diff --git a/README.md b/README.md index 435e0ba..b9d99e4 100644 --- a/README.md +++ b/README.md @@ -1,11 +1,8 @@ # Template -_Update: Feb 23 transferred files from [Risk and Reliability Book](https://gitlab.tudelft.nl/interactivetextbooks-citg/risk-and-reliability/) to set things up._ +This is the template book. You can fork this to create a book in as easy-as-possible a way. Focus is mostly on providing a clean and simple view to the key setup of our book repo. -This will be the future home of the template book. Design philosophy: -- people will fork this to create a book in as easy-as-possible a way -- minimal changes should be made to the book contents itself, to prevent downstream merge conflicts -- focus is mostly on providing a clean and simply view to the key features in our book repo (e.g., config files, scripts, markup flags, etc) +Minimal changes should be made to the template book contents itself, to prevent downstream merge conflicts. # How to deploy a fork of this book on GitHub Pages diff --git a/book/_bibliography/references.bib b/book/_bibliography/references.bib deleted file mode 100644 index 09caf27..0000000 --- a/book/_bibliography/references.bib +++ /dev/null @@ -1,396 +0,0 @@ -@book{adk2022, - title={Structural and System Reliability}, - author={Der Kiureghian, Armen}, - year={2022}, - publisher={Cambridge University Press} -} - -@article{baecher1982, - author = {Baecher, Gregory B}, - journal = {Engineering Foundations: Updating Subsurface Samplings of Soils and Rocks and their In-Situ Testing, Santa Barbara}, - title = {Statistical methods in site characterization}, - year = {1982}, - pages = {463--492} -} - -@book{baecher2003, - title={Reliability and statistics in geotechnical engineering}, - author={Baecher, Gregory B and Christian, John T}, - year={2003}, - publisher={John Wiley \& Sons} -} - -@misc{baecher2021, - title={IFCEE 2021: Karl Terzaghi Lecture: Greg Baecher: Geotechnical Systems, Uncertainty, and Risk}, - author={Baecher, Gregory B}, - howpublished={Presentation, YouTube: \url{https://www.youtube.com/watch?v=Y5w1p3uAe0I&ab_channel=Geo-InstituteofASCE}}, - year={2021} -} - -@incollection{cardona2012, - title={Determinants of risk: exposure and vulnerability}, - author={Cardona, Omar Dario and Van Aalst, Maarten K and Birkmann, J{\"o}rn and Fordham, Maureen and Mc Gregor, Glenn and Rosa, Perez and Pulwarty, Roger S and Schipper, E Lisa F and Sinh, Bach Tan and D{\'e}camps, Henri and others}, - booktitle={Managing the risks of extreme events and disasters to advance climate change adaptation: special report of the intergovernmental panel on climate change}, - pages={65--108}, - year={2012}, - publisher={Cambridge University Press} -} - -@book{ditlevsen1996, - title={Structural reliability methods}, - author={Ditlevsen, Ove and Madsen, Henrik O}, - volume={178}, - year={1996}, - publisher={Wiley New York} -} - -@article{Eijgenraam2006, - author = {C.J.J. Eijgenraam}, - journal = {CPB discussion paper}, - title = {Optimal safety standards for dike ring areas}, - volume = {62}, - year = {2006}, -} - -@book{moss2020, - title={Applied civil engineering risk analysis}, - author={Moss, Robb Eric S}, - year={2020}, - publisher={Springer} -} - -@article{vandantzig1956, - author = {D. van Dantzig}, - journal = {Econometrica}, - title = {Economic decision problems for flood prevention}, - volume = {24}, - year = {1956} -} - -@article{vnk2014, - author = {{Veiligheid Nederland in Kaart}}, - title = {De veiligheid van Nederland in kaart}, - year = {2014}, - journal = {Rijkswaterstaat}, - url = {https://www.helpdeskwater.nl/publish/pages/131663/eindrapport_vnk.pdf}, -} - -@article{vrijling1990, - author = {Vrijling, J.K. and van Beurden, J.A.}, - journal = {Proceedings of the International Conference on Coastal Engineering}, - title = {Sealevel rise: a probabilistic design problem}, - year = {1990} -} - -@article{vangelder1997, - author = {P.H.A.J.M. Van Gelder and J.K. Vrijling and K.A.H. Slijkhuis}, - journal = {Water for a Changing Global Community}, - pages = {554-559}, - title = {Coping with uncertainty in the economical optimization of a dike design}, - year = {1997}, -} - -@phdthesis{voorendt2017, - title={Design principles of multifunctional flood defences}, - author={Voorendt, Mark}, - school={Delft University of Technology, the Netherlands}, - year={2017} -} - -@misc{sympy_why, - title={Sympy documentation}, - author={{SymPy Development Team}}, - howpublished={\url{https://docs.sympy.org/latest/tutorials/intro-tutorial/intro.html}}, - year={2023} -} - -@misc{jason_moore, - title={Learn Multibody Dynamics, SymPy}, - author={Moore, Jason}, - howpublished={\url{https://moorepants.github.io/learn-multibody-dynamics/sympy.html}}, - year={2023} -} - -@misc{BFG, - title={Animation of the unit circle with angles}, - author={BFG}, - howpublished={\url{https://commons.wikimedia.org/wiki/File:Unitycircle-complex.gif}}, - year={2020} -} - -@article{kaplan1981, - author = {Kaplan, S. and Garrick, B.J.}, - journal = {Risk Analysis}, - pages = {11-27}, - title = {On The Quantitative Definition of Risk}, - year = {1981}, -} - -@inproceedings{farmer1967, - title = {Siting Criteria - A New Approach}, - author = {Farmer, F.R.}, - year = 1967, - month = {April}, - booktitle = {Proceedings of IAEA Symposium on the Containment and Siting of Nuclear Power Plants}, - publisher = {International Atomic Energy Agency (IAEA)}, - address = {Vienna}, - pages = {303-324}, -} - -@book{kendall1977, - title={The Risks of Nuclear Power Reactors, A Review of the NRC Reactor Safety Study WASH-1400 (NUREG-75/014)}, - author={Kendall, H.W. and Hubbard, R.B. and Minor, G.C. and Bryan, W.M. (Union of Concerned Scientists)}, - year={1977}, - publisher={Cambridge} -} - -@article{vlek1996, - author = {Vlek, C.A.J.}, - journal = {Risk Decision and Policy}, - pages = {9-31}, - title = {A multi-level, multi-stage and multi-attribute perspective on risk assessment, decision-making and risk control}, - year = {1996}, -} - -@article{slovic1987, - author = {Slovic, P.}, - journal = {Science}, - pages = {280-285}, - title = {Perception of Risk}, - year = {1987}, -} - -@article{voortman2004, - author = {Voortman, H.G. and Vrijling, J.K.}, - journal = {Heron}, - pages = {75-94}, - title = {Optimal design of flood defence systems in a changing climate}, - year = {2004}, -} - -@article{apostolakis2004, - author = {Apostolakis, G.E.}, - journal = {Risk Analysis}, - pages = {515-520}, - title = {How Useful Is Quantitative Risk Assessment?}, - year = {2004}, -} - -@article{faber2003, -title = {Risk Assessment for Civil Engineering Facilities: Critical Overview and Discussion}, -journal = {Reliability Engineering & System Safety}, -volume = {80}, -number = {2}, -pages = {173-184}, -year = {2003}, -issn = {0951-8320}, -doi = {https://doi.org/10.1016/S0951-8320(03)00027-9}, -url = {https://www.sciencedirect.com/science/article/pii/S0951832003000279}, -author = {Faber, M.H. and Stewart, M.G.}, -} - -@phdthesis{jongejan2008, - title={How safe is safe enough? The government's response to industrial and flood risks}, - author={Jongejan, R.B.}, - school={Delft University of Technology, the Netherlands}, - year={2008} -} - -@misc{CUR1997, - title={Kansen in de Civiele Techniek, Deel 1: Probabilistisch ontwerpen in theorie}, - author={CUR{\ }(Civieltechnisch{\ }Centrum{\ }Uitvoering{\ }Research{\ }en{\ }Regelgeving)}, - howpublished={CUR rapport 190}, - year={1997} -} - -@misc{CIB2001, - title={A framework for risk management and risk communications, Work{\ }Group{\ }32,{\ }CIB}, - author={Vrouwenvelder, T. and Lovegrove, R. and Holicky, M.}, - howpublished={CIB report 259}, - year={2001} -} - -@article{bea1998, - author = {Bea, R.G.}, - journal = {Reliability Engineering & System Safety}, - pages = {109-126}, - title = {Human and Organization Factors: Engineering Operating Safety Into Offshore Structures}, - year = {1998}, -} - -@misc{eurocode2001, - title={Eurocode - Basis of Structural Design}, - author={EN 1990:2002 E, Eurocode}, - howpublished={CEN}, - year={2001} -} - -@book{vrouwenvelder1996, - author = {Vrouwenvelder, A.C.W.M. and Vrijling, J.K}, - title = {Collegedictaat Probabilistisch ontwerpen b3}, - year = {1996}, - publisher={TU Delft} -} - -@article{starr1967, - author = {Starr, C.}, - journal = {Science}, - pages = {1232-1238}, - title = {Social benefit versus technological risk}, - year = {1967}, -} - -@inproceedings{taerwe1986, - title = {Mastering Global Quality by an Interactive Concept}, - author = {Taerwe, L.}, - year = 1986, - booktitle = {Proceedings IABSE Symposium Tokyo 1986: Safety and Quality Assurance of Civil Engineering Structures}, - pages = {317-325}, -} - -@book{raiffa1961, - author = {Raiffa, H. and Schlaifer, R.}, - title = {Applied Statistical Decision Theory}, - year = {1961}, - publisher={Harvard University press}, - address = {Cambridge, Massachusetts, United States}, -} - -@book{benjamin1970, - author = {Benjamin, J.R. and Cornell, C.A.}, - title = {Probability, Statistics and Decision for Civil Engineers}, - year = {1970}, - publisher={McGraw Hill}, -} - -@inproceedings{don2003, - author = {Don, F.H. and Stolwijk, H.J.J.}, - booktitle = {CUR (2003) 50 jaar na stormvloed 1953, terugblik en toekomst}, - title = {Investeren in veiligheid: de watersnoodramp van 1953 en de kosten en baten van het deltaplan}, - pages={79-98}, - year = {2003}, - howpublished={CUR rapport 212}, -} - -@inproceedings{vrijling2000, - title={An Analysis of the Valuation of a Human Life}, - author={Vrijling, J.K. and Gelder, P.H.A.J.M. van}, - booktitle={Foresight and Precaution: Proceedings of ESREL 2000, SARS and SRA-Europe Annual Conference. Edited by M.P. Cottam, D.W. Harvey, R.P. Pape and J. Tait}, - pages={197-200}, - volume={1}, - year={2000}, - address={Edinburgh, Scotland} -} - -@article{jongejan2005, - author = {Jongejan, R.B. and Jonkman, S.N. and Vrijling, J.K.}, - journal = {ESREL}, - title = {Methods for the Valuation of Human Life}, - year = {2005}, -} - -@misc{SWOV2012, - title={Waardering van immateriële kosten van verkeersdoden}, - author={SWOV{\ }(Stichting{\ }Wetenschappelijk{\ }Onderzoek{\ }Verkeersveiligheid)}, - howpublished={Factsheet, \url{http://www.swov.nl/rapport/Factsheets/NL/Factsheet_Immateriele_kosten.pdf}}, - year={2012}, -} - -@inproceedings{jeuken2013, -author = {Jeuken, A. and Kind, J. and Slootjes, N. and Gauderis, J. and Vos, R.}, -year = {2013}, -month = {01}, -pages = {}, -title = {Cost-benefit Analysis of Flood Risk Management Strategies for the Rhine-Meuse Delta}, -booktitle = {Comprehensive Flood Risk Management, Taylor & Francis Group}, -} - -@article{tengs1995, - author = {Tengs, T.O. and Adams, M.E. and Pliskin, J.S. and Gelb Safran, D. and Siegel, J.E. and Weinstein, M.C. and Graham, J.D.}, - journal = {Risk Analysis}, - volume={15}, - number={3}, - pages={369-390}, - title = {Five-hundred Live Saving Interventions and Their Cost Effectiveness}, - year = {1995}, -} - -@misc{TAW1985, - title={Some Considerations of an Acceptable Level of Risk in the Netherlands}, - author={TAW{\ }(Technical{\ }Advisory{\ }Committee{\ }on{\ }Water{\ }Defences)}, - howpublished={Report by TAW workgroup 10 'Probabilistic methods'}, - year={1985}, -} - -@article{vrijling1995, - author = {Vrijling, J.K. and Hengel, W. van and Houben, R.J.}, - journal = {Journal of Hazardous Materials}, - volume={43}, - pages = {245-261}, - title = {A Framework for Risk Evaluation}, - year = {1995}, -} - -@article{vrijling1998, - author = {Vrijling, J.K. and Hengel, W. van and Houben, R.J.}, - journal = {Reliability Engineering and System Safety}, - volume={59}, - pages = {141-150}, - title = {Acceptable Risk as a Basis for Design}, - year = {1998}, -} - -@article{jonkman2003, - author = {Jonkman, S.N. and van Gelder, P.H.A.J.M. and Vrijling, J.K.}, - journal = {Journal of Hazardous Materials}, - volume={A99}, - pages = {1-30}, - title = {An Overview of Quantitative Risk Measures for Loss of Life and Economic Damage}, - year = {2003}, -} - -@article{bottelberghs2000, - author = {Bottelberghs, P.H.}, - journal = {Journal of Hazardous Materials}, - volume={71}, - pages = {117-123}, - title = {Risk Analysis and Safety Policy Developments in the Netherlands}, - year = {2000}, -} - -@article{vrijling2001, -title = {Probabilistic Design of Water Defense Systems in The Netherlands}, -journal = {Reliability Engineering & System Safety}, -volume = {74}, -number = {3}, -pages = {337-344}, -year = {2001}, -issn = {0951-8320}, -doi = {https://doi.org/10.1016/S0951-8320(01)00082-5}, -url = {https://www.sciencedirect.com/science/article/pii/S0951832001000825}, -author = {Vrijling, J.K.}, -} - -@misc{delta2014, - title={Deltaprogramma Veiligheid. Synthesedocument Veiligheid}, - author={Deltaprogramma}, - howpublished={Achtergronddocument B1}, - year={2014} -} - -@article{sitar1987, -title = {First-order Reliability Approach to Stochastic Analysis of Subsurface Flow and Contaminant Transport}, -journal = {Water Resources Research}, -volume = {23}, -number = {5}, -pages = {794-804}, -year = {1987}, -author = {Sitar, N. and Cawlfield, J. D. and Der Kiureghian, A.}, -} - -@misc{usace14, - title={Safety and Health Requirements Manual}, - author={U.S.{\ }Army{\ }Corps{\ }of{\ }Engineers}, - howpublished={EM 385-1-1}, - year={2014} -} \ No newline at end of file diff --git a/book/_config.yml b/book/_config.yml index 52459aa..f5c1433 100644 --- a/book/_config.yml +++ b/book/_config.yml @@ -1,6 +1,6 @@ title: Template -author: Robert Lanzafame -logo: figures/cover_small.png +author: Books CEG +logo: figures/TUDelft_logo_rgb.png copyright: Delft University of Technology, CC BY 4.0 # overriden by extra footer/sphinx config execute: @@ -11,51 +11,22 @@ launch_buttons: only_build_toc_files: true -repository: - url: https://gitlab.tudelft.nl/interactivetextbooks-citg/risk-and-reliability/ - branch: main/book # for edit button; need to check branch permissions non-TUD user access - html: -# X START DRAFT # temporarily enable Hypothesis for published book until Library finishes comments: hypothesis: true -# X END DRAFT - use_edit_page_button: false - use_repository_button: true - extra_footer: | -

- © Delft University of Technology, CC BY 4.0 - - - Creative Commons License - -

sphinx: config: - html_show_copyright: false + html_show_copyright: true html_js_files: - https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.4/require.min.js thebe_config: use_thebe_lite: true exclude_patterns: ["**/_*.yml", "**/*.md", "**/*.ipynb"] - # Reference issues - # See: https://github.com/executablebooks/jupyter-book/issues/1090 - # and Milestone 10: - # https://gitlab.tudelft.nl/groups/interactivetextbooks-citg/-/milestones/10#tab-issues - # This next line was from Caspar/citg-jb-stack and doesn't work (see Issue 24) - # https://gitlab.tudelft.nl/interactivetextbooks-citg/risk-and-reliability/-/issues/24 - # bibtex_reference_style: author_year - bibtex_reference_style: author_year_round - bibtex_default_style: myapastyle extra_extensions: - sphinx.ext.imgconverter - download_link_replacer - jupyterbook_patches - # Local extensions are for bibtex (Thirza's hydrology hack); see above - local_extensions: - apastyle: _ext/ - bracket_citation_style: _ext/ bibtex_bibfiles: - - _bibliography/references.bib + - references.bib diff --git a/book/_ext/apastyle.py b/book/_ext/apastyle.py deleted file mode 100644 index 16828fe..0000000 --- a/book/_ext/apastyle.py +++ /dev/null @@ -1,17 +0,0 @@ - -# from pybtex.style.formatting.unsrt import Style -from pybtexapastyle.formatting.apa import APAStyle -from pybtexapastyle.labels.apa import LabelStyle as APALabelStyle -from pybtex.plugin import register_plugin -# from pybtex.style.template import names, sentence - -class MyAPALabelStyle(APALabelStyle): - def format_label(self, entry): - return APALabelStyle.format_label(self, entry) - -class MyAPAStyle(APAStyle): - default_label_style = 'myapa' - -def setup(app): - register_plugin('pybtex.style.labels', 'myapa', MyAPALabelStyle) - register_plugin('pybtex.style.formatting', 'myapastyle', MyAPAStyle) \ No newline at end of file diff --git a/book/_ext/bracket_citation_style.py b/book/_ext/bracket_citation_style.py deleted file mode 100644 index cab10f3..0000000 --- a/book/_ext/bracket_citation_style.py +++ /dev/null @@ -1,27 +0,0 @@ -from dataclasses import dataclass, field -import sphinxcontrib.bibtex.plugin - -from sphinxcontrib.bibtex.style.referencing import BracketStyle -from sphinxcontrib.bibtex.style.referencing.author_year import AuthorYearReferenceStyle - - -def bracket_style() -> BracketStyle: - return BracketStyle( - left='(', - right=')', - ) - - -@dataclass -class MyReferenceStyle(AuthorYearReferenceStyle): - bracket_parenthetical: BracketStyle = field(default_factory=bracket_style) - bracket_textual: BracketStyle = field(default_factory=bracket_style) - bracket_author: BracketStyle = field(default_factory=bracket_style) - bracket_label: BracketStyle = field(default_factory=bracket_style) - bracket_year: BracketStyle = field(default_factory=bracket_style) - - -def setup(app): - sphinxcontrib.bibtex.plugin.register_plugin( - 'sphinxcontrib.bibtex.style.referencing', - 'author_year_round', MyReferenceStyle) \ No newline at end of file diff --git a/book/_ext/pybtexapastyle/.gitignore b/book/_ext/pybtexapastyle/.gitignore deleted file mode 100644 index 49d0093..0000000 --- a/book/_ext/pybtexapastyle/.gitignore +++ /dev/null @@ -1,114 +0,0 @@ - -# Created by https://www.gitignore.io/api/python - -### Python ### -# Byte-compiled / optimized / DLL files -__pycache__/ -*.py[cod] -*$py.class - -# C extensions -*.so - -# Distribution / packaging -.Python -build/ -develop-eggs/ -dist/ -downloads/ -eggs/ -.eggs/ -lib/ -lib64/ -parts/ -sdist/ -var/ -wheels/ -*.egg-info/ -.installed.cfg -*.egg -MANIFEST - -# PyInstaller -# Usually these files are written by a python script from a template -# before PyInstaller builds the exe, so as to inject date/other infos into it. -*.manifest -*.spec - -# Installer logs -pip-log.txt -pip-delete-this-directory.txt - -# Unit test / coverage reports -htmlcov/ -.tox/ -.coverage -.coverage.* -.cache -nosetests.xml -coverage.xml -*.cover -.hypothesis/ -.pytest_cache/ - -# Translations -*.mo -*.pot - -# Django stuff: -*.log -local_settings.py -db.sqlite3 - -# Flask stuff: -instance/ -.webassets-cache - -# Scrapy stuff: -.scrapy - -# Sphinx documentation -docs/_build/ - -# PyBuilder -target/ - -# Jupyter Notebook -.ipynb_checkpoints - -# pyenv -.python-version - -# celery beat schedule file -celerybeat-schedule - -# SageMath parsed files -*.sage.py - -# Environments -.env -.venv -env/ -venv/ -ENV/ -env.bak/ -venv.bak/ - -# Spyder project settings -.spyderproject -.spyproject - -# Rope project settings -.ropeproject - -# mkdocs documentation -/site - -# mypy -.mypy_cache/ - -### Python Patch ### -.venv/ - - -# End of https://www.gitignore.io/api/python \ No newline at end of file diff --git a/book/_ext/pybtexapastyle/LICENSE b/book/_ext/pybtexapastyle/LICENSE deleted file mode 100644 index 579d367..0000000 --- a/book/_ext/pybtexapastyle/LICENSE +++ /dev/null @@ -1,21 +0,0 @@ -MIT License - -Copyright (c) 2018 Naeka - -Permission is hereby granted, free of charge, to any person obtaining a copy -of this software and associated documentation files (the "Software"), to deal -in the Software without restriction, including without limitation the rights -to use, copy, modify, merge, publish, distribute, sublicense, and/or sell -copies of the Software, and to permit persons to whom the Software is -furnished to do so, subject to the following conditions: - -The above copyright notice and this permission notice shall be included in all -copies or substantial portions of the Software. - -THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR -IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, -FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE -AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER -LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, -OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE -SOFTWARE. \ No newline at end of file diff --git a/book/_ext/pybtexapastyle/formatting/__init__.py b/book/_ext/pybtexapastyle/formatting/__init__.py deleted file mode 100644 index e69de29..0000000 diff --git a/book/_ext/pybtexapastyle/formatting/apa.py b/book/_ext/pybtexapastyle/formatting/apa.py deleted file mode 100644 index dfa5a58..0000000 --- a/book/_ext/pybtexapastyle/formatting/apa.py +++ /dev/null @@ -1,486 +0,0 @@ -# -*- coding:Utf-8 -*- -from __future__ import unicode_literals - -import re -import six - -from pybtex.plugin import find_plugin -from pybtex.style.formatting import BaseStyle, toplevel -from pybtex.style.template import ( - field, first_of, href, join, optional, optional_field, sentence, tag, - together, words, node, FieldIsMissing -) - -from pybtex.richtext import Text, Symbol - - -firstlast = find_plugin('pybtex.style.names', 'lastfirst')() - -if six.PY2: - def format_pages(text): - dash_re = re.compile(r'-+') - pages = Text(Symbol('ndash')).join( - re.split(dash_re, six.text_type(text))) - if re.search('[-‒–—―]', six.text_type(text)): - return Text("pp.", Symbol('nbsp'), pages) - return Text("p.", Symbol('nbsp'), pages) -else: - def format_pages(text): - dash_re = re.compile(r'-+') - pages = Text(Symbol('ndash')).join(text.split(dash_re)) - if re.search('[-‒–—―]', str(text)): - return Text("pp.", Symbol('nbsp'), pages) - return Text("p.", Symbol('nbsp'), pages) - - -pages = field('pages', apply_func=format_pages) -date = words[field('year'), optional[", ", field('month')]] - - -@node -def apa_names(children, context, role, **kwargs): - """ - Returns formatted names as an APA compliant reference list citation. - """ - assert not children - - try: - persons = context['entry'].persons[role] - except KeyError: - raise FieldIsMissing(role, context['entry']) - - style = context['style'] - - if len(persons) > 7: - persons = persons[:6] + persons[-1:] - formatted_names = [style.format_name( - person, style.abbreviate_names) for person in persons] - return join(sep=', ', last_sep=', … ')[ - formatted_names].format_data(context) - else: - formatted_names = [style.format_name( - person, style.abbreviate_names) for person in persons] - return join(sep=', ', sep2=', & ', last_sep=', & ')[ - formatted_names].format_data(context) - - -@node -def editor_names(children, context, with_suffix=True, **kwargs): - """ - Returns formatted editor names for inbook. - """ - assert not children - - try: - editors = context['entry'].persons['editor'] - except KeyError: - raise FieldIsMissing('editor', context['entry']) - - formatted_names = [ - firstlast.format(editor, True) for editor in editors] - - if with_suffix: - return words[ - join(sep=', ', sep2=', & ', last_sep=', & ')[formatted_names], - "(Eds.)" if len(editors) > 1 else "(Ed.)" - ].format_data(context) - - return join(sep=', ', sep2=', & ', last_sep=', & ')[ - formatted_names - ].format_data(context) - - -class APAStyle(BaseStyle): - name = 'apa' - default_name_style = 'lastfirst' - default_sorting_style = 'author_year_title' - default_label_style = 'apa' - - def __init__(self, *args, **kwargs): - super(APAStyle, self).__init__(*args, **kwargs) - self.abbreviate_names = True - - def format_names(self, role, as_sentence=True): - formatted_names = apa_names(role) - if as_sentence: - return sentence(capfirst=False)[formatted_names] - else: - return formatted_names - - def format_author_or_editor_and_date(self, e): - if 'author' in e.persons and 'editor' in e.persons: - return sentence(sep=' ')[ - self.format_names('author'), join["(", date, ")."], - self.format_editor(e, as_sentence=False)] - elif 'author' in e.persons: - return sentence(sep=' ')[ - self.format_names('author'), join["(", date, ")"]] - else: - return sentence(sep=' ')[ - self.format_editor(e, as_sentence=False), - join["(", date, ")"]] - - def format_editor(self, e, as_sentence=True): - editors = self.format_names('editor', as_sentence=False) - if 'editor' not in e.persons: - # when parsing the template, a FieldIsMissing exception - # will be thrown anyway; no need to do anything now, - # just return the template that will throw the exception - return editors - if len(e.persons['editor']) > 1: - word = '(Eds.)' - else: - word = '(Ed.)' - result = join(sep=' ')[editors, word] - if as_sentence: - return sentence[result] - else: - return result - - def format_volume(self, e, for_article=False): - prefix = "Vol." - if for_article: - return join[ - tag('em')[field('volume')], - optional['(', field('number'), ')'], - ] - else: - return optional[together[prefix, field('volume')]] - - def format_title(self, e, which_field, as_sentence=True): - formatted_title = field( - which_field, apply_func=lambda text: text.capitalize() - ) - if as_sentence: - return sentence[formatted_title] - else: - return formatted_title - - def format_btitle(self, e, which_field, as_sentence=True): - formatted_title = tag('em')[field(which_field)] - if as_sentence: - return sentence[formatted_title] - else: - return formatted_title - - def format_web_refs(self, e): - # Based on urlbst output.web.refs - return sentence(add_period=False)[ - optional[self.format_url(e)], - optional[self.format_eprint(e)], - optional[self.format_pubmed(e)], - optional[self.format_doi(e)], - ] - - def format_url(self, e): - # Based on urlbst format.url - return words[ - 'URL:', - href[ - field('url', raw=True), - field('url', raw=True) - ] - ] - - def format_pubmed(self, e): - # Based on urlbst format.pubmed - return href[ - join[ - 'https://www.ncbi.nlm.nih.gov/pubmed/', - field('pubmed', raw=True) - ], - join[ - 'PMID:', - field('pubmed', raw=True) - ] - ] - - def format_doi(self, e): - # Based on urlbst format.doi - return href[ - join[ - 'https://doi.org/', - field('doi', raw=True) - ], - join[ - 'doi:', - field('doi', raw=True) - ] - ] - - def format_eprint(self, e): - # Based on urlbst format.eprint - return href[ - join[ - 'https://arxiv.org/abs/', - field('eprint', raw=True) - ], - join[ - 'arXiv:', - field('eprint', raw=True) - ] - ] - - def get_article_template(self, e): - # Required fields: author, title, journal, year - # Optional fields: volume, number, pages, month, note, key - volume_and_pages = first_of[ - # Volume and pages, with optional issue number - optional[ - join[ - self.format_volume(e, for_article=True), - optional[', ', field('pages')] - ], - ], - # Pages only - pages, - ] - template = toplevel[ - self.format_names('author'), - sentence[ - join["(", date, ")"] - ], - self.format_title(e, 'title'), - sentence[ - tag('em')[field('journal')], - optional[volume_and_pages], - ], - sentence[optional_field('note')], - self.format_web_refs(e), - ] - return template - - def get_book_template(self, e): - # Required fields: author/editor, title, publisher, year - # Optional fields: volume, series, address, edition, month, note, key, - # isbn - return toplevel[ - self.format_author_or_editor_and_date(e), - sentence(sep=' ')[ - self.format_btitle(e, 'title'), - optional[ - sentence[ - optional[field('edition'), ' ed.'], - self.format_volume(e), - ] - ] - ], - sentence(sep=': ')[ - optional_field('address'), - field('publisher'), - ], - sentence[optional_field('note')], - ] - - def get_booklet_template(self, e): - # Required fields: title - # Optional fields: author, howpublished, address, month, year, note, - # key - return toplevel[ - sentence(sep=' ')[ - first_of[ - optional[self.format_names( - 'author', as_sentence=False)], - "None to claim their bones" - ], - join["(", first_of[optional[date], "n.d."], ")"] - ], - self.format_title(e, 'title'), - sentence[optional_field('address')], - sentence[optional_field('note')], - ] - - def get_inbook_template(self, e): - # Required fields: author/editor, title, chapter/pages, publisher, year - # Optional fields: volume, series, address, edition, month, note, key - return toplevel[ - sentence(sep=' ')[ - self.format_names('author'), - join["(", date, ")"] - ], - self.format_title(e, 'title'), - sentence(sep=' ')[ - optional[ - "In ", - editor_names(), - "," - ], - self.format_btitle(e, 'booktitle', as_sentence=False), - optional[ - join[ - "(", - sentence(add_period=False)[ - optional[field('edition'), ' ed.'], - self.format_volume(e), - pages, - ], - ")" - ] - ] - ], - sentence(sep=': ')[ - optional_field('address'), - field('publisher'), - ], - sentence[optional_field('note')], - ] - - def get_incollection_template(self, e): - # Required fields: author, title, booktitle, year - # Optional fields: editor, pages, organization, publisher, address, - # month, note, key - return toplevel[ - self.format_author_or_editor_and_date(e), - self.format_title(e, 'title'), - sentence(sep=' ')[ - self.format_btitle(e, 'booktitle', as_sentence=False), - optional["(", pages, ")"] - ], - sentence(sep=': ')[ - optional_field('address'), - optional_field('publisher'), - ], - sentence[optional_field('note')], - ] - - def get_inproceedings_template(self, e): - # Required fields: author, title, booktitle, year - # Optional fields: editor, pages, organization, publisher, address, - # month, note, key - return toplevel[ - self.format_author_or_editor_and_date(e), - self.format_title(e, 'title'), - sentence(sep=' ')[ - self.format_btitle(e, 'booktitle', as_sentence=False), - optional["(", pages, ")"] - ], - sentence(sep=': ')[ - optional_field('address'), - optional_field('publisher'), - ], - sentence[optional_field('note')], - self.format_web_refs(e) - ] - - def get_manual_template(self, e): - # Required fields: title - # Optional fields: author, organization, address, edition, month, year, - # note, key - return toplevel[ - sentence(sep=' ')[ - first_of[ - optional[self.format_names('author', as_sentence=False)], - optional_field('organization'), - "None to claim their bones" - ], - join["(", first_of[optional[date], "n.d."], ")"] - ], - self.format_btitle(e, 'title'), - sentence[optional_field('address')], - sentence[optional_field('note')], - self.format_web_refs(e) - ] - - def get_mastersthesis_template(self, e): - # Required fields: author, title, school, year - # Optional fields: address, month, note, key - return toplevel[ - sentence(sep=' ')[ - self.format_names('author'), - join["(", date, ")"] - ], - sentence(sep=' ')[ - self.format_btitle(e, 'title', as_sentence=False), - "(Master's thesis)" - ], - sentence[ - field('school'), - optional_field('address'), - ], - sentence[optional_field('note')], - ] - - def get_misc_template(self, e): - # Required fields: aucun - # Optional fields: author, title, howpublished, month, year, note, key, - # type - template = toplevel[ - sentence(sep=' ')[ - first_of[ - optional[self.format_names('author', as_sentence=False)], - optional_field('publisher'), - "None to claim their bones" - ], - join["(", first_of[optional[date], "n.d."], ")"] - ], - optional[self.format_title(e, 'title')], - sentence[optional_field('note')], - self.format_web_refs(e) - ] - return template - - def get_phdthesis_template(self, e): - # Required fields: author, title, school, year - # Optional fields: address, month, note, key - return toplevel[ - sentence(sep=' ')[ - self.format_names('author'), - join["(", date, ")"] - ], - sentence(sep=' ')[ - self.format_btitle(e, 'title', as_sentence=False), - "(Doctoral dissertation)" - ], - sentence[ - field('school'), - optional_field('address'), - ], - sentence[optional_field('note')], - ] - - def get_proceedings_template(self, e): - # Required fields: title, year - # Optional fields: editor, publisher, organization, address, month, - # note, key - return toplevel[ - sentence(sep=' ')[ - first_of[ - optional[self.format_editor(e, as_sentence=False)], - optional_field('organization'), - "None to claim their bones" - ], - join["(", first_of[optional[date], "n.d."], ")"] - ], - self.format_btitle(e, 'title'), - sentence(sep=': ')[ - optional_field('address'), - optional_field('publisher'), - ], - sentence[optional_field('note')], - ] - - def get_techreport_template(self, e): - # Required fields: author, title, institution, year - # Optional fields: type, number, address, month, note, key - return toplevel[ - sentence(sep=' ')[ - self.format_names('author', as_sentence=False), - join["(", date, ")"] - ], - self.format_btitle(e, 'title'), - sentence[field('institution')], - sentence[optional_field('note')], - ] - - def get_unpublished_template(self, e): - # Required fields: author, title, note - # Optional fields: month, year, key - template = toplevel[ - sentence(sep=' ')[ - self.format_names('author', as_sentence=False), - join["(", first_of[optional[date], "n.d."], ")"] - ], - self.format_btitle(e, 'title'), - sentence[field('note')], - ] - return template diff --git a/book/_ext/pybtexapastyle/formatting/pybtex/style/formatting/__init__.py b/book/_ext/pybtexapastyle/formatting/pybtex/style/formatting/__init__.py deleted file mode 100644 index 5ac42b8..0000000 --- a/book/_ext/pybtexapastyle/formatting/pybtex/style/formatting/__init__.py +++ /dev/null @@ -1,69 +0,0 @@ -from __future__ import unicode_literals - -from pybtex.style import FormattedEntry, FormattedBibliography -from pybtex.style.template import node, join -from pybtex.richtext import Symbol -from pybtex.plugin import Plugin, find_plugin - - -@node -def toplevel(children, data): - return join(sep=Symbol('newblock')) [children].format_data(data) - - -class BaseStyle(Plugin): - """ - The base class for pythonic formatting styles. - """ - - default_name_style = None - default_label_style = None - default_sorting_style = None - - def __init__(self, label_style=None, name_style=None, sorting_style=None, abbreviate_names=False, min_crossrefs=2, **kwargs): - self.name_style = find_plugin('pybtex.style.names', name_style or self.default_name_style)() - self.label_style = find_plugin('pybtex.style.labels', label_style or self.default_label_style)() - self.sorting_style = find_plugin('pybtex.style.sorting', sorting_style or self.default_sorting_style)() - self.format_name = self.name_style.format - self.format_labels = self.label_style.format_labels - self.sort = self.sorting_style.sort - self.abbreviate_names = abbreviate_names - self.min_crossrefs = min_crossrefs - - def format_entries(self, entries, bib_data=None): - sorted_entries = self.sort(entries) - labels = self.format_labels(sorted_entries) - for label, entry in zip(labels, sorted_entries): - yield self.format_entry(label, entry, bib_data=bib_data) - - def format_entry(self, label, entry, bib_data=None): - context = { - 'entry': entry, - 'style': self, - 'bib_data': bib_data, - } - try: - get_template = getattr(self, 'get_{}_template'.format(entry.type)) - except AttributeError: - format_method = getattr(self, "format_" + entry.type) - text = format_method(context) - else: - text = get_template(entry).format_data(context) - return FormattedEntry(entry.key, text, label) - - def format_bibliography(self, bib_data, citations=None): - """ - Format bibliography entries with the given keys and return a - ``FormattedBibliography`` object. - - :param bib_data: A :py:class:`pybtex.database.BibliographyData` object. - :param citations: A list of citation keys. - """ - - if citations is None: - citations = list(bib_data.entries.keys()) - citations = bib_data.add_extra_citations(citations, self.min_crossrefs) - entries = [bib_data.entries[key] for key in citations] - formatted_entries = self.format_entries(entries) - formatted_bibliography = FormattedBibliography(formatted_entries, style=self, preamble=bib_data.preamble) - return formatted_bibliography diff --git a/book/_ext/pybtexapastyle/formatting/pybtex/style/sorting/__init__.py b/book/_ext/pybtexapastyle/formatting/pybtex/style/sorting/__init__.py deleted file mode 100644 index 3430087..0000000 --- a/book/_ext/pybtexapastyle/formatting/pybtex/style/sorting/__init__.py +++ /dev/null @@ -1,12 +0,0 @@ -from __future__ import unicode_literals - - -from pybtex.plugin import Plugin - - -class BaseSortingStyle(Plugin): - def sorting_key(self, entry): - raise NotImplementedError - - def sort(self, entries): - return sorted(entries, key=self.sorting_key) \ No newline at end of file diff --git a/book/_ext/pybtexapastyle/formatting/pybtex/style/sorting/author_year_title.py b/book/_ext/pybtexapastyle/formatting/pybtex/style/sorting/author_year_title.py deleted file mode 100644 index c315c0c..0000000 --- a/book/_ext/pybtexapastyle/formatting/pybtex/style/sorting/author_year_title.py +++ /dev/null @@ -1,39 +0,0 @@ -from __future__ import unicode_literals - -from pybtex.style.sorting import BaseSortingStyle - -class SortingStyle(BaseSortingStyle): - - def sorting_key(self, entry): - if entry.type in ('book', 'inbook'): - author_key = self.author_editor_key(entry) - elif 'author' in entry.persons: - author_key = self.persons_key(entry.persons['author']) - else: - author_key = '' - return (author_key, entry.fields.get('year', ''), entry.fields.get('title', '')) - - def persons_key(self, persons): - return ' '.join(self.person_key(person) for person in persons) - - def person_key(self, person): - if person.prelast_names[0] != '{' and person.last_names[0] != '{' and person.first_names[0] != '{': - return ' '.join(( - ' '.join(person.prelast_names + person.last_names), - ' '.join(person.first_names + person.middle_names), - ' '.join(person.lineage_names), - )).lower() - else: - return ' '.join(( - ' '.join(person.first_names + person.middle_names), - ' '.join(person.prelast_names + person.last_names), - ' '.join(person.lineage_names), - )).lower() - - def author_editor_key(self, entry): - if entry.persons.get('author'): - return self.persons_key(entry.persons['author']) - elif entry.persons.get('editor'): - return self.persons_key(entry.persons['editor']) - else: - return '' diff --git a/book/_ext/pybtexapastyle/labels/__init__.py b/book/_ext/pybtexapastyle/labels/__init__.py deleted file mode 100644 index e69de29..0000000 diff --git a/book/_ext/pybtexapastyle/labels/apa.py b/book/_ext/pybtexapastyle/labels/apa.py deleted file mode 100644 index 59176f3..0000000 --- a/book/_ext/pybtexapastyle/labels/apa.py +++ /dev/null @@ -1,67 +0,0 @@ -# -*- coding:Utf-8 -*- -from __future__ import unicode_literals - -from collections import Counter -import re -import unicodedata - -from pybtex.style.labels import BaseLabelStyle - - -_nonalnum_pattern = re.compile('[^A-Za-z0-9 \-]+', re.UNICODE) - - -def _strip_accents(s): - return "".join( - (c for c in unicodedata.normalize('NFD', s) - if not unicodedata.combining(c))) - - -def _strip_nonalnum(parts): - """Strip all non-alphanumerical characters from a list of strings. - - >>> print(_strip_nonalnum([u"ÅA. B. Testing 12+}[.@~_", u" 3%"])) - AABTesting123 - """ - s = "".join(parts) - return _nonalnum_pattern.sub("", _strip_accents(s)) - - -class LabelStyle(BaseLabelStyle): - def format_labels(self, sorted_entries): - labels = [self.format_label(entry) for entry in sorted_entries] - count = Counter(labels) - counted = Counter() - for label in labels: - if count[label] == 1: - yield label - else: - yield label # + chr(ord('a') + counted[label]) - # counted.update([label]) - - def format_label(self, entry): - label = "Anonymous" - if 'author' in entry.persons: - label = self.format_author_or_editor_names(entry.persons['author']) - elif 'editor' in entry.persons: - label = self.format_author_or_editor_names(entry.persons['editor']) - elif 'organization' in entry.fields: - label = entry.fields['organization'] - if label.startswith("The "): - label = label[4:] - return '' - # if 'year' in entry.fields: - # return "{}, {}".format(label, entry.fields['year']) - # else: - # return "{}, n.d.".format(label) - - def format_author_or_editor_names(self, persons): - if len(persons) is 1: - return _strip_nonalnum(persons[0].last_names) - elif len(persons) is 2: - return "{} & {}".format( - _strip_nonalnum(persons[0].last_names), - _strip_nonalnum(persons[1].last_names)) - else: - return "{} et al.".format( - _strip_nonalnum(persons[0].last_names)) diff --git a/book/_ext/pybtexapastyle/names/__init__.py b/book/_ext/pybtexapastyle/names/__init__.py deleted file mode 100644 index e69de29..0000000 diff --git a/book/_ext/pybtexapastyle/names/firstlast.py b/book/_ext/pybtexapastyle/names/firstlast.py deleted file mode 100644 index 8f23263..0000000 --- a/book/_ext/pybtexapastyle/names/firstlast.py +++ /dev/null @@ -1,39 +0,0 @@ -# -*- coding:Utf-8 -*- -from __future__ import unicode_literals - -from pybtex.style.names import BaseNameStyle, name_part -from pybtex.style.template import join - - -class NameStyle(BaseNameStyle): - - def format(self, person, abbr=False): - r""" - Format names similarly to {vv~}{ll}{, jj}{, f.} in BibTeX. - - >>> from pybtex.database import Person - >>> name = Person(string=r"Charles Louis Xavier Joseph de la Vall{\'e}e Poussin") - >>> firstlast = NameStyle().format - - >>> print(firstlast(name).format().render_as('latex')) - Charles Louis Xavier~Joseph de~la Vall{é}e~Poussin - >>> print(firstlast(name).format().render_as('html')) - Charles Louis Xavier Joseph de la Vallée Poussin - - >>> print(firstlast(name, abbr=True).format().render_as('latex')) - C.~L. X.~J. de~la Vall{é}e~Poussin - >>> print(firstlast(name, abbr=True).format().render_as('html')) - C. L. X. J. de la Vallée Poussin - - >>> name = Person(first='First', last='Last', middle='Middle') - >>> print(firstlast(name).format().render_as('latex')) - First~Middle Last - >>> print(firstlast(name, abbr=True).format().render_as('latex')) - F.~M. Last - - """ - return join[ - name_part(abbr=abbr)[person.rich_first_names + person.rich_middle_names], - name_part(before=' ')[person.rich_prelast_names], - name_part(before=' ')[person.rich_last_names], - ] diff --git a/book/_ext/pybtexapastyle/setup.py b/book/_ext/pybtexapastyle/setup.py deleted file mode 100644 index a62d122..0000000 --- a/book/_ext/pybtexapastyle/setup.py +++ /dev/null @@ -1,27 +0,0 @@ -import setuptools - - -setuptools.setup( - name='pybtex-apa-style', - version='1.3', - author='Naeka', - author_email='contact@naeka.fr', - description='Pybtex APA-like style', - url='https://github.com/naeka/pybtex-apa-style', - py_modules=['formatting.apa', 'labels.apa', 'names.firstlast'], - entry_points={ - 'pybtex.style.formatting': 'apa = formatting.apa:APAStyle', - 'pybtex.style.labels': 'apa = labels.apa:LabelStyle', - 'pybtex.style.names': 'firstlast = names.firstlast:NameStyle', - }, - classifiers=( - 'Operating System :: OS Independent', - 'Programming Language :: Python', - 'Programming Language :: Python :: 2.7', - 'Programming Language :: Python :: 3', - 'License :: OSI Approved :: MIT License', - 'Operating System :: OS Independent', - 'Topic :: Text Processing :: Markup', - 'Topic :: Utilities', - ), -) diff --git a/book/_toc.yml b/book/_toc.yml index 146f8d6..8a2321d 100644 --- a/book/_toc.yml +++ b/book/_toc.yml @@ -1,10 +1,11 @@ format: jb-book root: intro.md + parts: - caption: Contents chapters: - - file: reliability-component/overview.md + - file: some_content/overview.md sections: - - file: reliability-component/contamination.ipynb + - file: some_content/text_and_code.ipynb - file: references.md - file: credits.md \ No newline at end of file diff --git a/book/code/cosinewave.py b/book/code/cosinewave.py deleted file mode 100644 index 744c2fe..0000000 --- a/book/code/cosinewave.py +++ /dev/null @@ -1,12 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt - -x = np.linspace(0, 2*np.pi, endpoint=True) -y = np.cos(x) - -plt.figure() -plt.plot(x, y) -plt.title('$y=\cos(x)$') -plt.xlabel('$x$') -plt.ylabel('$y$') -plt.savefig('cosinewave.svg') \ No newline at end of file diff --git a/book/code/ex_FN_curve_step_01.py b/book/code/ex_FN_curve_step_01.py deleted file mode 100644 index efc3ade..0000000 --- a/book/code/ex_FN_curve_step_01.py +++ /dev/null @@ -1,38 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt -from mpl_toolkits.axisartist.axislines import AxesZero - -# Probability density/mass function - -fig = plt.figure(figsize=(8,6)) -ax = fig.add_subplot(axes_class=AxesZero) - -for direction in ["xzero", "yzero"]: - ax.axis[direction].set_axisline_style("-|>") # add arrows - ax.axis[direction].set_visible(True) # x and y from origin - -for direction in ["left", "right", "bottom", "top"]: - ax.axis[direction].set_visible(False) # hide borders - -N_fatalities = ['0', '10', '100'] -N_fatalities_loc = [0.05, 0.30, 0.66] - -pdf = ['0.989', '$10^{-2}$', '$10^{-3}$'] -pdf_loc = [0.99, 0.66, 0.33] - -ax.bar(N_fatalities_loc, pdf_loc, width=0.05, color= 'lightcyan', edgecolor='k') - -ax.set_xticks(N_fatalities_loc) -ax.set_xticklabels(N_fatalities) - -ax.set_yticks(pdf_loc) -ax.set_yticklabels(pdf) - -ax.set_title('Probability density/mass function, $f_{N}(n)$', x=0.6, y=1.0) -ax.set_xlabel('Fatalities') -ax.set_ylabel('Probability') - -ax.axhline(y=0.66, xmin= 0.01, xmax= 0.40, linewidth=1, linestyle='dashed', color='k') # add dashed horizontal lines -ax.axhline(y=0.33, xmin= 0.01, xmax= 0.90, linewidth=1, linestyle='dashed', color='k') - -plt.savefig('ex_FN_curve_step_01_py.svg') \ No newline at end of file diff --git a/book/code/ex_FN_curve_step_02.py b/book/code/ex_FN_curve_step_02.py deleted file mode 100644 index d83d51e..0000000 --- a/book/code/ex_FN_curve_step_02.py +++ /dev/null @@ -1,38 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt -from mpl_toolkits.axisartist.axislines import AxesZero - -# Cumulative Distribution Function - -fig = plt.figure(figsize=(8,6)) -ax = fig.add_subplot(axes_class=AxesZero) - -for direction in ["xzero", "yzero"]: - ax.axis[direction].set_axisline_style("-|>") # add arrows - ax.axis[direction].set_visible(True) # x and y from origin - -for direction in ["left", "right", "bottom", "top"]: - ax.axis[direction].set_visible(False) # hide borders - -N_fatalities = ['0', '10', '100', ''] -N_fatalities_loc = [0.03, 0.33, 0.76, 0.95] - -pdf = ['0', '0.989', '0.999', '1'] -pdf_loc = [0.03, 0.66, 0.86, 0.99] - -ax.step(N_fatalities_loc, pdf_loc, color= 'darkblue',linewidth=4) - -ax.set_xticks(N_fatalities_loc) -ax.set_xticklabels(N_fatalities) - -ax.set_yticks(pdf_loc) -ax.set_yticklabels(pdf) - -ax.set_title('Cumulative distribution function, $F_{N}(n) = P(N \leq n)$', x=0.55, y=1.0) -ax.set_xlabel('Fatalities') -ax.set_ylabel('Probability') - -ax.text(0.8, 0.9, r'} $10^{-3}$', fontsize=20) -ax.text(0.4, 0.725, r'} $10^{-2}$', fontsize=30) - -plt.savefig('ex_FN_curve_step_02_py.svg') \ No newline at end of file diff --git a/book/code/ex_FN_curve_step_03.py b/book/code/ex_FN_curve_step_03.py deleted file mode 100644 index ec61816..0000000 --- a/book/code/ex_FN_curve_step_03.py +++ /dev/null @@ -1,35 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt -from mpl_toolkits.axisartist.axislines import AxesZero - -# FN curve - -fig = plt.figure(figsize=(8,6)) -ax = fig.add_subplot(axes_class=AxesZero) - -for direction in ["xzero", "yzero"]: - ax.axis[direction].set_axisline_style("-|>") # add arrows - ax.axis[direction].set_visible(True) # x and y from origin - -for direction in ["left", "right", "bottom", "top"]: - ax.axis[direction].set_visible(False) # hide borders - -N_fatalities = ['0', '10', '100','100'] -N_fatalities_loc = [0.03,0.33, 0.95, 0.95] - -pdf = ['0','$1.1 * 10^{-2}$', '$10^{-3}$','0'] -pdf_loc = [0.03,0.99, 0.66, 0.03] - -ax.step(N_fatalities_loc, pdf_loc, color= 'darkblue',linewidth=4) - -ax.set_xticks(N_fatalities_loc) -ax.set_xticklabels(N_fatalities) - -ax.set_yticks(pdf_loc) -ax.set_yticklabels(pdf) - -ax.set_title('FN curve, $1-F_{N}(n) = P(N > n)$', x=0.75, y=1.0) -ax.set_xlabel('Fatalities') -ax.set_ylabel('Probability') - -plt.savefig('ex_FN_curve_step_03_py.svg') \ No newline at end of file diff --git a/book/code/present_value.py b/book/code/present_value.py deleted file mode 100644 index ffbd88e..0000000 --- a/book/code/present_value.py +++ /dev/null @@ -1,16 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt - -t = np.linspace(0, 101) -y_2 = 1 / (1 + 0.02)**t -y_4 = 1 / (1 + 0.04)**t - -fig = plt.figure() -plt.plot(t, y_2, label='2%') -plt.plot(t, y_4, label='4%') -plt.grid() -plt.legend() -plt.xlabel('Year') -plt.ylabel('Normalized Present Value [$-$]') - -plt.savefig('present_value_py.svg') diff --git a/book/code/risk_types.py b/book/code/risk_types.py deleted file mode 100644 index 38f967f..0000000 --- a/book/code/risk_types.py +++ /dev/null @@ -1,54 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt - -# Given Parameters - -N_fatalities = np.linspace(1,1000,1000) # fatalities - -P_df = 0.1; beta = 0.1 - -alpha = 2 -k = 3 -N_A = 100 - -r= 0.025 -I = 5*10**6 -B = 0.33 - -# Individual Risk - -Pf_ind_risk = (beta*(10**-4))/P_df # per year - -# print('Acceptable Failure Probability: ', Pf_ind_risk) - -# Societal Risk - -C = ((beta*100)/(k*np.sqrt(N_A)))**2 # binomial distribution - -Pf_SR = (C/(N_fatalities**alpha)) - -# Economic Risk - -D_damage = (5*10**7)*N_fatalities - -Pf_ER = (I*B*r)/(D_damage) - -# Visualize - -my_linewidth = 4 - -plt.figure(figsize=(8,6)) - -plt.yscale('log') -plt.xscale('log') -plt.plot(N_fatalities, Pf_SR, linewidth=my_linewidth, label='Societal Risk') -plt.plot(N_fatalities,Pf_ER, linewidth=my_linewidth, color='r', label='Economic Risk') -plt.axhline(Pf_ind_risk, linewidth=my_linewidth, color='g', label='Individual Risk') - -plt.ylabel('Probability of Exceedance, $1-F_N(n)$') -plt.xlabel('Fatalities, N') -plt.ylim(10**(-7),1) - -plt.legend(loc='upper right') - -plt.savefig('risk_types_py.svg') \ No newline at end of file diff --git a/book/code/sinewave.py b/book/code/sinewave.py deleted file mode 100644 index 74a1d42..0000000 --- a/book/code/sinewave.py +++ /dev/null @@ -1,12 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt - -x = np.linspace(0, 2*np.pi, endpoint=True) -y = np.sin(x) - -plt.figure() -plt.plot(x, y) -plt.title('$y=\sin(x)$') -plt.xlabel('$x$') -plt.ylabel('$y$') -plt.savefig('sinewave.svg') \ No newline at end of file diff --git a/book/code/test.py b/book/code/test.py deleted file mode 100644 index 21a9781..0000000 --- a/book/code/test.py +++ /dev/null @@ -1,23 +0,0 @@ -import modulefinder - -finder = modulefinder.ModuleFinder() -finder.run_script('cosinewave.py') - -moduleslist = {} -for name, mod in finder.modules.iteritems(): - filename = mod.__file__ - if filename is None: - continue - if '__' in name: - continue - #if "python" in filename.lower(): - # continue - moduleslist[name.split(".")[0]] = True - #print '%s: %s' % (name, filename) - #print ','.join(mod.globalnames.keys()[:3]) - -print('Loaded modules:') -for name, dummy in moduleslist.iteritems(): - print(name) - -input("Press Enter to continue...") diff --git a/book/credits.md b/book/credits.md index d49744b..9694553 100644 --- a/book/credits.md +++ b/book/credits.md @@ -25,15 +25,6 @@ This book is created using open source tools: it is a Jupyter Book that is writt ### Acknowledgements ---- - This book is licensed under a Creative Commons Attribution 4.0 International License. -Creative Commons License - -The following items referenced in the text are _not_ included in the license: - -{numref}`risk-curve-baecher` and {numref}`risk-curve-baecher-2` are from {cite:t}`baecher2003`, based on {cite:t}`baecher1982` and described in {cite:t}`baecher2021` - -{numref}`risk_matrix` is from an online PDF document (located [here](https://home.army.mil/lee/application/files/7815/3809/1878/Tables.pdf)). The formal definition for the risk matrix can be found in Engineering Manual EM 385-1-1 (located [here](https://www.publications.usace.army.mil/portals/76/publications/engineermanuals/em_385-1-1.pdf)). - +Creative Commons License \ No newline at end of file diff --git a/book/exercises/example-quiz.json b/book/exercises/example-quiz.json deleted file mode 100644 index 53de808..0000000 --- a/book/exercises/example-quiz.json +++ /dev/null @@ -1,204 +0,0 @@ -[ - { - "question": "Choose all of the following that can be included in Jupyter notebooks?", - "type": "many_choice", - "answers": [ - { - "answer": "Text and graphics output from Python", - "correct": true, - "feedback": "Correct." - }, - { - "answer": "Typeset mathematics", - "correct": true, - "feedback": "Correct." - }, - { - "answer": "Python executable code", - "correct": true, - "feedback": "Correct." - }, - { - "answer": "Formatted text", - "correct": true, - "feedback": "Correct." - }, - { - "answer": "Live snakes via Python", - "correct": false, - "feedback": "I hope not." - } - ] - }, - { - "question": "Which of these are used to create formatted text in Jupyter notebooks?", - "type": "multiple_choice", - "answers": [ - { - "answer": "Wiki markup", - "correct": false, - "feedback": "False." - }, - { - "answer": "SVG", - "correct": false, - "feedback": "False." - }, - { - "answer": "Markdown", - "correct": true, - "feedback": "Correct." - }, - { - "answer": "Rich Text", - "correct": false, - "feedback": "False." - } - ] - }, - { - "question": "Enter the value of $\\pi$ to 2 decimal places.", - "type": "numeric", - "answers": [ - { - "type": "value", - "value": 3.14, - "correct": true, - "feedback": "Correct." - }, - { - "type": "range", - "range": [ - 3.142857, - 3.142858 - ], - "correct": true, - "feedback": "True to 2 decimal places, but you know $\\pi$ is not really 22/7, right?" - }, - { - "type": "range", - "range": [ - -100000000, - 0 - ], - "correct": false, - "feedback": "$\\pi$ is the AREA of a circle of radius 1. Try again." - }, - { - "type": "default", - "feedback": "$\\pi$ is the area of a circle of radius 1. Try again." - } - ] - }, - { - "question": "Enter the value of $\\pi$ to 2 decimal places.", - "type": "numeric", - "precision": 2, - "answers": [ - { - "type": "value", - "value": 3.14, - "correct": true, - "feedback": "Correct." - }, - { - "type": "range", - "range": [ - 3.142857, - 3.142858 - ], - "correct": true, - "feedback": "True to 2 decimal places, but you know $\\pi$ is not really 22/7, right?" - }, - { - "type": "range", - "range": [ - -100000000, - 0 - ], - "correct": false, - "feedback": "$\\pi$ is the AREA of a circle of radius 1. Try again." - }, - { - "type": "default", - "feedback": "$\\pi$ is the area of a circle of radius 1. Try again." - } - ] - }, - { - "question": "Determine the output of the following Python code:", - "code": "a=\"1\"\nb=\"2\"\nprint(a+b)", - "type": "multiple_choice", - "answers": [ - { - "answer": "1", - "correct": false, - "feedback": "No. When strings are operated on by +, they are concatenated." - }, - { - "answer": "2", - "correct": false, - "feedback": "No. When strings are operated on by +, they are concatenated." - }, - { - "answer": "3", - "correct": false, - "feedback": "No. When strings are operated on by +, they are concatenated." - }, - { - "answer": "12", - "correct": true, - "feedback": "Yes. The + operator will concatenate the strings \"1\" and \"2\"." - }, - { - "answer": "error", - "correct": false, - "feedback": "No. The + operator for strings performs string concatenation." - } - ] - }, - { - "question": "The variable mylist is a Python list. Choose which code snippet will append the item 3 to mylist.", - "type": "multiple_choice", - "answers": [ - { - "code": "mylist+=3", - "correct": false - }, - { - "code": "mylist+=[3]", - "correct": true - }, - { - "code": "mylist+={3}", - "correct": false - } - ] - }, - { - "question": "Which of these is the ratio of a circle's circumference to its diameter?", - "type": "multiple_choice", - "answers": [ - { - "answer": "$\\pi$", - "correct": true, - "feedback": "Correct." - }, - { - "answer": "$\\frac{22}{7}$", - "correct": false, - "feedback": "$\\frac{22}{7}$ is only an approximation to the true value." - }, - { - "answer": "3", - "correct": false, - "feedback": "This is a crude approximation to the true value." - }, - { - "answer": "$\\tau$", - "correct": false, - "feedback": "True for the ratio of the circle's circumference to its radius, not diameter." - } - ] - } -] \ No newline at end of file diff --git a/book/exercises/exercise-dam.md b/book/exercises/exercise-dam.md deleted file mode 100644 index 8adb8f6..0000000 --- a/book/exercises/exercise-dam.md +++ /dev/null @@ -1,154 +0,0 @@ -# Dam and River - -You are tasked to analyse the safety of a dam and the downstream river system. Downstream of the dam there is a dike ring protected by two main dike sections which must be able to contain water released from the reservoir. The dike sections are connected to each other and form a continuous boundary along the same side of the river. Let $P(F_1)=0.01$ and $P(F_2)=0.01$ denote failure probability of dike section 1 and section 2 respectively. There appears to be a correlation between failures of both sections, $\rho_{1,2}=0.9$, and the figure below shows the effect of the correlation coefficient on the joint failure of the two sections. - -%commented paragraphs were used for an exam question with a fault tree - -%You are tasked to analyse the safety of a dam. The dam itself can fail due to instability, and another failure mechanism is failure of the spillway due to uncontrolled erosion that could reach the body of the dam. If water levels in the reservoir become high, water is released from the reservoir into the spillway due to overflow, which happens approximately once every 10 years. - -%When water is released through spillway, there are two situations that could lead to a weak spillway prone to erosion and failure: 1) hidden damage to the spillway structure that cannot be detected in yearly inspections, and 2) a crack in the concrete of the spillway which has been missed during the yearly inspection. - -%Downstream of the dam there is an area protected by two main dike sections which must be able to contain water released from the reservoir. A dike section fails if the river discharge exceeds a critical discharge $Q_c$ with a probability of exceedance of 1/100 per year, which leads to flooding of the area. There appears to be a correlation between failures of both sections, $\rho_{1,2}=0.9$, and the figure below shows the effect of the correlation coefficient on the joint failure of the two sections. - -```{figure} ../figures/system-corr-coeff.PNG ---- -width: 400px -name: corr-coeff-or ---- -Effect of correlation coefficient joint failure, $P(A \cap B)$ (assume that $P(A \cap B)=0.003$ at $\rho=+0.9$, where the arrow is located). -``` - -**Question 1:** Estimate the probability of flooding of the area protected by the two dike sections. Assume that the failure probability of each mechanism is 0.01, and they are _not_ independent; however, you can use the figure above to quantify this. - -```{admonition} Answer -:class: tip, dropdown - -Flooding of the protected area occurs when at least one of the two dike section fails. This is a series system. Thus, probability of flooding of the protected area can be determined by: - -$$ - P(\textrm{flooding}) &= P(\textrm{dike sections 1 fails}\:\cup \textrm{dike section 2 fails})\\ - P(F_1 \cup F_2) &= P(F_1) + P(F_2) - P(F_1 \cap F_2) -$$ - -Based on the figure and the correlation $\rho_{1,2} = 0.9$, the joint probability of failure $P(F_1 \cap F_2)=0.003$ and the series failure probability is - -$$ - P(\textrm{flooding}) = 0.01 + 0.01 - 0.003 = 0.017 \: \mathrm{/year} -$$ -``` - -## Dam repair: probabilistic planning - -The dam has to be repaired. The responsible minister wants to make sure the whole project is finished within 12 months, and only accepts a probability of 10% that actual construction works exceed this duration. The dam reinforcement consists of two activities. The second activity can only start when the first one has been finished. The durations of both activities are uncertain and normally distributed. The first activity has a mean duration of $\mu_1=4$ months and a standard deviation of $\sigma_1 = 1$ month; for the second activity $\sigma_2 = 2$ months. - -**Question 2:** Compute the mean duration of the activity 2, so that the project duration would fall within the criterion given by the minister. - -```{admonition} Answer -:class: tip, dropdown - -Let $T_1$ and $T_2$ denote the duration of activities 1 and 2; $T$ denotes the total duration; $T_1$ and $T_2$ are normally distributed: - -$$ - T_1 \sim \mathcal{N}( - \mu_1=4,\sigma_1=1) \\ - T_2 \sim \mathcal{N}(\mu_2=?,\sigma_2=2) -$$ - -$T = T1 + T2$ is also normally distributed, where - -$$ -\mu_T &= \mu_1 + \mu_2 \\ -\sigma_T &= \sqrt{\sigma_1^2 + \sigma_2^2} = \sqrt{5} = 2.326 -$$ - -The probability of project duration greater than 12 months can be found with the complementary standard normal CDF, and should be a maximum of 0.1: - -$$ -1-\Phi\left[\frac{12\:\mathrm{months}-\mu_T}{\sigma_T}\right]=0.1 -$$ - -Applying the inverse CDF allows us to solve for $\mu_1$: - -$$ -\frac{12-\mu_T}{\sigma_T} &=\Phi^{-1}[0.9] \\ -\frac{12-(\mu_1 + \mu_2)}{\sigma_T} &=1.2816 -$$ - -$$ -\mu_1 &= 12 - 1.2816 \cdot \sigma_T - \mu_2 \\ -\mu_1 &= 12 - 1.282(2.326) - 4 = 5.018\:\mathrm{months} -$$ - - -``` - -## Acceptable risk - -The government wants to study the acceptable risk and the acceptable probability of dam failure. Two criteria are used for acceptable risk: - -- Societal risk (SR): an FN limit line: $P_f \leq 10^{-2}/n^2$. -- Individual risk (IR): $IR \leq 10^{-4}$ per year. - -We know that mortality in case of dam failure is $F_{d|f} = 0.1$ and that the population living downstream of the dam is 1000 people. - -**Question 3:** Plot the FN limit line and indicate the acceptable probability of failure according to both criteria (individual risk, societal risk). - -````{admonition} Answer -:class: tip, dropdown - -```{figure} ../figures/exercise-dam-fn-limit-line.png ---- -width: 500px ---- -``` -```` - -**Question 4:** Provide an advice on the acceptable probability of failure for the dam. Give the proposed numerical value and a short motivation. - -```{admonition} Answer -:class: tip, dropdown - -Based on individual risk criterion, we have: - -$$ - IR = P_f P_{d|f} \leq IR_{acc} -$$ - -where $P_{d|f}=0.1$. Hence, the acceptable probability of failure is: - -$$ - P_f \leq \frac{IR_{acc}}{P_{d|f}} = \frac{10^{-4}}{0.1} = 10^{-3} \: \mathrm{/year} -$$ - -Based on societal risk criterion (FN-Curve): - -Acceptable failure probability can be determined by the FN-Curve: - -$$ - P_f = 1 - F_N(n) \leq \frac{C}{n^\alpha} = \frac{10^{-2}}{n^2} -$$ - -Based on given information above, expected number of casualties per dam failure event is $n = F_{d|f}\cdot 1000 = 100$. - -$$ - P_f &\leq \frac{10^{-2}}{100^2} \\ - P_f &= 10^{-6} \: \mathrm{/year} -$$ - -The most stringent of the two criteria applies, so the proposed safety standard would be $10^{-6}$ per year for the given inputs. -``` diff --git a/book/exercises/exercise-fn-curve.md b/book/exercises/exercise-fn-curve.md deleted file mode 100644 index 62f9102..0000000 --- a/book/exercises/exercise-fn-curve.md +++ /dev/null @@ -1,68 +0,0 @@ -(ex_fn_curve)= -# FN Curve - -A small town is located in a seismic region threatened by two faults. Fault A has a 10% probability of occurring each year, which would cause 10 fatalities, and Fault B has a 1% chance of occurring, which