From 86fa30cb267d0f3b6273e9af7c84e5285dca956b Mon Sep 17 00:00:00 2001 From: Eliza Diggins Date: Wed, 11 Jun 2025 10:59:05 -0600 Subject: [PATCH 01/17] First paper commit. - Set up directory - Added github action to compile. --- .github/workflows/draft_pdf.yml | 28 +++++ paper/paper.md | 181 ++++++++++++++++++++++++++++++++ 2 files changed, 209 insertions(+) create mode 100644 .github/workflows/draft_pdf.yml create mode 100644 paper/paper.md diff --git a/.github/workflows/draft_pdf.yml b/.github/workflows/draft_pdf.yml new file mode 100644 index 00000000..82e1bf58 --- /dev/null +++ b/.github/workflows/draft_pdf.yml @@ -0,0 +1,28 @@ +name: Draft PDF + +on: + push: + branches: ["paper"] # run on main branch pushes + workflow_dispatch: # allow manual triggering + +jobs: + paper: + runs-on: ubuntu-latest + name: Paper Draft + steps: + - name: Checkout + uses: actions/checkout@v4 + - name: Build draft PDF + uses: openjournals/openjournals-draft-action@master + with: + journal: joss + # This should be the path to the paper within your repo. + paper-path: paper/paper.md + - name: Upload + uses: actions/upload-artifact@v4 + with: + name: paper + # This is the output path where Pandoc will write the compiled + # PDF. Note, this should be the same directory as the input + # paper.md + path: paper/paper.pdf diff --git a/paper/paper.md b/paper/paper.md new file mode 100644 index 00000000..a6605844 --- /dev/null +++ b/paper/paper.md @@ -0,0 +1,181 @@ +--- +title: 'Gala: A Python package for galactic dynamics' +tags: + - Python + - astronomy + - dynamics + - galactic dynamics + - milky way +authors: + - name: Adrian M. Price-Whelan + orcid: 0000-0000-0000-0000 + equal-contrib: true + affiliation: "1, 2" # (Multiple affiliations must be quoted) + - name: Author Without ORCID + equal-contrib: true # (This is how you can denote equal contributions between multiple authors) + affiliation: 2 + - name: Author with no affiliation + corresponding: true # (This is how to denote the corresponding author) + affiliation: 3 + - given-names: Ludwig + dropping-particle: van + surname: Beethoven + affiliation: 3 +affiliations: + - name: Lyman Spitzer, Jr. Fellow, Princeton University, United States + index: 1 + ror: 00hx57361 + - name: Institution Name, Country + index: 2 + - name: Independent Researcher, Country + index: 3 +date: 13 August 2017 +bibliography: paper.bib + +# Optional fields if submitting to a AAS journal too, see this blog post: +# https://blog.joss.theoj.org/2018/12/a-new-collaboration-with-aas-publishing +aas-doi: 10.3847/xxxxx <- update this with the DOI from AAS once you know it. +aas-journal: Astrophysical Journal <- The name of the AAS journal. +--- + +# Summary + +The forces on stars, galaxies, and dark matter under external gravitational +fields lead to the dynamical evolution of structures in the universe. The orbits +of these bodies are therefore key to understanding the formation, history, and +future state of galaxies. The field of "galactic dynamics," which aims to model +the gravitating components of galaxies to study their structure and evolution, +is now well-established, commonly taught, and frequently used in astronomy. +Aside from toy problems and demonstrations, the majority of problems require +efficient numerical tools, many of which require the same base code (e.g., for +performing numerical orbit integration). + +# Statement of need + +`Gala` is an Astropy-affiliated Python package for galactic dynamics. Python +enables wrapping low-level languages (e.g., C) for speed without losing +flexibility or ease-of-use in the user-interface. The API for `Gala` was +designed to provide a class-based and user-friendly interface to fast (C or +Cython-optimized) implementations of common operations such as gravitational +potential and force evaluation, orbit integration, dynamical transformations, +and chaos indicators for nonlinear dynamics. `Gala` also relies heavily on and +interfaces well with the implementations of physical units and astronomical +coordinate systems in the `Astropy` package [@astropy] (`astropy.units` and +`astropy.coordinates`). + +`Gala` was designed to be used by both astronomical researchers and by +students in courses on gravitational dynamics or astronomy. It has already been +used in a number of scientific publications [@Pearson:2017] and has also been +used in graduate courses on Galactic dynamics to, e.g., provide interactive +visualizations of textbook material [@Binney:2008]. The combination of speed, +design, and support for Astropy functionality in `Gala` will enable exciting +scientific explorations of forthcoming data releases from the *Gaia* mission +[@gaia] by students and experts alike. + +# Mathematics + +Single dollars ($) are required for inline mathematics e.g. $f(x) = e^{\pi/x}$ + +Double dollars make self-standing equations: + +$$\Theta(x) = \left\{\begin{array}{l} +0\textrm{ if } x < 0\cr +1\textrm{ else} +\end{array}\right.$$ + +You can also use plain \LaTeX for equations +\begin{equation}\label{eq:fourier} +\hat f(\omega) = \int_{-\infty}^{\infty} f(x) e^{i\omega x} dx +\end{equation} +and refer to \autoref{eq:fourier} from text. + +# Citations + +Citations to entries in paper.bib should be in +[rMarkdown](http://rmarkdown.rstudio.com/authoring_bibliographies_and_citations.html) +format. + +If you want to cite a software repository URL (e.g. something on GitHub without a preferred +citation) then you can do it with the example BibTeX entry below for @fidgit. + +For a quick reference, the following citation commands can be used: +- `@author:2001` -> "Author et al. (2001)" +- `[@author:2001]` -> "(Author et al., 2001)" +- `[@author1:2001; @author2:2001]` -> "(Author1 et al., 2001; Author2 et al., 2002)" + +# Figures + +Figures can be included like this: +![Caption for example figure.\label{fig:example}](figure.png) +and referenced from text using \autoref{fig:example}. + +Figure sizes can be customized by adding an optional second parameter: +![Caption for example figure.](figure.png){ width=20% } + +# Acknowledgements + +We acknowledge contributions from Brigitta Sipocz, Syrtis Major, and Semyeong +Oh, and support from Kathryn Johnston during the genesis of this project. + +# References +Example paper.bib file: + +@article{Pearson:2017, + url = {http://adsabs.harvard.edu/abs/2017arXiv170304627P}, + Archiveprefix = {arXiv}, + Author = {{Pearson}, S. and {Price-Whelan}, A.~M. and {Johnston}, K.~V.}, + Eprint = {1703.04627}, + Journal = {ArXiv e-prints}, + Keywords = {Astrophysics - Astrophysics of Galaxies}, + Month = mar, + Title = {{Gaps in Globular Cluster Streams: Pal 5 and the Galactic Bar}}, + Year = 2017 +} + +@book{Binney:2008, + url = {http://adsabs.harvard.edu/abs/2008gady.book.....B}, + Author = {{Binney}, J. and {Tremaine}, S.}, + Booktitle = {Galactic Dynamics: Second Edition, by James Binney and Scott Tremaine.~ISBN 978-0-691-13026-2 (HB).~Published by Princeton University Press, Princeton, NJ USA, 2008.}, + Publisher = {Princeton University Press}, + Title = {{Galactic Dynamics: Second Edition}}, + Year = 2008 +} + +@article{gaia, + author = {{Gaia Collaboration}}, + title = "{The Gaia mission}", + journal = {Astronomy and Astrophysics}, + archivePrefix = "arXiv", + eprint = {1609.04153}, + primaryClass = "astro-ph.IM", + keywords = {space vehicles: instruments, Galaxy: structure, astrometry, parallaxes, proper motions, telescopes}, + year = 2016, + month = nov, + volume = 595, + doi = {10.1051/0004-6361/201629272}, + url = {http://adsabs.harvard.edu/abs/2016A%26A...595A...1G}, +} + +@article{astropy, + author = {{Astropy Collaboration}}, + title = "{Astropy: A community Python package for astronomy}", + journal = {Astronomy and Astrophysics}, + archivePrefix = "arXiv", + eprint = {1307.6212}, + primaryClass = "astro-ph.IM", + keywords = {methods: data analysis, methods: miscellaneous, virtual observatory tools}, + year = 2013, + month = oct, + volume = 558, + doi = {10.1051/0004-6361/201322068}, + url = {http://adsabs.harvard.edu/abs/2013A%26A...558A..33A} +} + +@misc{fidgit, + author = {A. M. Smith and K. Thaney and M. Hahnel}, + title = {Fidgit: An ungodly union of GitHub and Figshare}, + year = {2020}, + publisher = {GitHub}, + journal = {GitHub repository}, + url = {https://github.com/arfon/fidgit} +} From 47c2f22e7e6f5ff339e634facdd626f5e393aada Mon Sep 17 00:00:00 2001 From: Eliza Diggins Date: Wed, 11 Jun 2025 11:00:49 -0600 Subject: [PATCH 02/17] Added paper.bib --- paper/paper.bib | 59 +++++++++++++++++++++++++++++++++++++++++++++++ paper/paper.md | 61 ------------------------------------------------- 2 files changed, 59 insertions(+), 61 deletions(-) create mode 100644 paper/paper.bib diff --git a/paper/paper.bib b/paper/paper.bib new file mode 100644 index 00000000..4e4544a4 --- /dev/null +++ b/paper/paper.bib @@ -0,0 +1,59 @@ +@article{Pearson:2017, + url = {http://adsabs.harvard.edu/abs/2017arXiv170304627P}, + Archiveprefix = {arXiv}, + Author = {{Pearson}, S. and {Price-Whelan}, A.~M. and {Johnston}, K.~V.}, + Eprint = {1703.04627}, + Journal = {ArXiv e-prints}, + Keywords = {Astrophysics - Astrophysics of Galaxies}, + Month = mar, + Title = {{Gaps in Globular Cluster Streams: Pal 5 and the Galactic Bar}}, + Year = 2017 +} + +@book{Binney:2008, + url = {http://adsabs.harvard.edu/abs/2008gady.book.....B}, + Author = {{Binney}, J. and {Tremaine}, S.}, + Booktitle = {Galactic Dynamics: Second Edition, by James Binney and Scott Tremaine.~ISBN 978-0-691-13026-2 (HB).~Published by Princeton University Press, Princeton, NJ USA, 2008.}, + Publisher = {Princeton University Press}, + Title = {{Galactic Dynamics: Second Edition}}, + Year = 2008 +} + +@article{gaia, + author = {{Gaia Collaboration}}, + title = "{The Gaia mission}", + journal = {Astronomy and Astrophysics}, + archivePrefix = "arXiv", + eprint = {1609.04153}, + primaryClass = "astro-ph.IM", + keywords = {space vehicles: instruments, Galaxy: structure, astrometry, parallaxes, proper motions, telescopes}, + year = 2016, + month = nov, + volume = 595, + doi = {10.1051/0004-6361/201629272}, + url = {http://adsabs.harvard.edu/abs/2016A%26A...595A...1G}, +} + +@article{astropy, + author = {{Astropy Collaboration}}, + title = "{Astropy: A community Python package for astronomy}", + journal = {Astronomy and Astrophysics}, + archivePrefix = "arXiv", + eprint = {1307.6212}, + primaryClass = "astro-ph.IM", + keywords = {methods: data analysis, methods: miscellaneous, virtual observatory tools}, + year = 2013, + month = oct, + volume = 558, + doi = {10.1051/0004-6361/201322068}, + url = {http://adsabs.harvard.edu/abs/2013A%26A...558A..33A} +} + +@misc{fidgit, + author = {A. M. Smith and K. Thaney and M. Hahnel}, + title = {Fidgit: An ungodly union of GitHub and Figshare}, + year = {2020}, + publisher = {GitHub}, + journal = {GitHub repository}, + url = {https://github.com/arfon/fidgit} +} diff --git a/paper/paper.md b/paper/paper.md index a6605844..91e17f43 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -118,64 +118,3 @@ We acknowledge contributions from Brigitta Sipocz, Syrtis Major, and Semyeong Oh, and support from Kathryn Johnston during the genesis of this project. # References -Example paper.bib file: - -@article{Pearson:2017, - url = {http://adsabs.harvard.edu/abs/2017arXiv170304627P}, - Archiveprefix = {arXiv}, - Author = {{Pearson}, S. and {Price-Whelan}, A.~M. and {Johnston}, K.~V.}, - Eprint = {1703.04627}, - Journal = {ArXiv e-prints}, - Keywords = {Astrophysics - Astrophysics of Galaxies}, - Month = mar, - Title = {{Gaps in Globular Cluster Streams: Pal 5 and the Galactic Bar}}, - Year = 2017 -} - -@book{Binney:2008, - url = {http://adsabs.harvard.edu/abs/2008gady.book.....B}, - Author = {{Binney}, J. and {Tremaine}, S.}, - Booktitle = {Galactic Dynamics: Second Edition, by James Binney and Scott Tremaine.~ISBN 978-0-691-13026-2 (HB).~Published by Princeton University Press, Princeton, NJ USA, 2008.}, - Publisher = {Princeton University Press}, - Title = {{Galactic Dynamics: Second Edition}}, - Year = 2008 -} - -@article{gaia, - author = {{Gaia Collaboration}}, - title = "{The Gaia mission}", - journal = {Astronomy and Astrophysics}, - archivePrefix = "arXiv", - eprint = {1609.04153}, - primaryClass = "astro-ph.IM", - keywords = {space vehicles: instruments, Galaxy: structure, astrometry, parallaxes, proper motions, telescopes}, - year = 2016, - month = nov, - volume = 595, - doi = {10.1051/0004-6361/201629272}, - url = {http://adsabs.harvard.edu/abs/2016A%26A...595A...1G}, -} - -@article{astropy, - author = {{Astropy Collaboration}}, - title = "{Astropy: A community Python package for astronomy}", - journal = {Astronomy and Astrophysics}, - archivePrefix = "arXiv", - eprint = {1307.6212}, - primaryClass = "astro-ph.IM", - keywords = {methods: data analysis, methods: miscellaneous, virtual observatory tools}, - year = 2013, - month = oct, - volume = 558, - doi = {10.1051/0004-6361/201322068}, - url = {http://adsabs.harvard.edu/abs/2013A%26A...558A..33A} -} - -@misc{fidgit, - author = {A. M. Smith and K. Thaney and M. Hahnel}, - title = {Fidgit: An ungodly union of GitHub and Figshare}, - year = {2020}, - publisher = {GitHub}, - journal = {GitHub repository}, - url = {https://github.com/arfon/fidgit} -} From 33a3c35789336684dfe779830c65383f780766be Mon Sep 17 00:00:00 2001 From: Eliza Diggins Date: Wed, 11 Jun 2025 11:47:34 -0600 Subject: [PATCH 03/17] - Added Summary and affiliations. --- paper/paper.md | 75 ++++++++++++++++++++++++++------------------------ 1 file changed, 39 insertions(+), 36 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 91e17f43..94f8046d 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -1,54 +1,57 @@ --- -title: 'Gala: A Python package for galactic dynamics' +title: 'PyMetric: A Library for Geometric Computation' tags: - Python - - astronomy - - dynamics - - galactic dynamics - - milky way + - differential geometry + - modeling authors: - - name: Adrian M. Price-Whelan - orcid: 0000-0000-0000-0000 - equal-contrib: true - affiliation: "1, 2" # (Multiple affiliations must be quoted) - - name: Author Without ORCID - equal-contrib: true # (This is how you can denote equal contributions between multiple authors) - affiliation: 2 - - name: Author with no affiliation + - name: Eliza C. Diggins + orcid: 0009-0005-9389-9098 corresponding: true # (This is how to denote the corresponding author) - affiliation: 3 - - given-names: Ludwig - dropping-particle: van - surname: Beethoven - affiliation: 3 + affiliation: 1 # (Multiple affiliations must be quoted) + - name: Daniel R. Wik + orcid: 0000-0001-9110-2245 + affiliation: 1 affiliations: - - name: Lyman Spitzer, Jr. Fellow, Princeton University, United States + - name: University of Utah, USA index: 1 - ror: 00hx57361 - - name: Institution Name, Country - index: 2 - - name: Independent Researcher, Country - index: 3 -date: 13 August 2017 +date: 11 June 2025 bibliography: paper.bib # Optional fields if submitting to a AAS journal too, see this blog post: # https://blog.joss.theoj.org/2018/12/a-new-collaboration-with-aas-publishing -aas-doi: 10.3847/xxxxx <- update this with the DOI from AAS once you know it. -aas-journal: Astrophysical Journal <- The name of the AAS journal. --- # Summary -The forces on stars, galaxies, and dark matter under external gravitational -fields lead to the dynamical evolution of structures in the universe. The orbits -of these bodies are therefore key to understanding the formation, history, and -future state of galaxies. The field of "galactic dynamics," which aims to model -the gravitating components of galaxies to study their structure and evolution, -is now well-established, commonly taught, and frequently used in astronomy. -Aside from toy problems and demonstrations, the majority of problems require -efficient numerical tools, many of which require the same base code (e.g., for -performing numerical orbit integration). +PyMetric is a lightweight Python library designed to streamline differential geometry +and vector calculus operations in user-defined coordinate systems, with a focus on +applications in astrophysics and computational physics. In many physical modeling +tasks—especially in astrophysics—it is both natural and advantageous to work in +non-Cartesian coordinate systems that reflect the underlying symmetries of a system. +These coordinate systems may be highly nontrivial, such as ellipsoidal or spheroidal +coordinates, where the ability to express and manipulate tensorial quantities is essential +for deriving accurate and efficient models. + +The core design of PyMetric emphasizes a seamless blend of symbolic and numerical computation. +Symbolic expressions are used to derive key geometric quantities such as metric tensors, +Christoffel symbols, and Jacobians, which are then converted into efficient numerical +functions suitable for use in array-based workflows. This enables users to write models +that respect the underlying geometry while retaining the performance and flexibility of +NumPy-style programming. + +PyMetric further supports structured grid abstractions and offers extensibility +for multiple coordinate systems, buffer types (including HDF5 storage), +and geometric operations. It automates tasks such as computing gradients, divergences, and Laplacians—critical +for solving PDEs or modeling physical systems—while maintaining awareness of the coordinate system +and metric context. This makes it particularly useful for scientific domains that demand geometric +precision, such as general relativity, magnetohydrodynamics, and planetary dynamics. + +By bringing geometric context to array mathematics, PyMetric provides a flexible +and modern foundation for coordinate-aware scientific computing. + + + # Statement of need From f5587d9eb6f146d93cc673942c76c996008fdd01 Mon Sep 17 00:00:00 2001 From: Eliza Diggins Date: Wed, 11 Jun 2025 13:13:40 -0600 Subject: [PATCH 04/17] Added most of the core paper. --- paper/paper.md | 134 ++++++++++++++++++++++++++++++------------------- 1 file changed, 82 insertions(+), 52 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 94f8046d..777c8bc1 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -27,9 +27,9 @@ bibliography: paper.bib PyMetric is a lightweight Python library designed to streamline differential geometry and vector calculus operations in user-defined coordinate systems, with a focus on applications in astrophysics and computational physics. In many physical modeling -tasks—especially in astrophysics—it is both natural and advantageous to work in +tasks, especially in astrophysics, it is both natural and advantageous to work in non-Cartesian coordinate systems that reflect the underlying symmetries of a system. -These coordinate systems may be highly nontrivial, such as ellipsoidal or spheroidal +These coordinate systems may be highly nontrivial, such as ellipsoidal (homoeoidal) or spheroidal coordinates, where the ability to express and manipulate tensorial quantities is essential for deriving accurate and efficient models. @@ -50,74 +50,104 @@ precision, such as general relativity, magnetohydrodynamics, and planetary dynam By bringing geometric context to array mathematics, PyMetric provides a flexible and modern foundation for coordinate-aware scientific computing. +# Statement of need +Astrophysical modeling frequently requires the use of complex, non-Cartesian coordinate +systems such as spherical, spheroidal, or homoeoidal coordinates to exploit the underlying symmetries +of physical systems. These symmetries are crucial for accurately and efficiently modeling galaxy +shapes, gravitational potentials, and relativistic spacetimes. For example, in galactic dynamics, +ellipsoidal models often benefit from the use of homoeoidal coordinates, which align with the geometry +of the system and simplify the underlying equations. Similarly, in general relativity, expressing +metrics and computing curvature quantities in adapted coordinates is a standard practice. +The Pisces project is an emerging computational framework designed to support high-level modeling +and simulation in relativistic astrophysics, galactic dynamics, and related domains. A core requirement +of Pisces is the ability to perform differential geometry and vector calculus operations generically +across coordinate systems and grid structures, with support for both symbolic derivation and numerical +evaluation. Prior to PyMetric, no lightweight and extensible Python package provided a unified backend +to handle these computations robustly. -# Statement of need +PyMetric was developed to address this gap. It provides a foundation for the Pisces ecosystem by automating +the construction of metric tensors, differential operators (e.g., gradients, divergences, Laplacians), +and coordinate-aware transformations in arbitrary coordinate systems. Its ability to interoperate with +NumPy arrays and disk-backed storage formats (e.g., HDF5) ensures that it can be deployed +in both interactive research and large-scale simulation contexts. + +By embedding geometric context directly into array-based workflows, PyMetric makes it easier to construct +models that respect the intrinsic symmetries of complex astrophysical systems. This reduces the need +for hard-coded coordinate-specific logic and enables more maintainable, reusable, and physically faithful +software in both research and educational settings. + +# Methodology + +The core methodology behind PyMetric centers on a mathematically rigorous yet computationally practical +framework for performing differential geometry operations in arbitrary coordinate systems. The library +is designed to support seamless transitions between symbolic derivation and numerical evaluation, allowing +for precise, efficient, and geometry-aware modeling. + +A coordinate system in PyMetric is defined minimally by: + +- A set of axes labels $(x^1, x^2, \ldots)$, +- Forward and inverse transformations between these coordinates and Cartesian Space $T(x,y,z)$ and + $T^{-1}(x^1,x^2,x^3)$. +- A symbolically defined metric tensor $g_{\mu\nu}$. -`Gala` is an Astropy-affiliated Python package for galactic dynamics. Python -enables wrapping low-level languages (e.g., C) for speed without losing -flexibility or ease-of-use in the user-interface. The API for `Gala` was -designed to provide a class-based and user-friendly interface to fast (C or -Cython-optimized) implementations of common operations such as gravitational -potential and force evaluation, orbit integration, dynamical transformations, -and chaos indicators for nonlinear dynamics. `Gala` also relies heavily on and -interfaces well with the implementations of physical units and astronomical -coordinate systems in the `Astropy` package [@astropy] (`astropy.units` and -`astropy.coordinates`). +From this core specification, PyMetric constructs key geometric quantities, such as the inverse metric +$g^{\mu\nu}$, the metric density $\sqrt{g}$, and terms appearing in differential operations, such as +$L^\nu = g^{-1/2} \partial_\mu (g^{1/2} g^{\mu\nu})$, which appears in the scalar Laplacian +$\nabla^2 \phi = L^\nu \partial_\nu \phi + g^{\mu\nu} \partial^2_{\mu\nu} \phi$. These are represented both as symbolic +expressions using **Sympy** and as numerical equivalents which are converted from Sympy into +native NumPy functions. hese quantities are computed lazily: they are only derived when required for a specific operation, +avoiding unnecessary overhead. -`Gala` was designed to be used by both astronomical researchers and by -students in courses on gravitational dynamics or astronomy. It has already been -used in a number of scientific publications [@Pearson:2017] and has also been -used in graduate courses on Galactic dynamics to, e.g., provide interactive -visualizations of textbook material [@Binney:2008]. The combination of speed, -design, and support for Astropy functionality in `Gala` will enable exciting -scientific explorations of forthcoming data releases from the *Gaia* mission -[@gaia] by students and experts alike. +Coordinate systems are categorized into types (e.g., orthogonal or curvilinear) that determine +how symbolic properties are derived and which simplifications may apply. This abstraction enables users +to model highly symmetric systems (e.g., spherical or ellipsoidal coordinates) as easily +as more general curvilinear systems. -# Mathematics +## Field and Grid Operations -Single dollars ($) are required for inline mathematics e.g. $f(x) = e^{\pi/x}$ +Fields in PyMetric are array-backed data structures (typically NumPy or HDF5 buffers) that are explicitly +associated with a coordinate system and grid. While fields behave like standard NumPy arrays, +they also carry metadata about their geometric context, including coordinate labels, spacing, +and metric-aware tensor properties. -Double dollars make self-standing equations: +Operations on fields—such as computing covariant derivatives, applying Laplacians, +or transforming between bases—are automatically dispatched to appropriate symbolic +expressions and numerical kernels based on the field’s variance and the geometry of the underlying +coordinate system. -$$\Theta(x) = \left\{\begin{array}{l} -0\textrm{ if } x < 0\cr -1\textrm{ else} -\end{array}\right.$$ +This design allows users to write high-level, reusable code that is agnostic to the specific geometry, +while still benefiting from the mathematical correctness and efficiency of coordinate-aware computation. -You can also use plain \LaTeX for equations -\begin{equation}\label{eq:fourier} -\hat f(\omega) = \int_{-\infty}^{\infty} f(x) e^{i\omega x} dx -\end{equation} -and refer to \autoref{eq:fourier} from text. -# Citations +## Future Development -Citations to entries in paper.bib should be in -[rMarkdown](http://rmarkdown.rstudio.com/authoring_bibliographies_and_citations.html) -format. +The development roadmap for PyMetric is focused on deepening its mathematical capabilities and expanding +its utility in advanced physical modeling contexts, particularly those involving curved and relativistic +spacetimes. While the current implementation supports a robust suite of differential operators in orthogonal +and curvilinear coordinate systems, several avenues for future growth are planned: -If you want to cite a software repository URL (e.g. something on GitHub without a preferred -citation) then you can do it with the example BibTeX entry below for @fidgit. +1. Expanded Differential Operator Support: -For a quick reference, the following citation commands can be used: -- `@author:2001` -> "Author et al. (2001)" -- `[@author:2001]` -> "(Author et al., 2001)" -- `[@author1:2001; @author2:2001]` -> "(Author1 et al., 2001; Author2 et al., 2002)" + PyMetric will be extended to support a broader range of tensor calculus operations, including: -# Figures + - Covariant derivatives of higher-rank tensors, enabling modeling of tensor transport and geodesic deviation. + - Higher-order differential operators, such as biharmonic or fourth-order Laplacians, + which are essential in elasticity theory, advanced fluid dynamics, and quantum field theory. + - Tensor contractions and curvature operations, including the Riemann, Ricci, and Einstein tensors, + to support simulations in general relativity and cosmology. -Figures can be included like this: -![Caption for example figure.\label{fig:example}](figure.png) -and referenced from text using \autoref{fig:example}. +These features will allow PyMetric to serve as a general-purpose differential geometry engine suitable +for high-fidelity modeling in physics, engineering, and applied mathematics. -Figure sizes can be customized by adding an optional second parameter: -![Caption for example figure.](figure.png){ width=20% } +2. Relativistic and Non-Flat Coordinate Systems -# Acknowledgements + - A key area of expansion is support for relativistic geometries, where the metric tensor is no longer positive-definite and may depend dynamically on spacetime coordinates. Planned features include: + - General Lorentzian manifolds, including Schwarzschild, Kerr, and FLRW spacetimes, enabling direct modeling of astrophysical systems governed by Einstein’s field equations. -We acknowledge contributions from Brigitta Sipocz, Syrtis Major, and Semyeong -Oh, and support from Kathryn Johnston during the genesis of this project. +PyMetric is explicitly intended as a modeling and analysis tool, not a time-domain simulation engine. +It provides geometric infrastructure for constructing and analyzing equations defined on curved spacetimes, +but does not aim to solve dynamical systems or perform numerical integration of time-evolving fields. # References From 0bd656953cb293100eeb02c6591cd42fe06d74df Mon Sep 17 00:00:00 2001 From: Eliza Diggins Date: Thu, 12 Jun 2025 07:28:42 -0600 Subject: [PATCH 05/17] Citations. First draft. --- paper/paper.bib | 110 ++++++++++++++++++++++--------------------- paper/paper.md | 122 ++++++++++++++++++++++++++---------------------- 2 files changed, 122 insertions(+), 110 deletions(-) diff --git a/paper/paper.bib b/paper/paper.bib index 4e4544a4..cdb599dc 100644 --- a/paper/paper.bib +++ b/paper/paper.bib @@ -1,59 +1,61 @@ -@article{Pearson:2017, - url = {http://adsabs.harvard.edu/abs/2017arXiv170304627P}, - Archiveprefix = {arXiv}, - Author = {{Pearson}, S. and {Price-Whelan}, A.