From e8692b7dea1eeab8efa6b0711d58bf5c82a026b5 Mon Sep 17 00:00:00 2001 From: Alex Clarke Date: Tue, 9 Jan 2024 11:30:56 -0700 Subject: [PATCH] Created the Abstract Algebra theorems and definitions cheat sheet --- .gitignore | 303 ++++++++++++++++++ Abstract-Algebra-Theorems-and-Definitions.pdf | Bin 0 -> 381503 bytes Abstract-Algebra-Theorems-and-Definitions.tex | 33 ++ README.md | 18 ++ init.sty | 86 +++++ part-1/chapters/chapter-0/chapter-0.tex | 7 + part-1/chapters/chapter-0/complex-numbers.tex | 14 + .../chapter-0/equivalence-relations.tex | 19 ++ .../chapters/chapter-0/functions-mappings.tex | 27 ++ .../chapter-0/mathematical-induction.tex | 9 + .../chapters/chapter-0/modular-arithmetic.tex | 1 + .../chapter-0/properties-of-integers.tex | 33 ++ part-1/part-1.tex | 3 + part-2/chapters/chapter-10/chapter-10.tex | 4 + .../chapter-10/definition-and-examples.tex | 9 + .../properties-of-homomorphisms.tex | 32 ++ .../the-first-isomorphism-theorem.tex | 13 + part-2/chapters/chapter-11/chapter-11.tex | 4 + .../proof-of-the-fundamental-theorem.tex | 17 + .../chapter-11/the-fundamental-theorem.tex | 5 + ...-isomorphism-classes-of-abelian-groups.tex | 16 + part-2/chapters/chapter-2/chapter-2.tex | 3 + .../definition-and-examples-of-groups.tex | 14 + .../elementary-properties-of-groups.tex | 17 + part-2/chapters/chapter-3/chapter-3.tex | 3 + part-2/chapters/chapter-3/subgroup-tests.tex | 13 + .../chapter-3/terminology-and-notation.tex | 36 +++ part-2/chapters/chapter-4/chapter-4.tex | 3 + ...fication-of-subgroups-of-cyclic-groups.tex | 17 + .../chapter-4/properties-of-cyclic-groups.tex | 33 ++ part-2/chapters/chapter-5/chapter-5.tex | 4 + part-2/chapters/chapter-5/cycle-notation.tex | 28 ++ .../chapter-5/definition-and-notation.tex | 5 + .../chapter-5/properties-of-permutations.tex | 43 +++ part-2/chapters/chapter-6/automorphisms.tex | 19 ++ part-2/chapters/chapter-6/cayleys-theorem.tex | 5 + part-2/chapters/chapter-6/chapter-6.tex | 5 + .../chapter-6/definition-and-examples.tex | 7 + .../chapter-6/properties-of-isomorphisms.tex | 26 ++ ...cation-of-cosets-to-permutation-groups.tex | 13 + part-2/chapters/chapter-7/chapter-7.tex | 5 + .../lagranges-theorem-and-consequences.tex | 37 +++ .../chapter-7/properties-of-cosets.tex | 20 ++ ...tion-group-of-a-cube-and-a-soccer-ball.tex | 5 + part-2/chapters/chapter-8/chapter-8.tex | 4 + .../chapter-8/definition-and-examples.tex | 5 + ...properties-of-external-direct-products.tex | 18 ++ ...modulo-n-as-an-external-direct-product.tex | 17 + .../applications-of-factor-groups.tex | 13 + part-2/chapters/chapter-9/chapter-9.tex | 5 + part-2/chapters/chapter-9/factor-groups.tex | 5 + .../chapter-9/internal-direct-products.tex | 26 ++ .../chapters/chapter-9/normal-subgroups.tex | 9 + part-2/part-2.tex | 12 + part-3/chapters/chapter-12/chapter-12.tex | 4 + .../chapter-12/motivation-and-definition.tex | 20 ++ .../chapter-12/properties-of-rings.tex | 23 ++ part-3/chapters/chapter-12/subrings.tex | 9 + part-3/chapters/chapter-13/chapter-13.tex | 4 + .../chapter-13/characteristic-of-a-ring.tex | 13 + .../chapter-13/definition-and-examples.tex | 13 + part-3/chapters/chapter-13/fields.tex | 13 + part-3/chapters/chapter-14/chapter-14.tex | 4 + part-3/chapters/chapter-14/factor-rings.tex | 5 + part-3/chapters/chapter-14/ideals.tex | 13 + .../prime-ideals-and-maximal-ideals.tex | 17 + part-3/chapters/chapter-15/chapter-15.tex | 4 + .../chapter-15/definition-and-examples.tex | 7 + .../properties-of-ring-homomorphisms.tex | 42 +++ .../chapter-15/the-field-of-quotients.tex | 5 + part-3/chapters/chapter-16/chapter-16.tex | 3 + .../chapter-16/notation-and-terminology.tex | 30 ++ ...he-division-algorithm-and-consequences.tex | 29 ++ part-3/chapters/chapter-17/chapter-17.tex | 4 + .../chapter-17/irreducibility-tests.tex | 29 ++ .../chapter-17/reducibility-tests.tex | 21 ++ .../chapter-17/unique-factorization-in-zx.tex | 7 + part-3/chapters/chapter-18/chapter-18.tex | 4 + .../chapters/chapter-18/euclidean-domains.tex | 21 ++ .../chapter-18/irreducibles-primes.tex | 13 + .../unique-factorization-domains.tex | 21 ++ part-3/part-3.tex | 8 + part-4/chapters/chapter-19/chapter-19.tex | 4 + .../chapter-19/definition-and-examples.tex | 15 + .../chapter-19/linear-independence.tex | 19 ++ part-4/chapters/chapter-19/subspaces.tex | 5 + part-4/chapters/chapter-20/chapter-20.tex | 4 + .../chapters/chapter-20/splitting-fields.tex | 34 ++ ...he-fundamental-theorem-of-field-theory.tex | 9 + .../zeros-of-an-irreducible-polynomial.tex | 44 +++ part-4/chapters/chapter-21/chapter-21.tex | 4 + .../characterization-of-extensions.tex | 17 + .../chapters/chapter-21/finite-extensions.tex | 17 + .../properties-of-algebraic-extensions.tex | 9 + part-4/chapters/chapter-22/chapter-22.tex | 4 + .../classification-of-finite-fields.tex | 5 + .../chapter-22/structure-of-finite-fields.tex | 19 ++ .../subfields-of-a-finite-field.tex | 5 + part-4/chapters/chapter-23/chapter-23.tex | 1 + part-4/part-4.tex | 6 + .../applications-of-sylow-theorems.tex | 5 + part-5/chapters/chapter-24/chapter-24.tex | 5 + .../chapters/chapter-24/conjugacy-classes.tex | 13 + .../chapter-24/the-class-equation.tex | 15 + .../chapter-24/the-sylow-theorems.tex | 29 ++ part-5/chapters/chapter-25/chapter-25.tex | 3 + .../chapter-25/historical-background.tex | 5 + .../chapter-25/nonsimplicity-tests.tex | 21 ++ part-5/chapters/chapter-26/chapter-26.tex | 7 + .../characterization-of-dihedral-groups.tex | 5 + ...sification-of-groups-of-order-up-to-15.tex | 5 + .../chapter-26/definitions-and-notation.tex | 11 + part-5/chapters/chapter-26/free-group.tex | 13 + .../chapter-26/generators-and-relations.tex | 20 ++ part-5/chapters/chapter-26/motivation.tex | 5 + part-5/chapters/chapter-27/chapter-27.tex | 4 + ...on-of-finite-groups-of-rotations-in-R3.tex | 5 + ...cation-of-finite-plane-symmetry-gruops.tex | 5 + part-5/chapters/chapter-27/isometries.tex | 13 + part-5/chapters/chapter-28/chapter-28.tex | 4 + ...ntification-of-plane-periodic-patterns.tex | 5 + .../the-crystallographic-groups.tex | 5 + .../chapters/chapter-28/the-frieze-groups.tex | 5 + .../chapters/chapter-29/burnsides-theorem.tex | 10 + part-5/chapters/chapter-29/chapter-29.tex | 4 + part-5/chapters/chapter-29/group-action.tex | 5 + part-5/chapters/chapter-29/motivation.tex | 5 + part-5/chapters/chapter-30/chapter-30.tex | 3 + .../hamiltonian-circuits-and-paths.tex | 20 ++ .../the-cayley-digraph-of-a-group.tex | 9 + part-5/chapters/chapter-31/chapter-31.tex | 4 + part-5/chapters/chapter-31/coset-decoding.tex | 13 + part-5/chapters/chapter-31/linear-codes.tex | 19 ++ .../parity-check-matrix-decoding.tex | 9 + part-5/chapters/chapter-32/chapter-32.tex | 3 + .../fundamental-theorem-of-galois-theory.tex | 17 + ...solvability-of-polynomials-by-radicals.tex | 27 ++ part-5/chapters/chapter-33/chapter-33.tex | 3 + .../chapter-33/cyclotomic-polynomials.tex | 27 ++ .../the-constructible-regular-n-gons.tex | 9 + part-5/part-5.tex | 11 + 141 files changed, 2141 insertions(+) create mode 100644 .gitignore create mode 100644 Abstract-Algebra-Theorems-and-Definitions.pdf create mode 100644 Abstract-Algebra-Theorems-and-Definitions.tex create mode 100644 README.md create mode 100644 init.sty create mode 100644 part-1/chapters/chapter-0/chapter-0.tex create mode 100644 part-1/chapters/chapter-0/complex-numbers.tex create mode 100644 part-1/chapters/chapter-0/equivalence-relations.tex create mode 100644 part-1/chapters/chapter-0/functions-mappings.tex create mode 100644 part-1/chapters/chapter-0/mathematical-induction.tex create mode 100644 part-1/chapters/chapter-0/modular-arithmetic.tex create mode 100644 part-1/chapters/chapter-0/properties-of-integers.tex create mode 100644 part-1/part-1.tex create mode 100644 part-2/chapters/chapter-10/chapter-10.tex create mode 100644 part-2/chapters/chapter-10/definition-and-examples.tex create mode 100644 part-2/chapters/chapter-10/properties-of-homomorphisms.tex create mode 100644 part-2/chapters/chapter-10/the-first-isomorphism-theorem.tex create mode 100644 part-2/chapters/chapter-11/chapter-11.tex create mode 100644 part-2/chapters/chapter-11/proof-of-the-fundamental-theorem.tex create mode 100644 part-2/chapters/chapter-11/the-fundamental-theorem.tex create mode 100644 part-2/chapters/chapter-11/the-isomorphism-classes-of-abelian-groups.tex create mode 100644 part-2/chapters/chapter-2/chapter-2.tex create mode 100644 part-2/chapters/chapter-2/definition-and-examples-of-groups.tex create mode 100644 part-2/chapters/chapter-2/elementary-properties-of-groups.tex create mode 100644 part-2/chapters/chapter-3/chapter-3.tex create mode 100644 part-2/chapters/chapter-3/subgroup-tests.tex create mode 100644 part-2/chapters/chapter-3/terminology-and-notation.tex create mode 100644 part-2/chapters/chapter-4/chapter-4.tex create mode 100644 part-2/chapters/chapter-4/classification-of-subgroups-of-cyclic-groups.tex create mode 100644 part-2/chapters/chapter-4/properties-of-cyclic-groups.tex create mode 100644 part-2/chapters/chapter-5/chapter-5.tex create mode 100644 part-2/chapters/chapter-5/cycle-notation.tex create mode 100644 part-2/chapters/chapter-5/definition-and-notation.tex create mode 100644 part-2/chapters/chapter-5/properties-of-permutations.tex create mode 100644 part-2/chapters/chapter-6/automorphisms.tex create mode 100644 part-2/chapters/chapter-6/cayleys-theorem.tex create mode 100644 part-2/chapters/chapter-6/chapter-6.tex create mode 100644 part-2/chapters/chapter-6/definition-and-examples.tex create mode 100644 part-2/chapters/chapter-6/properties-of-isomorphisms.tex create mode 100644 part-2/chapters/chapter-7/an-application-of-cosets-to-permutation-groups.tex create mode 100644 part-2/chapters/chapter-7/chapter-7.tex create mode 100644 part-2/chapters/chapter-7/lagranges-theorem-and-consequences.tex create mode 100644 part-2/chapters/chapter-7/properties-of-cosets.tex create mode 100644 part-2/chapters/chapter-7/the-rotation-group-of-a-cube-and-a-soccer-ball.tex create mode 100644 part-2/chapters/chapter-8/chapter-8.tex create mode 100644 part-2/chapters/chapter-8/definition-and-examples.tex create mode 100644 part-2/chapters/chapter-8/properties-of-external-direct-products.tex create mode 100644 part-2/chapters/chapter-8/the-group-of-units-modulo-n-as-an-external-direct-product.tex create mode 100644 part-2/chapters/chapter-9/applications-of-factor-groups.tex create mode 100644 part-2/chapters/chapter-9/chapter-9.tex create mode 100644 part-2/chapters/chapter-9/factor-groups.tex create mode 100644 part-2/chapters/chapter-9/internal-direct-products.tex create mode 100644 part-2/chapters/chapter-9/normal-subgroups.tex create mode 100644 part-2/part-2.tex create mode 100644 part-3/chapters/chapter-12/chapter-12.tex create mode 100644 part-3/chapters/chapter-12/motivation-and-definition.tex create mode 100644 part-3/chapters/chapter-12/properties-of-rings.tex create mode 100644 part-3/chapters/chapter-12/subrings.tex create mode 100644 part-3/chapters/chapter-13/chapter-13.tex create mode 100644 part-3/chapters/chapter-13/characteristic-of-a-ring.tex create mode 100644 part-3/chapters/chapter-13/definition-and-examples.tex create mode 100644 part-3/chapters/chapter-13/fields.tex create mode 100644 part-3/chapters/chapter-14/chapter-14.tex create mode 100644 part-3/chapters/chapter-14/factor-rings.tex create mode 100644 part-3/chapters/chapter-14/ideals.tex create mode 100644 part-3/chapters/chapter-14/prime-ideals-and-maximal-ideals.tex create mode 100644 part-3/chapters/chapter-15/chapter-15.tex create mode 100644 part-3/chapters/chapter-15/definition-and-examples.tex create mode 100644 part-3/chapters/chapter-15/properties-of-ring-homomorphisms.tex create mode 100644 part-3/chapters/chapter-15/the-field-of-quotients.tex create mode 100644 part-3/chapters/chapter-16/chapter-16.tex create mode 100644 part-3/chapters/chapter-16/notation-and-terminology.tex create mode 100644 part-3/chapters/chapter-16/the-division-algorithm-and-consequences.tex create mode 100644 part-3/chapters/chapter-17/chapter-17.tex create mode 100644 part-3/chapters/chapter-17/irreducibility-tests.tex create mode 100644 part-3/chapters/chapter-17/reducibility-tests.tex create mode 100644 part-3/chapters/chapter-17/unique-factorization-in-zx.tex create mode 100644 part-3/chapters/chapter-18/chapter-18.tex create mode 100644 part-3/chapters/chapter-18/euclidean-domains.tex create mode 100644 part-3/chapters/chapter-18/irreducibles-primes.tex create mode 100644 part-3/chapters/chapter-18/unique-factorization-domains.tex create mode 100644 part-3/part-3.tex create mode 100644 part-4/chapters/chapter-19/chapter-19.tex create mode 100644 part-4/chapters/chapter-19/definition-and-examples.tex create mode 100644 part-4/chapters/chapter-19/linear-independence.tex create mode 100644 part-4/chapters/chapter-19/subspaces.tex create mode 100644 part-4/chapters/chapter-20/chapter-20.tex create mode 100644 part-4/chapters/chapter-20/splitting-fields.tex create mode 100644 part-4/chapters/chapter-20/the-fundamental-theorem-of-field-theory.tex create mode 100644 part-4/chapters/chapter-20/zeros-of-an-irreducible-polynomial.tex create mode 100644 part-4/chapters/chapter-21/chapter-21.tex create mode 100644 part-4/chapters/chapter-21/characterization-of-extensions.tex create mode 100644 part-4/chapters/chapter-21/finite-extensions.tex create mode 100644 part-4/chapters/chapter-21/properties-of-algebraic-extensions.tex create mode 100644 part-4/chapters/chapter-22/chapter-22.tex create mode 100644 part-4/chapters/chapter-22/classification-of-finite-fields.tex create mode 100644 part-4/chapters/chapter-22/structure-of-finite-fields.tex create mode 100644 part-4/chapters/chapter-22/subfields-of-a-finite-field.tex create mode 100644 part-4/chapters/chapter-23/chapter-23.tex create mode 100644 part-4/part-4.tex create mode 100644 part-5/chapters/chapter-24/applications-of-sylow-theorems.tex create mode 100644 part-5/chapters/chapter-24/chapter-24.tex create mode 100644 part-5/chapters/chapter-24/conjugacy-classes.tex create mode 100644 part-5/chapters/chapter-24/the-class-equation.tex create mode 100644 part-5/chapters/chapter-24/the-sylow-theorems.tex create mode 100644 part-5/chapters/chapter-25/chapter-25.tex create mode 100644 part-5/chapters/chapter-25/historical-background.tex create mode 100644 part-5/chapters/chapter-25/nonsimplicity-tests.tex create mode 100644 part-5/chapters/chapter-26/chapter-26.tex create mode 100644 part-5/chapters/chapter-26/characterization-of-dihedral-groups.tex create mode 100644 part-5/chapters/chapter-26/classification-of-groups-of-order-up-to-15.tex create mode 100644 part-5/chapters/chapter-26/definitions-and-notation.tex create mode 100644 part-5/chapters/chapter-26/free-group.tex create mode 100644 part-5/chapters/chapter-26/generators-and-relations.tex create mode 100644 part-5/chapters/chapter-26/motivation.tex create mode 100644 part-5/chapters/chapter-27/chapter-27.tex create mode 100644 part-5/chapters/chapter-27/classification-of-finite-groups-of-rotations-in-R3.tex create mode 100644 part-5/chapters/chapter-27/classification-of-finite-plane-symmetry-gruops.tex create mode 100644 part-5/chapters/chapter-27/isometries.tex create mode 100644 part-5/chapters/chapter-28/chapter-28.tex create mode 100644 part-5/chapters/chapter-28/identification-of-plane-periodic-patterns.tex create mode 100644 part-5/chapters/chapter-28/the-crystallographic-groups.tex create mode 100644 part-5/chapters/chapter-28/the-frieze-groups.tex create mode 100644 part-5/chapters/chapter-29/burnsides-theorem.tex create mode 100644 part-5/chapters/chapter-29/chapter-29.tex create mode 100644 part-5/chapters/chapter-29/group-action.tex create mode 100644 part-5/chapters/chapter-29/motivation.tex create mode 100644 part-5/chapters/chapter-30/chapter-30.tex create mode 100644 part-5/chapters/chapter-30/hamiltonian-circuits-and-paths.tex create mode 100644 part-5/chapters/chapter-30/the-cayley-digraph-of-a-group.tex create mode 100644 part-5/chapters/chapter-31/chapter-31.tex create mode 100644 part-5/chapters/chapter-31/coset-decoding.tex create mode 100644 part-5/chapters/chapter-31/linear-codes.tex create mode 100644 part-5/chapters/chapter-31/parity-check-matrix-decoding.tex create mode 100644 part-5/chapters/chapter-32/chapter-32.tex create mode 100644 part-5/chapters/chapter-32/fundamental-theorem-of-galois-theory.tex create mode 100644 part-5/chapters/chapter-32/solvability-of-polynomials-by-radicals.tex create mode 100644 part-5/chapters/chapter-33/chapter-33.tex create mode 100644 part-5/chapters/chapter-33/cyclotomic-polynomials.tex create mode 100644 part-5/chapters/chapter-33/the-constructible-regular-n-gons.tex create mode 100644 part-5/part-5.tex diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..7f7bed5 --- /dev/null +++ b/.gitignore @@ -0,0 +1,303 @@ +## Core latex/pdflatex auxiliary files: +*.aux +*.lof +*.log +*.lot +*.fls +*.out +*.toc +*.fmt +*.fot +*.cb +*.cb2 +.*.lb + +## Intermediate documents: +*.dvi +*.xdv +*-converted-to.* +# these rules might exclude image files for figures etc. +# *.ps +# *.eps +# *.pdf + +## Bibliography auxiliary files (bibtex/biblatex/biber): +*.bbl +*.bcf +*.blg +*-blx.aux +*-blx.bib +*.run.xml + +## Build tool auxiliary files: +*.fdb_latexmk +*.synctex +*.synctex(busy) +*.synctex.gz +*.synctex.gz(busy) +*.pdfsync + +## Build tool directories for auxiliary files +# latexrun +latex.out/ + +## Auxiliary and intermediate files from other packages: +# algorithms +*.alg +*.loa + +# achemso +acs-*.bib + +# amsthm +*.thm + +# beamer +*.nav +*.pre +*.snm +*.vrb + +# changes +*.soc + +# comment +*.cut + +# cprotect +*.cpt + +# elsarticle (documentclass of Elsevier journals) +*.spl + +# endnotes +*.ent + +# fixme +*.lox + +# feynmf/feynmp +*.mf +*.mp +*.t[1-9] +*.t[1-9][0-9] +*.tfm + +#(r)(e)ledmac/(r)(e)ledpar +*.end +*.?end +*.[1-9] +*.[1-9][0-9] +*.[1-9][0-9][0-9] +*.[1-9]R +*.[1-9][0-9]R +*.[1-9][0-9][0-9]R +*.eledsec[1-9] +*.eledsec[1-9]R +*.eledsec[1-9][0-9] +*.eledsec[1-9][0-9]R +*.eledsec[1-9][0-9][0-9] +*.eledsec[1-9][0-9][0-9]R + +# glossaries +*.acn +*.acr +*.glg +*.glo +*.gls +*.glsdefs +*.lzo +*.lzs +*.slg +*.slo +*.sls + +# uncomment this for glossaries-extra (will ignore makeindex's style files!) +# *.ist + +# gnuplot +*.gnuplot +*.table + +# gnuplottex +*-gnuplottex-* + +# gregoriotex +*.gaux +*.glog +*.gtex + +# htlatex +*.4ct +*.4tc +*.idv +*.lg +*.trc +*.xref + +# hyperref +*.brf + +# knitr +*-concordance.tex +# TODO Uncomment the next line if you use knitr and want to ignore its generated tikz files +# *.tikz +*-tikzDictionary + +# listings +*.lol + +# luatexja-ruby +*.ltjruby + +# makeidx +*.idx +*.ilg +*.ind + +# minitoc +*.maf +*.mlf +*.mlt +*.mtc[0-9]* +*.slf[0-9]* +*.slt[0-9]* +*.stc[0-9]* + +# minted +_minted* +*.pyg + +# morewrites +*.mw + +# newpax +*.newpax + +# nomencl +*.nlg +*.nlo +*.nls + +# pax +*.pax + +# pdfpcnotes +*.pdfpc + +# sagetex +*.sagetex.sage +*.sagetex.py +*.sagetex.scmd + +# scrwfile +*.wrt + +# svg +svg-inkscape/ + +# sympy +*.sout +*.sympy +sympy-plots-for-*.tex/ + +# pdfcomment +*.upa +*.upb + +# pythontex +*.pytxcode +pythontex-files-*/ + +# tcolorbox +*.listing + +# thmtools +*.loe + +# TikZ & PGF +*.dpth +*.md5 +*.auxlock + +# titletoc +*.ptc + +# todonotes +*.tdo + +# vhistory +*.hst +*.ver + +# easy-todo +*.lod + +# xcolor +*.xcp + +# xmpincl +*.xmpi + +# xindy +*.xdy + +# xypic precompiled matrices and outlines +*.xyc +*.xyd + +# endfloat +*.ttt +*.fff + +# Latexian +TSWLatexianTemp* + +## Editors: +# WinEdt +*.bak +*.sav + +# Texpad +.texpadtmp + +# LyX +*.lyx~ + +# Kile +*.backup + +# gummi +.*.swp + +# KBibTeX +*~[0-9]* + +# TeXnicCenter +*.tps + +# auto folder when using emacs and auctex +./auto/* +*.el + +# expex forward references with \gathertags +*-tags.tex + +# standalone packages +*.sta + +# Makeindex log files +*.lpz + +# xwatermark package +*.xwm + +# REVTeX puts footnotes in the bibliography by default, unless the nofootinbib +# option is specified. Footnotes are the stored in a file with suffix Notes.bib. +# Uncomment the next line to have this generated file ignored. +#*Notes.bib + +# Draw.io backup files +*.bkp +*.dtmp + diff --git a/Abstract-Algebra-Theorems-and-Definitions.pdf b/Abstract-Algebra-Theorems-and-Definitions.pdf new file mode 100644 index 0000000000000000000000000000000000000000..48e8b90ee25f89e39ce1b633dee99aa65d95fbd1 GIT binary patch literal 381503 zcmb5VW3VX8mNmL;?q%D?Ubb!9wr$(CZQIsfwrv~l^y}NNZ^S+EedpDWs*KEtjHp>z zV~#m;B#E4m2n_@6Zzz(v#o<+`-}vX_;j)c7K%>RP;@f*4D|F+ zbRy;sj!yV&OiWO8QpPr>PG>e99wA_(0Vs#Dc>!`o}N1^fW4H46aMh|Jg1Xu>ML02_)V9Q1!adPwq$ zRSp#vQxCA4ipq|rGG9zgd5gs3$j-{}%R%ai&F$rjl1N&Ls>oc5pam7;_(jK!P!bo7 zs?Ws*XLdLr{Z#vF z6p5o%4ykM4{PEdhZ@c=IcA-3j8I-_|wP&#uraXKwzP9`j@3!+1gja?jJqIxU3BY%u?vZCex@KE8yKGiTX;Qz*}Pg^m*;j|t>) z!7t>`tH=QC{8aUYLOh$9#1e~DNzBzKYz|aP^s z*RocJQHc}D(}f_%HEv;Jiozc~H#8=yc_T%fwg>|+X+hkh(+dUlT!YXO{l?;~OSH_X z!!tG<_Q56<<)cG)oB@W)1D=RVDHqmprpse$=H43DFKkY)aEczHiwcTD8^s2e;~Mit zBg}3dSFy^>*9k^V=5;@oB2iT!6$Bf_;Z#lL#q_m9cGOaPjXwBsU+;7F@1!~7ka7zT zwIP$FlnVX}m<0Gz$NOGps>(|S40cwqWy6m!HYKbFLd6k%!wsVcQ^B-72JeamxK{3F z8*%bX^=#^SlxybqtYPO9@@LQ01iI%XYKC?C zP!>Z`)MkCkPAR5)Io(QXXKT$m;g0-^hS?vcZFbxb^y+V4|aF zARDtk1@HtJke{7zI>L=psVj>p2`KZ&Axo$TU=G9wJ)(-zh`D2D<4>M+&%vD}BbN-g z7Y8xGi4sM<5EWO|>FoXBXE6)NlXQ)^6Yg>23Tl9CR*r@1F~{hPQRWpE$NiE|QW2nx zlx*fFn-epqB1Y6jnyU{p@l!Z}11(eF%o3nBhsA}VpZCCL4!h){1+zLs0n!kH^NJQe z+?^IvpF#Mcz?y>`TVN28NlPRS)Q_o2{}rm1!ET>ps6Qkb6O1^s`Vfp;FAzM|7DG8X zxZ4bssgHn-K#xF9k|nS%2HgrCCmAE_&L8p$7YpOF$F+B7!?juQ%p%U`uY3O2SPgzoQ<7bgnCu^tPtZVns|v2Px!7j(KFfED1i z&VV|W*PRrFhBHkRhRufmIOk6{QWl>@i_9zm$b^7CA|N-1P#VZ<$ZX$Xg-;I%8vP{Y zhcrS#+Sge6IpP+gEr`FUl7-LQn9OfPZiX`2A4p>v@0>$x+Pmp3L0pY>sLdwq%K7k)5 z1nyv2cWgCG1cn1um`XPsiFCKG?X3}sHoCudXyMhFK^s%#L95e^$<0Y*dUrBYQQI!&CDJ=~bdIYX&E?D#YoFMD@B9h|yJo!jb1Q<}I`)dN^Zv=;JA z5Mqt{jmCPw!*{^u@NM^+mPx^iM$w~AtA}V4GM=mWZF4Y)YW_IAdQVWpA+VmyYXQs= z4)u+z|2P_DlCRS!Wtb&wHQw|?1Vd@;}mI5mSlL;Yx)^Si=o*q zoRzOyepdUD_Iqa_z#zv!m!0bYLpFCrY++d;PLr!s@g3c@onuh6Q9YTW)QD9jmV z`Id2VHX+|}`#9@OF=MU=W!Bsx8wFNTjU=s z*kyND8p(xAz_=Q;IAN=ASF!Zrvs5R%RflOC<4J(8omP<^y9dinNgpco1=mZ9Y(-mE zTvO1b(3&rA)1#J3>Em+f9?R)!t>4NaMLC{P9_pB7|(HJdIU8DMKICLta+H^3v zuIulTlMZI0-`IjlP!EY}Gf|$b{$qx(s1{>!jpxgyen&oQrdp4N84t|fn%1>A(d{-1 z)~{TxRIXID6>y?ErBsX3x?A=0xIftfRuOu{17dYF&BX2Y|uego6ODeZ6BU+kAcg$ZEtTVp% z7|a9`Nt0PSp}slmt=QiY?#R5W)-)Rn!1{TEJqNtu$_1`3q;9p%e9oATxQW^&=2}G{ zm-?fD#|zC(EWI;UU!;zyHL9{8oj)g`ku!b3Jqo;pp#i2$yF106292t<^CZ^uFI)MF zt>5g;<=N7r!5g$jrDvo|@)FD!l7YR~GK^UY zYIT}CGpwPNIdR6Xmz@7ZT7v=Wy}7^2o4kh23ZN@9tjs!{a@uU>+p`I;YjRE|)f zRlXd`Q@I+liF(s+Kr^QSGBED)SJ5=~s2L}aY0&Z+`P6RwDxoCG{QYzS96I+2&;}rmFtYvQ;5f(e+799)54rkAuo{$;exq5%nkS1)OsP2c`45%p&4c6IUs+zT zD=vk1F367ZL$Z?ZB_;o4)iQ2$v!W=W;5~m}9-;_Mcj9L7-@2UgTfFLlpWGLegGwes znt6GtTaVHL22N5PBWpasWZ&t;BU<^R_;6=u{AQrku-->4Ajqf5kR;swAfxUMPm9rJ za0}QT$fDzC{LVp(gebd>_nlyZ0k#ze7hbw=LD{%vAXQSLOflV@3bWW)D-GW-Y#9%6 z-(ahGf}cM@nD!?8?4#hMIH}55q5AnemN)6e-_>3Go1n4(&5B}YWctTJyGoOm-Jk~u zx%rIPJjPCV+o*Rjz`-YlmDaSa6C^K*PKu?)L;8AYv?P-zpyc21bIHmoa@pka`Fd~8 zXMM?Ybpg?Sv-f!XPI7=>kP`xOU(k%bi<8{9rxv6nwDma94iJz30P)vYE4cTS;;r2v z!2C5)Zw}t=_Xj~zKQrqCP$13UamAr#Vgf!)4}Zq?a(H}}^zFzIXkY1w$r#T^(Oip6 zxQ2>If*8zT0RxJ}(AqRDbZj$iCJ#?+tbawJSUly>KAn64BO$2RA&9;p~i7 zKqB2!Jj^Kxiyif$P5NIG$(n8aO+^odZ>nQ@`__T()4@ zq`3K5BlQ`vY>L>#wgM|?3};A@cOY-v)W(>t4Ss>U!PQV(q%`OI{vj<3+_lI~N%%E92v>rq5j%WnJcl0q36Ld5 zv;Qu!ayncBrU1?bq+AVke0F~2F!G(*572Vn>7C!HCx@l*&I)yX2DfxmkCsM@7SC$t z&Gb`OHYAK7H}T=0%L`;F4p7->#d3wxQ$m{KN*Y9HJNd=s7vP#3IE!*@Y?6kB9r4mL z)b3$p3>A-DWC-GCAK%+l7Ff$feA!g)=7!uVlkznNE2G-l{2_FF7MDoTQR};o8V@j> zJweFTKmk+EU>VMQ+4;7LUyWna`_qIgH74BP=X4H&T$z(S!4sPlLF~74a263I z&67PA^#~r#q6Ss$jSP1N2U7_+B}XuDiL2$BEq|(0@;YQG_nmCFo=Ef(7>?hTuwyaa zE-cA>6%W#*Z;Sy%Wa(jz${j2*Pn6?PjvV5Z*4__)F~HGdUm$#%V5o4K2OSC1M1j(j zMc_Q+g;hzhq0VmC{*+~wY5?f9oCPX#hv0A#F*H8bT*A<&^-`S2hJoDq^-J-#goC7_>5Kc$|TrTiV`LK~k3 zG%&U(iC=vn5Pty^+qfRUX&xYW+6a9Fc+@qJVgkBHI8^!piqn4I9V!YaNtfY7KqQ>p zGT2<7EIT1Q<%GKv9N#nU7~mNHJOw`Z96h!#+hWxcDx8C3LT2XFq6fz#!5ed^=x0|92GuF<^L&`(%H@lqQB-e2_sk z^jVDpJwL-eaA4pnXr=z6B6Kh#Q~_f!9_NUGd5hyFF#OFk7%szI;}ei(Hn8q9hgq$> z$^Ln0x3#_-9iXMZZt?eX>w~XTeLlA09Q3y}JjQA8#E^^d*azsZJYq65IiSUPc$*01 z8Br(HYC%DFX}~gt@NA$rQqR{onOb$@=5OUjiSU=5%Jz!W6T-C4HNB?1pK;zV7~jLQ z-Xi#TfA)BAkDb!~?1jK7awyeT7Yzo$QE_-3XN(@x&1%w~-l79u!2P&y?;+vz%;$&U zq}<)yJR$73O0~anbk{~0(@L+zC5|~DS}F@kg-!3HS5J%AE{K(qJ|lEK+eO@GXgR5W zA&+Vb3sl!*3C!j?y5VJB!1eyws|i)LzPci(TRVEPjOF|=GRJ5M;BmoLF9M5kpK)o= z5(yKoqFFe#B#{KNU5C2udgB_H8Vz(4`n_>79eekVdc6}U7*+7{dMH@*WlWwjYO?2t z-dmETJF5gc)$Gz?lgn8MeEO3acPh>~N^wk?Ev>7QCKJkZW=DzHdu@Byv7yxO9NH^d zb(IGt7A0=S`PW*;>rCkzUC2_VW@L6BThG%f&LeVZgnst-0VmRWU4ZU%6_2NcO z_+?Bce%+MQ)&ukC=;Y1Ld|x#^R(N{vi#J85SvaeJ8u=~!d3#^UTglgX9Q1%j4T_Vd z9_j*HC}I+Yr^&E>`)MdT2&V99fBva#al*9~wOy>f&vP8N>}?x?yTj_v%F-Rau#-1U z4*O<+>C5=F$ami<-3qpZYr3;M#AcAJ4NJ9^{}-YgVAd65!MyIP8e>pP4)mgQ}|dpL)zqwTGA>JHGQBb=B@suvxhd;;jGKZ_QYs#M{~@z)mEn)Io(?=CrMJ? zq-qB}CWVo^_2F+0>2%;&IB*s{nq5PsN+~3JOGAS-XVb8U)eo0b_X{-+oD9lXMAIA_ z4;DAlwVP44^HN| zk!i6vEfhZDbg^ulriqE_&cY(yo~hD2+}mhY4lLbN4deFhWf8*71|w$Y>C!Wi%5QaD z6e>>_#T{pc_MDkLbiMVGFG&VBc?bKd&dfb{wtzf2c~cwl`^T zj~^=gd!EZ{hb+pR=2QJIy0mmQWo@BKa%kBzRl@E;EfIV^RkC%I7Ao`#Y{p2*=wsu_ z$(}A4SHk#f%c5$30K6PpsBLK@BD8_-1|c)OD0`Ht9WGNRCt|cxZtzz$r#(7J@-JTT zb&bal&FaYkoySkDiR|-Jqh*WDB{q_3D7+OzO6TuNkfkXy8~Pn#b1ZMQ0#7ixR(9LL zW?9{O`X69(Y;U~+Pq4UlcHjQ1>l@NmaA1Ag%HhsVd+EnFoyKR9^k(wNy1uITmug}z zDX(k{ow=Kj@cyv1Z1ET zOe#T89pAeS)J1X7O>D4WMDQn{=0zrzgNUp8IunCBFG^xK2TSLG;@#L zOOmmpY%;^; zd@djMPIvlaLVosDY-IhXo_)g9$gso;3@Mc8(gC*lQD9Kvw-s6@PmGvy!uEU{ogdNG0m1-&A@-slQlJP;`iCzR-Vs7&bFFuxAW{16BBPAate zPK?u(opa7kej%ppJgL0X@wY)7nDrrge84K6w-NaT@tE|t0**vz7;h|?DasfeT?#=Y zJtEG7lg32X3^RUk4(w4q{J?8&_#YTFPxmuTk(oY z%gj8PDA#(QmQbofx3SCH#=Fi2>vaa}sX&NF zr0j7UA&dzp*m2EJI-VJFWcstc(pWUIN~)bak^+Lq$OsMj(HE*2Ah>-gnJUN6z+CVg zDYMi}^YB5t*s-Zc!{(re#J~1DN^*Vi82b`VMRdW2th~NcWYd{+uz`~DsNHRNN#Q!k0=H&a~qay98@l8#V4+ii~SX_(Q^?IbO zi{~B0gdhr$;j9=N$81UY?*Wn%JLqze$Aa@xnl-aj2;2uve4@uEeUbEK`^EekBq!h@ zjx%FT&S{W3-DNkuB-B+`&&}9YYBs3=*3JJtT76utzn|1ws`VJb{^G1@M%R8bL_FkK zeSC#FZGb@(7tO%i3~1v^b8@RlgZpr#mC5K2m?(55sU5}a!oF=VVKkbwhXga=A0ucz zOhYaj<-lE1bw$ClKN!z3X{4fQ51=7mnCxuIh<&^?FR<%!hO%z96Mkq)f+P&S$i?z| z=e0_iLHtA=ksnQk({P#ArH?<+Wj*;wZajUh*UN0Z#VUn$+i9zi0pvPyzuVj&hi0A4 zqIRz*g|vIH>qmngwvOqzP5$O+aTE?ohcWYJcU)^?^421SHZ>D=t5`d<&R^3JrFL*n zwcgPCbh8@r>C{T+Pj`Kx$yG+%h|1fegqFuROE<_KSrf!uCVx>V6m^M|Q+b~pHIfN& zm$k(D&j`BGYXX|0H6ZaIVNp|UwJ??yK?sfBJUQfriFYWo$y6EupKv21`3f%Fmx0*Y z_7Hvyx~p;a50d>Uif4*<$1zd9Y0KjRmUGLNPF(k8Fl;2g=>jsI$+C_@qqLx8*2j{d zG4nxG?h()dgF`ajuBKTi&05pF<-`%!wDXS?@}Rib@HTxuZ)S4py{^@)@3|S{RO6aZ zZAmu;gUqj01J1f~!Ko!fjp752%6sGN*v=GM>-uWLzHQ5Z>rey}M8@&?wHjwrQ#lZQ zgi0gZ68ceO)(D0BEYn#-C6NXko~c1o!}!IKs9&E*oS~5yp5`(R$|=cD1F?75FhRRi6M2}$-f@f+yn4DB@^moy$e^{iM=&vo zX0#p@ji1tXFVH9>FDmthiwT>gpGz#jRW-b`Cta%>QxO**S#rdV-W>)#ww>5t%qS`d zhO}{)M~E5|QDX3=BWo~QZ*Nu^FxR7fuF?P{nm#oxggLxN%E$dTshKN3vB8KDy#RB` zEqSY6Q~{zOd6!Bql91%qX+=;m1AL={iH(rkLlVlQR{uRV=?Fcqc!*QJLQWcxMYAU2 zW-LO2&d`{`-U?7WE)XKsoKb!i zxncEvy7J(~!$$|up9u&b>!|)y1lZ>rBcbd)ZPJi1IaB(#_pFe3 zFB~uQX5Bv3KlAt-6IRhRQGPC;&OEgiThtM7M((dIl&a^m&6K66O@VyG?1LQx8m`#= zKx<8a4ByWxz$Z3s0IGH@j594YEIOo&;(`*MrYw8ipE}daieGt-Tj*0yb4mOI6vgSgSsW-z-m1C0Xw!+mY=emv}Wz7 z5d)K1seCw)F$hxzWZPPiIv6AjU|4NN7WPPfrN3k7?!u2dxw+i*T3>?9&oiSYaFh_V zrk5LM=zmWLgYI6e6-aS5_0tNp*erHEo45fBy+4K4w}#;>8UpKT(fGuxgE9WOTB?dHfQu#;&nhUeKCVYN>^mokxT7viHMg zCQWjUB*+*dELK_Gh?T=7oVpwz^W#Gp5Xit4aBff)6UW-elO`yR(x*}4p>C9h6qh6P zqiA4NJp8Hlv-KCkg@-%izt{h&bGU~VqAgPTj3Ib{)mE>p44kR$P*S(1anqbhx@hgg z!A|9~^rvgLoYU>sA*0Vyv)knQU7^)XR*TB7(B~eO-?P~lelpTBYv^#=k!2iwacKpG z>&T~8R-q!?3cBbL9Q1`VK`MUa`<6E}Cy(n#m;)|J4w~5ldP;(t1;-NO8J)1V06Nx6z%YmLvB5uC*0lzofQA7fS5J9BcLKl8W<=85%@nGx6zQRv+ng#PB| z+c{=Io~+!e)S^kmF^iw3V=x+o!+RL000&|Sdz7?(Zt(6egBe3hb3IGdAY&=+(Pg{# z#O}5Al$R8k8kP+RaQR-n?ax`BgU_E3_hiGVw<+S2Q?0U&jZ^|o=zH;OJ(Eb$Ikq_* zn^KpTMhBYV!EL?V%t3>~|9W)zec%l~7uzICWyo3@7w)EaTIkDr^td75Vx`k#bv}_4 zi3T9+1BMYsGRUcnQc>=0uBRhp-F038Jc94A=Hplh4K1|`VbxJU5lJF_^{$<>BUSSa zXbL$T|DQm{%J4T*Gy@~czqIIo0Aw1{u73ep*N5t@$}N5heot%*Hs`hFe3#l4$(4UG z0wj%e1@e;6+mkjzo{&b1)X5TELvo}z|C~Y&&J-MKM4&nXcq&hUV{)I3bA^O==5&I@&2x&fHnO2$=M$E4P6k(|l zUnw64dHW)C%Yu=9@;$^BI;*~*fl&(Km5VMIf_*YP>zYZ4omDl7d31&&1H{efVBw)O zD3RM@3a(-BC_6R-^g?^}&*qHcHB13g?C1xl_C*AFNPoh#U!$USfQu~ba6EkX_>yo_ zS9V>2diw}L)M}SO!?Z&Xb(Y_1%(`EV5|)anw-VwXY!!>HY&ZUin*m5;aCRvKn?4Ri zF*o#P6tnf8&p$VbCl3sA4X{az{O%oUhoqM1r;zGCn|hs~DXu|54T9Rw@PgfuD8gLV zush3Z@>DV0&Bij;bW-{jS4Ge3o74`zzUs-9!6@4LruJNFPU=)0wbKo>RASQC^Y$qw z`hs9J6Pr&usZnVO61=(G~$1d6qnQwD>$h?aS{QwGIm zan9(R^DB{8+ntPLY4EP5J+oUS66ghxh7$XSPH66SlA7OGjgXs-;}g&lLdm8~8g#GS zI~ix5ZWv1P)HSdxiOujDL2aH;9pt_th>Vnb56 zK&n{@xcSc%8mPz7bw_A&G_HEJ>#raCQG7?1WhlNxc3{GnS?QoX*?MYAcR z-9izRgS+=pyY<20**sv9tz@orHtyN zbUYLT&3pH&_KfoZ7Swakr_#din@g!W{9mqpV%P zN?bA4SI`w0Etya$dB!~O8nBFFXkh}o$}sv_%T&HU2IJr**;F|)(QYixQKk@T7JKMhz!T*E2&(6T| z|5=3?SsB>>X{kJ|xeutrKujGb z;Ka^}lI@j;q2?BJX*h^l9-X8L9%`gB`{5#OdC~gscxEk210pTWc?J7srKMa?i;xc< z1v0MKjF5saGjo_nysWY?+>AvbB@|nUg5rxjq3O?QvBgQT>RnwyDjRZp2H(N(^v`Hw z)F;*qwa#9^f{~*+3E-yn+mT&=>M(-`8*{(VS8Y4K58u9s!2Xb*CCe9+3gr=cU#EnWk&FR$)HNSJY#U3kg z5IctA=-Jq@(r1J?3oC#f(pW~OrURQGwu)5I@!1FVrPbeKGcBWstMhVsy0G=UuY@Xc z_;@=y_F%`T=6<`V=lr~0ALoW1u%2w-$+Xr&qtbS>e}BJ*9<YBBw=ct0%x`hM)4 zCNP9nkzDxch)h-)0*73J7plNudDNsVnKtZy+#(o}7>4*Dj&AsB`L<=*IBw`-P_~D0 zcICjz1Yv6zD_b{7eH`??Y|Rd$9AKzaC$%raVk1QbGADX^&J3eLv|3pM2Vce*z@&xI zrc7KLg*C?6^v#XZ=M2t-fG^xE+|ByFS!zVVeYZSc;@%%Ge7xB9thQ`58&80g{R8P=2iNzdJ&?;M}qA*$(Z;4&p`$Vg+&k ztK--Gq0Dxsc6Uy42B%4OrV$8MAskuT^`q6x(Gr+(@cNz}qvuG$t^WnjEa@xP&@)#Y zomjk7&bkxGhz_gW<;_Ff#^HH-xe4pJ$!}XWtjyhqxILOP|2~D3s1kRNx?n-q*hw|I zG4QyY-F0qzlxb!6C83Y+b@CjXRY9#0N>P_O-0*i0EMdLdWW%&@gm?5!p(7k#>M}`V4wr5xU2nB<_;I{%A@^?y9 zhSqw2LtnHILcC(w0P1Ef`ExT-Qc>?EiSo-@IFKX--zu6Wf_i2hWpImuuPY_v!{9Q1 zZ?}#@wc#mi=&|pRim17Dh&6Zs0$^ooqYKTyrZ)@#DrA#AVrYp(lBr2^243^kDQex^ z8|_+Gz>@JZKF0zRK!OpH^F+G0M4aMKh?`j(YO%Yt#RCFxjPQC5a;5l4MND$PP1F zy(GWj!8v;WW|?q4tO58{4vvK?ok)X^#9S~3QUGlZ46rLuN3=1((9Z|a4gwIDDi4e# zG`7NeY50>iOOE>?7-o1_+OgMX1m?|BCzB2H{6yKOh@Kv11DM{I>rNRqw!gGs2LxN$ zW>XXd!04~D6mPAc4hS+CB6m1}R@MdnF!%N34{^hc((Y`qlrS)8ORbSTP>ZUI)AN>` zDoyV{Ph|_3u7?jwHN2H3UsHo#wNGdW9rhWt`B>du8khNF8dN+!3n5vkE3WoFvVbFx zCX@>jPsV>}j^K_tlqcdD{ruMhjG>Gl#sVP_^Pc%|DNa>T2iE=f|2BfJHDKLo4x8gv z1azSPw^2PyOfEUe@+b~NvgD3z43bi6m!w3NkhDqlNx>UlRKyWm{8%R2j z$@XxWSz?rizGJg=tu@u*ec5Zfl6HSfJx3+RYgIR(z;kLiGP1=jAHInWrjaY8G+)E% z`m(4c>g~5b9XZ~U^@afdd4bgUvn^mZF|cZI_Z(^*WKo(he1^im*Log|pjJFiQaaWCSy8_8aJsCgh zfFblKi~(HAO+V;TB>sopKwafu%Ybi+U?wuPRZi+@OF_9ymla_6S1|B9QLxgayB8#M>=PaL-s+zd-6IiTfWbE z!I{JrSWT_IH+HQi$@Zd>6{D^?3S*J$Et^oM7jgqhcum=`8_kWD(|@(IkZgm$Hsxj#w~x0F-k9q3pUBe!Nzs|p5n8SmWDCJL10*WYfK%r%81I- z&h*#X%Zon`g&UvEI*~U^Zuo1KfMC1fB>eZn1WF$VbeSAhm_t*L?7N?YJkB1oN%4}O zkZPv++y-YCSGAj!I%gU+I_TxefawOkM(S0DNEhz)C%sXRIz#T&dfZDjc$ccsF5G*M zu?qsa7}gfH?XV((8Uov(F2sA0G3cun#QS}XKYst{gK*N-_jot~X@|7!q%2&?2{gzb69cPcPTxBfSmf-+Y^eGrOg_D!k4xM&6SxxX!9r z&4uSD)Dw~1vz~;{mD`MR7Tn4`^Vz-1LZNP&*x)WR1Y7W)-E1%Zya1e?k{~1wZ%Ws!y*HLTAJ0;W8&zm(W7~GhgH=UPOc@xHg;SbXBsJwlR2$wUw zi70^)0(_?!>P^L+d3S-}{A-9i-S&BqC#$^@i;TbR=*w{Gi(QaE$y%1^+V7x0_!H}Q z84t*R@?qA$Tx|b)eCl7qDDz(;!$0M_OG%u6nI(~fU%sJYpAix-Ou2z9sL~LOD$(az zlEiGNizx_yaLHsO1UZr8+@w}`T57Uyve-l{kqg(zug{ekJJO(n0m|YN@(&@!g_HNh zMneKv$kp@NkE4XNAiUIHD@b}MAWYjRvvV1{)@dp?oh6f@ol`VYZ3o%hXSCE4!vM)+ zeiOxxUkxV>?$zg&CxHp$m))YB$NW`pK>C#$!MLeb%}a{_paq$06}PZ!w{CT-nPk$t z%1SHWu-+bggOMJmy{FiF$ptZt?!%+W8rec+hys*=KhchgI;rJ7>|R301C>T@9;4_R zYQf8I{_e}FhHf2K++a{=HozHqIiu8Vp%Uq@9egD%iw%!?w_*^^kJs?v5_<2@(NJ}# zos3%=w@gOS#50`@ptxEyvv<*P&t2hPQ3Q*6BJ2I83wo@44qISP@wCv6`O?L7@VwGR z>f5NW(n$%vTKur;ZZyZ(MAv|kP#o@Swb4W^#a>V{TfPZft{xm{{Q_5-)uRT#_fdac z(V|Blug{ZmW>*gEPBeN1+ZvF(`Mb~k@8!?`=-@2>GB5oDZ>)06G}Hh+LePzO1UG5u zh?P&qF=dm2EMa?isGcE3QkeDAo3%6|*EGFXClfZuuHD#ciD&ASg|eUAR1#SK7C&-; zeQ;it(I%xGjn-JW1hG$+Ic+p4Y9>06_Q{x-Z>Z(N~+@^VFnTQwJP}Wc~rrFq+K=MnT zu#EuvLNUPToWek;g;Su+kM#lxfmD3k=~%l{)cc}`S4s1=c=G0cL;(l==R4a7OCSz4 zz~i1-SP4?}ThV9pI!I?$-b&wYEVH14iOFQ8U>&X0&_^UWo~a^;2#%~?Y3IA8 z_}A+v)YKp5@^eZ$+3fTOChP5X@JZgO!SUTjo5&iwn~vPb37F6N%c&k0MRobN^eK6> z$xFA*0H^gC=~d_0qm+t6urjJ$@NAp`F&|1yHjw9p-k#YDQo1i~LLfB#T1!gVVnltY z?dF><3LmOVyr56%Sf-54Fva8{hx>1DnOdWHeS6 zpDgVQ_F~ttY*jsk6#^KEvjAgXTpBUAWoj>t5LRp@j|7l8@BhbF$XEcebT6ThkpSk} zZuQhwo)N5ZtUwGz;;wFg0^llXOkNyMBAmQ7eFx6oc zEd01X{1mDB`l9p5U=9&*w)eAXw@|keY9E9`W-(4|ub$BL?Qdfo&?;aix+}(OgCU^t z9qkT|bjfslPdPtpXKey$>K z_Ny*4N&L3yIzs&6N$3dqX523$anpkgme*NIY`8NfTJheiFN6W6bOpRA~(AB3^Tdgg)r6=ofYI>o%C67qeh^XgQX4`n)5Gqk&#?` zXuICmka)}EzB<^pbGcz_VKKtcX*fehr0zxJ_2U3B_>%|0jC_H>H)@OzAUotBClrrf zwmBufJLS_yjY2-`j_}HqCT@Lr@IaKntV(OAkrIpD-{*K_s93jrwNI#;*qJUgX{uf> zy}20IRz3voSSYqB-6li_Yt+{>;bv9MXXYUMj9ni`sf7@yL;2}`YY=y1Syg)a)M0Z@ zBm@9P`Wup9w>bPhbc21FLE8~2O*gJ2N*H1Gc5#f1<=X}m{72ims6F61DRh^{L138M!d4oC}NmY!5N|<`nG>zQ-FtT%m&pF9Dheqsr zdUTlaz&30t8GA*ndKIZj3)*|=XM7~s{o@Eg(m+ftSUCmZT8se*LOR|) zAjc`ciAk*%5BCt00}l7{$N(Yvti6H6*NocHm75j`lGr5zs)ve6FZ0zTC;&nW)gE%~ zAnUGoxw9tYnJ%j5S@@PwP(#|8d-1e3%loONrS_%4327u&edUx5<~|tDriOJ&sJjhvZueS2Prz7n^3SiEhG*eukBCYqdg>etKqQwRP`&6U69iyiW}$NT&(@ z@}eL0^lqXBT4K_5Py6+It8P$MmiJ|OEzw&_y+=-Wt5q^LX-q=Xqk{rbg3en3EL(_t z6>C+aQBKb^Dz)=ah{0vC=7XH(0O4WJw9#lPUjbMvu)^PLH)}ogSE22%bnd6m` z^e)mj_r!#6W-u3bK4Rdc$c}IVh!#y0YTJ#w25-bf6*OidDp_)zekS}3fQ@zjIr!0^;)=pCJx7q@e1=8kFOmjrw# zp0?z`6W~!1f&R#m*-PmiSr~t~y=VX;hZAwpnOGX6>J_kclVQuYF7tL!t@ELXaQ$1C z%4zeEb_n{S2=OrhiY$5eWhh&(vV?bcp+oQ@1BQP{fEIu~fiFo=b zpa_mFBvKW^!G16l_9Oey=f_>IG$kE3 z#t?fhRBs`cGa4U!tSsQMMrEum5*@6zx_IP>sR@Mr8O5u+-=5BL`ZLkFh}Am|1p@l= zN^^Bz9%0V*J^0ald-H~0bm{1Pyr`Z6Fb2{SA}42|i^E+E^vj5*+J=u@?ilie=v1TZ zlRq7MwIEZhZd@;bwJ?%D9mZr>ThAyqsCl)&fy-)w@I}(^rRBTcJbXP{C3}NYzny(M zK^RqY)I8YsD^V2viA1s#u-SnUw2*9+@!j1Mui?+E@j)IT2U~r;EQKCOpf91JZ{A(E zaZ)BoJ~%(6;7h5wX;l--jeanCji<4{0gh`@CUWjj4s4B?^_Ts2Q`D3QXU4=tN&7Qy z=%qmtNjz&^KMuYKK;zqFt{y9EE;SN7lqqu3q_6xkM7erV5HpVeFtv%Zf zljI6HKQS^tqjX7UazQ5R$(D3#<09tPDNf95StNx#4FaAi0b9IqyXfXVTVJST*8Ea84Pf-ka}PQNvage;KQl|<6!m{6tTy{YCduh9RxXY z?qJRSb^MCRFpjPy%pS!<%i3Vw$O1~&Ac>A4w00subt8bt8=`}5N|?}xd2^Sx5!r;o%J@VS`a{@wYwGLu(m4`c7xD_Xd5p;nk0+E-I zc{|j5Db!Mym2)&S9xC6^psld+F{c{$gVqdN9Mhh&Q;drp1E9juwXh#SITS_}$;*6+ zx01+vZ@m<{>j#EHz`|DcOlJD0QLRkv8x@LtTo`9*LHv8 z5$g^d)=FNzlH$i&cVe_#x!s_zULQgKk6_67RK5o(4MG!ELk)0SfJ=N~Hpgex$g$DL z@!!RO8Qkz8-Go7zgUMEQGCSp9HQ`g$;o3&L_Zew$X? zd*|3VjpS`Fr1>s_o<$qA7?5bCh$%xo65gv8F`lA;xEEjCUD6~H1n9bBW<_pJFM2UU=TEnmI`{i*Q3EY*71ou z3A0%zMDfN$RAWLZDs_l2%^)TRk*+1-xi6QYt4G!XK>wH#BinS$wDPu`jOVnT|D@+M z+!4UccCE|#L!Y}0?IAI=B~sq*iaWSucT?qS^*ikZ+|(XVA!xH-a`D0&#RWt4m8Gqz z!#lqrJRKnlO|r>RKSy_8BNM?EJmEyKpyQQy6oJa%O4b= zAPhzwZDVEhYQoT_V_c{Hp&4L?7&84wGFV};F4WtH4JxUwB>& zYz0u4YKD`JBgb;7KSwq_C0NjcxanmwOqN`lLd|Ue%FUW>K*Xpc6Xn?)N3E4OGeDzn z8{^Y2)>}Q+8fya)lKR*{*a^ITFL!8;wVX0k6<1h}_CyN_YhXIuKM=YO#}5k7O3?^N zD4cU0$$sp&=r*$n>!kk-R|2J~G5E1Fxy^=UE=O#yL3sK+G8IT+LRS;-9ADj;=;sYc zB*ueJU2zgJ(mvK6;DlU3M8ZlLu@9%HUlLJef04JcTS#$aZ{FxnHo|d+l}7H0Zl3MJ z<})O9roHaRs<&5fzw9fqto9@&dCjhA*db+hsju7EgA7=);^&mhG*0e>7}&iacP3^S0eNfF!9sKpn(7Lq?LaUl_)ov%AU+1CP#VS*MS0 z%=bSY%3_aN0+^v392L?^kV_+q6ziZu6ldbGV4gU>is2zuKg`IQz8SDl$NYGpXpDq< zI;bkeCxeU{10G_uf_%o@A}R2!lA__=X{{$Vu|F`e0qC-|kud6l$ z!!*P0rS<#NGoeo2z%Ox^-AMt@4!YX{{VU$Zok1@az*0|HV{D?YrxVgP+2X2(l5Ba@ofHbR&xVs{wo{~(#JkZ3&8BVOg$CK?kJg~>jT$9$hgkngtL zQjaoNbkE3j+-+p&?=eNn@Tfdbx!RE_)3tU%Zs$?%TZ|C2;5Wr%+ud4wu21m5v z%|e%HL@3c$0Q8N^P4O7!3+b63UoW>kd#F43^I$pW#-W9oc=x0V1zqHlE_G0Z-dpz&!jo(7!aHMV(JWTM$;_1Kqa~8imZ_vTPY={)hKk2(3YBf%pYb);P z+)2x8zuEfrv!uFJZk@W|0D8&ZcSVYqw?xQonfgM?XMl$~#k&ork54pad3JPfK-2bH z$^eaMfR~!WJKDNm@Cqy-jQ_#Ob1?kh)p;g%7N-BUI=}tDocyO61AE;B&g^Hx5+2E| z=VW=&O3E49DS$%!GzugY$g#*TA1}Nah;$@#`5&`g&nBqW$*4+z1QV5x7bH5LIlSC9Xb0O zG1?lO-=i#yn1iw1K>h>#C2T@P+cR+=FncI>}Ts))L9 z)$TtSyD_(1%pnTUMKT~)!XAeo?m=Dot)bG%8))pxbONgQ2x_sfk&&Z?Lp@%$_xI)H zl?>|>gzg(DSu>aHDSv|*u65_hnQULpbkeVQRHl8h9HUrB?~g#$d;#&R;xq2EO8ZqA zSdv0T_nG>d5y;p94JPz&&+sLeHu_mnk+JO;!v=5!ez&RB4qSPYv?}LB;;#Uqf1{2d zJH-Uw9Gtn|E-P+CQDt6a!|(zDE<@g}7QH|!mI$}$FsHkEZQWMd%%Skus#V9ixVYcB z-pSp#PV>ihZt!t_l20GfURB&9_eYi20fh}|&)n87F7)!@XYC=xxvZr&bjnWEuta`H z&cNPSbu62CM>qw+q)#6HeYxH8u8A$ZK-dm1+7cIbG|7qd`#3$kk!r8KxYoqD+|CX^ zxXwiRYyh-L7&sx3eN*&tJgOQNFXBC@kHSI$Cjgx_Jt)dHg@pi>5oxWwc~^GCl9W61?1Vu6H|9y@Ey}H zh*nQeLY7aPilp2?v>h$v@T-wc*)552^lD~nT{UBCh5tKUosOBnqR(FJ#AYfT3&hcB zd6_kXCk;XJJcf5n3DCFB+0HuC!=!jyvbtCo6~oBW+FTWjwn9Wm2kjrubn>2Zy`)8V-|sMRB%sJ^y_3Hc(=q5NXxah7A~5e*g+ zht^KK;;ZG_0;WP_G-3e+kz^bQwh6pF_ZF;2)oq26BAI?^I=#bdJ+|}Fh8lK4{qQ@ zxJaq6Nm$EBtAKnoG#WVxF`rIH52waG+-L4EF!VE-=&Borp61p7VEP0G@|h!$YHS3Z z4sO*q*ZRfH(jhTlac;r7QffVM%zPI_J8a4$dZl!e)%89N;lvwsqo>e}dv(coYkcjSDU(WTA(fNHaca ztf4YsS2*7bhnmY9ooMU4u0IO}p!**#NnbG`cBiuiw2?(l;}K4iE&xU_D4Om;jh1aK zb3V{56}egJhZ-6X5g-_c))|m96TKDJu$>;Bq;*`>?V@xOeJnuv46@*=>=WnO z#p}w$3qxXU4iw<6^b9P$dx`PpJD!eWZ^pv$;wQpE44+l7Te_Qaq%X9LG+|Cj zC}n`#4^<%rjc~?}x_1YffU;|RDgqu{Ovc{ODL{FZpsb`3=mVfwS(N=1r+AqLxDY}# zmj%g00Q{=pm5@ctX~|tQTpI9hC-Z@BXTJ!mq93~@e8!Pbt+~?%i1})OGvz>T=jUAT zzEk%=HFvW4)OhKCoU%;u!1*KxWHdNg&~psuJX<)5q({ZBs&QfGrVR_E zb^Ny8j|l5V=hkcQe01|Age;oK=^(4*hIGf?^l`~tR)DOM)oV!e>J8F$Tll$P{n!d} zhJ<7riR=+@)RP{R(JF3eF$|>`!NTOT#BHCUN*L~;!giw;QcE2BNeK3fFYgZUKU6<7 zE+5|;i=033xn8x(g;OQm5gGM)) z?Kfjs{VJC|&EdaBFL)iKKmRV0{qcjtpALp+yZL11y_9tvGLADrOm(1}UiSlKfQeOK zP!GGJv`G#>o%w*#p__LRBa)#@pxA^z_@?Xnej!^tXOee$>Bx51pp$yGlfH9UZxu77?6a+A6~6au zbN>}nHW;NxK301S!0D!yi)n*2e8~Tdk3OP0boClB%qFTNi8|G%hxe8Zi=rMQuXG6Y zG%*3N2513ZDEOPdd}sda5P~^3pxdAIO^tfHmUZ(k*ZbawtuBy z;)Z>2kNr81@sr>A16kYsyPY3I$kOhcq^7{kPjXq)5z*6Iaj_ z=TdkDU2!k z;^Uo0l*n-e(Wk~lQTX5TOZpkcC*X!FD$rS@VSzz0O3;9mz@nf~{r8iF?h^MMprBRhpwJ_Y>^%_GFa7|};zS0* zP^-(TfGKGo4q<<(O{FR6!_2U6RVxF=L}Duk2Uk5N*^_T z2B=WS=o#w!yWpe2Ydzh6!5CiZsEVAcz{AHQUJ(YW&g#b4A8}GrPe2k6F@nm>PmSj? z&3mqJ>TK*-_X+ZZ)c{yyU$>ZztDR#9&VCvz{G7M^VDHEjUHjwN3w3z-?AeGr(g@#c zQ~Dlfx9SIXm^8hdwY+>8TvhaV|9KyFe{MBEk^_G@xqQsl#TF6Wd6H;EHRiuj_!x;0 zWeKx(Xzz$L(#XKK+qDsVukm(*h2FDWMGX94t8F;xoDLV&)JC|VDNQGi+2pQ?EPBjk20?Ep zKK&2JQ@qDWNWEa0tat*GFbpgr8RLOu92-wmMn6pA%pr8~;B71d795gE$j3;JC6%-P z7mrw|O;m0xu+JWH3P)li8}|OIroA8sMAfNy)tc7esH>Oui)gZLeJEmy<-v_I7?;Be1 zCaiVQ;``y@ z+e*NZ>ekBVmknyK-mUSD9q+ad?RUzJoDYlVlk4H6=~0IHN+pk5sK`vlsoXhF^6Stjj-yZXe0)tpoo_Yg5#vr80EBgyteDe(oPwFF7ke}{? zUqh2u&bc>;^3oC|n^E0E&!mVF^O}|*!bz(_v|59&W-uyX=aI9@dbi`j*o5PEgqXlK zeP==}SRXq8+`wFt$86j$Ia0$P`joSNPo>+-m>=ryc9{Sd z1$+ETG<510T>e6+SNwX(Qd2p1<4Uz@L*XORv__bpgf5 zT7|skeaV#gWt|U@xvxzesH5pC-3%29pYqL!*Yg(f zVTZGNN-Tz?fV^Ks<%AM-Z1`2{y0KogB)^w(FZ<|R&{7T#^}c)ejPUChe`>zT4_BV& z9%%TK9cWytb#bp@4sV9Z1S=N17^qlnl^TBLi-|wam>@=GauU!(SE{ z`Mfv^k+~3-6S+^)UhSTwT~Gbrfs}*c|AgiL@9{t8|9;w2C8iT$}jdKDS%e|i?@|6L|yT!SBcE>nQvk zDc-}x^rgD>YtIsv`HXanTtth7^=r$QKM$@+w^;`adJun+_%s9H^F(opbxozP( z4|_)RXn0K_%p{3;*UB&%HB!zYsyVXQI)}gS^*>`f=yI)3ePcMF$ z_o9%H!aTL>#dDkwFa;6uspHWTvLXrhOte~;<;-P*pEcODf_LWzv!Wk`AXKM7Oaq=p z9lx@;lhE6W&13Or3TX|}Z^BDm^+!2@{!~9C#%mK-b+|yiJ)z3u$fO_Zt8AyStQ zZPv8D9=K})(Hc4rXw&Hq)ZI0+%9A?&3`un|@9@AS>cV zlUDcAnDccmEtAqy*h?D3q;kBpoDjeNDpBvBT|&K!qG&N#V)4ujiw9gyRncZE&8Y2y zuQRKv8LF%KFpCs~S1!_n@T z;ho*wwv6B@8bUPq!j*bWjW1z;3$|3$F`Ir{PyH~xNtez_`>d7DYu7NL20 zl#tC9erJ))1v108bo{S%EQnPM<;dlCe-HUTygHV#A{V-gB~5y@2K(74E?$nSKNF~mL*UiQIgns;!s zuL;V;B!ndpzIvm~U&;?Xp`i|(eN|$Ptg5Gs`BKnNlqmD#L-a2Iwo>ZU0N#Lut4%># zfuyY0N2_NLT34nCI@QAsQ|lqEFf@!hjPxPMXb&bP{S~{O;~y2Vu?O1rgX#_$;=3t_dqptfM(E9_xL0}AdIiz$d>qQFdEHMg_G$lyCZihr2 zee;+=ZbX|k?P3{QPw3)Q z7I4Lyf@406Viu5dvk5n<7u^kv0D&F})Bsy~rOam)?R^wfYR9?Diq%RPOhK*=Lu$oH z^%a7p!%dXb@AacD%_wQ$oQG2{-0J-B8b7VO*L*~aTmLlZ+i#LJ_GCb=moVIvGTh>9 zfkpnOtqc`8s;BZWGUu^9Zgy#IoUgd{_>aB>zOST9+^0IeVz5#^nTn-XT2t9n zw5HW0348R`n>y7Zgs3+-UfR^#;=GccDO-0_y-cpSI_dEyvvpoWRY;d_h~dQ<1>i@4 zgAu8S-xKG;sH{oSIISFQILDH++uOaWX5V(4~~9Won~^u_};tdW&%3g*&}+Xja0eNdBpy z6_Cr!gnTLz?6RwA2va)Jtz4WTG)(RPtxW%QX?84mR#gXxG@!p9k~nHg^4>5A)%sDP z=d-zLxZ8P{k7@nxb*rHwRUXp9@s~sPz@Z@p+MY< z1r;L^lngb%Ao|zzQZ~LU-q&z&UrSl;+2He1@@T*J^R143cTh`NG44dM%OW5Kfo&-l zQHHkrEInW*!y&WSeY_L^8F6Y~?movVpeC zJNh}`x%%}T0SZe2dsL}wq0VwW6Bg3CuGM?^?pX_NFZVeGYAryw)Y(EThA`xzpz-v#(&!^hbz9`14_ z*2}e>l+UWf#(Lj${Tf>?CZVMHkg`+_6Bq0jxQ@?}L{6GAm_F_8Los_@|q*aNNgbxqXCAYGa zjZEUhDJG#hJ)5ZRcgEZ*rQIng>tH))#;9Ovt&OyQ!+{it8%$QT7$!_Y6XKeL#;#6g z;FVQSC!n(yE*wsv^Dh|9N&P}qbjB;WufIV?K2PUrLG zAPt3Fr7cp1Zvj`sD-`OwL@+pzb-{EXn&+29|02libh#9TSqXchlJgn>VR8w34j%bu z>#u~p#Na=!*bX=;$5Rvr=GKaDrX$J~P>N!$rOyLVp%`Z7{ROqwg(i?`G_3pna2^55 zmNXosNWr-C(L%qM2d2+*CFUamDmU!F|Mf~;1k5C~F(qOVty(022C~9n$~E*mtv>Cc zG*)goR_2o5P(`1x(R#)}V$BQd2#Y}JgAlhrey8k9X`Z4zby5A7c${9(QO-z3M605= zHEa0b5%U4IK&)7dRg*riD0DvmK%itBk%V9r678b^aQ$uMGXSQFjtWC978l2e(=cr; z3C=GFHiv?j1J;vY;%nw@HT9oU#*GXM6=%_O z!l^R@8;_s629n@GT!`;^LMANbsJqg^%*pZB%+%gnDg7*@@h))^Cv{eI%R-n1ps)%u zFzgL5?iR4e-UY7OC_fD|w9JVnBrHjTR0v+6!}^dG9$YbJCIJ#TY@;V#$ej5|Toh#L z3kjoY?X&hEK$=?u0Q8j5X*~dAhpfUjNv<3a|JF{)vQC4@>8f?~pqa1Ja9=DCzKcT1 z-dp!!wY>Vv;!T?8#@PwdL$CUd)U%zAe7AgB%apHHG*8X=S$l`tc$f0ngQ7#ban#U0 zYv^?sG6Lcany7>44Cbpt$n3+`Ulau#;N_<+s_Y6&4 z1cQ05_On{E<(YC{n%XbtqQFjZ4}N08({3i;GL4)Q`Kx!j)^0|JLPeqe+cZ+|5o5)d z<|7p{C|;>Cynj`^hj2JM^4u04lzO9-)NR!au6tklve9d~P|AjaJeK}uVmV~)YD9gR zOteq;GgZ5UzjO)r#js6=Amqf+%T5pHb2S(|AenU)83pHqF)UHzuWCQWbIz%GPnA4h z`#KJVogWF6JP$c>XO797Kjq^FwiM^Y>v?)FtTxa65Ls=i|99L;FFRF8aUt|QYr~1< z6@QA3o4Yv-OCCOZQseJQqaxb4WchDC=;oE{R|Tic?i+tZlk-zQQwEJg3P!?P?fUFb z&u_8q0dsi(ZT{5 j|hvRXawsl1u9ZD$jBCK_YynPHuUeE| zg`z(RsC+{)I`NIjXsML-+~xMibT5DL58Zz-2rU0;5?AudMz5=Gf_Km?6b>chPlkam)4gorQld!J=M|pOeK!laC`xQvF-TFBso5e=>KK5W;MlY2l(sSDB83 z5!Jo5e0tiKz2DkVhZF@)pTqDUg;Ua^iUAVPtvvO4RL;QicHdv4JoWd@45ozN#DG zUJlE=?&2BF2N?ahioLBAdd_6Z!w>u30%cc_#ocaRv`753 zdL^XQ8ZePnXa5?H*W**H8tCa?%!5FlrXilW3e@qpOY^tOj^f1DdZD{rGe|^j11Zvg z4{3p62nB?ZjafFhoH)bf<+WbosL>|%SapSz1`$cOu*RxNB2~&*B@Ab)6Dhk{syBi7 z8|WvyoPhuW)@Ua28|ktbRBfuiAYD_60(4mK4(}5Lx}5hI_ljHwO3e>5DexzY&*#jg zxf@iS{5CW66RZufbsurGQAnkRmzeC)_SRfDRatvdR8-~8*C#R+HoxheWXQqEdFjd_ zW%8vA@9zdgILV?;jGzgJOU-%eLeWO-#fFh(+*)XPA~HYp5d08m{+#TdN!B0!qf)er|(I8DXc`crJZzQpr?Ja2TnKL;H%d&qq) zj&AAowza+{--pQ4OtY6(Z^n2v^1e~4Q;oGE8ijtz)N?YRT5{LWOnC1$wnW#nrGmCa z)W4J(^=;_MTK(C?Cb4tM=)!L8VQV0_(@O(1yxBpFtCTviBR_`|K+1pN*>6K64)Z?M zHk}sXukLdmm9POuox~mP*MAgXb zKiSpBm%2>gec}gxa2HOe{)A#;&BkB*ODUFDfn+@V&J~@}1Mj>f5A$Ah% zs?pF+INs)L`y_Uzd>>fHfnPTB1wFGEigA%6;V9G^7QM2K6bMAVT6x=DUx(+-j)0#v zN#W2;>R++!s?@}f2N8vW(C0;;e1q*E%|S8IU?pNtU)&NGik6uh3{mO)vBCR5oDd^0 zI)G6>AbWm!f7=73h)H~6fn#sL4nYv*E`Tx7hX$}~a(ibbTYXFHE3ZsRj+X>X!LQJx z6upsxKN+io8%Fpe8A07wq{1;i(QV;HI&2H6SsV-8j~lc>UW(vMY zJ)dWl1m}94x#4SWP2OME*Bg5LVqJTQXjW^7*E;!3b8@syZlV~SEt`LtQ7=zTZ|>uv zBWd)+(L=A>ufJby5pn8x#qi~KP1`H1ZCqGdExEPI%QVcsw8RzmPZ1_#$Av0Vi#Fqk z%FFHHKJ{0I$@{(b5&7=yen0=B54+V}5W_+8!7{wkoJacQEyy6o$qdZ- z?OLS^egHLL&Z)X0_8kM>9!Jg)*Zkg(! z0N%2)tgm`)hoobDw^99;yZm)Dw_C7iNtu=%yRS(dPXVx`MjN-wqwppXeU5{hy4??j z*)Zi%Nd&s5GfA8#b1|~XloPhkr+5}<=aFO3Bya7!ucOHCM3X$qB(J_qKNk+$2O|r- zoE-c|p9Pw|imgm@k+*7SV6tVB3z~wZBKgt-8P>Z|sZcM;tmF!Wqha9?SeBuZhCbid z3k3y|Y1kWx!Gcx>i6UjKO!=ZXGh;a?-!t@IO!FfRfh6QFNcyOUI1n@{# z!hB5#h~maYPe^xP9nIYBBHkgSyP}R!pG+-n=+p*1;5ncm_Orz86QHUJ>?EENu@n(0 z^h3c=BO-#cu^kW}Z!mp=*G|(kV`KH5JK2RNsQk62v0Y*Dc>(%krB&u+o!p~Tdn&0h z)r9a;HA|4!`07j*pWma-pYq3P<9+vlFbG)?_2xwd8}DU{;ts?!=3*8`Cw=!#Yj~*) zXmZ*>2|MtB5=f4_h^i)r7UblJc5J^e3Mu7WU+ z5k`S#wC9Q>mT(agDyqeooSs>Gj-91j9ZSb&fuBny^gv zzg@wG6HV+xuupIO?vNhX(~N1Qn9n`%BoJ%F-}+bg{RwjilI`dLs_dS7D5AFpZ7niD=A z`;#gJdv1roa=~=Zut%ZTprKhjDB-~cF|$<4k9c8 zIJIv)Cf}V1CFkiQuP6a_tW3u!KM(OrgChYLJHVTj^(7Xd84ir3X)-H{MLc5lda-!;J!xPXZoS9G~~$XMCZUnQU-Uz z^mn6G&I-@M@EAoC-E`g7%)cjG3#VY^c^@6PhuEgn?1^tVj7WPz!Ig=C-Wnz=G#`yx zknp0Qli8meaww_Hu2Ao@38++>jc{E#4w4 zF@XnBdS{n83pvNA$m|>Z-urp`AJGi+o6S#|OW}Sdz{Z;C$(P%_#d?26zOdlaVIEYs zkYZ>60uFBi%dj_FmjL*pQ`vaPK13foTAfgx0d(M#_L$=QjN{`i>#aW4ku_`xt^kdcKH$W(U6^-!?a>|?wj;^j+ zIiO3P^O05{jcpkXE)AFx6`IY@xNhmv)cIz%I4(vRs--X0SV^*3{84scS-X)rNMn-v zdyoa`a%Go<0lEe2!CxF8FYg<<^L8mOQl*{*P1MHaicZ5rX}iOnKsp(rs-HJj{^C^{ z+Ft$nK@d{^I8xJInB?j+-1t#{*KWmAc&fC9@u>noD)XR*NStIhb$~icNy2hU2XZs} z=sG_*7xv33${J`rZjb(A{=7gll{+POK2U?pWxsMi+ysnhMWPKZy=ulpC;d$O8bvf3 zd@T%jcY<;5%{v*7SP!m6$8VQ5(-3MxNaSGl(=+C#lm#Q~~TmtP5mc=PROZk7H`~7e)y5U@|G@}y{0Hs~BLmZaT^=7+ z<4*dQ{odTF)fJh_a&+MzN*K+KC!xq9szfN=kz^0oi)<7f)sy@2b%MMpQb<~6i-GhH z8{S|0?h3KIC(j*y1INs^UWS#X=tCL}Q4S|PTNSd*%aVk04Ma<=Y#!A%@pXGwOf04i zD>9{}LZ|l7{pkL_G$}f^DO(Y>0gp}>>abvXq=`(<5M?|DM zl!DeyU$XtCu9~0<`{qE6SRMr1@S-Yt1%zDF?D#WRFI27Z4Tu9lRr}@Hplua(a=;5X zWTm?JPW962AB_^q1P?S3kGP)x@SsA&6em@WKP9A-D3)!;ErCoe9?pQ@31yZp5J4_~ zm>sEpvp08Ei5(hKrVz%GO7WB|^-uZDvWuqe~Y0_gS^ZhV}h z2pmf>=K)HBSmVq5K*B{`?HPDY0!&3PQ_D6nz5lJB6y4{N^lq$FcXJX;*u-70DL)k zYEXc?g!aZ~hc;DIn(}H|V$K(8eVDO002|wb91FnUbke`~ON@Z)F*%p-lfWzlI<=WL z*YSu_ISm7+(2`Vm2$N;Sj)P@Pp=Oydsm0UsY5lnYBYMmVw+0hA(F7+l+H2;QRS8E4 z&g3@tE}z3uUh5``=_?R7a%YrH&5iuJq>TM!3$j}z?GGj-NHt?+G=%r6o!dsfyux4MNqYYib?}m zWv)f_STp~E!p29K4;WfyQycV>OBKq!EKFSo5yli|er`rAuzttG{{VmydwC2rFA*C0 zHMWP+j{_I0`%a}4`R?DTryYE6hpIuXbd__bmi3T~U2LEAmdOVqX|w(3?YL>a-Qe=q zYNToCKQLCw)q15Fli}B6-Q9Cy7`Nv^8Yt7`Gk{AxmDh@y9x&18sVt2TK}y z(c}IzD-^;5Az2hCn_otHA3O3icINSYN8kP6r1~Gkg!4a%3Cn-aey>*h-(xOi?3iWh z_cA64!kHz4k@*zzz`RYoWi3~z`Wny@Gi1L#_^ip+oX&}$FGP_`Q={`;?(xm{if zVb7<}QF*>9WQdU(W*!YYq#F!MV?*JAl$VLmZ13DYPI`PWDyA%>zefC9ZCdR!r& zOv5T0H#5Hu{l*y?>bj%y9y4vZ622r=)b_PyDRhbymsV~LWjZIr2OZG7;=U5u5-~B1 z5+kTe0Gi=tscj6CFrRe`9-f4|V|7DpsT#b@0&CJ1Yvc4}*OdY8Pl10dR8iD2H48l% zhpK)%^zv_HM`h&E;oNjKhv@b>tuLoqYcnW9*`WSrEPg>!ydDb#CM=PC+oeEewG8s& zwvJL^Z@@tN;OS)YRSB>+S*LIk9-NE^2PI9XE;%sA^mN~TmAm~79}6*}YfV#4()9S2 zq_xwOVW8|SkQ;x{*3P_!a@|^VK{E6jesc~W9m7-CEQ-}x!l5$bT$PItggLm~Y}RQ+ zvDl3#bU?&t&Z@K^z(K|)}+EY1>@e)?nzbESo=PYR8zXNbi z7UWeqUNGFa_eg&qWOCfNSDE!tY1Yrqe*fIKcbWCUI2%Y0+!HMPw+3Rm3Z~}cgJG++ zw3}X=NG=P>11Qc@2@fvsylS*%Hzlj!ny)q+!wai;;iu_-1{0&zrTumSjB;B|q<^uY z@@(>i#S}}A5O+a#mkqTd@0iTT?<%Zf3#{vpoC@M&0oC`--`;$p^#YU_JY&S2Yl}8X zTa(r1+(*VCl;_0!v&)nI-*`X2tBZoj5}w0!w#Jnn_Vsrh0K=R|j4}iYc;tH>82A!J zr)Fe;13YQ5etXtmvUJU%Vb)MP*Ia`543LGN5KuX!)Z-Pp>H8gaQEhpp;AWmD+HPJ? z;g;<+JOeN5u#dLV*EuPV2jc4G(y$t#9qU2gEA~GVk-FY7rR?;o$}%B+$;_>JCS_Zq zh8hM=vaF$T^&>Q5`Jz-hY$D+(3EJ}81wGi$8)CqZh-{hp3>AdZ1Fg$RKC^Be46RtXe+Cvh)`2B4f4 zGY$A9d-y_8Cw$aIm*>M{ku*qW2C?X-hRl5qs0j8Wu2tr_HSjzK(y>!f!c^$cJL7A* zHC4@)DCn5ZJx!8F0L5dUk8+{$@|^j)YHttWQ8B5o#T=ZFjCr(>LHXrvssK&qQb)&7 z*`%LahilAXfCteQ4m(+I!>WE(m+PLNs8){kBZFUaaf$HF+5P-O+*|VDS?KE{0ThO) zm+Cue-6K`063OLb$eE>wu(iYCn@&$Rqma-jg8TtM4}H|lP+@^xO76&vDsCITd{CA! z{kV4Vtkendo$gEW%{9Y7Jm_E97Hh@jJv(Lx-p9va5z0lwv}ZZv4G&%T$KsOb`t`z2 zkDuN_c3-GT43pcRDK;s+kJ=~H;d)?cR+MJChD~$Jx>M68QJfScY#Cxst+Jaxf)j)FrJijRn za6plmR^G=44#ybQ3@gr64bH51Ex>Yrql$<8noTLm?Y1M)7-vl!nXW4iu` zxkxAx3uCc?21c!jD1%EXvH%>bl2^Pk9W62u3S_kXHIxCi@vK@2l`?0Vb^3llGCCpb z4l+{1s;s*R`wS-if?I@t;bc{Ibc>)SYV>z*#lb=PrG2$QWNNc=ew>$SjGZHFBNBK0 zi2kmtPpg~yt`2hE!EPSV?Tve=gNPAA^B@@F=N*fLPO~AZg~>J6HMMnAQfgHLnf%4Ew_x_qVzuztdVQC@ zfF0QI(c``Gb(~V{0+$V-7~oR;+(CWpfMA*Pd^v`t%;2kXazTS_`Cbs5nglnecw>SIP@|XE5cGM;Zsv>RcCTQo2zlQ zLqpWA(cOq%z_SAd6g^f8hvIJ4dY7IeGcR2Kv25IfeRK2DU94orZrmdby+7sNuWVc`9el@;b#YW!L@TRcB!h=Qhk@gHRptG(* zN4ITw*y09-XnFr$Pz7apWRLb53c%O79#T1Gi=DFK{}{C&6KJOtOt@pu9*NE#fjeO; z1|OExu7kQHt`4Ij#RtZ$-!7Tf7SMm7)^1hD?6F_&Rv?6-q=*i=ruo;4M-M0Ty9BOj znVrfuxzk!Qn`YCXV-XExK}Ula&Qn81u$njfgHADofXQW^sU`+<*LiE?y%@d5-(Q>G zm$&zaw)c}=K;h+6c?H$nBDVLtYwr;`1;@@t&<(nrV6C)at5_ClS+xc)=jZg-$5v2^ zTS4$mgKs8K(LS28Y}cQGG5xyc@Fp zkqDF3?n&7X!y}K0QbZM{{>SFI3O>|F)|b%_S6?BSdxVstxl}yk02s-OX>r5eajrCy z5JjzL9K#`Alnv#Lb!phy&c7`}59cyOeA>_E=<+wnUu>pkUtEZ~j zUO}UO&`d7g5jRGWG#CJuLt%wi7@>)Du|#nqSQ-O1Azr1N!H&1u`|ns`^7Z_{wGJgk zu-JiQj9W=UQH`-|Y?m0#qJZ6p!b|KOnqN`{?r?IkCprtZQ3&hjn`uHv)_c<<_uUvY z@)hwK5X>F7M7Jn(8rFa0*&-#7kv6S>-D;$m!Bj<>ilj@~ zYu)I_`0h$o`Fj01J>W}8%yY@pLV0SSB7;nIiL0Q3^r+(!=y{B`BgnhL*@r-7)l#$l zlSc33GP#MY4uhBA2MBz0LGgd?!tDQ#UHJc|tg$k({I|)sD~n2F2{D*C0Ut13)XttoRq3oY*? zF*~nax?IGN(xp(z8yWWm?Q|5^s;e(IQc|O@m9*Eq$9yGNc59i})aTkRb61zQ2R5a? zq;AwsC@)-_)wgMUAAHK%@|Pn?(@MyRtHs(pd)A1)|! z&2?XmGhw$@l@l>d`E>AWL?$z*jA>D;@QF|e3bp^mef4QmnD0Z}m4jqa?h_)&88049 zAGg-};>5RhRI7R*nQ0Y5+~-?eRa_smLFCjL-D{H{XdH&amdDK0zVzI0kFXZK>fZR* zvSC-Gy^ylFk)*v;L)WYy*6eTn_S8(%aeJOYYz$=r#frX2g8``qc8Z+g-E&j za!14CZ3?`yq~9*9+(2%v;l}J2fO2~D=ie#acITP-)@?r81>AvWVB0$f=4{35xB$o-x|oxoU|pN|e2 zAytd!p~TTz&uF|&m{U4nu$?-iCSNb1Rb)><)q|u42pd)r*nkVDVqYcXQlg zRW!g^z)_xF^?gvaiXMEIl`K)Vnhu|mFvuw44_TN#2;!n+D?*BCmo?{zx_a9=!RcjG z455d&Z2LS;bOL&~B{O03C>L=vAu0IF+3wG5#HekGk;!sVe}p%MgQo(KizEW`d>n;R z`r+iy$Pu4*Nc(?e4*?O=9dM_hxXWIxBOuh^TiclWbd3Bw8sGZ;Q~_j48U)noD|2H= zKo7K}YlT(`^~4kGA#Lb3Spkv1v?>gMNF~B9Z8y5ttNH1@A>B!XRAE+aKnzeecQ@tK ziSsc&#0BA-4Zu+@NTL&?iJM~>ZvKWdi3Pm}LXMnnI+S3C*<}oyx&cPR6+b5-P zL*ddyAb~>>zZ;$!e4EYyH#d4w0q|hP6reTL&|Ch&iNyK$2=V&{#PE;TKN;T_Cavna3D3NpD~$BR=*Uq?)c$ zd?06|i{!45Rp}y`m5C2pDf+iDvb2vO9iPVz5@2t1mLC2A=x@&piNs*iyhBUE?go6n zKUSfZDW=<4RFG@bmI2a0#Lw>sbLGg)7}qHlCd)s=BTYncRxEa(1=*Kdg7_vCtyRR_ zkLmirv`8^#Zc-#|X@u7LCAB5@2P&``=%m0w;hpU?dtxU(EBKx7Sk7c@ATo$iJrQvE zPoYi*co7QhEAix{i;4!G>&05}{=sQW{p?FQp#eTGP{2JigwH*oMIftmSO7{oa{vn* zuOJNOKKOK@^p7*egB5%!y|c5(!X^hga@Pq#$xLVwG6D-1a<`}ORYnHU+~r=sICCJP zFw^O#{xFgtdQ{~soc)N2zHyYnENrTGYiD6|Y?jT0GrI2Wa7ueVfrq!Wlv z#L~)_wCmxSqroo2SEVT#`NOABRd>(NFyvVL1!5k_=5FL~X?+-|I|zcv^tB*%Hxm0+ zia%IRasT@xi3rFgx`mAEc5Mo&bifL19+$p8ZZ>R5F{x!AYn+=$buV{f%jT=B75?(l z@Er*TE(@Oj$N4-?j)}t+tNU?a)-{eRZL;AIRlM9N|Q6C@GpFnuVN4~p5Nd7gU<3hl;rb=@eW`SS;zF;2gXB-0Ij<8DFi z{({LvJu!B@Yy{LB;Pb9FV4ti&8m;LtH_6xWfie7&MD3OuRbR=Tp-LNMl@pQVEP@9L zBDY>iI2X8qJSTI1*`IBIZ`R*nALXo#7uqVux{8nZAGRL6@7B5KC(MzX2M_>?&#y(C9byKYjR0! zVRfJ{e6h_w)!fkBZ3WE{c-wx4O88&-EDXcdE|CKIb!27ZDvIfPIeP^!VVA(zkNBdC ztf2K%wY=ux_q9{~rJ6DLJ?V-7PjM^i)UEzu^ROf5(cFXn&emX=^cG_@=xhF@X#1IBTA1<8m&yo znSUmc2(*sgRIhX@Y2mA0^hI;l_Tk?7dRS#Xnd2o44y2S8-~nE*)C7Ejhr1S+AuNzsu5xB9WD@!0*$A zJ}F7*7PzZ{oE61K!zN+^pH=JNC?uQThAnM$>Y}M|r5|TN%jSS2XnfhJbo zw=(;!CEUi>erx~jKv@c@4;EYZ2MT5{IVhcxnKfz%N|H86@#Ke4U`&8P^Wpn*sRt13 zZ8P^j9DDzxFy#MEHvJa{iD0D(n+^J30V&n$A5bMro~FZmK!qZ>*#;YHI0<2108vVm zV!rQg$*}}!!CE@PRP5{NYZ&6y7|7>NB-M)-hon?@9$2h6Jl7oPKR16LqEwWupW$knq>cnnYkZ^b+i1_2HD9RY~lZR3#h%r{My zmKG_Bd6(|k7|vhF!e@zTf32|I^@cAjy?yR?jD?OV4DW*0q>&uor? z$M8}&<)P%UAS?K2I|YCd+~y!&dK0k0#x1+1417?7zb44l_MF?G;Mil2@c zoM7*yIH=jF$U-DbjCF#ECL9GL=v8q?kCWx$9i8(oIndnxhlRuRA6Rw_Y`zH?ew zjQ-Kd_v_swNvK60sjEZm^C`A6a%YDT5iz7Ffvvqgyp>O2K@1@}O=)h4@*Sh6O|qq< zN`t!muujdZ`yF~)hcOz(#AfKDeKTq4nf4!Rle2jWo2i#-iC(fsV;~zsI zQDc#GF;=@BI$9cPfiC1n+6yy_VUA2oAQxA1>S}v^We-=mg$Wo5S%&X$KsFa55462F z9T?)JCH}x-DJT+ByJhDd!d=YCF^;EkJwl?rekR?rdDvh6dQG}5s@m+&{Mg6(v=)G{ zG4x&7#pH`c0BWxje@&5c=v8}fy+z~mLo)B>@{{q$#P=5uXw5U_UkO735oe6XE}?Pg z=x_ozK}NK#teUR45m~5mX>oA{1hvkQp$JK38xPKRh;FQWICLT1Q z4{S`2vhin@|3KLl7b6tRYRS*?fz*IH@{5bXw^CBQtITsHU~SBh>=Z3SLkq;bp+prjZVL1`tWpi(0NgAQES;A{dB zShJ)Vrm3<59p#*u;otns_{EB6Agd#;Z~aQYh7K8Yp&@u!y|~l->3+oJOAr{T3tswM z0Y&3`@kv{usSI8@=zfCP{(LsE3OJ2dXL=%rr2Cq5v{pRj?g@cW{x1+|ez#chPG}Pl zX2@v{R6uYnC=m&a4)%hy+!eVjawwW~X_q7&kbDF(Ev!G%sztkS<5(tQTufexwB#{( z%WDI+O@$7suIlQ>nToG^4-usS#8RNBNo8GRJ4I6^Fib>!jDi#J(ZquA($Yf_4JG6; zOagT6D{pk#yw$i`u9uJUlIpwaWNBJ6G+TeUFFRSg| zs1}9+AF9@m(nmJOLoecXdFKHiF~C2sT3?q5ubmmn{%A)@dbF>S{hOM<$S!s?2`2bC z{yxGA%UZ+XiPZKEsPr25Zr$N9n&7ZJoe`@GY$h5)#MYj}<^QWg1E#~eHN~s1m z*Mk^h63LDhOTl}}>iK36HKADS*CRk?fMQNEUD+2+J?b-gdWSmbI9`HY=jptr7+5H{V5SljvkLBNIQpyhiFs2_on({u)CT3cSjtU+v?L zm{S_JyO8DBdm-Qqqd%SF(|aq@2V1L5>c)EuuvFjy7$s2`^}*8`_?~>0 zh}vhZFIc%c@K#EuPH0syNQc#+v^LC+_h!oCpU5z~h(^|R|1)$+sB?03J1IQTVtk$G zXmHjhYm5FUtPCkqNRfYx{}ujgRbjXY8fqA8Tx{X!iTvS6;cKMK^QxH|-brKnFUTx# zlHYO{Tz+!6@YRw&8Ik1m_4NZwM2Ox?fN+xP{&LA?I+(vhABN1j%Iz59uVWY7`Uz=~ zX>R+*u{ZfB#o{*QN=(FBi>D_svy0S5_bb!r z0_Z18l#(=l8A9NB<0Z8xDk%m1$=$(StK@}0jdMFgO|7pW-IRU67ks&=h2fTc4+Fs+ zC@Bb2(v$4Oxr4W@?CAO_q|B*a0*^kQtanM3M2q>48=n*hAer8X&Z4^w+cfkc`&k-H zTr{E6s_bQY?c0t*uKV&0u{hKlnJh<{O(c>KYU_}boCE^mRJqW+Cdm5_c#K)i=YN>A z%q;&ChrvkC{9jMnCJpi5$_>izr2Vbj2thm_%?5HtbBlYLkzG5HPVlFYXI2ZfYs|my zy!Zo91OSPTsnDX)1jO3D-FAWYj|m1OZcuH$eZF0vU%{qA{-40u#13OZ*n})Hs6RqU z;@4X}5$s#>ab_jl*;C!=zOA}Sk+WaQ6mnSR+jm${Q|_#Zr( zH!3sNcy@jrtJBNr590bO*DJ^s3m;>PJT3ODTP4o_`=~RyMAR%N_Ec-SX_Nh)~7d_;q>NjMn5K* z+ByC+x7P{=LQ;V~Ld+!>0T7yL zh_R8862$`J6(EX&+;Iq&>Rb6jMjz}^_(?!V7?~i(W#YgECBykN;^Q<=+3UE88niU) zLGCq=Xek+|Qk|2~a^NE~Tpo;x+44vZsNIG7YoSwfhrRdg%{Bnk4+{>)(IQC zf>+@k9zNZ>$4_vd^8<|!^iW;t^G5;xh{Jd$_ORe^s`mrLVm$~j4P#Rg?+b*+9HrLe z_(WU4s;8$F4jyE6Z0&IF|4Z~e#L?i}W9?4!X%gSdAdkHk z$$vm_me7oCpx7?sd%y4I2Lj`)ZfLfM&KGy?(9U}KBC7?nLMq2y&;X|PH|~>DBO71B z{6sh(2AGHN32Ggf$wF*oAwO<>A=(mmpM35e20KJE2RaI6C43eI5@5r!*^5Y0p17}O z;*i`Vuj*{MXaAEMcOABh*qAU#BnYk~0qnfX#8V!-f?k?#3?qMd(Cjq+k%A*uq#}Mv zHnNiEuiDdEa~PPit~6A36)8VmF&*-y$f{ebFR>`kAY>?x*ab*`TQri4+|8o` zUWZqSdst*&RBYW}CDjP<5Z87ZP#mDvV?qeCAYlZAJsWTFYae}Bd&(t;JT-kWHJP#0 zCXau@1Ep?-rX9(SgHeeYpi6hxFs$678gUPQFA&)BV#O07cEyEtRvuXE$t!DpL#js; zX@YQB7y(CBl9~OML~<~VF#ZwEkl6)BJbLt4KFtVX^aJ2Reh9E3_89r(q;0Il|533Q zG8mxzB`HTk|07#0s&0XU&-iTU%R6hgVI07WJD>JD?1dS<50<0L0X*ukZq`_~Xl ztyFF{D?y${B(PpB`IIY|Ztvy|zy&4wGcpto)M#`WCC#9bh*%_DdJ{2{5i|1cEx!s` zkxh>qyd_N1| zyk8{rz@77Kq)C-&gki`n4(2C`MVRiLD;!~3P}v6aFU0R(WzLm9wEa>8dJ{D(Ze^u% zV<-3sHp=I=;se(9^CfYBp2cff3CnxWqT+QPK+&6#6UMUX9f98yvH1wHV`EwPV#iey!UsROlkc?Ohp)j z+`9{-KM`Ne0?n+WvwZeJpJ`f>W()ShK#%j44Z12dJbH(Y`(MgXAxpA#kOEen0!fym z>$-I+w#Gt_Uo6Fkfjpini)iLiBJXh4+vXNW-Qy;__yk_@D@nelK(NnNg2rfZ>zGaj(n1TrkCNn>5Ek zS~&ttzq)c`7~YzkowxD!;8PD;58ht$#YJm=V@H7&K@puwvwT;~fTus^(a0t0Opv1g zia-qqX>3?SdrfBdIRd0f0?{)QpuRL)qu5nwK4&dX?G9!(Ar$f`mm4#uF3deYueY;o zAL?Cu9aIaM{i6~*!mWj|C*3R~CG!{fc)3hw{$&|~M$_aw9p8~d?FsNItXb$66OnT_ zl%I94IO}KBf65pz*e9M#SbRFRmn?-F%z8?e`RsBXnRnV&r!PjqjiC|NC-WaZTH~_R7T*$O_rzsxwEDH1)si>nDZab6Tg1Y|KW&bU}gBP@tRxzf4r6o zrdop+j4rvyDV2C6wu2ges1^Kn)w0WOGFo$s@V9qp0d+Vt$@vbIUAHf!#jw9w;o9Z94=Jj=$|On)NMpM8&eS$~PgQDcr~|7m1PwIz z&%-${&gD4so>agF>J)`Y zqXp~Y|Ke_`cWy1kzFMjzbqthP!7jaguU$txw3n4}S^R32og z&aHv`snMn%2nY1X^8;8n_jv&OvVxh=V=xWMn6TQy!7ii@nA-IzLi7) z7D+$rlhA3yTnS)BMhvSdvhOW?oj3pFg=M`feiqado}5ml-ENJ%~y zNv$z)R2KiBAV8l$3?k^iV8JZe(T)b`X@Io08{E14c( zgDDqDE0b5o(~laWIwMWtia2iE5&%!u2>4}c*6UrGsmc~3zYJPU>dO$ru8~o=^b#F0 zvv)Y2+6nBBte|)v!&)iI#Ogf*wE2nOxrEz zwVO(r7RgfhRi?utIP6hrgfK=RgF6=vsk-XE8^H$0gr%>elSSnaiREE137dI<>v73gQE2!Iz6VTDTs>;*}L0W&RP-Bi+5@Ue#f!eL3d@UW8K z>kF&YyPX`$o`ruj(kV9SaM+eQlQiEgFik+B^Ok%L953BH%6aB?B0Q!ast3`<^Od-H z*fCp_#%BNY!>2CJ!HC-#t#9{iD#fSAOH6}~2$0grC#%u~!%P>d%>zL_&66Dh*vwmg zdnpN8JGq;=@6=?jIxLMWgO)==bz2D>8(3znV&Q4lcv;=Ci|uv!GAU$4O^|tu{Eb0< zU(D_ekPJ>_lOTv;C^=?h<>jJQG~~pX9Inah9O4=d_&ojQ-WCUVa7DUy!FMM^bcM6M ztE$U}D@|nhOQh(?xe{HpXF+b>iuI4Z#CG>Y9LuK@ytlf!Fk#qkRM`-Uqx2rQVyEQt z7oQW|Ut3+r|2KwEUokoYQF_f79ju^jtfGbydqIY{GR}~iv?NNL8pG%sJufxPu<&mS z`gB7gS$qHnHpVBvRmX!cIHqF#Vw&52bST6wrR=xP_>O2*RpnJ_b8k^_^-y{ox8(98v-p$L@pbWoTf_{q4K)rJ@G{phwIgd^z2ip#JNWe3KGYsD&y;TE zpJ;3)m{%xN!yxFC(e7hkXcD5CHLbzFgl0tiL_Kq1r6(xVhXEN;-y^-xL*F5gVj2!@ z0~ z_<$i#daX5E$04k;1`scjAq=n$=GxP$L>I8--WJvjawX8KG$i83cOGzi;KB&#$5Y7G}r|^86!ge#-Q+Wpf zBA@rxsQJ41}DosIx;x zCj|u(2)sA+#_I$i(v+2n%ku*$^g_2r$LlR*0#iN=sn1k(g^3`Z*{bCKG_kBLc|8AP z@6@J-%s2S1X-#2B_eunt!T`I|Zo5qrlpd&jjYNGgsBVJSbS>=t zlKc}w!X`@;@z8`#R>N}sO)Auu10c@%M>80-ZeuRvwps`xX5nRqCMn6v_ftDZ(`-(as(c}Zqsu;Tnz)n9QO2o*e{ z2j5-}8+4^9-#Xv(>_4pLBU3X|%RD}8P;d!`5m{tm(^7EO5IvYb#v6apy` zxhZLGeu?-w$UoV1KFv`67-uGr7g{(_=HJBhC8+=>S%qo}HmPWJtYN_KTdcf`u1nV^ z4KSgKAYCBL80~>&Jr6pQJQnav`Q|O(ch<&pM|+pKAiK+&x}6#= zFQFb+JK8OrKZ``TIaXIEXm^w%o%W+nB*0mF;lU4gp754SeONlKwJd~QFd`kwOs7^t zegT???UqM$*RWM8{EZLE+m^7Kg(5I7Xk_Hyp?e@SjkMpsrh5VF{t?3e||XZmTE689}u; zIGPNH?JzhK0|+(J_~Xv7t*-PXX#2OvhA!^VQS^oAoT!&CH<(#j%HOAfkqi7y3u|d+t>gZI1izEpo)^zt! z!rCD9Y7UO+)Ft;>)XPG;6_$)j1R~`DJSv*9TB!SwMo%a4=CL?&lC6mpYDQYo4rJay z*HsSA03c~ReCXDxY$RoPTwc{CUcb&QxawmB;mnMa#-$ zOWXC;By@QAwPpY|KrTHLQkx)VB#~)011YjzQ1|WBfIU<)8O|CJ0*WUHNu<1Wl0M z%N(>M;J=5+gI--+>!