+ /i^RIt^RIt^RIHt^RIHtHt^RIH t H t ^RI H t H t HtHtHt^RIHt^RIHt]P*!]4P.t]P*!]4P2t!RR 4tR#) N) lsq_linear)Models Quadratic)Options Constants)cauchy_geometryspider_geometrynormal_byrd_omojokuntangential_byrd_omojokun$constrained_tangential_byrd_omojokun)qr_tangential_byrd_omojokun)get_arrays_tolca]tRt^toRtRt]R4t]R4t]R4t ]R4t ]R4t ]R4t ] PR 4t ]R 4t]PR 4t]R 4t]R 4t]R4t]R4t]R4t]R4t]R4tRtRtRtRtRtRtRtRtR,RltRtRt Rt!R t"R!t#R"t$R#t%R$t&R-R%lt'R&t(R't)R(t*R)t+R*t,R+t-Vt.R#). TrustRegionz Trust-region framework. c \RVnWn\VPW P4VnW0n^VnVP4\P!VP4Vn \P!VP4Vn \P!VP4Vn\P!VP 4VnVP%VP&4V\(P*,VnVP.VnR#)aa Initialize the trust-region framework. Parameters ---------- pb : `cobyqa.problem.Problem` Problem to solve. options : dict Options of the solver. constants : dict Constants of the solver. Raises ------ `cobyqa.utils.MaxEvalError` If the maximum number of evaluations is reached. `cobyqa.utils.TargetSuccess` If a nearly feasible point has been found with an objective function value below the target. `cobyqa.utils.FeasibleSuccess` If a feasible point has been found for a feasibility problem. `numpy.linalg.LinAlgError` If the initial interpolation system is ill-defined. N)_penalty_pbrpenalty_models _constants _best_indexset_best_indexnpzeros m_linear_ub _lm_linear_ub m_linear_eq _lm_linear_eqm_nonlinear_ub_lm_nonlinear_ubm_nonlinear_eq_lm_nonlinear_eqset_multipliersx_bestrRHOBEG _resolution resolution_radius)selfpboptions constantss&&&&Y/var/www/html/photoedit/myenv/lib/python3.14/site-packages/scipy/_lib/cobyqa/framework.py__init__TrustRegion.__init__s4 dhh> #  XXd&6&67XXd&6&67 ")<)< = ")<)< = T[[)#7>>2 c .VPP#)zD Number of variables. Returns ------- int Number of variables. )rnr*s&r.r3 TrustRegion.nLsxxzzr1c .VPP#)zl Number of linear inequality constraints. Returns ------- int Number of linear inequality constraints. )rrr4s&r.rTrustRegion.m_linear_ubXxx###r1c .VPP#)zh Number of linear equality constraints. Returns ------- int Number of linear equality constraints. )rrr4s&r.rTrustRegion.m_linear_eqdr8r1c .VPP#)zr Number of nonlinear inequality constraints. Returns ------- int Number of nonlinear inequality constraints. )rr r4s&r.r TrustRegion.m_nonlinear_ubpxx&&&r1c .VPP#)zn Number of nonlinear equality constraints. Returns ------- int Number of nonlinear equality constraints. )rr"r4s&r.r"TrustRegion.m_nonlinear_eq|r=r1c VP#)zF Trust-region radius. Returns ------- float Trust-region radius. )r)r4s&r.radiusTrustRegion.radius||r1c WnVPVP\P,VP ,8:dVP VnR#R#)za Set the trust-region radius. Parameters ---------- radius : float New trust-region radius. N)r)rArrDECREASE_RADIUS_THRESHOLDr()r*rAs&&r.rArBsE KKyBBCoo  ??DL  r1c VP#)z Resolution of the trust-region framework. The resolution is a lower bound on the trust-region radius. Returns ------- float Resolution of the trust-region framework. r'r4s&r.r(TrustRegion.resolutionsr1c WnR#)z Set the resolution of the trust-region framework. Parameters ---------- resolution : float New resolution of the trust-region framework. NrG)r*r(s&&r.r(rHs &r1c VP#)zB Penalty parameter. Returns ------- float Penalty parameter. )rr4s&r.rTrustRegion.penaltys}}r1c VP#)z Models of the objective function and constraints. Returns ------- `cobyqa.models.Models` Models of the objective function and constraints. )rr4s&r.modelsTrustRegion.modelsrCr1c VP#)zh Index of the best interpolation point. Returns ------- int Index of the best interpolation point. )rr4s&r. best_indexTrustRegion.best_indexsr1c `VPPPVP4#)z Best interpolation point. Its value is interpreted as relative to the origin, not the base point. Returns ------- `numpy.ndarray` Best interpolation point. )rM interpolationpointrPr4s&r.r%TrustRegion.x_bests#{{((..t??r1c PVPPVP,#)zv Value of the objective function at `x_best`. Returns ------- float Value of the objective function at `x_best`. )rMfun_valrPr4s&r.fun_bestTrustRegion.fun_bests{{""4??33r1c TVPPVPR3,#)z Values of the nonlinear inequality constraints at `x_best`. Returns ------- `numpy.ndarray`, shape (m_nonlinear_ub,) Values of the nonlinear inequality constraints at `x_best`. NNN)rMcub_valrPr4s&r.cub_bestTrustRegion.cub_best"{{""4??A#566r1c TVPPVPR3,#)z Values of the nonlinear equality constraints at `x_best`. Returns ------- `numpy.ndarray`, shape (m_nonlinear_eq,) Values of the nonlinear equality constraints at `x_best`. r[)rMceq_valrPr4s&r.ceq_bestTrustRegion.ceq_best r_r1c VPPV4VPVPPP V,VPPP , ,,VPVPPPV,VPPP, ,,VPVPPV4,,VPVPPV4,,#)z Evaluate the Lagrangian model at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which the Lagrangian model is evaluated. Returns ------- float Value of the Lagrangian model at `x`. )rMfunrrlineara_ubb_ubra_eqb_eqr!cubr#ceqr*xs&&r. lag_modelTrustRegion.lag_models KKOOA   xx##a'$((//*>*>>@ @  xx##a'$((//*>*>>@ @ ##dkkooa&88  9 ##dkkooa&88  9 r1c VPPV4VPVPPP ,,VP VPPP,,VPVPPV4,,VPVPPV4,,#)a Evaluate the gradient of the Lagrangian model at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which the gradient of the Lagrangian model is evaluated. Returns ------- `numpy.ndarray`, shape (n,) Gradient of the Lagrangian model at `x`. ) rMfun_gradrrrfrgrrir!cub_gradr#ceq_gradrms&&r.lag_model_gradTrustRegion.lag_model_grad.s KK  #  488??#7#77 8  488??#7#77 8##dkk&:&:1&== >##dkk&:&:1&==  > r1c BVPP4pVP^8d2WPVPP 4,, pVP ^8d2WP VPP4,, pV#)z Evaluate the Hessian matrix of the Lagrangian model at a given point. Returns ------- `numpy.ndarray`, shape (n, n) Hessian matrix of the Lagrangian model at `x`. )rMfun_hessr r!cub_hessr"r#ceq_hess)r*hesss& r.lag_model_hessTrustRegion.lag_model_hessDsw{{##%    " ))DKK,@,@,BB BD    " ))DKK,@,@,BB BD r1c VPPV4VPVPPV4,,VPVPP V4,,#)at Evaluate the right product of the Hessian matrix of the Lagrangian model with a given vector. Parameters ---------- v : `numpy.ndarray`, shape (n,) Vector with which the Hessian matrix of the Lagrangian model is multiplied from the right. Returns ------- `numpy.ndarray`, shape (n,) Right product of the Hessian matrix of the Lagrangian model with `v`. )rM fun_hess_prodr! cub_hess_prodr# ceq_hess_prodr*vs&&r.lag_model_hess_prodTrustRegion.lag_model_hess_prodTsa$ KK % %a (##dkk&?&?&BB C##dkk&?&?