would cause 100 fatalities. Construct an FN curve for the town. Assume that the town is risk averse and that the tolerable risk limit is governed using a constant of C=1. - -**Question 1:** Compute the expected annual fatalities for the town. - -```{admonition} Answer -:class: tip, dropdown - -$$ -E(N) = P_1 \cdot N_1 + P_2 \cdot N_2 = 0.1 \cdot 10 + 0.01 \cdot 100 = 2 -$$ -``` - -**Question 2:** If the town improved the safety of its buildings, what would be the maximum allowable number of fatalities that would be considered acceptable due to an earthquake on fault A? - -```{admonition} Answer -:class: tip, dropdown - -Using the limit curve - -$$ -1 - F_n(n) = C / n^\alpha -$$ - -$$ -0.1 = 1 / n^2 -$$ - -$$ -n = \sqrt{10} \approx 3 -$$ -``` - -**Question 3:** What is the maximum value for the probability of an earthquake on Fault B that would be considered acceptable by the town? - -```{admonition} Answer -:class: tip, dropdown - -Using the limit curve - -$$ -1 - F_n(n) = C / n^\alpha -$$ - -$$ -1 - F_n(100) = C / 100^2 = 0.0001 = 10^{-4} -$$ -``` - -**Question 4:** Create an FN curve for this situation, including the limit line. Be sure to clearly label the axes and the values of key points on your diagram. - -```{note} -If you are not sure what the limit line is, wait for this question until you read the Safety Standards Section (Risk Evaluation chapter). -``` - -````{admonition} Answer -:class: tip, dropdown - -```{figure} ../figures/exercise-FN-curve.png ---- -width: 600px -name: FN-curve ---- -FN-curve for exercise 4 -``` -```` \ No newline at end of file diff --git a/book/exercises/exercise-paint.md b/book/exercises/exercise-paint.md deleted file mode 100644 index c7197db..0000000 --- a/book/exercises/exercise-paint.md +++ /dev/null @@ -1,173 +0,0 @@ -# Paint System - -In this assignment we will consider a paint system that prevents rust and corrosion on a steel structure. A high quality paint system costs €40 per square meter and has a failure probability of 0.002, which assumes that the old paint system is completely stripped off and the steel surface is cleaned prior to installation, which has an additional cost of €20 per square meter. - -Common cost cutting measures are to use a cheaper paint that costs half as much, but is five times more likely to fail, or to simply sand the old paint rather than stripping it off prior to applying a new paint, which increases the failure probability by 10, but only costs €5 per square meter. - -During operation of the structure, if a rust spot is found it must be repaired immediately by removing the damaged paint and replacing it. The repair has an additional cost of €500 per square meter. - -Construct a decision tree to evaluate the different options for steel preparation and paint, then use it to answer the following questions. Assume that the owner wants to minimize total costs, that the paint system only fails once in any reference period and that the probability of failure in each year is independent. All costs and probabilities are calculated on a square meter basis. - -%**Question 6:** Upload a photo/scan of your decision tree. Make sure the values and parameters for each branch are clear. - -````{admonition} Decision Tree -:class: tip, dropdown - -This problem can be visualized using a decision tree as shown below. However, it results in a different interpretation of the problem than that shown in the solution. For example, consider the top branch at the far right, where 'No rust spot' is assigned a probability of 0.998. This is consistent with the formulation of a decision tree, but not consistent with the problem statement, which implies that the €60 cost associated with cleaning and painting is always done when replacing the paint system (thus a probability of 1.0). This is why the values in the decision tree are slightly different than those in Question 3, for example. - -Although the decision tree is not part of the exam, this illustrates an important lesson: it is very easy to accidentally make probability calculations that are inconsistent with the situation you are trying to evaluate! - -```{figure} ../figures/exercise-decision-tree.png ---- -width: 600px -name: decision-tree ---- -Decision tree. -``` -```` - -**Question 1:** What is the probability of each paint system failure per square meter over one year? - -```{admonition} Answer -:class: tip, dropdown - -| Paint | Cleaning | $p_f$ [1/yr] | -|------- |--- | --- | -| High-Quality | Stripping | 0.002 | -| High-Quality | Sanding | 0.02 | -| Low-Quality | Stripping | 0.01 | -| Low-Quality | Sanding | 0.10 | -``` - -**Question 2:** What is the probability of each paint system failure per square meter over a 10 year period? - -```{admonition} Answer -:class: tip, dropdown - -$$P_{f,10y} = 1 - (1 - p_{f,1y})^{10}$$ - -| Paint | Cleaning | $p_f$ [1/10-yr] | -|------- |--- | --- | -| High-Quality | Stripping | 0.02 | -| High-Quality | Sanding | 0.18 | -| Low-Quality | Stripping | 0.10 | -| Low-Quality | Sanding | 0.65 | -``` - -**Question 3:** What is the expected cost per square meter over a one year period if the owner uses the high quality cleaning and high quality paint? - -```{admonition} Answer -:class: tip, dropdown - -$$ -40 + 20 + 0.002 \cdot (500 + 40 + 20) = \euro{} 61.12 /\mathrm{m^2} -$$ -``` - -**Question 4:** What is the optimal paint system for a one year period? - -```{admonition} Answer -:class: tip, dropdown - -$$C_{paint} + C_{cleaning} + P_{f,1y} \cdot (C_{paint} + C_{cleaning} + C_{repair})$$ - -| Paint | Cleaning | Expected cost [€/yr] | -|------- |--- | --- | -| High-Quality | Stripping | 61.12 | -| High-Quality | Sanding | 55.90 | -| Low-Quality | Stripping | **45.40** | -| Low-Quality | Sanding | 77.50 | - -Low Quality Paint + High Quality Cleaning -``` - -**Question 5:** What is the optimal paint system for a 10 year period? - -```{admonition} Answer -:class: tip, dropdown - -$$C_{paint} + C_{cleaning} + P_{f,10y} \cdot (C_{paint} + C_{cleaning} + C_{repair})$$ - -| Paint | Cleaning | Expected cost [€/10 yr] | -|------- |--- | --- | -| High-Quality | Stripping | **71.10** | -| High-Quality | Sanding | 144.70 | -| Low-Quality | Stripping | 91.63 | -| Low-Quality | Sanding | 366.94 | - -High Quality Paint + High Quality Cleaning - -**NOTE:** If you're getting slightly different results, don't panic! Most likely you have approximated the probabilities computed above in question 2. -``` - -Assume the owner has decided to use the cheap paint system, and is simply going to sand it off (i.e. the cheap cleaning method) and re-apply the same system every year (i.e., for these problems consider a 1-year reference period). You have been asked to assess whether it is worthwhile to use a quick sonic test system to prevent failures during the year, and if it is, the number of tests that should be performed per year. Each test costs about €3 per m2, and if a weak spot is found, a new layer of paint can be easily applied, lowering the failure probability by a factor of 0.50. - -**Question 6:** What is the annual expected cost due to paint failure if no sonic inspections are done? - -```{admonition} Answer -:class: tip, dropdown - -$$ -E(D) = P_f \cdot D = 0.1 \cdot 525 = 52.50 -$$ -``` - -**Question 7:** What is the annual expected total cost for the paint system if no sonic inspections are done? - -```{admonition} Answer -:class: tip, dropdown - -Using the decision tree from above: €77.50/m2 -``` - -**Question 8:** What is the change in risk for 3 sonic inspections? - -```{admonition} Answer -:class: tip, dropdown - -$$ -\Delta E(D) = (P_{f,0} - P_{f,new}) \cdot D = 45.94 -$$ -``` - -**Question 9:** What is the annual expected cost due to paint failure if 3 sonic inspections are done? - -```{admonition} Answer -:class: tip, dropdown -The expected damage is: -$$ -E(D)=P_f \cdot D={0.5}^3 \cdot 0.1 \cdot 525=6.56 -$$ -But the 3 inspections cost €9, thus the total expected cost is €15.56. It is incorrect to multiply the inspection cost by the failure probability. NB: this calculation implies the inspections occur regardles of when the failure happens. - -``` - -**Question 10:** What is the maximum number of inspections per year that can be performed that are cost-effective? Note: Round your answer towards the smallest integer. - -```{admonition} Answer -:class: tip, dropdown - -For the investments to be cost effective: - -$$ -\frac{\Delta E(D)}{I}>1 -$$ - -Which results in a maximum of 17 inspections per year. -``` - -**Question 11:** What is the optimum number of sonic inspections to perform each year? Plot a graph, with the Risk, Investment and Total cost curves and clearly indicate the optimum. - -````{admonition} Answer -:class: tip, dropdown - -As shown in the figure, the optimum is 3 per year. - -```{figure} ../figures/exercise-optimization.png ---- -width: 600px -name: optimization-curve ---- -Optimization curve for exercise 12 -``` -```` \ No newline at end of file diff --git a/book/exercises/exercise-sample-exam.md b/book/exercises/exercise-sample-exam.md deleted file mode 100644 index 8c8ac10..0000000 --- a/book/exercises/exercise-sample-exam.md +++ /dev/null @@ -1,248 +0,0 @@ -# Sample Exam Questions - - -## General Questions - -**Question 1:** Indicate which of the following statements is true (multiple answers possible): - 1. A parallel system gets stronger if there is a strong positive correlation between failure of the elements. - 2. Dependence between elements is only determined by dependence in loads. - 3. In case of a full dependence between two elements $A$ and $B$, it holds that $P(B|A)=1$. - 4. A flood defence system that is a single line of defence composed of multiple dike sections would best be characterized as a series sytem, not as a parallel system. - 5. A prison with multiple walls and fences would best be characterized as a series system, not as a parallel system. - -```{admonition} Answer -:class: tip, dropdown - -Options 3 and 4 are true. -``` - -## Flood Protection for a Bay - -A flood protection system for an area at a bay consists of a first line of defence (a dam on the coast) and a second line (a dike around the bay) to protect the city against a storm surge that can cause a high water level in the bay. The design team considers two strategies: 1) a single dike around the bay, or 2) a dike around the bay plus a dam (see figure). - -```{figure} ../figures/exercise-sample-exam-bay.png ---- -width: 400px -name: flood-protection ---- -``` - -**Question 1:** from the perspective of flooding in the city, the function of the dam and dike together is best described as a (choose one): -a. series system -b. parallel system -c. a single component -d. none of the above - -```{admonition} Answer -:class: tip, dropdown - -Option b is true. -``` - -**Question 2:** how will dependence between the dam and dike change the system failure probability? (choose one) -a. increase -b. decrease -c. no change - -```{admonition} Answer -:class: tip, dropdown - -Option a is true. -``` - -**Question 3:** describe whether or not there is dependence between the dam and dike, and what the source could be. - -```{admonition} Answer -:class: tip, dropdown - -It is likely that both structures are constructed of the same material (e.g., local soil), which would respond in a similar way to the storm surge and waves. The structures are also likely to be operated and maintained by the same government agency, which would result in dependence due to human error and maintenance problems. -``` ---- -The damage in case of flood protection system failure is 1 billion $10^9$ Euros. We compare two different investments in the system. In strategy 1 the system failure probability becomes $10^{-3}$ per year at a cost of 10 million ($10 \cdot 10^{6}$). In strategy 2 the system failure probability becomes $3 \cdot 10^{-4}$ per year at a cost of 50 million. - -**Question 4:** for which value of the interest rate $r$ is strategy 2 the most interesting? (You may consider an infinite lifetime of investments). - -```{admonition} Answer -:class: tip, dropdown - -Find $r$ such that the difference in expected damage between strategy 1 and 2, $\Delta p_{f,sys}D/r$, is greater than the difference between the investments, $I_2-I_1$, where the net present value over an infinite lifetime is $1/r$. - -$$ -r < \frac{\Delta p_{f,sys} D}{I_2-I_1} = \frac{(0.0010-0.0003)\cdot 1000 \text{m€}}{50\: \text{m€}-10\: \text{m€}}=0.0175 -$$ - -Can also set up as solving for $r$ when comparing total costs: - -$$ -I_1+\frac{p_1 D}{r}>I_2+\frac{p_2 D}{r} -$$ -``` ---- - A full scale risk assessment is made for the system with probabilities $P(N>10)=10^{-3}$ per year and $P(N>100)=5 \cdot 10^{-5}$ per year. A so-called limit line is given with values with $C = 10^{-1}$; and $\alpha = 2$. - -**Question 5:** determine whether this situation is acceptable. You may answer using a few sentences, calculations or by submitting a sketch, but either way, you must support your answer quantitatively. If you use a sketch, indicate the scale and relevant points on the plot. - -````{admonition} Answer -:class: tip, dropdown - -First create an FN curve for the risk assessment - -**NOTE:** _the figure below is slightly incorrect; the horizontal lines should be to the right of the "dots;" in other words, the 1E-05 value should be above N=100. This makes it more obvious why the system does not meet the safety criteria._ - -```{figure} ../figures/exercise-sample-exam-limit-line.png ---- -width: 400px -name: limit-line ---- -``` - -Next, check that each point on the line is below the limit line: - -$$ -1-F_N(n)<\frac{C}{N^α} -$$ - -The probability of exceeding 100 fatalities is too high since $5E-5>0.1/100^2=1E-5$. The same is true for 10 fatalities. -```` ---- -The flooding probability is 1/50 per year and damage is 150 million € ($10^6$). It is questioned whether additional protection is needed and what would be the best solution between the following: - -- Strategy A: raise the dike -- Strategy B: raise the dike and build a mangrove forest in front which reduces waves - -The table below indicates the costs of the strategies and how much they reduce the initial failure probability. Assume the interest rate is 4%. - -```{list-table} Mitigation Strategy A and B. -:header-rows: 1 - -* - Strategy - - Failure probability factor - - Costs, million € ($10^6$) -* - Do Nothing - - 1.0 - - 0 -* - A - - 0.5 - - 10 -* - B - - 0.2 - - 18 -``` - -**Question 6:** what is the most cost-effective or optimal strategy? Explain your answer. - -1. Strategy A -2. Strategy B -3. neither A nor B - -````{admonition} Answer -:class: tip, dropdown - -Strategy B is best. - -Various costs (NPV value) are calculated in the table below, and Strategy B is the lowest total cost we well as highest risk reduction. - -```{figure} ../figures/exercise_sample_opt.png ---- -width: 500px ---- -``` -```` ---- -Consider the individual risk in two areas of the city by the bay, above. The acceptable individual risk is $10^{-5}$ per year. The conditional probability of death due to flooding is dependent on the water depth and indicated next to the graph. The individual risk level in area A is $10^{-5}$ per year and the water depth is 3 m. The individual risk level in area B is $10^{-5}$ per year and the water depth is 2 m. - -**Question 7:** what should be the maximum allowable failure probability of the dike on the bay, $P_{\text{flooding}}$, to meet the standard for individual risk, $IR$? - -```{figure} ../figures/exercise-sample-exam-mortality.png ---- -width: 400px ---- -``` - -````{admonition} Answer -:class: tip, dropdown - -Individual risk is: - -$$ -IR = P_{\text{flooding}} \cdot P_{\text{death}|\text{flooding}} -$$ - -where the values for the conditional term can be found using the mortality figure, and solve for $P_{\text{flooding}}$. - -```{figure} ../figures/exercise_sample_IR.png ---- -width: 500px ---- -``` -The norm is governed by the most strict safety requirement, thus, $P_{\text{flooding}}$ should be 0.0002 per year. -```` - -## Component Reliability - - - -The shaded region, $\Omega$, in the figure below is the failure domain of an unknown object (the shaded zone extends further towards positive infinity for $x$ and $y$). $p_f$ is the probability of failure of that object, such that: - -$$ - p_f = \iint_\Omega f(x,y)dxdy -$$ - -Where $x$ and $y$ are random variables and $f(x,y)$ is the joint PDF. - -```{figure} ../figures/exercise-sample-exam-failure-domain.png ---- -width: 400px -name: failure-domain ---- -``` - -**Question 1:** identify a specific real-life object of your choosing (it can be anything!) that can be described by this diagram and failure probability. Describe the object and provide a definition of failure using words only, no equations. Mention whether $X$ and $Y$ each acts as a load or a resistance. - -```{admonition} Answer -:class: tip, dropdown - -It is clear that $X$ and $Y$ are both loads, since high values of both variables lead to failure. There are many possible ‘objects’ that are governed by two loads: - -- Dike: x and y are water level and wave load, failure is excessive overtopping -- Steel rod: 2 loads exceed strength -- Beam: self-weight and length are loads (but this is non-linear) -- Island: x and y are sea level rise and settlement, capacity is elevation; failure is flooding -- 2 things on object with limiting capacity. E.g.: people on a couch or bench, birds on a tree branch -- Literally any two loads would be acceptable, as long as the capacity of the object was a sum of both of them (if not a sum, it’s non-linear) -%Honorable mentions: exam grading, stoof pot, student knowledge on exam material, ear damage at a music festival, dog and cat in box, exam desk stability, fingers squeezing a pen, 2 heaters in a room - - - diff --git a/book/exercises/overview.md b/book/exercises/overview.md deleted file mode 100644 index e0df0bc..0000000 --- a/book/exercises/overview.md +++ /dev/null @@ -1,7 +0,0 @@ -# Exercises - -A number of exercises are included in this chapter that illustrate the previously discussed concepts of risk and reliability in a probabilistic design context. At the end a set of **sample exam** questions are included. - ---- - -_Exercises are largely drawn from decades of old course material from many contributors; this chapter can be referred to using standard Editor attribution._ \ No newline at end of file diff --git a/book/figures/1.png b/book/figures/1.png deleted file mode 100644 index 5227771..0000000 Binary files a/book/figures/1.png and /dev/null differ diff --git a/book/figures/FN-simple.PNG b/book/figures/FN-simple.PNG deleted file mode 100644 index 7e8eea1..0000000 Binary files a/book/figures/FN-simple.PNG and /dev/null differ diff --git a/book/images/TUDelft_logo_rgb.png b/book/figures/TUDelft_logo_rgb.png similarity index 100% rename from book/images/TUDelft_logo_rgb.png rename to book/figures/TUDelft_logo_rgb.png diff --git a/book/figures/combined_risk_criteria.png b/book/figures/combined_risk_criteria.png deleted file mode 100644 index bb9f78e..0000000 Binary files a/book/figures/combined_risk_criteria.png and /dev/null differ diff --git a/book/figures/cover.png b/book/figures/cover.png deleted file mode 100644 index 2a2bfb0..0000000 Binary files a/book/figures/cover.png and /dev/null differ diff --git a/book/figures/cover.svg b/book/figures/cover.svg deleted file mode 100644 index 2e7f47f..0000000 --- a/book/figures/cover.svg +++ /dev/null @@ -1,8550 +0,0 @@ - - - - diff --git a/book/figures/cover_README.txt b/book/figures/cover_README.txt deleted file mode 100644 index 9009a0e..0000000 --- a/book/figures/cover_README.txt +++ /dev/null @@ -1,17 +0,0 @@ - -store notebook in `./book/figures/` and rest of files in `./book/book/figures/` - -**note** a video was made to illustrate gradient fill. stored in robert's dropbox for now - -- figures created in cover ipynb - - make axes and fig transparent - - export without background in savefig -- created doc in inkscape, set size to 210mmx210mm per OIT requirements -- OIT requires 210mmx210mm and at least 300 pixels, which is 36 dpi or 36x36 dpi -- Default inkscape was 96 dpi, which is 794x794 pixels -- import svg's to inkscape -- position figures -- apply gradient to lines -- delete three points -- export to png (default 96dpi is 100KB) -- export cover_small.png (45 dpi is 35KB) >>> for book logo \ No newline at end of file diff --git a/book/figures/cover_bi.svg b/book/figures/cover_bi.svg deleted file mode 100644 index 5154d31..0000000 --- a/book/figures/cover_bi.svg +++ /dev/null @@ -1,4181 +0,0 @@ - - - - - - - - 2024-02-22T06:19:21.170713 - image/svg+xml - - - Matplotlib v3.8.2, https://matplotlib.org/ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 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- - - -Created by potrace 1.8, written by Peter Selinger 2001-2007 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/book/intro.md b/book/intro.md index 536d98c..fdf38ff 100644 --- a/book/intro.md +++ b/book/intro.md @@ -1,11 +1,9 @@ (intro)= -# Template Book +# Welcome to the Template Book _Write book intro here. This is the first page the student will see when opening the url._ -This book will be used to fork other books and make it easier to keep various software in those other books up to date. - - +This book can be used to fork other books. It includes all software developed by the CEG interactive books initiative and make it easier to keep various software in those other books up to date. --- diff --git a/book/notebooks/Untitled.ipynb b/book/notebooks/Untitled.ipynb deleted file mode 100644 index b7f29e4..0000000 --- a/book/notebooks/Untitled.ipynb +++ /dev/null @@ -1,153 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "id": "9d7ffe9f-441f-4119-b5e4-0e872922a78d", - "metadata": {}, - "outputs": [], - "source": [ - "from sympy import *" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "406dc83e-b114-46be-baf8-073a72b47a36", - "metadata": {}, - "outputs": [], - "source": [ - "t, a = symbols('t a')\n", - "theta = Function('theta')(t)\n", - "r = Function('r')(t)\n", - "U_c = Function('U_c')(t)" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "df8fe246-6986-4ffd-9c39-6bd259176e42", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle - \\frac{a^{2} \\operatorname{U_{c}}{\\left(t \\right)} \\cos{\\left(\\theta{\\left(t \\right)} \\right)}}{r{\\left(t \\right)}}$" - ], - "text/plain": [ - "-a**2*U_c(t)*cos(theta(t))/r(t)" - ] - }, - "execution_count": 13, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "phi = - (a**2*U_c)/r * cos(theta)\n", - "phi" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "a6e55454-52c6-493b-a753-f901cee357bc", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle \\frac{a^{2} \\operatorname{U_{c}}{\\left(t \\right)} \\sin{\\left(\\theta{\\left(t \\right)} \\right)} \\frac{d}{d t} \\theta{\\left(t \\right)}}{r{\\left(t \\right)}} + \\frac{a^{2} \\operatorname{U_{c}}{\\left(t \\right)} \\cos{\\left(\\theta{\\left(t \\right)} \\right)} \\frac{d}{d t} r{\\left(t \\right)}}{r^{2}{\\left(t \\right)}} - \\frac{a^{2} \\cos{\\left(\\theta{\\left(t \\right)} \\right)} \\frac{d}{d t} \\operatorname{U_{c}}{\\left(t \\right)}}{r{\\left(t \\right)}}$" - ], - "text/plain": [ - "a**2*U_c(t)*sin(theta(t))*Derivative(theta(t), t)/r(t) + a**2*U_c(t)*cos(theta(t))*Derivative(r(t), t)/r(t)**2 - a**2*cos(theta(t))*Derivative(U_c(t), t)/r(t)" - ] - }, - "execution_count": 14, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "phi.diff(t)" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "52970004-5d18-4905-a61c-01c5d9a7f81c", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle \\frac{a^{2} \\operatorname{U_{c}}{\\left(t \\right)} \\cos{\\left(\\theta{\\left(t \\right)} \\right)}}{r^{2}{\\left(t \\right)}}$" - ], - "text/plain": [ - "a**2*U_c(t)*cos(theta(t))/r(t)**2" - ] - }, - "execution_count": 15, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "phi.diff(r)" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "id": "3bc6b6e8-cdba-4eb9-b754-e07cc74c6063", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle \\frac{a^{2} \\operatorname{U_{c}}{\\left(t \\right)} \\sin{\\left(\\theta{\\left(t \\right)} \\right)}}{r^{2}{\\left(t \\right)}}$" - ], - "text/plain": [ - "a**2*U_c(t)*sin(theta(t))/r(t)**2" - ] - }, - "execution_count": 16, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "phi.diff(theta)/r" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "bcae9e54-d38d-4128-b872-e4bcb11d19c5", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.13" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/book/notebooks/contamination/Exercise_Contamination_Render.ipynb b/book/notebooks/contamination/Exercise_Contamination_Render.ipynb deleted file mode 100644 index 0bbed65..0000000 --- a/book/notebooks/contamination/Exercise_Contamination_Render.ipynb +++ /dev/null @@ -1,689 +0,0 @@ -{ - "cells": [ - { - "attachments": {}, - "cell_type": "markdown", - "id": "bcb1b890", - "metadata": {}, - "source": [ - "# Contaminant Transport" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "ab31a602", - "metadata": {}, - "source": [ - "````{note}\n", - "This page is generated from an `*.ipynb` file which requires several auxiliary files, all of which can be downloaded using the link below.\n", - "```{eval-rst}\n", - ":download:`Download zip file for this exercise.`\n", - "```\n", - "````" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "06fa7af4", - "metadata": {}, - "source": [ - "The purpose of this exercise is to:\n", - "- evaluate component reliability\n", - "- illustrate functions of random variables\n", - "- see the effect of random variable distributions on reliability\n", - "- consider 'sensitivity' as a functional and/or stochastic influence on the limit-state function\n", - "\n", - "You should accomplish this by playing with the code that is provided with the notebook and trying to answer the following questions:\n", - "1. Which random variables have the biggest influence on reliability?\n", - "2. How does the assumption of probability distribution influence reliability?\n", - "3. Do the random variables act as loads or resistances?\n", - "\n", - "## Introduction of Case Study\n", - "\n", - "The case study is a contaminant transport problem, illustrated in the figure below. A factory located near a town produces hazardous waste, which can threaten the drinking water supply of the town that is extracted from groundwater wells (C). The regional groundwater system has a gradient that causes water to flow in the direction of the town from the factory, thus any spilled hazardous waste that enters the ground will eventually be transported to the wells. In order to mitigate the consequences of a spill a ditch is constructed around the factory to collect it (A). Unfortunately, even with powerful pumps, there will still be some waste that reaches the groundwater table. Our task is to quantify the probability that the waste concentration exceeds the maximum exposure level to prevent the drinking water becoming unhealthy.\n", - "\n", - "```{figure} ./figures/sketch.png\n", - "---\n", - "width: 600px\n", - "name: sketch_contaminant\n", - "---\n", - "\n", - "```\n", - "\n", - "### Contaminant Transport\n", - "\n", - "Once the ditch becomes contaminated it is cleaned quickly, but unfortunately a 'pulse' of contamination enters the ground, after which the regional gradient carries it towards the town (advection). The pulse also disperses due to diffusion, which results in a classic advection-diffusion problem (see red shapes in diagram, at three different times, $t$). Because the ditch extends a long distance in the lateral direction and the contaminant is buoyant (it floats on the groundwater table and we neglect vertical dispersion), the problem can be analyzed in 1 dimension with the following analytic expression:\n", - "\n", - "$$\n", - "\\frac{C}{C_0} = \\frac{1}{2} \\mathrm{erf}\\left(\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)\n", - "$$\n", - "\n", - "Where $C$ contaminant concentration (e.g., parts per million, ppm) at distance $x$ from the ditch at time $t$ after the spill, and $C_0$ is the concentration in the ditch (just prior to cleanup). $\\mathrm{erf}$ is the error function. There are three parameters in the equation which are related to soil properties and groundwater flow:\n", - "\n", - "- $q$ is the horizontal groundwater flow velocity (specific discharge) [m/day]\n", - "- $n$ is the soil porosity [$-$]\n", - "- $a$ is the longitudinal dispersivity, which describes dispersion in the left to right direction in the image [m]\n", - "\n", - "Unfortunately there is not a lot of soil information, so we have to take into account uncertainty in these three variables, using the following probability distributions with first and second moments (i.e., $\\mu$ and $\\sigma$).\n", - "\n", - "- $q\\sim\\mathrm{N}\\left(\\mu_q=1.00,\\sigma_q=0.10\\right)$\n", - "- $n\\sim\\mathrm{N}\\left(\\mu_n=0.20,\\sigma_n=0.02\\right)$\n", - "- $a\\sim\\mathrm{N}\\left(\\mu_a=10.0,\\sigma_a=1.00\\right)$\n", - "\n", - "It is important to check the sensitivity of the reliability analysis to the distribution type and moments. We will use the concentration ratio $C/C_0$ to evaluate this problem and compare it to a threshold defined by health regulations: $\\mathrm{threshold}=1e-4$.\n", - "\n", - "### Definition of Limit States\n", - "\n", - "As shown in the figure above, there are two locations of interest: the monitoring station ($x=100$ m from the ditch, point B) and the town well ($x=500$ m, point C). We are interested in evaluating two cases with a reliability analysis:\n", - "1. Whether the contamination can be detected at the monitoring station above the threshold level within 1 week of the spill, and \n", - "2. If the contamination level at the town groundwater well exceeds the threshold level within 1 month of the spill (30 days)\n", - "\n", - "Relating these descriptions to our variables of interest:\n", - "1. find the probability that $C/C_0$ > threshold \n", - "2. find the probability that $C/C_0$ < threshold\n", - "\n", - "We will refer to these values as 'failure probabilities', even though case 1 technically doesn't correspond to failure---it's just the way we refer to things in practice.\n", - "\n", - "Next we will convert these into functions that will allow us to quantify the 'failure' conditions. For convenience, it is often useful to define the limit state as a function, $Z$, such that failure occurs when $Z<0$. It follows from the descriptions above, that the limit state functions for both cases are:\n", - "\n", - "1. $Z=C/C_0 - \\mathrm{threshold}$\n", - "2. $Z=\\mathrm{threshold} - C/C_0$\n", - "\n", - "NB: *in the book another notation used for $Z$ is $g_X(X)$.*\n", - "\n", - "### Analysis Approach\n", - "\n", - "Our programming task is to create a function of random variables to represent these two limit-states, define the random variables, then evaluate the reliability with Monte Carlo simulation. In other words, we will numerically approximate the probability distribution of $Z$, then evaluate reliability as $P(Z<0)$.\n", - "\n", - "This is a lot of work, but fortunately a number of helper functions and a Class are provided in the auxiliary file `exercise_setup.py`!\n", - "\n", - "### References\n", - "\n", - "This example draws inspiration from Case 2 of the paper by {cite:t}`sitar1987`." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "8287dbcf", - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from scipy.special import erfc\n", - "from scipy import stats\n", - "import seaborn as sns\n", - "\n", - "from exercise_setup import process_negative_values\n", - "from exercise_setup import RandomVariableDistribution\n", - "from exercise_setup import pdf_of_function_of_RV\n", - "from exercise_setup import monte_carlo" - ] - }, - { - "cell_type": "markdown", - "id": "d104b4b2-4fa5-4b37-891d-39201281ed2f", - "metadata": {}, - "source": [ - "## Defining the Limit States\n", - "\n", - "We only define limit state Case 2 below, and will use a simple multiplying factor of $-1$ to switch to Case 1 using a multiplying factor `flip_LSF`." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "64c24956", - "metadata": {}, - "outputs": [], - "source": [ - "def C_C0(q, n, a, x, t):\n", - " \"\"\"Contaminant concentration ratio.\"\"\"\n", - " q, n, a = process_negative_values(q, n, a)\n", - " return 0.5*erfc((x - q/n*t)/(2*np.sqrt(a*(q/n)*t)))\n", - "\n", - "def limit_state_fun(q, n, a, x, t, threshold):\n", - " \"\"\"Limit state fxn, Case 2 (multiply by flip_LSF=-1 for Case 1).\"\"\"\n", - " return threshold - C_C0(q, n, a, x, t)" - ] - }, - { - "cell_type": "markdown", - "id": "d7410d16-14d4-45c6-9f93-81ae08de0594", - "metadata": {}, - "source": [ - "## Class `RandomVariableDistribution`\n", - "\n", - "The class `RandomVariableDistribution` makes it very easy to define Normal and Lognormal distributions for the random variables. See documentation and example below.\n", - "\n", - "NB: *you can use the code in `exercisesetup.py` and this notebook to confirm the result of the 2 random variable case in the Probabilistic Design chapter, and recreate the figures.*" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "8bbf80be-5124-40ba-b3de-0da3eaa12ef1", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Define a N or LN probability to use in MUDE week 2.7 exercise.\n", - " \n", - " Usage:\n", - " -----\n", - " Create an instance of the class\n", - " by default, the random variable is ~N(0,1)\n", - " Specify distribution using 1st and 2nd moments for N or LN:\n", - " --> use method define_distribution to change it!\n", - " (the method prints a summary of the change)\n", - " for example, copy/paste the following:\n", - " test = RandomVariableDistribution()\n", - " test.print_status()\n", - " test.define_distribution(mean=5, stddev=1, dist_type='LN')\n", - " An instance will include the following attributes:\n", - " - distribution moment and (scipy) parameters shape, location, scale\n", - " - dist_object: distribution object (scipy.stats)\n", - " - get_sample: method for getting random samples from the distribution\n", - " - plot_pdf_or_cdf:\n", - " \n" - ] - } - ], - "source": [ - "print(RandomVariableDistribution.__doc__)" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "a9b93099-b1cb-458b-baf6-8ad5dd39c440", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The mean is 5.000e+00\n", - "The standard deviation is 1.000e+00\n", - "The distribution is Lognormal\n" - ] - }, - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "example_random_variable = RandomVariableDistribution()\n", - "example_random_variable.define_distribution(mean=5,\n", - " dist_type='LN',\n", - " print_new_dist=True)\n", - "example_random_variable.plot_pdf_or_cdf()" - ] - }, - { - "cell_type": "markdown", - "id": "62617026-f251-462b-a93c-b7305cfd3fa4", - "metadata": {}, - "source": [ - "## Setting up the problem\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "4641ae3c", - "metadata": {}, - "outputs": [], - "source": [ - "N = 10000\n", - "\n", - "t = 7\n", - "x = 100\n", - "threshold = 1e-4\n", - "\n", - "flip_LSF = -1\n", - "\n", - "q_rv = RandomVariableDistribution()\n", - "q_rv.define_distribution(mean=1., stddev=.1)\n", - "n_rv = RandomVariableDistribution()\n", - "n_rv.define_distribution(mean=0.2, stddev=.02)\n", - "a_rv = RandomVariableDistribution()\n", - "a_rv.define_distribution(mean=10., stddev=1.)" - ] - }, - { - "cell_type": "markdown", - "id": "f3e0ffb1-6035-4f76-a550-4ff19c1b5946", - "metadata": {}, - "source": [ - "## Monte Carlo analysis\n", - "\n", - "The Monte Carlo procedure for estimating failure probability, $p_f$, is:\n", - "- For each random variable $X_i$ ($i = 1, …, n$) one simulates N realizations, $x_{i,1}, x_{i,1}, ..., x_{i,N}$. \n", - "- For each set of simulations $j$ ($j = 1, ..., N$) one calculates $g(x_{1,j}, x_{2,j}, …, x_{n,j})$\n", - "- In case $g(.) < 0$ a counter $N_f$ is increased by one. After $N$ simulations one calculates: $\\hat{p_f}=N_f/N$\n", - "- In case $N\\rightarrow+\\infty$ one obtains the failure probability $p_f$.\n", - "\n", - "The number of simulations $N$ directly influences the accuracy of $\\hat{p_f}$, which is an estimate of the 'true' value $p_f$. As an infinite number of simulations is not possible, one must choose a value for $N$ that balances total computation time, which increases linearly with $N$, and accuracy of the estimator $\\hat{p_f}$, which can be determined as the number of significant digits desired for $p_f$, or based on relative error (coefficient of variation, $V=\\sigma/\\mu$. The failure observations, $N_f$, within the Monte Carlo procedure are the result of a sequence of statistically independent and identically distributed random trials in a Bernoulli process. Using the binomial distribution, the standard deviation of of $\\hat{p_f}$ can be written\n", - "\n", - "$$\\sigma_\\hat{p_f}=\\sqrt{\\frac{p_f(1-p_f)}{N}}$$\n", - "\n", - "As $\\hat{p_f}\\rightarrow1$ this leads to the coefficient of variation, $V_\\hat{p_f}$:\n", - "\n", - "$$V_\\hat{p_f}=\\frac{\\sigma_\\hat{p_f}}{\\hat{p_f}}=\\frac{1}{\\sqrt{N\\hat{p_f}}}$$\n", - "\n", - "The coefficient of variation is a useful measure for gauging the accuracy of a Monte Carlo simulation: values of 0.01 are ideal, but 0.1 can be sufficient in many applications, depending on the need for accuracy. For example, consider $V=0.1$ for a target failure probability of $0.01$. Assuming the samples follow a Gaussian distribution implies a probability of 0.997 that the 'true' failure probability is within the interval 0.007-0.013. It is also useful to plot the calculated values of $V$ and $\\hat{p_f}$ for every realization $j = 1, ..., N$, as shown below. The figure clearly shows convergence to a stable value of $\\hat{p_f}$ after X simulations, indicating that for future analyses that are similar can use a lower number of simulations instead ($N\\sim X$).\n", - "\n", - "In case of a target coefficient of variation the number of required simulations $N$ increases as $p_f$ decreases. As an example, for $V = 0.01$ and $p_f=1e-5$ one has to execute $10^9$ simulations. As for this case on average only one of 10^5 simulations leads to an increase of $N_f$, the frequency of obtaining a 'success' (realization in the unsafe domain) is very low. In addition, for low failure probabilities the number of function evaluations is quite high, which may be practically impossible if there is a high function evaluation time, for example with a complex finite element model. To address this problem, variance reducing techniques have been developed which allow the simulations to be performed in a more effective way. In the following the so-called importance sampling or Latin hypercube sampling." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "ec7883de-544e-48d5-85f2-dfc7856e9028", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "MONTE CARLO RESULTS\n", - "--------------------------------------------------\n", - " N = 10000, number of samples\n", - " Nf = 18, number of failed realizations\n", - " pf = 1.800e-03, estimated failure probability\n", - " V = 0.236, c.o.v. of estimated pf\n", - "\n" - ] - }, - { - "data": { - "image/png": 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", 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "sample_q = q_rv.get_sample(N)\n", - "sample_n = n_rv.get_sample(N)\n", - "sample_a = a_rv.get_sample(N)\n", - "sample_C_C0 = C_C0(sample_q, sample_n, sample_a, x, t)\n", - "sample_Z = flip_LSF*limit_state_fun(sample_q,\n", - " sample_n,\n", - " sample_a,\n", - " x, t, threshold)\n", - "\n", - "monte_carlo(sample_Z);" - ] - }, - { - "cell_type": "markdown", - "id": "d00e1316-c4ac-474d-93ad-18abcda30cfc", - "metadata": {}, - "source": [ - "The method `pdf_of_function_of_RV` makes it easy to see what the distribution of $C/C_0$ and the limit state function for different distributions of q, n or a. Below a second distribution of a is considered:" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "c08e0e56-8a6b-45a2-ad3f-abe3ce869513", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "a has 61 negative values that have been set to 1.0e-03.\n", - "a has 54 negative values that have been set to 1.0e-03.\n", - "The mean is 1.000e+01\n", - "The standard deviation is 1.000e+00\n", - "The distribution is Normal\n", - "The mean is 1.000e+01\n", - "The standard deviation is 4.000e+00\n", - "The distribution is Normal\n" - ] - }, - { - "data": { - "image/png": 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", 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "C_C0_cases = []\n", - "Z_cases = []\n", - "C_C0_cases.append(sample_C_C0)\n", - "Z_cases.append(sample_Z)\n", - "\n", - "a_2 = RandomVariableDistribution()\n", - "a_2.define_distribution(mean=10, stddev=4, dist_type='N')\n", - "C_C0_cases.append(C_C0(sample_q, sample_n, a_2.get_sample(N), x, t))\n", - "Z_cases.append(flip_LSF*limit_state_fun(sample_q,\n", - " sample_n,\n", - " a_2.get_sample(N),\n", - " x, t, threshold))\n", - "\n", - "a_rv.print_status()\n", - "a_2.print_status()\n", - "\n", - "pdf_of_function_of_RV(C_C0_cases)\n", - "pdf_of_function_of_RV(Z_cases, case_C=False)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "695f1336-8d3e-4503-9196-9969d181ae10", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "id": "8c197ae8-3a6c-45fe-b304-75f601dbb9ac", - "metadata": {}, - "source": [ - "This is the density of the function of random variables, $C/C_0$, two values of $\\sigma_a$, and a third with the uniform distribution (not using the `RandomVariableDistribution` class)." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "53273645-453b-48b9-85c0-e69eb1ac579e", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Joint density of 2 RVs with failure realizations\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "values_of_RV_1 = sample_q\n", - "values_of_RV_2 = sample_a\n", - "\n", - "g = sns.JointGrid()\n", - "sns.kdeplot(x=values_of_RV_1,\n", - " y=values_of_RV_2, ax=g.ax_joint, bw_adjust=3)\n", - "sns.scatterplot(x=values_of_RV_1[sample_Z<0],\n", - " y=values_of_RV_2[sample_Z<0], ax=g.ax_joint)\n", - "g.ax_joint.set_xlabel('Random Variable 1 (chosen by you)')\n", - "g.ax_joint.set_ylabel('Random Variable 2 (chosen by you)')\n", - "print('Joint density of 2 RVs with failure realizations')" - ] - }, - { - "cell_type": "markdown", - "id": "75f127f7-c40b-425d-91cf-6c6ecad207a2", - "metadata": {}, - "source": [ - "## Case 2: exceeding the health threshold\n", - "\n", - "Now we return to the failure definition of exceeding the threshold (`flip_LSF` = 1)." - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "3ee884a7-16fb-46bf-9766-9899e662a9bc", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "MONTE CARLO RESULTS\n", - "--------------------------------------------------\n", - " N = 100000, number of samples\n", - " Nf = 65, number of failed realizations\n", - " pf = 6.500e-04, estimated failure probability\n", - " V = 0.124, c.o.v. of estimated pf\n", - "\n" - ] - }, - { - "data": { - "image/png": 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", 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "N = 100000\n", - "\n", - "t = 30\n", - "x = 500\n", - "threshold = 1e-4\n", - "\n", - "flip_LSF = 1\n", - "\n", - "sample_q = q_rv.get_sample(N)\n", - "sample_n = n_rv.get_sample(N)\n", - "sample_a = a_rv.get_sample(N)\n", - "\n", - "sample_C_C0 = C_C0(sample_q, sample_n, sample_a, x, t)\n", - "sample_Z = flip_LSF*limit_state_fun(sample_q,\n", - " sample_n,\n", - " sample_a,\n", - " x, t, threshold)\n", - "\n", - "monte_carlo(sample_Z);" - ] - }, - { - "cell_type": "markdown", - "id": "d1d693c6-df03-442f-a100-a065355b2c12", - "metadata": {}, - "source": [ - "NB: *the joint density and failure point plot is commented out here to prevent slowing down the kernel. When N=100000 (1e5) or higher, it will take around a minute to run.*" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "19a0f38a-f4e2-4dc0-8ade-0094f2a3cc91", - "metadata": {}, - "outputs": [], - "source": [ - "# values_of_RV_1 = sample_q\n", - "# values_of_RV_2 = sample_a\n", - "\n", - "# g = sns.JointGrid()\n", - "# sns.kdeplot(x=values_of_RV_1,\n", - "# y=values_of_RV_2, ax=g.ax_joint, bw_adjust=3)\n", - "# sns.scatterplot(x=values_of_RV_1[sample_Z<0],\n", - "# y=values_of_RV_2[sample_Z<0], ax=g.ax_joint)\n", - "# g.ax_joint.set_xlabel('Random Variable 1 (chosen by you)')\n", - "# g.ax_joint.set_ylabel('Random Variable 2 (chosen by you)')\n", - "# print('Joint density of 2 RVs with failure realizations')" - ] - }, - { - "cell_type": "markdown", - "id": "3e7d0cc4", - "metadata": {}, - "source": [ - "### Gradient Vector\n", - "\n", - "Partial derivatives will be useful for evaluating the functional influence of the variables on the limit states. The gradient vector is defined as:\n", - "\n", - "$\\nabla_{\\mathbf{y}} G(\\mathbf{y})=\\left(\\frac{\\partial G(\\mathbf{y})}{\\partial \\mathbf{y}_1}, \\cdots, \\frac{\\partial G(\\mathbf{y})}{\\partial \\mathbf{y}_n}\\right) $\n", - "\n", - "To find the gradient vector we need to find the partial derivatives of $\\frac{C}{C_0}$\n", - "\n", - "$\\frac{C}{C_0} = \\frac{1}{2} \\mathrm{erfc}\\left(\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)=\\frac{1}{2} \\left(1-\\mathrm{erf}\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)$\n", - "\n", - "Using $\\frac{\\partial}{\\partial x} (\\mathrm{erf} x) = \\frac{2}{\\sqrt{\\pi}}e^{-x^2} $ and $\\Omega = \\frac{1}{\\sqrt{\\pi}}e^{-\\left(\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)^2} $, the derivatives are:\n", - "\n", - "$\\frac{\\partial (C/C_0)}{\\partial x} = \\Omega\\left(-\\frac{1}{2\\sqrt{a(q/n)t}}\\right)$\n", - "\n", - "$\\frac{\\partial (C/C_0)}{\\partial t} =\\Omega\\left(\\frac{x}{4\\sqrt{a(q/n)t^3}}+\\frac{q}{4n\\sqrt{a(q/n)t}}\\right)$\n", - "\n", - "$\\frac{\\partial (C/C_0)}{\\partial q} = \\Omega\\left(\\frac{x}{4\\sqrt{a(1/n)tq^3}}+\\frac{t}{4n\\sqrt{a(q/n)t}}\\right)$\n", - "\n", - "$\\frac{\\partial (C/C_0)}{\\partial n} = \\Omega\\left(-\\frac{x}{4\\sqrt{aqtn}}-\\frac{qt}{4\\sqrt{qatn^3}}\\right)$\n", - "\n", - "$\\frac{\\partial (C/C_0)}{\\partial a} = \\Omega\\left(\\frac{x-q/nt}{4\\sqrt{(q/n)ta^3}}\\right)$" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "a761d424", - "metadata": {}, - "outputs": [], - "source": [ - "def gradient(q, n, a, x, t):\n", - " Om = 1/np.sqrt(np.pi)*np.exp(-((x - q/n*t)/(2*np.sqrt(a*q/n*t)))**2)\n", - " dx = Om*(-1/(2*np.sqrt(a*q/n*t)))\n", - " dt = Om*(x/(4*np.sqrt(a*q/n*t**3)) + (q)/(4*n*np.sqrt(a*q/n*t)))\n", - " dq = Om*(x/(4*np.sqrt(a*q**3/n*t)) + (t)/(4*n*np.sqrt(a*q/n*t)))\n", - " dn = Om*(-x/(4*np.sqrt(a*q*n*t)) - (q*t)/(4*np.sqrt(a*q*n**3*t)))\n", - " da = Om*((x - q/n*t)/(4*np.sqrt(a**3 *q/n*t)))\n", - " return np.array([dq,dn,da,dx,dt])" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "d6492f20", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ 2.84464056e-01 -3.55580070e+00 1.01594306e-02 -1.62550889e-03\n", - " 2.37053380e-02]\n" - ] - } - ], - "source": [ - "print(gradient(2.5, 0.2, 10, x, t))" - ] - }, - { - "cell_type": "markdown", - "id": "18ae1605-4c60-4c65-be4f-ce9cef2e40fd", - "metadata": {}, - "source": [ - "## Your turn!\n", - "\n", - "Now try and use the code to answer the questions posed at the beginning of the notebook, which are repeated here:\n", - "1. Which random variables have the biggest influence on reliability?\n", - "2. How does the assumption of probability distribution influence reliability?\n", - "3. Do the random variables act as loads or resistances?\n", - "\n", - "In particular, to evaluate sensitivity, you can consider two quantitative aspects:\n", - "1. What is the functional influence of the random variables and x and t on the limit-state function?\n", - "2. What is the stochastic influence of the random variables, \n", - "3. What is the combined influence of the two aspects above?\n", - "\n", - "" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "base", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.13 (main, Aug 25 2022, 23:51:50) [MSC v.1916 64 bit (AMD64)]" - }, - "vscode": { - "interpreter": { - "hash": "85471ad55176ca86192ed6be6d105faaef73891404cad6bd910e89e8513744d9" - } - }, - "widgets": { - "application/vnd.jupyter.widget-state+json": { - "state": {}, - "version_major": 2, - "version_minor": 0 - } - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/book/notebooks/contamination/exercise_contamination.zip b/book/notebooks/contamination/exercise_contamination.zip deleted file mode 100644 index 105f3ac..0000000 Binary files a/book/notebooks/contamination/exercise_contamination.zip and /dev/null differ diff --git a/book/notebooks/contamination/exercise_setup.py b/book/notebooks/contamination/exercise_setup.py deleted file mode 100644 index 51a9470..0000000 --- a/book/notebooks/contamination/exercise_setup.py +++ /dev/null @@ -1,247 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt -from scipy.special import erfc -from scipy import stats -import seaborn as sns - -def process_negative_values(q, n, a): - """Prevents problems with negative values in sqrt of C_C0 function.""" - N_q = sum(q<0) - N_n = sum(n<0) - N_a = sum(a<0) - set_value = 0.001 - if N_q > 0: - for i in range(len(q)): - if q[i]<0: - q[i] = set_value - print(f'q has {N_q} negative values that have been set to {set_value:.1e}.') - if N_n > 0: - for i in range(len(n)): - if n[i]<0: - n[i] = set_value - print(f'n has {N_n} negative values that have been set to {set_value:.1e}.') - if N_a > 0: - for i in range(len(a)): - if a[i]<0: - a[i] = set_value - print(f'a has {N_a} negative values that have been set to {set_value:.1e}.') - return q, n, a - -class RandomVariableDistribution(): - """Define a N or LN probability to use in MUDE week 2.7 exercise. - - Usage: - ----- - Create an instance of the class - by default, the random variable is ~N(0,1) - Specify distribution using 1st and 2nd moments for N or LN: - --> use method define_distribution to change it! - (the method prints a summary of the change) - for example, copy/paste the following: - test = RandomVariableDistribution() - test.print_status() - test.define_distribution(mean=5, stddev=1, dist_type='LN') - An instance will include the following attributes: - - distribution moment and (scipy) parameters shape, location, scale - - dist_object: distribution object (scipy.stats) - - get_sample: method for getting random samples from the distribution - - plot_pdf_or_cdf: - """ - - def __init__(self): - self.mean = 0. - self.stddev = 1. - self.dist_type = 'N' - - def print_status(self): - """Returns current parameter values and distribution type.""" - print(f'The mean is {self.mean:.3e}') - print(f'The standard deviation is {self.stddev:.3e}') - if self.dist_type == 'N': - distribution_name = 'Normal' - elif self.dist_type == 'LN': - distribution_name = 'Lognormal' - print('The distribution is ' + distribution_name) - - def define_distribution(self, - mean=None, - stddev=None, - dist_type=None, - print_new_dist=False): - """Compute distribution parameters and RV object from moments. - - Usage: - ----- - Optional arguments will override current dist: - --> default distribution is standard normal, ~N(0,1) - mean: float - stddev: float - dist_type: 'N' or 'LN' - print_new_dist=True to print distribution changes. - """ - if mean is None: - mean = self.mean - if stddev is None: - stddev = self.stddev - if dist_type is None: - dist_type = self.dist_type - if dist_type == 'N': - shape = None - location = mean - scale = stddev - dist_object = stats.norm(loc=location, scale=scale) - elif dist_type == 'LN': - """ - Finds distribution parameters of LN-distributed X, - which are equivalent to the mean and standard deviation - of the log of X: Y = ln(X), then converts to the - parameterization used by scipy.stats.lognorm. - """ - stddev_y = np.sqrt(np.log(1 + (stddev/mean)**2)) - mean_y = np.log(mean) - 0.5*stddev_y**2 - - shape = stddev_y - location = 0 - scale = np.exp(mean_y) - dist_object = stats.lognorm(s=shape, - loc=location, - scale=scale) - else: - raise ValueError("You can only use N or LN for self.dist_type.") - self.mean = mean - self.stddev = stddev - self.dist_type = dist_type - self.shape = shape - self.location = location - self.scale = scale - self.dist_object = dist_object - self.get_sample = lambda size : self.dist_object.rvs(size=size) - if print_new_dist: - self.print_status() - - def plot_pdf_or_cdf(self, plot_type='pdf', plot_limits=None): - """Plots the pdf or cdf (specify choice with plot_type). - - Usage: - ----- - No inputs required, but there are optional inputs: - plot_type='cdf' to plot cdf (pdf is default value) - plot_limits: list with 2 values for x-axis - """ - if plot_limits is None: - if self.dist_type == 'N': - plot_limits = [self.mean - 3*self.stddev, - self.mean + 3*self.stddev] - elif self.dist_type == 'LN': - 'Avoid negative or zero value for lognormal dist.' - lower_value = self.mean - 3*self.stddev - if lower_value <= 0: - lower_value = 0.01 - plot_limits = [lower_value, - self.mean + 4*self.stddev] - else: - raise ValueError("You can only use N or LN for self.dist_type.") - - plot_x = np.linspace(plot_limits[0], plot_limits[1], 1000) - if plot_type == 'pdf': - plot_y = self.dist_object.pdf(plot_x) - y_label = 'PDF [-]' - elif plot_type == 'cdf': - plot_y = self.dist_object.cdf(plot_x) - y_label = 'CDF [-]' - else: - raise ValueError("You must specify pdf or cdf for plot_type.") - fontsize = 15 - plt.figure() - plt.plot(plot_x, plot_y, 'k-', linewidth=3) - plt.xlabel('Random Variable, X', fontsize=fontsize) - plt.ylabel(y_label, fontsize=fontsize) - plt.show() - -def pdf_of_function_of_RV(cases, case_C=True, case_name=None, plot_limits=None): - """Plot the PDF of a sampled function of random variables (C_C0 or Z). - - Usage: - ----- - cases: a list of arrays - case_C=True (default) assumes C_C0 is given. False is for Z. - case_name: list of strings with the labels for each array. - e.g., ['Original', 'High sigma_a', 'Low sigma_a'] - (default will return Case i for all arrays) - plot_limits: list of two values that override default limits - for x-axis. - """ - bw_adjust = 3 # adjusts smoothness of Seaborn kernel density contours - labels = [] - - plt.figure() - - for i in range(len(cases)): - if case_name == None: - labels.append(f'Case {i+1}') - else: - labels.append(case_name[i]) - sns.kdeplot(cases[i], label=labels[i], ax=plt.gca(), bw_adjust=bw_adjust) - plt.legend() - if case_C: - plt.xlabel('Concentration ratio, $C/C_0$ [$-$]') - if plot_limits == None: - plt.xlim(0,1) - else: - plt.xlim(plot_limits) - else: - plt.xlabel('Limit-state function, $Z=\mathrm{threshold}-C/C_0$ [$-$]') - if plot_limits == None: - plt.xlim(-2,1) - else: - plt.xlim(plot_limits) - plt.ylabel('PDF [$]$') - plt.grid() - plt.show() - -def monte_carlo(Z): - """Monte Carlo analysis for sampled function of random variables. - - Returns a summary of the analysis and a plot of pf and c.o.v.. - The only input is an array of the sampled limit state-function. - Assumes that failure is when the limit-state function Z<0. - """ - N = len(Z) - Nf = np.sum(Z<0) - - if Nf == 0: - raise ValueError('No failure realizations in the sample!') - elif Nf == N: - raise ValueError('All realizations in the sample failed!') - - pf = Nf/N - - N_f_c = np.cumsum(Z<0) - N_i = np.arange(1,len(N_f_c)+1,1) - p_f_c = N_f_c / N_i - with np.errstate(divide='ignore'): - V = 1/(np.sqrt(N_i*p_f_c)) - - print(f'MONTE CARLO RESULTS\n' - f'--------------------------------------------------\n' - f' N = {N}, number of samples\n' - f' Nf = {Nf}, number of failed realizations\n' - f' pf = {pf:.3e}, estimated failure probability\n' - f' V = {V[-1]:.3f}, c.o.v. of estimated pf\n') - - plt.loglog(N_i,p_f_c) - plt.xlim(10,N) - plt.ylim(10**(np.floor(np.log10(pf)) - 1),1) - plt.grid() - plt.xlabel('Realization No.') - plt.ylabel('Estimated failure probability, $\hat{p}_f$') - plt.show() - - plt.plot(N_i,V) - plt.xscale('log') - plt.grid() - plt.xlabel('time step') - plt.ylabel('c.o.v.') - plt.show() - - return Nf,pf \ No newline at end of file diff --git a/book/notebooks/contamination/figures/sketch.png b/book/notebooks/contamination/figures/sketch.png deleted file mode 100644 index d2fd2b4..0000000 Binary files a/book/notebooks/contamination/figures/sketch.png and /dev/null differ diff --git a/book/notebooks/flood-risk/Exercise_Flood_Risk_Render.ipynb b/book/notebooks/flood-risk/Exercise_Flood_Risk_Render.ipynb deleted file mode 100644 index 09ce9bd..0000000 --- a/book/notebooks/flood-risk/Exercise_Flood_Risk_Render.ipynb +++ /dev/null @@ -1,792 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "e228e52d", - "metadata": {}, - "source": [ - "# Flood Risk\n", - "## Dike Ring 14" - ] - }, - { - "cell_type": "markdown", - "id": "6f028272-206c-4474-9083-43d7b52352f1", - "metadata": {}, - "source": [ - "````{note}\n", - "This page is generated from an `*.ipynb` file which requires several auxiliary files, all of which can be downloaded using the link below.\n", - "```{eval-rst}\n", - ":download:`Download zip file for this exercise.`\n", - "```\n", - "````" - ] - }, - { - "cell_type": "markdown", - "id": "6897cbb0-6e59-4ed3-a346-ae684e115bbc", - "metadata": {}, - "source": [ - "The overall objective of this assignment is to make a step from the simple FN/FD curves we have in the book to work on something 'real' and to make 'real' engineering decisions about how to modify a dike ring to meet safety standards. This exercise is based on a risk assessment of the Netherlands from around 10 years ago called VNK (veiligheid Nederland in kaart, or mapping Dutch (flood) safety. It was done in the runup to changing the safety standards in 2017. You can find more about the project [here](https://www.helpdeskwater.nl/onderwerpen/waterveiligheid/programma-projecten/veiligheid-nederland/publicaties/), and a report specifically about the case [here](https://www.helpdeskwater.nl/onderwerpen/waterveiligheid/programma-projecten/veiligheid-nederland/publicaties/dijkringrapporten/dijkringrapporten/fase-1a/14-zuid-holland/). The first website has some English reports, but unfortunately the Dike Ring 14 report is only in Dutch.\n", - "\n", - "*First the case is introduced, then some examples using the pre-prepared code are given to show you how to use it. Then you are asked to use the code to decide which repairs to specific dike segments should be done to see if you can meet the safety criteria!*\n", - "\n", - "*Our apologies in advance that the code does not meet the Golden Rules. Although it might not look pretty, we trust that it is clear enough to be able to learn about risk!*" - ] - }, - { - "cell_type": "markdown", - "id": "9b9e2b82-d018-4188-95ff-d75c290ec1d4", - "metadata": {}, - "source": [ - "## Overview of the case study\n", - "\n", - "The entire dike ring that protects South Holland is divided into 13 segments, which have been chosen such that the flooding that occurs after a breach is not dependent on the location of the breach itself. This results in significantly fewer flooding analyses that must be carried out. In addition, all possible breach locations within a single segment do not have to be considered. For South Holland, 7 segments are defined along the Nieuwe Waterweg (i.e., the river, behind the Maeslant Barrier) and 6 segments are defined along the coast.\n", - "\n", - "```{figure} ./figures/map-dike-segments.PNG\n", - "---\n", - "width: 500px\n", - "name: map_segments\n", - "---\n", - "```\n", - "All segments along the river are dikes and segments along the sea are dunes, with the following exceptions:\n", - "- Segment 3: Park Sluices in Rotterdam\n", - "- Segment 10: Scheveningen outlet sluice\n", - "- Segment 11: Scheveningen Bouldevard\n", - " \n", - "### How does a flood risk analysis work?\n", - " \n", - "We are essentially creating a probability mass function, where the random variable is fatalities or economic damage. Since we can't wait a few million years watch the dike ring fail to get a good estimate of the actual distribution, we try to simulate all possible combinations of floods. However, the actual flooding process is complicated: due to the river or sea conditions a dike or dune is broken (this is called a breach), water rushes into the protected area, depending on the flooding depth people may die and infrastructure is damaged. Sometimes we are able to warn and evacuate people, but there is a chance these systems do not work. Reality is extremely complex, so we simplify the process in our flood modeling studies, using the following steps:\n", - "a. assume a levee or dune is breached\n", - "b. estimate the resulting flood depth in the (formerly) protected area\n", - "c. calculated economic damage and fatalities as a function of water depth\n", - "d. modify the above value depending on the status of warning and evacuation systems\n", - "e. repeat this for many breach locations\n", - " \n", - "As such, each scenario returns a finite number of fatalities or damage, which is why the distribution is discrete. Of course, we need to also quantify the probability of each scenario. Although it sounds complex, it is actually simple to represent using conditional probability if we can assume:\n", - "$$\\textrm{P}(x_i)=\\textrm{P}(x_i|D,W,E)\\cdot\\textrm{P}(D)\\cdot\\textrm{P}(W)\\cdot\\textrm{P}(E)$$\n", - "\n", - "where $x_i$ is our risk metric of choice (i.e., economic damage or fatalities) and $D$, $W$ and $E$ represnt water depth, warning and evacuation status, respectively. Given the scenario-based approach where a fixed value is determined for $x_i$, it is clear that this type of analysis creates a descrete random variable. Furthermore, the equation above indicates that single values of $D$, $W$ and $E$ are used, but in theory one could integrate over each of these variables.\n", - " \n", - "An example of the flood depth analysis is shown below for a breach in segment 12:\n", - "```{figure} ./figures/flood-depth-12.PNG\n", - "---\n", - "width: 500px\n", - "name: flood_depth_12\n", - "---\n", - "```" - ] - }, - { - "cell_type": "markdown", - "id": "14231f96-55e5-44f1-baea-1f8a0e7e0e46", - "metadata": {}, - "source": [ - "## Exercise Instructions\n", - "\n", - "An Excel file has been prepared that includes the results from the risk analysis. Each row is a scenario, with a `Scenario_ID` and associated probability of occurrence (`scenario_probability`). The column `failed_segments` lists which dike segments are assumed to have failed in the particular scenario. Consequences are specifies in the last 8 columns (described below).\n", - "\n", - "Your task is to determine which **dike segments** you should repair to improve the safety of Dike Ring 14. Unfortunately due to the available budget, **you can only afford to repair 3 segments.** Thus, your task is to identify 3 segments to repair and justify your decision for doing so (there are some cells below where you can type your answer). You are free to consider both life loss and economic damage in your evaluation.\n", - "\n", - "The next set of cells will get you started with the helper functions, then you are free to use them to work on the assignment. First, start by importing the required packages:" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "5362403f", - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "import pandas as pd" - ] - }, - { - "cell_type": "markdown", - "id": "940f2cff-4c61-4cef-81fa-73b701f8b43a", - "metadata": {}, - "source": [ - "Import special functions created to help with this assignment:" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "1a4624ba-f457-4bf6-8848-713e6aa5ccfe", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "from functions import find_scenarios_with_segment_i\n", - "from functions import assemble_analysis_cases\n", - "from functions import exceedance_prob\n", - "from functions import plot_curves\n", - "from functions import sensitivity_analysis\n", - "from functions import compute_benefit\n", - "from functions import set_TUDstyle" - ] - }, - { - "cell_type": "markdown", - "id": "79bc6385", - "metadata": {}, - "source": [ - "Load data and take a look at it:" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "771b9c7f", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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Scenario_IDscenario_probabilityfailed_segmentscase_1_dcase_1_ncase_2_dcase_2_ncase_3_dcase_3_ncase_4_dcase_4_n