%_W#ZfFQzcw9Lj^9E~coz7z3R+bMpH%26r>E52=~ zxbZyAm5h8Bb7eEkAo%i8#9EFk?Mqq7BT7I9qv{K=gd%XsOPG2ppwZG|D_!!Dr;mNu z3u=5;5(|sLIhR>Rs4DG_j07?7EUM5Xel%~`gzt3(TM1&x|0IdlCVnY&&UNzq)1shn zg&!a`m9lP~WKpI#l}lIW{cy?b5l9fOPjgQZ1mgNI3W&R3m0yPOHd2>ddru5yn8PrblTQ*P}@0JM(;SOwrG;Y z_frE2N(ov3pBG%SQRf;RU+kKZB&QFYph#BN!~4yC2%9&j(sAUoj^oF^&ll8|=%^4c ztyyx$knQr_yQDK|B|9w*{ScdL$^>7vhX|AQ77BP=#=1lqr^vs8TBZ|3QqWrlP&lu5 z6ew)T1+S7WA~1pFEQeisM3!LSzw)vv+qLz&_T2j(Yp?mis+kr&w$$L&n{A*yQz)W! z#iz~Df*L+r`sLY+HcOK6zn4g&0Q4eIvM?PGgxu1p{WU%c?`4tZ=*|pF!c(_{42@j^ zWmZT3ev(aLtqi23;)^7Q?><*HJW`WevCYKp5VOt1JX-T^h8Si;$yhtuIa=j%*O3J~m8HGpq!oX22-4ggJY^n05z=<-6tSFT^lY z=AEnN+_Oq2W9Ad60*hen$P=F9AG$g|T{sO|FJ>;J9KqHa1De8f&F4MW%23Wz`F#`2 z#s5MW(?|6QG5T2B}XW-Qs4ss?i_yGBr4UiEQD)phvv=nW1BKi}Jh z@pxF?d7|(s&Tw|s1V)@!06yG@=D>ivZr?4&hMo&Hn1A~g0nWg&kR2-OSvPP;2^DvD zhqtAe`Bo=oslGccDHe9V&yOhE=BgQ9{k`nF*)%c2nDo{tx=&4@UEpiR`SX>=OHueC zH!}vJ?@VLgzO1rUEaEr~H(a(OJf=$bPTtXKIN@=n#>}`!GpV&d_JUKw(L&qD;)zYD z(QOMY8myNrT70<|K#fN@XX>5NS;|~e2;__HPnoR>=!cp1bVm8YZBoD6OTn6IIwzB) z0x}bzu^f@B!L;ZUB0|c$z?X2($FjE7)Y?vAu!d8+kLA_IVm|tk2>T|G;G}HL!XvHZ zmj_a@PpyA}2yt(U(RQ#cdi)7>+jB|u>^+z+wc9^U<`nU~!`x=^7v$8#XfCkuz=648 zqLh?{0U;Z!$m@POForYs#sx29;NY4iVH{YK~9s zE^?RuC7~vs&=pQm8U>#O1_bNd4Lk+50P(>xudBMaEeG9P*DyqE8I$Wqbm~*YwG;LT zNehwRqKERTN3(GPnv@^k;^V$iZspvd`%&l>M-R;)#(soOb2fy|0U1@OC9e(qN4p)G z03#1~^zVzIc-qMKkAC76&N7qBPVYxuFj|zLwHI)buU1gv$tot{jB+LABiYp96Q*}$ z%)KH%&Z-MIM7UV)PCx@(~B)XI=HvH)~3kBRsDxEp<4e?Y^FuEOeUu zeu{!%fJITb-#CfBJ=O(M>YoB)o+3j$Tq0ehehoLJ2(LoI{0eUhVpBMP)S&LkG&?6f zalrcPpmxhK9LVo9XU#lAkL<<6uc}k$`KOvLs!Kn{5;}RtwL`p6H01Rnzp(_>uGjnsGT)AJ*`^8e^4gfE|B zezURv?=+?Vx4siA%m3DQ`tR}YQ)<$-e^~#Q{smnwi!K2egT1lblM-Q&y%E-dUMrtm zZ`HpV;JWAL4~0OL+m;kI`WgS~+7|1;+x|v=$;|xtql!`_E2ULPB}!e0C1UJ|h7xIw ziW6f^7lx~rXdPm$I>*>}W~xmgTN9(+c=)(n8WF7_M~y-WM2*HV1opQ5u3ja$4T=Sg zA9BFm_!xnk+ai?wYp<3V2vk+DQr;Apeo(p2Xx<(Sr%5-H3{D^0z%&F5idjsvfEtPq zzL!Iw_FjKA0UO&Wtd3$N*3FUg&O^f~LN* z-<@GL02TEgEr%fumVRC{XDIrVw7ro2-Ocg?RHZ!z7>}|-#(9A)2!XOc==pLZ{Q+SF zW{5$6efYg0nxVT8cuR=!wM_UhuTihU?3ZjoaGdl6A@}YhNN6;3bwTWCS84?V_BUz; zvPwYNM1r+uBS_tfxx$(!s00I8YlKQl6dDzrL1vW9aLXWW2tnaZV1-k1(xPIN0PlY7 z1(w*wiqXqhU1fibfQ{uMkFjd47+qu8lJnakXO}vj>Ok89(yqutC5_%@9 zo@`tlA6MLdKbLk~&6sXHT$Nl(*DRN=sBSnoC@hyoD9`b7Zc;FE$lZUzJ_CHRcgkPR z#U9Jd$qB;Q#$AUKdUXOy!LgnW>N~jwPFZ^b-+F$XAHVNgHPG1ZT}~|2`!uv|qzH;# zu=@7w2%-4esDxcxbhNE+8#vx9s{VGOHZI^<(K9!;e0I3sjUPsIPk6O=Mqj8|ONa9Avr_IzCM3|^Ay6C}b|0+;426=e;&z;KFc*D1wi z4caW=C>@spL&Ws6Ee4h)^o^DJXs7jYR*HJ6m4#PKYB!53W{8*154CV1T>2(|TRfR< zt6unxSLEg)TJEMf6TJ}QlBZI$Rv5Yg0$lw#e`+6Rf_Vg#=2M`@IUwY-) zG{INi$99FvUR^x{rhBiFx8(|=&b}6FMcmXIUJh%YRO83c#zc12CAFj)2Ol~8EH#o@ ztq?<|gCbB=z=Qg2vmm*M{96ucPX9ciBJCT8lhXRJUVWyq(X=*FUVR`Zx@5%P{S?Sg z3EH77@d7&zqcJK-BY=ORw@z(l@Kfa6AOql@-` zP&-PAyoko(CeHO?tsBezkTRYh0Af0OQexr|PQ=Y2K0_Nd`guFys`v9S#!?I5rHi7~ z+RH@!$SJ55=|^c{33(XHtXr?r98*xsRy!Vh^|t*>aDaoBNim{GYn5PR$tb*^Pxpq5 zv<+)|+meMAE$lD!{KA|@eAv6Q<#~H$?b&~2W$&>?uYFy5J)sXB;>%#J4DyzwsDdq@ zrw$*|dHjt^i)TFX@5>^{>Z3ZMzYwDoK2HXhfT3&5)5b6gI^Pw+$bl3Gha!4V~u{p}LpLqL+L;`!%6Vy96LA z^{8$vNtllHOlNDuY0qY>cqBR3e5Pr?-s^J~_>jDkwqxvt1-8d|%L#_MVu9j=mRA>T z4e#`{>+I`DAU#idZw(7mLfg@V;caoY@`S4KrXZkyHK0*ex&)i8ZOn^6m*2x^%a~`J zAPN|6VE{Fi2ZkcU7mTKJM&W=SREG2Zn{_?|AO4^O=Dq~tTm+oe26I?naB=wys2u0% zD%y8LlcV(7!^(2_CfxBO99?iF2s@{*Wzt?gFGh?_UQRH|NQFq-TaVpDT9G|^IgB+W zhnjyD)fqykOz#wG6#Ia*DAwT_nq(u@_CNk1|AD>A$iV*psiJn!ir78#Z&toSgJAH_ ztrFbYm=S4tQG$d!mGaneZ?ajYj)ar^z1!E#0<0grT%ORH7^Sg6NXSjgDX?A@y##Nu>O#eV2~cnfnF7Zzt-Er3}k9=E|S# zZ_sWXXh|4UpTU!z-7lVhpK-h?zr4-&Z{7?n4yQKnZEX10^2|7k{xTFc0x^XoGt^_o zpqk|*#yEw~EcrURSmUmj`uneCSDv4go1BXNu?w^VP(_1cBYt|tAj~t++=#$(J;u_6 z;{m#Ae3n9dy+#&(&>Cx!tNLEvRuO*t=-0|&-qy)@l`J^pe}T7uQHA{aZ6bQmME`|G z4J$}i%~j*-20UE~AXhS-&`4sS<42m^rvDLE4Cw93q5&)935ZUXi4f}Qy%S8o#7bvf zCEq!1emlhrdE?{b#Y+_u!<=e)888^YBqY!SEA&yXP6rdMN=KO3WbGT;+bgM|gb+Hh z`_$ffd+sjJ&4mNWN=-ky5=1oM6KZBf!0v<&DELi&4>?5g$LS*&(L!JdEhKs>9pth= z3`^#r?900{@@FS4VD9yQ?wr~1h@+?uy!qIznbOR14i9&n7E{EI0C`uhGV&HZre>vG z?#JwlA4I4zAg=)e(MftR5p9-TbdH(Gwl<@1U_L$Dcv3!YPBd!h{U~w@;c_Tj)&y?a zki&1oj)eBR!VS&2ZjuUtD=SMd4TRMeEK#$U22`zD$35Mx5%?#%tFm@K+{@Xh#Npt2 z&?HRD53b56rDsGTZ&W(M+_OAgj~VBBz~6yct7&$ebAjl~qjtFXMQYL#@6}Iz-&^7C z1`X(R>=qzY>`y`gSVYTa=_iHCmvlO^(GL78F}wGRxkXwDur{c^Jt^iwAqG9M#D@a| z@|vQNZv=Kmw$rH{CP;i3A%Y9>23bMIAc|-m3A;)JzV1^k`MlwLfC%Ber=4Mc^%VRC*onu`PpaMXN(eR!fu z_~Q-rMgfrS0bJ`hmmr3XdBqToF5yJv6Z_3PVbSo%jX$b3{<-Rd0Ww$6R)$?d#{`i~ zM0y%5j^CYgV}zLAbR-ApfZor8C5zqlPX@6nqo`4jT;Q+4|oTtCVc%a+c z==3A&RL>I(w;tCP8+hplkvq2HixZ@C0ujQdK6_BfcRjCIM=i{f3 zvTbo-2W7hc>2#=yZ^6i0efvn!&aNPzEHIyxAQUOX7k+YO>PKLwD*`0dMc-SJrC-0K9wz4~L%&uIEG^6r_80nL%7=ncmP?1UM z-FTc8%($b%*d)c;Cq?$AI7v$e3Q z(B8v6LYHfJsJ|x#Dnmp{em5jZH(cBQ!Pq+m*|v4tx@p_CZQHhO+cRz3wyl}AZ98Xb zrfuE)_u2czjyNlBtd~AwJof%jORKe&`jzeF`|+(>nucV(yiM~Q;b;%m{ZP1BLOgOg z>bEVP5TNM4tpE$ZO7IuG)3EuZEz$ZxwY)*luQG(et~1jpJNg3Ho*FWnOTYrRV-zS; z8hiF6@tL4YXN2-`O2_Xtz#1$g4xfmM8(M`k|18EoU5g-%;>jN0z@(b}R`X2=Y?qa1 z#wG2ONCl7z5uAg~B#$H=fD?@Z>YccB&#~mD(s0bJBlCEermrHIWE+O*>J@Wv|Q{g+tyjJIPdtk}i z6AB>~kxHLCsiMYNsBDu?MGiDs(wQI~xlyba%dgvFJ+3ycg3vk{m%>x0EF?q#FS1iA zLwFy86Lp9f->o}+kRT2OV$Gj=$p_Mg^UVKC@&^@8WIdC&V7q=#H)_SvX3vHwf4Xd3I(tD~RHE~Pk{?R;q*njEv2 zMc?~AyO`M8&;VMJ1xX;~a5u^NHcCgjC(U~N=SNiM{7@@KDqmx}JJarZ*`rO}*N z>Ij_%+j~{lP2l1S1azdI|4rK~Ms4}4e~0~-N8a@(`92vO)XW4wM4F?xVXDyNH9>F%nk)d&w zUQef4o5X(Fvx6EX6DV2Lq5IoZw?VYDSkA9QyG#4a+oy;a4KDo;C)D4smpB0=X~b+v zayXJBJ_r5R!P4_PP(9-nn*Wo4~Bm@NSr zPuU_u;9>H}2w|vS`2dmNdWO+k)>76YvChaf^kzH-4l^ix4uO@KK^{_8b)yTF1aWA5Nf>v>|h9sr)J*mdjc!Dwo;3KNZ-Z zFBb;Bw^{=3TCXae_|M^6FQ-@=_%Zu9X|nc2Ql+pBqgDMK1*Ouk`G&HGmu;u^)|__6Uk~AU@k{lM zWG1A`@q14_Hde(sms_mWayRd;$_kVHh268+!Oz~EF^pjO{hKapK)j6^ZQ9y9_eeMx zaWj+I*akS6A)^oh?- zKmO{VCm~~PF%MVjj}C1s4Sv?FHXUdMw}H_Ye*(EG7+(VEOG0YI>f~RV*}{Pt*O4hF z4VJlY%ozx{x2Icbwz!Qnf@M_?dat{Z~6@tN|%Ma+Di#L!K;QCi%mMFsJBan%70Z>ymGRk&=3H9$T1PK9Bb3M&U zWXP3ew?xlCgEW6B>+I1o7}#)*Z&VTeM<}7f$}9XAwNs+ie!ib5yBZk_nH3nMUYOSW~5VAKDahZ`x^&0^DaBH zbyu7A-tZ$c4qvY>ub1QSQJ_W=L1GciTu7%u%CcWzp--PSXNzwBLcXNR;d1# z{c-bx0Dxg125+*T2${Rf(#e3KMZ*{r!#BZjNDm-_Z{loFd$by?-x88%?1r=o!1PdY z4j@Dt^#5F}gu~@$R=7#}SUXy(dAvv(6d*8euhb^>!Bj6_CT`CI*F}ByYHl|l6e8*CzsS1Az*JX zpX1b|flwD$0J#N4ti4=Ux0r4xKQj-l{P0qu!Y{9CoobryJhDJG$^>>jE$Bb|wbkFn{itQ7EaM4t zaD485Zt2t_Ljqk!YS|RWY{EIixr8W zv0%BV1dEpnAjU#6l46NOBru0j0Gsc~qP~}R$u;PD`^2R7F)>T+u}$Rj!7q=vUc_UR z*-~si_LEB~2Y;boX)=+z_x10K<=Ll%yXbP+p{m4Fau{I8f@DlsBDS7mz^t6PK!fF= z#zaN25Q%6zI_d#ZmZwa2Cjd3(``5vRecD}qpdMqcnpD;0$4td?!cm?I1gT7Yr#aGp zeykQQzCTmu{0`A_l{Bxg4p|gs{=-MxmwD6Yy# z02~1^;DRL%%H1RQyu-mUH>$pzzZOpZ)w_x27(X{ohi*o)90e!Mrr+{&1gy2Iv=Wkv z=ozwkqMy1l0y_hOt!RX`)HkcWu+a*$QsYqKeG(<&^;yU$wT)0_o2L~z7S4SM5q z(~GVtfXe=z$4PN+k6-!2|(=2a>(3j1FV^ zF{nLDHgLcVD9&_OIi9k(UCvxPdlnqv!_iQWfW}<6egJsdGth1vx7Q#ruQWaJgTq~% zIqs3AIIMEX0rn(Q<}i8|fe#8l>nPi2>-^?G!EOJfm_OS1{~pm<+5Y_?^8YI44MoAc z=Wg834V~mgDeW8{2#UpakkKLX`a|^e$ z`HMTun!MfVyc}JKR7SCEC7!HZGb!Xt5wmjQsWuzmq)$H0wB=7D)*Q%M^373qch%Rn z^^w^-x3|%cuqNmf2E!$!aRHH+S5p$nBL>0rIoNR{pP*aBREmj4%vF(rdjNL1WF^?v zv~sy@iJe4m{v1r^SHuHSn1ThoMH!@u%UEragl=r7dIMRf;ou=zQ5JSs)JlXT1FF^D zY@8mPGi1?hOVk-gvdYPW8RcdH&d&G_X)fd`FO9O=Upe}UWUIr%inV}vVzM|1!Qz@? zE|?sWIJSs)ZlCe$*6@tuhlj3;vMIp0DLFd)LrwYvil^UOJOhRX8D~SqWFzId^39Vl zTU%8a(KTHQ(HP{!n1eKikf>zm3c89DiW&Q^#S(lZO4kwDjx(RwSu^QuUiOc@g_V-@ z9@SRoxvRL2ZoK#Lx%g!6IpV@(n#Xx+k#}R;SwXLOYfgR++&LANG0j&{{-ZFv6pE6UD0@`N=c9$0L z$#1*W40@{;6kb8N*$OUN_+B@SQ6VReu=tHvZWah}t1rOhJX&xOjs%(P697}w_dXGX zUd0nn6U`Y4Q*v1T#ybKHSr5a()80=P^hENe&MQa6ulq;9Zq?QfJt#9|i|&0JoWC6N zOjguI*VU@>WIk>9GU1LM#1U(6oDis@rbgD2|13ipxk33Y$-tpf`B1W-V)RDn6EFr` zph@@<2wG@L9w(EozF!Y^r;b356nESKyIkHLIBhItpDrF@G|N7G)tq@3i5XvKE&o^= z_Mj>CQtAbn)(|AH);vpO>&pj91}lDkh)wu3gxk#s0UrtcXuPqujhknQJJ!#aqpN*y zh)X%lofp)}sh(42@I8_$a&V;AJ3xtxju*a9o`=-)6?uUs-8`Sok;}=1hxQ#k{8!&- zOUOIBjlsiGW7P{}3Fqi0Sikneb}H(`h`$hRAXKyVxzR<5eIacuJcj%$+|@~&a+^)c zu}5vQ)P)DmW!2mga7@aw6*_uyVW=F~c(>F>ocv{{a7ya#D-(UyhcCNF(@SKGFB}3A z*57aNec+%QU(|i2;!4O+EnqIauXZ#8t(xwhET{(I@+(o7y{1x9-b4js-ckl zGCBJsQ`Z8&!}D?s@q2(eN4>sVcVJXb>)ev~TB05{u4svSC;X}8u@zodwSVU$!=moE zTg!B3s3dAoEtn2KQlA&@_@i&$^;EM>{@L&Yrke1;>-(dB2S4q!=*LQNTTCexx_YX^ zBoy-*W=9}roj3DydI9{5o|kvHOrU}U3t{oDmMT2AJnvhs>DRA8+qB&me%heVM|Y$q z*W8+TeS9$0kq=YVdHy(Y@J&+JFgjckxU<5JhE2qTjb_K`A`8Cs*b~qzb|BHih|t&LYS;nZQw6bFiJnINbdvLz%F`Hxv)kHU_Xyv&I)~=?3w^~ z!;V5pLjLB2aopY7$~C3c@;?auz%amd8NSbV{+1e3{!h6-0`>xO1^!s{En5M`(1I@M$&rY|vC-i7ivSi? z5!(2VogJ>>n7vP@G5KqyMzyj|A1dpuY(a7Su6psvC8t!_u)Xd zW8Hl7HrSdIi0jMa5xR#DF%<*Bcl`YF?S6#5O^5z=*Ug!Im)70RmJW!;kRSv(ppJ?_ z3)CeaWCR(2Oq|~opCWwOn_s_LR^5!9pvGX{;WzMfT9$E=)#=ll43W>|1B2_%b|Qg295(6K_uUeb0dmCafyVf>j*r+9Tsv{ ze;lj6f0=@+`b(hwuIlX1Em}EWb*AmA^j2$q5ej``tlhnGWWF`Q7MfQakuy>LoLg_~ zfnHZv$IJOZg(R{BhpGrv21F5L30b?QUe~uo5+$Dq(9y?RBE2qIDg)h(T|!s)%l3U^ ztzke3DY#EKgN zGKvPTY<;ivv+rP*ZOdefAGc{Yc>yvpYzS*W-QA5?C_Muz9Gd;3MU49M4x8)MLyjL_ z{;ge)7aB9ELHu66+^rhoq)fZS0!Au9<3rj*N6dG$s(&A)t=R794F>5{rnmwv9I(Z9 zr4cQI4MPZ2ad`zugVrkT(Trou&fC2ldK3i%@dDa)$r!K#7hV6ldPZd2&`Wu8N2aa%`alT)qt>i9mBi;LxLGjuL%oEYLqr?O z_jpv?S}=7mRbzm140h@$M^~^4Q>dafTR(}Qi{)~x3sJR2agvgP7nh;x+wTwxTU**Z zmVjF{G5zCr?(fl8mU~0D9``hRM=nDd+SlaaR}nH<@G$mH8+?CjaAM4W#HXfo z8%@{pI>vY&Zgj)IVF5CsgLxxLHRH*13M}$I=-LlVUhsi6&D)`;NOJuH2C1jWt`+Ec=EPLy?8i1pL#+=&gmdC)ia()(i4 zShQM-UsEND$f>4vy)nF)Mo(T_GMY-}X(VkC`}tcC8(qdn0ktSC$|j@ciTnE$*Uq3h zvm>?$)5?9jflZ=@bJjjYoSoBx^?~cfS|2dvFqao6@Qg0)xOd#8kk`I*} zP}*+}OhLP)ZJZ)*wD4@~!Ukb4g>9ccqtHWIqt?<8^4AeqRo$WKxNOyq#omM^9dVhs zPW{(Qb585*gUg__QC*yxxvC+K;6zpT2EuGfmF_ivvw#H-#}H~!`i1S{&6?+(t{u3G z`|-KtaRxt}UH-jsjA{8r8C4565vouVAS$FQ?Y~P#v{#rgAVP3$m;h?`3_7kd?<^AsGk^=7e~1Q{DAVQzaC|79=gWVzZz)!y zu?A8ungP{7w_ry3)$Yix#Ms|x%4k<<*;JlnVkjQ$&$w_fs-#!*mvA(;snZ0!=w8ty zK^*Co@P&$PP!xKSA@p(Q|E?uiQ2S6Krt(rpp8SPLH2wvX!08~|!Yl#$09+!-(^%ah zml>#p@Jv3fDcj3uX@?MmlNW5kAK?YpS?{yB-9*=AdPH(X$V|t_lLMaX_{iBkVu+KY zC*7)(u!48lA#N3_PzoN|>tlp#ekDzzcU~NKB6G3tT-usfw_UV3*xI>&+xb0RFZq}S z^nk$@aA-HhG*k@~`*1dN(}dt2%M{lK@CAwYuxO7&1%OaQP;w^vm(K zF{G^$D;Rv5ZqPN--4SDYx zT;%~Ej$(6F2Mr{NY7s;WrA7e-;;u*S`+UcXy%>qCLz0rjhaM;1VI~RV5x(<`PL;wc zB3J#utauhFNfsIC$rq_1`;(a-1!os=nu*|U+(VRO!8TEEC`0=4E~gSdtjvn3r|9*-{v z(rV>3B}3{P!F;vxWo@0yD#CehbZr z;Qp^D;+GOC+Fs5aoi{AC|2P+#ab&$woX&heN?5HEQbs}$V8Us;BGM7%pmL3JXfie= zP5Q|ePc~T9Zx0#6<};L6D~}~dBFo$YATEh>Ww0ta2&$CCR7)5*3R&a5U?p4zz(mT$ zWK1Yip$DCnn)2F)rT$D1`-AuYD!BDd1 zpqw+9B^gO@0CAhn>HL~7sFsU`U9&js!mgjEs+pNlJ3l#{?n_P7D}9{p{eW_KdZA9+ za*VEmzuxKo8Hhh|(j>+@UI+}zS9_RO$}62LvSb3tLqjo(2K>uU8194b%U|D8PfBX{>2Q08?% zqTtW!JAPZi%+5P`b|!D1!?m?neUR6-%?XBFv#+DG&#P6Fti40@$%*Bsr*o^UANcWq zxc9z2yX@52@Bifh^<>R`S3ghtF9+z)Q&&8rF^{eH)A4ruQP)$M;KrqBt~aD03j5+| zdNE17ATQ_K_`-IiM|0Mg=V*_7Pqz?D`KcBa=m2;c2Q(=3?V4fFVWC%Y=4~QS1L|m0V1-%C2#~Yn(+mbs zQEU;PGRoFnyg_3I334k%TPU$O*l@{cpRtL;gP%(Vf5qba?@vemwW>?6qpnvMsw2as zULYQu0g-jB*N(~n=(l1kh&(-3k=Sx9uf2Cqn3c!j$_5a-^m#P1aM5~0i6Sf)U||!o zCVR<}!Ql0SF+5th#cORBn4_}xRVUA@l-RLPyccO)V?dk2IUG>@GmNM;;h%riYK>6h z{WnC_?GkJ)7#dWeeldaAI|88~{UxU4S`bsP_q`e@I`@AC*)?dA#2RqB%SZcyXQs9b z_Y&Gcw+Y&86widi{}h)6eFyQmzsQ>Q0{hZfkgHc}<*HGgm#I@>i>p-f-lTObA-x!+ zX#qKpFNwj}0Jr{((%E4AY#qULL5lKGpaU5{UVCi=4F>zLmZ~XKjUOo5%-)MtKAm~F zS4y9cJN69P*uQwOUgUasZ4F1P^%)O-8=G~Ji9fu8-t6=Bg77V!pf`lQeE?~oUYD^# ziRE3R!Gu2K$_8pEcVTLwM9=7QLWoIKg3XQ=6~KZGPPGlt{JfAhkJFSz5LR?(s~wf1 zgJ??-Ct-HoB1B+GVYL`5veRAL^f%~J-qyoE7408a;Qu?KH$|Ce~i<^OJ(&eiML zt;mGxJr3f9HzRVy$(b`=QV$768*7G;bS34;zk8qq=@s^b*_bWm6D1seNQ>{6t@##C zNppwZV%m9rI#aoMkSPEN)TGjMwaBIsNJR5XNONrMZBl%tfm8hYT@|^Wz9R*%5EKJ~ zdo|uS=ho~muNg3-0Q1Qy#(J-Ww9J7LY8jf>C(tu09n)@EM>+4ci;rw(T9QIFw0Ycd z87;w%da)kIu=sZBiq6@{z#TXr5l*O0<>96+cqEonD0C8V)fq^`9)oZmCm(07#*dZ8 zkD2V`r_QU{hj!*TqKlhs3_>)t=?lS9QTiZ=%>qf@D48PcnLQ&qN5RY#;@(-tH0qrc z46KTy^U!6`h0m;b`lM8TdLk!=A`F^v>uxrQj7fzk`=%b;MX8EGQwS5_+f`;dIE|tK z%hPvXzTMro{@pv%gwt&E5DIcGxT6$({>XdFz9!nO_F*(<^aH_J;|{Z<_oEP7&SViZ z3icn$XXFKXZbe_JOX0>iPm}#L9sN9A^`~x~S;?9L6NqKNEzu*2$ZF2-%Wv;*R=?wF zr;z{;f;jzo8IagVgR`sT#dj}`hA*x&?xV=!HHsxuCG&M<4DHXhv6-LR4%ER_`%5WHiQ(x`bYjQp{0b)W$t5~Gn<-^IF?tF5S|(sIE< zsU>#+VWrFE`$T0Sx`nr~*g?Rj;$HEurjAu4b~B-^e-{lbt$k;CIAQug5jN)tnyC!L zs<#2lQ0t_O2I4IJVg_6cM2#>K;7I&Zu3&2oNh^;3)R`={2~EYk6q<~#$V70jfNSbR zKG2QEM=Zw|qcMngr`DbZjsBx+X3BoeL{nB|xeBvTizVGzn&w730q|g$7*iJwd(8tI zHHXq{4QA<{?pl!NhN<`&sE9~A{T=QaA}wgJXya!})A$)@pbJP;40cc;b zjrdwrybz*v1iD0ZD%@rx+=!%}QS2#m6i@dhsL!Wm-0ivb{BvZtZO1j6lK`T8pFErM zWieFEjtR#I*%Bi`!!%cEUP>7Y5{AVgwR!k5R{n^ zk=2|@BnxWIUcK}34DKLCGVhDeoNar$L{w)FG^6MKbtg?aYCtdk#jgf#UKl5`Eg&i1 z;dCO&d34|4)V-JR!wwOHxS)V0AmDxm2dfbt3x<_cv?DdpShP`InY)BGjZh~Bd{oFG zL$A$cQhjTXS_zRgb}(PqoL#(BnDSJIMag-0UZmA0FPXn7Fl41!=aX!Gj}z9(tXZBf_*(x^Y^Rs}njej8 z1njFb>|iwZT7Vr+#gkwcbMb2g1SCZ+;3y!-OScK3jnIzt&55^(Mjt;Wa%iIsRK^W@ z76VkyT8UYCjk3UCDR9m6y6cP@b8DfXA?k|`)qjMeyk2qfZ2HQrb2)z`4#ZRy4?mY? z-xJ5tUF&_C)Nl_hBljdkfvVdrG$S$8lJzt4L1q{JF)@0_v~8vKR@u;2j-3CQ`5GMw z87lK~YxP5eho$@J+*d!684f7^dSDjxeW~w)7_t)u!*wPYTdF0e$Yqup63OfopbU2x z-g6$d64*wTACJkSfWU3k!iS(#Y4sjd5{D-~MIdD#SY(q4{*rz`uIOzZuHjZNiQ}LC z{!QN?SG+#HYZx)(t}z(JABPXas)P45@;JW}33n4pBoq+DNufrE-+xvKRhlqjH9I(2 zVj;u%G9?wDleQsS>lV}p#7S}`ftgg!YoOk7#?R#BCG~1n9Kt;=Zk6(TICv3>>-h@s(&QVsib zv=9h}Y8U}(eK-Z{3@rUL89es5pWxH*SE0R_*oR2<*jPh0+lJXh5tuFsk{bieU6 z<@3a@?f7T_dn5QwcE^$;X&Da3J$Spr#7;9E1_e^PO?~)K>sTjxn%41IplC))txk+p zm1C|@BaY9#Io)|rEXiZ5=9MX|`QbX&8h5oz#SVpP+5<&%U(m@821r_@7yhdudLGk( zA%^8Z++mK9V~2gYw(>cv@K(~NX*!e4UZ`4*@J{Kk_msQlCu=BLK!TiW7+TuK>#g}C zM_>O_L1mQN!G0sygGQH2efmgbkt+uBICv*a|2gk!)ewVd;i~1eMR6`=F=~sblAvud z^AG+pwmdtOD2OWrbci{GYclQ#BspOt8N#Vr5#az0X;=*^9mG8ua@_mWch`0mMHd8Wjt;QI=$!g%+pLrTBUrP74pam|rGijeB#pF$81jIQuyrx^&&2I}%lJ9Z zNE|RyKB)XHF~;Msc1FgA;l7u#(1tS=Hu)5QHlGX)RM??DHFGN4WnSNxPK(M8!6b{& z4nhR^g0#N;zJ}Rffn-U!5<>=DHyb-Dou38ML3brKv`?%{U%GJ<+C9_U3faVtC9Hqs zsW=9F{O!tUi=l{1f49!bqdah;`2v}8!*3=xt%JV>#o(tri*9B!oM_ z5eh(!FrB<;*cD4KF=8vY=5Cno7L0e8ag141<=I-Y!8>t7i6AFI1V9`I5Q}qJiL8rq z8TE&9_1xZh5X2G5#W`+@Gz1oVB+Lp)GCVd4eYERSGSmG=v-(!KfNbpLOf z=zygG4G@MnY^YeYyi}ed0fmp*z6~=uhE;ZHQ3kyNn4GfITE=Y9wRN-TV79H)tbZ*h zO$;1%nNa8W&&`}OJLw@QRCZsukT53I4W=^Oz&;6%DC)e#Bkf-!@326U1YjyC*Tlz1tOJW6gi}P@w8v2T+ogkU#g?p0j5Jgir8I~0^a2N_K?w@TQUHwz zPe33!o)hTIGEZ1@UW_DT8bfU0HAs@qs3aeDkik=sDQsw!ysE@5Q?DJB zi>XNLw|gT}9{F5^5lNs-$;Maz@|vv}w<@7o11t1LcJ20aHj9q`l=$wN7$m2jEg^n* zsE0n01)>QwROd0rdrfZ*+rZ!7oG_JNJoaiG$juBRaAObwJ(!bKRo}EVtChdCr$s0i!`uv{(0UE1rNY& zz93YX35UC>omt~(`h{XQhwA9|Fr%G5NZL#TXM0j6ch8VXa@m6klidKg(Ln+{XM&l$ zDY;zI4Ft|!CReAyLppQN$DNpu;r>HGa$2RhOgF0EpI9U_WdH{C?oJHX*_P z>~g!x4?tRifb^fl^&e9RSpI!B=Fv|I!GGTjs#%SQgb%;Z33Dlv`%IgZb}aK!pxMqB zttuqve7(~_gwqGWceXzw3G_L+H|+A|uy{r;{9TkiTg^*l$G>WeE+-NIjZ2M7h!?>^ zt5`y)lxfxx_Zv<|YLTD-Mf9VDiwd59xe1R#depLGYHioXK+AhRU#8on#~3=YI;Ts` zx==9b9NwMOw|G3Cl_BZ6$!B5xh2s@hb&*~p)0wapnax1dhdD&!{;4m)4$vvS9avU-)>=w z*Nt*j3r6{AzA{&^aCu=xA~8}HppXkw!Z{45fE(c%kwlmNpAkw)wnVF zZkvdr8BHh;1Ux67GqD6yyA_Pd;|k+Od7sp%*r}Cl*1*r`<+}Kl&n$Z6^d6q)qp4sR zY0#RCbdC}2Qvm1CSyTl(EAv(#FbVGvh}Z_;2b}@lC88(J<_5b`d8{!bq zMe6IyIdjMZ*e#P+P`~=6iWwch>H`$gW(D$B)mk8H1t0M997doo&Q5I&R5;L3}xjT;v{h-u3&ni~?*d)_Ed%M0ac~om$m=XGn zltmv|AX|S&6rzbI!GlqTf*!a6o~K~gs1KDzIP7un!+R?#vLJ*`M;k7*&{HbG$6uS> zvnoV?y_>yHQV$31UnD!RBC));SC+TD?aQ}HX!ayDO-A~%6dsK;Q5OX+Dx(9e73cRy zheS8~d11C+a|ma9?Y- z7Jz{K9{u~0pb<9Y{o6wQ72qJGO#}MMQ`0GYA)ipz>=9Rr7YTDvR}WGm5=ueuKoJJZ zDP_P;w5uOb7P+4fY&q&}5^WS=!O&9&%vdtW5kpBPs3SNKg0>ZL`bsL@7p~{5f-)Vq z*jCB;TK|70rsUZ=o#+IE^Mo zMkO}YR!I1>ae4vq4IA$sUqLI5-4$K@94;jjdJm~DidwE-60}tb^a$;Uc$Rh=p3O!pim5YG=9Xd|}ZsjaIvb;U=J`lxi=PT-SftU+3 zGu$-DFCUN#=S!>1`V_g44G!!-tQbn~!OJ54<_)CAtf|EqaFgnPxm&2_r*@%l1jsBk zE%5P>=qt@*G~>$Hoj>vLAQ^BAFTdzRU|POKVIF+?QqWs6kM8bW2EBR29}+5#fq$A! zB=$$-!plE237Y_Y2&U}YI>t1mU+=VT=3C*6Qexni)zdQ4@a!4D_C=a}1C#6norv8$ zCb)jb-`w9F>z@gY68%#t|3@4C|4={v#k#p_Oas(_00QXyd!)Kvq>Y>XGo5>lfe3ZN z`H&DoP)x|%HwG(+%??VOAqFu9_9(OZvTG12ND<$2pr>fK3@3Cog(KqO}p8qKI+O$8uh{qgY}dMbscatQ4GAn_j+#7PKWh zZB>7Fzc9oz*_2$+sevRDX9mW+M>8DV9^K=15*a6#zdDb{tN*`u3m*UXZov-S*Mx7^ zRuR zgaUEP4zid;P%3mALe!+4C^+&$bvyYwEz$IsJY8MO*HPIYSh6mvZGC~3q=`lHpX>l& zA1cJ))*fb=W_+li9wvxKEB@==X3vRJcYqiTl)ctT^YP-{Wfn4!J z%)<2MCHR25CUhbq2~ei32c9;{+gyQg=6N~FI5oQLqbI>e^HfQJvgB zy97jBkiC+M4dx;)+(%@h!Nf%>+`t$lg3zi4j`o^7mzj6lwOfZZ>ofvf(b0$dT_UZ% z1OzGOAjv?6BV4bEUH#MrE@NBD@=qQc8Us%{d-F7sZfWda2Q7RroUe9i8>ik^L;{{){+kztF{tM2XQz zi~wj(V8n>Gx#cztXo}~Wz={xAb0mHE4PCp~w@DB=Kt@hD3C)KS!f))bUG$1F`w#PH z0Wwf>M2j`@RvMLUoJ{nOljZ6V9+l`zlI7wT8QOC?C7Xsk_tN=qOt|Z5d zin2$}JCPEI)bfUMN}-(q#AY(OqL!amuc3NLPY>jgAAHLnARB`z4j&H?E^lYR6QKQ| z4_ZNV1rz=PPl+TC2*F3ymKHB2B@1HE zj{Sz*rHQ+DG?)Pd9C#Q5JX%$FN{foT{8b_cDL&%Ej7X8ZpnjO}Ya`a5e%t(yDg`Fl zrMPaga6R=)hk`bK$`j^LNf(*y47sXpEu+8pL>)`#93cfbwgF3M-s&(P|A!YF&3+r& z2X3Xn=4u~a*M7{yJAPi-Rhmze2s;n@Rb{PO6qKlv*n&nZ(LB80d){H`kTZA~G*d)fW z%rIhv_-SlBe8D+_5kBsLp$arSRa?|o{rwL68(i|GHfC*^0jUdD>t6hGG%@Y%KPrnu z8&v+A_jcEA#vdLBZ*G0%O&_Y8yf{*5?Lki`v)oaJwg*rn7mBW8eO$_a`j-tXY{aLq z39d;2bwLf^G`DgAY%ay&#Lp7~%U6g4BJU;ATWh-M-v_{+V0kg_(l7hM;tIh%`@g_D+VyO}m4!jj1!qvnK z7s#P;1XI{%c-kY5A-5d`7shL+(ba&JhQsdGa1x#oq+;?IR8BW6r!Xk;-8wgNPr6$P zF|2-g`qgK;pHKbpFAT8s23)kB*yX?A14c?~J*6ur_Q)OJkl>z8mH4Nu)MwQ&%;FsZ zkt<*TrC>aJHZ9}-1kEHjjq7epYJ(GMYub#>55^;V<^iEpo8VlNVb9}GGOBw-3C^%m z;+!-|DHZv)9Mi7wJc2KC=HhYTc{j^0nG^zXBH~{20^M6&+rHv4+@()t6SVI+hmjOx z4a3hKfCTA?Ky~S`ODa+%7x;``vF)cFhx1q^4?WtbgnT5q@D2S%tr;~C#rq3jUhJ3|mz3K>xZiJHOUcN@HfGM5bE=Q^ z_1FoUSHjJwh!u0^iaxyX7ZMa3@hd&InAB`cb=G9arZ%flb3^@N$50;aY$E0sS1my_9e-eGRe_-b@{vdV!_0U)S|MsOn znLP|>_Bh@WnG7> zy?XOSC-hZS=h_8K06(CVb*mgo>12eA(p3MJ^)tqIYVgJvugA@{^Eb7DeKdvOpg#E= zhkcVe`(Ffw5D=UabHj<2NxN-fBYrvF<%yO=H zACh8OGOvvj)eb^R!%AtuyE%$UDF#{y;6N#w{mN340z7hc#GfX}r@Eje;VE263U>bF z{UWdf5o_mEV`FSI#aRGd=AwJi&o&LG(nLyOvy(nQr5UqRLf5%5Zg@M>_%$&Cfs5JV3b7~ zdQ1hSvTSeDjyyx@nh4QR;1(5r#&$|qfAh$t?;?$``?)R7S_H$)5D9JGlr`#E2sK*g zYJ{&Y(`n$zL=0B9{XEyl*`Df2FfSqhsaES}6u65oP|ywgFKzJzyG!NIk}XzKXQtQ5 zojD|AqPfqRtuog+&(6xP3-mv-6%CXLkZ)ksZ=uzm^FAlsf_ZH+)_8B4@4k4lmh_c( z=FhghmQ`u8Aw!_Qw0#_zAfO-Q3XI~abw@{^#!60B{K&Df-kfO+g=-G(98$b-0 zzK#8^KWyYyuv(c#(@$IdD6T0WrsRItj4C+;H7Egt7Lxg1Pv_Kb)RR+edf}Ti_1aIc zd17D^J(^JTe{ID2G{huRm#PyBuR)J>V;LUaBkqv-k5S^v{zPr3ExjT$(%-%j4v`+O zLe4CE^Kl+?gjd>5OmhL82cOrez8~_tcAurT(8uy3l!ge4*OB01?%hZ(pBgVBNnK`K z&~OwY$VkkNMko7Qj!6JZahGb+MvqUHc4u4ebgI;M?W`Q#OUsjPOJNPcy~*_J6c}{G zbD?nOg!qvt(m)n95kqA;?Ex^H9nF{)ljfm5^T#s52Fnv`Y`hy2!)Mtl^SwR$d}>^Y z71cCp@px1^T5m({9fHk>0Lo|OMC1P@LEHG-gSD{v=8jPinZOQC6f;st!H5-W7Iu@( zI;7yXu94Zcm}S}J3OHisC)RAltj?dkvF^gU`N*re%ou{BZFtth{BlPPmuKn+A({ad z#gFLV{ZSeW<)c_^PI3`;ur#zb1QRZd--trwHV(Q_eGw->2V4Q#kP%# zZQHi(if!AfB%S?szuo&>=YRFtXMKFu_c`Zp&N1%c0n?n)$VbWUO4pl=QSZ`lT5}C2 z+11&2$jTKLFU~UH?!_X~?x8WaXlrY(pSLJt%|N z&Swh2#Gkb$5o2B-+eFkJoc3=G!ER^pRJt>L+T>QCk7kqUs$&lq`(+t*fb8ob-$14$ zv5@S{lQkNhSw6U;(o_7G*cj`tJL^Xs|J0k2%r07E=p4*RGp=8H>5{kdzkvruFj_yYhKZb1i1j1_YZk%<{&k{Eo~p?17P zg4r>hXaj-zuF={*NSB|If@J8pe7)#JP?Ux(=;tfd7}N~8M|#dO*D`s*fnmMiIF%tx zEgWVLjy;pv3p$shwktxyQC|rHh`%u((%&4NvV<{1XqLb!YKC}^xP?fxS{ul?lK3c6 znKg?&sA@(lupnXP`vVPe}sP4!`WiDtjjv15YP%fMAoR|J;^_DTo06 zGOke$EeWH*HD(m9hb0-YADyImqk84n(`$8B4mhIUwbzKCS(^U3x`9w(#74fW91B=|{@66~~XWcu5g4uZSxd_4X3(_ch(GuW;=aLj)I2rW=C3mig^ z&m;fsAptzT-ngqj9-^OavM@VcrrdBoph$4jrTdTQ{79_zbLvN;TQw=%Unbm?1@G56 znJ#u78EhvBg;)?s>?Unfh>JIH1gGtWFNsDz=+8s8o&>XgfU}mPMf)L(A>v|~?JB!| z@m%yAX2Jqm*5=>aY}%U;6E|4Rn#=w;#dozMA-X>L&h+CMDAS3>e>pg3yU5 z$sU$BOlz9jA@YFzl(68Hnb<@|tvYd>%EkLBa8O!i=QSn$3MOhZal=X9#OV=WgeSAC z-*Q=2w~|Katq8o$*+$0I!BD9Kei)25ow^y#dt_Z?0b|k{)s)odN~T$1!-@}^cKLA4 zQ?J>__fL=2&T^$)@aKXDyz!6e$$I9buxMdwMc)hGJuv#kOl^lc)hlvas5ww+T9K)@ zse~|2AEA;@18HJ`YW?Y{J}BiUMpH1C<=^9quQORyL) zT@IOQ5v8W?@wSzDaRER_gJS*Ut3MrC{XcP{%S&gM7G;l{cRO?XR|B2xr4Ajk>xrJm zjcM-#D2*_>EX=BogOkNjf|GWYCWxzXrn^x_|03>rL;9jA~=yQpd>y*bqzbE z3=~Q6UMHzy<=nF6*Z3lO*a{&GmGmcPL4h6x{0H_9NhmUBkk#2};~%V1+-5uP;jo4~iP5AN2jC-yDnQU!+R zDeFtCoFzt!7G`Ivp|ZswLX&3Svh_zm%CL6!7PLj7O0wt^Ju>fGMi94VMG#0>mj_~0 zC_|vK%OV+fwMH3O!KK(sS3T4bFBG=9gu$paV9}NVAJZhZWCe`xPTg1=wXBvfTU5&ZNg~DY@ewRM-^B#eTA1^?9BO-@+Yo!1i;zpS$$T| zWH>@@kJ(794hua5T1;$OU0tBPYld8focRi?YrBoThNW_d6R9C-PCgI}Ff)AQVAV^$jI97}@z8Dpp zSG@)3%VY#kl$Pf#cbb@m=SR&rt?n`DS<}z+u<46j*dfyeb9IBCV1q9^3`M>h( zPMF(okK5NA_X=P>tUh1P_d?I*Pi6fD z=N8#d=-_lWcC1TY9&V@mC!b=wtR^O#C1*fgp60uNwvvWRP0h^VbS%l?Mv*jR9TA0t z9Y8q@0rkAIwM4aWWu8rPni%aBGj)4^m=OUaUf{2Wnic>wm>#Uri2bm+h;yKhDH3ab{{#gJw{ zpl-txtrA@1)AM5K1T4oBwv!KVd|UPIH^)hr?i12in$!U)aEBxi{ikZ9g!OTrN_HPP zksnAv^c1`nVPYF>f(;Xm8p<@5Bm^Cgh^|~iTytv#vyZplT%|z;NwRxn+IjXE5^lxz zvc^udssr@iz|4`WtD%iQzX7qgMUtZ5Kjt&CFejTucNANI$m}jPlW$L>2W*%>{zLgE zoDLdVi!IQ%R)IHQM?CG93X2?LK@(Q1W?wjWX&ciaWAl?tWP&Mh)VsqK23TNrn{q9i zU7~h(D{TNxyuqD7cRK;!;PvLdd~ws#dtggzwgNv+)kyEs}@_I2M279@TgKx{<-R0Asts0_R>sB97i9M^QBr9+7T z>EvH6Ng(L6#a-EZ0Zae0oRGO%Z58DKVsIH}m;iGPC0gw1NN0_z%^a zneiX!56sN}Ke)g#Q#J#HNI};=5q$l?aI^xuYmL=wEG^}b6GXp@)_#X=>j%fH$;lUN zX6@pFMG@{aA%8tkv09hVNsM(d!SrKC9WIe@?zTDM_e1l4-&xs)(wLn>Bo0Q=Kj5yd zkL?H^LkMV(LVbltq;pDd3kjN2i`UuV6D`WdJm@VYdKO--R}F8Y7e7>MX3jU{rStwK zS@R@%;&t4oF6bP~|5ck}OCkeR{e1xA>9vZ(Gdh$~KzC)P&d$xh!qo4P43t_$R3XGvhz$0J)g|@Kc41+7&);}5NA4kgv9q$iy)8m)Fsp62jKQ7-O zQ@i&eEc!QNpWkV{OEG%v3_Om6_f-+&ke3_1oU|i;8IjsKn`4gvF zL;HB{Q>Hc@l43WWQ)=QAQtLyG!n>MySY!U%W|)r%Uu)C z5HC`!3rfmM(sh=>Pq-2(h3H1(z$x%2kcjH_@xD_Z&OSM*=gbca^qFz_JaAI+^7*_6 z5^-&2iTG(S)>2a5C$)%QtE+26V40VdmLPaiEQt=35Td9LKDilTwsF;qBsW2Iy9P*W3aPE#hs-2TooVkbH5{oaj*{w6k ziMe=L_1`CWD)VisX#RKrn?xG&!vBs!k%|U_G}a>ZL(lgsK-x9k`l4bs4&qR=+C4bJ zSlX;$gpmluN}|EwoLovS31ld zlNOSFzsxomi+R?Z3y?+n1$7W5SMh*Os#Dg#h72THm0ghyFJN!;0xaPOD~}Wc;psTX zcJw9yqGBZY5exxG!R#5PzgRWRUCn&49}mY81*(aS0~fR5>~lD*vo&vBz6VEtmH{1Sfm#p)f!;Xl&jBW;d#{uAlEIa_q zt$fodEVTK7rf)c4kN6-S4fQFVDP+Cmdb=4(KTD9(Mfj@U^SR@#R$3h)Kq{0SGiyaF zlao-w!4ZJh7dwqw7U!!>4xi<$ymOZHo;~U*o*(Nj{v@lPo~oI($(m->X*g52<62d>5I^~s4>tH!I` zAGfXCUT{5-(OM{+4g=gfqvZD7XQ)np;GMqmo5BI`+uS0W)^NbG91hlMMOn(sS|3;V zVEP$e6HAjAl``l}!%+zbSzVz{=_tq0GG#h45-K0Z4|aZjqY;yK7OeDR1HGas1MW|S z56lx|SeIM6Z8WgrSqHbh?m_y}wHy>Og5Jc$d-C)gsF)z}vUx8<=dtvutyN-&R9swb z5JA2H^v>kz-c$ho&!WUCGK%%QuwUKO@)JV6G0o^wq-ZcxhZE^D1FH>;SnNaw?1TE; zD9sCBO0n1PHghIU_8&29c{69xLzW&^5YC{{gY_O23&kL>ik`PNmF zZ#bN#wsOQtkZUpoFY1DzS+$7cu?U7pJ zy}T6nR{g~)j&1ER4T2A1`VhKI|3^7VnL(&3r7|ruVig<5tHzIkzWjI8AkbkC@RwsG zi3F%q>WX1z7}()7qv4e|HWddiu$GI1be5VtaLG7&W~vNbk=;pc~ObaF5;u!eD4yZo1> zQXKAE$n!nGRbBGe)|?&yS|l@?LuJmj=RtLqleNPCC`hgSeFwC8RW*81D*nOe&StW( z3BHu;Xi_VU)bc3_~LBKVk!^!;<`laK_0``BeHUYXb#KZ(98?lE?}x1ran zU6zQkss69kc`$J&m!nO>A5s8Ps?$C}Fs$B>^ci_Hw91Z&{4LWyKOky-8y9UVFn{3y zyV)lGVAq;pLf4F|XH~F(7V`S=CQ(bDv^yq5P$sRIb4whi ziiZ=nb<9;FnysleIWI~hlwB>kya*`Gp156D9kQP-54O+0jtNx!cknNcVJS)^biD|= z%k*wMcQ@bc_A%*QgMH&|*qJ;zhe_G;m)ON5-G;|RCK=_RZQ-?#6~CbJ5A32ege^!8 z$;plTTFF7igIxT%u_hxlY`#S)tT={)n+xK@gII><4SN-(76>irH(?%7VT)N836ojz zlG!7C@~utZDP?5mXa-n%d4`$KD;BdbF5W}M9#PN{yXiBUcUTEjz(NZ;vR&*C1RlBZ z_C8~AJ_w7&KTcPGy>1I=ndAVgJ5ixyUY;=K&L#uO43XNewUK6@VG&aMr(}>VJ=&cLjAB!5;UydEBP!wcpNx2GXU%uGCknN1Nd>_w4D7$(YK+ zJC}!awA8I{T&pk{YnHiCasFHe!K$uf1g>D#7OQ!87P^Du z#%Q*eArX~#xg^TRyz$ChZbfNR7H;N_PH;#N4a^E>4fTXuxLKJ4U!Z)B1)4 z0^%3BYdyg9a-;fi^vjW91iU2?b|xPGI^x>qH>!P5fqYP*h?#{WuzhKTq7A9UPUQ>i z#}2-pis!*e=N3hv+P$(@ON`9P-_oy}2~e{A<3z{=#2!?4DtcXOX*Srxkq^)&% zqC;pIaD24~4gExH)i_^QmjYBj0S%xeCG_hGd&ZW~(Es=mXg-NYM_>C^4Ovk23FXEI znatTvEiL-|9#ThjszDBnf>0nFl(a0qato1{)^O3R9qMBnW3h?`&}R=YfV(bQTt+Og z-_8z9Ro`}6B;W!H@g_B)7?kmT1=T1r$n(vpiRlid{W89#hk+{DE5ysn6`W-fjR{%G z;lK7rHV5^=p1GWUi5(7-Fn%*+qybgv#HPL6$lvC#YK$3dWDat0x0h(R_p|CozB^uR z+_JZ;6I59*^;ML^Su9F;WJa6=jBsoO*T2 ziIIQy9gpB$$NPKpxfFdjVefln_P1t(!){e4ope*jIbD7v!($SaX7bfs>*Wu*G2hfk zM}h@Ee_8P>MPxyN*PvAK@X>N&8Xz$SMVY}DkcgPeka0+JCCBu92N^4FDO{49o*^0& z)SSOB8-fppBXEiXj5Es!$Lb&H87m%k-qMQdKOBK#e)9*CwO+Lc(!BC?n&_{uZz~b( zQWT-}ba(qKp9%iJcf8_Z8~bl+jURQv_Fof%cGxFaD|7vi^f= zmYM0h1^?IY|GU|CX->p%G^2l?0JwQv#Nc;7Bvh3SIn&+nY-yu89O`q6xmakO6Hw!g zq+dPsfk=hy1nYkmjTcJ>nDbukXF3XXc5Lr%3h3{yK3;RwZ0Xpyk$_{xl zT%xguQ8sjNUHMGe;77DmO}~RG6O(`_4nBRgz1~hG8P50M_%|9e*1pfHt~PFd_Cn88 zufOSV#2}h@HpBNLv|^H1;J#}=M7!RcwD+tlCnR~st3Fp{ndw|*(1;hK;=f@de!Cji z?e0HSoP6ww&!nM=J#;pDm=e0xd5Jd+`Jdie1r(CdYi*|+HuTf$+n-$#Ys+fs)*Y4? zju$pW`wuh_2fC%FCz0};PW~*8*>j>8r977@qWuwv<3mbS{`Ko(yr#y}&J%f+3-X+w z|4AEoeqjI4TAFAd@%0mA)(2agPk7^wNRPbduU2xdT;V$t8x3{{CT$W)<5GkyFgbW| z67UZ4E+eGjgf=jDYk0Hz_q!IpMQkjr&qf|Q1mJKJyjX%Ny6(b#5GppgjY9Gz2}8Dr z7nZ>S!e7Hh5LCiBxZu2~87Z@K>b_bUIR44DCc4e-l1$N1w%XAR^-X?(EVva(J#?V4 zf_AXbvxeIe2~GObOVs>E=gRNgKRh7DY=2Co>KI>9J;XZY6X82NfBl&0;oHr(ecP4AE&MIpkw577v8C)@b*X#@Na@&ZUHlh&ph_$coxszIQ zmYNe;J|TZ2@6V?X7{Oe*4YvOFv7w&`8{?1foQ6VEx0F>Wk1C2$5Mr~)Ool)X11S*| zAfPovBX#$NdSxKi#QeU$Q$9bv>fjqlqY&J_smU*km{(`qTHp2x@~JZ|)^w-M+@!oG z4=COc;J%Uy#$S@KtDlxfBgd~g0s#?!hyr1GkOaZKnej2jn7YuL)R<>r4mOtaE1jZT zQf@ZlBkV1WaR+UkOKOoX>8uMA_V2F%5N)3)vO>P#^m=2xbbvcbh*KQhyws4Q_?^Ug zc19OQS(660#3kkpa6M;cib76+nL-pWO#?kCw*{YRB*6D0kAw9~rb9v)oG$@0u?&yL zQ|IF#3%7_O&#!X}o?;inX6s=Vje?cdrBZ+#fxq)y!$s$muf1J9j|&`G+i8JJhV_ru z&cUi~@o~+L%LfY2hRvr5hdB@*qC&CPS<4>+xs!y$ud-4MoY7pi!4!!a0yw+Ciwtq4 ze8U(Ali^$e##!(#akL1;D=4@vA4F{3Y%)7w(mE~+8=&_*kqh+n7xUL9&pY~GN=ch3 z&aK6G%>Jp7)My~DG|RwFbdv{!8pH&TGvS8YRoQSHXuKzr#sXmun$- z(n-cRoC*8F?wFvz;_m{$#o6!sSkgpAoQiK@K}5$eQ%6r7O&;4C2J6v|cXEIR3-eZbriFv#$s0j5h$PALAPS3sUzEpyGuMwpPwoeb#-G{3+UhM6UZD%Aj`N7%HO48CmZwd{gBQ>5sV6j7-iZQWgYmV?I`gCDk&I2jdOb$6hZX2>7d+(*#l4$xsH{Qhl=JUp7!`G zuRX&2J0#EAvlr*KImZCDHka$6opoY=tkqdfVB<%6v}RS+J`F$XP3RM8+~OG_h3uYM zNF~ij&*$i|8nHOWuX3fxi8bOXFln!wt1IEX++;6T`MvSL7+w@d=veweZi(b*hVZ9r$-sF_ zV~OQca#9GvqbGG{0Q0|~P5M?VCAYqCShvgkDu{xI2 zG#gex^!iJkB2z**scN@VKIoivByG(Pee{n(u}P%Q86J}@B7s#5fp3-gXL+FQd)0}v z!b!H#$@P}F>1GPf-OCV8kLLLIGqK#|yaP9r(1XHsn_`48l76%PM29pcDoe3S(?p4 z8A3Ie1mJ2A!{sX#HO*NmJ|%~;bT`@^GZRw^f0-w}Gp zD+O~kMUtFPuWCXC#Clj(2Ie@#Hq3YJ{BaF_D)mSt zlD16c9gsRI8a@PIUUINfb*Eu^t0^Dekq{S}p`5sss~_Z>L2bYmG^=su1+opHEM;KO z?dLV0&mR0HIUgtJE}w+|>(sm*`X<$75vLy~Mh>J2LbWR=PAP^n$V!Op=ZN^`Ct>AF zNOPCE!Bg+NPyq}cwEv>(}xpftlI(Y_k9NVL&0E`caq_~a48hi0j_a#jydZ+ zFW;o}JM2A%?9<@v)m3Yg;I7{pjWXI1suAy;r4^f4$B@MfeetToeEzHD1+H)DY5!#c z39QTssn^nXdb!+eB~Ox_v%ph$-U3qp~o zSl=rI^;cjcyZxIpqWkhP@#%wtvJe9%_{U!_*nIgeKoV2VHCAWigFKnz!{OUaYQff4 z=NoAC-)WtHno!vPVej*O8)N-XCzMU?|IKxfkRwL31vxEbvDkF^W5JUaB`52kV5MbB z5?4)1aockpko$6{L~NoZ=YS$chxy*$f~eqBpE^5sEpLANdVev7*dxie8!t+3n6P>% zYLQ=+YHkxAHEHa^PTAt zm0S`N_h)8JA8~(LybZjY8Vky40N;F2u<~##%;$9Ty>)z1b{}uo4Q9jaIH6umJgc^8 zr1nU|LLZCSAoURJkq)X&qL~jyPk~IawL^q4NL{4 za;unborHU`d_;7hF8CS-#D9jky{7k3jY19U~$c5rfJ1U6~j~*t10Shr~ zFJi9?bpnh5My=j}QlyeD%PAZNVd=LE+I>KPJaMaRntqfdcs2?0MP?@T(5pExvXY{= zkh=vLdAvp*Ze{uzcEA5vqxch=b{v;-!@j6G8?{&}rS-#aC9S~@YdfXlMwEd<;8^6& zm`}VpUo`i0@u)CH47U6W_V1jGUa6mlNl)r4iXLdlTzU zrl#)|Oo0wt{R796W+5DH=O_H;uK{EAXe**i5_B!yz1jqurhQmCHb8~9;6v+qE-HqW zE=Zc5w(LKWHjN%T0rwZ^Y#_Hn)TREoNSb};}V6%IGEi^Q+c0qtm`>eMn z7Rl5fR=vqzS#1rmH5z+jox>FvWA~+bo=X_Bw-M!f>Em8zR9aC|v)nRTC{*n6SsA9; z4i#R;prV5QmWwtpN(R^%)a+A3o-%l?BD@9>&+g;^^DFd$nmx(o)oUSGsiB(p2A3evM3 zmDF~&3_H4}QVxRM%+$|mm)h+durAh{bQUi05s(^bjm_Fa8ozx_Y4R02zcLkE#C!s*qP>>QNY9p5pkTIPDIUc1>F3 zjej)a_R+4Nfl@eavgP1UkZJt-$jJhJ-B!Fi>a=X&f3sCdJZoNKD{k-HmvIr@iV~oI65-kg3?|?k66MY?+~E>Yfq1UQ)`?d&`V>6km;Z zAH2Bl!|urLVG&E4)GJWlqK*%WAPybR2SiB;9is(sb{9J1F(Y!5qxS>O{wsP-vtQvX0x7OBKOT6I~v?FZC$?M z$n;r_@{M}BE^X;|AM8kj<2-x~34feNJDx3tAp+ifn?(D>=nop|JLEdHS`D=D>IIS< z4tg3n^Ez=9^TaP7b04pAxb#9z&E-k0yq+CcojiuozWU=kh3?NU#=eZI1$+K!O894V z{rA`ZaE~$czW^2gbu^#@yB=xeE41HipPx2n=4Trds-ukj5$;6FRrh}00VEMnD5PX# z{7TFZc17>EY1^Z_Gd2Y#@8cOfan7J#qo;4jMFgWr{BmH)g^VIOKn{Z|nwX|TM^1o3 zjGQ$Ml}FsBRWy&SOw2XYZQ4;e`Z1sJC|fu6R1xi)c?|1&-#qGin$p4ABj-9VukO2$ z-lg>~bw~M70ya3EmRodg@k((KYXv^?`|COEP`W<$_Xgyq?wvAq5L$jqrc5$G^J%eu z#e=GzEZ8mtsvs#9Rv;wq2rC#Xc`*#pN7NGnPEn{F`Pm+OCDn4UWXYlT;<7)`4|_K( z(3s<7#)*I>6-BfNyAjhyjPd2(NnF*?RW8=phJp1p3|f9U@=jN8tCA)>!- z-poNqm4x5W-^h@&o@R`vIz)q-`q1XbuC`&fvMuv8e*E5Vv5vWncEJC&5Q5*8k zJyI=2B_+?RHrHJr^fN#qf6uis;fLOc7}!_6x*}zvW+i};T=s6ICrSND-7yF<6a^V^ z(~#X&NOWm7pHhRz8q$&u6%jckEZo5mDdg|$e$8H8dBAkE-^sr(@1I<13Gz3| zVbQ};^g3p?MLv*Q(vT9{{5Cj$`K)KMRhFpmn3bQSl|wGc$N9rT0m~QEBLSBuWXiJ- z(+z-8f-y#^{BX66w64>eX+eyQhr`Zq#UX4`d-kF3h32@Y)%U{%DSM2<)9X*}=;3Z| zl+8){gFu{yg|$52)G^QMCak%&P*D9JWvUQ zTVxn>aHn8o#m({>y`_+95p3mD&bAvOM@$MpE{J?#bxIqVBGze)o3*iNzF+<*cM<~x zl9q`K!;kTZVC1DXP1<3DW5L6qbKOlM49c17byG$bBH2I@F+_fu}^z*p>%$O?_ zZ$|-?AFS0F4!FevSP1cqWl;FnO(7E#NIBdR=u01EX}!II_wq?Fr%G^>-NxO9|9Lc| z`WNb{7s_wsYCigyQ%AIJ{JZzRzs}HwlCIFc2j3^AIh;KX(tJ?SuPkn($W1$PKy9an zOFNIPReDl2U!kril-F>Tlq~GVmx74A~9g76403Tw3zG>6l-tw!TW zuw^~^80)fdL*b@SkvRV9_E?EtsSk~ACKws0qbIXI(;`OEu5NX9Cp#?~jS8I!8bsFT zvnXk8IPC1wz{;iS4>@i>1C^FetDR7@p_3Rc$6Vko@A>5rnec6JgvG7wg7ZaFb?d_O zFQ&MAAE$Az)gU%0nR_VtqWH>7rc`>R=;5E)L|&TmE`iMTB1 zMFdeC8Gk)!i!~oz>*Z-Ujxa&Oa&>CmH*3rfpXNjhuN85v?KHvyKc0n9W5)>+KmL9; z_8Jx(-9n%Gf)|!P5WEu%jU><$%8p7{q%JWH(_QnRPvo%Ti5sy ziey;-WOBt;?yBaLd$TZ`@fA}QdKs9Sa+j6QJ4I09wD-P}VwHM&q%$=5$^#DsU@3|> z-Kw`|9`}6p>W{QjV5F&brJyCTBpK3;2|TO+L`)kVoxmFy=94xQMpg|3o_7)Cq>8?O zS?`!|m{v2wUd8>5?NDMGhgS+g@W3{fLPnu+V*-EjX`I|A4L0o*fxn;8DX9zLZ$VWYzVw>hJJ0?Ud*kPr6%up?{;DH7I# zdV;k2Zi~oncU_h#wxAiWvpz!CmJx01VdM#@WL}JxjUGDcDj|XETeO0EJ=5X5n zVlKhGi?lq*Om+;bG=vb<@m)1uKDEDj`Fo2WW0q~JZS^|4S~p0ys@z=aHf?OGQ7-X) z+t)w;8hX}k7ILFkJib0IvS(!#J+|$1&We#=;jQi;*Lwm4-hIBrfS4C8J3{kr&!&O)^aMKEy1nXFi`Ai?PTjS7Ha4v1d)9qlpVyj;3W^3@~H~#9S50E zw6ka{^#*3daeMmw0Pl4+J|cAHWreLy!D>yKY%Med7_%|+z%=UwOzwV8;lN|h%d^j8 zwQ9}qUk>(~ANDIwv?{hoQ@#k&=!5J_jPKaajz70Q`{;kwB;{-vh7q)2m6x<&<&$Vl z;=i0foOrVfxDFI|_nN+gv0q}bUxtNr0r79trt}8i85Zaa;-4+U0I{i^JgAefz-6y+_AL}*614T`8SI$v9Wzwx)lkY0SK{KOw)6T=;HWk5=6OZYerPE+%Ef7C11Fb*e6zn%%|Gpn2)#5-Y zK#@^BNQUW#(aY5iiHAAtv-%IG6Rvmc4x-Z6K_+ zMqlzkND*<#FErXVFnF3H6I6tNpJUlXOpIsR`9w6HO<;5r=4o1J>kTgO0rmxR1A{M+ zUPbpg|4@GaRY?C|sCs7BZeCse6K6RL%H^t(3VT;nzOJb z03gRJh=IUJYA$`gInBUjD-2-sZv=4#1n04~6hsC4v>`fti29{yEC1^mrX z4(%_1Q&tMPzph=z2MKTYt!;~0#$Ff~!p4MY*94k$h=N5rHbH4Vm2muySmpzn7(`=B z2C%UP;LZWGUJeN@f|BTIA_ByW?)o}G1Jl67JKQd84Oz9T+&{LEbz)$f&YVvVJh(#XoiTG%j;^>U4_^~!6n`A(tHr$y z&g$yyrciMPknhl2OBB)!mtvlWb{YM2Ic552hGZF_Oar}q2mJnMdRgCbo=?p`(+Ba# ziH$7cH1ON9CaeVNQ{Xf`IK)XN`v&d2uw*~8Hi6O`0P}&z3G8ICK-p+mTfLX-dS5X)QX8%?2?u)0*Yk> zWA4Wai@yS$=opEEf--KVxQbG!24+G!F*?uG&YKLYK|3+RIF^S zUQAJ!Jnb_bS`G_(w*vn{YDKRg(@H>EJuiIwH7PP^VJA+=A|oHpM#sTRhShrTL(MbE zRKtntsvwO9ek2NW0wi-zRS8Z5bcbTxD6R>xfX1fGND%n9suwV}YFyhGK>232!{f$> zWb5RG_9F+Io1d@QdX4CCAX!Q8w;U>obW?jwT`&*v3u9xVn(I1 zF{=43xGHgMmG^Dxgl9mXpcBGKVoJM+zr5PveKE0Ki4&k#CFN+X<=543E4Te>+hq;@ zHW-Zy;`4#(VBw?BGm&1Igwd%(a6La{Q}QTy(Rw$!zYMBaS*a?Jg=AeDe(^I`IuvT|WLU?{lX7s?wTj3+?-;HZ*9;|$uRw-1 zsu|%{xfQ{mqMBWltwKNdRv$852LgrJ3r>Q7Rx7>Gn2G3VT|;}NCv{&i!347COUmu( zUpIMe+X&&#g|{jFvee!SW=q(Sqc-G*=gj?kN7)hG@QJ}nD2AekxW-*6AK=X|evF)+uF(VtK^b5BF(ENSb~Oa*w-4rzm)XnT_h1?$ zEBu1}$}<(EdN2;4c_DR1D5eMnH6UZ@YHvLyx+0;C1jxp3)G6|4^hm^k?1(ESkbAtn zoX}L8gp)l~OXq(Tyjp6F)~;Ss{#d^1&rSfRET%Ft4fV<;t^TS9nnecK7j6aBI2;TZBUvo~|hWE``z2o`YMU$I@5 zt8K;>7?5ORpOH0eoiAOwRfOS0Xt{h&8l0}FIF!Cx-P1jdfH5f!35_h_g8hCVSr1Hz z^Spy8?6?PZFa)CHLbRsF8&mbNEK79FlzwaU+#f^b`cd(eyk)T#&y0|@SbG>d16OHcy8jst@1cUnyZK*#+A{B!30j#$TIFh*p3Jp&7< z*?v^rFhNxn$s{H8b6Y@`6o+yk);!lMMXdgRQ1*_&k%sNxW{jDb9UC3nwr$(CZQD*J z$;6o0HYS#f?|dY{^TwyLZ9bALIn^S-a&?>IP00rfGt!^(I`2hiiHOl12a zjf+A6FQZ{>U*5Nu_j7*pRuV2_W&mMp5R?lvly^O!_gCU{8pGpR%&UCx<@=;-$Hc<< zmibjbg=jIJm{LW$3$Jq|tUTJqm|1n?U^LFxpASN4XG{OnlLpjQD#7wb;ovV`P~%Rm zN5P{h2>jV9L@om9U|JLYd^b-`!z%)wOOuv)Ca}v(kyL(@J5;Eqw_Xz%x&>9hn0loH zGQ!VcdZDx!S59BW;Yoj-mh2j9Y~eqg3oU@rrS?bc=1$!O)Ng3c`er$ZT!;1cn;miV z%KWHFU|KT>JsFh!lP}xaEJ~r9JJrbx0)388PcUGu6bXBO76B1`30dJMcNF=SK~tIq zFXh0{X@{NB(6vrR$zZ=H!+QgW-b8CxvyqZWj)Vur%TSZ%U zNC>%Mn?)6IJv#&HgPP@M@*jMHo=lY%$z!-HhMW01%z?i~jrmo*r8+WRRi=2|zXo8t zTE6-MM~m2Lb@j~oggu)-!#Nvt-r(Q-Q*Lk6X~k$%DMBdALZ1tuU~IzhEdom9j$5Hd z6Qrffu|=Br5sA;dVb8sUK*C}y0t0$ZcqBP9AVHsd#!XZW|HH<{%=jPZR!nUFy0PVTz{l|~=HQR-&*yh7o7WBVbDXE=;*o<0=* z_pS0q1i-$kldgKwv-cJ&gwi2RH#&q5)QFbELI!vZc6OK`Zjil5OB79;xK!8C2m0Xq4aF7E_ ztXjb`0;Byn=GBtNaFxXgm^lhr{L3!ym76X-_0ZAj_cWzwM%@$(0q~b$jLVqJxE;X| zgCQwn5Xtz*F~7?*!_O3wn~ zMasHB5b4EW4h-uAYNXiY>AFo1WpRb8Kcfe68;Jx8MoBN6_vE4!OD?i+I$Y81)N6V1r&Axi;z1lrD6&P~$KPb3~3ADvf9x zoiCDJRa#Z8m*4wau^vUgKpiH?#4Y|kKbg-J*UW@8c!d!zS>ZEu#xr|+@oUzwUz~WE z{8B6Sufcqxe&*CQ883Cqbf}2fXT#PBm6RVzi(f=P{=t@CGrS&mIS{X>!Jg%C;@0mq zin|I$xx^>%mxV=yfs-TqQmap%{Y<0ps~byR;L#$A5eL%RWAH#Js0<6F$i^sH5kiAD z5k$)sEDCQ<0L)6wMU0o$*dvP(m+64kib9OEq?7F5s>yf^t`CA+9gL_k47C}`s1+9R z-qEXdKQhJDv>ac)$8;$qI2wA0rKZJoF(~*<8U?|$r6Vl6KQLfDmbUw!a5`jbFLr)r z^sYWdPuMF-xQQs5NU52CtWv4fILjEME8>Z*!gG)#SfVBD)8lQrqVWLbnCf8%bl9PR z1%->%F&(UQf75bsh^tsXC(qBb&X(qxSAk3*Rn{2Ur#9K$kIvK9#oSy4(6)N9No2dgX5{^=_a?V&M`OL)Nv zy7Ut=0wi?SO*4TUJ-nS#9CQdlI57RspL{Xg2ryR>$jLOK)qfV6<~+-$$oBea^P&Jo z{T&1d6E^zuUdlC9G+*>akmm-IK6EwNPOK|k8@%7gau^hHw=(yXyDFkFF(%{U9D&ds@cUaaXV zQk8LGC7vYh$lWG~?f&$zvpmk_KF-&GpoNy{Uala2{5x<7S}YYWxA-njWDFkOk)L%D z%1#7usBgkf`GF|cFL>Swp;AKT*}ZKPD(+jKz>Mh84&jSvb2AWcfD64n#@#K3Z%!y{ zx(DlEQ~vydV-8)M&7o^3opm5Y=9?Pr`yT5!T7=2soBPQ3*X$CE^g1}CL`5U*`H@LbGmP8 zf_P+p>iG{Pufs&_A6Gb-K7na39B?ZWSjL~yhD*3!1HKwS#^HtIt;(094knsxxe>Xz z(#EOwtS`=u$)!q%7hiMB4Y^6y+GN5X*V<@_ZX*GI8dM*^$@3v9nA-AANMYOZuJnLT zKUbv?^bP9G(ft7AUf*u>fx2M^zwZ*djjb8Lzs)>egR6fP`+z;iFPHOm*r4oj9~%ZU zYQ5yq2b1%Ay<3kgk?g-K+$!FwQKvrbXhu-A8lf9?kjaPkJYDS3GLql@9JlJSv`gKY z&NppBNVhxfZ@mcmP5+vQ@x=*We5H0bMW@TzA_C8yfG4P#2jsrfw$dBE;LHBH`ITkQ zc3?$)r}pB&WlK3}sjStmr7n#oANY_ub`9j5MZErZ!Fy&4jkdAb_;I+qtdj+(X?OmJ zXu{AVw1um4VERWU-#YXwG~|M>uxAAEug>}6JK0$tUmL60L7-iqd7Adp2e(VOxIIHW zQ_*kPKbnsw1x;^O&JJDdi7Bz&gKXy3uh@(4$eKdtcIx5l}Z-wC^2SM10HzU*!E>04t`@NZe zluzV&6i~{J!35$arMHkrsy23T?)FF7o(7{1+!_q{4F9SV-Bay-^o3}V*8n%l>f8SC z_dC)^D=um90maLeS6aACOCYmR;vlrr_zVG!M)W!8;2du{jLa}-Z(~#WG%Xwm)8iC7 zRe)a2Cv+_x%N9txFs}i3e}X)|x2cDa`^<+D`K)}LP74(&cYTn6G5N8JICHB2PsA;p&!vD?!BfZj zz4Mws%(+Z}?O&&JX1w3fPWFjYf(ExL7W$ElV} zsm{~`FVi*|Zno>QYWYGtcwrTvCb<(mEy9dVj#z7K8RNst0}_xqCwKyM9&sr`?Cp#f zzD(Df?OsY(Exr9hP+|f^IH2Z)9t2U%L~tVKmQ?waD*o>2m$Y;Jcof6YeKQlmRg_8zwbEra9f%vw=nvl)>Dzvoww-jcND?BYW3U(!c_hHAUJCk9}T-U z83HP3($&pA9?AGI03dvWouKf@LKckok$v;eo#<^T1AtguA{Exf&HY0E9vA)mpEgyd z{{-D&XZT;RlK<}-N%j8~zo48Fp}ZkqJ?VQWE|x>!xv7Q$IW7{L0KklS2Y zz5%xrxZ!H&u4CSzdpS+0x&1SW;fX#2iHuI99-c!SmL%8b28oqLP)e>HQ;A^G0mWa; z6)8n&H4?XYI#m0w^71yLWj&WLtAic5nj110`RBUh1#0HGJ2H3c#U zi)hMIA@Pj^anW^~g_C}eyl6)(n;;0ZU+Hq@RkQKXG>_bR?Z|G(OTlWS(jCS+p0Y$C z^MoaPnSp9;P1N_X-DyM-$G6bmwZr8ZLCj@-FM1SHV<+V5dY0PV{t#Sacl@plIbHB8 z2j~zQ5}#OOZ!BP0+ul9j-Tg4`;cHDJu5`3ifgn+$ayb2T! ziBkW^%BQ_VAB$UQ%@}s`+sv|zJ9Nm*?Ued)D+8mzyxU0p7AGgln|A24j{26;yO3&b z-fynR!>UXv7l;&Qk@TsgT+|IZE%*z164+kRhizCI(4-_`K2mGn;;Aa!mP=GMJFC2v z3;*>;#pR%%QB1Q;vO*aLZL#8fZu-zzqXIu_OS>LHIq#yFHVDRZRLLNSja%rgV6%L_itYfX$H#ePI3^LEn&R(v+pbJ{J zt#P%A_Zh*^uEOaF_wyfXVjQ1IFhgM?5dM^dtSWylB72T6b!f@hZor{Y!6vVIt%9!G z+;10K#-E?H8Ce^$7*s-t$(yksdkD>1hO$U1*EE)%+Z9a+27mXW-WeTfC>)jD@{*%2 zsvATttsKdCSo=rf?9r&Cbf3kXy9QyD_a#yaJzj$kMxD={wNGy^T6ysj$EoB@;;QZ9 zDs7d#Ww_tuA;sC>crcH2w-bC1Fbyk$ywf7vySXS6+3U-`YryZH>%gXYNIbWKVJ6c_ zz<&D=YR~hG2qh-paRa|sl7K5%9gxxzVHj{GxUw`r4_Sx+t6|x_Y3Z+4>&;Ye?7Xc` zrB>_wy6;=H<)%woW-sgT_La4F3+=eH)%K+dFJnG3%WAu)GTZvaH~WiX4A=aOu*+sM z_aRq~We)QPEDo|CX1MsJpW!||GjbiHK!p-8M|~sAsZ{}?HsHAUPmpwN-CQV4I%BUB5!(nLN)k>qFAR$F zfI2S;oJtFgNr)QqpLE%Y-~M!e#|w~^@J4osRQ-eP!?0?dj-S2gHTOhv-8{gMy_J9s z(dvmEq_QJmm7X4d@mK~xdU1rhKRGgUITEdeGXaO$YVL>6I8|)Nl-0-a=(Jkn z)#{gQPgmK#dckCz-7mNjJHMZvS~Mz)LJB24jWn*iiD_9N}4}`U-=s zjZ#*GM*0~aG34Q2x$HpQ2O&uX+HVU#jM-nZ2rB2%4%VY|6ypCG2B}xOov!mdIEv)4 zLQD@Uj{ENV+yf57$^^+!F{k{wZ1T&$@s2zvIw(fB1g0)HoVv%vCWe8O#XcQP9IGm~hC*VqM4i%);UcGCb1Y zKrU2AIq!B-Gj$cjz;>?<3r}c-!9{6s{JDqSIcq%Dj)V1RZ&Wgerju#Hq8ZIW_iw~B zvP?DC2Woq(w}QD&odg#CeZB2sf6c36N9HJwMdxwsO-1L5E>WC1aHx6J&y3t&vzraA zZ^)USWwyR2st!k9%i}__KNoLb-fxm7(wIPJI5`Y=xmV*TIyPMhQX<8dk~kE@sW7hL zh@H{R5K&FsFb78KZr;`wM#816-i{&;mwhrB z$ZXjDodp7_2jIeXgXs1PN%vd5o(H=N{mwhIFb&;51M~1`Q_}o(V&K=2gdg0E_DibZ z(x2jwgg=KTi3I~MrTeOwEooFmVxdWbgvtrpTe3PkqYXLo(rawxvQBSsyENUIUAh55 z*OOwp0S&6}*PA?_=uc|#QhAs&^sEzG23jjFJKOBCPP^NI^-dV)_%yuOv($XpD}))- zM1qT8iLZ8TS@|$f;}j_Ct*&hUZ#^GThTA}){l$nv(8oa=u)_8xCv|5l7mt6Hq6cvb zVFnz(`=6|CTBh@00+5_VDNBy&=IH_#6@Sk*gF}62f^(Ap&E_Xh&S~j$YUoVBmt=Tb z8U~9`x=0VXPIS8Oi&KsUHZB1zr`^#q&3?#WV{FDl*?~1&DE!*|3?M?N^(ykI9>DUC z2R+h2Nn#x0->cf#HJ+P$b#SHOOfH_6I8$Zd|bCX+T}6- zX%?|^{_ofPjLiQFIsRX8a#UkGetiJFM)g*a88iIe=AkQYJBsx+008f+>glw}SJT8Fv7SXb*3Q@){_! z6dRz*;1IIvX~Nj=;cW>}>0~Y)GY2k3sk|hiAlaRFz;C{>4sE_mM*W}u6dTL`{-^%` z)YQM@-N}2+$lX`9vx!vNFgH*+w|#LJDaw4F6k|l$;NrWJ<&%XfMP_Vg`d4-=&q)GG zdm9xxA_*YaA3{${)jkiceq4SD&D3?BmQM=(I0OtCdyjd5De+Z^resI67De+i9>h==dNw z@aBsmtLx0&n+|j?kHRlRM-`j-PvKeRXb*8v{GYWRd}<=EG35U?n}~ zNbV+i{&9O)-Kk_gg}kM>nX})uKcWF871M!e&2f(IKaQHKKMQWFpvFyXAST701l-8| zQdTnSGr8o>Bv7gdE)3SSSJzcccIu9r9YbQP(^4WvD8Td|x z&H1_>u5;AUz?UQKqEpuQL*NB9wkJqaPT1kRHqaukSY~HJxRsNEQt+Ve2neijoU~Z` zfl^(uu$-F7m`f3vvMX3QPD_a&)~QUjIRL>824~@NB%r*$e;9-_Rn{iCifE+h&sn@X zEr0NvG__DrvQjZr^+ji~e8_p#5Msi#c8Fy!Omm7q-SIlM^J(gkEQ`&-(~oNUqMS5e zNvAOB$ z5e)dJnS9hSatD`ABF>tSf873?tg)-`dPq4FeRDkDn%!joQ!J5nUo4CR# zhTyRSz|noQz5P5YfOPkaudxfbn~-r$LZ`nY?_D1!(-2_#=_gcb-uU8S6PSIkUGi|| zHPb2B^8_T0^0XFz&D|EAUd8Tgo{8R)6QwBZiE#9a)H{mZ3#9!uJe>Fye&+bag&giw ztlW)poREkKgn zk2XJg-o7zue-F*$DI`*_{k+X*SO##j3Ok>Fzp@i(_R|aLN9->c8Fr1RLG&_?WuaT3 zJ5Yf}AbOfq!7+I*?O%-ZmU(<^L#OEyYDdVR?nKSmGH=U-Rs@d;G8N+JezJ}eqGO41 z11w=zc@!);I%=150}Lz3hjZ&YtmqpLH!jJ{kSC%~2-x@?MniAVMIcRm?L^q&k1UJk zQSmu@LM{$Y?|D$#c0mRh2~Z0Rm;T;5*xO-d`iCleaL=`3bDER{F2buLwNA>BZ1g<|MtI-W5yX58ozx>{4(XL?-W-G( z5#sjt@o@tsz%1G9hm0a#ew0W3OkzF)Jv5$(pcoZpR!JaQGFu=Ky8v@%LHX}!FyS3& zSFwQKu7ivFE67gnu6QwumkqfQLdF-!B0sHzRpQ^;FA04T{9BKu{CI94|E;9L!JH)T zN||OJ3yOvx7niT4l!H0s-42EFLnC2*|)RJn7f(|%Iao1 zY#y;1`boO$3n&~-`jAm%D)9DNWK%P-sP}TbY}?IxXS*ASuHiWrat9?t%1*k7w?ciU zYF1RWChU2@s#Heeqwc$Ht-R->DjoVtrY1FjlB66_sx=T8gC5>*dPq+-DJq$L>2d$f zTR^*b=numn&;7@l7_pNlR$UzeKhBm?_fidOv{k0+9rr37yvmn^^# z*1*L#26h7!g3YK+u;i#XGvs)h$Xc1@PM0N_G3x_Np)_LSEI)9MgzG1HRl{Z)yC?@M z>dw9_GJ+=z=%tEpQOzA&w6=B3VXJWpWEYVU4})zHHliwY5&v;Ja-mE_SXOxe<+MT}*gt zNM-a1B>LH~sQ%#C5N}!} z6Pu#;?T6|wp!O}s`xLZ{JWt15Bz7{VjjhKZwM-VQ7YHItAu-Hc9h@MMqc1?jfz;;= zLJ^t6X(j8=8lXNYzM)l18-}tAYbn#R8*h%bKL=Gsv)9*@YJP#BQ*-KaGqFgePqcsa zoVazx;67{7ySBrcl}H|&ikwjmE}o>-ExAchJ)+z-PZ)_j6I?JYL5-ptuoxAFOUo?& zvG^S!T?acq%dm-nI%gmgc#Q!PO;`dFz1O2JLO?$WSAhB)uYkyF|BP4`n#z0uH`M8Z ziiIQg=EZ1!x6ZVX-v%KaYS!k`0-fzhkItPUAYlD&jH#qt<(5iN{d#k`L4f=*`0GDy zC>;NR*8FXv`mfWKP3n^NXaA>u@|Y4F{aZgdD;%tjS$kY9MsJJQFf|Bf1FXA8De37R z5Vf}C2F{|2dT~s!57-ZLcuzY#-r?z0#bxnvdpnPR zkN!YK)l=79_*WSOOhgR^6jk=H^{m&TXKzwu5K5AjKdBQ;G+X7a8{GL#jou6W-J*mM z$IZEU@@vwar8DbKAs$nyeSackT7uSsgFq5(t_-SJulYe|suyiF?)SKW}kXt(3$u7(A4Vk(f+Z^J|0%nlH%|v>+5bV z5iL?9(#XuWsC5rF_?4?^M|&L|iRd|sCK%`%3*K)i70}&Q>Zo{V{12iGw*f$3rjmrc(A^RpwCJJror;OqV4-sJ4NIehd{C1dD2xol68+*YiPw&ohPm(87~x}B^!;6c_~&x-NSvGfCoHxydKm*C@f8T?cZy(&`7MgXi5sum z5{n8;)&)oSqpQjvoKX5x79@IISM~U}uhg9$0}svB%7PfA zV^G+9Q(o~66B9`K?;_;v!~{0is%wq~ky(vW!0Z^;{`i<)d~Id5xw_K8!bhR+GWcMl z&8vF6cx{q-_i=uN6LCU7n0O*@m`<5m4mA#+;)HaiS4Vi##>H3|TSF$88!OBQRkyx^!Tls6Nh|q(oRWL{^j0UI0?AZwMPzu*ef>(PPLlHQ95iA~ zZmGXWneRkpb4x>%?58ku#Hza!SX5BqZGPwlK%}Alg;x_uV>F#*k~L{5dbA|jBy`do zQZsq}5nleBh%R<|&0JZs>M;&tw;^9WYxB=RYzVv&7<_n%*eaxIPv^`8HR;fEHVf?M zH|BuDS4=z^?5&W`B+Ytc*r5gb?ztocFh6BN(ClQADH-Yqnz$}zfLJH9(P_wTwvt1P zH0^+D&hN`8&|gw}>!@sl@6Ga+PG+Lrq~dIpO}-xk&ptm>Vj*gD$RR5anLNObN+;(9 z$_g291P8Db#<})L;Hg{tzWWm=kbtAb56D0tSiappv+2m)h|52WF#BYmQ6y;)4rXCq zlxULb<0(KjCP#Scc$PiF-#n%gTba=7QYeBRJPpLmJXRW0*DNy|Sn}88YNmUE=*j@7 zo)XL_^hJsMw)tx_f=jsp(BLCb4?~x9O+mvFP5vH z-x3gkBd7^MK{2V4Gxu8ko^>9tdryZQng|!9^@iR=VTaXEkGt2y$Cd0#^^W_UR0{RC zkIP4{zYQNJAD>6&ZGI zd|B_uL&yAkl53%M#i`LZ03Z@_O3|UvhBeBzt)N24pfIVUi89049vi%vr%{ZxSnGej z1kF=CWEdmPj)@tEst?H(X^xPaTczk|Ekv6V!=XMZa~ro786AGfq!t-WRlIJwB+Se1 z70CO{S;Vcv)=3JY$lh{L!JVf<&)7kXp+=ja#}WkF#8!})Sg>OQJ$VSpdEnstKBsoMbcIG# zomD8s$y|!8__SL94gb1pS|zS9F>hXmLV=umI^x^(>$}$5$t}-R&x5qxalDSvwSkc2 z#&xklWY%!wt-1`S;(hP~Hb@g`*8jMB23Cr)qRom6{6p%CMLq`1jnc5;Sh1BJ5&r=^ zQqH$b85u~*SmBy^ivAT+yoAfbaWh4oc3>mKWvwWFaajbIy8|^(ly1>=rSRu|?Gx!* zL9QdM+6SS3;rwas+Z7X>vP!dkP|^o~O8P&4?nXbYCE#dS5qAk&d*LFvB5Ggey4QYi zb;!A_*Cv|^Jv-$(bm&vKn}wh5!@LKY7x8fUGUp+d^JX`aKXF>S@R`RF^lI)w->0Ep zpTJtc`&fZ#4drD8tgg~qDs*~zRtHkk9bu3Lhwm>2eZE`)iXrh#`ow!rpXPsLs5q4o z;)rBelfoTN3L9^)7PLXz)|9M#K@-7T0)oWg;HVwsKji(gIkH3%x_hQCF}v2UFc)X8 zFxl{D>En9cKY|<^2~1}B(^j8%|HG_i{(sEs|HVIMVr2ZUFB1;5B%RmT(Ef*itY)P} z)H{$TgP^-Bm#)n_FPs!iJkM6fbduz>d%yGqTF?rcA~6!lJ&(%1y|Y8Rr7h6jsx><_ zGh^ZVvGcxi$6Sa(7{QiBJ57)I4L^Pn3M3QC9(oztmA&12cy&upn?PS;0&Vwk|D=}F zhn0pyH5@&A)6G)XObiz^*KF@9Ul)+iw*-^}v6#G*l2~K9yW&~&Acb`qwux&o>0%l2w*Ax*<_mvjGtec2yZPmjge z`*b%gwtR$({YY(`V&{uHyM7L8F5cW*$^DkNxJJ+!K%pSMys%ho-8hf-;v z78`Z8j(4hoErSQ&FW;+Xp~#YQ;TJ1uFqGPx?O!FyGlyqf|C0k~42MR9M`7#_3}=y4 zr28d{EBZ8t^?ScA9LD`@WM!}~gy1$!>Q(!s?C^8qu=dY;X%x!GH27AG(Bp|kA zSrMe*gR`fsBV$>S@4Fy_8J1;fbLz_=rt%BqC|>8!Ct&jcbLYaXr|3Mf5k|WDLw6Wm zHq?$+dJcf+LbH<47N6L+JQsI;dkg30*4vLjI2P>_+}$LMG+^IxP5Z1{|B-^po*Dmx zgK45Tu8b^dRfc_wy`I()EJ=22jytH-rgLXM(0DMWK`l1;pdjx0cc`AdT8^|(?D5(t zvJRwVD_5X#L?$*@0$wueRnSaE8>lU5<^d=RpPo5RS=L!O(4s$t*HXzUO7dofJak>R zHuq0rm#fDo1?^9i32`;J1ohb7LB>7gB1!22IqA>V4YLm2G<|sH?3r;!1EsjXns3fd zF^(lW1#+T7AifbSN|4OM))c`G@wB(w0}*3}?ZDog2F?{NcL4@cjv#{!V#fjek##u| zz*VL;DKaC#38%16gU$GWBw!w{(-%|ZnQ=`wyd(O)Lgs08{Q|PH=2Sb(fLxH&pAPx& zso}zE+k4q{U5B1{Q(qOSZT~C8>M=!U2Do9Nk0cI{W|EW6s#f5FNTx5NbMEpTEMX5RVPcx1w0Mf4N;)|;$yLMsgd*F0UU~!qjo=Nxc(qsFo|Ku2k zn-&JRGMyPERqh;_4O z_%d=P9^k@gr1^V+P$>sRWywBJG)9I|hK!6Atiz-DiMJ9bcxLg9CoMUU5Hy~}Hd7(~ zdp>uxsr1OoUK)--*ArD%k@0(abe_C$`HRj1-zzuDbHn2bhDHq4q@iqHkKLoQ#A(c; zOs;!|s!E-$yBM{CYHQqtNy|ocq_R5eanMM*$&JZuL#)@Z-qa^M)q2g**9S%v*$>zH z%wf_vzp6SIt{o5113qHgiregZZAt-(z>WPI2VE4ap>}I7QSDrtD~t`;X}qqfykLja z(`bi*#g> zw!N%?L;X@Oj!h}S%pbske2`DAb+m(O?)pA+MyKs>?=Sz`s_cn)G*CD*HwqYUG0i|$ zdacYTx=e=!0S-Qy>n7}^-d=*Lnz4v+v^pkNk9mxLqKZZb!hmcfAACn`xFDgefU<&5 zdEn@@c$^Xbf>#FW;JCFTpC1}5(|=#kS>-%eJ})gCFivr+G_p8M@T+M( zti|2)@kzJ+LnR-1eJjmUHI$#t#Tn+zU(%6X18RLRWA0db0ON*SsZ(0$gC9N|-hKsV z$fJap{n%tw&DTb0z_2rvBI4lm=7n>%<}BG|@zt&5Vwv;hIZ7zxD+9?e4{4|s$&nS~ zRqBl!{nF?L$1scy{h~F@prCM*4}q0sLg)<_%V^cO?S$MphzR>5KDuM;(WBhHZ_yva z=RP+=1LPnB?F71-yLt;iGPdp?bq%s3cg#NA8Cy(R^5K-hdTgLPW}bIHWoz{utarGU zbJ^Q2b|&cg^7_8g1EPZv{2w+Fmj9&GVrJm{ui;7uI^P?~D0=ssIsI35hisq?lA@WLFZY}0=Ro(eJzM3jVZBM%Bv1@3aj165 z|Lsw#;W0i|OiJ0~&)Z6BPiW#J?GHwpN^ZYCu(xa>Vh)rbRrYG5_(TbY4KEqVxa}P+ zt@=Z9j9-}wq>-G6QxA*$!vq897jrrjM$M!`L@}^A4ud;8m)$+)BY*`$aJf;!1qhNc zSK+@&6`oN3tWatF(BLdcdA4>F)*agZuFBPvK_ix-aMf*|-?I^Jo4#~F;zH+Dkp zhg*`3rAi%yqHyWY$0I<~H=0T8clFa<<&o)t&9=E7+RDXI_WNGx{->Yd!}~=4rlJV! z2pkY74y@IT#gLY}dH>*Q1~(E=hO&jVo2_Uk;fJ8Q-KttnR}s%g_>KVh0;^%FM-o%7 zcnZTmnoaBIROvmEAb&}dTxc@9o5mQ^wLt9%(ZJPcbl|@G9Qqf7Lp{JAmi=NPP+~wMT z(_Ken>2E*O1mY11e8qyPpV0JC7KDT1wt73P>%b{Cnw~X_OEX?$ZS~?q921cuu}?5)1mCGBq^DY)*`udK;9WhJ&%UE`r#^tmG#j>2x!G>b6@q@+g7zJ zB`SrZ)K!uijq42ei5V;r4u~716OqpZwBM8dYkG(Cz%8h8j=*pTSHN7aNP87oGv~8w z_(=*u$)FVLQKV)?f<6|eV*0Pvnlz@fRex!-)*IE#K#b~7>G0CP6wOXB+2Ghc1OeQ4 zm@I6lm|#3{xHA=eGz3Hj{2E`m?TFX9$i%z)Q82vv%T4#Z#gQ~nN8*|hv(JjcXB^4HIK!k`TnokOw5|?{o1*^X?7wA!%Q=l(HumSfNNftOywLE2*ik;*7=# zFa1Lvq!;3OA@T2LncI}zpR+YMfZEQPw zQr2~(kkoDkz@8g2E7q(5aLl>RF^O0%*1Z#;Hj?y~A4Nk=cBAdr8BJ^4%P7Uxm(E(6 z98p20y z6l@HdVTy-u`bD(OS`=!VzE~(aodYlyZd0?dd&)f@B~On1x3rQ@9a`!V!4!Vz8H*6USn@~!);aOkSyL-?^TsaU9TjHWa-1s{%reljx$!K}i7m&b*g{9xv! z0Fq{HXPme3!g7wMX|=sXY~dtHu0$Gc+mQx5EJP|oud6a$lD&T4 zz}I|P2XGYF*2+bGZhU|!$D&8~XsrCg#sma|!yuc+_#O9CnOD1nOR~Vg=DjUQUI#Ki zEs5#*PgU(N6+d){{6`_G=MZtF08yr2Uedkje-l}#VHolX!cf4T9}g#B;>XGR!5K@4 zd8(0yl!c(C#7KCk?tz^52E8W8$?jmK8p;V`!lebk=b2$7&Yio;b#%!coyi`31|E8h z{?=V+o#!RGubCqojvv5$zIyXv>|ru*vy^*pvvF>eU)p&CdTXf^CwZAxYCehsU%7@% zjBH?Asy0pCr+xk$t9M%%H9<$Dvu+1ctf6jCKs^`2C}J^sQW*Iqi3jBE6lB(#Y}PD{ zUs`TayPGb3u}DZ=O^9*7&ennwiGPa%z3U)g@?g>L@*9l&uQd^`r}1>F;76V=P%65v z4f{rYdOVjeT3)P}wSu7uRA`@#&4&I=#CJpND$}UJBbUp~g#VcjAZR51YT!E57sC~N zV7`JK)ZijU?~tiFcX_rAqFVjuKW>86Z6z?eB$x)l(0t$DVKIg!S!!0@(Jhv53bg*^ z-NAuVawxcWKBEXu5^-bv>+M*Ia!d!?&`tum;C5xK?yo)Lzz$|!^v{Kd}q0ZGU@F_!BYIWTO|E^ctFhz)R7E2njxh#Y_*HfPE z%-9pcd;U0bzBsW{Jaiqt3@tf%e`uCYh3WY(I)nFawzP!X2+g>oxAJj zY<<3>lStO#2;Ct?WVIke?UT*mhqgSk`z#G;hujBl=hcmx}vcm|t1gdy+7a*_N+$KnV+8 z9|)A?04gg6_`ha$-O_MWIV=}WX)nErBH5rcz*)R}%jjhgX=1BI!u?X0>%L!q-@Mah zFvZt$9kH6=Z){gDMpCweVrwu>_{e(c)H4A3IHGhZc5Oz|oo!QuU1UuH{6hrG{geEs zaMnXY;SQ0jQ0Wr$cGk6LJ)ZOToD-imAVVSa=y2*)EZ>m;VPXq~0bvm@-zJ^-GRLjo zww_KhwfVMaMTpYFqD#hs*c>hlBW&j)sK)G46kI%4L!qaWjyrc!6ogwpkBau=)dGkz z3((HTrlEh&mCV@5SGpQ~W&vLP3p*<_9@{?>C2!NyllX^Wa8SqdKc+uUmW@9Fardr_ zZ%r>l>agv~7spM8`w_{7%Vr+raI5XXnlyh+;h-A*C~rwj*z9Hjb9iez?kCgyeD-lK zT{y7e6a1!pvRpBL03XG{yZ@d9;!BmI_@X)#^Dwjaj}L_ejAy-^)YU#27=}yEk%+Le z6RhBuHmec(8e81DvQ{3W2;iE{-OSQXoXi$=v3#H-!0ty&tsdzZB{wFuj?R+M()%+-)IU7nyY%XKZ$Y*5Z!m4ZseV>hqaf!3h63u36@g`{k~EfsQ3E|jb^3nx8yo; zX*7apbXCcKbsL@IR(2^qCGLAeq6^7qLLR;)BKvr8RP%ARJ$y%G!#GNPricI187 zKUB9?^yQ_(0yBb;eDYV6qkv&o^hURfJFZHuyIBiY1W}1_3^;>|LY_f+6P3(}ffUQ- zTr$`U0^qa_E4$VFyA^fTuz{U!<@Na2kygj|ZLyv90+L))$skCumynL-)zVX$+42Ap zc`V?E7e_cEg5AZ92L6Qp)x=r1F!_4U0o&?lF~+9^^rzmD%CP6a`;Oa;?>jH_8tF-| zTV#thVo`-3&hIiUFv;Ka$qjIVY@zq5opgiEB*s#|k?K*6WnB6J^Wjw*<``M_arkW) z`y?5EFM!IjvbTbMgZ>*9*hMEh z9;M#){&R(e=Wib3Xlqz2i?;T~7rNT`NgMx)nB8W*rl>YVuTaryN_5xCWM_MdYZZuS z^Og;R)}@Fy@z8prTK2T~4wZGxXem9ipY4TcG59>Mvn1I!S)NO=vu{gRRT1>4vl*N> z9+fF55U$3rU;Dh@<}}TwDA+k|k;mg_RFs+Brm~Gke@g5d+|79zWaFkAP*^z3cbu_* zfj?r==>4bX3}&YPJ>|#9!17-|XAFH?xYyW_y57{UC8k3dy7{xTnH0%$o6}EIN}-2~ zh^G~b!j0y*db)qoi6S#ma@J_)!hl5|>|U%v2e7;(&F+7|^Lln`Zm!dn$N@;?fO#}a zk#i#4iGWiWW;)H9B>uUBQkzw$?1TRD6lLOw@lTykpAH5it_7e`6UfL%NsH}5s_nvg zgAP+>P4*(Y%ByxTUXNdO$7wg+&4uxb+4!%iO>X?X4qX_w4ow>a8{^d zFl7tual}42@84)(tzIS)JZ6gK6J#1Utu@TNXc8^q4o+wDaYN@Tl;Cd)f1#Q=0d_8 z#bQ9egCDR1u$hBA{m>L8uzJtjfT8~?m2g;sVzBKmn*FZDO*}0gB_`Ilo)$T^dIsD|*Hzth^O>lTr;E^S5>RAX?rNXi{QLi)?45#ZZM%QX zXvMZ|+qRt*+qP}nwr$(CovheSRb9rspaxpD3}AMNQ;=3!CbL0jVisUjCrQJPcafiBPA%&}Z3tm#bS zAkQ!lFro02hok~$w1@9C_oDWyHxPd7j%Ma9`^!n@XxS>~M^oBt@bBu)Kfl89aF8hKqRw zG_$%%o{@kA8x9Rw8s-}z@st&o44njAw1c}X&*{h+dORk=91kn+7}8+K%#n4l&$^&l zuQr!}4%o$`@r1sQ_BMpG(m*T=4S#8{gFH{4BRBO0hy574-*;lS_YDN*ET}WB?Kdc= zKGW168X_hQtBf}o2|vaY$=@%D2fR955YkCayjKjK1jU}(cLn95&0b6uS>kIw(UR4z znr@ox&zbwRnpT@8l}4%+r6A|Xp}6;IVka&3fX|N5ZJ;9_M1Xjkp@wpWZ(V5t=LxRk zsUKRtUo)ZzZ${@E2#xEKU z1{dopQA56UwhvPDQ43=^Cm!B+zI}g;*ON^7ZyYpc=6|DVF#h-5jA;!SM=UnPf1Wbz zRg4JCJ@H9!JI&ok)mAF7l1F>5{E2zYDu3jq6jPFQdtvl?g7@vLL^cA4F)%?eqgQKn zfqxno7}=i}C^UTE_D|=faDvlm_#0+v+SVrj3|XWZq=Hx*E1xcvo@XxTToWOi(7w^Iihb%#Z7db73cr(TBV*tepQsI9_^XntE^{abqN28Y9eowyMRp!fz=+{#7P~%` z^7xUJ)_$*wuVB$sVxi!L^Rn}Ib+;*EYB&p-B%9!u z_ihXmZG2zLGDvlgp-PxS8w*G^X9%bc3M-=?YB?VsTsNJ)AZDPaxxQ2Be?ldG=;UDU zaZRC!nyqT6N9datJ`Ia$nsELd&g;TWnfT|*S3W6Ckl>AWD-s!M+AR2OT2m&zQ!tg- z%^EhX6c6yTiu|+O+f1{5)tVqvvn11m*BrCYx(w2YqLu>WM~698VzX=%Q1#JP9qJ_= zXKHD9haOor6XoAWuA2lSFLcvKB0P( zshew-Iz{_|lhZSUVo0(VM_)-p(E1I}6Rpa4;%cw*Ew5TNFQY}@=wx>O-_pCj!(YgF zDKr@m^~|HU@8{n|sW{}K@QtaRdo0gTr|S-F>^)-C9iE-e7s#Y2L@o9Y6hIB^H6Nu^ zD>dxF&IeZT*-$pb^Uxi{EH*TMH3-dnpO}eMBApQp(T%hQXB@FC4~=^zJd%)%Madz; zlnWYz%(CD-T4QD>4fEIugrNo%3;kI(_gu%FMaBKgvVEsqTQyTLLoEfHrK>Mu z+gj1wPllLbjlfkfSy*bAXh`0dqc`!kY@}s1iMds{79u_AiaUY6J%yduZ$vUM!_3ib z!a!JjsmrUwtMofPFmiR{>RM{Ok&6 zDlBSgGUeqaEt~?fh$~SP7sRSI8wkotGKIUb6}w=%gXa3xb6|6BfL4Q{(T1RWbV;z8 zikj>CnES};oBa4GCHe!5Mj^g3DI;d=Av4D)!i$-MsJ598=<^cvBB*E&`t9$ote-RB zQ7-(xp6xA1`TN_iDG|#SSw}V~eV9u4qC`IlN{+0`!RGrAfd3jJPCEMUNlet{^PZ#H zDn1CPG266DaLI;avbR!j)xptxgYuVNUJW_qRKadM|Fx0y+TLvol+rkU(O5c#E}fqW zW`YJp5sD7+Ch+Qpai?GTTR-<=9pQf;Z#aOclztBeFpAZuB1wK)qpkCYE0^fn$?F!bCazPd)w1C<#z+kCvT6`!7#lq<1nQl!t@9-6_#pMFWQ^$jn;n5XqlWZ z)L&;jwjj9D&@)PwY_!js>(ibjlx;yA>C%i}i_T6~@O(383RTt70p{Te^J(NlC#C%6 z`}HkUK3l(DhEKM8%BC)XKzdIdWh6Pws(vSXq(j43(}GSwK^;IOP-mtYAsp*VO}pGJ zAF$_xamX?bFn7TZ+f%>pyu#%u%-X84YX=WVoC>cXkao_>J$V5QcnuEnUW*$3khr|U zWGcUFE^HBQ(<}PY)~2q<(Ka|h>OxXNLwC~s9(?p?Pk|^Gv(z^ ztF0gi@#*vswMuf01bbyc?H=hq7=DrL9*=qETYTHIez0iI7f38s)H4Dydula3T;uY< zc|IO%J=Z6h@x*_((NsF{x~-5fn;5#4J4LxTdm*}#x{<_r383uafnl!(s;Qzvh{>s? zO0kA756Ku5hek+6#FSNU7I75{@+d{?fwL5nr6=5f=Wgv2WZzQ}bs&HT`Yg}phw6%j zuPdK*cZE<&tfwMEkUOu6Cs?{-4y9)8*J7;et?t4ar+0ZB9zL`h zgN6!un_WR|@vUyH`;5#LHrxE{{gd8<4}(g}#WY~BAKUIfk$1Ro5*Yfr0KT;24Iv70 zlZ)!AqT)KkHfg79Q@{6eaK(w8)&5E*f(*n_ZBq5ep5BDf_&hvI!BVTdJ`zXL^=9m~ zd>0QWcV74JF-09G+aWX@B+JZd zy=jvf)JYTS9O!XF3}_C%AX&)&c_m}a4|&Y&49fo&LZaZb-qG#;i&r-vnf-6KwSNto z{r?EP{#f8_Hbs%Q->KS){OlNS!~$s-251*t5b!rRbmm}@5aNmhjG|g}cbTvg2#@l~ z0Rb-)p>p@)MHpj?oAg;D5dne9k@ATQ>J zGX@T6ONSB!oa-FuC)*n?<_;2_qloca%u^lDxL&Ycr!WcK!o4s_ma&(E)Na*Zkb)x$ zNf2X{_JBAgFh~$b6r%iXG%H9i6sGD-;QKCy!!*BuKY(kMP2{W2;!^yPiRtE%Gtf5>s8|FMbz}xB2 z_V>e(Oowp1$QYzIJBJmZH`2t9klXuj8{nNzUe!M9s`cgA&}mjZ2Q2oa&|aMIUOha? z4%}^9W*`{LB2w@(`z4G2yye~xR!sX7oD(t9>5;EKzRfRsEGQ;sQ;AeQ5b-g^eu=8t z5k?Y3NOX#=EcPcT#d-vFuE3bSV-tB|u=*N&52-p){66vh6wy6oT5(!hLjKbs?tyTa zVu-MI`SZZsQ`N}jzZU8i9{Xlk(^t-l6x0tFTemWZE4*g84xA}Rg>R9l`lh6$Y`mQ$ zr=Qz%C$|_-#8Ole(lqi85X-%B=P$+rswoVI$M!gyhAI_>jw!5z(%xq6kF?5ooGBJBB%LD-Kxam?ubl5Onc+G%t}B}`28mQad86JT_o@f zhmcE6-;=4h7Tpw)oVOa0rrf)+e*Q<+yJ8oKLlXUI8Fo~MQ54{sCQ~m|*9$8hrNb-0 zvyty;{0-ibkY$fTJTGq^P3C1rD^J2mIVakNe5;8w&R;hOVbgmFSE%ak@FXsN%MO6ypmu>+|l+X`zz#&h{5Z|t`{Q^#jRf7GuXA#@~bHDk2 zcIFsZnc4o^0DiOD|K6GVr*rhfpLs53;$gPAOqcaEyHHB}nNO#1B#Va@El8w(?}P>; z@AEfgji7}C0CvIIe&X8KQ`p&i`yYN^WJcQ7v{93bNm40pZJ`JfnyV3%3uv7km}qy= z(A`vq_Pa!qC>0br-F+R4t@Zo?H6IvEsO%^Q!}_hY?9zF?P3g<75Qf;ly^H6bhk+*# z-zRSfi!a{v5sh?inhD^IIyI}!P+h9}^H0lM)OIUmBx1smsq_S4#DFr} zVCad7H3Qu2wR{q!8^o9pqlVRk5lTf_*k3l}~gxgzXQ4+yZl22s4Th3b%*fY62bc_+(cgvK$ImT~w|-PvkOW{{Z54|I9o$P2MS{nq<6K z902*+9=afLO}ZdOb5v=Fp6nldJ=4U8?0CKlm_76t@@hy{2D~kDi!000wNFwk~ylZxvqRC__YOWEd7qxnu;MzD1~94AxisU{Y`5CfazvFfiwG$5KzVIKw$fI z2nVxbki{7wGiZ^3NlPLoTP#~QD;z`Ej6^qMM&RsQOs6;iZ`aXRZROB&iQIKWS)_9u zcg@wu%9PLUHD5|)OPtAt9*x+LWZwA+Qjp=>`b6v^ATx46AIhbdZI#`sdw^ZfZ z$oAFNI*f%2T+XRsE5{x9ZP4L%W=ltMf`Ps@ZDPp(F%6~x!-3$=@36|uugK(`d#iv@ z{*JDl6WX}@($i+D3#ak_9@h#*7w4J4ZtO2K81h3CJV|5);{)^@TSpC)Bt87C9u2&i z^Ly(rv8|yC1ctF8)~1S(xG*ItAxe0pCm$=Jg`^_b`GKrd`DD_h>>K;C)lOXQ47Kh` zcA5JoGR8(!4go#B)65(=>-rMdu$GVoPqBI)3}#u4w3HN2i~VMF_f^Fl;@d#QWNdvM z=oLU9`%aI(xL*)A9aPbV?xu`skav;rlY+qiZ$Zy9yvc$rx27)R6 z`9u}~w;6qMfP~q;GtU%PSG{_lVe zBgg+>9sa)oYtw1}apQ!%JRo}jMU($Py8d5soP__#aZG`VYL@|3RkkNlrc7jMrUSNr{AjBKufSW(qdgth9 z-S6+Kt5t-WGAyw=tChSp3i@Ss#Lzb;mk&;n_Jk0H@YLxg%peUScFRF?;Vf$n7z|cO zrC8*bU&L)JMJtb2$7$e~Ur-8QhLBjuG*2us6!CIMB)gv@C&*|^E$fS`32iLt!#H;q z8^EYMRqLZVk3t6g_B5^nG+j~1Hk{(lcn4)TWXwGRHSdU}VQ8=YrD=?qJ9{XJi;56? z+XQ!f58Z|M)n=vUy_b(Rl#Jk+3V*ax0=tVT^V2>zC*zI~|M_z6NOL!YS))|NvLzgB z;Z&5MM>Dj=;0CXdjZUO$e$H*Vxnv$tSb7GW&~^r1_qrqDw@2Y>IOxTx9Z9}lYY-js zhN(44i!K9=lqn01^up*2lOUZffLQ}f7+4CcB0n<4Cn-6&tp`ED&U%@#u?=4Yb!m4P zMUdWRnBdXEPZGB=l(+cLk7RL7xPs6jYGg`aBU^Y`$;dLV9v(rLIpwE+0x_$*KBH{y z(~_5G9}l5$wrsOG-dIfu7!v4#KcYDBtQI~UueLU?r@PB-+PnRDG}E6%&OP_?;B6`0 zd#>))>~p8EQvG_4PS(xhxWq;dVKH*Gp+o6yF@ZHKFtQ)veJJ3<=&Qw?SF9>}mbGFn zJ@hMHr(8T&iPMwJ@Sb1)^;P6#q-(9q`y=QGFQ3fjYA4pqUAj1+4G&9P}q2bvhlpw>c%!^l#~Fia-rR9G03!D`MT{sLz>64r44wEP{X61w1wq5r`Ue{bihto zkW&q6aJ<+&Ov0m^MVz9I<>)ac_a5{Xo*}hY{=5ZEyO&B;?0NxOw43`?M?HeBWvlMf ztB9)3m1k&t7C|xvUGG1BMtx zoKb6mt1s()3%LB2IzL-3$=`b`cK#=OQ*2*^O^|5QhF9BeFu#4NtWksSdZYxHkYyaW zL42mXK1Vz+4$dERdv>^}u3p7R%|E}?*ROAh77=@{>MUGe_s1L%=OUVMhJ^!MhUn`^Hq5fD#oM*8(cK!^1{eF@N!N+12z2(;m|Gv1O53Z()&-T^BSJ-LrTJ^8LY&MyO1Wb{L0J|L zlTTc8M~kaIZW?SP{1wrwmM?NiMGe4`Nn$VEGaIkvHpK1#xgMz_{_TwamMUWSzfki3 z)fpL}2I%2MU%n!+67yF(rD`O8_e07C^ow9iRx83&pMQ_0p!T29+<4>l<}+J6r%BPbaqW$KDs)b46G;dI4@|T1=pSz`RU=(dgv|Bb(+DO< zC(-V|$-7omwm)@!$+n9<5SjT)N2{xE|L^uuWbLk9dmc7L_1M9^2f zOXDLa%XZu*3t_yrz(en%WB!4m0*olcn5vb=A4er*nVsD60xGsuJDP_WDS2JUkTjZ8Qps=LcdxW*3MkJ_4o)eoPqoChKR z330Uuub%%EYxeHSnGM=v$AL7_fCPVG+D_Y2^z$HTk9}M6B?Z<=^aN)c?o}o|gL@OA z3qI#2DB`{($>v3ToT5w_ZxNh;C^a%8B-a5Ezneinf?>x>xIMVnVtk@_(;6vJ9#K-j z4^eS9#wr1eH?%Y6y*6^ewt@1xAx+d@f$9@p1$>KeiTd<)u|U-lCaJe+9?Kt$N&E+% z7J8^*o#4EuF~y)!Ek_T@B&DVGNx1gn~i8AwG8+kGRH( zk!Mv_6xfhSp6HYvND38o8)p@l zMO6s0_zmLonQR%B3#wV$lG~!Hji(vh@J40VK{F!(6m!MAO ze4K2+T_J@Youc4tmzn|QS?9P1laG{qojtuc;_Y!-))h5k8uIs$AAAyV9lk+^KOhWn zpp@n|OCgZ&``=o_^Nnw^C>Y#PdK?N64~DHN@Yl3uK-9qt9_k)-i;T4a-Xeht>rF18 zNjH1wJ+neDUJTLt>OP!-5Qrqs2;aN@hjk;7ka0f}i^cuAc{pTuN9p>Q?vi+1 z=^yF$rMpsJgJ1m%A)ULUWHEjNE>-m%cH>v|p6E-F&9PivBqED~eP}P41(28#_Y?V$AXb$- z3LUN?*ss?#7#<9+6V>SKZCfLz_)(DJ4l+vJu`kgY;j*>>`==hjbX1<9Bl(pB(WO3- zrYeOw%CkCIil|7vyD}PYIJ+o5mu468(abBKfxK4dxRgQV_xc;y2pQ91i7GTs;tv@1 zVW%A|U+X-rVz^X__55vD(gWe+*QbI6urea1v;v2Bzkoj9h9^l_!kKUhCwXqK-fc3E z9hE!}j%7a&?l?2Tz!lSYJ;#x)AI97=TVtpEx&PvECBgtys`-YwAMYP6ia{TAzYX%n z*e}CcwfOgHljpjR;bxFyM`f`uSkG|lwAnUcISuRlSMulqz}_ zz>2&sB%$uCey<&fv~4j)F)4l`^muKZsY~%v-p+m#C)1ekkjH=__d3UpY)#y%*N{Pc zCTCNaw(_Y%%M7A^YUeh>3*!DGd`TWDxX!~lfw-OPDHF=1T1vBEL``6p&2c@m8MfC%it8B23&X$I2^lzkxPSlo{5O?b>Yv@e z|D>MHEePEBOg4nhSHd@CJ;OM&%@=`*m{64@nx4!?zI&jkMG%?ACuB<&BPIIhXzOBs z4DR#eS3$Bmy?NOuu90YTKWajH(JV!;hFAK321=wMoC8sr)HbBPvc0pr3Z$*W`Q)vQ z?erECBnUy%Um72;_Y+~yFBrzcjxYytQ_gn$;FEoa1=Zv zh{oz-FdvifrsPmDWGiJ5uPSO=kFMv`F{k5Q&1WUArETLc$=vIAb&c0W_lD=n0pK&7 zC9%P;%R;NB14m9hp6(xW&>*z0Fv zNYId+zx=cCySKLgbS8;YY#{QH#ZjEZmqzeZ=$KqM`vk5|P-;b3RT}w?je@V*BWg{R z(GCnJ?3Fni%)a36oAI-AicJ1ZEi!HkZ+;anPk)R6HO6hdy zo^jdPkNMfZY8+a_ET?Ncba=W&QBz{%(5|{qZ`hNA+k7)YZ>AD3&1bbPb>eJbS9oNw zao|6N#=~tfwTc*<#`*)R$?f1s@=xf(?KO zugXAi%aU!Ig0yYMO-9`(vBG7Z39S!hcMF15+weK==Jx27ZF}#B849WIr)sxjf9Eb? z3o3(Cydd5rB?c`_5Bg3&x^HTiHR_7ab9dM76UIf%KmIs8ukZ~+PpesqT>x4fLwJ+Vx@iIt*r3Ko3lE=NyOh4WN| zC$r>!XT@<7zVCqF4UmM{$-;uYY13{#4SeZfvHrS^QOwW_#6)-YZXw19+Jk2pMF%7W z{UtxR1D+0$HHo7=MObzr+u_=Q}{d^b&WMe9p82BK(ir@LRyEn#;;G2jDG@W_uRTPM@ z^n^|v7jJ&%c$D~kc+smXw#dBc1-v%eS6o+Eti+NH0In?lR|zde-hXZJvook-;_5LD zWwWnZA0i%v!XJrWUAZ^GSQ3QXz^Xv+_m2ba}?_qOKX9e!^Ho9QA_Y>%7x zB2+o)^Wh5ccC34KZ&BV@SuyGp!v~0IyhW{jD{wi}irb-NdU*e4UJV(JxW@TQ=ihJ? z+;8Z=1xxxA>DrB!;3bdLq{@XP>=dNd%YO$kgxcv^Z$73)PX6w2zww4N<{0+!W=S|a zu7z32Ve7lH-vL;SJ%*Y8X-5#K`1Zbx4K%x@r_c&xKgyPkzL2L)YyCPvUyk6%kHPwG zyDJGjI^uNT`lj{_JHT0dQ@Q^ARl)bjD2T6y&# zzZ<`;7g*iK-e(+VcNSLSU9jr_rKMlyx8p8~tcU&E8p4}>;sxRLF_CzGII}no1CU;e z*?<8bEDrx0fvjV&s3RfSw67BgVvA?dx%<_|D{(59K54>5g+?RC?VbEjCcRBGJ|Bzh z{^4PgY8ZU4HPl$k`=J%?$S?nur|A`*kOolvTqZ3z&e}@F2dVZ={wdfLWLX+F4wq*t zJQM?BE@#iUrzS{RDqP}tu>Mh0kt88x1woa@LV~#;;EIk>L7sIaD1=n(OyVWK6FKC` z#k>63ATlUrmp0#?qQZ6?yK-)2VK9Y4HwqK{fIJqO;awiv&o=ZY-7E4)6G0YWE-c3| zz9Rqa)^`m+=HTyK-8h7(%CpMOPUrfmkB^d!=Fl}i)3$m&yTjZ10-g7MgS;bS2Cr@+#2V4zr< zg%5|wj}^}1tby@jHBQs9(U%3dJS3VE?McsfAdgWPil2cpV@z_=dG_5q2Xt(%>(}zs zvGTTb3t`gX^m6HH*-a>O87ZBe$+K3qr}FVEI0S%pc>NdTuSD}ouWW6ML%G$!twC)`RA9f^tPi^I5eLYteAvHpOmbwT&zaFv3oB;d4B+5t-8Qy(K z^|@Cfiq1%;RbvtR+h6d8iR$EKuDxJ`A`UVEa)dDQ>)1Gl3ETmKbvL$D zalIXL+b)+@n~Gq`qzNDGo`-{nmb-z<2Df`9V--9t5dEzzTwHI$t%536pPubdfgYA4 z#GWR1OFX$n>o1zXwa%;0nt3t$K4dOrsYgjB^77#biz14vMj62t-%807>mI=ExMQ;1 zvM0sHA!h4`1h3kcl8WhkIhOEJ4aXvoE2d9nD<+7@c)wjnd6JGsjZJ*-ZJ#|xBs-qR(MoNp zx}uunnWU7)zWC6)4%nle9{$yck)<)sSs266$H?*)eF)Z#BGtoF^{(z}g_KRTpKb7IWgbR(W$5bzviJ`LI+)zC69G{(*?mA z`e(fnU^g@33IdoXfWg@(&xL2Cn!2ov_BEdiVRlZbijG61$(LFU;K(1X?*~8qijGKdoc1Q zoRVCwzS)5Z;_gpyf#$j-;$7`%;UR_q;ffkn-nC#)|C+tz;nY1+E~f~m?SFEw26oTIc%Zv&cA%k=|`2*PSweWl4xVF1(-2&I5TeoPC@?4Oc~&nBEELxu5SRs8L;%|Kxi<_tBu%Z<|aH#vz^!Ssh{l@;E(e| zUR&6&!I~Oa1)`>avDxH0$+I!E$d>sSN%AZc)>Jdr)AycGJx}0X&U=;Al3QBjb_ibW zFx)K^_EEYq!Q)!qxd)KY5a-_jnG;+oM>Tf%b0ZJ^eOv>jsdtsAF|*BIr9VZp*=R`XEMQE;y; z+nX)W^HGw!HU43^CNl!AyL1uDTpU5Y+o^Q^g-XDW4Zg$g*gM25x3=jmJyt~E6|PRY zjYp_IoJJow`9(VXVQpe*0ErB^woKP@kCAqlKmUPz;;xm@xRt}C!!EJvovn61s11Ni zu@CAiYPju8IPn+{Z&fq$Iwz1rq_#qk`YkVH#sz{kC!O;tg&@WR^J?zH);#O$_Qt50}BT`ihZ?pe01oW zpJ^WlTr;ipwZ{-ZCSuL1T8oGM!X|Qk#*I_fdLE|Ov@Z0L+{j)YLR&wZ5l&I42w1FA z$K(otH%t{xJlwkb`wC@~Df2WvuWw6q>$~97$-@)~Dzh(?^=tc62>>@}6Pg$&{xRxt z*MS;@K1yKoqAmzv$vnNIH;|wkpqlD(!U%$f!2U8 z`=9+2JeZ?M6r~iIxO{UfeB_DeJuU~;a>Y?QD=RLvm!0Z0=Z58M&D_2|_osJ#l05oJ z7~1tCLq~%bgwYK0-35xq(cm_RYu8`oj_O;l97v)j+H}6YZt2!~5`K-RKT7#DG+R&h zm~-`3RJDE`nf}b+D$2RGj>3K%qe_V3fQZv!^Zu}_K{TpS_Q{`}XO$<#sOg(go?sV3VxTz`UKs&MfLc?~ZC(TwVw2&6ez8=zsi zG5WU4e7{z#Hd9r+O$--*TfPE$Y=T?G;LbfKUx_QHayh^+&@Jz`fw2-VuHP*ULKL&- z!si2?z)DD%0D--hKE}>Gf5|%pU(*S6h_!geBy!}TP=*$+tXKo)3E0` znr##ptS^O>ju88o%-eJ9ndC(9btEsCe4> zo6Lpm6RM;4xDK^9D#fw~aAfNNXMKLVnG52})hn2>-%hug{nSfnCYYLMV*I>^gZNuS zl8|e8xij(Crc9ZaC4nRkWf7elJ%0Zz=%3yXCC~Z(#`6rJMO^b5UQ=(; zC8iDsn*Dey;N+4Dd%VGI(kL>42&Cab#66atWTw?s4(DdjO|2LlOe_e6dDt-};YKlf zh!sdc5z!5pxm9INtp&3TS<)(S#Mo$yNi1u0WP!|Kf{dj$hy&15>_$(}6)T0bEKGdX zY*G2rK;M4(WJSoIU=49XVcbKI;{LUWc}^K+-mu7G*>t1|$gyry<=lddevk=}#klCB zZs`k*MI}Xf9dHJHP7T2T>OwuY%h}@2c7C=KU)t^dp+Qwa$1ETM@8tzm`E-QxVP@2- z!WUrw72KDjk^!~Y+?GcanTSFD-QR{8}7X$~u8X zn~f$50T@bVW(G!OTs)W7)X0}X0)`oLJ~@b-uaIhc1woTL7BIlCjQZ`JeZOcH;3e$m zNQl23Mez~8kV*JF+nMP)Bfnc5~C*wLr|I9yt` zv8p5x<2z%CY5pyHyzX_#=u}3ZMKCy-=tQ1FbYC_Dv1ySs9U4kD?M(}p+Qy?U!