0.00/0.00 c SCIP version 1.2.1.3 [precision: 8 byte] [memory: block] [mode: optimized] [LP solver: SoPlex 1.4.2]
0.00/0.00 c Copyright (c) 2002-2010 Konrad-Zuse-Zentrum fuer Informationstechnik Berlin (ZIB)
0.00/0.00 c
0.00/0.00 c user parameter file <scip.set> not found - using default parameters
0.00/0.00 c reading problem <HOME/instance-2704532-1278561432.opb>
0.00/0.02 c original problem has 515 variables (515 bin, 0 int, 0 impl, 0 cont) and 559 constraints
0.00/0.02 c problem read
0.00/0.02 c presolving settings loaded
0.00/0.03 o 515
0.00/0.03 c feasible solution found by trivial heuristic, objective value 5.150000e+02
0.00/0.03 c presolving:
0.00/0.03 c (round 1) 6 del vars, 6 del conss, 0 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 110 impls, 0 clqs
0.00/0.04 c (round 2) 13 del vars, 15 del conss, 0 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 110 impls, 0 clqs
0.00/0.04 c (round 3) 14 del vars, 16 del conss, 0 chg bounds, 0 chg sides, 0 chg coeffs, 0 upgd conss, 110 impls, 0 clqs
0.04/0.05 c (round 4) 14 del vars, 155 del conss, 0 chg bounds, 136 chg sides, 0 chg coeffs, 0 upgd conss, 110 impls, 0 clqs
0.04/0.05 c (round 5) 25 del vars, 165 del conss, 0 chg bounds, 136 chg sides, 0 chg coeffs, 0 upgd conss, 110 impls, 0 clqs
0.04/0.05 c (round 6) 35 del vars, 197 del conss, 0 chg bounds, 136 chg sides, 0 chg coeffs, 0 upgd conss, 110 impls, 0 clqs
0.04/0.05 c (round 7) 38 del vars, 199 del conss, 0 chg bounds, 136 chg sides, 0 chg coeffs, 0 upgd conss, 110 impls, 0 clqs
0.04/0.05 c (round 8) 40 del vars, 203 del conss, 0 chg bounds, 136 chg sides, 0 chg coeffs, 0 upgd conss, 110 impls, 0 clqs
0.04/0.06 c (round 9) 40 del vars, 203 del conss, 0 chg bounds, 136 chg sides, 0 chg coeffs, 356 upgd conss, 110 impls, 0 clqs
0.04/0.06 c (0.0s) probing: 101/475 (21.3%) - 0 fixings, 0 aggregations, 0 implications, 0 bound changes
0.04/0.06 c (0.0s) probing aborted: 100/100 successive totally useless probings
0.04/0.06 c presolving (10 rounds):
0.04/0.06 c 40 deleted vars, 203 deleted constraints, 0 tightened bounds, 0 added holes, 136 changed sides, 0 changed coefficients
0.04/0.06 c 110 implications, 0 cliques
0.04/0.06 c presolved problem has 475 variables (475 bin, 0 int, 0 impl, 0 cont) and 356 constraints
0.04/0.06 c 32 constraints of type <setppc>
0.04/0.06 c 324 constraints of type <logicor>
0.04/0.06 c transformed objective value is always integral (scale: 1)
0.04/0.06 c Presolving Time: 0.03
0.04/0.06 c - non default parameters ----------------------------------------------------------------------
0.04/0.06 c # SCIP version 1.2.1.3
0.04/0.06 c
0.04/0.06 c # frequency for displaying node information lines
0.04/0.06 c # [type: int, range: [-1,2147483647], default: 100]
0.04/0.06 c display/freq = 10000
0.04/0.06 c
0.04/0.06 c # maximal time in seconds to run
0.04/0.06 c # [type: real, range: [0,1.79769313486232e+308], default: 1e+20]
0.04/0.06 c limits/time = 1789.99
0.04/0.06 c
0.04/0.06 c # maximal memory usage in MB; reported memory usage is lower than real memory usage!