010.000021125700600570046057004205700300
120.0000162140020014001501400140140099
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340.000004516003700160028001600260016001800
450.000004672040720307203071020
\n", - "
" - ], - "text/plain": [ - " Scenario_ID scenario_probability failed_segments case_1_d case_1_n \\\n", - "0 1 0.000021 12 5700 600 \n", - "1 2 0.000016 2 1400 200 \n", - "2 3 0.000005 2,7 1800 210 \n", - "3 4 0.000004 5 1600 3700 \n", - "4 5 0.000004 6 720 40 \n", - "\n", - " case_2_d case_2_n case_3_d case_3_n case_4_d case_4_n \n", - "0 5700 460 5700 420 5700 300 \n", - "1 1400 150 1400 140 1400 99 \n", - "2 1800 160 1800 150 1800 110 \n", - "3 1600 2800 1600 2600 1600 1800 \n", - "4 720 30 720 30 710 20 " - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "df = pd.read_excel(r'Prob_Cons.xlsx')\n", - "df.head()" - ] - }, - { - "cell_type": "markdown", - "id": "11d5077c-d8fa-4898-a68e-d3f6e6a96f9f", - "metadata": {}, - "source": [ - "### Evacuations (labeled Case 1-4)\n", - "\n", - "*As you can see above, the dataframe has 8 columns labeled `case_*_*`. The last character denotes either fatalities or damage with `n` or `d`, respectively.*\n", - "\n", - "The consequences in each scenario are dependent on whether or not there is a flood warning and time for an ordered evacuation or not. To account for this, 4 sub-scenarios are considered, and the probability of each is weighted equally in the total FN curve (cases are combined in `exceedance_prob`). For the response to a dike breach there are 4 conditions considered (in order of table on Page 139, Bijlage I):\n", - "- flood unexpected and no evacuation\n", - "- flood unexpected with an unorganized evacuation\n", - "- flood expected with an unorganized evacuation\n", - "- flood expected with an organized evacuation\n", - "\n", - "It is interesting to know how this is incorporated in the analysis, but you can ignore this when going through the exercise, since it becomes unecessarily complicated." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "5507ede2-4f44-413b-9f02-42a3adc81c8c", - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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Scenario_IDscenario_probabilitycase_1_dcase_1_ncase_2_dcase_2_ncase_3_dcase_3_ncase_4_dcase_4_n
count50.000005.000000e+0150.00000050.00000050.00000050.00000050.00000050.0000050.00000050.000000
mean25.500001.290931e-0612549.7800008603.36000012493.0000006631.50000012491.0000005988.6600012471.1000004269.280000
std14.577383.822669e-068887.7566778037.4451468839.0239216213.3141848839.7955125578.158158835.2880883965.545056
min1.000008.830000e-09230.0000008.000000230.0000006.000000230.0000006.00000230.0000004.000000
25%13.250004.402500e-085475.0000002225.0000005475.0000001700.0000005475.0000001600.000005475.0000001100.000000
50%25.500001.125000e-0711000.0000003800.00000011000.0000002950.00000011000.0000002700.0000011000.0000001900.000000
75%37.750004.797500e-0717000.00000015750.00000017000.00000011750.00000017000.00000010750.0000017000.0000007775.000000
max50.000002.140000e-0533000.00000029000.00000033000.00000022000.00000033000.00000020000.0000033000.00000014000.000000
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" - ], - "text/plain": [ - " Scenario_ID scenario_probability case_1_d case_1_n \\\n", - "count 50.00000 5.000000e+01 50.000000 50.000000 \n", - "mean 25.50000 1.290931e-06 12549.780000 8603.360000 \n", - "std 14.57738 3.822669e-06 8887.756677 8037.445146 \n", - "min 1.00000 8.830000e-09 230.000000 8.000000 \n", - "25% 13.25000 4.402500e-08 5475.000000 2225.000000 \n", - "50% 25.50000 1.125000e-07 11000.000000 3800.000000 \n", - "75% 37.75000 4.797500e-07 17000.000000 15750.000000 \n", - "max 50.00000 2.140000e-05 33000.000000 29000.000000 \n", - "\n", - " case_2_d case_2_n case_3_d case_3_n case_4_d \\\n", - "count 50.000000 50.000000 50.000000 50.00000 50.000000 \n", - "mean 12493.000000 6631.500000 12491.000000 5988.66000 12471.100000 \n", - "std 8839.023921 6213.314184 8839.795512 5578.15815 8835.288088 \n", - "min 230.000000 6.000000 230.000000 6.00000 230.000000 \n", - "25% 5475.000000 1700.000000 5475.000000 1600.00000 5475.000000 \n", - "50% 11000.000000 2950.000000 11000.000000 2700.00000 11000.000000 \n", - "75% 17000.000000 11750.000000 17000.000000 10750.00000 17000.000000 \n", - "max 33000.000000 22000.000000 33000.000000 20000.00000 33000.000000 \n", - "\n", - " case_4_n \n", - "count 50.000000 \n", - "mean 4269.280000 \n", - "std 3965.545056 \n", - "min 4.000000 \n", - "25% 1100.000000 \n", - "50% 1900.000000 \n", - "75% 7775.000000 \n", - "max 14000.000000 " - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "df.describe()" - ] - }, - { - "cell_type": "markdown", - "id": "021ad4a5", - "metadata": {}, - "source": [ - "The function `find_scenarios_with_segment_i` will ask for the dike segment(s) of interest (as a list) and return all of the scenarios where a breach in this segment is considered." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "096d2419-9467-4505-898e-36a670dd46ce", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Given a list of segments, return set of dependent scenarios.\n" - ] - }, - { - "data": { - "text/html": [ - "
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Scenario_IDscenario_probabilityfailed_segmentscase_1_dcase_1_ncase_2_dcase_2_ncase_3_dcase_3_ncase_4_dcase_4_n
012.140000e-05125700600570046057004205700300
899.480000e-0712,13110002000110001600110001400110001000
49502.450000e-088,12,13190002700190002100190001900190001400
\n", - "
" - ], - "text/plain": [ - " Scenario_ID scenario_probability failed_segments case_1_d case_1_n \\\n", - "0 1 2.140000e-05 12 5700 600 \n", - "8 9 9.480000e-07 12,13 11000 2000 \n", - "49 50 2.450000e-08 8,12,13 19000 2700 \n", - "\n", - " case_2_d case_2_n case_3_d case_3_n case_4_d case_4_n \n", - "0 5700 460 5700 420 5700 300 \n", - "8 11000 1600 11000 1400 11000 1000 \n", - "49 19000 2100 19000 1900 19000 1400 " - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "print(find_scenarios_with_segment_i.__doc__)\n", - "find_scenarios_with_segment_i([12], df)" - ] - }, - { - "cell_type": "markdown", - "id": "e4cdbb15-6659-4227-935c-cbeab4a5b927", - "metadata": {}, - "source": [ - "## Compute exceedance probabilities\n", - "\n", - "Now that we have explored the database of scenarios, let's move towards evaluating risk. Before assembling the risk curves, we will extract the probability associated with each scenario, and use a prepared function (`assemble_analysis_cases`) to make the process easier." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "f30a1a10", - "metadata": {}, - "outputs": [], - "source": [ - "scenario_prob = df.iloc[:,1]\n", - "damage_and_fatality_cases = assemble_analysis_cases(df)\n", - "\n", - "choose_damage_or_fatality = 'fatality'\n", - "case = damage_and_fatality_cases[choose_damage_or_fatality]" - ] - }, - { - "cell_type": "markdown", - "id": "984faaa2-c42c-4879-86df-6e25e4fe1f04", - "metadata": {}, - "source": [ - "The function `exceedance_prob` computes the FN or FD curve depending on the case that is provided. And the function `plot_curves` will plot them with the limit line." - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "1b360ec0", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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XWL58ORUqVMh0lDNNYmIiiYmJ2q/VajWRkZHY29vrbY8vIYQQQgghRPGj0Wi0e+wW5krfr1TS+OTJE4BsNwBOO5dWNr+aNGnCjz/+yLJly0hJScHZ2Zk+ffowZcoUSpUqlWW9xYsXM2/ePJ36FiJTtQBPwOS5Y5eB00DGfc6FEEIIIUQRdffuXSpUqFBo/b1SSWNCQgIApqamWZYxMzMDID4+Xqe+pkyZwpQpU/Jcb9q0aUyYMEH79dOnT3F2dubGjRvZJptFTXJyMocOHaJNmzbaBYWKS3+6tJXXunkpn5uyOZW5+c9Nhq8ZzrWn11IP1AaXFi58+eaXeFb0LNSfmb7IvVY077Xszhf2z0xf5F6Te62wyL0m91phkXut+N1rkZGRVKtWDWtr6xzj1qdXKmk0NzcHICkpKcsyaVNDLSwsCiWmF5mZmWkT1+eVKlUKe3t7A0SUP8nJyVhaWmJvb19ov4T01Z8ubeW1bl7K56ZsTmVsbGxY1HwRty1uM3PnTOKT4gmJDKHHqh683/p9mps3L7Sfmb7IvVY077Xszhf2z0xf5F6Te62wyL0m91phkXut+N1raQr7sbVXaiGc3Ew9zc0UViGKMyOFEf9r+z8CZwfSrEozIHV+/FeHvuKDIx9wKviUgSMUQgghhBBFySuVNFatWhWAO3fukJKS+UNcwcHB6coK8bKqWqYqRyYd4dO+n2JukjoKHxYXRutPWzP95+kkJifm0IIQQgghhHgVvFJJY4MGDTAxMSEhIYFz585lOJ+cnMzp06cBaNy4cWGHl46Pjw+1atXSbgEiREFQGimZ0HECAbMD8HLxAkCtUbP498V4LfLiwr0LBo5QCCGEEEIY2iuVNNrY2NC+fXsAfH19M5zfunUr0dHR2Nvb07p160KOLr2xY8dy5coVbRIrREGqXrY6hz86zODqgzFRps6dv3DvAh4LPVjy+xJUapVhAxRCCCGEEAbzSiWNADNmzEChULB69Wr8/Py0xwMDA7Wrlk6ePDnbFVaFeBkZK43pW7Uvxycfp075OgAkq5KZ9vM0Wixtwc1/dNu7VAghhBBCFE/FNmk8fvw4Dg4O2teWLVuA1H0Onz9+9+7ddPWaNWvGggULUKvVDBo0CDc3N+rXr0/Dhg35559/eOONN/joo48McUlCFAnuFd05M+MMUzpPwUiR+iviZNBJ3Oe7882hb9BoNAaOUAghhBBCFKZimzQmJycTERGhfaVtlREXF5fuuEqVcVrdjBkz+O2332jbti0RERHcunWLunXr8sUXX/Drr7+iVCoL+3KEKFLMTMxY0mcJRycfxc3RDYC4pDjGbh5Lpy86cS/ynoEjFEIIIYQQhaXY7tPYunVrnUY8unbtSteuXfUYkRAvn2ZVmhEwO4DJ2yfz7eFvAdh3ZR915tbh60FfM7jx4ELfJ0gI8epITk4mISEBY2NjEhISMv0gODk5Ocvz2Z0rygo7bn32p0tbea2bl/K5KZtTGbnXilZ/xf1eUyqVxWr2VrFNGl92Pj4++Pj4FKtfPOLlZGVuxTeDv6FH/R6MWD+CB1EPeBr/lKG+Q9lxfgffDfkOR2tHQ4cphHiJREdHEx4eTmJiIhqNhrJly3L37t1MP6TK7nxOdYuqwo5bn/3p0lZe6+alfG7Kyr0m95o+yuflXgsODsbKyorSpUsX+fVUJGksosaOHcvYsWOJjo7G1tbW0OEIQac6nbg09xL/8/sfm/w3AfDzuZ85dvMYq4atort7dwNHKIR4GURHR3P//n2srKxwcHBAqVQSGxuLlZUVRkYZn6pRq9U8e/Ys0/PZnSvKCjtuffanS1t5rZuX8rkpm1MZudeKVn/F+V5TqVTExMRgZGREdHQ0ISEhVKhQAUtLyzxdR2GSpFEIkWslS5Rk46iN9GzQk3c2vkPEswgexTyih08PvJt680X/L7C1lA85hBD5Fx4ejpWVFRUqVEChUKBWq0lOTsbc3DzLN/JJSUmZns/uXFFW2HHrsz9d2spr3byUz03ZnMrIvVa0+ivu91pycjI2NjbY29sTGhpKeHg4zs7OebqOwlR87mohRJHxZqM3uTT3El3r/fdc8LoT66g3rx6Hrh0yYGRCiOIsOTmZxMREbG1ti9UUPyGEyC+lUkmpUqWIjY0lJSXF0OFkSZJGIUS+lLUty873d+L7li/W5tYA3Im8Q9tP2/LBlg+IT4o3cIRCiOIm7Tl+ExMTA0cihBCFx8zMDECSRiHEy0mhUDCi+QguzLlA6+qttcdXHFiBx0IPAu4EGCw2IUTxJaOMQohXSXH4nSdJYxHl4+NDrVq18PT0NHQoQuTIxcGFAxMO8Hn/zzEzTv207ErYFbwWebF071JUalkFWAghhBCiuJKksYgaO3YsV65c4fTp04YORYhcMTIy4oP2H3B25lncK7oDkKxKZsr2KbT9tC2hEaGGDVAIIYQQQuSLJI1CCL2qXb42p6adYkrnKdrpFkdvHKXevHr8cOKHYrWRrRBCCCGEkKRRCFEAzEzMWNJnCYcnHqaSfSUAouOjeWvtW/Rb2Y+IZxEGjlAIIYQQQuSWJI1CiALTslpLAmcHMrTJUO2xbWe3UXduXf68/KcBIxNCiOLLxcUFhUKR7euLL74AICQkRHvM0tKSsLCwLNs1NTVFoVAQEhKSZZkDBw6gUCgYO3ZshvYVCgVKpRIHBwccHByoUqUKvXv35rPPPuPx48f6/BYIIQqZJI1CiAJla2nLDyN/4Ke3f6JUiVIAhD0No9MXnRjnN0625hBCiHyqWrUqzZo1y/RVvnz5DOXj4+NZvHixTn3u2rULgK5du2Y45+HhQbNmzfDw8MDZ2ZmYmBh27NjBRx99RIUKFZgzZ452WxUhRPFibOgAhBCvhr4efWlWpRnD1w7nzyupo4xfHfyK/Vf3s3HkRhpWamjgCIUQoniZPn063t7euS5vZGTE999/z5QpUzJNKnNj9+7dWFpa0qZNmwzntm7dirOzM9HR0djY2GBkZMStW7f49ttvWbFiBfPnz+fmzZts3rw5X30LIQxHRhqFEIWmnF05fh//O18O+BJzE3MAroZdpcniJizes1i25hBCiAKiVCrp168fiYmJLFq0KF9t3Lhxg5s3b9K+fXvMzc1zVadKlSp8+umn7Nq1C6VSiZ+fH+vXr89X/0IIw5GksYiSfRrFy8rIyIj/tfsfZ2eepYFzAyB1a47pO6bTellrbj++beAIhRDi5TRnzhyMjIxYvXo1d+/ezXP93377Dch8ampOOnfuzPvvvw+Q7ymyKSkprFq1ijZt2mBvb4+lpSXu7u68+eab/Prrr+nKpj33mdXzma1bt0ahUHD48OF0x7t27YpSqeTw4cMEBATw5ptvUqZMGYyMjFi3bh1vvfUWSqWS5cuXZxnnb7/9hkKhoGHDjDNo7t27x7hx46hWrRoWFhbY2dnRpk0btm3blufvhxCFSZLGIkr2aRQvu1rlanFq2immvT5NuzXHsVvHqD+/PutPrJetOYQQheZmTBLTAh4x8Ph9pgU84mZMkqFDKhA1atRg4MCBJCUlsXDhwjzX37VrFwqFgjfeeCNf/b/zzjsAXL9+naCgoDzVffLkCa1bt2bMmDEcPnwYa2tr6tatS1xcHDt27GD8+PH5iikrR48epUmTJvzxxx9UrFiRypUrA/Dmm28C4Ofnl2XdtHMDBw5Md/zIkSPUqVOHr776inv37lG1alVsbGw4fPgwffv2ZeLEiXq9BiH0SZJGIYTBmBqbsqj3Io5OOoqLvQsAMQkxeK/1pu93fWVrDiFEgVsbHEWNXUEsuxbBT3eiWXYtghq7glgXHGXo0ArEnDlzUCqVrF27NttVUl/09OlTjh8/ToMGDShXrly++q5Rowb29vYAef5QfMSIERw/fhw3NzdOnTpFSEgI/v7+3Lhxg+vXr2tXc9WX+fPn89Zbb/HPP/9w5swZgoKC6N+/Px07dsTW1pZz585x48aNDPXi4uLYuXMnCoWCAQMGaI8/ePCA3r17Ex0dzaJFi3jy5AkXLlzgzp07HD9+nPLly2un8QpRFEnSKIQwuOZVmxM4JxDvpt7aY9vPbafu3Lr8cekPwwUmhHip3YxJYpR/GGpApSHdf0f6h3GriI84Dh8+PNPtNlq3bp1lnapVqzJkyBCSk5PzNNq4d+9ekpOT8zU19XkVK1YE4NGjR7muc/r0aX755RfMzMz4/fffady4cbrzVapUYdKkSTrF9aI6derw7bffYmlpqT1mYWGBmZkZvXr1AjIfbdy5cyexsbE0b95ce60An376KZGRkXzwwQdMmzYNMzMz7bmmTZvy3XffAfD555/r9TqE0BdZPVUIUSTYWNiwdvhautbrypgNY4iMjSTsaRidV3Tm/Tbv80mfT7A0s8y5ISHES83jj9s8jE9Jd0yjVqMwynwfwOzOPU1Woc6iHzXQYG8wtiZKHaL9T1kLY850qqyXttJUrVqV0qVLZzhet27dbOvNmjWLTZs2sX79eqZPn46Li0uOfWW31UZelChRAoCYmJhc10l7XrFXr15UrVpVp/5za8iQIRgZZT62MnDgQNatW4efnx9z5sxJd27Lli0ADBo0KN3xn3/+GYBRo0Zl2mbnzp0xNTXlxIkTpKSkYGwsb9FF0SJ3pBCiSOnTqA9N3ZoyYv0I9l7aC8DXh75m/9X9bBq1SbbmEOIV9zA+hfsvJI2pskr/cjqXtWcpGp6lZNZX0ZDXLTfSuLm5MWzYMNasWcOCBQvw9fXNtrxarWbv3r2ULVsWDw+PfEab6tmzZwDY2Njkus7Vq1cBaNKkiU5950XNmjWzPNe2bVvKli3L9evXOX/+PA0apC7q9vTpU/744w+MjY21zz5C6jWnTQUeM2ZMtv0mJCQQERFBmTJldL8IIfRIkkYhRJHjZOfEnnF7+ObwN0zcOpGE5ASuPbxGk8VNWNhzIRM7TszyE2AhxMutrEXGty6po4mZ/07I7tzTZBXPUrJedMvKWKHXkcaiZNasWWzYsIENGzYwderUbJOUkydPEh4ezogRI7QLl+VX2qqtz4+QNm/eXPvvtFE2Jycntm7dCkB0dDQAdnZ2OvWdF2kjopkxMjKif//+rFixAj8/P23SuHPnTpKSkujSpQsODg7a8k+fPtX++/jx4zn2HR8fr0PkQhSMovUbTAgh/qVQKBjbZiztarRjiO8QzoaeJVmVzJTtU/jj8h+sH76eCqUqGDpMIUQhe3GKp1qtTreZfG7PQeozjTV2BWU6DmkEnO/sShVrUz1GX3S4uLjg7e3NqlWrWLBgAV9//XWWZfU1NfXKlStERkYC4OXlpT2eWSJVqVIl7b+tra0BiIqKynVfacltVitxx8bG5rqtzAwcOJAVK1awZcsWPvnkEwC2b9+uPfc8Kysr7b+TkpIwMTHRqW8hDEE+qhdCFGk1nGpwYuoJpr4+Vfsm4OC1g9SbV4/tZ7cbODohRHFW1doU38ZOGAFKBRgp/v0v4NvY6aVNGNPMnDkTU1NTtmzZws2bN7Mst2vXLkxNTenQoYNO/aUt9lKzZk3tFhaQmthpNBpUKhVPnjxBpVKlW9m1du3aAJw6dSrXfaWNFD5+nPnzrHnd8uNFjRs3xs3Njbt373Ls2DEePnzIsWPHsLCwoGfPnunK2traalecvXz5sk79CmEoOieNycnJnDhxgqVLlzJ27Fj69etHt27dGD58OJMnT2bLli3cv39fH7G+Unx8fKhVqxaenp6GDkUIgzM1NmVx78Uc/OggFUqmji4+iXvCm9+9ydsb3yY+RabyCCHyx9vVjutd3ZhUw55+FW2YVMOe613d8Ha1M3RoBc7Z2ZmRI0eiUqm0o2UvunPnDpcuXaJ169bpRszyau/evXzzzTdA6rOYeZGWhP3yyy+5TvZcXV2BzLf22L59O0+ePMlTDJlJG1H08/Pjp59+QqVS0bVr10y/T7179wbgiy++0LlfIQwh30njoUOHGDx4MHZ2drRo0YJp06bx7bffsm3bNnbv3s369etZvnw5gwcPxtnZmTp16vDZZ58RHh6uz/hfWmPHjuXKlSt53sdIiJdZ6+qtCZwTyJuN/ltgYO2JtUw4OoEzIWcMGJkQojirYm3KYvfS+DUrz2L30i/9COPzpk+fjpmZGTt27EClUmU4/9tvvwH5n5p669YtPvroI7p27YpKpWLIkCEMGTIkT200atSIXr16kZCQwOuvv57hvdGtW7dYvnx5umOvv/46AEuXLk03inr69GnGjRunlymigwcPBmDr1q1s2rQJyDg1Nc2UKVMoVaoU69evZ8KECRmm2kZGRrJmzZo8bYMiRGHK8zONv/32G9OmTePq1atoNBqMjY1xd3fH09MTJycnSpUqhYWFBZGRkURGRmoTnytXrjBx4kSmT5/OmDFjmDVrFo6OjgVxTUKIl1ipEqX46e2fWH9iPe/7vU9sYixhcWG0XN6S+T3mM7nzZJRG+lm4QgghXnYVKlRg1KhR+Pj4ZHo+L88z9u3bFzMzM1JSUkhMTOTBgwfa/RhNTU2ZNWsWM2fOzFecvr6+PHz4kJMnT+Ll5YWLiwsODg7cuXOHR48eUalSJSZOnKgtP3z4cHx8fLh8+TK1atWiRo0aJCQkcOvWLQYMGEBYWBhHjhzJVyxpatSogbu7OwEBAYSHh2Nra6tNVl9UoUIFdu7cSc+ePfn888/5+uuvqVGjBpaWljx+/Jjbt2+j0Wjo37+/TjEJUVDylDS2bNmS48ePY2FhQb9+/RgwYACdOnXC3Nw8x7pBQUFs2bIFPz8/vv76a9avX88PP/xAjx498h28EOLVpFAo8G7mTfOqzRm0ahCnQ06Tok5h+o7p7L28lw0jNuBs72zoMIUQoliYNm0avr6+JCQkpDseFxfH4cOHqVWrVrpnELNy5kzqjA8jIyNsbGywt7enWbNmtGjRgiFDhug0WFCyZEmOHDnCqlWr2Lx5M5cuXeLhw4eUKVOGPn36ZNh6xNzcnIMHDzJ9+nR+++03bt68SaVKlVi2bBkTJkygbdu2+Y7leYMGDSIgIACA7t27Y2qa9Sh1s2bNuHLlCitWrGDXrl0EBQWhUqkoX748nTt3plu3btpprEIUNXlKGi9dusSsWbP44IMP8rzssZubGzNmzGDGjBkcOnSIBQsWcOHCBUkahRD5VqV0FQ5/dBjvL73Zfms7ao2aozeOUm9ePVYOXUl/T/nEVgjx8nl+kZicuLi4ZLmCaBonJyfCwsIyrDK7b98+EhISsh1lfLH9nFas1YWJiQnvvfce7733Xq76Kl26NKtXr8607OHDhzPtY9euXXmKfdKkSUyaNEnbfk4cHR1ZuHChTEMVxU6eksbQ0FDtsse6aNOmDW3atCEmJkbntoQQrzYTpQmDqw/m3W7v4r3OmzuRd3ga/5QB3w9gz8U9fD3oa6zNdf+9JYQQr5rdu3cDum+1IYQo/vL0EZA+EsaCbE8I8epqXqU5gXMCGeA5QHvsh5M/4D7fnVNBuV+mXQghRKrvv/8ejUZDixYtDB2KEMLAZJ9GIcRLw87Sjs2jN7Nh5Abt6GLw42CaL23O/N/mk6JKMXCEQgghhBDFT55XT83Mw4cP2bZtG6GhodjY2FCjRg3q169PtWrV9NG8EELkmkKhYEiTITR1a8oQ3yGcDDqJSq1izs45/HnlTzaO3IiLg4uhwxRCCCGEKDZ0Thr9/f3p1KkTMTEx2gehFQoFAJaWltSpUwd3d3fq16+Pu7s7devWpUSJErp2K4QQ2XJ1dOXopKN8vPtj5u+aj1qj5vit49SfX59vBn3D4CaDDR2iEEIIIUSxoHPSOHnyZKKjo6lVqxaDBw8mKSmJGzduEBAQwI0bN/D398ff31+bSBoZGZGcnKxz4EIIkRNjpTFzus+hQ60ODPEdwu3w20THRzPEdwi/X/odn0E+2FraGjpMIYQQQogiTeekMSAgAGtra/766y9KliyZ7lxCQgIXL14kMDCQgIAAzp8/z6VLl3Tt8pXg4+ODj48PKpXK0KEIUew1rdKUgNkBvL/5fTac2gDAJv9NHLt1jE2jNtGsSjMDRyiEEEIIUXTpnDSam5tTqVKlDAlj2jlPT088PT117eaVM3bsWMaOHUt0dDS2tjISIoSubCxs+GHkD7xe53Xe3fQuT+OfEhoRSsulLZn5xkxmdZ2FsVIvj3kLIYQQQrxUdF499bXXXuOff/7RRyxCCFHgBjYeSOCcQFpUTV1CXq1RM3/XfFosbUHQoyADRyeEEEIIUfTonDR++OGH3L17l4MHD+ojHiGEKHCV7CtxaOIhFvZciNJICcCp4FO4z3dnw8kNBo5OCCGEEKJo0Tlp9PDwYPr06bz11lucP39eHzEJIUSBUxopmfHGDI5POY6boxsAzxKfMWzNMIasHkJ0fLSBIxRCCCGEKBp0ThptbW3ZsmULjx8/5rXXXmPcuHH89ddfpKTIJtpCiKKvsWtjzs8+j3dTb+2xTf6baLCgAf7B/oYLTAghhBCiiNA5abS0tCQ4OJikpCSSkpLw8fGhdevWWFlZ0bBhQ0aMGMGXX37J0aNHiY6WT+6FEEWPtbk1a4evxW+0HzYWNgAEPw6m+dLmLN6zGJVaVjEWQgghxKtL56UCo6OjuX37NhcuXCAwMFD73+DgYAICAggICNDu0Qjg4uJCUJAsNiGEKHoGeA2gceXGDPYdzMmgk6SoUpi+Yzr7ruxjw8gNlC9Z3tAhCiGEEEIUOr2sL1+5cmUqV65Mjx49tMdiY2O5ePFiumTywoULhISE6KNLIYQoEJUdK3N00lHm/TaPj/d8jEaj4dD1Q9SbV4813mvoUruLoUMUQgghhChUOk9PzUqJEiVo0qQJY8aMwcfHh7/++ounT5/KKKMQosgzVhqzoOcCDn10iAolKwAQGRtJT5+ejNsyjkRVooEjFEIIUZDmzp2LQqFg7ty5eap3+PBhFAoFrVu3LpC4dKVQKNLNACxIISEhKBQKXFxcCqW/7LRu3RqFQsHhw4cNHUqxVWBJY1aKwo0jhBC50ap6KwLnBNKrQS/tse+OfsekY5O49OCSASMTQoj/1K1bF4VCgYWFxSu3fsTmzZuZN2/eKzmTLS1BLawkUJ9WrFjB3LlziYqKyld9hUKBUqnk2LFj+g1MZKnQk0YhhChOSpUoxfZ3t/PdkO+wMLUA4E7MHV5b8ho+h3zQaDQGjlAI8SoLCAjg0qXUD7ESEhLYtm2bgSMqXJs3b2b+/PmvZNKYH9WrV6d69eqF0peJiQnVq1fHzc0tw7kVK1Ywb968fCeNeeXs7Ez16tWxtLQslP5eRnlKGt977z3u3bunl463bNnC5s2b9dKWEEIUJIVCwdut3ubMjDPUKVcHgMSURN7f/D49fXoSHhNu4AiFEK+qDRs2AGBnZ5fuayEyc+3aNa5du1YofZUvX55r165x4MCBQukvOz/88APXrl3Dy8vL0KEUW3lKGr///nuqVKnCqFGjOHr0aJ47e/z4MV9//TU1a9Zk8ODB3L59O89tCCGEodQqV4sTU07Q1aWr9tjOwJ3Un1+fQ9cOGTAyIcSrSKVS4efnB8DXX3+NUqnkyJEj3Llzx8CRCSFeNnlKGgMCAmjXrh1r1qyhTZs2VKxYkTFjxrB69WrOnz/Pw4cPSUpKAuDp06fcvn2bPXv2MH/+fDp27Ej58uUZP348ERERfP7550yePLlALkoIIQqKuYk5o+qMYse7O3CwcgDgQdQD2n3Wjuk/Tyc5JdnAEQohXhX79+8nLCyMsmXLMmDAANq2bYtGo2HTpk3Z1ouLi2P58uU0adIEOzs7rKysaNSoEcOGDePIkSMZyms0GrZu3UqXLl0oXbo0ZmZmODs78/rrr7Nu3bpM+/j7778ZMGAA5cuXx9TUlDJlytC3b1/Onz+fafm0Z9Qgdcqpl5cXVlZWlCpVip49e2qn4KY5fPgwSqWS48ePA9CmTRvt830KhSJdXKdOnWLKlCm0adOGsmXLYmZmRsWKFRk6dCiXL1/O9nsF8PDhQ0aOHEmFChUoW7YstWvXZvny5aSkpORY90VxcXF88skneHh4YGNjg6WlJe7u7ixbtozExIJfZC2rZyBdXV1RKBSEhIRw5MgR2rdvj52dHaVKlaJXr17cvHlTW3bnzp20aNECGxsbSpYsycCBA3nw4EGGNjNbCGfdunWULFmS0NBQIHUHhud/bgW1UE1WC+EMHz5ce788ePCAESNG4OTkhLm5ObVr18bHxyfbdjO7z/v168eFCxcK5DoMKU9JY506ddi9ezdHjhzhzTff5PHjx6xevZq3334bDw8Pypcvj4WFBUqlklKlSlGlShW6devG3Llz2b9/Py4uLixZsoSgoCDGjRuHiYlJQV1Xsefj40OtWrXw9PQ0dChCiEy8UfcNLsy5QPua7YHUN1WLf19M86XNCXokq0QLIQreDz/8AED//v1RKpUMHjwYyH6K6p07d/Dw8GDSpEn4+/tTunRpatasyZMnT9i0aRNz5sxJVz4pKYk+ffrQr18/fv/9d4yNjalfvz5qtZo//viD4cOHZ+jjm2++oWnTpvz4448kJCRQp04dVCoV27Zto3Hjxvz8889ZxrdixQqGDh3K3bt3qVmzJikpKfz66694eXmlW/TE1taWZs2aYW1tDaS+R23WrJn2VaZMGW3ZIUOGsHz5cu7cuUOZMmWoWbMmMTExbNy4EU9Pz2wTlYiICLy8vFi/fj1lypShYsWKXLt2jUmTJtG3b1/UanWWdV90//59PD09mTp1KoGBgZQpUwYXFxcuX77M5MmTad++PfHx8bluryDs2LGDdu3acfHiRdzc3EhKSuKXX36hVatWPHz4kM8//5wePXoQEhKCq6sr8fHxbNmyhbZt25KQkJBj+2XKlKFx48aYmZkB4OHhke7nZmtrW9CXmKnQ0FAaNWqEn58f5cqVw97enitXrvD+++/z8ccfZ1rn888/p0mTJhnu8+3bt9O+ffts7/PiKF8L4bRo0YIff/yRe/fusXLlSgYNGoSLiwtKpRKNRqN9WVtb06JFC6ZPn87hw4e5ceMGkyZN0v4PLrI2duxYrly5wunTpw0dihAiC052TvzxwR980ucTjJWp297+fftvGixowKZT2X/SL4QQunj27Bm//PILgDZZ7N27NxYWFly9epWzZ89mqKNSqejduzdXr17Fw8ODK1eucOPGDU6fPk1wcDBnz56lf//+6epMmTKFHTt24ODgwO+//86DBw/4+++/uXfvHvfu3cuQZO7du5eZM2dib2/P9u3biYiI4Ny5c4SHh7N69Wo0Gg3e3t6EhYVlel0ff/wxy5cv5/79+5w+fZqHDx8yePBg4uPjGTJkiDapatCgAUePHqVevXoAfPXVVxw7dkz7ev3117Vtzp49m5s3bxIUFERgYCABAQHaeJKTkxk5cmSWyd93332HnZ0dt27d4uzZs5w+fZpDhw5ha2vLL7/8wrfffpuLnxao1Wr69evHlStXGDBgAPfu3ePmzZtcuXKF27dv06JFC44dO8bs2bNz1V5BmTJlCkuXLiUsLIyzZ89y7949mjRpQlhYGKNGjWLmzJls2rSJu3fvEhAQwM2bN3F1deX69eusXbs2x/Zff/119u7dS9myZQHYunVrup9bgwYNCvoSM/Xxxx/TvHlz7XXfv3+fb775BoCFCxdmWLBn7969fPTRR5ne599//z0ajYYRI0ZkeZ8XRzqtnurg4MDo0aPZsGEDQUFBJCUlERkZyYMHD0hISCAqKorDhw+zcOFCWrZsqa+YhRCiyDAyMmJy58mcmHKCKqWrABCTEMMQ3yEM8x1GdPyrtfy9EKJwbN++nbi4OKpUqaKdlWRtbU3XrqnPXGc22vjzzz9z9uxZSpcuzd69e6lZs2a68+7u7rz77rvarx88eKCdnvfzzz/TuXPndOXLlSuXYR/DWbNmodFoWLVqFb179053buTIkYwfP56YmBhWr16d6XW1b9+eDz/8ECOj1LeolpaWrFmzhrJlyxIaGsqWLVty+tZkMGzYMFxdXdMdMzY2ZuTIkQwYMIDg4GBOnTqVad2UlBTWrVuXboply5YtWbBgAQDLly/P1Srau3fv5sSJE3h6erJhw4Z0I6EVKlTgxx9/xMrKiu+++86go41dunRhwoQJ2u+/nZ0d8+bNA1KvYfTo0QwaNEhbvmLFitrHzfbu3Vv4AeuJvb0969at0y4oBfDuu+/SsGFDEhISOHQo/boFM2bMQKPR4Ovrm+l9/s4772R7nxdHxvpu8PlvthBCvCo8K3tybtY5/rf5f6w/uR6ADac2cDzoOH6j/fCqLCu2CaEPHgs9ePj0YbpjGo0my73qsjtXmMraluXMzDN6ay8tKXz+DTykjjpu3boVPz8/li9fjrHxf2/1fv31VwBGjBiBvb19jn3s2bOH5ORkmjRpQosWLXIsHxoayrlz53B0dKR79+6ZlunevTuffvopR44cYdasWRnOjxo1KsMxU1NTRo0axcKFC7OcEpuTa9eusX79em7cuMGTJ0+0zyOmLRoUGBhIkyZNMtR77bXXaNiwYYbjI0aMYPLkyYSEhHD9+nWqVauWbf9pUxW9vb3T/UzSODk54enpyaFDhzh79izNmzfP8zXqw8iRIzMcc3d3z/Z82uhgcHBwgcVV0AYOHEiJEiUyHPf09OTcuXPpFu9Mu89Lly6d5X3euXNnvv766yzv8+JI70ljWFgYTk5O+m5WCCGKPGtza9aNWEfH2h15Z+M7xCTEEPw4mGafNGNBjwVM7jRZ++mtECJ/Hj59yP2o+4YOw6Du37+vHfl4MWl8/fXXKVmyJI8ePeLPP/+kS5cu2nNXr14FyDQ5ykxey1+8eBFI3S8yqxlmac+93b+f+c8wq+QrbVT0xo0buYrleYsXL2bmzJnZPn8YGRmZbb8vKlGiBBUrVuTmzZvcuHEjx6Qx7Xvz7bffZrnlXNq1ZfW9KQyZ7ano6OiYq/PPnj0ruMAKWGbXBVC6dGkg/bU9f59nldzHxsYChv1Z6pvek8by5cvj4OBA/fr1071q1aqV6ScrQgjxshnUeBBNXJswaNUg/G/7k6JKYdrP09h/dT8/jPiBcnblDB2iEMVWWduyGY4Vl5FGfdm0aRNqtZqGDRtm2Kjd1NSUvn378v3337Nhw4Z0SWN0dOp0+dzOCstr+adPnwIQExOjXdU0K1lNwXw+QXle2nTOmJiYXMWS5ujRo0yfPh2lUsns2bPp27cvlStXxtLSEoVCwcyZM/n4449JTs585eu0pCGrmG7evJmrmNK+Ny+uApsZQ05PtbS0zHDs+f9/sjufm2m6RVVmo4yA9oPe568t7WcZHR2d7/u8ONJ7FrdmzRouXLhAQEAA69atIzIyEoVCgbGxMTVr1kyXSNarVy/LXw5CCFGcuTq68tfkv5j32zwW/b4IjUbDgasHqDevHmu919KtfjdDhyhEsfTiFE+1Wk10dDQ2NjYZRvKzO1ecpU1NPXfuXLYJ8a+//qq9fkC7EOGLi3pkJa/lraysAGjcuDEnTpzI1/c8PDw80/eGjx49ShdTbqVtPzJx4kQ+/PDDDPfC3bt3s63/+PHjLM/lJaa0782+ffto3759juVF0ZX2s2zWrFm6FX3TvKy/d/R+Jd7e3nz22WccPHiQ8PBwQkND+fXXX5k5cyZVq1blxIkTTJo0iY4dO8o0ViHES83E2ISFvRZyYMIBytuVByDiWQTdv+7O+5vfJz7p5fkEUghROM6fP8+lS5dQKBSUKVMmy5epqSnx8fFs375dW7d27doAWS768qK8lq9VqxaQOs0yL1tRPC+r6adpU2VfnAaa0yhySEgIkPpsYmYCAwOzrZ/W74vi4uK0z0PmNDUV/vve5Gak8VVQFEb/8yvtZ3n16tV83+fFUYGnvxUrVqRr167MmjWLLVu28O233/LWW29pt+cQQoiXXZsabQicE0gP9x7aYz6HfGi6tCl3Yu4YMDIhRHGTNsrYsmVLHj58mOXro48+SlceoGfPnkDqrLCsnuF7XpcuXTAxMeHUqVM5TsMDqFq1KnXq1OHJkyfaPSTzytfXN8OxpKQk7fGOHTumO2dubg5kPQ3QwsICgH/++SfDuT///DPHpPHEiRMEBARkOL5mzRoSEhKoVKlShinCmUlbYXPlypW52s/wZZf2cymO0zfT7vPIyMh83+fFUYEnjVFRUfj5+TFw4EAcHBzo1KkTp0+fZuLEiZkO6QohxMvI3sqeHe/t4NvB32Jukvom5/KDy0z8ayKr/lolH6IJIXKkUqnw8/MDYOjQodmWHTJkCACHDx/WTsHs2bMnHh4ePHr0iC5dunD9+vV0dQIDA9PtO+jk5MT7778PpCY9f/75Z7ryDx48YP78+emOLV68GIVCwf/+9z9Wr16tXaU0TXBwMB9//HGWG5//+eeffPnll9rfifHx8YwePZoHDx5QsWJFBgwYkK582lYYR44cybS9tIVKli5dSmhoqPb46dOnGTFihDbpzIqxsTHe3t7p6j6/n+LEiRNzNWrWq1cvmjRpwrVr1+jWrRu3bt1Kdz4xMZHdu3czYsSIHNt6GVSuXBnI+udW1H3yyScoFArGjh2b6X0eEhLCokWLsrzPi6MCSRqDg4P54osvaNu2LWXKlGH48OFEREQwf/58goKCuHjxIosWLcpyqoAQQryMFAoF77R+hzMzzlC3fF0AktRJjPUbS9/v+vIk9omBIxRCFGX79u3j4cOHmJub8+abb2ZbtlatWjRo0ACNRqN9rk+pVLJ9+3aqV6+Ov78/NWrUoHr16nh5eeHm5kbDhg358ccf07WzePFievTowaNHj+jUqRPly5fHy8uLihUrUqFCBebMmZOufJcuXfjkk09ITExk9OjRlCpVCg8PDzw9PSlbtixubm7MnDlT+zzgi2bMmMGHH35IuXLl8PLyomzZsvzwww+Ym5uzcePGDAux9OrVC0h9E1+9enVatWpF69attXsGjhkzBldXV4KCgvDy8sLd3Z0aNWrg5eWFra0t7733Xrbfx7fffpvIyEiqVKlCo0aN8PLyolWrVjx58oRu3brlWD+NkZERP//8Mw0aNGD//v1UrVqVqlWr0qRJE2rXro2NjQ1du3Zlz549uWrvRQ4ODlm+2rRpk682C1K/fv2A1L0Q69atS+vWrWndunWmo7rZGTRoEKVLl87y2tMWc9K3Ll268NVXX2V6n5crV44GDRowa9asLO/z4kjvSWOdOnWoWrUqixcvxtnZmc2bNxMeHs6ff/7J//73v3SbowohxKuodvna+E/3591W/22ivf3cdtznu3Pi1gkDRiaEKMrSppp269YNW1vbHMunjTY+P0XV2dmZs2fPsnjxYho2bMiDBw+4evUqJUuWZNiwYdpN69OYmZmxY8cONm3aRLt27UhISCAwMBAjIyO6dOmS6fS80aNHc+7cOUaNGoWjoyOXL1/m5s2bODg4MHDgQLZu3cqwYcMyjXn8+PFs2LCBihUrcvnyZRQKBd27d8ff3z/TbTyaNm3Kxo0b8fLy4v79+xw9epQjR47w8GHqXp42NjYcO3aMoUOHYm1tzfXr10lKSmLChAmcPHkyx0VsHBwc+Pvvvxk2bBj//PMPoaGhVK9enU8++YSff/45TwudODk5cfLkSb755htatmxJREQE58+fJyYmBi8vL+bNm5dhE/ncioiIyPL15EnR+0By6NChrFixgnr16hEUFMSRI0c4cuRIrhddShMTE5PttRfkM4djx44lICAg0/u8T58+/Pjjj1ne58WR3ldPvXLlCubm5rRt25batWtjbW1NbGysdqUhIYQQYGFqwYr+K7CNtWXllZU8iXvCncg7tFzWknnd5zH19akojZSGDlMIUYRs2rRJO2qYGxMmTGDChAkZjpcoUYKpU6cydepUIOfVHhUKBYMGDcqwJ2R26tSpw6pVq3Jd/nmDBg3SJry5MXDgQAYPHpzleScnJ9atW5fpNc6dO5e5c+cCpEswnj8Oqc9a5mZVzNatW2f7uIGZmRnvvvsu7777bpZlciunvjKTVfng4OBsE+Ds+nFxccn0fFbH04wbN45x48ZlE23WNBpNnlYpPXz4cKbH165dy/r167Osl3YfpPX1oszu85d19VS9J42LFi3iwoULBAYGsm3bNlQqFQqFAkdHxwx7N9asWROlUt4UCSFeXU3KNmF0z9F4r/fmr5t/oVKrmPnLTA5cPcDGURtlT0chhBBCGJzek8a0T60g9aHeS5cuERgYqH2tXr1aO/Rsbm5OXFycvkMQQohipWKpihz86CALdy9kwa4FqDVqDl0/RP159Vk3fB1v1HvD0CEKIYQQ4hWm96TxeWZmZjRq1IhGjRqlO37nzh0CAgK4cOFCQXYvhBDFhrHSmLnd59KmehsGrx7M/aj7hD8Lp+tXXfmw/Ycs7r0YMxMzQ4cphBBCiFdQnifalipVKt/zj9M4OzvTvXt3Zs6cqVM7QgjxsmlVvRWBcwLpVr+b9tjn+z+n6ZKm3PznpgEjE0IIIcSrKs9JY1RUVJ6XwxVCCJF79lb2/Dr2V74c8CWmxqYAnLtzjoYLGrLh5IYcagshRPGj0WhQqVSGDkMIkQW9Lulja2vL2LFj9dmkEEK8khQKBf9r9z/8p/lTvWx1AJ4lPmPYmmEM8x1GTEKMgSMUQgghxKtCr0ljTEwMFy9e1GeTQgjxSnN3dufszLMMbzZce2zDqQ00XtKYoKdBBoxMCCGEEK+Kl2fzkJeMj48PtWrVwtPT09ChCCEMrIRZCdZ4r2HzqM1Ym6duRH3r0S2mHJvClwe/zPM+XUIIIYQQeSFJYxE1duxYrly5wunTpw0dihCiiBjYeCDnZ53Ho5IHACmaFCZum0i3r7rxOOaxgaMTQn/kgxAhxKukOPzOk6RRCCGKEbfSbhyfepwJ7Sdoj+2+uJv68+pz6NohA0YmhO6MjFLflsiCKEKIV0na77y034FFUb4iu337NitWrODgwYOEh4frOyYhhBDZMDU2ZUnvJczxmkNp69IAhD0No91n7Zi5YyYpqhQDRyhE/piYmKBUKomPjzd0KEIIUWhiYmIwMTHBxMTE0KFkKV9J4/3795kwYQIdOnSgTJkylCtXjs6dOwPw9OlTgoOD9RqkEEKIjBqUbsCZ6WdoX7M9kDq95eM9H9NqWStCI0INHJ0QeadQKLC0tOTp06cy2iiEeCXEx8cTHR2NtbU1CoXC0OFkyTivFfz8/AgICCAwMJCAgAAePnyofQFcunSJqlWrUqJECerUqUP9+vWpX78+9erVo169elhZWen9IoQQ4lVV1rYsf3zwB8v+WMbMX1NHGU8EncB9vju+b/nSu2FvQ4coRJ6ULl2akJAQQkNDKVWqFCYmJiQlJZGQkJDp1C21Wp3l+ezOFWWFHbc++9OlrbzWzUv53JTNqYzca0Wrv+J8r6lUKuLj44mLiyMmJgYzMzMcHBzydA2FLc9JY//+/enfv7/268ePH6dLIgMDA7l+/TrPnj3j1KlTnDp1Kl3WXLlyZW7duqWf6IUQQmBkZMSU16fQqlorBq4aSEhECFFxUfT5tg/vtHqHz/p9hrEiz7/uhTAIU1NTKlSoQHh4OGFhYWg0GuLj47GwsMj0U/jszudUt6gq7Lj12Z8ubeW1bl7K56as3Gtyr+mjfG7vtbi4OGxsbLCzs8PBwQGlUpmnayhsOr+LcHR0pEOHDnTo0EF7LDExkcuXL6dLJi9cuMDTp0+5ffu2rl0KIYTIRBO3JpyffZ63N7zNT2d+AuC7I99x7NYxNgzfYODohMg9S0tLnJ2dSUlJISEhgSNHjtCyZctMn/dJTk7m6NGjmZ7P7lxRVthx67M/XdrKa928lM9N2ZzKyL1WtPorzvdaSkoKhw4dol69epiamuYpdkMpkI+ezczMaNiwIQ0bNkx3PCQkhMDAwILoUgghBGBnaceWMVvoWKsj/9vyP+KT4rl0/xJNP2mKdw1vXte8bugQhcg1Y2NjzMzMSElJwdzcPNM3YEqlMsvz2Z0rygo7bn32p0tbea2bl/K5KZtTGbnXilZ/xfleS05ORq1WF6tR6UKddO3i4kKPHj0Ks0shhHjlKBQKRrYYyZkZZ6hbvi4A8cnxfHvxWwb5DiIqLsqwAQohhBCiWCk+T+oKIYTIk1rlauE/3Z/3Wr+nPbb93Hbc57tzMuikASMTQgghRHEiSaMQQrzELEwt8Bnsw09jfsLKJHX16tCIUFosbcHiPYtRq9UGjlAIIYQQRZ0kjUII8Qro6d6Tz1t+TjO3ZgCo1Cqm75hOxy86EhYVZuDohBBCCFGUSdIohBCvCEcLR/Z9sI/ZXWdrH74/cPUA9efX5/eLvxs4OiGEEEIUVZI0CiHEK8RYacy8HvM4+NFBytmVA+BxzGO6fNmFj376iKSUJANHKIQQQoiipkCSRn9/fw4ePFgQTQshhNCD1tVbEzg7kG71u2mPfbbvM5ouaUrQ4yADRiaEEEKIoqZAkkZvb286duxYEE0LIYTQEwdrB34d+ysrBqzA1Dh1c+GzoWfxWuzFX/f/MnB0QgghhCgqCmx6qkajKaimhRBC6IlCoWBcu3GcmnaKamWqARCTEMOn5z/l7Y1vE5cYZ+AIhRBCCGFo8kyjEEIIGjg34OzMswxtMlR7bO2JtXh+7Mml+5cMGJkQQgghDE2SRiGEEABYmVvxw8gf8B3mi7nSHIArYVfw/NiTVUdXyQwSIYQQ4hUlSaMQQoh0hjYZyqctPqVu+boAJCQnMGbDGAauGsjTuKcGjk4IIYQQhU2SRiGEEBmUtyrP8cnHea/1e9pjP57+kYYLG3L69mkDRiaEEEKIwiZJoxBCiEyZm5jjM9iH7e9ux87SDoDgx8E0/aQpn+//HLVGbdgAhRBCCFEoJGkUQgiRrd4Ne3N+1nmauDYBIEWVwpSfp/Dx6Y8JfxZu4OiEEEIIUdAkaSwEKSkp1KtXD4VCwZYtWwwdjhBC5JmLgwtHJx1lSucp2mNnH53F42MPjlw/YsDIhBBCCFHQJGksBCtWrODx48eGDkMIIXRiYmzCkj5L2Dt+L45WjgA8ePqAtp+2Zd7OeajUKgNHKIQQQoiCIEljAbt//z7z5s3jk08+MXQoQgihF53qdOLMjDPUc6gHgFqjZu5vc2n3aTvuP7lv4OiEEEIIoW+SNBaw8ePH0717d1q2bGnoUIQQQm+cbJ2Y03gO87rNw0iR+qfkyI0juM93Z8/FPQaOTgghhBD6VGyTxtu3b7Nq1SpGjx5N/fr1MTY2RqFQsHDhwlzV37NnD+3bt6dUqVKUKFGChg0b8tVXX6FW6281wL179/Lnn3+ybNkyvbUphBBFhVKhZNrr0zgy6QgVSlYAIPxZOG98+QZTtk8hWZ1s4AiFEEIIoQ/GBdFot27dCAsLK4imtVasWMGKFSvyVXfJkiVMmzYNAFdXV6ysrAgMDGTcuHHs37+fHTt2YGSkWz6dkJDA+++/z5w5c3ByciIkJESn9oQQoqhqXrU5gXMCGb52ODsDdwLw+YHP2WW7i7pN6lLdqbqBIxRCCCGELgokaVy6dGlBNJuOg4MDXbt2xcvLC09PT1avXs327dtzrHfy5EmmT5+OkZERGzduZODAgQAEBgbSqVMndu7cyWeffcbEiRO1dWJiYrh/P+fndJycnLC1tQVg0aJFmJqaMm7cuHxeoRBCFB+lSpTil7G/8NXBr5i0bRJJKUncfHoTr0VerBq2in6e/QwdohBCCCHyqUCSxsIwc+bMdF/ndiuLhQsXotFoGD16tDZhBKhfvz6fffYZgwcPZsmSJYwfPx4TExMAdu/ena5sVtauXYu3tzehoaEsXbqUTZs2ERsbC0B0dDQAcXFxPH36VJtcCiHEy0KhUDCu3TiaV2lO/5X9ufX4FtEJ0fT/vj8Hrh3g836fY2lmaegwhRBCCJFHxfaZxvyIjo5m//79AIwcOTLD+b59+2JjY0NERASHDh3SHh8wYAAajSbHl7e3N5D6vGViYiJvvvkmJUuWpGTJktSvX1/bb5kyZQr+YoUQwkAaVmqI/zR/Wpb7bwGw749+j9ciL648uGLAyIQQQgiRH69U0nj+/HmSkpIwNzenYcOGGc6bmJjg6ekJgL+/f777cXd359ChQ+lefn5+AMyaNYs///wz320LIURxYG1uzYcNPmTV0FVYmqaOLl5+cBmPjz1Ye3wtGo3GwBEKIYQQIreK7fTU/Lh58yYAzs7OGBtnfumurq4cOHBAWzY/7OzsaN26dbpjaQvh1KpVK9vtNxITE0lMTNR+nTatNTk5meTk4rMSYVqshRWzPvvTpa281s1L+dyUzalMducL+2emL3KvFd17TaFQMMhjEF4uXgz2HcylB5eIT4rn7U1v06JcC5q0bIK9tX2u4i8K5F4ruvdaVufl91rh9yf3mtxrhdXfq36vFTaF5iX5uNfb25v169ezYMGCDM87plm2bBmTJ0+mcePGnDp1KtMyU6ZMYenSpXTt2pXffvtNb/GFhIRQuXJl/Pz8GDBgQJbl5s6dy7x58zIc37x5M5aW8iyQEKJ4SlQlsvbKWvaG7tUeK2tZlokNJ1LFrooBIxNCCCGKj7i4OAYNGsTTp0+xsbEptH5fqZHGhIQEAExNTbMsY2ZmBkB8fLxe+3ZxccnVdKxp06YxYcIE7dfR0dFUrFiRNm3aYG9fvD6R37dvHx06dNAuKFRc+tOlrbzWzUv53JTNqUx25wv7Z6Yvcq8Vn3utV7debDu3jXc2vkN0QjQP4x4y7eQ0FvdazP/a/A+FQpGLKzccudeKz72W39iLCrnX5F4rLHKvFb97LSIiIsd4C0KhJo33799HpVLh7OxcmN1qmZubA5CUlJRlmbSpoRYWFoUS04vMzMy0ievzTExMitUvoTSFHbc++9OlrbzWzUv53JTNqUx25+VeK/z+XqV7bWDjgTRybkTXz7pyM+omyapkJm6byOEbh1k3fB32VkX/wzG51/RfXn6vZU7uNf2Xl3stc3Kv6b98Qd1rhrq/CnUhHHd3d1xdXQuzy3RKliwJwJMnT7Isk3YurawQQgj9quxQmUVNFzGh/X+zKnZd2EX9efX568ZfBoxMCCGEEJkp9NVTDfkIZdWqVQG4c+cOKSkpmZYJDg5OV1YIIYT+mRiZsKT3EvaM24ODlQMA96Pu03p5axbsWoBKrTJwhEIIIYRI80ptudGgQQNMTExISEjg3LlzGc4nJydz+vRpABo3blzY4aXj4+NDrVq1tFuACCHEy+j1uq8TOCeQNtXbAKDWqJn962w6ft6RsKgwA0cnhBBCCMjHM42LFi3Kd2f6Xlwmr2xsbGjfvj2///47vr6+eHl5pTu/detWoqOjsbe3z7BlRmEbO3YsY8eOJTo6GltbW4PGIoQQBamcXTn2TdjHoj2LmLtzLmqNmoPXDlJ/fn1+GPEDnet0NnSIQgghxCstz0njzJkz873CnUajMfjqeDNmzGDv3r2sXr2a1q1bM3DgQAACAwO1q5ZOnjw52xVWhRBC6JfSSMmsrrNoVa0Vg1YN4n7UfR7HPOb1Fa8zqdMkPu75MSbGxW9xCSGEEOJlkOekUalUolar6d27N1ZWVnmqu2XLlmxXLs2L48eP06NHD+3Xz549A2Dx4sV88cUX2uPnz5+nYsWK2q+bNWum3ctx0KBBzJw5EysrKy5duoRareaNN97go48+0kuMQggh8qZltZYEzA5g+Lrh7LqwC4Blfyzj6I2j+I32o7JjZQNHKIQQQrx68pw01q5dm4sXLzJ69Gg6duyYp7q7du0iMjIyr11mKjk5OdN9SuLi4oiLi9N+rVJlXExhxowZ1K9fn88//5yzZ8/y8OFD6taty/Dhw3n//fdRKpV6iVEIIUTeOVg7sPP9naw4sILJ2yaTrErG/7Y/DRY0YPVbq3mz0ZuGDlEIIYR4peR5IZy05wDPnDmj92DyonXr1mg0mhxfLi4umdbv2rUrBw4cICoqitjYWAICAhg/frwkjEIIUQQoFAo+aP8BJ6aewM3RDYCn8U/p+11f3t34LvFJhn1GXgghhHiV5Ctp1Gg0+Pv757kzQ263UdzI6qlCCAEeLh6cm3WOAZ4DtMe+O/IdTRY34WrYVQNGJoQQQrw68pw0tm/fnvHjx2dYeTQ3du7cycGDB/Nc71U0duxYrly5ot0CRAghXlU2FjZsHr2ZVcNWYWFqAcCFexfwWOjB2uNr5QNJIYQQooDl+ZlGFxcXPv/883x11rRp03zVE0II8WpTKBSMajGK11xfo//3/bn84DJxSXGMWDeCA1cP8O2Qb7E2tzZ0mEIIIcRLKc8jjUIIIYSh1C5fm7+n/82YlmO0xzb5b6LhgoacCz1nwMiEEEKIl5ckjUIIIYoVSzNLVg5dyZYxW7CxsAHg1qNbvLbkNb4++LVMVxVCCCH0TJJGIYQQxVJ/z/6cn3Uej0oeACSlJPE/v//R59s+PIl9YuDohBBCiJeHJI1CCCGKLVdHV45PPc6EDhO0x3ac30GDBQ04FXTKgJEJIYQQLw9JGoso2XLDMG7GJDHv4mMA5l18zM2YpALra1/YM9ofDAWg/cFQ9oU906m9woy9qHgVr1lkZGpsyqf9PmXn+zspVaIUAKERobRY1oLlfyxHrVYbOEIhhBCieJOksYiSLTcK39rgKGrsCmLFjUgAVtyIpMauINYFR+m9rxH+D+h4+C6nIxMAOB2ZQMfDdxnl/yBf7RVm7EWFIa5ZktSirVv9bgTMDqBZlWYApKhSmLRtEt2+7kZ4TLiBoxNCCCGKrzxvuSHEy+hmTBKj/MNQA6p/19BQaUANjPAP42FCCk7mxhgpFCgAI0XaS4ERoFCkfgJjpFYB8EfYM4yMTVKPPVfOSAFnI+NZG/w00zh8g5/SqKQ5TRwsUSjQ9qUANKrUtm/EJGFsrP73nILQZ1nHPtI/DLcSJlS2Nk09npIMQFh8Msrk1Hb5N/60c/8kpGCcotCeSzsPZHrs+ePP18q0TjZ1n6+fedv/Ccrhmps7WlLl32vWl7XBUYz0D8MCFZst4fPrkSy6/pQ1jZ3wdrXTa18i/yqWqsjhiYeZs3MOi39fjEajYc/FPdSfX5/NozbTqnorQ4cohBBCFDuSNAoBrAmKSk1UMll0UQNMC3ycq3YsUOFnCf2O3yceZb5iee/sP9m27fnH7Vy3rQZaHryToY0au4MztJF2rtquoHzHXhSogfq/B2NvpsRcaYSZkQJzpQIzIwVmyrR/G6U/ZqTATPncsbQ6SgXmRkZEJqkYfy7155J2i2j+fY3IZ5J6MyaJ9TfD8SR11PKtqg5U1XOi+6oyVhrzca+PaVWtFUN9h/Io5hEPoh7Q9tO2zO0+l+ldpqM0Kr73uBBCCFHYJGkUAgiJTUZW6X95xKk0xMWlFEpfGmDCuX+YXceBEsZGlDA2wtJYQYl/k1DF88Om/1obHMUo/zAsFSo2WqROrV18/Sm+L/mo5c2YJNYERXEvJoE3SR0xrlHSpMD661i7IwGzAxjiO4SD1w6i1qiZ/etsDl8/zMaRG3GycyqwvoUQQoiXiSSNQgAuJUyyHGk0AjqWLUGPCtao0aDWpBZTa0CtSf1aDalJpyoZgoOYWduBFCMlmn/PactpYP3tKMISVFnGUsZcSe8K1to2Nf/WV6pV8AgGV7IlSaH8d6RLw7nIBK5GJ2UWOgqgmrUpde3MADBWq+AJdC9vTbIidaQlrZ6xJgWeQNfyViSR/tzzbacl1+mO/fvV84m35oXyObenyVgui7rBz5K4m01SaGNihKVSQaJaQ4JKQ6I69ftfUH578IzfHmRcyEgB2gQyNZk0QqnQcCEq9VnIzKZCH3gYi4O5MUoFGCsUqf81UqT7WqlQYKJW4QL4BkVhZGycZdnUrxUYqVO/X8cexWFiapK+jEKB0kiB8b9to0qdqvwwPhkz1fPtKTA2Si2jzuOnLGmJskIB5hoVb1qCx97bfN24QoEmyk52Tvz54Z8s3rOYOTvnoNaoOXjtIO7z3dk4aiMdanUosL6FEEKIl0WhJY2urq4ANGjQgAkTJtCsWbPC6lqIHI1ws2Pp1Ygsz3/lUTZX0w+Tk5PZEwyTatpjYpL5CErbMpZ0PHw3yzY2vVaedmVLZN72HvjGs2y6tm/GJFFjV1CWSeOuVhW1sae2EcCG18pliC/1XCCbXiufZexFRdo1Z7YmphFwtlPlDD+vFG0CqSZRpSFBrSHx34Qy3fF/j6WWST02/1I4jxKzTvSzogFiUzTEpqggF/U1wMbQ6Fy1nTadeML5f3I1nTit/BtH7+ZYPq1s9UymMb9YxuHn6yQpjNMnlgooYaTmcwXU3RNMPEbcSUvy/02QoWCfQX2e0kjJzK4zaVmtJQNXDeRB1AMexTyi0xedmPb6NOZ1n4exUj5DFUIIIbJSaH8lQ0JCtP/95Zdf8PT0ZMKECfTr16+wQhAiS1WtTfFt7MRI/zCU/84mVCrASAO+jZ30+oa2g5MVI11t8c1kMZyRrraZJozZKczYi4r8XLOxkQIrIwVW+Vg0+kJUIt8HRWV5vr6dGc0cLYlNUROXoiZWpSY2RZP67xQ1sar//h2nKsAhTwNIVkNCJmPIFqjAEu7EJeeYpK4OesJIt5KsCYoiJDYZlxImjHCz0/szni2rtSRgdgBvrXmL3y/9jkajYdGeRRy5cQS/0X5ULFVRr/0JIYQQL4tCSxrXrl0LwMOHDzlx4gQnT55k4MCBkjRmwcfHBx8fH1SqvI9uiPzxdrWjuaMl626Gw90gxlcrhXdVhwJJulY3LsfASrbMDwyDBPAsZc7s+k55ThjTFGbsRUVhXvPEmvasCorKcjR3W/MKue53asA/LL8WSWa5o1IBQ1xsebuKHSoNqDQaUtT//lf7tQaVBlJSkuFiEN96lEVlZEyKRpNJnX/LajRoVCkQEsSH1UuRqFCmHldrUD1XJu2YQqWCSOhW3pp4jNK1mVZWqVZBPNS3MycOo3TtpWjARJOazTuaKXmYrCApi/nBauDrG09YejUSI0XqlGSFApZejcC3sRPNHC0zJJNAro5llnQ6Wjuy63+7+GzfZ0zbMY0UVQrHbx3Hfb4764avo1v9brn6OQohhBCvkkJLGt96660Mx27cuFFY3Rc7Y8eOZezYsURHR2Nra2vocF4ZVaxNmVPXkT13YU5dxwKdptmubAla2ldiz57L7G9bSee+CjP2oqKwrrmqtSlr/h3ZfH4LECPyPpo70q0ky65GZnpOo4GZtXOX+CYnJ7PnIgxysc3VdScnJ7MnBObm4vuUOlX5PBszmcacvswljrbP/N5NPX+dW92qMPvyE5Zdi8g0UQaI/feE6oUByxH/fr8VzyWTn/w7jdwoh2NpSWdmz0saGRkxsdNEmldpzoBVAwiNCCUyNpLuX3fnw/YfsqTPEkyNX94PXIQQQoi8yvs8LT2qVq2aIbsXQohc83a143pXNz6sXgqAD6uX4npXtzwv4pI2tdYI0k+t5eWdTjzCzS5fqxNrQLsXZ9p/07Y6yelY2vOSt2KSsmy/iVsTzs86T68GvbTHPt//Oc0/aU7w4+C8ByyEEEK8pAyaNAohRHGSNrIJqSOb+U3w0hLQ8dVSE9Dx1fKXgBYXLybKRv8my0aAVylz7eitvikUqavLZqdkiZJsf3c7Xw38Sju6eDrkNA0WNGDrma0FFJkQQghRvOg1abx79y6bN29m2bJlzJ8/P9255ORkkpKy/sRXCCFeJfpKQIuLtER5Ug17epW3AeBs58q0LVNCm0Tqm1oDv96PYeDx+0wLeMTNLEYdFQoF77d9n5NTT1KldBUAouOj6beyH+9teo+E5ISCCVAIIYQoJvSSNIaHh9O/f38qV67M0KFDmTp1KvPmzUtXZvjw4VhYWHD27Fl9dCmEEKKYqWJtymL30qxp4gSAq5Vpvqeu5oYGuBqdxJY70XxyNYLqu4JYFxyVZfmGlRpybtY5BnoN1B779vC3NF7UmOsPrxdMkEIIIUQxoHPSGBMTQ6tWrdi6dSvly5fH29ub8uXLZyg3atQoNBoNP//8s65dCiGEeElkNnVVqUhdaEifA5Bpzz2OyOE5R2tzazaN2sTqYauxMLUA4MK9CzRa2IiN/hv1GJEQQghRfOicNC5dupSrV6/Sp08frl27hq+vL5UqVcpQrmXLllhYWHDo0CFduxRCCPESeX7qar+KNkyqYc+Nrm6sySaZzO5YdjTA8n9XW82KQqFgZIuR/D39b2o51QIgNjGWEetH8GXAl8Qmxup+0UIIIUQxovOWG9u2bcPMzIzVq1djYWGRZTkjIyOqVKnCnTt3dO1SCCHESyZt6uqLx5o7WuL73P6LI//dkzG7Y/sePiMiSZ1lX0cfx+Uqpjrl6/D3jL8Z5zeONcfXAHDw3kFe++Q1fnr7J+pWqJv3CxVCCCGKIZ2TxpCQEKpVq5arvQQtLS25fl2eC8kNHx8ffHx8UKlUhg5FCCEMJrNkEsj2WK3dQUToaeG1EmYl8PX2pU2NNryz8R1iE2O59vAaXou8+HLAl4xqMQqFoqDWfxVCCCGKBp2np5qbmxMTE5OrsmFhYbJRfS6NHTuWK1eucPr0aUOHIoQQxUoLR8tszyepNdmuppqZIU2G4D/VHxcbFwASkhMYs2EMg1YNIjo+WpdwhRBCiCJP55HG2rVr4+/vT2hoaKbPMqYJCAjgzp07dO7cWdcuhRBCiCxNrGnPqqAoslqUNfhZMsuuRbD0agQf13fkaZKakNhkbExSP0eNTlbjUsKEtmUsOfhPnPacsdqWpc2W8smd3Zy9vB6ALae3cDrkND++/SONKjUqpCsUQgghCpfOSeOQIUM4ceIEY8aMYceOHVhaZvyE98mTJ4wcORKFQsGwYcN07VIIIYTIUlVrU9Y0dmKkf5h21dTnaQDVvwenBT5GqUjd0zGtXNpk0yVXIzDiv5VXLVDR0dKU62UnolA0wPzmbOITowl6HMRri19jed/l/K/t/2S6qhBCiJeOztNTR48eTYsWLdi3bx9169Zl6tSp/PPPPwCsWbOGCRMmUL16dc6fP0+HDh0YMGCAzkELIYQQ2UlbkXVKTXtq2phmu32HSpM+sXw+0VSTMelUaUBTuiMJDbdRz9kTgGRVMuO3jKf3N72JjI3U23UIIYQQRYHOSaNSqWTXrl3079+f27dvs2zZMm7duoVGo2H06NF88cUXhIeH069fP7Zv366PmIUQQogcpS2iU9/OXK97PqYxsqxApy4/81HHj7THfgn4hQbzG3Ay6GQB9CiEEEIYhs7TUwGsra3x8/Nj+vTp7Nixg4sXL/L06VOsrKyoVasWvXr1olEjedZDCCFE4XMpYYJCQcYhQx1pgLsJCvz6Lqd1tda8tfYtImMjuRN5hxZLW7Co1yImdpyIkZHOn88KIYQQBqWXpDFN3bp1qVtX9q0SQghRdIxws2Pp1Qi9t6vRQGBUAtMCHjHCrSOBswMZuGogx24dQ6VWMWX7FA5dP8QPI37A0dpR7/0LIYQQhUU+/hRCCPFSq2ptim9jJ4wApQKMFPr546cBrkcnsexaBDV2BbE/yopDEw8xo8sM7WI4ey/tpc7c+gzavYOBx+/z9t9hvP13GAOP389224+bMUnMu/gYgHkXH+dpexAhhBBC33T+u7lz505cXV359NNPsy336aef4urqyp49e3TtUgghhMiTtIVxJtWwp19FGybXtGdJfUdtIvn8M48K/vs6p2ch1aQujKMGRvqHcTtWxcJeC/njgz8obV0agEfRYfj98iZbjizm+1sRfB8UxY93orXJ5rrgqHRtrg2OosauIFbcSF1QZ8WNyEzLCSGEEIVF5+mpP/zwA6GhofTq1Svbcj169GDSpEn88MMPdOnSRdduhRBCiDxJWxjneX0q2uAbFEVIbDK2/+7T+PTffRrbly3BzAuP8I9IyNXjkGqg5p5gqliZ4lKiOk1e/52d+8bCk1OpZ2/7wJMzUPsTNGaltdt+jPQPw72kGVWszLgVk8Qo/zBtMgrpk9LmjpZUsTbV03dECCGEyB2dk8bz589TunRpXF1dsy1XpUoVypQpw5kzZ3Tt8pXg4+ODj48PKpXK0KEIIcRLK7NE8nmrg0z5O5dJI6QmeNdjkrgekwRYgPsqCF0FwV8Daojyh797Q60lYN8cUo/SYG9Ijm0rFOAbFJVtvEIIIURB0Hl66oMHD3B2ds5V2YoVKxIWFqZrl6+EsWPHcuXKFU6fPm3oUIQQ4pWlXXk1FxSAvakRlsrnKiiU4PIONFwHZmVSjyVHQuAYCPoM1Mm5jkWlgR33YjjxOA61Rs9LwQohhBDZ0DlpLFGiBI8fP85V2fDwcMzMzHTtUgghhCgUI9zsyG1+pgBOdazMs77Vedy7Km9Vtv3vj6ydB3j+DPat/qsQuhrOe0PCA1wsTWhfpgQulibZPkd5PSaJZvtDqfjrLcadfcjRR3Go1JJACiGEKFg6J41169YlNDQ0x2mnZ86cISQkhDp16ujapRBCCFEoXlx5Ff5bHMeI1JVYlf+uxurb2Ikq1qYoFAoczIyZUdshfWOmJaGeD1SZBIp/nw55eh7+7s3U0oHsa+vMn22dc1x8B+BBfApf3XhCqwOhlPvlJu+eDuPAw1hSJIEUQghRAHROGgcNGoRGo2Hw4MEEBwdnWub27dsMHjwYhULBoEGDdO1SCCGEKDRpK6+Or1YKgA+rl2J/G2cm10xdiXVSDXuud3XD29UuXb0XE04FgMIInIdDww1gXj61YEo076x5kw+2fICzuSZDkpqWlH7dqAzrGjvRrbwVpkb/pZaPElV8dyuK9ofuUHbHTUb/HcbeB89IUkkCKYQQQj90XghnxIgRrF+/nhMnTlCnTh169+5N48aNsbOzIyoqilOnTvHLL78QHx9P06ZNGT16tD7iFkIIIQpNFWtT5tR1ZM9dmFPXERMTE9qVLZFjPW9XO5o7WmayQmsLyjY4xBX/yfx58RcAVhxYwbFbx/hxzI9c7+rGupvhcDeI8dVK4V3VQbtq6luudkQnq9h1/xnb7sbwe9gzEv5NECOSVKwOimJ1UBR2Jkb0qGDNmxWtaWOfWjfoWRLrQ58QEpuMSwkTRrjZUVVWYxVCCJEDnZNGpVLJrl27GD58OL/++iubN2/Gz89Pe17z78MgvXr1wtfXF6VSqWuXQgghRLGR3QqtGq+f+fbwt3z404ckpSRxNvQsDRY0YPWw1cxx75UuSX2ejYmSQS62DHKx5Vmymt/DnrHtbjS77j8j7t8EMipZzfrbT1l/+ymOxhpWmUKjvbdJVCjRaFJXY116NQLfxk4ZRkmFEEKI5+mcNALY2dmxY8cOzpw5w6+//srVq1eJjo7G2tqa2rVr07NnTxo2bKiProQQQoiXhkKh4L027/Ga22v0X9mfm49uEpMQQ//v+zO6+WjaW7fPsQ0rEyP6OtvQ19mGuBQ1f4SljkD+dv8ZMSlqAJ6lqMEUNPy3/yPP7RMp+z8KIYTIjl6SxjQeHh54eHjos0khhBDipdfAuQFnZ53l3Y3vssl/EwCrjq3iT+s/qelZk7oV6+aqHUtjI3pVtKFXRRsSVGr2P4xl290Yfg2NzLKO7P8ohBAiJzovhCOEEEII3VmbW7Nh5AbWeK/BwtQCgNCYUJosacIPJ37Ic3vmSiO6lrdmXZNydHGyzrKcBgiJzf1+kUIIIV49eh1pBHjy5AnPnj3TPsuYGWdnZ313K4QQQhR7CoWC4c2G4+XiRb+V/bgSdoW4pDjeWvsWB64dwGeQD1bmVnlut7KVCTzJ4qQGXEqYZHFSCCGE0NNI440bNxg0aBClSpXCwcEBFxcXKleunOnL1dVVH10KIYQQL63a5WtzYsoJOlTsoD32w8kf8PjYgwv3LuS5vSGVbbM8pwa6l897IiqEEOLVofNIY0BAAK1atdKOLpqbm+Po6IiRkcx8FUIIIfLL0tSSsfXHMqT9EMZuHsuzxGdcf3gdr4+9WDFgBWNajkGhUOTcEOBmZcp10O7/qAE0Gu1aOCy4HM7uVhVz3Z4QQohXi85J4/Tp04mJiaFdu3Z8/vnn1KlTRx9xCSGEEAIY6DmQ19xeo9/KfgTcDSAxJZF3Nr7DwWsH+X7o99haZj2K+KKznSuzLjSWkNhkSpsr2RzylPAkNb+HxTLv0mMSVcgejkIIITLQOWk8ceIEVlZW/PLLL5QokfNGxyJ3fHx88PHxQaVSGToUIYQQBla1TFVOTjvJpK2T+PrQ1wD8dOYnzoSe4ccxP+LhkruVy12tTFns/t/f6tedrHj9yF0A5l2KSB2FfGEPx8EV5W+7EEK86nSeQ6pWq6levbokjHo2duxYrly5wunTpw0dihBCiCLA3MScrwZ9xfZ3t2NrkTq6GPw4mKZLmrJi/4psF6DLSudyVgypZKP9WqVJfcYx7b8j/cMIfpakpysQQghRXOmcNLq7uxMWFqaPWIQQQgiRg94NexMwO4DGlRsDkKxK5oMfP6CnT08iY7PejzErZSyynnSkUMCG20/zHasQQoiXg85J47Rp0wgLC2PDhg36iEcIIYQQOXBxcOGvyX8xqdMk7bGdgTtxn+/OiVsn8tTW/biULN8MaIDQ2JT8ByqEEOKloHPS+Prrr/PNN9/w3nvv8eGHH3Lp0iXi4+P1EZsQQgghsmBibMLSN5eye9xu7K3sAbgbeZeWy1qy5PclqNXqXLXjUsKELBdN1UClEnrf0lkIIUQxo3PSqFQqee+994iLi+PLL7+kfv36WFlZoVQqM30ZG8sfHyGEEEJfutTtQsCsAFpUbQGASq1i2s/TeH3F6zyKfpRj/RFudmT1OKQaCI5N1mO0QgghiiOdk0aNRpOnV24/+RRCCCFE7lQoVYGDHx1kVtdZ2r0W/7zyJ+7z3Tl8/XC2datam+Lb2Em7h6MR8PzA4y/3YgC4HJVYILELIYQo+vSyempeX0IIIYTQL2OlMfN7zGffh/soY1MGgLCnYbT7tB0Ldi9Apcl6CydvVzuud3VjUg17+jnbMLlmKZbUd8RS+V/62OZgKD43IvO1SqsQQojiTeaKCiGEEC+RdjXbETgnkCGrh7D/6n7UGjULdi+grn1dPJp74OzgnGm9KtamLHYvne5YzwrWvHXsDiRDolrD+2f/Yf8/sfh6laOUmbIwLkcIIUQRoPNIoxBCCCGKljI2Zdj7wV4W9lyIkSL1T/3FiIt4LvJk35V9uW6nuo0ZB9qmTzJ/ufeM+nuD+etRnF5jFkIIUXRJ0iiEEEK8hJRGSma8MYNDEw9RzrYcAI9iHtHpi07M3DGTFFXuttIwVaa+VdjSrDz2pqmji/fiUmh9MJR5Fx9z7Wki0wIeMfD4fd7+O4wPzv4DwLyLj7kZk1QAVyaEEKKw6W16amxsLL/99huBgYFERkaSnJz5amsKhQJfX199dSuEEEKIbLSs1pLT00/TbXk3zj0+h0aj4eM9H3P05lE2j9pMhVIVctXO605WBL5uxeCTDzjyKA61BuZeCmfupXCUClBrUvd1tEBFR0tYcSOSxdef4tvYCW9XuwK9RiGEEAVLL0njli1bePfdd4mOjtYeS3tQXvHc5k8ajUaSRiGEEKKQOVo7MtNrJtdNrzPz15mo1Cr+uvkX7gvc+WHED3Sp2yVX7ZS3NOFAG2cWXQlnzsVw0pbEUWWyNo5Kk7plx0j/MJo7WlLF2lRv1yOEEKJw6Tw99eTJkwwdOhSVSsWMGTOoUqUKAKtWrWL27Nl0794dhUKBubk5H3/8MWvWrNE5aCGEEELkjZHCiI86fMRfk//CuVTqc4oRzyJ448s3mLxtMskpuduPUWmkYFYdRwa52OSqvEIBvkFR+Q1bCCFEEaBz0rh8+XLUajWbNm1i/vz5lC6duvLayJEjmTt3Ljt27ODSpUu4urri4+ND586ddQ5aCCGEEPnzmttrnJ99nu71u2uPLftjGS2XtSQ0IjTX7ajUuXsToQFCYnOXkAohhCia9DLS6ODgQLdu3bIsU6NGDbZv305YWBhz5szRtUshhBBC6KBUiVL8MvYXvuj/BSZKEwBOBZ/Cfb47v5z/JVdtuJQw4bknULKk+LesEEKI4kvnpDEiIgJn5/+W4zY1TX1mITY2Nl25atWqUbt2bX7//XdduxRCCCGEjhQKBePbj+f4lONUdqgMQFRcFL2+6cUHWz4gMTkx2/oj3OzQZPIs44s0GhjpZqeHiIUQQhiKzkmjvb098fHx2q8dHBwACAoKylBWpVLxzz//6NqlEEIIIfTEs7In52ed581Gb2qPrTiwgmafNCPoUca/5WmqWpvi29gJI0CpSB1RzMysOvayCI4QQhRzOieNLi4uhIWFab9u2LAhGo2GTZs2pSsXGBjIjRs3cHR01LVLIYQQQuiRraUtP739E98M/gYzYzMAzoaepeHChmw7ty3Let6udlzv6sakGvb0d7bhbTc7RlS2S1cmLF5VkKELIYQoBDonjR06dCAqKorLly8DMGjQIMzNzVm+fDlDhgzBx8eH2bNn065dO9RqNX369NE5aCGEEELol0Kh4N3W73Jq2imqlq4KQHR8NINWD+K7i9+RkJyQab0q1qYsdi+NX7PyfOflxOeNygBgZZz6FmNzaDQxyZI4CiFEcaZz0tivXz/atm3L9evXAahYsSLffvstxsbGbN68mXHjxvHxxx8TGRlJ48aNWbhwoc5BCyGEEKJguDu7c3bWWQZ5DdIe2xu6l+bLmnPj4Y1ct9O3YuqWHM9S1GwOjc6htBBCiKLMWNcGateuzb59+9Ide+utt2jRogU//fQTISEhWFhY0Lx5c3r27IlSqdS1y1eCj48PPj4+qFTy6awQQojCZW1uzcZRG2lboy3v+71PQnICF+5doOHChqwcspLBTQbn2MZwV1u+uR0DwPe3oni7SsmCDlsIIUQB0TlpzIqrqytTp04tqOZfemPHjmXs2LFER0dja2tr6HCEEEK8YhQKBSNbjKShc0O6f9Gde8/uEZsYyxDfIRy6fogvB3yJpZlllvXrlzTHo5Q5ZyITOPckgTMR8XjYWxTiFQghhNAXnaenCiGEEOLlVadcHZY3X87QJkO1x3yP+eK1yIsrD65kW3fMc1ttrAyKKqAIhRBCFLQ8jTTeuXNHL50+v6+jEEIIIYo2c2NzfIf50q5mO97b9B5xSXFcfnAZj489+GbQN3g388603sBKtkw4/4hnKWrWB0fxJEmFvWnqYyrRyWrcLBR4FuJ1CCGEyJ88JY0uLi4oFFntxJQ7CoWClJQUndoQQgghROF7q+lbeFX2ot/Kfly6f4n4pHiGrxvOoeuH8Bnkg5W5VbryViZGNCplxpFH8SRrYPvdmHTnLVGx2RI2hTzFu6pDhv5uxiSx/mY4nsC8i495q6oDVf/d8/FmTBLLr0bw96MY5gIfnP2HD2qX1p4XQgihP3lKGp2dnbNMGu/fv69NBo2NjXFwcCAiIoLk5GQATExMKFeunI7hCiGEEMKQajrV5O/pfzN+y3hW/bUKgB9O/sDft//mx7d/pGaZmtqyN2OS+OtRfJZtaf7979gzD2le1oYqzyV8a4OjGOUfhqVCxUYLWHEjksXXn+Lb2AkNMNI/DA1ggQosYe3tKL65HYOTuRI7UyUtHC35sKpNAXwHhBDi1ZOnZxpDQkK4fft2htcbb7yBQqFg3LhxXLt2jcTERB48eEBCQgLXr19n3LhxKBQKunbtyu3btwvqWoQQQghRCCxMLfh+2PdsHrUZK7PU0cVrD6/ReFFjVh9bjUaTmg6uCYoiNxOUNECbA6F0O3KXXn/d5fVDdxjhH4YaUP2bWao0oAaG+4cx4t+EMTNhCSquRifxfVAUDfemvuf44Ow/3IxJ0umahRDiVabz6qnffPMN3377LX5+fvTr1y/dOYVCQdWqVfniiy9o2rQpAwcOpFatWrz77ru6diuEEEIIAxvYeCAeLh70W9mPgLsBJCQn8N7m92hRrgUt2rYgJDYZTVbZ3QvuxadwL/5ZgcSZNgq5trETzRwtWRMURUhsMi4lTBjhZidTWoUQIgc6r566cuVKnJ2dMySML+rXrx/Ozs6sXLlS1y6FEEIIUURULVOVk9NOMrbNWO2xvx78RZMlTTCPu5qrkcbCMtw/jGq7glhyNYItd6JZcjWCaruCWBccZejQhBCiSNM5abx16xaOjo65Kuvo6MjNmzd17VIIIYQQRYi5iTlfD/qabe9sw9YidW/hW49vsWn7G6jvbiI3w43elW153LsqYT2r8l4VO5SFmGwO9w9jf9gzpgU8YuDx+0wLeCTTWYUQ4jk6J41WVlZcvnyZqKiobMtFRUVx+fJlSpQooWuXQgghhCiC+jTqg/80f6raVgUgWZWE5sbHcOkDFMnRWdZTADNqO+BgZkxZC2M+qGGfZZ6p+Pelbx0O32XZtQh+uhPNsmsR1JARSCGE0NI5aezQoQPx8fEMHjyYyMjITMs8efKEwYMHk5CQQKdOnXTtUgghhBBFlKuDK4uaLWJ82/H/HXy8D5uAvtTiujbpez758/Eom27l1KrWpvg2dsIItCOOSkXqm5Y1jZ1Y09ipQBLHtMV20v470j+MWzLiKIQQui+Es2jRIvbu3cvevXtxdnamb9++1KxZE0dHRx4/fsy1a9fYunUrsbGx2Nvbs3DhQn3ELYQQQogiysTIhGVvLqNtzbZ4r/XmSdwTnsbcJfZIX6a+8THqCm8RGpeCm4UC7gYx2MU2QxvernY0d7Rk3c1wuBvE+Gql8K7qoE0umztasvxqBP6PYkBVMNehBnyDoljsXrpgOhBCiGJC56TR2dmZv/76iyFDhnD+/HnWr1+fbi/HtGW3GzRowIYNG6hUqZKuXQohhBCiGOju3p2A2QEMWDWAk0EnSVGlsHjnFLrW+4t1w9dhY2bDnrtZ169ibcqcuo7suQtz6jpiYmKS7tx3Xk4kJzuwZ89VzneuzOc3o/npzlOeJOdyydZc2BzyVFZaFUK88nROGgFq1qzJ2bNnOXjwIH/88Qc3btzg2bNnWFlZUa1aNTp27Ei7du300ZUQQgghihFne2eOTDzCrF9n8cneTwDYdWEXDRY0YMPwDXrrx9UqNYn8zsuJvsfuse1ujF7avROfwp070SiAT65GsKi+I0+T1JJICiFeKXpJGtO0bduWtm3b6rNJIYQQQhRzJsYmLOmzhNbVWzPUdyjhz8K5G3mXdp+3Y1C1QXRWd9Zrf1ubV+DAw1jmB4ZBAniWMmd2fSfmXXrMX4/j89Vm2tjltMDH6Y4vuRrB2sZOeLvaaY+tC3rCjAuPiUpWY2dixMf1HPF2K5nPqxFCCMPTeSEcIYQQQojc6FynMwGzA2hZrSUAKrWKDdc20P2b7jyKfqTXvtqVLcH+tqmPxOxvW4l2ZUtwtL0L6xs7Uc5ciaVSQTlzJW4lTHJoKWfDn1swp8X+EIb//ZAHCSriVBoeJKgY/vdDWu4P0bkfIYQwFL2ONN69e5e//vqL+/fvEx8fz+zZs7XnkpOT0Wg0mJrKFA4hhBDiVVW+ZHkOTDjA/F3zWbh7IRqNhj+v/In7fHf8RvvRqnqrAu1/mKsdw54bFdwX9oyOh7N5sDKXRp66T5fyVhzLYiTzr8fxVNl5i2SNhnIWxsyv60gHJyud+xVCiMKgl5HG8PBw+vfvT+XKlRk6dChTp05l3rx56coMHz4cCwsLzp49q48uhRBCCFFMGSuNmd9jPnv+twc7MzsAwp6G0fbTtsz/bT4qdQEth5qJDk5WjHTNuHprXh0NT2BqYHi2ZYJik7kTl8KpiAQ6Hr7LKP8HOvcrhBCFQeekMSYmhlatWrF161bKly+Pt7c35cuXz1Bu1KhRaDQafv75Z127FEIIIcRLoF2Ndnze4nPaVk9dD0GtUTNn5xw6ft6Rh08fFlocqxuXY38bZ5rYm+NsaUxps8J5esc3+CkHHsYWSl9CCKELnX8rLl26lKtXr9KnTx+uXbuGr69vpttqtGzZEgsLCw4dOqRrl0IIIYR4SZQ0L8nu/+1mQY8FGClS35YcvHaQ+vPqs//K/kKLo13ZEpzsWJnQHlU51qEyipyrpGNulL83VTMv6PdZTiGEKAg6J43btm3DzMyM1atXY2FhkXVHRkZUqVKFO3fu6NqlEEIIIV4iSiMlM7vO5OBHBylnVw6ARzGP6PhFR2bvnF2o01UBqlqbsqaxE0aA4t9XTlZ6OtHZqUSe+3oQn5LnOkIIUdh0ThpDQkKoVq0atrY5Pw9gaWlJeHj28/2FEEII8WpqVb0VAbMD6FwndQsOjUbDkr1LmHVqFvej7hdqLN6udlzv6saUmvb0d7Zhak17PEqZZ1q2haMFw1zt+KJR2Tz3U8pUFrIXQhR9Ov+mMjc3JyYmdxvohoWF5Sq5FEIIIcSrydHakd3/282S3ktQGikBuBJ5Bc9Fnvx+8fdCjaWKtSmL3Uvj16w8i91Lc7pT5Qxbdqxv7MTR9i5A6gjl2sZOeZramqiGm/9u1yGEEEWVzklj7dq1uXv3LqGhodmWCwgI4M6dOzRq1EjXLouFw4cPo1AoMrw8PDwMHZoQQghRpBkZGTHl9SkcnXSUiiUrAhD+LJwuX3ZhyrYpJKckGyy2Ya523O9Vjdh+Nbjfq1q67TsgdYTyRlc3pta0Z4CzDRUtst/d7Gp0EjV2BbEuOKrgghZCCB3pnDQOGTIElUrFmDFjiIuLy7TMkydPGDlyJAqFgmHDhunaZbGyevVqTp48qX2tW7fO0CEJIYQQxULTKk35e9rfeJbx1B5b+sdSWi1vxZ2IortGwvMjlIkqdY7l1cBI/zBuyYijEKKIyv7jr1wYPXo0fn5+7Nu3j7p169K3b1/++ecfANasWcOlS5fYuHEj4eHhdOzYkQEDBugcdHFSu3ZtmjRpYugwhBBCiGLJ3sqe6R7TuWV+i+m/TCdZlczJoJO4z3dn3fB1vF77dUOHmK04tSZX5RQK8A2KYrF76QKOSAgh8k7nkUalUsmuXbvo378/t2/fZtmyZdy6dQuNRsPo0aP54osvCA8Pp1+/fmzfvl0fMQshhBDiFaJQKBjfbjzHphzDxd4FgCdxT+jh04OJ2yaSrDbcdNWcmBnl7glHDRASW3SvQwjxatPLkl3W1tb4+fkRGBjI7Nmz6dOnD+3bt6dHjx5Mnz6d06dPs2XLFkqUyPtS1Fm5ffs2q1atYvTo0dSvXx9jY2MUCgULFy7MVf09e/bQvn17SpUqRYkSJWjYsCFfffUVanXO00jyokePHiiVSsqWLcvbb7/NkydP9Nq+EEII8arwquzF+dnn6d2wt/bYlwe/ZNrxaQSHBxswsqy1L5u79z4KwKWEScEGI4QQ+aTz9NTn1a1bl7p16+qzySytWLGCFStW5KvukiVLmDZtGgCurq5YWVkRGBjIuHHj2L9/Pzt27MDISLd82tbWlokTJ9KqVSusrKw4efIkixcv5u+//+bvv//GxET+MAghhBB5ZWdpx7Z3tvHN4W+Y8NMEklKSuPX0Fl6LvPD19uXNRm8aOsR0FtQrzU93YshpkqpKA8uuRfD1jUhm1bSleqFEJ4QQuaPXpPHu3bv89ddf3L9/n4SEBGbNmqU9l5ycjEajwdTUVC99OTg40LVrV7y8vPD09GT16tW5mv568uRJpk+fjpGRERs3bmTgwIEABAYG0qlTJ3bu3Mlnn33GxIkTtXViYmK4fz/n/aGcnJy0W4o0aNCABg0aaM+1bt2aOnXq0L17d7Zt26btVwghhBB5o1AoGNtmLE3dmtLvu37cenyL6IRo+n7Xl/dav8en/T7F3CTzPRULW1VrU9Y0dmKkfxg5zWVSaeCZSsPcSxH4WRZKeEIIkSt6mZ4aHh5O//79qVy5MkOHDmXq1KnMnTs3XZnhw4djYWHB2bNn9dElM2fO5LfffmPWrFl07twZKyurXNVbuHAhGo2GUaNGpUvc6tevz2effQakjkQmJ//3XMHu3bupWbNmjq8dO3Zk23fXrl0pUaIEZ86cyccVCyGEEOJ5DZwbcGrqKVqUa6E99s3hb3ht8Wvc/OemASNLz9vVjutd3TDJywaOwJfXIgomICGEyCOdk8aYmBhatWrF1q1bKV++PN7e3pQvXz5DuVGjRqHRaPj555917TLfoqOj2b9/PwAjR47McL5v377Y2NgQERHBoUOHtMcHDBiARqPJ8eXt7Z2rOBSKPP7VEEIIIUSmbCxsmNBgAt8O+lY7uhhwN4CGCxqy5fQWA0f3nyrWpjmONL7ok6uSNAohigadk8alS5dy9epV+vTpw7Vr1/D19aVSpUoZyrVs2RILC4t0yVhhO3/+PElJSZibm9OwYcMM501MTPD0TN0Lyt/fX+/979y5k9jYWG0fQgghhNCdQqFgZPOR/D39b2qUrQHAs8RnDFs7DJ9AH+KSMt9HurBZ5HIl1TRxqtxt1yGEEAVN52cat23bhpmZGatXr8bCwiLLckZGRlSpUoU7dwy3Ge/Nm6lTVZydnTE2zvzSXV1dOXDggLZsfg0ZMgRXV1caNmyoXQhn6dKleHh40KdPnyzrJSYmkpiYqP06OjoaSH0m9Pkps0VdWqyFFbM++9OlrbzWzUv53JTNqUx25wv7Z6Yvcq/JvVZY5F4r+vdajTI1ODH5BON+HMdG/40A7Lu7j6afNMVvlB81nWrm6hoKyqyatsy9lPPoocW/Y5IlFOpCud/kXstdGfm9VrT6e9XvtcKm0Gg0On2MZWFhQbVq1QgMDNQea9GiBSdOnEClUqUr+9prr3H+/HkSEhJ06TJT3t7erF+/ngULFjBz5sxMyyxbtozJkyfTuHFjTp06lWmZKVOmsHTpUrp27cpvv/2W73gWL17M5s2bCQ0NJSEhgQoVKtC7d29mz56NjY1NlvXmzp3LvHnzMhzfvHkzlpbyVLwQQgiRGwfvHmTlpZUkqlI/iDVTmvF2nbdpW7GtgSMTQoj8i4uLY9CgQTx9+jTbnELfdB5pNDc3JyYmJldlw8LCtKuLGkJasprdCq5mZmYAxMfH69TXtGnTtNt65LXehAkTtF9HR0dTsWJF2rRpg729vU4xFabk5GT27dtHhw4dCmV7EX32p0tbea2bl/K5KZtTmezOF/bPTF/kXpN7rbDIvVa87rUudGHY3WH0/ro3d2LukKhK5MvAL4k0j+TL/l9iZZ67BfQKwpfXIvjkagSxKk2mW3FYoGaN5W2mqd34wrMCbcrob5/rzMi9lrsy8nutaPX3qt5rERGGedZZ56Sxdu3a+Pv7ExoamumzjGkCAgK4c+cOnTt31rXLfDM3T31APikpKcsyaVNDs5tqW5DMzMy0ievzTExMitUvoTSFHbc++9OlrbzWzUv53JTNqUx25+VeK/z+5F4rXuRe03/5grrX6lWsx7Lmy/gj+g/WHF8DwEb/jZwJPcNPb/9E3QqFs7f0iz6qW5aP6pZlXdAThv/9MMtyIQnQ6a8w6tmZUcvGDBuT1KUoopPVuJQwYYSbHVWt9bOVGci9ltsy8nutaPX3qt1rhrq/dF4IZ8iQIahUKsaMGUNcXOYPmj958oSRI0eiUCgYNmyYrl3mW8mSJbXxZCXtXFpZIYQQQhRfZkozvhv8HZtGbcLKLHV08drDa3gt8mLV0VXo+JSOTlYGReWq3IWoRH68E833QVF8HxTFj3eiWXYtghq7glgXnLs2hBBCFzqPNI4ePRo/Pz/27dtH3bp16du3L//88w8Aa9as4dKlS2zcuJHw8HA6duzIgAEDdA46v6pWrQrAnTt3SElJyXQxnODg4HRlhRBCCFH8DWo8CI9KHvT/vj8BdwNISE5gzIYxHLx2kJVDV2JjUXjPBqV5EJ+S67KaF/6dtrDqcP8wll4Jp15JcxQoCmQEUgghdB5pVCqV7Nq1i/79+3P79m2WLVvGrVu30Gg0jB49mi+++ILw8HD69evH9u3b9RFzvjVo0AATExMSEhI4d+5chvPJycmcPn0agMaNGxd2eOn4+PhQq1Yt2Z5DCCGE0JNqZatxctpJ3mv9nvbYltNbaLSwEefvnC/0eMpZ6PzZPQBXY5L58U6MjEAKIQqMzkkjgLW1NX5+fgQGBjJnzhz69OlD+/bt6dGjB9OnT+f06dNs2bKFEiUK9kHunNjY2NC+fXsAfH19M5zfunUr0dHR2Nvb07p160KOLr2xY8dy5coVbRIrhBBCCN2Zm5jjM9iHre9s1Y4u3np0iyaLm+BzyKdQp6vOr+uo1/bSRiDVwEj/MG7FZL2GgxBC5IV+PuL6V926dalb1zAPlefWjBkz2Lt3L6tXr6Z169YMHDgQgMDAQO2qpZMnT852hVUhhBBCFG9vNnqThs4N6b+yP2dCz5CUksT7m9/n8PXDrBq2CjtLuwKPoYOTFSNdbfENfqr3thUK8A2K4v/t3XdUVEcbBvBn6R0ERLEgAopgAREEYzRgb7FEY4vGQtQkJGrsBRv2lmgM+WLsHRONvXejomIBCypFEBRQRBGkl/v9QdhIYIFll13K8ztnT2TuzJ33LgPZlzt3ZqmjmdzPTUTVj1zuNCrD1atXYWpqKn75+fkByNsf8cPy6OjoAu3atm2LhQsXIjc3F0OHDoW1tTUcHBzg5OSEly9fomfPnpg8ebIyLomIiIgUyKqmFa5Mv4KJnSaKy/bd3genhU4IiFDMTJ+NrnVw1sMCbiZa0FUVye28AoDIlMq10TwRVVwyJ42HDx+GlZUVVq9eXWy91atXw8rKCsePH5e1SwB5zx8mJCSIX/lbZaSmphYoz8nJKdR29uzZOHLkCDp06ICEhASEhYWhefPmWLNmDQ4dOgRVVVW5xEhEREQVm6a6Jn4a9BMOeh0U312MeB2BtsvbYs3ZNQqZrtqxti78uzTE+4FNcNbDAi7GeVuEWeqoQQWAqgiQNp3MFaDUlWGJqGqROWncvn07nj17hn79+hVbr0+fPoiMjMT27dtl7RIA4O7uDkEQSnxZWloW2b5Xr144d+4cEhMTkZKSgsDAQEyYMIEJIxERUTXUx7EPAucGws3KDQCQlZOFH/b+gL6+ffEm5Y3C4uhYWxdnO+Ttex3UwxpPelljahMTDLIwwDhrI/SsXfr1IfZGJ+OrGzHlFSoRVSMyJ413796FmZkZrKysiq1nY2ODWrVq4datW7J2WS1w9VQiIiLFamDSAJenXsa0rtPEZYeDDsPRxxHXwq4pJSYbfQ0sdTTDnrZ18Vtrcxz1sICnlWGp2296+g7n4lLKMUIiqg5kThpjYmJgYWFRqrr169dHbGysrF1WC1w9lYiISPHU1dSxfMByHBt/DCZ6JgCA6DfRaL+yPVacXIHc3FwlR/jvc5B1tEo3O8r73qtyjoiIqjqZk0ZdXV3Ex8eXqu7r16+hqakpa5dERERE5apH8x4InBOIdo3aAQBycnMwff909FrXC/HJpfvcU5461tZFezPdUn2QC0hIx5nY9+UeExFVXTInjc2bN8ezZ89KnHZ669YtREZGolmzZrJ2SURERFTu6hnXw/nJ5+Hd0xsiUd5SNCcenICjjyMuh1xWcnSApa46RKVYIScHQJeL0Xy+kYjKTOakcejQoRAEAV988QWePn1aZJ2IiAh88cUXEIlEGDp0qKxdEhERESmEmqoaFvZdiFMTT8FMP2/Pw5jEGHis8sCio4uQk1t4lXZFGW1tBGkWSOXzjURUVjInjaNHj8ZHH32E0NBQNGvWDMOGDcO6deuwY8cOrFu3Dl988QWaNWuG0NBQtGnTBmPGjJFH3EREREQK09m+MwLnBqJDkw4AgFwhF3MOzUHXNV0R9y5OKTE10tfAJldzqdrw+UYiKguZk0ZVVVUcPXoUffr0QXp6Onbv3o2JEydi5MiRmDhxIvbs2YO0tDT069cPR48e5ZYWpcTVU4mIiCoWcyNznP7hNBb0XgAVUd5HqHOPzsHRxxHnHp1TSkwjrYzgaFT69SJi0rLLMRoiqqrU5HESIyMjHDhwALdu3cKhQ4fw6NEjJCUlQV9fH02bNkXfvn3h5OQkj66qDS8vL3h5eSEpKQmGhqVfWpuIiIjKj6qKKuZ+OhftG7fH0A1DEfsuFi+TXqLzT53h3dMbc3vNhZqqXD5eldoKRzN0uRhdqrp1tBUbGxFVDXL9zeHs7AxnZ2d5npKIiIiownG3dUfg3EB8uflLnHp4CoIgYOHRhbgUcgm7v9qNujXqKiyWzuZ68LQyxKan70qsu6iFmQIiIqKqRubpqURERETVkZmBGY6PP46lny2Fqkre4zeXQy7D0ccRJx+cVGgs+Xs3OhppQE3CiqqeVoboWFtXoXERUdUgc9KYlZUlVf2oqChZuyQiIiKqEFRUVDCj+wxcmnoJ9WrUAwC8fv8a3dd2x4z9M5CVLd3nJFl0rK2Lu92tkTXYDmc9LOBmogX1DxLI3c+SUPdACLaGv1VYTERUNcicNDo7O+PBgwelqrt161a0aNFC1i6JiIiIKpS2Nm0RODcQvVr0EpctP7kc7qvcEZWg+D+Yd6ytC/8uDWGu9e+TSGk5AmLSczDqZhzqHwxFaHKmwuMiospJ5qTx/v37cHFxwerVqyXWSUhIQP/+/eHp6Yn379/L2iURERFRhWOiZ4LD3x3G6s9XixfDuRZ+DY4+jjgceFjh8WwNf4soCaulPk/Lhu3RcGx9mqjYoIioUpI5afT29kZ2djamTZuGDh064Pnz5wWOHzt2DM2aNcOBAwdgbm6OEydOyNolERERUYUkEokwqcskXJ1+FZYmlgCAt6lv0ce3DybtnYTMbMXd3Zt9L77Y4wIAzxuxePqedxyJqHgyJ40+Pj64cuUKrK2tcfHiRTRv3hw7d+5Eamoqxo0bh969e+Ply5cYNGgQHjx4gM6dO8sj7iqP+zQSERFVXq0btsbduXfxmdNn4rKfzv6EdivaISI+QiExJGblllhHJAJ2RJS86ioRVW9yWT3V1dUVQUFBGDt2LN69e4cRI0agXr162LhxIwwNDbFr1y7s2bMHRkZG8uiuWvDy8kJwcDACAgKUHQoRERGVgZGOEfZ9vQ/rhqyDhpoGAOBmxE20XNgSf935q/z7Vy/5Y54A4FlK0VNYiYjyyW3LDW1tbaxbtw6dO3eGIAhITEyEiooK/vrrLwwZMkRe3RARERFVGiKRCN91+A7XZlyDdU1rAMC7tHfo/7/++H7390jPSi+3vhe3qFlyfAAa6Mp1224iqoLkljQ+evQIbm5uOHv2LLS0tNC4cWPk5OTg008/xfr16+XVDREREVGl06pBK9yZcweDXAaJy3658As+WvYRwl6FlUufI61roF1N7WLrCAIwvKFhufRPRFWHXJLGn3/+Gc7Ozrh79y4cHR1x+/Zt3L9/H5MnT0ZaWhq+/fZb9OjRA3FxcfLojoiIiKjSMdA2wJ4xe7B++HpoqmkCAO5G3YXTQif43fQrlz4vd7LENldzGKmJCpSLkPchcJOrOaz0NMqlbyKqOmROGrt27YoffvgBmZmZmDlzJm7cuAE7Ozuoq6tj5cqVOH/+PCwsLHDy5Ek0b94cf/75pzziJiIiIqp0RCIRxrYfi5uzb8K2ti0AIDk9GUM2DMG4HeOQlpkm9z6/tDLC28+b4HeX2uKyj2tq40kva4y0MpJ7f0RU9cicNJ45cwYNGzbE5cuXsXjxYqipFZwX3759e9y7dw9ffvklEhIS+HwjERERVXst6rXArdm3MNxtuLjs98u/w3WJKx7HPS6XPuPSs8T/jnifhQhutUFEpSRz0ujp6YmgoCC0adNGYh19fX1s3boV+/fvh7GxsaxdEhEREVV6elp62DZ6GzaP3AxtjbxnD++/uA+3ZW648PyCXPsafSMGc+8niL9+npaNLhejYXU4FO3ORAIAOp1/hjOx7+XaLxFVDTInjRs2bICurm6p6vbr1w8PHjyQtUsiIiKiKkEkEmFU21G4NfsWmtZpCgBIzUzF2sC1+Gr7V0jJSJG5jzOx77HladF7MUakZOPeuwwAQMCbdHS5GA2zv0KYPBJRAQpfY9nMzEzRXVZKvr6+8PX1RU5OjrJDISIionJmX8ceN2fdxHi/8dh0ZRMAYPv17Qh4FoA/xv2BZnWblfncc+/HS1U/PiMHXS5Gw9PKENPtTbE5PBGRKVmw1FWHrb461ocn4llKFkQAGhtows1EG6OtjdBInwvqEFVVUt9p3L59O06dOlXksaSkJKSmpkps+8svv2DSpEnSdlkteXl5ITg4GAEBAcoOhYiIiBRAR1MHG0dsxNaRW6GlqgUAeBT7CC6LXbDx740QBKFM541Jyy5Tu01P36HJ0XCsfJyAP6KSsOxRAkbdjMP1hHTEpucgJj0HF1+lYvmjBDQ5Go6tTxPL1A8RVXxSJ40jR47EkiVLijxmZGSE7t27S2y7d+9erF27VtouiYiIiKqNoa2HYnW71WhRrwUAID0rHWO2j8GwjcOQnJ4s9fnqaJd9YlkugBwh77+SCP/U87wRi6dcXIeoSirTM43F/aWrrH8FIyIiIqI8dfXq4srUK/jG/Rtx2e6bu9FqYSsERgVKdS6f5jXlHF3RRCJgR0TRz04SUeUm80I4RERERCR/Wupa+PWLX7F37F4YaBsAAEJfhcJtqRt+vfBrqf9Q39lcD55WhuUZKoC8O47PUso2FZaIKjYmjUREREQV2ECXgbjjfQetGrQCAGRkZ8BrtxcGrh+Id6mlu7O30bUOznpYwEq3/NZAFAFoUI7nJyLlYdJIREREVMFZm1nj6vSrmNBxgrhs3+19aLmwJQIiSrdoXsfaugjv3Qihvawxw84ErY21iq0vkjJGQQCGNyz/O5pEpHhMGomIiIgqAU11TawZvAYHvj0AIx0jAEDE6wi0Xd4Wa86uKfV0VRt9DSx1NMONrg0R2ssak2yNAQDmWqqoo60GNxMtnPWwwGZXc6gAUBUBKsVkkCLkfaDc5GoOKz1uu0FUFXEOAREREVEl0rdlX7S0aInBvw/G9afXkZWThR/2/oALjy9gy6gtMNY1LvW5bPQ1MK95TRyPBh73soG6unqB4x/X1MGmD/ZptDPQwP/C3uJBYgbe5+QlqUMaGGBB85qw0ddAVlaWXK+ViCqGMiWNr169wvbt28t0jIiIiIhk08CkAS5PvYzZB2dj5amVAIDDQYfR0qcl/Mb6oY11G7n0k39X8kNfWhlhRuArLH+UAAAYa2MEG33eYSSqysqUNIaGhmLUqFGFykUikcRjQN52HCKRtDPkiYiIiOi/1NXUsWLACnzS+BOM2DICCe8TEPUmCu1XtseSfkswufNkqKjwSSQikp3USaOFhQUTPwXw9fWFr68vcnJylB0KERERVWA9W/RE4JxADNkwBFfCriA7JxvT9k3DxScXsW3UNpjqmyo7RCKq5KROGiMjI8shDPovLy8veHl5ISkpCYaGXImMiIiIJKtnXA8XplzAvMPzsPTEUgiCgOP3j8PRxxF7xuxBu8btlB0iEVVinLNAREREVAWoqaphcb/FODnhJGrq1wQAvEh8AfdV7lh8bDFyc3Pl1tebzH9nQq16lIBxN2Mx5OoLLLgfL7c+iKjiYNJIREREVIV0adoFQXOD4GHrAQDIFXLhfdAb3dZ2w8uklzKff8vTRGwMTxR/fTQmBb+HJ8IvKgk/PXkDANgV+U7mfoio4mDSSERERFTFmBuZ48ykM5j36TzxWhRngs/A0ccRFx5fKPN5Q5Mz8dWNWEjaETK/3OtWHMKSM3Em9j3anI5Ag0OhaHM6Amdi35e5byJSHiaNRERERFWQqooq5veej7M/nEVtw9oAgLh3cej0YycsOLwAObnSL7a3OTwRpVkPUQDQ81IUulyMxvWEdESlZuN6Qjq6XIzGVzdi5JpMLrgfjyFXX2Bm4CuEJmeW+TxEJBmTRiIiIqIqrINdBwTODURn+84A8qarzj8yH51/7IzYxFipzhWZkgVB0m3G/whJziqyfNPTd0Umk9/fipMqlp3/TIH96ckb+EUlYdmjBDQ+Go6eF6OYPBLJGZNGIiIioiqulkEtnJxwEov6LoKKKO/j34UnF+Do44izj86W+jyWuuqlutNYFtv/SQLPxqXgXFwK/n6Viuuv03D7TRruvU3Ho3cZCEvOxLOULFx5lYLv/kky/5vDHo9NQZOj4dj6NLF8AiWqhqTacuPy5cswNDSEg4NDecVDREREROVARUUFs3vORvtG7TFkwxC8SHyBV8mv0POXnhhgPQBdunaBurp6secYbW2EFY8SyjXO/leeIw2qJdbTLuZYLoDRN2Jx/XUa3mXlwlhVQBcArU9FIEOkinY1dTDFzgSN9DXkFTZRlSbVnUZ3d3eMHz++QFmHDh0wceJEecZEREREROWkXeN2CJwbiO7NugMABEHAn2F/osvaLnj+5nmxbRvpa2CTqzlUUPGnqwkAfg9PxN6oJGyJSAQAPEnOxKOkTPwenojGR8Mx5a50U2KJqiup7jSKRKJCe/xcvHgR2dnZcg2KiIiIiMqPqb4pjn5/FKvPrMbMv2YiJzcHV8KuwHGhI7aP3o4ezXtIbDvSyggf19TBpvBEnH+ZgoA36eJj+TNXv29shBUhyWWKbYa9CdKhiqxcIe8l4N9/5wrIzBVwIvY9ckrx8bOkxy9XP36LZynZ+PPjemWKlai6kCppNDIywrNnz8orFiIiIiJSEBUVFUztOhVulm747JfP8Dr9NRLeJ6Dnzz0xtetULO67GOpqRU9XtdHXwFJHMwBAWHImNoUnIjIlC9baIiA6HIta1EJCtgo2PZV+v8aZ9qYlTpMddzMWO8LlM012X3QyzsWloL0Jp6oSSSJV0timTRucOHEC/fv3R5cuXaCtnTeb/NWrV9i+fXupz/Pll19KFyURERERlQs3Kzf81P4n7I3bi6P3jgIAVp5aiSthV+A3xg8WJhbFtv8wgczKysLx6Lzyja51MKSBIbzvvUJMWjbqaKthUQsz7Hn2rshk8ktLQ+BV6WKeYmeCnXJKGgHA+94rXPbg3UYiSaRKGpcsWYJr167hwIEDOHjwoLg8NDQUo0aNKvV5mDQSERERVRz6GvrYP24/fr38K6btm4asnCz4h/vD0ccRW0dtRW/H3mU6b8fauuhYu2GhsqKSyfYmGjh+vHTnbaSvAV/n2kBweJni+q8QbtFBVCypksYWLVrgyZMn8PPzw+PHj5GWloatW7fCzMwM3bp1K68YiYiIiKiciUQiTOw0EW2t22Lg+oGITIjE29S36OPbBxM7TcTy/suhoSafKZxFJZNZWUXv6yjJF5aGOB4MTLI1RmBSDhIys2GiqYa62mrYGJ6I3JJPIfYmMxcDr77ASADh7zPRpEbx02OJqhupkkYAqFmzJr7//nvx11u3bkWjRo2wZcsWuQZW3fn6+sLX1xc5OTnKDoWIiIiqEZeGLrg79y48t3nirzt/AQDWnF2Dq2FXsXfsXjSs2bCEMyjWvOY1Cz0D2cZUG543YiESATklrYbzj1Ox7zFSB3A6GQEjLQ18Wlef23IQ/UPm1ZLnzZsn1dRUKh0vLy8EBwcjICBA2aEQERFRNWOkY4R9X+/DL0N/Ed9dDIgMQMuFLcWJZEU20soIT3pZY2oTEwy2MEA70+J2dSwsNj0Hv4cnwvZoOLY+TSyfIIkqESaNRERERFSISCSCl4cX/Gf4w7qmNQDgXdo79P9ff3y/+3ukZ6WXcAblyl+gZ0/bujjqnreYj6iENv8lAPC8EYswPvNI1Zzc92UNCQnB0aNHsWfPHhw9ehQhISHy7oKIiIiIFMSpgRPuzLmDQS6DxGW/XPgFHy37CGGvwpQYmfSkTRoBIBdA78vRWHA/Xt7hEFUacksa169fDysrK9jZ2aFPnz4YNmwY+vTpAzs7O1hbW2PDhg3y6oqIiIiIFMhA2wB7xuzB+uHroammCQC4G3UXTgud4HfTT8nRld4vzrWhAkBVyuzxUVIm1oa8AQDsipR+70miyk4uSeOoUaPw7bffIjIyEhoaGrC2tsZHH30Ea2traGhoICIiAl9//TWnsRIRERFVUiKRCGPbj8XN2TdhW9sWAJCcnowhG4Zg3I5xSMtMU3KEJfvC0lD8rGNPc12p7jzmL6jz7a04fH0zFqGcskrViMxJ4+7du7Ft2zbo6OhgxYoViI+PR0hICP7++2+EhIQgPj4eK1asgK6uLrZv3449e/bII24iIiIiUoIW9Vrg1uxbGOY2TFz2++Xf4bbUDU9ePlFiZKWT/6zjUXcLbHY1L9OU1fX/LJLT82IUhlx9wamrVOXJnDRu2LABIpEI+/fvx5QpU6Cnp1fguJ6eHqZMmYJ9+/ZBEAROUyUiIiKq5PS09LB99HZsHrkZ2hp5K5Pee34PbsvccPH5ReUGJ4WRVkYI6WUNcy1VqdsKAI7HpuCPqCROXaUqT+akMSgoCFZWVujSpUux9bp06QIbGxvcvXtX1i6JiIiISMlEIhFGtR2FgFkBsDe3BwCkZKRgTeAajNkxBikZKUqOsHRs9DUwoqFRmdvnouDU1a3hb+USF1FFInPSmJ6eDiMjo1LVNTAwQEZGhqxdEhEREVEF0bRuU9ycfROj2v67dsU2/21ovbg1Hr54qMTISm+0tZHczjXqZhy+uhEjt/MRVQQyJ40WFhZ48OABXr9+XWy9+Ph4PHz4EBYWFrJ2SUREREQViK6mLjaP3IzNIzZDS1ULABAcGwyXJS7YcnULBEFQcoTFa6SvgV+da8vtfJuevsO5uMpxp5WoNGROGnv37o2MjAwMGjQI8fFFPwT86tUrDBo0CJmZmejTp4+sXRIRERFRBTTMdRhWtVuFZnWaAQDSMtMweutofLn5S7xPf6/k6Ir3haUhAKB/PX2YaKhAW8ZPyd73XskhKqKKQU3WE8yYMQN+fn64ePEiGjRogM8//xz29vYwMzPDq1evEBwcjD///BPp6emoX78+pk+fLo+4iYiIiKgCqqdXD1enXcW0v6Zh/eX1AICd13ciIDIAf4z7Ay3qtVByhMXb7FYH6urqAICvbsRg09OyLW4Tk5Ytz7CIlErmpNHY2Bjnz5/HkCFDcPv2bezYsQMi0b+LF+dPR3BxccHu3bthbGwsa5dEREREVIFpa2jjt+G/wd3WHWN3jEVyejKexD1B68Wt8fOQnzGm3ZgCnxcrqo2udTCkgSG8773Cy5R0AED7mjoITc3F05SsYtvqqlb86yMqLZmTRgCwsbFBQEAAzp07h9OnTyMkJATv37+Hnp4eGjdujK5du6JDhw7y6IqIiIiIKonBrQejVYNWGPT7INyNuouM7AyM2zEOFx5fwPrh62GgbaDsEEvUsbYuOtZuiKysLBw/HoIjn9RHZLqAxkfDi22XWbEf4ySSilySxnwdO3ZEx44d5XlKIiIiIqrEGtVqhGszrmHqn1Pxy4VfAAB+AX649ewW9o7dC6cGTkqOUHqN9DWgpQKk50quE5/O6alUdci8EA4RERERUXG01LWwbug67Pt6Hwy18xacCXsVhjbL2uCX879U+NVVi6KrVvzHaHUVTk+lqoNJIxEREREpRP9W/XFnzh24WLoAADKzM/H9nu/x+W+fIzE1UbnBSalTbd1ij7uZaGNm4CsMufoCMwNfITQ5U0GREckfk0YiIiIiUhirmla4Mv0KJnaaKC7bf2c/XJe6IjQxVHmBScnTyqjY48diU7DycQL+iErCyscJaHI0HFufJiokNiJ5Y9JIRERERAqloaaBnwb9hENeh1BDpwYAICIhAjOvzsTP53+uFNNVz79MLbFOjgDkfvBfzxuxCOMdR6qEmDRWUL6+vrC3t4eLi4uyQyEiIiIqF70de+Pu3Ltws3IDAGQL2Ziybwr6+vbFm5Q3So6ueJElbLlRFJEI2BSeKP9giMoZk8YKysvLC8HBwQgICFB2KERERETlpoFJA1yeehmTO08Wlx0OOgxHH0f4h/srMbLiWeqqS90mVyhbskmkbEwaiYiIiEip1NXUsbTfUni7eMNE1wQAEP0mGu1WtMOKkyuQm1vM3hZKMtraSOo2AgBDdX78pspH5lF74sSJSjHvnIiIiIgqNudazgiYFYCPbT4GAOTk5mD6/unota4XXie/VnJ0BTXS18DkJjWkbvc8lXcaqfKROWns2bMn6tevjxkzZuDRo0fyiImIiIiIqql6NerhwpQLmN1jNkSivL0OTzw4AUcfR/wd8reSoytoVcvaGFBfX6o2F1+llFM0ROVH5qSxadOmiImJwcqVK9GsWTO4ubnht99+Q2JiohzCIyIiIqLqRk1VDYv6LcKpiadQU78mAOBF4gu4r3LH4mOLK9R01T8/rofD7eoDAOrrqJVYPyWnvCMikj+Zk8b79+/j1q1b8PLygomJCW7evAkvLy+Ym5tj8ODBOHnyJKevEhEREZHUOtt3RtDcIHjYegAAcoVceB/0Rre13fAy6aWSo/vXJ7V0AAAPelgrORKi8iGXJ3GdnJzw888/IyYmBn/99Rd69+6N3Nxc/PHHH+jZsyfq1avH6atEREREJDVzI3OcmXQG8z+dL56ueib4DFyWuODe63tKjq4wjRI+XZd0nKgikuuwVVNTQ9++fXHgwAHExMRg7dq1cHR0RGxsrHj6qqurK6evEhEREVGpqaqoYl7veTg36RxqG9YGAMQlxWHe9XnwOeqDnNyKM+ezUy3dYo93LuE4UUVUbn/rMDExwffff4+bN29i2bJlUFVVhSAICAgIgJeXF+rUqQNPT09ERESUVwhEREREVIV4NPFA4NxAdLbvDAAQIGDR8UXo/GNnxCbGKjm6PGta1S72+ERbY8wMfIUhV19gZuArhCZnKigyorIrt6Tx4cOHmDZtGiwsLDBz5kxkZ2fD1NQU48ePx8CBAwEAW7ZsQfPmzfH33xVrJSwiIiIiqphqGdTCyQkn4dPbByr/fJS98OQCHHwccPrhaSVHl7cVx2grwyKPtaupjS4Xo7H8UQL8opKw/FECbI+GY+vTRMUGSSQluSaNCQkJWLduHZydndGiRQusWrUKr169Qrdu3fDnn3/ixYsXWLNmDfbs2YPnz5/Dy8sLqampmDZtmjzDICIiIqIqTEVFBTO6zcDCNgtR16guACA+OR7d1nbD7AOzkZ2TrbTYQpMzsfXpuyKP/R2fBgFA/hKR+f8efSMWYbzjSBWYzEljdnY2Dh48iH79+qFu3bqYOHEi7ty5AxsbGyxevBhRUVE4duwY+vfvD3V1dXE7Y2NjrFu3Do0aNUJQUJCsYRARERFRNdPUpCkCZgWge7PuAABBELDk+BJ0WN0Bz988V0pMm8MT8c96PaUmAFj1KKFc4iGSh5I3kylBnTp1kJCQAEEQoKuriyFDhmD06NFo165dqdqbm5sjLCxM1jCIiIiIqBoy1TPF0e+PYvWZ1Zj510zk5Obg79C/4bjQEdtHb0eP5j0UGk9kShbKstvc5fhU+QdDJCcy32l8/fo13NzcsGHDBsTGxmLLli2lThgBYO3atTh//rysYRARERFRNaWiooKpXafi72l/w8LYAgCQ8D4BPX/uiWn7piErJ0thsVjqqkt9p5GoopP5TuPjx4/RuHHjMrd3cHCQNQQiIiIiIrSxboO7c+9i1JZROBx0GACw8tRK/B3yNzytPBUSw2hrI6wow1TT9jV1yiEaIvmQ+U5jXFxcqZ9JvHfvHi5fvixrl0RERERERTLWNcZBr4P4adBPUFfNW0/jesR1/HD5Bxy5d6Tc+2+kr4FNruZQAaAqAlREef8t6ebjFDuTco+NqKxkThrd3d0xfvz4UtWdMGECOnToIGuXREREREQSiUQiTOw0EVenX4WliSUA4H3We/T/rT9+2PsDMrPLd6XSkVZGeNLLGlObmGBgfQNMbWKC0+71i23jcOIp1PweQf+Px1j2ML5c4yOSlly23BCkeNpXmrpERERERGXl0tAFd+feRV/HvuKyNWfX4OPlHyMiPqJc+7bR18BSRzPsaVsXSx3N8NPjN8XWT80RkCMA73MEzLz3GrZHuVAkVRxy3aexJAkJCdDW1lZkl0RERERUjRnpGGHvmL0Y22wsNNQ0AAABkQFoubAl9t/er7A4zr5Mkap+SHIWVga/LqdoiKQj9UI4SUlJSExMLFCWkZGB6OhoiXcR09LScOnSJTx48IAL3xARERGRQolEIvSw7AHPXp4YumkowuPD8S7tHQb8NgBeHl5Y9fkqqEK1XGPIKsNkO58HrzHV3lT+wRBJSeqk8aeffoKPj0+Bslu3bsHS0rJU7T09FbNyFRERERHRh1patMSdOXcwdsdY7A3YCwDwveCLa+HXsGv0rnLtW0NFhIxc6TLHNCnrE5UXqZNGIyMjWFhYiL+OioqChoYGateuXWR9kUgEbW1tWFlZYdCgQRg2bFjZoyUiIiIikoGBtgH2jNmDDk06YPye8cjIzsDdqLtwXeaKsXZj0QM9yqXfjrV0cDxWuimq2irc8JEqBqmTxgkTJmDChAnir1VUVODi4sKtNIiIiIioUhCJRBjbfizcrNwwcP1APIl7guT0ZKy+uxrvdr/Dz0N+hraGfNfhWNOqNo4fDZeqzdxmnJpKFYPMC+Fs2bIFs2bNkkcsVdLu3bvh7OwMbW1tmJiYoHPnznj9mg81ExERESlbi3otcGv2LQx3Gy4u23hlI1yXuOJx7GO59tVIXwNbXM1L3K8xX2N9dT7PSBWGzEnjiBEj0K1bN3nEUuUsX74co0aNQrdu3XD8+HFs27YNDg4OyMjIUHZoRERERARAT0sP20Zvw4bhG6Chkre66v0X9+G82Bk7/HfIta+RVkYI6WWNGXYmGGxhgBl2JuhfX7/Iuu1q6si1byJZSDU9NSoqCgCgrq4Oc3PzAmXS+PCZyKoqJCQE3t7e8PX1xdixY8XlvXr1UmJURERERPRfIpEII9qMQFpUGv4X8j88in2ElIwUfLn5S1x4cgHrhqwTJ5Syyt+/EQDOxL7HskcJRdbb9PQdhjQwRMfaunLpl0gWUiWNlpaWEIlEaNKkCR4+fFigrLREIhGys7Oli7IS2rJlC7S0tDBy5Ehlh0JEREREpWChbwH/6f6Y9OckbL66GQCw5eoW3Hh6A7s85b+66vjbccUe//5WLIJ72ci9XyJpSTU91cLCAhYWFuK7jB+WlfZVv359uQQeERGBDRs2YMyYMXBwcICamhpEIhEWLVpUqvbHjx9Hp06dYGxsDF1dXTg5OWHdunXIzc2VS3z+/v6wtbXFtm3b0KBBA6ipqaFly5Y4deqUXM5PRERERPKno6GDTSM3Yfvo7dDVzLvLFxwbjI+Wf4SzUWcl7kteFk/fZxV7PLyE40SKItWdxsjIyFKVKcLatWuxdu3aMrVdtmwZZs6cCQCwsrKCnp4egoKCMH78eJw9exYHDhyAiopsj3vGxcXhxYsXmDdvHpYvXw4zMzP89NNP+PTTT3H//n3Y2trKdH4iIiIiKj/D2wyHi6ULBq4fiPsv7iMtKw2/3PsFb7a9wfrh66GnpSd7JyIAxeWg3HGDKgiZF8JRFlNTU/Tq1Qs+Pj44ceIE+vfvX6p2/v7+mDVrFlRUVLB7926Eh4cjKCgId+7cQa1atXD48GH8+OOPBdokJyfj8ePHJb7evXsnbpOTk4P3799j48aNGD58OLp27YoDBw7A2NgYq1atkut7QURERETy18S8CW7MuoFx7ceJy3bf3I1Wi1rh3vN7Mp/fWq/45yT11FQw5OoLzAx8hdDkTJn7IyqrSps0ent748iRI5gzZw66desGPb3S/bVn0aJFEAQBX331FYYMGSIud3BwECeLy5YtQ1bWv9MBjh07Bjs7uxJfBw4cELcxNjYGAHh4eIjLtLW14ebmhuDgYJmunYiIiIgUQ1tDG78N/w07Ru+Atlre3o0hL0PQenFrrL+0XqbpqmudahV7/E1mLvyikrD8UQJsj4Zj69PEMvdFJIsyrZ4qK2WtnpqUlISzZ88CADw9PQsd//zzz/HNN98gISEBFy5cQJcuXQAAgwcPxuDBg6Xqq2nTpggICChULggC0tPTyxA9ERERESnLIOdBeB/xHuvD1iMwOhAZ2Rn4eufXuPDkAnwH+5bpnJ3N9eBpZYhNT98VWy8/LR19IxYf19SBjb58VnIlKi2p7jRaWlqiYcOGMr2srKzK61pKdPfuXWRmZkJLSwtOTk6Fjqurq8PFxQUAcOPGDZn66tWrFwRBwLlz58Rlqamp8Pf3R6tWrWQ6NxEREREpnrmuOS5PuYzvPL4Tl+0N2Au3ZW4IfxdepnNudK2Dsx4WcDPRgoWOGsw0JH88FwCskrBFB1F5kupOo4WFhVTba1Q0oaGhAPKuQ02t6Eu3srLCuXPnxHXLqm/fvmjdujW++uorLFu2TLwQTkpKCiZPniyxXUZGBjIyMsRfJyUlAQCysrIKTJmt6PJjVVTM8uxPlnNJ21aa+qWpW1Kd4o4r+nsmLxxrHGuKwrHGsaYoHGsVe6ypQhU/fv4jPrb5GON2jsO7tHcIiw/D9ITpgBnwXYfvpP683N5EA5c96gEAGh8JgzZyJNY9/SIRWVmmUp1fEo61ij3Wivu9pmgiQZ7rBivRyJEjsW3bNixcuBDe3t5F1lm5ciWmTZsGV1dXXL9+vcg606dPx4oVK9CrVy8cOXJEpphev36NKVOm4PDhw0hLS4OrqytWrFiB1q1bS2wzf/58LFiwoFD57t27oaOjI1M8RERERCQ/cSlxWH1nNULf/Xuzwa22G75z+A566nJYXZXoP1JTUzF06FC8e/cOBgYGCutXqjuNlV3+s4QaGpLngWtqagIA0tLSZO7P1NQUW7dularNzJkzMWnSJPHXSUlJqF+/Pjw8PGBiYiJzTIqSlZWFM2fOoHPnzlBXV69U/clyLmnbSlO/NHVLqlPccUV/z+SFY41jTVE41jjWFIVjrXKNtWH9hmHGXzPwy8VfAADX464jLisOuzx3wcXSpcTr+C/DfU9KrPNugHy2buNYq1xjDQASEpQzPblaJY1aWloAgMxMyUsW508N1dbWVkhM/6WpqSlOXD+krq5eqf6Hl0/RccuzP1nOJW1baeqXpm5JdYo7zrGm+P441ioXjjX51+dYKxrHmvzrl8dYU1dXx48Df4TBewP8L/h/eJv6FpEJkXBf7Y7l/ZdjYqeJUk1XTYdqiVs3yntccKzJv355/V5T1u+ySrvlRlnUqFEDAPD27VuJdfKP5dclIiIiIipJ69qtcXPmTbSxbgMAyMrJwqQ/JqGvb1+8SXlT6vNoqhSfYGqVcJyoPJRpyw11dXWYm5sXKJOGsrbcaNSoEYC8mLOzs4tcDOfp06cF6hIRERERlUYDkwa4NOUSvA96Y8WpFQCAw0GH4ejjCL8xfvjI5qMSz9HEQAOBiRkSj9sacLsNUjypkkZLS0uIRCI0adIEDx8+LFBWWiKRCNnZ2dJFKSctW7aEuro60tPTcefOnUIL0mRlZYn3VnR1dVVGiGK+vr7w9fVFTo7k1bOIiIiIqGJRV1PH8gHL8YntJ/hy85dIeJ+A6DfRaL+yPZb0W4IpXaZARUXyZL9BFvrFJo01NFQw5OoLWOqqY7S1ERpxz0ZSgDJtuZF/l/HDssrAwMAAnTp1wokTJ7Bp06ZCSeOff/6JpKQkmJiYwN3dXTlB/sPLywteXl5ISkqCoaGhUmMhIiIiIun0aN4DgXMCMXTjUPwd+jdycnMwff90XHxyEdtGb0NN/ZpFtjv04n2x573wKg1AGkQAlj9KwGZXc4y0MpJ7/EQfkippjIyMLFVZRTZ79mycPHkSGzduhLu7O4YMGQIACAoKEq9aOm3atGJXWCUiIiIiKkk943o4P/k85h+ejyUnlkAQBJx4cEI8XbVd43aF2sSklW5GXv5iOaNvxOLjmjqw4R1HKkeVdiGcq1evwtTUVPzy8/MDACxdurRAeXR0dIF2bdu2xcKFC5Gbm4uhQ4fC2toaDg4OcHJywsuXL9GzZ09MnjxZGZdERERERFWMmqoaFvVbhFMTT8FM3wwAEJMYA/dV7lh8bDFyc3ML1K+jLd3mBgKAVY+Usw0DVR+VNmnMyspCQkKC+JW/VUZqamqB8qKeCZw9ezaOHDmCDh06ICEhAWFhYWjevDnWrFmDQ4cOQVVVVdGXQ0RERERVWGf7zgicGwgPWw8AQK6QC++D3ui2thteJr0U1/NpXvS01eJcjk+VW5xERZHbPo0ZGRnw8/PDqVOnEBISguTkZOjr66Nx48bo0qULBg8eLN4nUR7c3d0hCMXtYlO8Xr16oVevXnKLh4iIiIioOOZG5jgz6QwWHV2EBUcXQBAEnAk+A0cfR+zy3IUOdh3Q2VwPnlaG2PT0nbLDJRKTy53Ga9euwc7ODqNHj4afnx/u3LmD0NBQ3LlzB35+fvD09ISdnR2uXr0qj+6qBV9fX9jb28PFxUXZoRARERGRnKiqqGJe73k4N+kcahvWBgDEvYtDp586Yf7h+cjJzcFG1zo462EBNxMtWOiowUyz+I/s7WvqKCByqs5kvtP48OFDdO7cGWlpaahduza++uor2NnZoVatWnj16hUePXqETZs24dmzZ+jSpQtu3LiBZs2aySP2Ko2rpxIRERFVXR5NPBA4NxDDNw3HmeAzEAQBC44swKWQS9j91W50rG2OjrUbAgBCkzNhezQcRc2xEwGYYmei0Nip+pH5TqO3tzfS0tIwbNgwPHv2DD4+PhgyZAg6dOiAwYMHY8GCBYiIiMDw4cORlpaGuXPnyiNuIiIiIqJKrZZBLZyccBKL+y6GiijvY/nFJxfh4OOA0w9Pi+s10tfAZlfzQu1FADa7mnPlVCp3MieNly9fhoGBAX7//Xeoq6sXWUddXR3r16+HgYEBLl68KGuXRERERERVgoqKCmb1nIWLUy6irlFdAEB8cjy6re2G2QdmIzsnbwsOAXlJ4ocqx07pVBXInDRmZmbC1ta2xEVutLS0YGtri6ysLFm7JCIiIiKqUto1bofAuYHo3qw7AEAQBCw5vgQeqzzwd/RTfHUjttD01FwAnjdiEZacqfB4qXqROWm0s7PD8+fPS1U3OjoaTZs2lbVLIiIiIqIqx1TfFEe/P4oVA1ZAVSVvC7grYVfQdYULkHCpyDYiEbApPFGBUVJ1JHPSOHHiRMTGxmLt2rXF1vv5558RFxeHiRMnytolEREREVGVpKKigqldp+LvaX/DwtgCAJCW/ga5Qd8AYauA3IKz9gQAkSmcyUflS+akcejQoVi+fDmmT5+Ozz77DGfPnsWLFy+QlZWFmJgYnDt3Dv3798e0adOwYsUKDB48WB5xV3nccoOIiIio+mpj3QZ3595Fb4fe/xZGbQbufAmkvRAXiQBY6ha9rgiRvEi15Yaqqmqxxw8dOoRDhw5JPD59+nTMmDED2dnZ0nRbLXHLDSIiIqLqzVjXGAe9DsL72GosOTwTELKBpCAgoD9gtxio2RGCAHhaGyk7VKripLrTKAiCzK/c3NzyuhYiIiIioipFJBJhca8pmPPlKUCrXl5hdhJw/3sgdBnWO5twyw0qd1Iljbm5uXJ5ERERERFR6fl83AG359xGA8se/xZGb8f6vT3xNP6p8gKjakHmZxqJiIiIiKj8OZmZIXzmEejYzQVEec8x3np2Cy0XtsT+2/uVHB1VZUwaiYiIiIgqCVUVFXRvPQZw3gNo562umpSWhAG/DcB3u79Dela6kiOkqkiqhXCKk5KSgiNHjiAoKAhv3rxBVlbRS/+KRCJs2rRJXt0SEREREVUrHWrpYH+0PeCyDw4vlyLoyQEAgO8FX1wLv4a9Y/eiUa1GSo6SqhK5JI1+fn745ptvkJSUJC4TBAFAXpL4YRmTRiIiIiKisutQSzfvH2p6qN3qJ3zbuhsm+E1AelY67kbdRatFrfD78N8xuDW3uiP5kHl6qr+/P4YPH46cnBzMnj0bNjY2AIANGzZg7ty56N27N0QiEbS0tLB48WJs3rxZ5qCrA+7TSERERERFsdXXgLl23r2fK6/TMLLtGNyYdQO2tW0BAMnpyRiyYQjG7RiHtMw0ZYZKVYTMSeOqVauQm5uLXbt2wcfHB2ZmZgAAT09PzJ8/HwcOHMCDBw9gZWUFX19fdOvWTeagqwMvLy8EBwcjICBA2aEQERERUQUiEonQwUwHAJCSLSDgTRpa1GuBW7NvYbjbcHG93y//Dtclrngc+1hZoVIVIZc7jaampvj0008l1mnSpAn279+P2NhYzJs3T9YuiYiIiIiqNfEUVQDnX6YAAPS09LBt9DZsHrkZ2hraAID7L+7DebEzdvjvUEqcVDXInDQmJCTAwsJC/LWGRt7moikpKQXqNW7cGE2bNsWJEydk7ZKIiIiIqFrrUEtH/O/zL1PF/xaJRBjVdhQCZgXA3tweAJCSkYIvN3+J0VtHIyUjpdC5iEoic9JoYmKCtLR/50qbmpoCAMLDwwvVzcnJwcuXL2XtkoiIiIioWrPU00B9nbznGi+/SsXUuy8RmpwpPt60blMEzA7A6LajxWVbrm5B68Wt8fDFQ4XHS5WbzEmjpaUlYmNjxV87OTlBEATs2rWrQL2goCCEhISgZs2asnZJRERERFStbXmaiOjUbABALoBVj9/A9mg4tj5NFNfR0dTBppGbsMNzB3Q186azBscGw2WJCzZf2Sze7YCoJDInjZ07d0ZiYiIePsz7i8XQoUOhpaWFVatWYdiwYfD19cXcuXPRsWNH5Obmon///jIHTURERERUXYUmZ8LzRmyhcgHA6BuxCPvgjiMADHMbhluzb6FFvRYAgLTMNHhu88TIrSORls3VValkMieNAwcORIcOHfDkyRMAQP369fG///0Pampq2L17N8aPH4/FixfjzZs3cHV1xaJFi2QOmoiIiIioulr1KAGS7hEK/xz/rybmTXB95nWMaz9OXLYnYA8m/z0ZQc+DyidQqjLUZD1B06ZNcebMmQJlI0aMQLt27fDHH38gMjIS2tra+Pjjj9G3b1+oqqrK2iURERERUbV1Lq74xWz2RiXhXVYuLHXVMdraCI308xaq1NbQxm/Df4O7rTvG7hiL5PRkxKTE4OMVH2Pt4LUY234sRCKRIi6BKhmZk0ZJrKysMGPGjPI6fZXn6+sLX19f5OTkKDsUIiIiIqpAEjKziz2emJULv6gkiAAsf5SAza7mGGllJD4+uPVgOFs6Y+BvA3E3+i4ysjPw9c6vceHJBfw+/HcYaBuU7wVQpSPz9FQqH15eXggODkZAQICyQyEiIiKiCqV0dwMFSH7O0cbMBpenXEYPyx7isr0Be+G00Al3nt2RY6xUFcgtaczIyMC2bdswdOhQODs7w9bWFs7Ozhg6dCi2bt2K9PR0eXVFRERERFRtmWhK97iXpOccNdU1MbbZWPiN8YOhtiEAIDw+HG2WtcEv53/h6qokJpek8dq1a7Czs8Po0aPh5+eHO3fuIDQ0FHfu3IGfnx88PT1hZ2eHq1evyqM7IiIiIqJqq2MtXanbXI5PlXjss5af4e6cu3CxdAEAZGZn4vs932PAbwOQmJpY1jCpCpE5aXz48CE6d+6MyMhI1KpVC97e3ti1axfOnj2L3bt3Y86cOTA3N8ezZ8/QpUsXPHjwQB5xExERERFVS1PsTEo5QfVfKdm5xR5vWLMhrky/gh86/SAu++vOX2jp0xI3I26WIUqqSmROGr29vZGWloZhw4bh2bNn8PHxwZAhQ9ChQwcMHjwYCxYsQEREBIYPH460tDTMnTtXHnETEREREVVLjfQ1sNnVHCrIe7qxNAlkek7JU0011DTw46AfccjrEGro1AAARCZE4uPlH+OnMz9xumo1JnPSePnyZRgYGOD333+Hurp6kXXU1dWxfv16GBgY4OLFi7J2SURERERUrY20MsKTXtaYbmeCQRYG0FMrPnVUUyn9vcnejr1xd+5dtLFuAwDIysnCpD8moY9vH7xJeSNT3FQ5yZw0ZmZmwtbWFlpaWsXW09LSgq2tLbKysmTtkoiIiIio2rPR18BSRzPsaVsXzQw1i61roSPdTnsNTBrg0pRLmNZ1mrjsSNAROPo44lrYtTLFS5WXzEmjnZ0dnj9/Xqq60dHRaNq0qaxdEhERERHRB3ya1yz2+KIWZlKfU11NHcsHLMex8cdgomcCAIh+E432K9tjxckVyM0t/jlJqjpkThonTpyI2NhYrF27tth6P//8M+Li4jBx4kRZuyQiIiIiog90NteDp5Vhkcc8rQzRsbb0K67m69G8BwLnBKJdo3YAgJzcHEzfPx291vVCfHJ8mc9LlYfMSePQoUOxfPlyTJ8+HZ999hnOnj2LFy9eICsrCzExMTh37hz69++PadOmYcWKFRg8eLA84iYiIiIiog9sdK2DQ+3qir/WVRXhrIcFNrrWkfnc9Yzr4fzk85jdYzZEorznI088OAFHH0dcDrks8/mpYpNqcrOqavEbiR46dAiHDh2SeHz69OmYMWMGsrOzpem2WvL19YWvry9ycnKUHQoRERERVRK96xnAWu8Vwt9nQQDgbqYjt3OrqaphUb9F+MT2EwzbOAyvkl8hJjEGHqs84NPHBzO7z4SKily2gacKRqrvqiAIMr8497l0vLy8EBwcjICAAGWHQkRERESViINR3gKVqTkCwt9nyv38ne07I3BuIDxsPQAAuUIuvA96o9vabniZ9FLu/ZHySZU05ubmyuVFRERERETlw6HGvyupBiVmlEsf5kbmODPpDOZ/Ol88XfVM8Bk4+jji/KPz5dInKQ/vHxMRERERVSH5dxoBICgxvdz6UVVRxbze83Bu0jnUNqwNAIh7F4dOP3XCvEPzkJPLx6yqCiaNRERERERViIPRB3ca35bPncYPeTTxQNDcIHS27wwg75E2n6M+6PRjJ8QkxpR7/1T+5J40hoSE4OjRo9izZw+OHj2KkJAQeXdBREREREQSNNBVh6F63sf88rzT+CEzAzOcnHASi/suhooor++LTy7C0ccRpx+eVkgMVH7kljSuX78eVlZWsLOzQ58+fTBs2DD06dMHdnZ2sLa2xoYNG+TVFRERERERSSASidDin7uN0anZeJOhmGmiKioqmNVzFi5OuYi6Rnlbf8Qnx6Pb2m6YfWA2snO4g0JlJZekcdSoUfj2228RGRkJDQ0NWFtb46OPPoK1tTU0NDQQERGBr7/+GqNGjZJHd0REREREVIwPn2u8p6C7jfnaNW6HwLmB6NG8B4C86apLji9B5zWd8TrttUJjIfmQOWncvXs3tm3bBh0dHaxYsQLx8fEICQnB33//jZCQEMTHx2PFihXQ1dXF9u3bsWfPHnnETUREREREEihiBdXimOqb4sh3R7BiwAqoqeZtDX81/Cp+uPwDTjw4ofB4SDYyJ40bNmyASCTC/v37MWXKFOjp6RU4rqenhylTpmDfvn0QBIHTVImIiIiIylmBFVTfKvZOYz4VFRVM7ToVl6dehoWxBQAgOSsZfX7tg2n7piErO0spcZH0ZE4ag4KCYGVlhS5duhRbr0uXLrCxscHdu3dl7ZKIiIiIiIrRzFATKnnbJyrlTuOH2li3wd25d9GrRS9x2cpTK9F+ZXs8S3imxMiotGROGtPT02FkZFSqugYGBsjIUO6gJSIiIiKq6rTVVNBYXwMA8PBdBrJzBaXGY6xrjP3j9mO0/Wioq6oDAK4/vY6WPi1xKPCQUmOjksmcNFpYWODBgwd4/br4h1rj4+Px8OFDWFhYyNolERERERGVwEo3LznLyBXwdUAcQpMzlRqPSCRCb6veuDT5EhqaNgQAvE19i76+fTHRbyIys5UbH0kmc9LYu3dvZGRkYNCgQYiPjy+yzqtXrzBo0CBkZmaiT58+snZJRERERETF2PI0EcdjU8Rfb3qaCNuj4dj6NFF5Qf3D2dIZd+bcQX+n/uKytefWou2ytnga/1SJkZEkarKeYMaMGfDz88PFixfRoEEDfP7557C3t4eZmRlevXqF4OBg/Pnnn0hPT0f9+vUxffp0ecRd5fn6+sLX1xc5OYrZV4eIiIiIqobQ5Ex43ogtVC4AGH0jFh/X1IHNP1NXlcVIxwh/fv0nfr34Kyb9MQmZ2Zm49ewWWi5siU0jNmFAqwFKjY8KkjlpNDY2xvnz5zFkyBDcvn0bO3bsgEgkEh8XhLz50y4uLti9ezeMjY1l7bJa8PLygpeXF5KSkmBoaKjscIiIiIioklj1KAGSnmAU/jn+W2tzRYZUJJFIBC8PL3xk/REGrh+IsFdhSEpLwue/fY5v3b/F6oGroaWuVfKJqNzJnDQCgI2NDQICAnDu3DmcPn0aISEheP/+PfT09NC4cWN07doVHTp0kEdXRERERERUjL/jU4s9frmE44rW0qIlbnvfxrgd4+AX4AcA+PXir/B/6o+9Y/eiUa1GSo6QZE4ao6KiAAD16tVDx44d0bFjR5mDIiIiIiKissnMKX6l1OjULMwMfIURDXQVFFHJDLQNsHvMbng08cAEvwlIz0rH3ai7cFrohA1fbsDg1oOVHWK1JvNCOJaWlnB1dZVHLEREREREJCN99eI/4r/PFrDycQKcT0YoKKLSEYlEGNt+LG7MugHb2rYAgPcZ7zFkwxCM2zEOaZlpSo6w+pI5aTQ0NESDBg2goiLzqYiIiIiISEZ1ddRLrJMjALn//PuH2y+Vvh3Hh1rUa4Fbs29huNtwcdnvl3+H6xJXPI59rMTIqi+ZM73mzZuLp6gSEREREZFyNTfUlOpD/paIRDSpINtx5NPT0sO20duweeRmaGtoAwDuv7iPVotaYfu17UqOrvqROWmcMGEC4uLisHnzZnnEQ0REREREMhhtbSRVfQF5dx09b8QirALdcRSJRBjVdhRuzb4Fe3N7AEBqZipGbBmBr7Z/hfTsdCVHWH3InDT2798fy5Ytg5eXF3744QfcuXMHaWmcb0xEREREpAyN9DWwydUcKgBURSVWFxMAbApPLKeoys6+jj0CZgdgdNvR4rLt17dj6pWpeBjzUImRVR8yJ42qqqqYOXMmMjMz8fPPP8PFxQV6enpQVVUt8qWmJpddPoiIiIiISIKRVkZ40ssaU5uYoKe5LkqTOwoA7idmlHdoZaKjqYNNIzdhh+cO6Grmrfoa/T4aHy3/CJuvbBbvDU/lQ+akURAEqV65ubkln5SIiIiIiGRio6+BpY5mOOpugc3/3HksSUJmdrnHJYthbsNw2/s2mtdtDgBIy0qD5zZPDN80HMnpyUqOruqSOWnMzc2V+kVERERERIqTf+fRWq/4lVVNNCv+rEDb2ra4MvUKulp0FZfturELzoucERQdpMTIqi7uk0FEREREVA3Y6Gvg8/oGEhMAFeStvFoZaGto45sW32Dn6J3Q19IHAIS8DIHrElesv7Se01XlrMxJY2pqKg4dOoRVq1Zh1apVOHjwIFJSUuQZGxERERERyVFJK6t6SrnyqrINdB6IO3PuwMnCCQCQkZ2Br3d+jcG/D0ZSWpKSo6s6ynT/+dixYxg1ahQSEhIKlBsbG2PDhg3o27evPGIjIiIiIiI5yl9Z1fNGbIFyFQCbXM1ho6+hnMBkYGNmg2szrmHKn1Pwy4VfAAB/3PoDt5/dxh/j/oBTAyclR1j5SX2nMTg4GAMGDMDr16+hoaGBpk2bwt7eHhoaGkhISMDgwYNx79698oiViIiIiIhklP98o8Y/S6oaa6jgSS9rjLQyUmpcstBU18S6oeuw7+t9MNQ2BACEx4ejzbI2WHduHaerykjqpHH16tXIyMhA586dERkZiXv37uH+/fuIiIhAx44dkZmZiR9//LE8YiUiIiIiIjmw0deAhmpeKlBTU61S3mEsSv9W/XF3zl24WLoAADKzMzHebzwG/DYAiamJyg2uEpM6abx06RI0NTWxc+dO1KpVS1xeu3Zt7Nq1CxoaGrh06ZJcgyQiIiIiIiqNhjUb4sr0K/ih0w/isr/u/IWWPi1xM+KmEiOrvKROGmNiYtCoUSPUrFmz0DEzMzM0atQIcXFxcgmOiIiIiIhIWhpqGvhx0I845HUINXRqAAAiEyLRdnlbrDm3htNVpSR10pieng4jIyOJx42MjJCZmSlLTERERERERDLr7dgbgXMD0ca6DQAgOycb0/ZPw5JbS/Am5Y2So6s8uE8jERERERFVWRYmFrg05RKmdZ0mLgt4GQCXJS64FnZNiZFVHmXacuPVq1fYvn27xGMAsGPHDom3fb/88suydFut+Pr6wtfXFzk5OcoOhYiIiIioUlNXU8fyAcvhbuuOLzd/idfvXyP6bTTar2yPJf2WYEqXKVBR4f00ScqUNIaGhmLUqFHF1hk5cmSR5SKRiEljKXh5ecHLywtJSUkwNDRUdjhERERERJVe9+bdETArAD1X9UTwm2Dk5OZg+v7puPjkIraN3oaa+oXXbaEyJI0WFhYQiUTlEQsREREREVG5qmtUFwvdFuKWcAvLTi6DIAg48eAEHH0csWfMHrRv3F7ZIVY4UieNkZGR5RAGEREREREpSmhyJjJzcgEA8RnZCE3ORKMqsldjaaiqqGJBjwXwaOKBYRuH4VXyK8QkxsBjlQcW9F6AmT1mQlVFVdlhVhicuEtEREREVI1seZqIJkfDkfnP8iNvMnPR5Gg4tj5NVGpcytDZvjMC5wbCw9YDAJAr5GLOoTnotqYbXia9VHJ0FQeTRiIiIiKiaiI0ORNf3YhF7n/KcwF43ohFWHL12zrP3MgcZyadwfxP54sfwzv76CwcfRxx/tF5JUdXMTBpJCIiIiKqJjaHJ0LS8iQCgN6XozEz8BVCq1nyqKqiinm95+HcpHOobVgbABD3Lg6dfuqEBUcXIEeo3jsaMGkkIiIiIqomIlOyIGFXPAgAHiVlYuXjhGo7XdWjiQeC5gahi30XAIAgCFh8fDHmXZ+HmMQYJUenPEwaiYiIiIiqCUtddYl3GvPlCNV7uqqZgRlOTDiBxX0XQ0WUly49SHgAlyUuOP3wtJKjUw4mjURERERE1cRoayOJdxr/SwAw3P9FtZuqCgAqKiqY1XMWLk65iLpGdQEA8e/j0XVNV8z6axayc7KVHKFiMWkkIiIiIqomGulrYJOrOVQAqJZwx1EAcCMhvdpOVQWAdo3bIWBWAFqZtRKXLT2xFB6rPPD8zXMlRqZYTBqJiIiIiKqRkVZGeNLLGhMaGwMAissdBVTvqaoAYKpnitkus7G031KoqeZtc38l7AocFzri2L1jSo5OMZg0EhERERFVMzb6GpjXvCaA4pPGfCIRsCk8sVxjqshURCqY3HkyLk+9DAtjCwBAwvsE9FrXC1P/nIqs7CwlR1i+mDQSEREREVVjvzjXhgpKvuMYmVK1E6PSaGPdBnfn3kVvh97islWnV6H9yvZ4lvBMiZGVLyaNRERERETV2BeWhnjSyxquJloSE0cR8lZeJcBY1xgHvQ5izaA1UFfNe0+uP70ORx9HHA46rOToygeTRiIiIiKias5GXwPb29SVmDQKAuBpbaTIkCo0kUiECZ0m4Or0q2ho2hAAkJiaiAHrB2Djw43IzK5az38yaSQiIiIiomJXVt3QujZs9DWUEldF5tLQBXfm3EF/p/7isqMRR/HJqk/wNP6pEiOTLyaNREREREQE4N+VVac2MUFtLVVxuZGGajGtqjcjHSP8+fWf8B3qCw21vMT6dtRttFzYEvtu71NydPLBpJGIiIiIiMRs9DWw1NEMW1zriMt+evJGiRFVfCKRCN96fIu/p/4Ncx1zAEBSWhI+/+1zeO3yQnpWupIjlA2TRiIiIiIiKqSruS7sDPLunF2JT8OthDQlR1TxtazfEqvbrcZA54Hisl8v/oo2S9sg9GWoEiOTDZNGIiIiIiIqRCQSYaKtsfhr3m0sHR11HewYtQO/D/8dWupaAIDA6EA4LXTCnht7lBxd2TBpJCIiIiKiIg23NITJP88z/hGVhBep3KuxNEQiEca0H4Mbs27AtrYtAOB9xnsM3TgU3+z6Bhk5GUqOUDpMGomIiIiIqEjaair4upERACBbAH4JeavcgCqZFvVa4NbsWxjuNlxctunqJky7Mg2P4x4rMTLpMGkkIiIiIiKJvBrVgPo/WcP68LdIyc5VbkCVjJ6WHraN3obNIzdDW0MbAPAs+Rnclrlh+7XtSo6udJg0lhN3d3eIRKIiX8uWLVN2eEREREREpWKurY4hFoYAgLeZudge8U7JEVU+IpEIo9qOwq3Zt2Bvbg8ASM1MxYgtIzBqyyikZKQoOcLiMWksJ7/++iv8/f0LvL799lsAQI8ePZQcHRERERFR6f3Q5N8FcdY8eYNcQVBiNJWXfR17XJt+DR3rdxSXbb22Fa0Xt8bDFw+VGFnxmDSWE3t7e7i5uRV4BQQEoHnz5mjRooWywyMiIiIiKjXHGlpwN9MBAIQkZ+JEzHslR1R56Wjo4HuH77FlxBboauoCAIJjg+GyxAWb/t4EoQIm5EwaFSQ0NBQBAQEYNmyYskMhIiIiIpLaD9x+Q66+cP0Ct71vo0W9vBtKaZlp+Gr7Vxi5dSTSsivWnpiVNmmMiIjAhg0bMGbMGDg4OEBNTQ0ikQiLFi0qVfvjx4+jU6dOMDY2hq6uLpycnLBu3Trk5pbPg707d+6EiooKhg4dWi7nJyIiIiIqT73q6sFGTx0AcO5lKu69TVdyRJWfbW1bXJ95HePajxOX7QnYg8l/T0bQ8yAlRlZQpU0a165di7Fjx2Ljxo24d+8ecnJySt122bJl6NmzJ86dO4caNWrAxsYGQUFBGD9+PPr161cuiePu3bvxySefoF69enI/NxERERFReVMRiTDBtuCzjSQ7bQ1t/Db8N/iN9YO+lj4AICYlBh+v+Bi/XfytQkxXrbRJo6mpKXr16gUfHx+cOHEC/fv3L1U7f39/zJo1CyoqKti9ezfCw8MRFBSEO3fuoFatWjh8+DB+/PHHAm2Sk5Px+PHjEl/v3hW9ktT169cRFhbGqalEREREVKmNbGgEo3/239j1LAkv07KVHFHVMchlEO7MuYOW9VsCADKyM/DNrm8w+PfBSEpLUmpslTZp9Pb2xpEjRzBnzhx069YNenp6pWq3aNEiCIKAr776CkOGDBGXOzg4iJPFZcuWISsrS3zs2LFjsLOzK/F14MCBIvvcuXMntLS0MGDAABmumIiIiIhIufTUVTDG2ggAkJkr4H9hb5UbUBVjY2aDy1Muo6dlT3HZH7f+gNNCJ9x+dltpcVXapLEskpKScPbsWQCAp6dnoeOff/45DAwMkJCQgAsXLojLBw8eDEEQSnyNHDmy0Dmzs7Pxxx9/4NNPP4WBgUG5XRsRERERkSJ839gYqqK8f/8a+hbpOeWzJkh1pamuiTHNxmDvmL0w1M7bHzM8PhwfLfsIG65uUEpM1SppvHv3LjIzM6GlpQUnJ6dCx9XV1eHi4gIAuHHjhlz6PHXqFOLj4zk1lYiIiIiqhPq66hhQP+9mSHxGDnZHKnfqZFXVr2U/3J1zFy6WeflJZnYmZh6ZqZRY1JTSq5KEhoYCACwsLKCmVvSlW1lZ4dy5c+K6stq5cydMTEzQvXv3UtXPyMhARkaG+Ov85yTfvKlcDxpnZWUhNTUVCQkJUFdXr1T9yXIuadtKU780dUuqU9xxRX/P5IVjjWNNUTjWONYUhWONY01RZIl7TC3g0OO8z6nr7qSjt2F9iESicutPnueqTGPNQN0Ah746hIUnF+J/V/4nrqPoxXGqVdL49m3enOsaNWpIrJN/LL+uLN6/f4/Dhw9j5MiRpR7MS5cuxYIFCwqVN27cWOZ4iIiIiIjkLRBATWUHUc0kJCTA0NBQYf1Vq6QxPT1vLxkNDQ2JdTQ1NQEAaWmyb6ipp6eHlJQUqdrMnDkTkyZNEn+dmJiIBg0aICoqSqEDQx5cXFwQEBBQKfuT5VzStpWmfmnqllRH0vGkpCTUr18f0dHRle75W441+dfnWCsax5r863OsFY1jTf71OdaKxrEm//rlOdbevXsHCwsLGBsbF9Gq/FSrpFFLSwsAkJmZKbFO/tRQbW1thcT0X5qamuLE9UOGhoaV7peQqqqqQmOWZ3+ynEvattLUL03dkuqUdNzAwIBjTYH9caxxrCmqP441jjVF9cexxrGmqP6q81hTUVHs0jTVaiGc0kw9Lc0UViodLy+vStufLOeStq009UtTt6Q6iv6+KALHmvzrc6wVjWNN/vU51orGsSb/+hxrReNYk3/9qjjWRIKin6IsJyNHjsS2bduwcOFCeHt7F1nn0qVLcHd3h5aWFpKTk4tcDKdTp044d+4cfHx8MGfOnPIOu0RJSUkwNDTEu3fvKt1frqhy4VgjReFYI0XhWCNF4VgjRVHWWKtWdxpbtmwJdXV1pKen486dO4WOZ2VliecOu7q6Kjq8ImlqamLevHlFTlklkieONVIUjjVSFI41UhSONVIUZY21anWnEQB69OiBEydOYOzYsVi/fn2BY7t378YXX3wBExMTxMTEFLtgDhERERERUXVQre40AsDs2bMhEomwceNG7NmzR1weFBQkXrV02rRpTBiJiIiIiIhQiZPGq1evwtTUVPzy8/MDkLfP4Yfl0dHRBdq1bdsWCxcuRG5uLoYOHQpra2s4ODjAyckJL1++RM+ePTF58mRlXJJcREZGok+fPtDX10eNGjUwfPhwvH79WtlhURXz/PlzfP/993B1dYWWllaJm/kSldW+ffvQr18/WFhYQEdHB02bNsXq1auRlZWl7NCoijl16hTc3d1hZmYGTU1NNGjQAGPGjMGLFy+UHRpVYdnZ2WjRogVEIpH4syyRvFy8eBEikajQy9nZWepzVdotN7KyspCQkFCoPDU1FampqeKvc3JyCtWZPXs2HBwc8NNPP+H27duIi4tD8+bNMWrUKHz33XdQVVUt19jLy/v37+Hh4QETExPs2bMHaWlpmDFjBnr27Al/f3+FL81LVVdYWBj+/PNPuLi4wNXVFZcvX1Z2SFRFrVq1CvXr18eyZctgbm6Oa9euwdvbG/fu3cO2bduUHR5VIW/evEHr1q0xfvx4mJiYIDQ0FD4+Pjh//jwePHigtK24qGpbu3Yt4uPjlR0GVXEbN25E06ZNxV/r6elJfY4q80wjAatXr8bs2bMREREBc3NzAEBAQABat26Nv/76C/369VNyhFRV5Obmiv8IsWzZMsycORP8VULlIT4+HjVr1ixQtmjRIsyZMwdxcXGoVauWkiKj6uD06dPo2rUrTp48ia5duyo7HKpiXrx4ATs7O/zyyy8YMWIE9uzZg8GDBys7LKpCLl68CA8PD/j7+8PNzU2mc/HWUxVy9OhReHh4iBNGAHBxcUHjxo1x5MgRJUZGVQ3vWpOi/DdhBIBWrVoBAGJiYhQdDlUzJiYmAFDkFl1EspowYQJ69+6N9u3bKzsUohLxk185i4iIwIYNGzBmzBg4ODhATU0NIpEIixYtKlX748ePo1OnTjA2Noauri6cnJywbt065ObmFqobHBxc4NZzvqZNm+LRo0cyXwtVbIoca1S9KXus/f3339DQ0IC1tbUsl0GVgDLGWk5ODjIyMhAcHIypU6eiZcuW+OSTT+R1SVRBKXqsnTx5EqdPn8bKlSvleRlUCSjj91qfPn2gqqqK2rVrY9y4cXj79q30gQtUriZMmCAAKPRauHBhiW2XLl0qrm9lZSW0aNFCUFFREQAIvXv3FnJycgrUV1dXL/K8np6eQuPGjeV2TVQxKXKsFdWWqg9ljTVBEITg4GBBR0dH+O677+R1OVSBKWOs2draits5OzsLcXFx8r4sqoAUOdbS0tIEa2trYdWqVYIgCEJERIQAQNizZ0+5XBtVLIoca3fu3BGmTJkiHDlyRLhw4YKwZMkSQV9fX3B0dBQyMzOlipt3GsuZqakpevXqBR8fH5w4cQL9+/cvVTt/f3/MmjULKioq2L17N8LDwxEUFIQ7d+6gVq1aOHz4MH788cdC7YpaxVLgs2bVgqLHGlVfyhprCQkJ6NevH6ytrbFs2TJ5XQ5VYMoYa/v374e/vz+2bt2K5ORkdO7cGUlJSfK8LKqAFDnWlixZAg0NDYwfP748LoUqOEWOtZYtW2LlypXo1asX3N3dMXPmTOzatQuBgYHYt2+fdIFLlWKSzEaMGFGqvyb06NFDACCMHTu20LFdu3YJAAQTE5MCfyUwMzMTJk+eXKh+v379BDc3N9mDp0qlPMfah3inkRQx1pKTk4XWrVsLDRo0EF68eCG32KlyUdTvtXzR0dGCqqqqsHLlSpnipsqnvMZaZGSkoKmpKezbt094+/at8PbtWyEoKEgAIGzatElITEwsl+uhikvRv9dyc3MFXV1dYdKkSVLFyTuNFVBSUhLOnj0LAPD09Cx0/PPPP4eBgQESEhJw4cIFcXnTpk0RHBxcqH5wcDDs7OzKL2CqtMo61oikJctYy8jIQL9+/fD06VOcOnUKderUUUjMVDnJ8/davXr1ULt2bYSFhZVLrFS5lWWsRUREICMjAwMGDECNGjVQo0YNODg4iM/BFaGpKOXxeU3aPbaZNFZAd+/eRWZmJrS0tODk5FTouLq6OlxcXAAAN27cEJf36tULFy5cQFxcnLjs9u3bePLkCT799NPyD5wqnbKONSJplXWs5eTkYMiQIbh+/TqOHz8OW1tbhcVMlZM8f6+Fh4cjJiaGiy5Rkcoy1hwdHXHhwoUCrz179gAA5syZg9OnTyvuAqjSkOfvtcOHDyMlJUVcv7S4hnQFFBoaCgCwsLCQuMy3lZUVzp07J64LAGPGjMG6devQu3dvzJs3D+np6Zg+fTpat26NPn36KCR2qlzKOtYAiOfCP3jwoMDX9vb2sLe3L6+QqZIq61jz8vLCgQMHsHDhQuTk5OD69eviY9bW1kVuyUHVW1nHWr9+/dCqVSu0aNECenp6CA4OxqpVq1CvXr0i/7JPVJaxZmRkBHd39wJ1IiMjAeT9/5Pbb1BRyvp7bdiwYbCysoKTkxP09PTg7++PFStWwNnZudTPUuZj0lgB5S+DW6NGDYl18o99uGSuvr4+zp8/jwkTJmDQoEFQU1NDr1698NNPP3FfPSpSWccakDcVoqiv582bh/nz58sxSqoKyjrWTp48CSDvL/Bz5swpUH/Lli0YOXKknCOlyq6sY83NzQ179+7FypUrkZ2dDQsLC/Tv3x/Tp0+HsbFx+QZNlZIs/w8lkkZZx1rTpk2xe/durFmzBunp6ahXrx7GjRuHuXPnSr3/LJPGCig9PR0AoKGhIbGOpqYmACAtLa1AecOGDXH48OHyC46qFFnGmsBVeUkKZR1r+X+BJyqtso616dOnY/r06eUbHFUpsvw/9EOWlpb8fyoVq6xjbebMmZg5c6ZcYuDtpwpIS0sLAJCZmSmxTkZGBgBAW1tbITFR1cSxRorCsUaKwrFGisKxRopSEcYak8YKqDRTGUpzm5qoJBxrpCgca6QoHGukKBxrpCgVYawxaayAGjVqBACIiopCdnZ2kXWePn1aoC5RWXCskaJwrJGicKyRonCskaJUhLHGpLECatmyJdTV1ZGeno47d+4UOp6VlYWAgAAAgKurq6LDoyqEY40UhWONFIVjjRSFY40UpSKMNSaNFZCBgQE6deoEANi0aVOh43/++SeSkpJgYmJSaNlmImlwrJGicKyRonCskaJwrJGiVISxxqSxgpo9ezZEIhE2btwo3vQVAIKCgjBp0iQAwLRp04pdRYmoNDjWSFE41khRONZIUTjWSFGUPtYEKldXrlwRTExMxC9NTU0BgKCjo1OgPCoqqlDbRYsWCQAEAIKVlZXQokULQUVFRQAg9OzZU8jOzlbCFVFFxbFGisKxRorCsUaKwrFGilJZxxqTxnJ24cIF8Te3uFdERESR7Y8cOSJ06NBBMDQ0FHR0dAQHBwdhzZo1/AVEhXCskaJwrJGicKyRonCskaJU1rEmEgTuJkpERERERERF4zONREREREREJBGTRiIiIiIiIpKISSMRERERERFJxKSRiIiIiIiIJGLSSERERERERBIxaSQiIiIiIiKJmDQSERERERGRREwaiYiIiIiISCImjURERERERCQRk0YiIiIiIiKSiEkjERERERERScSkkYioinB3d4dIJMLFixeVFkNkZCREIhEsLS2VFkN1MH/+fIhEogKvyMhIZYdVqRgZGRV4/0aOHKnskCo8S0vLIsfayJEjIRKJsHXrVqnPKUtbIlIcJo1EpBD5HzZKevGDA1Hp1a9fH23btkXbtm2hpaWl7HAqlTZt2qBt27Zo1KiRzOdq0KABjIyMkJWVVWLd/CSpuFffvn3LHEtkZCTmz59fIX6XBgYGYv78+Th48KCyQyEiGakpOwAiql4aNWoEMzMzicdr1aqlwGiqFgsLC9ja2kJHR0fZoZCCjB49GvPnz1d2GJXSiRMnAABbt27FqFGjynyeoKAgREVFYeDAgVBXVy91OzMzM4kJq729fZnjiYyMxIIFC/DJJ58o7O6pubk5bG1tYWhoWKA8MDAQCxYswIgRIyQmwpLaElHFwqSRiBRq1qxZnAZWTrZv367sEIiqnaNHjwIAevXqJVW77t27V4i7gfKwdOlSLF26VOFtiUhxOD2ViIiIqIyOHj0KFRUVdO/eXdmhEBGVGyaNRFThZWdnY8OGDfDw8ICJiQm0tLRgZWWF/v3749ChQ4XqZ2VlYd26dWjdujUMDAygq6sLBwcHLF68GKmpqYXq/3fxlp07d8LZ2Rk6OjowNjbG559/jqdPn0qMLyoqCt988w0aNmwITU1NmJqaonv37uLpb/+Vv4jJ/PnzkZCQgG+//Rb16tWDtrY2HBwc4OfnJ6777NkzjBo1CnXq1IG2tjZatWqFY8eOFXnekhbCCQgIwLBhw2BhYQFNTU3UqlULH330EVasWIF3795JvL6iXLp0CZ06dYKBgQEMDQ3h4eGBM2fOFNvm+vXrmDZtGpydnWFmZgZNTU3Ur18fw4cPx8OHD4tsU17v1dOnT7F8+XK4u7ujfv360NTURM2aNdGtWzeJbfKdO3cOHTp0gIGBAYyMjNCxY0ecP3++xEWAUlNTsXz5cjg7O8PAwAA6OjpwdHTEypUrkZGRUWyfZfHheLh37x769OkDU1NTGBgYoFOnTrh165a47t9//41u3brB2NgY+vr66NmzJx4/fizx3NJeS0mLnXz4fZZUHh8fj++++w6WlpZQV1cvMGNB2p95eXn9+jVu3rwJNzc3mJqayv38Dx48wLx589CmTRuYm5tDQ0MD5ubm+Oyzz3Dt2rVC9d3d3eHh4QEg72f0w+ckPxyXiYmJ2LRpE/r06QMbGxtoa2vD0NAQrq6u+Pnnn5GdnS1VnEV9fy0tLcXTfrdt21YgFnd392Lbfujx48cYPXo0LC0toampCRMTE/Ts2RPnz58vsn5CQgKmTJmCJk2aQEtLC7q6urC0tES3bt3w66+/SnVdRPQBgYhIARo0aCAAELZs2SJVuzdv3ght27YVAAgAhAYNGgjOzs6CmZmZ+OsPpaamCh06dBDXt7OzE1q0aCGoqKgIAARHR0fh9evXBdpERESIzzVjxgzxvx0cHARNTU0BgGBubi7Ex8cXiu/69euCkZGRAEDQ1dUVWrVqJdSrV0/c/5w5cwq1mTdvngBAGD9+vGBjYyNoaGgITk5OQt26dcXttm3bJjx+/FgwMzMTdHR0hFatWgmmpqYCAEFVVVU4c+ZMofN+8sknAgDhwoULhY4tX75cEIlEAgDBwMBAaNWqlWBtbS2oq6tLbCPJnj17xO+niYmJ4OzsLBgbGwsqKirCsmXLivy+CIIgWFtbi9s0a9ZMcHBwEAwNDQUAgra2dpExlNd75enpKQAQ9PT0hMaNGwvOzs6Cubm5+JzLli0r8tq3bdsmfh9NTU0FFxcXwcTERFBRURFWrlwp8dqfP38u2NvbCwAENTU1wcbGRrCzsxPU1NQEAMLHH38spKamlvp7kP++zJs3T2Kd/PGwbNkyQVtbWzAyMhJatWolfs/19fWFBw8eCH/88YegpqYmmJmZCU5OToKOjo4AQKhZs6YQFxcnl2sZMWJEsT//kq4nv/zbb78VLCwsBFVVVaFFixZCixYthNGjRwuCULaf+Q9t2bJFACCMGDFCYh1Jtm7dKgAQlixZUuo2+e9Fafrr2LGjAEAwMjIS7OzsBCcnpwJje9euXQXqf/fdd0KzZs3EP+dt27YVvwYMGCCut2PHDgGAoKGhITRo0EBwcXERrKysxO9Zz549hZycnELx5P8ej4iIKPKaPvz+DhgwQGjUqJEAQDAzMysQy3fffVds23x79+4VNDQ0xOPV0dFRqF27tgBAEIlEws8//1ygfmJiovj3jIaGhmBvby84OTkJZmZmgkgkEgwNDUt8z4moaEwaiUghypo09u3bVwAgWFtbC9evXy9wLDQ0VFixYkWBssmTJwsAhDp16gi3b98uULdJkyYCAGHgwIEF2uQnjWpqaoKBgYFw/Phx8bHY2FihRYsWAgBh+vTpBdqlpKQIFhYW4nMmJSWJj23dulVQVVUVABQ4nyD8+0FYXV1d8PDwEF6+fCk+lp90mZubC61btxYGDx4sPm9OTo4wbtw4AYDQunXrQu+VpKTx4MGD4g+Zq1evFjIzMwtcw++//y4EBwcXOl9Rnj9/Lujp6QkAhBkzZghZWVmCIAhCZmam8MMPP4iT0KISp23btgnh4eEFyrKysoSNGzcKampqgpWVVaEPquX1Xh0/fly4fv26kJubW6D88uXLgrm5uaCqqiqEhYUVOPbs2TNxQuXt7S1kZ2eLr2HGjBkSrz0nJ0f46KOPBADC4MGDCyRi0dHRQrt27QQAwpQpU4p6y4skTdKorq4uTJo0ScjIyBAEQRDS09OFPn36CAAEd3d3wcjISFi9erX4vX/79q3QunVrAYAwbdo0uVyLrEmjqqqq0KZNGyE6Olp8LC0tTRCEsv3Mf0iWpHHAgAECAOHevXulbiNN0vjnn38WOndubq5w8OBBQU9PTzAwMCjwe0cQBOHChQsCAOGTTz6ReN6goCDh6NGjQnp6eoHy8PBwoX379gIAYevWrYXaSZM0CkLp3ltJbYOCggRNTU1BS0tL+P333wv8bjh8+LBgYGAgqKqqCoGBgeLyVatWCQCELl26CAkJCQXO9+zZM+Gnn36SGAcRFY9JIxEpRP6HjZJeb9++Fbe5efOmAEDQ1NQUQkJCSuzj3bt34g/1Bw4cKHQ8/3wikahAQpCfNAIQVq9eXajd4cOHBQBCixYtCpRv2LBBACDUqlVL/AH2Q99++60AQGjXrl2B8vwPwtra2sKLFy8KHMvOzhbfqTQ3NxdSUlIKHH/79q2gpaUlACj0oUhS0ph/V8jHx6dQjNLy9vYWAAguLi5FHs9PsItKGoszbNgwAYBw9erVAuXl9V4VZ+PGjQIAYfHixQXK8+9Cd+rUqch2+e//f689f/y4uLiIk+wPxcTECHp6eoKenl6p7zZKkzS2bNmyUHL85MkT8Zjv06dPobYnT54scsyX9VpkTRo1NTULff8Foew/8x8qa9KYmZkpGBgYCBYWFlK1y38vinuVRv7P4n/vNpYmaSxOWFiYAEDo3LlzoWOKTBo/++wzAYCwdu3aItutW7dOACC+4ywIgvgPRYcOHSr2GolIelw9lYgUqqQtN9TU/v21lP+8Yr9+/Uq1l9qVK1eQmpoKCwsL9OnTp9BxFxcXtGnTBv7+/jhz5gysra0L1fH09CyyHYBCzzWePn0aADBmzJgi98ibMGECfv31V1y7dg0pKSnQ1dUtcLx79+6oU6dOgTJVVVU0b94cz58/x5AhQwptn2FkZISGDRvi0aNHiIiIgLGxcVFvhVhYWBiCg4OhoaGBiRMnFlu3NE6dOgUA+Oabb4o8/u233+Lrr7+W2P7x48fYs2cP7t+/jzdv3oifnYqKigKQt33BRx99VKhdebxX8fHx2L17N27cuIFXr14hPT0dAMTPdwYFBRWon//MpqTtGUaNGoVLly4VKv/rr78A5D279eH4zmdubg4XFxdcuHABt2/fxscff1zk+ctq1KhREIlEBcoaN24MHR0dpKamFjnmW7ZsCaDwmFfWtXTq1KnQ9x+Qz898WV2+fBlJSUkYNmxYmdoXt+XGh6KiorB7927cuXMHr1+/RmZmJgDg1atXAPLG6dChQ6XuPyMjA/v378eFCxcQFRWF1NRUCIIgPv7f8a9ImZmZOH78OFRVVSWutt27d298//33BX7m6tevDwA4cOAAevToUeQYJaKy4U8TESmUNFtuPHr0CADg5uZWqvohISEAgCZNmhT6kJyvadOm8Pf3F9f9kKmpaZF7heUnue/fvy+yP0l7qjVq1AgaGhrIzMxEeHg4WrRoUeC4pA+wNWvWLPH4o0ePCsVTlPz30N7eHvr6+iXWL0n+NdvZ2RV5XFI5kLe0vre3N3JzcyXWefPmTZHl8n6vTp8+jYEDBxa7ANB/YwkNDQWAQt/HfJLK79+/DwD43//+h927dxdZJ/99ffHihcR4ykrSe2NqaoqoqKgij+e/r/9935R1LZLGlaw/87Io61Yb+Uqz5ca2bdvw9ddfi/+gURRJPzPFiYqKQpcuXfDkyRO5nldeQkJCkJ6eDg0NDfTo0aPIOvkJ7ofjbNSoUVi5ciW2bt2KEydOoFu3bmjXrh08PDxgZWWlkNiJqiomjURUYSUlJQHIu2NUGvkfcIu7k1mrVi0AQHJycqFj/70TmE9FpeiFpkvqTyQSoWbNmnjx4kWR/f33ztiH7Upz/MO7ApJI+x6WJP+a85OK/8p/f//r8uXLmDVrFlRVVbF06VL07t0bDRo0gI6ODkQiEby9vbF48WJkZWUV2V6e71ViYiIGDx6Md+/e4csvv8S3334LW1tbGBgYQEVFBWfPnkXnzp0LxZKSkgIAEpNvSeX5iemDBw+KPP6htLS0EutIqyzvnaQETFnXIulnU9afeVkcO3YMOjo64tVK5S08PBxjxoxBVlYWJk+ejGHDhsHa2hp6enoQiUTYuHGj+Li0Ro4ciSdPnsDV1RULFiyAo6MjjI2Noa6ujuzsbPF/lSV/nGVmZuLq1avF1v0woa5Tpw78/f0xZ84cHDt2DNu2bcO2bdsA5P3x8ccff0SbNm3KL3CiKoxJIxFVWPkfwhMTE0tVX09PD8C/07aK8vLlywLnlkVJ/QmCgPj4eLn1VxbSvocl0dPTw7t37xAfH1/kHSpJ78WuXbsAAFOnTsWMGTMKHY+OjpZLfKVx4sQJvH37Fm3atMHWrVsLJUiSYtHV1UVSUpLEO7ySkpL8cXLmzBl06tRJhsiVr6zXUtIfOvIT8rLGo6if+XwhISEIDQ1F7969i5yaLg9//PEHsrKyMHjwYKxatarQ8bL+zMTExODChQvQ0dHB8ePHC03bVuTPoiT539e6devi+fPnUrW1s7PDvn37kJGRAX9/f1y6dAl+fn64fv06unTpgvv370vcFoeIJOM+jURUYTVt2hRA3v5+pdG4cWMAeVMyJX04zd8PML+uLPLPERwcXOTx0NBQZGZmQlVVVa7PUkkj/z0MDg6Wy52W/GuWtIdf/nTY/4qMjASAIp9XBBT7/FR+LG3atCnyjpqkWPKv/d69e0Uez5+6+V/505dLc3euoivrteTfKcz/I8p/hYWFlSkeRf/M5zty5AiAsk9NLY2y/sxIukuc79mzZwDypvQW9Uy0PH8WS4pFkkaNGkFdXR2xsbFlniarqakJd3d3zJs3Dw8ePEDbtm3x/v177Nmzp0znI6rumDQSUYXVt29fAMDBgwcRHh5eYv2PP/4YOjo6iI6OFi+i86Fbt27B398fIpEInTt3ljm+rl27AgA2bNhQ5DNHP//8MwCgbdu2EqfXlTdra2s0a9YMmZmZ4nhk0aVLFwDAb7/9VuTx//3vf0WWa2trA/j3rs+HTp8+rdCksbhYEhISsGnTpiLb5Y8ZSc+hSSr/7LPPAADr168v9tm0yqCs15L/PFlAQEChY8+fPxcvsCQtRf/M5zt69ChEIhF69uwpt3P+V3Hj9PHjx+LEVVI7SdOD84+/evWqyER7xYoVZYq3LLFIoqOjg65duyI3N1cuv7dUVVXFC5rFxMTIfD6i6ohJIxFVWK1atUK/fv2Qnp6O7t27F/rAGRYWVmDaloGBgXhVz++++w53794VHwsPD8eIESMAAAMHDpTLnb8hQ4bAwsICL1++xMiRIwtMW9y5cyfWr18PAEVOx1SkRYsWAQDmz5+Pn3/+ucAzUKmpqdi4caPEO4T/9fXXX0NXVxc3btzAnDlzxM89ZWVlYerUqeK7Ov+Vv4rmsmXLEBERIS4PCAjA6NGjy22KX1HatWsHIG/639mzZ8XlsbGx6N+/v8Rnub7++mvo6Ojg9OnTmD9/PnJycgAA2dnZ8Pb2xpUrV4ps169fP7i5ueHx48f49NNPC91Vy8jIwLFjxzB69Gh5XF65Kuu1dO/eHUDeH4COHz8uLo+NjcUXX3xR5ufnFP0zD+Q9b3f16lW0bNmyyBVd5SX/Z+bXX39FYGCguDwkJASff/45NDQ0imzXsGFDAHmzC4q6s9u0aVPUqFEDz58/x+LFi8WJY3p6OiZMmFDgPZTVh38sSE1NlartwoULoampiUWLFmHZsmWFEs/Y2FisXbu2wB+wZs+ejU2bNhWajv/gwQP88ccfAAAnJ6cyXAkRcZ9GIlKI/P29GjVqJLRt21bi6797cr1580Zo06aNeP8yS0tLwdnZWahVq1aRe+KlpqYKHh4e4vr29vaCg4ODoKqqKgAQHBwchNevXxdok79PY3F7C0LC/mnXr18XDA0NBQCCrq6u4OzsLNSvX19c39vbu1CbkvbYK2lPO0n7MUoqFwRBWLp0qSASiQQAgqGhoeDs7Cw0atRIvCF9UW0k2blzp/hcpqamgouLi2BsbCyoqKgIy5YtK/K9fPfunWBlZSUAEDQ0NITmzZsLtra24u/RpEmTit2nT97vVf6m7AAEGxsbwdHRUVBTUxP09fWFNWvWSNznbuvWreJrr1mzpuDi4iKYmpoKKioqwooVKwQAgpWVVaF2MTExQsuWLQv06erqKtjb2wsaGhri/T5LS5p9GiV9byXtuZdP0pgv67V4enqK2zRs2FD8njdp0kSYMGFCmb7/glC2n/kPSbtPo5+fnwBAmDt3bqnq/1f+mC2pv6ysLMHNzU0AIKiqqgp2dnZCs2bNBJFIJJibmwuLFi2SeJ4OHToIAAR9fX3B1dVV+OSTT4RBgwaJj//yyy/i96t27dqCs7OzYGBgIIhEIvH+s0V976XdpzEnJ0do1KiRAEAwMTER2rRpI3zyySfChAkTSmwrCILw119/iffh1NLSEhwdHYXWrVsX+B07ffp0cf0+ffoIAAQVFRXBxsZGaN26tWBjYyOu6+HhUeT+okRUMt5pJCKFCg0NxdWrVyW+/rsvXI0aNXDp0iX4+vqibdu2ePv2LR48eAAdHR0MGDAAv/zyS4H62traOHXqFNauXQtnZ2c8e/YMISEhsLe3x6JFi3Dt2jWYmJjI7XpcXV0RFBSEcePGwdTUFPfu3cP79+/RpUsXHDt2DAsXLpRbX7KYMWMGrl27hoEDB0JHRwdBQUFISkqCi4sLVq5cKdVf37/44gucP38eHh4eSE9Px+PHj9G8eXOcOHECgwYNKrKNgYEBrly5gi+//BIGBgZ48uQJMjMzMWnSJPj7+yt8oaBdu3Zhzpw5sLS0xLNnzxAXF4cBAwYgICAADg4OEtuNGDECp0+fhru7O9LS0vD48WM0bdoUJ0+eFG8NUNS1mJubw9/fH7/++ivat2+PhIQE3L17F8nJyWjdujUWLFiACxculNv1ylNZr+W3336Dj48PrK2t8eLFC8THx2PcuHHw9/eXaXVfRf/My7rVRmmpqanh1KlT+P7771GrVi2EhYUhMTERnp6euH37NurWrSux7e7duzFy5EgYGBjg9u3buHTpUoFnw728vLBz5044OjrizZs3CAsLg7OzM44fP46vvvpKbtegoqKCY8eOYcCAAVBVVcXNmzdx6dKlAndOi9OvXz8EBwdjwoQJsLS0xJMnTxAcHAwdHR3069cP27ZtKzCTw9vbGzNmzICLiwvev3+PwMBApKWl4ZNPPsH27dtx+vRp7t1IVEYiQSjFmu1ERERUrP3792PAgAHo06cPDh48WK59zZ8/HwsWLMC8efMwf/78cu2rqtu6dStGjRqFESNGlLhvYm5uLmrVqgU1NTXExMSUeaEXIqLKhn9uISIikoMtW7YAyFv4SFE2b94sfi5z3759qF27tsL6ruy6d++O5OTkYrfr+K/r16/j9evXGD16NBNGIqpWmDQSERGV0v79+6GtrY2uXbtCVVUVQN5iQvPnz8exY8egq6uL4cOHKyye6Oho8b56lX1lVkXz9/cXbyJfWh999JHErT2IiKoyTk8lIiIqpfxpoVpaWrC2toampiYePXqEtLQ0qKqqYtu2bfjiiy+UHSYREZFc8U4jERFRKfXp0wfPnz/H5cuXER0djbS0NNSsWRO9e/fG5MmTxXvBERERVSW800hEREREREQSccsNIiIiIiIikohJIxEREREREUnEpJGIiIiIiIgkYtJIREREREREEjFpJCIiIiIiIomYNBIREREREZFETBqJiIiIiIhIIiaNREREREREJNH/AYzO4tTb9QJXAAAAAElFTkSuQmCC\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "N_D_ordered_test, exceed_prob_test, complete_table = exceedance_prob(case, scenario_prob)\n", - "plot_curves(N_D_ordered_test, exceed_prob_test)" - ] - }, - { - "cell_type": "markdown", - "id": "7dce7a21-f338-40ce-ae1a-35ae357301ba", - "metadata": {}, - "source": [ - "## Modify the system and see how the FN (or FD) curve changes\n", - "\n", - "The function above allows the user to choose which dike segments to repair, then the relevant scenarios are removed from consideration. Play with the segments and see what the most important repairs should be to improve the system risk." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "f2a8ecf2", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Segment [12, 13] in scenarios [ 0 7 8 49]\n" - ] - }, - { - "data": { - "image/png": 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n1vv373n//r3ud7Vajb+/PzY2Num2xpcQQgghhBAi59FoNLo1djNzpu+PKml8+/YtQKILAGv3acumVr169di+fTs//PADUVFRlChRgs8++4wJEyZgbW2dYD0XFxdmzZqVpmMLoZcjUBswjLXtFnAFiL/OuRBCCCGEyKaePn1KsWLFMu14H1XSGB4eDoCRkVGCZYyNjQEICwtL07EmTJjAhAkTUlxv0qRJjBkzRvd7YGAgJUqU4N69e4kmm9lNZGQkJ06coGnTproJhXLK8dLSVkrrpqR8csomVcbrhRcD1wzkbuDdmA0Vwa6xHb90+4XaxWtn6meWXuRay57XWmL7M/szSy9yrcm1llnkWpNrLbPItZbzrjV/f3/KlSuHubl5knGnp48qaTQxMQEgIiIiwTLaoaF58uTJlJg+ZGxsrEtcY7O2tsbGxiYLIkqdyMhITE1NsbGxybQ/Qul1vLS0ldK6KSmfnLJJlbGwsGBeo3k8yvOIqfunEhYRhre/N51Xdmak00gamTTKtM8svci1lj2vtcT2Z/Znll7kWpNrLbPItSbXWmaRay3nXWtamf3Y2kc1EU5yhp4mZwirEDmZUqHk62Zf4z7dnYZlGwIx4+OXnljKN6e+4eLDi1kcoRBCCCGEyE4+qqTR3t4egCdPnhAVpf8hrocPH8YpK0RuZV/QnlPjTvFT958wMYzphfcN9cXpJycm757M+8j3SbQghBBCCCE+Bh9V0li9enUMDQ0JDw/n+vXr8fZHRkZy5coVAOrWrZvZ4cWxbNkyHB0ddUuACJERVEoVY1qNwW26G3Xs6gCg1qhx+dOFOvPq4PHMI4sjFEIIIYQQWe2jShotLCxo0aIFAKtXr463f8eOHQQFBWFjY4OTk1MmRxfXiBEjuH37ti6JFSIjlS9UnpPfnaRv+b4YqmLGzns886DW3FrM/3M+0erorA1QCCGEEEJkmY8qaQSYMmUKCoWCVatWsXXrVt12d3d33ayl48ePT3SGVSFyIwOVAd3tu3Nu/DkqFa0EQGR0JJN2T6LxwsZ4vUjb2qVCCCGEECJnyrFJ47lz57C1tdW9tm3bBsSscxh7+9OnT+PUa9iwIXPmzEGtVtOnTx/KlClD1apVqVGjBi9evKB9+/Z89913WXFKQmQL1YpX4+qUq0xoMwGlIuZPxIUHF6g2uxq/nfgNjUaTxREKIYQQQojMlGOTxsjISN68eaN7aZfKCA0NjbM9Ojr+sLopU6Zw4MABmjVrxps3b7h//z6VK1fm559/Zt++fahUqsw+HSGyFWNDY+Z/Np/T409TJn8ZAEIjQhmxZQStf27NM/9nWRyhEEIIIYTILDl2nUYnJ6c09Xh06NCBDh06pGNEQuQ+Dcs2xG26G+N3jef3k78DcPT2USrNrMSvfX6lb92+mb5OkBAi94uMjNTd9I2MjMTAwIDw8HC9N4IT259U3ewqs+NOz+Olpa2U1k1J+eSUlWtNrrX0KJ/ca02lUuWo0Vs5NmnM7ZYtW8ayZcty1B8ekTuZmZjxW9/f6Fy1M4PWD8InwIfAsED6r+7PHtc9LO+3nPzm+bM6TCFELhAUFMTr1691o4cgZh3ZQoUK8fTpU703qRLbn1Td7Cqz407P46WlrZTWTUn55JSVa02utfQon5Jr7eHDh5iZmVGgQIFsP5+KJI3Z1IgRIxgxYgRBQUFYWlpmdThC0LpSa27OvMnXW79m86XNAOy+vpuzXmdZOWAlnap1yuIIhRA5WVBQEM+fP8fMzAxbW1sMDQ1RKBSo1WrevXuHmZkZSmX8p2oS259U3ewqs+NOz+Olpa2U1k1J+eSUlWtNrrX0KJ+cstHR0QQHB6NUKgkKCsLb25tixYphamqaovPITJI0CiGSLV/efGwasolPq3/Kl5u+5M27N7wMfknnZZ1xbuDMzz1/xtJUbnIIIVLu9evXmJmZUaxYsTh359VqNREREZiYmCT4RT6h/UnVza4yO+70PF5a2kpp3ZSUT05ZudbkWkuP8sm91iIjI7GwsMDGxobHjx/z+vVrSpQokaLzyEw556oWQmQb3Wp24+bMm3So8t9zwevOr6PKrCqcuHsiCyMTQuREUVFRvH//HktLyxw1tE8IIdJKpVJhbW1NSEgIUVFRWR1OgiRpFEKkSiHLQuwfuZ/Vn6/G3MQcgCf+T2j2UzO+2fYNYRFhWRyhECKn0H5RMjQ0zOJIhBAi8xkbGwNI0iiEyJ0UCgWDGg3CY4YHTuWddNuXHF9Crbm1cHvilmWxCSFyHullFEJ8jHLC3z5JGrOpZcuW4ejoSO3atbM6FCGSZGdrx/Exx1ncczHGBjF3y2773qbOvDosPLKQaLXMAiyEEEIIkVNJ0phNjRgxgtu3b3PlypWsDkWIZFEqlXzT4huuTb1GteLVAIiMjmTCrgk0+6kZj988ztoAhRBCCCFEqkjSKIRIVxWLVuTipItMaDNBN9zi9L3TVJlVhQ3nN+SohWyFEEIIIYQkjUKIDGBsaMz8z+ZzcuxJStqUBCAoLIjP135OjxU9ePPuTRZHKIQQQgghkkuSRiFEhmlSrgnu093pX6+/btvOazupPLMyf9/6OwsjE0KInMfOzg6FQpHo6+effwbA29tbt83U1BRfX98E2zUyMiJfvnx4e3snWOb48eMoFApGjBgRr33ty8DAAFtbW2rUqMFnn33GokWLePXqVXq+BUKILCJJoxAiQ1maWrJh8Ab++OIPrPNaA+Ab6Evrn1szausoWZpDCCFSyN7enoYNG+p9FS1aNF75sLAwXFxc0nTMgwcPAtChQ4d4+2rVqkXDhg2pV68eJUqU4N27d+zdu5fvvvuOYsWKMWPGDKKjZUI0IXIyg6wOQAjxceheqzsNyzZk4NqB/H07ppdx6T9LOXbnGJsGb6JGyRpZHKEQQuQMkydPxtnZOdnllUol//vf/5gwYYLepDI5Dh06hKmpKU2bNo23b8eOHdjZ2QGgVqsJCgri5cuXrFixgiVLljB79my8vLzYsmVLqo4thMh60tMohMg0RayK8OfoP/ml1y+YGJoAcMf3DvVc6uFy2EWW5hBCiHSmUqno0aMH79+/Z968ealq4969e3h5edGiRQtMTEySVads2bL89NNPHDx4EJVKxdatW1m/fn2qji+EyHqSNGZTsk6jyK2USiVfN/+aa1OvUb1EdSBmaY7Jeybj9IMTj149yuIIhRAid5kxYwZKpZJVq1bx9OnTFNc/cOAAoH9oalLatGnDyJEjAVI9RDYqKoqVK1fStGlTbGxsMDExoXTp0nTr1o3Dhw/HKat97jOh5zObNWuGQqHg5MmTcbY7OTmhUqk4e/Ysbm5udOvWjYIFC6JUKlm3bh3dunVDpVKxdOnSBOP8888/UalU1KgRf+TMs2fPGDVqFOXKlSNPnjxYWVnRtGlTdu7cmeL3Q4isIEljNiXrNIrczrGIIxcnXWRS20m6pTnO3j9L1dlVWX9+vSzNIYTIcF7BEUxye0nvc8+Z5PYSr+CIrA4pQzg4ONC7d28iIiKYO3duiusfPHgQhUJB+/btU3X8L7/8EgBPT08ePHiQorpv377FycmJYcOGcfLkSczNzalcuTIhISHs2bOHiRMnpiqmhJw/f54GDRrw119/Ubx4cUqVKgVAnz59ANi1a1eCdbX7evfuHWf7qVOnqFSpEkuXLuXZs2fY29tjYWHByZMn6d69O2PHjk3XcxAiI0jSKITIMkYGRszrOo/T405jZ2MHQHB4MM5rnem+vLsszSGEyDBrHwbgcPABP9x9wx9Pgvjh7hscDj5g3cOArA4tQ8yYMQOVSsXatWsTnSX1Q4GBgZw7d47q1atTpEiRVB3bwcEBGxsbgBTfDB80aBDnzp2jTJkyXLx4EW9vb65cucKLFy/w9PRkyJAhqYopIQsXLmTAgAG8ePGCq1ev8uDBA3r27En79u2xtLTE3d2de/fuxasXGhrKkSNHUCgU9OrVS7fdx8eHrl27EhQUxLx583j79i0eHh48efKEc+fOUbRoUd0wXiGyM0kahRBZrpF9I9xnuOPcwFm3bdf1XVSeWZm/bv6VdYEJIXIlr+AIhlzyRQ1Ea4jz7+BLvtzP5j2OAwcO1LvchpOTU4J17O3t6devH5GRkSnqbTxy5AiRkZGpGpoaW/HixQF4+fJlsutcuXKFvXv3YmxszJ9//kndunXj7C9btiyjRo1KU1wfqlChAr/99humpqa6bXny5MHY2JguXboAsG3btnj19u/fT0hICI0aNdKdK8BPP/2Ev78/33zzDZMmTcLY2Fi3r0GDBixfvhyAxYsXp+t5CJHeZPZUIUS2YJHHgrUD19KhSgeGbRyGf4g/voG+tFnShpFNR7LgswWYGpsm3ZAQItdpeu41ryITXu9Po1ajUOrfr29fYGQ06gTaUgPVjzzE0lCVymjjKpTHgKutS6VLW1r29vYUKFAg3vbKlSsnWm/atGls3ryZ9evXM3nyZEqXLp3ksRJbaiMl8ubNC0BwcHCy6+zbtw+ALl26YG9vn6bjJ1ePHj1QKvX3qfTu3Zt169axbds2Zs6cGWefNpGM3csIsHv3boAEe0TbtGmDkZER58+fJyoqCgMD+Wousie5MoUQ2cpnNT+jQZkGDFo/iCM3jwDw64lfOXbnGJuHbJalOYT4CL18H43P+4TSPK3E9idVN653URreRUWlqE5mSumSG1plypRhwIABrFmzhjlz5rB27dpEy6vVao4cOUKhQoWoVatWKqON8e7dOwAsLCySXefOnTsA1KtXL03HToly5coluK9Zs2YULFgQT09PXF1dqV49ZjK3gIAA/vrrLwwMDOjWrZuu/Lt373RDgYcNG5boccPDw3nz5g0FCxZM+0kIkQEkaRRCZDuFrQpzeNRhfjv5G2N3jCU8Mpy7fnep51KPuZ/OZWyrsQneCRZC5D4FjFUoEvlvPqY3Uf9+ffsCI6N5F5XwZFtmBop07WnMTqZNm8bGjRvZuHEjkydPTrQH78KFC7x+/ZpBgwbpJixLLe2srbF7SBs1ahSvnK2tra53LigoCAArK6s0HTsltD2i+iiVSrp06cLy5cvZunWrLmnctWsXERERtGzZEltbW135wMBA3c/nzp1L8thhYWFpiFyIjJW9/pIJIcS/FAoFI5qOoLlDc/qt7se1x9eIjI5kwq4J/HXrL9YPXE8x62JZHaYQIhOcaGiLhYWF3ptF2sXk9e1PaJ9XcAQOBx/o7X9UAq5tSlPW3CidzyJ7sLOzw9nZmZUrVzJ79mw2btyYYNn0Gpp6+/Zt/P39AahTp45uu75EKvbzgObm5kBMT15yaZPbhGbgDgkJSXZb+nz22WcsX76cbdu2sWDBAhQKBVu3btXti83MzEz3c0REBIaGhmk6thBZSW7VCyGyNYfCDpyfeJ6JbSfqvgz8c/cfqsyqwq5rCU99LoQQCbE3N2J13cIoAZUClIp//wVW1y2caxNGralTp2JkZMTWrVvx9PRMsNzBgwcxMjKiZcuWaTqedrKXChUq6JawgJjELvYrOjoaDw8P3f6KFSsCcPHixWQfS9tT+OqV/mdcU7rkx4dq1apFmTJlePr0KWfPnsXPz4+TJ0+SJ0+eeEuSWFpa6macvXXrVpqOK0RWS3PSGBkZyfnz51m4cCEjRoygR48edOzYkYEDBzJ+/Hi2bdvG8+fP0yPWj8qyZctwdHSkdu3aWR2KEFnOyMAIl64u/PPdPxTLF9O7+Db0Ld2Wd+OLTV8QFiVDeoQQKeNc2grPDmUY52BDj+IWjHOwwbNDGZxLW2V1aBmuRIkSDB48mOjoaGbNmqW3zJMnT7h58yZOTk5xesxS6siRI/z2229AzLOYKfHpp58CsHfv3mQne9rJffQt7bF//37evn2bohj00U52s3XrVrZv3050dDQdOnTQ+z517doVgJ9//jnNxxUiK6U6aTxx4gR9+/bFysqKxo0bM2nSJH7//Xd27tzJoUOHWL9+PT/++CN9+/alRIkSVKpUiUWLFvH69ev0jD/XGjFiBLdv307xekZC5GZO5Z1wn+FOt5r/TTSw9vxaxpwew1Xvq1kYmRAiJyprboRLtQJsbVgUl2oFcn0PY2yTJ0/G2NhYl/R86MCBA0Dqh6bev3+f7777jg4dOhAdHU2/fv3o169fitqoWbMmXbp0ITw8nLZt28b7TnT//n2WLl0aZ1vbtm2BmPUWvby8dNuvXLnCxIkT02WIaJ8+fQDYsWMHmzZtAmJmVtVnwoQJWFtbs379esaMGRNvqK2/vz9r1qxJ0TIoQmSFFD/TeODAASZNmsSdO3fQaDQYGBhQrVo1ateuTeHChbG2tiZPnjz4+/vj7++vS3xu377N2LFjmTx5MsOGDWPatGnkz58/I85JCJGLWee15o8v/mD9+fWM3DqSkPch+Ib60uTHJszuPJvxbcajUqbPBBZCCJFbFStWjKFDh/Lrr7/q3Z+S5xm7d++uW38wJCSE58+f64aHGhkZMW3aNKZOnZqqOFevXo2fnx8XLlygTp062NnZYWtry9OnT3nx4gXFixdnypQpuvIDBw5k2bJl3Lp1C0dHRxwcHIiIiODevXt07dqVN2/ecOrUqVTFouXg4EC1atVwc3Pj9evXWFlZ0bZtW8LDw+OVLVasGPv37+fTTz9l8eLF/Prrrzg4OGBqasqrV6949OgRGo2Gnj17pikmITJaipLGJk2acO7cOfLkyUOPHj3o1asXrVu3xsTEJMm6Dx48YNu2bWzdupVff/2V9evXs2HDBjp37pzq4IUQHyeFQoFzQ2ca2Teiz8o+XPG+QpQ6isl7JnPk1hE2DtpICZsSWR2mEEJka5MnT2bVqlXxkp3Q0FBOnjyJo6NjnGcQE3L1asxID6VSiYWFBfny5aNhw4Y0adKEfv36pamTIF++fJw6dYqVK1eyZcsWbt68iZ+fH4ULF+azzz6Ls8QFgImJCf/88w+TJ0/mwIEDeHl5UapUKX744QcGDRqkGy6aVn369MHNzQ2ImQDHyMhIb9II0LBhQ27fvs2SJUs4ePAgDx48IDo6mqJFi9KmTRs6duyYbnEJkVFSlDTevHmTadOm8c0336R4+uMyZcowZcoUpkyZwokTJ5gzZw4eHh6SNAohUq1sgbKc/O4kzr84s+v+LtQaNafvnabKrCqs6L+CnrXlzq0QIvfQrvmXHHZ2dgnOIKpVuHBhwsLC4swyC3D06FHCw8MT7WVMqP3EZrNNLUNDQ7766iu++uorvcf6UIECBVi1apXesv/884/euE6ePJlge/qMGzeOcePGxWk/Mfnz52fu3LkyDFXkWClKGh8/fqyb/jgtmjZtStOmTQkODk5zW0KIj5uhypC+5fsyvONwnNc588T/CYFhgfT6Xy8O3zjMr31+xdwk7X+3hBDiY3Ho0CEg7UttCCFyjxTdAkqPhDEj2xNCfLwalW2E+wx3etXupdu24cIGqs2uxsUHyZ+uXQghPnb/+9//0Gg0NG7cOKtDEUJkE7JOoxAi17AytWLL0C1sHLxR17v48NVDGi1sxOwDs4mKjsriCIUQQgghcp4Uz56qj5+fHzt37uTx48dYWFjg4OBA1apVKVeuXHo0L4QQyaZQKOhXrx8NyjSg3+p+XHhwgWh1NDP2z+Dv23+zafAm7GztsjpMIYQQQogcI81J46VLl2jdujXBwcG6B6IVCgUApqamVKpUiWrVqlG1alWqVatG5cqVyZs3b1oPK4QQiSqdvzSnx53m+0PfM/vgbNQaNefun6Pq7Kr81uc3+tbrm9UhCiGEEELkCGlOGsePH09QUBCOjo707dtXtxaOm5sb9+7d49KlS1y6dEmXSCqVSiIjI9McuBBCJMVAZcCMTjNo6diSfqv78ej1I4LCgui3uh9/3vyTZX2WYWlqmdVhCiGEEEJka2lOGt3c3DA3N+fMmTPky5cvzr7w8HBu3LiBu7s7bm5uuLq6cvPmzbQe8qOwbNkyli1bRnR0dFaHIkSO16BsA9ymuzFyy0g2XtwIwOZLmzl7/yybh2ymYdmGWRyhEEIIIUT2leak0cTEhJIlS8ZLGLX7ateuTe3atdN6mI/OiBEjGDFiBEFBQVhaSk+IEGllkceCDYM30LZSW4ZvHk5gWCCP3zymycImTG0/lWkdpmGgSpfHvIUQQgghcpU0z55av359Xrx4kR6xCCFEhutdtzfuM9xpbB8zlbxao2b2wdk0XtiYBy8fZHF0QgghhBDZT5qTxm+//ZanT5/yzz//pEc8QgiR4UralOTE2BPM/XQuKqUKgIsPL1JtdjU2XtiYxdEJIYQQQmQvaU4aa9WqxeTJk/n8889xdXVNj5iEECLDqZQqprSfwrkJ5yiTvwwA796/Y8CaAfRb1Y+gsKAsjlAIIYQQIntIc9JoaWnJtm3bePXqFfXr12fUqFGcOXOGqChZRFsIkf3VLV0X1+muODdw1m3bfGkz1edU59LDS1kXmBBCCCFENpHmpNHU1JSHDx8SERFBREQEy5Ytw8nJCTMzM2rUqMGgQYP45ZdfOH36NEFBcudeCJH9mJuYs3bgWrYO3YpFHgsAHr56SKOFjXA57EK0WmYxFkIIIcTHK81TBQYFBfHo0SM8PDxwd3fX/fvw4UPc3Nxwc3PTrdEIYGdnx4MHMtmEECL76VWnF3VL1aXv6r5ceHCBqOgoJu+ZzNHbR9k4eCNF8xXN6hCFEEIIITJduswvX6pUKUqVKkXnzp1120JCQrhx40acZNLDwwNvb+/0OKQQQmSIUvlLcXrcaWYdmMX3h79Ho9FwwvMEVWZVYY3zGtpVbJfVIQohhBBCZKo0D09NSN68ealXrx7Dhg1j2bJlnDlzhsDAQOllFEJkewYqA+Z8OocT352gWL5iAPiH+PPpsk8ZtW0U76PfZ3GEQgghMsL8+fNRqVTMnDkzRfVOnjxJvnz5aNasWcYElkYKhSLOyL+M5O3tjUKhwM7OLlOOlxgnJycUCgUnT57M6lByvAxLGhOSHS4gIYRIjk/Kf4L7DHe6VO+i27b89HLGnR3HTZ+bWRiZEEJA5cqVUSgU5MmT56ObN2LdunXMmjWLJ0+eZHUome7kyZOZmgSmpyVLljB//nwCAgJSVV973pIEZr5MTxqFECInsc5rza7hu1jebzl5jPIA8CT4CfXn12fZiWVoNJosjlAI8TFyc3Pj5s2Ym1fh4eHs3LkziyPKXOvWrWP27NkfZdKYGuXLl6d8+fKZcixDQ0PKly9PmTJl4u1bsmQJCxYsSHXSmFIlSpSgfPnymJqaZsrxcrMUJY1fffUVz549S5cDb9u2jS1btqRLW0IIkZEUCgVffPIFV6dcpVKRSgC8j3rPyC0j+XTZp7wOfp3FEQohPjYbN24EwMrKKs7vQuhz9+5d7t69mynHKlq0KHfv3uX48eOZcrzEbNiwgbt371KnTp2sDiXHS1HS+L///Y+yZcsyZMgQTp8+neKDvXr1il9//ZUKFSrQt29fHj16lOI2hBAiqzgWceT8hPN0sOug27bffT9VZ1flxN0TWRiZEOJjEh0dzdatWwH49ddfUalUnDp1SnrdhBAZJkVJo5ubG82bN2fNmjU0bdqU4sWLM2zYMFatWoWrqyt+fn5EREQAEBgYyKNHjzh8+DCzZ8+mVatWFC1alNGjR/PmzRsWL17M+PHjM+SkhBAio5gYmjCk0hD2DN+DrZktAD4BPjRf1JzJuycTGRWZxREKIXK7Y8eO4evrS6FChejVqxfNmjVDo9GwefPmROuFhoby448/Uq9ePaysrDA1NcXe3p4BAwZw7ty5eOU1Gg07duygXbt2FChQAGNjY0qUKEHbtm1Zt26d3mNcvnyZQYMGUbx4cYyMjChYsCDdu3fH1dVVb/nYz+Zt2bKF5s2bY2FhgbW1NZ9++qluCK6W9nm+U6dOAdCxY0dUKpWundhxXbx4kfHjx1OrVi0KFSpEwYIFKVmyJP379+fWrVuJvlcAfn5+DB48mCJFimBiYkLFihVZunQpUVFRSdb9UGhoKAsWLKBWrVpYWFhgampKtWrV+OGHH3j/PuMnV0voGcjSpUuTL18+vL29OXXqFC1atMDKygpra2u6dOmCl5eXruz+/ftp3LgxFhYW5MuXj969e+Pj4xOvTX0T4axbtw6FQsHjx48BKFOmjC6mjHxGMaGJcAYOHEi+fPlYt24dPj4+DBo0iMKFC+s+52XLliXa7uXLl+nVqxdFixZN1nWeG6QoaaxUqRKHDh3i1KlTdOvWjVevXrFq1Sq++OILatWqRdGiRcmTJw8qlQpra2vKli1Lx44dmTlzJseOHcPOzo758+fz4MEDRo0ahaGhYUadV463bNkyHB0dqV27dlaHIoTQo33l9njM8KBFhRZAzJcrlz9daLSwEQ9eyizRQoiMs2HDBgB69uyJSqWib9++QOJDVJ88eUKtWrUYN24cly5dokCBAlSoUAF/f382b96Mi4tLnPIRERF89tln9OjRgz///BMDAwOqVq2KWq3mr7/+YuDAgfGOsXjxYho0aMCePXsIDw+nUqVKREdHs3PnTurWrcvu3bsTjG/hwoX079+f58+fU6FCBaKioti3bx916tTh7NmzunKWlpY0bNgQCwsLACpUqEDDhg11r4IFC+rK9uvXjx9++AFvb28KFixIuXLlCA4OZtOmTdSuXTvRROXNmzfUqVOH9evX65LNu3fvMn36dHr06IFarU6w7oeeP39O7dq1mThxIu7u7hQsWBA7Oztu3brF+PHjadGiBWFhYcluLyPs3buX5s2bc+PGDcqUKUNERAR79+7lk08+wc/Pj8WLF9O5c2e8vb0pXbo0YWFhbNu2jWbNmhEeHp5k+wULFqRhw4YYGxsDUKtWrTifm6WlZUafol5PnjyhZs2abN26lSJFimBjY8Pt27cZOXIk33//vd46ixcvpl69emzfvj3F13lOlqqJcBo3bsz27dt59uwZK1asoE+fPtjZ2aFSqdBoNLqXubk5jRs3ZvLkyZw8eZJ79+4xbtw4zM3N0/s8cp0RI0Zw+/Ztrly5ktWhCCESUNiqMH998xcLPluAgSpm2dvLjy5TfU51Nl9M/I6/EEKkxrt379i7dy+ALlns2rUrefLk4c6dO1y7di1enejoaLp27cqdO3eoVasWt2/f5t69e1y7do03b95w7do1unTpEqfOhAkT2LNnD7a2tvz555/4+Phw+fJlnj17xrNnz5gxY0ac8keOHOG7777DxsaGDRs28OrVK65fv87r169ZtWoVGo0GZ2dnfH199Z7X1KlT+fHHH7l9+zaXLl3Cz8+Pvn37EhYWRr9+/XRJVfXq1Tl79izVq1cHYpLN06dPc/bsWc6ePUvbtm11bU6fPp0HDx7w+vVr3N3dOXPmDC9fvmTVqlVERkYyePDgBJO/5cuXY2Vlxf3793F1dcXT05MTJ05gYWHBvn37+P3335PxaYFaraZHjx7cvn2bXr168ezZM7y8vLh9+zaPHj2icePGnD17lunTpyervYwyceJEFi5ciK+vL9euXePZs2fUq1cPX19fhgwZwtSpU9m8eTNPnz7Fzc0NLy8vSpcujaenJ2vXrk2y/bZt23L27FkKFSoEwPbt23WfWezPM7PNmzePRo0a6c77+fPn/PbbbwDMnTs33oQ9sa/zXbt28ebNm3jX+aBBg/Dz88uCs8lYaZo91dbWlqFDh7Jx40YePHhAREQE/v7++Pj4EB4eTkBAACdPnmTu3Lk0adIkvWIWQohsQ6lUMr7NeM5POE/ZAmUBCA4Ppt/qfgxYPYCgsI9rGnwhRMbatWsXoaGhlC1bVjcaydzcnA4dYp611tfbuHv3bq5du0aBAgU4cuQIFSpUiLO/WrVqDB48WPe7j4+Pbnje7t27adOmTZzyRYoUibeO4ZQpU9BoNKxcuZKOHTvG2Td48GBGjx5NcHAwq1at0ntebdu25dtvv0WpjPlqampqypo1ayhUqBCPHz9m27ZtSb018QwYMIDSpUvH2WZgYMDgwYPp1asXDx8+5OLFi3rrRkVFsW7dujhDLJs0acKUKVMA+PHHH5M1e/ahQ4c4f/48tWvXZuPGjXF6QosVK8b27dsxMzNj+fLlWdrb2LZtW8aMGaN7/62srJg1axYQcw5Dhw6lT58+uvLFixfXPWZ25MiRzA84ndjY2LBu3TrdhFIAw4cPp0aNGoSHh3PiRNz5CqZNm4ZGo2H16tV07do1zr7Y13lunJjKIL0bjP2mCyHEx6J2qdpcn3adr7d8zfoL6wHYeHEj5x6cY+vQrdQpJTO3CZFaTZc05dW7Vwnu12g0Ca5Zl9i+zFDIshBXp15Nt/a0X0Zjf4GHmF7HHTt2sHXrVn788UcMDP77irdv3z4ABg0ahI2NTZLHOHz4MJGRkdSrV4/GjRsnWf7x48dcv36dAgUK0KlTJ71rRnbq1ImffvqJU6dOMW3atHj7R4wYEW+bkZERQ4YMYe7cuQkOiU3K3bt32bp1Kx4eHrx69d81pJ00yN3dnQYNGsSrV79+fWrUqBFve9++fZkxYwbe3t54enri4OCQ6PG1QxWdnZ3jfCZahQsXpnbt2pw4cYJr167RqFGjFJ1fehk0aFC8bdWqVdP9HPumgpa2d/Dhw4cZFldG69WrF3nz5o23vXbt2ly/fj3OuT158iTOda6P9jrX94xwTpfuSaOvry+FCxdO72aFECLbMzcxZ92gdbSq2IovN31JcHgwD189pOGChszpPIfxrcfr7uIKIZLvZfBLfALjT7jxsXn+/Lmu5+PDpLFt27bky5ePly9f8vfff9OuXTvdvjt37gBQr169ZB0npeVv3LgBxKwX2aRJE6KiouIlSNrn3p4/f663jQ97Pz/cfu/evWTFEpuLiwtTp05N9PlDf3//FMWTN29eihcvjpeXF/fu3UsyadS+N7///nuCS81pzy2h9yYz6FtTMX/+/Mna/+7du4wLLIPpOy+AAgUKAHHP7fbt20DMtZxQcq+9zhMahp2TpXvSWLRoUWxtbalatWqcl6Ojo947LEIIkdv0qduHeqXr0WdlHy49ukRUdBSTdk/i2J1jbBi0gSJWRbI6RCFylALmBRLtLczuPY3pZfPmzajVamrUqBFvoXYjIyO6d+/O//73PzZu3BgnadT2/CV3NFhKywcGBurqJdXDktAQTO2X9A9ph3MGBwcnKxat06dPM3nyZFQqFS4uLnTo0IF8+fJRqFAhVCoVU6dO5fvvvycyUv+M1wnFo43Jy8srWTFp35sPZ4HVJyuHp5qamsbbFvu/m8T2J2eYbnal77wA3Q3e2Oem/e8iLdd5TpbuWdyaNWvw8PDAzc2NdevW4e/vj0KhwMDAgAoVKsRJJKtUqRLnLoYQQuQWpfOX5sz4M8w6MIt5f85Do9Fw/M5xqsyqwlrntXSs2jHpRoQQAJwYHTMBib6eerVaTVBQkN79ie3LibRDU69fv55oIrxv3z7deQO6CQg/nNQjISktb2ZmBkDDhg05ffp0qt7zV69eUaRI/BtqL1++jBNTcmmXHxk3bhwTJ07UXQva9+3p06dJxpOQlMSkfW+OHj1KixYtkhW7yJ5iX+exZ/T9kPZay23SPWl0dnaO8/vTp09xd3fH1dUVDw8Pzp8/z6ZNm4CYOxSpWetGCCFyAkMDQ+Z2mUvzCs3pv7o/zwOe8+bdGzr92okRTUcwr/O8rA5RCJFDuLq6cvPmTRQKRaK9YG/fviUsLIxdu3bpngGsWLEirq6uXLx4kc6dOyd5rIoVKwIkOEnMhxwdHYGYYa0pWYoitjt37uhNGrVDZcuVKxdne1K9x97e3gB6n1eEmGcZk4pHn9DQUN3zkB/GpI+joyNubm7cvHlTkkaS/tyyM23vvvY6zw03olIiw8+2ePHidOjQgWnTprFt2zZ+//13Pv/8c93yHEIIkds1dWiK+wx3Olf778vashPLaLCwAU+Cn2RhZEKInELby9ikSRP8/PwSfH333XdxygN8+umnQMxosISe4YutXbt2GBoacvHixWRN6GFvb0+lSpXw9/fXrSGZUtplDmKLiIhg9erVALRq1SrOvjx58gAJDwPU7n/x4kW8fX///XeSSeP58+dxc3OLt33Tpk2Eh4dTsmTJeEOE9dHOsLlixYpkrWeY2yX1uWVnZcqUSfN1npNleNIYEBDA1q1b6d27N7a2trRu3ZorV64wduzYRLt2hRAiN7Exs2HPV3v4ve/vmBiaAHDL5xZjz4xl5ZmVchNNCJGg6Ohotm7dCkD//v0TLduvXz8ATp48qRuC+emnn1KrVi1evnxJu3bt8PT0jFPH3d1dl5xBzIyeI0eOBGKSnr///jtOeR8fH2bPnh1n24IFC1AoFHz99dds2LAh3kiyhw8f8v333ye48PmhQ4f45ZdfdH8Lw8LCGDp0KD4+PhQvXpxevXrFKa9dSiOhpFY7Ucn8+fN59OiRbvuVK1cYNGgQJiYmeutpGRgY4OzszOPHj3Xbzp49i4uLCwBjx45NVq9Zly5dqFevHnfv3qVjx47cv38/zv73799z6NAhvbOX5kalSpUC4NSpU1kcSeq4uLigUCgYMWIEq1at0nudz5s3jwMHDmRRhBknQ5LGhw8f8vPPP9OsWTMKFizIwIEDefPmDbNnz+bBgwfcuHGDefPmUb9+/Yw4vBBCZEsKhYIvnb7k6pSrVC5aGYAIdQQjto6g+/LuvA15m8URCiGyo6NHj+Ln54eJiQndunVLtKyjoyPVq1dHo9HonutTqVTs2rWL8uXLc+nSJRwcHChfvjy1atXC1taWGjVqsGfPnjjtuLi40LlzZ16+fEnr1q0pWrQoderUoXjx4hQrVowZM2bEKd+uXTuWLl3K+/fvGT16NLa2ttSqVYvatWtTqFAhypQpw9SpU3XPA35o7ty5fPvtt1SoUIF69epRqFAhNmzYgImJCZs2bYo3YUnPnj0BWLJkCRUqVOCTTz7ByclJt2bgsGHDKF26NA8ePMDBwYFq1apRp04d6tWrh6WlJV999VWi7+MXX3yBv78/ZcuWpXr16jg4OPDJJ58QEBBAhw4dkqyvpVQq2b17N9WrV+fYsWPY29tjb29PvXr1qFixIhYWFnTo0IHDhw8nq70P2draJvhq2rRpqtrMSD169ABillipXLkyTk5OODk56e3VTUznzp0pUKAAZcqUoUCBAvHOPaOeKYx9nQ8dOhRra+t41/m0adMSfSY2p0r3pLFSpUrY29vj4uJCiRIl2LJlC69fv+bvv//m66+/jrNIqhBCfIwqFq3IpcmXGP7JcN22Xdd3UW12Nc7fP5+FkQkhsiPtUNOOHTtiaWmZZHltb2PsIaolSpTg2rVruLi4UKNGDXx8fLhz5w7W1tYMGDCAyZMnx2nD2NiYPXv2sHnzZpo3b054eDju7u4olUratWund3jeiBEjuH79OgMGDCB//vzcunULLy8vbG1t6d27Nzt27GDAgAF6Yx4/fjwbN26kaNGi3Lp1C4VCQadOnbh06RJNmjSJV75x48Zs2rSJmjVr8vz5c06fPs2pU6fw8/MDwMLCgrNnzzJgwAAsLCzw9PQkIiKCb7/9lgsXLiQ5iY2trS2XL19mwIABvHjxgkePHlG+fHlmzpzJrl27UvQ8W+HChblw4QK//fYbTZo04c2bN7i6uhIcHEydOnWYNWtWvEXkk+vNmzcJvt6+zX43Ivv378/8+fOpUqUKDx484NSpU5w6dSrZky5pBQUF8ebNG/z9/fWee2qfrU2OESNG4ObmxpAhQ/Re59u3b4/XM54bpPtEOLdv38bExIRmzZpRsWJFzM3NCQkJ0c04JIQQAvIY5WFJzyVYhliy4vYK3oa+5Yn/E5r80IRZnWYxse1EVEpVVocphMgGNm/erOs1TI4xY8YwZsyYeNvz5s3LxIkTmThxYpztCc32qFAo6NOnT7w1IRNTqVIllixZkqoZa/v06UOHDh2SXbd37960b98+wfKFCxdm/fr1QPyZdGfOnMnMmTPj1Zk4cSLz5s3TtRd72K62DX1LyDk5OfH27VvdjLUfMjY2Zvjw4QwfPlzv/pRwcnJK8SMNCZV/+PBhnJl2k1sPwM7OTu/+hLZrffHFF4wbNy5VE8nEbjc5syOfPHlS7/a1a9fqrlN9Ero+tCpVqsTKlSv17pPZU5Np3rx5eHh44O7uzs6dO4mOjkahUJA/f/54azdWqFABlUq+FAkhPl71CtVj6KdDcV7vzBmvM0Sro5m6dyrH7xxn05BNsqajEEIIIbJcuieNse9evX//nps3b+Lu7q57rVq1StcFbWJiQmhoaHqHIIQQOUpx6+L8890/zD00lzkH56DWqDnheYKqs6qybuA62ldpn9UhCiGEEOIjlu5JY2zGxsbUrFmTmjVrxtn+5MkT3Nzc8PDwyMjDCyFEjmGgMmBmp5k0Ld+Uvqv68jzgOa/fvabD0g582+JbXLq6YGxonNVhCiGEEOIjlOLBxNbW1owaNSpNBy1RogSdOnVi6tSpaWpHCCFym0/Kf4L7DHc6Vu2o27b42GIazG+A1wuvLIxMCCGEEB+rFCeNAQEBKZ4WVwghRPLZmNmwb8Q+fun1C0YGRgBcf3KdGnNqsPHCxiRqCyFEzqHRaGSdWiFygHRdcsPS0pIRI0akZ5NCCPFRUigUfN38ay5NukT5QuUBePf+HQPWDGDA6gEEhwdncYRCCCGE+Fika9IYHBzMjRs30rNJIYT4qFUrUY1rU68xsOFA3baNFzdSd35dHgQ+yMLIhBBCCPGxSNekUaSfZcuW4ejoSO3atbM6FCFEFstrnJc1zmvYMmQL5iYxC1Lff3mfCWcn8Ms/v8jQLiGEEEJkKEkas6kRI0Zw+/Ztrly5ktWhCCGyid51e+M6zZVaJWsBEKWJYuzOsXRc2pFXwa+yODohhBBC5FaSNAohRA5SpkAZzk08x5gWY3TbDt04RNVZVTlx90QWRiaEEEKI3CpVSeOjR49YsmQJ//zzD69fv07vmIQQQiTCyMCI+V3nM6PODAqYFwDAN9CX5ouaM3XPVKKio7I4QiGEEELkJqlKGp8/f86YMWNo2bIlBQsWpEiRIrRp0waAwMBAHj58mK5BCiGEiK96gepcnXyVFhVaADFT139/+Hs++eETHr95nMXRCSGEECK3SHHSuHXrViZMmEDr1q0pWLAgGo0GPz8//v77bwBu3ryJvb09FhYWNGjQgOHDh7N8+XLOnz/Pu3fv0v0EhBDiY1bIshB/ffMX87vOx0BlAMD5B+epNrsau6/vzuLohBBCCJEbGKS0Qs+ePenZs6fu91evXuHm5oa7u7vuX09PT969e8fFixe5ePEiCoVCV75UqVLcv38/faIXQgiBUqlkQtsJfFLuE3qv7I33G28CQgP47PfP+PKTL1nUYxEGihT/uRdCCCGEAFKRNH4of/78tGzZkpYtW+q2vX//nlu3bsVJJj08PAgMDOTRo0dpPaQQQgg96pWph+t0V77Y+AV/XP0DgOWnlnP2/lk2DtyYxdEJIYQQIqfKkFvPxsbG1KhRgxo1asTZ7u3tjbu7e0YcUgghBGBlasW2Ydto5diKr7d9TVhEGDef36TBggY4OzjTVtM2q0MUQgghRA6TqUtu2NnZ0blz58w8pBBCfHQUCgWDGw/m6pSrVC5aGYCwyDB+v/E7fVb3ISA0IGsDFELkOnZ2digUCry9vTPleM7OzqhUKrZs2RJn+8yZM1EoFMycOTNT4hA5X3h4OCVLlsTR0RG1Wp3qdmbPno1CoeDo0aPpGF32Ies0CiFELuVYxJFLky/xldNXum27ru+i2uxqXHhwIQsjE0KkhjYxS+q1bt26rA5ViCzl5ubGzJkz2bt3b5Jlly5dypMnT5g6dSpKZepTo1GjRmFpacnkyZPRaDSpbie7kqRRCCFysTxGeVjWdxl/DPsDM0MzAB6/eUzjhY1xOeySpruqQoisYW9vT8OGDRN8FSxYMKtDzDK2traUL18eW1vbrA5FZCE3NzdmzZqVZNIYFBSEi4sLpUuXjjPRZ2pYWVkxfPhwrl+/zp49e9LUVnYk0+kJIcRH4NNqnxLYJJB13us49+Ac0epoJu+ZzPG7x9k4aCOFrQpndYhCiGSaPHkyzs7OWR1GtjRy5EhGjhyZ1WGIHGLz5s28ffuWUaNGoVKp0tze559/zvz581m5cmWu+29UehqFEOIjkT9Pfo5+c5TpHabrlkI6fuc4VWdX5c8bf2ZxdEIIIUTmWr16NQC9e/dOl/YcHByoWrUqFy9exNPTM13azC4kaRRCiI+IgcqAWZ1n8c93/1DEqggAr4Jf0e6Xdnz3x3dEREVkcYRCZB4vr7dMmnSa3r0PMmnSaby83mZ1SOluyJAhKBQKWrZsqfc5q+nTp6NSqWjQoAHv37+Ps8/f358ZM2ZQvXp1LCwsMDMzo0KFCnz55Ze4urom6/hJTZDj5OSEQqHg5MmT8faFhIQwadIkSpUqhYmJCXZ2dnz33Xe8e/cuweMlNBHOunXryJcvHwMHDuT9+/fMnDmTsmXLYmJiQvHixRkzZgwhISEJtvvHH3/QoEEDihYtSoECBejUqROurq6cPHkShUJBs2bNkvN26Ny8eZO+fftSvHhxjIyMsLKywt7enj59+nDkyBG9de7evcugQYOws7PD2NgYGxsb2rdvzz///JPgcV6+fMkXX3xBkSJFMDExwcHBARcXF6KionByckKlUnH27Nk4dWJ/Jh4eHnTu3BlbW1ssLCxo0aIFV69e1ZU9c+YMbdq0wdraGnNzc9q3b8/du3cTjCc0NJSff/6ZOnXqYGFhgampKdWqVeOHH36Id/1B3M8zMDCQb775hhIlSmBsbEy5cuX44YcfiIqKilPHzs6OgQMHArB+/fo4z/s6OTnpyt2/fx9XV1fKlClD+fLl9car/ZxKlixJgQIFsLa2TvJzat++PRBzzeQmGTI89dKlS4SEhKT4PyAhhBCZw6m8E+7T3Rm0fhAH3A8AsOjoIk7dO8WmQZuyODohMt7atTcYMuRvFArQaEChgIULr7B6dWucnStldXjp5ueff+bEiRMcO3aMJUuW8M033+j2Xbp0iXnz5mFkZMSKFSswNjbW7XN3d6ddu3b4+PigVCpxcHDAyMiIhw8fsmLFCsLDwzN0wh3t98jLly+jUCioWLEiarWaxYsXc/LkScqVK5eqdiMjI2nVqhVnzpzB0dEROzs7vLy8WLx4MTdu3GDHjh3x6syZM4fp06cDULhwYYoWLcrJkydp0KAB06ZNS3EMly9fxsnJibCwMCwtLXF0dCQ6OpqnT5+ydetWQkNDadOmTZw6f/zxB/379yciIgJzc3McHR3x8/Pj8OHD/PnnnyxZsoSvv/46Tp1nz57RsGFDnjx5gqGhIZUqVSIkJITJkydz6dKlJOO8dOkSs2bNwtjYmDJlynD//n2OHz9Os2bNuHDhArdv36ZPnz5YW1tTqlQp7t69y+HDh7ly5Qo3btyI92zt8+fPadWqFbdv38bAwAA7OzsMDQ25desW48ePZ//+/fz999/kyZMnXiyBgYHUr18fLy8vKlWqhEql4sGDB8ybN48XL16watUqXdnatWtjZGSEl5cXBQoUwN7eXrevcuXKup/Pnz8PQJ06dZL1OWkTy8Q+J+3xISahzk0ypKfR2dmZVq1aZUTTQggh0omtuS37RuxjSa8lGBkYAXDt8TXquNThzPPc9T87IWLz8nrLkCF/o1ZriI7WxPl38OC/uH8/9/Q4mpmZsXHjRlQqFZMmTeLWrVtATI9P//79iY6OZvbs2XG+TAcFBdGpUyd8fHxo06YNjx8/5tatW7i6uhIYGMjp06dp2bJlhsY9bdo0Ll++TMmSJblx4wY3btzQxfDixQt27dqVqnZ37tzJ69evuXv3Ljdv3uTu3bucO3cOCwsLjh07xrFjx+KUv3z5sq63a9myZdy6dYtLly7h5+dH9+7dU7W0x5w5cwgLC2Py5Mm8fPkSNzc3bty4QUBAAFeuXKFHjx5xynt4eDBgwACUSiX/+9//CAgIwNXVFV9fX/bv34+5uTnffvttvLXQv/zyS548eUKtWrV4+PAh169fx9PTk9OnT3Pq1Cld0pSQadOmMXz4cF68eMHVq1d58eIFnTt3Jjg4mJEjRzJs2DAWLFiAr68v165d4/nz59SpU4dXr16xaNGiOG2p1Wp69OjB7du36dq1K0+ePMHLy4vbt2/z6NEjGjduzNmzZ3XJ+YeWLVtG/vz5efz4Ma6urjx69Ii9e/eiUqlYvXp1nN7NHTt2MHnyZADatm3L2bNnda+lS5fqyl2+fBmAmjVrJvk5+fn5cebMGdzd3RP8nLS0SeOFCxeIjo5O9D3OSTJsIpzcONWsEELkNgqFglHNR9HYvjG9/teLey/uERwezE+uP+G/yZ9f+/yKqbFpVocpPnJNm+7l1avwBPdrNGoUCv33wfXtCwx8j1qt/3uKWq2hevUNWFoa692fUoUK5eXq1f7p0pbWwIEDdcPv9Hn79i1WVla63xs0aMD48eNxcXGhX79+XLp0iTFjxuDl5UWTJk3iDflcsWIFT548oUKFCuzduzdODyRA48aN0/V8PhQcHMyKFSsA+O2336hYsaJuX9WqVVm6dCldu3ZNVdtRUVGsX78+Tk9lvXr1GDJkCIsWLeLYsWNx2l68eDFqtZohQ4bw5ZdfEhQUBICpqSmrV6/mwoUL3L9/P0UxeHl5ATBhwgSMjIzi7KtVqxa1atWKs23WrFm8f/+eJUuWMHTo0Dj7OnbsyPfff8/XX3/NL7/8ontGz9PTk0OHDmFoaMgff/xBsWLFdHUaN27M4sWLE72GACpVqsSPP/6oewbe2NiYhQsXsm/fPk6ePEnnzp0ZM2aMrryVlRWzZ8+mTZs2HDlyhAULFuj2HTp0iPPnz1O7dm1WrFiBtbW1bl+xYsXYvn075cqVY/ny5cyePTteb6OBgQGbN2+mSJEicc69Xbt2HDhwgD///BMHB4dEz+dDT58+BWJ6j/X58HMKD//vb5C+z0mrYMGCKJVKQkNDef36da6ZzVhmTxVCCEH1EtW5NvUaX23+io0XNwKw9vxaLj26xPYvtlOpaO4ZridynpcvQ/HxCc204717F8m7d5GZdryUsre3p0CBAgnuNzCI//Vu1qxZHDlyBFdXVzp06MDRo0exsLBgw4YN8dam27dvHwCjR4+OlzBmhjNnzhAaGkrJkiVp27ZtvP2dO3emaNGiPH/+PMVtV6tWTe+XfW3v0IfPXmp7HvUlWIaGhvTr1y/FvY3FixfH09OTP/74gyFDhiRaNiIigsOHD6NSqRKcjbNTp058/fXXnDp1SrdNu8C8k5MTpUqVilenV69efPXVV4SFhSV47IEDB+oSRq1y5cphampKaGgogwcPjlenevXqADx8+DDO9t27dwMxs4vquz4LFy5M7dq1OXHiBNeuXaNRo0Zx9rdp0yZO4hv7eAcOHIh3vOR48+YNQJwENrbYn9OgQYOS3a5SqcTCwoKAgABevXolSaMQQojcxczEjA2DN+BUzokRm0cQHh3Obd/b1P6+Nr/0+oUhjYfE+wIhRGYoUMA0wZ5ESF1PY2JJoZmZYbr2NKa31Cy5YWhoyKZNm6hZs6Yuofjll18oWbJkvPVa79y5A8T0wGUFbQ+Pg4OD3r85SqWScuXKpSppLF26tN7t2iQ89mQ4b9++5fXr1wBUqVJFb72Etifmm2++4dixYwwdOpSffvqJ1q1b06hRI5o2bYqNjU2csvfu3SM8PBwjIyPatWuntz3t6L7Y74f2PUwoPhMTE+zt7fHw8EgwzjJlyujdbmtry5MnT/Tuz58/P0C8yYpu3LgBwPLly9m4caPexPHevXvxziOpWBI6XnJoJ95J6MbIh5+Tk5MTTZs2pXnz5vE+pw/lyZOHgICARJPynEaSRiGEEHH0r9ef8CfhLPdazo3nNwiPDGfYxmEcv3ucFf1WYGlqmdUhio/MiROfYmFhEa9HDGKelQoKCtK7P6F9Xl5vcXBYo3eIqlKpwNV1AGXL5kv/E8liZcuWpUSJEty7dw9LS0s+++wzveW0QzBjD3HNTNoEQJsQ6JPa3pu8efUn8drrI/bjVdoEUqFQYGZmFi+5BjA3N09xDO3bt+fQoUN8//33XLx4kbt377JkyRIMDAzo0qULixcvpmjRokDMBDAQ0+N47ty5RNuNPXxSG3ti8SUVu6mp/kcTtIm8vv0J3VjUnsfNmzcTPSagN9FKyeeWXPnyxfw3HhAQoHe/vs9p+fLlej+nD719G/NctK2tbYrjyq5kyQ0hhBDxFDUryrnx5/jK6Svdtu1XtlNjbg2uPLqShZEJkXb29vlYvbo1SqUClUoR59/Vq1vnyoQRYMqUKdy7dw+lUklgYCDffvut3nLaZCKhL9MpoU0iEvpSr2+ZCzMzMwBevXqVYLsvX75Mc2xJ0SYqGo0mweU4goODU9V2u3btOHfuHK9evWLv3r18/fXXWFlZsWPHDjp27EhkZExPuPa9KFq0KBqNJsnXh7En1gOX2thTQ3sef/31F2/fviU6OjrBc0hpL3pqaRM6f3//BMtoP6cXL16wefNmRo4cqfdzii08PFyXwCd24yOnkaRRCCGEXiaGJizru4xdw3dhZWoFwMNXD2mwoAGLjy1GrYl/112InMLZuRKenoMYN642PXqUZ9y42nh6DspVy23Edvr0aRYtWoSpqSlHjx7FysqKVatWceDAgXhltRPPXLx4Mc3H1SYvCSWADx48iLdNu0SCp6en3mRTrVZnysLp+fLl0yUWCQ3j1A67TC1ra2s6d+7ML7/8ws2bN7G0tMTV1VW3FqK9vT2Ghob4+vommtx8SDvRT0Jxv3//XjeENTM4OjoC6GbvzWjJeZRCO2Owdjh2YqytrWnXrh1LlizR+znFpj1He3t7XbKcG0jSKIQQIlFda3TFdZor9UrHPN8UFR3FhN0T+P7K97x+9zqLoxMi9cqWzYeLSxO2bu2Ai0uTXNvDGBQUxOeff45areaHH36gWbNmLFu2DIAhQ4bES+g+/fRTAJYuXUpERESajq19hvDKlfgjFHbt2qUbxhdbo0aNMDU1xdvbm7/++ive/v3796fqecbU0C4tom9NyqioKDZv3pxuxypYsKBu0hofHx8gZgho69atUavV/PLLL8luSxv3iRMnePz4cbz927dvz9Tn7bQz0v7vf/+LM4w2o2hnX03sHLXP7OpL/BKj73OKTbuUx4eT+eR0kjRmgqioKKpUqYJCoWDbtm1ZHY4QQqSYna0dp8edZkKbCbpt115eo9b3tTjleSqRmkKIrDZq1Ci8vb1p1aoVX30VM+S8T58+9OzZk5cvX/LFF1/EKT9s2DBKlizJrVu36Nq1a7wE7ezZs8lOlrSzny5cuDBOz9aVK1cYNWoUhoaG8epYWFjolpb46quv4vQEeXh4JFgvI3zzzTcoFApWrVrFypUrddvDwsIYOnQojx49SnGbvXr14tChQ/ES8p07d3Ljxg0UCoVuFlKIWS/Q2NiYuXPnMn/+/HiJkK+vL0uWLGH58uW6beXKlaN9+/ZERkbSo0ePOMnNuXPn+PbbbzPtPQTo0qUL9erV4+7du/Tu3TveMiXv37/n0KFDKZqlNDGxb1aEhuqfeblOnTrkzZuXq1ev6k1kU/o5aWnXv8zotUwzmySNmWDJkiWJjssXQoicwNDAkPmfzefI6CPkN4t5TsMn0IdmPzVj1v5ZRKtzzyLGQmRn8+bNo1GjRgm+YvdI7dmzh/Xr15MvXz7Wrl0bp53ff/+dIkWKsG/fvjhJoLm5Ofv27aNQoUIcOnSIEiVKUKlSJapXr46VlRWNGzfWzcCalIEDB1KxYkWePHmCo6MjlStXpnz58tSpU4cmTZrQoEEDvfXmzp1LzZo1efToERUrVqRKlSpUrlyZatWqkT9//gQn8UlvderUYebMmajVar788ksqVqxIvXr1KFSoEFu3btUtt6FSqZLd5pEjR+jQoQMWFhZUrlyZOnXqUKRIEbp37050dDRTp06NM8trtWrV2Lp1K8bGxkyaNAlra2uqV69O3bp1KVGiBEWKFOGbb76Jt1zI8uXLKVGiBJcvX8bOzo6aNWvi4OCgu07q168PoHeCqfSmVCrZvXs31atX5+TJk5QvXx57e3vq1atHxYoVsbCwoEOHDhw+fDhdjlejRg3s7e159OgRJUqUoEGDBjg5OfHNN9/oyuTNm5eePXsSEhLCoUOH4rUR+3OqWrUqzZs3p1ixYgl+ThDzPOOBAwfIly+frsc+t5CkMYM9f/6cWbNmxVngVAghcrLWlVpzdcpVqtjGTOWu1qiZeWAmzX9qzvO3mTNkTIiPmZeXF+fOnUvwpV2z7sWLFwwbNgyA3377Lc7C6IAukVQoFEyaNClO0lG1alVu3rzJpEmTqFChAo8ePeLBgwcUKVKE4cOHJziJzodMTEz4559/GDx4MNbW1nh5eaFUKvnxxx8T7a00MzPj5MmTTJgwgRIlSuDp6UlwcDDffvstp06dytT1I6dPn8727dupU6cOb9++5f79+zRq1IizZ89StWpVXbzJtX79eoYNG4a9vT0+Pj54eHhgampKly5dOHXqFLNnz45Xp0uXLty+fZvRo0djZ2eHp6cnt2/f1tVbv349EydOjFOnWLFiXL58mWHDhmFjY8OtW7dQq9XMnj2bnTt36nrgUjMDbGoULlyYc+fO8eOPP9KkSRPevHmDq6srwcHB1KlTh1mzZnHixIl0OZZSqeTQoUN069YNlUrF5cuXOXXqFG5ubnHKaXu09V2LH35Ot27dSvJzOnjwIMHBwfTs2TNL1jjNSLLkRgYbPXo0nTp1okmTJlkdihBCpJvCloWZUXcGN5U3mXVwFmqNmlP3TlFtdjXWD1pPS4fcNSxHiOzgw56kpBQsWDDJkU6tWrUiKipKtzRJbDY2NsybN4958+YlOzbtMiexFShQgFWrVumtd/LkSd3PHy5pYWZmxvz585k/f368euvWrWPNmjXxjjVz5kxd719szs7OdO3aNd45ajk5OREdHR2vPa0ePXrQrVu3eEu4/PTTTwDY2dnpradP586d6dy5c7LLa5UsWZKff/45RXUKFizIihUrWLFiRZztarVaN1y4ePHicfbF/kz0Seo6TGz5C2NjYwYPHsy3336brB7OhD5PrT59+vDll1/qbcve3p4dO3Yk2n6dOnVo2bIlBw4cwNvbO87nGPtzSmxpn9iWLl2KiYkJI0aMSPzEcqAc29P46NEjVq5cydChQ6latSoGBgYoFArmzp2brPqHDx+mRYsWWFtbkzdvXmrUqMHSpUv1rsGTWkeOHOHvv//mhx9+SLc2hRAiu1ApVExqO4lT405RLF8xAF6/e037X9ozYdcEItUJL54uhBA5XXR0NBs2bABIcJhtdrV7924CAwNxdHTMsvU4s4sFCxYQHR2drJsjiTl9+jSnT59m5MiRFCtWLJ2iyz4yJGns2LEjffr0yYimdZYsWcKwYcNYtWoVHh4eREcn/1ma+fPn0759e44fP06+fPkoW7Ys7u7ujBo1ii5duqRL4hgeHs7IkSOZMWMGhQsXTnN7QgiRXTWyb4T7DHc6Ve2k27b4+GImn5vMw9cPszAyIYRIu9WrV3PmzJk42/z9/XF2dsbDw4MiRYrQsWPHLIouYS9evGDhwoW8efMmzvYjR47w5ZdfAsSbBOljVL16dVauXEmpUqXSlAMEBAQwY8aMeMOEc4sMGZ66cOHCjGg2DltbWzp06ECdOnWoXbs2q1atYteuXUnWu3DhApMnT0apVLJp0yZ69+4NgLu7O61bt2b//v0sWrSIsWPH6uoEBwcna2rnwoULY2lpCcQ8pG5kZMSoUaNSeYZCCJFzWOe1Zu+IvSz9Zynjdo4jIioCr0Av6syrw8oBK+lRu0dWhyiEEKly5swZhgwZgpmZGXZ2diiVSu7cuUNkZCSmpqZs3LgRExOTNC9Pkt7CwsKYMGECEydOpFixYhQqVIhnz57h6+sLQPv27Rk+fDghISFZHGnWGzx4cJrb6NSpE506ddI7RDs3yLHPNE6dOjXO78ldymLu3LloNBqGDh2qSxgh5oHvRYsW0bdvX+bPn8/o0aN1UxEfOnQoTtmErF27FmdnZx4/fszChQvZvHmz7j9E7cUTGhpKYGCgLrkUQojcQqFQMKr5KBqVbUTPFT25/+o+QeFB9PxfT47fPc7iHosxNTbN6jCFECJFPv/8cyIjI7l48SLe3t5ERERQpEgRmjdvzvjx4ylfvny6Pt6UXgoUKMCMGTM4cuQIjx49ws3NDVNTUxo2bEj//v0ZPHhwpsycKnKHHJs0pkZQUBDHjh0D9N9R6N69O8OHD+fNmzecOHGCVq1aATHrtPTq1SvZx3n06BHv37+nW7du8fYNHjyYr776KlMWNhVCiKxQo2QNLk26RJcfu3Da5zQA/zv9P87dP8cfX/yBfX77LI5QCCGSr2nTpjRt2jTZk6FkF6ampklOJJMdk12RPWX/Kz4dubq6EhERgYmJCTVq1Ii339DQkNq1awNw6dKlVB+nWrVqnDhxIs5r69atAEybNo2///471W0LIUROYG5izrfVv2Vl/5WYGsX0Lt7yuUWt72ux9tzaRGfXE0IIIUT28lH1NGqnFi5RogQGBvpPvXTp0hw/flxXNjWsrKxwcnKKs007PbGjo2Oiy2+8f/+e9+/f637XDmuNjIwkMjLnzESojTWzYk7P46WlrZTWTUn55JRNqkxi+zP7M0svcq1l32tNoVDQp1Yf6tjVoe/qvtz0uUlYRBhfbP6CxkUaU69JPWzMbZIVf3Yg11rGXWtRUVFoNBrUanW8ng/tDQbt/g8ltj+putlVZsednsdLS1sprZuS8skpK9eaXGvpUT4115parUaj0RAZGYlKpUrW97XMptDkktu9zs7OrF+/njlz5sR73lHrhx9+YPz48dStW5eLFy/qLTNhwgQWLlxIhw4dOHDgQLrF5+3tTalSpdi6dWuiQ11nzpzJrFmz4m3fsmULpqbyLJAQImd6H/2etbfXcuTxEd22QqaFGFtjLGWtymZhZCI7MDAwoFChQhQvXhwjI6OsDkcIITJVREQET58+xc/Pj6ioqETLhoaG0qdPHwIDAxNcdzQjfFQ9jdrnCBP7H5KxsTEQM+NUerKzs0vWcKxJkyYxZswY3e9BQUEUL16cpk2bYmOTs+7IHz16lJYtW+omFMopx0tLWymtm5LyySmbVJnE9mf2Z5Ze5FrLOddal45d2Hl9J19u+pKg8CD8Qv2YdGESLl1c+Lrp1ygUimScedaRay3jrrUGDRrg6+uLmZkZJiYmccpoNBqCg4MxNzfXe40ktj+putlVZsednsdLS1sprZuS8skpK9eaXGvpUT4111p4eDh58uShSZMmmJiYJPp39MMlVDJLpiaNz58/Jzo6mhIlSmTmYXW0/yNKbEpk7dDQPHnyZEpMHzI2NtYlrrEZGhrmqC/yWpkdd3oeLy1tpbRuSsonp2xSZRLbL9da5h/vY7rWetftTc0SNemwqANeAV5ERkcydudYTt47ybqB67Axy/43x+RaS//yBgYGKBQKlEplvAlGtMO7tPs/lNj+pOpmV5kdd3oeLy1tpbRuSsonp6xca3KtpUf51FxrSqUShUIR7++mvr+jWfUdLVOv6mrVqlG6dOnMPGQc+fLlA+Dt27cJltHu05YVQgiRvkrZlmJeg3mMafHfqIqDHgepOqsqZ+6dSaSmEEIIIbJCpt8KycpHKO3tY6Z5f/LkSYLjhR8+fBinrBBCiPRnqDRkftf5HB51GFszWwCeBzzH6Ucn5hycQ7Q6OosjFEIIIYRWzuk/TwfVq1fH0NCQ8PBwrl+/Hm9/ZGQkV65cAaBu3bqZHV4cy5Ytw9HRUbcEiBBC5EZtK7fFfYY7Tcs3BUCtUTN933RaLW6Fb4BvFkcnhBBCCEjFM43z5s1L9cHSe3KZlLKwsKBFixb8+eefrF69mjp16sTZv2PHDoKCgrCxsYm3ZEZmGzFiBCNGjCAoKAhLS8ssjUUIITJSEasiHB1zlHmH5zFz/0zUGjX/3P2HqrOrsmHQBtpUapPVIQohhBAftRQnjVOnTk31bEcajSbLZ5SaMmUKR44cYdWqVTg5OdG7d28A3N3ddbOWjh8/Xqb8FkKITKRSqpjWYRqflPuEPiv78DzgOa+CX9F2SVvGtR7H959+j6FBzpugSQghhMgNUpw0qlQq1Go1Xbt2xczMLEV1t23blujMpSlx7tw5OnfurPv93bt3ALi4uPDzzz/rtru6ulK8eHHd7w0bNtSt5dinTx+mTp2KmZkZN2/eRK1W0759e7777rt0iVEIIUTKNCnXBLfpbgxcN5CDHgcB+OGvHzh97zRbh26lVP5SWRyhECI3mz9/PgsWLGDGjBnMnDkzq8OJQ7vmd8mSJfH29s7qcMRHJsVJY8WKFblx4wZDhw6lVatWKap78OBB/P39U3pIvSIjI/WuUxIaGkpoaKju9+jo+JMpTJkyhapVq7J48WKuXbuGn58flStXZuDAgYwcORKVSpUuMQohhEg5W3Nb9o/cz5LjSxi/czyR0ZFcenSJ6nOqs+rzVXSr2S2rQxQiS9jZ2fH48WPd7wqFAjMzMywtLXFwcKBu3br06dMHR0fHLIzy43Py5EmaNm0aZ5tCocDc3Jzy5cvTpUsXRo8ejampaRZFmLAlS5bw4sULxo8fj7W1dVaHI7KxFE+Eo30O8OrVq+keTEo4OTmh0WiSfNnZ2emt36FDB44fP05AQAAhISG4ubkxevRoSRiFECIbUCgUfNPiG85PPE+Z/GUACAwLpPvy7gzfNJywiKx9Rl6IrGRvb0/Dhg1p0KAB5cqVQ6VScezYMb7//nsqVqxIt27dsmwB8I9dw4YNadiwIfXr18fc3JwrV64wefJk6tSpk+aOE0NDQ8qXL0+ZMmXSKdqYpHHBggUEBASkW5sid0pV0qjRaLh06VKKD5aVy23kNDJ7qhBCQC27Wlyfdp1etXvpti0/tZx6LvW443snCyMTIutMnjyZs2fPcvbsWa5evYq3tzevXr3i559/xtbWll27dtGoUSMCAwOzOtSPzunTpzl79iznzp3j2bNnHDt2DCsrK27dusXkyZPT1HbRokW5e/cux48fT6dohUi+FCeNLVq0YPTo0fFmHk2O/fv3888//6S43sdoxIgR3L59W7cEiBBCfKws8liwZegWVg5YSR6jPAB4PPOg1txarD23Vm5ICgHY2toyevRorl69SuHChbl79y7ffPNNVof10WvevDnTp08HYPv27ajV6iyOSIjUSXHSaGdnx+LFi5kyZUqKD9agQQM++eSTFNcTQgjxcVMoFAxpPIQrk69QsUhFAEIjQhm0bhD9V/cnODw4iyMUInsoWbIkv/32GwCbNm3i6dOncfbb2dmhUCjw9vbmxIkTtG3blgIFCpAvXz5OnjypK/fkyROGDx9OqVKlMDY2xtbWlrZt2/Lnn3/qPe7MmTNRKBTMmjWLFy9eMGTIEIoUKYKJiQkVKlTgxx9/JCoqKl69devWoVAocHZ2Jjg4mClTplC6dGlMTEwoXbo0U6ZMiTNXxYfevn3L1KlTqVSpEnnz5sXc3Jx69eqxcuXKBBO0qKgoFi5ciIODAyYmJhQtWpShQ4fy4sWLpN7eVGnSpAkAAQEBvH79Wrc9JCSEuXPnUqVKFfLmzYuFhQV169Zl2bJlet8rb29vFAqF3kevFAqFboWCP//8kyZNmmBubo6lpSVt27bF1dU1Tnnt+659RrZMmTK6NhQKRZxr4ezZs3Tp0oVChQphaGiItbU1FSpUYMiQIVy8eDGtb4/IIVKcNAohhBBZpWLRilyefJlhTYbptm2+tJkac2pw/fH1LIxM5DQR797hvmIFWxo0YGWZMmxp0AD3FSuI+Hc29pysU6dOFClShKioKP7++2+9ZbZu3UqLFi24dOkSpUuXpkiRIrp9ly5domrVqixfvpxXr15RuXJl8uTJw5EjR2jXrp2u50yfN2/e0Lx5czZs2EDBggUpWbIkd+/eZdy4cXTv3j3BRO79+/c0bdqU33//HTMzM+zt7fH29mbevHk0b95cb+J469YtGjVqhIuLC15eXtjZ2VGwYEEuX77MsGHD6NmzZ7yRCNHR0XTt2pUJEybg6elJyZIlyZ8/P2vXrqVevXrpNmFjbPpGQ7x69Yr69eszbdo0bt26RdmyZSlWrBiXL19m5MiRtGvXjvDw8BQfa/ny5bRv35779+9Trlw5oqOjOXLkCE2aNOHu3bu6cgULFqRhw4YYGxsDUKtWLd3zmA0bNtStEb5v3z4++eQT9u7dS1RUFFWqVKFgwYI8ffqU1atXs23btlS+KyKnkaRRCCFEjmJqbMqK/ivYNmwbFnksALj/8j7159fn139+leGqIklv7t5lTfnyHB0+HJ+LFwl8+BCfixc5Onw4a8qX502sL9c5kVKppH79+gAJPuYybdo0ZsyYwcuXL7l48SI3b96kfv36hIaG0qNHDwICAujRowe+vr5cvXqVp0+fsm7dOlQqFXPmzEmwx3HFihVYWlpy7949XF1d8fT05NSpU1haWrJ3715+//13vfV27tzJy5cvOXXqFB4eHty4cQMPDw+KFy/OxYsXmTFjRpzyISEhdOnSBR8fH77++mtevXrFrVu3uH//Pjdv3qRixYrs3LlT1+uq9dtvv3HgwAHy5cvHmTNn8PT0xM3Njfv372NhYcG6detS+G4n7cyZMwBYWlpia2sLwPDhw7lx4wYVK1bk3r17uLu76x5LKliwIEePHo13zsnx3XffsWbNGnx8fLh27Rq+vr40b96cd+/exVlCpG3btpw9e5ZChQoBMUNntc/Jnj17lurVqwMx67Or1Wp+++03Xrx4wbVr17hz5w7BwcGcOHGC5s2bp/HdETmFJI1CCCFypJ61e+I6zZVaJWsBEBEVwddbv+az3z/jbcjbLI5OZFcR796xo3lzQl68AI0m5gW6n0NevGBH8+Y5vsdRu0b1y5cv9e7X9hgaGMSsvqZQKDA2NmbLli08efKEggULsn79eszNzXV1Pv/8c7744gsgZl1sfaKiovjtt9/iDKFs0qQJc+bMAeDHH3/Ue2MnKiqKJUuWULlyZd22SpUqsWzZMgB+//13goP/G4a+Zs0aHjx4QIcOHfj555+xsLDQ7XN0dGTLli0oFAoWLVqk267RaHS/z507l0aNGun22dnZsXbtWiIjI/WeV2odP36c2bNnA9CtWzeUSiVeXl7s3r0bgI0bN8aZDbVWrVosXboUiJkUMfY5J8fgwYNxdnbW/W5ubs7ixYsBOHLkSIrj9/LyIl++fAwfPjzOCgMKhQInJyc6duyY4jZFziRJoxBCiByrdP7SnJt4jjEtx+i27XHdQ/U51bn4QJ61EfHd2byZd76+aPSs4wygiY7mna8vd7ZsyeTI0lfevHkBEkw6BgwYoHe7djjr0KFDMTExibd/9OjRAJw/f56QkJB4++vXr0/VqlXjbR80aBAmJiZ4e3vj6ekZb3/RokXp3LlzvO0dOnSgRIkShISEcO7cOd12bdLVv39/vedRpUoV7OzsePjwIc+ePQPA09OTJ0+eYGJiEiex0qpRo0aaZ61v0qQJjRo1omHDhhQvXpwWLVoQEBBAuXLldIn20aNH0Wg0NGrUSNejF9tnn31GsWLF4p1zcgwZMiTetsqVK2NiYkJgYGCKl2IpXrw4AQEBHD16NEX1RO4jSWM2JUtuZA2v4Ahm3XgFwKwbr/AKjsiwYx31fUeLf2IeQG/xz2OO+qbtrnZmxp5dfIznLOIzMjDipx4/sX/kfqzzxixO/fjNYxr/0Jgf//pRZisUcdxavz5dy2VX7/7tKY3dAxdbhQoV9G6/d+8eENNbp4+9vT1GRkZER0fz4MGDePsdHBz01subN6+u91N7jNjKly+PUhn/a6lCoaB8+fLx6t24cQOI6fHUJmofvrSTzjx//hxAF2/JkiUxNTXVG2e5cuX0bk+uc+fOce7cOc6fP09AQADVq1dn1qxZXL16lfz588c5j4TeY6VSqXsf9b1XiUloDUftsd+lsAf922+/RaPR0KpVK2rVqsXEiRM5ePBgintARc4nSWM2JUtuZL61DwNwOPiAJfdiHoJfcs8fh4MPWPcwIN2PNeiSD61OPuWKf8xD7lf8w2l18ilDLvmkqr3MjD27yIpzliQ1e+tYtSNu091oWLYhAFHRUYzbOY6Ov3bkdfDrJGqLj4VuWGpiNBpC/PwyJ6AM8uTJEwAKFCigd7+2J/JD2qQioXoKhUKXgOhLHBKqBzGTr6RXPe0alG5ubrpE7cOXtnxYWFicc9PGr09i+5IjOjoajUaDRqMhODiY69evM3369DjDfJN6jyHx9yoxCX2u2oQ8pc98f/XVV2zYsIGqVaty7do1FixYQMeOHSlQoADDhg2TtUA/IgZZHYAQ2YFXcARDLvmiBqL//XsarQE1MOiSL37hURQ2MUCpUKAAlArtS4ESUChi7sAo1THDnf7yfYfSwDBmW6xySgVc8w9j7UP9f2RXPwykZj4T6tmaolCgO5YCdEOp7gVHYGCg/nefgsfvEo598CVfyuQ1pJS5Ucz2qJhnNXzDIlFFxrTLv/Fr970Ij8IgSqHbp90P6N0We3vsWnrrJFI3dn39bf/nQRLn3Ci/KWX/Pef0svZhAIMv+ZKHaLaYwmJPf+Z5BrKmbmGcS1ul67FE6hW3Ls7JsSeZsX8GLn+6oNFoOHzjMFVnV2XLkC18Ul6WffrY5S1YkMBHjxJPHBUK8v47QUhOpFaruXDhAkCK19U2MzMDEn4WUqPR8OpVzM2z2ImQlnafPto206OemZkZAQEBXLt2jWrVquntpYxNrVbrzi2xY8VeEiOjJPUeA7rlP/S9V5mtf//+9O/fHz8/P06dOsXRo0fZvn07K1euxNfXlwMHDmR1iCITSNIoBLDmQUBMoqLnO4QGmOSe8P9gYstDNFtNoce554ShSrqCHl9d079OlLbt2n89SnbbaqDJP0/iteFw6GG8NrT7yh18kOrYswM1UPXPh9gYqzBRKTFWKjBRKTBWKjBWaX9Wxt2mVGCsirVNW0elwESpxD8imtHXYz4X7SWi+fc1KJVJqldwBOu9XlObmF7Lz+1tsU/nRDc7iXj3jjubN3Nr/XpCXrzgvaEhN54/p9KAARj9+wUqvRioDPi+y/d8Uu4T+q/uz8vgl/gE+NDsp2bM7DSTye0mo1Lm3GtcpE3Fzz/HJxlry1X8/PNMiCZj7N27Fz8/PwwNDWnVqlWK6pYrV043k6c+Xl5eREREoFKp9A6FvJvAzLOhoaG63k99Q0A9PT31DiXXaDS6ZyBj13N0dOT8+fPcuXOHatWqJXle8N/QzSdPnhAaGqp3iKq+5y3Tm/Y8EnqP1Wq17n1M63DZpChi36VNQqFChejZsyc9e/ZkzJgxVK5cmYMHD+Lr60vhwoUzMEqRHcjwVCEA75DIJEcriZwjNFrD09AovIIjuBn4nqv+4Zx7HcY/L0I57BPCnmfBbH0cxLpHgay4H8CSe29ZeOcNs2++ZorHK8a6vWTktRcMvexH/4s+uoRRHw0w5voLrr4J407ge56ERPL6fRRhUeoEhwF9bMOJdcsbfDmc5/8ubxB+7x7/jBiRocsbtKrYCrfpbjRzaAaAWqNm+r7ptFrcCt8A3ww5psj+KvTti1nhwihU+m8cKFQqzAoXpkKfPpkcWfp4/PgxI0eOBGImuylatGiK6rdu3RqAlStX6l0n8JdffgGgYcOGeodCnj9/Xve8YWxr1qwhPDyckiVL6p5RjO3Zs2d6e6wOHTrE48ePyZs3Lw0bNtRt79q1KxCzxEdyh1yWK1eO4sWLExYWxoYNG+Ltd3Nzy5THglq1aoVCoeDs2bO4urrG2797926ePXsW75wzQp48eYD/hvAml6Ojo24tRx+f1D1aI3IW6WkUArDLa5hgT6MSaFUoL52LmaNGg1oTU0ytAbUm5nc1/450io6Ehw+YWtGWKKUKzb/7dOU0sP5RAL7h+mftAyhooqJrMXNdm5p/66vU0fAS+pa0JEKh+renS8N1/3DuBEXoCx0FUM7ciMpWMYv3Gqij4S10KmpOpCLmC5O2noEmCt5Ch6JmRBB3X+y2dbPTx97272+x/7+t+aB80u1p4pdLoO7DdxE8DY3Sc8YxLAyVmKoUvFdrCI/W8F4d8/5nlAM+7zjgE39yAQVgaqAgr0pJXgMlpgZKVAoNHgExz0LqGwp93C8EWxMDVAowUChi/lUq4vyuUigwVEdjB6x+EIDSwCDBsjG/K1CqY96vsy9DMTQyjFtGoUClVGDwb9tExwxV9guLxDg6dnsKDJQxZdTJ/JKmXd7g3YsXgAbFBx/uu3+XNxjk6ZnuPY4Aha0K8/e3f+Ny2IUZ+2eg1qj55+4/VJtdjU1DNtHSsWW6H1Nkb0ZmZnQ/fjzmuvT99+aBRqMbF5+3YEG6Hz+eIddjRnr9+jVbtmxhzpw5vH79GkdHxzjLTSRX7969mT17Nk+ePMHZ2ZlVq1bphlNu2rSJFStWADBx4kS99Q0MDPjqq6/Yv38/pUqVAuDs2bNMnz4dgLFjx+rt3TIwMGD06NFs3bpVt8bk7du3dQnwl19+GWeo5hdffMFvv/3GmTNn6NevH4sWLYrT2/Xu3TsOHz7MxYsXde+DUqnk22+/ZcyYMUyZMoUqVarQoEEDICbZHjhwIIaGhum+7MaHypYtS9euXdm1axcDBgxg3759lC5dGoDr168zatQoAEaOHJnhw1NLlSrFnTt3OHXqFBUrVoyzLygoiGHDhvHll1/SpEkT3RDg6Oholi1bxtu3b8mbN6/emwAi98m0pFH7H0P16tUZM2ZMht85ESIlBpWxYuGdhKehXlqrULKGH0ZGRnL4IYyrYIOhoaHeMs0KmtLq5NME29hcvyjNC8W/exsZGcnhw/Bb7UJx2vYKjsDh4IMEk8aDnxTXxR7Thhsb6xeJF1/MPnc21y+aYOzZhfac9c2JqQSutS4V7/OK0iWQat5HawhXa3j/b0IZZ/u/22LKxGybffM1L98nnOgnRAOERGkIiYqGZNTXAJseByWrbe1w4jGuL5I1nFhbvv3pp0mW15Ytr2cY84dlbHd7EqEwiJtYKiCvUs1iBfSd8gsNfXxIcABUdDTvfGKWN6g6bFiS55EaKqWKqR2m0qRcE3qv7I1PgA8vg1/S+ufWTGo7iVmdZmGgknuoHxMbBwcGeXpyZ8sWbq1bR8iLF+QtVIiKn39OhT59sn3COG/ePFatWgXA+/fvef36Nd7e3rr93bt3Z/ny5QnOnJoYU1NT/vjjD1q3bs327ds5ePAgFSpU4MWLFzx9GvP/rqlTp9K2bVu99YcNG8a+ffsoV64clSpVIiwsTDfks2PHjnz11Vd663Xr1g1PT08aN25MxYoVUSgU3Lx5E41GQ+3atZk1a1ac8mZmZhw4cIB27dqxbds2/vjjD8qXL4+FhQVv377lwYMHREdHU7du3Tj1Ro4cybFjxzh8+DANGzbEwcEBExMTbt68SZEiRXB2dmblypUpft9S6vfff+fevXvcuHFD915FRkbqhqy2aNGCmTNnZngcPXr04PDhw4wYMYLff/8dGxsbAH7++Wfs7OzYvn0727dvJ2/evJQtWxZDQ0O8vb15/fo1CoWCn3/+WXdTQeRumfZ/Se0fM29vb/bu3Uvt2rUZM2YMPXr0yKwQhEiQvbkRq+sWZvAlX1T/frtVKUCpgdV1C6frpCotC5sxuLQlq/VMhjO4tKXehDExmRl7dpGaczZQKjBTKjBLxah8j4D3/O9BQIL7q1oZ0zC/KSFRakKj1IREqwmJ0sT8HKUmJPq/n0OjM7DLMwtEqiFcTx9yHqLBFEoc24NGoUCRSM+kRgFX16xlW51P8Q6JxC6vIYPKWCX7Gc8Pn5fMW7BgzJf/vn3jfPlvUq4JbtPd+HzN5/x58080Gg3zDs/j1L1TbB26leLWxVP1HoicycjMjKrDhmXYzYqM5OXlhZeXFxCTPFlZWdGiRQvq1q1L3759E1xOI7nq1q2Lu7s7Li4uHDlyBA8PD/LmzUurVq0YPXo07dq1S7Cura0tx48fZ8GCBRw5coQ3b95Qvnx5Bg0axJgxYxKcsMbY2JgTJ04wadIkDh06hJ+fHyVKlKB3795MnTpV71BYBwcHzpw5w+bNm9m7dy937tzh4cOHFC5cmE8++YR27drx2WefxamjUqnYu3cvP/30E2vXruXhw4fY2Njw+eefM2fOHJYsWZKm9y658ufPz4ULF1i0aBF//PEH9+7dQ6lUUrt2bQYMGMAXX3yRKTdwtRPcbNmyBS8vL27evAlAQEAA5ubmbNy4kb///psrV67g7e1NREQExYsXp02bNowdO1bvmpwid8q0pHHt2rUA+Pn5cf78eS5cuEDv3r0laUzAsmXLWLZsGdEJLD4s0p9zaSsa5TdlnddrePqA0eWscba3zZCka1XdIvQuaclsd18Ih9rWJkyvWjjFCaNWZsaeXWTmOY+tYMPKBwEJ9ububFQs2ced6PaCH+/6oy93VCmgn50lX5S1IloD0RoNUep//9X9riFaA1FRkXDjAb/XKkS00oAojUZPnX/LajRooqPA+wHflrfmvUIVs12tITpWGe02RXQ0+EPHouaEoYzTprasSh0NYVDVyoRQlHHai9KAoSYmm7cI8keZxFBWhUbD/UfP+eHuG90owYV33rC6bmEa5jdlzYOAOMkkoNtW+qU3hUd0J9zXD40ipq2AR4/wuXCRC7Nn0/34cWxirRuX3zw/B78+yKKji5i0ZxJR0VGcu3+OarOrsW7gOjpW7Zisz1GIrBC7NzGj2yhZsiTLly9P1TEKFizIqlWrkpzR9EPm5ubMmzePX3/9Ndl1zc3NGT9+fILDZfUxNDRk4sSJ8eqo1WomTpzIvHnzUhS7k5MT0dHRBAUlb6SIVt68eZk2bRrTpk1LVnk7O7sEn99M6rnOxD73L774gnHjxuk95379+tGvX79kxSdyt0xLGj/XMwtZShcs/ZiMGDGCESNGEBQUpHvQWGS8suZGzKicn8NPYUbl/Bl6l695obw0sSnJ4cO3ONasZJqPlZmxZxeZdc725kas+bdnM/YSIEpS3ps7uEw+frjjr3efRgNTKyYv8Y2MjOTwDehjZ5ms846MjOSwN8xMxvsUM1TZlU16hjHHLXOT0y30X7sx+z2pUKooPi+fJdrTqFYoCLa0+S+R/vffQf++3wrFf4+cLfh3GLlSAYZhIYz9rishgW9QxXpeUpHE85JKpZKxrcfSqGwjeq3sxeM3j/EP8afTr534tsW3zP9sPkYGufeGixBCCJFSWTp7akZPIyyEEOnFubQVnh3K8G15awC+LW+NZ4cyKV6jUTu0Vglxh9aSO4cTV+jf/7/JbxKg0Gi42uTTeNs1oFuLU/uvdqmTaA1UO3cQi7cvY3o99Yn1vKQ+9crUw3WaK12qd9FtW3xsMY0WNOLhq4fJODshhBDi4yBLbgghRDJpezYhpmcztQmeNgEdXS4mAR1dLnUJaE5QvndvzIoUhgSWN1ArVQTlK4Brw/Ypbrvm6X1oklhjTKOAW+vXJ7g/X9587Bq+i6W9l+p6F694X6H6nOrsuLojxTEJIYQQuVG6Jo1Pnz5ly5Yt/PDDD8yePTvOvsjISCIiItLzcEIIkWOlVwKa3WmXNzArWBBQ/Jfk/fuvxiY/q6asIcIk5c/zmge+Sdbzks8uXcalam2OLllGxDs9S6MoFIxsNpILEy9QtkBZAILCguixogdfbf6K8Mj4a9UJIYQQH5N0SRpfv35Nz549KVWqFP3792fixInxpkYeOHAgefLk4dq1a+lxSCGEEDmEdnmDliuWU7RePSxLl8akfHma/fYbndxv8bJI6VS1G2xpgzqpnkZAGR2F6sY13L4Zya9l7Xlz967esjVK1uD6tOv0rtNbt+33k79Td15dPP08UxWjEB+LmTNnotFomDFjRorqOTs7o9FoWLduXcYEJoRIF2lOGoODg/nkk0/YsWMHRYsWxdnZmaJFi8YrN2TIEDQaDbt3707rIYUQQuQw2uUN+pw/j/PduxSfP5/KQ4ZQobB1nGc8lYqYfxWQ8NqO/7rWpHOiE+wQqw2lRoMCiHz1iq3NmuntcQQwNzFn85DNrBqwijxGeQDweOZBzbk12XRpU0pOWQghhMg10pw0Lly4kDt37vDZZ59x9+5dVq9eTcmSJeOVa9KkCXny5OHEiRNpPaQQQohcRPuM5zgHG3oUt2Ccgw33OpRhTSLJpEoBbo06EJSvANFK/c9L6qNSRxPmm/DkOBAzXHVw48FcnnwZx8KOAIS8D2HQ+kH84vYLIe9D0nbCQgghRA6T5iU3du7cibGxMatWrSJPnjwJllMqlZQtW5YnT56k9ZBCCCFymbLmRrhUKxBvW6P8pqyOtU7j4H/XaYzZZoF69W7yfrBOo4YkeikVCm6tX5/kou6Vilbi8pTLjNo6ijXn1gDwz7N/qL+gPn988QeVi1VO/QkLvZJaa04IIXKjnPC3L81Jo7e3N+XKlUvWWoKmpqZ4espzIcmxbNkyli1bRnR0AlPJCyHER0BfMgnE2laUiJb3uLNlC7fWrcP3yhWIikq0TYVGQ4ifX7KOn9c4L6udV9PUoSlfbvqSkPch3PW7S515dfil1y8MaTwERRLPVYqkaRcVl//nCSE+Rtq/fdq/hdlRmiMzMTEhODg4WWV9fX1lofpkGjFiBLdv3+bKlStZHYoQQmRrsZ+XLFy7djKW4VDw2twGr+Dkzegd8e4dld1D+PmiPVN3GDBiP1TzCGfkmmH0WdmHoLCg9DiNj5qhoSEqlYqwsLCsDkUIITJdcHAwhoaGGBoaZnUoCUpzT2PFihW5dOkSjx8/1vsso5abmxtPnjyhTZs2aT2kEEIIoVfFzz/H58LFxAtpNByo3Z6pBx/wfdX8BEao8Q6JxMIw5j5qUKQau7yGNCtoysmL7uQd9hmGr1+AQoGlRoMFUPIltHCFFSHbqOF9he1fbKdmyZoZf4K5lEKhwNTUlMDAQKytrVElsK6nEELkNmFhYQQFBWFlZZWtR66kOWns168f58+fZ9iwYezZswdTU9N4Zd6+fcvgwYNRKBQMGDAgrYcUQggh9KrQty8XZs/m3YsXoGeoY7RSxTtLG641aI8amOT+CpUC1JqY5Tngv+chF7k+Yfx3XVEFvonZ9u8zJ9r9ZmHwxWFY2P0B9V3q82P3H/m62dfZ+n/62VmBAgXw9vbm8ePHWFtbY2xsjEKhQK1WExERQXh4uN6hW4ntT6pudpXZcafn8dLSVkrrpqR8csrKtSbXWnqUT07Z6OhowsLCCA0NJTg4GGNjY2xtbVN0DpktzUnj0KFD2bp1K0ePHqVy5cp0796dFy9eALBmzRpu3rzJpk2beP36Na1ataJXr15pDloIIYTQx8jMjO7Hj7OjeXPe+fjqJsdRKxQoNBreWdqwYvIaIkzy6upEfzD/gPbXGucOYvH2ZYKT6qg0YBEK1R/AJYdIRm8bzYm7J1jtvBrrvNYZcn65mZGREcWKFeP169f4+vrqtms0GsLCwsiTJ4/ehDyx/UnVza4yO+70PF5a2kpp3ZSUT05ZudbkWkuP8sm91kJDQ7GwsMDKygpbW9tsP8IizUmjSqXi4MGDDBs2jO3bt/PDDz/oZgAaOnSo7ucePXqwevXqtB5OCCGESJSNgwODPD11k+M8fOyDX958XG3yKa4N28dJGBNT8/Q+NP8mmwlSKOj0sjCXHHwA2Ou2l+uzr7Nt2Dbql6mfHqfzUTE1NaVEiRJERUUR9e+ERpGRkZw+fZomTZrofd4nsf1J1c2uMjvu9DxeWtpKad2UlE9OWbnW5FpLj/LJKRsVFcWJEyeoUqUKRkZGKYo9q6Q5aQQwNzdn69atTJ48mT179nDjxg0CAwMxMzPD0dGRLl26ULOmPOshsj8vr7esXOnOxYu+nDt3jqFDq2Jvny9DjnX0qDfTpp3l4cPXlC69nTlzGtGypV2q28vM2LOLj/GcRfJoJ8epOmwYk9xesvzum3g9ikkxD3yDMolp0BUaDfmjTDgw8gCfr/0c/xB/nvg/ofHCxszrMo+xrcbmqKFq2YWBgQEGBjFfUVQqFVFRUZiYmOj9ApbY/qTqZleZHXd6Hi8tbaW0bkrKJ6esXGtyraVH+eSUjYyMRK1W56he6XRJGrUqV65M5cqybpXImdauvcGQIX+jUIBareH8+Wv89NM1Vq9ujbNzpXQ91qBBR1i79qbu91ev/GjVaieDB1di1aqUTxaVmbFnFx/jOYvUGVTGioV33qS4XrClDflePUs0cdTOxOpUuhXu093pvbI3Z++fJVodzYRdEzjheYINgzaQ3zx/Wk5BCCGEyFLpmjQKkVN5eb1lyJC/Uav/+3IY/W+3xMCBR1iz5gbm5kYoFAqUSgUKBf/+G/vnmHp+fr5s23YElUr5b3ni1PPxeceRI95641i9+ibm5kZUrGiLUqmI81Kro/HwCCYk5B5GRga67X5+IXz11TFif6/Vxj5o0BEAihUz/3d7FB4eoeTJ8xRDQwNdzAqFgqioKG7dCsPC4jkGBjH7tHfAPvxZW+e/n5Pan9DPKSn7X/uPHwcl+HkNHvwXjRoVpWzZ9O9xlJ7NnMne3IjVdQsz+JIvCsW/zyxqQJ1EvWtNOlPSyy3xQrFmYl1dtzAnxp5g5v6ZzPtzHhqNhiM3j1BpZlWaN1uGxqpOvBlaB5Wxwt48/tAkr+AI1nu9pjYw68YrPre31VtOCCGEyAxpThr379/PN998w4gRI/juu+8SLPfTTz+xbNkyfv31V9q1a5fWwwqRrtasuaFLTvQ5c+Z5Clv0THUsP/98PYkSfya7LY0mJumNb3citXYmu/3sSK3WULHiWmxs8mBmZkTevIaYmcW8Yn42SuHPMb9v2XKHIUP+AmLe17Nnr/Ljj1dZs6aN9GzmAM6lrWiU35TVDwLwDonELq8hVkZKJru/iumt1jN76vWGHWix+3fMAt+gUic9E+vgS740tC3N3C5z+aT8J/Rb1Y+XwS95GeTL1r3doNRwsPsSFCoUgFIBC++8YXXdwjiXttK1u/ZhAEMu+WKqiGZTHlhyzx8Xz8B45YQQQojMkuakccOGDTx+/JguXbokWq5z586MGzeODRs2SNIosh1v7yCSeHRJ5CAREWp8fUOAkAw7hvZ6GTToSKp6NqXXMvOVNTfCpVqBONs+K26hSyQt/+0FDPy3F7BFoRIsiN5M3fF9sXj7Eo1CgTKRmVjVQIXDDylrZoRd3vLUa/sn+4+OgLcXY/Y+WgZvr0LFBWiMC+iesRx8yZdq+Yz/z959x1Vd/XEcf12WIEPcGw1xL0Rxa+7MTC3LlZqKo+JXWbk1LfdqmFGZ4iy11ByZI7fmREVz75VbFAFlc39/oKQJCN4LF+T9fDzug3vP94zPzZveD+d8z8HDKRunQ6Poufsqcfy7q2vsg1lRn91XqZs3Ox6acRQRkXRmctIYGBhIvnz5cHd3T7aeh4cH+fPnZ+/evaYOmSX4+fnh5+dHbCLnjIn5FS/ukuRMo7W1gfffr8Knn9YiLs6I0ch/fhoTXkdFRbNx4yZefLEB1tbWj9V5+LxTp5X8/fetJGNxd8/BkCE1iYszPvaIjo7h8OEjlClTFoPBKqF89epzbN36T6JJr8EAtWoVolEjN4xGiImJ5cyZ07i7l0jYnMNojN/6OTY2jjNnzuLu7o6VlSGhv4exP6z7ZFnSz//t/2nXn/780bLAwBscOxaUZKKfO7c92bPbEhYWzb170URFpd3/R0YjfPDBBj79tDa5ctmTM2c2cua0x9Y26a2zs+r9mKdO3WHmzEOcPRtMbOwtSpa8Q7ly+Z7eMA0llkg+akbZskz+4g8qb/+D6luX4h56nbPOBdiTxE6ssUY4ERrFidAowAE8p8OF6XD2WyAOgnfDnteh3HjIXRfiS6mSxJL1RxkM4H8mONl4RURE0oLJSeOVK1eoVKlSiuoWLVqUI0eOmDpkluDr64uvry8hISHkyJHD0uE893r0qMjEiQGJXjMawde3CrlyOTy1n+joaPLnt8XdPUeSO2ZNntyAZs2SXgL644/NaNy4WKJ9r1p1hRYtvB7r+/XXS1GmzMyEBOtRBoOBOXNeTpgFi+8jmBYt6iS6XfiqVSG0aFE3w+/8durUnSTfs5WVgV273nps5i8qKpZ79+ITyLCwqIRk8vHn8a8Te75x40XCw2OSjGf16vOsXn3+sTInJ1ty5rQnZ077B8lkfEJpMMDMmYcTvQfVx2cNrq7ZcHd3xc7OCjs7a2xt438++tzWNvPtxvloomx8cFPh0qXzMnyiXNzRlmgHR3Y3bsffjduyIPsZhtwvQThP/lLAAOSysyI81sj9h9OEBuv4Jamu1eBIf4i8DtG34WBvKNYTXngfrFL2/1usEZb+E8qrhZ2omccBq0y0656IiGRuJieNjo6O3Lx5M0V1b926RbZs2UwdUsTsSpbMib//S/j4rH3wpdaIwRA/2+bv/5JZN1Vp2rQ4Pj4V8Pc//MQ1H58KiSaMyUnP2DOK1L7nh0lXzpz2zzReuXIzOXbsdqraxCee0Vy6FJriNnFx8Npry1NU18bGCmtrI/b23z+RVCb23NbWwJ07t5gz5w/s7W2SrWttDWfO3OHs2QM4ONg+kbDa2VljZWXk0KH7uLpeIXt2O2xtrR9LdA0GIyEhsYSERHL1avATGxfFM6bpxkXmkJqdVw3ArmYvUMLJlqCoWPoF3mDeubvxG+64VgPv3+DYEAjaEt/gwgwI3gflJ1E8VzE8nO04HRrFhfvRJDGJzonQKOqsv0AhBxvaFnXmjaIu1MnjgLWVEkgREUk7JieNFStWZOvWrezdu5dq1aolWW/v3r2cP3+eunXrmjqkSJro1q0CdesW5scfD7Jr13Fq1ixD796V0+TL7IwZzenYsSxDh257cE5jHsaMqZfqhPGh9Iw9o0jP91yvXpFkk8aqVfNRp04Rbt+O4M6d+Me/zyPTZHlsTEwcMTEQGRmVypanU1F3SwrqLHrK9R+SvWowgL//IcaNq5/iqNLTozuvWj/cyffBNasHLwzEz5761yiYcL9hnmw2DC2fh3nn7v7bmV1OqOQHl+bAma/AGAN3A2HP6wzqOpM+tdpyKjSKMivPJJk0PnQlPIapJ+8w9eQd8mWz5vUHCeSL+bJjowRSRETMzOSksVOnTmzZsoW33nqL1atXJ3pv47lz53jrrbcwGAx06tTJ1CFF0oyHR07GjKnDqlV3E13CaU6NGxejfv1CrFq1ihYtWpg8VnrGnlGk13vu18+b6dP/TvK+0YULX00yWTUajdy/H82dO5HcuRPBhAl7WLDgeCKzbvF9eXrmo1q1AkRFxRIVFUt0dNx/nscRHR1LZGQsQUHB2Ns7JtT5b93o6KcdKmF5RmP8RlQZ2cOdV2efugWXzvBR6Vw0LJSD9dfuJezE6lPC9YkNav571EecEYwGK3DrDjm84Eg/iLgMMSG8M/MNjl34kAltJzyRpFobwMoI31TNj5ONFUv+CWXt1XtEPfgM3YiM5YfTwfxwOpjcdta8VtSZtkWcaZTfETtrJZAiImI6k5PGHj16MGfOHHbs2EGFChV4/fXXqVGjBq6urgQHB7Nr1y6WLVtGeHg4tWvXplevXuaIW0Qk3ZQsmZOZM5vj47M2YTOfh2dTPm0JsMFgwNHRDkdHO4oUcWbEiNosWHA8ybq//pp0Avqo+HtQk/+Fg9FoJCYm7sE9nZGsXv0n9es3xGi0SjLRjIqK5f79KPbs2Uv58pWJizMkWjciIprjx09RtGhxYmNJSGajouLrREbGcPnyVVxd83Dy5B0uXkx8ma7RaKRYMZenvl9L83C2Y0TFvKy6BCMq5sXW1pbGBRyf2u6/R338u0NrPQpU2cTR3QP489AyAKZsmMJfp//il96/cKJliYQk9cNSuehWMk9CUvq2uysh0bGsvBzG4kuhrL4aRsSDeyiDomKZcSaYGWeCcbW1onURZ94o6kzD3PFtz4RFMefCnYRkN6lzIkVERB5lctJobW3NypUr6d69O8uXL2f+/PksWLAg4frDjSpee+01/P39sbZOekdBEZGMylzLYdPzHlSDwYCtrfWD+w0NuLraUKSI81NnZKOjo7GxOUGLFmWSrBuftN6hRYv6idZ5NKk9fz6MMmVmJjq7ajTC/v3XOXjwBgsXHuf8+RCKF3ehR4+Kz80RJMnt0Gqs/hvfb/6ej379iKiYKPZd2EeVUVWY0XUGIzxfeyxJfZSLrTWdiuegU/EchEXHsfpqGIsvhbDycljCJjzB0XHMOXeXOefuktfGyHQ7qLrmHJEG64RffCR2TqSIiMh/mZw0Ari6urJ06VL27t3L8uXLOXbsGCEhITg7O1O+fHnatGmDl5eXOYYSEbEYcy2HzWr3oD6ZKD9+/Mq6dRfw9JyLtbXh32RmYkCG31nVHAwGA+81fI9aJWrRflp7Tt04RWhEKO1/bE+vur1o4tzkqX042VrxppsLb7q5cD8mjrVX42cgf78cRmhM/BLlsJg4sAMj/57/+PDGSZ3/KCIiT2OWpPGhatWqJbsZjoiIxMtq96A+TJT9/R+e03iTZs28+Pjjrdy7Fw38e/TIQz4+aylSxIkNGy4+NgMJMHPmoaeWZaaZyipuVdj36T7e/eldft79MwDT/5rOn85/Uta7LBWLVkxRP9ltrHitqAuvFXUhIjaO9dfusfhSKMsvJL2Rk85/FBGRpzFr0igiIpIUD4+cjBtX/5GlqxUICLjBjBmHEq1vNBpp1mwxVlb/zkBOmLAH4KllmXGm0tnemXk+82hctjG+830JjwrnQugFao6vyfdvfU/X2l1T1Z+9tRUtCzvTsrAzb0VFw53E6xmB8w8SdxERkcSYPWm8c+cOYWFhiR66/ZCbm5u5hxURkUwoLCwaKytDkvc7wpMzkCkty+hnQCbGYDDQvU53qhevTrtp7Th69Sj3o+7z9qy32XB8A36d/HCyd0p1vy842SaZNGKE4o7P90y3iIiYxsocnZw8eZJOnTqRK1cu8uTJQ/HixXnhhRcSfSR2JIeIiGRNxYu7YEijUyEengGZGZUvXJ4dA3fQtGjThLK5O+dSbUw1/v7n71T31/mFHEleiwNaFU59IioiIlmHyUnjgQMH8Pb25pdffiE4OJhs2bJRpEgR3NzcEn0ULVrUHHGLiMhzoEePiomef2kOmeEMyORkt8uOb2Vf5nSfg1O2+KTuxLUTVB9TnWlbpiW7oue/SjjFb3JjxYNzHw3waK4+6sitVPUnIiJZi8nLU4cMGUJoaCiNGzfmq6++okKFzHP/iIiIWFZiO6saDPFLTZNatppSBkP8TGZm19G7I7VK1KLdtHYcuHSAyJhI3vnpHTYe38iPXX4kR/akZxH/a1/zF5h94R7n70WTz96a+efvcisqjtVX7/H54ZtExqIzHEVE5AkmJ407duzAycmJZcuW4ej49IOOJWX8/Pzw8/MjNjbW0qGIiKSpR3dWfbj7aePGbrz00hKT+o2LM+Ljk7JdRzO6kvlLsnPwTvov6s+3m74F4Ne9v7L3wl5+6f0L1YqnbOdydyc7xnn++2/1ywWdeHnLJQA+PxyE9SOJ+8MzHN8qqn/bRUSyOpOXp8bFxVG6dGkljGbm6+vL0aNHCQgIsHQoIiJp7uHOqgsWtGTcuPo0aVIcf/+XsLIyYG1tSPhpMMQnNMmVPWQ0wmef7aBjx5UMHryVU6eS2gkmc7C3tWdqp6kseXcJORziZxfP3jxL7fG1mbJ+yjMtL21eyInOxf6djY01xt/j+PCnz+6rnA2LMtM7EBGRzMrkmUZPT0/Onj1rjlhEREQSJDYD+XDmMLmymzfvs2HDRQB+/vkYVlaGTHsMR2Je93odLzcvOvzYgd3ndhMdG03fX/qy8fhGZnWfRS7HXKnqL79D0l8FDAaYd+4u3qYGLSIimZrJSePgwYNp2bIl8+bNo0uXLuaISUREBPh3BvK/kis7fjyIsmVnJZQ/el9kZjyGIzHF8xRn24BtDF02lElrJwGw4uAKPEd6srDXQmp71E5xX5fvx2BF/MzifxmBC/dilDSKiGRxJi9Pffnll/nuu+947733+Oijjzh8+DDh4eHmiE1ERCTV5sw5kuQxHkajMdMew/Fftja2THxjIn988Ae5nXIDcOn2JepPqs/41eOJi0ssDXxScUfbpI89MUIxR7Mf6SwiIpmMyUmjtbU17733Hvfv3+ebb76hcuXKODk5YW1tnejDxkb/+IiISNo5dOhWksd4GI3x158nLSq24MCnB6hXsh4AsXGxDP5tMC9PeZkbITee2r5HCdck/3vFAWfvRZsxWhERyYxMThqNRmOqHin9zaeIiMizCApKfrXL065nRkVyFWHjJxv5tOWnGB5MG/559E88R3qy+cTmZNuWdLbDv0bBf89w5PEzHJf9EwrAkeDINIldREQyPrPsnprah4iISFrJndvBpOuZlY21DSNbj2TdR+vI75IfgKt3r9L4i8aM+mMUscakj3Dq5u7KiZYl6F8mN+3cXBhQNhfjK+clu/W/6WPDjRfwO3n7mXZpFRGRzM3kpFFERCQjqVgxz2NHbzzKyspAxYp50jmi9NW4bGMOjjhIk7JNAIgzxjHqj1F8tuszrt69mmQ7D2c7xnnmY0Gdwoz3zM/AcnnY3/wFKuXIBkBknJH/7bvO63/9w+1InSEsIpKVKGkUEZHnSo8eFZO9/vCIjudZfpf8rOm7htFtRmNliP+n/lDQIbzHerPu6LoU91PaJRsbGrk9VrbsnzAqrznLthv3zRqziIhkXEoaRUTkuVKyZE78/V/CysqAtfXjM46ffVY70x+3kVLWVtYMfWUom/ptolCOQgDcCL3BS1+/xLClw4iJjUlRP3bW8V8VFtYpTG47awD+uR9Dg40X+PzQTY7fjWTwgRt03H6ZPnuu0nffdQA+P3STU6FRafDOREQkvZltK9N79+7x+++/c/DgQW7fvk10dOK7rRkMBvz9/c01rIiIyBO6datA3bqF8fc/xNq15wkMjN9F9MCBp+8m+rypX6o+AUMCeHXyq+y/uR+j0ciYVWPYemor83vOp0iuIinq5+WCThx82Ym3dl5hy437xBnhs8O3+OzwLawNEGeMP9fRgViaZYcpJ28z7sRd/GsUpJu7a5q+RxERSVtmSRoXLlzIu+++S0hISELZwxvlDY8c/mQ0GpU0iohIuvDwyMm4cfUZPrwWJUrM4OrVe/z22ymaN19MlSr56NGjIiVLZo1Zx7zOeRlWfRgn7E4wbPkwYuNi2XZqG56jPJnbYy4tKrZIUT+Fs9uyoaEbY4/eYsShWzzcEic2kb1xYo3xR3b47L5K3bzZ8XC2M9v7ERGR9GXy8tSdO3fSpUsXYmNjGTp0KB4eHgBMnz6d4cOH06pVKwwGA/b29owZM4aZM2eaHLSIiEhKOTjY0rBh0YTXa9eeZ9KkAMqUmcns2YctGFn6sjJY8UnTT9g2YBtuueLvUwwKC+KVb15hwOIBRMek7DxGaysDn1bIS6fiLimqbzCA/5ngZw1bREQyAJOTxsmTJxMXF8fPP//MyJEjyZcvHwA+Pj589tlnLF26lMOHD+Pu7o6fnx/Nmzc3OWgREZGUOnXqDgsXnnisLDbWSFycER+ftZw+fcdCkVlGrRK1CBweSKvKrRLKJq2dRP1J9bkQdCHF/cTGpexLhBE4fy9lCamIiGRMJi9P3blzJ3ny5OHVV19Nsk6ZMmVYsmQJZcuWZcSIEfzwww+mDisiIpIiM2cewpD4CRyAkS5dVlG8eA5cXOKXT4aERFG8uAuNGrmxceNFzp8PwWg0cvx4EFeuBOPu/gujRtWladPi6fUWzC6XYy6W+S7jmw3f0H9xf6Jjo9l1dheeIz2Z1W0Wbaq0eWofxR1t4/+7PuXYRsODuiIiknmZnDQGBQVRqVKlhNd2dvH/6N67dw9HR8eE8lKlSlG+fHlWr15t6pAiIiIpFp/0JX4tLg52777K7t1XE+o8TDDHj9+DlZWBuLjHG9+8eY1mzRbj41OBGTMy7+oZg8HAh00+pHaJ2rT/sT3nbp0j+H4wr333Gh82/pAJbSeQzTZbku17lHBl4rGgp45jNIJPCVczRi4iIunN5OWpuXPnJjw8POF1njzxhyafOXPmibqxsbFcv37d1CFFRERSrHhxl2RmGuOTmkeTykdf/zdhfJS//2E2bEj5cs6MyvsFbwI/DeSNqm8klE3ZMIU6E+pw5saT/5Y/VNLZDv8aBbECrA3xM4qJ+bRCbm2CIyKSyZmcNBYvXpyrV68mvPby8sJoNPLzzz8/Vu/gwYOcPHmSvHnzmjqkiIhIivXoUTHJmUZTDRv2V9p0nM5yZM/Br31+5bu3viObTfzs4r4L+/Aa7cXi/YuTbNfN3ZUTLUvQv0xu2ru50KeEKz1ecH2sztXw2LQMXURE0oHJSWPTpk0JDg7myJEjAHTq1Al7e3smT55M586d8fPzY/jw4TRu3Ji4uDjatm1rctAiIiIpVbJkTvz9X8LKyoC1tQErK0OyM4+pceVKmHk6ygAMBgPvNniXXYN3UTJfSQBCwkPoNKMTPxz6gYjoiETbeTjbMc4zHwvqFOaH6gX5qmp+AJxs4r9izL8QQmi0EkcRkczM5KSxXbt2NGrUiBMn4nemK1q0KN9//z02NjbMnz+fDz74gDFjxnD79m1q1KjB6NGjTQ5aREQkNbp1q8CJEz3o39+bdu1KU6NGQaytTc8cCxVyMkN0GYunmyf7Pt1Hp+qdEsrWXFhD3Ul1OXntZIr7ebNo/JEcYTFxzL8Q8pTaIiKSkZm8EU758uVZt27dY2Vvv/029erV49dff+X8+fM4ODhQt25d2rRpg7W1talDZgl+fn74+fkRG6vfzoqImIOHR07GjasPxB/DUaaM6ecGjx5d1+Q+MiJne2d+6vkTjco04n8L/kdEdAR///M3XqO9mNZ5Gm/VfOupfXR3z8F350IB+PF0MH08cqZ12CIikkZMThqT4u7uzqBBg9Kq++eer68vvr6+hISEkCNHDkuHIyLyXHm4ZNXHZy0GQ/yGN//dPdVoJNHdUx/q3r08jRsXS6eI05/BYMCnng9ebl60+roV/4T9w73Ie3T278ymE5v4psM3ZM+WPcn2lXPaUy2XPXtvR7D/TgR7g8KpltshHd+BiIiYS5oljSIiIhlZt24VqFu3MP7+hzh/PoQcOeJ3+Lx7N/6cxiZNirF+/QXOnw8BjBw7FsTx40FERsYnkV27lrdg9OmnQqEKTK47mT+C/2DernkA+P/lz66zu/i1z6+UK1Quyba9S7iy9/Y1AKadCVbSKCKSSaUqabx48aJZBnVzczNLPyIiIqZ4dMlqYh6dSYyOjmbgwIV89VX80VErV56lQYOs8e+ZvY09/l39aVy2Me/9/B73o+5z5MoRqo2pxnedvqNbnW6JtutYLAcfB94gLCaOOWeDuRMVS267+NtUQqLjKOFgwDsd34eIiDybVCWNxYsXx2DilnMGg4GYmBiT+hAREbEELy/HhCWrK1eeZfLkBpYOKV29Xfttqr9QnXbT2nH48mHCo8LpPrs7m05swq+TH072j28M5GRrRdVc2dhyI5xoIyy5FPrY9ezEMj87/Hz+Lt1K5nlivFOhUcw5dQtv4PNDN3m7ZB5KPjjz8VRoFJOPBbHnRiifAX33Xadv+XwJ10VExHxSlTS6ubklmTRevnw5IRm0sbEhT548BAUFER0dDYCtrS2FChUyMVwRERHLcXa2pnbtgvz11xVOnLhNy5a/UbFiHnr0qEjJklljo5eyBcuyZ8gePlz4IdO3TQdg7s657Dm3h1/6/ELZ/GUT6p4KjWLbjfAk+3p4t6jv3mvULeCCxyMJ36yzwfTcfZXshlh+coApJ28z7sRd/GsUxAj47L6KEXAgFrLDrHPBfHculIL21uSJjeClvWsos+k3Qi+c59cXXqBCt26Ufest7Jyevx1vRUTSWqqO3Dh//jznzp174vHKK69gMBj44IMPOH78OJGRkVy5coWIiAhOnDjBBx98gMFgoGXLlpw7dy6t3ouIiEiay5/fMeH5qlVnmTQpgDJlZjJ79mELRpW+HOwc+LHrj8zvOR+nbPFJ2PFrx6kxtgYz/pqB8cGuQjPPBKfoTEwj0HDDBV7dconXtl3i5U0X6bH7KnFA7IPMMtYIcUD33Vfp8SBhTEzMmVO07t2UfBMGEhSwh5jr17myezfr3nmXmaVLE3T8uKlvX0QkyzF5I5zvvvuO77//ngULFtCuXbvHrhkMBkqWLMnXX39N7dq16dixI+XKlePdd981dVgREZF0d+VKFEuXXkh4bTRC7IOsxsdnLXXrFsYjCx0t0bFGR6oVr0a7ae04cOkAEdERvDf/PeoVqke9RvU4fy86YVfap/knPIZ/wsNMiscu4h59xvbA6W4QBsDwYPCHP8OuXWNejRqEu3kQe/sW1nnyUa1HN170eVszkCIiyUjVTGNipk2bhpub2xMJ43+1a9cONzc3pk2bZuqQIiIiFrFhQ0iy9/Z///2B9AsmgyiZvyQ7B+/Et6FvQtm2K9uoOb4m9vePpWim0Vy8tq/E5c4NrOOSOOM4Lo7okBBsDu/H/spFrA/t40Df//GtR0nNQIqIJMPkmcbTp09TvnzKth3PmzcvR44cMXVIERERi7hxI+mZs7g4I19/vZ+jR4No1cqDV18tQZEizpw6dYeZM+OP9XBxib9nLyQk/liP5+FeyIfvL+h8c16zr8y62LGEZTvP6ZunubDkFeJK9IfCnf49APPvm7D4JNyJJCKnHQc6O0Ip6PZCDiZVyUdMHIw6fJNpZ4KJvXKP6C0X+OLOTaJzxsCLxaCgY5KxVN26HKPBkDCzmJhHc1irB/Wib95kXsNGXF+ynfNGO4o72tKjhKs21RERecDkpNHJyYkjR44QHByMq6trkvWCg4M5cuQIjo5J/2UvIiKSkeXLZ5vszFlcnJE1a86zZs153ntvPcWKuXDxYkjCjqsPcxmDAaysDEycGIC//0t061Yhfd6Amc2adYiePf/EYIhfqhv/05f8TTdzvegfRMdGwckxcGcPhjKjMM48B1v+SWhvDArns8/uYt3AwNAVbcmTLf5rSd8yufl+xiGY/jcxBgN/GY0YDffg93PQuxKGF4tivHoPtlwi6uY95hWKJKZkDpwvXUlIBFPDOi6W6GtX2TJrLrsbtcNggInHgvCvUZBu7q7m+s8lIpJpmZw0Nm3alPnz5/PWW28xb948cuXK9USdO3fu0LlzZyIiInj99ddNHVJERMQiGjd2YenS4ESvGQzxm+Rcu3YvoezChRDg3/seH3r0Xsju3dfw448HyZ7d9kE/hgd14rh16xZTp/6GlVXid5MktVT2v8VGo5GbN2/y/ffLEm2TXD9Go5EbN24wbdryhHoGg4F796LZvPlSou2ur21A2brVOBYSANYxYB2DzUo/og9VSrR+7ObLHPzzPLkaFsXa2oqws3dhxqH4HXKMxvhNbx7enzj9EG1d7Fg8eS8YDMQajfwGGI17CcWBnDzbvTdGgwGvLcvY2ahdwrauPruvUjdv9sd2dRURyYpMThrHjh3LmjVrWLNmDW5ubrz55puULVuWvHnzcvPmTY4fP86iRYu4d+8euXPnZvTo0eaIW0REJN0VKmTHjz82oXfv9f+ZXQN//5d4++3yHDhwgxUrzvD99we4fv1+ivrdufNqMlcTT8yezYWnV0nS+VTVPvaXE9Aw4XX0U+q/8caKFPVrjDOyeNLeBy/is7uHKfk+qlLsGd+jldGI07nL8P5GyJkN3ihFXKW8+J8JZpxnvmfqU0TkeWFy0ujm5sa2bdvo3LkzgYGBzJkz57HfWD7cdrtKlSrMmzePYsWKmTqkiIiIxXTtWo4XX3TD3z/+PsXixV3w8amYsGtqlSr5qVIlP8eP3+bXX08QF5f65ZLybPbjRRPW40QY1sSlqm0cEBaTHYLC4x/j90CDIsz/sCrn70VT3NGWrvltiFqxiCNz5nDv+nUc8+en/Ntv6/xHEXnumZw0ApQtW5Z9+/axceNG1q5dy8mTJwkLC8PJyYlSpUrRrFkzGjdubI6hRERELM7DIyfjxtVPtk7x4i4p2jnU2tpA375efPZZncfKo6OjWbv2T5o1a4atre0T7YxJ3LuXWPHjfdk8tf6j/UdHx7Bu3TqaNm2Kra1NQv1Ro3by7beBTyy9BbCygk6dytKrVyUiImIJuxdJz/eWcueaNY9vRfMvV9ds1KpViNhYIydP3ub8+ZDEA0tGFNmYRh/6MA0XQjASv1Q17sGoyf1xGIC9VHu8cPM/XKxViIsV85Lv8llsxvbA5c4NeLDZTvC5c1zZuYudI0fy5oYN5C5ThqiwMI79/LMSSxF5rpglaXyoUaNGNGrUyJxdioiIZEo9elRk4sSAp9YzGuGddzxxcnr8vrnoaAMODlY4O9slmjSmRnS0FU5O1ri6Zkt1X9HR0Tg7W5Mrl/1jbX19qzB1amCibYxGGDKkOmXL5k0oc3bqQLNmi4lfTPpo+hb/evHiVjRuHL8a6dSpO5QpMzPJWVpra0OiySrATfIxkQFUIZBq7MWJUO7hSD5uYkdUojOQsVgRhhOBVHmyw0UnsSuZnd6PnP/If89/vH6dRY0b02bFCpa++ir3rl5NeJfBZ89yZedOdnz+Oe02biR3mTKJxi0ikpGZfE6jiIiIPKlkyZz4+7+ElZUBa2vDY7OOBkN84mNlZcDf/6WEpa2ZyX/f36M///e//Hh4uD5Wv2nT4vj4VCA+lTI+8oBC1f+hordDMn3/+99r3Lh6Sc6OPhRFNnZTEz/+xwQG8y0fMJX3CcMJIySkjXEPIgjDiWn0IYpsT3Z2J/Lp5z/GxhJ25Qq/NmxI2NX4+1Mf/nE//Bl29Sq/vPgiUWFhyQcvIpIBmXWm8dKlS2zbto3Lly8THh7O8OHDE65FR0djNBqxs9MOZCIikjV061aBunULJ9z/mCNH/L+Bd+9GPXEvZGb03/dXvLgLXbuW5eTJHYnWnzGjOR07lmXo0G0cO3uFEMNFqLqGK4XP4DnyVxb0WsCLpV98rO8ffzzIrl3HqVmzDL17V8bDIycFCjji47M2YRMio9H41EQysRnIMJzZSzUCqZJ4wggQHUvVX+ZjxICBpAcxApGhoUkugTUA927coO1HE7j1Zg9GVsxL04JarioimYNZksZbt27h6+vLkiVLHrvH4tGksXv37ixYsIA9e/ZQtWpVcwwrIiKS4aXk/sfM7L/vLzo6mpMnk67fuHGxhGWoaw6toeO0nwmOhKt3r9Loi0aMeHUEQ18ZirWVNR4eORkzpg6rVt2lRYs6CctjH01Wz54NJjb2Jj17NmDZsjNs3foPwcGRXL1677Edbg0GAznzurL7ek12UzPlbzAkCmeCsEomYYR/50+fpvzMH5iwuRjN3iiFTxsPZtQolPJYREQsxOTlqaGhobz44ossWrSIwoUL061bNwoXLvxEvZ49e2I0Gvntt99MHVJERESeA43LNOarel/RqHT8fghxxjhGrBhBs6+ace3utWTbPkxWf/rpZbp0yUPjxm788EMzjh7twZUr73LqlA/9+lWjXj0n+vWrxokTPbh2zZeJE+vj5GSLtbUBJydbKlfO+9QNi0JxfuperP+9UzMxBiBHXDCcDobxe/AftJUNj5zrKSKSUZmcNE6cOJFjx47Rtm1bjh8/jr+/f6LHatSvXx8HBwc2bdpk6pAiIiLynMhpn5M/3v+DUa1HYWWI/1qy8fhGKn9emfVH1z9zvw9nKT/5pCBjxtRJWAbcv391QkM/JCbmE0JDP+Tll1/Ayir5dG8fVZ+aED6Tzf/w/uxDadGziIhZmZw0Ll68mGzZsjFjxgwcHBySrGdlZYWHhwcXL140dUgRERF5jlhbWTOs5TA2frKRQq7xyzVvhN6g2dfNGL5iOLFJbUBjBj16VHzq/ZD78SIEF2KT+NoUixVxyd7xGM8I3MXlsbIzs4+kPFgREQsxOWk8f/48pUqVIkeOHE+tmz17dm7dumXqkCIiIvIcerH0ixwYfoDmFZoD8RvcjF8znk93fcrl4MtpMmZiu8D+d7nqw/Mfk9t9da9TsxSNZ08EvnxLTXZiRyTG2xFmfDciImnD5KTR3t6e0NDQFNW9evVqipJLERERyZryOuflj/f/YPzr47G2sgbg6O2jeI/1ZvWh1WkyZrduFThxogf9+3vTrl1pevWq9MSS1Ye7ry6hLRcpxi1ycZFiLKEtExlArwVfEp0tR5KzjQ/LnbiPGxd4nd8YwETy2gVxKjQqTd6XiIi5mJw0li9fnkuXLnHhwoVk6x04cICLFy9mmZ1TN2/ejMFgeOJRrVo1S4cmIiKSoVlZWTHw5YFs7b+VojmLAnAr7BYtvmnBwMUDiY6JNvuYDzfWWbCgJdOmNUv0DMr/nv/ox//YTU26+FSlWctyNF+2lhCcHzmB8t/TKA38u1GO1YPnToTR48bXVFr8N7PPBpv9PYmImIvJSWPnzp2JjY2ld+/e3L9/P9E6d+7cwcfHB4PBQNeuXU0dMlOZMWMGO3fuTHjMnj3b0iGJiIhkCrU9arNn8B6883snlE1cO5EXJ7/IxaC03SPhv7OP/ft7c+qUD+vXv0nNmgVxc3OmZs2CrF//JjNmxC+n9WpeA/fv1/OboS0XKEYY2YGkd1W1Jg6X6DtUnvUTPruvclozjiKSQZl8TmOvXr1YsGAB69ato2LFirz55ptcv34dgJkzZ3L48GF++uknbt26RbNmzejQoYPJQWcm5cuXp2bNVJwHJSIiIglyO+VmSLUhnLY/zZBlQ4iOjWbnmZ14jvRkdvfZvFz+5TQbO7EzNj08ciacM5mY7u9Up16T6fj7H4LpfTAGHU9251UjUG3bMnbfqIh/2dyM88xnnuBFRMzI5JlGa2trVq5cSfv27Tl37hyTJk3i9OnTGI1GevXqxddff82tW7do164dS5YsMUfMIiIikoUYDAY+bPwhfw38i+K5iwNw5/4dWvu1pt/ifkTHmX+5qikeJpuFc0Q99YuWFeBEKJy4w8bFJ9IjPBGRVDM5aQRwdnZmwYIFHDx4kOHDh9O2bVuaNGlC69atGTJkCAEBASxcuBBHR0dzDAfAuXPnmD59Or169aJy5crY2NhgMBgYPXp0itqvWrWKJk2akCtXLhwdHfHy8mLq1KnExT3t+N7Uad26NdbW1hQoUIA+ffpw584ds/YvIiKSVVR/oTqBwwN53ev1hLJvNn7D4O2DOXvrrAUjS5xj/vw87VtFHBCGMwBHf/w7zWMSEXkWJi9PfVTFihWpWLGiObtM0pQpU5gyZcoztR0/fjyDBw8GwN3dHScnJw4ePMgHH3zA+vXrWbp0KVZWpuXTOXLkoF+/frz44os4OTmxc+dOxo0bx549e9izZw+2trYm9S8iIpIVuWZ3ZfE7i/lu83d8/OvHRMVEcfruaaqPrY5/N3/eqPqGpUNMUP7tt7m8c2eydQzAXuI3yQu7G4Xzr8f5tGwOSqdDfCIiKWXWpPHSpUts27aNy5cvExERwaeffppwLTo6GqPRiJ2dnVnGypMnDy1btqR69ep4e3szY8aMFC1/3blzJ0OGDMHKyoqffvqJjh07AnDw4EFeeuklVqxYwZdffkm/fv0S2oSGhnL58tPPhypYsGDCkSJVqlShSpUqCdcaNGhAhQoVaNWqFYsXL04YV0RERFLHYDDg29CX2iVq0+6Hdpy+eZqQiBDe/OFN3mvwHl+0+wJ7W3tLh0nZt95i2/DPuHfjBtaJzDnGYkUYTgTy4PuC0UjYz8cY/mIhfimRzsGKiCTDLMtTb926Rfv27XnhhRfo0qULgwYN4rPPPnusTvfu3XFwcGDfvn3mGJJhw4bx+++/8+mnn9K8eXOcnJxS1G706NEYjUZ69uz5WOJWuXJlvvzySyB+JjI6+t/7I/744w/Kli371MfSpUuTHbtly5Y4Ojqyd+/eZ3jHIiIi8qgqblXYNWgX9QrVSyj7bvN31BpXi1PXT1kwsnh2Tk503LIJW9fcGCEhbYwjfgOcMJyYRh+iyBZ/ISYOVp4lst82NmwI4ZvjQZYJXETkP0xOGkNDQ3nxxRdZtGgRhQsXplu3bhQuXPiJej179sRoNPLbb7+ZOuQzCwkJYf369QD4+Pg8cf3NN9/ExcWFoKAgNm3alFDeoUMHjEbjUx/dunVLURwGQ3L7qImIiEhKuTi48HGVj/m+0/cJs4sHLh3Aa5QXCwMWWjg6yF2mDP+7dJYqo77kopMHt8jFRYqxhLZMZAA3eWS3VCMQZwQjfPvtdcZuSttjRUREUsrkpHHixIkcO3aMtm3bcvz4cfz9/SlW7MmtqOvXr4+Dg8NjyVh6CwwMJCoqCnt7e7y8vJ64bmtri7d3/FlQu3fvNvv4K1as4N69ewljiIiIiOkMBgM+dX3YM2QPZQqUASAsMoyus7rid9CP+1GJnyOdXuycnGgy7CO+LziQCQzGj/+xm5r/zjAmwmCA0A2X0jFKEZGkmXxP4+LFi8mWLRszZszAwcEhyXpWVlZ4eHhw8aLlfmt26lT8UhU3NzdsbBJ/6+7u7mzYsCGh7rPq3Lkz7u7ueHl5JWyEM3HiRKpVq0bbtm2TbBcZGUlkZGTC65CQECD+ntBHl8xmdA9jTa+YzTmeKX2ltm1q6qek7tPqJHc9vf/MzEWfNX3W0os+axn/s1Ymfxl2DNjBB798wE+7fwJg3aV11J5QmwU9F1C2YNkUvYe04hIaRXAq6lvdDE+Xz5s+aymro7/XMtZ4Wf2zlt4MRqPRaEoHDg4OlCpVioMHDyaU1atXjx07dhAbG/tY3Vq1ahEYGEhERIQpQyaqW7duzJkzh1GjRjFs2LBE60yaNIkBAwZQo0YNdu3alWidgQMHMnHiRFq2bMnvv//+zPGMGzeO+fPnc+HCBSIiIihSpAivv/46w4cPx8XFJcl2n332GZ9//vkT5fPnzyd79uzPHI+IiEhWsvHSRqYdnkZkbPwvYrNZZ6NPhT40KtrIYjENHHiJEyeS/g5kRyRe7Kcq+3AmFLtcOSnRvhnO9etjlcwv5kUk67h//z6dOnXi7t27yeYU5mbyTKO9vT2hoaEpqnv16tWE3UUt4WGymtwOrtmyxS8VCQ8PN2mswYMHJxzrkdp2H3/8ccLrkJAQihYtSsOGDcmdO7dJMaWn6Oho1q1bR9OmTdPleBFzjmdKX6ltm5r6Kan7tDrJXU/vPzNz0WdNn7X0os9a5vqstaAFXS915fVvX+di6EUiYyP55uA33La/zTftv8HJPmUb6JmTnd0FWrRYlui1vNygD9NwIQQj8fcPxd2+w43vv+fe8uW8+ttv3Ni3j2Pz5nH/xg2y58tH2S5dKN2xI3Yp3AwwKfqspayO/l7LWONl1c9aUJBlNsgyOWksX748u3fv5sKFC4ney/jQgQMHuHjxIs2bNzd1yGdmbx9/g3xUVFSSdR4uDU1uqW1aypYtW0Li+ihbW9tM9ZfQQ+kdtznHM6Wv1LZNTf2U1H1aneSu67OW/uPps5a56LNm/vpp9VmrVLQSk+pOYm3IWmZunwnAT7t/Yu+Fvfza51cqFkmfs6UfevllD3x8KuDvf/ixcjsi6cM0nAjDQPzZjQBWxC8GC716jQW1a0NcHGDAgJHgs+e4umsXe8aM4c0NG8hdpozJ8emzlrI6+nstY42X1T5rlvp8mbwRTufOnYmNjaV3797cv5/4jeZ37tzBx8cHg8FA165dTR3ymeXMmTMhnqQ8vPawroiIiGRe2ayz8cNbP/Bzz59xyhY/I3f82nGqj63O9K3TMfEunVSbMaM569e/Sc2aBROyQy/240JIomc5AlgZ4yAu7kFCGR/vw5+h166zqHFjosLC0iN8EcmiTE4ae/XqRb169Vi3bh0VK1Zk0KBBXL9+HYCZM2fy8ccfU7p0aQIDA2natCkdOnQwOehnVbJkSQAuXrxITExMonXOnj37WF0RERHJ/DrV6MS+YfvwLOoJQER0BL3n9abT9E6EhIekayyNGxdj5863wDF+xqAq+3ha6prUYV2GuFhCr1yhdbWPKdbkV2r1WMO6wBtmjVdExOSk0drampUrV9K+fXvOnTvHpEmTOH36NEajkV69evH1119z69Yt2rVrx5IlS8wR8zOrUqUKtra2REREsH///ieuR0dHExAQAECNGjXSO7zH+Pn5Ua5cOR3PISIiYialCpRi5+CdvNfgvYSyhQELqTq6KoEXA9M9HqvY+FTRmVCTvpAZgRIn/uTihovsmnOEZlXn0nPiHrPEKCICZkgaAZydnVmwYAEHDx5kxIgRtG3bliZNmtC6dWuGDBlCQEAACxcuxNHR0RzDPTMXFxeaNGkCgL+//xPXFy1aREhICLlz56ZBgwbpHN3jfH19OXr0aEISKyIiIqazt7XH7y0/Fr2zCBeH+J0HT984Tc1xNfHb5Jeuy1XtrePnD0NxTmJhaspYAU482JQwzghG8B+0lQ0HNOMoIuZh8kY4j6pYsSIVK6bvTeWpNXToUNasWcOMGTNo0KABHTt2BODgwYMJu5YOGDAg2R1WRUREJHN7o+obeLl50X5ae/Ze2EtUTBT/m/8/Np/YzPSu03HN7prmMZTycOXAgZvsoyrFuPDM/cQBYTg/XmgwMOyb/TSeabkNCEXk+WGWmUZL2L59O3ny5El4LFy4EIg/H/HR8kuXLj3Wrk6dOowaNYq4uDg6depEiRIlqFy5Ml5eXly/fp1XXnmFTz75xBJvSURERNKRe153/hr4F32b9E0oW7xvMV6jvAg4l/YrfSZOfBGA/XgRgguxSXwtS8n9jnup9p9GRq5cTN97NUXk+WVy0rhixQrc3d354osvkq33xRdf4O7uzqpVq0wdEoi//zAoKCjh8fCojPv37z9WHhsb+0TboUOH8vvvv9OoUSOCgoI4ffo0FStW5Ouvv2b58uVYW1ubJUYRERHJ2LLZZuOr9l+xzHdZwuziuVvnqDOhDl+v/zpNl6s2bVocH58KRJGNafQhDCeMkLBUNY74hNGIgVhD4l/ZYrEiBBcCqfL4BSNEhSV9xJiISGqYnDTOnTuXCxcu8NprryVbr3Xr1pw/f565c+eaOiQADRo0wGg0PvVRvHjxRNu3bNmSDRs2EBwczL179zhw4AAffvihEkYREZEsqLVnaw4MP0BN95oARMdG89EvH9HGrw23791Os3EfHsFRomZlFhQZyZ4i3biXuwz37PMQU6g8bsMmcXf+n8TmzvsgoYy/D/JhQhmGE9PoQxRPnvF8bfc1ClSZk2axi0jWYfI9jYGBgeTLlw93d/dk63l4eJA/f3727t1r6pBZgp+fH35+fonOlIqIiIj5FctdjK39tzJs2TAmrp0IwIqDK/Ac6cnCXgup7VE7TcZt3LgYjRsXS3gdHR3NqlWraNGiBba2trQHol49zbH58zkyezbHD57l9n179lKNQKokmjA+dP3ATQZO3c+E973SJHYRyRpMnmm8cuUKbm5uKapbtGhRrl69auqQWYJ2TxUREUl/tja2THhjAn988Ae5nXIDcOn2JepPqs/ENROJizNln9NnZ+fkROXevem0Ywcj712j2K9rCcj5YrIJ40Nffb4jHSIUkeeZyUmjo6MjN2/eTFHdW7dukS3b0/9yExEREbGkFhVbcODTA9QrWQ+A2LhYBi4ZSMupLbkZmrLvPWmp/5ulKeKVnwerVZMVHRTB+IXH0j4oEXlumZw0VqxYkQsXLjx12enevXs5f/48FSpUMHVIERERkTRXJFcRNn6ykWGvDMNgiM/OVh9ejedIT7ae3Grh6KCQmwsYUpA1AoM7/kHpVr+lcUQi8rwyOWns1KkTRqORt956i7NnzyZa59y5c7z11lsYDAY6depk6pAiIiIi6cLG2oZRbUaxtu9a8jnnA+BK8BUaTm7I6JWjiY2z3N4DI9/3glTs7nry97NMWnQiDSMSkeeVyUljjx49qF27NqdOnaJChQp07tyZqVOnMm/ePKZOncpbb71FhQoVOHXqFLVq1aJXr17miFtEREQk3TQt15QDww/QqEwjAOKMcXy6/FNe+volrt29ZpmYquTDZ3z9VLUZOWJ7GkUjIs8zk5NGa2trVq5cSevWrYmIiGD+/Pn07duXbt260bdvXxYsWEB4eDivvfYaK1eu1JEWKeTn50e5cuXw9va2dCgiIiICFHQtyJ8f/cnnrT7H6sG5iRuObcBzpCcbjm2wSEwzBlQn98svpLh++K3wNIxGRJ5XJh+5AeDq6srSpUvZu3cvy5cv59ixY4SEhODs7Ez58uVp06YNXl7a6jk1fH198fX1JSQkhBw5clg6HBEREQGsrawZ/upw6peqT6fpnbh69yrXQ67T9KumDHtlGMNbDsfG2ixfr1Js8tAadF99LkV1HfI4pHE0IvI8MuvfatWqVaNatWrm7FJEREQkw2lQugEHhh+g68yurD2yFqPRyKiVo9hycgvze86ncM7C6RZLtzpF8HuvMnu/O/jUusM/r5MOEYnI88bk5akiIiIiWVE+l3ys+mAV414fh7VV/O03W09uxXOkJ2sOr0nXWAL8mtJzaM1k65R61Z3+b5ZOp4hE5HlictIYHR2dqvoXL140dUgRERGRDMHKyopBLw9iS/8tFMlZBIBbYbd4ecrLDFoyiOiY1H1PMsX00XU5dcqHQYOqU7l2QWxz24PVv0dynNx+GbvSM+g351C6xSQizweTk8Zq1apx+PDhFNWdPXs2lSpVMnVIERERkQyljkcdDgw/QMtKLRPKJqyZQIPJDbgYlH6/MPfwyMm4cfU5sP0tom79Dxs3538v3o4k+mQwX3Rbi8H+S8Z/fyDd4hKRzM3kpPHQoUN4e3vzxRdfJFknKCiItm3b4uPjQ1hYmKlDioiIiGQ4uZ1ys+J/K/jizS8SNsPZcWYHniM9WXFgRbrH02/OIWLOhyR+MTKOwe+tp3T1eekblIhkSiYnjcOGDSMmJoYBAwbQqFEj/vnnn8eu//HHH1SoUIGlS5dSsGBBVq9ebeqQIiIiIhmSwWDg42Yfs33gdornLg7Anft3aO3Xmo9/+ZiomKh0i+WbsbufWudkwHW+mKHlqiKSPJOTxpEjR/LXX39RokQJNm/eTMWKFfnpp5+4f/8+ffr0oVWrVly/fp327dtz+PBhmjZtao64n3s6p1FERCTzqv5CdQKHB/K61+sJZV+t/4p6E+tx7mbKjscwVcztyBTVGzNiRxpHIiKZnVl2T61RowYHDx6kd+/e3L17l7fffpsiRYowY8YMcuTIwc8//8yCBQtwdXU1x3BZgq+vL0ePHiUgIMDSoYiIiMgzcM3uyuJ3FjO141TsbOwA2HNuD1VGVeG3/b+l+fg2ubKlqF54SPpt1iMimZPZjtxwcHBg6tSpNG3aFKPRSHBwMFZWVvz222907NjRXMOIiIiIZBoGg4H/NfofOwbtoETeEgDcDb9L2+/b8v7894mIjkizsT8YUiNF9RxcbNMsBhF5PpgtaTx27Bg1a9Zk/fr12NvbU6pUKWJjY3n11VeZNm2auYYRERERyXSqFqvK/k/30967fULZt5u+pfb42py+cTpNxpz8dkXyNy/+1HpDP6+dJuOLyPPDLEnjN998Q7Vq1QgMDMTT05N9+/Zx6NAhPvnkE8LDw3nvvfdo0aIF165dM8dwIiIiIpmOi4MLC3otYFqXaWSziV86GngxEK9RXizcszBNxry2+g0GzH0Z7K0TvV7KOz+f9KyYJmOLyPPD5KTxpZde4qOPPiIqKorBgweze/duypYti62tLZMmTWLjxo24ubmxZs0aKlasyKJFi8wRt4iIiEimYzAY6F2/N3uG7qF0gdIAhEaE0nF6R/rM60N4VLjZx5zQpTzG8I/oPrE+OP27FLVarYKc2NPF7OOJyPPH5KRx3bp1vPDCC2zdupUxY8ZgY2Pz2PX69evz999/07VrV4KCgnR/o4iIiGR5lYpUYu/QvXSp+W/S9uPWH6kxtgbHrx1PkzFfeLk4fNsYbOK//l25di9NxhGR54/JSaOPjw8HDx6kVq1aSdZxdnZm9uzZLFmyhFy5cpk6pIiIiEim52TvxJwec5jZbSYOdg4AHLp8iJrja7Lpn01mHavH7isMPxQEdtbg5gzAlXMh2FeaRfa839O+/WmcCkyj31d7zTquiDwfTE4ap0+fjqOjY4rqvvbaaxw+fNjUIUVERESeCwaDge51urN36F7KFyoPwP2o+0w5MIWec3tyL9L02cB1V8OYdfZu/IvNl+DhcyDyUBAxd6OIjDQSdTuCLz7ejMHhK8YvPGbyuCLy/DDb7qkplS9fvvQeMlPy8/OjXLlyeHt7WzoUERERSWPlCpVjz5A9+NT1SSibu2su3mO8OXzZtF+4Dz90M/7J1Xsw/e+nN4iIZXDHPyjd6jfWBd6gVo81FGvyK7V6rMFnwi6cy83EkGMKBoevsMs5lcKVZjN7edrsACsiGUOqk8a5c+eydu3aRK+FhIRw//79JNt+++23fPzxx6kdMkvy9fXl6NGjBAQEWDoUERERSQfZs2VnxtszmN1tNvbW9gAcu3oM7zHezNg2A6PR+Ez9XgmPiX+y5RIYDClud/L3szSrOpddc45wceNFds06zMxBfxF27DaERENELNHBkVw5dIvubZZRv92KZ4pPRDK+VCeN3bp1Y+zYsYlec3V15eWXX06y7S+//MKUKVNSO6SIiIhIltGpeie+qPcFlYpUAiAiOoJec3vReUZnQiNCU91fIYcHmxTeDIfUJp5GIM4Y//Mpti06yU9/nE11fCKS8T3T8tTkftP1rL8FExEREZF4hZ0K81f/v3i3wbsJZfP3zKfqqKocuHggVX2NrJg3/kleh1TNND6LT4fvSNP+RcQy0v2eRhERERF5Ontbe7576zt+6f0LLg4uAJy6cYqa42ry3abvUvyL+qYFnfBxzwEvFk39TGMq3blh/nMmRcTylDSKiIiIZGDtvNuxf9h+qharCkBkTCS+831pN60dd+/ffUrreDNqFGJ9p7Lkfb8KGACrtJlxzJnPIU36FRHLUtIoIiIiksGVyFeC7QO382HjDxPKFu9bTJVRVQg4l7JN8xoXcOTGlMas39+Vmm+XJ9eLRcAzL9iYL4EcNbK22foSkYxDSaOIiIhIJpDNNhtfd/iape8txTW7KwDnbp2jzoQ6fL3+6xQvV23smY+dM5sTtLkDp7Z2ZOjujnz+eSGylXLFOo8DTmVzMfHXV/GZUP/fWckU5JX13ixF51fcn/0NikiGZWPpAEREREQk5dpUaUMVtyp0+LEDu87uIjo2mo9++YhNxzcxq/sscjnmSnFfHs52jKiYl1WXHAkd/Ca2traPXe/YrDjDvtnPlYshFHJzoWK5XCyYeZiwy2FwPxpi4hPVDj3Ks8D/ZaKjo836XkUkY3impPHGjRvMnTv3ma6JiIiIiGmK5S7G1v5bGbpsKJPWTgJgxcEVVBlZhYW9F1KrRC2zjNPYMx+NZzZ/rOzHftUZdOAGE9adhwFbAbj9zz2zjCciGdMzJY2nTp2ie/fuT5QbDIYkr0H8cRyGNN7qWURERCQrsLWxZeIbE3mx1Iu8PettgsKCuHj7IvUn1Wfsa2P5pOknWFml4Z1IhZ0glz3cjmDLlkvcvx/NfyYqReQ5keqk0c3NTYlfOvDz88PPz4/Y2FhLhyIiIiIZ2CuVXuHApwfoOL0jf53+i5jYGAYsHsDmE5uZ030OeZzzpM3ABgNUzgubLhEZGcvWrf/QuHGRtBlLRCwq1Unj+fPn0yAM+S9fX198fX0JCQkhR44clg5HREREMrAiuYqwqd8mRqwYwbjV4zAajaw6tArPkZ4s6LWAeqXqpc3AleKTRoC1a88raRR5Tmn3VBEREZHngI21DWNeG8OaD9eQ1zkvAJeDL9NgcgPG/DGGuLg4s411O+rBSqgKeRJ2Vv12+kEa9F7HlStRZhtHRDIGJY0iIiIiz5Fm5ZtxcPhBGpZuCECcMY5hy4bRfEpzrodcN7n/WWeDmXEmOP5FwDV4cNJHzL0Ydsw+ynvvXeDdL/eaPI6IZBxKGkVERESeMwVdC7Lu43WMeHVEwl4U646uw3OkJ5uOb3rmfk+FRtFz99X4PPHqPfjx70Tr+Q/azoYDNxi/8BjO5WZik88P53IzGb/w2DOPLSKWo6RRRERE5DlkbWXNZ60+Y/1H6ymQowAA1+5eo8mXTfh8xefExqV+s72ZZ4JJ2A/xjzPJ1m3ecgmDO/5B2LHbxN4MJ+zYbQZ3/IPSrX4zWzJ55UoUDXqvo1iTX6nVYw3rAnW8m0haUNIoIiIi8hxrVLYRB4YfoGm5pkD8ctXPfv+Mpl825Wrw1VT1df5eNMYHy1E5fifZujGXEz+78eTvZxNNJiu+viJVsfT5Yi/vvXeBHbOPcnHDRXbNOkwzr7nkq/WTkkcRM3umcxpFREREJPPI75KfNR+uYdzqcQxfPpw4YxybTmzCc6Qns7vNTnE/xR1t42cajSRsgGMuJ1aeY162nOy5dhgHBzscsllj/+CRPZs1DtlscLC3Jns2Gw6eucOswdsT7efmrms0qzoXn/H1mTGgunmDFMmiUpU0bt26lRw5clC5cuW0ikdERERE0oCVlRVDXxlK/ZL16Ti9I5eDL3Mj9AavfPsKb5R4g2YvNcPW1jbZPnqUcGXisaD4F6VzweUws8a4ZMkdWLLB9I6M4D9wKzt2XeFeSBSOTrY4XLpC2y7fYYw1krOwE5MnNaBbaw/TxxLJAlK1PLVBgwZ88MEHj5U1atSIvn37mjMmEREREUkj9UrV48DwA7xc4WUAjEYji04votmUZvxz+59k25Z0tsO/RkGsAMMr7mafbTS3Y8tOc3HDRY4tP8P+/eHEhkYTdz+GoFPBdG+zjFJNfrF0iCKZQqpmGg0GwxNn/GzevJmYmBizBiUiIiIiaSePcx5Wvr+SL9Z9weDfBhMbF8tfp//Cc5Qnc3vMpUXFFkm27ebuSt282fE/E8wvH1Xl3Ff74i88WLJqAKq9VZqAn06kOq58+Wyo3KkikdFGoqPiiI6OTfgZExVHTHQsMdFxXPzrHwhPwUY+xuQvn9pwidKdfufE/FdTHatIVpKqpNHV1ZULFy6kVSwiIiIikk6srKzo/1J/ahavyevfvs6tiFsEhQXxyjev0P+l/oxpMwZbm8SXq3o42zHOMx/jPPOxoUt5hn2znysXQyhS1IkuNe7h49OcCnejOfn72VTF5Oubj8GD6z91mWy515ZxbNnpVPWdlJMLTjD3/ap0rJbXLP2JPI9SlTTWqlWL1atX07ZtW5o1a4aDgwMAN27cYO7cuSnup2vXrqmLUkRERETSRE33mnxV/yt+ufYLK/9eCcCktZP46/RfLOy1ELfcbsm2b+yZj8YzmwMQHR3NqlWrADix4nUmLTrByBHbCb8VjkMeB4Z/XocZ844kmkyWbvkClSun7KvplOG1abb89FNnElNq8JR9dJzX3DydiTyHUpU0jh07lh07drB06VKWLVuWUH7q1Cm6d++e4n6UNIqIiIhkHM52zizps4Tvtn7HgMUDiI6NZueZnfG7q3afTSvPVs/Ub/83S9P/zdJPlCWWTPZt456QcD5N0yr58BlXh5mDt/97BIgJru+7bnonIs+xVCWNlSpV4sSJEyxcuJDjx48THh7O7NmzyZcvH82b67czIiIiIpmVwWCgb5O+1ClRh3bT2nE+6Dx37t+htV9r+jbpy4S2E7CzsTPLWIklk9HR0anq4/uPq1Etxz/M2+3I6eN3uH83kuw5spG7QHaOLT+TqlnI2NPBFK3/C3ULR5Kt8A2aVyucqlhEnnepPqcxb968vP/++wmvZ8+eTcmSJZk1a5ZZA8vq/Pz88PPzIzY2BTd5i4iIiJiJ9wveBA4PxGeOD7/t/w2Ar9d/zfbT2/ml9y+8kPcFC0f4r4IF7dj8Y9Mn7oHsOXEP/oO2gsEAcSnLHq/vusYSYMmSBVjlzEbpF4syZXhtmlbJlwaRi2QuqTpyIzEjRoxI1dJUSRlfX1+OHj1KQECApUMRERGRLMY1uyuL31nMt52+TZhdDDgfQJVRVRISyYxsxoDqrN/flZpvl8etsRsOBR1T1T7uTiTHlp2mWdW59Jy4J42iFMk8lDSKiIiIyBMMBgO+DX3ZOWgnJfKWAOBu+F3aft+W9+e/T0R0hIUjTF5jz3zsnNmcC+vb8b/OZZ+tEyP4D9rKhgM3zBucSCZjctL4XydPnmTlypUsWLCAlStXcvLkSXMPISIiIiLpxKuYF/s/3U977/YJZd9u+pba42tz+oZ5jr1Ia926lXv2xkZo0WopDXqv48qVKPMFJZKJmC1pnDZtGu7u7pQtW5bWrVvTuXNnWrduTdmyZSlRogTTp08311AiIiIiko5cHFxY0GsB07pMI5tNNgACLwbiNcqLhXsWWji6pytZMifvv58fDM/WPupSKDvmHsPX9wLvfrnXvMGJZAJmSRq7d+/Oe++9x/nz57Gzs6NEiRLUrl2bEiVKYGdnx7lz53jnnXe0jFVEREQkkzIYDPSu35s9Q/dQukD8zqehEaF0nN6RPvP6EB4VbuEIk9e4sQtHj7xNh+7lyf1CDrIXSt19jsQZMRrBf9B2yr2+jHWBWrIqWYfJSeP8+fOZM2cO2bNnZ+LEidy8eZOTJ0+ybds2Tp48yc2bN5k4cSKOjo7MnTuXBQsWmCNuEREREbGASkUqsXfoXjrX7JxQ9uPWH6k5riYnrp+wYGRP5+HhyoKZL3PrbC/uXX4Xnwn1n6mfY0tP08xrLvlq/USxJr9q6ao890xOGqdPn47BYGDJkiX069cPJyenx647OTnRr18/Fi9ejNFo1DJVERERkUzOyd6JuT3mMrPbTBzsHAD4+5+/qTm+Jpv/2WzZ4FJhxoDqrA/silXObM/U/uaua1zceFFLV+W5Z3LSePDgQdzd3WnWrFmy9Zo1a4aHhweBgYGmDikiIiIiFmYwGOhepzsBQwIoVzB+o5l7kff4+sDX9JrXi3uR9ywcYco09sxH9TYln70DI48tXe05YbfZYhPJKExOGiMiInB1dU1RXRcXFyIjI00dUkREREQyiPKFy7Nn6B661/l374o5O+dQfUx1jlw+YsHIUm7k+15m68t/0DZKt8r4Z1mKpIbJSaObmxuHDx/m1q1byda7efMmR44cwc3NzdQhRURERCQDcczmyMxuM5n59kzsre0BOHr1KN5jvZm1fRZGo9HCESavaZV8+IyvY7b+Tv5+lkmLMvb9nSKpYXLS2KpVKyIjI2nfvj03b95MtM6NGzdo3749UVFRtG7d2tQhRURERCQD6lyjM5PrTaZCoQoAhEeF02N2D7rO7EpYRJiFo0ve9x9X4/vvi+HWqCg42YKtaV+TR47YbqbIRCzPxtQOBg0axMKFC9m8eTPFihXjzTffpFy5cuTLl48bN25w9OhRFi1aREREBEWLFmXgwIHmiFtEREREMqAiTkXYPmA7A34bwLSt0wD4addPBJwP4Nc+v1KpSCULR5i0ggXtOL2mBba2tgCUbvUbJ38/+0x9hd/K2EeQiKSGyUljrly52LhxIx07dmTfvn3MmzcPg+Hfk1MfLkfw9vZm/vz55MqVy9QhRURERCQDc7Bz4IcuP9CgdAN6z+tNaEQoJ66doPqY6nzT8Rt61ev12PfFjOrEiteZtOgEI0ds5/61e7gaYjAWzUno9fvEXLufbFurbNbpFKVI2jM5aQTw8PAgICCADRs28Oeff3Ly5EnCwsJwcnKiVKlSvPTSSzRq1MgcQ4mIiIhIJtGhegeqFqtK+x/bE3gxkMiYSPrM68Om45uY1mUaLg4ulg7xqfq/WZr+b5YmOjqaVatW0aJFCzYfvkMzr7mWDk0k3ZglaXyocePGNG7c2JxdioiIiEgmVjJ/SXYM2kH/Rf35dtO3ACwMWMjeC3v5pfcveBUz386l6aVplXzx9z2GRSdZJyYiNh0jEklbJm+EIyIiIiKSHHtbe6Z2msridxaTwyEHAKdvnKbW+Fp8u/HbDL+7amKsCzkme90qV7Z0ikQk7SlpFBEREZF00bZqW/Z/uh/v4t4ARMVE8f6C93nzhzcJvh9s2eBSqe47nsleL/9aSWr1WEOxJr9Sq8ca1gXeSJ/ARNKAkkYRERERSTfued35a+Bf9G3SN6Fsyf4l1BhXg1PBpywXWCp1q14g2et/Twhg16zDXNxwkV2zDtPMay49J+5Jp+hEzEtJo4iIiIikKzsbO75q/xXLfZeTM3tOAM4FnWPw9sF8s/GbTLFc9esv96W6jf/ArWw4oBlHyXyUNGZQfn5+lCtXDm9vb0uHIiIiIpImWnm2InB4IDXdawIQY4yh3+J+tPFrw+17ty0cXfLO7bv+TO3eH7TFzJGIpD0ljRmUr68vR48eJSAgwNKhiIiIiKSZYrmLsbX/Vj5p+klC2YqDK/Ac6cnOMzstGFnybK2e7ZzJMzuvmjkSkbSnpFFERERELMrWxpZxr41jmPcwcjvmBuDS7UvUm1iPiWsmEhcXZ+EIn9SkQdFnameMzXjvReRpTE4aV69enSnWnYuIiIhIxlYtfzUChgRQ16MuALFxsQxcMpCWU1tyK/SWhaN73KjBNZ6pna2LjuKQzMfkpPGVV16haNGiDBo0iGPHjpkjJhERERHJoorkLMKmfpsY2mIoBkP8EtDVh1fjOdKTbSe3WTi6f5UsmZNZs5qnul241vlJJmTyx7Z8+fJcuXKFSZMmUaFCBWrWrMkPP/xAcHCwGcITERERkazGxtqG0a+NZm3fteR1zgvA5eDLNJjcgDF/jMkwy1W7davAqVM+NGjljrOzFQYHG7BO/l5HY0TGiF0kNUxOGg8dOsTevXvx9fUld+7c7NmzB19fXwoWLEiHDh1Ys2aNlq+KiIiISKo1LdeUg8MP0rB0QwDijHEMWzaM5lOacz3k2XYvNTcPj5z8ufhV5s0rQeRdX3ghR/INcmp5qmQ+Zpkg9/Ly4ptvvuHKlSv89ttvtGrViri4OH799VdeeeUVihQpouWrIiIiIpJqBV0Lsu7jdXz26mcJy1XXHV2H91hv/r71t4Wje5JNu1LJX2+f/HWRjMisq6ptbGxo06YNS5cu5cqVK0yZMgVPT0+uXr2asHy1Ro0aWr4qIiIiIilmbWXNiFYj2PDxBgrkKADAtZBrjNg1gpErRxIbF2vhCP/VrGlxKJA98YsFsvNSk+LpGY6IWaTZrbi5c+fm/fffZ8+ePYwfPx5ra2uMRiMBAQH4+vpSqFAhfHx8OHfuXFqFICIiIiLPkYZlGnJg+AGalmsKgBEjo1eNpumXTbkanDHOP3zzbhRcu5/4xWv3Kbj+PIUrzcaxwHcUrjSb2ctPp2+AIs8gzZLGI0eOMGDAANzc3Bg8eDAxMTHkyZOHDz74gHbt2gEwa9YsKlasyLZtGWcnLBERERHJuPK75GfNh2sY2WokVg++ym46sYnKIyvz55E/LRwdfD1ie7LXZ4zZw5VDt7h//T5XDt2ie5tl1G+3Ip2iE3k2Zk0ag4KCmDp1KtWqVaNSpUpMnjyZGzdu0Lx5cxYtWsTly5f5+uuvWbBgAf/88w++vr7cv3+fAQMGmDMMEREREXmOWVlZMaj5IEbVGkVh18IA3Ay9SfMpzRm6dCgxsTEWi+3U6eBUt9m26CRzV2jGUTIuk5PGmJgYli1bxmuvvUbhwoXp27cv+/fvx8PDgzFjxnDx4kX++OMP2rZti62tbUK7XLlyMXXqVEqWLMnBgwdNDUNEREREspjyucsTMCSAlyu8DIDRaGTsqrE0+qIR/9z+xyIxRcU82/2Vvu+uM3MkIuZjctJYqFAh2rZty/Lly7G1taVr165s2bKFEydOMHjwYAoWLJhs+4IFCxIZGWlqGCIiIiKSBeVxysPK91cy8Y2JWFtZA7Dt1DY8R3my6tCqdI/HLof9M7ULu3rPzJGImI/JSeOtW7eoWbMm06dP5+rVq8yaNYt69eqluP2UKVPYuHGjqWGIiIiISBZlZWVF/5f6s23ANtxyuQEQFBbEK9+8woDFA4iOjU63WErVK5xuY4mkFxtTOzh+/DilSj37eTOVK1c2NQQREREREWqVqEXg8EC6z+rOioPxm8tMWjuJbSe34ePuky4xTBxai2a/nQJj6tplc7FLm4BEzMDkmcZr166l+J7Ev//+m61bt5o6pIiIiIhIonI55mKZ7zK+av8Vttbx+2nsOreLj7Z+xO9//57m4zetkg+f8fXBQPyDR34mY9SE+mkZlohJTE4aGzRowAcffJCiuh9++CGNGjUydUgRERERkSQZDAb6NunL9oHbKZ67OABh0WG0/aEtH/3yEVExUWk6/owB1Vm/vys1u1XArbEbNbtVYPb2jpDUbKKDDQO/2Ishjx/WpWbgM12bRErGYpYjN4zGlM+/p6auiIiIiMiz8n7Bm8DhgbTxbJNQ9vX6r6k7oS7nbp5L07Ebe+Zj58zmXFjfjp0zm+O3/TKEJJGshsdgPBUMQeHEnQpmZu915Gj2a5rGJ5IaZj2n8WmCgoJwcHBIzyFFREREJAtzze7KL71+oXeF3tjZxM/0BZwPoMqoKizZtyTd4gj48e9U1Q9Zd5He/qlrI5JWUr0RTkhICMHBwY+VRUZGcunSpSRnEcPDw9myZQuHDx/WxjciIiIikq4MBgMtirfAp6UPnfw7cebmGe6G3+WNH97At6Evk9+cjDXWaRvEndQfMec/YQ8/+lRKg2BEUifVSeNXX33FyJEjHyvbu3cvxYsXT1F7H5/02blKRERERORRVdyqsP/T/fSe15tfAn4BwG+THzvO7ODnHj+n6diGXNkwBoWnqk3cbZ1lLhlDqpNGV1dX3NzcEl5fvHgROzs7ChQokGh9g8GAg4MD7u7utG/fns6dOz97tCIiIiIiJnBxcGFBrwU0KtOIDxZ8QGRMJIEXA6kxvga9y/amBS3SZNxqvSsR0D91pwhY5cqWJrGIpFaqk8YPP/yQDz/8MOG1lZUV3t7eOkpDRERERDIFg8FA7/q9qelek3bT2nHi2glCI0L5IvAL7s6/yzcdv8HBzrz7cPzcx5NSf5yFzf+kuI3PwOpmjUHkWZm8Ec6sWbMYMmSIOWJ5Ls2fP59q1arh4OBA7ty5adq0Kbdu3bJ0WCIiIiJZXqUildg7dC9danZJKJvx1wxqjK3B8avHzTpWSWc7Zvk3h8HVwcMVcjvE/yzilGh9+/K5dD+jZBgmJ41vv/02zZs3N0csz50JEybQvXt3mjdvzqpVq5gzZw6VK1cmMlLr00VEREQyAid7J+b0mMP0LtOxs4rfXfXQ5UNUG1ONeTvnmXWsbu6unBpck0GLWtFheRt6T24AV8ISrRt57DanT98x6/gizypVy1MvXrwIgK2tLQULFnysLDUevSfyeXXy5EmGDRuGn58fvXv3Tihv2bKlBaMSERERkf8yGAy8Xettwi+G8/3J7zl29Rj3Iu/RdWZXNp3YxNSOUxMSSlN5ONsxzjMfAB3e3wAYgCdPIDBi4NMp+1kwtbFZxhUxRaqSxuLFi2MwGChTpgxHjhx5rCylDAYDMTExqYsyE5o1axb29vZ069bN0qGIiIiISAq4Obuxc+BOPl70MTO3zwRg1vZZ7D67m599zL+76qq/b0ASR9ZhNMZfF8kAUrU81c3NDTc3t4RZxkfLUvooWrSoWQI/d+4c06dPp1evXlSuXBkbGxsMBgOjR49OUftVq1bRpEkTcuXKhaOjI15eXkydOpW4uDizxLdz505Kly7NnDlzKFasGDY2NlSpUoW1a9eapX8RERERMb/sdtnx7+bP3B5zcczmCMDRq0epPaE26y+uT/Jc8mdxz9Uekpp8MRgIc7U321gipkjVTOP58+dTVJYepkyZwpQpU56p7fjx4xk8eDAA7u7uODk5cfDgQT744APWr1/P0qVLsbIy7XbPa9eucfnyZUaMGMGECRPIly8fX331Fa+++iqHDh2idOnSJvUvIiIiImmnS60ueBf3pt20dhy6fIjw6HC+/ftbbs+5zbQu03CyT3wDm9SwbliUuBVnEr8YZ8S6kXkmW0RMZfJGOJaSJ08eWrZsyciRI1m9ejVt27ZNUbudO3cyZMgQrKysmD9/PmfOnOHgwYPs37+f/Pnzs2LFCr788svH2oSGhnL8+PGnPu7evZvQJjY2lrCwMGbMmEGXLl146aWXWLp0Kbly5WLy5Mlm/W8hIiIiIuZXpmAZdg/ZTZ/6fRLK5u+ZT9XRVfn7n79N7r9AaFTyFRadpFiTX6nVYw3rArVUVSwn0yaNw4YN4/fff+fTTz+lefPmODml7Lc9o0ePxmg00rNnTzp27JhQXrly5YRkcfz48URHRydc++OPPyhbtuxTH0uXLk1okytXLgAaNmyYUObg4EDNmjU5evSoSe9dRERERNKHg50DP3T5gXk95uFgE39248nrJ6k+pjrTtkwzbbnqnOS/E0Zvv8LFjRfZNecIzarOpefEPc8+logJnmn3VFNZavfUkJAQ1q9fD4CPj88T1998803effddgoKC2LRpE82aNQOgQ4cOdOjQIVVjlS9fnoCAgCfKjUYjERERzxC9iIiIiFhK+2rtCTsXxrTT0zhw6QCRMZG889M7bDqxCb8Ofs/U57WLd59eyUjCZjn+g7bSsVlxGj/YfVUkvTzT7qmmsOTuqYGBgURFRWFvb4+Xl9cT121tbfH29mbDhg3s3r07IWl8Fi1btmTWrFls2LAh4ZiN+/fvs3PnTtq0afPM/YqIiIiIZRR0LMjWflsZsmwI3276FoBfAn5h3/l9vFvm3VT3FxubyllKI/T7ai+Bc1qkeiwRU6QqaXRzczM5abSkU6dOAfHvw8Ym8bfu7u7Ohg0bEuo+qzZt2lC9enV69uzJ+PHjEzbCuXfvHp988kmS7SIjI4mMjEx4HRISAkB0dPRjS2YzuoexplfM5hzPlL5S2zY19VNS92l1krue3n9m5qLPmj5r6UWfNX3W0os+axn7s2aNNV+++SV1PerS56c+3A2/y+mbpxkYNBDywf8a/S/F35cdHW0JDU3df6tj+66Z7bOhz1rG/qwl9/daejMYzblvsAV169aNOXPmMGrUKIYNG5ZonUmTJjFgwABq1KjBrl27Eq0zcOBAJk6cSMuWLfn9999NiunWrVv069ePFStWEB4eTo0aNZg4cSLVq1dPss1nn33G559//kT5/PnzyZ49u0nxiIiIiIj5XLt3jS/2f8Gpu/9ONtQsUJP/Vf4fTrZP329j8uSr/PVXWKrGzJHDijlzSqQ6Vnk+3L9/n06dOnH37l1cXFzSbdxUzTRmdg/vJbSzs0uyTrZs2QAIDw83ebw8efIwe/bsVLUZPHgwH3/8ccLrkJAQihYtSsOGDcmdO7fJMaWX6Oho1q1bR9OmTbG1tc1U45nSV2rbpqZ+Suo+rU5y19P7z8xc9FnTZy296LOmz1p60Wctc33WOr/WmUG/DeLbzfHLVXdd28W16Gv87PMz3sW9k42rZMk7VKgwl9RM4dy9b6RFC/MsT9VnLXN91gCCgoKeGm9ayFJJo719/AGpUVFJb2/8cGmog4NDusT0X9myZUtIXB9la2ubqf7Beyi94zbneKb0ldq2qamfkrpPq5PcdX3W0n88fdYyF33WzF9fn7XE6bNm/vpp8VmztbXly3Zf4hLmwvdHv+fO/TucDzpPgy8aMKHtBPo26ZvkctVy5fIxc2ZzfHzWEBeXorcA0Uazfy70WTN//bT6e81Sf5dl2iM3nkXOnDkBuHPnTpJ1Hl57WFdERERE5GmqF6jOnsF7qFWiFgDRsdF8/OvHtPFrw+17t5Ns161bBU6c8GHQoOp06FAmvcIVSZVnOnLD1taWggULPlaWGpY6cqNkyZJAfMwxMTGJboZz9uzZx+qKiIiIiKREsdzF2NJvC8OWDWPi2okArDi4As+RnizstZDaHrUTbefhkZNx4+oDsHDh8XSLVySlnunIjTJlynDkyJHHylLKkkduVKlSBVtbWyIiIti/f/8TG9JER0cnnK1Yo0YNS4SYwM/PDz8/P2JjYy0ah4iIiIiknK2NLRPemMCLpV+k68yuBIUFcen2JepPqs/Y18bSr1k/rKySXuxnZW0gLrmjOAxQrMmvFHJzYeT7XjStojMbJe0905EbD2cZHy3LDFxcXGjSpAmrV6/G39//iaRx0aJFhISEkDt3bho0aGCZIB/w9fXF19eXkJAQcuTIYdFYRERERCR1WlRswYFPD9BpRie2ndpGbFwsA5cMZPOJzczpMYe8znkTbWdXyJGIS8nsqGqEixsuchFoNuswPhPqM2NA0jvzi5hDqpLG8+fPp6gsIxs6dChr1qxhxowZNGjQgI4dOwJw8ODBhF1LBwwYkOwOqyIiIiIiT1MkVxE2frKRz1Z8xtjVYzEajaw+vDphuWq9UvWeaOPsU5GIz3ameAz/gVvp2Kw4jT014yhpJ9NuhLN9+3by5MmT8Fi4cCEA48aNe6z80qVLj7WrU6cOo0aNIi4ujk6dOlGiRAkqV66Ml5cX169f55VXXuGTTz6xxFsSERERkeeMjbUNo18bzdq+a8nnHJ/YXQm+QoPJDRjzxxji/rNtaolahaBBkVSN8f7nO8wWr0hiMm3SGB0dTVBQUMLj4VEZ9+/ff6w8sXsChw4dyu+//06jRo0ICgri9OnTVKxYka+//prly5djbW2d3m9HRERERJ5jTcs15cDwAzQs3RCAOGMcw5YNo/mU5lwPuZ5Qb2TFvNC7MgyuDh6ukNsBbJP/yn5m3/Vkr4uYymznNEZGRrJw4ULWrl3LyZMnCQ0NxdnZmVKlStGsWTM6dOiQcE6iOTRo0ABjak5C/Y+WLVvSsmVLs8UjIiIiIpKcgq4FWffxOkavHM3nKz/HaDSy7ug6PEd68rPPzzQq24imBZ3wcc+BP0DFB/c99t8Cl5O5z1EkjZllpnHHjh2ULVuWHj16sHDhQvbv38+pU6fYv38/CxcuxMfHh7Jly7J9+3ZzDJcl+Pn5Ua5cOby9vS0dioiIiIiYibWVNSNajWDDxxsokKMAANfuXqPJV034bMVnxMbFMqNGIdY3dKNmbnvcsttgXy5Xsn2WqJY/HSKXrMzkmcYjR47QtGlTwsPDKVCgAD179qRs2bLkz5+fGzducOzYMfz9/blw4QLNmjVj9+7dVKhQwRyxP9e0e6qIiIjI86thmYYcGH6ALv5dWHd0HUajkc9//5wtJ7cwv+d8GhcoSOMCLwCwzi0HzdbPhcQW2Rlg6vDEz38UMReTZxqHDRtGeHg4nTt35sKFC4wcOZKOHTvSqFEjOnTowOeff865c+fo0qUL4eHhDB8+3Bxxi4iIiIhkavld8rPmwzWMaTMGK0P81/LNJzZTeWRl/jzyZ0K9plXy4TO+fqJ9+Iyvr51TJc2ZnDRu3boVFxcXfvzxR2xtbROtY2try7Rp03BxcWHz5s2mDikiIiIi8lywsrJiyCtD2NxvM4VdCwNwM/Qmzac0Z+jSocTExgAQB/Dfo9Ezx1Hp8hwwOWmMioqidOnST93kxt7entKlSxMdHW3qkCIiIiIiz5V6pepxYPgBXq7wMgBGo5Gxq8bScHJD5m/9m1mDtj65PNUI/oO2suHAjfQPWLIUk5PGsmXL8s8//6So7qVLlyhfvrypQ4qIiIiIPHfyOOdh5fsrmfjGRKyt4o+A++v0X7z90WdJzyoaDAz7Zn+6xShZk8lJY9++fbl69SpTpkxJtt4333zDtWvX6Nu3r6lDioiIiIg8l6ysrOj/Un+2DdiGWy43AGKCHcAYl3gDo5ErF0PSMULJikzePbVTp05cvnyZgQMHsmXLFt577z3Kli1Lvnz5uHnzJseOHeO7777jjz/+YOLEiXTo0MEccT/3/Pz88PPzIzY21tKhiIiIiEg6q1WiFoHDA+k+qzsrAu6Q+NapgMFAITeXdI1Nsp5UJY3W1tbJXl++fDnLly9P8vrAgQMZNGgQMTExqRk2S9KRGyIiIiJZWy7HXCzzXcZ7dl/wwztxxCeO/1mnajQy+gMvS4QnWUiqlqcajUaTH3FxSUyti4iIiIjIYwwGA9/37kerQS+AwciDfVQfMNJtXG0duSFpLlVJY1xcnFkeIiIiIiKScsvHvsmyna/j6HX938JCJzkc/SFnb561XGCSJZi8EY6IiIiIiKS91jU8uLN7ImR/cH9jUFH2nttHlVFVWLJviWWDk+eakkYRERERkUzC1saawt5F419EZofbhQgJD+GNH97gf/P/R0R0hGUDlOeSybunPnTv3j1+//13Dh48yO3bt4mOjk60nsFgwN/f31zDioiIiIhkKXUbFOWXLfHnpBeMbsNV/ADw2+THjjM7+KX3L5TMX9KSIcpzxixJ48KFC3n33XcJCfn3jBijMX7a3GAwPFampFFERERE5Nl1benOL5/vBCD6Zk2mDajEhws/JCI6gsCLgVQdXZUfu/xIh+o66k7Mw+TlqTt37qRLly7ExsYydOhQPDw8AJg+fTrDhw+nVatWGAwG7O3tGTNmDDNnzjQ56KzAz8+PcuXK4e3tbelQRERERCQDae6VH6uc2QC4dfAmnbx7sHvIbkoXKA1AaEQoHad3pM+8PoRHhVsyVHlOmJw0Tp48mbi4OH7++WdGjhxJvnzxW/76+Pjw2WefsXTpUg4fPoy7uzt+fn40b97c5KCzAl9fX44ePUpAQIClQxERERGRDMTKygo37wLxLyJjmbfhApWKVGLv0L10qdklod6PW3+kxtgaHL963EKRyvPCLDONefLk4dVXX02yTpkyZViyZAlXr15lxIgRpg4pIiIiIpKlNWjolvB88ZpzADjZOzGnxxxmdpuJg50DAIcuH6LamGrM2znPInHK88HkpDEoKAg3t38/tHZ2dkD8xjiPKlWqFOXLl2f16tWmDikiIiIikqX5vFoi4fn+vy4nPDcYDHSv052AIQGUK1gOgHuR9+g6sys9ZvfgXuS9J/oSeRqTk8bcuXMTHv7vWuk8efIAcObMmSfqxsbGcv369SfKRUREREQk5eqWz4NVbnsAgv++iXfXP1gXeCPhevnC5QkYGkCPOj0SymZtn0X1MdU5cvlIuscrmZvJSWPx4sW5evVqwmsvLy+MRiM///zzY/UOHjzIyZMnyZs3r6lDioiIiIhkaT0m7iEu6MGZjEbYO+8Yzbzm0nPinoQ62bNlx7+bP/N85uGYzRGAo1eP4j3Wm5l/zUw47UDkaUxOGps2bUpwcDBHjsT/xqJTp07Y29szefJkOnfujJ+fH8OHD6dx48bExcXRtm1bk4MWEREREcmq1gXeYNbArYle8x+4lQ0HbjxW1rlmZ/YO3UulIpUACI8Kx2eOD91mdyM8RrurytOZnDS2a9eORo0aceLECQCKFi3K999/j42NDfPnz+eDDz5gzJgx3L59mxo1ajB69GiTgxYRERERyareHbAp2et9+m9+oqxMwTLsGryLPvX7JJQtCFjAJ9s+4eA/B80dojxnbEztoHz58qxbt+6xsrfffpt69erx66+/cv78eRwcHKhbty5t2rTB2tra1CFFRERERLKsszuvJnv9zOZLFGvyK4XcXBj5vhdNq8Qfiedg58APXX6gQekG9J7Xm9CIUK7cu0LdiXWZ0mEKvev3xmAwpMdbkEzG5KQxKe7u7gwaNCitun/u+fn54efnR2xsrKVDEREREZEMxBj5lO+HMUYubrzIRYOBZrMP4zO+PjMGVE+43KF6B6oVr0a7H9oReCmQyJhI3vnpHTad2MSPXX7ExcEljd+BZDYmL0+VtOHr68vRo0cJCAiwdCgiIiIikpFkS8HKPSMQZwQj+A968j5Hj3webO23lRbFWySU/RLwC16jvNh/Yb+ZA5bMzmxJY2RkJHPmzKFTp05Uq1aN0qVLU61aNTp16sTs2bOJiIgw11AiIiIiIlmWY5X8qWtgMNDvq71PFGezzUbvCr1Z2GshORxyAHDm5hlqja/Ftxu/1e6qksAsSeOOHTsoW7YsPXr0YOHChezfv59Tp06xf/9+Fi5ciI+PD2XLlmX79u3mGE5EREREJMtq+aFX6hoYjZw9H5Lk5dervE7gp4F4F/cGIComivcXvM8bP7xB8P1gEyKV54XJSeORI0do2rQp58+fJ3/+/AwbNoyff/6Z9evXM3/+fD799FMKFizIhQsXaNasGYcPHzZH3CIiIiIiWdKol16APpUgpXvWGAyQ1yHZKi/kfYG/Bv7FR00+Sij7bf9vVBlZhT3n9iTTUrICkzfCGTZsGOHh4XTu3Bl/f39sbW0TrdOzZ0/mzZvH8OHD+e2330wdVkREREQkSyrpbMesAdXpUToXxs2X4GY4OFjDpkvx9zL+l9GITcOiT+3XzsaOL9t/SYPSDeg2qxt37t/hfNB56k6oy4S2E+jbpK92V82iTJ5p3Lp1Ky4uLvz444+JJowAtra2TJs2DRcXFzZv3mzqkCIiIiIiWVo3d1dO9qzEoM/r0GHSizi9Uxl6V3q8kpUhfjaydyXsCzunuO9Wnq0IHB5IrRK1AIiOjebjXz+mtV9rbt+7bcZ3IZmFyUljVFQUpUuXxt7ePtl69vb2lC5dmujoaFOHFBERERHJ8jyc7RjnmY8FdQpTIUc2eLEouNrFX7S1gpbu8EUDeLEobtlTt8CwWO5ibOm3hQEvDUgo+/3g73iO9GTH6R1mfBeSGZicNJYtW5Z//vknRXUvXbpE+fLlTR1SREREREQeMbJi3vgn1g++3jvZQocyUMARgNGV8qW6T1sbWya8MYE/PviD3E65Abh0+xL1J9Vn4pqJxMXFmSV2yfhMThr79u3L1atXmTJlSrL1vvnmG65du0bfvn1NHVJERERERB7RtKATPu45Er3m456Dxg+Sx2fRomILDnx6gHol6wEQGxfLwCUDaTm1JTdDbz5zv5J5mJw0durUiQkTJjBw4EBef/111q9fz+XLl4mOjubKlSts2LCBtm3bMmDAACZOnEiHDh3MEbeIiIiIiDxiRo1C5MlmnfDa0drA+oZuzKhRyOS+i+QqwsZPNjK0xdCEzXBWH16N50hPtp7canL/krGlanGztbV1steXL1/O8uXLk7w+cOBABg0aRExMTGqGzZL8/Pzw8/MjNjbW0qGIiIiISCbhYP3vnJARaJAvu9n6trG2YfRro3mx9It0ntGZG6E3uBJ8hYaTGzKy9UgGvzwYKyuzHAMvGUyq/lSNRqPJD619ThlfX1+OHj1KQECApUMRERERkUzofqyRM2FRZu+3abmmHBh+gIalGwIQZ4xj2LJhNJ/SnOsh180+nlheqpLGuLg4szxERERERCTtHQyOTJN+C7oWZN3H6/js1c8SlquuO7oOz5GebDy2MU3GFMvR/LGIiIiIyHPqYHBEmvVtbWXNiFYj2PDxBgrkKADAtbvXaPJVE0YsH0FsnG6zel4oaRQREREReU4dvJM2M42PalimIQeHH6RpuaZA/C1tI1eOpMmXTbgSfCXNx5e0Z/ak8eTJk6xcuZIFCxawcuVKTp48ae4hREREREQkGQbil4ym5Uzjo/K55GPNh2sY02YMVob4FGPzic14jvTkzyN/pksMknbMljROmzYNd3d3ypYtS+vWrencuTOtW7embNmylChRgunTp5trKBERERERSYbtg2/5l+7HcDsyfZaJWllZMeSVIWzut5nCroUBuBl6k+ZTmjN06VBiYnWCQmZllqSxe/fuvPfee5w/fx47OztKlChB7dq1KVGiBHZ2dpw7d4533nmH7t27m2M4ERERERFJRHR0/KaTsWHRsPA4XL3H3+k02/hQvVL1ODD8AC0qtgDil6uOXTWWpl835Vb4rXSNRczD5KRx/vz5zJkzh+zZszNx4kRu3rzJyZMn2bZtGydPnuTmzZtMnDgRR0dH5s6dy4IFC8wRt4iIiIiIPGLWrENcu3YPgNjIWFhxBj7ZzI8zD6d7LHmc8/D7/35n4hsTsbGOPxp++5ntfLT1I1YfXp3u8YhpTE4ap0+fjsFgYMmSJfTr1w8nJ6fHrjs5OdGvXz8WL16M0WjUMlURERERETM7deoOPj5rE722YOg2Tp++k84RxS9X7f9Sf7b234pbLjcAQqNDaf1dawYsHkB0THS6xyTPxuSk8eDBg7i7u9OsWbNk6zVr1gwPDw8CAwNNHVJERERERB4xeXIARmMSF43x1y2lVolaBA4PpGWllgllk9ZOov6k+lwIumCxuCTlTE4aIyIicHV1TVFdFxcXIiPTfttfEREREZGsZNu2f5K9vnVr8tfTWi7HXCzps4Qe5Xpga20LwK6zu6gysgrLDyy3aGzydCYnjW5ubhw+fJhbt5K/qfXmzZscOXIENzc3U4cUEREREZFHREUlv0Pq6UuhrAu8kU7RJM5gMNDKvRVbPtnCC3leAODO/Tu08WtD34V9iYqJsmh8kjSTk8ZWrVoRGRlJ+/btuXnzZqJ1bty4Qfv27YmKiqJ169amDikiIiIiIo9wdrZL9np0WDTNvObSc+KedIooadWKV2P/p/tp69U2oWzKhinUGV+HszfPWjAySYrJSeOgQYMoUqQImzdvplixYrz99ttMmDCBWbNmMWHCBN5++22KFy/O5s2bKVKkCAMHDjRH3M89Pz8/ypUrh7e3t6VDEREREZEMrnBh5xTV8x+4lQ0HLDvjCOCa3ZVF7yzi207fYmcTn/DuvbCXKqOqsHjfYgtHJ/9lY2oHuXLlYuPGjXTs2JF9+/Yxb948DAZDwnXjgztyvb29mT9/Prly5TJ1yCzB19cXX19fQkJCyJEjh6XDEREREZEMrGLFPKxefY64uKR2w/nX+5/v4OjSNmkf1FMYDAZ8G/pSu0Rt2k1rx+kbpwkJD+HNH97kvQbv8UW7L7C3tbd0mIIZkkYADw8PAgIC2LBhA3/++ScnT54kLCwMJycnSpUqxUsvvUSjRo3MMZSIiIiIiPxHjx4VmTgxZTukntl3PY2jSZ0qblXYN2wffeb1YWHAQgC+2/wdO8/u5Jfev1Ayf0kLRygmJ40XL14EoEiRIjRu3JjGjRubHJSIiIiIiKRcyZI58fd/CR+ftU+dbYy6FU6tHmsY8V7FdIru6VwcXJjfaz4NyzTkw4UfEhEdQeDFQLxGeTG963Q6VO9g6RCzNJPvaSxevDg1atQwRywiIiIiIvKMunWrwIkTPbAr4pR8xfAYds05wsvVF7BhQ0j6BJcCBoOB3vV7s3vIbkoXKA1AWGQYHad3pM+8PoRHhVs4wqzL5KQxR44cFCtWDCsrk7sSERERERETeHjkpECVfE+vGGcEI0ydeh3PdistfhzHoyoVqcTeoXvpUrNLQtmPW3+kxtgaHL963IKRZV0mZ3oVK1ZMWKIqIiIiIiKW5RgVB4an13vo6PIzNKuaMY7jeMjJ3ok5PeYws9tMHOwcADh0+RBVR1dl7o65Fo4u6zE5afzwww+5du0aM2fONEc8IiIiIiJignrlc4MhFVmjMf7hPyhjHMfxkMFgoHud7uwdupdyBcsBcD/qPm/Pepuec3sSERNh4QizDpOTxrZt2zJ+/Hh8fX356KOP2L9/P+HhWm8sIiIiImIJ/d7xTM1E478MBoZ9s9/c4ZisXKFyBAwNoEedHgllc3fNpf9f/Tly5YgFI8s6TE4ara2tGTx4MFFRUXzzzTd4e3vj5OSEtbV1og8bG7Oc8iEiIiIiIokoWTInM/1fwsrKgMHakPKlqkYjFy9knI1xHpU9W3b8u/kzz2cejtkcAbgUdonaE2oz86+ZCWfDS9owOWk0Go2pesTFxZkjbhERERERScLDnVQH9vemQ/syVGpQ9OnJo8EAeR3SJb5n1blmZ/YN20fFwvHHhYRHh+Mzx4cu/l0IjQi1cHTPL5OTxri4uFQ/REREREQkbXl45GTcuPosWNCSg5vas35/V5ybFUu6gdFIqVdLpF+Az6h0gdL81f8vXnJ7KaHs590/U210NQ5eOmjByJ5fOidDRERERCQLaOyZD98JL2LoU+nJWUcDGHpXomb5PBaJLbUc7Bx4t9K7/NTjJ5ztnQE4ef0kNcbWYNqWaVquambPfIPh/fv3WbduHadOnQLAw8ODpk2b4ujoaLbgRERERETEfHqUcGXii0Uxls4FA7ZAjBGcbGFkHQwFHPEp4WrpEFOlXbV21ChRg/bT2rP/4n4iYyJ556d32Hh8I9O7TsfFwcXSIT4Xnilp/OOPP+jevTtBQUGPlefKlYvp06fTpk0bc8QmIiIiIiJmVNLZDv8aBfHZfZU4WyuIicWQww5DAUf8axTEw9nO0iGmmkc+D3YM2kG/Rf34dtO3APy691f2XdjHr31+xauYl4UjzPxSgtXfrwAAMklJREFUvTz16NGjvPHGG9y6dQs7OzvKly9PuXLlsLOzIygoiA4dOvD333+nRawiIiIiImKibu6unGj5772L1gYDJ1qWoJu7q+WCMlE222xM7TSVxe8sJodDDgDO3DxDrfG1mLphqparmijVSeMXX3xBZGQkTZs25fz58/z9998cOnSIc+fO0bhxY6Kiovjyyy/TIlYRERERETEDD2c7DA9ubLQ2kClnGBPTtmpbAj8NxLu4NwBRMVF8sPAD3vjhDYLvB1s2uEws1Unjli1byJYtGz/99BP58+dPKC9QoAA///wzdnZ2bNmyxaxBioiIiIiIpMQLeV/gr4F/8VGTjxLKftv/G1VGVmHPuT0WjCzzSnXSeOXKFUqWLEnevHmfuJYvXz5KlizJtWvXzBKciIiIiIhIatnZ2PFl+y9Z7rucnNlzAnA+6Dx1JtTh6w1fa7lqKqU6aYyIiMDV1TXJ666urkRFRZkSk4iIiIiIiMlaebbiwPAD1CpRC4CY2BgGLBnA2L1juX3vtoWjyzx0TqOIiIiIiDy33HK7saXfFga8NCChLOB6AN5jvdlxeocFI8s8nunIjRs3bjB37twkrwHMmzcvyWnfrl27PsuwWYqfnx9+fn7ExsZaOhQRERERkUzN1saWCW9MoEHpBnSd2ZVbYbe4dOcS9SfVZ+xrY+nXrB9WVppPS8ozJY2nTp2ie/fuydbp1q1bouUGg0FJYwr4+vri6+tLSEgIOXLksHQ4IiIiIvIcOXXqDsbo+MmJmOBITp26Q8mSOS0cVdp7ueLLBAwJ4JXJr3D09lFi42IZuGQgm09sZk6POeR1fnLfFnmGpNHNzQ2DwZAWsYiIiIiISBqbNesQPXv+CXHxqwJjQ6MpU2Ym/v4v0a1bBQtHl/YKuxZmVM1R7DXuZfya8RiNRlYfXo3nSE8W9FpA/VL1LR1ihpPqpPH8+fNpEIaIiIiIiKS1U6fu0LPnn8TFPX4bWVycER+ftdStWxgPj+d/xtHayprPW3xOwzIN6TyjMzdCb3Al+AoNJzfk81afM7jFYKytrC0dZoahhbsiIiIiIlnEzJmHktx3xGg04u9/KJ0jsqym5ZpyYPgBGpZuCECcMY5Pl39K86+bcz3kuoWjyziUNIqIiIiIZBG79t8gqSMKjUbYFXgjfQPKAAq6FmTdx+v47NXPEm7DW39sPZ4jPdl4bKOFo8sYlDSKiIiIiGQRJ6+GJXt9647L1OqxhnVZLHm0trJmRKsRbPh4AwVyFADg2t1rNPmqCZ+v/JxYY9Y+0UBJo4iIiIhIVuFkl+zluNBods05QrOqc+k5cU86BZVxNCzTkIPDD9KsXDMgfsnumFVjGLFrBFeCr1g4OstR0igiIiIikkW4lckFTzsIIc4IRvAftJUNB7LWjCNAPpd8rP5wNWPajMHKEJ8uHQ46jPdYb/488qeFo7MMJY0iIiIiIlnEyPe9Ul7ZCG06rcxyS1UBrKysGPLKEDb320xh18IA3Ay7yUtfv8SQ34YQExtj4QjTl5JGEREREZEsommVfPiMrx8/22j19LPXw47dzrJLVQHqlapHwJAAquarmlA2bvU4Gk5uyD+3/7FgZOlLSaOIiIiISBYyY0B11u/vSu2uZSlSxPbpy1Wz8FJVgDxOeRjqPZRxr43Dxjr+mPu/Tv+F5yhP/vj7DwtHlz6UNIqIiIiIZDGNPfOx+cemDBlSKGUNDAaGfbM/bYPKwKwMVnzS9BO29t+KWy43AILCgmg5tSX9F/UnOibawhGmLSWNIiIiIiJZVKFCdviMq5OC2UYjVy6GpEtMGVmtErUIHB5Iq8qtEsom/zmZ+pPqcyHoggUjS1tKGkVEREREsrDvP67G+v1dcSqbK+lKBgOF3FzSL6gMLJdjLpb5LuPr9l9ja20LwK6zu/Ac6cmKgyssHF3aUNIoIiIiIpLFNfbMx28/t0x6xtFoZPQHqdh59TlnMBj4sMmHbB+4nRfyvABA8P1g3pj2BjOOzCAqJsrCEZqXkkYREREREfnPzqqPX+s2ti6NPfNZJK6MzPsFb/Z/up+2Xm0TylaeW8mLk1/k7M2zFozMvJQ0ioiIiIgI8O/OqjXfroCVa7aE8ry5HCwYVcbmmt2VRe8swq+TH3Y2dgDsu7iPKqOqsHjfYgtHZx5KGkVEREREJEFjz3zsnNmcz79tnFA2bWrW3Tk1JQwGA+81fI9t/bdRMHtBAELCQ3jzhzfx/dmXiOgIC0doGiWNIiIiIiLyhCEdy2BX1BmAkMNBzF3//O4Oai5Vilbhi3pf0K5au4Sy7zZ/R61xtTh1/ZQFIzONkkYREREREXmClZUVb/aulPB6+MQ9Fowm88hum5153efxY5cfsbe1B+DApQN4jfJiwe4FFo7u2ShpFBERERGRRH3zoRcG5/j79C5svMje03csHFHmYDAY6FW/F7uH7KZ0gdIAhEWG0WlGJ979+V0iYyMtHGHqKGkUEREREZFE5XLORu0O8UkPsUbeH7vbsgFlMpWKVGLv0L10qdklocx/uz8D/hrA8WvHLRhZ6ihpFBERERGRJH07qAZYxx/guHvRCW7czVyzZJbmZO/EnB5zmNltJg528bvQXgi9QM3xNZm7Y66Fo0sZJY1ppEGDBhgMhkQf48ePt3R4IiIiIiIp4unuinuz4gAYw6L58Ot9lg0oEzIYDHSv0529Q/dSrmA5AO5H3eftWW/TfVZ37kXes3CEyVPSmEa+++47du7c+djjvffeA6BFixYWjk5EREREJOXGDqqe8HzJ9L+JiY2zYDSZV7lC5dgxcAeNi/57nMnsHbOpPqY6Ry4fsWBkyVPSmEbKlStHzZo1H3sEBARQsWJFKlWq9PQOREREREQyiPb1i+JaOS8A0ZfDGP3zUQtHlHllt8vO+5XfZ9bbs3DM5gjA0atH8R7rjf82f4xGo4UjfJKSxnRy6tQpAgIC6Ny5s6VDERERERFJtfc+8Ep4/s2U/RaM5PnwVo232DdsH5WKxE8ohUeF03NuT7rN7kZ4TLiFo3tcpk0az507x/Tp0+nVqxeVK1fGxsYGg8HA6NGjU9R+1apVNGnShFy5cuHo6IiXlxdTp04lLi5tptp/+uknrKys6NSpU5r0LyIiIiKSlj5/uzy2BeNnxu7sv8Hiv/6xcESZX+kCpdk1eBd96vdJKFsQsIBPtn3CwX8OWjCyx2XapHHKlCn07t2bGTNm8PfffxMbG5vituPHj+eVV15hw4YN5MyZEw8PDw4ePMgHH3zAa6+9liaJ4/z583nxxRcpUqSI2fsWEREREUlrNtZWtO5ZMeH1kPF7LBjN88PBzoEfuvzAwt4LcbZ3BuDKvSvUnViXHzb/kCGWq2bapDFPnjy0bNmSkSNHsnr1atq2bZuidjt37mTI/9u797ioqrUP4L9hgIEBBwQEMUUEUQHjJheRSuiYlzSJJLOTHVHzWGb5Hq3UhCNeSvLSzV47pb7BOYpmVuZdSkmPCmVeMA6iQCB4K0QUlTs87x9+Zh/GmQ3MMOwBfL6fz3yKvdba+1l7nj3Omn1Zb78NMzMzpKamoqCgAFlZWTh16hRcXFywc+dOvP/++xptbt++jdzc3BZft27d0rnNzMxM5Ofn86WpjDHGGGOsU1v7t2DIbCwAAHkHipBdpPv7L9PfcyHP4VTCKQT2CQQA1NTX4JXNr2DS55NQUVVh0tg67aAxPj4eu3btQkJCAkaPHg1bW9tWtVu+fDmICC+99BKef/55Ybm/v78wWExKSkJdXZ1QtmfPHnh7e7f4+vbbb3Vuc9OmTbCyskJsbGwbeswYY4wxxphp9exuheAJXvf+qG/E7Pf4bKMx9XfujyNvHMFY97HCsm2/bEPQsiCcvGi6qU467aDREBUVFfjhhx8AANOnT9cqf/bZZ6FSqVBWVob09HRh+aRJk0BELb7i4uK01llfX49t27bhqaeegkqlare+McYYY4wxJoW1bw8FzGQAgCOp53Dzbq2JI+paFBYKzBg8A1/O+BJ21nYAgILSAgxLGob1x9abJKYHatB4+vRp1NbWwsrKCkFBQVrlFhYWCAkJAQD89NNPRtnmgQMHUFpaypemMsYYY4yxLiFsoAP6RPUBAFBFLf629rSJI+qaYgJjcDrhNELc741PautrsXDXQpPEYm6SrZpIXl4eAMDNzQ3m5rq77uHhgYMHDwp122rTpk1wdHTEmDFjWlW/pqYGNTU1wt/q+yRv3LhhlHikUldXh8rKSpSVlcHCwqJTba8t69K3rT71W1O3pTrNlUv9nhkL5xrnmlQ41zjXpMK5xrkmlbbEPf+VQZh9sBgAsHXdKayc7gEzs+bPR3Guta5O03KVhQrfvfQdlu1fhk+PfirUkfrhOA/UoLG8vBwA0L17d9E66jJ13ba4c+cOdu7cibi4uFYn84oVK7BkyRKt5QMGDGhzPIwxxhhjjBlbdQng7DzL1GE8UMrKymBnZyfZ9h6oQWN1dTUAwNLSUrSOQqEAAFRVtX1CTVtbW9y9e1evNgsXLsTcuXOFv2/evIm+ffuiuLhY0sQwhpCQEJw4caJTbq8t69K3rT71W1O3pTpi5RUVFejTpw9KSko63f23nGvGr8+5phvnmvHrc67pxrlm/Pqca7pxrhm/fnvm2q1bt+Dm5gYHB4dWxWIsD9Sg0crKCgBQWyt+s6760lBra2tJYrqfQqEQBq5N2dnZdboPIblcLmnMxtxeW9alb1t96rembkt1WipXqVScaxJuj3ONc02q7XGuca5JtT3ONc41qbb3IOdaS5cCG9sD9SCc1lx62ppLWFnrvPrqq512e21Zl75t9anfmrot1ZH6fZEC55rx63Ou6ca5Zvz6nGu6ca4Zvz7nmm6ca8av3xVzTUZS30XZTuLi4pCSkoJly5YhPj5eZ53Dhw8jMjISVlZWuH37ts6H4YwYMQIHDx7E0qVLkZCQ0N5ht6iiogJ2dna4detWp/vlinUunGtMKpxrTCqca0wqnGtMKqbKtQfqTGNgYCAsLCxQXV2NU6dOaZXX1dUJ1w6HhYVJHZ5OCoUCixcv1nnJKmPGxLnGpMK5xqTCucakwrnGpGKqXHugzjQCwJNPPol9+/bhr3/9Kz777DONstTUVLzwwgtwdHTElStXmn1gDmOMMcYYY4w9CB6oM40AsGjRIshkMmzYsAFbtmwRlmdlZQlPLX3rrbd4wMgYY4wxxhhj6MSDxmPHjsHJyUl4bd26FcC9eQ6bLi8pKdFoFxERgWXLlqGxsRF//vOf4enpCX9/fwQFBeH333/H2LFjMW/ePFN0ySiKiooQHR2Nbt26oXv37njxxRdx/fp1U4fFuphLly7htddeQ1hYGKysrCCTyUwdEuuitm/fjpiYGLi5uUGpVMLX1xdr1qxBXV2dqUNjXcyBAwcQGRkJZ2dnKBQK9O3bFzNmzMDly5dNHRrrwurr6+Hn5weZTCZ8l2XMWH788UfIZDKtV3BwsN7r6rRTbtTV1aGsrExreWVlJSorK4W/GxoatOosWrQI/v7++OCDD3Dy5Elcu3YNDz/8MKZOnYrZs2dDLpe3a+zt5c6dO4iKioKjoyO2bNmCqqoqLFiwAGPHjkVGRobkj+ZlXVd+fj6++uorhISEICwsDEeOHDF1SKyLWr16Nfr06YOkpCS4urri+PHjiI+Px9mzZ5GSkmLq8FgXcuPGDYSGhuL111+Ho6Mj8vLysHTpUhw6dAjZ2dkmm4qLdW0fffQRSktLTR0G6+I2bNgAX19f4W9bW1u919Fl7mlkwJo1a7Bo0SIUFhbC1dUVAHDixAmEhobim2++QUxMjIkjZF1FY2Oj8CNEUlISFi5cCP4oYe2htLQUPXr00Fi2fPlyJCQk4Nq1a3BxcTFRZOxBkJaWhlGjRmH//v0YNWqUqcNhXczly5fh7e2NTz75BFOmTMGWLVswadIkU4fFupAff/wRUVFRyMjIwNChQ9u0Lj711IXs3r0bUVFRwoARAEJCQjBgwADs2rXLhJGxrobPWjOp3D9gBIAhQ4YAAK5cuSJ1OOwB4+joCAA6p+hirK3mzJmD8ePH47HHHjN1KIy1iL/5tbPCwkKsX78eM2bMgL+/P8zNzSGTybB8+fJWtd+7dy9GjBgBBwcH2NjYICgoCGvXrkVjY6NW3ZycHI1Tz2q+vr44d+5cm/vCOjYpc4092Eyda//+979haWkJT0/PtnSDdQKmyLWGhgbU1NQgJycHb775JgIDAzF8+HBjdYl1UFLn2v79+5GWloZVq1YZsxusEzDF51p0dDTkcjl69uyJmTNnory8XP/AibWrOXPmEACt17Jly1psu2LFCqG+h4cH+fn5kZmZGQGg8ePHU0NDg0Z9CwsLneudPn06DRgwwGh9Yh2TlLmmqy17cJgq14iIcnJySKlU0uzZs43VHdaBmSLXBg4cKLQLDg6ma9euGbtbrAOSMteqqqrI09OTVq9eTUREhYWFBIC2bNnSLn1jHYuUuXbq1Cl64403aNeuXZSenk7vvvsudevWjQICAqi2tlavuPlMYztzcnLCuHHjsHTpUuzbtw8TJkxoVbuMjAy8/fbbMDMzQ2pqKgoKCpCVlYVTp07BxcUFO3fuxPvvv6/VTtdTLInvNXsgSJ1r7MFlqlwrKytDTEwMPD09kZSUZKzusA7MFLn29ddfIyMjA8nJybh9+zaeeOIJVFRUGLNbrAOSMtfeffddWFpa4vXXX2+PrrAOTspcCwwMxKpVqzBu3DhERkZi4cKF2Lx5M86cOYPt27frF7heQ0zWZlOmTGnVrwlPPvkkAaC//vWvWmWbN28mAOTo6KjxK4GzszPNmzdPq35MTAwNHTq07cGzTqU9c60pPtPIpMi127dvU2hoKPXt25cuX75stNhZ5yLV55paSUkJyeVyWrVqVZviZp1Pe+VaUVERKRQK2r59O5WXl1N5eTllZWURANq4cSPdvHmzXfrDOi6pP9caGxvJxsaG5s6dq1ecfKaxA6qoqMAPP/wAAJg+fbpW+bPPPguVSoWysjKkp6cLy319fZGTk6NVPycnB97e3u0XMOu0DM01xvTVllyrqalBTEwMfvvtNxw4cAC9evWSJGbWORnzc613797o2bMn8vPz2yVW1rkZkmuFhYWoqalBbGwsunfvju7du8Pf319YBz8RmunSHt/X9J1jmweNHdDp06dRW1sLKysrBAUFaZVbWFggJCQEAPDTTz8Jy8eNG4f09HRcu3ZNWHby5EmcP38eTz31VPsHzjodQ3ONMX0ZmmsNDQ14/vnnkZmZib1792LgwIGSxcw6J2N+rhUUFODKlSv80CWmkyG5FhAQgPT0dI3Xli1bAAAJCQlIS0uTrgOs0zDm59rOnTtx9+5doX5r8TOkO6C8vDwAgJubm+hjvj08PHDw4EGhLgDMmDEDa9euxfjx47F48WJUV1dj/vz5CA0NRXR0tCSxs87F0FwDIFwLn52drfG3j48PfHx82itk1kkZmmuvvvoqvv32WyxbtgwNDQ3IzMwUyjw9PXVOycEebIbmWkxMDIYMGQI/Pz/Y2toiJycHq1evRu/evXX+ss+YIblmb2+PyMhIjTpFRUUA7v37ydNvMF0M/VybPHkyPDw8EBQUBFtbW2RkZGDlypUIDg5u9b2Uajxo7IDUj8Ht3r27aB11WdNH5nbr1g2HDh3CnDlz8Nxzz8Hc3Bzjxo3DBx98wPPqMZ0MzTXg3qUQuv5evHgxEhMTjRgl6woMzbX9+/cDuPcLfEJCgkb9L774AnFxcUaOlHV2huba0KFD8eWXX2LVqlWor6+Hm5sbJkyYgPnz58PBwaF9g2adUlv+DWVMH4bmmq+vL1JTU/Hhhx+iuroavXv3xsyZM/H3v/9d7/lnedDYAVVXVwMALC0tResoFAoAQFVVlcbyfv36YefOne0XHOtS2pJrxE/lZXowNNfUv8Az1lqG5tr8+fMxf/789g2OdSlt+Te0KXd3d/43lTXL0FxbuHAhFi5caJQY+PRTB2RlZQUAqK2tFa1TU1MDALC2tpYkJtY1ca4xqXCuMalwrjGpcK4xqXSEXONBYwfUmksZWnOamrGWcK4xqXCuMalwrjGpcK4xqXSEXONBYwfk5eUFACguLkZ9fb3OOr/99ptGXcYMwbnGpMK5xqTCucakwrnGpNIRco0HjR1QYGAgLCwsUF1djVOnTmmV19XV4cSJEwCAsLAwqcNjXQjnGpMK5xqTCucakwrnGpNKR8g1HjR2QCqVCiNGjAAAbNy4Uav8q6++QkVFBRwdHbUe28yYPjjXmFQ415hUONeYVDjXmFQ6Qq7xoLGDWrRoEWQyGTZs2CBM+goAWVlZmDt3LgDgrbfeavYpSoy1BucakwrnGpMK5xqTCucak4rJc41Yuzp69Cg5OjoKL4VCQQBIqVRqLC8uLtZqu3z5cgJAAMjDw4P8/PzIzMyMANDYsWOpvr7eBD1iHRXnGpMK5xqTCucakwrnGpNKZ801HjS2s/T0dOHNbe5VWFios/2uXbvo8ccfJzs7O1IqleTv708ffvghfwAxLZxrTCqca0wqnGtMKpxrTCqdNddkRDybKGOMMcYYY4wx3fieRsYYY4wxxhhjonjQyBhjjDHGGGNMFA8aGWOMMcYYY4yJ4kEjY4wxxhhjjDFRPGhkjDHGGGOMMSaKB42MMcYYY4wxxkTxoJExxhhjjDHGmCgeNDLGGGOMMcYYE8WDRsYYY4wxxhhjonjQyBhjjDHGGGNMFA8aGWOMMcYYY4yJ4kEjY4x1EZGRkZDJZPjxxx9NFkNRURFkMhnc3d1NFsODIDExETKZTONVVFRk6rA6FXt7e439FxcXZ+qQOjx3d3eduRYXFweZTIbk5GS919mWtowx6fCgkTEmCfWXjZZe/MWBsdbr06cPIiIiEBERASsrK1OH06mEh4cjIiICXl5ebV5X3759YW9vj7q6uhbrqgdJzb2efvppg2MpKipCYmJih/gsPXPmDBITE7Fjxw5Th8IYayNzUwfAGHuweHl5wdnZWbTcxcVFwmi6Fjc3NwwcOBBKpdLUoTCJTJs2DYmJiaYOo1Pat28fACA5ORlTp041eD1ZWVkoLi7GxIkTYWFh0ep2zs7OogNWHx8fg+MpKirCkiVLMHz4cMnOnrq6umLgwIGws7PTWH7mzBksWbIEU6ZMER0Ii7VljHUsPGhkjEnq7bff5svA2sk///lPU4fA2ANn9+7dAIBx48bp1W7MmDEd4mygMaxYsQIrVqyQvC1jTDp8eSpjjDHGmIF2794NMzMzjBkzxtShMMZYu+FBI2Osw6uvr8f69esRFRUFR0dHWFlZwcPDAxMmTMB3332nVb+urg5r165FaGgoVCoVbGxs4O/vj3feeQeVlZVa9e9/eMumTZsQHBwMpVIJBwcHPPvss/jtt99E4ysuLsYrr7yCfv36QaFQwMnJCWPGjBEuf7uf+iEmiYmJKCsrw6xZs9C7d29YW1vD398fW7duFepevHgRU6dORa9evWBtbY0hQ4Zgz549Otfb0oNwTpw4gcmTJ8PNzQ0KhQIuLi4YNmwYVq5ciVu3bon2T5fDhw9jxIgRUKlUsLOzQ1RUFL7//vtm22RmZuKtt95CcHAwnJ2doVAo0KdPH7z44ov4z3/+o7NNe+2r3377De+99x4iIyPRp08fKBQK9OjRA6NHjxZto3bw4EE8/vjjUKlUsLe3x5/+9CccOnSoxYcAVVZW4r333kNwcDBUKhWUSiUCAgKwatUq1NTUNLtNQzTNh7NnzyI6OhpOTk5QqVQYMWIEfvnlF6Huv//9b4wePRoODg7o1q0bxo4di9zcXNF169uXlh520vR9FlteWlqK2bNnw93dHRYWFhpXLOh7zBvL9evX8fPPP2Po0KFwcnIy+vqzs7OxePFihIeHw9XVFZaWlnB1dcUzzzyD48ePa9WPjIxEVFQUgHvHaNP7JJvm5c2bN7Fx40ZER0ejf//+sLa2hp2dHcLCwvDxxx+jvr5erzh1vb/u7u7CZb8pKSkasURGRjbbtqnc3FxMmzYN7u7uUCgUcHR0xNixY3Ho0CGd9cvKyvDGG29g0KBBsLKygo2NDdzd3TF69GisW7dOr34xxpogxhiTQN++fQkAffHFF3q1u3HjBkVERBAAAkB9+/al4OBgcnZ2Fv5uqrKykh5//HGhvre3N/n5+ZGZmRkBoICAALp+/bpGm8LCQmFdCxYsEP7f39+fFAoFASBXV1cqLS3Vii8zM5Ps7e0JANnY2NCQIUOod+/ewvYTEhK02ixevJgA0Ouvv079+/cnS0tLCgoKooceekhol5KSQrm5ueTs7ExKpZKGDBlCTk5OBIDkcjl9//33WusdPnw4AaD09HStsvfee49kMhkBIJVKRUOGDCFPT0+ysLAQbSNmy5Ytwv50dHSk4OBgcnBwIDMzM0pKStL5vhAReXp6Cm0GDx5M/v7+ZGdnRwDI2tpaZwztta+mT59OAMjW1pYGDBhAwcHB5OrqKqwzKSlJZ99TUlKE/ejk5EQhISHk6OhIZmZmtGrVKtG+X7p0iXx8fAgAmZubU//+/cnb25vMzc0JAD3yyCNUWVnZ6vdAvV8WL14sWkedD0lJSWRtbU329vY0ZMgQYZ9369aNsrOzadu2bWRubk7Ozs4UFBRESqWSAFCPHj3o2rVrRunLlClTmj3+xfqjXj5r1ixyc3MjuVxOfn5+5OfnR9OmTSMiw475pr744gsCQFOmTBGtIyY5OZkA0LvvvtvqNup90Zrt/elPfyIAZG9vT97e3hQUFKSR25s3b9aoP3v2bBo8eLBwnEdERAiv2NhYod6//vUvAkCWlpbUt29fCgkJIQ8PD2GfjR07lhoaGrTiUX+OFxYW6uxT0/c3NjaWvLy8CAA5OztrxDJ79uxm26p9+eWXZGlpKeRrQEAA9ezZkwCQTCajjz/+WKP+zZs3hc8ZS0tL8vHxoaCgIHJ2diaZTEZ2dnYt7nPGmG48aGSMScLQQePTTz9NAMjT05MyMzM1yvLy8mjlypUay+bNm0cAqFevXnTy5EmNuoMGDSIANHHiRI026kGjubk5qVQq2rt3r1B29epV8vPzIwA0f/58jXZ3794lNzc3YZ0VFRVCWXJyMsnlcgKgsT6i/34RtrCwoKioKPr999+FMvWgy9XVlUJDQ2nSpEnCehsaGmjmzJkEgEJDQ7X2ldigcceOHcKXzDVr1lBtba1GHz7//HPKycnRWp8uly5dIltbWwJACxYsoLq6OiIiqq2tpb/97W/CIFTXwCklJYUKCgo0ltXV1dGGDRvI3NycPDw8tL6otte+2rt3L2VmZlJjY6PG8iNHjpCrqyvJ5XLKz8/XKLt48aIwoIqPj6f6+nqhDwsWLBDte0NDAw0bNowA0KRJkzQGYiUlJfToo48SAHrjjTd07XKd9Bk0WlhY0Ny5c6mmpoaIiKqrqyk6OpoAUGRkJNnb29OaNWuEfV9eXk6hoaEEgN566y2j9KWtg0a5XE7h4eFUUlIilFVVVRGRYcd8U20ZNMbGxhIAOnv2bKvb6DNo/Oqrr7TW3djYSDt27CBbW1tSqVQanztEROnp6QSAhg8fLrrerKws2r17N1VXV2ssLygooMcee4wAUHJyslY7fQaNRK3bt2Jts7KySKFQkJWVFX3++ecanw07d+4klUpFcrmczpw5IyxfvXo1AaCRI0dSWVmZxvouXrxIH3zwgWgcjLHm8aCRMSYJ9ZeNll7l5eVCm59//pkAkEKhoAsXLrS4jVu3bglf6r/99lutcvX6ZDKZxoBAPWgEQGvWrNFqt3PnTgJAfn5+GsvXr19PAMjFxUX4AtvUrFmzCAA9+uijGsvVX4Stra3p8uXLGmX19fXCmUpXV1e6e/euRnl5eTlZWVkRAK0vRWKDRvVZoaVLl2rFqK/4+HgCQCEhITrL1QNsXYPG5kyePJkA0LFjxzSWt9e+as6GDRsIAL3zzjsay9VnoUeMGKGznXr/3993df6EhIQIg+ymrly5Qra2tmRra9vqs436DBoDAwO1Bsfnz58Xcj46Olqr7f79+3XmvKF9aeugUaFQaL3/RIYf800ZOmisra0llUpFbm5uerVT74vmXq2hPhbvP9vYmkFjc/Lz8wkAPfHEE1plUg4an3nmGQJAH330kc52a9euJQDCGWciEn4o+u6775rtI2NMf/z0VMaYpFqacsPc/L8fS+r7FWNiYlo1l9rRo0dRWVkJNzc3REdHa5WHhIQgPDwcGRkZ+P777+Hp6alVZ/r06TrbAdC6rzEtLQ0AMGPGDJ1z5M2ZMwfr1q3D8ePHcffuXdjY2GiUjxkzBr169dJYJpfL8fDDD+PSpUt4/vnntabPsLe3R79+/XDu3DkUFhbCwcFB164Q5OfnIycnB5aWlvif//mfZuu2xoEDBwAAr7zyis7yWbNm4eWXXxZtn5ubiy1btuDXX3/FjRs3hHuniouLAdybvmDYsGFa7dpjX5WWliI1NRU//fQT/vjjD1RXVwOAcH9nVlaWRn31PZti0zNMnToVhw8f1lr+zTffALh371bT/FZzdXVFSEgI0tPTcfLkSTzyyCM612+oqVOnQiaTaSwbMGAAlEolKisrdeZ8YGAgAO2cN1VfRowYofX+A8Y55g115MgRVFRUYPLkyQa1b27KjaaKi4uRmpqKU6dO4fr166itrQUA/PHHHwDu5emf//xnvbdfU1ODr7/+Gunp6SguLkZlZSWISCi/P/+lVFtbi71790Iul4s+bXv8+PF47bXXNI65Pn36AAC+/fZbPPnkkzpzlDFmGD6aGGOS0mfKjXPnzgEAhg4d2qr6Fy5cAAAMGjRI60uymq+vLzIyMoS6TTk5OemcK0w9yL1z547O7YnNqebl5QVLS0vU1taioKAAfn5+GuViX2B79OjRYvm5c+e04tFFvQ99fHzQrVu3Fuu3RN1nb29vneViy4F7j9aPj49HY2OjaJ0bN27oXG7sfZWWloaJEyc2+wCg+2PJy8sDAK33UU1s+a+//goA+PTTT5Gamqqzjnq/Xr58WTQeQ4ntGycnJxQXF+ssV+/X+/ebqfoilldtPebbwtCpNtRaM+VGSkoKXn75ZeEHDV3EjpnmFBcXY+TIkTh//rxR12ssFy5cQHV1NSwtLfHkk0/qrKMe4DbNs6lTp2LVqlVITk7Gvn37MHr0aDz66KOIioqCh4eHJLEz1lXxoJEx1mFVVFQAuHfGqDXUX3CbO5Pp4uICALh9+7ZW2f1nAtXMzHQ/aLql7clkMvTo0QOXL1/Wub37z4w1bdea8qZnBcTouw9bou6zelBxP/X+vd+RI0fw9ttvQy6XY8WKFRg/fjz69u0LpVIJmUyG+Ph4vPPOO6irq9PZ3pj76ubNm5g0aRJu3bqFv/zlL5g1axYGDhwIlUoFMzMz/PDDD3jiiSe0Yrl79y4AiA6+xZarB6bZ2dk6y5uqqqpqsY6+DNl3YgMwU/VF7Nhs6zHfFnv27IFSqRSeVmpsBQUFmDFjBurq6jBv3jxMnjwZnp6esLW1hUwmw4YNG4RyfcXFxeH8+fMICwvDkiVLEBAQAAcHB1hYWKC+vl74r6mo86y2thbHjh1rtm7TAXWvXr2QkZGBhIQE7NmzBykpKUhJSQFw78fH999/H+Hh4e0XOGNdGA8aGWMdlvpL+M2bN1tV39bWFsB/L9vS5ffff9dYd1u0tD0iQmlpqdG2Zwh992FLbG1tcevWLZSWluo8QyW2LzZv3gwAePPNN7FgwQKt8pKSEqPE1xr79u1DeXk5wsPDkZycrDVAEovFxsYGFRUVomd4xQYl6jz5/vvvMWLEiDZEbnqG9qWlHzrUA3JD45HqmFe7cOEC8vLyMH78eJ2XphvDtm3bUFdXh0mTJmH16tVa5YYeM1euXEF6ejqUSiX27t2rddm2lMeiGPX7+tBDD+HSpUt6tfX29sb27dtRU1ODjIwMHD58GFu3bkVmZiZGjhyJX3/9VXRaHMaYOJ6nkTHWYfn6+gK4N79fawwYMADAvUsyxb6cqucDVNdtC/U6cnJydJbn5eWhtrYWcrncqPdS6UO9D3NycoxypkXdZ7E5/NSXw96vqKgIAHTerwhIe/+UOpbw8HCdZ9TEYlH3/ezZszrL1Zdu3k99+XJrzs51dIb2RX2mUP0jyv3y8/MNikfqY15t165dAAy/NLU1DD1mxM4Sq128eBHAvUt6dd0TbcxjsaVYxHh5ecHCwgJXr141+DJZhUKByMhILF68GNnZ2YiIiMCdO3ewZcsWg9bH2IOOB42MsQ7r6aefBgDs2LEDBQUFLdZ/5JFHoFQqUVJSIjxEp6lffvkFGRkZkMlkeOKJJ9oc36hRowAA69ev13nP0ccffwwAiIiIEL28rr15enpi8ODBqK2tFeJpi5EjRwIA/vGPf+gs//TTT3Uut7a2BvDfsz5NpaWlSTpobC6WsrIybNy4UWc7dc6I3YcmtvyZZ54BAHz22WfN3pvWGRjaF/X9ZCdOnNAqu3TpkvCAJX1Jfcyr7d69GzKZDGPHjjXaOu/XXJ7m5uYKA1exdmKXB6vL//jjD50D7ZUrVxoUryGxiFEqlRg1ahQaGxuN8rkll8uFB5pduXKlzetj7EHEg0bGWIc1ZMgQxMTEoLq6GmPGjNH6wpmfn69x2ZZKpRKe6jl79mycPn1aKCsoKMCUKVMAABMnTjTKmb/nn38ebm5u+P333xEXF6dx2eKmTZvw2WefAYDOyzGltHz5cgBAYmIiPv74Y417oCorK7FhwwbRM4T3e/nll2FjY4OffvoJCQkJwn1PdXV1ePPNN4WzOvdTP0UzKSkJhYWFwvITJ05g2rRp7XaJny6PPvoogHuX//3www/C8qtXr2LChAmi93K9/PLLUCqVSEtLQ2JiIhoaGgAA9fX1iI+Px9GjR3W2i4mJwdChQ5Gbm4unnnpK66xaTU0N9uzZg2nTphmje+3K0L6MGTMGwL0fgPbu3Sssv3r1Kl544QWD75+T+pgH7t1vd+zYMQQGBup8oquxqI+ZdevW4cyZM8LyCxcu4Nlnn4WlpaXOdv369QNw7+oCXWd2fX190b17d1y6dAnvvPOOMHCsrq7GnDlzNPZhWzX9saCyslKvtsuWLYNCocDy5cuRlJSkNfC8evUqPvroI40fsBYtWoSNGzdqXY6fnZ2Nbdu2AQCCgoIM6AljjOdpZIxJQj2/l5eXF0VERIi+7p+T68aNGxQeHi7MX+bu7k7BwcHk4uKic068yspKioqKEur7+PiQv78/yeVyAkD+/v50/fp1jTbqeRqbm1sQIvOnZWZmkp2dHQEgGxsbCg4Opj59+gj14+Pjtdq0NMdeS3Paic3HKLaciGjFihUkk8kIANnZ2VFwcDB5eXkJE9LraiNm06ZNwrqcnJwoJCSEHBwcyMzMjJKSknTuy1u3bpGHhwcBIEtLS3r44Ydp4MCBwns0d+7cZufpM/a+Uk/KDoD69+9PAQEBZG5uTt26daMPP/xQdJ675ORkoe89evSgkJAQcnJyIjMzM1q5ciUBIA8PD612V65cocDAQI1thoWFkY+PD1laWgrzfbaWPvM0ir23YnPuqYnlvKF9mT59utCmX79+wj4fNGgQzZkzx6D3n8iwY74pfedp3Lp1KwGgv//9762qfz91zra0vbq6Oho6dCgBILlcTt7e3jR48GCSyWTk6upKy5cvF13P448/TgCoW7duFBYWRsOHD6fnnntOKP/kk0+E/dWzZ08KDg4mlUpFMplMmH9W13uv7zyNDQ0N5OXlRQDI0dGRwsPDafjw4TRnzpwW2xIRffPNN8I8nFZWVhQQEEChoaEan7Hz588X6kdHRxMAMjMzo/79+1NoaCj1799fqBsVFaVzflHGWMv4TCNjTFJ5eXk4duyY6Ov+eeG6d++Ow4cP43//938RERGB8vJyZGdnQ6lUIjY2Fp988olGfWtraxw4cAAfffQRgoODcfHiRVy4cAE+Pj5Yvnw5jh8/DkdHR6P1JywsDFlZWZg5cyacnJxw9uxZ3LlzByNHjsSePXuwbNkyo22rLRYsWIDjx49j4sSJUCqVyMrKQkVFBUJCQrBq1Sq9fn1/4YUXcOjQIURFRaG6uhq5ubl4+OGHsW/fPjz33HM626hUKhw9ehR/+ctfoFKpcP78edTW1mLu3LnIyMiQ/EFBmzdvRkJCAtzd3XHx4kVcu3YNsbGxOHHiBPz9/UXbTZkyBWlpaYiMjERVVRVyc3Ph6+uL/fv3C1MD6OqLq6srMjIysG7dOjz22GMoKyvD6dOncfv2bYSGhmLJkiVIT09vt/4ak6F9+cc//oGlS5fC09MTly9fRmlpKWbOnImMjIw2Pd1X6mO+rVNttJa5uTkOHDiA1157DS4uLsjPz8fNmzcxffp0nDx5Eg899JBo29TUVMTFxUGlUuHkyZM4fPiwxr3hr776KjZt2oSAgADcuHED+fn5CA4Oxt69e/HSSy8ZrQ9mZmbYs2cPYmNjIZfL8fPPP+Pw4cMaZ06bExMTg5ycHMyZMwfu7u44f/48cnJyoFQqERMTg5SUFI0rOeLj47FgwQKEhITgzp07OHPmDKqqqjB8+HD885//RFpaGs/dyJiBZESteGY7Y4wxxpr19ddfIzY2FtHR0dixY0e7bisxMRFLlizB4sWLkZiY2K7b6uqSk5MxdepUTJkypcV5ExsbG+Hi4gJzc3NcuXLF4Ae9MMZYZ8M/tzDGGGNG8MUXXwC49+Ajqfzf//2fcF/m9u3b0bNnT8m23dmNGTMGt2/fbna6jvtlZmbi+vXrmDZtGg8YGWMPFB40MsYYY6309ddfw9raGqNGjYJcLgdw72FCiYmJ2LNnD2xsbPDiiy9KFk9JSYkwr15nfzKr1DIyMoRJ5Ftr2LBholN7MMZYV8aXpzLGGGOtpL4s1MrKCp6enlAoFDh37hyqqqogl8uRkpKCF154wdRhMsYYY0bFZxoZY4yxVoqOjsalS5dw5MgRlJSUoKqqCj169MD48eMxb948YS44xhhjrCvhM42MMcYYY4wxxkTxlBuMMcYYY4wxxkTxoJExxhhjjDHGmCgeNDLGGGOMMcYYE8WDRsYYY4wxxhhjonjQyBhjjDHGGGNMFA8aGWOMMcYYY4yJ4kEjY4wxxhhjjDFRPGhkjDHGGGOMMSbq/wELDlhR7SRHWwAAAABJRU5ErkJggg==\n", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Segment 12 (Katwijk scenarios) used at idx: [0,8,49]\n", - "segment_repaired = [12, 13]\n", - "segment_table = find_scenarios_with_segment_i(segment_repaired, df)\n", - "idx_segment = segment_table.index.values\n", - "print(f\"Segment {segment_repaired} in scenarios {idx_segment}\")\n", - "\n", - "# idx_segment = [0, 8, 49] # enter index of segment of interest\n", - "N_D_ordered_new, exceed_prob_new, complete_table_new = sensitivity_analysis(case, scenario_prob, idx_segment, N_D_ordered_test, exceed_prob_test, complete_table)" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "a20111d8", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Old fatality: 3.04187862305\n", - "Old fatality: 2.6691130726399996\n", - "Difference: 0.3727655504100005\n" - ] - } - ], - "source": [ - "old_costs, new_costs, result = compute_benefit(complete_table, complete_table_new)\n", - "print(f\"Old {choose_damage_or_fatality}: {old_costs}\")\n", - "print(f\"Old {choose_damage_or_fatality}: {new_costs}\")\n", - "print(f\"Difference: {result}\")" - ] - }, - { - "cell_type": "markdown", - "id": "4ed2eff1-97dd-4df2-9e4e-a2fce6a6a360", - "metadata": { - "jp-MarkdownHeadingCollapsed": true, - "tags": [] - }, - "source": [ - "## Assignment Answers\n", - "\n", - "*You don't need to answer all of these questions, but they will probably help you arrive at a desicion.