~M. and {Johnston}, K.~V.}, - Eprint = {1703.04627}, - Journal = {ArXiv e-prints}, - Keywords = {Astrophysics - Astrophysics of Galaxies}, - Month = mar, - Title = {{Gaps in Globular Cluster Streams: Pal 5 and the Galactic Bar}}, - Year = 2017 +@article{harris2020array, + title={Array programming with NumPy}, + author={Harris, Charles R and Millman, K Jarrod and Van Der Walt, St{\'e}fan J and Gommers, Ralf and Virtanen, Pauli and Cournapeau, David and Wieser, Eric and Taylor, Julian and Berg, Sebastian and Smith, Nathaniel J and others}, + journal={Nature}, + volume={585}, + number={7825}, + pages={357--362}, + year={2020}, + publisher={Nature Publishing Group UK London} } - -@book{Binney:2008, - url = {http://adsabs.harvard.edu/abs/2008gady.book.....B}, - Author = {{Binney}, J. and {Tremaine}, S.}, - Booktitle = {Galactic Dynamics: Second Edition, by James Binney and Scott Tremaine.~ISBN 978-0-691-13026-2 (HB).~Published by Princeton University Press, Princeton, NJ USA, 2008.}, - Publisher = {Princeton University Press}, - Title = {{Galactic Dynamics: Second Edition}}, - Year = 2008 +@software{hdf5, +author = {{The HDF Group}}, +title = {{Hierarchical Data Format, version 5}}, +url = {https://github.com/HDFGroup/hdf5} } - -@article{gaia, - author = {{Gaia Collaboration}}, - title = "{The Gaia mission}", - journal = {Astronomy and Astrophysics}, - archivePrefix = "arXiv", - eprint = {1609.04153}, - primaryClass = "astro-ph.IM", - keywords = {space vehicles: instruments, Galaxy: structure, astrometry, parallaxes, proper motions, telescopes}, - year = 2016, - month = nov, - volume = 595, - doi = {10.1051/0004-6361/201629272}, - url = {http://adsabs.harvard.edu/abs/2016A%26A...595A...1G}, +@Manual{einsteinpy, +title = {EinsteinPy: Python library for General Relativity}, +author = {{EinsteinPy Development Team}}, +year = {2024}, +url = {https:/einsteinpy.org/}, } - -@article{astropy, - author = {{Astropy Collaboration}}, - title = "{Astropy: A community Python package for astronomy}", - journal = {Astronomy and Astrophysics}, - archivePrefix = "arXiv", - eprint = {1307.6212}, - primaryClass = "astro-ph.IM", - keywords = {methods: data analysis, methods: miscellaneous, virtual observatory tools}, - year = 2013, - month = oct, - volume = 558, - doi = {10.1051/0004-6361/201322068}, - url = {http://adsabs.harvard.edu/abs/2013A%26A...558A..33A} +@article{perret2016dice, + title={DICE: Disk Initial Conditions Environment}, + author={Perret, Valentin}, + journal={Astrophysics Source Code Library}, + pages={ascl--1607}, + year={2016} } - -@misc{fidgit, - author = {A. M. Smith and K. Thaney and M. Hahnel}, - title = {Fidgit: An ungodly union of GitHub and Figshare}, - year = {2020}, - publisher = {GitHub}, - journal = {GitHub repository}, - url = {https://github.com/arfon/fidgit} +@article{yurin2014galic, + title={GALIC: Galaxy initial conditions construction}, + author={Yurin, Denis and Springel, Volker}, + journal={Astrophysics Source Code Library}, + pages={ascl--1408}, + year={2014} +} +@article{turk2010yt, + title={yt: A multi-code analysis toolkit for astrophysical simulation data}, + author={Turk, Matthew J and Smith, Britton D and Oishi, Jeffrey S and Skory, Stephen and Skillman, Samuel W and Abel, Tom and Norman, Michael L}, + journal={The Astrophysical Journal Supplement Series}, + volume={192}, + number={1}, + pages={9}, + year={2010}, + publisher={IOP Publishing} +} +@article{sympy, + title = {SymPy: symbolic computing in Python}, + author = {Meurer, Aaron and Smith, Christopher P. and Paprocki, Mateusz and \v{C}ert\'{i}k, Ond\v{r}ej and Kirpichev, Sergey B. and Rocklin, Matthew and Kumar, AMiT and Ivanov, Sergiu and Moore, Jason K. and Singh, Sartaj and Rathnayake, Thilina and Vig, Sean and Granger, Brian E. and Muller, Richard P. and Bonazzi, Francesco and Gupta, Harsh and Vats, Shivam and Johansson, Fredrik and Pedregosa, Fabian and Curry, Matthew J. and Terrel, Andy R. and Rou\v{c}ka, \v{S}t\v{e}p\'{a}n and Saboo, Ashutosh and Fernando, Isuru and Kulal, Sumith and Cimrman, Robert and Scopatz, Anthony}, + year = 2017, + month = jan, + keywords = {Python, Computer algebra system, Symbolics}, + abstract = { + SymPy is an open source computer algebra system written in pure Python. It is built with a focus on extensibility and ease of use, through both interactive and programmatic applications. These characteristics have led SymPy to become a popular symbolic library for the scientific Python ecosystem. This paper presents the architecture of SymPy, a description of its features, and a discussion of select submodules. The supplementary material provide additional examples and further outline details of the architecture and features of SymPy. + }, + volume = 3, + pages = {e103}, + journal = {PeerJ Computer Science}, + issn = {2376-5992}, + url = {https://doi.org/10.7717/peerj-cs.103}, + doi = {10.7717/peerj-cs.103} } diff --git a/paper/paper.md b/paper/paper.md index 777c8bc1..a9f4b3b9 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -1,5 +1,5 @@ --- -title: 'PyMetric: A Library for Geometric Computation' +title: 'PyMetric: A Geometry Informed Array Mathematics Package' tags: - Python - differential geometry @@ -18,65 +18,78 @@ affiliations: date: 11 June 2025 bibliography: paper.bib -# Optional fields if submitting to a AAS journal too, see this blog post: -# https://blog.joss.theoj.org/2018/12/a-new-collaboration-with-aas-publishing --- # Summary PyMetric is a lightweight Python library designed to streamline differential geometry -and vector calculus operations in user-defined coordinate systems, with a focus on -applications in astrophysics and computational physics. In many physical modeling -tasks, especially in astrophysics, it is both natural and advantageous to work in -non-Cartesian coordinate systems that reflect the underlying symmetries of a system. -These coordinate systems may be highly nontrivial, such as ellipsoidal (homoeoidal) or spheroidal -coordinates, where the ability to express and manipulate tensorial quantities is essential -for deriving accurate and efficient models. - -The core design of PyMetric emphasizes a seamless blend of symbolic and numerical computation. -Symbolic expressions are used to derive key geometric quantities such as metric tensors, -Christoffel symbols, and Jacobians, which are then converted into efficient numerical -functions suitable for use in array-based workflows. This enables users to write models -that respect the underlying geometry while retaining the performance and flexibility of -NumPy-style programming. - -PyMetric further supports structured grid abstractions and offers extensibility -for multiple coordinate systems, buffer types (including HDF5 storage), -and geometric operations. It automates tasks such as computing gradients, divergences, and Laplacians—critical -for solving PDEs or modeling physical systems—while maintaining awareness of the coordinate system -and metric context. This makes it particularly useful for scientific domains that demand geometric -precision, such as general relativity, magnetohydrodynamics, and planetary dynamics. - -By bringing geometric context to array mathematics, PyMetric provides a flexible -and modern foundation for coordinate-aware scientific computing. +and vector calculus operations in user-defined coordinate systems, with a focus on applications +in astrophysics and computational physics. In many physical modeling tasks, it is both natural +and advantageous to work in non-Cartesian coordinate systems that align with the inherent +symmetries of the system. These systems can be highly nontrivial—such as ellipsoidal +(homoeoidal) or spheroidal coordinates—where explicitly handling coordinate-specific +expressions becomes tedious and error-prone. PyMetric provides a unified abstraction +that decouples the underlying coordinate representation from the operations themselves, +allowing users to accurately compute gradients, divergences, Laplacians, and related geometric +quantities through a consistent interface. This makes it easier to prototype and scale +models in complex geometries without having to rewrite operations for each coordinate system. + +The core design of PyMetric relies on a hybrid symbolic-numeric model that balances efficiency, +flexibility, and accuracy. Symbolic computation is used to derive key geometric quantities, such +as metric tensors, Christoffel symbols, and Jacobians, directly from the structure of the coordinate +system. These symbolic expressions preserve the full geometric context and can be reused across +multiple evaluations. Once derived, they are compiled into optimized numerical functions that +can be efficiently applied to array data on structured grids. This approach allows PyMetric to +support coordinate-aware computation with minimal overhead, avoiding the need for repeated symbolic +manipulation during runtime, while maintaining high accuracy through analytically correct geometric +expressions. The result is a powerful and extensible framework that enables NumPy-style workflows +in complex coordinate systems without sacrificing physical fidelity. + +In addition to its symbolic-numeric foundation, PyMetric provides structured abstractions for grids +and field data, supporting a range of coordinate systems and buffer backends—including in-memory arrays and +HDF5[@hdf5] storage for scalable computation. Users can define fields over geometric grids and apply +differential operators without manually managing coordinate-dependent logic. + +PyMetric automates core operations such as gradients, divergences, and Laplacians in a +geometry-aware fashion, enabling accurate and efficient modeling of physical systems across +disciplines like general relativity, magnetohydrodynamics, and planetary dynamics. By embedding +geometric structure directly into array-based workflows, PyMetric offers a modern, extensible +foundation for scientific computing in complex coordinate geometries. # Statement of need -Astrophysical modeling frequently requires the use of complex, non-Cartesian coordinate -systems such as spherical, spheroidal, or homoeoidal coordinates to exploit the underlying symmetries -of physical systems. These symmetries are crucial for accurately and efficiently modeling galaxy -shapes, gravitational potentials, and relativistic spacetimes. For example, in galactic dynamics, -ellipsoidal models often benefit from the use of homoeoidal coordinates, which align with the geometry -of the system and simplify the underlying equations. Similarly, in general relativity, expressing -metrics and computing curvature quantities in adapted coordinates is a standard practice. - -The Pisces project is an emerging computational framework designed to support high-level modeling -and simulation in relativistic astrophysics, galactic dynamics, and related domains. A core requirement -of Pisces is the ability to perform differential geometry and vector calculus operations generically -across coordinate systems and grid structures, with support for both symbolic derivation and numerical -evaluation. Prior to PyMetric, no lightweight and extensible Python package provided a unified backend -to handle these computations robustly. - -PyMetric was developed to address this gap. It provides a foundation for the Pisces ecosystem by automating -the construction of metric tensors, differential operators (e.g., gradients, divergences, Laplacians), -and coordinate-aware transformations in arbitrary coordinate systems. Its ability to interoperate with -NumPy arrays and disk-backed storage formats (e.g., HDF5) ensures that it can be deployed -in both interactive research and large-scale simulation contexts. - -By embedding geometric context directly into array-based workflows, PyMetric makes it easier to construct -models that respect the intrinsic symmetries of complex astrophysical systems. This reduces the need -for hard-coded coordinate-specific logic and enables more maintainable, reusable, and physically faithful -software in both research and educational settings. +Modern astrophysical modeling requires a high degree of flexibility—both in physical assumptions +and in computational infrastructure. The Pisces Project (of which ``PyMetric`` is a part) +is a general-purpose model-building framework for astrophysics that aims to unify and extend +existing tools for generating models and initial conditions (e.g., DICE[@perret2016dice], GALIC[@yurrin2014galic]) +under a common, modular API. +Its goal is to make it easier to construct complex, physically motivated models +of systems such as galaxies, black holes, or relativistic fluids by exposing a simple and extensible +interface for defining models, fields, and dynamics. + +A persistent challenge in building such extensible modeling tools is the limited and inconsistent +support for coordinate systems found in most existing software. Codes like EinsteinPy[@einsteinpy], +DICE[@perret2016dice], and yt[@turk2010yt] often +hard-code assumptions about coordinate geometry, making them difficult to generalize to new physical +contexts or non-Cartesian coordinate systems. This lack of abstraction limits reusability and complicates +the construction of unified modeling workflows across domains such as general relativity, +galactic dynamics, and fluid mechanics. + +To address this limitation, PyMetric was developed to be a lightweight library that standardizes +coordinate-aware geometric computation. The library is designed to serve as the geometric backend +for Pisces and similar modeling systems. It provides a consistent abstraction layer for defining +coordinate systems, computing differential geometric quantities, and evaluating operators like gradients, +divergences, and Laplacians—all without requiring the user to manage low-level +details of tensor algebra or coordinate transformations. + +PyMetric emphasizes extensibility and modularity through four core interfaces: + +- **Coordinate System API** – Enables the definition and use of arbitrary coordinate systems with minimal required knowledge, while supporting symbolic derivation of metric-dependent quantities. +- **Buffer API** – Provides a backend-agnostic interface for array storage, allowing seamless integration with systems like HDF5, XArray, Dask, and unit-aware arrays. +- **Differential Geometry API** – Implements low-level, coordinate-independent formulations of core operations such as gradients, divergences, Laplacians, and volume elements. +- **Grid and Field API** – Supports flexible discretization strategies and a variety of field types, including sparse and dense scalar, vector, and tensor fields. + +Together, these abstractions form a unified symbolic-numeric pipeline that allows high-level modeling code to operate naturally across diverse geometries and data representations. By standardizing geometric computation and decoupling it from specific coordinate assumptions or backend implementations, PyMetric addresses a longstanding gap in scientific Python infrastructure. This foundation enables Pisces to offer a powerful, composable, and user-friendly environment for building physically accurate models in astrophysics and beyond. # Methodology @@ -96,8 +109,7 @@ From this core specification, PyMetric constructs key geometric quantities, such $g^{\mu\nu}$, the metric density $\sqrt{g}$, and terms appearing in differential operations, such as $L^\nu = g^{-1/2} \partial_\mu (g^{1/2} g^{\mu\nu})$, which appears in the scalar Laplacian $\nabla^2 \phi = L^\nu \partial_\nu \phi + g^{\mu\nu} \partial^2_{\mu\nu} \phi$. These are represented both as symbolic -expressions using **Sympy** and as numerical equivalents which are converted from Sympy into -native NumPy functions. hese quantities are computed lazily: they are only derived when required for a specific operation, +expressions-using SymPy[@sympy]-and as NumPy-backed callables. These quantities are computed lazily: they are only derived when required for a specific operation, avoiding unnecessary overhead. Coordinate systems are categorized into types (e.g., orthogonal or curvilinear) that determine @@ -133,8 +145,6 @@ and curvilinear coordinate systems, several avenues for future growth are planne PyMetric will be extended to support a broader range of tensor calculus operations, including: - Covariant derivatives of higher-rank tensors, enabling modeling of tensor transport and geodesic deviation. - - Higher-order differential operators, such as biharmonic or fourth-order Laplacians, - which are essential in elasticity theory, advanced fluid dynamics, and quantum field theory. - Tensor contractions and curvature operations, including the Riemann, Ricci, and Einstein tensors, to support simulations in general relativity and cosmology. From d1641519f76f282815ec957046d722f1ae513365 Mon Sep 17 00:00:00 2001 From: Eliza Diggins Date: Thu, 12 Jun 2025 07:34:58 -0600 Subject: [PATCH 06/17] Fixes. First Draft --- paper/paper.md | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index a9f4b3b9..fea0a897 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -13,7 +13,7 @@ authors: orcid: 0000-0001-9110-2245 affiliation: 1 affiliations: - - name: University of Utah, USA + - name: University of Utah Department of Physics and Astronomy, Salt Lake City, Utah, USA index: 1 date: 11 June 2025 bibliography: paper.bib @@ -42,12 +42,12 @@ multiple evaluations. Once derived, they are compiled into optimized numerical f can be efficiently applied to array data on structured grids. This approach allows PyMetric to support coordinate-aware computation with minimal overhead, avoiding the need for repeated symbolic manipulation during runtime, while maintaining high accuracy through analytically correct geometric -expressions. The result is a powerful and extensible framework that enables NumPy-style workflows +expressions. The result is a powerful and extensible framework that enables NumPy-style [@harris2020array] workflows in complex coordinate systems without sacrificing physical fidelity. In addition to its symbolic-numeric foundation, PyMetric provides structured abstractions for grids and field data, supporting a range of coordinate systems and buffer backends—including in-memory arrays and -HDF5[@hdf5] storage for scalable computation. Users can define fields over geometric grids and apply +HDF5 [@hdf5] storage for scalable computation. Users can define fields over geometric grids and apply differential operators without manually managing coordinate-dependent logic. PyMetric automates core operations such as gradients, divergences, and Laplacians in a @@ -61,15 +61,15 @@ foundation for scientific computing in complex coordinate geometries. Modern astrophysical modeling requires a high degree of flexibility—both in physical assumptions and in computational infrastructure. The Pisces Project (of which ``PyMetric`` is a part) is a general-purpose model-building framework for astrophysics that aims to unify and extend -existing tools for generating models and initial conditions (e.g., DICE[@perret2016dice], GALIC[@yurrin2014galic]) +existing tools for generating models and initial conditions (e.g., DICE [@perret2016dice], GALIC [@yurin2014galic]) under a common, modular API. Its goal is to make it easier to construct complex, physically motivated models of systems such as galaxies, black holes, or relativistic fluids by exposing a simple and extensible interface for defining models, fields, and dynamics. A persistent challenge in building such extensible modeling tools is the limited and inconsistent -support for coordinate systems found in most existing software. Codes like EinsteinPy[@einsteinpy], -DICE[@perret2016dice], and yt[@turk2010yt] often +support for coordinate systems found in most existing software. Codes like EinsteinPy [@einsteinpy], +DICE, and yt[@turk2010yt] often hard-code assumptions about coordinate geometry, making them difficult to generalize to new physical contexts or non-Cartesian coordinate systems. This lack of abstraction limits reusability and complicates the construction of unified modeling workflows across domains such as general relativity, From 3be991d78f420b8650ac484a4b2e4d58621033ff Mon Sep 17 00:00:00 2001 From: Eliza Diggins Date: Fri, 13 Jun 2025 11:04:20 -0600 Subject: [PATCH 07/17] Fixes. First Draft --- paper/paper.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index fea0a897..5f174751 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -69,7 +69,7 @@ interface for defining models, fields, and dynamics. A persistent challenge in building such extensible modeling tools is the limited and inconsistent support for coordinate systems found in most existing software. Codes like EinsteinPy [@einsteinpy], -DICE, and yt[@turk2010yt] often +DICE, and yt [@turk2010yt] often hard-code assumptions about coordinate geometry, making them difficult to generalize to new physical contexts or non-Cartesian coordinate systems. This lack of abstraction limits reusability and complicates the construction of unified modeling workflows across domains such as general relativity, @@ -109,7 +109,7 @@ From this core specification, PyMetric constructs key geometric quantities, such $g^{\mu\nu}$, the metric density $\sqrt{g}$, and terms appearing in differential operations, such as $L^\nu = g^{-1/2} \partial_\mu (g^{1/2} g^{\mu\nu})$, which appears in the scalar Laplacian $\nabla^2 \phi = L^\nu \partial_\nu \phi + g^{\mu\nu} \partial^2_{\mu\nu} \phi$. These are represented both as symbolic -expressions-using SymPy[@sympy]-and as NumPy-backed callables. These quantities are computed lazily: they are only derived when required for a specific operation, +expressions-using SymPy [@sympy]-and as NumPy-backed callables. These quantities are computed lazily: they are only derived when required for a specific operation, avoiding unnecessary overhead. Coordinate systems are categorized into types (e.g., orthogonal or curvilinear) that determine From 88965c45b59414fd3e127f09adaa48c8df5af66d Mon Sep 17 00:00:00 2001 From: Eliza Diggins Date: Fri, 20 Jun 2025 08:21:00 -0600 Subject: [PATCH 08/17] Edits --- paper/paper.md | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 5f174751..de0eacff 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -24,7 +24,9 @@ bibliography: paper.bib PyMetric is a lightweight Python library designed to streamline differential geometry and vector calculus operations in user-defined coordinate systems, with a focus on applications -in astrophysics and computational physics. In many physical modeling tasks, it is both natural +in astrophysics and computational physics. The library was originally created to provide a +geometric backend for the Pisces project, an (in development) general purpose astrophysical modeling and initial conditions +library, but has since grown into an independent library due to its size and complexity. In many physical modeling tasks, it is both natural and advantageous to work in non-Cartesian coordinate systems that align with the inherent symmetries of the system. These systems can be highly nontrivial—such as ellipsoidal (homoeoidal) or spheroidal coordinates—where explicitly handling coordinate-specific @@ -59,7 +61,7 @@ foundation for scientific computing in complex coordinate geometries. # Statement of need Modern astrophysical modeling requires a high degree of flexibility—both in physical assumptions -and in computational infrastructure. The Pisces Project (of which ``PyMetric`` is a part) +and in computational infrastructure. The Pisces Project (of which PyMetric is a part) is a general-purpose model-building framework for astrophysics that aims to unify and extend existing tools for generating models and initial conditions (e.g., DICE [@perret2016dice], GALIC [@yurin2014galic]) under a common, modular API. From f6bff8161ebf0367695eb75750de1e471c200f72 Mon Sep 17 00:00:00 2001 From: Eliza Diggins Date: Sat, 18 Oct 2025 11:47:40 -0700 Subject: [PATCH 09/17] Fixed Einsteinpy URL typo. --- paper/paper.bib | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/paper/paper.bib b/paper/paper.bib index cdb599dc..5d1ec3ea 100644 --- a/paper/paper.bib +++ b/paper/paper.bib @@ -17,7 +17,7 @@ @Manual{einsteinpy title = {EinsteinPy: Python library for General Relativity}, author = {{EinsteinPy Development Team}}, year = {2024}, -url = {https:/einsteinpy.org/}, +url = {https://einsteinpy.org/}, } @article{perret2016dice, title={DICE: Disk Initial Conditions Environment}, From 2a4a0d567adf73ff635fd3c73db5431222ab80ca Mon Sep 17 00:00:00 2001 From: Eliza Diggins Date: Sat, 18 Oct 2025 11:48:32 -0700 Subject: [PATCH 10/17] Added DOI for YT reference. --- paper/paper.bib | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/paper/paper.bib b/paper/paper.bib index 5d1ec3ea..41b443b7 100644 --- a/paper/paper.bib +++ b/paper/paper.bib @@ -41,7 +41,8 @@ @article{turk2010yt number={1}, pages={9}, year={2010}, - publisher={IOP Publishing} + publisher={IOP Publishing}, + doi={10.1088/0067-0049/192/1/9} } @article{sympy, title = {SymPy: symbolic computing in Python}, From 7a404da6c2309ae5bf52e0788e0900399eb6b483 Mon Sep 17 00:00:00 2001 From: Eliza Diggins Date: Sat, 18 Oct 2025 11:57:11 -0700 Subject: [PATCH 11/17] Modified the index.html file to redirect to correct docs. --- docs/index.html | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/index.html b/docs/index.html index 39b2ca92..8d3d695f 100644 --- a/docs/index.html +++ b/docs/index.html @@ -1,3 +1,3 @@ - + From e631ef692b597ea54105299c4e9d5a8f4bda8358 Mon Sep 17 00:00:00 2001 From: Eliza Diggins Date: Sat, 18 Oct 2025 12:29:46 -0700 Subject: [PATCH 12/17] added minimal example directly to repo. --- .../example_cartesian_gradient.ipynb | 184 ++++++++++++++++++ minimal_example/readme.md | 10 + pymetric/_version.py | 19 +- 3 files changed, 210 insertions(+), 3 deletions(-) create mode 100644 minimal_example/example_cartesian_gradient.ipynb create mode 100644 minimal_example/readme.md diff --git a/minimal_example/example_cartesian_gradient.ipynb b/minimal_example/example_cartesian_gradient.ipynb new file mode 100644 index 00000000..ee16dbda --- /dev/null +++ b/minimal_example/example_cartesian_gradient.ipynb @@ -0,0 +1,184 @@ +{ + "cells": [ + { + "metadata": {}, + "cell_type": "markdown", + "source": [ + "# Cartesian Gradient Example\n", + "\n", + "---\n", + "\n", + "This example provides a very simple demonstration of how to compute the gradient of a scalar field defined on a Cartesian grid using PyMetric. We'll first install\n", + "the PyMetric package and then create a field and take the gradient." + ], + "id": "2baca49099618917" + }, + { + "metadata": { + "ExecuteTime": { + "end_time": "2025-10-18T19:13:05.178616Z", + "start_time": "2025-10-18T19:13:00.988588Z" + } + }, + "cell_type": "code", + "source": [ + "# Install the PyMetric package from the source\n", + "# code.\n", + "! pip install .." + ], + "id": "e84ed94947390571", + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Processing /Users/ediggins/Dev/pymetric\r\n", + " Installing build dependencies ... \u001b[?25ldone\r\n", + "\u001b[?25h Getting requirements to build wheel ... \u001b[?25ldone\r\n", + "\u001b[?25h Preparing metadata (pyproject.toml) ... \u001b[?25ldone\r\n", + "\u001b[?25hRequirement already satisfied: numpy>=1.22 in /Users/ediggins/Dev/pymetric/.venv/lib/python3.12/site-packages (from pymetric-lib==0.0.2a2.dev26) (2.2.6)\r\n", + "Requirement already satisfied: h5py>=3.0 in 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/Users/ediggins/Dev/pymetric/.venv/lib/python3.12/site-packages (from matplotlib->pymetric-lib==0.0.2a2.dev26) (1.3.2)\r\n", + "Requirement already satisfied: cycler>=0.10 in /Users/ediggins/Dev/pymetric/.venv/lib/python3.12/site-packages (from matplotlib->pymetric-lib==0.0.2a2.dev26) (0.12.1)\r\n", + "Requirement already satisfied: fonttools>=4.22.0 in /Users/ediggins/Dev/pymetric/.venv/lib/python3.12/site-packages (from matplotlib->pymetric-lib==0.0.2a2.dev26) (4.58.0)\r\n", + "Requirement already satisfied: kiwisolver>=1.3.1 in /Users/ediggins/Dev/pymetric/.venv/lib/python3.12/site-packages (from matplotlib->pymetric-lib==0.0.2a2.dev26) (1.4.8)\r\n", + "Requirement already satisfied: packaging>=20.0 in /Users/ediggins/Dev/pymetric/.venv/lib/python3.12/site-packages (from matplotlib->pymetric-lib==0.0.2a2.dev26) (25.0)\r\n", + "Requirement already satisfied: pillow>=8 in /Users/ediggins/Dev/pymetric/.venv/lib/python3.12/site-packages (from matplotlib->pymetric-lib==0.0.2a2.dev26) (11.2.1)\r\n", + "Requirement already satisfied: pyparsing>=2.3.1 in /Users/ediggins/Dev/pymetric/.venv/lib/python3.12/site-packages (from matplotlib->pymetric-lib==0.0.2a2.dev26) (3.2.3)\r\n", + "Requirement already satisfied: python-dateutil>=2.7 in /Users/ediggins/Dev/pymetric/.venv/lib/python3.12/site-packages (from matplotlib->pymetric-lib==0.0.2a2.dev26) (2.9.0.post0)\r\n", + "Requirement already satisfied: six>=1.5 in /Users/ediggins/Dev/pymetric/.venv/lib/python3.12/site-packages (from python-dateutil>=2.7->matplotlib->pymetric-lib==0.0.2a2.dev26) (1.17.0)\r\n", + "Building wheels for collected packages: pymetric-lib\r\n", + " Building wheel for pymetric-lib (pyproject.toml) ... \u001b[?25ldone\r\n", + "\u001b[?25h Created wheel for pymetric-lib: filename=pymetric_lib-0.0.2a2.dev26-py3-none-any.whl size=259935 sha256=25a8ab74cecc3a17193c28d3aa6675f536eff72b198bd9934afc762a7012129e\r\n", + " Stored in directory: /private/var/folders/wb/hm_py6x1025cwdg8jjs1rg_w0000gn/T/pip-ephem-wheel-cache-9mekzsk3/wheels/5c/a0/f2/adc1bf06554787ce9ad3de709272799b2f3e991ebe4c4ae46e\r\n", + "Successfully built pymetric-lib\r\n", + "Installing collected packages: pymetric-lib\r\n", + "Successfully installed pymetric-lib-0.0.2a2.dev26\r\n", + "\r\n", + "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m A new release of pip is available: \u001b[0m\u001b[31;49m25.1.1\u001b[0m\u001b[39;49m -> \u001b[0m\u001b[32;49m25.2\u001b[0m\r\n", + "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m To update, run: \u001b[0m\u001b[32;49mpip install --upgrade pip\u001b[0m\r\n" + ] + } + ], + "execution_count": 2 + }, + { + "metadata": { + "ExecuteTime": { + "end_time": "2025-10-18T19:25:51.637294Z", + "start_time": "2025-10-18T19:25:51.576159Z" + } + }, + "cell_type": "code", + "source": [ + "import numpy as np\n", + "from pymetric import DenseTensorField, CartesianCoordinateSystem2D, GenericGrid, pg_log\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# Disable the logger\n", + "pg_log.setLevel(\"WARNING\")\n", + "\n", + "# Create the coordinate system and the grid.\n", + "cs = CartesianCoordinateSystem2D()\n", + "x, y = (np.linspace(-0.1, 1.1, 104), np.linspace(-0.1, 1.1, 104))\n", + "g = GenericGrid(cs, [x, y], ghost_zones=2)\n", + "\n", + "# Define a function of the coords.\n", + "func = lambda _x, _y: np.sin(10 * np.sqrt(_x**2 + _y**2)) * 5 * np.cos(3 * _x)\n", + "\n", + "# Create the dense field from the function.\n", + "f = DenseTensorField.from_function(func, g, [\"x\", \"y\"])\n", + "\n", + "fig, axes = plt.subplots(1, 1)\n", + "Q = axes.imshow(f[...].T, extent=g.bbox.ravel())\n", + "axes.set_xlabel(\"x\")\n", + "axes.set_ylabel(\"y\")\n", + "plt.colorbar(Q, ax=axes)\n", + "plt.show()" + ], + "id": "c806469c678a6c5c", + "outputs": [ + { + "data": { + "text/plain": [ + "