-L*I z!^6{W%c-74;TMBLT}bN46Y1s*SA}v!nZa>+tc^tCqgV_FaWCJRpBYP2zildqV>Pxh zJYUC1?{Lh6{1fh8C))&rnx1c9IXIsX9t72S9ZLoIi#O3zG{YB00ESP|A}k$wTU}Rm z+s8xDPWXX5Va9;Mou9w!>Ne}uimy9)Bqt7WqWrZa`B<#9G?ud``*Yf&K%~Mh#Yz)? zJ4V}!Oqiv$Ad1yRNh_cm#~rE#wzU;!*0>`EuTuuRwiZ05`i|zMwASDJbplx)khNKt zB(-v?dcd}t^9JvyJbe#^kf2}R-UkH?h4YccZF9nuZ^a+z9GZoIL4_YTk3DpTrWYGS zwsl-li3nPX?WDpd>d8@3(hz0cQ`JovjDB6}i7~&oLoY-(l5*o%kCK}pNNfZ^ngFSk z(FO|i$(m)!@eY4!vWWXQI-zL8p zFQL4$J!U1on8dG#3s1lImZxkO12cHjx?pHSq#kN`tQ0|0M zc$bsm?Wab!v>IjiNnplmeC5t9x3O2KeppOBlD6kLcZ$H2JIC9C#%V9~*gnFiZE#Ta z^>kYBQ{D6}&}=AovinX3QhTBOUFxoHW!H3nw;LVoYubeXdgQva|`(1P+`NTVoc0Ca(A9a1==8w95SGT`aQ3;CRnxD}}+&h!hd~qamT$&cHX(;(rd?{n8#`OKd z({5iSPkddI%$g~OK>(baoz3e68z56SlRR8Uo8;>)^`dfChY>+P9Q>HNqbK}F3%V#y zim6{-c;Wo0Bn?s!Niq^NN{5y)Y@9-qqJ00V;@;M&{o(MbA~YXADDEf=-A=4AuqtdX zcIJ_ZGhubp!)k=Un(OVTUug1pV;34m8@?RN+_4 zUMYkceK-8Y_nIn;N?6)HoT3I>N7!N66O!?a$ws~co_3Cf*2JB&*ECU9mmTd zEnk2IxI>*Hj5$Iv8bb3>=GS74ZL{T=tvcGJ_O^4b-|J_)l^UuYj4Bm_L_`1x!Bac{ z?QTbRBl9j_69|nILQj9X-VWuE<@fOv)&(BlkDO72`!E=`B{<8dK4M?8SAjI2;iM8JVADpvWqEZ0jskLmM4DG8rQ>0ujs zO=M@IPrN2lTl;mk)jO*pBt?D;%#u%EV~M+}ZqM!kh1a?s7QOhhtY1ALACrB2>%#<;wY7CKke?CCV3on|9^WJW2uQ?QSXpgzoj=2*KMoaq z!C`f0jCiwEN>EI6ra290H-|4UCe80a*hAl$ePR*De(%r=jFo%2;=^5lD))M)z4WVw z?)vVC*ef~$cVd88)Ww~OV>hbyHBJBeEhaO))Cf02qLiz4sulIK3|T`_XnMjA=m2A5 zk14p}@)w4I_#t9M=m9k9#@M@_5Y%P-+*5U&0edz=!j!t-9Ux%nhHD|0>QN*=+RCbu zW#dcUA{VutqHt>o5lstm~Hesv_yZjCD{6($bfD2^w@$UArrkDcqsd?5D z$DM4PnT|9J!OJq>%>0Zcql$El*&g1ye_qtpi@8!2KWVzVS>}w9Dt+6A&R0l{kM8#G zKhB4{`v^f>zNtv_%ZdU}aUg^VqPi$KE-1pur${c5)CT`@j(Q*XGz*HFvA;^%F zY18m(Tb>uQ!*BiWrmeh7LG4j!CI)P+Z}!MMYYMh{~*+oQ&qi-1^ilO zmp;7?F|fUO3gq}eIkX=wLFWjl$AnpyfgY9zDy!((J;!K)U(@A|O! zPu6E4Ohjz#+g%J%S>a^q0hEy3sfk2ab1*dV&`qM8dm2T-nV9K?Wn4_s`y?6@bbbj$ z5a$0}^6<-5dWoa;^Gpwu%;&*<+?B|_=Rk$tXDd3{RMK#&2u7_0jwca(5?DXoFd>EM zgIb2==+7OCHXj!QNvr4}w&NVukU^OOTg5GGHLzpe5&{%96?FYHAuxy`autd_na9y( z5cA&J-N9eto(`c_&rX1WuDs${F5S_k*Az2OL( zcEyMw{a1m`9&qG2S|ic zA3%knYL3H#{0F#X3Kl~uKjo>ut+?%UX~2I7J#(Ogpwa&WJb+co?c=zgJD4fpY^`lC z>va!%ffO*-CR}DHsoWS#!$66_*kXMFD)q`t`fO4jgav9|@QKu^9J*}bLV2hL_UsR{ zPzm4}NnE_QX%9Gjs9x?5QcrF$MOgk(C#3gJ!I^AUowi|%P0Q~x&4Th`IW6o3&HRvg z&{!lmz`Jtl(c6@mgnPkd<9&mygpiYukP3ne}Re|BJD6;1PA}wshGxc4?Pw+qP}nwr$rg+qP}nw#{8#U*En-r|(Jn zB=0YHvohCQbB^&0&5aK;bgp<4F3GSCjhj}D!~Lkm4TV`Xg(kM^jhbXS(d2kfU|GSL%eGs2Q`X6^0t9@ z*zwKRpTKi?ICDn@zuPhJ-)ns?$ymd{YI)u_woO~W$WM0H%X>URH3O}t%Pt>6muh_P zHOaw@C$Ces48}g+D%QqFB;o-S@qC`wb7fr{o?QcYtkB-Mu64k?E4yHLx>D!z;XR2S z^&4hGxzXNh)lUchQqG1>3E(|z=E{N_*Rl(fZYAK}N9+>tkj!VN^Z^Wl^0>+rBG!GR z6^sbMQd7kZT0jxKGKt;FrsU6l^F;{YQVJtJD4;xvM%?$PJLxcK%l4r#tw21Raw!Nx zvdFf51}0aOB!8UFgHdu28f!LqLZ!a9FGKh9&%s+p14;_Nt#Vsu*lT**XyxiCAt$W3QkMShti+G+#jnrut# zuru5)kAXPe!c*FF+lmh!C!)b-znppQZ6`jT31eh!W?$!6Tj>*59Vr-T$af_|RMQLk zJ+A}c&RHM2xE=q-5oQ6Ypw=veADE91xmP^Yuat+xvBru$Y%q`e+Ksa&VZqMmN`*@A z0iXRMe`_X1)6gu41ZhVK{-ZF?LKsIjdr8@!RA%qYu2lk&qTVD9p8jKUZA;F@sJiKJ zz*^DRrMbH~zGGkg?!A+8eU8D@)8j1b*#?xI<~!+a##3^CeS1;Oq?SEJ!TR~sn|J== zYxzNaQ>@vhqgcu-iRZF5fV>imx`Ljco=x+Rj$jQ5t*A5Xt`Yjrlb805Ac)dTJfcaa^#kpoV$AXj@H*D(8# zypQbabY+O5M-!@LWrt>0IRmu4RWwpbB?ZClno|LsoF6i7tx-(*%J!`aK#_B@VWquZ z@PNj~3j{kv#kASJSURJE{sg0m_Oi+5D_Rp6k3O)OI;E@gcr)!>W46|_jXxf3QN6HL z?7r4x%GxR^{Yh=f*bj`uB>w$rbA`GkD?osXXcHL5P{`!c3AK(568_Nxm^268^bc(< z6Wjl-Qu+5eD*xJtIQ8R+)?$U(no&K4W3Cn*p5ef+t{kF^5W)!!x&v?`DUCP36thdNxsIaL2Q zs`82dJ_ETp6R4T8+&p~9oRfA1u|f)LDctzxItLPSK$Aq=W(K=5GA4?DfKet#81fT? z`|Oi8jlvio&Xhw8$iJ810#h-pXaB2^ZD;t6KUSm3z=sVrX; zCgh?ab+sUtldL;LQSArRi+n_>D9{Kr#!aUWB8cvs0_{|!465x^Bp)I- zJ*Hf49LqY_9MXAzlV2%gD4Cqmq970t1G76J0gDZ-47qfVoIS+pAtKo;u^rZRJ2dQ{ z-wRbF;-=~5igFz8a>a)Cxs_vw{OW=)5Wn+>e}0$=T%hZEyh;tVlir4wmQ{1?0yNVF zAMKApLf7{L=fp9vO^F;H`(MWgX`?tZsXV8@zc~*1FLF{ zOE|n}w${~4$Hs+F=t$1?jjvC0&-#tRpQx$l`(uwB8k+fMq~JaM%vQ+*qtdVe;E?!| zi(9`#Y+o;YsZ#iQ+V~U`S5rCA;e%^H$BXH3$#li5YuHD%HqTk3(QR;Od_JCt;dBo- zVBHp38(SUjjjIJ{w%1n%>zteIn}v}y?(dJOY3^^w7Ji}XmyU}s&7AayPm>R)m*?ZH ztBS3Sfzm&nx-Pz-&QAkVACLXkcg;c*T|xO3npt3S@S(8{^G{@y91RBR54~)iIsKro zaRLPyl*4^15_|H?(=lsgl=K(h1SSUr^c}j-Y1{64e4jOjBrk?6r=MxCK75mCy9>@P zNKqe<2?e_XYZfRQ4)T%y_S8qi{NF-ktXj(Sc5_qNk1kqq_inO{~>{bF?&7`bd{koG-(hjA5g$s9%=U z8^MMtG>Kq_i&)vfj#=ufWZIc)`=V+O*Xx6bKS(W<7$AFv_-j>yXws56P=KTI^(LOf z4{aF{Ql`4n;36~sLTl|Ayl`qie#)di`^o6~@vfXv>J63f*T~i>BLpm(ST1jJu;HI^^wQUA|o-ee__dcm&wg2H;!GqT2iFZxj(g z9SUk_-8jupm#h^z)Vt39vR$y7QU>;=*u1G8sK-=}@(!hUO$ZM=oDP0O(8snw2JjQLiJ30b7b?p!}JUx>0M-CQ7*zDPczVMqjPYII&Nz(C2lsuaAnH6nW~bf9Q%K^7vg^}WZ6+Fh zifb0>+^0GS&@e0k#r3io(R1LuIW5-&0A#0qp%8~#sT%520b!{O7oO?N_z6b(K-JZALyKX_d+=)LO?Oz~5!yo*syomteK;&BKlO5^ z>tG|}wEtc(tNv?y#Keq*!+%yD)Cp;}uk)>vzEOfm`Vb{wu)n6E-0-t(hFFMwFV%Y* zQu@91c`>-Dwd~60z^>1@(P9gzVuLuE0;XAzI$%X*jjwHVL~Ia$le*R9bhl2Y#YsSb zTdQ(6LC)OJCTy?s<}mH%kmrigEc_Q~RfB)xI)=F@VXqQekMD+Q@Hf{A-}X90|JB4e zuE$@)Jp*`QV&%YrFZEx4qRZsql+<2~R;CSk!I0e^BRh|*r8PkCi1>`^eED-c@1Gw; zZ;(_=!Bcz9B5BN9jFfBrI#kS(`h7ueFS~bzgs^>@+@cHX_t{6AVKm;dFL=N&G4spX zY!Jq5h)}_B1DTLTJPyNg-9MK`Jx@E?HGC;DT~c#!7dGs`2rwIoJ%%wA&48q#Mxpsi zZY%pp#Q?kI{2*Q7!Lm*CK^|6qyG5+!`S3O^d~I#cW1hLUOU1 zG=01f3SgPT;PDwdZyr7M^@wKt=P912jZ-ie2WGv?SBeFCeF+VU%kB4veJ%1LHFF2D zXgK&xibLRl_G}~ZE_BlkPeS+$Un#>9^v>oU9MRz5piJ$_#@6n9=KvA9IWRMz`fWApMv zG*w$d*5KDW5Qw;Bbth-K%tj<=06v7D8;9f8BO1(#P(hv(B2XPK%1gCVT$7I$Tm zNjsH_Mv@d(NBc&V&(t=L%1GVyN@jnl)auiXD{uc@G*$Xhg4lMIWcpL}-v*NM7jIV% zI1tsV7{8V;cZ`bSvuAH-FQ<)Bi0gWmO;ou4nA9k2lGX$=OazPRD7c`0hW~`HE4jR2 z*mMzq(n(Svt4>Q43GGraA*&#+!?s#m?-4Ru0=)-h|kl=iR{FVRowY!HqnD314fU_~URb7b7ri^npI@ zK40-!h6aTHt~hnHDsMKqh^8Xyme38=1~Ou)4kosAYGnNF1=j+ats}mQEn_6E5l?}> zefV2MCa0M122{Bd%Iwsq>b~-sBmpc5wi@tu+g97l`tR_riWG{lQSg01Jd1*+2_Wx- z-&{vdQz5ti06RButI322l0Dd&3azhEP6kjIw}CGQ)u-I zqHrP3Sz%>eyf!B@)E4+z3uAShY3MMMW! zb|2KNX+hMm+n;w&xl=iRx7&ke;9)Dk&x$}xt>9FY-3Q(Bfx0^fbPS)3yLjK4A4*;Vul7>wH#40FE@$8f|luEIFE<*6n^l2H7E?^!nw+|>%*;7Af>dV*t;Mn;5$QC2Gvq10sbEl--khP)H+r#dy$dnw>-ap-W+(3E)xUhAi&B zUC~*^V*V}hN@LFEI428p# z+l((=ou}B5e!qr`RYu$;!FS;dl`0Qe&J#}C<_V{z+T&3|Tb~ujE_xy!2Y}nETrSH5 zopo&hNOuq1%z|87$(ySbNQ4!o>4Kv2VvVFaL+(%qH8+F7nMuY#N!7{rI0GbsN)zX_ z5umgcl0f#$D1=lSVglS{l9q~**`{>i{r#-zwT;^UE}{ydsFi+^IxnOifxZxwww&y{ zsM8(XsrqeSKDLIv)BPq-;S%r8&Wu(mW(iP?D7a_9$oqUquN7DBAEgWGw(&;R=4vg` z>i5JFa+3y>n~D2Gb5ye-TmnP}auR?i#mF(7vR@aPqG7CcpsG_3y-Rlb&gZ|q`QaBl zM3?OX$7!mySrB3xPzLvVz`<+NDv+y$$I8~UtZ6t1i3VDFsA&;rQHR&PU!CnF)44jo zMpsrBje{!t7yf(GVv0zH&cu_EL~449E?Ag=YmUGaDbGvFMb%w z@>MgI7t}p1=qa5gfKVdvk6_I2LrFI`V%HZ>W0El*J4I=DdXcD&M-(Tv@DCo(U3K9d zHE7ji@WmRGhDC}XW-$#YrZB-^9`{pzsUc zLL;s3s+L!o!j=+X3PO~8jlFEg)~&-#{7nPL=`EHg>-K9&F7rblgzb+-$|dQUXf|n= z$#RdP{UeOme#EZ2;Pr#$(tx4jrQn#du*XQg{x4nAMHJEC&4fecPl@FD*Q8Vid#krv zbg&QeRh@u`422LNXWDm?^0W&?FnjvrpCRFMk&m$06-W++*ytUOeNjw|4gFI~mpc8y z^}(-{d&=d8jaSD!A^s-^uvl0oLgK3C%!KcMua|UP_4UC1>010T68{g~7ZdycNy+^e zChBM<>DWvUYX9)4HHzBCJN>+#TVHvuy=D zz|;B>Pz{Fgsp}wtn-jzc4cP>VNrCDF@TEtohsTmruBY3RV>#-4Xmb5#31MJK zy&W{bGN2&E3+Dd?f#@OCm%)E>;O5>ZETN~S2*e)h9Y<&Sr@euhNBMhuIPN)DY!^za zp3S-yW0+8$^TpdjdPRSBTiX`(4Gg8$@xaUd)`syH&R#+40|sy5ixqpRU$NB|T7+ax zrHK8?UtJKhKDj=&QB3N1Jz)d=OTTxWoWH<=hcqDnaE4gu{z2-_!1&*^f&ahJtw~)n z_J9Sc`=y4?K^@b~@vYcxRgfeTlZX%LQU(ug^f0$>shK2YG5#|B%r}Q3!Gp!P!(W|g zHlB zZGqf&8Czee|LSK`o3r;6-AH6SAKB?kGx52|<(Xc&{uYUM?%0Gz#g4j!tLxbCzXgP* zz|&)L{CpAVo%FSJ1QjHIP?QOJ= z@+Vfj(tPy=qa_~N2aBnNLzL{r*uO6a9>4|e&6fNr?s#S4bpb_sUKQS&jQl$ zfw-`QX1@@HwGhbXWlp7)Vu=<@bz~Dg2?$9&$n?w3g6^C0$8=Bj9bG0V?IH@f*i|{D z&^sr!ntK%paw;Kx;N#a>Uv0d7B51K4>N5|u7u95<&ZC7x9Vin?Z)S^yY;$C3yfwTE zJ>nM#UVv!@0}F=mmqGgSp9Iy9ZXODJ$M`-Cvzy~ae}tF7s2uG8P~EkEl;nq$_>J1= zSH5P!d$?`qss&p@s4Vgff)u=`_@t@uss!fJD8z5~6`;fYN!ry&cs3Jkp`Qx@$gt5r+@GK#Ld{XZi{*AZ;Ac9Tn zj~dpatbGKKk4SrP;VmWSw00!Hzpd*J(aX49qJyZ^Ed1u=1;-MIxozb#Wp&=QBa=Fh zdGTwo33M@o-OL_T0HJtlNp4KMG>LK$JQYie)H=o=n`&6(0+%Zowe=`V_H7!z0AB9% zQNaH~j4lo*))3Zt0}U^>EfupIGdzDjXQ%Sm$cb4UJt&*)FA~-C)Gi?!qPBudJw7`A~!B` zeJmE}U8Qhny_w9Jem%(d>gz>ge@x@LkwZgz&RT|Xts5K zngHt{F-9>nfV^z+7XTtZw2ni^Lyr^ieFP)@E>>k3iedlL+K$RhfU7)mpdU)B=ngyd z`!>Q55Fo&NJJl=Pfhdi@yNKBCU#M9mF6o8og>H1MKBo#Xj#k4>IfTVJ%W{-Dw74%} z!*qRTIp!^LnpePxYX%Hp&LoFP!614#bAs5pnO=ch^CO?$fo^2`R@j~fo9zRZ2qk1| z=+>!p;(+nUR% z7v56~aCl!GdDn>hq3{&ST!Xj_JWIjIy{V&i;1PK4jO=I45@g?&6V2wVVeLf#T1m*(m*J8!y-tek7}>TUi~p(_`^dBm9iWGKvhr@v z7EZdf;a#VM6{v4SKYggTcq2(-*bKIw(dL0Hc?9g!2_BPP@?neapV)%k5p)e_O~r*a zU;+*4>6eI*!u7nwdf-B@xS6H5SAm#Dg7d?;Rqj1F&$x{nZKXrk#8H$Lz<2>~0H3;e zVRgJfd!ksp9tsJqUvI*)$36hS82>$yOTAs;0=%Foh>Vw`b`o+*(=ZSmz+5m?6iv4G zqb8{#4!V?wkc5b~%9$Xh3h=JMZMKf&R*UtA0EXs&-a=n=buTWR0e+0xs2dnUlJpb3 zQ>#M}Fj~B-1h5d3U&G^fGpYP!KPK8nD3`Cq2VIDp-py^Flod`7-S8(XkrYY~G@<|X z1amUH3l;;Z?lh5^$6*B)ifrpk19&!OKLKkTl!jteiqr1xvZRRW-ZXXdm6(@1ZK;Jt=>{3wHm2q#S&~M%8p*7)=XFlK8 zRIv)Xn}muUC92#@1x7CQt1RB1Fy!Jb6q(x+kN%+)|BNrchvsz>?x^7tCkS5Z)&0!K zhmA{}%{(p$j;ub&R%`X{1f^wuM)-Qc;^aoVX1<=&StU`?)D4%XgsrBn5qOQ@?5nJx zmbLf~+BrorEDNX9FqUH|8&pJbf1=_qihM?lRbt1xs|2x_#M5HJpc;Fh5^%^^;8oNE zQHUrQDi?C@LA&0kQK&2`C=+uYxS@41%n~AdrNPM<~G*Z2l~$U z{g|$U1v!~YBUUDP&Rek1t6cQb&0{6o-I1p%CL$`LX(Qm%9uhxYvg?}RC}(=x^wxLO zNjQ4)5BTP&nA6{zOm94vF4d1}x#71Ri|lutlADrf1Oh$fj{B}DJI6aN7KNOD?*Ww2 zc-pTonnt=>}w1N-7H35w`toa(##rjxYZDE#M z(f_IUqW_29i2u(~}JO ziN#(qC6j12rfUvV`ZX78Tg_^iWrdv8S$*r|L#;AH8$}d^PY5C%A^rOY2}BHqEtDi4 z;e4Oc-o@Fw+=xlz5vk!yu+6AL(x%QY~&(QR?g-pYaYs|Z8B$Yh1rV2->nIt}qB z#0654H`_0ydNKdozdC4vbcSP~=PJUJz&vODCp6cJ7|v%6vzB$PJBzQA`x-x+}BmmcI%{5{}>XJdkt7?YPTr?{0 zkm%hvaH6VEj;~iK#Bq1b@yH(Zi-&BqGVyb>=#w>k!<;r)2I$k8gNmAApUL!n(PO6F zzvv;~H8)q9@iaPeO0}+b3*N2ujb#)8WU*e?K^Udr`BF1C2TtnPgHgsS;+0e->#WY_ zaXb$ZOMIDE0lM1(l2K5oN`@u7_`E4qd;zK~DwY26X#SI6mY(fj^DnOc^DJmZ?4J1< zx#~n=b_*$}AJV07{n^47LrVt(B1#M#o@x$WO&}cO-umWI7M4iyI2E-;0|YuGipW3L z#;XwPUZr~7AHc@V>FM!&$i!<@7n`bVFtC5A9ff5K*1%Awv)l;4y~YvML*yIJD)KL~F8g2(wQYZYv)aEP@A z#7>yT9AB_6MWre*%GI&)e*1ul<_LEbgm{ms3=0EFd9NiBGEaAQ-+RmX9S*In>b&1LHf5gY`XPeZEp<5sHAnxY_%)Zw?yX?fCnoTv9K*St;k90geRm*)jLqR)!w43Bx z>pU8R>KXM4-;>5_Gm@5!f4`5q7OpC1eZ2}Dineef1=hnuNGyCI3@W4H6jI%!NF;8zjEB1lJCT|XVMNR5|nHN93dKTywur|y9e9?86k6FXybYt~2vB=fNB zk}zywK&+$$rC8cFZ!q~di5gk0R(ypHdfUpcJSyZv2vDH$+Z?ZGLLW7b z^dfuUEX`GVi<|@r$CML7YN37<9LSF4w7MD7Q#)o6U*(d$!1T>+o9-4vnHC;4Pnb{+ zo(<=y&*n8!_5No3ChuTKfLKK*CdJLJVIcUx!WVj(i!H~r@`N&dD3!3pns%bdEOS`p~lG?Xbutr8+Ia*8~A6<^=GkNU5Z zp~1rkgX5VT#01=m<5m9~0!f10CP#!>j1i8RhV$)I{YH^^XB(L!;OUgmf$IJ)SY3Pu zbI?kVFkd)Yd+=|UwsB(cabiD1JRW77yMfuC0&_9Z99ucT!!>sG$m~anPZ{TirM3kh ze5+JffAjU1&m_1V@JQj;YBNY*yc9ZRbhd=%D^~?GPpCrRu;+R`?!a+a(^xfT=v6zk zuc~upe#}8LV-o%Ej{wD^AfnYg_#7{GZQk-%lrj-i+zL3Tfx_y)Wm+#u?c@H$E2YsC zV66PlgW=0BBR_jp;buriBXq9>&|O;wUpeGrJbB9m&tZPk!pBbGmO+B*`&~1pnWD(J1D(regbC3J9f|_ z;+OdiFM zvT?nRQwXXc3$Y5hCJkmB6cyFt=DS+kAwd!H+DVp2r&Cy>_D zi|?ejF;^+_rW;i~!YoJ>L;Vhj79voVCXs3|*E6I2faIhTJobHxF#4r3<6DDuG8+)G zV;$J8x`}DBKWR*Eq@JKD->sSJSjZe<)_JQ5PQ5`#f zr3S8KUY)yv7fS{!W}4(nkb0~NpsIF~y-}0axkn6t?P0hY#LR^@uYaIRFBCs1&Ca(~ z7J8Gp`0Vorp}RA7dT|LfVw}#&*bbp%=p2yQ0AnNq zV2nmx*K)j3cSO(K~$vGziZ5Q+>z~ddjy3vOFmP8F6=YF@T+9Y5Lahq zkdtDb4BQ>H{Zef?Y#r2rlMKbdgkbdP>^&7I{#N68zcn_I%z90zNu$uzZDawS)azj@Y2Gu9t^4{I^Qv$TKUu&C)H9L`?iXx{IId26u7xOuVuGy_; zi=Fr$+K9zQ#=dYwTbuyILOBi%{EW)nW##2AT*x9nsWx|(z&zI&w5uglVrgfb3_Pig z^zS5y@&_HjyD(f~^`w{$=R@Wh$t2&@Oza@Qb(7G9rpdNJRgjoA z6RHSIGIEMzD5t!eq|tIxQmi5`s(n-Zbh-k22wmotdkP@R5YtyYs6%9zz#8M5SH~Eh zMu_d!^jma5$8M;9aMaQg18t_S6((OrklKWjqSt)<+RF3=*4%LN`=`!^@gK4o7#NuT zPuKl#2A-OU2W+T5H@fknB`&|6Qk7BQ1!tzG6$I(!w5?F7;ID|_DZ+F;5 z6Kum19${{gG|_W1r;j+Hw7FRp66 zNpGIT3}@L841b28g!I*rGs^hS(_d2Ql@szFM6zme17T++Q4INQU`T%zjk=Xs1ObT> z$pE5QuEVao*j zJ!$&u)kI`nkB5V73`-}g26+gBaILVJ-I9_yP70|1Cc5dd!40?s<&i?0I`arlb6O&i zn`5-h$bzWyptwnFr|UQ0wk3bzE=UT-kUy9sqAmz;{0dnr-fZ)L57klfKmYsY^Q}~= z9l<7OsuWo1D>F_3QR-`zWOEUq-c9A6-R8W~sL!>>%sLT)DG{W+Tb$q*J2MHa2~!vH z-pec`*A+JyaVqRAQT=NhCg{5Lij}-M3VAG6R&dH|7^!0DR4t0+>~*E4uwg%I0Nc2) z=7SYyhYj8IOZlXx%2c?ip_k_{34N>TK07~I%xg~$?#2mW}bW(`4jdV zLE|xhmP$Rfui3#a3WFI(WVUalRFKo}CR#BpEhu}j*gK8v!YLd8IJ@v!Nf@bLr&KJ( zENpAZNE7o7tOW?sGU?hK?Mpwjrs7tMwS%;0b}<(%Y$rPZ<3u027J0cv{-o-`CS(^r zk0>W+s2Ic)u{!v4k?(SHt~b?13cmndE)xfgmTfKtdHlGwmjOP7Dte4DA1LiP#P3ZH zA`Js3UKSP*nmez(%-0?_Xuwodg}#qs;2Lr(o*vRfUjl(rnJKdUGCzRK8;d&N4%%fj z5BJE$0=#$E4BSfzapXZOBq`w|DL{}3(&jGz0Gf`{b&kqse|HQ0)gyXflW!+;k2ns? zDwtAn;Q#~2wBIzzaE!r~7?7TfTB^()=>7{vsg_b26s6iLNH9m^k|2Zh)7d)o2%}zV z_Jr)Il%Bb7yH;y4v-WX`oFalgGU8<-%amJ>+AFOK#%%c!lTbd&u{6~RBI$$)W5vUa zV7o93pchj!iS|s$06bJ+O3@ndr4N@CXC6R3*2i5tL0SVlLl)n`NihHuin#OFi5(W-37o4YSp@w;4ZO#gB9yI0FW>gIG#ZOq+e{cLKOJ@*vG{egmMJ1%i>+#T>Y3()yh{K?U95SPvU}a2c zB0ykUF*nQ1ff?dOfZA6ajqZ2hCU9Z-H`|+o6;M1YT9i-L+fT>kiptTc3~k@R;3wQW z1IS&xq1mnsq!wY1S*xMT-xd+#LEsWZ(32ABJ7>t)SeT`gzM?3?J>~e+lJt;i03_G$ zSdvCIW@X(7H5-jvP`EtRw`{hsOnE{_-@WIWj(Gb&I9sxHhr6HK9}70FA_x@RvF3Zl zDLD#Lc^kKuN0te7nv)5B89$Tm$Sd1P+5MLGX21MBq`vCyq&@%CCv=e9Z_UsKL`Em- zjr6JE8yX(_HPP+JiC`UV=**H6sK(y1<3W9)4m*mzyqZ4Q&ZpoW!h^TBJwf48&RM2sv40R?e3# zuwd2gB4n3{6%$s9&dfk?reU=p!u$kNAH6aKzUzopKfkOZl}?$&_CrMv3c`_-7D_cU z2;)Lok$3nTshy;(CwsqOgGrs{kn*M^>bFG1L~dvg*rQi}?_Ky-LG}zm;&b>`OOXB$ zYdr2u*71ufeuk`@2!R+Z7&#}b$T~P-8lt|Ut^n}0|B;}&vcA0#M1agh>C|&=hl76K zO4sfA7GO#N=j=9)9)+8PZ#*FFu1cI3+()Z@Gt5U0iN@gfFWMuFYEp}{yBN1lzH3{9n`G=u1jy9 zJ4%A4ncY1dZ}3Qqgr)z~7X55||A&@<{lC}1|6&$drSf0E)Bi+PO(#L1*~-|6pEIS) z&@5M-`N!i&B1cZfIpKVL(BKjYV<#-6>j;HGUmgs!>?D}HU{3LD&%S!Kw7EM{DuHFt z#r@v6WGo9ScPlm*=2KlWN&QN8#P1{nOq<+s4aA8|uuS)@-GEb#yUBR&e)W8Ccfs}o zDl0UaCY_QfhG1l9-S}m-vSE0;?}cnPva@O7<5Qk6NEQ?Nm4~6`*V`M+^wu1wyxoR} zx1-4edrkg8yWCad`C=Jb_i2#%F~I7Z8_QFhy?NttY^n_&`VcjqrT`fLK{ZGETt+QH zLLf?qj~AdhI&$l9LT|AC@fTKA;;4ynuCqmR<5Mwr>bgIZ^rhs&6%eKk3RVLF)I{Kb z{8GInR5BQ2gnEjuNbdDe!o&_oaA^+1F+HJi?`lctw!aWjG0B<&QIIT$*2Zmfb{KWpHC6~x`|c$GxIj^kf)J_#QF8&HCKE`LD%&3*=|O* zr>L7%$TIho@NO$UG=lZu60+}jPc)MU_}t8lkAte1Q-gd z%|4KCJfq>F=mpsVcX_i{t50LKVR)Ks?`~y@OPiO{nf)-d>J_GOdBTKw4Q){^NqyctHqNm>o(9^qO@YK`agkkr6HA~}($rW8BN@bEGPZ0)g- zdY(Ut<6;68Yi|hcfihcn`CKxk8T#kX=HdhUd*{Ksa#|vDlwa_uKu5)cZ2+BF?w3#L zuBv#}7^*(+$u_Nb{1FLe- zvfKsxwb3Yf^Nt=^QfqtldUWa_+d_~?cDH0%7+4f#f~U1&ofK8=%{C;I4~fhUx{>Fy z3fgI+Nk=X2!QLmL(bAeJi>h}b7KA7~0lreZ{_t^ptZSKCiSti2;D;FXKWYF2%MT3k zUwRalG=5_1Mp3&zROwi2EmqIGF;n5yhYe>A<1$Jqz+>SNKqW8~gMbuhE_P0yfS3SS z&^Tzu*a1N@qE~FcwgXgKC_CTZP~ld3bh_RjG-*_m2#ZkFwXaluqU%;A6ari4D=IRV zLN9Gy-v-J`SFnqPhELxQmS}HZVE>a>kotMFyVK2Ei8&_Y49Y9+^3ckitnB7o{`qv` zrJF43>+7tl^pvsrW@8uy`bi^EF;){&v0MAp4LVkW&%xMHHyjUF$-Uh$%p7y2VtMjp52J zc`Ng7CXamJEn~~LNyc{6tn?c#5&oj`gt*yB(S`bWEPhkJ+^XV~pD1}%E=Ms4V$$_y zWy2xd8nOe5hEc45-3uEKx#s;QlkqWK zypPn%Hb1x9~%3)%N!@htceM%-{De zCII^lC;1SQWR+%F_$QywR;t)gIFMLHx&2l2~&Edv|loVt`1?CFPy!Dm5a zSJ7-9@&kQXc7#FSY}{C7^wr^{CQ|>y^|MmyPq{!$BOaKJ{)_>Yxi*V4u;44gI6BT; z#04_92bAZ7f(%kOQ8es?UCSg?W9$SR28MR|%d&IxHBnt2${SOw<2abq=J!(4@rfcf z#_Nu_$_A(cQF2mv;{ZiVWH+2k&OrGb?0l@E{}sq2ui>99>i}tEzKDTtuh(+#MD@&h zf`~70rGSLAi~h43m}}@_M{2a)sBLMo&i#0G^VZZBeWTfEQOT=J9mIc zD(U(Tfv|Ix;^R8pT`ta11w8GtS~8GBKA}3myHp+_{PH)$-u8t z>fOF>9u}2WPIc{_Mb^UUpFC zJ_4j$)8&3Lzj}Z|PkfhOR#-Mc{YG%Jy%(+ zApH3R4!vykT^Xk3?7TN8L3r1je(u3r&{(6r<5N0rp(@YFJ-Gy3MXO=yA*C%A4;^1jq_P zA`Q-fL5C6L$&WjN@n?dV!_Ly*8L+zlGl9v51BDXmnO2Ytj+}`<@h(nm5CV^_nI}4oYBRw^CtA)szWZJ~%SXLX6%o6a7Zy~e4 z=wT|J)#nijHNEQRf+JS!L4tgIy!sJJq%ldiY&x}*J+v{4)Pow;0ug(`F4O(DRQeOr zaP3j3gT9|BUiB{%fFc?KF0V5_d^aZbAcQcw=TDPgX4Vu!%_n>xPZKu`N*fAGzPJxx z^d=eCd(!rr=tD|p5q>MP5!y%+hSZGOqd{INWzbOjcqM}Ppt1#YV*U(9VrCt)k^;LQ zTWVFp8E1itVwcLSsrg{6sL}vW@YYDizRluEU;4>eSo@5)FNaiZb?`r=XX54(y=>l& zJdxnbVIp|Dd>Pv?nwB!DV3)#)3S+58|!%P#TQk*c?|k8aOdRuT@0r8AbJj0uy`lKw>eGrN2(t2qJ2 zUDSTCh}C~H@WCs&gU>?oMKRqF%;Bao0i5`*ya8D;Y%43Mt-AScQ9^n^uJ6$P*t958 zq};G#&kzeXYg{lXynWx+K%N+sCNPyBcEo2$l78I{pwmRqnYTwXpwg9R4VN~<6HG=j zjWa##bD%!KA|bNJGQ%)mVMJ1%Pk{*V?1+&}$i6>aaYWMv-A_~80J91-i;zv(IRJsI zkE+D5q!1rko7m+0Q~LD>0;M#(#yiAWCuOldhK!Izt|#?oPnQp?&1h&y#7k=M<0%Tt zU9`tD4jny8WV>vdT@E92dIl>Mk2YS*7UYj3!1`7GXCXO#@e zejS`e)@FJ%f}E~-3ASa>=6wTOux;)#g0x>@Gyvh-EY7_Dnha*IrkK@RvlgM zFb5#$++x-Jh0h)AmKCvHqzxHk@=2}PJ*LANGob4PgI{YKw;uqcc*sVE@wm z&NaVL5Vty1RtB1(c`fpZ5E-}Yj(Kd!I*wlj{w17R%V{cPb$nIL!{6d+|C??M19UV> z2c`VvicDv|cQID_yteoE9(!OjJxYDCQz1DaUU|Harj1$P!ceLl8rCllMY zZQHgcwmq?}34gI|+qUgwXKVMZ+O7Rp?R(Spoa(D{ar*Sr_O(wW$Ya3j(o>_*q`1BCjLTt^%GukBzW>j%3wGz8%;u z(FuR+PBBy}cmHU$!WB+X1#WewB;|r{s>s)!J5`R%$Z48?g`Kgua#or_g4y-N&=NFh zGXgB!sD?mwNQ-4Wd$BGa0!loAkZ3uV2h|fHi*s0Uuu(vRTl6fyd+K-B^l(1Zzsr8Q z!ej~?;j$yIW5$fKi*-+z_sD2KES_;6tTxu8=>t7Bu2pf*gpKZfHMOC(lV3!Tm# zfqRnp1J^)$q!hx1V2E;t?8=>3`0Qf~yTkyW0L11<+r*M-I{rXt=nq*U){f!vl#AklPzT|)34j2Q3$f-Sh?kMEA6`)-rF zjkNrJFrD)=oyF^M@Bld-nlcd`SH!*s7l41IH_}HDq$MmIC}MXdXz>`)S`mW~u=_9I zf=@K`2Lx%Q9V$XGXu*he1c=CeEB{dhpTP0c!L+p8B*xIby4W`u*HZ;GlhRzXGpX@J zBpJ2_8IWQ&UpK5l!^AdU6!R>HK$azy(Hq1vO4DpITx^HqsV%8R)M}(pPC(`2EJ=`> zl;AqNBtUX3H^oAfPH07}#`K1L`DM}`I4@aLsqxoDjyhPo!`XoChO$yzxUC{#}E@hKE38&h1%NYy+g8Ug?cT8(l{P5WsFt_4x^K@ zZ3RK~y;{`1V!qDc$W0n<@ENf);IP6%M1_P+b$6M8>!*&ai|EEFcAt=X2Ze$6fn$5z z?(3g{o;;53=pGK5%WLb7w)JiA0w#a|CcmDxu5V|T`nE0fJo*p2hZTVn0ll5jcq-1T z*{%Cul-xai8$ieQUm<(Hf4jrkShQNk!bf)B#6f$W#3fOoOkiQLae61k1||=MIO2jt zvx-OkW$~U+q1;;aANg>G3|4y3Y{DfKaLm|wmY`QA5rW+}<{tH=r4)&>AIUT@eRm|GT zjFYA5Gzu4}h4jo06Nb%+Fw%=8PGyFaEhDRda?TdyvZu(!eZD>kJSUDA(M;%OcNySG z>^1>;MS320H29I}E5AOM?U}}x9jS85lEDe7&&z7jClh{*m#!15E8eHRze#mxOgpWy z2`=7;;*^C2YGJME1t$YfQ1LdR8eH<~=grM$&$PE-ZFemy;-EjNpGpMCBl2_N;TEFo zvY+!5oxRIG<^MIvuq%o{i9-g77K?rBJeLmo>v4cJN{^b6#qjQ{M2IE?{pxmiytQhC zd*x;(2;LX?0*e!tdy_dz43TM^nT^voh0B_}ITNxkRq<3@gFR06dHv-?YAs8(y=43A zRP-3|58iq8q!gLG0UXH-ERZ(JvOC1@gFrh(qV<7bNY5xTPT4B@v&;n{&spMz7GvHw zo{!yzbX~~|^9(o@8d^iI_N;|Mz;*|G&{Xr6uElD*^XE5lXGXT?bwQ^Y00TiCKlG1?;mT z*#qnPI>P8<2`Q{^FMF4h{N_VT()Ms*5S@rhcnIN#FNuZ8BhWdz-GyBjwJWvL7Rm}( zr1Dh!ZGP$h`mCs^BKStbay2)>vgI%7IgphTIF{g-uK?)A2N`)Zdk@6 zj&T+>47#)#1Tb4BoHJ!88YiYy+ibti#{3)W_kAcdHN^BUMl;AzCaYM#Sekf2`GT@+ zb!7K`G=B0Mw>notJ4k%qTO(<*XV7Hq8bvRLn8HVr3X!#J4+zXi1|pcMQ`eSt zL;+Gl0P7UKU2$a6RcQ99XuF0jyEd(qyQOzx-IhFi8V1n^HDkXTw0dD#=bFf3T1zoI zl|gKkS{>tdw8SeT0pnqw{+z$$^ood%iu0alFGM6;gT3e5ytN`ckb8n~A?D;_OeVAi z-(oawBH)CYN-Q4hQMQ(1cgi&P2O5)Y^^Ov2tQOiF9u(W53QiMbzoOQ2&2Hz2C%%Ue z)`e@_;c@vd2C$)kFLwh=?%sAfH&ZN#+XZ9|x+`WcF22>P*#pO&~Zh=-# zxsvf^xOXipeBTai&yV#dc-`#O@ zWNBv!@p~^SbVRhTs?|n2p1I>u|M|1T|9Me`U_nSPITzy?LXGu6p`2i;a06uXt#{c$ zGY%rWxL+!iK=do#kp};v4C=+dpesW{bWYSQc=ilsvnb?33DA`*)&xHbUP=zlwuy6! zuT6f#FPuo#l1^#lOs21n`#6)oY^Y}%fh3lkLauu)h&U|c}O zuk_yo#akKpJbWha+PPv0OZ4CO#2ig zu$i@Yz`(+xTMRla1_K*CzE9NGfg!IK%<8q=8VJiB2Q(W-rAKEX8={l9iY|7_0OT2w z!GRJpI9>=YU6G4r6YbmF;o6$QPoxFr+!hY5+khhMKYFYp8Nrt*%?#<8f@&?fecPvD~ngPOdBBLq#tkVaYpj*poM*FpFMkCDhV;mQ(hJr z?H2?27>Pa&*^4NgeD|k#quwH1Axm8iIYHM43S{d=-k_(A-yIdkh2$`OgcptmHA3do%j!U}L4IaI-n?MHBso5Q?rt~-&SF#~^2U4RVm@Izu` zq7P1Og^;N)H4FBxR0$x3kNtI-1u&5AF@gFq$A5%~SicsZ@T4hco;02m;_7o8PB`CJ zx#E-^ts)4!{|^$1M^(^jLFxoPP_)nv_Y=N1iK28N}V$bJDMJTHOe}Uz^uP%lVV#y zbD_dZ8Z?8LFRwU!KDOX4 z>~k7XkxQ{i^PTw*Wq(j6%s+GoRO@30y{{uH4g0V%%B3fYIYgfrj!fqKvV98%FJTKZ zAehgh-Rigchm~ms08^yhPMp$ruK+qL?fIh0vlby{Mk-o955%GC+h&xB$D?*3Y6HvL zyaqdNZ#({kkjW4h@OzD3gTo6MZDPzg@R6ciK{>`{*$TnvbAV+0m?uRHxE%b%w#&5D zkt*8ld8oi8WkgG%+$1dL$Oc}XHuLqv7m-(U<>J_`-KL=-tp>*q!2k!Nppavp4h{0A5HJpfdk0QPx@ek zx;LP5EM#t=)fjbbiWEXH_kimVmx&k;P)8PH|1nmbK+ye(j_^OO6TUAPt{5QcH2qsy zW-oxh?j4ogWqZHrUE8*H1qtgljL1AWd^3jLlQE+0ohC1oqW{R!Fg0r$HuZt}YD@Ki z)uIW2l*HLhFz@}g{o<0*U?TJ`(9ny6yS7tEhL#Ou?B|{tfHsi#LJWEzHT7On+k(AH zAEY0R58my{eD`>~CZ|7SKIa}lDxW*cEh;AFm`ecf=abmo>l11}^2TdXd=Gz>7yz|2 zR|d1QbW)G{GKW&RP8H+h2JIB&wBB%TG|=c7WCZW=pswJ>4Fvp9kK(dr=c9?Y}%ng@V=<27D@JN<=;9}a3{k> z1D(5>#6S>1xnzT!<{bOSFK_ULe2WgQT?cp0lMKSaRErRnn@OXw?rlY3%hY(Lc3Thh zkYu-dP>0*p+5BuX{dFoF{sU{UTDFOJw_x_W3~?&V&=$h1<~951=Zvr@f;+U^&fk<- z%`q}hC~)ECD%?0bC~st>_ei2dChG|-%q*{E;hmr@-no^N_=BT?8gI9}g^6g;vWevJ zYxFHgCR#;??pu$CW2r(7ial5drAc42fOxG|uZVo}>8?o%Z7SdI^pTc?WHMa5rZB80 z>{gTs&zO9KiZNAg@xWlhX?iz|kOZ1Gf?z@y*IhMD7i3~LoXMcIK254cpof=>sW~kB zbbRMP?xSEWp};CfXZuE>{EvUQkt^!`RvFiEkz7tWwWRnIJSY}2TpBRlhaE0PQtrlHCJS|$Dm8t3(L)Fuy;?~Dj*qtu^jt2CG+ol z4W$zN1P%=)Bsrx8~NBVC`+AJ)dxxI_7oB@YBUmH>;62 z!CP)tce3e+MZ%~BGix(p=d|k)?WYYLK#<+;O>331qa@h}SV@D$X%r$yhV#py^f1dn z5aTB-?R}Y3)v8V`gTyftjjp1(uc2J0jqj@~IBXT9Hq5Xyj-=&)Dbm%zAE(eLtm<`Q zR9oRV(8xuv%6ma_y`zj#QWYq z2=B{sn0uEzgD97VQJjm?Ev|JiBTZv4gT?*T$374NI@UQB#cQNCwqxJzqEGmLXmx&ruUIkD7Up zlW8#53esPf(EOJL{;qcmrISihrJ3xosr75D($L3X(f%rtL}i_|d5Z4K_F0l_l_98-IH zar590&mtQ8GBt3}vUj%)20R*WF}DT>6pL2L!$o)p`~eQkKZM6eLz5@&Awlkx#@%^b zfAQGi71cFDuQV`5szc=WUk%e4`z01U`CWCo=~8S+)5y8Z zE-!W&Q74_eRbLOQK6*Pls533DLTK);e2oO-8Pm2+z&Ng9Z76RX?uc)3lLrC=mB(U* zn#Obq`nF3E)qchk0wY{X8~9!~fvL3!uQS*e&`gs#yd3@k9PYUh^Df7WwwcR!%Y?QvMx~&$E86fklT^J?z96@z^ zkVw?fpb?!#8Slmj@t_;|4d)+e93NjB&aQs{&OHQM0NcuKu>#+PU2y}KC&LA@yoRoL zhr8Y~2ArcOdY1#ZlVnhUnnSNA$hz2oF<>b=YNWO2a+E57a;Ty1iWeMZ%g(en-q-)dGpwupo9LVM-j9YI1m!izV~O7dfoZo>gc2zXVVyf;dAz;18j8Ai3y^a|rp zU&=aXghHE_rO19<9)Z7Z-3MQ?zWEG#!8{7K#(N9?%^$*P7?`yB^D0j{8(v(JXJ5sq zdZ&|>kyv%!IN?#X;gQ*>8>}1%_WKTrZFJdM6eFOxE!b#3)vO|nrepGXMjp}kM0c0J zwqA<=&?-B);00U3;p#mSLXr6M9pz+havuMXjzr}y?%ZcZ()?`gHR!J`5&*U84g-#d zz0GZf>$3L0$~riHz>~1GJO4v2#_^wYFF5`Snf2e8cgj(db65~W>Uz;gM{O=I`}hi6 zgpE)qqR-!?glus_sfxs3qeuVA)wnW{2w+P<2iHQgjD!0xuvqJZe@)&sAzGx4<0 zZ26^-Q;VGVrR&2b`cOcrNtFRBmXu9pDE>}qFtJs0J4{bBi)tdT5K{pZND%CFv#Y`3 z9A*qwT?$1Y*c3jAuLLq27x6)B!R_|8yFbeK=Q_NrwCep_gFUwrP`RaGP&2XYfc7-M zVaJj=e5P0sNW&%m8}&#e@D{Yd26M9*QO-kx%!sLMGl0yPwUsoR1pbfyNMn=X88Qv> z1eVN>*cuM)cEn%fZ8FUwaZ!yW24_AeRXzw*2*3Ogat@IJznHWjuI?YACvJsMbRybJe2{+U$b44Vyo3NSs~ zGi@_I(>8)bvDL&@v5knbcWTNXL$o~SZo1s|Yn0kQQD`SIIML6>Jtuu5)fWOU^vqIK z(|;dlE4MgPB-c6oe6ddcNIYjbZif}1FZ2xIIJvufQ(gv$#J47%bn$C^4f~_>6AaT= zK2exJNDMpcz3T}uL%4VN&bbk1sWCp4vD%$q-3%yIcd&{S?$gfcTEYwGqB*L#`gy*2 z8{VnQbv)>p*f6Ff|z05MXdi$sY5mJ%+n^ppMBkiqr}l@ z=m>^B-|-Q{)d?I%$j;wBXee}Nbe>C(WspG=LYwnE0HPb zOJ~7ls?B{g5?$>yRQ57fcIfI#_cQ}L-4lq!x!)jN3rJSB8ctT0*75MLGL@da^oJ{) zRD;9Kxf#%M@D?5xkz7##dn>y*3tmoX;Q*Q7-UQ6p2$Ig_na<^vo(@DSE4%rl1n}4g zj=*Wx$^<&Z0-AqzFP(NgBzZ>2l}|m!pzr1Ud4tMlE`?xpadDadn!qD6wK+GnvbBUv zU~#QyYyuZ&Wd{J4uj1-twtIfZ!&2+RVq!uPh>Lr8ctD8gSU~*#<>F_}9net{4KBF0 zxVAVpwFq{rF$Ux%qO;(iHVh~Oqqe`*Q?M6jxfleNwTDyMrTE1Lt< zdkTb3r42gCyU;J@{?@y;NT>i)yb&dT20;>HMg003AZ)3w&q zLC^-xuyuKLPl3YRDg3E$);Tvoui&@f=pnbnDvi{Py6v`ANtq$%$Mu zFiUUcW~^M(;%?8Bj{Mev^aOi3ncQ3i@0}hT931O|XLJKg_r}s;{6-gCTIhQ;5I*jS z3uJrs=2_(dnhY>Yf7i~;0Qu?l;=ygt0MX6XmGkZTp?Wn4GBJlp*Tm@nijke7yW0Ks zge1ty{F>_h@Mw4hvSa}siO24JT$%9~I0N}LIk-JN{1E@%QDGRjo^HgMM`F6vb{=F)_mazuf`Xi6ITJ}?X`Fw+& z|NauB2>QK}*2(ASEC;OW51|(xnKOp<8vXY3(E2lR__LGpb9D6MHv8iszF))6{*$Eg z_4oFNlmpNNxch8@aCFww3(z65K->iH_^GNidVe{G+1N<`G{{JaCU(ROxtz57-Vm3u zaFRh(K^2q1G>PsRIl6Ia>cN;Ao}X5o+g`h`Edv*vnH+rdH|@P*Zie6|obJu|OdCaO z<^91`o}6CYKCGoPF**Ul;^xBk?q>p)hz!la-<^Wfl|WUA_m^V|NbH;52DbzO!Z?9t zZ1f2FxDe-B1&$H+$N!SU0}|g87=$)NdlS(G5}y+ogf~R{U~pmv9=Sne0>vW#MuH7c zx<{-B!7BMiVr-uz1QAdB66rm4_J_jK`$hyVqWMf~4VXj!`RAPf=hXQA=cM+JfbT7T z4-aT7{~|V|KmQ@OHw61D05&;!iwMlZ@-EUl8S^7!+Y8kjKKmU1Y~V3zd5;KYZu4#c zrcZpZbMPbqtQoLI_!&+6bK3YFYX9SSo3^>VbVm3ri2mSD#7G(~@CIzteCt{V)P3*I z8eoz7BWNhC{?A-3|1)>&|IAafe*(7V1>wx4pbF2f;*SUd?e@0D-9(<><-P|9Co{T{F zcZrYmz%9pb6_DA{wZ-N6)$QSL!qBf0lk?|ziU!aePEf*I0sDZrPiPPy2y8vtY}p?t zhu(eN&8r_HAluXn0i;!nmVa-6_~H)-KKoACrx|d~_Y>I5?)`NJH=CSRv9MF{eL}_L z?gsKacVrOHcboHu_;azbvA8&}h-L3Kw*Bf7p{6G}ViJqg&GXfVw!`}tD2~I{^-`%) zcEN(;3gh3;xGKH!A4Tbx`B`W6KaYD;`*Mtd0kkk ze>U_IB1%8XY!wW_dnea>Iiz-QOOU%v@(FjlGcnb1kw815q~{`H>R*KrI($leb(hiJ zp46#-!xmx}U>FPuC)j3m`w4<=v#9;E`FdVN44YdsMMtv!NK(IM``>a$>M*=*>>3C8 z>AdaK%Nsafc9Zt3_mF~i3gjl0Jz)vUq)ixpr=bl=g^QtQAfMB*J$R7dayKlYc+}pf z#wy&z9AuwDMx_wnOoa_$(_AIN#^Qi>RP zk2uepEu+jTl$>FqFaql+e{o!6`{3-YgtaI?x&DO4!^S?Om~d`I*xG!X<11>iwNbKY zo>oOeMzo?7--{#HVdcG*in7w2%yG4|dTen}E>u`#MwY!51Z~_=CAjc5tD0`xoJ*4U zH_|UW>P?upe51)r)sQX2dD(Asx~lEp(VuhT>#R*4FX!<)za4AgP47OwSUR|QaPHwq zLRHUQxYO>#!@=5eeCevoB@T}JhbIEyRw!}BelfNJ~ zYeEp}MP8yhNblJ0Yvg4X8+>XoO6sG9Tu2L5s=VyFqF|N0hq^hZ=tL9v_+TAB9?4bo ztyz;V@-%7UKCfTMV7KanyAV=5dod&mHX;*J-6^n>ESO^X*2n8$HXXbF>?xUn72H|h zi91)D)=gA1m@WoSFL-wqO1mC21uDP1@>r>piQUs`n8e_m1RFz>rXD*?y3(?~r zTKfRZsV_*_{Z0r17U##w08dQA&4_Q>xP+WIWF;oJ6o@Ft7HPRY-nX!O{FrG{kS|lR z7{m+E#%9nYC8UZ*y90>kb}siCw&rGt%#^Pdvq+Up<4q!ky$)UGO??ryF`>gaJ3(R# zVLOg8t%AWLxqrgTT@z%4*Gp#~h#}NZ+FA6+@M>n0BP=ALIP6<5iv9rmWNWW{=4MqV)je!s zJ$kEX=SS10qsm@lF`-aJ5&%be#Wq)VZ1{rW4~pSmOTQopDLt?$!e>yy9AW1-#W($n zJ%WGSKoHWxxf1>fZnhBTMP>?#`m?}zkk3^9rr&LW>>Znjdq^W5P?zuu4yY&+%-#$Auy!r!xR)x;3< z8bALb?Kk>ofb}t@l=T!8tGO6Kn4Up}kqt}RD%&7Ip>?^u6{_>oHOWuS`-n8(`g6&z z+)~GH5ovR^0)^`l>zx>|0BcatUC--2xM8kIz%OUU6wJ9)nv%PNaBuU+K-Lyoc0}I! zirPAGonS;HaXmANdVAVDCBy}=_lr!x3A61^E8^+YzX0bx1~J)RHn?GpT2e+Ha zOHx_|pfS5yeZCz~gI0o-Rl*WkIb5nIDvz{3BWjqR8wcPCKk7j~DaKX)44oz_FhtxU zsK&}M$5`oxv_YmWRBT*Ir<XS8fQPnT6sHI9y?9G14f~LhX8VJ$U`&`jh$G@V-YT0fdU6XDhT9?1GA*VB z@!HBZG)YpkuyvGPT0(QqyHDEEhZ&7(qZm1pD^BzdOARx`KmB9<=Aj+wB+q5e_L3UlaxNl?aqo=wF)D!+$ zJO4=+-oYILcFTxrd@GPb1A zF1pU^8vW&nw{+YF77>=R?em9u`;*o*s1`{rZyRmoYEuS2?uAFhlzOcqI8BA0zwKDS z^=CqrKnHovMg#2VUVX+=%?6kDn|=I>d(7YgN@ufC=y7aOVT+-r z$&s%HfW;0^;qhS``-@J$WVm74Ai0h}t)u|pMMSe%daEyjSOm^Wa!6Qo$Y`~WWOGPN z$G~7ZWj{HHi52~?R3=D~bfr{E@d*Db(uD)bBUC}p^`g_D{S(Tx|x_;Ux4(ODCEg_9*Swt-NqFsn%Zm(FP_ zim|mAZmIIP8vPD7p4aftVPU?|m#SOm*4<_m$|G{+Ngm%^m>j5=r_aPqQ@IJk*3S8Z1W(_^!X*(X3|(CqIOBi%I&F@XAL=yoG#Dp^XXbj z)+~M}fqfJjR=|tas@a>=Wuo=Kac_lN6A@;BN_A30nYd;3Qm$e*%hi}T)8NFVTEqPJ zhY4S53w}}y2lAa(zOO`PFTumTWdm*KstS?ORLB($x&A)L18o6@nv4UuKfhaGADeyQqi z!DfFa2>)c4ejP6KDtpcu?G#^fE(-oKrh$SfG6*%)D9LmJP?3C8L$Qmshh5pPDWRyH zFC$4G)G^F%3GSfpdkBF{=5y@`e6y6D{`5zc!VbS+G@^>ve3eQQLqKDTr2Ea_iWnai z(u`)vOE3OJmQ_4`b(phv^SIVf!i0W%IO!&!j22w7mf?_{tWW8e_)Zbgqo5hP04;x& zqim!6o(w!sd?}*W6!^8{AQel)S`i7j((>YT*j<2JM2$TAF$PGuh%-^XyU()}8tm&pZ){R44) z{m#ivG)E=BDaLi4IA#Qq?iK(Ebm89+sR~$sr9iutS#{u7`$-l)b3w3S-iz`R@NIWy z^}XCxtYZh`oR{20(zA{iYja~xgQU90SEE@nu!eB=n{p2PWDjjK>ZSf^-fI3*_9A>z zxVP=?E9U5SIGfLs=BUNmD~Z8{q=zwFKJJv)jN#{8D3m+;kl;r=BsaZAe` zwZlCGyAfSvIdqr9iQeBq#}Z;ZRGjCd`I2D5i2Jk$;PLqXsX^9~J_?6OLO+U#sWPAU z1WSWI?@qxlQQkq(It~bGud^~Mtqi6;T_+F)tDFfYtETEC1BX!Ea#PF-*6eQS*Gpaq zma2k3vd&s6_uJDoH0_0D`;J0Khbn?VmVYtq^BN;hn_>5r2D)&YoNDAy>M?n;zc_SH ztMJ5?i5ksIhc!Xlb=vAK`caJ*;JD{P6UM z(qzzf_$*{esVnMc^Mm26R{yqf+9)wv?jw;$Mt!x8T<6J8KcitgPMDi$+y%pQQHfXo zo_f9^D;G@Ndku7KATlI2|4sxfulz*S;?vv|&>PB_hn_)n5R_kxUjJGC`qk<|^$y#z z>Fx2vFKHM=+)>Wc<7Xt$f6@q)mIuq6BB515LmqDwwyEbFY`o3rfyxPEcu;-`8tOKdY<&l@5;+p)8FwWYk&S@SWhZTokp3P zX{R1MuGvij>Dzf`IqtgbPj*gv23ioEPh9`qj*zXGh2mPVMZU+!Z(-`r$--pBF@PS4=?)Za9tbM;% zu)Q|1uyhkeaqmZK-Yd1ruqWl9MA0x=6G{aRpD3gBN_?(!g)IeA)1`5xcD;6m4&>_8 z@@uIlJ~%5EH*e4+2U86`p)G1^W?lym-o3&joD(gYq=fm>83h$zws#k90G(aI#_tX- z5m>^GNPbSSh$`$>ee93&=eS8(S^t##KSpq`@Fy&3Q}QZ~yhHVZw@)Nu$1FmRb{3?7 z&1D&AjpBQ4U$gY%sXby|VEVm@tg!7uTr9pAd%J`QPZ3@AIu40@Yzzx+uv&PArttaZ|j;z@X3EE|(N#;jDsVi#sATK3oC) zm`N-F$v!1?UzEL>iDH#w+(8WutN5D{9>Sd9SKAh^jmP#NK58v;@vSe?*!ag^F9X8% zoUYQ`--cN%K_GMz5`8$J)lhhFiRGEF+++xwYse8&dBdL+WA~!l;-a(SP zjvJNm!ZS{WtIuV=7!E(1vQj05=zV)+~JXNR&P1}O2tNt6fmhlK{(suqU zxcG+r-W+7KDaF2HfZZ<;t;=JAaSM`VCxT#MV);bQ9tOaBxRu^`G0KPVIVgR5VxbO2 zgdY50os2AS2Ww!B0P#wfee83+P0+mc?aX)%tA#)M(wM~ZA#38!OM! zI^0Qwfzl~=yVth%## znU3l-NKhMD&#zw+fPBG$|d=CQjl+@qvSK_E?^f+;xds;;9a|iLWwW{4JlS`DBB3B#{Vk;AWPYw9*DN7q~qcK&lvt;gOjP{fvf&N^x0qmN)yW*zVm zZ~;M>_2alt-)NaZz(ux6S9g(38lHA{u!Z#^x#9N2n)2)GuW8H_o5_o4YUN)8v_*}z z=W7Ctg3>J-3+KlR*$SF3--&8s5bx5t91E9ZSG-8!7tNY07YaERiTjg9Kj@nf4yINyG=d&?9JJweZvsL{`FlPWst zkx6WuI8yY#AjGgfV|K2R@Aq_1TBY>EG9fI+)@Z+Rz$lrUsuSf5!?JUm;mu`wO^q#k z_W0E?!H`w^0vHbV-Z5=Ym0o^j@rk4CMNk_^dR87%pmU@Rq+AH`xe;$Pm<)j4SITUi zt9yIvz0D%WluVR*io)ANKKSYBtm#IzM1>g;g*F10L4bR6Wm~6cksu=&kb`^? zWhjhz9M@8&_$Em93cUE?y-%Wi(Yur5I1WMuE?1JFCLz-1KJ>ex48;hL_UL`hDnl-8 zMNq?ylahQS$>dUFnqiaCPRusPTy>;hnH<5IowydX!ve2qJ_7MLD>nTwGJc5K7$B=F0+{X zh3ECa%~1cgy!4r;=o@bDtJhxD3dh`0lgb7#ym4Elv%O%9 z<-ExDZ+5mOCR-7y5uu3pPi4^-J2G7D6>{duy$2*k*s@%oaa2wukgrVb1-2x)D5(w} z)9Hb4qjPtBq#wjdgVFWvz-?=s5EDzj6j8B`4x!@Oe>A%=nAi|q&pi!)-@$)yG@7bd z7XxLKZoZvxf8b9vrr{0Xbw80UpxsyRpOq0NJw^iz$S#1`NTVIeR8mZ@g_hENCCr;@ zAE>v;o~y~sgQ*-rPL}3XScKq0&ZhiAg-Z46lVgHNdM>xjED3fT)ZdR6<&Kt_78T2e z?WsN+IEy&U1%f-P%0vQ7=m{?Vn5QHeDkXftJFq1Wz1V)mwTm8=U!M+o3@H5S!4SN} z>-lBWE$}VHrmnFszU~hXQq&ZwK-c!p{2kadMxwgz$#>%mD>7g|YA$3$l+5#5>FME- z&j$I;>cosWXxuUXsM5n?NytQodKoH@AG+gy?=1&rp@-G~Im8XCXvv(savY{|X%N!x zA+@vNFcvwCqqg)thOzOQJcqrO+kAwa@^GrYHkT?RvkpO4zHvs|4xMA4jll4kx@I-p z(JK;n13qX}>4mgCv4 zuNIznE-d&I0rTc~sE?#t0i2!+L2KqlA~t&3&2b&H1q~O{p?mI8du(lu{Am2|9!?=W zI8PU;aYhfb6Jo*>uj77fuEe-@j{#r0DPOX5BMnx=#*R9ve@l|i44HbxJ9ct`exKHnH^+kis~2^IUGF~u|1+v@U{?2u_UD-r<<2o0vOQvqohoN1NT$Z%s5wj$FJb0*vra}X%dtO`@p%FZ z)Z~JYUiH#_QaF_km%nxW%1k)i@#tW^QvF4vk(28>a7S5n!cgIuc|_6AQ+uy|*B4AE z)Heb?Vnit&ckZG4Cb}$sk#e3fUARdA9&ouSJ|tCXEy_K9%$~rRB|qjS@+C;RS;o3C zbbz&)HRgBiZ+L$@ml+$3a^BGyy8yupC0)-}X{T>QvOu$ny;JieYaXQRQ^oLxpTAcXWqHQJtCi2Ti#oFz48dyEb?pke=CDX& zsQl5krEV;Fc$jasW$f#Dj~lwL-$3LM9(VG&ANKYJ7%b)fC;m|(a{$?-vbprdH-*{) zmnFZnEUJ#VMg7eNAGJSTS>dji-zof-s?d+J)Az9=bw8s$a`;eExAA5Wt`C~RQ5VBqfD!dNsACu&7vhEw*3i=4s7AmmwDRGDw& z+0f>G69ivq7s*+vB14o=uA`pVfQfw_u_|z9m@!H}2ryr7!$xzVDxSN+ZogO$$*(KcO{QQO!xbAo0!dYq#Rao7Hd+)i=cYkg+s= z>+}W8;1#H16BxBw1YLlGHgrQesNK(2Fp;|h^2mna(w`LyV61W*$RaUM_^y4X3ILVU zc&TI&6Ag_7MVs~1qja?j3LQ)KzaQk}*4LS}HY6dm%jb4eP|SA=?ZMSlGK5)}x%T=* z`>VM`c*i0$ePQp65sk|%ZX^`qqTVj4&7&wUVMW*sJ6X}+CYv(RcrVIp)eF*;OW4w2 zBPs5auxYL}@wl?i8B!~}{>E@el$(BP2?fah#2IV;<6!~+b<+~Nk`thwqiXv*)jY3& zD$|P5ntEV_IRO^)Fm>gtR#QWDDN(~kb+RwL{L8T1C{8+f+5m|XB;DwpHv)rio1aFq zu+iRze&w|Hfg#}zrb~cs70}p99O&nd-kvGf?swI5R;3j%m_U-?5L=q&Le8$GMaN1F zgTaeZ3mh|(oAzqhJt*2o$ngrtqdNFRK`OK-0$!I&XOxJhc`tv7O~Td1SS2(-h%gfV z3XfMT7udJ{nQ75MoH9^mcGJ7V*007S0*3iAD7-}jgB1CG5AhfBS_WC+v@vU@jK@Xb z1P}IapHx%Cg6PCmh6}UGaDNp`j@HDSM=kaFy?&m|mOlTq?}w-N5$%zPA0SwUlr=BH z;rDv-Xth-&@jUyZ73c20JfL#2M6gOo)f;I0Y8r7ZqGQ&vvS$?|)91Xa zJiStl1`$Lv+i&vqkycW_w=R(6MH%H+LQ<>)0zk<@3kFeAMOO#XL6gIZ41(41E?uGob5juc|9RywMSe0?n@7inrVDE(yYXdiM4qRh(RB0|iGv z#*{9 zgccsz(gK37Mxvj^Z=4A^ZR&u12%Ida{{{Lrv^4qkphVBsRrb^2Qf%MpQ>tzp#1I) z;BLF`EOKC+_7PaY6U7XELz%;H2BRo6NJF!sF-PA@_}v{@9VHW%<*0TTx+%v(kP%oe zkz+>_a!hv(^aW}sYP_uJ124feltK|IU{qsp^wF;GDHzA@+g_P22Mzm3Oab`u_`STa z-FxaV!U$qCEB|0kR4xx8yC0Ev@jn=Qr{-J~sLeKBvF&7qD>mQQwr$(CZQHhO+qP|| z_qphx*&{GND>xh1-=3#xS73Ozk#68)Iq>&o)VJAH2z9BdAn{MUMK7<^e*<{77kMm0nq$o@d@Xterbd1S! zkM^SzoPv38eIQJ}C=0AasvcqDcI>Y}ZqU5=Hc#O3bklmk!Kg^OHWm19!jaK&ts7QK zgCO05BW=ZkF8W-YP5#(KXy*Nop;n7a4G&I#J;VgWwk$8TX{K%XMzCa$nyHLotfB}# zF{RCNQ%38UATmY|yMf3&aX~hD(`G&RRL5|jLlE+cp&{CezP*l-;~kBjiEF9A$=H4^7QzDomN0+Di4A z#C_LVEapYUP=XYa=YoGPp)IEQ{hqlfxgHYF+``?-HUIgxO57i)KBzlAnl!k+sL&Se z%7zDDI{`@vq;yiIq5*udgc6_xJlH!yvO&!0u#0rrhwHl6G0S?iCHmXE#@9?ww~o}5 zF?a-+`D!JAF7C-=d%2#T@_FJEEt;dEgZ$8nuv4f^T;}4YzR~nkCoJhl3T=qQhILFz^3d!t1>OSVk?W3w{B81%Swm$SH&h>%^K^m@RqCJB=0Y(|4G<1R zWuP?Zb`%GkXFS{&i`8uc=pHTWXi(1)t=c_wJJh9-aLL5ZPpA#@%YAdLd z2E1*=Dth5d&W_74;|Bi+f0x|VvVvX*4%(9Fn%YUbC!NScl4gZ*oKP!bxCFk8HiDEo zU%#i36^g;CShN0Y9b0@pzx!@al{oR4(U0h8=sI%mOT?bitVP$)rc~sP_F|tnNc6zL zBZ8k7YkNBSaq9h6=p~lknePPu+6L${4b-#h6DnDChnP#AZ7fiNJO}lkoD{4{-fcUv zdAB?Mq!;k(GfhTr6pD%@&V6%q8oU$_`|N;{lV|*Qdz#9by{Gv(5peW;hBbvOk-I`E zMV9^8+%8Xkrs_a7*VJ7kbteM2WqLcLl<2*-Kd{hryxMkP(6e*dd6C_?uXKsn8dMOB z)i38+b21Ulcr4^#3f03e<&iDqbQTGnU~R;Cb5Cig?F*&dLZZd1?cWXPmC53kZb5sl zw_Pu!V5VhA6tJ2~y6@-3VPG~mx*#*9-S>nein{cT=QPV(R!*nRkaSqm8|VrGw>^kT zkr806hY@k*7YWI6yUl?olpkoYoPCbvJxI;efB)p$u#UIfGN9D5YZq1)xrS;o-(}x= z85s;XMe^)%aas{AsiifK*-oWA?_<{1hALS^#Yb4;(XBGF&BFkpVC|!w25Pq$IuvuZctT|%i-cg;FQhl1CI|_&isN{;k%)EZ>kx_pF6wclifb zF17&$_mG9EtZi^I)hPsy;`*<%s9M6R|HgtqspuI~{RB4i-QWZ;^lFK`R@lKgjLQyH=unu#1!t4;h2dtEZN}5Tb zAj9u>ru^7=de86SCLOwoL6GrIM!)nT4CLl$G=$E6`dORZP7;>W!)yo{^_52NAbXnc z{mvG@PWroC;q{VK5Fd4bK1-jw#@skk*_<0vp})q`aDa_AX0cXg8dWL-*+{j{acsGh;@}j|FPJmpvrtO)WIY&L+if`=f1j6Dm|t2N9oLwwdHq zH3J>Qv8SvDH*02fxjtq~Bw|%!UG>;$3gpZi|0a$_Bkn^dl5ti>ozLW)1suUR`b1r& zk6ac@;qOzfJ%pql^vES*{@;?zCuX}^1FaD=3`qM8m%5$pgjvEF6GAOCvA*of5H}Xn zcPXo1A`gX8yiIm)V8CXR^i%wRj`$YX;=e=Q0%UmP`qOeea>k}OjK|q57*)xQL~MWt z71%I{rHEMkI5`eu*0{P>Is_FXj|{FAj03u6w3%zzd#OsL%{H-OZagscl0Gx!Bl^aG zeE3B5FD*aDE$&f^cUa1AX!x|V=DxP-HRrbnoiv*0qkcEhOej*6w0s*K0IttNH2-RK z$?9HF^5kLF`|{kjE+yRpKK}W!T*On5H7QFx;*3ufaAQ2R=|wbBLAhT{F;KV4@wELqH~^52MGFwxSL#N zuJVwJGR{?o^28q-zABDfrY;b04mCq2>^6fdq@#w_z|^lUGOx%aHPOvTM9(0y7qL3+ z4h3*C<@|)t~w0fC>=+>DX556MQt?b5&Yo5T@oRD(@+jdNjqJC z15VYF2yyg$&4cL#829+RO{@IH7WK@J2{>fUSA-~i4|Y`ojAMVn?os$JlxwblwaIS1C zszL1}?R(=ks@0!L+Rs1PS7mM7s!Y?HTiJtAXMNIE(((4l)hZFGZQ=l>xx?D8kYl~s(k9_bcpD`p}0CuW^&t!r_-0I z{pEYeX~%Op%3(bqQrvTVre5xfQBm@VX7S93n1u1*OTWv$urRNOCkp-jSXSqp_nN3) zdqdo03IVwtzV^9WII3A2Vq@-$mVn{0GQkrzZhC9Ui~5NyRA6)*pWkt9XFVaLMP!Fp z#ZfpSWoRELE3AKFlTF*Y0y<5KTbV@>%UPjaVx1v;iefaX#ynZp9PS`YWxO5Rx8cbk zr+JZ$#Ac|3g6FIhL*w~x-*$bFX$&FIGsvbGkhG|{2vuiS+el6)xf+>%a^`JaUZGYB zJl~Qx!bYN6GAl}BSRUZHo)ye9h$$1Eof1AO(EWTUA8lQIrt1F}Rgzo29kv4&Ia{}l zGdISb*wL6J(E_QN|8!Xl)hI@e`X+<7<4r4$U}^=Mrs?Xt}zc6Sj({UZu)U0e=y z-jO8Oo+N&d)7`jIK)NlM7w_*|YJ$&dgg*5S&Z9&(*7nQuE2jhtcPT50ldcwA{%mmc z7r*AP9yY!03AVbUie)MrUnTg=Co>-{44Mja+IRI)=Q7&RR&^80DpBbTPZAUr6T#TW z`bj|iOYxRdW{McbY~;83a?|cYknpjIt0{478N|H{MuvY1$B7fX6ZER07{JUNr5T1? zS0;x;@qmGZvuMAa9yq9IYW#rmuQ!zQ9SDJxX24~6r$wd5uRBid1{FJ9@adBN zK7Y6S-o!DIX1i1*u$7v`qKu>15SL?HyQ*s~VH8is0X+3-pV_vxITQr%?iX!}>=aVt z`T+96hN+|_xDu%s927tCV>LO31q-+te_5&SIc46ysU<4^k}4>To`bEIXGR07vlMjU z&};`$isc~ed&RtSCY8>qY?NKDjUcEW`HX}xYxe8ZjiPuNk zTEX48aT$j6&i5GDv z4=!AmCp&8^f&b9MGfxZeIL)??(kmbP4I-xO32pnp&1sMvLKnSEsy7P7ndxGSh_0S- zL@*C~|M@;*J)G35%%PK31?x+p?}l(tc4(IZMe2Xga~Pa7tGu%eo5J=lG7Yek6-HVX z1`QhIyo_dpOXX?QT9MxKP@;+TS$JAuFzDhImQc-OZ0BenQybvFbf>#}Cx+pVb7a#| zOo`rZtrC);scz`Xh+U1p*q{g$Z6l+C|fx0Y9F zdF!Xw$aq`+jKNF>HfxOi>z#0&zuaQhwF>tH{(5TieugIET@w>dY{VTvg^v^Gl21G* z&Gl4a3VKV6Hg)s;ibEXw9KqN$O*2Xg)`s)K;H(_CfQ2uh?OPf18q52s;UHEaikyNB z9L5-yc8rmw6{OIAaZ)4#>Ug9!?n*XWp%#M zk!Q1gZ_}QJM6V_@0E029@g&fxT;Q$ZNv1O!ilTr=VUsYX1{b>5_{a><)V`E1wiJt* zK2mKYngM%g0%eVB-}Ntf%uTCB78($}IM`SC&{D!}NDtJ3)O_$I<3osn+VTGtSZgj9 zQNcba*KL8$GI!HmYE{YDKihR$YLq38jFNhFTqadng2R_Xsp;-NT`&-UPy8{rOZk)P z`L)~`7>TQ7>0T%{CUjvM6Ar9dV`&d6z~>PLT;JJaFbf9Ur8f(z;xlF=#3B9OLT~wS zn>IeY0^@fyf_rS#V8scnKA%sG3SC7uuMNX*AD^m&>3mFGm3L$TjPMf~FGFG+45E+| z@=qLHNOf0^#jt{dA|S?(|Jwm9YTT)`#$dv42L|lK!O?i8_>p#S3CNexw41|x?o^$B z_ox3yfTIiuqsO!~6fL$tz;?ro4&v^=7q=5}*vIT&bRrP=Po=F*Hzf_Gu9>WT!)aiA zB$0O#-M|QOdj>$KsG|5#L2^exO7X>~@^i4H(#G;Rr7Xrk$eXlf$TxSGG1bS^ZS58k z`nC||Ip&7|7XNDHl*#!>EvuWPOYs_cV-FFl5)Onk3R|4oM!zKn7MeqKZ9y@ZAhM_W zFU8|0xM(U1=5|#aUa~AU2lXJt#xNH@C&7+XxQ;`bjZL-GPdP90qZ-YdHu_aT)+O+C1g;Mc4Hjf1|#m7jrgpwI%nb z@KZ2I;YJ(Gl^&oD873osHwBa!pb5JW8~b4*0Tob4;2n?6&F>C?Xp`wEc^Bs*06_@q z9Tux3zw_N?3b{numHAQ0i+10!bPv~YOtIvQ#n~DCsdn#x+p#Tck*$^qVtTY&YsOIwK?Hm(Ezgs$R44E!UjJOMl=+&!WiT&5L)-hIfYBbJ={%%fv_Zo2E}$48!r@Y=9KJ0Cm^2~V-S%0YL=cFY_GA)!lA1ul;~}hXIzqHr z*k?jlF>$*_Gurms2R3Ax{g!L+>#C|}3O~Esk6^+V<9{H%yeJkRHgeGcU%p~BFQy?q z3YT8!(rS?=Rm4@RT3`5`YG<>Z5bkT0dZqdGV5oiMDLbl~2gP+@w-Cfiy}>qtfsVua z7fnM8-{fl4kqDEVb^x5Ey|8b2eEp>>da1s&m|a}!7)6e*hvK()zb9`t#cddq089ir@VM7#b z{YjCeB~F~qZ+$bI&xP^Ho-Bjq>1>J#s875KwT_86cf`rjlMO+<>XIIh%*U#qqP-n6 z%(E-fm&V2uA(tRR2W{1icBcFm{q;7(wp|92+{D45zL-xABHe0HGFP>w9i?y<&Gy-DuG&#K5tMY~_OeZ2;~w@}^+XK7*@U9nc_tJ& z8=L!TVR7fc?lAYjzPH@bye!PdFP1;nL|a*vp1NaAbQ!XQ!#a#A%WAo68iNP*8@R9x z(ZF%grm2>r?8&~=8p#S{QhBnzZ91y*;518Ms1WQcB+voIX;X?{3-001(?%IRmI(Ce$;sc&Um8(CAKNO zdi~iNHEAITR)GaT0nurar!;`AEdd{d16N5i}>v-igX#aig>EXRNd{ocpkG4SBsAP@d z#;Wek6>F*W=0!cIHgf5bbEy7N=*Py@>=~Zb;u^5_kB2&`M)zokmNZIVj6NsTe;Zgj zmuWtmV2=~DxWP0?l@l+T8a(~GQFLi;-XNMtD%YcHjD6|o+rW}p(D7U7nBOvCdswO- zwW12__c;ndYY7J8^v~hNMLw3^X=o;fEEAQSIzSy^-So5maW{9T{E0HmKoC``X|N=) zFMqAsWf$pgCwqR}HC$X`396SuoIT>_NbPZLRW4A@Y$VH&h7%EIg>2IJIdEt!mTRhN z0M|Cv-(%3JNmp9fH-M5nG2|a*WCV8Rdqd!DuZi%ZgBb?Liu@L3Q705*Yv?snJ)5)w zfiS)+)uT8d91rOW)*-8{wCRjS1wVTToU6UTd^yG-MNgXyME*)*%k8m&!n_Wy^l{I|nTg zSoo+suLixhy<>n%LR%X&m#P;N_Ov|Yc!$yI3YLbEZaGkPMZm>UOM8*29DkSHMaL%Ibfx@nPdJ(i68%d&U6*mm{ zc6A2#r2H}DKLa2WRmwLrOEyaGSW%0DK&&BPm83W4{Ivb=6H_SN0DihMW1pb;doBVo z!QOhu+W}rEWpVxXVm~^%zl4G1noV6Ql$;NFiP=8!g%}BZNQj4~>6tU__YI@Q3T%=v zLBiRK;_)H@CjU9#ZET_>gM&{>37QD`?Mq=@;W#KZ`$7`)&`nv(^=~>>>BF<6tQCi#fIl03uXGu@)53dlsuw>-%W-j@TUo>*_8uz8Ck7-=iI@DjWaHeF@HKn0I` ze#!m+_`F%Qg+Nn@5Nl%uEs8uMSkO=Y9YI`Y$1wA~=*0Dp0w&lc^v^7GoX3-K-7yqo z!5iO&K8=>J2+KvxTE(tQ6+k=o!G;$?!#{Q5FjniIJE(#DZHB;a_Lb4cdmJ2w%2-f4 zvmsEge?qw%b`ao(P?o1s`g`hMqJ-56M8O06gYq`Os|kf31ZMJ%Z30K@x`<{(5Q~EP z$5SZC6}~D0MfB>XKk;8TzIXG>^bpHcjc1@hQU~u*&?bU7nhL6O?^uqm3St4l(>G0g zKV*~4a?d(5A(bl^@wxR7^gZghw3$!EJNVYx`DjjS-c58&^bDgp>cZHh|A~c!pTkvF z4G8#vhf5ab@Ah&MNxF`TLQ9`FYe+;>9{xOD@|wswN7X8D^<*C*50`S6Lyctaz%qCB zUeZG~ubFOpI>y6AG0t+0eA|r$*`pc=F9p!b_WtnlI0^3StcExl-!TqDM+T!t*};EH zUhzj1fJL218K^-(+w-;~Ri~F-rIW6<;_ov)1c?*3x2O6it^{ycr|FkN)g%>Rm73kL zFQz~U37Jq>DVa5nlKyZbg>BqxY4bJ20M`^_XJz$AY5urpEn)Jd%TT3&z>lS`IaKo` zw7Ui+LKv|VP?4Z|)70~W1sO}u0uZtfHag7!NAN&$O5Pp+p3ANPxwGAPC#ykPMTWBzvDT#Zv)1jKdaI;_f*8I6F}B7T=NZ-n z{8S}y1$>?_5+W@|3KXq@}q z@6?rvQ61LF{gU!P_fa@P0gb)bD1quZKA!zJ0ZrPEWFM$bAOHxR z-1Nu;ZM?h??Oi>-aE0F|fMPtT^3)L$-f2Q~&IwJ=@yuiqJ{!5`~gDjbzq_r!?E(|tdZ ziem}c3Rw%q&1J!CpAc?@(;U(paOLob33CaXGSb61yGc0-=CXvq*1t{yY!zbRjn!U+&IRlkiE(O>V-Qcy(p6V7JHf%_9F~ z{GfeaKU|MItUBln{lhF!8z0z4*@F{9OpedWfnUg}JT>31hg22EP7$pX-(Vthp9wnL z0;t62qY1I@YhW9YWZ*OZvD$7$!Uoffl75TN=s+xlI)hMXH**n$N1oi<+md5DPu(Xu zMTy8+kRLSA=wfT05A|0Zgl(6`tki!Hs}EwvihLbBCp+E+V|mamaO1D@p>*N${f6>U zU=YrO+v4sHt6vwR*?XyO0tZy*dh}Y4zMc$gmx*~G!j1}`wNSF^he0b~!L~+6feY(1 zoW0^;AL})4hbKX_m9bnx&1@mL)V%A+9rjz4dh1f`Ny|#v@QO#TFw`ZZ*4b2p5uw>f zP>pqtmwmBB3b|{FbUHW18^0jVv8{=R497)%S9qt=vb!T75Bj_jY18$KKJ?L7CagJm zh(NPuUI0YYX!R#_lvw7u{wrA1d!h2!p5|V9ua9pqO?+AwGBg z@vyOK>!b}^hm~4Ip}HD=p(|>__HBbNt=>Q82!etOigv=mymT$(r+)-n(HDjO$-oQm z<;RO%t~W+h{qV$1+S|xCkrLTLADjNr01kiXQ9u=eijeALR@0pY$oH&__S9Zm}N(#9L@reTFh(`ub5(@^&X2oj!;F77gVI-PZI!T0hvR z{`bFJC{BaNMpV9530MdSNl%pLv?PkF%@5h!5|MC!@HWp~h^1qbedY#Q{N0x) zQ#8%2Oi?k=;rFJ3u0VkpFVaSA+e)dp0c>F`k_TX!Y;|+Z)`s2wW7tmRJ1;mg z-l$N-@gZYU*z0?@5A*vM;uBJcVjbt}mdouEB%?rl?;%sO@C>b!jxnO@-29k{k^zEZ zCBc39gM)H;&!XQ>j58tnPjVGPFP4)yZ@s;WX4?kl|(fxhAajB1&VTTiaq$E;j>p`Qkh?(B)ZJcYte7c`}VWr(!J)=xMX$dBq@M!D*pkJJs~j^h5|ZHK5+#D49MS0i;s|wh^Y}C z)*R-0Q+lil#@Q)=Xs_TGhVT#)oM@g$9T7QNQLqnqVx|QMp9d&5k0LgX0ugc#97OmB zT!=ja#E74k9+EE_CNIiQFdH)681dyMhF+42q+_~Q2iQu_1t>Nw3~}_<$u9|S2?+wC zAJ~Gh2yF>|8ws`n-0W{3J;lN|0qNRMRh*coyp4^jsw!<9#z^RK`-k7$T_q_5Xc<7CMG7dtAHu{Ad#FXPzMK} zrZ`%jK0@#>aODrM9ncRC4iEyyZ13cE_ID*B><zHN8u6d1 zSWlFb{X~qATwD~m=R$9mJnCtGQKNWVTyJ>UEI~!v2IPHl(COKS4pxy7O+9Z^?a~67 zl*C_bAvc8I2y#hLp%8&U`~?EOfXYCDE+ASCew1}axA8x?#vUi5cluzAW9$B?<)!+0 z^i$`Z@d_lNjDbV*adHZF%l&fQ$wtP7{sHp$j|XxrBZZZD%e^pTTRMo1?(q^$!|8(z zJHbZ)db@nRWkX@^CWLIO{`B4Jy-od0u9%<#FE;gM{c)Ajz}|=8vww&LVs{7kGwXqd z1`Yyy1Je1WE`$pB20+~LwoBN-fbkv8Hk}!MtPauoqWE3g+Sh^ps7vDco6w;4y$~ee zfP(w!Jq4crW?u9v{@B9)Dj)v}Km6j0?X0i7xTamZe*HoQUg@>m_=3(AIg1p4=Y{Z1 z0{!gD0nP~KCH`6w{o*MK1k5qU1!!*kd?M=0JkYaI2%&_4X@2id5d2o^VmAi&=Vw5Y zuhqsv`z8K?{Hn#&P}9SC3LS)!9@{0N&|v$uqWtscFJUj(2o)hD5C><#7Sz0IR0|jo z1%4AUkzDI8DukV5Ka!XeG*EXIMjyz&*xMzKyPp7%O{Q+oE?LIktuwmiUTY^!n6_ZkGX+_ln%x-r&XBw1MA zOMrx4D&=iqLB8qoM}x)3k$%P1S%^zekw`|zmcT~(dK21pgjE^v){B~g_x`+8xZ#@8@)mQEtP80AP%9@xb4tr@8B&)5b@rg{t^mr-}Mm$nF>7_nmxL zRkuP~G61@ylUue1WjX~MrCHsK*q>1~xdq+CBm&t&XqW*D2Oim<;xnH+`){{G(ku zA;c@s6ondLkm%Wk;~W<3Y4PkXwfnvD7QUkuB8evVd&(DlkV+>?HKny!xn@@M2p`J*NBDCZ9u&>5Ut_m z8+!7lhohYO+=Jp`v2#3f)`t0ly$|emcI`PGxGTr#>rK{(-Y0T|VzqaV`e`SQvG#iS zxQ>lW!P!CiK3*kwTmZuThT(xI*2D^=X5~A%b$c&VEgY=nO{b~!NG+y3^X_S9Uq=qI zN$dqv>y*|vR#g&3g7fnSGAX}t`21VYStudQdV)d9jKGNDe%OQ8yxr82&xT+fDo4-Q zpR3YU;NzwcaQ$c~m~neuh9oSE+L2GRTiAb(@#s;b;DGIw0`lvPUdI-_B&*a-s9dgVN;uawZbKfZcgYVb>9u(U)wpal*`) z9;t4l$`>wq2rLcUZw_YI2h#%RSyC`hF1+W4ua!7 zf-cPmSVy03p!`zB>}}n(Q|2K=;Mb{t)~Ab4P}O3KnFOycts;k4uJa1oQjvETZ8{o# z^$ZaJgGAo}#M5(M6SDQ=bkKEqkv^_y-LH00mG3DLZ0X#fg#j6!Kc}L!8IlLeSAXLl zs;j@|S5K@ZrMqcNNbH-8b2J@eYxHZDpqNYc=&&FhP`-)zlcG`hkz`lvq*19aw-_BT z6V)UFxLrnhnC&!uAD!Xjop4^J*jMhoF4;xhOS8m3GA&wG54pA<)^1*>VA(<9@Xm=h z;sLXk8Mb2g`mZ}GvzxaJouwK9m!2a%Nu}u7Hg5OzV#8BKpvGK`wP+>UZYieW71f$W z=Wc>L%15g8T`wH?I^N%j{3>G#*9EgSlc}?3!>h|(SF^OyN9ANTV~g2<8|>syC?fyBievMe+tD9=~rLPke!_$?ipp`ZxmLZft1l$6fsrN)r~B z-7m&cuhIS?)#po*2U(@gYlm3`$bo|Jv8joy6XwgQuGp0cZ%ve32r&Ue0H&r`32`C| zPwM=_O%Z11!f>2=MVNch+#~F3gX#_EWfb)$>?h9%cEc7Dr4Qwk$w%Vcu6}K{EH=dd zc$kl#6y6w@Lwn)^k3kGYGtl`(iOuD+5XIqU_y#}I6 z`RHrh>U9&(dW`=#X%qrS4teXf!|>!h5*lOOQjKsBhge`wDCxejA$M%NOVPzAF(!Mf z@w?vR`dV>#S>={B+oQ>!DDA9G?MfnhyMX^nShXjTR@l*@7XrgSvf*^ESV1UYhUPss z%R$QhJ7h|{98C06UsLwQridCPuw@chl`W~J($!rp;5lU5BiGT5)fIF2=Mt^gr3Sv0 z8L_-&yljIl4KJz68pIPJ;HIO9I9G(pe=>8#q+9$=b?VleN1Wzm0wE1Jb0}qv_U6~c zcq(PuH4j)$+20f+h?Qk_DLw+$v+}_Z`87oVAN+^+M5{r#d)T_j_d`-{ehXF(p*-?2 zj_txp+XJhuR~hfwwR){N+8Wawl;uqu79KfY#-Cv_*ZoV}wgd}$Qx?|I-X$2P zP>8HC-6UiB8QLvW?I5WCV5N*Jk&8{ZB6fjKwgnl)#fH6@e2s#jdRQGiDb7grrF@wF% zM^D!-NiGeHS*FnhAxbGz0MyedX~EG-MJoo2)G)xSr1w z0S58T?c~PFq>BuTs|Z=>d?`EWDp8ZuQkk2>dcYCrQ^qLS2korvRsr5K4@{sv?z{nx&@)9Mg&KNxgDog(MYe4r|?o+@>@_?IEq@@ z#S&w68pcR_uz6&CE0q<^7>({(^(>Q7rqrs1{~xuzgT@p9DJMa`TZwB47F^o*T@+wJ z2zcx|uixI7A`@sByHg!tFkn@OwtYaoG1GM9 zh?fPXhiaE!5jrbO(+7h_7qA`H92FxEBk#6wG*sM^9frQfOCL|JNen;h2APHm=c4MuU{xJB!C-NLpQV>9KD-Y<+D-`!d~oW!((B|R8MTXlm~I-&3+IrJqqUb(E7*; zB9`RT-CDR8PK0RH4Ey|;URqEn8Yc{_E3qX5*QYJaZZ;`V#^@9J*=ID|DF~hA9w+T~ zjci^YIz6UNm{AUzu2V||-HIk%-)AbpbQcvuAkS zV^`*%bASr^8p3pll5`@uZwBh!{QXaODgNEmsnow&PS*4s%AOs)Da}sG6`Q(k z>)e3`NvEBT#)nea2h7Gd>N!hk6dG;~&)Ob6um-gO>J7uI)Iek40bOGF&}_)FMb)Wx?9Z2wx<8YXLGo44=*%z`oTqBm`2AKc+i%vygJB7 zs6s`t;RwR<(AxHQ&_@|8XH=z%@>8bM)a&tn$)Y$-XzTCk11E)YIKWiFyMU z=Agw}E%h(#W`&J({D4#8UAvNSM6R@Po-zLAH{Rk+>ktIr&^D@2==*9^DW%3rq>&x` z8~AB>ZSN;Jqy!k=%+Y&f}^a8D3_v>KcVSF(Q-vE@VKhZiH ztLhL&Hu9|zHY!m1Ixk;C%O)_Oc*U-DaNYN#NmoH?vSV)qUVGPX5AX4}Rq=gd%B}+T zowLGf{6~&6H5cT4v10=^bd`IY;GXLFZPvupwB7fe%DY=hCyfqq6Kq(4w-tVsai~Q* zv_W^mW2v?P!gr$m8c$ft6%oL^%8^Ma7`y%njLV;ekK-~*D$AYm>)Z(^e z6bvV{_<0R49IeM5h0L_CZrXIkZ=Xu;^OBx#uia(}&0ImMySa=_CgNFdDe!Hu-^Z>C z#zOQT10i28RJy`oy>ynFk?^iREJ7ZXKBHIQrtbyFB>E z6+zAcC&~Am_1OH-P@jd2krIg4h&x|T%9zz9{2V#8J|;Li84OhO zSMvV(pAH*>xznI{-L!Mx+Vw8g<1+aECJhM zL1lO9rV=N-y3kAtF7yM2sMg|W1k{(X5s#|iWW5-4arM@1g|B{A*`}Ai_n=J!UW0gqcqK9vCCRt4%N38y zrNsjCJN}u)4d(5q8&H{RE#rE0hjzfctEi!aD4WkPsjG7@hl1V%lvQ}M@gdaf$jw-+ z{?7AJz?tPyU6yA*krZd4Y`Fq7B}Gi&o+%EC{%sh~1O3az=s1`R{|!Wb>19x< zip@v!)Thom?h^#_ex}uhjcTX9gY~vBS~*?0&+6&x0QEN!X3L1D9|s6FlCR zP5d<>_LZGFnIE*O>9Y+59@_SGx)9DP+MhmVns0>BbQNbI06s#G2W`8 z%jcD|u~g+B0Me7Zs39z+hq(JTyy>~?-4gin3@b>3V@6IS9l>Zl4%-g8LlBFRRA$Gx zG>7gL_RLJiX_ZpNkC^+QbE0n@1=(VO`0F~L2*i79=h}V?`$PHtuWm!aO-_YT=ogVs zxMFOWs6%@qbFI~68XUC1j1A|~Og{P-O}?Kh>*&0*tf-^tsNxmmVK?!WzJHZpYJhVs zhacO@B@WvY6X5YRQ(feeRj19+Op>9MiVe|?Aj!1RH{Qr}zm_;D1v_1b3yZRPt?h#` zQ?FU8bA%}UAx+iSv0q2&w2CHBQa>$;#f#m=?(YL_S_Qk=kF(^t@Bvi_EzG?mGQjq< zkG0@sN}+o6&jgBG5LE({0@veXwO#o740zogPG&R{$WY*-&^p@<5vu&cX+R=zV0Y^L zQ4{@rw(tuKibcB~wuKq%mw0}>U=~mz!f^FKK02H>nq~L+<-mRfyA};v||2mm~xYGmYjKQ*9=9elvUV@L3cEs z#Ah2CC?}^Cf-_~dDQ*oF!Z+#WbPL+gNhYgVxY2UrF>lFqlZ0L5my;^-voKQsg`GZ^ zEKs*|qqG{qIFf{AJr5StUD*2;%6pK&iL=Ku)l@i*gnm9!OZ{Ii-d1hWmyMEf=sut` zrR_QG#?Sm@qAlY>ua)nUNa9W2gvm3>hn?f=I&=G{-Cmb$w2`W8`0zXqOox7ZBEz&g z1BbDjH!Vp5%gg1+#gvU|6VT@Quel7W-mek3e6*M8aN9%vVQk82O-cWUZ>u0%n{UA% zE(n(N5rX@w)qd>DFV1`jFw3_M%1-p3a+Y%FBp)Q})73}dqiRGEgGI7^m_N!^z4{N? zRK-?n@RDa??RF&U61c|N1vW_qzV}lv{9_e^Tv;>5wU%KYn~M8JvX;MW6~k>ikmT^N zbmVmckgwPe%C5A6+wUJMsu#sA?^hi=;?-=KYfUPEj&Is!{UD{x8ibmQj16aX0dzV{ zVE;6N@W-u4%E$&!_{6gvVYI6}&OGg*telMItp7AAk}{ktAGn6fqr5t4hoPZ|D?AL1 zq(H)M6s{X%rO60r23!6+R!JE2)27A}TBM+c>E$W_Xaj%B6dIq>!zSLk3(=9>_m$%^ zdrE_LBF1Er+;Zyth$My;U|@9dcwXnqTN_L~v#~B^nQL2EwH!0#<*m!?t^GT;xA=1o zsE@rs%tu;W1V+Xx&hp)k%`C7?&-Omgja(E<@h3H(mFBYPZGMw?aDG+Dl_H%qer9Bj zDP53FuiX5@l>Od_q?9gE4far`OiIC?>vB`T98ySogF#hc_(P%3xsB-|u@|ahgR=+C zI42|GcYohcGY3X6l)hbZLJ010@<7{^X@|rDBsIqoS_#AJl-6IyGnXq&T!Cz!TpvxW z-S}?3phPqfr3fi$W5yhjzA5 zMjZ)VYnH;WW^5j8TTy~PAY#btW$%X`&IRrNuWKta#aALCTf zs%<4PbyDwUdmSIMDUmA5{KosU2L;{nYsU+b__??$ekty4j_`I=GddKALxo+2=w)#_ ziP`Olc1g}J8c(Hg8J62R9m=IQ{`Y}DjpFJEmh-C}IWpd~OUffDC0RF*%McgoQi_vH zH={EIv`2i#w!Pt=xSM-aA?N{F7uwsPYxshzWqCG7@shXATnJYP7l|;`&uVdE| zl%0hgHt*^Nat{UQ4vO~}#T^<9WRS2%ZOXyU)D~=M zW#(Ex)0YO=YUK)uhk*g9hW8u@iyRWf0xke}iOhX1a-Xu%D+&1KwsW006e%ozNw#_pRNStSF#La z8<;moFahp@`YixhWkeu(`DGJ_C&we80R4Tv!2B^accET!;1CxO4IU70i|i127j}$e*VXMGBOBhnN%ycKS%ixVb6p0o{vAyjc{~r zWK*xUdceW{);@^lg1Ay@ziU)TEBf8?;n2H{g`sm6eT>;&5czr24J?{^_0W8ncpG&%vR z@LS~2S9q84rVuiF?*{)-@O1!?_5xqt0Qz=weQT$1k3d5PvAcgEe;s?fCOje{9zwEw z>3>>fRZwq0?~YLsf$bil0Rg?ffCK>ILxX>PQ|CeWe{F!@WNQ$oz~B%*D>p+8KU7C? zeWCrXZ};`Uzg(%E-vTWN09t&7Y@m>VG#A^Yap6|M`G4&BaZgTq zTb2CO2m5=$qjbg40R-^*cGTcizx;v#dc5EhAwt}~Lf8{;2id zDh9##eSWo`!yf=c0lMY?0tN$iz5D_S19ZXt0uBRo$^7#1;QOJy*pk2PdAU9Q3{J!E zIsdSF%>mYC;s8C!_5lm(u*$ySed!`sZ~qAk#rP%a2mkpU@Wn-j7=kv4Zl;57MTM`g zg+FhrNX~ya+QCfBGT31l(>s09=5y-U-ODd+SUu{}5Z0O~^11SEXv*(%A?Ox!J?-56 zfaC6>RjBcK5IbGH_q2^JW5*NOJ? zG<=M#e{-tqG!dSq_5)rIG~6>{`DMS#$TOMT@l|t6kwzXhZZ1ay!7E+&HgQu#kvRR{ zLmlpw%FC_zG4R>u{pe(A*9EsFLLhvc^y(4?W(yY|aqh}?&Uu{a1(ZTGziy(>YI)@)UTP5)d+X0@6lS=!m>BJRd~P8N%g&wri{TuvY4<~MG=@sc$kC9 za$M!<3mvw9`Y>0x4$w6!ix*5d-1~{lxRE1a4ZM^!9D4+NNP{saLErmpQ!pV$FSf?p zcuk74MfN%oC!hT1a~_4+m*wb9rq%FThcj!Ps2U$|fFeZm=V3wVtkY|W*?z2jhn`!o z=C@J*C*^2>4hw0u^1etn^>B76!CmZACy)3-p*(Z}K#N=T&-Ke%nN*@&Sg6M@VPJ4R zWd!z^bSvD)4ynRiE#Y1^#bbS*tkROQ>jztRJlq9~Lg1%+^MYe-g?zp1;=mJQ{awj6 zT?4I!#;X>m6tL`R!!Gk=(QX+674;=!^Qn@82!&C^nC6QOM8ht{R*~Jwg;BZHaF2&( zutSFyI`qwzO`3GLc##eDN)sh2KDvfF#y??R{N`>m&PJxOZ;uW4J2O}xWL$X6Ni$?c z9fYcsDD*NU=|g+P?^IGtij`mbce?lV8$itQR~4~U9ABWo+Mj8G!Uj($!>&ZNsv1KB ztsn68azbr;DCa;Ik4W-^&|c*}M%?&kZDSOHE2e2!=Jp`Zy(&z2b=&rc7RNF-Uz6Bk z988yHx-Q%bR9s>?2F^7|40vczd-5NQM+6 zo(wiA2L8xAu}_wP8g0L4Z{;sDBy27GoG-3qZ|rU5wyv46nB+9r(i1($N2-P7A?k@7 z&`6M`Vt-S2lX`uJn+!Z{t^$~EZn72H7>)WeeF)2NQ5G}U{Xd`60n70b2|!#c)MkkM z%ao_yI=7?*lLE9EjVzz%>84Q-9uV!Nk7ag~&U6){rd=>O1*l3El5-x9D7!!3PcKHU zQnkSTjo|c#jQ?&}CGhJLhfPUN#}`CP1-us!m3KFRXsNPzf$SY1KB6Z9uoYsfiFKS3 zA0yGiRrSMlWGhpu8gq}#a#n|fK`Wha!-&Ov^l|JmR5a9Lii-LTGKi_jv+YawPP6Y7 z3a>THYo@hHDdEXlX0Y=few9H5HgQ-4$E@t^S7UFPd$fVvLE@F9LiP8W3ZH!s`V~SH z$?2v*NXr0DYwZLf!cPr|MhzVr-6zRCKgd-QqPT^$FLb{&3fLh@P5ai0{2-D#av)f& z&P(f!W$7|0u5?qkOJEQAm9#Hv%!qOhbze{;Hs|f(~jr`e--GTv$0mPI{gHtS)EOF)ldqH5A5D zxGKYl4*P{cI>faV;|=(KOE_lw*5YL}wYK`%VJ{s8pMSis8ofVJKzNeeO~R3mQjdea zWr^U_GJY5EqnN5LjAZPt)4-y}HACrY;bnBg|!ecDnj2mFnO5j>$QjOpTmMonA*imFiv4GG_ zxl_b$l~?Wvfk|@;5dc_?>^i9!eXCqbi_(gl6-x4&2bx(6FtmZ9c0tsz-V*uR*&4ZP zj&twbz%H_{r&~8sLeE^>~>9a-IYy^+@V>;6pu?`)}j@f z&S5$1b-XANZ^$?PL8FMsVHA)XQy!l3o$pLfUfXPBmSLsmq1BZp`Q0Mm2zV4(- zCT~=r@0?GFvbfLwZT%9m?B0@Vr9;gSz09hGfIF4mCnHKUVnRYBkZm z^jYA}5s9g98<2XYVu!*G(5!m!qjuigB&!C@Bm7Y{UdA5KFj_OYtPcWI0M&cIWJq}F z(3fN;uP1M9!bA`QF-w1JWC=OWs$t=8B4R7qd1<+V7)y&piZqzzO26FnC!L7$6$ZLr z)JV-I(o07hpVrw3UI zub8a>yFyKaEkniF(W97T+HF4rG3=%sD?EBhHJh^QBgiWqYv{6>Fh8!Xa`WvOSfK)N z1AHX4QPA%FPWJM$dUt`Ve#T5wOa)uf!}v-Cv~>{IcPi5rwRp4jAxJ0F2ibA%+kHft zVa}b8?u}zX*3KIn8tb)`;WRTUNprX@CoE__MJ>24Zc3%197LImYC`QLg3Lc+BlkLu zG*1G%fVGcg85(PBdBc$cJN{9k| zBw_g=EH3?OqYut>zY^B-VQt>{eUOW$Gpu{xcA%pahwdn6(9cPDwij!TN3uzYArV%i zhfcHmq^T<##W28IP$2jED$$>=@lezL690(U1YX4G`ycj11QsV$73Uh38V9@KQ7vFB z3Maz2(Au~zV{@ojnJ1Tv**%K71$?(<_QrO@ET}HP9SJi}p;U-Pn@YFqsVo$pOXGhXdLN94s2l0;EHN zf6|u~0_&9+efQ2zFia$K>=$|_6BZY?4z?cza&_uiaafClVkJDMV_hG!u;l;`F}29nkaJ4emNNuD_4pBfcjY$@4g_jdJK+_PBdD#PnO_A27r; z0|X5TN5~SK$BIUgS_45=>r;xdlL-4*CDXj;dhk{i5|_iUgRpRHm^9+XOp%J{+>)O; zZuN8}NmRqU_HLDd?# ziz!?j{t&7NRiotDE(8^4Wm@92vnNs*q|AkkR!d$yQTmo<=R9^_H{UP18Qr1{92tg= zzsQG&^BEsjNB93+y2Tb#(gWn{<5$jY6BcUKxyfo)q>N7uqecNqiVYXg_h&v$xx! zz9zSQ2tvEmS3HC)HX8@$B|ry(=`qE{)2+vDv@{KIUe#6kdiF|uI5g4}(5!eMh)##FY2jI2e@s=xn@iMCB9hVBirz=9 zs!>tVc3*-V=cZ{SBN*E3s5;g@#SZCSLZEl;zE=w9z=z(YLTY1NuVCW499kwwg50f9 zHX-jU5I1^nY}>hsAsNy|`0$#96m+4+RW`a_#((Li+*jKaOzr+#r1AU#MY%MGn zTK2t6kf?SyBjXh>V#S)!p~1jP>0;BCoSqwq!!v-it}0l(D(rDnXb*-XtT%C8m_j3! zc*!~nNh>4canL@(VkNFGfwje=F?&hh;$T|JaK~IIqI(ZZyJxqa<{Ob*JeCmGABQVq zkQO0$?tr?L4nSTyGu#Zqzk5s%|4R5&gRdq�as*Qy^;9tk+aO1G%c1zv zxescr@ay(GSEeUtCu^ueX#TC*>;VMZ=Axr-c|C4Vj$p=ITFt2{@pPaK`Dazx*X2c! zGN;67e@`9TJyJefc|7&S{^&IG+1VeSGDAGx5#(a?S{oKNh%U<2+r?Y@4*TRoQ!_+6 zgZR-KXwt~i@I4V?}{+ZVy(KN=;ETg(~h%~@Gu-`p2Q zQ|IPMo;vQRrf)J!1U^9vE#i3kwt<&+sVU40NW;>YcDq@)DblgH#wl;^{G(4NKIG-H zlr-!%b`Ht zJt`BdZ>aNhinSg(N?{>*yU<&x1__0T(72u%x9D1sB?Zv6_2sx^4MT?7s6<$UB1Ds17EE_+IvAh z5sm8w_-OuezeBXs?uxWthuVp6)rO1;q*(@oj-^G82EUqA;I60YGMTLNKAp%!6wR7K zgX{?rS*N2Xp!?D>*hHs=Qde3czN3u6Z1a>lk$(hDw{$o-qDmCeu}_n>iW-E@ucf+p zAReSmKZ59!4R9thjGE}xzy00#!jUEpTrZ`9BFTia7K6KC#rfl@!@w(a-gr?EBDcj) zKumn@;Tzn7Vag}`TnQHtm)d!f(MgVm*20Di1Yw%R(~XHiZ{f3_*%<;|?6INy?qY1! z1{~eTnf3aIcrz!!hbA*M*CmUcU6&`F(F-+JDMH$YYnb^XYj0aaE?ffAbH+Hwm7{mU z>>VEvpu8!Rai^A4F%O!)D~b{z8YwOO3BLYHF~MzVmr(tD0echO4zhPGt0c7m#+7<4 zl1x#$%;CWr53lDFvX-XV7jXk`O_k+eZ@y}FAyDu-LCx8EV9U#Ax-;HtB;;3L(>);{ z95CrPCywq(CD|Ka$nJj)T&Kpp$T(6J-hYdDDx?OR1ZMM;1mGI~VHJW*52B6Sp z6Z}-nSlb1X^R-2Mb&_-y@hveL?kXiH%aQJArBcJGs6mADw9*w=r|q!j2o#Qck%w4B zmoTs${`83Q`2mJuFS{l}%TqqhKx)x-WU+l?84ba8bIfv&5XZCFjQt{cxg(<=Kl^7r>kwT2JgY=A~M4?Upwi8oFhLaCRxPCV5 ztN`;d*sgb^lpe1Qv3m2CWfSzzchfdP9)3`8YKxQv>W>#o^`yT}#`1!+lPCSe+ap{l z+!U`YQvi$MI=4A1o||Y2J%nVrkY|mFjZ3+)Bi~Izyv5zTwrz73RYji&Zo16N_!s8j zXV+Cj3o~PSsTVD}3j_%2b8My6=TroT92Qr=o;wEcJ;l*apyssMkaOnli(o>ve&Z%P zL#5KS=tAw_pDb5Sp;Eji<>foQE)o+V!#&reQL5-D=0w=$gvW@06&w${nK1$7IZf;?+=uu+OGW+-T34GQc+!yt9UoX>OY z-hoRavI}_#TrJ4==jeE4R$F8JZ7*BT$>C_QUhohnV`-KsS4zy8&O3;+kR96fC2g@= zl1mH=)bCRASD!?QqlRh%=k3su1qo8Abw44CliIo??xSUCfyg;z^1JQlIfawz6+m_v z{az6@;8`y!XZQOC)CjpYZkeHflc&iuSrQO)6YR}kyano*xylw3i8-ir1{=K{yBIxa zSn{D{PuKmseNi9oA|dWoXft@`5c1lb$=y7Rul@6`@>|XL3NLiGdQWy~xcJn7aE=ws zzCw=ofK{e!mUEK6n~#&&4v?IZ+9p#3z~ECW>q%rN^Ezd7MIoirGH`GmE64l@>4?ib z43LjM>6|}BILUdW5b+8qe0%crovq6D_EmdU<ehJZP*BB6PfWR6 zmEd%?%d*+|bp6xuj`W13LfuhhxKK{tm985YPfBDcaV6>%=CJCqOs3W&-w`RG2kJm{ zmb&mFAR3~-pD)B7eX6#RZgolBcA8G7%GMoG$g-hzh{dGq`$A-zO>yjxee<%SE4CbF zxjuUS4IOVc!?{J~M6L_kI{^?$2ddN&w*OhZ8!IIVsS4_Y`f+Gn!qc23?cuZxNG#;( z(ap=G1X21{(BsfzaX})6EZpH~{1ZQi7@~f?Oi!a!Z@am3M7TDn%t|Y<+(Z z^5sBX-|FGR{kM~+)ijM%mi0Pgdx$RtjveY&)L!&9jGOQUw4B_b17hm?T%qDIoo3Ym zZXKbSA@na#m%!UXo2<{@bz+&v=6tTf$cga$PBB@mM(@)9^$TZ{SR$Ik3g+T0{hHgDoT1{u6_(28)R%ZqDH&SNdg_z00RA6gmU*VQ z$DaXGwd(=8EVD@gGDG<*83(P}k9*TZR&X8QTv0BH=>nW;ZI_t#32ASQ#hdllDz0`( zP4~$oGznd#IPK7wiLpPE@z;w|6nmagOOu8=K+cygXa+a}U+afwRUHe{mbsq7?k!zH zukR%L$XJ`w5VwKaK?)Vj;ds7e!@y}zqcyC7ouOGbBrN>fMRqo~h~ER8+)NVDN9U-= zFnuW>{|o_K&$(7W33rok=EwUWY`o_!x)s@r7@rl0n4{f?8n;VI5T7;{%ENwma(IIX zhB*>)+AC`@nzUaprVRnt>_#5_nBgI75l$pU1F#qZZu?IBZ>t$XdNo?lKqG(@+w2ek zV?67Ky4S<#q)q*`N9aWgNxvpmB%EF%xvTh)v(cnCg@~P36+dBv?uTfxCc+?hSly+> zy3p>xD^!PtHdIHZQR49^*XU$wZMHkl0V`xY7Aaq(-VPuPHUiNN+#`pOz3T+Na59nL7?i|9-d7%*6Byor# zM>M>r!;d<>LcE{)-+g{yhS}1U*_Upxr<02i^I6buF>PH8KWzwXj*>Nw4Rl&mY%2d< zx0_#@Zb^yN0#%FU)g`jOE zqo*QXgB*D+!;D!AcFH?8gfWr|mMq5U>c(W>tA!D`S7UixxF+d9rG;lM5=4iTT>YX~ zKsFR~>ZW53AiBKCXniQj#Dz+9sKP0hQg>*q3)YzG4F>=H2l#P5AH+7dJD8g_;5Lnj zE_kWX#dVk>3t7H}GZ(IGX#(mV54^)_lx>Y`h1c0LYr3`)Bo19W5Z}06IP9OCt;Q&# z`UD==13Mld=@|mfSzN^{i#c!N^Q2*PeAsf$uAv3&G@rhA}>2@_GN+32@t@?zk?CW(C zq5J`&y^Ew1Ws-fIQRPuV}7nIOVlNPd%;dBR-&$v=;;Z)U?#{!SZxC? z(d5R#miWDU=%K1PiyR`(w}_`U<&|0EYfRR?