*\n", - "\n", - "\n", - "\n", - "1. Which scenario contributes the most to risk?\n", - "2. Which dike segment contributes the most to risk?\n", - "3. Is there a certain region that seems to contribute more to risk?\n", - "4. The above questions look at risk, but you can also consider probability and consequences separately. If you look through these details, do you notice any segments or scenarios that stand out as contributing a lot (or a little)?\n", - "5. Which dike segments do you choose to repair, and why?\n", - "6. What is the total reduction in expected damages?\n", - "7. Could you get the entire curve to satisfy the safety criteria? What is needed in order to do so?\n", - "8. Consider the dike segments you chose to repair. How might you actually go about repairing them: would you focus on reducing the probability or the consequences? Make a few suggestions for how you would do each improvement and comment on the feasibility." - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.13" - }, - "vscode": { - "interpreter": { - "hash": "2f56e53acab938e533261baa35aac2c581caa9f2f4a01ed69448e50e809c0ddc" - } - }, - "widgets": { - "application/vnd.jupyter.widget-state+json": { - "state": {}, - "version_major": 2, - "version_minor": 0 - } - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/book/notebooks/flood-risk/Prob_Cons.xlsx b/book/notebooks/flood-risk/Prob_Cons.xlsx deleted file mode 100644 index 9d5f9c5..0000000 Binary files a/book/notebooks/flood-risk/Prob_Cons.xlsx and /dev/null differ diff --git a/book/notebooks/flood-risk/exercise_flood_risk.zip b/book/notebooks/flood-risk/exercise_flood_risk.zip deleted file mode 100644 index 992a414..0000000 Binary files a/book/notebooks/flood-risk/exercise_flood_risk.zip and /dev/null differ diff --git a/book/notebooks/flood-risk/figures/flood-depth-12.PNG b/book/notebooks/flood-risk/figures/flood-depth-12.PNG deleted file mode 100644 index c3dc0c2..0000000 Binary files a/book/notebooks/flood-risk/figures/flood-depth-12.PNG and /dev/null differ diff --git a/book/notebooks/flood-risk/figures/map-dike-segments.PNG b/book/notebooks/flood-risk/figures/map-dike-segments.PNG deleted file mode 100644 index a172d35..0000000 Binary files a/book/notebooks/flood-risk/figures/map-dike-segments.PNG and /dev/null differ diff --git a/book/notebooks/flood-risk/functions.py b/book/notebooks/flood-risk/functions.py deleted file mode 100644 index 7519bce..0000000 --- a/book/notebooks/flood-risk/functions.py +++ /dev/null @@ -1,163 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt -import pandas as pd - -def find_scenarios_with_segment_i(segments_fixed, df): - """Given a list of segments, return set of dependent scenarios.""" - idx = [] - segments_fixed = set(segments_fixed) - for i, row in enumerate(df['failed_segments'].values): - segments_row = set([int(seg) for seg in row.split(",")]) - intersection = list(segments_fixed.intersection(segments_row)) - if len(intersection) > 0: - idx.append(True) - else: - idx.append(False) - segment_table = df.iloc[idx] - return segment_table - -def assemble_analysis_cases(df): - """From scenario dataframe collect damage and fatality information.""" - econ_damage_case_1 = df.iloc[:,3] # Unexpected, no evacuation - econ_damage_case_2 = df.iloc[:,5] # Unexpected, unorganised evacuation - econ_damage_case_3 = df.iloc[:,7] # Expected, unorganised evacuation - econ_damage_case_4 = df.iloc[:,9] # Expected, organised evacuation - - fatalities_case_1 = df.iloc[:,4] - fatalities_case_2 = df.iloc[:,6] - fatalities_case_3 = df.iloc[:,8] - fatalities_case_4 = df.iloc[:,10] - - scenario_prob = df.iloc[:,1] # scenario probability - - cases = {'damage': [econ_damage_case_1, econ_damage_case_2, econ_damage_case_3, econ_damage_case_4], - 'fatality': [fatalities_case_1, fatalities_case_2, fatalities_case_3, fatalities_case_4]} - return cases - -def exceedance_prob(cases, scenario_prob): - """Compute exceedance probability.""" - case_1 = cases[0] - case_2 = cases[1] - case_3 = cases[2] - case_4 = cases[3] - - key = case_1.index - - # Combine Evacuation Scenarios into new Dataframe - scenarios = [pd.DataFrame({'Nr': key, 'N/D': case_1}), - pd.DataFrame({'Nr': key, 'N/D': case_2}), - pd.DataFrame({'Nr': key, 'N/D': case_3}), - pd.DataFrame({'Nr': key, 'N/D': case_4})] - - scen_combi = pd.concat(scenarios, ignore_index=True) - - # Sort values by key ('Nr') - scen_combi_sorted = scen_combi.sort_values(by=['Nr']) # useful if scen_combi_nodup.sort_values(by=['Nr']) in case of no duplicates -# scen_combi_sorted = scen_combi.reset_index(drop=True) # Reset index starting from 0 - - # Create new Dataframe for scenario prob with corresponding key - prob = pd.DataFrame({'Nr': key, 'scen_prob':scenario_prob}) - - # Join both Dataframes based on common key - join_scen_prob = scen_combi_sorted.join(prob.set_index('Nr'), on='Nr') - - # Determine Exceedance Probability - sorted_N_D = scen_combi.sort_values(by=['N/D']) # Sort N/D based on ascending order - complete_table = sorted_N_D.join(prob.set_index('Nr'), on='Nr') - - N_D_prob_ordered = complete_table.iloc[:,2] - -# N_D = join_scen_prob.dropna(axis=0).iloc[:,1].reset_index(drop=True) # N/D -# N_D_prob = join_scen_prob.dropna(axis=0).iloc[:,2].reset_index(drop=True) # Corresponding scenario prob -# print('N_D', N_D) -# print('N_D_PROB', N_D_prob) -# order = N_D.argsort() # Sort N/D based on ascending order - -# N_D_prob_ordered = N_D_prob[order] - N_D_prob_cs = np.cumsum(N_D_prob_ordered[::-1]) # Take cumulative sum of reversed order - - exceed_prob = (1/4) * N_D_prob_cs[::-1] # Reverse result (1-FN(n)) and /4 as 4 evacuation scenarios are considered - complete_table = complete_table.join(exceed_prob, lsuffix='_orignal', rsuffix='_new') # complete resulting table -# N_D_ordered = N_D[order].reset_index(drop=True) - N_D_ordered = complete_table.iloc[:,1] - - return N_D_ordered, exceed_prob, complete_table - -def sensitivity_analysis(cases, scenario_prob, idx_segment, N_D_ordered_original, exceed_prob_original, complete_table): - """Docstring incomplete.""" - case_1 = cases[0] - case_2 = cases[1] - case_3 = cases[2] - case_4 = cases[3] - - # Dropping segment(s) - case_1_exc = case_1.drop(idx_segment, axis=0).reset_index(drop=True) - case_2_exc = case_2.drop(idx_segment, axis=0).reset_index(drop=True) - case_3_exc = case_3.drop(idx_segment, axis=0).reset_index(drop=True) - case_4_exc = case_4.drop(idx_segment, axis=0).reset_index(drop=True) - - scenario_prob_exc = scenario_prob.drop(idx_segment, axis=0).reset_index(drop=True) - - # Determine new exceedance probability - Excluding segment(s) - N_D_ordered_new, exceed_prob_new, complete_table_new = exceedance_prob([case_1_exc, case_2_exc, case_3_exc, case_4_exc], scenario_prob_exc) - - # Plotting - plot_curves(N_D_ordered_original, exceed_prob_original) - plt.plot(N_D_ordered_new.dropna(axis=0), exceed_prob_new.dropna(axis=0), marker="o", linewidth=2, markersize=5, color= 'darkblue', label='Excluding segment(s)', zorder=10) - - # Plot dropped points - x_point = [] - y_point = [] - for i in range(len(idx_segment)): - row_i = complete_table[complete_table['Nr']== (idx_segment[i] + 1)] - for j in range(len(row_i)): - x_point.append(row_i.iloc[j, 1]) - y_point.append(row_i.iloc[j, 3]) - plt.scatter(x_point, y_point, label='Dropped Points', s=45, color='darkred', zorder=15) # Plot the points corresponding to deleted segment - plt.legend() - plt.show() - return N_D_ordered_new, exceed_prob_new, complete_table_new - -def plot_curves(N_D, exceedance_prob): - """Plot FN or FD risk curve.""" - plt.figure(figsize=(10,6)) - set_TUDstyle() - - # Plot FN/FD curve - plt.plot(N_D, exceedance_prob, marker="o", linewidth=2, markersize=5, label='FN/D-curve',zorder=0) - - # Add acceptable limit line - ND = np.linspace(1,100000,100000) # fatalities - alpha = 1 - C = 0.010 - limit_line = (C/ND**alpha) - plt.plot(limit_line, linewidth=2, color='darkgreen', label='Acceptable Limit Line', zorder=5) - - # Styling - plt.yscale('log') - plt.xscale('log') - plt.grid(True, which="both", axis='x') - plt.grid(True, which="major", axis='y') - plt.title('FN/D-curve') - plt.ylabel('Probability of Exceedance, $1-F_N(n)$') - plt.xlabel('Economic damage [meuro] / Fatalities') - plt.xlim(1,100000) - plt.ylim(10**(-7),10**(-3)) - plt.legend() - -def compute_benefit(table_old, table_new): - """Compute new and old consequences and net benefit.""" - old_consequences = np.sum(table_old["N/D"].values * table_old["scen_prob_new"].values) - new_consequences = np.sum(table_new["N/D"].values * table_new["scen_prob_new"].values) - benefit = old_consequences - new_consequences - return old_consequences, new_consequences, benefit - -def set_TUDstyle(): - TUcolor = {"cyan": "#00A6D6", "darkgreen": "#009B77", "purple": "#6F1D77", - "darkred": "#A50034", "darkblue": "#0C2340", - "orange": "#EC6842", "green": "#6CC24A", - "lightcyan": "#00B8C8", "red": "#E03C31", "pink": "#EF60A3", - "yellow": "#FFB81C", "blue": "#0076C2"} - plt.rcParams.update({'axes.prop_cycle': plt.cycler(color=TUcolor.values()), - 'font.size': 16, "lines.linewidth": 4}) - return TUcolor \ No newline at end of file diff --git a/book/notebooks/overview.md b/book/notebooks/overview.md deleted file mode 100644 index 41cd6e9..0000000 --- a/book/notebooks/overview.md +++ /dev/null @@ -1,3 +0,0 @@ -# Notebooks - -This chapter contains notebooks that can be used to put your risk and reliability knowledge to the test in real life situations. They have been rendered as individual pages to show you their contents, and each page will have a download link near the top to allow you to download all files needed for the exercise directly in a zip file. diff --git a/book/notebooks/traffic/Exercise_Traffic_Render.ipynb b/book/notebooks/traffic/Exercise_Traffic_Render.ipynb deleted file mode 100644 index a15a33b..0000000 --- a/book/notebooks/traffic/Exercise_Traffic_Render.ipynb +++ /dev/null @@ -1,2250 +0,0 @@ -{ - "cells": [ - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Traffic and Transport Reliability" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "````{note}\n", - "This page is generated from an `*.ipynb` file which requires several auxiliary files, all of which can be downloaded using the link below.\n", - "```{eval-rst}\n", - ":download:`Download zip file for this exercise.`\n", - "```\n", - "````" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "\n", - "Have you ever sat in a car during rush hour and been annoyed at the amount of traffic? Have you ever marvelled at the recklessness of fast drivers, watched rubber-neckers gawking at an accident or thought there must be a better way to design this highway? Today you will get a chance to give it a try on your own!\n", - "\n", - "One of the reasons traffic networks are difficult to design is that they must operate well under a wide range of difficult to predict conditions: think of severe weather events, a large number of vehicles on the road during a few key points per day and the unpredictable behavior of human drivers. This all suggests that a stochastic, or probabilistic approach can be well suited to traffic and transport evaluations.\n", - "\n", - "For this assignment you will consider a highway route between Dordrecht and The Hague (we will call this route the ‘trajectory’). You have data measuring travel time along this trajectory during two months, all measured between the hours of 5.00-11.00 (the morning commute), which we will use to estimate the probability that the travel time exceeds some critical threshold, and the threshold itself is determined based on travel time as a risk metric.\n", - "\n", - "## Estimating Traffic Patterns in Practice\n", - "\n", - "Before we begin, note that this exercise is a dramatic simplification of reality, as it uses simplified methods and a single dataset to evaluate one highway trajectory. In practice, this is done by setting up a complex network-based model and using stochastic processes and probability distributions to simulation things like vehicle flow rates, accidents, road closures, etc. Travel times are then described using probability distributions that are based on a large number of simulations.\n", - "\n", - "In other words: assume a distribution of flow rate or vehicles on the road, use stochastic processes to consider the range of highway conditions and the occurrence of accidents, then let the computer do the hard work. In the end you get a histogram of travel times for your trajectory of interest. You can then look at the database of simulations to try and make inference on what leads to undesirable conditions. For example, take the group of simulations with the longest travel times for a given trajectory and see if it is caused by insufficient flow capacity or emergency vehicle response rate (i.e., ability to clear accidents quickly).\n", - "\n", - "In this exercise we will not simulate an entire traffic network, but instead use two simplified methods for estimating travel time, each of which will give different insight into possible design decisions.\n", - "\n", - "## How does this link to MUDE Weeks 2.7-2.8 Risk and Reliability?\n", - "\n", - "This is in fact a relatively simple probabilistic design problem. Just as the simple example for computing dike height to withstand a river discharge with failure probability of 1% (a one random variable case), in this example we need to design the highway such that travel time on the highway only exceeds the threshold amount 5% of the time. In this case the only random variable is vehicle flow rate. As you continue reading, you will probably think the computational models and method for taking into account interventions is a bit complicated, but remember: you only need to design for one random variable!" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from ipywidgets import interact\n", - "import ipywidgets as widgets\n", - "import warnings\n", - "warnings.filterwarnings('ignore')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Traffic Variables\n", - "\n", - "We are interested in estimating tavel time, $t$ [minutes], measured along a single highway. Key variables that play a role in determining $t$ for the Dordrecht-Den Haag trajectory are:\n", - "\n", - "- Vehicle flow rate, $q$ [vehicles/hr]: typically measured per link, but for our purposes it will represent the entire highway trajectory. For the morning commute, the flow rate is typically 5500 veh/hr.\n", - "- Capacity, $C$ [veh/hr]: the maximum flow rate of a link. For our trajectory, the capacity is 5600 veh/hr.\n", - "- Delay, $t_{delay}$ [min]: additional time required to travel a trajectory for a single vehicle. Caused by an accident that lasts $t_{accident}$ minutes.\n", - "\n", - "A few other variables will be described below after we introduce two methods to calculate travel time, but first we will introduce you to the Python code that will be used to make it easy for you to solve this problem!" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## `Trajectory` class\n", - "\n", - "As the objective of this exercise is to focus on the probabilistic design process (*not* to see how fast you can use Python), many key steps have been automated for you using a class, `Trajectory`, which is defined in `exercise_setup.py`. An instance of the class is initialized with default values already defined, and many of the methods can be used without the need to specify inputs (see examples below). Observations in the attached `csv` file are also initialized as a dataframe attribute of the class, so you don't even need to import the data. For most methods, making a user-specified input argument will allow you to quickly see how a design decision may modify the characteristics of our highway trajectory. \n", - "\n", - "An instance is created in the following cell, and the class is used repeatedly throughout this notebook to provide usage examples. We have tried to provide informative docstrings to help figure out what each method does, so you should not have to look in the `exercise_setup.py` file unless you are curious how the class is defined." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "from exercise_setup import Trajectory\n", - "t=Trajectory()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The class is initialized with a number of default values (explained later), which you can check using the following method:" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Print current values used in Method 1 and 2.\n", - "Current parameter values are:\n", - " alpha = 0.15\n", - " beta = 4\n", - " t_0 = 28.5\n", - " C = 5600\n", - " rCf = 0.2\n", - " q = 5500\n" - ] - } - ], - "source": [ - "print(t.print_parameters.__doc__)\n", - "t.print_parameters()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "It's easy to create a second instance of the class, which can be useful if you want to see what the affect of varying parameter values. For example, here we change $q$ from the default value of 5500 to 5000:" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Current parameter values are:\n", - " alpha = 0.15\n", - " beta = 4\n", - " t_0 = 28.5\n", - " C = 5600\n", - " rCf = 0.2\n", - " q = 5000\n" - ] - } - ], - "source": [ - "t2=Trajectory()\n", - "t2.q = 5000\n", - "t2.print_parameters()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Part 1. Two Methods for Estimating Travel-Time\n", - "\n", - "We will introduce two methods for computing the travel time, one that focuses on *flow rate* and *capacity*, the other on *accident duration.*\n", - "\n", - "### Method 1: Bureau of Public Roads (BPR) Curve\n", - "\n", - "Method 1 computes travel time as a function of vehicle flow rate, $q$:\n", - "\n", - "$$t\\left(q\\right)=t^0\\left(1+\\alpha\\left(\\frac{q}{C}\\right)^\\beta\\right)$$\n", - "\n", - "where $t^0$ is the free flow travel time, which is the time it would take to travel the link if there were no other vehicles on the road ($q=0$).\n", - "\n", - "$\\alpha=0.15$ and $\\beta=4.0$ are constants, especially for our simple case.\n", - "\n", - "Later in the exercise we will make changes to the highway (interventions) that will influence the parameters $q$ and $C$ and $t^0$. For example, adding a lane to the highway will increase $C$.\n", - "\n", - "Method 1 has been implemented in the `Trajectory` class as `travel_time_method_1()`." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Compute travel time with Method 1.\n", - " \n", - " Keyword arguments: q, alpha, beta, t_0, C.\n", - " Returns: travel time as float or array, depending on input.\n", - " \n" - ] - } - ], - "source": [ - "print(t.travel_time_method_1.__doc__)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can use it to calculate the travel time for given variables." - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Travel time computed with Method 1 = 32.5 minutes.\n" - ] - } - ], - "source": [ - "print(f'Travel time computed with Method 1 = '\n", - " f'{t.travel_time_method_1():.1f} minutes.')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "You can use *keyword arguments* to change the default values for capacity, free-flow travel time and flow rate to see how the estimated travel-time changes!" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Travel time computed with Method 1 = 31.5 minutes.\n" - ] - } - ], - "source": [ - "print(f'Travel time computed with Method 1 = '\n", - " f'{t.travel_time_method_1(C=6000):.1f} minutes.')" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Travel time computed with Method 1 = 28.9 minutes.\n" - ] - } - ], - "source": [ - "print(f'Travel time computed with Method 1 = '\n", - " f'{t.travel_time_method_1(q=3000):.1f} minutes.')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Using sliders we can look at the effect of capacity and t_0 on the BPR curve." - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "```{note}\n", - "The widgets displayed on this page will not work in the website version, only when you use the `*.ipynb` file with a Python kernel (e.g., in Jupyter Notebook or Jupyter Lab).\n", - "```" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "c0bdaad2190343f5b8c103bbd6bd9257", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "interactive(children=(FloatSlider(value=28.5, description='t_0', max=32.0, min=26.0, step=0.5), FloatSlider(va…" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from custom_widgets import method_1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Method 2: Delays Caused by Accidents\n", - "\n", - "This method takes into account accidents that may have occurred along our trajectory computing the delay experienced by a single vehicle, $t_\\mathrm{delay}$. The delay is related to the length of the accident itself, as well as the traffic flow and trajectory capacity:\n", - "\n", - "$$t_\\mathrm{delay}=t_{\\mathrm{accident}} \\cdot \\frac{(q - rC)}{2q}$$\n", - "\n", - "Where $rC$ is the remaining capacity of the link [veh/hr], approximated as a percentage of the link capacity:\n", - "\n", - "$$rC = rC_f \\cdot C$$\n", - "\n", - "In our case we assume $rC_f$=0.2.\n", - "\n", - "Total travel time along the trajectory can be estimated by adding $t_{delay}$ to the travel time without accidents. This is similar to the free flow travel time, $t^0$, except we must take into account the fact that accidents don't have a significant effect on travel time until traffic flow is already reaching the trajectory capacity. Thus, we introduce a cutoff time, $t_{cutoff}$, above which accidents affect $t$:\n", - "\n", - "$$t=t_{\\mathrm{cutoff}}+t_\\mathrm{delay}$$\n", - "\n", - "The value of $t_{cutoff}$ is estimated using Method 1 for a condition close to the capacity of the highway---100 veh/hr less---which returns 32.5 min, computed here:." - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Travel time for q = 5500.0 and C = 5600.0 using Method 1: 32.50 min\n" - ] - } - ], - "source": [ - "print(f'Travel time for q = {t.q} and C = {t.C} using Method 1: '\n", - " f'{t.travel_time_method_1(q=t.q, C=t.C):.2f} min')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Method 2 has been implemented in the `Trajectory` class as `travel_time_method_2()`, which computes travel time for a single vehicle and a single accident. The class also assumes $t_{accident}=10$ min as a default value, which is close to the median accident length during the morning commute. " - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Compute travel time with Method 2 (delays).\n", - " \n", - " Keyword arguments: t_accident, q, C, rCf, t_cutoff.\n", - " Returns: travel time as float or array, depending on input.\n", - " \n" - ] - } - ], - "source": [ - "print(t.travel_time_method_2.__doc__)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can use it to calculate the travel time for given variables, which is set up to assume that a single 10 min accident has occured for a vehicle traveling the trajectory." - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "A single accident duration of 10 min is assumed by default. Include argument t_accident=? to override.\n", - "Travel time computed with Method 2 = 36.5 minutes.\n" - ] - } - ], - "source": [ - "print(f'Travel time computed with Method 2 = '\n", - " f'{t.travel_time_method_2():.1f} minutes.')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Investigating the effect of accident duration is easy because you can change the default argument values just like for Method 1 (see documentation for complete list of input arguments):" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Travel time computed with Method 2 = 44.4 minutes when accident time is 30 min.\n" - ] - } - ], - "source": [ - "try_t_accident = 30\n", - "print(f'Travel time computed with Method 2 = '\n", - " f'{t.travel_time_method_2(t_accident=try_t_accident):.1f} '\n", - " f'minutes when accident time is {try_t_accident} min.')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "There is also a method to compute delay:" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "A single accident duration of 10 min is assumed by default. Include argument t_accident=? to override.\n", - "The delay for one vehicle is 3.98 min.\n", - "The delay for one vehicle due to a 30 min accident is 11.95 min.\n" - ] - } - ], - "source": [ - "print(f'The delay for one vehicle is '\n", - " f'{t.estimate_t_delay():.2f} min.')\n", - "print(f'The delay for one vehicle due to a {try_t_accident} min '\n", - " f'accident is {t.estimate_t_delay(t_accident=try_t_accident):.2f} min.')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Interesting, the previous calculation shows that if the accident time increases by 20 min, the delay is only increased by 8 min." - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "```{note}\n", - "The widgets displayed on this page will not work in the website version, only when you use the `*.ipynb` file with a Python kernel (e.g., in Jupyter Notebook or Jupyter Lab).\n", - "```" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "d00800ac309946df9291756aa1ffcbc4", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "interactive(children=(FloatSlider(value=10.0, description='t_accident', max=60.0, min=5.0, step=5.0), FloatSli…" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from custom_widgets import method_2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Part 2. Importing the Data" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here we do 'the usual': import data using pandas, clean it up and explore it with a few summary statistics and visualizations. Luckily we've already done this for you in the `process_observations` method in the `Trajectory` class, and class is initialized with the datafram as an attribute." - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Create dataframe with observations.\n", - " \n", - " Steps:\n", - " - Import file defined by string attribute observations_filename.\n", - " - Extract all columns with observations.\n", - " - Set up and return new dataframe:\n", - " - travel_time_df\n", - " - Set up and return new arrays:\n", - " - travel_time\n", - " - flow_rate\n", - " - t_accident\n", - " - dataframe and arrays are added as attributes in init\n", - " \n" - ] - } - ], - "source": [ - "print(t.process_observations.__doc__)" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [ - { - "data": { - "text/html": [ - "
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" - ], - "text/plain": [ - " Travel Time\n", - "count 22021.000000\n", - "mean 34.344555\n", - "std 9.524935\n", - "min 28.524847\n", - "25% 30.146187\n", - "50% 31.284827\n", - "75% 34.625918\n", - "max 129.301866" - ] - }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "t.travel_time_df.describe()" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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VY2Oj5+vuu+/Wt771LTU2NiopKSmgdQEAwMDh9yWhoqIizZw5U+np6crIyNDq1avV1NSk3NxcSRfuLTly5IhefPFFzzEX7005c+aMjh07psbGRlmtVo0dO1aRkZFKTU31+hnXXnutJPmMAwCAwcnvwJKTk6MTJ06orKxMzc3NSk1NVXV1tZKTkyVdeKO4L78ny/jx4z3f19fXa9OmTUpOTtbBgwd7Vz0AABgUArrpNi8vT3l5eV0+t379ep8xw/DvPUy6WgMAAAxefJYQAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwPQILAAAwvYACy8qVK5WSkqLIyEilpaVpx44d3c5tbm7W9OnTdfPNN2vIkCEqKCjwmbNmzRplZWVp6NChGjp0qO666y7t2rUrkNIAAMAA5HdgqaqqUkFBgUpLS9XQ0KCsrCxNmTJFTU1NXc53Op0aPny4SktLNW7cuC7nbNu2Tffff7/eeust1dXVaeTIkbLb7Tpy5Ii/5QEAgAHI78CyfPlyzZkzR3PnztWYMWNUUVGhpKQkVVZWdjl/1KhReuaZZzRr1ixdc801Xc7ZuHGj8vLy9PWvf12jR4/WmjVr1NnZqTfeeMPf8gAAwAAU4c9kl8ul+vp6FRcXe43b7Xbt3LkzaEW1t7fL7Xbruuuu63aO0+mU0+n0PG5ra5Mkud1uud3uoNVitVoVFWmTLdzo1TpRkTZZrdag1haIiz+/v+sYyOhxaNDnvkePQ2Ow97mn+/YrsBw/flwdHR2Ki4vzGo+Li1NLS4s/S11ScXGxRowYobvuuqvbOeXl5Vq0aJHPeG1traKjo4NWS35+/t+/6+jdQrcvlCRVV1f3bp0gcTgc/V3CgEePQ4M+9z16HBqDtc/t7e09mudXYLkoLCzM67FhGD5jgVqyZIleeuklbdu2TZGRkd3OKykpUVFRkedxW1ubkpKSZLfbFRMTE5RaJCk7O1sNTad0fU5Zr9ZprXpC40deq5qamiBVFhi32y2Hw6HJkyfLYrH0ay0DFT0ODfrc9+hxaAz2Pl+8QnI5fgWW2NhYhYeH+5xNaW1t9TnrEohly5bp6aef1tatW3Xbbbddcq7NZpPNZvMZt1gsQf2Fu1wunT3nlLOjd4Hs7DmnXC6Xaf4Yg90n+KLHoUGf+x49Do3B2uee7tmvm26tVqvS0tJ8Tls5HA5lZmb6s5SPpUuX6qmnntLrr7+u9PT0Xq0FAAAGFr8vCRUVFWnmzJlKT09XRkaGVq9eraamJuXm5kq6cKnmyJEjevHFFz3HNDY2SpLOnDmjY8eOqbGxUVarVWPHjpV04TLQggULtGnTJo0aNcpzBufqq6/W1Vdf3ds9AgCAK5zfgSUnJ0cnTpxQWVmZmpublZqaqurqaiUnJ0u68EZxX35PlvHjx3u+r6+v16ZNm5ScnKyDBw9KuvBGdC6XS/fee6/XcQsXLtSTTz7pb4kAAGCACeim27y8POXl5XX53Pr1633GDOPSLwm+GFwAAAC6wmcJAQAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0yOwAAAA0wsosKxcuVIpKSmKjIxUWlqaduzY0e3c5uZmTZ8+XTfffLOGDBmigoKCLue9/PLLGjt2rGw2m8aOHastW7YEUhoAABiA/A4sVVVVKigoUGlpqRoaGpSVlaUpU6aoqampy/lOp1PDhw9XaWmpxo0b1+Wcuro65eTkaObMmXrvvfc0c+ZM3Xffffrv//5vf8sDAAADkN+BZfny5ZozZ47mzp2rMWPGqKKiQklJSaqsrOxy/qhRo/TMM89o1qxZuuaaa7qcU1FRocmTJ6ukpESjR49WSUmJ7rzzTlVUVPhbHgAAGIAi/JnscrlUX1+v4uJir3G73a6dO3cGXERdXZ0KCwu9xrKzsy8ZWJxOp5xOp+dxW1ubJMntdsvtdgdcy5dZrVZFRdpkCzd6tU5UpE1WqzWotQXi4s/v7zoGMnocGvS579Hj0Bjsfe7pvv0KLMePH1dHR4fi4uK8xuPi4tTS0uLPUl5aWlr8XrO8vFyLFi3yGa+trVV0dHTAtXxZfn7+37/r6N1Cty+UJFVXV/dunSBxOBz9XcKAR49Dgz73PXocGoO1z+3t7T2a51dguSgsLMzrsWEYPmN9vWZJSYmKioo8j9va2pSUlCS73a6YmJhe1fJF2dnZamg6petzynq1TmvVExo/8lrV1NQEqbLAuN1uORwOTZ48WRaLpV9rGajocWjQ575Hj0NjsPf54hWSy/ErsMTGxio8PNznzEdra6vPGRJ/xMfH+72mzWaTzWbzGbdYLEH9hbtcLp0955Szo3eB7Ow5p1wul2n+GIPdJ/iix6FBn/sePQ6Nwdrnnu7Zr5turVar0tLSfE5bORwOZWZm+rOUl4yMDJ81a2tre7UmAAAYOPy+JFRUVKSZM2cqPT1dGRkZWr16tZqampSbmyvpwqWaI0eO6MUXX/Qc09jYKEk6c+aMjh07psbGRlmtVo0dO1bShftE7rjjDv3iF7/Q9773Pb366qvaunWr3n777SBsEQAAXOn8Diw5OTk6ceKEysrK1NzcrNTUVFVXVys5OVnShTeK+/J7sowfP97zfX19vTZt2qTk5GQdPHhQkpSZmanNmzfr8ccf14IFC3TTTTepqqpK3/jGN3qxNQAAMFAEdNNtXl6e8vLyunxu/fr1PmOGcfmXBN9777269957AykHAAAMcHyWEAAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAMD0CCwAAML2AAsvKlSuVkpKiyMhIpaWlaceOHZecv337dqWlpSkyMlI33nijVq1a5TOnoqJCN998s6KiopSUlKTCwkKdO3cukPIAAMAA43dgqaqqUkFBgUpLS9XQ0KCsrCxNmTJFTU1NXc4/cOCApk6dqqysLDU0NOixxx7Tww8/rJdfftkzZ+PGjSouLtbChQu1b98+rV27VlVVVSopKQl8ZwAAYMCI8PeA5cuXa86cOZo7d66kC2dGampqVFlZqfLycp/5q1at0siRI1VRUSFJGjNmjN59910tW7ZM99xzjySprq5OEyZM0PTp0yVJo0aN0v33369du3YFui8AADCA+BVYXC6X6uvrVVxc7DVut9u1c+fOLo+pq6uT3W73GsvOztbatWvldrtlsVg0ceJEbdiwQbt27dLtt9+uTz75RNXV1Zo9e3a3tTidTjmdTs/jtrY2SZLb7Zbb7fZnW5dktVoVFWmTLdzo1TpRkTZZrdag1haIiz+/v+sYyOhxaNDnvkePQ2Ow97mn+/YrsBw/flwdHR2Ki4vzGo+Li1NLS0uXx7S0tHQ5//z58zp+/LgSEhL0wx/+UMeOHdPEiRNlGIbOnz+vhx56yCcYfVF5ebkWLVrkM15bW6vo6Gh/tnVJ+fn5f/+uo3cL3b5QklRdXd27dYLE4XD0dwkDHj0ODfrc9+hxaAzWPre3t/dont+XhCQpLCzM67FhGD5jl5v/xfFt27Zp8eLFWrlypb7xjW/o448/Vn5+vhISErRgwYIu1ywpKVFRUZHncVtbm5KSkmS32xUTExPItrqUnZ2thqZTuj6nrFfrtFY9ofEjr1VNTU2QKguM2+2Ww+HQ5MmTZbFY+rWWgYoehwZ97nv0ODQGe58vXiG5HL8CS2xsrMLDw33OprS2tvqcRbkoPj6+y/kREREaNmyYJGnBggWaOXOm576YW2+9VZ9//rn+5V/+RaWlpRoyxPfeYJvNJpvN5jNusViC+gt3uVw6e84pZ0f3gawnzp5zyuVymeaPMdh9gi96HBr0ue/R49AYrH3u6Z79epWQ1WpVWlqaz2krh8OhzMzMLo/JyMjwmV9bW6v09HRPke3t7T6hJDw8XIZheM7GAACAwcvvlzUXFRXp+eef17p167Rv3z4VFhaqqalJubm5ki5cqpk1a5Znfm5urg4dOqSioiLt27dP69at09q1a/XII4945kybNk2VlZXavHmzDhw4IIfDoQULFujuu+9WeHh4ELYJAACuZH7fw5KTk6MTJ06orKxMzc3NSk1NVXV1tZKTkyVJzc3NXu/JkpKSourqahUWFuq5555TYmKiVqxY4XlJsyQ9/vjjCgsL0+OPP64jR45o+PDhmjZtmhYvXhyELQIAgCtdQDfd5uXlKS8vr8vn1q9f7zM2adIk7d69u/siIiK0cOFCLVy4MJByAADAAMdnCQEAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMLKLCsXLlSKSkpioyMVFpamnbs2HHJ+du3b1daWpoiIyN14403atWqVT5zTp06pXnz5ikhIUGRkZEaM2aMqqurAykPAAAMMH4HlqqqKhUUFKi0tFQNDQ3KysrSlClT1NTU1OX8AwcOaOrUqcrKylJDQ4Mee+wxPfzww3r55Zc9c1wulyZPnqyDBw/qt7/9rT788EOtWbNGI0aMCHxnAABgwIjw94Dly5drzpw5mjt3riSpoqJCNTU1qqysVHl5uc/8VatWaeTIkaqoqJAkjRkzRu+++66WLVume+65R5K0bt06nTx5Ujt37pTFYpEkJScnB7onAAAwwPgVWFwul+rr61VcXOw1brfbtXPnzi6Pqaurk91u9xrLzs7W2rVr5Xa7ZbFY9NprrykjI0Pz5s3Tq6++quHDh2v69OmaP3++wsPDu1zX6XTK6XR6Hre1tUmS3G633G63P9u6JKvVqqhIm2zhRq/WiYq0yWq1BrW2QFz8+f1dx0BGj0ODPvc9ehwag73PPd23X4Hl+PHj6ujoUFxcnNd4XFycWlpaujympaWly/nnz5/X8ePHlZCQoE8++URvvvmmHnjgAVVXV+ujjz7SvHnzdP78eT3xxBNdrlteXq5Fixb5jNfW1io6OtqfbV1Sfn7+37/r6N1Cty+UJNPcl+NwOPq7hAGPHocGfe579Dg0Bmuf29vbezTP70tCkhQWFub12DAMn7HLzf/ieGdnp66//nqtXr1a4eHhSktL09GjR7V06dJuA0tJSYmKioo8j9va2pSUlCS73a6YmJhAttWl7OxsNTSd0vU5Zb1ap7XqCY0fea1qamqCVFlg3G63HA6HJk+e7Ln8huCix6FBn/sePQ6Nwd7ni1dILsevwBIbG6vw8HCfsymtra0+Z1Euio+P73J+RESEhg0bJklKSEiQxWLxuvwzZswYtbS0yOVyyWq1+qxrs9lks9l8xi0WS1B/4S6XS2fPOeXs6D6Q9cTZc065XC7T/DEGu0/wRY9Dgz73PXocGoO1zz3ds1+vErJarUpLS/M5beVwOJSZmdnlMRkZGT7za2trlZ6e7ilywoQJ+vjjj9XZ2emZs3//fiUkJHQZVgAAwODi98uai4qK9Pzzz2vdunXat2+fCgsL1dTUpNzcXEkXLtXMmjXLMz83N1eHDh1SUVGR9u3bp3Xr1mnt2rV65JFHPHMeeughnThxQvn5+dq/f7/++Mc/6umnn9a8efOCsEUAAHCl8/selpycHJ04cUJlZWVqbm5WamqqqqurPS9Dbm5u9npPlpSUFFVXV6uwsFDPPfecEhMTtWLFCs9LmiUpKSlJtbW1Kiws1G233aYRI0YoPz9f8+fPD8IWAQDAlS6gm27z8vKUl5fX5XPr16/3GZs0aZJ27959yTUzMjL05z//OZByAADAAMdnCQEAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANMjsAAAANOL6O8CBgv3qWbt2XNYEydO7PVat956qyorK4NQFQAAVwYCS4gY7nM6I+ndg5/2ah3XsQPBKQgAgCtIQIFl5cqVWrp0qZqbm3XLLbeooqJCWVlZ3c7fvn27ioqK9P777ysxMVGPPvqocnNzu5y7efNm3X///fre976n3/3ud4GUZ1rW4SmKn7GkV2u0bHg0SNUAAHDl8PselqqqKhUUFKi0tFQNDQ3KysrSlClT1NTU1OX8AwcOaOrUqcrKylJDQ4Mee+wxPfzww3r55Zd95h46dEiPPPLIJcMPAAAYfPw+w7J8+XLNmTNHc+fOlSRVVFSopqZGlZWVKi8v95m/atUqjRw5UhUVFZKkMWPG6N1339WyZct0zz33eOZ1dHTogQce0KJFi7Rjxw6dOnXqknU4nU45nU7P47a2NkmS2+2W2+32d1vdslqtioq0yRZu9GqdqKgoWYOxTqRNVqs14D1ePC6YPYI3ehwa9Lnv0ePQGOx97um+wwzD6PF/QV0ul6Kjo/Wf//mf+v73v+8Zz8/PV2Njo7Zv3+5zzB133KHx48frmWee8Yxt2bJF9913n9rb22WxWCRJCxcu1J49e7Rlyxb96Ec/0qlTpy55SejJJ5/UokWLfMY3bdqk6Ojonm4JAAD0o/b2dk2fPl2fffaZYmJiup3n1xmW48ePq6OjQ3FxcV7jcXFxamlp6fKYlpaWLuefP39ex48fV0JCgt555x2tXbtWjY2NPa6lpKRERUVFnsdtbW1KSkqS3W6/5Ib9lZ2drYamU7o+p6xX6/ztudmyxib3ep3Wqic0fuS1qqmpCeh4t9sth8OhyZMne8IigosehwZ97nv0ODQGe58vXiG5nIBuug0LC/N6bBiGz9jl5l8cP336tGbMmKE1a9YoNja2xzXYbDbZbDafcYvFEtRfuMvl0tlzTjk7ut9fT5w9e1YdwVjnnFMul6vXewx2n+CLHocGfe579Dg0Bmufe7pnvwJLbGyswsPDfc6mtLa2+pxFuSg+Pr7L+RERERo2bJjef/99HTx4UNOmTfM839nZeaG4iAh9+OGHuummm/wpEwAADDB+vUrIarUqLS1NDofDa9zhcCgzM7PLYzIyMnzm19bWKj09XRaLRaNHj9bevXvV2Njo+br77rv1rW99S42NjUpKSvJzSwAAYKDx+5JQUVGRZs6cqfT0dGVkZGj16tVqamryvK9KSUmJjhw5ohdffFGSlJubq2effVZFRUX6yU9+orq6Oq1du1YvvfSSJCkyMlKpqaleP+Paa6+VJJ9xAAAwOPkdWHJycnTixAmVlZWpublZqampqq6uVnJysiSpubnZ6z1ZUlJSVF1drcLCQj333HNKTEzUihUrvF7SDAAAcCkB3XSbl5envLy8Lp9bv369z9ikSZO0e/fuHq/f1RoAAGDw4tOaAQCA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6RFYAACA6QUUWFauXKmUlBRFRkYqLS1NO3bsuOT87du3Ky0tTZGRkbrxxhu1atUqr+fXrFmjrKwsDR06VEOHDtVdd92lXbt2BVIaAAAYgPwOLFVVVSooKFBpaakaGhqUlZWlKVOmqKmpqcv5Bw4c0NSpU5WVlaWGhgY99thjevjhh/Xyyy975mzbtk3333+/3nrrLdXV1WnkyJGy2+06cuRI4DsDAAADRoS/Byxfvlxz5szR3LlzJUkVFRWqqalRZWWlysvLfeavWrVKI0eOVEVFhSRpzJgxevfdd7Vs2TLdc889kqSNGzd6HbNmzRr99re/1RtvvKFZs2b5W+KA5j7VrD17DmvixIkBHW+1WpWfn6/s7GzdfPPNqqysDHKFAAAEn1+BxeVyqb6+XsXFxV7jdrtdO3fu7PKYuro62e12r7Hs7GytXbtWbrdbFovF55j29na53W5dd9113dbidDrldDo9j9va2iRJbrdbbre7x3u6HKvVqqhIm2zhRq/WiYqKkjUI60RGhKlDFr3f0h7Y8bbzkqQ9H3woSUHtFS642FN627foc9+jx6Ex2Pvc0337FViOHz+ujo4OxcXFeY3HxcWppaWly2NaWlq6nH/+/HkdP35cCQkJPscUFxdrxIgRuuuuu7qtpby8XIsWLfIZr62tVXR0dE+20yP5+fl//66jdwvdvi7I6/TO2l+vlCRVV1cHZT34cjgc/V3CoECf+x49Do3B2uf29p79D7jfl4QkKSwszOuxYRg+Y5eb39W4JC1ZskQvvfSStm3bpsjIyG7XLCkpUVFRkedxW1ubkpKSZLfbFRMT06N99ER2drYamk7p+pyyXq3zt+dmyxqb3O/r2IYYeiq9U7mPlWtMXLRqamp6VQ98ud1uORwOTZ48ucsziAgO+tz36HFoDPY+X7xCcjl+BZbY2FiFh4f7nE1pbW31OYtyUXx8fJfzIyIiNGzYMK/xZcuW6emnn9bWrVt12223XbIWm80mm83mM26xWIL6C3e5XDp7zilnR/eBrCfOnj2rDhOtc87pkssVMSj/4QiVYP8tomv0ue/R49AYrH3u6Z79epWQ1WpVWlqaz2krh8OhzMzMLo/JyMjwmV9bW6v09HSvIpcuXaqnnnpKr7/+utLT0/0pCwAADHB+v6y5qKhIzz//vNatW6d9+/apsLBQTU1Nys3NlXThUs0XX9mTm5urQ4cOqaioSPv27dO6deu0du1aPfLII545S5Ys0eOPP65169Zp1KhRamlpUUtLi86cOROELQIAgCud3/ew5OTk6MSJEyorK1Nzc7NSU1NVXV2t5ORkSVJzc7PXe7KkpKSourpahYWFeu6555SYmKgVK1Z4XtIsXXgjOpfLpXvvvdfrZy1cuFBPPvlkgFsDAAADRUA33ebl5SkvL6/L59avX+8zNmnSJO3evbvb9Q4ePBhIGQAAYJDgs4QAAIDpEVgAAIDpEVgAAIDpEVgAAIDpEVgAAIDpEVgAAIDpEVgAAIDpEVgAAIDpEVgAAIDpEVgAAIDpEVgAAIDpEVgAAIDpEVgAAIDpEVgAAIDpEVgAAIDpEVgAAIDpEVgAAIDpEVgAAIDpEVgAAIDpEVgAAIDpRfR3Aegf7s9atKf1jCZOnNjrtW699VZVVlYGoSoAALpGYBmkDLdTZ5zn9e7BT3u1juvYgSBVBABA9wgsg5h1eIriZyzp1RotGx4NUjUAAHSPe1gAAIDpEVgAAIDpEVgAAIDpcQ8LesV9qll79hzm1UYAgD5FYEGvGO5zOiPxaiMAQJ8isKDXeLURAKCvEVhgClxaAgBcCoEFpsClJQDApRBYYBpcWgIAdCegwLJy5UotXbpUzc3NuuWWW1RRUaGsrKxu52/fvl1FRUV6//33lZiYqEcffVS5ublec15++WUtWLBAf/3rX3XTTTdp8eLF+v73vx9IeRjEgnlpSeLyEgCYhd+BpaqqSgUFBVq5cqUmTJigX//615oyZYo++OADjRw50mf+gQMHNHXqVP3kJz/Rhg0b9M477ygvL0/Dhw/XPffcI0mqq6tTTk6OnnrqKX3/+9/Xli1bdN999+ntt9/WN77xjd7vEoNGsC4tSZKz+UPt2bNHe/fu9es4q9Wq/Px8ZWdny+Vy6a9//ask6aabbupVPcFaRwpOEHvooYf87k1f1gNgYPM7sCxfvlxz5szR3LlzJUkVFRWqqalRZWWlysvLfeavWrVKI0eOVEVFhSRpzJgxevfdd7Vs2TJPYKmoqNDkyZNVUlIiSSopKdH27dtVUVGhl156KdC9YZAKxqUlSWr6//45oA+IjIq0SZIamk7p7DmnnP/XqjCLTZ+G9y5EBW2dAIPYl+3Zs0dnnOdlHZ7SL/V8ORhK5gpiZguYwJXOr8DicrlUX1+v4uJir3G73a6dO3d2eUxdXZ3sdrvXWHZ2ttauXSu32y2LxaK6ujoVFhb6zLkYcrridDrldDo9jz/77DNJ0smTJ+V2u/3Z1iUNGTJEQ04369RvHuvVOrbwMIWZYB2b1aL21J/JNkQ6Z4J6zLqOZy2LTVarf7neGjFE7e3tskYMkWGNUFhkZEDrfFnQ1rHZ5Ha7VV9f36t1JCkyMqrf6omKilJ7e7saGxt19uxZSdL//u//6v333+9VPR988IE+//zzXq3xRcHoczD2FQir1ao5c+ZoypQpnlCI4LtS+rxly5Y+Wff06dOSJMMwLj3R8MORI0cMScY777zjNb548WLja1/7WpfHfPWrXzUWL17sNfbOO+8YkoyjR48ahmEYFovF2Lhxo9ecjRs3GlartdtaFi5caEjiiy+++OKLL74GwNfhw4cvmUEC+l+jsLAwr8eGYfiMXW7+l8f9XbOkpERFRUWex52dnTp58qSGDRt2yeMGu7a2NiUlJenw4cOKiYnp73IGJHocGvS579Hj0BjsfTYMQ6dPn1ZiYuIl5/kVWGJjYxUeHq6Wlhav8dbWVsXFxXV5THx8fJfzIyIiNGzYsEvO6W5NSbLZbLLZbF5j1157bU+3MujFxMQMyn8wQokehwZ97nv0ODQGc5+vueaay87x69OarVar0tLS5HA4vMYdDocyMzO7PCYjI8Nnfm1trdLT02WxWC45p7s1AQDA4OL3JaGioiLNnDlT6enpysjI0OrVq9XU1OR5X5WSkhIdOXJEL774oiQpNzdXzz77rIqKivSTn/xEdXV1Wrt2rderf/Lz83XHHXfoF7/4hb73ve/p1Vdf1datW/X2228HaZsAAOBK5ndgycnJ0YkTJ1RWVqbm5malpqaqurpaycnJkqTm5mY1NTV55qekpKi6ulqFhYV67rnnlJiYqBUrVnhe0ixJmZmZ2rx5sx5//HEtWLBAN910k6qqqngPlj5gs9m0cOFCn8tpCB56HBr0ue/R49Cgzz0TZhiXex0RAABA//LrHhYAAID+QGABAACmR2ABAACmR2ABAACmR2ABAACmR2AZ4MrLyxUWFqaCggLPmGEYevLJJ5WYmKioqCh985vf7JcPVrvSHTlyRDNmzNCwYcMUHR2tr3/9614fdEefe+/8+fN6/PHHlZKSoqioKN14440qKytTZ2enZw599s+f/vQnTZs2TYmJiQoLC9Pvfvc7r+d70k+n06l/+7d/U2xsrK666irdfffd+tvf/hbCXZjfpfrsdrs1f/583XrrrbrqqquUmJioWbNm6ejRo15r0GdvBJYB7C9/+YtWr16t2267zWt8yZIlWr58uZ599ln95S9/UXx8vCZPnuz5xExc3qeffqoJEybIYrHov/7rv/TBBx/ol7/8pdfHQ9Dn3vvFL36hVatW6dlnn9W+ffu0ZMkSLV26VL/61a88c+izfz7//HONGzdOzz77bJfP96SfBQUF2rJlizZv3qy3335bZ86c0Xe/+111dHSEahumd6k+t7e3a/fu3VqwYIF2796tV155Rfv379fdd9/tNY8+f8klPxoRV6zTp08bX/3qVw2Hw2FMmjTJyM/PNwzDMDo7O434+Hjj5z//uWfuuXPnjGuuucZYtWpVP1V75Zk/f74xceLEbp+nz8Hxne98x/jxj3/sNfaDH/zAmDFjhmEY9Lm3JBlbtmzxPO5JP0+dOmVYLBZj8+bNnjlHjhwxhgwZYrz++ushq/1K8uU+d2XXrl2GJOPQoUOGYdDnrnCGZYCaN2+evvOd7+iuu+7yGj9w4IBaWlpkt9s9YzabTZMmTdLOnTtDXeYV67XXXlN6err++Z//Wddff73Gjx+vNWvWeJ6nz8ExceJEvfHGG9q/f78k6b333tPbb7+tqVOnSqLPwdaTftbX18vtdnvNSUxMVGpqKj3vhc8++0xhYWGes7T02Zffb80P89u8ebPq6+v17rvv+jx38VOxv/xJ2HFxcTp06FBI6hsIPvnkE1VWVqqoqEiPPfaYdu3apYcfflg2m02zZs2iz0Eyf/58ffbZZxo9erTCw8PV0dGhxYsX6/7775fE33Ow9aSfLS0tslqtGjp0qM+ci8fDP+fOnVNxcbGmT5/u+bRm+uyLwDLAHD58WPn5+aqtrVVkZGS388LCwrweG4bhM4budXZ2Kj09XU8//bQkafz48Xr//fdVWVmpWbNmeebR596pqqrShg0btGnTJt1yyy1qbGxUQUGBEhMTNXv2bM88+hxcgfSTngfG7Xbrhz/8oTo7O7Vy5crLzh/MfeaS0ABTX1+v1tZWpaWlKSIiQhEREdq+fbtWrFihiIgIz/85fTmht7a2+vxfFbqXkJCgsWPHeo2NGTPG88Gf8fHxkuhzb/2///f/VFxcrB/+8Ie69dZbNXPmTBUWFqq8vFwSfQ62nvQzPj5eLpdLn376abdz0DNut1v33XefDhw4IIfD4Tm7ItHnrhBYBpg777xTe/fuVWNjo+crPT1dDzzwgBobG3XjjTcqPj5eDofDc4zL5dL27duVmZnZj5VfWSZMmKAPP/zQa2z//v2eTy1PSUmhz0HQ3t6uIUO8/zUVHh7ueVkzfQ6unvQzLS1NFovFa05zc7P+53/+h5774WJY+eijj7R161YNGzbM63n63IX+vOMXofHFVwkZhmH8/Oc/N6655hrjlVdeMfbu3Wvcf//9RkJCgtHW1tZ/RV5hdu3aZURERBiLFy82PvroI2Pjxo1GdHS0sWHDBs8c+tx7s2fPNkaMGGH84Q9/MA4cOGC88sorRmxsrPHoo4965tBn/5w+fdpoaGgwGhoaDEnG8uXLjYaGBs+rU3rSz9zcXOOGG24wtm7dauzevdv49re/bYwbN844f/58f23LdC7VZ7fbbdx9993GDTfcYDQ2NhrNzc2eL6fT6VmDPnsjsAwCXw4snZ2dxsKFC434+HjDZrMZd9xxh7F3797+K/AK9fvf/95ITU01bDabMXr0aGP16tVez9Pn3mtrazPy8/ONkSNHGpGRkcaNN95olJaWev1LnT7756233jIk+XzNnj3bMIye9fPs2bPGT3/6U+O6664zoqKijO9+97tGU1NTP+zGvC7V5wMHDnT5nCTjrbfe8qxBn72FGYZhhPqsDgAAgD+4hwUAAJgegQUAAJgegQUAAJgegQUAAJgegQUAAJgegQUAAJgegQUAAJgegQUAAJgegQUAAJgegQUAAJgegQUAAJje/w8yzHCVWBJLIgAAAABJRU5ErkJggg==", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "hist = t.travel_time_df.hist(density=True,\n", - " bins = 25,\n", - " edgecolor='k',\n", - " linewidth=1.1)\n" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "bin_count, bin_position = np.histogram(t.travel_time_df, bins=25)\n", - "travel_time_freq = bin_count / sum(bin_count)\n", - "travel_time_cdf = np.cumsum(travel_time_freq)\n", - "plt.plot(bin_position[1:], travel_time_freq, color=\"red\",\n", - " linewidth=3, label=\"Relative frequency\")\n", - "plt.plot(bin_position[1:], travel_time_cdf,\n", - " label=\"Cumulative empirical distribution\", linewidth=3)\n", - "plt.xlabel('Travel Times [min]')\n", - "plt.ylabel('Relative Frequency and Empirical CDF [$-$]')\n", - "plt.legend();" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "Text(0, 0.5, 'Empirical Exceedance CDF')" - ] - }, - "execution_count": 21, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(bin_position[1:], 1-travel_time_cdf, label=\"CDF\", linewidth=3)\n", - "plt.yscale('log')\n", - "plt.ylim([1e-4, 1]);\n", - "plt.xlabel('Travel Times [min]')\n", - "plt.ylabel('Empirical Exceedance CDF')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Part 3. Fitting a Burr-Distribution to the Data" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "It turns out the Burr distribution often is a good fit for traffic flow rate data, and we can obtain the parameters using MLE incorporated in the `scipy.stats` method [`Burr12`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.burr12.html)." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The standardized form of the Burr12 distribution (with location, `loc` = 0 and `scale` = 1) is:\n", - "\n", - "$$\n", - "f(x, c, d)=c d \\frac{x^{c-1}}{\\left(1+x^{c}\\right)^{d+1}}\n", - "$$\n", - "\n", - "The distribution has to be shifted and scaled to fit our data, which is done with the location and scale parameters that are returnd by the method in `scipy`. If the Burr distribution as shown in the introductory video is a two-parameter formulation, and if it is used with the location and scale parameters as follows, it is equivalent to the `scipy` formulation (four parameters):\n", - "\n", - "$$\n", - "f_{scipy}(x, c, d, \\mathrm{loc}, \\mathrm{scale}) = f_{video}(\\frac{x-\\mathrm{loc}}{\\mathrm{scale}}, c, d) \\cdot \\mathrm{scale}\n", - "$$\n", - "\n", - "The CDF of the Burr distribution is very easy to evaluate:\n", - "$$\n", - "F(x,c, d, \\mathrm{loc}, \\mathrm{scale})=1−(1+x^c)^{-k}\n", - "$$\n", - "\n", - "*NB:*\n", - "- *In the video the parameters loc and scale are a and b, respectively. c and k are used equivalently.*\n", - "- *You are asked to make a calculation with the CDF below, one of the few things you are required to code on your own in this notebook.*\n", - "- *There are actually twelve Burr distributions (yes, 12!). They were 'invented' in the 1940's to avoid tedious hand calculations easier. The scipy distribution is equation 12 from [Burr's 1942 paper \"Cumulative Frequency Functions,\"](https://doi.org/10.1093%2Fbiomet%2F64.1.129) hence the name*\n", - "\n", - "In `Trajectory`, the distribution is fit during initialization of the class with `fit_burr`, and the parameter values can be printed using `print_parameters_burr`. The example below illustrates the use of `scipy.stats.Burr12` without requiring to dig into the py file." - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Parameters are:\n", - " c = 84.137\n", - " k = 6.421e-02\n", - " loc = 12.00\n", - " scale = 17.49\n" - ] - } - ], - "source": [ - "t.print_parameters_burr()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we will plot the distribution with the histogram to check the fit visually. The PDF is calculated two ways: one using the 4-parameter version provided by `scipy.stats`, the other using the shifted and scaled 2 parameter version. It is clear that the restuls are identical." - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# Plot the distribution and the histogram\n", - "from scipy import stats\n", - "from scipy.stats import burr12\n", - "c, k, loc, scale = t.burr_parameters\n", - "x = np.linspace(20,130, 100)\n", - "plt.plot(x, burr12.pdf(x, c, k, loc, scale),\n", - " 'b-', lw=3, label='PDF using 4 parameters')\n", - "plt.plot(x, burr12.pdf((x-loc)/scale, c, k, 0, 1)/scale,\n", - " 'r:', lw=3, label='PDF using 2 parameters')\n", - "plt.hist(t.travel_time_df,density=True, bins=25,\n", - " edgecolor='k', linewidth=1.1)\n", - "plt.legend(loc='best', frameon=False)\n", - "plt.xlabel('Travel time, $t$ [min]')\n", - "plt.ylabel('Probability density and histogram [$-$]')\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "#Burr fit on the data with 4 parameters (red) and with 2 parameters (blue)\n", - "fig, ax = plt.subplots(1, 1)\n", - "ax.plot(x, 1 - burr12.cdf(x, c, k, loc, scale),\n", - " 'b-', lw=3, label='Burr-fit 4 params')\n", - "ax.plot(x, 1 - burr12.cdf((x-loc)/scale, c, k, 0, 1),\n", - " 'r:', lw=3, label='Burr-fit 2 params')\n", - "ax.plot(bin_position[1:], 1 - travel_time_cdf,\n", - " 'k--', lw=3, label=\"CDF of data\")\n", - "ax.legend(loc='best', frameon=False)\n", - "plt.yscale('log')\n", - "plt.xlim([25, 60])\n", - "plt.ylim([1e-4, 1])\n", - "plt.xlabel('Travel time, $t$ [min]')\n", - "plt.ylabel('Exceedance probability, $1-F_t(t)\\:$ [$-$]')\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "What do you think of the fit?" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Part 4. Evaluating the Trajectory" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The requirement for the trajectory is that the 95 percentile value is no more than 10 minutes longer than the free-flow travel time:\n", - "\n", - "$$\n", - "t_{95} \\leq t_0 + 10\\: \\mathrm{min}\n", - "$$\n", - "\n", - "**Using the information provided above, compute the 95th percentile of the Burr distribution in the cell below.**" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": {}, - "outputs": [], - "source": [ - "burr_95th_percentile = None" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "**Use this cell to check whether the trajectory meets the requirement, after you compute the 95th percentile above.**" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Replace the variable in the cell above with your calculation!\n" - ] - } - ], - "source": [ - "if burr_95th_percentile is None:\n", - " print('Replace the variable in the cell above with your calculation!')\n", - "elif burr_95th_percentile > t.t_0 + 10:\n", - " print('The requirement is not met, interventions are needed.')\n", - "elif burr_95th_percentile < 0:\n", - " print('The trajectory meets the requirement.')\n", - "elif burr_95th_percentile < t.t_0 + 10:\n", - " print('The trajectory meets the requirement.')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Part 5. Effect of Interventions on Travel Time\n", - "\n", - "Now it's time for the fun part: let's look at a variety of interventions and see if we can improve the travel time on this highway trajectory! The following sections describe the interventions and illustrate the Python tools that are available for you to re-design the highway.\n", - "\n", - "## Description of Intervention Effects\n", - "\n", - "The following interventions can be considered for our trajectory:\n", - "\n", - "1. **Extra Lane:** widens existing road by one or two lanes \n", - "2. **Hard Shoulder:** adds a hard shoulder to the existing trajectory, providing extra capacity, especially during peak flow moments \n", - "3. **Max Speed:** sets the maximum allowed speed on trajectory (current value, 130 km/h; maximum value: 170km/h)\n", - "4. **Alternate Trajectory:** constructs one or two alternative trajectory options (e.g. a second highway or large road), decreasing peak flow rate on the original trajectory \n", - "5. **Incident Management:** speeds up towing and accident clean-up services by X% which reduces time duration of an accident \n", - "6. **Accident Risk Reduction:** employs cooperative intelligent transport systems, C-ITS (vehicle to vehicle communication), to reduce the number of incidents by X%. For our case it can also include a number of measures such as smart signs, lights and lane control. \n", - "7. **Modal Shift, Trucks:** decreases the number of trucks during the morning commute by X% by promoting alternative modes and commute times for truck transport \n", - "8. **Modal Shift, Cars:** equivalent to the above intervention, but for cars \n", - "\n", - "## Implementation of Intervention Effects\n", - "\n", - "The following table indicates which Method can take into account each intervention and how, as well as key information for using the Python tools:\n", - "\n", - "| No. | Intervention | Variable | Method 1 | Method 2 | Keyword Argument | Values |\n", - "| :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n", - "| 1 | Extra Lane | $C$ | X | X | `extra_lane` | `None`, 1, 2 |\n", - "| 2 | Hard Shoulder | $C$ | | X | `hard_shoulder` | `True`/`False` |,\n", - "| 3 | Max. Speed | $t_0$ | X | X | `max_speed` | >0, 170 max |\n", - "| 4 | Alternate trajectory | $q$ | X | X | `alt_route` | `None`, 1, 2 |\n", - "| 5 | Incident Management | $t_{accident}$ | | X | `incident_management` | 1%$-$100% |\n", - "| 6 | Accident Risk Reduction | $t_{accident}$ | | X | `accident_risk_reduction` |1%$-$100% |\n", - "| 7 | Modal Shift, Trucks | $q$ | X | X | `modal_shift_trucks` | 0%$-$20% |\n", - "| 8 | Modal Shift, Cars | $q$ | X | X | `modal_shift_cars` | 0%$-$20% |\n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Method 1: BPR" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The expected travel time changes when the free-flow travel time ($t_0$), flow ($q$) and capacity $C$ are modified. The interventions listed above have been implemented as keyword arguments in the method `intervention_method_1`, illustrated with an example below the docstring:" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Compute travel time with Method 1.\n", - " \n", - " Keyword arguments: q, alpha, beta, t_0, C.\n", - " Returns: travel time as float or array, depending on input.\n", - " \n" - ] - } - ], - "source": [ - "print(t.travel_time_method_1.__doc__)" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The baseline travel time is 32.50 min\n", - "The travel time with an intervention is 28.17 min\n", - " (the difference is -4.33 min)\n" - ] - } - ], - "source": [ - "travel_time_baseline = t.travel_time_method_1()\n", - "travel_time_with_intervention = t.intervention_method_1(max_speed=150)\n", - "print(f'The baseline travel time is '\n", - " f'{travel_time_baseline:0.2f} min')\n", - "print(f'The travel time with an intervention is '\n", - " f'{travel_time_with_intervention:0.2f} min'\n", - " f'\\n (the difference is '\n", - " f'{travel_time_with_intervention - travel_time_baseline:.2f} min)')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The Burr distribution can also be estimated for the same intervention using `plot_distribution_method_1`, which relies on `intervention_method_1`. Here it is set up with widgets to let you play with the effect of each intervention:" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "```{note}\n", - "The widgets displayed on this page will not work in the website version, only when you use the `*.ipynb` file with a Python kernel (e.g., in Jupyter Notebook or Jupyter Lab).\n", - "```" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": {}, - "outputs": [ - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "7974564f725f4bb1ba9a4b1d8a221aca", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "interactive(children=(Dropdown(description='1: Extra Lanes', options=(('None', None), ('1', 1), ('2', 2)), val…" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from custom_widgets import method_1_interv_dist" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This function will compute the 95th percentile for the baseline parameter values:" - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "42.5\n" - ] - } - ], - "source": [ - "print(f'{t.burr_ppf_with_int_1(0.95):.3}')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The same function allows you to check out how the 95th percentile changes by applying interventions.\n", - "\n", - "*What interventions could you apply in order to meet the requirement for the trajectory?*\n" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "33.4\n" - ] - } - ], - "source": [ - "print(f'{t.burr_ppf_with_int_1(0.95,alt_route=1):.3}')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Method 2: Delays\n", - "\n", - "Interventions for Method two have been implemented as keyword arguments in the method `intervention_method_2`, and can be used the same as with those for Methods 1, although there are 8 possible interventions instead of 5:" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Compute travel time with Method 2 (delays).\n", - " \n", - " Keyword arguments: t_accident, q, C, rCf, t_cutoff.\n", - " Returns: travel time as float or array, depending on input.\n", - " \n" - ] - } - ], - "source": [ - "print(t.travel_time_method_2.__doc__)" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "```{note}\n", - "The widgets displayed on this page will not work in the website version, only when you use the `*.ipynb` file with a Python kernel (e.g., in Jupyter Notebook or Jupyter Lab).\n", - "```" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": {}, - "outputs": [ - { - "data": { - "application/vnd.jupyter.widget-view+json": { - "model_id": "892aced71d0140a48243e07efbf54f4f", - "version_major": 2, - "version_minor": 0 - }, - "text/plain": [ - "interactive(children=(Dropdown(description='1: Extra Lanes', options=(('None', None), ('1', 1), ('2', 2)), val…" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "from custom_widgets import method_2_interv_dist" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Part 6. Cost-Benefit Analysis\n", - "\n", - "Now it's time for the fun part: coming up with an optimal design! It's easy to use the intervention functions introduced above to find a combination that gives a 95th percentile value that meets the requirement. However, in real life interventions cost money, and we will take that into account here using the costs specified in the table, which have also been implemented for you in the methods below, `benefit_cost_method_x`. These functions work with keyword arguments, just like the intervention functions above. With that, the assignment is simply:\n", - "\n", - "**Maximize the ratio of benefits to cost such that: 1) the maximum cost of 250 FCoins is not exceeded, and 2) the 95th percentile is less than $t_0+10$.** Your 'answer' should be in the form of a specific set of interventions (using keyword argument values), costs, benefit-cost ratio, and a short justification for how you came to the result.\n", - "\n", - "Although the assignment is simple, there are a few things to note, in particular: Method 1 and 2 are different, and *both* are simplified versions of reality. They will give you different results because they are different methods, not only because Method 2 includes more interventions. In addition, the costs are defined in terms of FCoins, which are not 'real' monetary units, and have not been scaled to reality; as such, the benefit-cost ratio will does not need to be greatere than 1 to be a viable project.\n", - "\n", - "| Intervention | Keyword Argument | Costs (FCoins) |\n", - "| :--- | :---: | :---: |\n", - "| New Alternative Route | `alt_trajectory` | --- |\n", - "| 1 lane | --- | 150 |\n", - "| 2 lanes | --- | 180 |\n", - "| New Lane | `extra_lane` | --- |\n", - "| 1 additional lane | --- | 70 |\n", - "| 2 additional lanes | --- | 100 |\n", - "| Create Hard Shoulder | `hard_shoulder` | 60 |\n", - "| Increase Max Speed | `max_speed` | 7/percent |\n", - "| Accident Risk Reduction | `accident_risk_reduction` | 5/percent |\n", - "| Incident Management | `incident_management` | 2/percent |\n", - "| Modal Shift Trucks | `modal_shift_trucks` | 5/percent |\n", - "| Modal Shift Cars | `modal_shift_cars` | 8/percent |\n", - "\n", - "NB: *the \"/percent\" cost is determined per percent change in the intervention basedo on the pre-intervention value. For example, changing the maximum speed from 130 to 140 km/hr is a +8% change, thus it would cost 56 FCoins*" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": {}, - "outputs": [], - "source": [ - "from benefit_cost import benefit_cost_method_1\n", - "from benefit_cost import benefit_cost_method_2" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "These functions compute the benefit to cost ratio, which you need to maximize without exceeding the total cost." - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The benefit-cost ratio using Method 1 is: 0.095\n", - "Total cost for all interventions applied: 100.000 FCoins\n" - ] - } - ], - "source": [ - "BC1 = benefit_cost_method_1(modal_shift_trucks=20)" - ] - }, - { - "cell_type": "code", - "execution_count": 36, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The benefit-cost ratio using Method 2 is: -0.058\n", - "Total cost for all interventions applied: 100.000 FCoins\n" - ] - } - ], - "source": [ - "BC2 = benefit_cost_method_2(modal_shift_trucks=20)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Good luck!" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "base", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.13 (main, Aug 25 2022, 23:51:50) [MSC v.1916 64 bit (AMD64)]" - }, - "latex_envs": { - "LaTeX_envs_menu_present": true, - "autoclose": false, - "autocomplete": true, - "bibliofile": "biblio.bib", - "cite_by": "apalike", - "current_citInitial": 1, - "eqLabelWithNumbers": true, - "eqNumInitial": 1, - "hotkeys": { - "equation": "Ctrl-E", - "itemize": "Ctrl-I" - }, - "labels_anchors": false, - "latex_user_defs": false, - "report_style_numbering": false, - "user_envs_cfg": false - }, - "vscode": { - "interpreter": { - "hash": "85471ad55176ca86192ed6be6d105faaef73891404cad6bd910e89e8513744d9" - } - }, - "widgets": { - "application/vnd.jupyter.widget-state+json": { - "state": { - "0187e7214d8a445dbb5c831f13f34dd3": { - "model_module": "@jupyter-widgets/base", - "model_module_version": "1.2.0", - "model_name": "LayoutModel", - "state": {} - }, - "08f445fa1f7a42dab8956fa6ca209e16": { - "model_module": "@jupyter-widgets/base", - "model_module_version": "1.2.0", - "model_name": "LayoutModel", - "state": {} - }, - "0953d24691094e3d9b652d497901a09a": { - "model_module": "@jupyter-widgets/controls", - "model_module_version": "1.5.0", - "model_name": "SliderStyleModel", - "state": { - "description_width": "initial" - } - }, - "0bb275f5ec1542b5ae0ef636577f1b72": { - "model_module": "@jupyter-widgets/controls", - "model_module_version": "1.5.0", - "model_name": "DescriptionStyleModel", - "state": { - "description_width": "" - } - }, - "100c0581cfc747c8af541fc9d5145845": { - "model_module": "@jupyter-widgets/controls", - "model_module_version": "1.5.0", - "model_name": "DropdownModel", - "state": { - "_options_labels": [ - "No alternate routes", - "1 alternate route", - "2 alternate routes" - ], - "description": "4: Alt. 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\n", 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\n", 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-Here is a code block that is parsed from a python file: - -```{eval-rst} -.. literalinclude:: ../code/sinewave.py - :language: python -``` - -Which is the result of: - - ```{eval-rst} - .. literalinclude:: sinewave.py - :language: python - ``` - -We can toggle the code block by nesting it inside a `toggle` directive: - - ```{toggle} - ```{eval-rst} - .. literalinclude:: sinewave.py - :language: python - ``` - -Note the single `-triplet at the end of the toggle. - -````{toggle} -```{eval-rst} -.. literalinclude:: ../code/sinewave.py - :language: python -``` -```` - -The Python file saves the figure, so we can include it using the regular markdown recipe: - - -```{figure} ../figures/sinewave.svg ---- -name: sine_wave ---- -A sine wave -``` - -```{figure} ../figures/cosinewave.svg ---- -name: cosine_wave ---- -A cosine wave -``` \ No newline at end of file diff --git a/book/prob-design/01-one-random-variable.md b/book/prob-design/01-one-random-variable.md deleted file mode 100644 index 2555a3d..0000000 --- a/book/prob-design/01-one-random-variable.md +++ /dev/null @@ -1,78 +0,0 @@ -(prob_design_1_rv)= -# One Random Variable - -Consider a river that is protected by dikes, earthen embankments with the purpose of keeping water in the river channel and preventing flooding of the hinterland. The dikes should be designed and build such that the height allows the river to safely pass the maximum discharge every year, measured in m$^3$/s. A rating curve ({numref}`rating_curve`) gives us the relationship between discharge and water depth, $h_w$, so if we know what the maximum discharge is, we can build our dikes to the critical height, $h_{dike}\geq h_w$. But there is a problem---what is the maximum discharge in the river each year? How would we even go about determining this value? One way is to make observations and find the highest recorded data point. For example, in 1995 the Rhine River reached a discharge of around 12,000 m$^3$/s, the highest recorded level to date. But even with over 100 years of measurements, the record is not complete: there could always be a bigger discharge. Another approach could be to come up with a number that is, beyond a reasonable doubt, impossible to exceed. Many experts believe that 16,000 m$^3$/s is getting close to an upper limit, and 20,000 m$^3$/s may be physically impossible. Which of these two values should we choose for the design of our dike, and why?