&BB C r1c VPPV4VPVPPV4,,VPVPP V4,,#)a Evaluate the curvature of the Lagrangian model along a given direction. Parameters ---------- v : `numpy.ndarray`, shape (n,) Direction along which the curvature of the Lagrangian model is evaluated. Returns ------- float Curvature of the Lagrangian model along `v`. )rMfun_curvr!cub_curvr#ceq_curvrs&&r.lag_model_curvTrustRegion.lag_model_curvks_ KK  ###dkk&:&:1&== >##dkk&:&:1&== > r1c VVPPVP4RVPV4,,,#)a% Evaluate the objective function of the SQP subproblem. Parameters ---------- step : `numpy.ndarray`, shape (n,) Step along which the objective function of the SQP subproblem is evaluated. Returns ------- float Value of the objective function of the SQP subproblem along `step`. g?)rMrrr%rr*steps&&r.sqp_funTrustRegion.sqp_funs? KK  -D,,T22 3  r1c VPPVP4VPPVP4V,,#)as Evaluate the linearization of the nonlinear inequality constraints. Parameters ---------- step : `numpy.ndarray`, shape (n,) Step along which the linearization of the nonlinear inequality constraints is evaluated. Returns ------- `numpy.ndarray`, shape (m_nonlinear_ub,) Value of the linearization of the nonlinear inequality constraints along `step`. )rMrkr%rsrs&&r.sqp_cubTrustRegion.sqp_cub=" KKOODKK (kk""4;;/$6 7 r1c VPPVP4VPPVP4V,,#)am Evaluate the linearization of the nonlinear equality constraints. Parameters ---------- step : `numpy.ndarray`, shape (n,) Step along which the linearization of the nonlinear equality constraints is evaluated. Returns ------- `numpy.ndarray`, shape (m_nonlinear_ub,) Value of the linearization of the nonlinear equality constraints along `step`. )rMrlr%rtrs&&r.sqp_ceqTrustRegion.sqp_ceqrr1Nc ^Ve VeVfVPWP4wr#pTpVPR8dpVPPWVR7p\P !V4'd7WPP\P PV4,, pV#)a Evaluate the merit function at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which the merit function is evaluated. fun_val : float, optional Value of the objective function at `x`. If not provided, the objective function is evaluated at `x`. cub_val : `numpy.ndarray`, shape (m_nonlinear_ub,), optional Values of the nonlinear inequality constraints. If not provided, the nonlinear inequality constraints are evaluated at `x`. ceq_val : `numpy.ndarray`, shape (m_nonlinear_eq,), optional Values of the nonlinear equality constraints. If not provided, the nonlinear equality constraints are evaluated at `x`. Returns ------- float Value of the merit function at `x`. r)r\ra)rrr violationr count_nonzerolinalgnorm)r*rnrWr\ram_valc_vals&&&&& r.meritTrustRegion.merits. ?go(,LL(A %Gg ==3 HH&&q7&KE&&)>>> r1c >\P!VPPP.VP P V4..4p\P!VPPPVPPPV,, VP PV4).4p\P!VPPP.VP PV4..4p\P!VPPPVPPPV,, VP PV4).4pW#WE3#)a Get the linearizations of the constraints at a given point. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which the linearizations of the constraints are evaluated. Returns ------- `numpy.ndarray`, shape (m_linear_ub + m_nonlinear_ub, n) Left-hand side matrix of the linearized inequality constraints. `numpy.ndarray`, shape (m_linear_ub + m_nonlinear_ub,) Right-hand side vector of the linearized inequality constraints. `numpy.ndarray`, shape (m_linear_eq + m_nonlinear_eq, n) Left-hand side matrix of the linearized equality constraints. `numpy.ndarray`, shape (m_linear_eq + m_nonlinear_eq,) Right-hand side vector of the linearized equality constraints. ) rblockrrfrgrMrsrhrkrirtrjrl)r*rnaubbubaeqbeqs&& r.get_constraint_linearizations)TrustRegion.get_constraint_linearizationss-(hh%%&%%a()   hh$$txx';';a'??