molnarg · May 9, 2026 08:16
diff --git a/highs_sc_bug_repro_inline.py b/highs_sc_bug_repro_inline.py
 """
 Reproducer for HiGHS 1.12.0 semi-continuous variable bug.

 Symptom
 -------
 When a MIP contains semi-continuous variables (integrality=2) and the LP
 relaxation places one or more of them at their lower bound `lo` exactly,
 HiGHS may return a "feasible / Optimal" solution that its OWN internal
 feasibility check passes (`row viol. 0`), while a separate post-validation
 rejects it with `infeasibility = X` where X equals the SC variable's `lo`
 exactly. scipy/linprog surfaces this as
 `status=4, message="(HiGHS Status 4: Solve error)"`.

 In the verbose HiGHS output, the smoking gun is two adjacent reports:

    Solution status   feasible
                      ...
                      0 (row viol.)
    ...
    ERROR:   MIP solver claims optimality, but with num/max/sum
             primal(1/63.125/63.125) infeasibilities
    ERROR:   Setting model status to Solve error

 i.e. the solver tells itself the solution is feasible (row viol. 0), then
 a separate check on the same solution finds row viol. = 63.125 (which is
 the `lo` bound of one specific SC variable in the LP).

 Workaround
 ----------
 Replace each SC variable q (bounds [lo, hi], integrality=2) with:
  - plain continuous q (bounds [0, hi], integrality=0)
  - binary indicator b (bounds [0, 1], integrality=1)
  - two coupling rows: q - hi*b <= 0  and  lo*b - q <= 0
 The feasible region {0} ∪ [lo, hi] is preserved exactly. This routes the
 disjunction through HiGHS's well-tested integer code path instead of the
 SC-handling code that has the bug.

 Setup
 -----
 - scipy 1.17.1
 - HiGHS 1.12.0 (git hash: 4f96ee8) bundled with scipy
 - Python 3.12

 The LP data is embedded below as base64-encoded numpy NPZ. 866 rows x
 696 cols, 78 SC variables. All row/column names removed -- only numeric
 arrays remain. Extracted from a real failing optimization.

 Run
 ---
    python highs_sc_bug_repro.py

 Expected output: original formulation fails with Status 4, the
 binary-indicator workaround returns an optimal solution.
 """
 import base64
 import io
 import numpy as np
 from scipy.optimize import linprog


