From e6d547c43dfd45c852244d684d4d531e350bae40 Mon Sep 17 00:00:00 2001 From: turtle89431 Date: Tue, 5 May 2026 01:46:16 -0700 Subject: [PATCH] Scrape wikipedia-science: 3626 new, 2846 updated, 6627 total (kb-cron) --- _index.db | Bin 66498560 -> 66826240 bytes .../wiki/A_History_of_Vector_Analysis-0.md | 48 + ..._Mathematical_Theory_of_Communication-0.md | 2 +- .../wiki/A_Metric_America-0.md | 22 + .../wiki/A_New_Era_of_Thought-0.md | 106 +++ .../wiki/Extensions_of_First_Order_Logic-0.md | 28 + .../wiki/Felix_Klein_and_Sophus_Lie-0.md | 43 + .../wiki/Finding_Ellipses-0.md | 155 ++++ ...Fondements_de_la_Géometrie_Algébrique-0.md | 46 + .../wiki/Formulario_mathematico-0.md | 2 +- .../Foundations_of_Algebraic_Geometry-0.md | 30 + ...nova_theoriae_functionum_ellipticarum-0.md | 21 + .../wiki/Games,_Puzzles,_and_Computation-0.md | 24 + .../Geometric_Exercises_in_Paper_Folding-0.md | 60 ++ .../wiki/Geometric_Folding_Algorithms-0.md | 45 + .../wiki/Geometric_Origami-0.md | 69 ++ .../Geometric_and_Topological_Inference-0.md | 23 + .../wiki/Geometry_From_Africa-0.md | 32 + data/en.wikipedia.org/wiki/Geshu_bu-0.md | 33 + .../Glossary_of_Principia_Mathematica-0.md | 245 +++++ .../wiki/God_Created_the_Integers-0.md | 27 + .../wiki/Grundlagen_der_Mathematik-0.md | 39 + .../wiki/Grundzüge_der_Mengenlehre-0.md | 22 + .../wiki/Harmonice_Mundi-0.md | 2 +- .../wiki/Harmonice_Mundi-1.md | 2 +- .../wiki/Higher_Topos_Theory-0.md | 31 + .../History_of_the_Theory_of_Numbers-0.md | 38 + .../wiki/Horologium_Oscillatorium-0.md | 32 + .../wiki/Horologium_Oscillatorium-1.md | 82 ++ .../wiki/Horologium_Oscillatorium-2.md | 37 + data/en.wikipedia.org/wiki/Hydrodynamica-0.md | 52 ++ .../wiki/IJP_The_Book_of_Surfaces-0.md | 35 + .../In_Pursuit_of_the_Traveling_Salesman-0.md | 40 + .../wiki/Indra's_Pearls_(book)-0.md | 51 + ...l_Encyclopedia_of_Statistical_Science-0.md | 24 + .../wiki/Introduction_to_Circle_Packing-0.md | 33 + .../Jade_Mirror_of_the_Four_Unknowns-0.md | 874 ++++++++++++++++++ .../Jade_Mirror_of_the_Four_Unknowns-1.md | 710 ++++++++++++++ .../wiki/Journey_into_Geometries-0.md | 28 + data/en.wikipedia.org/wiki/La_Géométrie-0.md | 54 ++ .../wiki/Letters_to_a_German_Princess-0.md | 47 + .../Letters_to_a_Young_Mathematician-0.md | 16 + data/en.wikipedia.org/wiki/Liber_Abaci-0.md | 25 + data/en.wikipedia.org/wiki/Liber_Abaci-1.md | 371 ++++++++ .../wiki/List_of_books_about_polyhedra-0.md | 59 ++ .../wiki/List_of_books_about_polyhedra-1.md | 93 ++ .../wiki/List_of_mathematics_books-0.md | 2 +- .../Making_Mathematics_with_Needlework-0.md | 29 + data/en.wikipedia.org/wiki/Math_Curse-0.md | 31 + .../wiki/Mathematical_Cranks-0.md | 41 + ...ical_Foundations_of_Quantum_Mechanics-0.md | 297 ++++++ ...ical_Foundations_of_Quantum_Mechanics-1.md | 135 +++ ...thematical_Models_(Cundy_and_Rollett)-0.md | 29 + .../wiki/Mathematical_Models_(Fischer)-0.md | 32 + .../wiki/Mathematicall_Magick-0.md | 48 + .../wiki/Mathematics,_Form_and_Function-0.md | 37 + .../wiki/Mathematics_Made_Difficult-0.md | 17 + .../Mathematics_and_Plausible_Reasoning-0.md | 41 + data/en.wikipedia.org/wiki/Mechanica-0.md | 24 + .../wiki/Method_of_Fluxions-0.md | 53 ++ .../Methoden_der_mathematischen_Physik-0.md | 21 + ..._Riemannian_and_Non-Riemannian_Spaces-0.md | 18 + .../wiki/Mishnat_ha-Middot-0.md | 112 +++ .../wiki/Murderous_Maths-0.md | 34 + .../wiki/Murderous_Maths-1.md | 41 + .../wiki/Mécanique_analytique-0.md | 41 + data/en.wikipedia.org/wiki/Number_Theory | 0 .../wiki/Numerical_Recipes-0.md | 2 +- .../wiki/Numerical_Recipes-1.md | 2 +- .../wiki/On_Numbers_and_Games-0.md | 160 ++++ .../wiki/Opera_Omnia_Leonhard_Euler-0.md | 44 + data/en.wikipedia.org/wiki/Opticks-0.md | 25 + data/en.wikipedia.org/wiki/Opticks-1.md | 48 + .../wiki/Origami_Polyhedra_Design-0.md | 27 + data/en.wikipedia.org/wiki/Origamics-0.md | 24 + .../wiki/Pasta_by_Design-0.md | 30 + .../wiki/Perspectiva_corporum_regularium-0.md | 46 + ...ophiæ_Naturalis_Principia_Mathematica-0.md | 46 + ...ophiæ_Naturalis_Principia_Mathematica-1.md | 25 + ...phiæ_Naturalis_Principia_Mathematica-10.md | 68 ++ ...ophiæ_Naturalis_Principia_Mathematica-2.md | 27 + ...ophiæ_Naturalis_Principia_Mathematica-3.md | 16 + ...ophiæ_Naturalis_Principia_Mathematica-4.md | 22 + ...ophiæ_Naturalis_Principia_Mathematica-5.md | 25 + ...ophiæ_Naturalis_Principia_Mathematica-6.md | 15 + ...ophiæ_Naturalis_Principia_Mathematica-7.md | 17 + ...ophiæ_Naturalis_Principia_Mathematica-8.md | 43 + ...ophiæ_Naturalis_Principia_Mathematica-9.md | 33 + data/en.wikipedia.org/wiki/Photometria-0.md | 39 + data/en.wikipedia.org/wiki/Photometria-1.md | 35 + .../wiki/Point_Processes-0.md | 25 + .../wiki/Polyhedra_(book)-0.md | 31 + .../wiki/The_Fifty-Nine_Icosahedra-0.md | 51 + .../wiki/The_Fifty-Nine_Icosahedra-1.md | 58 ++ .../wiki/The_Fifty-Nine_Icosahedra-2.md | 43 + ...The_Fractal_Dimension_of_Architecture-0.md | 32 + .../wiki/The_Fractal_Geometry_of_Nature-0.md | 23 + .../wiki/The_Geometry_of_the_Octonions-0.md | 37 + .../wiki/The_Ground_of_Arts-0.md | 24 + .../wiki/The_Higher_Infinite-0.md | 33 + .../wiki/The_Petersen_Graph-0.md | 26 + 101 files changed, 6136 insertions(+), 7 deletions(-) create mode 100644 data/en.wikipedia.org/wiki/A_History_of_Vector_Analysis-0.md create mode 100644 data/en.wikipedia.org/wiki/A_Metric_America-0.md create mode 100644 data/en.wikipedia.org/wiki/A_New_Era_of_Thought-0.md create mode 100644 data/en.wikipedia.org/wiki/Extensions_of_First_Order_Logic-0.md create mode 100644 data/en.wikipedia.org/wiki/Felix_Klein_and_Sophus_Lie-0.md create mode 100644 data/en.wikipedia.org/wiki/Finding_Ellipses-0.md create mode 100644 data/en.wikipedia.org/wiki/Fondements_de_la_Géometrie_Algébrique-0.md create mode 100644 data/en.wikipedia.org/wiki/Foundations_of_Algebraic_Geometry-0.md create mode 100644 data/en.wikipedia.org/wiki/Fundamenta_nova_theoriae_functionum_ellipticarum-0.md create mode 100644 data/en.wikipedia.org/wiki/Games,_Puzzles,_and_Computation-0.md create mode 100644 data/en.wikipedia.org/wiki/Geometric_Exercises_in_Paper_Folding-0.md create mode 100644 data/en.wikipedia.org/wiki/Geometric_Folding_Algorithms-0.md create mode 100644 data/en.wikipedia.org/wiki/Geometric_Origami-0.md create mode 100644 data/en.wikipedia.org/wiki/Geometric_and_Topological_Inference-0.md create mode 100644 data/en.wikipedia.org/wiki/Geometry_From_Africa-0.md create mode 100644 data/en.wikipedia.org/wiki/Geshu_bu-0.md create mode 100644 data/en.wikipedia.org/wiki/Glossary_of_Principia_Mathematica-0.md create mode 100644 data/en.wikipedia.org/wiki/God_Created_the_Integers-0.md create mode 100644 data/en.wikipedia.org/wiki/Grundlagen_der_Mathematik-0.md create mode 100644 data/en.wikipedia.org/wiki/Grundzüge_der_Mengenlehre-0.md create mode 100644 data/en.wikipedia.org/wiki/Higher_Topos_Theory-0.md create mode 100644 data/en.wikipedia.org/wiki/History_of_the_Theory_of_Numbers-0.md create mode 100644 data/en.wikipedia.org/wiki/Horologium_Oscillatorium-0.md create mode 100644 data/en.wikipedia.org/wiki/Horologium_Oscillatorium-1.md create mode 100644 data/en.wikipedia.org/wiki/Horologium_Oscillatorium-2.md create mode 100644 data/en.wikipedia.org/wiki/Hydrodynamica-0.md create mode 100644 data/en.wikipedia.org/wiki/IJP_The_Book_of_Surfaces-0.md create mode 100644 data/en.wikipedia.org/wiki/In_Pursuit_of_the_Traveling_Salesman-0.md create mode 100644 data/en.wikipedia.org/wiki/Indra's_Pearls_(book)-0.md create mode 100644 data/en.wikipedia.org/wiki/International_Encyclopedia_of_Statistical_Science-0.md create mode 100644 data/en.wikipedia.org/wiki/Introduction_to_Circle_Packing-0.md create mode 100644 data/en.wikipedia.org/wiki/Jade_Mirror_of_the_Four_Unknowns-0.md create mode 100644 data/en.wikipedia.org/wiki/Jade_Mirror_of_the_Four_Unknowns-1.md create mode 100644 data/en.wikipedia.org/wiki/Journey_into_Geometries-0.md create mode 100644 data/en.wikipedia.org/wiki/La_Géométrie-0.md create mode 100644 data/en.wikipedia.org/wiki/Letters_to_a_German_Princess-0.md create mode 100644 data/en.wikipedia.org/wiki/Letters_to_a_Young_Mathematician-0.md create mode 100644 data/en.wikipedia.org/wiki/Liber_Abaci-0.md create mode 100644 data/en.wikipedia.org/wiki/Liber_Abaci-1.md create mode 100644 data/en.wikipedia.org/wiki/List_of_books_about_polyhedra-0.md create mode 100644 data/en.wikipedia.org/wiki/List_of_books_about_polyhedra-1.md create mode 100644 data/en.wikipedia.org/wiki/Making_Mathematics_with_Needlework-0.md create mode 100644 data/en.wikipedia.org/wiki/Math_Curse-0.md create mode 100644 data/en.wikipedia.org/wiki/Mathematical_Cranks-0.md create mode 100644 data/en.wikipedia.org/wiki/Mathematical_Foundations_of_Quantum_Mechanics-0.md create mode 100644 data/en.wikipedia.org/wiki/Mathematical_Foundations_of_Quantum_Mechanics-1.md create mode 100644 data/en.wikipedia.org/wiki/Mathematical_Models_(Cundy_and_Rollett)-0.md create mode 100644 data/en.wikipedia.org/wiki/Mathematical_Models_(Fischer)-0.md create mode 100644 data/en.wikipedia.org/wiki/Mathematicall_Magick-0.md create mode 100644 data/en.wikipedia.org/wiki/Mathematics,_Form_and_Function-0.md create mode 100644 data/en.wikipedia.org/wiki/Mathematics_Made_Difficult-0.md create mode 100644 data/en.wikipedia.org/wiki/Mathematics_and_Plausible_Reasoning-0.md create mode 100644 data/en.wikipedia.org/wiki/Mechanica-0.md create mode 100644 data/en.wikipedia.org/wiki/Method_of_Fluxions-0.md create mode 100644 data/en.wikipedia.org/wiki/Methoden_der_mathematischen_Physik-0.md create mode 100644 data/en.wikipedia.org/wiki/Metric_Structures_for_Riemannian_and_Non-Riemannian_Spaces-0.md create mode 100644 data/en.wikipedia.org/wiki/Mishnat_ha-Middot-0.md create mode 100644 data/en.wikipedia.org/wiki/Murderous_Maths-0.md create mode 100644 data/en.wikipedia.org/wiki/Murderous_Maths-1.md create mode 100644 data/en.wikipedia.org/wiki/Mécanique_analytique-0.md create mode 100644 data/en.wikipedia.org/wiki/Number_Theory create mode 100644 data/en.wikipedia.org/wiki/On_Numbers_and_Games-0.md create mode 100644 data/en.wikipedia.org/wiki/Opera_Omnia_Leonhard_Euler-0.md create mode 100644 data/en.wikipedia.org/wiki/Opticks-0.md create mode 100644 data/en.wikipedia.org/wiki/Opticks-1.md create mode 100644 data/en.wikipedia.org/wiki/Origami_Polyhedra_Design-0.md create mode 100644 data/en.wikipedia.org/wiki/Origamics-0.md create mode 100644 data/en.wikipedia.org/wiki/Pasta_by_Design-0.md create mode 100644 data/en.wikipedia.org/wiki/Perspectiva_corporum_regularium-0.md create mode 100644 data/en.wikipedia.org/wiki/Philosophiæ_Naturalis_Principia_Mathematica-0.md create mode 100644 data/en.wikipedia.org/wiki/Philosophiæ_Naturalis_Principia_Mathematica-1.md create mode 100644 data/en.wikipedia.org/wiki/Philosophiæ_Naturalis_Principia_Mathematica-10.md create mode 100644 data/en.wikipedia.org/wiki/Philosophiæ_Naturalis_Principia_Mathematica-2.md create mode 100644 data/en.wikipedia.org/wiki/Philosophiæ_Naturalis_Principia_Mathematica-3.md create mode 100644 data/en.wikipedia.org/wiki/Philosophiæ_Naturalis_Principia_Mathematica-4.md create mode 100644 data/en.wikipedia.org/wiki/Philosophiæ_Naturalis_Principia_Mathematica-5.md create mode 100644 data/en.wikipedia.org/wiki/Philosophiæ_Naturalis_Principia_Mathematica-6.md create mode 100644 data/en.wikipedia.org/wiki/Philosophiæ_Naturalis_Principia_Mathematica-7.md create mode 100644 data/en.wikipedia.org/wiki/Philosophiæ_Naturalis_Principia_Mathematica-8.md create mode 100644 data/en.wikipedia.org/wiki/Philosophiæ_Naturalis_Principia_Mathematica-9.md create mode 100644 data/en.wikipedia.org/wiki/Photometria-0.md create mode 100644 data/en.wikipedia.org/wiki/Photometria-1.md create mode 100644 data/en.wikipedia.org/wiki/Point_Processes-0.md create mode 100644 data/en.wikipedia.org/wiki/Polyhedra_(book)-0.md create mode 100644 data/en.wikipedia.org/wiki/The_Fifty-Nine_Icosahedra-0.md create mode 100644 data/en.wikipedia.org/wiki/The_Fifty-Nine_Icosahedra-1.md create mode 100644 data/en.wikipedia.org/wiki/The_Fifty-Nine_Icosahedra-2.md create mode 100644 data/en.wikipedia.org/wiki/The_Fractal_Dimension_of_Architecture-0.md create mode 100644 data/en.wikipedia.org/wiki/The_Fractal_Geometry_of_Nature-0.md create mode 100644 data/en.wikipedia.org/wiki/The_Geometry_of_the_Octonions-0.md create mode 100644 data/en.wikipedia.org/wiki/The_Ground_of_Arts-0.md create mode 100644 data/en.wikipedia.org/wiki/The_Higher_Infinite-0.md create mode 100644 data/en.wikipedia.org/wiki/The_Petersen_Graph-0.md diff --git a/_index.db b/_index.db index 96f49e3877a55e07f32967fa8ef6c8e405e7a880..9491ccaa5bbe2dd440cc8a0f37c6ae90009ea877 100644 GIT binary patch delta 315198 zcmb4s2S5}@+yBnYmaBU-m8P6vLjeyI6;TljsIg#)B}R_}4mbr4?;wgPNQ$Nq!Dw7H z>Y^q_qsA7!Bu38?6XRR|=4ms| zyLdik-o@`@>Z8ohaa_h8uIax;U3!z}w&%XsUDrlG7w%m#}kON*5^vet&d#D#!KSxI2pDdQI3(cGjlN>7`4RS7O=P#isINDzDu6KzS!w z;<(fmHHW6`T=z(RvN+ph`N1-Kr)k?vORE_Mo~xOR4Ui&gzUt4J1w!b?B1RLDqm+cO#ryp|O@EAe?7HjGhI!sck4}1Y|L*;SY?BNr-0yUPr0B}& z2eJHkeyH$>@wD-S9r?(q4b(d zf2lU`Bn*C;dwVw;l=kF}|+*ID6h*Oc}+3o4_V9$8-EC@XVCHWhFe7KR7& zBo=BcbyO5P0bDa%Hx--VE-njeO1nzSogpTkq=!S+B4?SiBFMs%c5vaG168`poN^FP ztZ-f6^5(lAaC%&(rVRP+vV5nf%xhS1^+D>p`XGz$DRA5fZmS|~W4UCSQoN0|5BZ2b zONWxbiH)4%ekZSy1)Q>`AucSa1G|Sh63d*k6P+GMqPtLOzhYr1b^N5fw2gICR&Qsi ztsGYq*i^_=?DAH)Jynn?@d2k|^@-u4<6rUYUaFQZ_OlL(dpqlHva-RDwbWVRapfzs z&bJE{9Y1ttW2sub{8JLU;Lq(0hzAmYMBks=CH?noDmkD?4Z3?N?Wf$|pqna$lCQ}D z-@XPNBh_8lcv|fCxJ%qcuFBFxw>RHaQsRJ?;8lt(rI#($mYSI2IR2kyOm@8gpJlW; zj@ei~ZPntn;R_}LK_@6Tys53JC5mB=Cllsr4DvVfF?ox;Pqafk6aqsKVbXfp;Gt{WN++YI%Fazl>6W(d~*tp8BIU0m#BO4U@VjtPcvpB;cvP4ubQSdc zH~dk43t!KB`TKYqZ(!HiUiLJb#9Gr+bO{|#JCa|?dt?JyKnlrF5(RG-&U(;tr=tSq zS^*9Lb)YhYbXL=r4I#bM`o%*?D>WZ*ggVaf8;ul4j7enEsJeQ=X3|+o>7d@e>f*bx zHa>?chAr`vcpSOvt>x`m6diR+$$Tk3L;2>__*KfKhWOU3=dfZ-+@oFjmcA7K998CR ziGNEe*$^M&%ia**kt+UI;}ev+SK_U{+E?O}sp8lYAEPW<6Cdr%SrcDLc9&cDZLE+C zQY33oDuuuOtU-!$${JMKHkzf=5=UZDqPsK^W{&gDxVAa=`t0q4UTVh*xK9*mV9+$t zvcs^+Qlk_O3>w69zro!N1A`L!M6onl;>vS+5*>MteAk^Ck{uua+uv-C^UAi&pm<;Z z%%EO!NpJ~Fah%_dd`E#3M}LX4qQdF%CRVr;9f?)$%Ce%w+l(yV&=<8)cK_+(aWXy>d(<7>w0MvK8`s4yhzujyCQvHCH(zjeFmQeBZQPWoDU znJnh~(qzdZ`o;NTZ)y=VlZp}dVxC=b7ND{=t$JjZ=T%7JGDk&lSV+j+tcvd6jSmFV(_S>iyx zhESN*KZeG28eV44sq}a&T@}rrae~M3fU^WXlYP9S#OZ}$92KUJlOfQGiu4^?AC=*PXH1|sfj4DO8mAkh>!KslDd{!oImsi9lai$%@dxp^xJ9fL zXNn`lcu^;ODI5_t2u}*d!Z4wWpySW+uk(-dxqLr9oc+$uvpsAjdzejReOL&+=?gA5 z52DHzCC#eHtI|5fwq^ZkaaDoGT~Jl#D0SsKTC$ZBo!A(vZd-niwpVf&rL9tKC~57L z@0GOb0DpfZtQ+w6(IU(|DHMxxX_m)1^sb9tImQCDK_`m_Y~(!FO%2jz>E zXlx;8G4E4{vF^@ej&u@sE-_T)xL&y0Io#r=mp5M@=+MqLWPVNjReJ;H&EtCqR zAySOQ#0%nnagF$>m=8;LN0A7h34URTP%2~z5&SJS$a2YY*s{(t&ob7MXbF*jme0z2 zses+ah1D3Ds2|QTaKAzTb{8mn~i0w|IdZ{_l>s2!j;}^!w#@WWf#t_4Yh8GMo488Q<>i6gu=*R10b=P%o=@#fF z>$*zcN!z7Ir7X!Lo)K4z#bOWPvY-kDLW;oir}>S1>sd5|3gmsVntPp0BptY4h=DuB zf%F!mY@eo!RfER-N)4^O_E9KR4RI9~y7DVaDxx}Z9D7h>V(P_>XQ^H(S`yb&ag2(I z3zUfR+JRl#b4nbQURNFnSmT@yue%IItd2_Nlx}fL-^@2qev(3ZH$B8;D1nC*x$}f z648yusqBm#gVIK|+pm<-};WRCW3>b9fM zX-X$G?!3~zQ$h!IK;AA`;UY&V$=Pk<)c$ZKwT1El+e5zBKHF7MY#;4(7L+(=yFD|b z+U?Hm#_uOR6~USiL-oHX9jpl>eC5`JC><$N7gY-^Mp0v?xA7h9lF*Z=!Rka77vl03 z1B0~}I}%5^3JTm6QAvTOUGOeuVGA5x6Mzzdl7PAc*?^LLj;<-|?q%b-Mn#&J(w%ZY zD81&TjH7V<PYUNZ%LrX}^+qv=g{yl%vX@nCEuSM9s)s=_z!8 zGSgD%XjCpnMaLLY;$qsfp%kzVG>_Mn`v~>a=NR zNe?AvMcO*iq;g_$r7|!&I?8u>McP|n8sNCl;!0GToU6AFjwCa^lqoVVLwVIYn z^beBA1>;wx`Nps6yZvVCOpw% z@5a7lyV&Dw0*j;<=>|GmrkUhh@(L*+UAe2=3Ux-~B$lMqx%UXl*01`d+qv$B2<`PUONyL%9)~NxS&OQQ{4=09VIH;oa~%owH$p)h39yoF zx00C7A9N#$O=rrD57Oh*2hTmlf@oxSWz9$F9lE&73Y?|RvI?&qxLk?Do_%OzlXhl@ zXC2y@=W)%dbVmN6Z2ux8)?fcq5*r3A2Y7+nxa1io)5xTNLc1_$QK)MEC5g@D9emB; zz;}FgP(JIY#{ZebI;$5?=CWuSk*d@Tjfqok?PwFNz606UYM)tc`&SZ+(zG9S^U>+7 z1C3Z8c&&kB7YSjVk`hydSPWc9J%lh~&U`51Jj>n{xu)qTVBfdxh;1Ukj~M-mg%j9y<;BbA?4 zW+f%WDz>hNb?S3}C$V|+FQzZO*pDYkig2;tc$3A(EwOm$Y7${u;48S;@4ShUpVYC# z-(y|;{Q-{SpyUV!>NK z^aJV-Gyo_AXdqA~&>*0}Ktp_Q{V;S`IT@n}xmlyAVUIE{H*1`4eQwrcI`X`)t1D{} z>41hkR~bAe5u{9~!&Bl7u!-A7Nt@#X--Q`jai_#@xK!>vPU#aAJt3BiWL@Dq-lV7L zE=xKs28sAMsUc?W8~M6?T;43tUz8aoX{@Bwp)>?V-@_a8Ifv4|dhk%CXK-|QYEL#3 z9-LSnP+5^JA&aVLR#_9hO)6_kCUw$R6CC}y9yCX`)m7>!a;nMSr;{+>yr}3Wc%P7y z{Z|am)uCXTv>dcNW68EyFj3nJJ?>KbFh^-A=m6y|JD5O5I>D-5;BiJJ2j4Ge!adn3qEZvAk5!NFpU#45#BR+xp*_o}%$}3|fs*Xf#VR?EWb0JcTj8}Z46i1&&{5t&9_G1HC03vKjE2)z4`~xyt#;*8QC*plPh0yEAI!c<12c5r*ts-p!O-e#pkYA6fkpt` z12ht76wqj(F+e#$V}Zs2jR%?lbT80Eph-ZJfu;c62Q(GvexPYU(}CIr)>6bvgO-QJCeG>pA(oSn~Z&<*%{%;cCr?TUe-&?D({( z>duWY>iA^A+hg;A3V@tIg+N6>#Xv5g89+0EN_=mRE$#o0NV33W^`TG7Da+7QUQqk* zD~nrDI=0MLI@Y~pIu7jnxwD+*Q_E|Xr!3PgJuEu;EBRgdC3y~5!@J0w`Kznhxe~3mCumic7?q13`UmD|{!sC%i0F3zLOjLJ)tA-^V}C zm+)ixR_q#kgJlBye4lQi57M!;GdOBKCws{vQbZ)~Ea|@}Gdw(r*(px*LXRWA!cme~ z6fo*lDJQFb3X8TmcBit^yD}8GV41;XTD`GeCXtfOu?xL5%4e5zz*+OAds#JJYE`-l zE2|t z!{<&CX7e>}s@4^+ptGoBy)tEwd#4igy1SENe%<||V%YAERgS&k?#!cSNoo9jQLHlM zEq4bcVY_>+(ta=GTlbdxW##yG_i!E!E6Sx4tz(qZz3yVA%?@{bK++sN_ZW*%Ztiuj z
DGdQ9Hb*xZc-{($N2JUc2E5UwuM@9C#$1C^mfZ82?w?}FFrn{^1q2HazcVwfe zaw8(is)X-yPf?!P;Vuwz_?q@q{T^i45u&3WbEp?j0NGz^1}}IIOUsN(7eo@ z?n13)>ZR@vu^7?uWGu_3YTK?)u(mX}jS{@ueUe9Wy87^sb*!^!e;Jnpb@igBXp};H z?jefxHFp=~=1%wHO1;k=uMG9M+!+*@L^F7e$HG-pJk_>C_&Yy(V+Bg^u_DEG zSs$~Y1?N8U0#yK20zCjU8)yzt70_Iu2Z0^}df0dFqer@>vmz3&NI}){6#m+Rs$Udg z-JRj8z_p>fVhpZs*9FJH3^2TxIja)U;@vzsTz3oVXMAIWtG5m4O%`%JxVJf4W?XN~ zr^)0J*({%uSILFO_Hv~8vU#a_x;f5t$W(9m#&nPII`=l2Lb>63peBo(av_?csyat&!_5P|397egcR zHRba!b^BxCV96dhHI!EqmrrLYG~(rey98UOUVQR2i}GD<^sb{y!?*U6 zNpcS`2ktRfn+Mb0O5gJ8JY{Wp^<$)!a-(!zj52gq_04J&xR75JYratU(t(bMeJ zBRG*TPm$JxnllS}uw|A*=>OBQG;z>o0m|Lnoh@_wk%4Hr-3xYms(rgX^F}|+`f&3V z>H54;6#h=QJ}<8SaIjr}$qupAtcndsyODEFMS%NyvHC((k`mphBqgFFJHO>4HY+(d z=EW^IcYPjE4bY=Nj{!Xn^aRj+panor0zC!vG|)3ZwLs4TEd;6qss~yG^c>J)pd~=h z11$wofR+I*2U-F2g74h*m7Pzl2DeGPFFv=;$Cd?r<0_!lKE6@?`g!gIQ<#*3@Wv&9sa#{rB*U`o@O1DXaAkeFtzUoz`uI zN5g+z*(7?$Wa|YBUx72RpxG?cvID>B!CZG`Me{j?O$6*gs(tJg+N#>|C4R{}6*@{v zph`3XwXEt|H#X(2Oo^rL0w+lJg%EcE4)~UNui%Q?vcl%P`7n2@G#fsIEucpfN_A=q zRIoX|=+7R$yI3Jkb_flDnXFiU-x;RI4@f0Jzp!U&o>P4-FLp>6|nfwdlkvHCX>S7VYW5*8R%TLo{eW5-Qs)I zw&rCrS^F}H`HnJFeW6lENmYfGY*FPmDXa(@fUeUP#$InC8nhsQrP-j>vK1GW_E?j% z;O~?*Kx=(}r>v9OvVq)_ij=diH-*0ga@GwC@LXVYg2johZfBW28zv@;J@9wST!E z)X!?iI-nPUUh-8t)<3Grr~T9`d3wnv^Lyqe&Ew7OO+T9sn-r77 z)ZIjl?;C53LyTs_XNGx(@rG#qRsACUFpxtp>o(|S>(X?xbY6N%DwVp3zlkr2GsJ$P zK{z2a2p%DW|BZi-e}bRDN3*MJ19Pz?`VW0Cgf66$Xe{}O>;^@2B)I!NSd4|x?VGEDh&}&NXmz&)8}gn6JF|+QI2vw6{l(T+rXVq_Wl$?Ljtx?yu&LQKU+j) z=DGCGH0zUMIh8JJK5Df={hYQ@9zCC)8LsNyJE+fmU?3sX++V5rAia;W zC>#{D`@x)HrV+gYMks6K^OSGvO#r{`+_~VOP0);0gWaX&l@;1dio6xjGW~> zE84YEy6-0=4GDP3)tRrvur@UK>3~94J!qD^^po`OwS`X2dGAA%bl%m}DJAIB^wwy& za4DBQ0JH3{Pt&utW+@lPUoq2=Cj(yhh8SlX<;bV$MVes+`>xaNUNm&Em$@HsV2}XB zE;*d`=6O?DYImY}r2?D*;9Q9OCom+px-Nt$`Jbg1Dx@MJP90s>g{IL6UQGtWNu2WS zXX*3Mo-|UkrYJev+XN}*-t?DY%jlG^yx3b3t^Zv$U1<5c>IfF-CgzN4T9z4;Wp zd8AFV&!`vmAF_5d{6$4Ro!(WG2i5(Dx`8GeytT<>2v?G_?adbjDr5w#MppJA>!4PH z8R<3Uv$N@7)&ZlR67=ao~q40O2ZRb6{ zb+(-bYDs2J+L93;e=(?ydUV-EYM_qSd>2x7cG6SF&IM9Gq}PCU`J{fk|9&hill;P& zj+$1QN_3q}J&ivaeYB&}djIZrl>FlBxqtUQ5*T?o@9h?JS{#NWDqWc+M8~Oh5rc`L z!=d#7Ar0M?_8bhBK_47=C}5}n$A#XAg5VeMkSOgUjz%unad0<~59oEEH-O#*+5_|! z&|aW@Kz^Y8KnH*h0v+=0IQaIs@1h5BYdKv9Viq#MnEJM~OmgxGQZn}m8?U>nL~lD> zvM95)x*xp9v1<2o1+2C2{INk<|YOjjiXc>A5qyJShGsNj#LJAOwXOh&Wti@ zj8i?aY7giOTW9V9&&H=a4?n?^1!`t~9J8)=$1#KQ?CXc8D3nIWMr$?AJ@i(QGfV#3&f$G#~n5SFe)E$9@CQgBN%O5Ki|M59zYCLk2`5{r$Ll2bRMbf@~$USUbTuT!r1htlePJwi9`TJ!yS8H@IA?_V zYn`d_6(ynmTBgrkf6cC=^fSe=;##7jo;VxiKmPhEwu&n4$LV6*3`Y}iXPCK~3E18R zT}AOxt(38=u60mX=Q>&Ng7B5sfW8F!3g~N~Z-Bl9`VQ!OpdWy)1Kj|+3G^e-Pe4Bd z{Q~qW&~HG$1N{N?C(vI&e*^skbnBV$m81>`fg&&j9zj455hMg1f*!$uU_>w>m=Rg>AHK2;`F3zfKM1s<7wBR-m4=X$q+U9!hFxq!X8LOYqXigv zDw+H^&GN5^jv_x2eh^dQ#-RcB_S ztyL)~io{de+HZrz7o-Oo!$8r8AfU>C>$%Y`3$Hb!8z@ z#9tN?O%|_0v*0xD7zet)39Q`L%m>ZSm?xOqny#9*n&y}?O(Dih5C;2*aRiwE{s3|7 zfZ;{M0>ezh7()+38~va93;IL)m$_s5$3b-&AU~&7EP9!c?_OX%OkF`@VZy`MH7Iw2<;GJ5UdF85n>VI5IP`qMCgRj8KDb8JVIB5 zZU_koi3mvu-HHFzeKs=wl1NT)Q@Mkx)R0W38MuSA6ZxH-p%1AAa3d*$=0kvRsn}Jx z2H^se1Pg=!RrBfWSGJS6SvPu(u5m)}H!^`HlP74;sNhvVC^YEO$}F8Vf;!$%e}UT0 zWzead4l-7t!R$_cLnDN2+V!X@k|tfLW|(m!5%Z)}u?0x_xT~5&yn5gUR6Ujg}?cOcKml zu2_!xf^sc{EXv`1!4At~GTQcgDa+iJ5z1z_rQO1YA!K30P_nNfix4Z$vgzD$?zYWm z5V*NMkT=K=f$6;inBKnxtIsO)!{*869%k9}mFb}A1u(ulO;+P?#(l=eVfNXK2E%#7 zD~7p-EJHh(cW1%)J_}6miF%{1QMW}`rz_J<(hbyEq#vXc(pCsyn=YkEVGwwDM%-L2 z)`%0uPQow3JHk?77BwNlL5MdMw-lvmv2dF|bXeJFOKah9G zDpEo2A+ZpJeEUCSC57lCPn?N9a&07H$XTT~vE=T+?JXETQ0P>}gIUC?raUnLgs7?` zStNcn+~~wor}y3m35cn9>qHibTKsUgj{Yf!vPd=ogY9^#wmWo^#?hgfYQuY3WV3qU zZO9~y;%lO)^6|1O*);2@I`U{1*{^;Aztm`}TcP6tm)F~JFl8In$?6A(vq+M9YCq=v1nxYfz6m8_wa}wNm_^_wNKWew zdoG$cU)XXBR=<-)x(I{$8VT(76;A`3$<0?+AHxUD0UWNG>Q%@2C>AS@uGUucZ|6P@ z>Su1A{{Uq8hN#P-ifHu{cvPgi`FIu?t=@t=vFaJXQGqnXHjP!EhUQt-KOjdtbsD4- zwRd+`IcK{(EsYujV%4V)WRVW44f^+SwF^`;OnnvZjMMCG>hterkrx&=W|4)B*+9d9 zh69ZNx(8?^&?unMKx2S%fW`uiBl{Z16Mh?+q6+gSkXcmduRZ{Y!TvpfeRwiTIj}4> zTs6T5Pi~L#8in8_MyrLUR_fl!I?0K#m9IS5q(!cz!O zBRqppi|{PMLWDYmdW1y?&mk;ESc338!cqhUVHv`5gcS%cAgn}Kg|HeyCH^+^8_3sb z{Ye;?1+i%m+2+#q*9A*gq?aX^)J^*X5Pm&hD_VuWgtNj{VZJa;=qU*N z*Zc|Yl&ag`Kqjis0cNT>gCQi4$8aXK=7ncjr05t4F8Dd>#jW#LjKBAR268XUM%A}z ziORogc>Im5pn37S9oCRo;PkqR?lQRjg|}< z<-G=Ct2=k3f%wlISwp%Nu}MT$CEHq}K$Ha}S3|OsdIT_QAhs4<=b+cQfvus@uSKJh z9Y6kmf44bq){RbHO90j(yom4;!g_?45jG%fM0f>Z6T)VMEeNk7Y(?0HupMCs!cK(O z5OyK#M(`oLj_?M;n+SV|e{}L&WcP70Zk4c?%qN>yJ-wH--@9cmDU!(x>PdAJNmK{H zl$#NWHr&G7F*(q)iA@`Eoa*t7PvZC5p$Sc8r=9|#=^rQqun)nHupi+7!a;;X2yY`C zMtBF|U4$bD?;#vT_!q)4g!d7SBb-2JL^z4?0m6p}A0eDVI8FTjSk92=c1p=zk~uE; zm`Zj;lT`n)LuW|e+OErC|3L3zmdZHuGI~mXFSp!$LcS>1DkPAtklXUbXf6$zQbiEW`A zTY*;47SShSpH}b|JJgtrHDs9o)YP*il~BGCwEpN3QqTDFmM&a|AH(JTMW|(g+SPuR z*hMZ`^Ncpqy{vQHZny<-4&gk)#|WPwd`kSg?Vpj+7n8Ed1=vrKe4pVD{XNDd=24;^ zChaESAt6~XvC;guNV z7wb~mT9UI8^l6+9`xKh;f)@QNC1^~Q(`5Q5$A(68hc>{$Lu*&bmI_xFD1S8|qA z-^16m!3scTPxMxJK>37NUCkGg2;25baqlmhfIvGb0~azo>s*U#~CLXXsn& zzSF&}dqL-cXke@Kt8^TKb{>`{NZlkVo)fpj8t)h(risDASHb}ZSgR5y2;Bt(f0aMT zujc211uX^kwtUUrVhdR=OM&p=)AR-EqABE0@;1!XLXttkVWa9%4%G4MTh0RLcNorJ(g0W+h1PfgRTW%YF)*U4gm*B>*J?B>{B@vH>Lnr2zE+>Iswz)Qj%R?M=!4K*ZI4j{8bhWRE;b7R`S1 zY_kp2yS1jNrZDhf%{OKkTN%EA52P4M4Sfxg{v-VweU*NUzN79>-FrGk=Y-v42|7K5 zYVVVlN@bR_+mE}>i4Q`Y$w{yp9uJjIk4TVd%tBY z(*MQuPH^f#onY%j{emrx-cnPNNDl1!OWVy~5;o|5l^?TI>Am7^$pbdrhjfY3D{`aY zwse8_^ongQd!#gyqxNh}gYW19yoS!%)PUzkg^in5xbFA7LfrrAstz1Kng#n$pG>1q zv9RtO?BU}m>&<4t3IXxYKmm(7Y@0P1D~etDUVbZ7#%sPT|M634G?CDh-slgDQ>|yx zs72N>&M<&g(_&chNO!Hcngp9vgT+?Az>>Z%;GLVdy)`rIgZ`=t!aaEn=9OHWGPbKV zM*ZrOG`f?Q3%FGEQY!+EGuSOFsJVX}W0L>Gr)hLBArV@zODn81Nl6~wCJr2FAzk5; zey9YWNQtX!xR6Ex`XZzw^h4;6FaRL~VIV>#!XSjf2tyEtB4io%LYnRjF|dZENDQgi!tnAHpwyTV3H+hTjc1lc7^GPT7_gDg+JnI52)^ zLNP|bRz%s)Ci%@}3iSPizY=k)oRS0tt9z=Ku z;bDYF5ULU8A=Dr|itrf1;|Nb6%tu&&@Fc=h2u~wCgHVg`EW$#BI)r+JMF`I!EJj#@ z@I1m&1O;Ik!g7Qa2rnS4L|BEe8bL*9Kv;vY7GWL2iwG|vtVehmVFSWOgjWzYA#6t2 zg77NBR)lQ`+Yxpk>_m7CVHd(~1Ruid2yY;~iLeLZErh)Y`w;vH`w zgm)0$ML2@+9>P(Ce<2)0cpu?7!U=>%gp&v#Abg1M5yB~i(+Fn}&Qkw7ADyEEy0H{# z{3_`@ZA+!`dpn$`iBbaEf=dH?mcRj*SgP$=YRScKAiKvvA5WQj=|nMWTelKw0QeZ; z6NFC@K0~;Ga1r4W!spb#Qo2lwyF?G<{2cd>crTc;uL`e$dNEKC`9^*PD1TXMJKJSC z-JrA4;SleCm26d?gc}krC~4V1;VhuxM}IuxP)tVKJ(Y=Cx9w zUS5f=-4$H7sn2B!@CEg6>T`uoYEvD`6>?v3mW!6du({V^Nw@_R_f5{*SnKr?G ztYiAk`dWR7ex$ymUetZbeMKU4yWr@M;kr=Rc>K1sTyjYLr15RUo8Va7AU-A*ikV`x z@T>5F@FJ}4!-Nj}AF!2h2fvV?0p5|0yn+1yQ3#va6Kopm1*ZmlNe|E!)JsRgp&{4F zF|rGG&OAu$WbmTQR`+3)Z_#b9_1zNpU1Ijzuuh7_j@$X?LO5w4`yJPG%h7XKy$BIz z5$dOaOL%k~CtZ`RpSO4^>SE!w+ z7jv%ASeBYw-IVH?`-qn6*mRwe`%qIVIrqUpO0wn7#kE~Me(MxV5vLE<{9FU;ud
iqk&POc^zqPS}2sTcy4_?Fx-i|AAI?_P-D59&(xZU9_E_!8kOgs&04LHHKoJB05M zexUw;GOknBAetW~ed!Z$63Z7A{)aDKr-b?+`usW-jaa*}ZvJ=IDZmYco76x5yC3Nz zkLrm2OHThKtMUa~`;;<&mG>t)t4PW9w-NL`QCkpU0!Y>HFBK(H% zJHj6be^v_@!y5RMRm5Qz|l5RK55`42w==A0TbWR(!Z zI#WShl@P-wn)oB!^TZ6NC=C|Pd+TG^&x~X#HJ)s%l5s4x9is!XL1KrUhBk|x32p3S zFy;cbJOyGd>_ai;BC3ZL$kuvHS@ZceTEtv79x@S?q9j*j$Elk(KFdPtyzpoMD?)pO zSmyT%actpzlI0=TAodZbm>S_E9Lou1P-93ewJi1(G=_v*!0N>fVRH&veScbJc!6PbUVL8-a-T|m1P$!_yKwW_1fw}^914;l&Wc$jK z7@1eiUE%t1FLJOV9E0^>3T&r1%U)qKEr%>iEYmEV;53Ru^3(GD5P*Ey{Hpl@IOR%& zD6Lhn(X^HEh_S*r&=?9X{T&7uRC3eMo+Rmi(C>xiX*_He{y}$8XVg@=k#<0WWnFBZZspQkVb5oT)3!KIFOwCyw z1t+eMb6P-_b@kkS%%tWlo56VX{Z$s&*SqZP^~*sNfc=z)Y;-}}^D3hxrTrubAA9z6 z`muoi_kRxFyiduA6h)A#19cXIMdp1$s{CGVx(#Rdktaf?` zGJMY_DQWMohse+!5E^NFqMmhE!~^Rae6!wPUq=HP=}OlXYE}*%T(1T;xWLOxYP;k8 z;82;6+S=}{*2Zd+S#1id?ZIk$vf5Nu+l$rqX0?4-Z5pfX%WBhEZ9i7qpVbavwHd5- zAgj$}wS!pgU{*VX)edE~S*$jj)ed8|!&&VJR(lVt9m(Dr#e^J5+QUhE^g|$u)^80O z&t8zK>-#Uk<8@$vTEio7UgBnIbJV=e420A~z>$S{?#c?d)WM~hiC%X}WrZ_v9c!ji ze!jCDj1X``B;-NHSAaLMDR&zx78W{ScR}FCew36!3abt4!3Y+CqZlJh5Vo(=wI0k! zRUlsA9s$ zfSvKTe}wJ1&94*Abg(fszZwqEXs)Og;o;b)nSntnh!i-ATLxnpfOE(A_X4eKAXPAC`l-)1brotGX~zj zIa@cXYdZC)B=Do1h;Z74tNDfJQe#*u9JPaw+69ZS1aWdlg((-0VTB{(Jjj~E_ z)7RvQPzL?qJbz~}37iHP>kFkQ(^2i);iI}z!8sdtbT!om@7VPAW~NOisMp0)ts$7b zJEk=%JR?o7yV=t-wXn{rT0pw*-hG6oTn&^5YqyHLttum(!@WVc%YTTgkA ztD1&`44yc!CGs)6`HrTsnPH@d)>~a@2{|*OCR^~x(!KT!v5`BnaR;8n?!c_tL z`vUijlZXVCTKF(c&zQnQZK5}qsgB|$cTpLHa5W7s*slhshz7nL^iZfooB30RVBo;z z(6dc1SJMu@7;c%n-GClMLcd*L_QDK<_k#i7{CdM+W;gwY@0Y55#%dfp6%2ewfd)^~ zQvqH=W3)J;JI7K1f+24|q93Eqa>xp$hA^qg(bV+*Nd&%<13wIWPcbDvx;sb=SZ^dD zl6j&eMw(iKzRgot^B|V_YJ!s)+GFi4h+b#O1I?`+$!lu@{1R5kfCm*db>Kbx?HSgy zc@==h7y^S5=5T96=T?&$D{wUN+C1PG8lQq(9eJvaetdtC(%J5sYVB2K5doscn+KSQ zQmv1nKnky|Rgfwmz-m3nD4X6kjS7_|Ma?UNji^U{cg5adLFbl-71zW-_ve6_%D###*O^}U2Mkrto zF`0v8*?>P-3 z^Z)$8`&-fTQgz1D*HJzaAV%@3mf|7xiI!rJ`anxjNFC8qutzClx0V87IAfQV0^L31 zH7y0INXAYr1%8i=9a;)Yy!>e!zW%ZwK#uEMEY|r;!#1zz$daMBwPdp6yR=nPHuUFW%dFg?l zGs-tK-6XTM!u=rQ_Ong*GPX80r`8;4PL=HUSB;p+>iG5<4{L?d)f1+*0iMT&ebJop zjW7N2VD=5L-`q6$T~htY7Pwux~DQG_4&%)v&^H+QTOQdMa{c&o5Ez( zSyQI6uGLLy#9azeqAjTu&h}_hIGS@*S9tHX+c{T-~XGAlUk%iMPa2(LA-%9`V-EUENb!HQDgRNL=)hJ~s> z&;5vnRyVzeE8iN3+Jc(kN#)v+US(b@zMZuc&N*{|fY#L7GAkZ@hB8Njmf2fb1kuD5 zUh8Z}mDlPnw1VJN25UWVYb!YMu*QG~$BLUF;g-{SyLIM#FVyA%9}u*!R3$T?X06p{ zuUvwoRM&c2kq|X#;bhhZe4ALz<*^Pfad^ERH#BOT(+l>Md?$7j_>deW@Se~ERI8TU-slX^uY`~aPr_ZD;I(#1PD@SseBR;|TXN6%1ZX^DR4xp7He7jcVtb?6 zI=k3y&2#311p@BhU-omP^8HJSG!;Gq>=bcZM?q8;1Z_C2_m+Xg4ogBs6?Xn8_gqJ5 z9_|iJu%guM_F#{|M#RbrcZ;lno`cXb zy)%f=TBweNp%Wcj?1Ug=e0T{AcMyv}WC^qrMt8mk4)yga12dL{RYT*j&tXgB11MA^ zSSw&hybE_~T4B4)Y`oVr5x}jkT|t-q+j)>=%`AZ-2J$G@>V=j=>mf#>6b@m8#uPZg z(*aZU0jCxIfCOvp1QJqNix+T|XuS%Jv^ok30-XaVG%EvRsv=bbZ((u|oRrh!tX z9r_5B|F_BJDpO9*s0}mUnO;fO;Y!UdOPWzT(JR2Cl(EY#q4)La+p}li)ILec$;o|s zrgXE}`r2$W^B}yy4ZGa}x&O_6fM;gb9O@sG?uvT_ZnU&wVOX^+L z*Sq=QNQYHBV=Q2qZF!~cTc5z9f=V3Lqt7|tTLOlrqcyH+@oMm<0v4Lst4D7fve1pN zr40^Ga?Qa(G6etq0oXnceQt$<;d{a0QO&hb&45-lx`^&BFybAcY53uL+@wiQ305IQR3c+{Ml$|7N z%hz!g!MK2rSTWmeb!(%bso^llVT_h|f!$Qyd1?X{9^!)CW7>&p)-GdkADK5^t79Y# zlu__*a5x*Z&DsUL=^!fMev>LV<^9$Z6C$c_zX^6r5sp3Q90#h|8jHrk4|~;NsKL1Q zR%#Oseu2Bijslo?#V*jA@hwYA+&CLrzIqqv_Sq0E4&9$%1!b$)Q4R@U`kI9zFc6)S z@kWKS6iy_Cm?7)XN{DfD!pHKukw-y?!Q`lL;?ps11&$$rST(#4Tcn++I)Ua5b06lV z+v+WL&xVYJxW>V`Dm7Q%2s6YdStmeafq|&=Iyzaa2oxBBO~5@clQ^*6N;tIy8lzrH z|CF@u2v2cC1zxxV?4;=fX?^KJEg$#D1!SR^1Or5IZL zfE!g5Wz_f1HbZeJl;Q(%2o%HcK%NZW*%3IJPfG(QD)XX32R(Ub#q~nZL8oKW)I~>@ zvCsqbOTrk!u;P?}GALNqI-%aO*z`qHi@je)@70TFSuSY0nXVjWg@RhYMInwFM zD|5}&o;h06*0m(oPyu^Dtnd$c03QeCRIN!h(>9&pO>yCc$M)~9bttmIKpNNWrirEG zRMoVpjz#9}jZLx+!ew?i3LWsFu%mK3Zs5_SUh5>Sdj`X29^|wRh5@0)AVLlp*rVX< zYi$giGaq2D32A5_~(XR3sG(%h*^jXytinM$K)t2 zITVv4@7%oyl0uDEZUiL78m;2tkYqJlBZg_okytDnlC(xkW@$;S-l1BC`!T~1Em?%g z!K@k^uf5$MxZRY@yptUG|2TUS__)sUURZP9Go#VWNHf}HOP0oxWlOds&uEu-d6DTx0+2oeUEx{ zO-U<#(7q6UDQtyP;k(1#;bmcOcI#}#tM{m~?9`Rrn%6S3>=FP_w>K8=h_|FaYl4~2 zQ$};UzAT2&L0{E+JkGOK9uI_pEa)?o2)B5B$}lLH<>eW}92lUChBweroC0Bd9>gjH z5+(%)+l*|``|#hVbcJQ6Au5FshL>?e;RJFD?p8ic&gge{8a~8o%hVhZK`B4#7a6`; z;PHf`{(Y6%E46H18iTCgZ8t|`p!^^TLAMC2M1aC_eRUqA4`LF&U1}(x7Ja=!3p}K% z3N2!nYsl^)(J@6RwcO+FM-&}?&EXXrIY>4%JWX#VT}ig-J%#tqjFdz2m70JZi&MUZ zqCH^i!AS_8*#20+?edN;hrTDlk%J60SM=_DGIFi5eFjW7}9zsLY8GihJ42jFyq{ za+l#9o*on^!d)9A)nL1Hsif%xQH+CJ-)@F93j7joupW2pQwC-9((-0cHXtuKk&-S$ zP_LFjV-rG5&_Oy`kAXwfB@=bovcOzWWSastqMr}@m54y4wg!=`v2SO!V2zjUTJF!W ztWMV$IWyy=vh+%!!S(+BpvRMfw4a4H0i?&_5$P_huiEsILUCuRO2aq=iTN#KUcd4U zz)Deu$&MA8KJD1;jBckg!QH#xZq$kaHggWEK__q*1SeA}8%~f~G|d77dY7Qj-l8tO zO>kW@Tmkif`_ae^>HrgA%5xBhz!lS*(4n}Zc@rb;SY3WZC{@1m35Z7>$UWrojrEhS*JY;+O5{z9zoyoAAnXd>Sxu{#Cp>g1-Qmh*4m#6st^ogUgnxfSV10Qh3ua0-1G>8z$xPPJK-a zCGaLC@cXbk=9j8HTQmgh&OKiL7#MMYlZ$%RdwiPZ(tSCKlQT&@ggdtvp>l)7S8mz) z?aB{RQ%Cj1Dw|BNBW&j#>~Wp>Itjh!8F1h-N_+`xB(EcL=LDbEVt3HMgfM&=f@s&- z|F~P3S)X*i$|lVSI|p6xAapbR&d$F-F0yoI{f?Q`vk<<=^L-*xH>=@q6U@o=Esgj> z@nB9#7gvL#Xc zcGD-stFy^Z1OzqW#bHlC;aDb5c<{2eR^MXTgbduxjtqXFJl_WRy=pib(qwL`s$*QFP4FArb78lmBQ` z*T(uy_|# z)Z}9!aGV$%0!KOmF4tb(0M^JZg_NaWDcKL!G?4@{19>k}Lix$87*rC^Fc`At;J zIv{|Od6cf}P;5~KUl{>k2@wp?F7N`l33A|!zc&Lx3`Z$q9rpnk&^`uvfk_NL;{;JS z0DkP$7|wkT+L<>pFeyk%oi?fR0`Ckqdol@$8Tho}MsTOYD1nwB3)F%ik^791*O~vI zj~`^XPzn|jsCFU=$x%j53Pz33$mGs5NDv-^)g6?jK)+#0z?sZ+iDQ!ikikDgVaeq5 zz}V1qL-fe>5>j}ng=BE-nuIg~QzVBqw7?g+y5Mi^*A+yQxxn&}V)TuX zsI0fE{`1SKv?CMqaGg^>C+WZ;q$8oUVG5FzOmi~bPK);8lIK-XYGK3pZpWR6j_uyR zBl9u1&EyP_D8-$!(#QpgK2PGHA~Oi_6nTDd{=`8P7l2IAV9{=P$qirx69_6mLymqCa*$;mozfu3-bWLC zlr;8FaVIT+9n?#%SQgrTrBr!J?gSst9Y=`ZV=ZzLQ6~gQAlhV=U1l0mr*nhQa{vrT z!^+aSb4u9=I}SZGp_2@HiPis+=UZ%vJQrMuHtexWs;VC1y?9fstE;)CYY{sv0CF=1 z>bX1#7ON<&(v4Lk&vbR9>xr?_%AbR{a03_wh)*~XBI^uhoO=c4j!vLOB%sLzjI+Bx zyHeFN(%kPFU#>A`kN52{N>WkQ&h?bqqw}>#GqoceT~DSrzgzieo#3i{6veEILPP?2 z3#$;CfkGSt&@nW+1wt#_?r=iiMbVIi@__&jV2X}m>mfK0Bv??mxP{zKQsrVD`f;Sh zHtPS`D6_wP{_CpdL}zoChW0bqin8e^l60h_>AGNow%N1V-4?9+BYw`oIVB)fq(%oY#27^snvG6b zXCL}%$>fl&-3u7XO(aCZh< zvAV(DlzYvn!v1cK*0t8Ji^kjAplkuN3kmz!;JSFMDISY;tlioZYl$^?wso~OM0X!O zdLSBWX>Dn2@9Ju4i0(fUjkU*O&CSgX(WA}Vc5jcyo8ujw9W9-m=+oE`QOnqA%tBpr zEY`-(Y=cCN)6x=;Zi6VTDcZZU$r*8j#tXMxuIdIZ00L`Hf%0qIIXwvd6@`zx&jFp* zB?p>N_dbjd^86uDiU5tsNpjw<*zlC9#3*+RV_^o-^wy^6?M)5Q?h(!kb_ztK<4w`l zI8{xpEisOA>w#!jM`vTKv9-0eu`Slw5pUF^ZH~8hb;jE>J;oT=|0c{ffCrs;3vlmE zzSaH^WG>K-ulLSfA00eBiOhzl*FlOm0l8X&E`tmD6mN{j(6cs7Xd|HYhz3yGbNg|% zJPb`)bM*fE`yBwWKXUmwwd#}xs0L2B+u5%6uKMWR@y^cp3FKNR@&a!YCVV$qp9C5IOa_v$kwi=uJ-nLbIT%}3pDY&qfjRFYR<{T zvU%m<6UrM~r9PGwsK*bIDms4?_?LfhTjaA%NAT~=Yy(u-kE;4hXVY_sB1a#r+W1Uk z#|%;VQGd>@k_TB=S8rXNdMoqj#hM$G5}C2cgMqYMBWgY;rjc_P&taY>Nr^P#l&2sB zcLK44me>a+i4$iKL?iXXiKrd?`3V*3+&^{(Y8Pl!!H+R^kO-*{0{dZ~ou`o6ZRmy$ z*bg^;5tK!&g<@xR#8FHV5E5Ec&!_uvxWfy+FTumLdmT#ug(7wq!WNS3f!4gAXcI>pDWfr3 zZp%PKbAkhHAO#f=X;?X(s5C+cVGQ7M_|Yi{RU~+@qvLR|(GJ8)`cNco5FLTEe~PV~ zheB5LG9ZM2t1&51Z)jZ%XnCB%(;#u8qlpP1-@$X9q?Oolwy4RS25d{mY+};YPzd}$ zNlGafCmn(XYx#FhEU9)+Z;<+l0nCg`^l}}TrhIG?zNh~~75k>Jo|EhC!xz4$N{+Q` zcj1#$xnMy=yn;1_Ro*G$b*v$4+Kw2Ikh=jh^1SBiuGcU&F?I?)!u_gA`=9PPp-Q%s zZbnJa>=5`2Vn~p?vKnVUP-!?oS><{;I$1f)g&ma`i61J#?9mVXwJNjz{Mc|fMdA;N zWgO#UBt++xYodmk1PMHp#BN!^0#-`Y_*P=jENVYZpN`;Z1`w zA(=fJKa;fnZBsfg<-)6;o>Pgr4`H%#RPyu(u>^qGH$4slLF#r$7}-Y9Hm-9~1dj7* z5Y03&j;^7~6SM5HjIvbRPHdJ`I$;+Q5=5-VVO)y&BRInFf&AGd-ty?)Z$*Cii=sA= z9_X)2>44{?N)g3DByXJ|d5-xTMDjfxcu3L?)`AJ3tu6I;b>-iL^6YC@{!kU)-P*P; z4n0z9M`yfs5fZ-@_Pim8#^Xnzv59OvUA5||6CM4;x*PpD^T}bY*T4BheQJ@b$zlY% z=+&YdKsPnI;A?IlgjEA}P;v@O51Ut9_E1_ohI0eQ9u8hm>Jx*5(K?|5go{{MRR`7% z^NP7~N)kr(ngf1C<%X3V5j-Z)drD-%_4c*DeoU36wj&&Ja+otYIyMb5n2Qkyfu`}J z0H)qKAZTUh;)orkrWagIznI5^#?*uf{+-KYaTZJ(0!^r4?WZ^NQPcJ{q!#o=KIA^*t9?U zOXZ1dzNvYPAI;&kLU+gyCnR?RNN2>^17}F}w(!uDE+8)K!y5*Rt=a!)vp<54!vu&1 z{aQp~#s2F@i&`j3m=LKsffeHgoZ=76&VnTx9u#g@FG0P%{DbdO#VHO4f3S(Q1B ztXM}3XeR{#C>w`C8xElnnkrD7f=zEnM&G5D_6cWC9FSy+PRe9ux?l{V%gR_~DglXS z0ENObEF84k5SAK4!y1d}j)iO}!AQPqm0E9CNe}GystqjS*gNZF5M>otJ zXcwXnkJEq%eVU4;kqe!$k=axlb|z5{07!PMp9W7C;~2q@hX-#@qKT+`fq$ zNKRm@wx*8GSZl0p5w=>mTni&GKJn@a^$K!}ReFN0?J)XjYHp3Sw$9eScCXs(DFO0p zjWxB!+uK{6>e7LawOFs``g^xKmM6})&Bi~Kv|YYy_u!nRMtz8?^Jyv8tweN zntijd7s-KOed_&(D-}z7)ojJmljnCxio&ZL_ocaG6pF7m{QWSQ5*4A;vdIVx+y}g^wW3mJd%2NKi^VDAF4Hvz zsF<5O20dqSZdYk;uuSxv@_n2NoVjBV`8OQjlxrCU#DAnRCY= z@m`mPx%!O$cv;SNr0s&SA@VB@oKEUWQY#IwL=DDm1bPp%xVY9&Ck`20QFUoL%Lpx$ zIpGBc*?m&^MM?_L)D=ZcpC(3hfrq@1=xZg2boPSj6Vn}5%t^}gWJ4SdOe66tEMZF_RW@%m5KGy@sGE&_#0KGy?+Fy%m*+ z6kc!mv=>pzDY@MfOpZR&DW=YVrw>nML2T6Y; z0biNV@AGJ$3O#2b4c_0k+rW(EE3Fwx?%%peTYydUhw;1_*cP zC(s(fk z*NR_xhUFgv%75Oviho?gD`!+c)8@Op_8AwG{F)mAx6tEy#gDd&jRInao-B=#Q{lpIXwO|{n za@=`MI73e0>dA_aJ1hJw%;K}3aaMTl96(^Tv$%58Ecodhykl}AE2@qZEnHJ6aLQTM z6t?dW7=y z?q@wuOlzBaAl1>VC(gKF`Tk?Tus@QzThpKQ0=xsMlW?;^LtdhQD*2kv3xReVmr%m^ z7?SuxdC$ugm{FJ$@UkWYNpjn27}SJ%OR!pbu`V;@%kKo>!`Op`Pr`4EZ`n?#Xu;(& zl?UgV)8eTn_iX^2Bn`5iqS>Yb_vhTyDDTvHXi}Wp9&Izi@2U~<3%W>leQz47^LZ?* zTU;w}ARXCb1ON&XgQuoX1FNOv*=-1|ltGgT zNte@;IwMF&!ih=Hq;wnN2SttpCa<@^->iR-Gsxi=5%>0iw1YZ0#n+<>Rw`r$-EUib zbSq+EMmZhM5Cb0pZEU5)fZG+C6Cf8!conUw*I%~8ZW-0JS1$XOww$1PkK#Syj z8BE<^qk@JE zAs^5$It;%SIMW7&Z&N260}$R6C==`@-;@CjhFVvKs;eRej#UU7tT-uFAu|3b#t-uY ze%C3^x@-ajLB79i&u#NApnQMWgHZi=3qGbiS;d6a9Q7tAyC6g%!gfGC0881PN2@*>$$uks`!OoW;dK_0x4mP^d z$cD=~DHZTZ-3>OP`9oNVOXnsk}a`^NIt3#e3RA<0|V2#{qYVcqU zV5sAaV2w|v2GtHY1|jU!nt_x7`!BZ;wp|9fw<{$UA?!(sa?#ml$1;Q;Pvip2NO@4^ zd6j#Q;|rQ^$!NVEb4KC`$lVSz97JrWV7M>{1CB^893BgUg@utwZlWlZMZwdX8AjN(sRR+w%)3$DGcoUT=RDVfjkzQR7QUsv5le zXa!t|#2OsZLG5^x`BsEKWRK^q8=x2;!x1UI6eGBzEUF1k1HhP&^MFeqfZRyJ1_)n` zM4)FR8J~z4GVWz$`eCz9v%cum9%QGYq!byDBv3e2o!Uwrl86y!kPv=BL{Gdyfe7#b z+7oSo_OsJme7}8i?0JY^oDRXE49Htr)?zVAmqi*42OaKVkxpjH?1UA?a1y=;=$vDc zkEYNN>=Pgs7>CdWrVMzL5p`<=1ueCOyq?S|Iu<=WIRlj?a z@SK6DQ4d$@7a1CbbW%MNB*EB!YyfHn{gtcgw&Lc;me_$`TvP@2wU@tT6xKq%obgxV zgp7?#H9R;_Gvv?EEu5o9dQHbXNZwBEUp#vEj##|yL==64S{7)nX#vzaMexq{SnpOv zJ=6m2Mtxi1rVg3X4V5)ZW$nMIvSv1Jo_*q_P; zy@gVkOUKf4Ly^7bt2&-3?wI5@hKK3M4H+k`*PnZEbqZcTH~YCR78}nOakm`25pVer zdgYGJPK>S-`dR=2gokiWqGAJv2->r6k)cCkv`=q;h}GS3U<)nqtJ(ttC8UiR=;unEgNLF*Gg5?8UmmoDg0{SdEunGl8flXQQe~*`?+(=d$@-DuHO* z(kIc6FOY8%*s(Jq!lscKO@5$;haiQUODpLz9zrtBbT^}dg$6(3hbDv1Ojp!;{BJ)R zgu$BB3PlNvy8=gz6X@S_3{7TiRKmJAoP>%9(o9aIHvgY;AHf{V z>izt>l8uCajn{#YA%}LM06hhefy}@dMqu3p5wxHlv21bOuB>bCtti3Dx^Mx&LF@wV zcBl%)(~16|v>7B46$3b$d+GjA!iqJ)vg4%`!jQ3~*wiv|%qa!qx-dO3r#K0&fuP&Z z$!IEb4&Zyo%*~a^15)u8QYo2+VXO>hZ65Ju3|j@?@*S!d9Uz-ZLcHuESn<-eY%6w;(xV|Z&zslO=Y1m%<&rR^M) z791XkIB2`sQ99hwNqQIucC?#>0Zga$;9vu(mHFU#Bs>jujVp*5s*x$ej7`Z2hs8o!bb<3RGHtqUvztsCUy!ary zZf|O7YiVs?Y<+PPUVZZ?=L@fx&-SU0n9ugBli7yala+HBqU`Zh%_pLVz|DIvZA#Cb zn*B`9r24rxFfSFiUky*HEwM|Z>A7UV@pN|8&ZlQO(uxTDI1o5ht@z>WHZIK5Y`yu| zP`&+d>(7l)WIyCf!;`&rJy337QS0rW&b;3!gPR1@d3+PiyxG5?I_Kp&9YlbTxJ_G& z>D4|p?`ck*GiP)^D1~Vd4?Hsuof(5Jo;iS{I4z0mSt6q>1T9oe)FApgM;9p3{)wyf zIIvdMKRx}mB?Ypq;ww(%On|fB{Q8fLGHd;&zX@1>`MIZqDZMAb{!S5x4LVMN=qPFf zUx=2bh{Gu%5fwS~GeGs&+4O>htNB3GnHzr2r*!2f1oJ(V!p=|x=Q+KDmK>n19cr_k zudVdcn=4a5U$?`0BzbzxvE+0glqxhm8cx7E0+5AyggbuUAi4h}b0rLOb5c%=21$kD z4jqEdI9lhpK4un$tEX3mimPrMKoFrvkHYe47&c9~JcpUQ?Ou1BbI;MQ9ynMQCP@kg zcD(VHX4oUjfS?VxnE1ASZ^mfY*=X!%6@0oUQQO>m10&)@(b)kF%c(a=#rM=%b= zOmH!2^Xwe#lh755r43I{=Nb0i!l`7Fz}ncLxR@`p5TfT*#vt~NQfWs^yrbjEp%Q?> z2=EP`$w^JMSTtc@o&N8tcp%;(XPJ8@L=jG57)foQ97vpYyQ2?(O%XbdsiM^*jN#an zrRH3L^c_aNJAAjW^MK9#KTZ^;aA*!djS3Y5+6VriJ2#&YuQ+nF58_|)6vAvGxh{GKu{Wm{%32uP zIC}~DcdAoSVLvpt(t~r**pr4C0AnpG7M}n3&MnvnPjBoTVEGx?Ju|G7elMa740i&I z6Qc!ayDLmX%3;E=s*};`B*+(lI2G3}Kj$7MGu6@%#s}JmYF`Z2-F|0aQk@(=)f7Dh z5jp8LcIo^WoZ&M_0kJ%=edGmY5;U2XBgU9W&}DaX141uqyf%;VZlar8x`4LhUG4T) zXA$_w{>j)c4R6t{Qry218BpdMe#5NJ3jDrVjVQ{q%i(3|F;`xK9%@%)_hePeGyNT7 z#K*h+Ian!VyFCpoi+Cc)dNycXU2?3>LUMI8yi1-lEF_*!C9T&k78IuBS=4=Y3=6G` zWge{qDMKT+ZLo(2lLl-JKtGD@g|Z|@MB$ERfmOC9VT48g7G<~}L8dw=7@u%Qq8LBH ze0L8Go*A4Ni{|Xb>cBdDu)%txcX8gg9qzc$53_yXNB_q^^qYqR3-_-Wy0p=W`V zX(f-7n;^^MKybG172H0sk~G5sQvptxR0$~{>=R&<{L7bBwSSxV+7C|Jo_hum!>iRk zbpJaLR2lKxP?`N=;1N}0zyFyps>)?89KNnNgAiaItjB5JJ#bAeEdj{Tq6~fMLy$!m zOW3pLz6j~Tv%nD9ZC%m2jE!tdV_R#iv9q(Yy}hv=9U(Tz;DrO|Frq!sitMxpVx-FUxf7=HHl zECZkY-J0pp#xNO^hw6E#gb6fj1BORW<=~?yEjk9cc2tfjFhC37ZGYm-FbvV=0T4ES zKsgYmEGh;BisV8Vms?P<1F@FKg%%gr^sm!DOa+Mo=@&77O4GBf-=P;YHl?*Th+iR> z8esaKL2hKy#KI064sZcEEodHuyK&KF0^mna65>@DG9_T^IX1hRJ98#I(`Exx(PkT zU{l=E38VQ%1|I0qV&pcpFuK9JU=Xo$_RkQNywMv1{Tl0R>WFu?w6)t?hJFaQt{)%# zp(^`RGpSQ@zC?Z5oEwwp7Z{kQvXQy=d&ApPy6z`cbb2uex>d- zp7i|4vmxt}1sAv5&2+~veKXWIpU8mea0{sdeprCiOXuuEgpa2vRYAmlb=m``^yj6S0BystPnSt z6~Bumxs@LL!m{7JxSjBSO%<0QgwGB3=IQ9m4?gu;3j*7H?C0JveUxziIukNu=YOwX z)kk`6eB6!4%cL>@NmomAyE`LIFF#-<4pr5axSwoy$rFaq?zUciY}HC>so1G<@q7CZ z6Jb@MCmW)%_LjDeSX{$!dgaUaTd&`F93B1U+CXGd>eFTm0HU3CT0N<%U`VDwti(dG`Py5^TJTFbxj;T1JKpkDA`E!mx=lOGiKQn6fwVaD;+qsUVSr@XxC-eR;?~dI6 zmb)tS(U3nl5%`C|Atary_rE{;7umP@W_??{A4cT)`_!|>uZ&}!S3S|Jr(Sz?qnTcD zz1+U~`8SMOopvE_aoPpztMzqJ>y3Z@qR)CZ{FUq*-+ETpm6Rc}PTRWXj;59lxNNx) zQE`2#b@(*4Z|2*e=948~gOy%>plbeAXu+#~>$U#x7CDu+H^Kj@HRgotNk^_PvC;)g z5l?+dt2Zw>gK+FqV-EJRuYLZCQ6+D37rn7wx|CB=syo@%6l;sO#a#5Y;=27(&YY^P z+yjgC-u;rQfnbZ169L|*Cwgy_R1Ma(@n@?lep3nis{ej&I?O{0A`Er4wYkQT(d(r| zxAu2$?^ThY4s?VN^8G{ha)f)2+OPiAy(%v-|J*+NkALqec81^F)ZWz*YjfN)(>>Qq zth2*kUSUTrc|DcEqcmxz4{BoA>dwxu{iEOioT|vlJhflzu2tnuP4T8S9POF?8oFL= zovp2_4NfFhP4*t5$;YJS`9fuN?(R{5wfoHWyzNO+=)N-x>2aR8)w+Lj*iUHUU0q8dNVJ- zy7(rOeDbsQwQo$S%C~s8{2!lDCB;~n8%*{exL#nz-|4H)$(YXCZ@mALDw>lqE4Q!4 z-!Sy2i|uFA1=p?k$j57n;P)tm_4G*ZL8$rQKQJ|BB|h)1D!$d53Hv0@*4h7>Y`h{veJ+4UgAs{s3Eutw#_Lcj|rD16F)HsFOGTX42~y&j3ua_3Y=oz@&>FCI0IN9rPJ%Yl^p`Q|_!4 zT+boIuP7Yo-9~jxazK#MZb;8g+b@0ib)(XXZr@<$-~6)s>ysMDVxTA5W6fPICR%yj zuL-K3e(r;z{6k z3a@1DuwMJq!3sb8J0*>Wou2MhMZh1hB5!SLZtrwSk;>~nEB|VFU9n4fy2#@o!lRDb ziMM$@HE;3maNtKqDQVF*;3QNUcc(0H-D|&oHLPmFPIyW;1Bvze;i{_KOiMj*db1DK zenc%Tx;et-L)Y!}mB&;~a6uqB`$^D6m5ZLd2vW!)+u9a~luMh}m34NspgM1!%Qy%n zxE=fYQdJpQ{4gR65T)oAd6R$(#oN z5B-1Se|R=O(&MT3+TVTTA;p{$iN-$b?7yW7jl_Rm;WPZC)a-X3d0187*I~Yx)t2>P z1w!gW!K861SReR5flma|ft`Uca@W2;rx#4(5B;C;zb)&-S>N=udVcA@&GU-qotFR5 znswHxLu*!8|K-_8k=1>CO^vulj8P3rV!LZQ zU%pbOMP(lYB?!{c1Erc&<%Sn1UnTSNp1Q{JC>9S-zZ|U14v)n&o_A;+{3{R<=2Q7!kAU)9TapZ&Po6%bWO4 zTqW(R-+G%WwqN|_2UOYYzHh%x{cUy1wr{^gvu3}UH5<#y3NOuxQ5y>i2eR9xw3zcF z(FN=P=eEGg3rP-~jq%+hp6~DH>zEE;l#RD*!w3uKG1BE8`FCF%qNL&8{YBv%+Uu93 z1GJP*uY+CmDNk;|fC1v%K71bv!V3PCO3xz!+}vHpGHZQol|Ka`8ancA9bfEbgZJgY zJZ>&Z(?jn}K>^G%y@y&Wy(K{!S*m*RgJ?v#ar+-GUsTm8RD ziwI4F=MLd2h*)lrupw|cN=8yGQ)U1;E&9(u)dkDZxeX{%V=8E}(sMGZrZAqAWwSny z51%xYHM0xDx%ffe5Uj#FzVjkHmgCHi@F0A$+BD8gV~q+h;i{)#MJ3|HLGTGTm^yqq zf(UbceUotHsKFgFX8_L7sRR77RvDvX>8A@lABo~!gYqFD0cc3P#q9xDX);~8evjhS zh`|P#DI$_)KFRYk0n6N8R)#EN=aL!F=%_>$o4s&fn5*R5R54*?*&bQ_eO%P7ehe}l z#)9FW4Z(bt0y~F>=~Xb-imRnYHvId>X(Ty!1os=wY|6?(>*Ai};VhvuVyEZ2;mPBv zhx-ru(}1#Z_(z~O-`VeZBnzgLaO6lAglqCp$mlyzPP4@rOy1!)vq~xwJH$4{GSoi(x%vJ2K(n7c-Pfz&Hh#--l zWeJul6KD82{iqxc5pY~Uo3emA5g#-?w-R;1E*CBgIR-8ZxGw4CGMSZzkw9xp@pv=$ z{t9k~yW~}Y`IL*Xr{H8S)97Ks<&XJ;OMjE(i*%Lvx&L0N0-k5(M0)a$ z&|I?GR8UzFk~-176{dpqw4TisUV{T(3B&1%6%{L55oDCXu~8JYtXHz5fCt`jzkTPE zeX2Ia<3rMYb#9fJXdyN@z}Z~MpBDbW5CVRJ#-vXZE& z?1$06hExQlZmVUD_XZ^{U#U;fQwdLqebVIyJ9NA{c_GT1u*nKh}_IM3{##!0Mr8$`3p0vSt_xb%P96CXcOi~hcvmbqx{7rB0 zp|P!<%>jjRVmO_67%pH;#JPifkMToqi73nX_=Fd!a{xh`_+qKbVPFE0o;aAL!Q{S| z1FS~y1R{8j3VuyBpgWt=#iqfdh`_jh4-Qz=B^%XL9zX$c$Es>GFdxOnsSNevtIce+ zNpMrXbI7hjrz`>K+)aBhc&IdK5T`y_fPl;57(o<*X!^sA-@;sEYeM zf;v{@m2uu$8Uid3_WHzl7qxBS{cgC*i37r1Grrta0H}-%hw|1b&qxN+)2mFAiv09k z1wRQE@i$xfV2n3?x&((gkBwGB?meE5cX(t`?TV{?h_{zV5~b{(LN3-rLVs0qk(coP z4*qQ6QdO1kvXPK`hL~gd8WKDA7p@UNY9d6e-n~O`N(Gnt4DtV(bjWLS)b zOlG_jBB&9EK2)0kX%4%}^rb`s1zjGA)|?yz!AIxz2|7!j0y+~45y%~Nvq0S0_dKF| z;IDy-xMv=O$HaLo?f1L!d|XIA#id+*I|qDF_F97+C*6dP?JG=^ww~BIK5Wj>ViY)#2TS$6`tEE+$jl z65rp2+jYRtII+;J$=VLm^CfhULIN)V@phh+=@!CO6|G)risWw{En;3tGQ!#hsqlaHIT%pWFr^l zqoM!->OQYmLN{tSn8ED36P{k4gRX5mNGzW&=QgW^FSv-6HO1aa;vn6a?Uh)G>AAHi z63jM8*L86Hx6m6*$krmS91kkSkiO&jg`q$Jrr@EH0&XmWaCN&E4m_l3iHnkk%orX| z$uq$755m%eZb9!NKqTbh)NE>!MQ^$yVFeJ=z;y!hCoi z1&i_#xi-HsQVO4=bWNZrciD-uKyFcPuqiKG8VH5f7NACWzlWFQ79gx`VR2q(Zm?o$ zXl0P`gI_9tzW06L&U1_wtSO0;r#ukm=(zjCQ4ffk#E;wwIc8d|4r~{*-4n(Xi zh%R=ol(Yz7;dHl0x1!6JheOEA`Qf-Jzj0EVC+wsrQk!8gsSoFkghlBpqfD(}c#VVtFE+W2msv znZ`-PWrX1p9wBT6EJt-uZ+JD>4?8go83z!(Z6Fn^S8O}&eDf;2w_IbW z#l6ylMHe_L;GGbd4+h6lgr~ zxQIGZk+x`>#K36g1-eC2u%JB{9npJ(AmI3TA;lSoM=uA?j~K2kn$-o9z!5B7CfyJ8 z3qztQFYM&tqahF}0KkTBRT~rTfV@Ybp!4*g<7`Nf|LB56mX$<%m^eLCkc7etFYx6L zsZ}X_1dylcEumIh5#s@x!~cu>c#tv2KGF@^b$CO zSt>Zo1!OV8barEdbuzqlgGOViw?<<(*j%-)yTLlaNsTqXLvKWvvMdV{S3Z6c!kmI+ zI$U+|-HjdTAT3g_ti9_U3O|qV=lA&YsG41S*JJ7%w`H3>Svmh^_Ix7$*#qm$`p26< z5=3rGRc(HEdB^?y76c)-4=^;1MIe$&HV%rh$dlWzsWoCOQh2km$b@~>T&@Z`=S@ta zVqzjh$1zy6-SWjeTDHIX;a_+vj_!iFH_X+sL}M2i92v35o1)vNqqlR%;^i>}Ud48X z6{7|W1WH06){WMhW(4p=#cBr&%ElTOMSHPz7QD-v-m6(9@4PyJDlCG}kG1*h@#~M|l zIK7qT-8eJ0ltfVr4b;);y-kALwxjP55{*J&AhxYXnF=d`Y~-}qb?r_h)TQGjBnKG` zXq|WPDFD)eSd!{!bO1FAP>KT+mLST&n~XQj5LwuJi@v1cthhMQjSCjYiPKmLZg`9z z=L>ckhO?k0tP2kTqNFCIdV-DcEn48C1>ex}R`*C|b0Dd0l;L{Bf|H=KfFg7}wfQeo zTy73*k@^1gDALfwoQsC-efm><5RJi!5dH=9^aWGGVY&t9JA%=p_n0QQ!ciTgO>AK) zEz=?|qB9bJ4&lsG?rS}-M7)4uQ~+c)gE)CKZNy11U%S}O;>gzZhL z2r*8hw8kOWtc6D#v3Wq-jKkZjad^;reXCuMAgQ-9SsP3)c7qkuwy0RX$zIczZ^$&3 zeCs#sqB}@Eij}T2&%423an6tGm4|bbR{-CNUMVi>#l$D*A=If!Ozgkif*X$~P7jZP zhH$An%&+SVz;O7Jh*PAY!^vvNoqH4^-jajSql_0iIyrNI67b*e(2GP)S__@X?HR3WDY*t1vHOn!IXx}GIqm7 z;V6&~!~}q3ji3>3a`!00ImZyP8r{=tLCyhANSUOhTpI)kWjtw8u=Fhxm13{B0`1hh zl&Bhpp-H$T3bDo74lo8EA`8KCe;aI}oPVNF1rN~b%ewX_rA4PE;dVVfJOic)AcXen2vNv| z3P%ihodC~}y9P2x<}CR5olDkBGjKHmD^GNUL5)VM5soqe`{XesndN?i>kG~-t_S_S zC!4D6Yj?cYDA{lm{K5m3Rcl`XR5U#bhKeqUV1}U7M*Xt$5QkyRK6~ZgjrQbQ*t`xV zZ$@p4OKc>f!KeNVPi1YGU@uzW{hHBBc65?yg*WoT?vOLE{iyJU?%|@9rp(^C=L$M zeZsa}e-jH2-$)#wSSZj(j(;rgj!57fY)V88q@sH6xzn~M`(vtj)kGgce@re6=U#X8 z46_#iL*BNRevjPxosv@KNVbzB*B(MXnLXAQE*~qg$M1egK{*0C^V5IzPPH^O!sNne z8~=#pOQ=%dKtQy^9_^Z@Xc5QqF3_P9gWA_a^BD8J#-!*K8`MN4SswWwdk3`xk)fIX z#JIS)0HU4w9o!2fD_LTHml>75okmhQiOTCFLnRgvC(kJ>{O5Tkhe$~X5NK+U@rkhE zWSHXb!Vn>{$=+%a*EtTMx|Rm}THrpTa21{Bxz-5PD{g%*D^6O^yN zDZkSXgIddx@FWO2 zPBRF@Gs&cN_SZ&-n_nJY5eM~J-Gs8*7MqqW&f=UwGJ^}Ku*)l!nuByf`sbrE2+T6hk*$qzAn9t1wRChec4+6wZe+g{e@+kG6HjwS=?5{=Kcw>*W1AfYC2|_c+;w&ZO?;eoY&k(eFQ_?#+qBa) z{69ycyWsdOF(k0abajT9uG((;;(#i(pXzx;6 zeS_l=HM@;aHsX+okRzmkwGiP7f>tM3mGGqK58MEpM@S5VJl&)n9k)tEtU}Ccw1Wdu z=dY4OKs>oY1RxF8^aKtDa-2Z$fM~=7iIRr^;3nK|Xi7Y3{qn*6d8K+6O3wuUJEwsa z|8MEeTVRuC*UqY?Oj)(qu=OTf<{&291ME|>CxDF1%l&s{g=fPLhP(29mG?^COkQj5 zzvsS^dw=exTwmyGq4$RF4b=pH68vazCfFSKRbVdg&cN+~nw)RvJeM|Fizb z{ddjgzgmn?gjWyc*{{ZWJ*M?S^S!WMzxM;)_x$%t|0n+C&eR^$I{dejEA43RWfe4* zzGB6Xr&igK?Gq|&Ecuv~xFfIHdhu||XMN<^=L-$*4(qkUscj1$|Je6np<({Bm46pL z`|8X+Dq<`>U?uL~StFm>fB5+gDs27piPRD6Z7=sab^WL}RWe_P{hhv-RiUwTpY{4L zKe)m=c_fu*Z~DS<6|sKr-qa&c{PZ#P#82Oezjxv9arMeiFDdgR(h~k4D`&OwgHPli zD*HR5^HMhq`wE8A#Z|XGb+{v)Pt-rO5cOwZ9WL{Tv;b8psQlpp>+EE_e!*dMYd=pO zf^S8&X1)MiM-Q=LNLYkMoj)kvx{PdOdjbS*Me!ocF1s9@pWRZ?rh!P|o?`^lNBz>^#LB2#m$(1HdR?vdI@> zawL@&`n-_)MM<)!f<|wLI%@(vKr%Y_DN6Mc(4@X+ z?VKKiNoLFHYSRHyMA_wP*wFVL1XMs^jYBSVd5|gIG7jU;OyG<~4Lnh|3jd7nfDCbB zPRpUlss62VMv4~W(Y|h2aboR*Z#hPr{|J{B1|IcqTeM z4j%Xz78D5fjxku*V%+$5U}E~zDQNlt4g$wI#mf%Z83G=TB5eVL4H+U}LF2;!GGJ_~ zR;(>O?B|0=8h6#JgJYl>Gv*Q+ffm8zOJUU;w#=h3ZR6 z0A?1U`cg|qEYE26QhWNBml62yMD~|eVADPb-+5~5T_6DwbofLO*T7SSePc81A7n00 zMY3hP+U)oXzcSi>C)9H@X}s8p{HEjNEs!0t80(6`Wv4NA`7kV7Ruv4U3#*PkbALxV zOq@Bm5N86VGy+M`R>wN)k1nxZ{Ql=E$}^4~c)i$99WF3G_=YOJZ62nGlt2(<0y)4} ziURBY1qAk67P*1Ov9H!Vsh0LKAlL{LC$8es=^p^o*)}uexai4>(dw0PiU=JI@N;5+ z!YW268ZMB-qY=&gXT$a-djN*h;zJ3>MI`$ocu9~Sf;12GHr5srg|TT-agL4+PJ%^C z(DDW-li8_QseEbwdd;jV-Uyv?<93kpz8i7Fr)K-^NvX~czsEfRU5&t3v6BP%BlWRoL&6;Fss(0xY+p;vH|z&PlF z3mz~=5vG(}Y6G;!kR9R#)$wNWATd0C28ti(qXDLz9sS^jDFd5>6F0LQ%o=A3?9)Srx%B~xC#GZaElPvdtNQ~nbTQ;(^e!h+`z0Zn^ogwSgbV{ zjHJt}?tV{UN4k{gZv;A3MV%hP?0=22P6&b;=*xFk1mXZ*{-@{?ec(mL!OrZU5@~YRO8uCRB98Aad>n4Wv;CfV&38U>Ko`IVjz) zV?a9+Uzw}GKs`9^aiUYKiS?M6`(ujc2Ug8D0=fplG~AU+45uWt2A7J*5y?}>_zL55 zCRoI(DaTdU%Ml0DTN@L8~YGha9bjyJdFontSKbC^&|}u>mMvrinO3 zT|^!UVjP}=S~$O<8Z-ry8q2D5_XDTti#T`!|c{f1_{*lJt*+BO908wH^sZ|y>hb(y$S4A=+m zpO}c>8WDWr0aXK{M!?q7{G();M~2#87rcus$_7F!#rrC7|KNZmjmhIjniXjE^TcH=~KZ89BPKw59*cFFJ20-H`nIDg7;gLg0VqYI%71^}{5MszDhT%am}5@e%m zaRAIuXw4~v6ZNG+?0}=eiccW!tv=ZK3GGSj#2N%5=(=qfgFk~PWAI?aR6)1N!%ebV zB3Cp`;Lk&=ouFZg?%rNR=|FVWN&5|$xE3KbRJ_anap?C|t;yco*MhUE*8a@nmsMdE z!w-U|T_iKjgxv!H6s!JQRkRebnn1cR;+)WKBsz5%{eFA2>=_cjl=Irx_V%m76<|JS zQ%CLe4eKvrW704v`g`9ric%R!05@<0Bmi%N+Q-s4XJyhcswAEl8!&+faOYqiF>6?N zOcE)l?s@ofYSoaTDOMl}H_>`@%AS7aUyXt>NG66zbFyj|9K`I2qr%|}cNaacBMH#V z0#aJT;>6#ll-l`Rs=`;Siqcw!m*1^x7U4=iWCHg0^0HOo7M>cy5@UosGc*980tjBA zlUme5EPDSvc!N$MjQbilgY(XkGMTv_85KzyIs;NBH~LyRm!X&cC1ei1WgJsq5>iRqyj^cN^ct8)pJi z+1IWYdWx&uJ+OfD&4ql`lk>@}oKG4XuXdN%)h|A&{w8&Gv$%1?tNsHowTugU+~09{uQ`QsPJ>pLZK(5?NIBo1=zK zi^vai#X*Qyn{|Ff7T>)`(j)R|p2w#(J^ItN$P@)KhdG(x+ALMKVT3Saqtl<<`wRpO z!08|lP{S^jjpGUKR2&qCQe)N#85r-VIU^g`5K0O_NeC=gv@mP@L2%viq!H zg~tS`pW;fO{xfuel&g!FBN$8p!Rq^@$`M|2!2&fIe#c^k-Nn~yyj~cE(N%_bOFS4J zjv%Pg@PKVa7iZ#PDMKN{+TcV=4;fz-8-AEYLzg}YcS8B9#qcrjwX6G{Bd

}*#Fz4Qb+;ccrY6OZ8w%1mDR(^c?E)J5Pvh}EHQcuK}{ z*povuMi>)k7Oc^rwCmp;t}swe_3T% z&m>yC4S1msr>WDza^)XPiD{p^%g%XnkR=cJAvx**LACNBEkI_p%NHd0k|}EOD!nIB zJ=_ZEB;WwweFieMgAjN7mS+TJz_~(F1F@jfgN>e4whnsjd{poAlQ4vNklV=)#?bck6efWR=%2Spy zy;Q)u16hNh5cKb6e`0{LDLN?g2I&nEcA^JhI(T<&Ngbkl076j?kknIB0RUx4 z1%6dn3a4uq=^carv@_v3n-s8!JNruvA0%yfc19`dmg~+RwTZq3< zUU49tUl7g@%D|;ZSZkToys?@WR9OrHzk0jQ<}9Z&CfJUWsTgJlFj)|a1) zl-jEyey_b{=+f6e|2`xhfADK-16rsPxKYZ}s)=5a072wHF2RutK|j^iilhV-Gtk2f zWWAHvW>Sls4$&G?Ga$mIhz%D_Opv$^>jhP^V!ojaM+EUlY|@og(#F_&{a3ystLf`a0qZA4`-{tQ z)J?((g=h6m($QZM{}H6Ui?udG+=n?*Xi4<_SyKE*~m;%xL7)^Z*}*fF$LS|fsmqjWADB(J)lV-QqyPawVh zIXnH%SK*Lx>)6Q8R#~bz1nGVz2(lHQx>D+y)cEJG-}{CU@LswvJ=Ze((B#jJCSRWD z0$SUen$fMcxc!$ic=|--3H3ze3fzUCROYjmxy2Jrxy%T|bLIVw@O5-}Pn&fTx?vZ+ z$4?l1QfvBfos!5N5>P-M|R#!D*NFtc-#!0wX5@a*|-E zz-aAYsczG3Zf{S4v7>`GJkIe#3hh+hmKZXY=@;NjP#5y1d(u7Cc+=6`+U^uQqr9#0 z=4Pkhpz=a_+eV&|)o(G(7Q{1l8Y@>uhAUM@2MRG1$2P-EwZ>aoo%#|gyA=@|JINzT zPu7}7riK>fg~FUXtc)>d0dFf|6t*tna8WoOlb*3JYj0q94KL!Z#xaaqzx}xvPat#{ z2Tv#bqy%PI@55JXh9&mL7KTHfZd0i#S$d>yH%K}wV?Wt4&kIq~xx zw87?NP>oC`J;#U}6T%oX4oIrbB;zd+C^oBkW?Laxk`As_F9mjR8A_K*DsDuI0DB?J z*33cH6H@vWQb|h)j6D*Qt581M%J&Y>1EPwhN>x9P&+b3Bi@jK5xFsy?#F^)8CVciQJTR} zS2c>;SY{poh=<&y6uh+HaUH^ed5X2Lg@wVic3_0Od`O^GqTXzj4%FZw0@R=e25`z< zD7lfMd>=u#v2F}zSGkFkNl?Abh&=Gl1$qjl@>fZrW zeB@9OdWl6|jfT&bZc(Zw2Cm~63Js;CM-tIyLk-H7=I`y*72&Oa4XPg;m2VNA1R?U+ z&E>dS!o9Wxvz-x`2@u!J&&z75cst6jl^8n*m}*`E?}elm+06$P_aFMgfP4?i;5Ok3 zV*?QIaA=jUWX_SC81uzYBdJ3COh~Wf&1#8h(j(Q%gPi~<%po^*EoX4MbW2{LaTgjr z+)=4qna5SQM2|6n(yznP7QbJ$20z)-7W;Eg6{c`~QMI%srwxRI9c+sW5m|xX4MigC z;&*LahjY@nY&(QJ!nkC$fM3v9J43Euj2KugDjumVVyu~CIrxc66P&*tTKp*6GAt3< zWDIPeQsHM8zd;gb52A&!QYqNQ!5z{yvuitK2#vTbJf`>{j`|U(W>3KLed32|&Jz(G zI=Bm$?K1HVxB?EsqI3E8@^DHoXAsRs9zA;;Y{1h#kh{#@^aJYn`Fe<5IuO8+(zSJr zNONqjVyP~bO|dEV4hMEb#<3SyEj&RgWhMCHsEMB*)&bOm5i#^qkXx{q@f`Eg%ZYmK z7O)CQpZ2g(03SEhdR(rM7*N$3>g(9+4Mlj2ErOvi?A+-feo8odT?`R*hu*9_5KqZ+ zk?OeTw2$v9q?e9tH^jQuOGjn(dsyOxEGq$bTOk(|cmSQ=jQh2ORIDT*zYSMdY3xGA zh3aG&AHD12xWW=QV^SCe53_*M?8z=Yy$m0;TMk>!z*5jUU7bAArF~Pj-8zWkyAY`! zYqy6<)zjUWW>8YN#oa?IqdXId(HOj~nu~gxL=5pZAvWF2`938lq@bA%a>VVy!wZ7E z37cteodDKGgR?BVBwvoKZkb-51A@R(X&lD5W|+2S!v`7^7KYBNY}0H3QLVd`uE~}b z34Npgm$vtSuk$SLhIO8C_Fmf3(Xf^!S(3H9Ez3*Z+fHo9K3cY-X${-5lbk#yEtHZt zX?Qt6n>-0`Nk2%SjD9bjDAewt3qo6HOJ4|W8KrL<0;P1q_y1q_b7UvbuW!GR{CxC` z`?=?JU-z{y%>@C%LDn>&B-d*IF2kkuo8o+in0!F$>v+l7uC6UYgldGrX~>QxR&29S zK=Hj2SMGj7|NTNK$$$_a4SSTkF(os}lP{~YQV#NhCMcI3nHBOvM%OHa1QA0Aq3f88 zP-ug0P1}G4;HNjF<416HO_PX+YwU$@kLs};_vv8+J#J4C{;gr@jF4dfHlE6a`y;D; zxTz@>0v_UWJ>IjA4{2IA7FCwINS3-+s84nkLR54@@Jgqq^*bFp%ERmSAdl54iF`K% zG$bo68>P+9&I~fh*96hPBZeS@O_~8+1XfKt*s1G62}`psX|@kj1OVmUYDJ&WJt=vS zfOA$LLa-~A9YP;tg-RFZP7X^P#@#5y?(dM^O7Fu0 zsIu5=SK-&H7TQRjqN|t_nc^-@h)u5fX-)6yN6k_M%m)2|RNZZw){7VT;5fpA>FlX| z3~4SioGHwDj&Vp88Bu0(7D^;i)}SoJ4x-^@fl(RJPFe0c4%D<~KK3MR{kStMy(uZ> z_e8jeB?f+5N*HO;>TVUhxRsN7AK-$xmaQ}cw_^!}HPeU@&L+W9Fd19^YN4URyRVVB}2Yip`xb3_MzZ&C($Epqoj7@#7d~{fM3gSza`X$XU@Kt^LVD z@uviLAw=K`1mb~QAQpvSFA;^jFA&8is6K)#UgK{(f)CUFSZOp6O9cF7;ZRF3l5CAd zO9QcZG!pSg`~m!*g18Z{<7_61N68*Ehko+wPz8R_6#hlmgcAYCA_JjxED(%_(2FGQ z_y7XUP;DR@>clWY&%XLat@&2-%TMa~c}ibte)*^MFRp|e&B;VjQP*F2_n4EBPutN) zpVrr#TO<1;$(7x>{8<2v4}lHYpQPikiVGsk9hcE+a8yo==tzxdVKb8z4dAR$L)`P`%%49^Y~XDdE3+a@4B@9Tl9QsSebkK)A|)7 zzn$U0CAPaSx*gj3q9V^fila>axnrQDaJw~MbJ~ksPDn^)Kk;A-!e+(ZWd= z`|hJiCHT@GmBFJXmcI4xc!-~O^5?(t=Ux2C^XJ|A%D>-wkM4O6=^@RI_v){%d>y~< zajiVk^eZeNw&x?y=slWe z!^&n{{Hxo(^@(TnffStG3z=3fIKFq~>3pm;;8>VjZG9*5nIP0m=gRBfd`?fSsUL8yEz%#-2ej{KFS_2TUD7(dJH5r8S3Mu{ z%y@b{0pP5)c5U=|eb|0GexH{~x3_nGK{q_``yN>+@3lWw@w{GFs$4!Vta?UXfDzNg zrJ3>``;|boUhjc07pvc$w_?6p`}eIU_1Ma{W6$gHKlHf#j~DqLH}YS(80nxP=RfJU z*8lbM{COXL{yTqujz90`&kOwddH(z#{P}>svi`3>sQ=;394r9Zje|wr4$t3te%bR@ z&t8wuIOx9Zew+KCJ7)gA`Ix!iOd6jvo{oGn@@Qmh_}{~K!qeeQ=zoUZ8#)n+27f2` zXmBX-FM(eSOb5FC-}S%WpY>Px{shSbhJB6RZ+SoLyg`uAJr9S{2PR(B?^lcQ$T$C7^Vzl2FY3>!uc8lq9$%Gw`sr78Bjo^Y%>4dHEMfl} ziUgjH!HtW#HHv>Yw+2*Uzx>mB*sdIXQLo}>>+I)ld`64e^}{dfi_V50ISN;c zFMn{8j&Q1fl(#;&34M9b$%OrfC^IB3W_A=KtIc2eJW>M8{qEmr)mr$w`J)v+)oFXv z(-BC*$3|Y%2lB7nd7<6@NcF7l(^3!SJNFc$3*LizIDf?VwxkyNBMw!b)Y#v|2c7nl zKY38E(h?Q<=YRKwI{V0DU)92P^yj{=87uq7Uew>`%6AT-j*h?iS69S7@ady^sg`KU zKlh z+>81Xb1&iFhw$&i`1cF=_YwU2DE@s6|2~d?zleYTC;t5p{QCs{{SyBDGXDLF{>iyt z)$?u4>g{Ajy!AYC1Fby&%&+MqpL6xv=G?FAzvlaT;4cEN1b!>_shWU)otqZtHaER8G)&%`kvEs1YHJfIj zER;?qSSCRFmU--B9YFPw2;_bcFQPz}lH9#?59jXeM zraK%9`I0Hbzu-_p)!qh^Z4QO5RJehygnJ`X{LpEhjk-SXHPAPkRhqY!)bt7^%h2I@8G#Kmps3gux!d z)e@?P2_+_wF<>7Su8Hhe14&!2Zf56XI76&>i;keTXqBB3Y75 zxHZYXf$Mz;wQV0nlNC9G=ASBi#5r=Sdt_`32W_p9Iw9MiS7Y&Md^)IkCI#5A+QR2` zVWuZ>!%6D_xHCnyVpt$@$7FJfAJV;;OPHhKRbi7Lam4j(B{gA6;3g8Pm~M@yPQGr)wb&JYach+>waKph-NsM_i{W+!HoMzcTGCLFT40< zikpLOLD*!xPe_>MW zpYgMs(a=+y*0|VyC9zV6Y|OB*)e>lZoIKwiB8r8iU^s8k@F1PIvQ?w--|CfIC&Cd9 z7#@UzQIGUD$2{IGGq;u4mlz`s1F2uER|V!Yj^1n`!@>fE|HAz^jvEJ?+C!rOZe#_o^tf ztlhj+TBJOnLyDibjjO2GF7nGVxV^XY>_Wh@^mX6)tK3s^k~DU@Lf8 zqD?v)koCF_HL$Atj1G&)WlZc^9=2A5gT6$pc2)CE!+L50HVq2TL(s!rv5UiPfbk3w z0HuA0iG(Hp&QSpzfr38Hpk#;GLfH`j6z#F}Ug;Q23UO|B3E~M8(?tL(gRUj&`X(?^ ziVnANA+dV=s?0#rlto9TmV%8G=4UhuNN>T*a!M_i1p*uG$?uNp138KH?P`?%?37>F z%|TKDdmg~A$c}nBP32se&?HBY9U5$@d(ePk;N9xUW=~$%?m=9l6$9Fa*i&;(B z@9pfX36r8qxFfy6ba^Vto3+7B-h@$V)Nml~q<33$MWB?Qrc-9FKT|8UlqE~HMcJqD zO%hXWCF`T|aVj2)#uDEBDYg*v`3AlIHSAu0#0m-3MeAceSYKVekqwmg6}MFcpi#lI zL;KP~-gZ?-O89PfWsMQ>1?$*iz1Le2=oE6!)3%p*aRah);YGZ+Aq}}9n%i6wZBIsv zS(6p_WH^?jiD@Wl+9~~SNu?9m<|vs8Z72=}N?3C3rePlveh}~o1v>=EG4FuiDqG{G z)hD+PXb^<4f;OQ74Yx(EaB)gRuYH`v6<`W`d^0P65D^=7Cm!}QuYiM@xg8%tPP3V1 z#v@Sa9#SxAg%gY@k_ogAOIE5@syX%ne_a++7bUQaTsOS1ubM-sSRU&L6wjN4p^$zzu4h@toQ4cI zck|=4>s};{o862AJQ$uFkK2J2VI2+wP!({0qwa=*ne3_oRItNGT2d+D^+r6{WPj=( zv8neobDGLLl5$Dryr&j#Gt_{Lm~L3P!qQ9a<#uk#QGxuuUe|S0hWoNIEJ4`H*xx~I zYd2Km(IC?rmCbv&2<%#5t7$9?ohTjcHGK19@U>QlB(>#MyJ^@p-y4OAo3{|K5Q-qa z>2$l{PJXFCn!Y7mlJ+NC8X%91mscZ*e=?Cmq(sbw-5+T5Ed4Wz@x=anE5CW)x=1Tol zkUU1qW3kBg80;Ql%a}-)#p2;~Ae>0XpSbu*{gW3F2kTYuyNy4EaAw=D*w02=v_tmB zZ>`r#?c8(k(?{%2c3gr);ECs6cSTqJW&6weU%Kq}_=H}jh2LqjgFn;O9TR^(V%^d4=fl<=7yi72ZGb-? zux>w$KR;{TzKK7NTDO<+=UMCawW6Y}XRO;xxO>jJy?{T@Shug>&(B!5XNrn?Tddnt zxPzkoLH@a7-M);c1J>-HJ^d7E|n6#o1KsC4{!4D?Jg9Pqy)*iwiVEF_116bULhK_)U#T|fYC;nW; z?GF3};B3c-c@W`6Mg31;FXPYWp~uI=KL!1RF`WPhf`?y$3?F~K0Gbis!6F;hQvL4$ zMUFqR<)IyaqJLJ41a>--kOLYn1GmoZ!ppO} zKF^;o@aIqY^Jn_X*+m_!>F1lMrRCR<3~mIm zQ5UR_7rUO^gBRx&Z+ZJH`sk@mM*NDSmBBR$UwM(^1SL2#$*9lR9J~*L;skac!MJmQ zHbbAGDL3DQ7f9&jtN={<5vT%D@KEdw8d`@5oR(&{^fAG3=u1d&HAqK6r zn(`On>O9EjR}*x*;ovz$JUy$6mH9cmL#idP5**MDybvW{?m?*^%#d(LFt>-lt}4P0 zw((#}@}Ror^{meKDDF3TtbY5TU$}qv;mQOS3SB$x zC!y2;;S8|CY0PP$Cyi7-{1WE_IPb>c}K@+%>39SX2p^H@xDm(w&QMkoR= z9^F{F$}B?nQ7eo=!Gr!Tqzw@Goa~Y^l|u$x78FPj5=#w@0tl%I(j>T1i?hclTi+mL z5I68~T}KRMKpw6~0AolQJqd?PwY&Eh5-8@_dx8mM5RA46uT12E5@2b9mE$U~tR++7 z@d^2IT+^}`6Tj-sO>VD&ghkA`$$1(z=+{B?cB+uDjW=gBq=JN@vGf>130-6U zIIiiz)#PuS4Y*y*j4mlewdJzzm%w6J8&EQZvBgAe$X@T#@pBVmiP`aSLa~(KWcf(c zWkw93faSC>Nk*>9l+wwT!J@1VYfsz z9}>dM56>d9JGeGN>QT4JSg@%1JbG~w|8TN$!&C^;0cipBM=DMWzb(()_%E>h4tm+w}q=@E6Iw^S22{tbb zv4WvbPQq77*yN=*j~w}eER~S zE26_=24Nr6@pzvI$6+olN$&(;*1-pg(MMD_w^L58#9qXgDN{#~QR_CZ;b*ouhNQQ5 z5!Zt0N6dh+0>?#Y-6%Wiw4_sPASe!VDz69AgjLJ$&lz5EVi)vG6kO|50_4^0u#Rvb zMi^Ig4?{kQ7>Sd1oGyhdw+#cE3UHFmhO_OVFv*CZzt#${t*W6u;(+*Z)}wQV^&PS< zhXPPrKwf0jov%)YSjO1FUw{dIVO@vvhOP}`+jFaXbXa1PhC-1jED{Eit$aO6fk^#5 zCm(?h_CA=r(`Y(~qYPb{@CCj5S!ZQGe`Ci;>?Gmf1|lE_Ju&#$lU01vwvUxUu7{us z4!HyI0Tz~{J;V~05(Ggxf@^Pz*!MVh;T#S?1@bXXhY*?MjE1~_*v0sgf>RS zLYF{Sg4nij=9Jx4DGLWwq~ju@lNLJ}A;4;kAh*gQ#NE z!47*^stBoZ$C&+?ld@HZB4cKZXT7AEYry0YEnxoZH8ZNFR4?!o~J>Xbd$BO+N+iDe0ra!7o*gmbu1Eo6#Q41YmdkNvCAwUJ5e zKY{w~x;dF$oJFhb?HpKfWNVc#Srizb;#f8UD^W#4$r#H`V+nB))e21_mm&fxWAWuE z-U-4B*I9gYlj{n^O`NW#Uy}J=GqfB}WOf-S!vxhY_!ouGh+`z;IG{u90fsq_%Fg1t zWmymc3{BxYJwJ*Ai~A;R8t}Zr)+7np2**{`7H+l*Q+`HLnbw|#Y(|4xuRm_;(86H- zSw5oc*O+^eaJEfqKSZZm_V)fLitA>(m39H5v~f-Yuv&9{Z##2nW>JJlcR+|6PSB`< znZz`xnH-c!;6(0X8c1YV)Ffx73AzcL&656^Vs9zh$#SGHd}BH^_4zfl0Z)512_uJ~ z^HC1xoYa%3`Yw3)f}}#!5H)@PH??G|>u17YlxGNWugoSypsLQCuL)-wC@~JbhWqIf zu@sEuxrw;%dyv{&u&aF8pt~<26&h&)f@d707%G*H@6?S6aen7~z=UfO6`aF9J>y^F zsLU>K3N-H5C2kvbFDGE68}12440VRXF2Yb2n}vkJ{j%|EL1ay!Mm_-n$Sj=fa>C>> z&8sC-TSl))n->!^tMgH4t_qPW!{`;8@gmn#+Zk?cGqvGitUuxXqUl|Ak!G*9<5@Z7 zyn6zcmk6rj!UpNZT4K&F|E!>^2Zt0am2|7Wb*)@o+1}xha0i@;O97o^hg6H2;u|I3 zE0oT7=U$r=(bwTHv7Br~#2o-9LX8l=*dePWl5lrQWUC%uAY=x-A&+mj5(Gy!>%zU% z^TYFUcCPgs^juSr2`DRsM`&V{R_tloL_<&i`xrv*TuV4smIM<2+iJychrd*R0@ z0nMGwyd@Q(W!#=v9Hw%KL<075QRI$ni${Z%mCK7CUF4Q=@y~Vqe33tY!Jq%hpD*#}%lvtjKVQ*TjEjG% z*LSQmUA#~Ki^whGxxd7t=l)91d_*~|DG5SRr29VT^O=O?`UGeUBmj35*=H09BJx@U zjsVl>;nLO+szJu>!jod40ia-|LHEOHd6-Eklztx)(+T*4qAb?3pI@3PY41*+Ah2PF z)1JyZO5OZ1j{%MvpHk*K<@O@#4zjOg(GK69Ee8xYBzJWNT>z0Dfx|?C$)8(px`i(h z3sG!LAgDgJH6Z&3nZ?JTgk*l^pzE=R@nV^JFx!FtTrhl8XO@R=9-1nmT%5;KOQ~aKqA7D zWaJm|1lGN7gfd_XVn!;V?)DNb?i1EJDo3w)@RJoB&8a@38_4;xnp!tw8U%kwQrrke zi-?q-CRQuy%w_|!a7jOin)x&wL)D|^ei4@&Zj3f(#UQ&WK8W5XLPof3c;^s$t%{ z@FsIxyY8Px^+U44JF8`7O4+XpE=2!^ZJc%Joj6(S_!0ih@!fu_h+2%kA>c1OJHUcB z_#+zVAY5v2eO*II9|%cSu#KPfS$+b+)eLFJDyzy6dbBhrIM-T7hliO(Yj^T$6SX*vyy}3aTLnEh%rSPk z-4ZB=vn)B8m!WBySDF^V7A)j;n+Rz!kyZGEPu3@VRIdO~*afSYr*yyl99E_{r-3z%(fS}Z}#$`EK50Ozkwbr)*7EInXG5{G)wsS(+7wYbDsg+AUXCTg6rHh zRoQNsh}+L|LQsU;G#SmX4970P2|DWe38d^IVY37G_xW`DGw5K2xE_pC+_x*q9%Mya z*uZgQbQhRn!7|7_t|SrMp*M6NgKuXUds{ilO&M-rz$wg$V6k-&N8(t$y%~i;y+c*2!7PEpQh<#A&KJF6&*xw$n-ec2Yt%&fN!9^Hqe=L2wc@S%(Mx z9r&5m4Wy4GKEO>DMCXJuUZNGv0}_e|!`+XYArtsi76>;8QUu)?ws|9buTHzn^x6ze z&ZSul4-?pkLYJtxJHbu3y71ND5S91sIQNd#YWUgrYsA3W-S9e~5AaU*yIs@m!~Z;r zDCuZZ+-M*N05?&Ip9i>f{5`1N7IuloqFhzm6Zj8w-O20^b6BU*uS2|Q`&64+-S zO7$7~B#B?vb;?i=!);(+B}x2N>B?qeiz>)-Szh>HE5#N^YPf^; z$z!kmIW$sxe<_}Cs^^IIb2j&zI>I`jSNybBN;Xw;cNrnhdnd<-c|~v<#~m-h!|0TN z;6YrqLO4Fd#eeJ}+xsu0dIsVEe4XIOH`st6kjwJ0gxwa~hqZijkOPZ%!>UQ5EpcAN zgKVaT?U%2Cwiw%kQ&`I?!>sZ+PKOx=YQZe;MX{g-yAE87)^RI=(bq1XAGL;NuSI`K zb8Z6~UO>WHynIj$k9c*01U zM-63qM?z-@7;p)DB-`VR0L}f5gj}+@L)1AVW->c*up}M~MmLxyLS;;WfdB#Sswm!D zQ3@s$=PZUs{1?%4h;JlENE>c3*@~-d!cDOOp|!Jkq=l?r==Cu$u8pF0gesq=2Hff( zR@$$Yk!a8gOYipT1_EQCF&@!fby7iv<{R%=4|n|@`p)J0@Zm|#1J?FZ_9}KNk>)NK zcTGqj5ORhCtZ%FC!O$MS;iWmhCxon zEWjD7&GO>InS)z4%5K5^c}OB~7^r!F!0jHM1-p$k;nYXnn2f2Z!iiRGm=dZJh6})9 za53oz+8jZ`7+3<)Af{1wOX5`AiabTvOs6s-ZJ`}N5MESW=RN?*WeXrR<~=9;-~oJn zjdQmXhFFF0>@Wet<8=VAe4R$@mfNu>?-9u z-^qyJm!o?_eCOUeA@(CySBg~xI^2iFgvBp(OgcW-#9kdcT*=)Xl-;i|lGtX6F05)m z1HI|*s!YT5kFCzd`AtpBAyVBXp-`#@rae?Hd7{M|St4q6x`LqbLdENWqH?Z|s~iLD zqZNuJk`j3IRg73Jx4HGpvrsj(aE5)lb_KJ&9Szi0@6>(s z2(F%`Jk&YPu>w>Ak@mg7$+R{Lt6tjCh5sOuGsED)xWjhTqhW6wNe67h#h1ODWX!Cx%oFWw%BCF6;aP%Hu#xE5@2JQ7@6o@T(PvPifxlU{A;KP^6rZ_s}y@`h=RK)QtW!j+X1`sOM+|%F*m0T z$2wXV8{pO(vsay15?e_>Q@AJY;Xt)=a2&!%EmSBjTrTYQ6tR2=rhXKS*Wx;kB?24} zvE(dQ4W2-sggh)jC4`4<1UcyEKq@MV96qj48*Pt5A#LoA*F&^7I*K?+C{7j!MAwAm z=~3pq{XD2{$~je~%+b+I>3)-lN>EvpZ9ok_1!UDl>f`~#1-vMzW{qheA{5Z3+yz9P zs-P!>f*oW5MA}v0+YugZk*6r!4j)E=N3emQ&Ld@YQhG4RODG9&Ch}^M+oXhGJtVU1 zy`Iego`LQI+|M^d0*u_P8!bP`*|GWYsb!f&)(XyxH}^U^+Ux#pR3D*^BD|My9a$t! ziOj7>yhiL)QQAa(>u9K!3brIYbOQhq2-d?^Cn{YnCIaY>iZba2uR~F<;H9##gm9@W zdq}Dp<-1}_d?rFc(XF?N`X(_rkZWP3r7%md5-eQpV-2OHidYKQ^3#UkgB)BLiPqRi zAi~DOO?(r(e1dNT!&F@1mx*YJn9YX8>^3AOxZtGmMU8mSUy!LRBZBn%B383-o@sHN zfJmwI0lo+~mZw6jtkSpB&+b)ks19$9fNE2g>B5*zdC~rGLycx;AB0)8gSa|$-xMQ| zDGkt3G;8hjXf$KvF>ED;sc$lL#_uC({V)yECOL*mqQ)G7y_G)*7f8=oek5r7p>*8D zlXZNz&i){lt}5rA9!8{K9NaXRJ7SviYDe+#&2Yq}K>;H%Ki}kGg$-n0%H+xbLm}sD zuVK*k7bpt@+5pt+njzSbRNpJAkN|CuU30{+a6!T4q|m+nV)b3e2Tg)~_i#llpCW|& zNupVs`1X_(PqIg}IY88TC1+^TO-Uvy(gc)SOFACG1)P3?qC(PA>@6}%AwcvJlIZ}4 zQhs^_+{I`PiO(IW$8NVSfj|e?#tzxIdtn~wE`{-nVVEUgKMFX*(o7xU;J|aBo(g4X zA!c+4xPhnK-f^-PWrhd5Dw9;fu!>8)rUA-3(U%C~h#NTroHgDy;cb;w%RR?L*f7Ip zF9r=+_D)oF(lBXr2OxkQzssssMkAfPF5{S~&xaaT&Y29KZU@(1Fdi2AxzF&9F{g*v zA`Eew19iTf*m}qZTbl7KIJiy>K866fYj#$3LTE4iR12DT2-F}l%&IUAGn$T!2#T^< z1aYTA&nisxIkN*3pUO8a8A%{jrX+R5y108_`!X;I|#?&qe zhbMHvUOAc8c_@w?z}o@Bu-|I8A4Wa(xnh3pH4Hezz>pQV6`#U~?=*3Be5^P%>owM!CVeiSvO% zA%49$C~VoH5unW!6c3Dcs2JunLZsf{7|E+U(bYb6`aXx&cVLG;1{}mMLIpjDJdMtYZY#BI3Hbs~DI} zVaNf~{w$^|DX}PWs0pw4azcvSt{JsfXcuu<*n1Up^e`T*fzwKs`{e+8D94=PM>J+K z5d!EO*IZbX9XoJ&6_z6NBg9lEgal2c)_B3~5?Qf^MVIK?yG0DX6;!h;SzBxsnQo$E zPDB?9JqYcMgPdjb)iU})!5CzR0P}!UvK`$TxJaakBgzpDF95!DTEta^sZ*^Y0@wk6 zD{+(~7jpuV3C`jGChA=BeiFQM;BjRv1pZ-R!Zrz9405qkAq5e) z6?b!2qADV&dEhEc5TT=1qOZ!_NKA!O@D;#>jN;XhVM6}PnUrn#*o7Y_IeYr#_)IsLMG@d~!G_&r zLHxU|IW=Q09rWb_zgIpDM@QmLL%Rf=( z5<1VA9!NV?|7+P7Op{7O;!I~4QkT1UxSVwNB3)tNVdN2X*zI$4!@{@k_3HM(qc;$6 z31q0Ne3qMQnHr(wusF+HB>B{)yd5`S?=Kj!btd44lg0`Hn@j`xZH)UM3U2Y3^jt#M zY2JeK0naYFl_e{TQ*hL|=f{|@M@65rHbUtsrZKyy603%Im^f|-C9|-HEnt*>xS+Vq zEv0xI3Tgs;xEv(m<2N+?Mka_ZxAZEUCgbu8G;+#eH!&}y5C+w6xj4W^9uCI@UqpE_ z4uO2rT)XTCF%jh^C1D5cAIEi#pGVOimJZu5;6ar-xk3UHr9yOe1FJCJGeJzqLT@F9 zo|HXSAi+HKs3Pr-Lc_^;#PMJxQbs2LXh6@z-%<(1YJ6KT7Fp+yoDZhRCx+r+4I}X| z40j^2SS*nU!4#}KT9!-rJD`t+w@fe@i!6-r{M;fEycsv27;=%#T-`@Z(}QdRYKKT|-4c`^ zW}t||U)b6eKJt#x8bgnzdkT|ARAww2{ zX%_m<6oi@FYM9wSa z#1OwLrNuX)g3XD@c$Y{R+d@(+^@m%zX=?a$2JVL<-N5w`LGZ+38R2-s%73?m`^M+h zkcCGQFd4uBr6o+C|XeI$s`Z57Vg_p2)AJj#WQCfY=YCf8r-hq zCf@9$jXaN)!h8@GKzO4jiZq*9Q7t)>^_;YJ8k8U;y9li~(+xzP$LJ(vmADb)9Td@* z4!~CzPh~2PP;H{&CrK;#M*9@Wa~*Lx8(05`H}+KmX_p2sFBDDs;5VZUg~ ziv4#z>$g!{(kc@v1dCw0&3?pYU&tt@)K22NtL*0*H<&VshA&K9h5c*jX03Qu&MP|^ zL33@ue!>q3I~Dg3Bu?V<-3|b5VoyN-K$IuttGF(;0iH*72HL@Xs$r3&p~D*%q%&Sa z>pKgg>nJWush*RE=iQp5aX5mfdtiSFiUJfHra%a|olLtigQ)+cln5lHJZV%Kj#V(P z2U)@|4zWQvg)7H5>DC6p+`E+#E;r2~Fv-aHq+kn@vl&RrA=|baf9!@HYjrcp19X=P z7i@9+R%4AjPN|Uymx`QlkKKG&ZfQNxqn1pLc9 z)VqYxZX-0qPyyLlMro%aU39}q5O(;ekB2sn$a#c#=cXp3Hx-1hqD!~h%ej3TaAsrw z7DR9G9ml*B?z#*U>3szol1@J-*dU3~s_A6qXCNme`vpEoa5r#~{Z`Ca9r&GV81a7W zqGT;Ij0`Ko99ge~tXG*Z8M_pkZ}0-Bf{xRS7Ee>SL8w3smLscQ3+%eEuiJh zGOHHxZ(){)JtErZTs6iKzeXIDyDSnT;aFoJbZ-(>Hh>l=ya7KuU|NVFt;MX}NEee7v~=AV7LKk1cUQgO!?0oM_@+uX z7#>9#m`u_(LQF<^Tvrn5kHM^wTnF82$Z8xU@2rCI6OilhXg6>Rz>3}=B6wP-d*OZR z&;SRxzNvP@g98!OpccW{WfBBt5MRSuV_Ya;wzgmxcGX*Mz#c>$^@Oup4~%N%OJbs( zaNfzn5EOfJgY+NzVDwl9C#W-KVC$n9%I^@uoU9`{Mj|*4n@TJ=Y+*P6`GRde93H9jHcFv;jI54Z`B%YFxH%jA&83BmEv z;ug$ixjPBjh;Y3q1QU|0HiQgSB~f3BC!+Cm80NgnM1;yIY( zh@e6CNm{reO-{l}9!pt|>14yoaRx4O1fumobW4O!1I-X5yv9Vfe1i~vV%Q_JP8&+z z6axX0b$eyMX257#Z?)}CUy7<@4+7U7(+|f$eqU(YLkS-KxuENh{p?L_tB)c(O8GI9>>~Pl* z9YSJ^yr{SlLbwhojIzu(BXK@)j^TTrRD^@mIa!oi!