[^expensive-option] - -```{figure} ../figures/rating_curve.svg ---- -height: 400px -name: rating_curve ---- -Rating curve for hypothetical river. Relationship is $q=C \cdot h_w^\beta$ where $\beta$=2.0 and $C$=4.0. -``` - -This is a difficult question because the actual discharge observed in a given year is random. In addition to other variables, it is largely dependent on rainfall in the drainage basin, which is impossible to predict far in advance---certainly not for the entire year. Furthermore, we don't have a way to accurately extrapolate our past observations to identify a logical maximum discharge. For this reason, we will use a continuous probability distribution to quantify the probability associated with a specific maximum discharge, $q$, that might be observed in a given year, defined by the PDF $f_{Q}(q)$ and CDF $F_{Q}(q)$. The only other piece of information needed is a design standard---a probability that defines the discharge to use for our design. Other chapters in this book cover the derivation of a design standard, so for this discussion we will assume that a flooding probability of 1/100 has already been determined as the acceptable level. Because there is only one random variable, we can use the PDF to determine the design discharge ({numref}`design_1_rv`). - -```{figure} ../figures/design_1_rv.svg ---- -height: 400px -name: design_1_rv ---- -PDF and design value for river discharge with 0.01 probability of exceedance: $q_{design}=155 \: \text{m}^3\text{/s}$. -``` - -In particular, we note that failure occurs for high discharge, so we must use the complementary CDF to find the design value, in this case probability of exceeding $q_{\mathrm{design}}$: - -$$ -1-F_{Q}(q_{\mathrm{design}})=0.01 -$$ - -$$ -q_{\mathrm{design}}=F_{Q}^{-1}(1-0.01)=155\:\text{m}^3\text{/s} -$$ - -after which the water depth and minimum dike height can easily be determined from the rating curve: - -$$ -h_{dike}=h_{w,design}=\left(\frac{q_{design}}{C}\right)^{1/\beta}=6.23 \text{m} -$$ - -Recalling the *safety margin* limit state from the previous section, $M=R-S$, we can see that randomness plays a role through the load variable, $S$, such that - -$$ -M=R-S=h_{dike}-h_{w,design} -$$ - -If the condition $M<0$ defines flooding (i.e., failure) and if $q$ is the only random variable, we have successfully ensured a situation where the flooding probability is 0.01. - -**Reflection on the Simple Example** - -Is this an oversimplification of reality? Perhaps, but it gets pretty close. Many flood protection systems in the world use an exceedance proabability approach to probabilistic design: choosing a specific and making sure the component or system can handle the load. This works well when the primary source of uncertainty is the load: the river discharge in this case. - -We also took for granted that a simple relationship between river discharge and water depth is available. However, this is never the case, as such a relationship depends on the cross-sectional shape and roughness of the floodplain, which not only varies along the river trajectory, but also changes due to natural phenomenon and human interventions. This introduces additional uncertainty into our assessment of whether the dikes are high enough. - -Fortunately there is also extra conservatism built into this approach. For example, duration of high water plays a role: if discharge exceeds the capacity of the dike system, but only lasts for a short time (minutes or a couple hours), perhaps the dikes can withstand the overflow without eroding and causing flooding. This can be conceptualized by considering the joint probability of a high discharge *and* degradation of the dike leading to flooding: - -$$ -P(\text{flooding},h_w>h_{dike})=P(\text{flooding}|h_w>h_{dike})\cdot P(h_w>h_{dike}) -$$ - -where the conditional term represents the probability that the dike erodes (fails) given that the water depth exceeds the height. Assuming failure when the critical water depth is exceeded is conservative because it implies $P(\text{flooding}|h_w>h_{dike})=1.0$, whereas in reality this is not the case, and the 'true' flooding probability is less than that computed in the equation above. - -Later chapters of this book will introduce methods for taking these realities into account in the design and decision-making process. For now, we will see how our probabilistic design changes when more than one random variable must be considered. - - - - -[^expensive-option]: Although the 20,000 m$^3$/s value is tempting because it is the most safe option, it is probably prohibitively expensive to build! \ No newline at end of file diff --git a/book/prob-design/02-two-random-variables.md b/book/prob-design/02-two-random-variables.md deleted file mode 100644 index 2843d63..0000000 --- a/book/prob-design/02-two-random-variables.md +++ /dev/null @@ -1,191 +0,0 @@ -(prob_design_2_rv)= -# Two Random Variables - -The previous section illustrated how a decision for dike height, $h_{dike}$, can take into account uncertainty in river discharge. We used a maximum allowable probability of flooding to derive the specific value of discharge, $q_{design}$, that should be used to choose $h_{dike}$. This was necessary because there was otherwise no way of establishing what the maximum discharge should be. The only variable considered to be random was the maximum river discharge that occurs each year. This section considers how the design process becomes more complicated when *two* random variables are considered (two load variables). - -````{admonition} Distribution for $q_1$ and $q_2$ -:class: dropdown -On this page all calculations assume the same lognormal distribution for random variables $q_1$ and $q_1$, where the first and second moments of the distribution are: - -$$ -\begin{align*} -E[X] &= \exp\left(\mu + \frac{\sigma^2}{2}\right) = 100\\ -VAR[X] &= \left( \exp(\sigma^2)-1 \right)\exp(2\mu + \sigma^2)= 400 -\end{align*} -$$ - - -For the `lognorm` method in `scipy.stats` we need to provide the parameters shape `s` = $\sigma$, `loc` = 0 and `scale` = $\exp(\mu)$ (see explanation [here](https://mude.citg.tudelft.nl/book/probability/Loc-scale.html)), in this case: -```python -import scipy.stats as stats -s = 0.198 -loc = 0.000 -scale = 98.058 -q_1 = stats.lognorm(s=s, loc=loc, scale=scale) -q_2 = stats.lognorm(s=s, loc=loc, scale=scale) -``` -```` - -## Discharge from Two Rivers - -In this scenario our objective for choosing $h_{dike}$ is still the same, except now we recognize that our location on the river is downstream of a confluence of two smaller rivers. The discharge at the location of our dike is thus the sum of the dicharge from Rivers 1 and 2: - -$$ -q=q_1+q_2 -$$ - -where the same rating curve applies, giving $h_w$ as a function of $q$. As before, acknowledging that the maximum discharge per year in each river is a random variable, we can approach the design problem in the same way: choose $h_{dike}$ such that it retains water when $q$ takes a value with probability of exceedance 0.01. For now, we can assume the distribution for River 1 and River 2 are the same as in the previous Section, and that they are independent. - -*Compared to the previous example, now there are two distributions---how do we find the design discharge and dike height?* - -Before presenting the correct approach, three common mistakes are illustrated. - -### Incorrect Approach 1 - -Find the discharge in each river, $q_1$ and $q_2$, such that the probability of exceeding each discharge is 0.01. As in the previous section, - -$$ -q_{1,\mathrm{design}}=q_{2,\mathrm{design}}=F_{Q}^{-1}(1-0.01)=155\:\text{m}^3\text{/s} \;\rightarrow\; q_{design}=310\:\text{m}^3\text{/s} -$$ - -*Why is this approach incorrect?* - -It considers the simultaneous occurrence of *both* rivers exceeding a design discharge with probability 0.01. This is a joint probability of occurrence, $P(Q_1>q_{1,design},Q_2>q_{2,design})$, which can be evaluated with a multivariate probability distribution (or the marginal distributions in the independent case). The scenario is equivalent to observing two sixes after tossing two dice simultaneously: if the dice are fair, the probability is $1/36$. Thus, for this incorrect case the probability $P(Q_1>q_{1,design},Q_2>q_{2,design})$ is not 0.01, it's actualy 0.01$^2$=0.0001, illustrated in the figure below. - -```{figure} ../figures/design_2_rv_error_1.svg ---- -height: 400px -name: design_2_rv_error_1 ---- -'And' probability for Incorrect Approach 1. -``` - -### Incorrect Approach 2 - -Find the discharge in each river, $q_1$ and $q_2$, such that the joint probability of exceeding these values is 0.01. Since the two rivers are independent, we can solve for our design probability, $p_{design}$: - -$$ -\left(p_{design}\right)^2=0.01\: \rightarrow \: p_{design}=\sqrt{0.01}=0.1 -$$ - -$$ -q_{1,\mathrm{design}}=q_{2,\mathrm{design}}=F_{Q}^{-1}(1-0.1)=126\:\text{m}^3\text{/s} \;\rightarrow\; q_{design}=252\:\text{m}^3\text{/s} -$$ - -```{figure} ../figures/design_2_rv_error_2a.svg ---- -height: 400px -name: design_2_rv_error_2a ---- -'And' probability for Incorrect Approach 2. -``` - -*Why is this approach incorrect?* - -It only considers one scenario! - -There are infinite alternative scenarios that also result in a joint probability of exceedance of 0.01, for example, $0.2\cdot 0.05 = 0.01$: - -$$ -q_1=F_Q^{-1}(1-0.20)=116\:\text{m}^3\text{/s}\;\; \text{and}\;\; q_2=F_Q^{-1}(1-0.05)=136\:\text{m}^3\text{/s} -$$ - -which results in a totally different dike height. - -```{figure} ../figures/design_2_rv_error_2b.svg ---- -height: 400px -name: design_2_rv_error_2b ---- -Comparison of two 'and' probabilities for Incorrect Approach 2. -``` - -### Incorrect Approach 3 - -Since the 'and' case didn't work we can use the 'or' probability, or union! In other words: find the discharge in each river, $q_1$ and $q_2$, such that the probability of either of them being exceeded is 0.01. - -The union probability can be found as follows: - -$$ -P(Q_1>q_1 \cup Q_2>q_2)=1-P(Q_1q_1 \cup Q_2>q_2)=1-P(Q_1q_1 \cup Q_2>q_2)=0.01$ implies the exceedance probability for each river discharge is $\sqrt{1-0.01}=\sqrt{0.99}=0.995$, thus: - -$$ -q_{1,\mathrm{design}}=q_{2,\mathrm{design}}=F_{Q}^{-1}(0.995)=163\:\text{m}^3\text{/s} \;\rightarrow\; q_{design}=326\:\text{m}^3\text{/s} -$$ - -```{figure} ../figures/design_2_rv_error_3.svg ---- -height: 400px -name: design_2_rv_error_3 ---- -'Or' probability for Incorrect Approach 3. -``` - -*Why is this approach incorrect?* - -As with the first two incorrect approaches, it also only considers one specific scenario! There are infinite combinations of $Q_1$ and $Q_2$ such that the union is 0.01. - -### Correct Approach - -The discharge in the main river is the sum of the discharge of its tributaries, thus it is a function of random variables which has a distribution $f_Q(q)$. Thus we can use the distribution of $Q$ to find the design value $q_{design}$ directly. Unfortunately, although $q$ is a linear combination of $q_1$ and $q_2$, because they are lognormally distributed we cannot find a simple analytic expression for the distribution of $q$. However, using Monte Carlo sampling from the distributions of $q_1$ and $q_2$ gives: - -$$ -q_{design}=F_Q^{-1}(1-0.01)=275\:\text{m}^3\text{/s} -$$ - -This is equivalent to integrating the joint probability distribution of $q_1$ and $q_2$ over the region $\Omega$ where $q>275\:\text{m}^3\text{/s}$, illustrated in the figure below, along with the contours of joint probability density. - -```{figure} ../figures/design_2_rv_correct.svg ---- -height: 400px -name: design_2_rv_correct ---- -Correct approach: $P(Q>275\:\text{m}^3\text{/s})=0.01$. Also illustrated is the region $\Omega$ where $q>275\:\text{m}^3\text{/s}$ and contours of joint probability density. -``` -### Comparison of Approaches - -All four design values of $Q$ are collected in the table below, along with the required dike height. Clearly the method of incorporating uncertainty makes a difference, as the height varies over 1 m across all options, which is a significant increase in cost for a structure that is many kilometers long. - -```{list-table} Comparison of design values for all four approaches. -:header-rows: 1 -:name: design_2_rv_comparison - -* - Approach - - Design Value, $q_{design}$ [m$^3$/s] - - Design Value, $h_{dike}$ [m] -* - Incorrect 1 - - 310 - - 8.80 -* - Incorrect 2 - - 252 - - 7.94 -* - Incorrect 3 - - 326 - - 9.03 -* - **Correct** - - **275** - - 8.29 -``` - -## Reflections on the Simple Example - -% Dependence considered in componenet reliability part (and system!) -% Design point consideration NOT included here, and probably not in this book!!! - -We need to be explicit in what we are trying to evaluate. In this case, it is the distribution of a function of random variables, $Q$. - -For non-Gaussian distributions and for non-linear functions of random variables it is often not possible to get the distribution of the function of random variables analytically. Fortunately it is easy to find it numerically through sampling techniques. This will be discussed elsewhere. - -The 'and' and 'or' approaches (intersection and union) are simple, but really only limited to discrete cases. As illustrated above, they cannot be used in the case of continuous random variables, or with functions of random variables because one must integrate across all possible scenarios leading to failure. Nonetheless, these approaches are extremely useful for many situations, and are the basis of *system reliability* problems. - -The situation illustrated here is often referred to as a *component reliability* problem, where the 'component' is defined by a function of random variables. - Although nothing more than a function of random variables,is nothing more than an integration over a specific region of a multivariate probability density function. Often this region describes failure of a component, which we will try to keep below an acceptable level. \ No newline at end of file diff --git a/book/prob-design/example-river-system.md b/book/prob-design/example-river-system.md deleted file mode 100644 index 384bb3d..0000000 --- a/book/prob-design/example-river-system.md +++ /dev/null @@ -1,24 +0,0 @@ -# Flood Management Case Study - -```{note} -The flood management example is covered in the plenary lecture on Jan 9, 2023 (see Brightspace), and has not yet been added to this book. -``` - -As mentioned on Introduction page: -> Throughout this book we will repeatedly draw on the field of flood management to illustrate risk and reliability concepts as this field requires expertise from all perspectives in civil and environmental engineering and geosciences, from climate and hydrologic processes to evacuation and recovery. - - - -```{figure} ../figures/simple-city.png ---- -width: 600px -name: simple-city ---- -A simple city that we would like to protect against flooding by the river. -``` \ No newline at end of file diff --git a/book/prob-design/exercise.md b/book/prob-design/exercise.md deleted file mode 100644 index d834ed6..0000000 --- a/book/prob-design/exercise.md +++ /dev/null @@ -1,13 +0,0 @@ -# Exercises - -Elsewhere in this book we have covered methods that will allow you to solve the discharge problem on the previous page, for example, propagation of uncertainty, functions of random variables, etc. Try the following exercises to evaluate the distribution of $q$. In each case, you should be able to define both the distribution of $q$ as well as the value of $q_{design}$: - -1. Define the distribution of $q_1$ and $q_2$ as LogNormal using Scipy, then evaluate the distribution of $q$ using Monte Carlo Simulation -2. Approximate the distributions of $q_1$ and $q_2$ using only their moments and use error propagation to approximate the distribution of $q$ -3. Use the moments to define Normal distributions for $q_1$ and $q_2$, then find the distribution of $q$ (hint: it should also be Normal, and you can solve for it analytically) -4. Use the moments to define Normal distributions for $q_1$ and $q_2$, then use the multivariate normal distribution in Scipy to define a correlation coefficient and explore what the effect of dependence between $q_1$ and $q_2$ has on the result. - -```{note} -Solutions to these exercises are on the next page. -``` - diff --git a/book/prob-design/exercise_solutions.ipynb b/book/prob-design/exercise_solutions.ipynb deleted file mode 100644 index 2b6f30c..0000000 --- a/book/prob-design/exercise_solutions.ipynb +++ /dev/null @@ -1,308 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "12d4c736-839c-41c2-974e-e472550b1ec4", - "metadata": {}, - "source": [ - "# Solutions\n", - "\n", - "All code required to solve the exercises is provided on this page, with the output included by default. To use the code interactively, click {fa}`rocket` --> {guilabel}`Live Code` on the top right corner of this screen and then wait until all cells are executed. You can also download this page as a notebook to work with on your personal computer.\n", - "\n", - "```{note}\n", - "On this page we adopt the notation of lower-case $q$ used in other sections of this chapter, and do not use the upper-case convention to denote a random variable.\n", - "```\n", - "\n", - "First we import a few packages and define the distributions of $q_1$ and $q_2$ as described on the previous pages." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "baaf5a2b-e837-46f1-bf9d-56bf9cec708c", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "import scipy.stats as stats\n", - "\n", - "s = 0.198\n", - "loc = 0.000\n", - "scale = 98.058\n", - "q_1 = stats.lognorm(s=s, loc=loc, scale=scale)\n", - "q_2 = stats.lognorm(s=s, loc=loc, scale=scale)" - ] - }, - { - "cell_type": "markdown", - "id": "a2724e09-9815-4f02-af62-2d595019c1b3", - "metadata": { - "tags": [] - }, - "source": [ - "## Part 1\n", - "\n", - "We can use Monte Carlo simulation to evaluate the problem easily. Remember, there are four essential steps to Monte Carlo Simulation:\n", - "\n", - "1. Define distributions for random variables (probability density over a domain) \n", - "2. Generate random samples \n", - "3. Do something with the samples (deterministic calculation) \n", - "4. Evaluate the results: e.g., “empirical” PDF, CDF of samples, etc.\n", - "\n", - "The solution below also uses the method of moments on the MCS sample to compare the Normal and Lognormal parametric distributions, as well as includes the \"exact\" analytic solution for Parts 2 and 3.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "0b46ebdf-1a24-4de9-a426-286f3f2720a7", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The 99th percentile is index: 9900\n", - "The 99th percentile from the sample is: 275.9 m^3/s.\n", - "The inverse CDF of the Normal dist gives: 266.3 m^3/s.\n", - "The inverse CDF of the LogNormal dist gives: 276.4 m^3/s.\n" - ] - }, - { - "data": { - "image/png": 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "N = 10000\n", - "sample_1 = q_1.rvs(size=N)\n", - "sample_2 = q_2.rvs(size=N)\n", - "q = sample_1 + sample_2\n", - "\n", - "q_as_N = stats.norm(*stats.norm.fit(q))\n", - "q_as_LN = stats.lognorm(*stats.lognorm.fit(q))\n", - "\n", - "plot_values = np.linspace(100,400,50)\n", - "plt.hist(q, bins=plot_values,\n", - " density=True,\n", - " edgecolor='black')\n", - "plt.plot(plot_values, q_as_N.pdf(plot_values),\n", - " linewidth=2.5, label='Fit with N')\n", - "plt.plot(plot_values, q_as_LN.pdf(plot_values),\n", - " linewidth=2.5, label='Fit with LN')\n", - "plt.plot(plot_values,\n", - " stats.norm.pdf(plot_values, loc=200, scale=np.sqrt(800)),\n", - " ':', linewidth=2.5, label='Part 2 and 3')\n", - "plt.xlabel('Discharge, $q$ [m$^3$/s]')\n", - "plt.ylabel('Density [--]')\n", - "plt.legend()\n", - "\n", - "get_index = int(np.floor(0.99*(N + 1)))\n", - "print(f'The 99th percentile is index: {get_index}')\n", - "q_percentile = np.sort(q)[get_index - 1]\n", - "print(f'The 99th percentile from the sample is: {q_percentile:.1f} m^3/s.')\n", - "print(f'The inverse CDF of the Normal dist gives: {q_as_N.ppf(0.99):.1f} m^3/s.')\n", - "print(f'The inverse CDF of the LogNormal dist gives: {q_as_LN.ppf(0.99):.1f} m^3/s.')\n", - "\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "1fae3f87-afc0-4c3d-a6f3-f634a5422304", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "id": "13773486-ddd6-4bc7-a012-b44fc1f67ed8", - "metadata": {}, - "source": [ - "## Part 2 and 3\n", - "\n", - "Error propagation, as introduced in previous chapters, is a method that relies on a linearized approximation of the function of random variables and assumes that the random variables themselves are normally distributed. This results in the relatively simple equations for computing the moments of the function based on the moments of the random variables, applied below. In this case, since we are only using the moments of the lognormal variables in Part 2, the distribution is identical to that described by Part 3, so the solution is the same.\n", - "\n", - "The expectation is simply:\n", - "\n", - "$$\n", - "\\mathbb{E}(q(q_1,q_2))= q(\\mu_{q_1},\\mu_{q_2}) = \\mu_{q_1} + \\mu_{q_2}\n", - "$$\n", - "\n", - "And, given independent random variables, the variance is:\n", - "\n", - "$$\n", - "\\sigma_q^2 = \\sigma_{q_1}^2 + \\sigma_{q_2}^2\n", - "$$\n", - "\n", - "The partial derivatives have been left out, as they are all +1, and the covariance term is zero. Plugging in values from the exercise:\n", - "\n", - "$$\n", - "\\mathbb{E}(q)= 100 + 100 = 200\n", - "$$\n", - "\n", - "And the variance:\n", - "\n", - "$$\n", - "\\sigma_q^2 = 400 + 400 = 800\n", - "$$\n", - "\n", - "Finally, we can compare the distibution to those found above (see figure). The two normal distributions are very similar to each other, which tells us that the asymettry of the lognormal distribution does not have a big influence on the distribution of $q$." - ] - }, - { - "cell_type": "markdown", - "id": "6da9930f-5409-4bee-a8ea-e4c505355425", - "metadata": {}, - "source": [ - "## Part 4\n", - "\n", - "Here we will use the analytically computed value of the distribution of $q$ and compare the design value $q_{design}$ to the value found with a Monte Carlo Simulation using `scipy.stats.multivariate_norm` and a covariance matrix to generate a plot and compute values. The solution is more complicated that you were expected to provide, in order to illustrate various approaches and insights.\n", - "\n", - "First we find the variance of $q$, which adds an additional term now that the random variables are dependent:\n", - "\n", - "$$\n", - "\\sigma_q^2 = \\sigma_{q_1}^2 + \\sigma_{q_2}^2 + 2\\sigma_{q_1}\\sigma_{q_2}\\rho_{q_1,q_2}\n", - "$$\n", - "\n", - "Resulting in:\n", - "\n", - "$$\n", - "\\sigma_q^2 = 400 + 400 + 2 \\cdot 20 \\cdot 20 \\rho_{q_1,q_2} = 800(1+\\rho_{q_1,q_2})\n", - "$$\n", - "\n", - "Design values are computed below, and as the plot illustrates, increasing correlation coefficient results in a higher likelihood of observing high values of $q$, and therefore the design value increases. The opposite is true with no dependence, as well as negative dependence.\n", - "\n", - "The code cell below does the following:\n", - "- define the analytically derived moments of $q$\n", - "- set up the expectation and covariance matrix for $q_1$ and $q_2$\n", - "- sample from the joint distribution of $q_1$ and $q_2$ and compute the corresponding sample of $q$\n", - "- evalue the empirical design value, $q_{design}$\n", - "- print and plot relevant results\n", - "\n", - "_Change the values in the cell below to explore the problem, especially $\\rho$ and $N$, which can have profound influences on the result: $q_{design}$ and the accuracy of the MCS, respectively._" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "5122d9c9-f239-4914-aa54-3e0cfef79f2f", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The correlation coefficient is: 0.50\n", - "The mean value of q is: 200\n", - "The variance of q is: 1200.0\n", - "The design value for q~N(mu,sigma) is: 280.6 m^3/s\n", - "\n", - "For N = 10000 samples, the 99th percentile is index: 9900\n", - "The 99th percentile from the sample is: 279.3 m^3/s\n", - " ^ this is the 1% design value, q_design, from MCS\n", - "\n" - ] - }, - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "rho = +.50\n", - "N = 10000\n", - "\n", - "mu_q = 200\n", - "var_q = 800*(1 + rho)\n", - "\n", - "mu_q1q2 = np.array([100, 100])\n", - "cov_q1q2 = 400*np.array([[1, rho],\n", - " [rho, 1]])\n", - "\n", - "q1q2 = stats.multivariate_normal(mu_q1q2, cov_q1q2)\n", - "sample = q1q2.rvs(size=N)\n", - "\n", - "q_1_dependent = sample[:,0]\n", - "q_2_dependent = sample[:,1]\n", - "q_dependent = q_1_dependent + q_2_dependent\n", - "\n", - "get_index = int(np.floor(0.99*(N + 1)))\n", - "q_percentile = np.sort(q_dependent)[get_index - 1]\n", - "\n", - "fig, ax = plt.subplots()\n", - "ax.scatter(q_1_dependent, q_2_dependent,\n", - " color='black', label='All samples of q')\n", - "ax.scatter(q_1_dependent[q_dependent>q_percentile],\n", - " q_2_dependent[q_dependent>q_percentile],\n", - " color='red', label='Top 1% of q')\n", - "\n", - "print(f'The correlation coefficient is: {rho:.2f}')\n", - "print(f'The mean value of q is: {mu_q}')\n", - "print(f'The variance of q is: {var_q:.1f}')\n", - "print(f'The design value for q~N(mu,sigma) is: ',\n", - " f'{stats.norm.ppf(0.99, loc=mu_q, scale=np.sqrt(var_q)):.1f} m^3/s\\n')\n", - "print(f'For N = {N} samples, the 99th percentile is index: {get_index}')\n", - "print(f'The 99th percentile from the sample is: {q_percentile:.1f} m^3/s')\n", - "print(' ^ this is the 1% design value, q_design, from MCS\\n')\n", - "\n", - "plt.xlabel('Discharge of river 1, $q_1$ [m$^3$/s]')\n", - "plt.ylabel('Discharge of river 2, $q_2$ [m$^3$/s]')\n", - "plt.title('Samples of river discharge')\n", - "ax.axis('equal');\n", - "ax.legend()\n", - "plt.show()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.11.4" - }, - "widgets": { - "application/vnd.jupyter.widget-state+json": { - "state": {}, - "version_major": 2, - "version_minor": 0 - } - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/book/prob-design/overview.md b/book/prob-design/overview.md deleted file mode 100644 index 2f447ef..0000000 --- a/book/prob-design/overview.md +++ /dev/null @@ -1,41 +0,0 @@ -(prob_design)= -# Probabilistic Design - -Stated as simply as possible, the term *probabilistic design* implies the use of probability to design something. Although this may sound complex, it is actually not much different than a deterministic approach, where values used to design something are not assumed to be random. For example, the load on a beam, or the maximum discharge expected in a river. In a typical design process, the problem and functional requirements are first defined, the system or component is evaluated and then refined {cite:p}`voorendt2017`. It is ideally an iterative process, where tradeoffs between competing requirements must be considered in order to arrive at an optimal configuration. During much of your university education you have probably learned a variety of techniques to evaluate interesting problems in your field of study; however, only towards the end of a bachelor or master program do you begin to *design* things and take into count information beyond what is written in a simple exam problem to make decisions. The design process is often challenging because there is no single right answer, and it turns out that incorporating probability in the design process can help. - -Consider some arbitrary object--let's call it a thingamajig--which we must design and eventually build. We would like to apply the *factor of safety* approach, which compares load[^solicitation], $S$, to resistance, $R$, such that $FS=R/S$. As long as we make sure that $S$ is less than $R$, or $FS>1$, our thingamajig will never fail. We could also use the *safety margin* approach, where $M=R-S$, which also quantifies the point between safe and unsafe, although here we make sure $M>0$. These so-called *limit states* make the design process quite simple and is a great engineering approach for many situations, for example, if: -1. the values of $R$ and $S$ are precisely known, or the range of values is negligibly small -2. $R$ and $S$ never change (at least not over short time or length scales) -3. $R$ and $S$ are easy to measure in all locations of interest -4. the model used to design the thingamajig is nearly perfect -5. the consequence of a failure is negligible - -In situations like this you can make your design decision and rest assured that there won't be any lawyers knocking on your door in the near future because the thingamajig broke. - -For many situations, however, a deterministic analysis is not wise because we cannot guarantee that our thingamajig will always survive. When $R$ and/or $S$ can take on a range of possible values, all of a sudden there is a chance that our thingamajig is *not* reliable: there is a distinct probability it may *fail.* Part of this book is concerned with the quantification of what is often called the *failure probability,* $p_f$, for which there are many different techniques. These techniques all rely on probability theory because it allows us to quantitatively account for the following in our engineering process: - -1. imprecise measurements -2. model error -3. randomness in some of our important design variables -4. risk-based design criteria and safety standards - -These are just a few examples, where items 3 and 4 are the focus of the following chapters, and items 1 and 2 have already been considered elsewhere in MUDE. - -%Sometimes we have criteria, sometimes we do not. - -## Chapter Overview - -%Terms and definitions first?? -%Aleatoric and epistemic. -%Sometimes we don't have a structure. Then we can consider just the *hazard*. - -A probabilistic design is illustrated in the following sections, first with the simple cases of one random variable. Then an example with two random variables is used, which can be referred to as a *bivariate* case. This is more insightful than the univariate case because it allows us to consider the quantitative and qualitative influence of dependence, as well as the functional relationship between two variables and their joint probability density (e.g., union, intersection or limit-states). - -The evaluation and design of a river flood protection system is used to introduce key aspects of risk and reliability, as well as the design process. A distinction is made between using probability to assess engineering components and systems (reliability analysis) and to derive design criteria (risk evaluation), which are introduced formally in later chapters after the general risk analysis framework is discussed. - ---- - -_The primary author for this chapter is Robert Lanzafame._ - -[^solicitation]: $S$ stands for solicitation. While this letter and word are much more pedantic-sounding than simply using load, or $L$, it is widely used in the structural engineering field, where component reliability methods were pioneered. Here we take a broader approach on the subject. Classical texts are {cite:t}`adk2022`, {cite:t}`moss2020` and {cite:t}`ditlevsen1996`. -%[^pattern]: The word *paradigm* is not used because it suggests completeness. The examples here, are meant to be used as illustrations for key concepts, and extended to other situations and higher dimensions, so *pattern* seems more appropriate. \ No newline at end of file diff --git a/book/references.bib b/book/references.bib new file mode 100644 index 0000000..658a4ca --- /dev/null +++ b/book/references.bib @@ -0,0 +1,6 @@ +@misc{jason_moore, + title={Learn Multibody Dynamics, SymPy}, + author={Moore, Jason}, + howpublished={\url{https://moorepants.github.io/learn-multibody-dynamics/sympy.html}}, + year={2023} +} \ No newline at end of file diff --git a/book/reliability-component/contamination.ipynb b/book/reliability-component/contamination.ipynb deleted file mode 100644 index 84093c7..0000000 --- a/book/reliability-component/contamination.ipynb +++ /dev/null @@ -1,555 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "49a19d81", - "metadata": { - "tags": [ - "thebe-remove-input-init" - ] - }, - "source": [ - "```{custom_download_link} exercise.zip\n", - ":text: \"Download Files\"\n", - ":replace_default: \"True\"\n", - "```" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "bcb1b890", - "metadata": {}, - "source": [ - "# Contaminant Transport" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "0e18b539", - "metadata": { - "tags": [ - "thebe-remove-input-init", - "thebe-init" - ] - }, - "outputs": [], - "source": [ - "import micropip\n", - "await micropip.install(\"seaborn\")\n", - "\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from scipy.special import erfc\n", - "from scipy import stats\n", - "import seaborn as sns\n", - "\n", - "from exercise_setup import process_negative_values\n", - "from exercise_setup import RandomVariableDistribution\n", - "from exercise_setup import pdf_of_function_of_RV\n", - "from exercise_setup import monte_carlo" - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "id": "06fa7af4", - "metadata": {}, - "source": [ - "`````{admonition} Interactive Python Page\n", - ":class: tip, dropdown\n", - "\n", - "The code on this page can be used interactively: click {fa}`rocket` --> {guilabel}`Live Code` in the top right corner, then wait until the message {guilabel}`Python interaction ready!` appears.\n", - "\n", - "When this page is activated:\n", - "- Several packages will be imported automatically\n", - "- Code cells will **not** be executed automatically (you do it!)\n", - "\n", - "The download button {fa}`download` provides a `*.zip` file with everything needed to run this analysis on your computer. \n", - "\n", - "````{admonition} Which packages are imported when this page is activated?\n", - ":class: note, dropdown\n", - "```\n", - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from scipy.special import erfc\n", - "from scipy import stats\n", - "import seaborn as sns\n", - "\n", - "from exercise_setup import process_negative_values\n", - "from exercise_setup import RandomVariableDistribution\n", - "from exercise_setup import pdf_of_function_of_RV\n", - "from exercise_setup import monte_carlo\n", - "```\n", - "````\n", - "`````\n", - "Here we use component reliability methods to evaluate the probability of a contaminant causing dangerous concentrations in a groundwater well. The contaminant plume is transported on the groundwater phreatic surface due to advection and diffusion.\n", - "\n", - "The purpose of this exercise is to:\n", - "- evaluate component reliability\n", - "- illustrate functions of random variables\n", - "- see the effect of random variable distributions on reliability\n", - "- consider 'sensitivity' as a functional and/or stochastic influence on the limit-state function\n", - "\n", - "### Instructions for Interactive Programming Exercise\n", - "\n", - "This page is designed to lead you through the analysis sequentially, so we recommend executing the cells one-by-one as you read through the page. Afterwards, you are welcome to use the \"run all\" button to execute all cells on the page.\n", - "\n", - "Once the interactive feature {fa}`rocket` is activated, you can use the code cells to answer the following questions:\n", - "1. Which random variables have the biggest influence on reliability?\n", - "2. How does the assumption of probability distribution influence reliability?\n", - "3. Do the random variables act as loads or resistances?\n", - "\n", - "## Introduction of Case Study\n", - "\n", - "The case study is a contaminant transport problem, illustrated in the figure below. A factory located near a town produces hazardous waste, which can threaten the drinking water supply of the town that is extracted from groundwater wells (C). The regional groundwater system has a gradient that causes water to flow in the direction of the town from the factory, thus any spilled hazardous waste that enters the ground will eventually be transported to the wells. In order to mitigate the consequences of a spill a ditch is constructed around the factory to collect it (A). Unfortunately, even with powerful pumps, there will still be some waste that reaches the groundwater table. Our task is to quantify the probability that the waste concentration exceeds the maximum exposure level to prevent the drinking water becoming unhealthy.\n", - "\n", - "```{figure} ../notebooks/contamination/figures/sketch.png\n", - "---\n", - "width: 600px\n", - "name: sketch_contaminant\n", - "---\n", - "\n", - "```\n", - "\n", - "### Contaminant Transport\n", - "\n", - "Once the ditch becomes contaminated it is cleaned quickly, but unfortunately a 'pulse' of contamination enters the ground, after which the regional gradient carries it towards the town (advection). The pulse also disperses due to diffusion, which results in a classic advection-diffusion problem (see red shapes in diagram, at three different times, $t$). Because the ditch extends a long distance in the lateral direction and the contaminant is buoyant (it floats on the groundwater table and we neglect vertical dispersion), the problem can be analyzed in 1 dimension with the following analytic expression:\n", - "\n", - "$$\n", - "\\frac{C}{C_0} = \\frac{1}{2} \\mathrm{erf}\\left(\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)\n", - "$$\n", - "\n", - "Where $C$ contaminant concentration (e.g., parts per million, ppm) at distance $x$ from the ditch at time $t$ after the spill, and $C_0$ is the concentration in the ditch (just prior to cleanup). $\\mathrm{erf}$ is the error function. There are three parameters in the equation which are related to soil properties and groundwater flow:\n", - "\n", - "- $q$ is the horizontal groundwater flow velocity (specific discharge) [m/day]\n", - "- $n$ is the soil porosity [$-$]\n", - "- $a$ is the longitudinal dispersivity, which describes dispersion in the left to right direction in the image [m]\n", - "\n", - "Unfortunately there is not a lot of soil information, so we have to take into account uncertainty in these three variables, using the following probability distributions with first and second moments (i.e., $\\mu$ and $\\sigma$).\n", - "\n", - "- $q\\sim\\mathrm{N}\\left(\\mu_q=1.00,\\sigma_q=0.10\\right)$\n", - "- $n\\sim\\mathrm{N}\\left(\\mu_n=0.20,\\sigma_n=0.02\\right)$\n", - "- $a\\sim\\mathrm{N}\\left(\\mu_a=10.0,\\sigma_a=1.00\\right)$\n", - "\n", - "It is important to check the sensitivity of the reliability analysis to the distribution type and moments. We will use the concentration ratio $C/C_0$ to evaluate this problem and compare it to a threshold defined by health regulations: $\\mathrm{threshold}=1e-4$.\n", - "\n", - "### Definition of Limit States\n", - "\n", - "As shown in the figure above, there are two locations of interest: the monitoring station ($x=100$ m from the ditch, point B) and the town well ($x=500$ m, point C). We are interested in evaluating two cases with a reliability analysis:\n", - "1. Whether the contamination can be detected at the monitoring station above the threshold level within 1 week of the spill, and \n", - "2. If the contamination level at the town groundwater well exceeds the threshold level within 1 month of the spill (30 days)\n", - "\n", - "Relating these descriptions to our variables of interest:\n", - "1. find the probability that $C/C_0$ > threshold \n", - "2. find the probability that $C/C_0$ < threshold\n", - "\n", - "We will refer to these values as 'failure probabilities', even though case 1 technically doesn't correspond to failure---it's just the way we refer to things in practice.\n", - "\n", - "Next we will convert these into functions that will allow us to quantify the 'failure' conditions. For convenience, it is often useful to define the limit state as a function, $Z$, such that failure occurs when $Z<0$. It follows from the descriptions above, that the limit state functions for both cases are:\n", - "\n", - "1. $Z=C/C_0 - \\mathrm{threshold}$\n", - "2. $Z=\\mathrm{threshold} - C/C_0$\n", - "\n", - "NB: *in the book another notation used for $Z$ is $g_X(X)$.*\n", - "\n", - "### Analysis Approach\n", - "\n", - "Our programming task is to create a function of random variables to represent these two limit-states, define the random variables, then evaluate the reliability with Monte Carlo simulation. In other words, we will numerically approximate the probability distribution of $Z$, then evaluate reliability as $P(Z<0)$.\n", - "\n", - "This is a lot of work, but fortunately a number of helper functions and a Class are provided in the auxiliary file `exercise_setup.py`!\n", - "\n", - "### References\n", - "\n", - "This example draws inspiration from Case 2 of the paper by {cite:t}`sitar1987`." - ] - }, - { - "cell_type": "markdown", - "id": "d104b4b2-4fa5-4b37-891d-39201281ed2f", - "metadata": {}, - "source": [ - "## Defining the Limit States\n", - "\n", - "We only define limit state Case 2 below, and will use a simple multiplying factor of $-1$ to switch to Case 1 using a multiplying factor `flip_LSF`." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "64c24956", - "metadata": {}, - "outputs": [], - "source": [ - "def C_C0(q, n, a, x, t):\n", - " \"\"\"Contaminant concentration ratio.\"\"\"\n", - " q, n, a = process_negative_values(q, n, a)\n", - " return 0.5*erfc((x - q/n*t)/(2*np.sqrt(a*(q/n)*t)))\n", - "\n", - "def limit_state_fun(q, n, a, x, t, threshold):\n", - " \"\"\"Limit state fxn, Case 2 (multiply by flip_LSF=-1 for Case 1).\"\"\"\n", - " return threshold - C_C0(q, n, a, x, t)" - ] - }, - { - "cell_type": "markdown", - "id": "d7410d16-14d4-45c6-9f93-81ae08de0594", - "metadata": {}, - "source": [ - "## Class `RandomVariableDistribution`\n", - "\n", - "The class `RandomVariableDistribution` makes it very easy to define Normal and Lognormal distributions for the random variables. See documentation and example below.\n", - "\n", - "NB: *you can use the code in `exercisesetup.py` and this notebook to confirm the result of the 2 random variable case in the Probabilistic Design chapter, and recreate the figures.*" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "8bbf80be-5124-40ba-b3de-0da3eaa12ef1", - "metadata": {}, - "outputs": [], - "source": [ - "print(RandomVariableDistribution.__doc__)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "a9b93099-b1cb-458b-baf6-8ad5dd39c440", - "metadata": {}, - "outputs": [], - "source": [ - "example_random_variable = RandomVariableDistribution()\n", - "example_random_variable.define_distribution(mean=5,\n", - " dist_type='LN',\n", - " print_new_dist=True)\n", - "example_random_variable.plot_pdf_or_cdf()" - ] - }, - { - "cell_type": "markdown", - "id": "62617026-f251-462b-a93c-b7305cfd3fa4", - "metadata": {}, - "source": [ - "## Setting up the problem\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "4641ae3c", - "metadata": {}, - "outputs": [], - "source": [ - "N = 10000\n", - "\n", - "t = 7\n", - "x = 100\n", - "threshold = 1e-4\n", - "\n", - "flip_LSF = -1\n", - "\n", - "q_rv = RandomVariableDistribution()\n", - "q_rv.define_distribution(mean=1., stddev=.1)\n", - "n_rv = RandomVariableDistribution()\n", - "n_rv.define_distribution(mean=0.2, stddev=.02)\n", - "a_rv = RandomVariableDistribution()\n", - "a_rv.define_distribution(mean=10., stddev=1.)" - ] - }, - { - "cell_type": "markdown", - "id": "f3e0ffb1-6035-4f76-a550-4ff19c1b5946", - "metadata": {}, - "source": [ - "## Monte Carlo analysis\n", - "\n", - "The Monte Carlo procedure for estimating failure probability, $p_f$, is:\n", - "- For each random variable $X_i$ ($i = 1, …, n$) one simulates N realizations, $x_{i,1}, x_{i,1}, ..., x_{i,N}$. \n", - "- For each set of simulations $j$ ($j = 1, ..., N$) one calculates $g(x_{1,j}, x_{2,j}, …, x_{n,j})$\n", - "- In case $g(.) < 0$ a counter $N_f$ is increased by one. After $N$ simulations one calculates: $\\hat{p_f}=N_f/N$\n", - "- In case $N\\rightarrow+\\infty$ one obtains the failure probability $p_f$.\n", - "\n", - "The number of simulations $N$ directly influences the accuracy of $\\hat{p_f}$, which is an estimate of the 'true' value $p_f$. As an infinite number of simulations is not possible, one must choose a value for $N$ that balances total computation time, which increases linearly with $N$, and accuracy of the estimator $\\hat{p_f}$, which can be determined as the number of significant digits desired for $p_f$, or based on relative error (coefficient of variation, $V=\\sigma/\\mu$. The failure observations, $N_f$, within the Monte Carlo procedure are the result of a sequence of statistically independent and identically distributed random trials in a Bernoulli process. Using the binomial distribution, the standard deviation of of $\\hat{p_f}$ can be written\n", - "\n", - "$$\\sigma_\\hat{p_f}=\\sqrt{\\frac{p_f(1-p_f)}{N}}$$\n", - "\n", - "As $\\hat{p_f}\\rightarrow1$ this leads to the coefficient of variation, $V_\\hat{p_f}$:\n", - "\n", - "$$V_\\hat{p_f}=\\frac{\\sigma_\\hat{p_f}}{\\hat{p_f}}=\\frac{1}{\\sqrt{N\\hat{p_f}}}$$\n", - "\n", - "The coefficient of variation is a useful measure for gauging the accuracy of a Monte Carlo simulation: values of 0.01 are ideal, but 0.1 can be sufficient in many applications, depending on the need for accuracy. For example, consider $V=0.1$ for a target failure probability of $0.01$. Assuming the samples follow a Gaussian distribution implies a probability of 0.997 that the 'true' failure probability is within the interval 0.007-0.013. It is also useful to plot the calculated values of $V$ and $\\hat{p_f}$ for every realization $j = 1, ..., N$, as shown below. The figure clearly shows convergence to a stable value of $\\hat{p_f}$ after X simulations, indicating that for future analyses that are similar can use a lower number of simulations instead ($N\\sim X$).\n", - "\n", - "In case of a target coefficient of variation the number of required simulations $N$ increases as $p_f$ decreases. As an example, for $V = 0.01$ and $p_f=1e-5$ one has to execute $10^9$ simulations. As for this case on average only one of 10^5 simulations leads to an increase of $N_f$, the frequency of obtaining a 'success' (realization in the unsafe domain) is very low. In addition, for low failure probabilities the number of function evaluations is quite high, which may be practically impossible if there is a high function evaluation time, for example with a complex finite element model. To address this problem, variance reducing techniques have been developed which allow the simulations to be performed in a more effective way. In the following the so-called importance sampling or Latin hypercube sampling." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "ec7883de-544e-48d5-85f2-dfc7856e9028", - "metadata": {}, - "outputs": [], - "source": [ - "sample_q = q_rv.get_sample(N)\n", - "sample_n = n_rv.get_sample(N)\n", - "sample_a = a_rv.get_sample(N)\n", - "sample_C_C0 = C_C0(sample_q, sample_n, sample_a, x, t)\n", - "sample_Z = flip_LSF*limit_state_fun(sample_q,\n", - " sample_n,\n", - " sample_a,\n", - " x, t, threshold)\n", - "\n", - "monte_carlo(sample_Z);" - ] - }, - { - "cell_type": "markdown", - "id": "d00e1316-c4ac-474d-93ad-18abcda30cfc", - "metadata": {}, - "source": [ - "The method `pdf_of_function_of_RV` makes it easy to see what the distribution of $C/C_0$ and the limit state function for different distributions of q, n or a. Below a second distribution of a is considered:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "c08e0e56-8a6b-45a2-ad3f-abe3ce869513", - "metadata": {}, - "outputs": [], - "source": [ - "C_C0_cases = []\n", - "Z_cases = []\n", - "C_C0_cases.append(sample_C_C0)\n", - "Z_cases.append(sample_Z)\n", - "\n", - "a_2 = RandomVariableDistribution()\n", - "a_2.define_distribution(mean=10, stddev=4, dist_type='N')\n", - "C_C0_cases.append(C_C0(sample_q, sample_n, a_2.get_sample(N), x, t))\n", - "Z_cases.append(flip_LSF*limit_state_fun(sample_q,\n", - " sample_n,\n", - " a_2.get_sample(N),\n", - " x, t, threshold))\n", - "\n", - "a_rv.print_status()\n", - "a_2.print_status()\n", - "\n", - "pdf_of_function_of_RV(C_C0_cases)\n", - "pdf_of_function_of_RV(Z_cases, case_C=False)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "695f1336-8d3e-4503-9196-9969d181ae10", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "id": "8c197ae8-3a6c-45fe-b304-75f601dbb9ac", - "metadata": {}, - "source": [ - "This is the density of the function of random variables, $C/C_0$, two values of $\\sigma_a$, and a third with the uniform distribution (not using the `RandomVariableDistribution` class)." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "53273645-453b-48b9-85c0-e69eb1ac579e", - "metadata": {}, - "outputs": [], - "source": [ - "values_of_RV_1 = sample_q\n", - "values_of_RV_2 = sample_a\n", - "\n", - "g = sns.JointGrid()\n", - "sns.kdeplot(x=values_of_RV_1,\n", - " y=values_of_RV_2, ax=g.ax_joint, bw_adjust=3)\n", - "sns.scatterplot(x=values_of_RV_1[sample_Z<0],\n", - " y=values_of_RV_2[sample_Z<0], ax=g.ax_joint)\n", - "g.ax_joint.set_xlabel('Random Variable 1 (chosen by you)')\n", - "g.ax_joint.set_ylabel('Random Variable 2 (chosen by you)')\n", - "print('Joint density of 2 RVs with failure realizations')" - ] - }, - { - "cell_type": "markdown", - "id": "75f127f7-c40b-425d-91cf-6c6ecad207a2", - "metadata": {}, - "source": [ - "## Case 2: exceeding the health threshold\n", - "\n", - "Now we return to the failure definition of exceeding the threshold (`flip_LSF` = 1)." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3ee884a7-16fb-46bf-9766-9899e662a9bc", - "metadata": {}, - "outputs": [], - "source": [ - "N = 100000\n", - "\n", - "t = 30\n", - "x = 500\n", - "threshold = 1e-4\n", - "\n", - "flip_LSF = 1\n", - "\n", - "sample_q = q_rv.get_sample(N)\n", - "sample_n = n_rv.get_sample(N)\n", - "sample_a = a_rv.get_sample(N)\n", - "\n", - "sample_C_C0 = C_C0(sample_q, sample_n, sample_a, x, t)\n", - "sample_Z = flip_LSF*limit_state_fun(sample_q,\n", - " sample_n,\n", - " sample_a,\n", - " x, t, threshold)\n", - "\n", - "monte_carlo(sample_Z);" - ] - }, - { - "cell_type": "markdown", - "id": "d1d693c6-df03-442f-a100-a065355b2c12", - "metadata": {}, - "source": [ - "NB: *the joint density and failure point plot is commented out here to prevent slowing down the kernel. When N=100000 (1e5) or higher, it will take around a minute to run.*" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "19a0f38a-f4e2-4dc0-8ade-0094f2a3cc91", - "metadata": {}, - "outputs": [], - "source": [ - "# values_of_RV_1 = sample_q\n", - "# values_of_RV_2 = sample_a\n", - "\n", - "# g = sns.JointGrid()\n", - "# sns.kdeplot(x=values_of_RV_1,\n", - "# y=values_of_RV_2, ax=g.ax_joint, bw_adjust=3)\n", - "# sns.scatterplot(x=values_of_RV_1[sample_Z<0],\n", - "# y=values_of_RV_2[sample_Z<0], ax=g.ax_joint)\n", - "# g.ax_joint.set_xlabel('Random Variable 1 (chosen by you)')\n", - "# g.ax_joint.set_ylabel('Random Variable 2 (chosen by you)')\n", - "# print('Joint density of 2 RVs with failure realizations')" - ] - }, - { - "cell_type": "markdown", - "id": "3e7d0cc4", - "metadata": {}, - "source": [ - "### Gradient Vector\n", - "\n", - "Partial derivatives will be useful for evaluating the functional influence of the variables on the limit states. The gradient vector is defined as:\n", - "\n", - "$\\nabla_{\\mathbf{y}} G(\\mathbf{y})=\\left(\\frac{\\partial G(\\mathbf{y})}{\\partial \\mathbf{y}_1}, \\cdots, \\frac{\\partial G(\\mathbf{y})}{\\partial \\mathbf{y}_n}\\right) $\n", - "\n", - "To find the gradient vector we need to find the partial derivatives of $\\frac{C}{C_0}$\n", - "\n", - "$\\frac{C}{C_0} = \\frac{1}{2} \\mathrm{erfc}\\left(\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)=\\frac{1}{2} \\left(1-\\mathrm{erf}\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)$\n", - "\n", - "Using $\\frac{\\partial}{\\partial x} (\\mathrm{erf} x) = \\frac{2}{\\sqrt{\\pi}}e^{-x^2} $ and $\\Omega = \\frac{1}{\\sqrt{\\pi}}e^{-\\left(\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)^2} $, the derivatives are:\n", - "\n", - "$\\frac{\\partial (C/C_0)}{\\partial x} = \\Omega\\left(-\\frac{1}{2\\sqrt{a(q/n)t}}\\right)$\n", - "\n", - "$\\frac{\\partial (C/C_0)}{\\partial t} =\\Omega\\left(\\frac{x}{4\\sqrt{a(q/n)t^3}}+\\frac{q}{4n\\sqrt{a(q/n)t}}\\right)$\n", - "\n", - "$\\frac{\\partial (C/C_0)}{\\partial q} = \\Omega\\left(\\frac{x}{4\\sqrt{a(1/n)tq^3}}+\\frac{t}{4n\\sqrt{a(q/n)t}}\\right)$\n", - "\n", - "$\\frac{\\partial (C/C_0)}{\\partial n} = \\Omega\\left(-\\frac{x}{4\\sqrt{aqtn}}-\\frac{qt}{4\\sqrt{qatn^3}}\\right)$\n", - "\n", - "$\\frac{\\partial (C/C_0)}{\\partial a} = \\Omega\\left(\\frac{x-q/nt}{4\\sqrt{(q/n)ta^3}}\\right)$" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "a761d424", - "metadata": {}, - "outputs": [], - "source": [ - "def gradient(q, n, a, x, t):\n", - " Om = 1/np.sqrt(np.pi)*np.exp(-((x - q/n*t)/(2*np.sqrt(a*q/n*t)))**2)\n", - " dx = Om*(-1/(2*np.sqrt(a*q/n*t)))\n", - " dt = Om*(x/(4*np.sqrt(a*q/n*t**3)) + (q)/(4*n*np.sqrt(a*q/n*t)))\n", - " dq = Om*(x/(4*np.sqrt(a*q**3/n*t)) + (t)/(4*n*np.sqrt(a*q/n*t)))\n", - " dn = Om*(-x/(4*np.sqrt(a*q*n*t)) - (q*t)/(4*np.sqrt(a*q*n**3*t)))\n", - " da = Om*((x - q/n*t)/(4*np.sqrt(a**3 *q/n*t)))\n", - " return np.array([dq,dn,da,dx,dt])" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "d6492f20", - "metadata": {}, - "outputs": [], - "source": [ - "print(gradient(2.5, 0.2, 10, x, t))" - ] - }, - { - "cell_type": "markdown", - "id": "18ae1605-4c60-4c65-be4f-ce9cef2e40fd", - "metadata": {}, - "source": [ - "## Your turn!\n", - "\n", - "Now try and use the code to answer the questions posed at the beginning of the notebook, which are repeated here:\n", - "1. Which random variables have the biggest influence on reliability?\n", - "2. How does the assumption of probability distribution influence reliability?\n", - "3. Do the random variables act as loads or resistances?\n", - "\n", - "In particular, to evaluate sensitivity, you can consider two quantitative aspects:\n", - "1. What is the functional influence of the random variables and x and t on the limit-state function?\n", - "2. What is the stochastic influence of the random variables, \n", - "3. What is the combined influence of the two aspects above?\n", - "\n", - "" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "base", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.11.7" - }, - "vscode": { - "interpreter": { - "hash": "85471ad55176ca86192ed6be6d105faaef73891404cad6bd910e89e8513744d9" - } - }, - "widgets": { - "application/vnd.jupyter.widget-state+json": { - "state": {}, - "version_major": 2, - "version_minor": 0 - } - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/book/reliability-component/exercise.ipynb b/book/reliability-component/exercise.ipynb deleted file mode 100644 index c0199aa..0000000 --- a/book/reliability-component/exercise.ipynb +++ /dev/null @@ -1,498 +0,0 @@ -{ - "cells": [ - { - "attachments": {}, - "cell_type": "markdown", - "id": "bcb1b890", - "metadata": {}, - "source": [ - "# Contaminant Transport" - ] - }, - { - "cell_type": "markdown", - "id": "a05b1f14", - "metadata": {}, - "source": [ - "_This notebook and associated files were downloaded from the book [Risk and Reliability for Engineers](https://gitlab.tudelft.nl/interactivetextbooks-citg/risk-and-reliability/) (Lanzafame, 2024) under a CC-BY 4.0 License._\n", - "\n", - "Here we use component reliability methods to evaluate the probability of a contaminant causing dangerous concentrations in a groundwater well. The contaminant plume is transported on the groundwater phreatic surface due to advection and diffusion.\n", - "\n", - "The purpose of this exercise is to:\n", - "- evaluate component reliability\n", - "- illustrate functions of random variables\n", - "- see the effect of random variable distributions on reliability\n", - "- consider 'sensitivity' as a functional and/or stochastic influence on the limit-state function\n", - "\n", - "You can use the code to answer the following questions:\n", - "1. Which random variables have the biggest influence on reliability?\n", - "2. How does the assumption of probability distribution influence reliability?\n", - "3. Do the random variables act as loads or resistances?\n", - "\n", - "## Introduction of Case Study\n", - "\n", - "The case study is a contaminant transport problem, illustrated in the figure below. A factory located near a town produces hazardous waste, which can threaten the drinking water supply of the town that is extracted from groundwater wells (C). The regional groundwater system has a gradient that causes water to flow in the direction of the town from the factory, thus any spilled hazardous waste that enters the ground will eventually be transported to the wells. In order to mitigate the consequences of a spill a ditch is constructed around the factory to collect it (A). Unfortunately, even with powerful pumps, there will still be some waste that reaches the groundwater table. Our task is to quantify the probability that the waste concentration exceeds the maximum exposure level to prevent the drinking water becoming unhealthy.\n", - "\n", - "![sketch](./sketch.png)\n", - "\n", - "### Contaminant Transport\n", - "\n", - "Once the ditch becomes contaminated it is cleaned quickly, but unfortunately a 'pulse' of contamination enters the ground, after which the regional gradient carries it towards the town (advection). The pulse also disperses due to diffusion, which results in a classic advection-diffusion problem (see red shapes in diagram, at three different times, $t$). Because the ditch extends a long distance in the lateral direction and the contaminant is buoyant (it floats on the groundwater table and we neglect vertical dispersion), the problem can be analyzed in 1 dimension with the following analytic expression:\n", - "\n", - "$$\n", - "\\frac{C}{C_0} = \\frac{1}{2} \\mathrm{erf}\\left(\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)\n", - "$$\n", - "\n", - "Where $C$ contaminant concentration (e.g., parts per million, ppm) at distance $x$ from the ditch at time $t$ after the spill, and $C_0$ is the concentration in the ditch (just prior to cleanup). $\\mathrm{erf}$ is the error function. There are three parameters in the equation which are related to soil properties and groundwater flow:\n", - "\n", - "- $q$ is the horizontal groundwater flow velocity (specific discharge) [m/day]\n", - "- $n$ is the soil porosity [$-$]\n", - "- $a$ is the longitudinal dispersivity, which describes dispersion in the left to right direction in the image [m]\n", - "\n", - "Unfortunately there is not a lot of soil information, so we have to take into account uncertainty in these three variables, using the following probability distributions with first and second moments (i.e., $\\mu$ and $\\sigma$).\n", - "\n", - "- $q\\sim\\mathrm{N}\\left(\\mu_q=1.00,\\sigma_q=0.10\\right)$\n", - "- $n\\sim\\mathrm{N}\\left(\\mu_n=0.20,\\sigma_n=0.02\\right)$\n", - "- $a\\sim\\mathrm{N}\\left(\\mu_a=10.0,\\sigma_a=1.00\\right)$\n", - "\n", - "It is important to check the sensitivity of the reliability analysis to the distribution type and moments. We will use the concentration ratio $C/C_0$ to evaluate this problem and compare it to a threshold defined by health regulations: $\\mathrm{threshold}=1e-4$.\n", - "\n", - "### Definition of Limit States\n", - "\n", - "As shown in the figure above, there are two locations of interest: the monitoring station ($x=100$ m from the ditch, point B) and the town well ($x=500$ m, point C). We are interested in evaluating two cases with a reliability analysis:\n", - "1. Whether the contamination can be detected at the monitoring station above the threshold level within 1 week of the spill, and \n", - "2. If the contamination level at the town groundwater well exceeds the threshold level within 1 month of the spill (30 days)\n", - "\n", - "Relating these descriptions to our variables of interest:\n", - "1. find the probability that $C/C_0$ > threshold \n", - "2. find the probability that $C/C_0$ < threshold\n", - "\n", - "We will refer to these values as 'failure probabilities', even though case 1 technically doesn't correspond to failure---it's just the way we refer to things in practice.\n", - "\n", - "Next we will convert these into functions that will allow us to quantify the 'failure' conditions. For convenience, it is often useful to define the limit state as a function, $Z$, such that failure occurs when $Z<0$. It follows from the descriptions above, that the limit state functions for both cases are:\n", - "\n", - "1. $Z=C/C_0 - \\mathrm{threshold}$\n", - "2. $Z=\\mathrm{threshold} - C/C_0$\n", - "\n", - "NB: *in the book another notation used for $Z$ is $g_X(X)$.*\n", - "\n", - "### Analysis Approach\n", - "\n", - "Our programming task is to create a function of random variables to represent these two limit-states, define the random variables, then evaluate the reliability with Monte Carlo simulation. In other words, we will numerically approximate the probability distribution of $Z$, then evaluate reliability as $P(Z<0)$.\n", - "\n", - "This is a lot of work, but fortunately a number of helper functions and a Class are provided in the auxiliary file `exercise_setup.py`!\n", - "\n", - "### References\n", - "\n", - "This example draws inspiration from Case 2 of the paper by {cite:t}`sitar1987`." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "0e18b539", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from scipy.special import erfc\n", - "from scipy import stats\n", - "import seaborn as sns\n", - "\n", - "from exercise_setup import process_negative_values\n", - "from exercise_setup import RandomVariableDistribution\n", - "from exercise_setup import pdf_of_function_of_RV\n", - "from exercise_setup import monte_carlo" - ] - }, - { - "cell_type": "markdown", - "id": "d104b4b2-4fa5-4b37-891d-39201281ed2f", - "metadata": {}, - "source": [ - "## Defining the Limit States\n", - "\n", - "We only define limit state Case 2 below, and will use a simple multiplying factor of $-1$ to switch to Case 1 using a multiplying factor `flip_LSF`." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "64c24956", - "metadata": {}, - "outputs": [], - "source": [ - "def C_C0(q, n, a, x, t):\n", - " \"\"\"Contaminant concentration ratio.\"\"\"\n", - " q, n, a = process_negative_values(q, n, a)\n", - " return 0.5*erfc((x - q/n*t)/(2*np.sqrt(a*(q/n)*t)))\n", - "\n", - "def limit_state_fun(q, n, a, x, t, threshold):\n", - " \"\"\"Limit state fxn, Case 2 (multiply by flip_LSF=-1 for Case 1).