rJV#PQL z_h=9oh;nX&(%^gM_<=p#VT<}YOj5lv*c-_#nHkjR2`LO}u)QU)0dZ=|hf?fs$o9O- zUJA*nt8-geO|H)RG(b)&;r4mlnLzhkwe>3+`Se<|Qnk^jC^|4)74VlxfJ8J^Pys%j zLx@_~2AXi>-nWuI1mOLE{!CKkzJ_`s_<6N-53DxY*kqZ3%X>G=!1*yFiyHRI1kstG1K zpSx)&`vi(vz-KOChD)Rk%>Q$v8yo(V+_hFG87pxR#OESP!4;}VH7DMsZd+?Z!y$ZH zpG(**s#r5xr2`oouwlUyCq@=^-_?;V$l|Rib`m+~IS#~e&ofnX7+Q;oIH$tmO@?4t zdEUhbYw(bgrQ3<<<{@A@0;3bmR7KEy2+QhhXtm`I^#!K}s@iVF+8#3&H>5B`G1 zz-0`AnP7%z&r%PetBnyqlROSg6fb8kPPlo_TeW}!SD5XGT`ls6hsDG3f^Tb0iE_!J zc5sD)Jt4NxotceT>_LBZl+kN~$Ea}CgEBc$!x}NWwqB@On+#r#tPYhJc**Y9P9q-(XCG_-MbIU9%9(&f>nAh#@q_8c_z&B3J{CKBr z5n!(8UY)YYJ4Uox7|e54i}&mYGjm;Ihtbnz0#z1+ZUMzA zY;~kI7e!0|z<7tmkm02}COL#eFr}ydpGEy2rthk$+p8?1D-!bsJ_B1E2u@^I z$eaHjGE_h0jc_EYD+RKI|G~|T+}8GXF`qr#`e*XZE9dE`x;oW3v&Zxn<7=W^Vx>7l zq$ZmWzyw>sR@%Dy8VEqb1fqw=!<7{P3yTaY3kw{vg#|ShtLGjbEMha<-0)r`%cq4o43FPF`Nx#oZeKd+@x-=ynW@9v&J~RL}UOq(~$h->>knc&g zb6qegKi^jHzL|laUAy0xAF4RmGh0(eM@La`GRC-8*fA(Qb3=HLvI+9~HurXVz$rdd zUyO|PPL6=@X|5@&t7#rT*dJ0`u(&^};A#GrU#`J5Cp0WFHZ^~1SYCXU$3Ilj?Fx(e zQ4?a|;P~P)sTOp3NkqoY$(aR8ja0J^8D)qf=lj;}$!G~Zj%wL)`i6AO|05VfG@W=9Yq ze)t}onI8dwwzRhVeR_VCzGwvuOu^OG(mDZo0IIF{#C!_^hxsOb_3x0|*4zML*82p< z;PgH(pLcCX_ShTkK-N8f>3=`-)Qg*!lwg=Jel?$bmk|+TbO3Zs;CuiW!CA5VvIA40 z`zEJB?>=|MEKFE_O&;KN-Q$Xh{C;(V`m;aa&0~FKfwp_mf^qM9>y@zkkzhdPzA@a0 zSZr7v@3209Z|i?IkAE#Uej^@!4flR&$uL|!KYOXqeheRe8|WPC>R*3aVckNuxBEWx zt{`@x=6;!%L4PcxNwBY}e`;lRreV5J4)Ce&j2Igo>+9^lC2bBV4G%$^j9OXX(`?QjN@#)Z#{|i0$hQUt>U;mf*{g+_+`IngfFLC)VH2?E2Fh{%8!Om z^)C2h6he#WPF9O<)pz-@XQ4Vk2P1rf+Z%RpVE92%D&HUi>yoIA8p?7{hO*bgU~V zAleDur#%z49|B+(moGf#HuO?n3p+ZpJET8G@J(Nfv@|cilG;C|(OP;dGJBPi_juqy zKjM8CU%F$EGbjHfdOdtUt-rp`UwGGs;I40IkE{cnDkavA%qC(zCwUylbC$<7|EV-M@hSu#fMHz;?uV zd6T^g-~aAOZf<~X(l&QzVeY7(@xESV0rBUc&0?CEZp~=W4K$G!Ty#lfj>fxKXZnLV z?k*o;18!=V{73yg>WbzDnNMHKgzszCzso|Ur;uU_T17aywOBY4qhm4Tf!ZXUt?N?o zT+(=C44`;(+9=x{uc%yHFw-0Y{#M!1W-x_t*$$bU-KS;MzMM3~7zLYUP~J>b)9#sL z$*9ZajTjc}-M_!F$>#}d3^#625myYGns6SKYx#yp=aR&aVRIWj#oF1~!v9UB-<WA1qQW(y;equy{Lz?_ zLr<=ree}dT8L9mMjMP5nn-lKo|Dy&X>S{=` zDd__GjR!4RgK-~O&ZDf+dif3_YLgpPRI}}nvueQgdD8M}kd7qp+<6pgFi?~td%{*; zf2F{RfOXrdH&jcvLO&3;Uy>HZz=91GF|0`;LlnR7As}O3NlYF?!#z3WtC*7&e(?cR zZii;?CGWp6E6{@OchLQ#5aR4*iGcf-xt>K(PCbsqX#+9qbbeF$yM@&Q-AJasowjy7 zm=k1j47l=d)GusANW7#HT(7Q}K%1NvyTO0&`Yz~lJ>KFeX2)MDul6|43v{YX6f1Ad z@>0)U4kJN+!Q1f&&)hkRZf9$o*@uwGiz{AYR@P&netE6ASjFpwW|z{egV{FiPZQOUtf$` z*#db7pUq2(MzZ!RZ?_a}P|0HJqk@E%VM4sz)oSRO%~6pGh8?IHRS;$yd+r6=3povB z09+&4I21il!r%LeAuo!T&PoD!q&VTccgsxfwjrQC>XaIND&%km?239d0O)zg78?Q~ za3&6j+2X(i6;v4dG@1*eJw1ODek8Q0vuxUfD%Pt{6WkAU-Bocz<~K9jihwkom>q7$ zob$i6h}5vGw~+`v7Ce%~?X;}Vf&}f-SGk+$@ztDAeV3QgH7b|i2Dcq;^navpwe3nN zl3`L_Z=@Pnsi>gz`Ckmp+wMzA&Q@gV)487=8FppuDb`P@pQo~@t+ogepm0B@BxP!4 zP_we8X`q{k^O@D0fSf_q(!bPib*SzLfQ|6s~8>+@ZT4soPzrj%gVEt=Zs>)ONVM&8nG z^e8c?1IPlziyPNS6IK2Vn$cOgg};$D=b5G+=FRc6&+rw0cCAK+@HkU4H&eu=Jpf>MVc5+giMsT#Rn2RAyHH3 zWzAzd_s4SLGjb*UGEiQ$F%_%OE{yDk6o+H^>ACi{!grON^@E>;5NP$1n^nBeix6SH z%I9#gp=(Askidz;eo{xJkSMvY8sHYMTx=nDDJIhue^qq$e`9{P?EGV^$x~KegAK|N zLT<>ko!kV#tt5#TBV_YTsF>=ym3B=Zoy}hPL}Zj$d#7$X`hfd3HWw1lw$u7gj)b^0 zgamcG%qL#%gR?#(vdCYNC7)}Vh8q>5Ib3bY?6#L+h&*#Ida{9~#x>P#og5sxp}Q5N zN(4*AQ4JH^VGjq1CN*Aas8VLDmH4PBYAU?`PmX}Yx}2t=0G>2b)I!im)}=zE5|BI zR~VXvjK-3fhwbpBOCFcetV3-ctPKC;nJHr8ZYyyJ*lpS_mrPa@!a34b=FF8=-|PR=v4*G=l~XuWIPWh65zkIC z78Or4i^_faT?3S<>Y52sgmJqu$XD&$*D(S_RYbR2Bb1`xVqjttS?yUH9UpHsMk?_- z=~gRQjO)a-p^jjE30|Wbr7@@lM#R!^rOwjzi7BXc(d@S8--TBo*$D~~CxN8TG0Vjm zSNF$W!y3|k3^9v748A>jB_JM~w&@hT+Wf3!CObB@{ogT<_CaMy?6~g$MM}(A@UhV> z%M~01AVbHWk0l&0@DZLUiy~xle5Sp6wTlZjO~tC6&f)mGpkP01c!Wl4#-1K}zp$&b60ac&GSKCM9O1NYW++RrxdiW< z)OA&jjy^T&`Geb}N`5m1k1NI+<@ASXo!We53dPGwyTKM5ni-KG92>&>HqPcA5LLC$|c7Emkok`C3-v6q!3ru6~ za3Gv-qGOd9Gg+xsKVN1)4I$lq#@eb!_c`r*K}GBP;)}FUEG-^T&HF-DknDqx9nb38 zHMaGc9@SQR_KUnA4}qZe78vbc`xYUd052Hre+mBK7z==_l>nP}yon;PXRCSfkBk|F zQYh&@sRQvI56T!I7Y%vZsIrf|lM-nGIVHxMn@CE|R)KO|0pm~ou~BBqebNdnFdj%` z7R@hMk0)$Q`be`G1_adAU;u%)iQgP8##^}=w_Cf>f7rn>G2N*3@EBJ2lv|kRd7?my zDTznptunheHx?-?_t+R#R`)E!C4G(B+>NR zDy^uPPYr)(+s<+g7gXLAjv$n%)cu%AWfM7`H4X0mA8}zK z9dyx@bFrFB8R>m`_ibEdlsjFb+d9KMeh^7~;osuw?0VEE<_)((QUHw&RuRKOy>|H& zy!c~IYZ1w^%4va`OyKOw9T~%34KX`p2BT38vYz3M!l%o-hw$<=tansaUizQ10<{siVCQRux-AoJ#*mztF)LSq#X z^H(n}HKvPlzM{OhYf1*6!k4k5A$dv07NwUY5bXzPk1}@qp2_EyP#}A-luoYsl7|*W zZ|pMh`OqSmi)Z|OQZ?|JG9i;AH*Eh|z&!V77W2ik;d;4r`Zifq3Ng*+I5o(OYnoIO ziV+DSOU7VV&#J?!c_n$qt-II7$xx*#b3@-kJrEV-Uu7eRsnse3&wIyWIpYtX;fq>A zB$ujIfmL0vDr!BMs8{&7zzGlPU(LvVMWAg1vawq$pyA!8igCub?K4?5)W?hK-p^QT z&Qvkb!(R);z0mdz4N62r0^Sr^NF^Y%qYT0B8Em=wKG63u^5m-@Wxa-=` z15D2%zNn;mZ>y`GO@!jOU_ihSrLt++@7cfBD0%Z%Or?%*3$oaYJ`L-ReDfs;bCl9muA^sHO)3;;pI*3K z4X4ip&xQ)`yUgH^f;Q3D?C56=%H2oA3 zz**_>E*88jGN;-%G#w9AMSci)F_NcA2wVpFE_taxH?j@a=92Sr$Y`MDRascg2sR=` zkF9|et=5o<8tJ&zidlv!zT7SXNXjMxI&RMc|8hj+-H%?_ytrW?18clLaE1z8?Yylg zX3%aGR68)x>U}{@fM}vMMIL@#Al024eTG zk(c$^kfX#VJqV9#qnQ4Ipni*DtQtR;Sz~|NzT3NU>0EdJ)46aHg&J>#f19(@^Am3w z@h92BH@a*el#KH$TeS}JV##&~t7%Y)S2pO2wwAm9MV1Sr!JT*&YciZ7^=V`3YLfr1 zpy`0?(tK7IdzqJF0Tl14xgJmKF)GR^5)I3pN9r`}{#<|`FRjZ^O-4~dsaC!ODGr04 zR$C}*K01Whkfwh21^%0^qHZyQynZGI8e$i667%KNPQB7QW&3d~X)xl;k0NETXuzNn zRJ=JEU%6j9F)_w9Eslw7smhPki$m*4F&C;JO9%Lq=mj}wyOa}i}I^9PU)9A zA0qW#)m?7u*JvD?CW;h@u5zD%@B;xF=$j?J8F7gmgOrUaWO8#M;uq@OO; zA?XxJyMldQu!c1In!pNwC0yH|6~|dl^JicwbX62pjAfl2Y{MtXPQnM1Qn;J0mukCV zgQL^sD#}&QR1pqdI{t* ze=n4tepC^u8M(1#)`6h#{%Be8N-*P+58~rq=cdcH4;|pc-M(&_l_sOBy1jS`ouOPS zM;qux2&~?JO72RVqv1R#)dR#`zPa{5BYJQr!Wlu{YmiclzM1Y%MZSU9PTncp_ zo9nlJiOynLDAyZO?z<$J5t1QmGE+N+SF7Zmexnj;&=i$xW?mFe!e`;icf^&8N>y)# zmF3s%T*hu>@nnQHX@>~E?(dr{!>F}fZOYA&h4Ve~gnxw@E3JV znQsRE$reqn(5_`o==Cqhro?aGN@D7psyUz;4 z_$I?aXeSD_mOM82v+G6P?90cB_#4EszF}5jFR+d56BuLZ-jVBg;-kofU3a`wfgrgA zG@VR@+sJ3gMAEtx+dccF>AQL{cMypIZeA?Jj2?eSm|euptNE;5DQ%o|BHFyABT;B6 zOjR~Qf;pX(v})wXZ9Q_3N`vYS`~V*It(V(Sc1mat-F z9a3h${w7ILc1?Ef`k`1e9`#g6vO;VkEv~z)i4s_}`ff$ssu11|!3>=Z=H5?4aJ3Eq^jKbJa?k8n>c%BVT}CDr{N=CaF!bc(=_E2it{K1j9FkkpmP zjJktnSnSeFy`YNHUhldNudV!LAtYCcmHf*{{m*t`Og)Z#HMEi5fjSnh^f0y1^H}5E z_=&83u;w74ko9~rj-R9-AZkxAOXvbI4I{t{$&DqVA>|tQ#gIb;o-itDIunFbbwH zUqW`fmMVGk)8y=kNXvhAhYd5~Hg!Obta7Nuh}A*8cw64rBtsY+-j14~PckoOje1lw z(FCQN$hszOA{9n|!uCi>Sd>hyl+g42kBJwi0fj&xtdbg~*?z>t9IaE2>;|+v)Gg&U z)j9`Ey{?Yk#2!&lp|U!vnq?T4tP>T=uGabVyerP$2)18f;C$j%+k#DpaCrHEW#}b2 z1nJ!SN{ihw5EbHS$AFtc-(Q~8gpCDGx$M_-R%d6P=awcz3_t;j>UH#p4?blI^4vm} z5WyPjGM_sxJgRH`w-?Rx3VBn&Da#K*PIvKp&mFT1aHS4fa6r=Lxa?Rw=c81K??$iK zY9+afNz4fD4tj8AhF;5(A(RzbYzXrOq;s;XEX6fx5Ej(U)ecpNa|9zVlD=_&E?-I1 zQB0n~05j*EbcP{n#b-B0HyGm2>T|XG4PUO(E-^1L8&P+>GF8t2M$9W|pHSw`@K8K& zI20A)j}S8UlTiQVqqto`ymg&hmPPwKmp~h+MiH{9rMYJx3p{&`1EeXU*8#g!UwN^~ zI2cEo0&-7vR{OQMp+jxFh3NZN!wk)ao|VI@sR*eqU4HD{*;Y+U3^_0iYl3Ys%UgHk@l%cJ-E+=BTOXl5`s=hKOrxpY4>7T!|rh;fX2X zO35y2WASeZ2ztLl8wDb7NTS5vb}sJ#r@LL>;dXtugrjwxw3SjXUKDEYFJZ{&eLE%r z%uH>)`M#xg7Yd0yCQ*x>eO7!c!G+q?Yc&7Rsz}fZ4n3GuzK}Xd1W!T&TOM+lh(O#^dyGYhm0=XC*W>GZmVddg}=Wb2Oc;L2I&gZzJ<355*el1{kK)88kIV zMIpIIDQ_JF2&}W5i_!kI{HvlHDMWf>x1%;0lkdAZkrUrvn@_N>YqYDT81i!`9N|U@ z-a1B9qi@{RW-KUg+gQ#;lPQjEq2{BGzp0Sfj^moh0~LKwDzS>03^&zDcWrQ=8Y-s~ zp{y#&v^V?D`xMck85k&I>-X{{A?1E&&iX?UD3PEtxtE&cR`B!Si*sFXE}AL&iC3_u zsS-rI=Bo++z=msx_ zcQ>EK8oU<8>@$U3sYm{Q|O#0F)w@u55NWOK`no}`49zyy$%)ks&) z58XRb>DWcQY;WRI_K!v@7||)0YlM=p(2&lvL^SFDVWxg`Y7uA|4Y1&sA8(qDUR;T` z*4&kI{P+Kv$BF`}nzHMLMrlqjKkZtW>7O#+PbcBk#o2jp4O-N3zN4G{A6w@Toe9@8 z+Nfh29ox2T+qP}nwr$&X(s^Rrw)MYj-F0W*gsPllgu$tF$oKn?^0kBo_Wth)FD`XAGG_ z0w#YPaV3y@%FQtG6a(_SbY-(%(tY+wUI1yF$a4TJgK&=n%^f`m5kIJ}E z)0~!L%@yS>UjtaYeCunvxA6WJaWIPe+;$61?m_^2=`I zqm@f01yzrUl-k(LlY?(ot9wxAlXOh?x~XYDAt;jITNW=U4dEXf>+0fpMzSm)>JG=& z3s1;~ucrsak!B}Qx&omofx134m3kZr19vkfkq3LWU3ip?I9mHoD-3~aQ7g+rO zh4?%%HZ<$LdllzNmWTvD`25)L87cY1rTlQr+S*eI`{l~aV^Pz4!6oh&Ltxc^H~_gq zFrwjbS6vYUkap<0&Y0+y6zJ(SE}JwteXn;0h-dH5eMe;|dQigGHXteW^M?K zmDh#VQ}>;W*BzI?DAD^GjAza@!3H8J+tALfrQd=9D_G9a(R_7GjAytNsy)vEKif8M znrbPbnW8yGG7(AOUmIPN?B6U0M)eoZj%^unCx`Of_-~Pq5$$8A4lZE+bZ7G<6Fud7 z?nkMq4lAKhSnojOsI{Q=sW{8Gi3iJX8x1UL1Cd2GOm;<@*3;u$Z zHpl#~rvChcn+IBHt3$84&9%=2)SNmHIt7rgl z=zd;3NCp4&rg%FNV$>Gqxevd3@_~arT(8ccwNG&f(J|!hwuf&&rEPO1t$BMWnPr#* z=kC$xiW8Q=HBhHv6`4DEgTp*tF_qNz@SO*nQ?VXARkKiFY29R3Bmzo)RkjFbtz2Bh zncM8&a-B67ou)wJ=82>QyL;d)fD{x0B2>O|tOZG^#q)~VW{Ea(%hnFPntXBHu2BVNT zDm#W8P7$=(XL-lbZC#h4OP#0%_D#;}!+Cqx3up4Ru|#152S`^NF$%r|tC2*Q@Fz!) znU_3aiUXR3nb<;@R1>7ufLz}by-H>*SlKybGm9F2qDO^taUwLy4jtGcF^@a!lqHTY z5l7>i0AbyBD=iBVf zDyD9^F${W2L#ZDrbxB-qS0kR-Gi~TZOmW@5keK<^z{M$eJH&n86@Mj5Fer5t z7puoY9w=`?Xy1Etcl=`Nkd_MZBeiNCG;^3{80YD=r8WEZUuFxyzsC_?XC?$vJjLCe z=W%?D_xoN$yd_8cjHVmfB^0M0w%ws`i#v&vs4f%~{2;4R8IO?uWLtR#_1*P^#Goso zBG9RhzBm()*IMO6)+X(hacB#%QL`hUIL-agL7PXbbadSJ-hb6z2Lla`7d`&d4C#jx z$LUtpR9)y9r)8GNUZ4^wab`v3ypfbF^z&;ae@te8+EfY$yUpe zbV_h@4ynqn?M~L4;IzTAaRJVgF!aP>DUnmsMIDsQUgQYcI-0A^ zXpKe8hJ6Cz5l$3WU0gfHpnAyv%2ffw!>ju6`3csO0JPUsq0=!8HGl4}r+kg_w-r>N z1tlb{Cv{Zo5M8b|TXe-0itjpX9{)M3Q-Y7#AcN@}b4+mk)i_>IKEJ~E1E^_`_!H>} zp&S?m7JVb*|CilWB%mc*W#^!M5sp>74UyxUw_ssKTmAASQp3GCo9pTG^Xmgv7W}o} zw)mLV0Nsg{HI%r38QoROK4a;%5fN&tum&}dE2wwWY6u5_V92Jj*)k$?OIX@_h*3JO z-7`8^a1!e>yZX`;eDqGMy?gp;c_=SLF7h*W6B-++)PEelsTSUyO=3t%z01O7q+;ucKG&um!w^Ug~<{t`dj^w__(6PsLH+`0*UczD>k7czwT_ zI`-`tx{#VVnJZOkqa3m*Ih&U12?W5W)}NAPU#RDt0?*Rfd_PXYNBX`deuh}mN1_2D zBmh6!)9f!eM<7#Tz3Rj1XE(V2f_p2uN9d;Es~5nz=;B{GDn+=ERIJSM3r(z&M7Z+s zV!cZn+_D8>iLb;KP+X8oJtYAx-pR_m|6E#Qyp!B~COducxR}zd40)%go9k5y_$X{$ zR8+nR%ca)4qRsi$L64xB3^v~`Rvne@zoL_L4oo3x=%%iO#5&AkGMiiQDs8NlIYzHRBvY*CiGvN!1?-W$mPoNH2Xxw2~ z5KMW^sh;3K<6keK#p5kr7F%RrH%~opfF)~tD{w}IyMbJud8Os`2x_&6Vqeyi44)q3 zO}Isqh|?d6La<)x6U8QW)T}i-O>3|po>Z`XmjDlw<{2*PSzGPu$TPt|3Xm7BiS$>MRDg6@o$JCJQFCP6R8u}Et zy5fDCg@<+ezO1KN5uN$BemMdrvPW)loT$P6zwVNGVSm5=!=4J2w3H!|uh$Q?bn)m^ ze8i3`7YFx5Q9Dq|ry(tq8Fx?pbjDp>-9L&HFN9d^f38o!Q3wAR&R^ABfTch18r1%| z&?FR2_3?6z?t+P6i+Fi&A6Wxv9O$p0_NOOlnF;+}m^vw8K5S^}9&YA$yEjrG6$Y2A zTbqZo#0P#iriERCe51OKbp{;y1W`&VJ9M_@7G+e0( z`0rGr`K&~qz2`ocx4C_pZ+jg{ePJ~}H@SzDRf*plr6%2CkF2UdBi}4IeA-pD!e6^6 zT@sd4jwM)aYvg1x@Z`wQC=EB}?--Kg<4$S&Z%mwuRB$J0JT!(PSY}SIL|}(!hs|bW zRXnz2P}N6;>8-Z;yZuVoF)NaE9DEhD;VaNKa z+!%$&fP7sVHT_o-#hySlyj04|>XfQ%1r_;<$!j6qIcA5+@*S|HUQ<$^!6fkPEnJZ9 zA-GX7hpx;%IrLN%QEz8X5clVU=3~C9#LZ=Fy4bN!mzt@ney9iSBd9q97ySr(bJ^*F z#Wmd~-Tp{)VYvF8!QOLR%daQg71biI&Rj|0#lbBb`p>H2hLt7olZTXXT;|l^$0i!e z+(kBSbh5<*C+&{T%$8@3bx~X97+7qHj2*)GpiwmNPNG^lJ1Ciwo_M)b@SSL~PK~kG zOyPuybNwDXS5jeO?N{#naSFOHQW^?g_JKri4X)_>LWrp>9$MvQHS!Gx0UsL-2s_)t ziI850gp+4;q6xCgx0pFwpoSPAY0N@if2s1ar!r6cv8`Wh|(j5;dFy0b=LAgAH$W83|5NRxbCcnra^VD9Li z!L4fWZptmmsxzr`hLuKsp-3iffF-{|4#&)l4X4O-`+7aWK*5TAn$76IO5Xz6KeHXU zoUxmAKolLn3H6yOAhlNOZKPD_Ua+yp;8htdHPJdH3JPctF9hS1r!0S{-oQ2HLCIaz zsg^xPlYG4EFD6cjj92KC1K>OyY|4C03C%3gNTl?hBwN&DII`#1_n< zEtIGf@-b~xY9C|8I9qbE{MP>JQ_fggqnAVR(FGl1ZqEmTmlif5Xp3o5z2 zf|^t@)Y0axZyr~TOp*?0>uluJL+H5XowuL0V%<5y^kTtS8{hm<;YW7<&c;2+?O28p zR|GOmoK%&;$4BT+CLj|AohT2y)KoyNTT?Kr(ZVO!)=kl zm5()_VUAwV zzw}XiNb`?7mKj z{Rp-V?4a?FjuNgN&R3nQ#fI|kMFFn8)jPMdY8gsqPEaI=4P^GCiH;|Z5$rUrX~D$F z&2&Oo2skD^cPr7*BBpXegp*fxsQY5sEBH>5eBU3GJ#zU(ig+)+b9QEb?hKuK)%HD- zHQuB7mc!v~R8}TiU!8grS0Ka>Y%3RWtmdr?9ICn*jyAwjx4Ts*1Ush9u&4M8f1#4A zTZ2|E;gRvj zW0CSS%Yq}EeA z==?2F<7tHuT{qS;R~Oy(aQu@rp351j@IcVOJJ5Tm>ez|QSS?IdYK||p_UaLFpEg;v zuA*a_WAJ#dN9?&m>S~y=8?W#<>?R$Dj9mkNO;dGl#-#H`U4+De_1HI6opt<*96Jnc zj(q8#2O7*4PX$>36UerE@C0AJj+0w++Amd{;Gc(GUY?_r_Av~)Z`%=aO75jw3Vy%_ z{O5XQSmPPVMgbWZbNdP#m>lF-wMeT>+5sS{U;``K7{50kys1Mn=-_KMiBSg;6MXbz zWea%&-zt(x@S0Ykn1H(nkKw#%LCT5lY}C%h_sG1I3_vSC$~~zR=mUP;Qeidyo^}kkMHd8-alNYVerA9y2c1E$fFKHw}7pj z@glBVl*@6>z4bc0D$0pXe>83GhI&p*_tPQ)W*Q71dpymb5$ z9A9nNX*yWuG`41u>XrP(*Xve(VXhf*koGH3rs%pmGZm9cTj8dT>^}oTe)L~t3OJ01 z)_pCe*{H(kjVFv4+C@YI<+&y!rPSvck$*IO{8LmhtWHvNvdbT<4!ltXY319;G|q)f zz5VfVMUo;Nqji@IqW=?*eht|o#K!+687HuNzq|=?O7%s2estHP|If@&*{C06^uGU3 z*@)?1Mvb=esy7^`##`vZ3S~`gA{( zF%JI6{(`Ctq~u$Ak|Y8S!P#U93-!7H%oN7p{>PqnpPJ(1k>}`lE6-1BN3YD@q`fVx zo!D|lexD#Ad-YEY%>@2@;2n5vdkRz(czOPKcFPfzLJ53_ojzJ(N-cGm+FF%Nwc194 zYmHz=KLoY^j95EtAs1~Y$bitsr99~B!y!M z7C|jn=DP%Mmuej){=f{XyQA{z4=q!#UiYaR{rr9Yz6MNl$g8&TMPwO zKEeikRBvUE+7KR&kvd)sDila=wz!{`-QaH859MW+8F8f~LB^`tkGLez^1>>cJ5-k$ zfN_=3Y7I1vly|Tv$=dWuxq=e$YjHC;Y6*x<2Jj5qr)(6#!__(s$f!t7TUb&9xmm6< zqj`|H-k^OFik|&hImlEpFen6vXiXo44&q~~^pCA#GHc;-nC!#;)_1F;EW^Kr!~u_^ zX=l(O4He489>jA~VlSD051z(pmrOP8r7YBLY-jhlZCzW?UF}4f@ z2B{PwU945GEcTx2MUwQhgp?ti%0uzMF|7fXBBaNr>xW#e+o?_q7aHx{A!9b*?d>Zoq2C~q zEMV81(BDQ#1@{=mPpsCms zUWethQ3W|?irDIg*ImW{ZUvOyqyws|f-5cjBcSHgoUg`ce27%Niqs`vS6>$a!TwN* zJ(h4sE)R*VK3PwRiK#Ru_@y3Mvv1q`pAEYgVFc6_pk54dWX}m)u@M zRSsZ+_Y~;6v1AH4D|s+=s*4nyNS}U-Y=ME^uX4@@jOUCsf$YdK$+nTMgVJ9JM^4h1 zZzPWNc>qSq0F|F|btJ1f6S7lF24h+|bp@mu*7M z!*#QmuB5=Sl>P$SZI8D6(JfI$Lrj|)YKuv)WrmEWgm@)g_Xd41ffL40UEPeu_&fyJL= z9{;e_&4}x?%CNP)bv=_v=M8IDNYY{%>^87y+FuOBwD7|X6ZyiWNE(c*Q$A$9uF zHXonC)|)ZHoNnmAcCnI=#I}beoUGh{f_!{uHB=lsGR=%H?8OKdZ^>3Hx3ie-x`1UZ zCaAL}YtoTV9SVRRZys1u{Ib6L^n$}jF(l`_Cs!~JI3Q^ZHh(3j0BrE7aE~pk+ON00XYhF@#b+}KQ;ArDZ|Cf*vhFaa-Aa17r z(gm{9=$mc6giZd|Nsd2F2Yeo-GUyHFh!-1rl%y><+DU#SxEF`VAfC9`{0EVHAHB6y z&_z2PDC(!E$;~oQtcYSYCU>ccejt!yOw&7z7M~1Ix~+*rICvmNS%$3Z$44upqtZb@ zk+x-66{Pg5#y;^@g#39;eYl}$Oa;azlGA@rCmb~W<^6C6SvuK_MYZc_^ECbUhsKI) zHjDMzdCT=!??iqURJs+@Z1Wz%NLKCUBV0#8-~Tld3q?ManhINkzfBs<&zAYK&Ja1< znk3SoBvIEhsGe}<2Cks^YjW<^-BC}j@ca4C#%O1^ctqyoNRV9;Sff0xdU^w)AbR(B z)w)aQe_oBD=?Y5RU*(2dT+&BV@4SEHyVY6pW5`7;q5V+oJ_r?bepzf4KP+V|JAhTwuI5fPi+d?flJaZ`@W(;O=$h^x& z;<3$YYZ9@iNn9P+5C#KI2+LTC=}oc&&+=OI5<^sQ4dBM0-SSKgF9}(5}*AxsByaCw=q@t>z=0 zaBJ=d{tC^d%mx!jOpR@X=|+YK!tj>Y;n?>ArtX2L3Df35Y4Ad1@1lDCVqH4KAmWGV znxwDNDz0M7MdcF9Ts@zJrU^oX;|Nu3u5z>OyYAIy(4y)@N3+kLt>?Ni6f$r7`2xLlc zfKt=J1gZ2St6znPX}kn#-tyL8x5QW0>OJ>5U0ls6w@yXo{gr~fhu&NW`;=OQKF+U# z^(wwOr}^C+sZ|;zKl|pqW3r1V)ec=4Q{-CxM0JeQR$*f~E*Dq4Q7Tz}B|a8P5V^6Q zZ55K3jU?%>ace@onGxTb<&b{PW=V@H=&bczLy&FoM&0EXhJ*@jh@=Vuk>QayssG}A zTV^c|CDC5!AeH@XVyKd8ibT4za|Ol#bQ0z9=K|EhMTYkTP1i?0Ann zlkU12TU6NC6$R9>P~J)_mgb2yM1T3%e>lR|I?bJ^rCo7pn1-(_>sAFhq?a@;*9*j3 zCF<6hK6Xa;2qpE_xSZq?h0(>!M7;3@LcL^>TxmS*`8iP?jKn*Uf*bM^CVY@R5_-aG zsX)gKR(i-*9w}Vy&m60myPF_rUz+Iw+VvXL5!L> z!SX+T?K!O)+fB_1*JdMQomsn;UK*O5)og$EASyA0d|M)KNQ(mhHPks1GT2RNC|@e# ze!A&))P|n@q9FJk?EBL2aH-2YOaBxkO&3(xYof3ojG70~!;$~|+W3{ysX@GgW50-gwr zptAh?o&+E43%MD*woM5xbnP5PCon`Z`!5hS9R@+K+%m9ek^VHt9S3Mt(ViPHZDabwjoxMgQbu+i5nCd09kQ!whQXc+$wyEkZ`qTX!trJQmYVafBM>`@X63YL7(7c`xk$$YiV`^>$_ec!(*IVi?g+hMH2 zS0>gdRX%V{3A3`!-+!=ww+6|7(U`ZfqIrNhhGOoNh=(U_*7TRN2a z`(qG+dEF~jaVHB$1b~U;my`l%V$KuL#eK+J@NxHv!YEW05{)Y*M}IG$HmxHcZU$yV z1wKpdnQ0Ez_jzcf2p8PeA8q3t+Vy6e6n0OL)2|m_Y6_&qGNu}gVg;cRaSNeu-Vn+g zr@$*hIY!FTcSyO#6?{+OWxfC0<5mQYNK-40z$&3bRTCI0-1YBwqwaQAR=c5xaJOyM zjHB4XHaeO8H83Wz+{kDPU2r0y3aA-1;X&YDQ=}~b6wTdOYc+Y%J+4a|I)>ldPahNI zlsfeY05wwBwE{2PT(oVn|B@1F-^F0)LPZB5EWRG$SX1YJL-^)LdRz=zi7A0?++;={ z(@*ZKaqH>Z(Zt4@MBpA?;Dpl$&N&o=-nb2`&^etzGB^jBgYDsozix5!gE9xgIAuT+ zIFrxb5zY(e1EJjw>$cL$tfGhVOmM#?Hn!Zv8~Hwx&jMSG*Sn|6Q}`VBA53OpbpVqi zBJnV<##(2d+bUGC^Bl3L$PAN&@iB#OEtpgdT4u(NR zuC%1g+Q%`(&w~zfteX%uG^-@6LN|w=RI^lcaWu(5t1}vS{L=%{c7=BF%NP@PP<-X( zc|qN3e`nb^uZdhn$|wX&UDN86Msk_9NY858&*nlbG7-)dWjXa3XRn!j-uMyjVB2`& z3LkQ8(KTkMyZl7-f5VRVeag^VNCgHpDSwnSM`bk3&gDOl#A=kPpX$VElSDtQr3%3bFCxGSDWMHLqos~M5d_>8 zaUGcShim*&N>G)Sa3g3`k6DnxShEpOS{OVN{kb>;F!kx~4!YRU$8|T7ESfOu)%841 z9o*3}*X~-N3%3A+Cn_NbqR6d)_$^x{u z8K$;ub$B0bg2bd(#m=US(Xjz2R6-miY4vXm-27DMGPmL!GwChgKlXdbXR;z2D`ARr zsNyDSMtKzQ3FFD0Q~nbsXuhS~>)R?T^xjc1JZh|BnJOxFEU=ef?&4pC7kIY&!Twrn{>h`$#cuX%IE$3xaPv$K zQCXukyF!NSnq9=uTN!(?Drt7TG}$N>75t~;>2X;MW8&C-kxI{MJEGQi31Moe=CK7;#6WHsr=m_F zxY?_wZ`8;G;s2MBIS==#g@fddi)~MVsl@Qz3iZgJDS}{_F{$BpB=4;lmKJlcsz~$5 zJxbz^nnSFtX_hPx1lBmGV4~m;H{OcY3dxj?8W$A}QTXTPh@NOcxUn){|4j8Xm3t!7 z^~XtIY5LH*&E>oGp@;&30r9YmKe&R|H=(7z`osg*Po~4$8lC79AR`>Pw(PL2B1hJG z;EYvKC!~oK`bY7Xk+#aaczAA8JRf6p|P~s&g%-auTuA5O`TG4$)bL~=@AilLA#&MHMezQUI)}kG}t9@~~ znB*J9d)~rrjKDY3*80uO;wECF;lFnh$0!suArMA1nz}{wU>sdEW|!$LVmed>1Vxh) ztz{4`IrwI&oP{_K&#-(mJ8L3NI8W9Ht`dA-C6+B~$V*F#CaM3X9?k(Va_lHWS+sg7 zBV{qlIE4H)X%F{Xo)v&1T}^hmO3%=5xTj-=?Rg0GN|UQ9#t?b75UX zkHZ;qhZPq>q--~_^S|Khu=j>K+oO~Jps?BKC2I7p5%mk&N#*^8#=ar)L-K7@)Xp=9 zxHq4&3)$5nR|lriMa0R8^38}3ldsd^xYeA!Tay?&?$30!+W$bQRJM~qD^c`jvN; z-O1B~^koX`b=BG)yTbvf>m8=?oW_R9e1$vrpl)LfxhJI~_t8m7KgK}b@ZEf|N7d$4 zl(s!2rHXx?1o=ryjo%Eiy--)clDNHdKv7mu}3nI6@5 zk%_FJA&PdD1rrXrzI*HIl@{#7nE>3188tK^+9}{otE5=i*b5&Mlz=J*p|Qd2*n%T?pB_J_)>) zyt__Kq(RDv+=V>xjz^&wWmO)Xa8rOS0VJRxVC^o8FPF^vd{oC|LDOIk2w1Uau`Akw z$C}noG7KRwZ^lo70vnT-m;)O)5+lLt$cB+Dd!_9qd8qjirp=D4g0}i&T)=A$*bI$$ z+Nh?2e!K8!-WPSctfa*J`QSVym_lKp%3vwz$e%JY&S<$jV;2rf^Ed{5=%7q}c^K&t z(KSk4-_byk*mhyaBraAu3gP0OYIq&957>7w0-6dfa>PLwjWvQ(-p$uabLZkh4zZ|e zU4=YGh-3S?sI#A2KPnkp(^+ZP!h_7xf}zcwAQb+4XC;)QjCp>sdjoiPu||4^m-Y)W z2Bawd=%T~v#y|nbWAS1iNrh$va4@n3C_LlYsuA;9GqRTbGCob7KyS*Bex>>C`6m}^ zpuUUdAD`1oWf@<>q8p@(3FgZ#vFzt=9OWs)%?vvdj6b32Miy)Fg?|CUxE^g+2;?0hg+ly(f$PNEf8}pqQDJ4_m+kXK z47-PerO64%C^tH5wRB~3-hm5E#bogt*t-Ic%CyOIst%$^T2fINYa$WcO<4Zgq$(J;%yCF~ zUbd7al({&YGw}&@df5_@=>j+;P049DV4N{x zKAN@YPc*On+i|+jHa8WqGG?8lNy;eliYdKKp47o~QMsYf38#(;z%*DwCDSW8+1?W^ zLZz_b>a5@J#|&x9$evrl^m`IY_<3k3a%K8=zhMC|^_2B(Aj~bV@W!$TEmAllflExE zgRGvpD&7kXfRWxAY)suW52PF@^_3>a{H7hcAfJsi7#%GiTZ~UmVLejotH^$&CAE3K zS9=eZ(OTWMQJ;vC{2pS&j%O)ntBVgJ%kb^%>1?A-JG(3XB6DShI*pVu%`B+d{X4o@3IqaOv z`*}9e2H=L;P(X>zRSk}C11E!;FAxJYL4&1&OFc)5K~!m(n|^?CcBQ^>+KX<1+b)#S-a&9(4@TIGkp1}FkwSk8zVoZbHLFKLu%`-C+Xa6J?E_A* ztaCpokkD-kwdhTkic31nSAbSgRwM}o2i3hArp?&WPslcRSpRMQU|F z8@b{jndes8kw=_;EUfX2WFp)2Uz9CN(0IWY5q7T(YYEr&*V?ojv5ho&$L)}-NisNi z@*li9~B6ePuGpa&AHA!noS8`Df)MYcSNcIR82MgFV zauWhdqA0DF-AXz#QRW|_7T!1)AlreJ3q#@w&YTkSNoKMa$nSC>M7%l8C37?;qyyf_qLRMXKshqlfpT>D zv5lTDr$dDtC3LpsCwlo)Ec=a!$^MB4-NnWKsn+<(p>@`R>)Dw14RM}NaPE27E<-OD z+0Oz}Y8z#qx{6Hd7gy>^D2h|x^t}mWN7!Mx+IUZ_V_F#KDakm%D5xm=qd5*{yGh9} zIu$!*Q3ScrP~t%Rw5gH~2)4>{t)$=)zLZwOuL&-JL{b4&Ne-?< zmI&%uOvP>F(aql1fn;eaJ@($DU{19*7MmEFVw64JyazZq?1mM`!b{C+0)$DcHE6#c3jKNxmI$k=UU+kx@WGJ?l zcV0q8HDBq)>Eu#@^AD zT@|3w|2$x36(`(6BzzA}9eKVAwyZ^2ht`e>dxLwKcBQ%!S&S!nfC>EP1kPuGE4dCi z_v!6NqbyqGtgvQu^^E=w$fq-|!D;tey&Ny1K001G>Q{T(xbhd91>)@5sqd3nn+^ue zWb`rYBIXHh#@@o$-5rZgB<~bx$|mpGY=bo~0Qk*sdiT%-bL1{k@>f@qBU;qslcLln zI?}Wywg2wT-2=|rIUeZb<L%&92)K~PuEr7)F7Rq*@ra<@zGvQutd5a9*7My2$ zcw(E{erhy?A^Y{jQA*RLzQDDZ4Q7K2cJgRwG>EtSHFI=tYD~1-p40) zG+Brx9%m8ysGKE2jb8=N*B&Lo=o}dvlW!&Z17?S~(y<$jC0zd$RCo|^t59CsX=J7( z4dDV*OQUgd=rrvW^ETH}g%HLHB3)e`-;W`|xY*)~dsw$bRC>6a)+8vEB|lWDHGY;D z7EXgfpSQJU1ktiDp6Aga%7eoj-+r*(8L}-HrwMR@9MnjM+J%9b$mx2Ld5Wo{O89@~PA@uZU|CO^-nz44uC+$K|087coUqAg~cwUwOWsJ*AcKKE} zE@4vHlawv`Z@oH%K7Kp00d(|Q;F+Y~i%TlOcn*7dmn?vCPukQP;yXrgND*Wr|JJ~e zUtZ#Qob+5O~w$L6Mu`UoQC|b>| zy{}{h57^q++(y2tf5-64k)89Al zx4-qzJ5ySc|E_qQ|IJ)s(Yb*d3zB-5;L6}e3cv(~1TX=i>9WEgA_9R$K?4U8k?81< zIkZq;(Q`wkW5FIni4&RpL>C4H2?EsFR3Sg2DxyVzZag|c1d4zXLSQA7z#+jRfC3l% zkrFAe0;ooC><|EGAX|b&26-epR1)s|s9W<;zOHln{=hs6dO#9dT1tEA+yawuVL`%# zkO6dH*I>@wT}aT5e=vy)9WXa;@d-VSasU?YScZo9`1pho+2x4H#}sqaKzD(~xjY?LI;dd_>g$L@ zUPNJl2p~W6MIx%nAExjR-~zjauIeEB^WcFisIfo@)Ukdh=TM@8x{G;3dG_o0ol$?V zPO4_CAidE_vT9LXzY`322zMBOu#f-1jC`@*&7nX+f;EH-&jWF15dRf?aDSp^p4oqWull9vpdY~Y zAmv8{dV74#_ur!qT_;AW^YdTyZ`F8<3k=Q5qWsNI`30q-CiVr!6hvYSD2QkQLj*!b z!2p$ziUI=p#hUo4VZXULx*5Ei;}?4s7`RSs2-1+^OMhsnSC#P3p)0sOi;6}2(XY1bpBz?o4iK|| zr;y(*Iv_zr#5ejYtAPSKb)1n$skDBAwdJp`M=4e?RLfsyfXE0b5F#q{fw_Uz^FFk*!0*vl zpy=|fQqTlf=f@{6 z*5sSRyxY2je!s5ddr}2`XVpTUL;lbE)Qr#tQASe(oa2F-6)?8IuU5Eq z-tqL5P{HLb`afN)-d5aFeSZ*H+iW@>bcC{>YHTzZ23dBIP@B6l8hV1z~aaIwiRa~xHp)?(e?bbE23^;nJC$_zSXThuvl47w1|Kl3I42xEDM-$^o z4@JA3Fiq?{&(Q)>(<5#NDkP)9>3ZZhJuUjS#uIyjOGOLo=woh;MyrD!mq?!q{ojfC zCXHa|?eoWTkM2p66?bv%V@Fjp@@yCHtJSio(cEX}VwZN-jC3!sSSRjNX^%jPohs0x zPa2`A2Wi8X6|HZZtX=P`dX>7h>yNBZJRWol$P)nB27c*~PoM>2{9SHxf(n zU!b%TnE6-RGs=kQOdSv!ePAO9-e&fc0nB{`Z-^LK_c7Yheiqcv;?%P!{py9Rx;@Qp zdRn1NQkKFYaTBt1L&72-PRQh|Sj6>lgO5~5VW0KaQa83tLClC|AjJG}mYPG_Ikn^De3r+KKh~bsN5znY~d@~IEdD$_idp*{ju)xCgg@Y zyB24&(C+xz%}G3=v0Q^|gWj~i#79 z_&4-(JqtpVzBTMA*R&kZv)vAPuQMYh3aRm}lG5Z1x1|u$&*=+uZheOjI#Op>FKU62foZwWx$qeglS@!e8$=GLMzWeKNLFyiorLp^Dac~dCP0N60Z)yd9#jmR*D?G9-SMFHGW`=TxdP^I?>}< z+>+>nVHzJFgh0x$rro#y1&;~9Yq)H8fxIupsjp^7H0OO{&KD1tHtG(>+7k0#&UvpR z{$m_n|1p01J&&g?r9=>R)@`pUfe1C9`#twSLO$$irUu?F)=p7|c# zpo$PYqi@oxE$_E-<>p(=rJGa zdVR;X`Wptn)$aLFDzg0qTkwP%tE+jF|2o~CJ?)s3gPV+%s6ws6chk4wTc}pWXi`xT zwBu{r5h8Xvr|7kk_(LbKe2Abj7w8gV^#`PL=B3E6usGJvhDg2WK3|xT_P1&@J@Db9 zOKVXlhHE6$nE2IF{U2lJ5M2out=m*mvF)6g6|-X7wr$(CZQHhO+o~8R_WNJsj`13| z@pfzVcW-^)nv)-oeNp?@*lYXwYP-4S`TSLG%PeqJ;%(tZ$5#3?<5%5ASZ6+{Nx&bZ zd6;QS$4rJwVnN8Ho|;z)M~wTUj^7d>O1lSVF&4jAFXlhr0S2EwGTL)5w+fU=h%A!8 zyF}3((f36wDQ-!g2lHD7?!6M1oP-Wlku!#g)u|Uqj;i?b1J`#8uG`1M0R{JwjV;ekH{lK zV!A3C^rAm$Qy2VTf6dfCjc#QS4(r#n^IY;;j;Kn+qeadQ0!j89SW5#?u~g*r)+cMn zt!!AtvmciSZ%4@ajf7nLH;5MIOEuHDuh(a-(lI`GI%Xo5uI- z9e~*}j$|4-V;*4ct0J*u_7^HH)oo)h2qjts&d&5cW| zqg1nfpzxNrD~CCv({te{bs>%bc72=*vVrNJ{V#39&dVry#Nlhxeqzj>;?McJG+Nyx z{glsVI(i{2-oquRnm?VucFDlo&*TbTd+& zg=?Po6*>KIRk+59bwsI*C3=FKL)5J}+iJ_p-hABq9oI3vaWKws4(7K!Pb(C>s9==H zyEg)=t?9T%gHnM}?eDv+hwVDcHj%yqbBBY)zxG9E2c)j<3*0C^)_VmMu&VK04_`vQ zdmL5O!^VY)nswqDg-9N152oJow|k!{Ry*;(N1aPa-PSU-G+OEi* z@Z}x^4fNV_@WXdz+66PPuxEm0+|8K? zRmwS8p|hYq*7giezgXAobLz}pu1=<(I)|)XSHG|DcC$%1KcI+kQK*HPPDX}k=?ifJ z+jtj|!;dF&)=JCzJ$d;MV9(EhT< zEu?C4Yb*%6rD09oUj29qc``m^1S)#P9KNzZTquVf3SjIieZ;9)HMai6l z#+7ls-(k@{mzOxM>Or=)>#wU1z5jMO-N}pPGRzk>ZOYRG6Ei-88&*qS)@Haz<4?a; z=jjCw1Fov#q_J>tEuStTB9;{=QN$!>wgF^zaP8LsC^}^N?m4+A+4f#%8QM-;(q2VQ zkK}?;r1o_8AaZ&BS7r5b=>1w5 zMKcCRrp1IO35rPlk0S;>h5naSQ?tXd*b3uqjEPlr346NQ1#d`oTPTW z-SSp#6P2BR{EgI{-1(Si-05kWx{Ykw%^oc@JOf9-r@m#DBj&c6dGFNP5wEe9FeNbJ z1*SaU%X~_6zm&f|+F;NV4MJ8Xe_@+lo^z4(81T+W>gwJeGm`66>Q9VL#q8>Qgvd+} zB}o<@OrL?Sk&8hp#8SC9A8wRD=zA;$KgD7bu>Ol*A%~* z_5Q2#@bBQJ3TI!vsdxQd2nVvBi0W}mVxj-XoE;yR*u(zuA_Y@8j+k*U?P~-qhY>I3 z5rq|Y&0+I{SJnMIN;qi~by&re#&XQC#88IM`dkNTV!@tVEGl^xz@+UH)P$)#$TNy{ zG_;gjN#&)i;mTFBS!+5ZpW7viMRJ9l8QLqP@^|X|@I?bP0tMnydMHbw7Ai=VgnP#`9NL><( zN9@Qhs5Jhh?IP^50!>9$YN+8;2eHXF|6QV2g)K#kH64Qk7O{vi+( z7RTO6rMbTXAZ4VPp76&6KpPJBYg*m}r=i6@)$n)lC^pWQ>JhB> zQ{89ouIs-cg+B+0iI2^~OeU^6e2BEz8s;d>VIFY6WInMa26mHNk<(kzPTBL)=_Uwn{KX=`kWaH^)u5oF|-puMVIwd@xe7Hiw0?+r7?QN za>+RO$}`7eya#3r`;5o&*VKxb?TgbTo~;GLcb47mw2;WA$KP7duLBHK;!<#~%bcj% z9D9n_Wbfa38X=TVj88$H=8noSov$>5g|lAhf=KeEFkiKmdiR0%SQ_1xldZDajXPGf zQ}H!v8KS-l9>;k#rN*MDoZ0}=-oKr=o`F~|Wrg~F^wFHmF@BNE@6KA$ZBr6IDv@*r zwLWHiDnpWzcOzIE5aL($vg?N|rzsT0naJY}F=fiV3JQBpP(nPK?iq)f;Z@aQ*jaIt zNt4)_6|J8*!N8S2bE6oq)aarg;mVFE1h*iu*z3?5PSBgh%e$2 z83)8kO!V&x6Amw0=XOn6r}I40m&(!gG&LCYIh1S_WfhSsK1Pi>dYGQu*IiH?Hua@V zVx{5W*U+wV*WA?BXeJ{i6Da`T})X!rGr15Uct9-X0VYbMqet8_`%sh+!E z%2Zj?P7kSL8Sslm&5R4v*n3F*;B_c2&@uy^5gglm#>b_X?f7-06Kev7wx*)1iFK@Y z`jjmLSdR7Xu{3;405}RRDQk3qb3zG2!%0Jt`G)+o*$ z?~?;M=+L1y06rAlt|522-nBtZ!_@fIEXJXm4^b`8iSfek(a~97BOlmMGX<)qU7DJP ze+*~fWWa)cJz_q`5+%1wAC#-=uF_-iw#;!qW)V=|5keF6t%)Ln-VU#Hku42u9VH^U z{_eqg@n1f9+ERVj;Nj-_H2K$xn>kDxb9gKe*A!+eEVapn+%sf>PXn3d1F;elD{O5V z#a%$4e1gr;c7s$ZWEGzdrs#1o!T$B|(A;;#1CUa;DWXGdF^n@x;S*n`ipXLHgvpnu zjjM*dasQg76VS3!(@0sYQYsr_`zUiMFDQ_)MA{g!Wcs@te6PbDDds*WUOGky+S)R~ z!I-n0p|B{zmPNlcWv~UIRpGb&N6UI_x6B*adS-QRM5;37PT{WvlGu5w z4zcLQL(M$S_hYq(vly2sv)QT~X?UfFb5}9YXsdaCJ;Do^m6oPnib)+@@spdJ@%{yafTxq7#`u=$#gA{HiQ>7eBC$>+iH{T)Vd}}`HO7}Q-`5a z3GZsF=%?9qCO*~!c-fJH{0weOQkmrnHZTO~b53(!zr2P61!o=YU7u#Ug-bWl|1@cgg}oH;@Ig7TWf-UPPPq_;W8zzhPLdIW8VjV>11F6bz}pt< z{?v%xGYyFb(;V2HoM;bnq&#lD@=DPj_i*x*k-Hk(xiv&ApWXXwpE*i#3%@>6FCU+Y zq%x*}C4LVed_QzW+-YP_((Xl_EG|({Uy)=an>2un35P4PCX{$psbbF_IoNj*9 zKD+XXmhxD>LUU{H_sHk7`^>`v3@rn%XyGYK+4l2Y98waNtty56yFUk)csVsZ&7-Y3 z?f*4k&fg<#2q(D}_DKs#f_#j71kbN1uockfK zBOiX~%XeDl3l8`PuXC>{5Q>gHlU9&`am?eF}dL>na?yPLAQ-L_lHL_Y` zsqYL`lM*&BmKGj<#HNsqOwah@%;w&{NG4~l%}+miR*p~R>3WR1RgUPfOYOOCwdE_Q3*XF(`A{uZQ5y`_oNTsS9Ch> zixK6e&W|Igx;yM`G<(sGcrZvO+FNkTkf>0jgsL4pM2G3(taI-5DmkEZjx zYJrH}SNSo#gv6aiI+RLzXmGd1-W6ecnZ+>1{95kcrxm*$Sct`-Y*Mg-Na=*dtv@WN zInuszv|d}9)fyL=ROh8vp5-Y13ACjm{XTT`7TD(e_h5xtaF>_N=X23FEN3+)wy1E4T|G8< z>^TH0Ok3Ss`mx_6@MAbd$>}4GFBZ`_}^#h&{%d$`8p-O*F*oBeOw$6_s@$v ziCbf@$z@IE!{gAmeWH)bo?i5sSX(dz6)Q&zW<(gUWO>o>xPQY{RAh5mA?MO45?AbH zI8k3<<^CpWv^B1=%2+gz(c0jcuD6?1%zd+T^?nFv$%zV-{vEff8qYW=FlwvOAgJ%#Qgu{ z(2N|6Ow9iiOEVKP{Le_p_?Lx^@&8vV`T{PGx4Gyab%?{=4v$0FE(CS+du^YspD?KF z|30fg)b0N!a0(9XXWm4g@0ZFO+DiT2)|H(qFBt)m()?*cV{02Iv^EGXhI$632T);S zlM;3HU(?gp(bLn_;>ya@gpgAEe#hd+B!z z-}6`tpz7}K?Pou(kWd=GuK7hF^!=*?g0SZ=u7yd!r2HFOkfF}@-}#8lU#Ic#tlcxx zvvYE=;j6E(Yp$i=EY5$;5<)Wjqs$YS|NG4X@u|YZKid!Udb@~~P!2+EO8DVNm0Tl( zmkodA@6R4UHVy^V>gVL}8yD;v#I6i1xuh55*v5a~58Ll8?Y}F@y_sM242_@c+kHJh zFuy^6uC4WrjcrVfKwQBCWPXtoN)htwe!><7MS=13gIIs26$F&@JZ1F-B>fs+?7y4Y zzg>n0ITVZp32KA+(aGycz#ktS$Xy^Xep8E)_6zZ_YQkDqAKsjVfpV=Ed#B-3h{vBl ztGTU}{^`|*t#4so|Kc+S1;x$!R0(Y;f={BxGQNaLM)_)+$$~nMn?^eW+1EckH9R`~ z4Px_)ACrW+v=2evq2o} z>0|t%nf$pd{@IHj#;2wISzY>^+W!%=(+6*K{%RZ9I^*Q*t_i4q+G6tmsjJ|;)9a#v zWr6ss`K4Er95k@S2^Ao-Cz=@$l9Q0}rRNym!!ZtSUJc^N!1S@U{-0U&eQi)9u%92? z%4=RvZaNE-`Qc}w$0j3TWQ*DGhb`+z5qrI_CVOZP^9>VhFZIIj0SOFO1NW!Jry4IC z1dNLdOs%+W%8vxWpKEF>69-J^JJ%Kjm1KSM;6IC7)83cH{5J4_u!8pSUhy`S_gY#l^e(eLb~LL+Pe(_zOen z0I^3z;a$j1A^B%s3vGq(F|}nA;5nuF)i?Zrq4a>*a}M_{Wd}QH{GZzPS#0njHSPfL zr3DenALdu?0U|B>Ll)b2cJ1&k*53we!t@Q?O4htn>IN@~fJ> z0ML3ezb4UbX$h{X@-O*4-_ep}@$q09qQmJ$@!qA8H1kQz4#z%5zU@w8QvbQ|Gpl9^$x+{i=Sh7g%4d9B2c` ze;7q__Ox@p1MGYpzQ@eFRZf72-crL)cAt6IERM}hURry7c`I!zUx+_nBGA7( zL1N-D{#D2Df~T*6H}9-KA#*Zc#Xbz=mTX(pGeu*b5pz67$ei1ZQkj|lnMjVHe{KxF z%ygTC-r6;(nbGUGT~1=bj=gKKN{XsoY1_iNVR=|hL{6S{V(^KW2fU@68CpMtAT)j1LOx`3rs z9iNgm1BXl2LT#NI=rESPrY0OINk-)j%x36)Y?@Qc<^yRz1u6NyZH}lH!#NxDuviw6 zsR<#8^yX36_BFna;|Ay7{619I9lgB`HM{MMOn%0V^#M_YYNsrF@#l;5Gwi5E&R(e# z+X3YcWEcbXirt41%UNoytUVAOGr}kZ`u-<2v9az#T@#~IQE~b6clb?Bm=Q&t3>4PAnwnD6A z=?N#QOD_vn3s2O=t~<9J-U1fRE=2klCG`?ED76hCSIUIEBH!ZhxIcH55oyAX_*w=? zfLQecfjv!VsV8?p{TaRn{7S8NqBbeX=yJ>V_Z^%P^_x;#!{nwQieB&RR1BoqO6@w2 z)Q@3raz3{+ez^Lv#lrvb2ox#!CF*o8MUEu*0q$2VsY=iAZ zbz$D{dGQpYXv;yb)UBYIB-Wh<0;L50M*O$as*&XgF;}6oamt$39Z(%Eyk}6KdFLCttICnsN99t2K?>w3e=4) z^??+HsZF2ky%Ms@YvvYqzDQ6y8|WDPPNXy_^vgpdcQ61B|1G|_AbznkmR^i|(y{eS zP#&6=HXZ5`-if0*l_a^H7+OFLAovp_3Cyl!vAk=Nq=HRUs!kJoD;!>_lRABCK456N z1wd9!N1Z`8dUv?Fb|HQM;DHvuc^)pS74v_M94+BrB|(Znr5(jPhbl0P9+e`XxNqV&V2x_Z=gLjisz9%S%YM%_lM0*aH>wwZbp0mc@NMyR?gRBX7LPt^N#?fKOZ>#_d7bxFXjQbnwWz;3g$FcdCIn6b3~~iTTEUE<(d?1Dn$; z6@r0Tqc_J$!zW16zw)rPA@(2Ry}Gt~+2bxB#BwJ3yqqH>HS0;RtGdFRhLx<;eu;h1 zQuxp-ZYE(28i@xmc@4c-6PxP8$2+@dtu^-RIw^#e;`-uf{nJtcH9o$qrm6lF83jYe z?=VA?L4$DI#a^7+{F))IVyl<~Nu~eeidu%V&-a++(|1*7S!rd(r*!k}Mm2_PtFTcZ~WzUUKdqy9OEPtQ8k#uIa>;%3Ci+~$W zxGQHRRDh4F*$4>4bHHyTFwsLJ>50f~50(I!#u0CB;m+xyZR=b@VUzW;ABvwH^r}T* z(<=2jIuzX9WsF`i->UCJayAm4_{s6bnzFywYRV`1nvieFneo{7WLG3F_z;(ojb}}D z(ua!e_lVvMxFCTAyPAu#?>rl~9YR_!PkZX2=98yMGj(`fiU8f8r_-@X;<(VrRDO+Y7!IF{+2Fzx=? zLCb#FbWdd86_jql(IH#_LgUdTfa;%L`Aoh!f5bnLM^$@4BVgp3&t4Xw!& zsn`iq!{TAz*7Mq-^a;c{gFfN2jx_B8r!QZ%O7B1?H<6L*(;#WdIr;W~Rf$i@YaUcv z{>y>B&CjX$f#qfNn4)#-RJ{z@xx%{Cp0rmrkvX$D^UJ0PAxud4@XOd|XiLJLq5X9# zDtmF8Y&Yp??RB;(LiH7`cWMy<)V8VCXbRM$|7xlzt%IBZSi_a&Hh|`4s8uUzTP*po zqkY+aAIwfxoA3yI#nH7B{{3}vWrix%eOdzJK$n@Z5G~AibQ99nyW*_jLL9kH^CaL| zYefLDhjW1OFVqmJwxYE}n|l`e5Y3=8budE9mPtp8tjFsIJj4jQpdqQ!tecV`>(=vV zU7Ps)DQY^c)2r2`gRL`~a3qmGx6T{Qm?|>F3+^Tl^^LwC&lAnxQ zK=L#eLS~l?fowSW!Ksskm}lGfd#G?OBBcb!ck?F@|dJH22;q-c@$T-jz$wg zyimQiU5}uQ?=U!k9`;Wq(jbbW42)~D2F{jTy_*r`~7IF^3XUHarqqX zqtl<+kO%5;aCsvbXP+o2IiI=q+MZh(l~|8cm$EIs>+)C{T)Lb0i)<$?BaPwP7u28Xw%c#2f`nm-rHRL1gUl zLmG{N37yLyr*EzI?&8b`_sC5FwtdvncoSSN19E#}_D&-vL*D+6vvFpunV@ut^6K1> zMssc~dZktis0IvhXnce^mh%jv1Z4U_T4h&JY!IQm0TIFA zKzF8`oRHu7aG_go)B&KVmil;Jah@S$$)OSsoD~0H?{Vx^WT~&bb*CxjY~Ou-bKLkA zv?BvK?1Q3+pH9B&LDO`dwK~*oZH3MPJTWuGD8-8<17;su%<`4}WpD6~-)g3lVqiGl zfxZsYWsClS?*wwuh2nWz*_~e3fx^u6+j{)xmq?!PG-jvczeHq~M{b4QVadNiBRtS@ zwBTYl<5T6{m2hj%Hq+U;A-f$+!gkWkM3Re);INJYo75B>l3gLq5L>j0sHjY6(#$F; zz%Y~YV=BdPy1vJktT)QWM|uKpN0PVJkclNP=b}u|pP`;P6_+c976Ed)F5YBW*m_J5 zrBdhXpBGy)qiO$v<+@gbp`C;bhy4^h=nZCwC1&=x{g}_p3efqfk)8JbYO4n^cN8{| zI>4Ltq+-bQHe2Rs8uIEKvYHSy8}pqdwj`l9x9nxzIZWje7M=A;*GY&>a)g`w zpDS3|dNP4A(TBZ7uapS?yrzYb+X^~hZh3SSw=nNZChEeRlZ%n(XiDo&WdcI-(MMkBO#i)xvP@A|_&H$_!1xNbNv@O5hUAia2}+zKbH_PHzKQo6$4K%gHaaQ=YK z4K6Dl!y~c6L$E9Z@w?FCR?%_bc{oNYSAc;XYX$eH*q${$scL(1t&jQ!kKiUZ^w)56 zMVNtg*l-gsL;Fnql!xI6WogUJ0WL0Ia0%Z2qT%ZJLM2d`V>NU>^kXoWaipyRNhdBk z#^zM;nMnit^pNaMx|Z->mlsuVdT51K)Krk;k`Y?;9@E4z88{f~wJ>1-4Hcr zvBt)k2$MS5|t8}?NWuj5+$UNo{n92(E+6v?>5lQ~W zxFIl3Ke)X_bo_l!a%QGgwoXthpDL=9;-*_97TTRZR)~~A;DAe;f!Jicj6iys(?1(& zZ$+_E4oVuCRE68cW2w&kHf%Fg8erYcryfm5$^S>!wtc+WP&|32Kb{0k|9@O zVSAm*y7$cHYZ1#3kQFp2Y@JH(qL<-F0ZOSA^QNR60?mK>QmH^62*=^At5?dX1KBBi zhpQlo;$L+{By^ZmUiLUJb4pqiFCpn1O8Fj-JVS#YC^u1ow3brgI%2=A@G75uLOQK+ z4LzbqqE5dWB)Q4ew6K*uw3+>Kib3j{Th~xz5fIv(9spo4`qFiiSs!uS=ap}#v{dp30Lf^Tx zPs<=(UYaA(#rHQ z0v!8izm9VQz2SJH+zIX8iyC*RvC{G(3W}Xte;H{OphtYxY8NG)yUs1~JjrT=p2(gL zvAkH~7c2x4{=4dy;LQUb(=w8nM~`HdSzy57UlAj;wv+Cx^{A%)nT}C=N)oOCtDw@0 zL@F2*GFWfhR5?(^CM98oNU41$k?KY?EK~wBQ35rY#1Iqb~rD~Q5QkA zz?Rp|+&y*A7n&7eE8R)X;kNPQ*6zDPy_a1=pya5^McS^!rZ4T}?AG*h;+SddZ-Vef zUYuB9EdRoN2zSCsG{^KxF%UMh6<3Re2=ndYB!u(xSA{5ASDJC3|^;?G-LBRvd#fjBWaGp=oxRMkW7X;?_e=_Zca4y zjI3%(+fic=QcZ6GkFDDeiTfT~(2#F*5mauG=2mJ#-bp_&@pl$Ku^5J~rjh=NGTPO* z_M~$4?dmfJ0X!x;zFr0d{velZI$hu8`HA1C%0u`>k#$AVQO+ng?+-aZv*!mb`eNC) z@2!x#JM>o8xn&w8w=Cw$d{$~(;^O5@TC;OG4w$qxNd1nLC7!!}`goL-b}Gr(0%|B4 zLYcvo;HO;4{eZR^t^>$sFT5Y?R+)1U?CxOQTMbd)!n5VuZKSz`UWGt6*+rYBAH_X% zpkKhCO z>iTQ9)krTul74FY2LuY+L;4JYBJXP^o7+R*;*QMQ{&;F)i(;q)uut7?ee)nmkXW6c zHyT8P(80%Ai@9lO+kn#tVaUS&3z-{-zLtO&UKk~tz*KTv&^hi$Fu6wY2)ZF^Hi5}w z#U&D~@^kt9@WVpiJvf_7b%b<=z`3R!%xZmBwEtGZ*={3E1CQq6Pj&KiPMk5AO%yuX z0W^1Z3zhYK5A5yPE=n54k@GZZ?(=Ovx~WgtX&c`A_Fs}@n0+b#TK8$=5>=^z^DAG4 ze^NxSY6`IVPl%-W?+p1i*RX8b(wC++;%idAM8nhd4~9=?75R^fgNUw8&!o>EcxU3C z&{Bve0YUe_^Ts44{`(!4p0ph{&B;GmN0wl&y+)W!H5ffaL#Cy|9bpvjI8P=o-kt7( z!O@UC%jOQ=fQro;%Ti&k-Daxe9)l2ohW@x`)?0{cPV+22Y!={L5>Fo14`PYKAvEz=m;zLC0Su3>Y*$#U`W@e^~xJqt0Lp#S+<3Nlb{DPE$Z`kv*EIw|J7#48a^2|&4^-ci`l+0=W3}vxM*Jm> z%-*#Mf%JvptOCrXTX{v^vJ8%LI!UEesS!%!bFamR`<(~6q_FG?IY3vGqqR^L7ADc# zOa~GijiMH`iXFiMZ8H3mi5`M@bUeBeZEET~K2Q=sD$`Lj0cL&n^ar7ys=ErWmtOHk zSOmW#Ey;67?jDil>2$p7_^w#SQP?W%&9}mhz#Hl5Lza#f_ztH(GL#8pNW2_azfp~r z2rjfGi3IMQJ{>ZcH(bO`==2C5SjLkqX5_o}{nyb<-h6@A!SLH6b`m`{lb2K+Eb9jr ztdO}SbVdQwm6sTbZ5>ZAbTO7)VP5ukcdg%(ZNaBij4v-k zT=r1PSrBTsSY6A2{I(WhGEM3dtSpq(f;^3unYU^}K-yU%Ef%v0E$X4}IImPH`E&*L7vhQ8x0Vv%qgr&yK)BjP}F zcrn>K&3iZxOb!hmfh?FaxG$T~EKwS|yhyUTWcN9w#TZF6w0_CNTa-1i0YZz5O#M8` zE=>)8mq}!5o7yMe;#4IvLEs6>1DVR8jR?pi5q3`9*P8l#e}3alzXKbd4$TK6x7cKe zP(K<!xdkG9P`-{RSeV3{d{ zUGO41C$n?@Vz3o_@N+gYccGZ0p35aqZUULjvd$@A17KGE|GV=GFL zOS!E=V=7vRr>>X-F^|Nz_dsAFzzNckCnmY?{!@bIEM- zsd(vbI2c_ef5|{7}gfaz0%L6 zCGQGeWqMW9FVgq0p%>9ZFL#{-uV>eqf+rK@z%&Cn#l%Wo)gft5!pPaZVFNu`4P)_% z!HzyJx>^45m@~J;_%El$j~@Llyhzmpz7zbbmrZNc&3TZ&C~i8S3s{r0Hycmq0c4JV z`}B+;j`%xKZ6fYbOah@u751MP3n83E;wEm~X7h^EnW>k!nn)6PG8{K}TVLF0l7Fg? zPowf}2WU8Q@e(QbZ`u}HnS;uLgt2@1H$_$S11~AwbCU_~hs6A{{T18W#|l4vUT-?0 z1~Lpy2G*5fBMlK~>A0f$gXq4IuV0|=@%tmrm)@v*!^^E%P_x_p;}a-)lttA0mP|a@ z5=p$vqb;*>N|G@FO(%J?GabH!&Dd^RL_8j}ZBeJ{38XnIze})gI*-z}af6@GMU|(> zU~Mwyjq?j*Lz|3kOVM7RkYib1M?@hB-)Ics6Ymq~yU}ZZ%;8MnO?TdG4I7F$5>vdFQ_ra&b9st8 z$Q*Y3mXe_C$z|p4k1PrPEA2mHL+7#*^!&B%78WgYJiEcsk7oQDOZ#*7@Gn0(FGH7E za{Ls6rCeLB&d?591w($QpxzBt2cWYs8`^5m@efC`IBtq!Y()-ah&`Vb-5+(l;zj>k zs}n4%5RTAM_R9|42iD6Im)jM@&*pVi%5mSmUWiex#D|9xd&(3hIY7LB*fq;YAmK{& z0JgkK{?de3y{J8EcH0_^(HfDeFtMDa!Yg&79HZ@Y&arpSO+2t(ct2t{YO}OUGc@13 z~Me&=z#aX*T&!ZqaC$oyI~<*i2vEu zO#!%u&#)q^t(Nxa|D>>nnAG{=vv=-{>)LZX4XC3fUUcv?YUHF4zZPIx6gCetPoC%> zdG^)YMLkz+@>fdlwlzvr62TGe*ip6UXhRyrlkL(XC_Z00GF zc9L$w+#;dbawOTouSGOUU!{y~=;M;b$WS{Q4@JNfWt+|TXO zQ}br$dEhC5&g2KskJp*rkAlSXA)>g1bA9y&+1FX*fjsLUbl~LhE7^3!l7piZDQ8mB z=7JHY0(3Zj=iYE~wJtFb@`v;d3wlZ50;0iYH_K?%FxF0F4mWo9%`AoLZ04tX#>=d- zzRAet8)=Ah#k)yanYwqaKwI+16X#RaTig}|23lJhxY~a88vM<3o1HJj_od%KH5@K4 zq<6Ga$z7QLCm<)O;b2Pf6x?6elzwN^V6N`KqksmGaEScbLSWx4>u3njJ$WBF1&>vK zsH{6i*B81Upbj)~l$nj+S38`U%PlGt{Nzn+=9Wb`PdJFA*K-US(}m9Ni5gW`iPc#@ ziYts19rKgne@WVIWVWPIld=D7#18O5JXOzCzCz@g6?7S*KSTdIUTZQipkP^D;zEa2 zIipyn?G{S?%*c+3^w_{Q$+;Vb2V2)t*+vSMNXUSRtKG`6nVTOEJ34EOf?bHXvPEXN zZ%<*hdy4rytT5+_YB(01Ix8kzxVAOdOa**|PkK!opHZNoR|{R;{6W~Rt7N3Diu=7* zFZ^HIJqurX3sYJ{MB3u5Q)jx8m)=%E97b>Q%Cxj4>gaEp*HV11u;2&ZrmC; zGDDzVwK((~m8K&@6z#vp9Fe&v7(pw-3uXXKH94m`E!5yu16GI3S_c6q@XoOE+@k4) zQQp>=OmOx`(N<1|U1vtKFQJugi+VGI&!sW)A-Cf;D=4OC=^-j z(JcxKsr1Dp=1rr|akd>P!~$H(lb?@@a&X{Z2_77Lk+~Mta-}wSASn?LkLzJ=mjm5Z z+%>*ar3E8~g~0t2#YPA{bIMrBv;0yg6mDj!T}hJ9U2qK|lu7Y&|1H**NPj`ofG9m5 zej!%=J=j>u!RFR2!G8UIYp~VRGO&pXMwrpdCp|Z$bCh@-x05X`jKM3;DJ*;xv7h!pDD|gBOKS*feE=Gilr=^Qcr@( zEJDjJ$xU0sz|qgOU`C4ToR`vdcfTpG(^ozZ7!OH&`YeC{x6=0wqr>$_QmRnDhu0K{ zz}VgiO_4s}FK+Kq)x7wEQ5eB7ac91C89YCk+Ey2%Vq|`$W`f-iYI2#eB=us)CHLcVsUE^L?5NqvxIOb+U5Gb(ni~cc9xF17Elj zvqc8(gDfP)Kk1U#AzZWM|sb z%}%PQrfWVazTpz%m<@g2Wd7IgK|%%{O!DH@#A*FGrG9l2$%KtwMg2j)Xg#@>kCduN z5aK3cP(NWD62NUHlEtz&J*Zj<|Kw)~LO(0&kZePXPr2AV!5-02l|~874kzrf=2og6 zW`SqHn@ST05juluX_8)7%EE)wO9Zy#%nr}Mp++UTXRfi5BzD^J`tGVMdhu^E^{U_- zQdgOUJBuWrfs%RJn#g(o&DgA7!@w-M^4I0`rY7B=-OBgZ~nqP~bv3e98heEfCw-shs@2hY9 zf?0I!i7lOT!rG*1LY+XCgBm%HVSCME7 z7gjXHPr33mM$14pKGwD8VkpZQ?mRrWxrJyb=rO;tMpG{`;32t`AUG_&pwoN_=vX#* zeXP9FCl49wm=*Bpn^Fa9VV*SGiZ_!Jg;JSRBMAW~8gv?LnQS?2@r_|~m~DPj9&4Ma zQCvSfEv)%{WVAgwG+;n=uBF)|jFGLoVD-ic0+K?l($=bO1Il$X=<({f7A{WBhT0w+ zWs(=`ZA4OZn>a&Noxask1qTK=Wb$|Q4%T>^ur>%wqAcq;sII-k1Lq@{RRJOP+ zd*pt$_dLfZuhe7C$7IXGZGdHtJ?`0(`Y4 zSiMwa5$3(>oWK+{UA^AFa7?aX`>N~>!2&$a@$S1f1dO%O+l#)ZgUd@ZeW_=)t1VXC_YNW?=RyHL!5_FgqAw}Q%dKE z4SPb5L4xWWheoA4Tfb_TrBcJ>d{@fjPg(BFplIak*_fid+TLFP0|$?tS8yo#WbE#f zH&hbTK~JLh6zS58)SC39^JsQhB$;lbZsP`F<4wr!!NcCjkF6IpBZ@eoIILTAZ!-uiFjKVn$5pEoq~`grhcEv$$;6) zHgrE2(Cze>*n{RYYH+&@*Ju)BHO_rZqV2JgdS92OFu+}uTUzF0IR?CDYSW_kSqIOo zaso|0C&KoeCSEX}WSvqIPq3xO+v&Ew=25B^F&j~|G_(2U(&I{$W>hY9de#G~g8j@N zE5H~1_dLyvMqj?hez?UdsaKdEZ!$@5_ECk*;t2nSYwN*GI#`Exv=bfGg~OE3aD{hvb?0mt$jnX2eF;U&=hP0wY4~{GV&vvw zC?2)Lzev>2j2bj+a`$~u2d)+cam0!aysv1XR3sS-;%Ur)Nw9!{mu#Q@jxht|vq3EG0c(Hzon0}rX)a*UHB*&eB1p0Gb$0k3FED7D zmvWy?NEU`j(JnGjGdpvH!4a&WFq>SDr6!O6_Zb)h`t8nLes{<>49n5mRD416Iy$2* zV&>)6FIpoiO-4K3eC%Y$@|TO)-e&q^((vF)fz3@P(Y1+?xMMMuG@D~TWTe{~O|3#95kfU@#-kr}4GRmC;M*|7j z3@<6NUIMq|MDlE=+{89LUJGQg4u>S#-tU6YF(N_qV*)|182>4MG2Z(NPjVLkdV~D~3wvMdCDrgRXdK+E>IE64w`Blj z(ehb?)tJyxHwEj>t={u8E|=y}lVZ*p67*C?6L**jvF{A*^qTqjn@hiS3aU&kI$mfA zU%c&2Rv?;!EDM!FdB8Xi?=HYbUK?+n2D+O$5sP#Nms4K&6x|o<4(r*aFg%r7rK5>;N3>iA zNA;;TQ~U+|{frJ|!{+2n5I4lL!^zU~Pgn*M5=qRQ4h%uhv}pvx*>uS>h8bLGBzO#C zV~JNrK`xlHPYFsHTVLQ#iE_U0vdz-&a|M-)4?@Y@b0K|15O&_F=&8RXza#3)O6l1` zRIS>{q_E~5Ogo3nlgrey8FBM9r|^7ZD@6Q4ivB5@QGgh4sY?%ljZ(Fye#^tzUPm?? zja(7T)|0h52X-CQ$$wi(%w`-F<~(}H_N&(1lpZ$C1kv$m!dYZ%+aRd$OQ3KYvf}iN zz~?o?@#uO^GJ21?$t_A_*!lx2Wrcq3Ad!EIJ@LK^O|V1RGyHOTX<`HRSybBm(p#}M%0bSe)>oKaIur~%!kvbs{s4s zQ%Y@rGp!ui-n$&|CM|X(_u5x1-Z?9E_$hNAqSZ2QP)OD-y;L;Z*ASH9np`mBmO_sn)K0h@`xwuBX^%*?Q9~u^2%|}hy z{sRx3Lyzo2HI0ji7O}Wxq>Nm$;o12_QdR;@y=`56-+oc-KRPRB%e!Cx)+zPDXe50K z;Cf8Vi>{F9us`iEu>>!D;`G05T&9X1L$kwuxh|VhocE0jkaT8Zm9*A}y}%d&3&HI@ z5u;A?R0}a?4X*fw;80Ll!HHZOTC39a4|nBHD{+UX)cJeTk>CL_v%PP=RF)CK_uPmj za{dQMmVt85odw_0tJynwhu2Mu%LGOdkT`K?R45$$O4O`dT!{bb@bEc(ySnh045xhn z!E%!4fsOk8j{b8`i}X!SIj3(oH|2&9B|^> zFNr+PL`#KLL71xXT(3oXlH8)VtXTaQ$?){`C;@MX&&#xI64or~*N*yzQttsM{~Z8S zcKAh7_3YXg<55tiWKnmoH|A`blz@a}>lS15WVDp+!|1fbTAv=!6TkJ{833j3y+bVL z-^1JLlPNnB{PT!vTmfl*q6kFXK+Wna@oT;2>lL#sim& z7m`}EQC7WNj^Wh^0hJP7uReT}99NC7KC7o>N^XuuB;4KMi|5>3&S<34cR`Eyruj%t zWON>^H-0%3;)_sK1>0$@SKN?hvTDb&VX?Vo{Pm&jKI&x_HRPvzHYPprWZays0Cuw< zv|7%-GQsLPjX01eF!j3RIxzsb758O1j6SPpc4c}ZcUyy&d=cZ{#m3#xd;z>HfCWLL z`NyR2bzN{6P5GMmYLv&42Td~+xKM0v8MkUR zvMzf0k4c_aMOju$f_zv*GyuLG6vRS7LS-O4mG@Vme8NDNDZ7xzm-9 zEyGPZ_zL6@s4;fA77;&bIo5B(R;h#+zW+{J*OFVNN94(hj1JvzAo3U($H;EwxrMYT zg`x1uAlyNO2$0cP=(>zUGam5^y6X|A;CD5X@$We=gNrv!m?!teNcpN9Z0ouo=rFhC z>B!_Fe4J+INTR{M4Mzwt4cHCT0;Cox!2cXkPpW$<##^GYh(Y`>qM_$Yd2Ox}T?sHe zG?iUhBCkZT#VOQD-W)2cPZlvZEs?^B^-!Bj}OR~p8LQfwAa>Be|Ich%7k=}5OsEudKcxuh$v2&T9@Y{Nft{4-f> zXB~*lH$=^YW@r(qU%2$uA&A08)7TE4xW{$)%X0&v6*`CttrdR2Hed&j81HOuqcB3X z`3GjEthae0=0%|%yz!j%*t$ID8jqTzKHln_F6xW$?k=n9SzkxX*!)_lt7x`1 z$>-BciXfjwb}=_F%UpO=f%C0aqED-=*0D8x`6=!$o|0X~zMk&#u=x_#c- zh1$-~Yd;gn^+tzI*22*9SAS1AjB$G1=PaaoY<^u(^6E<5ScG{y+#86di}kIwU`|qQ zhM@<^c|CXHFx#du{(j#h?6pgb|mHE!_!~d;^Bd(cnvf5yH3-MVCBG$Q=dK zw2)DPxRKTBI10qv3P$#hF4!Fa9}joF9_$`RekytvlnM9r^yA}&7b$2a)t+RyY=XxY>u84q`17P?bz}(VAf}P|OUcVP+ zL4X5xx8f`^>P3JXM1z1C=DeJ`$<9!kR|aZBzB4&7@4QpKL>O=xOXM8_gx*S-$tD@8 z164`!Gf?l&V|?6|jNtr;l2*rhi`F+Wd0pX1Qiku*A(FYWKqKvGru5qd%rLftP*M3a|d?FfiIW?HiXk-oSzYY-gu9X$s%mJx~^r|qIESs*%l9HRD_%!1nF~`v%PfLtDpnRF9p{$Mrb>&D#<>H zy>gZ}!IvJpH9Bp5jpMT&I@2}{fmV)fN)3m)%M)+;>`7iom^i(QJ6n& zF`d&(&k(UMRN7pPM_1-Xi{PWG18^;xfuL&SozTe-0<(*z&Q;>iWUHaLh*0n;>{TR! zUL&CLL*&u{Q=u?(O#yLdp6ep1rWrjQA2}AlY$1p7Ae<@L%h^&$PaYcS+kM66L-{mN_~%Ms0ux*p*a?W+ zw=NYohhS++^}>1K!&#B8ty9bx@nU=NL4InjI=h=3ZY(>UIs2slvlZ2&>TbIoSspCn z_@KJC+sep;(o_<{O~b4VRou*ORXfgAoq5tR`pVdkw?4Qy4gh|uz0Z_ulQBAR^4=4N z3C??oucS#w82q5eLX)o?h>?yTO1;mDvUFV3w#!g#d+cfl^mEM27OQ$}Ox0`b-V8Qq zqm<&^n25T(yU95YQ-~_}@7MFErx5EBn1(<&mJQ&)TPV%DUXUqPNIIlT?!nUv5`$CFw6RW9>w4*OBW`resAY=s_JfknR;HF zk!IDKS9>By4No0vq4k_CcWT)@FI@Sw#0}_Xv=djxB@QCcpA3iSsnEYe6G-Hi)|?TQ zrgR$0=iG)Q6M2tbTSsSjI@EE;q5-K8?&lP%R625*^Dl87ewDYRwLZr4)MTgzeB<KLkvyc?Z$70k|e)Bm4=Il5d!LnB1M7>_4Vy>e znlMuwwoM_k^)uzDuA`e-=`(rzDZhV@y+GCCeC4c-;5i`?f%UCpBkS))=tLW{%T|g| zE?LDHb;1i+IrxLLgi3vZT~LTEm`TbUzqq%S^I@OOC$)4m;qJG2sw5WGZ-~G7V0ol< zC!gB5JH;jxp>d(V5~3)ev&6YdD9VExSJnsb%#QKetTm7xN@hC@^^m2OUE4T{>fo|W zl{ic2dlydT{{HEmDyC1)f{5ydKx)OnT|IMmvtvQ1t*SU#cf&l`25 z2?A0XBr5lX+*R*E=h)@&JH{h!36%z-(d^wUyf;lb&O#LxIvJO&Nrzh`({n3gfjcy2 z1AxYb=m-bw&+7`0`y9LP3qqJ+px++?&+qCaK(()nc`z4Vi}=Au#p{`WK0h^|4c`@$+1$1MU|wf7G$SaieK(4p9@S3ceB=P{{6ISs_X)- zTlgf76P7FwzuqvJPdqxJoEtuD8ggF?F7aFlEFXRuUZ|JW<}R6uI+0P-Vcq)CZ@NX8 zv4@4X#%<0>M@JU&iZkq#ABxz6fyDJh9O6@EJzEVrc3@=r1CzAVG z^ygcuk+PE^YmhSP)G?BjU#w|Z}I)WrP}$?rQWuTsW~{8n0`QI?MM-09g+|?-=bW5C&uOUgq!b) zaBz}J`khoaLfYFGcIAuHAgUr=1*6{88PKk;bJh&1AN%3;>mz-Bcd2-Z(&r&T= zwvRds4>ET4Qq#e(@e)=YG}z_yJdoK8Urw3qsPxQ9U*>Eo1G{9|$xfPxsM(d3w*}SE zh0Y~DS*a(|L-9z#SZrZ^th*7WtBm{eGd5DZ113uYg*L3|!%Z#3#~-pRvf+74C2{`G*F%aLAZcY~ zp?G`7yE;Znt!5Z*ro?K@SDiG)UQRmbroMb~u2CeQP2z``nV;#SmRi*1GXMzgi z#SJA6tsYUgtvqa7ysv;B!bH!Ybdd!tF4t~tgF%rQsZdv&Xe#SjGjO)wr7-=ZHPU3K^afEOR*gXpU+UoWd4$Kw$5`3n@?*HYO(}ltzVm`I09P)XL()C& zKnzow^W^0tp=|Dus+si~a>Jh6y$4i!08tzUPxN8pr}wbY5Mqx(?vO7{Usa?(e4}Xp zT`N02T4DRg*2QLVW%AR)B1yHVZzEoTOhUGZxu>c~EN~Bj?XtKX9G$+&TA-l423RO+ zS~7U^hR984g!42{ltz5!m-SOeu3v_gS{HQwTrMt6KN8OzvUbYK^b--smZn=q7UMGh z>T-h-?az0TtO14~$7R%&Kx6`^a)1pc15Cj1q)AfLuEs0@olL{kitgQK2R(S^S0x>Z zI4BM&RNM2gM{rt-nCP=|{|wQM81TsfWx4pXT&)#7B+eI2Q#W#d^C+-`Dn7b&Jy^Hq z68~DyxJJ=Mil%B~J%Gs;i!ciNLq^%^q!SJ!wk7xuB6HZ)K#yaPiSCvZqEw6=I;0P5 z2rv_%qQ_+t9M(+YKDW-mt&3 z!Hu8Jc$Xx2l9K7*ML6(#-L69NT=5u(_N5;crD=Tu;Ntj8R_Y0Y)4%%_(X+VGCw3h2 z3YLdbYo^61KJ^!1Q@k?ejYVb(YFGW1Sx&bVTl+_;tb7!r!p~R(O47~ZMUKoXsE++` zvGq$l2#TG11RO689KtvvM-5%C4ImA5&r*L@M?Vm^b5d^O*8>tByeT-%O?>Q4P{LL% z-$>Q|<+BpFH612U^GCPV<|_?QoM+qVc}<}ROZD8Zxt!wzm})IXP}FhT;wnojxw2Ai zoadgw>yu9Tft5pW6$^uv0)D{Fpk3Jd) zv6W+GvK-MtP*%Yz-`x^w!qjL@?Y|53FuXo#p)5i*>5Lc4sMm@$ny*o^!aBhY~sQK?O6tsU^pOcT~?)C_)N~;57j3E1v3qa^92tnx194h zNgPgO49t;!xz`hwQZu2gW+8tHB-O&|*MA3jVO9d->{PN~u_FoH8BmyKQ|6u7^7g>V z;rrG9uv)*II)$D2)uTJSeQ!>Wom0hF{7{W2G=W-JPySc@7~B7XA7f-;Wc?q=*#E1+ zVqyEA>i?vVv9mG$fAF#YD-9N?%JSVRT}i)xz6*1*|ML7IuY^>P|ME0|@N_>zGerf# z&JL+C<&H$8M4CTEL2@z+#5wyY=ignn*IK9Be^X{2Zg)SoXC58v&oH3L`4Ze182>r2 zAfN+_1E{#Tu#f~0BvcSUkN_PVF$Wgt>iet!(jZ|@0L6)l|I&h>pv31 z4YVRaEUwI;9YBk70NfnVG3@))w-RiE&%if}3ixqucDfTZJhbYyI-qNFR}bCI+6EYq z`sCBP_V*om2q-wPH;3heZ=bA%3-v7;*lWT9stR^?4kB2<_t*WZ98h3@c-{00`LSI^ z3wRQL|3SSvfGq#6At=bR6B>hT?;w{Je6E330eu%a`xgWp=659)x`hNVxDiZ)A5uJ1 z_axL|U$;H9VQ~xk_hB!>TEyW3p#ijo8U6wM;4jRd0KzzP@yE@%Lq6Ev_0e799mUc+1dGf-$RyYka!op043q9DYnH$X!`Lk5ZX zSs3E&cfiL`fsYO4_zjrG?|GoF?C3{i;4KFKUfT+c0Sfq?3Ozv|#{BYiH*owIGr0;N z#r}N5@|$3w$@y)9X9WR){2Ad!bcD>Og)+T@?ytq8jxbK}C#66+eZt-lAQS{aih%_* zGKT}$Bv$m-w?+et01nyjbMX_E%#VNKCqhFM3g0{QQweb|R9J8I4FcU->^t6D4jb?` zK|v>TFqk3}>?v=e0|tY{3! zF)?UI<MChT-6eh%k<9jb-1dVReP~n06u{gpS9~*J zR95@m1{mIZ_6Tz8A!xBoRC$5S)}B$G%Pia`s_uM3h!;LnBU|$x)zXwo8m<~%R9T|V zugn#HhO_}=tN*Dr|J=7ReA7z(1eP)ivpcA*!jEC|Gr%H1**4Fv?cMkx>b!pxao)1b zy@UuL>4OlqKoY9qD|y3Kl}|7^d|7{vK&A@%0IwNgRmE3hj1PUxiCF{^uOMikLwJH1 z^S_nC`(qrhDv9P1L_F%BVf6(>>T=ty%G1G$4u{FYO8&`RDsyhEkaY zk_H0@J5b8#R6MhCt2V_N&OfA{F;TqMNMs;P4sQ$1anHx~0mrILEU10nzP|uJiRS-i zLON`ofMl=`t!cG2w;vngn-f9OOH&_}H`Lfn6KW5l%Q%fFCXWo`_>r};-iYfh{9b-k z2ZzaV?I?~0TXhOtn)BHq&C^lutnnUI`W*DEdQ(ZhHHcyoxRhd}txG>6iR_awR~%6> zPaV%h;jeYzy1Q7(+jd#>OwFNpT5andhxEHw&~SGylG7HQ5Xs{AN3e51hIg$_)yn9^ zIG%)&MEm}-mcSG}hcBxz1%XP;?Ty$xzqAl?8lbxNU+>g`5UUrl6{h?f%M${u8q~X# zD&AB$(>2P7QH>5EB8se$it=RP8C5Kq{+UMQfZ$z4&)>;idz4Skl#!@l4a&9GoG8`D zu#Kco1utCpoSdNKqd?xLBoyB4xL)8%pt0>h(qZ)VfF}zhtPBtA@(VBWVB9 ze&amfwue7VN?(c*mdN@a%{k!n+TZ-A5Gya!<@e-V61(;5(HT{4hC)j(soo`XKxeGr z&j6O`#*sI% z8y*>~Tych13#Fo8rv5FTft?Ifem*zcie04XQi#OSw2d-xBb|)(6=S`asmy9Q#g{N# z0E}*Qw=cpz`y9g;4{Cysx&o(`1*<^X5$gYz;nLD63U(K!+NEE_y@BAlkjvu!V7E+5 z$OEt5gqIo|PoWc(X`ofvj;Zo?nG|# zSHzbYa3B%cu8GqP=P~{6Ahtl!Z=9?<6YTGs=oed+$C+Ek)6&+&isBnzlFTxx<#K?Z zH%hh0a})DYxA$$CNo}OS@xr03(|+Kk9x(NKPaj!3`D}qCm)7vpUnVdfzflxCt3?vJ&Epw*zI5o)sFq{*kwZW&BkKSWPA7O zCe@S;j#Qz)29T!v62&;(_9b>I4-Gb27ur11fziiZ8N#&?`9km5yokL=*?kz=Ys-t} zVld570XtPexo-OJm_gI3VH)M1ZnMMMj|3StpwU;xk6f|NZv$_YD8p{A|A>uQ*{^GI z+f$-;WtfWbZ*wHu`aMT=o9WB4Pk((`aCa1OEtIOzser>&9&ywN-(0Qb4e*c3g>e&w zYK%!OlqI&=T8Uk9?0ofT;?g*_H`DP|`fuxa@c`4_-6r^db5_PLAdW(2S#P1MqMPJf zsdoAes(w{vXE!~K{wYvAY#HUY8#E^>?tRk{*N6FR8;Xwab`tnr{IWmeihqc_L!vwZ z16AIV@|8RP<|q~`L00(QYytBqG{uI3?!;>M)L!67W?5W`p*~{Gyv&U(rJjf>ZfP-H z<9159anu`;VKOD%M-?SOT6?$>=ArP@)Zs@kVi#A^l1yq{2CysB_;xOQLh?>I_HMa{ z@z=~8BtA-hr<@p-D}Y^?0;oa<&V#01s+8LPgrf~QM;9K()0mdDUguVpTzwW_n@`Nz zTsl81;+Bu;k1ix=+Cy@ z^%(cWR)`yHB8^%7Gutyz^*x8J7?BCR z=z4#-0`JI78%!H|n6_&s6SS`GjaSFtJ4UF$;eX@SuPewgH%QOkq_i`EMNt|Lz=PI_ zWEJ`FI9-NusI`W#xO>n~irG4fV(@)1O0-C&mffCbb?{>lX#K)`@j+7AKWQpT1ABdds5TWT_D8oR@32b7TcsL+R=D$@|X;F2{EL=(uqe9F-(%5?Ob7 z))*d)Iy@=c88y47kF3ay$jb||tbz`#GFxh$)FQ2Ue87QKE+IQzIbcB$g0UsuA8r=iFpqkGkMiI_ z;p*0%0{_h-|7O$L4>ia6@kcf9BxkMrPW*>6a+d6c+3OJKaEE-3`oFcX?#1uSbu=O- zjzed$P;Lv(jXA&L7Yf^G%)v3@yEbXnMs>xe%-PBmu=5HeL51#P7XNF*;fE)N5N%zmO9=+!w-d2WZcO;gPa;$ z5X6t%jyD8#^yN}C@$Ie!O6TuZ)GtpKdo1H(+ru@j5^$~QQx!bJZ5{u~fWWQj8R=hs zVwPTOW^S@CyMS0WY}dXxAIxW@YaJbEtTLEFrh3dCQj9{zB3FiTeaBM* ziSTnvRYeyAYA+{_bJlNV<(SDL?gp|%Q_SkzAU0?`%(E_T&3NhG=LGE|FX=ax}(G}_I1 zx|*=u`+(@&z;h3vEBWb8UCN=4Xi2?i!Bx68My5@HwX68v{2(vOO8QcM*Om;PnBa5B zC2$2Y5@;!Gu?#XtI^Bft&w*Oza+SVwT3JCE4Btuba}iouMr9+Tov!>R0N~Wh3*^n( z#FxDzWvfi-C4hYI&;_WVM50#rZU?{IT;&Vg1Ko#&CxpsxdPsk zbG$f7vDVSoOukE+SZ|lR2*Ve*{9r;upy}?fRizz}S3}}DTYqSrX!)dUR?QjOs6bRh zIM=x6{k(Ljuv9^PhWnJh_x~fy9mG4;FmW31nO%2Dq-DxVjh>0($Za>VEuH?urCVG7 zM+D1BCbBU8HFN+WthJr}U+Y~`A4+8bp$jvhuPaS{#9Pnq$|?!M2F64_UC0*13Q(+- zxo%wfI)?cJ`Xt1Hrsy0`A0Ge)!t>>r1(_ljK8NIr32W-0?hC}p>?^z9Z(o7mF?(03 z$V+bx*hH(pco|W8_uLfMTKa1IVI-<#RIXS1y4{>@Q#rfoc9qa6vcbS6*T&8Fo5tg3 zC5U@~c#T?evv)@JTp(Fok&Hi1Q_LBx7Ttm5odT!(+YAqfR)0bt=tY%?KkL%78PY&B zD^Y|^SQYJ{X(p}XQtH87tlg);EA8P5@XoASH8X+kpsw(s>5l(KxhqmDEEG!)#fFdp zAu>!n6js+}adRJ^=a-nJtjihBQ-9}C%qf5G*yD?S=#V@jx{0UIn%>dL-E|aMCgfla z8)VFf;cTT{-(DeL@m=1J z2~f_%Z-*nI#&_nN4-N53mfZ!9pgoKzXSPAv!mZ!|hKEzDylD!Mvjp{q?<5VYjcXI1 z*dO2lLY1i{BXo2F^ryE{{7(OZ>MJ05`lR%%6jp3G%BdgjVf$)vDZ*K6^eYpKt^5v- zr#AZO198yL!A+Ff#bpoCG$QRt{dWm({5|UNc8R)$M-uCB)|bMCkaNe-rOgAW-B=7N zV*cTxTEw4dN8H@ywwr1iHt5gw9!9*xvEBHI_=_WB?)%XDi7ss4Mt7>{E*xy`W}O_w zV!6%_!=hN(@^p8|h!LfiM?y1eEFmtmi1W7r5MVrfKZp8`y_%jHJ^k1$*ME$TH8pp# zX|C1}oi6uMoz5inKd}+SOXfo~H9H%llb9zyRR-K7ZpdR$mtwc=zVB@SN#!L6XOB3`6jAk4HvQ)$t>T@`8s}^ z1YX%g`TI)5S%25y>({Vuc7z(C$2Wla+J{%Zg+4MfkwH;)GQu`>=P~wIa_3^>qz2G9@3Q z7MDB|*FBf`RRr-yk$*@k+dq3mh++;>0xUBAKAfzi2L}vFZgDhqG%+e(A^kdueBMXD zs4CU=jSO5HjBGeQx8M|rOC_3$IGvp#^{77$cD;ewbVo^eK1YZGq zg6^QR_i1KUrlwUJ6kuM|Txp-Dw!Pzg6vyDs<;!fFzLzF;v|hH%h9z$qp&_k|aQlj=VETZ8%Rl3_ z?EX7`X`bk&ASCsduEr9j{-Uijy~>JT_2Bz;HTn76HH}PDaLd{9m~kRS2OI$~obo<9 z{=sl6LV>O)Z9vzR2@K^(QPM_S2l6Gs&Sfd z)6807)?BFLDlx~G8SleP84Ro+4ho#E-gS zYP`&>4#;Zy7fMh|=@xx6BX6VqsvQ}BWY~w!N0T!XjnAfMWgkuAyR8L-7tGF%ya1J8 z!^{(mq?G-Mz|%YRBtg&{4E-m1Iasew2U#9j&ef6+BaC)qi+rSF#swJZz9FE7fbL2e zkK1TDQt60Rk3&uS*ip+twRWz+kcq)dJ@j!f)xI;;7Bg#7#}j02cK$DNh&V_+;fj8- z?nIc%qA`mHtbghs))ae1<4<5aL8FJ5Y&0Hi4fCY9>FS6k^F@D)dS;Ky+{G=1iuQU@ zX|2ikfyp=cNw`)-NX16v*-xARB?n2add56igIj-8szayv65I)uBzC&A_ zMMAZbGp6iM#@=~6oBJPAUxXKn<=$8FM?1$9G zGcIHK~!o&`014ZWI9XAGIHm3RUf6jE&8@y;`u18MnJ#5DsF~ktzMZz65es393 z_tLB@%C%j>DY8;VR7J-jD*C5w}Nu z++KHjnoaet%=(eJ^5? z!Q{2(RN-{K{^!_)*kWFh&GDZr-6uX_1Z!&xEA}=~j>`55e9w%?dyZ=Z1YX98VFiILDs`<2Tc`u+Mx<3~Ze-51Bxrf>}-)zt>D^6;bc(#8Ilv#^_Qi^8U#35oH>ET^SxAgm7BN2?GYxEOsX(4nyx zjO(E@elB7n()e^^0}daLIwf0HtcT0L;WJ^fqat%yEO9O`#e)nA#DIK)3f`&5!0qJi z-j$Z_oDWIH%rdwy!Y>iSQa$do(a+>11A)mx-pT=^#|TM}3p7 zb}|KHengFrp0+@uC~TX!`2m+z9PQjsQPT1zU%w*2;mR&0cGRXBKvs&d0E6zJHTB^4 zzCKai@Z3aj6S7A#2wyCUyHf41lrhOM{cX^>&~EhQ#L_acY2E2Gs)nzR0K?ysj(AsEJscn<>2mRY!AF_&lG6*Mm+6r+i+8~pV7I5pRj*5=B zx80)HR4MOTk-e%ZG%jT2tt)_3aBwFoW#V(E*N$_yQ4nTxNSwnD_|2N}GW#w)>r*%_ z_tJHr7_Th1ujX`3PU(4xVwOyitt#|ErDUH;hB$W{Wkh{_7L1;JH&5${L(xShC%2o_ ziAL}yXUMg!#GT^E44c)!$)9vJ8MMOb7Mbv-EJllQnc0brTod55(1nob+E4gIf^(fbp?=3=LCUyd#^)!7Fu;^ z4+6l>%F4p7s_0>+o}Q2j4#3<83(y8;>7O+qSFZ=%cN+pgRrb2i%V{uL1Zb`%ob}se zHB5D2S0-oJUoZe?1Q*W1XV%F_Ga&CjIslOMAoZ^V#`rX^U(5rX_V2p|126*p(Y>v^ z-U}g^=TH2P6=?VhSE>LHu?%GZ*#HczVw$XRaO+^^Pq}>PmS2&>e9gGGyn3JS!wLFre(b=<%K_#9uzYL+>;tg`KmNn?ayE4Z1K>_B zU>~o4JN_GCf0Cm{iI2Y9h?Z~<62xY+?95QrVX`}pDW-(}QHA%D?e z|0h=-Y6$~8#{WV0@t*!e+4V04(Eqg^41oVGrUHAEEf_%mkID_%x!KJhe?b4wTK^;E z|4-t-tNh5!0m`t)J%Ijis4n==tyKnF zKwRwq*DDV|B4^AAn8okK6xPs9OWllvR- z^8(mR|3=*W0Jg_HxBtiTn?IYyzaS@o&FWu}3&3XmFUSpGgZvBf0N8B)1s~6{{TF;Z z%>EzvC`>l!zu+THhkuCiJ)%c>!TzDb`55nD{jbv=-)=U?f5As;PXB_B)SUl@Jdao6 zY-j5HFYcg6vhaT($76Z-Kj44O!raBl>2X+ptkC12{)7K`5y4=0usPBmCyZC)H8V5j70YD4^?+pF*tDxiI9_Hg&7OK~ z)KS)ZaGkSI%IsKCn#ImMoIjaL@VX$Qp22BG$kk1jpb#i_>P1i^kHGD~5Vf%C)uh4k zrmO9qOK_uoULwP*5b{~2t)sdmL+J$>zs}D!4fsd1eyvUJU&M6TYxXfg>yd_GDJp5y zib8EynDK5^xGP@<`xo$f$U7qf6kG#0k6wks@uUU&$)vc@s&p3ep50~_yZ%VS_cD_u zkbI%3oJ*xajM*=lm-z9J*zgvJre~88W}SffgBYhZFKxTf8s?vJ#mU_j#FvsiMg7() z+{;2}QAWeR?c?m*!3m;^ZzwB+8+KS7V=eRjny#Yb6CijaF&Z^21wTZn+RHQ<6zSp9}aDdoh&gu;!i1T_YSh15mfb_-A3 zHM=v)B}y}Lbp#Tc%cE98hOT2BK}NX#_E#A`McB+bi2$wiEZvMaeeqkq`4X=xmGC&< z-ltP&XCEk@^HVxM6PC-eAb0dKTN9&P$Jh7IMi>S3XB?#0$XbdARY3wT{WGJZN9xeB*B9TUimKP>(~lm#gT-Q$w;A z+4dBp%iY}!5h(x$348=gy9juH$Tvb1#9TRl18&XRk!1le%zz{xxPUwSYtxMqzA0si zJ5mwyX6W~4sK!`4%+bPv3lT8pF_klU0^Q<vGj=Dzkr-1R0 z9nXgr`#fY`J9d4;>FY{Cw6h7p+&$kcMo7rmB8y?LnRs91j3i=LTuoY%%u!orwLPAS z;-IzFE{3km=JmS8>_8EuqMLQsN=|zHW)@E1FI7xF@ap@C;A&4KGxJ@@hrLD#eRXcm zR8*f1b>22-4M59~Hy62S&&P-ximG?Qe6yvXq#XUjzttQ>{;QX2JGq@GhzWSJ97u*9#0Tg-S=!Zelf5M|0sJN|P_dJsO# zm*z!8*}TwlP^S`U7`JwZ4EyfQM6k%7vIf!9C$l(XAO;J^tP4|Sq1ix6jpU?>E{S4& zzi-C5waGb6AEz!sf_XZn1G0;Ce>2^(&&ZtygI=T5`QC_;fm@Vo&xq87sD4f?ZBAVnIr;DzL>&>CDP{`XOrb-U(ir+(0+U?TXiE@tdI6M&Ap=; zdr#$MS>_u+@AgvLN4YPU=N6qng7Q5(;(XrzkKUzf+C12ha z+KSgv`69kSD?c^Np#eI*nZt^jUlc3pKpT?CCZV4FDH(4Zm_cNfv*;oj^hGyb&swfG zyh4d}e~m`V+{u^Bx&O6fn!Ls^aZ`BxAl;1KoW)n3O1k7XCn6Duap!RwD;+L6v+lr? z3=t3eh)*-=v@57*?w?Sz4dvjFt1p$2w}VFY?yOmeKHv&GW8KXY6_(#%-IUWfE75o(hDJ#8 zHfM`Nb#Fj}ke+InSn)Yy^+FXz^j&ImBD{O>%{JQHv*UegK`M4e(m_mA1h{P74QAT| zkzEy^f<8{Hcl(M4-+k(k$P^>L&bbX6POL zEkd?BC#9`H2^L1`yQTEKT&~*eF^Dn$i%|+%kNkJegLdLmgDISh@755-+-;e~5WU?y zHWt`&g1?PV4kphssLlw9hjfwP>HX4~)`>(G2nn?_vgzWo)3C+A#&HjDjLj-A+`YrK zW10<8CH;IYDwC++foQ5bav*0Pl)0B%YiO4>gTX6eUdnhQ1(q(P@W!ybt-vm` zzz`+)?bx$UZN4AWtv#7z6!xGqKhqudJL~V@81W`c$^L03#EiqdSniddLtnVja$vjN zDs9Pb_#1L-w0`H0_EItU3tD>4t+tZ{ZtPCy+seeiah)rC5v?oUIdN= z{$K{kQ+62-$K6kvRq=G95cg8t>CPfzXSJDyD0UNOY}l4x{|fpAd>hh$k9qS1eziJ$ zxV2(ZH+OeIaZTVH-B@hN8dlzg2K{MmUNQ7gk_SDN=8iJpiUGbtyY=Cu>nLja(4+kI zbCGZ8Nj{?0)VX27n`W}Z!UV8pkI~hs1OQsEr>fk$%GO)DZ8TQ%z1;3+O}z)VM=Pg4mH0xb5)5=vrgGW|TNrR%xk*HG*%<-XP(~`0lNElMjpM z!U=ZFyv3oQp!?&>zjsLaav})uokY$BB! zn@PHCQC6R}dG`73Lm#mXYjpB;#<^HVQk;+a(ft=D`)nCX{%NV{+@aE=$_)(cC_9wA z_7_y8^PBpbb$6jq6{NzAz{st&WFW}x6)R7@yn8wx(y$q&|FFQ2)WF<$aH;U;J-P?= z7yCa$&CzEVwTx~3IF{ji)$`zL8gD-vx!?k7k2vr*cIG(laou9<3)Z32EA8RT>zItU zLQ#g#iWIqadI#iBodDueV`8ptUm{*P zP)&Ux(hTH-T~8#@)N_cMF5679%&a2%3Row;PrCw*5HxWq4&~EIZM*n?pCVsFOF|^k z4A)=5UBR*Tn#~FsrD;ELk24B#jbju_1Zzt=iuFd)?ygI+-q1mH3xZyr=!h5+-LRVi z5lFMJ-?fL69QYWy-v+vBST-@h^KtW?mA>v2+$>5uXGR(8iunP1b{cYdA*#u3?Sp#7 z-&PXgv|ecbW{`=zmKJ@ePNySsbKr2!3YA_ENz7~5{s?lu+pX~dfVy04Wn-McXdEX; zfh*_j-h`8;bj`?9CWK1n27LD95&nvzWGUTynOf@5w~`MdVvvQc*HbANVo3YGd;y6s z&)wm!u~}uT;RKf2b+53o-njR8+3zCMnS@4%UsD2i0t~)yGLIbJso&gd)aHB`oo__$ z!w&O*hf@j2qzRx1*6cUmXJ2iR&CAwsl^*++NcqG+`@NMB^-PXksER?}uI^!;&QT196>z z%*>=>^#{~{{F;v)zpe0?=DYgGs5cJjqkTOtfzC#Wb(&o1Y;~kW-(p5^&FgLhXHDmq3ZCGPKBDEnb4 zRgg1_aP^)W=?$Yze}>$TEA4O)8UmD}mn{{y+6}SJM6)qH-l|ND)U<-md4f#N^|L#M z^j7!h`8NznpBw^_Ct@Z~Gmc6aUR|fu^^z0q8o1`lNPJRyCY!?N%2D19H09RA+#dbH zH6NVyi~rI>Wk8HG-H=}wo)wc;HKV0;f#-KbBe1{mVj`V*E`MxF4~hQ_kHsj)i`MvR z3-r>A*T<7Kv>eD~Wcl*>z)NoWYCECQr>G;C9a6L`Mg-MQawY|9;#7N6HF!?i5=MWe z>`A~v1@q%m0YS;pH2AEhPq^4xI$2(Oo;Vm=q|~ixe%avIT(&iBRf~o(c$)fziulcM z2dCP~9?tnnrE<3)b5FrU5XFqd<=gCyCmItfFb;bT$f^p;6bh;XVL!v)AP>abH;sl; zz#`frgd7gh0u*$`K2{DR(DbG(E@s&xz@EEkg>EcNM){MXoCQM`o|a3q_1A|tZ=O|h z*+4hnskg&>TIW<{Zbg7Rcxu|>PpI|2?WH#l-@IF3lX!F0Nskm0nI!fM`U)66fkSjC z*SWN~Q;^7xzFyyA**W9HJhNeeK(QKiGQ2=t6a3@QvGtNE)%jKw3tCWu-|8FLeAw?Id5*vy?ml7O~LshovQd`=aznqJZUOb zWNqHc+34acAGwKOIzH;uhZi~s!p(~@*0!}FnF%pkXbP9-ddm2WNqoa^zIpyI2fvTP zuN@DOW+>B0dfHBv!h_uF)_9y7vUW^Knm)yujMqv>$3yKr&}P3IL@sY4%x+F&HRgUD zWO+ms$3bre+Q+>|*;1z^A_U^yr#ZY+jchzca@7~hkt2DSGK=%OnSLkx`r`1_c$%RS z_h4S~^RL(QH`563Ff9ua*}8Ce@Kn#wJrd)_!-BNdhxt>zqi&2;XHdSFB-(t~{Z2eP=&x&syC-IV=+PH3Bb_Ov-zo^6KI;cK=Hu-EU z;xh>r*n64`(%VjIXX1hv#1^rYhyrVI5iy>t(?Vo;qlq%kLJ>ga6od@2jT=cN`%j8gimUtbkmHkfLm0CzA?p z7g5UfB3MN2B;Sen`>A|CjR*0MD=}n*QYcG#bzx=CnkHAxx30!1ucogvQHA|m7?}4Sm^u7~7;l9q7qjA`03Eh2qhQ<9e9xLi! z8@YFXmKonU&}wjZg=s3xyaA+r-I!`}`jw>DzU4AY5}p^mgq;z;o|(sxh2NJ5s$iBV z<~_iX4X#n0mimGt4cPo@+xB(Hux?m2q`&w?pCnT3(i)nYB*1uFyj34ArY@S66x5(5 zO)TZFd1_b{ab3CxSe(n*$S$l7u9B=HzCH~(Rkl`FPspBdR~}7yFXcLCv>VxyGkbnr zIZ;%;s!+!GQEM#^xIle6Vf~#nWcC=MYs^hB_&(_+v8m#SR!P~*(^s>=w+L@PvZCxA z00R0_j3G;e9r=o^~PfD|%ui@brM*<>r;fM8B5- z)r{AN2d#*7A|_5tRyewm2uw z4UUL`}YKPM+NcUr8SOVE%^X3 zJW~WMM1^;Do%AGd()0S%T+*;OdRAUqTvPUz=4`H2_T=YjHK2DHqO6)%)t;7or7A8+ zd4=ah(4@vv>B*4q`}M7G9NIl5Qu4~D1A0?KHf{keoCA|Jjs2rF5fa+;FPR)y>Yxu-DtbRa}(TjZ4MX0eDdiil6JbY zjA~Om=L&mlJdw;ee|g)qI0>+ly%1)~la8pvVIge1s?*BO!D9uSC-f-S1xu_6zDRIc zj`h>qEmmbll!ner27{y=oqX#$&X;NO(we-inm3eHXAwg06{BNJQ}^l&7!?+tYMDLY z`sj`!>bcLki&eW!xhMn{22bTrU4|*TjG4Vd!bk-^lw(A&`c2!eKKo35(%b)Qd6gk> z!u6ZY88u}&=CYyU7+SjfYc67v^Ge6A9T#gXdW`tyr$|gw**#sx*@&bzQZ2^>djhi! zn|`9pr8sZTA9!r2TT|Fu2l_SM=yIhnm+MJ(sd=F1v>5*4Ypx6{$zwBy8TMV5zDeQf zCUPiCOUA!WXZr}Hd{^9>T8rN0?NbVO&2jGdcm&OQZ!YE~dD5DVXCC4N zjm64LuOvdG!5qdhHAWOQhX;elAOQXkj7Wp z!P-dgYPziUwey(!gC_Zh4v0__eY_kvbjJ;Sznj%rt1j?CO>Jcw)f^4&DCOzi%B>tZ&Bm*CP02N}TtR1kF5l6JelHOPOI>6wF0Cn*@lEqW%H=ZyTl}#kV z=j0vGc(g2i*J4Dcd2;9qZ&omMnKE)Pw&qBN;#|xGxva|P&0f11$)LNQ_iTpP6FepF z_1gK}bi${QIUB!*-v&8O_S_eie@IujOZfc#lqW(H<0xLfpM6XiKf}gbRV_)O$nW>x~mjrt`Bka^_Di|fe&;^RI? zrf5ywE(^;XUt&WnMiZ)`m@283$DK`AEfjV#jvwrOnt7|&7}iRC7Ezkk%G2t$PU1zY ze#2m$MjOW;GO%eh#*aNpwqjh%Tyi5=Kw?KWF^eHzu+7#v*d}lkjWIJ_HD{Q1*(p7> zDi_`O@QEXcgEr)@bjB{xKKh7!cB)?DKwtV?i3m|B|; zpCrH3f;xU0pqei^@Z<{}?}gZzhgF%-Sa%FO>_fBC(L+}?|HJ7Zwt~QE z9oK4AGzt;JPMN4H!J~UN?{^MY?;|G~0Kl3p&C7{QbyKt2TsJK3JnIav0CnaMuYbkv z^bHf$wSg2#&AMTWXwO9J;%7WJuYFjt>%Mv%O;wPQ-b|l{bMya* z{H-C}QioIgirU6cbUhYaPgVYh~ zwe%{pCeip|ae)WO%2^ypPy@Iem&bKE;CrskEyf$`m>%F=f9Bkd~lhuN`AMa#8ykI@9hXnu5Q{LO6_t9$w~;kQUc3t zaq^NX+HJnnzPp^7OEU>`Gc!as=Vys1DH1>{Jc1+?*Y8h1L zQ0`uzVBp+C*}W_(pC!ab-Il{tIt+I=hLl{L!b!!@#Q9O@wcKB3b{CAYPJOV7A{^Zo zT@G~)us8dOkWfKhUEbyP1A>y)VO*S1duV`qD$(Vpml5OKXzP-mRTOC?cw>EG zqUg}9)r@`1 z)Za?>9t^zHcNUssU&y^{+|Og}xXqC9mmbw1qWAX6w~fGA$PQ0Gt}$fkpZaEy`=rQG zrwLy~-GC&v=(fx{+9i=;ls+zJr6iU)1l2^+sp{o~I0crz!+lM5b^oG2@Qa^T!#!dG zA*V`{v1baoy56qhmp!Z+vA}!&LBF2fZwk!QgZKC<=BJ`lZ)dI+Oo%LFqHvF^>=h${ zLLlih&ais+n4S;&Z_~1)bw?Y7nas%B42~78z&mo5Lt0U$v-%&jEu?-bR-q)3?7P81 zoGFT(2q_tv3(MFSrTLNr{q(KCkLrB)R?xv7X`L#XRo{rU3jLbbvFxZWu$Jf$wG=_Adb6DI z6!KE?`ZPXW;Ros#;l8qM>nG?G)H>lB+?yNJ5)DB0Qmn<#gcPcD43#o06=~>tHn($X z1}ZXkY)9!$=*iCB8>UB><8_*7C|tcSm$KGPc=D8Wh)iMo#V-WpNz5py+`^q;Y-T5P z=lx`oaTI%ny3)sOo2zvyKt5*tR587P)=aa@ksYl=)Gov!b)=5+!pE-&!k|dd+;uWp z=xrT}QO78Z-zm&);)>_SS2k3aMWTzIjHw@SbhGW2ez@HbsN1$ZC@RE7XP@|yFYp}{ z)k2yS&6!jn*j$*X<&)Bz<@IMoczzf1DxwJJ$Suj9xDjn6*qMke1E&6w`XBtZ=p@$M zhqkPn*7U5VaSoMQQepfA+n{fP7E+N;Dj(<6RszMC?gMUaabAUXH&IGxMeXc`DWXyU z8}80Ju<7t{(q0>Wt_h}Ro4fbp@kk-n&sLkfS32<;&tD8b)yjRZP$<)Fk-Wv4hhDup zRc%lXHaa-3`JP!unQ`R@u?rgSw4=D;^p$37IAQC=j<)GUd11)3%RCxLoW3l_T;4yx zx-hq+RihKYmkGx>lG>4^xlCdoCYVGB=W?KVXNYTdkj;EPx}4`RCRsIxq@$W#&jd<~ zUy7l`VR`DCUr`(n%ci>eD=51}f{>yyR_LoUXv$<})>q)E$ zhG~P*aCt&>#U{Psk4wtXukcgCVRU#|=X~tq>Is!bohiGRfC7f+fNmmj z@nzk>cK4697H`tEFDk>ADafCl9QpAQ5klV%k#=IEl1WS8^h_+{JVa75o`JSlM+I|| zG+6dp0llkITsA_xgb?eeqC$;M+tv)H8XQ)NJy-HO?2%7xZW(P{ z@eT1)$~IV0xmi_FTjr#{+Y`m1CK{l`RP24DNBi{Zcud4)k2q^n?n=IB=7T_2LmJY1 zvsW_{3kvI;lL+&CJ3$`>AU{iCV(V8~Sb;tFpLLsb2^~5Y;!?6!QOD+_SUF|1>&2zP zcx5cXU8_zh9Gj*2GZAcnGsDs2{H~HyI1Xmv-D2eJdCuPWKBeGEv=gh#*y^MzjlsvU zg98OvdZ3x1jpXLD<)o!qKjCyUlcsJ=`5KYnZ{Q( z_o*(Msgv2uJcGOVLlqGM20QSVs20HHtnnf)+tb^|iW~ma_1MS|tvKCPIp9TYC$`%L z?vp`zsbjPzk$mw+u3UHyadEPRQ}0xtyT$yA@$|8Dgk9BWxwYwK?=21C(g?E|aB8!< zWeqZ3+oonjs_Z8bOl>YSn1GhP;O+9)%NEH%ge*O3N5>sQdK&7N$mj};;JYf>Z|hEU zlak_)IJCV&^r$!|DKUEz5k{`c#y?2 z79nS(B$F)LU61W*WN%_> z3Nbe{Fd#4>Z(?c+JUj|7Ol59obZ9XkGB!6h3NK7$ZfA68G9WTAF)%j@FHB`_XLM*Y zATSCqOl59obZ8(lF*Y+XARr(hAPO%=X>4?5av(28Y+-a|L}g=dWMv9IJ_>Vma%Ev{ z3V7O#w*^pK3A8N=1PShLjk~);aCZwXjk~+MySoMmZoz`Py99Rv1PcTUyw1$rN#_1v z^+^%=;Ul^Z^!$Gfv6ME$OR-5Gjajh$=lljWL#|kENlQ4PF@x+US?(hD>F0C{}|dk z@dCt*+$>E2@{9l(dpn>r9EGU8gQt_FxrGae=6^l{s7+`9EId41^nbYnL~MahmL^7a z0C^)93!p8C(Zt9GplWYo33T!NPY7y$3l|p$UM41YcXvi3TW3alCv!m>dVss7iv>Uh z=nQmn1DXPU6%0@?vIYKK86zA8K+VF^`ER+Zy_t)oeOnAqDo7}_r5 zY4fW@re9$|T^6@96}7ju1=_hd!~M!n%+d*H0&2S_)8CV|wzGG)^Zo~zS=yPJ{VKxL z)qzRf&eG8pC@uDn2}lI@TV@V)0dO!gGjs8<1AvYIpofVC)35Mqo({mjlq|o*pbC7w z9qb(dW}qT~zLsV{&>uK&XCpTtz{SZG=mk?%g|k4}doV z8#{o3m4gMq!_5ug;$Q~&{x^z}k>x*GF#mRywllK_@cf-Ds7wEou-iZLr~c zrC<+QS|EV>_m1l_b1<8LezE*NZ~9*@|9=bqE6V?E$NzUi60SBjf2pbe(*J+dMz)qV zp8pttcGlGewEyzz?%hhil#u1zjheF#As*l0&)R>%JT)7**n4gnkXj+ zfJx++=x@XcV0!l(aRHb_e17H&W7jZEIm?VB9766mvZ^Q~q1WHZqHv)xG|BXPYY5t3NK=ki_BaqJMU&I1R)W`(1Pyb5TL7Ya;parvZw*Kt| zO4|500wrneWMpCu1ig^VTz<>h{+0iIRsSkLEGEAz1_d**w*hU`zntv9B(}DHHveT{Qe=%vBrV&Me*V?RO7adEf*!vWN6*FPX=PHuldP#*4o>=?-V4>DFz zc+Wo|XbfJz+X#x}1$6qG>OT)&6IUnD99;f-HG&S~fAC-b=Kz5oKohvtC3_RT5UYle z&igtMe0PR}DS>&41I-K?2Jcm;F4spSm{gkDoS-eIJCW4UK9u!6aq3&)HR7M%r)^Cz z;qA%F9Zx>b28k-O2OV%LGgw2@C8r{dgM_dI3~IuMK0h6OGy<*Pw1IcaP!u@2aw91f zq2Id?NP095R(_cXTRKoatmTx2f3BQkh*gi#4J==vC^XJp#36-tVIX`jqZ+Go4=y?GdmO?yw`dcyl-}=-(`2xhy+4$0 zIZdQ5Vs%aK*ru@998-H8D5%^!om}fvQcUwwGj^s|OtO4cwBc&xP=V(;=zYv@^g4#2#%$1{4Og+iOl>5#>*ok31kZ1zM2aXr zFdu%7#op8%HrW{4z-a!&gJdX9*wz)WYo62K9(b~$Ml!nYF(SQiCF3<0;dZh|YlCt5 z-6Y$7sQYlz+0+(SA3T+!xj9JSxUM}lUksiOKN_nsm(cZ&rwtzpFP1DdC##^1tyu|v z*g&u0;1r%FyY{$a&>ikRV({x8Mx}b?t4M8i0e22+39J-MeB47TMEK66E0*NU4zJiI zTKJAkMBEE?SkaAUb>Ge8=bH0F6Im4IPmp(n))$b zc*|wmX`y_+Nx%h#yn6RX0@lIDz!H3|Us-oJB4P)EU{x-n(87+Ci9 z_vg2TUSxGYpU6*p48sgH=NR&P6O=Y`0S5OFOn}cL8DtR<<2QYNvp~boraFs*7;4&G z1tHT9wuCK5ve|C*dsc=?2wZ>v;A<3aVf7f;E`>22s>wq$`EiTz{x83iWR67r|{6`_39v~Gt2 z%*Pv~E24TKjjRuI*dBA)TEK56_zsq3W3mXnnaC&UT#BcanxNhbT0hWL|FM z*>WLL)-bET-&$!19e>M%mBqn$Vwp-89P?QQ%A*#6x3~CkefmP%SLJBheE5LJuXg6d z<-|t)5z~vLQjaR!N$5$4){J=T-X~%4ZkD=8{JUiDP`5Bt2Lh^{b+(_^G4OmXYOq-G zPOyJ-PbM#>Q6!%xZz`iITxS3ly5l287NL4%zrar@&x=?bj$2HJl*>;l`RYGDU87SD zGk3OsKu-vwN@Lj0u4v#!Pn~sG51v(m(KE0Ov!HVLIJZaVk?J<7hY(VoEMWAW0Vo`fkPw`POyS1!i)|HWi=Ff0>Qx` zxxdfi4_gWdLA9=F>$;t{Cr+-Rb=t!6c2TXaQ<{bpLU_o^+=SoVCE3gg177$#;Y~}S zKdsx0*~3oawXyz0NLJsuxpnQ~+|3YOil)FD)KJj&Q}rZSY9g)gZmDC3T)r$# zJm5A}BDJz>H38tnoTaF5)6(>kdr|1J9=Gdl62BX8V%|`t;hxU0ts7d?sv)#c*Hq}` z^&@j~sH`yP^iqpgpNYtjusQQW0ck~wzOENfAV9r;sT>h^Zc>I>)zPm1%J1yV^rHug$KJ0 z$2q2~LJj9WSjhLPAIz1skKpNVr7Q?mUdvYKhH3ZMhK_jwKr zuvKdY#Z1wySNidijLGXBHLixkD)n8`*nKTHfQg$@3K32NQq|I>^op%8oK)MTxI5FR zHbsrZVcBpYuVD&`UvbvRJdD6##}w7_-fA2$bWpdF$TYXU|Lm!?1>5z3M6cFsd0lv! zu_d750TY4aJQ8f0AwF45u8G6IX;tdrq}tIusJxbm$mys&2<6y(vQ~*AIobp8(e!I~ zT8~G;g2+#k)4`0f_UXc+XKm9B>JVDqynFjtQ^Sa&A`$sVCF78oFb2Dl#PE|^7sw<% zvgXprAschb(Rtv9^lIeeG-D1^^jTU(aafK7#Cml#i$~lI8@Fzr4txU|@P`H5333O~ z?5v?vLKM0Q>QC}3WmNs11IW5X^cqK55@1-s1IaRUtjHQXE@wMD20sZNq2 zSY)!`X%O&g(NpFH#_WW|9pd74j2uymqI7E?zEaVQ8?dhue)g5sF07?%HeC|bH`&yP z<{Uy}7JonFLO=2o109#yhyI zdPodd0G;y#rcMpsrO&1aNqh9kbHdkpbSo{1T~VT6kiFV&?NGfTPncEC)N8tBuVM)3 zDHj9RPVkBAbn%9&6V~@-1hQydrKL}-nk)GJDHaftjtp%xPq z9Hgat3BE^^Tn!9{!>ivmAGrH>-xkvNaLu_{En^WZxeuY{eYtdS;?<}6n8ONf%C zXAI5{DBE8qjbTijGKkx*za(nnu^{=2kZ##&6-`{RG=q1rhuS3u$`bY}iZWm+h*azd z@L-#B2%Kx`drVGHLwN)?4ZN=9iTe}P^{%;aW25*g`7b|S3_qVu~o6;hb`-KVl%>G9zGo;Au`)d8a{^Vh*Hg= z)Wr1Gz+VEZf&OCfidc!XJy71vl%A<+0vCvQz>>Vek?)zv-H6YG(7pt%(Y{w({(ZH) zt^YbOC>MoRU&0rUm`n&k3I8zeQvd_>^Mzj;o^8LM)n!Uf(pw2P0*xU6air|!3L^@P zE|qrC-B8^3_d!wl=&^*65lcRYXgriKIbDNDn`Ta2$U7|o%AJ08tqcG;j!0#+gL5XG zD2Ofs9G&E#07Vs7U^(`);DO}8G<>NS*ki4g(s(VsmF7`k3YN-RjVo7^BjQ=dy_KyE zTv${VTRzG9B`%LsQphP@tR?ITilOTOH%S8rIbNd))`-b9W%E;y9PlAWgiT2NE{;(JCI1}~_!iVbU^gqbios#(+LPtQ@| zm~>-suc1AVM_!4Kc(_Sp3DPJkL$C}N+Aj){d1n?{fSY?ts8R+2W9hvwMb^Y_0Z$zY zUVv{t=+_Cy{h47YZux6y*CdAUJ+<#yHqLY8A(mPWv>Lp8dQON^b$yWGg~LKbp@f}d zk1$M>D95&K+qP}nwr$(CZQHi_jBR^n-~D)#O>X~*KIuMHRj3~G2CeEQ7XmJH3`(Y} zhP1=M_Q&p*enNs5TC@5uk`~*NawrJ)Y{xGU+MK{?cjOj?hY zIOU`Ys}oBK#|uHbQ6@CrLgm>@pEhL8#YPx6WMYmdYB}?Qa2G!Gx)-ayS$lm?>aL5b zCt0YB3)sFVW*Bc}p=Kn8aPd$Fz|7KhhvDOkYtLKm)GSxo|KY?ilIPCocGF#NHUcBy z_W%mj^BwoAV$QQe18I?2s2xQ6SqrQtfGokOdR&b!2?*b*-k=DZOd4IOq}$!>Fl$=y z*;ueqhf}L^rkm|_n|o#32DLxjXj@&bZ@H>Pz<%^y`Iz3$`sLlc`mniM8o-Hm?0rdfoL!$*Aad}jQ zwQ`YWH)iF$GZF6iuHib&%LW-e0QrJj*$IT@M?dB<9UW{9~71;?Rr zNBSie;3@}a^Qaq;yICK9?vFY3GVFX#&(v`>uwjhv8?6v1zB%C!@%+JWKj;3d0Q@b0 zb*WshY-_8pxmES^Pyy#28EnU6=C|WD`Ce&47eK~exINi*tX3O_!_gLGn@c#tckB>kO@!{B=Z(0R>seiMF}5x&qm z5vBZbxEej=Xq0+M6S|FdMoeq}k$iRz$^YIRIiMDy{>l_EZIN%t&~^vo46-pN1&$u zQ9!S2GfdGDA>K1MrDPOrfJTjT;34ahf+$H^Ey;!q?oNg0xBq7*HCHI+?Zv2crZCVe zOaNj0xNs?%`~rN>XISF{Rkym95;Y~;tvg^FZ<44x`Ac|=*jg34 zCV3Ww*y&*P+Z!a5fWdd5w};pW3TGzM2+z1xdYwoxuERnM-g-SpeA+{RE2F`H>m7bp zbPqlwTd~uT=^nl3(h|wNGH}q`~-KObyT}CX9EDif3`e7z^Y?A@Ptj? zjay?Isx`r$ny`b8w@&J=B`TObV$ERB43QJFJ}VUZ=SQEEOXuVNL=3c_N0LkvpiV72FKf>&ezNovIQ_B@LRF4N;aWf3cjCG=0lte#3Rf zcyc;4XoZu2ry47fZ&kNp2rmW)GMJ!B1s?b`4;aSoMC#3$f3Rrn?21LT6`xYn`qfR- z(7$?hal;4L5J_c%wqO_Gul1<)u}4&iw*$ zlm6*a{C3?m97e$0^DSNH6|ayt?)!Z(x<~|mt|F*eS1_XXs0irdKyy8aJ0~;Au+OZ< zy-w^>E6hkJElC)*weY@y((}^w-xoWWTTH;O7g%gmmLR83&0<0<;!Gmz%N~;e__ezw zj32F5vD=-aPaMJk?PtdxLO*WP)9gfn($Z)2yo@7qE1fbC=mI7Tc2uzuZR2l=PBS_? znNArI!z+lC2anYyslAgIf;UcTSjw`yZpoSQkg-?_u5|gy_$9f0pNjr!l#+KzM4Q&O z2LsOs1$$H?4~h71p=cayMkKk!gB3|G9*{pG@P;JY=G=8)gb%R#O5)w7Ii-Y)MNcgX zg-m#2V}6l(<7a6L;u{9Xf&(7@)0x_T#YxI(Rzj^@NPQ?&4T(Wr*{E)?58$7nC6CMI zo`4Lb+_PNPNL~#?k@0&fbQOVy7V*kw2<4`qKoB!#S~H5k3j>cppilO+4m;(X^c7p7>D+uMz?jd*sO*S9ZV-sZ17fw|HwcX0GF-g zAGh%wRtaS=NtY-{?`-=5`C*pqrR!QLT99=Uesr>Y>*=EzYaDpE^qG+%0OPCAanD%~U=CyA1LYLlz(*@A$eK_dw=VR?{Q z%Xjk7SLi(`lQ-IOsaNGce;9qtxMCho+b!#(^XF4o)`pGFi-^PR7>spRHZ!FmiTcnlN`{PiSMVAl;S<)@qQ7#M{fwH zYvy{Ud+607B9)9X%UCl}v3SjFl+KuLLeGJO7r-5s;-{)iujZ1?kkg6icc=<-Sh-%s-kM$)Rr=aMe@#L54LXQ$8t=X`CYPawo}&Cn0Eck#4t?t@3&VE~gv<<9N=5N6Q# z)a0jy!r#E0rAtBUM{N0B880%$mx0+RyFvWw(=fZ{^CGPJ!%cW!MXAU+P4uW?Bd~I7 zlxvyOMdZ|A_Vzt>Z00Q89{p)n=V&n*yj(n;YCUM=KdQ0dl4$mM7fYS%hccFL>j5B< z{y1`MKF&1wHuM6ock!s*8RkY*EvK}o@I9iXZtH7ls7vuvG*t$+5d2nXs?Z1pDnACP z2EyTX)J%3eg8>6I6SwEA%SfCwWNY8+{^{iUaWodfcr><6%6y@ z(l4|w1$qCexSZsqWHam zYnvITB$8JAFONI{fU`q7Pvugwfz7;|o)JA(o0HALcR7Y~1Sd#i>R+KvB}3=;=tI%G zE?XEaD!vZWoold|SP&^7AIx1dR$o}G!F4-)I$L({wYGM+)KG3`!&spUZ`#cNWPpX2*J@}J;{{mobF!kKc^8VcedGC*HB zZwx0Bd6U96xJeJQm4VkZuw@lLoxNWhgs;3sO^|06YRm?E2nlV64?YUJQ?jZf1!_DT zpDyx{S>&l3o?dZ#HP0I!s1sMJiLTdEQkGo;1W-U@IGwVYJ-1;K)ng)>Y;`rAjaCFP zh;3D)^>}-5!$%4Sl4kTLUdr6{?RrsSTi00;?HeNVH4@B`kYBbe%lo}9wf%Z&&ZjBw z)RtKJ5{UIhT@a})KDkCckx;?M{80ZTzs-XWpEHr!c;iB%TZ{wk5cZ%kIX!gN^Iy$l z;25Oe8#0^r?PoCk8Dp9j%9qReQFmy9Pt-g$I|z(Bmu%t{xkUG4-;*%MIcg4otfoZ@ z_=D>k(0|Xi?ek5s5D_RO65D{bzK>iK8nw*c5@#h-=X8iRqOo+Ljv)v{*p>%=AInf6 zv8026@G#B>eq^rTU+W1^lFsQk48U2m@FCjfUj`NKl0e97m|eCmwZAz z<3zvBVm}<)MF{-fY3`EQek+kd{LnKbNxC=Btq?$`UT9i)x>u;1$tHpu6R%I zW~WT#;2ootJkLd{62lt%2jhz4RX(2?|7Fm?&QnoGYWT0kdSj`j)!B88F-aoGF*8G1 z^U;EGN1^Ap4C%@{B@5QI>PhhaO>_bg2_}b7V``q9VTG-I?(jD@B~Sdf`sn>+hqPS9=w}}@>d>&lvq2LT4#Mt=Y#V|)yLxk6*^d53gx0&k_d+R+o;g=d=daLorz zI2Gkp^x(z)n?~?QwNK;Q*TG>EDC(#kb<|d}VtTV-T=zU{zVXBlB9+DpOqrF7jogLB zhoyE<3q^Wi3=z;QMiE~2Ek+|p#lGu!=ULobQ0+8}$nahsZ#fo1E(6`-R{z3mzB`wg z*=JnNHFt6$SY-D-zuhcuC7l-{VlDgU^_2o0RT^V1bGA)^P{P4v_|&}fnfi)8K6D9{ zk84z+Kg}J%nsbhw7ckv8qQ6LoK-$kOlx^@qE+Jx`5822Z&{u1&_;IjHy|L<-`8pK@ zuAOvh26d_h5R~Mlaxk~t1m=oTCumevs?X1R+`o;|I2|=5m#xhgYJMkY#ji$bFLvR7 z4NEf7P}5=@<|nby4jg#N1WD4kv4$R3)K6vPKzVE4_6T`#n_d6^?s+T=5MPA^csRZej^>bEcL zcD4I0lFIG_ky)0nGeZ)B8Fkrf^b)Pw87n^=@0{VsWt0Ch*8CU@hv$+ z(hW2|=3%dBo&(CfZzeDlMXA684R6rS=4rS%Xr33z!H#IJ^B|K46<>vAc$+Jf^Jb_{ zDnM|nOjIzY9OY!c_{)Mp&Ln1|kI7VeWrR!{#qmyM*^KX2H8C0OaHYI4}t%)yyk*eUrKD0gv6!-@N z{=0h@mGc46GdAt($~m;?)?*!K8m%+@ieG}+tf7%Sbgs@Hw=~BZ)r!UsjJ4!