-U9+gpkygBB6#@!6S;hr2(92 z#Uq9>DU3FWz*!O&(YQt1KR}oea%)6EwX0`|6cu|>?b0|QJxU*PGG+XN}Xg+7cs*tta^jg2MZ zfpYMj;gWa&I@f3bEN~(XQ{P}5y3+ELKj{yaRdDz|lPrPv*iPtpg3waAhP6OJ#7&p^B13G!`rNNB!Y&3ljbWp=&J#Lwhux z2nXTVlt5k}e+Vza@U%~Y4GskmR5ad#*qmu}B3xTlQWo%s;Xdz=Hl_|o{CF0PCu6A; za{@JoGl3K&pRj$7`jcrr9Q1!O^Htr5dNt#{MZW9Cdskx7-L5B$wLf_u2&MQ1%U3=0 z#FjqG3?ZxP1+Nc&({1C*LAUMFm?S}7&cCw!4@vv8kNujSiSAbKF6?pM+0n-z(<@Fn zk28hGOmT83OEQLeLjL2oDl1UuhW@ThAvF+szz=3dX4~xVZwk1I^KoxaJm0ltPs$#D z={44QW5JDhF(Hu-nrAi~BrEAt6$3Lf$<%0}FAE!y(Rdy? zJO=@eBTOVSn%RlCQUd3N+&WC63EvvY?t>gYs=-#@YIFI2`{GbZ?w-baP(Aql%hF~m zvZgF#4kMiw(yKaC;50kdn%SF$E(1MZyxVMhWu6mkR)AjuF@UW?sl<}xyEBAeViaws8l4CKeF8QYNA zCp&_4Jveb&Gfb5OE_%LgbUu4+1_@%7i#9$-MxbHjxJS|+NnJlW#&cq9v^}#6NnMvS zERVw(39zx7GE=$PYi&Rvvr|jl!Z_gM*UWaO~F_lwa2 zVB4?15O$T>+wMQFXVMNxURVYD3$x=F2J%mKzgn6n#x?#cTlS)YKfVXe3D?EAl|0jIq5Hr*`aCl17AR=di1U$l?r->M}_xKIEex*AAw z-Qgu=wW0D6=iC0*LGSK;?U}<1i`U@7E=#fx;$FCKBRABkEX+f)NM$sPjK^&1+U42l z4D^WjcTcrh(%aK{>nA2lOAd`)LttM&si)FA&}$@!p1F!(bCTgy_Ou-yf4g3t zbEd@stm}Y%M6@C(!#UvctV$!MHYp$e&}_8=fV1*37ifqM8_3%=j`_ei7bIgJa{JB} z_Bk?=y|D^EcdKM?$|BC`+qGoRLZ%6k7aby4rgVI27P-urhBOPA=phweE!z_8VkR!!yof(TY@?Rz$kx?5m zR_QP{E{G>&GiQE!ru!G7@@`zV31!`$Vl5Ig%WQbNuv1OP&a5g@SDx`t=(St%rMQxW#mrwdRF ztPzDRIsq&N2SiEv?R4XwIk2B{e^E;X1Qj9A9U#blwB#Ln+J1TeMcsrSBaHZwjT-s3 z3TW9uI)w*!ca3U#44G2FV99V5{HVi#76FCibXhoXQl!R7#-NGF3JJ%-ykZHkPpOv7 zFqBGW0RvwxA%KLG&XNjqwGWE>%v+Big<;PeLz~RN9wKuoyD&Kh47__{7_{!l$ON$T zJdUFMvzYz`Bu*cn%1+`0Iyf;iIeTqkasq8FEo3j*SN{3WTs?v;Qx39R#W4y|J^z`v z6?droUw!Sp>wEe-I{!nQxr$aC4ETc|yrOwl+!w#9e?PKf9Qms5ivEHb{i+`I7>^eD zJB>$$Oj(=b-gT{t0$0XJS4 zn7J_ERD@?z(S^OLq6@6(!rnqf7ZztP9FU6U$J#pDr$G)l>Ee)|9$n+fhUPaS4O^yA zC7wx@8K+9Mr}k#gJDuaw7V7-3*YYDO5%iyb&A+3hUQHN*61@V6rBY`S9tT#lLE29} z^I62L0zufVwu2xLQeI=%u^gpQhCk82&7`HTIGm=1ifeT3G;&P;}Ge7<2VO z)Wn|P{aq3W(COe5LU?B%P6vAD!&+r4r$HWWSiIayJbpL1WGgG-J0=KRMFelC)js*s zKkAM7E5=VH+NWosS}F9(89NdVBFE({kPvVe_U;0DM?5sMod3$kGl~4%jo&lvznyuP z?k~%ZlU^z`$Fc6g?qFU>dp7(%t)jX;vlpqbF)!$*Qz?_&L(ankU^@S){Mw{c*b3!6 z++cC~!LA97lFcGH1l&r*0?dk5a4EyGGrxC1PZi?{mWr(wQaEQoFkZDgm;Ovk*dLjB zpYF3i(DvVv?fsF36hfc=^Oj*fXb>F8Bvm&~7wnbJ{{H^_m6OHEiya-@ z-N&!t7&tx)arz8>hf$&-GdSCxIj}g|4ju_^3bQj{TYf~hqzi~Eu!tSJ1m2`T#^OL- zfc3+ey}*cChh=f|#rcNohYfs`*ZH010YHDoXdqZuA-7*Gz(&D`XcE4~&o_%3e>OlcSK}Hzj8KRXdOO&E*%0KmqRBDQo4=i?&33_LMz~)Cmnvutz1$7H57bG2d zs6rDcBY9rYCqCm>u=`rrB%?mIG`gHQwlo4KGE5Gq9hrvbfw~>yApg|TTN6Kef*nee zI6H4&uPU=$ffIT%|6AjYi0c3Kk0W8h2Y&uvU7@3()8NZfK=Xt=RKE&)vev+pPAQ?U z!5v?dyv0D}gmdcf9Y|Un%Z}tf_1nJG+5&L?5G)f5V~H3*LmgT3`M+PkshmV9IAf5> zi81#dLH5pVo3qU&kz?ONZ{v%!AlwTpTJV&4MZNj&lBSM?_z{Tlv#9sj<8e}992 z-^9Pa#lQcBe}9L6f3H9L=xYcH_f^}(-{)M-uvd9a|IVITZ@D+=4Ix_454?-s&wD@P z{T=V8ywl!c?l~=9T z^fGtuC72#2-899FY4QikLEa%nI{$>#pOE?k-)=tiX+8tdQ_DK8P6QD^Er~0T9exNp zGq{|FM1@fc77$DXp;yZ!cAwiRhlMkw4%k++su8%&u!iyuoc`*A@{UW8F1Y36@(v`E zh60C0;Wo=Z6JQuzSrT5Z{F7Mui?_X|PaCfKm3@!D zrhiRR`<1yWIu>W=(90m~U>?IA#Atq8F5{Bqg%{V;xTf*Sk{dS{aWf+0uIRWn7Id!W zm;6W+$l9Qn1mJj)h_V8A@W5d$Zs#T0(fJ8O4K>kmZDKwsZ^}CsB>u4f)^FT;O~=o- z`13k{zRjQS@aG@&mEXAaU47@b+*XnQ(}pGV_L9-|jzJjmMNj6cx4m<)?41y`&V%iJwS zU6k;CFi)KV)&)LNtSQm$z0ZKKu<>We3OTrhy9+yQVkU+fBo$7k=FHv7?V%tZx*w1Ee~&Y)Ak8B}j2`Y6H`A zj;AQ+M2)<@M9E%eb%jxAkNR?tym0!6SsMjmJt9!Rilp%|xD>VBEpcxpupe1JQBlrE2R%}0+`Ur@~c91lb@hE8mR@#ZNCZm|1n4h1W zZD=S(jw)06O$RW9!=3HDNG{mj_XbV_i}oYYBM{&!_n_%-?}CO? zFzb_b4rYZhqVs9wO{mpA>i?Y9^nZg|JO8&(>lQ%m&LxOorvSgJm!k#E4QLcNF@YZE zObg-_q@h+&jN-8%X@%5)aWBo2x&)IxHMP)ccc!yoJUiCH$n6aAAcm3weGRz^)=Us! z6GU4$n-Lgzez{o$mq25SvzH)I1(c6C)Ru4(*!(Ogm8_zK*%|wl{r{k)&LJ)uktF2~ zt8^fS1ZPJ%D+B|gb-)}oOwvCxGz)NsWQT{x7U|FpSQAwx(OykJap!N_A$2fB4O?bhs-s;>b>M(t#%&!s)u&QFYWxZ9KD9;Xx{+AVVF^Af(kvq8f&} z45$pU`*HgR;U8$J95?dnx6T~Mf=Ky$D-$6a1~P^C!I`m6K_g>bs#h}*R#S})ABK5G ziN)ay4G_AhCKcz=y>(7NSWe{w`j`XMKuSky9J7Oixsx+S!7Kzgnx`Tzu6cm5A;Jii%R)^yc0Mbi{~7|GPWIamIgYI_OIg7c_ z3MkZa^*~ZClRnu_18R0g|!SC801 zuc4jF0!v&*npP(MJ&)@N$?1`*?w66KwtoXc*5mB};XcO^0j)x15#Dl73iTl@Iw3>%IaSUT_Lzkmq*{*O-^)Yas>&<%fuKU@#J= zJhvhlmj>%5X$sDJBMkJQ?mBhGAdwe73F3ikHoH~}BZJq(Jz*rI%m`v(!lYKNFKXs| z7SbZ;i}e~!g*$xaU|*H?Lc4N<4FpkGws3C&0QU}aFE8t-<) z15kZ$#WIZO&0w)k`ANiYqCM*!UlgW5!BnlMjTX4_Hs zbqnnBoXai^Q3a-)n*h?`z)V%Xnq_z`xiU02%uaED;1&R9#?t3}F|1EuW&{SAvvUXu zz-5Ea2STfYQlszJs60TN2N*8PhX9Q^&2t@@HEHrL^^WTv(9_~|Aor~f z#Hv`v8eISdwwvAy#g#3ZPt+GA$xuQ--K}KS>h`>gLAM18*QSyP^@&+26g^phIalR< zt00&26ek&R6c!)Otlo!EWl{%5(LD{Ltzof`moY3O`rRbs4@uighzd>NI428*w+B@0 zd3lG(ano6FwKTPq2h%WKbrv^N46|$JI%g$y>esO%7!-=askpGJ>j1>EWl(t^(hwuk zfK+wB=ttB}S{bUzHP^Vb-0V2+ z;Nh%CQ-`A|e`Oe9%_kVk*_mK$mut?(d)O7k`GjbHu)CVL{Q|zzG|fka3dqw!^Jf7v zNC!730LP?lRz)*|9!SqmiJ`V!rX@1qog5eOGQi&v`l1}Vy(Q@~uPlL5QlC}1-~^a; zU~(hOSwRV@f(Mb!8A{hlaX68Bs}USQ6gcYBQAs$UMvvIK%1%oPaxRt`x<~Fxffbx# zo(6u!LxA5*v_&%!&_*^nx@7?`Qyc*&9Dan+n<6&D9pAz(Y8o_#s<46Xk5Y9F5ZS~S z>__FUOoK=E42U8HHHZj^XjNda)LQ_!QgDOCP*08__`_BBTT2t0lcqUA4{-Hvho)Z} zL+TM}J>)Vd6IO2!3mBV8z1dJlQ+(MIf#RNW+5q11Ay!1(TTvd!wfjtOC}kwY*;dum zfXrB&0j$g#23pJVh6Ai~3gN{iCsKx#ItPbbYAGRfbV?%b9o!DZf=ULCudnZN!Q;WH zs<&R#!TVck{UMLS3{1c@QniCXzA$f=>zxCdTPgRPcQpngh``hhF+3BnY(rA)P;n4Z zKM^`J6paVM@jxi(PbU$3Gnxnn=@9FK&crk_rAxOAGO2C>Rai+Wc$InfmNQ$k^QLhVe#k2S!9YREVp3 z)K#T{6Iq@i#aLfAE^%DO%69a~*-7)tYWVFL6wzY*G(JRh+rS7#V33H(;)+FLRP(@V zSYdUx0JC_>X?TZkBV`D5#H3}?(0L#SKpS5?g2=I0c($2pG`nd6DmUS>)=AB+3})0v z3p_q@^8HnqYEs=yR3>dBwKi8rt^otEN#z@KA|XhWgV+F*bCVGYIRR+cLLyQONG=hx zZIL1P)HhpEJ8ZyKN0#0rUT0D?XVnL|-T2vobuN#?->44{0s$grfi!&1<$>g0p*ePB zs1RjXwdm1cv<_(zLC*O?b9qL`aKsSbNv~?)&b_rx0r?#- ztxA*3n<5SLYdT1Bb-mjafH4}Pj}>~074^r)HV0`RtLmtuSFU`x#)aqwFwa-d89gU- zYJ_lDvAGe!)};SWm1@sI* z2zm9OI*z?L*0J{uN3d5zOy$B9Cm3Y??jD@d0uv)*C5R)?=_pcOFlLZ+XKAN%W=r4P zu!L8Th7s)0%%w$!K9lzMBa99|fit7E`wizgsA|oFPSbEml|3Uz31?xFt~Rn@xmX1p zOA3=v=?cz5i08OvI-l)fCWkv-5Najvl0;@utq8_j5B8w|mpN-d6F|iC#f+vBt*Mzs z+~_wR_aOB&kV-SKK~)_)3X*tX(TR#6!`cUI4ft3Ev7HQ9LdQK-rSBf%0H-BlrsTLD zXuEj7?w*CfcNMm`iW`ztx*asHtQ*$~F?;UP3jEUDB$~}uIv=ypVeka%c)bE6J4vjl^zbSaoekb909AV?yhJiHsva=EOVRO>&~2v zD?)-_9fms;sAp$CcjA1OGg;b0R5Y$619O}#ACNQIi_H>jFr#KLd|n;2+*sE$0d*Y9 zXWMWdFBUaku&;9*4cfot@}isy z$e>=Xbxvvy;$b02d3Ay`g>)M8RRtQB3>jZA4=Q~1)VEuh7JwZ@-}O^IAeDJ!fRS?D zE`52-fnTc#;lIPkED;WdQ}7bUc^*N)Y-Ilk;P6HC?r0`HDIAt^0#f3 z0&j!jN)fzmcP)49=SSb8H`=$5#Kd2J`-KZ)zfOAn!jVGh3kNA7S9E_{cmDN>hIIae zzw)u#9HpCkadN=eh>{mrSb&^|^nC)NLohRt8BZWQIt0QjI5d;l2jw}Wl9|rl{_fVy zu2GzEu%?g-Xp+uQDa<`MpE(VCa;fszEZCAo7+wJ1i}e9Sh_f>SEQ=Fe5W+zQq-=Xs zkrA@NlrqgyxT*w8V$Dtd4#wd2D_{7yRuZIQMA`dIP1%3{FI(W?5Yfy8NO0P{rI zl&W-eLWJTpXB2}(Oh%^AkkqS$xY;Ral*E)1??pnj06Rd~EkLsXtr*lM=+)>fWL8St zR~R@g0!9J|oC)=g^ip*)2g+Myi9l0u7NK@MGlF0+v`v7}6{@QyXciWrGJ%ah49}rl z*gpnOR8fCW01teQ=|P)&mzH68x6nv2Gu8u&GN)#8C)iF)(9-hR$XK%&kd2G2drrD5 z9df$i)G0Qmq!(Ht)q~MHrj~f zfpJK{E$m07!T9ttUI%))z*n{38nXyiGRbe8n&h(=KAJqYP*DBg15&&Y_^3fG<8D<0pz1B` zCQc3)ueAUY$d&-aL?d0N0|e{rGAuM+*ET7{wD~_rOmET}^=|C!Xz%Ol>hA5fKLy-Y zJpG^G!F$z4M&NOeb;nRx^_{W*Cs@@r|H1zXR$YG=tFAwRCEr6kZtTkABgh#`%OmP~ ziTWIkx-!IpK2P~-lK%sD&PE8RQ56#$=JkG#y~RZ<=(9jXH$y4luD z?N9-mK}iLr{M}NuP$}3|=f9>G8x-{01A%vIiTsm)_Hj>c^+apWG}Z2AMYWt*Du{`n zsolSp9i_jUtNY#WK~xMtyp$wHAkpa|RT?S~YmZzA3>> zL2>^%?)Rq&4?I}hM(9a5P1~$Yc5$y;LHXMPOtMJy~29()` zwwu;@RK=mp2qY0O_*IFQV$-7nh_F}%_uVO>=lIHm}fFxKPoE*hyN zTC35N4QGnHqpR55MItX$%B8#qo}B9F?M0HJFaRK_H;fEMEOf273x}CnAv^$^IKW_- zGBK0C_>cJ#S8aaVyS|yqu|+h9$QpR#&@i=k4X#OS+&w6$yMoyxG-!>^Vflu(We{RC zP5V^p-=PjBhIfu?+M{Bgl-E1V6|lBRS_KFR1O+g_l9KdHzUDnmz5kzK+_wJ$#?=F# zeDW`K6JZIyUF4h4zWs^Vk&>@z8{YxX^-*|vl~{OdF&S)FK zIOvct+BQ$+hyBsO8okMm9{!#dDmy6l8yA`eS>^)DTsX!ui;K9$4~)%xNDw@=UD+(>=3a9BLIq99LVi4 zU@H)UK<8?&iLs7@RPB$Qds2_L%hbaJ#F< zqll)8eF9?z3zk^msDljo#vOcRQ{Da zo`n6ylE?K>4*MB<9Db(QmBWn44*TM%2lonm?$X;USAd zDLaMT%2phsSD0fmET<3xjNqlrJ1{OzHr-1&0+6<%+{+- zvja3j`VBk@+zdG&+yN1TAB852V}f6wQy1P8EKKo=U{?*StOg8VfTg`NUez>K%)a&P zm$j5ho9x#7%6-1gYJ+$E#~b`jWMR+7_5JOg8@gc2yA6&c_G`1>)69blZ^j;ri}x52 zJsw9IulU1OWA&wX7WY|oL_!byTyH=^u$P9xjm%R%^Uoho+OOR{st59a_icZL>S8Sn zwhJZbq;PZzh7?QF7Y-IoY}-2Rr{=$)m*$(Exft2vyw0q?hLr@ykBJ_;jsqW)EJPG0 zW+4Mf1-Mp{XQT?iw%Q-P^Km`tg0axmkLl_BQ{LtT0uX?ngkRQzeewMfSE>f<0-gq7 zD;q%!wuB{te;b@Qv4(c`&QU$F1D-KtOywx!;Rx0c#|Cv=bTA^d4;O%C5>6S4I%i;D zM+=cfkQB7MfQ4l~)b!o5E%5!pi7Z3FXC&Fk1!Mn`MuXlK*U~T^uG;ARU#z_en4ITT z=c}r(s+a10U$k^}YimipRqw6MYVDG>FScdJZns*kR$INf7g>@mR|=9zLYxqdofJuM zzK99QK;TKtfHH8I7$b(u5Xi)YNf-taI}jeoGk1uYgk)eK_xC^VSJmB;oVjK-so{!{x zwO}UfSUTXvk_=Bx`-wle6{=1GPnV%ltN@!qT!GxBP=9H#;4zD;eX30aA)s|mWn53? zkS?vpDPxSZmGtY3vBqRFCEk|FWw|DlIr;9k4^GE(qGg+bi=icSltHO0quVW0ADW5vN6|Siz}Q|KxW*<5fM{MjXQZ znsE9T#YaHm)Ggsx#<>PFLCNRZMN2ZPvb?j_>~un!=Xm_<#J#_|^Cp{z(t-xLDcR{0=1Q$>I3WvsZ6y$zET( zvFV1<^m&3XVWSBrnT!ASEB?ngX^&P?0bP^08VfH zodfl`^sc_s?_9O3rdZwGFk;NTYj&?`=-F%B(@A13xl6m|+uwdAp72i||7Li%qZhSr zM=$&b{^8?ZbzwJ@tf#F%(cj(MZP;Z1|U=HzuY_?-8jB_Uq4h>s~^F&e+?HnKD5RI$m9JU0l{1nk$ zODQs_X3^F-uDN{#!)5M~VBte9P(7jV<}YmtVwi&d@%qI_6FR+F;`4W{oQbZ?s&d?wx zP0%W0p61Q{pG#4$049gF0^6{aGWl(LtfM0Yyd2#U2$T1JjGao5C#7~{K?;i zOB8MjKTe20$cWGNGzt>bVUzygdw|j7DgzXptOua-=V8{-$w7yMF5Sssu1*@Qn7Pc! z;cjMFMxDOX4!{OOIez=8?pH#U6>bD0I{S3GFw#i^NB?-6QKDGM++ADzr+=L-E&|lu z+1B6N(c9Ny1gNIuzNBK~3kOqo#w>#K!(KLma}k%=XK?6a=HAKdAvFOD+Y|mYE&S!Dn zOTQjzsY=KD4@Q!`1J1uS(bv)ER$W2M+U)260f<^*h4+A|#6H9i(Jcjx&HXjLPu_rV zYbS;$nC29`i{RxD#3)Tbb;bHDQEM&b&Yyxk2SX54X5bl!k16zRE~clDHs& zV+%k8gbskSG0ySs`V0ga>(qFGxy6?NJmTNzTzaT`eN__k?S=R?@O@sLE}R!7q$^x; zU4{mn)(|jsLoaeR&y31w9T*8vX$K4A6mo%{-bKu!dIAh0OK?rF5Mt*R9g*i2F2eK_ z<2}V*zB)RK8f~;Ced~`uP@fdAVP#AcHgCbe&{@>y2L%af>);WQP?rzT;iKbH!ASGq z<8@~$LRB|B3%QsR)nN29qtn=M9IOmTv!gShChJ0x=&VU3U?vglRXtMKecZ$@PAGO# z>~2O+ynA8py!fvL%s+|V`Ae-jLxTeGp8Ss;ZF`0g55rql(2_ek{RBq1q> z8(jvrcDjlCV&ZeexsOdux1Jup3S{ro&;=`I;)st_szQ)`7c8P$TaHdHLV=X~NXQ8p zXO=kn$k>Il29@Q$ZXh*Nb_l@ffHGFiKtGV;c6agF7dQnYH zOD5g3!A<`Wj5KI6kwEYdU}P~#gV@)kmDQO!l$rP9juXRg`;e`7kn4jifcznBnx=1t znB2AdP%Gr&kUze{>|jzI%XTtzk7sNMZ)xVCORC&t!r?kbL8?8Y1JhIe|SY~ zBJ!|!yayv&UMMB8Zt3Y84Le>O>$@fn?=+r_)9A^lII*rm-Qa+n6{rW#tHYX2e zpA8*fe8!v0LJJq)A_q~ng@s8c7LANr!bW2*4h8n$Y(|TVS(_vf%XXG&CaICg=Apb5 z6dKCnLi{NrdSOTm%gEj?f*f>Rn1=;4<+AZ?DB#=LoZtcW(ZZxtRMS7&w=3fZ z$Bce8fj6Wjb9!73mkjfWOiP?PbU@;tlw68v=jY<7i!K`~K6)Yj+z!9a@)ZeO?s#&m zl-Xkk#-{~xlx3qENs=O6B7N()6TlpGVoPyCW`p&EkQxp)!6J~P-C+ZLl){TWmObPq zhC9!b*xTqagd=0D=2NMzY^k9H8KMv@qW`)75)L)&wqbN_viOf@bbPx7T(*9KnRY4W z6i28GDjA}c9(<;zGX3~x-jjR6EhQ%*v`HrpYEceow!Hj3(U}8jou&|5(Fz%S9ZiSp zx09DZC*&0jFEU+VQTA`%{ z&Vf3xo%qr!h|quS52K-qmZcQlN$bofJ7n@Y0Q9{uMD*K|9=`SS6@J5w?}zjK&VPQ% zt7z1DiS{9rU*R+d*h9`9Zcrw5SL6Oa4ONvIc{PnNhCGnNzq$D$rnGPO|4rEliWn3E zW>#^Ly+SosQS{p64T<_=+V`v}(+Otzt#^J@E1}q5vCJHJI#`^x5tsz?Mqh{uDgF8U zy56^?MfcFgL^omjiSFLsWl@6nCvzfYOM(O?1Rpg5c{4*G^8*4|b~lAwNWVFdyYX#@ z)w(Q1@Lt;HNE;zuf|La}VIW#&s1o&XVO8j+E#R1=Fk?~$8T5QI={zBTm&&1u3F5ZM z9h)#4M|sVu-^_r6$r{(DeIN&m(JSfKz7Ve^ zm-0BbCWCgQ3k+J6%Q3pdtnrIY$e4{O$-H7a6LAzjTvJEN2%)Xd<^)*-&;Rr*2SzF% z2pW}rIy0IJ=q}B81|1|+2q6$62>LRcrju9o zd!BQitZbaJIzF5P4eE@sC}a`<^@B0@FnGbrG)jS-15vbtYpXPm?~J#jWY`q{)_Xt3 z&(8Q>evkQ$fAES|(e{p+@pyaZrgxyNyby2h+}l2e2J#HOJ5OsJ-1O~O7XonK_>&KZ z2jCk54sAIX_J5A@dB!YyKU|TY_I~(Mjd?14xdM-7jSraTI@`JVnEV+fA7F1f9QK(^lG|v%F`T-@o4;{ zR%q|FDQtFdnCw`zk33gbuqGHcoGhEZ)%RpYj1+C!@bu(5MIoI&c|S8TWtVYaBBD(QPVMnMhO7=6_|){^$<1PgMrY=S%=W7 z$giXMG+uEU{`E`a$vAU;YCH&O&Ne(xzFO%FmO@X834)_^dlAwGKn{{1z@J0F*g>hj z94D$4tUvYUI)ib}YLf&`XqbfMnxb`nL}JW$ni0ea>8(CTv}%L$WrVq2bJU z{j$$q@G4gJ_jPkZSgN=TSfQ5~qvtRAKm48R;W+Ht!_wZOkdSQ(8FGwUqh{8CMwn95 zp%9$1IA&p`%PuALVz9V2K0~>d>qMS_g7%mh^8L>~^DZwx zx#SSZY>q`NMSw-d#@5CHa=lv-4$kvZr0*hur^+~GM3;88$L>jS)`xbK2`JQ5utKQT zSePODSo9_N^O?=(pRE5uxH6BU92~r~;7<%~_I9G_cckMU3f9rl*4@+D+rK=+gMA9s zS;DKmKeUY&m9 zkLGeJoWWd{Sl%5vu6O<6f0Y-i?hVLNR+_PAYR93V`!EBg>_h+7IvhNd-bIU&?OQC& zVoEBPu7I<}dH0Q9&j@T{Zze{sX45zdsxV+eUG>a5NF5>`4L=5!4?)fu_BjEEK{)s{ zxc~9_Jo6EQ4*1Xi&kuMjbDh;<-enA4a|SL*g261RQT4C~-U3f3bR|>d^7k8CUiB(# z$@6RG$%o|)?9J8<3q&T3qi`6gh*KC7@C;!PAn9l|n9s5>`L0Z_TkvG5L&pz(0StFg0vZ*-!2EQmr`+{ZgZ!UbFlBYY zWIHtve~um!u!$RYvR!ug%{KNxS9fq>7KFH-8P6Oi&LF)gsh#<+yWFH15r|!*V;MJK ztF>soPWthQpCtv3ah77hvmG%h%vsLm1?GWy378^{kl4K#tZ-2v;RAKoCA4z#7-|Ak zjNX}|33S2M*)xG|1iyf6+pJ#3fzymQv!nUS2F=MlKb?N(-?UD@r_nep30eg10VPGGAyy%9+_gkId!#1sIR~y~CfG1LV_-9sCq>n%MsaX28BVVfM1&2^z zbs14H!PWGPMs;Y~Y4@Bz*d@n>TjI!c+Yeh;ZVXcKF4fm%I5)n{*i7cqiRXW=8Y?ZQ z0e?^d!s|Kfbs*fCE@ZFVb|~8cxU}Dv8o2HTgAoh^!gTx$jp4TfgxuElHGh{e5h~qavTS>p_3*B9!G?URm6owick88jK@nQ4yC}Y1V6*qF3e< z&Ce0rKqRt^R8qwOVn<|$llcDzK9U&$t6ATX7aL6_x*jN1Ad=HRG9YY_<|$F$QtRMy zf;>#!XD5%5u1c#9If1T0Hf$8)K}hATmloBW#^nuf1Sm%7UCl)Jl`NMtH;PRcil&vH z^LPFC;!utMzLozP=Y`p`uXyF{I%uTxfGLAtCn`sR z^zRuAlm1L8kf5QG?Sa|c0$eD`z+f?+w-&3@Wk3lYEdLv@{8OaC* zB{Digdp>p5l5Q~+3Ayo0kLbvRksRZ&rw{H6!x8WiakB>>%a7j2vg9#RbuDW;h9c?8 z-)4g8n}0T6)vT3r3G!(H`Dc+5EXNPO@%qbN&)ZU_yNG4a*8gq&o%eo{$vjy8SSs4E z@5Pe7R7gzWV|io=X5KLrZpISgG#dXxPOU#QaxJ{FYA~B!91idyGmZ`o`i*~hBviF` zP=*|RCM0vu(2ct^@jvbvLgYYipCRn9<^EoK#Ts^qi3(5Hdla@~7;cTi4SQzE2jUMO z`yP&&Uw*2|%S{(uIZ~W{=b!&VLDvZw8d#Y@;SLF5$YSdv2M}(gxz@}n3MORaLfhSD*|UKjmV@x=5!5^|vg~6Ge_eM6 zTz@baDe0J&ycZ1@O~9u+g}k6tlRqJwP4aD%bdaV9b6Cp~yQO+S8DAY2t&!k|kL7kb zTipZ=rWaDv>r_*S65uuYkyg?-f32(zSsuygw1LBx-v+|1Gfdg8rB%duc?pT%`QqY( zquFN68*VF^&JMx(A{taPyc=y23Zze5tgMb&b(nPM*9xoZC50-VFGae8 zkW-O<{>v}b7;Kj?kIH@~Ria#Efr~p|5@c;R`k&}uG+_q)TQH_Y_)5Ewu?=gxLzoab zPx*hC|6=}7{+7HS=KX%&hhHuGt*UT1 z@8*g8^e5siP3idF?UCv|u;Uz?CcGYEsbTO8GtLxL7417)Z1K)CereFBia$dB*NyoG<A5}ZcxlFjDe@H2`}K-qaQ z-ZXj@PFF4+L2ZKZS;$rT>FqNc{qO8A3l*eScE426i3i`lVTrH7cH>JC1Y=)KvI70t zV{*a^0vwG0O$Iu0VbXvkdAx$qS3{rT2FSX3gbA@IS|*ahoHRF$h`mge|*8KNtgcH z`iTGSM_=~J{ZId7Rj4-o#wR{nc~n`~-65zjGFN9=T+g!MVY)`Wjz;4_Df*R2U96B2 zE<*d31hDy~e{~^T-GH+eCKQssnu#t8TmTKBYimls)_S-iX-uQ#6_gSV+mErQ&Noby z(>%_(YsLjr<(n(DiiiQ*Ob7;O0-WTVYTrANmDN+H%ccN?kyl|FXe~NW)|*hW~MEkNc48Z zn-3~L2PHTIvq~Brt$n?n-K_+QbhZw(#cS_7JR~YNywKM4(?9C(Gt!d0A8EOV*X`(R z>+9|49OzkQtG+MQVx(CGCgm_F%rjU%nks2Hesf=6sz9vnDE1jrohh2Jb-ME6eX=~H zU;ob^+?4+A?|!V#A4j}I?R>fpaV@L%w<|El*Xugd@G>Phz3hyHk+`iU9)mJ7^< z$J}*zXKgxF6R8YsOuzYfRef?G(IKj^tTKSpo3nKrl&NJL}$D-2bTejd1ZAOYs~~K`R4jq82O*dTK`f z^kc8oq<E;+14gsFG<~}#2<-=pD@}*4(Z|9^GLKbGC3th z3T=zwg#~tg=ID`0E-*$+Z=14D;9@oi!9A%n` zU;)wE+}YPdlO%8eap>>-xCJ|LV4z3Bh!7_(ls+M7rq~E>8m^5@Gze`B@*Lz=2}xQh z&H)LPbMelPzx6YrU2XTJ5%{r#b5+mkOS z7hR6aT3b>>N}jES9ZUEG_%~AXY^VOSRo}IG=6mY7wJ)E{QoTdwY`BLhFOTkqn%fL4R|${yS%K(iOz$3v zaAU6lv8_foHblc#zPebWN>#59`97n_Nk;SVh#p5_MbYHLym)MVZdj#>&svYloofX zQm3&Po4MTKk;TdtW!~lGD4JU9ybZWgd^w~hqEnjk3_BZ ztE(FR4vpl|n89IPlzfJFdgyIL36W15M)WC_?j2RYCehqN>W*Mlu8+bIFIRb%Y#_Fn zwK-woPO{TRrHpxZ>@u#TTULern9aM(%flq&^0``-?=cd=k~P>S+Ry|vno{}U9K01c zpx6z{Z5m0{DNE*Dv)ZPvcDA7RaiRE5YJqFDRj0l+sWR4$BTDOgNBeI5I{U_QN4M*e zl*puXw#yPS{*GLtK=rTog+5oHhdXohHzHiyq8>}b`dwJUsMc2OE7gic3dkuegE(c| z^}BMdeX}mEH{aJLFWq#DCBK@XD;mqSzRzACo z%O}X@29ByKdtvC^IV3M@%zJ2EUT2tRHqE2$YIU$!2)HA)B3F~?DHHClGSpmE66RJb zX$tx09Mz~bp2PZPZ$$xbol{|Un*W^UbzJCPTW^WZ4hbO7=c&Q-?gnS$|G$SerM!%pXEyC%_7tB*EoAD;@xCI~=q-oFM3!+|oDlYfF7i}GT2 zWcGN1Te~79I;fNa*-UWbtmRhjPg{NWQhoJg1Am^eGo;)9JBGCpauy2pQ}zgW8`(P? z$qfp;y3P8ymp?8mfOL!wqZT|5rC93D2@SM05*?qxK4TNojo$J?kBo5}_U3q;aXO&h zUB?+vlD8pYs2R_X3}YjMTxp6q$yAJ-r=vzcJZ?0{`7;*f&xU9OksHv6u3fR?YF#vH z>|sEv%EIIf&Wy}pz1qt=KS~@he&(q=2Q{1?FLxAxAjdLb8k#4SG)3oto8WQSOXeY& zPUG2;S+0sGsXJ#?RQ{k%B(*Ipy449Lof@OKJTT8@_z$*uxtAv^)i9hfgk8Pv&3C8J z8G}e9KbyQ8FvUa-ezAaa`(4lGgud|A_x|$AP_i7DMHY%fVGkS#{!lautkv=3O|I`# z0@yo)jJdf?jW&4^<|XuFVB2c0d-)1Af`1a>KB+f08}pU#Q>LvM9jmo}9;?^uMaB}W@?5TM8ePxLllpE|Wsua+ zh&+HcjWxyxUO1gYwq!D8X>|I%1GIrhGY00}1+bEVE0mI{|mm_-Zd=x%I8R)^IYqfD10oHJFDQ?XmWE*A3;Q=LxN*^aj!4xA)Q56BEo44hg5b_(4Z2UMt#>z@=_%wFDb1k zsx2yul~q<2tSqf9T3=aMRbEkA9*dRK7FSl5Rn}Hk6jv3MuPIwc;?hD|ja8V|KK#8E z`QHwIPnn(mI=uD+?4rF^mnmHr)MY}AHA}$21gFfDyyDaU^b;RUj2y_`8{*!g*6Q+d zef{EVSg%!eGmt?qzwLuXmlXfI@5fn=vW#Cjd(NwmWBZa4f5I}4N;`34cmalQ%@d`Zc|=xF<@?y8FjZmx&QCN^)2#RK*d7?i_W5fdaTt%eN@M&4sc<> zyY7K6z293!1?aBscC{C8Mni@&vL$}#&?c&gqd&t#Mwvn~S~R?+C30iv(5%a)RvM4()E zE0Hx9CR%$o`Jwc`^eQ{`vWAvfOuULE{Z5T30>+dj!KBgA&%r4YH{bX#&Un?$Aj26H zGZ|C~Fa&M$v{W)u@}LeRnS%dMtN%4#;3NO#pUaZL%jirqugi_)!t_;XHBV(qnVU}h zG!fQ#Fpp1ML}x@Qyi=<0Kr9*nqmBeo1k#X`32{$g1?nR#eD9A%-j?{ex7`jnil5lK zpY~7{V$l_pTMv+jOu?*R;T2R(&FDpW;Rq>rAL}3I7 z^@0$lwWG7OBavCQ76-F!nGG(~V!PwZ(bdgl-xglBIrm~gc5jSQCvD0|PlhA#Z>)dZ ztEy;;U(rtP?!cI0dG=c3{#zSg^;ULdXV%r))7{b9(Vgh(Ze_HG_aBY-cC@h@`r72L z!Av_kyZSo);a}hG^(GfbbQeLqS3}p^*45SD)4$wgJ(eY?BC?Cxx}`zHFI2-ymmYY! zA@NdI-=vHT2LdPS*<9r)Qr+!WM?bSg?vT*}^FWs?_26v!yFYoRa`1rN(Y_jFQ=W1; zoKHbWaG%18HJBxP^89nT8v*+y*NLhkV)gG$a! z&zOfPoy&Pko>gv}F7HA5eH=h&9ej5Q8g!ND=?3SFX3rHHMyzU<7LKo0i zWsIieDJfRv&LW!@Nw%y7>3xln)(wWE6g64;`lIRFA zyw2jZGC}$GGnZ7~#NtusP)Xw(tYMNt)O5!|ApJo$u4>4ME@hm6n3kX;I|LRL1|qvK z_B)cT;KAjJ^wBb#)LIOD#^dvy3Z){hTXh`>g8^D*C0RVQj5w-%Gj2o{&NZ7(d~`=e zAGUFFE|_@7o+CXWKw5%Gdsm*9yF zEb~O`w9ovZl=f|wALJbX7No-A6@u6hVAyb+pl{#APgf_4vq*6I+UIbE>gnt3 z>%t4EqrZOuE8mHud*X>?f~3I%=+I9bJ+v1e(T;)6zJ4A)Nd6bnd|V!vEfjsM2t+3a zN`rLP2?^L{(Gv5c7U<~6F)a{<-}mf^pB(H=v_04*e`VVYw$57SW+9$hQ%ORHspgWy z{!vCehoD>e?Anx!*bh%nTqG%&YqG1W?NpaAw-fiJdmHW@7}yklOzl6O;Q_!Zp@}2t zm<}G2*orjTn z=bSAxA*J`_s8qxn5{R{ztr!xZ>}J zTRuRhhQs9}siKCXA12jcz9{cVUVeaI8OL#UGv0~mx8`~h=}*20V^0JN8=iX*;q%ZL=@DbuEC zIW*%bJkrcMEHp7M5%IH`#9%=P2yO^6CPJuCtz;7m$ihSdsw6zH>ob!+%Zh~yASg^O zNcA{E+l0E2{m(+3*|eAN@PiyKy-i9!v)f^#l?7RPNLm(OhM!&vqu`TH`-CbB((?;Z{%e2oH1WCY80-!5Zq1Uly(HSkH(&rpstL*j%$B9K z6+tuSysbvGe;iiAOFDRwq3r%s&eNPB8)y8t3O|O=$We~pOG?hx*&A;j;3Vi8=;b8n z?%;qAPJ+&^j=uKJfj)*vVB4Y7r;o)s4RHDBAAnsueEQ6Bm`wLr^x*!p>rC8tcBiK} z!Tvu_?|%(|`_8N%Qpe2tI+<8s|2^~S>ga}leA{{H@sF8T*L~+THP`0xc9jg5MDHlmWd3)YJ|gv zAaeDs_kN;PMnCd);6vai-u+dt+Rxiw5GqQy|G{T+9y~(auZvE1={41W;#pmws_2ou z0Rt{h)J-kZt|kC$qYlMk`@@$%Naoo8u=P}Fdgr;_IlVX(SjXm521uv_4+lFcc?z_% zcFmQ?in3dLtCE%biDQG|N@QN68cU~7{Fv_)1jQWtULN)JV*Q1SNW0|x~@tq5lw+a{SCHDxrs zE2;Z_!wXWA$veUvEoh7W_+aZ@%U~o|E5qYy;>d%L7yMj?l_?EgV#4qJcfaqI>?a9b zrk1o*(3lrG>zV;N3!^MxIC2D@<#=?Em|n3oxay3v?C8q<=buW4Yb%!ELS{+)*9*== zg*nuejy!`Vz%Vn8Mdu#07&0K6_cgvI!I-V`Hm4Zk4Ng)9=Ox{Ma_$&arU;>p9eY8+ z6pKlikX>#Aho3YWC}YXpW9~$3{!3Zru2jrCsPnm|p-wN*J6pUHxDqu#O5zUCcM6uC>T_ zPZi6alfnee>6s+>!w}vUW^Oo{jpCL-fsxs9af)ZMg#9Z7PeXk!d(4NfvA#^SqUN&%&%AJJb|PfB?I9gGnjPZT1#)C+enV~rC&%aAXhqXBoCHHfNrRhj+5d9h$-(nHfl0!X;1&5ap%fU!i zCmEFRE|Cr*iKCA?s>d7-OfiS>tTNZ^PO|*nP+v7$uu@E6bdja7qKrQynSON#^AbaA zF^kZlyoj?@?Bl^h*f9vs2yAmrIUb1RTx(KCWSDslr<#k-q}-jOX6tNb`{eI1Vz%-# z&btE_hg3s#q{7ql>6~!R@W?RXfdM>lgyIZr zFQn@5B5?WxX1s?NPDFB?3Kh$iUf3-o?HsNcDhiwd+2g!4GCI6KSeM!KDk%cUeAIEO zu>qUPd~U%yjJ$%>5x&2o!OUQ=_5YTou1-cg2&FTE&Eo;YTjseGi{QDG>7&(?(d#5% zKOYI5cNWAw5!{e4WvQQ1it}1N1e{{@yH9Is7QMAOIcO{#GU!Ppf)BJ%Lq^C}23#CU z?TW~LV@B#SzxAhNzA*!qCtF=B-cC%%%;>wY;f*uTR`aK7HwTx|0&HvLsSQQ^lecY* z`hJ*|<&!QUgpLrZ$0G5)u#^d2|Tt9~;sc1doQpW5W)9xetZ&#veM5=r%Hf z6P4|y-BkM395P-S#niYA+yDch4|>!fWYsj{HW}L5WJ8^lWo}+3x1(mw@_&}eZ7`3W z9${0rD$Z97c-}?4a}3sub89MWhQ&6sCCm69_FN@OgY`4jIc_aw(@n+8D=FB^b_%e0 zmlxqIVIXFu4n^{y;2Js4%|cF7Q)GyBTbU88bGAhx+XE48>XVFM_lB(jz9ek-TryXs zUW$*(;c7K+tgKuqUp4&r0HprJJrARc<{;-E(SS!pPNoEkD!CG@+Y~OAV^!k89ZB8n z(aoOAGAs^^=|-deToi8BZPVppHF8l`PwCG}JxMj|W{EDhzVoJhSl(QzR;%Fc49e|h9BuafZU?V%S;6Gx2#2-ufl}ZqThfYR>}Fj@knc z=;x8v9UkWS-rl1AHHJU?^}!asGQFkAT-VO-i0jE(s>)LYT9?O%_30yP5@FlzO?q%l zw`LmpG?MKP=*~H7uT1TAK?p-lHPL=+so=DYFrvTvcSOSSRuc7{am&ixvg3vi8HzL; ziH@R70wv5PfD;&BLX{uBlhm>Lj5)=X$-VXHfO?)*pJxQ=b+-Irt;~^P{`Bc;K5EV{ zja+t^3s9R@c&8nHxw+n&+Uo3QG?k8Rh(E10zML=K>WP`0Xm9{(B@URM$<6|UuV7eXOOvpv zS1(~z6TkF%W<$6*s5skHB=X)GmBjOX&j>+*8FI@LlC(UJIzwSI~IMraQ)@-+% zL$*CD?%A}?KXCWV;=v) zXx#(V0?&G3b#iU(YA|r>vW{vk{JyEQOBe_o# zDr}CJYxUYDF9+K&#umr!4CFv|<$tA9o7(i#@IH2`=B}?WCQaPn0=tM^_Kl;Vcir%R zA7Bq8t%ud>9hWqkJs}X(r`k1!4Z3aKr_UMA?$*nXHj2FDrgrGz8oj+Hb|7l*F?H?w zc_lC38tu_H)z|FH?RxowT^`kC%-+};$$6ZesN1Jk>rSt^N2dNYFDikPZ>)ACtluy2o%aKG8(d@ zJ~s~gh;;?lQgG|_{4B16{)RHG>ZCW>ZV28Q; zYJpDYdnEh_HefjB*hu->ms7ACF4=g-!vbr0GRH{;Vxs#CYuA*Q;0%R(Qwg<|%c!Ev+gott_uCEG(j!b7`!!qM&3|VG{+Miwet2%h&hva!GM$wz}RrW*JCZ!D}en#OS5;Tc7P~c1{M@@BHT2sB<#NJSAW0 zvW!CJj9~9Mx2whX-u}s=<5hgObX8^?KaC#hjHx=6K!Z96F5QBxOFUr{$vBWPj-b|~ z((d@x_(7`DV7t3`(JwoF&a2uyh)x4j{D7Q3e#`(cxA;5$ahM8o@xT0xSMUGPLmv)T zr$6|foi%G*5vz=?33be3_ozqHZ$30yJ(*RwFuF;6yjS*?=KiaohpG7Ap!$$*S}Y3`!aWbjiDF{o_}@&xeWX*Z1|jTdY|VWw@RtY%(?!h{+y*R#g>$d+D$haNgR|AIv1b{A{9vWpeh#AIkk)Vj& zt+wa9mAgA}-s$S<>nHa!{&Avn^oBEn8NWJ-d|uw0j6!myTLRbgxj%m2%Caup*m`Bo z>FYOp4tc}WezLO<=b&!d?^s;FmS6|Syq5J-y6;9rD>*tobA5blE6HqBdpzrR)Y01C z+27sT(b1b|9f&{sEap$+>u%hj3Xt5c+VPE=AN9ZZflrZ$EpRYo;4H?TONxzm9(*|4 zOD(uZQK789EnGJn5VynuQ@i3^*MmU@_k%3Z8NNZMt4F>GpeCl8CGY^w_&Lhi%=t{U z9vLkT=0Gwsmg^cJ=ikmaL*187-Rlk2*M> zrWGriynZg1{CD$sZW4v1sVnm>z%g2Kbhl%_Hkwoyk^s0ruOr9}?fmnfK#WvMRya!? zhyCaiRjEn5%^}^W7aP%=ADZWY{KoFkyPo6cLlO;6i(%NNKh-8fu8rnA0-Iq$eyw5< zw-Lyt1JQJ4`y;thOR}xuK6$t{8X+|UPsNuW&x=6wIlZO-JXb;p2+YFL$PNG3{^fb^ zCz7FR1mC6-oPhIs*GQyW^GHGSIs%-~g5p_6X$!52l~uH_Ee=)ksJybL zZdL8t5X?Z)!HP&}qlC-tMb&5Z;@a}F71g<=YOKAwu3)!a)HH0Y5G%7@Z&a@>h*h<0 z;-h4!W?kM+F@aq%@s*oaZP4p$^Y-M&by2mxc5S6T$?wR|sjgouZ}w0Gy<=NJBrmoq zT3Ajsw!Jqtzm4bNUYMQvC34e(M>P5wyG|cU#Yuo)eU_cG>1)jHQVxI$&E$o zJl3Kw*W8HZ>Yc{Oy0s^DqdFDIxAB%1Y^W=ELeI)_^HaI{q`U^kIFwtkniv#xHAPi< zCSg}R(p{s+6-9b`eMw2(qq=CWYwvDSld1CRGJ!2t(zkkLER^JObz@(&szI|~m0BAr z595BnvZ$gaN8hdPE^jK)qelyi^}DHfM^V2n`nNXZM!lGFtbqa)xCwOCaUwJ?ogbEJ z&s4O1;3D=lejWw-SCBm~@M7%+HHr!tP;!+F?KO#H zr*Qn~wjBPZ3JQVKw!QIHdUIC5Ox0)f6pBjCXTw|j z^l_6(jQex*sMCgDi?~>6poaF=#iGeP&P8;r+9?P1^6qHDL;2lZj1Up3YaM**D6>};X`}t_DOf1&CXu-^5g~qs=+H6fUe=ezF zc=C-3y5AHDk0XCb*L++eKK~13ze?VwtvUCy4Q!Ao9V;8bn2xFcnn-w-uTPoO{YW`s z9ajHVglC}8gq(fo#H7R%Rp>aI6M0;EHYcps649iwGZKp^U3EevX)2!qXXT8oUFxPX zlH)R31wvMN%UvEbwSF0(ziu zL~*1qwrO8ItFcYy0{_$r0ZnEn zGBQByt80x&AO-k%Ik|A34#`c;mB`^R5x;rC8lcrnIk|y5E8#da*pO#ytJT<^;}IT~ zUCm3fyxeJ$2%6U-5^${2G(r2dM-O*s2e004q#Wz4Hx{yaHn-nW&*0Yn;dX2J(a^-7xVqVyZ;?_O^5*iGH$9tV zp_=%WYPU$V$`W20HigzUFLDJ#8!|b!CZu;Vt)qz9xE6fDMK76#PYv{#qH2?dweAF~ zZf~0kt0+p+XSvtXn4#sm0;lX_SbqD5&wGV&qj`x)begp6Y)ggeHJHj!Xn7;o^LO#u z`q*L&r$5Gx5mOT7Zqh>J)IFeCXc9FS6*?worSUC4KaO_qd&RUr11b{I#Y9McdlMl+^xGg=XfE>8~XOhrWSP@ z87$aPWH{5BulxC_@`Qfo?!BZ>DmR1(2=_K`T2+=`QeIW5R|*f+So4+xA^(axHJ+lN zy-c5^@^r_J<>)FR9MxK0^(yOhU5ftcb#-lTMXg?o=uekksqRYZ+J;|zM0aATCj0ih zY=NP|R6e2OyixCk&qJ%%Gm=!exzdic{UyAAqqamSys6gC2m@{ELA8+TvfYx}k^te@WwM0?QFZ-<9MhL5$U_zCaE0Ckn<>Ux98pr&75mMXUKblPGTJyp@BhkM8McV)ef;U_dh3yiDS ztbJRz-;7%IwI1KET=l@CdTz*5+HzKH#gCS#=~X?o#tx;b^sB5s6%R?jzE-a!QY9jJ zrhp`R6rRQg5iQcD?X=-F>P}~>K!hY!VSjfB=%rPK5NTShKU|ULMev7201S5mbu$o~kc-Qa+jG=t>uvEr$RLX+BpcM$Nla)k8k*N=#4c`Y zq}vsuPqka5vOiHG)m zy6jJi4t9h+i(=L3RH1IxsnJ&bIpRg(LPrA5r7nW8k8^657N9X4zKB(4udYYJ8h~z} zt@1*=eO7k~bcF$PJEvsx<}+kCpdKr$WKW}!==DpaL4!-N-zAs=@oo(`o;4hDuw>@w zkyBGzQr%rtT2%b5W0j@Fs~cO6Y+O}YURPRKR#sS18mlNPsVFL{t|V--sHC#Ero61I zq_UtWR^C{$sytR-UR*!~W?6YztmIPZ=BB!}Yl=AQ%Ls9d6>Ta1$?jbR#pM-+1wTR9 zWJzJFytbgMy0RBNVXTP%YF8E)6&4hfl#~>Iapv1zv@|!;OWBo3uWIydj@13sJ5qO^ zEbSX^X#AHYeUD2;*XOD*`@`4IlF703_z%L7Ekk>hDtfsJ?x_5+?Ec~vDm4GG=&Rm_ z!o%pOR90o~`sHE&wU6!aDz_8Ag`Pw{`9wJ=6N-|{II(>IXM2~^kcwc+O6WY@mpBGK zeQ}*vRc$#~Iiyq(N2&}o0;C>Jzw!^EiX%bdB%H96`RUpP(#|Vwo#}lD0U_{9ML8JO z!<2BI!!?gmL(@dO9GV(wle3+8Xfm>+HJX_8zw!rg$DJ4E6u2TG*T#pM2;~_mtz4)IrIW8w{YCn|7Boo~J7fd4 zxMzXGlI;bxdPk=H%`Zno1y5QNxQeULE@>E1S>jE375~F&i;i)S!dg!345^VxL9Q!x}6D6O*Wlrzl$f}`^EX<5h zXPxxN1ii?CoyD>gzQFjR40H14Fts20J9L8NA{RU~TtzAXtHnVkt=g1;ua=P+MsY>m z?_!`xs?8^iZesKzabU8TxMBy)6VE~w9uPk(Oa&9rRDmxfYcl<-oBHJN1&M!@Rg|8V z{Md}p&6{b1DDnBEw5~xn0l+f#h~pCr@(UUPD-HrHlNyPrn#1o@ZK%wdT?Bw)px~WW zi9y4*%cGGyOesogJ%82Fd;||>+Pp=^!1PY)cd@;vzlQr27~y;aWulH#ue3c$OT_WIqmk(X`ELt zwGv@VXeXJFNAUh+Gi#xU03aLYRQw$NkE0X*n+w11RisOPcsM%1wi}E;sMNv?g6LtR zU{E+E*mo5zP?s8sRScZ4YH*&2wfSNHzY?mj(f^hAzYkaLEgyc-%O@a?Fw#ugR-;&1 z1X~=pw!dPG)tM5|Sw89|;fCyYE2&|^koK28Koww{FNh{$1NrTL9}d+OE`d*r|Ba8m ziVK}XO>M!&PKh2HCM6*I&H^hLXE2Io9;oabVs;=h4xF~pKvA5w7wb8>g(3)XjLcfW zHZbQ^BGE0)zdv1fI2`qV{p@+KD74j2eC()KSswJp&>;3kHT*^*@heGcn90@$*^q`i z`+^Pj0w;=jGn3tc?XO8?2F`;Zc2Q46ipYD7;YQ2t3O$Q9*~g2n$jjSki>F`v-n9yk ze0~1#r$}&IXVwop2t;=*&pxD(KhjTOPj zR-4WgqPAe`#Wh*xA#J^ZX^>ByakRv7x45`CS7Uha-}BfLUP%$tQH5TY`qjVngHa0J z1X-1!sAn?cu*!v((fWvTw!}w>k-9Vrgy%+;1I+=7n{#umoHOJg10RX=!j({43><*; z4qu_(pAvQxnl2z4$OR)#UBLyj9`UVs^7p|m*m<&i%u6Qgsv`dKxit<$X4ToMT=u1UKHYrcFxCV2r3d3y$zgjOYOr_r%k8LrU9V?z| z8B$o)5RZoTFQi`^-(Kne^R<`51%$`wf#Kx-1=0gD`y~^+&(oGqeCiReW_^FJh(jhz zMC(IDpAWNSU>f@)Q*J5!Pk-_&b?GmC?Tx|)?P_Od4EEt-D>Nw3n8+l_-WWjx`QLMj~W)ShTz> zTVP_1A8Jb^unYygKsg1zVd=cs8W!J2v+h7=?*M0+lWEuarw7<19)j%#mw*9Kh>v0m zPJ=x@oGI>o_fY-NAJ0Gr1*;279O&UUg2Ip@scrGD9_`xf@G!>p_XaV+6nEfbdKMEL zw@EW-+w}~~Y@^0=LbAm2&J(vd6}XpR)?~$5rRwwexWE=#dR#O38a=@v_ZQ(h|7Yj_ zE}U1-5S7nJB}GPIm>gk@cQG#iO>!r%rta3DeEIcMp zh)OXWxbyQ`q%qlO`&6#RP|D#KMp}smgp-eqrb|BYqiX+`{^|o>;h80`u(Cu}N?Ce$ zu!&xO`+xf{Zv!vdiWO-O4oo0UO>Ys-y z{TH_WxdNo8jWIF?Tq)>b@*yvxE-Ixn#RtMiRz^~!s0WM#3GB6{@UMW5*|Jj(QT&T8ptOvZC4#(;9 zR>+vm9+W3{$&nc)hqG$t+Lf?@)C~wv8orWf$WE~g9!5Qn60>4*A)X?O@^jEf+~qHF zAjq-{6XTb`bCAbHAsQ9cR_2KJ-}=T6!&PMM$W{aHbjyNM4#KV*sf1D(ZyXFPK@OCU z^kM2;v?tg`MEp_0*+r`(g}DqBxCAjP4nvnYLlf&TW`mLm6Q~gQ&BNhYqW#>fIAff- zM9yVL^ppZyo+2h2f+AwUf)PRXR9;>2J)%W6=pd(a2LxLQmGK=R@=z_Q*Z^rUsfVW? zA8qe^RFW%e6YqRfvqeHgY=q^skoHG|QjY;M%m9^R+~%jo0>qk&Ki2WMO%ErDOmjSU z{yWw!A>CBN)UFODx5V*YxB7_NfR-LMbpBl3GJ;;DhYK6fak`_M{+nzpud+3C9d+Qggg+Qj$pTHW1k z9sOODXm`Y9!yJ<25^^xVgpxRCxA(5d|4*J@HuJ4;y9(nS^V(iGn7VV#QJ9zZWhsp9 zn%3#bDbi2l899Xxgh_x?UE)CNneG3SlAAR-+EQv@)&kQF)*dq3^?1n)sfHupJF8 zvJPsEfo4nP!KmWjdgsp$qNtG*wi9ITg0fCiwaF)heu~D3tqP=$nOQ_J z8q_$YIdtdrX)+X;7=M0Y7LI6^J&LSj8(c~b^=^702%yQhf~R(gSS&}G97SDR-Vtby z;#F+-+TwldoiE!m_&@oHFNVtfKYQpO!bRy*JLk&%6Tf>soLesmRFx3ULk6`bivvoR zz3W(2(hbMq0oBVT{A;NlJEJ6sak1B8=iNIn0v20svLg^B2S=dy)wJy$@Np@^i%Pjr zZgS2sYl5(|h&Ji}_RAmg%7+6?wMI=aGdD1j@SI`DOBzFwXaq%lEf3z6D%UC6+%xSL zI%C-nJv2Db;&*(#4evL8LP$E{UgR$rG~J3{*wi%K@p!9^-_(bQyex&VLG7_pNO4rl z)<@cD&}cmqG6vu1Nwy(QOme%qdIUUxTN?#^XVWv6>T~j%z>ZO*S^u?TLte!>*v<^t z0$*2cV$ImUdL>!;W z*fTu^tDL_1dmF30zTP(f=JU@%m~~D=5l364+816gvb2_?Cm?WHB?k+6?W%Rg-UqQ3 z-K>OnV)E`D0vbi|Bu)w=bj-6^>D3*o#<((iHt(2HCCM*%e56;2%)m$o9JVL~)yd<* znSvCLq_Lz*F&$hQ_y7F&Zh0&H(eHoQtJ$dCbeiMb>S91n0j_P(jFu@7Ow%9uZ%uVc z*fMPi=dXKd7_&t)6!1~387PuYFeV%_S*(CHbG8m7PBho>HNo5a&DnSHW$;It0}i=k zVo6)1Sh7Vo4xBS+E?zxMOd*M7knsU3l-p8cZuNimQ!jhX$t;g%t3E~XI?HmCCBPUo zSPPVEYD9{Fd%zWp+m_Jj16b&6KhRuRn4rCaL568o@<51ti%V8uEVjf&o|_{VZ)-RK zd6@^R9GwpyXY>v#+;N6hr_WnvNKnKPYkCrs=cY}xy$HUUN^BXV^?CNlbEj^Iy7_x| zUiM1;&!)c)6XF;pv222d2dzBee7S&{84P!3>OV;GbLXZ)GBSEQ{9MN8ak=Mi!W;sKhVb35ca8x@azYALf zh?ri6R1w-mLedKwFi30TG8WT+?E^o+p3E?jEav?ew*Q=0U*zD=(Q+FPBRqE3t{;F$V_tyBSul}-E z;lKQ!&Ux$ncmC*AuP`4;{Ti0n+2Qob{~oLMzq#k@USTqObB9zL86Albn`LzQM4&K1 z>XIF7p{wFn%-{U9T+X+}FD%3#lI(ec>-`hMETMaRhTm`!*fmIPgoeraU-t**?^F9lyLSethF8Y-pD?X#yf7mbcG9sX`bmD+-P5h?hZYTxXtg`7-JK+8<>TSY zSdzhsLz8S>>FlKX^nc+`qoHkn87;2qK00z#3QQ(zEUczV@WoQlXO=dzq;qZlm$y9b zC1L?qB}jW}ZSB6REg(5^2_mF*9^*_B6gz2pFr(3ZyO#5VmIs1{hwg3o5@^CPO$ZSy zZQG`f^~ZqF=gh`_~rOx{wII%F^cqk;Yd|+%}jvG(=3hipHTJmk@WD;BLnGOf4x0F z{abHrr!41x{$;Nw2CeHHXzTCq?n}R3@&`5kHFf%5Jowz5Z7&lz4IXtZ3OY|LGS#s43rMORyYS4U58@I|WTc31k=cN*8ey`mtU zIN!he?H~KM{_{uhis`+&VNkH8ePbD2Ba{d&bRWOIu6vJalk)a+1m&Gvh<^ z(w^FyJvrAHyhcxMb< z8g4y0e&NEj--vg@>f+^h{WstBArORdbhVKgmi%5Nfq zZU|m==+rnz4k=HEr%W4aA*oN-^9Yl#EP; zZ@2g-zw?9e+T0=6u77h=v9~sFF!S?;#2ew2_GJefWT30RFPKg9?Jen7etXTj^yl*j za_UE?EW$G@u25~9TPH4En@gwu{!6RvrKgszhEx+7S+`P-Y)WxrI?lyh_xTi}%c z^yXr3P3Ff3`j!YYCZm&(3-CXI$RaC4j%@cD&&HFLfqWOF4|GMFtDk@q2 zWHx>CuNp-Lx&~MZf(A46x$}0DUv}pQ;r0GIyT2DMtjm11hXePTP3)8ug7fo!*>ArY zUX%XHhu0R=zTHdy$*Hg-T3!8ZL>>-giPp~Bjp^6l^Zj7hwfl9RJ5!7hm_(>lO_>}z z>i@SrANST8FpA#(rJKKm3@!k7^|ZlCb@yiWZQkv;|K=-S53hBTiR_sLyWJ@z_!hYv zc2rgJb$44&Kc!*=th{o&;lnpME6p3!!_6z*(a^nS$g`qOlVj_fVn^gOGBkL8cqD!Dm&2=;{Pu^x`cXW9^ld)? z=|F+y_P|Fzw0fMLV9FzJv$x7QBZ`>lA^xPq8_@k*DRKeN_=Z zL|mxWDBkou*qX{Ga}r#itGTjTk!koiE0IwX&cg|Lml5-^hc_SfqBB^)7t0$>;h~QU^kMa3F)uqwoPYk>R8u%IF*=^qDi$lR zOZ&MJrBS(9O9Vjvwz2%Gu!j!9L8mwxMG>K;*&qmPaAk_9*q8}^;KNyq^Rb*J&&xx8 zjU47JPNddc@V9AUp45{k6e6_6Ztk=Kb0myYv&CT#52+yfXfL4#=jl*Tz2xOijZ?it z4=n(vBPTj1H-z9PmEJOi$sHgcC&9@q2%@OK)C!`4aFM5-bHZklkFc(tuC8OaHBYZ> z_bib|PH|m<7da2X4G<>bMQ~SC_}%|Y+nYc~nq~E!74gNU*h3N8rBp~ttG)XKdPlv4^pn2F#2(o?(9f`@WErRbAaab7p8t`Ng-q?|tvxci(&W{_p?t;A1aX z{rsxp7!<+eqR)0BQI^lc1p+KuJV8e|yfjmiyjX1GpfUfMOdkq`&A(%$I~KqJVZAH8rNA7cC5`Q@t|iGc76BYsxd)qb`-Rm(Zrb&NoObrm!^&GC0Z@ zuKqc#5WA@UKL1EEQ&LxtXmndN*eM&5NrEjGG!VY)DL01FO3xLm#54NQpunv-!BajJ z6PH4j{%Zb*rs2a2hrmAb&5EreuiazG*clC{7kH@BzLnEM7V?n^S%gX4LT2q^T=8DX z9^H3H)fr=G)gta@AYWljX&k+J8}hmZq(|NQCL^Ep_6ia;;Vu(XF~fK=lE6SF7~q02 zrw}(%LKG}Id{0sD@Iqk&t~;G^F=Xv+fsw5tQ6MWPHBcr$oKnHV+S?*r{d&3+Q;*#0 z^pPR}D|@}*4UWr_RF|`iw@C%ujs{_|GFqaGQmZhni6?=Pt0p=~wC6O)&&soXDy1V7 z5?=wNCDI3byWw!;g^CKPbU+`cV;&m!6jZ3k;rXMWK8{Gg%f`J@es+o{)0Gz~2-}Vu zP}hva#+o6on45{H3ZeZa$u*9@W%!^1mBR%tm0;>Lg-zt8^~|{Xy>hHY*PeV3Zivv@Yb z+7hZ*WY^U+eZ|E?suE(&-vd4=qji4(`aERq0yiJ_f_J!+2ubFVZK}>S(+aI&o8C0b zLRk>vqqs{gk-h7Ac&7<8)}_6XNcCSaEZPX{;v2=sn5gV_sd>kALtM&eYdBcqefI8M zYX43fg8TGQOU75!u6rl#Z?`GxsgOvMY+8(lLNeDey{VEDZie1VAX7M7X-;(6^V<}E zS~;r_%csn7*tGrGaNJGBgG_BlTN1M{4F-0qRUH#!Qip^3>TxxAxHGHk$RTpIM1&~xQ&LksmTh0SD5n)(c58&Wi1;$BpQKK4s%Awmsx%Gou||icfm}jW zI(CX{PSY8~=gwes8ULSgy4u_Thwgn_6I{^C2AE&wdD}^PyFOaD-Gowl_*lkSwKImi3i0C2TdsPO`?3Ojlx;ayLFegDW6b%QD>4oljFQXfL+F9OV4Z^ipRqtF)}#) z0=+5ZKNd+X5qzgtMQpP6KcGtVX+@jxAmZZn`*ks4-?!bL9z+D!rzz#Nq^YH5tshRq zI;;CN6drj}o?5!y&GV-O$=Tf9X*_;(1jXeL&)drgo8;;UbaitNn9Lkq9_+J9BIL4L z?+nG4g*h`9xIbOw!jR|^&O=#}?sBVgVM|nFs_2-i{f+WNDi{{v<%is|pW~}6_DLRFUJFQn z!)P~6`P4Z=1=iL*JgIEFcMgs+v*`9d9J0Ayz9lZr)A~F9I%5LY@e@V zIBQrO=CL!P2!IFmu6=asGM{>5LhARTzHOf=-GVKco3yBG)t?jk&guPHXOC9`%@%j5 zZn zd`D)~&I#3^Z!Sc|Pll60ew=fxw3eqirMu7QmR-hyeNOUrLceDR6m~nh+0jV1D%3mN zKYRsB7w*`jKgK>9J#KupM(S4)KS()nQ)M0q^7JG2N*te7OIYssU0YP8w94;TPT9;d z&WQ^W-m6Cbh@4|%llYzDTt@Y+82w$NbV;savE=pATt-IHqVgK_k}mx@7D{&WwVBP1 zMBu0z89Dd7VoR!H&1^C~ zZ`1@&Rcb7ljc(4Ql7)CSogk1jk<29Ejmsr^)8xd2PA;A4Og3DA*Nu#vnGUGlGEEJc zL{EBCGM6j2BzT!3^5w<^n(xqy8 z*+DXa>o~Hv)9m$dZ{T+URcT(b6&EbCffnwFTd=I-U4jc>FLYMj;7dg#Ra9SzB z=PS7NZau92>wo#Z-cU-;BlD<{&tk0lwU^)YT8`sY17n1P832Hf-_!;ki;w}CTqFV@ z-qL+TcF7S0kjxyEph$S9bA4C4c7A|+IKBEMFM6Jv3(E8%Y}F0I^?)6Zd# z6fTP29xRfu2`(51kN|*fS0AI3V<&mafAFyOG}_N2(wfusz3*nH~^UjeO@fu@Z%O$X=OFg zbSgiC3wH70!#kwA!a2h*P$yulpY5k7LC@d6yQq*N>vhB)k;PRB76r(_Ngo(*Z$Q@8 zi)ZD=hr4Rbv=^wUp@F11HjbAyUC>Y2b9nuQKwS;IHZY!gUiJTna?GAc170 zy*ppJClJZu>KDgny+UwksQRB~Kjn2toIAOCEkT0Qz-aXe|6YnNE#CwW{IGiGzkb>~ zHT5luchS-agJS2cE(A^}10ot>g(T`T2+Hz<)!+UfZ^P&Wrdjc?3@KIGsa$|#{Kh;A zsHz48So3U2Q7zqPNF#rT=4Nn{I6%DrZEA>f7y6y&pZI%Jo1h?+&cG8Yi`1fo|AG~! zoQGwFGzhb_OnM^1ff<;F48}HwLIRgLbxv9Epz`}Ad_Hd#pC1Jz;zOMTh`&!NTHazm#V1x zH%bs?E)s5LaZ6U)Wn&9-fIHrz2UID<5$i3j?l%n$hHsfzP00kR9}j9744jK$T8q%& zNww(WV*d@rv+0xcLreojSQbsGiuQm`(={J?>59B>JOI{1D=1(;UPsYxYocIZwbp>I zYgkysjk=tm610@`VTs92*=k&X(L+Ka_>P)-TC8z6zJ5ITtmSs^9UiGNkozxaaE7uYcMDfq(A*XsrJB=C{1i zlqo$Mb9|hmAfV^{&R-i<79uvfyWfO*t<|k-S1Xz3vHvCo@*%7niVg?Y(8R>h^U&aL ztFxqw)RT+Q zyKLXFqLqDWS{z4(3tGF^rL`>Ir$0+>XLrcO^7SX1pp6k|5B35bB8vTr|y${$nF`5-46esnX%lBjJ1T{}aSz$Bjak|Z=?~b= zgxJW~s(*WmU7mKTM$op|-WahfJ#j4KxXAtO;1%qrN|5B73@ecU$y|C=zmsksXf^;d zJSDZ)pYg&^=I=o&UfV&QmwC6gq23V+5u?gfBU?nSB^a6U>D>;i#211Q=yi}-XLC7V zMlCa#z8F@znJ(Q_zl*oL975+l5Ka{@5iNABvbiHFOQ7sM1KNtSwWrEvgV^E4l#cBKu@P*{_D&(Gd$SVMvkb^_&-=l7~6E9ST?fD_z_Iy|&pbbaKu%tvZ_a zf+7eX;P9^UxYUe4yS=bjd8tAdm&S_Ju{2)rute0_r6UvrssbOi%w$IkbWEt_$gcKg z(j;g&%lM{EAUTyN1e;?yK&l_zdxo>u+0*k{)xC!;xUExtlf>@2ko(e0T)c*Hj=6#o zM13|9g%S8E0m6RF7><7Ct>#gpm+p1n2+R z1FIxd8>~ijDY=$Lr-ffTEmaP-2etRG2F?4Bh*w|!k!f$o`B3ONxx)f+2f*|l>=tGQ zITi{o(hjmoSK7i}c#+i*f_9mbP-D0ND0Yw^w|iYal9ufCFyQ%t)!XF$3finw59XM5Q%gJ?`TEWX4ylmi)c zoEaT98I7Rav9HJwd@2-Hf+oIWf?p@d1x89zM3~mywR^u zOMTGn@!-p{N1WCRE4%G`T4d#UMcS{jx6Vk($SlU?vs>+^tliWmt$JI}@067#rZ%{y zKk&uzV6)xSWTe0kOxejJ^xA&R^V1R@*}bFTzztU? ze%uWQF;JsQ@t~=wu4eo2uo?k^K)G9tJFW4$hyyd3TrLz%+xR=n9WQAz$cMuagG#n! zHSZ&04$r2wuk^D>ssSJC`D!dGfkB z?#c6KPS&lqN+uRXb4mI6Gt4Pd-y?CajG4fF*B11uEFW$F=Hz#u_uFl2y*%W*8xva- z0gTFFv9VeH4BFIu%*H`ipfMOAG7Mjnr{G>Nw!-ewDK~S;_6C@v?zz-?GJVGy<=0pV zYeq2b(VEvMU+=K#$-IQSy(s&3pOuwI-o&%UjN>~ChC>nNDw`V4aPgH$V2ua$>2^u$ za!SKGk~e{B*U)o)XCOUM%xSgqPMZ%mkp1SAKNb+iouIUCvJgt-8XMJ=EtYeKgnXhn z(nrceIl!t#0%psKPOVt30EWTnD$-bf-PQE92)~zG9C4;WLO?n>K_DdplJ0&v_sDoS zpaoSZ5Y+#h<04OfK*BHuHIZaw=FQz24f8=mLI>H;@4ZJd1ljGtc~z*jANeXR{Z@d*sHxrn95u5<%^{u6rp4FROpd zs>X4k|BjX}DZQxI92F-`@;og`E9rqyYE~f^l&M%6WxJsRFHC#QdCgt)t#qiL)$3{X4XzZ+VSQ}8qf75CNo6hCXIm=9>+R+xFxJgV zNcL(LtK7cXjMI7DeckRDjZn!KD_$t%R(~gTS5$suTZrmcd)TqnYIUm)wj4`!Ar1NC zTJ6R*nXP-mX6$Y~k+s1s9lhOL;FHxaQsYhKH1Ep1o;OT~IipUiBJbIf`J}QUT81{* zGoAl@yVhg9tV3+MY)c#5s9Me%wx>hmZNF)H^VV&(cN^RDFtpVO=xJ_fBdbiw25R#e zXM~RnMp7BYVTdef;V{!7H=?G|_jus8+LKYw`fjss+^2Th))@@k_j@iahyK;-*ZHKa zWi9b4DH|;NV|wUaEzSyBNOVNa+B&)N#3Q8-I9A#Ffu(yMu75KO1lcIr3xf)n%w!TuISZMWV}LP z`Z^k=q%;phX=VQWNdUy#>g7%8RV@(UhsP=WPAyU__+ z$p$u85B=D**E47eP)n9kFN#8N1Li=Q6Op>dG~SI3x+x&$*hL;2C|CNLHnnEp$;^oa zGm(Y;GS`&ASCJ$MPD83W6Hky3C!Ow!7n-(`awo-&$t-7}+03SsiA*Y0e}_FEs5;j=5($x(Uk1TCMS~VZP_?p6Wknd#byflN{B`XhJNvd z_9+z6)%5!ftcc8BVZa`Yr81~EJ1mw_h0(hDI(sb>kN+DN zgVjhTAa+If%t}kDoQ-LBPS4@Gz+-XwA!td+<}qZ*BI3t?JHtQDl)zZ^Z+_)_aX8AQ zP>WWpeVYFonSmUcC!9OZjE4nIhDa`8SldwVT78`{%E;l{f*_A{ah$a`V}~?5 zn%?b<=Q91a9u5x=j3XM=pU?buptxmS!*TBh^WZ1bETjsRaAjBL z;-}}TmA`x2Ygzrdt8>|iW1n69^3|o0YW7p%z^26I8Xs*5=BJ0h>Ww~krhWNWy&cUP z?lInCIiKWOUrw+7)UDP;ioP*kOcUQ~ z*RSq{9+Dm<7rU|D)9G*|32SHUws?}nPvQoHScEu_AaVoE$huH6qCPS6>=4YI>yJy? zmdHS++nG^uMVPwOPi9zo4G<2Q!S9!W(Nfd~C-sSW;5ExPmy1((O85@?2nu8&OF$)< zFxIK?_B<#azANz}@)I3L{H}2&oFlv%vCylJvW~b_gj0t93`pse(!)9YGHc`=@>ML9 zR{woNTQa2XT^;)Izn0&Hez4GaQJo=4wl>zc+D9s|brEVfdkK+C^9$8)Ec|n?&}g^W zXvDkW^M}nAS1Wg_`SZRL27-(t&Ae|vk2JhD}TvKS8{puys7>p z_<))w;gBOQd%&Vpo`*`B^x258c;(LJ1X(A=jImf zS=`n99pf`1>h9zZ6TTka@*W%n5C7y%FSi9v$P7e4H@;l;4{rK-GpWeQwU> zd%FdL>T}BsyWTezaJr$_<7{I&Y_kIm=XAObPsHOC-Rn~smneVwnCt5 z-Zv@eJJ4@v)vr~DJ%I$u_sCD6b`K%a@>xCgI^6Xr2j|bTCZd^XT7f_ALCWQvj7&Pd zmvf^$(U4$T78NI1JZ!U^y=`q7x1lwufhnij8=PRU?h+TxV_Xp8tge2r^SW1vQ-P!K zs)OjS9{9EI_1dck|G{rU`~T%X`)6KP_3NMdtzaU97-)%7qZ+OL+>TE(3oQOYZ)CU5 zPZ6|F>poZ(W$R2yb11ptAd9roE$(qN4ZCURd+Z7U=Ti&S!0PvVg}k1>gnFc(uE=e> zGWVdG`x~<)mo$K=SrB7+)Kwtc`4YF$F+|&?S;Z)c3$I#K8Mnk@uN63P<-VUd_Ypo8%kaM!Y6+^ z795(aeuu)H(9`^2DN#$=WC$pd3mIcUE&pKC{h*o`n^9cBlGvF)a=vp7wL; zY>8pQb0)FwlnrkOwbFuWX>OSS+Q5w;4i*NjOcW~1ONWzUE~QD>lZwZhCVolb0gqw& zFCJOOZ?T%&+g+#*cKq95w7U3%Ut-72+nDaoPE8>M?03oc?%o6^n5Joyh~2}*ZAL*r z#=^;w$+7;iK~f?TAOGC;;(|X$wW6A0dWB?u2{s5=G#=nS@y8YAO$nAHwtYI~!ppep zXJMXT{2Mou|3Tb#PZTFuV$n{vUh|jQ_8I6l8>N1hQuioRHFvXkfD&i*bN}>zF6?*1 z%Pj`ndJtK+wW$`M8#{;Aqc6l1i*%LLo&<1y^_NRt)2^|JB8yEt{e5`up|D_>+XvMa z`_gL0B+Ft2UrhCW^AEyYYjd0bF>5b%Z7p5G98L`u7u>R;o5ea1t%Yti2{)M=UmPR0 zMKeg0?LpMQbHZ+&q&?XJqA7$0)8d>4W1}TLf+bcL52|0e@mIZU|HdZK8zC#!6!Z}N zb4H7!D{iMLs+fiT>NoCuz#Oyq<9|xr{y%uFJ1mUuUpg=wAwTXcUl_7<5N=fA#+3vxGoZ0!f`6OG!kGmus|DYpHDJ{|JX1u z@M~}$OuhC#4!{A5YxRRO?=^Td>FW3Wi+{J*=`&x4d}J@N7RKt7ScenL4ciE3d^!I@ z-LHhsDiQ%QB6{p=ePl{%@knYzGjwnqK;=H-#BVXjb#5BirE?krTh zzVk17JIbfH<@#B>r3SYmnD@c;m$(I1*Cq0_-kV+9Na$`zG*qB3{t&{zwo$wL^0G^z z$Z{NDS8W}vTlGqnr&(G0WK=mDivKqK-QQoF;PBt_@A%~S>ctbKLV5Jbo9_-k?Votk zTbPm7m**p4lo5YuVx8;V1t+U22*&}@e=g%nTfNL)ZnokCz)?_V;)|0&ZqSJ=Ml zz%5`dA!+_kJ;eAD6zaiT8M5YeTnR5S7@^M=ZB*(iTsNI}6%j2yc6v9cHzJ>E5(fwL zI3GDQ=)P0mzPq@SlY<;h+R2egot@z9*woN4hvRm7Y*eSmI6XS1B1ZMtu#QGJ8sT3W zk+#!a`d1JZ7T(s3L*umL(BRYlaW&}fr#pEc2a`|xc^L;2Pj`+D4RbL5w4e8IF!ppO zui;>nn}>BU@^t42|IizwPx@Wq>JZw>#+Q25A%f_dC&him5r&PM3s%aS(nkB#+Xe$3 zGCoc4Vce>b3s{MXw6w5roE5(31Mi)OQ!6es~BQD@~ukt$IRNGIXnM^4d&X=QCa%$u-m0uY9M;s z8A99ux~$pD@0|~S>C^)czT(x&pI0Wnt&aJK3LG98*gd#=Y|IZ__fe+dCw{x@uzt<2K$uWmS-y>W zDsJln&A;BG6es zI|_DAjFs5Z7hg5Cc8NHBjj$uN^+y~XfRdx_Yz6`R1>X&{?o_~SO% z0nO%L{rZpnDT%v_+m_c7Dh-X+bUIXyG?UvHyX#i_+S}=fAO9(~qktk=wf)|Y{#@}W zi#@0*fA{bGJs`!L`~C0vDPfCQrnrq99{~HLt0-n2l5ma{tuANSi@)UA%nTIo{UWiaqehp0T^ zU%$C%T%;DK05FkVj)hbA8LjmUE{mZK{OrQbZr5cWGDTdz_3ZC1-TFs=gJ*yF^Y7gH zN`=R^K~7Bb+?qRy^x0WUaLue85;)nEZ!F$uMsQY}>w%O$-)S zFmqtlonv)6xB8!+e7dPzgI~j(N-!SPG$DenREx(k-wQA7`w9NN%YXOyZ$ZG=fBzl)U)X@L zFQor#ISNe% zch`Q-_~5^ng+S{JQ(pX)L!q!4fG|Gt0I9SWr*U#Dtvv%O)uQ#M^+NI|V_aUlHt&Uv zMW^y?RyAoS?0W%_%{AS+9kAAVMVh^!;zM~c>1hShE5B?vCG>X;#*~|ea?@8FBQo|5 zzWX;g-Y0StVqfh8bSt5|EL^c$=*MwO5h+-ZRc;HYV7v1mA2ymF58_$x59hX61nA6I zP>)!u)ELRh!P;DC23m=;oe09fJDt5?B)H?1R&rdT6D!YN)%_ta2y*G!>l| z4&^!zHA5?cbh%EcwDbf+3R-b!4s znjDx_fNZAx?bM%kA%;3CEkY7?8Gy+?IB$@(Gcd_m^IX?gjRwQFFu793HR^OVp3lTy zrjrFK&J3e<a4QM^Yn(GVK&B&3lsPfXgHe`{7UtNf=Xtt zp$6BFq}NIg8QLcr1~O?tO*PpKjoMd(VcS5ux*h;fj$PFsQjqpw7%3sK8jYbyw5%32 zB7hlHHvlpS`?M@hQQVHiZ^h!MRFc|f1G`>#A8%9?>^1gH*BBo|D8lFe~b2@RH zo}*>#Eu)c;*7dG;rVK(ngKRHl5@9HWZ6@YU9(pMrC{q^=y$1%SI_Jf(w3s=?^+-<& z{t!X^YZ{l)D3h1{K18AQsUD$=kYo_fV9xH+wAN5G4wSD9P<`lx53sR8Fafk$8!l@E zBn#^i71(AX?Wx95(D+|{&3I5+-XE`|ou1D2PVIJ3)o%F&taJupy6TMSjWL~)m zDAg(flh$ow`dpEqerv8ACxJVKJ+qIR^y*~T!riU`A%T6l3~!C%yVS3$?M_e7TJ3u`Y?Hn`_@>=s z^(~rCYe3rIiP04Go zCYtMy%#(-OvAB-8dqp6wn&`%ZA>~@7Bv90C%?G04 z#=3Ah+};?D20a7gPV}{!w)s@3xXt`qHaI`)ak47WmW+iPe z78;sU*X&1M>-mb?(fo^-<3*LvN|Zt zP87p>-PUZZJ(|qc2il26h!*PFqp4(LxVc>qxA1UV7`R_7)fMPw<&+r&eO8|iM+@O- zrdyA9hGPxMxL)!v<03=%*lF@uT70IO{k#sT~g}i})6C_u{Y2wuZ zjG7LX6ut#X24E@_8e;Tb{jjGt1A0ual@$I_IT#7f)7dsd9EfPN*x@N_+_P@=q1k`4 z&HncIi>CdJKv|Z3Q`NQ(sJ`LSBC7tu(pyF;!7d452!yOXhK-94yXig@t z@+u8PNqf9C$v?X)=wBy72f)=gHdqa;yQAvvUR#7+QFjORJE&J4($QFE`|u(vN;&^L$m_JGp3$ zhr$+;?Y}h+ZyW|}!ZnaLDb)+1%SoA*^}tQ*jJi4( z5izaqZzg^MT$3Yru`h~1WmocNph`3nQk3OdU*x^0Z-aIdNLNT-Yww~U-^lD{^n-hX z@F_~>)LrG{y#JMu(R=Ck$HicnWT0B`Sd;qejgngPlr^tL)FW%%LLmLTr^daY((Wa3 zLjj_j#WSMG(dvIV5|R_r^+7IF=YVi!TeZ$mX3SQtDm}+KUCrk@Zqjt2&cEiAof_tW zfMiZRzZybQG{>6?6ZwW#ZNVx%aHKi6fTnohzhO|in)igtwYnVl)%z>9{@G&`G2>rsEiB{w6=5P2RFsRhN0mKmE2qkiPMfW)7cR0%VZvs~tSM)- zF_O#0>*1KHPi3-65V+|iWF|+`NjODd7D=aGNi{UbvzcsnE}e(XBm=CskS=8Mi3Io7 zmlK6#eKt{_PeY7SpGjsLQVq#m92OIyg6p&GsZ=Thd>HZ+s7V@f6qMq9S?51~n!N>0AnWlN@FA zCbP|rsrq<2+mq!a5cz2(0$mwk6d3A=f6^TBIPnseH|-Gv3rWhSnNk+gMrQE z?h=vPhj6>k;t^b0TK&eIOAW0wm3^Gtx^oY-WfCcZv~2aafAybv;1IDnTXg)r#nn&! zoulp59pNP}J-lvGqXswcu8_3>RLRCvk*Yc-JIAep0eE%Sj|E!F8+%!wD=}GKA`RMQ z+Y$T84b-l9CNK@UD1AEI;iiqeWp~+tB$;%bfeP5_IbSnvLGV3c7z4#i zvQU<>;Ob^8u-iS-Z9TvT!871qr=6yXT`PaBJYv8xR&bsm=~2^dBvx69y;=qW|Hgde!L=*{L<%kST5 ze$$%QXd;#nVBGTCT;g1TJt zeD&nk&w1lz&`-vSJpWNE=JRaGzEkP0l#nT<`3)}i;P;Zi=Bo1_eSg=Q`>4*(PNz7A zQvV8@uA9&2uIgX?g_dIP>TmziuSHhBnECZ+`l{}M7o0C-k+FL5le_ZO<3I2N!PE)6 zBBy|lAYxT;#?O66XO@cJl;+s~3x&GKnC-RsyD%eY#cx%E1$LIq};Z=v=|CxW`& z;dup45ul!QgtxF&`tAhh@6ojfIFiYI%3E>wv*~nCl~zCa@1R%#$$rTYKWhSQAL|IH z=5Rik%gJf}M<^4pJqwKJ#o|R$yeuw1diK+BfAI=|hHL<->4o%SIN(%3gLaFSN=)Rl9OiAAZ z1gHe_cr)&j&K%ybq6s-D8!_gh36%g-U5w*F>CU7>?br6_dtzyzyLghR3;PCB@dJj~ z17zXDpEq^(vZV|I@B>AQf&xHbEWpMB*1Tj9CMI*1P;pIVL+@nYd;>_KDUNAc_XeLr z%ZP=^d0f^xQfdt)h$(tR9m$<@Pv{EuA+=XSU7jbLLtR`V|1sCs@|AO142cU&q@7RZ`lb4pw ze&l3p8low}Yd1>LJns8!ZWMXXh zDCt(dbSmGl^v%@S>K}e)u#u!*@gMd`>Q$V)=cT@{ovntSsq1w0Iw`nZrmhK}zy6oV z+STb&b5*;KDy`lR{mQ_`G+k~DnaP`-eyR$?Z2aYdO*ZJ=E${9CATq#|)c-&hgDgByM`{`EfMwH+_ECJ%4%ri3|MV z`La~nM+zA3pZKN)jJN_0!;UALo@DWuq8mtGCBT_ggM3H*Yo9VcqLMz+R(L)^woM_` z__T>K69RO7vZ3)0GdtTlR1{Bsda(~T)5uu=t2~Cyr}~*&?|9AGHDd=dQvyl8 zdT;l4Hp|qD(1IsY9Q6Ga4nR@up-lATh8P?jo zRwtq+7H2IDU9FO9BW$hBYmz)TIyqh*B3@*Wd~~EhW9j^H&+efb@DP(^7j7R0!=dGw zJ1fF+uxLjPj<_V3)&ax9zXN!2UjIW{qcD;_u2$ue8+Cxr6u>(pz#+aSD@j89aTQ`2 ztX#$}{EzlpVjf|^%5zl5^7grOeP`#D)b1{c1|6TKG?&uq)dpnQ)+K&h?OAWnH5u0C z)Tuc?|K5j(>~kss1&6Sn#Sr!YJgpxPB_*(%cYdTtibv+6OY=9;kyEQ*4kz~d+Wgz* zGwTX|5~t(qw#)zil)uZb3v5_WuMYjSC)-Y~t;nB;l5SYa)4tlOu5E>huJPAPn)=wP z5%wXdTlKR)^aZa_{f#p{UbrmOcMYA)B<`aSU3iW1V!CYz^9Nos;5Ea=A>fklUITIg z{T(nH?KXz5^}T!Tp~^14JM^~&uD`+U9a;6F^|1|XD74lntBXIF zZ7#cgxT0-L;_-B?$D{$oQH0n>>qStvD(&iKiQ8~1 zZ)<6N4&y~--DLK$G`4ifB5yXVjPi~mlDZD^1pJa)exX=(>bYuxi2>)N@#!zMP+KJ7 zru2DBk!pZY@Ktm&h!!BE#03Lwo#yXswKDe;UVhqj(Db#wYkj4s@6PJqnWsi=Hmq_e%6X-fbuUd;olqXMP>J*8NHzPwj25}r$3bV+$;J0 z+$(42HlCQFqH{M?35F_dQtL-sII_$H0z}3+1tHNGw2Y(%rFD!3CICp(xM-2xyG8~P z3Pn@1;I6F$*>(>h&!hY|QvKTap9J%p*MwLVMXIm$jXr(X{vFYeG1a3wG#2*q-B>W; zIUO}jF$EN#t=geVW4sopLFlmQJ zb(r8V^(cH!k)crXZ7Z1@2nrLa2V3ZK|=Gyj#Z&&k2wrh z?72sFs84#f%wfDzufvBNhVAp8E!hpP>FfhLw8!4&(5qYsMk>$ldoR?-F6sKBogC2N z0*9f>86Do!*>c5RahGFApLF^The6;e9NxB@)jZGUb#tXphqvtPULD@Fd+p+m%@JROW9f?J}Wcp>xanIFwO%=D)JB>gMtPp7Y>J5s-s`s=B;Q(ehFNKQrnKzw=eJPss6_At_0J+__ZrLFNRk?_ab-x_R9TGb>YrG^y-5xzrOm7;o7M$ ze5KFJ{Nl~mcK*%4Up@$`%0Pc1AN2S2_@Ez3JA?OTTBKT$L~EfnATpJPx*k}JfK@tw z%DYJrItnbnLCDqZUVtMxe2&0H<1ARtFSIEPip1^{Mxf2}Fq^s}DouD*L1XeRbMKn@=At?<*JBd5Hur6P8}&XKeXFOYm*7eN57qyBCIZZnVCTjuB5 zT%!ei89FhMhMC*?P$*osb)oOVyX<*D@D1$(Ns@sqt_4HdxHt#fL-R9Tqr}9WV$2wQ z5-UdYr=vpyJY5}{LsuK#m~%LgPRQ)4hFPp$msB!r<6^tE-8h@9cn3BxR@88TiS7VSrZCQ)O9xkX6O zCU%tdvPk=;5HcT(+uQ_6lU+PuQmi$;aWPjwQfnKNLmCCsF)``Z!%s71}8ow zoJ?b+GuD}pjEAGKdSP*rsmWw4I~4_{1_UKBULQ|9HDpC(tP%%-36ds$HPbLgCJppj zd&|}ffh^yD3<@TgFacX^+MlZ1luzlfwY9r>qA3z+6e(P1q_q%>+_N7Okyv)Hr@daa zi-&i{;#-e`7QrCx+F^t&e{80l9PADv5$c8m8vfZ-w@?}}eA6_Ofl~6JvO1_&=QFLA z9%NL<(Ib{ki^+>)Pyzu4l=;%zG4dUzS&W(A@8qdt^y?nA2R9Fwh6Rjppa z_N2lRA-rX$i#t6JgVefw^4qWs()ESPNn={e6ixkWvWsfq!8XPMTH)9ZsWF0jyQ`_f zzz4x_1lOJ+5v`U5ur%Cg&_VD#zA}EloYaRl7#RI1^kpSdKhOI}RW57-Qq9)fH6jqd z!ofo+u?mUKJd{V`gjoNrLyB3gWn+M+ianqF3FNV_|%c?W5gn#e*bsEl^Cia_Xy z+hcKQ5z1C>kp#4t*5#z+RXJMbl zb7j+qrUI5JxQhIFJi^q+l0~YsnZao^xtg=y6(eA!+}=bsQFRQbZioPvNOGE6BdnhJ z*zpD1TzCw$vn4BD`=CM3LJRatpt36tv}2Fvf&oA|*75zUAPm*7)z31x%9YYu0VCmZ z2xA&;Z%TeD98&nQ-xIc$I2sO{Q60H&<@q|2?4-(!FlZ+ENzOsd)Evd@geZ5#oR!e; z4o6(nk`wzO(ASIiH3ro)mtvNg@C~8LMz-}eG_cgLg-T7Gq@X4@j0BS4+HOnKu-*EI z>ok*+Ham?+x6^|f*>j<~HLQkvs3jbxSOJ7=On8#@1%beDGvZf6C7J%)%1Tl$PPblU z(Ik+CD`6-^u3N#0HOV*@@i)-CJq?9o3n(Uy!)DVMn=M0AcPMPsCrAqO*?>n zIfRHSw^LANzP9|?6Z8XH`5^eY!)!MLaf zYJ9)?@+BAZvRBW&lT@iTgdDl}F)d&FA|ZTtv+Q|Q!$#d`!5w*x@&;iShb|U#WST_@ z=J*yZY*9Kwf<3@Sr>bdUVY-0xw*-?6CTV}%ZXr{f6QxoxtxVYK1VOHh1bz0teD0jA1! z8wqb~hrOW)+FOlPQ@TT5)c2aZCb=9A!|e!zYZW zAnQ*GO`+JbpVz~Q$+Aa&UEAQi!3{%~8@!0v8)}R7HwY%EHQiM&iYDMECF@h0p|b~$ zRptYwKgn6?z$Cm&UwQ%ne$7DY1pKr_BolX%U~MuPR&VHKHrR+50rPI~VwI3UgZXGG zC+bHD=~*;#V_Q7$v+yTHRY^lvuvS{A2uCMOo`rlOodDC9$mCOnj%+HMNjD}_ zpaq+A(1d~<B_!j>R4lAW40YwU^^t9 zt!WrQ3#o=|Lnd2JXOoQ-U7v$PG}jnUC$sr@eIZWCi2}LN>Jym+@5pb8=YS*D=MrhI z)~8dc?lh#LiA=n)K2cxjNWvQmMQJi#Xz6U+DT>ghOlt-RVWB>r$pK)jr{dW(pu}W0 zooz~SC6khIE*A9u_=UQ^ktmgi=-P_mQ-x*xRT)Tcj*HBf}-C%9nj=HnNw!5>>;cPy1t*>}~0p=+micq}l z2Z7)NSRH8ll_s32$K=+#wFj`^!-t4S@!1y%#FZV~6^@m8>l6#Id!?J41!EwCxo}QP z%L@I#I9|Mei**HoXGM50?C0951gN5sQ23x6nM#L8M%O?xj~}2oP$$(7F8^e(akb_3 z%V}5^<{mzVCmQMp=p$QIB zCqI<}@T>%ZBn|(yI3l&Tp$;z7zEdvD!_mXMS|DIbuZ& zRCCv-z5G_0=3Rvaw(}YJ)HL#AtT%o2$7Vn2HNWDzzPOQ%Pu*_SxUAU8;sslCt3g#Y zdSbFxBTAfi7{p_uFS6O(|OUvZ?2;csp5<d%lN?X z(D>*e)QEsvPWs@Mn;UcnpSc0*_o<^yMcIq*cJBTB^@+#QHy2}dw?U6!DeI?87yBJq z>uT=De{#oawq-P&np?T93)ju>z54b@d;a7p_W(^myVU&Qb4wp{+L16AKnzEl_?C_? zld?;0?P`@IiyiS3zy|4j)LgYl2u?$W!{XUzAJCM=%a5M@6qItG@ft%zG*I<}rG`Mh z`g5cYYizZ4{-z{h)$|SUp5<>*qYeHgd~imeu;j4GH5KEC9x#q-1&v7HkZ0Y6r^#w zsedS44h9<>K&>YDbHyfM{0i&mq-?7{|4;swmxrIvp$RoIRXINKE-rhsxVo=km8osciowPK0#PdTRz8uV8wLGrCrP3P zC5>`M*5t|0hgo|cgZmhW4pu%QqgI_S2zh||#pAE9?pSL`?Brl3Kpkvo(dvO)|BjrT zUpijG>5ew?KMl7r$A11h1;5D6$>kd6R6S)C62q#Izk&gh%)k*y_#ZUBmLSb^8(bHT zVQ%h;5acYbBe>p+EV zh}pq&4x)%+1S{l)E_$YTWA!_hXB$1>Ce^_FUk;9$;yUx3;)20qZt0`yb8KL6Y-nt7 zbm!pUp25Ky_0C82Vf7nd|EJza>!(E8kTm~IDsw892p7W5UFm$~*{14GLUaGwFAUCl zO=X!hH&15T3fX3vQj@vHbVEaGb6q-~^y3rTcZFM{nXY&*W>t2*FUC{3Lier!w#R_C zDVL4L>Q2{_5}UnuEZiQBbsy@J$+a_8zpKzxm&>JfB{dLB^!MajWPXh|KZ?b6=%_zR zisHJWs*vsCN#b}pEL^FJCzD45-FiWu_?K*JTRn^0XhVRA$Urz53uofvu}B+vR*N^cc5rZ5NU~}LhViA z7={<#Qi#SQa2|AQ&0wL!DicXZ8=KoUr5lNrWak>~>mctI&qsTk&nbel`Y-o?#_KNg z*=@Uf!wthJbwZ-Paa$}|7fq+P#?!O|-{^&R7Iuca!{Km8xGhkW?Kzo_XWOG}4|?kw z^hr(KeGQ3tq@XX)Mk6hCn>Jx^pibfTSgw1jB}$%zK5Ce$s}B{ziF93kU8pUR4#$(E zUb2=YP&7GN7mcT5?fF2r-VyJKG>3N#$Ks(V@pY6H-LfYUY3OLIO9zyJj;6n+)3Ibv zeYCM>OS+Bi8_yNkq15k~NQMR%Z(u{%hv2*}&JOle$~zPH?cyEUj-_(3F73*KBseiX zGBTxcPYDybOVJb{Gs73&ob?WtIbElHf8KI4#nq7A9g#P6D)&}^zfX_oZ=4v=i&g4v{DqF2}dkgt;Hnp=? zHl^*wNflvtJv^s-Q#*9xB^|yrtXpDux#^U|<&J!+goU44rB6a8@tE!B3qLTDF&|U>>)Fsvo>vG%iH#xj@Yt8Cesy7c@j4dz-QB$`G>lA_O2>*L$90D zA7^GP?@|}%+V!r@I^A!UQ}ePOQKd`Prn++1Mpisch^^U}Ez4g!o+XT2N}RPz?pj*; zyWUlkjClInV}d+sVsuI^GY-=T0|qtsBEK#K%g!66M3}Gk%9~b?X$qc#o7|y1gybkB z!w1<}INs;HRmxFyP=)7gcv&=UPlD_9dcm-@x()F{F!*@E5?JZR*LF4Qp;7Y}nWWt0 z)>DDXHuHN8a52{%#E5uDOg7!RSG*h814#`dDQuXG?IATN6}!S9*jdRVu8SorzsQTX zR)3iRwe?U@PYy-770e0ea(KI-(o~3mRl%qZfSkjapKG8?qaAO;>TVxZGMA- zI?GMYrrNP>OkH3-l8A(+sUT_TRM@5-&R?*eGwZXmUJV(w#;`6!3L_tzpTHDHvRrJ` z{-iDj)_rW27c$+%!|yvs+Yt_5N6}Qfg0qBYnOl6DB=k&^#>UM-b?xal^!H-BQ$0R(HGC?*+_1i_@W5DIOFURQ%33F?<>cno{JRR}bkTizN zmD4VR;3!vsMYxn?DsEPzq)Wr%ghad3N<6K@l1e$DKWBB%n`*!VHmC{+DC zqA^sx^iQs_FDC_9>Hd03yLu(~IuGL!=ng4e<_GI_uGVL#RpK#gib)=X z2FrY^>e1F9N&0Z?&B1nNS<*PyU02HmdqEFw!^7=+Sxrc`bIVdMf9CbwyA#1@KS2v| z_%gm%=^^F%tA@Qs&;UEu|--_IK5sBCPf*%P*KA@JPOg9x!$)RLT%A7 zQvnbyW?DKyCFiQ&M@?JGLBXn|c-}HnBAdbLq{7Z=oX}J>vDD!WTLHFh*Y`Y*IOYC{ zZK_Fk)WcF%%Q(qp%cNGxX|k%l?MfI73=+VXYgAl05sdxC{$w(rE&qj~?A=V$o^-M? zS?ux9Zxhgdg-Rr zkG=Iga|^&Rhsrf0K?GDTAbt zKi!7&WH5M-fqIyG$#^`^gs#I!WZnfbiI8337mQ5+GDOj*sdCDkr^0D z?8+(YR2%BYY^}jQkBiwxN#ZL~l&6g*0`;p55LydKARdW$%tpc)mDL>zt>9&6?$$5V z7?s__ZT+V9m;`)(yISKlWk`)ywwjxLFDIIun|*+7?R9t@;_X^W9;(C>HF2wyv+Is` z>47(;g3ouE`(1O(ZoQR73aSGWJ<}z>qjy3K%n}guDX87&u)GUMM1uzI?)(g!TwdkarGpwO>*rxsMjE zjbk<+n7^v%d5 zkG&T02%&Y0rX^z%u@%4zHsu|bK)qw@nis7nwr#`-*tF^>e1bOB17>6WMh~B(F720% zEN*EIajpJvXx3{x9FyntkczYp)@oob6nB*9vb*>lF=4vyJXcA6Y=(b-X)zV5tN!dS ze7Co0k6Tph6CX+cfNnKiwT0uyTClyTc3@RTk^49*YOc1tpl#LvovL(|)v(=CO17O{ zu%%sxRPjC&VuQ78vsuNZOFk9jT8EzM(o^labsHN5Ua-d+KH?a+v`Tr3FCC~OR!Tno zceLpq2-PiPxAfD#1JQ)HZK#HdFtw&KhFr&Y>6oO%{H+&gWXhHoN0oc_qyZ-AeTL~N zZn)4Jf#*%AARB;D+Y!{M(;sMIS{Y#VK5CmpwKEc#2Z*AQ zObs{2f`SxJ#hLT#d)1<^#!Sjo&PYjcL{+dcelX#k&&Z#n|H()brjd#&UXGo!uyqdcjHSyoK78(e#U}@-U z-Ao!<7G~DtET7=av#se7_0zJ6t}!lE#!Wlbm5+p&1V00DYD0*XV zscgv0XEuI=F>4*oh1*OH`?P&OOIB@+nr_{AggxlhEgJz4l%4X z))*{I(k5C*(%%k#qC~Cg!`*c{8(}b%0|zBqi&`YVr@^5SWLk(Gy#TOMbyr`uXjcUT zflEGoZw;nm@)irl7obp@_l*G>X<>(4>DG%Nh-7mqRonZ-x?sP$cuEV+a)l1Bcu;ep4$&aI z0O6%`B9_l~l20RVaS*fwsd5%p*pEx@+T)(FK$X?+^SLQC_2Th(#d3tRW@ZEe(Bx|{S+uMX>Mt+?}=P8gBk zds8NM212vp-!SEA(=)2ct?^aeSJc};DpI0;nu#i9yE?NRRg!fA>1rgrZy0Q;vm4fO zdreDd+_40LD3(7(vjgnYc-m$|?X()MNSK2`vbAlv%brF^DQ8bx07!?Eqw?&cEG#Yv zLQ9-J4U~gk_?>rb>pLlIw6_nS%5%Uf+iIxk_XR?4mxjqS%M8md*b9z~_{S_fS>wy5 zaizhNxV|*4TSB1#+Dq0y0*01LvyP#)UzfIrflt{M%7%C^_&SY#%{GJmCOD^*s9HSy zu3gRo&BJTR%whU{S2R?8D?01#m}^vVUMMNF=)*a{U^aYD^3r<%ngGz+2RQNh3t!aX*6L65uC}Wo(h|E7dx*PVWeLoHy2RnT zOoa?%B<5_SJ-5X)QZP_!o@_8&l4lJ)&AoSRo7`(5E4I)phlACBLHS+fQ1B*QW*<1L zF`T;V8*sE(K3YSRNi{vR$#7KSa9?jbr$00L`JSY%GN_e$h3z$fGfknU3wkzleT5aj zbXdD4-B5cV7}AJBUY9E6+Sccc7kN}7l^S#N5tV}~t2KNxktTT4{LMZYmZ`AT9=ALX z*CKjT_h;Oa#dKN5fNWYoFN7UwsYbmP=Wo(}4{A%!S=#(=pfYLZLYrC->7Lj91~8G^ z!Um-_1Kl+^oSI@9({kV~*{hzk6>KD?!jAXv*-ll)g-=ZBaIX>m+1dTow_>wiL&q== zUn0Br24nAGndxuzf_km4a8E~BIx!fE&EvG3Sz8nhg+sB$o8VwfzHFH>6|-fAEFw$c zDDx=ZLRv}#(sV(kf&Bs2Po30Fhr%AIs2D@6lD&$TZO<#KJ%XfN`72(Wcxky(9sA!E z&ONXt>kg{-ps+cU!-fR7m&RL?!yT1{cy>D}tuy&1vSKFys^wLQLIW&$sYHg&YaS?Do>z<% z8dKCNPKNDlo_yC3;w4%elg;(@iN;JWnO8vC9^1^OT|iovydar=$;LpR6fW}xqi>sJV7CqYO(rN75HY3s)Wuaq zZ9)OQj|GmELtt71>fMMV4e!>|M>SJbIwW^2YACatqm0eY^>wiW6m$o@<%0={r@<#8 zG_EFj+ZCrx1=)p;5CY`WU%H&}o2y^vD>}>C43FB{uO{v9kjLFtVm720gOte2l`9<( zr-NZiw+v~e)uj*W)7)1X%)ph8T6BgiO%u0m>2cT=`w=xw$u!BB<|d2OIvy?aT{ZjC zcE6F&aQST1aOQn_sDX*|N^@>YotfZt>P}sF>DK&x|53HlM3mr+hh}Cv!3}Ra)F<6{ zlwXUgOdAGqF{M9~1+xN)v*AF63zfbec-3G3+P-<8X$Gw_u4qZnL+l-PWNnORqE4^4 zd1;qdw}7@?aD6L~ENp)ysT!w_Mt}fKgdRxkB z%8Tm@mS=iD>K%LyNCST(nOGODVW}(5Yj!=P_4T0i@->igu~Eg z&1k1>+fDWk%MUa>_iHwsP>1df!JTb}Punf(jJC*lvuTtbj<82VGvX$~?Y4Ny*|^$M zJrEaI!FDF`I%M~D-41h?cILE7xhMHNr0?$2=-iBHknB8nYE@aLOXkToisYz)D<^H3 z9${#}o#Ga?3tspU3{&f7-X65?63Z5~$NNo6H}JT!`Pn%HyK$mpC;2WUhP;dE0+p=M z)nQeAvHBUR+EX5&lDB$ot`CJhGf4Du(|K(#TFuwmA?cY?L%wouL;GG(4PQu@1=8k$ zEd-E2k;eOMnjjWL@U8yFvRJj2-Y`Tp(; z<X7QGuoK^s#RETC3 zI1q|HEG*zBtEP-`DSCRdu*X>ughf>7bIe>U2pM7t78BBF4te^NHu$2AI!y+8O~+2y z87hEKkHpDc9T@D1coB1CqT`56P3xvC)j8j1n08B#AmjmN2p5QZTq7O7W_Xr@2&!!$ zKzpxIK`rxq=NQeipbL#c+q`v9-JU09{5q9J-EfCtBmnV5;45Q+A4&$~CQEJF2QRU#)NY=CL);FScbptrF&}GTGjBNEnq-+|5D9}Z@xiwTXI5IXkHpI>TaWaMh zY&2f=LW88g<8<@mt`{tkwhA7KPheDl-mV(lTuVh!sAhV|XU$Vnm>mu(KBAYm-Z!)_ z0??HnFm4E_(bln97?#)?3-Pft)J2pYxeuRM=z_Syd*RqB(MvFG zfTQvC*ss@D@e1_O=o#aj`!vwKUKmZZOcw&WS7f>nNC~m^YFJGn5kpSbWqv@KF!PWl z49&1!ZVQIURY|W>uWsvGuwy6&`7lZp)-4nvMwwdH{t=Ap6Zx>W1fWUdb5Foo(6R2e zH#PQiRMA+Q;|*g>hET=Jru722v3+MBRKEVZ-yUeIT>9O=<+W6nf8*N&p~}@1mer58 z{c|dL{`}YfmRDan`o{+-v;5D3f7?q`GFv|v$b@#I=H#E!=$^d zIW;(9pu1Z%b6BuFV_<&Rz`7m-YEkkqFB->{u6iCBUOQ#ov{(lbX%WkwhMZ3t$85H> z^^jNjzgd!IV~o1=mHP&OhlvJ~$F1W@_XlI*f!&vmt0#;|7>K3&dZ?A^8{p4)P=-`d z3SVz^A%q&iWKg}bP3(rn^a#$M)B#VAa<#QPq5**VL8qF;O;nCXMW7|fF=+bI)vE-s zL+&>Dx|leSDpPwurk88s{&1#NgrZK%Ra1*^zHnLq_G;xyTKjLh*B-q@Dt*cnfu4o3 z^N0K*MeU%$WL?c|@zw_s@*tf0V;*2;oI0T$v)H!-w#Nh7l|wn{Aahl(6YceFE%^I_ zMZ^dYli*@cx#Z*ZTA|2fUkInESPU=D5E;bN1BaR$YtyM(Sr60O2h*usQi;y9BqXn? z%OsjJ=~}Xgw{6R2xJ>4gb>t3DXX~00%}27xc{Ix=YMMI8GM=sJB0+g7yEjR9xq5P% z*VGYKRGU6qQ{UK-O4rqVb1Ku6PS>RpWAvc@(?k?CG$d-ic{;lj17=+v!e%n{%C4c> z{+g{db@jD1O|=OGzD#`z;qT-}%b&*;vU2;oy}8(zs`4-KR(06 zTScQ{Ns9`^z9sE(KYq$=uDGspeWO6zsc<4X-8&4v56L9~a@xb4$HI8`Vetw;OFJ*+ zkKC|hmpUa(;T)D?1_&X2U{EYHd@NgQc>ILt&2Z@R>}+{Umb@en3yMo}J}&50DnDhA zVP~$-4o<>XRS0m-g+eRK!p6qH^;uLsc?JR_JL2}q5m#>NkU)x}K;j4X<4btECYDL0 zbG;Z)$p5FWiE>SayvGddD3?X2x7FqKU}*Nu(k#$>i(fm9Oz}Z^CG81DmgZm~d8rHj zt+lnTHP-=$Oym$;QuP#Eh#H0zDm#hZK?~Q#Y+q`vy(K0c#CDV6oj(#1%VZ*$aR^p= z<&ML=VK5`@M7{1x7CqrFfgP27Vca_V(4V>YBF1TLk9O&PB#r=9wDk6{o!n^xX)$~)lTQEO zPX1WUo!y2sOcjpPu0v~r;;~W_Kou_c+ESS&wV$jo;(j_nI5$s4`9rHq{nvxRgWDtwv;F<$LQ3x7-Y3d0xa*vGC|?$ z2lK}5nOJ&C6;wnS->2tNRygy4Esn`Qi^94$>iE;A<$2qlGzSA{mQQK6-Qa8CgTp+; zy~8S=K}Q31c$7c+eCV>S}td zJ(w2XP)(Cv%ykTXPUG*_d3UB#RHI2DfS z#A2tcil>5`B2F5{n$Y4p-fYh2NhpQTZ)VAyg)Rv_22ucTK= zXn(R1EZf&i4MW-*=2o+!>F(o z=Q?se6r7r40nhP)6L?_$K5d&zc8Y@Md>x*>bs8R*cZ@DEb(T^3f9eYug2xrc1pn?0PjCq^&=aHav-0Tbn;sqO=`ys~Fx#sW;k)Aif=mRBPI` zGW|0n?X@PoHEb8`MIvuiu3Y~#*jI`o8=FSXmZ~5b@lrJEV@<8ztMQ=muYC+^`}=ah z4~A=lEe{)rO2Ez5mVIkDsA_m0ALmPT<*jY8AOVz&kJop&%6Nv!>ASf$@0Y_!m7~xmHY|SbqaE2O$ZVpA!Y6N0#8WFPjNC~&5FvP#elG)vw@jK>P5zK<>QnTwpj~-%qA(0uB7_zGNE2q`H2R(rxI; zrW4bw2HJzOW;N!7Y4W-XJ*n_0a~GGf?tFK3`51=MGX?z;KUcGN@6AwX#%Qic*`m`!i*LChdSVXCN3=y+JP;}6CIdUlSgc)GoKq%m zM^;k~6-`7N^crVM*Md`&(@zWsYgija}S6s#hfU7;wvm=iWdGm}YULN%(FwT3z6926ZBqpNw<+c7wA zvlERvgu{T1SA$;&OPOz-8$voru027aaji!~Wc3g^yNd8Re7e51&eM4K!_=?p3`80j z4T0j;pM=_G%8e?`-x03wVuv&psi|-peQSo$Cl%)?tm4qYj2C-MyyeX7Dw-+*-`x_1 z5Q~8|Xxhpx%lFi*Ls*5c+o2e#n^rJ-!_OG<+UivQqGzk-nx_Mu+M!d>*9@qPmYaf6 zzv#A4k~{q}l&n-B@LAa_Zfa7ci~(GiRRDQ%*& zXb+z%w{DFCdbOS92H@NfsTh?8c~O-U$nZi7jT%|lix3ZB?g!e-SMd~8xyuV$=CeU> zjniL&%JL{9}#O2ke z$-9wkY^@tirnYBNZQ0toW0Vs^2+v?TO=Y&XVS;U~O{a62bWOT7+0j{Bi(K8#Bg%zg zE6pQMH>FxIlGc*iqoJXOvSVcNXl<#fIo*(I>q(_r`)X^m$wa26jxuDa+lch7yqu~- zC`ZGT%{C=S{Lz%k@?xsCDP5Ors_kpqn$M(=wXq0iEyt(H*ID1B`q@N3n)4Yjmnex* z0<4g(TBwLC{orSB zBW~?@FgiI!PBVj19gh2gsBVG6px|s*)TQx~PV>TyS<#GD9*tm(;y?(&82+s@4a#eu7$7F*6(X`2MNWs<4gr5)+K1ygK51vSad@PpZ zvSgMvp`;^X|ox>50;w>A1 zMKoQ}VVr(lci-27t{GAq5Mh|qSnp{tujspFr?7`LS~E)XtH)(ScrO;H{1aB;xH(B( zQ5R1nU-VjVZhw1gvURt4ruOS@*~K*O({;VY7#dO9bx${vhhzb$Ia_CbPl*}ntL`Ol z+gMM?MscUEZ=d}-u0f6+mR=`*$JAWs0qc--}*EN8S8+xuI~)jh2!CHdPg`{AJMHuEKaJ- zWOG9s_467V6pz~(*_I%+PdK_2mwZ1kHl3|aMxw3T8k=@dn-k1lUl)C;Awnoso;gG_ ziEy+%+Lj47)^_5k3j>yK?W>PO!##5u%_WNyQ!3 zB`G7@MHW+{kdv*uGM(8-nuZp+yf@YoZipvxmCyg!2+=8gx-;F>l-jy4QAe;VA4LaxZWp0eO$7*xo$RIo-izkspKUgmjx=VH7QG#6 zu5ai|ZjD8@Mp^^An14-OEKPVuLo}QXClrszdo}T{M0j_yDTYm>C9avrh-42pHV&rP z-4=tgY&aHeOcEMiQzB96fj~FLz1nyxn$FaRTjF(uVCTYdGSMNfG$bR5*l-+30fORN z>(Z)&9RNsb$Y2_W*ko#3Yomm+NA>aW_Hd#*8_C5Z$y8mJqUXJ)NMk)&Pub2$UG1K1 zT{^b625bdM420{mvD#>?vAKRIUTMGmDb7nm21~*fc^&lQ#+#eP_>i4$^T0oHLU?0D z*zHt=Lz&#xlyRq42fEyw5@sAK#|^U^MQs%4jXM&5%jST4!rD8J%y6ELUe$-shAUTX z6r$dH)i^CAS>7&Od`Mg@rENJXOHv0Ev5k_;4K7G6_s$wxn^61syb=B5GJ&+f;zEuF zHL%Q4!?U6vS7yYN356yDpZS1}*M-2(+1KL9(_Ej>{Bx$T-4}(QH>xDwbeCkf%TTZa z{Swg*6qXZF`v@JEAxY2?acy&z&oY@qB~zEU2=!T^+3h<$Mw4%tw-Foav;f~zVsj3K z0ns?>`b0Y48Dw$eNf3m^(8ua(YMMK?4+N;F9thXH+7-)h*MO&}@Xm+NtGnnULgX0N ze$98w0fGHs^S0Br@H?_<7SJ-9xwULjqnnkMO@**mlY67`j~RIWHI3)24bs$#7STSW zWx;;}8Qq?=3vHKEJz4w2fWb?TU60x(j0qMRkJbsK&f9$}w0)rR`+TA;ECoiXl73mB zr%vyxof)3r;oR{%$)64a45sE>ES#zJlA)l*n2LXR7!E*OjZZ_Jh8Kk6PPLtRqlcY> ztc#Km=QMUlr3e>f*pS#Y@^QJ~ACd|2xXVOPvoWJzV1$QCdg%kRgqKsA z{cHEs;|ZgkLmK(A?Sz>d=51kWx3*~yIv<(^;SHNv*&^hTwxUQx7z;fYE zsE@txtN)I)^=DO@%U+m$^_}V<5f;KxZf)Z?eTl>ei;H{}$BO0>O*Um!tKS zPlLBg@{t&b97!c~F^^tJIHB@UJ(}8M zNiE7-gonz}BkHK`R7d=%p!td2jOEp^ls=$acII!YRqd-yrP{2>N@ieNG}+c_OIK%q z&#FN*S`NG5NQ+Rq9nqsJ4+JLdQ4R27b4_Y6rOx*ykJ)=vyoS@rHol(I&!%pDu~$vo zM$Yeuq;-|9JC;V#z-RkfO2e60O_#lSTHTzjJ+6~>tTVh_P0wXJ`V$SFW!!)1J-rgj zrE7A?Qi&aDq_XsmR0ByB`*$|fB;NSu=5IYVJDASy-jz!3BW5yD-rJvhujy!QDmhS> zC|{#?aXN-vSTxrvKCos@0Kl@*1C~QJR3O_?Jf86G>he{-pKuysqv9gL98@)sVjBP-_EKuOVUwc`#$ez^`fLb77N54JjXYtUs&s z<~`xDm0+;6EETF5&UT5y_SGBga9DwzcG^7BGNP@JKO)cf4CwD0ah(QS!uYP9-_ajq zq|4h)6LZwgv*EAPIws~K{<;?XR9x8cpk5`->{1D1;W>uCb>x*)IJz0%F`*nVq0A!c zNrdNi-YYBMEs!q28AjpkE zNPZNw%+i)*hdk{O6)+`)a8S+8g)Kd^X!OodtXd_>1sarh3o)jV{iV*<0-XuP7gv>C z*!07fx$|a(AgC4R`FW1tJ<)j8;g(@b6+7^>#C#W<^!CniF(NHTbfo)DzoP|T^TPr( zkW;l9SuA0i?JjOu9GvMnSGD+qQhZ#`;{ZyZ%)Os^!%_mMPBA~^GIqU>A`LD7Y^ za?0i~XOil^O7PWBF_deDIccyg3(TA$yV?l37Noq?ln2a;k{6=hR?D9~Mg%Ruuw4Vc zg`tAQG+NP%z1V#Iv@*!B%Jk~2a7U#yEEC*rW)E9EGxw%;V5MdfBFgVpjxnVDyU1j~ zTVvdLNsesFKzvAVr+p`9+qavQWg0h@25GiOkw3g5gTSm3PDo>*H%{W;r&W;PZF-!S zFh6mlN+t%Cf8M^`i?|WMd+HJMerz<&4$PW;l%bM7!F3BBX(GH(6Ts~GZ*x#$P zFjpek0kKJEjIvMY&~)q16+=5OiLjhDExMIeaA?eOaFa=vjt{D*^RMXoRLa)8-V2hc z&bb;qwC{{c?w`gp+xW^|G_Cv`tB{7raGA|@zD1d@1@J8tHj!?4jym;9>F3bJ2u=qs zO@htvh$l`+%711*kFJj+BQ**tTWUa=QQ0($r$eOGUS1;Nmfbq50grh&K`*W5V8haC+UoDmAPz1uxsw zEw<{gRwv&ja2-c|i~5|NfwfZLOi~KE>b{3Ls5I{aDheT|ZQ8|CL`{HZ zKuZ-0dj;^6X%Bb${tHso&tuo{FvrFyKW=My&8ygLiP+rak9_y>{CA zIS+ciJyLma=hGlkAzii$K{yJ#TbC08$sSumi}XDtUdn9!H)F=goDqs{5#Bc8t<60T z&tVj2QoFf-PwTx^O0E?XQ*PC0e22DfR~-DD#e)g47ET1yD&;N96&_&H@SW4-@i9N?09ThJtOC~XxT#WY&DD6T z9*P4&nN0n;(~RT-sq=+L2faKTNhq%gswa@B3WS5}q}_mO&Pd25$Gl1jBSnDt}>h$lNHs%E778SKl6d^ zAL!8E(>j<*i+Ysup?okH0EKI+S6y;9edjtpyh?LLKhp9(3YAET0NxVW2Xn>9PBG&~wyIB3J9hgbWcJ?0M}0ctzG zzf5rt>~gxRrF&;X9uWb3Z@Ft5vZNN@&{WfI`*ze%sBoP(FUF!S>jYmI<@Y1 zkB{IZ#5}L?(w#mm+6H$H?DkO%iC(+Z-+7bmM$&Na-AyDwS?7}r5T4542MU_Ib@aCB z&o%7~u60aGycReM4P1n`k_Qv0KY@pa0QrQ5%5i`aU({tUO9=@gh}d_v=iRwL zqLO><)8IwNOBiRJEB6UKwCGQb1eR0eMC96nF)c6GqU4tyO{pjPci%|H!hPFJcWzc* zL*_g6&R)G=d)!cIyM-8U(>t-(`zrLvZhliw%lUN7PK`x2TfGcZ+P9qt>x%)=J{IGZ`%JLgMc(W(jnYBGg-zu8 z@>jG=xlr=uyeFlYaSPy`f@C72*;+j^Jjt*v2IrMvcyie`=7ye7tVkrLUDqeXr4D;Q zWwO0(un&R2V#Ly?|yaol9fgiEl34E ztHr#Ly`{5xRjBXP-fry7}n5VF* zEDzn*26pRDr*Qjwhjr=9XN@A}2gU^_ryI9gCpp2w)m^3!J*qnkPA0H3y2qL%?C*$a zs`0v_&FOP?Yrh4Wh(rqHu8U8*WT>xCn$9V$)uB*i!LMUv>@KCCB(Dmwz7fH1tN=aG zLZwYnAgQ5jEJS(0PHwZlRz9vpJ8%5O>*Dv`ase*3egmeH7vDy>>OZ-;ige^x(5c9tNH0jThE$enl z#!(5HFPz}s;gIv*a`8C_D<1(1JGP~8*;pjeP2qt#F5B^Rfgrbt-TW$TPM2hw?1}d6 z7jAq>Krm_DAJP4*4WLxUvCybpTeigx+2axWYswQ#@$imbKd3*Zqq@8%fGLN~5^KuO zw*-dA%J%l~4K?hx?n)MDmG8B8t*aC2y5_N(bm)(Ls@0x9(QnJh3G8pC4{bDPva#GT zw)KQYYZ1-_#+$ZPEBeTIm@W3#{PYfr5iZ>@zL%0pPSI{ebI4Gqu@!lWQ_U-PuMt83 z(D!)b)lkT4#8v$raRptPURhULW6m28{f&UwuX<4MGZC~&oBWBemlKQ_WhJxnoS50q zyjK}|{nOw+can^D#yXs`*4D#_<3XLya&ttpX**|~Z4q*rvVAeTis`S)W^~zo%7mh{ z+U2NG0|OD$R=bQ|7Q|ZKj;F6AV`FQ#0f{AeN6C}|IZJr7l;!HCt?;-pW_$Q;c@=s^ zk@kyFyrpg}VaT?dtr&DU+m|_q&do>&uAo*H*byf_V3kvD!g(!xzu#&LFO|1>qBRd) zO3^VP+R_m_FD)@W_H3HAi0g6GVb0f3j9H^Y9qnp$CgN#E8s-DDi7*v@TR%qaU)jf_ z_f4EN63wr%s1`N{j#1$osc@D}u3&jML$q?7kGY>(@Mlgl&Isam=*k$28oQ@I2zvBs z`?F8KO(mKV7~3}1>E3qzG`{BpUD*L@sSTI7&gw?J`mimv1eg|tZlAG)zSLHvSk?`=TP;Hl5^6r-nBtEGnB z!N3!KXeqa#=HL>XaHX?xw-+Yw#S)mRmxj&dAh?k4bn?;nv9&C%&KKT>moa@xmxtnx zT*T5}@!WCrgIs+eneBl=Q>z!6Eee|&)70dltU#kv5~dt7G2@_Z!JS}Webe1ExSgSD zLK+=RX?38K>)G_ZC)vxJZl3hSPRz|drgpv0ey2U$p%5Pzwk}J@R^_giJ$+;pa1JX zt$Gg!g1_;TKS`flzY$3Ni|_lsfAQIG`K`}?+wXkaSKQ51();kwxyy{_egBWR%hx^c zFMruxzUI|d27dcnadQsDfAdR!_qTuG3%~t?-_N*Q=fCxBezVC?M_qbXx-pe0U+Kg# zs)qy=sm8`6i7J|UYsjs*wWd7R(@mwPG!ak@sd8s}M^8(N?2fe!4cT&Y3;tZGbduy1 zwV8$*j2*;W!I0G_aSS7@sWH_Mrp8ih-ABLn%if-^?t#ntOi=Leu-%MVu`{@6#r7s2TadAB_!cx zj9s-?^@yl*)4AT}wK>tFY@a;pS2ClH0ehAEj}86uqS(6E^cESmpQ$Elu{2ibv*=#B z%S&nFWiNxPgd1Mt&Pn5&Y_pCU9oX%2OfRd;eQx&Cy3V;gzq)_uWi9=Yas`3BdILt+Z@2Vstm&&byC8SPx=AP;9Z=rU6B~KKwt?g%dN$vGP3wEy|Y>? zDsF`X>ome`J))G=wMr$87Fvg-0k!Zk8~Ra!L#Ms4$3wxdWx6XR-cF-fT8*%gDL$@| zx#0C7qe}xTzpTq>w6J$E-XyWGDN-dF5d7o;t?_}*z;TH zRA1i_YK?{JYtjuhbyVeOIh9CI2oC=w<<@DbO*Lmz#D0!T)TFpuvN@f|4QFci5ebR_ ziX53zoi}gG+LqWy{CWD{hZhs2O69iUAjM(!Z`o4wyIz04t)40t*Tjxs!bcM!Tli}U zcZ#-48tDpqfqnW*;G($8SB{qo)G(K@`$N>5B9^tC~U1k0gYbb9r8U> zgIG~VHiE%G;z8kU=3;tjyLE%5P(31l7%^BXJWE{j0k(m7Gk^2$gLtqy*;}Urs4e{K zi0F*1RQCy(tJwuL;rsA9`YhnSeaBv67V+v;JJ#iHfb}gF{6S4S7?aj&@5%V?<_zH; z^HdbF_1Dq_m>8xu8a*o3<$q(v)C(W!1X1S}bo+ow`si3OgWq^h?6m>lK;Fnv_5 zw=hu!8rgu3kU(#W4C3&%?rAoVBzS&(b!ugH*%nW)KsQl>x&{M5D)N#yMn*Jld0}Oq za*uMX+FD6E@K2P89Y>Y=OaOx+b;DpP)QaSO;o>8??|fnzV8Z3*uPEQs5 z&23344SI=Ldh#o`hFiUu%0pXT8MjEMn67d;+2a{6zEXUsn-Jjd-F(O#9pQHDblDtzPXdFN2SBG?EK#` z`NlpRa`|suFXWn0hn$RHxeZ;~l;sAo5qh5Rq7q-YrWuz?-TJ6eoYdw}=M^-+qUtdA za1s<*J;X=Dfs%jwT~Hg{W1w>VrR4hM-bi6Y;&l5n&yZYHWxVuZ04j<)I=*gUS5FV3 z9OB+4l5F#29tecjh#vO8h1FiVOnbj{cx9XHh@ar=ObAn?d3&aXiZ%(@9Dgh7K&sUZ zzGxD?&4ajSJ0q<2P9!?8mmBQ?g(h3qg$TJoL5;Gyxk)us$-{qG_J#s!&=mF5HVx|5 zFIAvs1;_p?X6N3>N7cov7}H|lN17- zH2LhaB$j9((xeW5>Rf#)lStGkksprhb?B<)JfF>GQGdghq>-{x#Kk1Y0a2T)t*L3? zn-Rm)K zLD!ABeN}crKWobMUL44<8h-4K`ha>(I}akirxG5l3JnxIslj0ny=IX-P4)}neqKC= zeH8gq;4aVTz2z-C+1nL&{_JV9A$xTJ=dA1n)u^>zb0BOW3GN*>&PtS4@Kg!PbsI|OWX-G0!R3XSEJ_%_sL=s>ZJxGs(=JEC=l z>PU4QfgS5$_a@obmo6#}tOU}qxocSocc-$pDrVT*XkNs@+x29?tInyFv@Ww?5BY%D zvy;!T1nQVD<`p!u)vulmq!e`ZlnI~>l*Ni;%$Ce%>xQ=jS_Q#(iTmBHh!?lQl71^X z-|t1=S;nhmbI|7kVM^5&=G`2#9|Xzg=C9I)QGvN;!|ZC`V8AQDKD(f@t;$*GUTrV}M@csFMDOcrN~MV= zqPT)JUof(!7iTs>BxXpWzbVaZ>?*J$ui2 zQEH;%Xr#@i*Yb9Jlqvt|!^QO~d!ocwTU^x`6Km(r^!J6f2nI<3_D)tUX?GlUIO0_#^_Qi!3c$vJ4x>HL4Oo zdL7?quf#*qHz7$zqO=STN#P~Cy)}Oghr0z~Z){je)qT&^tFN`)b-tC*6@hTC233ObFn1^&8h-C_ z!=+h&uTNj~&WW|n^S18L0&T~AK0@!Ik16^`^^{M3b^C2;fowPh0@VD|7exaim9{>J zUtB1S`4@SfI`TDHNFwQSMGZ5Ad@7F;rr(BKj>pi?EN0ytbz~A`Wumw|hF>hb$-1-@ zlZiT%mqdW3n(8PdL((Sx*Qh%2DXhcUEP*GY-EAleR7^(nK1D&Agfs)eZ`~6AjbNpA z`PaSu(o9|sj(^9?<&PKZX3DiYu6?m~tejR==9yR=V#3icF7~1;>V>;?qJ@>3=(U>a z8-K88qI<+|b)Q!EpKo>lsw%I~_4fBIOs^F2%M~15vi6n5u6x18lxy(pt(d!&@2>3l z?ym-$TQ;k4n;4mQO;@S%Tlv!8|7*d9!+TtD=YfgA;k;rrRXRBTY;p0mC7hDQ#8XOF z-jDeK(hO2Jm+<(WjcflyZGGG-6L|ZzlkAzYC@;9l`>nev=exdK@f{h7Q zRP}EG+{%xJzn5g-6yoJ;aM~&pMR8x46OFUl4WticTAoTW_FenlbdO3EKY9ogm_H#Q zngO{Qwzyo*VAH2^wCHVq5(YoAKoQ}>YNhbUe}xQa)W3!5 z<1RK|{k|0#)>^1*N~W(b=dBX8=Al9Ri{Y;vrKyz>PKBve09tkBs{=$_d0eeGUwD)1 z(kju6+Z3Oo@H7Rkk#jd{lP8-hm;UbKV6yUuKO7GI|SVCHr90th=rS|2oP$O7%&MEm^usrkv6ayRH0rD>_3#_BEBSM) zsF3oPO&{YQZc0s~0LXLtbljwOLl+6mb0|1?)I(oc@SXWJ4!3DlTnU} z?sNu5#|CVJVLvv$KK&Q#ssETC7#kYhIQD;exgLL@LbGl>oNLg+g1!h$D9!fU#-H@% z&sJ*p|5LB2qyf6U;Z)>bURs)8RSo%NmZGr8ThpdQw0R&XD3OMSe4^m%MtQyozGsAG z^H=fjEKUsa;tgs zrp|Z!mD`0GpL^_3u7+*JxjLVyrm93*d>K{Ib%XtA3kp zf(jtSsDQBYn2FkOno0(wY_=V2=0SO+A@3&JTFnVVF zUKo3?0H0g%~c;D&!VavMv(keo0~b?jM8^^KTwylMsA0Uco$j!^%Y~&Aa|4NYk6RAdSwZcJZ;zjFYh&bES|>2b?J10 zW&F(b@JEZ-fB|6MgyoP(zLe>HJ%jU%vP)UOcDM>7*_$Q%= zRq)(e9vPi|>;d68&eIOLv7F!Y?>=lk%Bz5mb+|hFj-r=2WbkkPrw%$OS~M}&m>L)Z z@E|rEp|ioE%Ko4D3tmIzccQDo)NUP)vHnpxP}I*qcPIKaQ(scFgf!5!>SpyKf4A!KxSdS@=fD^ zFR){y_uy*@2m!k{v&7;&25;LIuPqVvsNFG8f-}6yI#$wdb$)zcmEh)cTEu!k)^1G%r>1-AxO8da( z9zW8FuJY7pmZtMsd=X3dVfNeqGGNQztF2DvQr;Jn4;u0_)GK`xq#o9s4=^>cqBeX= z_${&~B1JE(E*QLM)Qc}_fms-zy<|X|Fg}v#zd(-0^!