 # Base64-encoded NPZ archive of the failing LP. Decoded at runtime.
 LP_DATA_B64 = """\
 UEsDBC0AAAAIAAAAIQA0moHe//////////8FABQAYy5ucHkBABAAQBYAAAAAAADcAAAAAAAAAJvs
 F+obEMnIUMZQrZ6SWpxcpG6loG6TZqGuo6Cell9UUpSYF59flJIKEndLzClOBYoXZyQWpAL5GmaW
 ZjqaOgq1CmQDLmMQ2N10YNZMIPgZcSANBG61HmAAAYt+uDilNCHzIPL1BMzJOHD2DBBI9ED5HXB5
 iD+KqOZe4ugKOtuXgSFOmb8xzaOVv1Djt4Ni82DplLrhgZtGzyeDK11QKx0PFXcPlDuHSvjQ279D
 P1yIKzeI9Sep5Srtwo8BAhpG6VF6lB6lR+lRepQepUfpUXqUHqVH6aFIRx6A0QBQSwMELQAAAAgA
 AAAhAE/Cp5b//////////wgAFABBX3ViLm5weQEAEAAAlEkAAAAAAGoyAAAAAAAA7N1frGxXXcDx
 W/6lEBNqgoohMVdCWiQNWgulELBDQUBAaEvLvZgYIdLCQ2O1GKNB402Mb8ZqTEzAxFSMPhtNTHzi
 8CC+YCLCC4kxxAdIDAgRYyw8YO+Z2ff2rnP3mf1n7b1/a63P56HTOefMzD7nzOw1d76/s+dP3vfI
 zz/woVsu/MaFT97x0Uc/8ctP3vGmi3e8+bF777jz4h2PPfHkrz/5kV/5pSee/OijVz/+jo88/olH
 n/34Jz7+kV999Nnzr773nnvuvHjPG+/5iTsv/s7FSV5yAQAAaNvJpZNbT//n25/dn//gyf4Th9Mr
 D558/6rf3R0+/v7D6aXD6eWTFbbyWQ8kt5ee9vnA/vNXku9rd/30u6ff4I8cuZ6Fddu3O/xcryS/
 l/TrTi6df7pLznc/p5Pr13/zDXnZbn/6od025287+nW3nJ6+fH/+5PLh4688nHbnX70/3V06nP+Z
 w9c/dDh94PDxtx2+rrvcxWQ7ohj6c+v7/P37092Dydenp/m37+a/r8PPeZf8/k6639ddh9MPHk7f
 fvj67vd2+D6u3H+4XPd1rzmcpt9Xtz237s7/PjZy5ZHDz+ne3f4D3c/xVfvTK8n9+sLth49f6jmf
 3v9vT86/Kvn6uw+ff+Rw/g2H04f3pyeH0wv3HM4nP+9nf683/J7P3C9zS34+z95/9rd/5/58931d
 u7/dvjvdzX//FWfuj93H95c7e/6Gr7/2e7gtuf5XHk6v397+tNuO5Od1k+tNf343ns/kyrv313vl
 vYfbffhwO28+nO/uDz91bTv2p6/qOZ/b9evvfg83/D6e83O58eN9j/fx61D6+z89vfZ77r6uf397
 4+9t7v6mu34AAID5nv7UVV85vM54+eT07DPd64gP708vPLz/+Kfed3L3VX93eD326QdOHjt1+PoP
 d687Xt5//PPHXx/uvm7/76a3nHz89ANvOXq5m7ry0H777r588s9feNad11/3PN38f+i2L3kd9cr1
 101fePo/Lzi59/R6nn/yxavX84ULh+376cPpXYfTO49u5+On38/Lpn0/53jR6X//77P/erp9L8h+
 /aU7/bF/7fLu06f358u70/vDNw7/jv/q4fwX/ue+0/vFG5PXda50r3fdvTu9nr9+3+5jp//ztsP1
 PLC/3k/t9ucfv3Q4/6OH6z3c7le6613e6d31O5d3N5x+qbv97vXvBw/fz+H0a29Zbfty+cFH3vn4
 f+0u7/72b+7+8q1/9K5dd/61X3z9T371qfdcO//DT/7iL/zLS9+x+8vnf/Yzb7rl8u7HX//+V7zg
 tnftHtrdfevFFz68e/Q/f/O/3/3OB3av+fI9n3zgHz+w+7Vn/vSJZ1704O559z/62z90/6Xdd3b/
 du9/PPWOa9f3ub96+clnXvqz187//ddffum3XnHfbuufxypOPrDb/8+bdt3jZX9/f/H+47vk9bEP
 d59/4eHjh9eNrz2u2nFYdw77hcPP5+nLu9edPkC/d9/p4/D27vXfH0j2G4fXWa+9fpzPe7/+vfff
 /rHLu7te/P0r/3Txtbsfe89d//7dp969u/DHz3v7S277ud0Tn37lN275/EO7Lz35zdd866Xv2f35
 W//iDb//uUu7bz72xO/92R++9drj5H+/8gffeuplr8u+faE83d2fn7mvW1dOP/7V6+vKfn140f7x
 8aF0v+913GV8+76ttwAArkvmtgDgXNYNAAAAAICYzKMAALXTqwEAAAAAYtKrAYjAegTAHOZSAAAA
 AABi0gEBgFrp1AAAAAAAsenVAESQrkc6IwBjWDcAAAAAAGIylwIA1EqnBgAAAACISacGYEtpR7Qu
 ATCH+RQAAAAAgJh0QACgNvo0AAAAAEBsOjUAkaTrkt4IwBjWDQAAAACAmMynAAC10acBAAAAAGLS
 pwGIIO2J1icA5jCnAgAAAAAQkw4IANRClwYAAAAAiE2fBiCidH3SHQEYw7oBAAAAABCTORUAoBa6
 NAAAAABATLo0AJGkXdE6BcAc5lUAAAAAAGLSAQGA0unRAAAAAACx6dIARJauU/ojAGNYNwAAAAAA
 YjKvAgCUTo8GAAAAAIhJjwYgorQvWq8AmMPcCgAAAABATDogAFAqHRoAAAAAIDY9GoASpOuVDgnA
 GNYNAAAAAICYzK0AAKXSoQEAAAAAYtKhAYgs7YzWLQDmML8CAAAAABCTDggAlEZ/BgAAAACITYcG
 oCTpuqVHAjCGdQMAAAAAICbzKwBAafRnAAAAAICY9GcASpD2RusXAHOYYwEAAAAAiEkHBABKoTsD
 AAAAAMSmPwNQonT90iUBGMO6AQAAAAAQkzkWAKAUujMAAAAAQEy6MwAlSbujdQyAOcyzAAAAAADE
 pAMCANHpzQAAAAAAsenOAJQsXcf0SQDGsG4AAAAAAMRkngUAiE5vBgAAAACISW8GoERpf7SeAQAA
 UCPztwAAAABALnPna0qbzyltewFgS97PDIAprBcAAAAAYD6BmNwvASCfuV20tK5a2vYCAAAAABwz
 tZ9G667RtgcAIvJ+ZlAOj08iMz8DAAAAABCTvgAA65naTaP11mjbAwAAAABwTPQuGn37AKAF6Xqs
 iwIwhPUCAAAAACAm8zgAMF/0Hhp9+wAAAAAAlrJWD9VdAaA8aUe1ngMwhbkcAAAAAICY9D8AmG6t
 Dqq3AgAAAAC0pa/j6rsAsJx0ndVpYTue91IS6wUAAAAAQEx6AwC0p6/f6roAAAAAAOPk7q36LQCs
 J+2j1mEApjBvAwAAAEALdBRK5H4LAHHl7qy6LQAAAABQi2OdUwcFAMZKnz/oqwAMYb0AAAAAoAXm
 MCiR+y0AnHWsb+qfAAAAAAB55eqW+icAMFTafT2PgO14/FEyc0QAAAAAADHpDwC0IFev1D0BAAAA
 AGIrrX+Wtr0AULN0XdaHARjCegEAAABAzcw1UDL3XwAYrrTuWdr2AgAAAAD1WrpL6p4AwFhpT/V8
 AtbncUcNzOcAAAAAAMSkQwBQg6V7pN4JAAAAAMCS+rqtngsA60nXXZ0YgCGsFwAAAADUyLwCNXA/
 BoD69fVaHRcAAAAAqF30Hhp9+wCgZmkvtS7DejzeqIn5GwAAAACAmPQIAJguegeNvn0AAAAAAHPV
 2jtr/b4AILJ0/dVbYXme91ID6wUAAAAANfG6LTVxfwaAfrV2zlq/LwAAAACgHbV0zlq+DwAoUdpN
 rcuwPI8zamQOBwAAAICaeB2Xmrg/A8BZtfTNWr4PAAAAAICh1uqfOisA1Cdd3/VWWI7n09TEegEA
 AAAAEJMeAQDDrdU99VUAAAAAgHWM7aX6KgDUI+2y1nkApjDnAwAAAEANdBJq5H4NAMsZ20l1VQAA
 AACAdTmOAgDQsc7D8jzOAAAYwxwuAAAAAMC6lur65gUAoD76LABzWEcAAAAAqIF5CGrkfg0A4y3V
 P3VVAAAAAAAAtnBsfiT9vHkTAACAuphfBAAAAACIyZwOAMR1rLOmn9dlAQAAAACWEfV4CFG2AwAA
 oFXmdQAAAAAAYjJXAwDbi3o8hCjbAQAAAABQmq7D5uqxui4AAEBM5msAAAAAAGIybwMA5en6a64O
 q+cCAAAAANxo646a+zgMAAAALMPcDQAAAABATOZuAGB9W/fT3MdhAAAAAAAozVKdNL1ePRYAAKBu
 5m8AAAAAAGIytwMA+S3VR9Pr1WEBAAAAAPLo66ZTe6oOCwAA0AbzOwAAAAAAMZnfAYDl9fXSqR1V
 fwUAAAAAmCdXJ819/AUAAADKYo4HAAAAACAm8zsAkF+uPpr7+AsAAAAAAK3r+ujQTqqnAgAAcB5z