&jq9>G z_cQsrZad$)-NW~1kT>|UjgR7b^jNU)W(NC@_^ybX0&&|{vl<|whskVd9UaB1KbZVlYbuGXccgGi0+SVW%K^;;e z9#S;K&kd(W4J~HeDk&({LS#b)!0U4TZ*JamWfr0QbrCF=9_ZR&Rg+D-KCeNggLy#p zZJ|5A;9}d2buf6#J*vLw!NT^W>9<8Ogb?bcLlXYcuexq=+4UP=%8IymjSonLWptxo z`nqmuYL&gG)PpD`JK{M&L@~I@G|C&Uono_SU3r-!s$JeLd>>;`?C@gtzA?MREY3Qd z)&HE?``*7+HH|4nhIoW%z^bXh{Z9uCo}1E+!zj3-4DW|Vx*@??{K!ff7#%G(5t(T! zk&jf}a$fUhLv>WvZzlZ%m)P?K?A@7cQmEh$G`uPo&1s@i9TS3BZ(l{Nwd7>+H#DL< zQg2|$$T!24!(+>>augQAWk2S~HfC;)?-NfNz_u94^GT%WD1o1iW@_vu*lzGFN$xX@ zwRWbFTI^fsb})Fb=pX51vDfm*59Xw-U=hj$p%a#Mgk-x?FXlFbin!HuX}}+<_oi6! zthFAQX!W62n9hCYbKaM+I1%=_uX<1au4rf63cN^12gS-(ENmDxWuehNaRi2env3`YtpE<*6_4q*9y)%|*}`ccy`Jf%HPHT>op zf<@n@?_2PUnA>VN=t^SgG*d{aLgDcDNp;&6j$gxKX;k277;(wVhfd6evTJxAa&0Tuh0I0EfLop#z?K0oC$Jm#{}XKRDQ ze~g8txP?9dzL)Avz~$q(xFYaos9lN^uuYW{^9><{4;f#=dQID`zF^@-Gofhp7kk^~ z_4i!XQFl}Y9C*D zz=+L4+whh-GOQk_R~CIkFW@ZqUUL`ijmIMnT01SDviH<>w7Di6VUS!~!ukwJaH?=m z_&^oq|7Nf6GoOVN-1C`CO{*D7mf?~l#+L3&hKUd0g8@`ATJ^d6YVv=o$+x1!~)#5}dn$x}u<@S-e2 zzo^R9_LlV=#$+)sZizAtXx3{(!Zbu|^660N z)6%Ih?~oYSA`#zng|LdnNi7>X*j>=Hmj>LkvY{>ks z)X_N(=9fqlOj3WSE$&x0ecap-+VF$!G+auupOJfJg<+x2P|EUBvaan^90NUZjxSHe zDleWmfG&@~6;b_n11yd40vS1s%}Ex#Q8K?GY(+ znC#g+y3uU=jqt@7BH@ZqMMi(=YD!JDbtA`DNd4p`?X7g|DR5IyyQs`%LG$ylCO+9hK1sq?E`{>~?DSUMlH)2D&$YBm z_dsoKveVeF`z&XKzk945%%AKnnjaO{F0p}m%7_t7$NG6BZN$O8A0vT;L8%5<{ z0(U!Lli3)d^DUf2dRm~x99CaQamARJIBf>x)0$#>ZRPoZ=631)X0U<+e)4) zz4AZ?%>Fx4GV}!L;Z0$+>c3BTy=_8dkNs-X@Bw$C)^w>(1MgH`YxWRYA>)rGSFGTH zDWfn(DF3xW;tay2bg1*!^#-ru`6~=P-Je5<+p1|rl=ja6@}6sHD>Ff@SLw<$xbjgX zB`AO@4hs}n7oUChTh1!T0PzFD_Ex&3P>Qf=K`Toae-`AsbC!E=qW1vnnQ?E+W+)v* zG;4G2=6b7RC=|iA?DeHwPMI&&RhXo0;FTRp(sDO77#7V1Hy^)B5!b$0xk~`oLKgAv zHOP-^+3Ykd*Ri>Rds?z`Y;N$q_7GjR!^!l1B_5JXIk;g?fIRUG}NZ zp9nU?u^6eB@`u_K29poh7%lZL)7#NSbEPk-94|I)f1ZL(&<@D?+x#_S37(8%*k?|O zdbd#99;hDNXA+kA^n@Bdg>sx+EP`I|!o zv}+=<3d(I|H>6=A&e^fyc*VNVHC9x3?PX=E|htmYOPODi9I-Z}bA) zcHu;T^0ZvEU1v_3^7ZV#sHuJ{M0a&(zTozbGZ2hZfhZvqqg|c^2-V9v661jG`vHh$B$Kr28<&Tyibbh30!q~hnLih_ z3qCyHi4g7ss!PAjC-ZsPXm;|Ip>{)|YU8sf9e|3ms$>zAM<*p~Uo(J78hzn_&jY+F z%EZG<)RB7f>$Cq9kTnrhM%&-82aOLm8t?(}ITvjVj}z?ld4aDu;~tekfIDw%#bHsRQAzUGDQ@m8>pt|MNq!6JK06AP&uuC~L~=g^%l5kNOX zoqPP5B(rA=VF4XkYBJNz(z->Kj3+u#t}ZCI`6j#XIOm#_Zw7lU`TSPV>cqlL{127e z8zMhp9NJYpL*HR@8L3}G_F2Bf1Z73gi6qtoh?bAIx|JP`2y3dAYAu^)BND(ck^#z` z^Za=*ttkwu=Kc$H5jY)MNmy?sj-y9jcLzgx%$*a0R^{&zN)kVKy+W3Wdd zD|6+U{1IYEl*}=xHd9=9BnQDipx(8H>%G@_TBFeRBJ>phA(F;=&Sm*2Sz!f57?msj zO(A?lfab$8KX`FX@4aMepFJMkL2W1eQAG_hN=l0s1S`tIuz$Q(H7S|}MNk`T-@W~0 z!-M)^VvK3n1_-cy*UBO0iCyv=Z~_Q7W3SiOG8tuh(m=(vFf?Bv3!seJ$Fm>B5jA{B za3L*LyrpsKUnVbf`>iB3~*~+_%F1 zDUE>UXy=U!ZB@-mf;MEJPSWfm__ra>w8s8*8i@e9N;h)WF=Z2Cte%UA+y2$6sjsWF zUcP`HPVd;qF&begc_2gv>v*V{pICF2J(@YcYo>icB9w9|_;&bO#B}gj+J_U@bgy1) z>5m_6MYzlhx1)0Nk2|JEZ%rtwWF`9XR{b5&=_v1#MYKp4l{>tX7 zJD;j*Q8MpHt})2fl@$JLIF_I)CZZx-I`aK^ZheG$+v%T^i#O~D!DL&PIG90!8^HXC zmZVvQL2qv)-aHfE_N@WZ9x#g@RsV`vJIx+L=kkuh5I<}Vcq?@&m2KtuhqlB#iRl>${^}obac9>goN2NYn`rQkA2PnQ}Y~&Jp-pa|L-FPnYKLEnkzC2gA}@ z?Y?aQ85wS{lSoLjLr%!DG6gXxnrRbq6xvLYg|DFV7Q2-3N|9QEYDSaquYgoo`3Fmep!` z>v`gZ?#LHrkG8lX?Q{N%ezrR?PT&YXH)$3nBx!w3$w%;Em(FF}%U4)w@WK`jwz7O0 zFBjA;ccAX`>C^nbhqE;{dZA6+QfV(!PK0}am&hIc%tZ3jqNPG!VO-g=T03h@6(K{;_R zy-ca_Qr#&V_85<^?8aq5UMN+)KD2f0`Zw-d_g^UFk-vhiT<&x(XG-X>E;pV6!KmGh zKbZ&Zi#qWA$+rEHS4utR1`!SEJl{LB5_w*^COj@iQKjs$EfRaPO1QrBS-{lf__7_E$bBblyNiljzC4od@RIHUi? zt$Xz8@p<$ELHC!`0{U1wkt!Xb)SKLAjS<_swxVO0X(HDTU`(!3k+?noa|!h9FxzcE z|4&@n5JE1EzZhbrwscalUw|iS!8*m0SFx5-l*om{$J<~e_7EZT@+hA_{Q1GfM%Uc| zdpu2PcBpkV)4WtJOGE7fu0JBvcY3tLm1Pg#k3OU$tQ?s`d+|_8uF&@(wI*uCVB|IB z0oYg-tp@NhHz|y5cFK1ZIV3S+W7A?29UYRI;sQZAJQ^uBsEt`IL+(|kmbt#`9qb3qzc4M#E45gCVZ&x4tbN0#kO`Z2Jx-_ z4;_<%sVDInF;Qcv^rJ4^$osn9BY4Q)oAtIn#HPs>?LhBS)+4}o2X_*t_n61DLM<3E z=nL??)^eQ$8SilXL=;E+7cowvLDirIiupT*saMlt{2}0F;Lk$L34_(^9oQic_$1l~P|i%GdoroQ)4?{4~+dWwoR+SzcPTn&3)o0NRhTijz2C zTIE_?r;M6C#rhGRpGIclNbWo*W3jWDqG17|^*zBo=1jnKdRK$Fot`>R?Z{Kunu3pcKGhct})i<+Tm70b;msfc)`$5}$v>UmJcZs`NRed@N+=pq*~Ss*EKY&%M> zVn+ZC%Ux%r#c#F@A?kS;f@BQL)b=*~t{ z)oRwTv)FG$Hsa+n10nX{spw%*7#nj7uymv8Y_mJBuT(Mqkm$5$BAGrw41sY6hT-d$ zMn9v)zzsyf5ybKL%IG%h+}p+uaj$NPEJowVlW=3kcvn( zoHmW<;l%g1VfQR{EcI#h_3QX4Ul8in)uw1-_z(7wxWQPeVv`YS{A1B}tth<(d26JN zn*29dh49n7da?huORjs#VZxz}AM)&-tQ`*|bMuyTRu;dcv=R-SeKk?hy!%0m6v|D< zP*HiNJepk7S}N|O82q2F?OT3oLV}b0Hz)*9DUuG935>~Iaz0|-d`PbEu zjOx|Tr)+F=5{ond9n~k&G$3%%^Ez2ZGG>wVeQP+e56DDLrMh$KVx6_DQP4|=n+U(n1YMbp z5O`)ce7NNQ2dqR=yUFAf zZ2mMV<-cqbLCr7B>wU-Vuio@^yUijsQQR~dYFLZ>rlwWfbR25tr~r6LpH-;wGJY~* z=(nXW%$#W-dp&i4^97l_oN}r))F-)@0KZstd34iIHV*#jIzk2WD2NwXk;~Vnq28li z!v67@JP~SewAYq?{Dy}Q(YWk`u=$+t&txC?##xX;i|2|twTGKX1ddU(%y3^3SY~lrBZoFds^B~4D z4I~nz3j3vGBV9(a!t${SfS~}s>N3sTw#u_@uzABou7FiF**s|}%A*+4oQ#G_cs{%| zikz73GNx{?*PC2hE(~=bj7wV83JdK?DeHRN>L0FA`YB(?%>XiRsv;!YCMR|8Dm)tU zQ+XFl4r3|)E-jA}#aO%r4)28|ysDxOU>eK%BY#2l*5FpYQ&ZdZE?t7C>U}#JeVm(* zS>Gu$W3gBcTHFF~qCgh#sbCmcdIJyE=^ zr=B$ARt_%z^Lw&Q>}xclwFY(D6w*+yn^I^;hL8S6SzAChhK&&k*zxQbWY1&xig8^zJI)FhtW_ z3zXYTD;wy`24y*lq3P>vlr=k44kQl6Ih8~w&&oKx`(ky#go}lo8N9JZZ#-LkX4})GGDJQz0v-h@L2kAO1)>^vG=o2iS|# zx~2gA-8bciMoC0eIV0qIr+KycrS5^Y@yB|0R36Zz8~=xsdXN+x3Y%fXi^0QwHyOb% zNmQTFM{v*PH}~9EN7_dL{eHhS(u=y{6*Sv@Q29|08|O|d75ZOf zt==<5O8S?V_~9-I*4j$DKvG!pBfKCaALRoS1P@szguN}veS+DNW=X~`lw)<^Y5 z+4I-;KTAi|?LC0?tANl3G!+s1-{m}@?VUv~Tx@cyyb1w6Uw&1ZA5cLU#T^(Ch3_pT z=+3=d6Hg!kR>>5`;z#V|(_SP({Y^k|ZhCZuDUzX->i3;Ve83Vp(Q2p`c@QDDL(G?^nC zX*4SW9Wq`rZ(=CQcr0O!m<91p6QMIv2z6OqD7l($(ER#dzH9q&>R}w?(aR=axaYWH zemeU0q?&{$w*AVRuv4}@%NHpvnpf%!p^--j4dUQxGdcia6Mj)OGcXrUPwz( zGKNx4J%WO@u`a?iAQu1*c$P`R5DkBBO9x%gFaBe-QE?`*wyTeq}b=JcRrZS z*ZZyRv3(C;Ik!QO+Zxa>1I?w~`Ac!K+~X-c%D9%TepZrg!Zv2Nr{?%PXS|Dnn70Aw z=UEZ;#(rIz;zA`cul3=i2Tb>PJl;XNqF#)^g_|v7SRfZqV2E!BX8>5+Cg+SA`d`*1 z_PW5}0nQ6iT(65=XzR$EW(;9%qWDLEd;<5b{mZ7o(~Jf10O~S_ZLARd@ET9zZdM{% zuqWC!!vbk&sbRWhy901X-J^@LP#C zTa|MW^gXSp2z(+f=&ri_{al*>UBSW+0Dt$|>|jyj;Vj5#!Wi4KvfVg6CcfNOV~x2* z*t|ivA)|pvsU<4cb|MUl+ou2#RFt<%cQlIAi z1+S2a91BZ*VH?!Brb&p7OM zCyZeJ-0dc!T~eAL(2Yjn&kLhhiypV*z@1P#IHDys3N@h(B94gH9EhIYOPO`p3GMNH z`MqKXGs~3;EYEAXy*53k-0g%Gfz{x;hl~1htOILj4T;|OURrh#uZ(3ce$AWL|Wbj zV5|E#bio;w4eSlwQ3Ms+@F*E5GY;atB=(-ReRUliRX%xkE+fI>K3)`LzJ5Nlr#)@) z=O1~G48wuI6#FzqI-#0Wc|+z?*DnNee^1r!rjZsapUgolb~8;U$IL+N)R+U0tOrlz_O2$VM&K;3E05W)%K@W|HbT@v%jPGjEXmh8FV#bfV6w9~d%mgSEpfa3Cd)PZX{iDcYe~y_h{}ZIye+`cn zT*VRTbyPQoBiYlkzShJhpJD%5Vi;!M;au3v%T#(gQ+eNiF*%eblEtT+BTkIo@bG-}`&?!D6d#F~NWzzN zvT<7~s!gM&cjJsYT>LSjv1eITi~OU5O`w2n1Il}wyH#EFX_priVFhc0CM)e%X6 z=i`_9>?M{F5P?0iN+c?b(MsP)eG56DU_ygg#_C(>t=cbx>C@ljGz&LJfG3}L_Jb@! zU?k^rJAlIu$i1wNWb(9w6g zxAnExs|q~w_@)ME~*V$Q)iF4*u1@{=kUK7q`$T}sEU0E0K_R$w7jX{Cv96G1Iuv=l=v z8$2jX7JK9Tdn!_~pA73?L70(&`thK7*&_*fl#IcEb7UsPkA|tkmJFx0JC7koYF#t^ z^%@csh=(hOI0t-q6{QU{s%^mGX?JK?|`-7LLQ>@)4XmD7WJo|g;) zQ}?H?trGb=iv86-@F!dQZ=sA``r5RS%WPhj<|0U42|Qe;(tTc1 zvczROXx0A^fx?5zRIL&HhnuaP%W3jgV63Mv@8WR>Y9&t=Eq?B>{fb5iC!!?h3iK>p z!dpmJM28f1eG9_W({Fx+YX^Sgq%|QXqOO)8`Wl8}iIWxCwmyS4C@9&jZ_=~uA7{-( z%Y+x86pbU2xoLe63*EJI)64LAc;H+O5m(0^yI`ft6JCgtS(|BCIvuH^zW01%1ZAlr z@On?oeMoWnDL@C(bT2ZFRK^hb!t7QSfNpHQ&G(P2D_$1*5Fg0)c=B%!JB76Z%d;nT zPTNXME)q}cu@aJeZA1tPoVxq~Rt(TV(?c2?)vFIq6JWU}{Q(Y~$H}uNqfi=|gVL}x zq#MQO$>Ia0B7#KL)OnjheqTYLYnQ*gaLy|DlzC{a1`z+W;rHQ_^KkJ{S85xs03*|S ze0XEkmb);PEZY3DVR-&HTKJUi*VpEnLF0HH-@6eFkAU~BQ*)dCP~nf*?p&EN}g4R-1#X*)ar zuHv!qvp4qyxi7ucsRMu3hcdSz>msvLAOOcRJB1#@xDg+R+`P>KFqx4**#Y&}PYOlZ z!ak{pqZ(@M>6LAaP&^H&BzkFk0xN(5;S^#d7nblP5mGxQ0SbTbs3;t3Qxo+!GJK8d ztHr?KgT9BZG7Ch2;{ZyMDIK74n+oFzE@cO#?<%y6s>{B*qT4V}#>niYi`yu#%Pcz6`KvSio^u-y;65q9E<1q?x zt@=lu^xG%IXKm6_apQxB{A)Ve_ozgUP$QTC9of3lczu_r0uKc(ELfR>QXpX&wc0{y zA;z0u1Fywt9dy)=!&mbg$&JA9Jr75~Pu?fFzA`KyY8WEh-lD8vqk?8dU3xHEuh7lm zrh2AS@oQ1)(|8VsF)Bq7jc6f;Sf}*g9~Zy%sec-&l3A%uy5K$Q;S4D7Umm1GK)by_ zDzmE4&ERays|DSQY1?QIoik|zBiz2k5^wrO8-5Ui`oF+vym%Z@y{JNM>n99tCjWeF z3{>iN(V|Ttt=9(-ekiLfdTLkzlj?y!mb{K3rQ<>ZnZGXHP;=Tek#`<^fG|EGPVO)J z$H)rxn9V--Z_6Cmn;u4-wv{Xtr(cseY$8OTiz|j$xrTT_)6S#n zZM<5q^QMleyfluIJ`Q89e3a0TFN`S13vNO5!Tj(762u_PUpNu++u&2aHKk!o((7os zwlw)lctUHqsPOBD$46iA_dywyy2A43P4SXP^6?9P zQ&m0PM{r_ezWxvNl*h4JCtz44(9UMDHp0xpDiVH;L6FWn^Gs<|O#v^Z)mr#}FEP4Ez>t#e?ozT2 z00_@45bl-|ND%MhF6|QRlHvxHL_bEFHX6kS>4%S3rad?f}3j z*^kqkQ?SNfA7}aV1ZC200O$k({n-3<0GHwr$SFiKz)%3awgPtan6UtC1GgHaEkIDO z|AQL*UK(3nRg6ep9v%(`zTO`KbZwhgSsw6L&%se4#%EBI)w3&fm=~h0IT8@GVsTu{<9na`@XUX z(81C15C59}awnj;hBt2r1>G4$g!v!F&M8*3D7vE8wr$(CZTnr@w*9Vc+qP}nw#~ja zY15B>^k?T}@9&eWWQ{q;W8gqlfSQ6Ago3PE`rz_nGAu-><_{alW@jJ%cmIt+8SmQH z{9f!tzkntrEWulSfA5AH^vt5$v1jk-~dgvFZ-YKld*E(Ag*>nl%iiI4-~+kcuirQ0B-_>aQ!%V z2nQe`9$IS-zp&L8$KbF0qYql&tG?Au#2bhvPivq9=;lD4AHXi%z8i$R%0}#=)z96? zUoikWx;)aQ0aSCi`p^M@UlBhP;i{jZ*g>~YPaypOy!KI0knf-GZ__UcdTEZSolE>j z{*y_{{IW`t(uc3vnBNsisR7=Aohu$50asf-1ckU%__0}Ph^OyciVK4?eO3P-2UUN~ z{(wL~v`=@bU&^)b+IQyPW^9_i-@mM~f(^DWFMeg|zjObJPYuA!x>xnVVzXSFe2#jdz8s(peyu9N-<`}<2~rf;!+w{k z+5+)k1%OO#eqR}dbdB?K5TsqoDnq7ojo+1P9=*n|@)^Rpwm?5V)c_lu0t9{wy|!qe zJ4Z7IkK^P0$_Qek9(O5C4AAT+cdoK}UmfK_im)<4|^YTNdG1hI^h`v=`hRuji!lo=sant`qO8XR}V`W^q(f z&Qe@3(s`hPbL70XBfn(4dw*ve16FN>Q84$b9^>E}1yWs^#GrKp_S~fncg@mYG9Tx5 z#NjhYNGtqzN7TKj$e-(G>r53~&nNV51z^ru+jul^SSa@aa&NdOa`({GY(D;#=?aEuLny$4>4Z&C`h|ajsXWC26cZ>^+>S z%Gq$z3EETB!+dWw`QzI@UD?~81R6^;o5-K;>VFVOHA9T>++?oZiAl3+i!He`bfoH0 zuJyt-jf@B8L^HWYR(Jk<&C0G!&qH&I6Vg;1IRW1QS!Cy3P1|YGUCbNh2eSa^Cp*_J8yBIcmnZ@{nw<7MZmiq7*EI0=Z!^>a`G#b3XWU8 z+uiswM7EX@>iP~?OXqV?KU#MTd%v0W2L5T;H2D1V3P)&jwZgdm)*iF=jsk@_6j6Au zF=ck|-QBHlS>sxzGV8|kZp+&a))B$yq1^QuR;&u!jv9#4vrcu3)0d~H)KXw|B^4}6~!MPdkRi_2vyN8hTNRBadJky zOd{iKwRHu`S4RxviF$%<@LB=)Zvv9nui z7U3q=-fuRPd&~s0>s1w*cZ#ymx=}n^nv;AmWnWUCp%4sleITM6fe+1+yQXfz%e3}s z)8nd>jj6%`Z6n+MDW(Q?68GHSPqC2`aiO?sw3|qcXtm$&5&~PC{1)GV2d`5M>7i6B zE8!`>h;K$7=~yT_%G6Jx-(`RBaDx%=5$oj2yT*lCGnvMPSos7{!itAml%pN|YQrI7 z=XC5T;6?Y&=rVdmPWH=pOW`fOQ%7H@^<=GdmQ2AS$)=>F#srLsU4!x@xNWW$Y+oNp zoD24e_7ob=s4S~jkQ9u_<)LttTYwCD9zkD>5`9g z#rZ(bE-^nU;Xn+kRgAit0yB-y|1ml3iB!qhl0yI*;(Ni4v4*zZhu@|h$IuP_G_$Z;6woN*Gcyd+mh{IHoX_%m{p+{mEHoEVA{-c`bT4am9 z9n*4J+I;2hS~;vN6uWwTB?})RCL`fd<$w**K?0GHt=MlBr+CVXY?BvMNu@=?^Nh|r_tn+1 zvoy%a!!(IIS5&8#C{|Ln)S5d<(4FJLo0IQ}Q$i%PI4N0_*W+9@r#ajQ_p)n+YT*4j zPka+R$i2Yb3$|O6e#Hv{ngKTe+jBCxCi=+CwWP}3Y6Y=AGf&b}(Sg zLBmzr`9^5Xpn%Rl^qv_@*Bs>l>MBT((aI$p~4Ff~gwMWruz9 zkqCfC(9GkW^f_yIM$z}Xna_k9{d6+-ItRA1?E_xPLQ|HCeE(x&vq`srl(LdjBCBC; zJ|Bz)6`oHysGOkmE7*V)l!UwuIES zwra6-7Y(EE(_nI|v&N={0&tf#vguzk=5hvOL>|?u$ka={m->y$ZCK2*`=YF^UQtSW z*H3?HvT94*Bf(w)F5k5s&wk896}5E)%{Gh%aehuISBe)F<&)+9K@0il(=wUghb(NM*K)C}eFj)*Db@X^ zpSd`@yS#CnRy>^Nke{ijPQ3cW`42)?n@YVQTI9Pjh8fj#&Xq8gUq7_6Eh-|fp%|&3 zXYM#C*~?0O@dC19Fnk89y*i+Gw4DN$ws_Jh_up)sFnChjp7IKZg99DKwKqHd@} z@8a4F7o3>3f3d->U3Vi3%8(m zf(+gY#6CTWoE?KypyRU4#giy5kFtVjI*3i{G>A(Qgk#=agS`dBt7&nVGIxy}1s1PW zna3&7?{|BbZM(3CY+VSe3xbz0ThR= z=pkJ3Kt@faBqX=^FaJrukwI{45y0rBt znAjr4Q@B*5ZgUbk8tv#aRVW3ZO4i5cvuL%$GZ!rF%pqVZXaeT#b{kb zISp%8)945QhU6bvgR3o4v)wdhb=bcp8ZnaL&{fPuQ$%vdyFG^~QQb_W^T@>H6XD3K zYA=LbA51@+Gc0n$&Q*m;c+c_Xi3EgqHs{21!@rilaTySQ%A_ zIvs1NTp8XX#)YC6P|Ek0v$$WHL&93_)~q%ezr(@GSSxW5pC#`aM|?D#p)En0im$aJ zbwlK`+x{34us#p~vH;eGbdvsX{96q+*U#7c7W25Q(D24smLDj9ct}}zHA*Jz@$>+N zQk5;RKayS-^&uJc+=h(DbI#Kl>-To7N#AAM03R&%2$N8G*tAC@4K=k;XjkB@We)2N zNAJy&v^Ssy!Ot>yXC8^M&)zzoRxD+{;#g3;d-{vMq=`a=T(D6pds9NqHgb`~6CNw~ zhHYaU>(SmcCb$F!7uJ@5CsU6v&jHn9fxILJ*2w&T}8n`+^wtIUbTVA1e&Obp7vlojVPMVW!4U)3P z5?8LDvW0g024IV3c_hjB+6Ah zv%z0+mP-@R>jiQxQuK7X+AY|~IL1&$+CTHMWCsw_uD!bLh)2YS5zS8(8JwyhnlcK< z!|y`ev7i0|K*vG>>nsS@AgpI0WIxhiWSbSGwPeF49VLS`F z2s@xup{)NnfmP+N5-`P_IP;WVPo)P}IbeIG_ugQ5Z{7~Ao_dZfq@itz!utR&jEvzI z$Nf{u?mz-FtEXB$A!+i8xPD4{XT{RE9;D(tcnc7JL98%}^YXH0>>E@GF!k+zT9W(Da%~>aWJD*GQ*urvA-cJ_OjWf`@y%x5=Q>u*&#~;~ znu9{Vp=dR(ij-{H_)dJ4TBgy3BKgR1i}cGmlbmZ5;uC${g#LiS^p8@h&!w(N2`?n@EG1v0j>XDuAtyqsiOt?}&Zv_p ztpL@;G~Ni5!HmR{SL;Hm=g&!jv$axPd5cCaa#;9E z!_gww^@Um4)nezVNW0dd13DlEyx{qpXH8e zR=vAN8yZY6}XbsAe(UIF$&olb@&8|SkQhR%N%K#jy&DrnZ%jR(AIl{V`58*!b_q^`vN}- zu292v3xpiVL56Y7#O`U|Xr8-^H-d*_Tw0`hy_lgfyR0(v0cP7-C7g=~7O^ zV!!!mVB|T0DwI1V@pHUR&cR~0Ey4aK3rzb-FL^hh?xpl&`6&3A z;YRgzU1)Z_1V8azYyLeF-R^9E&N#}D7nFpa^_PL8VT~Paiv%l+3o-Fx?}H;LH3{Qv zIcS~2j|gkVjWVo_`|~5}A98lKm2hoJw_VHTx^CdV+Q@995K|ywSR}p*)KQ74^A6Er zIQc>FT8{i0b0~zaM5o@s$#e`PUQk1bCPfOIIlIG^b9lSN7L-U_@!oC{bCq)M1aj=n z7_XBIPt7075lYTSbyeGdhoM|~2C?SIDwC2^py22JFa4b_cfq>!pPaghFmxBmgO#8a ztz`b~_2Cwwopq@hBcf_74+o=kk;vIbNhKe z5|gC|8DQo`kV&KQv3<1CrOH9*=LyV@C)N8&L$oWPlX$6o3Owhr;BMS)M43I=o%;pb z9qa0y0}-`l!xlB6ut((eRgC{4h#|9@rhhiuFY@OQF@_uZUSi2Oa{7c@9)wMoXu>#% za5)ox^E76!dm%3`G~c-RxB5^o&PX}a%hP3kEhXI|MGxN34~g`QUaQM$iQ_U)J1EnU z-G%~OpbCx)@gtf%6g1I1Fd2LW3_I|?y09`hwTL0K&hC@^emBUtyKDlz7we$Bw82p; zq)?I^F$g5x8kxbA0%8pPoJ*Q0Qb>$RpCeti{qTkd>* zmkq&%O8s*#LNJ!=4alI=;s$O&e2_AGgu(%SY0B5>EG3m!vHr&B`WOW#Y9IrZJG{d~ z=rL}U`&OqnSrH3@hKU}>dIqjTi38I^1-l842+)w zc43EM!0$3ptoRg<>)X*e*FAu3*6`hHt~PP?%WIBHWM!(UH5ef+?&mqyUPmd@AR!*b zrle$y6t+!uRKcdW$PBpjMY_I=qS~Sk(2zv3B$5{=Z>4V|1&Io$9Fx3@?nrZ$BXb=~ z^S=#b^Ab%Xjy`>snGb2M$bDNHbPHL5a(01MMCfBdbCwmW1<*GtHwJEl8!(^i#ID|k&QadF& z)zZ|hW4M#Vx(!Fn&xkCqdcK6y5g{7_0wD;|1bED?KL_TLM>hWG0z*xA51^+5Vc%vT z;Hlzg9(Dv-C1(Pv0~t2J>VWl#Mrc{qgam9_b*J1+5aw)859?!(;r7QGL6NM>8p={4<8;PB_ zzyEddxTXkgUhsK$p!kufkSrIQDEH&+qTf4%#du;2(2}O-LXth45rJl?)&?gnB2XIa zLn>n1W?vBSzRqhPgG}HME8`i+`ndjFkU*$Zrmt~#9T{St{cRX(svr2xV4~$ zeIghQBdjfV329zP;@n;R$f33KlWV#F@!PnpPC9YOKGcaZfhR2d| z4l7{g)?APRH}MK(80}Su(>%Uz=fz8o;euwjvKy%yY zZsy(^a$}#YqWp&H;g4lZ&Vd~-iLNJLCI7mBeWefg$9>S~L^Yv1@uxMLT7sOIK!udS zrJF`g$Yqs}^V5rszr)SAM^VJhz`n3I)u=iogxENHUVz#y{;{^oQOv+gzwbWXQdTF- zHxz`CH4gV%=}lwN&roc?!o4!X4jK9?>tEZ#3i$dwCUM}-LzJTZGlq;Ryh)1x)DCK| zEz&n`yt}6e0XTfz{WNv@NPcG3krZ&^_zGCYXF8-QP)tGpkO`=NlHqw0iU&^46%4U- zs~@+5Zw!mLrnPe2p#C)bH?F?*6pN5#$@jHiAIbCnehCsfL&8jVLJgvC6_P8f5h;4e zgES%~`Wqc($;Rv)Ts~eeF%Wx5%j&M?ZI;YdiMe2@c!bs4UNOeIzd--sdaDkKhT|BX zi*MQcZN`+i-#D3@$ltsVFU)1sXsMd3DT!FsG4L;@O`R!L@cGEHkM+3id9QvU5)%rK zeaEQor(>lKha|(CcecE~Ol6U?gw$T#RBtQcTT1MQ(Ea3J`q&p=;9qU6sGqp<=(mWd z$OWUjw==pEZX;dkENH&$$~b{~WU7o|Qlu%qD$j0%>+8fo4RnEdkrZ6Px?QMoZ5n#o z{e`5iwABtT$k)I5NGwsD>f!4yi1(D8A6@nZ&~$9``kFZlIDDfJU7^eBPHyF@hr=TusrqX#$j!u7oF ztXM)Z{!3&bNN-2lD(0x??jYlXp(Bj4vxkFf`5L>wLUT%(!G`XbPsHYlB7=SPL?OSLA+J+2>=QHpoWoGSoe0?$)I z{}uD|VWS=V6J|LsYh%Jce;N3S8QJo|3>!MWooPxVH$d>cKNa-wx`8bm*DMp;2RvCy zExCIeV+?pWu0hCuUG^MM8qnd9v!e?8Q1v;yi?#Y<-PoN|M<6%Xel-=;veFn6qc2TW zIYtb%>iItGL|u&_F;<|%&DkC**X;>khK?BTToulS@Dh?)k3xX$p}gfZugUK%L**ZrC3+j8fxeVK&^ zHXFRTbOk+W2_ugz<*Ob<24t~E(AQnbLwCIl-yzSKGZvr-J9Ft$dVlc~-6=Y-w)aeP zy4HAFqV%#3s-N3vX3+am_QsyMtg1EGK)sk1P+NV6zMkq~&&v2XVB-X{xy&s4)x)MB zVLw>hJrbCD@fa@HVOB(@W%_VuC;bc%3WWp#W|&aIpz_VEaCEvPKQYlHj`NPC))iux zL0?ao(Kx+`P6^cb(-8Jm=FxjXH(z_vG3?emXUvo(TwY3Qx_TRCj6Io zya^Vl#Beg}7nC#T%juq4Z8dGM6UKWL26Jz!Lg_5H{HlRlB@_&!I6}2gwl`k-LZ-&~ z2!Op_{@-)T_Eu7!xK<$HSB3bu9y!Snef)Hsk7-c(9-rA}* zNZa4wpMzJ2nKELBS2VVWA7mf7Rr-FUgdW6Wz?=c(#>B&o*?I0qPvHI@1kmcL!C<|~ zivhFGC0p&+Xi#zelL~U-(;5wq8CnYE_wC&3-Vk3jn)=s)mD0oO_j>n<2eq_**~z*f z>a8zS>1L4fBPU^*blhj4el&+-sS3S)j5?=!GdgGzDE!uAxhJ~e%C0V*RdIQ}Gy73L z<{vA8*zT>jkY=*j({wiI%m95v${bA>P)-6ypGBDROe*>+S^r@2Fi%EqLn=w#bW);* z2XM^Ifuua#@%lFfR`!4Ua4o~eE9w+nHQUPDWj6>SQ5&gQ548w(3%{HQHysad#Sf5x zxvVbmFu-_|crNe1H>sd@1*Qr5%`$($kCnR7*XueUSE-c`zKUNP#{9dzy;-Rn0s{uH z$IGjiO46dy)&4?qyZnGjW@-G0rs3~Qun5K&MEXsa+Wmlt4i4~rwzwoS48KC9i}=@1 z>tNjXjKoXOOx$*wD#MV=29I{Eg-barUeg=Zf;>D84A1|azVcky#6LCjr)pR0Y*9-F zjjCqrwHx;sqn~oiomr4AukeFRt6C)p{>tdHv2<=_^YDbjRX%$m8*+(nTgi%EKZF8k z0z(_FS1d$mvW7xTIV0Uft-$d@Q#{NSP1#4jo(Bxki0t631cMSL6@V==6BcX8m`}j4 zB{$S)c;{~<{-aN*(LblB%g9Vm0+3u4HWhY))>5JQjj(ibImj39Ki#ZjYzFIOMT2g* z^RFUJ5Y2)H0hn2l+l4x=-7sz7KmsGRV90BQ;sTC-56-o@#-u2QAHv0I} zZCZOHP;mv;=f94`d)SO?BctqVb*h_cFGsW@9uq{K3$Fbudrrqq! zSh6oe(xUW~nwEliT)A`!94bd*>TUHZDj$Mgo%F2ZfXdikH}ns<*6z{k8y9@9Y~Cp} z=57_SsU&P2tBIlE7Wu{Sn;8Wx_M(R#H?wS^`h9mtxl4z3RJ=ur71`J}cUc zZ-&$!hYG6D60u>5U^g_A} zOYJ&^*81lwa=4-BwqTG6Hsv2|G|@Iv-QDRyCH(Ow&eD2vcRZFcOksBDVT-@tpAYdl z#rZc{l!)-bsX%S8Lxvf-rxmyONv>*s<-TO!aD52`6P4Md_WdehB3)pisANhB<%dLc zVd8+u30TybObMfx9uMjV=wHbkG1Vmoqt-*_bNZ#W#fxf5@ncJoI!~?h#PYHG7+#baQ=@*{(pPp*%_EQ{tKV{|L~J;peo4L zyX@Huf1!xQM$c{%Y!!qsjQT*>Fo4C_1A|!t2?)cTr6Pi**d*kR<^iNXS5dA`$=sOc|1} zpXg~J=YS%g0txpTekW@}g98;Yvbiuq92Uj<0J(N-0T3De!;7lIlV~775I_Tre~!Zi zCV-au`546gdk_S`0mD4w0hST)d?nHvp`nzI^~C|;gV70yh>1z>$Z_%x;6w)q3^)Yv zqa6b}jHrbAYyp%(K)^)bzllL(yP%1@pdJFx?1N(nLf(Q|UJHat-z=ODfvkYt%{PRn45TO1d z0r>C7^y2p0>OsixtbxNg0dpJR{II}*nO9%{_oco6#t z!?qP-4Q%5=iF?F<-N@sH1`9E0zasxQRoB=D)AQ`rHX_5^oIQDgh}*&capIU-#IC6R zX$2P(eZbFVMgffj2oO+OU;-#32Z#)9gZP!RJvjyZHbQx?9(lq?*$cP>;P@lv57wWR zmxiAJKwk%s;xFVW90c^!x}S>_5f0IZ2qp-KlQ+Y_G49u3w4_klYdkeg{Kwp%6#|$C z5#a3gbeCKkrUeJlp1t?C?YCWL|I?I94ejL15A3H^QWZ4-3XuI6H)1)In-GA>k2Pw2p%?4r{qx1+hYXBYe(V=^ySMR+AK+*A+uXCW{k#6*i|rR*t&V$Y`qqvctagV2=H(d?1FY|N za~bIaUH3UZhQaRjx5cus4+E~OFMIo^TO=)&3NN-m0R=GNXEO8;>JaLqx%;2Hw^5McxRYE`);)yaLp#?9DG8uH36ix~5T{`bNgxD* z!2En-lyC5UfIoyBKp~KT1|!fw9E5Qsy|>CbU@Ax4EI}#+J zrhfkZ=Lh-^_;SMe<`lukwpf7iQQj)(>#k~rj+^TCHX?tJ+DzZ0)fo)n-e*1ovly~l zxyZdi-<3(be|e7&)M0awk3Ci@{jXEN21cvPN9_DS^)^T|qiefK({T%LF=;o{%5Qt5 zy~XEbJb3RWnCFP5P+LJeg~8Kq&uL|CRV18FJ{6&LcXeABPlxQEB&{E@n(hs1sSOWvFxoD#U~o&Q&P`*3&XKyTsY_WNMtiZ_3#-{P%+x-h0 zcx0jn+L|^T?y0L^mA0hUlpuzj;L%*v<~I0?v~apWV3ZBmLv58@+))#2*H&=NZ?ES0 zxAZje?Jy9x78FR(sRhR^5Jx6!$J=oydQ17PaI%f zb~Je|-*EdcN8fs-AZNS*eP^N|MHZ3N+mtoSH>F^kS};1GEZ1q*y%}+f%I_B^IOn|_ypvOKvyJ;`eD=S*#h20u zBwQbb5sy9hLNe}TeSP%?5gu#hzsGG`N0j-=%5Z5SHrztVET%o6Zw9ZF(o~8{K05 zBc&QwLhT9I0R10lZm& z;AlE@nH2E!bD^KPp7|G}k!`VE;OiA?_Zfz%tAzj~@8zIjvhqzOc&1UURLncFX}0tt zBe|)EBDXGHfKMkC=2l}zk|Ii`%NNIure*WyVaN+tVng9%04PUxHLf2DDtZ^AFBshW zS&kzQBG%Y3ByCY};!m*`60&bQFqff|kUoRY-iYQ%*igMDE;Ie5E zD=tF@C|Wp3!Egn=xJ+-=IPlV$C7q(!q}yioOzmsPdB^I+G5J=Q)MvM70n!)1;7uvl z4evHdHN=)uZAt$<(H@0NA=)yA)P?5*+`<^B@{w3G`|87P0>5%8dsLv9yxthiS^m{BGtR2bqLyp^ zSy(e(gP_-AQjR@x@~4YacELf_XOCQ81uxLc2W6fY5+D3Fq;H60vV>#Qv?ZaeDQ zd*i8j)H*vB5KU3PB-h#VPTt@pYE;qasmZnTCU>dWE7K@0llA+V&Y>q|$5mIqlw?TS!KPp{zHqZdABF}5#nmJD5T z=-|rX38cSE1!Tv$ldn~cg=2cMal__dM`OZfwAUbK4pem~!F!TZSEm6lRmI|{Vu|)^!jHe=54Da`J;i2CkvNSLQjeO6auuyZ|p{5e8m-4MlUvx-=OGlK!o^(ZUXs5T~ z1raTekkV*>xi}ftBwvBvvG+;M_pVj1HiqVf9q!)*K<2Bdsi`x@=YmiirPp$fa;p~7 zTlCX0kSdd5<$8lAJoq>I5^w4!0$AjIk&}`-SJUn19N3{(A{*#c zP${PGDM9)?3?H$ESN^nRIg7<{fP{|4CO3Nc-K0+!=oW?(i4g%Q8uHN@#7WohmZgGH zE!m^cH3;r+Dj}!-4v{aE@s~FhL85rLEUTqNQ73bI<>;F=;_NBhHE)2s)^Nm7+2I>E zPy(z4$JN&b@3goCId`Nf>UxFF3D>AKL`uoqOS{R6v zyr)g+<6lr$DSF01EPTdm$C#!U=xxRDX@{8@!b=ld$tPnag*eTT70T@edaU#$?`L1Kx!I zp1b^&nWpAB-)<#T8>5ca(VA=x(YhO9yo6IxnYe@ZKH@NgrLh+=qB}5l1Pc!QDBMWc z0PBjtvlt|2S|GEB*1}==R6)xFF=I9~bw_Y1w{Y9EbkwahvYY z=G)ebuu6Wsy*`Q8)E5?7OJILq^Q}#+H`i7wr?;!oCm8;;Tb%f(l5@uB=|7HgpIcoD*QnL!$VJKodk?1U3rH-KOecn;~?>gZGT zKB{P5`{yeNj^f&5K~G;EY@B!EN!brC0ve%QAE?M{h*1N7RnPz;X5txmO> zS~M5%ua$=X)d&CG$WR*9RGRCYD&ova>}D# z1gN&<&LW>3xXa0X3qUnT<4tgBwS&H`Z&tl?cGntjEqkGXFK#3bBa=)oVpvw5UImKQ zics3)4W)w)1YeAz>}^qW8{0V?`C5X%51@!#(01%Xs|4`b6}xa!3yiQEYdYWd$%*}L zW7x7Z^P?3ILMEI{gjd@wy(5kEVvy^ii1E zlL#(tBOcu(&api$Ztwzx-t1N*sj;wATP~-9WgR0Sf)E|18 zxN@xQ567K=xS2lqZwbXP6=SpYqu6r}0k&G5{w7G`=+azb1k_dSdpu+1;&M!&lw5R~^js&YI8FoeYo0)(hXe%B82& z=lQl7lPZ(x!!6%2EYIrpfDh(!D!H&-HSXQinGjS55ca@7E=BCu38_irBvD$` zEiISa4WW+GHDm@Eaa0}Jvb$ke7Y2T zRsDPi=AL*-mLbJc50MzF*^3c#-t%5$kYcz4UN%6Lk1|UEU6Wt~Wk#EIrgvj5Ni<%Z zk56GUHU4Yt z-lw}t?kZcJZoI#@Zk!^BV5oM@iyx-4wDiQ`CDESwFSqyB7j<5DYTVMrHbkWZjixs; z#p~b02=T1q#yq_QVTYX2b9yrVOi(`{JhMb3$pY0g-&+Z@5Zi%FE80+XD5jGFY0}GF z;$HesBOMIOp9;+){i{d{-HV*Nb#CVG% zbP!}P*y9vXsV0JDxzFjnmBvdH{HxY4!eap^wZgY}6twg*G;P>_DVZAK9iK{Gb(Z4h z$ucC*>h2kHL#i0FGMOk+&uXO|B%EY#A$q7dXJ4U%^u3cjdc3`JxCrM}3Q;w!T6mtz z`4@DG@I^-?Q|WnG-pr+@vp>j=%T4PECBdXF`1Z2Jvl1S>D%!?U-whx{F=VEgwSyv4ll8mPBb)PdgzuL}3?w(K`Jg4D^;3bC7^=_AEd zKUBtb-rMbWs9&98WB8+9Jn<2?v24g!rP5UAMLvffgGXzgDmc|$TV>7VQrzgXa)v## z(ljAw_pz2~jqUFu3F;mb=d--z=RW23F>WtZ;V4mEA0Obm{>GcKF{_jIESZ+js^;96A3NqJm^av&3a>bZKLnB zT81bKF2}CHK1{f`9o9#4l?8=D`JiaJ0=E%6t*aPLIzD<^m*yj2Kd{o{_l?Yq)VWC_ z16cqg7$USFx~vW@39I;P9YYl?lCYWFk|OX=z>%T(6PtD1HKHWmg)RDxF<+As1{N#y zGS*oITavW+_+GX1)zwKi`p+#_M*W;EtWu+8Q(n*TrCv>uUW@g-crj%BBDsQh3C92I zn9TCd0t?!9M{c>3Yz3DGMk72erZP$)=@kuv1-eTHj zDCW>6SI`s9_k7cU@?Yz~!Ezq5d1h9Jy*))?2~pT=ieBOc_ga_0o;Wp)8fs2{3%++A ziR;;1h2ywBY&r>Jw^84~G5Tx1EbdUj>NTX?*S4{N^`rO?*K*b{TgyYI*gePqY4`fl{@Z8;sM(4QDtDI8ERX{fk2sZ@PYQs6;o>!&h1k}HOFN@UkgbPJJy4) zom?>*4&!TF^^-;{P9+^%2=8v@59sA1J;^s`Kh$ucrIBI$$~6EX;yLxzu=vI)x@l zsbg^CUkR0L@~ZQTWFe1Zy?2r*x&orrWaie`j-nuWx)lR!4%EIs<&qPk0+TwP6O8wj zzCn?Q>O28FWpnrz#Y?kuvkpUmoIK;Dd^kQc8{is);I-AILta^6qwQw+pX9yk^T*{z zOa6Gkh1n-EtKPV?K0wSa8%~3^$wK(03p!XtOFLmV`cVGSijoX8GjDn4_Adgir?H{4 z&6N_tR``=<%N7{P_w_SX_SK)ARlP;#6KZyg5t;?aQXiZMfPW0tZvPp9g^<=AjX(== z)+=~*C9hq_f0FHJXAM_?tD!+eX2{d-W9q{8E3LaTziAA|OPjI6iJI4%|I|-=rRPL# z>s39mssGMUafChu`yWqv*^JF`S4feiSn&OBo}8Gx$6mso-_v#*+ysk5^P@w()_C3J zP@{RI>4hk0*%!HbOj7kYHQiNbmSuS;*IJ=B|XJjtKHj|c^MAzZ+` zPxolK%3oJXH^iAMb-wQjyRm0Ex8B9M_JRs?A_XMnAROX>Z*b3Ko9arCG9(+TgWPVK zNCo5p7h0TxcVH7jZO?y#%iD=3`}6Rxt}ZoWFPV`6JH zxo3rQ?%$D8-cZ}~im^0HaaMo76M4PFZ9|i_Gon?0xl<7T|?K&p=1C^))ZeFn1eH9>^z%!Zzz4lNW7 zJt-sD!HBE%5lOV^w0x9sqNLofL%utTzxJu&-Qr;1up{cX1KLbZ17BoEAQ3{u75vvIeb zu{{lw4X{S!ylN+^{zk)Y`ca+Sa9-Fv2ZUemhNbKIs~l+yH*#n-lPUwB@dJO`aNJn9 z`r%MWfoUVE#X6KoA(Ss#;a0_`A(1w&K30M7Y^{TQ7EKP%#@In|OOw7N7c#!Ac-yXw z)=Yg8tn1x2OrT|}$pTU;d~faG;N9Mxl`O+uE|u!u;E0djtEDduop!`*r%2ug?K$nq z_;}e#Kllr?Ih*pGvik^aAL|8MNaK+nd+_`h?%{{c3o2~<8y zYmo+~9}-C$$iUvMb?*j?8o}5I8&iG-56I})_z(d|yxbfLfStW<{ok3huxJ*br@y14 z;;g1cxBzJggZPe03j~rekYlw_T1(1|1n8 z63^`Lrv{+31`zRrn1jq#o!IHeg=%OB<;i~F%LM>)5(OyDBjB6Nwf7IkMSx;t3jt7; zHdx{BEJgk|4*;O?aza2j`O%}m5Uw(y2PbrORZ~-ARpKIJ^(tGo5=HZ;f-r@h1K|YB zr{#z4yLAMtC~@uM3#rdv1Zt`lkoC)GzM?UxDUm1G8wUW(049``1DrvCCP2A!X62U> zz|1=V2>v>*`bq?v~O_uA=}=a??nzE@C%fgp1!`uktVz$2uJNh0s#YBGEQ07 zx1~q(rx-eDEu>f*|Do7f8b$$OW$|)+Bi=$GpvniN_o=wOy~vu%Cjd`J&P0az>J)t0 zwaB5>05c>su`>e??#r6`U?qRzryb0HuQ zGs_En+QpM2ee$zb<;U<(3knL-i$?}<1_9Wfs$TaaTXl5<_#ymF&wcXp;#}hbpw5*9 z@C>33ko%qE$(Gjf2f$duJiC6kJLpB^BqQqsGKK?A2dw5tc=BuD%LqvI+b^9F60ijj ziY@Iw1hN16`J7$dEM0G?3-jOpb@*M>b|rzuNZO{EcI={AkLVMAJ5bt)|m9KM2(IE8S z%=%*3-8rUmec69=NB>v+x9j{n^WcYh_ggKtf(i38$oN(A%U4y73vu#BqvDT7VAlCNP1z@%>&g#g2>LTi5}0KyV9O8ff-tr9QLFGi`45}Y z-$wu;zr6$b^eF&X=jdqvMR#LSIc1ZJ2U}X|@g)S9n|jh4mmHA3sr9u(ORLN4Pk~~2 z5&N@rKsE$@cjT=p1f92;3kg=&C~##UN9bSr&;^+KBLB4eeRK*^H~G!_ul@W5;JWA+ zPvF1(#dp@q=^EwNUn;)mx3{=|<)<^v2d53-I_ZbgmWwcUtcTcZ;bnH#3zVZ>^#kew zc$McT00_YKhX2+iaP{&Vz%8ektGntqFSm~Slb>6}#m(b@KtK0@AHtpGrPszOE^JWyxA?gn0iNKAZqScqaSQXK z2<*jdJ%{s~?`^gd5~Krgdj7QJdOCz}ZOPlby(ZE9e4>Menp2?jnKUC|*$Hmr;tLv@ zB%q%0`y1*>kto0Sarht%WBn@qje)^A*4U=oF?X4lDGKOt@yAi zffG^mM*NkO#8^=oI z+&fpnQqM#^QN`^vC_9WAE!;^pQ1oH?8(W{Ysli(ly9B?2-AG!z_v96&B7`gBv09=2 zfd_NJAQ;>Fi>r(8R($*vCEcGZ+{mR4)jT&wE#LJlw!_2BC!}?$Zrpyt0QqI@n7zqT zsEGW6s3^;E%56Jr9p&hamHH6k5k>Yj+gYRtOlGz%Wc40S2FA(SU}(Fweiuf>i0iIY zIlE#gydsqtYc#YxHm*#u6rqtQ<}=AREV~t}`bY~H&Z6=+#|39RU?LVDz^<>e!KKajSW-P^mXB2K#aKyL|T3n*M^n2BicU?*u!p&eVN12rEz#1 z`rZxJelQ~yUSSyz@DNjF$YF3$4$YV?Lnhx~G$MPA@MycKKLp@C--Z4uqN#Q0#*lj* zhG;z5lG1DU3X^uTAYyz+L}!x&=hJpF5ggj0l3h*Ro@ps|&|a_&ly9PI@S?0xh0(k- zxb)Yrmk=EqBxTq~b3pCt?;@61PH}8!?T#|HKzQllAq4^fR{CDdQk5!A-3eq)%)jn8 z5pGhc-DjZgF1&=P)f`P1rhYl{`b{TMTT7b?Q2MEyl(*z-CB|*ru2JnQDO-thV+B3= zZgF9r5!8!kk-9$x8sul>;*_ELTk069XB>gkQne~qk9oPMLPiIYFuX?Bi{k8=9p}L` zx4eb6*%YEnp}%+{P(WW_N0uUNwae|GhL%zRhUosTv>3^$px!~^uxD~|23?~LCUW8* zz*O5_52xJz^j5H4Uibw3rJ~jU{`VZXzs}MM@ytzxXfesX22$`ga^X7E}uD55v)V5bRBa(36~ea2v2Qh9F2JqQdHQxI9{(R%uuA*h6*Bm> z&fXFIO_%kKNB6cV`ESrEWx@QPjFHrA$0aRya}M~YKWcWse`Q8SPTc7C??J`ZKct4q zuyl)iU~WxXdqaOy%lRJ{=-m`@MR>_!TJx&K41QSDE^xpO1zvQN#>om^0z2^Vcm=_|%ya&z@U}j^brvz`~%Hz@HMsW^YM6 zZP^Q*4MM^Ho-)`#qQe6WpG>!?dhYji9K-9X4YD7+ZyQyyw;Qv9Bc)yj=59LQPR%%3 z&fA0LSnSfOFRdXw%HN!~Fq7B;S<&VhfYBy_QS)yP+!F{hz&Qt*Nr~Bc9z7)3Y2%^y zxw!LsjqaWZR={}VPxSA^mTi#Hy0R)RYMGc)Znp`lW>|^g>h!0XZ+BRNzvb;;XTQBG zUa6rj=^EX*s#S3dRZ#<%p3l+%o6v3Vd<{fe(^!4uobNq}#4#q$Ca`=2L9u=_?D)va zJ$*r;n%%OcHj(yYdPsy@Y@e^Tb;K!;h_QZYZJjgj>NqDTDPkZvHOIuI&}ul@ z3={oBnia_o)mKAmxiiXEbL2^CBIh$cCf|y3UFPwaRZwjDw2(ec()RGH2WPFE`>>Eu zdG>qu`s;2WGy>z!7Rx~OlS+IS|8;;ia|vh(k}7h}b5Mlwbz_4P5xxLAX~&j%I3+ff zx_d9t(x#S}Vf7O$KI4QeMcchhBa;u*qofPs0pPBr!m-0=NO}l;QUof7N&`ouxO?H6 zYZLcQ=wZoV=Xv0iO2hswK;Kjs=xhb#MAE%2aQ^Bb7aS~SrQfu8G@(Wn*KM~a*~hH=S`wGKyPC>x5d#dT^{UElq8i7FHja`y?{yfigmev5B9byq}d?_XM~dxnVJt*B4sb@lnh zXL3ga(x9r7G5AT`bpyJiD`J1OGe!lb1!^SbF#m+cqw&md;;YgX=jZq;BRAJ#L(n|R zH%MA21!J{|*kIQ9hQ%JEdSdEIP!qhKwG~Yrw}W6QMGshBY|V|>@lTUF-V~8=Z*w4} zDRN@_E17eC1@76Yck|0FvU6RbX>CoF0Sdn|Yft?b9S*2F2P$TgXXZV_%gskNQxp|D zOco*sQ)_BM@_Asml^?nmeN>8pK~aV%#55qmPwE^(7M6lnh{!cYKqy1f`b^udVQNs3aMku|30(p5EtVXc9i8&`s&wLBd2;A9 zJw>O4*S(sUp`UsCArfplTT8Dl1^E(5YgwDAwgo1#3|!bjqqZ22Q}!>F2HyYtw0Bw$ z&fGiGDFV&{!yi3kBWgbAN{h&6IH>AM*cz&QY!aN(bK}~CR@XURG+0Qm;t0V7iJ}~p z?x62O;jQG1>1-iwD)Z%ZeZh=uG&<;Sl<%1cVfK15K`?r(~Ynh1>bbufwjn_H<9nh zLEHV9Jl`I7@WRhiUzT8nZOjj3KCanrfU#LyqN&Xn)8` z$cnbbtmu>BRdfp{sq3Ha($Qtz+^_SKJVy;f^a*Vuem2SnYVjS3>6JK7I=FmSkX)_0 zT&%xNpcKRe(|(gOL*e87Kh#AX<`T2fb(1O~21#w&(JO6{h<>EeycksiV*3UvDFWWl z1(=xNF6i)?2PqNd`5eIWX%U#%oTleuE+iM!1SqP0%YG9!LcFBW41 znPbAzeitZ8C=0nXCs(!DvU53Z&@NXqdM6<&`b_TI@piE}o zoveym(nFFB$zFvHD_3n(y^U!QRH`L86plkPTP)}h5B5S$zoPhjd9^V#cCIua_MG)< zNi=r^X$RpkpWJLxfQWHz(o)sT;5Z#8T+P)@orr2)n8U~*ut>hv&~L3JHuK$Cdxz(c z1y${E5+q55V%asl|7F9)>)-{|}m_5tgn1!fLUl?8!r$PLD zRe3>S$4As7Z|&X+fqgQ4dcW{|a7gbURCck& zzDJF_C32eV;3~IiNm7j9BT`h^)u%{n6fY->qgkAen9tXjUvk$_kRM8+ONlcl>QT_x zd@`h|U25Af;!X_2Rq!NMwqYE;9taw)E&jfsidLU{{~T#|ry->jgZF!&K0Z-#ud zJGQ8h<2kvLgEkt?3*6QxVOeDY1A$Qb^cblqP-H9E@w=I7@r)5!N(x$q6kclmXUH|} znzzVHn&r{tPxc$v8~UMUIbtAsUspg>$IxO$UQd03{Xo$N$m0|9E{VL=$)hgBhzEu@ zwzt+L11iVjunu>=aDv9V05FPu7$G<-HiMN|V;pi^+VDbVik`?6CHQq zSz7Y*wTc=I{3(q&7GNC6AIrUm`1oquMsLvO9?7nGk`WE9ycn7=5I%~xQD|Semvi`8 zv2mmW1%mUa3!+6G+`X;HM|;ZZZ7HJ~agtU2v~g@mgOKBUj`;B&^St!EnhGb!+g7W=LNP_LlAMcws9N|Ku&)pj-?uBNTf7i}rU z>M8rXcuJ2wP@RK*$d{j}<7g8pUj_?gziv@u?3%ie=uage$zP#qi(t;a)`_%|fq>jO zyh15YjQA0KnQ0+ZQf!HV7~ZPc1_(6PoVSGn8pq7KDFJJz&d!CQcsK5vyyS zG$hPD+?AEE1m@mc3qKJ}!s)>c5~jIYkRn5aeL}JO{|-NMK{HPj#NiCg&qrK^-fi!j z)t2L4uhJCkn3i?_L{eY$PpH4BtJ(?p>X<)+U4h;UspM1$aBauOq$c3YF+Bh-_IeLt z{UWgW@3y&q7`ao8yt@X;m4c|RIh}e@ze+T~E+A}|7cpY|bto0}#ZG|Y?$r{Uc*?ws z<2hSEZERURa``1_Nj^y2{vO^F$m+RCf3M8;V!SPRqaqBOatO>x;!z$o&33yHI@7K! zCvYp<*=07SkbdHh7=PQY^Smb+JO319wVnR7{p|XX1(#jQ;agDtEjh*| z{3^*s))F-y>GY4M%q!y-Th5WWpkib6vcNS=?d+-;n%`&!!d|XJkGI zj^1X~5vguQr=e#wR~)%UXOSL-9hIOQ+I3SWx7dzWsr`p5cJMGMled>jgx75%oYJS{ zha~x^D|1@>K?b1ErIF2yRMuOjWqbfY-bfJ4oT;u z`pkmqg=f=IxTy0J;PrYlT->}XUnQ)LaU?Z&ixC3vz#d8zDzBzMjk;f6Iz64Ar0$Sy z+jmHOUVKg*-DrG)GaI7w^ZYHOVL^I=lqVaz+XrEBP3q(lm6~9tO3Jn$4-VdshxxW8 zhf%#{$B5eR%zTft5|P zLs5%;SE+EZyd84Z;Z7xNThKh}VarKo)8AS?9O?`L2BM5*B6X*)cHD*UVP*qLn)ZEl z$b+eHMmKjN=;Hu7(3jx5{CY&x=cc=F@fVT>UWtkD>sg17>sqjT=|Q^5{oRTh9IB=B z(u;Lk0E*9{Qm;7i+@b->YHGa~|NaqmVGLIRZn}-rZ*SX_1+GC#3VKrn;E93r#HiG? zh9D@|yfy-Ial>T4sa? z7f&6}t;o0o4jK%wtjcdCvw5~wCc|zenX#$zIXj%K=#-Qcww1;fVF8TDI3uwM>&-Jd zaA^MMTEN>pWraeZQzIgTx%h+>f*qa0C!XMskrb^GkH_`&=TNA^!{4qAhEcx%yao5Ps0T0-|DECQtv zKk)rmpm*ix?-xyhj-F{!r+__BZ1Edv<~s%qi$U4B2!A@0H28E7Z>4s6x5enZE~9je z-!gjp2AEn!OC!kk z@q&aWr-||^MESW)t^8K>_1q|p6M&Qn!4k&c>S90|a|Qm&S%A-4Y3-eYvZ{N0s3}3O z|57^?iIp;zI{wjW=*8I154(*W+h`sQ;nBZdP_%NMt(|~3;ThXA)_07sLQIU*PJ>AB ziwC;)3vJ*?W8-~&6ceM6Z~KmHvOS>5!R4iazUZ< z0kcl50@Lv}-Ca3LWHt{YKn0aYSEoIXl2;9f?P!@>B3gvMH(l`EpVbVC&s82#dwRoY z1j@uY42BPQR*0+KjDMffsj6KC26>roHzHrtf4?|EOEnY?-U8rPu#6EN%0bi^R zR=9ZD7s7XbK?UB4eYIcZK2j=*7*9LkK2Q1Y(?H5rbW)oJV!O)Qe4%omqCZh2h+3Kl zUU(>c*7QDkoVqEL@0t%)UZuZ#bHlIeEY6;*?sA})D+VB}`xN?2F_>S{X)F+?>KdUp zP#-Zux4b%&pwCTRwg~=E32aS{-hr1cewvjZbT7L%42UkY?5b9$W&%%U<$P;Q? zN(Jc-<$t-Yq?KIM(XZ6Fadm`W>V|^McKiDBTr<_Wk)e#MbE2zXIyEJ#*_U3h0=L4Oo8<4~P%YX?u^=?p6Sf`C}El>Rynb!H!hq)H|Q1F#a7bez#ny4hY zY$^0)lCD{#_Z?&Cib=OB2@kt%s8&kKK{N|Dq(WaXjT`=OhTrY;6x~fx8n==(H-INkBvb3ZjBbtl@FYpR6dFY&|O8L^7RCTP!V5GR?JKto{)lpZXnN>Cu70)Ub zf*|9p&+le{DVg6ynOmoM=P_W_(sh8+F6;8d^4UOmV|y2i!_xBfIN1u+iHt~Vh(nIqhUy@XaavY3JF&i`o;;i zo!UxaNa3OK^>Ba_f4d{=Z*OI+pwb2HIB$KAVIgxvtroANmD)Qou{>0s%3_Xs>Xomk zJ8)EI$=!?44WeK$b17z(Jin~F`r&@52_o|%7l9l776ifn!C>2)q-w#&G2q&nZO-^M zwTp&Kui5eWn%^ygORaoykb2=Dw){rq76`ar|2N3di}mYCjLRjlxsu6+Sq(T~xcPR! zcwYgj(GVWWIPlc-H2b?m&iGw_413wOo*!>gqF+D01qp5Isqsm5pvEyI?D=j0XH+cJ zU;a>!;-jrsn3W9Ck4_dF)-WIV$B|1pE1|3EWv9n+R}NO#2u*@F68Vin6s0>W;^e}R z%h*xt5BzXUVovg_LHC8WYKz`9zY>e|+9J*+anG(aXQnH}tivWzJ+|Zk$YFt&VvFXY zq4renvcz4Wk!s*x(cmVZ`sw?J35_gC9P%Ub4N1QNdVnn`rnCwTRn9E2f*^z02Gj_a z!}ckL%MDd$Tzqgm)toTzt5dW~3^&n7;n{nz`hDaKNda=(nR0p`zPtu}+wf_3I?T=Z zic#U!Zs~flp+#GoCh-kIM12~;tK$8%}URF@C8&`uto8r zLBOq$N61z+wnl1=lv}6rbdiZ=8?-IC8l#GQ(4ysbf#RFZzHS{2KkY{2E2Xvr+3uh9 ztGN3`2eUs`YY~mqd{)h&oh)@%wm6r!CrIy4HWht1MC^izJr+fW@%f7`>%iN_f`vTv z=U%Y|8rY1TzVK}E2KDPtVfkHjLtquRY#oI>@^B9JGfs9d#F$G@U_GV|-;NITaPeQ` zH&sY<&m|z|46E(}H8W7P#&oIW#@)4OyHcx{!22Sn4l_Df9c~pM6C)#C+Jd!yN`=Kmgj>ZX zl8zA?FBy6pp9m>?B`OjrAYG`2?+3>t#ClxR4;a7s_}0J-(>wdiT8$)P_y$5y8`)u9 zjg|&)u_Z{Ezy`MHS0p1ZbLzM(FiHoLRjYb93z@mY8QkoH z25C16GxAi4xNC3p-kus{9pd%Kw>H^1C$u^rGf!cSvinji=r-)6bjtUPY6@3;?x+${ zh`(KDxpy| zimW!IPa3Irj;aZ3^-;JzK%;aej3vNv^69t-q<;l?Ec~qf5r!D3?ou!E=8e^)HIf|FM}h zR&ZUFH@yPImBp>&ADBatial6O#S16`0%~~X8-$DvOO7J`-b&BRX%Wn~L# zevNhA!I$U=Zq$4J!rtD^YcYt2vPQVSW`M2$IG`L&0_nu`u=s4l>7tPL)x#l}O{icy zDOH=5-V<;Oz5@HnCB^i}WRg(2SN#!;IP+k3;{Gcyt*dKdL+{ldXpOR)vC`2pG^^&Q_3?;neoxT zs{hIb>L0yIEGLm`e19uuAGohd{`I!;)^-^vynbNe%`lQuom-^pf`=5Z`aFmrOl%KpzHYVC+GHu^2SM4u=ZhIGb9#uTJrr5 z+NLX9bPH%Jb+Ft;b|GMNdXVK*Gh=MqhWHU`7)iOWk)!+vO zgiFi15c?(9<%Ox|Gb1eG(8|`j#kOy%7XENTa4VHGq?5NuGSdk=?JSqc(dc2iy}7HB z4KyQjZ*}66bgVbknm%HOO*YApC}DN&C7j~L4a!=2g_i7xKt*d)Ko`YAjJsaQ*~D;@ zL~A$LsXflpxO;T|$HvD222(a_kgLP>Ci!Ujh&R9Eh*N_l7vf>G^GDX~qx1Dj@T)^M zyRY^RGsm$VHS${^#}oGuN_O~g9hY085s|WtH_W{_nqCel9^z%91Dts%@!Z_uKhNJq zuzCUt^{^I{7`r)ji*GY6T6!2aHkDGZ5{aOTiw zmX}^SljvD=TfyML(h@>Y7CuTGp|;Ul5NGA4AI(b$&>~VZIGN@sG31WQ64SCn{?PF{ z0Q8{tH?eb%80@~w!F=5Kr6%~(;%5@6V<$;XnebmYwujjH$`%Sx`YWRQ{9%&GM60wi zG4w+?BFT-Q?&+==b#C2SXLsd{>|;`XzT-O+S_}L4_9&@{fs!M zNAus%laUKQ;A2JJ5MZ+dDK!KTqcrCs^eMs9^YcRx5KvMOkdDv7BOINky=fs{&_c>L z+&eb_o8JTF2oe%tz(o-)O^fa z3e<#S2e9h*F_F(fg1o+`LAzRrv2V#F#?4MnMy-yZjzGJ(xexTi-Z=(x0X+%O$9IyA z!QFA0__xGRoz*V6JE#MI#md(4fzIZ=*wbOVApijSXZsUCz!)3=)&sW#BeVkNlv@Eg zZ}G?TrLg=e?}2@(;P?a7_W5mnn|yC3ARoaSVG|%+T$lpiI|Q-=TxItW_{T<)(rsbS zz}5wV?#Ip908l=70$>Y=`W=G zYhW6dLb$kq3hdEm?cP&xvjLoa@Qd~AqGP)bD0)W1KE8X29$NB^G%|JqcuLa^{5wQP0$NCGr_~jseySY7prQZ{u zkpb-ee!tJsL4yolDH<4krZeAZUSr5t!x^CK!VG{?s*rK(KuES_2Ug24uat zVdZ5H*Cm!E0^kE2Qr-yY`XylUk3$CvA(jRR#{mX-k$215jX~uf8aD%WsB>ur?C?j} zoWuLk+NaAH<1_JNeX`5nv&+cL;G**2fqW%-U`r<$6f<|!ADU*D*_bUk{n6Nu~rTNgl-P zcr-~!YW!i&5?eLeIoWO}q&l~JxBqk80~>;z6WE_?whc$%$wl5g*rqNz1vc-Hh=&`{ zjQJN+EAsxzCRjag&UN{9pi_43#VNwapDOPyF`gkC>_?Kf)(QW(n1c8b%X@4oi#}&< zn|g7Of7|{G?zmX#D@D)?XIU;6w(+eh|M+;e{o4mqu+)ylvr>eLSfWhaCztUAmJD7# zf#jIiCXle6GF+Q7wU~ra0kvJUp(al=s(MSh_u5Vh3*o`seohs}qX?OO;YH6vyG zQiG$od1H#Oed+os!!1-%$XzELz@O<=2nEb6kLDFg_g%$Mo3DsR+>ct z4f~KDcrci{S5976t9L>c386_m2`~!Y+pCnI0=mQvyM;}+D@7JKUcNE@tfJ78iL=%N zhVSI0+kN#^*>)fvh-25{XNz|U*#*diw}3bkN`m=(Z0ENrZK;UX@jYZLTuB2(w~_(; zy5T^4Oe!62VRlw%(dJS)#gmqdfv-PV|BtY|K0mWrUVBV(d5jGuCLunzOt{>Eqq3-4 zvpON?gD7c}2B{2pI-kA80f>ggEkQt?>tTZKteo?t@INpXuK=}F%-76m>Yw6(llPZe+XK3mS?t(HnWM{s+#n;x&XPdZs-2iQ z7w+4*(&;aDhq=xE)Ryb&mAgx%>);_*aTP~@iY^H4opgeQinc8|G$ZpByTWzfo#^8o zCc|C#A7r(@D@jRrrlD!aQi0F4>yvM2P!a$Jz)kPq;5pG^Rr<N!<;T#1&1=o>JhRKB}bxdDMGs zIi394-8X4xVZP5Xp-#&x@DcJvV0g2ivYjDV&;L z;4v?NYWf5%u$)sLzM1} zS&ZHnawc5LIY&eaQzE>$hgS#}=!wmBMiR}eb_5!%<#Z^6lr3$mr|wqCw)VfVNsj;R z#~t%wFE&t+KEu!RJfkk2M9n!qC*wGj-IX3!wLOB3g*icTYKM>Ot#1Ui9xvCr&?xMz znt0F{C!uVX!&kg_)B)E94|Lffog0A*!R5eWUR12Ee_BMR#0-=X+sBE@RBl4Uy~A;L zB9BZ%Y1*EgXR>HGLmj;|E)5VVg%_(iuOH<0VCzCXNdMixF{?3iWTu`^*H}RH2emFkDjGwzB#TndfhZovuwIVXY!wA6^LdIa9Qfz*7`VKrd>bz5 zm8;(q(+{gWK>LwgdG!%B>S5Zt)ivF@vl`-b+Q7w}>o zX39-@#;OdcIH%-*Cg^sTqzTr%0@cD;b~BDS(=tHE#f%*MbZplU;&(h(qknCnRenE) z8g@fZrqjrJGgPOOpGL!EfUEIkiJ88Y&J@}dq&ZE`R6lH)k);VA>bHQ*l&M2oxx2IN z8G3e+inSIEs+Q|#bvGloLKTBXcCk7l#GOrtDnfEyu;rmn$Qj-ni^?*Mpd3S>>3$BT zHo>&kS1~17ifv^Qk=9K~P`@*XegFY|6Ons?pE#B)b?Ppfb{!Dwp#t8BZWjPcW4$Qt zoqp>cU8IE;;dC_)`1bDgN(AS(%+Ok-{R6+fRY9-0g@X-o*+4Pb!oHi3y+0zt!QC8! z?ytm%3n`L>=Ul+!RV7LPp#j${Zf$lObr2sFF7=a}o3|{CacA7Rv3@LQG zs~sbtyA;#^cv3$!43c9{-vitre5-FM@Y`5M<+*&H%ig4Xb!aL9s5-A6F_t|VzD&)< zoxpH6Rk%u>RP;iO5ci=m7Tv{Bb20l>e!xH}Bq*EcZbTmK)S?OtdX+eXh@(P{@z0x88`oQ+j|@OGd5QZ3L=sCZwT z?JxSHmGuJT@ z{w5^d{3(wblcnLEmYWYdp;YUrFBC^7maig{!Ca2yVp>vr0Y_`tufxx~!>as9+0#tb zn+P)LpM+AQF6nNz*s;$%HD|-@DBpd}?XxNd~)IKS0u@al{!~!zN z-R)gj(!v}}EA)N0WboN(RnthpJ;S`4zb$r2S?8^z-;O`CvBtJkOs+8R*^#CB@|+M} zmCWlwNkEX~($lz82kJ@mG+>GhX~Irx968&>URQGrXu?hR(<5I^3o#r*2ellBL)vW_ zvR8F%V||Jvo{ol0_tO2|;LAAO-{ARhqR1ZDl-ftx;9w|$Kc$A}82u`e>1N%`=e^(* z`}(ZOZVOs!DlxT_r@D8)g>7l4tAPC$>Y+!`#CNO|l5PY06qei^(~CKALs|0PrAx_# znd)B`H!~ZBQb=RnW>!34s*hvqJ_kL>ZWH=YDZ0m6yOy=G!%B4L zp_7a>I#*|rpD*-ir0?i$1YTN6G}4l5wRX6-O@8W6zSO7osioK6dXeD`YKrUAJ=!aN zVPErQ6t74SC?5iA=UAndu!Fq04l)P}uh-{yKeG?u0zd8t6fiNBL1=UGB4ds%LBus0 zd6;mWtjFXA^BG+?=Zado!?FaQgpaz=S6%DBjdav-JC@rNIGHK|8EG{}Oa4{W8pWvGO%lcJuJ-~i521{%ncSuRyOPW=*kp4DY<_P0Y zSG%v|r18+me<4-~wS2V+;yq&$X0;8M;-C|qk50Odb~;V)YvuTytpCe2Xm17NCdz#D z;<0SltZlHao@pC{|8vD|(V5R|q(Gw%70IC!myj*HmylKbLxGZsBF^-MuV@Z=J9L9w z!7J$Fes!g27k*`J@{_b0o@n^xd1yw`+8DdXx9?3SzIE1-8=Z6@Y&>D9y~W=Q_B174 z>UBl|HOknoeTUD-)QiEU=I7Q`-nezPifRqC@0~@2RQi_7`O}B{#sSrCt(ogq)QNUV z(=9zbs#?6velm1iXJ&J~^KPS`;V*&E@0-%pgF-a9v9A^9hhqvBAT3M@dy(@t+xBFljqbA6C#xE$BA3D@Qt^PHWFkpR_k zhX{vUtKoQ=r_@5%(C%Y3S%pDjnrhXo&<^`9^zWRim}Mcg$Vx524e^-2vj#4@U>$hA z5=V6}EBAk`w!6}_xofE=pWmL?sLlrSswU)!av3P~R zo@xD+HC5VoI_xq~rT9*)DQU8|{0BXBjXY<{m=~<*94H`KMB8ARt3?QLXt&qMt6-?T zR7WqebRRZGoE` z9U*`i)`nrEgC*5mMRTtAvvLA^cBdqL;taR1{V&GOAxN-b(Y9sVwr$(CZQHIcv&*(^ z+qP}n=I{6s4}&{+!yKMjp4@w{^|Rz`TYJePVLZM@uWs!nD&a=AubRG6J}fV3Ohx%` zF%>!lF(BiT=t}wI02*p?m4<|z0HU|e>PorpBNjAZ0dQMLhVc$~QJg<)rmE2}RU~=! zUD#<7{}Ef?f77pZN6yEz9G`_v*b-Tm9gyOId&h_6`MLqbpnd47@3?V|+3^0p?DIoV zZ3Z#nrx9QWRf&Nk_s8ix|AM-BpPzpeBJXj7bO`}{>H*gY_IWlV~Cx< z6?z#-`sgnOYM+1ul3@+%6BfrL9Vfh0S#o!D_!fa@4yjBn;x$5u+DfbPnsSS*01wv{|6fqI-1 zdMeFLo`fR{wZ_3#k?89<$k0BHwyx>FL>fGYD>wXpO2HgvE%uhC?958-sai+;N-{j^ zo<6mp)fAUvkZjq;5I^QDa@-km%&Q1ins3UIKEhh)IxE${`AsNTQQn~uZ&Be_A~(1( zy=XmN(t$E+Img1@$iQ@cIO6kJGi#*1rRyZBz-#F@h@sY&E~jcNW+U;Um{N)))bit) zHwb;{?~xCC6r=Qe;*B*UswTzp8@ahIP{i}1R7sXy7)r?6s-v+lbcgu;sS;F*7bKS{ zr4WB72Pz)qa)_tEhC+I#+Vbc9E8au33xmMxioOE|Q#yZ*Rv6fwMBMqkFV)6E1u*F8 z_>4O|%#G|a3&A2X9*13l))3lej*H>$b<1_K_BEuGyk2a{t8+dgUZ17+&T87<(-kpg zUfMSL#dvCyc_}4$-Sy!hboME4qhQgQH09R2bvv1t94pN7IN19ro@mGRGJ8lYX`Xs{ zcnWJE1UVglD<1Sfan=<6CNz%TSelz>bE@)RKfff7s6>7S3o*88%*(V`Bzq|twNXZR zR77V&?QVI`DWu@?6q}eK-F@B@f4Is}PkglUW64Sj1X~-i>B3k%t`r_CPdY9^%z&eb zZl?3M=+QS$M`Al(1J}Hluo1zn`^MGQ0sQ zN9ma-Ydu<3^kM~>)i!03<>xN>Bm-c$?2n=biK7*uBdY& zl?-*KIn8^Z^a1u{<(z1-4|XZdLd2(iubny_W*Rl@G+ZEaMw%F5L5g~r3e3=@nOe0; z#sOa=`MsPS<^()9FUcdkS>GxNevCE7;x2#l$>!~9WJ^Z)nwOsuvJ2M^LaPVC_&RCH zAU*KJ3hoKMux-Ja$$_3V3hTB}8+r-{emQ~TQ@U=_fUY=m(3idrxtLQGR@*{?26DQX z+gjS7lVttDFX+jlmRNe{xM?RJ-;qS~w0Qv_RB1Y9B22fB2k@0EUqmOr2&OZ>5%~_e z0`}Z5sfwMK_|Ki!Iit20=*w7t%BKoRSb*;Z`66Ewo8gJR=&BvaYVtEDQ$_ul#X65G zsJRp_9=6x1crP)<9%fT8-Find6b9kLv8Xuoo5z4i_ zfW&ebDYW*Jk0u3RYEQojvA?2Pn@Udc@3xz4TDQQ@?~>EZ430g{yQBp1ksIiXiBJ&^ zq#nF+A^!xyt2&uY1Z+N^ZikUNp74p@z$PRdq9lc)fTa5b$B>>-I1C?Z6r7^AZ3G;A+XV{dYQNAFKn%72rh{yraG@F{uhpo z!*c_l>Dq*~I#Fv|9{ouVv6781gT<@92raUeZZ@>=&2Tu`zSXG)qV=ewR5CW2?Ecns z%c4qb-cpw?aHyJz{NxjG_4wJ@gY#ho&3w8>wxm>xRMWWK4LTD=_sf-xlJzJ%2(Iwo$r+7_}yxA!KELfmPK1HTM0bUPb66tNC&8^`bN6*yW{<` z(BpDBc%W6GADf^oa_5CxVjnp&IBt$E{<&nznoB*;7;aWG7+cU$dx#u`)^9>e9xD^C z!K<-f`G zp=y>Y4+Naq3UI)a~2*>u5L zi{j_<$JfmREJJr!(}26N<~FbGcGWnmu<$iH;?c(hVMC0X&<5pyK+?QKW&o||NU>(x z-dE_`%-ao32nZSUqm}ON+0yK02C~nkdadumUeJp!P~Kzv)5cgheINO?D)a8GDWta$ zEyi@kF+9y*z9Y+(Mo~5#AsGQ10D4czGR?j(!5%b2{!M`EZ2Ga9;Uqru=FUWXBy=K6 zqVI_S?6HNUqO9dZe@k+)t5<_NQ&StNY>2IT9?{7d?@gQ%R{oRB4fgM&AC~eyz5K>X z;9h(TR<8{IuC&eGKOG7j?t7rW8Ffx#`@`LmZkNS;zOr9ce=J5JXi@i8+hkKRlr|6| zGjTI;KUCt@b9VRz426r~7~9VtUDev;+QTj8n1uqKmVVI8DiiS&=mPf|#oecn*Uz46 zUDD`B(s_#=mlx{C-HRY|F;qlFPe$9SSEOkJf_XxLN5x(hqGRstFTuE+%_P$1jV_>Y z4|17ShNi9aYN;yDn(koC+l#Yd zM(V*a=&`-o7!-t8zg3!#l~gxKPa_|;2&Hhbd`Ra-ASUB07C%#ZnPWA3AIkEXwe zuC94SeXgJs`w`(bO7l+eyNAltoUl2mHGmZPiQuSY*6!QVnG-|x&txziT%vy5q(qi& z5DcZN!zGBrZ5+21rFcoZG4zN$UM-bL_4(`zXA6X&SpzF#HI^f6VgoA$IT0$V{&$-M zK8DMk;B6tjojNgMd%^f?C2~|hxLuC=Wh`o|3&xUHqCb~D3XUSuR{u2AvHSolBrqGac7pJZH5BAISs0OySL8Nc*YMg z71{1ov2VaP&&NMoDbF)9V<~|A*FXb}#6hx-U;7xH9haY@D+`EVTssR5jMr9fwAO#m zgAvnnMYeNdR{#wyKx*&EZ0t+ryZ`yQICN z{zY3w_KnwY;m5QZNcMoe?{ni@TXe#(X1L!obQwUzIcJi2uZyek*3$*obPoKDgs`>l zlo~l(k{O;jDxmD7wCsp5n2yo)2^eZ>47A}_n<7|OsgNS)WFIRqHL##(=GN;Xc)Q?^ z+74X*g7zZP^~LLjhe4*5I*p;fy}{H{k>Ibkr&^+;AhdQ-Qc6AR!sWXYjH=-j zyGe3l`Lr(kZT4(){90k5YdTJ)t(TABu{Sq?_O)cu0_JDBu)iprS z$9#`^(xH11qu@V{QsgoEikSQ!T6gTYL{X?cGgKK|vM0J5qxV|Q%ktQv&>O4Y`!5b2 zkVIOyb7*R>t#gnior;(MkZ$WL7x)%r1gy&vjz#$A+A|m8sh~C$WUF|X`05KEVvew~ zYL`e_^wYFI8M^9RB_oa93VYfPV|sp9ZOSP2?eyw$Y4-D@Z!ntlLt})6DqbzP-+6IR zu)aRvReGA!4BblgdqIZ%l907^W6U^*!Kb}9C+T!Ux-|YMXccQih}P~Qq6^;f(VS@V zTarn65!0(VM>nR$ds;<0F2EqQEBHEn zVuQ1Hupb!{OUB~s7L9ZRQQUE%Hy^ZwdclPV^jyVQ(GpHU?a+9{&S@=5ox7xqU}kR6 zl75+F6iTh4(`Z6rZ~}2qqb!+OdE`XnX_?CwH<3=rAzs|?m?S(c_w$IZMy8BobOK*m z_jSk`)zoXk#!r!>SLEW}PEOT~1h~Tq2@K^~B6FpRj-!3x<21KAD6K$(_2|MmVj$!K zi@J07{orJ^jdQjG5x`R>e!jg!8|+#1{)p7SN!3utuBuf#=A2nQMu7~-%{I7Mw1-^| zvk4OB%bdbNm~vIg$ev}w4oTX5kelMC<%Q~_F0iBK zjV-WrE+`)Ne6dkl7C0p6noH-(Q%y~>6CbSN=15*WgEmZ5*u%kxJqZ3pBcBl zIHWleQ!vt65b?D-OYI+6YIlt<0e_Z&QBunN_)(={y5i6>Y4ZAd9&aWM0bv+%&pzM3TpjFRp) zWEw6U{P+IcKAPK{(K+`w8lr;;snVRHVpfJgR!PCrqg$%@K(%F71B%FDGo- zI;{s}shVl!=Wx&XaK*$Qv_X&926fF@@wrrSxzK`#YNGaD6JzU!{CZr8)AcHIF|>QK3uOS@l*1Q`)OgK5q77(+X6RB&&{6Cxs5vDOGh|qG7h_qye6X1I_U1P*PDylQEE?F{z!1Lw#_+gv8L?0a)yf11p zu@mbC+MG9cp%s4+UUcBzR*DUdKUW_7VDku90XW&*r z>TUaU2g0sD4&rhy3O4z=!dRl0kkmyPN8$5}fso#qO8 zA{oQOp_C3K_3_XUe>b$ud!0X?iTM~5-Lv3^5L{Fj(YpV1XzA6(1!lOaKTHP!K?pO81YM zgbosK`e~87KsOPh26IrqQF#}TVFwUtSSaFq=f-mYxc}srG@t;J6n{)n1ql9-K#=^> z6OAYX=7Bwn^#Obc{DA|59aXxoH2N3dK%lGR7-stO0tIIU0~&aGYS!Y!A2{4VAtCYc@d;2sK@WL!=%AwkzY#dp03dUq z-JHXQ0s6thF#IXl^CtsVx(A-pL0sc+qa49J1%3_&h5$g?2N5@h#MHCE*g_Uq!!f9+ z24`>yEBuXn{y`W5@Sg<(01N!py|I6(6@qxWH7QF(20MlmJw&uX|HBLf365cP2I$zs z!3cl?`zabsRF5IVw}c%jAcPAUyqhfyh($F5Kw;R|duW)=gLuP1gAgU~gQa+&jyXVC zS!h^+fdUmXVp#6?TpD^8%#9d>OMicAwmpY|-}Jj1!VCoK{KE<|HK{v*^Y`v9(7N)w z7=fVT*MQCe2LLD`H9kHCw2v3SL7!YbLjQRB?&fY+@Qyx>K`^hEdjxk+1_KB$+#wX% zuk5Q{!JY%)^c)oa>3284zox9u003q`7?@)~7r~<9SB1RK;gsKc;MkkU2e5@8@TCu6 zu6DLJ*ADpzbTBXe?RU<9w>Ef%*4CBQc%C2mm)q?UZ3KOfo(>ivH8q8JOjQYwfSMc_ z;>#SBnBu@5J@2>3sxX@o;GKUON$y-9*88{HKfiYe0qmu@Kg1kIM4wQ&OA_)l4 z9XRqAM9}9C8j}D}_{bgvCBQ&*0DyTk`Eso_C?JUfL=*Z8y3}**gq&VZ4oJ{98i3)Z zf3<%nCfsWXx1y}PVHS$;?MiTqU#;5y9il!KQKr64tW@1iMDQNS4)25eGV$yJ&STp# zKxG?GoZZup=G&PHK-k#o?O>0aF6Zm%Leqnz$OUh%y=@fw)A!n?Q-FSmVNF|CvTW?f z)En)5TGUQ|%90wxy3+-TOpCTvvD5p#CAZtKm>=*TARbPWJ;}qq;qs$qdxTMqM;+~< zXYEbKA^nG@={u%HHh*s^oS<<2j%BRLAK>40HoiuGw-?!&%N&>TZK3T{RVLJZnX4&3 zE*?){$?hwf2u?0o4Wa<;IN@dUa>%Z$;WCE+P9&9SkhH`{tuJaf1So|8Pj>-OL{GwT z<;(bo<>}7kiE62cptADPPrq_&YvT4X&y%uL=5#|gxzb_2pVo93+t-LxfU1gYb{k42 zvGpp%DlAnW?%i*yz%BTN@CI>jj2U)}jJ#qX$hPxE5HS|CH-YmVh3`Lv>AC8if+Di$ zn8kK8k(J*EXZgeLJqC}_;OUPE0xh%3i25$qTr(%C$4kXmBiHD$5vFf9jK$3vNxWKO zzN|j%McrjCm!eU|9R$@}*1?A2&SKt`5bl*l7bQf) z7qCA7voQ!?%L&yowum+IMSF^iZ*7q(t#}p*^17Df&H zz120=#;;FN&2G>O?lJ8XaFpd`&_v(E92v<>|FzH9_{IxkuNhtSli!ZknZ(p@# zX_`z}u5^>$h+KQ#j2xvvDm|90UsLIvD86)5k7C;^CB7Js{klU&x$rXRceAH!HgXd4 za6gPjT6t5RjKWIOvh$;mUtFiahc$I|Ym(A#7YOhf%NKlp^5TFeA?F>xNl6J;dxLUN zyGUc~$jl8r>tY!>9!4IVjvLn@)fGQH4?|n0<=(m+0q^<91J~5Q=;bv^n^`QZ73wiu z<3HQPfy+70w@azB(=S)kdPIp?rTSCOQ(mZ+ltHyY5!I5%>z!UQ9RlT#;~zzSw}~iO z=Cp9{q#oVc?V<(?)!9a)t=7}#<`|sjtHZyfIDx028EuMd`iUSq=+F#j2+qeI=;)F0 z+Ol*KlVA2L26=KJi1!d;Vy7gWkLt7vqbuxAnve51MySB(j#VElVY}0w> zrO+n;VJ@#9N%kn-{a7?Ch1u-7i`?oh7@?Zz_@qA&lK8e0@sw7A5VYL0?dy4KJ~;$a zZQF7y>lJfBM>SrsG+7YzE)e$7&=%bl*88Vd{zxrs|zd+)9i}zWm0y?5sMk9QH zn3Dt*p*ZlPAKP1v_U&RRwAL7T5r&VUyrp)&c!a68zg240y}+Bs{UTd!M(|sh<+5kG zbGcdEdQ+IBX1Lor3ly-juT45eM8IJtq>hU7qHF4F_bMboY(A6VQV*dsNX2pdk>u=C z*Ho8@<9hKXc|jWVW)0WCuU}-ol`l_ew&2W1@8Mn*hm?4u5J}T6@_iA&DD%!FZ*QH` z-8niMZL!OIFjx|bGhxXclcw6iCFd#jTiO+BjNt#iqwL)OV!W4P*9hXzR23>>dE zCq?mhznKl#F?6fFwGy1KicAQWPV&lSey9F!DhMg zR;T}^s^E^u+}QUYtMn(;I7pi$S#>rsU9U$XbD8DlM*mX_L2D7ok{7hOD)tFtF58RH zyRAe}amE>{!x`-*M7rKt;tze@mybi5Q0Gv|E#o7dusV)5-?hN#@m-M}`S$C`g{`SK zFG?0FZGX|jqv$sx?4!(+50IlcAB&qeuwMX%=b&zT?l+r`#^1|-yJq0}x)lx4aDj-R+s-0i z815#46);itW;%0a%m5K;S2yyHT_$5B`>-=Xv3Qc4qRKTw z`E>lV&pOK|?gx$CV^;~@&J&rvx2B_MYtK)1A^b7U+G{&gdIg5n8&9y#CIs2tX7K*oHXUX%->MbM*eUG%?!0kIn@b9Jt{L=sM?{p zvWZt&*zPM-(;W_tYcyTV7Q0b%_5`*^`#DF7iJl5A6aF7q{-!T>`x&FxIT||2c6`V# zVICvl5v?KduFG5|imVGVXPRdLM1z9^XD^5^0M;dU@r3f=S(X4(h^NB!8VqLNlxd5@K(G$UQYC3P6a? z!!3|g*Gg<&keM%sWJxDkseGxya$C97*$oC0XOQP*0s54U7FGgx4v7{oI*z&`K_k8! zmHZ&Py z1!?77S{I|5pojh~Z)M1k`5`ViONkWMtW!z4sycs4M|%~exSq8Zc7)eEi$c*hGfwS% znAlC=Tj>nBCyC@&AtSeP+gX(!*9vcGM8ECQu5X%~|Mwp>)^gfXVBik%T+Fh!vB=K< za-pVAH#HAU_Jtmd}xxnA|khV;qC?0iLh;Uq-;58X9aq&xqs z^rV6XJt+ju{V7fQC`t9+w70leJHW_=^*2C<471!0nN!hLU=_1SZT=hWJf9aBo(=}t zIWc!8%&)Dxa6qoLcZ7xOmC`o38EcKcZ3IofhC@f(tDn)7!jh-=fTfsqBRI$=QaqH4 zh$=&+tLLi7&%d1K&h9OOmL&32nMwBYu%I@!NU!GfW2A;@L?buFpWb2FEo|t;$lw0}g^*1l!NB&^@>Uwo#VFpMpn91xf(UA+&zNw{{Jl8otN2J(S@bt5|R<<#J zh2Dy3l+TMKu)VZiJ}vRshcB<`aO>X?8Kh*+xD93940&ppC0%C2(BAm>m253FuMA$d zmtlK$)&!-Kv4QXQPp|GhpC`QC%3{Q^GaZlW?7Xq7PGimS6>hGhh4)oAdZ6l)12cW1 zQcCeAdX%lhl79=b_GA;P#M%8fdmXY+o@}EwX5q?>J2=XKX5{XdnWSZQ`xfU&onY2< zz_zZpc}_lBROuyaXOmErTt1JdlX)ifF?d9Tsjo{gz5K5*8g$ z)YlRt96_sO&YltYD8xX&;U{`$bx({LxJW^4%n!B@>3>gp+spc}1h+2}<*1wklbqlk zYI0L(=65zdj8t6*E+ zb#4Kw$GlR71BA|U1ma~PwPR)LWQW7@Pbvm(mZsy#i`^~zj~tdVb2uY^%-!!uUFV&i zwd~;M-Ibd88d>GFFwxF+x_))OzK5UMwbfgEIb&Jhte>Kp3efU9VGP650 z-454evy?{O%|(ka@mHZ;9At(iM)80-dt1z`RMIU``a(8(&b`v*MOo{2l86IwzT%SM zHI+4DH5Dru800Glz(cT1N~>hj5A7A78?$^)wM&!admjPEeUqmOYeHB9%{wIg`WF2q zTB_Yycl5X~`!WCM65WGW$)p@~pN|Q+Bdir**$l*H5Xhm0wRkisdO(0?nyHW>IeP-~ ziz6}fv2-SR_Kti@&Yy5bE%^5s+cwsSn$exsE~OFPLfG{u@;xf#Br+Iq2mu8A}`WbuQuL5$9LaN&R`YO_cj`j zm|foure#Vq_-CXutahMd6{~V{EaF&)shgR>Tzg=PAZm$|PHhDZzuJOUF z?Lpys2b{|@wuYal>m3&*6L%QgW-?d{=jk>uqz}V9d;w>A7T5(7>8#%H+|WMN@&lQAofs?~p=oi#<}pWv z>15HY<2hXwiabBNQ+Qh{5_t?8~fdLpW02gM4wt7 zNkczj(#D_<<0!vF({N`oBZ_$j;hZ%jdk0z9$|RtDddTE1IY1C%?jiI6OdB)KcRCLa zaZ|-&*4`6H9nL%I#>&tTIBQy4B}qGYiLT~cqhy+rJMqT#fIONp@ZFLf>Q%dCb_`N{ zg`uf5tlBHz2%&yN(?c&*+1ITJ4&ec{uTYXbWu{xVarMDdyD;f%hcGRx77iti#gBo< zhJ;t5%ACGS^|he+XO8UfjnCCbV|kY-4ki_Ryy=8)`WPj@M1G!-!+TFQloWDOi#zAm z5mQ!dIVk<-q^lo zInG?#WM~-Zq9c(P3y}NA!uU_^o0?e}8^5Xl}5{|FT5kU9AsH z%vUu+;a{W6`U->!H6s~bim43*bx(ywb|t8;8|8mcnqK#8sVbrF=;Y~b#0&eDa_?MvSG#MDcyy0{EG zqbv0#rrPl{bG`-_$9Kz-3kcG_c){W$Cy)^ecK_M4LXjon+nVL?KVl=dV{mU0uDmMa zdu#4n#m(;)hQH|;U2{PX@f~s#Q8szZTr{Z5F>8pYo|l!LtU9~2Q%TW1xm9>=|`(};zK)3nV!v3U_%3nOPn*J?&MtfP4DE%^iDBPd(zGMdyHhKUIXq?{PITH!*8dv#n(UJxqUnb|1mpb`cK&z3lrP_a7Ne|Ihp?J z^uMz+c1AXi|8sWc3a*m4xk9TOO@vznk^hR|CGI88C9xa_0zn!;^0ZU=M*>_iGEf2) zfs^H&s9OS25T!`s7WY@Q6^GnVnGv>0Dg3GcVZ9I$ zK^={P>h6#d76e#SK%apk0D3AV&?VF_FmT({z6A_WNYb}Hh$;(C;IN?;0!>V5tPqeZ zk8S{wkpQBkCL*OK0|o^Y*yLAOxX>ifGJzfhh5|mwk|5ze20$v+#5Ve02bY0^miJlW zIP?i{l=%2~q_1Q+6}O;5LGWdS3{%r?tA;KB~WE2#@(T|@>klHR}v`ac_nyc$; z*uXYJ0g9$VqFjPG>;P9FtU*SHCUhLIFHVL#xFOgdZzhC4&=wcLeP1K83UC_s5Lj?S zfHe>lI1&A(9z=!?EC{Wfb0XUC7JG2wKV+BRWDr2VS+EKqBoFTG{OkPCgmJwIgbEZB z)3||8q6D}Ba1iPoa{|Kf!O#6rK!g%&@Z;DEk@I0xzlAnT%wirQchZUBQn1+s(vQ`nzf!+xP6 zzk(f+K|VSQw*uhW2=@XYz&UQf_hJJ)`U5nY$a&^|{lR~_fx^Q93?V4cEa2Tm2mpUo zM*AJYcCELL3laGQtQq9Ii3ILuXLsdWI6V6mB-D5P&w6jvHKbRE#x&ITUWfcgRa6xC z1pEmZ85AVMgn%fBh-d+m5)uHxembKGLGDXo@A%s{B*0M=PTX7Dj6dW@_54BlK1XqU z`utZrf(FXb;Euk6sev#h&*^BniFFvTJKB@mjXM}bT z|61B0Sr)wY9KdIV4r~HH?8`tun@t}M7z2yfy@eYZ5Hk=H65?5DAtFP92KT!hK!pK! z0fR7z8fA<2<6k4wep=J00m0Y>4B@%AXgX*ZU;2z$y?JzPui#*%lluSY=zPCB>i^cy z{eB-ZDndvQf`x=V01R?+1#O=%=>3>TV6X4RCV31H5d#NGf7&pC1K=oF_D-84|Bwa@ zydXTuKcWBGl)$)w`n9a-WyCoO74S0p0UIg~7`U+jxta4L`n7_%h!8t;@;?V#z4l+} z-2rlFgU5kN%MlPfCd$$mWx-XaWcGyi#U^iW3z3~cRtsWuk*Ojg{ImRdhaIpwvBN>!-$-Bl%OJZ3vjy3 zpQnBJToGB}iKQW%Auiq+PN7bTq|;)URAaIhVBdQbhH7yky8=G$N?{H3kY<~qUwchq zLy1taxRjAswr$LZ4)hQ?h?i0Z8jQFNbTwM}Twix@-`2%6>ICh;O-?vgT!LZoOoJADs;3}y$#oDPcB7|vI$Ft$xS}j{OAXYMJ zuuI2UMhpbquy^myU~RiVk|JGbLQI60<;>n*&^)dtelG#Bh?jvmLtUkpvf0Q)cV{s7 zD_bj+l9NiArFgCH?JupLUT@P}M?@T0?r{QF%j5p!bET(ToGyGm+UDI#gU{Q6q{ek1 zCenYYt;a3xHnL`}@{o=Y0SiEqfJ;QkbVKYIx<;?Dn(>V$+7BBxwWZvqp5Bu0g>^yS zq#$AOnC3d=k*?YeXqS1hebJRxKSTRr8nIKIRF5NbOcxw|sE=T%3)-$evB)lnmfpxP{ zFQKxFI8h}W?+$wQ7Pz}Gyf;*2_W(J2Wi1e>+_wB99hmIxT*}=#+Ex?^0;sbyLb@uAiQ>1Dq{Ex-~^gBNu))~`e+mrFB8hFDgs z*j@LsCB`=?ev<*ueU2~|ewqNPCxU2#*iq_GYVlChIZP{gEQhQe)?U9(Swu!rBWQgH zaAgQ}waVw`a0^$SrnO?k+1vKF2et`XDn`E3Tz7nKODY|;<|K9T1a!=jZJoimxf)hj zDFgapE=}0$v45Xij#5Y*}v`XfKpw@&hQh(~1v#@*RpD#lY(-ALmdFP6)-0oclF!5lV9HZK( zGX@vE5$}4Os2Y>@uejSKYWf&_MfOQme?@L}AaXwe`ID@XarPNsBlY7(9kHEuV zop`q0;d&Gx=#wdaHd~h_DH*|KZ8BoVNBARY@Gf?%3ndZ@rwsIq^cC zPesG|s151l4Sg!{le8qs6c`WaJ&G|R?%PUCzL}KVH>$rx{taY~VtqZyN5*m~ zN6ceR4{Ps@@?wlH+q;FIK9_cK`PV9+x$j;=Cyi_{UX~gy@Mx9iobN*VLBd8s5j}lZ zja7(A)Ezlu6KP?uuE?zDU9c}MJsX6D_l_jO0#>wo&1jsjZ7)iOyLlCzVfqwR)0q8R zNBDF6KbS^Y=eE>#HtlPp53YXx(}XwwF1JbNumw8_XU^%ulmMl;r7Cw?i!bvP~5*pjB@N$2SW?zH9f zhb{H)S3afbas5#>2DnvUCS8cUJRWj3G9Aqwx$n0d?!I14X$+VP)-Ig(lf?4?8@xTg zM0Y4#yJM1V$0*_shoq|80*s!_rFoYFO~rES_sFsTWPC?4$>Ia#U|5+__?r3vj#bna zyDx99`*KcC8p@I1@z4q{?hg^0p;emW;9(eUT?R&;169 zE|%Lld=nL{+RB!8c&WX^j|);qTMq|*vY`*ggqCLg_lRvK_xWor_k^^?=rV?d~2mx=^3xB58ei{5i0CE zb?ix|%c)Q%VTp-Y$}LC0cX`LrACgh*+ZUwKlDtEnnLf;MXImI$$aL-0rgQD>a5*`o zo}~Br7l)lm>y*u*9VvZot)Z+c?rEh??2K9`k>(q596kA#FtcUgH?1{+$5t#%b-ri~ zk(J$FByl)glJjYW9BcSPk|(+zU*|@u6uERvg)z^M0-E@St-S0aIZMn6j*KcgFJm(y z?$MX#dn5VEzRn}KZW-|PN>HM-N*OR(Bnard9UJ<6(7!=lsGb*=En-xNJnGbu0jG1} z2PKWsvYoA?M~UQ(N%Eoa=0)jj<~+nFMnb#Wh-Bi`LV=otse#5Iju~1c!Z)weoeF#@xSq zrwx0GP6J{q?|jrP|98gaj$858ut(x|+-WMn(t{_^sXy7bL3r3Fx2$k#cZ`^IlS zHdVZsBWY=biENmKCxxY4ErAEOc;=*fD8_6I45itaYp%90kHzIZ=TTiY#1%%(Ea@7I zyhtx47$0UWrH*iMHfl8WqJXo`0m}$s`vjMSqJATbEWS}Tynq&Uq)9rU#2?MPalF%> z3mV!V?ubwqvT9TU zB`*X9SzhemVPET!-`a(>$Gv2<8jE)v51hYnPG++mnSKd zA}Z+qI#Mt4*m?D05UOM)?L3>q!W4Tbi=Qhf39~5aVt^=w!kSj9VB)r|SaHw4`6akp za=dkZ%6FblC`8Pm(#z&vup-+yagNYW#*H*6(=!s;sXC_qmUs{6flja24ZysCzb$~T zSC=cP^i)dy_@|l;^0V=2Z+hObYd0Fz>*?E8 z%sWv>U_aL4a_q;1403XN=%$h`sjMjT zgY*>phxROzIQ(5YpS+uE^37s;MO$n&u!yiChQ2W+BpB;NJg_eC`65&etS|QGO?z@l ztS)Wf`t#^rvb9Z)9zEmvPw`S3@ygR%q~&DiwksJ%o(yc zCo6pU@-p9w^Nw$lrq0)LR8os$Kz-70f2X_EL(^*c2}4m#-a#A%LLnbdNE_b`&Gm!( zBS$f%c4Xr_RfStIkulQU5N6&quN{5TOozYM1zg+dSDVGh2rI3tXqCjl^^Fxyun_bZ9c-moa z7HIUUYkCHueeihEnX6$GnsV#6WkHD3|1em@;so9`$tpV5gI>~m%XU0nxEv;;-Yu^R z4b(f#e|j28$JpWnRnV}opJunZKG8xe`Eer&b|H&)A$4@3rY3U)S--|BrUPHQ!rG}? zAF59YEtH1;E_2`OBtZ2zSv4hYKuJtHT|uf$Pndxdapw{?E4 zQ8PJ9S^BF?UD_10ngc2G57RR9!#zMmY_0E%=DA47Ymjm~k)61wZ=PS?3$gl__= zo~32s%e`aF`s6RuYDkRk`nn@}bGmgBcUr zq1(Ocxju>|BFLsXF|g287E$@!Nar#cBXrOyPU0FNzvmB7C7(K`v-T;STDfEHc^lNE z<@mkI5(yZpds*)ueSXCw=9xN)a%?j>(XvNQ_r*;0>-<;{QhAL02q1`tB}ZQ<+jKO@ zB1*_SC$8Gf6@@JBe7}TXGQ;{;o>>{qaU;JR@OeLLFV5VNl|v0)DI#rf>3(^?UyyYE zx0o%-v?;XX@?CqDlMPx*k3>hvD*UX09-HF>Rm%&>j_QLkv+ulVnJAM%l1x72ttxje z{^2ga8G#Tew_EG8kvk|*RYqkKz}Rsg<1!aNp%k&Qmd+|hS}aXjeV;LUdo%lw%&|MQ zd4flC40rL!WJF_9Hl%Xu+NJFSXm#+nH+kl9eAj?*B25XVzT=Yl)>Bu)uFNG3Fl|^W zdC5TKN~G^0)IXLc+-CHZf-)DsRF4ZE`L&i!G+K#6edS?3kMW`v`nCP~z((pDZGzoq z>$j*hE<4el4^Pu}q>5!qgJ_ieO{De$cDLU_KDwu-&q6af>J`^7&tPi$el?Lb@~m=s zfSa(gP45;=Jvw$BkPTrk4IiA{(?%VyBKggH+;Uitp_~Rst>xQg?oe1KpdI&Yb9)B; zdIg*Fgi4lb)W%qW=~D*GV*RnXR9yczLEZ2_lI+$)e&(#W*7pyS|FhZ_9@5HsZ3Iw3 zv^>obeKdGZ4gaQ!zE($UsKR86*bcHqf?3H-*u1_w1H;V2CosAdM9y)_%@J9I=v{(t4 z8SN=Hg!f}>NqJdWZttn4=4*4YS~~zi9g38J>Z_fru%@Ynv~hkbevm1xmKq)mNr~56 z52$&O&tWoOk8K+h=tZq8D3 z9`Ik_yp2hpxX=3HjQ8Dh>aWIqv!TwM^G)Y5Y8T*2pXZxL+Cc)Z<}1!R%i!Bq6}{b4 zJ8JM_e?#r?rO~c#jc3M#lFUvMiiI1!Xj(m5|4bwQAuWDDXwwcU7=ABPJT3!LjahQYFr)x;t|q zo)qKYId#-8=}syF3lQ94Is4hl{n=hN(Hx@&T{q2ft5N}&5mHN)mlt5cL;u3GNbh24 z+o0Fe8^0CbwbiTVWt}uz`3F$caB3(3GP;T`K9JMm!;ckPwhLQooy1XF&oVuD#_S!f z9;3SLW_5L$z%&MrI zKQt!}2kDW-_?-X#BYjiIsCjt|uTm5U#gczxnL?U}@^ zP)=!f8xYY$1GVg7h$Vc2bW=O<40QHb>D!)PGO~S{ytdxfpi9I(dz>KNxc3I9OcrIq zfq-|J%=9cMm*2UVWaD%;)mKr0+(JgoSzqFX8dYeU*^3y^*&lo0$O}y%n5bi%GC`|s zAD@$uB`Ce1xW!=uVHhtd<}^WT(v^M9pXFMiG>g@~x4~t4%nZ2+Uxo&H@L}?G;&~z! zFcy}Gqr3kHpPiPt{cz&WP|=$ubJC_b+m3@*!#iTv64k1e9639BV!Sg9%y0=KsIm7x zcMt(Zj&ph1DAZQhACf^ebm>3q3cXzTeI217#&5W9qvUN$4XbR6g-&&=yQ7lG?DV;E zYr~(KUxS)@i>QWLU!iofb7yF6jM~doZ;+8`HPZD^a^3lNNBS>*#{zMS$z##{zo2ga zN7|e^()K|6t~TI>ncQ}pu{$`j3Wa6$X(;rE3>8Z@Y>u@iMHxmbFY4~+{-8M={F2^E z1ee>Fwnuh>(Ze*3zLt=8z^i;YJ|#5o%!BxXBfdy*F1EQ8q|W>_{WByhz0GEW15f^{ zHo@r)SbQn%N46vY>+2q&VcB?>2I&W{RA_F?? z(tyA4%K|i$y%l9LOZ4y?L8tVB$5aBn`R{IdoBu;$f5wsyzl zHUXyx>>vBM&vvSto1MJI!$hyuZx!|W1`7M3k-XMbbxBIqY!q^R=l;7j?1!9c$7P{^ zk~+yk9V-`vFdj$MaQ@UAf=EDWWcSU9ug;~LI|yYj!|vCwori$y1TYMm2VKi~n;f=h zY{o`19UIeqOJU2)w;c&5^NfTsz7wTp$0i7>iFIgLBdFQC^n1h2R=ci;R1K?UNS@l! zBSY+rJ-v*-ylca-SQM!!j=Yh9p{lg<3+PUj%B)TZcFfQ38@wd1ZRbUE(w z@zlU-mt4ufxzuH@t6ss?_i+X=(2@<qt8*6SGT(Je|D!uC#2yYRvx9)U*u z{>V-gT4Yz3b_1H5TN@B9+z5W`w%6=W-`(_+j9H?0>h+KASKI1raOhzVSX4XcIt&G{ ztAD*ieIqmwNeb%;CkNp5wNCZ*bv6YHOC~`$?mfRN3YKkt6Ews%!FwHqqyl>e5%bY6Ej>MKCjeZU`e-1@KOQoE?8Oe|{;j^7KvMKe`yy5U_kp zSf`Jv0>IYb_AD-7z&bGQc+UBO6V{QH0ibgj_Z{4P!a5KI7Z9#*)aqw-0OtL>AwY+E zr*F58zNSA7h~s)whi z%JJFdYu0`Fi&6kgM^^s}>kz-SGoxD=r{MPbPXFuQ@`Rf>Q@uFN%>f}K8+&+X|MvXv z0(q!o7#2TXH~H2+{Ms7e^__t)eiKNi`ugu87-)5IHd^rbBx(h{%e!=S+pFnoLQdgA`a7MOhaaisUpfWsT3OE3_D zY~299-9OiF`T_?B02+Z)1b@tVsAK=fxyw4U{1g4}&+i;TJOH29wbvtn`oD+IJNBV9 zxF!JZb&p@<-!oz}&751Spe@oSU{V12WJLw~S8 z0N>WmDFJ8%>R*3XDPifoazX7uE7syo4h~I?|NczDJI4Ka{L$_N5&m8Eb)M39t>QnK zfja^8f_M4Q7k6r?Vc9#O^Sw9161m-CIy4QE}0I)sq%lIMU`^!G! zBLUP){-wRI1KKeCA%OeKzTzK()KB~f>j1EQ{2~2S$^YPczF2+>Zv(K+{3Z5Z!Fm48 zSD`KWh2!^|y~6iUG5^v3INI5u{SB(y_WK=F0ZjSb!vpc3ZxfA)?4cyg`g z#;(?-9q=R8wfdbs0j=BohSXKs{)N;v-u!p!y!jK1Rp0s3`grj*0RDs4PvQC{K4D#b zcv*C<2i6k$ZE*Uw{juKso$#rdywHEwN_pzLZvjd3JFtfQoAsd`c=>M@xb?rYH@}?I zDw??e9)dUbzt?(xhkqzYuGHqS%H*90r_)0|~ z59wK*`?WJ~82qw_5j*%@6`fAD)vqrXnGgQ^6NCJ=iulfbp6o*c{nyUD>}e0eYU!;d zm#vGRC<(O}!KkoiJY-M_@p*aBuw?DZJVi}Xg=*eruT?xPQzKmuc@g%ezS|`}_y@-u zxB7I(p(N+*`Zp@>F(KoKsB9|C|#xhP^#7X09z{|IZ)78h2C@Mnujfk_O#z^Ov+pIy+1K zI`D>2ZszjM?Y$&K9ykOC#XS)m1G&Ma0gkUlzL2l^UA_!HR+pMzV} zfo`2B>t+qrCb1K6sW}*2qgbGy*sMCOWJ-*Ay`8=m`9u(1M^r}fJu{N6Nc06lXK9WS z|2d3qe+wtVub@eLW$a9GZ3)Q>M=9?|htcp9U#s3xSk^KPc-A200wppW zu4$whY?2bA16Ungnb2*(r81|9FN1r4@x4QL(fMt$9%UQ*eqb+0|EjqJO(dxmb!N*l zN~(IylefYyL69Lw=CEk&K(?3=E9ds*EN?QMPB`)=*FdU!B?Wp}Y)n?us7cI$%{CnT z!bZo=o{42DF$QDd?f^f(nL+}~Rjk;NF!y90b%&apnn;p}T z*;N14tj2Patj9S!v%%4PptP;KC2uahz7J8 zq=BoppH$M1jY)t{3G0ILXa&wTeLVNjKL7#FtTK?C)8tffwD+y*F7J{aw^ zS8#huNn7=RGOepGGrvUr-k=Cq3dE#m1_2xveU0-4eZNZVwh2kHdmDo}h!9dhkkvEd zgkbp@jh~1A<#dWZafFP*I;9fxN|#L@?;-y;0Rz7|$I=EkRP@B2Ssr*JID;3{pc8Q& z!ov=mI41{$|4dFCwD$Qqm)qAI; zGK@{7=V^Jvo!sugxcid#Nia`}r$#$MN#Eo6_XmQ%qWE81Qn%NS-USO4w^ zW-`(kFVskFlEsUpA-HegdK={D0Vyk&B*0g-P%T|xfsAXiw6b^Ll#a%DsyDR3y+p>Y z-|A^tn36apLMAi#8r+*;VBNH~`W&l9^FqBo$%bbMWj$k3d1j@xO97+du}aCYm4Hch z-uPtei_p-yf<2GJG!S>$Y!UEnKR%_}UE(#&6$ESxxjKrZQRvLTrF4)EB`bIi3=V8a zy>?mO4+KoR9Z;dovo%i^^>I!9w^FNPLC!(q27EV|{&A(zpzhx;7VIM%gJU-6hCO?g z$ltek9$s?n$4YGr5r{ru(!xPeHt5#FKJqbG^v~H*xLeQ7hNKWjUQ4G{uAvQw#UWW{ zu&Q?(kYV5x4q3i!1Z|68L0(wyf-@EWN9+|S`-L&$Rs!oUiYxVuwn3NtVxsx!ps=(& z5h%#(Pv$%_VgGp(hC~)_p1s+fscLUzMdQAcyU-~cmy*V^qt-+3uinJ2eTSqb&;IWZ zd&Lca(cRa&iNUz(^+^s(K>YXTGbv$a-&&VXV-jki!b|C@&_mAT$Bta(b#dbYJV#%6 zhg_Rny-#5~Hw2P3LxK$v%e_%V^;YL-TJ?oNPeTX%%MN{17+jzTbPkM^9u}TX?UF>b zLWav&-56@#y-RC;I5|BUOill#`EBpR{G%|zSRx#*opCbugRx$y{qJbY1BchVHB$4d z%cjtARJ#lt?!_KzL)}CDhv^6-ug$bcRdqYrn9b}RH@73zQiww zFD^su!6tv;rr8$nnJ(BFLnx+iIgqq@h`sF%5XGw^p`7Hm?aTOkv^M<3xE=$A8FUlj z0iTmiWd2p{0RGXpXUi1X`K=Zl0L@Shp15N&DhQjX3{p9XPda%C@-q6xctv zL*2c(lpH}MQzHqa4pNBb=J<+1QShSF$7_nQi?1WFZ6HdDX>v@hkBtTBxQ4d=FM1a8 zQ+H#6?i}Uhn|P;O%J%$X=7X)~-ErQ&gGYO7@9m)_eVWyL(4ha1`x1PL-C4`L-El|kBmTgwjn#v#>HH8s(2P;l#2I~B)meoT=&CgZata`G*Z({)_6$4%_< z?{=@!fn!53{PrWEX^7)VL{uDIf1f1e7}BD^g$?`y)$}!#NQ*e7KPTNEvBcQ(dndmlzfN z!q587*?AcpgI=`oTaNNF3GA`;hr#ZVM9z*CmvT1?*HXvhEWvgOy_bvPkM$Z-)F$ow z_~UB!vDcsup7uB>y^?TXGjr8iH_}*E875aj&gp=HeX}EU8w7lr94!10({y5nj>$6pr!k*4S+KT!#8i~s9lDQ$L~1G*H()1>iGb%K+p;Aur>L5yuq_2K{ZOYN z<(_sdihyCynczFqs41b24JFPj{cnH3070SzmCGO0ZTwzT9oLwsQ|b^bJ}_FpzD}BK zfee;#8<}@OvzM>^@JwdfFwY0T(ck!dY*qx)*@}q$=1NdkTK(+_B8t72FTqU+`IO<0 zxx4ip@B>U^;FJGEPcZLGy4d4HU7yZ`spln^d>LP%eZnDzDy`iA?t2c&fKSmd%6%KT zS>v)>#K)Z+#b6gVf`I~SENW8oxB}LmsC(Gw4;S86;ND9^Itm>g;qzdZ4X3ceo|eGh z?+WYg8JXCrkQtYB`#|iSmIONsJAnbXU6$ntCg?TDLB!DE|4ode zRN?S(gGn$sFzn`(TcfWPtgkCy1n(?Q^}QhN7ouXhDHE z6xbPNWpH{j-%DF^8m>kIBQEt-@LrM4DN3iNg8i!Z)OtzX_`0l$N2hw$La~tkl%S{7 zFlNY=KnmwOk5_ekR=`r+f?~@QXS1&rcl?-{>B?&`*oQ}VM6;%S3LN1$ktr1#5;s}M zuv}2Uw)EVwHr(QzE0a1xQPl+%N> z_3mo`5h7(gW~7#4ot668Ak014rWrU156G|_|5BLp<@BdpDUe7c9GtUD`p{;jH4ITQ zaV4unOT>}c&7k(yqDf3tgU<=Xr5Bm+oT=|3R?s-sm48YaCnEeo*^J~LB%-`) zB{|G$w`bzLPdku6hl)!}tAUCLcq%8GIP@7A@jrHa1<%ePjPSHx91yn4uFEIIeXY{M zQKPE6ma16_5ofOq4k)?*A(gz!S!aJpo!SR!`{nh10W5k0G=&@h?tYz)j3+HpjQCwP zJQAmihqPi=Q*`sVU1+~bYTABY@{Xa=Rs46@p#?^}Vr*Kr%)Um4eo)cL4u1)Y?|My_ zAd$(Jl}5OVU;ZfH#-f%{qcb++z)nF^#J&HNRnEM<{=55rHs4To&XL#}F@H6{W{a(QoIOTGtj z^}2+`XzxiS@_ghBM{RJkCc6_U>gQx-R!jUt)_p^1IB>sfW_Ys1jEIuVbmTX1!pI&S zL|HCttg%x(RWi8jd9q6;IQ)ZZyEWO<&OUISzMt`hLs^On=H(Kpe6Os)mn0zr3Y2>i z#KaLrxWBhqow@bO04CGhOu}5d>Nf}ubgvulf5d%B_2xw(AZ7cgjMmXrq>LvI)LGWg z%N|a{xjf>NdbCu21NW8*ZeI=)my@9o=nQ8Riz5|jIc@5ypjf}YAmy|{O@N#?H00VL z3GeUq9S<8CebTqtRvYR16<-OV6y5C0_59Yp$ zFJSPL3n*R|hUQ!j#@LR2Pok2iD{}I>4&rf4wrmye$4;2g8_Hu%*rPxo`*4*TjX}7i zUgLCbM|o#mhH)-~nVQ9m-ZM4dp1k7!{F4cH!V{Bp^8V@#HouP{(ievvOH+7>0dRR) zKE1p)P(hKlY-B1i+lUV@h-mm|+vWQ`r30!>Fff#@Lu!Ql*E>3YX77&ZVk}^y?(_Y$ z5kd@+<&}|oavV@n4U~SOSSN(=&AWeI)s=GYE}RUYt0ScSyH@Tun*DrAUy zmsUD&%|g#2r1J)*N>>uhIP;zEJixTWY>uPjJ{;yYQT$)Y&SY?aVg%cC70Co+I-1o2tRg(A0(G#ZDx2n*D}jCOwNn;Qj@%L%wwpXw@jK zE&{^waBo(>zV>py4nyvpcrBe$ zrBs~3pC5lQ&CiM26>E99kyi9eY3ZIXXx_Sc;WYS^-A3=J=Bbx;^%65hH8Z*x)cCsK z!p#rv=yWnq#~nAjMh(8Aw${_cE6?PovVV70CU8{=9T~CsACzwW=XGI}fMgbf!#bBJ z2}INzJ86m=^IhW2|HWVm0Y#Uy8B&&vSUAbkQ;-uJCQhAlLbPhga5c@3hH`$j0 z_oaA(#lc^TqiLF?#vL$odd^*cY8!>9;5AvWS8d>1H7sev-kz6#Etm|lKD&0ceA;Qe zvD86fq^Df>bGO#&zrGg8URP%IdBAV!?SvBb{-ltQ8?kHS<-4T)GOHl2;djl_ZV$C; zRQ2O*GUD_$UY2m|*H-&`{)|F|D;lvt?sQ;y(F$r91TN}1a#4Q`?@miAxaatRz7e0v zKnz;8x>QP91c1^Ay#i%bagAGNab1xF$J$d`oz<;x>+)JIu9N=BmWBsDPVbVvo<(3$!1^>|FGkv2xq( z1=(Xu`1<7vhC_2F`gL4js#sg^>Y2Ad};Zbj^1}Bh;^%EP;k0fU5I$41x3>SMQT>{No}+umiUu zTM4n9Sz6``nku}?tVg0~`j`YIDXSKxAo>8~W0UR|K6w1LOF{MFn>v%l8tMYb!~4dh zzu_&|RR{dSnK86tdyckaOUxT3TNBRn0b<1Y!b5a#Yd(n2BMQEuCkI%-kGf*e^o@LX zDy)J%@cvmh1G64!Qjyv8b4`tT0$jT`jrEv0`LN-uJu@QHzjjByv>vL-LB2ZvZ+&w% z>#K$!0sHhnp{F!z+<4Rie97~_rfiUO+?ER|m?INCdqFCO6}XKt9>V}-JZy5`EZgAM zp_U^odYkE-1DnOt2)mvr_JhnwtQBOd zC#q#}tVF!s!XZm)Hpdhy2vIUZd(W~p6h$4o6?|h4^7Miwe{XFeaLPVEKWkMA4EMJ6 zY>Cfh7PD-Q^}gwt{Jz1lQ28w84?FfYG-@A}(Ggy=#@`-N+HOE9_526m?tjGCmH8g( zCHE9zHONYl-!ik!aAgS@$d?~CbwdlQtdvKNV;j`(0ahnDXM*;cGY*qksPrWWQEKKG z?CMM0;k&89ZC1$Q)xk}BqM{jF!n+Bwj4#7L37$oX7{j`#zm0+I@J++v^)!ze8PCnB zf?<^`SYwpv@>fkFRBB?Ubkb`a&9Tz;mxZlE=9tpdB@o6jfp=ibfh)7_?NBWlJ_A`U zKp)2`y^a`FvMEy(xFLeEnDATR_2*D&QfUU$+j+7>O~1zJ^Ts-%C92z#puT{-iz zQ16%^=c3dWHy&rwd#=N0C7P5QJKMyrsMQ7!t3)T*raV=LJMiA(T;lU*#_8dsA(yKa zcDfe)W%w;}yC6sBtDxX;o`~x@F=ze1T$@7(rag;7vkBaMZ)$~?S%lY}0k!*q_4#(` zCDtuO(56lKIn*BQTP4wV#K@^f84P7S3WbO3u0@48Om4oz2MSW}gGP*8s}w+#5Rc(ZnI#B0jb`C$C; zi75a$wEJ;}s~nHpwI3@J!hc$-F9>o_RLJYM!lsEjOHyP8SDt zWlE49iH#J&?pPwE;?--?nB&c8Kt-C<5bI@CPZ6bEo%z@+gk1eDTAe*l#I3&B7Hm}* zNp&!S4Q>2_xgJ+f$r2Jqpv+_cJ&pR3G}QvCdipij$cFtguB2sCU(z`Wfr7L-AfeWH z{Zl4joB*!2zp48bD6>h?-WaTu*YM821%O(&oi|CIr~vK52!;2d*NlCIYN?}IO4kxOcqU8&7j_YUw)VZ) z64IJ?Lm3&cnP1EAnDsYgU4#-fYss917WEde<%g1C9?yoj!Yc-lvCp=nN`jW8c;3Xg zeST0rhF5zSb?C)Z|IgQo>PZ-!QT~ZnL$$svEP4GGI}}~IRneC7U^@&D$6t2%Z1dti z;%vc;(9D=*eLy&eKST>Su|)(aTdq2gh87a-j#HpF`CNJk~oj-c!u|J;H*L z%iETgrn(nljmRwEQT}r_ULf61(Cvj(JKyvR$pQrv8_b; zA|X*wrGPz)4uZ(0nBc2 zQym3IA8k4w;~hcttBo3KzV;-;Vs8HHGzSD(K-n?<8jzC}=HSSJWEuU(oC4ZyUBHNZ z5sT$v?xNOaL!fML;*!fHA8;8aTzOuF(Cb|m(jAI59Wk2HIkhv^=}JkD{Q}6+bwM+8 zq;y8Ov9-M=4sB4Lv9{Kfh{o@nJw&{fz!(n@I9Lh{mKN!?yFc&{_IYTR52?xdWgs;~ zW97;vg=6kr>6a*Rvx;yof*|EEu|_*nQw}ys*<;1`d6-o6+O@cpvS6?Fn2h6;ma*0G zvKhwSv}~$?^kCwUt&dOLq47?