`b27v_bEz&rE#63fG|{Z|)@ zGe)NkxvxC5I0cPt^Bd}o{h9@Eea>Tg3CI>PEv(MLhAe+Y6pg|5w4m-l~r6lkncFRG4SgA=pC~My?~}h5A+Yg;PsD;4m^jZ z9J*P3hKut)*HZrYiJ_%0bopp0Rz*wg|K}fh-6bC_JtuVf2*Us800ZyIAIsm=zH&yi zDO%j?#Rv06WB7V>O{r zUw})%4UeB==qhi0aVprf@vnaS2UFRx{^5K#7)u4#WJ;}k_*VxHPnp`BjyLn+C}h(KD;XjN)=OQ4etNkkcm|&okCTR|{Y`$$;*| zuUnO5Y>sYxbh46Pp0zyU9Og%mHjae9O@{h5Stchra|R_ZnrsU)Fg1jL*gt(6_uu=@ z#*OdVyER$)3;&`yn98Uj9|3I$ELJOD|L9i(9mCy)dHhCJ(cI_HFCi5PfnO-X60gAA z9wTaQiJHsg2FYJVFmuBxZ2ao)mYeE#KLa$2Zuj?WeE7euHB^4P{#r1Ts}6moDB+zw zDNb+v%vauRsr=Nxn)0GBR$5{yLe?BpBqGT9Tt#y)T(X)MH|>aqAo40EB{MSi!1k;? z&E~7M~!WjpW6A$UZV6!h(hA_yiq_f;AGL~s=2wjD{j%B!7Iim+vf3c zLoE53qO2A~x{An8shFul@|1Stb?zICOwam13{d$a9jH#H_I`cxP2_U}NYqSz8hTB| z&cMd8FMoEl@}y-0FWl=8<1baLd2nlK7p-Z*Tec8@0>n-{1K;e0ko=o?6o3RW{AlKlwYPOsEr+yLUR+bi+imxa@!?sdDttQUE z1qs_b&uzpKszeU2lw_M~T%lIBcVYHTH*z0+`Q2BA9ev)1qNi`-w_+z!54AM5*-O(b zG;6TH+MHqepRlQmI=ld6buJrU|2O|rLuqlTid(?X`GFB_Qoh^g_ux1l!)8oQ&Vmxf z!WACwv3+CRtOB3gY0#PpcWlm6czEd8cOkFhJHGs2i=~O1aS>*6kq~lY+oYHjLK1s# z@*cA>h}Qcna8yJYI;G4KEFh*4FsgB7nwTj>MFv!q3pQYhP1QiG0|v#OE*a#&b+8!d zKl9yFeNs^8OD9gb8CBP~FyDLO;iFH=l%iSqBe% z)h;daYF95a>qS1(sRj6YS<&9brNw7&tuAkTxcB(p68bs_%l#XhFW=|g``0($z0bS% zFZ1p*w{D2{`9@8k2-nkoOr`VmC0oAd`^nP}7R6OJg#Y4KdD9s@OqT}|_Q|K6h)c6` z4{=yx>o{O{99FMRxERz=bPoEVIoKvwQ3 z-2V8>Voco17R4=bh8_cZC(oV8cf%viuI|}re{{Hh&c0DSGj_x{KO7KRpD#>V-xmuH zoPEQ|c307e0+3h17VGZdyr4uD4Z`BWuyGf7EbfHODNgrP0>i_PI7srv-v^MaPNE?&M(*W@Qo`PpX7ns;cEa(w5|;)hP&;dhH~!$wUump-srX~T z_{Q&k`-8;Bul>uPi-+^wI7V!gzxOBFHm?4YztpOX%f?I(bbOMl{L$xsla$%#1k>`otRIXuEv z$m2mw$Sf{}XgLduMN=urXis+z;H6=a?h5h`3{uKahZL-1v?^edjw+ z8Gj*vnh#z_y^-&}e6Hul&2!iD!{a04drX`t#MKaooEln zE5H2n#{-Edur}B~Fid?x4-(2 z{`nihU;oCZ`##Fw4@M$4x5R%ic=N+!4gX(+0l3fzoOOr}xQlC4Q#2QSlE`M2VYW3E zO%u`{E5{U?G9Pi-jt4BJ;5PmiBkc+p=~6(4<xDHkGh*@Ly7~`t%5g5Aj4f<^@P-u1?x z31R`Q37LWE<~B>VD`xT0CTc=uIdiCTFuP zFWU#zVa}#x4Xje*KDmQ_d>bFS&!7FrRj1KJxn zBwqKZ+_j_lg{HA`yJ+Pjf@*PYSXy1;pI+0y$)mnk1j|%6PhDrG3dY)QG<{1?d*wS@ zP6QGiAOCmvFIS!L?{8{*?q8A$6@DA?y72>3yP7wC=qLaCj$O#S7eT@%kU)f-xLoD7 zrckWI>l{A3arD-St<8`VusJ5d)%+O3lm8Tx+Og!H_i{;7@;jPZ`QV)lIi4K4@4y)X zLPdUfus(@-3oCO9%Yep#=vHM*rO(aIxJ_d`-{Fs*YMCT2q4R}wVEz#2iB1)xjYMLs zfoAvND^72`DOj1&7@9jH_s;x9CJAAcU@XG8AejYw2I7lJiHrOwOm~O`$vRnl*6zo9 z0}~@dMy^B~2gWC!F=6^cH-fq77ElU+2kS>yBpp?!CR*q7t)lKGH;Vy8ZTBaA5MHW( zR*j+lOzlg?f3m=M z##H|15C3eirSi?UYQ5%3aa42<88zL5PpBd7Ce2DG%wAn8pe})FK=V+Q0*x)$gq{(m z?XL!V=qm-#0m|j2Qn*u(hWb|;ekRr|R(DegOA<1@WVYG%d-sF&m7o8uEU~GGPa6aO z;UDGlJ`0a3TLR?FO#a5B;sSco$rTwb@R7MVQ}lL})M?=bkn#Iv_|ND))gR2s3^r7( z5I}*03`9KNq>EnJ_ke)QzxhxJb@Ml*&3PLQsEvlzV%evw&16Ci^YxYD#$m7ctYn*1Wa?}e7lI)A$N(OSzymMKCItSpTy|G5wW># zl>h0EHE!QL(1O(G4~SOmM}Mbl#NmNM|7kq%f=DoWV4%NmY;bURbhz>}ppvG=|18|& z#Ohe`J6gk+xXGhUH$(#=<8q4`sk}uDg#(-wCfz?)yIx&JqyQLG;M;e zHg+_eX)M8$vfIv*=it@nvMsdGn9;%v9&#qtj*bm;eqd3ZK8$sx0g#4<81oGrxK1L7 z7$n99zR>BV*{KyjRbxSqEbjIKZHR{@Ug}GF)WY^%cd^8 zs&%x!E>U~i!KZpYg+IeX$NFEHEXi%i))0o>t@YHr!+Yq`*5ok+j$Bxm7vSciAtY?- zNp0j{F@ZeZ3B*f*Z)|WPS04mglzz?GuBe zM-20`1%Je#Fq1-@>xq*Ga9SFMgkZoyQK$zjz%xE2h5}i=*~;K6U-9ZnCJ_{>C;&!@aw2&!geG!*zC5V(k!W=xD8{x`Q0i!a$k=5rI zqw|x7)~i;u=cqvb;p1iWf()YiW%r$`aR;TIs$^lHmiim&E0BhO;0q!ZvmA(cd!exL z;YW?RlDRp$Dai-6VAeJ^%Rv!6IruI0D$J>U4&(Ub3xMUr7G$Yef`W86mmap$4` z*Rbxye*xBwl6hJV*zayh>&NE?yo&u1vR+n!~AJ{_pz%z97H+>PUx^Jq+lCVD5v2M0%cU&(hb6rM;?RyV<-0cqzVj;$#w{|9w~Kpl<13(D()o11Z>*~>+5uCep9XVXc78Nh*PlF* zN>j5Od487T!y{w;%<=*i)X>Na)m`Bbt!%E|H}o+~C!^1IGBGkRI!q^5&|f&+sv#jW z$2wkoqj2n2{l=TWw~+iO^oL%gBxb>sh;rJMch3PB7}QuY(wvf)Om)X>PxGh1H&{TP za*x*d`Hk29s@-E4^Tip~1}#K?b({me!~J8u1N}pzW4#mk?ivUq3+HwNU-6I&SjrO`K?NE)_uoS}Wd>TPE%)vr9ef?IhOYsi|4MfMObK+LOPy zv3zK#zC;L*9S=n+Ez!Hb3=9cU=c2&TW-jDc#a7Dke$B0u4e|8sJD~q%1rk^9vjI9Q zm;`z^wnZkVG zoyVNc3va?uKue9U70gyS>4K?m^CG@@%j0M!z>_d8>8w)(( zb;wuokwjIvV)-4QgvWzLyQ~kd#n~&^7U*^5XQr`wfWxIY*`!5d8~3ooUFeotE;rA|~+1S5gOCUk-+(N;8Q#CHLm`UR?sf){sRF z|D4uFun(>^$X-AEjwOa6*`rD4fUw{QUYkGJ^Q&k>W|!Gz?y9Zr`{fPMJIHDYE@Q6#9LFh2@VztH(+M@}+)u@768%CW!m zxnOhD{A~tDDuuuLV_y9UzU_H@XleEi?Q!=a2A>0d??SFs)1uCe$l^o!v+7@fH!ZRDLR=+ER~L_ z1cJAh=EY}?i8q}G|1W~k^<)ORf!tFyClvHZW-_=n4nE4ODaNr_-1x=Of7;yUL}YQU z4(@y))K@mjy-oEcxoUIM_VofxBxq*_-$U7oxM`7Ik304}9oCxheE8RaKk;_P>lCYd zb#9yU70d5CqqDp)!tU#)BLj%5AyO;F{lM((3^CNU9<-G(15YaZpuab8G&V%-(^}~uWrx9 zyuh6;R}VGt8-p(6a&L2Ny67> z24W1*Oj#V%)xJP{ zia?^0pJhqy=g8_o{su|Tu1(g9Z))|pLz9kjmnw9-$Fo6indn{JUu(<< zy+J7tFrxZD4+LU(Ih%#ny?>r432QX*RGEZ8xRLOShmE!6IuhEELIJ7By?s9rohc|BLLbp* zCrCdb{@Oh*?eL;;f-E7OX8?+SPZ2#nL)(=e4Iy+Lt>Y=5}z`DaMS+QtjL-seUxJNu_LJ(fETz!9C@NYo)FO8GbCZ*EJ)*h>LD;KL-P0V`bg1{mu;`Gvd*$%MzS4q9p@b$;6`MW|zs z8-eSy&PxJ(5K`L&*GajZih$J&O36C%Beb+3%}p$ zIesG;63KMmpd6bYVJ@&yzS-AA%fN-vnLXsQU(dZXvj^O}w*2ZgwpN9Z!?<;xYU0p9PYVNRR6V@R$k( zPYBmkiXofOa411CRWb@BD2AP?$tl5)Rlu$%KPr{4$!w6V$z@CRsccgnX8&4p2i0aM zjGf8VX8E1UrJAzTx314LQht|wg^h_!Lt}=lL!=4HklTPn`5CHYCzF|6wwAOA-?{x0 zpBjF2lmvrqWC_CTQT{|(niC1sWwY(45T`SQTlYy(+&WXBR}(c?#6d^0@V-KjBZs!z_5 zijgQygkFK3S}&80Z*6_SA4InoB9Pnf=w>Mpp2R!Vf2KTcNPWDf5sucn+(PPOCXm3Z z2k}Ahee z{XiL)e2|n`q=T_WZLa#4|BHfkD8W#5_`fearG#3qV14V&G^xxM5H72|w!T0K=^sj% zSb^s#6%pK({zc!MCFvlvMrj+Wx84rKh;&&*kEvCmO(7VPqon)z-Ah4Fv`-Iic_BD= zjb4j!JU~sXDqYj#BW!|<7OwG)Kp5K(8N^EV?idJE{p(HAuj*9moy$hrbQOW9ns=6a z03Rg9{u(8(svz+ui#;!MifaLntvv;S#WSJow&vZ`_%QWIb%1zktdWI;63%?Ht8){4 z${}OEY$&99d((Bd;zi|_xw-0-=OHbt82@>!LB}l}J zn5atf5=sfw^~$~=iS}J09xd~N7psOtyKn3dKsu+EX5?02bD|L${#4{}6DT1%GIDCu zcv>6tiqp^^+dztHDGJm*anw(%QtnKUw5c%bufXZ2RFED#k1?$YDfpeh@G=DZN&ofi zk{b%^Q9h#DM4UDE1@bG3pe0hI+AJT4XFW1llh)bBb<~R?@GD5(Uz>;IFkUMPX{|n- zU3QJg2fx1Hk}TTzFITez>DQH0mK{iwJY%_m5<5w(9E+#IRLZ72OFEpc?IW8jyXR`# zjJp(mdf_;UdJH?#kB8HdKZdi1{UW?J#MiaC8ov(DNUafEEmwa3!L#5Me3Y@5y1A=G z9w1VVKaK5LG7vWBYB!J4P_-bQ+lNa*3P8^J5M18vx%9I(#hPa*vqt)kpNdEy?%RHH zXEocOH9qR+^;5$|usR&M`{0E@Ncvy*V{52Ho}pw?f0StmI-0FZ)^e3eLRGW547q}{ zQ0yG3`AE=LLyGf62I5W1A*C8Ecagn>HKmjk`UKrYU{IP7*3Nbu!jHA zbvbekwU8nZx}9zy;U8H5GitCAc;k3`>Gyof{Z$g4*Zdz!HvI9d5`;&hbuGyjt#Yax zwi$o1hs>v)dIN#ic@kIB;rA(Uuk>>A+k43GvS%)QZ|QPazJhEbj~2OV395@ZuE^_) zbpwkU*Kc?w-F}nH{Vsv_jNTnHkHRHg_Tf@U7jMzxnCHp$uE_1%lw=&nO;0b9fpJ7F z)Ed+>iU|Gj4EMLfRp4f(%TAo@a41{g^0c|NEvPZ>d1ItJ*WI(u%}$pc<_xE|$cv0~ zn(jTqwT@5d=00=6v-ex^sAKTDi^H9os@J{G%p>iQM473o$#Bpc!l7=SOUsZ=M!Io^ zSJIM%Ja3#)Yc?Oi01a}zNMCj9yu%lCU7lb%e8a9O=Q3XY>e0YwcJZWPR*rb~i}&S6 zNVnF^%8~D?adTVZVcHz|-c)zomABxs@=dmoT$7;{X>mqnITNS*$qhEaTH6)`&Czd} zrw82J)NqG+`)Sjk1O*c(bJ5x+Wu>M@J9-Scfog-{{#bZjIiE#cLH-61dfG=b=MFLnAMM0nP0jaevi>; zJzsM!sk+?n1@Vw}Qz`BB~ZGR}{5 zqh_T9f37o7AG(h)6YU9iQM||=>K1X>z9u+AaOJydFd%o`f*nl#?DIl0eY*BXl@)xD zv1kWM>|Md2r;DrX?G%+SQb>y4uG8`a&IDj%qS>K%T{6?8wDytXq;7}TizF}a-@09Q zqSqVl0@8uhS*vWA>Jm8AHor>AGZK9Vyl}j)t2La?g=1m$m<(u^^?Eb>Zu3A%opqEO zQpvENEA-jBCbB7M3w z9ZBdGp2fVSh1eI0l84rnOw=y#Dv`u|TJe$O(-(}KgsxgtfNOsNO_2KL=`2rcV*EKn z=|;KuyB4qeGDr0Q_JnCdHa!joWn+t*2lKuPT^bBugFZ~JIw0RuvZB=LyN$BGehb7% zvf3L)W0sD)amaHt6!pW<{O5y|P@pgEet$4JL*!{e6>Wti%jXjw$`rRMeL=dcj`5U+ zXBAD$rG#Z|*OM-8S`n^ttChwpTjjeUZJL$cT2ifraze|FJ`E;smi*f0SK}6^#SZY8 zM~X7VoUlArrFyj;p>%Qc+cyN6+f`tvd^#9hQqdoG#?U-IZDkeTk7%_Y>icuSFb+vG zEV&NGEh@?)X8AL-(&-(V(XB`j6^=jogYnJDr*9^$SfX%mQ#?RCu&!b;6`sY>dM<{- z294~rI|iymK*r(m`aO+_NRq;`Kazb{&tgQ!NdVp@9)G-Ti`~Yl|@j8Z=HoYJnF6+Pw1X z8frQl3@LopbvPM}IYXnqAf#|74pXbN<@T!w77^CYk!!0&(rjnmFam|MX7Q+VAjtRP zVlYsy>alT?2#%UJyf*zu`luxn!bs3$zdQePL=&QAE{c>JA3y zC_3bx@1^cHs$YIENfN{caj$@lV6fM9U|+Re5ibN0qDzfBZUsQV5_-dM#T#0bnUMh_ zWJV3j$Acks{k)-fUk(S6(|yd~6(eN^4( zW7~iXoGlzScr}PlT5}Q--GvANMyVn?t71wewE3sFFH03yxl#dRnnQ_-Ja{0uU*&7T z=n7hFk~=t*dXz-D3PpFFUl%@l$xGrBqPSrqSi!DhRZdY9cY0F7nEiYu7$e|OvB<2a zPRt>}qK!$TA0eszx(i7x|3B2dd6eAQRp+UQU+nvmdrHd4lu~PEDi=wq)V^;eRjEp< zeNjcGQpzmlBIQyl$yF7OfrevjV;ciOvp8(J54Hi*;69ic2BzAmm}v&aOE;$J!_dd( z52nYQ9`H2G(9?aI`F!vDMP#ZB7|-!PX^ry;qLu6 zZ55XwFNwrxa&vFTrcfn_Db+3d={14te3W)J8NDAs*_IW}1{M>v(CZyffmdR1HfC!y zhqS^L%iu67Mz(5H_J?x}wi?BC1y}`WQ52H!Vxd_Di)93E!D=>1fDi6ypT4DFv1U*) zrajvLpE#7&AhS|_qkA>+=d?Gg1BP;(CA#lG#e64XuWS>b60QayOo+FWf?4e4XuF;y zi+2N(e{)xLm4Dsp(PV@C&K3`d9%S2+c>`=Ut;=M#5VK;I)zkPKKx5vljwON#%RJ`q zLlMQx(V(Uxrfii5hegFVzL4w4#i@hL?rq@bE$hF!ZLQ{r?Gq}b0dNxv+q4C)ha&E* zJ9wzs=41NXgC;CFLU>$-|A36z0&%J(fjiPU-X__+6Yhj!FT&|r4#TMYq2A}G1EcT{Y07?!5OO67D@Qeb#61a z(Cm|i^ZU`|G1;dx#S|8UJ?V6zi;Ti8DhN<)!I0mQNnXmQ+EDRL_0Q~_NfopJ0fJN<+O{E-`IG9yn?P|QGCZY&;Z0;cVbsHR zIvJCdQp2(4i(x1P{$s=Uk&s8ax8^q~FN*i@KE6PQku3-=N+#*xeaH(bunr-_aJT~+ zNc4tV8GMfxKp|ddeRd(<%EG34#&%;rDWpZ07;C|cH;#Y^pScr>Tj66du!@zgc(@1- zClE%%4u_4;ZE#Z(5t=7mHDq12Lu^B2ZtaL*2BkCU4KIY_xNls5mYbX~I?{;=9Z5<< zEy7_-#Dvg`8(ZIOHrL@l;HAmIHYVX4t5)(BAK#;n%J~2OhFT@(=vlQ?u)#@ z4lz+d(`wfyorv@26`(HTz4d%36w#?mq>Y8|ATRRzwH&6LHDzGnZN{i?YQ7W>bI^q!x$B186 zniCom9qbDyaElOVyok@ir}C|lh%!US5^8I}% zIOxSJ#>YfwQS)=qP4O*}*Lb(&3@f+9K+5I4N=2K0D`;3ZFhi4QAi?KS zuoCu(f&{DGL`n%#+7lE*Ks{B#r|N+SaYs;D)3!<`@d)-5rzRfAUY6lY%O-O8nnw{P zlVo&9Y$xtH-?IZiFOm*f1ueAa;cF6tscGmbV9Gro^y^jF0B?&DQzuMW+titM@zH8D zA_bi08^|*ma$Cg7sGGIZ&cr;&P}RXf@ve3oxk<4>N@Q8E(ZdU-1aA*U=kE}~F3XO# z;@Mc}fhbQ?3Z#Vef=)W~+=y|nmsnTEMz8hPPAq=zV#SNNXmNihyqKGI^#9#HuHCYfL5vVxJ7<--K+Cd0tDX&9@Q`DZJkAuQKk% zT>MyLhpYxY4vV-Q^<+?`#T-}FxAVrWwi$^s#%I-r$Yk7;&SFYM*yvU#9L5T+Y7~d0;It$<2S9Ox zSJ!}^HMGsE+v-G^T3_nHwfKw;$gF;wLn6-_$kWsi>ED)Xi+s7Dj=ne=l6YG|=`zX@4~MX}(4Qdu4B~;wV4^A4-ADR)K*k_94r}iU zf}N3HJ-lzof%Zt5TqBHEf-y|sXl`Q3n&WUVp_mMJZpCe!%7tjqge)G42il75VoDdL!uU$J|}oOD&(d zIq<&$Q@jy+y9b?k4x|vmPQ}DzY^h^0lfZ1Rq~Z>z#W^~S$oCN?sUUs=O?-CnEG88h zne5|kYx!U#>}W}|$3v0Inhi{ypJ?vQw_Q{$U=?ni@xy5hI};+;?IB1LaJLPvPfuBl zjd7QdJcDNn-RA|DGy3zq0ClE!P`_W%pJ|C8w{klxx_Hj!aFI9=jBjptU^QnVA`*k4 zu&-CVhF2&M4#gVTan~Sc_6Q1Nxqw#Nz=JgJUa;Qq32^+$N21|mUKQ=oZPS%}9vz%w zyMzdNC98EW}R0WYA!rzw?}Y^R`a zM>m>#p(Rz!bz~A*TF4~x#T13g(*;!g7L^DpX3?-STN9W9sPi*f$mfeV%<$sBlxt7) zrzsqiYHRH*v?uay8@m#1>0+`alcMQNwulV@D*~m0i?mA5Z8^&Rby2JjKYbFt{$v}0 zcBw+4$S5;~{BaBksQf>EJh0Vi?VevJ_|Id*90!A`<0H`O9)>Pjz@Q-pH*T_zZ{RVt zeY_zQaYsHJPQD44EoRd(*0d+(x$z-^>{BA4rZE$S;tq$%bq$KVvKzsUFyF?@dt&Bl z5u#V3p3zcKsW)N4*h9fQJwZkBPp7!+dm(&A#69~Qaw!p%)S~9kPOcfGC=iGHHO`-m z5UjhR>$@S3Dr{~i;?tG|Rf5wH!i;PV`hC%yO{a-f5@R#gcn*p)jrX95ZAF|jRuEgxt^5Og4W+;i_oc*=eDspalo!Rgd<4{2;5{TrB_i% z)7O5QW1W zgoi0Pt>PifU(=jI+9a{9tSg2(_zbKn6>CnLTaRBr%+(Pmp9r2X=Z*;#hr^o6j%v}Y z`fmhbeosV7{n=2&3N5X9L+`{q3EBpmQ%DYU#b&GomUc#^T}XT}Q}<}K7rb@H!gz(o z?}ox#n-ai+X1q5P;&c+2BSuJRV*M?I^|yVb+4q^J(@f_Bu8<;S- zUX<2)Gnl+jf?&?7JNttPL8C-luTE-^b~%7n1ZaT8A&Nw_;Wji#pMqOJ6W zV)5xV;vyLR#>3AEwH`=}j`wFMD$S1*$=-c!`mr15< zTA={BBPLy#FkPowMA2VNm^d5E5~h_L35T4tYvd{)k$xhwb{~5kQJ9hnMQ?VjI}c)n zcENU_p;TUovIR8{mzSv@M?z66BgV%zHm&Pu+%IzJ2-}N9a&Z1p&5IT<`@j^w+;4h= zxyWiYqXek1M48>A$s<~g$e9;&TJmt`?pSYjPfYJ*D!a^K6cHjPFYEneZ#7ZSWsc&^ zSevz)ExHbE^{n8yO|(U7*>@QB)6qcwsK(IN)Bcp& z+Wc&gzdeINxz2m5+eJhAHy-2ckL=(+;q2#POm9~wOzSo%1+}H`!WxYl89Ofq!mpL5 z7IENf3GnPI|Er@YgC6#PH8OmcBQ@HpdT$ibTCN-al9(-iX>WF6*C1`Hdn>Ox(NY~6 z*i}RrTo9UQT){x(w&ijF2z-e#e+A)0q)dl*r0NNGwgqD|M4ysS85&{;gG<*Pc8C9J z@rO6NO{SJ#xNh5Ih$r6=dSpl+Y>juAZKKZ`As4YO)ku`BC@J2Zrx5;)B%v0B{RTDWEjH!#_@3{*Yy#zGDC~T@O!=BZSHGU2Mrx#VVkD7D;!xC zYx2gRREcOOcN#2(8FxYiC`)9r<$ugLf?)8VV!Vru)R@l8HVUA z!z7J~0CFdd2?=_ABv5z)V==7X?F@Hx`${)He!;`EN3ADYnXm?gQsf9Ta|ajJj6W}U z9z`|WIw9@c=F5ttkH>vEM-aI{A!xSjq`6;>OYA|O(N}u&Kq#@6IMxAUJ|yu$59drS z(mpxs1+dK<%%I;ZdDI=G1jj z4QGuKVQ|rQgDGUX(=jO4!Z5 zv1x`PB)Y?F${sCfxS{*eL^NSw;Qce&7&p!)8`mjk6$IHbZyeQ7c3luu31|#)epb{# z^83q3W#Y@iOFixI3qspgeKlxM+V`v$;w(mco4dM>TI8TsKWdgxaovL6$_450T=FS# zmJ~~cilq&*2zLp1J9cmFC5Dp*D#564dvLg&jI84x6dguLrXnx}sOE%k@-Bh45ZyPT9OnWtu+tiZJ$VqEBS8TNlkKmZhR{Z(f~$-G`$vD z3$3k*LO!QDzr^h)3q%OeS2EXvi2%bwA(6>pVZaVhzyd&_;DTNwj-c3*%(fj$Zcgk= zC)){%EhO@-xkN`g*Of|c?!e-J(Ex)%LRqS6q2qy)GXjJfMu64Wu*yo}40n*Z9MQ&^ zwv}ty^5UjV;h-3SQ2Ua|Tenf-D>~x_TNCFtUX#EFAt7JH`Un(|PmG2Ww2r6P_&F$2 z#VsS(`Gl;1vMlf$J`Oo<2w_JLi$FdT<5ly(R~xXL1ZVNYD8txpYf2z&WN6| z?OwN2)sE>Ah1W=e0DCcFvp-c?GF*I4f=9zlb`5Kr9BV?2gj{lEsEm!DaCA_{h#LoL zb%3`iob;RT)82aAsDh-#%`)@bkz_;hVk{I=DRc+G))*TIB~T2}Y}_vdV;nMHUN)D9 zv4gZ1fn-wp!eMhYs|YDGgxceNFM%q?4SX7m*FcYHQU+Uazw@fd&Z==a!YXvW$tX^j z33f+I(kBX)?ow}S|Hi0MPm>Mqz<|YX488;vbNa+q<^@26&%!aHw+T^4pS4l6n;#1w z8trSrw?qkg4RFo7_QLiM`jlDy1-X_s$Lx8N1w#pVEQHh~lcCmZH=YnvIOZW9)h+3) zMKw3@q1tVr70r3g78eJU8&Gx7<}GsOjuGT~h!|6LR9}cQx%zyMPTaIa+cQj9GQq6y zZ_tr1##XgJ^B{wBSbiw?>!LfjHW87R4CFOAZiumAeM`TA{@!-y%?5;@c6ZyLV-I{ ziLM=~$c|pIzN#Y1NVuI3PxR({@{vTl6o-NBWBL73FnSBoXsl4o1_)mbc%570qh0BI zA3Bynzb%qZ_G>gV~aULq(3j-y{&rAMA53=<^LMt@CA?8>OIvO%JeNjBs2 zFX7*IyH8{-ORu*>8U}~%0NyUOc1>gg?S$M|2tl@EcX?sNN9lG_Q?JS2XPZ!02fZYR zY-b-dy3ia!K9|MVA?=G!#nqgTXsDywcozCwO&V^g9io%m))fM+Y7FwxRj4{2SzS?5 zOwfdzSL8oq)&WP&Vnp%-;d8`^mber~t*6WDu z1WSrBm9lwgNZ`c{)?QjqsDZEIT` zmbFGn7HskH2`sOX%PtNTu8Y^%Kmebz6ba5+m;@+P!T8zS-C>>JA2^c_Meafa2mh{t!FK^U<$#>_Pur>50Pn4k zN6fh!&B;(msZ@Q|u`>ku)S#z@h$peESXE2t|BOkJA&+wD4y3mf7pwYRKK(q30-~dz zjt3QuB@2l-?>KiKNl>=qY{$NENO>q6R4_+dav@;G!%TH&D6H-PiAhMr$67)y@LzZ~ z9F8elnw_RLKyLMdocA>pKz??|T^%Cgz;j70Z1GQo!@k2)Ozc94aB{yDX{{A+nFimS)B9c$}t@#2e8xAk+Qu zb2K91L@0vY1mDSp)>QVrIu}s{ahc_ zP%_%My?GHP3uJE9&0HV>|LwnHs=qs=U?m#PcwtMV>EOF36O1<#MskY}Zw2Db1Z8ep z61+h|f%!GS^v1LTcwWi!i!g3j&!J{4bOv4F%QV^v_-}yDah69WKqJQ&2!sT$V9&I1 zcMCkl!C*r6mC1%BC*uOcBv>?|&@Us0zdZD?jB1XUVvUAvG3+NX3T7fkrLF|t+6Bzl z0!8?0FcfQKGIi7K2t}6hFW6ETEik;|Shp(|2Z(5K`x(|zruvc zSXjFN@TTWgFs3^Ql1a&8v$Qp|jHfMf%4E$!Et`?~s|pxgM{lkvR7Lg4e6;FEz%*iP z=!4ycRA&Cp=#h=k%%ipz`$WN(IxB2H)BH?$+#Mz4PA#u6SWW{hP#*BMZwMJyKMa=*2t%rF3qs_lLt)mCc6@M{hwX+h*GY zCUrX_BWU+i7BYjft)!K1nQ7{faRNh_qa^R4D4)z%;(6quA>EIaAY<)QVF_>HIHb_R zX~Z~Xxtir|EhJ_!Va_ZpWoaO)^Kxri!^MiUsD)r~k-e>@4}(M~^+9*D{Dfw$LG5?k&4=xyReyz&;?!hZotiTz*Ai#Bvy znB88IfxiSJh2I~q6HZ3?+;OWS6Qvk1;feE7L+BA4Hk!qJZfpn3xJe1C6yM-Mq} zTC&{<`Tx^09Td~4_7r(4dO#j zVZq{Pbr?gDPWXuU^!gbnDu&_E0v~(tHwc``F*__iQ+RgEoeMr}WGHUJ{#l{|SYquG zAr>Wcdk4MiUm}O~cbI!lBLTpfB*E^6DF54n+ErZzV4M z_{pGbehc8ewZN6pd6_ZATARP z&~O%<$Mxkh5BrnbZtut_@>gZ~4a@6#knWER1=PmE2YA@;p-0x^2D?jIU0T3kJoN zR|V#mI3r@ox^1NwWS_a@#inEzvxt4eaw<;2?=^c1QXP^of87fyDZCpjlD`$Pvze<| zaIK*gbi=Ob(IgoS^r&$p!vW)!b@F)cU}3|om0w-tFIujSog3n~Dg zm!x(i5MEK7vEzUzw^`t<;YI+B%_a)0$<`E7USJ1^r?K?U$gsbL(S<1X@QPkn%cLCR zo81w3njK`zT`6@HSUU zTxRe1T0|eyV>q_+IiUm&6#qq9VJ1eC7^IM~( zj%cf{c6MjOq21whq#&DEN4(INj$uDz|HV6Fu`YOjKZiyGiB^nru~cg~mW;)_qF62o zc_cHQ-pnPE@$PseeZWq8bZ62Xfnm9lijhdVBNmRvlj%sjjnK1}a5S((NRte=r_z}J zTBEVfa5&PfuD9(@bab3(L1pnt$7zG-zLk6Wq#JFH>zqj$`e(!2 z*(8b+p{QSF%I$5O5pwxxFAQ|6>+3d{CrILk!fKG*U`PL~Vct4>TwAKF0gk>FkYp6o zc|gHkGXGQPo^1NYFm}bbXMRWsBZ9P%WNoU)oVY+M)t$1UH=2J8$0y>`*;BIf_AEeD zc$r)g@S&r_y7%~=^f`6D?Yyok#}csz`f*^>p?=-2MkJ)~Xy0hL2wrSEmnA^kg655M zjhL)t(;|VI428Bf0k0XDMzKGvU7`ZSvDtY8gJ6%1*M5csfECHri?ZhGT)Yc0p~O)1eNd*A9Di=6`~r~Oa!MR4W(60NBkIP zLGgM;LSr?AK7m5njM2}9xSMPj=?G->JD+&G!2xaeY!%Mz#C}ThY?0{Es`S4xc#(J7{#jXT5+?pq-EW1 zttM@Ap(nzh#C}iaEXT5;=v4v;Okvg8gF}{QbnSL zHqX*QwKGe6DJZYD^CV`(gv_34z_dCTi_9tqC5&CLdkUMW2!Yl#Mu-rz6nGbdGB<0# zzr4{93R#S|3}p^0#>w`|9)b&y{}=4g&oM(P!!L}83}ndC)Yy&FAw#l0T0I21vT z)6|A4GHkRFYx#P4Zgq`Wl4~wT#DEZh?)2qoIK(kkF0{pZnZNd|23{ez7q{{#7Agtt zW_D8GOG~&sg1vRkj(0&2wMbBEW-?vz_NU?+@Uyb(-kbKnKklsR0_j1Pb&(~XV^h6} zlO3g2#>{EBQ0k>ftQ7$Yd9iaWsZm%C1yZ&uY({_*IPr7&@P0B7WgjRlo&zsolf0zW z>F2$}+T!i^$F!GwlGQCjm1WXjbER9`#Op@Xi!j#1bbS^Zy+*^UR&dw3q1GsPH820{HcKD-!qD&L*kN{oGG6K?ucK9_C7#a_&}aPU5xNad5QnPk!ggLF>1JgMyzOy7cjO$I!j z)K4eLIG8PPh@J@gLW@HBbE#}w79~7gDHhT3ap-3Xy-)l%;dV0Mc3>^YbaJqNI87$K zM6Ny6m)M+0zM>p`2?Y-%GsPCp-uD&rXy3V=$yA%hLis;zQCi74*Jh*PbBhZ zQ=OTP-c){1v4b4EQrH8T!Uq1oVZ%Eu|DrYcH_>-W{1b^(zVD_f@sZGmAH2d_zY`w5 zXGSuk+ps!30}X_m(MmiyZd=^aVZ5XTyKzWZRvk6DjFhB8YHpu4!#xHt$P&yQ3@~)V zVNJHk=J90Cj93`E^>!NjG>6L;m!zUfy;F`Sy+_R^3LC97T@ z)4tli`{}f!Xxd3HfdddXHN`1}RsFuj@B6YeT#QYvxCh=XjZHg^~Nnu5@ZWsgsh^x}{!#ZU84UcG`$h1=O zSwc4Q`v?Nb_Hk+?wTUbeN+Xc~2Zm#x*pU5SvY*L*-wWAt_E>gP=09itb>^2dAI`j% zIhWa-{;Txwr9YE?EB$nOFda_)aq3r7A5P7rPNg;{|5Nh!lb=pLNIseDO?)fy+lik{ zyp}ka$jASE{GIqu#qY(h#`naNvHvahF!qUe@?cmnrW)0I>mR%R(_Y^@`@i_fz;VCU zS!i`b;!>!V&&}=rwbCaaKNjl#;8Rr8&F#D1)AOU@@fTI^Y+o#{y07K=+THkX?S4+b zW~Y`1A1QnDguTG+=8uC`WynvgK36*P#+^B8RvB-gUK3&Ew`M4&gg2AI-E*?$)#qD2 zSF0UB^(DRlX0=E+Uk@5!PvwWxlx*&H4RAxoSd^~sB~ea z-u`r1bu61=a;E*qk3(O!LQ?E6_Yi0^`n{~xFPIhyH%H2A?jXrQVddq4M?rE zM;)2zHE8n*^=1CRPq|W0eraWjO;X8*_GhVT zLsnV#qe@6x{Pc3E(Vbsh3||#qQoZfZ&W%bn7ah3xU`l6y0B@rbqNz6;BE{+&7~$8} z)RJ5Es75zhtW~PxIBamZ!8fY?#=Iy;i>4u)S{avh;{ke8XcW{R@-b`n7G{uT zEyAlM_&VkAZd2Luf|XUifw=&G4AbQ^CQe--r3X}T90yVjuvzj)CH5Y{Rs%JbqEa6P zi>T#O8`-g|rF&Af72O$m;p=@WT;8}bH$4c*>XrCmuQk{=RR7eoKN0Mz-Tdk2vQt#U zp&RP|Xxaj8nJ$-5>)mf3@(i%7mRun-y#+Mx+~EW&Q&rU+b_>AMB2of(PC4`ZRiyFy zr*8j{*IF6-llOmoFaPZ;v3)5}rs@;wd8l*=fGw>@qh-qYHL?S<*L+8hs}VZI4qQT7 zq-qUVptZh91xdANVCHq|2w(yd)Kx2*>VJ@BT*%dijV4MbZbZe(neNR3E;XyZTnokssMPeqTiFYJ-T)4w5SG zJ}%a!a{a4c`{&-E>oQB1*RM35Tt8j^)^EHUC{~_ubd7R9{x_x5<`Mk6?z;kCq7y<* ze`wmixbn1lmNa8BS;|ihDm8~<2&fvSjlxi%30S_r*@Pre>H}#>*LFIqRl2x1vp`8O zRYsem)~T&|?Nfhrp;&KcjSKas^f#eeSNsRI*FW{?XIXj;W#004tqr22s=ln9A@#wv z`*S6QLb$%kg^l&NF)W7dHXtuhfot5O(JsO7-xW0g^^3}L@tz?%aNwg1)tf~;Y zYF-{FqV}cDSRm6@Ywml7><`1$SX&$aKsC z=++#?cL8>pq6s3=?x{E-;I>V1V-d7in6@}bw}P-}p(Sg{h7ciUdtd;fWSOeOT5a9s zM>f#S#V37k(Abj@XJFsJ-X{5^CJZb5x5H_ubmFEcT)CtYIXCMc8~R_0%o5Pe9>Yiegn{6Eu4 zR_&27cl%i{NG4-@;|9G^(?KsE#mdJ`#!`ItN zsX9S_#VB}5{BvT7LH_20p0pekA#%q3#`l-;NC`YSF+ zl0CZ+h&KzL`(N%NIM)JM?1g6nQ4Uy&LQvB{tzD5Z+kQR$p86j=4SM7qvV1G{1}+(@ zf#4altLLeVbw?pu{&g4bO}UN??0~AeKQ1Swn`2((v6RBXT@o%+v0_<*>B+21G2tGO z?;9JX^>AC3cz4&-LA!Y?9EC#rtE+DMy%>XN0E;Q1Q8#L9X@=K6L{Wig;a;`BXZqvi z@oKLmjC+Ayfjh)HT7cv1cPKkuA36Ay;C5H#dh5fVyZ(5YVoaRiU%q}t!jgjOtk$2e zKMn4$eQS1GTkYq6{qucD?MF(FQ$k~Lfhx3c{b>rdHttXa_J&_P5K6UHD{%l~Wo6;5 zZs!yV4| zF3!o(6 zG8jGVL<_ZJe6TQV22vhqAR-vOm(d35{eG*D}NhRJx$@aHW$}F<-p56KSmW_AmTI zcSYrl8(V|Tf+>iyrqcLK9YqmAtkE03s0Pk4KexBm?;_J#oCE|uklIi^P7;H}x@g%D z9aSO5VUvcb9Ki^Mhk@uk#M>ktWSnpN7#Cm}0ZXtV!=y>WQjZoFhDuj!A8WnXdd6^6 zkk`nFQ_!kXtF*cQ6<`Mnnb-v?B8LlWT_ZL&VR-GtXaCWDM{Ev%XJYehde_MC5EZ@l z?%!MgV&|zq`|a;Q+sf+{u}JbmUiICGBb7fAZ<5M?D5b1b{&8;SKb%bNTSq3HMi1da z7ZpCfMm=Qq$^FLqqS_Paq0NF$O4uVrup~1Am<*CQnx(ar0cp-@DlEo5SyM!0tuTC< zolw4E`{9u5sx)hP{o5)G#FW!pd^>5t3;J0 z$*C48o*KQt=j^_jd{_bCTasK2RAk3suW9W<!rIh}8M|q4S8=>j53Ex?~W2(}cCJC_71Ln;-fgMHA zHVX>66IL_95IWa~z^zHsnVDLQVD{;~+xh@%!>F|TFoB7amHJ3P$i$(E`sBsgrI#hM zzeeRhAWOUcc>Ay~YF|^?ns1y~NET#~>_vl$0fm)xgHg5+a(#+yuE3Qv! zRRcTy#Wnf>PgiPG)=V(H;Y2g1GT(GUOlcPQFDdJVc(-`ELtHRVfwgF!OO9`?2!=j6 z%+i|RJ5M42anag4SHIFez#WQVG_cB%9iQ>Ch){W9t;rmVH|rzk|I}-%JvN?9)ONT2 zqj=>qHSgUlT+b9rMme-|UyT0mLfG}@KYM4?xCOeICcJ)#10{?+H<=KN<+h=?I-5|) zIQ@p70j^&C^RERbYOj8?E%rSij;Fs1;uucKClpJ5bVK$7*>L81`fHSE`pHyV^4F@R z(rW>84*kdIuVK2Ux@R@`g(J1EerBLA-n2#40{?PzUw!t|AN01i?msxPcW88M-@frN zr!-bKeBp4dH@taE{h#d__QHWH^YLe?aJ?bfwL)i(`(=Oz&o4llGG3@_2WPPNw2Lh&{m!n8*W+I8`TJj8sef$b>p|CLgCY4-jeKFEHgekQ zs~vx_7*67G#(%zW{Tvp){BQk1aFgARH*eRz_=WjLb|FieCVUz<`$Iy@uAW2k&#h<9ap}vzn1^SY@ah2)V^3- zEV-ZcFMjC{f^8)?k4G(|LaU(n3mf8p?)}2AWtTVk~p> z?83p)+RNtP&|ZGZw+miXMrj0Y7!Woav#&ydsUz$UAHu&>R`|c|_J+ldSMQh3SsD&n zS}0S*S9xYjw=nlD!`Ws^&rUBqn4ZI}G*5c*2ja6PXiqP2B3hw?=tTFiu_8L0pzPhk zK=H*$+Y{DpKOh6@5g!4s- z>^f=OF^z@;Y>BF~b8v$d6I`_$;B*Y7_A5vCceR=r4fiGS5T%3>3uaMZ>%aN&n%7?c z{0BeawbhfK`{Q7${_21Ipx1uFhpUFVygF&%v6T|Y>5Liwn$}>6U}j7eofo$FJ{;q?GB#>yTyNxX ztzG_`qwN`uqJcB`0gwL82feO})`H_Nv(rSm0DjxKE5}5fTjel8yxAM^6!H?zHw1d($g80 z(O!@`#S}(HWs$Cb_3U2-+bgxTCi8u{g zsBdDG?xCJRBvbC#wi14P9CSu=U$3K~2IKb^41tD%-tG&{9xup(I|#?{1q8V|iAGa% zBcsD>oewz!GFj{q2g@9FL~!99X_vKXJTkGK2ECVBFF}L8O`&-YS@!L#Yg?%NZM2Y9 z)@d~#N>v}eojY;6XZMdD8NZblEj{f*9dTu)qg6iDr#{Kx~@!9r;|a2HO*q4h@QAkW{l&u6^Zq zCtB*=6Tk1}>tFuO-}iEr(lZvgX3)A;=3LX_{QbWLT3S+PN+RPo!*#X?XqEqo>~f_k zGw|x5hEx3oBi#MYPmbpuitP*8K3!XyJ}fQOErPTuPINSP;^ZndPM9QYoV!3!>Mu4s zaLFmcv-Od8lVs2laa>zA_8le*nlaNLq|fOvT4rY*l(K0FflN$awn%zjcj~g3ulzpp zq>=Q>R7OX9%k1byj#abti%eFh@tv{j<;J|t)9Dmp+tbr4rcgYJ6dH%&jm+4KoVFHN zWhg}@7BRRpbDwU=PAa<`ebq-U{i)Yd`L;*W7ayIqgES_+QrT*IJ05tY(H;iJgQc@i zocNRX|KsJ-2`ooDMu&&Tb_%`U)6hIfV0l!8NoNV~p1oCBC_SO04AXq+ZxCpm=Hj$I z3|KQxqHt@k(ecYcOvtMO9oVhjF#EnvcdBjQ{UrSpYaps5CM5aHG+DI`MlcrMUEL@9 z9(K&zNCyUrC5@1iQv;MDl5tk08_Y8|dVe2&|@tmv$MQ8Aa6p3`#<$sF*1 zM!nGZ$bMX8>i0^A)u6R^RK|7Of2n)z{T?gXTCrEQTFKOBa8zxJJ#DF8CaEzyMq`sS z*1i~0h0-ayF5CC=%oV9M%P90*RdN}{3;IdC@`Qi4)eG*!9e9J63CN`Zd$+`l{JYF( zFA=78d&E_swMlQcv8xkT5LUmIT*vBy+OR51t9GfW>pKehhSA6)$r0KKK=zVeWxBli zEO$E;BnY&4z09vIHlSCPo1@izsn-E4fO<*(x(&}-hib5BQ?mB#%>|?Hn+tX+gYc0%`5jz#Bfuu094@qpw zYOHFU`(*az3}5N$;{DYJrE8Z@4311(HXeU<8ZkiTcO;?{D~u6-afW0SP|c?Ndu3*} zHv5Oao9y*XX3i(kG}YtW!MtXEh5D2AIj^Ob>$x*v?z~HoV%#NAX_Kerk~m9<35)BS z@9>Hp7~fgC2G0|)PvM0?D3n!e348xQ=~Q{1KnC&n^VmvJ6P6d}?A#;{B+9(Na&I)6 z*BY*k>0X>5x5Yc+xb@zbuX`;?(|>hj6`RDri~hXV{q*|gPpdg(1;6L-y1V!EcFz14 zb5deZhoq2CqVp0$0iwEiDVgWpXx20b5L51Ir;Z9T2ZhhA!;Yyw0yD!91Mf~8OTY%P zs0o`|;NRVDsh@uS>%n|dKp2v3-fyh(of^Z0Chm;nOrRjf?_20q*Uk@~#4tar@R!@A z7aslwXX9sxJ(Z0^IE$5B>!l?)S61Z7TQh|+077ll3ezN{--pxTN57VFPP@Y*E42e!?H@4~j3NPg%t zweEc%`KJFbl(beJ?ceqf_x(()5zuqmKm;AJlYL|uD2^ZM^%*ZAb>?~(iB#Jnu@a(uIO`EJaS z>jT4s_aVuHirw_-z~nSiuLvY=3JJf9GC>j9%XdPGHPYnYfI6la|zXdFb?zh&$w4 z&ovNJu;oi6`_SB+ro~;xYx4Zk^3c%Gp|uvAn;31dJiFdI#J*g#N_}9W>`Ev+Z0dQW zVFAD#(~8?wcXIpAFknS--&)0EQ7)A=WXD(>>=X~i)W#+h5iq`Y6d3c>S?U){a9*0_ zgsr>`R~~+bZ4ICn@tdG8U!BI3p^b7DKi0!fFS6Jd%Tr_?0XRGS*))nsWQ~-hKMx1 ziyyjbep3C6ph_L{seA+I-?sW=>(-f}3UBcSH)3yV)#*w{?bY!tl_X`xwM4?K`@+Q?6MF`006?+XqtvfqWT-@oN=Ezc7W1~Hyld>QjQDO6P~SW z+C~l1OYcfj78U(4P)^PpoB94{HYEDJ zpON|gW8TpZ<3$fRV)~=W1~HBOgT3fq{kK2-U3k&giK4Yn{`%(!(>u-(6^`_FP^739 zf2DQLRSXwUNVqw62ylxy);nOiw)Gl9?_isVdppG)#q}ynx?U*aeYh2o^%nD0KeF>P zUS~wx7D4KGPi!;s8+5p?MOtgv%Rygb>xM0|fmlSGzt|jB;JhD%L5*osKvFG4kD=~h zs0!{uD&8q=`f7Qegf|ejJNNm387vH5ftYCD*MHz^JA>^RNZG#9#Z~5qc(A|T+xLfF z$3aO7%_vg0xlQ1v!-jZ*7%Mg-yQ0#FJ}PHbeCDv`PY`8mcxe4S!+`uysS%!XmB*#V;rgHa*#Ctc#_V1!nQyfB&%n?H-T*c^p*~;%P&Wxi?@6s-F?39*shB8A1A5}; zk28KEE~{3Eo)KM@U4_z8qSSo8IB5bJWagxt;>`d^RD%mTa|H#2V4#W}|)PTS0Gt|CyF;T3r2`qdQ+oeAXmY!jmXrSS#FA;n! zlX9gx!{l1<09pqMQ6DL}*koW4m_~%z++3e;6SeV53X%9A{BrT0;3YJ8Wu~}(i|im3 zZt1r^{fUD;-l6ZAGv9uv{;93+cVSV`K&w4HOul|!i@QNo* zpmPQ}dN)@QF+nDjpp1%mvHMTMFK!c1H-|ahsD+)UfZI&NDBTgSD95qJc(-01c-bp$ z1h*V{DUJJ^5UO^9;3B!dp4`6Zb;d8jjihs5t>v0@_6hxBJ=8ZtGdm6XQf<3#^hQCi5 zlL8GbfW&oB``EqJVt2_x^}#TOH7V|dQwggJt1_wAKlb4Jy^fNjqIyVdl2R#=+{J}I z8H+8~EC2Z~Io}3WYP*?DpD{cNcrBZmZ~4T`)@)VZerZ8;wqG%G@>n=+1w~=%3>3Oq zzG2Dg*y--D+Iw1eOh3s+fY@5M_4j{ii`Q|(CdEDZ$Yg#;sI_H63UhPvWeNNu0D;p} zfSExNSOqE6=3>x|E?4XfmlZa(Ww}A1oeIa+f99|1-lqE3f7=U$I{3iN%bHl@4)u{Q zf7omF;4bxFdHZJrtv&v!GTX@%h4O)=SW{%jTLZP~e?Q(*-}Yz!F<9WN1s(!L_HpXQ zCI=G8*T+f_oIn{*L^&WfHYfzaZ{?a0vGG5`4GFzze5yGu(-uLUJJvs8vasSA^l&1i zAj-%`*47cmBXL)#sBhO+SzSB}gXaIM>?YTMRt(~$4uno_Kemb-`*VbbFQV;UySG>? zAA9wHQGgSVP=Igu);$`e;hUZr%o;(d{YB+SYh}Z}4Y8~I*>LQq`R^zB?=Aj&zy1E( zjz)a6?JMu+e}T}3PjXr!`okeCK*QB{)0hU|i0782p?>LHOHXMX$_Zc!`@`p~>S6$o2gG~xF)uA{0?U_am2%~?8BFW2zf zRF1v}DREb%1i+f$-iuD_Xtd4n44FzfAYlzrh=v0Knm}>=5e0iTKypY9G5TL!_o7QT zDrP%#A8_yjI-yz=uBo#s<%h!SUq&tOn0s_Whta1%Jon|Z&1&Y>b0HMHDN&5{ZSM6^ zC3t$nz5BE~PwpNRD}fL(`#y|!REU~3TvGzC5@N$ zd?=WF1CfvrI;i#>_rQWgPcGS5fwUKIs*QdNgQ19IB(kSj3zq_%kZcZ&+_Ka#ceFdxiL8bG7bcz|;m#45W_uLXis%y>7=xuLFS zJGPQlM-Q0ImL24iCE7t^j6a+`0c93o{^W7UcH|S$dsL$$Y#rU#a)UT1Y>bjAd)+mu zfMJSE1Dlm=x|)o5sPpb(Yu=97XaKPTd!AKEB%Awv&)~#J4m=+S-Cl50Ck<5~TA_-P z!sB^S$)@sqw~mosgwT3_PR|8HiX-JQ0O@_URhjT$1+Lx86n{Y*WAOB(hC^Om~?gDWho52tEZKxvELO}F6j@SfT_O1cUvq6nnSva~#C ziPzn%$PJ=+ejBd_Ij-D5_GqBw=Qp>3oD7gwPdVM}ip)r$tNTqIEk}CXXVpM3AIm`tibcGY4!O)i)g^21O;l?t%@FGbo`rCz0>RIZbps_ASo-;q*dR9MZ? zBrhd%U8*BPo!Cr@nlb5*^#7hOEqvl}q=l^YeKpFc*@65V|~KY+he<E)xad zKBJD3JJ#zi$!&$9gSF$;N}zfqq8(01mfgT<8w^uBSsP1DRda#J{~x zU8H=0Ko{XL%0UuF!Xt)Ci9CM}$w1ucy3ETx+eOVu+1!{G^XKJRFM=ruiOxN5C4;bv zcl$%QQEFs}G{$Qk50Ndl36=qHVo_Yk9&HXpZYYC?-`Ike0EeY%8Qr#54ytB{p>IXq zAA-^4S`f+XeoUPwoJt>l+U7S>{~iY{8?Pj*=KTFxe@Y4vuZiJ;zoW6mkb9|hyi8b2xY zU!zRmg0PEAa&+J3sGRtSeZD0SZF1|B4kr&4$R+L4toXCON=81(75bbY0xH|NPpJ{= z*tj5>IQ)dwL(?Phzt3{xx%b+{!<#%?t!#aSW$VuC5PDav!M^DkXz*h_qr&`Ie;}plEI#bm74OZKB8WmI~CGEqkiS|v)36$=QCld54bZJG$2$s8#JN`U9f4{C{$ z$Y}Ha+sf!%CfG`{osFm!k)fGE)@HfVNd0PHXnUsBcyojF9ab(rgK~9Ky2JQ1#d8AD z?w0V5*TQyWSkT+_Si2=Lvo;o6sDmtqZ9R^IlochAwBE*=G-oqqK9t4Ly_E>2&4~ij zTSvl9P*{r4u0~S@OGs#aR5LpQQU73|-$Z9nY1CYEq>DC|DS(jrv!Z}lTPLl`ae(XC zxE}BDxwwA6pk#B_!j;#MEX1=lhr64_vK=c4Ob|TdQzBG3XD;J4zTOi^ed#y8^s8U~ z{x4U*^xu8ySKQ6Bfy9@8pz`GpeEIvo^v;*R&)uUG@;Bc3LgVUKh*C!IRjQg(mMsT= zO^}Qo=A0qTImz6LxlA^ZC*L`_+sK&JLdkYgswLpYML2L)Dco|f{ZzUokxjS4(G&S% zK2HL-R53wDw=5aiwiigGo=fpgGTly=bQnC1(NVUw=v*p?HpD;Y9s0HWm5x2$@ei@H zJ>Nh5a>J#9BGL52e+Qdq?W;Tg^t(90J-X(et~{aOybE}t@U^;9R0QOi0Y)a4*H`B# z3*l@-3TAhQ#{837vX;R)@LFM}aalH?K4STH8qQ8rs1XbP<(7 z2xTuZGmC2GJSs`DZX7aG<@6h6(eweAnCQ~tluoKI-=400Lq@^*I|-&`&-C<8{>-Fx@1bhTW8i-1`BQ}%M&xukbpikf8CIIfed!0sL8NON79DPn(MFT znq!bTijpfDT}y6lO9C#fbovX@IPmRTeK~nqzw>|o55bmJK%oF~dB*&_VR*M{<#)F1 z{hs-T=D!1-EH@$|_YDpQlOKA#`fkvty1fmm8~-k-?%j90e5%{`ox>{Y$GtxYwAViS z>!06pRIxuN6+lH0iG@3kYGF934b@o{V!6{pS10?>-Y%zyT!7EVd5Xm0(Q?% znQ;{Qg_ff_YqxF?^o4y)Hhp<|ouDNqAWU0#RJ}3K`hWSsuLd_B8)|GeURCNdBOhv1Ywo$CPUaq4*y}pMD`{ovV)k&CML+-g=QDXE7;zCZ3=LR;@zxS5zK|A zpP>V$B2d9Wm!wjOW{(~k}L_iw(kiQ(|e2I7P8TEo(ABXk;dBEZ+e^k44833 zy`FZNxb$E~n{`8G ze|TY?i@hYYKIrIgrw&1P^&x7S$PBN;rNr|!8qjqKD&HUUC?m# zU?AO$5%57Mr{0`HP1Ze^p;U21fj^C5y%u#kxCS%tMG!U#+;QW%3W8xjQ_t1DCC-y_3NYRFdz#|D08dY^rp*SZatYSObR`t?)j5B> zTN}9QF6ifudZ5JdN(st1Ufy{wL9j_WLeB){rT*^P_mdWwmUEb zt_W4^RTY#WU{oAz_@>n3S?8bD&*wv7Ro-nZUfR{(wP7C(a2gjaOsbvhkYY`WGH@4h z=eBY&5$@KqDhZfP+7^N>J69$oXtsj+&F+k0=ti__0`oa9>ZgR|g)ZD)!D#PQue*>) zw<$5c zW~x*3xMchpQDBP$fX=bJ{!jE(w2-yqN!{o5>J`k z&PKG&neFt+%h=3h?DoIRYpmq!nz#eW9ecpnM~!1sbX8&sum{FR4qv5D2L*|<%NC0XWvHjBf!f39Mxlg{?EC!& zPhWtikBO%r!0nY`LRfY&i0fC_IU@9PhOOfQH{BzucW}T3Ylgc#wl3TyBY>SV?w*19 z_J*?qtq09IsfJz&Chw3VoG*Qp)Xmqa6bEedbB}YFStEszjYRE*D81rRM(U*%Y{QC^ zVlnMS952hus3g{=Yv)KX{Q9Edt3G(yMboh5bhW<%gHgzgF5dDb2sIP|U)a+6xj7Y} z{8#x7p>ys%il-T=$%yi|x0|3~om1Lyk#K3n{JA$P>_SVh1rn-<38HGI2ncfxR}&mF zae{;%UeZBQd#w}*-yo#TZ=@%fwDj-|&!661491fhrZqb25#EPx7Ul)}E+DtDNP6Lv}QUy}svq7CFlJ#<~ZKshpY0wl_woee~F zKpR5|Hvr9*qy1jgkB4<1bjs=F&+2_}0A8$UHoJ`d>DO@=Ymz}0Y|lr#$I_ugSpORg z*}CcQIkH`hP)@lC0z6EOBE1I2N$PCt+_dZbrg1({#UJiT3LL9{;na~(+|fp&Nd3p1 zc*GXxth$^vHf0<=gOCuq)=KR`G6}eLw-_H+Gu@}$Jb341N4_r*A$sqYWKin^?~R=f zGeW4jo>MKRiZxCR4*5WJm&3P`yY!Q~@;b!bK&Fg%x;$oj_WT+jH#AIVA8~%^mBSXU zqQ2wD2uAlke*%Bk`3#uml*jE3evuXNxeL#OupIqg?de>am8 z%T1n0K5qUmHI*l_hCqA&&CP2OCVF^#t-QJQ`}X=uAA5uZ<~u7(0)~|w!T}~OIw4K23x48rlsG|#!y_;1MVh1Xzh(gA~Fj!W>!{R zNo#EsKO;m@5B*nnI2gGoEBpAE7rjMLa}$A2PJ{w$uJG+r;9ilw*4 z+Isq9_;{?`p7l2n^4#8puspeI!ZCb7=7#gqslzwYKEF344&!1)Jl8v~HTb*n?O9srduc;Ox>h(n;c`Gc>e=$SLH8!e*Vr@QiT6M zN)i5WRd@mi9>F-v&pnjA;XJ+N^Dad#sew6nPX)bw`$-5OrKmUP{ayLFhe?d^fLAu# z0et=HSJvdmz2L|g6ji@DgwKKe_wnnwbxFLv;249^-Rq{DKV0SKu%$52&F9GvK<_L3 zEC#&^4P3w5?Lhy1er=-%Zr;~yB6hf6cON4I0VxFD;BNki7pxp$cxrf~hWF0d!1oVx zvCE@Dic!7A?=vA8C^qnmU?=Fay}cL5E2S~d@w%Gdt0GA6s%D=TIK)(bMz^`cxzRxmFX!giS{)Eq2 z`MKs$_Q{^|@GbQ{p>*!mZI;Ac-%JLvoLK7+0rs)Jso40(RkPWBbWp2G76%(LZf|~C zV~3Qz{is&!fd=ue>O0*ETG|SO@Oc%0a$glKqHZ$^p@Z9Y!=E=bnDdx+2$b?)%m;#% z3FfA04wDW8h*-B-Ns>S+5cvKyJS`rDJoKV0GI)@m`V*`15hzm?jmQe|tZd}Df^0(AmU z@AF`oLXbM`zUme)JVVwoYOD!4bq6F9qM`ZSr{gip_UKKzuC}o+daG=xI-1gParbW7Auu*0-W@msQa@H+ zT1Rtc37kcw(<1O5JBdJh4QGg}gF==S!lVqw{GPTVf*zuh9W+~mcUGOe5R5v-1-NTW z540b!&`8cV61Z7Gnyi`w5;Xy+tV>sW5-Q62wmO^Do}ulSh}(&|#zcqN(GiTiRY`2@i6qhsF?!(W16r-- zqEZYEa#n<~+DjojUw7nlz0#dBiC$YGYbCA45~}%7cxkZ=_kOsVpvGtT?O?o_tI7Xx zC=rr>mn$aoU_0ShV4Fyom9RJTQcF970HzwtMB|}tLEhX`ZLy8hpAwk*y9P5_l1eot z(s6qP3&1k%h!xF*qHH4Nu5x^8zL5NXJA2pIxUwz3PgUofdcTWRe3M0qqD1i_QW7ar zFH(=ztJU37x4P9Wsc(yBs+J$BzhM$`{`0)>am z_H2iEgAjib=_!_?wMY(FMHiwlkl@~D44@3{0ekJ7=DZ?OQB!-l>m|yIenyGrvg|r4 z**S)Gh(OCIotLy|ZaJd9o!fw^#A!@QNi^A`-)(B@`+DLj1;Waf7LEUsicDfKOy%(b z)A={k@={Z_aB8-+I34*E=vAg}1ZO zt?7k|QpBXtdfSjV@mfP=jIL?qPwizs89#WGqNBLS!y5iA#VUmD-18o@Be2w7!PCu( ziv)9$Pp>V^c4#j)KNw{M8y@`9ONQ%I%Q2cV&>Sjy{w8^WZm!ScSq`ifSH}z{D&%|v zb-K3YZ}`?ukJrbK7FZE;v9mjiP9cVCBVP34WEC+nu_Hi#egfk@mP+dv**u(#nMY?p z1d+}iz(mirE`3WjYa{wMbG}d6LcbYhE8oORJXfV-yzGr~e(_E=P*NO}($KRxF z;e{q?R)m9pAwFH}E^|r%hjM9E%PyBIsmk?OLuzR@ z!!(a9ZKGVXB<$K7PbyD2{FOd4Mg+~1Y3?atkaCVM2LayRG$8Gj0oL7!ZGIhIC~z+L zQb!Rpj3N$l+U}f71J+tvrT-k?Y^KKP;r;A+h%FGjHl{sKfHaRd)bU+IT)p=e_6RjL z*g@RyAR-9|LdZ$Y^p)T@zwMT@Gx+7S0MRU2H+4xy<0hm9wjnh?XW=%CFRc_U(#8iim7@=HxGF^A%SGfm&DkWi z+kPT4gc=j;Z3}#b(nTP_X@Ds`2(ZIrdaws*WNzO1XdCB)WK;x`%gh*USL+a<*W6T0 zXXy(Pp^_7Lvw@1sp9VxtM{>GDi9J5H^ej0ixgs`qI<}Hh#s9F2XHdW~wyT9}j@Z;P z|Ig-YbR*74&2Cmp{iV)op2U=Laj;aaRPy=0LXHHK!eB=&SC}t$6`F%#uH25TyzWUo~6%j1~rNptCYRV`QOQ>=8B ze6~{Ozg#I_F7%gaGMs5AN;X@`U;|(c{DX~wX=3!Jrbukh{yls4Z)HmVx!3Eg0C9iM zFAre__>Y+hMLSpt4R@lB1wM7H=K{rFOW}|FjWbG7-mq zZRbCZaS-Hvqdw;@*EaSB0sd3<%Cej4$;d)$Pt&-{RXl5v=Naf;h--&Szn_d!%#j21 z?in*-N}#*rCtTk;H<^!4MTjlReeD@2y(?zo3;mxbw$*&T9W+j2 zNZb~rETGRYRFtUWz*N)SmkQ{33LE?7r4X>{ zr+gwV!hgdHe`1aTO^+X6@uSH73fLK0?cG#=@X60I-Ok8h&L=%ftO8ohPacMKsKBj5 ze9q$S4qrh)?i&H}t=WZmx^}p07PBIj`AFIrg0xid9yXBCc|+0(M;WYMEW|{zC&occ z^!ib+utdgc3@D5dtT2k}&Kk3DIubT-(S34bHH<_G(=U@QDa@H2%Iu^|6m|U1OQhK- z7mnb>zb`yefI-dZ5T7w6wyNEGTb=acnud%uUz4GW7GhAlhEv08bwx5(&iBDr-X^9!f#X|& zNzrny;Dldh*STs6%@IG@^5Qx`>?JONU@RWD-51)mg~*rkecF`t3ull@MLO1h!?8>O zhkn~s$Z&vfXBJwmW0O9qXx5e30r*NX@40;_KMGpJH=8=>R`T^%XkWXXzkObU|SQhL+u38kqf4YkRjil zvF#J34&@ZG;7-z`IJTat&I@~F^Ed~dY*Wt}pc`tpc&ayPPf4tK=w;{<9JSw!UNn-B zU0)k-CvR1%M1*bEj0U&&Z$Q{Iy>k|mn@;?}nTQSAB+mF*($!s{qT*^yn7Zu;7Q*Rp zu&Qi2Lo`k9hKWyc*&J$tW79V2Z%i67TI%#NJLTykYC%Nd?ZUNj=5V#HnFM*G(o@C< zyW?mfu3LlK{&FDc(qth|>o@}+L%C_ zXiD!eh4$I0wC=tN67M?l7ktwK98V(ek;)knfF}$c4p=z^9V@30qhwh#l116Bl&SC>4edKc6y0t z_+(^O8jYAIjw~yu9YMeL<6tni)Umf`*M9G6*lOHpq(HtA%C1)4FIIcnlp+GGo;FZwP5y!6G2SjTjyInq;;(a~^p92K@yiYTcU>(oA8Mz%<}0G#Eb}jAH=Y1@k_l za$I?McRpMK|CXMFVk+WQUlXyVvr;sB#&5`Glq)uRI;-jA{#*{D4CX4a>7)XZBnoLG zdN6?DG_y5eDRyDp?g+S?f^phmuzyTVrDfRe-E3!7Dlxc)%lqWOs zKJe7a#cE2lSWbUR&+W$w7Ij&7D1QBh3C3^OB!A^I=PP&2B|(ljo-f$D_O?ssJ-ntR zFnkm`=IbOG*NC%qoU{*RG*;QmlF?wMZ3#J!TB}405dFifzGukU_HLuF0eqTRwZu1P zqy}hFcJR$8kjaV&IoKa&gE89xZGoPo>6hEoeru9|KW8Vh7iBy`u^zyhCb5>bwE{mmD#O%_&T2WmcHv;;*N`? z@HjF{6BRpsR$924Hxh3b#~U_7;MI>i1lbSu`?;b%R-DQ!(!N755~a%`NwH7yXB-8R z6(dRwsq6hL619s;STu{-MMNhM(@x|sT|oyM7B})5bYh4y=y^-TWEfx$5kC{H^^vF- z3%Ousr^~*;^g@~P?nLSMwrS0weOM~OSTZ}`R_eRpC!SarkZsh!aQ$=v54Pk-UP)uw zHC`!d9tMDxK;s7gUb)hCE^zHVSvQu-#|4KcK72FV_+g)i-D0&bkw}_W+id9KV?nU= zI`n-i>bH&wobp&VqhVkMJK|fP9WiY>Zssr80d^vYgF!81ZT2Mz&(V|I(ZnMZA^fj) zfh8{;Cw}WeJn^Yt=?m+#Ad?ICH_c~|v{P=(rXUdR5>r16OuRE8GS@9mbe9;|Wc16dJrV z1MjLfI`~n>x$*ErD#~M#76S84^3T=%0*;*%Pdhij<@=@;Xa;XW@%br>U@;8K$#%ot zy11kld@iGn3qr8X6pmX=4dO1ipNtp=#ZJrCP1FX9|U~LfUebPJHTx3VL(~t-8RMe4$2Vlr~i6 zQl$&!xL6}kG+)XTQSM75o03h+b#hQU__dDWpDXtkOBMdfXR~d^Tw6Ir3-8Ql+XhOd zLg#Riywm*QN~u&S@^GP2{HnLohNHex%vaj@xzI-hUNMs?S8|;ddF1o8S{;`^`L3Nz zs6hFNX`<}18Ai>K;o4atiS<+=-%lU_d9A(0N-<;H937+Qb3k)L zz9e^G!J5DYJC@!f)YY}i(ir$p+cA=|eK1gb=rKQ&+?N=xBo2-vDDuc2Xt}vJm+({H zt|(1Kc6=ehe#JAnmvhuuUmCZEbr`o;yy=1$qar{yX#(b2eQDgS{dh8*yeD((v=F;3 z9$#S6Lc@74{t%|8v#r{|Oi9>`i66HzinGIo^NgeUMJ5dn{UAgZLh3yi^qxmLn4X#) z{)I^BgVdVM!80Bm!IS$!VtZI%Ro)jfPB)LpIq>c^%g*GRQ%Rnk{Nw<79ZRyaKc@U{ z+460HeXs?{+K%m4E~rYwPhd?%aNDsw-(@k-x#531)roM0vC15LxHL(SBh$Cj=2^Sw zk^3k-|KLaB_Ay5auEK(!`8P#dV7Eku>MJ|bGl6x-8w_Bj$M_7^mK>a%MlMJ(bnO7>%6&@%;;F%-iE;-#m+=-GL3aeV_lUeU0G@F zq!tDl2Hj;M_Na*mQv-_eOZVc(el86la<8N)AHDM_rQ`e zMSX0fbBFeiSXe}NVk~p2QImVO)X|p=dhexm$NrA;=?YZ=@I-X`>BU1a1?tz!$wVp$ zXYix)-rmmHFwax2orSb|y^ZPCW3 zR5?ve&D}n}r+fv4OgbokWhM)~`U4a%^bm{FH^kn+W};pTEd>Ta66PiQO4#&$OLs9p zr!X}WBsi-TZebL8yM!QZX&|;?-0-#3H1mu`@>>qCE!Mb*gqtS<0#QxYHv`T=>~E+} z5mjARc^q*#A!1wPKQqXjfMl29{=CMX+mi@fSqX#IQo5zBnyc$VkX|QG8E(7)!fMSM zi4^_aB4mw(%=1ZXW+olk8@p5i#^CX>WQ)7Au!Atx_fQsr_Et=+IS|bMJC$)kc&6nP zWx}z}RgN49@E~5cC47FhTl1iNB8iCBGSW%4=geDuQFt*1z9jp`bNvUzigE)n{AV$L zDSJg6Z?5SJTN9;Bdi=HXqBWXHVP5gWv;Be4w0R<()sw+ZJ&>BZtbc;qReM{%eVL$q z1$5GJO}{k>5~P*5<3V+aY3*Ko5zb}4PIAX|{>XTwd#S)dD!vnYiMoP#r2srE=|xxS zV$9~!y{&MMLgCDZ`n_{Sf7_4h??ktzSUovvkpa!P?|(=`j@x#^uDwGdo{~K zGi(=IeSmVgFdHdNjad5YRs%~%I@0u2!VUD*0aEKynI)gL=Z zFfeSW;!?CIN&x9#=4vnYP#s$_eIWx2ZO4Rzy$I-T(+1+6@h`pgp67k{0@QiK=L)GJ za7F}W5zAu*ahNJHjB9llUz{ch!fcqV5`PobvLX_(6A+_u)Wr<{y}0{^nT*V?bwsm& zjuru`>fu_u%rC?!D_4#l-)^`$w3LT07Wf)59Nl^lg5sZ3dSF~|JuLf!k%uzeOytxJ zg@noG8ZK;h>*((>5ExPBi4tTG0p?5~g}`QYSZ|)36{UW%DuTi4M0BHtU*CeLBHo2tFl>R`Q-`mU^{U6FpOQv6+(@c%N@4!x_H@m}$EH&#H zsI}*^Z1BuwslM3xE#llr`h-u}w+J6*Y@bc_*hBffr__*x<7}FhB{$ZSZrL;vUJ$C1 zK?Eb>n=EFXvne8phZwXUFsi-k0`D`mq%|SXY5$07R(##R_k_)2yHcT zbz3>&d0$g-@ZEQ8-pwMxo~+j0JmLJcro$g%bknmWQH}U5`uIR@7d8?a6}mhVmVfAZ zA?+F+3H15C8oNbnmLyOGGwdn^yb1o;)T~*eddjNOHeU4&od{F?`)C^c=Rm z+2inEK=HRz|47}5rKA(a;z2HqN#M~91A6a;fVFua_G*fT>?0OcnOeGt;|J~82I$hA z^@2!CY;+7eCt?Eitn>qyzSAmGqKD>;rjaLt5w`D&XgVR9Bw!~2g$luWZTu0v5i*Jr z5{fdt{EmX2X<9$gsjn`sY>I{;NJ?eB3|-7OZH$a~1=9P7H;eWjIhP zej*tK!EAdD#w_MY=O))bx*-m7&}KDmlDuM%jC0lGO(SzK`Z|g-Mc&6#g+*%V1Ov&S zWWcAql*&`u@p;Khyo&5#qLj-dK9E_-{>pQxMFsM+ws8NVEheBEAf6#ND=qr*9M$K|p3AIwQd4Cs0r5dm5 z7o__%%pb_G)0`~_1fiPt*P`AAQ^!=(+(r=csWZbi9}}<*^aZ#}iRE)(vztov8;JGh#h9Z#}3R`h^X(+>>*`96;4b?(Bk^9w5p_*&Yokr1xj9(+BDfhuCJ2o$mD9OX=y(Etpxu2fvp4c zO)nq*X>uZ}3~T6bR#7x6ae-5cJ4n^m(y#fOpUAe9%89{t5q0e7 zjS`^*_UhC&(T;o=Fj#)?X&p!QX~GL-j)nb>DW~3(Ii4GCJ8jXJUi+z2I=JG^lL>^F zj$r1t1fIdEYaDwkkC8qjeQTMJP~=YJMesq#`%6pCFf1f+IAUZZ=n(5?0aq6#8;|rdbwzA7el4SPOrllhw(}C(JT@7`;?AgCRvLxL2K?6?UID zY7un~d9;CydGoyuLY?85a?C`4Q>oi9UOG@f2F>x=Tc?SjtEshp8aAC=m$SiOFlYfT zW6a3)I7byR11?U{IO-{?hPGNnN6e~f3hG4@h5N*V`^Jev=`ID?w)R*SwXIU^tYfB1 zZN1+6Pw85X>^pa=+?k*vT#Rg!L^hkqjFvlxVnYZU>10nL$fS~8y?xn2dzv_4^t;Mb zHIq%I+DUYcjTK9YTDrZEsuYtsy`pf0dB6J2LUtf#kO<|88MOUOXS0KMHIb_IzcxF>_(%AO^EYSmG&L8r6NNK;p!j`_Wi9K;R>?yc4ll$o)^WrdI)B>ycxd zADeL{;29-+Zg9Gl7SVX`zqE7coGpw@W+Ww%93^N;SKxU&%;5(NXp(kjCMma;;}|32 zAfej(Mmw2F=$thX1a(>wZj$#~x)atS?9I^s_jN5ao!fi5G+os+<_@%{;&Pq8(Nf|8 z0+q%V1)olv94=MZlWtasas_Q-@F&tV2@|MK+)cBW4r7^LI(Ze5$Bh{NV zbJK|f@K_^24yU9zByNYSg>hK?euJuv?zq+AdlQ)0O_DpGXwxX3DAnR!XtF=SLO{O5 zMU8OvvgSIY)N`>;t}X9Fb9}-Uir0}ri}Q{POlZ7!dfHUl?0i=tj}E;qB?eoo-Feo~ zO!B}}6WHZUICbx!{7tv9{qbV5JFqWmt6Oj$O9V8hK`PKMa>!55YQnu)gQVocH9_p8 zn=IFx?Np&4TIJmjhJgc>@#$$r+;DmbMj%J4vQKo>cMd9s;GtOv#gQ*0J(`g?j6TcS zR2@{fH0`C=tw0905(i?9=J|oOM{@VPACPE?Q}0{G4=H3Giw~*lsX3LCS%}FgA3BJr zsj>KCU1Y{nE0}7fygX4bp%jq2mQdFmOe}1b6rQ zsqHElPIWj;*bBRA=5fypUJ{E3;Dp#8QY=T&|1A{Zr#IriM&TX4Iv?;w%RcO5sxY47 z*y367rO=5h7Xqy5Ty#h^6PbVi+yr2(HOFQ99^5ItVOzT3Cl$438nJQN%L#wwnT{Nz z=yZ}^$T7dzarS;J?x$SLu<4F<$vo)*@km_5w3CBYq`;VnFnm;Ze1W!2A#PhE+KpBD zkh6pvekl2P`w2narOtog6SGA+Gi>1vPqT2?K;-1)h~J+=v`xh&8`~t#X5i-{a2tOX z(_iadn!o{5S;Y`|6%vtxC>`0f-7#ive9@Q|eV)Cw2a$rSXRE$rPPSD9Yr0avn)VH% zSD5@x81rn9SPPw*)6Vs|av~X(MH7ATveP1hM>1$K0pn17uc)KPE<;c{5x9!gwl5c8 z|4OvB{r}oj#C^Cj3E*gH@WPr`cHs!#5$+V1dPP#0(n_=mV$x-eYzZtAMm;v2i|$8e zc8vnn*mU&kAu|`gZvsKTg}GRk*7vj(8DfvK*7UR+-sYr(PqJ4QAR0 z{q|Apycl-H7&Yi~)2-zv!jMxTdCUy0LgiN~IhI?gpSTG>!sJ7G(+RLG}NNp(`# zW?a%c*W(#0{NhT?{Bk?4^k6_~{wR7w^G*1OAxhhh>l=aEl8Nm#7VPAN;utn0d`5s! zG`>oyAtM(p0N>pm$}{~{;6gOHVIvP zU>OlaXrF26#yX)g?4FBn6;Trqf*D-%(X!V~_}5*pnbSg4yvODw&;>#8P+emq8_01y zi^%YX3u4&eeWIinR#3il$Qd)n4h(y9*uouW3DqIqB;s5`-q%DO3YW|{(F5mlOihSE z`TPwmebSPJ)q_E>N>-DoL35e#lTiUi_7xl3@nj|Zps(yq>xOa-%1)tI>+SZ$loq$W zmLyuVb2Pl+<#omWEi3C%L-hy7&uxo7v1983=^L)8wBurr;M?oqu;a!jw4~|M>skHtanD|3B<8(-m=GK2`9T+&iN1JXJuuy2IYp5+(-e-_ zaY6Lv(j!Dw#ZMY-HLx=RecRFwj0B?ch$)P1ee=gZjrDCc{>OhD_cMnOrsRrgc5R*N z`Hfij)_*$nCp3ioXYcIH3SIW&M0hBL%qW@XuE7Gyy)gvQ%)UWl*tUM++m_RapNl}*VG4M~_`|+OPcvo* z5H_dma3IMHSywmLRqMzx#G?`y5bbTEb14g=66sS&>hbb(%N^BBbjY7I5Y*$|6B;r& zL9mA504@{BAM)%5xg7EbGja>}&)@IIvYVvzcXY zdJ@14ZCOLp)5M*5z_-l`w3jaZ#T8~a9DwQ;Vig+s%oD_>ieL^?4tW{e08ckqQp<8r z(}@>UuinPGbJ8QjsGeGjUJlq`gN7M8PUif$j!2zlgC5-&&<0o3jlrD&y<~DJ3D(xC zY0m}{XS^!es`R(et-keHe_~7p}_Gal`zaLg%|)l4H|?d0S+WCJjs3b-U2x z1{nEZ;c4Wvs1c9KVH>(*+)g~sg=da^Njz0yG})p}B<(>pGBR`Q=7NasaRd$nxtAb< z;Hezx2GCB>)=*d%yIo!<3ymoBzS!N1Y%dv{p_QQHF*|w4I%3k#NqE|Z^fyEPg~-g=smyQ&7L2izZmuq_NhUL3k(=XsM%lD(;?rDvW;&=b8`2#prz4w-0B|9h z!lEmQ4%TgI0xIq$caAQQ+dy zQ$Pxw!gM`5DAe(6fnIIiIh(R%vNt6>oI&~nKO7y0x*<`GNKWiY!Wb(b~YBiV0 z59+>LAGw31@|Cc!rjzLmwPhK%vOfrr^s)ovNyX0O4(C&S&{R- z;r|<>ALoC(fLn>ptCQ`>|T;XmK1n*9$?{f337Vl7;2Hq z;<#zHnQ_ffdygz?&reunT>ZM8O*10!o0l|$TSn_Tq(e-jbOMUl2G4X3)yxOjM{GXP zd)olbBy|u!=QNBZaFbZMoHkdD$^?-CJyrck?0sBAd;_uf=*W{JCCBy5q0eLtZ|<2T zOCN!1UVkTlBBJ@QWV}|y=%(blx$4mnlNgsTAG4An&2)RazFt2%sOwj%#k~zZ z@S<8DSJ>BlIx{p2TX<+KAlMLQ_O7V|MSZ#4OBQRuXnraPax zM731_mkJt^jtref=(t8?MTCo#YkDc`o^GlO89(_XD+mmslk(GL;RuF(=zlHlZAwbi z^xs#dQaVklI|n>h6Yf#$e@hs`wSp!Z4R|UMJlT|x*TR(b1oe_BTDSYRX9(w<4y<0p z*onTWG&UWvl8L6MU-^JAQ9WT3c!p7p2+$2cZDQPD3d@}{{q&-8BTLy}TEe^#d!LHV z;`fu|UHGe`m1qcBm`5XihUTYM)NZ_wtof0Rgu{guhUS|*V*n(pMj2sx_oyh@X1EZ` z?&_)@O=XUwmz{}DX+1ERaLR()l`Be(bsvvmMp4GOou0+O(=1!?8i)rWz`#V;`sE(k zS=R2rf%t42^2(D1U?cRnLwQ0|NHoPSu@1||8Ht~>7#AbAkfu||F^HYpbmP{$yUA+A z7-?eB0o(%5fy$F`7eIS}n;>O_QPUJ%UDAg3X~^92!kNRks`yQVoQTI4Y%$Qk)Go7& zS)OE3f`g4qhYJ-Qwg1(R#0f?g<_t^G8cZmuTkzT43x4H zWo|jvUTW*$p?lVAR2`Cr!J@zgIHrHipIg7D8*t;Al!-}6(F>*LRYiI>YOY>Yx* zI-V2k^WCzT6(DoL7VlmIo3ZNtxM#|MK?hQWh~WU-^;}2lYw__l1g0GW;2d%y(wG>! zHqfGHAH*{-g=YMWHmO-KTV{CJ2!vWY%7y1ow=0Muti0j13QPRpPFhWihM*{X(LR}S zxoUY)GC)TRxtg-lc=lBzWhl19&Tf2-`6P#&bTj15Ig-WIXCT486EbqIpynx8M0q0m5ZhEd_%UY zV*VIJRm4gK=El9hwI}`Wy}$KO%Z-`8>h=C?m@cfP*`@w{f2H^MSNRX}-Lq=S<9hpU z{r1)0i4VWM{)hi0aCtflTmO~+-^8n*Thh(~4Rb!Ucsun(xxUj6xWR>Mt|c>VJ*-y_ zO+_B;^u45C((U93rb_zwHeoxcfoE{tz4`N zOk{S}bt|{__8%<&t7^CnNmu@T`Tlt0BJF833Ac!b%7~4!cHpKa4Rk0!vdS-3 zx!>K34S#WsKl~WAkLF#h9lhLv4e)C7=)1%IM!VQhYc`qR1s>XmNd%*n(yyYT0VUks z7)`*pR!qEBy~SOt9}V*Ck!xq|dVN_>FNZp6|McRibyKFL4!!BDs~K(dCZ{GEo7nC_ zee1bvZD(Gx^f7gxQqeZLg)NX)OnVx=1Y~QaCDY_**?yxIxFUqyG;BO5N$!EDK$>fv z!wT>(uo_#h(86`*5q`T~&TN2stud>pwI^1R@x})WtW4_%Q*AhCuLUM+A7{<%2+H1R z=58(CtX)~_MNXh?sNdO7G$r&0sEx{?MN96_>7pJ?mzVi0p{q(1` z+-@GY_030N?6`4Gj20yJFC3XTGCejyE3~Pb6Ei1{O`n*Y9G{(-nwg#)nV2{+G4XhD zYzYHMi}muv?)GUv8=<$RW77i>n@(-B>9-R<{aweUkGrwPCdOCquP;ZQxLqt^*GFRx zjybPA-TLDP|7*OBvWen}i<@uH{C9I5VPmHe9hfNYN^iX9yU`V*SM?y(RcdT($^a!; z?JQwwcN;^IB$Q4oY#yLR6*=v$CDZC|64rhh_gUC#qw8pCD_8s1Ui$0N7XEHF7OaJ# zF&T&Bjv=t?igsZp>g1x{$MOQ$4xM+M+%&h{0C0PUylt3sjr-}e_k3&e^2c6BeL*{X zf14=o!(xeY*oyt)zm8YK6ODiO7u4eP*GKsfH9!6J#z7?wZ{TcI6gph;*`s&=NL)>L zwlUl|?T#Eb+ufa1f8{~9iFzVpY}-8SfB3b(2Ele|W|VV)COK2>IG_}e*u&b^_2+*z z-WGCgdlzWIw*7g9_Kezx2kv|a$;N*K5|NX3z;(G35ovE|%tgqpYG*Y>dpK=2>378u zx$8*ZHO5k-N4#FWzZuPSBN4fR9h&0XGr#B6KiZknZX}_*rgBj1ZjNckY7}_jn85-F z#HlWADmr+J9Rp4UNRQmt-Lb^2U;P8*fO`p-np9c&c)$1|(rDw_As(C(c( z_eNdKz%nr$3NZj8x^ildCgnYXfR<^l?q;l(ZyVO@xUpaj*-u1*2e?8-hmEa&x%}U< zU%Y4mzO%wgR@rpdS&WseQ^Nwt(RB{qutD>_HDk}MgMcyBrR{yovT2<*bjMQLKRTc- ztv!4y2Y`FSUNs8b`y&E{nCMiuu~LJEUB6FGc5~hfj&EcC$A3|$Xrch4b+DB$R^hMs z;jKxgaZ@4Q^=mSb)tZS{DT;z@mZiAU%o%=W^*MXQgL$Ez8GlAf*>r5uuzRF zW9x65pWi=eoOJ5{7bkuDzyEJr)wlk=*NyOhZWTbEAc6Wnr~vvuY>)lc98!HDHP<0| zJtfod-HeNa{QuGc?cE)0s_n^Y@;kIi8E?B%$$Y7pO*LtNM5v&&;IP?6Q+jH7e}?cr zWl0qKWxLqW9gpJPXFbs-ZBrHe*Ari`T|^O-Z7o{BeG^MIW%=HOPdmRG-$}z#8Hd>xte#4R=9`>pa73?(&Ji`dPqx zSGTfU?!3jX9f~6dTHL6NKalCO^^!6{@Jul4Igo(>+Oe}-D~hZL-BfMV1V6Y zc&Rm!J`kbDz#U2v^ZA}$d^WCk-qA-2`zZU*UT4PU!J5^z*SfEIorM73M@KR!CEws% zA%!2HO`o(F?zJmMP4<@kaV<$BeqiXYPo#14n~irS9-lde?_X$tYMXq%uqyes4L*&m z6viX~P`fpvuO-r_cnF(z>TJ5L8t|bxnjzAhyQqkNM2N)4r}6kyL~_7BdiE+Zzk$21pyJh%Ph zmvL>Hp7{i*a24R3?L8@G(|h5nX4!8bG8kL{{!Cbqab^1Ti4q2I5Ph28W*{_Fj0UBj z-;7?%#O1kQEbU5ms_&94Q~k2>A1#Tfqx(t8opHCH>=zx}0x+z^_I4;9`qLA$tU(}K zjr+$Zj2UJs)bxZvz|Am_%;bzFG<9r-S8GyV!*|?~ zz!&peBo6k?6~|&00$M0d6kYxF?7qU2a^5mXi_erSkvN(<6o8$HV)BZB;y-L!88-i# zLb~@Q`wnKZ7h)lI20d-XD&c{tWZF`IgRw$YK9hX2tC-e@sbKPGw;XgqJLblqy&Ct) zVZ?BBTY-1}WV2456M1Y{Q*SfUYAG|}weDcnRN=HsS|P=uX`QO&l0K4(#Y1B4KX^L3x7g{a>hUO{hC^|r9 z6M-sN@TeB?+|>@Wqh*|mzSNz3dVl>zbnXxl@^E>P;AzPVmjF9`3N6Tkc6-DrY~U(V zD1tqGno!wC3iuU9os*>&}@C&bU{@b2X_zJ6m(nxe( z^~oL6ox-VWtm>A?mJ0PYzJNaE$#5@tHc8juu3LQk!lG*D#fuMgcjzQ)PKeuFlgBD| zd?>D8tPWq-6Xawaog$jtK(%6tO5>E+ zkk`mp21RW_+=92t^)WEn=G?@zbs7XJH$6T$4AvnXXM)TLTf(cN9M*b`_hj*uz*g z`<0iDI_8E8Oh8i7O{)ZF=rd~}_MZWg{db60ESl$>9DMbd)sV-0Ig9KBKpsjwM1)sH zs}WSEmr@ImWlSz^Hf=Gspd*H|7zCD8?9Q|$LXYl;E@aYJRr7$W5{Iw&Ax#d% zvvu~3sC6yoWJ{nH%*rYP;3)gv3l5FeG*rhx-36Td zUndU2qJ2zs$#}}~G2ErU9m}_@dBd?YiWV?Vc?w=DxEQaxrrc&r%rc5QP4e{;W)bq8 z-DY(Wll;=Hnt`8UbztA@$-TZ$Mk?Rz^&@QROY=$#78as0tT>n}aQ02nxSfhU@l4b@ zL7}0o6@5T6y@%x8yjUbZpBv>LLU>-o%Oydk8?FalC;RT@Mh#lS;%rn2vvvsCFEVq+ zM(0K1(+@g&1mtwJPtPQJ`cp-HD0R=Y6+|70D~-X^@`Gvcb4=AL4w9EooO_bQ6{Ydh z0LQhp67udF6X)>{5|}j7MSXLXHrIdTG!vIZ8T4$0a_9V`{|JPl8hS=`&G=jz$=7u& zMSl3k<;t)gCmA}M=~316Y={14G9A$?yQs{TFXY2oovP_=)h2yv@;Qo^t6Q1smD9PD zTIa-CQ@^cBMmAyDZMj;RTIjj#bX&8(lEvFwrFwc7W!18c98Oz2#D%l!a9Srnx=`pK znz};FHC5f(vNKs#ek)~gB=e~=U$5RBkn4-I^Iz;q{~PZY@_qe|SNmBHy;e(etNmkt z`Ofhb`M%~->8*c$@aJCV*8HIbuV*`H>g|m?)mrI#D~GCaP)@Dkt-`*ad+j}NZkJj$ zD)-cNjG^m|kH;J5)%ttu_xJq^uO46A-1_(b*I)7ujg3ZzEDT3aqeimM?SYK)d zuV}mg*iwG?$xpr7<%i4GZxbsOhA!EVGz|7oMWJ&0jw=OE0amtX2=0-Y(Y3X0P-qHc z%s)Tg7H+skzF5XKxB;Jz9e!AxWPiQyY^v!A+^%`GbV43+gnJA_(tr$5M+o0uE$*X}MVL^6jnMh@Rk_n4D zT_f(@1IQQhbQ8zXcK38lXHTBJZT|T`saNkSLEDYhn)lYgfB73;-`hX<&n}eqnxkQT zc~|pfZ2`thT(Zj9+8EvX{rb$M=M>52JGg;p%TZf9Tb> z{@&mDyI#>3r~KWqFTF348!xQs=hox@`{&-pk+V^+Xb9m)5C8{^;cdXMv?N~t_8Yd}kfkv|C{TR+pN%`<=H# z#cETXgiT`(d&2s>RBuyn)S|-PiT|XqSqnl&IM4JxzG`J_fI;z#+IYj z)4MN-`0rca>aFtOzwOn2@@Mi8HpV*i!W+P#)>>H_5C&eFte6wC)FEg+ZATl}I9kn! z8wV9vz%6fo?Mbuq{%X|k7+|=5;)3~xy6o}+_>s!SHUMsArkZEl(Zu#u1w7E~c^H>7 z?Tm$oJMFkfiMXJ`{nl@J*&hXd&{@?fNeew_=9iN<-oSr@MBR*qvV7#REJHPMw zZ~fou?RTCHHFY_nrY_B)#KfX}gOR>DrdU||Kspe5Pi6aP=Bzv1 zHOnwK=qggjR2BzKVF7p$;h9*+NvPTxrftyl#6`L=o~~nQ#6TonV-XGL$tJItZrMW) ziB)RSm3bO$;Z_6NA{}=e%Ptd^S?!gIG!UU6J;YfUW-uTrmL$6O6p2(jO4p3CDy&kT z*7%0b9H6v=g=W($OLDVo*rMNr49$Y-+{ZqXb>gW@!{xNbvZQ%M9kp8O&*uqJITcwa ze4C&McBH30^Ah-HA$+H{CA=(g53+tppmK^ih4)w136ycT_^l=8$_U*&u4Y?2YBk%m zK?4LYYJ5`@Np1v43(qW<-+s9q1TJjZL7yV%4|%C9bIX>LYI^_6s>SNvF_g+;Ta6S{ z%3(+awe{HENROpsBh5jTTjdnxkI0IAif2K)d;3E=Rk@^FQ_cfl#Tel-?j1aRIsmsY zmTLw_0@{69=%F@lCP5=uHc^`KOpsL%COc18&=yUFy@;AB=d^?81sNtzXx$LuV`#L}7_h@bC~>dfG&No`S3ukKWoI_88$uK(hs%HQR;_ z+3N+bq*=OA5(iZ*<0(nO@DVUCjJ*$(neu{V=VwMoJ)cm=h<@_wfYch|8$UqH)DR-s zpJ2Eo?U4D{fLM5-Cij`LoYn`)*cRp>eiv?@bVeW{@GTNMWthI739&MCT*SDxP z_R^FJSrLXCFVYcnnQS8&chbwO zieemoK$Uu4_N++$8YevqG5-6$SyD;ORND`mz?_xm7N9!QO zw=tOcV5!k~A0<@BL>sKpuX>p$E3j=qs+2l|6|LrF`CH`jZCa#A`ixl137i707>J0H zE|B6$J5+*_46}p?=QupHoubouT!46a{p8~228vchubOfm6J^wENoKi|R=C&zg)5YW z8l4^t#SP9T1Cu|U0qw)67n2?BEA(GcS0zUZnsOs@l<1|Q@mG5(UDwR@BF1pli+{%g zwbNJPNpxCQLD=x21HOWW3n;ky6F*dLqL5R-zS&E1h*S3*^sM^|HA1l2S~+WX@^w)5 zQ?Y*Ttp-wJ-|fPs3}8=)uX((B^@DK(8f3uyXJ}iu9hkB{fYjP&n?PVA%6=@r8llP`;k!I)GtAReN_9a5U7N_{4 z0Vv}IQMqeF4KkaFsuddnD3wFBXvSKxgpGmo&4ws)R@&?5g^!~?V$|r(RFH8L6*p5d z=f5r%eMX{p56t|Ww)+yI#}jK0qA9GXTG3H+R0soY>0i0lXF{7>y;z@_hs`SHJo9?# z4cR^SC(2&bkV!a@&pH9CM3lbq|3%$7CHwQi49&V;v`WMXJ+EcV=_n-NC04b*#SDkz zo~le|BMoPVDtCDkD>KP=D^=uSrnze+2;~0^YH> zN3Hm1v&sAg1rY^X!!JjzcHChw_Tv^zx@k@gnD!YO`n9(=e(m>$z%=KLHGuQRhiYi# zNM^Iq50D-*UTc6=xn?oTu>?amYAg{`Ml#;$P z-Iw^aLhGue^O|0EI>z|aMa{J(>@cWJV#YACDe>a- z)-rj85XM+px+afGP3D05!^C<4(wLB-X#lTT|gm+zaV1 z?OxhodD>?UKqo#bA*{%=Axu9>O&s&W^SKfCmX-BmuWdli)Vel`a|p4#u8DwR-F%=Rd7GwqH#R zh6i%ci@(&i8y^V;zNcFT4kMkzM>x;*0{#3_N9A5u{Q4dcXm*eJabAd|%>_>Wb?SiI zV&8~9PoJo{CCzUIY%YvWES-Ql~RRzaxj$o2vnKT))!KjkSow-at-`hszmu$Y!mMv7<%5BAL zsgSSW+@O6-vC9g>kW`kbjFbyE^Z5!TT}cuv&;zzu>Fvcyk*n0&s2Izo3Z9K}VNpqB orE;#E&$Q!I%@m6D4l>j7b*j7K2&os!l%vV1IZbvi)oTj>4<5o2yZ`_I delta 72792 zcmaI830zgh8}NT-<}7zThfM@Tc2H0h5D?q|H{8X2Nd<%}kjh0CbIZ$Zkron6bIk3a zmRVNr-mLUurrG9FnP!Vxnyuzi+3x#1=VHI!|NrxOt>?>}b7tnu%$enxnP+bO#cPrE z7tcpFcd!oS5n045bC0xcY3b?NJu>z*W-rJzrK?*YV8+^&wyJV!|9Q{+ssvSW52H$F zChXa=v?NttXVZSt*6p$FoUIKN+%w87VyQ(G+#?{EptN^?Gg{CXArc{GLTrTC2jf#e zK&3Hll?^A(<5=kI*Wve&c_Ive%*V;d@@rL@q+Z`Wh-QP;cPDSi3d_%{J+*CzB z;D1%oIx>-0&!aDMziR4dz!OnTJJJ|wsnCH)vIy^F)RHFrO=!x(iUe@oGHy!LGrg8Z z6C2zCFDb=y<~T&pV|DZek&?YUa}oX3RW~~h(&>SxwdIbA7;tX~cTH7A6gXSZSsVeb z)!?eCtFEc5sI3Wy>t%TDs15_?VsJWV);L1I?F9GS;>yxsaF>9)qNX?qoRh&>UIz~< z0^n*GT+OPhEX4xq-48At3yN!0xJUzcsk3fotqm^X;iAM@U2Oq(D7uSli)&19VdSK) z)+sl9y_kBwUd+PNrFVpU;aRTiWJM&Om+xfJ;m^`1=pgbpIYTy*d88|mg?AvV?;rnY zCyN)seLqjp<%N9uE;dQbWKOCVvr?8S7q)g{W2o+W`g0P~@aHZDB7#UDvgglTiuoFw zMCWp)#WaD>XffTR6w#hkC09I$T1<@SEhh#Oh5z}L_1T8Gn@u2Q5DSPE#O9g1*}m!} ze|Y-WcuI zQd?e8QX}r*r>CfKy!nAn7XDJw-qChwtGu@6frJo# zsyh zeszFfM^9n2-?I@=#6eui^_xyD+xfk@e*O8*T)(b-RQ;PK{?oI5S$t=nU!tdPo?oU) zoci!(u`G*!y49~o!-dg)ApV{UqXS~XJauUM zSbg+`Y?{Pxq?uy)+zSEi6s!u_WHwhW2Bh=87XvaZOrjsrb+m$}bN_n#jiHVyPtd>OE2x?;TVRe@V_1H1C9+`vifSMoexo*TG9FODGWT|Vai&{$pX zNSKvJtlJz&r7!v6v3{|}e>7|NQI6T(rDa_kUj{U3iX?W70=Q?_iqLz7K5@xO?*PNZ$N2mG!*tb{41m z6-F_UpCbOMC;LX=bb>im%Ci_J@1(_|N0a_o&I}gOaN%YkNDxRn&xM=8!{&MtTQ_{F zHHcO1K|(_M3SS7q7o>^|B7Wo}qKkzhVQ;X9ctlm`JpN)-ay%KzSFFFodb;0oMnH%MAV3*GBRo3E4K| z9=NieeWc;Y)=-cz&ylSiaw;;v7e)wg3+hNUUF~51&Hkxvjqw?1Gk;ilaD@j)z!sq`lOnC{bh({kE@oFH!AlAAwVRO^M+ zJlZv25Kqs`58?Iw^V9fF*MI`giM;%$%=*3eoFkE*2ZrZAC^kq@;UFDBB0wTRqC8Sm z^qmV4GldTXZH=}-o2;d3?bP4ZuhjSHTWXaWXuoCu@Ts_%ZIph$@4c8?glY%)VH%Uf z$E03O^nB3sYCYj!vzT@b&x-|X2B~k+5$bBSQ0;90%YM}Uqy9SWksHqqAJdcpd#b&)m2a>w$n zg(k+7dUGsW#r8!l2+DuKyOpT^VrU>O5Wsg##M9P=t-SR{7Bso(0MtTvNRxe2u z-x1e|6`^8pQD$e^64r_SM!jSYSxSZz3#5wgn$)EajsZWeywN{GFM9ebXejZw>e&%J z`r~XGtH10jWXUva44*f?OPqdc{A3nD!wU2j@BIdKzyA3Mh2NRp#l)i%y2j~65x+56 zx6jzT)kzvHIuy7)zlc&HAnfLm-;mInQTO z=?6Y<2D~C=(NEM&{c?4GeIh(-nq=|Q_x)DSX7c`*hs5v}*Si*4Bl6}xrdYfP)?I(p zv#<4e??Zz0*3jEDfNH6j+Q;>(V||$HNtw{aO?mOzfEbT9xyu>GcRd*!$EUq^zt!WI z)@3a*jV!LMbyWM$^T7KRvaBU`SxelqmiT2Y3CmhKEoKhwgB%M96GqnOLc4U1ipSP+kgewj$76S%*@@8pIQogG~i}bu) zp~X|ro!QzL>TmmAuvZn=RyZnalWU^b0IJ`4I+}HmN1lO~M)G;jCU)S>rCJz&qEzc^ zyp;9Kdy%JBXkGc8a;;g^9uXeYPyKbCc9Qd-N&;;|xBq>f#`A;ECPw>3upA1ho#m{a zTik_Bp?Y`AS(YHrSb!J2`wPz{@bM0<1}k?VuUc6V!av)ZIKW6SOCM6cY-i&Bok?Pg zm`4)?J?nZs>lJ5fXT5CQWqs7z%WAfKZrN<9u%yvO^KEmhxyqbp4lrFb?a-^iYn+Ar zN%oS5NTzTEhurS0T6F7|Zr8IIzOH@x2>wx0*8=Vj4M4B@;|jCV(BV8azkMu^xEvM3 zE4p+|*4Y)6IXIKQ|vVuLtGkGCe{!Q#UQ5 zIW&U&ZC+xYX6|DSH~nS$%=Efxy=kuH4O6zMopM8YpL{{Qq=mT2Ow!w~Dld^RZfeeM z^jvPvzD;;kaJbBW2o4{lM6*G(qPUW8+7lA$8N4#POf*HZJX*f6%E4C*H3idtt9emS zcr?!r3U_%v2?`%c_~`cG4j#ESdy8mP=A}VhSO+@lwCAg}*{>7dy(O>yPCL-yTR8~{ z9|cWrB-Jn8`H)2^Gvv)iAYxuj!WzbH$o7oe&}-Mtpd3)8Ku3K_E7iJ~`l`3pL+XP( zthx7iUe(;YgLyYyK+~aM1YUe4AVzPUQo?MWL(RPx67nja_j&JVeQ`n^>&V}{(7O*` zv8s0*Z&~$aFb!D7^FHVu%U}L(zrQDDW$z1pT;w&-G@oI#fF3ZNGd*jnF?ChGV!w%r zvPwl|v-FAdoU~XPE_Eci+6irwHb>l~byt5=-xi)x*Q*Y-yE4Uo$NrAJiA}YSu_v$u zdc$^&%(oq~&9q2iC0AoC}2=FR50<{b98 z*`mbB=j0dU*_GWeWB>ifNiArfqnbL?Y#J)^UDHi5dgKd1ER0`1vNewHNDT|1;7eZFv7!br)gqUOWX{U>rorY%m^w^8$4_SmYShz2L~;`iVk*G_H?p#CFx^aUus=C`)Wx+{G#weWLqZOt@7 z^NZuI*lEBcM(TJ==))#{@$l9lW17O}9{Slz10vc!){!nu;X7Y_Mq*MP-HAdBJrK?Zw>W%iDDnJIR4#Sk7Abmmlf#iVXg5-hp2N?h|(DV9FgN9U*QCun- zJd%$u8a$TTVm(`n20v&b2fT}Zo6PnR&xLyj$DWY{p^IrgSNy^!d5eoaWYmP6UNH6o zah|my;jE_6Kw*QRy`ep>Mi9I`wqY_LqS#G0=Nr_C>`Th(OqV)Ib7#@xYl!?eS+&@@avZ}L~ZP_`@cluq(( zP!b$+UztiDORFS@lqNCpJs9H3#Z>k)JHi@6*i;rvFVG!yDIH0}$T#E_@*oLR`|I@= zlUdM{g97zap6{usUr#>^wJ_uoKfN>`W}t7XEL0A7hCC=_t-LWXM!)~SS>{JWzFc{F zaE!k3mR#D zq5doe6(4J{?y4w(8Q}Vy5*qC3xFr83#q|>vrj5|ndv)*b;Qmjh$MK8v4=H-zMTOAv z!lr_HVTxJ3Fy9|D0)I`GQI46_#Wk~w!zTOY%gx^wF@GAm-&bW1jafv48V0%YL56?~ z1sMi19ApH@NRUw=qd^Kl#(<0k83!^RWCF-UkVznuL8gFA1-S=g8pw2z86brqMIgnV zL9UtJQ{r%8hrmq*CAoY=LCGZ6LaX`af|3T2%o0R?y`UshNuB0^+|J;|KOW8GzkPc& zuHnrwB_O3B4v<+OWgz7s6(IM5%m$g`d2`I%zW>M&c!03ZqZCx;5PoUumQFn7!ZmAxDZVAYDnBXTEBBZE*>g%cdzh85 zJn4HDPJaTev{9NR&Zk>xy_743i9c%}S~_YwVS%TZPSdhAfAw3MtG;5srOr|N+kdv7 zq3!K^?JMn0`!Mn|IRTTw-)tvsTW$9bB+rq0Qb4-GoUn)aJz_CEZkh?>yq|K_dc(R8 zbnGeS@yY?=O>4GQvHW0p%d*Zg&ysI`&Ai%tk5Xg$&U6eEnD=)(2a7n`>+e1CIwY`Y zIDdPeb939+yrYpt@o64sJh#2#OcXn?Y^wV`_5gIsMXCJr1I{?!=QXF3yI*&X<$Vu2 zBYDU{XTBK2@~Pf2>0#E97PaRyyw1)%#p`^CZ-31>M(oP&q5A!|nqaO~_#D6fsxy}V z_^NX%S6+86GTzE_1`dsqyB|tnB~(9jtB`f!A0LDi8HwDu;!)axzj??xkbmxlpoIsW z@k&}|N@q5X>Ytx{oW;t;4;V`M@B@#r&a|kIAKL3o;7{&#KGV)-6SlzmWpY_HEIuZe zI%+D)DwDaT#x)JJU=pt<$_H6Dp0~%jKulnxsebavBQPB(euiIr#hJuwUIp~s~Zc9)#XB`HgDZOsIV{!s?R8`M8K`xISvpdn}ZXeZ{#R)$Js{ zX+UTk?S7Jn9B`)cCk{aIK6b!4j+0lN)qKON&g5mS&SkAt%Ub6xYpvejS|j?2{e&$7 z4>?scIavHu+#;4jNqxiCK($JyztBUp+B5$YXr;V9;pY&2qjMiq^y|%!vv6KI!}UJQ zLl-OjlQFK3jG>P=k9Em<)4fSB4fTJ7r%rJt=(7iZ%KREW`KSh@7NibjKFEC_3qTfv zECN{!vIOLQ&nF)(?b4ggB4eOecO~*PKi4xRA(joL_g2&zDnGaSyCV3`pR5vjfG-Vq zg_?T=XPBN6#?N+m#`wE-_OomE3Aw_Xg77ApL?oV7;L1#*i_~}2N7R9|ul5G0Q?F9d zem^;E&($6y%k7fwU1Jc4w0>>XJ(UHnD8k2_sY%eI>`%ZPBJ7Y)t10^N5twE#eXyB@ z(6GJSf2ymKern+~=#axkarXz{zon@Zr{E)ep>s?2VQ83vU`ez*UC8`AUyXHLmVEk5 z%FxfG)$c`^ypMkK2pc9EG4PjKo^1zn1mDGX^8M|oc+;nM`QASL+9Rx(pT4~{PH!&k z%_RK`nDv|We#fUUKYj5}kFbY%@wmza9pA0!8y6KbnfEJn^&x?t#f7d%{W6Dv01Dev(VG@MeV${S6i-?YaP|U)%Vng)JbX&`)&Jcc9(qs&#iLJl<5qb zC49s;SGgV}kMSFGw?y(m^ISLi__7Z4}v@d@-WCUkOq)PKpq8o4CHZ;Mvx~!mV-2bG=r=F zc@ktL$SRPhKvsirkToDrgRBKv=lSIN`c5ZZ(5~AaJke5%`OqZouDG5Qr%2AnYTZgujP;?yT3~FFtz<m2+=fTo-)L(I19$Wx+mI7TnCb2m-mr7h<5^fA}Kk2dOqn1#*BT z({EycOvo6QP-^VRNT321`Zm!z$kIBg?S3;jFA_yJoUn2{-0D+=m4VA@ehW8N?AG zO6AVFvT}FpVhj`)i0p_@lBhhlxYkhz@kPO9cfE7>S6Gxj78nOh`i|-fOy&~(UccR} zlWZcD?$%oUOSnkyVP+LIbKQp(2v%(-kN^g;4vjZ~vvmpHWYjs^eK;JP6(WTKXkDaF z3)syP$IG;))_u4OCW45x8Zw>;p4y45t`hE3a7Qs#HOB$v18%D%Rm`ezltOs8n$D!U znhGq=2)GKOkfO&k$iDviQ-QnLvjuYToP{+NcT1x?CN5SX5NkVdjgr|Si07~$zPT@x zOB^+|&T8LVW{V=O5xEcB!DBijrAD+l-c9XyvkzzokyShHbGI&lhY?J6l$1Jap@=bW zF8$rKZJ?PdnD6;|M2~GOUEc&to#vi{$P<*_{w^oq|Ae@zX}Ir66;HE{cr}n ze;QL3R5*OMZNB`Gg}x%oO#pAPWAq5)T9?fL9FmmsYLG#QMQ{5RJ zbrK~<@f`*0+LESoBdbMR9gPJu^#MRT>I zq{675?!(DORwdC{TvF~njICfEe!)yL#hhTKd&s5*6<8bb>5L|5RC=#sYP||+xFan;27>#a#WYp!2eYdfYIL6BAFa)M+ zcp5TNhFWr1Yjf5>h0)J}*WP0!h85JPu9=cF7YY_~XvEkH+gz{}FqhG}kj*3voedpC z4a99U&IGLgx!By@8Q3D=6-2*x=W{Hf6iTBQ!o=b;1?ubkV#snA@IFO0zKlOO?Z%hE zn+_(`R+K<1GKwz(+vQ<=^AgF|{J=SgkveEdSi>r&Q_O6wzIyj_>~H<~{m-#*7pzV} z1;p3&jsfre7@6I6oiAc^9pPpm^kq=KzJyFQ-VX1AGP1$L5DA^hOsXk{Pv+~@WKnih z`?@G2Cy_?W!M42!Qr1=%Via+%!-DM*drh}lPkQA!)-6YromioutZKo(zXd;l2(C`h z896K6hZE3qsA#I2Th-Pp`a$O0;U)^L4Kmk!;5oM1pDE>z%3?_9}#HHvxVA1y4mekODA}X?E&g<^|xB= z!Kxp;%x1OPG>bjZ9q!*=)ogZ)7VPi0?9_&3r#3D-r5n4z)9FI4oNCD##suk-^p>IgO7{*V2veW!hueSv+NJ=Y#* zH`#u$owDtMp{YKcw$)V$GLY>tC1+>c?Ip^+?yp>PBV5bGCf zG|%&$x0ewyjt!@JUiDcP=~@3l%XP^&SGv@cLOOb0I@gj%c-8rqF04nF^L*p^mVTb8 z=UZNYMPvFBS5h|R@nI>OrrOw6HjWAOCH#V(ms2)9M<%;Bg~Rt5;fEcBjhW{ztf}=4 zOq+}fpN@liMYVfVFn-03qG?WXi31zI?@px^!%af;m!NAl0!_;n#p=~PHWf7dowf;N zv*+)$ElNk0BOKyN!Iqvpw_wW<)bz9XJJ%K1rMf3j(p`EZi}zT^Z24VfQ^`!O6m8ip zeNWu>b^K7#7B{zb-5Tqg616_Q0fIRDQ6>oiDhKtP<@`Swt>p}mbN9ih9 zYkf*9(^AxH@O9kkP}Sdl#=gxyk4zvYVXwWf-A|0QUAFDE)!Rnff~{XzcUvE}##qi- zHd#t63FedLr(q{4-E1|THN9vmF(oQDmHlL^QlsQ3cKL+dBoCEU=|hQ2V_UVNw-r!KpFKC1SYv5wxYH@dN> z!MsF+j>3C*)^_G3x(C4?pxLGGF068p|>Hym`wOo453rZtS4QQ^a90 zdI7{BuKa0;?AzjiJS%!1$a9v@$O5hdz3cw!#-`F`r?xIT_1v;k+m@Yre*dW#!~$_5 z1M7*fsO>LMakj_5K162x^VscC{Cw>875eC*7f6C$c;l>SoEX2y%0|!&Q1ADQ=95$Q3@2ATn^X3{B=_~;FVZ|0()J{n>9D{CrOzIay&(HM zN}v6IKNyfh=L@!XZ0l`vObNDh*m3mmkk zrM#)EQ5<4dB~|#0N9{a1M>K6S6|Tq&=B>@KF?#n;N?EYy{LZ5V&X`J7(`=ah}ij9DP_MNBN}!HEMOCYT-}3a&!u^4{`$JB*-a{(;y#! zd{mr@2+PhXAmOl$dS zA1sd7+b8R-QBOjFZ+PyjE`0TKUp++&-{Q&JzKWuS#~Ma&`wHYT$Q94%ZC~$h7$9yE zO2EuSx`#|5$>as{FfE0htuXQnIVmm?Cy8k=E518PozC)D95c}$w98;6^`h3S)oPQ8 ziO)#68e@Z=!E0M9C5ShKFZlA5tFa?rF|Re>YaVG%Gy9otf`!0ZQ>7^dI)%N;d?iZ> zkpG0e- z4I%5Vf_ww=Ey#Bu--G-B@*~JKke@)VgWLeQ333bMXOLe&eg(M=@*BwSAb)`T3Gx@n z-yr{h+<81?J!t|#Py|DW2niu06od(3MpzJ5gbiUws0a<=hww)PAOaCVh<1oz;tg5f zp8PPtueb1&04wn;={+=noF>hB@Wu9IHrem3hrb;q*zMHGH$4#Zm-5KdNZaH-3L zX~H!@J);V06qw)ahb5IEc7NM>+ZNj#TZT=xo`KDWYHL5M#d6K^fn}d%jb*W=&@#Z% z2@Ds0GJk0HnAe#Xm?xOi)F;9I@f7W%MQQA3MXz8atX#+Hm?-SCc#kjT7{$ z(63oY)60j#37{h)0uhObLPR5C5V43jL_8t^(FxHRk%&k_bU}1QBqO>Zx)blqhf>J6 zOERQjvhb^}w4{>hdL^)%z7ZHD!?$fmPU_(=q>|8h^{5a)%N(_}FhNPKsf8I}80!f) zDq-eW0@Kapw3M_={Z|P1iN0xbDjC3fbnfAE>D@Q=he>Q|=hP;A0!TyjK%^rw5SfUc zh%7`lq8Fk!q7R}kq8}m$kxRUrHs_I&zr~^Ckf5tA{mGLunNJ3i0KEk+M(Fo%=}%(y zvK=aUTAv5*;HE>66z`!;1IU1DxF$7?4H8VVSOcuz4KnpH1%NTqA!U_vuac`oL1%M8 zeobC4-!IRQb5I4BK9^pV)`4l#P$@?IMf_B|q#f0^X!Y6{Em;eIFMLjYP2H?Ms#b|3 z#jc_i)&}2Z+tlGuU2oe@*q^m8v5&JS*@^9(ZHH|cf2<`jd2prZg$3gVbBb9qT{ayt zZ8bHpolud=g`ZeHOJEB9jvfQ+$SOLJhL9gfD|w2*BGZ5VrL);oKds5EyKTf^T!pVH zhlPw1-WvKvJC-tHpdP((Ac=!cPwA*%S_4k+4&WZb8;Z3EUQ(UVa;Rl6EV;PkDq%X9 zW0@?|9xHd&9?_<0DdaINM4GPtAw6bJmhZ^t<$dah>Wik&Uox&mLg+uypNp zSXjP6->1*e#dIu9q=GUOwjm3&vn%of`6<6IB)#VNU=pq;zm1#+94Pi+6;%IW(POL| zEt%g&k-W!8Sg7?Vb!9*o1@9z@t^*=J07cuh4JMuS zrNAlrYwr&x$@=}kC_UmGyq^m%>n5U|GS>zijiJLA>)RmeA!a2`Fgq5&Tu%Q9B8v*g zot;_6;)St9XEe5yjFgPzl>7<03Ngm$R^Uj<94SZ+{UiqRrH^II=xHqc>W-6x$vS<< z{~qZ>An9F0+Ot%MdwxYtP4R!@wdz*LevIyZZ!ihdyT1u}^-md;r|lKgS&q3CmDuL1 zeD4Oc<1zXW$nPlK4gOx#SA)A%{|R!f>l)-SRc`_=X`4;`G#SeF3`9QEy9kQmdtz+o ztS;#jt+&F<67>y`l?WqUj)ji37HGb(d&VsO&8!PU;<(yViIC9VhUm^;vU2_ z#B{_AL?NOGQH+?0C_$7W9Ee$nGDJC|0&y>5HewE9E}|0QL{uT>A*vBIh+0G)Vm{(N z!~(=Z#3ICE#1h2)h@}V@q8{N!Jb-u*@etx+#4E@qTiA6X{aMCO}hA zQZ^H=Zw4l;C=m7I;22Ef!u6lP5y7*s`A0R4O5IEVTM*A6o<(d$JcrnZcpmWrVmsnR z#7l^m5jzk&5xWq(5ql7O5&IDP5gx=Vhy#dM5w8*NsMOcV{u5-(2I(MKw&96`B#QiW z@Wq3qTqURV)A~s0u=+#IzSmd3b*$eV4I@gu^30>4r~CsC0f!J?L@VMj;tj+R#G8nt zh+~Mi5XTX3Bi=#0i+B(5KH>!8B;pj}G~xrqhlr05XAmC~??2jE^5h;Ry>q%C_`j#S z_J)%T?|Vnil3tBT@7rOEr<`Rl!M=u`F;CDM>?hTm>Kp1>u#N7m21_+2r}m2UxqXVB zQgDt`upmLuTjA@s!>=FVJqb5Wl*T@&-zZ3+aV+zmYlp_2Bj>3icV&Vg))^);O6qVp zd(`U}J-YLFmg((3@f>N#ZN zA=SI}$ec}Ni1!Q_duI?z-r(-M{9#IZ;(0KIU+bMd{Tz9hP)J%*;W<($cbjNz(x0LS zS*ND`a0~DW;ymJ0#Ak@liFbeD7i84Mu7hbXoW@C=3Wpqiw63y`l+DsPX}h#UN|kKl zr)-3{TXfr_z!c|#^13%I_X14nKwq$A@YYLHGFW=jZf|h^3nYc8X0!>c1tXPOLnD~B z_XiqEM|9Jj11^wD7I}>zCqTJ$tkPR=d`u$r1u%8$L&NO8hNGlTg#A4lZP=c(^vtea z>!1td2|~@;JJt@qKp=~^`NgKRj@Hz{T?HX%*uPpwh&44IcJ1i8f9-ieM~TzD{zER1 zE`;>aQ+8`KxMi8qtQ$Q0+ z$l@OT@X_0(gOZZB3a(WCdH3y6w$#{5wwZ!?isKm3VW8-zGlAL`J)q0yzyd|kV>bAdHtfZ=zcpM z&r{3hI6YTNJZ(03`8dNN<}^CUtX8}MPY_;T!8=ovL7HR_J#Jr_CVW3+e>gbW&)VnTEIl` zkaZ2r(??hntb*mdWiK2ssDN2|N3c{sZQgEv*j!}pZ4L$#!S_thnI14rHKoDC;!EX# z(yWvz{gig{4^YT!;WWVzIZC=Mosgb|p3FCTe>y_k1IGnQ;KWFKc8i?=#s48z#QK1( z$ zfa#|UH%`FuHNP=kjnz4vUJH`_p>v10(U94D;!HM8hLNnB@0gh$1&8=Fy`VUo4iHUD z$l`g0YB~%ty*$Q|8a`v#BH37Fl}Uzqju3$>=3zJl&GlJIo~r4?!sWnrFdiQAnIfZs zu;N>emjl2|B<(s{A;aRBj>v2?fOYJEdhf7Z}a(Vnn^{qREXtc zlA%GnJ8LAp=#Tf9;yw8}q?ds5({|7&F)!2K1cv^U4H4b` zP+;Kvko%uZi*0IwQ;vXMh~5Y|=GSteFQOkJ2a$`&L-a=sKnz3-LJUUaBZeS`B8DM` zBSs)bQg6$JQMB|rOA#A%<DWi3DWCu`1~C>f4ly1v0WlFV2{9Ql1u+$I4+3I5_R)023`8NK2vLlf zi6}voA{>ZWh%!Vuq5^R*Vm4w9VlJW*;Y3s+<{_#PHHcb79b!J>KEwjVLc}7(V#E@} z{fMOq7or~FMm&Ic5b+S=VZ<^-1L6_Hqlm{4k0TlpPau{fnh?#16^JJhD-o*@Pa#$# zIARUrX~bH@I>dU!2E;~$j%Yz_LTpBCK|F(a7O@ra9AX>ddBh8d?T8l_F^9 z>_Y5D>_O~B>_hBFco4534j^7dyoPukaS(9`;YG9}4kO+`96`K^IEpxicnfhH@iyWe z#Jh<15bq;SAWkAqAx0^%a#65>nhU9Wsa%R7hl6TE`( zk32z6f*pmuFq-7Tf&5eATJ5+VmGTvxVWUIg%;wi*hqJn@yZ#8=dY%mDH-gh6x!*(m z6-r%rJ}Q!LKDIwr&mI0VbeJ!tenroUCEWPg^dYf9jdo#bHO9*didR)_+ zFJGe)pY%|E3XdKO=chs%_qA)Ca1_EDEa%rlD=9Rrkw*5=EvZaPCqyv z`h$8zeL;OfoeO7Kli|$XkM{TJKlYc2#NuH`y}#WCn$SU5ay-VCvdQd>Pn6&mlGRl4&WFjf~W)I$od!1>J$Fab;PolUxP zU0=fx&&W$-WmF$o{Vo{jPXEjol_|Aoah72KunBenBjut+smww3A4}G-uJYs^ z#*@<(@WfiQL`sAsIgp5%ZK=p8a_N;buFwwpQDAhNd3KHl262Uukxekb2+_JR7o?+d zy{>z%fNJ2q4k^x{`f^Bev|a{WDWZw4ZlC%kjqnbhaE10ICfpP#tE-s9=gp}O(l0_* z&RB3_R95Y*t8wsX%gsP})L+Ir#f{KH66&p(a)k!dLq%68RN;}rTY_#$`I?R+7xfwN zw?aP(97+o#ynd;0wnW9GP0(GCly*iD_7SsL9hjT%C;@AJ!(maKA<;hW(XLujIc%9xN-lbo{1FNXGR|PgL z`|&yj+(6u<-eo`DqDvnzQMOPpf5R4f{F}4pGVj8gpXt0ZUE6bmO6H6n-Fl|=$jZ!U z`tAJB6z~h;SHx|^Z;0O!e<1!u{Dt@%@ekq-eeJjN%$6bdg7UF_s0aBGHjC2V^?GpR zuP9LY$%09e_dU2uhr>8UeAm#(NK_4i^|kOr1B3J>@EZf&{{O!*z~MIr$_)jDe-Uvx zls_~e@OAEQ3Wu}3v-ZJ;an|@!=GVj{2?J2(<&lidEr7)$sfw`@eGc#_EEe(R>w%&- zV;*B8tdtJc^Oi8s-Zub`5xo~IAmmW(n10;FSOiNMIiu<5QpNxxLPE$01z|#%5f+3M zVMEvvDndi}A^Z^mh(JUTq8%a_(H;?k2t|Y;Iv~Ok9hvv&QmB}2(tm>#$vSQ57Re^6 z!c)X9KP3;4?cy=x`r>pIG%MPc+ z)v^mgvY(ZHLUiu_JRp%5{LyUU(?1LN#W0l6Uq8N^1$r{Zs;BHtQdKMi#3AAl35ZUJ z&WJ=r5~2&DDKHS=|d;(gh?+_*y##X6DniPU;7$+N@4g18jfTj@#U}EHwIw*85Bb z>jhnV=R+1qLyq}Q=N7&Fu;|JCu=h+jMSeLThF_n3LG}zk+q*yUnT{+kSP{s7KG%DZ z?~vV{-R;Bq*z>(N`+h?scgzZjul?y}2!HL<-rIf0iwZLx%%peR6-aFS)Mvfl@xZY; zJHdl)8F+#&mhU{*Tcco}Q~62n2L08cC2)i#tgG+P-izy7PJ6y22^Eq@yNYf1!6h zzhPbjCm)@!Me@$4;ZUjZ>mMnfbhqeLUz)&t|GU$@Q%GZX)|kQ?Q(0pgYwW=q(^+E% zYs_SgJy~NGYs_Yiy;x&!*4T$N_GOLzSYr-r%w>&vtg%099Kad}vc^HIaWHGlXN^Nx z<51Q(j5Q8tjU(9WBbij7m}&)6t$E;zydZB>!AQ1F;d4lOivE53aqLl7leh|h-MJccf~iV6bTTNubi4xlXX}HLk!4 zyRyVEKQ=BInjarY41i6!bVZDeuu=(z39tk;o(6$krwjINYJ8WI(QfldBHEmVG6_vF z+aC0yCiqQ(O2Y=x2snt)nI*nJ!4zzmi(%wx3z^A8IKz%tkbbZdUg*28)e@xyqNoEK zZR1fq1*^82nhIA5n4TJUW>S+AOdhK%9hf{!g-JBk`b-?}-pK+BT}Np}t>Fb;FpWs1 zV8q#$&S)xviE-OSB2(r&<~XbFdcBvLD!_)W2F>t}B%&>+J%yMYuHtI2Grn7VAyl3P z$u}~NDG;bsVVGJQDa@cI__-sW6|ygd9U1(@K&caKWABz+AhlMOEG#iz40e|ojxsO+ zgWV!>LqPGN%G_33lituxCs=dss4)!Is-mjLC(pjwdqM zuFomG`=ShL!7pi~rY*}wlvO+D`n<=0F=+Mwl70^{l{uVq9koXJL)NVE6wH1dl`fz6 z{#2}XIA+5I{M41G`Sp^5V7+klTe?9PoovxZ4Nzt-eC&N-5aM8;M*hDqsf> zmi}$uw3N!u`yBJZR^519NoWOT2P$#IWNT+I1e)cVQ|ExM-WLDxg$zEqv$W242eQ4y zS1I9p$)Pz+np2E+wMJxP&=S{|f;=LFi6mOs8c*(HVs)AEPW*;o`i-X?44L`Un0GK2farZ)7dgFFqLY=d~83AUY z{=sUycJ?^4YO$$!Ho@>Hf`4lu4EGd(9!aZYh9rU%Q;pMv52{0bI zEqzASW@o969@mkBAd#!&N&XSQTKVuCnhkwhu&ls-ZAQbcOt))E1ZbE}~Bc2?KuY$V>nOFr)p{%^^K_Agvi9!DN0tXdq>)=q0FZul_tAld~MkHWh zT|K{I{=XF}l!&$E#cdHS!gB#f5@QG)^)#!p$r{qGgUxCWZYNT(?KQ$XMac!tu=|R!8X4u^>3;>DKp7ObF9q{Lz}z0%4pu%$P`~z6Hu|l* z?ZXdF8yJlTQ=3W|bd}%}I*_hPx9*fVtFb?UmTQXXgy$cOELTyv8v5_*w#!*A30h}c z?N*8X(!u(Z^(P-Xap1(OCtmc0kVLyp1q*aPusT=$t$uc^pMOArpKA9D^!HN(0)jOE zcA8(HO$z|abbFB1PtyYYZK_p+sjTWB7=+gAHcNX;kVW-t2Lb$T?fe430zSa5X;y2P zJwUbj*+Znx9=$En3r^!jTLx3Nac{z`S<~$1v#>DpmI1~g#v>*$@5iYVSr@RE4-;0I{{sD`?^eCw`aqT>TSi#=Te9?exX9F- zbHAi1K(u_*rE0U;o#C)8O|){-6IDhxTtOuB=Zk8ma{x zG28zQx+F_CVYT5B!PRKE7`PrVTohaj3>U!=mobD4_bLq+hMj7-Fl>S0!mxu47l!R) zxCpq?E@D_02JUP)F>r+8!oWd>3j{J5A)qP%fcQ`p5wW*1#v1*XCsC|F+G zr_(0aswoUG6>$&qx>ikN4P83i!k_&+uI)%utcTxglvjcZnb|YVeIyBnp$Vo*^qYzJ!eUzmU}Ieanblx^|!uri8$f)OkbIubbjXQX*R zdQYPx!O&Kjl{>4@6LjHjv!Q8XR9aP!Py(sH7dqCqC{h@XpBP)3g|+pQ7{w9_hZ!qy ztiUT5=qhuoKqrMuD4(8|NM@;o^D}iNKE)UPq}Z_^!k?=_*sI)NF{x2z0{y+LCc%tlIbrat%kAu^A z#*0Dqr1Pl=>KY7o7+W_A=jh;@8RMyu(w@W&c4sveb1SgpH*WQJ!SGp)<0@XpB~mzW zSZydo#^dh9+@^WrFpRNwhm)G1fuR%DQw-hG@Cm<$)AlK5QtAZt2z`w9sfBgzFvh`#Mu~To z97Bb~S`*;!R+;f_;nOcwGKe(0(s|$AI@p`QWTmpK4nAmGd_g#O9ZbZz(3IM)GMK5R1O`!OC00&&S7L>kneVEUm>mdXp9$Z$9NUc_ z98C-DG%(P@C=SX-gxPHhh;fkxdZnuvl#aVeO(SOb-PV#i7-ZW%;vz~wr%VciAF`Fg zyGvn;7Hx@#rq@>1CeUv1FsYGv$6XB)BOlTJ-^MlsW_i{4+hjg(V@!BT&aOmMcB+AHS58N=dAN1NV@UfRPancMaWN)KA?p@SaowCple?wohp>6h_Q%K}VRB-Pcy(^N9q|N9O&)_MN@INcj>}VBQ<=5z}%_SSMG)i z*$Wz2TOR}(vZ4AJ{$L&oRnbuKusBo^lrp;tCkgFvcu3YNjeN2JFlo@=}DR0`bqi{ffbJeH!^nG$qkP3+60%(To*7+B*Wi@8)z?UB+m ztL<_!mDAEw({R|urxjFA&xR$QyJ5{#&d5$pF&-O7T)XS5cQv!*>0)ZnjJuwo%g)Y7 z_eGG-XeQo=xCV-(E!Js__JlzmQ#Lm~h|#ROAvKX?z-I~(xYGs(iXH2`8UF3Dq>FB9(08vv(1@9SawfL z8N}sgor4TL0}~9kbJ*lC4Z(c~b!n3|$Hz;5*J=ya=h zheQ{w-QXGxB#pw4I>GQ14^wTz=EnDAu%G~I2$)z%_ZTA0@(po#1wSR?#I+UQGng+!oe8TE@EG1!Hx<4)IN@ncd{1h);dX62%;|f2T^0#!q9Q=kTcC&41Ih$2-fQKBRQ1V};zKnh?HX-n7FN_Hg|mFFak6Wd2lvEyi+ zI8Jfajs=-cHr;lLH_66vS<6mw;Aeu3?Cf-+Npcm4-)&qsR;;9po-6d{W7W*2P2A@JpG#_eL zn&Zi#sG}G1f&Fne3R1{tb>3yRCY?2y?ReoFM9^YOdm`VwIFl#^6*Cp+{^N0zNvy)% zWW1k8QuK8+8a1mqb6b}`5KohpE)kM%w!-sbiNOIIWmUsO7_Pnhq*vyGSw9NkNpdXN zw|ditJ|0*`iS_U^*pyBgB|dZ+P0AeTT@0RgB%3d*a`QwyJ1T1hvIeLnR(`|l0VE0mM!%NF6Ie*WYOuNnyn>>~j}Z5oh^*fB z+~V0F0gy8RU+{$=GxL&~d~Z1L;A^g{iuu{>V(KJaFR@BWuUSSnWy|F`(g|QkvQ6st zTOF2X#2x>u5RXeYvv=(_RY#|}mRRP*z}Vo#h{+auY@Vq)Iy(cG8XFU9)UV;HOE3g7 zW9sMLAUQcaaZxi(KkpAR-q3EWR9AMGqNB5|=ydg0?{&#ba5qU?))Z2phOkMgk@U)y zmR2F5j15Yf)T3Q9Oz>4*Si?7q4D8`dEDu%8FqKmR)kMGz)+qpHWQ##OyV?5yXJ5v{MeKiehAvNJ_Y#m}NN zn4Nr@U~YB6Mbk5Md(>v2=1F?nLs<-o=dttKo7W^_!DDAni!5ks8C7|7(C*0=pI5gqwtF+JT^x85>g1*17bGJv7#8Z!=!_+6j zu~>W@=A+6^3(Cg#d$z0FFEPtnxRKnNMJVi9mV6Xg8r5oSso7mEt#i`>!>RY?kq;7$9f8e0 zUilET5moopb{Cf!!