 PAAAAAAAMZn7AYB8ui46tI/qqAAAAAAAZRl7HIah1wcAAECZzP8AAAAAAMRkLgcA4hh7HIah1wcA
 AAAA0Lq1u+ix29NpAQAA6mA+BwAAAAAgJvM5ADDf2j302O3pswAAAADb0F0AKImeAECJrF8AAAAA
 ADGZmwEAptKBAQAAAABi0oEBKIH1CoAamJ8BAAAAAIhJjwQAxtJ/AQAAAABi04EBKEG6XumQAJTI
 +gUAAAAAEJP5GQBgLP0XAAAAACAm/ReAyNLOaN0CoAbmaAAAAAAAYtIjAYChdF8AAAAAgHWdeZ9u
 fReAipxZ5/RIAApk/QIAAAAAiMmcDQC068z7vei6AAAAAACb6vqtjgtAjc70SesdABUwbwMAAAAA
 EJMeCQDt6LqtfgsAAAAAcHNn3hc7U0/VZQHgrDPrro4JQIGsXwAAAAAAMZnXAYD1nHl/lUwdVY8F
 AAAAAMir73gK+ioATHeml1pXAaiAuR0AAAAAgJj0SABYX9/xFHRVAAAAAICy9B1vAQA47sw6qpcC
 UCDrFwAAAABLMocA03n8AEBcfcdbAAAAAAAgj6m9VGcFgPHO9E/rKWzO4xDmM88DAAAAABCTDgIA
 y5naSfVVAAAAAIAyDe2vOi0AnF0PdVJYn+elAAC0ZOi/O/37FAAAAAAgj9xzCeYcAGiZ9zMDoCbm
 cwAAAABYgn4C83kcAcD2cvdUfRYAAAAAoGw6LgAt8X5msB3POwEAYDz/bgUAAAAAiMkcBAAt8H5m
 ANTA/A0AAAAAS9BNYD6PIwBoj34LAAAAABCbjgtAi6x/sD6POwAAGM8cLgAAAABATOYgAGiJbglA
 yaxjAAAAACzB3ADM53EEAO3RbwEAAAAAAOo0dA4k+rxI3/ZF324AYrJ+AFAjc4AAAAAAADHpkwBQ
 nqH9NXqn7du+6NsNAAAAAHDMsQ7bfX7tXqsPAwAA5GXOBQAAgJLphwDUzDoHAOU51l+7z6/daXVh
 AAAAAIC9tMOW3mVL334AAAAAgE4671r6/Gvp2w8AAAAA0GfqPK65VwAAgNjMuwAAAAAAxGTuBgDK
 N/V4CjouAAAAAEBsXc9duuv2Xf9atw8AAFAq8zcAAAAAADGZdwGAdnUdd+me23f9a90+AAAAAEAu
 x/rqseMR5LqdpS8PAADAMOZeAAAAAABiMj8DAHEc66rHjkeQ63aWvjwAAAAAAOfrOu5Sx1NIP57r
 9gAAAAAAapfrfcSGzgV73zIAAAAAoFRT51KPzb/mnnfNvZ0AAACczxwMAAAAAEBM5mEAYHtTe+qx
 4xfk7rS5txMAAAAAIKqtOmqu2x36/mV9H/e+ZgAAAABAVFvNpea63aHvX9b3ce9rBgAAAABEkXv+
 dOz861xr3x4AAAB75l4AAAAAAGIyNwMAy8t9/ICxxy+Ya+3bAwAAAIDIovQ17zMFAOTmeQXAMOYl
 AAAAAABi0rsAIK4onXXu3/kDAAAAALRmaIed22v1XgAAgG2ZpwEAAADWog8DjGO/CQDlGdpf53Za
 nRcAAAAA4EZT++raXVYHBgAAAABaM3Xude15WfO5AAAAAADDpPOwpczxAgAAcD7zMwAAAAAAMZmz
 AYDypT22lOMwAAAAAACUYumumvv6dWAAAIB1mLcBAAAAAIjJ/AwAbG/pnpr7+vVfAAAAAIBxui6b
 9lm9FgAAoGzmaAAAAAAAYjKXAwDl63ps2mV1WgAAAACAcfqOdzD0cgAAALTFfA4AAAAAQEzmeQBg
 PX3HOxh6OQAAAAAA1jG0o/Z9nQ4LAADQBnM9AAAAAAAxmd8BgPUN7ad9X6e/AgAAAADktVQ3nXu9
 ei4AAAAA0Lql5mbnXq95XgAAAACAebo52dzzsuZvAQAAYjN3AwAAAAAQk7kbAIiv6625u6uOCwAA
 AAAc09cTj3VGHRIAqJXnOUB05kEAAAAAAGLSmQCgHX3d9ljP1XsBAAAAAPIa2mnH9lz9FwAAYF3m
 agAAAIDW6NJAKeyvAKA+Q/vs2I6r+wIAAAAAbCPtusc6rw4MAJTO8xmgFOZpAAAAAABi0psAgLTn
 Huu7+i8AAAAAwDS5++zY4ysAAACQlzkaAAAAoBV6NFAa+y0AqEfuLjv2+AoAAAAAAK2Z21uHXl7X
 BQAAAAAYZ+7c69DLm68FAAAAADhflPcNM48LAAAAAHCjKMedNY8LAAAAABDD1Hnb7nLmdQGAUnje
 ApTGfA0AAAAAQEy6EwAwted2l9ODAQAAAIBWrd1bh96eDgwAALAOczMAAABA7fRnoFT2XwAQ19qd
 dejt6b8AAAAAADfK3V0dLwEAAAAAII/cc6/mbQEAAAAAhjk257r0HKw5WwAAAACAmzs257r0HKw5
 WwAAAAAAgJszBw/l00MBAJbl+RYAAAAAQEzmXgCArejIAAAAAAAx6chQLo9fAAAAgLqZvwUAAAAA
 iM0cH5QrffzqMgAAy/A8CwAAAAAgJnMvAMBWdGQAAAAAgJh0ZChP2l08jgEAAADqZP4WAAAAACA2
 83tQPu9nBgCwLM+vAAAAiEDXA4CzrI8AwFZ0ZAAAAACAmHRkKJf3M2MJ7kcA0M/8CwAAAABATDon
 ALA2/RgAAAAAIDYdGeqRPp51GgCAvDy/AgAAYEu6HgD0s04CAGvTjwEAAAAAYtKPoXxph/G4Zg73
 HwA4zhwMAAAAAEBMeicAsBbdGAAAAAAgNv0Y6pM+rvUaAIC8PL8CAABgC7oeABxnvQQA1qIbAwAA
 AADEpBtDPdIe4/HNFO43ADCceRgAAAAAgJh0TwBgaXoxAAAAAFCatTqqXgssLd3P6DYAAHl5fgUA
 AMCa9EUAGM66CQDrW6uf6rQAAAAAAONE66fRtgeIL+1D9iOM4f4CAOOZzwEAAAAAiEn/BID1ROum
 0bYHAAAAAGCqrbvn1rcP0CfdP+lDAAB5eX4FAADAGvRIABjP+gkAx23dO7e+fQAAAAAA9s78PbLe
 CgSTdiX7KYZwPwGA6cz1AAAAAADEpIMCQBxn5tp0VgAAAACAU0t3Td0UqNWZ47/oT9yEdRAApvP8
 CgAAAAAgJh0UAJbvmXopAAAAAMA0tfTMWr4PIL4zx+22/wEAWJS5IAAAAJbg9X0AmM96CkDLaumY
 tXwfAAAAAACl9cvSthdoT7qf0pV4LusYAAAAY5T2ukJp2wsAAAAA0Iql55bMRQFTeT8zAIB1mOsB
 AABgCV7XB4D5rKcAENfSnVXHBQAAAACoi/4L9PF+ZtyMdQMA5vO8CgAAAAAgJj0UABhK9wUAAAAA
 iEn3BVJp17GfAABYhnkaAAAAcvJ6PgDkY10FAI7RewEAAAAAYtN9gWPS/YT+0zbrBgDk43kVAAAA
 AEBMuigAcIzeCwAAAAAQk94L9En7jv0FAMAyzNUAAACQg9fxASA/6ysA0EfnBQAAAACITe8FhrK/
 AAAAAFiXOVwAAAAAgJjM0wHH6DwAAMvyfAsAAAAAICZzNQBAH50XAAAAAIbT3QCWoVcAAGN5/gAA
 AAAAEJP5GgAgpe8CAAAAAMSk7wLkZb8KAMxlzgYAAAAAICY9GADo6LoAAAAAALHpuwB5pftVvQwA
 GMvzBwAAAACAmMzZAAAdXRcAAAAAICZdFyCPtIfZvwIAc5m3AQAAAACISQ8GAPRcAAAAAIDYdF2A
 ZaT7V90MABjL8wcAAACgj84LsC37YQBAzwUAAAAAiEnPBcgr7WL2s5TM/RcgBnM3AAAAAAAx6WkA
 0C4dFwAAAAAgNj0XYFnpflY/AwDG8vwBAAAASOm8ADHYHwNAu3RcAAAAAICYdFyAZaR9zP6WErnf
 AsRi/gYAAAAAICZdDQDao98CAAAAAMSm4wKsI93f6miUwPMEgFg8fwAAAAAAiElXA4D26LcAAAAA
 ADHptwDLSjuZ/S4AMJc5HAAAAEBvAIjJ/hkA2qHbAgAAAADEpt8CrCvd7+ppAMBYnj8AAAAAAMRk
 DgcA2qHbAgAAAADEpNsCrCPtZfa/AMBc5nEAAAAAAGLSgwGgfnotAAAAAEBsui3ANtL9r64GAIzl
 +QMAAAAAQEzmcQCgfnotAAAAAEBMei3AutJuZj8MAMxlLgcAAAAAICY9GADqpdMCAAAAAMSm1wJs
 K90P62sAwFiePwAAAAAAxGQuBwDqpdMCAAAAAMSk0wJsI+1n9scAwFzmcwAAAAAAYtKDAaA++iwA
 AAAAQGw6LUAM6f5YZwMAxvL8AQAAAAAgJvM5AFAffRYAAAAAICZ9FmBbaUezXwYA5jKnAwAAAAAQ
 kx4MAPXQZQEAAAAAYtNnAWJJ98t6GwAwlucPAAAAAAAxmdMBgHrosgAAAAAAMemyADGkPc3+GQCY
 y7wOAAAAAEBMejAAlE+PBQAAAACITZcFiMn+GQCYy9wOAAAAAEBMejAAlE+PBQAAAACISY8FiEVX
