x432 =E= 0;

e332.. -x18*x113 + x433 =E= 0;

e333.. -x19*x114 + x434 =E= 0;

e334.. -x19*x115 + x435 =E= 0;

e335.. -x19*x116 + x436 =E= 0;

e336.. -x19*x117 + x437 =E= 0;

e337.. -x19*x118 + x438 =E= 0;

e338.. -x19*x119 + x439 =E= 0;

e339.. -x19*x120 + x440 =E= 0;

e340.. -x19*x121 + x441 =E= 0;

e341.. -x19*x122 + x442 =E= 0;

e342.. -x19*x123 + x443 =E= 0;

e343.. -x19*x124 + x444 =E= 0;

e344.. -x19*x125 + x445 =E= 0;

e345.. -x19*x126 + x446 =E= 0;

e346.. -x19*x127 + x447 =E= 0;

e347.. -x19*x128 + x448 =E= 0;

e348.. -x19*x129 + x449 =E= 0;

e349.. -x20*x50 + x450 =E= 0;

e350.. -x20*x51 + x451 =E= 0;

e351.. -x20*x52 + x452 =E= 0;

e352.. -x20*x53 + x453 =E= 0;

e353.. -x20*x54 + x454 =E= 0;

e354.. -x20*x55 + x455 =E= 0;

e355.. -x20*x56 + x456 =E= 0;

e356.. -x20*x57 + x457 =E= 0;

e357.. -x20*x58 + x458 =E= 0;

e358.. -x20*x59 + x459 =E= 0;

e359.. -x20*x60 + x460 =E= 0;

e360.. -x20*x61 + x461 =E= 0;

e361.. -x20*x62 + x462 =E= 0;

e362.. -x20*x63 + x463 =E= 0;

e363.. -x20*x64 + x464 =E= 0;

e364.. -x20*x65 + x465 =E= 0;

e365.. -x21*x66 + x466 =E= 0;

e366.. -x21*x67 + x467 =E= 0;

e367.. -x21*x68 + x468 =E= 0;

e368.. -x21*x69 + x469 =E= 0;

e369.. -x21*x70 + x470 =E= 0;

e370.. -x21*x71 + x471 =E= 0;

e371.. -x21*x72 + x472 =E= 0;

e372.. -x21*x73 + x473 =E= 0;

e373.. -x21*x74 + x474 =E= 0;

e374.. -x21*x75 + x475 =E= 0;

e375.. -x21*x76 + x476 =E= 0;

e376.. -x21*x77 + x477 =E= 0;

e377.. -x21*x78 + x478 =E= 0;

e378.. -x21*x79 + x479 =E= 0;

e379.. -x21*x80 + x480 =E= 0;

e380.. -x21*x81 + x481 =E= 0;

e381.. -x22*x98 + x482 =E= 0;

e382.. -x22*x99 + x483 =E= 0;

e383.. -x22*x100 + x484 =E= 0;

e384.. -x22*x101 + x485 =E= 0;

e385.. -x22*x102 + x486 =E= 0;

e386.. -x22*x103 + x487 =E= 0;

e387.. -x22*x104 + x488 =E= 0;

e388.. -x22*x105 + x489 =E= 0;

e389.. -x22*x106 + x490 =E= 0;

e390.. -x22*x107 + x491 =E= 0;

e391.. -x22*x108 + x492 =E= 0;

e392.. -x22*x109 + x493 =E= 0;

e393.. -x22*x110 + x494 =E= 0;

e394.. -x22*x111 + x495 =E= 0;

e395.. -x22*x112 + x496 =E= 0;

e396.. -x22*x113 + x497 =E= 0;

e397.. -x23*x146 + x498 =E= 0;

e398.. -x23*x147 + x499 =E= 0;

e399.. -x23*x148 + x500 =E= 0;

e400.. -x23*x149 + x501 =E= 0;

e401.. -x23*x150 + x502 =E= 0;

e402.. -x23*x151 + x503 =E= 0;

e403.. -x23*x152 + x504 =E= 0;

e404.. -x23*x153 + x505 =E= 0;

e405.. -x23*x154 + x506 =E= 0;