0.04/0.06 c # [type: real, range: [0,1.79769313486232e+308], default: 1e+20]
0.04/0.06 c limits/memory = 1620
0.04/0.06 c
0.04/0.06 c # default clock type (1: CPU user seconds, 2: wall clock time)
0.04/0.06 c # [type: int, range: [1,2], default: 1]
0.04/0.06 c timing/clocktype = 2
0.04/0.06 c
0.04/0.06 c # should presolving try to simplify inequalities
0.04/0.06 c # [type: bool, range: {TRUE,FALSE}, default: FALSE]
0.04/0.06 c constraints/linear/simplifyinequalities = TRUE
0.04/0.06 c
0.04/0.06 c # add initial coupling inequalities as linear constraints, if 'addCoupling' is true
0.04/0.06 c # [type: bool, range: {TRUE,FALSE}, default: FALSE]
0.04/0.06 c constraints/indicator/addCouplingCons = TRUE
0.04/0.06 c
0.04/0.06 c # should presolving try to simplify knapsacks
0.04/0.06 c # [type: bool, range: {TRUE,FALSE}, default: FALSE]
0.04/0.06 c constraints/knapsack/simplifyinequalities = TRUE
0.04/0.06 c
0.04/0.06 c # frequency for calling separator <rapidlearning> (-1: never, 0: only in root node)
0.04/0.06 c # [type: int, range: [-1,2147483647], default: -1]
0.04/0.06 c separating/rapidlearning/freq = 0
0.04/0.06 c
0.04/0.06 c -----------------------------------------------------------------------------------------------
0.04/0.06 c start solving
0.04/0.06 c
0.04/0.06 o 494
0.04/0.06 c time | node | left |LP iter|LP it/n| mem |mdpt |frac |vars |cons |cols |rows |cuts |confs|strbr| dualbound | primalbound | gap
0.04/0.06 c t 0.0s| 1 | 0 | 0 | - |1414k| 0 | - | 475 | 356 | 0 | 0 | 0 | 0 | 0 | -- | 4.940000e+02 | Inf
0.04/0.07 o 141
0.04/0.07 c b 0.0s| 1 | 0 | 0 | - |1740k| 0 | - | 475 | 356 | 475 | 356 | 0 | 0 | 0 | -- | 1.410000e+02 | Inf
0.04/0.09 c 0.1s| 1 | 0 | 375 | - |1733k| 0 | 69 | 475 | 356 | 475 | 356 | 0 | 0 | 0 | 1.121111e+02 | 1.410000e+02 | 25.77%
0.19/0.21 c 0.2s| 1 | 0 | 419 | - |2144k| 0 | 90 | 475 | 356 | 475 | 357 | 1 | 0 | 0 | 1.124286e+02 | 1.410000e+02 | 25.41%
0.19/0.30 c 0.3s| 1 | 0 | 449 | - |2247k| 0 | 93 | 475 | 356 | 475 | 359 | 3 | 0 | 0 | 1.124762e+02 | 1.410000e+02 | 25.36%
0.29/0.38 c 0.4s| 1 | 0 | 502 | - |2399k| 0 | 140 | 475 | 356 | 475 | 360 | 4 | 0 | 0 | 1.130000e+02 | 1.410000e+02 | 24.78%
0.39/0.49 c 0.5s| 1 | 0 | 566 | - |3097k| 0 | 77 | 475 | 356 | 475 | 361 | 5 | 0 | 0 | 1.130000e+02 | 1.410000e+02 | 24.78%
0.50/0.59 c 0.6s| 1 | 0 | 631 | - |3346k| 0 | 143 | 475 | 356 | 475 | 362 | 6 | 0 | 0 | 1.130000e+02 | 1.410000e+02 | 24.78%
0.59/0.69 c 0.7s| 1 | 0 | 703 | - |3566k| 0 | 163 | 475 | 356 | 475 | 363 | 7 | 0 | 0 | 1.130000e+02 | 1.410000e+02 | 24.78%
0.79/0.82 c 0.8s| 1 | 0 | 746 | - |3685k| 0 | 181 | 475 | 356 | 475 | 364 | 8 | 0 | 0 | 1.130000e+02 | 1.410000e+02 | 24.78%