 AwBy8/wCAAAAACAmczsAUC4dFgAAAAAYSx8EqIteBADxWJ8BAAAAAGIyNwMATKUDAwAAAADEpAMD
 1MH+HADiMz8DAAAAABCT3goAjKX/AgAAAADEpgMD1CHdn+t0ABCP9RkAAACojd4M1ML+DAAYS/8F
 AAAAAIhJ/wUoW9rh7Nepkfs1UBtzNAAAAAAAMelSAMBQui8AAAAAQGz6L0Bd0v26XgcA8VifAQAA
 AABiMkcDAAyl+wIAAAAAxKT7AtQh7XH27wAQn3kaAAAAAICY9FYA4Bi9FwAAAAAgNt0XoE7p/l23
 A4B4rM8AAABAqXRmoHb2cwDAMXovAAAAAEBMei9AXdIuZz9Pydx/gVaYqwEAAAAAiEmvAgD66LwA
 AAAAALHpvQB1S/fz+h0l8TwFaIX1GQAAAAAgJr0KAOij8wIAAAAAxKTzAtQp7XP29wAQn/kaAAAA
 oBS6A9Aa+z0AIKXvAgAAAADEpvMCtCHd3+t4ABCP9RkAAAAAICbzNQBASt8FAAAAAIhJ3wWoW9rp
 7PcBID5zNgAAAAAAMemtAEBH1wUAAAAAiE3fBWhLut/X8wAgHuszAAAAAEBM5mwAgI6uCwAAAAAQ
 k64L0Ia019n/A0B85m0AAAAAAGLSWwEAPRcAAAAAIDZdF6BN6f5f1wOAeKzPAAAAAAAxmbcBAPRc
 AAAAAICY9FyAtqTdzjoAAPGZuwEAAAAAiElvBYB26bgAAAAAALHpuQBtS9cBfQ8A4rE+AwAAAADE
 ZO4GANql4wIAAAAAxKTjArQp7XfWAwCIz/wNAAAAAEBMeisAtEe/BQAAAACITccF4Kp0PdD5ACAe
 6zMAAAAAQEzmbwCgPfotAAAAAEBM+i1A29KOZ10AgPjM4QAAAAAAxKS3AkA7dFsAAAAAgNj0WwCe
 y7oAAPGZxwEAAAAAiElvBYB26LYAAAAAADHptgBcpecBQHms3wAAAAAAMZnHAYD66bUAAAAAwFL0
 RoC26VAAtMB6BwAAAAAQk7kVAKBUOjQAAAAAQEw6NECb7P8BaJH5FQAAAACAmPRLAKA0+jMAAAAA
 QGw6NECb0v2/rgdAC6x3AAAAAAAxmV8BAEqjPwMAAAAAxKQ/A7Ql7XbWAQBaZI4FAAAAACAm/RIA
 KIXuDAAAAAAQm/4M0LZ0HdD3AGiB9Q4AAAAAICZzLABAKXRnAAAAAICYdGeANqX9znoAQIvMswAA
 AAAAxKRfAgDR6c0AAAAAQBTR+mq07QGgbem6pPMB0ALrHQAAAABATOZqACCOaF012vYAAAAAAGyl
 tq5a2/cDwDbSnmh9AaBF5msAAAAAAGLSLwFge7X11Nq+HwAAAACAtY3tuLovABGk65FuCEALrHcA
 AAAAADGZpwGA9oztt3ovAAAAAEAex/qsfgtASdKOaB0DoEXmagAAAAAAYtIvAaAex7qsbgsAAAAA
 sI6pHVa/BaBk6TqmTwLQAusdAAAAAEBM5nAAoDxT+6tuCwAAAAAQU65uq/8CsKa0P1qHAGiReRwA
 AAAAgJj0SwCoX65eq/sCAAAAAK0opaOWsp0AtCFdl/RFAFpgvQMAAAAAiMlcDQCsr5R+Wsp2AgAA
 AABMdebvPfVTABgs7YnWUQBaZL4GAAAAACAm/RIAlnNmbkg3BQAAAAAoWq6+qtMCUKMzxyfSRwFo
 gPUOAAAAACAm8zkAEEeurqrPAgAAAADkVVpXLW17ASjTmePKW38AaJA5HQAAAACAmPRLANheaT21
 tO0FAAAAAOhTai8tdbsBqFu6PumKALTAegcAAAAAEJP5GgBYTqmdtNTtBgAAAAAYKncn1V0BaFHa
 Fa2HALTInA0AAAAAQEz6JQDkl7uP6q0AAAAAAGXruqw+C0DN0nVO5wQAAKAE3b9f/TsWAAAAACCP
 XPOy5m4BqJn3MwOgZeZ0AAAAAABi0i0BYDu5OqoeCwAAAADAzejBAGzB+5kBAADAcf69DAAAAAAQ
 k/lbANbk/cwAaJG5GQAAAACAmPRKAGAqHRgAAAAAIDY9GIAteT8zAAAA6OffyQAAAAAAMZm/BWAL
 3s8MgJaYmwEAAAAAiEmnBACm0oEBAAAAAGLTgwGIwHoEAAAAZ5nDBQAAAACIybwTAFvSEQFogfUO
 AAAAACAmczMAwFQ6MAAAAABjrNWl5t6OfgYAAMASzFkAAAAAUANzFdTI/RqAyNbqjHNvRw8FAAAA
 ANjGsd7Z93mdFAAA1uP5NwBAm47N1/Z93lwuAAAAAFCr3HOtejwAAAAlMh8EAAAAABCTeSQAIsp9
 XAK9EgAAAABgWWl3jNoho24XAAAAAMBS0jnaqHO1UbcLAAAAAGCu3POrua5vrbla87sAAAA8lzkh
 AAAAAICYzPkAEEnurpjr+tbqnboqAAAAAFC6qP1x7vusRf2+AAAAAACGijqnOvd91qJ+XwAAAAAA
 3fxptPcdy71dAAAAMIZ5HwAAAACAmMwTARBB1xOjve9Y7u0CAAAAACjVsa4YtTvOff+yuZcDAACg
 buaKAAAAAABiMu8DQATHemLU3phu19TtjPr9AQAAAADt6fph7o6Y6/rGbp8eCgAA61nq3xMQmbkf
 AAAAAICY9AoA1tR1w9z9MNf1jd0+HRQAAAAAaE30v4tKt2/qdkb9/gAAAIjF/BAAAAAAkZl/oGXu
 /wAAAACUwOtYAADbWuo4ubmk2zd1O6N+fwAAAABA/dIuvtRxbXNdn+PZAgBAOaK/bwYswRwQAAAA
 AEBMegUAOaVdcKnjIuS6PsdDAAAAAAA4X/S/g5p6XIi+ywEAAMAY5ocAAAAAiMw8BC1z/wcAAACg
 BF7HAgBY11LHyc1l6nF9+y4HAAAAALC2qceJnXs7Q7ej7+v0ewAAKI/n8bTIXBAAAAAAQEy6BQBz
 TD3OwNzbGbodfV+nXwIAAAAA3NzSxzGYe71Dj8cw93I6KgAAAEOYQwIAAAAgMvMPtMz9H4A1LX0c
 g7nXO/R4DHMvp58CAAAAAEtJj4Ow1HERch2HYOnjNgy19e0DAEDJojyvhy2YAwIAAAAAiEm3AGCM
 9DgISx0XIddxCJY+bsNQW98+AAAAANCOsf0v+t87pds19vgMQy8X/ecAAABATOaCAAAAAIjI/AN4
 HAAAAAAQm9evAACGGft3G1GOQ9sn3a6xx9cdernoPwcAAAAAoFx9x3ud2sH7Ljf0OLJDr3/q8W1z
 MScAAAD5eF8JWmYeCAAAAAAgJt0CgPP0HS9gav/ru9zQ4xAMvf6px0fIRR8FAAAAAKJa6jgGubrj
 1O0aezl/5wUAAEAO5oQAAAAAiMg8BHgcAAAAABCb168AAPJY6ji0uf5eZOp2jb3c3OMFAwAAAAD0
 6Tve69rHtR17nNnc2zeWuQAAAFiO59u0zHwQAAAAAEBM+gUAz9V3vIC1j4sw9jgFubdvLD0UAAAA
 AIhi6HEWct/O1MtPPb7C2Mst9XMAAAAAAAAAAIjGfAQAwDhDj7OQ+3amXn7q8RXGXm6pnwMAAAAA
 wFbHRZh7nIKpx0fIxTwAAAAsz/NuWmZOCAAAAAAgJv0CgKu2Oi7C3OMUTD0+Qi46KAAAAAAQ1dzj
 LPRdbm5fnHt8hbnHdQAAAAAAAAAAqJ05CQCAaeYeZ6HvcnOPSzD3+Apzj+sAAAAAAAAAV201l+T4
 MQAAAG0yxwgAAAAAEJM5HgAYbqvu6fgxAAAAAADnW6p79l2vzgoAAMBV5nkAAAAAAGIy3wMAxy3V
 O/uuV18FAAAAAFhGrj469np0WQAAgDqZ8wEAAAAAiMm8DgDkk6uLjr0ePRYAAAAA4HxpF3UcBAAA
 AHIwtwMAAAAAEJN5HwCYL+2hjoMAAAAAAFCXvq56rLfqsQAAAHUz9wMAAAAAEJO5HQDYXl9PPdZZ
 dVgAAAAAgHGG9tG5HVWHBQAAaIP5HQAAAACAmMzvAEA+Q7vo3H6qvwIAAACcL+0f3XldBAAAoE06
 OwAAAABATOZ5ACCOtKt25/VWAAAAAIDzje2e3g8eAAAAAGAdY+dgvZ8QAAAAAEAMS83bHrtec7oA
 AAB1M98DAAAAABCTuR0AmG+p4yUcu14dFgAAAABo3djjGOTuo3orAAAAAMDNjZ2DzT0Xa84WAAAA
 AGCYse83NnV+dujlzOcCABCJ56eQn7keAAAAAICYdBEAGG7s+41N7aRDL6fDAgAAAACt6jrn0u9L
 tvRxFgAAAAAAAACAdpkvAABgTd3xCXIfpyC9vqWPswAAAAAAULu+eYKhcwa5vw4AACLyfBbyM78D
 AAAAABCTLgIAx/X1zqEdNPfXAQAAAAC0quubuTpn7usDAACgLeZ9AAAAAJjDvAIsx+MLAK7rumau