e406.. -x23*x155 + x507 =E= 0;

e407.. -x23*x156 + x508 =E= 0;

e408.. -x23*x157 + x509 =E= 0;

e409.. -x23*x158 + x510 =E= 0;

e410.. -x23*x159 + x511 =E= 0;

e411.. -x23*x160 + x512 =E= 0;

e412.. -x23*x161 + x513 =E= 0;

e413.. -x24*x34 + x514 =E= 0;

e414.. -x24*x35 + x515 =E= 0;

e415.. -x24*x36 + x516 =E= 0;

e416.. -x24*x37 + x517 =E= 0;

e417.. -x24*x38 + x518 =E= 0;

e418.. -x24*x39 + x519 =E= 0;

e419.. -x24*x40 + x520 =E= 0;

e420.. -x24*x41 + x521 =E= 0;

e421.. -x24*x42 + x522 =E= 0;

e422.. -x24*x43 + x523 =E= 0;

e423.. -x24*x44 + x524 =E= 0;

e424.. -x24*x45 + x525 =E= 0;

e425.. -x24*x46 + x526 =E= 0;

e426.. -x24*x47 + x527 =E= 0;

e427.. -x24*x48 + x528 =E= 0;

e428.. -x24*x49 + x529 =E= 0;

e429.. -x25*x82 + x530 =E= 0;

e430.. -x25*x83 + x531 =E= 0;

e431.. -x25*x84 + x532 =E= 0;

e432.. -x25*x85 + x533 =E= 0;

e433.. -x25*x86 + x534 =E= 0;

e434.. -x25*x87 + x535 =E= 0;

e435.. -x25*x88 + x536 =E= 0;

e436.. -x25*x89 + x537 =E= 0;

e437.. -x25*x90 + x538 =E= 0;

e438.. -x25*x91 + x539 =E= 0;

e439.. -x25*x92 + x540 =E= 0;

e440.. -x25*x93 + x541 =E= 0;

e441.. -x25*x94 + x542 =E= 0;

e442.. -x25*x95 + x543 =E= 0;

e443.. -x25*x96 + x544 =E= 0;

e444.. -x25*x97 + x545 =E= 0;

e445.. -x26*x114 + x546 =E= 0;

e446.. -x26*x115 + x547 =E= 0;

e447.. -x26*x116 + x548 =E= 0;

e448.. -x26*x117 + x549 =E= 0;

e449.. -x26*x118 + x550 =E= 0;

e450.. -x26*x119 + x551 =E= 0;

e451.. -x26*x120 + x552 =E= 0;

e452.. -x26*x121 + x553 =E= 0;

e453.. -x26*x122 + x554 =E= 0;

e454.. -x26*x123 + x555 =E= 0;

e455.. -x26*x124 + x556 =E= 0;

e456.. -x26*x125 + x557 =E= 0;

e457.. -x26*x126 + x558 =E= 0;

e458.. -x26*x127 + x559 =E= 0;

e459.. -x26*x128 + x560 =E= 0;

e460.. -x26*x129 + x561 =E= 0;

e461.. -x27*x130 + x562 =E= 0;

e462.. -x27*x131 + x563 =E= 0;

e463.. -x27*x132 + x564 =E= 0;

e464.. -x27*x133 + x565 =E= 0;

e465.. -x27*x134 + x566 =E= 0;

e466.. -x27*x135 + x567 =E= 0;

e467.. -x27*x136 + x568 =E= 0;

e468.. -x27*x137 + x569 =E= 0;

e469.. -x27*x138 + x570 =E= 0;

e470.. -x27*x139 + x571 =E= 0;

e471.. -x27*x140 + x572 =E= 0;

e472.. -x27*x141 + x573 =E= 0;

e473.. -x27*x142 + x574 =E= 0;

e474.. -x27*x143 + x575 =E= 0;

e475.. -x27*x144 + x576 =E= 0;

e476.. -x27*x145 + x577 =E= 0;

e477.. -x28*x66 + x578 =E= 0;

e478.. -x28*x67 + x579 =E= 0;

e479.. -x28*x68 + x580 =E= 0;

e480.. -x28*x69 + x581 =E= 0;