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" + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "execution_count": 29 + }, + { + "metadata": { + "ExecuteTime": { + "end_time": "2025-10-18T19:28:22.741360Z", + "start_time": "2025-10-18T19:28:22.597770Z" + } + }, + "cell_type": "code", + "source": [ + "# Generate the gradient vector field for the scalar field.\n", + "grad_f = f.gradient()\n", + "fig, axes = plt.subplots(1, 2, figsize=(10, 5))\n", + "Q1 = axes[0].imshow(grad_f[..., 0].T, extent=g.gbbox.ravel())\n", + "axes[0].set_title(\"Gradient in x direction\")\n", + "axes[0].set_xlabel(\"x\")\n", + "axes[0].set_ylabel(\"y\")\n", + "axes[0].set_xlim(*g.bbox[0, :])\n", + "axes[0].set_ylim(*g.bbox[1, :])\n", + "plt.colorbar(Q1, ax=axes[0])\n", + "Q2 = axes[1].imshow(grad_f[..., 1].T, extent=g.gbbox.ravel())\n", + "axes[1].set_title(\"Gradient in y direction\")\n", + "axes[1].set_xlabel(\"x\")\n", + "axes[1].set_ylabel(\"y\")\n", + "axes[1].set_xlim(*g.bbox[0, :])\n", + "axes[1].set_ylim(*g.bbox[1, :])\n", + "plt.colorbar(Q2, ax=axes[1])\n", + "plt.show()" + ], + "id": "e963bc0b3c9f7e30", + "outputs": [ + { + "data": { + "text/plain": [ + "
" + ], + "image/png": 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MxPRCL6aPokSWKGp4f/3Xfz38uT/35xjFU8eJBqjS+B9qhHcVqYOUKFkPa+J5r2jVQsFgD/uSXY9FljxpbIkn7z/kixK02uJ9Jm76k5/85GL7iw4HvIncy+d71WUfiQ33nRiRxipQW0JW7rt377LVet04wS7XW7puOhzdRPt99md/Nqc1oO+SxouQp6oGZC9Cum66/rKvhLtLCI6EQuP0fKCYQx3Pezhvb5eNhNybf/tv/20ejEvu612E6Dw0mJMGZBI1QIReVhTJCSIWJhSi+IwJ0TrIGkbK0btld5Ft3f77lNe//vX8LP7sn/2zbAUkhUwDVceUg0Qo2uZejglFXZLgGGP3+T/7z/4zntc6PdveX3o/audOUZlkfZftZDnMedqtjt06AhTpCoUUGVG1anStLjdXum46HN1E9+zrvu7rOHADBdSga11H1eu6qcu91Euom6YERyIaH3mKf+fv/J1aRt8uUUNpyAUZtk9PT9nbjEZt8ojXQPy+pI+ZuqJCHXeKdkS84lrIx00sKGKFwX1o+Ru/8RvNdmRxfO5zn8uKTegVotg857h2DLJgEze91kiuC/XaErJS4rnca6EP9gu/8Au500AhZ6kTQe5nWl53P0ipUShforGI/Pt//+/Vy7WNUJ3UGNHxiTfcus+kMD/xEz+RQ//i8f17ILlBpmSZp5DG1IFCXjKNcSDqDEVjWjd2oUuXLldfum46DN0kHjWaSC/R9VH+r3UeoK6bulyWPPzww2aqgalDHc/bPVNXVIjPTBnWaTAn8Zglyzw1NpRZntYRZWJKWFiiTpDViMKAEn2CXmJqeGv8YAo5S5ZHGshJypLoFxSmlnJy1HjyPtwoDTIlugcNTqUGjPYn8PFP/sk/4eVN5XnPex6HiKWxG5QTgwaV0kDieyXkbqYQvHT+pIT+m//mv2FwRQlOiZtOz6QllL2dvFo0uJXCyFL4WbmXFBp2G6FnR6FmKQgGWW5IeZJyooaEQoV+/Md/PFtvSGhsFz1H2o4G4hLHnSg4tB01SnJ/JdQv1UWNFN3fWgLGl7/85czJ/+RP/mQOP0tjaahzQ+8jvU89I/2uA313s3Tvun+XLlOk66bD0E3onaL7RzKV4td1U5d7pZdINqnjUMfzdjB1hYU664TQyY1POTbIkkOub3JZk1L5oi/6otHOvAg1QkQDoEaGFBLRdyjvAsXm9/sTWKDY/X/hL/yF8IpXvIIVHSUI/J7v+Z6CBuSFBgCSdegv/aW/FL7zO7+Tedz0AVADTTknthFq6KlxpXOgMRx07fdKYdGA6L/7d/8u339S+iKvfvWr2SJKdD8aIEn3tyZkMSRLH330NMCaOhekxCgy1bYKi4R48k996lO5g/C1X/u1PJ6FcoqQYqQoRSL0bH/iJ36CIxCSkqNEd3T/KFGiCHUC/vJf/svhta99LStX4r2TAqopLHq+P/7jP85jG0jxUn10jfRu0fvYZXuhiEfLHYkEq9D5/l3ujXTddLm6CYXALLXJdD+m0i67bupyr/TSReimyxjPO6P46Bd6hC5dunTpsnV0IxrU/+3/+sPC/Q/VB0VPlUd+cxk+46N+lqlHyEvv0qXL9RUKP040SAJFBE66dDkkvXRddFP3THXp0qXLgcshBKDo0qXL1ZNv/dZv5QH6RK/r0uWQA1BcZelgqkuXLl0OXCS54W51XH2F1aVLl2nyQz/0Qxx846u/+qs5AS8FWujS5dD00nXRTR1MdenSpUuXLl26XCOh8V80TogCO9A4oS5dulycdDDVpUuXLgcuy2HG0651dOnS5WbIuqAbXbocgl66Lrqpg6kuXbp0OXBZ7iFq0vIaUCm6dOnSpcv10UvXRTf14PpdunTp0qVLly5dunTpsoV0z1SXLl26HLishjlPu9Vx9a1/Xbp06dLl+uil66KbbhyYosRuv/Irv8JZlCmJYJcuXbrsWyh932/+5m9ygkpKHrirdJrf9Zeum7p06XKVdFOn+d1gMEXK6hnPeMZln0aXLl1ugLztbW8LT3/60y/7NLpcAem6qUuXLvdKum7ar9w4MEVWP5IP/2NfHhbHt8NsFcJMQDHNZyFwYJE0H45CWM1ngTyZq+MQhkUsW54MPOJsdULTiteHk1UIx6sQ5kM4Ol6G2dEqzOdDOF7E+Ww2hAXNHQpfDTN2lZKn83w5D8vVLAyrWVidz8NyOecTGc7mYVjOwoyms1kIq1mYn4cwP6WTDGF+NgvzMw7YHxZngdfNVkOYn6bl5cDr58shzM6HsDgd4rUvV2F+tuJ7MDtf8URC29NEJzVbregkeTlOcPJsQJ3F+Yzu0ywEsnbwvZuHQPeObu3xnNcN83lYHdM2s7BazHh5mNGctqHlEJY0Pwp8T3mZ7nm61zyndUfp/qfl+KyGWE7nckQ3gu55CPPFKszovs8HXqaLpdOkZxGX48RXwtfjrST0fOJ9js9qFgaa021ZxRdltaTf9KxCGJZzfn70jML5LMxovqR7Sstxzs+K73l8jvwM6TnRlJbpWdHzpG15P3qesi0/R9pWnmM6/9UQ32e+NPes5DVP7zc/L57Se003hU77iO55fOf1/V+k95/uOT03eRbHUj7EspMh7kffxNEQZotVWJwsw2wxhOPjZbh9chaO5qtw3/FZuP/4lJcfOr4THlrcDUfzZXjs0aPh/sVpuDU7Dw8vHgm3Zmfh9uwsPDx/NJzMluHWbBkemJ+FRRjCrdks3J7N2C52NFuEo9k8zMMsLOifs+wTjeA82b/Oh2U4oxs7DOHRYQh3hiGswiw8MhyFu8MinA5H4X3L2+HR4STcHY7Ce5YPcNkHlifhPWcPhNPVPLx/eTu89/R2WNLy6Ul45OyEl+/eOQrnZ0dh+f7T8PaX/RVtb3aV1R4iHsUvu8tV0E1Hi9thcZq+5yW18/G7np+uwuKcGyJeni9j2zyndpvbiFUIVOa/e26X0/d+NA/DIrbNK2qX6Xs+kuX4/a9OYrtN7TN/37O0vIhth+rCpCN5Tu2pLtP62BazbuSmcQiB90ltNJXrcprzuZKOlDYqXUhSMVHg4mqfRNXIPbOrVOenCqSp5D+xrQ/+91DZ15fxKUO52d7WWZx6yzi/jdF+rKlY04zkww071bO1rL0Pa+6deRZj283q21WWZ2Pntk+nSuue5te0vg2UGTWBF5bKV3fuhLf9pa/ai27ah166LrrpxoEpoU8cz26Ho3A7N9oDvnixg8lKIykD6iezkklgKlCnkRTLSQjhdgJTt5Yh3EoA6uScARUtnxwtuaNIh6bOI4EqlUGySMcOOoGp8+WCO+xnZ4swTx3z5dlCwVQ4pZMJDKpmBExSh5sAFS+f5g44HT+CqQge5qSYFwQeVnH92cBp16hjSYBiNo/KeTZL50kd8iUsj4EpupykpCOwSmCKO+MEsGInfbVIwOpoFpZHcV+acyeeNiOlncDU7CTd8wWVx/mcO/ax087K+9iBKS6niwsRQPFyAk0ErBjvrTYCU6IgaS7LBICXS+p00AXQBGCKflMLcT7PYOocwBS9Q3RaCKbomdF10jKdOwEmfobx+TGYmsn6CBQVTNG1CAhugSlnLIjPKL3vCUwJWJLf1GmaM/ClZ5GeydEsLx+n50Lncys/l+FWAlNkULgVwdT86Dwsbs3jvT+eh6OTWTiaLcPx8SocHw/heLYMJ8fn4dZiFU5mIdy3OAq356twezaE++dHgV71+2YhPEj7hxWDqVsEisMsHM/mPEUwNa+CqVVKDki4k+0OA33Gq3BrGMKS9hvm4XiYhzMK97qahwVNBK7OFzxfLo/CrbOjMKOys+NwcnISzlfzcHT3VlicnYQZfbvz47A6W8T3Adqbw0ja2+MNHbLIu0JGPgJT8/Rt01Nb0LdE3/9iCIvUHs9nyzAbyBBG65ax3SYgtYzLULEiHAZTC1JcZI6YhdWM2uJ5WJFBazFP3/4sLJMxhdrk5XEGUNxGz3JbHI0vCTyx8SUDKAFb1PZyOyOAC5cFMGmbBMt0hros17IGSK3p4HLb7bYREMVd9BpgMr9HwJUHUqMd9AQIWttMuJZRme3WcR+mgKmpx9lE1oKV1K768qlgagdAVZzFvWKmwSvVVCcbgCn9uQfdtL+kvfNw1eXGgSmRaOmPHdTgPwxq5FdJaRDOiNggAhhSEqmN0QaHK0yYIikE9YSw0osAi5YXBKa8ZY1NgHO23JEXgJQjYRquI3WISXnmTjAXRP2Yjilt+Gy8DYLydGCpkyuSa9HCiXczH7m6lyge8+3SddG1pkPLaa47pFvPxyvqttspTnbb1HabLHLgWbyG5jYTZKfzmCqbPMqxdVOUv9uHb5MxqeEXYHtL0SY929spe8k2TXjfUyXxyPYCjV4q5vlL6iNcuuxVjIrIRhE1kKjBJLVDDKjSx0ZzA6ZomTorpJOiFWGo1hPnxVjwiQ1UrS02+sC3HeBpiAd2y6Tj0rVno2eqXLcfb/ttuVWC9rwcQMLtt2n3umwuo/d1jy0svpTSASnK3XLtPKe+d5uc1y7ru1yq3FgwNT8nj0ykUMTGOreubKFn83/SSUy7i7QFgkJRIc0Y4Gj7ngAUeT7Ieni8WLJHajFbhdvH5+yZWswGnhOo4j3TIckzRRZu8kwRfYvWE31MQBtZDZk2xmdMRkVZwQbGaG2k64iOEbUS8rcny+CV4PMXAIaAbOx7FW0mZjyRGoJDy1xrvdaTFZa2axUFX60XymY15Sg3WK49XQjdfbrXAuh4EzA1xQ73Ji0jPc32XqlfAPdxRDY99BYil7qJd75Kq/DnOqzfM5Jcp1ygACoPb2TyZNntRO0TtXLx/JFBhOZsKY+evwyk3Is62SqwmUTv9Y6DhfcQdanLPZCp6FxAE03skUrT+Xk2EiZhb9QiffSL6EWPaovawsrx3bm0DHNVabXX0LYXbTbpN/lmWNdloyFXoUgtFdU6wK1zKRcLYDXZG9XYRz1eRV3lPmrQuQqgbOzdqK2/yGPj4SceVw21E7ZHLK8Hq+1X6QZx8WzLezLldahZ9Zw0PVIXKPvQS9dFN91YMEXjTaiDJBQrC6YSzzs12qSYGNyku0XAhTxWzLkSxEMfIVOZiD5GtKVluHVE40OGcN/RaThZRBB1nMBUPFzskhGQOl8RcWkWPVjLgcdN8TgdolGs5vH4fByikCUvFZXxO0iUw0jNivSJdP7SmGSWRzzuSsBWHuuUvV1UWmklaq2HamEktGdEJN1msZ5mpR3BB/+uWP34VNSjkYAP9FljPdGDh7uqVRUbNQPk6JiZjy/bZicTPM9tpOb+Ek+iHmikM3KvLE81IDS2rd+u9lvBaaUzhZvC81t/6Eh9ZWOBr2PPhkrrC0vACScCUfq5yDKU6bTD+zMi1DbQtGsdXa6QpHaZWyxqQ2RggXiiwCPF9D4aN7VchtnZufVMqUdrwZQ+GsdI1IeBaRbJvNT4oLQWUQE7vkIEOtgrxpWLAQr0iCgMAUzSfmpP16qdql6yR2yvHqaAqwaI8tuNAC27PHI+ByeVh72LftxE8H7h0hb3To2ZmwCwdYDKnpqqvqJ8F6nVM6XvcI+A1L700nXRTTcXTPG4oETzA8NyNttHsMSgib05kfoXB/lWGlDT0RqSFyrS+mic1BFR/ahstmJvFXcQk1ckepTiWBxaNyclx+N6kqKUzltSLEj3Y/ADlg2lQ8B5KU0RykTUoGYG+G7RIBiQkH5MtBhuJd7SudZidg9cPpvK2D0eazSFBbOv+7dhRXtxvnhcjgs7X9xmMps4j8vJOu4V9NXXBV0ORWRcI/yuzkWSsUrAFVgsYJvGmFfADLwsbDc8B53v6A1ufde1tsgsg3uhus3Ix7cLkKqVV5ZNOIQ17oXeTGwil3i3prbt96L9n1D3gfVsbqTcWDBF0ewWFO3tHMYlJWueRDWjOQULoEG3RAck7w9vS3EVqDx5esSVsliswjEFm1hQtLLT8CBHK1uGB45Ow63FOZP0yDPF458oAlzSmqerRTidLdjVydRDGiQ/j0EpqP7lbIgDglkn0iDhASI0Rcsle6UWabnlmdJl8XJFkBZ1lXin8pep5VNdGOJBQhzlQQ/S+ZIYGl8LFMFcsGQ+q2yujB4v31tIHql71jb7m1DdIvcDptxi3RgHa+8Ld9gHIp66ZgeidXryfD04UmqlrU48THGZBsOnCGLOVhGXxUd0sYoDvUzjIu9bMnbAI1rXv9tGOs3v5kgM2iBtOLXnAyynqHz87aTOuXywwyoMFM3vnAJQJDdWGtfJ7yUb6eDrEcDEtHYIIqFTjqSq4EoYDrXl4kLyBTGLQJovNiLCODC6LtK9+s0gWoJFYzUUJbXpjW2cY7EMx2psW9D1ah6pQ5YWEKg5n4AmX/JCy203Ov4a2dYjtb5S9y7peSWjwRSKoPNO7f38Guuqh6pZNy+4z9NpflluLJjiKHarFY+dYm8TD9xNKxOoYMU1UDS26I2iSGW0giObSQAL6c0SwCIwtViG46NVuO/oPDyQwNRDR3fDrfmZeqYIMLF7lKIrceC5ozBfHWkmaQ4PztQ/yi4dPU8E/GgvikQ2m6exUzSQmABfOmdWrqx4SeHa8V/Rq5WWeXucopYTA2D2dm3iG5ePGSiB2FuubK+Dp6VToMAqB6eQMqlSjyU3KgUJ0PXrcczFy5QGzHuYpu7TqmhL8WPNpF/WdIz5YI5FBwIuDKl/FamQ6fKk7tdcvay7CMmfw3S4JmczgxdavsV9y36S9l59hXUTJLbZYBDjyHiJ8pdAjuod7BTy+KkUzY9of9jAUEhQimTKUdPzWCQJly5RV+Pcgaqk3xTgCfASEDWbZonAMbFEqUajl2gALlMDE3BoC6/Uju1A8YlOoPOl4+qRNzA2HbRsbJFbs/EUKiC6Q9fJvb63YO31pznatFdsAJsfe/36yUDqHsj+kvbOw1WXGwumGC/FIPnxPeT8PLnBZkCRxlQR/GHjHm1Lxj2Ol+4sOym8NnmlCEAdz8/DyfycPVG35uc8cTQ/glHsmZqH5WwV8xbNZuF8xgHKmRK4SOHPeHsGSXEfoftFj1L66tJvsT7WDGpaXpukDryWNJ4rhkPfx91Wm5ZiLDl24cVoKeJalejxaoG/q6jk8GLvmTdtvRiP4pgCroLnvfjP9iTxXFr9PlCjbr3xhXbpcjHich0yiFFPUPRUcTYLSUGhFHBs/MWgIR6cOI+sBAFrAqQ8cIqgSkKYx+MnNgN+ytix2/SDqLUfArIK4JQNfju54lsNyEQ6H0nVUzERVF3pNgPw98gmO8tF3aNhU1tk0feBDsvYQdZtM1UadQxXumNzveXGgilKVEt5Omiekx1K0ASx2lE+jUWYH801v8bqJI5nOj8DCyGNbVoM4dbxWXjo5G64dXQeHnfrkfC4Wx/g3DkPLe6E2/PzRAeKHwF5oc5oQHCYhUdXx+FouQrn5AVL6wlcnaUIf7QfebyijqQcIAS8KOjEUFD70FPGOyRFmEOrR++UkpSSRSMq5KSxwcpRjKXaUHRws3L1QUO60LPoFTHeptpc63fbQX1yiEtTYqp5tzyJ3ZxOe6GdxFcBvolUXwV/6/YZhrimP+VS21ckvk0kvlMzZMemQa/1myxeKpnIF8x9yxTZ716LJIvetY4uhy8xrx49b2wz45jdyCifx7QZlMNOPPGUx28pP2JUvxj+HNI3pIG3tO1wvODkvaTPeEqJejkhNyWll9xSlLQ76T6m/Emi3kT/y2BLjHrOcFczfqVLUrqfkxgCaSj3M2BxTzIGhBRAjXitptRTq6O172XJFCCwxitTGEY3lCpQXScbbI9R9csDV+oy9yJH/m3KBLy19hynbLTOC9U6ARgPeUh66brophsLptjLRB2l80h94MS0FA0Ju42khMgCyMlT52F1GsEOJS+ksVRM8+PcHXE65rFSZzw+6sHju+HhozsApihNqOWIng7kp4qoh45KYOo8gSyq93i+CucUdYlZGkNYEK0veag05J0AJ7BkGn57ZcyUV3Qxeo3wL0CBCdVinyYhGZ+G1D3DmwCvnwMDSpOvggQAbEVkgEvUVi33x6Z1bCv7uPTiWcBzgp/rjmUV7b1uPJVIlJZjl62tdySKXwRQ8dOQ7dM3eA+F2oldqRDXITHiTZCYODul30hRUIXuzRTzo9jEkZGPcBPT+zhBOimk2A4qkCIjobSHic7HVD4CVClBr0wxKX2MWptBUzLUYZRYp18ESKHeMayH6kXKAjQcuMg0wJqHYI1UvF3jN9suV0NETPQ8jZ7IIQMplG09f2a/e9S233OL3LQwshd7WtvXPhyoXrouuunmgimi9XGeqcFkjo9tt+2UzygnBwWHOI0dyPnJPMxpjC+FSE8JdQlMnSzOw/2L03Df0Vl4cH4nPDS/E45my/DA/G64NTuHPuksnFOCKH6JVuyFou1IaEwVTfTNcrLfRPfjwBQKpDIoyoosWk2EBmi8ITjHtoCXJ/SC2wb8UmAMVDWZbmluzPSNC3Yj1f0PuzUxlwzVDkqq92JCZ6YOjg9Ftjypq29o63JJwoCFx0mJN3eI6SxmCUglfLQ6jhFgaZofpx3IW0Xhz0mHCIDiOuchHJE3asFeqdXxPAwEno5nYXkcARR7xGQu+Qv9OKnCG5WBlHNeT/oGCm8GeAniopgvhu0aoEk6C0DUFNAzVme68Jv6+e903feo/TehzzdV5pc0NqnL4cvNBVNnBJyWYXYac3LMKAIS5efgsVSkuRLsYYvfjOl+BLiGE7plR+H0QaI+zMOKkuwercL8eBkevvVoeOp972VA9bRbvx6eePSbMWnv7IzBEnufCBZRBL/hKDwynGgEP/qSz2gc1YK8UwsOj36yXIbzRQRZFGJ9QZH8yAvGCYWzd0oCT8S8VwB+nHeKRDDL6Biq8m5F39nUZA1tFAXb5Mm0TxfZVqXjxbD08Tz3huGmVFALU38TpPJMo+E80YfuUaS+mohjF3OG7iZiLtnvlRAtWALU7FJHl8MXYj4QzY5UD7dX5DWiyLOcOD4CIDIC8vIpGfki3W9+dxnfu0eOorGQ1RjTJ0I4OQqrB24xmDp/8Dgs7z9iCt/5ffOwPImeqeVJpvIxtU/GUUn+Qojsh9Q+E4wCWBLqvMZk1l4qwSg8qIp2wTVRhdappomgalL5SF1rz3OT88mVbr7PLrIWUGy53y6y5/u1lvK3z/PZl2zQb7hXrLl96KXropsu9Qre+MY3hk/7tE8LT33qU7lB/e7v/u61+/zIj/xI+J2/83eGW7duhQ/90A8N3/qt37o9zY+ofULvO19Gyh/Pz8Ps7IyTH85Oz8LsbpxIWfF0SlEAQ5w45PbAkfxuLc7Cg0d3wkNHd8LDC5oe5enBxR32Tt0/Pw33z07DffNTpv2Rt+pkdh6OaUrBKgh0EQCTKXqnoocKg1CIU6mwCLoyw6bwXimfz2T8jpnZLq1NM4LnPcgHqCw16PbuXONNA0d7oq9E8JQszynoyWXdzL0d9YIugbrJ+5i6HL5uEhAjHqLoMUo0vOMItghQsVfphCYa97RgQx95nQJF/kvBKVjSOKlwfMTb0La0H42V4jnXleqU4wjVDyfxTGnACokuaKnmeh2TL1h8OY467Jc9/dvVMTpN2b613pdXrZAbfPjbdsRv6ud7iPfr3rPUJ8u9HH60L720vAYv96WCqQ984APhoz7qo8JrXvOaSdu/9a1vDZ/6qZ8afu/v/b3hX/2rfxVe8pKXhC/8wi8M3//937/xsWPnPVL8mFfOE4WUXYbhfBmG0/MwnJ6G4e7dMNy5E4ZH74Tw/kdCeN8HwuwDd8LizjIc3R04cMTJ0TLcpqATx4+Epx+/Nzzt+L3hiYtHwwfNz8Jj5+fhwdky3D9bhvtm5+HWbBlOZkseSyUTJ/INceKB7il8eqb3JSqhjuNIYZjRo1JRZE1Qdc8MLrvXNtsDnilyJl2gXP0mAWQs0MKF3k8Jj568Vgc6OFXHU8nyZZ9Ql2uhmxi4EJhR4BTYa7Q6CWF5K023Qzi/fxanB2fh9KF5uPuYRTh97HE4f9z94fyDHwjnH/xgWD7+obD84AfD2eNuh7uPPQqnj1mEs4fm4ezBeTi7fxaW983COdV1Ox+DJzg2B6FgUBeDHkUQFfMt4hgqk3NK6ObolZqtGa8koGodkLoXU+vYGfbly4PpUjwWXbaWnVTL7B5OXQ5eLpXm98mf/Mk8TZXXvva14dnPfnb4uq/7Ov79nOc8J/zYj/1Y+Pqv//rwghe8YLODc1AJyohLAGpgz9RAND8CVadncZmTINLgqMQ9f/8Rcy/my4fC8cO3wmI5D0dn5+GEIvjddxqeed9vhI+6/fbwAHmo5qtwX2pdz3lk1BDOhll4dFjynOL4LSkkeliEs9ki3J0d8zfD3qkVjZmaRe8UBZ4YZOxUHisVcylJ6LvBUvFaXigpbnycvJ633dPXm6h0G/O3ploXZVuc++VCJlIVN5ZDSHC1R0Gqzb08bLJvCP1PEvgeokbRPFOYu+2CpNP8bo5uWp0MYXkrpeygifMZpoToFJQi5TikHIkcCGk5C4sHZjyOd3FnEY4fOon5E0XHhRDOHj4KZw8dMVBb3o6R+9j7dZyCTAiNjyl8eQwU0sGNcQ51jKf0iTjGRP4B66ssBWcBrH1Xyi7YrMGdNJppU1110+SaXfOB2uquhHSa3xUdM/WmN70pPP/5zzdlpKjICtiSu3fv8iTyvve9z3b0U8JezsDO3ilajsEomG9OIIsjTZASo43nTP2jpL+BFBbVMV9xfikaK/XYxaPh/sVZuG82D7fS2JxTTrYbgQ7txkBpIBpfTMRLc+N50mATaqNPnbW8XXbHbNDr7Y3GhYi5rRqb/hrLBXul8lsvvw9PvK0i+dAu7Hg0cnJXKkQcfdnl4HWT0OrScKc4qC++W4OGR0+pOUg1kcWBAlIsqWwR5qtZGM5SkKW0bvnALCzvn0cPE1P7LJWQwRCPw4UkvRXQZBL0SplcwBQgtU5qzefIZxXzUq0XVZX7lGsGKrp0uQy9dF1005UCU+94xzvCk570JFNGv0kJPfroo+G+++4r9nnVq14VvvIrv3KDo0h4sehRSSEK4v9VSrhLkf+SopIxU+RFOp6FcDKbhVthFo7CjFL9hhWBH8idpF1FtsqVrbE4huI+dv3Gr+w9cxEnDXiIOKIrvC5dulwh3bQ6GkI4jgY0oyJEJ6QyMgIqsJKk88RqOCNUFfUYl9Gux0fhnCL5zWZhOY8Tl6cE9dmzZM+lAEKt9t3TyUe22bdn6NBUzoXKjbrYPUi/X6X0e3IhcqXA1Dbyile8IrzsZS/T36TcnvGMZ7RBlNAHBl8WKYGsXCiEOodST8oq0fFOZiHcN5uF27N5WMwimKJ/NO5JQRXP6zlu0MKNQEqoRHGd5l4c/ybu5Qcj94e1/4EMHpFBYz2UaZdrIJ3md3N00+p4COEWogQ37kjzC1JKjqgblotVjOi6OA+rk1POS0jh0WVM3+r0JJydnYTVahaWS4pCG9+FgeZKlcYcf4COak2oADr5O9bMrqNob+tR2kbPbKoOLpu5vYsuvYmq7xD6HjdIOs3vioKpJz/5yeGd73ynKaPfDz/8cNXyR0KRlWgqpBgUK24c0BISx1qjIqU/gGaUipQSKy7DIizDClKEim9LyHkAmTijdgrTvZvO6dLlmsjVeNsnD9Hbk1AKBZp2raPLFdBNHB2vAaASiOLiowigaFocLRlAHR+fh1u3TzmBPAUyOqLxT0MIZ3dDuHtnFlareQhnNHAqGQxpaLCAqFUrEIOLsifnpHZGOddIQdzrMNVtQNo+5ZoNhb32cojsmGss+9BL10U3XSkw9XEf93Hh+77v+0zZG97wBi7fWFgppWzwpL04dCwRysmfJMkOyYtE5HKKXjTnXB1hvgjD4+4PZw8fh9VD87A8PgpLsvrdmYX/dPeh8O/uPi7cPz8Lj1ncCQ/OiQ8vYGoVzodZuDPMw3mg+VE4DUecW+osLMJ5eilxiqg/Ai6Za0wHTuaYLiRZEc3gWq/8fD6nxi3ZSmvg6Psi8MUWXEMfxWbK7jU3X/WC968WEVDfiNGsF3yJefzgYYv6j9Uocuhn3OVK6KaTVZzI60RvVgJM9EEsFsSCiAGJTo7Pw/FiGU4Wy/DwyaPh1uI8PPb4kfCM278R7luchiPaZkaaZxZ+5e7DPN1dLcJ7794fPnB2KyxX83Dn7DicreY8Fut8uYh6hQPbRo+VAq1inqPb5eUI3FQwOp8HVH541SFbEnPu47Z0wHU95Do04f1FvHlg6v3vf3/4hV/4BRNelsLKPu5xjwvPfOYzmQbx9re/Pfzdv/t3ef0XfdEXhW/6pm8Kf/bP/tnw+Z//+eGHfuiHwj/4B/8gvO51r9v84AlEcVJeevsWi8Q5j+AnlmdO3exoEcL993Eej+GDTsL5w0fh/IFFODs6CqenJ+HunXkCUx8cHljcDU89fk94woJS9FKACdKLFJmMkvWS52oe7q6Owt3hiEHUGZUNEVDRHhlQxQ4aAyk31cBSaVHMc2SMjA7o5W224ELArFq+ZSNVDHiuHcIrMgfotsFz28qNaccu6H5i0JWDFzFqyPKFHiq2H7vW0eUK6KbjCKYYRJHuIC8T0fhoTO7ROQc7OpqvwoO37ob7js448NGT73tfeDDpnY+471fCY+aPMpC6TRTAMA8/e/cJ4S13Hx8+sDoJv3LnMeHdpw+Gs+UivO/u7fDo+TEDq9PzBc9XS4pYQcAqZrMmoMUGA5pLqE32YiWElDxaJmGtibaXPFYCqJAi2HLx5qgWWnTRb2/7+00f95gOWpee45p+ehfFor+U+zU7gDr2cT938QRfgl66LrrpUsHU//v//r+cl0NE+OMvfOELOeHhr/7qr4Zf/uVf1vUUepaU00tf+tLwjd/4jeHpT396+Nt/+29vHhYdjGo6+Ijjjs85Mh97qUQkHvlRTIgoiRE5QzwnMiSwM2cldHd5FB6h1PWzITy6OgqPzo8YTB2nHFL00hFwojmCJt6fX8rkjUovqLyoSAc0lMBKi2NAU/WiR35PvnFTZOTjWDOI+WrJlTzpw7tzOtTuCoCoS6D6dZrfzdFNcSzUwLQ90iU0pzG5HOhosWJvFAEq8kTRdDsBqgeO7sb5/JTTcxyHIdxKYIrKaaL6KNrsbTb0DZwjkdafL4ewJLDEn+KcI9myIS/A2NMUiVaRUYowKG4bTs1R7QU3kEgTSDX02gV/ZMLsr6+Ry6icRKeW7V3uIR7Yn6gtYfsz59Q2V+jCO83vQMDUJ33SJ4VhxAtSyyBP+/zLf/kvdz72cESqhKxvKbENU/6I2pBCpDMPPGWOJy/W8SIsH7zF2ePPH1qE5e15OKfkiRQZ6XwehrNFeM/p/eE/3fkgVlo00PfR1Qkn5L1vfsrJeXHs1OnqKDwy3OKX6JHVSXhkeRLOh0W4szpmUEbLp6tFOF8tmIZBik6pf2QtFJpfheuu9PpKMkE/plnXjXqsIBz7FFnjCcpA1rFE7rFFSrwgO8sGt+bayZbAOHoLc7AVTk7t7FMmLcAF3WD8hLp0OQTdROOfjo+XDJwIQB0dRSofgar7js8YPJ3Ml+GDTh4JDx7fZTr5005+Izy8eDQ8/ujR8OB8yR4pUu7HFAhpmIXHzO+Epxy/Jzy6OmbdcTRfsp45mZ+HD5zfCqfLRfjA4hbrGqL73Z0fMSOC6H5LGndF38h8HoZlajFpjmOJExDjLVl1Ju8VyhiVT5XCBHb2Lk3BunZpDTAyLRSeKJ7TbFq9h6wyJqnh4fKolTsfegJtc0xGQdMOfRhuc2rvz7QTGj+HQ37hroFcqTFT+xQCSdyFI/oehZVlPoX07AF5UDjZxTysTuZh+cBJWN2ah/P752F5i3J1xBCzpHCG8yG8//RWeNfdB8Pto3Pmta9m83A0W4YHF3fCrdk55JCKYOrOcMwAiRQcgSgKXkHl5L0iEHVOim0FHqwVDSBONL9EvaD5rMZlH5kwKf20m7UBYEicuvFN3dExyMc9k/yMdznytW2fdLzbPuoZP4QeZlauY5B1wREZ7wVNb1fhju2OloZd9+9yb2R+tAqL4+h94rFRR+fhFuuUgcHT/QymzsPjbj0SHmbwdDc88fh9DKYeMz8L98+W4RZ/O5Syasbf0YPz0/DBi/eHO/NILycgRDqH2BBHi4GBFW1IoOp0Tinmk9WZE/jSWKj47qzYcp7ad3XlAF1CAjOJTk3lmlC+yY5wwSsqy/fCOzVaPQaHpUupfU/Jg1fb15e3PWGXK3tpbqfWMcqNHN9t63s32wPt86KeW6PeaNhpHzQN8b+Seum66KabC6Z4fC1lgZfetISITS/tkIrIg0XA62jO1L4VZYun8jTlCmdM9TtbHYX5MionUlZHszl7pWTsDnUOCawRYGLKH42T4vFSNG6KlvN4KQlA4cdMaccP3DkFQHLcdZJiPYAroxDtndr+Js/Wda49qBqvbm3OE637wLrFB3Y6O8k+rIWX9IyifX2qfUAs7TnAy3CJXkqiYtG0ax1dDl/IeEAgKlL7YtoNGiNFyd2J6XA8X8Zpds66hSYqJwI5kcQz3UD4BPHvIm3DdcyWYTmbxXpWy7CaR28V6Z0FTUR35/xVRNgQirnQ+JLbIH3H/I2gQUT6fVO/g5buChPHV02+sev3Y7wHgMmfp5a1+rad8reZHOL94i7WgSltfnfHzmnCTbwAwLUPvXRddNONBVPkaSLVw8+QGnPKGUUDfwFLkadqdZyA1PGMPVLsobodYgb5o8ghJ+pDWM7D3fPj8L67t8LJUaRPUP2krB5dHDNHfZYUGgEqCTyxSsEoHl0mL9XymAcE0/o7y6Nwd5mofsvkpWLvVKRbsHeKqBQwUSLhWfJW8bKn+kneLPwdasv7McCw7vWDY7g8KeCa5wLL3TbABnH7ONSYpiLxMYPalDT5XjSYiAAd5XJ6HVsee7Z7HZjUs16xLW4ZmKKnKXqZ1rBAL0QkRQEvUXROKKlvT59TCgCTQNW0QbIAwrp02UKOjgYObU4eKQJVFGSC6H0Egh4iWt/RXdYvDy/uhIcWd8ID87vh9uyU2Q/EhKD3e8nvL4EyiVxOY3cpaUcI98/vhocWR+F4dhzuHB3zN3mH9M+K9NWKvVe0B+mbs9kiDo8inRIjqaegSFQTja1KzhjhyvJrPz7uQ5vexKgwv5F6LuI9Oq26W+UIgHBxpK3SjVDvtLaDH9H4UlGchwganOyNALCNfrsX96Zl3C1OZ2LH514+zzX3iA0dNSaJfxaXoXxviNxYMEUeKQp3rk4ZGuxLAEUBQPRAEXgiMLUkrxQBqWMCWEQTTB6q5G8mWgNFR+LISGHOPHSiT5DVj+SMQ05EqyApSKXuhRmDKaL30e9M84vgKQKoOEWaH4WxlV5unpegCS82AyjdjhvP1OUz0f7ijgpCdm5gBdVEjr0HVw7qaNkIG8TMbX2Vk0Xq2CUxCYvlqftdkJdjW9nMEz/WA7qsixIbvczbFkiBfO5r2ORQe5VO87s5wgEnUsQ+8hBx+PP5Of++xcEjIs2P5rfnZwyioneKNE+k6Mnrt2LDQTRkkCHvKMzCyeyc9yOhObEiSCiYBTPHhxBO5wveh5YX83ny2KzYUEcy42i40VNlgBR6plriGBVaJnqoxqqY0nwMO9iZKoALLfnKWESvVWtZwKRHJy2P11UBUhfZbO/odLknjIpNz2XqtsMeDKP8fZYf3kW/ap3ml+XmgqkEhughsmUNx26QokiAiqP28RTCiqL3xVRU1gqfQA1nlydr3nJg7jl5lphKMaO4ShQjKSpIUkP0l8ATWflOFUzNwpkGnEgAiiMFxrC0cbxU6tWyJyrOmXphvE0lqFIaoAdbFcWVr2mDGypKxBaMbm+AkJ/XTq1B82uuvyzZRqlfEr7wbZg8k9HTGQW06BkcvygPV8T30zIgXqRRzfbV2kdRkAXUv6KfdwGKIRK4dqNC7Lp/l3sjZGyLUzS8MQiaR0McUf2ErpdG/fJ3Jl8P6xX2ICXQk97JJUcwz95V+fbkWAuhAcoxiOZHgW1nc16PXv34g2qKgEqPogEpkkI14hoVv9wwIBmwVdsXj9AorxZ7oORxTwMs6bAv7LfCsrn0K+CN6iKCL909BFKy7d70v0Pse637YvTSddFNNxZMLU/mYb6Yh9mCrGsCQOJbx7Sm5HWi7SKQmqWgE5HiR8AqLLJnihQPRfW7c3oUjhbz8P75LVZepATJ8neyPE+c9yUrp5yINzCAIu8U/aaxVjRJqHUCZUui+FFUJcr9cR5phTQxnY+nUMwz5W+Iv9l6GK+Vr9N4q1IEJncf+Owmf4iZtqeda3QFQW/Ye6OMk032w95zpbOenlQqWOeWv9ekq/XhTbdy1Ji4+HsUvN9gqR3DBGBcNvtswhXJ4CnSLjOgkqATg+34XbCrLhrY23ErNT2BbpOuAJP2Hnggiy6HLwyc5jGCH+kMitxHE+mOW/Nz9kqdzGgdga0Iquj94zG3YUiJ4XP2F3pn78o43PQ1CZCK46fOecwU1cvv9YIMfItwzp6pSPfj8bsUuVbGT62GsCI2Bxn4WKmsofa1vE1o/EvrazQ/67HarDU3TZJUlICOAiNdVywWl2WcWA1AFetuUP4q53ZZhvlL90hNkYZHb+t712LGTLEF73CsqmzqrWwBdA/ua+dw2c/xmsuNBVOcI4qy6UKDrl7SREdjGl8CUjw+ivNKpf2E4seVxYkoeASCqA4CQUcMkFbhboqORMrreEaUiciJkISf0RtFwSiiZ4rGSJHii+OjIuhi4CWR/GRyIdHHKH+t31lJuV6gKrSJX6D5wNd7paplUxqUsQS9Y8c7RAvhJthgnSdxW5ldMG2isR0mUlZAlX44bGdqvhfeqXW3NgOpke33rLi4Pdixx7Xr/l3ubQAKnuarSPtLHiMCT+RFEhAl3428k6QSKGch5nvKRoLsUZU3mBOEiHcKPV9s8MvnEaPxwVhTMZwUjIQJss6Q1PJGgeVm0zdZgY8s8HJuc7b2NjX2ycsNyp+TqjPvkIHURZ/sBvm8trl3e22eZxe0b+0kN/Q0bYrVLkMvXRfddGPBVIzMF/NhFOOMEs2PaYBpO6L6RZofjJXCnp04e5YcT4lzdZyer9iSt5hFrxMppfM58dqFlhEFwRSHpqU6yLpIoIoAGoVep0my0WvwCe+VihMCrGIcVaGgkvUfgdPUjxXzjORCe1+K3m8qqHmccPuaF8vXib9hm/rpg/mzctq18Nyby44J97bxVm17wE1QCXqt0KrXfMZQjvNsq9gApFcQ547h7L2UR4i1o/fJeKXAQp6Xw4VKHzN1c0SNCmBoCEWzHb1MrCdmMQosBYsgVsHdYcWACuWU8hbSWNxAkWOTp4nH7OI73fDHcEjwpCcket82H5fxOiXDH27jPFDZW+VA1BbfWv3KEFj6dXZn4wVJnXr1QE0BYV0OUOw7Xl1GGdNx1ZrXvahrskdtApxw22QoWHuSe5A+ZirLzQVTlCPqaBY4arlrtDnkOYKpo7R8nDxU6ffAOTjAs8VUvDho9+6CcnlEbxQpvrurldIqfN6cGGiCwFTgIBYErAg0nZ4vmN43JEC1IhB1PmcwxQCKzp2XaZ7BVHNCj9TKRfbjC89Kc3dJSR018IR1OYhq1hngEHS+mX3MOCsXOkDWq9W0YcWSaHKC6VKEOev12PQeJNrXNJfGePWbOAKRHnNRmC/3Y1RMuzdrKCZz79PT3sitJJbzEjfHsjhmY1eJVnv3PoqVP9H34qdiSIjqVc7LGWx16bKbSBtVvk34HkZa3yLMhyGcDkfcptMYXdId5F0iiYY7AlNHPJEpj+YMqmi8A4/btZ7WIM0uRwgDcCdt5lrPkG1g+Ds1Br7MoNCy/BHmvIkGULn5VM8KtlcCgmBZ7mmZR6oemmbmAJWoG4NFHaCKgAsRFlR2iNL0RtVPenYRh8X7VdtoE0Pg1PUbAKoCLG11E0biyfJ7VbEaeuBeObfRbbpcmNxYMBXBUDIr+e9VOu9zm1NKPFJluG+SpIxcMAoCXASWaHseyEuLrtcdg02kwcOSnNfnlzIR/KQHCL/12I3JXKCcMRRs+9GJpsXftanYLyV3nNKAFccr583Th3Ow1dd8ETdDGjpxvWz6rHg7C1PGgkzU5YLhCbwG/lNCd5yWi4W6+s5d3JkOyZOwax1dDl+sQad8y3KznvQEA/65zpn7wJ2xGOgo54OJlJzo0bIGgbZ4M8OEjlrt1L2OauyPQKr4yLzHauwcxrxKcg1Sn4IqvNAcXsN0Tv11epfXbN0yntBVUzwNILU/+2speL9M+YZAae8ygWu6/rMa3bc63K7xDl+W7EMvXRfddGPBFHmbaKIQr/67UDBFTDoZK0X0vhTNz3ilxNjEACflnKLxUxQ0Yj6E+WoIp4FofktutM8Lz1QCXvxSRnoggS+yLlJAC8kpJTQ/8kQF9EYlz1rTMwWeKBuQIgedyIEnRIHJBckNWedOkUvJsdnKdQ6IVjxRCq7c1ASwUofv5POUz1l3dV6UXdraeItSwIEGWC3AbkPWKqR9NJjNi02gFt772n0uQCwuj+0nnRXM+aUAS8ZhZG9hPaofltkbOobXWxJrkHxTfp14GeNcgsRkrxRY8RPNTz+ZXPnehTvCO/YOdt2/y70RBEpEQ495nWZhNUveqGHBT5Joe4vhiLenBPGceJcofhyBLwegIJEk8QSq7g7H7J3iFBw8+WTx6G0Fr7tgALW9Vd4nb6hzukW9UsGVsyPNeaxwG1e/rhu5h7rgnRypE+qZRTWMKHoD23jERaOUvy4byT3BBpiQd6pXCn4P+wBSuH7sgsU7qtvsg4txeHrpuuimmw2mji29QAQ7lRwanYNO2InXCwcpZG8RUfLoB9H9Yrj1WDkBpJjro+RmRWUZrYkxal8Mmb5iMAXjpARIKZjCsVJ23BQCp7ycfhN9Q8ZXEYIzEf4o4p/tIWpnvwWqpCcckJY3a06ab2ou99COoTL6stJT9qAsn0OtUXQeKAyBv60YBAdW1GIb2aLCqzO5vS44iaKptPwdL2fW9BwWp+HusVlfA11wwfn1yIBJQVUaEJ9hi612Ximje7vN46w4pBVEyWD9HNkPgVUCUAXIqr24XbpsLgpi0hQ9TtGrxMBHghzNjvibIGof0fqIKk4h03nsFFAE6bUUEEadlkdXxwyoqC4EVZL70IMqBh4VKrMYFPKEBiQBRhgoyYIl0b3qjfKGPT3ISHvZaju9x0hXZMDj6wO2nz6HvNtQq2qc8neAwGrUcFcrL6yVF6ib4Bmb5rNF+dtEVE07ILRmeRQ87ePZjtWB4D8VsLdKXakTQVmXeyI3FkxxNL5540X0nXXIK2U8KLqxaJlMGxRFqIPr4Hv03b+YPwo6aYbeFwNN8LyST8oqsAmTXG8656JxreEl31veoFGrdrSr69ckRm120msAwZkRq8lK9iN4/utktpECS7bfikV0P5IAbVk8totKbV8woG1Q39gzQft3e7vyEGO9mEo9Y5Z2yISVN5czKoH0Rek0snnsHoBib6fT5R6IgHudAOQrwArzCKhSWHQep0v/APXk8VXEfojLmjRevF4CnkyCAlEHzmK1zuPe0Dm1zx0BjR7F66laU4HtYs0YWjs3D3iKkxi5nk23OUAgNSrNtqECpLaqZ3L1I3Vv1vcodt92r02f4y7P3aN1Xz6bsFypdD8jjC9GL10X3XRjwRQHnzhOOZmg82roajOk9cFyAajS7imRLuuAZaRlkBWBkihSTg5WUTy3wtbHtB/RA2mZKUTn5ImiyBchzGhZg06AJ8pT/lpeKRN4wtP7IOeU3ALpYRp+Q/piax8PF4HSRTCK98qXSRh6LQOPiNtWvSRmf1vmT6ElkXq25/E4AmyLMljGeWX/mvVVL2uLdr0qLdec5EbB+w/PcvD7wr233wSETpYqtBqg9Wl+qbTsoGm0Y7gXc41IDSvHvSR1QgkKYm3Y0cwTK4bkFdBQ0tKB1c8Bxplg/BYJPqGd37BXkehru9bR5fCFxs/GoERzzuFESdwp79NiNuN0G/RNEF2c5vRMz2ZLft9iUl/KG0X+J/sC8pgpjt43Y0ogJYknz9Sjy5MY6Y8Tx0cP1Vk6NgMwSSAPqToQ4Eni+FoSeZ2bMtBBMO63pJqXNrAxup+K72+jAQgATs2g7/ujOV+UVBzbKVPPUHqiav3a6xLZb639a1/HuRf3a8QrFS+xonda57SpYbJ1D9cYAuKu8ka29XgJstbngrssvXRddNONBVODjJmKQY/slwudR6H0CaDK1DTbIkduO/fGYoeKglcsI7WPBtcJiKK5tziIB0pA2IBgSkKg1+h9rXFSSwRSEDIdKH7FYA+l97keYk2KBibdjASOcmNU7ld0lx3oqk01IJankeh9axpjxAoXJQU4Wqchxqy9e5Cq9wh/r8njpR0Ht6zbIvLTYugNFTQ/P2YKqgMq4GbXWN6smCknz/012SmPFxmP5CfPE4PP3JvORpfrK9xBSYAqBjAigLNi49wpRYXl3FAxYS+9j4sZZZ6aMZiiMo4Y615C9kglzxQliOfIfgSmVscxNUcaUyWRZQVMEZA654BIOTAS6SelnzO1PekpBEOqbzJgKqdkzAwump/q5AapYIwijZ3IBoCqbNb8zcci3e83gmXT/5VrwHFWALyauvGQpGjYd0g0P+lY/kD2eBcCqrBP4cri5Ttr5rp6ivI1N0hftNnmgErfbdKdcNL48raWu1yY3FwwBTQ/aeQU+fvO/LzhITEVgtIQs4pS/0jhwDFcDgBaF4cjVfjn4oECJeW9Sz5Jr2IMPJZP0IvnTap4Dx+arSKDK2mbde477q5zju1L0fnHbVtngJ1y3e8SWpJ1h5yIVXc5/GwbxVLZSZ9TLejHWNVuO/vTAy6BMnYbBFkeN297rzK4Asuzwjs8u3wEg5Mq40jM49y3BTDRunato8vhS7TJSeCJnMtlRt4lAjnUu9dxUPE9Ji8TzecEdmBcqKicWEf0TMn4qHM/RkpAk6f+AQUdgVDREIDuEh3EW4heqnmgeD9ouhvLsl3hGRnrdNZAjd++ZdwfSdRb7euONbaTG+JDkQqQ2qaaVhu4rrILu1/D7ts1wVNj37F3gtd79N/YrwHkLxsg7UMvXRfddGPBFHml5nT1AmS8iK7AkOhE86NnTt4lTNwrooCHvFJpZ+q00Xhh8lQla7u3FGjoc1qhnqlM7VOan9D7xCN1Pguzc4jmJ+VVjxVr5TJABYIuVZRTv1CbA0q9UhQhESh7lAS5CELh6JJI+RMAK/UUQBbuYQZqiCIzmtTT0qnuus+dD/t81t6JsWh+9hA6LzoECH7TOnOKE+pvSnGtFpnYfonrMYxN5qJ8tk17oXLfJVmvRuaT1yNtk2ORRG8VlVM6AfUJYeS/HfXtYABV8kABnMNgE0r5c0En8J7J+Mhom9j17C4m0/x1yDJ/E4Qiui6WFJEv5pCK30f8FkjofSTPFM3PVkv2Rp3NiQYYcxlSEIr8rUVhwJTeYaH4Udmd5bF6pO4sj3hOnqrTZUw0T3kPOdch0/wo1+G8HMubkshn9kOm/jEVCSLLxmWk/6X2bqJnqrCJWbtkUYbAUjrppq+eQFPBYBePk+gFNZjEAg2bLptfBY9TS9aceE1fXRnRfsIaqniL2je6PKLoJ56XHNLoTi1vIHhY5r6QBKVYA7J45NTO0bf2r5eui266sWBKI/ONjGmUiHNmPAiERNdOPDb44oGa4SD/SAHk973ysUhYdZakmLguXhYAlZb9mKkKlQ9N7hoWveCje5rfJiAqX79bcFH9JFlvCZxqIdC14UMg5sdK+eMXHXu3Di7cAKaqdsg0tCl3It+uyhiZVoQGc+hZ29JabGtOcdoJCvW0du6zChhORbVT9sArH8Mt12iCCUjJGKkIXnNi0ngaAFMUQEkVQAmsYLpNBW8tvvq1gfc2VLql+OVIZ6neqsu6S5fNZLWiibxQpGsoOt88zAhgAaCS0OcUDp3KIsCKbytHjIXEvyTigaL3nEOkJ28UUf54jNQwD3eXkfpH4IlAFVMDeZ4ofonmF6l9id7Hh8pzC5Rq46SA2ifgCnSV6qdg278iXPoGTpCaM8pjMO8QQBBVrxvyUI01RIfulTK6Z4/UvgNqBwtid60fkbYs+hEXAaRa+w1rBo41ABXrXE/5O/zHcu3k5oKp5HHid9JZv4zlXjqIfpxU48PRJtbQ/OLcvPB4PB9W1ljsZmDRc0oK6X8AkkrwhOOgbLmhAuJJrQVW7iM3gQkqLRF4ndAtoWATboF5Tv5wUEexTn+3zj2XY0d9qhic0wLgk2trgKV9yVRE6PfBuS8HYFV8C7XvofmNyBxzR9U+r30n7MVkUFpSwa/5rOTMzBdiEp7moBTm6vb8XHsAipsjEpCIAxHNCcgMYUlGPAJKqxi9bz6bhTMFVnFOnikBU2qMEG+WRu8jSmAGUzHYRMw1FcdI5cTxEh5dg06IN8roKgnitD6irNFJfFI+zxSAqsqyAVGN/nHtszMASXQgtmWVfmsLBFWb1dq2Y+P9Dx1gbSqbtnVjD+miZE39o6DYACk4+SnbTxHf78RyP9CuBaguSXoAiiw3F0wthrA6IuCROz/VAY8y+JQBVWzNGYhV6uQGmRQEjxOCFlO9VZitAj4QUUq0LB4opu5lz9T8HAAVUfvAS5U9Vom2p1S/oUL5w3xSGWgxCEPl18ot5aK5aZe4QvHjZaI30gR0Pxu5L1L+uC4X4EM8gybgB3q2dLv0XFxv3DhfRGkKpQNygK0DVBk8+TDZHvk5RGg6E7Nxi9+URnHKNps0sAhKDQawERbz9jbBb22IH9YrvR+k+QkEEQofT84jJb/3KflRxC+Thu6jE9dQ+aoBJ2LHUiKi8WTGlGSAdREKTo63ax1dDl8oWfv5OUU+it/NahGBDX0rBHbOFgteJiB0NI/UPppHel8GU9L28fsNoc8luAT9JjofASkCTKfLBLIoeuD5gt9nznt4nvIeUqRZopvTeyiRZqnylKheKOgSWEITyqegSQqaAEDZXFPx+qsR/YIFQrVvjFkmNXQl1D5oz1Q7C4hyjAQ0slab1KRcSG8KSOPZpE9sQiN9yZ9q6x4XsmOE2eYhoPtk8MQYlWgTKU66AZKmAKkmqBo7TweQKqeRXxOHzGuAyr9SrfID1EvXRTfdWDAVUpjzaocWO5atiHG+o6m9SQEnSLGCwBTmANmaJ94m5JRHkISeqQa1D6l8BjRlkBTnECLdWP9sGHQNi75WpLXLyiX+9mOpMpAsxkbVOuXu/vr1Hli1T0+ss3i6o3CoLgKy0wWs80o1O9QerG5xDuuF7u2GAUVwtHrjnpqy2gn7G4qAqnY4pfrJmCp5TS6u5afv0d/++DuetGG86m9P+0PPFNIAR557ly4biETLI1CjYzzZLiVU5QisSFZDBFDLIYIqjvQ3r0fzk6AWETwlMLVaJCofgaxFmkdAlT1kkR44YL5DoPMJkMLxUqqb+ODWa4UR/ArgJMt8IxoAqvGNtfqksq7aT03tkfZZsa1zfWel/gHQ8iCs2smtPuQ9gYILkNFxaa581y4w4gVTKGWwnJ/TBd672Q7Lpp5159dwXTbBj3uZaoCqOIeuj+6l3FgwJXmjhBTNM2xFoVOIHfja2PIi8o9UQbxyYyHA1hgOA8omKyXglxuQZK17uq2GPHeWP9M7dJ35GiqofnyVrxJDoJsOtAClDKwQUBVAaNbu0Kt3BMrx3ntgZYGvaOFhvN3Twk0pZbkDPmW7qtR69jj35dtIJZweOs7a+40BpDYazQN9May5eKhsXilbTb4ZGC491+Pms+1489EzlUAV9xDzuKcMmPLZKaBSKh90U83zy4rxIkCVJGvdtY4uhy8DgRcCMWRIYyo6BY8gNZHeTO6HJTDFuQwp31QEWEzzExAGoh5U9UzF3xRsgvNHJS+UjpOiPInJG8Ugig6r43nT2CjwSGmUWZOGw+ouA74EPLnQ6AiiWgCqOcZ5DbAyKjr1x41XCcuhjRmm5j66mFQ++5V9ndw+dNRFNEeb1lnTbVM8Uv44DcPhuHg06qKjFMupYOT9v9ct/D700nXRTTcWTHGOqYUG3GNloR6ammWe/iRPVhVQpY41KxZ638kzRIpOVtYq1P5+in6kiicpKQk2kSh/htpHAQWXcfLbzpeDlodqAt8U2a8yrqrplXK9Vw+YmM4nZjpH+fPUPgwwgeOoTKCPyhTLY3TESPFzHkP4jZQO6ZzzJ6udehsUAbHcZuLGEGAQAuNqK5//rPouQNmuMmaZguehy6Y8TbWolVgH7FN7DvIsNEKfThLFL4/viI81R/AzFECl/1Vx9aQQ6DFpb0y6CbaI9Ol5T1NO3LvUHD2xsykKRMFX8czXuUw3F6Fp7VpHl8OX4XwelmfRM0TfEiV8J8BD3xF5ic7J80Q0v+UqLCh/IVP7YgQ/+W4KI4cmlU7BKNI4KAk0QYBJPFTsFTuPHz6BKsqXyGphCdQ+iiQrICoFRKJl1UeO2ucZFAisBFwVcz5xvIi86N9kBD+4AVL/jCE/Ue+1iRQgJO1wzVAG7akBTfeqF9s6xgRdsVdHzh48Uij++eytQl9nBTjVchKOAimto3G2294YfQkrRnezDIjd63fOaeoi+12w7EMvXRfddGPBlHbKxTKGno7R/Rq/vRUBpdbYqvUNrHoCrFwUPs015SMfrcqgEzgQxEfws6ZzAFH+vDbqlIO/AAAWd9Lx/lRAknpIoCNfA1TF+uqzKrUujo8aF+sl2Yts2JhVsUoLiE2tsKXkKwh/yruPTpjR4/oiH3reIcz0xlS8iPm5tAyC0yXWlY9u1SielQ99jlQ/rQkogHn/ixsz1eXmCHf0mV4Xv5uYNSN6m5apQZNARjHc8aAeKjZKNDp6YiSInqhI3Vs6MMV2NvaMJWpf8mChoUjbJWBQoCfKb1uL1udBVA1Q6UlLuzHyXcW7kXMa5v0q/dF11D63PKb+zM29yv3B1gVW+jIXdZmT7vNFHXjK8qZ9wwuTkZft0m5ilxsLppjiJ2HOYbwSifEYiFTCcxdg2hgxrMuWI/lh7V6JpKh9SJGoWfdq+aMUROF+XIbjpBINMAWgMFH8dMBHTWIwjTJAn3PnJCDlI/bFQBR5e/FKFVESTZCJ7LUamh4P0ZbxBuJ2+VztRUnulX1IiuGRf6/dIQFl3bjitXIdiLTVXkWiJ5aS4YuhZYY2AI6/7b2321vejlQJDkvIHyW7QR4qA77qpxwvJ3mA5Roby1iavVM22MSqMon3SX9DDqr8HrjnuWeF1qP53SCR4A7kS+UPhmh8ybtO/+fJS5XCotN3Ni887fYFxDxoMl5KgFOM1icgKr3f5JGifYgRkXQQ0/pEH7FnKrZpwpTIQSfAY4U6jU4ADYcu+ESeu3QjSaoY0Rjhk45lvZsNHR4nYVQ/WYnUviLJ7wjQavZe14GrQxgvZU7B9E4mbL8BACsPU253EUBkjb43uac8WNL+ha9zgnLe9FqK92qou1Vx+UCkR/PLcnPBFAGplLRXe1aJ8uda6Pr+rQ8GlYCxkNk6s0UOQJTQ9VKoWY3EB+U058h+ic6n1D6mWCSqnibphah+CUhl5QbR+5wnoJRGbDXTsUZKHyTmZe5WiujHADaBq5SUV4CWbKuT68Br4mTnvbKR/cQU6sAW4oJW4t4tpUrxs+6K4rljGw9YQ5f19A1exGiL27WmOP5MDQM1WiWKw3+4ffGMTB15nJQA3EyvhGS80gE0Ef1ymeR79pIPRSNKzFWu1TX4WJTmR1Z6pfJRxL4UKjqFkJboZ35SOqCMuRyjdu4gneZ3c2R2Ng/hdBaGo5S7g3QV08YDj2GacVTZIcznOUCFpy2bTh+G7meGd/Y2SXAJ3gYSxjOlz4+NigO31MinICnpIFpnaH6r+vIogGpQ/JrjpGoR/Lg8GwAjXdJio1rflMuRRQVjqmQDAV0GQ236WW0KpPZuUcNlAFFjYOkCPVIXKjWwlIyA7X3cutkaIFW9MY0b5i3y8tMDeDlejfJX27e1fuo2W0qn+WW5sWBKPqhMl4DGtZUPSn5Ofe6VF9dG0QOPGPbwBGBBmadIVKkTgCcKpSSeMd9OrOuYT7K+QGAJsw58Cxg+2+DKRo4p30HP1ZXHKY5rf7c741NaFrvzMHpAW7u9mDq4WiuNdn3Kbv4RbVSBl7XKo30cv6vL2gTleb0n2k06rw3FvIOpwEbny2eA2+VHmM7SeSn3PV6qyw0TyduUxvXw6yTpNURkNTduQ5ixtyp+9TIvJYN+BVCQN0q8Unp8Y23AnFLZEpH1zWyUzrdWd/kyOeOyqXBXVFntUJJ6m8as/Dt9stBL3Ut9rurLkDX3/cKPXXtWW1Szk27b+t7fA+TZAmBTtu9yIXJzwdSC3DnZjk0WOEmpFK1PQ+XDhi+81kFvvayuo6XbeeqDRPDToBMVj5WOnRrq1j/xOmngCRvlL1oALc1PlzfBFkDbY2+TCTqRvU9xmpm57oM5pCRnlOSk8lMl15TdJl1LWgZHWexsiFdELyFv76FP7bHhFobe1bpta6yqCmx9IIrywCOPYtgeOHi6pd5TyBPmYin45eIZEeVPLePgAQSPVI7GlwNMxIAUFNqZ/EE5SAXS/fLvzXJQyXccMwXkYBTQH3SUPgFUdlnyabAnSid5DxIEhHdi7wEo9hA16Trk8rgJMievz1kGUxzKjyPPSlubviumqVsPcBhLLwB50HAcFI/RYhAlaTgyoGJvVErPwXoElrNnyiWWr9DVdUyVGfebI+kWxr80N2/sUO8gSnvWxkqxHSGwSNERsa6C2ofHcJH9PCDDcVfG+n+dxT+DTTvo7v4W5VuAKBPx19QtaLp9CtZQW9key6vHSDW6YzRPnd8Zd9PkBdNlLJcXtRKDvxFognXwPXoR96GXrotuutFJe2mSyCeslFLiXJOn1oyLbymp1kHoz8x+26vKMkbwQ4XUBFMYnc+W5TqSFkgcprgOlRfGg15j8sNCAFMarS8l51VlL4l7E8jCcVI5mS9Q93QudbhocvM8NidOCQinuXDnlN6ic6CO4XppI+VBjLR8OTS2v1XQCkvnGTvT8oylfR5TQn6fKeJRgT+tUaVhy3GMVDlOrQSvVZqlA1V8CM0lBYdNCz5pr04MqDKoQi/VpqzqHGQCwqE7QBUT8aZofTBGSsZGydgSAVcxX8/cJPLN46d8hJT9Saf53RwhIDU/iyBHDU9E4da2cTBJ5HN7l/bHjmQs4b8GMCAdFUGUABui9gWI1Ffoo+yJYmof6Cxj3INgSrG8AqAa1L61Bn4MYZ46oSkAYn2Zvv0UbVfSlghIMtQ+wUY18IQBKwAAICPrxsie2zgSfV5S/9R76vSbdr2qem/Ciet+04GU6reJVduxeeli3XuVl9MLZqwE7ga1AP0FPCeRTvPLcmPBVO4YJhSfWtLYWDYerLEMrBEEUt7SJgpEykZoe6bMGVx8PVoX7ldrF1od/E0uWG9RxU+AkaErHfNiPcwxcl9pIaqU49GxUXOdd9nOlm0js+3X18DPhrVPk9Zza5nPWuWbnJg7HrbxAGbV56PLALhMGrJ4o/Kjgue3kWQ7oMev664E6X2x4wa0Ptc5zTnqLlZ5dbn+ou19iuYX+0exxx7BgyzLB5N6+tqGVnpUoI+sIUaoexI2MLEjVJ+UuQ49QEKvk9dhWL6W5pfObaM+r/MYmWEmleUCJO0om3QJ1lZUW74MqTSUBT4/eBku7t7vAKR8NfYs9/Bi7u2F7LKp3FwwRVY9mtiqnKhJMvhWcy658RA1S9mwHkDpvl6ZgPKyEfzE+mdpE5m6B5GTmBIItL5oPod5CkQh16TcpHRSa4MZOMsHhj4nT1KoeKPccg4skZYFUMFvDVYh1tdKQArrHRGvlOxjg094L1Scy28gcmkfBM1BE8VR/MyddCC59u74IBMeJF+oAHgtrHkCah39r07tA3BsJqD2QfCJ6MREel/KH4VeKNnWPKs66FonEfTkVL0UFS3mmxLqX6IqpEASOehE9FQtYVJ6X4Xylz1TaBHYn3TP1M2R2WkI86PsqY906AiYcvtJlDVpVOTblMak8ZzTB27aGqHzISjyAIr0UYCgEx5YSQAK44GSZQh6BODKGPy8UbA4Z3+DYLUwDgQ4oZeowoxikwgDMFgJgEG8WZ7Rr56o2QW1we66NjoOnOtepQWkWvbVNcdH/WLqudfNEt5vXQYFjd+S3x5uSssWucl5zJqmPxsNOi6PBKS4JBDVPVNZbjCYSgrKWJaFggCgyvmp9FUvGv01IEqWjfXOcs1FMRlg5ah7rdDo3mpoo/VZU7q2FRvgqPg7KXe1iMIyKH7sBGQQBR0BF5nPAiwAVdAxx0671JE78Xm9WohMJz7nmwIDrgFSOfLThhozPcc8VsbfV+hYT1FO8rywvFrvdiIKTfr8BkpWAJZVOPVIflVAJbv4aH0apS8DqriL38aWacJeM+5twvUykMqvv39MmENKKHw6hooVhYSRhoS9Qu3TsOlpUD9Rh8ygsv1JB1M3a8wU0/wW6VWisVELMVxxyqlU7jt6ld4ZChpufBCkGuDh+WztOKhiWcZDVRL0FgYmPZekr9y5VgU+MTV4yqVX2FAGJEEd6q3Cct3Bgad9Aympdt/gbF8datRVG2y/9bEuC1BttJ2n0so2+7jpqf+otzLdFAScAqgM0LpcfmkHU1luLpiCDnj1g9ZGdYcv3VEWrGeqjH6khkXX4/PUv2KcpKf0oZHFd8QRYFXvS2VULrQcmowXE/VC1bXcRNbiU1mffmPkvqJj7oEVnq9r2MrOdgaR9qFsKOmDr+DlhlQ8FBNAUc0Qtru4i248h2qbhrTMyjYeO5p6YRnBLe5txlU5TyFuu0ngCbTxxWVI06vOWR9wov079gUhSa96o9xF7wn0drm5ooYx/y1WEUKt0W9U7EEUiU8Er8CnNPSNLqtFIn2nLp+Uzy3Fy6CLmlR2uHYPeBQE1ZYRWNzUMU3rZCp4nbrdPcN647VMvRSV1rgos01ed9GvUQGoLqTuLvuWq58pa0shisSMI/qliZbpTTOBDYRylqMmFSAA62yAIBsoIkVN0hxQbmqWDcV6jdqXzO4+f5Sdi+VvXUMECjoFlojBI4S+l8ok6IR6nWRb542SoAZI81vAsqcAam4qCDyhniz7DOIAbPBKAb0PcxqZHEdylZu0UeDREJdO7kR7ZJf3KTsNFUPXML5s4VsC9x4P4j3RnVywEPDoSeRF3ce/17Begoa0wK/1DOYXzt7/HGBCo/iZ6Io2ml/0RMUgFeLFwsh+6x8XUfkyhLJDNuJvpu3JXCh+KbeUeKPkdzmh1ypuawb0XwCgquW42mbaRF71qleF3/W7fld46KGHwhOf+MTw6Z/+6eEtb3mL2ebOnTvhS77kS8IHf/AHhwcffDD8kT/yR8I73/nO/V78DZM50fzO0vw0hMXpLE534zS/G3hapHlczusXd2ibcsJtTB18DPqd1vGxcjlOdF4LOjczDXk6p3nMhcgTLtO0HOJ0jpOsi1NLB/K6Qk9KxFpgbSAtvqKTZ2ORBMMaUHfZMrURnFxZ/don14DjtDfYfqf72jLsGetyacyLSXordD6j+4ZmmdqCdX+nqLedKnXpcfb1vA9cL62ugaXj5oIpeXkZTKWXGTrnMXpcBUCJBX+sctcxLhtyKIdw5zmfh1MkEAYdrYVYl5/HKY+PwnamfVOk0QHLvHSkU3JdDIMe71Pmzuk4Kj++pojc58JuA63PRPer3PvcefcNph8vpdHbdRyOXOMun625feZeu8507eaiAayxPMUKWDt/3bQAVGBOqwCh/JqmZ+YurVBchZJxx4Ttjc5KgLYYB4WR/Fx5VGA2GuB03ULBZGrR/NynJ2OgUvQ+DYOOvwU4IaVPxlylyorMAntWWvF8ZztNm57Sj/7ojzJQ+omf+Inwhje8IZydnYU/8Af+QPjABz6g27z0pS8N//Af/sPw7d/+7bz9r/zKr4Q//If/8H4v/oaJJGYXgDFLoITnPM14mqU5UQL591mapIzLBdTEct0HJ9nnPB8D5zwlkMNlAHoiOMplfjn+HmCqg6VC5/n1aJh0+g6phZKsvjBqVoydRVtdMYAdVBdv/0MxdwJSlwI0QY8XQa78cpiw7IGV3662LZ6HK/fJ6b1Rt35N4crKPvTSakPddKhGvhtM88voP1os0JIPHlagCnCgCv/m4zZhXeMM/HQHsJpgy1vOcKCur0tdKJUEvUZxtF7ddDFFY5I75LnTjLmlKt4LA4y8p8MDKAe+9Bh1UIURqBVAyU3G394dZG7KdC8V7wHII87MESr30d5qA2YRaN8LheUBEa7wRoLa2CeM+I3gCetuWN1EkeS7Bp5CAbkO4OZAIe27XAVVbnyu7JknD6hy7QqQDLUvw76cWUDGSQnkA0WQbp5SqK64vP71rze/v/Vbv5WV15vf/ObwiZ/4ieG9731v+Dt/5++Ev/f3/l74fb/v9/E23/It3xKe85znMAD73b/7d1/SmV9tEcChOgiMQ8o6l9/w/c3GvnHUQ7xRwwjnaHkFXU9BDTAgaiHQk7WhaezTc5mW3zAOFbGtgVPPYPyh40adoqq8QvPzqrtVps9hqox04IdN99m3bKBzqn2ITeoZEb7PeF83vcf7kBpIKtajtm8DqZnbvi65/9h+D/KLGt/Fxo0xL//N4rD+aDLyEaA6Pz8P/9P/9D+xke9nfuZnwgMPPKBGvte97nVs5HvMYx4TXvziF7OR75/9s392Yed1dKNpfkTfg29D2va0RWznaTui5qUiFRi8WtTtFQhmlMcBvjVPUy3oBFrlmOIgkfkgbwcOAgZFppSGdNJVF7uiicqHix1q+tOK2sdJJRO1b5E8TzSnydP4iObH63N5NYIfJP7FIBU8aX4peo4JQBVUP5/nCKLBidIdaYOk8yx3RjvRhSeirEQHduedASSnvC34vhWA2L5PyAKYLAKAzG/wQOF6D3BrURQx6Ad9O+BtjF7ddLJzT7FMEfwc5Y9+Lxr0P59jyo6dKu+4gKVoF5mVo6U4ih99FkMGTGzEzkfhXFMYzY9zUAmtL5Wv4uSj+OVIft5wcX0CUBB4Innc4x7HcwJV5K16/vOfr9t82Id9WHjmM58Z3vSmN3UwtaUsiC7HjInU9sg3RiLtYGWcqTF21aTS5ngQpeVmvFPqUNYCVIge0v0yfc7UJx9c7RzwtxdzTdDLl2sUHQT9SzNvGa9U2ed2ukjC65dHpBZ8x+9nLnG2aafe1mP01jZtzZq2YB2Qqu495TxcO44GsH0AKh0XWxgDXbn3Qnn6X7rIDJLKfaYBKCepjnyZaciAuQdoItBCc5VFlJUbFIDi9Qdq5Lu5YIr/REuBV0jmQ8TWGV/rmgnL0+l8pxiBlgNddW9UadlDq17LK92U6kfHqQxzHbXKCCTBvdEgFOpxQqrf+OTH4+ByjUbmy6vPqnKhHljBpWRr05QbB4Cqej+LaX2legq1jveerH+F4vanVVHg2ucwij5rDr08/wx025qWFQ8UvCYCsiAkenlq9XFSY48fDXX+usoJgklgRL9mQAq7XQ5A4YJObPAeXBaYet/73mfKb926xdPovqtVeMlLXhI+/uM/PnzER3wEl73jHe8IJycn4bGPfazZ9klPehKv67KdCE0uRhaNgIGNz7SM77Z4p9KydP5qr0mVzmVYDTWjjzPmCYgSYIVJ52tjkBRkQaQ+T4HXednKSomem48WDYEn5Lr1Pom1Xq4FOsC+WdUyOXfxAO7SuW+BqmLMzvqqamrAd7c3EvB81GRdnVsDqeb57A6ipt37xnysjobelP5j9ThTRHdNfdBwNWXfYOp9W+imQzHyXfqYqde85jXhWc96Vrh9+3b42I/92PCTP/mTo9t/wzd8Q/jtv/23h/vuuy884xnPYHce8SM3Fe/BMONwEOEoDRDQUNHqlz1Ss0nNat3qRNcUmgNdtXWqsBrgq2ywXBCCeFOqU+5AI7UPwJN6MCQghVgMZV8XbEIsrS4selkflgMChWfjnyF6neTC4ylkL1QLCzRl8Cm57N5FQ1h7xv65OGmexx5bWUPFTAeVjpjS9wpAa7fz+0lPzPPXvWdKQFMeF5XDomuYdJ5WJhQ6Qp8MZdZcJ3uiKp9bGkPFwyoSSMYcUxT+nM8gKQjxSInniT1ZkGvKAirnnTpgoXaTqA8yEQd9nRCt4t/+238b/v7f//vhpshl6SYcsxQnH7AhB26Y1YI9FAEiXHkRGGIIMwggMeMgEi44hBvDxdvQGCiZu/FSxJ6Yr9w4KT9+ygWPkPHDeRxxXl8HeqXeQz2pbb/z7FtD5G4f6+S9nVFv8r77tcm0ZVcwtMm297h9LA/n+nAFKIq/dRPTN1wPpBoqtNwI6s/Ham02bPeemNO8Vy/TvdNNh2Tku1TP1Ld927eFl73sZeG1r30tKytSRi94wQt4MBm57byQ2+7lL395+OZv/ubwe37P7wk/93M/F/74H//jTOt59atfvTnNL1HEBqEGUQefOlwEBISiMHPjpRpjp8Ysf4YOMXFZvFLlNjl/hyohPwjXf3dg0hzUGxd55Wjaa36uSjfJNL+AdL60TOUrpvEJzc/T+8Yj+CmtTyL1abks5zJL8xuKDrwkh7UDQlPgEQFXqVFlfv2a90W79kLx88BKvBEVsGsof7iX82R6Zb9101expok3ET2ECJIzkKp4GOG5eOCVA4Lki5Lvip4L0ZUoSt+CKH1zitiX6H06jxH8eC7bpTJN7OuCUKyTeOvhnybtjetiXy0l48Vkvek30f3Oh3k4Dwuex3U5cp9N1ptBVU6ACu3HAXqm3va2t4WHH35Yy9dZ/ohv/o/+0T8Kb3zjG8PTn/50LX/yk58cTk9Pw3ve8x6juGigL627ynKZumlxGt97bmOpoOad5/LYYBhvfdq+kKpOqIxhqhnwEs2v8Dz5sVFFHeV+8bfrrK4z/kjFugxGIcrtpoayTPmTtpVyv6nJeMyAOeWEvGzQKBW3f6L7557bZTY94GUbjvx77+6rMYRXtwfrN2yTM8BY67gx1EJdBcAaO1Xpb0gB979Sv8xXUU08XRNxqdZXjf4+IM/U2zbUTWLk+7Ef+7Fw2XKpnilSMi960YvC533e54UP//APZ8V1//33s0KqyY//+I8zAv3sz/5sthjSoLPP+qzPWmsxbIqxNNgyszy10aw11P6391a09vWKLZUbz5Svr6h43AyUlfLIhWknHBP1IviaVel+RUS/Vv4pURpFB916Q3S5AhTKZetl9I+vtAJt07ogiPIn6mSsrKXgdzytyRvJc5Lykf0LimWaG1wJ9zS9OY5aCeWmzE0auGLDS8Pzrdzm8nctpXAOMqH+MB0jl85a+onqjZpdaAdjn+FnSVnh1FJYBEIJSH3Xd31X+KEf+qHw7Gc/26x/3vOeF46Pj8MP/uAPahmBjV/+5V8OH/dxHxeuslymbpq1krTXQoZLuQ8b7qep9RTpOGqJ4n1YchgjJWUYgVbH/sq6Oq291HsVjxRLBml8v7B4XfvZ+DZ36w5u8MFvcKCDB1KHcizsL9TW1ZY3rV9n5VEKIFXr45jzaA0cmHBTZof1PPcdGv3hiboJjXw//MM/3DTyoVy0ke/SwBRdLHEbkdc4n8/5N/Eaa0IWP9pHFNQv/uIvhu/7vu8Ln/Ipn9I8zt27d5mHiRMLhqs0ZjZwDcjyJi80flPSyarRuyq9PPRKeeDUpjL441V6jjXxiMLT+ySPlFD6IKeUhkc3nqVaDqnS85SpfvW8UtHrlYAQ5JnKwQ8ghL16pyDQhA9BahozF+WvcWNy59l6rCSCW/7dePao5P0yeKnWGLKKOsY3tKHNbQVuuQKEEMDWqH6WBhjHspUKo6Rbytgo9RRisAnJL1UNjS5T8jRCct91Unql4nVlBpEFSxqiVcKkQ7h0n0/KTzb4hKPzXnEhq9//+X/+n+x1oTC0RJGg6dFHH+X1RMP4gi/4AvbgkEKjtpnABwGpqxx84rJ1k1LuOKdTXKY5LvP6U/yd81JVaX6Yt+pM8kbFOrjuVBceS/NJCe3P5JKKE9P8hBroloXON/fUPhMqvU75y+HSIwgTOh+CM+TyNljgEcBNBVooU4ynfnu3bLwPG+5fJnLYRLm7qlubTqnCWaDMeLea/tvuFOuC9qlaBFl36OKAVX3oPFW4nTBdzIsEm+C+ajN2g9fHnncLUKFt059rs64tbu410EmHbOS7NJrfu9/97rBcLpnHiEK/f/Znf7a6D1n9aL9P+IRP4BtKYRG/6Iu+iEMjtoQ4l1/5lV/ZpPmJe1U7itxpk44pvX3Oo+KKm9avWueqAoyKcVAYMQlAlgzyxTFSaMFrYb7Rb04G9Hr3sPcKSbJeHCsF1L6ctDcuE9VPKXrrEvQKaPLJeotofgSqbDLl3GnPgEpBkxkShhHh8rqayK2VmxA73Rk46XprHHXAaoK3Ap8v/G6Cp0kNIe3tLGR8Gi7sv5xiFSjlZRs4pAKs8FlAND+m+GHCXoziBxQ/jebHFL9U7vxDOXnv1P6NqFUEUSmSHyXpTWloEFhx5D5I2ouUPqX+QWQ/ifQ3rAhQCe0zUvvmaDzZoyho27GOTeSv//W/zvNP+qRPMuUUGYkobCRf//Vfz0CD8ngQOCAq3F/7a38tXGW5bN3EQCakb8oZOqQhMx11aDTGHnGViq7lNoCEbZdcEIrgaHwQzc8Hm9CFEdpyvBbsUWLnFPWvGNni9csx82GkUQZ9lppEUXHYQgrDfW+gqjJ2dG3dbq6gYN2+m7YvY9tP0Detd2fScXdrtuoHLu7vOjpfBUgZ6qgAJvf+Qb8hb2PPY5PLG9wLqNQ+rQR+DNPU/EZygHqJZJM6yMhHBr7v+Z7vUSOfGPdovCoa+SgoBXm4vvRLv/TCjXyXHoBiE/mRH/mR8DVf8zWsrH/qp34qfOd3fifHkv/Lf/kvN/d5xStewdE+ZCJOZhj55oovY1ML1ZTNwYomv7MHoxxQqxuhkmvUu/EJolFdJtymFn3PHxKUfVb8ZbCDYrnoJFSsT0WjaOl7ZnNgG5Y92g0i+FUv0P6W/kcJmioHsG1zY0xbZXnPUsV2/pla01jt0m1ZTWlVqsPnkyBqHrOmdzQ9o3yHqzek/knm/atG0aLjZI8qeabyGQqQLul/XBfQ/sxLfEHPbx+JEWnaRNirV5kESJFQcAYK1PDrv/7rnMyX2uSrPl7qsnWTGs5SpJQ2vQ48PWuS3trEuHZ/PAYmz1XKnjHwyfbZKsGgKlkVcoJd8SZlGmDNsJgNijAYFYFbslyZvmYN9Mk6P7/A9nSyeAtZs729BNnX/bmo+7xGv4zvsyHqqzyXrA2kvPUch/VTbb92rOArIfvSS6sN7gIZ+ai9JCPfU57yFJ1onKsIGfn+4B/8g2zko3DppJOoTb5IuTTP1OMf//iwWCyKrMRjvMYv//IvD5/zOZ8TvvALv5B//xf/xX/BCvxP/Ik/Ef78n//zbCH10gqtqFHfnItWkv0VH9aGjYXBDXII7yaXOawvlUwFF8B+Y6ETxOLHioovOM45gMbcWe8qFyD7Rw9E6ZlaiWdqQct5W/Q8rdRjhZ6q9sQUMo34l0Kjo0cq3VDNLaU5jbw3RIAVUM700qZFd7CPCgaHWtRYAl/zDO02nj1qB27Ds6xhiSrILs9ZAKM8PwTCNkFyXo60TRdwwuWdMsDbBQHhWCbuOZicUeqNkiATQvVbuQh/MRBFpv2V77gAZkyAaCfxStXJMhKpL3qdyBO1COeaY0o8ULVpFlaruC9H/kveKR7k7p4xlXe5mnLZumlxGt9/NVC74AvG+5FE8+i48rwBrG4Yc0ygiVAPJKH7Q6K9TGF3DAmzDMqmZrDU5Zy8MbYp0n5FxkjUxTGZRzxHAvhpOYU05/bP5y9CNb5Nx79iQGpW44yC3gilv4t9nNXtsqRtx2pvO2WbPV6XMQY26rZjfD1YGtbuH98poPq5PqH+hJd+9NOToF9ybnpfUpJpqAP34aBG8o3vOeXGVZShGF9Rihj5aLpXcmmeKQpdSNxG5DVSmEP63eI1PvLII4VSIqU39QajmHw3CqwQ8eDHNsa/akitgy1VVQCTAVLOuGI73FGBaDvR6lxnFw0oZduJHp10jFSiVcgkiXiLZLwyZiom8C2i9y0S6GpE8NOxODh+SuhjOk+ejPQ7RvHLkeM8oMrjp1zQA+c0az0+M08aMIfDhjK5uQCcEETl5+RCZzvwVXiuKq/b2qZUAobAcn4f7GTofRCOPk7wjsxb+8eTNkl75f7WgBRH7ZNofTmyn4nASNukdSZpr0LaCKJqYV7zSKm0zP09+xvpfULtixH7FpHel0KjE3jSSH4aJh3HUCUgpc81RfBrGT92lH0O8u1y2LqJxhstzlZhzlMe0xTHOK3C4u6KAZcZ53Q6fdKxT6Y8HSuNocrjsWJ5nvJ55eVVmJ+vdLzU7HwVp2WaaJ2OnZJyN4bKe9vUW4beMc1p4IJT1FkbbQPklmI657m/UNClYf0krCFAaqrn5QLlQg+/5zZRxT8TLKstGyBVHyeVf2ejLHbOqkDK9yGhLr+9gP+8s5yDW5Z9sEN4QM9h3wEorrJcamh04jS+8IUvDB/90R8dPuZjPobDz5I1jwYxk3zu535ueNrTnqax5j/t0z6Noyz9jt/xOzhc7S/8wi+wRZDKRXFtJw3TyUU/38ZL7YEVbjvplIzVQ9wVsdXOCXqzBdDuCId0Xg20rNW8HtVOemXsTbF9OrRa/KDBK76xdHO0nQGQm5PB5nUzv60zjBorEJbqSdU2QDNl/TnZGzn+3Ga7NHS4MxqQHZD2+zSM01WLqW5TU/bV3zZpsoChHLXPPpsMluBZVQJOFAqodv7wq+ahkqNGmwTQ/DLUriftlWATSA3EMzbvy/4bjssYM3WT5TJ1k1LvxMUCr5QJAV4LyNL8SNoDhLLxBsY2QVnJpvBlzktVEwmHroOX1A+j5xuvNikrPYk82EkN86LP4NLs71xQb9/HZV1zvrF4r2HR+d/2KP7CL0j2fkOczHZbP6aetz/20Hx+48CoplnjTjpGDz1M5gXF59l4ttu80LXTusJjpg5VLhVMfeZnfmZ417veFb7iK76CB5E997nPDa9//et14C9F30Br31/4C3+BG2Oav/3tbw9PeMITWFl99Vd/9RZHx7xD6WXnBr72kqc9BH80nnuzXXS0CfVIuTJv0d7ZUKXgJSkW8h4IjZEV4qzRwc6Ur7yc8khh0AnyNiWaX845JV4tT+uDaH/UtyAKYFqOdUDUPg42YYNPWC+VpfjFVwS8UQKs9BlDfqnWfYL7bvsWNjy2fa7ODOY9TbVni79hW7N/WgbDWfv55jRhAJzzO4ynyNfhyyogWJeB9qc0P/2dcn7xdtYbJfdbg0xwrimcUm6plF9KPFUxGIWL6ofPcfR7kG83BpuIVKB0ewfxRIWw5GkWvU7qlcrL5wPlloL8Us47JVS/6JWKFD+m9Kkxkmi1Kb9Nlysrl6mb5qfLMF9JVAf4uNHYhOUofswr7zDWZ68AoYLWZ3/bdsqNZ1orlrKYGzmXRD5R/LidIT+0ofYlOh8vpGAUie6X78uEM/Htnezrlo3Hydfvmv5yfbaCFuNLBTxuo+Rlf7r/hte9pTTekTZtM+xfxgxlcCLlsxqm5Zdy6lo/KVeeA1k5csdsBECNBbUScA/b8NucPlSk/PHiVoDJWUiL5Ysbz9vlAMAUCYU4pKk1qBfl6OgovPKVr+RpV8mR3ZI9zEUmMFayckW73lhtKa0yA548ehvpbI+KJOW1fWt7NeOhtE1eKQ6FnioyYc0FWOXIfKbjPTY2Cul9bp6pfybGLcxzol4pM14OM07K+yS8hoitlzEOJRDlt+GZ0PvkN+4nt7D2zBBEN8ATLuf3KJ27e1f4/qIOUSCV5x5IWYWC46Wg4yB1ea4/3Osa+DKUhgSePKhCWp/S+3SsVBw/ZYFTSfVLZoHitY23Rjp9jbFSQEuQyH2JcKj0PTOWCiL4SXh0scRJWPRM3bw3NL9d6+hyBXQTUegk6zO2x+l3/uYrymikz1R9JyvjNON2HkC53/lwFSvTiEAkQqQySVsSAVTWv9HgJ0BJGjYYY5KaI2kLq0b+yecGl1vrmxaga6i3kVi2rdT2rd1mvh0JcIYLlEsCUuu2N4aDFkA1FmpALWYsIvQNGlH7FEhNBFG6qz4jLHPvr77eyWuFnqwpsgb0ulM+2KS9V1kuHUwdmojFIVuhZETrlnVNKKt+AJs0WNiQ+/10NK4FWabzjYeWG6CdZdvpNiAro5eS2ocAq+iQ12l/te1wyiHQ8bIh7Dk2eDg+yligpt/YGlAyRR7s+g7LlMiL0vn2+2/6/B3QKpZNmQfSEGq5QuvU06x1EEA55VQD8gpZsORpfQVYAvBb65/UpNZnyo/F5pmyFL1arqlYzkCp2Cbth0DbhGXOc1aCe+5wdJrfzZHZsAqzFQX0RwA1lB4q08DkZ1tVV+Z9zMAIO1n2hUZwVQKuovKx992cYzZTSUsNq4yuEpAk6yJDcBuUVJztRuXbbpv7EA2QtSvguki5CMA0RWr6CtcV5RV03wJSY/v5YzaofQZIbfD4jPPQ6Oo9B5W4x8+t0/yy3FgwVf0utbOdXbL53dyiEXedbU/zqh7aWxLWVC8WjNqFZT0UN4rHB7dy0fCgNwIAknigqIxpeZmyR9sZut4R5JmCHFMc7Q9ofurFSvQ+rovLB0sjw+ATEHhCA06QF4SpIOD54NNyUf7MjZ76/HxHGgeAgYfKPNe43gcZMe8DvAuzde37psC69h7I2LZQA7yzwjtoApSgJzENtrZl8kwyoBqP4BeXY16pXM5BJ1Jkv5yg11L8iseTgkrE682WWQVSklsq5ZeKXif6nT1Q5wW9b8HBKHh5JTTA5KFaJW+WUP00ml963jSXCBeX1RnpcuVldkpgit5O+Ybz2++Y2SVyWmd5KH5boARHsvuMWZbqV1ExvGQ9oqfujZWka2jMmFD90jVT+8JR+5Le2spY0bDOFN4Nv+zKmsY/MDjpuF/sRPt6NlH2uN0ubYtEPhyrYxuDnsMf2/aNzSErdYw+K29gKJ4l3G/vfWrcFEPtAyBVRvYbtyaompL3N5FWo7GgAaj28by73DO5sWCqCJW5b6kqrrFtt/1iMuQDI15KRAwDagREeQKb4diD1dN1qjHseexA16mAhq6n+0AyXlRCfiwOUvkKml8sV++HXAvOjZfE0fB34l1Zzke2ScGdZEUPmtO0+hO452P5UrYQYxWF0ykDergOAnQIKpdoyk3IZh2zBuPT0jOIOZ/RO2XDnmeaX3q+Wi7VtxGlKqnKrRMwZW0Y4IGCiH4RyiWKX/JOMekQog1JAmdcLk7vAj1Tu1IhroP17yYIR7ubkWeKfxkLm8NWsseGRiL948pqn1k9IfxakfHH2JkVOyW0NSr0Uc7SnBoM6GzyL/nGsL1Z04UdP792h7xYbu3jrwMBVW1fA6Qmnl9tQ3gltpKJ+27ySu21ZVn3HFpgdAw8jdVtqLN22YyRCg3AtfaGgjc2BWCBz2Fkb/lgDhdQ7UMvXRfddHPBVCE7Ns7bHXLrRog/M2ctizxcsJowgPKjf4TSBd3QSocZgRKHRp+Nj3Gq0ftMniI/NkfBkt02O39KEGXChToglQNP5I64brfBU0UDrPYvPJBynWejPWHbIty9Ow0T8h7q3eidSA2tw27tsVJSXuvQeBAFnQNjcTUX2aJignfJj40yXisg36Xj5TDoCKhQyZleVTrJNO5xKIGUD4fOCgAj9KVw9zIuSoCUBVG0LLQG9EpmBDrmed5VuMod6zxQfdzFCwWfYEDV6EVVGggDXMYkNWCzqS/HNi+ddBhh0C4E2NPjsbcpNWD6F0HEGKCoNAH2HMpxT0VV0j66srXLviY0WGkZjC0t9rQekkOQXU7DqwSsb9c2x/ZVdhA/PqrQlY5r36D2FQEpWhdeWVU/r6z6tgs8MeUQI8EpDkAvXRfd1MFUbPUvD/xvA6hwHBRTHmYQgSZFQNJOXQ4tW0YswPrsmJhM7YPofBK5zwWaoAh/w5GsFxof5JvyyXo1DxVS/oZEGxyY7qcJYT3FLwWfYGofnRYNVoZOO3XOs5cExlPVb33t5mb4BR4G5QZj4Am8v8VUo/9BAArv1RjV+hu8JwZg2+eq3kIERhLwwwBZmExURfAwaiLlFAwEkidHCl+i9dGzSiCKfh+l6H2aawq8UjlRr3ipMqDCVFfNZ5nGRy05ot/A4IdofRxpWjxRKfgEB5sIMqWAFCkoBeecwkh+TO+bxflqHlaruSbrjQl7U/AJpvtFUDXrSXu7bCtnyxBW9OZWpPFa7e1t28oLJXPUKelPaoAVGHL7k6l96qWidhyPLVQ+sRr6zqAq7HWoCgx4uOyMQEb3ofEPjUlOR+LtsvXlk8VjmnOozcfuLR5sX9L0Rk6XdUOSFCRsXLHbD+9VY3ltBD8wvioCxDHYSOcz7IqhDqDU+OcuXC7a2/tStfbtoG8jnrsEVYkBK8L+n6+wJvZQdZdSOpjC/BVXVQRb6fgpMHcYddPWxFbR5Ch9LC6hqzZMQvVDzxTuX9tHO+/DiFJzlrtUhvo5Xw2Uu8bNtMWG0F21zZr1DfNvuyFCD5S7hLLuUmKY3/FtRsUpHhPi31NREFBjJ4GL7H55feV5VY4rIDbUPFMCtgA0AXTVC89V24S9U0RrEnsCzCOoEm9VGQJDPVIpupBQAtWLBSHyIy0Bbu4FeqVCOodd43VRHV2uTgCKKyGp4xit6jD+SZSRKB/IZxwZINiYisGv5WKfAJjGzq+2XPfP1du3oq1D1oRvU93xCuDlFMNlf5IH37MuPYC15eK1WbuMusaNs6oBJ9eHqBtos+dqqHQqY68M3mX5ZsxBY9k9Z0ldol66Lrqpgylpvw/1zW00GvyxiTuav1tVUemjFfgETXjCWEXd2gDYJLwIqnDclJbJOKlKOHSz7MOia5AJ2W6o0P7StanXIy1DfqmcGNZ33G2HfKMOuOmE57ExUt7yRmm76zvTDW+UBqBw+2zGaEiWLKdwEEhZEOWSLAMIxuftgXAxhgoArgmJDnTM6Nh0YdFdcAlTjt4pzTXlgoeMPDsssY8GAJGCpjQ+yoQ/z2VC9csh0WXZhkVnPZg8U+KRkvdj36HRezS/GyTLZQhDwzN1qdKgEkrwF24EZKyU6yTKmCitCcYciiXQdzDNN9QCWmYLrcN4kNDLMdKembbSz91y9fP2Hi5f32R6QUNQf3tdvqus8TCNbrONoBGvdp9r246eigddta3dXqLD/GGBBohDKfz5IDD2px2/B0hMje9uenZxG/BCcZCw3UGUATfDxT7HHs0vSwdTqWW8IIPylEPLolmIY6CAmQdsPV2Ghl0BFC2sMPzsGi59TdEwVRAUB4KmRS7jCH0zn3wXk/lWckzVovkJeErR/MKiEb1PQVSkjwmljJehc85XIB6SKaJgqdJyossOtmVrLIyXyTS+/FDzWKhM8TMATNvidM6oD3h9fDGbl6GnlO1Y+LzNqZtgIpnu1xoDJ2ALQZcFVxEAC8hFgKsR/OaZ7se0vjRR5L4YwS9G8VtgmS5HCiD2dyqPTcETlq0S3Q+T9OpEkfs4gt8izzmaX1zm9T5hb4rit1xBFD8+QIrkB4OzZmnadwCKLjdIzpchzM/zb7Hu3CvxLv68IisgnUFZamc0iSwHkhBacfJaoYdKnVMpKa+n843hB20UnFXflfnxnjUmhG0n7W/vPJOIplI3AihkVXgP1yhomNKPHO4BoMLjTC3f5VDuulsA1Wyr965B6UMgBc9D1gnI8a9tdRyVvJ0Y2ErPqwzk1XyMahuIC6zX0/CMXBcaF7YUBE56yq4/0vXShcnNBVPFS3WJyLhm1gCGRPPUlIde7s/7ZpQ1fkzT4IOibCqgWsJXm8G+6AXr76SMqkrNutslLHY+V2nc7C1QW06rDzAmznxo8I6/b54wX63H/fadg3Xh0Cc2eM7uu5m0nk9t7oxqxQX4ZwHRFuNrAeHNc39LvYjaB4vdLudJ3L7l989RvFToscrUPfBAivcKg05IUkGM4udHt/vlPSutFUaL3KGOLldAVu4F4sV72AsSup4/pOiSWgAYL7q/M8HLWBJZ5lXgiZJqJ7aBel4Tym2bZkFYAaigHTQdeV+Xb0crIGHyBY3JRYOoLWSvrckUcCn9lCnbt9ZXn6G1YuaewMQqEcBV9sF3rfboDuRxXppeui666eaCKUDsKpf4RldZstKwJzeU0PikA8rLZOnDtoB+zpOlr9GhLxp+DFSQLIeRdmdpftGTlMvEM8XLQtnz3ijjpYrejOwBSb9TKHTxRIk3SsCXyRmVPCAxIpx4oOQOYtCJSBUbbfGRyqfgCbxN6sa29L/olZJOM1p+KvQ//A3HrQah2FaMlQuecQMQq7pwgBiDTpgAFLKvLstzzBxGpFtmah95oiCnFAWcSB4nofJpfin1ROF4qhrAkn6Y7dDhrdTofToGKgWeYK9UmouHKgWdyLmmsmdKPVSrTPXjwBNpHgNPkGcqB51gz9SYN3FL0QiCO9bR5fBlWC7DgDQ/5RibrfZ4RNdICvgxxeB50iJpc9BSkiJJaFn8JuL4WwFUcpB0DantUv1WGbzfPD9trh2FWQFSpbwwBFbaSecNKbxRUp42McEPXBtcDYwA1zL2JDfuYu6jZ75GbY5gh8bGleU125ux07UT9L+93huL4GfSd4CBFsdl66uN+9l8lVMJeVQHBwlDIDhm6N7X42zevtlB6aXroptuLJhqPruLRsi1BrVWDg28GvYEcBnKX1IWNGhR9BTz001LXz8WOlu085w62hjhzUTzQ2AVj7My9L9Q0P/icjpvpfnF6H2Dlid6H4yTkuUIoihyH3TamdqHIbgTvSzdH0ne68XiF2gOUyuXvRgIpJAPgiDKgae0TsfPrBpjpvIJVPNPrcF/JR3BG4pR2QtYdp0FM4dAIqZDgGPaeNuctFdomNx3gmh+ZowUUPw0uh8DKQBQOm4KAJWOmaK5XFq8OXIbOa8nbxfXUvQ+eXY5gl8GVEsETiFS/CRqH/2OiXrn4WxFyXpjwl4BUgyqUhS/lVL9KJKfRPGLlD8Doq9I/IAuByhLQh80bkrARqO3sY8eSG0kPRjYMqjK88H9niWdEWl8qTHi5QSs5vP4PYhhUMZPSQeT/4B3qn6ieUynnGNFf3nwNInm54xGxkuF9wR0bw2MIejKv6FRrwALw8aoiHTCJ8kGnfR11aSTa5zU+jqa3Si97rEDV+qqgiX3HKTmYlubhxIZEXleplpZF82vFSW4OP+kqzQBgAZsWbOjnM/YOKrCTYflNdx5wf3bGyw3FkypUexeHW9SA5dscxqVzzUcNX0K22aABYGVfEcb9pN6DVVPjlWx5rWU0djv6jZjljr4na1AFolYCplekda5aXNRGH7HLDqtxqjiXYpbuu0bXqi1CqxxyOa1ehaaVzD4/N1ctjen2npWoljgucTfqJwSbHXh6uNpoBeqcU9G70H9Qx7WTjl5b8w7lcG1BKsQIEaFCLINkIanXPVC7kl6AIobJD7izQQwtc0rl40U694LUD6+w65z6CUbfvkUZdQ8OWhdYPNa2wabVMHQ2KXVGh5oBxFImfV+Ks698VQ2+gynPJ9rJrP2cqGP/H6t8rFDTaQRbAOkRusb+243AcTOmNvcBqrel/QAFFluLJji7ltqlTWQgK6z850lfRjr2AsGDKW5RtiUgBS0AHmkmELB9UdvSNS/65MJ5M51Je+QzFOuKabwgWcqrov5pWTZ0PmKABRA7xMvluQqkgAU4JnSoBPJM4UeKc5bVE38Ol1/th6SeKF0PA2MkTFR/lzPXDnDlSATdjv7ctWSvGp7vcnLBw1vCWbt8zXTSBJmS7t01lvIMUVzfj7pOc3nFHhCgk9Ej5R6qQLkmRJ6nwuTniP5bfb1qccKkvUKMOKIfSmKX84lFT1TZ2lCeh97q1JOKQo6oRH+Vkjzw4AT2UOlASj27JnqYOoGCeWY4sZTaG/pbTYIwlsPNtdWUcdULFBCz+Pl9EctIGLpyvOBPFDcHEQvFFeMuQ5Jj6DnqQpezIDKUiqGOTQCildqLDppbLvSmF+MJuvax9Fl571XOprzaI3lPFrnjfLXTawTWmjlcJ4sOwYT3ElaljK9X/n3MDo216ICiQBcrhOFKtQ9543K0aHiZo76V809ZZL2AszH86x2vbLBjTfRqH1Unw884Q0Rm2lCk6DX77j3jm0HUyg3F0w1TBxafFEWZjxipaE1Fj+h+UFHGVejJ8G2s5IIbuQ84HiDHyeVllWRCIDSDnii/cE4KR0/VU3EC3VwpL6c9DWPmUpUMdTZAJoia8SOzbFh0aXhy8EPpgsGH8j0Pn1gALz15jmApG26o/UZil8eBtZ4KO7HJmNvCmVeB8paZgBU6lzI83VjpmziXrgISZgMwJZAlB0vlQGTLEtkvwi0VnkMnPdSbdi+6m2WoBEyXkqBVE7aK2OmcLxUBll5XFUEUikQxWDHS8UxchFI5bFSafzUBbQdXW6GDCsiraYxUzlreJ4X75aMj938pYuR9wDIxNLcZogVj5bYuCbbJy2kjZ7oqtp5otZre1pySgeMSuMBkY1kU4xx0vYv6bECFJU0QLnkNmCz46GGTYAU6lkT6GDiA9LblcbdbAuoVI9dTL9mVFrXquAyS/XUPKjS+2/HROVtsmXSjpOKR7DjpKQKAVuW5he3KwFXcXrJ6l0YzAUTuUevY35reabgRmz0qNyNVGDlbk1XTRcjNxZMscDguUo/dr+yQSOIAMqALPk2cQMsxzqmnA8qGykbUyoYlKJitav9rikubQTdNWgHGiLCSR0aFS41bjVDpukPVO9CpVVvWW8QcBsQ1dAMnnvSOnJlm11tMtVLcNhPD4QKHjswuN4vN05Yxu+pokKlk9ab/FPy7HJXpzgkXhEqueaFg77Ax2U9ihLFD7yOSu/L0ftksgl6AWgX+cYqPYFa+R6kR/O7QSL5MAwwycslbto2WaKGfLCfmOoqUFqxB5iWkWaBL7vXQL633AZSunureYVt9IhJYaBR0YOnoiNeM9A7MFQHVJV2FNumynEuVOTRaOd7zb0dWXcQrYJRBA3QuUYflcpkRLm7ek1UYFw12p8AIDWp3zf+jCZ1EUcP1e6D1MZm70N6NL8sRzdbX6XuWmqBPd3PtqAbStFpzZYQ1n2VjmvUV42ofQg4CNTIefGA30bHbuTcrGcq3QdI4moDUOTtaoEmTP4pDToxuMh+meoXYH2k9g1htogTe6Pm6Td5M4RCprmlwFtVi+A36hKI1j39hZ1kzfMAQSeU7lfrRCNfDu55xWtV+509V0DZXPfcas/RX6F2ApL3MG2nHigExkDfxFxSJq+UibyY6X0x6ETFM5VofJHuF38fQTnnljK/85Qj+kkAEQlAYYOJyG3E+8VBJ9IzjfmkZjFyn07ijYL8UlImUwo8wbQ/oflp8Ino3YpBJ5J3KtH7Zo1pn9Kj+d0gidFN9KEbr5NpiGSGFqDkGXHCuq6mypJSyl6otLX+ToFpWGetwkxofLNGI7SuT+8vtWLgiXpHM3/n5ZTvMDUQ2lZhUvgwpr8g6bzuZ/Rb2ytV04sa+RbO33pLXDlc32SpdcZrve5EB/ThKkZzC91r2p8HrX6Zfw/1PorzDhYnruXOwJfqxNdVZxARWFdLHQqkXGAKd55GLyX6Hkrcqkbn89JIR7CNOK8UJpPft/RoflluLJgi0TEyZhwMdJB9J3nT+rPxzH4k+Ns0uG6crl/21XADGs812xih3paIgiIRBRJaCiiPnTI8c6eMUEkJFcwn7M3rICQ6eqnEG+XofDg+qqT2hYrHo/08ihsxgkH1ndAbISucOwTelTEA5bfZaxI9o6ikcwQdA9Qi2DmAy/PrPL3FTAKqiueUw9LnEOg4dir6gsx63L4SkKIFpMznmSL40VwAFHqaYjAJCXGex06tYBJ6n4RBF8of7ysASsZLyXenB6889y5dtpHU8BDdT38LaII5t/jFe1bv3eSEuK6zLd+5WPsS64H1SkomqjxwPhXsaMIxzfKmaCF98QJ4hP0g5+2AFjYM2aaFEUuBPeF0k92n1ubZ9q/pofLJed1ybnd38F5hH6HWnrTKZfXUNuhetlUeNG+6n7+vqKfMtqhsKwBOFmvjpByQ0m2gvlnrcbibHllE8Ek2gDAXr/Uu1oy20DFsdmTgVnS9dGFyY8HU+te2sXbblxE+ItFbBaiqLAujr+DiJh0rYK2ap6pxSaK4ULHob9GbtWVnoctWQqwrN3JqvUvja2Sdz12ktL3UMGL+KPRA8WkjZb7wTLUekLcWpU6xbm29Sy5GIND9Rlp/B7hnxd9UXtu/ESK9Kgiw8X3R9fktqAGmoj8Fy56eWZsGVDqpzA5jSOPbAFQJhcLkjjJjpKzVr4S41VtmlvPjw/D2lr4ngAqpfjFsugVbOOk4KQyTrz29bHzx46X2bWnLx96tji5XQKptgWmgoMg91Gb7hBH17Oax7ZGPWpSNS7Cr0fpguRA3SAX0jFmv7Qkuy3rZ1G6b9VQEW1ZvpRYD2yl3Whmc1dq0Uhe2lvUeFUBqDWjaFEitM8JehOzRsFddXrfPJveqhWakD1DUl40AAorMq6piPq7RQ/vPQNm5rf3StzRu8q3IOiv51L7DJtvcQ710XXTTzQVTvoMkVD9eiRtuZulR0OM/ZukA+/cOGuxo2ZDC5KFJHbMcta/oPWbgte6lxo5zBTSpJS+43FJIg0jBJXhdkXMKqH1M+aMIfbDM+5VR+/giF3mZKGKR0peDTmAEP4n6Fhy1L4fjds8ELD6xEw23DX9D9L5M+0zvRdpIqaCVIBOSW4opXpJrym1b++1DaidMWbxviqHSe4DRiDNQzvQTBL3Wc5g9jlVPo9L6PEVTkisLzQ8j+KU5UPhi5L4cjCIHnpBAFCm/lIvmp+B4Qqufn112EAlAOieqX/JCRVpfyiWVKH4cyW8VJ1p/xjmlYnQ/offhRHmm6ADkoYoJejPNTyh/SPvbp/RofjdJyDM0TPBIOdS+rkfi10dqQ2Ip0DeXPVCitDIdXhqnZGavWfewXgOQhKKHlpccga9YDxS+2D6lMhM9Fj1RyI6IVHRDO0/MCk/tq9ICfcRSuRW6naX9iYGpAGjVDj0uV57VhO8z8k82yD01VdZjiPVSA7G4zuFs1Vs1PVa7v3qKXlHai8hjrbMBNs4zCyYbbnOUv9JL5Yx8laAUocIUku0T5E7PK49ORJvGsMmzGHs2tT4r9iF8v2VP0qP5ZbmxYMpalrFz7dbzsjPpN17G3GWvOw+kCmlL1QAInWRD8yvZF6bB8vVPbuiwMavQ/LTTXVlGJaeALHmfCvoEjMdRRaTHkIZMGrxM88seKaujosLHqLw117y9F6aNwX6HPAP9IWBLgBSs93XBexN/5/fCteuwPTZsjWeE79w6aZnAQBll5SV3r1RoreWSsiLj+PLgLn0m3pOIQScg1Hl8FXBO4CmBYAiHvjGQqtkXwPPEND70PkmZ/k50PpmbydOBLcVTATUC4E2eY5cuXkzjMwak/D5bHEfAkVE8qX5REi0vlRdTbBtjbc0RQHnPFLY52iz7gEfeW2U9XYVHKbSpfVjOx4NOuH7CBb2vTQ/M19oK6z0CpGTdsKZMnsH+4dTOMgak/PKkt7UFRGuXXqPzqerLviDfl9DqFVS1qX22zvI0hjV6OUfSm/D8quAC3KsVA2y9s2Lrap1el93lBoMp7L7dgzfMvcXmc5IvXAq1cc8WDQFU2k6LDoTlte2rVxryXQIoUr65C0bhAZJRWuK5EOCUKH3Z25FCn0uPU5aJ4peWqx3y4MdM2U660WEjXObcNfdrc7OK7mrZ1hh/sQGTjTCSTa1nP6FTXdWtrX3Mw/bgOLfwhbIP42WezmJ+07P1HR0OQJHmbDTOQSN0/NOsPlnvU75Bsw1BlHwu+Dgina8eEp3HSKWAExz2PP2OY6MAXFWmAkjx2Ck39s2PmQr7lX3gs65Er4ig9Qwtbhd3wHpZblwrIKgy5Ya8MkE7lTnBQNuDZfRGyXbquUoe9YphzxjunL5S3TQCrBRIVcpjmfc2beCR8g19tScODYfvTF/HXjBcot5fKW8BKVwungfXlJYxV0nWVaW3Kq0zuscCKa0e6pfPwkgau87vsVD+Jny+Oz9aMAbHc4A+Cd4aV7YP2ZfdcAhXX24smOKOUaJj2c5y9krEDfd40KIxAFCF73+KnkQdVu3A1aL2+Te5ZtWSVe7YzWh+kHOqSvNzlL8atc/nlIrbeGpfBFI5OW+m9hmvxhzBFOUkytS+qGdz3oiWVNdqEl5I1gu5hPK7ACZOWU6d6dSDTx3qTOsz7XiF0qdtMlqWnF4YFRlMrsonB5zwwEjXFdH6MmjOwAkS9ULnI3sYJYJfuu9C84PnxDQ/pvvZSZP1OmqfAC8BzuukwKomp1RQz1KO6Jepe6fDUaL5HSVqX6b6RZofRfGLkfxiND8KPJEi+a1SJL+lUPvyvBrJj1xae5RO87tJQlQgCKcjHe29HkKML9gTzQYZUUqchwpB0Jy6ajIocm7WcR4qyUUVOdqx/eE5bJuAEVP1aB23OQksLWj7BKwkgh8mewc9JDRlXDaJ4StU5lYApaoB0Ww7VA1QqsdFP/tG3KX/aD+PmgcqHKRs1Iw4Uk91ve+bNJbjsWtBkSopOoDWVx+PnUCR90h5zxQCKA+mimsRltNgKH/txyhR/vbgaWx6pVx/w6/fUTrNLwuSpG+UYBhs/s1/auaQPUul8dDjj1phZnUgVAFoaE1rURuyErCdauxE2+3K+qvUvsrUsgBa7nKlwVNrESbzxUhvNfd9XWSslH0QsB465+KNGmXOIBDSB+jWNx6n2a9R51qZhrrKbfmybXnLa4X4sa28QBnhs9IJaX5l0InNL9yKsSuot9lONpdUovnJMoU7TxRAzTsl3ihc1hcEwXXduNGjJnXZSVqN2cgwpZ0PWFTsgkFoKZr1AWRVA084cCbeJ7NvbDEwgp8PPMGtiFKVbd1C9VOQA2ocy1FRIJnAlLWil4YKkEIPVK3bIPX58jWPYaPyqyKNd7kmZbNZcfOP1efWyVtT2y2/ntDXQGWelv0jXvc4Zpf13EYA1WWczk2TG+uZqnqgfO7DFoVrfdX2g0IPFJQbJodsQxYxGbw+d8dMGzH1jyoDV/LYuVQ705WgE2ZsFC4v7HJcnzxSArR4WbxU2QulIdCdN0pyFeWxUjbEtoTZxnDbJvGrSwJbSv2mFElcwStVDhRCYGU70MaV7jxPteV6x3uDHnd63rYsdyiKzoJ7jvKc/PP1URplXXx+FvgikGqFrs8BJ8AThfmnkPanodMxn1QZ4t58dpKjLTl/4qci4Cj+Fq+UhD/XeWMS6p9Q/iQ8eswtlb2TmeaXAk2Q5RGDTnjq3z5lHwCtA7yrIZzLibxC5M2hEOlUiIAmShw/JYoAvphWu2LGOkGkJP5f0u8iZgKgNELxYw8We5nAK0VeoSDL82y84+AR4nWyQSfIW5UNfOKdqnmioE0Dj5S2bVKfY1tg+2c9U8kw6PJIqV40wSgskCpzS1V6r1N6sthJQJ6Yfeh1XXBIMhVtmPvj72F6vwuA6rb3dD73arf1Vtyn5piVT8GjkAy2GpelwVwc5U++Uxh22DLuN2WYqBdguYgQfBG6aV+GwyFcebmxYCpT+2RsTJ6H2nyqSEMnH7DbX4AWbwIgixprDUYhSRJTfRhqOS6jaW3UiVyYUnRXM04KyrwCwU64RHZLyzlpb43al4AXACtuZzyYkmh9iTIWl2N0ODoTLkuNHlL7NongBzfE5h1K74D1RNQof5kSKp1oaZTQC5HBU4Jabhttn7kMo56Mi4DuQpd6AOWsp/a5lWCpSNpbAC87vi3S/OxzUxBFCXpNRD8b1U9pfpKgF5P1ytg4B6qKdzmVCYNOxkfRz6Uk68XkvGlslCTlFeDE1D6K6CfzRPmj3xS1j7dNCXsjxS9OMWJfHCfH9L6l0Po81U86wHuUfdAprgGV4iZITIxLX0IM4UoU6IEiSbKkBoXbmJVGd5tQa2Uzn5w3NRBC2fOAScASAyRXLvvr8jzR+wg8RTClND76bWh8kfIn46UkUt+Kt03AipelbZpl3cPgSyjm0HbhckFN9/otRejz+RIrqTxs6o+ad8qBAr3Vw/pvsgaYfB8C+xeH1gFdBx6x21IbK4X74X0t7nUJasRZqmOcMF2KS86LyxlQ2f3y7wSKvC2idf3aUQPKX+rEjbffzq2qNwhm/nmnbTVBL9Sjtbj6sC+5F9kTzS9cA910Y8GUUHXMe4Veg3sl0ICqpwo/XIxC65bjd2PpakW9Nc4yNP5Vr4bvlDeWfYNXNn5+8KfnNHtes80XZQ2i0Pi5S2xJ0fbgvUo3pXz+jsJVWy/L2AB4fVB7Jru+X6hAR5RVe4MqvrSn5J8l7KO7mueCd9F5DoH+p1QKpGlWvYrTn6+ct3oZTY4p8TwixQ+ofxJcQsZbJXAdPVHWa9n0Lpobd4HWvy43SxDgSEOPjYqhNKR90HVb62lLnTDTH/mDhDYaO/C435pgE3IWUgcEltDGHZY1HLrUL3Q/o0twXo4PLdoqc+5lBx2b7hoN0OhM3E56qb7Db+5xZXlMKgbX4vFVHudVkeK0N2nc193PViOrxygb6hYgmk0uHHsQ4xe17jE21/l+RssIOxZNePQAXfYhNxZMsRddOkprOsfVztTUF5PpA7P13ihptKmMDJKyO56OdxNPOQc3xop3o3mL5oeUiBHLXbTyDXY5VKh9KSmveKYkaAHtZ/JJJQqYp/ktPJ1MO+SQHwLuVr4l8WLVy6S3DH4LoDLeqPR41SOFg4fSPhi5Tehe0olejVP+aoyQYozN2PtVHZTrOx3QQcJyCTyBEa7QQ2USLGOkrJxXKj5HCDyRlinoxFGaNOAEeZ4S5S/S+aIXKv+Wvk8eV7VOECjFOA/JM5XyStER1CsFHqplyJ4o8Urx+lXMKWU8Uy74BAWe4OATkEvKUPucV0qof/uUtWP4JtbR5QrIfME5n/RxrSjwTvpFXk/hp1M7iCZrA6hq4kARzzInquqNQo+Vo/GpRyp5mphSsUgeKKbzgQcqUfvIKxW9TckblbxTq6NcRh4pbpd4OZ4jzaP3KueOoraJHXapnZJtRz1ThpHh2jrVhalct4WcU7Kf3ELsuPvfcJubwsrfPS+k9q37Zg8YaBVGXG+PRIDqDLv1e1y7z+sofzbdSqgEoMjYPo//zXks9azNZ1O93iEFlODDTknOi6OMsSLHksqnUNawxrint/GCANU+9NJ10U03F0xBclb+XQNV8KJimrxa6MlRelbFwoL2QwFW0gYIyJI6eDf5jfVNMZK0wBSANx/Bz5SnEOeeLmaoffMGtW8hoc8xal+D2pd+x4YsgSwO8mQj+MXLwPxSedkk5xUgBRdugVZqyNALAQEH9F6jd0LNmhlcKSBXIOUBOgCqSln50qx5sFULHVpas2V3qAApLDcdjZl/1pnOGR9EpmgyIOZnSnTMNAG1L0fuy2OmNEmv0vmynwjzUK3ve+SA6jFqXywzY6QEPGkodEjWy7S+lMRXQFSi9BmKnwIqBFKSqDePlcpJe+24qX3T/Ho0vxskBFICASr6MCXUsmRvJwBlE/pG3bVB+HQZD5WW1SqVxjXF9RipLy1DVL7ZYgHAKi8LhU/GSRXUvgVG8yMqYDLuIMBSmh8k5x2j9gmgwqS+leS83kBoKX11ap9pA2t0sxao0nu9wXMfpoOkGDEOLbPhcqSlj3Cdn1f2t0DKbmLuud+3YLsgYEKWC46TcqwXzJUIACuu9+bZ8XvBgGqSWVAurnx2Bvdg520YucnVcdx5OAICq32+Kz2aX5YbC6ZKqXSCt6jCuJSgofOYCtdjvig1MlaYHbK9lo+9f75hcqDKAKxKuXKZVXGgQinLVNEIavAhy7W+TPnjYudtMiwQ8T6ZBm18EGhNBDShARdBVr543AEAGJTXbhv/9u9LzTC57p3a4p0zbVDjmZr1I+XV5woo0OxaJEy2Ufq0H4aRklwUPx8OfR0n3WPQDK21ZgBauQwpfjmSn89HJQl6XRQ/XXbKSL2RVmEZ4NylyzZiaHQjXs6kE4QNOKn50GATcCzbs0zh0Ou0vCJUunihkLInBp35CLVP1mmahjLhLlL+PO2vKEvXNIWG7u2lbR1oG/wih1Twy+4JoAJvPsA11D9+tuuU/QFK5XSrAKuqwyrKs6V4K/dXV6dG2egVWNZAR63nWekl3DNpepvAoDu2z5TyLnuVmwumkoVZO8vYwnIZovzGuKSaF4okGxTTHDwmtfFPnE8qtaHooXI9RwgU4xZA/CWMgSm0vBXRjjIFwgYqyB4LzB1lqH3kkaKTM3mkkkWI59HbRB4NQ+1Tz5SNEOcDUBgf0+SWLneM5XkX9D6J6odeS9le6HscgMB1nOH9UdoXUP6UyienXvk95f1qXFbxLNEbJfPcscE8LY7KCbQ+edY58AR6pmKAEHo+HHQi0failypH82NaH5XLPC1n+p94qbJ3Cp83Ct1KsfgpYOKAE3nck3in2CPlaH2UQ8pQ/CC3VMwvFSl/584rteK8UnbKuaRc4Amg/O2b5pd7jzvW0eXgZXZEanmROGw8kC/MVumFIpdnisASPfGiKFJQm0kHsAAqdihtAIq4LN4oF2gCgkrEtgO8VAspE8ofXQpR+1J5ovlFr1IOQMHUvtROEeVPvU5I7TM0Pwg04SL3mXZt4ZdT1L6FbzOB2gfUdjECGsqf6di3Ov6Zhu4l62+n1GVjb5CND9ca/O614Llg2ZT9cNmA2EoEv8LbhwAWjbPWMIveKUvtwyl9J/h8wGOF1D7dVo415VLRALupgKG3WlYz1tati2rkMxTA2vaHopeuiW66sWBKuZ7GRNV4OddVVliS3E7wUaBnXs5DrCNankAYL0J9xTcw1ripdS3/NssQ6tXS/GJ8KFQ2kpxXFRJ0tEUJYdQ3G60vNW4ApjQ5ryynqH0ClhBMYb6pVuS+dSJ0vzzZ/EHigZAbZimfFUCN1qGxBqsymeYWdcOmF+We9bDGiqvLjcSVhTVXI/thNMb8TItxUxLVj4FSWa6gSUByovppAl/1bMkp5Jsj34XeRnieJohEmnzYcwZPOI4KKH5LpPlJwl+I4MfHgvFSCpB9kt4EuAVQDXtP2tvHTN0YWczDjC1S8S0f+CVLXwC9h2Jxl16WmU8QGCdl5i4Jbx4zBdH6ZJvFAsKa57FUApqY4ocASsKdJxqfgClN0GvGRoneAWqfhEUX+l9qw1YYOl11k0vwuxD9llJ30A9vONS2EaL1GUCFnXUHpNItTEfR5cLrIZtCpF71OtXAyqHJOiXljb0IlECU9TJWT+EJLKP5KcMFgl0pOFKvlACkkgURX3WI2peOY097/cgnva6i4zdd4idc6eThb+13VI7hjbXpp946Y/jdH3DpY6ay3FgwFQVeqlpnmZdh83UPfF2DCOtxPBXPKsvBtbXFefhvwlh9po+ZUqCWcm1gRxwbL0/9y1xmR+0z1joBQdBhdvQvjJdQNIK4zS5tgHOPI7CSguq4ObhxZcCSqg5N29o5ylbAqfFe+Wery1je2gaWPaCqjQ1A+mV+lgSQqG8CiZUdKMLt9X3AMVKVqEv+IsViiVQ+rDGCKqDm+SS9g5uA3odJexVYJxRqovnJ6aWbLopKLgEtgftTV11unLBXSEKjyxiqGCY9zCU6UbK4Cb1BrXKh0VjAG1kFUpXAE3wu2QPFQKpG6ZMyDWCRPOEwTlPzSFUi+0UdBHPdzhmBvKFIj1Fvw3BCkkG9vSv3sW0ofNhbgijcpwqoTJ0VA+1VEbx3odInwe1qc7/ebDOFQ531Va1eNdTBMzWjq/F3sS8eYez4iTK7gY2jeSW1CqpGWr9jTbpmuii5uWBKInMZOl9aZzpFtc5Uu1ppNFS/pYY6xXjJ1L5aoAmgBkplur52IN9gVRufBpjSCH4ZQPlcRDoYV71UkcIX12MOIhe1rxpsIlL7YtAJ6sbKMlD7NOhE9kgh7as1rBMzQ2SangSYkI5y9GJInqnCM5U6yRy5LWndmkfCeCDYTOo60oUVqJw3t8OHR8BWfo09a/RKAVD2HZBWkssi6SXMJXqfeBs1+MQcovhRkIkUwU/nHIRiyZPQ+SLVjyh+mfanYCwpOIhfpq+4fm5AoRAQFWl9EfzE/FISdMJR/IYjmFxuqVU5LZcQfAJofrNlCjxB+aUo8oXkmUq/OZLf8qJofnvoUF2lDtkNloFofrMjjuIX24dE7UtmYEPvk94W9rpGsVTDK8VYKVEUTAS/5HlifSV5poKj+aUEvUr/E0+SeKayxyrS+XI+KaXoAbUvR/PLy8R4FD1kAlMI5Q/1lI/mlyLNxuBISF0Hj5R64GODi/R3S+2zRia8rfleT/nQci7CqPsrPP4Wta/Wo5/Wy784cadeHWqgzTgYZM2+lTHavL42WLmk9Nnl9GprORhxwYPF1D7wUgVn4EXrWBWGpLG5eB8yvoZIzps8l2Jb9w7U+qapz2L6GHKbav2NQ9JL10Q33VwwZb9iMFm5bWov9pigFUmW1eNUNpg4hsofftQgVQNO8FsvDwGUB1gYvU0AloIp8EaZKEfQ4AFVkKl9rJCzm90kdk1gC0OcCwWM94MGLQ/vKal93lJUNlLgufAh0dONyeHP0/YyR0uQ90ikfTEMem0qeMppXuzTeHQbCT5P+e11b7yphZKyFlkA1ECZwE5DVkhZMeVxbYnal0BSSe+LoZ2F5qdAysDg8n4IcEJBMBXxLdD7kocpJu+NXimk/AmVL065rPBaAdgunjGMmcPxcXBCMWnvnpVDj+Z3gyQlvI3R2oTalzxSFC0MuTV+npbL/rcLOlGbV8dMRWpf1AM4ZorAj1D+cjh0jNYXt8njpARYqZeKt4/GIBPWXGnI4q3ykWRzuY/c58sUCLl2zxoRW9S+sch9LnhB1VvVkNgZAK+iKPuK1czLaKfgEqQASm5dAYIc8Kr1TwRYFfu5e2yYMY4lA4wI3tyMmULFLP0MqFbAVu1SjUsxG8HlGNmeEZ8l1S0QbSMxrtR8ujVQVe0A1rZvle0gPZpflhsMpnxnuVwuQqCvY1LUDoNGI3H7ig6rbFPs63uXXioNkymvASpH59Ow5qqQssUud7BtiNiopFJjJGOkxBKUvE228w1ASi1EOet4BlaODqj3avPxUhiJTcOcu5uhHikDoHwj5jrVUJZPyaO8+jlt02T490Yr4lNwLxOuc14r05moTMar5ax8OM/BQITil0GwAiYATvI7U/3wsFZp6e1NHQ3fLQTMkoFUQd0jgJSAEgGqBK6WZl0EVAy+EEixZzJ7Jfk8MCS6B836O45hKSyDXbpsKuzFoS8mhl3htlU8ndHFLj+y9cfMK8EoauOkdFZS/TIVT6h9dlm9VBLuPNH8dJxUyh+VveGZ/he9QglAAbDKQAiXM0DSyH8w1hPTdpgyTOtRhEZ3aR9a4Mkvxxtr6WMVENXS5YWkRl064cZDdcXaj9KA1+qjAEgy6115UQeCq7rxLS/7iMHlNia/VFqBkYLrehrOwZ3uNo9r2j6NcVLwW26fG11R9lXpXdviPLtMkxsMpqRXZswh7Zj9yc5gfk/5Gvw3QEAjoSTNvSjUPqkPI/75c27UXetoa7mMN2kFnVAPFICs2rIJNJESuQKdz3qjXFJejtwXGzGig3EVQv9TL1WiAlaofZ7mt25YKFL5ynExifJHxl4IiS2eBwVWQvMrvBNA7fNR3DB6n/dUxRPLOniDFrgYGyVACUAyVwmdB9/B0N+m0wFRrCQqo26Xk/VqbinxRKVIjJ7eh9OR0v3ScgpQPq+Mo8LnSltJV1JeWREc5ySUPio7S9H7OJ9UWITTROk7VZpfitqHiXs1kl9M1isTRfDTRL1M83P5pJjW5yL5ybQcwnwZwrC8gN7QFetgddlOhuOjMMyOIr2P2xjydGbPVPZGIWhCN3zlRam598UYI71J8UZp0Imkp6TXmSh/MgZK1om3SYCVjpESz5R4rBLNT5cFOEnC3QSWVtQrSe3TaG6pGs1PopFi7igJQLFw3ihpXKCc9Vvwyw0AZfDo+McZN03MiNk6D5XtsOcKvEXtgmXioQpD7hh4NMAKjLX4W5BA4Q20z6Kk9tkEvciiwDyVmdqX9E9ajq9/heJXuR/s3UrGWfF0bexd8UMMuCx2xqr3Dwy9VaYL9l+xj5qddRejQ7peYrnZYGrT5WHDF0ksTvLhiw5kY2NqMROQQmOh6kX3bfpPtTpGynmjWkEl7EBeS+nTOorEhT7ghCxjNB1szKzLPFO7aknyXGCKiu6HW7pWbDuTI/Shl8ogTo3qV3nWuL0AbWyk5LczslVPyK/fpCEyuN/elLpCA23vWQP4/KUOfKawjSRC9NzzPLYNwtuDV0qAU6b6CSBGil9dZ8e1ZRb5HFwiAWEAyZpLij1ScRxV9jzlQBT6u0rvQyAuyog8UlmJFdxzeNkuyjPVaX43SMSrs5onwxtZf0IVTHHHkz/PiWAqKZpsnIGeKQaGSJQ/9QQlsMVAiMo1T1QcJ6UAynigAExVvU0QiQ+CUCgIAm+Up/GNeqY85W9W8UaZRLyoy+S+QA/U6dMmiBr7vESxoNdJgVPyUF3Bfmmhd8b6JFju75UHUmvqK6l9QBnH4FX4rAQEwdgpsSUoGMP610nqx8U0vbs8u4wwjeoo+gypt2FeOUSnuS9jytJys2+yg3SaX5YbDKZc7xJRPXSOt3r5jOUpLcJwqbwqt6rCvVVQVTlu9X3zlp4AikPKPHgyy5hDIwGrYhlofuqB8iHQMzAibxSdUfRKQXAJ7XBnS5HJMwXmFBtNZ314Us0VJR8mWHu0+67R2uQ35plCip/1RpkxMt4iBA2eHy/lO93NvOitd6110RUg5Kc81s1R+7AzAx2MIjIjjHcTQBX7ePXnpt4mDSphqX0IwGJ5Bs7tZ5r4jXp7ohcxgqbspRLgtEyeqbgsQMqFSIdw6LJs8koBtS96JVPQCcwfJePm1CMVaVjFe9KlyxYyHNGYqUUae5caNnoX6fOUQBS6sVjFkcZQe/ksmILepc5NlL3kpdIEuyQKikrQpHQ9GRsF3qiYRyodA/NCGa8SUALVwwTBKDCoBHqmXG6oZv48bfsq46NA56GhUMfWgIFJOt21W1ptwE3UvrhNNKzK/bWAamPZNwLboL4mkDLgs2bkc+v89kUdMA7KgV6zGw4L0GUYw10EmPBJ5GWewdjotW8pNa1X1FczuDqjrumjeBqf74dAn7brposRz6K55/Ka17wmPOtZzwq3b98OH/uxHxt+8id/cnT797znPeFLvuRLwlOe8pRw69at8Nt+228L3/d937f5gaVjxJ2haHmWue8kK8BKyyRrO/f4w4OYVJbpVumNZ2WQkgrOJ0xET5B9FjiFchJlJIkLZV9SXFweyzhany7LFMtomsnko7vRtFiFxYKofTSPFD6mg1HUN6WCxfLcKc/L2NnmW1QZHFre5wSG1CsBYbIrdD8ZF2PyCIlrnTvR8uxhrIx4Jnw+IfVaWJBVA121KDujHqrGC8ZWWrHBwXvlo/U1f2tHohbFD2l+QO/TKT5LmTgJr1L9BojcB88WAJUALN7eUP7a35A8Nw0UIWOgBhwLNQ9nwzxS+gJR+GLi3hzNLyfuPV0d8STJes8wih9R/IDmxx3YFM0vgqaZi96H9D4so6h++zYB7mnqcvC6aXW8CMPJIqxounUUhpM88e9bx2HQ8mM3l2U/pXXHbn6S6uM5lB3T8WkZzkWneZoWYXWclmVupllYHs/D8mQWVsdxWvJE1xh4Wcrpd55i4t44hThR+REBzTzJuuFoCCue0jrSZ0egC4+cfkv6j3Wa0P3SMuo2bANbExsJgdqOUxm4B8GDH+SCbX4J4mqi9Lh9iPMijeE6UY9NL1Rle+nxl0ZeoP41x6wJGMrzmPPQl7spUfcwmESLOSNBsXAs1b4l6rO4gOyHar8A8136m+qXK0Zf2+cAJs2+9cC+9NIQrrxcqmfq277t28LLXvay8NrXvpaV1Td8wzeEF7zgBeEtb3lLeOITn1hsf3p6Gn7/7//9vO47vuM7wtOe9rTwS7/0S+Gxj33sdidQCzLhl1lappU1lp0NlqWRUVrH1EuoWHKGseVKo4ac5TIDOTZspWvdWPHQKlTkGnKUP0MZy/uF2vK6eyDgQhor3z4VieXABiXbG6uPGwDsHkfVCGlPaPzcUYdu0oi0rIDV9S6C3wiox3V8Sp66op0C92xrIWeLBLwIlir0vhZodJ+J0TXoXcRcU5V8UdUgFUWIfKvcNMR+ZZIs93zqqKDCBSmrfLQJX8KUOrocvG5K3p4ZfgvyMfA7mr6ONP4ytlcbeDagwY1tQSpAb5Q22BAQwnupYCxVpvmleh09T2mBswrFz1DJS5qfXiIuV8fzVgLsiNd9sn5zZSPLsf0aRvsWfnwUl0Hjhm3c6PO6F51Ndxw5zUn7bbFcqOSqTqsoU9PgAqCS1ZV6LEAyyVRyORwLg1F4IT2x2SMZv4taj7wspnM28RAOjEFXr1x/cHrpeuimSwVTr371q8OLXvSi8Hmf93n8mxTX6173uvDN3/zN4eUvf3mxPZX/+q//evjxH//xcHx8zGVkOdxG1As1Aflrp3cUcEFjJN9EWtZv1H0b+SPO9W3k6cdGyTVGFixlJeCVDSsXjNqHVAcIMKGNlpQJnQ8CTZBIDiJZj3SwMWofBp2Ipx3LxVXvW+BqZOB0cdrhdp1qjOyXO8sYAtt2ooXKFUygCTt2RvNPiZdzxFLkO95jEgeG+42yRlDcV/VQSefHeqJMRwXmNjx+fAbSkcEw6OptAk+jBqFIuaSkzHgdqRxzSykEql23Hy814NuglD76raHN2VuVKHsUlIK9UznYRMwplSl+QvMjT5TMo1cKAk9A8BH0SmVqnwtKwc9+yJS/feeZ6nJjdBN7eRbzSOnjAgg0Qe8XWImGIhDFelF9wY13mqvOAAAVAChB8l1Zb0KVmzLJI5UAFdLuKoEkFCgh/c/T+fyy6LO0bQZmgw06IZ4npPU5PZfHhEokWgeasJMt+48ZgxTX0rMSgCo3ntpTAFRoSZWuwLqe+r0CV6PvDpwLLPu+iPY9qkZeoFziM9A6hkbQibyN+Wm2czR1GUvl6H9m+3SF66IG07YKqCrPAt4OMMwhlDO12XIFVAiAXBka9hpjd2vgqjD+dbkeYIoseW9+85vDK17xCi2bz+fh+c9/fnjTm95U3ed7v/d7w8d93McxleJ7vud7whOe8ITw2Z/92eHP/bk/FxaL1Ho6uXv3Lk8i73vf++JCzYJcgKU0NqK1TWWVAUhYDoBKNiwsM1Nect+Q1YIPqGIEvjiJKJVUXh0bhYkKRbEUuaPEzQ6gCcZESaPGHWtJxLsmap/Qwcylmgh+ORiBnSPNDzwXydsAuS6dB8K72dOyo/lJo2UAEQIoBFYV8GQbP9g+PZ7xdtutdc8bn2sLLNkB3tlSm+l/6ZlDVL+SyrLSuSbqTdQ+itKXqX6pPIGqmKDXB6ZIiq1xxfzMkgV3lYb2CsDiW57GP2k0PzraMEsJexcMlJDaJwl8dcwUR++zICqPmZrzoP+cqJcQW47aF2qUPk/30zFUe9ZYtfZqmzq6HLxuYoocg6kMlHLQvgSmYkOnekUT+U4RFwXURvfLYEjAlhpnzLJsA+OkcBuMxAfAiyL4qRFHxk/58OUFQPLjpLJew2AUGJVPEvVO1W96WwBMZQ+HA1NrOt1RvYuOwq51KhsAUEnnXG5+qx8gx/L9iIuUMcfIbGRbY8xFrx4iHwekdN+h2NaOU4PnYzxTmIwXwp4X9D0cwyv1pz7KJiiDx7jFE23tpUAqf64wpMAadHUMne4rCziWOwMo36fQ9fngur935O31vdmHXromuunSxky9+93vDsvlMjzpSU8y5fT7He94R3WfX/zFX2QKBe1HXPQv//IvD1/3dV8Xvuqrvqp5nFe96lXhMY95jE7PeMYz6hs6IEWN4WzXhz1iwTFTq7w2ue0KypbzRPnJZxm3PGWpR6w5yfqjDVbJBZf1BS8ZlQ00aGoRgm3l3Fu3pfYYkNpXINdUltelBqxVKzZQ2iuoHdQfp6wPH4Ut309r4S1/5aWnI9UUoX9fYP/YnoMikxpzP8vS+VAxAV0ivwsZYVpvVM064Z+MvzgkDYIuSXQ/yS+lEf0kFD5Q+nLEvxTAAvJSKSEV6aBg0cuKzLFOeD12biuWwX3JsKepy8HrJvUEqcEjRcYT702xvOkkNLtynVL1YLs85tJH33PrIdR5Nu4g1c8ad0xSXu89B3BmFQMYCNFwVCQeb+g3sHyJfjM6jssclV3bNX46Ba3MS2ZTOHqZ6axXtFGN0lZsEw5PHJDKkq/HMG5q19DQadVl0FO5TwKbVbZTFOHOr9TLGzSgE58FQPHmuqGGpPCQxaGdxqzs4163ss5D0ktDuPJypaL5rVYr5qT/zb/5N9na97znPS+8/e1vD1/7tV8bXvnKV1b3Iesicd/R+sdKSwJQJDER/FAqL6R5SemdHsRSkTnSxhO1xtjUlDpGMOuNBUjWO3d7qVCwLNMgdJkameSt4GJMykteCqD51ah7mRqWc0u1qH1M2NKEeeuiu5VzyRnFnWroTOdQ1ynYhOSXkqATq1Y0P5gSvUuXxSsFAShqtL6wBa2v9syL6welUYwhAE+jjV7lAk1gp6U2zgCCocQcnRB0AgJN5GAiQPPT3FIx8IR4ptg75ZL5YvAJuWR760RdZI8UzckbRbXTc450viMOda6eqBADUVCeqdNVDjwR59FrJZ4ppv0taYpeKaH55aATcRk9UTnPlASacBH9kAbY5cbIPnXT8mQe5keJ5ifNOns6Pa1HwqJv3hkxY22TJctQw3WcVAJ2CnjQSwWAKi2rNypF7uNjFdH3LJ2Py9EbJTQ/bZ/K5Ls6FgrrgOh82ROfqQDieQqebeHnel9wOd0aB3hE/RedXfY8JY8ibyfUvvwccVnrgS6FKbwg4TPY9Di+D4Jllf4I6pcxQ68td/QNE8IcjHsmPQca8pwBEPJISZ8kVMZxr71fWz4PE4BTb1S8Wfn9QYOe6/xVvFJ5SpoS+hzxUhI13fdVulwvMPX4xz+elc473/lOU06/n/zkJ1f3oShJxEdH2sRznvMcthYSNePk5KTYh6Iq0eSFPU9+gFLrRauBqJokQMW7uLFSsdWqVFsp130av2su9KqHiioXpULb1BISCsUr1ccgqgBQ2RMlSXgLMMXAC8ZJpfFT0ogJtc+HylaP1jogpfN0fyGCH7cRjr7H4IlAVAqnXQQZSOu1hQcA5RuuWeW32WcqkFrXoNWUmrf6eaAsz9BbgP2yWnptAmZcVhqMjJUy0fwSkJKIfpK814ybSmOjUsS+PG4qbWc8WJi01z1rR3kQD9IKovjRNhLynMdJJZofJ+2lJL0MoGSeAVWk+aXxU2681GoZKX4RRKXEvEjjayXqRfpfovhtMoZlkgAVZKc6uhy8buKod0eY2yzrldx+0HuWLXWbPFnfV8ttiqXrGZAFQIjrwHYF2x8FUyWAQtBUbKuUQFweRkOgK4DC5VAml8/UPaT0uZDZwLDQ27IRvc8XWmsqU/tSa8fNvEdP3IuWTgNdjKKwi+sAp7pNF2Tqi1QzEmNfJLT6Jc7oizRAPL4BtnLP0aPok/LaCH26XqCLAVC53+HnY7L1Y5Cx3EDtKwIcCeDSjw37GHCzE2uq2fcwx6yv3+uYqX3opWuimy6N5kfKhax3P/iDP2ise/SbuOc1+fiP//jwC7/wC7ydyM/93M+xIqspq41kDZDaSnwjgVOrvAKK0KqTLTsVIDVb00i1rEFpvXGPg7JBip/lJWNDBDzlVIdaklxeIQwWpceecDuFV279GRjdzbYpaPGxyeVwX2/hAdCUD2znWF7pyJjfG3Z01gkYsPRgNXxWVWju/cp14eDf3LnIHQeMzJgtfYaX7qM06nbF2Vc/KgTLVeOb0vdyst7BU/YwYl+N4uc8llifeTe0twcnB51Z0et5faT6mcSpexY77m/7qcvh6yaTzsLR/EwZB3OQ3E0bTItaHb4ef7xWGVICWxNSBbNnyUTsK1I4QIoQQ/1zXg1PA5TAEt4jhR3sIsw2dLZBv2WANU7vE31XbYmdDr76XcaKzKYty/ix6k0wY6vgHhZKGEAW7o7bufVmWIHTSQnqQkld+9j1E6W6KfQ98HcxhECWs97x69MaW1Z0gIpbt1cdtS+9NFwD3XSpND+iOLzwhS8MH/3RHx0+5mM+hsPPfuADH9AISp/7uZ/LIWaJW07yxV/8xeGbvumbwpd92ZeFL/3SLw0///M/H77ma74m/Kk/9ac2P7ij+Y2Jdp5qMkyzABbtx6yxr2EbusGbUurLUNHAb95WLHQkkLBQv05JvpvWq/UGE/FCAlfxTIk3is4xe6aE2mcjwOU8Drk8niZ4pkYkd3jTb03OC0BKc0hFOpjpMGs+qZDpfULpEg+V8TwJtS+7yQ3ND3JLaeME7vTSU1XpZFcaR3xf/DvRAtfYiSg8U7jOU/60XCy4lvqSqX3kjYI8U5JbCuh+MQhF9j7FoBORjBcnofUJtdNepoCl/EtUXA4+QVQ+nnPQiVirBJcQz5RG8BNv1CB5pWi+KHJLsVdqCVH8lkLxa3ijilxSWD6YHFN7zzPV5cboJsnHVLQlzKYA6h+Ub9RBKjq50KbwcqbtYTsS24z0TWLYcqT8Ke0uR+1T0CRAsdgWIvQBoCoi9GkdNvpebO8yRV11mgAm8UZJ+2YSuZaUL71FFRN+1SsFiXmjwa+h2DOcYB0jjqgr11LUxkiZ96dC44NtTH9F+iLwPOO2/lllA2wut0EnSDQCvxtyIL9DxfinpzbqshHPYVzOxrdiq7ip9lGkf5Jvluo6ZMnIzsaAh8uNYQjQRvj2wpT5OrtcLzD1mZ/5meFd73pX+Iqv+AqmQzz3uc8Nr3/963Xg7y//8i9zFCUR4pN///d/f3jpS18aPvIjP5KVGSkvipi0qfjB5BvLhvuuMVJAWc0q4wBUzeIjHWIpA7Ck9VaWhcKXLXJZAenYpwJMWX6yHQdlw2nnnEMumk46j/VAynYUSppfGb2Pj4KAC4GXiaRT5hOq0/Ugmp88TLeP4tOiPI1rqLnjpzRu3mDlOj/xWdvOj+8AWY+m6+BUFBsmQ8yUPjf5KH0wLmrm1pt3QJ8iXjj9yiAqvtGWwhkhWRw7xVMCVjRJhD+ZNEw6hkKHSH4SvY8j+AkdNAFuAdEy8TMbo/bVpl3blprsQxF2RXoldBMDKQBT7PlUw5+LzoVtyVRp6JVyWaL5hQa1D9sZmzeKy5CiB2W1MZsCkJTylwyBsmyi8kFodGMghLQduIzpPHKobE/7CtXljW8qKRS9vzI2Kj4gDqedjKi2vTsAQVvWmm0KIFXZtcnaUhzhABevg4BHaPA1gUGSec2xZCxAxmBIYLStUPv0lHC5IgISGQQrNK5vCGR2c2M8zU+P2LrnI/2Fog0wk41CLUAKbuf+ZF8AbQhXXi49AMWLX/xinmryIz/yI0UZ0Sx+4id+Ihys7ONNRaXmy2ogyu9Tc5mbxsk2ULWBuCWlDwdzxnm29OQGKVqA6IcfGCqNWj7PqaokNZXVVHsmgSsCKcwxpXO4n2jp0YNkD1VB56pZefxJtk5+W0XmQDMCKWQkesBV0Ppgn7yfey/MPmixhY4IKiUMIuFAE46N0kNUHjYqJXvp8pwzpQ9pfQyggMpHY6ji71SexlORNytOBLgaND/NM5ZCobs8YtH6V1oFUYFhpzchvjjtU/qYqRujm5TmR+8eF0BjmXJLSRuk4bWHLV8D0z5ITxYAFBjpBg+s6Df9gAAUfN5cBp4k75lyHqYCnHG9efxmrMOFNa/li2p5o4Rh4Y2GmNewBqw2uJ8cvp6AbuGYqoAmqZ+dHZBnqtlD37Ps4zi+36HlDV6700XN+nwdoJMyCJYN80XgMxM7QJzZ6MG6jQFPfuDAfgTDoq9Fpqq4wWrq13Mp0s/LPkxBB/TKdV/gR+vrY6YOBkxdmoj1eergFrfpxjLxXalS+GBux7eMWHrMb4iI41zrM694BPQkaheJeqNSgIlM4YN8URJ0opVHCgaDbpLPQT1QAoSca9x3jrkPi7999L7UWTYR/CBBaxnBD/IMMc0v0cBq3qaGB2o2VbH5ZXwnZEIrL8xz9KqS8hen3DmxUa+gI2ICikhuKaDzpQAUErFPcksZmp8Gpkj7Ac1PwZmCX8oplS4bOxRpq+iBotudc0sJfY/KiMLH0fzCPJzxcqT5RWpfiuZX0PuSh2q5iN4povlJXqnlnCl77JEylD4fZCLO55BTSqP5JYpfp/l12VaWt0KYUd5fBVPYUcqdqapXqqHGvNGlaF+kateJFWAUt4PcUj6kuQdNBmxZAFVsI8EjpH1DAMWeqbSPyxc1q+WLwhyIqtMsUEJDkXS81Rgolz/FU5G2EB2FjTc7qFBnp/AThmmRgBTvKbtfNKDa9jgtap++P21qn++b2N+e6mfZMVyF66PE54UUPxdIwgwziOeGgY/AJ7SW5ldE1ttQsoEXM2bmb1qPnvoiatiTGwsBJ0yS3sSaKCl90F+RNsKDra6aLkRuLJjyVBy2yhUvGWimXV7AhiWmWqVTeKahwm1qICpMB1LeC2W8EY6HbF3k0pCJN6LekLWpfTvcR6HsIb0v3oS0Oo2BEhAmliEFN67BKoCQj5JTRs2pAShrXSof407WIPOsncVYrMlGUZVgq7WuDEyB74rvfHgeuqPz6bgoDD4BFIzmMyWrtiRkzhGtJCeUgq5U40qpfZnmx94npfaJVwqn6KGKFMFM7xOKHwNsAdBJGakiw2S9CqLFA+USN/P6FIxizyNq90Ed3Dv1sMuFCAVsWC1mTLeVtit6Pqz1WTtlSVrlcSXUXwFV2hZw2awKsBRAOeBkDDwVYJUBUqTteUDG33+K4BcKYFXxQoE3yo/zFd0lhkC/bOl8FjBZ2ldsw1oSW6vkhsJ7KwEDeJWAqPxc4n45sh9UZvHNBYEqOYfRC2vsV1tfG35QnLZ590YsjCYnV1lv9j7VgVTWW3IW8WPxzzN7qvD57/lm12h8Arr9oWrfrZy+298YVpwRpXw40B+5IBC1L0r77BrophsLprygtx1Ki8ZyfUXj68w702hQRCxdbwRIablY7mAZwVMt07soI0fpo+EAAoQUNEGOIB+9L3qbkO7Vova1O9a1NiZ7pTJVLzggpcDKDPp0VC4FVR5Exd4CWniq83SsAkQhyKpdSKWRmKTMUDH5HRBImd9l58h4rXA7U2YHfok11wcQ0fxQbp2C66TohPqHzPE8Aqr9zBFQyd6ZzpcpfDFKXxwrVQNP52tBVfJY6jgp9FA6614BnonC54AT/k7zvSuufSjDa6CwboKsjkKYH0Wan+omiOoVO+kVe1+jkxZ3tMtF57gBoLTNoOXK+Clsd5Si50BRQeETYGWC4eSkuzmsOegsSd3A5wFBCTCFx6wBplC/pZuYPRYOOBlKmNVV+XbKTaBzjrojg5R0zdIRVtpfhlKcg8o/n+LBCZrapPOxheRLWX+kWWs5X4gF5Q48FX0Z55XS7azHUPoS8d7ZoCH+Gaqe0aEFuc9hqeZI/9uwjzeB0lexr8KHBEZgZdxUplpFFRBVp5yXQMrM9yX7AmlDuPJyc8GUWJXhIzLfE5hICg70bEOrTrMRmj4OKneuRwZuYsMkjQ8EnbADcTPI8lFxoos80rwwX9QsRXGLDZNLvjuR2if7FvfI3SgFUUjzE2+FeBV0eEpKyIvR/CC4AEbv42fpvRHgidCgA1IuEXOgvHSt1yfuXOvFTWh4agCq4mlCj5INMOHGH+hg76Gg+8UIWXmgtkTAUqAkFD+i8VGOKaD15aS9OXkvJ/BVqp9Q+zwAr38iETTJ5ap6YwDkI/idhRzB70yT9sZEvXdXRwykOGkv0f48xW/povjR+7JMUfyU2pc8UxjNTyh/nvqnlL9E7Ut0v9Bpfl12pfmdlDQ/EqHyqLSMOL5sLZhqACjUPdKuOGCl7clsjOYXj2ijAEIeRAVTNnG8oXfVovJJTrxifC+ZXpyHXT3lQk1PlzvSu6yBKfE4YXNPp6wabhDAVKJZBFEMlwQzuYOqcfcimxGsvxjrVdnWL8vzkv09YHJTnd6XpwiGkT2TAXFezr+RGcNa3/VnbGCsbSL4rZf8Dkh6DWvw1e08YwaGKzCgku9aDbY26BVS/Owy9EUctU/LoB3R6MRd9i43FkzJN6wNiGtY8IUTy0f+BPf/Nha8Y3NwUWw1K0+rgQKrWovq5xoq24DlxiYHHrBlcTu3DvbFe+evZ/Re6B8U8EQ50IXoIzZYeNOcucyHIU2c9cIaJOWmnjp48pYhU5+3ME259grI1vV6adaSPKbMDJ3PrcsKEakSNsiEDTgRn2+M3idV2Gh9+TAYMqR+rb483y7rmUJPo1L+BghAIZ6r5LGKgSpswIkIwO0YO+ttzMvKP3f0ztZUvg97biN6AIobIxKAQpo2P+7Btym6TbWydhtSLa8YcdYbdbJXyXuhpBNtx1gBjQ/oetp4mLFReTkaBrO+sW2VNwZmHaeeKfWYVyh/kx8OhMc2wCk9A6QspwdYBqVID6Y6tOASZcpNsDi+vk7BOPRXNj2W11VJ72AfxYM51UWubhymgL24nW9+5Tsc6h03uwxpXmK56/RVAkuYfkZ5MHtOlVEhuj+e9z6kB6BQubFgSsc61DqxrV6erk+moxGZ5I3Sb8y7uf22DmRJPo0GqKqNjeJNjEeqZs2zyyZHFK5HzxNQvuRcFWiJtcjdR9VHeO913FOm6fG2MmYGc0pJHqm0reksm3xS+BsaKc0rhb+jxQc70diA1TvM9lHiKzGCh+x7IkrCv4MZ++X5CFiqBalAS6/+hrwtNhIW5hNz1j1D7fOBJsgjWdL/ItVPr6p63QKQk6HXlpODJ0XnE5qejJcizxSVkxfqTLxUKfgEeZ44RPqqnLieVcwrlcdL5QAkOdAE0Pz8mCktz3mlovcSfxP9b99gag9K8JA6bl2asloMYXUEwQmMhbpuoLkwMCWVVzzi1TLyMAVL9zMUPvU8AUCScl2PQQhAX3HQCQRTWTcJdU/BkrIp3JjedFOQKjalGydNlN5mfjYZKYkhisthQw0+kcZQmbFSWmetwzHhhEyHfM328oLs0mnFd0PqdHoqn47vn+DkwJCZ4/PKL7z1JsUj2OcK43vTuVkQlcG1eQeqN68xWg7Y22p+hBQtvJz6D3nMtl3GOrT/kSt0IMqBqjBm1IXgFLX6fN/lkPTSNdFNNxZMReoWWD3CeouLaY+k9Rh7M2cTAZSUa8PkLDoN0OS5xq0AE9phdqCIylqJ7SS/kEbwAwA1Ru3DQBM+JKncW8nVMDY+ijq7JELhU4+Ci+AX8wUJtS8lYJVtICmvTdCbwbQ2MCaan5Qhza/0RBReiXwhxhS5rvEamsqq7LhIwAnM3VKN4CedGJOsF8YpSH4xoclICGGh+KXnq5Q/TdQrUwZVlKSXy9hblQKUr6H2USkBItqG59r5yKHuGfykuQAoE81vOOKJaX4pMa8k7ZVIfhrRb0kR/DLFj6h9/K4IxU9AlCTpTZS+uU/UK5H8IFHvXBP4JiAldL8uXbaQ4Vai+ukgUNeGQGdrxF5ht619hIbu5zrGNVBVo/YV5RlMoZ6ScVK5PLc90ZiTL1Kofax3XERZXOYmLukm1WU1AOVAVGh4MJq3UDrF0LTT9c5TfL5M84vQiE5Zuwd8AxNcIg+WhPlzz8wAtYlighOk29vYcPfOqtFNtu/iDX2ToveBJ9L2WxBcIagCIJ2Oj8/XjItDSl+6MQbLuY/JvwdC46zdBB+dT6GaS8Mi/ZPgjcNK65Mcl3VmRDq1TOnT8bvW0CvBkky/pBLND8hH1wK4HKLcWDClbYw3Ock3hN+T+7Z2bZssl9qDpTr4issOZJk6ykGcWI4WHS7G63GAMtP4cp2Guueofb6+dUa22r0Tyw7PYJ7HTGGgCZszaiisPLmh0gZLNnS/a7Q9uW355Pz+DjzhOn9R274otftZezdEYVW2tZ2ioQHyLS8Ro+/JO2Osf47OZwf9OronWBS9ANQ0vxRUI73P0/1MYAoXpALofDlcfplXyhy/asHLNxVuT/ncdVmSM0MYyX3KPpRgV6JXQtT4MdbW8CddaBKwwlSkZdWxTGkLoLB9UdCUQRECJ80NJXUoRc9R91SnuI6z61CvY01IHQqs1IsBY3RxW+hISyd7vWRanwxiikEnkrcNaRYQD50OMxnbbNKhuIxvGIET/h5jeG3QH5hybDXQwtwAJjO0ID/7OI9n7k9jE0Ada2iU1/S+rst9h7ydBcFVdVHrV9Tof2Mn53XGRbw7+wJnQ7jycnPBlCD91JBpo5Dadx382QBURryVxpXhdmrNw228VcevC6CM0LojyseVZ2WEPGMb7ahm5ROvRI7gZ+l8WWHBKUMnm3+akLLTvhAFSS3PlFL98rw2/kWjtBV0v1rQCfJAiOJDa4+ExoY8U2LtQbClJw7YFXHJFGm8I7isXim46eqBgt9I5TPrNAhFDkBhc0tJYsv8LuTgEwMEnUhBJiDvlASfMNS+FuCCcXby0DlvTQoTLPQXBkwJIEVqH9H5FoVnSuh+cYr5o85kLlOi/ZE3SgNPrMQjNY8UPw4wkXKHQQ6pYtkEoBBKH+aZspQ/jaixL+lg6sbI6mQIsxNKD1Ax7nhjUK2CdWC+pq/kINnQnrfFMtBDhrpXWc5gCSPJugATwpDgpG2xrbBhzeO2rIMkIFJDN1m6l+gpNPAAkGt8DNjljjaSqPjjo4hASvsCq9TecnsVx06t0r2vp1qZLmKfKQunf8cwvKst+PxH+jiG8hnWGPUM2EIjr/VY6TtiEizHEylBdAmeMVqwHXoQqgBb5jUvZSqZdl+xz5IuOP7247XTkaqUv3hT64EnnIGvYvjNyxCoorGNZ9J0mt/FyM0FU+4lMMYhZ2yaalkZoyOrRU8OhvPUUKPiysuNABOFZQ/Ajdl22tioKrWv0iB5+kQ8DzkftApNu21tal+m69XAlAdQsaGCCUNfK82v3gDlfEESGhsaHU8H9I0TPladbxkau0Xvk3USvlg7KNAOF+ApUfygXMdJQdJeDS1cAKkYla8WvY+pfbIcMHofBKwogJVVVfnzs14iDl2eAklwBD8CSLy84HUyNorofxEwxbFQDLISzU/HTuF4qUTvYzDFQCq+EzlyH0T0w2h9OiVKX5pbECXrE71PgFWXLlvIcDwwoPLW6djWuGgGlddsLa3Yd4Rlnhoz3yHGzrDmjlILkhvDq53heioObW+k85yOqfqmGKObjTFSjmkafMcZQZQcu27oa9wbjMaWlCrRvmSZPmvpK8TUFEl3JsqfGIV4DOW2gGrUIrthVXuppQ6kCnqf6auMTbVxUnldfDesZ8mDIQ+cNeBII4KfHbtd0j23JRMoh0cTN7sIxAl0CZAS0CR0Pzvl/ocYdu13X4IlTN+BwxMMzS9F8zP9mS57l5sLptLLpYpDXjBFUY3lrcWBJXMiFUsP7iMn6+vz5S1qn2kEHQAao/bhKQF9C7/GvH/l9NeINEKhNtdloGWhyxyi+8l+GGoUrT1oCbIcZQeU8BaZDoyz8Pl97S2Zdh8Mei83NtV5kJ3mhfUYwTmUadhi8z7Z+r0FV94dnSOQxsG+qKwMxW+dpE4HXqvLJ4YwTOh84rUikGUofwqyMVw+8thRsVkF5sGxyTSfNsbPyCo1zA4tF7Evc92eoyZdg4hJN0Ikip1pt+T1irnNxp6pvIZVMd/90AwoZvQOdp4NQyKfr7QBQvMzHocaK8JH31PjnbAjKmAKPFMZTOVtMrWvAabcNZc3LrVGccM01ikHlMjtVVyiY1N7YspMm5b28G39oYp/laCpXIvQm++PFJT7202Qsgf9C1DIaLTNO8J4ONefqZ2G9om27tJhH6R2NW652j+o8PJ9X8L9NiCqdlq1x+P6MBfyDu5DL10T3XRzwVTSHso7hwB9vo+rlD8tGPkSK99U9T2ZknwXe6ZrAk1oOQCoerAJ7yrHABM5maGn9hk3uwFf0vle/6UWcHCM2lcEm/D5pHIACs4tReWQS0r7uErtm5V5ozSKX+5A20ATif4FnW20ClUbN9PRGbl4eD90kwo4MkEnWlG0ClpfjuCXg1PIOAeJ5JeiZqVJPFLRGxU9UzqZfFKJ2se+oxx0QoNPJG+VWpKTvTaCnkjji/0tSc4roYTjO8AR/NJ7EQNQRDqfUPskhxR5pmLQiRiAQuh/5IUy+aVSbikKPkEeKQ06kQJPhGWi+qknqpJXqpZnioNQJC8U55VaRc/UMuea2qfsg56xV3pHl4uTk1UIt4hDpj1Z0xkqwyo7Wfeca4Cq6HWW5QJcdL10Sh2FTwMEiM5IjAe/7AMbZereqgBIGjEWIoxaI5C0N+kGVMfQ1G+H2kIkmW7STTFTVWyfJFYVzTXwBF2usv5yoIl4LPEqiL8KDbfRa9UOdIAn5+Y7S6IqouHQb+EVmns3qnrKbWeT9ZbsGj9eDpe1j6LeTKT0QV+l4ZnCvoqAMNUws2nvRPvuYUAJ9EplO1q2sWFfBKmAsm1OEl/zPI32OSA6sQxBaAWd8PXtUw/sq77ZNdBNNxhMCSiygKo2ZsoYlia0fyytBmltRD9P92v9dhQ/HMCbtkOqRFhD7YsAynofVGFVIiPh4M0plh6JZuPLagBKQ6EXHgcHpoD+J42TNlwQwS+7zyt85ASgTGMDlD8dPyW6ocJBlnK0Avly9zaMvjc1wBRRbQm0cJ1ajgFIcY4XBFVK84OkmECPEEBlwpzXkvJqNMcyJLodP5WumZ5JysGSrz9+TDjqTgNKJCAVI/nFyQCrRPmLy3GsFE8ErGQZxktppEem+EWanwBqieTXCoNukvgCxU/ofELzSy6xPHXpsoXMjlch0FT1TPEWqVz/bN7Z9uCJl8Gaj0a99Bt1iYIVAFjoadJOLFDzaNt5lVZuaVtkwFFDH1K2BHhBYBujrxDs6WmPj4Th5jldsNL5QM3HNimBpjTnPisvRz3F94Dbt3zbUtdCjbTGIFucwYY9+l2keR7pbGpAW/bz9cg++NsZfk2ZAVX2d2Y6xBrLvobrgyAzQrfNz1rnsza1b1Px7Nr4+SmaVNOyHkW3FxZN/pazgcQHlRCgWx+WgP0T7ItUPVm+X6IPq8tFiDCgb5x4q0zxbTmvwl6aO9/Q1JbxZDxcB6Ckm9UaP22U8oXWzl8UUm5o8GusAMLKqW4ixXfvLK3WCIfgKl6BjewHgzmrGcTrjYy38sRb4KxC7gq1X+Hra17lhuIBEpbJ6bllG6mv8Q65KYJ3tMiB5c7l90DlJCS52uFwm0nvRY727EZUgafSU/vcb03Om7xYfirH17kokIX1Dz2U5fuRyyPFKq9LlKv0Ausy55PZs9Ya9jR1OXihYAzqKWbP8Sp7jxfyexVmvJwmXB6bFrCt7rMyx4zbwDks7Lnkc5Pl6MGWoDXxdxp3iV5uSa8gZWKcUS+4lPsgN2kyAXEqAXDEmIOTXw/5E9UQZDrs6dsVL4m0h6YzjvoVdKg8wI0UZGNc1T34VlXVVfVH/QSqekctjVBzsw8D25tDQhncZ/yt9xh1F9Zh9nP6ytW5ieDZohdK1+t4Ked9Sjott72z8ah8rp8SL9ON73b90rydLastG0/VoemlYfNDv+Y1rwnPetazwu3bt8PHfuzHhp/8yZ8Mlyk32jPFRhp9ye3TNIMSZfVst4ACpnwdtc80SNOofd5CSOuRooc0CbQYZmqfDTeKjZIqlHReuelo31+hE4TKAE2p2SffJTGdYvIopM5wDH0dI/TFoBOuk7yy0fuidylH8NMkrGl9MWATthELEHqmCmpf0VhBp1rWT3hHsI31yxh0wuSWAvBloviZSfJKpZNP3qkYxS/T+2Ikv9QxQkqfdoTQM4U5pvJv8UStu1jxUObB23Z81Lkk52XPE9H5iMIXc0phoAkuT1Q+2kfySYlnSuh9S5dbij1S57MwO0+eKV5uRO5TCl+ZW0rLJRBF8kzF5VUINHXpsoUcnZyHxa0zk6cmLqQmx1P79LOboqB8xxd+GiOdtd4byrjomLSxDwYQ9YWliUuEPksft3Q+2c94odCoUw00ka8rJ45319W+C1GvMOUubr1KbiS7X86Fl7sLccwUG2Kks76x0dVCCd9JvxdSPVzFI9U28vl+S8vQl2nmZYCsclnH2bl3Cel9rWEL9h3dldoH/Qy96KSvTOqW6MEsqH06jtsNP3AR/NSolyIIxz5Kg+ZHegvLajS/FHRC+zS6fAEJ5S9Bvu3bvi287GUvC6997WsZSH3DN3xDeMELXhDe8pa3hCc+8YlXwzP1whe+MLzxjW8M10LWvFOzvVTvGqZWeHRYX+7ToPb5bXjZDsq1Efwc+MLoa2Z8lY3Uh4ozn6YFWc0bAA0OF5kgA37KoMqXRWAF6x2QCpVlDYOuEzRa6beGPq94JbARM56KdG2t7f1jn/6upGXtO+UbbgNKOO/UrB7Bz2wvkfxYqaX3J9EGLbAGKqhaeBOtT567dID0PYCoSWuuMU7yrGisG3qboscpRvQTWh/9jlQ+nRL9TyiAeV0cQ3dOiZyHBKIGoPgh9TPR+hRgS9JeB6wNqDY0P4zol4FU0qgXk2uqy43QTUfHq7A4wmkZp6I8TcerMD+iaTlhWoV5pZ45Lh+vwhEc++g4HZ+mRVwXpyVPxzytwtFiGY4X6Tcvr9K6+PvETbT+ZC7bwjTP63i9bDMvp6M0Hc9X4WhWTlUPVyWlgwA0pCkLnZABnHbU5SllMDcb43R7SWjMsjF27WnsUaZS+4TpIOWqUiteKVCayJjJICrrlbzsgiDB/ff9GW/4xVP11L7tx0jBbzhKBlUZMHnEad4KBFFSId+ikcBYa/ofrX1w3zhJLsRw5eXVr351eNGLXhQ+7/M+L3z4h384g6r7778/fPM3f/PV8Uy9973vDc9//vPDh3zIh/CFkAJ72tOeFq6siMeJrVFpfAmW71y5L6lYBrEBwnVirSmshnY/bGzwSAVfuMJPR4BUHN7XN3KV4meYEm7WROxTgJWOYAAVAC8PwMAzVc/X4BsXC6SqfGNtCMt7UgAlfIz8GCa2UC0FBcAHfxtQhFY/B5YYSNXqwgkH45poWDiwF9+PHJREOxt+v4IKaO9DLhXTgn1TMDhFBlYZHCl9L4EtBU06AZBiz6VM6R1KAFzeKwVRBlxna56Gxod8UaKIMo1PFFPmLObfUL5HQXvJLnVcZ7kuuomAwXyxNJ4pbXpw/BRI4a0aEduuYznXlA1kEIaa18Nykd+pkvNH2occfa+dFyp7oEovFR5b2pq6F2r9B4JjovgzVcNV/E1eKtlKgkqozk19BC6XsVD76SisO+k0d53wTQx32OxOaUhmI8tZ6ZX9GL+MfQzotxjKpB4jM19kpVAus7GuBKyqe6AOG8VxP40xBmmFpj+vh+1qdHLz/MwO0E9Jij527WxfxuusvA+Csno/ZRdD70XrJRJ55O973/sCyq1bt3hCOT09DW9+85vDK17xCi2bz+fc9r/pTW8KlyUbe6a++7u/O7z97W8PX/zFX8yuNuIsfvInf3L4ju/4jnB2dhauinjk7stZCo21yQEqk5TjNmFskCYAHs3FAB4mnWeThR2gmTvDNQ+V54hbOkVuiMRCxL+resMBHhzjUkuwC+vIe8DBBpL3IHoUoodBlletiSO00Zw6zZI7KFL9lN4nUfucdwE9E3nKngm7LTRmuOwBm3t/pjYy9Sh+kd4nniYNItGk9OUAEzmiX0rQq9NYFD9JyCvjEspxC0c4B49VbayVBUwCopNXyUyR2se5oUIMKEGUvhhc4oiXYwS/OPH61RFPd2Vaxt+ny7TNch7OlotI8eMpviscwQ8mG71vxjQ+mYTGh8s0j+td0l6k+GkAiutD8zs0bvp11033HZ+G+0/Owv0nND8N9986DfednPEkvx+4RfOzcB9NtI62kd+jU6rLlVNd8Xg0l2PlsgdO0jFprtOZ+30aHuBzj/MHj+O8OR3BXKezcP/RWbiPpgVOpzy/nX7frky3FufFdEKTerJW6s1azGiqRSqNlGUTTAcNSdBzzSDyIqTR8U7LSkSs6RhfVut7rDm0VlUZqlCk2PD9FgmUJEwI0w8CSl+hhypBJRho53Ix7Hm9g+UmB5nr0/ipdQMMTU+NFeCJAsMuDktosW2K8brCmoHhBibacPpt+xmJRVPJhVl4r0Q/yfoY0WuS8/Qy5RnPeEZ4zGMeo9OrXvWqYpt3v/vdYblchic96UmmnH6/4x3vCFcqAMUTnvAE5iv+63/9r8M//+f/PHzoh35o+JzP+Zzw1Kc+Nbz0pS8NP//zPx+ulFS8Emu330Wqlh6/Dge0Qu8crEKmPfO5NYCmpx4pDBZg8lBl65CpA6yV/rTXiUl8qNZVF2hAw59jh9s2VDakaNlYCdIgENW0/rjGqO6ZQhMlACa0vnhO/AjY3tha41NPeADeWBavFB/eKSzjmYKT0mde8UJ5K3MeR1d6pnhdAaVr7wk++8pzNMA7epUkRLoJNpE8VrqNo/dxOc8T2MYEzhrRMb0HBiSX3kxUWvZ9SS+ro/UVnql9aywzOG6HaUtu+itf+crwUz/1U+GjPuqjmJv+a7/2a+EQ5TropiOixwlNjmh1iebGlLaFTJlWF7ePv9dPK6g/T1hnrJeOm7fldYl+F48VgYmh5ikdL9Xv6HmZkgdlZJyp0vYcdU+Xl9VE4uN0vjzP1GXfKUedaMdold589HqI7PF7N/prk2+2vq05s9lmQGrStp5R4cEWz7My9d4oY72u3HPjbfJeLTeGD6MCWupg3bbdvl9gTta+jMwr45/AI1XcJNPHQO8i3kAHkEEnFX0VvG218dthZCz3voHUvvTSEK/9bW97GzMMZELv06HLTgEofvVXfzW84Q1v4GmxWIRP+ZRPCT/90z/NHMa/+lf/KiuvQ5Y01jQLvWgztywvn/v6cFVZ8YRy/aJrPXDrneJVtd65GySMACvuUzkV05JYhZAbuCz0HXLODCFq6f1Id2CYRu2TunI5eqogNDp2tgV4YRJWaMB8g2YS9ho6l+8w24aq5llqjofCdfqoNqR1eYXlgBLfI/VQYTAK2N6NjaqNkzLLyTOFodAVHM1Hol5hVKxifNQYgMJ3obxw1AkRNHF2KvZURSBVCY2e5hSQQoGUeDDTMgewYG9nyj+mQAo9lfmdmE0Oh14LjQ4gyo2X2vsg330owmE3bjoJcdNf97rXMTf95S9/eThUucq6iTwvdM7yuKTtC76/BPS/3PlbLyUQsFS+UAALZCfUA0zIfhrKPDSCBrhy3E+OE88HTTD22P7c9X4UyyncedJVMTKorFvlTrGqA/pHDWs2PLJOVWzgOwcbCFjKRP/ZSLSNzvAG4rsTm+9c+V3opopBTw5aGPykPA9VUIBkAphYLx+GR+dNIGR6Pj37HkXZvc1tRhbWvgg8PzUlWs9VfKZjww/qxrs8L8dxF32V1tze9gJ8eSbW7jdsTwBtiLOHH36YpzF5/OMfz+3jO9/5TlNOv5/85CeHKwOmiC7xvd/7veFbvuVbwg/8wA+Ej/zIjwwveclLwmd/9mfrTfiu7/qu8Pmf//kHrbDc1xKj9wU3dmrAcliu/eZKcoOS0/dhQzTi2nAc49zo5Dq0QWpZZjzXPKGDrPxsE4C/swWocavghvBSRFnltqg09Dd4JcAjxUl3U0NT5pMCF3qK0CeJejWaX4rsFzSCX0zAyiK5gwac++V0SRAdRzvQzoXeBFYeSE1sWIxRyizPXFAJAFJC54OAEkOxDBH8gO4Xg00kJUa/BUQlILVIlt9I9YOwxSbnlCTszSDLeLaq7056NgggdYrPguh97HFiyl+MyCeR+zivFCTnFYofLy9TZD/aNlH8VilBL9H7Ig005ZQSal9aZnqfJt91wAmi9xGlj2l9SvfDaH4RNPkcU+qxOlCZwks/ZG76dddNRJc7PoFEn94whWNMC5PYFPGgBOlqtoOKoMeMo4LxLZyPMG3HENAEN4LtedvYnsS6S52Egm1KCSXLK8oqHcCnGKd4+CNQ0NMUR0Dlsqy54xzrjMl2UwQ/HTM19Y5PHEqJAHm4hE6t000GNGEfpVZm1kP/w9QnwxHyumLoATAieLfGODsL6q3HcKvrdlH6BPAqkFIWDfZVwOArQwykLs6F6TxYEBQr9i8kv6HQ/mz0vbwtjKXCKMOV/onp2+hYX0sfvMpycnISnve854Uf/MEfDJ/+6Z/OZavVin+/+MUvvjpg6ilPeQqf+Gd91mcxd/65z31usc3v/b2/Nzz2sY8NBy3yYu1gbNLvdtP9jElw/f662g/ucvWgVU9+1Kt2QM9Y/9z6xt7jnghoUGAZVaIJGwoNDrKZMxiL+5qx/VifLIMbvTBWVYCQseQ4PVG9TSD+Vu1kFZTTr9xVaYP1PTGAvXJSaEFUhWaXxfpn6X2+DLcD0K10i/p9aQkCKrHyGqANAKsYc4c5pmSsnXizYBtN9oxezOAsgRV+eQmUswLy+0gwClFUyO2IwPqCovnto7M0ZF46ClH4/uJf/IsbcdN/9md/NhyaXBfdJPS32DSK98S1nU3T12ZiPDD+GwfAoyALgJM2NwCOyNhSgCyoQ9YjSKPyON7Ag6lNOsfR86RAU9rIGEMmESko9Hn6vskoyG1S+tYTOBLtpoEmnLaTa97uU3QWpcnrNqx7l10b1RjjcG0fi3rLuSy64Qnti819klx9flfLdzDsKK2b4J9L1iU6zMBtq14p2UdeSNMXWUO7hm2rOgq3wePA72p3ztvzd5V9gfhhs82Jyk0Bhj76oz86fMzHfAyHRv/ABz6gDIorAaa+/uu/PnzGZ3wGD0ZuCSmrt771reEqiKH6bQOo1h4gV70WRGFn02yL46ccqIIGB+uw66GzZ1zpVrgR4GO11EWkTUSPXFTyWI1+40BJyZQ+2T95nnBclM8tBZ1hpmpBBzlbdyCfVLIGYTS2uF2y6ED0tnLMlMsk7ixD3htV5S/jxdfE3WvAhwXNDyl9Bhy5ZaHuFR4rsRZqWTrh5K0SjxR7L2HAr6f3aR6p4L1TNlx69kr5Ab3SZSI1nD8C+cTQMiz0PapVglHEsuil0gAVmGeK80lRLilajoFMziWISfJcikdqSJ4oDUaSPE/8rMVDJR6pFrWPPVLifUpAKtH8Iu1vVVD99in7oGfI/sRLRypFzSt1FeW66Kb756fh+Ais4kiAA+8GemC2EvQ4gU4wniIARYUOKbxYEIkPaVoAqDQfnQdvUE8+lpVhjSeHwRQ7kKRtiTVHfZZaHdqeFRh9xOn+RacTt50KsBKgikwVOfrEe51OSGl8fp0x8vgxNe5ihwnLm0oLME3AE9agVxp04zyXiwdK+i2xb5MVqQ117gx7zuAXau+c8V46DysYAcYkewwR3mUjH+e/VEMvznMfx+aUQuqme8arinHP5LxMy3QGLuos9kGqQSfS+6AGv1SHAWb5Avci+6INzjas4zM/8zPDu971rvAVX/EVHHSCDGevf/3rC8PfQYMpGsx7HcRhldiQSgMo44F2PQCaYLyLvGXp8dQ+LHdWGGxk5EtpWfJ8oIkxGVcbmXJSuQoDoBBc+eS8NtBEAlMEnNhlK0l5heInSXnz+JeYLwgi9yVgFRuP1GEWIJXKMCGvuNY10ECrcfKNGP5WrTl+P9e/G6kmBki5vAaozJgpjJrENL+cmDdH7ov5pHSsVKL1RUBVp/FJDhZN3KtRrlIUP9nHjaXy7wE9U3rv4ugEO1Ijepni82bwlLxMTOtLYCrS/GxyXlnmpL64TEl6lwKmEr2PgVSO4oeR+yJwkt8WNMUIfhKpL4S55JVKgKoEV0MIRPWjDhqDqgSsDlSm8NIPmZt+3XXTg0d3w8lRNEJoZ63SIsck57tY/+rUKARSkc4btzXboFcAgBNS/mqAq9ZWjHmgmHIPnVh3+jHqqQLLuAeFN9cIsrBM/2KC3nRVYkiVcVPUXM6G2G5Jm5U7BRPvqRgK9Q4X+qGFjXiuisCDqwrQ8pXsIFUgJXpHeuFo9CvKfNAJR/Nz8xJElWWRDmpp5BpGH/s+jvpXA1Ktp9f6tqSvUgbBagfDwjyXoUjfAsAKjbyG9peDJGU6H9D7an2RWmJfF3G46dm64vLiF7/4Uml9ew1AcaVFXir5jqa2l5u0q3uB5bDOHLfcx5+WACfboAwbXp94F6aJHyOFFh6xyHlush9HpYM5GxnDsa7yxOLJGwsMNiTwu2p8q7jBm497i4bJbJ6NzRk8iWLzurMGqiy2S3X6UahWCRoKaDPykfM4+YHBucswcp3y3oifE7dNHkjoJCGNrxb5UZP66roarS97L01QPXeTamPfvHWPzwoofXZfKNMXPVH/9KHsWWPtQwkO14Obft1FotZZS3ilw8fAYIcDGe8QFo+PZTJtBHoJHHjK5hNHG6y8iLW8UXClqR2I2+gZSz9UqX0JeslwXu3vxx92OVL9UoSlarsv5573qp0Z3JQScraXN/IoTtZI20nrNMeajJF9pGzWGA9erxlNbYWtMf8GRY62RqzXU9D96VWf47rxbEYJT6hPFxBI1fURrk94s0TcDT2GWDarfPimK3Xt9e3ZFzgbwpWXmwumRByg0vZVOrVuef9Aqt0A5WWY1ZQOerD0ouJ87ekKH5+vLW8vlL/4Y7wWPCOfYBIB0lDxUlnPFASeEM+TWHg0xHU8H/FMKc1PAk0QfYvEu86TxSaHuwb6n6EHwgBN8VpBY6XzQo02bogUtXSp0Qguch94nkwE0dTiWs9UovylIBRaDkEnhOY3n6/U8hfpfBKIInum0EMlHqiikwUdptrli1U23kLsWqFnKueZkgAU6plaUb6p0jN1uop5yZDmd57KODhJ8kiRZ6rqlWrR+yTQBAShyIEnctCJGGQieqCK3FI8Cnn/SXsvA0wdKjf9ussDR3fCrUX05461rxWYs7EYf3El5Dd6nfI+2GED67+J8gnbGmDlrwh1HhjJ/FkKtZx3BwpW8oXlABKS3DsqxaUBQtSQ0li0WdyLI/3FYEqkOmKzmtq4CWBn8HMc/yveqYrhsOwo1zrazloGy9t0QSZhN4c+oq4pgdBQ9OKzTpJlG3RCzyJ7PMdyX1byYPrxURlEOSDvvJxjQMr3jixbpmTStIJkxUATaMyTgBJ1AJWDSdS9TvnltkEnpD+Cv9cGyGp5tPYlHUypdDBVAVQKXirjqbhh3heoKqw7aJrwpod2HTW7lTRa699SIVKsDxM6XofskwdeSlAAEmmEWNmlRkQapzCF2ieUPuElGzAFDUtyrRccZBPlJnWkKw2OWW65y0Xj+0AX6xSdA0xxOXH284OLvzFCHwIujOCnwMsBK55jst7UIXI0P4rgp9H8NBdLAlW0ThNYRh9SrNrSd1oSVWC8OdjFko5F7PAImCIAFfNICbUvj49KcyqXZQJQDKZiGYdHpwh+9K5IBL+lT9psI/iNjpPCZL1C63PJeU3UPj9W6iICUFySHCI3/brLg/PTCpjKyzuNk2qIgJ5QA0NeA+DYp1EPk0KYybBPQJMpU72S7oFQ+zgfXQx9Hocy0vhaohbnBpP+kX0tHz2Cr0QoB0pfvDDTSZ9wyibQDepM1Z15DI0ZS1zcJfuczQpY5jPcd4cYDys6pdb/8H0RX1YALIjyqjS/dUDK0vl41yJyX/ZQZV3kEiqPXKoa9TBAFrAdFHug0beavsWPl4r9kbhPyaiJ47Pd+CeXy9CDIwOEHJCq91ts9L4qkLoequngpIOpQ5DZ9qtnW9bZwoOx8Re+/DSljQoeLYeCRE1uBt/PBGsQrq81RKKUatpIlYyekDXH5X6C2652MVtK6241q2x4q4rTQ5Dl9vO/rSUwW/KyErMA3Fr0/LIdG6GqZ+1oUczvgucKY+Vg0pDFmqQ3lbsIfsZq6IOVwPg7eU/Gxrx5hdMC1qZMLr2w8CXFnrVw2LfsY6DvtvsfGjf9ugtR/I5mEa54GSfX7ia19AY1Wh62C+XZlcBpk6h88TsuzXtiO+NlafQ4El8CbEx5THqLGSZJj+lozQyUsHYcHj1rakf0w5XASRpm7aQbENzo3u/5Ic72vnP9BIucUpX9Cx1hwFWt7hKs412reUd53QYXXb7BlW0UCOeXTZ8x/EaTg30HsiG57Gs4EGyWYdyUroPOQAsI+WWwfnubxsjjupIBKA5RbjSYgnb0iokNT71dFclzwDeh0hpOMMzlviR6prK1x3ij1GJjvVXRG2U9U0Ln02ATo9Q+cIdDol67DAEmMFIOLJsAFLScLrDpQp9yi+Vewn0dWvmkpNx5mDhSn3ikkM7nAlBkal/yRlH1mmOKpuyF0km8U+KZgmUTuS95qzCBZ+t6+flGbVpY0BPk4PkyeaDot+SToveBKX2J5kd5o3KeqeiFotxSNMXcUinoBNH8aH6ekvRS0AnIJxXnLoKfLudgExp4AvJJqYdKKX4ryCtF0cGQ9pepfgPN9ynrQulOraPLwcuDizvhvsW5hvpGmUDc3lpqgKceoKLeAFoI4corp22CLUgZN+cWkqGRJRQ5oiI0isFuYntC1D7WXylqXyzPgSXmvH/0tK8mdASkn5qNfpjGI7drtjNdejH0mnFw7NiYGt0GT2TEW7WplMg5VVvpfUuUWP2Ny+lkcI7BrjDNRtUjZSPKquGvllfTAfnskWqLB7XoNVRmDHo+Ew1dx+ua55i8VJ49I882LWM+KTOEQPoXEhBLWDKNwFiF50r3T2WYTwr7M77vAuV7zTO1D710TXTTjQZThQHqisjUfFBN0eiFGOoc7oe82GPmggaAsgEosifCj5NSACWUP6XzlWOjVAH5BiqdRwQ/ELkvtBqf2dqIN6bx8coNx0pN4R/XgJRbZ4JJqNKqRO7z46i0fCi2U1AlY6UwWpLQ/JLi4s6F/JZEvOkJ2mh9WZGNXXB8j6JXym8pz5+243Dmmqg30vokmp8NiZ6mNGaKE/oStU/mFLmPOlvLHA5dk/RCGPQYGj3TPhVAC4VPgZXQ+qTcTwLKk1W8QvNjC/kBR/Prcthy3+w03DdfgWHi8iS2CyT7fp8lsl6lHPzg/BmlsU8S/ZPAEYc4jxajFEMieoZjePQInoSOP1CUzTCLkfpSeaTBtwNP1MR4JFDfYYwaCLLEy/AAPXgs1ceI90rYF5XyvTwaS1Uolsc9UuXwhAyE3DKCJQRUql9iffH5lGPvoKfhIvhNu0gEUpkl44YpuDFTJmBWaFD8kBmRbkkGyX6MFND+xqIIj9L52mOkqv0aeUxMA+y66SLk5oKpy3iftGWYMBZqV9EAEnlMVFQ68FvJD0NB8dM6xg5hgFMqU8pDvRGKCgb2V4Vjo7DlcKK1KQWUSMeSwcK5LV+fT8qwDWoKCX6bRzVBeTmdacUrq1p5GF+f22dvHbR+9xxCPykizAvlI/WlenAdDgizHqlaDyS+V/JOyZun9wPGSiV7YrYwY3LeBLQitS+BJknSC3PMSybj6jQPmYLvDKDxXWgqHLcNWgXzhOOiKj0oE0Zwj7KPKrsOvTLR/I7DMnloLlf0u5/t513LxQkaQDLiOM/WpQiWYitCNiH6KONnlrwRnPkhBo+YM/AceDsNpp4Mg97xNOZZz1vAORi9ljfM+i+vc60kzEXHSR3OumY6vbN7+y1PebaFjqksY1U1ml/1cDAGSoAUeqZyD6PQaaYO8F6tk9qYvNj3cM8Og724Jl6euwJk9/z0PVa9AoZc1DtyMAO+8m2tjnnCcrk/zXcJ+zoXoAD2peqGcOXl5oKpeyqVnrkub/4WaTRXpjaU+wtUita7GAI28snjx49qIkYptIAqAy1ft/VGZU8EKB0TvSiPnSpc5SYRb6Jy+NxRtOsG1D6M4Gci90k0PymvdKZLt7mbi6cB8EtTKtY7DCKhQSegTNcBvQ+DTcQpBZqASaP3JfqflPN7IRQ/8UJJ1D4JOpFySOUAFGX+qLgfWBILVRQBUGz4JeoWdWrgXUl70ADxSO0jml+O4CcBJgg8EZ3vdHXE6++ujmLQiUTz46ATSwlAQdS+heaWMkEnlN6XvVKRrgcBKHwEPw46IdH8hOaX6X24HPNKreJEL/IyR/Hj7+wCPFOXOWaqy72VB2Z3wv3zw1LNm47Uip7pSqdVTTMuqIR2maMXSlqaSNmbheWMvNgxRDq1QzFteMxhx4YVVoiLsKJ1QwgLDkqRKIDpGDr+S42FlfOGDnM09EAgAgxQAPrPrBNdJiyLeDOsjcWMCc7riw6x76TXTnZTlNsy2NU8UIr/XP+l6r0Cul0qE0+Tepsq0frm4KGKND+3LdSRvVdQrgZBC4XXiRm761K2+EATNaNdZNLkaMN2WEIy5Ln8ltoXQeoeMCSQ8id9Fe2fuKEKOahWSsmBQxjccAbppF1EAIo+ZtYMaNYAANeLSURBVCrLYbXY11Rsm1e0mFuIpeeNWdqMR4r2SW14ZpvLdmCVSbSJ6hBjjEgEFybeJuUeoxKqNE663isTUUImxGjLemOtPaPBA1rr9WLg7nrrD1qQ1nz4o08UIlUV1D5cVsUGv9VUJbcI6H2yDYRCT0Zd8ErlZTNuSoGWVGXBlw0VAXQMc73xLZJbld8t6ITIGLnkgWKKn3qjaFk8UDifl9Q+Xo5eKxlnp9Q+MwmlD7yUotQwcp8oJ1VSmeaXgXcaF5V6RDL35RfqmepyY+Rktgy3Lt8ptZPEvmB5ESbCK4yNkm1ZN6SxT3E8yzyFL1+lZfq+CEjRWChgUtCnyJ6p6KEiIEVBKSjaH+KnrO9a5w0tnTEYotcin7dcbKaGwbgq/YPi14N3Q47j9E2xDHXt9Jq4nfU0oLxIzmv2rxiJMWARuE8wCJL81iS+CEtNMuiS2uchOXqopt4LHO8me5rchs4ojOZnHKagfRW4gZlRs2Y8HDzn2AexbBrfX8FyPxUeK/NAI7VPfjtHYpc9SgdT90AE0KQWBhoEXG7LWOMvK6Xh1sZFytWLpRRxGCsljUWlUaxQDWRT6UCX1D7vjUrKgsdHwT5kxBeLEHig1lL7gLalIdBTfTJmSsdS1cZJuYamCazcLUEZa4jMLUOFpIAJzWt5O6NLcX/wXnmgpXXgGCoATdISo9Uvc9NrNL+8XsIeQ1yMfFmjLTES+1KAE0i0m4FTCo2eQhlznqgErhQwpfIIutK6BJ4USDlrIS0jYNJ3x1jywLIH8yLzPA/oleASSSFhWHTVuLXpArDUPurs+O5KyDHR/K5Qj6f2WqEXB7fj4A+pEYl6CJalfWSPEn2Ic7ccw8UTWFKDl9LE4jeajTv1c9T50KDrwXbRAJQ73hksQYe72gkH6jp4tzJwch3s6k2c7f/7beinwvuE2/h9UP9oWR4XVbgrxJiHu5iE0M6TVQAp9GxZ+t86se9eZXwejo3S55eBVezT1EKho6EYQdRY/wWHH9ghB1VgNAKccr+lHgbd1m2BVHFjdpV96bohXHnpYOqeCIAmREa8PA1Q8Qebh0HZVdyHjitjI26QkxkGFYFVpvzl82u7yrERUoWT8kTZbdw4qUpeBm3AdDntl6h7/FPoWiQbUPus+9t5JNw4GIzm16L+SYNlGjp4Hk2pACmcMLiERuoTYOSofRipz28b6X0ugp+AqETnM5H85jFiH9H7NFGvRuuTZYjkhx4qDURRD1OrbSp0oKSDxLQd9kKlQBPJM0V0PVomWh/R+Gg9zSlZ77lE9uNpDhH8MrWPcksxvY+OeR7pfQSo5hLBj6LxnSdK3/ksLmuEvuSFOk+/OZqfTc5LUyxbmWh+GLVv5pP1cu8LUf2eZB90imugsG6CPDA/DQ/OxZRxOCJtuynTqVIu46EAkLAxBcFJMjKxYSWVLRMrYj4MaTmop4kpxcSsZRof7Z87vTGYTty2ev5K6wJfu0Zsk88307rYaIMAKS1jmgYzdtNMGJMGaX4wbhjHT8kcO8/pRpoEwq1veKI+Mr9VlTvXHZZjGQAktT5CtD0BRAYc6bIY99KTKBLz4v7ZQ6XV4RiqDRpCP/xAynLuqPxbqZn4DIX9gO8NRvHTKMOQ7xKCZSl7BoYrFPmioP9RGPUqQShifyUCKTMsQaIQi6FQXjBvTN4zmNoLRW8IV15uLpi6DMufACEFPA5cTZKJ4MsdUw+Nniq/6YwU1VC16vhDGjc5hIRtA6lM5TPACxRJHszpqA6ghLynaV1AAdUHXknBRfqGphgYWrunSWTb6phho5iK5E66bCh/uB5vu7ESJjWH+/kprS8iJinPHIARJEI0ASka4Hq95L01wITLF+VzSFEnKwaXyPMcaAKXax2YsiMSFQ1ETfLKKnmXsoepbu0zvai0Xab74b5pvBQosC5dtpGjsDpIxRz7i2VLsKo0gPLtx1UxFHls0GJkPfZYJ9AUP6HodaJPVnQQe9STt0m8UTGceYRO0Q4Z65UO+RR16tVDOprZ0xqHMp1LffsOWBpmL+ixWnoI09B7D1Wx8YSL2US8Idavq+mokf31J0btU4+T3LF8hwVIlZWYUB+mXjzbqWP3mpgTVuT+hjUEYrOuR/XsbeTnw3aGvjfSV5kUdEIuxOs11DG4LtS3MWzMrpcuTA6xzb7egGqdyAfO3HAAXbJONUZcEIucgBkJTJG/6ASQpFzrzd+rJtKrWB7TFoWLPIcEteuRU+xd4zoQV6h9YsEhSd6muAwNjKf2oRVGx1Xl+2Pc6GD5aTVm2ADpTZFbJwsj1pdm4CUDhDKQKqiAHlhJAAr1RMUehLIINJ9U2s+ESgdqXwo8UWSXR0+T90AJxQ+shTheqiWilLgjBLdR3gul8yULNIZA1+VVDpOuY6VWcZIQ6BIOXayFebxUegfYG5WCT0AI9GKS4BNpmoslL+WeEjqfnxhApQG/6p1qjpfas9baR5VdkV4JOZ4NPI00LXuXZufTLbOmccHD2GACDaR0oVMgc/YUSVgjopaLgUU0V/QuxXDmtJdAqxhJJwaUyNtJGHTX6Z54jbVRoNnYg1S+XI7rszEHl52XCmwvqlMx2NKIFypKabwstkNjaOvhrbk5cbfKmKiaEQ/G7Npl/I3zbLzzdsT4HiDtvAW0wMhXA2HV67F741AEG2Di/2/v7YOtS6ry8D733vedkSiChTBxGERQQUGghEAgQjQSoLRM+ENDAAEBofyF8SOgfAgBERQwOAGUQEAnWBaEKbRipfxAcJAKBipEPgIYICWIUODwUTEwAZl533v2r7p7rdXPWr16733OPfe9597Ta2a/t3fv3t/79OpnrafXClJXckrZuW8lV6bneSxGvDJ9Qd6TigQLxjw7D4pzSpn9cC5vNXZxmDTut2TGNa5B+aiyqeMN4dTLVnAJXvnKV4Y73vGO4fLLLw/3u9/9wrvf/e5Z+73xjW9MnfPDH/7ws/f+vImN9vfCnbVYQyyQwU6jdBa1EtD0Blw4sa7sE+lVsh4HtmX+Cg5y9YA3J1PFYAEp8lqkZcGS6H2YHwiDCUieoDhoBqpfLKu5MF4eoXbwAeyYVNnreFzFZ0Q8UQyKKFeMofZVi0Pvq/JLCe0PIvgxxY/BUxx/CJAiuh8k6S1R/CyYWurEvJaC0dDNhcKDoczjwnmhMGcU0fYoel+O3EdLWj+QyH2F4refk/PGPFOHBKoSzY8ofunb2QvhcK8k4z3U9L5I5ZMIfkLjg3Kk+l3MlL68aKofJ+QtND+i+jGXJybpvVRzpo66dNl6vRTnTF1Gy+Vm+ZpjXOy5+PznaUnrQW8/vxjkWmObc9w+xPDuOcR7ngO2TCHfD6QuL1x3QOVE9k2RRYdcpnXJgWeC4qwkJkiEDK7FU76XDT5GR6a5mzxXU9IzkLdc5nG29ae2sRQQpWj2jfk2YjCUe+A9HMC1shh6iugudJPAtoo5UdplTxRVY3AJd8Fz0ntUwSnAEMinmgRSHkhG3WTeEYBkPSaisRDPyTXvVY1hOIqfRBouAZBkfCLzeMnQp8YkBLKcgEgyj1e1h1yHDgUQcyAq8GTGNRv1Tm1KLw3h1MuJg6nrrrsuPPWpTw3Pe97zwnvf+95wz3veMzz0oQ8Nn/vc50b3+8QnPhF+9md/NjzwgQ8Mp17gQxr/pkoHqiIA2cO1DuLUaytZrQwQ1BVqAygIAXVGSeG8KHMORhXKiI/beA4YKhRwfyv3Od+EUVSqM+GnN0Lhs1FuRvtuhyKpZMqkPINCkS/NWgCNXq2UW7mRMlkX1sXKZ6h+QK1wdSZw2r2LbvaPaO0znHNF+XPmH3i0PjtYUYYE4KuXpIjOxNzCKvGtdflj1RN4ZTt/8PSPmsWO39MZ0Aw7Liepl9husq+zIKhl/5gWe47qOhawkCdbL6Wf4TbYh+S5mRzkBvshp0+CQAX8m1KBCxqifoZGt+pfJugq0WPc1vZrGEgCu4bSLu2nQBJXYuQg0Il4UXKARjS/k5QGT0y9Aww+wVUMjnAdAZfQAa3nCsubfAhgkFa6icSj/cm4yAkiQm2awMAbi0xts7pq5NjedAb+q15Z9QS6nEkwdc0114QnPelJ4fGPf3z4zu/8zvDqV7863OIWtwjXXnttc5/Dw8Pw6Ec/Ojz/+c8Pd7rTnY5+EY2vrUnhOg7xwBEDBF7FDlc6bifajAE1OSeC7z2ynil3wbae54miqxWLTfZEtZYUza8KZV2i8S1smbwI2uJjF7D6eBMzbXS3kc6qhLo2AGxMQMPLq0QQxNssagGqnniuKKiEyjmVtmPACR7dFGqfeKem6Hwc4Y8HN952hkmN34C26to5TeSdSgEnMp0veqYu0CLhznkb5ZLKf/OCdZnqtyCvVMwplRfxZoI1UOeQMtQ+WCK1Ly65TNY+yCcVuCwR/cgbRTmlmPYX67RXCkZaGxSxPh5x6bL9eul8WIRzi0U4oOUcLefTspeWc8e2LNwlXVNa8tyAtCyiF03/3Q9DOEhLLkcP00HyMsW66HkyAW8s2FJgqf5gxdNgvBBL42FKHiSOHkqpF3h7iRRK0UMrr7qdt2n/+l4LbykDcTQw1sbDfHOls02R38CgqPXTmoDLjnPGvE7lQqDelCuwVJSqjsSHEfz0fF01hxfpgWE90d2wnmYgANgAKcXCcd9tHUSkjF94TEE6iN+PnYaAfTCPP2CcIttbwShwPNLKlUlpOuwxcczjo/2T10uLM6CbThRM3XzzzeE973lPePCDH1wuaG8vrb/rXe9q7veLv/iL4ba3vW144hOfePSLMB2MGCcuBZCypjLng2ILCXa4tZVE83rZaK7oBml6R4uG0AZbhcJH1CoBZ3keTIvax+Aq/UU6n5sTSOcFYlqfDI4tWKpofDrZnfrr8I6reVPK2uNEwKlNmm0R8ESRphrhzZHSJzQ+Z85UqR9M4l66QKL1ZSCVIwhzFD9OglgS9taR+qplJGKffJPCPQdAxYMWocoU0JSBFIOqTPHLfwk4UV1ahNqXaX0pMW9M0hspfkTzy/S+vMhcKQRR/P1AvUTwu2gofjJvigEVRPpLiXnpL69HIHXoUP3ixK1jAlJddksvnVfgJS8MohBQbX5xjh3Pnc4fl2BAFgEpAlfpbwRUaWFQRUAqJQbP5QSoDCkrz9lEQNWeMyaeIhWSnAARASkBUEzLU0FvDHCi+ZgItAq9r9DYVboGlwZW9C5Op5TOnKhgKmCOvqmJRXvdXZ3k1RuwlA8BwAjaVRH8nDYZLOl1bi+UPAmJXiL4FcaEnc+LjInVovV54tH8FDMCch42gRQm5XXmS2VABfO+BbSUsYyMTzBxL+Y/9NJ1mHW1nwVQhgKoxj5qO+VCxKBLXc5WAIovfOELyZp3u9vdTtXH9Y985CPuPn/2Z38WfvM3fzO8//3vn3WOm266KS0sX/rSlxoWmHCCEk8+MniFy5MyVKb4EhBinYNS6GZ5sm91m0zdM5cwOB4z5HgXAwcoB74XalfmcvEfoPrhSVr0O2XBa7m5faUkHY5qW/aXZ4j7hKO/rmFsfeoEnmfLerNaxxOlBhZBpP1V9JgWkreTgqFF+s7yyST0CQU30e1M2GEbVhazzEO5ivQHIYtt1L5qDkJwIiNVoJnuTSx0HnimAUC1XX3I9slUz9TN29LlVMil0EtjuqlSTYscliHW5m2bV1bxl5fCjpvvNkXik47fdnz5SmJUPm9snvYXr5Pe4o3V16F1lQEy0NEVRc+ZS1OBMTPwhmPyFfFc5HJ5ZcAuBs4KtZhdZAXpL9Bv4bojl2SIsopbyARJyaqBNX2taOvDlnphQlwCUeMSE0wlj4dKuyqmkNI5i9Exist6wVv3tnvjHP4S7TjJiAJJXf1ccjlV0fxuvPHG8JjHPCa89rWvDbe5zW1m7fOiF70o0S6sqO9uovPA/s/2hbOEd2Kl42kcPm7qyLmTIuVlkFSKhJT+FiXFCVLNqFc6B8Za1W+M+crCE64boKG9BLjga6V9+SGSRYfLsg9H5Uv1ZXvO9QS0PipzDqg6gh/Q/9J2bOtF9pv+K4NmuP8p642ar0R/Cwiqw6Bb71SVT0qVi6WP13E/qYfIfsXCVwJQKI/T3rg3Kh8WrYSQWwoUIg5S8ldH1lJVHx062b7M0fo4IW/0RsXvgb1VsZ6DTsRyzCcV1yOtjwNOpL+UWyrT++jhRc9TzC81UKAJyi1VUfpwnal9WL5IkfooAEWm8xWKXzRBcj6pRTRH2txSOK+KIo9tXJmNDLJWOkaXrdBLY7opgqf9RUxvS+sCorhsFEjqbuYrJQH62K9TH8Dbypgt53eKEiPspUTswkDiwXAOspMi8HGwS+r+Uy8BKkyDxJJ8t6VULZXPGl0QEHH+OptuIdXRNvRAlUTh6K3K58i04nx8dUymtMfzgXeqClDAg3HRgSODcgOkVHAJM7C27808rBnvnv61aBa9UlIH7Yz3qbRjjxPTzXWyXfFUkcJVKTog/5S0V2k6pm6YjHnq/sr4g7+RKMV4R2QC/Jbw3cV6eq84h5ypfTyWkTGNBJ/A/JcwniGvVKHbgUdqaATEgvGMGPM85g1R+7htNbZJDwF+Y1OP86T00hnRTScKpqLi2d/fD5/97GdVfVy/4oorqvYf+9jH0gTfH/qhH5K6ZRzQxBs5OAgf/ehHw53vfGe1z7Oe9aw0kRitf1dddZUe5I6JZ0JbQ1iplGM47g1l9QJXugPGsoLK7fKm4iWIyth2Ms0bGBn36WhDDLYcAGXAlLRl9zeX+V4ACJXQ6BogKWA1TIc4lw7HaTuWlFeAFOqRxgNJj78yxelXJGVe92h+nHjXAqtUzsCpasNzpiKwQiAFSoyVlUq068yH4kngDJawvQ5GAXOnGCjRM+DEz3i/HBY47pHBVAZVZdCS50klgEXzoeLghRPzLp1w6ClkOpUzZTTPx/MiJhWwBJRQG8GP50alKJAcrS9pV4rWZ+dKlbDoNLlQLWq+VP4htKwSR5JN0DM6vWN79NKYbtpPAcKNNyqmuGiBqdSFrAamrFEw15EZL/0c0MKXW+jVrIjyV8+mPDawqD2gD6kZEDlvVOs6C0gq3iMeJDPQIlpd6n9oXpTMk4L8dRWYwr8Muur5UTYSHAbOqUCUoYKpAE7WmyH6cARIgcg7P/KA2DAJ5LAInMxSXiIAMQBX+Jc1AO3HOkWBMGqHdkcBYHQ1asjV+LRxD6kTDyGwGWzoc/PuFKgCpgSPa8SThZQ+HrvIGIKNvsiMQPqfpt6puoahV+U8tBH5nHlR+i89nU2BnYZsija4OAO66UTB1Pnz58O9733vcP3110sY2aiE4vrVV19dtb/rXe8aPvjBD6q65zznOcky+PKXvzyDJCOXXXZZWlaTkTd7BEBVHX6FYyVVFH+cQKlIq7QxlxnI5Hweav809p3/xSqgJJXgdbITZ+HQEmlwqi2U7aRavhe/o/CjtcmDIlFUP3yQULavoNl2TKxyWuUbMfuqU1pvlgX/ELWvWAVhV0Pxy7QMnASsz+9dtvcIeEBT2wL0xF416LAhajkEcRr41IFQkK+erYQOeFYKq+TyYADdBs+eIiLvlDp+K6AEDiGRFzLznXfZarkUemlKNy0cIGV/oQu39VxhA0mo9uUEubqlTYxLhrwRccyFTp+hfz6KroeGOzfwRKnHwbL0I+i9kjDYCMgMHVDoerYO6jGwAXQReEODLctNtmnuLpAS/LqJQceqYhUp1bmXYqYPCBKSGzCb2vPhNin83ZbuvHim1DtW77vsXEAUjH1wHlyoc0j5OqpB3xtpX9XzDSlw5PyY5j+YLmeN5hctc4973OPCfe5zn3Df+943vOxlLwtf/vKXUxSlKI997GPDlVdemSgRMd/H3e9+d7X/rW51q/TX1k8KDlJx3bTZOGDKmsgpE1CS+uxdKh0pUb1SlJ9yMEv0y6d0PFNMD2xcZn39dQjQohigzNeuJttSvVhuNPhpeqN4UNz0MEFeBm87ryvvVjvJXUXtU/dkHl/jQenw5DAQ8LxRGFzCKXNACU3/ozqM4JfqOPoR0fo4AEXMyQI0v32k+JEXSuWYwuhK6A1ViiZXxkdKzjN5hSjRmpteD1BrlkDni3WRzhePF+l8Ma9UovkRtU88Vof7ydKbA1BATinIT5YugHJIpXfJuaQgop+i91lqH0bwO9TlHK2PA02UCH7y19D64OMPxypdCZ59vUT9d/JMkck/O69LR1OXCpxa5RzB0PqKpslJeHlLHoBmTVO8C7THwKT08Y8zg6CSPkfoc0jPY+8RhaDIXqVc5jx1y6q8nyl7IQe1YU+4UIgpqE1qm4LdZK9VLheaMfdPQkmm6KH55288WSayLZeFFsbsDM49xANzoKCLTmR9hQP3FsA6zi5GGekcIAUeKKT2YQS/9FYhOl/aTXJQgb6S461zMy3WzRS1r8xry15HiHQctwu1L3bxOeAWl8t7LDQ/mbYAHiodVKKUua0XaAI9VrquBEfieo/+V0X2Sw8BjIL5oZRXvCFPknnoXbYBTD3iEY8In//858Nzn/vccMMNN4R73ete4c1vfrNM/v3kJz+ZIildUlnVuzAmqKU8pYOgK6Ml1azsXip5AJ87WgBZ9GvJDAxzA3JYPD8rVOeaq/wLBmCxkoD20hYpDPyjZtoeWHpsGFBxkbsUPc01Vm5uzwtxFGpfq35CUtM5VAlnkeh9qp7Blab06X01V53/VtQ9DoeOFECASsWjhbZhqmFKH/1dEqCy946WYImqBWGGczj0XJ8GRHGwEnRSTJ6rUKh9Osx+CYNeaKIqgp8b7RETHVJEo8wLMgkRSx1HvhCKX1JQCKLgY2oA8I3KJgZSXemdCr2UQEvyRhVSXx3Agf5bQ08VIMWfL87Rzf+y4USgVrye1PUohVX6hRGxPw/0BuSfWgk4o+ZGmbDnMUpo7LVS3yJgq/Q1QucjEIbgTEX4E8ofJual9WUj3YMzTwrn25T5NTRvOJSIb65HCnUR6kXcbuuPS6x+8so8gKD1AqJAFbEOkb/l4suuJRkvr68i+mjOdhMYywIpHeq8rlfvEQGUsgQUkIzMCBzbqDlOLaMvzJOSdjg2gXELsmxUmHT1LdHTMd+SPK3j+I429X0O4dTLiYOpKJE64dEnorz97W8f3fd1r3vdRq6hMZZeDXQp4FSfIOkdPAFE4GufAEJLWJqfOQR3NLmuPm7uY2qQpddJ0Y54pXg/ReczICsJAx5jeWNvlO4wNJVrjNbntgv+ujoPtzE33QJS9bPDnUwZvgXX4wm3jGXFkESvkPFs2UVR+0hx4QTedDixEvJu/IUAj50e1FgoYvto8idXWsvrtpH6MCRxa5EJ3jZXVbYWsqU3DUrAwscKTRSQl0cMeOfCI09tS5jYAqwRMNmkvaW+Tlwib3Li6XU5bXKieql0+hu07M09NUMoIbIK6CrdKCud8t2brrnk0U7Ah/+auSvisSr9geo3pP/IYXIQ/Mj8KDbSMIiCvsXrb1rbdH/Fng24buPlwIF3mSppWBsuUFr4nifYz507dZJdjCgV5yIYWGGVGOfKPq2veBJQzfwJ8LeGM64kYBa+vyqSI4BfAEQ6aEgBzdWHrsYlRScpcNWcsuCBonoulbQ3r6N8L+ohSFmNg+z2LmcPTJ2EVOGmpay/WKRxqW/QnycqP3zFKefOAEejcioLqLz12nrIB0g/cO646DzZDe70Ph52M6BJqmy96E5LO7DAqJ6UWQa41FbR9KCjQTe2ieaX20JHY7xXsp+M7KepfRXgso9rGAdSGiTpCH4VzQ+pfUD5CzboBNdLPqmgaX60LQEpyS2lPU9M81MUPxWEooCrdDixLFqvlP1U2BuJNuuirHAwJEEnKHFvouJA1D7OJ5VpfntpSR6rw5xTSjxTkpw3e6hS9D7OQRapfReLV2qPKH+W3ufR/jLlL0fvk8ATkqw3U/pKPqk6gt+gckuVCRRItt22ib5nYZLvrkgBMmWukueh2vQ5818OQFEofqULhbLUx7DqFO0PDPiU+ibmXKe+IYOmFDGPPE2eB+lCzERF1L1I00s0v0CRQNPfA6Hr3ZxoeYXap2h+QdP8UhJw9owDzS95yMkzFctVND8OfiP5Fk3kvtQVZD+/RHeLz4WTunI96hrL1AgTnqoZv+HRYFoQ/0J7nOgtjxkKLSiCOnvK4o3ioEi8LxgB8ebQu9W8uULtUzR0AKyi9g21Dyl/DI5VFEbxOOY2cce0Td5rfp/Z4+gY9HiqAlDxeHzCbSTwEdYbil9sk48xOMeAXFI0zqlBWJnnqDxT/LjVyrBVeums6KadBVMo5T160N8fFw1HtaSM0vsgpiycPx0Wj+0EpJDO2Ps6vYv26HxyMCp6oAk7fG+9srR43qWGN2o5sk2dE+rUtdWu7vxcEB152xsy8S1gvedJcgNI2L9crkAY0vrgZlUdJkPMNyShzZHuhx4q8WCVhyrKsfG9ayyOFj8CU0DzE9oOhhQG+kwVbrjyTEFSRKbLAB+dv6lq7lwj8WGt6HIEP47Kxzx0lVeKIvgVrxTUJ1RpaX8b1VP1Czjqsc+Awtolyb+50uEfD0yvz1kgUgFMDKOKrqi1Zg45XX4OxllcBZDgABAlpxx7mnTo89J/UKL4ikZsvVJ7TS9UmoOlovaVIDhI31N9mQTBQYoYUMX4GUAwijKF0lAPxgCT1aNGpt67ZyvV72jioBYdNUe4oJPQnOboNPARATOivoTp+VPKAq3qS/dbfifI4mdgJZQ+OzyB514omzwGwTyarJT98Ykk5zXjmzHPk65DFoVzkXbMAwO3xYgnqmLihC3TS2dEN+08mILf4Gq91jonYo8VhTDH+skyeKj0JWhPVfl35CKbfSSafUBfKiBlQZXuWCwtjwe9EgwiaU8zCGZri0zQ1RFy5rjF0zFGQFbqUBA0DUd8papvpXcDjwb7XPFM4eNyPFZyPAp7zkBKA6p8ozaLPM6bEg8UhDa3Ufw4NPoYgCqvmSx2JseIKCnqrnkwI9ZcCEec50WVeQqS/wWswDw3AedJJasghUFP6yn4BHgnRzLHq7lSPLqTsOceBRDCoVd0Phwp4WDyDGiBLlsl2dMzJAd0UgMwL6W0od/1sF4kv/L1FpBUwFLMJ1V0ifZG8fWV+vyzAq8U/9SkX8iAZTDzo3jukwR+4LL1TKVySbEQ24pXifsXAlOcP0oCTdDcTA54wWCqzNOEvgfyTKm5UZI7CkOgo12F+ilvnhQGnZBgE/WAV/Qkr8NfT19tVNSngycd+cttjcepyi1lvElIL/c8W3gVCA5lKATPoYRAx7LvmRLw64RF1+C4vFOk+JUPHcYcnEcK1nF8osYoJtCEBVWteVLVmAe/H/pBqvGReo06Kqd9xV02K7sLpux8FPqRj35nq+mrel/+MaSobyVnlB/Nj0fipo4tKNi7UFk64zETFVzbMIYsPbAk9bqNAKgoQrXjRL01n7hJwTOR/aq2jXDXY8Arlwffi9V6VxOiMCfnWkLNYOmhvE1oepi0l+h8QvPjqH0QvU/WM7UvHwODThT6nk3S6+WaKmALEvS27jV9a0UhaUFqH4EpshhjsIlM7cuDmkLt20+LRPAj+gzT/HLkvkzzixQ+ofZFOl/iDWX6xB6DK0jKG+l+i4scoQ+pfTbgBEXyA5ofJ+eVXFIEsHD0JL/dMlEiHLd0mt/uyCGBKe7yE+inX2gJTMHR9XIrXp8jqwGosv2QABPS+sRGQctFofOVvHMRCGFwiNg3xKtNtDwCQaocGCjthwuBIn4ygAqLcNMy0vwKjY9BUqzn/W6WCH4ZkMWfcKL5YWS/RO/LbdjAE6OHsjEo0fwYbCX6X+waqG+KzwEivTGAyh501oWF8icDaut5Wo6AKPt79X6/q1oBrZ6y4AnLyt3BxmAGTzqQRKoGQ58AK1WGY7g3aG6Xxj8y15wuwna5dWj8fIbiUUSanwOU6b0htU9FZJTcUiUprwp+FHUQ0PUyaMr6KV2xl3BXMSUo6BEeI9SR/dSYKD+gakxUAShvHLpB6TS/IjsLpgQ3gAVl8+9zBNUoIIVACeh+Aqjoa0MzjZRLVIsCsGZcWotgPQKaZD/VZhxsVUBqwqsk/ffYuv3xWYtNg9ond9xSVqtKUwE5db6+dL2i8gjVzeOxBofip61+3LZYCfEySMHNyveB+WTq1qzA+IjNid+mvtD/dF1WZsWSyBN/dYASj2LhW/LE6qcsgoWXrml7AJC06flI4Hsjgt/2UY7RZevFEOqgwwf9YLbNyfukj6//QjdpwFYZcFcgi3aTCNCK5gfBJsRLVdOA0VNVhUknEMbtD217lXy3Po7bFwH1uNANca5NnedOey+KJ6QEN8jvAalmluXRovapZLzYzc/tb9xxxDzBy6VbcPVRHpognHEAFx3RdWCZU3C7xRpjqDzU8fUQdtOqa7e5yOyZuY3oFhupGK/GoflBOzJ51GMkfGT23VqdhccDCyYy/JVHCg6m7gzHOVOOgpPUS2dEN+0smLIja+VZUFts+zXFdHq+d8qcR22bAFX8a/Guc6ozVuszABR7wbiOrSPojWrVk/YVnICBJpDyB8eY8kRVnqkw0yM1IVWfbTRFM+gE5pBqBKBQoAi9VPwdwn6yTjmmbBh0XGpvVCbYyNwpQ8WwoWr5GWWjYMw3Uz8zVJ0ChIBGk3KzIL2PytoaTAEm4vbDRcojlY6VvFJxiSb64pGKs9g5d0ey+BlvlCpLDinKHRW9VeyJ4nqZK8XeqOKRKut1FL8ceMLS/+AT4fxw68Ss7tIl0eKGcDF5o/h3GsMuFNDEnqr82yUr/EoKiuBRAj8FLlkAlT/v7IVK18X0PvBGxTbRsZsDSmTPVAkuQTQ/8EZlL1UGS9ozdUD7kCeJckhxAIqbh4PkWWKPFuaIYtCVvd4UgILz1qUAFMUDhQEoCs24BKDgPil6LGJZAhZAUAmJ6saBCSC3VEaO4JkSvVTPKa7A1SogamWxIBxOYK2McCEKOHG94pvZ+brcbjNDplxA67IzZGlS+wAgL00bmo8ri7xXNOQhaGJvlFgHhJGjc0Q5AbNGcku15kkVQ5+mBy5a1L7GGEfV8WM8A8BlG2W3wRTPSeF1+FsFCtiEIAji9WqwOuJeQk8V7o/t5/xQ7DHcsgZQQt3zrDGN0OVevabumblRBkzZ/Vr1TSCFff4chdV4LLhNwBFpC8GeDIr4MQEAqgJQ4LwojuDH54D5U2muFETwE4VlKH4+iPKj+am8U5BkEe8YJ+l63xNOJUYwxXMVoiLKA5gyyOFofkLzi+UInCRRL00M54ELJ+elBL0FSEF0JFV2gJWpsxH8kiKTCH5M8yuR+xaDofuJ24wVna+ZjgVIbUIJdiV6KuTCsAwXIIrf3hCT+DItVwh/pMLEFj5bdPcHXiiaDxUld8UZPEUQFf8/dL1QGURlUJXBUi7HuU/0+xYwFSl/+wpMxfVEBR4OZI5TBlM2+e4BRe7LZQZCN1GZE4IXAFUi9fG8q9gn8fyp2N9IzrsKQGkwVZLyUtQ+nh8FYKrkHwo+tQ/ThGBkP3gh7lyqqbdrjatum8Y2C5Js2eyn5z5VF0ltwDi3NvVDJ+ZNw5yKal7CKrSi9tlcYDaaXzImMIhSUfvgfZJRL49byLCHkfpUPkMAPfFHAXQ9Nb/X5Dz05v1iuUxzIK3bovZpjKtfD88i2bRq2hQ4G8Kpl90FU/T2PBzjDaQ3/q7th10BKx2pT22z+9lK/DVN0fmqcu2ZUl4oBVg8LxZ1MlCPZQXM4HgurQ/L2Neba7adx2jeitZ98/qU0sGKsbaoiIxS8q5OvFg0wNH7ezdrQs+C3U4y00OkJby8Of0pfo7eXIwSJr2AK1RcEPKimuSLlBqJBujk8SgTgL1F5/NYNKx22upnqXwIvPmk9lvmsorIMv7wrNFjA9LnTO2OcECHPQluU36FyQCQAJVWGOu82vx5Wy+VrmdPFP8UwDAvND4Vlc+UkXanaMAQka8Eoig0v9wWk+xiRFCi+Ll0YhMV1ETp86jILp0PopQK3RieBfZD+q96uM08UtNAamb/cdQB8tx9rdKl8hy70WKt+9B71fN1uR5AlWpbdE915Uq/gB5D/SKNQbvacQiOZ5wxSjXuoXXlLfKmPdAH5jgBy/cCD64xPDAPyjPcH136nKkiuwum0HsAguN8VbfOKdIHDFYW45ESMJJ+s2ZehtphxauwHXFrVzvxNYwAKK/eiU6EVremJylaeGh/+RE1g1JMtynX5oQPNfc3W++MeCpt1L6qfq9B+eN6Ci5R6oZmJL+cUyrnkmLvVNy35JbKQSlSbimi8+WhSPE65UODR8rJJ5Vr8ocpgwXKbqZye4gCo6ATNOjJEbKKZyp6m5jip2g2FNEv/U3eqJApfmwZTHml9srEXprImz1MXCYgVXmjSAGBFyp7nCj4hNSxVbB4opDal7xPJuhEovghvc/+qFSWypW+tC5dlNwUPTVhEfZodBcpfpTFKP+mhQJYzBzre6byv6o7hblPGEhCU/sisMn9Ru4DMoDKniZN7bNBJ6LnSAegIG8TUf6Sl4o9TCZfVKL8MV0v5plK/Yz2THE590OZ8pe8UeyZYm9U9FDE6yOKMQebKB7yTDWQ5OEckIAH4ELpMp4p0U9aV2KexfTOPJDFnkZPZ7tGXT1CTsOIgr/HvVVTBkCF9EwbOze3cZ5i8LMopQh92XTNM8Y5GOLcJFJuUft0FEY7B87zTJUIfiWPFFL6wEO1NBT0KJbOV9H8GvmkkFWjviUKNoGeqWwB0a9o7PHJuHP6EXdZXXYaTFUeg1YHg3+nBD/UBc6PAvMKdnZSxRaUwbfWpGh/Tv3Yhcz0SlXRhLg8Aqy0W7kOCFCDopJzodnGOwbOnxrZt9yLXpdX4SmuKUEgJWVnnhS3tWUGSEjnWwxO0l7+W+ZQVRH86O8iAqlE2dOR/ArNLyuw9BeiKJUgFbRIpCV4LBRRMn2mEPLdPi+ZXA4hznmwwhSeFM0PgBPTaTK9Jg9gysBlLwGopEOI2hfxDM+VSjSLNHcK50U5YArrCUQJyFLgisAThEKXvwSk9Fwpk5w3a/PqOyluwrn+vxWkPRZZ7Rhdtl4ikLppCGGfFART/OI/3EXkVUzmO9/j7H1KWJeYTRJcIkfnK54aBk2cBiEDJ/b2cD0n63apfQCm2BMlCXdDjMQXKX9A10tzsco8qQymSpnBFCfnFQDFYdJ5bqaAqSCJepNBiABW6s9i38OerNgXBYjulh6OLsuDkzpnflSa5zYRGp1HABODYfuOPRUvgMrrvlkn2YM5ZY7OJ1XWXiTNxy+6lV8K74uHNym+ymIaRMUdclJo40l0qH2pOVM1hSlR3iuDKQHHAKY4rQtaEyRSnwAh0k0Nip6aogD0Ph9MDTMS9UKaFzXeAVBdPzoIVrZleumM6KbdBVMz3yX1c0XWHCO5HlYFlmbmoWoezDvj1I05Pwav3gIWaQvnQCOWB7wQa0ycr0nrw4GEuS/MI7URIDUh6ruwOaS4zs7HGzkG6F3nZmEn8WJBuFlsBgizOEvm3zR7qFphlunIKjKSRMXCKFoUIhkjZOloWrWFECMplYSHLTqfBdS1gtE0PyenFK6n7wctgg3g5Ir3rDqY6rKeZANFNmwgoS8OolIZjSK0zyrwvdXlp7E+eZiKgT1eSz6DgCryVkWPVA48w0EnijEl534ygWmkvniyVS46BmKUlyo9BzHalBx1S0UPNAm/GxFD9SA7jHsppEsoA3funHm7AksYvZaVgeg8u25fhnH7e2WWqReMY4W5Mre9AVJoP1r5WNXl5gFNXtfzpeyBdZcMZoURal/9XvGd1fQ9vTOfged3l2tRRl3v5pwyRhdWC1eOXIulBx6zxpknHUyJ7C6YEgsNrHvbjgKkuLfgHwNS/kYvDTuP4cgfnpqjZPe3nYYggTGA5CfVVW0N1UENcB36n20jx7PRAe05oANaNEHfas9L6TcFmJygE+BdcoNOCLUve5q0lyrT+cRLxXmmxFvFASjII+UEnqg8U0z1I88U1o9RLfB7iN43MohhtSgw9khFYQ8U53QpND8aIC1jTqk84GHPVKbTaJpf9EylE0Rr8MWSU0pofU7QiUTlo1nxe0Lty56olGtK8kjFaH4c2c9G8DP5pHKYp7IsTRS/yVHGMXiluuyU/N1wEM4Ni5i6lrqX4p1qeaNQY9gvsHSJepDJZQFTPIk/eZsKlVfmRsG8p+yBylS/BGiknqh2GMEv5YtiT1EMOlGS7yqaH+0nninOEcUUPQlAQXnpkmcq78fHYw9UpBZbal+VO0pyDdlAE+SxANqXRHdDbxTS+iDoBAcnwIctOi/VOV6o1mDee5FV/Ya4W+CJqsc9oODJoCd0cTbusYagNu1ekAx2CazS/umZZP1oDXkMoBiKeJ6pHFAC5+Mita9Q/pKxgN8xUDVtPil5h5BHSgWaAM+UovOhx0pyTo20Rw+UMRZK/in5fvwofvm1nAE0csplZ8EUTvgXsZ6GCTf4vBNpz1IGVLxiOk2nnKLYHOV3MswtA0DiyzMAKrWy4CcKzmuSek5wR/dhMod7QKk6xhjIsp4Ie81j90uXV4kF1w6QquopEp8KgT5RFrDOQCrhCIjcB4tE8KtCodegStP6ODFvoQhZT1ZLcFIvPj5Wj2449DRoKqGFbejhDKzyIgMYVnZMsWCwJGVet3OmTPQkE01JhUdnRQUgStYTpSKDJPkLAGrWXCn5luCjUOvbM9G3c+VPh8SodTcJmCIDiUTzIw9rI1eP7aJYylheb2FvE5fTgJTmQfFvXganyTu1NwKm9hyaH813orIk8w4QlY/mQWVvVKHr8TypDJToeELzy+fJkUJLn5MT7kIi3lTWiXjjPR7agTb2RelhaDBVIvUZEOWEPK/mTrV0aEuQmOKBKvO+GVys/QNfNMCTqde6o5xLqUS0LU2ERy/f4zCaLU15mlTACS8fWHCofcUTmUEUAigIg44R/Gg/O09KJ88t9D4BWwKEaAmarie6asywzPupegOk5CEAaB2x9R2XbEIvnRXdtLNgalLWAE/CVZ5x6GECdKnyUWQCXKhoQwqsGEuatYRgudrPURoWGFG1B35cTxde/5QyOopYB95ipicTABW2L9sHdUwVLl0eSLHyCZ0vtQfFBWApAyhQYMZJgpcxNQF4Wr9rah/T9XD+VC7DpPUmzUZTbcrMdj/EPibctTS/0Jiwqyl9BsyrBaIhmQAmsmJBVOtByTs/Bu/UJr75M6CwdkEScEhUuJw9KnubswUqO67zi0wQwXxmrUTcaAxBYet+KgOAYupe8WcX+l1cz16lYlDhvzk0OgejKfmi0Eul5lVyDjqYP5WDS9AcJwhuUxL05rJQBU1EP6YE5j6nBJdAT4Xqh1RwAh5wM7qEgXZ6kBO5o3A7Pnx+PxVSqN+V0q2sc7Cd9VYtjvrDHy5JB9LEhWrOlPZLYdfM60Lpc6l9DJ5w30IdL4xuaM9jFsOiqW7Z0018T55egn14f9sm72si0MINiDG60f+PAinT7li6/02NxYZw6mV3wVTDrKcG0LbcEujQ0kcfj4M9h1OepPzN6iRH9jXl0RCtzg/fDTqBZTN4VR1RaLVhiw5gB1FSpszXsZzwRuE9eh2gt27FM+/y3xF6H1P2knDQCCqraH5A78M6+QZVMt9C80uBJzC31J5H7Qs6h1TlpQLQJaCK7oNpFkDjSbcNDzcrcgyBXAYssQ4HPDopZqTikLU6Wo8pOpZQ+y7u5QneKYLfXpn0q4JNFE/U3kXwVkUKX3TkXcxR+oTmd5GT8kLACY7kB4EndD6pNrVP/ibtixpaflT0l92IgHY3HBq9y+7IV4bLwt5yL/t7EkWXBlyW6kdeKh5Cjk3097pABEr8u86GEl2nw5ozmMrzldjbJJ4pBkLgmUJvVOoXyHvFQSeWkE+Kg1Fw8IhcDkLtS/mikFp8mKOGSvJdiuIWz8PBJZIXiuqZ4lVyDYEHCpLvstciPU0w9CgKn01KTw96MZFWZNIzZV6cvE/WP01UMiG8vzoobjdGPWffKW/T5AVETz+Ng9gQkDxSAn4cz5QCSAU42XxSuY1OsIxBJ0quMB2tT0XuY2qfRPArND9F3fPqHJpfLtugEroePVQ59yE9rWVjzBP3o9dkHtToo+9yvNLBlP0O1/BITXqWGmWJ8qcuAn38K5y/Os4EL3umB8oFSFwGa50HhCqan3OM4IImYxmyc6O8exi5x6PMlRIgFVoeJ/A0FZ2rvE/KC8VUPnlN6I0q7YR3Ttuq0OYSnQ9DQOjxvfq6VDh0BEv5O8mPljvpGA6dE3lC1nhWSjDw8nO9lLwwcSDD8xMyoAIvFYejZYXG34uXCNHS+DK60+Fp+fvA0LMqUp8GTMVzZZbQqONlGBthwEvcoHSa3+5IDA1+07AX9hcxcbSdK2VBVX6pEvFvBSlAKigPExpW0m+YAFQu5zOzl4o9TJwDCj1MNuiEzHdi+h+lT4jHYWqfpFIQz5QGU0z5i4aZRAWkqHzSvyTQFA04ZT4Ug6kyuA5qnhSGOC9l6MwxotuIZ8pS+qyeG9XHVlqImD04sD5LjIGweY6x+g30aumSneseRs5QPFAQOAQpftiGvU8CutDjyF4qbw5cfF9I96MFohCXBLoApCw9D3SQgCPUT86cKfX9ONGLK4COD2w44oM/onSaX5GdBVOucWgKSOEgeBNfgDUApZV5QSo8EQf5DHAxyeV2QI+iH4CFrkXL89zl3nbp273zcTfqACy1j3OvszApepvmhju36x5okvLgzJ8i61wFuABYyTlKcl79fRbvUwZf6IXS4WinovkNFbiP84Ro0EFIki3PeVCFUfmQckNgigYtiuJnqTSS14NuXqyCFL1PhZuFiH6Gn14sewVYsfJiwFQUHM6N4u1OAJPm749Nqt43pD1Taa7jsXdYaxyjy9bLTSkAxV7YY5rfYgxA8e/8KGCKQpwjmCKXO8+T4u2pTHmkuA9gyl8GQ3UACsk/B0FqGHgxJS+Xc3+h8kJR31I8U+QVA8CV+5+gPFMZLIE3ivMO0ZyonO2A+x4McQ6ACcOdQ1m6AM8bxSCLHzBvN+v4Eux7Y89NJVxvdmg1nyVoxDPHZD1UfVdzbUUy7YFjUuqD8Din1VUWah95lNj2VQEpDZowcl8y1AENvQJLCJYFABXjsJ3XxCAZARQCK9QlVrdo+nl5RkhJR3DC+6Nest+RrDvPsP4mjuRWbLykDemVIZx62VkwNdohNICUet+rAKlhZq9HP4pWWOpZ5zDlFthoJ+UtdZYb7M6HqmgNTn3DoyWD4xYI4w4Jr8cpe8/C4uJhDpDistSDVwpADwadqMo2Wh/mlOJofRx0InHVqC6K0P9Kgl4BSZbil5RQofkxiPIof3Cr9jGlwcvCcFPjgEk+C1BYZW4EzamApLxpwENJeZnyxx6pGMGPBzgpct/AyXnzA02UCab2XTRBJ4DqxxH84hKBUKL5MeVP6HwczY8offz3cFm8VJEaeEjUvkQTpHL6ayh/FljZgDAAoNIvN4ZR3OOX3qXL6nLj8vKwPNxP86RwzlTlmTLJt9H4tJgAUFjGABMJdIDnudD/MoDC+VES2Y9AloQlh9xRar6T8ljFXE+Qf4oCRrD3yssRxaApgynKa6US7hKFmLar4BIJQJUcUUL14jIOqtG4A4Nm9tqrAEpUV+kvfsDmr7yXkXEAvjvFFuZBszOeSN1SY1A9T/hAxTYkf5zIfLLeAkKymal9JsREulbH+Gv2z01b3igGWfSe+R3zfDihdTrJljGnFBjvhGXDBjzSO9JGaH7Bp/mpfFLQxovcp7xVBUgpECXjI8PMkW/KKqNxR0DaZdOAqsuOg6mWzPnQ1vVIzensjoLQS3/YBFcqLKsFL9DeB0LU8cD+FnDZeh+QlWM0AVJL8XhlO97F7at0HC3PpNfnT3ip0CulPFNi4DIWQfgLY3Pgsdf1SOXjMb20w0O6psVyN0kpAQVAFBUPtsRCbSZvC8WPBzF1sAkddKIkSMQJvzYABSsR8U7Z78hYAZHqZ7flyb3W+wSR+6QM3wy86Oqdu98UuwfxJYTNiv2NrnuMLqeC5ndu2I9BxtN6jnO3p4BUfJketQ89Vy2xgSUwsAz/RS8V/9YxwATmdGJqXwI04MViDxN6pjA4RJ4zBXOtCHhdNGHNJahEqicPFASbSINmBk4wN0oG1DCIRnqXG+7cJmuNwsBKyvwgJ6h88BqaDAr/BZU+vxHUKnVF2BcJONnwj3yx5jbSKXyN1oOSrpKeFwefqA5BVkwLoPK+SOfj45VgFJqdXTxVSu+IvtHr1bgF6mrvU93W9UoJ8HZCoNsxi1rAG6W+L/Oe07OlB7zquOek9dIZ0U27C6YmXNVHRe+tTvC4Ppo23Y08SVg/AqTkOBAkYi1vFFvunPMUN/bI9oZHyr3mlR6UeUwOmIlKibf5dLya0qeCUhDYwXoLruo6niNV1psh0AVIhcozNTYJHSUrObYWakAlVkBQXjwPigEShj1nK3Eux/qcyyN7ptgrBXOkeNAic6UorxTTaQ4NOIJ8UhL2HKx8BXwVKp/OJVXmTkmIdAgwURTfiEfK+4AqME1oN3mmFpeyu5p9jC7bL19dng+L5X6eM5U8U0uH6qc9U+XdTtP9CmgqQCmgZ4qS5eYyH7EEmmDQhF4oqQcPlASmYSqweLVLIAme75RAU9CgKYMpCiRB8y/TMahfEWofzsMEj4SeEwX9ThgLMGG9UWW+VNpTdFpjnrDRcU1D4JggJoKI50L/28QPecx70dp2hPMK8CO9gxiQ+9ryeAD8gA4qRrxC5xOjHweaIHIBK2MFmJ35cBhoosxrKvN3C80PvgM1b9dQziF0OnqpsK4aL7GOsl4pz3CNDwa+s0INTXz98ueYgdUm9NJZ0U07C6bQU7C5g0J5Q3n0Zp8PkEGb2udYzZpgpZiQWtQ/j7qH9RWYarWVNnpuVMUtDuvRJsoDMGVQHt6cKQWcbIQ+/oaYzaUi+9GcKEnMW6L95fKgaH4S2U8i/Ol8UUjzkyS83l/xSuHLqR8CR/Azf+rJvDaCn1iEeaDEA56Sx0XmNSw1tU/oNpHeFx9CpO9dLDQ/ySOVIvQVSgUn5pXcUheHTPMjqkVMxpui+UXaHyulFM0PQRXX5Qn9OlHvso7eN0rzg0Iq0xypSO9L734vottO8+uyttx48fJw4fAgeaQSNnfAVJRYV6DO/DlTHFxCe6UYZDFY0h6rKBY0HcL8KQ5Mg6HKxRvFc58UmGKaXz4ne6DQ080JwTOFr4AlmyNKEraO0fl4Ls0sAAWDZ9ZDtN+ogdDRu8qIyZ2tJ7qh22xxKQBVU+grqG503p7Kk8aDfriQotLLuKNgB/ZGcRdNQD8CJ3qmErWP5sIJA6KRlFdF7pMIfvkBK1oeUc1Z31TR91oUPjYA0jhIBUXi8VPUSVyWgEg8PioRAMtjJ8PJMGG8j+2Yjn4WUMopkZ0FU6dOWv0XIMK2d6rx1/mtLUZAmQJStt4pq/NjfQMsVcDPlqfu76iS+p+F+2CqUxgw5nq4EJDhrS68/UvkPvRU0VhdOT7K4Ik6V7hKjOrn9aM8OLJUIFkDIMVWa8kXxXMoqL/GeRW5DdSbfFJsvdCB8erIWALkR6gWYuUzda3t5aSwrl6In5B39LMSIIXvEQFW2KysPobxj9Fl6yXS3w6IOpfsLYtFSdpbRfMrlL+54lH8rGdKKL3QXnI2SQQ/pv/plAlM/8O8UJgvio/Px8CEu5quV7xUbMzh6+C+paYRY8S2knw33yDOE9bhzFU/5Oo1v75ppKz050SHkAa+hDRwELzxAfGUBXIDnYS9ZsgjJd1w8k7Z/rYEmkjrajJz/Kd0tmzwE5CMeaeY1knvxQZjrcYcoI9q6h5E8xvRNZ6OSldjaX90XmDvO7pMG0b4N85t13sJxySb0EtnRDftLpiSL3hLZM6lmA7ZGLP0j9Wpa9UjB1zaeKCnBZwUj7xFFTQdhrqmtkdq1OI3U6Qfhr860EQNjDw6X5vSZ4JR7LW9UeU46I3S9D8V+tzNH+Vsp8h+xXo4/kB4QjAqLBU1iZQTR/Ar9JtsGZYIfjTgkUnibGE+JK8U53Ehr1TAoBNkFUwWPDOJVyb2emWk9Ek+KSgDxc+W3ZDo8lCg3kqVHZVfVo6CmDxSC/ZMbT4AxSa6q23q7rq05e8Oz4flxQPyPEUwxRmdCrVPwNRi/lyp0rL8vtEkI7l6IOgEljn8OQIrCTrBnikARcUzBcFr2MME3igEWeJ5ovDlAqDAM4XzoDhvFIY4Fw9UFZUPAkWAN0o8U+RFoIegE/A2dGBpy2XfCjemr/RbI0Mm1SpPFMwxulRj5VVHuYo+Ht8JB6+ges4ilTwp5gb4O0x/VWLdUmbvI3sic7ddgoyUKLEApPl9I6VPvFGlTtHyHOoeb1N0vZG8USo8unxrxXtV5vcaal/1XekEvtUrcb8DMPTB2EaNdbZoGL04A7pph8GU81Ft8oUOR92HO9WRNqasgFILWCFISXUtS5wpN4FQ6SS8eik7+RMQRLkKyl5z9YxmivUaedu9eVJA05OIfAySeD9M2svzpHA/ovJhWSX4lQ5vGJ0npaP05e1lrpSm94H9zr3d0j+3gVR6ZUDJ4RDoypKMND8CUzG6FpeZ2ifJedN8qPgwIngiQEWDmQKamPJXqBKRyhcpfFjHZU7aq+ZLUbQ/AVJE+fNofKjM/OeFiV10fUXtY1C1F59Bp/l1WU/+38Xz4ebD8+JtEjAleeWi6AA0qe2cQVIFoGqAVXmpTNLuEnimeKZUQAihBWuPlUTao+MhmMK/OAcK5z4VKpcePA9ejigboS8BpdoTXgbXuW2Tju7Nj2LKgWf0o7ajIkC4gCUx/Mlc55Lk1nqrUvVxgqopvQnC3xMC+nRpBKhKxYhmstQ+CBxRyhjZT797+R5GqX2a5qci9Snq3qIGRYbmhyBKtscljIEzSOBLuqe01aHPXWqfPLiRF8/jF3y0m07V0aWS3QVT2yYODaAJHhxApdp6gATbojKo6AimjEvrnMPq9VUbc277NDbZFTiYtSixsbZ4S8azNTQ8XNU6HkUml4HjQ4AVrZpQtVmJtrW2nAJfqvS7JUztYmJieomMBPWQx0OHqkWFh5GUIBwtX4dZJql6Zj+kTUg7tJDRiSpKqiBIXIqyKkgSFL8VfGjyPswL5he26QmZ3mBtnWN02XqJEfP2I9Bgz9SwyF6qQQOq9Bugj5vX1/dMwZxJpkpxFE/wTGFAmjJ/Css0f4oD1lB0PaQCYu45jASqABSDJu5rICfd0ARQBRSJN0rAT4kcKsY92q6AlAOOaiOjHam29diorAmQxLYzF0idxDiaro0BlTzEqWdjFDF/o6Vc2sk3APrF/lVjEHh3OWQ7fC+OHqr0Dh7HfieNcVj6kod2OzWdQfZRD6M9zcG8V9fmZxts2DO1Eb10RnTTzoIpG4BicalefmOQ1XRzevUtGh9us0BGoQAf0DSVSWPSraoz+aK8QXDZPox7w7z7aT2LliBIwnUY+2JZrDnkbeI+Fj1Iss3NIQVUPZtbirfDfhh0IgaXSB4lk1tqD3JLiYeKLNKeV6qZ/JAGSslzRvMwhkYbHijJRHS0OkuizELnYWof03MOKcDEkAJP0ENb7uXvg/JHSfS+RO2jvylflM4ppTxRylsFQSWE7kf5oziPlND6lsozhR4qCY2ezPNA78M5VsoqXOZCJWofRu8jz9TAeaaOwxJ4BhROl2n5fxcuCzdfOC8BJtKnBTS/KIXWq9enRPoCA6hwXcrUtvJMgVcqR9rT/YWAIgRQTN0TOl+m8eWfHgMs9kBRnjsMa25pfAKgyhwZHUgC9JyEOAfAJHqpnp9ZDXxFGYzQzueAKd+CVQ0JVBS2lMok6wp12BXAF55/mDvAHuVdoRut3leofgT2GVDl5u3jlu8P5r4hoAJDXgHSOE/OzJEDKyfrnfQomREB3wzSx2O7FOTIeJgkoiy2J88SHqOU6beJnifwhKqgE0j14/2qsR3/1nk17oARpHwrNHulBEseR0L5LrsLpqQDKeP6MlCSikvobZqodwEFWjUckFPqF/M8RCMAy1cwcH0TwGsMRFXH86619bxG+gV5pwikFtPJeXGelEv5W8wtl6h+so5AigAUm72a86RsAAqg8mlANfEsZNBUb7TzpLLlGcoyr4HmT8Hk8hIOnSzXRO2TUOikvJIyi4CKQRPT+6As0fsUpY/nQzkLRUQqc6NaIdIpaS/T+yzlTzoC52Mj5ZPxlKApvTCAOqY5U112R75y8Vy4eLGAKQWaVLkQdeeCqSgYdEJF80OQlQsQiIIDzOiAMwHnVwGY4nI6BvUfqe0S9uOkqjQXRgbRAJAweIQCUTgfCgGUAUk1UBqZB6Xq2hS+USZHGzPVHS93JaTHcHMV1rql62AgbfOJe+eaBF0zDcw8jp86WBzw6+tq7yRAScojND8Ie86R+wobgv4CgKqofRXND0BWa87USPLdQiEEOp98l5CUlwCY7MfUPshDpcdG1FbW7TcCiHbsfcjY5BiCI3XZcTA14huda+hZS1YBUsO8suuJ4rL1REl9XbY/2MrljfV4fgfE1edwgNSEjL6DYbUdh9Z2xJnGW+lewMJbhtG6NOm2Oja8EEnGi3wC3bYMoryHPeeh+N+5axWEwRUmQOScM7ZeUf9UxD490LF0B80dby8Lh96HC0bnK4l4G98gfov4EJzRTsMUYoAUAixBuBvvQTYx0fcsTPLdBTlc7qf5RByAooCmEWBF7aYkf+bgzxIHA1B5BUxZj1QuZwCFfUEwFD7waOGcqHhIpu5xMAEFmgqYKpE/zeDYqRODobAjvLDmI4EmkPInOYpmsCamjJ0g3EUMKww0ytAEPEHbOhCWMb0dUDEqnLe7/ia5C0dQZfSKKjvfh2LFAJBm9Dqiaybr0dgcRvZj2nloj7msEXtUzW+RbEIvnRXdtLtgCj1Ti2nX+8ov3PNKOZ2wLU95oJodt+r8y7mbtDynXAEjPpeh8Kmy6QjGvFHV+fCZeHX2HqdkMfL4jadJub+ZkhfqPFISPMIEjJDpQORlyh6nUlc8WTqKXwW4iMo35plKu1cR/PQga+rBxMGP85kbPnoul8hacZJ4SZSp8kxRAIrDw720pMEU5ZPKVIu97JFiix/T/KAu0SaIdpFoFTZy32HOKaXrDM0vUvoGL7cUeKPGckmlH7v+RvMja4xaKm9UCGF/LwwYzW8fqCabEvO7WfsYXbZevnzz+XBwjj1TjjdKjMsIpMr6tCCdr6zrsv6b2tLcqPyTMTRAC65MqHJMripthbZXBr4ljUIxwiThfEBmwFyAEAIr1kWLdtRZpdMM/c/qpYZnwK574wPRQ3zcEUOfaSp1ad0Lm36JJZ2ao2EsrJcqe6HMVZf1xjUru9bQovkVA53ySBHoLmAcksF71D7xGkGZdVDldWLd5NdLTkPWSY63SuWqEkA/g9rHZfvwZ4sTTAuMucO26aUzopt2Fkzxx1ZX+t6q+Qc2QKZ58tVAVNP7M5POV9rMBFFTAMta9CyoSuVh3Os1cj/N8oRUTRvepgQcEEBxPToVDPji7UPDI6XaNj1VxcQl0bWpvqL24TaTQ0rd8YRylUGSU4/hZ9ESXSaEE4WPqH2SQJMjbsU5U2nyWEmWqRImskLjMLQcKYkVDEdR8ih8Ngy6V0/Kxw2BzgmxWHHZuVL4wcyZvG+pfeiZgmh+w4Kofl26rCE3XTwIhxcPSnAJAE88X9IKz6tZVbzfvwAgPjKAqRJ0xrQFcFUNenGei5rz5HmxW4EBIC8UAyspl/aVkc8AqFyuqX5Wx1ErpSObj3ik68D2jEPURjqmC6DwAEjjOylA5ZyXcxYWQMUe0nIXcs2u4PflACgEVtXfedQ+eXdI1+O/JlEvbxewNXj1AKSgjYrUh3OmEDjJNAjNnlDjrdbzsqh7TKSNGfzUA4guG5KdBVPxyzxSn7Qu4GoBqREgUQEtF5QUIFUpAc9DNQWWpq7V3HuNV0oDez0ukFr1XXieJ/9CShnbIHhy2tgAJdLWWbw5Vn6bAr4gTVFdzxZomXRuQBkNnnibr+BNlkTcpG6ogCqk8vCcCJ4n4YUwFkwCWec5x0vMRF8PjmDCLw5+FDByKBVQhwMg9jQh3U9b/Rzw5D6ICanmSely5qGjx8p+WEeXTvPbHYke4MXhngJTUfJnN0iUP5TVPFOyV+UZ4KOowSxVVt4qS+3FgBZsXEn7RiML3QEPcql+IX0IGAKpnPsDC5rWmwuVjscDZ7lJqvcGtSNsikpQN440le3YEN6tux8OUi4FiIJztE6X63POqIXTvoCneRdr25fchxZgOwFIXBBudQXMjQLAXeuTOTS/YfQbq7bxvZlvSJ+bNnB5DEh5wgwbOwbCMQ6PQ+a/llnSaX5FdhdM0cA0W1ZGOq3Rj3hGm3WA1BSgsQDKAUtN+twYiBrbBmV7LF3G+SuNa8fzjD0jbz0dxC9bYKT6ZAE1xTqDLvASJMKJxIcBKCRSX6by4Xah/DG9Lx2jUP44F5X8pe2eZypF69vLkbz2MNcUW6qJ5pdvryTtzY8sqzQeyHiPUwY5PH7BKFsSdCLP39C5pThqH4U0JppfUnKUT4oDTUiwiYtMtQBaBQSa2HPLOeiErMt2pvMB5Q9ofnQzOnJflV8KNTj+EBfTYMok502Pdz9S+3IAiiFS/iLNb8NgyirjtY/RZevl5pv2w+HBOQWkxPCiAk3Q7/8In1oZyBrgBJP/yyAXBromWAAfAwe66IEqHY9D1Zui7vE1Slhzasf1rcExRS4dHfQ6ZVc3r/DbUV0J7wcBJeRcXsAIQiPpT2s8srgEwCoZ42CQTxeuTktt4nvOLETeTsl5W9eH35T80/ZGoQdKgLeJ4KdA9xS1TwWYMEEokJZX0fyAHUHUvkxZd6h9TAOE/dKdccJerucPIJbhWZQPAz4WT9DSEhzAZA26UVXz72tb9NIZ0U27DaaSEKBqmoY2JC0g5bSZBFI4UJsAOqNteJtznup6HMDlHbf6cVkw512TJyu8C08hVUAKtlVlh+anjmnAV1Igylvktan3YQDFc6TQM6XnSpVtJfMLOkRonlVthJIHguOXWdG8ZHI50/yKR0oWnu+A+V8snQcoFkLNEUWjB0/KG6XKkMgQQ8rydvkWSyQ/pPMVQA9eKfUweLQ38WFZIOV6pqxXipYzoBy6nIwcHu6H4WLxTKH3AjtNBFFzgk+wsOeoqkdQBXqmDHg1La/YI4prQsCXAUhyIEvdA7BT0fQm660es+Bs2sg42wi5glR0Pj4O1Q8eaGIaH6CV5LXzwp8fN5CSG4GLdrfBKl1/2TTeB3oe0Sw1dU8BK4zqiJEc5X0CHdRhN+jvAr5FpPlxe1bbXujzShehR6v2XtnxkfLoNNhE6ZdK5Zz4uAWo8G9po+dJMYviiNaXLk3ZXTAVsHMii4qN2c9t5IOe37HOBii23v6gRtrbH+CoIlAdzkxlYsCSBXl4/qRaRxSQe9xVxe7kIYkGWEqnBk6cAk2MVKgs4wG25HgTOatyAVjilVJASoMsjN5nB00CnhBwqR65Fh7YlH6SlJJ9ESYUsg2HHqo5UybRJoc6Nlnmme5XgJSeByV8c88iqJQTUPVsTg+25Cmw5UXyQ0DFys3U81Ozj9QqGlZQDpBKOaUIQHGZKX+b9kxtgk5xFqgUuyDRwxvBVH7penCU+wZI5bBBMCV6DrejN8oDVXxhOJhVA8gaMFnaXRLPAwUD4xYlyzvvWvrNbsd6W/YEgW370ebtDdAkgMruyIAKBiMVwDpmUacyIA8ZETwOmHpc+I0hAM96rPZMIbDS31PZrgEO6yCIIqs8U1RvABHqnVJ25jcB7U+BJvIw8bbSvnieBHDxg7XhC9fpr824B3NJIRsn66gVjjt12k7zE9ldMOUMxIkYxcQ/rlQWIf4Q3ZePfGzc35QRoMjlOD8m3bmjwnLAllUaeKwxEDVD6YzRIRSIaniqKoXlPZuxOnloa1D7AnQgltrXAEgqgh+W099M0+N2thxUfY7WV2h9hdKX6H00CNKJOIuXKqsc9mbpHFP6kWWARCz2otBoQrBuXHxdGMpYaH40Z4PBUwo2IUl7OegEgynyVlF+jiHS/XgCsI3cJ7Q8LNP3YGl+F71ofhlA7V3MdZyclwGWJOodWtQ+ov3l0aHjrSJLSXqQxhUgygiS80ZaH+WWGoDmFw6I6keJRzcmpr9Y+xhdtl6Gm/bDsL+vqVJV/4fKZN0T4YrxIGEb8DyVeutxqusVXQ8HoqHhHRgLbOTMd1LAylyHCn0+BZasXnafz4S09BOts2MBQZPdzqcTyATjDqk8aaeC9I8YdIL0GkSEdZSUXkVvZqg9nc1AJRDBT+UVg+S7Uo8UPUy4y8njWfcwaEJ9hBQ9rz7t5yThXZfax+DrCK9FULcxDuMYR8Y926SXzohu2l0whdLwRK0lc4CUPX3jfKVtS3E1PE94bqts7DHM+a2ycYGP9+NvHRtvaF0g1ZBmc8/T5F1QyzPVGsCQh6n2TBEMB6+U8k7RNhVIItXpwVJxfkjXWF0G37lv/RS2Orxv3ZKBVMEU4KkiJVdyw+h1FWTC8tjHJgI7EZU8r5S+EEPRgLCzOtBEXhetLL+JBmga/cZ0hMeinLRlr7QxnipYOpWiy5E8U9EQ0QRSVNiEObfyOpmy5QuzjpEOz9M1ul5+33S8Mphs0O5M2PLRZPCjSeKdY6PuHLnvClhNSKtp0wvFO3mgw9u+DUCKBkfpUgxNp7q8xgOxc/DcOXehQQ/FY9sxiywYYMKjh2pgb6l4XFdR9Ey9GJFb+9lrdYC8sokcAUiVB2FObacddDlW2W0w1QBREJbi6ODKnK46lunwqzpvflSj/ZQ3Sv2Aj0z5k4fVvDfX2zZHWj/8EY+U1GE5/c3R1UT3W9BkLTZmkeARZp6UngsFniiss22oXIc/B+8TPWjdhsorPMj8mhwYBtZD8UxRAs0U4hzq7XwpDodeQqAXml+m5HDuqOyVaoU5ZzClJ/yyh8kLf17oeaks86ggmp/QMWhhL5V8g0449JYIkDJgCuh8OQCFofnh301rL6uk1z1Gl62XxYVFWgogH0YA1RFP1jI0IFjCS1B9OtCruK7SH/U8plQ7si5hzz1anzq2oQeGEb1mrq/SV45ennq0gAvE8+Qdyg4hZN2OP/DAHvhy1o9dhoIIc5HQYbp24kIQN5GZPb5oABU8bxTVpWMB8OEIsUnEG8UBJTjdRqnD+ia1z4RJt3OmVL4oBEy4HwabkO8UvFXgeaqjAGIgpDXECTRRxjiFiaNZOccQGn0TeumM6KadBVMy8JUKM1jHDte2UweSA46czO+8p71Ki0b9CNCZ2u4BI2+/MAa4hknaxKSyMs9nrqgOZJTaV3jDHlBS1D0GQ7Hx3kTkPrXdJOdFAEaR/TKljwCTUPsQQFnQhH/LdoniN/V8WPkZ4ITb7TypuEsEUoeEKpnal2l+eyqnVNr/MCbopQcHEfwSre8Q80gZQKUS9QLFgqL2cX2m9mV6hfxVVAuKlEQ0v6zcNM2vBKUw3ik12QOAk5UIihhQMbUvASWi86WofTmyX47gl8HVcEDR/DactHcT3PSzwEvfBdm7sAh7N+GPHeZ60qrIpsDUhKFOt3E8T2O6R62PhCZ39heq1FgbA6Qm9VLzvmCDh4i8Cu9d2AHuCKACuMz4RFc4skH77qQw2BFaIpXlvghQ5euqFZQLnuTAVGfLCKL4vWPuKGEz6DJ7NZMeMgDJRvOrjHpYlyLD0v1Vkf2yLhF9hbml4HtF4DSL2jfxQuXb4DFGqtSgKU0nGKP20dilz5k6HtmKzJKvfOUrwx3veMdw+eWXh/vd737h3e9+d7Pta1/72vDABz4w3PrWt07Lgx/84NH2TZn8oE7o7cppRW1NAiVVngJS5niLlW9/AkjZY3qWi7kgC8WbM20VmVJitbITy42zr9Qt5h1/dKmuEel83OvqIHD2odoofqsOmjwgxRckgSf49dikmtxGhT8ug6HSU2M9X35NSVX0Cug4ywBpmKRd5PZUyfvII3MCThxFqvcsYRcN5Q+2mTqcANzldMqJ6KXARoiylOTXEJYZy96ijBjz2vE5eN6jvQ68Frtfe50MLbJMtW94s5314pEoNGHbh4j3oNm3YMRP4y1o6FfuYxTVi9uMvVe7vo4eXLf9bJnZbxmQxFVmmmrZrrxQpb4cBjxToBbK/vbcqNiRulcAlqaCt6l7eFwFDmw773i8X/pLuhs9UeaZbZzah8+u+iwagSe6ajqbYOq6664LT33qU8Pznve88N73vjfc8573DA996EPD5z73Obf929/+9vDIRz4y/Omf/ml417veFa666qrwkIc8JHz6059e+dzKLe18YG6uhDU+RAuGqo4BnBg4UK1+IU7nW/ajda+zsAPTRudiLXx1+4Zr2p6/8QzcR9cCI9aLZD1LXpAItr4wtQ/aeAEmMI+UBI3AJXmkaq9UqmPaH9D7ch0EnUjeKZ1HqoCoQvcrHiru90o772F74/QyFmDqXknAiwEkovcpLcu9sqTtsZypfskzJcseLBBwgqh+EmyCJ/BKwAjIKk8eKTWAswNCNViiYBPKO1U8VDIpGHNJwaBIvKcwQGr/bO18KKDxUcCJ6JEaOPgEeacGzjPFC+eXkr8b1ljDhpYuW6+X9m4KYe/msuynvwu93GTWcbkwsT7jWPmc9RLr973ruxD888X6IywxGM0eLSkwDax7S24z5EA1F6nfiH+pzPWSr24O0PSoxwLmcr/Df1WaB0MT83Ss/V1Wc26w7XGKB+yUYayMSVTwCJnGiuOWorQx9QbvK1TxBIKZNs5lpI5zDik6pgL1xeiQvVHkkYJ3VYIf+SDeXyCHYWublO06zO1l2jl7pSxYV9H8Jvpq6+1LdYayJzS+BY1RaAxkaH+b9kxtTC8N4dTLidP8rrnmmvCkJz0pPP7xj0/rr371q8Mf/MEfhGuvvTY885nPrNq//vWvV+u/8Ru/EX73d383XH/99eGxj33s/BPb0X18md5H1nrJU752r7Mc6zRNe3RW8N9Jj1ML1CAoChuk9tlz2Gvma2nUNwUNUXPmRo2EPq9AmcyBAoDF1L0wJ5qfBWV04xK1DxAuAyJKzGvDoeNcKJtnCsf35faB6gcvLZfIojfUk33lVZIyi4Ap6SkOcR40tY+BU9IFOE+KEvUmpUdUigyk2HLOAIppfs4C1D6JiNRUWIbuJ4oKygyeWsl55QmNfXzoxayDSiiAlRL1RpofRfGLbfdpPUX2o2XD5j+xoB/xGF22XC8xzS9+Uy0vOYk/KGpYDqgvmNvcNdw5Oquy98ygoK9M26v0UR1K2juH7Ofd06piHCFybBoHlCh9ecZ1LhddtrCR+8xDT9thDGLX5fo37VUY6vGMjTjI94d6nPs38COVQb77nDGcvh9avx3IqFD07JyoAlp1Oo5UxwY9pt9586OUbhoaNEBdL0ZmKcP8qqWZ2xsFaX5Nap/WGKLTcTxTHiW8DCdQjaL2IagqgGub9NJZ0U0n6pm6+eabw3ve855EiZAL2ttL69G6N0e+8pWvhAsXLoRv+IZvCJdMjs1Nih3UjM7fUxoWvK3yjQ7TGxbH/UhaA4hWp4Jl26mAAhvmjC1A+bWP7yTsNaDOvRYEWOx94k10XI3vJ14c9sfNpshRZ2ofWwqZemGpfWhAg3UIYVuie3ig2zx88IjWtIg20NdeUCfPh6pjRcQPxVAB4VyNx+QCqdpjhe+Z1zmCnwHtx9ZHdDnreqnlBbGLb7Dg4C/eMu/Yc7wyMpdkLiXPzE8Z8xLoyf1cx54A8P6YgbKcA+ev8O/e0P1WWbDvSe/HY3Hg+zMdTRPQnbrxY92piU5QFdRWeagmgJTsYw+Oz55AajVO0hH6RIcgCJ+gkOvjFR2lvgFz4/WxgQVhdV39gJpV/mdRD3zEGAyb86NoTK5GI3KXs+WZ+sIXvhAODw/D7W53O1Uf1z/ykY/MOsYznvGM8E3f9E1K8aHcdNNNaWH50pe+pLYnz0KywvgWFYxWMyWzvlHvx4YjfmtdUwPVutwajHrl0R86Hlu19xPKraIsBhh/qjaNB9YCTKOBJkxHIR4o7HSSpYZOj9Q/E3Qi3pCmDVovFB+XvFEBaH3p2OB9wjL1zrFOAJR4p2wwCmrL9Xyv9DBTEHTK75EtoeWhyutSXHaK2se5oTjPFJeXWC6eqeyNIkpfDNmcgk5kj1Q6IOeTSmXreYKcUvQ354ji8qCDTgyUV4pySpW/2jNVvFMQaAKpFfj9seeq+jg9ix6Apj1L+Qsqn5QEnUj1tB7TbMXywTHMmVrVMNI6Rpet0EtjuinS/BJLtNgs2oMjR7zBUot+7X4TzlwPW26yE3Bw6ukzta+22FfHaB1r7Pxj9zdmTBkTxziWumGuZ88Nl1O3kDtq7HpE/YH+o+FHfR3kGaq8U5dC+Jzqw+OUG/ai2ZO1mAYJDm0wrXKwngHKTO1L3wNT/bKxoHipTHJ4KVPUvip4hC5zm2DzSfHxggkwUXmpikdKovhh1D4TbCJpasyhBgU9NGq8cGOwU+MdovfJ+ASxrLBrqM3elumlY9RNn/jEJ8ILXvCC8La3vS3ccMMNqU/+0R/90fDsZz87nD9/Xtp94AMfCE95ylPC//gf/yN84zd+Y/jJn/zJ8PSnP/100fyOIi9+8YvDG9/4xsRXj5OEPXnRi14Unv/85/sHWNiOw2wLOoJNXhm5oAnQYQ7rK6kNUvtUuUHnq46lzj1M3ltLqVlR+Ame99zf0ErUvjCD2gfASuh8dENM+fOAFM+laodDJ/C0V5cTsIKXiA4QBFzFh1SeUFHLGUQVQAXUEn5WdkKwBJ3I2yKICgygJKcU0vyY017CocscKVZ4wllH+gTSKsYt4QyUlJKybVnJDQ6QImWlkvIWYr7hqDs/bvXDoWeHlD5F74MQ6AigmELB1D4ux3YbVg7WirruMbpsh14a001pvtA+VLS85SirDrgbIEoONQG+mpQ/1cbP8Tamw1ww1aKQN2iGVpRBsN7oU3IXzhiBwRJ0GcW4VUCVHiiTF4UvgbuarbZtENBxE8QTuMGXNjomMhH8WDdxmb8Dp5yAU3CofcYLqetKQt6sq2pqn9UvAoiwrVwLbQNgVfQSjJPwHHSDLWrfZIqTkd+y6gcwubyMbTJLojI8G3C1TXrpOHVTNH4tl8vwH/7Dfwjf+q3fGj70oQ8l+vaXv/zl8NKXvlSMWHF+azR8RTr3Bz/4wfCEJzwh3OpWtwpPfvKTTweYus1tbhP29/fDZz/7WVUf16+44orRfeODiErrT/7kT8I97nGPZrtnPetZaSIxS3xwcXLwJbH2zLGKHcd5WgpvhWtpgr45x5ijKRreJ1unjGPWAAaWGqzjfayxTB3LbK/2scdubVN1BHyqeytKScCSaqOgUHU/AkCNiB0AwD6DJlWGScIcyS84IEtF70MMAopFWQtpXVErnLJarKKq2gEAUhN27YLKyb7kiQ8Tv08HSLFS8utgGwc7MdvZCtjldMql0Etjuom9sfhhK3LE2Kc1tm100DsfSFW6RWi2BgAN8ynpeN5Jr5OqH1a6bm8bUq5F7/AkIfYQ4fUBEcDzHqnuxZ6e7xlBmt1+Il3HDKVN1yaAaoYMUwEtuCw7gOJX31IBpfkvgi/43oxe8XSQqgNAYPWQpfi5+kyNsVB5Vk9B3Y8S9SjNh4RlBE0MyTDAhP1wVI4p2D/sjjzsYQ9LC8ud7nSn8NGPfjS86lWvEjAV57tGanecDxu9VXe7293C+9///jRv9tSAqXjh9773vdMk3Yc//OGpLqLIuH711Vc39/uVX/mV8Eu/9Evhj//4j8N97nOf0XNcdtllaWmKWJuAzrcJs5FHOYBtStmojgX2N0rHteg5ikm2edfSUlj2WOYBuMpq7Bkt/DbcAYzug/0r960KuJQwn+w5wnI6B0atMZS+YLxRnBdK0fpUFECTT0qVYTSAy56O1pc9T3rJt8JBJSAQBYKuxoMqFD9ep/uiB5z1gQFKSPMbGjS/WBepfYrmR94oyi1VovZxlD4CWJIPCqL3GZqfneTLdD6dZ6rQ/0rUpELpUwl89YSu8pHhIEt9Xw5SZeVkqX2cX4pzSIlnigNN5GAUy4NC7ROaH+Up2ZhUCnrNY3TZCr00ppv2bx7CvjXVNoxLTfEG6WOCoKbVflWw06iT8wAYq+vMuRrXNGnRxu2r0Mpl1A79BusFZbwiQBU9Eoy/Yp8mfTP10xK1olyXyn/L19oIUHHsYsc91RhI0/tmdyUwthFvFB6AKXzB5I2y1D4GPBLdz3ibIqU8HQNzQLW8UeCRYlq6ZUOoY5hEvOK9Aq8WU/ha1D75np0nNwKgBSSp6QwYnQ90GIxnuJ7LQvfbMZqfJ1/84hfVXNY4D/ZBD3qQov3FyK0veclLwt/+7d+mVBenguYXLXOPe9zjkvK5733vG172spclFxxHUYqRkK688spEiYgSb/C5z31ueMMb3pBygEQeZJSv/dqvTctKYq1DmwJSKC3w07gc2ceURy1vc4yVI9cxpbBa17SWrAqkcIIlTq6ENhVoMuDLWmeKRQeOgYAMgwgIGALgZkAVg6Xyt4AluXSTjDfVWxAljMWS3HfsQbb65aDofGVKUd7HofYBmOLj5gVpffQAiMvOCg6zzEtEP+GROxPNLZBSFAuwBuI6cdKLog11MhNF6Zuh8fElyMuoqX2ZykdzoKCc+efMQefw6YWXLoOnDUmn+e2OXkphvvf9z3dyKt7Y9jnv38Nwc/SRC5LKxlleKls3Vi/bV/ioWw8P9YCpSoZWTrKe5kMt3OECeqtcj1ZxdDWHGJseeqwsSN+jmyoJeUExT3YkFkBBHYIoLNM5kdonZaDa6Qh+ZR9Vp/RRTfOz9ainZLuANwBDilXhhznHsRYCp9G553YcajeaIBOVl4q9U7JNz59CrxSOdbaR5vclE9Ng0hmyovzlX/5l+LVf+zXxSkWJffW3fMu3qHY8XzZuOzVg6hGPeET4/Oc/nxRRvPB73ete4c1vfrPczCc/+ckUSYkluueiS+6Hf/iH1XFiPpBf+IVfOLUji1WHXpXCgR+qR6NYWeaAKnH5j1hCZ4CnljdKDiN9ah1oAoGVXBp2HHydZj8NrGAkgJ0Nz5NCwJT2BZOrug7OKUVVGA6de1qgAqburxF4Z1UpICpfDIKqfHYNksrfUg6mPioPmSeFykRx1mESsCgg3G4Wm1xT1hk4QSCJtB1AVBhJrjkmdsTD1j76MzSi+JW8HSVMulgHCUAV619RYscxZ6rLjuilQNbymC/J6xhMnfuZefsNM5pN9PkaQA0TAMpRsaijGueU37nd1mJ6zP2dpT6AoIE5EMMjVGNGzZX9xBVVNtpq8Sy19KJCYeHSiEVxqWzmPo3sp7rNOYYiNQYBBd2g8SlDWfDKBTCxztDGtZqu59H8cl2Z72TbKYOetx/Pn8Lzu0YB+IaPMg6T8QV9o2pMA+/BAiy5CqCe41hmS+WqOAVnRv8Z01NEA9aYfPjDHw53vetdZT3m/IuUvx/5kR9J86Y2LScOpqJE6kSLPhEn8droHBsT03NKZD80I11KaXQmU2DJVUyuAhxXcK1rmvrtuX3yzB+sR7FoUfqUhYbbsqcorjjJeaUN/VXBJVrUPo7oh4ErUlQ+eoASXKL8TcEliPKXPFDUPkfuyyBrjx7SnorgxwpZ0/9aL8SrRS/IAOsxd1RJ3pvpeinPFHmgOCmv5JMi75Mk5Y3H4Uh9FHI5fQ+chFdofkzXg/xSWH9RB5mQ8MsxkWZ8bJw8E2kVGM0Pgk4Uul+pT8/cA1nI78cRD4AppE5IoIkEigq1r+SQygl5Y32J2hcSzS8uQSh/x9B1HEUh4zG6bL1eijS/A0DjzbHrpgZFHtByO5rGZXh5c0YAU0s3le2Df4vrfL9qrlnxKikDHBrHcK4j6KMURIgBCT8causBLxk+GBBjvVWXVFL3R94mDzkKULJ3xM2or9WHdM+jHjA3YsNcqi9lYTkQUEpvyQSVkLGOpfZxPeoPolj7EfwGVb+nvFRA4YtU83RtGkiVPFJA6UPjH3uk5L6NV3ZKcGzDc3CpXublylxda8QrUf0wOnGJ5mfGQNuil0I5xqc+9alwy1veUnmmPHna054WfuzHfiyMSZwfxfKZz3wmfN/3fV94wAMeEF7zmteodnEerDc/lredKjB1cgI9irUUnQSQmqLdeUpvhVM0244AKfcgG3o2LlfdnKuKSmPLrePY9s5xK/ofeqCUpcdQ/cx2OS+My8ulaHDEc6jyeB4zP60hsJucRah9kEOq8kTli629UiWoRClrqyBP/LUKLlP/NAXDsxSKlc8NRGFyR0kdZpGXG4WbH4nWhWAfTMzas2k9Uzb4BAMt8kiZvxLpD4D5pkOjd5rf7kgyIvBcTO5HnO9pI0zSpsfH+VimvENjAEodY8V0G0cQtqMUYwrV04bKWaPmWpaOXAJOIFZAne3Q/HAsYSOuXlIZA24VtW9s/3yT6rtD4GT34b+tABOyHfWAAWGsbzwd4pRxcC9MCOk/NVVcMyq0t4q/5azuvUBI5ZlVQAoewuTvYUwESGHOQ/MoKyYF7Iv7qPHMYmtpfre85S0VmGpJDF8elzkSPVIRSMV5sP/xP/5HxSiIcv/73z+FSo95Ac+dO5fq3vrWt4a73OUusyl+J5609/TIBr6WJiia/rBHFVioO5CNibLemXpzUehGnrvoH7gFOECpMu1VWXmP6jppD5Mv2fMU3H01tU8DKehh+WGnY+ceRSh9EniC50LB3zyUJyAFhxr5DHLfXYAQRuXTgIm9UHEulL9PCX9O2znQBM2Lyn/ZSgjzpCjxZxWaloEUWhZtwk4Kb47bZA6UzJ3i7RQKHcCTAlLOPCmtsOwPgJ640PmcaH0JEFFgCfZGwV+ZE6W2wfyofW31y8Epws5I9Mo88YlPTLzzr/marwl3vvOdEz0j0t5QYi6PBz7wgSlceKRzxIANXWrZuzjUy4VjWlrn8M7fuhbYnrzN3vXLssxtImCM64fOwtvnLCZAjXir2QhTJf+F+ZjQ11ThtlWfoweNCwSFrHMbQPOE4NM8mRoruGMMT1nXoMiCIdEncCxOJm0DTRQ9QfNvqU7enczhBUA0mchZ0/c0/TzrHuuh0ufUYMwHcE5y+dYzNuDITiFTjAnwSultxjCMOgj1lPJKbWhewSmRT3/60+F7v/d7wx3ucIc0TypStyNtm+e0RnnUox6Vgk9EHfYXf/EX4brrrgsvf/nLVaTVObLjnqmZkgwycShWTFljxp7GIWrQY600Y6L2gzq0jk1Y+1YStK5Bjoy1wZoBY0OzXgeY8AJJSOdik/Nayh/S/KTDAWqfE9nPA1a6rOl+mJSXQVSm+RW6H1L6ONgEU/4YaCkrliPVY6fQ5rINI/fR3wycCrVPABXT/yjPVDoW5JFiYJUUAkXn44S8ogQNrSKVTVLeKm8UJPXNyXmBPmGSJypaBVL7GHQJkDKBJzwsxQVr6QuW2geBJw5ypD7OLSXgifNISQS/nKg30f72iPK3XwJUbUzGFPMqxzjluTx2QfZvGsI+0VdHX97i0g+uq1NaA4anj1Y+d+NH3LhfO9dW9HQ6kr5oicKHVnwVkZUqWTdQNDZun8s4/TLqE31hPGcq/QUdurWDWKb2Kbcb38ic/Z3jeZ4p64ECUJVEMRvIcBfaeaRYlzBgEuCEkfiULtFGQKGSE3Daq4yEuF8x9oVVqX2sn1jneI8fxz0yPwrnOzG9D8cnGKUPgZMBUdGwB/XLLab5bVqihykGnYjL7W9/e7WNvdBf//VfH97ylrekpL3RexVTY8S5sqvqpQ6mxgTc9Nsol6xvlk7WlFfZfy6QAnGBlOnv7TFVgAlu51H6zDXkYxLQ8hY4lkKtMANVdKogZ+wfwXzJQGru83MUsQekeL0AqkLxEw8NgzBW9NhG6grdr9AsjAkNFSM+Csdip62AYBgoF0yPEL1PxsKX2poQ6Ef6YWpqH3qrOPCEtQqypU9ZA82i6jYs20rTu5S5PHZBxMMy3XJz35kFRe72kW/Qq58ZhQW6y/bBkUandiavOAAWntuTj10ekN6dGoM+QywhgAhtirYftgNmvCFou47KPBHlPwfwjd2IS+EzQIrfCeoI2r4w+3h6RZXNdquTxOuE57c6CHUYXrzyZJExVO0DAVha1D77vLznawwBtt4aCirDghkHtcYuMATY+LezrXopSpxXNTW3KkrMCfiOd7wjHEV2F0zZj3BLP4hpRbOpk0ych56RKJsVT9Gc12QP5s2NsoCqQftTf21uKQZKmIdKPFPZy1Q8VkW7Sgh08FLxkiYl4zwp9EAJvc/PHSVGKojq13oBDH50Hc6PAnBl5kcVWh/UA7WPg04kQKbCnUOUPqH3FZpfoVOQ18pQaYr1r1j3qvwenE9KPFCoMDGH1Fz6BORCGQuDbOLTS34pQ/GT8r5fl71U7JkqVsDlwTF4pk6ZHFcuj12QvQvLsJcSF03IhuflzQVU6hJWaDt+bhcpqRPg7SqDWmtgyf0B6Y5cRY1SQAnu04vXmj3d6XeOuaMoD6XvaZqDQlYXz2go9Uc6qNH5oowAeKTVFe9pCkQpyp/xTvFfS99DHSRlOIYJcS46KAoHPEoGCt1GsRuA3ofrlb6BeVVFB+n5f5VHShf045JvFMc4JhQ6tJFE8CbQhJR5eoQXdALr++SeY5HdBVNReAC7kZm8G5RNGN7nyipA0vS3K+kPpRQwJ4JzPARUmHwXOxknOS8mpFPUvsUEtW9vitrH+aXyOkfqK3OjSjnr5lJf5krp7WrO1ExwmvtuDHued84MBPY2lXlUFbUPyqmtE8HPi9wnCgjofBxJCal7NZiyQMoBWUilUMl5zTrPu5JBl43cx2gfIvep7w+ofUSZSM8uRevLH0UGTZHex2VI1EugqSTnzaApR/DL9L7UJkbySzmCNj3QxXs/wjFOeS6PXZD9m5Zh/xDAVG1LOXbZDmszeaR4FSL7CBZgt5QDuvIcVwg0kcoIGLJHOvbnOdBn8USnPif2DQlYFUDFnjCh8SEuodNt5NF5xkfr/Fmzi4meodwVILWPHty6fYwCEfAQGDRROZ8S5kkJUNEBjCzlr56n60TwY4+V11btZ+brYlJepprbMlP3gNKno1g2qH0Tb0IZihk02XlS9O2q+eRI6UOqnwJQMIdXzZsK26WXopyBXCIdo267bNs3tk4Hbj1PZnNlZbTgKTjeKG8f1TEBJrWu7TFqnz0eASW1r3OtJuI2nKZ4uXB7aWaObZ4LLsoIxkAKPFccF7AwEOyNl4NxBL+a317PveP5fcpah+3NxXq0C3Nhet3Wm8dSPZp1fxM4cZcj+kH+jgLydW6OWsEV75brIY1Kbc1LbF76sJklSgz+EHnivHDiWS+XRxxgji1xvhTKcefy2AnhIAqwLC7xErZhgUieQtkynmquryKuSb/V6H+CGSCHkbnHpn90ZRPjSXuoFY2Vq1yCe2jXqzIh+EwcfSI0S1GD3gCAdIujU7ygEVI216l1EkTnw3r8Nuy7tu3xJrXiNc9phNqH4nlQZb0aGNQeKm+cgsdw1H11nqk2J6SXFts2zl1DdtszddzSGBhakW97Ux9Vw9tExjhjTvMuRHcPChTgvnOug4/lgRnTKYzOc2rVM40v7o/R+ZI3KbPn3Yh/iwa1z9D8hN7HeaPk1w8eqNS2hDNWQSfMQ+YAFKk86pHyqX3pLwMn6mk5cl8qxwnSwXqjYh6p7IZjml+m9UFSXuOZyl4oDjThRPEjSyAHkhBLoVgLwStlPFdxW5zsqyNtAbCCaFvVQMiiysY3pylQNjISBZoIQONjLxV4o0q0Pq4r5eSNImpfzjOVD5fq4rLFPL/TnMtjF2TvwmHYW1KynCgbdnLOllV10czrrIkglQUKyqSw7O9a+t1iDCl0aRNKmr1NdKzkQRKDRxx05z4yhS9nKhWvxz6Qg00ALmDv1NoyNejdtLT0tq1nlxtvmzyutVw6lD4BMjWtjz1SApCQiocJ4T1qH3qjlGcK8kXx+SAin/ZYGaq5Au4ObVDuTwN69Tztw/PAUsvAW83TlcekckvVgSacyH3EsFCRZjvN79ikg6ljEgRIs2QTli2jZ5qnMVH5VH+KIIt/4GIeWd1aZst4KA8oyX14Efpwv1YiXtmPwBLWI3XPq6uofYXCp/9iuHMCUgCsclJeutsSx0AAVlLguL31nrx6UF6YUypH5dMR/BBMJeCURvs6n1SmWxCQYkoGcNTlLyc65Eh+Jmzs+DwpqJPoSUDzA9pECZMOVAqk9gmQGvnIVWb48t3mqFtE8dvzqH2UqFeUEAGn1KZE7QsQ/ryALFBexwGmxqziqxzjlOfy2AVZXFiGBYKp0yKTuoEod047ZXBTg88CmrIxUIOozCwg/4fVKxx1b4+DVFBbjM4bzx37Ij5+zKNEYCDPjzKRKFJ/tKHAH8YouJbXYJX2FXAyhlfR/SP31/JeMTCScqmvovWlcmmLgKfMk4Lchg26XgllXlP06nrWNTpanwqHLqCO6tP1FSOfnSclgAqfRWvuXxhj3PjJeRFAZZ0Fzj9Jz1EogGUb6yNI3XFsNL/NjF3DGfBMdYy6LbI4we8PjEju9Uxdm1UGqBQaIKkFtKqAEwjAjPKxxysdFFoyG1HXzLXV5RpILaqofeWp6Uh+ctUlIS+g18WaL1QzWQSWyU2W/tyeodw0R+1L7Q0tw06ubVEhkD6haDKKT44LPQtD39A31Ejkac8d1hWFavMhaQQmVsBKkeE3V5RaUVxaieH3uelpmO25Z6stpz2Xx05IdC+fimWcntdcqvZoVDH55NRgFr3VZVudcJV6R+xbULAtVI6opqPLigeqVIG9qJUucubJK3DkLKFdXjjHqCiTXN84h1DKcf/ZNL+iZ+rrrmmgVpd518d6Sj1u9/tpiPNR8cigqrOUFRwLlZGEprQ0xl5yxQa4rQXYL4FeWmwxk2OudM/UNgl9+GY8rkSMRtjQWpjoWNx/eNQ+ZXyCbfaUs353jUZqQIkdxwjAmqL0WRDF7mwGPB7lr3ihaHvLIxWFI/cFyCWlqH0FUKUlna9E7Steqty5qyh/kw80Ahz/DbA+kEATJllv8kylcVjJHRWpfRzqHINOiHeKckIl5RXLElSieKfQC8XBKDiPlFj8JDDFUOrdPFO8HayHSMeQ4BM8T6KU5ctsKTDv4Yo3ihUQA6ISwU8CTIg3KgebSDQ/8jyl4BILziFF1r4DWtJ+hU6RAlDE5QxY2rYxl8cuyOLCxbCIfNGtlkX7N9jq46rtZMiQVfQwWWo4t42eJeLcKV2QvUu8b/I2xWLsn2Ofx14p7tuT8SkrPqU6UZdy5WIThkrwPszYR+lHqa/3XrmbQfBB0TIwlPzKx0CLpwIpmuanaH2sQ3gbRNyrPFJzqH0QRMKjoyc9bGmA6IVyaH4J5Mu98H3hHDt4CIP3YOQfM/YpQEl0UxqTAIVPxjCQioPrE0Oi1C0TNZ3KXE9MCdnPlIdT6PQ+DdLB1BaIAlAtaYAldxu2wRMMDaBlLwb253HsWBTephXeAiiuW8wHVeKSXvhlnvOUVAK6sCsgBvQ9njM1Re2DCH4FVJW/DJz4fFxeqDL8Vbz+luiN2qhWKHqxnPr7BKQwpxTNiSKDbGoPCXlVmel9VK/Dz8I8KQZWRrFVZaMEK8ofUCgYUMkkc5gf1fRajep8ZxC3cBL0skKL1L64wvOk0ncQARTT+FiZkUKT+VP02BL9TysvAVbHwUufawmdOsYpz+WxC7I4PAyLrR/xGCBEdW7fZmm3AKaKRx8UFJUZPJW+ltrE3yLpNGbuZhpgCa+XaHuxPkXlk6tTNGk6C1wf7TxLIU+LOP2tUdHtp4wx0WxX3gWvvNYF8uMlI54dI9i2vAkvEj1PYoMk+ngwYMmZM6X/zqD2wbyqkkoDo+8Z+h/ObVL1+hhW95TrwnxScJ+qP/bm8BogZdgw+F1wWTEk+PtRND+I6AeJeu1YRyX7NWBM6rZJL0U5A8bH3QZTVU+3ZYJ9fEPm9PtjbZTnis/pOEcmv/XGCWyQCT5nBbQskGopIG+eVbQ64jEral9WFOjBQgVWjgW9pihw+ou3odli2uuO4wanbkzcZww5pLjjYnxRqH0EsrieBw0CvIpVsCgCbzKw3qYoFaR4PEWIbVyF4wAi9DY58FH2WcfIMLjh0HmbTtJbQs7SXCqh70GkPgFbJcSstAXOOmao3zSYkmd7xGN0OQWSrSTb4d7k308lDG50nVjbcX8VvQHK/NvFv/bU5WwK7HBwiOoAslMeEPN8qjo/VC7YI6wNpDyd1bgZhT9wQO0dc6q8ScF79y6oQgCmna1TXh3tqRoFUo5eGSu3dZCmnBfF6YAAGw3S3IuaHzUlzvsRTWcHBaKH4LKszjJUcgWyHPaOAlGmvOlvZxN66azopt0GU1GGY+6XZgCiyeN4AIclTaaFc0GUIflAuY0xwMk5YL3SnTOuu0XnqwBTaAMiXLc0vqoevE04iFVtUh2BKEvtC3p7yyPF+aTSpVCEvjwWZ5qfrYN6egEcaCKfZs7D1BCDFTyHP19WQSdyHSbrVXmk0DuVABF4oyKtDwJNlDwcmlbB22xej1ImWp6iBA7NgBTp3KaclR4EpyiosChLxwJY20N05L4yP4o8UwyKmNrH0fxS7ihI0BvzSZH1L0fty4ElMJ9UovRRZL9E7WP6X6dSdDmKXLiYA6TM1hkrDPRGAdIK7Rt1EgpbNhnLU8DfpLMd6bhpG/WGkoqAFFwMKtH0UkGCU+5PUsJdgGQwx9QaY1Z6Lmx8gUOpV+HpwIbB0GNvYH1Tz64qMC4QsAChCgfnoQj+tMcQsOHQ+oKh7eF2FcEPDHuJlleo5OlREB1dyg1qX2FDYBvNkgheGfNG2XlSxjs1auBr/a7gOxfDXRrbQB1Fl2SdU3QTPRpF+WO2hAkukfSYw5RABkVqdwaQyxbK7oIpr2PYtIyBoBVk0lhmQdLgz6+yoMvbv7rcuZ02KgJvkGuVCisi3oYKw3qW3PoRIAU0vhbVTwEp8ETxX1bMHk1PIvH5YwRa0SEi5j5HBlJiJeUjGKZbCXK3MOVyVgFSEniCHoRkmS/JEwXQkPIr1D3Hg+VR+sw2VGyK4oegiZWWyR1jHkZ5IvhQ8KHbbxmBFHujwOvE1L6gaH6lvo6YZLLHS9kPO5uXYWuT9nbZcokJe1P4zRXeF0Whm5LcF60CpLzBIQAf/wSwnftUUBAIkNJ2GFTK/YCewj6WkuiK4oh9Cx1P3T9tT9H5OLY5nWBDatk/hgFC6q+tMzquats6/rEOJnizadQCUvweLJASkBUmPVJYX82XmgBiSOkregxykwnd0NDGWd07+cn4k20CqebH4z9YPRYCQ4Idnzg5DpH6V4BXKdcGZj0msvViNN6U9KS9IrsLpk5CEPTwulNOIGiizRp9pACqVFysc4DxY/NhPCVSWdWsB8orN71UEGiCOw8+bipbIKVpfRWQgrlR7I0SMGSZYtV8qOKNYuBUPUZz72o7eBJVCHoAUpa6x2fSwInKHGQCaH4ZPNU0CwFUjoWwhKjVyqo1RwqVIfLSa2Wqo3Ehs7KAq/o7T4GM0wb+iOlHgt9t9aKQDgFBJ5DmJ8EokFde5kqphYJMFDAF4EqFny3zNDYlnea3OzIsl2GIP7DWAKOqls5i+tjxn5Z1x+3//XlQ4smoaH0AoNiahwotAZvGMbkvtIBElEcGXqkdG1b4Xiz4Sn/XUGpjzVW/siIo8kBWuSt3veWJaoK4xgfQHDbg45n6dppGrgaQApC1mEvtMzTyCmCpcglrbttW9D/QL2o73wvWp7oRw17r4cv33XoD9lvBhO8wT4r0j4AfjhiLc56QSi5lmusLgAsp6bm+GKA3JZ3mV6SDqVVl7DcztpsBSLmvRy657tisVwnbVHrCgi3vOP5tKJlzT+2OXJeHhgLBepf20KwfXJClLTUAogggKeXMND8EUcHmk+IIfgSoxqh9AqRoyo2MLxhscT9Z1t3nKQ8VgBM9MPEuEZjCPFJI7UuUvtjmsETwGw4hp5RE4gNqX4rgx3Q+S/NbONH4kPrHZZj8K0l7ITGiJFA0+T+MNwsthvxA1ONKGIqoPbLBftwWQDF9oiTjzd+AieAXl5Rwd6Gj8mGZKRdE54t0P47mxwl8k9I6GLY+aW+XLZeLFylMqEcVWJHSN1fGAJbTcUnONtxX/XUAV9ol/+6oU60MIGmVc8CR8UNdVrz3eIg0r4x6Vr6UVMVzqiANxNz7bwEk0F2VNwAuzuo20VGSfsHgDMvAqJgUaEwk3QavqVXWF+Tcpx0vzBHomoXKaUBJ8QKRLomnaAEk0keVYQ5pfl6i3hROX+sRNPKpSH1E4VNUwPg2kFYOnqykq+S+DHui9TzxwSLgVd+1XlcGPgY+MB830fKCl4iXcyAitY+Mf14QJI/yB8fvslnpYGqmBeZ4T0gJA1fZy3qvyqGqzpLBiQvAWJAGOHKlzQZVR1IrIlRWsyx7E0BKr2tvlN9Oe6iUNQk9URW1j8cDpT3XlTlRYAbTT8x7iu4D9MZNWFR4A8rCRGCvlaL24WK9U8UyaK2LyuvUUIj+X02nyPU2WzwOCGnDLIU1MgBQA7YyCJRkoFDHc6eCsvAxzY/LsI/1XAHXvaL+Yd0mZZWB4dgxumy/5MmN1tJC20wnsCkxQKicrxWhD/pPVDTsXgL2rRgNExBa1h29uKTYWkj9LwWQKPcL3mguFxSVS5Wlcd69o/nGHQJY/TQiyqMEz7SpPw0DowJ2eEXNNlOyCnJqCCblVfXo1SGdAu1qvZEv2NMhlqkgqt3RPXjuyhvlebVA7xT6XrmZAqS0p0Td8xz9xAXnO/CAtAbV9A2OtNFjnDoQRXD3M9MitkkvnRHdtNtgigeXqYwmoxV+PMctrKf4dwb6QwEqxFAWUIURUGVkyvji7mNBENabDt/WKS+UDTaRrDMFoEggCS5LnfFIBQ2cZP4KgC5cdKhz6AchmAQCrDJvKj8xnPgstzPqt24/fDU/ih4CBp3AOvRYcTj0HGACHmIal5Uyz5MSWgXPkVKWQAiLjtxzpPzx5F/LYW8pMgFaJiS6KDrzmxsbMDbmauicUho4DVVuKVtv50Fx4InsdSqWPQiRXmWWH45tkm+n+e2QHB6GYRE/pOH45ihYKZYhU88wBQAXt+dVNR8K/lLHiDgp/fYtMEF9JG1ZD/OOTtu17rMBSHAd762YyaBOt68Gumab0jfBaQe3Vh2ft5lrdQGfd41jFtMVPiOZO4v7KRBFNHEp035VSPOibypjnJ0LBeHVQ+VVspRziNznzpOi40eBNBzWSKhkzvMxz1pAObyviilRgZ7isRJqHuSdkv2A1lf01Xg5G/nonR/DfN5O8yuyw2Cq7nFEaVhB1/alFARP1DcoQMVFo2Dwu5RBamO7PZ/9qJtWDNPpt5RNpTTG6H1hBqVvzBtlIvQNXr6oRWN+FGybS+3LQAoS9PJtMfAaedr+OCkfpUwrQhA1Qu3j3FFcdnNIAUhiioWJdqToE5bSZ9omAzNsD4bKlxSWMzm4Amj8iChJ4lQIWvE0ed9ja56U0CMwOS9HPgJqXypDhD6m9gGoivVxPyxHut/ygL7FRA8cOs2vy9oyHEb+7cVGJxH/3zzVL/d/Hpii4CyqYfmtJb1oQRavJ96zBlgpVDlyo/l4sW38kSZjGCu5Ar6Kc+roelhodzyGBv0DDhbt1WYOd0AAhekTav2E2/EcCszBMeX6VNuiC5uADgXbuQIPs/UoZbM5GAIneXgFIDFYEYATdBAjL3CEqm/klrIUcQ9M1dQ/oJqTXlHGPaT3saHPDTox+jDr5w5AXKh9MA9qMKk2gkfho/ollm3yXZ4j1YraJ+VB15PBr8vmZXfB1Khpx8oJAKmGEU55qLgOGQ9mxyokenCsgrjaGqh6AgrJ6+CtNc0qBNyOx1D11rJnAJEGY2B1gzbF9QEmkOraAAB51D4crwuQ0kZZ05eWccSsh2kcMgKkdGAKnFaUimIWhZfnWhGd8xqaH1MwrFdJPSKzqMeK+wmQLyCpKGCrrIoiMxc999HpuRUArADhVt+QB9JVNCVL2wPlhxGV5Hh2nt4mpUfz2x1hfq7zvlJy1WN4jaMOn+bGnChXsjWhXkplpP1p+l8evPJ+XNmwDjYnEbuX1N4++rs0Hbj3GNAQaHZVIMzqKuc0VT80ctkueGq0dQGXgqf1Wn2AkVDouI5AygAstT+g1CY9HI5bdAeo7xE9lEyQqs4Oasw2q3Mw91RL5NscaeO97ApAA53fqm54t+50BTMeUt8Z7Ndqo6Y5bEp6ND+R3QVTUZQp6hjPsxjRBy3gQ9sqoITtQAG5FD4qS9+BA/251w2H8upVG1vfsMQ1I/St442ynYTQ/wyQMuXsaaKBvpNPKo+r0RsF3isGUhL23FABGw9ZXhcm4qUNuU/nkOjsnQIvlNQbah+3FS8U0yWI7sd5PjD0eStbvPFYta2GZpIvW/lgYq+2FtYR/ITyh7/B0e/QGwDAM2TrXyqTNZ08Tx61b0nl5I2KwSRSIAmI4CdeKqD3GS9VKSO9j4JQHG62Q+k0v92R4XAZhvhjwkGfbKR/qne5ysudoMmqeu4waYgtxqhiScq/Neo7UC/FflX0Ds53cqJz8twobjs5cK1F+tSKbleAElKBkWJVgR/SJal7sl4nNKSYbe5irgmPN5sGaK/NvkY0GPoPR8W60gU5SBtEGTCU69pzbsVLhXmmGknfcbscD9JpVB4llX5Dz8dVhkDOJyX9J+aR4k/ZztVtGfZGHq183zjGIc9R0NS+8u2U4BKKwkcsCfZcqUASUh5JycHGv6iTLOWPjrFJRdBpfkV2G0xdSsGxIAMgKouVDvTKyoAK2qbDNgAbr05e60R9a56UACiu9wCUUgzrg6gKSOH63hiIIgAE21rUvtoLhdQ+GyYdxg3eU7YRVyFBb0XtQyBlaH5pP5gnlf4S5U+FQcfIfTAPqtQhQNLR/FRodEi+K1Q9tR356ph1vgZdtSds5piphVBhwm7hmev5UQy0Cn0CgNU+zY2iiEgpKh+Uhf5HQEmofVIeMrUvRfaL5SErrZ4Yscu6En9DI2BqaAKsOd9cHXWPjyHR91Tz0lkLfTZVF5CVo+9lJYMqLnNdC8BRljUAVgVIAdeOt69C61N6BfqCpm7RUdWUk1/NbQFvNdKIXWqfoXShQdECI++61P3Qmzb1CuuwDpsjahxQDtoEUGMgircxna9F7QNgVRnnJml+9A1YOjromvp4pKPS+YxegnoL5PI9IpBykvM6n2J+PzOpffRdybeiwJIJcsRgqxW5D0EWUPtyeTD1NHaCeb1dNi+7C6Ycq0xVfxLjITTQ4aXY+UwWeM0BVeqA5Tit6/BkDETJYVsWtspTRUCq0VbORzduzy20PmlrHhwej69ObbcASIYN9bOoQBUoMRgvzEYGOhfgOLXP7D14+2BDx1pYfdcOqMF2Hs0Pj6EerVVKeI7q4mY+H/mgR/ZjyoQa8PBcDOebc2h5CoTxwGrC2iyWPpzPAGA/lzfcedh3uO4xupwCASpShZsaoGk2TQZ+V0PrN2ercB80+lG9ChIBxxgx6K0sDghwOni6Du9Eug33CciI1hzt0ndUj4lEHcMDS9iG94H+qKJp4Tlat+Dd8ooye9exT8r27x61D/4qHWOPMQLkRP23dJu9N7iOih4Ix3SV6gypmzkvz2Hk4LpHz8PvyIvQp0C6+fa84/r6Cx/oFumlM6KbdhdMRYGvsuoIbKcwR4w+Ut6jGe0R4CDjwfVQsR7j/Rrz8tOPyut08JRTvavTX1T7oZJpASgERRMdAHqjpB1G6pMcUdY75ZQjdY+vQcpDpvexDmWqHtH8cn2h9u1RLzyH2ud6pdDWpYDUCLWPHpx4oDjoBNH6SnJe9khxkAnjjeK8H+SV0ta/Opqfm6B31uRgU5a/mtOuwqfjw1C/hzwfo/r41DcHYYdN0AmOiMQ5pKJlMNL4AuaTio9J5YhiLxXnliqeq7g95ZPiABQHAwSjIGtf/J6iFXB/CIseza/LusIAZiDPhGeMsHVHnnOQZz8pZSLdLygR1D2S940BFTVYZ6BfAZFiFCn0Pfhb0fSgvegQDHRB/YF4lUofgV6ETM1Cgwptl8SnhZLleabUXEqVXsFpi2+w0onFK4VGxGpQvqq0PhMH0CwqsGTQpaXMiWfKzMWFyH4e5c+j+YnXCc4jbW3+KEP348h/NeCzdQ5dFl4IjVbM8MwAbnlfAIAqah8miS/R+lw6H9PJgdoXLLWP621aDvZAqf04AAV5q+L6xbAx6TS/IrsNpgqM2ggyroZ+DS9TcNtQQ3EpwUHD/GATat8RnCQgawaQUh2+U668VXMBFLZXisaAKFtv68BTUIOqcTofjxgshS9dGrdPK2tS+6oHz/158U5V1L70V5eDieDHZqycksaAKqZZAKWvKhtQ5IWl1UCKKBMezQ+VoUmCqC2JlXbzf3fybTqWABOSuQB3VFia2sfBI3TSXgJNPDdqQUBK5j4Z5YUL0CpEeUVFxgqNly5d1pL8uyj46KjeqHX3i78poDvZ0XscoKV5M5abvo5wJ0yLHE5FA4J+H73PAJIEaFlgpXWN9BVo8UdQZesBQOlj2LKmFUoKD3sdcC8KMOFwxGtbPbYj9DMOgFKHbOWOQu9ONfepBlLV3CgDpnSqjkIP90AW08oryp9qi3OjyOhprkHyGtJ9VFFkZXyVdZBoevuezLfpUvu4TLqHgbVK1Mv6yqbcwAh+KipfKRcdBHXpGEMJhc66iQ1+XTYuuwum5lhoSLDjkDbr6jEYfI8OJEfqiWmhwVADGDX1HLZv6MGVQVSwiqEGUlZB1DQ/mBvltK+AFAA2r5yftQY95ZqHGjThNgWq9FNZdeyA4AkOU1H7CrDih1Kay2fnJuRtKTde8nFR8WB7VV+dUD0u9xzVNvt5tegVVpSVm/a2zxoHHLRPZR20VD/+y5Y8q/icgZEMnqrIfYbeJ20y4Fbf+6Ykcf6PqASPun+X3ZQ5RrcJXQEWJ+gYnB+K2W4HqxgQo4AnBFV4HEPfVYBLAxarhzwKHqdmx/qKTmXvAZ6DB+xcHYjGRNwfn+msznT191c1q9xiPpBCHaO2wXqrLDok3boxwOG52ehcXaOdjGzu5wjjtXLbLY8rAikztuHNGEJ/BOB7ZavLWsfRNHPf8FyWYbv00hnRTbsLpkLjB4t/07eHrpk1f5QL3aEpCh/Vpz88UqaJuNiP2d+xRJZtbFdtW9c0dc28/6iCtJ08/ahVnacwoFPA/YxianqjsGOAiIC5HCl8pdNgOl/LM4Vgqk3tQ4/VMPsxNql99IBqah/kjuI2TO2TCH7ZA4XltMTWnE+K6l1PUwwwQdS/iroXc0hxAApjBfQmB6syWvhgu0qqSM9iMdfYoAYPoFjyiyjfi4ngV/J2QAQ/ofmFUk55oSiaX4rER14qofkh5S/T+5geOEiZAk/Eb+dgmSh+i4sbTjR1xAGBHKPL9gtaai7FO5trGZJ+maL7CbCBJUXpAy9TBYCcPFOJSlfXZSs+de7xL3iWuT17m7GcI6nBhH/qG8RDzccA2p5EXzPUq3w+nROoeBZgMIuBBVhPsUcrXb8DoNzBsUmtYPVtE1gd3Xi8rkcKDXKyvhz3QlVJ4El3NL1NnOi9CkYBXqpg6IHIjODw6amIaTrkVstjNLY8BEzcFsEVGvI0nS83UN+PeJ2A8kdMiKSPwAOVy0VnST3Q/DIFnTxQJgBFYN1EnqnkkYrTGDbpmdqEXjojummnwZRKxHvcL5MHh1SuABX/oAVQ6V/4WLAJ3ledDs61jqwKoKa9VACcFPUhX6jQKNR+QOFLbQyI4mOZcn6uDISKvmfg1ARQ3CeCa6W04e1ip1rhYRbrVjGiUUdLdbINyonGx4Y3MTlRPZSVJY/WkRaB1AvMQl9ZFi21D5ShG4XJKFNthChKTB6AtUq2HlcccBXrghyxDDwWjhIzND4TwU9niOeBlRd+tuamlyUrLaZMFAqFXpKy6lSKLmvL4hKeapVzFVAkkf9wsJkOtxjxRgH4UiBMOt5GXfndl9+88TI1/irAxb97uiYBUPLX9Cmip3zPwlgZgU8LPNXgyiToHQVVLTfMCuIBqbAOtU/rIY/9oPSLp3sa9UUHkQa1VD1sqyyW5XqLLnLW1cNr9NkWROGztkCKQDy+V82GMMDcUENlHhR+r1SvQLwAMdZDfH7eRjfKQCoZmmnZpGeqi8jugimLPtw28wZ/o4LAydR7xyyAin4AfJ3AfnJBlbnuObc3dd2jAIqvTwa1TvvFSJn3N2BrtjfKPUYBRQVI6blRmo+WO2AVgMIBVUwtmAwSNUHtUxH4VOqlctG8j5xVhUO34EkDqqLgFj6H3eb54PlS1hLIj8lTcvzolBKDG2zRDPWDmZRsR8gffckNYwF6yeWhKQ8wqLIAypsEbJLzShlBGP7lc4nC4vxk0QvK3s/NKqzW+GnVY3Q5BUKDttz9Y4JCEO77N5rsUnt982UUAIUDR91RAsCROgc0yXFsO72PpeOV+ho8FVAEnmnPS4RzKsEjpQa9CozZAXMNiko/YOZJNYCTrVfAacKAqQbo5pXhJ7HmW9cHWYnaN2KcAz1SdEQLQHH+wQYgs/tW6zYRvA+kZj8QGYOZDQv7Tpy5eRUA18EoXL1UeTvBM2r0Ee+P9QigBFRJubBxFJNnS/TSWdFNOwum3IFeVUYUsWJv1TJ0QH360J05Tbib5gjnhq3DriXmFt0Dwq+l6vArgDThlUI+OP/opT303B6IArqempjDEfow+a7Q+fTgtuSRYrBkvVT5aeQ+coLax23p3yozhfVISeS+MWofvWOm+Q06h5Sm9vF2yB0VE++yVwmT8CZqH0XvkzLUH+qymghsgk7gBF8/lxRbDElBVpN8nS9YWQigpCesFRDESooszZnWUKh9MtGXo/YlmkRun+l8nKgX6BEUzS99d0Dty1QJovlxoImUTyrXL/YztS9+f3v7y7B3sAzD/qZpfhvINH8GsszvhKTvPdLaltkwkgCVbsK6o1Yew/peKAZQ3HFG2UP6HoArqS8DyrR3pONxu0TRK23zdmzD1D2qD5baV9oOQvNbuDQ/nVsutKl9ONF/4VOvZLBqvNoVtY8pxKZeDC7K8OJ7sTzDYssImdbV+4I2U9JyulQAZMQjBTmlikFOe6RCg9aH+kHKUm+jvUIwitDOJ+UBL9FPcP1J2w6r9YFCz8QHrcYxhtZnwRKWmfFgGBIpcTyti95JOqbsh/VFT+VxkWZPcERZpvnRi4t6iiIULw5yBOPhwnK79NIZ0U07C6aSTACpY0PLxvIxP18UbXSsJjxGzUBi3mXILXvt0aSD1rDKMjNSrxTCMAKyADBhuHMqywOY8kYh6AFqX6H+4Xii1CPNj4FUPpb523pMcMh6lWl8iMmB2mf7ETWXlrbzzo5F0LMUtqgULfqF195mi+fHXrezdc5kYPNclJWSK1wLAYAoed82UhfSefAvWIkxCWJa17mktALEwVS9aLpGcDxTFFqfgX+XLitK0QUMpGrPlJAW7GeW6saMFQ3lwGBIOkpuS3OcWl6lVNSgCqxYUtZtCu2u9kiN0/ywXn7LAt4MtY/OV1H7DOjR/Qh6qUw/YoCQLVdAKYx7qFCHWZ1YvSrTfhODE5faJ2W4BAuqjP6pdBDoCgRfvs5ogCJzblCeKqS5uj7btpKZQKoc2TwwD0i1/yJrAkG16Bz1/dWeUVVvALpiS4gOAuMzU/tYFy0M1a/LxmV3wdTIYM9iiVFhhYaUvKm2a5RFn1acQUYsBvTMlcaNzqUcVO1XAFG5rqb6jVL61DlMoAk4twSaEP1fe6BwbJAhDowjuEv1fNh4306nqz4tfn+keDD8ufS0leeKvFFKgbCnSisxDapQuUHwCbH2sTcL5kK5QKum66nJvg2lqB8NWBud55Ofdf7AVT42F0CVFyMKJdhw52hJBmu1zRqPc6LEakjfHVv21JypMk+K+ekSXpb56BFAEYjai96pY1BYm2AObph52OW4ZG8vLFL4G/oBiTUFLCsJZyEnnCT2E86LLr+3lgBwgbY5WAR4m8BjpUBW0B4m8SrFteRd4v3Iw2TaD3wO8Drp+U57+vddeQB0AArxWEO4c/Q8ibfKUK/Q4KIGwzjPl40zDbBlwZo70PYCTtjt/OJAxdv3va5XSu0mesgHRL7RDHQQH9Mx1LWNde02eiknUCwHPF9j1CN6fKzf4weRhm+ihOqHhKBb1DYDeljn78TmmUJKqdVBonNa9ZZuTuwIr5yupwCoFHwLDH17yaO1OUWwKUb74gzopt0FUyOgSkXw28RLJu9TKo6AJbHkwA9cD9z9G1jVSNXsgB0ANXj1Da/UJHiSegBFmIgX23uUPo7Uh8dTSXYBWFEHkut14AnrkUI6n3ixDJCSR8DHwScPLwb3GKX20QMrIdFpSVH5SmLeJEz/s5H6MG8UU/oOkfJH3xRuN9GQFM2voutBuapzIvihcm39buQDZyWXB4QSnRJ/AOqbISXGiTZRSRHNT0fzY0BUyjGCHwMoScTLeaaY/segK9H/kEpBSQ8TbYLoE0SbiLS+GMUvKqr9g8Owv7cMYeM0vw30RWdAYe2E7OdEMWkgVKwx8rd2PGnANV8faE9U8UwB8GoBKEvzQ3DEnigEVhaQEQ2wJMstYCpR+qQN/9YLmCpGFEjKTWUFpjCqGg9OY/v4pBQtGMAPgCz0AiiPwhi1z3q3ERyZnFOp30Oau6K8e+UZQGpxjNQ+SaJr5khFwfm3I9Q+qzPctsGJGAvgqrpWy6iAbUofzQFV5teDAAoBlbzjVoLevTa1j0GRUPhIN5VvFOh8Kq8hRY/FpL1iAMz6KJ2bAyBROUWXjYa+/Wjo2zAFfRN66Yzopt0GUxWQIjf3cbzYBohqlnndXqtTVwGeudczUu+CKFQEbj0CIAO2PDqfrbNKwx5TtYWBA+4HrBAGT4Xuh0DKMl/KvqnKjOebj67xrdgBjzGyKW3JlD+uk7lSwUTuC75nSnmQ6OoWI3RA5TFChegqp7b1sPlbmfH7SdhJvnfzIzDfV3pjoOyUVTD+he8SLYAymKqUXLEu1/sUwI+DKo9Kwd7PTDXNXlI25J8JU1uXExEBLK3tTt26X5tL4VOdqKHzIXBywNSi8mK1qHsmOqcFWkJ3Qpof/+5b+yPFyouq1ggKIH/bUft039CuU3/N+XFdMy4MeBp70XiMdd63rUBEZlSt6uMt8PIMZ44usYPtygNlj++t2+Op63O+fEPeAdWx2g/FjEsEWKkxEn5HU97K+jtVnlEDwGsKoNFD7JWib8meD+eH4/q6306XcdldMFUBKWdw2Cg3v8U4AENAxg2HGR4qaudam3BO1SbEHMvtvLGPxR9g1elrgDTMBFE8YNV1NViapPTRQLbUEVja88KeQztOwWinCWA751nxnnUdlK3nCTxSeTsYmpdAAZQQ6LRdglDQkjxOQOmTfBo6Yp+K0kfbFDhCD5OyJmoPk2tJFNBmgJWh+pXtE9pLaTpHcTUyy8uACcESWaMxP4eiT2A2eclDZa1/YB2UMlsE2eJH1j4JOjGEfbL+Hewtw35M1LVhz1SeW3A0gHbU/btcItnfD4sQPz7qYVWH4U/4XuvdolLB+U4MnKTegJ1Uz5aDcpzsjTJepShSF39nsJ+i8yHNL3qsCuUv9beK0svR+wzlzws04UTuxLJubwJMtIJRsP6a8kxZbxPM/23T/kr79LqtLgxHMKDKjhqYWONauw2giBkGuMoQB3ppzFCX9YvWN2oIIeVGgl9P0niL3mHsS129ju1R95Q69ECpd8+U0ip6rAlAwTpFPKLwLQK9XL41CUABuaM44AQAqpratyTD3jLRzqNuioyJqKs2S/M7ul46K7ppt8EUoIg5QKpqM3LoFp2Py1UbOYFzDrRWrStjVi7vPLZeOhTdsSuLG/+VbRYQkSIBBaOOp6h9VETAxVH7wAOVBrYCnBAwGRBFdD5ul7o/A7KwXACWfvJj1D4JhQ5zonCOlAJY+JfofBLNT4BUKcvfBHpMBD+i/yEtT4AUKzBL2zNtJXqS16aiZFDyROlMHUtkvtkRfQ/zPdjwYL1QCKJwEjkMbFLkowB0vkSPKGWOmMTJEJnqE6P4BYzml6gWQOnDMtH9UvQ+TnxI1L6kpPaXaYk0v4P9w3CwvwxDyny8QaH3c+RjdDkdNL9F/ACpL8oWF/lN1cog1+U5VlOCIc/tJmtZMl4lqF8gzQ/nQAnAguh7FpBBBD/ZBsl1GYTlOY8lsl+h9AKdz0TxlHoc1GK0PgQ8FeBqgCWz3ypgSgMlH0Sle6Vj1HrYeLDKa1xJlKMcxz3mk1m0xjtsxKM6Udumz0djnQeybGAjnHOzGAVYRVd4hry8vz8/itWLjMPiO7eDd2VYKH/RqKc8UBDCXObWVUa88o0Wml/5ViRqH1L7bNQ+pPYhsIK5u1JOieNjOeqmrHv3DjK1L+mpg2joizS/w+3SS2dEN+0umKKeTH5CE0CqKk+I/IBbp0ZwNWdH79yLzQKqytrlWcfwkjwglY5jPU4N8DVatt4sA6QAEElH2QBvNZBCRgvcVzFGjSBn7T5ULYymY9whWhD3w/q0rl8Oj5us5a1Fk1DWRXNhVkmViwOFhAEjnMVVxlO/h4ntLeDOf/UjASoEKDX8rloUi2Hqr6L5FcpERZ+QCElm7Mg0P1rSJN9O8+uyriD4SJ9R/PDIepE+RsfaVjgRM44v/9R1HpiCyHgCxCovFbUXbxTMmfKAlI3eB8CqzKMq+ymKFRtUQpjMP1XAj6ULGm+3S6ui7WFFep/tf8Yi9tl1C6RAjr1H8fRDrd7r9jP0y+g+XN+6FqwzUh7Rik9nMV5XdE9NF+W2Y5RO/H68b8VG7WvRS2uqoPF8Vt8kjolYJ/Hn32l+xykbTN+1vrzyla8Md7zjHcPll18e7ne/+4V3v/vdo+3f9KY3hbve9a6p/Xd913eFP/zDP1z5nDL2HhmEblScDlR+SHgZToet9l9nsSGd4UeJkWNwbkiuJ5ewhNasI8sgf5et+FKfrDBUT4u4pHmEL+csmbpx/kluQ9HSIGpabqPr4iCWI9akcvpbOhE18E36VQebkExRCKpGRH02nCtKeZ54KeycpcyBMp4pDjgxuoB3Cj1R4qkqQSXwr9pWeZ00BUNofE5wCfZKVeCsoEZSbp7WM8pFAkmYAZXQ8uw6TCCXJW+TIBIxT1T0SlFOKamXpdRxsAn9dyjeKaJVpO85TuylvFKZ3hfpEnlhr1T0RkWv1Ln9ZTgX/27YM8V0iqMuXbZbL0VZHByExcF+WEQP1QEvB2U5R0tad7bPWmA/Ppb9S+V8PXkp+9Lfc3p9SMsB/c0Ltiv1e3n9XFz2wvJgL9XJsk9LKi/S3/jbju3ybzz/1tPvOdWXYDK5XazH333+jXM77idU0BlVXvj1eyNlE64669Wsv1BfonGmmiOTPgCjc50BuyqvMkAGT1M1V5YPaz1QZpDSovNZb9OYV8ptS0EnMIGvt4i+MQbDeT+uMDI/DwFK0T8lWl7WS6x3gqeXsC3oFvnO9hvfFuqh+N2m75R1EOokWigAEgebKHqp6Kekm/ayXsr6aZlo6Acb1E2b0kuLM6CbThxMXXfddeGpT31qeN7znhfe+973hnve857hoQ99aPjc5z7ntn/nO98ZHvnIR4YnPvGJ4X3ve194+MMfnpYPfehD613AlAVlzn6bsIhQvesYWKy5IFhywJXt0AX0cGduM3BbALWwIMkAKxNWuixOnYAjXV/Aksnlg6AKLDAMojhMtYAsBFHG1eJR+9yJre5nAEl3+a+h9ilgFRk7ROEbFLCivzyHCpIhihIDICXudanjqH4l0l+VcNes52PGhIhO9nnVRgMp9GaVp+BbGcVAEHCSrp7ozZZmsUwjoBIFRYoMlBQPkmy5gKuiyGpgRbQ+ahOVkwApD1ClJSfn5SVR+0RJaSAV/25Uhg0tXbZfLwE4SqAKwMziHK5D+dwKizqeWa/OhWANQZsFUACceCEwmAAT/c3tI0jiv1zG9QKeMmiistTxOgEpHsg6xpQMnHAQW0AWDnBTWQbBOEhugS1dVikVxDhJFC07h8roZDZc4oRUz2NRebOszAZU6IKhXZ2+YoH0Prtt7O/cuVGiw+w8X8dQB7pFqOXmHsb6tznjpTI+snNxecF1BNSkewRcayCF30v+Jv1vqdQPDSBVIvVJYl5Y0pgoRuxLizb2icFv7zDsS1jGLdJLQzj1cuJg6pprrglPetKTwuMf//jwnd/5neHVr351uMUtbhGuvfZat/3LX/7y8LCHPSz83M/9XPiO7/iO8IIXvCB893d/d/j1X//11U/eeoHH/WLHOshNLmPns5YwlyIHnUww9WjKgm2t+rqMZiVDu8N5zVAvrms6k6L9q9E8SrmehTk+nhc9UuPCZy+Hz38XZn54Te3j/aXvoAKWZT+pY2Vm/uKtwaurbgO3GaVW0SwquqAJQ2ufq0cvrB/V5EYOe66shuXWfYqORPXL2z2ajTUguJPLyfupqRVAMZVy+WspffYvL11Or5yoXmKKHIcU55xNuG6DPayzwNwlOT4fM/2lBbdBTic0gKh9TBs8VwkYAduq3zF7BDDPlJeU2wlJ3aBNtSKtebThVeh8dnurDvUoGpi4//E77xUA0ohMHsLogKoejzUyGLYAp9JDE13ipAHzOLtUGQDAVeA7kndl36n5rmTw4rXX29L25vw6+/22v7M8J5wCcRnjcvmpE/MG5pV3OUNzpm6++ebwnve8JzzrWc+Sur29vfDgBz84vOtd73L3ifXRYogSLYa/93u/t9rJpzqNsfZzT+H0Yu53vIEOc9Y1OPODuGw7ENUOwZMHjngACu3lfKgkqjbA4YWAERrwQG4o2EeXy301A1BAfylgzLnfVoeOgSdE93Ai3TAetY/XlxxogjxPGUSRF0rqua4EnlCBJnCSL+1ng07YQBLpRNYzBRZE2xZzfLSsj9pD5ShPfuJj0ZMwYpJ8F2WeggykcLCUgklQm31d5pwzbOGL9clSbSk5NlLfAeeWihZBAl6R2sfWvoNlqkvWPgo6wbSJqKSiF+r8/mHyhJ4nr9Qy5prapDSiuK18jC7brZfia4o0ub34UaY1sc4v7Dv08i9MSdW/QwWlGVD1Zs6U6kShjZrnxL97yTOlyzIAFTDGv/VSVqAKPAS5DANZZSDRk//TI8GoaqretEGDi9lug0t4A99SN5KEV+lLLpeOU+vqxvuy73LOO3fAktd/q9Nhu2D6f7tuvAvKNmvofahvXF1idQxc62LqOdjn4Sl4b18EuEjz4+/AgCb8Rr0IfqmedVBUs6SbRE+hPoK2g43ah7mlEqWPvq+U65B06gFE7TsoUfuiJ0r0FAWgiMyJuG250TxTG9BLZ0Q3nSiY+sIXvhAODw/D7W53O1Uf1z/ykY+4+9xwww1u+1jvyU033ZQWli996UvzLCXH9W7ndoAbAG5jAGqy4xaAZUDUYk6giWEWqFp4ZQRHUEbQZIESAys5jm3Pp2YAxsde9UUIkGLwVEAWAymBamYOFffSDKBULk4+LgOpBHTAEwX1CjQZvnndBsGRB4oKbc+bB6Wof9YThZbIYUrJ5ehJ6hNVAB5AlXxHJbwxD2JQYUlZFE8OiR6cpIasvAQomXDokjwx50rN9FWK2pcAlaJQZOWVKBQUdjbx0DmaXywvlhsHUzi4OMoxumyHXhrVTZEiF8EUAKmUrDduK/+IyDzFue+XB4ZOfVXGYBgQdKKAAb1dDCAJOFF/J2GkS0hzBl7FG4RACNvTbRnqlaq3QIfpWMGh1WEbPCcco4AzBzTNiNTngix6JLlOGxVdQ2ZLV3uvbBVAhRH8DJCq2go1wNa7l5nXcVxl9InoJNsWAJc6l43g512rXGq8r7JxmIGlQF2X703KUCffmgbx+K3JdxT1B4LxSmcZECV1hRLqhUMveaVwqkSZGpHmilM49JyqI5cTsKL6NH9qb7O6aRN66azopjMfze9FL3pReP7zn3/pXmzcubk/RIY5DmlduNcxNzruUaBEZZfKh72d2mZ7XscjhECKq0q/pnp8Te3TvXvZBwJLqOP53qgpKWHOaR2VDZ8ew6EjdY+vCCMbp/YArJxj5dtjF41DrzDKSJvYNI61AKlScDMTIZbqiR8IKngLqJQlEF8yWASBmlPKMAgco+2oARBZD7neBGGRieEwyMrzBenBVSyqEtQkUfkg2ElZIqiKyusMxHrtcjK6CSPhpY6D/jaSEab+eGzE7YnnKradLhg2Cn0JQRadHz1XCITEuk8eKcrFoz1T+Lsu81LkNyxh0qFevEYYra/2Ilhvk/I8sVcrNICSBVI8oF7RG6UH6/is5W22dbGst/vbFWI4tg6gy6hb8DKsjmjpFXssq2PMeaqLGFMtE2qH1IysjAzDqnWlQs370zQ/+LbMX6wv29gbC8DJfFc2KInWafRtYR4pGS95c8VJN1VloJ933XT2wNRtbnObsL+/Hz772c+q+rh+xRVXuPvE+lXaR6oG0i+i9e+qq646GqKe2q/Zux0j/G6c0/VAYRktZWNtGCS5YGwFOh+0zzobvFGik8F7NOGNQrClxwI6Ul+ph/0mpKb2GRpfsGUGS4vSloNNxE1EyyvJeHPACeWNQmqf54UCyp/1PHllRe9L59C0C1GCSCFsUS/oRmc9u/juPEDVAvZMMUKLMQyoiiUwT+DlwQ/n6mhS+5jCR3mkpC3l5MgBJ0xS3giiOHpfBEyQTyp5oPaA2rcY0t9I74sgisvLTeeZ6jS/M6WXxnTT8vy5sNw/0NZ6sNK7I8VVXq07YAdLlrFqIe0J25Y5IBBCHHJEye+agRNvh7bqNw6Aqgw20cNUqFWY26fQA306nppjBTS+2uNQAyq1XbU9Ip3P1aOkZ8felZXoseSQ9TO+ATmc8fbU/T0kgg8zjHEVtY/ryrxbdyYA1jeA3GxBg93Ec1PGPLoQDZB8Sqn6viARb+WZooBHSd8ob5Oh+XHALgxioqh9pKcstY+DayG17yCzI3IEv2UyikZqX/RGMR39YHEYDjfJmug0v+0IQHH+/Plw73vfO1x//fVSt1wu0/r9739/d59Yj+2jvPWtb222v+yyy8Itb3lLtSQZjrCcpFirl2MZ8awk7X1wsn2rHYQwlwU5ZrZet1k462WyZAFSuc/COVIGaJk6bFf0Oh2XH1c1BpgHpEQMkKKqAp64mXrgeuzD4x9e0jYAVGWBdgJuCpCqvkMBSAC8PAXX4rdDHSo1VU83qpT1zN9ABeTNt1oGWzBnAb1RqLBkQjpGzOL5GCaa1kidRNmSdRO2uKJT6DD8yRu1FxUWKTCzRIpfjJa00YhJ8TEtN7N02Q69NKqbDhInJwz7FOEuhQjfT+shhhTnkOkxoS0vByssaj+OukfnU+fMS4rAJ2HKvRDmlFz3oA5nLmHNYZ2j70kUPojGlyPtlTovWifPlcxR93KfEAesHDlNQlGTsSVTgBuhzk2Ez1Yfgn1DjnhrQptjWQ3KSwfb0smsh11dHGUMHFDHvNKwxOvHVbkYEau5Sw0cqI7jXYw3frJg7SiC4H+kWVa5NvCJfS9AKUVjnlpQZ2mvk2pPbVq6iCMhj+ujMErtQ53E5QyqhqyLom5ivUR6a9v00uIM6KYTp/lFy9zjHve4cJ/73Cfc9773DS972cvCl7/85RRFKcpjH/vYcOWVVyZKRJSf/umfDv/4H//j8Ku/+qvhB3/wB8Mb3/jG8Od//ufhNa95TTg1sjj6/sPc47YsX7ZHXMyl+Zn9j+KNcsoERTRlDwER1fFVtr1ReXvZFjZC7UO2DQIsqeLcUalcQJKEPqd6HfFPenkDoDSQwnWr5DxPklovj6M+hlJqJuws72eOMW49jA97UHo5sV/VN4bWb1ZoMD8q1ePEcDN3SihBlsZnc4OYgZGh/LGCQipFVFLJOwUAKv5lwMR0vn34u6/+RqvgGdAOOywnqZcyAIhIIP6GysA2dyTQkdl5JquK+R2WQxu+tdCgPI8VDGDRom+8UcXqb+iBSMNVRpW6TyheJeNhUsfQx8P+xPNWybGdgbWiAcY+QcpQbwfjqb7WnfJ8gjNvqnonI+9r6n1PtfH6dty9BW6MoW2WrnEAlKjlxjV6umotBsTYTvgeYF0opQrkGqp58lZa76kGXul4lRcLDYQ4B0qvD44+ysbjUBv2MLdmWifPFAEo9lLF9TSfl418Z2GC0hbKiYOpRzziEeHzn/98eO5zn5sm697rXvcKb37zm2Uy7yc/+ckUSYnlAQ94QHjDG94QnvOc54Sf//mfD9/2bd+WIibd/e53D6dCFita9OfuPwWaJsq5U3HmQtl6C6qOBKB0eww2wcdSwSgYHLFnio6lxwB4DK6e33mMUfsK3qBOV5LzUgcLwKnQ+AylL7arAk0U6p6N4Fc8UEDvY89VzCUF1qG0PSbqZcVmEvTmOp0rKh07tCP4xQGdBlwGPdpJv/gypC0MpnAz/VW0PvBOpYASQKVAb1UwwSNa1D5F8xPKRGxf6BNxPdF2mFbB1D6y/O0fZDpfpE6cA2pfLkdq38VE7YuKKkXz24tUik7zO81yknppeX4/HMYcUqm/YCtO/pO7Q12nxP5GRYxFqtpkglJoq5SiPql1BjTUuRdQYQGPTV8AA1InkASfQ82NagSEQKrgKIVvMU7tK/fCdcWjVP2lY3jgSBmN1MDdGhz9V9QUwNaqDvfnNhhcQhQXAnHYzTOUGQPaFMNBU/v4Lxg3Lbgy12cphbxt9JHQfVaAqvX47Bgm1dWhzAUUeYEkuI0KHlG2IwVdaH5AQc/7DUY3Ic2P8kjF80j+qJAS8aZASItCO0/BjyhqXwRNrJuSnuIIfqSPEs1vL9L8luFw72LYmHSa3/aAqShXX311Wjx5+9vfXtX9yI/8SFqOJGJqcOQEkXsTSM2oz/s2AFGjLCAKt8+dD4XHgnlO2KYVmU8fx4bOthH6NEASqp4DpPRlrfkeW1MVVIHOAJQIa72zVQzMZARhqX24Tjvlx689UqW+YQFsKDxP+cFj1veG2+2nYS2NejeoKwM4D0TJoZQiM5btynLMUf60osNBUWWlNt6o2mI4+Emk2QqYQs9CkAmwBGbvVLYGYgCKjfch+H6Pcowu262X4muKXikeuMmPJ/dtqv9I1fVLTYaXqtJ5/Xz8SodU1ihn4OkAKwMkqrmP8Nu1IKt4o40HSg1wW2DKeLT5d10dD7xKNviEAXLJuKI8U7r97PlQLTbIXDBlwZJX3xLVnzsHN/29227GefxbAcWpVX1pv2p/xGBxClDNAFH5vZi8TxCcRH4vuN0p+9957e10dREEP8q/i8GtTzdGOom9U0zlk8ASQO8reqgwJnI5/1Vz5LdBL50R3bQVYOokZHGSB57TX83tbGVQOgNEKaXpjIiVGalRb0fVEAlXekrjgUpFj86ngkqUJ+EHm8jbEbBpva+vuQJSXkcMwmBHAymm5ZVGJQS6jtqnc07hfCim+BnAxMEo4jozwgTolFxRuS38lXrIJ8Wep3h2m01eAajsZfLnTdETcKyEzedGConDpiuAZJ+92qcMvlJ7OyByFJLNIaPBVJkPoXnmZpIvTvDdByVFHqtM7wPaBAWbUHOiOBz6gudHEX0i0SlK/fIskMC7nIgsz0ULd/xQy4A0/co8AGUGvwVwzQBTvEP6O2b4yAVNZTMWfWpXg41C3VO/dQFTFtCYKHvoSbLUvgQ8dT9SDDENMFUNhCeCSvC5FUiEuU0NAJXrx4yU9kX4854W8VmNDTT5OOmlzx/VLOZ6qHh95vxbz7jn3Oq8K423Tm3l7lLdIo8nhhpQhbm6h9cV0MEokpopURnklMcKg0fAfjboRCqXCLJ6vhQY9FgfJZZEZEjEPHeUooPmQvFcqZRDitNzxLoAZUrVkSh/IQOruH4mJihtoewsmJLOwAM3ozw77GVs/YzTttrMqZd+tdEb2boxy5hq0wBWbr0FULaunEtAjuOV4v3TQNyALKT55WbQBtrl45VrzH2hY6lFRThMU/tKiPM1qX0UxS+1BxofRvMTYAUUPknEK7S8HFGpjtQH9el4mq4nXiXcD3JKaWof1DngSl6zZyFtWU29dRyA2YGZzR2FCo2VmYmCFLfnuSWspEB5Ic2PlFeiBAqdj6P5EbWPIiLFCH6JThHn/8fISEkR5ShIKYJfSsibPU8czS8CqPN7luZ3MVzcJJUi8Ps7mvnuqPt3uTSyPLcXDmPgBzbxmEGutvS7HdpM/QLUPvNXrPLQ8WowZUAWNa3mOyJ4YVuSeJDqNqN/kcbHXWjL2+QArxqQDW2Qxfcv9YO7Te67qUP5mmaMGdxXif0wvBzbByfdtnqgdFDR9sR5u2dYawArpPcpsAX7KhCX1if6JLgwBlZNQGVvAQcp6l1Bmef1VYY8J0Lkvi0T/VRFl23R/IgyavUYG/oONJhK+ohyHAai9iVAFQES0c45qmyqizQ/ofPlcqH55ch+UTcdpDYXt0ovnRXdtNNgyi1HWa0/OrpsAkhN7LtyeUI5NOl86lgaBNV/weuElD0HSJVja2qfvfS1Bedy2+/BrFfBI0y7ArzwjqDAQKph+XMVmYgOg+vR9apgFOq8DjiyF2n/NpqiPm+9A/c0atDSyBdVUYbs4KYuT69DDiljhZbtkE9K55aq83UgnSJa/uK3yuW4bFT6nKmdERloIYVYNkKhIJ56u2fo8Aacqb7uSJXRTwCBD6wQYJSkvTUgkmPYeUsOoLG0X29bWuycqJG2mno1L8luBaSMLqxShsxNO4KyGOlEoR7BxJG6l2H1ulWZYYu5Y611DjoYQDW2gzuG8nVMNc5p6BL2Ytnvp9Ynje9HqHuF2lf0Twk6oejmoHts2eY6tNtEL1F5/JmtKH3OlMjugqkoDatGMnhsGFB5yqkSWz+HwufV2f08ZYoUhFa9/EXQA+1adD5qJ9sc6l7+W3uW+FwqN5QFZYAGRLmkPzXQxNUaI5XBCnqgUhm8T7kePFb8F6l9SwBPSO3DEOgmqETak8OaBwoogfXKG9Uuq8Wh+KFXqqZoAPVPv8rmZ1o/4HnRk6w3SluXgUrByil6nnjApCx+JQAFUikkGIXUZzpfOiZkky/7keVvv2SOT9Q+joK0nz1TcULvvkzsLZN5ObcUTvKNeTw6laLLUeTw/CIsDsDHYAajuftrjKjRoILVzR81zA/B7YjjFGjy6H1wDgEZ3MHDILQBoKTMx4CoamoeVGu/CSCFA1o7V6reFzpAoAqi3msOwOmJuc+6qfP5hRk63+ABiCEDCLX/fIACalPrDDln20DIZe+blOPaY+N3uMpYmS4jzxXOvjn1GOABjCY6wW8UjssR+fB70AFJyOPE9V7EWKDzed6o4qUiHcQMCvJAMeUvXb7kNyyR+mI9U80TU4Jp50Ldy4Y80TscgCJoz1TyRpHBL9alSLNdNx2L7DaYCm0rXgXeTV+30uFbneoIqHK9UBNlF3R5QAn3X4zXLxptEERp0GTKwQFIOA/KicA3L1Jf3Y3qIBZFMjgaB1IYCr0k4kU6HwEs3k4GGU3zK2UGTrnMYApAE1L7qFwATj1nKoIrRd3z5knxK0FAZSL0VcdwFR+ER5/z0Y/os8oqDQMYq7xSG5wHhaHNJXqST+3TEZMKiMqUP6b6GeUVb5KoFJyUl+dJJQCVQFSOjJSiJRFoytS+TOeLZQFTUZFFMJVCKm46ml8B4Ec6RpdTMWcqAarGoLb8Nv0fnmd4nqKXW9Dk7oegys47aZUdml/pA2wEQJhvwsdwA1PUYErKcoxBHQ/bWoCU5qu41+cYHNX9NfSmqjPGyaY4Aw7ctEBARXOp7LYR8S5FA6O8BphRnx8j7I0CMr88efvNC69vrgL+zX3t90t63fFmMm21OR8q7pfymrGOKQCrStorugmofRzFL+klAlT7Zp4Uz9llal/SR6ybDsN+NPaRUY9DnnPi+AimzjvUvlRegKEvgqlNRprdhF46I7ppd8GU7QSU6eOErmnNsObzAlBMHHMFIFW7MHRZ9gOPkvZG4eEav6IKvKGnauoVmZc4rEDtE4peg86nvhvUzOb0rXOj9c9TSjwfiurRa+Qed/RcpWgphNW9DKt3cPFWFjObt+Yj6Nw1us6jTXj1q9D+cLJ5i9I3Ro9QlIpgFt43lcNGpc+Z2h0R48KMQerc3+0UmFJtjI4Qw9MYaBoro1fJoe3lezb7zfI2tep8Cp8P9mjAW/VBbRCVtK1bz+UGihjrEyr3C1UoIDUfPLnHX3X7HIC2iXPDAYXK6Bxi1S5VnRZyoVkqJ+ucUX0Txil9XIffoK4HlpBaIPgRj41cnRQdtpbSR8FtLeUv6SNiWzjUv7WjHDvS50wV2VkwheN/8VxsElBZT9YcMDSjnd6n0XHbjn2sw8eOBQCZDV++8ABO0xvlU/p4XUfu48NpqqBcstPW9s42rDofyNcP5eGNUfvE6yTAisslHDpS+3I+KaT2lbKAFqbugZcqeZyEusdeLPZGlf0WMyl/qsweJvBEqb/8XKcGZ57wYxwxqPK6RO9iMBNXXG9UzC0Foc+V9W+c2iflvSEFmijR/DhiUg40kQDg/jKVM80vW/8StY+9Uckzlel60QIY80il3FKG2pfL6JlaJitgXIZNe6a67IwcXhZCOKfnRiYZm+84Vo8yAqpci7+1Fwkogu12sCll53ePbSaT3zr7LRpAaGK/3M73QCXwhW2lTMe329L6DOOkNXCOSQJIprFCFhpYxSuugk3MAVmeUc1sU7c2BuIdL5VEdl1XDH7MVXmtrNeX7T5nBkh8XJcaavKbgWdKviOkoKNuYp2VAhuVgEdZj2FAJI7gRzkNOTkvUvvEG8XUvsKO4AATcZ1zHLJnCml+MRCSBKBYkJeKaOeZ/ncY9iPI2nQOxC67DaaScKex2DygmgukNkbnU38bAGuifmGPgYBIQE/pZVXwCFungBO1kS012PKj9lFbKrsWlQpIQWlk0DFF7ZOzSUQ/BlgEIJDax/tzBD+k9JG3qSifOoIf0gBHI/dxez5uK5pfKhcgZal9qFCPAqTGtsncCnewBEk4BUwBh92En1XUvkYyRImYBOHQmT7BZaH5UdS+YOdJ7bPCivzzEgpdaH6LQvPLSioqp1zOVIrcJodGPwaa35EDUGzqYrocpyzPh7A4B/ppxm90lTnlK3mpWvQ+qHdpfKZcA6G6Xateg6yZXiei+VVgb29kLnGT2jdhkLT1jWdaHm6jLcKFlqeqdZw5QGpCGqpUB0IS0KTbwuvZuKQ7l+/ODyEvwD2Vp2inJkl83G71UdQhUYtyxL2gAZRP8xvaND9F7cvlpIPi3wSmeN5uAVCsjwRMpXDnGUBxKo6omzKYytS+rIMAZJE+SiBrkedMbdTQtwm9dEZ00+6CKWvxmwJUm/ZcySWYr+goQAp7szGLmVIMDSDFxWpfVDa+N0qAj+yrQ5krbxReigFSq7ujx18K5oiiCvpbU/sEMFG7sp8hYg/OXzyuAi6G4ifghuZHVItDMTTKDfW8evUt62Pryc1s27IOjlGC9OCIrHxoKfTy00gbn/JXtWdlJfXGaq0iJmk6BUZIyuv5O5UofULd47YQwc/Q/uQY8x/9zAffo/ntFs2POE9SiQ1aO848vvfjdXREGZiW37RHBZwDoOx6s53xBCE9StePHcffpx08ol3frLPPzO0Qja6WztPRH3wMC5ysm+YYpKk1T7C7yACq3H+JZMi/C5NsOm2jFedbHP0OWdWqsvnmPf1jkki36H8cuQ/1j/7LCeKL3pkTrY8TxFeRZbmcCCCgm4COvrkX1aP5sewumHIA0hSgKlH+Rsi9M4GRAKnFzPZTnbgaVU90/hUQmvBGIeji8qINolyvkxPBLz/KRvJdVVcDq5Y+8ipVRD7xQBkQ1aD2Kc8T5phyckfNovYp75Sm82m6HgEsqmu25dehvFR0x45HSlH8LBAcA1XyvMvzkVXv264UlxOtzyTixXK27kEQijFqn42YhEl5mWJB1r+oYfLEXrL+HRTrX/RGJW/THufkIJofRUEqASi4vARq38WcMDEl7T3sSXu7rC2H50MIccHIbd7vsmWHm/gNq82LGW3tb9m2MQNVr86lBVovkQVM1Ebtx6AI2tVtR8CR8XLZ61b11b1q5sWk/i9P0Az+qY7HE+ohQ5vEScYxiK5LVL+ppL54CY5HqbnwVVsDnT3musLfCYU35+dgsaeHReeH8tf6h78TCVrC+gbK+S/pnRFqn47mZwNNcPRYui/QRzkRbwZXUQfFckoMD96oFAgJqH0cVIIT8V6W8huybspBkITyx0EnqIyeqViObTfOmuiSZLfBlJWZgCr/KNkVP6NXOSKQWqmM665CoB+1BVG0XYU2xx7UJNat2gLYatXnqolIfdV9OMFPHb0zKdbIiwl5gdqX1iFqX+WpwoS8YM6apPY1IvXFbRXQ4fKyUVagyJZLJD7bNowBKUv588T5PWA9jgnKgAXmRrFyCj6A0mAKqIDmr67LCqvsR5H7ILu8REvizPLMU6fEhymbPIdDj4qNQBTT/FhxpQzypJCigorrEUztS3lInPRI/YvrG5Xl3MHbxDG6bL3EORiR5peMdyt6osZ+w3Pofba+DGDNb9vUV3jAerEUUBrqSHze8aci7uF5cIJ/amOAkgVQDf2nAA+O2Vvtj2R559lAdD52xwwzcrRgXzwpi9VbWOBkdMr8c/siKsTqFDTSwe17d9AEULydosJKPS8GQAndD5JCZ5pfHRq90llE7St1BKyqiIAQSTbpnkjzAx3ENL84X3cPgJXQ+Jjmlyl9rHMSBZ3KBTRRmY17CViF3G7TumkTeumM6KadA1MxS3iU5Ve/OgPwWIuVt93pWB3rvJwf/m0duz5Pg+Ntzz9TQaR+alG3y/1XAT/IH8/7DLAvAbIKcKFnCi4H9lFzo8RgZ0ATgC9PMDKs10TN0BqcQBO0n4AmXgfvVGrHgIrbUN4oAdMMrMQbBaHQycPEQGwhbWE+lPE28b7ijULvkvVMDV55aLYRoBbDpfPnwM+O29IDsxOLq1czjH/r4o2KK5jLY2killXeKKJYRIsfddQS4py3x8AfPC+C50zFOrYQHsI8qXNlkm8KOhG/8INlWrJHa5mXaLHbPwzLGF42KciLYbm3DId7y7Dcu5iU2+HeYTjcu5Da7sUJvjThd2/vYgjRM5UsrMtwuFiGm//fBXqURzXh0mPt0fzOvPC3cvHiVylp7wRA8uob4/wK7KAs5g1UJ0GTOuZIPiYLiirgRVqv0RZvstqvAlye7tR1yLaonwfch9Fp89EEazhnV9E1qMtggME6RcraUGeNdanMt6NScUB/Dyk1ZD/WX1Df0h/aGAiP06ThUO35mpRRD++h6CTnFYw9Vt1EgWyHPu4Y8mzbtD06bywoWoKeOizUveKNAi8VG/CIKSGGvIsxAATXZ8/UksBUBluHqT5qzmFvGYa9GMyI9FSaizuEw/0YXCLnizrcu5jGbLFtXE9jtBR8IgegSCk6YtswJL0UDYEXvrw53dSj+e0wmLrxxhvT379+yQtO+lK6dOmyA/3N13/915/0ZXQ5Rbrp47/2iyd9KV26dDnj0nXTZmXnwNQ3fdM3hU996lPh677u6yBCzHrypS99KVx11VXpeLe85S3DaZR+D9shp/0eTvv1b/oeotUvKqvY32xEegCKMy9dN52tezjt1x+l38N2yNbqph6AYnfB1N7eXrj97W+/0WPGj/u0/khZ+j1sh5z2ezjt17/Je9io1a+DqTMvXTedzXs47dcfpd/DdsjW6aYOpkQ2HsG3S5cuXbp06dKlS5cuXXZBds4z1aVLly6nTrpnqkuXLl26bJN0z5RIB1NHkMsuuyw873nPS39Pq/R72A457fdw2q9/6++hh0bvcla+5R25h9N+/VH6PWyHbO099NDoIothU7F7u3Tp0qXLxiceR37799/laeFg/2iK9OLhTeH6j/5q+OIXv3jq5w506dKlS5fTr5fOim7qnqkuXbp02XLpeaa6dOnSpcs2Sc8zVaSDqS5dunTZdulzprp06dKlyzZJnzMl0qP5denSpUuXLl26dOnSpcsa0sFUly5dumy7LIfNLF26dOnSpcs26aXl8eumm266KdzrXvdKCdHf//73q20f+MAHwgMf+MBw+eWXp+TIv/Irv7Ly8TuYmpBXvvKV4Y53vGN6yPe73/3Cu9/97tH2b3rTm8Jd73rX1P67vuu7wh/+4R+G03QPr33ta9NHdetb3zotD37wgyfveRvfA8sb3/jG9ON5+MMfHk7T9f/f//t/w1Oe8pTw9//+308RfL7927/9xL+lVe/hZS97WbjLXe4SvuZrviZ1UP/6X//r8NWvfjWclPzX//pfww/90A+lzO/xm/i93/u9yX3e/va3h+/+7u9O7+Bbv/Vbw+te97pwonSKoy5dzox03XTyuum066UoXTd13XTiemk4ft309Kc/PT1fL5jGQx7ykPDN3/zN4T3veU/4t//234Zf+IVfCK95zWtWOn4HUyNy3XXXhac+9akpJOV73/vecM973jM89KEPDZ/73Ofc9u985zvDIx/5yPDEJz4xvO9970sdZVw+9KEPhdNyD/EHGu/hT//0T8O73vWu1NHED+3Tn/50OC33wPKJT3wi/OzP/mxSwCcpq17/zTffHP7pP/2n6fp/53d+J3z0ox9NA4krr7wynJZ7eMMb3hCe+cxnpvYf/vCHw2/+5m+mY/z8z/98OCn58pe/nK47Kt458ld/9VfhB3/wB8P3fd/3JUvWz/zMz4Qf//EfD3/8x3987NfapcuYdN108rrptOulKF03dd20C/JHf/RH4S1veUt46UtfWm17/etfn77ra6+9NtztbncL//Jf/svwUz/1U+Gaa65Z6Rw9NPqIRAvHP/gH/yD8+q//elpfLpepA//Jn/zJ9GO08ohHPCL9KH7/939f6v7hP/yHybX46le/OpyGe7ByeHiYrIBx/8c+9rHhtNxDvO4HPehB4QlPeEJ4xzvekaxpc6w923D98VuJ1pGPfOQj4dy5c2EbZNV7uPrqq5Oiuv7666XuaU97Wvjv//2/hz/7sz8LJy3R+vef//N/HrUMP+MZzwh/8Ad/oAacsaON39Kb3/zmSxqC9sF3+qlwsHfE0OjLm8KffPwVpzr8bJcsXTedvG467XopStdNWbpuOjm9hLrpU5/6lNJN0et21Nxan/3sZ8O9733v9Du7zW1uE77lW74lGZRi3xcl9h3xfvB3GA02/+Sf/JPwf/7P/0l9zBzpnqmGRKQaXX6RSsCyt7eX1qNVzJNYj+2jRAtJq/023oOVr3zlK+HChQvhG77hG8Jpuodf/MVfDLe97W2TJfYkZZ3r/y//5b+E+9///olKcbvb3S7c/e53D7/8y7+cFPFpuYcHPOABaR+mW3z84x9PVJAf+IEfCKdFtur3fEqoFF2OX7puOnnddNr1UpSum7pu2jaa31VXXZVAGi8vetGLjnh5Q/ixH/ux8BM/8RPhPve5j9vmhhtuSN8yCq/HbXOlh0ZvyBe+8IXUQXgPOVplVnkpq7yQk74HzwISeab2h7vN9xCtS9F1bycZnpbrj5372972tvDoRz86dfJ/+Zd/Gf7Vv/pXaeAQqQmn4R4e9ahHpf2+53u+J3VoFy9eTB3aSVIpVpXW7zlasf7u7/4u8e27dLnU0nXTyeum066XonTd1HXTtsmnHM+UJ9Hj+JKXvGT0WNH7GKl9N954Y3jWs54Vjls6mOrSlBe/+MVpomzkqseJnadB4g/nMY95TOJxR5fuaZRIU4jWyzgBcn9/P7mo47yASK84CYW1jsRvJlos//2///eJhhGV7k//9E+HF7zgBeHf/Jt/c9KXd/okRTs6omepR/PrckbktOmms6CXonTd1GXjegl0UwRScyjokZYZPU5jcqc73SkB/+its6AseqmiQeC3fuu3whVXXJGogCi8HrfNlQ6mGhI7vNhZeA+59YBbL2WVF3LS98ASJ+pFhfUnf/In4R73uEc4KVn1Hj72sY+lybExMg4qgCgHBwdpwuyd73znsM3vIEZJinz0uB/Ld3zHdyRrVKQ1nD9/PlxKWeceolKKg4c4KTZKjB4W52w8+clPDs9+9rMTFWPbpfV7jp39Jbf8Dcu8HPUYXU69dN108rrptOulKF03dd20FXopyorH+MZv/Ma0TMkrXvGK8MIXvlDWP/OZzyQ6ZAw4EoF0lEhbje89eld5HuBb3/rWFO1x7nypKNv/1ZyQxE4hWl1wkmLs/OJ6fPiexHpszy+l1X4b7yFKjLEfrTRxImOLZ7qt9xBD/37wgx9MVApe/tk/+2cS9SZycrf5+qP8o3/0j5K1jJVtlP/9v/93UmSXWlmtew9xPoNVSqyAT0vMm237PXfpEqXrppPXTaddL0XpuqlI101nU+5whzukeX28xDD+UaLh4va3v73QPuN3FOcx/sVf/EUCWi9/+ctThMiVJEbz6+LLG9/4xuGyyy4bXve61w3/63/9r+HJT37ycKtb3Wq44YYb0vbHPOYxwzOf+Uxp/9/+238bDg4Ohpe+9KXDhz/84eF5z3vecO7cueGDH/zgqbmHF7/4xcP58+eH3/md3xn+5m/+RpYbb7zx1NyDlcc97nHDP//n/3w4Ldf/yU9+cvi6r/u64eqrrx4++tGPDr//+78/3Pa2tx1e+MIXnpp7iN9+vIf/9J/+0/Dxj398eMtb3jLc+c53Hv7Fv/gXJ3YP8Rt+3/vel5bY9V1zzTWp/Nd//ddpe7z+eB8s8bpvcYtbDD/3cz+Xfs+vfOUrh/39/eHNb37zJbvmL37xi+laH3zV/zc87Jt/5khLPEY8Vjxml9MtXTedvG467XopStdNXTedtF562CXUTX/1V3+VzhOfLcr//J//c/ie7/me9B1deeWVqa9ZVTrNb0RiONnPf/7z4bnPfW5yY8dQitEixhP/PvnJTyoLR4wSE3MYPOc5z0mTGb/t274thVuMiPi03MOrXvWq5K7/4R/+YXWcyIeOicxOwz1sm6x6/dFKGfNFxESCkcYSc3hETneccH1a7iH+BmKI1/g3cuqjSz5SXH7pl37pxO7hz//8z5MlmIUtT4973ONSwsO/+Zu/SffBEkOoxvCz8T1ES1W0ZP3Gb/xGoglcculzprqAdN108rrptOulKF03dd20TXOmjltiYmfP+xi/5Ziq4CjS80x16dKly5aK5PO48ic2k2fq06/ueaa6dOnSpctW6KWzopu222zSpUuXLl1OTZ6pm266KVmGo+XXhoD+wAc+EB74wAem6GvRwh3nv3Tp0qVLl1MqG84zdZqlg6kuXbp02XZJbIqjKqzjv8ynP/3pKfePZ8l8yEMeEr75m785JcyMoZQjNSuGWO7SpUuXLruql4ZLopuOW/qcqS5dunTpcmT5oz/6o5Qk8Xd/93dTGeX1r399mu9y7bXXpshJd7vb3ZLn6pprrkkhibt06dKlS5fTKt0z1aVLly7bLhukUkQvES6RmndUiTlOnvSkJ4Xf/u3fDre4xS2q7TFx4oMe9CAVPjlOlo75df72b//2yOfv0qVLly6XWDrNT6SDqS5dunTZdol5XTaxUESuOHmYlxe96EVHurQYwyhmo/+Jn/iJZu6fGGWLo2ux8Hrc1qVLly5ddlQvLU9/QvlO8+vSpUuXHZJPfepTKmLSZZf50Zie+cxnhpe85CWjx/rwhz+cqH033nhjeNaznrXxa+3SpUuXLl22XTqY6tKlS5dtl01QIWj/CKTmhJ992tOeljxOY3KnO90pvO1tb0s0PgvKopfq0Y9+dPit3/qtcMUVVyQqIAqvx21dunTp0uWUyaYoesPpp/l1MNWlS5cuOwSm5kpMZhmXKXnFK14RXvjCF8r6Zz7zmTQf6rrrrgv3u9/9Ut3973//8OxnPztcuHAhnDt3LtW99a1vDXe5y13CrW9965VvpUuXLl26nLB0MCXSwVSXLl26dFlb7nCHO6j1r/3ar01/73znO4fb3/72qfyoRz0qPP/5zw9PfOITwzOe8YzwoQ99KLz85S8P/+7f/bsTueYuXbp06dJlU9LBVJcuXbpsuyxTQo8NHONkJAa6iHOrnvKUp4R73/ve4Ta3uU147nOf28Oid+nSpcsu66UT1k2bkg6munTp0mXLZRiWaTnqMS6F3PGOd0wR/qzc4x73CO94xzsuyTV06dKlS5ft10uXUjcdp/TQ6F26OPL5z38+TYz/5V/+Zal75zvfmfLkXH/99Sd6bV26dOnSZTel66YuXbZPumeqSxdH4sT7a6+9Njz84Q8PD3nIQ9JE+cc85jHh6quvDt///d9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+ }, + "metadata": {}, + "output_type": "display_data" + } + ], + "execution_count": 33 + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.6" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/minimal_example/readme.md b/minimal_example/readme.md new file mode 100644 index 00000000..9fc9d8e3 --- /dev/null +++ b/minimal_example/readme.md @@ -0,0 +1,10 @@ +## Minimal Example + +--- + +This directory contains a couple of Jupyter notebooks which demonstrate the +basic capabilities of the code base. Each will attempt to install the package from +the local source code and then run the example. + +For more detailed examples and tutorials, please refer to the +[docs](https://pisces-project.github.io/PyMetric/dev/auto_examples/index.html). diff --git a/pymetric/_version.py b/pymetric/_version.py index 6c7d66d0..a5076793 100644 --- a/pymetric/_version.py +++ b/pymetric/_version.py @@ -1,20 +1,33 @@ # file generated by setuptools-scm # don't change, don't track in version control -__all__ = ["__version__", "__version_tuple__", "version", "version_tuple"] +__all__ = [ + "__version__", + "__version_tuple__", + "version", + "version_tuple", + "__commit_id__", + "commit_id", +] TYPE_CHECKING = False if TYPE_CHECKING: from typing import Tuple, Union VERSION_TUPLE = Tuple[Union[int, str], ...] + COMMIT_ID = Union[str, None] else: VERSION_TUPLE = object + COMMIT_ID = object version: str __version__: str __version_tuple__: VERSION_TUPLE version_tuple: VERSION_TUPLE +commit_id: COMMIT_ID +__commit_id__: COMMIT_ID -__version__ = version = "0.1.dev22+g0f5941d" -__version_tuple__ = version_tuple = (0, 1, "dev22", "g0f5941d") +__version__ = version = "0.0.2a2.dev26" +__version_tuple__ = version_tuple = (0, 0, 2, "a2", "dev26") + +__commit_id__ = commit_id = "g7a404da6c" From e4b5dd8a8c1ecbe76165329778e0ddc95a55d337 Mon Sep 17 00:00:00 2001 From: Eliza Diggins Date: Sat, 18 Oct 2025 13:56:56 -0700 Subject: [PATCH 13/17] Revisions to paper + example in the paper. --- paper/example.py | 75 +++++++++++++++++++++++++++++++++++++++++++++ paper/paper.md | 79 ++++++++++++++++++++++++++++++++++++------------ 2 files changed, 134 insertions(+), 20 deletions(-) create mode 100644 paper/example.py diff --git a/paper/example.py b/paper/example.py new file mode 100644 index 00000000..73facd12 --- /dev/null +++ b/paper/example.py @@ -0,0 +1,75 @@ +# noqa: D100 +import matplotlib.pyplot as plt +import numpy as np + +import pymetric as pym + +# Define spherical coordinate system and grid +cs = pym.coordinates.SphericalCoordinateSystem() +grid = pym.grids.GenericGrid( + cs, + [ + np.linspace(0.1, 4.9, 300), # r + np.linspace(0.01, np.pi - 0.01, 100), # θ + np.linspace(0.01, 2 * np.pi - 0.01, 100), # φ + ], + center="cell", + bbox=[(0, 5), (0, np.pi), (0, 2 * np.pi)], + ghost_zones=2, +) + +# Define scalar field F(r, θ) = r * cos(θ) +field = pym.DenseField.from_function( + lambda r, theta: r * np.cos(theta), + grid, + axes=["r", "theta"], +) + +# Compute Laplacian and trim ghost zones +F = field[2:-2, 2:-2] +F_lap = field.element_wise_laplacian()[2:-2, 2:-2] +R, Theta = grid.compute_domain_mesh(axes=["r", "theta"], origin="active") + +# Plot field and Laplacian +fig, axes = plt.subplots(2, 1, figsize=(6, 6), sharex=True, gridspec_kw={"hspace": 0.0}) +vmin, vmax = -5, 5 +norm = plt.Normalize(vmin=vmin, vmax=vmax) +cmap = "seismic" + +axes[0].pcolormesh(R, Theta, F, cmap=cmap, norm=norm) +axes[0].set_ylabel(r"$\theta$") +axes[0].text( + 0.5, + 0.9, + r"$F(r,\theta) = r\cos(\theta)$", + ha="center", + va="bottom", + transform=axes[0].transAxes, + fontsize=10, + bbox=dict(facecolor="white", alpha=0.7), +) + +axes[1].pcolormesh(R, Theta, F_lap, cmap=cmap, norm=norm) +axes[1].set_xlabel(r"$r$") +axes[1].set_ylabel(r"$\theta$") +axes[1].text( + 0.5, + 0.9, + r"$\nabla^2 F(r,\theta)$", + ha="center", + va="bottom", + transform=axes[1].transAxes, + fontsize=10, + bbox=dict(facecolor="white", alpha=0.7), +) + +cbar = fig.colorbar( + plt.cm.ScalarMappable(norm=norm, cmap=cmap), + ax=axes, + orientation="vertical", + fraction=0.04, + pad=0.03, +) +cbar.set_label(r"$F(r,\theta)$ and $\nabla^2 F(r,\theta)$") + +plt.savefig("fig1.png", dpi=600) diff --git a/paper/paper.md b/paper/paper.md index de0eacff..4124f512 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -25,38 +25,38 @@ bibliography: paper.bib PyMetric is a lightweight Python library designed to streamline differential geometry and vector calculus operations in user-defined coordinate systems, with a focus on applications in astrophysics and computational physics. The library was originally created to provide a -geometric backend for the Pisces project, an (in development) general purpose astrophysical modeling and initial conditions +geometric backend for the Pisces project, an in-development, general purpose astrophysical modeling and initial conditions library, but has since grown into an independent library due to its size and complexity. In many physical modeling tasks, it is both natural and advantageous to work in non-Cartesian coordinate systems that align with the inherent -symmetries of the system. These systems can be highly nontrivial—such as ellipsoidal -(homoeoidal) or spheroidal coordinates—where explicitly handling coordinate-specific -expressions becomes tedious and error-prone. PyMetric provides a unified abstraction +symmetries of the system. These coordinate systems can feature complex geometric structure which makes the +explicit handling of differential operations cumbersome. This is particularly true for exotic coordinate +systems (e.g. homoeoidal coordinate systems). PyMetric provides a unified abstraction that decouples the underlying coordinate representation from the operations themselves, allowing users to accurately compute gradients, divergences, Laplacians, and related geometric -quantities through a consistent interface. This makes it easier to prototype and scale +quantities through a consistent (and coordinate system agnostic) interface. This makes it easier to prototype and scale models in complex geometries without having to rewrite operations for each coordinate system. The core design of PyMetric relies on a hybrid symbolic-numeric model that balances efficiency, flexibility, and accuracy. Symbolic computation is used to derive key geometric quantities, such -as metric tensors, Christoffel symbols, and Jacobians, directly from the structure of the coordinate -system. These symbolic expressions preserve the full geometric context and can be reused across -multiple evaluations. Once derived, they are compiled into optimized numerical functions that -can be efficiently applied to array data on structured grids. This approach allows PyMetric to -support coordinate-aware computation with minimal overhead, avoiding the need for repeated symbolic -manipulation during runtime, while maintaining high accuracy through analytically correct geometric +as metric tensors, Christoffel symbols, and Jacobians, from a minimal set of coordinate system properties. +Once generated, these symbolic structures can be converted into efficient numerical routines that operate +on array-backed data and are composed to perform higher-level operations. +This approach allows PyMetric to support coordinate-aware computation with minimal overhead, avoiding the need for +repeated symbolic manipulation during runtime, while maintaining high accuracy through analytically correct geometric expressions. The result is a powerful and extensible framework that enables NumPy-style [@harris2020array] workflows in complex coordinate systems without sacrificing physical fidelity. In addition to its symbolic-numeric foundation, PyMetric provides structured abstractions for grids -and field data, supporting a range of coordinate systems and buffer backends—including in-memory arrays and -HDF5 [@hdf5] storage for scalable computation. Users can define fields over geometric grids and apply -differential operators without manually managing coordinate-dependent logic. +and field data, supporting a range of coordinate systems and buffer backends. Because the PyMetric field abstraction +is only minimally coupled to the underlying data storage, it can interface with a variety of array backends, including +in-memory arrays and HDF5 [@hdf5] storage for lazy-loading and chunked computation. This design enables coordinate-aware +operations to be applied efficiently to large, multidimensional datasets without compromising generality or performance. -PyMetric automates core operations such as gradients, divergences, and Laplacians in a -geometry-aware fashion, enabling accurate and efficient modeling of physical systems across -disciplines like general relativity, magnetohydrodynamics, and planetary dynamics. By embedding -geometric structure directly into array-based workflows, PyMetric offers a modern, extensible -foundation for scientific computing in complex coordinate geometries. +By automating core geometric operations across coordinate systems, PyMetric simplifies the development +of physics-based modeling software that requires flexible geometric handling. Its design supports a broad spectrum +of scientific computing applications, from simulating relativistic fluids to analyzing gravitational fields. In +doing so, PyMetric establishes a modern and extensible foundation for geometry-aware computation in Python, +enabling the creation of accurate, efficient, and scalable models in complex coordinate geometries. # Statement of need @@ -81,7 +81,7 @@ To address this limitation, PyMetric was developed to be a lightweight library t coordinate-aware geometric computation. The library is designed to serve as the geometric backend for Pisces and similar modeling systems. It provides a consistent abstraction layer for defining coordinate systems, computing differential geometric quantities, and evaluating operators like gradients, -divergences, and Laplacians—all without requiring the user to manage low-level +divergences, and Laplacians; all without requiring the user to manage low-level details of tensor algebra or coordinate transformations. PyMetric emphasizes extensibility and modularity through four core interfaces: @@ -162,4 +162,43 @@ PyMetric is explicitly intended as a modeling and analysis tool, not a time-doma It provides geometric infrastructure for constructing and analyzing equations defined on curved spacetimes, but does not aim to solve dynamical systems or perform numerical integration of time-evolving fields. +# Usage Example + +To demonstrate the basic capabilities of the Pymetric library, we include a simple example of +the typical workflow computing the Laplacian ($\nabla^2$) of a field in spherical coordinates. +We use $F(r, \theta) = r \cos(\theta)$ as our test function, which has a known Laplacian of zero. +A visualization of $F(r, \theta)$ and its Laplacian is shown in Figure 1, demonstrating +the library’s ability to perform geometry-aware computations directly on array data. + +```python +import pymetric as pym +import numpy as np + +# Define spherical coordinate system and grid +cs = pym.coordinates.SphericalCoordinateSystem() +grid = pym.grids.GenericGrid( + cs, + [ + np.linspace(0.1, 4.9, 300), # r + np.linspace(0.01, np.pi - 0.01, 100), # theta + np.linspace(0.01, 2 * np.pi - 0.01, 100), # phi + ], + center="cell", + bbox=[(0, 5), (0, np.pi), (0, 2 * np.pi)], + ghost_zones=2, +) + +# Define scalar field F(r, theta) = r * cos(theta) +# This is a good test case since Lap(F) = 0. +field = pym.DenseField.from_function( + lambda r, theta: r * np.cos(theta), + grid, + axes=["r", "theta"], +) + +# Compute Laplacian +F_lap = field.element_wise_laplacian() +``` +![A scalar field $F(r,\theta)$ and its Laplacian $\nabla^2 F(r,\theta)$, computed in spherical coordinates using PyMetric.](fig1.png){ width=85% } + # References From f8f8ac653e1f4c58f2078471ca2e5a8374d130c2 Mon Sep 17 00:00:00 2001 From: Eliza Diggins Date: Sat, 18 Oct 2025 14:00:30 -0700 Subject: [PATCH 14/17] Adding figure to git (whoops). --- paper/fig1.png | Bin 0 -> 184120 bytes 1 file changed, 0 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00:00:00 2001 From: Eliza Diggins Date: Sat, 18 Oct 2025 14:19:05 -0700 Subject: [PATCH 15/17] Improving figure caption. --- paper/paper.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/paper/paper.md b/paper/paper.md index 4124f512..d1fa49d0 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -199,6 +199,6 @@ field = pym.DenseField.from_function( # Compute Laplacian F_lap = field.element_wise_laplacian() ``` -![A scalar field $F(r,\theta)$ and its Laplacian $\nabla^2 F(r,\theta)$, computed in spherical coordinates using PyMetric.](fig1.png){ width=85% } +![A scalar field $F(r,\theta) = r\cos(\theta)$ and its Laplacian $\nabla^2 F(r,\theta)$, computed in spherical coordinates using PyMetric.](fig1.png){ width=85% } # References From 15e524a4d6471da3d78dac73a46baa9c962d69f7 Mon Sep 17 00:00:00 2001 From: Eliza Diggins Date: Sat, 15 Nov 2025 20:33:17 -0800 Subject: [PATCH 16/17] Paper revisions. --- paper/paper.md | 14 +++++++++----- 1 file changed, 9 insertions(+), 5 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index d1fa49d0..e7ae00e2 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -122,12 +122,16 @@ as more general curvilinear systems. ## Field and Grid Operations Fields in PyMetric are array-backed data structures (typically NumPy or HDF5 buffers) that are explicitly -associated with a coordinate system and grid. While fields behave like standard NumPy arrays, +associated with a coordinate system and grid. The grid handling supports flexible discretization strategies, +including cell-centered and node-centered layouts, as well as ghost zones for finite-difference operations. +Support is currently provided for single-grid configurations with arbitrary spacing; however, multigrid extension +is planned for future releases. +While fields behave like standard NumPy arrays, they also carry metadata about their geometric context, including coordinate labels, spacing, and metric-aware tensor properties. -Operations on fields—such as computing covariant derivatives, applying Laplacians, -or transforming between bases—are automatically dispatched to appropriate symbolic +Operations on fields, such as computing covariant derivatives, applying Laplacians, +or transforming between bases, are automatically dispatched to appropriate symbolic expressions and numerical kernels based on the field’s variance and the geometry of the underlying coordinate system. @@ -155,8 +159,8 @@ for high-fidelity modeling in physics, engineering, and applied mathematics. 2. Relativistic and Non-Flat Coordinate Systems - - A key area of expansion is support for relativistic geometries, where the metric tensor is no longer positive-definite and may depend dynamically on spacetime coordinates. Planned features include: - - General Lorentzian manifolds, including Schwarzschild, Kerr, and FLRW spacetimes, enabling direct modeling of astrophysical systems governed by Einstein’s field equations. + - A key area of expansion is support for relativistic geometries, where the metric tensor is no longer positive-definite and may depend dynamically on spacetime coordinates. Planned features include: + - General Lorentzian manifolds, including Schwarzschild, Kerr, and FLRW spacetimes, enabling direct modeling of astrophysical systems governed by Einstein’s field equations. PyMetric is explicitly intended as a modeling and analysis tool, not a time-domain simulation engine. It provides geometric infrastructure for constructing and analyzing equations defined on curved spacetimes, From f7d4670c12a0e25e58ffc9551371fb36de48f61d Mon Sep 17 00:00:00 2001 From: Eliza Diggins Date: Mon, 24 Nov 2025 18:37:17 -0800 Subject: [PATCH 17/17] updated DOIs. --- paper/paper.bib | 7 +++++-- 1 file changed, 5 insertions(+), 2 deletions(-) diff --git a/paper/paper.bib b/paper/paper.bib index 41b443b7..9f4e1925 100644 --- a/paper/paper.bib +++ b/paper/paper.bib @@ -6,7 +6,8 @@ @article{harris2020array number={7825}, pages={357--362}, year={2020}, - publisher={Nature Publishing Group UK London} + publisher={Nature Publishing Group UK London}, + doi={10.1038/s41586-020-2649-2} } @software{hdf5, author = {{The HDF Group}}, @@ -18,6 +19,7 @@ @Manual{einsteinpy author = {{EinsteinPy Development Team}}, year = {2024}, url = {https://einsteinpy.org/}, +doi={10.48550/arXiv.2005.11288} } @article{perret2016dice, title={DICE: Disk Initial Conditions Environment}, @@ -31,7 +33,8 @@ @article{yurin2014galic author={Yurin, Denis and Springel, Volker}, journal={Astrophysics Source Code Library}, pages={ascl--1408}, - year={2014} + year={2014}, + doi={10.48550/arXiv.1402.1623} } @article{turk2010yt, title={yt: A multi-code analysis toolkit for astrophysical simulation data},