 vpn7+gAAAAAAOF/aP+f2UD0VAACA85gLAgAAAGAOcwmwHI8vABgu7Z5zO6iOCgAAAABwvq5nju2a
 OigAAHheDGsw/wMAAAAAEJNOAkDLuo45tmfqnwAAAAAAQDRL9f+h12v+AAAAgJzM6QEAAEB8OjFA
 m+z/AajJUl1y6PXqogAAAAAAe1t3yPT2t94eAKBenmcAtM28EAAAAABATDoeACXauj+mt7/19gAA
 AAAAwJqmduZcfVrnBgAAYApzXgAAAMyhUwLAcqyzALRgaq/M1Tn1UgAAAACAG83tlGt1Tj0VgJJZ
 xwBgeeaCAAAAAABi0ksBqNHcPrlW39RRAQAAALiZpf++XB8CAFrj+Q9AXuYdAAAAAABi0sUAaNnS
 f1+ukwIAAAAA5JH7eAg6KQAAADmYDwIAAADm0q8BlmH/CgD5j4egjwIAAAAAEEnahbvzejEAAABb
 MmcFAAAAABCTuSIAONszu/M6JwAAAADAMEt1x7nXq4cCAACwJPNFAAAAAAAxmRsCoARL9ca516uD
 AgAAAADAeEM7dfd1ujYAAAA5mPcCAAAAAIjJfBAAHDe0d3Zfp48CAAAAAJxv7U459jgLAAAAAACt
 +v/27idEj7uMA3hSbUlFSIRWIgGJJSwSpBq2/yxqpmlta1JskibdrSB4aXspBHtS9LAg3sToRUgF
 qRU9iwfBk9uDeqmgtJeCSPDQgvQPWBFiDzXZd367+87u+M4778zsMzOfz2Uy7zvzm/ed99/yfJ/8
 pus+2Hn7dAEAAABgN8X+P32DAACLKV7HsmwJwHz0PwAAAAAAxCT/AmCMivml//cNAAAAABBTWZ7p
 //sBAAAQgX4iAAAAoC55N0C7fM8CAAAAi1JfAAAAAACITR0XAAAAACA2dVwAAAAAgNjUcQEAgLrK
 ruOZbnedTwAAAAAA2jCr36Xpfhj9NQAAAESkPwsAAAAAICb9RgBENCtfbDp/lGcCAAAAAOyuLE+c
 93YAAAAYIn1HAAAAAAAx6WMCYC+V5Yjz3g4AAAAAAMRTN48u7ifXBgAAYBH6zgAAAAAAYtIXBAA7
 1c03i/vJSQEAAAAAulU1/zSfAgAAAABAt6r21erHBQAAAGC7tvr7mrqeEwDAWKW/i4pLAKrRDwEA
 AAAAEJPcC4AhaCuPbOp6TgAAAAAALKapXNP1mwAAAGiSPiEAAACgaXJsgGb4PgUAAADaou4AAAAA
 ABCbOi4AAFBXU/MJFccxTxEAAAAAAIuYtx8mba+PBgAAgD7QXwUAAAAAEJP+IwD6bN4cMm0vvwQA
 AAAAmE9TuWLZOHJLAAAAAIB62roeW9PjAwAAAAAAzXPdOwAAANqgbwwAAAAAICZ9PwCwONe9AwAA
 AADop6avfyd/BQAAAABoRtPXv9O3CwAAABBb0/188x4HAAAA9oJ+BgAAAKBtcnKAenx/AgAAAF1R
 hwAAAAAAiE0dFwAAhqPp6yHNexwAAAAAAOazaN/GXu8PADAW6e+m4hKAavQbAQAAAADEJPcCoI8W
 zR/3en8AAAAAIK628rOq48rvAAAAxk1fCgAAAABATPp6AKBcWzln1XHlrAAAAAAA3eoqPzVPAwAA
 wDDo7wEAAAAAiEnfDQB0p6vc1DwNAAAAAMBQDS3fHNrzAQAAGBv9NwAAAAAAMenLAYAtQ8s1h/Z8
 AAAAAACGoiynld8CAAD0i/4cAAAAAICY9OEAwPCU5bNyWwAAAACgb5rKM9vOReWuAAAA46QfBwAA
 AAAgJv08AIxZUzlm23movBUAAAAAIIZivrpo3iqvBQAA6Dd9PQAAAAAAMenLAYA4irnqojmrnBYA
 AAAA6Juq+eWs7brOQeWuAAAA46Q/BwAAAAAgJv08AIxJ1dxy1nZd55/yVgAAAACAiWK+2Xbe2fT4
 8lkAAIBh0dcDAAAAABCTPh0A2FLMNdvOOZseXy4LAAAAAPRFyimbyiu7zj1nHU8OCwAAMA76dQAA
 AAAAYtK/A8AQpXyyqZyy67xz1vHkrwAAAADAWLWdb5aNX/W4xe3ksQAAAMOmjwcAAAAAICZ9OwCw
 pe1cs2z8qsctbieHBQAAAAD6IuWSi85TUHf7RdWdRwEAAIBh078DAAAAABCTPh4AhiDlkYvOU1B3
 +0XVnUcBAAAAAKDvZuWVi+aZdceve1z5KwAAwLjo5wEAAAAAiEkfDwBDNiunXDTHrDt+3ePKXQEA
 AACAvkg5ZFN5ZNl4beWdVceVtwIAAIybfh4AAAAAgJj09QDQRyl/bCqHLBuvrZyz6rhyVgAAAABg
 bMryy6bmNZh3/LrjAQAAMA76ewAAAAAAYtLXA8CYlOWWTc1rMO/4dccDAAAAAIgm5Y5N5Y+LzqfQ
 1rjyVQAAALbT3wMAAAAAEJM+HwD6IOWNTeWOi86n0Na4clUAAAAAYGzamheheH9xu7rzKchXAQAA
 2E6/DwAAAABATPp8ABiytuZFKN5f3K7ufApyVQAAAACgL8rmJyjbru44beWZVceVpwIAAPD/6PcB
 AAAAAIhJ3w8AEZXNT1C2Xd1x2soxq44rRwUAAAAAhqqteRFmjTvvcRedBwIAAIBx0/8DAAAAABCT
 vh8A+qiteRFmjTvvcRedBwIAAAAAAMagbm5ddT+5OAAAAH2irwwAAAAAICZ9SABEUjdXrLqf3BIA
 AAAAYD4pT4yaK0Z9XAAAAIyDfiQAAAAAgJj0FQGwl1KOGDVPjPq4AAAAAACgDV3nx00dT+4NQGR+
 pwBg7+j/AgAAAACISY4KwJB0nUs2dTx5KgAAAABAt6rmpGXbyVkBAAC4Qd8PAAAAu5EnAsDe83sM
 AM2rmo+WbSdfBQAAAOiHrnOW4vHkPAAA7Up/bxWXAOxOvwMAAAAAQExyLgAi6TpXLB5PrgkAAAAA
 0I1550eQawIAABCRfiMAAACgbfJygHp8fwIAAABdUYcAAAAAAIhNHRcAAMZr3uuTmU8IAAAAAADa
 1/b16vQLAQAAUIV+MQAAAACAmPT/AMBObc+XIT8FAAAAAKin6XwzjSc3BQAAoA59QAAAAAAAMekH
 AoAtTeeaaTx5KQAAAABAs9qaT6Gt8QEAABgmfUEAAAAAADHp/wGAndqaT6Gt8QEAAAAA+mqv8sqy
 48pPAQAAmIc+IAAAAACAmPQBATBke5VTlh1XbgoAAAAAAADQjtuyyfKpbG/WD83cbv/G8vBkfX01
 v/2OfJnWPz1ZZiv5+pfy7c/ny7P57Q/m26X9jm4+jmdueGM1e+HKdddWsz+/ct1b+XZX8/VX/n3y
 xt1XPr+6ud/GYu1Cvr48GedXX82e3fjHg/k4ZyfjXskm68+t5OufyMfNj/t6GrfqeSu7/1T+PM8V
 tt9aLt/w3ur08tV0/HT+zuXPJ1++8cWZj2/31ys/z1nh9VtPr9eJfPlkvnwo3z69bvnzWMuf13ra
 7njJ80uP50D2sYuPPPfO9eP+5tfLrx340aOb63f+9e7PXr18ZnP9489//Wt/Ofhw9osP/f6l+/ev
 Zp+6+/EjHz70aHY+Wz5w9OYL2dP//Na/Tj9yNjv+2j3fOfuHJ7JvXvvJpWu3nMtuOvX0d28/tZK9
 l/3tvn9cfnhzvJd/eXj9pYNf3lz/7ZuHV7595GT+PC7m5+m+wnk8lt9feF/vW8pvXylZL77/lwrr
 xwrbL+f3X8zX782X+ft4Pb2f79n9fF9/Xade5+L7cv2JfP3+LH1eJu/3W/PjFt7n30j33zx93M3P
 VeH8XH//TI7/menntfl+W8o+2HBkx/sx3T7Zb+f61PZrhc956fdPfr73pcdROF+7jFs8f2l94zT8
 biX/XsjPz4ur2V0bH9D3T258DpfS/h8tfG8cmz7+2unJdmuP5esX8v2+MH3e9n1u83FMjbNt/bE3
 33986dnV7MStH6z96eid2SfPnPj7fy+fzvb9+KaHPnLoK9mlF+54a/8fz2evPv/28XcPnsl+9sDP
 7/3+yyvZ289c+t5Pf/jA5ufkP6//4N3Lt921Y/z0Oky9HtvOy/TtZZ/3+X+Hiq//5PwVv4fLv2+n
 X8cDk+WL6f187WT6Xdm4/erW78rk9+GWyev9VDoeAABA4v8tAgAAAADEpo4LAAAAABCbOi4AAAAA
 QGzquAAAAAAAsanjAgAAAAD0g3ouAAAAAEAs6rYAAAAAAP2gngsAAAAAEJs6LgAAAADAuKkTAwAA
 AADEpo4LAAAAABCbOi4AAAAAQGzquAAAAAAARKBeDQAAAADQLXVZAAAAAGBs1EUBAAAAAGJTxwUA
 AAAAiE0dFwAAAACANqlDAwAAAADEpo4LAAAAABCbOi4AAAAAQGzquAAAAAAAsanjAgAAAADEpo4L
 AAAAABCbOi4AAAAAQGzquAAAAAAAsanjAgAAAADMR10VAAAAACA2dVwAAAAAgNjUcQEAAACAsVEX