##   hh%%&%%a()   hh$$txx';';a'??##   !!r1c  VPVP4wr#rEVPPPVP, pVPPP VP, pVP \P,VP,p\VVVVVVVV\P,3/VP Bp V\P,'d\Wg4p \P!W,V84'g&\P!WyV , 84'd\ P"!R\$^4\P&P)V 4RV,8d\ P"!R\$^4\P*!VPR,W,, 4pWi,pWy,p\P,!W2V ,, R4pVP.P1VP4VP3V 4,p VPP4R 9d<\7V VP2VVVV\P,3/VP Bp M/\9V VP2VVVVVVVR,3 /VP Bp V\P,'d\Wg4p \P!W,V84'g&\P!W|V , 84'd\ P"!R\$^4\P&P)W,4R\P*!R4,VP,8d\ P"!R\$^4W3#) a Get the trust-region step. The trust-region step is computed by solving the derivative-free trust-region SQP subproblem using a Byrd-Omojokun composite-step approach. For more details, see Section 5.2.3 of [1]_. Parameters ---------- options : dict Options of the solver. Returns ------- `numpy.ndarray`, shape (n,) Normal step. `numpy.ndarray`, shape (n,) Tangential step. References ---------- .. [1] T. M. Ragonneau. *Model-Based Derivative-Free Optimization Methods and Software*. PhD thesis, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China, 2022. URL: https://theses.lib.polyu.edu.hk/handle/200/12294. z6the normal step does not respect the bound constraint.皙?z=the normal step does not respect the trust-region constraint.@rdebugz;The tangential step does not respect the bound constraints.zSP",8EdSP"V, V,p SPAV SP P4R8dV )p \PB!WZ, W, .4pW,V , pW,V, p\ERVV\P,!V4344p\PD!\P,!V V(,4RR7p\PD!\P,!V V(,4VR7p\PD!\P,!V V(R3,V ,4VR7p\GR V,R \P8P;V 4,4pVV8:deSP P%SPV ,V4p \-V 4R \-V4,8d\PH!WV4pV\P,'d\3WV4p\PJ!VV,V84'g&\PJ!WgV, 84'd\LPN!R \P^4\P8P;V4R SP",8d\LPN!R\P^4V#)a Get the geometry-improving step. Three different geometry-improving steps are computed and the best one is returned. For more details, see Section 5.2.7 of [1]_. Parameters ---------- k_new : int Index of the interpolation point to be modified. options : dict Options of the solver. Returns ------- `numpy.ndarray`, shape (n,) Geometry-improving step. Raises ------ `numpy.linalg.LinAlgError` If the computation of a determinant fails. References ---------- .. [1] T. M. Ragonneau. *Model-Based Derivative-Free Optimization Methods and Software*. PhD thesis, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China, 2022. URL: https://theses.lib.polyu.edu.hk/handle/200/12294. z8The index `k_new` must be different from the best index.rcP<SPVSPP4#NcurvrMrSrlagr*s&r./TrustRegion.get_geometry_step..chhq$++";";0TrustRegion.get_geometry_step..s% !8FF5#..!8s%'r$@g{Gz?g?z9The geometry step does not respect the bound constraints.rz?The geometry step does not respect the trust-region constraint.)r[:NN)zlinearly constrainedznonlinearly constrained))rrrPrsqueezeeyerMnptrrSgradr%rrrrrrA determinantsxptnewaxisr absrrrr Trrr3TINYrrrmincliprrrr)r*k_newr, coord_vecg_lagrrrsigmarstep_alt sigma_altrrrrtol_bdtol_ubfree_xlfree_xufree_ubn_actq g_lag_projnorm_g_lag_projcbdrkrl maxcv_valrrsf&& @r.get_geometry_stepTrustRegion.get_geometry_steps> 7== ! !