0.89/0.95 c 0.9s| 1 | 0 | 807 | - |3709k| 0 | 161 | 475 | 356 | 475 | 365 | 9 | 0 | 0 | 1.130000e+02 | 1.410000e+02 | 24.78%
1.10/1.11 c 1.1s| 1 | 0 | 860 | - |3734k| 0 | 174 | 475 | 356 | 475 | 366 | 10 | 0 | 0 | 1.130000e+02 | 1.410000e+02 | 24.78%
2.10/2.13 o 115
2.10/2.13 c E 2.1s| 1 | 0 | 860 | - |3761k| 0 | 174 | 475 | 356 | 475 | 366 | 10 | 0 | 0 | 1.130000e+02 | 1.150000e+02 | 1.77%
2.10/2.14 c 2.1s| 1 | 0 | 860 | - |3761k| 0 | 174 | 475 | 356 | 475 | 366 | 10 | 0 | 0 | 1.130000e+02 | 1.150000e+02 | 1.77%
4.49/4.52 c 4.5s| 1 | 2 | 860 | - |3761k| 0 | 174 | 475 | 356 | 475 | 366 | 10 | 0 | 44 | 1.130000e+02 | 1.150000e+02 | 1.77%
5.79/5.87 o 114
5.79/5.87 c time | node | left |LP iter|LP it/n| mem |mdpt |frac |vars |cons |cols |rows |cuts |confs|strbr| dualbound | primalbound | gap
5.79/5.87 c * 5.8s| 2 | 1 | 1510 | 650.0 |3873k| 1 | - | 475 | 356 | 475 | 364 | 10 | 0 | 128 | 1.130000e+02 | 1.140000e+02 | 0.88%
5.79/5.87 o 113
5.79/5.87 c b 5.8s| 3 | 0 | 1510 | 325.0 |3878k| 1 | - | 475 | 356 | 475 | 364 | 10 | 0 | 128 | 1.130000e+02 | 1.130000e+02 | 0.00%
5.79/5.87 c
5.79/5.87 c SCIP Status : problem is solved [optimal solution found]
5.79/5.87 c Solving Time (sec) : 5.85
5.79/5.87 c Solving Nodes : 3
5.79/5.87 c Primal Bound : +1.13000000000000e+02 (27 solutions)
5.79/5.87 c Dual Bound : +1.13000000000000e+02
5.79/5.87 c Gap : 0.00 %
5.79/5.87 s OPTIMUM FOUND
5.79/5.87 v -x515 -x514 -x513 -x512 -x511 -x510 x509 -x508 -x507 -x506 x505 -x504 -x503 -x502 -x501 -x500 -x499 -x498 -x497 -x496 x495 -x494
5.79/5.87 v -x493 -x492 -x491 -x490 -x489 -x488 x487 x486 -x485 -x484 -x483 -x482 -x481 -x480 x479 x478 -x477 x476 -x475 -x474 x473 -x472
5.79/5.87 v -x471 -x470 -x469 x468 x467 -x466 -x465 -x464 -x463 -x462 -x461 -x460 -x459 -x458 -x457 -x456 x455 -x454 -x453 -x452 -x451
5.79/5.87 v x450 x449 -x448 x447 -x446 -x445 x444 -x443 -x442 -x441 x440 -x439 -x438 -x437 -x436 -x435 x434 -x433 -x432 x431 -x430 x429
5.79/5.87 v -x428 x427 -x426 -x425 -x424 -x423 -x422 -x421 -x420 -x419 x418 -x417 x416 -x415 -x414 -x413 -x412 -x411 -x410 -x409 -x408 -x407
5.79/5.87 v x406 -x405 -x404 x403 -x402 -x401 -x400 -x399 -x398 -x397 -x396 x395 x394 -x393 -x392 x391 -x390 -x389 -x388 x387 -x386 -x385
5.79/5.87 v x384 -x383 -x382 -x381 x380 -x379 -x378 -x377 x376 -x375 -x374 -x373 -x372 -x371 -x370 -x369 -x368 -x367 -x366 -x365 -x364
5.79/5.87 v -x363 -x362 -x361 -x360 -x359 -x358 -x357 -x356 -x355 -x354 -x353 -x352 -x351 -x350 -x349 -x348 -x347 x346 x345 -x344 -x343