 BQAAAACITR0XAAAAACA2dVwAAAAAYKjUPwEAAAAAYkt1XPVcAAAAAIDY1HMBAAAAAPpBHRcAAAAA
 IDZ9uQAAAAAA/aCeCwAAAADQD+q4AAAAAACxqeMCAAAAAPSbOi8AAAAAQGzquAAAAAAAsanjAgAA
 AADQBfVoAAAAAIBxURcGAAAAAPpCPRMAAAAAILZUx521BAAAAAAgJnVdAAAAAIB+UdcFAAAAAKAJ
 6ssAAAAAwNjpywUAqvsfUEsDBC0AAAAIAAAAIQAi6e/F//////////8IABQAYl91Yi5ucHkBABAA
 kBsAAAAAAAAcBAAAAAAAAJvsF+obEMnIUMZQrZ6SWpxcpG6loG6TZqGuo6Cell9UUpSYF59flJIK
 EndLzClOBYoXZyQWpAL5GhZmZjqaOgq1CmQDLgYQ6DjswIAVqIyKD0pxQursHbCLm0D5hkTaB+Mb
 E6keBiLRxBVwuAcG1NDEcbkfh706U6B8E1TxA9E4zIHZhxYOG2oJ2Ivuzg/2RLkPDtDDZbiLo4cX
 DFArH1gSpz6gGMr3I9F8LVTxB40O2NXbEWkuWvrEqc4Whzq0fFi1HMonNV6IVUcrcwmpy3Sgrf20
 FiegziHFgTRzYeUnme5oCEaTdyTNvJap+M2HA3LrK1zABU0dTB+x5QS11aOVBwx6BNTrOWDno6s3
 g/JxxYcGmjix/jHCYR+6PLp+ardHyBVHdx/J5jjgV49ef0jgUE+o/YIr3kitb0g1n1rqiaxHCaon
 1V5KxclNr0SHGw7zYfkRV31OajlNrXikdboabOYPNnFax+9ApR9i2znUrv8pVYdwt1Abo/c6JVz9
 NcL++6YR039oaThBdSLr3B9WpURgqGt9HbhDjtUKLv6494xyfYKcA377Q6DiiHIm+m2ivkiDs8MO
 OaCJER449AVAxZ3g8srfOBdwnJjicH1xgS1XeiAOfQh3eKktL2OzmIzTfWfPAAFPuIOBMQjIw+Vj
 f+qcZ57R7gCW91HG0AcKHpF1Ug7g8AhFhOe7jV8Wck9ox2kfunh+2pfFjCSoh4Gw2nXbkv5jugvs
 3ieY8XZ6oeu2z291McTXqz5pnqeKo5/2A9Oc0skSLGHvcPXrKO9P/RQI6Y1jS3fArw4h7j3p+S+7
 4gKi1eMSN8kMLj3vUwxJV+FuBNW3vptkoU1C/+73Oo5//+Ux+7mlcqL/p1/toNj9lIkzMBhuE3iy
 YGkvAXfIO8iDEvw/JwdwdjHWhdN9h75qxPCT2p4i3Z2bla+Wz7vag9OdQaAC5aKdQ6EtFzAqHRzS
 04BAzYlke8hS5wAr3zwh9AFEPvl5oO//IZcqCL/BHcO8pvDTc2eudMAQNxE0s9lrglnO4VI/ayYQ
 fLQgWj24HHuHqd7mvn/v9DprDPF+UDy/xywXqkEVxi8c5dEXTPNBpaf7T0xzvoLqp6+Y6ie9rbE3
 /Yc5fmttxvRxV5wmhjgu/4KTxVtMe3GpB6enl5jqIYDY9AvrPxFWr9Y1YddZrQkO4HD2x0wnYPcE
 QuspBw8HcH1+1RVDHSSfYsYHuHx7jll+Q8IXRz2Xh5b+4PMs6OPbCqjisPFs+Pg1dBwVPj4NbcfA
 xyNh44+wfAR1J3x8EFrewsedYPbBxoHQ+1EwWg+NNkOTxxhfgNKwfjRGvxlKazjA2mOwdhCsXQNr
 p8DaH7D2BKx9AKv3YfUdrB6D1UOw+gVWb8DqCVg5DSsHUcoVYDqDpR8AUEsDBC0AAAAIAAAAIQCg
 Ab+x//////////8NABQAYm91bmRzX2xvLm5weQEAEABAFgAAAAAAAJ4CAAAAAAAAm+wX6hsQychQ
 xlCtnpJanFykbqWgbpNmoa6joJ6WX1RSlJgXn1+UkgoSd0vMKU4FihdnJBakAvkaZpZmOpo6CrUK
 ZAMuBjD48H+UHqVH6VF6lB6lR+nhRo+CUTAKRsEoGAWjgBLw+Lcy62TLD/aXmA4/lNT9YB/RkdmY
 YfrBvlBi9dr9th/sTZ/cSRdvCHKInaT2z2/tB3uwJgdLh63agbuFtn62N5tyPSDOWdSht/mhyLaY
 X/Yb7+r4K11mcfixYY/nznvf7a/+3NoeE8bhcOTRp/Uy9h/tH6xmtbH20Hfw0lw6Jcjrg/2ax8tq
 3jlCzaUDsMy+quBg+MEeRtdJHCyWd/tg//4dCHA5hN+Q8dhy6Jv9pOn9Vdsff7M/cnGh5z9Wbgd6
 uY9aoHT5jEqXFR/sT7yR6p5fxOAA4ys1zvG/FPDXHsbXUXjQ/tafyaFOimtTxZUP9uERzVyKpxgc
 FC7lx7PrfbE//v1FWdbFH/btLo1PNPK/2BeWnbnFvuu7/XT19c0n4z7aP3rl7/L7OSPcfAvPuLbV
 esxwvph55be6n5wOAx0etAYvT8xrXFHyxd56ozAQ8cPzi3hsyUXX63YOB8XD7V8Aw8MYDEwcDDkn
 G3BO/mDvVM35VnWLkwNImXisEDxfDbR/6A1KBaZP8GD/aH/U780Rvxxjh9w9i2d9Tf9gvwUMfB3m
 bTpqOXHXB/ttubeByMYBVm5AwlPFQUnmkKLMoY9UD7egeft49Po+2OvKfbRbeFHKgc897qlt9j97
 5lkc0vPkGBxO+KXa8bZ+tW+V3bQy6/Zf+4qmL2qzGT/a26Z0+uxhYneA5ZNn61SfNMuJOFDbfYMF
 wOILzJng7wCrV2D1CKxemaTiOUmF08lhwiP29JTpmOU+AFBLAwQtAAAACAAAACEAMcqW2f//////
 ////DQAUAGJvdW5kc19oaS5ucHkBABAAQBYAAAAAAAA5AgAAAAAAAJvsF+obEMnIUMZQrZ6SWpxc
 pG6loG6TZqGuo6Cell9UUpSYF59flJIKEndLzClOBYoXZyQWpAL5GmaWZjqaOgq1CmQDLgYw+FA/
 So/So/QoPUqP0qP0KD1Kj9Kj9EilVRxQ6UgoreaAXd4QhzxMXwiUNoHSAVDaCa7u7Bkg4Al3MDAG
 AXmHde4Pq0TWSTm0vg7cIRcajmYejNbC4R5jHOoJ0ejuRqflHeRBDvrn5AB2prEunO479FUjht/S
 IWiHXOvri3YOhbZc1xcXODikpwGBGtSfDjD/e0LoA7YQ9YHyUHkPh28aMf2HrrricJclAfe54AgP
 WDjpQWkNNHkjAv5HN2+w0IZofGM0Prr7caVfEzQ+urm40vVA07j8g55eYHw/ND6u/ENpPqJWusGV
 L4nlExJH0JdyO2MK/kc45Kxn3Wv+IQLO/7BovcLZLwj+pNP1Hvs/RzicXui67fO/CId+UL5/H+Fw
 89z34Mc/IxxApZb7VygN5GudFji+61uEQ+OFqh9GQPVa/Xktrh8jHJYwqd92AJoHLibeRjiUOgh9
 ywXyweXBywgC4Uqt8EbXZ4ImTmz4kis/0PmHUPihl4uE8he6v9DzG7HpFt1c9HJ/sIZfpIPXsvU9
 RcB0DK7Pn0Q4OFwLXr3+U4TDjWbPjx8/QNP1jwiH3ul5Qs3AfLXr7unaT8B88emSb5LAmwgH07hd
 njxAvo95p2MC2fkAV3ziqh9x0ejlox4aH2YPen1KbPoh11+I9hoAUEsDBC0AAAAIAAAAIQD3S0kA
 //////////8PABQAaW50ZWdyYWxpdHkubnB5AQAQAEAWAAAAAAAAmAAAAAAAAACb7BfqGxDJyFDG
 UK2eklqcXKRupaBuk2mhrqOgnpZfVFKUmBefX5SSChJ3S8wpTgWKF2ckFqQC+RpmlmY6mjoKtQpk
 Ay6GUTAKRsEoGAWjYBSMglEwCkbBiAWMVKJpDci1f7D5Axcg1l3Uii9c/qW2+UOdZhok9GD370DH
 01CN16EafgMd3gPtn6EafoPVXcM9XskND3QAAFBLAQItAy0AAAAIAAAAIQA0moHe3AAAAEAWAAAF
 AAAAAAAAAAAAAACAAQAAAABjLm5weVBLAQItAy0AAAAIAAAAIQBPwqeWajIAAACUSQAIAAAAAAAA
 AAAAAACAARMBAABBX3ViLm5weVBLAQItAy0AAAAIAAAAIQAi6e/FHAQAAJAbAAAIAAAAAAAAAAAA
 AACAAbczAABiX3ViLm5weVBLAQItAy0AAAAIAAAAIQCgAb+xngIAAEAWAAANAAAAAAAAAAAAAACA
 AQ04AABib3VuZHNfbG8ubnB5UEsBAi0DLQAAAAgAAAAhADHKltk5AgAAQBYAAA0AAAAAAAAAAAAA
 AIAB6joAAGJvdW5kc19oaS5ucHlQSwECLQMtAAAACAAAACEA90tJAJgAAABAFgAADwAAAAAAAAAA
 AAAAgAFiPQAAaW50ZWdyYWxpdHkubnB5UEsFBgAAAAAGAAYAUgEAADs+AAAAAA==
 """