(<7`er9aAsGXwOho>vywwIeP;Eckk&|lA#&r7Gq+C z4iCv9(b1G}(ef@&4>2}AVCReFx)Y>c2Zqa$PI*c*h8()-s~s+6vMd76fhnkXk$}lh z4MRFAF)d>Gkq+lVK(-cFjM=Gw zP5(J;V9J46ZEOqDt+M4cBLZW_FmVreEgqo{qA1TfOPWAy^s3qxb}0UJ`5zZPkI8HH z87ZDo?FB#33NwzE;LI7^O@B>O=@D+}@OwQ6gn>6CA~4)2+-Kc|sYMEA00b`xjs z?k$3)@5aP3JBVZ%TajWJdT6~8F!9AbjSGgmT2j^GFtBn;n9xBrR3@>&!~Mp~2Y5BC z(|j=B4Q^vfLxWd@B(EKXkN))ck-5e~!<4r)@d~5iuH66;GIiF%dnp#`B;$(5>1DuZ zt$f5Qvsm6n!5<+8X|-|A|7Kj~S1Sxp^k?7Zb{wn*c2$pPw2H)O+mAG4YNH!ochj{c zDIH%LSc}K^<+E`ng%}~U(cO58;fdJwX#si;Ju zori%5cF)%;ZcIXSj3P8FI$iT!)@HVlQ?bliU)A_ncu8$v*hjI!9G7_L$LXw{%oC3~ zNs-MXPu?51+&u!KU;}@I#$1Z=CKu;EVkIDgU3_a zPf71>HAGKCztXSB`?V*r_TR%G(Li@!FBs(cbu<5B&i~g<2Z3zCel(c5qH$UL2{8vJ zY1z`#5**YMF#t8f$X_AimcmI*!mA{}B&YEQX-NJ|SRHPayh}ptbQR6HDo`Gm8ba3E zoHW5?6kd{FkO;zE?nd>ami6BD3w13F=AR?^gR2`~X@=R_K-lL`Hf}4J`>WNm=LA0` zeis(N)K-YLRkI(I3RiakfDD~%_oJ%fJYBsZrmxt!`6aC6qy`~u=fy=sKd1)v@Kw_j z^a%14%83ah;=FDP3U5l0IOE!YTz>b4M(x$X`g>~#Z6ca;m%wDaE>uy9dj2W>sfPZ} zlw@tk(X=yx?2Fj2T+-F4{c@g=qzI4aIUvt~D?2ZjIb+X#} zRQuUF-206^#}ZpzZ4{J60211N`DV-#v6b(#g!X zxj_Y>e#b!vZFZOSrNz2(9Z|TKozcO(Ynl9VH-*s>3VP>2ED+!1CJmfQl2GA12U+43 zFvGZXGpMan*-A-i4|W^U%;kMtb?cuxH(L|5Mm6tC0}4U~bE#Uhc|3>H^AbwO1U)@) z7S`v+(QuQ?T1^6=2cIR=o!4ctydK@!H;Io4r?Yr3C>dq)jLz$KT0H_^^*~q3lv2tX4V;O>Z(!OShCLvpq!5X`>=2lv1@CM8&b!EQW9`_GU zCc=WtXpPiBR(c!}UqZvX6qaw?4Mn@fZV#dS__KKIejVvN5q_2*&09kvLP6-%(VAt& z0wb0ZdfC}n)~!K^OJI&6;O1i`*Sp9}_r16fRF>pj+H2k@!HROt{BagBAv=Tdc+-NC zK~xOb@5s2FCd&j26e*5981e~D^`4C6xz%EK!Q`c0(6!IjO+%~5Fd^Pb@APOhvW!ti z*Y%vQm6{uJuF;E+yuj}RA0_F9AGkc;om70Aq+?Rn!a>n8e6H!@CxMY>Adex=3KibtyglZlWFqK`YZ=!9-SBix{8? zt<=^&zEy~Hy~#Z7jA3sVx9d+yvW%z6tFd_C_cNQN#hNpy3wvD2LE@7R3tf-Dt2J)i zUE5Iz^+bdQuMp3X%s+DTvV#v1I3d2W4~Mm`PNT8^w*X^X{8qx z&4=7WJ}cBg_Tda})PkT#2|C_Ym#sGQNcAH5d%Z7bs1HqtjFjTGb?_HJh$iNY%=b+r z0VrYlNluOo({ zDv&I4hN!tRfN2>YLpY`9^JA*-w?2_??IL&fe;DMaV&o;H4nYcZk)kzz0G1}wqsPMc z#ZXRXVjgd-hEjT>bm1@6A8!n&Ej+*rC(IlegR@0ZQx-oSfcT~^*4 z$_X6pEh05!McahcNjdqWRTz|L#rm=NQ46qM=&bNlu!v6~;~A?Lq)IFC($UzM z@ECm=T6;-RW4LHUzu8{}rMZj8mMb5N{&4Ahx zen2rwL3sgrQh37a>`@&;!-3L}Nem;&}j6G)Nbr? z9?wEu45k@)Pjx~-o)V@nix3wA)+IA~cVF26SRnSsE8crZ!y^4RN`?51^4zX5y9j}OwtPJbT zqYhhwHJ}UPtgFF5(|bAk)3cpx<`lS(r(unE6g!!u-rhL6(a-ll=D5iO4qh9-^Ui2* z8G-9C-&E%TlfD&gvJKPA)&&IC*APfQt;QYZw$yERVt)RxXHrrdgRM~I$IB|GFF{Qx z=GM@*dkGcMHj)&`r=ozt?D4#ns($1!iD7*fhvS6au%D^V@lyeB4 zjj(BIk;A3TwZ#(ey5%F&5Q$DPC_$$VrwN|a0~^Q(j=(x?U=2%=Z*>=9l{9U6g3?a1 z%+3x%!=sghG(ntt3whI$dJ0jxW>R1rxsCUeR%ni`#Bs&G&E#nzs*MnE~6JsNOOr&phnS>=3AROV2eX*G)Bb z92FKhJm>;VWyHl{-_8dImfBUS{7lmc`J=ZxH8*N$i6bvUs6DA_T>Ei@olDSLh zjWWV{4N14Ne(BTwjd+I+{(fh-8v#h#XYCcmPtv`-nRH5``va#6Mrw86fHc12`hR4@ z83%g9z!-B3*wQ$>_Msh82_~ig(WHv)P&z5~ntMSyXYWnEW?6`c(9^z-8Y!B4BT@Br{ePi}7^JRxo@r5IpMUhTT`+)nPjeMeqg zgN)yre|xQ&=k!GRxsLs<(Y(wS#%Dd^eP*AKYKKwV4NmTo=l>XR&tvTu-Aw?j~u9AYkjonUBYW?OA<4n6aKw2f=F#)s<9=LXYID=miy3uC6HPEVEm?jVXy^xsOhd zet9P>h2}DZpEGSD3t-qW3zxpog3f*^mb;cQ zf6K2DLPA%By}$CN^!uiks0!jXp(Zh;$LPm@=toRcE&}ic-Nql*k83$AIPvi>LbYTv zyDkJJ{va^Qz#2<%DgvmGg57kRp*|7=2sSc|om}-6n7R}>z{VJ_DM)uNw~SM}EFq7t zj=(+~KgBZgM$1>H%-|e|$M?j?#t$C*733wTeRl{K>wHe}#Wl_r9T&q=`2GR#@Onz zvdYjC8}*ddm~GKJy`O9N)rp`i!92Wf z_WD+z80loX@joaZNSgU)iAa3meDq>k@-#}g^?*;iUnbI0G@nBx6H84W&tu3ne&cKB z7!36#liBchbves7f#D~ zIZ}#r%d4R}1=RX=9|nhz+iX7ZId|YqZW9Cz$&JX<*UO~NyFCi}c;TmEaP^>gI7vz0 zjRUkdOtd9aoC7WAY93f@tW?v$P^y~uhv#I{nb3fBbLl6nn%+a8$*s zG$q`0T&-%h3Z@fb;^cUW@jxTR5!z0OiZ6PZ=lh%d_BElV*FC#$N@OKSc0#~cI0cUs zZKf1szp$-7at!ylbGx?HI$1vMwE4+qHKE z(U(v9CTjBDY%^~H8eNfW#F6omJ0pEE%2#p=GFg=ble zOdZx28bMf8M4qA4U-8ALPF zXb!0;^SwtD|KP5TpW(k20a&wpHzk z(V+~A5SAoOK7v*)kPH#b>v@*zR3huB;5%gV$6*oRp3jw}RB-kVZHTBmyHUDU$?T$- zX4;{aSN-j9rdQ;d(&%d(#r*r)cH$CC)@GL|RQQDK^F^v9X!TcuU0V*&4A1&2MWQ`U zq?N&;fcYg;dTMH5GY-wH-c2xQ40BW2uno<}?J({cU>?jSUNV=#II2L3yx#m7f{t_C zUQ-u{C5E_r)}ymlYCNn}3b(jd_J*fRXx-ec@GAwhzNj*U4g;B}zYsz_las5o)#J(Q z&W%Dj>GZW}4FI~M8|v>$v$68pOrp#$aS4+b(nK0^6j{XFtA*0sKr)dxT4CvySY%eQ zagHwX9y>JyEbVB0;}+7X8|;JMdrYAMVJ@0pl3?ftU53tQ8cc_SD@}#|)}zYCCD`fN z*)M8>7m`~zS`GZYi;$jbJ#F()@iYy&oH*DPJj^wd=d04`zg?7GP+YJ#5U~JtxoPE} z!QuSaDe!Ui9U(BmASpkiJyn9o^GI& z)+Q{ix9tMUxZQZW1hyffV5?F`if$ZdtA$pL*7;O0Y{^{2-Yf5+)72Tbtqlg{?k!NT zfX=%*D(E+cKnII05Q^Uut9RX(n6BP)K(d`nXfj+BVZV}SKe91E0pobwGGA-xbTG{r zzT;L|2K8fy2Iz&m<^shP&6?`4AaDBjGc3O72w#++Zifgz`6MKMxSohcuOx6F! z4y_tSQe|G^trm51WnIDQi`L6>FqZy_;luS*YtdoVFkN^IM_}Si1cPDyc9|3FnpxC* z`y;Un(1o~Arn&7hZB;oSi1Xl~Xv2SE=cBDsfRgS0XQwoRQ>4u1U1HZE!w_9j zi#p_RkycB?dITp@BFB)-bA7p!*0bu^IN)D?|j-U!h2O4 zbVknMmsaDegX85|p|;|)u)TZsi@<{Hu-gj^+UMf-8mJeCGW<;ruU{vyA0flSE+GAL2z7PQpC zqQ!#LoMqmT0VTenc{460%exSrn;(%NMgi^7QduiK9tqV~h?$z2fbnYu8WOk?)LB-@|J- zTf`H{A_aYP+NigNLmEX3$-om{f(;<>$0fV8OM!@~GwP8kUC2@iL9h{uOG%M#F5YSj zE!=cjt8pF>k3qM*$V4A_AM|NMOFC8np((h+%bLi1Ty;bk6)*J*r_^kfd>rajb-1MC z)CY>jm0|5#n3>J<*v!F|S@b1Tp2*5H`rsm}w@$p7gQIw1{>>jSmvfO}msn zB6eTFA3&TqPxBZPRowmlzkUKI9EudxIKxubOm|>fUCfTH+s-?#_YQ znu|J{VyEkz<%B@Hu#_z~rRkQ@PW=PUN|du%edc(0>`w`v?AtGgl0!0lgpwnfCNBZmfPk$Jdfib?}?5xXJ7gpgiO_j3LWjv-=(h$%Ny+FBZwxdX_?J{sA> z6wcNplj0##&qlgfIB0R2big+HWI_I^f@YixIO*bNN)!TvZG5o&K0=aDg#<9SyJg?< z#_=o8Re$+zN!OzS8@t@eu6(T&lAFq{P#XFXTUMsmvdQj-D3kWZ;7ByMM&7P1No?yU zdpOvr= zu9&mYY*l>|zvC6zA8l;Bfk&MU%Ve^3{NQm%yPvCBZ)_a0%)*Y~R!FYx9|&nC$o$FK zg4Cc}&9xj*Xx>)6U*MDC_T>Ng81~P9dJLPHp8a3XT{Ge{)3Y-D>)n4o|CyPco%O$b z{}|XbE;#@aCDzM<>4Yc5B22xPZAz#)7$NEEO*b!@Av06oH45J4GmSClWa2AFSI zNy+dB1bF=iA0cW)FW@0LBiMc3=5LYjb9G#qQHjC7sDhXg1xb|tN9T}qXW1DywLy`$$M{CE#gzh`oe%ozMfPMdc*?D3&Ce&de;1c7tIZp zv&F?n$lioi!%71*g}}cgTRA7=hka(j27vYZl6j(X=S4t$B0>)m+53PX*P=%~0(CX; z;@=MU!wAF{N(7c;i}E5IO$sa;%mb2B(~aj$xXyD#*2}i~kzI`Qc^VZ+YVgAdF);99 z;|ifQE11K?D?NmEa|*6MMx6TX;Y9xrek#Y4-f`8?L(dMd9f1#lEcIlcLl+DjB%pa% z->V{@VTUeu>7N6eG&C_VczWUH)KVaTS71GOOyG^KZqj6cPut$7iFw>!0SH&1ZE-7L z=stJX0 z-nIaZUoT$vIh5nTQFkz(X`g$4aw1oQ7frE^eHz}^O7a5WfCTmtAoz5|{Yn*uNrd?# z+#%jvaG{VNRdK$4vkbcJ0w!b~C>-6ZjsSKs<9}H28+~^`91%s7XdwAtsI5%UfP#u$ z+g~;8pW@GW-tl;gtj}bES-Vh(Uuk-9pIT}T)4-B9 zZ#Gp77{VKXR_RGsS2z0NV9WT^eL#{ThTfz5AvpP^Ut2Y=Y|NX6KGMkWqX3~|LZEfs z#Ts(iJZcc>t+Kd!({LC-auBexg~0$IknGUc{YdJMSwiZdzNeRI-h?awrC(Sj-2lZs zTM&SJ(mq7WYyb`KSQG$qWm{qqm`C?m6!Lq;tZjL}d8NKeais|mOC+BK@#hymdwGB2 zf&}m}k6mMNX%MZpakW~X`8CRAzgs5xBWj+xzmt)^VR-rZJ|)Vx4qw0w@FE4*r@bB_ zHg4I`P#}9%-PmmhyrgG9OvuO`VO5qJUOQ$bLR}oruB#KK$Ri(0VPR#gBirHXc;exy zH-LI`ERZ<}P5M|lY=BzYu9fftnW@~N4%#UjGqmX%W0&WbEq94#cBaLr$y z+0gTdXz(sHq?1}!S7&^*3j#7MyfzA50yr~j{<4dS(0iq@kv}{246Ds9(PW(_W1q{N z>he(MI91ek%&+GxnbVlF9q7un`#hmH)+?f$^;z{|^NHdu)tj3Myx260nM?K52>tZp zQIHS>7sa0RC`y2SymeG@W~Zt_jlyg-27@NeI$9hM74!si+F`j|X(?z)&Yg!0xC%G4 zZ<{hssU`RUK^hhU51j8^l$|?L?ecEq@|IX+>mIynUfT1%Og`dZK&KEbgW*BDcur)H zKirTOSuim4i!GOtt5LY_QW!?>S!$8Z{DK$ngrSp;QNO5GoW@&u@J)GM|?Ham{!|XY$E*cg=%KqG8l*c{5Sw-l;f-3e`T4ViyY|qzB z)zD0tnCZ{3oB+{2%D+7C8*-tfC-KK(9oV|g%1eTj#)lC7$*AdVVI>bb z74&0-5TwI3E0GJAS|&lRRcVtB*=_ead4Umza03lI@1eVkgD;fM%X6xBGDG=`N?KlpxV!84MLZO`s>?dIAkKJt3=1F92&x|Je6(M z?+RdgQda-aY?XJAx&v3fkQ{NEhU{dRvXd^w@kNn(e*kWx7bF-4mDtbOK<_40{5CYU2%2Z~LhPec_Pk*4QDn=D&s|F$sp$(a{il4)gVc$tfOW>vgDl5&!%o=%JGC=pNZ zcay^iWv@~Qmbq`QLPA|F?V`iWx_fcsl}L6dwfUQef*Cl_yph){e}xoMwSji^Q(Qt8s}%T!p;ta9`)>Lk^Nl z<7eI>>Qsc$$1PXWj7r^ZA1I<&;93YoZ<3~P6$8n14EAAf91gRc^H!!)$phH$_{W&~ zE9dm&+_AKHmL06#P7NW?mK02gH4lqq?RUzj+mZ>jRjh>x!bdy2`<2D$0!GtC_Jzo$ zv>`1<0}*k@Mns#~a@e0hI6y*Ktnvr`{GZ(@nHOD$JhXW4^14vHG4iK4r4x|fje5V5!L1;jP{V* zj`oy>!p}bEbI?@%RoP>9SyQooP1&D1cSKn`dKY1`sPC-egN4@3tmIe0)h{+~uEp5w zq1b*q7=n|tsps+I1oLe9b3$Y2>~jVRl=8&rxwMngknrkdc_p0sk9&1OK^ocT-n2FE z2cMyuoT8qGADs;&r>f>GTGcen6hSJfdqUXZjkc6T zrF>_j9)oq$^p)j7SXnRErGFk}W#eM|m|H00g0PmxO>P^LMOz=sG0mp#)ZD`ri9$54X}lZs(4PM1yEHdn&&`%u_B`A3lOH!Y8183hlwrsCd@$NoMs3 zwQWNeUD0+1wfmlXD48)UMJ4F6ge3*yvPt2@jmMugE)J)9QZ2g~*=N_S>>!F0XA)uUzfbYI^XBvV zlNfP;HY2LCYzwOjPdc7-_^Sykpd9CF2RjnwN1mXa2~g-OU&Hl9G#Yxxv3urZ(@JWl zPPCf%OJy=#YR05-*!v$%XtQ$Ix?-4=$OYrkGpQH9@nPnS2YcZQdeQ`(BFT~;pT{s` z3sa~VQUxte+>+!e7lqKlBw$qI)_!Yly_@%$tsv!~E1A0h=D^(VI` z1VE9>ch;51uvCT7t?C0~aVSX5+E;4YRlKdGA0->os7opv>7u*R7!B;YxN-wjIfY|e z_5>&4vEoSpOjg>7pCc_ZSSi>JpOa?}l`Jz_s@O-g#aL}Tjn!iH{YvXTn&^{O;@d_o zADMZjC^)MHA(3J1^>f-wy@S1v?-CqG-G1+2K6~UosxO426F+tSgj|Rj6H&OJ{dW95 zG*>21oSNwaFWz_~u@w9`vsJ{ws3$odRg$zHC!1L%l#f=lDE^jwHUeXCXV1H7Q5#Rz z+vrU``SPqLl{W&T@>kb`iS-H=WlS=0rTnSSZn=u@_HOP*Ks>sAgn}dU zyx``W;~qw7@B+_M9<6^lLOzD)Phgy{5}#4|1TJkBYIpPK#?hL07irK7i>ZsVC^&Q0dxx_ZQsvOd zXzz|oj)Y!zh@7Q0&hqnuUrUq1I?*-1%LMK!PBr(E=lu%-qq~TaDMu19(-!cbo{~+h z3d~zzK^nz-hrtlDv>92muDyLmyZ4l4AQDNa149Qi9bk95T%1f(^wT$pF7lq7aazP# zytn=}X0d=517;L&+c@O}e1S=^01-EB=7epnwyXv%f(K^TCO`T)1*Wjx&oX-;0 zh~N~|V9f^lgg#o^YY?(JeSY86P_g(F+c2h2xhdt}S3X{Z=ZsEXWEMVGF;QqFIj%tK zgh&<7glJFbDnN&bbQlKg+xM^g7Y4VZMVXFNNOs zo|`q}WH*PgqS6CNae(aK7D@nE^jpZPE{c@n=TDldpg627zAETl2G$~)Fxd&!5nIk^ zlEbVZV7H~4y0L0mmBv`N>ob6Z34y1_hT&#Se*?GN0|CbcER$CJdmEx#OQ7(|h=jNl zRduPiKIFUo{EGm&^TV7pP`zDnLo8o=;+6xi2LqkQ1WdXGk7h~=QL-qaR64D z$wgk*?RBTkoB2}T?&cvyD5oUqJ6k8jQ_SSmQVZ4JVWK0rCUcb;W}jwu7u`>h+B7p9 zt=w6Y@m`}lQL0t~N1aOXOOI zk(ueoSfbopw#m+)x+zqw0(&i}OR_h{UeKpk-c)pS8zY{(egJV0iMR3$fC8!Ms- zMhB5uroL^pBhz8cSUK_7J6}zQH)=gc zvbcQp4Z@yu*u!`+X`VakV73k#Le2xx9*T-xIH?jLlYSSOmA)O^E}ssD-SgF)yfaRS zlDnDGisXHPgF#L5{m1r??QiWLJ}WcBzqfk$kaQwumX5~u_;ezc`i{mz#)dXV#*jQb zkPeRa#`;!}uB%qc(l)#F$n8g}u5byfzyr==KqvyWcLa9JR?4LdIs^~`4?Tf zQM&#~R&d!jch7EvxZ@j5NfScK7n4%GqLVrkEgg;pDfwGXMcbFO7Gq;G%pY)ul!_5` zM`Vw)4F`kw=RDe`XN8w|)NUK`A(F--i%Y~-n`eWH)o^V-OkJc0c2A_?5!tjepn`g_u%|!- z>dHwU^!8f^GnwG1HawFZ?3HO=Sky_DujXV^UQavBJRoyNm5kaO?R9UOX3pjg>>03N zjOcJGR4OSQ7r#EfmT_UyyiaaM-QL(RNH^4?D{CvpU+QV3o2)jatM@$z5`}9Zr4&C{ zlcqyAyz@yDM~|K%mFpoB8SB*s$!)`|0ON8Bd)HBWdv||BqJn?V^rw@nRix@Ww8^Hr~&ySOE=6fMQ5L;3NJ3`ys^mhS4rD(eQaQ2%Vf{|ia zZ-IAcFT~lCO9i{xKX*#KMF)J7D!H_RHpAU?nbU`)%6j-p zn6-+e(h}t{I`jn_o*A}H=WbnU@Q<=#|35=EWSQr*4>?t7Kfs?VF5wdI7MSZ;oD~hN zM`Y(R&Klhec4Hi@q1+S;E)Z}hdmN{G3iE2cHk3B-gD>!D;A54YR^W)9v~e%=^==OL z*3Zemvu8Q_&EHiSiTT7Hz@IptdbKh z)1wd!GY$u8T1KVEFsB^1BA}*@EY`ED4i6gmV-Fe@VC+9aEKEc@EtnIcq2*H3Dgrv< zsigF|=^WsUOIsbDR};?#mZ%g0gp0V?&D6_oE5vELom_p!bbh`lP=q}DK#XJ;4mVhW zM@K*T&NjgI6~b#Dx`yf6>jqCSDbO9jJp!VJi1r$I*Zly!>=s?J#|Fn3pu)eDZ97bu z(+ZS1r!i!=>3YcK2+rOPaU?BtO*gE%^Sn>tl%CFpnC#i?Rgk?F>`ifk$+R6v?-??$ z=!c{*1)m;0DJCe(ECgVRi10m_GCD%XECl)@FqMpihZ!4wx=q$UHBCm4aY>6pmcb@V z;%Oa!-y)wg6_NU~UOapxGQh)1dD9|4dL$yRf_z`x)3*054$7{HI7;ig{1>at`sZ{q z8r~!E5FT0gZ#@xZk>R{?o%A1xPkCkD_a2E;Wsy~QWjdbT67_hP^0 ziYL7{MDKN7xv(tF#n~rseA1G(Xs(A3bg##JfU>R$rs4^2El+>03R;K429K;S9}7xB zxiNt~tFhpuaiZ-N|YJAv;_nunPZ5{+(!H0VhzdqK3%5_M36LV_17v zgvqqu+q%(Jy*DF@r)=zY#Plz=ZxZ}XFdquDEGFGQ^q*l%ih#)SGYQxTGGc-=fBgoS zBqo#rk%^Df{q-C2HYk&UjE9*RW1&a(cUF$90LO+lr3{B%ro{6)`H4fGKo%CuU5k9o zx8ZnMEA2Yu#ZN`#mXjaL2e=GPd1fkkr;#bIABx|tahct)%W8N}#=(B8Wc)~6^xIV) z-Ddwx#btg=Bxov5g-2H7`>**U@o%|tJh{yVO(~9gWh(64#Y2o(^hl?J0WnQa;(iy*xMh%{U;ugF=v%g#Dvz82&*vEKL99 zkmmGnAq~FcUm*>T*bkCmIAyf%`ji$Y#*yylCfe z=*}c}%*2%JG_wwEjkTzA+HrLSkEQ=cBqB&!b^ z$!DdqD)rUxkH=&Sl#x>kv*@ovxI$BYOAd*3Ri~8<K87@8dB~(_b3pVGEb!<&7>|)sQ#V0IH=t->&E$*GIB14~Sh={g5W>4&#`6Qv zVu>zU^(4==sEjubaAr4dpnn_uG;k6n81)~hSCGf<326F9{O^Od;TSq@u}BGa2C$|+8Y zVeKZf+2Vyx&PJCVQ-ijIUQYT>UR%O6mqoJ?*!G5B0@eqyKR~e%$#_nq79oRsOT8nX z_UGemsX5I4cq$Kiic8#-)o|lINqLHc?Z|T6|HwDIBCF`gVs;Y?!1cPsc`12HnXL3G zytBx{@V;Oo>Ujm(%um7WqeYQ>Jism+hgzC!Tl zdt*=^!ON`I+tq~CBXXYjjfGI$!xWg>EdImLPhYb!jjrnJ6bEZy&5EB+L5B4@^lJJ& zzb>`Rjlp=&125a@4NBuTZ0%*$SDyR^-ZaAxzcYc+1D}kVmL$gB^M!A56OG5A3)pV@4^d& zW8AVAd|GmL9dYvw^a~8k@VF*TD-Fg6Tq@oBH(2tZaRX=JQ#$Z%%XP0~kaK zJLDg~Ki_jN_%;USkX&5puDa{uBHo=0E)ei_1ZTe7-$kA(g9e z!%Jswjkn)GIXs;?an2|=H6c9=ucUFiBz4xuoj+Y7Z)_ZByO~*Xa%pO=m~(OS)+}{W zH96}&t&ncjKU{AQr!{ivP;%CKlVZHdH~IPVoPTb7X2gF_%d@ZOp6TRf~FX@FlFn37k&&jXnSeJd4hFs*(B7Wz6cCD>r z^`DnK(d{2xaE&YVA+#E_EB6yPnIWHX%sfJKNuA&K2j10hRkQ0ekM?iX9!Y18r`^1)U@gaQZX7?cv7V^zNp0%%|=16j~K3-)=ZMHjgR^H;d>o z0Tt|Ke8{4I69@)|_K!iSLq?SS32IP&D(DXAA!`3ou)&p8q}pp|pyU?oP=nYOt0>ON z8*1QNr?mlE5f3S>`RH;%mYU!@5e!Q^M~09_Vhv&>vYR;)N_bAJtKuhaqJ=_)u@3V~01vLg8cSQ`z?T=a1-Q3-F>`$BooYThBDuZR*S;D{iqP~ZS zOyfOT;E}bdJH0e%kK^3$1i!Vu<95s|z9Y!&bwahabOGM>l{=ncNmn#CBLKQL^PS*5 zY(Y29r`iT-gtS6IPp1N4${(5!n!=|B;}k(lA)b!$jd2$N3Kl`@fao(DHx@#lBnP;o zPv>uC&}S=}1aw26%oZ8!vrPfXw(e`u#H(`oiC5M3-gH(qY1_bu83Ikg-fDkx!)~B! zrVl^m*)DQUGd;Z>OJ2ya^g^CwEiYE84zHtU&F^VV{srf7Xz=)D#1;cVv<`2U&kZ;SxHpk1LMghsFUGA z0kLi2ki5Nj$8qez zPQ7r2&*e`omkT7MsB{PL@-@mc%yHYuLRB0~4oc2>s|DSGYVLetf!b2qkTWdqu|aLH z*ru$bo}X!t)52pUX`L;7chf$xy&=C|XH^@k*5I7Kgi|LUVv{H+ zJYd=1L?GAk?ms|bC>~-VS7+B9Y*i^1cG$097G$`%x!`U)DW-?64#L}b_YloX{hnkeD}u&x4dbBTYJ($3S=a&yD%bkLDlMZG zsrFdZ!d9!*)q^7UYkt%J=^usg_X%QrR;GVn&xHTK#t@VPjgAC&tN$}YfcnOy;^e|oOmk1?=Kjt` zWs4@?*@#lNVd7eEq^xl@%Yv!4lg#XHrasf(Yx$$?g}Vf{BRcM)Wd%<9FGpbQ+qCaY zGie;OHXo;XF@9B?Ymk-VvY)id`E^##+1*Extm9aHQf#?Y@8pBf*BFfoF>+dnN&DS} z;+%hXp|5w$$$h08PW-90Cutd6Fds#V&+t;ZudDacZ#|bb@hd40FRtrY#d=(7wCYyQ zjX4jW?d<43KPI;mZa>|arCMw7m6cV~=Ij(xyyv`=@ee#lW^1*;3M;yss{?=Hp1^E`^en`F7I0~|$GGg3F4&yOF82!HpWk1g_lrXm!0SVL=bvqiPP z3Bu)Fe&{zrxcwglq3W9;Sp2^cg#RdX;%L1x8NUg_kE|l8S1#lKL=ZULy&g&(w${LB zxEuc>2ut;cuef+^M1K*4;h`>=aGlX@I;!Ymjeisk>)+jjm6`s(9;5yS-k|>`8Xm=hyd9b~T)w@do4auCR_e{@WT&>`S(uXkgT0lLY zn99O|E5^&!?LI6psts?*Oyb65f4-Yg9(ozGc7HpOJ>>x;f*?cfN#>JZo4G75l+!=PTh9@{2>%O24s zN3L*;z!gAM{CxyaK~6BPe=N9%JoZwKwsH2ig~;Jmul zaJJj-;(v@ zx`Yv;$E8jx|H-*F_4?WHm(>hzB-}jO{hQTD|A*Cdru}cXnvMTet3mSFkNjzS+SGm)XUCLT=(o zJhB*1Zli%yilkndwJQ&k>vUTmvo}9?P&#=@r*vD(^2uCI9v8EE9B2$K}^Rtft^T97u|k_y_HkO zrcJ0E1<{pcDZdRpzcIC|pWWpU#^3FiTcK`FZ#=kg zYqT|NT48b;{z^jduZq9qDi zIZg2tw23H;l#|oN`UHW>?V$bC!FBU%V%OE#dQ@QM0MmW60L?4_;4+gne8;=h$I~j3 zG)UWku304a$?HsTsU+F_)#`J;?m3gGVDk_>7MOBG<#mOC511(|R`jZQHmQYuotfqp zl|}0xO&PSo(;7LEO2ldabR`tl6o*8r$Vq`VDa(qEk<;Fdo}FBIW!!?J5t%>jj~fK1YV#bDYhJ> zUTCgBSvwA0{gS67{L*qdXZ5P|Ge&W2B}eW+c48(`T{EL&_OZ&GimMolXu#&>BufxtyI+<@;|!&I)L3@ez~nq#j(+V_`L9bdF3 zIOM$bqISZuZ)y_lH6p)vpG+`l55Wv=D}Ehf(3QY$$t8STIX!lor?kAjy*};t` zTf1;Ie63oA5T33=5A)m81#ReyDDb92<|dr{uUD1v(zT}>*JWqB)yS$EHHj9)u?Z99 z{+cffY0k~tcl(J7#Y)TBsKqdIW$FZ(8b*+LRK6eCgx!e%)Bxb!Z!iFG_}8c~01rxI znq0mtzA%8WzJ*}L*Bmp>|@Vo+X;<9w|Z0@9Ir1j9kFGNCMe2qJrERDW)y z0g6LwN%9?~#6G{4f=4MV#4D^wA>>l4gudc?F)dB}3=FC(&NMV5=$! z(@Ds8$;E#BqFqlIDkV=J7L$_a)rD=#mv(GdjUk3+^~*E4EuGWs!h=pDgE247(4}}? zc^(U815}qA6gIZmQLN-8?RtM7Y>R@Po&-;_ZIYqR+_5Y3MZa5M4`|c<-%$Kb<77=BCQ9GWj9kea5EPx$CGpMI>_!7$KRV%8NzQKvvD55 z&vSX*e^g!3c6wWeegV?horwOUs{aA*|F>23ll!A5?xsv1Timc0ri=~6QJ!%O{S7$j zuQ6Ub4%oMwGCAG+_#bLfUUggg!G;W7*YI~#bxHc?MNk+w(B?t2xp=K}2VvfA+K9ku zcw13L%^v8wj|27;hh4L~H_RPKeNzMPL-Rvs=(+oiXpe>ZDQDztzLlo2aBJv6Q(g3Of!1_L60pRj&(_jLemLxX00$2cG0bv73!^o+Z z1p)HGPy@pPED#x#3J3GU^s#Wc##0WUxJ#z&8mJTG?LtRjq6(-DX!4C4ut|1AfWSdP zHX3Au0dSuK`Dy~&Ztr751=7NX!CE!UGXmoJKB)^tjd0&(s{>(zqN^)v&OR4D^B zDh&9zKV^KV6>NnZ`3Vg1Q%n-JOk8>So8*@B|z0R3op5qr*Q-4>eX!6x%2 z_VgM?dF4yT^vfge<7({ON7wkvBkki#`&-|2{}*NN03G?$G>m398{4*R+qSKVZQHhO zYhrG)v2AUh9{E?&`v4@Yh79eiQg}{%HvO z6v_M`5PtNx0Dj^mn_G@=#JEhHsPE_V;1_K)&E=L;^-$hx&&dRG7-Q~V2=SaFtcv;H zBkS+zePx3|{RDN6JW=|Ov-&@nTyU`c|J#B8zf3Nu|LvO4O1)%NpO9fkDp^GOkFJMB z-G4}nYmeks^t=-6; zN864Tk}d^~wX(_)2#9Ug!yDZ-s0Y5$)%eaEM9%Q7pBp<(x2(&;)BjsV`uwFLg}=Yx zcb0O?258<-Jc?|w|La~skJ!GdnJ+MgD8rzl;YIXPkweXYci^#){vR7_E`9Z9I)zLA z0*^PYn8#*Ic-sV0o4-fw;fStDy{5iyn(=b~ z9&e2SU)r$iGoEIqnIo-*y2o3AB5gFbKdt#~5*&KXq?BqvH&j0_hEy8`WM@}}UXb~v z!~fBcMw|YCqG$S+J+5ecf?Va`C<%oDAw{Z-Yc1Q(DQUbKqhc`_>I4PHcYo>?wa><+ zc^j$pV!mR~?%Wc@3?Ey1fHatN+ZR9+1vdy23izeSoEEkfT5f59`rH=QZ!G>R~C`$j@$ z3KV4DZ(`Xf@*HNgJp?RIK1x!blJz|VPG;YvB(}c{LH*{}-=vbmS+D0XE+S^SXI%Ww zSoAhuC$Dw#v2K>k#r+;KmA1{zc74r+zs%h{^D|f9CTV+SCcn(!EUs8g{=2zb=C3!} z!)^1*Ykry1C#}x*UM%?^IUtNphQIVjj65&BIj9_A_d!DDG&ml)E4x~Qso!@a^8czB zJ}Ce2|3+$C5C0$M&wnt~;AHv#ZZ-OE*Pj0}S&F_0;Z%hjn+{(b@UzgVeT0tOh*d>K z{XOgd(~l*juL>gJgZJ*;?EQSx_vMARN$%%E({nZI&-X$BxR(6G9rm|Bmvw*67N*@t zuC_V8a1Riyer?Uw2nt0dakVAQHUid=0|Y)TYFK4cusO@@SeYR*|0^$ zwUM{}WU?_u8f37(?+y9tqW42_Gbkv@?`?PXajRI-pfu$hWf%FCJLNv&)Qs|=59-sp z+mypHNvk3T6;4OMKyt$VN}( zmwS)V$xHLjPw!DgX6<^heFIRFiqAK*~)0f%P9#O zsug23wX;$8DSzw6qm+v?*BaGbg)>$i2tm*YC`M$#?}q(IWC5rFM1;i=uzj~tBoK-q z4Vh2@zv!dfsgMf$3L^$O!9W};$UtR4&;v~1ze|Il1(<@t!zoXdWP*W|W~HoeejBBH zrT$*B&IA&N$!%O$Dk>V2lA*kaEEoibKAOxNQ>+%Xr%Wx6K?MRSBb6~-xEL_N7%mb5 z7QUnsO#5n`TsekbWy{UBCY(G~My_+M+B`^dQwZ20_bcAb&m zJ;`BNU73EV*69~sJQe>jljD4E)QgN8c=O0Pa^!%dW_(C%N-b_l2$QACIh#|+{HPq9 zXG0K{GP}6&jZJe#jU>MwYDg3NY2+?8nlbDOW-WT@L|@x0w1m7EqpcTsSX-ad`H;HM*6Vb% ztU=%PkXlV{aOiZahOgjtdr*{Y2f~G4PqqDbLPRe=jHr9}KCqx1E8c12Wr72+bCoD2 z@cJBMz%%KmIwxR@Gl%{krX>6SL#d?d>0nC8pkQpJ;$jQUAWz7|$oP-Hos+W*Ar~k6 ze_0u_G5zoVy#Lu7Z%9|m9%m%YZ>9dv2$pV$-rM&d7!ln=H+E}rCL{>Wn`vB$qG2Vt zZ+~C8cDTfVS<$l8$g7wOR()lOkfpe z37MsBYK}4&R|BxFu*)|S;pbRA3IeT*I53~dk0OLDlJ+xKO9ojg$I{H5l1a?|@YceX zC6y`t=JHxxpFJ9zAH9?IvQ8P+DH;eo3ZUb2+{dF-P6W>|BUUEvQ!Uy2^QQrMQ=Aqd z6F*taMVR~m)iZ8-9Gu5=oeU!H4i0bJnH2i4$Hq!^8nblRf}fcS`$kBbZP+q8(K2S` zb(BZ=j^A*cojf42!a~S_S3&~P6nfrFZ1$2|m^pTglzE*pnUwY~DPaOJeWpts+0*P|R^7}G7JvctseDmbXummLE>Fkf-;Nm#AvDtYnZlQW4 z=ME`x(D=a=-V&Tx@}*nLlEL!~B$0C(IG899YOhgH9Sb}Uq}(do!L_s!q0R}Hgce06 zmoa6=G}@@J<~~t`LM?4WpuwL7?6U1S<_Q!evkO$`bBj!t8b}GvX`0zsTir*1wruiB z!y#mg7mRgOo?KMQ)aHxq_qlPPXQGfGKewUATryd_G@{uxX_^JfTZ|nskKFvJB=2`t z?|e-zKxv+-pgc*GgJ>2bq>2$e32nSC$al#>LjaV>8xnl#@A_+&Tv;axfxjM$+qT;% zXnDBrrVG6v7kc{xAmp}9*a^5<6V-QjJMn)%uFeu$uq=SlJqcs#5K$qm1VGndi^nak zLm~3ICt-3jxSZ`|SmyC>9n-y|mWZPskHX~CHJ8bo&F;g;`zK=nkM+d6+oPYp87ioio4xzYgPr^mZy>QyQ2|;?8jad5rY#m#1Dk$Jx#Ho>5p4$M?&kTA36zoainlP$J5eq%PzP6`?!1;$W8j7S zqpLrf@{)d)l`AGXnkY#91yPXli!T2Y*lH&LQ0V7B_DxL1vS}%%YhNbJyoi>0>*R}M z>__lne%? z`Lr}WZ%Hlek*`=Qu*{OeJfD1_31RAujNoGHa^g?3_sj2Rcbf-(h_|;n?>~ba;lesX z=C>epvXUNha+LgsiLaNe5sTp}NQ(gRm2ooO1T$quUZFtH3tfj`(ME3AS+GPcBWhS! zwh)UYWHopg($n{o1}k zYYszES4H0lEehU!g~_aT6wP{QRGB;U3{;DakVTB(h+B$AZD>-N;qXo+?tQNexkYRg}qkk z=;ef4HjA)~QB`Xo^s-ZG%UOYq&S#{fZzV}`B|o5Ky3rH)@ZeWq)yXi`ln&q-POT_7 zBA{^|jE@W@!cK%=Bx|>^yminH>k4$N2MGzVRv7)X-ub@vQO4i(S=QDpAVJ6L6TQn8 z4V&4nB`cQtdkEHuvR9ClHXkj*kP=f^5jIgoSJy;dUj7GC0iI9ZG-SK3CGIkXFHs8iI;K^d#asoXc6c_k>Je9t?0 z7~YB~R3Strq&I6j4kNms>kwXl6{)_~SkEvU?*^HPurn4}-e53HCM<5L#3L$+-`GgA z$vLhjWZQtI!l}OmjkbYoaQ+a>-j}!7GdY8>SmaKky1pa|Wuu9F#NJ9IlkA8{0wjyS zGtBc*k18XghZ|sU@(}r`EvOx&SwuHsVYEx ze{*t9!SMZEaa0JW80PH)&rkXwTL>=dInAP4i)_grz=4X|{%bH#UE+tbE)HU#&DuIJ zn;55yQVGTFin+uL#Tc!kq^a2hrpr~{hK#MJWl{`dxhqs`3z+8JseYacYbxF>D@H&K za$^?(P7m-#?lq5c8E@7~|%@PEYVPc`kFL;)^)L2xNfXR7noD0wn zZS5%UD^qWqal^Osz3!GGTfAC&kG3LgAC`d(o^cy`l9Jso>6@$y)IirnqADNKUFW3d z?7)bYeEZSbnbHx{7fLIJKcobsCpWsOVL`qmM!UZnPj_8P z2!R(%o0g0_j3@J(J1}_2-78kwqBL(iK&H)v2nt{#3}ytoasrFyRMj*}{s+>sN9biA z*|_nJ(x+x$pAKXsIYCjy(SbNe^_s|M+L0A{llD!`cE(dChgES$f>|+B#yKVO528|L zpm0t4CMs@9qGjpYce#{!8H=$`e%*73A^M}!#uZ$`ntfy@k{Ci*>p2X|1#NZ)73M54 z1z5kFw7h7xa0XYUwZRY&0=-HVra0YV<-B67p-8c+gn;_wL{y+-H^;FE5Ov=FfS#Xf zI+;duV$5==FsZq!P|AFDP;KwNZ+##3?7K`po6X!Yjl8=wGRd+1a+QMau4pAkBZiuQ zP3WXENZYcG+wf>)qH7+D+p+dqVk@3a0!>y$A6eV2#qIS2No{!jYKS&Ca1E@f zjK2f7HP{kn%7zshxD<^AN#u?*Nz64=j-pPwG7wWvqj^`jUn!MR&{IMtwgzD=Q#8>= zrIF{6v(s>+cQ9!w4Kdf;YYoO!hqHCj3Y5`jA=SrP3p7Xd*#s~ z4~Q?*U!^7ZA>P}AdJ1Z=oO%Op&p!YOux6-|f5b>BatLo2cR zMkP2-I1rNR=eEX?vHkq^FwU-MB8{cw2EV6JEnGC+_ds1}rDg<`r)edpWnZeLcWRqQ z8d6Izb%JAd5giNJEJo9+8~L28NUzY&8xhCAg@G5!phvg!qCDFiEnj>-RY`H;RAh+3 zqi4+J=Y}TUGT`LG7y8x*G!escHgvUgkJYVYu4gjuoj0`#GV)K94=&bo@>%N}3YeZO z6zviuV!ONg^NfxONeSlM@s{QY%q+$aqA>sbjmaQWz-p>lS2HiI!C9UrK7~Y&z-$lA zcVj@0Wc^{>TJGB0oq{z7U9Yn@?j40Y8^6E!^Vgm`F%cF9Wp0GtsI+v^lp_^%?mj{( z*3;q2Y(*>Hlbi-aMb11-Mcz&*J)B4$@&f|TZKcok&f#dI&-l^O z5ZbY-urA}(6;{O;8?l$H2G6BiDq>IsMDDwdBgwANr6DJ*TpzvyHN}H{UG3`BOmdXM zlB{@tk45R^TWOS3?IIMlyCIS9&ELnmHP?MVJX{BmtQ`65jNY00hXn<%>pu;%k$a)* z8TME1Q1_I)cv(FKve|xzVNn0hxYKbLbB)hSp}ni^_+&ckUN|%Bb7BNj#+FE*db;T@1!pWd&wMEkyjX!& z|5ktf*yG$uxeYCzGkWpz{kt2o*xuQ?rnwcj?P&ppuDaY$HoN+Dh6{s>l}DYo{6~Q; zm-ijw$u|<@z~Okk>K$hv1)h2W0k4nWMAj5G8gUbf@JoK|2_xQbPpKwL@`vyJx5VTt z9?;>}_Y-GtPglLBdGqkWI@f@jpLoG6W)untQCfYJgVBxO$j8nnzLigTDls4el*d$w-;-< zCMfaydtYr^E3fpl@uVI~YGHjc_wBk1&eb#@s@Bq~RZ>&743O*9QdC>>`DVZ?bj{q& z9qd0dBr4g99{_VYv+kAZ$Z0|ZI=S@yFmrS1@?OXkChH_i@8+Iw_bu4D2>h&nx)>a9 z9geI)rqoF-;1W;mCu7v-^OITfd$!Y5YU;@vWM1PDw0URwUGtE2HoU9JdrCjTTN|vs zUi;i)p??-;BfMFfGUN1v@h2MP!!dcYUxWej0Y^iJr>!Z92z3e?dPvvqjXkBmIh3ZFaar(*_D|8L<6R+vk z-8d`OdEDKub*;=~4e_sTe02YLc%%(&Nb?Dw+8k5M3**!a!>a z$QDZ~toR}2=C2PovvGNL@^T%7q9E{;vm^hSnPV`;3E|2jDj_9KAdmwyU#lK`SwQ-* zz+jKh=kY5I(OokL&3+W#p#PwUuK%jxhrP9oqOVN53^l%fy_`kDB1s&v6=u`wk+l;i zWly*7!$cQ{hpr3GhfK*0qnXQ!{}Xt6mY+ur@j9DF4BVJojRJ*4$g&k_Gmvc z;-rJf}vI_@CS9!JHFKv%WR!D@>=t;l9 z>nvHIoPrce=DXIGAad9*_;cM2CI*(s;)tF@w-IJmSUnVx-(H?~d-4q$z}?w^B?9Xz zI`aV8UG)3oDfthkV_&~_p~B~52?_>%eq%qk7uunM7=Pg!6uMb!J%}rP;ZymAjp0dYwl_fl7W7;fLdDdvvCbE}!_n~S5 znTD#{`>a`b=)<2M_rDL;>_5GnoZbN%CB)g!{YqiX%UV9gS}lo2au%Ls&AGM!yb{9h z)NWDj_;y_H75%tl0I7BNMZ~Y>m!)tn0pp}*2i_dlcYAYodRXtG1poD!PvFU43-0XT z3~-D1@CgX7SJ!*TznwIhAa*ny=>DE~e=D-rEQaaYd z0ZZ+!PHSm%M48H5$mijTO`seNl`ixKn}vHo!|De%|?H;U-Hx{vnX3aDcw1hto2^Om2lGH zgerFNK{@T{_0BdPG^Req+f z6OI|+6#FPR>Ii$b3sGKih~S{wiaWKaNUqxwoq#9$^n9!mS`GAhvsU8E86}r_1WWd+ zE7m6;Jbbx?da39Tt8@#&8dOJcKms8~Eusg8a73>kpxuJYM5NI!+7MlXA$#?S>=0Wl zcU>*UTP`QlK=9MQz59OyhrufT5Bf+Bj{okt^MBGuGBW>{K9ZS{<$vA5{m=TyQcb;T z(l#XDe1kcE!WvbBq&`epLIx-)NKY6~#sg&Z7!^$t4%y>$Rala0c zQX2>c<0`6~6&t z5~d!MREGT#xJs00v{8nI5JsV5gWu<@WFZ>+j0TM=b)HGcaN#*?*6^XxM@b2k9XPQ} z0tc|BN%tN4djYugt~3&}A+unS4k-a(1hRARLJqR76ZeMn?}&hrqU&PL8d!nR9JEU? zC?{ynm>*n3ctSxr{RMM0*@ zG^E2bl!pl=VsS#!HPfbv5xAhoOd7S*lmIU#+3YwqMKxg8p~^P^a*a8oRtNl*x;kdh z3Jh=`sGfxBQRNB~QiTN%15c3z5llN35sDS=yj3+slPdYcJdnmeNL>Vid3|m#*@V@= zG<7a+m<_+dtmOtXGlQ8AQ(mr7tVN}EQG3_n`&q~jx)ph$ptLh|WLcsxZ7bRY++Bu3 zzBw?gkJ#}7ytps-Agd>GaS`NeWjbuHW63CA;h?e83!xxN!ll2zitLE`Q|6XZYg9|v zP57NErXqgKO&{J&al|9|f9(9+i9_)J`#0Y{pMb#ctv=uH-Dwr{N}$K+p__I0d18Oy zO5pF;Hls~js+;dL)w8!K`n0;Sb!G7}QOft@ZGXewpHH&rGDO+?5Iihq!z?1X`t!Fl{4rRnIE5IPs@_j2^N}FB8H_4nl)CctN{YDHGvvK<8muq#+$IQ zfyGJm;8h?sox`N*Np#*W&uCH6~2_RPXSVvAOhz zah3Dc;ar;-l_plxSAp1g7KI{Oycl@n;tJ~wZK1k_w?9m|3tm+RRD?cBLk(_yLcP&ZNcAD>)l4pDkpxM=Zeh^7^6X+ z$aR%n39wwjnTw3?d|Ik?PZXu#ALcpzwP-F=K6oaFX#{`j5qfVGdPp5|LLH*l*&m6} z-DXD=wxtG1aie@$C!AigYmKAuX4g3Tak8{tYAxTL#$(+xUH(e; zdEC1=QSk4URG`$m-$_}V8fG6YV3`$9+Z`vjt4%oq)0~TfrzElc&X87zv zXhBgM-^C{MzKC|6F4;|Hv-Ip=&k$WMYU|b>s@HbR9$4d(CTk-UXxtuJ(TR9L9DrD! zwAM#PKPZk{$+a!-VqeR5nNp6qH%xK#wyz#oqhKKHR`vp}s&&G1*}7a;(+jm`X5h>X zW1kN@gwPWTQ$WU8Zf15u7+%D)l`On$@+WWxpo`&~R4txuDbqM)0rgVaR>mqKt@#S* zX9sGMPS(D)P{(?5Nh_qGJ@sZiv4c4_O+4r>aiZi$C~^jn1G$q8TsN(V^(s6Y^m@*F zY&%+K56p`OmHwA9J+Rc?23uYjk=!@fmlgY5NxVwsE7eTDe8h4+S^$;k3JE|NjU11{ zukn(t64<7Bn-wv&+68cC@(;-G3h{ z6*Ma1Jhy<-FHoz+II9$N)F523({J%sKEp`N0V@)#RRChUPQb#c1n$`ej+*A6V+m}r zCjg}qbcZbyZ-%^(U8!-t5ouU!FTURYBkt{x3&g)*w3-m(m|0J!8S@uo84Z+<$K|4( z@(J;r((7nA=*IcNC3$MeSFE&~y`q}L{zvhydZTg6&Q((E+Z-oT#4i!nK+A^_f zjkB|%f-Mr14yT2pO_|OON!@D8xzo^2sqX0_m(z3ZMDdJz?jf)|^gsb2?gM(gf6;8o ztBbs>i~Ogio|3Nk!N}u{NKt3fg-bcHPONf_B^^(SCe-u)UaN)3f+dUaluWr9i2$ zQLcc2yzuu-0p*3qm5n+Q7+}t z2KS9{oVh$8Z!^&smClr#eD0ORoJOI9F)fU{+=G6I`mt2H!}+LGx<9QDR}}v`9CG%7(eg#<9pb4f7W~~ujdMU+`k*lkCir@ zgV{0^U%6^mOGeaM$zfsF8eQu-{M|i#IMV@rEHAHzTYcN{ec{mZLuf+T$yx1(LhCr$ z3*GDp`QF}HGZ!JluhJuvqnC9$Z-%Q!e$IQl)zM(=Y_r_Z(u!x;8=u;<*`hK2sz0PH zlBC>(f2Y#H9awPD(dhuCfwm&&^?cgnGkMY&j6&DDm?6HY9nQc0V_bjLLt^%cyH<^K zH6zY*Kn=6CN{Vt)Err4v>=4hn(Uc-?ts^Igz8Kxsrdy(`3I3z;cU|rI5)jd$Yb5~; zO~XP9vf!&h5Ogqwru|ny5YU85zk!5MWXGwXeBReIFags-ZZ179I_(|c?~7@#_8bpf z~lHnM@PN|d=bz?PB8DV>v_VxVCjJ_ZbK+Wv0EY>uHq;4xEV8vK<)_SQkvC z>w3proIR>|3)EwwG#!n5QF7@kjfZeKf@Kv-_&$ zY%6Z8DU)mh?kP&x3CwtUbXXqjumsRZ(PKb`51z!nrZi|xh7+VV6-Qeu6blqLx=bqML3#+ z^62sxeo<|?Lg?=KGLz@{qaHNOLFUSz` zn;0vhJTW$+IZ`1sLVa4OJ6*Kf;BJ+SIQw~rjJoK@oRn+|4!4eRkzrqUcf>u+A$6C_ zN*nUs55MaPULnkPW(7u49x^1jut^j{`wUMHNAA{Y&#jxZ*z=WgHWs<v^LmO7vVhB_rkD@;tsb^v3;I z_wGZ@sFwN}B3dKE0$a3vhy|Vq^D^gJrmdSS?VF2?ec-q+=fxyMkA4Y3 zZ@1se^UcYF|J5W9&6OwrG`972hx$)$uhw{3TfQ5VoAoH`keNQA3fr zj%sxA+~zt&HM|IVx=zif!J1RR%-z5r#GN1yw#`s1nvydMc06=R!=5VVBAF_A?G~L% z8P}OJ@l#jxD57V%46qxkcBqA=@!J(RfzxSv=%~w(10$$~wW{c|yt>zclG8y0<|iZd z!RlRlS^qpbZdW(QGnf)X!6mM_!XlmlSoM|2TpjqD>TptzHmD{-eK>ccWft^zwS z?eTiN+_5xACreLd@y`DKeUDF{VX$W~;BPalsD5@fxL^vVjzAMv8&ap*4A*F=Gn4Td zh@#}TZj_~d0k>8|^Z!-tnXCH#QAOUWvL+0p6xOM%93ca((H(V2FMSqeezw9XrDc}z z3f8D0+)`uk$E>vbg<=U9gH2^MzQ@uf*NoO?+zHpl9&?K@9w+75>83s=T#?pbmh0uB zG+aSrniVOflE!2~X9)HW9tKTa&F^19FfmDesomU!`(YU0#5NI{kQPZeJxey;>*)rO3|fl#)<4_T?U} zFCkd52cHC+DQ1B7+gu$6>>_b2NauVcv&DE*jB!J@q!C};kQ0ujZ4*T#jc_op}AB`?t&^5|1*29e`FN- zXyjNSKM#O-jMe&hrDApV(!eH_t1I5)Rl(iyUIyWiI8onunk|yp<_I_;1g&%Ykb~Wd zU=}6nQSvh|yd|x-brghYsULbBRz7eI6H~FPFv$P=LQC+l62C`M(&;4RH-1PEujv|FYfgG}UDjj&` z>*A*({p%t`xn%xp@;z7dbZIV)<t_qH2+DA5^P3Dijfi!1D`nQq}WQ%4~quI^^V{kg#P#6nO8Z6yTW^#OI6c|SHcPmEa$>u=p^+t_Mi+6&7a8YMl2aQ7`XasgG#a>S%s z8|1Q^D}M$6*BigcQ(Ia@Q2OaB5JAOwAK3WM8dttExiomolP@l-$}$hX{Q^U`UC5Z$*)O-||y} zjS-icpve%`nrAcPzm)eKS9<<2RepMjuO|83_R6y({3iW?qJ@+i+oJ2&%Lx8QOX}5> zS#Pxls;U5Ao!j!itKMo#zNr;8ii@En&9W=!PT{L)A^_Q9|KjOUF{TRr3Bj<&A{`<; zl+eH$m^k62I?Q>Fkj@+zeQ2Daf~sn7*+iyxd*-2-r3xHm)g}QqnNz;mwru3mfZnaN zii*Wj9h0_>5F=kU@~Zsa&%X=q{vRi2={s#dKTiY%KJF%tHTAQtL{|T{UZkv3ITbdq zlqvHmm8ftBAVBwY#vZT`-P3O^xs1o>_r6Uq82G=qY29y~jVK7bJB)}mB3xbmW;HSp zmgZ4uS6K%W^Kv!4>~bbHO*oLHmfm}hki+nE&o->)=FbHamXjjOlPW6lN|PGVd7eZG zUva3XP&N>7^Y#YUFd*2<>t{Og;3qLsp9f>0NT7$QF6i9Nk)p29oMARU%>8xOd%AvQ zhvEUZKjA5jhN{flCjfai489W=VkBz|Fj*j9IgiJT#k+BSW#R-=xAliCTKWp`;lh&tH|;QIlp2DiIlW zKISun=qU_y2re`+@datIOvKhu)&h|xv;I}wslK}O$6Y#~JAm7$r5Fn9(h|!~v2BlX zM=r4iX*GQnmN&ZI;QwN`K{D-)*!KdET9urf6x&6NX%%%Se(6jB?1Eg79zEt|NvMNG zP5-6|Fz%!)f_3OfObv7iPf5+OJ17E7(AV%CGMg6YVpY(CIv`)Y9Y)r`qQXF>rBZKw zHJ6S9C_jI`+3>h{#G_ab8!-WrBZ~Y*#X34LM1+b%=9~qU<=enITe$I<1Dx}<)3^A) zD%Y^~3ALxpHk3L`rmL>xFi>u}weYtN#_ABB5rlFKh@cBCpE=(~>2>fzlPmg>y*0e4 zf-cs-471wMWEN$`GJYLJZ#Es@?S4P6g-}NU)uJY$GOC39fD2}vw6HHxJd$Ju)u-R9 z%j@i;EbbXq4=@4+Ps8req7G6Ast(qg>1SBRZ{f9lQ59@%<=`Mx9ACV=5c#krg8n0lm z(E5vE@Wq0tLhH!@TgVHyEvD7;3@QeT@H&o;+F_A!5nl@-<@5Hg9-Y0_%xCp?cbJRS z9UOnlejB#Qc5cOWA?MaVAoihkg`;*^Pic6@)@^CN>{1AHj31m5U$ z1Di-}y0}bF+d1sY>+JV1om^l`adYsIO{$1G$3_)|s3ig&EJmIk9Vl=3?X0lH*Vl}T zyuYoK7X@58uIaqVTgk0WL%8_bAccVj=B0PJc`0`13BQP1y-7{y)`V2t{&3Q6e_JXwEveoYfdNk6Z2x+*4aC=W zFe$j74O+7}rG`&&OBg{PAR_hCh97fae-s+2Oqo}KS(Uyh1hdgfFJZdKxbVXP{)?%b z)nsIXG#n1*-WJ$Uxgly)JXnq1mh<0dzLWeq#Z+IptOnk`cpo9ku#@)40lcPdv|eu$ zBha<;Y}3+TNN3oyrw^Cbw8`SV1^&}puDCfbWmY5onH_x1AVm+(Sp=9(Yt=~Fj5;0h zYirah2p$Fh>Mlp3*pBUV8t-Vf&wbT#j(SgAlnyPTG5)gE>_b0LYhHIu9&r}HILa0O zI&`i(f$bGX_nQTd@O685^ZTrU!L#`Q3BhF>;*5upiQGGcyDLAgdm{y;w)i`M%`BC*u&P;c$>y_VPT79#n8_>16I}-H}<@4NVZ13a~f>Jsz0u!>B zXNFThf0X_2;lv9RN2+G=k=zbLvG^uRg+LczVIR|7t%Q(2nXy&d!tDA7;ve=@u=~Ce zGL;&&sUKLj@#E}Xy1O^_3Ls#~c>IYEnNdA+1DFk_B=Xjg8((pG=4==bRP$b<8xLrg zYSeBr1w09gaO%7o=9Gue#ZAU!Faz@ujqR!4UI;@kT~a`_^fMaJ@6Itud`F-^udjLu2{6}^)LsIDVkmYYwocu-S1I{Rnb^O&Pziv#+~Th z^cCsWm$Yz|Jnq>)^v07MguSN9wNMb8iqAomhfe%?TlYrky?#ZKuxa(sSM0n+9Oriu zRw`Kk%B+%?tp*C!5_+Q}De?Tl&Qs5_N^D#K^XjjQDa05%3vzMOPnPqOqtHr*6QTo- zpv5i%+m3&TZb z;S*IJiaxk{!-@vDd}lZh!*kAU6Uz+{4w;sWQyNuE3-iFTYnwdAcCAJWYFO!#$PdFiyF9ZG#7Pc_ln? zO#d82+}^z(4gEAJEW|6}PUItsv|<-*iY=b9#3)>SHKbyuy4r*TQm~h|1p7 zv-*b?oD z7;``rSsYeU2W4Kx4gp*ojFqlsn8h^Rol@M*Gu+q%%Uk%CDV1#DyZwSC z`Vi>Q^|YceIg1)XOK;viGe*d{N!8dHGqn{j=_r3$XBm$py8kJw^)Df67BvO;gmGE@ z?S!v#j~RRjQ6mU#iMRi3e%AD)@88r&G-ozcRj)lW62~X|QQ+gb$rU(9`H%k4hX4yT zzeF%vz%`3)moPO`uUL?ps;T+i=NZyD11+FoCI@ zJjb`PRE_rx*Tyylol@>c>h5f2c5=;yXNmLYGV!8tkj%*y$z7 z1OJv*4E?&~gwe^%!Z1-YHw3l={3Z|`i{(7a=jwi_G^s_L$YOy5u|QH#dvrYUf6Ig zVU}?`gcx!Vp#%^_dkYf2X|88oHd|uOeFbu3&oNP|R`-hL*T7qDcTg1P zt={P|Lr1UF1=(VYk6K|873;3CK!2gP?@>|OKKjrDQ8l#JmHvFlBH0B$n+ zwNi5h4W8+4!w@j=BQXpZynbxrH zFJC0q8z(62(#T^+wr9kdVkIPY6b1Td4n_>fvJl?{V4{o$LXwCSMsXDIEZ2s-~KBO!Tab^vuju&iz8)cTw{)=}wD|Jgb#gK_qhgRT z^>nv)0ytBC(fAjlrM;c#SGG(-N>OfRMrKwSW~LU<&w3y=i3QYzobws4AvOFYan%V{Bw+_fG>!D>OYB}xcZm*|lwOStQI z-}l^e?)#qe-gEAmKc1QI^ZCwvpE+k{o|*X;AAjc{NT9p3K=426P?VCF0$f5wFQa|B z`?+0)K9N->YX1FC6qNscY9_C6d0~HPzAO(QS~45E`*{-kiFlj;e^(c@Hi2;inLch> z@8$8dEYY=lkaR)J9aG8;UX-Cau1?I~BD?wd`AWh?ltE3=jfm!->>uxpe+%0k$~gW| zR@KX8p_llIy`wkDCRW~=WWF0uOLgn%Jxu_MxV|n@T`I9^5($3tjH68bqRYJEd;fFP zeI{<2F1Y-)=9<-+em1fqTK$tG!d-B4q@1tooJgXmftGikf_sJ&{i&_68~Kg<-HE05 zSLkRbEavwD%{?tE5JSq1;Cphz<{%e@raerl6>e$NJQ@{A_y~rV8WciC_Os{gy(2WaHiu z-1V)IlfK{Jo6)MvL`@=gzkp73WCBybUwP`OS7|msUcW7}RQCCQ_33w@oY!*IRzJ`JKj0 zhHNf}hvZUM7*LyCF{3j}lahDahX72eeLX@!#M|-Yti_beg!4_5@f>+xE>e0_xf}KA zk@2ciC-#XpjQ76MTmRCcqkF)(8;}Ijl(~ABhOyFYJ~1`m^#L6|LV@=)_-?;8I?0=H zg74$OJvl@xNPR5(Os=JuFPw<$*h?_c#~^h(I=79BYkBoN<~j9lSXG1@7(=XP&fNb zg4EfY&ZgJ(O|l#4rZ`r{;=zl*2I?taxO>w@F7pb!VI!@kBf41tb&8F^wKaazlxZh$&J6BE~HkAa* zzNLB$dMkd{p83a*;{HuLS*2Yb%WjO|JllRvatQrB_Rb5{Ph8}HU7sHsCe(h6DYFSn zhi{nugkE!JH09M0w4=+TQR`whe+Z!q1*`8Wm%Zyx+icGBr5}e`atQ|1o&ECvR<-+M zj49{XsoL@6_wLU=e#~t2$yD*D! z?O$%lIENO1zP3*>Me_gKwc%eCplvMNJ!qs2{M_6_1?*%5WR(?x_B7I#Ug7S4=V_#^ z1?*%6H_~6LTu?DvnfD9`5$o={pMJSoIAe)?h|8Lk<{RT>)u zJEPgZz!a5UvXpjNK2DO`H=*?byj7^zCGG?CqsX~3sD7(+nNuWi9zr;l=`{vwhY$_zr3o(*q<{)TElyY*a4rtLS&{TG$f?)zK#1-}=B?9}_#6&~2rOc!VC#>pE#g<6oC7E7 zHL}NUt69SU1M(5&eGqeNh?-$Z6=B}49ibCZ3gG&q+>i_SGzEP52gj6Y?b={%DD`W7 z9MIR%{9Ae2QNO?}qIe}bMs^5KmuBR+{wsHkZWy0$G4(rlym2he%kk5p^;jdW@b=?~ z7zL@Cdhv%kn-KodbZT<5LCaHm#Y9c1W>ycl06A^PXemLfL ziP3_W^KG0GF&f4gQ%nsJqvzG+wPw8Fw#$$5I>$ah5?>ia7|SmZZbe)Gwy$r$A9LF! z_K^IuGtNOXKNgv?+6(*c5~&f??cg8lP@937N2!bDh@^k!+kmCgf3@ ztT7I32C4V@l#R<9f#8m0yK!HniBG+3*&7bHlHIPtJYyInnu;>&(-Aud zs%1tTOBxPL0w#=Mpq!{?5;}(4B2F*YrkrXWmB~HEq{a_LJ++e7tRri!mAThOYjB6R z*E{V1)_S>XzjoB}%u=!QNH7Vl*E@)6cB+%?Ht!6>DvN*J;8_dZ-y_P_xE4CVh7W(< zJj2i^W{vf>r8{I_<&ufccPz$wtg6_U9e@&yn@I<;gB~`+PA8UOE%0c*&ln>P zt$P{)U&Cw>(SQW@zHcw+t;8~8GuEDl(oQ1a3po`PVJJFh$b z90YNHQ!q1&jadEu6+axJ;xSVFC494MzwSC-&}QDKdRs)hfY$FBY8@MCLqhA!ERiT& zdo2eWU_&bI%vP1CP|H4v4WA~lpQb7hNEoW6XzWy+W>9q!*@};<#E<(^&L`IUGYof8bDt2p;X8G1LRpm5ec)RFwwluvUun0_!~B6m=G3!X{Oj4VtW# zf|8?vPH#Et$13>#%%k9_g8pq-Iwq%wE@L$vBz>~2T3X@ zWssBNU|jPa`(T2N>L-^l=5CfS>h8|a>)ioLQf;n{haG=?A#}h#g>(ys@^;IGkasTy z3w6I#oUFAIu&SBu2uEYct1K{>j+urCI$g_c?FU=Y{5EO9jIqLyBPN^B;LO-nk0S;i zvuek1Y4u>TDq)Og2hIBk_9|}7I@Y^xGx1#{?KHoIkuz*|7dLmv8An@cxtdab|1&@ z_t1=5gLJM|T5bk9rZ-iQ7ILUbPutgGoI7sB%Ix_12= zM9N{ujv&j`V2&5^wV31}t=wzIQctLQME}V~8_Z!WDpfYg5u@G)p~(ZwG&==gSK|9A zUeQ*b{Vmnd0~;KNF<hirV-QDIE!sO?QZ1mYgGN*XgAy#f$Nv+q`igd@nd`sur2&_KE18jynWuh z-P^LAfr0W)@NF4aw_oVAX0GRuKz$M#LE5w4CD8ATUKY~oCyeKgJj_S z7mqat6m=5iNM9fZWBZIew90PQJ4;b%m#@W9xp|Z7P%^1bQ>9vN>Mf+qNt5DwztGrF zu%uNe2sGurH#ZNK$So=*0KBY206aKvrV~uFkV~gib;KaWmwI z5t>RumQ@VUA$cpc|3R7E3@XJq75(7mLuUK^rX?5~HCs$& zA97Nw%$%pHMHEUXn69^~5R7)wL@OhQ9FsZnz;%r-(4L8u%Iu7{hh*B7e>%SZ5Rhq5 zq0@^+vvK^jEV}K$6R`&CSx9MTixEG!I;$QgdnJC$nt+6pom*8^+t}TSCH@^56 zV?$l(q)-)yu4S0)q9m>#_$z6~(Z2zQ?r-dPe>sXA1a>KI}I z-G>*zG&xO{e?@Bm%2!xLqn2pR2igM8*UpAc3J!pt(BT;bTG=Ns?!oW^qP>|!(Gfm| z%IK+SFl*yECIZ%BmvrTrz{$0$Axy_5Myg-<6OkkAQ5$_8LSET3V0Z=5uly>IVeQm{ zFsG5yxki=GG)|( zzwP?UyEtOAn^bp%R(VcNw-3y9{gr8GW-~ zs)aT@AVZ%C>35o(f~@PJ^?aMz26Pk8KgH;MH;1gDfUNoMg#-^?rb^F3ZZ}xmFSWpT z2+$hlHgdPUUBjr4;$PZ?I5m?Zon` zgy5vSK=HtEd0l=x3+82o$7DlI72A#kx2?b`C=8jc`)A~Ko`cTZt76@LBmLXlpv|<3sJbrxOncBU+xHxB zTbi+vU6!weNw-{ycw!EnG)k2p;u7i}i=tx=#Ood_qZdvceC-Xk+c7M5*5k+J z8(TkZx!U*pr&|hpV|GgG9t)*k3^%!KdT?FXiZuEm_hVW(?V84qGu!y=LdLq!kI)#e zrKP7<@DD$IguoX+shZ9MpG2tYh3;XQ`J&vOpo%ybdr-Qef6&a)Ye_<9Ta(N`*M%ZC zI;h%}e4b=RMm%xM{%)4R-pX3^ObCsCopwP>x1>BB57>`jdDHK#)|ufssT;x>qxI}U zigV8SOk3#uCG*I3`p)PE!}7Dn?{e3!GA#3p-WrxUUuKH&mU)!8-*k=D6S72Sf+)T! z)OBp8r$!EpNZjX$4PA?2G)5FB33nYc8mS!Ofer>sN z#+=GLO)M1!2yxT*bEwhey%6S1P)zH(V%$lWM_vDhyxy5%@M)71-(V6&EfYJ|#fHqt z`MN|BTP=$f*4u{M$C@2Q z?NRY{v4+x&;FVirbN6T*y11PpVQy!RwhhA@vTdJ^`IaNncK_d*DHGP1I`^PKM~wwS kjMm#?yMI083Jh`%2nr?MRM5x+6%_&UG{V9lGhLeh0?Ih=+yDRo literal 0 HcmV?d00001 diff --git a/Abstract-Algebra-Theorems-and-Definitions.tex b/Abstract-Algebra-Theorems-and-Definitions.tex new file mode 100644 index 0000000..c1f5e9b --- /dev/null +++ b/Abstract-Algebra-Theorems-and-Definitions.tex @@ -0,0 +1,33 @@ +\documentclass[12pt,letterpaper]{report} +\usepackage{init} +\usepackage{import} + +\newcommand{\E}{\mathbb{E}} +\newcommand{\K}{\mathbb{K}} +\newcommand{\dist}{\text{dist}} +\newcommand{\lcm}{\text{lcm}} +\newcommand{\characteristic}{\text{char }} +\newcommand{\gf}{\text{GF}} +\newcommand{\fix}{\text{fix}} +\newcommand{\gal}{\text{Gal}} +\setcounter{chapter}{-1} +\author{Alexander J. Clarke} +\title{Abstract Algebra Theorems and Definitions} +\begin{document} +\maketitle +\clearpage +\begin{center} + \thispagestyle{empty} + \vspace*{\fill} + All theorems, corollaries, lemmas, remarks, and asides are direct quotes from Contemporary Abstract Algebra, 8th Edition, by Joseph A. Gallian + \vspace*{\fill} +\end{center} +\tableofcontents + +\import{part-1/}{part-1.tex} +\import{part-2/}{part-2.tex} +\import{part-3/}{part-3.tex} +\import{part-4/}{part-4.tex} +\import{part-5/}{part-5.tex} + +\end{document} diff --git a/README.md b/README.md new file mode 100644 index 0000000..8fb73b2 --- /dev/null +++ b/README.md @@ -0,0 +1,18 @@ +# Abstract Algebra Theorems and Definitions +This repository houses the LaTeX code (and the corresponding generated [PDF](Abstract-Algebra-Theorems-and-Definitions.pdf)) +that generates a packet of all of the theorems and definitions contained within +[Contemporary Abstract Algebra, 8th Edition, by Joseph A. Gallian](https://a.co/d/eLi1WCJ). + +## Purpose +The purpose of this packet is to provide a useful "cheat sheet" for viewing all of the theorems and definitions within the +textbook for easy reference when writing proofs. + +## What's Included? +This packet includes all of the following from the textbook: + +* Definitions +* Theorems +* Corollaries +* Lemmas +* Remarks +* Select Examples that contain a definition or theorem diff --git a/init.sty b/init.sty new file mode 100644 index 0000000..e768970 --- /dev/null +++ b/init.sty @@ -0,0 +1,86 @@ +\ProvidesPackage{init} + +\usepackage{import} +\usepackage[utf8]{inputenc} +\usepackage{pgfplots} +\usepackage[english]{babel} +\usepackage{amsthm} +\usepackage{thmtools} +\usepackage{hyperref} +\usepackage{cancel} +\usepackage{mathtools} +\usepackage{amsmath} +\usepackage{amsfonts} +\usepackage{amssymb} +\usepackage{graphicx} +\usepackage{relsize} +\usepackage{listings} +\graphicspath{ {./images/} } +\usepackage{array} +\usepackage{tikz} +\usetikzlibrary{arrows} +\usepackage[left=2cm, right=2.5cm, top=2.5cm, bottom=2.5cm]{geometry} +\usepackage{enumitem} +\usepackage{mathrsfs} + +% Math Functions +\newcommand{\limx}[2]{\displaystyle\lim\limits_{#1 \to #2}} +\newcommand{\st}{\ \text{s.t.}\ } +\newcommand{\abs}[1]{\left\lvert #1 \right\rvert} +\newcommand{\dotp}{\dot{\mathcal{P}}} +\newcommand{\dotq}{\dot{\mathcal{Q}}} +\newcommand{\Int}[1]{\text{int}\left(#1\right)} +\newcommand{\cl}[1]{\text{cl}\left(#1\right)} +\newcommand{\bd}[1]{\text{bd}\left(#1\right)} +\newcommand{\lr}[1]{\langle #1 \rangle)} +\newcommand{\lspan}[1]{\text{span}\left(#1\right)} +\newcommand{\ldim}[1]{\text{dim}\left(#1\right)} +\newcommand{\nullity}[1]{\text{nullity}\left(#1\right)} +\newcommand{\rank}[1]{\text{rank}\left(#1\right)} +\newcommand{\ldet}[1]{\text{det}\left(#1\right)} +\newcommand{\ltr}[1]{\text{tr}\left(#1\right)} +\newcommand{\norm}[1]{\left\lVert#1\right\rVert} +\DeclareMathOperator{\sign}{sgn} +\renewcommand{\qedsymbol}{$\blacksquare$} + +% Special Sets +\newcommand{\R}{\mathbb{R}} +\newcommand{\N}{\mathbb{N}} +\newcommand{\Q}{\mathbb{Q}} +\newcommand{\C}{\mathbb{C}} +\newcommand{\Z}{\mathbb{Z}} +\newcommand{\F}{\mathbb{F}} + +% Theorem Styles +\newtheoremstyle{break}% name +{}% Space above, empty = `usual value' +{}% Space below +{}% Body font +{}% Indent amount (empty = no indent, \parindent = para indent) +{\bfseries}% Thm head font +{}% Punctuation after thm head +{\newline}% Space after thm head: \newline = linebreak +{}% Thm head spec +\makeatletter +\def\thmhead@plain#1#2#3{% + \thmname{#1}\thmnumber{\@ifnotempty{#1}{ }\@upn{#2} }% + \thmnote{{\the\thm@notefont\bfseries\itshape#3}}} +\let\thmhead\thmhead@plain +\makeatother +\newtheoremstyle{case}{}{}{}{}{}{:}{ }{} +\theoremstyle{case} +\newtheorem{case}{Case} +\theoremstyle{break} +\newtheorem{definition}{Definition}[section] +\newtheorem{theorem}{Theorem}[section] +\newtheorem{corollary}{Corollary}[section] +\newtheorem{lemma}[theorem]{Lemma} +\newtheorem*{lem}{Lemma} +\newtheorem*{remark}{Remark } +\newtheorem*{aside}{} +\newtheorem*{example}{Example} + +% Formatting +\setlist[enumerate]{font=\bfseries} + + diff --git a/part-1/chapters/chapter-0/chapter-0.tex b/part-1/chapters/chapter-0/chapter-0.tex new file mode 100644 index 0000000..8dd7a10 --- /dev/null +++ b/part-1/chapters/chapter-0/chapter-0.tex @@ -0,0 +1,7 @@ +\chapter{Preliminaries} +\subimport{./}{properties-of-integers.tex} +\subimport{./}{modular-arithmetic.tex} +\subimport{./}{complex-numbers.tex} +\subimport{./}{mathematical-induction.tex} +\subimport{./}{equivalence-relations.tex} +\subimport{./}{functions-mappings.tex} diff --git a/part-1/chapters/chapter-0/complex-numbers.tex b/part-1/chapters/chapter-0/complex-numbers.tex new file mode 100644 index 0000000..ac252f4 --- /dev/null +++ b/part-1/chapters/chapter-0/complex-numbers.tex @@ -0,0 +1,14 @@ +\section{Complex Numbers} +\begin{theorem}[Properties of Complex Numbers] + \hfill + \begin{enumerate} + \item Closure under addition: $(a + bi) + (c + di) = (a + c) + (b + d)i$ + \item Closure under multiplication: $(a + bi)(c + di) = (ac) + (ad)i + (bc)i + (bd)i^2 = (ac - bd) + (ad + bc)i$ + \item Closure under division ($c + di \neq 0$): $\displaystyle\frac{(a + bi)}{(c + di)} = \frac{(a + bi)}{(c + di)}\frac{(c - di)}{(c - di)}=\frac{(ac + bd) + (bc - ad)i}{c^2 + d^2} = \frac{(ac + bd)}{c^2 + d^2} + \frac{(bc - ad)}{c^2 + d^2}i$ + \item Complex conjugation: $(a + bi)(a - bi) = a^2 + b^2$ + \item Inverses: For every nonzero complex number $a + bi$ there is a complex number $c + di$ such that $(a + bi)(c + di)=1$. (That is, $(a + bi)^{-1}$ exists in $\C$.) + \item Powers: For every complex number $a + bi = r(\cos\theta + i \sin \theta)$ and every positive integer $n$, we have $(a + bi)^n = [r(\cos \theta + i \sin \theta)]^n = r^n(\cos n \theta + i \sin n \theta)$. + \item Radicals: For every complex number $a + bi = r(\cos \theta + i \sin \theta)$ and every positive integer $n$, we have $\displaystyle(a + bi)^{\frac{1}{n}} = [r(\cos \theta + i \sin \theta)]^{\frac{1}{n}} = r^{\frac{1}{n}}(\cos\frac{\theta}{n} + i \sin \frac{\theta}{n})$. + \end{enumerate} +\end{theorem} + diff --git a/part-1/chapters/chapter-0/equivalence-relations.tex b/part-1/chapters/chapter-0/equivalence-relations.tex new file mode 100644 index 0000000..fd7142b --- /dev/null +++ b/part-1/chapters/chapter-0/equivalence-relations.tex @@ -0,0 +1,19 @@ +\section{Equivalence Relations} + +\begin{definition}[Equivalence Relation] + An \textit{equivalence relation} on a set $S$ is a set $R$ of ordered pairs of elements of $S$ such that + + \begin{enumerate} + \item $(a, a) \in R$ for all $a \in S$ (reflexive property). + \item $(a, b) \in R$ implies $(b, a) \in R$ (symmetric property). + \item $(a, b) \in R$ and $(b, c) \in R$ imply $(a, c) \in R$ (transitive property). + \end{enumerate} +\end{definition} + +\begin{definition}[Partition] + A \textit{partition} of a set $S$ is a collection of nonempty disjoint subsets of $S$ whose union is $S$. +\end{definition} + +\begin{theorem}[Equivalence Classes Partition] + The equivalence classes of an equivalence relation on a set $S$ constitute a partition of $S$. Conversely, for any partition $P$ of $S$, there is an equivalence relation on $S$ whose equivalence classes are the elements of $P$. +\end{theorem} diff --git a/part-1/chapters/chapter-0/functions-mappings.tex b/part-1/chapters/chapter-0/functions-mappings.tex new file mode 100644 index 0000000..4a1ae17 --- /dev/null +++ b/part-1/chapters/chapter-0/functions-mappings.tex @@ -0,0 +1,27 @@ +\section{Functions (Mappings)} + +\begin{definition}[Function (Mapping)] + A \textit{function} (or \textit{mapping}) $\phi$ from a set $A$ to a set $B$ is a rule that assigns to each element $a$ of $A$ exactly one element $b$ of $B$. The set $A$ is called the \textit{domain of $\phi$}, and $B$ is called the \textit{range of $\phi$}. If $\phi$ assigns $b$ to $a$, then $b$ is called the \textit{image of $a$ under $\phi$}. The subset of $B$ comprising all the images of elements of $A$ is called the \textit{image of $A$ under $\phi$}. +\end{definition} + +\begin{definition}[Composition of Functions] + Let $\phi: A \to B$ and $\psi: B \to C$. The \textit{composition $\psi\phi$} is the mapping from $A$ to $C$ defined by $(\psi\phi)(a) = \psi(\phi(a))$ for all $a$ in $A$. +\end{definition} + +\begin{definition}[One-to-One Function] + A function $\phi$ from a set $A$ is called \textit{one-to-one} if for every $a_1, a_2 \in A,\ \phi(a_1) = \phi(a_2)$ implies $a_1 = a_2$. +\end{definition} + +\begin{definition}[Functions from A onto B] + A function $\phi$ from a set $A$ to a set $B$ is said to be \textit{onto $B$} if each element of $B$ is the image of at least one element of $A$. In symbols, $\phi: A \to B$ is onto if for each $b$ in $B$ there is at least one $a$ in $A$ such that $\phi(a) = b$. +\end{definition} + +\begin{theorem}[Properties of Functions] + Given functions $\alpha: A \to B$, $\beta: B \to C$, and $\gamma: C \to D$, then + \begin{enumerate} + \item $\gamma(\beta\alpha) = (\gamma\beta)\alpha$ (associativity). + \item If $\alpha$ and $\beta$ are one-to-one, then $\beta\alpha$ is one-to-one. + \item If $\alpha$ and $\beta$ are onto, then $\beta\alpha$ is onto. + \item If $\alpha$ is one-to-one and onto, then there is a function $\alpha^{-1}$ from $B$ onto $A$ such that $(\alpha^{-1}\alpha)(a) = a$ for all $a$ in $A$ and $(\alpha\alpha^{-1})(b) = b$ for all $b$ in $B$. + \end{enumerate} +\end{theorem} diff --git a/part-1/chapters/chapter-0/mathematical-induction.tex b/part-1/chapters/chapter-0/mathematical-induction.tex new file mode 100644 index 0000000..1f6fb98 --- /dev/null +++ b/part-1/chapters/chapter-0/mathematical-induction.tex @@ -0,0 +1,9 @@ +\section{Mathematical Induction} + +\begin{theorem}[First Principle of Mathematical Induction] + Let $S$ be a set of integers containing $a$. Suppose $S$ has the property that whenever some integer $n \geq a$ belongs to $S$, then the integer $n + 1$ also belongs to $S$. Then, $S$ contains every integer greater than or equal to $a$. +\end{theorem} + +\begin{theorem}[Second Principle of Mathematical Induction] + Let $S$ be a set of integers containing $a$. Suppose $S$ has the property that $n$ belongs to $S$ whenever every integer less than $n$ and greater than or equal to $a$ belongs to $S$. Then, $S$ contains every integer greater than or equal to $a$. +\end{theorem} diff --git a/part-1/chapters/chapter-0/modular-arithmetic.tex b/part-1/chapters/chapter-0/modular-arithmetic.tex new file mode 100644 index 0000000..95acd55 --- /dev/null +++ b/part-1/chapters/chapter-0/modular-arithmetic.tex @@ -0,0 +1 @@ +\section{Modular Arithmetic} diff --git a/part-1/chapters/chapter-0/properties-of-integers.tex b/part-1/chapters/chapter-0/properties-of-integers.tex new file mode 100644 index 0000000..99c73b0 --- /dev/null +++ b/part-1/chapters/chapter-0/properties-of-integers.tex @@ -0,0 +1,33 @@ +\section{Properties of Integers} +\begin{aside}[Well Ordering Principle] + Every nonempty set of positive integers contains a smallest number. +\end{aside} + +\begin{theorem}[Division Algorithm] + Let $a$ and $b$ be integers with $b > 0$. then there exist unique integers $q$ and $r$ with the property that $a = bq + r$, where $0 \leq r < b$. +\end{theorem} + +\begin{definition}[Greatest Common Divisor, Relatively Prime Integers] + The \textit{greatest common divisor} of two nonzero integers $a$ and $b$ is the largest of all common divisors of $a$ and $b$. We denote this integer by $\gcd(a, b)$. When $\gcd(a, b) = 1$, we say that $a$ and $b$ are \textit{relatively prime}. +\end{definition} + +\begin{theorem}[GCD Is a Linear Combination] + for any nonzero integers $a$ and $b$, there exist integers $s$ and $t$ such that $\gcd(a, b)=as+bt$. Moreover, $\gcd(a,b)$ is the smallest positive integer of the form $as + bt$. +\end{theorem} + +\begin{corollary} + If $a$ and $b$ are relatively prime, then there exist integers $s$ and $t$ such that $as + bt = 1$. +\end{corollary} + +\begin{lemma}[Euclid's Lemma \text{\normalfont $p\ \vert\ ab$ implies $p\ \vert\ a$ or $p\ \vert\ b$}] + If $p$ is a prime that divides $ab$, then $p$ divides $a$ or $p$ divides $b$. +\end{lemma} + +\begin{theorem}[Fundamental Theorem of Arithmetic] + Every integer greater than 1 is a prime or a product of primes. this product is unique, except for the order in which the factors appear. That is, if $n = p_1p_2\dots p_r$ and $n=q_1q_2\dots q_s$, where the $p$'s and $q$'s are primes, then $r = s$ and, after renumbering the $q$'s, we have $p_i = q_i$ for all $i$. +\end{theorem} + +\begin{definition}[Least Common Multiple] + The \textit{least common multiple} of two nonzero integers $a$ and $b$ is the smallest positive integer that is a multiple of both $a$ and $b$. We will denote this integer by $\lcm(a, b)$. +\end{definition} + diff --git a/part-1/part-1.tex b/part-1/part-1.tex new file mode 100644 index 0000000..4d69495 --- /dev/null +++ b/part-1/part-1.tex @@ -0,0 +1,3 @@ +\part{Integers and Equivalence Relations} +\subimport{chapters/chapter-0}{chapter-0.tex} + diff --git a/part-2/chapters/chapter-10/chapter-10.tex b/part-2/chapters/chapter-10/chapter-10.tex new file mode 100644 index 0000000..242a861 --- /dev/null +++ b/part-2/chapters/chapter-10/chapter-10.tex @@ -0,0 +1,4 @@ +\chapter{Group Homomorphisms} +\subimport{./}{definition-and-examples.tex} +\subimport{./}{properties-of-homomorphisms.tex} +\subimport{./}{the-first-isomorphism-theorem.tex} diff --git a/part-2/chapters/chapter-10/definition-and-examples.tex b/part-2/chapters/chapter-10/definition-and-examples.tex new file mode 100644 index 0000000..82da21c --- /dev/null +++ b/part-2/chapters/chapter-10/definition-and-examples.tex @@ -0,0 +1,9 @@ +\section{Definition and Examples} + +\begin{definition}[Group Homomorphism] + A \textit{homomorphism} $\phi$ from a group $G$ to a group $\overline{G}$ is a mapping from $G$ into $\overline{G}$ that preserves the group operation; that is, $\phi(ab) = \phi(a)\phi(b)$ for all $a, b$ in $G$. +\end{definition} + +\begin{definition}[Kernel of a Homomorphism] + The \textit{kernel} of a homomorphism $\phi$ from a group $G$ to a group with identity $e$ is the set $\{x \in G\ \vert\ \phi(x)=e\}$. The kernel of $\phi$ is denoted by $\ker\phi$. +\end{definition} diff --git a/part-2/chapters/chapter-10/properties-of-homomorphisms.tex b/part-2/chapters/chapter-10/properties-of-homomorphisms.tex new file mode 100644 index 0000000..60a083a --- /dev/null +++ b/part-2/chapters/chapter-10/properties-of-homomorphisms.tex @@ -0,0 +1,32 @@ +\section{Properties of Homomorphisms} + +\begin{theorem}[Properties of Elements Under Homomorphisms] + Let $\phi$ be a homomorphism from a group $G$ to a group $\overline{G}$ and let $g$ be an element of $G$. Then + \begin{enumerate} + \item $\phi$ carries the identity of $G$ to $\overline{G}$. + \item $\phi(g^n)=(\phi(g))^n$ for all $n$ in $\Z$. + \item If $\abs{g}$ is finite, then $\abs{\phi(g)}$ divides $\abs{g}$. + \item $\ker\phi$ is a subgroup of $G$. + \item $\phi(a) = \phi(b)$ if and only if $a\ker\phi = b\ker\phi$. + \item If $\phi(g) = g'$, then $\phi^{-1}(g') = \{x \in G\ \vert\ \phi(x) = g'\} = g\ker\phi$. + \end{enumerate} +\end{theorem} + +\begin{theorem}[Properties of Subgroups Under Homomorphisms] + Let $\phi$ be a homomorphism from a group $G$ to a group $\overline{G}$ and let $H$ be a subgroup of $G$. Then + \begin{enumerate} + \item $\phi(H) = \{\phi(h)\ \vert\ h \in H\}$ is a subgroup of $\overline{G}$. + \item If $H$ is cyclic, then $\phi(H)$ is cyclic. + \item If $H$ is Abelian, then $\phi(H)$ is Abelian. + \item If $H$ is normal in $G$, then $\phi(H)$ is normal in $\phi(G)$. + \item If $\abs{\ker\phi} = n$, then $\phi$ is an $n$-to-1 mapping from $G$ onto $\phi(G)$. + \item If $\abs{H} = n$, then $\abs{\phi(H)}$ divides $n$. + \item If $\overline{K}$ is a subgroup of $\overline{G}$, then $\phi^{-1}(\overline{K})=\{k \in G\ \vert\ \phi(k) \in \overline{K}\}$ is a subgroup of $G$. + \item If $\overline{K}$ is a normal subgroup of $\overline{G}$, then $\phi^{-1}(\overline{K})=\{ k \in G\ \vert\ \phi(k) \in \overline{K}\}$ is a normal subgroup of $G$. + \item If $\phi$ is onto and $\ker\phi = \{e\}$, then $\phi$ is an isomorphism from $G$ to $\overline{G}$. + \end{enumerate} +\end{theorem} + +\begin{corollary}[Kernels Are Normal] + Let $\phi$ be a group homomorphism from $G$ to $\overline{G}$. Then $\ker\phi$ is a normal subgroup of $G$. +\end{corollary} diff --git a/part-2/chapters/chapter-10/the-first-isomorphism-theorem.tex b/part-2/chapters/chapter-10/the-first-isomorphism-theorem.tex new file mode 100644 index 0000000..990e81b --- /dev/null +++ b/part-2/chapters/chapter-10/the-first-isomorphism-theorem.tex @@ -0,0 +1,13 @@ +\section{The First Isomorphism Theorem} + +\begin{theorem}[First Isomorphism Theorem (Jordan, 1870)] + Let $\phi$ be a group homomorphism from $G$ to $\overline{G}$. Then the mapping from $G/\ker\phi$ to $\phi(G)$, given by $g\ker\phi \to \phi(g)$, is an isomorphism. In symbols, $G/\ker\phi \approx \phi(G)$. +\end{theorem} + +\begin{corollary} + If $\phi$ is a homomorphism from a finite group $G$ to $\overline{G}$, then $\abs{\phi(G)}$ divides $\abs{G}$ and $\abs{\overline{G}}$. +\end{corollary} + +\begin{theorem}[Normal Subgroups Are Kernels] + Every normal subgroup of a group $G$ is the kernel of a homomorphism of $G$. In particular, a normal subgroup $N$ is the kernel of the mapping $g \to gN$ from $G$ to $G/N$. +\end{theorem} diff --git a/part-2/chapters/chapter-11/chapter-11.tex b/part-2/chapters/chapter-11/chapter-11.tex new file mode 100644 index 0000000..878befe --- /dev/null +++ b/part-2/chapters/chapter-11/chapter-11.tex @@ -0,0 +1,4 @@ +\chapter{Fundamental Theorem of Finite Abelian Groups} +\subimport{./}{the-fundamental-theorem.tex} +\subimport{./}{the-isomorphism-classes-of-abelian-groups.tex} +\subimport{./}{proof-of-the-fundamental-theorem.tex} diff --git a/part-2/chapters/chapter-11/proof-of-the-fundamental-theorem.tex b/part-2/chapters/chapter-11/proof-of-the-fundamental-theorem.tex new file mode 100644 index 0000000..a7e65dc --- /dev/null +++ b/part-2/chapters/chapter-11/proof-of-the-fundamental-theorem.tex @@ -0,0 +1,17 @@ +\section{Proof of the Fundamental Theorem} + +\begin{lemma} + Let $G$ be a finite Abelian group of order $p^nm$, where $p$ is a prime that does not divide $m$. Then $G = H \times K$, where $H = \{x \in G\ \vert\ x^{p^n} =e\}$ and $K =\{x \in G\ \vert\ x^m = e\}$. Moreover, $\abs{H}=p^n$. +\end{lemma} + +\begin{lemma} + Let $G$ be an Abelian group of prime-power order and let $a$ be an element of maximum order in $G$. Then $G$ can be written in the form $\lr{a} \times K$. +\end{lemma} + +\begin{lemma} + A finite Abelian group of prime-power order is an internal direct product of cyclic groups. +\end{lemma} + +\begin{lemma} + Suppose that $G$ is a finite Abelian group of prime-power order. If $G=H_1 \times H_2 \times \dots \times H_m$ and $G=K_1 \times K_2 \times \dots \times K_n$, where the $H$'s and $K$'s are nontrivial cyclic subgroups with $\abs{H_1} \geq \abs{H_2} \geq \dots \geq \abs{H_m}$ and $\abs{K_1} \geq \abs{K_2} \geq \dots \geq \abs{K_n}$, then $m=n$ and $\abs{H_i} = \abs{K_i}$ for all $i$. +\end{lemma} diff --git a/part-2/chapters/chapter-11/the-fundamental-theorem.tex b/part-2/chapters/chapter-11/the-fundamental-theorem.tex new file mode 100644 index 0000000..c90c6c3 --- /dev/null +++ b/part-2/chapters/chapter-11/the-fundamental-theorem.tex @@ -0,0 +1,5 @@ +\section{The Fundamental Theorem} + +\begin{theorem}[Fundamental Theorem of Finite Abelian Groups] + Every finite Abelian group is a direct product of cyclic groups of prime-power order. Moreover, the number of terms in the product and the orders of the cyclic groups are uniquely determined by the group. +\end{theorem} diff --git a/part-2/chapters/chapter-11/the-isomorphism-classes-of-abelian-groups.tex b/part-2/chapters/chapter-11/the-isomorphism-classes-of-abelian-groups.tex new file mode 100644 index 0000000..7fb9674 --- /dev/null +++ b/part-2/chapters/chapter-11/the-isomorphism-classes-of-abelian-groups.tex @@ -0,0 +1,16 @@ +\section{The Isomorphism Classes of Abelian Groups} + +\begin{remark}[Greedy Algorithm for an Abelian Group of Order $\mathbf{p^n}$] + The Fundamental Theorem is extremely powerful. As an application, we can use it as an algorithm for constructing all Abelian groups of any order. Let's look at Abelian groups of a certain order $n$, where $n$ has two or more distinct prime divisors. + \begin{enumerate} + \item Compute the orders of the elements of the group $G$ + \item Select an element $a_1$ of maximum order and define $G_1 = \lr{a_1}$. Set $i = 1$. + \item If $\abs{G} = \abs{G_i}$, stop. Otherwise, replace $i$ by $i + 1$. + \item Select an element $a_i$ of maximum order $p^k$ such that $p^k \leq \abs{G}/\abs{G_{i-1}}$ and none of $a_i, a^p_i,a^{p^2}_i, \dots, a^{p^{k-1}}_i$ is in $G_{i-1}$, and define $G_i=G_{i-1} \times \lr{a_i}$. + \item Return to step 3. + \end{enumerate} +\end{remark} + +\begin{corollary}[Existence of Subgroups of Abelian Groups] + If $m$ divides the order of a finite Abelian group $G$, then $G$ has a subgroup of order $m$. +\end{corollary} diff --git a/part-2/chapters/chapter-2/chapter-2.tex b/part-2/chapters/chapter-2/chapter-2.tex new file mode 100644 index 0000000..582f73b --- /dev/null +++ b/part-2/chapters/chapter-2/chapter-2.tex @@ -0,0 +1,3 @@ +\chapter{Groups} +\subimport{./}{definition-and-examples-of-groups.tex} +\subimport{./}{elementary-properties-of-groups.tex} diff --git a/part-2/chapters/chapter-2/definition-and-examples-of-groups.tex b/part-2/chapters/chapter-2/definition-and-examples-of-groups.tex new file mode 100644 index 0000000..1055ed0 --- /dev/null +++ b/part-2/chapters/chapter-2/definition-and-examples-of-groups.tex @@ -0,0 +1,14 @@ +\section{Definition and Examples of Groups} + +\begin{definition}[Binary Operation] + Let $G$ be a set. A \textit{binary operation} on $G$ is a function that assigns each ordered pair of elements of $G$ an element of $G$. +\end{definition} + +\begin{definition}[Group] + Let $G$ be a set together with a binary operation (usually called multiplication) that assigns to each ordered pair $(a, b)$ of elements of $G$ an element in $G$ denoted by $ab$. We say $G$ is a \textit{group} under this operation if the following three properties are satisfied. + \begin{enumerate} + \item \textit{Associativity}. The operation is associative; that is, $(ab)c = a(bc)$ for all $a,b,c$ in $G$. + \item \textit{Identity}. There is an element $e$ (called the \textit{identity}) in $G$ such that $ae = ea = a$ for all $a$ in $G$. + \item \textit{Inverses}. For each element $a$ in $G$, there is an element $b$ in $G$ (called an \textit{inverse} of $a$) such that $ab = ba = e$. + \end{enumerate} +\end{definition} diff --git a/part-2/chapters/chapter-2/elementary-properties-of-groups.tex b/part-2/chapters/chapter-2/elementary-properties-of-groups.tex new file mode 100644 index 0000000..a4be982 --- /dev/null +++ b/part-2/chapters/chapter-2/elementary-properties-of-groups.tex @@ -0,0 +1,17 @@ +\section{Elementary Properties of Groups} + +\begin{theorem}[Uniqueness of the Identity] + In a group $G$, there is only one identity element. +\end{theorem} + +\begin{theorem}[Cancellation] + In a group $G$, the right