e481.. -x28*x70 + x582 =E= 0;

e482.. -x28*x71 + x583 =E= 0;

e483.. -x28*x72 + x584 =E= 0;

e484.. -x28*x73 + x585 =E= 0;

e485.. -x28*x74 + x586 =E= 0;

e486.. -x28*x75 + x587 =E= 0;

e487.. -x28*x76 + x588 =E= 0;

e488.. -x28*x77 + x589 =E= 0;

e489.. -x28*x78 + x590 =E= 0;

e490.. -x28*x79 + x591 =E= 0;

e491.. -x28*x80 + x592 =E= 0;

e492.. -x28*x81 + x593 =E= 0;

e493.. -x29*x82 + x594 =E= 0;

e494.. -x29*x83 + x595 =E= 0;

e495.. -x29*x84 + x596 =E= 0;

e496.. -x29*x85 + x597 =E= 0;

e497.. -x29*x86 + x598 =E= 0;

e498.. -x29*x87 + x599 =E= 0;

e499.. -x29*x88 + x600 =E= 0;

e500.. -x29*x89 + x601 =E= 0;

e501.. -x29*x90 + x602 =E= 0;

e502.. -x29*x91 + x603 =E= 0;

e503.. -x29*x92 + x604 =E= 0;

e504.. -x29*x93 + x605 =E= 0;

e505.. -x29*x94 + x606 =E= 0;

e506.. -x29*x95 + x607 =E= 0;

e507.. -x29*x96 + x608 =E= 0;

e508.. -x29*x97 + x609 =E= 0;

e509.. -x30*x98 + x610 =E= 0;

e510.. -x30*x99 + x611 =E= 0;

e511.. -x30*x100 + x612 =E= 0;

e512.. -x30*x101 + x613 =E= 0;

e513.. -x30*x102 + x614 =E= 0;

e514.. -x30*x103 + x615 =E= 0;

e515.. -x30*x104 + x616 =E= 0;

e516.. -x30*x105 + x617 =E= 0;

e517.. -x30*x106 + x618 =E= 0;

e518.. -x30*x107 + x619 =E= 0;

e519.. -x30*x108 + x620 =E= 0;

e520.. -x30*x109 + x621 =E= 0;

e521.. -x30*x110 + x622 =E= 0;

e522.. -x30*x111 + x623 =E= 0;

e523.. -x30*x112 + x624 =E= 0;

e524.. -x30*x113 + x625 =E= 0;

e525.. -x31*x50 + x626 =E= 0;

e526.. -x31*x51 + x627 =E= 0;

e527.. -x31*x52 + x628 =E= 0;

e528.. -x31*x53 + x629 =E= 0;

e529.. -x31*x54 + x630 =E= 0;

e530.. -x31*x55 + x631 =E= 0;

e531.. -x31*x56 + x632 =E= 0;

e532.. -x31*x57 + x633 =E= 0;

e533.. -x31*x58 + x634 =E= 0;

e534.. -x31*x59 + x635 =E= 0;

e535.. -x31*x60 + x636 =E= 0;

e536.. -x31*x61 + x637 =E= 0;

e537.. -x31*x62 + x638 =E= 0;

e538.. -x31*x63 + x639 =E= 0;

e539.. -x31*x64 + x640 =E= 0;

e540.. -x31*x65 + x641 =E= 0;

e541.. -x32*x66 + x642 =E= 0;

e542.. -x32*x67 + x643 =E= 0;

e543.. -x32*x68 + x644 =E= 0;

e544.. -x32*x69 + x645 =E= 0;

e545.. -x32*x70 + x646 =E= 0;

e546.. -x32*x71 + x647 =E= 0;

e547.. -x32*x72 + x648 =E= 0;

e548.. -x32*x73 + x649 =E= 0;

e549.. -x32*x74 + x650 =E= 0;

e550.. -x32*x75 + x651 =E= 0;

e551.. -x32*x76 + x652 =E= 0;

e552.. -x32*x77 + x653 =E= 0;

e553.. -x32*x78 + x654 =E= 0;

e554.. -x32*x79 + x655 =E= 0;