 def load_lp():
    raw = base64.b64decode(LP_DATA_B64)
    data = np.load(io.BytesIO(raw))
    bounds = list(zip(
        [None if v == -np.inf else float(v) for v in data["bounds_lo"]],
        [None if v ==  np.inf else float(v) for v in data["bounds_hi"]],
    ))
    return (
        data["c"], data["A_ub"], data["b_ub"],
        bounds, data["integrality"].tolist(),
    )


 def expand_sc_to_binary(c, A_ub, b_ub, bounds, integrality):
    """
    Rewrite each semi-continuous variable as continuous + binary indicator.

    For column i with integrality[i] >= 2 and lo > 0:
      - relax bounds[i] = (0, hi); integrality[i] -= 2 (SC->cont, semi-int->int)
      - append a binary column b with bounds (0, 1)
      - append two rows: A_new @ x <= 0
            row 1:  q - hi * b   (i.e. q <= hi * b)
            row 2: -q + lo * b   (i.e. q >= lo * b)
    """
    n_rows, n_cols = A_ub.shape
    sc_cols = [
        (i, lo, hi)
        for i, ((lo, hi), integ) in enumerate(zip(bounds, integrality))
        if integ >= 2 and lo is not None and lo > 0 and hi is not None
    ]
    n_sc = len(sc_cols)