+K;JHes7DqW=f|hay4T(!HRiwLO+b$ug9lsPt`dEbpd^Xua0Q zbw{hC&f96G%qcntzs7VDy=22S%2GZL339!mP|O$0n2DuuPtU^QbB+*;dNtb>5KA7aUkqOj(C&As}B<^@aiM39lP;w%?ZNK z&3)7rr}{qgh}#%l`DAI*6@yy#=ht5Sy-a1{)sH<|El>TzwMX0?cVw|e#@%;kW!rGu zm%lvs6Z2l!`0H-!yN!>6tCe`?iQ3fOSN`z2`)DHkS)e~}d2ZgL?v;7RUGVDFpnTgL zmHv>M`i-v>1${6KUi~`&K$aYD{Zi@qME?M->K}Cfa@g#Y>&)irf>~3jKBY{m55X2P z^Gp1EL~90PAsnW2e&>8(t|q^7ckJu?!p*6t-2#V|EqtA`pr?FnT~~fvQNAAYU2D^9I&;|cB^cU0VoB@MC7Qni>r0< zDCQJayp-r#ZGJGN>X0*nv*vgeO4rdGhfdI`2>0@BT;T#%66U(ZnGG&>Ne$V_`MH!{ z=i)(C+vMo#J}&eujAt&N6M~oE#q2$+v%ra2`}gtK=9@HzI8V~EcW?t61j}vo#Z4?f z^(t%KX5(2z?M;c9ItCAc%rpY?7r@d11f)^;uK3504Hp;JXhiOdCop}U;2ZSWyVMKd zb&Yygsj97Q3@~eHxw2m7{*f$)d%z%)XeoJ1Z|H?VQ*oAofHK-U7v0-|jgN4_pL^Y1 zL3Wp@dlvtKQ9k?ck6OKmUub zyN*NkCAdBSo$8o7onX_v*Um_B?v15cq+DxEpo>XdBSk#6G$UTBCaerU`b)2)bSK5X zP0$h&R!1T|Iy!=(_{8w^Xx=I$G<}@pJy%=hG8c!# z-T(P@$J&}aJ9;sEM(6RbZx27g$%&RXsjRW{MqA#%6?k;Jx7}I4FH9JPe_a!GBBActCZc#M$zhJpE+X2< z(r>ed1c=dr@IdbyZhklK9hy9WdQ7YJTpy-8nFKY+%jIYd`{%#mTEb%-+wzbuZBo|+ z#qig-wD5Lu7I6YS+zDUg2NP|#er81^c)&d+aDF04o*OS!j%Slu_vH@Y@S` zNfm(%4y10qfc|C<9&6eyDE?}hxSvaiY-*heVC&?XwhCf^R*higgeIqF?gfL6^V4&^ zSfU~itn@0Al#Nesgq0E-;2Gz`>yv>eX))IAvDDZA>ioE$2wYhkB+p<;S5u4~?C>I} zRn+Jl9v�a#vh%##n;@1(&NU9_0PutIOVSvzLgM8-=ZpbK`MBae$(fEF>OqazhY9 zd(qHu3y-dN!*yok1EW#LhCj%K`Rx|np^iU5sZw0sy;lR>68_1`H{6{0m`wZwJGeEn zTeqHc9MW+(Uplq8Z(BJQZtH);byu_QacPs?m~&&n1QL*}C#GrH8Z_S)rX&cFz#x9s zAno>ROzVTbG#)Sy7y~Qa5CoGJP@>KQ?~RePo=7Q-8nqk5 zKMT*$?8lugjg6;8i0kEyI6EXwHChAb2vpDd|1I54AHN-66fYR23pKi%4}{;`{f1i_ zKDy@(*IshO-bVz!I^jmcPjj^`{Bw@;s?311fH|LwdK^hnYqF8ZQv38a_1h7t32ORI ze&jUWACPgOK1EsT81@^6sK^^)1hPW2@C3HI^CL$3B97j4Dsn%}j{5XKJr<|VHlJJ) z7Wcp5mJkbbDq_txdsm@@ojN^uR-Gf(vBzZ*Pg%IpeoWl4smQd`yksh>!KXF;Yjj8@ zOiZq^S$|yK5CJa;(91N1Z1A~oD17yHdJ=nu z_05j(Tl}0?4H7ff5}-ZlPvhC;gjUyX9$XU12|G1*L7<~G??I#Fg8}CK@l(?zw#1=I zMI(Eni!WpHP|0Iz(;kh^2Krmlwn(SXg)iU199wQAA~HM?OPw7Yme?>|V_N8kd==eD*c`_AHGhv(aTC`gc!JRAP_-@f7ct8sa$ zHJpRE#vvSa_MHxhRJrkb`GIxcnExKmkJuaz1&JT8@}8t z5fRy|=h_4_R^n_{E+J5T+dsVFO6X7|)=ZBq@Uw9$!u2=YB0??4!t0#PttNxPX)AmU|F0HhTL>0wA=s~`v?kI%L{3%~Yr-aV z+MumhqShhNeYbaQ>Gv%tw|uT~hozb-5mm1vEOH2}*eL8xotLNunB2lo{nHz6^@h^} z=WZ~JhJb}`+*=B)588u3QzUBMf_SDLrx(8dzus_nRC8Lx#DJFG2-Xv8TY#+WS*4_r z7G|MwG<2WhK=Cf5B24jce3tKyR6=omA|e~(-R4i!kPIc9%}uR__wF;EurRWe>GmPW zDsLlhYgTRU`~TB*w{|-O_%-4C#-@cV`Of%t z*U^`Vyv8ET;hAoN^aQF%v_k1YVud-z!#mw|a1norT?)&=byn9z5;Y4y zv^AIOD}&T@=wi2OSZD2Qm=VEf&1Vk?q;Gh%@8s?@&n{M28iQ-&v%=w19~c}N#iw4c z{H{bmoCPz{NNPh6oH%IKL=zIzK|lyA^w!H*>@VR{&>CtzzcWco?%EY3Pf}b0jK*~_ zV8#}eEgHKwNSvAozn#49T3M(c!^7u&anL<;py;u;SU=@4_ZmIbjaC$$YpXU2H3lxDTAwj&%!Uw2)DNjaU3 z*1J$?Od~PHX>&X`IeY=3`SO?r%ZgAMTsn&UjO2#H@$3!Hzh5s#3e^7KUEcezj@%!9 zEOXth0l8UA>;kGeY2&JUlD5V*8|TF`#ETB$auNC3S1$-sIJCphfeVDfi`ZxMOowFoq4FOF$U-JMlxL;ML--1f0aAkr;sj;Ly4BoBX^@O8FTDSI%95~ zS&3_%u{hp=VIMhv^O;!0-Idx9AJLNyPDhl|%;bAWDlKCE%t zH3wzt)cD91zDnah3Fz+$!fGOxvMYR~47s-e7tR$M;9IB1wiNEHTz7Mio3dPg*A+ZV z7VfJLTuy^RB+ib8+nea_YLKzm3?G^y(%KTpwyUM8mq1h?oXudc z#E7~w-FdrPG}oI>h;|>Di;W)X~x;(AH_qk1s_GN1JEU77IF z=IgGfC*et3lyw*@f_EjDi&;IsFrFF-|B-_2;hYwxTM4#?D6D3x_MPERb9L_BE zh`WI^8hpJBVOW+@b^J=PsXHFPxiw(Jsj41GNVL;L0|Fbjtz-ak*=?9)#mJZ5wqLz;OPVh688za2k@Bp=$o#jG-qrGGKMFQxypCwo#6-O@NS%q-u%)Hd&TH_ zL|ki2vpEmc5l0+{C)HRYs*xoIs7|`eK*Evp~5kJ%7u?69_1&m}hL3q8< zqNp1`IU*SqFHCln_7btvS}Hg7AP_ec8`|^bN=vD+*wR`8V7#fhSgcfvv-1S!WV14{ z7qbL#7n_LWZfHROZ>uylBKRX{w^k6zi^XyU!Mo5{Lc%X}G!O$$+4gPK9MM38`N%}y zTrT7*gox*}&4d7z3ay1~8IivcOFnn>Jb^^zhHOJ?xl+tx(9bt^V#DVV^n~J;0vC(< zM~af~OZj4BrGyh8$DyUEMI{I`H!UFxVhJ9Aa<-IjE51@5a=}-LE9#nCHKCp?uBkN$ z_5bVt+dv_Pw6-dq*w{y)ZxmJ#{sd7&bE|H3-==6}m&D_`yNHoF5Rb3n)TY$>czo^Z z=p1Eky&{n`>u|}<2sm=_O$6|W3pVr#2pB7qC$PeQVU?xjYT&F zKIsGWzH$)TqYxw}=f52U73c9gXGB8L1kW#bbE8Kutki>}TwfpU*R&!Yc@144-a-W{>{CK{ve-V?V$P%ugq zT;)GtdwBVk7u!GCox(|jv~aHMURJSAmxDAh%jZuMG*fTv!cnJX$SA8duGVj| zg>6UpfE?Szq@g0V?%@{T1%L>kh)EdC)#$7sgmI_fCjuMd|Sv<=Y&# zYHyPDwLdi@QYUlHZ_A>U#khbApL*mK*WPX$vG_XINBgfBk88#1>}pG$ZOMh zwfdoTcarR)@l&cx!q(9lo2~dY#VoClq||5K#7be)9UHb-ZGAM|YSL7HIQy>G+_HXc zm||mfO3t=MybS@{qfFZ_=Ox&_LpD!q_9BPeXqIBA#G+9#XL#Lkh&)dxzEI18%V_6ivuI0-Yccq zy%BL@#7`p?eIy<{F`}H#Mfm$-iI!#a*38ENNws1r>`*ZncHaM*>*%)`F{Gx=N4%=b zPrH$n&S-jQppG~%4XZ;Ipy$wqdc{ILv_D+*z-w+v__G|ln-D4`j2i7X`do~TaOu(4 zWW#0i8YEiH-&Q2ifr|`P)Jfcv;V;rQ@QRXHi*9P)i6k>VS=X?4(QTK8W$Q9Y*RGVA8Ild<>Jo=hj zG$%o5qT&*a>iVPTtoo-nhwuIZ?Ro?a%$y{udWSgRJ>-;*jQa5uZEZ|Q3$m{w#+6fz zz*ELvHfm|Q4`VTr_A@+^dkFWcf6br$-fQke8_6vQY!Iv7az=B%E5)H2e)kVvQzWQ{ zPBZNmV!_lvY0~@5<(}KF(&td@L~!+yT4v&-p4bPu42xW>fpODa^^yj)YSMB#Y{Ygm z+lEg?nTtjx+ei=?*IqNVtTpQ`7_kPz&OajZ4LzCEPU|W4^1kp2SLauQfR%t(^>A^^ z3ggf7m|u6#-53|oUQ%gh@qll5+Fi(wI+m%ks7diwejY$36H2{S-3Mvrc^gauq%}_Z zo^|BL4~&f2{OspFN0yt&zAH#imL|zRHC@*hwsg4kzd_!Mu*LI6J-Z*>(l!h87LdUC z@DnS&EL`!YuerH(Bb26MA)MsWN>ZAM#v!_2TC}PeOAvf-gd@_%zl_;3{MeUZSyi;^ zdMuJUp_Y+J>HLkJ>Im{=B_h5eAR`PDL_)X;+vp(TVwBEi6S|b9Q37PP zDfd93)Yw`fnx&BAp=@&#h02RdjfF+n$cdJzlo79s50zVq%g>d{n90kz=7!Psd?nXb z&K5DbmzuDNH^`RWn!`Tcm@6S&(`*EK#o7omE;eiFr&Gi3f32FGOOMSett-C0@QuRJ z{7>e_vY*LzXWkF6;@FJ6hwpfPY~!%wa8id;I-J&FM2E+8IHSX;4r4lu>u^?wb8c#E zF|UOm)+E7GFRO0iv;aF=N4XF`qDFnwSSrGJ3-PK zWMc$pQ*mV~_QdpT+k)c9G_$GB?Aplw6)%06^&)(gV|Vy1j&n8=2_qLlogc7p!%B_M zEf3Ns$yM^T+m&^G;m~@rE1X;T2EjE+OoJGy^!RozHzqmUYC8XlByMe6y)|tv_eVxs ziFO-cDUmTsjCoabOZBd@_lvPFNjRRikKxxDG1NQlrWEj6u`wBc;(TqfEq&|LNwS;G zn5ODaCo;AWdyA*BvqZR}=^L)+!Gh`6W{h2tjNxdtQ|2m6Lwp}Qb;g9=NGR2%J>FHR znhyoIwrzpsN52GIN!4QGZw=qk{0%p6RTODvoT5Wc0=S&M@mOSA*w6VRT6AwC=6B?L z_y;ZDaJ>ZZV=H1wUYHj9!=UI}vk&A38sM-Moo9ViulSg%c{1Jxm(7OjCSnR?hDRCv zg%JT;^YlkPJiTj6GAV&oreb~Y9xRC?n8nNr zV;xipKRlbBY^IAZn&+raE*l8}2+JLGLNx(sg7P_yvu(`ibJVQ0h(sb3`O0f8X8el> z4kHMkh9foRD)`PJ3|rqs4Cl4S8|EPiyLx8djF@6|#$|6Xu4@?Cv=z@A4+pb)EY|RXctX(E;Stf3}^H4(@Tzw%HPheky1gTDRGNS zoFeqWi$?M|f zCHAK61Z4xt!P0Cauv892`!*|7n=9F2++-1JJ?TpX^jh{nulM;#d8&8DVI*KLdsY`f zk|$2S_kgv}?3O6qe-2z_{DI%w`U(hYDSA{hU~wXG2@e6ktcNP>bP7SLMhQm;gq1UK*7I1S;o6pXX8Z)X0OX5` z?p58MATu56&O2lUR=7Lzm>sU(arUE|!uO55?n?J0PRWnvX(6xCNxUf=DJ}pFo1yjA z9&8ENGiTkpoMh%)NtG_|o z{aIs`;%%ph3qfX_;on&&?pv z#mSUM=$R&20_e~SEfrXen7{>&O+o{s4?Ey+A4T$-=%W$ul=Yu}Y{wzx2Yp>Ko?=q4 zm7@8-52j<-XOi}Xt5_Qby|4!!2pLNr4M@GxtLTcl*0UmPeGlzE%>2_-6jAUwP||eX z3{g`PWM%ozxQZr*^hQnBx|AE)t!fN1E0<-DHP_~GOqvZ@l zM-yw1rDv-}4`>Y?*V8yMNT$_9B}}Q*wQK2I;^;;%L?&KLY$*kVNh}Z_RBLy}Q)fp< z!SkUJT0w|0D@n7&@&QbSV)RXVUuE zCpPKH{_&)ABkQBJsTrPF!j9Esk;U=IEU)u}X5NNgG@`gH%$KUUI`464BX%Z}Tv3mc z(L49%?49DZt;Ql(TiTm$tRUCp=4h zEJ%!>AtWQ>6WtC-0J#fQafX>5YYYe-WsXgoVF0OOlUqz&kvfX9eRfP8F4JAu@xIsH zErlrH#zuBmxZ?eTGv*U;V(-^f5B2%fmFcl;r<1h! zbTIf$$;E3IcS(VhtHgK%Pn?Tu%;&Q%Nt@DaxF>DnLqob^wF60KCM_-M8xy#HPEec8 z=k)vUB;-18aj)~_I!#;-ld-2=k8%_T2Pvi=J>}vTZ>T!>E$B7-#AZp3T?cGx9h5p| zZT2qfhEiaY$3&|bSZ2hMP0#bA%nwZ-HTCX5kxSN`H7=`IYo>Vkmf&fZ-xj1Gk4u&% zULk(KlP6kbENruier<`lZwRPgC$fI`UN{y8Y%3LE+L~>75P@{?!_D{vvkt3d{ zp)uc5QtS}QUuQ$5Iag-W)N%uP(fNkf)?AfT=f+ZV4t=e;rLnQ4jG{<(LaDr{Ay+Cj zHr|g1q^Y$zUuh&PsiD{o;!PP>Mv>Z4*Qm9SYX?ZDM9T`5mIcL93tC!pKDV}%MZrX& zEHvU&p=FI^LsZJU3az4NXL+Y(<1Q*V39)u!ITaeYGYyglL6_dn&5&wqm>hpL9qWjhNf4%g4P=4C|Y*79_*FP0};dHz;`+UcP-{&}dzYhOFhyUoN zIv#w+{S`*I?X%Lq8{01Ql{K;I^Qqsc=TriipGwF35Vw2CT`nX^fmzYq7*7q>ZRkCk z8q=64nqMc7GENN-PUsnaLRb)h6(b`L_F$)*EPcsN**i4aU)L)0QnO z+M}sstVxY+#m75Pg{kWYARJ70ojm|zACA#C8);O#tTUkXvE-aEtEq}VNl5UyHyJdD zC^#{UVO({q%a$kIIbo#Ok1at;R##J8dj#S^5RF$BRo$IfmCxU#(ali7OgpkloaLAF zcL5^B;Z^1{+S;omRtL`-hlH{ z>-u6SA>^j|uIxHsu#V^IPj-=nPS5(37km6hvWtF_=3>$18p@u`p>AZm;VL?k7aUbT zsa?}q1MI!7YyngV5r&3wmCIrFJwH+pmemu@o)D=q+0pPIY3tD#j0&31hnB0@IUiXr z;w7X!mKYOGk4B5}zj8CSo?dlp-d1Lvwl9jJr+aQhO%^rUfcs;AZF4$jqH8r0H=Gs5B@ zwVYd17Q8tq5zBTRT~94p0GAjTH>KOkFN}kHGBHd#$z=EnVQp>I86j&{qJg=2Bf!fR zCRMaIa2DHVWm<_IGkMm2?Uauax&J*q=r7Hs6gYF$bay66#6X%zCO}rAa{DdO(LQFG&vdl&?evK7`uv9hRcLdD z_mqzg;9fF`NDUuTYB!V1SO;BDTO3bc=C)6LP>HQ|^uDToO}Ye(&xnd&17P_PxMW?% z!^@AGjIGbfb~eR4dVn=&PuyFm?MHW%A*ml1cSX>As(f7nxlR3{hLA^Sa*%$kBzE>f zRSJgP+7MK*9U~18FHNv>88nqVrrSzmrBFtw$RW)jr!?mXyUsTeOAY8A_G7}ZL0l;m zL1zJ_FNbtOPGz}VZZ1>`n5Y{XfNVkh;Ezq_%MDnPi|s^W2=b)@DonmgY&Y@U&n^4a zXf1xx~EMbSVnM1v&gwoqD<@ zmK+==S08dy_4j$FnohfJ@~GY9Gb2|sx-0cs0}Nf8YiZ zu8NM~{X=c8E0HXPUhC4mM%KxRv(*a-_!_@A$@b(uN1fM+m9V~GTElzZlpSg*p{jyx zP``L~BO114QU?p&^O83wHrAV}ao?$Yqw0?)_1mJ5kAlBOy}V%V7{ zN(G~=f5jjn12@)HRYru~j2r?W%2-5w*&$*UOn_9eLp*o`tk$|<9ggBt0AxwkRgneX zD{^_}f~i7tghQi9+32BOPy>9zWc`zXW}YMua(d$LiDAse&gNf2gl4pEQXA{0t6B)9 zs(vu;Qyz7`^373&rn7sMMrq%`^S7-4Z3q!i!}CyO*}D3A zrh=Cg=4<(3))>>n&D^A$dm}Ae=VyFIpiZA4r$FnU&JU29;RSE~S}k-kvoTn0vswHm z4X4(AVm7I-e)fB=51rt-?r81P<?bG@0Xt}HEtG2bZ z+!L9QbnjLnzf8}%y$b)2Xsi?fG=@xoH_bl53#;AmKHTtSo@0T;^l0)f|A}viW6(7e59g5??jLhp~O--AE7d2OjO5SIKsfLBo+%d60(fmA#J-=?jziDC8t@OkVn|VAvS)J6| z?cJEId5TbJUL8TR>j7|N^bbZRZ@pEoXj^n|T8lX}Gha;UO*s8LGC(|6hXn9I05PHK z4Oq!(pcs{}64F6uMd+70&62-ZF&!Tq>uq45r37r$g3Wg|x*^2~(ZnW?xl zwX&~NkHuJ3)ROct)`2L?lsPsoy23hZ|3nnTx`7{0jr19vGx9Elf6k2=sgZP?eVXMr zV&>CJgaE@o5$Vc_R^``>^styR{wL6WRBAeHN~GvgQoLByIfrNHKDw7>Celv3K%R(1 zG@CZ{>=-?X1Hg|e##;PF7sj|q_Q){kIulhDn3-9DJCYQHh|EZSJS$763ONwy^{-DJ zQ0%{&;58~vlNpOwlbo*`j&LaZ7v0DT3R2R@EP-~5@_@0F?uu6pfFVMdRKe7RL8S=U zE8|AZ9!`>bKF}^89!QTWq2H>o&Po8-q9S0m@DJnXUz-3o)FybWfOP^}1c(ocWlVP&<4npF*?TjY%V$Wn)C0*}F`cgF@~Lb-l}V=3sZ=VR zZOBxf@Bf`hSqL#CrnUxstN*QF=Z)VhdU-}SAskq!7)76m zo?eCCPux%>%y*08$5Nrwb~bUToAva2ti`N)y=W+H`DA52(UAWt5Hm=@TzzhnY{~0x zio!(3KZWXdBmNQJKSGEKvMI-#A_uYmK~BCUEP^7b=!f$4-V`9`D@mEsp!Q`7ch9~p zE8t}BNYX2+@zm&u_QOEI=`AwuTl%UkWKW)DkB;dG2$lfwU!xcG2oUUl7k4nz^rqLy z@^+Ii{9k*Zr;Tw{y~#VS+i&94_C2^#>p+dFc>E@Z)| z}Q?>7y=JC;^i*G_Yw%S_LvZmVU@|(RM=vej9Imn_gpe~m1vh~fbh5C2{ zkb(SE?L|1N#leLfiRfTt#+Dmu)>f~c^a}SsXuU0y13pjC$9nM4P1qmyzMEk`Jathr zF}uS;UR909sbTG&GkO^$A8Xw!O zC7>CDHHkPD{eE-GRutHxMn1$8xRJCZP^G%Jc>!DEu+kWgoJ#fu!6naPXiROFR=M-0 zoY4Q=?!4L1r%R18^a-EZCP;ThqDa)DW|yq1Mk;wFQjDziTTCzNZNcQdvTb!^qLM2{ z%8}jP>>H>E*2`e7ue`5aDc}B~doQ4uaZ20R zw{AdJVb~3`H*Z}%^K%1@ma-HgHl))^*0?0kww1thJ&X=|R~(FR!ra}A)Qu~Ua~ zs-zn6EJnWqSPYG<{gh#mFPe2RhuILhc}4_(u?k~^&EXj-U=JcxU+9o+O+@79 zb4}n(774#69Tq(ateQrgCaqxFHv@~00|k`(a-}U_ZW3fovEjL+e;BDe@4p5A$k*f_ z*@#nQKAgK^O3Zw?f4R__UR^f`Av(?%A8VUw7UBu6EgUszNvAtVqGs8gkMNkCdmxqR zYw&>w_UIySFY>RMcf)4nYpIc_!m^{1cM?qGtw+(VewmQiX)n58OIfCnuV{tYk~n8Y zYq)*8wY{XHp|=MQ+^{_PCsQ-6Ph8^ly$kns)QwPF(fd}+Fhu$1@J2?)DF6G)41<&&LUgXh z-LzRMs)y)DZ=3QD0X*;RQ_<}XZ={NTvA2k~RPnnWX?n9Kh0jwMLfvQ;J;y#Slap0% zx#ALCK$NeyUPUEV*G*W_?{%_c`J#``&~xv^b}uYMFMD>m`|6CpmB5 z^1rG8U(U30`KLEWmagcD?wPpAdfPpoHYLe7KU%kY`A65!w0%X--#XI(7F~-#5v%4D zR-LCkr9$MT*3_ah$++Gq7L_LmPkVu=B%O>@rZd3BZ&=9ur3=$mGXHz+OiP)+)NC#o zJ%1@)owk_ydjiK5gy{Stx0CHP#Ww0EzXnYW(HYxAcq^K}vC@n6x`P+2zN4V}`bpBg zC6mv86X=+KZj?c(qFm^~1?FeaGfPj&&c;;{^g*vi&7X(f*xivL^*)`J1h>>-p%efUA4vR`G=;V=N_KkXU19wfP7>M^tVUwsG)GH%;NfF*XU&^Th`!98`rb2E>uqLAtWMh!eVIGFJ<MOp34=urivM@* z+Uf9xQ%}1UE3Mg&Zpy$pa1ZW_hS zUmM`YpjiX(F`QRe%e7Gr3R^}@XeGNgMuEf3gHfzf+#J+RLRCE4(Y0ayY>MfaLSa8~ z25P%@l1GjMHaReUh6nfoaENflt*+KEeTI-&2F{GzwQJ)PC`zfkc9yesN&vlfk_!9o zAz3j(iSw_$Eg@Fm-?CDXuBl4;fzL>~Hp=z$fD0&OoIc>!JvZzf{+%h8I)%Bw3LK|EV+4M5?KG?> zpFgxTv($$!Upt{D?Q}%|%Z4Y;O$cxqcPL_nm)ap0ace z?z%O|Mh;@@AQ8a|br4Y)e)zT;mO($s4}?$2k$vsB8kfNHjID@LkJYIM#4M(?isfWd#HxUC~;%mvSi)4fUdHXZ%@Np*v<=M8oha1HG|+w9Do!TZj`pJd6HpIgd zt(t5$cA6QW9oRNx*M>gukI%SfApshBo#NXbUc5vhO4hCi!;f%(1KkaDl6B!CaL%A; z+0(9_rQ-GMi6>*VejCZRC`rJk{NgCmz^G*>;q7F-a4?*y+6u?R>4L>IS?Qya53K*! z#SxKQp?O}@vfWB4I1p4-rDp9Vn+|HOGWGlm$^G(ROE!#$jLwngPY(~!WU(HWg{Vcn zgf(J7^<9-yu)dM)?cO1O?UZ_%@KAlcP6GlUuvv}_gn#_c&$tyJ6A^w-Y_tv1%Ebgj zig+{^HZ$!MYiOO;rLQ~&8Tf3eXgHjWj0Srso;ZU!jJIfj*|=_Wc=(*}%^E<(!bOTW z@O~m0c%3z7Hcr^H(R@K3BVz8F*xJ3MF|yHwjm<;%!MyxHil?8n&RQg*9kSC##ar>5 z7{a#Z=%dw!wT1$A?UY36)x~6zOIHZkBm42%Fz4r)ZM@>Bm~$O%>DqA>UYw&Wx9msb zA_Ce}gMmofT2y1(I1-KE7;0*pKDb3Q@?MIETgI*u`hv;=6-5!O4C$z=yDhMtp#czHIXb zdlh?D8K{KE6|l8vwJ28%<}to!{Q;YTIz9McSiAJB>p5a$sb%qGB5{g=rya(*u!obJ zrl>O;+q*5z2T)uXjxoB{G!raUQ<$FlPov8~HPUbE!ykR(S+_j=8pk>9LWnj3?_Hs( zV<@;!0UdubJbU?BH@BI%cLkwdnO=(WE_W_meT5nz)CsoBjA(O10COd9+IQ@ILHzPS z#Aa5+Ql+>Q*nOhr^_*mjK42Us9^$p6HyJY8>~l)$_O!Mrso_|a2rRJ4*h;T8N0j-54BJ{8!l|d8b;|n2 z^HDXS5of zy?W>Ud2!Y&CTd?B2IQ*bH6@VhO=p#bh>?4qy53vo6zPg1GVENri6Nhura4 zz?0`HjR8;I8t(t8XJL}Q3zx`$aBYCwx!Nr>W*xW?*&<=OmWo6r zu@QEu2^)Q}(kfWCQWHfh1U$8|gSKLs$X+TQk`=2=E>bRcR2!bmVS5w>J`obto10w* z_aV#wtL(51l3GKBo7!llFt?B=Vv3Er3vGA=IB(4XPC+BsrV;Rp=4`3Cp#_1x#J`mW zHsa%ULOy)|M@Z3f`ite>1~K}gL#o22m=FJ z1L#&3(Q)k)V8Y(U@PmJGOgY%Wg<)LBM$S&SGm%8xLoBtXr&hgtVr*vu$!q@ZBT`fd z_e?lOr19K3qa7{ZBfTJg4@iIVuiIc)_a;eg@lf}+%9B?aKf~h^C2H$?X_I2*Y?^IK zkbF8Zq68abr>l)T2EyO_)-l(-k|gDGoVVjZ_V~T*aA|Is9@!FP1CX)9hwkPlgBGSUS#1G2-7M)5L zzwd930WZ}5?PG3!M^PlHuGt^xGd60OYm=pfa-V$HUyKlX)(fwY6hB?@mu zW!7}pI>;tg6t*ec5uxDQ5TKRgueFBGzMH&!WCr%2W=U7yKVhPw`nr}kG^S_)9wlf4 ztB8_mkEEi=MnC-nG15kV?$NB{SsuT?5)S?T!){HL7_A{OPa6!feM1e{BzF0z*4 zjrM{$xY@zv=m`8!3N89T8dL%VG4Xq8K)tozSYmwO6#Gotcn^Ue&l1OHb2DD(_Tr2^ z+pIAQKlWcAcCGWke=Pbgu98LFv|= zmjp|1v$VDr+SQyKQ0rPWIENa={FnDW?3WRBKRBy4<|9 z3;)(af372rP`9^r?HsfOHU6;%ftEDP**ZIuOaMzFEyyT$r}0F47+3+xskXSCjmVy%dqJnNSl2{z(v24-z23nR?}|fdih}UwtZk?^3!H z6gkm}X5Ymuq>uZ>cMDtli~yu%}3eRj;oO*5m?A)vuXFXZ>?PSc`n z%vw|A!$+gifl1GHYqf@s1oZfp44C!cof8+Py>UQ4aGYMM`>i=kEZr=-~8rn z`3m7IbAM)|wN}~VEJqB~NMMMhr^Jj7*w@HDIhb|ndbT!e z0OY!4aGMFNw%|3TD1B6HBC->S{@EFu7n_W_T&a4(3E2btlti-KcAP+1i~6RK>=^MS z$+;cKu$-EG*{uURv2Nyl+(J*)L34kOHS5WrIpSI|GmVah|H5heri`g75;hJW%*4gN zMg0qm#prBLft92*lmx1W?{5#Xb=;8fT zKO)?YsM(l!d}2d1#cvO^&Dx3<#s^{3#9i9j zvfKo#i05OJ7zxXhM_qH(s8c*s9Gk zWUfJ1lA=Ea}@go*g(GPmIT${0_pwU`c&I$)eVYQ zErgj}(%cXSZZX;zC5ANW^0`>M7+E8~E~Gg!IjBPxlw@G$LbH@?cX_P0Xeg&hXFGqz zFG{Op77A=j*Ro8Ku*6FeXKQ)+8{xL*vsfNpyLi+sTOSarVFY%c;SGAG&nZ5cF|vK}sMOQ)yS z?rh)%Xrn1mnDMR+c`Z$YfkVB%m$XeeTv159>VwO84)J^WT9$c9UVzsRwZ<@p#^yJb zI#=FGnrp z=jHIXDZi(h7S62iPO+#blbIQALKVE%26t{UHL0X(wc(VyFVS@d=}-!#v3axgty^ei zx9Pa+Zm`B|r%m6OjakiDk;`ge!7-6PWh{2znhZYxA=U&HO%|f9IIj)Eu`_M8Zmll` zza^(lkVowu?8dHKI5C$&Rp7$=fBC3ezD!$m+Qb$6Jt|r_MrN!JdRM=y{|Kw$Wdq?m zxBRK=3K#w7qi!pz`@n#hw(4rma=gQw0ze)NMx6O}jF=IX-Yu znQjp$M9Rl}1Lkq`JBBHbd)AHycJvsOwZx`6Wwyj}TjO4NH|KjVo>em787Hw_EEbn8i?50Nnc$E|=*8kv8MBesbA<+KXz0x50LGeK zs5NDa^B*Zt5&H=iOMoReBD9wXl5efFHFuS|vds-xsw+(mkGAD*TR>CTVuZL)B>V<& zE{cV25S^tzNT5e)AQ~RSw_;lm;{^tW>ha3k-tB_7g~1n|cZ=>cc|MLA8{>BIi}^kr zchdb0Jjqt~(^*qGwa{-il}KktQq$2155-_5D|;)eY)bZqU%BOoYkt_4FXLSR(TxpG zj0_pk^5`;C`&EgV$j+FhX)hZv;XpV3r}61c28M}l^8$~X!Z8LIT+z;xm9Tl^5x1<2 zg-)`grp{dgpbvkL%Y8|k#-m|w(-HhDCpj)$jJV>hSDIA{xW~Oy7ZA^wreMooOSpaW z5%wE>7ss~n&p5X33IP6v#O%R!#z!B6pf{{5u?49_MzOp$GP~*wU@pSo@c9AQhxqM6 zG@bC%TaLKd3vK-@f;=NRM(s8^ym5^(SBBtVVjrg$h0kw2f_D$ovrsBc{&|RP6SWXf zUAxIjNta^hP%t^AeAD^0?j#%Foj&XHm3@aGKw($%EbW#6kb9np7CE(Rf<${ZkC2$A z9?7{JzXYD$$pgbajmZ60IrTk?pg6% zp^=Z9HP_zIVG~fVJ|>%;c?QLc#us{M@`!`4wM`y)#Gh|uoO!Js5KRJ%=G({tVZdCDD5#wTcp38%MsRgSCdSbh?L+`=S`vD}`R zj`~sULx~7Y#6DmnBCz5`259tTswGG%*Vgpc6KX^Z{xVDaoZ9>wrz*=Sue~)fAB|NmljafEFI32d^{NB8S@yMf=*x@Smxw_h9@21Z%4k zaTOPb8C+Y5^J@hGp-E=UJ-FeA*b!l18*kp7jwDshxc>0BPBTV_BHR54omgAkDqR;H zQ>xQGqRWvur1mcG>X{}nza~=Z-gVfv&?amOjq>p7S`s{uF!tCHl+0&2E&b% zF%-6q9dWmW;~cx#!h}5j)8|cNGcjea%Z_1e#B_5*$YXgQ4-bqV!P=DqL&|ewo4npG zqsGn;QV}q>mvc8~OlOzibkVC%^zPlZ(;g9Rr2GqrpP3n15<(Y*lN>CPx&_Ks#-`3$|ux z91h|O47Z&>;*P?|hybKI(Hxt63Ix^GfP;0yRrzCK-vvelu!%_!9wLq`xjiRXTb9}k>>~B6zC)u>=5u+kUbVp`&WsLdX%T6)AiNFQ zV5?iI=z^AMX&=7_QvwLgT9YVAR;zdHXdX9dlCQ9|X+XmnNq)8x$q=mwlAL8l(i;Y> zs|vCzoC?hRe=m;9dc+iNVh`VKOG&jhJ7rD;)i*3f;!bHIkDC^+YqNE&&-jdYg!Fo+ zgYGS|Fftp_wSxaP4z>y@(vz%~rj2Sv$KrFwy^MzEi~HK*CT6ku_H}r;nF2hmZ@$f? zE<}02Ha}ByGh989wZ%ir+i-$IGM*qd=i^t7xJ6qbR60R(qB~)BK+fbO6Y#N-z$WqB zjTn~(j6%v+2okhj_~ma`aJar-BT zPM8=vO9O2-X5yJiA1AJr-6n1dG%0wgO{WZ`A~bGa&DxYR&$(J7JxFLoR{sWd*PM8O z;e%RERQR2O7Q5w6x5zW8HD+*}gf0qEunqhTl}KwuL6s=}lw!XmeJfZKfnueX@H zbwdU1S2*5b^~bTy9!Vi;7__#H$F3j)ijz&PsHU@Ny+0$I3O~DR()xw7ZUiBIG#O!c zs~h-vl+eC#>L(-y1WmbYJ2vtbjNwS^WL6=>V_!!qM|kgQYeCLO%*R@8+x?XrD|z-0 zpG{^ehIVZE6?Q8uG)WskDrdhFvPb3;QuU+OAn8%T5|kv3oGVs92<0;x_^k~tXo zJ96OVajiw$7Ur`J&Aj1Jy{xgLxq%%CX+H2lAOf?^Iev>)@P1qTRw~`Io==yba~z&` zQ|a;x?w>-kHeR2V`Bd!n7k9Qy_1t;geG!D)t?zmp|6`BB54;tijLo)3q4Cdsv0(Ma zwQFjhT}-bwv&r8ke_HU{0P1Q>ELhXm$L4?bz*e>-h)!>h1shhc)dS*y`(yDMI~8vNQu$=?};Z*36hH> z2Gw|AW!!eT(k<}OxQ4+}_`#>xEiIL5sJH>sq!mi8p!2wx{D)f2rUCjx_OTpg*W3-A_ z-QbB<+s4Apj8KKZ0jOj4se*Ey>(Kpi>>{^hR}I5DQ2z}bplXc*>;ga$-a%L0U%JC^ z;Oz#upc8`DupeFVTm&!Ub7oZi+8KFg`u!N&wD>5=0evx79x}8I4bh^GbS82s_zDSF zte!q=)I-5BnCUR~e}8X&OrT8sC5*7Q+5%E&{UvPmJ_a1zMO!d@ z4M$n`MMaqF^F5_XTOobR9LEOV6C?Je)YErgJSON8)tOpi1~vcg+YDtxoiVq|!)&O? zC2$KLyC7xUmzo<(2!=-Qp!IDreA=vQ{@yM^F@Yc87nO8Dd}yiyIJJHRnVjzTWG3jE z4&r~#Uoth{s%nhoZvYC`zc2%Rq54{dl^Tu~K19=w=X+H>VNS)8FtxyKRS%e|qdXmR16o#+W zoK}f`pQW~#c*^-3OC3#Rz;_~wT@z!==^>J7PT>%+7WBj&kWc>naiX?CfwW3?$Fs;z zIL#yCQpGJUb+*1GyA@ha&SbR7xv!yfCUS>5BNxjWuCA2HdWUbq6i>i`7C~#mU2K&- zEX=S;phK+QH5U9NY(dpA&ZJ|>*DvX;$qNL`pS3-st?*{%ziuHXW>WCTo;Co-N zB&(sK7NbvMx5PS}hT6C@EzQ7+E+!kyFbDNzhb_fyaSt*_Q*WXnkzupo!rVk-Q}V`~ zk0Be4pNd*=n!P5mT0}&?07^47LhFZ(21cl5Vs&yy9+EVpp>@Jrun?o?+xZG%2`Z+^ zezhkP!2Ao**6OG-H72LOVp|OMUMJN%;{axlffr^|K;+P5C?59QYKCZZnrE`Ni^t5h zd&PhdR8qMS2w2Ot#`-~hr@OGpnT{=@QEC{~(^cQ?w8*hGviNE&4}6lUKv#0_Ky ziYpqogma(FHB65rf;R!J-$bAR(gO7qkunfWh{IL#xFQ6=3v9?uee&|V-GO8n^gZtu zJip}C7aWHd-PDp-|1bBaQ~3pn4`pV}TJ!bNZ>IN#4R3poTkBSqR!tq?>^B1e^1nB} z=x46}-b2Nn@T>dpcCF#pzyCdMZ#s2XP$R4Sn^$AMwWc@h`|l@QGCcU+-*xliZ4*;Z z{)hJvL>-U+($&Z3WO}X^KfgW`{+Ivw9{2rWCB%GiwfxEP^3+q$yvO|(*ku23b@kEe z!l`rbc#nHLh~0Jd#mT+B;pt!aR=lCJJWPykVS{@-ewqxNNxknxP}>_vFxejd+|zAT z)&Edq5UzOdBW_K+{lnpN&%ej*2p|93w{fTM9gh~D|7R|6_yHY$P=_DV;i?Wl?56(t z`S-fyOR>%{(f1?ntFgAJ*ZB8GVpDHh^CK>ojtyfz{1NxAAXWSM*5^C7{D|Z5qdL6L zO?7U0zx#{xZcgg?F!izbyY*AsIsRi(9ri%D=@ajFJD>joM-Cs*A#_t;_{2-Dd2RT@ zH(zo=x^LyiwQKvUPHeHvV$_RJ;#sO>63_sgI_{Q|nW? zaB=yA4&C-xtYg-f!guiFgYWsytxZ>7eP-|5uGT7ZzJ;1k0 zU6bzl!1sMQUJA=U@#pbi>Z#F}-H*ktzVy*yN{qkk#)91TSrcK5Z`2VQp%US0i(Uz;EHJ@&({7;jk>Rt8_@**-osAAYR; zEb4x9_}w$T%o^*1bd=!OYz3a)!Ju1)O+>O16Ru7ml&6o z;oviW;(D$=a^MQvT^;xDIK2OLSGJ+J`rNM{ZHWhW+1oA}D+pJec-eg(oj<>!sM$&;0#|dctMAb$$2(<576-+{^B{bN`9IkMj33{QWF{ALH-m`1?42KhNJU z@b`=S{Stql;P03D`_KG+(!Fx-Q|{`D?Ao=P*KS(5ZsW$j=Rf%VPr0cNzW-O;iQkWH z3KQo(?S7^7-Q1t&zLfjD+<(b^D)+J6Pfq<7S3e$`di%tu-MVzVkPd(O%BS7mlv1^+ zy>3=h9LB@xZQ(Dx<EvR%Z{uy@ z2g*z1hr-R@SsULKe&F2KIe+e@@5ajEJ6^iiEt~4y`KtRwOsK7g+|<(BUUetaQy>2E zA9F`y&wumqtB%8GbhxI&XLa~h9ez!R|DwaM>+l;o{H6}SrNeLQ@H;yEt`48m;qy9t zL5JVd;rDg;12^@}!++@JypUd%UNx)q^QDth#jpOM`$|eYY|qrHzxYG<`}YUAJ+bvu ziT*FTzldG^%8UP_IsE6HUvy7Ry=~VQ-S5Qdnpfsp*Bqp4UYYa!L$`j>armz~{E-fS ztizwUsfTX;Z|1yxQcWbW&HJ1*+p6x)>Fjq$2s)+b=|nhY|7R>GwMWt~Wc>I*#G; zMb}-i7*Bw!rX^mxLahs{TjwU^Scw zUs`tE^$@6iYT(QTc9KVqEG}Jo@0+(x!0S_QU+-Rr6fMQY@W^b-#e}vaG<8RUr@H6< z7>7mzJPG#DHERl+-d!dxMG3`>@OTnw3Zx;Q-D- zcioH&C-IQ(?l!5kH+l_Q~Pnt^?2rQy6 z+1_tQ_|Tf`ZV!0*+U838{e@qiHxO?P-wg!!U#_$)G*7sz;^`D>p&q|iW*E5Q2a~7#zR~7>tb}F?3ixK&pk15f}@o<;5nAoy0J$ zThBC^tQ|L=QYRfxoUwsWZ){I9lbK8>)9KqzqPNPUzX_cG-Y?HV1cs8&fUV zTk z@z5QROJG7q=zDfpIqQ8L1KprDVJ|E$qjGQYduyfwEcl0fnmX1_1v^;=PlYfOg(}lJ z)+>&~Y^iE}YfHmj;3F{vSl&S-c>N7E!egqf2UYX#`W5DK9;*?*vcE@?NS*+kqfODO zkum)1%0oL9=fQa^tAn8i*@{$f)zeANi!ZFFk+pt|(;U<~zH4PkYGmt*yEjZ>-=%~& zb0cSR00F71$_0MzGU=|hVqDF?#wKXZaD^4~f*83Kvmn-f(+~-Jk|kc8P1W+&Und<* z3erDvjm+1cgs|)WX_|&xm6-pHo-klpxo^;2z=KKl9KG+BDCncZV=BK^tG|r*8CUCd zZRPsI3yQC86xTfd4R5+ozW37KO=ow%swn3Qi{grPb40Ur71{yonNgiVBuTG9!2yKm z73h7@{K0AZ8WYgN0!~~gK&1b?H0o`SDTZ`mI)h^IwarsO14J&yFt2*tUTJSa<(79a z>S8swp3iFT9RdP`HbOhGzIf#hA~1>!V^F;3DD9+J=$Q&yJB&%+zHZ=|OsrfF*ntY5 zNhYdC+>2?60&7=Rdx}$^nqoY_s)(rUT|nb#&7NYoJG(QSgwNGOplX3wnlN`TcWz1)8nbeEc>LHLuVtbh^cbFH zYgacC#cwT5(@8++?E5j!jNepz?cS-N9rY7yri9p`?q{pbl5fz1)-YeUnYVRYpD1qG zP2O&)7o~zX?^w4_IJ1aSp*id{=AtJG{;@nS91sfN!&ecm_>i$OT z8d9y%{l~1&tFZ0Na5COfochcZDw81pWMs8>)#lgLo8-VJdE+t!SmF%jHMr86(+Zgq z@CW*G+$4yvuTx9av+cGhtjIZ9QKf2@yCDV?%abrmN z;^l8V|C3k0a{2Um-xFo4vJKf>x&`9{{52D}F6t0;M<@^t9(*0Cns(e7xu$GgBTftK z54FuK;7z8R6S+H2CEC#PX|mJ85oR$Jn}hIY~Eq+64jF3?PvK`?@3GOKE?Tb53t z9|$l?N{7iO_x)q=5{IGj8;T~^s zkFG9#|Cz~PT?GGlxD@~8!QuG2aD|Bk+ z>D%hBaV(1BDLk z=i)rYQ3J=!!NLpl5blY-V*L5Z;QFBOwf5p|?9E{B`r;q4w+jUENZ~>kQDxOMVwKUD z*zm>*mj*c8KCb$_r82Mw4p0P5jnFcr`Ua6VC^P$M6RwvPjr6A9pbYHx$_?5Gh;GwW?A_Ag&?o#rW(oN?FC!5?q*l4hW z;TPq5M3?wf@D7e^7nLTU9x$*UpxiFpt#L(Hd(P7<{J4h~@a$$bU&_1FCtP8ZD|EZh zcDqw+-NP>CPU(}=+2j@yQS^q=nJ-TUgOPaD#=hTLU;IXqbl#hcn#uW+K{2ufKrwfK znE!e^`-iI{Wa8zVQX-vnb~$Up?5FG9vwPfQ^IWgn>>fSl3VYZq1nv$VT<9$2es?n1 z9H%UsAZ#$L+W=mij$psFwM? z;}O@%o^mrg63h1j^emjOs_a|Scr%vGrpLB*BvZ4t1HQZ|o86nO&onmNn8|zs-)UW{ zE7LB$((LIOx6=F^x`K!XklcmPLdoy@Ho~o(NW}CBZvFe(*D|LV8&ERh;!zj;HBr?&b zZ~LG)_{!|FE4!kxC-O{zOU3`{4;IE!*X#|;yNc^RbvdXnEm*&TUq$2iH9YLzJ#Wjah z|3o4RQl+`$(EcNFIDZ=1#ZP*;G808|skx)iuOJwTTG+m3#o5b(aDMJ{P5QY99cF&E zA~wm-M)1u1bpJmSSW)9r3RmT-OK*Md3Z^=Dvefg%E5W<2_}s#~gSrVzbW?}TrTY`u zdJem$j?qJ-z|2JR66ef5&fr0+WOpaKP&m;Y$*Q)=wRA{Zcp$~WDh>`GRSX^M9n6m_ zXgj;mob`_>@O2#YGW=K26lH)C(t|E_=JhjI0yZCL^Y7aHT$^8L^B+O!^)vq&-2OrQ zLPfeNdZFTHPh)dgF!A{C4`gz|x&QlnDk`FX2qkRSGCc7@$kYdsPJHj$?KFRTHGO(w z_7F?( zO1cZdA^WUZq`hK-#n-KX#My#h_XtuH{pe`Z*S%5wMCad!$$n~>WWORN+oj7Ux4EcW z&NhfF(+`Pe8%Z88u%B@UaGYee!C4e>wlSlOA-r*1CrFP@OA1n7BJ#r_6g4`Fi|J6F zk*$J_+4cxqm*_>j8KF3wM|RTUtsL^oLfp&Rvpz<$2XxVtkN9O}2SC5WIu$)SG%>7* zq=H0rLev2V(ut}=I0vERVE-x@RQoXjIdzs1>q80}qvR0IAhnh*eBq;4vhdjGJL*=3ScS{Ur0d24m%V>QK3X1PT^_}Qp_XCl-M zajC`1b*#tmPJKfpt>YGRpy*Lqa2 z3|eV9&QE*nk3ybgUI|_KzdV~J7F*dB3QOFAXgP_951Xf7}+-Ei|?V;Gr*Ui8VI=lhDzSsuruJxcuDOIy& z>f&NaK!C#s_~##)t%_S~^yQ-=)WS+|_WmMFuk^Bdw?4LrivunqLM=hE_>TavEdynJ znAIR)2Mm741lMwPb0As)>u`La-wqOEU>6{G86Rf;s&p|3qT#T3?+xX>@fheq3fK+- z_!PQm_+g4CKxS021_~~Yu#mSwhdpo%qk?W%4r+e|K*R$?Rc$~;;S>E`EE5MYWTI0( z4Y_cgp(Tjr$xMnBU1z0PM1;lHl?fJ@`qk!k-y)mH>%P{7EFZNQzOpc*egOt(Bab_8p0}|{hkP->awzHoui$Z>steD zpkev4c#D)M^@=9SrJUpY5U&68DepGWoASG?zunMA%58qRfZ!HmEm$K!IpuU288+-Z z{vznmfxJHZ3Iu-)SXM}m{1G335xy>V1h{9hG=4_H_WXcAw!OVRk`=rv^?c<=tQCvL zV17XLmuOe@@R?*Sx39i>&Mn@aWzSq-kYY<|(gh>pxK_ywUaNa7^@||!=_4yd{R%US zxv$N`h1y#AD6g)GCu8-o>*mztu=`$Z-Dxo{Uu%l{0q8>X9dh0JjIy-H=h78m*)}_r zQaM-3L9BmPdM0FwFL%d2g}vZr_~1bo;*T-x8Wo9;a|695D|5@Kz8+TzZQ6?nDSs)? z0TLGHfH*(|BPzG>2dQZiWiN-HxGfqNnn&XY9*5V#6;`;oc!G7#r(gsI>^y*6-N7T^ zyY-z6hY=_?AsHb7VHc8)g-gBcRssF=sqq0>>J{?O+Qp%$grmbcev?4=mc@E-BPKi) zhH5jvi5{GBFqMVaB#yx*UDXoTV{>Emwe_{}2Kdng zNw%zRmj;l(d(N$M;@5m6)c^U0QEHQaqXj}o49C+v0MP{XAcQN1&;Dde7*YrVT(yS% zp)I{F!Xo>!3EbPbt*`o+bsO`n++dccMNar_k*nL`D(5A^6(|vJqNRm;KPuUs3{t$V zlJ1>#Cs4G(Yj)MpI;oI#b@$;9q1z0r%I;_?0sJTdZC?`Z6A(Oef(jo22k8`f(1B*cR`#8pv5MH(oR z5a}O$g0;2CT>y2;*2j?w6z(ZQB&Q$vx<(gkqZOauUr`nLF7~m)>rL^}%r*Joy+|o` K_Lsqb&-x#?O&=)$ diff --git a/data/en.wikipedia.org/wiki/A_History_of_Vector_Analysis-0.md b/data/en.wikipedia.org/wiki/A_History_of_Vector_Analysis-0.md new file mode 100644 index 000000000..cab08fde4 --- /dev/null +++ b/data/en.wikipedia.org/wiki/A_History_of_Vector_Analysis-0.md @@ -0,0 +1,48 @@ +--- +title: "A History of Vector Analysis" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/A_History_of_Vector_Analysis" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:13.416934+00:00" +instance: "kb-cron" +--- + +A History of Vector Analysis (1967) is a book on the history of vector analysis by Michael J. Crowe, originally published by the University of Notre Dame Press. +As a scholarly treatment of a reformation in technical communication, the text is a contribution to the history of science. In 2002, Crowe gave a talk summarizing the book, including an entertaining introduction in which he covered its publication history and related the award of a Jean Scott prize of $4000. Crowe had entered the book in a competition for "a study on the history of complex and hypercomplex numbers" twenty-five years after his book was first published. + + +== Summary of book == +The book has eight chapters: the first on the origins of vector analysis including Ancient Greek and 16th and 17th century influences; the second on the 19th century William Rowan Hamilton and quaternions; the third on other 19th and 18th century vectorial systems including equipollence of Giusto Bellavitis and the exterior algebra of Hermann Grassmann. +Chapter four is on the general interest in the 19th century on vectorial systems including analysis of journal publications as well as sections on major figures and their views (e.g., Peter Guthrie Tait as an advocate of Quaternions and James Clerk Maxwell as a critic of Quaternions); the fifth chapter describes the development of the modern system of vector analysis by Josiah Willard Gibbs and Oliver Heaviside. +In chapter six, "Struggle for existence", +Michael J. Crowe delves into the zeitgeist that pruned down quaternion theory into vector analysis on three-dimensional space. He makes clear the ambition of this effort by considering five major texts as well as a couple dozen articles authored by participants in "The Great Vector Debate". These are the books: + +Elementary Treatise on Quaternions (1890) Peter Guthrie Tait +Elements of Vector Analysis (1881,1884) Josiah Willard Gibbs +Electromagnetic Theory (1893,1899,1912) Oliver Heaviside +Utility of Quaternions in Physics (1893) Alexander McAulay +Vector Analysis and Quaternions (1906) Alexander Macfarlane +Twenty of the ancillary articles appeared in Nature; others were in Philosophical Magazine, London or Edinburgh Proceedings of the Royal Society, Physical Review, and Proceedings of the American Association for the Advancement of Science. The authors included Cargill Gilston Knott and a half-dozen other hands. +The "struggle for existence" is a phrase from Charles Darwin’s Origin of Species and Crowe quotes Darwin: "...young and rising naturalists,...will be able to view both sides of the question with impartiality." After 1901 with the Gibbs/Wilson/Yale publication Vector Analysis, the question was decided in favour of the vectorialists with separate dot and cross products. The pragmatic temper of the times set aside the four-dimensional source of vector algebra. +Crowe's chapter seven is a survey of "Twelve major publications in Vector Analysis from 1894 to 1910". Of these twelve, seven are in German, two in Italian, one in Russian, and two in English. Whereas the previous chapter examined a debate in English, the final chapter notes the influence of Heinrich Hertz' results with radio and the rush of German research using vectors. Joseph George Coffin of MIT and Clark University published his Vector Analysis in 1909; it too leaned heavily into applications. Thus Crowe provides a context for Gibbs and Wilson’s famous textbook of 1901. +The eighth chapter is the author's summary and conclusions. The book relies on references in chapter endnotes instead of a bibliography section. Crowe also states that the Bibliography of the Quaternion Association, and its supplements to 1912, already listed all the primary literature for the study. + + +== Summary of reviews == +There were significant reviews given near the time of original publication. Stanley Goldberg wrote "The polemics on both sides make very rich reading, especially when they are spiced with the sarcastic wit of a Heaviside, and the fervent, almost religious railing of a Tait." Morris Kline begins his 1969 review with "Since historical publications on modern developments are rare, this book is welcome." and ends with "the subtitle [,The Evolution of the Idea of a Vectorial System,] is a better description of the contents than the title proper." Then William C. Waterhouse—picking up where Kline's review left off—writes in 1972 "Crowe's book on vector analysis seems a little anemic in comparison, perhaps because its title is misleading. ... [Crowe] does succeed in his goal of tracing the genealogy of the 3-space system, concluding that it was developed out of quaternions by physicists." +Karin Reich wrote that Arnold Sommerfeld's name was missing from the book. As assistant to Felix Klein, Sommerfeld was assigned the project of unifying vector concepts and notations for Klein's encyclopedia. +In 2003 Sandro Caparrini challenged Crowe’s conclusions by noting that "geometrical representations of forces and velocities by means of directed line segments...was already fairly well known by the middle of the eighteenth century" in his essay "Early Theories of Vectors". Caparrini cites several sources, in particular Gaetano Giorgini (1795 — 1874) and his appreciation in an 1830 article by Michel Chasles. Caparrini goes on to indicate that moments of forces and angular velocities were recognized as vectorial entities in the second half of the eighteenth century. + + +== See also == +History of quaternions +Hypercomplex number +Vector space + + +== Notes and references == + + +== External links == +A History of Vector Analysis from Goodreads \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/A_Mathematical_Theory_of_Communication-0.md b/data/en.wikipedia.org/wiki/A_Mathematical_Theory_of_Communication-0.md index d28fda6ae..dc719e84e 100644 --- a/data/en.wikipedia.org/wiki/A_Mathematical_Theory_of_Communication-0.md +++ b/data/en.wikipedia.org/wiki/A_Mathematical_Theory_of_Communication-0.md @@ -4,7 +4,7 @@ chunk: 1/1 source: "https://en.wikipedia.org/wiki/A_Mathematical_Theory_of_Communication" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T08:36:35.522445+00:00" +date_saved: "2026-05-05T08:45:40.516645+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/A_Metric_America-0.md b/data/en.wikipedia.org/wiki/A_Metric_America-0.md new file mode 100644 index 000000000..ee834dcb0 --- /dev/null +++ b/data/en.wikipedia.org/wiki/A_Metric_America-0.md @@ -0,0 +1,22 @@ +--- +title: "A Metric America" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/A_Metric_America" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:50.989387+00:00" +instance: "kb-cron" +--- + +A Metric America: A Decision Whose Time Has Come was a 1971 book by the United States National Bureau of Standards (now the National Institute of Standards and Technology) printed by the Government Printing Office. +In 1968, in the Metric Study Act (Pub. L. 90-472, August 9, 1968, 82 Stat. 693), Congress authorized a three-year study of systems of measurement in the U.S., with particular emphasis on the feasibility of adopting the SI. This detailed U.S. Metric Study was conducted by the Department of Commerce. A 45-member advisory panel consulted with and took testimony from hundreds of consumers, business organizations, labor groups, manufacturers, and state and local officials. +A Metric America: "A Decision Whose Time Has Come" – For Real (NISTIR 4858) was a June 1992 follow-up to this book. + + +== See also == +Metrication in the United States + + +== External links == +A Metric America; A Decision Whose Time Has Come +A Metric America: A Decision Whose Time Has Come - For Real (NISTIR 4858) at the Wayback Machine (archived November 12, 2011) \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/A_New_Era_of_Thought-0.md b/data/en.wikipedia.org/wiki/A_New_Era_of_Thought-0.md new file mode 100644 index 000000000..5210e7ef8 --- /dev/null +++ b/data/en.wikipedia.org/wiki/A_New_Era_of_Thought-0.md @@ -0,0 +1,106 @@ +--- +title: "A New Era of Thought" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/A_New_Era_of_Thought" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:55.623559+00:00" +instance: "kb-cron" +--- + +A New Era of Thought is a non-fiction work written by Charles Howard Hinton, published in 1888 and reprinted in 1900 by Swan Sonnenschein & Co. Ltd., London. A New Era of Thought is about four-dimensional space and its implications on human thinking. The preface was written by Alicia Boole and H. John Falk. They also rewrote Part II which Hinton had sketched. The book has xvi and 230 pages. + + +== Context == +A New Era of Thought is inspired by Plato's allegory of the cave and is influenced by the works of Immanuel Kant, Carl Friedrich Gauss and Nikolai Lobachevsky. It influenced the work of P.D. Ouspensky, particularly his book Tertium Organum where it is frequently quoted; Scientific American writer Martin Gardner, who mentioned this book in some of his articles; and Rudy Rucker's The Fourth Dimension. + + +== Synopsis == +A New Era of Thought consists of two parts. The first part is a collection of philosophical and mathematical essays on the fourth dimension. These essays are somewhat disconnected. They teach the possibility of thinking four-dimensionally and about the religious and philosophical insights thus obtainable. In the second part Hinton develops a system of coloured cubes. These cubes serve as model to get a four-dimensional perception as a basis of four-dimensional thinking. This part describes how to visualize a tesseract by looking at several 3-D cross sections of it. The system of cubic models in A New Era of Thought is a forerunner of the cubic models in Hinton's book The Fourth Dimension. + + +== Contents == +Preface +Table of Contents +Introductory Note to Part I +Part I +Introduction +Chapter I. +Scepticism and Science. +Beginning of Knowledge. +Chapter II. +Apprehension of Nature. +Intelligence. +Study of Arrangement or Shape. +Chapter III. +The Elements of Knowledge. +Chapter IV. +Theory and Practice. +Chapter V. +Knowledge: Self-Elements. +Chapter VI. +Function of Mind. +Space against Metaphysics. +Self-Limitations and its Test. +A Plane World. +Chapter VII. +Self Elements in our Consciousness. +Chapter VIII. +Relation of Lower and Higher Space. +Theory of the Aether. +Chapter IX. +Another View of the Aether. +Material and Aetherial Bodies. +Chapter X. +Higher Space and Higher Being. +Perception and Inspiration. +Chapter IX. +Space the Scientific Basis of Altruism and Religion. +Part II +Chapter I. +Three-space. +Genesis of a Cube. +Appearances of a Cube to a Plane-being. +Chapter II. +Further Appearances of a Cube to a Plane-being. +Chapter III. +Four-space. +Genesis of a Tessaract; its Representation in Three-space. +Chapter IV. +Tessaract moving through Three-space. +Models of the Sections. +Chapter V. +Representation of Three-space by Names and in a Plane. +Chapter VI. +The Means by which a Plane-being would Acquire a Conception of our Figures. +Chapter VII. +Four-space: its Representation in Three-space. +Chapter VIII. +Representation of Four-space by Name. +Study of Tessaracts. +Chapter IX. +Further Study of Tessaracts. +Chapter X. +Cyclical Projections. +Chapter XI. +A Tessaractic Figure and its Projections. +Appendices + +A. 100 Names used for Plane Space. +B. 216 Names used for Cubic Space. +C. 256 Names used for Tessaractic Space. +D. List of Colours, Names and Symbols. +E. A Theorem in Four-Space. +F. Exercises on Shapes of Three Dimensions. +G. Exercises on Shapes of Four Dimensions. +H. Sections of the Tessaract. +K. Drawings of the Cubic Sides and Sections of the Tessaract (Models 1–12) with Colours and Names. + + +== Notes == + + +== External links == +Hinton's writings contains some abridged passages of the first part of A New Era of Thought, from ibiblio. +A New Era of Thought (pdf) from Australian National Library +A New Era of Thought from Google Books. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Extensions_of_First_Order_Logic-0.md b/data/en.wikipedia.org/wiki/Extensions_of_First_Order_Logic-0.md new file mode 100644 index 000000000..396bf4a14 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Extensions_of_First_Order_Logic-0.md @@ -0,0 +1,28 @@ +--- +title: "Extensions of First Order Logic" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Extensions_of_First_Order_Logic" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:44:39.252783+00:00" +instance: "kb-cron" +--- + +Extensions of First Order Logic is a book on mathematical logic. It was written by María Manzano, and published in 1996 by the Cambridge University Press as volume 19 of their book series Cambridge Tracts in Theoretical Computer Science. + + +== Topics == +The book concerns forms of logic that go beyond first-order logic, and in particular (following the work of Leon Henkin) the project of unifying them by translating all of these extensions into a specific form of logic, many-sorted logic. Beyond many-sorted logic, its topics include second-order logic (including its incompleteness and relation with Peano arithmetic), second-order arithmetic, type theory (in relational, functional, and equational forms), modal logic, and dynamic logic. +It is organized into seven chapters. The first concerns second-order logic in its standard form, and it proves several foundational results for this logic. The second chapter introduces the sequent calculus, a method of making sound deductions in second-order logic, and its incompleteness. The third continues the topic of second-order logic, showing how to formulate Peano arithmetic in it, and using Gödel's first incompleteness theorem to provide a second proof of incompleteness of second-order logic. Chapter four formulates a non-standard semantics for second-order logic (from Henkin), in which quantification over relations is limited to only the definable relations. It defines this semantics in terms of "second-order frames" and "general structures", constructions that will be used to formulate second-order concepts within many-sorted logic. In the fifth chapter, the same concepts are used to give a non-standard semantics to type theory. After these chapters on other types of logic, the final two chapters introduce many-sorted logic, prove its soundness, completeness, and compactness, and describe how to translate the other forms of logic into it. + + +== Audience and reception == +Although the book is intended as a textbook for advanced undergraduates or beginning graduate students, reviewer Mohamed Amer suggests that it does not have enough exercises to support a course in its subject, and that some of its proofs are lacking in detail. Reviewer Hans Jürgen Ohlbach suggests that it would be more usable as a reference than a textbook, and states that "it is certainly not suitable for undergraduates". +Reviewer Yde Venema wonders how much of the logical power and useful properties of the various systems treated in this book have been lost in the translation to many-sorted logic, worries about the jump in computational complexity of automated theorem proving caused by the translation, complains about the book's clarity of exposition becoming lost in case analysis, and was disappointed at the lack of coverage of Montague grammar, fixed-point logic, and non-monotonic logic. Nevertheless, Venema recommends the book for courses introducing students to second-order and many-sorted logics, praising the book for its "overwhelming and catching enthusiasm". And reviewer B. Boričić calls it "nice and clearly written", "an appropriate introduction and reference", recommending it to researchers in several disciplines (mathematics, computer science, linguistics, and philosophy) where advanced forms of logic are important. + + +== References == + + +== External links == +Extensions of First Order Logic at Cambridge University Press \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Felix_Klein_and_Sophus_Lie-0.md b/data/en.wikipedia.org/wiki/Felix_Klein_and_Sophus_Lie-0.md new file mode 100644 index 000000000..1d0470dec --- /dev/null +++ b/data/en.wikipedia.org/wiki/Felix_Klein_and_Sophus_Lie-0.md @@ -0,0 +1,43 @@ +--- +title: "Felix Klein and Sophus Lie" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Felix_Klein_and_Sophus_Lie" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:44:40.437862+00:00" +instance: "kb-cron" +--- + +Felix Klein and Sophus Lie: Evolution of the Idea of Symmetry in the Nineteenth Century is a 1988 book by I. M. Yaglom, translated from the Russian into English by Sergei Sossinsky, on the history of the notion of symmetry and the mathematical works of Felix Klein and Sophus Lie besides other mathematicians, such as Camille Jordan, without focusing on biographical details, but on their ideas. It was published by Birkhäuser. + + +== Editions == +The original Russian edition of the book was published in 1977 and translated into English by Sergei Sossinky and edited by Hardy Grant and Abe Shenitzer in 1988. In 2009, the book was republished by Ishi Press as Geometries, Groups and Algebras in the Nineteenth Century. The new edition, designed by Sam Sloan, has a foreword by Richard Bozulich. + + +== Contents == +Felix Klein and Sophus Lie examines the evolution of mathematical ideas that converged in Klein and Lie's work. Yaglom based the work on his lectures to graduate-level students at Yaroslavl State University; Douglas Quadling described it as "a sharply-focused (though appropriately discursive) study" rather than "a catalogue of names and dates." The book begins with Camille Jordan, who discovers an unanswered letter from Galois among Cauchy's papers. This discovery leads Jordan to become the principal advocate of group theory. When Klein and Lie set off for Paris in 1870 to meet Jordan, their visit is cut short by the Franco-Prussian War, but it proves long enough to direct both mathematicians toward the applications of group theory that would define their careers. +The book's central chapters trace three major developments in nineteenth-century geometry: projective geometry, non-Euclidean geometries, and multidimensional spaces. During this period, the scene was dominated by figures like Carl Friedrich Gauss, who attended a lecture by Bernhard Riemann on geometry at age 77, where the ideas presented were "so far ahead of their time that only Gauss could have understood them." Other prominent names include August Ferdinand Möbius, Jakob Steiner, János Bolyai, Nikolai Lobachevsky, Arthur Cayley, Hermann Grassmann, and William Rowan Hamilton. +Alongside the main text runs an extensive apparatus of 312 footnotes that occupy nearly as much space as the main story. These notes provide additional mathematical detail, biographical information about minor contributors, and discussions of deeper philosophical issues. + + +== Reception == +Douglas Quadling praised Felix Klein and Sophus Lie as "a work of considerable scholarship" that "tells a fascinating story in a style which consistently commands attention" and recommended it to mathematics teachers and advanced students. Quadling suggested that the book could serve as a natural sequel to E. T. Bell's popular Men of Mathematics. +Ed Barbeau found the work both informative and frustrating. While acknowledging it as "a 'good read'" and "a useful source of succinct accounts of the principal developments of nineteenth century geometry," he was disappointed by the book's failure to maintain focus on its stated theme. Barbeau wrote that the thread of symmetry gets lost in "the wealth of material" and disappears for "large tracts of the book" only to be "quickly dissolved into a discussion of group theory" when it does appear. +David Rowe delivered the harshest assessment, particularly regarding Yaglom's historical methodology. Rowe wrote that "many of the standard weaknesses found in historical studies undertaken by mathematicians," with interpretations that appear "based on a combination of folklore, conjecture, and superficial reading of popular (and sometimes notoriously unreliable) secondary work." Despite this, Rowe acknowledged the book's value "as a popular introduction to the historical role of symmetry in modern mathematics." +The absence of an index was criticized by both Barbeau and Quadling. + + +== Original version == +Феликс Клейн и Софус Ли. (1977). + + +== See also == +Vorlesungen über die Entwicklung der Mathematik im 19. Jahrhundert + + +== References == + + +== External links == +Limited preview: Felix Klein and Sophus Lie via Internet Archive \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Finding_Ellipses-0.md b/data/en.wikipedia.org/wiki/Finding_Ellipses-0.md new file mode 100644 index 000000000..08432ae49 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Finding_Ellipses-0.md @@ -0,0 +1,155 @@ +--- +title: "Finding Ellipses" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Finding_Ellipses" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:44:42.735764+00:00" +instance: "kb-cron" +--- + +Finding Ellipses: What Blaschke Products, Poncelet’s Theorem, and the Numerical Range Know about Each Other is a mathematics book on "some surprising connections among complex analysis, geometry, and linear algebra", and on the connected ways that ellipses can arise from other subjects of study in all three of these fields. It was written by Ulrich Daepp, Pamela Gorkin, Andrew Shaffer, and Karl Voss, and published in 2019 by the American Mathematical Society and Mathematical Association of America as volume 34 of the Carus Mathematical Monographs, a series of books aimed at presenting technical topics in mathematics to a wide audience. + + +== Topics == +Finding Ellipses studies a connection between Blaschke products, Poncelet's closure theorem, and the numerical range of matrices. +A Blaschke product is a rational function that maps the unit disk in the complex plane to itself, and maps some given points within the disk to the origin. In the main case considered by the book, there are three distinct given points + + + + 0 + + + {\displaystyle 0} + +, + + + + a + + + {\displaystyle a} + +, and + + + + b + + + {\displaystyle b} + +, and their Blaschke product has the formula + + + + + B + ( + z + ) + = + z + ⋅ + + + + z + − + a + + + 1 + − + + + + a + ¯ + + + + z + + + + ⋅ + + + + z + − + b + + + 1 + − + + + + b + ¯ + + + + z + + + + . + + + {\displaystyle B(z)=z\cdot {\frac {z-a}{1-{\bar {a}}z}}\cdot {\frac {z-b}{1-{\bar {b}}z}}.} + + +For this function, each point on the unit circle has three preimages, also on the unit circle. These triples of preimages form triangles inscribed in the unit circle, and (it turns out) they all circumscribe an ellipse with foci at + + + + a + + + {\displaystyle a} + + and + + + + b + + + {\displaystyle b} + +. Thus, they form an infinite system of polygons inscribed in and circumscribing two conics, which is the kind of system that Poncelet's theorem describes. This theorem states that, whenever one polygon is inscribed in a conic and circumscribes another conic, it is part of an infinite family of polygons of the same type, one through each point of either conic. The family of triangles constructed from the Blaschke product is one of these infinite families of Poncelet's theorem. +The third part of the connection surveyed by the book is the numerical range of a matrix, a region within which the eigenvalues of the matrix can be found. In the case of a + + + + 2 + × + 2 + + + {\displaystyle 2\times 2} + + complex matrix, the numerical range is an ellipse, by a result commonly called the elliptical range theorem, with the eigenvalues as its foci. For a certain matrix whose coefficients are derived from the two given points, and having these points on its diagonal, this ellipse is the one circumscribed by the triangles of Poncelet's theorem. More, the numerical range of any matrix is the intersection of the numerical ranges of its unitary dilations, which in this case are + + + + 3 + × + 3 + + + {\displaystyle 3\times 3} + + unitary matrices each having one of the triangles of Poncelet's theorem as its numerical range and the three vertices of the triangle as its eigenvalues. +Finding Ellipses is arranged into three parts. The first part develops the mathematics of Blaschke products, Poncelet's closure theorem, and numerical ranges separately, before revealing the close connections between them. The second part of the book generalizes these ideas to higher-order Blaschke products, larger matrices, and Poncelet-like results for the corresponding numerical ranges, which generalize ellipses. These generalizations connect to more advanced topics in mathematics: "Lebesgue theory, Hardy spaces, functional analysis, operator theory and more". The third part consists of projects and exercises for students to develop this material beyond the exposition in the book. An online collection of web applets allow students to experiment with the constructions in the book. + + +== Audience and reception == +Finding Ellipses is primarily aimed at advanced undergraduates in mathematics, although more as a jumping-off point for undergraduate research projects than as a textbook for courses. The first part of the book uses only standard undergraduate mathematics, but the second part is more demanding, and reviewer Bill Satzer writes that "even the best students might find themselves paging backward and forward in the book, feeling frustrated while trying to make connections". Despite that, Line Baribeau writes that it is "clear and engaging", and appealing in its use of modern topics. Yunus Zeytuncu is even more positive, calling it a "delight" that "realizes the dream" of bringing this combination of disciplines together into a neat package that is accessible to undergraduates. + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Fondements_de_la_Géometrie_Algébrique-0.md b/data/en.wikipedia.org/wiki/Fondements_de_la_Géometrie_Algébrique-0.md new file mode 100644 index 000000000..a91775da3 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Fondements_de_la_Géometrie_Algébrique-0.md @@ -0,0 +1,46 @@ +--- +title: "Fondements de la Géometrie Algébrique" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Fondements_de_la_Géometrie_Algébrique" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:44:44.112183+00:00" +instance: "kb-cron" +--- + +Fondements de la Géometrie Algébrique (FGA) is a book that collected together seminar notes of Alexander Grothendieck. It is an +important source for his pioneering work on scheme theory, which laid foundations for algebraic geometry in its modern technical developments. +The title is a translation of the title of André Weil's book Foundations of Algebraic Geometry. +It contained material on descent theory, and existence theorems including that for the Hilbert scheme. The Technique de descente et théorèmes d'existence en géometrie algébrique is one series of seminars within FGA. +Like the bulk of Grothendieck's work of the IHÉS period, duplicated notes were circulated, but the publication was not as a conventional book. + + +== Contents == +These are Séminaire Bourbaki notes, by number, from the years 1957 to 1962. + +Fondements de la géométrie algébrique. Commentaires [Séminaire Bourbaki, t. 14, 1961/62, Complément]; +Théorème de dualité pour les faisceaux algébriques cohérents [Séminaire Bourbaki, t. 9, 1956/57, no. 149]; (coherent duality) +Géométrie formelle et géométrie algébrique [Séminaire Bourbaki, t. 11, 1958/59, no. 182]; (formal geometry) +Technique de descente et théorèmes d'existence en géométrie algébrique. I-VI +I. Généralités. Descente par morphismes fidèlement plats [Séminaire Bourbaki, t. 12, 1959/60, no. 190]; +II. Le théorème d'existence en théorie formelle des modules [Séminaire Bourbaki, t. 12, 1959/60, no. 195]; +III. Préschémas quotients [Séminaire Bourbaki, t. 13, 1960/61, no. 212]; +IV. Les schémas de Hilbert [Séminaire Bourbaki, t. 13, 1960/61, no. 221]; +V. Les schémas de Picard. Théorèmes d'existence [Séminaire Bourbaki, t. 14, 1961/62, no. 232]; +VI. Les schémas de Picard. Propriétés générales [Séminaire Bourbaki, t. 14, 1961/62, no. 236] + + +== See also == +Éléments de géométrie algébrique +Séminaire de Géométrie Algébrique du Bois Marie + + +== References == +Fantechi, Barbara; Göttsche, Lothar; Illusie, Luc; Kleiman, Steven L.; Nitsure, Nitin; Vistoli, Angelo (2005), Fundamental algebraic geometry, Mathematical Surveys and Monographs, vol. 123, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-3541-8, MR 2222646 +Fantechi, Barbara; Göttsche, Lothar (2005), "Local properties and Hilbert schemes of points", Fundamental algebraic geometry, Math. Surveys Monogr., vol. 123, Providence, R.I.: Amer. Math. Soc., pp. 139–178, MR 2223408 +Grothendieck, Alexander (1962), Fondements de la géométrie algébrique. [Extraits du Séminaire Bourbaki, 1957--1962.] (PDF), Paris: Secrétariat Mathématique, MR 0146040, archived from the original (PDF) on 2011-11-05, retrieved 2010-03-03 +Illusie, Luc (2005), "Grothendieck's existence theorem in formal geometry", Fundamental algebraic geometry (PDF), Math. Surveys Monogr., vol. 123, Providence, R.I.: Amer. Math. Soc., pp. 179–233, MR 2223409, archived from the original (PDF) on 2006-12-08, retrieved 2006-09-27 +Kleiman, Steven L. (2005), "The Picard scheme", Fundamental algebraic geometry, Math. Surveys Monogr., vol. 123, Providence, R.I.: Amer. Math. Soc., pp. 235–321, arXiv:math/0504020, Bibcode:2005math......4020K, MR 2223410 +Nitsure, Nitin (2005), "Construction of Hilbert and Quot schemes", Fundamental algebraic geometry, Math. Surveys Monogr., vol. 123, Providence, R.I.: Amer. Math. Soc., pp. 105–137, arXiv:math/0504590, Bibcode:2005math......4590N, MR 2223407 +Vistoli, Angelo (2005), "Grothendieck topologies, fibered categories and descent theory", Fundamental algebraic geometry, Math. Surveys Monogr., vol. 123, Providence, R.I.: Amer. Math. Soc., pp. 1–104, arXiv:math/0412512, Bibcode:2004math.....12512V, MR 2223406 +SGA, EGA, FGA Archived 2022-07-04 at the Wayback Machine By Mateo Carmona \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Formulario_mathematico-0.md b/data/en.wikipedia.org/wiki/Formulario_mathematico-0.md index 1f591ca28..230abdbfc 100644 --- a/data/en.wikipedia.org/wiki/Formulario_mathematico-0.md +++ b/data/en.wikipedia.org/wiki/Formulario_mathematico-0.md @@ -4,7 +4,7 @@ chunk: 1/1 source: "https://en.wikipedia.org/wiki/Formulario_mathematico" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T07:23:53.723865+00:00" +date_saved: "2026-05-05T08:44:45.297151+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/Foundations_of_Algebraic_Geometry-0.md b/data/en.wikipedia.org/wiki/Foundations_of_Algebraic_Geometry-0.md new file mode 100644 index 000000000..24d662c53 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Foundations_of_Algebraic_Geometry-0.md @@ -0,0 +1,30 @@ +--- +title: "Foundations of Algebraic Geometry" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Foundations_of_Algebraic_Geometry" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:44:46.432627+00:00" +instance: "kb-cron" +--- + +Foundations of Algebraic Geometry is a book by André Weil (1946, 1962) that develops algebraic geometry over fields of any characteristic. In particular it gives a careful treatment of intersection theory by defining the local intersection multiplicity of two subvarieties. +Weil was motivated by the need for a rigorous theory of correspondences on algebraic curves in positive characteristic, which he used in his proof of the Riemann hypothesis for curves over finite fields. +Weil introduced abstract rather than projective varieties partly so that he could construct the Jacobian of a curve. (It was not known at the time that Jacobians are always projective varieties.) It was some time before anyone found any examples of complete abstract varieties that are not projective. +In the 1950s Weil's work was one of several competing attempts to provide satisfactory foundations for algebraic geometry, all of which were superseded by Grothendieck's development of schemes. + + +== See also == +Weil cohomology theory + + +== References == +Raynaud, Michel (1999), "André Weil and the foundations of algebraic geometry" (PDF), Notices of the American Mathematical Society, 46 (8): 864–867, MR 1704257 +van der Waerden, Bartel Leendert (1971), "The foundation of algebraic geometry from Severi to André Weil", Archive for History of Exact Sciences, 7 (3): 171–180, doi:10.1007/BF00357215, MR 1554142, S2CID 189787203 +Weil, André (1947), Foundations of Algebraic Geometry, American Mathematical Society Colloquium Publications, vol. 29, Providence, R.I.: American Mathematical Society, MR 0023093 ISBN 9780821874622 +Weil, André (1962), Foundations of Algebraic Geometry, American Mathematical Society Colloquium Publications, vol. 29 (2 ed.), Providence, R.I.: American Mathematical Society, MR 0144898 ISBN 978-0-8218-1029-3 +Zariski, Oscar (1948), "Book Review: Foundations of algebraic geometry", Bulletin of the American Mathematical Society, 54 (7): 671–675, Bibcode:1948Sci...107...75W, doi:10.1090/S0002-9904-1948-09040-1, MR 1565074 + + +== External links == +Extracts from the preface of Foundations of Algebraic Geometry \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Fundamenta_nova_theoriae_functionum_ellipticarum-0.md b/data/en.wikipedia.org/wiki/Fundamenta_nova_theoriae_functionum_ellipticarum-0.md new file mode 100644 index 000000000..8a159c528 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Fundamenta_nova_theoriae_functionum_ellipticarum-0.md @@ -0,0 +1,21 @@ +--- +title: "Fundamenta nova theoriae functionum ellipticarum" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Fundamenta_nova_theoriae_functionum_ellipticarum" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:44:49.966123+00:00" +instance: "kb-cron" +--- + +Fundamenta nova theoriae functionum ellipticarum (from Latin: New Foundations of the Theory of Elliptic Functions) is a treatise on elliptic functions by German mathematician Carl Gustav Jacob Jacobi. The book was first published in 1829, and has been reprinted in volume 1 of his collected works and on several later occasions. The book introduces Jacobi elliptic functions and the Jacobi triple product identity. + + +== References == +Citations + +General +Conway, John Horton (1980), "Monsters and moonshine", The Mathematical Intelligencer, 2 (4): 165–171, doi:10.1007/BF03028594, ISSN 0343-6993, MR 0600222, S2CID 121787388 +Cooke, Roger (2005), "Chapter 31 C. F. G. Jacobi, book on elliptic functions", in Grattan-Guinness, Ivor (ed.), Landmark writings in western mathematics 1640–1940, Elsevier B. V., Amsterdam, pp. 412–430, ISBN 978-0-444-50871-3, MR 2169816 +Jacobi, C. G. J. (1829), Fundamenta nova theoriae functionum ellipticarum (in Latin), Königsberg: Borntraeger, ISBN 978-1-108-05200-9, Reprinted by Cambridge University Press 2012 {{citation}}: ISBN / Date incompatibility (help) +Jacobi, C. G. J. (1969) [1881], Gesammelte Werke, Herausgegeben auf Veranlassung der Königlich Preussischen Akademie der Wissenschaften, vol. I–VIII (2nd ed.), New York: Chelsea Publishing Co., MR 0260557, archived from the original on 2013-05-13, retrieved 2012-10-14 \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Games,_Puzzles,_and_Computation-0.md