e555.. -x32*x80 + x656 =E= 0;

e556.. -x32*x81 + x657 =E= 0;

e557.. -x33*x34 + x658 =E= 0;

e558.. -x33*x35 + x659 =E= 0;

e559.. -x33*x36 + x660 =E= 0;

e560.. -x33*x37 + x661 =E= 0;

e561.. -x33*x38 + x662 =E= 0;

e562.. -x33*x39 + x663 =E= 0;

e563.. -x33*x40 + x664 =E= 0;

e564.. -x33*x41 + x665 =E= 0;

e565.. -x33*x42 + x666 =E= 0;

e566.. -x33*x43 + x667 =E= 0;

e567.. -x33*x44 + x668 =E= 0;

e568.. -x33*x45 + x669 =E= 0;

e569.. -x33*x46 + x670 =E= 0;

e570.. -x33*x47 + x671 =E= 0;

e571.. -x33*x48 + x672 =E= 0;

e572.. -x33*x49 + x673 =E= 0;

* set non-default bounds
x2.up = 1;
x3.up = 1;
x4.up = 1;
x5.up = 1;
x6.up = 1;
x7.up = 1;
x8.up = 1;
x9.up = 1;
x10.up = 1;
x11.up = 1;
x12.up = 1;
x13.up = 1;
x14.up = 1;
x15.up = 1;
x16.up = 1;
x17.up = 1;
x18.up = 1;
x19.up = 1;
x20.up = 1;
x21.up = 1;
x22.up = 1;
x23.up = 1;
x24.up = 1;
x25.up = 1;
x26.up = 1;
x27.up = 1;
x28.up = 1;
x29.up = 1;
x30.up = 1;
x31.up = 1;
x32.up = 1;
x33.up = 1;
x34.up = 1;
x35.up = 1;
x36.up = 1;
x37.up = 1;
x38.up = 1;
x39.up = 1;
x40.up = 1;
x41.up = 1;
x42.up = 1;
x43.up = 1;
x44.up = 1;
x45.up = 1;
x46.up = 1;
x47.up = 1;
x48.up = 1;
x49.up = 1;
x50.up = 1;
x51.up = 1;
x52.up = 1;
x53.up = 1;
x54.up = 1;
x55.up = 1;
x56.up = 1;
x57.up = 1;
x58.up = 1;
x59.up = 1;
x60.up = 1;
x61.up = 1;
x62.up = 1;
x63.up = 1;
x64.up = 1;
x65.up = 1;
x66.up = 1;
x67.up = 1;
x68.up = 1;
x69.up = 1;
x70.up = 1;
x71.up = 1;
x72.up = 1;
x73.up = 1;
x74.up = 1;
x75.up = 1;
x76.up = 1;
x77.up = 1;
x78.up = 1;
x79.up = 1;
x80.up = 1;
x81.up = 1;
x82.up = 1;
x83.up = 1;
x84.up = 1;
x85.up = 1;
x86.up = 1;
x87.up = 1;
x88.up = 1;
x89.up = 1;
x90.up = 1;
x91.up = 1;
x92.up = 1;
x93.up = 1;
x94.up = 1;
x95.up = 1;
x96.up = 1;
x97.up = 1;
x98.up = 1;
x99.up = 1;
x100.up = 1;
x101.up = 1;
x102.up = 1;
x103.up = 1;
x104.up = 1;
x105.up = 1;
x106.up = 1;
x107.up = 1;
x108.up = 1;
x109.up = 1;
x110.up = 1;
x111.up = 1;
x112.up = 1;
x113.up = 1;
x114.up = 1;
x115.up = 1;
x116.up = 1;
x117.up = 1;
x118.up = 1;
x119.up = 1;
x120.up = 1;
x121.up = 1;
x122.up = 1;
x123.up = 1;
x124.up = 1;
x125.up = 1;
x126.up = 1;
x127.up = 1;
x128.up = 1;
x129.up = 1;
x130.up = 1;
x131.up = 1;
x132.up = 1;
x133.up = 1;
x134.up = 1;
x135.up = 1;
x136.up = 1;
x137.up = 1;
x138.up = 1;
x139.up = 1;
x140.up = 1;
x141.up = 1;
x142.up = 1;
x143.up = 1;
x144.up = 1;
x145.up = 1;
x146.up = 1;
x147.up = 1;