    A2 = np.zeros((n_rows + 2 * n_sc, n_cols + n_sc))
    A2[:n_rows, :n_cols] = A_ub
    b2 = np.concatenate([b_ub, np.zeros(2 * n_sc)])
    c2 = np.concatenate([c, np.zeros(n_sc)])
    bounds2 = list(bounds) + [(0, 1)] * n_sc
    integ2 = list(integrality) + [1] * n_sc  # binaries

    for k, (col, lo, hi) in enumerate(sc_cols):
        bounds2[col] = (0, hi)
        integ2[col] = integrality[col] - 2
        b_idx = n_cols + k
        A2[n_rows + 2 * k    , col]   = 1
        A2[n_rows + 2 * k    , b_idx] = -hi   # q <= hi * b
        A2[n_rows + 2 * k + 1, col]   = -1
        A2[n_rows + 2 * k + 1, b_idx] = lo    # q >= lo * b

    return c2, A2, b2, bounds2, integ2, n_sc


 def main():
    c, A_ub, b_ub, bounds, integrality = load_lp()
    n_sc = sum(1 for v in integrality if v >= 2)
    print(f"Loaded LP: {A_ub.shape[0]} rows x {A_ub.shape[1]} cols, "
          f"{n_sc} semi-continuous variables.")

    # === Original formulation ===
    print("\n=== 1) Original formulation with semi-continuous vars ===")
    print("    (set disp=True to see HiGHS internal 'row viol = 0' vs "
          "post-check 'claims optimality with infeasibilities')")
    res = linprog(
        c, A_ub, b_ub, bounds=bounds, integrality=integrality,
        options={"mip_rel_gap": 1e-7, "disp": False},
    )
    print(f"    -> status = {res.status}")
    print(f"    -> message = {res.message!r}")
    if res.success:
        print(f"    -> objective = {res.fun:.6f}")

    # === Binary-indicator workaround ===
    print("\n=== 2) Workaround: SC -> binary indicator + coupling rows ===")
    c2, A2, b2, bounds2, integ2, n_added = expand_sc_to_binary(
        c, A_ub, b_ub, bounds, integrality,
    )
    print(f"    Added {n_added} binary columns and {2 * n_added} coupling rows.")
    print(f"    New shape: {A2.shape[0]} rows x {A2.shape[1]} cols.")
    res2 = linprog(
        c2, A2, b2, bounds=bounds2, integrality=integ2,
        options={"mip_rel_gap": 1e-7, "disp": False},
    )
    print(f"    -> status = {res2.status}")
    print(f"    -> message = {res2.message!r}")
    if res2.success:
        print(f"    -> objective = {res2.fun:.6f}")


 if __name__ == "__main__":
    main()
No results found