b/data/en.wikipedia.org/wiki/Games,_Puzzles,_and_Computation-0.md new file mode 100644 index 000000000..dac8820fd --- /dev/null +++ b/data/en.wikipedia.org/wiki/Games,_Puzzles,_and_Computation-0.md @@ -0,0 +1,24 @@ +--- +title: "Games, Puzzles, and Computation" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Games,_Puzzles,_and_Computation" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:44:51.099239+00:00" +instance: "kb-cron" +--- + +Games, Puzzles, and Computation is a book on game complexity, written by Robert Hearn and Erik Demaine, and published in 2009 by A K Peters. It is revised from Hearn's doctoral dissertation, which was supervised by Demaine. The Basic Library List Committee of the Mathematical Association of America has recommended it for inclusion in undergraduate mathematics libraries. + + +== Topics == +Games, Puzzles, and Computation concerns the computational complexity theory of solving logic puzzles and making optimal decisions in two-player and multi-player combinatorial games. Its focus is on games and puzzles that have seen real-world play, rather than ones that have been invented for a purely mathematical purpose. In this area it is common for puzzles and games such as sudoku, Rush Hour, reversi, and chess (in generalized forms with arbitrarily large boards) to be computationally difficult: sudoku is NP-complete, Rush Hour and reversi are PSPACE-complete, and chess is EXPTIME-complete. Beyond proving new results along these lines, the book aims to provide a unifying framework for proving such results, through the use of nondeterministic constraint logic, an abstract combinatorial problem that more closely resembles game play than the more classical problems previously used for completeness proofs. +It is divided into three parts. The first part concerns constraint logic, which involving assigning orientations to the edges of an undirected graph so that each vertex has incoming edges with large-enough total weight. The second part of this book applies constraint logic in new proofs of hardness of various real-world games and puzzles, by showing that, in each case, the vertices and edges of a constraint logic instance can be encoded by the moves and pieces of the game. Some of these hardness proofs simplify previously-known proofs; some ten of them are new, including the discovery that optimal play in certain multiplayer games can be an undecidable problem. A third part of the book provides a compendium of known hardness results in game complexity, updating a much shorter list of complete problems in game complexity from the 1979 book Computers and Intractability. An appendix provides a review of the methods from computational complexity theory needed in this study, for readers unfamiliar with this area. + + +== Audience and reception == +Although primarily a research monograph and reference work for researchers in this area, reviewer Oswin Aichholzer recommends the book more generally to anyone interested in the mathematics of games and their complexity. Liljana Babinkostova writes that Games, Puzzles, and Computation is enjoyable reading, successful in its "purpose of building a bridge between games and the theory of computation". +Leon Harkleroad is somewhat more critical, writing that the book feels padded in places, and Joseph O'Rourke complains that its organization, with many pages of abstract mathematics before reaching the real-world games, does not lend itself to cover-to-cover reading. However, both Harkleroad and O'Rourke agree that the book is well produced and thought-provoking. + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Geometric_Exercises_in_Paper_Folding-0.md b/data/en.wikipedia.org/wiki/Geometric_Exercises_in_Paper_Folding-0.md new file mode 100644 index 000000000..1c4e93674 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Geometric_Exercises_in_Paper_Folding-0.md @@ -0,0 +1,60 @@ +--- +title: "Geometric Exercises in Paper Folding" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Geometric_Exercises_in_Paper_Folding" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:44:53.464312+00:00" +instance: "kb-cron" +--- + +Geometric Exercises in Paper Folding is a book on the mathematics of paper folding. It was written by Indian mathematician T. Sundara Row, first published in India in 1893, and later republished in many other editions. Its topics include paper constructions for regular polygons, symmetry, and algebraic curves. According to the historian of mathematics Michael Friedman, it became "one of the main engines of the popularization of folding as a mathematical activity". + + +== Publication history == +Geometric Exercises in Paper Folding was first published by Addison & Co. in Madras in 1893. The book became known in Europe through a remark of Felix Klein in his book Vorträge über ausgewählte Fragen der Elementargeometrie (1895) and its translation Famous Problems Of Elementary Geometry (1897). Based on the success of Geometric Exercises in Paper Folding in Germany, the Open Court Press of Chicago published it in the US, with updates by Wooster Woodruff Beman and David Eugene Smith. Although Open Court listed four editions of the book, published in 1901, 1905, 1917, and 1941, the content did not change between these editions. The fourth edition was also published in London by La Salle, and both presses reprinted the fourth edition in 1958. +The contributions of Beman and Smith to the Open Court editions have been described as "translation and adaptation", despite the fact that the original 1893 edition was already in English. Beman and Smith also replaced many footnotes with references to their own work, replaced some of the diagrams by photographs, and removed some remarks specific to India. In 1966, Dover Publications of New York published a reprint of the 1905 edition, and other publishers of out-of-copyright works have also printed editions of the book. + + +== Topics == +Geometric Exercises in Paper Folding shows how to construct various geometric figures using paper-folding in place of the classical Greek Straightedge and compass constructions. +The book begins by constructing regular polygons beyond the classical constructible polygons of 3, 4, or 5 sides, or of any power of two times these numbers, and the construction by Carl Friedrich Gauss of the heptadecagon, it also provides a paper-folding construction of the regular nonagon, not possible with compass and straightedge. The nonagon construction involves angle trisection, but Rao is vague about how this can be performed using folding; an exact and rigorous method for folding-based trisection would have to wait until the work in the 1930s of Margherita Piazzola Beloch. The construction of the square also includes a discussion of the Pythagorean theorem. The book uses high-order regular polygons to provide a geometric calculation of pi. +A discussion of the symmetries of the plane includes congruence, similarity, and collineations of the projective plane; this part of the book also covers some of the major theorems of projective geometry including Desargues's theorem, Pascal's theorem, and Poncelet's closure theorem. +Later chapters of the book show how to construct algebraic curves including the conic sections, the conchoid, the cubical parabola, the witch of Agnesi, the cissoid of Diocles, and the Cassini ovals. The book also provides a gnomon-based proof of Nicomachus's theorem that the sum of the first + + + + n + + + {\displaystyle n} + + cubes is the square of the sum of the first + + + + n + + + {\displaystyle n} + + integers, and material on other arithmetic series, geometric series, and harmonic series. +There are 285 exercises, and many illustrations, both in the form of diagrams and (in the updated editions) photographs. + + +== Influences == +Tandalam Sundara Row was born in 1853, the son of a college principal, and earned a bachelor's degree at the Kumbakonam College in 1874, with second-place honours in mathematics. He became a tax collector in Tiruchirappalli, retiring in 1913, and pursued mathematics as an amateur. As well as Geometric Exercises in Paper Folding, he also wrote a second book, Elementary Solid Geometry, published in three parts from 1906 to 1909. +One of the sources of inspiration for Geometric Exercises in Paper Folding was Kindergarten Gift No. VIII: Paper-folding. This was one of the Froebel gifts, a set of kindergarten activities designed in the early 19th century by Friedrich Fröbel. The book was also influenced by an earlier Indian geometry textbook, First Lessons in Geometry, by Bhimanakunte Hanumantha Rao (1855–1922). First Lessons drew inspiration from Fröbel's gifts in setting exercises based on paper-folding, and from the book Elementary Geometry: Congruent Figures by Olaus Henrici in using a definition of geometric congruence based on matching shapes to each other and well-suited for folding-based geometry. +In turn, Geometric Exercises in Paper Folding inspired other works of mathematics. A chapter in Mathematische Unterhaltungen und Spiele [Mathematical Recreations and Games] by Wilhelm Ahrens (1901) concerns folding and is based on Rao's book, inspiring the inclusion of this material in several other books on recreational mathematics. Other mathematical publications have studied the curves that can be generated by the folding processes used in Geometric Exercises in Paper Folding. In 1934, Margherita Piazzola Beloch began her research on axiomatizing the mathematics of paper-folding, a line of work that would eventually lead to the Huzita–Hatori axioms in the late 20th century. Beloch was explicitly inspired by Rao's book, titling her first work in this area "Alcune applicazioni del metodo del ripiegamento della carta di Sundara Row" ["Several applications of the method of folding a paper of Sundara Row"]. + + +== Audience and reception == +The original intent of Geometric Exercises in Paper Folding was twofold: as an aid in geometry instruction, +and as a work of recreational mathematics to inspire interest in geometry in a general audience. Edward Mann Langley, reviewing the 1901 edition, suggested that its content went well beyond what should be covered in a standard geometry course. And in their own textbook on geometry using paper-folding exercises, The First Book of Geometry (1905), Grace Chisholm Young and William Henry Young heavily criticized Geometric Exercises in Paper Folding, writing that it is "too difficult for a child, and too infantile for a grown person". However, reviewing the 1966 Dover edition, mathematics educator Pamela Liebeck called it "remarkably relevant" to the discovery learning techniques for geometry instruction of the time, and in 2016 computational origami expert Tetsuo Ida, introducing an attempt to formalize the mathematics of the book, wrote "After 123 years, the significance of the book remains." + + +== References == + + +== External links == +Madras edition and Open Court edition of Geometric Exercises in Paper Folding on the Internet Archive \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Geometric_Folding_Algorithms-0.md b/data/en.wikipedia.org/wiki/Geometric_Folding_Algorithms-0.md new file mode 100644 index 000000000..c1dc98faf --- /dev/null +++ b/data/en.wikipedia.org/wiki/Geometric_Folding_Algorithms-0.md @@ -0,0 +1,45 @@ +--- +title: "Geometric Folding Algorithms" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Geometric_Folding_Algorithms" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:44:54.562391+00:00" +instance: "kb-cron" +--- + +Geometric Folding Algorithms: Linkages, Origami, Polyhedra is a monograph on the mathematics and computational geometry of mechanical linkages, paper folding, and polyhedral nets, by Erik Demaine and Joseph O'Rourke. It was published in 2007 by Cambridge University Press (ISBN 978-0-521-85757-4). +A Japanese-language translation by Ryuhei Uehara was published in 2009 by the Modern Science Company (ISBN 978-4-7649-0377-7). + + +== Audience == +Although aimed at computer science and mathematics students, much of the book is accessible to a broader audience of mathematically-sophisticated readers with some background in high-school level geometry. +Mathematical origami expert Tom Hull has called it "a must-read for anyone interested in the field of computational origami". +It is a monograph rather than a textbook, and in particular does not include sets of exercises. +The Basic Library List Committee of the Mathematical Association of America has recommended this book for inclusion in undergraduate mathematics libraries. + + +== Topics and organization == +The book is organized into three sections, on linkages, origami, and polyhedra. +Topics in the section on linkages include +the Peaucellier–Lipkin linkage for converting rotary motion into linear motion, +Kempe's universality theorem that any algebraic curve can be traced out by a linkage, +the existence of linkages for angle trisection, +and the carpenter's rule problem on straightening two-dimensional polygonal chains. +This part of the book also includes applications to motion planning for robotic arms, and to protein folding. +The second section of the book concerns the mathematics of paper folding, and mathematical origami. It includes the NP-completeness of testing flat foldability, +the problem of map folding (determining whether a pattern of mountain and valley folds forming a square grid can be folded flat), +the work of Robert J. Lang using tree structures and circle packing to automate the design of origami folding patterns, +the fold-and-cut theorem according to which any polygon can be constructed by folding a piece of paper and then making a single straight cut, +origami-based angle trisection, +rigid origami, +and the work of David A. Huffman on curved folds. +In the third section, on polyhedra, the topics include polyhedral nets and Dürer's conjecture on their existence for convex polyhedra, the sets of polyhedra that have a given polygon as their net, Steinitz's theorem characterizing the graphs of polyhedra, Cauchy's theorem that every polyhedron, considered as a linkage of flat polygons, is rigid, and Alexandrov's uniqueness theorem stating that the three-dimensional shape of a convex polyhedron is uniquely determined by the metric space of geodesics on its surface. +The book concludes with a more speculative chapter on higher-dimensional generalizations of the problems it discusses. + + +== References == + + +== External links == +Authors' web site for Geometric Folding Algorithms including contents, errata, and advances on open problems \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Geometric_Origami-0.md b/data/en.wikipedia.org/wiki/Geometric_Origami-0.md new file mode 100644 index 000000000..4cfb3b468 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Geometric_Origami-0.md @@ -0,0 +1,69 @@ +--- +title: "Geometric Origami" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Geometric_Origami" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:44:55.725835+00:00" +instance: "kb-cron" +--- + +Geometric Origami is a book on the mathematics of paper folding, focusing on the ability to simulate and extend classical straightedge and compass constructions using origami. It was written by Austrian mathematician Robert Geretschläger and published by Arbelos Publishing (Shipley, UK) in 2008. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. + + +== Topics == +The book is divided into two main parts. The first part is more theoretical. It outlines the Huzita–Hatori axioms for mathematical origami, and proves that they are capable of simulating any straightedge and compass construction. It goes on to show that, in this mathematical model, origami is strictly more powerful than straightedge and compass: with origami, it is possible to solve any cubic equation or quartic equation. In particular, origami methods can be used to trisect angles, and for doubling the cube, two problems that have been proven to have no exact solution using only straightedge and compass. +The second part of the book focuses on folding instructions for constructing regular polygons using origami, and on finding the largest copy of a given regular polygon that can be constructed within a given square sheet of origami paper. With straightedge and compass, it is only possible to exactly construct regular + + + + n + + + {\displaystyle n} + +-gons for which + + + + n + + + {\displaystyle n} + + is a product of a power of two with distinct Fermat primes (powers of two plus one): this allows + + + + n + + + {\displaystyle n} + + to be 3, 5, 6, 8, 10, 12, etc. These are called the constructible polygons. With a construction system that can trisect angles, such as mathematical origami, more numbers of sides are possible, using Pierpont primes in place of Fermat primes, including + + + + n + + + {\displaystyle n} + +-gons for + + + + n + + + {\displaystyle n} + + equal to 7, 13, 14, 17, 19, etc. Geometric Origami provides explicit folding instructions for 15 different regular polygons, including those with 3, 5, 6, 7, 8, 9, 10, 12, 13, 17, and 19 sides. Additionally, it discusses approximate constructions for polygons that cannot be constructed exactly in this way. + + +== Audience and reception == +This book is quite technical, aimed more at mathematicians than at amateur origami enthusiasts looking for folding instructions for origami artworks. However, it may be of interest to origami designers, looking for methods to incorporate folding patterns for regular polygons into their designs. Origamist David Raynor suggests that its methods could also be useful in constructing templates from which to cut out clean unfolded pieces of paper in the shape of the regular polygons that it discusses, for use in origami models that use these polygons as a starting shape instead of the traditional square paper. +Geometric Origami may also be useful as teaching material for university-level geometry and abstract algebra, or for undergraduate research projects extending those subjects, although reviewer Mary Fortune cautions that "there is much preliminary material to be covered" before a student would be ready for such a project. Reviewer Georg Gunther summarizes the book as "a delightful addition to a wonderful corner of mathematics where art and geometry meet", recommending it as a reference for "anyone with a working knowledge of elementary geometry, algebra, and the geometry of complex numbers". + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Geometric_and_Topological_Inference-0.md b/data/en.wikipedia.org/wiki/Geometric_and_Topological_Inference-0.md new file mode 100644 index 000000000..e3c6e624b --- /dev/null +++ b/data/en.wikipedia.org/wiki/Geometric_and_Topological_Inference-0.md @@ -0,0 +1,23 @@ +--- +title: "Geometric and Topological Inference" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Geometric_and_Topological_Inference" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:44:52.312144+00:00" +instance: "kb-cron" +--- + +Geometric and Topological Inference is a monograph in computational geometry, computational topology, geometry processing, and topological data analysis, on the problem of inferring properties of an unknown space from a finite point cloud of noisy samples from the space. It was written by Jean-Daniel Boissonnat, Frédéric Chazal, and Mariette Yvinec, and published in 2018 by the Cambridge University Press in their Cambridge Texts in Applied Mathematics book series. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. + + +== Topics == +The book is subdivided into four parts and 11 chapters. The first part covers basic tools from topology needed in the study, including simplicial complexes, Čech complexes and Vietoris–Rips complex, homotopy equivalence of topological spaces to their nerves, filtrations of complexes, and the data structures needed to represent these concepts efficiently in computer algorithms. A second introductory part concerns material of a more geometric nature, including Delaunay triangulations and Voronoi diagrams, convex polytopes, convex hulls and convex hull algorithms, lower envelopes, alpha shapes and alpha complexes, and witness complexes. +With these preliminaries out of the way, the remaining two sections show how to use these tools for topological inference. The third section is on recovering the unknown space itself (or a topologically equivalent space, described using a complex) from sufficiently well-behaved samples. The fourth part shows how, with weaker assumptions about the samples, it is still possible to recover useful information about the space, such as its homology and persistent homology. + + +== Audience and reception == +Although the book is primarily aimed at specialists in these topics, it can also be used to introduce the area to non-specialists, and provides exercises suitable for an advanced course. Reviewer Michael Berg evaluates it as an "excellent book" aimed at a hot topic, inference from large data sets, and both Berg and Mark Hunacek note that it brings a surprising level of real-world applicability to formerly-pure topics in mathematics. + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Geometry_From_Africa-0.md b/data/en.wikipedia.org/wiki/Geometry_From_Africa-0.md new file mode 100644 index 000000000..e323c206a --- /dev/null +++ b/data/en.wikipedia.org/wiki/Geometry_From_Africa-0.md @@ -0,0 +1,32 @@ +--- +title: "Geometry From Africa" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Geometry_From_Africa" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:44:58.111842+00:00" +instance: "kb-cron" +--- + +Geometry From Africa: Mathematical and Educational Explorations is a book in ethnomathematics by Paulus Gerdes. It analyzes the mathematics behind geometric designs and patterns from multiple African cultures, and suggests ways of connecting this analysis with the mathematics curriculum. It was published in 1999 by the Mathematical Association of America, in their Classroom Resource Materials book series. + + +== Background == +The book's author, Paulus Gerdes (1952–2014), was a mathematician from the Netherlands who became a professor of mathematics at the Eduardo Mondlane University in Mozambique, rector of Maputo University, and chair of the African Mathematical Union Commission on the History of Mathematics in Africa. He was a prolific author, especially of works on the ethnomathematics of Africa. However, as many of his publications were written in Portuguese, German, and French, or published only in Mozambique, this book makes his work in ethnomathematics more accessible to English-speaking mathematicians. + + +== Topics == +The book is heavily illustrated, and describes geometric patterns in the carvings, textiles, drawings and paintings of multiple African cultures. Although these are primarily decorative rather than mathematical, Gerdes adds his own mathematical analysis of the patterns, and suggests ways of incorporating this analysis into the mathematical curriculum. +It is divided into four chapters. The first of these provides an overview of geometric patterns in many African cultures, including examples of textiles, knotwork, architecture, basketry, metalwork, ceramics, petroglyphs, facial tattoos, body painting, and hair styles. The second chapter presents examples of designs in which squares and right triangles can be formed from elements of the patterns, and suggests educational activities connecting these materials to the Pythagorean theorem and to the theory of Latin squares. For instance, basket-weavers in Mozambique form square knotted buttons out of folded ribbons, and the resulting pattern of oblique lines crossing the square suggests a standard dissection-based proof of the theorem. The third chapter uses African designs, particularly in basket-weaving, to illustrate themes of symmetry, polygons and polyhedra, area, volume, and the theory of fullerenes. In the final chapter, the only one to concentrate on a single African culture, the book discusses the sona sand-drawings of the Chokwe people, in which a single self-crossing curve surrounds and separates a grid of points. These drawings connect to the theory of Euler tours, fractals, arithmetic series, and polyominos. + + +== Audience and reception == +The book is aimed at primary and secondary school mathematics teachers. Reviewer Karen Dee Michalowicz, a school teacher, writes that although the connections between culture and mathematics are sometimes contrived, "every mathematics educator would benefit" from the book. +Ethnomathematician Marcia Ascher suggests that the book would have benefited from an index and a map of the cultures from which the material of the book was drawn. Nevertheless, reviewer Richard Kitchen evaluates this book as "the most complete volume available on the ethnomathematics of Africa". Reviewer Steve Abbott writes that the book "provides many opportunities for developing cross-curricular and multi-cultural approaches" to mathematics education, and that it is "an important book that deserves to be widely read". + + +== References == + + +== External links == +Geometry From Africa on the Internet Archive \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Geshu_bu-0.md b/data/en.wikipedia.org/wiki/Geshu_bu-0.md new file mode 100644 index 000000000..8497b2fc7 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Geshu_bu-0.md @@ -0,0 +1,33 @@ +--- +title: "Geshu bu" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Geshu_bu" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:00.452687+00:00" +instance: "kb-cron" +--- + +The Geshu bu (格術補), translated to English as the Supplement to Geometric Optics, Science Updates, or Optic Updates, is a book on optics written by the Chinese Guangdong gentry and intellectual Zou Boqi (1819–1869). The book was written in the late Qing Dynasty period in China. It covers the principles of lenses and is based on mathematical theory. + + +== Background == + +Zou Boqi wrote two significant works in optics: the Geshu bu and the "Notes on the Mechanism for Capturing Images" (Sheying zhi qi ji). The Geshu bu tackles the Chinese principles on optics and its related literature while the Sheyi zhi qi ji delves more on the results of Zou's experiments as well as principles on photography. The Geshu bu was published in 1874, after Zou Boqi's death. In the late nineteenth century, Western knowledge, especially in optics, began to influence China. Zou's book, Geshu bu, introduced basic concepts of optics and lens, building on earlier Jesuit translations. This work challenged the traditional Mohist views and laid the groundwork for geometrical optics in China. + + +== Contents == +Based from one fascicle of the book, published in 1877, it aims to expand on ancient Chinese mathematics. The term geshu highlights thorough investigation as explained in the preface by the Chinese philosopher Chen Li, drawing from Western lens-making techniques. +In the book, Zou discussed different mirror shapes and principles. He also explained convex lenses, focusing on how they concentrate sunlight to ignite a fire. The focal point determines how close or far an image appears. +The text introduces trigonometric calculations for lens reflections, providing a mathematical basis for understanding convex mirrors as well as adding details on telescopes and microscopes. The book also corrected some mistakes made by J. Adam Schall von Bell and Zhen Fuguang, writers on optics in China. + + +=== Reception === +Due to its unique approach of integrating mathematical calculations in lens-making principles, the book received high praise from Qing scholars. In 1886, Zhu Kebao wrote about optical methods in his biography of Zou Boqi. Zou's book helped circulated the knowledge of optics and lenses in the print market. Such circulation was reflected in a winning essay from the 1889 Polytechnic Institute (Gezhi shuyuan, 格致書院) contest, linking optics and the "mirror that lights a fire." + + +== References == + + +== External links == +Geshu bu (1877 edition), available on Google Books \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Glossary_of_Principia_Mathematica-0.md b/data/en.wikipedia.org/wiki/Glossary_of_Principia_Mathematica-0.md new file mode 100644 index 000000000..c4c9032fb --- /dev/null +++ b/data/en.wikipedia.org/wiki/Glossary_of_Principia_Mathematica-0.md @@ -0,0 +1,245 @@ +--- +title: "Glossary of Principia Mathematica" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Glossary_of_Principia_Mathematica" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:01.640169+00:00" +instance: "kb-cron" +--- + +This is a list of the notation used in Alfred North Whitehead and Bertrand Russell's Principia Mathematica (1910–1913). +The second (but not the first) edition of Volume I has a list of notation used at the end. + + +== Glossary == +This is a glossary of some of the technical terms in Principia Mathematica that are no longer widely used or whose meaning has changed. + +apparent variable +bound variable + +atomic proposition +A proposition of the form R(x,y,...) where R is a relation. + +Barbara +A mnemonic for a certain syllogism. + +class +A subset of the members of some type + +codomain +The codomain of a relation R is the class of y such that xRy for some x. + +compact +A relation R is called compact if whenever xRz there is a y with xRy and yRz + +concordant +A set of real numbers is called concordant if all nonzero members have the same sign + +connected +connexity +A relation R is called connected if for any 2 distinct members x, y either xRy or yRx. + +continuous +A continuous series is a complete totally ordered set isomorphic to the reals. *275 + +correlator +bijection + +couple +1. A cardinal couple is a class with exactly two elements +2. An ordinal couple is an ordered pair (treated in PM as a special sort of relation) + +Dedekindian +complete (relation) *214 + +definiendum +The symbol being defined + +definiens +The meaning of something being defined + +derivative +A derivative of a subclass of a series is the class of limits of non-empty subclasses + +description +A definition of something as the unique object with a given property + +descriptive function +A function taking values that need not be truth values, in other words what is not called just a function. + +diversity +The inequality relation + +domain +The domain of a relation R is the class of x such that xRy for some y. + +elementary proposition +A proposition built from atomic propositions using "or" and "not", but with no bound variables + +Epimenides +Epimenides was a legendary Cretan philosopher + +existent +non-empty + +extensional function +A function whose value does not change if one of its arguments is changed to something equivalent. + +field +The field of a relation R is the union of its domain and codomain + +first-order +A first-order proposition is allowed to have quantification over individuals but not over things of higher type. + +function +This often means a propositional function, in other words a function taking values "true" or "false". If it takes other values it is called a "descriptive function". PM allows two functions to be different even if they take the same values on all arguments. + +general proposition +A proposition containing quantifiers + +generalization +Quantification over some variables + +homogeneous +A relation is called homogeneous if all arguments have the same type. + +individual +An element of the lowest type under consideration + +inductive +Finite, in the sense that a cardinal is inductive if it can be obtained by repeatedly adding 1 to 0. *120 + +intensional function +A function that is not extensional. + +logical +1. The logical sum of two propositions is their logical disjunction +2. The logical product of two propositions is their logical conjunction + +matrix +A function with no bound variables. *12 + +median +A class is called median for a relation if some element of the class lies strictly between any two terms. *271 + +member +element (of a class) + +molecular proposition +A proposition built from two or more atomic propositions using "or" and "not"; in other words an elementary proposition that is not atomic. + +null-class +A class containing no members + +predicative +A century of scholarly discussion has not reached a definite consensus on exactly what this means, and Principia Mathematica gives several different explanations of it that are not easy to reconcile. See the introduction and *12. *12 says that a predicative function is one with no apparent (bound) variables, in other words a matrix. + +primitive proposition +A proposition assumed without proof + +progression +A sequence (indexed by natural numbers) + +rational +A rational series is an ordered set isomorphic to the rational numbers + +real variable +free variable + +referent +The term x in xRy + +reflexive +infinite in the sense that the class is in one-to-one correspondence with a proper subset of itself (*124) + +relation +A propositional function of some variables (usually two). This is similar to the current meaning of "relation". + +relative product +The relative product of two relations is their composition + +relatum +The term y in xRy + +scope +The scope of an expression is the part of a proposition where the expression has some given meaning (chapter III) + +Scott +Sir Walter Scott, author of Waverley. + +second-order +A second order function is one that may have first-order arguments + +section +A section of a total order is a subclass containing all predecessors of its members. + +segment +A subclass of a totally ordered set consisting of all the predecessors of the members of some class + +selection +A choice function: something that selects one element from each of a collection of classes. + +sequent +A sequent of a class α in a totally ordered class is a minimal element of the class of terms coming after all members of α. (*206) + +serial relation +A total order on a class + +significant +well-defined or meaningful + +similar +of the same cardinality + +stretch +A convex subclass of an ordered class + +stroke +The Sheffer stroke (only used in the second edition of PM) + +type +As in type theory. All objects belong to one of a number of disjoint types. + +typically +Relating to types; for example, "typically ambiguous" means "of ambiguous type". + +unit +A unit class is one that contains exactly one element + +universal +A universal class is one containing all members of some type + +vector +1. Essentially an injective function from a class to itself (for example, a vector in a vector space acting on an affine space) +2. A vector-family is a non-empty commuting family of injective functions from some class to itself (VIB) + + +== Symbols introduced in Principia Mathematica, Volume I == + + +== Symbols introduced in Principia Mathematica, Volume II == + + +== Symbols introduced in Principia Mathematica, Volume III == + + +== See also == +Glossary of set theory + + +== Notes == + + +== References == +Whitehead, Alfred North, and Bertrand Russell. Principia Mathematica, 3 vols, Cambridge University Press, 1910, 1912, and 1913. Second edition, 1925 (Vol. 1), 1927 (Vols. 2, 3). + + +== External links == +List of notation in Principia Mathematica at the end of Volume I +"The Notation in Principia Mathematica" by Bernard Linsky. +Principia Mathematica online (University of Michigan Historical Math Collection): +Volume I +Volume II +Volume III +Proposition ✸54.43 in a more modern notation (Metamath) \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/God_Created_the_Integers-0.md b/data/en.wikipedia.org/wiki/God_Created_the_Integers-0.md new file mode 100644 index 000000000..b99822649 --- /dev/null +++ b/data/en.wikipedia.org/wiki/God_Created_the_Integers-0.md @@ -0,0 +1,27 @@ +--- +title: "God Created the Integers" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/God_Created_the_Integers" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:02.760295+00:00" +instance: "kb-cron" +--- + +God Created the Integers: The Mathematical Breakthroughs That Changed History is a 2005 anthology, edited by Stephen Hawking, of "excerpts from thirty-one of the most important works in the history of mathematics." +Each chapter of the work focuses on a different mathematician and begins with a biographical overview. Within each chapter, Hawking examines the mathematician's key discoveries, presents formal proofs of significant results, and explains their impact on the development of the mathematical field. +The title of the book is a reference to a quotation attributed to mathematician Leopold Kronecker, who once wrote that "God made the integers; all else is the work of man." + + +== Content == +The works are grouped by author and ordered chronologically. Each section is prefaced by notes on the mathematician's life and work. The anthology includes works by the following mathematicians: + +Selections from the works of Euler, Bolyai, Lobachevsky and Galois, which are included in the second edition of the book (published in 2007), were not included in the first edition. + + +== Editions == +Hawking, Stephen (2005). God Created the Integers: The Mathematical Breakthroughs That Changed History. Running Press Book Publishers. pp. 1160 (Hardback). ISBN 0-7624-1922-9. +Hawking, Stephen (2007). God Created the Integers: The Mathematical Breakthroughs That Changed History. Running Press Book Publishers. pp. 1358 (Paperback). ISBN 978-0-7624-3004-8. + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Grundlagen_der_Mathematik-0.md b/data/en.wikipedia.org/wiki/Grundlagen_der_Mathematik-0.md new file mode 100644 index 000000000..e04dad791 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Grundlagen_der_Mathematik-0.md @@ -0,0 +1,39 @@ +--- +title: "Grundlagen der Mathematik" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Grundlagen_der_Mathematik" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:06.338584+00:00" +instance: "kb-cron" +--- + +Grundlagen der Mathematik (English: Foundations of Mathematics) is a two-volume work by David Hilbert and Paul Bernays. Originally published in 1934 and 1939, it presents fundamental mathematical ideas and introduced second-order arithmetic. + + +== Publication history == +1934/1939 (Vol. I, II) First German edition, Springer +1944 Reprint of first edition by J. W. Edwards, Ann Arbor, Michigan. +1968/1970 (Vol. I, II) Second revised German edition, Springer +1979/1982 (Vol. I, II) Russian translation of 1968/1970, Nauka Publ., Moscow +2001/2003 (Vol. I, II) French translation, L’Harmattan, Paris +2011/2013 (Parts A and B of Vol. I, prefaces and sections 1-5) English translation of 1968 and 1934, bilingual with German facsimile on the left-hand sides. +The Hilbert Bernays Project is producing an English translation. + + +== See also == +Hilbert–Bernays paradox + + +== References == +Sieg, Wilfried; Ravaglia, Mark (2005), "Chapter 77. David Hilbert and Paul Bernays, Grundlagen der Mathematik" (PDF), in Grattan-Guinness, Ivor (ed.), Landmark writings in western mathematics 1640–1940, Elsevier B. V., Amsterdam, pp. 981–99, doi:10.1016/B978-044450871-3/50158-3, ISBN 978-0-444-50871-3, MR 2169816, archived from the original (PDF) on 2011-05-14, retrieved 2011-02-01 +Hilbert, David; Bernays, Paul (1934), Grundlagen der Mathematik. I, Die Grundlehren der mathematischen Wissenschaften, vol. 40, Berlin, New York: Springer-Verlag, ISBN 978-3-540-04134-4, JFM 60.0017.02, MR 0237246, archived from the original on 2011-05-17 {{citation}}: ISBN / Date incompatibility (help) +Hilbert, David; Bernays, Paul (1939), Grundlagen der Mathematik. II, Die Grundlehren der mathematischen Wissenschaften, vol. 50, Berlin, New York: Springer-Verlag, ISBN 978-3-540-05110-7, JFM 65.0021.02, MR 0272596, archived from the original on 2011-05-17 {{citation}}: ISBN / Date incompatibility (help) +Hilbert, David; Bernays, Paul (1968) [1934], Grundlagen der Mathematik. I, Die Grundlehren der mathematischen Wissenschaften, vol. 40 (2nd ed.), Berlin, New York: Springer-Verlag, ISBN 978-3642868955, MR 0237246 +Hilbert, D.; Bernays, Paul (1970), Grundlagen der Mathematik. II, Die Grundlehren der mathematischen Wissenschaften, vol. 50 (2 ed.), Berlin-New York: Springer-Verlag, ISBN 978-3642868979, MR 0272596 +Hilbert, David; Bernays, Paul (2011) [1934/68], Grundlagen der Mathematik I — Foundations of Mathematics I, Part A: Prefaces and §§ 1–2 (in German and English) (1st ed.), London: College Publications, ISBN 978-1-84890-033-2, MR 3027390 +Hilbert, David; Bernays, Paul (2013) [1934/68], Grundlagen der Mathematik I — Foundations of Mathematics I, Part B: §§ 3–5 and Deleted Part I of the 1st Edn. (in German and English) (1st ed.), London: College Publications, ISBN 978-1-84890-075-2 + + +== External links == +Hilbert Bernays Project which aims to produce an English translation of Grundlagen der Mathematik. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Grundzüge_der_Mengenlehre-0.md b/data/en.wikipedia.org/wiki/Grundzüge_der_Mengenlehre-0.md new file mode 100644 index 000000000..f225d4103 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Grundzüge_der_Mengenlehre-0.md @@ -0,0 +1,22 @@ +--- +title: "Grundzüge der Mengenlehre" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Grundzüge_der_Mengenlehre" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:07.505560+00:00" +instance: "kb-cron" +--- + +Grundzüge der Mengenlehre (English: Basics of Set Theory) is a book on set theory written by Felix Hausdorff. +First published in April 1914, Grundzüge der Mengenlehre was the first comprehensive introduction to set theory. In addition to the systematic treatment of known results in set theory, the book also contains chapters on measure theory and topology, which were then still considered parts of set theory. Hausdorff presented and developed original material that later became the basis for those areas. +In 1927, Hausdorff published an extensively revised second edition under the title Mengenlehre (English: Set Theory), omitting many topics from the first edition. In 1935, a third German edition was released, which in 1957 was translated into English by John R. Aumann et al. under the title Set Theory. + + +== References == +Blumberg, Henry (1920), "Hausdorff's Grundzüge der Mengenlehre", Bulletin of the American Mathematical Society, 27 (3): 116–129, doi:10.1090/S0002-9904-1920-03378-1. +Gehman, H. M. (1927), "Hausdorff's Revised Mengenlehre", Bull. Amer. Math. Soc., 33 (6): 778–781, doi:10.1090/S0002-9904-1927-04478-0 +Hausdorff, Felix (1914), Grundzüge der Mengenlehre, Leipzig: Veit, ISBN 978-0-8284-0061-9 {{citation}}: ISBN / Date incompatibility (help) Reprinted by Chelsea Publishing Company in 1944, 1949 and 1965 [1]. +Hausdorff, F. (1935) [1927], Mengenlehre (3 ed.), Berlin-Leipzig: de Gruyter Republished by Dover Publications, New York, N. Y., 1944 +Hausdorff, Felix (1962) [1957], Set theory (2 ed.), New York: Chelsea Publishing Company, ISBN 978-0821838358 {{citation}}: ISBN / Date incompatibility (help) Republished by AMS-Chelsea 2005. +Scholz, Erhard (2005), Felix Hausdorff and the Hausdorff edition (PDF). Extended edition of a chapter in The Princeton Companion to Mathematics. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Harmonice_Mundi-0.md b/data/en.wikipedia.org/wiki/Harmonice_Mundi-0.md index f72013b11..f667f27b3 100644 --- a/data/en.wikipedia.org/wiki/Harmonice_Mundi-0.md +++ b/data/en.wikipedia.org/wiki/Harmonice_Mundi-0.md @@ -4,7 +4,7 @@ chunk: 1/2 source: "https://en.wikipedia.org/wiki/Harmonice_Mundi" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T08:33:39.488056+00:00" +date_saved: "2026-05-05T08:45:08.718356+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/Harmonice_Mundi-1.md b/data/en.wikipedia.org/wiki/Harmonice_Mundi-1.md index 84360a1ce..1d72864c5 100644 --- a/data/en.wikipedia.org/wiki/Harmonice_Mundi-1.md +++ b/data/en.wikipedia.org/wiki/Harmonice_Mundi-1.md @@ -4,7 +4,7 @@ chunk: 2/2 source: "https://en.wikipedia.org/wiki/Harmonice_Mundi" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T08:33:39.488056+00:00" +date_saved: "2026-05-05T08:45:08.718356+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/Higher_Topos_Theory-0.md b/data/en.wikipedia.org/wiki/Higher_Topos_Theory-0.md new file mode 100644 index 000000000..795501468 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Higher_Topos_Theory-0.md @@ -0,0 +1,31 @@ +--- +title: "Higher Topos Theory" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Higher_Topos_Theory" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:11.067998+00:00" +instance: "kb-cron" +--- + +Higher Topos Theory is a treatise on the theory of ∞-categories written by American mathematician Jacob Lurie. In addition to introducing Lurie's new theory of ∞-topoi, the book is widely considered foundational to higher category theory. Since 2018, Lurie has been transferring the contents of Higher Topos Theory (along with new material) to Kerodon, an "online resource for homotopy-coherent mathematics" inspired by the Stacks Project. + + +== Topics == +Higher Topos Theory covers two related topics: ∞-categories and ∞-topoi (which are a special case of the former). The first five of the book's seven chapters comprise a rigorous development of general ∞-category theory in the language of quasicategories, a special class of simplicial set which acts as a model for ∞-categories. The path of this development largely parallels classical category theory, with the notable exception of the ∞-categorical Grothendieck construction; this correspondence, which Lurie refers to as "straightening and unstraightening", gains considerable importance in his treatment. +The last two chapters are devoted to ∞-topoi, Lurie's own invention and the ∞-categorical analogue of topoi in classical category theory. The material of these chapters is original, and is adapted from an earlier preprint of Lurie's. There are also appendices discussing background material on categories, model categories, and simplicial categories. + + +== History == +Higher Topos Theory followed an earlier work by Lurie, On Infinity Topoi, uploaded to the arXiv in 2003. Algebraic topologist Peter May was critical of this preprint, emailing Lurie's then-advisor Mike Hopkins "to say that Lurie’s paper had some interesting ideas, but that it felt preliminary and needed more rigor." Lurie released a draft of Higher Topos Theory on the arXiv in 2006, and the book was finally published in 2009. +Lurie released a second book on higher category theory, Higher Algebra, as a preprint on his website in 2017. This book assumes the content of Higher Topos Theory and uses it to study algebra in the ∞-categorical context. + + +== External links == +http://ncatlab.org/nlab/show/Higher+Topos+Theory +If I want to study Jacob Lurie's books "Higher Topoi Theory", "Derived AG", what prerequisites should I have? +https://www.math.ias.edu/~lurie/ +https://kerodon.net/about + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/History_of_the_Theory_of_Numbers-0.md b/data/en.wikipedia.org/wiki/History_of_the_Theory_of_Numbers-0.md new file mode 100644 index 000000000..424eff04c --- /dev/null +++ b/data/en.wikipedia.org/wiki/History_of_the_Theory_of_Numbers-0.md @@ -0,0 +1,38 @@ +--- +title: "History of the Theory of Numbers" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/History_of_the_Theory_of_Numbers" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:12.238942+00:00" +instance: "kb-cron" +--- + +History of the Theory of Numbers is a three-volume work by Leonard Eugene Dickson summarizing work in number theory up to about 1920. The style is unusual in that Dickson mostly just lists results by various authors, with little further discussion. The central topic of quadratic reciprocity and higher reciprocity laws is barely mentioned; this was apparently going to be the topic of a fourth volume that was never written (Fenster 1999). + + +== Volumes == +Volume 1 - Divisibility and Primality - 486 pages +Volume 2 - Diophantine Analysis - 803 pages +Volume 3 - Quadratic and Higher Forms - 313 pages + + +== References == +Carmichael, Robert D. (1919), "Recent Publications: Reviews: History of the Theory of Numbers. Volume I: Divisibility and Primality", The American Mathematical Monthly, 26 (9): 396–403, doi:10.2307/2971917, ISSN 0002-9890, JSTOR 2971917 +Carmichael, Robert D. (1921), "Recent Publications: Reviews: History of the Theory of Numbers: History of the Theory of Numbers", The American Mathematical Monthly, 28 (2): 72–78, doi:10.2307/2973042, ISSN 0002-9890, JSTOR 2973042 +Carmichael, Robert D. (1923), "Recent Publications: Reviews: History of the Theory of Numbers", The American Mathematical Monthly, 30 (5): 259–262, doi:10.2307/2299094, ISSN 0002-9890, JSTOR 2299094 +Dickson, Leonard Eugene (2005) [1919], History of the theory of numbers. Vol. I: Divisibility and primality., New York: Dover Publications, ISBN 978-0-486-44232-7, MR 0245499, Zbl 1214.11001 +Dickson, Leonard Eugene (2005) [1920], History of the theory of numbers. Vol. II: Diophantine analysis, New York: Dover Publications, ISBN 978-0-486-44233-4, MR 0245500, Zbl 1214.11002 +Dickson, Leonard Eugene (2005) [1923], History of the theory of numbers. Vol. III: Quadratic and higher forms, New York: Dover Publications, ISBN 978-0-486-44234-1, MR 0245501 +Fenster, Della D. (1999), "Leonard Dickson's History of the theory of numbers: an historical study with mathematical implications", Revue d'Histoire des Mathématiques. Journal for the History of Mathematics, 5 (2): 159–179, ISSN 1262-022X, MR 1793101 +Fenster, Della Dumbaugh (1999), "Why Dickson left quadratic reciprocity out of his History of the theory of numbers", The American Mathematical Monthly, 106 (7): 618–627, doi:10.2307/2589491, ISSN 0002-9890, JSTOR 2589491, MR 1720467 +Furtwängler, Ph. (1923), "Literaturberichte: History of the theory of numbers", Monatshefte für Mathematik und Physik, 33 (1): A6–A7, doi:10.1007/BF01705606, ISSN 0026-9255, S2CID 116618046 +Lehmer, D. H. (1919), "Book Review: History of the Theory of Numbers", Bulletin of the American Mathematical Society, 26 (3): 125–132, doi:10.1090/S0002-9904-1919-03280-7, ISSN 0002-9904 +Lehmer, D. H. (1920), "Dickson's history of the theory of numbers", Bulletin of the American Mathematical Society, 26 (6): 281–282, doi:10.1090/S0002-9904-1920-03305-7, ISSN 0002-9904 +Vandiver, H. S. (1924), "Book Review: History of the Theory of Numbers", Bulletin of the American Mathematical Society, 30 (1): 65–70, doi:10.1090/S0002-9904-1924-03852-X, ISSN 0002-9904 + + +== External links == +History of the Theory of Numbers - Volume 1 at the Internet Archive. +History of the Theory of Numbers - Volume 2 at the Internet Archive. +History of the Theory of Numbers - Volume 3 at the Internet Archive. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Horologium_Oscillatorium-0.md b/data/en.wikipedia.org/wiki/Horologium_Oscillatorium-0.md new file mode 100644 index 000000000..f7aa5a304 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Horologium_Oscillatorium-0.md @@ -0,0 +1,32 @@ +--- +title: "Horologium Oscillatorium" +chunk: 1/3 +source: "https://en.wikipedia.org/wiki/Horologium_Oscillatorium" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:14.621466+00:00" +instance: "kb-cron" +--- + +Horologium Oscillatorium: Sive de Motu Pendulorum ad Horologia Aptato Demonstrationes Geometricae (English: The Pendulum Clock: or Geometrical Demonstrations Concerning the Motion of Pendula as Applied to Clocks) is a book published by Dutch mathematician and physicist Christiaan Huygens in 1673 and his major work on pendula and horology. It is regarded as one of the three most important works on mechanics in the 17th century, the other two being Galileo’s Discourses and Mathematical Demonstrations Relating to Two New Sciences (1638) and Newton’s Philosophiæ Naturalis Principia Mathematica (1687). +Much more than a mere description of clocks, Huygens's Horologium Oscillatorium is the first modern treatise in which a physical problem (the accelerated motion of a falling body) is idealized by a set of parameters then analyzed mathematically and constitutes one of the seminal works of applied mathematics. The book is also known for its strangely worded dedication to Louis XIV. The appearance of the book in 1673 was a political issue, since at that time the Dutch Republic was at war with France; Huygens was anxious to show his allegiance to his patron, which can be seen in the obsequious dedication to Louis XIV. + +== Overview == + +The motivation behind Horologium Oscillatorium (1673) goes back to the idea of using a pendulum to keep time, which had already been proposed by people engaged in astronomical observations such as Galileo. Mechanical clocks at the time were instead regulated by balances that were often very unreliable. Moreover, without reliable clocks, there was no good way to measure longitude at sea, which was particularly problematic for a country dependent on sea trade like the Dutch Republic. +Huygens interest in using a freely suspended pendulum to regulate clocks began in earnest in December 1656. He had a working model by the next year which he patented and then communicated to others such as Frans van Schooten and Claude Mylon. Although Huygens’s design, published in a short tract entitled Horologium (1658), was a combination of existing ideas, it nonetheless became widely popular and many pendulum clocks by Salomon Coster and his associates were built on it. Existing clock towers, such as those at Scheveningen and Utrecht, were also retrofitted following Huygens's design. +Huygens continued his mathematical studies on free fall shortly after and, in 1659, obtained a series of remarkable results. At the same time, he was aware that the periods of simple pendula are not perfectly tautochronous, that is, they do not keep exact time but depend to some extent on their amplitude. Huygens was interested in finding a way to make the bob of a pendulum move reliably and independently of its amplitude. The breakthrough came later that same year when he discovered that the ability to keep perfect time can be achieved if the path of the pendulum bob is a cycloid. However, it was unclear what form to give the metal cheeks regulating the pendulum to lead the bob in a cycloidal path. His famous and surprising solution was that the cheeks must also have the form of a cycloid, on a scale determined by the length of the pendulum. These and other results led Huygens to develop his theory of evolutes and provided the incentive to write a much larger work, which became the Horologium Oscillatorium. +After 1673, during his stay in the Academie des Sciences, Huygens studied harmonic oscillation more generally and continued his attempt at determining longitude at sea using his pendulum clocks, but his experiments carried on ships were not always successful. + +== Contents == + +In the Preface, Huygens states: + +For it is not in the nature of a simple pendulum to provide equal and reliable measurements of time… But by a geometrical method we have found a different and previously unknown way to suspend the pendulum… [so that] the time of the swing can be chosen equal to some calculated value +The book is divided into five interconnected parts. Parts I and V of the book contain descriptions of clock designs. The rest of the book is made of three, highly abstract, mathematical and mechanical parts dealing with pendular motion and a theory of curves. Except for Part IV, written in 1664, the entirety of the book was composed in a three-month period starting in October 1659. + +=== Part I: Description of the oscillating clock === +Huygens spends the first part of the book describing in detail his design for an oscillating pendulum clock. It includes descriptions of the endless chain, a lens-shaped bob to reduce air resistance, a small weight to adjust the pendulum swing, an escapement mechanism for connecting the pendulum to the gears, and two thin metal plates in the shape of cycloids mounted on either side to limit pendular motion. This part ends with a table to adjust for the inequality of the solar day, a description on how to draw a cycloid, and a discussion of the application of pendulum clocks for the determination of longitude at sea. + +=== Part II: Fall of weights and motion along a cycloid === +In the second part of the book, Huygens states three hypotheses on the motion of bodies, which can be seen as precursors to Newton's three laws of motion. They are essentially the law of inertia, the effect of gravity on uniform motion, and the law of composition of motion: \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Horologium_Oscillatorium-1.md b/data/en.wikipedia.org/wiki/Horologium_Oscillatorium-1.md new file mode 100644 index 000000000..254398ae2 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Horologium_Oscillatorium-1.md @@ -0,0 +1,82 @@ +--- +title: "Horologium Oscillatorium" +chunk: 2/3 +source: "https://en.wikipedia.org/wiki/Horologium_Oscillatorium" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:14.621466+00:00" +instance: "kb-cron" +--- + +If there is no gravity, and the air offers no resistance to the motion of bodies, then any one of these bodies admits of a single motion to be continued with an equal velocity along a straight line. +Now truly this motion becomes, under the action of gravity and for whatever the direction of the uniform motion, a motion composed from that constant motion that a body now has or had previously, together with the motion due gravity downwards. +Also, either of these motions can be considered separately, neither one to be impeded by the other. +He uses these three rules to re-derive geometrically Galileo's original study of falling bodies, including linear fall along inclined planes and fall along a curved path. He then studies constrained fall, culminating with a proof that a body falling along an inverted cycloid reaches the bottom in a fixed amount of time, regardless of the point on the path at which it begins to fall. This in effect shows the solution to the tautochrone problem as given by a cycloid curve. In modern notation: + + + + + ( + π + + / + + 2 + ) + √ + ( + 2 + D + + / + + g + ) + + + {\displaystyle (\pi /2)\surd (2D/g)} + + +The following propositions are covered in Part II: + +=== Part III: Size and evolution of the curve === + +In the third part of the book, Huygens introduces the concept of an evolute as the curve that is "unrolled" (Latin: evolutus) to create a second curve known as the involute. He then uses evolutes to justify the cycloidal shape of the thin plates in Part I. Huygens originally discovered the isochronism of the cycloid using infinitesimal techniques but in his final publication he resorted to proportions and reductio ad absurdum, in the manner of Archimedes, to rectify curves such as the cycloid, the parabola, and other higher order curves. +The following propositions are covered in Part III: + +=== Part IV: Center of oscillation or movement === +The fourth and longest part of the book contains the first successful theory of the center of oscillation, together with special methods for applying the theory, and the calculations of the centers of oscillation of several plane and solid figures. Huygens introduces physical parameters into his analysis while addressing the problem of the compound pendulum. +It starts with a number of definitions and proceeds to derive propositions using Torricelli's Principle: If some weights begin to move under the force of gravity, then it is not possible for the center of gravity of these weights to ascend to a greater height than that found at the beginning of the motion. Huygens called this principle "the chief axiom of mechanics" and used it like a conservation of kinetic energy principle, without recourse to forces or torques. In the process, he obtained solutions to dynamical problems such as the period of an oscillating pendulum as well as a compound pendulum, the center of oscillation and its interchangeability with the pivot point, and the concept of moment of inertia and the constant of gravitational acceleration. Huygens made use, implicitly, of the formula for free fall. In modern notation: + + + + + d + = + 1 + + / + + 2 + g + + t + + 2 + + + + + {\displaystyle d=1/2gt^{2}} + + +The following propositions are covered in Part IV: + +=== Part V: Alternative design and centrifugal force === +The last part of the book returns to the design of a clock where the motion of the pendulum is circular, and the string unwinds from the evolute of a parabola. It ends with thirteen propositions regarding bodies in uniform circular motion, without proofs, and states the laws of centripetal force for uniform circular motion. These propositions were studied closely at the time, although their proofs were only published posthumously in the De Vi Centrifuga (1703). + +=== Summary === +Many of the propositions found in the Horologium Oscillatorium had little to do with clocks but rather point to the evolution of Huygens’s ideas. When an attempt to measure the gravitational constant using a pendulum failed to give consistent results, Huygens abandoned the experiment and instead idealized the problem into a mathematical study comparing free fall and fall along a circle. +Initially, he followed Galileo’s approach to the study of fall, only to leave it shortly after when it was clear the results could not be extended to curvilinear fall. Huygens then tackled the problem directly by using his own approach to infinitesimal analysis, a combination of analytic geometry, classical geometry, and contemporary infinitesimal techniques. Huygens chose not to publish the majority of his results using these techniques but instead adhered as much as possible to a strictly classical presentation, in the manner of Archimedes. + +== Legacy == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Horologium_Oscillatorium-2.md b/data/en.wikipedia.org/wiki/Horologium_Oscillatorium-2.md new file mode 100644 index 000000000..8872fe792 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Horologium_Oscillatorium-2.md @@ -0,0 +1,37 @@ +--- +title: "Horologium Oscillatorium" +chunk: 3/3 +source: "https://en.wikipedia.org/wiki/Horologium_Oscillatorium" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:14.621466+00:00" +instance: "kb-cron" +--- + +=== Reception === +Initial reviews of Huygens's Horologium Oscillatorium in major research journals at the time were generally positive. An anonymous review in Journal de Sçavans (1674) praised the author of the book for his invention of the pendulum clock "which brings the greatest honor to our century because it is of utmost importance... for astronomy and for navigation" while also noting the elegant, but difficult, mathematics needed to fully understand the book. Another review in the Giornale de' Letterati (1674) repeated many of the same points than the first one, with further elaboration on Huygens's trials at sea. The review in the Philosophical Transactions (1673) likewise praised the author for his invention but mentions other contributors to the clock design, such as William Neile, that in time would lead to a priority dispute. +In addition to submitting his work for review, Huygens sent copies of his book to individuals throughout Europe, including statesmen such as Johan De Witt, and mathematicians such as Gilles de Roberval and Gregory of St. Vincent. Their appreciation of the text was due not exclusively on their ability to comprehend it fully but rather as a recognition of Huygens’s intellectual standing, or of his gratitude or fraternity that such gift implied. Thus, sending copies of the Horologium Oscillatorium worked in a manner similar to a gift of an actual clock, which Huygens had also sent to several people, including Louis XIV and the Grand Duke Ferdinand II. + +=== Mathematical style === + +Huygens's mathematics in the Horologium Oscillatorium and elsewhere is best characterized as geometrical analysis of curves and of motions. It closely resembled classical Greek geometry in style, as Huygens preferred the works of classical authors, above all Archimedes. He was also proficient in the analytical geometry of Descartes and Fermat, and made use of it particularly in Parts III and IV of his book. With these and other infinitesimal tools, Huygens was quite capable of finding solutions to hard problems that today are solved using mathematical analysis, such as proving a uniqueness theorem for a class of differential equations, or extending approximation and inequalities techniques to the case of second order differentials. +Huygens's manner of presentation (i.e., clearly stated axioms, followed by propositions) also made an impression among contemporary mathematicians, including Newton, who studied the propositions on centrifugal force very closely and later acknowledged the influence of Horologium Oscillatorium on his own major work. Nonetheless, the Archimedean and geometrical style of Huygens's mathematics soon fell into disuse with the advent of the calculus, making it more difficult for subsequent generations to appreciate his work. + +=== Appraisal === +Huygens’s most lasting contribution in the Horologium Oscillatorium is his thorough application of mathematics to explain pendulum clocks, which were the first reliable timekeepers fit for scientific use. His mastery of geometry and physics to design and analyze a precision instrument arguably anticipated the advent of mechanical engineering. +Huygens's analyses of the cycloid in Parts II and III would later lead to the studies of many other such curves, including the caustic, the brachistochrone, the sail curve, and the catenary. Additionally, his exacting mathematical dissection of physical problems into a minimum of parameters provided an example for others (such as the Bernoullis) on work in applied mathematics that would be carry on in the following centuries, albeit in the language of the calculus. + +== Editions == +Huygens’s own manuscript of the book is missing, but he bequeathed his notebooks and correspondence to the Library of the University of Leiden, now in the Codices Hugeniorum. Much of the background material is in Oeuvres Complètes, vols. 17-18. +Since its publication in France in 1673, Huygens’s work has been available in Latin and in the following modern languages: + +First publication. Horologium Oscillatorium, Sive De Motu Pendulorum Ad Horologia Aptato Demonstrationes Geometricae. Latin. Paris: F. Muguet, 1673. [14] + 161 + [1] pages.[1]. +Later edition by W.J. ’s Gravesande. In Christiani Hugenii Zulichemii Opera varia, 4 vols. Latin. Leiden: J. vander Aa, 1724, 15–192. [Repr. as Christiani Hugenii Zulichemii opera mechanica, geometrica, astronomica et miscellenea, 4 vols., Leiden: G. Potvliet et alia, 1751]. +Standard edition. In Oeuvres Complètes, vol. 18. French and Latin. The Hague: Martinus Nijhoff, 1934, 68–368. +German translation. Die Pendeluhr (trans. A. Heckscher and A. von Oettingen), Leipzig: Engelmann, 1913 (Ostwalds Klassiker der exakten Wissenschaften, no. 192). +Italian translation. L’orologio a pendolo (trans. C. Pighetti), Florence: Barbèra, 1963. [Also includes an Italian translation of Traité de la Lumière]. +French translation. L’Horloge oscillante (trans. J. Peyroux), Bordeaux: Bergeret, 1980. [Photorepr. Paris: Blanchard, 1980]. +English translation. Christiaan Huygens’ The Pendulum Clock, or Geometrical Demonstrations Concerning the Motion Of Pendula As Applied To Clocks (trans. R.J. Blackwell), Ames: Iowa State University Press, 1986. +Dutch translation. Christiaan Huygens: Het Slingeruurwerk, een studie (transl. J. Aarts), Utrecht: Epsilon Uitgaven, 2015. + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Hydrodynamica-0.md b/data/en.wikipedia.org/wiki/Hydrodynamica-0.md new file mode 100644 index 000000000..64b4f1f58 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Hydrodynamica-0.md @@ -0,0 +1,52 @@ +--- +title: "Hydrodynamica" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Hydrodynamica" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:15.780405+00:00" +instance: "kb-cron" +--- + +Hydrodynamica, sive de Viribus et Motibus Fluidorum Commentarii (Latin for Hydrodynamics, or commentaries on the forces and motions of fluids) is a book published by Daniel Bernoulli in 1738. The title of this book eventually christened the field of fluid mechanics as hydrodynamics. +This book introduced the Bernoulli's principle, stating the first form of conservation of energy in fluid dynamics. + + +== Description == +The book deals with fluid mechanics and is organized around preliminary versions of the conservation of energy, as received from Christiaan Huygens's formulation of vis viva (Latin for living forces). The book describes the theory of water flowing through a tube and of water flowing from a hole in a container. In doing so, Bernoulli explained the nature of hydrodynamic pressure and discovered the role of loss of vis viva in fluid flow, which would later be known as the Bernoulli principle. The book also discusses hydraulic machines and introduces the notion of work and efficiency of a machine. +In the tenth chapter, Bernoulli discussed a primitive version of kinetic theory of gases. Assuming that heat increases the velocity of the gas particles, he first demonstrated that the pressure of air is proportional to kinetic energy of gas particles, thus making the temperature of gas proportional to this kinetic energy as well. In this chapter Bernoulli introduces a correction to the volume that appears in Boyle's law, anticipating the Van der Waals equation by more than a century. However most of Bernoulli's theories of this chapter were ignored historically. + + +== Table of contents == +The book is divided in 13 sections: + +Which is the introduction, and contains various matters to be considered initially +Which discusses the equilibrium of fluids at rest, both within themselves, as well as related to other causes +Concerning the velocities of fluids flowing from some kind of vessel through an opening of any kind +Concerned with the various times, which are desired in the efflux of the water +Concerning the motion of water from vessels being filled constantly +Concerning fluids not flowing out, or, moving within the walls of the vessels +Concerning the motion of water through submerged vessels, where it is shown by examples, either how significantly useful the principle of the conservation of living forces shall be, or as in these cases in which a certain amount is agreed to be lost from these continually. +Concerning the motion both of homogeneous as well as heterogeneous fluids through vessels of irregular construction divided up into several parts, where the individual phenomena of the trajectories of the fluids through a number of openings may be explained and a part of the motion may be absorbed continually from the theory of living forces; and with the general rules for the motions of the fluids defined everywhere +Concerning the motion of fluids which are not ejected by their own weight but by certain other forces, and which concern hydraulic machines, especially where the highest degree of perfection of the same can be given, and how they can be perfected further both by the mechanics of solids as well as of fluids +Concerning the properties and motions of elastic fluids, but especially those of air. +Concerning fluids acting in a vortex, also those which may be contained in moving vessels. This is a relatively short chapter, in which Bernoulli tries to reconcile the vortex theory of planetary motion with Newton’s Law of gravitation, as well as presenting the theory of fluid vortices, and some interesting experiments involving fluids in accelerating frames of reference. +Which presents the static properties of moving fluids, what I call static-hydraulics +Concerning the reaction of fluids flowing out of vessels, and with the impulse of the same after they have flowed out, on planes which they meet. + + +== Reception == +Leonhard Euler, friend of Daniel Bernoulli, sent his criticism as soon as the book was published. Bernoulli accepted some of the criticism but considered that Euler's work on fluids was too abstract and did not describe the real world. +A rivalry priority dispute started between Daniel and his father Johann Bernoulli who had also written on the matter. Johann claimed priority on the Bernoulli's principle. Johann's book Hydraulica was published in 1743 but falsely dated 1732. + + +== See also == +Analyse des infiniment petits pour l'intelligence des lignes courbes by Guillaume de l'Hôpital derived from Johann Bernoulli's work + + +== References == + + +== Bibliography == +Mikhailov, G.K. (2005). "Hydrodynamica". In Grattan-Guinness, Ivor (ed.). Landmark Writings in Western Mathematics 1640–1940. Elsevier. pp. 131–42. ISBN 978-0-08-045744-4. +Bernoulli, Daniel (1738). Hydrodynamica, sive de viribus et motibus fluidorum commentarii (in Latin, source ETH-Bibliothek Zürich, Rar 5503). sumptibus Johannis Reinholdi Dulseckeri; Typis Joh. Deckeri, typographi Basiliensis. doi:10.3931/e-rara-3911. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/IJP_The_Book_of_Surfaces-0.md b/data/en.wikipedia.org/wiki/IJP_The_Book_of_Surfaces-0.md new file mode 100644 index 000000000..5f06f96ec --- /dev/null +++ b/data/en.wikipedia.org/wiki/IJP_The_Book_of_Surfaces-0.md @@ -0,0 +1,35 @@ +--- +title: "IJP The Book of Surfaces" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/IJP_The_Book_of_Surfaces" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:16.947814+00:00" +instance: "kb-cron" +--- + +IJP the book of surfaces is a book by George L. Legendre, with a foreword by Mohsen Mostafavi. + + +== Overview == +IJP the Book of Surfaces was released in 2003 by the publishing arm of the London-based Architectural Association School of Architecture. The book features six essays on the notion of surface written from an architectural, philosophical, literary, mathematical, and computational angle, as well as several lighter asides ranging from cookery to poetry. These threads have been given a particular typographic and graphic design treatment meant to weave them together into a continuous narrative. + + +== Background and literary references == +The book addresses some significant developments of the decade, such as the explosion of computational tools; the emergence of the 3D surface as an architectural signifier of the Digital Revolution; the profession's fascination with the formal possibilities of surface cladding; and the rise of innovative manufacturing technologies. It can be compared to contemporary titles like Mohsen Mostafavi’s and David Leatherbarrow’s Surface Architecture, an essay on the phenomenology of architectural façades, and Ellen Lupton’s collection Skin: Surface, Substance + Design, which explores the working metaphor of artificial skin in Materials science, fashion and the visual arts. By comparison, Illa Berman notes that IJP the Book of Surfaces withdraws from external cultural currents and their contexts and emerges from within the formal and computational specificity of the surface itself. As a piece of writing, it is indebted to the literary school Oulipo. Its treatment of one theme as a collection of vignettes written in different voices (linguistic, mathematical, computational, mock-literary, and pop-cultural) nods back to Raymond Queneau’s 1947 Exercises in Style, in which the same trivial event is told and re-told in different idioms. + + +== Form and content == +In keeping with the literary/mathematical spirit of Oulipo, layout, typography, and pagination form an integral part of the book's thesis. The pagination taps the formal affinity between a publisher's book spread and a mathematician's surface, both of which draw on the concept of mathematical matrix. Similar mathematical references apply to the title of the work, which combines 'i' and 'j', two symbols commonly used in matrix algebra, with the symbol 'p' (for point), introduced by the author in reference to Euclidean space. + + +== Reception == +The book's argument and restrained use of computer graphics by the standards of the day (dominated then as now by computer-generated renderings) elicited a mixed reception. Historians and theorists noted its withdrawal from the wider cultural context, its consistent argument, graphic sobriety, and theoretical reach. Some readers noted its lack of engagement with other pressing issues of the day, such as sustainability and ecology, as well as its blank and solipsistic tone, occasionally questionable syntax, and pedestrian graphic design. The book's reception may have reflected disagreements in the architectural community at the time over the meaning of innovation and the finality of computational tools. After 2015, similar disagreements arose between the trade press and the self-identifying avant-garde movement of architectural parametricism. Legendre has since distanced himself from the broader cultural claims of the movement). + + +== See also == +Design computing – Computing as applied to design +Digital architecture – Architecture using digital technology + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/In_Pursuit_of_the_Traveling_Salesman-0.md b/data/en.wikipedia.org/wiki/In_Pursuit_of_the_Traveling_Salesman-0.md new file mode 100644 index 000000000..3b88f825f --- /dev/null +++ b/data/en.wikipedia.org/wiki/In_Pursuit_of_the_Traveling_Salesman-0.md @@ -0,0 +1,40 @@ +--- +title: "In Pursuit of the Traveling Salesman" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/In_Pursuit_of_the_Traveling_Salesman" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:18.117712+00:00" +instance: "kb-cron" +--- + +In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation is a book on the travelling salesman problem, by William J. Cook, published in 2011 by the Princeton University Press, with a paperback reprint in 2014. The Basic Library List Committee of the Mathematical Association of America has suggested its inclusion in undergraduate mathematics libraries. + + +== Topics == +The travelling salesman problem asks to find the shortest cyclic tour of a collection of points, in the plane or in more abstract mathematical spaces. +Because the problem is NP-hard, algorithms that take polynomial time are unlikely to be guaranteed to find its optimal solution; on the other hand a brute-force search of all permutations would always solve the problem exactly but would take far too long to be usable for all but the smallest problems. Threading a middle ground between these too-fast and too-slow running times, and developing a practical system that can find the exact solution of larger instances, raises difficult questions of algorithm engineering, which have sparked the development of "many of the concepts and techniques of combinatorial optimization". +The introductory chapter of the book explores the limits of calculation on the problem, from 49-point problems solved by hand in the mid-1950s by George Dantzig, D. R. Fulkerson, and Selmer M. Johnson to a problem with 85,900 points solved optimally in 2006 by the Concorde TSP Solver, which Cook helped develop. The next chapters covers the early history of the problem and of related problems, including Leonhard Euler's work on the Seven Bridges of Königsberg, William Rowan Hamilton's Icosian game, and Julia Robinson first naming the problem in 1949. Another chapter describes real-world applications of the problem, ranging "from genome sequencing and designing computer processors to arranging music and hunting for planets". Reviewer Brian Hayes cites "the most charming revelation" of the book as being the fact that one of those real-world applications has been route planning for actual traveling salesmen in the early 20th century. +Chapters four through seven, "core of the book", discuss methods for solving the problem, leading from heuristics and metaheuristics, linear programming relaxation, and cutting-plane methods, up to the branch and bound method that combines these techniques and is used by Concorde. The next two chapters also cover technical material, on the performance of computer implementations and on the Computational complexity theory of the problem. +The remaining chapters are more human-centered, covering human and animal problem-solving strategies, and the incorporation of TSP solutions into the artworks of Julian Lethbridge, Robert A. Bosch, and others. A short final summary chapter suggests possible future directions, including the possibility of progress on the P versus NP problem. + + +== Audience == +The book is intended for a non-specialist audience, avoids technical detail and is written "in an easy to understand style". It includes many historical asides, examples, applications, and biographical information and photographs of key players in the story, making it accessible to readers without a mathematical background. +Although In Pursuit of the Traveling Salesman is not a textbook, reviewer Christopher Thompson suggests that some of its material on the use of linear programming and on applications of the problem "would be well-suited for classroom use", citing in particular the way it links multiple fields including numerical analysis, graph theory, algorithm design, logic, and statistics. +Reviewer Stan Wagon writes that "any reader with an interest in combinatorial algorithms will find much of value in this book". Jan Karel Lenstra and David Shmoys write that "The writing is relaxed and entertaining; the presentation is excellent. We greatly enjoyed reading it." And reviewer Haris Aziz concludes "The book is highly recommended to any one with a mathematical curiosity and interest in the +development of ideas.". + + +== Related works == +More details of Cook's work with Concorde, suitable for more serious researchers on the problem and on related topics, can be found in an earlier book by Cook with David Applegate, Robert E. Bixby +and Václav Chvátal, The Traveling Salesman Problem: A Computational Study (2007). +Other books on the travelling salesman problem, also more technical than In Pursuit of the Traveling Salesman, include The Traveling Salesman Problem: A Guided Tour of Combinatorial Optimization (by Lawler, Lenstra, Rinnooy Kan, and Shmoys, 1985) and The Traveling Salesman Problem and Its Variations (by Gutin and Punnen, 2006). + + +== References == + + +== Further reading == +Ellenberg, Jordan (March 10, 2012), "The fuzzy path may be shortest (review of In Pursuit of the Traveling Salesman)", The Wall Street Journal +McLemee, Scott (March 21, 2012), "Algorithm of a salesman (review of In Pursuit of the Traveling Salesman)", Inside Higher Education \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Indra's_Pearls_(book)-0.md b/data/en.wikipedia.org/wiki/Indra's_Pearls_(book)-0.md new file mode 100644 index 000000000..bec017896 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Indra's_Pearls_(book)-0.md @@ -0,0 +1,51 @@ +--- +title: "Indra's Pearls (book)" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Indra's_Pearls_(book)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:19.251800+00:00" +instance: "kb-cron" +--- + +Indra's Pearls: The Vision of Felix Klein is a geometry book written by David Mumford, Caroline Series and David Wright, and published by Cambridge University Press in 2002 and 2015. +The book explores the patterns created by iterating conformal maps of the complex plane called Möbius transformations, and their connections with symmetry and self-similarity. These patterns were glimpsed by German mathematician Felix Klein, but modern computer graphics allows them to be fully visualised and explored in detail. + + +== Title == +The book's title refers to Indra's net, a metaphorical object described in the Buddhist text of the Flower Garland Sutra. Indra's net consists of an infinite array of gossamer strands and pearls. The frontispiece to Indra's Pearls quotes the following description: + +In the glistening surface of each pearl are reflected all the other pearls ... In each reflection, again are reflected all the infinitely many other pearls, so that by this process, reflections of reflections continue without end. +The allusion to Felix Klein's "vision" is a reference to Klein's early investigations of Schottky groups and hand-drawn plots of their limit sets. It also refers to Klein's wider vision of the connections between group theory, symmetry and geometry - see Erlangen program. + + +== Contents == +The contents of Indra's Pearls are as follows: + +Chapter 1. The language of symmetry – an introduction to the mathematical concept of symmetry and its relation to geometric groups. +Chapter 2. A delightful fiction – an introduction to complex numbers and mappings of the complex plane and the Riemann sphere. +Chapter 3. Double spirals and Möbius maps – Möbius transformations and their classification. +Chapter 4. The Schottky dance – pairs of Möbius maps which generate Schottky groups; plotting their limit sets using breadth-first searches. +Chapter 5. Fractal dust and infinite words – Schottky limit sets regarded as fractals; computer generation of these fractals using depth-first searches and iterated function systems. +Chapter 6. Indra's necklace – the continuous limit sets generated when pairs of generating circles touch. +Chapter 7. The glowing gasket – the Schottky group whose limit set is the Apollonian gasket; links to the modular group. +Chapter 8. Playing with parameters – parameterising Schottky groups with parabolic commutator using two complex parameters; using these parameters to explore the Teichmüller space of Schottky groups. +Chapter 9. Accidents will happen – introducing Maskit's slice, parameterised by a single complex parameter; exploring the boundary between discrete and non-discrete groups. +Chapter 10. Between the cracks – further exploration of the Maskit boundary between discrete and non-discrete groups in another slice of parameter space; identification and exploration of degenerate groups. +Chapter 11. Crossing boundaries – ideas for further exploration, such as adding a third generator. +Chapter 12. Epilogue – concluding overview of non-Euclidean geometry and Teichmüller theory. + + +== Importance == +Indra's Pearls is unusual because it aims to give the reader a sense of the development of a real-life mathematical investigation, rather than just a formal presentation of the final results. It covers a broad span of topics, showing interconnections among geometry, number theory, abstract algebra and computer graphics. It shows how computers are used by contemporary mathematicians. It uses computer graphics, diagrams and cartoons to enhance its written explanations. In the authors' own words: + +Our dream is that this book will reveal to our readers that mathematics is not alien and remote but just a very human exploration of the patterns of the world, one which thrives on play and surprise and beauty - Indra's Pearls p viii. + + +== References == +Mumford, David; Series, Caroline; Wright, David (2002), Indra's pearls (Hardback ed.), Cambridge University Press, ISBN 978-0-521-35253-6, MR 1913879 +Mumford, David; Series, Caroline; Wright, David (2015), Indra's pearls (Paperback ed.), Cambridge University Press, ISBN 978-1-107-56474-9 + + +== External links == +Indra's Pearls Web Site \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/International_Encyclopedia_of_Statistical_Science-0.md b/data/en.wikipedia.org/wiki/International_Encyclopedia_of_Statistical_Science-0.md new file mode 100644 index 000000000..d72eabf4d --- /dev/null +++ b/data/en.wikipedia.org/wiki/International_Encyclopedia_of_Statistical_Science-0.md @@ -0,0 +1,24 @@ +--- +title: "International Encyclopedia of Statistical Science" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/International_Encyclopedia_of_Statistical_Science" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:21.535662+00:00" +instance: "kb-cron" +--- + +The International Encyclopedia of Statistical Science is a statistical sciences reference published by Springer. It has been described as one of the scientific projects with the largest number of involved countries ever, since it includes contributors coming from 105 countries and six continents. It contains the last papers written by Hirotugu Akaike, Nobel Laureate Sir Clive Granger, John Nelder and Erich Leo Lehmann. +The team has been nominated for the 2026 Nobel Peace Prize by qualified nominators from Cambodia and Spain, with additional nominations anticipated . +The first edition, in three volumes, was edited by Miodrag Lovrić and appeared in December 2010. It is published by Springer and it is available in print and online form. + + +== See also == +Encyclopedia of Statistical Sciences + + +== References == + + +== External links == +Publisher's webpage for this Encyclopedia \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Introduction_to_Circle_Packing-0.md b/data/en.wikipedia.org/wiki/Introduction_to_Circle_Packing-0.md new file mode 100644 index 000000000..7fcc3cb5e --- /dev/null +++ b/data/en.wikipedia.org/wiki/Introduction_to_Circle_Packing-0.md @@ -0,0 +1,33 @@ +--- +title: "Introduction to Circle Packing" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Introduction_to_Circle_Packing" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:22.697059+00:00" +instance: "kb-cron" +--- + +Introduction to Circle Packing: The Theory of Discrete Analytic Functions is a mathematical monograph concerning systems of tangent circles and the circle packing theorem. It was written by Kenneth Stephenson and published in 2005 by the Cambridge University Press. + + +== Topics == +Circle packings, as studied in this book, are systems of circles that touch at tangent points but do not overlap, according to a combinatorial pattern of adjacencies specifying which pairs of circles should touch. The circle packing theorem states that a circle packing exists if and only if the pattern of adjacencies forms a planar graph; it was originally proved by Paul Koebe in the 1930s, and popularized by William Thurston, who rediscovered it in the 1970s and connected it with the theory of conformal maps and conformal geometry. As a topic, this should be distinguished from sphere packing, which considers higher dimensions (here, everything is two dimensional) and is more focused on packing density than on combinatorial patterns of tangency. +The book is divided into four parts, in progressive levels of difficulty. The first part introduces the subject visually, encouraging the reader to think about packings not just as static objects but as dynamic systems of circles that change in predictable ways when the conditions under which they are formed (their patterns of adjacency) change. The second part concerns the proof of the circle packing theorem itself, and of the associated rigidity theorem: every maximal planar graph can be associated with a circle packing that is unique up to Möbius transformations of the plane. More generally the same result holds for any triangulated manifold, with a circle packing on a topologically equivalent Riemann surface that is unique up to conformal equivalence. +The third part of the book concerns the degrees of freedom that arise when the pattern of adjacencies is not fully triangulated (it is a planar graph, but not a maximal planar graph). In this case, different extensions of this pattern to larger maximal planar graphs will lead to different packings, which can be mapped to each other by corresponding circles. The book explores the connection between these mappings, which it calls discrete analytic functions, and the analytic functions of classical mathematical analysis. The final part of the book concerns a conjecture of William Thurston, proved by Burton Rodin and Dennis Sullivan, that makes this analogy concrete: conformal mappings from any topological disk to a circle can be approximated by filling the disk by a hexagonal packing of unit circles, finding a circle packing that adds to that pattern of adjacencies a single outer circle, and constructing the resulting discrete analytic function. This part also includes applications to number theory and the visualization of brain structure. +Stephenson has implemented algorithms for circle packing and used them to construct the many illustrations of the book, giving to much of this work the flavor of experimental mathematics, although it is also mathematically rigorous. Unsolved problems are listed throughout the book, which also includes nine appendices on related topics such as the ring lemma and Doyle spirals. + + +== Audience and reception == +The book presents research-level mathematics, and is aimed at professional mathematicians interested in this and related topics. Reviewer Frédéric Mathéus describes the level of the material in the book as "both mathematically rigorous and accessible to the novice mathematician", presented in an approachable style that conveys the author's love of the material. However, although the preface to the book states that no background knowledge is necessary, and that the book can be read by non-mathematicians or used as an undergraduate textbook, reviewer Michele Intermont disagrees, noting that it has no exercises for students and writing that "non-mathematicians will be nothing other than frustrated with this book". Similarly, reviewer David Mumford finds the first seven chapters (part I and much of part II) to be at an undergraduate level, but writes that "as a whole, the book is suitable for graduate students in math". + + +== Publication == +Stephenson, Kenneth (2005), Introduction to circle packing: the theory of discrete analytic functions, New York: Cambridge University Press, ISBN 9780521823562, OCLC 55878014 + + +== References == + + +== External links == +Ken Stephenson's CirclePack software \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Jade_Mirror_of_the_Four_Unknowns-0.md b/data/en.wikipedia.org/wiki/Jade_Mirror_of_the_Four_Unknowns-0.md new file mode 100644 index 000000000..0ea669d9d --- /dev/null +++ b/data/en.wikipedia.org/wiki/Jade_Mirror_of_the_Four_Unknowns-0.md @@ -0,0 +1,874 @@ +--- +title: "Jade Mirror of the Four Unknowns" +chunk: 1/2 +source: "https://en.wikipedia.org/wiki/Jade_Mirror_of_the_Four_Unknowns" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:23.909555+00:00" +instance: "kb-cron" +--- + +Jade Mirror of the Four Unknowns, Siyuan yujian (simplified Chinese: 四元玉鉴; traditional Chinese: 四元玉鑒), also referred to as Jade Mirror of the Four Origins, is a 1303 mathematical monograph by Yuan dynasty mathematician Zhu Shijie. +The book consists of an introduction and three books, with a total of 288 problems. The first four problems in the introduction illustrate his method of the four unknowns. He showed how to convert a problem stated verbally into a system of polynomial equations (up to the 14th order), by using up to four unknowns: 天 Heaven, 地 Earth, 人 Man, 物 Matter, and then how to reduce the system to a single polynomial equation in one unknown by successive elimination of unknowns. He then solved the high-order equation by Southern Song dynasty mathematician Qin Jiushao's "Ling long kai fang" method published in Shùshū Jiǔzhāng (“Mathematical Treatise in Nine Sections”) in 1247 (more than 570 years before English mathematician William Horner's method using synthetic division). To do this, he makes use of the Pascal triangle, which he labels as the diagram of an ancient method first discovered by Jia Xian before 1050. +Zhu also solved square and cube roots problems by solving quadratic and cubic equations, and added to the understanding of series and progressions, classifying them according to the coefficients of the Pascal triangle. He also showed how to solve systems of linear equations by reducing the matrix of their coefficients to diagonal form. +Jade Mirror of the Four Unknowns consists of four books, with 24 classes and 288 problems, in which 232 problems deal with Tian yuan shu, 36 problems deal with variable of two variables, 13 problems of three variables, and 7 problems of four variables. + +== Introduction == + +The four quantities are x, y, z, w can be presented with the following diagram + +x +y 太w +z +The square of which is: + +=== The Unitary Nebuls === +This section deals with Tian yuan shu or problems of one unknown. + +Question: Given the product of huangfan and zhi ji equals to 24 paces, and the sum of vertical and hypotenuse equals to 9 paces, what is the value of the base? +Answer: 3 paces +Set up unitary tian as the base (that is let the base be the unknown quantity x) +Since the product of huangfang and zhi ji = 24 +in which + +huangfan is defined as： + + + + ( + a + + + b + − + c + ) + + + {\displaystyle (a+b-c)} + + +zhi ji： + + + + a + b + + + {\displaystyle ab} + + +therefore + + + + ( + a + + + b + − + c + ) + a + b + = + 24 + + + {\displaystyle (a+b-c)ab=24} + + +Further, the sum of vertical and hypotenuse is + + + + + b + + + c + = + 9 + + + {\displaystyle b+c=9} + + +Set up the unknown unitary tian as the vertical + + + + + x + = + a + + + {\displaystyle x=a} + + +Then use Pythagoras to isolate c and b: + + + + + a + + 2 + + + + + + b + + 2 + + + = + + c + + 2 + + + ⟺ + + c + + 2 + + + − + + b + + 2 + + + = + + a + + 2 + + + ⟺ + ( + c + − + b + ) + ( + c + + + b + ) + = + + a + + 2 + + + ⟺ + c + − + b + = + + + + a + + 2 + + + + c + + + b + + + + = + + + + x + + 2 + + + 9 + + + + + {\displaystyle a^{2}+b^{2}=c^{2}\Longleftrightarrow c^{2}-b^{2}=a^{2}\Longleftrightarrow (c-b)(c+b)=a^{2}\Longleftrightarrow c-b={\frac {a^{2}}{c+b}}={\frac {x^{2}}{9}}} + + +such that we obtain: + + + + + 2 + c + = + ( + c + + + b + ) + + + ( + c + − + b + ) + = + 9 + + + + + + x + + 2 + + + 9 + + + + + {\displaystyle 2c=(c+b)+(c-b)=9+{\frac {x^{2}}{9}}} + + + + + + 2 + b + = + ( + c + + + b + ) + − + ( + c + − + b + ) + = + 9 + − + + + + x + + 2 + + + 9 + + + + + {\displaystyle 2b=(c+b)-(c-b)=9-{\frac {x^{2}}{9}}} + + +Combining everything, we obtain the following equation: + + （ + + + + + x + + 5 + + + − + 9 + + x + + 4 + + + − + 81 + + x + + 3 + + + + + 729 + + x + + 2 + + + = + 3888 + + + {\displaystyle x^{5}-9x^{4}-81x^{3}+729x^{2}=3888} + +） + 太 + +Solve it and obtain x=3 + +=== The Mystery of Two Natures === +太 Unitary + +equation: + + + + − + 2 + + y + + 2 + + + − + x + + y + + 2 + + + + + 2 + x + y + + + 2 + + x + + 2 + + + y + + + + x + + 3 + + + = + 0 + + + {\displaystyle -2y^{2}-xy^{2}+2xy+2x^{2}y+x^{3}=0} + +; +from the given + +太 + +equation: + + + + 2 + + y + + 2 + + + − + x + + y + + 2 + + + + + 2 + x + y + + + + x + + 3 + + + = + 0 + + + {\displaystyle 2y^{2}-xy^{2}+2xy+x^{3}=0} + +; +we get: + +太 + + + + + 8 + x + + + 4 + + x + + 2 + + + = + 0 + + + {\displaystyle 8x+4x^{2}=0} + + +and + +太 + + + + + 2 + + x + + 2 + + + + + + x + + 3 + + + = + 0 + + + {\displaystyle 2x^{2}+x^{3}=0} + + +by method of elimination, we obtain a quadratic equation + + + + + + x + + 2 + + + − + 2 + x + − + 8 + = + 0 + + + {\displaystyle x^{2}-2x-8=0} + + +solution: + + + + x + = + 4 + + + {\displaystyle x=4} + +. + +=== The Evolution of Three Talents === +Template for solution of problem of three unknowns +Zhu Shijie explained the method of elimination in detail. His example has been quoted frequently in scientific literature. +Set up three equations as follows + +太 + + + + + − + y + − + z + − + + y + + 2 + + + x + − + x + + + x + y + z + = + 0 + + + {\displaystyle -y-z-y^{2}x-x+xyz=0} + + .... I + + + + + − + y + − + z + + + x + − + + x + + 2 + + + + + x + z + = + 0 + + + {\displaystyle -y-z+x-x^{2}+xz=0} + +.....II +太 + + + + + + y + + 2 + + + − + + z + + 2 + + + + + + x + + 2 + + + = + 0 + ; + + + {\displaystyle y^{2}-z^{2}+x^{2}=0;} + +....III +Elimination of unknown between II and III +by manipulation of exchange of variables +We obtain + + 太 + + + + + − + x + − + 2 + + x + + 2 + + + + + y + + + + y + + 2 + + + + + x + y + − + x + + y + + 2 + + + + + + x + + 2 + + + y + + + {\displaystyle -x-2x^{2}+y+y^{2}+xy-xy^{2}+x^{2}y} + + ...IV +and + +太 + + + + + − + 2 + x + − + 2 + + x + + 2 + + + + + 2 + y + − + 2 + + y + + 2 + + + + + + y + + 3 + + + + + 4 + x + y + − + 2 + x + + y + + 2 + + + + + x + + y + + 2 + + + + + {\displaystyle -2x-2x^{2}+2y-2y^{2}+y^{3}+4xy-2xy^{2}+xy^{2}} + +.... V +Elimination of unknown between IV and V we obtain a 3rd order equation + + + + + + x + + 4 + + + − + 6 + + x + + 3 + + + + + 4 + + x + + 2 + + + + + 6 + x + − + 5 + = + 0 + + + {\displaystyle x^{4}-6x^{3}+4x^{2}+6x-5=0} + + +Solve to this 3rd order equation to obtain + + + + x + = + 5 + + + {\displaystyle x=5} + +; +Change back the variables +We obtain the hypothenus =5 paces + +=== Simultaneous of the Four Elements === +This section deals with simultaneous equations of four unknowns. + + + + + + + { + + + + − + 2 + y + + + x + + + z + = + 0 + + + + + − + + y + + 2 + + + x + + + 4 + y + + + 2 + x + − + + x + + 2 + + + + + 4 + z + + + x + z + = + 0 + + + + + + x + + 2 + + + + + + y + + 2 + + + − + + z + + 2 + + + = + 0 + + + + + 2 + y + − + w + + + 2 + x + = + 0 + + + + + + + + + {\displaystyle {\begin{cases}-2y+x+z=0\\-y^{2}x+4y+2x-x^{2}+4z+xz=0\\x^{2}+y^{2}-z^{2}=0\\2y-w+2x=0\end{cases}}} + \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Jade_Mirror_of_the_Four_Unknowns-1.md b/data/en.wikipedia.org/wiki/Jade_Mirror_of_the_Four_Unknowns-1.md new file mode 100644 index 000000000..d76cb2ac6 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Jade_Mirror_of_the_Four_Unknowns-1.md @@ -0,0 +1,710 @@ +--- +title: "Jade Mirror of the Four Unknowns" +chunk: 2/2 +source: "https://en.wikipedia.org/wiki/Jade_Mirror_of_the_Four_Unknowns" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:23.909555+00:00" +instance: "kb-cron" +--- + +Successive elimination of unknowns to get + + + + + + 4 + + x + + 2 + + + − + 7 + x + − + 686 + = + 0 + + + {\displaystyle 4x^{2}-7x-686=0} + + +Solve this and obtain 14 paces + +== Book I == + +=== Problems of Right Angle Triangles and Rectangles === +There are 18 problems in this section. +Problem 18 +Obtain a tenth order polynomial equation: + + + + + 16 + + x + + 10 + + + − + 64 + + x + + 9 + + + + + 160 + + x + + 8 + + + − + 384 + + x + + 7 + + + + + 512 + + x + + 6 + + + − + 544 + + x + + 5 + + + + + 456 + + x + + 4 + + + + + 126 + + x + + 3 + + + + + 3 + + x + + 2 + + + − + 4 + x + − + 177162 + = + 0 + + + {\displaystyle 16x^{10}-64x^{9}+160x^{8}-384x^{7}+512x^{6}-544x^{5}+456x^{4}+126x^{3}+3x^{2}-4x-177162=0} + + +The root of which is x = 3, multiply by 4, getting 12. That is the final answer. + +=== Problems of Plane Figures === +There are 18 problems in this section + +=== Problems of Piece Goods === +There are 9 problems in this section + +=== Problems on Grain Storage === +There are 6 problems in this section + +=== Problems on Labour === +There are 7 problems in this section + +=== Problems of Equations for Fractional Roots === +There are 13 problems in this section + +== Book II == + +=== Mixed Problems === + +=== Containment of Circles and Squares === + +=== Problems on Areas === + +=== Surveying with Right Angle Triangles === +There are eight problems in this section + +Problem 1 + +Question: There is a rectangular town of unknown dimension which has one gate on each side. There is a pagoda located at 240 paces from the south gate. A man walking 180 paces from the west gate can see the pagoda, he then walks towards the south-east corner for 240 paces and reaches the pagoda; what is the length and width of the rectangular town? +Answer: 120 paces in length and width one li +Let tian yuan unitary as half of the length, we obtain a 4th order equation + + + + + + x + + 4 + + + + + 480 + + x + + 3 + + + − + 270000 + + x + + 2 + + + + + 15552000 + x + + + 1866240000 + = + 0 + + + {\displaystyle x^{4}+480x^{3}-270000x^{2}+15552000x+1866240000=0} + + +solve it and obtain x=240 paces, hence length =2x= 480 paces=1 li and 120 paces. +Similarity, let tian yuan unitary(x) equals to half of width +we get the equation: + + + + + + x + + 4 + + + + + 360 + + x + + 3 + + + − + 270000 + + x + + 2 + + + + + 20736000 + x + + + 1866240000 + = + 0 + + + {\displaystyle x^{4}+360x^{3}-270000x^{2}+20736000x+1866240000=0} + + +Solve it to obtain x=180 paces, length =360 paces =one li. + +Problem 7 +Identical to The depth of a ravine (using hence-forward cross-bars) in Haidao Suanjing. +Problem 8 +Identical to The depth of a transparent pool in Haidao Suanjing. + +=== Hay Stacks === + +=== Bundles of Arrows === + +=== Land Measurement === + +=== Summon Men According to Need === +Problem No 5 is the earliest 4th order interpolation formula in the world +men summoned : + + + + n + a + + + + + + 1 + + 2 + ! + + + + + n + ( + n + − + 1 + ) + b + + + + + + 1 + + 3 + ! + + + + + n + ( + n + − + 1 + ) + ( + n + − + 2 + ) + c + + + + + + 1 + + 4 + ! + + + + + n + ( + n + − + 1 + ) + ( + n + − + 2 + ) + ( + n + − + 3 + ) + d + + + {\displaystyle na+{\tfrac {1}{2!}}n(n-1)b+{\tfrac {1}{3!}}n(n-1)(n-2)c+{\tfrac {1}{4!}}n(n-1)(n-2)(n-3)d} + + +In which + +a=1st order difference +b=2nd order difference +c=3rd order difference +d=4th order difference + +== Book III == + +=== Fruit pile === +This section contains 20 problems dealing with triangular piles, rectangular piles +Problem 1 +Find the sum of triangular pile + + + + + 1 + + + 3 + + + 6 + + + 10 + + + . + . + . + + + + + 1 + 2 + + + n + ( + n + + + 1 + ) + + + {\displaystyle 1+3+6+10+...+{\frac {1}{2}}n(n+1)} + + +and value of the fruit pile is: + + + + + v + = + 2 + + + 9 + + + 24 + + + 50 + + + 90 + + + 147 + + + 224 + + + ⋯ + + + + + 1 + 2 + + + n + ( + n + + + 1 + + ) + + 2 + + + + + {\displaystyle v=2+9+24+50+90+147+224+\cdots +{\frac {1}{2}}n(n+1)^{2}} + + +Zhu Shijie use Tian yuan shu to solve this problem by letting x=n +and obtained the formular + + + + + v + = + + + 1 + + 2 + ⋅ + 3 + ⋅ + 4 + + + + ( + 3 + x + + + 5 + ) + x + ( + x + + + 1 + ) + ( + x + + + 2 + ) + + + {\displaystyle v={\frac {1}{2\cdot 3\cdot 4}}(3x+5)x(x+1)(x+2)} + + +From given condition + + + + v + = + 1320 + + + {\displaystyle v=1320} + +, hence + + + + + 3 + + x + + 4 + + + + + 14 + + x + + 3 + + + + + 21 + + x + + 2 + + + + + 10 + x + − + 31680 + = + 0 + + + {\displaystyle 3x^{4}+14x^{3}+21x^{2}+10x-31680=0} + + +Solve it to obtain + + + + x + = + n + = + 9 + + + {\displaystyle x=n=9} + +. +Therefore, + + + + + v + = + 2 + + + 9 + + + 24 + + + 50 + + + 90 + + + 147 + + + 224 + + + 324 + + + 450 + = + 1320 + + + {\displaystyle v=2+9+24+50+90+147+224+324+450=1320} + +。 + +=== Figures within Figure === + +=== Simultaneous Equations === + +=== Equation of two unknowns === + +=== Left and Right === + +=== Equation of Three Unknowns === + +=== Equation of Four Unknowns === +Six problems of four unknowns. +Question 2 +Yield a set of equations in four unknowns: . + + + + + + + { + + + + − + 3 + + y + + 2 + + + + + 8 + y + − + 8 + x + + + 8 + z + = + 0 + + + + + 4 + + y + + 2 + + + − + 8 + x + y + + + 3 + + x + + 2 + + + − + 8 + y + z + + + 6 + x + z + + + 3 + + z + + 2 + + + = + 0 + + + + + + y + + 2 + + + + + + x + + 2 + + + − + + z + + 2 + + + = + 0 + + + + + 2 + y + + + 4 + x + + + 2 + z + − + w + = + 0 + + + + + + + + + {\displaystyle {\begin{cases}-3y^{2}+8y-8x+8z=0\\4y^{2}-8xy+3x^{2}-8yz+6xz+3z^{2}=0\\y^{2}+x^{2}-z^{2}=0\\2y+4x+2z-w=0\end{cases}}} + + +== References == + +Sources \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Journey_into_Geometries-0.md b/data/en.wikipedia.org/wiki/Journey_into_Geometries-0.md new file mode 100644 index 000000000..6c43b4ab1 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Journey_into_Geometries-0.md @@ -0,0 +1,28 @@ +--- +title: "Journey into Geometries" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Journey_into_Geometries" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:25.051504+00:00" +instance: "kb-cron" +--- + +Journey into Geometries is a book on non-Euclidean geometry. It was written by Hungarian-Australian mathematician Márta Svéd and published in 1991 by the Mathematical Association of America in their MAA Spectrum book series. + + +== Topics == +Journey into Geometries is written as a conversation between three characters: Alice, from Alice's Adventures in Wonderland (but older and familiar with Euclidean geometry), Lewis Carroll, the author of Alice's adventures, and a modern mathematician named "Dr. Whatif". Its topics include hyperbolic geometry, inversive geometry, and projective geometry, following an arrangement of these topics credited to Australian mathematician Carl Moppert, and possibly based on an earlier German-language textbook on similar topics by F. Gonseth and P. Marti. +As in Alice's original adventures, the first part of the book is arranged as a travelogue. This part of the book has six chapters, each ending with a set of exercises. Following these chapters, more conventionally written material covers geometric axiom systems and provides solutions to the exercises. + + +== Audience and reception == +Reviewer William E. Fenton is unsure of the audience of the book, writing that it is not suitable as a textbook and would scare most undergraduates, but is too unserious for graduate students. David A. Thomas identifies the audience as "people who like to play with mathematical ideas". +Fenton criticizes the book's style as a little too glib and lead-footed, and its illustrations as amateurish. H. W. Guggenheimer faults the treatment of projective geometry as "rather sketchy". Nevertheless, Fenton writes that he found the book engrossing and well-organized, particularly praising its exercises. Both Fenton and Guggenheimer recommend the book to talented students of mathematics, and both Fenton and David A. Thomas suggest it as auxiliary reading for geometry courses. + + +== References == + + +== External links == +Journey into Geometries on the Internet Archive \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/La_Géométrie-0.md b/data/en.wikipedia.org/wiki/La_Géométrie-0.md new file mode 100644 index 000000000..156d3e0c6 --- /dev/null +++ b/data/en.wikipedia.org/wiki/La_Géométrie-0.md @@ -0,0 +1,54 @@ +--- +title: "La Géométrie" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/La_Géométrie" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:44:56.902470+00:00" +instance: "kb-cron" +--- + +La Géométrie (French pronunciation: [la ʒeɔmetʁi]) was published in 1637 as an appendix to Discours de la méthode (Discourse on the Method), written by René Descartes. In the Discourse, Descartes presents his method for obtaining clarity on any subject. La Géométrie and two other appendices, also by Descartes, La Dioptrique (Optics) and Les Météores (Meteorology), were published with the Discourse to give examples of the kinds of successes he had achieved following his method (as well as, perhaps, considering the contemporary European social climate of intellectual competitiveness, to show off a bit to a wider audience). + +The work was the first to propose the idea of uniting algebra and geometry into a single subject and invented an algebraic geometry called analytic geometry, which involves reducing geometry to a form of arithmetic and algebra and translating geometric shapes into algebraic equations. For its time this was ground-breaking. It also contributed to the mathematical ideas of Leibniz and Newton and was thus important in the development of calculus. + + +== The text == +This appendix is divided into three "books". +Book I is titled Problems Which Can Be Constructed by Means of Circles and Straight Lines Only. In this book he introduces algebraic notation that is still in use today. The letters at the end of the alphabet, viz., x, y, z, etc. are to denote unknown variables, while those at the start of the alphabet, a, b, c, etc. denote constants. He introduces modern exponential notation for powers (except for squares, where he kept the older tradition of writing repeated letters, such as, aa). He also breaks with the Greek tradition of associating powers with geometric referents, a2 with an area, a3 with a volume and so on, and treats them all as possible lengths of line segments. These notational devices permit him to describe an association of numbers to lengths of line segments that could be constructed with straightedge and compass. The bulk of the remainder of this book is occupied by Descartes's solution to "the locus problems of Pappus." According to Pappus, given three or four lines in a plane, the problem is to find the locus of a point that moves so that the product of the distances from two of the fixed lines (along specified directions) is proportional to the square of the distance to the third line (in the three line case) or proportional to the product of the distances to the other two lines (in the four line case). In solving these problems and their generalizations, Descartes takes two line segments as unknown and designates them x and y. Known line segments are designated a, b, c, etc. The germinal idea of a Cartesian coordinate system can be traced back to this work. +In the second book, called On the Nature of Curved Lines, Descartes described two kinds of curves, called by him geometrical and mechanical. Geometrical curves are those which are now described by algebraic equations in two variables, however, Descartes described them kinematically and an essential feature was that all of their points could be obtained by construction from lower order curves. This represented an expansion beyond what was permitted by straightedge and compass constructions. Other curves like the quadratrix and spiral, where only some of whose points could be constructed, were termed mechanical and were not considered suitable for mathematical study. Descartes also devised an algebraic method for finding the normal at any point of a curve whose equation is known. The construction of the tangents to the curve then easily follows and Descartes applied this algebraic procedure for finding tangents to several curves. +The third book, On the Construction of Solid and Supersolid Problems, is more properly algebraic than geometric and concerns the nature of equations and how they may be solved. He recommends that all terms of an equation be placed on one side and set equal to 0 to facilitate solution. He points out the factor theorem for polynomials and gives an intuitive proof that a polynomial of degree n has n roots. He systematically discussed negative and imaginary roots of equations and explicitly used what is now known as Descartes' rule of signs. + + +== Aftermath == +Descartes wrote La Géométrie in French rather than the language used for most scholarly publication at the time, Latin. His exposition style was far from clear, the material was not arranged in a systematic manner and he generally only gave indications of proofs, leaving many of the details to the reader. His attitude toward writing is indicated by statements such as "I did not undertake to say everything," or "It already wearies me to write so much about it," that occur frequently. Descartes justifies his omissions and obscurities with the remark that much was deliberately omitted "in order to give others the pleasure of discovering [it] for themselves." +Descartes is often credited with inventing the coordinate plane because he had the relevant concepts in his book, however, nowhere in La Géométrie does the modern rectangular coordinate system appear. This and other improvements were added by mathematicians who took it upon themselves to clarify and explain Descartes' work. +This enhancement of Descartes' work was primarily carried out by Frans van Schooten, a professor of mathematics at Leiden and his students. Van Schooten published a Latin version of La Géométrie in 1649 and this was followed by three other editions in 1659−1661, 1683 and 1693. The 1659−1661 edition was a two volume work more than twice the length of the original filled with explanations and examples provided by van Schooten and his students. One of these students, Johannes Hudde provided a convenient method for determining double roots of a polynomial, known as Hudde's rule, that had been a difficult procedure in Descartes's method of tangents. These editions established analytic geometry in the seventeenth century. + + +== See also == +Claude Rabuel + + +== Notes == + + +== References == +Boyer, Carl B. (2004) [1956], History of Analytic Geometry, Dover, ISBN 978-0-486-43832-0 +Burton, David M. (2011), The History of Mathematics / An Introduction (7th ed.), McGraw Hill, ISBN 978-0-07-338315-6 +Descartes, René (2006) [1637]. A discourse on the method of correctly conducting one's reason and seeking truth in the sciences. Translated by Ian Maclean. Oxford University Press. ISBN 0-19-282514-3. + + +== Further reading == +Grosholz, Emily (1998). "Chapter 4: Cartesian method and the Geometry". In Georges J. D. Moyal (ed.). René Descartes: critical assessments. Routledge. ISBN 0-415-02358-0. +Hawking, Stephen W. (2005). "René Descartes". God created the integers: the mathematical breakthroughs that changed history. Running Press. pp. 285 ff. ISBN 0-7624-1922-9. +Serfati, M. (2005). "Chapter 1: René Descartes, Géométrie, Latin edition (1649), French edition (1637)". In I. Grattan-Guinness; Roger Cooke (eds.). Landmark writings in Western mathematics 1640-1940. Elsevier. ISBN 0-444-50871-6. +Smith, David E.; Latham, M. L. (1954) [1925]. The Geometry of René Descartes. Dover Publications. ISBN 0-486-60068-8. {{cite book}}: ISBN / Date incompatibility (help) + + +== External links == + Quotations related to La Géométrie at Wikiquote +Project Gutenberg copy of La Géométrie +Bad OCR: Cornell University Library copy of La Géométrie +Archive.org: The Geometry of Rene Descartes +Facsimile (fr) : La Géométrie Archived 2019-11-28 at the Wayback Machine \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Letters_to_a_German_Princess-0.md b/data/en.wikipedia.org/wiki/Letters_to_a_German_Princess-0.md new file mode 100644 index 000000000..0a1ce4b58 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Letters_to_a_German_Princess-0.md @@ -0,0 +1,47 @@ +--- +title: "Letters to a German Princess" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Letters_to_a_German_Princess" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:26.216400+00:00" +instance: "kb-cron" +--- + +Letters to a German Princess, On Different Subjects in Physics and Philosophy (French: Lettres à une princesse d'Allemagne sur divers sujets de physique et de philosophie) were a series of 234 letters written by the mathematician Leonhard Euler between 1760 and 1762 addressed to Friederike Charlotte of Brandenburg-Schwedt and her younger sister Louise. + + +== Contents == +Euler started the first letter with an explanation of the concept of "size". Starting with the definition of a foot, he defined the mile and the diameter of the earth as a unit in terms of foot and then calculated the distance of the planets of the Solar System in terms of the diameter of the earth. + + +== Publication == +The first two volumes of the 234 letters originally written in French appeared in print in Saint Petersburg in 1768 and the third in Frankfurt in 1774. The letters were later reprinted in Paris with the first volume in 1787, the second in 1788 and the third in 1789. +The publication of the book was supported by empress Catherine II with her personally writing to Count Vorontsov in January 1766: + +I am certain that the academy will be resurrected from its ashes by such an important acquisition, and congratulate myself in advance in having restored this great man to Russia. +Russian translation of the letters followed in Saint Petersburg by Euler's student Stepan Rumovsky between 1768 and 1774 in 3 volumes. + + +== Translations == +The first English translation of the Letters were done by the Scottish minister Henry Hunter in 1795. Hunter targeted the translation at British women, believing that Euler intended to educate women through his work. +The translation of Hunter was based on the 1787 Paris Edition, of Marquis de Condorcet and Sylvestre François Lacroix. The translation differed from the original letters of Euler in its omission of "... the frequent, tiresome, courtly address of YOUR HIGHNESS". +The Marquis de Condorcet's translation, made during the Age of Enlightenment, was notable for its omission of Euler's theological references which Condorcet found as "anathema" to teaching science and rationalism. +Translations followed in other languages including Spanish (1798) which differed from the original book by a footnote describing the newly discovered planet Uranus. Subsequent German edition (1847), and French editions (1812 and 1829) were also noted for their reference to Uranus and four minor planets respectively. + + +== See also == +On the Connexion of the Physical Sciences + + +== References and notes == + +Attribution + This article incorporates text from a publication now in the public domain: Lee, Sidney, ed. (1891). "Hunter, Henry". Dictionary of National Biography. Vol. 28. London: Smith, Elder & Co. + + +== External links == + Letters on Different Subjects in Natural Philosophy, Volume 1 public domain audiobook at LibriVox + + +== Further reading == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Letters_to_a_Young_Mathematician-0.md b/data/en.wikipedia.org/wiki/Letters_to_a_Young_Mathematician-0.md new file mode 100644 index 000000000..6ad0bd10f --- /dev/null +++ b/data/en.wikipedia.org/wiki/Letters_to_a_Young_Mathematician-0.md @@ -0,0 +1,16 @@ +--- +title: "Letters to a Young Mathematician" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Letters_to_a_Young_Mathematician" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:27.375942+00:00" +instance: "kb-cron" +--- + +Letters to a Young Mathematician (ISBN 0-465-08231-9) is a 2006 book by Ian Stewart, and is part of Basic Books' Art of Mentoring series. Stewart mentions in the preface that he considers this book an update to G.H. Hardy's A Mathematician's Apology. +The book is made up of letters to a fictional correspondent of Stewart's, an aspiring mathematician named Meg. The roughly chronological letters follow Meg from her high school years up to her receiving tenure from an American university. +Reviews of the book were generally positive. Fernando Q. Gouvêa's review for the MAA calls it "full of good advice, much of it direct and to the point" and later, that "while it won't change the world, it may well help some young people decide to be (or not to be) mathematicians." In Emma Carberry's review for the AMS, reacted differently, saying that "one does not so much feel the benefit of a ream of practical advice, but rather of exposure to the inner realm of mathematics". A review in Nature was harsher, however, saying that "there is a general lack of information ... [and] too much jargon" and that it "suffers from being written entirely for a US audience", but even this review finds a bright note, "The letter in which Stewart tells Meg how to teach undergraduates should be compulsory reading for all lecturers and tutors." + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Liber_Abaci-0.md b/data/en.wikipedia.org/wiki/Liber_Abaci-0.md new file mode 100644 index 000000000..27762c6a0 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Liber_Abaci-0.md @@ -0,0 +1,25 @@ +--- +title: "Liber Abaci" +chunk: 1/2 +source: "https://en.wikipedia.org/wiki/Liber_Abaci" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:28.580605+00:00" +instance: "kb-cron" +--- + +The Liber Abaci or Liber Abbaci (Latin for "The Book of Calculation") was a 1202 Latin work on arithmetic by Leonardo of Pisa, posthumously known as Fibonacci. It is primarily famous for introducing both base-10 positional notation and the symbols known as Arabic numerals in Europe. + +== Premise == +Liber Abaci was among the first Western books to describe the Hindu–Arabic numeral system and to use symbols resembling modern "Arabic numerals". By addressing the applications of both commercial tradesmen and mathematicians, it promoted the superiority of the system and the use of these glyphs. +Although the book's title is sometimes translated as "The Book of the Abacus", Sigler (2002) notes that the word in title does not refer to the abacus as a calculating device. Rather, the word "abacus" was used at the time to refer to calculation in any form; the spelling "abbacus" with two "b"s was, and still is in Italy, used to refer to calculation using Hindu-Arabic numerals. The book describes methods of doing calculations without aid of an abacus, and as Ore (1948) confirms, for centuries after its publication the algorismists (followers of the style of calculation demonstrated in Liber Abaci) remained in conflict with the abacists (traditionalists who continued to use the abacus in conjunction with Roman numerals). Carl Boyer emphasizes in his History of Mathematics that although "Liber abaci...is not on the abacus" per se, nevertheless "...it is a very thorough treatise on algebraic methods and problems in which the use of the Hindu-Arabic numerals is strongly advocated." + +== Summary of sections == +The first section introduces the Hindu–Arabic numeral system, including its arithmetic and methods for converting between different representation systems. This section also includes the first known description of trial division for testing whether a number is composite and, if so, factoring it. +The second section presents examples from commerce, such as conversions of currency and measurements, and calculations of profit and interest. +The third section discusses a number of mathematical problems; for instance, it includes the Chinese remainder theorem, perfect numbers and Mersenne primes as well as formulas for arithmetic series and for square pyramidal numbers. Another example in this chapter involves the growth of a population of rabbits, where the solution requires generating a numerical sequence. Although the resulting Fibonacci sequence dates back long before Leonardo, its inclusion in his book is why the sequence is named after him today. +The fourth section derives approximations, both numerical and geometrical, of irrational numbers such as square roots. +The book also includes proofs in Euclidean geometry. Fibonacci's method of solving algebraic equations shows the influence of the early 10th-century Egyptian mathematician Abū Kāmil Shujāʿ ibn Aslam. + +== Fibonacci's notation for fractions == +In Liber Abaci, Fibonacci's notation for rational numbers is intermediate in form between the Egyptian fractions commonly used until that time and the vulgar fractions still in use today. It differs from modern fraction notation in three key ways: \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Liber_Abaci-1.md b/data/en.wikipedia.org/wiki/Liber_Abaci-1.md new file mode 100644 index 000000000..3578ac765 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Liber_Abaci-1.md @@ -0,0 +1,371 @@ +--- +title: "Liber Abaci" +chunk: 2/2 +source: "https://en.wikipedia.org/wiki/Liber_Abaci" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:28.580605+00:00" +instance: "kb-cron" +--- + +Modern notation generally writes a fraction to the right of the whole number to which it is added, for instance + + + + 2 + + + + + 1 + 3 + + + + + + {\displaystyle 2\,{\tfrac {1}{3}}} + + for 7/3. Fibonacci instead would write the same fraction to the left, i.e., + + + + + + + 1 + 3 + + + + + 2 + + + {\displaystyle {\tfrac {1}{3}}\,2} + +. +Fibonacci used a composite fraction notation in which a sequence of numerators and denominators shared the same fraction bar; each such term represented an additional fraction of the given numerator divided by the product of all the denominators below and to the right of it. That is, + + + + + + + + b + + + a + + + d + + + c + + + + + = + + + + a + c + + + + + + + + + b + + c + d + + + + + + + {\displaystyle {\tfrac {b\,\,a}{d\,\,c}}={\tfrac {a}{c}}+{\tfrac {b}{cd}}} + +, and + + + + + + + + c + + + b + + + a + + + f + + + e + + + d + + + + + = + + + + a + d + + + + + + + + + b + + d + e + + + + + + + + + + c + + d + e + f + + + + + + + {\displaystyle {\tfrac {c\,\,b\,\,a}{f\,\,e\,\,d}}={\tfrac {a}{d}}+{\tfrac {b}{de}}+{\tfrac {c}{def}}} + +. The notation was read from right to left. For example, 29/30 could be written as + + + + + + + + 1 + + + 2 + + + 4 + + + 2 + + + 3 + + + 5 + + + + + + + {\displaystyle {\tfrac {1\,\,2\,\,4}{2\,\,3\,\,5}}} + +, representing the value + + + + + + + 4 + 5 + + + + + + + + + 2 + + 3 + × + 5 + + + + + + + + + + 1 + + 2 + × + 3 + × + 5 + + + + + + + {\displaystyle {\tfrac {4}{5}}+{\tfrac {2}{3\times 5}}+{\tfrac {1}{2\times 3\times 5}}} + +. This can be viewed as a form of mixed radix notation and was very convenient for dealing with traditional systems of weights, measures, and currency. For instance, for units of length, a foot is 1/3 of a yard, and an inch is 1/12 of a foot, so a quantity of 5 yards, 2 feet, and + + + + 7 + + + + 3 + 4 + + + + + + {\displaystyle 7{\tfrac {3}{4}}} + + inches could be represented as a composite fraction: + + + + + + + + 3 + + + 7 + + + 2 + + + 4 + + + 12 + + + 3 + + + + + + 5 + + + {\displaystyle {\tfrac {3\ \,7\,\,2}{4\,\,12\,\,3}}\,5} + + yards. However, typical notations for traditional measures, while similarly based on mixed radixes, do not write out the denominators explicitly; the explicit denominators in Fibonacci's notation allow him to use different radixes for different problems when convenient. Sigler also points out an instance where Fibonacci uses composite fractions in which all denominators are 10, prefiguring modern decimal notation for fractions. +Fibonacci sometimes wrote several fractions next to each other, representing a sum of the given fractions. For instance, 1/3+1/4 = 7/12, so a notation like + + + + + + + 1 + 4 + + + + + + + + 1 + 3 + + + + + 2 + + + {\displaystyle {\tfrac {1}{4}}\,{\tfrac {1}{3}}\,2} + + would represent the number that would now more commonly be written as the mixed number + + + + 2 + + + + + 7 + 12 + + + + + + {\displaystyle 2\,{\tfrac {7}{12}}} + +, or simply the improper fraction + + + + + + + 31 + 12 + + + + + + {\displaystyle {\tfrac {31}{12}}} + +. Notation of this form can be distinguished from sequences of numerators and denominators sharing a fraction bar by the visible break in the bar. If all numerators are 1 in a fraction written in this form, and all denominators are different from each other, the result is an Egyptian fraction representation of the number. This notation was also sometimes combined with the composite fraction notation: two composite fractions written next to each other would represent the sum of the fractions. +The complexity of this notation allows numbers to be written in many different ways, and Fibonacci described several methods for converting from one style of representation to another. In particular, chapter II.7 contains a list of methods for converting an improper fraction to an Egyptian fraction, including the greedy algorithm for Egyptian fractions, also known as the Fibonacci–Sylvester expansion. + +== Modus Indorum == +In the Liber Abaci, Fibonacci wrote the following, introducing the affirmative Modus Indorum (the method of the Indians), today known as Hindu–Arabic numeral system or base-10 positional notation. It also introduced digits that greatly resembled the modern Arabic numerals. + +As my father was a public official away from our homeland in the Bugia customshouse established for the Pisan merchants who frequently gathered there, he had me in my youth brought to him, looking to find for me a useful and comfortable future; there he wanted me to be in the study of mathematics and to be taught for some days. There from a marvelous instruction in the art of the nine Indian figures, the introduction and knowledge of the art pleased me so much above all else, and I learnt from them, whoever was learned in it, from nearby Egypt, Syria, Greece, Sicily and Provence, and their various methods, to which locations of business I travelled considerably afterwards for much study, and I learnt from the assembled disputations. But this, on the whole, the algorithm and even the Pythagorean arcs, I still reckoned almost an error compared to the Indian method. Therefore strictly embracing the Indian method, and attentive to the study of it, from mine own sense adding some, and some more still from the subtle Euclidean geometric art, applying the sum that I was able to perceive to this book, I worked to put it together in xv distinct chapters, showing certain proof for almost everything that I put in, so that further, this method perfected above the rest, this science is instructed to the eager, and to the Italian people above all others, who up to now are found without a minimum. If, by chance, something less or more proper or necessary I omitted, your indulgence for me is entreated, as there is no one who is without fault, and in all things is altogether circumspect. + +In other words, he advocated the use of the digits 0–9, and of place value. Until this time Europe used Roman numerals, making modern mathematics almost impossible. The book thus made an important contribution to the spread of decimal numerals. The spread of the Hindu-Arabic system, however, as Ore writes, was "long-drawn-out", taking many more centuries to spread widely, and did not become complete until the later part of the 16th century, accelerating dramatically only in the 1500s with the advent of printing. + +== Textual history == +The first appearance of the manuscript was in 1202. No copies of this version are known. A revised version of Liber Abaci, dedicated to Michael Scot, appeared in 1228. There are at least nineteen manuscripts extant containing parts of this text. There are three complete versions of this manuscript from the thirteenth and fourteenth centuries. There are a further nine incomplete copies known between the thirteenth and fifteenth centuries, and there may be more not yet identified. +There were no known printed versions of Liber Abaci until Boncompagni's edition of 1857. The first complete English translation was Sigler's text of 2002. + +== See also == +The Book of Squares + +== References == + +== External links == + +Pisano, Leonardo (1202), Incipit liber Abbaci compositus to Lionardo filio Bonaccii Pisano in year Mccij [Manuscript], Museo Galileo. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/List_of_books_about_polyhedra-0.md b/data/en.wikipedia.org/wiki/List_of_books_about_polyhedra-0.md new file mode 100644 index 000000000..0d208aeae --- /dev/null +++ b/data/en.wikipedia.org/wiki/List_of_books_about_polyhedra-0.md @@ -0,0 +1,59 @@ +--- +title: "List of books about polyhedra" +chunk: 1/2 +source: "https://en.wikipedia.org/wiki/List_of_books_about_polyhedra" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:29.884776+00:00" +instance: "kb-cron" +--- + +This is a list of books about polyhedra. + +== Polyhedral models == + +=== Cut-out kits === +Jenkins, Gerald; Bear, Magdalen (1998). Paper Polyhedra in Colour. Tarquin. ISBN 1-899618-23-6. Advanced Polyhedra 1: The Final Stellation, ISBN 1-899618-61-9. Advanced Polyhedra 2: The Sixth Stellation, ISBN 1-899618-62-7. Advanced Polyhedra 3: The Compound of Five Cubes, ISBN 978-1-899618-63-7. +Jenkins, Gerald; Wild, Anne (2000). Mathematical Curiosities. Tarquin. ISBN 1-899618-35-X. More Mathematical Curiosities, Tarquin, ISBN 1-899618-36-8. Make Shapes 1, ISBN 0-906212-00-6. Make Shapes 2, ISBN 0-906212-01-4. +Smith, A. G. (1986). Cut and Assemble 3-D Geometrical Shapes: 10 Models in Full Color. Dover. Cut and Assemble 3-D Star Shapes, 1997. Easy-To-Make 3D Shapes in Full Color, 2000. +Torrence, Eve (2011). Cut and Assemble Icosahedra: Twelve Models in White and Color. Dover. + +=== Origami === +Fuse, Tomoko (1990). Unit Origami: Multidimensional Transformations. Japan Publications. ISBN 978-0-87040-852-6. +Gurkewitz, Rona; Arnstein, Bennett (1996). 3D Geometric Origami: Modular Origami Polyhedra. Dover. ISBN 9780486135601. Multimodular Origami Polyhedra: Archimedeans, Buckyballs and Duality, 2002. Beginner's Book of Modular Origami Polyhedra: The Platonic Solids, 2008. Modular Origami Polyhedra, also with Lewis Simon, 2nd ed., 1999. +Mitchell, David (1997). Mathematical Origami: Geometrical Shapes by Paper Folding. Tarquin. ISBN 978-1-899618-18-7. +Montroll, John (2009). Origami Polyhedra Design. A K Peters. ISBN 9781439871065. A Plethora of Polyhedra in Origami, Dover, 2002. + +=== Other model-making === +Cundy, H. M.; Rollett, A. P. (1952). Mathematical Models. Clarendon Press. 2nd ed., 1961. 3rd ed., Tarquin, 1981, ISBN 978-0-906212-20-2. +Hilton, Peter; Pedersen, Jean (1988). Build Your Own Polyhedra. Addison-Wesley. +Wenninger, Magnus (1971). Polyhedron Models. Cambridge University Press. 2nd ed., Polyhedron Models for the Classroom, 1974. Spherical Models, 1979. Dual Models, 1983. + +== Mathematical studies == + +=== Introductory level and general audience === +Akiyama, Jin; Matsunaga, Kiyoko (2024). Treks into Intuitive Geometry: The World of Polygons and Polyhedra (2nd ed.). Singapore: Springer. ISBN 978-981-99-8607-1. +Alsina, Claudi (2017). The Thousand Faces of Geometric Beauty: The Polyhedra. Our Mathematical World. Vol. 23. National Geographic. ISBN 978-84-473-8929-2. +Britton, Jill (2001). Polyhedra Pastimes. Dale Seymour Publishing. ISBN 0-7690-2782-2. +Cromwell, Peter R. (1997). Polyhedra. Cambridge University Press. +Fetter, Ann E. (1991). The Platonic Solids Activity Book. Key Curriculum Press. +Holden, Alan (1971). Shapes, Space and Symmetry. Dover, 1991. +le Masne, Roger (2013). Les polyèdres, ou la beauté des mathématiques (in French) (4th ed.). Self-published. +Miyazaki, Koji (1983). Katachi to kūkan: Tajigen sekai no kiseki (in Japanese). Wiley. Translated into English as An Adventure in Multidimensional Space: The Art and Geometry of Polygons, Polyhedra, and Polytopes, Wiley, 1986, and into German as Polyeder und Kosmos: Spuren einer mehrdimensionalen Welt, Vieweg, 1987. +Pearce, Peter; Pearce, Susan (1979). Polyhedra Primer. Van Nostrand Reinhold. ISBN 978-0-442-26496-3. +Pugh, Anthony (1976). Polyhedra: A Visual Approach. University of California Press. +Radin, Dan (2008). The Platonic Solids Book. Self-published. +Sutton, Daud (2002). Platonic & Archimedean Solids: The Geometry of Space. Wooden Books. ISBN 978-0802713865. + +=== Textbooks === +Alexandrov, A. D. (2005). Convex Polyhedra. Springer. Translated from 1950 Russian edition. +Beck, Matthias; Robins, Sinai (2007). Computing the Continuous Discretely: Integer-Point Enumeration in Polyhedra. Undergraduate Texts in Mathematics. Vol. 154. Springer. 2nd ed., 2015, ISBN 978-1-4939-2968-9. +Brøndsted, Arne (1983). An Introduction to Convex Polytopes. Graduate Texts in Mathematics. Vol. 90. Springer. +Coxeter, H. S. M. (1948). Regular Polytopes. Methuen. 2nd ed., Macmillan, 1963. 3rd ed., Dover, 1973. +Fejes Tóth, László (1964). Regular Figures. Pergamon. +Grünbaum, Branko (1967). Convex Polytopes. Wiley. 2nd ed., Springer, 2003. +Lyusternik, Lazar (1956). Выпуклые фигуры и многогранники (in Russian). Gosudarstv. Izdat. Tehn.-Teor. Lit. Translated into English as Convex Figures and Polyhedra by T. Jefferson Smith, Dover, 1963 and by Donald L. Barnett, Heath, 1966. +Pineda Villavicencio, Guillermo (2024). Polytopes and Graphs. Cambridge Studies in Advanced Mathematics. Vol. 211. Cambridge University Press. doi:10.1017/9781009257794. ISBN 978-1-009-25781-7. +Roman, Tiberiu (1968). Reguläre und halbreguläre Polyeder [Regular and semiregular polyhedra] (in German). VEB Deutscher Verlag der Wissenschaften. +Thomas, Rekha (2006). Lectures in Geometric Combinatorics. American Mathematical Society. +Ziegler, Günter M. (1993). Lectures on Polytopes. Springer. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/List_of_books_about_polyhedra-1.md b/data/en.wikipedia.org/wiki/List_of_books_about_polyhedra-1.md new file mode 100644 index 000000000..43d1eeca0 --- /dev/null +++ b/data/en.wikipedia.org/wiki/List_of_books_about_polyhedra-1.md @@ -0,0 +1,93 @@ +--- +title: "List of books about polyhedra" +chunk: 2/2 +source: "https://en.wikipedia.org/wiki/List_of_books_about_polyhedra" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:29.884776+00:00" +instance: "kb-cron" +--- + +=== Monographs and special topics === +Coxeter, H. S. M.; du Val, P.; Flather, H. T.; Petrie, J. F. (1938). The Fifty-Nine Icosahedra. University of Toronto Studies, Mathematical Series. Vol. 6. University of Toronto Press. 2nd ed., Springer, 1982. 3rd ed., Tarquin, 1999. +Coxeter, H. S. M. (1974). Regular Complex Polytopes. Cambridge University Press. 2nd ed., 1991. +Demaine, Erik; O'Rourke, Joseph (2007). Geometric Folding Algorithms: Linkages, Origami, Polyhedra. Cambridge University Press. +Deza, Michel; Grishukhin, Viatcheslav; Shtogrin, Mikhail (2004). Scale-Isometric Polytopal Graphs in Hypercubes and Cubic Lattices: Polytopes in Hypercubes and + + + + + + Z + + + n + + + + + {\displaystyle \mathbb {Z} _{n}} + +. London: Imperial College Press. doi:10.1142/9781860945489. ISBN 1-86094-421-3. +Lakatos, Imre (1976). Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge University Press. +McMullen, Peter (2020). Geometric Regular Polytopes. Encyclopedia of Mathematics and its Applications. Vol. 172. Cambridge University Press. +McMullen, Peter; Schulte, Egon (2002). Abstract Regular Polytopes. Encyclopedia of Mathematics and its Applications. Vol. 92. Cambridge University Press. +McMullen, Peter; Shephard, G. C. (1971). Convex Polytopes and the Upper Bound Conjecture. London Mathematical Society Lecture Note Series. Vol. 3. Cambridge University Press. +Nef, Walter (1978). Beiträge zur Theorie der Polyeder: Mit Anwendungen in der Computergraphik [Contributions to the theory of the polyhedron, with applications in computer graphics] (in German). Herbert Lang. +O'Rourke, Joseph; Vîlcu, Costin (2024). Reshaping Convex Polyhedra. Springer. arXiv:2107.03153. ISBN 978-3-031-47511-5. +Rajwade, A. R. (2001). Convex Polyhedra with Regularity Conditions and Hilbert's Third Problem. Texts and Readings in Mathematics. Vol. 21. Hindustan Book Agency. +Richter-Gebert, Jürgen (1996). Realization Spaces of Polytopes. Lecture Notes in Mathematics. Vol. 1643. Springer. +Stewart, B. M. (1970). Adventures Among the Toroids. Self-published. 2nd ed., 1980. +Wachman, Avraham; Burt, Michael; Kleinmann, M. (1974). Infinite Polyhedra. Technion. 2nd ed., 2005. +Wu, Wen-tsün (1965). A Theory of Imbedding, Immersion, and Isotopy of Polytopes in a Euclidean Space. Science Press. +Zalgaller, Viktor A. (1969). Convex Polyhedra with Regular Faces. Consultants Bureau. Translated and corrected from Zalgaller, V. A. (1967). Выпуклые многогранники с правильными гранями. Zapiski Naučnyh Seminarov Leningradskogo Otdelenija Matematičeskogo Instituta im. V. A. Steklova Akademii Nauk SSSR (LOMI) (in Russian). Vol. 2. Nauka. +Zhizhin, Gennadiy Vladimirovich (2022). The Classes of Higher Dimensional Polytopes in Chemical, Physical, and Biological Systems. Advances in Chemical and Materials Engineering. IGI Global. ISBN 9781799883760. + +=== Edited volumes === +Avis, David; Bremner, David; Deza, Antoine, eds. (2009). Polyhedral Computation. CRM Proceedings and Lecture Notes. Vol. 48. American Mathematical Society. +Gabriel, Jean-François, ed. (1997). Beyond the Cube: The Architecture of Space Frames and Polyhedra. Wiley. +Kalai, Gil; Ziegler, Günter M., eds. (2012). Polytopes - Combinatorics and Computation. DMV Seminar. Vol. 29. Springer. +Senechal, Marjorie; Fleck, G., eds. (1988). Shaping Space: A Polyhedral Approach. Birkhauser. ISBN 0-8176-3351-0. 2nd ed., Shaping Space: Exploring Polyhedra in Nature, Art, and the Geometrical Imagination, Springer, 2013. +Viana, Vera; Matos, Helena Mena; Xavier, João Pedro, eds. (2022). Polyhedra and Beyond: Contributions from Geometrias’19, Porto, Portugal, September 05-07. Trends in Mathematics. Birkhäuser. + +== History == + +=== Early works === +Listed in chronological order, and including some works shorter than book length: + +Plato. Timaeus (in Greek). +Euclid. Elements (in Greek). +Pappus of Alexandria (1589). Mathematicae collectiones, liber quintus. apud Franciscum de Franciscis Senensem. +Della Francesca, Piero (1482–1492). De quinque corporibus regularibus [On the five regular bodies] (in Latin). +Pacioli, Luca (1509). Divina proportione [Divine proportion] (in Italian). +de Bovelles, Charles (1511). De mathematicis corporibus. +Dürer, Albrecht (1525). Underweysung der Messung, mit dem Zirckel und Richtscheyt, in Linien, Ebenen und gantzen corporen, Viertes Buch (in German). +Maurolico, Francesco (1537). Compaginationes solidorum regularium. +Jamnitzer, Wenzel (1568). Perspectiva corporum regularium [Perspectives of the regular bodies]. +Kepler, Johannes (1619). Harmonices Mundi (in Latin). Translated into English as Harmonies of the World by C. G. Wallis (1939). +Descartes, René (c. 1630). De solidorum elementis [On the elements of solids] (in Latin). Original manuscript lost; copy by Gottfried Wilhelm Leibniz reprinted and translated in Descartes on Polyhedra, Springer, 1982. +Cowley, John Lodge (1758). An Appendix to Euclid's Elements in Seven Books, Containing Forty-two Copper-plates, In Which the Doctrine of Solids, Delivered in the XIth, XIIth, and XVth Books of Euclid, is Illustrated by New-invented Schemes Cut Out of Paste-Board. Watkins. +Poinsot, Louis (1810). Mémoire sur les polygones et sur les polyèdres (in French). +Marie, François-Charles-Michel (1835). Géométrie stéréographique, ou reliefs des polyèdres (in French). Paris. hdl:2027/ucm.531073766x. +Schläfli, Ludwig (1901) [1852]. Graf, J. H. (ed.). Theorie der vielfachen Kontinuität. Republished by Cornell University Library historical math monographs 2010 (in German). Zürich, Basel: Georg & Co. ISBN 978-1-4297-0481-6. {{cite book}}: ISBN / Date incompatibility (help) +Wiener, Christian (1864). Über Vielecke und Vielflache. Teubner. +Catalan, Eugène (1865). "Mémoire sur la théorie des polyèdres". Journal de l'École Polytechnique (in French). 24. hdl:2268/194785. +Hess, Edmund (1883). Einleitung in die Lehre von der Kugelteilung mit besonderer Berücksichtigung ihrer Anwendung auf die Theorie der Gleichflächigen und der gleicheckigen Polyeder (in German). Teubner. +Klein, Felix (1884). Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom 5ten Grade [Lectures on the Icosahedron and the Solution of Equations of the Fifth Degree] (in German). +Fedorov, E. S. (1885). Начала учения о фигурах [Introduction to the Theory of Figures] (in Russian). +Gorham, John (1888). A System for the Construction of Crystal Models on the Type of an Ordinary Plait: Exemplified by the Forms Belonging to the Six Axial Systems in Crystallography. Reprint, Tarquin, 2007, ISBN 978-1-899618-68-2. +Eberhard, Victor (1891). Zur Morphologie der Polyeder [On the morphology of polyhedra]. Teubner. +von Lindemann, Ferdinand (1897). Zur Geschichte der Polyeder und der Zahlzeichen [History of Polyhedra and Numeral Signs] (in German). Munich: F. Straub. Reprinted from Sitz. Bay. Akad. Wiss. 1896, pp. 625–758. +Brückner, Max (1900). Vielecke und Vielflache: Theorie und Geschichte (in German). Treubner. Über die gleicheckig-gleichflächigen diskontinuierlichen und nichtkonvexen Polyeder, 1906. +Steinitz, Ernst (1934). Rademacher, Hans (ed.). Vorlesungen über die Theorie der Polyeder unter Einschluss der Elemente der Topologie (in German). + +=== Books about historical topics === +Andrews, Noam (2022). The Polyhedrists: Art and Geometry in the Long Sixteenth Century. MIT Press. +Davis, Margaret Daly (1977). Piero della Francesca's Mathematical Treatises: The "Trattato d'abaco" and "Libellus de quinque corporibus regularibus". Longo. +Dézarnaud-Dandine, Christine; Sevin, Alain (2009). Histoire des polyèdres: Quand la nature est géomètre (in French). Vuibert. +Federico, Pasquale Joseph (1984). Descartes on Polyhedra: A Study of the "De solidorum elementis". Sources in the History of Mathematics and Physical Sciences. Vol. 4. Springer. +Richeson, D. S. (2008). Euler's Gem: The Polyhedron Formula and the Birth of Topology. Princeton University Press. +Sanders, Philip Morris (1990). The Regular Polyhedra in Renaissance Science and Philosophy. Warburg Institute, University of London. +Wade, David (2012). Fantastic Geometry: Polyhedra and the Artistic Imagination in the Renaissance. Squeeze Press. + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/List_of_mathematics_books-0.md b/data/en.wikipedia.org/wiki/List_of_mathematics_books-0.md index 70466567d..1051c5309 100644 --- a/data/en.wikipedia.org/wiki/List_of_mathematics_books-0.md +++ b/data/en.wikipedia.org/wiki/List_of_mathematics_books-0.md @@ -4,7 +4,7 @@ chunk: 1/1 source: "https://en.wikipedia.org/wiki/List_of_mathematics_books" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T08:15:30.833032+00:00" +date_saved: "2026-05-05T08:45:31.111931+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/Making_Mathematics_with_Needlework-0.md b/data/en.wikipedia.org/wiki/Making_Mathematics_with_Needlework-0.md new file mode 100644 index 000000000..90765fd1f --- /dev/null +++ b/data/en.wikipedia.org/wiki/Making_Mathematics_with_Needlework-0.md @@ -0,0 +1,29 @@ +--- +title: "Making Mathematics with Needlework" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Making_Mathematics_with_Needlework" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:32.269533+00:00" +instance: "kb-cron" +--- + +Making Mathematics with Needlework: Ten Papers and Ten Projects is an edited volume on mathematics and fiber arts. It was edited by Sarah-Marie Belcastro and Carolyn Yackel, and published in 2008 by A K Peters, based on a meeting held in 2005 in Atlanta by the American Mathematical Society. + + +== Topics == +The book includes ten different mathematical fiber arts projects, by eight contributors. An introduction provides a history of the connections between mathematics, mathematics education, and the fiber arts. Each of its ten project chapters is illustrated by many color photographs and diagrams, and is organized into four sections: an overview of the project, a section on the mathematics connected to it, a section of ideas for using the project as a teaching activity, and directions for constructing the project. Although there are some connections between topics, they can be read independently of each other, in any order. The thesis of the book is that directed exercises in fiber arts construction can help teach both mathematical visualization and concepts from three-dimensional geometry. +The book uses knitting, crochet, sewing, and cross-stitch, but deliberately avoids weaving as a topic already well-covered in mathematical fiber arts publications. Projects in the book include a quilt in the form of a Möbius strip, a "bidirectional hat" connected to the theory of Diophantine equations, a shawl with a fractal design, a knitted torus connecting to discrete approximations of curvature, a sampler demonstrating different forms of symmetry in wallpaper group, "algebraic socks" with connections to modular arithmetic and the Klein four-group, a one-sided purse sewn together following a description by Lewis Carroll, a demonstration of braid groups on a cable-knit pillow, an embroidered graph drawing of an Eulerian graph, and topological pants. +Beyond belcastro and Yackel, the contributors to the book include Susan Goldstine, Joshua Holden, Lana Holden, Mary D. Shepherd, Amy F. Szczepański, and D. Jacob Wildstrom. + + +== Audience and reception == +Reviewers had mixed opinions on the appropriate audience for the book and its success in targeting that audience. Ketty Peeva writes that the book is "of interest to mathematicians, mathematics educators and crafters", and Mary Fortune writes that a wide group of people would enjoy browsing its contents, However, Kate Atherley warns that it is "not for the faint-of-heart" (either among mathematicians or crafters), and Mary Goetting complains that the audience for the book is not clearly defined, and is inconsistent across the book, with some chapters written for professional mathematicians and others for mathematical beginners. She writes that most readers will have to pick and choose among the chapters for material appealing to them. Similarly, reviewer Michelle Sipics writes that in aiming at multiple audiences, the book "sacrifices some accessibility". And although reviewer Gwen Fisher downplays the potential pedagogical applications of this book, complaining that its teaching ideas do not provide enough detail to be usable, and are not a good fit for typical teaching curricula, Sipics calls mathematics teachers "perhaps the greatest beneficiaries of this text". +Fortune writes that, though the book increased her appreciation of and understanding of needlework, she didn't gain much new mathematical insight from reading it. In contrast, Fisher argues that by using only "straightforward applications of traditional needlework skills" the book is accessible even to beginners in the fiber arts, and that the book is "much more about maths than about fibre technique". The real value of the book, she argues, is in the scholarly connection it forges between traditional women's activities and mathematics. Pao-Sheng Hsu says that it would be "a great coffee table book" for browsing. And Anna Lena Phillips calls the book "an excellent synthesis" of textile crafts and mathematics, providing inspiration to those interested in either topic. + + +== References == + + +== External links == +Home page \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Math_Curse-0.md b/data/en.wikipedia.org/wiki/Math_Curse-0.md new file mode 100644 index 000000000..0ab71bafa --- /dev/null +++ b/data/en.wikipedia.org/wiki/Math_Curse-0.md @@ -0,0 +1,31 @@ +--- +title: "Math Curse" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Math_Curse" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:33.411156+00:00" +instance: "kb-cron" +--- + +Math Curse is a children's picture book written by Jon Scieszka and illustrated by Lane Smith. Published in 1995 through Viking Press, the book tells the story of a student cursed by how mathematics is connected to everyday life. In 2009, Weston Woods Studios, Inc. released a film based on the book. + + +== Plot summary == +The nameless student begins with a seemingly innocent statement by her math teacher: "you know, almost everything in life can be considered a math problem." The next morning, the hero finds herself thinking of the time she needs to get up, along the lines of algebra. Next comes the mathematical school of probability, followed by charts and statistics. As the narrator slowly turns into a "math zombie", everything in her life is transformed into a problem. A class treat of cupcakes becomes a study in fractions, while a trip to the store turns into a problem of money. Finally, she is left painstakingly calculating how many minutes of "math madness" will be in her life now that she is a "mathematical lunatic." Her sister asks her what her problem is, and she responds, "365 days x 24 hours x 60 minutes." Finally, she collapses on her bed and dreams of being trapped in a blackboard room covered in math problems. Armed with only a piece of chalk, she must escape, and she manages to do just that by breaking the chalk in half, because "two halves make a whole." She escapes through this "whole" and awakens the next morning with the ability to solve any problem. Her curse is broken until the next day, when her science teacher mentions that everything can be viewed as a science experiment in life. + + +== Math problems == +The book contains actual math problems (and some rather unrelated questions, such as "What does this inkblot look like?"). Readers can try to solve the problems and check their answers on the back cover. + + +== Stage adaptation == +The book was also adapted for the stage by Heath Corson and Kathleen Collins in 1997. It was first performed at the A Red Orchid Theatre in Chicago, Illinois, in 1997, with subsequent productions at other locations. Its West Coast premiere was in 2003 at the Powerhouse Theatre of Santa Monica, California. Collins directed it, and the cast included Kerry Lacy, Thomas Colby, Will Moran, Andrew David James, and Emily Marver. The play met with warm reviews and succeeded with its audiences and local school children. + + +== In popular culture == +The book was featured in the first episode of the seventeenth season of the children's series Reading Rainbow, narrated by Michelle Trachtenberg. + + +== Awards == +The book was critically acclaimed, receiving several awards and accolades, including Maine's Student Favorite Book Award, the Texas Bluebonnet Award, and New Hampshire's The Great Stone Face Book Award.[1][2] \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Mathematical_Cranks-0.md b/data/en.wikipedia.org/wiki/Mathematical_Cranks-0.md new file mode 100644 index 000000000..dbeb84750 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Mathematical_Cranks-0.md @@ -0,0 +1,41 @@ +--- +title: "Mathematical Cranks" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Mathematical_Cranks" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:34.587603+00:00" +instance: "kb-cron" +--- + +Mathematical Cranks is a book on pseudomathematics and the cranks who create it, written by Underwood Dudley. It was published by the Mathematical Association of America in their MAA Spectrum book series in 1992 (ISBN 0-88385-507-0). + + +== Topics == +Previously, Augustus De Morgan wrote in A Budget of Paradoxes about cranks in multiple subjects, and Dudley wrote a book about angle trisection. However, this book is the first to focus on mathematical crankery as a whole. +The book consists of 57 essays, loosely organized by the most common topics in mathematics for cranks to focus their attention on. The "top ten" of these topics, as listed by reviewer Ian Stewart, are, in order: + +squaring the circle, +angle trisection, +Fermat's Last Theorem, +non-Euclidean geometry and the parallel postulate, +the golden ratio, +perfect numbers, +the four color theorem, +advocacy for duodecimal and other non-standard number systems, +Cantor's diagonal argument for the uncountability of the real numbers, and +doubling the cube. +Other common topics for crankery, collected by Dudley, include calculations for the perimeter of an ellipse, roots of quintic equations, Fermat's little theorem, Gödel's incompleteness theorems, Goldbach's conjecture, magic squares, divisibility rules, constructible polygons, twin primes, set theory, statistics, and the Van der Pol oscillator. +As David Singmaster writes, many of these topics are the subject of mainstream mathematics "and only become crankery in extreme cases". The book omits or passes lightly over other topics that apply mathematics to crankery in other areas, such as numerology and pyramidology. Its attitude towards the cranks it covers is one of "sympathy and understanding", and in order to keep the focus on their crankery it names them only by initials. The book also attempts to analyze the motivation and psychology behind crankery, and to provide advice to professional mathematicians on how to respond to cranks. +Despite his work on the subject, which has "become enshrined in academic folklore", Dudley has stated "I've been at this for a decade and still can't pin down exactly what it is that makes a crank a crank", adding that "It's like obscenity – you can tell a crank when you see one." + + +== Lawsuit == +After the book was published, one of the cranks whose work was featured in the book, William Dilworth, sued Dudley for defamation in a federal court in Wisconsin. The court dismissed the Dilworth vs Dudley case on two grounds. First, it found that by publishing his work on Cantor's diagonal argument, Dilworth had made himself a public figure, creating a higher burden of proof for a defamation case. Second, it found that the word "crank" was "rhetorical hyperbole" rather than an actionably inaccurate description. The United States Court of Appeals for the Seventh Circuit concurred. After Dilworth repeated the lawsuit in a state court, he lost again and was forced to pay Dudley's legal expenses. + + +== Reception and audience == +Reviewer John N. Fujii calls the book "humorous and charming" and "difficult to put down", and advocates it to "all readers interested in the human side of mathematics". Although complaining that famous mathematicians Niels Henrik Abel and Srinivasa Ramanujan might have been dismissed as cranks by the standards of the book, reviewer Robert Matthews finds it an accurate reflection of most crankery. And David Singmaster adds that it should be read by "anyone likely to deal with a crank", including professional mathematicians, journalists, and legislators. + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Mathematical_Foundations_of_Quantum_Mechanics-0.md b/data/en.wikipedia.org/wiki/Mathematical_Foundations_of_Quantum_Mechanics-0.md new file mode 100644 index 000000000..b6bb914a9 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Mathematical_Foundations_of_Quantum_Mechanics-0.md @@ -0,0 +1,297 @@ +--- +title: "Mathematical Foundations of Quantum Mechanics" +chunk: 1/2 +source: "https://en.wikipedia.org/wiki/Mathematical_Foundations_of_Quantum_Mechanics" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:35.818465+00:00" +instance: "kb-cron" +--- + +Mathematical Foundations of Quantum Mechanics (German: Mathematische Grundlagen der Quantenmechanik) is a quantum mechanics book written by John von Neumann in 1932. It is an important early work in the development of the mathematical formulation of quantum mechanics. The book mainly summarizes results that von Neumann had published in earlier papers. +Von Neumann formalized quantum mechanics using the concept of Hilbert spaces and linear operators. He acknowledged the previous work by Paul Dirac on the mathematical formalization of quantum mechanics, but was skeptical of Dirac's use of delta functions. He wrote the book in an attempt to be even more mathematically rigorous than Dirac. It was von Neumann's last book in German, afterwards he started publishing in English. + +== Publication history == +The book was originally published in German in 1932 by Springer. It was translated into French by Alexandru Proca in 1946, and into Spanish in 1949. An English translation by Robert T. Beyer was published in 1955 by Princeton University Press. A Russian translation, edited by Nikolay Bogolyubov, was published by Nauka in 1964. A new English edition, edited by Nicholas A. Wheeler, was published in 2018 by Princeton University Press. + +== Table of contents == +According to the 2018 version, the main chapters are: + +Introductory considerations +Abstract Hilbert space +The quantum statistics +Deductive development of the theory +General considerations +The measuring process + +== Measurement process == +In chapter 6, von Neumann develops the theory of quantum measurement. Von Neumann addresses measurement by outlining two kind of processes: + +Process I: during measurement a quantum state of a system evolves into a mixed state of eigenstates of the measured observable. This process is non-causal (the outcome of a single measurement does not depend only on the initial state) and irreversible. +Process II: when the system is unobserved, the state evolves according to Schrödinger equation. This process is causal and reversible. +Von Neumann was concerned that having two incompatible processes violated what he called the principle of psycho-physical parallelism, indicating the need that every mental process can be described as a physical process. Von Neumann argues that this issue does not appear in quantum mechanics as it set the border between observed and observer arbitrarily along a sequence of subsystems. +The sequence begins with a quantum system whose observable is to be measured. When the system interacts with a measuring device, they become entangled. As a result, the system does not end up in a definite eigenstate of the observable, and the measuring device does not display a specific value. When the observer is added to the picture, the description implies that their body (including the brain) are also entangled with the measuring apparatus and the system. This sequence is known as the von Neumann chain. The problem then becomes understanding how collapse to one of the eigenstates emerges from this chain. Von Neumann demonstrated that, when it comes to the final outcomes, the chain can be interrupted at any and a wave function collapse can be introduced at any point to explain the results. + +=== Interpretations === +Von Neumann measurement scheme is part of the orthodox Copenhagen interpretation which postulates a collapse, however alternative interpretations of quantum mechanics have come out of this idea. Eugene Wigner considered that the von Neumann chain implied that consciousness causes collapse of the wave function. However Wigner rejected this idea after the formalism of quantum decoherence was developed. Hugh Everett III developed the many-worlds interpretation based on von Neumann's processes, by keeping only process II. + +== No hidden variables proof == + +One significant passage is its mathematical argument against the idea of hidden variables. Von Neumann's claim rested on the assumption that any linear combination of Hermitian operators represents an observable and the expectation value of such combined operator follows the combination of the expectation values of the operators themselves. +Von Neumann's makes the following assumptions: + +For an observable + + + + R + + + {\displaystyle R} + +, a function + + + + f + + + {\displaystyle f} + + of that observable is represented by + + + + f + ( + R + ) + + + {\displaystyle f(R)} + +. +For the sum of observables + + + + R + + + {\displaystyle R} + + and + + + + S + + + {\displaystyle S} + + is represented by the operation + + + + R + + + S + + + {\displaystyle R+S} + +, independently of the mutual commutation relations. +The correspondence between observables and Hermitian operators is one to one. +If the observable + + + + R + + + {\displaystyle R} + + is a non-negative operator, then its expected value + + + + ⟨ + R + ⟩ + ≥ + 0 + + + {\displaystyle \langle R\rangle \geq 0} + +. +Additivity postulate: For arbitrary observables + + + + R + + + {\displaystyle R} + + and + + + + S + + + {\displaystyle S} + +, and real numbers + + + + a + + + {\displaystyle a} + + and + + + + b + + + {\displaystyle b} + +, we have + + + + ⟨ + a + R + + + b + S + ⟩ + = + a + ⟨ + R + ⟩ + + + b + ⟨ + S + ⟩ + + + {\displaystyle \langle aR+bS\rangle =a\langle R\rangle +b\langle S\rangle } + + for all possible ensembles. +Von Neumann then shows that one can write + + + + + ⟨ + R + ⟩ + = + + ∑ + + m + , + n + + + + ρ + + n + m + + + + R + + m + n + + + = + + T + r + + ( + ρ + R + ) + + + {\displaystyle \langle R\rangle =\sum _{m,n}\rho _{nm}R_{mn}=\mathrm {Tr} (\rho R)} + + +for some + + + + ρ + + + {\displaystyle \rho } + +, where + + + + + R + + m + n + + + + + {\displaystyle R_{mn}} + + and + + + + + ρ + + n + m + + + + + {\displaystyle \rho _{nm}} + +are the matrix elements in some basis. The proof concludes by noting that + + + + ρ + + + {\displaystyle \rho } + + must be Hermitian and non-negative definite ( + + + + ⟨ + ρ + ⟩ + ≥ + 0 + + + {\displaystyle \langle \rho \rangle \geq 0} + +) by construction. For von Neumann, this meant that the statistical operator representation of states could be deduced from the postulates. Consequently, there are no "dispersion-free" states: it is impossible to prepare a system in such a way that all measurements have predictable results. But if hidden variables existed, then knowing the values of the hidden variables would make the results of all measurements predictable, and hence there can be no hidden variables. Von Neumann's argues that if dispersion-free states were found, assumptions 1 to 3 should be modified. +Von Neumann's concludes: \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Mathematical_Foundations_of_Quantum_Mechanics-1.md b/data/en.wikipedia.org/wiki/Mathematical_Foundations_of_Quantum_Mechanics-1.md new file mode 100644 index 000000000..85c4ec2cd --- /dev/null +++ b/data/en.wikipedia.org/wiki/Mathematical_Foundations_of_Quantum_Mechanics-1.md @@ -0,0 +1,135 @@ +--- +title: "Mathematical Foundations of Quantum Mechanics" +chunk: 2/2 +source: "https://en.wikipedia.org/wiki/Mathematical_Foundations_of_Quantum_Mechanics" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:35.818465+00:00" +instance: "kb-cron" +--- + +if there existed other, as yet undiscovered, physical quantities, in addition to those represented by the operators in quantum mechanics, because the relations assumed by quantum mechanics would have to fail already for the by now known quantities, those that we discussed above. It is therefore not, as is often assumed, a question of a re-interpretation of quantum mechanics, the present system of quantum mechanics would have to be objectively false, in order that another description of the elementary processes than the statistical one be possible. + +=== Rejection === +This proof was rejected as early as 1935 by Grete Hermann who found a flaw in the proof. The additive postulate above holds for quantum states, but it does not need to apply for measurements of dispersion-free states, specifically when considering non-commuting observables. Dispersion-free states only require to recover additivity when averaging over the hidden parameters. For example, for a spin-1/2 system, measurements of + + + + ( + + σ + + x + + + + + + σ + + y + + + ) + + + {\displaystyle (\sigma _{x}+\sigma _{y})} + + can take values + + + + ± + + + 2 + + + + + {\displaystyle \pm {\sqrt {2}}} + + for a dispersion-free state, but independent measurements of + + + + + σ + + x + + + + + {\displaystyle \sigma _{x}} + + and + + + + + σ + + y + + + + + {\displaystyle \sigma _{y}} + + can only take values of + + + + ± + 1 + + + {\displaystyle \pm 1} + + (their sum can be + + + + ± + 2 + + + {\displaystyle \pm 2} + + or ⁠ + + + + 0 + + + {\displaystyle 0} + +⁠). Thus there still the possibility that a hidden variable theory could reproduce quantum mechanics statistically. +However, Hermann's critique remained relatively unknown until 1974 when it was rediscovered by Max Jammer. In 1952, David Bohm constructed the Bohmian interpretation of quantum mechanics in terms of statistical argument, suggesting a limit to the validity of von Neumann's proof. The problem was brought back to wider attention by John Stewart Bell in 1966. Bell showed that the consequences of that assumption are at odds with results of incompatible measurements, which are not explicitly taken into von Neumann's considerations. + +== Reception == +It was considered the most complete book written in quantum mechanics at the time of release. It was praised for its axiomatic approach. A review by Jacob Tamarkin compared von Neumann's book to what the works on Niels Henrik Abel or Augustin-Louis Cauchy did for mathematical analysis in the 19th century, but for quantum mechanics. +Freeman Dyson said that he learned quantum mechanics from the book. Dyson remarks that in the 1940s, von Neumann's work was not very well cited in the English world, as the book was not translated into English until 1955, but also because the worlds of mathematics and physics were significantly distant at the time. +Max Jammer observed that Paul Dirac's primary motivation in writing The Principles of Quantum Mechanics (1930) was creating an exposition in physics, treating mathematics as a tool. In this regard, John von Neumann's Mathematical Foundations of Quantum Mechanics, with its uncompromising emphasis on mathematical rigour, was a supplement to Dirac's book. + +== Works adapted in the book == +von Neumann, J. (1927). "Mathematische Begründung der Quantenmechanik [Mathematical Foundation of Quantum Mechanics]". Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse: 1–57. +von Neumann, J. (1927). "Wahrscheinlichkeitstheoretischer Aufbau der Quantenmechanik [Probabilistic Theory of Quantum Mechanics]". Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse: 245–272. +von Neumann, J. (1927). "Thermodynamik quantenmechanischer Gesamtheiten [Thermodynamics of Quantum Mechanical Quantities]". Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse. 102: 273–291. +von Neumann, J. (1929). "Allgemeine Eigenwerttheorie Hermitescher Funktionaloperatoren [General Eigenvalue Theory of Hermitian Functional Operators]". Mathematische Annalen: 49–131. doi:10.1007/BF01782338. +von Neumann, J. (1931). "Die Eindeutigkeit der Schrödingerschen Operatoren [The uniqueness of Schrödinger operators]". Mathematische Annalen. 104: 570–578. doi:10.1007/bf01457956. S2CID 120528257. + +== See also == + +Dirac–von Neumann axioms +Heisenberg cut +Timeline of quantum mechanics + +== Notes == + +== References == + +== External links == + +Full online text of the 1932 German edition (facsimile) at the University of Göttingen. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Mathematical_Models_(Cundy_and_Rollett)-0.md b/data/en.wikipedia.org/wiki/Mathematical_Models_(Cundy_and_Rollett)-0.md new file mode 100644 index 000000000..c83c4653b --- /dev/null +++ b/data/en.wikipedia.org/wiki/Mathematical_Models_(Cundy_and_Rollett)-0.md @@ -0,0 +1,29 @@ +--- +title: "Mathematical Models (Cundy and Rollett)" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Mathematical_Models_(Cundy_and_Rollett)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:38.192969+00:00" +instance: "kb-cron" +--- + +Mathematical Models is a book on the construction of physical models of mathematical objects for educational purposes. It was written by Martyn Cundy and A. P. Rollett, and published by the Clarendon Press in 1951, with a second edition in 1961. Tarquin Publications published a third edition in 1981. +The vertex configuration of a uniform polyhedron, a generalization of the Schläfli symbol that describes the pattern of polygons surrounding each vertex, was devised in this book as a way to name the Archimedean solids, and has sometimes been called the Cundy–Rollett symbol as a nod to this origin. + + +== Topics == +The first edition of the book had five chapters, including its introduction which discusses model-making in general and the different media and tools with which one can construct models. The media used for the constructions described in the book include "paper, cardboard, plywood, plastics, wire, string, and sheet metal". +The second chapter concerns plane geometry, and includes material on the golden ratio, the Pythagorean theorem, dissection problems, the mathematics of paper folding, tessellations, and plane curves, which are constructed by stitching, by graphical methods, and by mechanical devices. +The third chapter, and the largest part of the book, concerns polyhedron models, made from cardboard or plexiglass. It includes information about the Platonic solids, Archimedean solids, their stellations and duals, uniform polyhedron compounds, and deltahedra. +The fourth chapter is on additional topics in solid geometry and curved surfaces, particularly quadrics but also including topological manifolds such as the torus, Möbius strip and Klein bottle, and physical models helping to visualize the map coloring problem on these surfaces. Also included are sphere packings. The models in this chapter are constructed as the boundaries of solid objects, via two-dimensional paper cross-sections, and by string figures. +The fifth chapter, and the final one of the first edition, includes mechanical apparatus including harmonographs and mechanical linkages, the bean machine and its demonstration of the central limit theorem, and analogue computation using hydrostatics. The second edition expands this chapter, and adds another chapter on computational devices such as the differential analyser of Vannevar Bush. +Much of the material on polytopes was based on the book Regular Polytopes by H. S. M. Coxeter, and some of the other material has been drawn from resources previously published in 1945 by the National Council of Teachers of Mathematics. + + +== Audience and reception == +At the time they wrote the book, Cundy and Rollett were sixth form teachers in the UK, and they intended the book to be used by mathematics students and teachers for educational activities at that level. However, it may also be enjoyed by a general audience of mathematics enthusiasts. +Reviewer Michael Goldberg notes some minor errors in the book's historical credits and its notation, and writes that for American audiences some of the British terminology may be unfamiliar, but concludes that it could still be valuable for students and teachers. Stanley Ogilvy complains about the inconsistent level of rigor of the mathematical descriptions, with some proofs given and others omitted, for no clear reason, but calls this issue minor and in general calls the book's presentation excellent. Dirk ter Haar is more enthusiastic, recommending it to anyone interested in mathematics, and suggesting that it should be required for mathematics classrooms. Similarly, B. J. F. Dorrington recommends it to all mathematical libraries, and The Basic Library List Committee of the Mathematical Association of America has given it their strong recommendation for inclusion in undergraduate mathematics libraries. By the time of its second edition, H. S. M. Coxeter states that Mathematical Models had become "well known". + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Mathematical_Models_(Fischer)-0.md b/data/en.wikipedia.org/wiki/Mathematical_Models_(Fischer)-0.md new file mode 100644 index 000000000..00230df49 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Mathematical_Models_(Fischer)-0.md @@ -0,0 +1,32 @@ +--- +title: "Mathematical Models (Fischer)" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Mathematical_Models_(Fischer)" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:39.351961+00:00" +instance: "kb-cron" +--- + +Mathematical Models: From the Collections of Universities and Museums – Photograph Volume and Commentary is a book on the physical models of concepts in mathematics that were constructed in the 19th century and early 20th century and kept as instructional aids at universities. It credits Gerd Fischer as editor, but its photographs of models are also by Fischer. It was originally published by Vieweg+Teubner Verlag for their bicentennial in 1986, both in German (titled Mathematische Modelle. Aus den Sammlungen von Universitäten und Museen. Mit 132 Fotografien. Bildband und Kommentarband) and (separately) in English translation, in each case as a two-volume set with one volume of photographs and a second volume of mathematical commentary. Springer Spektrum reprinted it in a second edition in 2017, as a single dual-language volume. + + +== Topics == +The work consists of 132 full-page photographs of mathematical models, divided into seven categories, and seven chapters of mathematical commentary written by experts in the topic area of each category. +These categories are: + +Wire and thread models, of hypercubes of various dimensions, and of hyperboloids, cylinders, and related ruled surfaces, described as "elementary analytic geometry" and explained by Fischer himself. +Plaster and wood models of cubic and quartic algebraic surfaces, including Cayley's ruled cubic surface, the Clebsch surface, Fresnel's wave surface, the Kummer surface, and the Roman surface, with commentary by W. Barth and H. Knörrer. +Wire and plaster models illustrating the differential geometry and curvature of curves and surfaces, including surfaces of revolution, Dupin cyclides, helicoids, and minimal surfaces including the Enneper surface, with commentary by M. P. do Carmo, G. Fischer, U. Pinkall, H. and Reckziegel. +Surfaces of constant width including the surface of rotation of the Reuleaux triangle and the Meissner bodies, described by J. Böhm. +Uniform star polyhedra, described by E. Quaisser. +Models of the projective plane, including the Roman surface (again), the cross-cap, and Boy's surface, with commentary by U. Pinkall that includes its realization by Roger Apéry as a quartic surface (disproving a conjecture of Heinz Hopf). +Graphs of functions, both with real and complex variables, including the Peano surface, Riemann surfaces, exponential function and Weierstrass's elliptic functions, with commentary by J. Leiterer. + + +== Audience and reception == +This book can be viewed as a supplement to Mathematical Models by Martyn Cundy and A. P. Rollett (1950), on instructions for making mathematical models, which according to reviewer Tony Gardiner "should be in every classroom and on every lecturer's shelf" but in fact sold very slowly. Gardiner writes that the photographs may be useful in undergraduate mathematics lectures, while the commentary is best aimed at mathematics professionals in giving them an understanding of what each model depicts. Gardiner also suggests using the book as a source of inspiration for undergraduate research projects that use its models as starting points and build on the mathematics they depict. Although Gardiner finds the commentary at times overly telegraphic and difficult to understand, reviewer O. Giering, writing about the German-language version of the same commentary, calls it detailed, easy-to-read, and stimulating. +By the time of the publication of the second edition, in 2017, reviewer Hans-Peter Schröcker evaluates the visualizations in the book as "anachronistic", superseded by the ability to visualize the same phenomena more easily with modern computer graphics, and he writes that some of the commentary is also "slightly outdated". Nevertheless, he writes that the photos are "beautiful and aesthetically pleasing", writing approvingly that they use color sparingly and aim to let the models speak for themselves rather than dazzling with many color images. And despite the fading strength of its original purpose, he finds the book valuable both for its historical interest and for what it still has to say about visualizing mathematics in a way that is both beautiful and informative. + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Mathematicall_Magick-0.md b/data/en.wikipedia.org/wiki/Mathematicall_Magick-0.md new file mode 100644 index 000000000..7241a9e74 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Mathematicall_Magick-0.md @@ -0,0 +1,48 @@ +--- +title: "Mathematicall Magick" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Mathematicall_Magick" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:41.682100+00:00" +instance: "kb-cron" +--- + +Mathematicall Magick. Or, The Wonders that may be Performed by Mechanicall Geometry is a treatise by the English clergyman, natural philosopher, polymath and author John Wilkins (1614–1672). It was first published in 1648 in London; another edition was printed in 1680 and further editions were published in 1691 and 1707. The work is dedicated to Charles I Louis, the Elector Palatine. +The first book describes traditional mechanical devices, speed, siege engines and the modern guns of Wilkins' era. The second book covers Wilkins' theories and observations on land yachts, submarines, flying machines, and perpetual motion. Wilkins thought that human aviation is feasible, if only sufficient exercise, research and development is directed towards it. He envisioned flying machines that would be large enough to carry several people. +The book repeats tales about early attempts at human flight, including Busbequius' 16th-century reports about Turkish flight experiments in Constantinople. Wilkins also mentions Anglo-Saxon flight experiments during the reign of Edward the Confessor. The researcher called "Elmerus" in the text is probably Eilmer of Malmesbury, who experimented with gliding flight in the 11th century. + + +== Abstract == +Wilkins dedicated his work to His Highness the Prince Elector Palatine (Charles I Louis) who was in London at the time. It is divided into two books, one headed Archimedes, because he was the chiefest in discovering of Mechanical powers, the other was called Daedalus because he was one of the first and most famous amongst the Ancients for his skill in making Automata. Wilkins sets out and explains the principles of mechanics in the first book and gives an outlook in the second book on future technical developments like flying which he anticipates as certain if only sufficient exercise, research and development would be directed to these topics. The treatise is an example of his general intention to disseminate scientific knowledge and method and of his attempts to persuade his readers to pursue further scientific studies. + + +== First book == +In the 20 chapters of the first book, traditional mechanical devices are discussed such as the balance, the lever, the wheel or pulley and the block and tackle, the wedge, and the screw. The powers acting on them are compared to those acting in the human body. The book deals with the phrase attributed to Archimedes saying that if he did but know where to stand and fasten his instrument, he could move the world and shows the effect of a series of gear transmissions one linked to the other. It shows the importance of various speeds and the theoretical possibility to increase speed beyond the speed of the Earth at the equator. Finally, siege engines like catapults are compared with the cost and effect of then-modern guns. + + +== Second book == + + +=== Various devices === +In the 15 chapters of the second book, various devices are examined which move independently of human interference like clocks and watches, water mills and wind mills. Wilkins explains devices being driven by the motion of air in a chimney or by pressurized air. A land yacht is proposed driven by two sails on two masts, and a wagon powered by a vertical axis wind turbine. A number of independently moving small artificial figures representing men and animals are described. The possibilities are considered to improve the type of submarine designed and built by Cornelis Drebbel. The tales about various flying devices are related and doubts as to their truth are dissipated. Wilkins explains that it should be possible for a man, too, to fly by himself if a frame were built where the person could sit and if this frame was sufficiently pushed in the air. + + +=== Art of flying === +In chapter VII, Wilkins discusses various methods how a man could fly, namely by the help of spirits and good or evil angels (as related on various occasions in the Bible), by the help of fowls, by wings fastened immediately to the body or by a flying chariot. The whole of this chapter (and of the following one) concern the possibilities of flying. In a single preliminary phrase, he refers to previous reports of flight attempts: + +Tis related of a certain English Monk called Elmerus [probably Eilmer of Malmesbury], about the Confessors time, that he did by such wings fly from a Tower above a furlong; and so another [probably Fausto Veranzio] from Saint Marks steeple in Venice; another at Norinberge; and Busbequius speaks of a Turk in Constantinople, who attempted something this way. Mt. Burton mentioning this quotation, doth believe that some new-fangled wit ('tis his Cynical phrase) will some time or other find out this art. Though the truth is, most of these Artists did unfortunately miscarry by falling down and breaking their arms or legs, yet that may be imputed to their want of experience ... +He writes that sufficient practise should enable a man to fly, most probably by "a flying chariot, which may be so contrived as to carry a man within it" and equipped with a sort of engine, or else big enough to carry several people, each successively working to fly it. He used the next chapter to dissipate any doubts there may be as to the possibility of such a flying chariot, should a number of particular items be developed and tested. + + +=== Perpetual motion and perpetual lamps === +In Chapters IX to XV, extensive discussions and deliberations are set out why a perpetual motion should be feasible, why the stories about lamps burning for hundreds of years were true and how such lamps could be made and perpetual motions created. + + +== External links == +1st edition (1648) at the Internet Archive. +1680 version at Google Books. +4th edition (1691) at the Internet Archive. + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Mathematics,_Form_and_Function-0.md b/data/en.wikipedia.org/wiki/Mathematics,_Form_and_Function-0.md new file mode 100644 index 000000000..6be70fad3 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Mathematics,_Form_and_Function-0.md @@ -0,0 +1,37 @@ +--- +title: "Mathematics, Form and Function" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Mathematics,_Form_and_Function" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:45.216076+00:00" +instance: "kb-cron" +--- + +Mathematics, Form and Function, a book published in 1986 by Springer-Verlag, is a survey of the whole of mathematics, including its origins and deep structure, by the American mathematician Saunders Mac Lane. + + +== Mathematics and human activities == +Throughout his book, and especially in chapter I.11, Mac Lane informally discusses how mathematics is grounded in more ordinary concrete and abstract human activities. The following table is adapted from one given on p. 35 of Mac Lane (1986). The rows are very roughly ordered from most to least fundamental. For a bullet list that can be compared and contrasted with this table, see section 3 of Where Mathematics Comes From. + +Also see the related diagrams appearing on the following pages of Mac Lane (1986): 149, 184, 306, 408, 416, 422-28. +Mac Lane (1986) cites a related monograph by Lars Gårding (1977). + + +== Mac Lane's relevance to the philosophy of mathematics == +Mac Lane cofounded category theory with Samuel Eilenberg, which enables a unified treatment of mathematical structures and of the relations among them, at the cost of breaking away from their cognitive grounding. Nevertheless, his views—however informal—are a valuable contribution to the philosophy and anthropology of mathematics. His views anticipate, in some respects, the more detailed account of the cognitive basis of mathematics given by George Lakoff and Rafael E. Núñez in their Where Mathematics Comes From. Lakoff and Núñez argue that mathematics emerges via conceptual metaphors grounded in the human body, its motion through space and time, and in human sense perceptions. + + +== See also == +1986 in philosophy + + +== Notes == + + +== References == +Gårding, Lars, 1977. Encounter with Mathematics. Springer-Verlag. +Reuben Hersh, 1997. What Is Mathematics, Really? Oxford Univ. Press. +George Lakoff and Rafael E. Núñez, 2000. Where Mathematics Comes From. Basic Books. +Mac Lane, Saunders (1986). Mathematics, Form and Function. Springer-Verlag. ISBN 0-387-96217-4. +Leslie White, 1947, "The Locus of Mathematical Reality: An Anthropological Footnote," Philosophy of Science 14: 289-303. Reprinted in Hersh, R., ed., 2006. 18 Unconventional Essays on the Nature of Mathematics. Springer: 304–19. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Mathematics_Made_Difficult-0.md b/data/en.wikipedia.org/wiki/Mathematics_Made_Difficult-0.md new file mode 100644 index 000000000..3eecaf48d --- /dev/null +++ b/data/en.wikipedia.org/wiki/Mathematics_Made_Difficult-0.md @@ -0,0 +1,17 @@ +--- +title: "Mathematics Made Difficult" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Mathematics_Made_Difficult" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:44.083466+00:00" +instance: "kb-cron" +--- + +Mathematics Made Difficult is a book by Carl E. Linderholm that uses advanced mathematical methods to prove results normally shown using elementary proofs. Although the aim is largely satirical, it also shows the non-trivial mathematics behind operations normally considered obvious, such as numbering, counting, and factoring integers. Linderholm discusses these seemingly obvious ideas using concepts like categories and monoids. +As an example, the proof that 2 is a prime number starts: + +It is easily seen that the only numbers between 0 and 2, including 0 but excluding 2, are 0 and 1. Thus the remainder left by any number on division by 2 is either 0 or 1. Hence the quotient ring Z/2Z, where 2Z is the ideal in Z generated by 2, has only the elements [0] and [1], where these are the images of 0 and 1 under the canonical quotient map. Since [1] must be the unit of this ring, every element of this ring except [0] is a unit, and the ring is a field ... + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Mathematics_and_Plausible_Reasoning-0.md b/data/en.wikipedia.org/wiki/Mathematics_and_Plausible_Reasoning-0.md new file mode 100644 index 000000000..8fd891462 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Mathematics_and_Plausible_Reasoning-0.md @@ -0,0 +1,41 @@ +--- +title: "Mathematics and Plausible Reasoning" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Mathematics_and_Plausible_Reasoning" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:42.860670+00:00" +instance: "kb-cron" +--- + +Mathematics and Plausible Reasoning is a two-volume book by the mathematician George Pólya describing various methods for being a good guesser of new mathematical results. In the Preface to Volume 1 of the book Pólya exhorts all interested students of mathematics thus: "Certainly, let us learn proving, but also let us learn guessing." P. R. Halmos reviewing the book summarised the central thesis of the book thus: ". . . a good guess is as important as a good proof." + + +== Outline == + + +=== Volume I: Induction and analogy in mathematics === +Polya begins Volume I with a discussion on induction, not mathematical induction, but as a way of guessing new results. He shows how the chance observations of a few results of the form 4 = 2 + 2, 6 = 3 + 3, 8 = 3 + 5, 10 = 3 + 7, etc., may prompt a sharp mind to formulate the conjecture that every even number greater than 4 can be represented as the sum of two odd prime numbers. This is the well known Goldbach's conjecture. The first problem in the first chapter is to guess the rule according to which the successive terms of the following sequence are chosen: 11, 31, 41, 61, 71, 101, 131, . . . In the next chapter the techniques of generalization, specialization and analogy are presented as possible strategies for plausible reasoning. In the remaining chapters, these ideas are illustrated by discussing the discovery of several results in various fields of mathematics like number theory, geometry, etc. and also in physical sciences. + + +=== Volume II: Patterns of Plausible Inference === +This volume attempts to formulate certain patterns of plausible reasoning. The relation of these patterns with the calculus of probability are also investigated. Their relation to mathematical invention and instruction are also discussed. The following are +some of the patterns of plausible inference discussed by Polya. + + +== Reviews == +Bernhart, Arthur (1958-01-01). "Review of Mathematics and Plausible Reasoning". The American Mathematical Monthly. 65 (6): 456–457. doi:10.2307/2310741. hdl:2027/mdp.39015008206248. JSTOR 2310741. S2CID 121427033. +Rado, Tibor (1956-01-01). "Review of Mathematics and Plausible Reasoning". Philosophy of Science. 23 (2): 167. doi:10.1086/287478. JSTOR 185607. +Van Dantzig, D. (1959-01-01). "Review of Mathematics and Plausible Reasoning, G. Pólya". Synthese. 11 (4): 353–358. doi:10.1007/bf00486196. JSTOR 20114312. S2CID 46957889. +Broadbent, T. A. A. (1956-01-01). "Review of Mathematics and Plausible Reasoning". The Mathematical Gazette. 40 (333): 233–234. doi:10.2307/3608848. hdl:2027/mdp.39015008206248. JSTOR 3608848. +Bush, Robert R. (1956-01-01). "Review of Mathematics and Plausible Reasoning". The American Journal of Psychology. 69 (1): 166–167. doi:10.2307/1418146. hdl:2027/mdp.39015008206248. JSTOR 1418146. +Johansson, I. (1955-01-01). "Review of Mathematics and plausible reasoning, I and II". Nordisk Matematisk Tidskrift. 3 (1): 64–65. JSTOR 24524537. +Prager, W. (1955-01-01). "Review of Mathematics and plausible reasoning. Volume I: Induction and analogy. Volume II: Patterns of plausible inference". Quarterly of Applied Mathematics. 13 (3): 344–345. JSTOR 43634251. +Meserve, Bruce E. (1955-01-01). "Review of Induction and Analogy in Mathematics, Vol. I, and Patterns of Plausible Inference, Vol. II, of Mathematics and Plausible Reasoning". The Mathematics Teacher. 48 (4): 272. JSTOR 27954884. +Savage, Leonard J. (1955-01-01). "Review of Mathematics and Plausible Reasoning. Volume I, Induction and Analogy in Mathematics. Volume II, Patterns of Plausible Inference". Journal of the American Statistical Association. 50 (272): 1352–1354. doi:10.2307/2281238. JSTOR 2281238. +פ., א. י. י. (1957-01-01). "Review of Mathematics and Plausible Reasoning. Volume I: Induction and Analogy in Mathematics; Volume II: Patterns of Plausible Reasoning". Iyyun: The Jerusalem Philosophical Quarterly / עיון: רבעון פילוסופי. ח' (א'): 48–49. JSTOR 23301574. +Stein, Robert G. (1991-01-01). "Review of Patterns of Plausible Inference. Vol. 2 of Mathematics and Plausible Reasoning (R), George Pólya". The Mathematics Teacher. 84 (7): 574. JSTOR 27967294. +Alexanderson, G. L. (1979-01-01). "Review of Mathematics and Plausible Reasoning: Vol. I: Induction and Analogy in Mathematics; Mathematics and Plausible Reasoning: Vol. II: Patterns of Plausible Inference, George Polya". The Two-Year College Mathematics Journal. 10 (2): 119–122. doi:10.2307/3027025. JSTOR 3027025. + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Mechanica-0.md b/data/en.wikipedia.org/wiki/Mechanica-0.md new file mode 100644 index 000000000..a9c32a384 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Mechanica-0.md @@ -0,0 +1,24 @@ +--- +title: "Mechanica" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Mechanica" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:47.561752+00:00" +instance: "kb-cron" +--- + +Mechanica (Latin: Mechanica sive motus scientia analytice exposita; 1736) is a two-volume work published by mathematician Leonhard Euler which describes analytically the mathematics governing movement. +Euler both developed the techniques of analysis and applied them to numerous problems in mechanics, +notably in later publications the calculus of variations. Euler's laws of motion expressed scientific laws of Galileo and Newton in terms of points in reference frames and coordinate systems making them useful for calculation when the statement of a problem or example is slightly changed from the original. +Newton–Euler equations express the dynamics of a rigid body. Euler has been credited with contributing to the rise of Newtonian mechanics especially in topics other than gravity. + + +== References == + + +== External links == +Mechanica Vol. 1 [E015] – Latin. +Mechanica Vol. 1 – English translation by Ian Bruce. +Mechanica Vol. 2 [E016] – Latin. +Mechanica Vol. 2 – English translation by Ian Bruce. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Method_of_Fluxions-0.md b/data/en.wikipedia.org/wiki/Method_of_Fluxions-0.md new file mode 100644 index 000000000..ebc43b8e1 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Method_of_Fluxions-0.md @@ -0,0 +1,53 @@ +--- +title: "Method of Fluxions" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Method_of_Fluxions" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:48.700102+00:00" +instance: "kb-cron" +--- + +Method of Fluxions (Latin: De Methodis Serierum et Fluxionum) is a mathematical treatise by Sir Isaac Newton which served as the earliest written formulation of modern calculus. The book was completed in 1671 and posthumously published in 1736. + + +== Background == +Fluxion is Newton's term for a derivative. He originally developed the method at Woolsthorpe Manor during the closing of Cambridge due to the Great Plague of London from 1665 to 1667. Newton did not choose to make his findings known (similarly, his findings which eventually became the Philosophiae Naturalis Principia Mathematica were developed at this time and hidden from the world in Newton's notes for many years). Gottfried Leibniz developed his form of calculus independently around 1673, seven years after Newton had developed the basis for differential calculus, as seen in surviving documents like “the method of fluxions and fluents..." from 1666. Leibniz, however, published his discovery of differential calculus in 1684, nine years before Newton formally published his fluxion notation form of calculus in part during 1693. + + +== Impact == +The calculus notation in use today is mostly that of Leibniz, although Newton's dot notation for differentiation + + + + + + + x + ˙ + + + + + + {\displaystyle {\dot {x}}} + + is frequently used to denote derivatives with respect to time. + + +== Rivalry with Leibniz == +Newton's Method of Fluxions was formally published posthumously, but following Leibniz's publication of the calculus a bitter rivalry erupted between the two mathematicians over who had developed the calculus first, provoking Newton to reveal his work on fluxions. + + +== Newton's development of analysis == +For a period of time encompassing Newton's working life, the discipline of analysis was a subject of controversy in the mathematical community. Although analytic techniques provided solutions to long-standing problems, including problems of quadrature and the finding of tangents, the proofs of these solutions were not known to be reducible to the synthetic rules of Euclidean geometry. Instead, analysts were often forced to invoke infinitesimal, or "infinitely small", quantities to justify their algebraic manipulations. Some of Newton's mathematical contemporaries, such as Isaac Barrow, were highly skeptical of such techniques, which had no clear geometric interpretation. Although in his early work Newton also used infinitesimals in his derivations without justifying them, he later developed something akin to the modern definition of limits in order to justify his work. + + +== See also == + + +== References and notes == + + +== External links == +Method of Fluxions at the Internet Archive \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Methoden_der_mathematischen_Physik-0.md b/data/en.wikipedia.org/wiki/Methoden_der_mathematischen_Physik-0.md new file mode 100644 index 000000000..ba7569092 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Methoden_der_mathematischen_Physik-0.md @@ -0,0 +1,21 @@ +--- +title: "Methoden der mathematischen Physik" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Methoden_der_mathematischen_Physik" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:49.831629+00:00" +instance: "kb-cron" +--- + +Methoden der mathematischen Physik (translated into English with the title Methods of Mathematical Physics) is a 1924 book, in two volumes totalling around 1000 pages, published under the names of Richard Courant and David Hilbert. It was a comprehensive treatment of the "methods of mathematical physics" of the time. The second volume is devoted to the theory of partial differential equations. It contains presages of the finite element method, on which Courant would work subsequently, and which would eventually become basic to numerical analysis. +The material of the book was worked up from the content of Hilbert's lectures. While Courant played the major editorial role, many at the University of Göttingen were involved in the writing-up, and in that sense it was a collective production. +On its appearance in 1924 it apparently had little direct connection to the quantum theory questions at the centre of the theoretical physics of the time. That changed within two years, since the formulation of the Schrödinger equation made the Hilbert–Courant techniques of immediate relevance to the new wave mechanics. +There was a second edition (1931/7), wartime edition in the USA (1943), and a third German edition (1968). The English version Methods of Mathematical Physics (1953) was revised by Courant, and the second volume had extensive work done on it by the faculty of the Courant Institute. The books quickly gained the reputation as classics, and are among most highly referenced books in advanced mathematical physics courses. + + +== References == +Constance Reid (1986) Hilbert-Courant (separate biographies bound as one volume) +Courant, R.; Hilbert, D. (2024) [1953], Methods of mathematical physics, vol. I, New York, NY: Interscience Publishers, ISBN 978-3-527-41447-5, MR 0065391 +Courant, R.; Hilbert, D. (2024) [1962], Methods of mathematical physics, vol. II, New York, NY: Interscience Publishers, doi:10.1002/9783527617234, ISBN 978-3-527-41448-2, MR 0140802 +Methoden der mathematischen Physik online reproduction of 1924 German edition. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Metric_Structures_for_Riemannian_and_Non-Riemannian_Spaces-0.md b/data/en.wikipedia.org/wiki/Metric_Structures_for_Riemannian_and_Non-Riemannian_Spaces-0.md new file mode 100644 index 000000000..347857c5a --- /dev/null +++ b/data/en.wikipedia.org/wiki/Metric_Structures_for_Riemannian_and_Non-Riemannian_Spaces-0.md @@ -0,0 +1,18 @@ +--- +title: "Metric Structures for Riemannian and Non-Riemannian Spaces" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Metric_Structures_for_Riemannian_and_Non-Riemannian_Spaces" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:52.170085+00:00" +instance: "kb-cron" +--- + +Metric Structures for Riemannian and Non-Riemannian Spaces is a book in geometry by Mikhail Gromov. It was originally published in French in 1981 under the title Structures métriques pour les variétés riemanniennes, by CEDIC (Paris). + + +== History == +The 1981 edition was edited by Jacques Lafontaine and Pierre Pansu. The English version, considerably expanded, was published in 1999 by Birkhäuser Verlag, with appendices by Pierre Pansu, Stephen Semmes, and Mikhail Katz. The book was well received and has been reprinted several times. + + +== References == \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Mishnat_ha-Middot-0.md b/data/en.wikipedia.org/wiki/Mishnat_ha-Middot-0.md new file mode 100644 index 000000000..05553fa66 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Mishnat_ha-Middot-0.md @@ -0,0 +1,112 @@ +--- +title: "Mishnat ha-Middot" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Mishnat_ha-Middot" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:53.273259+00:00" +instance: "kb-cron" +--- + +The Mishnat ha-Middot (Hebrew: מִשְׁנַת הַמִּדּוֹת, lit. 'Treatise of Measures') is the earliest known Hebrew treatise on geometry, composed of 49 mishnayot in six chapters. Scholars have dated the work to either the Mishnaic period or the early Islamic era. + + +== History == + + +=== Date of composition === +Moritz Steinschneider dated the Mishnat ha-Middot to between 800 and 1200 CE. Sarfatti and Langermann have advanced Steinschneider's claim of Arabic influence on the work's terminology, and date the text to the early ninth century. +On the other hand, Hermann Schapira argued that the treatise dates from an earlier era, most likely the Mishnaic period, as its mathematical terminology differs from that of the Hebrew mathematicians of the Arab period. Solomon Gandz conjectured that the text was compiled no later than 150 CE (possibly by Rabbi Nehemiah) and intended to be a part of the Mishnah, but was excluded from its final canonical edition because the work was regarded as too secular. The content resembles both the work of Hero of Alexandria (c. 100 CE) and that of al-Khwārizmī (c. 800 CE) and the proponents of the earlier dating therefore see the Mishnat ha-Middot linking Greek and Islamic mathematics. + + +=== Modern history === +The Mishnat ha-Middot was discovered in MS 36 of the Munich Library by Moritz Steinschneider in 1862. The manuscript, copied in Constantinople in 1480, goes as far as the end of Chapter V. According to the colophon, the copyist believed the text to be complete. Steinschneider published the work in 1864, in honour of the seventieth birthday of Leopold Zunz. The text was edited and published again by mathematician Hermann Schapira in 1880. +After the discovery by Otto Neugebauer of a genizah-fragment in the Bodleian Library containing Chapter VI, Solomon Gandz published a complete version of the Mishnat ha-Middot in 1932, accompanied by a thorough philological analysis. A third manuscript of the work was found among uncatalogued material in the Archives of the Jewish Museum of Prague in 1965. + + +== Contents == +Although primarily a practical work, the Mishnat ha-Middot attempts to define terms and explain both geometric application and theory. The book begins with a discussion that defines "aspects" for the different kinds of plane figures (quadrilateral, triangle, circle, and segment of a circle) in Chapter I (§1–5), and with the basic principles of measurement of areas (§6–9). In Chapter II, the work introduces concise rules for the measurement of plane figures (§1–4), as well as a few problems in the calculation of volume (§5–12). In Chapters III–V, the Mishnat ha-Middot explains again in detail the measurement of the four types of plane figures, with reference to numerical examples. The text concludes with a discussion of the proportions of the Tabernacle in Chapter VI. +The treatise argues against the common belief that the Tanakh defines the geometric ratio π as being exactly equal to 3 and defines it as 22⁄7 instead. The book arrives at this approximation by calculating the area of a circle according to the formulae + + + + + A + = + + d + + 2 + + + − + + + + + d + + 2 + + + 7 + + + + − + + + + + d + + 2 + + + 14 + + + + + + {\displaystyle A=d^{2}-{\tfrac {d^{2}}{7}}-{\tfrac {d^{2}}{14}}} + + and + + + + A + = + + + + c + 2 + + + + ⋅ + + + + d + 2 + + + + + + {\displaystyle A={\tfrac {c}{2}}\cdot {\tfrac {d}{2}}} + +. + + +== See also == +Baraita of the Forty-nine Rules + + +== References == + + +== External links == +MS Heb. c. 18, Catalogue of the Genizah Fragments in the Bodleian Libraries. \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Murderous_Maths-0.md b/data/en.wikipedia.org/wiki/Murderous_Maths-0.md new file mode 100644 index 000000000..062f90080 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Murderous_Maths-0.md @@ -0,0 +1,34 @@ +--- +title: "Murderous Maths" +chunk: 1/2 +source: "https://en.wikipedia.org/wiki/Murderous_Maths" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:54.477242+00:00" +instance: "kb-cron" +--- + +Murderous Maths is a series of British educational books by author Kjartan Poskitt. Most of the books in the series are illustrated by illustrator Philip Reeve, with the exception of "The Secret Life of Codes", which is illustrated by Ian Baker, "Awesome Arithmetricks" illustrated by Daniel Postgate and Rob Davis, and "The Murderous Maths of Everything", also illustrated by Rob Davis. +The Murderous Maths books have been published in over 25 countries. The books, which are aimed at children aged 8 and above, teach maths, spanning from basic arithmetic to relatively complex concepts such as the quadratic formula and trigonometry. The books are written in an informal similar style to the Horrible Histories, Horrible Science and Horrible Geography series, involving evil geniuses, gangsters, and a generally comedic tone. + +== Development == +The first two books of the series were originally part of "The Knowledge" (now "Totally") series, itself a spin-off of Horrible Histories. However, these books were eventually redesigned and they, as well as the rest of the titles in the series, now use the Murderous Maths banner. According to Poskitt, "these books have even found their way into schools and proved to be a boost to GCSE studies". The books are also available in foreign editions, including: German, Spanish, Polish, Czech, Greek, Dutch, Norwegian, Turkish, Croatian, Italian, Lithuanian, Korean, Danish, Hungarian, Finnish, Thai and Portuguese (Latin America). In 2009, the books were redesigned again, changing the cover art style and the titles of most of the books in the series. +Poskitt's goal, according to the Murderous Maths website, is to write books that are "something funny to read", have "good amusing illustrations", include "tricks", and "explaining the maths involved as clearly as possible". He adds that although he doesn't "work to any government imposed curriculum or any stage achievement levels", he has "been delighted to receive many messages of support and thanks from parents and teachers in the UK, the United States and elsewhere". + +== Titles == +The following are the thirteen books that are available in the series. + +Guaranteed to Bend Your Brain (previously Murderous Maths) (1997), ISBN 0-439-01156-6 - (addition, subtraction, multiplication, division, percentages, powers, tessellation, Roman numerals, the development of the "10" and the place system, shortcomings of calculators, prime numbers, time - how the year and day got divided, digital/analogue clocks, angles, introduction to real Mathematicians, magic squares, mental arithmetic, card trick with algebra explanation, rounding and symmetry.) +Guaranteed to Mash your Mind (previously More Murderous Maths) (1998), ISBN 0-439-01153-1 (the monomino, domino, tromino, tetromino, pentomino, hexomino and heptomino, length area and volume, dimensions, measuring areas and volumes, basic rectangle and triangle formulas, speed, conversion of units, Möbius strip, Pythagoras, right-angled triangles, irrational numbers, pi, area and perimeter, bisecting angles, triangular numbers, topology networks, magic squares.) +Awesome Arithmetricks (previously The Essential Arithmetricks: How to + - × ÷) (1998), ISBN 0-439-01157-4 - (counting, odd even and negative numbers, signs of maths, place value and rounding off, manipulating equations, + - x ÷ %, long division, times tables, estimation, decimal signs, QED.) +The Mean & Vulgar Bits (previously The Mean & Vulgar Bits: Fractions and Averages) (2000), ISBN 0-439-01270-8 (fractions, converting improper and mixed fractions, adding subtracting multiplying and dividing fractions, primes and prime factors, reducing fractions, highest common factor and lowest common denominators, Egyptian fractions, comparing fractions, cancelling out fractions, converting fractions to decimals, decimal place system, percentages: increase and decrease, averages: mean mode and median.) +Desperate Measures (previously Desperate Measures: Length, Area and Volume) (2000), ISBN 0-439-01370-4 (measuring lines: units and accuracy, old measuring systems, the development of metric, the SI system and powers of ten, shapes, measuring areas and area formulas, weight, angles, measuring volume, Archimedes Principle, density, time and how the modern calendar developed.) +Do You Feel Lucky? (previously Do You Feel Lucky: The Secrets of Probability) (2001), ISBN 0-439-99607-4 (chance, tree diagrams, mutually exclusive and independent chances, Pascal's Triangle, permutations and combinations, sampling.) +Savage Shapes (previously Vicious Circles and Other Savage Shapes) (2002), ISBN 0-439-99747-X (signs in geometric diagrams, Loci, constructions: perpendicular bisectors; dropping perpendiculars; bisecting angles, triangles: similar; congruent; equal areas, polygons: regular; irregular; angle sizes and construction, tessellations and Penrose Tiles, origami, circles: chord; tangent; angle theorems, regular solids, Euler's formula, ellipses, Geometric proof of Pythagoras' Theorem.) +The Key To The Universe (previously Numbers: The Key To The Universe) (2002), ISBN 0-439-98116-6 (phi, Fibonacci Series, Golden Ratio, properties of Square, Triangle, Cube, Centred Hexagon and Tetrahedral numbers, "difference of two squares", number superstitions, prime numbers, Mersenne primes, tests to see if a number will divide by anything from 2-13 and 19, finger multiplication, binary, octal, and hexadecimal, perfect numbers, tricks of the nine times table, irrational transcendental and imaginary numbers, infinity.) +The Phantom X (previously The Phantom X: Algebra) (2003), ISBN 0-439-97729-0 (variables, elementary algebra, brackets, factorising, expanding, and simplifying expressions, solving quadratics and the quadratic formula, "Think of a number" tricks, difference of two squares, coefficients of (a-b)n, linear graphs: co-ordinates; gradients; y intercept, non-linear function graphs including parabolas, simultaneous equations: substitution and elimination, dividing by zero!.) +The Fiendish Angletron (previously The Fiendish Angletron: Trigonometry) (2004), ISBN 0-439-96859-3 (scales and ratios in maps and diagrams, protractor and compass, SIN, COS and TAN ratios in right angled triangles, trig on a calculator; normal and inverse, sine and cosine formulas for non-right-angled triangles, triangulation, parallax angles and parsecs, sin/cos/tan relationships, sin wave, bearings.) +The Perfect Sausages (previously The Perfect Sausage and other Fundamental Formulas) (2005), ISBN 0-439-95901-2 (areas and volumes, ellipsoids and toruses, number formulas (e.g. triangle, hexagonal), speed, acceleration, stopping time, distance, force, gravity, projectiles, Money: percentages; simple and compound interest, permutations and combinations.) +The 5ecret L1fe of Code5 (previously Codes: How to Make Them and Break Them) (2007), ISBN 978-1-4071-0715-8 (patterns, logic and deduction, prime numbers, high powers, modular arithmetic.) +Easy Questions, Evil Answers (2010), ISBN 1-407-11451-4 (formulas, working out square roots by hand, π, Pythagoras, paradoxes, problem solving, metric prefixes, large numbers, vectors.) +Related puzzle books have been published also: \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Murderous_Maths-1.md b/data/en.wikipedia.org/wiki/Murderous_Maths-1.md new file mode 100644 index 000000000..f5fb19d47 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Murderous_Maths-1.md @@ -0,0 +1,41 @@ +--- +title: "Murderous Maths" +chunk: 2/2 +source: "https://en.wikipedia.org/wiki/Murderous_Maths" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:54.477242+00:00" +instance: "kb-cron" +--- + +Professor Fiendish's Book of Diabolical Brain-benders (2002), ISBN 0-439-98226-X (mazes, logic, coin problems, number crosswords, shape cutting/rearranging, number squares.) +Professor Fiendish's Book of Brain-benders (a smaller version of the above) (same as above) +Sudoku: 100 Fun Number Puzzles (2005), ISBN 0-439-84570-X +Kakuro and Other Fiendish Number Puzzles (2006), ISBN 0-439-95164-X +One title that covers many different areas of mathematics has also been released: + +The Most Epic Book of Maths Ever (previously The Murderous Maths of Everything) (2010), ISBN 1-407-10367-9 (prime numbers, Sieve of Eratosthenes, Pythagoras' Theorem, triangular numbers, square numbers, the International Date Line, geometry, geometric constructions, topology, Möbius strips, curves (conic sections and cycloids Golomb Rulers, four-dimensional "Tic Tac Toe", The Golden Ratio, Fibonacci sequence, Logarithmic spirals, musical ratios, Theorems (including Ham sandwich theorem and Fixed point theorem), probability (cards, dice, cluedo etc.), Pascal's Triangle, Sierpinski Triangle, chess board, light years, size and distance of moon and planets, orbit, size of stars, shape of galaxy.) +Kjartan has also written a book entitled Everyday Maths for Grown-Ups (2011). + +== Reviews == +A recommendation of the series by Scientific American includes a quote from a Stanford engineer named Stacy F. Bennet, who described the series as "very humorous and engaging introductions to such topics as algebra, geometry and probability". On 22 November 1997, that same publication said of the series, "Have a look at Murderous Maths by Kjartan Poskitt. It is a truly addictive reading book, and was leapt on and devoured by my children. The book is full of awful jokes, fascinating facts, real murders and yes, the maths is good too. This is a brilliant book." +The Primary Times released a review of Professor Fiendish's Book of Diabolical Brain-benders on November 25, 2002, describing the title as "intriguing, fun to do, and not at all dry", and adding "I warn you, once you start, you'll be 'hooked'!". The Times Educational Supplement also published a review on the book on December 6, 2002, describing the title as being "action-packed" and reasoning that "behind the non-stop fun, serious mathematical principles are being investigated". +Kjartan did a presentation for 350 kids and 10 teachers at Wolfreton School, Hull in June 2004. Reporter Linda Blackbourne described it as a "stand-up maths routine [that] has children - and teachers - in fits of laughter". Carousel issue 16 (the guide to children's books) commented on the event: "...he possesses a prodigious gift of the (Yorkshire) gab, appears to be incapable of not enjoying himself, and plays his audience with the finesse of a maestro. Maths will never seem the same again". +The Times Educational Supplement described Murderous Maths as "A stand-up maths routine has children and teachers in fits of laughter... maths has never been so much fun". The Western Gazette said: "It is not often that you see a grown maths teacher cry with laughter...", while The Worthing Gazette said: "The kids went wild, they absolutely loved it...". The Stockton Evening Gazette said: "Headteacher Barry Winter said it was a stroke of genius inviting the quick-witted author to open the resource centre". The GCSE book in the Guardian said: "Those who have experienced Poskitt "live" will recognise his commitment to getting readers involved with the learning process" (Nov 6th 2001), and The Press (York) described it as "...charismatic..." + +A review by science writer Brian Clegg described his views on Murderous Maths: Desperate Measures: It's the usual clever mix of light historical context − mostly ancient from Israelites and Archimedes to the Romans − and real insights into fascinating aspects of something that sits nicely between maths and practical science. There's plenty to keep the reader and interested, and even adults perusing it will have one or two surprises along the way. Because it is very much applied maths, there is also a lot more opportunity to have fun with practical things to try out than has been the case with some of the Murderous Maths series. All in all this is a great addition to the fold. + +== Spin-offs == +Killer Puzzles (Written by Kjartan Poskitt) +The Urgum The Axeman series (by Kjartan Poskitt and illustrated by Philip Reeve) + +== See also == +Horrible Histories +Horrible Science + +== References == + +== External links == +The official Murderous Maths website +Horrible Books and Magazines United States +archived Daily Telegraph article \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Mécanique_analytique-0.md b/data/en.wikipedia.org/wiki/Mécanique_analytique-0.md new file mode 100644 index 000000000..f97577ea3 --- /dev/null +++ b/data/en.wikipedia.org/wiki/Mécanique_analytique-0.md @@ -0,0 +1,41 @@ +--- +title: "Mécanique analytique" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/Mécanique_analytique" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:45:46.353463+00:00" +instance: "kb-cron" +--- + +Mécanique analytique (1788–89) is a two volume French treatise on analytical mechanics, written by Joseph-Louis Lagrange, and published 101 years after Isaac Newton's Philosophiæ Naturalis Principia Mathematica. + + +== Treatise == +It consolidated into one unified and harmonious system, the scattered developments of contributors such as Alexis Clairaut, Jean le Rond d'Alembert, Pierre-Simon Laplace, Leonhard Euler, and Johann and Jacob Bernoulli in the historical transition from geometrical methods, as presented in Newton's Principia, to the methods of the calculus. The treatise expounds a great labor-saving and thought-saving general analytical method by which every mechanical question may be stated in a single differential equation. + +Lagrange wrote that this work was entirely new and that his intent was to reduce the theory and the art of solving mechanics problems to general formulae, providing all the equations necessary for the solution of each problem. He stated that:No diagrams will be found in this work. The methods that I explain require neither geometrical, nor mechanical, constructions or reasoning, but only algebraical operations in accordance with regular and uniform procedure. Those who love Analysis will see with pleasure that Mechanics has become a branch of it, and will be grateful to me for having thus extended its domain. +Ernst Mach describes the work as follows: +Analytic mechanics... was brought to the highest degree of perfection... Lagrange's aim is... to dispose, once and for all, of the reasoning necessary to resolve mechanical problems, by embodying as much as possible of it in a single formula. This he did. Every case... can now be dealt with by a very simple... schema; and whatever reasoning is left is performed by purely mechanical methods. The mechanics of Lagrange is a stupendous contribution to the economy of thought. + + +== Publication history == +The work was first published in 1788 (volume 1) and 1789 (volume 2). Lagrange issued a substantially enlarged second edition of volume 1 in 1811, toward the end of his life. His revision of volume 2 was substantially complete at the time of his death in 1813, but was not published until 1815. + +The second edition of 1811/15 has been translated into English, and is available online at archive.org. + + +== See also == + +Calculus of variations +Lagrangian mechanics +Hamiltonian mechanics + + +== References == + + +== External links == +Lagrange, J. L. (1811). Mécanique analytique. Vol. 1 (2d ed.). Paris: Courcier. +Lagrange, J. L. (1815). Mécanique analytique. Vol. 2 (2d ed.). Paris: Courcier. +Lagrange, J. L. (1997). Analytical mechanics. Vol. 1 (2d ed.). ISBN 9789401589031. English translation of the 1811 edition \ No newline at end of file diff --git a/data/en.wikipedia.org/wiki/Number_Theory b/data/en.wikipedia.org/wiki/Number_Theory new file mode 100644 index 000000000..e69de29bb diff --git a/data/en.wikipedia.org/wiki/Numerical_Recipes-0.md b/data/en.wikipedia.org/wiki/Numerical_Recipes-0.md index 27192c18e..e2186f6b4 100644 --- a/data/en.wikipedia.org/wiki/Numerical_Recipes-0.md +++ b/data/en.wikipedia.org/wiki/Numerical_Recipes-0.md @@ -4,7 +4,7 @@ chunk: 1/2 source: "https://en.wikipedia.org/wiki/Numerical_Recipes" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T08:36:39.090279+00:00" +date_saved: "2026-05-05T08:46:00.240449+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/Numerical_Recipes-1.md b/data/en.wikipedia.org/wiki/Numerical_Recipes-1.md index 91ba82be1..58f023a41 100644 --- a/data/en.wikipedia.org/wiki/Numerical_Recipes-1.md +++ b/data/en.wikipedia.org/wiki/Numerical_Recipes-1.md @@ -4,7 +4,7 @@ chunk: 2/2 source: "https://en.wikipedia.org/wiki/Numerical_Recipes" category: "reference" tags: "science, encyclopedia" -date_saved: "2026-05-05T08:36:39.090279+00:00" +date_saved: "2026-05-05T08:46:00.240449+00:00" instance: "kb-cron" --- diff --git a/data/en.wikipedia.org/wiki/On_Numbers_and_Games-0.md b/data/en.wikipedia.org/wiki/On_Numbers_and_Games-0.md new file mode 100644 index 000000000..a6e1ad3b0 --- /dev/null +++ b/data/en.wikipedia.org/wiki/On_Numbers_and_Games-0.md @@ -0,0 +1,160 @@ +--- +title: "On Numbers and Games" +chunk: 1/1 +source: "https://en.wikipedia.org/wiki/On_Numbers_and_Games" +category: "reference" +tags: "science, encyclopedia" +date_saved: "2026-05-05T08:46:01.406278+00:00" +instance: "kb-cron" +--- + +On Numbers and Games is a mathematics book by John Horton Conway first published in 1976. The book is written by a pre-eminent mathematician, and is directed at other mathematicians. The material is, however, developed in a playful and unpretentious manner and many chapters are accessible to non-mathematicians. Martin Gardner discussed the book at length, particularly Conway's construction of surreal numbers, in his Mathematical Games column in Scientific American in September 1976. +The book is roughly divided into two sections: the first half (or Zeroth Part), on numbers, the second half (or First Part), on games. In the Zeroth Part, Conway provides axioms for arithmetic: addition, subtraction, multiplication, division and inequality. This allows an axiomatic construction of numbers and ordinal arithmetic, namely, the integers, reals, the countable infinity, and entire towers of infinite ordinals. The object to which these axioms apply takes the form {L|R}, which can be interpreted as a specialized kind of set; a kind of two-sided set. By insisting that L