x148.up = 1;
x149.up = 1;
x150.up = 1;
x151.up = 1;
x152.up = 1;
x153.up = 1;
x154.up = 1;
x155.up = 1;
x156.up = 1;
x157.up = 1;
x158.up = 1;
x159.up = 1;
x160.up = 1;
x161.up = 1;
x162.up = 1;
x163.up = 1;
x164.up = 1;
x165.up = 1;
x166.up = 1;
x167.up = 1;
x168.up = 1;
x169.up = 1;
x170.up = 1;
x171.up = 1;
x172.up = 1;
x173.up = 1;
x174.up = 1;
x175.up = 1;
x176.up = 1;
x177.up = 1;
x178.up = 1;
x179.up = 1;
x180.up = 1;
x181.up = 1;
x182.up = 1;
x183.up = 1;
x184.up = 1;
x185.up = 1;
x186.up = 1;
x187.up = 1;
x188.up = 1;
x189.up = 1;
x190.up = 1;
x191.up = 1;
x192.up = 1;
x193.up = 1;
x194.up = 1;
x195.up = 1;
x196.up = 1;
x197.up = 1;
x198.up = 1;
x199.up = 1;
x200.up = 1;
x201.up = 1;
x202.up = 1;
x203.up = 1;
x204.up = 1;
x205.up = 1;
x206.up = 1;
x207.up = 1;
x208.up = 1;
x209.up = 1;
x210.up = 1;
x211.up = 1;
x212.up = 1;
x213.up = 1;
x214.up = 1;
x215.up = 1;
x216.up = 1;
x217.up = 1;
x218.up = 1;
x219.up = 1;
x220.up = 1;
x221.up = 1;
x222.up = 1;
x223.up = 1;
x224.up = 1;
x225.up = 1;
x226.up = 1;
x227.up = 1;
x228.up = 1;
x229.up = 1;
x230.up = 1;
x231.up = 1;
x232.up = 1;
x233.up = 1;
x234.up = 1;
x235.up = 1;
x236.up = 1;
x237.up = 1;
x238.up = 1;
x239.up = 1;
x240.up = 1;
x241.up = 1;
x242.up = 1;
x243.up = 1;
x244.up = 1;
x245.up = 1;
x246.up = 1;
x247.up = 1;
x248.up = 1;
x249.up = 1;
x250.up = 1;
x251.up = 1;
x252.up = 1;
x253.up = 1;
x254.up = 1;
x255.up = 1;
x256.up = 1;
x257.up = 1;
x258.up = 1;
x259.up = 1;
x260.up = 1;
x261.up = 1;
x262.up = 1;
x263.up = 1;
x264.up = 1;
x265.up = 1;
x266.up = 1;
x267.up = 1;
x268.up = 1;
x269.up = 1;
x270.up = 1;
x271.up = 1;
x272.up = 1;
x273.up = 1;
x274.up = 1;
x275.up = 1;
x276.up = 1;
x277.up = 1;
x278.up = 1;
x279.up = 1;
x280.up = 1;
x281.up = 1;
x282.up = 1;
x283.up = 1;
x284.up = 1;
x285.up = 1;
x286.up = 1;
x287.up = 1;
x288.up = 1;
x289.up = 1;
x290.up = 1;
x291.up = 1;
x292.up = 1;
x293.up = 1;
x294.up = 1;
x295.up = 1;
x296.up = 1;
x297.up = 1;
x298.up = 1;
x299.up = 1;
x300.up = 1;
x301.up = 1;
x302.up = 1;
x303.up = 1;
x304.up = 1;
x305.up = 1;
x306.up = 1;
x307.up = 1;
x308.up = 1;
x309.up = 1;
x310.up = 1;
x311.up = 1;
x312.up = 1;
x313.up = 1;
x314.up = 1;
x315.up = 1;
x316.up = 1;
x317.up = 1;
x318.up = 1;
x319.up = 1;
x320.up = 1;
x321.up = 1;
x322.up = 1;
x323.up = 1;
x324.up = 1;
x325.up = 1;
x326.up = 1;
x327.up = 1;
x328.up = 1;
x329.up = 1;