5.79/5.87 v -x342 -x341 -x340 x339 -x338 -x337 x336 -x335 -x334 -x333 x332 -x331 x330 -x329 -x328 -x327 -x326 -x325 x324 x323 x322 x321
5.79/5.87 v -x320 x319 x318 x317 -x316 x315 -x314 -x313 -x312 x311 -x310 -x309 -x308 -x307 x306 -x305 -x304 -x303 -x302 x301 -x300 x299
5.79/5.87 v -x298 -x297 -x296 -x295 -x294 -x293 -x292 x291 -x290 -x289 -x288 x287 -x286 -x285 -x284 -x283 -x282 x281 x280 -x279 x278 -x277
5.79/5.87 v -x276 x275 -x274 x273 -x272 -x271 -x270 -x269 -x268 -x267 -x266 x265 -x264 x263 -x262 -x261 -x260 -x259 x258 -x257 -x256 -x255
5.79/5.87 v x254 -x253 -x252 -x251 -x250 -x249 x248 -x247 x246 -x245 -x244 -x243 -x242 x241 -x240 x239 -x238 x237 -x236 -x235 -x234 -x233
5.79/5.87 v -x232 -x231 -x230 -x229 -x228 -x227 -x226 x225 -x224 -x223 -x222 -x221 -x220 -x219 -x218 -x217 -x216 -x215 -x214 x213 -x212
5.79/5.87 v -x211 -x210 -x209 -x208 x207 x206 x205 -x204 x203 x202 -x201 -x200 -x199 -x198 -x197 -x196 -x195 -x194 x193 -x192 x191 -x190
5.79/5.87 v -x189 x188 -x187 -x186 x185 -x184 -x183 -x182 -x181 -x180 -x179 -x178 -x177 -x176 x175 x174 -x173 -x172 -x171 -x170 -x169
5.79/5.87 v -x168 -x167 x166 -x165 -x164 -x163 -x162 -x161 -x160 -x159 -x158 -x157 -x156 -x155 -x154 -x153 x152 -x151 -x150 -x149 x148 x147
5.79/5.87 v -x146 -x145 x144 -x143 x142 x141 x140 x139 -x138 -x137 -x136 -x135 -x134 -x133 -x132 -x131 -x130 -x129 -x128 x127 -x126 -x125
5.79/5.87 v -x124 -x123 -x122 -x121 x120 -x119 -x118 x117 -x116 -x115 x114 -x113 -x112 -x111 -x110 x109 -x108 -x107 -x106 -x105 -x104
5.79/5.87 v -x103 -x102 -x101 -x100 -x99 -x98 x97 -x96 -x95 x94 -x93 -x92 x91 -x90 x89 x88 -x87 -x86 -x85 -x84 -x83 -x82 -x81 -x80 -x79
5.79/5.87 v -x78 -x77 -x76 -x75 -x74 x73 -x72 -x71 -x70 -x69 -x68 -x67 -x66 -x65 -x64 -x63 -x62 -x61 -x60 x59 -x58 x57 -x56 -x55 -x54 -x53
5.79/5.87 v -x52 -x51 -x50 -x49 -x48 x47 -x46 -x45 -x44 x43 -x42 -x41 -x40 -x39 -x38 x37 -x36 -x35 -x34 -x33 -x32 -x31 x30 -x29 -x28 x27
5.79/5.87 v x26 -x25 -x24 x23 -x22 x21 -x20 -x19 -x18 -x17 x16 -x15 -x14 -x13 -x12 -x11 -x10 -x9 -x8 -x7 -x6 -x5 x4 x3 -x2 x1
5.79/5.87 c SCIP Status : problem is solved [optimal solution found]
5.79/5.87 c Solving Time : 5.85
5.79/5.87 c Original Problem :
5.79/5.87 c Problem name : HOME/instance-2704532-1278561432.opb
5.79/5.87 c Variables : 515 (515 binary, 0 integer, 0 implicit integer, 0 continuous)
5.79/5.87 c Constraints : 559 initial, 559 maximal
5.79/5.87 c Presolved Problem :
5.79/5.87 c Problem name : t_HOME/instance-2704532-1278561432.opb
5.79/5.87 c Variables : 475 (475 binary, 0 integer, 0 implicit integer, 0 continuous)
5.79/5.87 c Constraints : 356 initial, 356 maximal