and left cancellation laws hold; that is, $ba = ca$ implies $b = c$, and $ab = ac$ implies $b = c$. +\end{theorem} + +\begin{theorem}[Uniqueness of Inverses] + For each element $a$ in a group $G$, there is a unique element $b$ in $G$ such that $ab = ba = e$. +\end{theorem} + +\begin{theorem}[Socks-Shoes Property] + For group elements $a$ and $b$, $(ab)^{-1} = b^{-1}a^{-1}$. +\end{theorem} diff --git a/part-2/chapters/chapter-3/chapter-3.tex b/part-2/chapters/chapter-3/chapter-3.tex new file mode 100644 index 0000000..0fe7749 --- /dev/null +++ b/part-2/chapters/chapter-3/chapter-3.tex @@ -0,0 +1,3 @@ +\chapter{Finite Groups; Subgroups} +\subimport{./}{subgroup-tests.tex} +\subimport{./}{terminology-and-notation.tex} diff --git a/part-2/chapters/chapter-3/subgroup-tests.tex b/part-2/chapters/chapter-3/subgroup-tests.tex new file mode 100644 index 0000000..79fb80e --- /dev/null +++ b/part-2/chapters/chapter-3/subgroup-tests.tex @@ -0,0 +1,13 @@ +\section{Terminology and Notation} + +\begin{definition}[Order of a Group] + The number of elements of a group (finite or infinite) is called its \textit{order}. We will use $\abs{G}$ to denote the order of $G$. +\end{definition} + +\begin{definition}[Order of an Element] + The \textit{order} of an element $g$ in a group $G$ is the smallest positive integer $n$ such that $g^n = e$. (In additive notation, this would be $ng = 0$.) If no such integer exists, we say that $g$ has \textit{infinite order}. The order of an element $g$ is denoted by $\abs{g}$. +\end{definition} + +\begin{definition}[Subgroup] + If a subset $H$ of a group $G$ is itself a group under the operation of $G$, we say that $H$ is a \textit{subgroup} of $G$. +\end{definition} diff --git a/part-2/chapters/chapter-3/terminology-and-notation.tex b/part-2/chapters/chapter-3/terminology-and-notation.tex new file mode 100644 index 0000000..4f5e770 --- /dev/null +++ b/part-2/chapters/chapter-3/terminology-and-notation.tex @@ -0,0 +1,36 @@ +\section{Subgroup Tests} + +\begin{theorem}[One-Step Subgroup Test] + Let $G$ be a group and $H$ a nonempty subset of $G$. If $ab^{-1}$ is in $H$ whenever $a$ and $b$ are in $H$, then $H$ is a subgroup of $G$. (In additive notation, if $a - b$ is in $H$ whenever $a$ and $b$ are in $H$, then $H$ is a subgroup of $G$.) +\end{theorem} + +\begin{theorem}[Two-Step Subgroup Test] + Let $G$ be a group and let $H$ be a nonempty subset of $G$. If $ab$ is in $H$ whenever $a$ and $b$ are in $H$ ($H$ is closed under the operation), and $a^{-1}$ is in $H$ whenever $a$ is in $H$ ($H$ is closed under taking inverses), then $H$ is a subgroup of $G$. +\end{theorem} + +\begin{theorem}[Finite Subgroup Test] + Let $H$ be a nonempty finite subset of a group $G$. If $H$ is closed under the operation of $G$, then $H$ is a subgroup of $G$. +\end{theorem} + +\begin{theorem}[$\mathbf{\lr{a}}$ Is a Subgroup] + Let $G$ be a group, and let $a$ be any element of $G$. Then, $\lr{a}$ is a subgroup of $G$. +\end{theorem} + +\begin{definition}[Center of a Group] + The \textit{center}, $Z(G)$, of a group $G$ is the subset of elements in $G$ that commute with every element of $G$. In symbols, + \[ Z(G) = \{a \in G\ \vert\ ax = xa,\ \forall\ x \in G\} \] + [The notation $Z(G)$ comes from the fact that the German word for center is \textit{Zentrum}. The term was coined by J.A. de Séguier in 1904.] +\end{definition} + +\begin{theorem}[Center Is a Subgroup] + The center of a group $G$ is a subgroup of $G$. +\end{theorem} + +\begin{definition}[Centralizer of $\mathbf{a}$ in $\mathbf{G}$] + Let $a$ be a fixed element of a group $G$. The \textit{centralizer of $a$ in $G$}, $C(a)$, is the set of all elements in $G$ that commute with $a$. In symbols, + \[ C(a) = \{g \in G\ \vert\ ga = ag\} \] +\end{definition} + +\begin{theorem}[$\mathbf{C(a)}$ Is a Subgroup] + For each $a$ in a group $G$, the centralizer of $a$ is a subgroup of $G$. +\end{theorem} diff --git a/part-2/chapters/chapter-4/chapter-4.tex b/part-2/chapters/chapter-4/chapter-4.tex new file mode 100644 index 0000000..cc35492 --- /dev/null +++ b/part-2/chapters/chapter-4/chapter-4.tex @@ -0,0 +1,3 @@ +\chapter{Cyclic Groups} +\subimport{./}{properties-of-cyclic-groups.tex} +\subimport{./}{classification-of-subgroups-of-cyclic-groups.tex} diff --git a/part-2/chapters/chapter-4/classification-of-subgroups-of-cyclic-groups.tex b/part-2/chapters/chapter-4/classification-of-subgroups-of-cyclic-groups.tex new file mode 100644 index 0000000..fd7c372 --- /dev/null +++ b/part-2/chapters/chapter-4/classification-of-subgroups-of-cyclic-groups.tex @@ -0,0 +1,17 @@ +\section{Classification of Subgroups of Cyclic Groups} + +\begin{theorem}[Fundamental Theorem of Cyclic Groups] + Every subgroup of a cyclic group is cyclic. Moreover, if $\abs{\lr{a}} = n$, then the order of any subgroup of $\lr{a}$ is a divisor of $n$; and, for each, positive divisor $k$ of $n$, the group $\lr{a}$ has exactly one subgroup of order $k$ -- namely, $\lr{a^{n/k}}$. +\end{theorem} + +\begin{corollary}[Subgroups of $\mathbf{\Z_n}$] + For each positive divisor $k$ of $n$, the set $\lr{n/k}$ is the unique subgroup of $\Z_n$ of order $k$; moreover, these are the only subgroups of $\Z_n$. +\end{corollary} + +\begin{theorem}[Number of Elements of Each Order in a Cyclic Group] + If $d$ is a positive divisor of $n$, the number of elements of order $d$ in a cyclic group of order $n$ is $\phi(d)$. +\end{theorem} + +\begin{corollary}[Number of Elements of Order $\mathbf{d}$ in a Finite Group] + In a finite group, the number of elements of order $d$ is a multiple of $\phi(d)$. +\end{corollary} diff --git a/part-2/chapters/chapter-4/properties-of-cyclic-groups.tex b/part-2/chapters/chapter-4/properties-of-cyclic-groups.tex new file mode 100644 index 0000000..636f2c4 --- /dev/null +++ b/part-2/chapters/chapter-4/properties-of-cyclic-groups.tex @@ -0,0 +1,33 @@ +\section{Properties of Cyclic Groups} + +\begin{theorem}[Criterion for $\mathbf{a^i=a^j}$] + Let $G$ be a group, and let $a$ belong to $G$. If $a$ has infinite order, then $a^i = a^j$ if and only if $i = j$. If $a$ has finite order, say, $n$, then $\lr{a} = \{e, a, a^2, \dots, a^{n - 1}\}$ and $a^i = a^j$ if and only if $n$ divides $i - j$. +\end{theorem} + +\begin{corollary}[$\mathbf{\abs{a}=\abs{\lr{a}}}$] + For any group element $a$, $\abs{a} = \abs{\lr{a}}$. +\end{corollary} + +\begin{corollary}[$\mathbf{a^k = e}$ Implies That $\mathbf{\abs{a}}$ Divides $\mathbf{k}$] + Let $G$ be a group and let $a$ be an element of order $n$ in $G$. If $a^k = e$, then $n$ divides $k$. +\end{corollary} + +\begin{theorem}[$\mathbf{\lr{a^k} = \lr{a^{\textbf{gcd}(n,k)}}}$ and $\mathbf{\abs{a^k} = n/\textbf{gcd}(n,k)}$] + Let $a$ be an element of order $n$ in a gruop and let $k$ be a positive integer. Then $\lr{a^k} = \lr{a^{\gcd(n,k)}}$ and $\abs{a^k} = n / \gcd(n,k)$. +\end{theorem} + +\begin{corollary}[Orders of Elements in Finite Cyclic Groups] + In a finite cyclic group, the order of an element divides the order of the group. +\end{corollary} + +\begin{corollary}[Criterion for $\mathbf{\lr{a^i} = \lr{a^j}}$ and $\mathbf{\abs{a^i} = \abs{a^j}}$] + Let $\abs{a} = n$. Then $\lr{a^i} = \lr{a^j}$ if and only if $\gcd(n, i) = \gcd(n,j)$, and $\abs{a^i} = \abs{a^j}$ if and only if $\gcd(n,i) = \gcd(n,j)$. +\end{corollary} + +\begin{corollary}[Generators of Finite Cyclic Groups] + Let $\abs{a} = n$. Then $\lr{a} = \lr{a^j}$ if and only if $\gcd(n,j) = 1$, and $\abs{a} = \abs{\lr{a^j}}$ if and only if $\gcd(n,j) = 1$. +\end{corollary} + +\begin{corollary}[Generators of $\mathbf{\Z_n}$] + An integer $k$ in $\Z_n$ is a generator of $Z_n$ if and only if $\gcd(n,k) = 1$. +\end{corollary} diff --git a/part-2/chapters/chapter-5/chapter-5.tex b/part-2/chapters/chapter-5/chapter-5.tex new file mode 100644 index 0000000..00e9b22 --- /dev/null +++ b/part-2/chapters/chapter-5/chapter-5.tex @@ -0,0 +1,4 @@ +\chapter{Permutation Groups} +\subimport{./}{definition-and-notation.tex} +\subimport{./}{cycle-notation.tex} +\subimport{./}{properties-of-permutations.tex} diff --git a/part-2/chapters/chapter-5/cycle-notation.tex b/part-2/chapters/chapter-5/cycle-notation.tex new file mode 100644 index 0000000..1022a8d --- /dev/null +++ b/part-2/chapters/chapter-5/cycle-notation.tex @@ -0,0 +1,28 @@ +\section{Cycle Notation} +\begin{definition} + Consider the permutation + \[ \alpha = \begin{bmatrix} + 1 & 2 & 3 & 4 & 5 & 6 \\ + 2 & 1 & 4 & 6 & 5 & 3 + \end{bmatrix}\] + + The assignment of values is as follows: + + \begin{align*} + 1 & \mapsto 2 \\ + 2 & \mapsto 1 \\ + 3 & \mapsto 4 \\ + 4 & \mapsto 6 \\ + 5 & \mapsto 5 \\ + 6 & \mapsto 3 + \end{align*} + + Although mathematically satisfactory, such diagrams are cumbersome. Instead, we leave out the arrows and simply write $\alpha = (1,2)(3,4,6)(5)$. + + It is also worth noting that an expression of the form $(a_1, a_2, \dots, a_m)$ is called a \textit{cycle of length $m$}, or an \textit{$m$-cycle}. +\end{definition} +\begin{example} + To multiply cycles, consider the following permutations from $S_8$. Let $\alpha = (13)(27)(456)(8)$ and $\beta = (1237)(648)(5)$. (When the domain consists of single-digit integers, it is common practice to omit the commas between the digits.) What is the cycle form of $\alpha\beta$? Of course, one could say that $\alpha\beta = (13)(27)(456)(8)(1237)(648)(5)$, but it is usually more desirable to express a permutation in a \textit{disjoint} cycle form (that is, the various cycles have no number in common). Well, keeping in mind that function composition is done from right to left and that each cycle that does not contain a symbol fixes the symbol, we observe that $(5)$ fixes 1; $(648)$ fixes $1$; $(1237)$ sends 1 to 2, $(8)$ fixes 2; $(456)$ fixes 2; $(27)$ sends 2 to 7; and $(13)$ fixes 7. So the net effect of $\alpha\beta$ is to send 1 to 7. Thus, we begin $\alpha\beta=(17\dots)\dots$. Now, repeating the entire process beginning with 7, we have, cycle by cycle, right to left, + \[ 7 \to 7 \to 7 \to 1 \to 1 \to 1 \to 1 \to 3, \] + so that $\alpha\beta = (173\dots)\dots$. Ultimately, we have $\alpha\beta = (1732)(48)(56)$. The import thing to bear in mind when multiplying cycles is to "keep moving" from one cycle to the next from right to left. +\end{example} diff --git a/part-2/chapters/chapter-5/definition-and-notation.tex b/part-2/chapters/chapter-5/definition-and-notation.tex new file mode 100644 index 0000000..ebb0d6c --- /dev/null +++ b/part-2/chapters/chapter-5/definition-and-notation.tex @@ -0,0 +1,5 @@ +\section{Definition and Notation} + +\begin{definition}[Permutation of $\mathbf{A}$, Permutation Group of $\mathbf{A}$] + A \textit{permutation} of a set $A$ is a function from $A$ to $A$ that is both one-to-one and onto. A \textit{permutation group} of a set $A$ is a set of permutations of $A$ that forms a group under function composition. +\end{definition} diff --git a/part-2/chapters/chapter-5/properties-of-permutations.tex b/part-2/chapters/chapter-5/properties-of-permutations.tex new file mode 100644 index 0000000..2e0d1f8 --- /dev/null +++ b/part-2/chapters/chapter-5/properties-of-permutations.tex @@ -0,0 +1,43 @@ +\section{Properties of Permutations} + +\begin{theorem}[Products of Disjoint Cycles] + Every permutation of a finite set can be written as a cycle or as a product of disjoint cycles. +\end{theorem} + +\begin{theorem}[Disjoint Cycles Commute] + If the pair of cycles $\alpha = (a_1, a_2, \dots, a_m)$ and $\beta = (b_1, b_2, \dots, b_n)$ have no entries in common, then $\alpha\beta = \beta\alpha$. +\end{theorem} + +\begin{theorem}[Order of a Permutation (Ruffini, 1799)] + The order of a permutation of a finite set written in disjoint cycle form is the least common multiple of the lengths of the cycles. +\end{theorem} + +\begin{theorem}[Product of 2-Cycles] + Every permutation in $S_n,\ n>1$ is a product of 2-cycles. +\end{theorem} + +\begin{lem} + If $\varepsilon = \beta_1\beta_2\dots\beta_r$, where the $\beta$'s are 2-cycles, then $r$ is even. +\end{lem} + +\begin{theorem}[Always Even or Always Odd] + If a permutation $\alpha$ can be expressed as a product of an even (odd) number of 2-cycles, then every decomposition of $\alpha$ into a product of 2-cycles must have an even (odd) number of 2-cycles. In symbols, if + \[ \alpha = \beta_1\beta_2\dots\beta_r\ \ \ \ \text{and}\ \ \ \ \alpha=\gamma_1\gamma_2\dots\gamma_s, \] + where the $\beta$'s and the $\gamma$'s are 2-cycles, then $r$ and $s$ are both even or both odd. +\end{theorem} + +\begin{definition}[Even and Odd Permutations] + A permutation that can be expressed as a product of an even number of 2-cycles is called an \textit{even} permutation. A permutation that can be expressed as a product of an odd number of 2-cycles is called an \textit{odd} permutation. +\end{definition} + +\begin{theorem}[Even Permutations Form a Group] + The set of even permutations in $S_n$ forms a subgroup of $S_n$. +\end{theorem} + +\begin{definition}[Alternating Group of Degree $\mathbf{n}$] + The group of even permutations of $n$ symbols is denoted by $A_n$ and is called the \textit{alternating group of degree $n$}. +\end{definition} + +\begin{theorem} + For $n > 1$, $A_n$ has order $n!/2$. +\end{theorem} diff --git a/part-2/chapters/chapter-6/automorphisms.tex b/part-2/chapters/chapter-6/automorphisms.tex new file mode 100644 index 0000000..d5aa206 --- /dev/null +++ b/part-2/chapters/chapter-6/automorphisms.tex @@ -0,0 +1,19 @@ +\section{Automorphisms} + +\begin{definition}[Automorphism] + An isomorphism from a group $G$ onto itself is called an \textit{automorphisms} of $G$. +\end{definition} + +\begin{definition}[Inner Automorphism Induced by $\mathbf{a}$] + Let $G$ be a group, and let $a \in G$. The function $\phi_a$ defined by $\phi_a(x) = axa^{-1}$ for all $x$ in $G$ is called the \textit{inner automorphism of $G$ induced by $a$}. +\end{definition} + +\begin{theorem}[Aut($G$) and Inn($G$) Are Groups] + The set of automorphisms of a group and the set of inner automorphisms of a group are both groups under the operation of function composition. + + When $G$ is a group, we use Aut($G$) to denote the set of all automorphisms of $G$ and Inn($G$) to denote the set of all inner automorphisms of $G$. +\end{theorem} + +\begin{theorem}[Aut$\mathbf{(\Z_n) \approx U(n)}$] + For every positive integer $n$, Aut($\Z_n$) is isomorphic to $U(n)$. +\end{theorem} diff --git a/part-2/chapters/chapter-6/cayleys-theorem.tex b/part-2/chapters/chapter-6/cayleys-theorem.tex new file mode 100644 index 0000000..e905027 --- /dev/null +++ b/part-2/chapters/chapter-6/cayleys-theorem.tex @@ -0,0 +1,5 @@ +\section{Cayley's Theorem} + +\begin{theorem}[Cayley's Theorem (1854)] + Every group is isomorphic to a group of permutations. +\end{theorem} diff --git a/part-2/chapters/chapter-6/chapter-6.tex b/part-2/chapters/chapter-6/chapter-6.tex new file mode 100644 index 0000000..d04ff82 --- /dev/null +++ b/part-2/chapters/chapter-6/chapter-6.tex @@ -0,0 +1,5 @@ +\chapter{Isomorphisms} +\subimport{./}{definition-and-examples.tex} +\subimport{./}{cayleys-theorem.tex} +\subimport{./}{properties-of-isomorphisms.tex} +\subimport{./}{automorphisms.tex} diff --git a/part-2/chapters/chapter-6/definition-and-examples.tex b/part-2/chapters/chapter-6/definition-and-examples.tex new file mode 100644 index 0000000..d4831dc --- /dev/null +++ b/part-2/chapters/chapter-6/definition-and-examples.tex @@ -0,0 +1,7 @@ +\section{Definition and Examples} + +\begin{definition}[Group Isomorphism] + An \textit{isomorphism} $\phi$ from a group $G$ to a group $\overline{G}$ is a one-to-one mapping (or function) from $G$ onto $\overline{G}$ that preserves the group operation. That is, + \[ \phi(ab) = \phi(a)\phi(b),\ \forall a,b \in G \] + If there is an isomorphism from $G$ onto $\overline{G}$, we say that $G$ and $\overline{G}$ are \textit{isomorphic} and write $G \approx \overline{G}$. +\end{definition} diff --git a/part-2/chapters/chapter-6/properties-of-isomorphisms.tex b/part-2/chapters/chapter-6/properties-of-isomorphisms.tex new file mode 100644 index 0000000..ea2db4d --- /dev/null +++ b/part-2/chapters/chapter-6/properties-of-isomorphisms.tex @@ -0,0 +1,26 @@ +\section{Properties of Isomorphisms} + +\begin{theorem}[Properties of Isomorphisms Acting on Elements] + Suppose that $\phi$ is an isomorphism from a group $G$ onto a group $\overline{G}$. Then + \begin{enumerate} + \item $\phi$ carries the identity of $G$ to the identity of $\overline{G}$. + \item For every integer $n$ and for every group element $a$ in $G$, $\phi(a^n)=[\phi(a)]^n$. + \item For any elements $a$ and $b$ in $G$, $a$ and $b$ commute if and only if $\phi(a)$ and $\phi(b)$ commute. + \item $G = \lr{a}$ if and only if $\overline{G} = \lr{\phi(a)}$. + \item $\abs{a}=\abs{\phi(a)}$ for all $a$ in $G$ (isomorphisms preserve orders). + \item For a fixed integer $k$ and a fixed group element $b$ in $G$, the equation $x^k=b$ has the same number of solutions in $G$ as does the equation $x^k = \phi(b)$ in $\overline{G}$. + \item If $G$ is finite, then $G$ and $\overline{G}$ have exactly the same number of elements of every order. + \end{enumerate} +\end{theorem} + +\begin{theorem}[Properties of Isomorphisms Acting on Groups] + Suppose that $\phi$ is an isomorphism from a group $G$ onto a group $\overline{G}$. Then + \begin{enumerate} + \item $\phi^{-1}$ is an isomorphisms from $\overline{G}$ onto $G$. + \item $G$ is Abelian if and only if $\overline{G}$ is Abelian. + \item $G$ is cyclic if and only if $\overline{G}$ is cyclic. + \item If $K$ is a subgroup of $G$, then $\phi(K) = \{\phi(k)\ \vert\ k \in K\}$ is a subgroup of $\overline{G}$. + \item If $\overline{K}$ is a subgroup of $\overline{G}$, then $\phi^{-1}(\overline{K}) = \{g \in G\ \vert\ \phi(g) \in \overline{K}\}$ is a subgroup of $G$. + \item $\phi(Z(G))=Z(\overline{G})$. + \end{enumerate} +\end{theorem} diff --git a/part-2/chapters/chapter-7/an-application-of-cosets-to-permutation-groups.tex b/part-2/chapters/chapter-7/an-application-of-cosets-to-permutation-groups.tex new file mode 100644 index 0000000..574525b --- /dev/null +++ b/part-2/chapters/chapter-7/an-application-of-cosets-to-permutation-groups.tex @@ -0,0 +1,13 @@ +\section{An Application of Cosets to Permutation Groups} + +\begin{definition}[Stabilizer of a Point] + Let $G$ be a group of permutations of a set $S$. For each $i$ in $S$, let stab$_G(i)=\{\phi \in G\ \vert\ \phi(i) = i\}$. We call stab$_G(i)$ the \textit{stabilizer of $i$ in $G$}. +\end{definition} + +\begin{definition}[Orbit of a Point] + Let $G$ be a group of permutations of a set $S$. For each $s$ in $S$, let orb$_G(s)=\{\phi(s)\ \vert\ \phi \in G\}$. The set orb$_G(s)$ is a subset of $S$ called the \textit{orbit of $s$ under $G$}. We use $\abs{\text{orb}_G(s)}$ to denote the number of elements in orb$_G(s)$. +\end{definition} + +\begin{theorem}[Orbit-Stabilizer Theorem] + Let $G$ be a finite group of permutations of a set $S$. Then, for any $i$ from $S$, $\abs{G} = \abs{\text{orb}_G(i)}\abs{\text{stab}_G(i)}$. +\end{theorem} diff --git a/part-2/chapters/chapter-7/chapter-7.tex b/part-2/chapters/chapter-7/chapter-7.tex new file mode 100644 index 0000000..775c294 --- /dev/null +++ b/part-2/chapters/chapter-7/chapter-7.tex @@ -0,0 +1,5 @@ +\chapter{Cosets and Lagrange's Theorem} +\subimport{./}{properties-of-cosets.tex} +\subimport{./}{lagranges-theorem-and-consequences.tex} +\subimport{./}{an-application-of-cosets-to-permutation-groups.tex} +\subimport{./}{the-rotation-group-of-a-cube-and-a-soccer-ball.tex} diff --git a/part-2/chapters/chapter-7/lagranges-theorem-and-consequences.tex b/part-2/chapters/chapter-7/lagranges-theorem-and-consequences.tex new file mode 100644 index 0000000..2615361 --- /dev/null +++ b/part-2/chapters/chapter-7/lagranges-theorem-and-consequences.tex @@ -0,0 +1,37 @@ +\section{Lagrange's Theorem and Consequences} + +\begin{theorem}[Lagrange's Theorem: $\mathbf{\abs{H} \text{ Divides } \abs{G}}$] + If $G$ is a finite group and $H$ is a subgroup of $G$, then $\abs{H}$ divides $\abs{G}$. Moreover, the number of distinct left (right) cosets of $H$ in $G$ is $\abs{G}/\abs{H}$. +\end{theorem} + +\begin{remark} + A special name and notation have been adopted for the number of left (or right) cosets of a subgroup in a group. The \textit{index} of a subgroup $H$ in $G$ is the number of distinct left cosets of $H$ in $G$. This number is denoted by $\abs{G:H}$. +\end{remark} + +\begin{corollary}[$\mathbf{\abs{G:H} = \abs{G}/\abs{H}}$] + If $G$ is a finite group and $H$ is a subgroup of $G$, then $\abs{G:H} = \abs{G}/\abs{H}$. +\end{corollary} + +\begin{corollary}[$\mathbf{\abs{a}}$ Divides $\mathbf{\abs{G}}$] + In a finite group, the order of each element of the group divides the order of the group. +\end{corollary} + +\begin{corollary}[Groups of Prime Order Are Cyclic] + A group of prime order is cyclic. +\end{corollary} + +\begin{corollary}[$\mathbf{a^{\abs{G}}=e}$] + Let $G$ be a finite group, and let $a \in G$. Then, $a^{\abs{G}} = e$. +\end{corollary} + +\begin{corollary}[Fermat's Little Theorem] + For every integer $a$ and every prime $p$, $a^p \mod p = a \mod p$. +\end{corollary} + +\begin{theorem}[$\mathbf{\abs{HK} = \abs{H}\abs{K}/\abs{H \cap K}}$] + For two finite subgroups $H$ and $K$ of a group, define the set $HK = \{hk\ \vert\ h \in H, k \in K\}$. Then $\abs{HK} = \abs{H}\abs{K}/\abs{H \cap K}$. +\end{theorem} + +\begin{theorem}[Classification of Groups of order 2$\mathbf{p}$] + Let $G$ be a group of order $2p$, where $p$ is a prime greater than 2. Then $G$ is isomorphic to $\Z_{2p}$ or $D_p$. +\end{theorem} diff --git a/part-2/chapters/chapter-7/properties-of-cosets.tex b/part-2/chapters/chapter-7/properties-of-cosets.tex new file mode 100644 index 0000000..bf126cd --- /dev/null +++ b/part-2/chapters/chapter-7/properties-of-cosets.tex @@ -0,0 +1,20 @@ +\section{Properties of Cosets} + +\begin{definition}[Coset of $\mathbf{H}$ in $\mathbf{G}$] + Let $G$ be a group and let $H$ be a nonempty subset of $G$. For any $a \in G$, the set $\{ah\ \vert\ h \in H\}$ is denoted by $aH$. Analogously, $Ha = \{ha\ \vert\ h \in H\}$ and $aHa^{-1} = \{aha^{-1}\ \vert\ h \in H\}$. When $H$ is a subgroup of $G$, the set $aH$ is called the \textit{left coset of $H$ in $G$ containing $a$}, whereas $Ha$ is called the \textit{right coset of $H$ in $G$ containing $a$}. In this case, the element $a$ is called the \textit{coset representative of $aH$ (or $Ha$)}. We use $\abs{aH}$ to denote the number of elements in the set $aH$, and $\abs{Ha}$ to denote the number of elements in $Ha$. +\end{definition} + +\begin{lem}[ Properties of Cosets] + Let $H$ be a subgroup of $G$, and let $a$ and $b$ belong to $G$. Then, + \begin{enumerate} + \item $a \in aH$. + \item $aH = H$ if and only if $a \in H$. + \item $(ab)H = a(bH)$ and $H(ab) = (Ha)b$. + \item $aH = bH$ if and only if $a \in bH$. + \item $aH = bH$ or $aH \cap bH = \emptyset$. + \item $aH = bH$ if and only if $a^{-1}b \in H$. + \item $\abs{aH}=\abs{bH}$. + \item $aH = Ha$ if and only if $H = aHa^{-1}$. + \item $aH$ is a subgroup of $G$ if and only if $a \in H$. + \end{enumerate} +\end{lem} diff --git a/part-2/chapters/chapter-7/the-rotation-group-of-a-cube-and-a-soccer-ball.tex b/part-2/chapters/chapter-7/the-rotation-group-of-a-cube-and-a-soccer-ball.tex new file mode 100644 index 0000000..f4b396e --- /dev/null +++ b/part-2/chapters/chapter-7/the-rotation-group-of-a-cube-and-a-soccer-ball.tex @@ -0,0 +1,5 @@ +\section{The Rotation Group of a Cube and a Soccer Ball} + +\begin{theorem}[The Rotation Group of a Cube] + The group of rotations of a cube is isomorphic to $S_4$. +\end{theorem} diff --git a/part-2/chapters/chapter-8/chapter-8.tex b/part-2/chapters/chapter-8/chapter-8.tex new file mode 100644 index 0000000..35954c1 --- /dev/null +++ b/part-2/chapters/chapter-8/chapter-8.tex @@ -0,0 +1,4 @@ +\chapter{External Direct Products} +\subimport{./}{definition-and-examples.tex} +\subimport{./}{properties-of-external-direct-products.tex} +\subimport{./}{the-group-of-units-modulo-n-as-an-external-direct-product.tex} diff --git a/part-2/chapters/chapter-8/definition-and-examples.tex b/part-2/chapters/chapter-8/definition-and-examples.tex new file mode 100644 index 0000000..72325ba --- /dev/null +++ b/part-2/chapters/chapter-8/definition-and-examples.tex @@ -0,0 +1,5 @@ +\section{Definition and Examples} + +\begin{definition}[External Direct Product] + Let $G_1,G_2,\dots,G_n$ be a finite collection of groups. The \textit{external direct product} of $G_1,G_2,\dots,G_n$, written as $G_1 \oplus G_2 \oplus \dots \oplus G_n$, is the set of all $n$-tuples for which the $i$th component is an element of $G_i$ and the operation is componentwise. +\end{definition} diff --git a/part-2/chapters/chapter-8/properties-of-external-direct-products.tex b/part-2/chapters/chapter-8/properties-of-external-direct-products.tex new file mode 100644 index 0000000..2aa4ce9 --- /dev/null +++ b/part-2/chapters/chapter-8/properties-of-external-direct-products.tex @@ -0,0 +1,18 @@ +\section{Properties of External Direct Products} + +\begin{theorem}[Order of an Element in a Direct Product] + The order of an element in a direct product of a finite number of finite groups is the least common multiple of the orders of the component of the element. In symbols, + \[ \abs{(g_1,g_2,\dots,g_n)} = \lcm(\abs{g_1},\abs{g_2},\dots,\abs{g_n}) \] +\end{theorem} + +\begin{theorem}[Criterion for $\mathbf{G \oplus H}$ to be Cyclic] + Let $G$ and $H$ be finite cyclic groups. Then $G \oplus H$ is cyclic if and only if $\abs{G}$ and $\abs{H}$ are relatively prime. +\end{theorem} + +\begin{corollary}[Criterion for $\mathbf{G_1 \oplus G_2 \oplus \dots \oplus G_n}$ to Be Cyclic] + An external direct product $G_1 \oplus G_2 \oplus \dots \oplus G_n$ of a finite number of finite cyclic groups is cyclic if and only if $\abs{G_i}$ and $\abs{G_j}$ are relatively prime when $i \neq j$. +\end{corollary} + +\begin{corollary}[Criterion for $\mathbf{\Z_{n_1n_2\dots n_k} \approx \Z_{n_1} \oplus \Z_{n_2} \oplus \dots \oplus \Z_{n_k}}$] + Let $m = n_1n_2\dots n_k$. Then $\Z_m$ is isomorphic to $\Z_{n_1} \oplus \Z_{n_2} \oplus \dots \oplus \Z_{n_k}$ if and only if $n_i$ and $n_j$ are relatively prime when $i \neq j$. +\end{corollary} diff --git a/part-2/chapters/chapter-8/the-group-of-units-modulo-n-as-an-external-direct-product.tex b/part-2/chapters/chapter-8/the-group-of-units-modulo-n-as-an-external-direct-product.tex new file mode 100644 index 0000000..1d36384 --- /dev/null +++ b/part-2/chapters/chapter-8/the-group-of-units-modulo-n-as-an-external-direct-product.tex @@ -0,0 +1,17 @@ +\section{The Group of Units Modulo $\mathbf{n}$ as an External Direct Product} + +\begin{remark} + The $U$-groups provide a convenient way to illustrate the preceding ideas. We first introduce some notation. If $k$ is a divisor of $n$, let + \[ U_k(n) = \{x \in U(n)\ \vert\ x \mod k = 1\} \] +\end{remark} + +\begin{theorem}[$\mathbf{U(n)}$ as an External Direct Product] + Suppose $s$ and $t$ are relatively prime. Then $U(st)$ is isomorphic to the external direct product of $U(s)$ and $U(t)$. In short, + \[ U(st) \approx U(s) \oplus U(t) \] + Moreover, $U_s(st)$ is isomorphic to $U(t)$ and $U_t(st)$ is isomorphic to $U(s)$. +\end{theorem} + +\begin{corollary} + Let $m = n_1n_2\dots n_k$, where $\gcd(n_i,n_j)=1$ for $i \neq j$. Then, + \[ U(m) \approx U(n_1) \oplus U(n_2) \oplus \dots \oplus U(n_k) \] +\end{corollary} diff --git a/part-2/chapters/chapter-9/applications-of-factor-groups.tex b/part-2/chapters/chapter-9/applications-of-factor-groups.tex new file mode 100644 index 0000000..750358e --- /dev/null +++ b/part-2/chapters/chapter-9/applications-of-factor-groups.tex @@ -0,0 +1,13 @@ +\section{Applications of Factor Groups} + +\begin{theorem}[$\mathbf{G/Z}$ Theorem] + Let $G$ be a group and let $Z(G)$ be the center of $G$. If $G/Z(G)$ is cyclic, then $G$ is Abelian. +\end{theorem} + +\begin{theorem}[$\mathbf{G/Z(G) \approx \text{Inn}(G)}$] + For any group $G$, $G/Z(G)$ is isomorphic to Inn$(G)$. +\end{theorem} + +\begin{theorem}[Cauchy's Theorem for Abelian Groups] + Let $G$ be a finite Abelian group and let $p$ be a prime that divides the order of $G$. Then $G$ has an element of order $p$. +\end{theorem} diff --git a/part-2/chapters/chapter-9/chapter-9.tex b/part-2/chapters/chapter-9/chapter-9.tex new file mode 100644 index 0000000..a636d8a --- /dev/null +++ b/part-2/chapters/chapter-9/chapter-9.tex @@ -0,0 +1,5 @@ +\chapter{Normal Subgroups and Factor Groups} +\subimport{./}{normal-subgroups.tex} +\subimport{./}{factor-groups.tex} +\subimport{./}{applications-of-factor-groups.tex} +\subimport{./}{internal-direct-products.tex} diff --git a/part-2/chapters/chapter-9/factor-groups.tex b/part-2/chapters/chapter-9/factor-groups.tex new file mode 100644 index 0000000..c8ae3b3 --- /dev/null +++ b/part-2/chapters/chapter-9/factor-groups.tex @@ -0,0 +1,5 @@ +\section{Factor Groups} + +\begin{theorem}[Factor Groups (O. Hölder, 1889)] + Let $G$ be a group and let $H$ be a normal subgroup of $G$. The set $G/H = \{ aH\ \vert\ a \in G\}$ is a group under the operation $(aH)(bH) = abH$. +\end{theorem} diff --git a/part-2/chapters/chapter-9/internal-direct-products.tex b/part-2/chapters/chapter-9/internal-direct-products.tex new file mode 100644 index 0000000..0b0a258 --- /dev/null +++ b/part-2/chapters/chapter-9/internal-direct-products.tex @@ -0,0 +1,26 @@ +\section{Internal Direct Products} + +\begin{definition}[Internal Direct Product of $\mathbf{H}$ and $\mathbf{K}$] + We say that $G$ is the \textit{internal direct product} of $H$ and $K$ and write $G = H \times K$ if $H$ and $K$ are normal subgroups of $G$ and + \[ G = HK\ \ \ \ \text{and}\ \ \ \ H \cap K = \{e\} \] +\end{definition} + +\begin{definition}[Internal Direct Product $\mathbf{H_1 \times H_2 \times \dots \times H_n}$] + Let $H_1, H_2,\dots,H_n$ be a finite collection of normal subgroups of $G$. We say that $G$ is the \textit{internal direct product} of $H_1,H_2,\dots,H_n$ and write $G=H_1\times H_2 \times \dots \times H_n$, if + \begin{enumerate} + \item $G = H_1H_2\dots H_n = \{h_1h_2\dots h_n\ \vert\ h_i \in H_i\}$, + \item $(H_1H_2\dots H_n) \cap H_{i + 1} = {e}$ for $i=1,2,\dots, n-1$. + \end{enumerate} +\end{definition} + +\begin{theorem}[$\mathbf{H_1 \times H_2 \times \dots \times H_n \approx H_1 \oplus H_2 \oplus \dots \oplus H_n}$] + If a group $G$ is the internal direct product of a finite number of subgroups $H_1,H_2, \dots, H_n$, then $G$ is isomorphic to the external direct product of $H_1,H_2 \dots, H_n$. +\end{theorem} + +\begin{theorem}[Classification of Groups of Order $\mathbf{p^2}$] + Every group of order $p^2$, where $p$ is a prime, is isomorphic to $\Z_{p^2}$ or $\Z_p \oplus \Z_p$. +\end{theorem} + +\begin{corollary} + If $G$ is a group of order $p^2$, where $p$ is a prime, then $G$ is Abelian. +\end{corollary} diff --git a/part-2/chapters/chapter-9/normal-subgroups.tex b/part-2/chapters/chapter-9/normal-subgroups.tex new file mode 100644 index 0000000..4bbf7db --- /dev/null +++ b/part-2/chapters/chapter-9/normal-subgroups.tex @@ -0,0 +1,9 @@ +\section{Normal Subgroups} + +\begin{definition}[Normal Subgroup] + A subgroup $H$ of a group $G$ is called a \textit{normal} subgroup of $G$ if $aH = Ha$ for all $a$ in $G$. We denote this by $H \triangleleft G$. +\end{definition} + +\begin{theorem}[Normal Subgroup Test] + A subgroup $H$ of $G$ is normal in $G$ if and only if $xHx^{-1} \subseteq H$ for all $x$ in $G$. +\end{theorem} diff --git a/part-2/part-2.tex b/part-2/part-2.tex new file mode 100644 index 0000000..9322ca0 --- /dev/null +++ b/part-2/part-2.tex @@ -0,0 +1,12 @@ +\part{Groups} +\setcounter{chapter}{1} +\subimport{chapters/chapter-2/}{chapter-2.tex} +\subimport{chapters/chapter-3/}{chapter-3.tex} +\subimport{chapters/chapter-4/}{chapter-4.tex} +\subimport{chapters/chapter-5/}{chapter-5.tex} +\subimport{chapters/chapter-6/}{chapter-6.tex} +\subimport{chapters/chapter-7/}{chapter-7.tex} +\subimport{chapters/chapter-8/}{chapter-8.tex} +\subimport{chapters/chapter-9/}{chapter-9.tex} +\subimport{chapters/chapter-10/}{chapter-10.tex} +\subimport{chapters/chapter-11/}{chapter-11.tex} diff --git a/part-3/chapters/chapter-12/chapter-12.tex b/part-3/chapters/chapter-12/chapter-12.tex new file mode 100644 index 0000000..cc8f8ae --- /dev/null +++ b/part-3/chapters/chapter-12/chapter-12.tex @@ -0,0 +1,4 @@ +\chapter{Introduction to Rings} +\subimport{./}{motivation-and-definition.tex} +\subimport{./}{properties-of-rings.tex} +\subimport{./}{subrings.tex} diff --git a/part-3/chapters/chapter-12/motivation-and-definition.tex b/part-3/chapters/chapter-12/motivation-and-definition.tex new file mode 100644 index 0000000..a43b04e --- /dev/null +++ b/part-3/chapters/chapter-12/motivation-and-definition.tex @@ -0,0 +1,20 @@ +\section{Motivation and Definition} + +\begin{definition}[Ring] + A \textit{ring} $R$ is a set with two binary operations, addition (denoted by $a + b$) and multiplication (denoted by $ab$), such that for all $a,b,c$ in $R$: + \begin{enumerate} + \item $a + b = b + a$. + \item $(a + b) + c = a + (b + c)$. + \item There is an additive identity 0. That is, there is an element 0 in $R$ such that $a + 0 = a$ for all $a$ in $R$. + \item There is an element $-a$ in $R$ such that $a + (-a) = 0$. + \item $a(bc) = (ab)c$. + \item $a(b+c) = ab + ac$ and $(b + c)a = ba + ca$. + \end{enumerate} +\end{definition} + +\begin{remark} + Note that multiplication need not be commutative. When it is, we say that the ring is \textit{commutative}. Also, a ring need not have an identity under multiplication. A \textit{unity} (or \textit{identity}) in a ring is a nonzero element that is an identity under multiplication. A nonzero element of a com- + mutative ring with unity need not have a multiplicative inverse. When it does, we say that it is a unit of the ring. Thus, $a$ is a unit if $a^{-1}$ exists. + + \noindent The following terminology and notation are convenient. If $a$ and $b$ belong to a commutative ring $R$ and $a$ is nonzero, we say that $a$ \textit{divides} $b$ (or that $a$ is a \textit{factor} of $b$) and write $a \vert b$, if there exists an element $c$ in $R$ such that $b = ac$. If $a$ does not divide $b$, we write $a \nmid b$. +\end{remark} diff --git a/part-3/chapters/chapter-12/properties-of-rings.tex b/part-3/chapters/chapter-12/properties-of-rings.tex new file mode 100644 index 0000000..ac358d1 --- /dev/null +++ b/part-3/chapters/chapter-12/properties-of-rings.tex @@ -0,0 +1,23 @@ +\section{Properties of Rings} + +\begin{theorem}[Rules of Multiplication] + Let $a,b$, and $c$ belong to a ring $R$. Then + \begin{enumerate} + \item $a0 = 0a = 0$. + \item $a(-b) = (-a)b = -(ab)$. + \item $(-a)(-b) = ab$. + \item $a(b-c) = ab - ac$ and $(b-c)a = ba - ca$. + \end{enumerate} + + Furthermore, if $R$ has a unity element $1$, then + + \begin{enumerate} + \setcounter{enumi}{4} + \item $(-1)a = -a$. + \item $(-1)(-1) = 1$. + \end{enumerate} +\end{theorem} + +\begin{theorem}[Uniqueness of the Unity and Inverses] + If a ring has a unity, it is unique. If a ring element has a multiplicative inverse, it is unique. +\end{theorem} diff --git a/part-3/chapters/chapter-12/subrings.tex b/part-3/chapters/chapter-12/subrings.tex new file mode 100644 index 0000000..3afdf62 --- /dev/null +++ b/part-3/chapters/chapter-12/subrings.tex @@ -0,0 +1,9 @@ +\section{Subrings} + +\begin{definition}[Subring] + A subset $S$ of a ring $R$ is a \textit{subring of $R$} if $S$ is itself a ring with the operations of $R$. +\end{definition} + +\begin{theorem}[Subring Test] + A nonempty subset $S$ of a ring $R$ is a subring if $S$ is closed under subtraction and multiplication -- that is, if $a - b$ and $ab$ are in $S$ whenever $a$ and $b$ are in $S$. +\end{theorem} diff --git a/part-3/chapters/chapter-13/chapter-13.tex b/part-3/chapters/chapter-13/chapter-13.tex new file mode 100644 index 0000000..b428d21 --- /dev/null +++ b/part-3/chapters/chapter-13/chapter-13.tex @@ -0,0 +1,4 @@ +\chapter{Integral Domains} +\subimport{./}{definition-and-examples.tex} +\subimport{./}{fields.tex} +\subimport{./}{characteristic-of-a-ring.tex} diff --git a/part-3/chapters/chapter-13/characteristic-of-a-ring.tex b/part-3/chapters/chapter-13/characteristic-of-a-ring.tex new file mode 100644 index 0000000..5037df0 --- /dev/null +++ b/part-3/chapters/chapter-13/characteristic-of-a-ring.tex @@ -0,0 +1,13 @@ +\section{Characteristic of a Ring} + +\begin{definition}[Characteristic of a Ring] + The \textit{characteristic} of a ring $R$ is the least positive integer $n$ such that $nx = 0$ for all $x$ in $R$. If no such integer exists, we say that $R$ has characteristic 0. The characteristic of $R$ is denoted by $\characteristic R$. +\end{definition} + +\begin{theorem}[Characteristic of a Ring with Unity] + Let $R$ be a ring with unity 1. If 1 has infinite order under addition, then the characteristic of $R$ is 0. If 1 has order $n$ under addition, then the characteristic of $R$ is $n$. +\end{theorem} + +\begin{theorem}[Characteristic of an Integral Domain] + The characteristic of an integral domain is 0 or prime. +\end{theorem} diff --git a/part-3/chapters/chapter-13/definition-and-examples.tex b/part-3/chapters/chapter-13/definition-and-examples.tex new file mode 100644 index 0000000..cb37d22 --- /dev/null +++ b/part-3/chapters/chapter-13/definition-and-examples.tex @@ -0,0 +1,13 @@ +\section{Definition and Examples} + +\begin{definition}[Zero Divisors] + A \textit{zero-divisor} is a nonzero element $a$ of a commutative ring $R$ such that there is a nonzero element $b \in R$ with $ab = 0$. +\end{definition} + +\begin{definition}[Integral Domain] + An \textit{integral domain} is a commutative ring with unity and no zero-divisors. +\end{definition} + +\begin{theorem}[Cancellation] + Let $a,b$, and $c$ belong to an integral domain If $a \neq 0$ and $ab = ac$, then $b = c$. +\end{theorem} diff --git a/part-3/chapters/chapter-13/fields.tex b/part-3/chapters/chapter-13/fields.tex new file mode 100644 index 0000000..79d9d30 --- /dev/null +++ b/part-3/chapters/chapter-13/fields.tex @@ -0,0 +1,13 @@ +\section{Fields} + +\begin{definition}[Field] + A \textit{field} is a commutative ring with unity in which every nonzero element is a unit. +\end{definition} + +\begin{theorem}[Finite Integral Domains are Fields] + A finite integral domain is a field. +\end{theorem} + +\begin{corollary}[$\mathbf{\Z_p}$ Is a Field] + For every prime $p$, $\Z_p$, the ring of integers modulo $p$ is a field. +\end{corollary} diff --git a/part-3/chapters/chapter-14/chapter-14.tex b/part-3/chapters/chapter-14/chapter-14.tex new file mode 100644 index 0000000..e17d59f --- /dev/null +++ b/part-3/chapters/chapter-14/chapter-14.tex @@ -0,0 +1,4 @@ +\chapter{Ideals and Factor Rings} +\subimport{./}{ideals.tex} +\subimport{./}{factor-rings.tex} +\subimport{./}{prime-ideals-and-maximal-ideals.tex} diff --git a/part-3/chapters/chapter-14/factor-rings.tex b/part-3/chapters/chapter-14/factor-rings.tex new file mode 100644 index 0000000..5c545da --- /dev/null +++ b/part-3/chapters/chapter-14/factor-rings.tex @@ -0,0 +1,5 @@ +\section{Factor Rings} + +\begin{theorem}[Existence of Factor Rings] + Let $R$ be a ring and let $A$ be a subring of $R$. The set of cosets $\{r + A\ \vert\ r \in R\}$ is a ring under the operations $(s + A) + (t + A) = s + t + A$ and $(s+A)(t+A)=st+A$ if and only if $A$ is an ideal of $R$. +\end{theorem} diff --git a/part-3/chapters/chapter-14/ideals.tex b/part-3/chapters/chapter-14/ideals.tex new file mode 100644 index 0000000..7b85fab --- /dev/null +++ b/part-3/chapters/chapter-14/ideals.tex @@ -0,0 +1,13 @@ +\section{Ideals} + +\begin{definition}[Ideal] + A subring $A$ of a ring $R$ is called a (two-sided) \textit{ideal} of $R$ if for every $r \in R$ and every $a \in A$ both $ra$ and $ar$ are in $A$. +\end{definition} + +\begin{theorem}[Ideal Test] + A nonempty subset $A$ of a ring $R$ is an ideal of $R$ if + \begin{enumerate} + \item $a-b \in A$ whenever $a,b \in A$. + \item $ra$ and $ar$ are in $A$ whenever $a \in A$ and $r \in R$. + \end{enumerate} +\end{theorem} diff --git a/part-3/chapters/chapter-14/prime-ideals-and-maximal-ideals.tex b/part-3/chapters/chapter-14/prime-ideals-and-maximal-ideals.tex new file mode 100644 index 0000000..8ef44e7 --- /dev/null +++ b/part-3/chapters/chapter-14/prime-ideals-and-maximal-ideals.tex @@ -0,0 +1,17 @@ +\section{Prime Ideals and Maximal Ideals} + +\begin{remark} + A \textit{proper} ideal is an ideal $I$ of some ring $R$ such that it is a proper subset of $R$; that is, $I \subset R$. +\end{remark} + +\begin{definition}[Prime Ideal, Maximal Ideal] + A \textit{prime ideal} $A$ of a commutative ring $R$ is a proper ideal of $R$ such that $a,b \in R$ and $ab \in A$ imply $a \in A$ or $b \in A$. A \textit{maximal} ideal of a commutative ring $R$ is a \textit{proper} ideal of $R$ such that, whenever $B$ is an ideal of $R$ and $A \subseteq B \subseteq R$, then $B = A$ or $B = R$. +\end{definition} + +\begin{theorem}[$\mathbf{R/A}$ Is an Integral Domain If and Only If $\mathbf{A}$ Is Prime] + Let $R$ be a commutative ring with unity and let $A$ be an ideal of $R$. Then $R/A$ is an integral domain if and only if $A$ is prime. +\end{theorem} + +\begin{theorem}[$\mathbf{R/A}$ Is a Field If and Only If $\mathbf{A}$ Is Maximal] + Let $R$ be a commutative ring with unity and let $A$ be an ideal of $R$. Then $R/A$ is a field if and only if $A$ is maximal. +\end{theorem} diff --git a/part-3/chapters/chapter-15/chapter-15.tex b/part-3/chapters/chapter-15/chapter-15.tex new file mode 100644 index 0000000..dead182 --- /dev/null +++ b/part-3/chapters/chapter-15/chapter-15.tex @@ -0,0 +1,4 @@ +\chapter{Ring Homomorphisms} +\subimport{./}{definition-and-examples.tex} +\subimport{./}{properties-of-ring-homomorphisms.tex} +\subimport{./}{the-field-of-quotients.tex} diff --git a/part-3/chapters/chapter-15/definition-and-examples.tex b/part-3/chapters/chapter-15/definition-and-examples.tex new file mode 100644 index 0000000..970df6f --- /dev/null +++ b/part-3/chapters/chapter-15/definition-and-examples.tex @@ -0,0 +1,7 @@ +\section{Definition and Examples} + +\begin{definition}[Ring Homomorphism, Ring Isomorphism] + A \textit{ring homomorphism} $\phi$ from a ring $R$ to a ring $S$ is a mapping from $R$ to $S$ that preserves the two ring operations; that is, for all $a,b$ in $R$, + \[ \phi(a + b) = \phi(a) + \phi(b)\ \ \ \ \text{and}\ \ \ \ \phi(ab) = \phi(a)\phi(b) \] + A ring homomorphism that is both one-to-one and onto is called a \textit{ring isomorphism}. +\end{definition} diff --git a/part-3/chapters/chapter-15/properties-of-ring-homomorphisms.tex b/part-3/chapters/chapter-15/properties-of-ring-homomorphisms.tex new file mode 100644 index 0000000..6817480 --- /dev/null +++ b/part-3/chapters/chapter-15/properties-of-ring-homomorphisms.tex @@ -0,0 +1,42 @@ +\section{Properties of Ring Homomorphisms} + +\begin{theorem}[Properties of Ring Homomorphisms] + Let $\phi$ be a ring homomorphism from a ring $R$ to a ring $S$. Let $A$ be a subring of $R$ and let $B$ be an ideal of $S$. + \begin{enumerate} + \item For any $r \in R$ and any positive integer $n$, $\phi(nr) = n\phi(r)$ and $\phi(r^n) = (\phi(r))^n$. + \item $\phi(A) = \{\phi(a)\ \vert\ a \in A\}$ is a subring of $S$. + \item If $A$ is an ideal and $\phi$ is onto $S$, then $\phi(A)$ is an ideal. + \item $\phi^{-1}(B) = \{r \in R\ \vert\ \phi(r) \in B\}$ is an ideal of $R$. + \item If $R$ is commutative, then $\phi(R)$ is commutative. + \item If $R$ has a unity 1, $S \neq \{0\}$, and $\phi$ is onto, then $\phi(1)$ is the unity of $S$. + \item $\phi$ is an isomorphism if and only if $\phi$ is onto and $\ker \phi = \{r \in R\ \vert\ \phi(r) = 0\} = \{0\}$. + \end{enumerate} +\end{theorem} + +\begin{theorem}[Kernels Are Ideals] + Let $\phi$ be a ring homomorphism from a ring $R$ to a ring $S$. Then $\ker \phi = \{r \in R\ \vert\ \phi(r) = 0\}$ is an ideal of $R$. +\end{theorem} + +\begin{theorem}[First Isomorphism Theorem for Rings] + Let $\phi$ be a ring homomorphism from $R$ to $S$. Then the mapping from $R/\ker \phi$ to $\phi(R)$, given by $r + \ker \phi \to \phi(r)$, is an isomorphism. In symbols, $R/\ker\phi\approx\phi(R)$. This theorem is often referred to as the \textit{Fundamental Theorem of Ring Homomorphisms}. +\end{theorem} + +\begin{theorem}[Ideals Are Kernels] + Every ideal of a ring $R$ is the kernel of a ring homomorphism of $R$. In particular, an idea l$A$ is the kernel of the mapping $r \to r + A$ from $R$ to $R/A$. This mapping is known as the \textit{natural homomorphism} from $R$ to $R/A$. +\end{theorem} + +\begin{theorem}[Homomorphism from $\mathbf{\Z}$ to a Ring with Unity] + Let $R$ be a ring with unity 1. The mapping $\phi: \Z \to R$ given by $n \to n \cdot 1$ is a ring homomorphism. +\end{theorem} + +\begin{corollary}[A Ring with Unity Contains $\mathbf{\Z_n}$ or $\mathbf{\Z}$] + If $R$ is a ring with unity and the characteristic of $R$ is $n > 0$, then $R$ contains a subring isomorphic to $\Z_n$. If the characteristic of $R$ is 0, then $R$ contains a subring isomorphic to $\Z$. +\end{corollary} + +\begin{corollary}[$\mathbf{\Z_m}$ Is a Homomorphic Image of $\mathbf{\Z}$] + For any positive integer $m$, the mapping of $\phi: \Z \to \Z_m$ given by $x \to x \mod m$ is a ring homomorphism. +\end{corollary} + +\begin{corollary}[A Field Contains $\mathbf{\Z_p \text{ or } \Q}$ (Steinitz, 1910)] + If $\F$ is a field of characteristic $p$, then $\F$ contains a subfield isomorphic to $\Z_p$. If $\F$ is a field of characteristic 0, then $\F$ contains a subfield isomorphic to the rational numbers. +\end{corollary} diff --git a/part-3/chapters/chapter-15/the-field-of-quotients.tex b/part-3/chapters/chapter-15/the-field-of-quotients.tex new file mode 100644 index 0000000..c466be6 --- /dev/null +++ b/part-3/chapters/chapter-15/the-field-of-quotients.tex @@ -0,0 +1,5 @@ +\section{The Field of Quotients} + +\begin{theorem}[Field of Quotients] + Let $D$ be an integral domain. Then there exists a field $\F$ (called the field of quotients in $D$) that contains a subring isomorphic to $D$. +\end{theorem} diff --git a/part-3/chapters/chapter-16/chapter-16.tex b/part-3/chapters/chapter-16/chapter-16.tex new file mode 100644 index 0000000..caf2a3f --- /dev/null +++ b/part-3/chapters/chapter-16/chapter-16.tex @@ -0,0 +1,3 @@ +\chapter{Polynomial Rings} +\subimport{./}{notation-and-terminology.tex} +\subimport{./}{the-division-algorithm-and-consequences.tex} diff --git a/part-3/chapters/chapter-16/notation-and-terminology.tex b/part-3/chapters/chapter-16/notation-and-terminology.tex new file mode 100644 index 0000000..386f2c2 --- /dev/null +++ b/part-3/chapters/chapter-16/notation-and-terminology.tex @@ -0,0 +1,30 @@ +\section{Notation and Terminology} + +\begin{definition}[Ring of Polynomials over $\mathbf{R}$] + Let $R$ be a commutative ring. The set of formal symbols + \[ R[x] = \{a_nx^n + a_{n-1}x^{n-1}+\dots+a_1x + a_0\ \vert\ a_i \in R, n \in \Z^+\} \] + is called the \textit{ring of polynomials over $R$ in the indeterminate $x$}.