x330.up = 1;
x331.up = 1;
x332.up = 1;
x333.up = 1;
x334.up = 1;
x335.up = 1;
x336.up = 1;
x337.up = 1;
x338.up = 1;
x339.up = 1;
x340.up = 1;
x341.up = 1;
x342.up = 1;
x343.up = 1;
x344.up = 1;
x345.up = 1;
x346.up = 1;
x347.up = 1;
x348.up = 1;
x349.up = 1;
x350.up = 1;
x351.up = 1;
x352.up = 1;
x353.up = 1;
x354.up = 1;
x355.up = 1;
x356.up = 1;
x357.up = 1;
x358.up = 1;
x359.up = 1;
x360.up = 1;
x361.up = 1;
x362.up = 1;
x363.up = 1;
x364.up = 1;
x365.up = 1;
x366.up = 1;
x367.up = 1;
x368.up = 1;
x369.up = 1;
x370.up = 1;
x371.up = 1;
x372.up = 1;
x373.up = 1;
x374.up = 1;
x375.up = 1;
x376.up = 1;
x377.up = 1;
x378.up = 1;
x379.up = 1;
x380.up = 1;
x381.up = 1;
x382.up = 1;
x383.up = 1;
x384.up = 1;
x385.up = 1;
x386.up = 1;
x387.up = 1;
x388.up = 1;
x389.up = 1;
x390.up = 1;
x391.up = 1;
x392.up = 1;
x393.up = 1;
x394.up = 1;
x395.up = 1;
x396.up = 1;
x397.up = 1;
x398.up = 1;
x399.up = 1;
x400.up = 1;
x401.up = 1;
x402.up = 1;
x403.up = 1;
x404.up = 1;
x405.up = 1;
x406.up = 1;
x407.up = 1;
x408.up = 1;
x409.up = 1;
x410.up = 1;
x411.up = 1;
x412.up = 1;
x413.up = 1;
x414.up = 1;
x415.up = 1;
x416.up = 1;
x417.up = 1;
x418.up = 1;
x419.up = 1;
x420.up = 1;
x421.up = 1;
x422.up = 1;
x423.up = 1;
x424.up = 1;
x425.up = 1;
x426.up = 1;
x427.up = 1;
x428.up = 1;
x429.up = 1;
x430.up = 1;
x431.up = 1;
x432.up = 1;
x433.up = 1;
x434.up = 1;
x435.up = 1;
x436.up = 1;
x437.up = 1;
x438.up = 1;
x439.up = 1;
x440.up = 1;
x441.up = 1;
x442.up = 1;
x443.up = 1;
x444.up = 1;
x445.up = 1;
x446.up = 1;
x447.up = 1;
x448.up = 1;
x449.up = 1;
x450.up = 1;
x451.up = 1;
x452.up = 1;
x453.up = 1;
x454.up = 1;
x455.up = 1;
x456.up = 1;
x457.up = 1;
x458.up = 1;
x459.up = 1;
x460.up = 1;
x461.up = 1;
x462.up = 1;
x463.up = 1;
x464.up = 1;
x465.up = 1;
x466.up = 1;
x467.up = 1;
x468.up = 1;
x469.up = 1;
x470.up = 1;
x471.up = 1;
x472.up = 1;
x473.up = 1;
x474.up = 1;
x475.up = 1;
x476.up = 1;
x477.up = 1;
x478.up = 1;
x479.up = 1;
x480.up = 1;
x481.up = 1;
x482.up = 1;
x483.up = 1;
x484.up = 1;
x485.up = 1;
x486.up = 1;
x487.up = 1;
x488.up = 1;
x489.up = 1;
x490.up = 1;
x491.up = 1;
x492.up = 1;
x493.up = 1;
x494.up = 1;
x495.up = 1;
x496.up = 1;
x497.up = 1;
x498.up = 1;
x499.up = 1;
x500.up = 1;
x501.up = 1;
x502.up = 1;
x503.up = 1;
x504.up = 1;
x505.up = 1;
x506.up = 1;
x507.up = 1;
x508.up = 1;
x509.up = 1;
x510.up = 1;
x511.up = 1;
x512.up = 1;