( JI J(JJrvva%@A  KK % %  GMM "  dkk&?&?@XX__  $++ - XX__  $++ -   <   KK GMM "  ((t);UC KK % % ) )kk''++At ,JK L (+1t.B+B'CA4??# #$"   < J   KK GMM "  KK,,T[[8-CUK y>CJ &DE 88==  224;;? Cc#B+F#C(FVGmGFlGVmG3 HE11ef91ef9%)?@J iinnZ8O5%488::%%/D4;;ns*ns* "%sBFF3K!8  ffRVVHgX$67EffRVVHgX$67EffRVVC! $4x$?@#N$*dRYY^^H-E&EF# $ 8 8 h.!I9~s5z)99!wwxR8 7== ! ! (CvvdSj2o&&"&&Sj*A*A #"  yy~~d#cDKK&77 /"   r1c  RVPVP4wr4rVVPPPVP, pVPPP VP, p\ PPV4p \VVVVVVV V\P,3/VPBp V\P,'d\Wx4p \ P!W,V84'g&\ P!WV , 84'd\P !R\"^4\ PPV 4RV ,8d\P !R\"^4V #)z Get the second-order correction step. Parameters ---------- step : `numpy.ndarray`, shape (n,) Trust-region step. options : dict Options of the solver. Returns ------- `numpy.ndarray`, shape (n,) Second-order correction step. zHThe second-order correction step does not respect the bound constraints.rzNThe second-order correction step does not respect the trust-region constraint.)rr%rrrrrrrr rrrrrrrr) r*rr,rrrrrrrAsoc_steprs &&& r. get_second_order_correction_step,TrustRegion.get_second_order_correction_steps6""?? L# XX__  $++ - XX__  $++ -%'        GMM "  oo   7== ! ! (Cvvhnr)**bffRS.5H.I.I 5"  yy~~h'#,6 ;"  r1c VPVPVPVPVP4pVPVPV,W#V4pVPVPRVP P VP4VP PVP44pVPVPV,VPV4VPV4VPV44p\Wx, 4\\WV, 4,8dWV, \Wx, 4, #R#)a Get the reduction ratio. Parameters ---------- step : `numpy.ndarray`, shape (n,) Trust-region step. fun_val : float Objective function value at the trial point. cub_val : `numpy.ndarray`, shape (m_nonlinear_ub,) Nonlinear inequality constraint values at the trial point. ceq_val : `numpy.ndarray`, shape (m_nonlinear_eq,) Nonlinear equality constraint values at the trial point. Returns ------- float Reduction ratio. r) rr%rXr]rbrMrkrlrrrrr) r*rrWr\ra merit_old merit_newmerit_model_oldmerit_model_news &&&&& r.get_reduction_ratioTrustRegion.get_reduction_ratioIs(JJ KK MM MM MM  JJt{{T17WM ** KK  KKOODKK ( KKOODKK (   ** KK$  LL  LL  LL    0 1D3  !< 5  )S1. Kr1c  6VPVP4wr#rE\\PP \P !\P!RV)4V.44\PP \P !\P!RW!,V, 4WA,V, .44, R4pVPV4p\PP \P !VPVPVPVP.44p\V4\\V4,8d\WV, 4pVPp VP VP"\$P&,V,8:dH\VP"\$P(,V,R4VnVP+4WP8H#)zr Increase the penalty parameter. Parameters ---------- step : `numpy.ndarray`, shape (n,) Trust-region step. r?)rr%rrrrrrrrrr!r#rrrPrrrPENALTY_INCREASE_THRESHOLDPENALTY_INCREASE_FACTORr) r*rrrrr viol_diffsqp_val thresholdbest_index_saves && r.increase_penaltyTrustRegion.increase_penaltyys"?? L# IINN 3- iinn 3 S(89 S(  # &,,t$IINN HH&&&&))))     y>D3w</ /I':;I// MMyCCD   A ABYNDM    !//11r1c x\VPVP44VnVP4R#)z! Decrease the penalty parameter. N)rr_get_low_penaltyrr4s&r.decrease_penaltyTrustRegion.decrease_penaltys+DMM4+@+@+BC  r1c  VPpVPVPVPPV,VPP VR3,VPP VR3,4pVPPVPVPP VR3,VPP VR3,4pR\,\VPPVPP4,\\V4R4,p\VPP4EF pWPP8wgKVPPP!V4pVPVVPPV,VPP VR3,VPP VR3,4pVPPVVPP VR3,VPP VR3,4pWr8gWrV,8gEKW8gEKTpTpTpEK# WnR#)z" Set the index of the best point. r[rrN)rPrr%rMrWr\rarmaxcvEPSrr3rrrangerSrTr) r*rPm_bestr_bestrkx_valrr_vals & r.rTrustRegion.set_best_indexs__  KK KK   + KK   A . KK   A .    