5.79/5.87 c Presolvers : Time FixedVars AggrVars ChgTypes ChgBounds AddHoles DelCons ChgSides ChgCoefs
5.79/5.87 c trivial : 0.00 0 0 0 0 0 0 0 0
5.79/5.87 c dualfix : 0.00 21 0 0 0 0 0 0 0
5.79/5.87 c boundshift : 0.00 0 0 0 0 0 0 0 0
5.79/5.87 c inttobinary : 0.00 0 0 0 0 0 0 0 0
5.79/5.87 c implics : 0.00 0 0 0 0 0 0 0 0
5.79/5.87 c probing : 0.01 0 0 0 0 0 0 0 0
5.79/5.87 c setppc : 0.00 0 0 0 0 0 0 0 0
5.79/5.87 c linear : 0.01 0 19 0 0 0 203 136 0
5.79/5.87 c logicor : 0.00 0 0 0 0 0 0 0 0
5.79/5.87 c root node : - 1 - - 1 - - - -
5.79/5.87 c Constraints : Number #Separate #Propagate #EnfoLP #EnfoPS Cutoffs DomReds Cuts Conss Children
5.79/5.87 c integral : 0 0 0 11 0 0 43 0 0 2
5.79/5.87 c setppc : 32 10 222 1 0 0 6 0 0 0
5.79/5.87 c logicor : 324 10 111 1 0 0 6 0 0 0
5.79/5.87 c countsols : 0 0 0 1 0 0 0 0 0 0
5.79/5.87 c Constraint Timings : TotalTime Separate Propagate EnfoLP EnfoPS
5.79/5.87 c integral : 3.45 0.00 0.00 3.45 0.00
5.79/5.87 c setppc : 0.00 0.00 0.00 0.00 0.00
5.79/5.87 c logicor : 0.00 0.00 0.00 0.00 0.00
5.79/5.87 c countsols : 0.00 0.00 0.00 0.00 0.00
5.79/5.87 c Propagators : Time Calls Cutoffs DomReds
5.79/5.87 c vbounds : 0.00 2 0 0
5.79/5.87 c rootredcost : 0.00 0 0 0
5.79/5.87 c pseudoobj : 0.00 27 0 0
5.79/5.87 c Conflict Analysis : Time Calls Success Conflicts Literals Reconvs ReconvLits LP Iters
5.79/5.87 c propagation : 0.00 0 0 0 0.0 0 0.0 -
5.79/5.87 c infeasible LP : 0.00 0 0 0 0.0 0 0.0 0
5.79/5.87 c bound exceed. LP : 0.00 0 0 0 0.0 0 0.0 0
5.79/5.87 c strong branching : 0.00 0 0 0 0.0 0 0.0 0
5.79/5.87 c pseudo solution : 0.00 0 0 0 0.0 0 0.0 -
5.79/5.87 c applied globally : - - - 0 0.0 - - -
5.79/5.87 c applied locally : - - - 0 0.0 - - -
5.79/5.87 c Separators : Time Calls Cutoffs DomReds Cuts Conss
5.79/5.87 c cut pool : 0.01 9 - - 23 - (maximal pool size: 236)
5.79/5.87 c redcost : 0.00 15 0 96 0 0
5.79/5.87 c impliedbounds : 0.00 10 0 0 0 0
5.79/5.87 c intobj : 0.00 0 0 0 0 0
5.79/5.87 c cgmip : 0.00 0 0 0 0 0
5.79/5.87 c gomory : 0.41 10 0 0 488 0
5.79/5.87 c strongcg : 0.40 10 0 0 707 0
5.79/5.87 c cmir : 0.05 10 0 0 0 0
5.79/5.87 c flowcover : 0.13 10 0 0 0 0
5.79/5.87 c clique : 0.00 1 0 0 0 0
5.79/5.87 c zerohalf : 0.00 0 0 0 0 0
5.79/5.87 c mcf : 0.00 1 0 0 0 0
5.79/5.87 c rapidlearning : 0.04 1 0 0 0 0
5.79/5.87 c Pricers : Time Calls Vars
5.79/5.87 c problem variables: 0.00 0 0
5.79/5.87 c Branching Rules : Time Calls Cutoffs DomReds Cuts Conss Children
5.79/5.87 c relpscost : 3.45 10 0 43 0 0 2
5.79/5.87 c pscost : 0.00 0 0 0 0 0 0
5.79/5.87 c inference : 0.00 0 0 0 0 0 0
5.79/5.87 c mostinf : 0.00 0 0 0 0 0 0