\\ + \noindent Two elements + \[ a_nx^n + a_{n-1}x^{n-1} + \dots + a_1x + a_0 \] + \noindent and + \[ b_mx^m + b_{m-1}x^{m-1} + \dots + b_1x + b_0 \] + \noindent of $R[x]$ are considered equal if and only if $a_i=b_i$ for all nonnegative integers $i$. (Define $a_i=0$ when $i > n$ and $b_i = 0$ when $i > m$.) +\end{definition} + +\begin{definition}[Addition and Multiplication in $\mathbf{R[x]}$] + Let $R$ be a commutative ring and let + \[ f(x) = a_nx^n + a_{n-1}x^{n-1} + \dots + a_1x + a_0 \] + \noindent and + \[ g(x) = b_mx^m + b_{m-1}x^{m-1} + \dots + b_1x + b_0 \] + \noindent belong to $R[x]$. Then + \[ f(x) + g(x) = (a_s + b_s)x^s + (a_{s-1} + b_{s-1})x^{s-1} + \dots + (a_1 + b_1)x + a_0 + b_0 \] + \noindent where $s$ is the maximum of $m$ and $n$, $a_i = 0$ for $i > n$, and $b_i = 0$ for $i > m$. Also, + \[ f(x)g(x) = c_{m+n}x^{m+n}+c_{m+n-1}x^{m+n-1} + \dots + c_1x + c_0 \] + \noindent where + \[ c_k = a_kb_0 + a_{k-1}b_1 + \dots + a_1b_{k-1} + a_0b_k \] + \noindent for $k=0,\dots, m+n$. +\end{definition} + +\begin{theorem}[$\mathbf{D}$ an Integral Domain Implies $\mathbf{D[x]}$ an Integral Domain] + If $D$ is an integral domain, then $D[x]$ is an integral domain. +\end{theorem} diff --git a/part-3/chapters/chapter-16/the-division-algorithm-and-consequences.tex b/part-3/chapters/chapter-16/the-division-algorithm-and-consequences.tex new file mode 100644 index 0000000..f3c78fa --- /dev/null +++ b/part-3/chapters/chapter-16/the-division-algorithm-and-consequences.tex @@ -0,0 +1,29 @@ +\section{The Division Algorithm and Consequences} + +\begin{theorem}[Division Algorithm for $\mathbf{\F[x]}$] + Let $\F$ be a field and let $f(x), g(x) \in \F[x]$ with $g(x) \neq 0$. Then there exist unique polynomials $q(x)$ and $r(x)$ in $\F[x]$ such that $f(x) = g(x)q(x) + r(x)$ and either $r(x) = 0$ or $\deg r(x) < \deg g(x)$. +\end{theorem} + +\begin{corollary}[Remainder Theorem] + Let $\F$ be a field, $a \in \F$, and $f(x) \in \F[x]$. Then $f(a)$ is the remainder in the division of $f(x)$ by $x -a$. +\end{corollary} + +\begin{corollary}[Factor Theorem] + Let $\F$ be a field, $a \in \F$, and $f(x) \in \F[x]$. Then $a$ is a zero of $f(x)$ if and only if $x-a$ is a factor of $f(x)$. +\end{corollary} + +\begin{corollary}[Polynomials of Degree $\mathbf{n}$ Have at Most $\mathbf{n}$ Zeros] + A polynomial of degree $n$ over a field has at most $n$ zeros, counting multiplicity. +\end{corollary} + +\begin{definition}[Principal Ideal Domain (PID)] + A \textit{principal ideal domain} is an integral domain $R$ in which every ideal has the form $\lr{a}=\{ra\ \vert\ r \in R\}$ for some $a$ in $R$. +\end{definition} + +\begin{theorem}[$\mathbf{\F[x]}$ Is a PID] + Let $\F$ be a field. Then $\F[x]$ is a principal ideal domain. +\end{theorem} + +\begin{theorem}[Criterion for $\mathbf{I = \lr{g(x)}}$] + Let $\F$ be a field, $I$ a nonzero ideal in $\F[x]$, and $g(x)$ an element of $\F[x]$. Then, $I=\lr{g(x)}$ if and only if $g(x)$ is a nonzero polynomial of minimum degree in $I$. +\end{theorem} diff --git a/part-3/chapters/chapter-17/chapter-17.tex b/part-3/chapters/chapter-17/chapter-17.tex new file mode 100644 index 0000000..13d4463 --- /dev/null +++ b/part-3/chapters/chapter-17/chapter-17.tex @@ -0,0 +1,4 @@ +\chapter{Factorization of Polynomials} +\subimport{./}{reducibility-tests.tex} +\subimport{./}{irreducibility-tests.tex} +\subimport{./}{unique-factorization-in-zx.tex} diff --git a/part-3/chapters/chapter-17/irreducibility-tests.tex b/part-3/chapters/chapter-17/irreducibility-tests.tex new file mode 100644 index 0000000..aa26925 --- /dev/null +++ b/part-3/chapters/chapter-17/irreducibility-tests.tex @@ -0,0 +1,29 @@ +\section{Irreducibility Tests} + +\begin{theorem}[Mod $\mathbf{p}$ Irreducibility Test] + Let $p$ be a prime and suppose that $f(x) \in \Z[x]$ with $\deg f(x) \geq 1$. Let $\overline{f}(x)$ be the polynomial in $\Z_p[x]$ obtained from $f(x)$ by reducing all the coefficients of $f(x)$ modulo $p$. If $\overline{f}(x)$ is irreducible over $\Z_p$ and $\deg \overline{f}(x) = \deg f(x)$, then $f(x)$ is irreducible over $\Q$. +\end{theorem} + +\begin{theorem}[Eisenstein's Criterion (1850)] + Let + \[ f(x) = a_nx^n + a_{n-1}x^{n-1} + \dots + a_0 \in \Z[x] \] + \noindent If there is a prime $p$ such that $p \nmid a_n, p\ \vert\ a_{n-1}, \dots, p\ \vert\ a_0$ and $p^2 \nmid a_0$, then $f(x)$ is irreducible over $\Q$. +\end{theorem} + +\begin{corollary}[Irreducibility of $\mathbf{p}$th Cyclotomic Polynomial] + For any prime $p$, the $p$th cyclotomic polynomial + \[ \Phi_p(x) = \frac{x^p - 1}{x-1} = x^{p-1} + x^{p-2} + \dots + x + 1 \] + \noindent is irreducible over $\Q$. +\end{corollary} + +\begin{theorem}[$\mathbf{\lr{p(x)}}$ Is Maximal If and Only If $\mathbf{p(x)}$ Is Irreducible] + Let $\F$ be a field and let $p(x) \in \F[x]$. Then $\lr{p(x)}$ is a maximal ideal in $\F[x]$ if and only if $p(x)$ is irreducible over $\F$. +\end{theorem} + +\begin{corollary}[$\mathbf{\F[x]/\lr{p(x)}}$ Is a Field] + Let $\F$ be a field and $p(x)$ be an irreducible polynomial over $\F$. Then $\F[x]/\lr{p(x)}$ is a field. +\end{corollary} + +\begin{corollary}[$\mathbf{p(x)\ \vert\ a(x)b(x)}$ Implies $\mathbf{p(x)\ \vert\ a(x)}$ or $\mathbf{p(x)\ \vert\ b(x)}$] + Let $\F$ be a field and let $p(x), a(x), b(x) \in \F[x]$. If $p(x)$ is irreducible over $\F$ and $p(x)\ \vert\ a(x)b(x)$, then $p(x)\ \vert\ a(x)$ or $p(x)\ \vert\ b(x)$. +\end{corollary} diff --git a/part-3/chapters/chapter-17/reducibility-tests.tex b/part-3/chapters/chapter-17/reducibility-tests.tex new file mode 100644 index 0000000..6da4977 --- /dev/null +++ b/part-3/chapters/chapter-17/reducibility-tests.tex @@ -0,0 +1,21 @@ +\section{Reducibility Tests} + +\begin{definition}[Irreducible Polynomial, Reducible Polynomial] + Let $D$ be an integral domain. A polynomial $f(x)$ from $D[x]$ that is neither the zero polynomial nor a unit in $D[x]$ is said to be \textit{irreducible over $D$}, whenever $f(x)$ is expressed as a product $f(x) = g(x)h(x)$, with $g(x)$ and $h(x)$ from $D[x]$, then $g(x)$ or $h(x)$ is a unit in $D[x]$. A nonzero, nonunit element of $D[x]$ that is not irreducible over $D$ is called \textit{reducible over $D$}. +\end{definition} + +\begin{theorem}[Reducibility Test for Degrees 2 and 3] + Let $\F$ be a field. If $f(x) \in \F[x]$ and $\deg f(x)$ is 2 or 3, then $f(x)$ is reducible over $\F$ if and only if $f(x)$ has a zero in $\F$. +\end{theorem} + +\begin{definition}[Content of a Polynomial, Primitive Polynomial] + The \textit{content} of a nonzero polynomial $a_nx^n + a_{n-1}x^{n-1} + \dots + a_0$, where the $a$'a are integers, is the greatest common divisor of the integers $a_n,a_{n-1}, \dots, a_0$. A \textit{primitive polynomial} is an element of $\Z[x]$ with content 1. +\end{definition} + +\begin{lemma}[Gauss's Lemma] + The product of two primitive polynomials is primitive. +\end{lemma} + +\begin{theorem}[Reducibility over $\mathbf{\Q}$ Implies Reducibility over $\mathbf{\Z}$] + Let $f(x) \in \Z[x]$. If $f(x)$ is reducible over $\Q$, then it is reducible over $\Z$. +\end{theorem} diff --git a/part-3/chapters/chapter-17/unique-factorization-in-zx.tex b/part-3/chapters/chapter-17/unique-factorization-in-zx.tex new file mode 100644 index 0000000..965abee --- /dev/null +++ b/part-3/chapters/chapter-17/unique-factorization-in-zx.tex @@ -0,0 +1,7 @@ +\section{Unique Factorization In $\mathbf{\Z[x]}$} + +\begin{theorem}[Unique Factorization in $\mathbf{\Z[x]}$] + Every polynomial in $\Z[x]$ that is not the zero polynomial or a unit in $\Z[x]$ can be written in the form $b_1b_2\dots b_sp_1(x)p_2(x)\dots p_m(x)$, where the $b_i$'s are irreducible polynomials of degree 0 and the $p_i(x)$'s are irreducible polynomials of positive degree. Furthermore, if + \[ b_1b_2\dots b_sp_1(x)p_2(x) \dots p_m(x) = c_1c_2 \dots c_tq_1(x) q_2(x) \dots q_n(x) \] + \noindent where the $b_i$'s and the $c_i$'s are irreducible polynomials of degree 0 and the $p_i(x)$'s and $q_i(x)$'s are irreducible polynomials of positive degree, then $s=t, m=n$, and, after renumbering the $c$'s and $q(x)$'s, we have $b_i = \pm c_i$, for $i=1, \dots, s$, and $p_i(x)= \pm q_i(x)$, for $i = 1, \dots, m$. +\end{theorem} diff --git a/part-3/chapters/chapter-18/chapter-18.tex b/part-3/chapters/chapter-18/chapter-18.tex new file mode 100644 index 0000000..921653a --- /dev/null +++ b/part-3/chapters/chapter-18/chapter-18.tex @@ -0,0 +1,4 @@ +\chapter{Divisibility in Integral Domains} +\subimport{./}{irreducibles-primes.tex} +\subimport{./}{unique-factorization-domains.tex} +\subimport{./}{euclidean-domains.tex} diff --git a/part-3/chapters/chapter-18/euclidean-domains.tex b/part-3/chapters/chapter-18/euclidean-domains.tex new file mode 100644 index 0000000..7b4e519 --- /dev/null +++ b/part-3/chapters/chapter-18/euclidean-domains.tex @@ -0,0 +1,21 @@ +\section{Euclidean Domains} + +\begin{definition}[Euclidean Domain (ED)] + An integral domain $D$ is called a \textit{Euclidean domain} if there is a function $d$ (called the \textit{measure}) from nonzero elements of $D$ to the nonnegative integers such that + \begin{enumerate} + \item $d(a) \leq d(ab)$ for all nonzero $a,b \in D$; and + \item if $a,b \in D,\ b \neq 0$, then there exist elements $q$ and $r$ in $D$ such that $a = bq + r$, where $r = 0$ or $d(r) < d(b)$. + \end{enumerate} +\end{definition} + +\begin{theorem}[ED Implies PID] + Every Euclidean domain is a principal ideal domain. +\end{theorem} + +\begin{corollary}[ED Implies UFD] + Every Euclidean domain is a unique factorization domain. +\end{corollary} + +\begin{theorem}[$\mathbf{D}$ a UFD Implies $\mathbf{D[x]}$ a UFD] + If $D$ is a unique factorization domain, then $D[x]$ is a unique factorization domain. +\end{theorem} diff --git a/part-3/chapters/chapter-18/irreducibles-primes.tex b/part-3/chapters/chapter-18/irreducibles-primes.tex new file mode 100644 index 0000000..9684731 --- /dev/null +++ b/part-3/chapters/chapter-18/irreducibles-primes.tex @@ -0,0 +1,13 @@ +\section{Irreducibles, Primes} + +\begin{definition}[Associates, Irreducibles, Primes] + Elements $a$ and $b$ of an integral domain $D$ are called \textit{associates} if $a = ub$, where $u$ is a unit of $D$. A nonzero element $a$ of an integral domain $D$ is called an \textit{irreducible} if $a$ is not a unit and, whenever $b$, $c \in D$ with $a = bc$, then $b$ or $c$ is a unit. A nonzero element $a$ of an integral domain $D$ is called a \textit{prime} if $a$ is not a unit and $a\ \vert\ bc$ implies $a\ \vert\ b$ or $a\ \vert\ c$. +\end{definition} + +\begin{theorem}[Prime Implies Irreducible] + In an integral domain, every prime in an irreducible. +\end{theorem} + +\begin{theorem}[PID Implies Irreducible Equals Prime] + In a principal ideal domain, an element is an irreducible if and only if it is a prime. +\end{theorem} diff --git a/part-3/chapters/chapter-18/unique-factorization-domains.tex b/part-3/chapters/chapter-18/unique-factorization-domains.tex new file mode 100644 index 0000000..34c0d59 --- /dev/null +++ b/part-3/chapters/chapter-18/unique-factorization-domains.tex @@ -0,0 +1,21 @@ +\section{Unique Factorization Domains} + +\begin{definition} + An integral domain $D$ is a \textit{unique factorization domain} if + \begin{enumerate} + \item every nonzero element of $D$ that is not a unit can be written as a product of irreducibles of $D$; and + \item the factorization into irreducibles is unique up to associates and the order in which the factors appear. + \end{enumerate} +\end{definition} + +\begin{lemma}[Ascending Chain Condition for a PID] + In a principal ideal domain, any stricly increasing chain of ideals $I_1 \subset I_2 \subset \dots$ must be finite in length. +\end{lemma} + +\begin{theorem}[PID Implies UFD] + Every principal ideal domain is a unique factorization domain. +\end{theorem} + +\begin{corollary}[$\mathbf{\F[x]}$ Is a UFD] + Let $\F$ be a field. Then $\F[x]$ is a unique factorization domain. +\end{corollary} diff --git a/part-3/part-3.tex b/part-3/part-3.tex new file mode 100644 index 0000000..652cc49 --- /dev/null +++ b/part-3/part-3.tex @@ -0,0 +1,8 @@ +\part{Rings} +\subimport{chapters/chapter-12/}{chapter-12.tex} +\subimport{chapters/chapter-13/}{chapter-13.tex} +\subimport{chapters/chapter-14/}{chapter-14.tex} +\subimport{chapters/chapter-15/}{chapter-15.tex} +\subimport{chapters/chapter-16/}{chapter-16.tex} +\subimport{chapters/chapter-17/}{chapter-17.tex} +\subimport{chapters/chapter-18/}{chapter-18.tex} diff --git a/part-4/chapters/chapter-19/chapter-19.tex b/part-4/chapters/chapter-19/chapter-19.tex new file mode 100644 index 0000000..1477437 --- /dev/null +++ b/part-4/chapters/chapter-19/chapter-19.tex @@ -0,0 +1,4 @@ +\chapter{Vector Spaces} +\subimport{./}{definition-and-examples.tex} +\subimport{./}{subspaces.tex} +\subimport{./}{linear-independence.tex} diff --git a/part-4/chapters/chapter-19/definition-and-examples.tex b/part-4/chapters/chapter-19/definition-and-examples.tex new file mode 100644 index 0000000..1bdb76a --- /dev/null +++ b/part-4/chapters/chapter-19/definition-and-examples.tex @@ -0,0 +1,15 @@ +\section{Definition and Examples} + +\begin{definition}[Vector Space] + A set $V$ is said to be a \textit{vector space} over a field $\F$ if $V$ is an Abelian group under addition (denoted by $+$) and, if for each $a \in \F$ and $v \in V$, there is an element $av \in V$ such that the following conditions hold for all $a,b \in \F$ and all $u,v \in V$. + \begin{enumerate} + \item $a(v + u) = av + au$ + \item $(a + b)v = av + bv$ + \item $a(bv)=(ab)v$ + \item $1v=v$ + \end{enumerate} +\end{definition} + +\begin{remark} + The members of a vector space are called \textit{vectors}. The members of the field are called \textit{scalars}. The operation that combines a scalar $a$ and a vector $v$ to form the vector $av$ is called \textit{scalar multiplication}. In general, we will denote vectors by letters from the end of the alphabet, such as $u,v,w$, and scalars by letters from the beginning of the alphabet, such as $a,b,c$. +\end{remark} diff --git a/part-4/chapters/chapter-19/linear-independence.tex b/part-4/chapters/chapter-19/linear-independence.tex new file mode 100644 index 0000000..21fcaa0 --- /dev/null +++ b/part-4/chapters/chapter-19/linear-independence.tex @@ -0,0 +1,19 @@ +\section{Linear Independence} + +\begin{definition}[Linearly Dependent, Linearly Independent] + A set $S$ of vectors is said to be \textit{linearly dependent} over a field $\F$ if there are vectors $v_1,v_2,\dots,v_n$ from $S$ and elements $a_1,a_2,\dots,a_n$ from $\F$, not all zero, such that $a_1v_1+a_2v_2+\dots+a_nv_n = 0$. A set of vectors that is not linearly dependent over $\F$ is called \textit{linearly independent} over $\F$. +\end{definition} + +\begin{definition}[Basis] + Let $V$ be a vector space over $\F$. A subset $B$ of $V$ is called a \textit{basis} for $V$ if $B$ is linearly independent over $\F$ and every element of $V$ is a linear combination of elements of $B$. +\end{definition} + +\begin{theorem}[Invariance of Basis Size] + If $\{u_1,u_2,\dots,u_m\}$ and $\{w_1,w_2,\dots,w_n\}$ are both bases of a vector space $V$ over a field $\F$, then $m=n$. +\end{theorem} + +\begin{definition}[Dimension] + A vector space that has a basis consisting of $n$ elements is said to have \textit{dimension $n$}. For completeness, the trivial vector space $\{0\}$ is said to be spanned by the empty set and to have dimension 0. + + \noindent A vector space that has a finite basis is called \textit{finite dimensional}; otherwise, it is called \textit{infinite dimensional}. +\end{definition} diff --git a/part-4/chapters/chapter-19/subspaces.tex b/part-4/chapters/chapter-19/subspaces.tex new file mode 100644 index 0000000..d402290 --- /dev/null +++ b/part-4/chapters/chapter-19/subspaces.tex @@ -0,0 +1,5 @@ +\section{Subspaces} + +\begin{definition}[Subspace] + Let $V$ be a vector space over a field $\F$ and let $U$ be a subset of $V$. We say that $U$ is a \textit{subspace} of $V$ if $U$ is also a vector space over $\F$ under the operations of $V$. +\end{definition} diff --git a/part-4/chapters/chapter-20/chapter-20.tex b/part-4/chapters/chapter-20/chapter-20.tex new file mode 100644 index 0000000..b89fb09 --- /dev/null +++ b/part-4/chapters/chapter-20/chapter-20.tex @@ -0,0 +1,4 @@ +\chapter{Extension Fields} +\subimport{./}{the-fundamental-theorem-of-field-theory.tex} +\subimport{./}{splitting-fields.tex} +\subimport{./}{zeros-of-an-irreducible-polynomial.tex} diff --git a/part-4/chapters/chapter-20/splitting-fields.tex b/part-4/chapters/chapter-20/splitting-fields.tex new file mode 100644 index 0000000..39871b5 --- /dev/null +++ b/part-4/chapters/chapter-20/splitting-fields.tex @@ -0,0 +1,34 @@ +\section{Splitting Fields} + +\begin{definition}[Splitting Field] + Let $\E$ be an extension field of $\F$ and let $f(x) \in \F[x]$ with degree at least 1. We say that $f(x)$ \textit{splits} in $\E$ if there are elements $a \in \F$ and $a_1,a_2,\dots,a_n \in \E$ such that + \[ f(x) = a(x-a_1)(x-a_2)\dots(x-a_n) \] + We call $\E$ a \textit{splitting field for $f(x)$ over $\F$} if + \[ \E = \F(a_1,a_2,\dots,a_n) \] +\end{definition} + +\begin{theorem}[Existence of Splitting Fields] + Let $\F$ be a field and let $f(x)$ be a nonconstant element of $\F[x]$. Then there exists a splitting field $\E$ for $f(x)$ over $\F$. +\end{theorem} + +\begin{theorem}[$\mathbf{\F(a) \approx \F[x]/\lr{p(x)}}$] + Let $\F$ be a field and let $p(x) \in \F[x]$ be irreducible over $\F$. If $a$ is a zero of $p(x)$ in some extension $\E$ of $\F$, then $\F(a)$ is isomorphic to $\F[x]/\lr{p(x)}$. Furthermore, if $\deg p(x) = n$, then every member of $\F(a)$ can be uniquely expressed in the form + \[ c_{n-1}a^{n-1}+c_{n-2}a^{n-2}+\dots+c_1a+c_0 \] + where $c_0,c_1,\dots,c_{n-1} \in \F$. +\end{theorem} + +\begin{corollary}[$\mathbf{\F(a) \approx \F(b)}$] + Let $\F$ be a field and let $p(x) \in \F[x]$ be irreducible over $\F$. If $a$ is a zero of $p(x)$ in some extension $\E$ of $\F$ and $b$ is a zero of $p(x)$ in some extension $\E'$ of $\F$, then the fields $\F(a)$ and $\F(b)$ are isomorphic. +\end{corollary} + +\begin{lemma} + Let $\F$ be a field, let $p(x) \in \F[x]$ be irreducible over $\F$, and let $a$ be a zero of $p(x)$ in some extension of $\F$. If $\phi$ is a field isomorphism from $\F$ to $\F'$ and $b$ is a zero of $\phi(p(x))$ in some extension of $\F'$, then there is an isomorphism from $\F(a)$ to $\F'(b)$ that agrees with $\phi$ on $\F$ and carries $a$ to $b$. +\end{lemma} + +\begin{theorem}[Extending $\mathbf{\phi: \F \to \F'}$] + Let $\phi$ be an isomorphism from a field $\F$ to a field $\F'$ and let $f(x) \in \F[x]$. If $\E$ is a splitting field for $f(x)$ over $\F$ and $\E'$ is a splitting field for $\phi(f(x))$ over $\F'$, then there is an isomorphism from $\E$ to $\E'$ that agrees with $\phi$ on $\F$. +\end{theorem} + +\begin{corollary}[Splitting Fields Are Unique] + Let $\F$ be a field and let $f(x) \in \F[x]$. Then any two splitting fields of $f(x)$ over $\F$ are isomorphic. +\end{corollary} diff --git a/part-4/chapters/chapter-20/the-fundamental-theorem-of-field-theory.tex b/part-4/chapters/chapter-20/the-fundamental-theorem-of-field-theory.tex new file mode 100644 index 0000000..88fc4ba --- /dev/null +++ b/part-4/chapters/chapter-20/the-fundamental-theorem-of-field-theory.tex @@ -0,0 +1,9 @@ +\section{The Fundamental Theorem of Field Theory} + +\begin{definition}[Extension Field] + A field $\E$ is an \textit{extension field} of a field $\F$ if $\F \subseteq \E$ and the operations of $\F$ are those of $\E$ restricted to $\F$. +\end{definition} + +\begin{theorem}[Fundamental Theorem of Field Theory (Kronecker's Theorem, 1887)] + Let $\F$ be a field and let $f(x)$ be a nonconstant polynomial in $\F[x]$. Then there is an extension field $\E$ of $\F$ in which $f(x)$ has a zero. +\end{theorem} diff --git a/part-4/chapters/chapter-20/zeros-of-an-irreducible-polynomial.tex b/part-4/chapters/chapter-20/zeros-of-an-irreducible-polynomial.tex new file mode 100644 index 0000000..12bddf6 --- /dev/null +++ b/part-4/chapters/chapter-20/zeros-of-an-irreducible-polynomial.tex @@ -0,0 +1,44 @@ +\section{Zeros of an Irreducible Polynomial} + +\begin{definition}[Derivative] + Let $f(x) = a_nx^n + a_{n-1}x^{n-1} + \dots + a_1x + a_0$ belong to $\F[x]$. The \textit{derivative} of $f(x)$, denoted by $f'(x)$, is the polynomial $na_nx^{x-1} + (n-1)a_{n-1}x^{n-2} + \dots + a_1$ in $\F[x]$. +\end{definition} + +\begin{lemma}[Properties of the Derivative] + Let $f(x)$ and $g(x) \in \F[x]$ and let $a \in \F$. Then + \begin{enumerate} + \item $(f(x) + g(x))' = f'(x) + g'(x)$. + \item $(af(x))' = af'(x)$. + \item $(f(x)g(x))' = f(x)g'(x) + g(x)f'(x)$. + \end{enumerate} +\end{lemma} + +\begin{theorem}[Criterion for Multiple Zeros] + A polynomial $f(x)$ over a field $\F$ has a multiple zero in some extension $\E$ if and only if $f(x)$ and $f'(x)$ have a common factor of positive degree in $\F[x]$. +\end{theorem} + +\begin{theorem}[Zeros of an Irreducible] + Let $f(x)$ be an irreducible polynomial over a field $\F$. If $\F$ has characteristic 0, then $f(x)$ has no multiple zeros. If $\F$ has characteristic $p \neq 0$, then $f(x)$ has a multiple zero if it is of the form $f(x) = g(x^p)$ for some $g(x)$ in $\F[x]$. +\end{theorem} + +\begin{definition}[Perfect Field] + A field $\F$ is called \textit{perfect} if $\F$ has characteristic 0 or if $\F$ has characteristic $p$ and $\F^p=\{a^p\ \vert\ a \in \F\} = \F$. +\end{definition} + +\begin{theorem}[Finite Fields Are Perfect] + Every finite field is perfect. +\end{theorem} + +\begin{theorem}[Criterion for No Multiple Zeros] + If $f(x)$ is an irreducible polynomial over a perfect field $\F$, then $f(x)$ has no multiple zeros. +\end{theorem} + +\begin{theorem}[Zeros of an Irreducible over a Splitting Field] + Let $f(x)$ be an irreducible polynomial over a field $\F$ and let $\E$ be a splitting field of $f(x)$ over $\F$. Then all the zeros of $f(x)$ in $\E$ have the same multiplicity. +\end{theorem} + +\begin{corollary}[Factorization of an Irreducible over a Splitting Field] + Let $f(x)$ be an irreducible polynomial over a field $\F$ and let $\E$ be a splitting field of $f(x)$. Then $f(x)$ has the form + \[ a(x-a_1)^n(x-a_2)^n\dots(x-a_t)^n \] + where $a_1,a_2,\dots,a_t$ are distinct elements of $\E$ and $a \in \F$. +\end{corollary} diff --git a/part-4/chapters/chapter-21/chapter-21.tex b/part-4/chapters/chapter-21/chapter-21.tex new file mode 100644 index 0000000..997c4e4 --- /dev/null +++ b/part-4/chapters/chapter-21/chapter-21.tex @@ -0,0 +1,4 @@ +\chapter{Algebraic Extensions} +\subimport{./}{characterization-of-extensions.tex} +\subimport{./}{finite-extensions.tex} +\subimport{./}{properties-of-algebraic-extensions.tex} diff --git a/part-4/chapters/chapter-21/characterization-of-extensions.tex b/part-4/chapters/chapter-21/characterization-of-extensions.tex new file mode 100644 index 0000000..28cb197 --- /dev/null +++ b/part-4/chapters/chapter-21/characterization-of-extensions.tex @@ -0,0 +1,17 @@ +\section{Characterization of Extensions} + +\begin{definition}[Types of Extensions] + Let $\E$ be an extension field of a field $\F$ and let $a \in \E$. We call $a$ \textit{algebraic over $\F$} if $a$ is the zero of some nonzero polynomial in $\F[x]$. If $a$ is not algebraic over $\F$, it is called \textit{transcendental over $\F$}. An extension $\E$ of $\F$ is called an \textit{algebraic} extension of $\F$ if every element of $\E$ is algebraic over $\F$. If $\E$ is not an algebraic extension of $\F$, it is called a \textit{transcendental} extension of $\F$. An extension of $\F$ of the form $\F(a)$ is called a \textit{simple} extension of $\F$. +\end{definition} + +\begin{theorem}[Characterization of Extensions] + Let $\E$ be an extension field of the field $\F$ and let $a \in \E$. If $a$ is transcendental over $\F$, then $\F(a) \approx \F(x)$. If $a$ is algebraic over $\F$, then $\F(a) \approx \F[x]/\lr{p(x)}$, where $p(x)$ is a polynomial in $\F[x]$ of minimum degree such that $p(a) = 0$. Moreover, $p(x)$ is irreducible over $\F$. +\end{theorem} + +\begin{theorem}[Uniqueness Property] + If $a$ is algebraic over a field $\F$, then there is a unique monic irreducible polynomial $p(x)$ in $\F[x]$ such that $p(a)=0$. The polynomial with this property is called the \textit{minimal polynomial for $a$ over $\F$}. +\end{theorem} + +\begin{theorem}[Divisibility Property] + Let $a$ be algebraic over $\F$, and let $p(x)$ be the minimal polynomial for $a$ over $\F$. If $f(x) \in \F[x]$ and $f(a) = 0$, then $p(x)$ divides $f(x)$ in $\F[x]$. +\end{theorem} diff --git a/part-4/chapters/chapter-21/finite-extensions.tex b/part-4/chapters/chapter-21/finite-extensions.tex new file mode 100644 index 0000000..8e2e161 --- /dev/null +++ b/part-4/chapters/chapter-21/finite-extensions.tex @@ -0,0 +1,17 @@ +\section{Finite Extensions} + +\begin{definition}[Degree of an Extension] + Let $\E$ be an extension field of a field $\F$. We say that $\E$ \textit{has degree $n$ over $\F$} and write $[\E:\F]=n$ if $\E$ has dimension $n$ as a vector space over $\F$. If $[\E:\F]$ is finite, $\E$ is called a \textit{finite extension} of $\F$; otherwise, we say that $\E$ is an \textit{infinite extension} of $\F$. +\end{definition} + +\begin{theorem}[Finite Implies Algebraic] + If $\E$ is a finite extension of $\F$, then $\E$ is an algebraic extension of $\F$. +\end{theorem} + +\begin{theorem}[$\mathbf{[\K:\F] = [\K:\E][\E:\F]}$] + Let $\K$ be a finite extension field of the field $\E$ and let $\E$ be a finite extension field of the field $\F$. Then $\K$ is a finite extension field of $\F$ and $[\K:\F] = [\K:\E][\E:\F]$. +\end{theorem} + +\begin{theorem}[Primitive Element Theorem (Steinitz, 1910)] + If $\F$ is a field of characteristic 0, and $a$ and $b$ are algebraic over $\F$, then there is an element $c$ in $\F(a,b)$ such that $\F(a,b) = \F(c)$. +\end{theorem} diff --git a/part-4/chapters/chapter-21/properties-of-algebraic-extensions.tex b/part-4/chapters/chapter-21/properties-of-algebraic-extensions.tex new file mode 100644 index 0000000..73af884 --- /dev/null +++ b/part-4/chapters/chapter-21/properties-of-algebraic-extensions.tex @@ -0,0 +1,9 @@ +\section{Properties of Algebraic Extensions} + +\begin{theorem}[Algebraic over Algebraic Is Algebraic] + If $\K$ is an algebraic extension of $\E$ and $\E$ is an algebraic extension of $\F$, then $\K$ is an algebraic extension of $\F$. +\end{theorem} + +\begin{corollary}[Subfield of Algebraic Elements] + Let $\E$ be an extension field of the field $\F$. Then the set of all elements of $\E$ that are algebraic over $\F$ is a subfield of $\E$. +\end{corollary} diff --git a/part-4/chapters/chapter-22/chapter-22.tex b/part-4/chapters/chapter-22/chapter-22.tex new file mode 100644 index 0000000..b45a0a3 --- /dev/null +++ b/part-4/chapters/chapter-22/chapter-22.tex @@ -0,0 +1,4 @@ +\chapter{Finite Fields} +\subimport{./}{classification-of-finite-fields.tex} +\subimport{./}{structure-of-finite-fields.tex} +\subimport{./}{subfields-of-a-finite-field.tex} diff --git a/part-4/chapters/chapter-22/classification-of-finite-fields.tex b/part-4/chapters/chapter-22/classification-of-finite-fields.tex new file mode 100644 index 0000000..5f6b792 --- /dev/null +++ b/part-4/chapters/chapter-22/classification-of-finite-fields.tex @@ -0,0 +1,5 @@ +\section{Classification of Finite Fields} + +\begin{theorem}[Classification of Finite Fields] + For each prime $p$ and each positive integer $n$, there is, up to isomorphism, a unique finite field of order $p^n$. +\end{theorem} diff --git a/part-4/chapters/chapter-22/structure-of-finite-fields.tex b/part-4/chapters/chapter-22/structure-of-finite-fields.tex new file mode 100644 index 0000000..4d75155 --- /dev/null +++ b/part-4/chapters/chapter-22/structure-of-finite-fields.tex @@ -0,0 +1,19 @@ +\section{Structure of Finite Fields} + +\begin{theorem}[Structure of Finite Fields] + As a group under addition, $\gf(p^n)$ is isomorphic to + \[ \underbrace{\Z_p \oplus \Z_p \oplus \dots \oplus \Z_p}_\text{$n$ factors} \] + As a group under multiplication, the set of nonzero elements of $\gf(p^n)$ is isomorphic to $\Z_{p^n-1}$ (and is, therefore, cyclic). +\end{theorem} + +\begin{remark} + Because there is only one field for each prime-power $p^n$, we may unambiguously denote it by $\gf(p^n)$, in honor of Galois, and call it the \textit{Galois field of order $p^n$}. +\end{remark} + +\begin{corollary} + \[ [\gf(p^n):\gf(p)]=n \] +\end{corollary} + +\begin{corollary}[$\mathbf{\gf(p^n)}$ Contains an Element of Degree $\mathbf{n}$] + Let $a$ be a generator of the group of nonzero elements of $\gf(p^n)$ under multiplication. Then $a$ is algebraic over $\gf(p)$ of degree $n$. +\end{corollary} diff --git a/part-4/chapters/chapter-22/subfields-of-a-finite-field.tex b/part-4/chapters/chapter-22/subfields-of-a-finite-field.tex new file mode 100644 index 0000000..b06fe65 --- /dev/null +++ b/part-4/chapters/chapter-22/subfields-of-a-finite-field.tex @@ -0,0 +1,5 @@ +\section{Subfields of a Finite Field} + +\begin{theorem}[Subfields of a Finite Field] + For each divisor $m$ of $n$, $\gf(p^n)$ has a unique subfield of order $p^m$. Moreover, these are the only subfields of $\gf(p^n)$. +\end{theorem} diff --git a/part-4/chapters/chapter-23/chapter-23.tex b/part-4/chapters/chapter-23/chapter-23.tex new file mode 100644 index 0000000..eaf204a --- /dev/null +++ b/part-4/chapters/chapter-23/chapter-23.tex @@ -0,0 +1 @@ +\chapter{Geometric Constructions} diff --git a/part-4/part-4.tex b/part-4/part-4.tex new file mode 100644 index 0000000..58ca3aa --- /dev/null +++ b/part-4/part-4.tex @@ -0,0 +1,6 @@ +\part{Fields} +\subimport{chapters/chapter-19/}{chapter-19.tex} +\subimport{chapters/chapter-20/}{chapter-20.tex} +\subimport{chapters/chapter-21/}{chapter-21.tex} +\subimport{chapters/chapter-22/}{chapter-22.tex} +\subimport{chapters/chapter-23/}{chapter-23.tex} diff --git a/part-5/chapters/chapter-24/applications-of-sylow-theorems.tex b/part-5/chapters/chapter-24/applications-of-sylow-theorems.tex new file mode 100644 index 0000000..518d6ff --- /dev/null +++ b/part-5/chapters/chapter-24/applications-of-sylow-theorems.tex @@ -0,0 +1,5 @@ +\section{Applications of Sylow Theorems} + +\begin{theorem}[Cyclic Groups of Order $\mathbf{pq}$] + If $G$ is a group of order $pq$, where $p$ and $q$ are primes, $p < q$, and $p$ does not divide $q - 1$, then $G$ is cyclic. In particular, $G$ is isomorphic to $\Z_{pq}$. +\end{theorem} diff --git a/part-5/chapters/chapter-24/chapter-24.tex b/part-5/chapters/chapter-24/chapter-24.tex new file mode 100644 index 0000000..93acade --- /dev/null +++ b/part-5/chapters/chapter-24/chapter-24.tex @@ -0,0 +1,5 @@ +\chapter{Sylow Theorems} +\subimport{./}{conjugacy-classes.tex} +\subimport{./}{the-class-equation.tex} +\subimport{./}{the-sylow-theorems.tex} +\subimport{./}{applications-of-sylow-theorems.tex} diff --git a/part-5/chapters/chapter-24/conjugacy-classes.tex b/part-5/chapters/chapter-24/conjugacy-classes.tex new file mode 100644 index 0000000..0ad187a --- /dev/null +++ b/part-5/chapters/chapter-24/conjugacy-classes.tex @@ -0,0 +1,13 @@ +\section{Conjugacy Classes} + +\begin{definition}[Conjugacy Class of $\mathbf{a}$] + Let $a$ and $b$ be elements of a group $G$. We say that $a$ and $b$ are \textit{conjugate} in $G$ (and call $b$ the \textit{conjugate} of $a$) if $xax^{-1}=b$ for some $x$ in $G$. The \textit{conjugacy class of $a$} is the set $\cl(a) = \{xax^{-1}\ \vert\ x \in G\}$. +\end{definition} + +\begin{theorem}[Number of Conjugates of $\mathbf{a}$] + Let $G$ be a finite group and let $a$ be an element of $G$. Then, $\abs{\cl(a)} = \abs{G:C(a)}$. +\end{theorem} + +\begin{corollary}[$\mathbf{\abs{\cl(a)}}$ Divides $\mathbf{\abs{G}}$] + In a finite group, $\abs{\cl(a)}$ divides $\abs{G}$. +\end{corollary} diff --git a/part-5/chapters/chapter-24/the-class-equation.tex b/part-5/chapters/chapter-24/the-class-equation.tex new file mode 100644 index 0000000..ca30be1 --- /dev/null +++ b/part-5/chapters/chapter-24/the-class-equation.tex @@ -0,0 +1,15 @@ +\section{The Class Equation} + +\begin{corollary}[Class Equation] + For any finite group $G$, + \[ \abs{G} = \sum \abs{G:C(a)} \] + where the sum runs over one element of $a$ from each conjugacy class of $G$. +\end{corollary} + +\begin{theorem}[$\mathbf{p}$-Groups Have Nontrivial Centers] + Let $G$ be a nontrivial finite group whose order is a power of a prime $p$. Then $\Z(G)$ has more than one element. +\end{theorem} + +\begin{corollary}[Groups of Order $\mathbf{p^2}$ Are Abelian] + If $\abs{G}=p^2$, where $p$ is prime, then $G$ is Abelian. +\end{corollary} diff --git a/part-5/chapters/chapter-24/the-sylow-theorems.tex b/part-5/chapters/chapter-24/the-sylow-theorems.tex new file mode 100644 index 0000000..4c8372e --- /dev/null +++ b/part-5/chapters/chapter-24/the-sylow-theorems.tex @@ -0,0 +1,29 @@ +\section{The Sylow Theorems} + +\begin{theorem}[Existence of Subgroups of Prime-Power Order (Sylow's First Theorem, 1872)] + Let $G$ be a finite group and let $p$ be a prime. If $p^k$ divides $\abs{G}$, then $G$ has at least one subgroup of order $p^k$. +\end{theorem} + +\begin{definition}[Sylow $\mathbf{p}$-Subgroup] + Let $G$ be a finite group and let $p$ be a prime. If $p^k$ divides $\abs{G}$ and $p^{k+1}$ does not divide $\abs{G}$, then any subgroup of $G$ of order $p^k$ is called a \textit{Sylow $p$-subgroup of $G$}. +\end{definition} + +\begin{corollary}[Cauchy's Theorem] + Let $G$ be a finite group and let $p$ be a prime that divides the order of $G$. Then $G$ has an element of order $p$. +\end{corollary} + +\begin{definition}[Conjugate Subgroups] + Let $H$ and $K$ be subgroups of a group $G$. We say that $H$ and $K$ are \textit{conjugate} in $G$ if there is an element in $G$ such that $H = gKg^{-1}$. +\end{definition} + +\begin{theorem}[Sylow's Second Theorem] + If $H$ is a subgroup of a finite group $G$ and $\abs{H}$ is a power of a prime $p$, then $H$ is contained in some Sylow $p$-subgroup of $G$. +\end{theorem} + +\begin{theorem}[Sylow's Third Theorem] + Let $p$ be a prime and let $G$ be a group of order $p^km$, where $p$ does not divide $m$. Then the number $n$ of Sylow $p$-subgroups of $G$ is equal to 1 modulo $p$ and divides $m$. Furthermore, any two Sylow $p$-subgroups of $G$ are conjugate. +\end{theorem} + +\begin{corollary}[A Unique Sylow $\mathbf{p}$-Subgroup Is Normal] + A Sylow $p$-subgroup of a finite group $G$ is a normal subgroup of $G$ if and only if it is the only Sylow $p$-subgroup of $G$. +\end{corollary} diff --git a/part-5/chapters/chapter-25/chapter-25.tex b/part-5/chapters/chapter-25/chapter-25.tex new file mode 100644 index 0000000..916de1e --- /dev/null +++ b/part-5/chapters/chapter-25/chapter-25.tex @@ -0,0 +1,3 @@ +\chapter{Finite Simple Groups} +\subimport{./}{historical-background.tex} +\subimport{./}{nonsimplicity-tests.tex} diff --git a/part-5/chapters/chapter-25/historical-background.tex b/part-5/chapters/chapter-25/historical-background.tex new file mode 100644 index 0000000..2296a63 --- /dev/null +++ b/part-5/chapters/chapter-25/historical-background.tex @@ -0,0 +1,5 @@ +\section{Historical Background} + +\begin{definition}[Simple Group] + A group is \textit{simple} if its only normal subgroups are the identity subgroup and the group itself. +\end{definition} diff --git a/part-5/chapters/chapter-25/nonsimplicity-tests.tex b/part-5/chapters/chapter-25/nonsimplicity-tests.tex new file mode 100644 index 0000000..1dd2d84 --- /dev/null +++ b/part-5/chapters/chapter-25/nonsimplicity-tests.tex @@ -0,0 +1,21 @@ +\section{Nonsimplicity Tests} + +\begin{theorem}[Sylow Test for Nonsimplicity] + Let $n$ be a positive integer that is not prime, and let $p$ be a prime divisor of $n$. If 1 is the only divisor of $n$ that is equal to 1 modulo $p$, then there does not exist a simple group of order $n$. +\end{theorem} + +\begin{theorem}[$\mathbf{2\cdot}$Odd Test] + An integer of the form $2 \cdot n$, where $n$ is an odd number greater than 1, is not the order of a simple group. +\end{theorem} + +\begin{theorem}[Generalized Cayley Theorem] + Let $G$ be a group and let $H$ be a subgroup of $G$. Let $S$ be the group of all permutations of the left cosets of $H$ in $G$. Then there is a homomorphism from $G$ into $S$ whose kernel lies in $H$ and contains every normal subgroup of $G$ that is contained in $H$. +\end{theorem} + +\begin{corollary}[Index Theorem] + If $G$ is a finite group and $H$ is a proper subgroup of $G$ such that $\abs{G}$ does not divide $\abs{G:H}!$, then $H$ contains a nontrivial normal subgroup of $G$. In particular, $G$ is not simple. +\end{corollary} + +\begin{corollary}[Embedding Theorem] + If a finite non-Abelian simple group $G$ has a subgroup of index $n$, then $G$ is isomorphic to a subgroup of $A_n$. +\end{corollary} diff --git a/part-5/chapters/chapter-26/chapter-26.tex b/part-5/chapters/chapter-26/chapter-26.tex new file mode 100644 index 0000000..f4de52e --- /dev/null +++ b/part-5/chapters/chapter-26/chapter-26.tex @@ -0,0 +1,7 @@ +\chapter{Generators and Relations} +\subimport{./}{motivation.tex} +\subimport{./}{definitions-and-notation.tex} +\subimport{./}{free-group.tex} +\subimport{./}{generators-and-relations.tex} +\subimport{./}{classification-of-groups-of-order-up-to-15.tex} +\subimport{./}{characterization-of-dihedral-groups.tex} diff --git a/part-5/chapters/chapter-26/characterization-of-dihedral-groups.tex b/part-5/chapters/chapter-26/characterization-of-dihedral-groups.tex new file mode 100644 index 0000000..b48a0a9 --- /dev/null +++ b/part-5/chapters/chapter-26/characterization-of-dihedral-groups.tex @@ -0,0 +1,5 @@ +\section{Characterization of Dihedral Groups} + +\begin{theorem}[Characterization of Dihedral Groups] + Any group generated by a pair of elements of order 2 is dihedral. +\end{theorem} diff --git a/part-5/chapters/chapter-26/classification-of-groups-of-order-up-to-15.tex b/part-5/chapters/chapter-26/classification-of-groups-of-order-up-to-15.tex new file mode 100644 index 0000000..2d85cd8 --- /dev/null +++ b/part-5/chapters/chapter-26/classification-of-groups-of-order-up-to-15.tex @@ -0,0 +1,5 @@ +\section{Classification of Groups of Order Up to 15} + +\begin{theorem}[Classification of Groups of Order 8 (Cayley, 1859)] + Up to isomorphism, there are only five groups of order 8: $\Z_8$, $\Z_4 \oplus \Z_2$, $\Z_2 \oplus \Z_2 \oplus \Z_2$, $D_4$, and the quaternions. +\end{theorem} diff --git a/part-5/chapters/chapter-26/definitions-and-notation.tex b/part-5/chapters/chapter-26/definitions-and-notation.tex new file mode 100644 index 0000000..efd67f3 --- /dev/null +++ b/part-5/chapters/chapter-26/definitions-and-notation.tex @@ -0,0 +1,11 @@ +\section{Definitions and Notation} + +\begin{remark} + For any set $S=\{a,b,c,\dots\}$ of distinct symbols, we create a new set $S^{-1} = \{a^{-1},b^{-1},c^{-1},\dots\}$ by replacing each $x$ in $S$ by $x^{-1}$. Define the set $W(S)$ to be the collection of all formal finite strings of the form $x_1x_2\dots x_k$, where each $x_i \in S \cup S^{-1}$. The elements of $W(S)$ are called \textit{words from $S$}. We also permit the string with no elements to be in $W(S)$. this word is called the \textit{empty word} and is denoted by $e$. + + We may define a binary operation on the set $W(S)$ by juxtaposition; that is, if $x_1x_2\dots x_k$ and $y_1y_2\dots y_t$ belong to $W(S)$, then so does $x_1x_2\dots x_ky_1y_2\dots y_t$. Observe that this operation is associative and the empty word is the identity. Also, notice that a word such as $aa^{-1}$ is not the identity, because we are treating the elements of $W(S)$ as formal symbols with no implied meaning. +\end{remark} + +\begin{definition}[Equivalence Classes of Words] + For any pair of elements $u$ and $v$ of $W(S)$, we say that $u$ is related to $v$ if $v$ can be obtained from $u$ by a finite sequence of insertions or deletions of words of the form $xx^{-1}$ or $x^{-1}x$, where $x \in S$. +\end{definition} diff --git a/part-5/chapters/chapter-26/free-group.tex b/part-5/chapters/chapter-26/free-group.tex new file mode 100644 index 0000000..3cc85f3 --- /dev/null +++ b/part-5/chapters/chapter-26/free-group.tex @@ -0,0 +1,13 @@ +\section{Free Group} + +\begin{theorem}[Equivalence Classes Form a Group] + Let $S$ be a set of distinct symbols. For any word $u$ in $W(S)$, let $\overline{u}$ denote the set of all words in $W(S)$ equivalent to $u$ (that is, $\overline{u}$ is the equivalence class containing $u$). Then the set of all equivalence classes of elements of $W(S)$ is a group under the operation $\overline{u}\cdot\overline{v} = \overline{uv}$. This group is called a \textit{free group on $S$}. +\end{theorem} + +\begin{theorem}[Universal Mapping Property] + Every group is a homomorphic image of a free group. +\end{theorem} + +\begin{corollary}[Universal Factor Group Property] + Every group is isomorphic to a factor group of a free group. +\end{corollary} diff --git a/part-5/chapters/chapter-26/generators-and-relations.tex b/part-5/chapters/chapter-26/generators-and-relations.tex new file mode 100644 index 0000000..650c778 --- /dev/null +++ b/part-5/chapters/chapter-26/generators-and-relations.tex @@ -0,0 +1,20 @@ +\section{Generators and Relations} + +\begin{definition}[Generators and Relations] + Let $G$ be a group generated by some subset $A=\{a_1,a_2,\dots,a_n\}$ and let $F$ be the free group on $A$. Let $W = \{w_1,w_2,\dots,w_t\}$ be a subset of $F$ and let $N$ be the smallest normal subgruop of $F$ containing $W$. We say that $G$ is \textit{given by the generators $a_1,a_2,\dots,a_n$ and the relations $w_1=w_2=\dots=w_t=e$} if there is an isomorphism from $F/N$ onto $G$ that carries $a_iN$ to $a_i$. + + \noindent The notation for this situation is + \[ G = \lr{a_1,a_2,\dots,a_n\ \vert\ w_1=w_2=\dots=w_t=e} \] +\end{definition} + +\begin{theorem}[Dyck's Theorem (1882)] + Let + \[ G = \lr{a_1,a_2,\dots,a_n\ \vert\ w_1=w_2=\dots=w_t=e} \] + and let + \[ \overline{G}=\lr{a_1,a_2,\dots,a_n\ \vert\ w_1=w_2=\dots=w_t=w_{t+1}=\dots=w_{t+k}=e} \] + Then $\overline{G}$ is a homomorphic image of $G$. +\end{theorem} + +\begin{corollary}[Largest Group Satisfying Defining Relations] + If $K$ is a group satisfying the defining relations of a finite group $G$ and $\abs{K} \geq \abs{G}$, then $K$ is isomorphic to $G$. +\end{corollary} diff --git a/part-5/chapters/chapter-26/motivation.tex b/part-5/chapters/chapter-26/motivation.tex new file mode 100644 index 0000000..c5964aa --- /dev/null +++ b/part-5/chapters/chapter-26/motivation.tex @@ -0,0 +1,5 @@ +\section{Motivation} + +\begin{remark} + In this chapter, we present a convenient way to define a group with certain prescribed properties. Simply put, we begin with a set of elements that we want to generate the group, and a set of equations (called \textit{relations}) that specify the conditions that these generators are to satisfy. Among all such possible groups, we will select one that is as large as possible. This will uniquely determine the group up to isomorphism. +\end{remark} diff --git a/part-5/chapters/chapter-27/chapter-27.tex b/part-5/chapters/chapter-27/chapter-27.tex new file mode 100644 index 0000000..8a6bdf6 --- /dev/null +++ b/part-5/chapters/chapter-27/chapter-27.tex @@ -0,0 +1,4 @@ +\chapter{Symmetry Groups} +\subimport{./}{isometries.tex} +\subimport{./}{classification-of-finite-plane-symmetry-gruops.tex} +\subimport{./}{classification-of-finite-groups-of-rotations-in-R3.tex} diff --git a/part-5/chapters/chapter-27/classification-of-finite-groups-of-rotations-in-R3.tex b/part-5/chapters/chapter-27/classification-of-finite-groups-of-rotations-in-R3.tex new file mode 100644 index 0000000..8787746 --- /dev/null +++ b/part-5/chapters/chapter-27/classification-of-finite-groups-of-rotations-in-R3.tex @@ -0,0 +1,5 @@ +\section{Classification of Finite Groups of Rotations in $\mathbf{\R^3}$} + +\begin{theorem}[Finite Groups of Rotations in $\mathbf{\R^3}$] + Up to isomorphism, the finite groups of rotations in $\R^3$ are $\Z_n$, $D_n$, $A_r$, $S_4$, and $A_5$. +\end{theorem} diff --git a/part-5/chapters/chapter-27/classification-of-finite-plane-symmetry-gruops.tex b/part-5/chapters/chapter-27/classification-of-finite-plane-symmetry-gruops.tex new file mode 100644 index 0000000..31a8bd0 --- /dev/null +++ b/part-5/chapters/chapter-27/classification-of-finite-plane-symmetry-gruops.tex @@ -0,0 +1,5 @@ +\section{Classification of Finite Plane Symmetry Groups} + +\begin{theorem}[Finite Symmetry Groups in the Plane] + The only finite plane symmetry groups are $\Z_n$ and $D_n$. +\end{theorem} diff --git a/part-5/chapters/chapter-27/isometries.tex b/part-5/chapters/chapter-27/isometries.tex new file mode 100644 index 0000000..c613435 --- /dev/null +++ b/part-5/chapters/chapter-27/isometries.tex @@ -0,0 +1,13 @@ +\section{Isometries} + +\begin{remark} + It is convenient to begin our discussion with the definition of an isometry (from the Greek \textit{isometros}, meaning "equal measure") in $\R^n$. +\end{remark} + +\begin{definition}[Isometry] + An \textit{isometry} of $n$-dimensional space $\R^n$ is a function from $\R^n$ onto $\R^n$ that preserves distance. +\end{definition} + +\begin{definition}[Symmetry Group of a Figure in $\mathbf{\R^n}$] + Let $F$ be a set of points in $\R^n$. the \textit{symmetry group of $F$} in $\R^n$ is the set of all isometries of $\R^n$ that carry $F$ onto itself. The group operation is function composition. +\end{definition} diff --git a/part-5/chapters/chapter-28/chapter-28.tex b/part-5/chapters/chapter-28/chapter-28.tex new file mode 100644 index 0000000..f529858 --- /dev/null +++ b/part-5/chapters/chapter-28/chapter-28.tex @@ -0,0 +1,4 @@ +\chapter{Frieze Groups and Crystallographic Groups} +\subimport{./}{the-frieze-groups.tex} +\subimport{./}{the-crystallographic-groups.tex} +\subimport{./}{identification-of-plane-periodic-patterns.tex} diff --git a/part-5/chapters/chapter-28/identification-of-plane-periodic-patterns.tex b/part-5/chapters/chapter-28/identification-of-plane-periodic-patterns.tex new file mode 100644 index 0000000..f14354d --- /dev/null +++ b/part-5/chapters/chapter-28/identification-of-plane-periodic-patterns.tex @@ -0,0 +1,5 @@ +\section{Identification of Plane Periodic Patterns} + +\begin{remark} + A \textit{lattice of points} of a pattern is a set of images of any particular point acted on by the translation group of the pattern. A \textit{lattice unit} of a pattern whose translation subgroup is generated by $u$ and $v$ is a parallelogram formed by a point of the pattern and its image under $u,v$, and $u + v$. A \textit{generating region} (or \textit{fundamental region}) of a periodic pattern is the smallest portion of the lattice unit whose images under the full symmetry of the group of the pattern cover the plane. +\end{remark} diff --git a/part-5/chapters/chapter-28/the-crystallographic-groups.tex b/part-5/chapters/chapter-28/the-crystallographic-groups.tex new file mode 100644 index 0000000..2ea6c56 --- /dev/null +++ b/part-5/chapters/chapter-28/the-crystallographic-groups.tex @@ -0,0 +1,5 @@ +\section{The Crystallographic Groups} + +\begin{remark} + The seven frieze groups catalog all symmetry groups that leave a design invariant under all multiples of just one translation. However, there are 17 additional kinds of discrete plane symmetry groups that arise from infinitely repeating designs in a plane. these groups are the symmetry groups of plane patterns whose subgroups of translations are isomorphic to $\Z \oplus \Z$. Consequently, the patterns are invariant under linear combinations of two linearly independent translations. These 16 groups were first studied by the 19th-century crystallographers and often called the \textit{plane crystallographic groups}. Another term occasionally used for these groups is \textit{wallpaper groups}. +\end{remark} diff --git a/part-5/chapters/chapter-28/the-frieze-groups.tex b/part-5/chapters/chapter-28/the-frieze-groups.tex new file mode 100644 index 0000000..3ad4d8f --- /dev/null +++ b/part-5/chapters/chapter-28/the-frieze-groups.tex @@ -0,0 +1,5 @@ +\section{The Frieze Groups} + +\begin{remark} + In this chapter, we discuss an interesting collection of infinite symmetry groups that arise from periodic designs in a plane. There are two types of such groups. The \textit{discrete frieze groups} are the plane symmetry groups of patterns whose subgroups of translations are isomorphic to $\Z$. These kinds of designs are the ones used for decorative strips and for patterns on jewelry. In mathematics, familiar examples include the graphs of $y=\sin(x)$, $y=\tan(x)$, $y=\abs{\sin(x)}$, and $\abs{y} = \sin(x)$. After we analyze the discrete frieze groups, we examine the discrete symmetry groups of plane patterns whose subgroups of translations are isomorphic to $\Z \oplus \Z$. +\end{remark} diff --git a/part-5/chapters/chapter-29/burnsides-theorem.tex b/part-5/chapters/chapter-29/burnsides-theorem.tex new file mode 100644 index 0000000..ce96a8d --- /dev/null +++ b/part-5/chapters/chapter-29/burnsides-theorem.tex @@ -0,0 +1,10 @@ +\section{Burnside's Theorem} + +\begin{definition}[Elements Fixed by $\mathbf{\phi}$] + For any group $G$ of permutations on a set $S$ and any $\phi$ in $G$, we let $\fix(\phi) = \{i \in S\ \vert\ \phi(i)=i\}$. This set is called the \textit{elements fixed by $\phi$} (or more simply, "fix of $\phi$"). +\end{definition} + +\begin{theorem}[Burnside's Theorem] + If $G$ is a finite group of permutations on a set $S$, then the number of orbits of elements of $S$ under $G$ is + \[ \frac{1}{\abs{G}}\sum_{\phi \in G}\abs{\fix(\phi)} \] +\end{theorem} diff --git a/part-5/chapters/chapter-29/chapter-29.tex b/part-5/chapters/chapter-29/chapter-29.tex new file mode 100644 index 0000000..13ede09 --- /dev/null +++ b/part-5/chapters/chapter-29/chapter-29.tex @@ -0,0 +1,4 @@ +\chapter{Symmetry and Counting} +\subimport{./}{motivation.tex} +\subimport{./}{burnsides-theorem.tex} +\subimport{./}{group-action.tex} diff --git a/part-5/chapters/chapter-29/group-action.tex b/part-5/chapters/chapter-29/group-action.tex new file mode 100644 index 0000000..8a70bd5 --- /dev/null +++ b/part-5/chapters/chapter-29/group-action.tex @@ -0,0 +1,5 @@ +\section{Group Action} + +\begin{remark} + Our informal approach to counting the number of objects that are considered nonequivalent can be made formal as follows. If $G$ is a group and $S$ is a set of objects, we say that $G$ \textit{acts on} $S$ if there is a homomorphism $\gamma$ from $G$ to sym$(S)$, the group of all permutations on $S$. (The hommomorphism is sometimes called the \textit{group action}.) For convenience, we denote the image of $g$ under $\gamma$ as $\gamma_g$. Then two objects $x$ and $y$ in $S$ are viewed as equivalent under the action of $G$ if and only if $\gamma_g(x) = y$ for some $g$ in $G$. Notice that when $\gamma$ is one-to-one, the elements of $G$ may be regarded as permutations on $S$. On the other hand, when $\gamma$ is not one-to-one, the elements of $G$ may still be regarded as permutations on $S$, but there are distinct elements $g$ and $h$ in $G$ such that $\gamma_g$ and $\gamma_h$ induce the same permutation on $S$ [that is, $\gamma_g(x) = \gamma_h(x)$ for all $x$ in $S$]. Thus, a group acting on a set is a natural generalization of the permutation group concept. +\end{remark} diff --git a/part-5/chapters/chapter-29/motivation.tex b/part-5/chapters/chapter-29/motivation.tex new file mode 100644 index 0000000..32cd5f7 --- /dev/null +++ b/part-5/chapters/chapter-29/motivation.tex @@ -0,0 +1,5 @@ +\section{Motivation} + +\begin{remark} + In general, we say that two designs (arrangements of beads) $A$ and $B$ are \textit{equivalent under a group $G$} of permutations of the arrangements if there is an element $\phi$ in $G$ such that $\phi(A) = B$. That is, two designs are equivalent under $G$ if they are in the same orbit of $G$. It follows, then, that the number of nonequivalent designs under $G$ is simply the number of orbits of designs under $G$. (The set being permuted is the set of all possible designs or arrangements.) +\end{remark} diff --git a/part-5/chapters/chapter-30/chapter-30.tex b/part-5/chapters/chapter-30/chapter-30.tex new file mode 100644 index 0000000..d9386c9 --- /dev/null +++ b/part-5/chapters/chapter-30/chapter-30.tex @@ -0,0 +1,3 @@ +\chapter{Cayley Digraphs of Groups} +\subimport{./}{the-cayley-digraph-of-a-group.tex} +\subimport{./}{hamiltonian-circuits-and-paths.tex} diff --git a/part-5/chapters/chapter-30/hamiltonian-circuits-and-paths.tex b/part-5/chapters/chapter-30/hamiltonian-circuits-and-paths.tex new file mode 100644 index 0000000..1e39aa8 --- /dev/null +++ b/part-5/chapters/chapter-30/hamiltonian-circuits-and-paths.tex @@ -0,0 +1,20 @@ +\section{Hamiltonian Circuits and Paths} + +\begin{remark} + Obviously, this idea can be applied to any digraph; that is, one starts at some vertex and attempts to traverse the digraph by moving along arcs in such a way that each vertex is visited exactly once before returning to the starting vertex. (To go from $x$ to $y$, there must be an arc from $x$ to $y$.) Such a sequence of arcs is called a \textit{Hamiltonian circuit} in the digraph. A sequence of arcs that passes through each vertex exactly once without returning to the starting point is called a \textit{Hamiltonian path}. In the rest of this chapter, we concern ourselves with the existence of Hamiltonian circuits and paths in Cayley digraphs. +\end{remark} + +\begin{theorem}[A Necessary Condition] + Cay$(\{(1,0),(0,1)\}:\Z_m \oplus \Z_n)$ does not have a Hamiltonian circuit when $m$ and $n$ are relatively prime and greater than 1. +\end{theorem} + +\begin{theorem}[A Sufficient Condition] + Cay$(\{(1,0),(0,1)\}:\Z_m \oplus \Z_n)$ has a Hamiltonian circuit when $n$ divides $m$. +\end{theorem} + +\begin{theorem}[Abelian Groups Have Hamiltonian Paths] + Let $G$ be a finite Abelian group, and let $S$ be any (nonempty*) generating set for $G$. Then Cay$(S:G)$ has a Hamiltonian path.\\ + + + \noindent *If $S$ is the empty set, it is customary to define $\lr{S}$ as the identity group. We prefer to ignore this trivial case. +\end{theorem} diff --git a/part-5/chapters/chapter-30/the-cayley-digraph-of-a-group.tex b/part-5/chapters/chapter-30/the-cayley-digraph-of-a-group.tex new file mode 100644 index 0000000..235f82b --- /dev/null +++ b/part-5/chapters/chapter-30/the-cayley-digraph-of-a-group.tex @@ -0,0 +1,9 @@ +\section{The Cayley Digraph of a Group} + +\begin{definition}[Cayley Digraph of a Group] + Let $G$ be a finite group and let $S$ be a set of generators for $G$. We define a digraph Cay$(S:G)$, called the \textit{Cayley digraph of $G$ with generating set $S$}, as follows. + \begin{enumerate} + \item Each element of $G$ is a vertex of Cay$(S:G)$. + \item For $x$ and $y$ in $G$, there is an arc from $x$ to $y$ if and only if $xs=y$ for some $s \in S$. + \end{enumerate} +\end{definition} diff --git a/part-5/chapters/chapter-31/chapter-31.tex b/part-5/chapters/chapter-31/chapter-31.tex new file mode 100644 index 0000000..3ce9c2e --- /dev/null +++ b/part-5/chapters/chapter-31/chapter-31.tex @@ -0,0 +1,4 @@ +\chapter{Introduction to Algebraic Coding Theory} +\subimport{./}{linear-codes.tex} +\subimport{./}{parity-check-matrix-decoding.tex} +\subimport{./}{coset-decoding.tex} diff --git a/part-5/chapters/chapter-31/coset-decoding.tex b/part-5/chapters/chapter-31/coset-decoding.tex new file mode 100644 index 0000000..b877652 --- /dev/null +++ b/part-5/chapters/chapter-31/coset-decoding.tex @@ -0,0 +1,13 @@ +\section{Coset Decoding} + +\begin{theorem}[Coset Decoding Is Nearest-Neighbor Decoding] + In coset decoding, a received word $w$ is decoded as a code word $c$ such that $d(w,c)$ is a minimum. +\end{theorem} + +\begin{definition}[Syndrome] + If an $(n,k)$ linear code over $\F$ has parity-check matrix $H$, then, for any vector $u$ in $\F^n$, the vector $uH$ is called the \textit{syndrome} of $u$. +\end{definition} + +\begin{theorem}[Same Coset-Same Syndrome] + Let $C$ be an $(n,k)$ linear code over $\F$ with a parity-check matrix $H$. Then, two vectors of $\F^n$ are in the same coset of $C$ if and only if they have the same syndrome. +\end{theorem} diff --git a/part-5/chapters/chapter-31/linear-codes.tex b/part-5/chapters/chapter-31/linear-codes.tex new file mode 100644 index 0000000..f35d2fb --- /dev/null +++ b/part-5/chapters/chapter-31/linear-codes.tex @@ -0,0 +1,19 @@ +\section{Linear Codes} + +\begin{definition}[Linear Code] + An $(n,k)$ \textit{linear code} of a finite field $\F$ is a $k$-dimensional subspace $V$ of the vector space + \[ \F^n = \underbrace{\F \oplus \F \oplus \dots \oplus \F}_\text{$n$ copies} \] + over $\F$. The members of $V$ are called the \textit{code words}. When $\F$ is $\Z_2$, the code is called \textit{binary}. +\end{definition} + +\begin{definition}[Hamming Distance, Hamming Weight] + The \textit{Hamming distance} between two vectors in $\F^n$ is the number of components in which they differ. The \textit{Hamming weight} of a vector is the number of nonzero components of the vector. The \textit{Hamming weight} of a linear code is the minimum weight of any nonzero vector in the code. +\end{definition} + +\begin{theorem}[Properties of Hamming Distance and Hamming Weight] + For any vectors $u$, $v$ and $w$, $d(u,v) \leq d(u,w) + d(w,v)$ and $d(u,v) = \text{wt}(u-v)$. +\end{theorem} + +\begin{theorem}[Correcting Capability of a Linear Code] + If the Hamming weight of a linear code is at least $2t + 1$, then the code can correct any $t$ or fewer errors. Alternatively, the same code can detect any $2t$ or fewer errors. +\end{theorem} diff --git a/part-5/chapters/chapter-31/parity-check-matrix-decoding.tex b/part-5/chapters/chapter-31/parity-check-matrix-decoding.tex new file mode 100644 index 0000000..78df4d2 --- /dev/null +++ b/part-5/chapters/chapter-31/parity-check-matrix-decoding.tex @@ -0,0 +1,9 @@ +\section{Parity-Check Matrix Decoding} + +\begin{lemma}[Orthogonality Relation] + Let $C$ be a systematic $(n,k)$ linear code over $\F$ with a standard generator matrix $G$ and parity-check matrix $H$. Then, for any vector $v$ in $\F^n$, we have $vH=0$ (the zero vector) if and only if $v$ belongs to $C$. +\end{lemma} + +\begin{theorem}[Parity-Check Matrix Decoding] + Parity-check matrix decoding will correct any single error if and only if the rows of the parity-check matrix are nonzero and no one row is a scalar multiple of any other row. +\end{theorem} diff --git a/part-5/chapters/chapter-32/chapter-32.tex b/part-5/chapters/chapter-32/chapter-32.tex new file mode 100644 index 0000000..80d4b45 --- /dev/null +++ b/part-5/chapters/chapter-32/chapter-32.tex @@ -0,0 +1,3 @@ +\chapter{An Introduction to Galois Theory} +\subimport{./}{fundamental-theorem-of-galois-theory.tex} +\subimport{./}{solvability-of-polynomials-by-radicals.tex} diff --git a/part-5/chapters/chapter-32/fundamental-theorem-of-galois-theory.tex b/part-5/chapters/chapter-32/fundamental-theorem-of-galois-theory.tex new file mode 100644 index 0000000..d0c0df1 --- /dev/null +++ b/part-5/chapters/chapter-32/fundamental-theorem-of-galois-theory.tex @@ -0,0 +1,17 @@ +\section{Fundamental Theorem of Galois Theory} + +\begin{definition}[Automorphism, Galois Group, Fixed Field of $\mathbf{H}$] + Let $\E$ be an extension field of the field $\F$. An \textit{automorphism of $\E$} is a ring isomorphism from $\E$ onto $\E$. The \textit{Galois group} of $\E$ over $\F$, $\gal(\E/\F)$, is the set of all automorphisms of $\E$ that take every element of $\F$ to itself. If $H$ is a subgroup of $\gal(\E/\F)$, then set + \[ \E_H = \{x \in \E\ \vert\ \phi(x) = x,\ \forall\ \phi \in H\} \] + is called the \textit{fixed field of $H$}. +\end{definition} + +\begin{theorem}[Fundamental Theorem of Galois Theory] + Let $\F$ be a field of characteristic 0 or a finite field. If $\E$ is the splitting field over $\F$ for some polynomial in $\F[x]$, then the mapping from the set of subfields of $\E$ containing $\F$ to the set of subgroups of $\gal(\E/\F)$ given by $\K \to \gal(\E/\F)$ is a one-to-one correspondence. Furthermore, for any subfield $\K$ of $\E$ containing $\F$, + \begin{enumerate} + \item $[\E:\K] = \abs{\gal(\E/\K)}$ and $[\K:\F] = \abs{\gal(\E/\F)} / \abs{\gal(\E/\K)}$. [The index of $\gal(\E/\K)$ in $\gal(\E/\F)$ equals the degree of $\K$ over $\F$.] + \item If $\K$ is the splitting field of some polynomial in $\F[x]$, then $\gal(\E/\K)$ is a normal subgroup of $\gal(\E/\F)$ and $\gal(\K/\F)$ is isomorphic to $\gal(\E/\F)/\gal(\E/\K)$. + \item $\K = \E_{\gal(\E/\K)}$. [The fixed field of $\gal(\E/\K)$ is $\K$.] + \item If $H$ is a subgroup of $\gal(\E/\F)$, then $H=\gal(\E/\E_H)$. [The automorphism group of $\E$ fixing $\E_H$ is $H$.] + \end{enumerate} +\end{theorem} diff --git a/part-5/chapters/chapter-32/solvability-of-polynomials-by-radicals.tex b/part-5/chapters/chapter-32/solvability-of-polynomials-by-radicals.tex new file mode 100644 index 0000000..2422201 --- /dev/null +++ b/part-5/chapters/chapter-32/solvability-of-polynomials-by-radicals.tex @@ -0,0 +1,27 @@ +\section{Solvability of Polynomials by Radicals} + +\begin{definition}[Solvable by Radicals] + Let $\F$ be a field, and let $f(x) \in \F[x]$. We say that $f(x)$ is \textit{solvable by radicals over $\F$} if $f(x)$ splits in some extension $\F(a_1,a_2,\dots,a_n)$ of $\F$ and there exist positive integers $k_1,\dots,k_n$ such that $a_1^{k_1} \in \F$ and $a_i^{k_i} \in \F(a_1,\dots,a_{i-1})$ for $i=2,\dots,n$. +\end{definition} + +\begin{definition}[Solvable Group] + We say that a group $G$ is \textit{solvable} if $G$ has a series of subgroups + \[ \{e\} = H_0 \subset H_1 \subset H_2 \subset \dots \subset H_k = G \] + where, for each $0 \leq i