x513.up = 1;
x514.up = 1;
x515.up = 1;
x516.up = 1;
x517.up = 1;
x518.up = 1;
x519.up = 1;
x520.up = 1;
x521.up = 1;
x522.up = 1;
x523.up = 1;
x524.up = 1;
x525.up = 1;
x526.up = 1;
x527.up = 1;
x528.up = 1;
x529.up = 1;
x530.up = 1;
x531.up = 1;
x532.up = 1;
x533.up = 1;
x534.up = 1;
x535.up = 1;
x536.up = 1;
x537.up = 1;
x538.up = 1;
x539.up = 1;
x540.up = 1;
x541.up = 1;
x542.up = 1;
x543.up = 1;
x544.up = 1;
x545.up = 1;
x546.up = 1;
x547.up = 1;
x548.up = 1;
x549.up = 1;
x550.up = 1;
x551.up = 1;
x552.up = 1;
x553.up = 1;
x554.up = 1;
x555.up = 1;
x556.up = 1;
x557.up = 1;
x558.up = 1;
x559.up = 1;
x560.up = 1;
x561.up = 1;
x562.up = 1;
x563.up = 1;
x564.up = 1;
x565.up = 1;
x566.up = 1;
x567.up = 1;
x568.up = 1;
x569.up = 1;
x570.up = 1;
x571.up = 1;
x572.up = 1;
x573.up = 1;
x574.up = 1;
x575.up = 1;
x576.up = 1;
x577.up = 1;
x578.up = 1;
x579.up = 1;
x580.up = 1;
x581.up = 1;
x582.up = 1;
x583.up = 1;
x584.up = 1;
x585.up = 1;
x586.up = 1;
x587.up = 1;
x588.up = 1;
x589.up = 1;
x590.up = 1;
x591.up = 1;
x592.up = 1;
x593.up = 1;
x594.up = 1;
x595.up = 1;
x596.up = 1;
x597.up = 1;
x598.up = 1;
x599.up = 1;
x600.up = 1;
x601.up = 1;
x602.up = 1;
x603.up = 1;
x604.up = 1;
x605.up = 1;
x606.up = 1;
x607.up = 1;
x608.up = 1;
x609.up = 1;
x610.up = 1;
x611.up = 1;
x612.up = 1;
x613.up = 1;
x614.up = 1;
x615.up = 1;
x616.up = 1;
x617.up = 1;
x618.up = 1;
x619.up = 1;
x620.up = 1;
x621.up = 1;
x622.up = 1;
x623.up = 1;
x624.up = 1;
x625.up = 1;
x626.up = 1;
x627.up = 1;
x628.up = 1;
x629.up = 1;
x630.up = 1;
x631.up = 1;
x632.up = 1;
x633.up = 1;
x634.up = 1;
x635.up = 1;
x636.up = 1;
x637.up = 1;
x638.up = 1;
x639.up = 1;
x640.up = 1;
x641.up = 1;
x642.up = 1;
x643.up = 1;
x644.up = 1;
x645.up = 1;
x646.up = 1;
x647.up = 1;
x648.up = 1;
x649.up = 1;
x650.up = 1;
x651.up = 1;
x652.up = 1;
x653.up = 1;
x654.up = 1;
x655.up = 1;
x656.up = 1;
x657.up = 1;
x658.up = 1;
x659.up = 1;
x660.up = 1;
x661.up = 1;
x662.up = 1;
x663.up = 1;
x664.up = 1;
x665.up = 1;
x666.up = 1;
x667.up = 1;
x668.up = 1;
x669.up = 1;
x670.up = 1;
x671.up = 1;
x672.up = 1;
x673.up = 1;

Model m / all /;

m.limrow=0; m.limcol=0;
m.tolproj=0.0;

$if NOT '%gams.u1%' == '' $include '%gams.u1%'

$if not set NLP $set NLP NLP
Solve m using %NLP% minimizing objvar;


Last updated: 2022-08-11 Git hash: f176bd52
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