5.79/5.87 c leastinf : 0.00 0 0 0 0 0 0
5.79/5.87 c fullstrong : 0.00 0 0 0 0 0 0
5.79/5.87 c allfullstrong : 0.00 0 0 0 0 0 0
5.79/5.87 c random : 0.00 0 0 0 0 0 0
5.79/5.87 c Primal Heuristics : Time Calls Found
5.79/5.87 c LP solutions : 0.00 - 1
5.79/5.87 c pseudo solutions : 0.00 - 0
5.79/5.87 c crossover : 0.00 0 0
5.79/5.87 c coefdiving : 0.00 0 0
5.79/5.87 c trivial : 0.00 2 3
5.79/5.87 c simplerounding : 0.00 19 19
5.79/5.87 c zirounding : 0.00 1 1
5.79/5.87 c rounding : 0.02 19 0
5.79/5.87 c shifting : 0.01 10 0
5.79/5.87 c intshifting : 0.00 0 0
5.79/5.87 c oneopt : 0.00 4 2
5.79/5.87 c twoopt : 0.00 0 0
5.79/5.87 c fixandinfer : 0.00 0 0
5.79/5.87 c feaspump : 0.00 0 0
5.79/5.87 c pscostdiving : 0.00 0 0
5.79/5.87 c fracdiving : 0.00 0 0
5.79/5.87 c veclendiving : 0.00 0 0
5.79/5.87 c intdiving : 0.00 0 0
5.79/5.87 c actconsdiving : 0.00 0 0
5.79/5.87 c objpscostdiving : 0.00 0 0
5.79/5.87 c rootsoldiving : 0.00 0 0
5.79/5.87 c linesearchdiving : 0.00 0 0
5.79/5.87 c guideddiving : 0.00 0 0
5.79/5.87 c octane : 0.00 0 0
5.79/5.87 c rens : 1.03 1 1
5.79/5.87 c rins : 0.00 0 0
5.79/5.87 c localbranching : 0.00 0 0
5.79/5.87 c mutation : 0.00 0 0
5.79/5.87 c dins : 0.00 0 0
5.79/5.87 c undercover : 0.00 0 0
5.79/5.87 c nlp : 0.00 0 0
5.79/5.87 c trysol : 0.00 0 0
5.79/5.87 c LP : Time Calls Iterations Iter/call Iter/sec
5.79/5.87 c primal LP : 0.00 0 0 0.00 -
5.79/5.87 c dual LP : 0.24 20 1510 75.50 6265.66
5.79/5.87 c lex dual LP : 0.00 0 0 0.00 -
5.79/5.87 c barrier LP : 0.00 0 0 0.00 -
5.79/5.87 c diving/probing LP: 0.00 0 0 0.00 -
5.79/5.87 c strong branching : 3.45 128 16520 129.06 4788.52
5.79/5.87 c (at root node) : - 44 9583 217.80 -
5.79/5.87 c conflict analysis: 0.00 0 0 0.00 -
5.79/5.87 c B&B Tree :
5.79/5.87 c number of runs : 1
5.79/5.87 c nodes : 3
5.79/5.87 c nodes (total) : 3
5.79/5.87 c nodes left : 0
5.79/5.87 c max depth : 1
5.79/5.87 c max depth (total): 1
5.79/5.87 c backtracks : 0 (0.0%)
5.79/5.87 c delayed cutoffs : 0
5.79/5.87 c repropagations : 0 (0 domain reductions, 0 cutoffs)
5.79/5.87 c avg switch length: 2.00
5.79/5.87 c switching time : 0.00
5.79/5.87 c Solution :
5.79/5.87 c Solutions found : 27 (6 improvements)
5.79/5.87 c First Solution : +5.15000000000000e+02 (in run 1, after 0 nodes, 0.01 seconds, depth 0, found by <trivial>)
5.79/5.87 c Primal Bound : +1.13000000000000e+02 (in run 1, after 3 nodes, 5.85 seconds, depth 1, found by <oneopt>)
5.79/5.87 c Dual Bound : +1.13000000000000e+02
5.79/5.87 c Gap : 0.00 %
5.79/5.87 c Root Dual Bound : +1.13000000000000e+02
5.79/5.87 c Root Iterations : 860
5.79/5.88 c Time complete: 5.87.