KK KK   A . KK   A .   $++--1 2#f+s# $ t{{'AOO# 1177: KK''*KK''1-KK''1-  KK''1-KK''1- >esl&:u~!"J"F"F#($&r1c \P!VPPPVPPPRVP \P 3,, R,^R7pVfRpTpMVPPV4p\P!RV\VP\P,VP,VP4R,, 4R,pRW@P &\P!V\P !V4,4pV\P"!W%,43#)aO Get the index of the interpolation point to remove. If `x_new` is not provided, the index returned should be used during the geometry-improvement phase. Otherwise, the index returned is the best index for included `x_new` in the interpolation set. Parameters ---------- x_new : `numpy.ndarray`, shape (n,), optional New point to be included in the interpolation set. Returns ------- int Index of the interpolation point to remove. float Distance between `x_best` and the removed point. Raises ------ `numpy.linalg.LinAlgError` If the computation of a determinant fails. r[raxisrg@r)rsumrMrSrrPrrrrrrLOW_RADIUS_FACTORrAr(argmaxrr)r*x_newdist_sqrweightsk_maxs&& r.get_index_to_removeTrustRegion.get_index_to_removes"2&& ))--++++//4??BJJ0NOP      =EGKK,,U3E  (C(CD++&     (,GOO $ 'BFF5M12bgggn---r1c \PPV4pW P\P ,8:d;V;P VP\P,,unR#W P\P,8:dD\VP\P,VP ,V4VnR#\VP\P,VP ,\VP\P,VP ,VP\P,V,44VnR#)z Update the trust-region radius. Parameters ---------- step : `numpy.ndarray`, shape (n,) Trust-region step. ratio : float Reduction ratio. N) rrrrr LOW_RATIOrADECREASE_RADIUS_FACTOR HIGH_RATIOrrINCREASE_RADIUS_FACTORINCREASE_RADIUS_THRESHOLD)r*rratios_norms&&& r. update_radiusTrustRegion.update_radiuss% OOI$7$78 8 KK4??9+K+KL LK ooi&:&:; ; @ @A++DK  @ @A++OOI$D$DEkk"OOI$G$GH DKr1c VP\P,V\P,,VP 8d:V;P VP\P ,,unMVP\P,V\P,,VP 8dC\P!VP V\P,,4VnMV\P,Vn\VP\P,VP,VP 4Vn R#)zx Enhance the resolution of the trust-region framework. Parameters ---------- options : dict Options of the solver. N) rrLARGE_RESOLUTION_THRESHOLDrRHOENDr(DECREASE_RESOLUTION_FACTORMODERATE_RESOLUTION_THRESHOLDrrrr&r)r*r,s&&r.enhance_resolutionTrustRegion.enhance_resolution9s OOI@@ Agnn% &oo  OOt44  O OOICC Dgnn% &oo !ggdoo(/(?'@ADO&gnn5DO OOI<< = L OO  r1c zVPP\P!VP4V4R#)zd Shift the base point to `x_best`. Parameters ---------- options : dict Options of the solver. N)rM shift_x_basercopyr%r3s&&r.r7TrustRegion.shift_x_baseZs%   !5w?r1c  hVPPPV,VPPP8pVPR8pVPP P V8pVPP PV8*p\P!V4p\P!V4p\P!V4p\P!V4p Wg,VP,VP,^8Ed\P!VPP4p \PWR3,)WR3,VPPPVR3,VPP!W4VPPP"VPP%V43,p VPP'V4p \P(!V P*^,\P,)4p RV RW,V,V,%\/V P0V )V \P,3RR7pVP2W,W,V,VP4V&RVP4V(&VP2VV ,V,VV ,V,V,VP6V&RVP6V(&VP2VV ,V,V,VV ,V,V,VP,VP8R&VP2W,V,V,VP,RVP:R&R#R#)a  Set the Lagrange multipliers. This method computes and set the Lagrange multipliers of the linear and nonlinear constraints to be the QP multipliers. Parameters ---------- x : `numpy.ndarray`, shape (n,) Point at which the Lagrange multipliers are computed. rr[Nbvls)rmethod)rrfrgrhr]rrrrrrr"rr3r_rMrsrirtrrfullshapeinfrrrnrr!rr#)r*rnincl_linear_ubincl_nonlinear_ubincl_xlincl_xurr m_xlm_xuidentityc_jacrxl_lmress&& r.r$TrustRegion.set_multiplierses--1TXX__5I5II MMS0((//$$)((//$$)&&~6 ))*;<((  (4+;+; ;%% &() *vvdhhjj)HEE1*%%!$$$^Q%67 $$Q:$$ $$Q' )E[[))!,FGGEKKNRVVG4EBEE>DK+-> ?rvv C25 DK+52D  ~ .36D   /7:uu"!!8D ! !"3 49rrsZ%%(:! xxhhuoAAr1