\"\"\"\n", - " return threshold - C_C0(q, n, a, x, t)" - ] - }, - { - "cell_type": "markdown", - "id": "d7410d16-14d4-45c6-9f93-81ae08de0594", - "metadata": {}, - "source": [ - "## Class `RandomVariableDistribution`\n", - "\n", - "The class `RandomVariableDistribution` makes it very easy to define Normal and Lognormal distributions for the random variables. See documentation and example below.\n", - "\n", - "NB: *you can use the code in `exercisesetup.py` and this notebook to confirm the result of the 2 random variable case in the Probabilistic Design chapter, and recreate the figures.*" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "8bbf80be-5124-40ba-b3de-0da3eaa12ef1", - "metadata": {}, - "outputs": [], - "source": [ - "print(RandomVariableDistribution.__doc__)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "a9b93099-b1cb-458b-baf6-8ad5dd39c440", - "metadata": {}, - "outputs": [], - "source": [ - "example_random_variable = RandomVariableDistribution()\n", - "example_random_variable.define_distribution(mean=5,\n", - " dist_type='LN',\n", - " print_new_dist=True)\n", - "example_random_variable.plot_pdf_or_cdf()" - ] - }, - { - "cell_type": "markdown", - "id": "62617026-f251-462b-a93c-b7305cfd3fa4", - "metadata": {}, - "source": [ - "## Setting up the problem\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "4641ae3c", - "metadata": {}, - "outputs": [], - "source": [ - "N = 10000\n", - "\n", - "t = 7\n", - "x = 100\n", - "threshold = 1e-4\n", - "\n", - "flip_LSF = -1\n", - "\n", - "q_rv = RandomVariableDistribution()\n", - "q_rv.define_distribution(mean=1., stddev=.1)\n", - "n_rv = RandomVariableDistribution()\n", - "n_rv.define_distribution(mean=0.2, stddev=.02)\n", - "a_rv = RandomVariableDistribution()\n", - "a_rv.define_distribution(mean=10., stddev=1.)" - ] - }, - { - "cell_type": "markdown", - "id": "f3e0ffb1-6035-4f76-a550-4ff19c1b5946", - "metadata": {}, - "source": [ - "## Monte Carlo analysis\n", - "\n", - "The Monte Carlo procedure for estimating failure probability, $p_f$, is:\n", - "- For each random variable $X_i$ ($i = 1, …, n$) one simulates N realizations, $x_{i,1}, x_{i,1}, ..., x_{i,N}$. \n", - "- For each set of simulations $j$ ($j = 1, ..., N$) one calculates $g(x_{1,j}, x_{2,j}, …, x_{n,j})$\n", - "- In case $g(.) < 0$ a counter $N_f$ is increased by one. After $N$ simulations one calculates: $\\hat{p_f}=N_f/N$\n", - "- In case $N\\rightarrow+\\infty$ one obtains the failure probability $p_f$.\n", - "\n", - "The number of simulations $N$ directly influences the accuracy of $\\hat{p_f}$, which is an estimate of the 'true' value $p_f$. As an infinite number of simulations is not possible, one must choose a value for $N$ that balances total computation time, which increases linearly with $N$, and accuracy of the estimator $\\hat{p_f}$, which can be determined as the number of significant digits desired for $p_f$, or based on relative error (coefficient of variation, $V=\\sigma/\\mu$. The failure observations, $N_f$, within the Monte Carlo procedure are the result of a sequence of statistically independent and identically distributed random trials in a Bernoulli process. Using the binomial distribution, the standard deviation of of $\\hat{p_f}$ can be written\n", - "\n", - "$$\\sigma_\\hat{p_f}=\\sqrt{\\frac{p_f(1-p_f)}{N}}$$\n", - "\n", - "As $\\hat{p_f}\\rightarrow1$ this leads to the coefficient of variation, $V_\\hat{p_f}$:\n", - "\n", - "$$V_\\hat{p_f}=\\frac{\\sigma_\\hat{p_f}}{\\hat{p_f}}=\\frac{1}{\\sqrt{N\\hat{p_f}}}$$\n", - "\n", - "The coefficient of variation is a useful measure for gauging the accuracy of a Monte Carlo simulation: values of 0.01 are ideal, but 0.1 can be sufficient in many applications, depending on the need for accuracy. For example, consider $V=0.1$ for a target failure probability of $0.01$. Assuming the samples follow a Gaussian distribution implies a probability of 0.997 that the 'true' failure probability is within the interval 0.007-0.013. It is also useful to plot the calculated values of $V$ and $\\hat{p_f}$ for every realization $j = 1, ..., N$, as shown below. The figure clearly shows convergence to a stable value of $\\hat{p_f}$ after X simulations, indicating that for future analyses that are similar can use a lower number of simulations instead ($N\\sim X$).\n", - "\n", - "In case of a target coefficient of variation the number of required simulations $N$ increases as $p_f$ decreases. As an example, for $V = 0.01$ and $p_f=1e-5$ one has to execute $10^9$ simulations. As for this case on average only one of 10^5 simulations leads to an increase of $N_f$, the frequency of obtaining a 'success' (realization in the unsafe domain) is very low. In addition, for low failure probabilities the number of function evaluations is quite high, which may be practically impossible if there is a high function evaluation time, for example with a complex finite element model. To address this problem, variance reducing techniques have been developed which allow the simulations to be performed in a more effective way. In the following the so-called importance sampling or Latin hypercube sampling." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "ec7883de-544e-48d5-85f2-dfc7856e9028", - "metadata": {}, - "outputs": [], - "source": [ - "sample_q = q_rv.get_sample(N)\n", - "sample_n = n_rv.get_sample(N)\n", - "sample_a = a_rv.get_sample(N)\n", - "sample_C_C0 = C_C0(sample_q, sample_n, sample_a, x, t)\n", - "sample_Z = flip_LSF*limit_state_fun(sample_q,\n", - " sample_n,\n", - " sample_a,\n", - " x, t, threshold)\n", - "\n", - "monte_carlo(sample_Z);" - ] - }, - { - "cell_type": "markdown", - "id": "d00e1316-c4ac-474d-93ad-18abcda30cfc", - "metadata": {}, - "source": [ - "The method `pdf_of_function_of_RV` makes it easy to see what the distribution of $C/C_0$ and the limit state function for different distributions of q, n or a. Below a second distribution of a is considered:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "c08e0e56-8a6b-45a2-ad3f-abe3ce869513", - "metadata": {}, - "outputs": [], - "source": [ - "C_C0_cases = []\n", - "Z_cases = []\n", - "C_C0_cases.append(sample_C_C0)\n", - "Z_cases.append(sample_Z)\n", - "\n", - "a_2 = RandomVariableDistribution()\n", - "a_2.define_distribution(mean=10, stddev=4, dist_type='N')\n", - "C_C0_cases.append(C_C0(sample_q, sample_n, a_2.get_sample(N), x, t))\n", - "Z_cases.append(flip_LSF*limit_state_fun(sample_q,\n", - " sample_n,\n", - " a_2.get_sample(N),\n", - " x, t, threshold))\n", - "\n", - "a_rv.print_status()\n", - "a_2.print_status()\n", - "\n", - "pdf_of_function_of_RV(C_C0_cases)\n", - "pdf_of_function_of_RV(Z_cases, case_C=False)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "695f1336-8d3e-4503-9196-9969d181ae10", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "id": "8c197ae8-3a6c-45fe-b304-75f601dbb9ac", - "metadata": {}, - "source": [ - "This is the density of the function of random variables, $C/C_0$, two values of $\\sigma_a$, and a third with the uniform distribution (not using the `RandomVariableDistribution` class)." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "53273645-453b-48b9-85c0-e69eb1ac579e", - "metadata": {}, - "outputs": [], - "source": [ - "values_of_RV_1 = sample_q\n", - "values_of_RV_2 = sample_a\n", - "\n", - "g = sns.JointGrid()\n", - "sns.kdeplot(x=values_of_RV_1,\n", - " y=values_of_RV_2, ax=g.ax_joint, bw_adjust=3)\n", - "sns.scatterplot(x=values_of_RV_1[sample_Z<0],\n", - " y=values_of_RV_2[sample_Z<0], ax=g.ax_joint)\n", - "g.ax_joint.set_xlabel('Random Variable 1 (chosen by you)')\n", - "g.ax_joint.set_ylabel('Random Variable 2 (chosen by you)')\n", - "print('Joint density of 2 RVs with failure realizations')" - ] - }, - { - "cell_type": "markdown", - "id": "75f127f7-c40b-425d-91cf-6c6ecad207a2", - "metadata": {}, - "source": [ - "## Case 2: exceeding the health threshold\n", - "\n", - "Now we return to the failure definition of exceeding the threshold (`flip_LSF` = 1)." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "3ee884a7-16fb-46bf-9766-9899e662a9bc", - "metadata": {}, - "outputs": [], - "source": [ - "N = 100000\n", - "\n", - "t = 30\n", - "x = 500\n", - "threshold = 1e-4\n", - "\n", - "flip_LSF = 1\n", - "\n", - "sample_q = q_rv.get_sample(N)\n", - "sample_n = n_rv.get_sample(N)\n", - "sample_a = a_rv.get_sample(N)\n", - "\n", - "sample_C_C0 = C_C0(sample_q, sample_n, sample_a, x, t)\n", - "sample_Z = flip_LSF*limit_state_fun(sample_q,\n", - " sample_n,\n", - " sample_a,\n", - " x, t, threshold)\n", - "\n", - "monte_carlo(sample_Z);" - ] - }, - { - "cell_type": "markdown", - "id": "d1d693c6-df03-442f-a100-a065355b2c12", - "metadata": {}, - "source": [ - "NB: *the joint density and failure point plot is commented out here to prevent slowing down the kernel. When N=100000 (1e5) or higher, it will take around a minute to run.*" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "19a0f38a-f4e2-4dc0-8ade-0094f2a3cc91", - "metadata": {}, - "outputs": [], - "source": [ - "# values_of_RV_1 = sample_q\n", - "# values_of_RV_2 = sample_a\n", - "\n", - "# g = sns.JointGrid()\n", - "# sns.kdeplot(x=values_of_RV_1,\n", - "# y=values_of_RV_2, ax=g.ax_joint, bw_adjust=3)\n", - "# sns.scatterplot(x=values_of_RV_1[sample_Z<0],\n", - "# y=values_of_RV_2[sample_Z<0], ax=g.ax_joint)\n", - "# g.ax_joint.set_xlabel('Random Variable 1 (chosen by you)')\n", - "# g.ax_joint.set_ylabel('Random Variable 2 (chosen by you)')\n", - "# print('Joint density of 2 RVs with failure realizations')" - ] - }, - { - "cell_type": "markdown", - "id": "3e7d0cc4", - "metadata": {}, - "source": [ - "### Gradient Vector\n", - "\n", - "Partial derivatives will be useful for evaluating the functional influence of the variables on the limit states. The gradient vector is defined as:\n", - "\n", - "$\\nabla_{\\mathbf{y}} G(\\mathbf{y})=\\left(\\frac{\\partial G(\\mathbf{y})}{\\partial \\mathbf{y}_1}, \\cdots, \\frac{\\partial G(\\mathbf{y})}{\\partial \\mathbf{y}_n}\\right) $\n", - "\n", - "To find the gradient vector we need to find the partial derivatives of $\\frac{C}{C_0}$\n", - "\n", - "$\\frac{C}{C_0} = \\frac{1}{2} \\mathrm{erfc}\\left(\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)=\\frac{1}{2} \\left(1-\\mathrm{erf}\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)$\n", - "\n", - "Using $\\frac{\\partial}{\\partial x} (\\mathrm{erf} x) = \\frac{2}{\\sqrt{\\pi}}e^{-x^2} $ and $\\Omega = \\frac{1}{\\sqrt{\\pi}}e^{-\\left(\\frac{x-(q/n)t}{2\\sqrt{a(q/n)t}}\\right)^2} $, the derivatives are:\n", - "\n", - "$\\frac{\\partial (C/C_0)}{\\partial x} = \\Omega\\left(-\\frac{1}{2\\sqrt{a(q/n)t}}\\right)$\n", - "\n", - "$\\frac{\\partial (C/C_0)}{\\partial t} =\\Omega\\left(\\frac{x}{4\\sqrt{a(q/n)t^3}}+\\frac{q}{4n\\sqrt{a(q/n)t}}\\right)$\n", - "\n", - "$\\frac{\\partial (C/C_0)}{\\partial q} = \\Omega\\left(\\frac{x}{4\\sqrt{a(1/n)tq^3}}+\\frac{t}{4n\\sqrt{a(q/n)t}}\\right)$\n", - "\n", - "$\\frac{\\partial (C/C_0)}{\\partial n} = \\Omega\\left(-\\frac{x}{4\\sqrt{aqtn}}-\\frac{qt}{4\\sqrt{qatn^3}}\\right)$\n", - "\n", - "$\\frac{\\partial (C/C_0)}{\\partial a} = \\Omega\\left(\\frac{x-q/nt}{4\\sqrt{(q/n)ta^3}}\\right)$" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "a761d424", - "metadata": {}, - "outputs": [], - "source": [ - "def gradient(q, n, a, x, t):\n", - " Om = 1/np.sqrt(np.pi)*np.exp(-((x - q/n*t)/(2*np.sqrt(a*q/n*t)))**2)\n", - " dx = Om*(-1/(2*np.sqrt(a*q/n*t)))\n", - " dt = Om*(x/(4*np.sqrt(a*q/n*t**3)) + (q)/(4*n*np.sqrt(a*q/n*t)))\n", - " dq = Om*(x/(4*np.sqrt(a*q**3/n*t)) + (t)/(4*n*np.sqrt(a*q/n*t)))\n", - " dn = Om*(-x/(4*np.sqrt(a*q*n*t)) - (q*t)/(4*np.sqrt(a*q*n**3*t)))\n", - " da = Om*((x - q/n*t)/(4*np.sqrt(a**3 *q/n*t)))\n", - " return np.array([dq,dn,da,dx,dt])" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "d6492f20", - "metadata": {}, - "outputs": [], - "source": [ - "print(gradient(2.5, 0.2, 10, x, t))" - ] - }, - { - "cell_type": "markdown", - "id": "18ae1605-4c60-4c65-be4f-ce9cef2e40fd", - "metadata": {}, - "source": [ - "## Your turn!\n", - "\n", - "Now try and use the code to answer the questions posed at the beginning of the notebook, which are repeated here:\n", - "1. Which random variables have the biggest influence on reliability?\n", - "2. How does the assumption of probability distribution influence reliability?\n", - "3. Do the random variables act as loads or resistances?\n", - "\n", - "In particular, to evaluate sensitivity, you can consider two quantitative aspects:\n", - "1. What is the functional influence of the random variables and x and t on the limit-state function?\n", - "2. What is the stochastic influence of the random variables, \n", - "3. What is the combined influence of the two aspects above?\n", - "\n", - "" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "base", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.9.13 (main, Aug 25 2022, 23:51:50) [MSC v.1916 64 bit (AMD64)]" - }, - "vscode": { - "interpreter": { - "hash": "85471ad55176ca86192ed6be6d105faaef73891404cad6bd910e89e8513744d9" - } - }, - "widgets": { - "application/vnd.jupyter.widget-state+json": { - "state": {}, - "version_major": 2, - "version_minor": 0 - } - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/book/reliability-component/exercise.zip b/book/reliability-component/exercise.zip deleted file mode 100644 index 37314fa..0000000 Binary files a/book/reliability-component/exercise.zip and /dev/null differ diff --git a/book/reliability-component/exercise_setup.py b/book/reliability-component/exercise_setup.py deleted file mode 100644 index 51a9470..0000000 --- a/book/reliability-component/exercise_setup.py +++ /dev/null @@ -1,247 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt -from scipy.special import erfc -from scipy import stats -import seaborn as sns - -def process_negative_values(q, n, a): - """Prevents problems with negative values in sqrt of C_C0 function.""" - N_q = sum(q<0) - N_n = sum(n<0) - N_a = sum(a<0) - set_value = 0.001 - if N_q > 0: - for i in range(len(q)): - if q[i]<0: - q[i] = set_value - print(f'q has {N_q} negative values that have been set to {set_value:.1e}.') - if N_n > 0: - for i in range(len(n)): - if n[i]<0: - n[i] = set_value - print(f'n has {N_n} negative values that have been set to {set_value:.1e}.') - if N_a > 0: - for i in range(len(a)): - if a[i]<0: - a[i] = set_value - print(f'a has {N_a} negative values that have been set to {set_value:.1e}.') - return q, n, a - -class RandomVariableDistribution(): - """Define a N or LN probability to use in MUDE week 2.7 exercise. - - Usage: - ----- - Create an instance of the class - by default, the random variable is ~N(0,1) - Specify distribution using 1st and 2nd moments for N or LN: - --> use method define_distribution to change it! - (the method prints a summary of the change) - for example, copy/paste the following: - test = RandomVariableDistribution() - test.print_status() - test.define_distribution(mean=5, stddev=1, dist_type='LN') - An instance will include the following attributes: - - distribution moment and (scipy) parameters shape, location, scale - - dist_object: distribution object (scipy.stats) - - get_sample: method for getting random samples from the distribution - - plot_pdf_or_cdf: - """ - - def __init__(self): - self.mean = 0. - self.stddev = 1. - self.dist_type = 'N' - - def print_status(self): - """Returns current parameter values and distribution type.""" - print(f'The mean is {self.mean:.3e}') - print(f'The standard deviation is {self.stddev:.3e}') - if self.dist_type == 'N': - distribution_name = 'Normal' - elif self.dist_type == 'LN': - distribution_name = 'Lognormal' - print('The distribution is ' + distribution_name) - - def define_distribution(self, - mean=None, - stddev=None, - dist_type=None, - print_new_dist=False): - """Compute distribution parameters and RV object from moments. - - Usage: - ----- - Optional arguments will override current dist: - --> default distribution is standard normal, ~N(0,1) - mean: float - stddev: float - dist_type: 'N' or 'LN' - print_new_dist=True to print distribution changes. - """ - if mean is None: - mean = self.mean - if stddev is None: - stddev = self.stddev - if dist_type is None: - dist_type = self.dist_type - if dist_type == 'N': - shape = None - location = mean - scale = stddev - dist_object = stats.norm(loc=location, scale=scale) - elif dist_type == 'LN': - """ - Finds distribution parameters of LN-distributed X, - which are equivalent to the mean and standard deviation - of the log of X: Y = ln(X), then converts to the - parameterization used by scipy.stats.lognorm. - """ - stddev_y = np.sqrt(np.log(1 + (stddev/mean)**2)) - mean_y = np.log(mean) - 0.5*stddev_y**2 - - shape = stddev_y - location = 0 - scale = np.exp(mean_y) - dist_object = stats.lognorm(s=shape, - loc=location, - scale=scale) - else: - raise ValueError("You can only use N or LN for self.dist_type.") - self.mean = mean - self.stddev = stddev - self.dist_type = dist_type - self.shape = shape - self.location = location - self.scale = scale - self.dist_object = dist_object - self.get_sample = lambda size : self.dist_object.rvs(size=size) - if print_new_dist: - self.print_status() - - def plot_pdf_or_cdf(self, plot_type='pdf', plot_limits=None): - """Plots the pdf or cdf (specify choice with plot_type). - - Usage: - ----- - No inputs required, but there are optional inputs: - plot_type='cdf' to plot cdf (pdf is default value) - plot_limits: list with 2 values for x-axis - """ - if plot_limits is None: - if self.dist_type == 'N': - plot_limits = [self.mean - 3*self.stddev, - self.mean + 3*self.stddev] - elif self.dist_type == 'LN': - 'Avoid negative or zero value for lognormal dist.' - lower_value = self.mean - 3*self.stddev - if lower_value <= 0: - lower_value = 0.01 - plot_limits = [lower_value, - self.mean + 4*self.stddev] - else: - raise ValueError("You can only use N or LN for self.dist_type.") - - plot_x = np.linspace(plot_limits[0], plot_limits[1], 1000) - if plot_type == 'pdf': - plot_y = self.dist_object.pdf(plot_x) - y_label = 'PDF [-]' - elif plot_type == 'cdf': - plot_y = self.dist_object.cdf(plot_x) - y_label = 'CDF [-]' - else: - raise ValueError("You must specify pdf or cdf for plot_type.") - fontsize = 15 - plt.figure() - plt.plot(plot_x, plot_y, 'k-', linewidth=3) - plt.xlabel('Random Variable, X', fontsize=fontsize) - plt.ylabel(y_label, fontsize=fontsize) - plt.show() - -def pdf_of_function_of_RV(cases, case_C=True, case_name=None, plot_limits=None): - """Plot the PDF of a sampled function of random variables (C_C0 or Z). - - Usage: - ----- - cases: a list of arrays - case_C=True (default) assumes C_C0 is given. False is for Z. - case_name: list of strings with the labels for each array. - e.g., ['Original', 'High sigma_a', 'Low sigma_a'] - (default will return Case i for all arrays) - plot_limits: list of two values that override default limits - for x-axis. - """ - bw_adjust = 3 # adjusts smoothness of Seaborn kernel density contours - labels = [] - - plt.figure() - - for i in range(len(cases)): - if case_name == None: - labels.append(f'Case {i+1}') - else: - labels.append(case_name[i]) - sns.kdeplot(cases[i], label=labels[i], ax=plt.gca(), bw_adjust=bw_adjust) - plt.legend() - if case_C: - plt.xlabel('Concentration ratio, $C/C_0$ [$-$]') - if plot_limits == None: - plt.xlim(0,1) - else: - plt.xlim(plot_limits) - else: - plt.xlabel('Limit-state function, $Z=\mathrm{threshold}-C/C_0$ [$-$]') - if plot_limits == None: - plt.xlim(-2,1) - else: - plt.xlim(plot_limits) - plt.ylabel('PDF [$]$') - plt.grid() - plt.show() - -def monte_carlo(Z): - """Monte Carlo analysis for sampled function of random variables. - - Returns a summary of the analysis and a plot of pf and c.o.v.. - The only input is an array of the sampled limit state-function. - Assumes that failure is when the limit-state function Z<0. - """ - N = len(Z) - Nf = np.sum(Z<0) - - if Nf == 0: - raise ValueError('No failure realizations in the sample!') - elif Nf == N: - raise ValueError('All realizations in the sample failed!') - - pf = Nf/N - - N_f_c = np.cumsum(Z<0) - N_i = np.arange(1,len(N_f_c)+1,1) - p_f_c = N_f_c / N_i - with np.errstate(divide='ignore'): - V = 1/(np.sqrt(N_i*p_f_c)) - - print(f'MONTE CARLO RESULTS\n' - f'--------------------------------------------------\n' - f' N = {N}, number of samples\n' - f' Nf = {Nf}, number of failed realizations\n' - f' pf = {pf:.3e}, estimated failure probability\n' - f' V = {V[-1]:.3f}, c.o.v. of estimated pf\n') - - plt.loglog(N_i,p_f_c) - plt.xlim(10,N) - plt.ylim(10**(np.floor(np.log10(pf)) - 1),1) - plt.grid() - plt.xlabel('Realization No.') - plt.ylabel('Estimated failure probability, $\hat{p}_f$') - plt.show() - - plt.plot(N_i,V) - plt.xscale('log') - plt.grid() - plt.xlabel('time step') - plt.ylabel('c.o.v.') - plt.show() - - return Nf,pf \ No newline at end of file diff --git a/book/reliability-component/overview.md b/book/reliability-component/overview.md deleted file mode 100644 index 4f4b4a5..0000000 --- a/book/reliability-component/overview.md +++ /dev/null @@ -1,127 +0,0 @@ -(rel_comp)= -# Component Reliability - -This Section gives a brief introduction to some of the mathematical foundations of component reliability theory, which is focused on determining the probability of a 'bad thing' happening (see {ref}`intro`). The topic has also been covered in the {ref}`prob_design` Section (especially the {ref}`prob_design_2_rv` example), and is a key part of Step 3 (quantitative analysis) in the {ref}`risk_steps`. - -## Definition - -In short, a component reliability analysis evaluates the reliability of a particular engineered object, where reliability is the complement of failure probability, $p_f$. The analysis is performed by defining a function of random variables, $g_X(x)$, and mathematically specifying a region of interest, $\Omega$, often called the failure region. The function of random variables implies a multivariate probability density function, $f_X(x)$, where integrating over the failure region $\Omega$ gives $p_f$. - -$$ -p_f=\int_\Omega f_X(x)\:\mathrm{d}x -$$ - -## A Simple Case - -The most simple reliability analysis is a univariate case with one random variable. Consider a water distribution *system* that relies on groundwater (i.e., one *component* within the system). Suppose we can model the groundwater elevation as a random variable with the normal distribution: - -$$ -h_w \: [\mathrm{m}] \sim \mathrm{N}(\mu=5,\sigma=1) -$$ - -If $h_w$ drops below 2 m, the pumps run dry, and our component fails. In this case our function of random variables is simply: - -$$ -g(X) \rightarrow g(h_w)=h_w -$$ - -and failure is defined as: - -$$ -\Omega: h_w < 2 \mathrm{m} -$$ - -The component reliability analysis is thus: - -$$ -p_f=\int_{-\infty}^{2} f_{h_w}(h_w)\:\mathrm{d}h_w -$$ - -Which is easily evaluated with the CDF of $h_w$: - -$$ -p_f=F_{h_w}(2)=\Phi\left[ \frac{2-\mu}{\sigma}\right] =\Phi[-3]=0.00135 -$$ - -This is nearly equivalent to the {ref}`prob_design_1_rv` example using river discharge from the {ref}`prob_design` Chapter, the only difference is there a load variable was considered and therefore evaluated with the complementary CDF. - -## Not Simple Cases - -The example above is 'simple' for three reasons, specifically. It has: -1. only one random variable, so the distribution of $g(X)$ is also univariate -2. the function of random variables, $g(X)$ is linear -3. the distribution of the random variables (variable, in this case) is Gaussian - -These three characteristics make component reliability problems very easy to solve. In fact, you should have already done this earlier probability courses with (co)variance propagation methods. For example, solving for the mean and standard deviation of a linear function of random variables that are each Gaussian is straightforward, as the function of random variables is also Gaussian. Unfortunately, as problems become more complex, so do the methods required for solving such problems. - -In this book we focus on simple situations with up to two variables (the 'bivariate' case) that can be solved analytically (linear functions and Gaussian random variables). Random variables are limited to continuous parametric distributions and linear measures of dependence (correlation coefficient, multivariate Gaussian). If these requirements are relaxed, we will use simulation to calculate the failure probability numerically (i.e., Monte Carlo simulation). - -With this in mind, a generic procedure for using component reliability analysis in a probabilistic design context is: - -1. determine probability distributions for each random variable (*marginal* distributions) -2. specify dependence between random variables (or independence) -3. define the function of random variables, $g_X(X)$, and region of interest, $\Omega$ -4. integrate multivariate PDF, $f_X(X)$, over $\Omega$ to evaluate probability of interest -5. check probability requirement, and if needed: -6. modify component (i.e., modify 1, 2 or 3) -7. repeat 4, 5 and 6 until the requirement is met - -```{note} -The term 'failure' here, widely used in civil engineering, is used here as a matter of convenience. Component reliability methods can also be used to find the probability of something that has nothing to do with failure, as long as it can be desribed with a function of random variables. -``` -## Two Random Variables - -The example with discharge from two rivers in the Probabilistic Design Chapter can be considered a component reliability problem with two random variables. The discharge of both tributary rivers act as loads because they both are proportional to the main design variable, $q$ or $h_{dike}$. The reliability integral is thus - -$$ -p_f=\int_\Omega f_{Q_1,Q_2}(q_1,q_2)\:\mathrm{d}x -$$ - -where the failure region $\Omega$ contains all values of $Q_1$ and $Q_2$ such that the river level exceeds the dike height: - -$$ -\Omega: h_{dike} \leq h_w(Q_1,Q_2) -$$ - -Note that if the dike were constructed to a height of 8.29 m, the component reliability would be 0.01 and the failure region would be equivalent to {numref}`design_2_rv_correct`. - - - -% save for later: compare Z=R-S to and/or and explicitly show how the generalized method can incorporate higher/lower together or values related to each other; lognormal case - -%To simple slope problem: *this example is borrowed from Moss, which is borrowed from Baecher and Christian. Both are excellent texts on risk and reliability analysis in civil and geotechnical engineering.* - -% THIS IS REMOVED FOR 2022-23 SINCE THE SEPARATE PAGES WERE NOT COMPLETED - ---- - -_The primary author for this chapter is Robert Lanzafame._ - - - - - - \ No newline at end of file diff --git a/book/reliability-component/sketch.png b/book/reliability-component/sketch.png deleted file mode 100644 index d2fd2b4..0000000 Binary files a/book/reliability-component/sketch.png and /dev/null differ diff --git a/book/reliability-system/exercise-simple-city.md b/book/reliability-system/exercise-simple-city.md deleted file mode 100644 index d8e852a..0000000 --- a/book/reliability-system/exercise-simple-city.md +++ /dev/null @@ -1,136 +0,0 @@ -# Example System - -A pre-fabricated bridge design is being considered for river crossings in a remote region of the world, as shown in Figure 1. Cities 1, 2 and 3 are labelled C1, C2 and C3, with bridges labelled B1-B4. - -```{figure} ../figures/simple-city.png ---- -width: 600px -name: exercise-simple-city ---- -``` - -**Question 1:** If the probability of failure for an individual bridge is 0.1 per year, compute the probability that you cannot drive from City 1 to City 2 - - -```{admonition} Answer -:class: tip, dropdown - -$$ - P_{f_{C1-C2}} = P_{f_{B1}} * P_{f_{B4-B3-B2}} = P_{f_{B1}} * (1 - (1 - P_{f_{B4}})(1 - P_{f_{B3}}*P_{f_{B2}})) -$$ -$$ - P_{f_{C1 - C2}} = 0.1 * (1 - (1 - 0.1)(1 - 0.1 * 0.1)) = 0.0109 -$$ -``` - -**Question 2:** If the probability of failure for an individual bridge is 0.1 per year, compute the probability that you cannot drive from City 2 to City 3. - -```{admonition} Answer -:class: tip, dropdown - -$$ - P_{f_{C2 - C3}} = P_{f_{B3}} * P_{f_{B2}} * P_{f_{B1 - B4}} = P_{f_{B3}} * P_{f_{B2}} * (1 - (1 - P_{f_{B1}})(1 - P_{f_{B4}})) -$$ -$$ - P_{f_{C2 - C3}} = 0.1 * 0.1 * (1 - (1 - 0.1)(1 - 0.1)) = 0.0019 $$ -``` - -**Question 3:** If the probability of failure for an individual bridge is 0.1 per year, compute the probability that you cannot drive from City 1 to City 3 - -```{admonition} Answer -:class: tip, dropdown - -$$ - P_{f_{C1 - C3}} = P_{f_{B4}} * P_{f_{B1-B3-B2}} = P_{f_{B4}} * (1 - (1 - P_{f_{B1}})(1 - P_{f_{B3}}*P_{f_{B2}})) -$$ -$$ - P_{f_{C1 - C3}} = 0.1 * (1 - (1 - 0.1)(1 - 0.1 * 0*1)) = 0.0109 -$$ -``` - -**Question 4:** Suppose there is a critical facility (e.g., a hospital) in City 3. How many bridges would you need to install between City 2 and 3 to ensure that the probability of someone not reaching City 3 from City 2 is less than $10^{-4}$? - -```{admonition} Answer -:class: tip, dropdown - -$$ - P_{f_{C2 - C3}} = P_{f_B}^n * (1 - (1 - P_{f_{B1}})(1 - P4)) -$$ -$$ - 0.0001 = 0.1^n * (1 - (1 - 0.1)(1 - 0.1)) -$$ -$$ - n = 3.3 -$$ - -It is necessary to install 2 more bridges between City 2 and 3. -``` - -**Question 5:** If you had 1 extra bridge to place, which bridge (i.e., B1, 2, 3 or 4) would you place it next to in order to have the biggest decrease of the probability of not reaching City 3 from City 1? - -```{admonition} Answer -:class: tip, dropdown - -I would locate the extra bridge next to Bridge 4. In this case, adding an extra element in the parallel system, making it more redundant. - -- $P_f$ next to B1 = 0.00199 -- $P_f$ next to B2 or B3 = 0.0101 -- $P_f$ next to B4 = 0.00109 -``` - -**Question 6:** If you only had 3 available bridges, which of the 4 bridges in the figure would you remove first, to cause the smallest reduction in failure probability? - -```{admonition} Answer -:class: tip, dropdown - -I would remove Bridge 2 or 3. If bridge 1 or 4 is removed, a whole path is removed from the system, while by removing only Bridge 2 or 3, there is still an available bridge to cross that river. -``` - -**Question 7:** What should the probability of each bridge be in order to make the probability of not crossing from C1 to C3 less than 0.01? - -```{admonition} Answer -:class: tip, dropdown - -$$ - P_{f_{C1-C3}} = P_{f_{B4}} * P_{f_{B1-B3-B2}} = P_{f_{B4}} * (1 - (1 - P_{f_{B1}})(1 - P_{f_{B3}} * P_{f_B2})) -$$ -$$ - 0.01 = X * (1 - (1 - X)(1 - X * X)) -$$ -$$ - X = 0.0960 -$$ - -Since the bridges have identical designs and have all been manufactured by the same contractor, positive dependence is expected between performance of bridges B1-B4. -``` - -**Question 8:** State whether or not dependence would increase or decrease the probability calculated in question 3, and explain why with 1 or 2 sentences. - -```{admonition} Answer -:class: tip, dropdown - -Increase. - -The probability of failure would increase because the system mainly works like a parallel system. In this case, when there is full dependence between the elements, the probability of failure equals the probability of failure of the strongest element. For instance, $P_{f_{\text{bridges 2, 3}}}=0.01$ for independent case and 0.1 for full dependence case. -``` - -Assume each prefabricated bridge is made up of a single road deck and 5 separate frames that are joined together. Each bridge will fail if either the road deck fails, or 1 of the frames fails. - -**Question 9:** If the probability of a frame failure is 0.01, what is the required failure probability of the road deck to make sure the bridge failure probability is no more than 0.1? - -```{admonition} Answer -:class: tip, dropdown - -$$ - P_f = 1 - (1 - P_{f_{text{deck}}})(1 - P_{f_{\text{one of the frames}}}) -$$ -$$ - P_f = 1 - (1 - P_{f_{text{deck}}})(1 - (1 - (1 - P_{f_{\text{frame}}})^5)) -$$ -$$ - 0.1 = 1 - (1 - P_{f_{text{deck}}})(1 - (1 - (1 - 0.01)^5)) -$$ -$$ - P_{f_{\text{deck}}} = 0.0536 -$$ -``` \ No newline at end of file diff --git a/book/reliability-system/overview.md b/book/reliability-system/overview.md deleted file mode 100644 index 9ecd09b..0000000 --- a/book/reliability-system/overview.md +++ /dev/null @@ -1,137 +0,0 @@ -(rel_sys)= -# System Reliability - - - -A structure or system in civil engineering generally consists of a set of *components* (also called *elements*). Whereas the previous chapter focused on the reliability of a single component, this chapter addresses reliability analysis for systems that consist of multiple components. The consequences of the failure of a component will depend on the type of system that is considered. In some cases, the failure of a component leads to failure of the whole system (progressive collapse). In other cases (and system configurations) there could be no failure if a single component fails and other components take over the function of the failed one. - -The techniques introduced in this chapter essential for carrying out step 3 in a risk analysis: quantitative analysis. - -## Series and Parallel Systems - -In reliability analysis two types of basic systems can be distinguished: series and parallel (see {numref}`sys-series-parallel`). - -```{figure} ../figures/system_series_parallel.png ---- -height: 400px -name: sys-series-parallel ---- -Series (top row) and parallel (bottom row) systems: the building blocks of system reliability analysis. -``` -Within a series system, failure of a single component will always lead to the failure of the entire system. An example is a chain, which breaks if any individual link fails. In our flood management example, a dike ring protecting a single area that is made up of multiple segments is also a series system. Within a parallel system, failure of one component can be compensated by the performance of another component; it represents the concept of redundancy. Drawing on the chain example, it would imply using more than one chain capable of holding the maximum load. An example from flood management would be to build a second dike ring inside the first dike ring. In practice, a complex system can generally be represented by means of a combination of parallel and series subsystems, just as the parallel system of multiple chains (or dikes) is a parallel system of series systems of links (or dike segments). - -```{figure} ../figures/system_series_parallel_ex.png ---- -height: 400px -name: sys-series-parallel-ex ---- -Example of series (top row) and parallel (bottom row) systems, illustrated with a chain and dike ring. Each component in the parallel case is itself a series system: links in the chain and dike segments in the dike ring. -``` - -Systems are often schematized using a system diagram, as in {numref}`sys-series-parallel`. This also illustrates the function of a system as an input-output diagram, where one can considers the ability to travel from left to right on the figure. It is analagous to many scenarios involving flow: electricity ({numref}`sys-lightbulbs`), water in pipes or transportation routes. - -```{figure} ../figures/system_lightbulbs.png ---- -width: 400px -name: sys-lightbulbs ---- -Series (left) and parallel (right) systems illustrated as a string of lightbulbs. -``` - -### Definition of Failure - -Whereas in component reliability problems we defined failure using a function of random variables, in system reliability problems, we define failure based on the continuity of the system diagram. Failure occurs when we are not able to travel from left to right on the diagram due to one or more broken links. - -## Reliability Calculations - -Equations for computing parallel and series system reliability are described here with the notation $F_i$ and $\bar{F_i}$ to denote failure and non-failure of component $i$, respectively. A system is made up of $i=1,...,n$ components where the probability of failure of component $i$ is $P(F_i)$. Note that as a concept, "system reliability" is almost always going to be quantified using the failure probability of the system, $p_{f,sys}$. This is sometimes misleading or confusing because the mathematical definition of reliability is the complement of reliability, $1-p_{f,sys}$. -### Parallel System - -A parallel system is often described as redundant since *all* components must fail to cause system failure. This is also simple to calculate as it can be described mathematically as the joint failure probability, or intersection, of all components: - -$$ -p_{f,sys} = P(F_1 \cap F_2 \cap ... \cap F_n) -$$ - -If the components are independent, this becomes - -$$ -p_{f,sys} = \prod_i^n P(F_i) -$$ - -Although we will not quantify the effect of dependence in depth here, it is easy to see semi-quantitatively that positive dependence increases the intersection probability, and therefore also increases $p_{f,sys}$. Negative dependence has the opposite effect. In fact, if parallel components are mutually exclusive the system is guaranteed to survive. The case of negative dependence is trivial in engineering reliability computation, but something that is used to motivate the incorporation of resilience or robustness in our risk reduction decisions. - -### Series System - -A series system fails if *any* component fails, which is - -$$ -p_{f,sys} = P(F_1 \cup F_2 \cup ... \cup F_n) -$$ - -For two components this can easily be re-written as - -$$ -p_{f,sys} = P(F_1) + P(F_2) - P(F_1 \cap F_2) -$$ (sys_p_series) - -Although it is straightforward to write out terms for 3 or more components, it is easier to re-write the union formulation as the complement of joint *survival* of the system: - -$$ -p_{f,sys} = 1 - P(\bar{F}_1 \cap \bar{F}_2 \cap ... \cap \bar{F}_n) -$$ - -As $\bar{F}_i=1-F_i$, we arrive at the following simple relationship: - -$$ -p_{f,sys} = 1 - \prod_i^n \left(1-P(F_i)\right) -$$ - -The influence of dependence on a series system is most easily understood through consideration of {eq}`sys_p_series`, which allows a direct analogy to the parallel case through the intersection term. With positive dependence, the system failure probability decreases - -% add exercise to show equivalence for 3 or more components. - -### Quantification of Dependence - -{numref}`sys_dependence` quantifies the effect of dependence on the join probability of failure of two components. The joint failure probability is calculated using the multivariate normal distribution which has a linear dependence measure, the correlation coefficient, $\rho$. The blue line shows the series system failure probability, equivalent to {eq}`sys_p_series`. The figure allows one to evaluate the quantitative effect of dependence on series and parallel systems, and even illustrates the bound of $p_{f,sys}=P(F_1)$ for the case of $\rho=+1$. - - -```{figure} ../figures/system-corr-coeff.PNG ---- -width: 400px -name: sys_dependence ---- -Effect of correlation coefficient on failure probability for a series system via joint failure, $P(F1 \cap F2)$ (computed with a Gaussian copula). The arrow is located at $\rho=+0.9$, where $P(F1 \cap F2)=0.003$. -``` - -````{admonition} Tips for Interpreting the Figure -:class: tip, dropdown - -{numref}`sys_dependence` is interesting because it shows the effect of dependence on *both* series and parallel systems, since they are related with {eq}`sys_p_series`, the value that is shown in the blue line. Note that the distance between the blue line and the top reference line is the value of the intersection, $P(F1\cap F2)$ (also called the "joint" or "and" probability). Note that without a joint probability distribution (in this case a bivariate Gaussian), you can't compute the joint probability of two events, except for three special cases, the vertical black lines in the figure---do you know what those values are? This is related to the concepts of dependent, mutually exclusive and statistically independent events, which are easy to confuse with each other. - -It is also common to think about dependence in the sense of how "one event happens given that the other event has happened," but this is not quite right. Dependence is describged simply by the definition of conditional probability - -$$ -P(F1 \cap F2) = P(F1|F2)\cdot P(F2) -$$ - -which means the correct statement is that dependence quantifies how the "*probability* of one event *changes* (or not) given that the other event has happened." -```` - -## Chapter Overview - -This page contains a brief introduction to the computation of failure probability for series and parallel systems, and describes the role of dependence. The following section illustrates these concepts with a simple exercise. - -### Additional Information - -The word 'system' in the title of this chapter refers to a reliability analyses made up of more than one distinct components. It may or may not be the same as the system for which the risk analysis is being done. For example, in the flood risk case we look at a dike ring, which is a series system of dike segments. Each dike segment can fail in a variety of ways (e.g., sliding or eroding), where if *any* of these types of failure occurs, the dike fails; a series system. Thus, the dike ring is a series system, where each component also a series system. - -% add a note about systems of systems, and being able to simplify problems. add figure too (there was one in Chapter 3, originally) - -%Sometimes the distinction between system and component reliability is made because components are very different. Sometimes it is a matter of convenience, as two components may share a number of random variables through their respective limit-state functions that influence failure. - -System reliability analysis can look very similar to component reliability problems, especially when various combinations of discrete and continuous random variables are incorporated. In reality, all of these problems are generalized by the concept of a multivariate probability distribution. The concepts are separated following conventions in engineering practice, as well as for the convenience of illustrating analytic and numerical solutions. - ---- - -_The primary author for this chapter is Robert Lanzafame._ \ No newline at end of file diff --git a/book/risk-analysis/definition.md b/book/risk-analysis/definition.md deleted file mode 100644 index 046f09b..0000000 --- a/book/risk-analysis/definition.md +++ /dev/null @@ -1,119 +0,0 @@ -(risk_definition)= -# Definition of Risk - -Almost all activities in life are characterized by some level of risk. Especially in the design and management of engineering systems, risk and safety are key concepts and need to be taken into account explicitly. In social discussions no unambiguous meaning is assigned to the concept of risk. Two definitions given in the Oxford dictionary are: 1) a situation involving exposure to danger; 2) the possibility that something unpleasant or unwelcome will happen. - -The first definition focuses on the consequences, the second on the possibility or probability. Quantifying and evaluating risks based on either probabilities or consequences (not both) is less realistic. For example, the risk of losing € 100 with a probability of 50% is different than the risk of losing € 1000 with the same probability. Also, the risk associated with losing a given sum of money will depend on the probability of the event. -An often-used definition considers risk as an expected value: - -*Risk is the probability of an undesired event multiplied by the consequences.* - -The unit of risk now depends on the units of probability and consequences, where probability of an event is generally expressed as the probability per unit time, for example per year. The consequences of an undesired event often measure a diverse array of damages, such as material, ecological, injuries and fatalities. In many applications engineering consequences are expressed by means of a monetary value, in which case the unit of the risk (or expected value, $E(d)$) then becomes € per year. For a case with one event scenario $i$ with probability $p_{i}$ it yields: - - $$ - E(d_i) = p_{i} \cdot d_{i} - $$ - -A more general definition of risk has been given by Kaplan and Garrick (1981): - ->Risk is a set of scenarios, $s_{i}$, each of which has a probability, $p_{i}$, and a consequence, $d_{i}$. - - -This definition allows the use of various so-called risk metrics (or risk measures) to quantify or depict risk. The expected value of the damage for a set of multiple discrete scenarios $i=1,....,n$ , can be expressed as: - - - -```{math} -:label: eq_risk_definition - -E(d) = \sum_{S_{i=1}}^{n}p_{i} \cdot d_{i} -``` -For the set of scenarios considered, the expected value quantifies risk precisely; however, it does not give insight in the magnitude of probability and consequences and the contribution of individual scenarios. For example, a single value does not indicate whether the risk is governed by a large number of scenarios with small consequences, or a few scenarios with large consequences and low probabilities. Therefore, an often-used companion risk-based tool is the risk curve, which shows the probability of exceedance and consequence for all scenarios. A well-known example of such a risk curve is the *FN curve*, which displays the probability of exceedance associated with $N$ (human) fatalities, schematized in {numref}`fn_simple01`. It is easy to compare the probability of exceeding a relatively low or high number of fatalities. - -```{figure} ../figures/fn_simple01.svg ---- -height: 600 -name: fn_simple01 ---- -FN curve, showing the probability of exceedance of a certain number of fatalities N on Log-Log scale. -``` - -The FN curve was originally introduced in the 1960's for the assessment of risks in the nuclear industry {cite}`farmer1967,kendall1977` and is now used to display and limit risks in a wide variety of industries around the world. It is an extremely useful way to quantitatively compare risk associated with a broad range of scenarios, and to make decisions. A famous example of this is shown in {numref}`risk-curve-baecher`, which compares the risk estimated for a wide variety of engineering infrastructure. This figure is described further in the {ref}`risk_curve` Section, and also illustrates the concept of acceptable risk, which is discussed in the Section on {ref}`safety_standards`. In short, it allows one to begin answering the question 'how safe is safe enough?' - -```{figure} ../figures/risk-curve-baecher.PNG ---- -height: 400px -name: risk-curve-baecher ---- -Risk curve for various engineering projects, showing probability of exceeding a specific number of fatalities, $N$, and damages, $, on a Log-Log scale, making it both a FN and FD curve; see {ref}`risk_curve` Section. Source: {cite:t}`baecher2003`, based on {cite:t}`baecher1982` and described in {cite:t}`baecher2021`. -``` - -## Hazard, Vulnerability and Exposure - -Engineering disciplines that are focused on decision making where natural hazards play a significant role often define risk as the combination of hazard, exposure and vulnerability, as shown in {numref}`risk-hazard`. -* Hazard: A dangerous phenomenon, substance, human activity or condition that may cause loss of life, injury or other health impacts, property damage, loss of livelihoods and services, social and economic disruption, or environmental damage -* Vulnerability: The characteristics and circumstances of a community, system or asset that make it susceptible to the damaging effects of a hazard -* Exposure: People, property, systems, or other elements present in hazard zones that are thereby subject to potential losses - -```{figure} ../figures/risk-hazard.svg ---- -height: 200px -name: risk-hazard ---- -Alternative definition of risk as intersection of hazard, exposure and vulnerability. Risk is the small triangular-shaped area where all three circles overlap. -``` -Often these terms are useful for framing qualitative discussions around complex topics where a quantitative analysis may be out of reach, for example, as done in IPCC reports on climate change {cite:p}`cardona2012`. However, they can also be used to simplify the risk analysis by subdividing it into parts that are (computationally) independent. An analytic expression can easily be formulated by expanding the probability term of Equation {eq}`eq_risk_definition`: - -```{math} -:label: eq_risk_definition_HEV - -p_{i} = P(N_i,E_j,H_k) = P(N_i|E_j,H_k) \cdot P(E_j|H_k) \cdot P(H_k) -``` - -where $N_i$, $E_j$ and $H_k$ are the vulnerability (fatalities), exposure and hazard of scenario $i$, respectively. Combining with Equation {eq}`eq_risk_definition` and taking the sum over all combinations of variables ($i$, $j$, $k$) would give the total risk. In the case of our flood management case, an example of each term could be: -- Hazard, $H_k$: a high water level. -- Exposure, $E_j|H_k$: breach (failure) of a dike due to the high water level, $H_k$. -- Vulnerability, $N_i|E_j,H_k$: fatalities given the broken dike and high water level. $N$ is usually modeled as a random variable as it is dependent on factors such as evacuation effectiveness and flood warning systems. - -% Point out that this formulation simplifies the calculation, promots the use of tools like fragility curves, and give earthquake hazard assessment as an example (DRMS?). - -## Other Risk Definitions - -This book uses Equation {eq}`eq_risk_definition` as the primary definition of risk. However, it is useful to highlight some risk concepts used in other domains. - -Within economics, risk is generally associated with a deviation from the expected return or the probability of loss. In social sciences risk is often considered as a contextual notion or social construct. {cite:t}`vlek1996` has summarized 11 formal definitions used in social sciences, see Table {numref}`risk_definitions`. In some of these definitions (e.g. numbers 2 and 4) the perceived seriousness of the undesired consequences plays an important role. Examples of other, more informal risk definitions used in psychology are “the lack of perceived controllability”, “set of possible negative consequences” and “fear of loss” {cite:p}`vlek1996`. - -Substantial research has also focused on factors that determine the perception of risk (e.g. {cite:t}`slovic1987`, {cite:t}`vlek1996`) including: degree of damage, controllability of and familiarity with hazards, extent of benefits from an activity, and voluntariness of exposure. - -:::{list-table} Formal definitions of risk used in social sciences {cite:p}`vlek1996` -:header-rows: 1 -:name: risk_definitions - -* - No. - - Definition -* - 1 - - Probability of undesired consequence -* - 2 - - Seriousness of (maximum) possible undesired consequence -* - 3 - - Multi-attribute weighted sum of components of possible undesired consequences -* - 4 - - Probability $\cdot$ seriousness of undesired consequence (‘expected loss’) -* - 5 - - Probability-weighted sum of all possible undesired consequences (‘average expected loss’) -* - 6 - - Fitted function through graph of points relating probability to extent of undesired consequences -* - 7 - - Semi variance of possible undesired consequences about their average -* - 8 - - Variance of all possible consequences about mean expected consequence -* - 9 - - Weighted sum of expected value and variance of all possible consequences -* - 10 - - Weighted combination of various parameters of the probability distribution of all possible consequences -* - 11 - - Weight of possible undesired consequences (‘loss’) relative to comparable possible desired consequences -::: - diff --git a/book/risk-analysis/overview.md b/book/risk-analysis/overview.md deleted file mode 100644 index 2fd0574..0000000 --- a/book/risk-analysis/overview.md +++ /dev/null @@ -1,13 +0,0 @@ -# Risk Analysis - -This book splits risk into two parts: risk *analysis* and risk *evaluation.* This chapter considers the analysis of risks from a broad perspective, beginning with definitions and key steps of a risk analysis, illustrated quantitatively through an FN curve. The next two chapters explore quantitative analyses (component and system reliability) before returning to risk evaluation concepts of decision theory, cost benefit analysis and safety standards, where the principal focus is on making decisions and answering the question 'how safe is safe enough?' - ---- - -_The primary authors for this chapter are Bas Jonkman and Robert Lanzafame._ - -% The relationship between safety standards and engineering design is indicated in section 3.6...may be useful to add - -% It is noted that a (probabilistic) risk analysis is different from a (deterministic) scenario analysis. A risk analysis is based on quantitative analysis of all (known) undesired events and their probabilities and consequences. A scenario analysis considers one (or a limited number) of design scenarios, often without considering its failure probability. Both approaches are complementary, as a scenario analysis considers one of the scenarios from the risk analysis. - -% In the Netherlands, scenario analysis is often used for evaluating disaster preparedness and designing the capabilities of emergency management services. For example, in the design of the Green Heart Tunnel which is a part of the high speed rail line in the Netherlands, a single accident scenario was chosen to design the emergency exits out of the tunnel. Analysing a high impact, low probability scenario in detail may provide helpful clues about the effectiveness of particular safety measures or crisis management actions. While such analyses may be helpful, it would be wrong to assume that such high-impact, low probability scenarios should always be properly manageable by emergency responders. This is because the probability of harm should be an integral part of any cost-benefit or cost-effectiveness analysis (Jongejan et al., 2011). \ No newline at end of file diff --git a/book/risk-analysis/risk-curves.md b/book/risk-analysis/risk-curves.md deleted file mode 100644 index b76dc49..0000000 --- a/book/risk-analysis/risk-curves.md +++ /dev/null @@ -1,86 +0,0 @@ -(risk_curve)= -# Risk Curve - -As introduced in the {ref}`risk_definition` Section, the risk curve is useful for evaluating the expected damages for a wide range of scenarios. In contrast to the total expected damages, it allows the comparison of relative magnitude of probability of occurrence and associated consequences. An FN curve tends to be the most widely used, where the 'N' refers to number of fatalities and the 'F' in comes from the CDF of the probability distribution of $N$, $F_N(n)$, although the curve itself actually represents the complementary CDF, $1-F_N(n)$. It is often plotted on a log-log scale to allow comparison over a wide range of scenarios. While in theory a risk curve can be derived from the probability density function (or probability mass function for discrete cases), the distribution of damages is rarely known and must be approximated by considering a finite and suitable set of discrete events. Thus, in practice, the curve is constructed using scenarios as defined previously in our risk definition (Equation {eq}`eq_risk_definition`). - -Although the FN curve is widely used, the risk curve is not exclusively applied to evaluate expected number of fatalities, $N$. In principle any measurable quantity can be used to evaluate risk, referred to as a *metric,* although it can be difficult to apply this to some situations. For example, assessing the value of environmental characteristics can be challenging because the benefit is not easily related to a measurable quantity. The area of impacted wetland habitat during a flood (e.g., km$^2$) can be used as a risk metric, but this may not properly represent actual damage, which may recover quickly or slowly depending on the frequency of inundation. Financial damage (e.g., €) is often considered as a risk metric, in which case the FN curve is called an *FD curve.* - -```{admonition} Fatalities and Damages -:class: tip, dropdown -In some cases it is useful for planning and design purposes to equate $N$ and $D$, but this places a specific financial value on human life, which raises difficult moral and ethical concerns. This topic is discussed further in the {ref}`value_human_life` Section. -``` -%(risk_curve_examples)= - - -(risk_curve_famous)= -## A Famous Risk Curve - -A risk curve is often useful because it can convey a large amount of complex information in an easily recognizable format. University lectures and conference presentations around the world which focus on risk, especially for civil engineering applications, will often begin with a casual reminder that 'risk is probability times consequences' and show some version of a risk curve. {numref}`risk-curve-baecher-2` is the most famous risk curve, having been shared widely over the last decades, perhaps because it so nicely compares a wide range of engineering projects. - -```{figure} ../figures/risk-curve-baecher.PNG ---- -height: 400px -name: risk-curve-baecher-2 ---- -Risk curve for various engineering projects, showing probability of exceeding a specific number of fatalities, $N$, and damages, $, on a Log-Log scale, making it both a FN and FD curve; this figure is also included in the {ref}`risk_definition` Section. Source: {cite:t}`baecher2003`, based on {cite:t}`baecher1982` and described in {cite:t}`baecher2021`. -``` - -{numref}`risk-curve-baecher-2` was created as part of a risk analysis for a petrochemical storage facility in Tokyo Bay, Japan, where large tanks, constructed on soft soils (hydraulic fill), are vulnerable to damage during an earthquake. Of primary concern was to prevent the petrochemicals entering bay waters, thus not only failure of the storage tanks, but also the containments systems in place to collect spilled material (a complicated system reliability problem). The client needed to convince the regulator that the final design was sufficient for keeping the risk of loss of containment to a sufficiently small level, which the project team was able to do by comparing the risk calculated for the Tokyo site to other engineering works around the world. The figure clearly illustrates what the estimated risk is for each project, and by making the assumption that these already-constructed projects provide a level of safety that is acceptable to society (primarily via regulatory agencies), the 'acceptable' line can be used to approve other projects. This concept of acceptable standards based on risk curves is covered in depth in the Section on {ref}`safety_standards`. - -The origin of this figure was described a Terzaghi Lecture by Professor Gregory Baecher, which can be viewed on YouTube: [*IFCEE 2021: Karl Terzaghi Lecture: Greg Baecher: Geotechnical Systems, Uncertainty, and Risk*](https://www.youtube.com/watch?v=Y5w1p3uAe0I&ab_channel=Geo-InstituteofASCE) {cite:p}`baecher2021`}. The introduction to the Tokyo Project begins at [16:16](https://www.youtube.com/watch?v=Y5w1p3uAe0I&t=976s), and the explanation of the risk curve is given at [27:00](https://www.youtube.com/watch?v=Y5w1p3uAe0I&t=1620s); however, the entire lecture is well worth listening to and closely related the subject of this book. - -## Construction of an FN Curve - -The following three figures illustrate the computation of an FN curve for a system with two mutually exclusive event scenarios: -- Accident 1 with $N_{1}=10$ fatalities and a probability of $P_{1} = 10^{-2}$ per year -- Accident 2 with $N_{2}=100$ fatalities and a probability of $P_{2} = 10^{-3}$ per year - -First, the probability mass function is created $f_N(n)=P(N=n)$, taking care that the probability of no fatalities is included: - -$$ P(0) = 1 - P_{1} - P_{2} = 1 - 0.01 - 0.001 = 0.989 $$ - -The cumulative distribution function, $F_N(n)=P(N\leq n)$, can thus be easily computed, as well as the probability of exceedance, $1-F_N(n)$, also known as the *FN curve.* Note that if a risk metric such as damage in Euros was being used, we would call this the *FD curve* and use $D$ to denote the random variable, as in $f_D(d)$ and $F_D(d)$ - -While the curves below illustrate probability and consequences associated with specific scenarios, the expected value of the distribution can be computed, which is equivalent to the area under the FN curve. This is useful can be used to assess the entire system. For this example, the expected value of fatalities per year for all scenarios can be computed as follows: - -$$E(N) = P_{1}N_{1} + P_{2}N_{2} = 0.2\quad \textsf{(fatalities per year)}$$ - -```{figure} ../figures/ex_FN_curve_step_01_py.svg ---- -width: 400 -name: ex_FN_curve_step_01 ---- -Probability mass function (PMF), $f_N(N)$. -``` - -```{figure} ../figures/ex_FN_curve_step_02_py.svg ---- -width: 400 -name: ex_FN_curve_step_02 ---- -Cumulative distribution function (CDF), $F_N(n)$. -``` - -```{figure} ../figures/ex_FN_curve_step_03_py.svg ---- -width: 400 -name: ex_FN_curve_step_03 ---- -Exceedance probability (FN curve), $1-F_N(n)$. -``` - -```{admonition} Practice Exercise -:class: tip -You can practice constructing a simple FN curve in {ref}`ex_fn_curve`, although some of the questions require knowledge of limit lines, introduced in the {ref}`safety_standards` Section. -``` \ No newline at end of file diff --git a/book/risk-analysis/steps.md b/book/risk-analysis/steps.md deleted file mode 100644 index 154fe6c..0000000 --- a/book/risk-analysis/steps.md +++ /dev/null @@ -1,144 +0,0 @@ -(risk_steps)= -# Steps in a Risk Analysis - - -The previous section made it clear that risk is a function of probabilities and consequences. Risk analysis, therefore, consists of an analysis of probabilities and consequences associated with undesired events in a given system. Alternative terms used in literature are risk assessment and quantitative risk analysis (QRA). - -A risk analysis is carried out because involved parties (e.g. designers, managers, decision makers) want to identify and evaluate the risks and decide on their acceptability. Outcomes of risk analysis can be used in the design process to decide on the required safety levels of new systems (e.g. a new tunnel) or to support decisions on the acceptability of safety levels and the need for measures in existing systems (e.g. a flood defence system). A quantitative measure of some form is needed to transfer decisions on acceptable safety into a technical domain {cite:p}`voortman2004`, such as the height of a flood defence or the strength of a building. In addition, risk analysis can be used to analyse the effectiveness of risk reduction measures, including management and maintenance strategies. Whereas the primary goal of a risk analysis is often to support rational decision-making regarding risk-bearing activities {cite:p}`apostolakis2004`, it also provides insight in the way a system may fail. As such, it can also serve as a tool of communication and management. Insights drawn from a risk analysis can be used to optimize system design and management and often there is a direct link to quality assurance. - -In general, the following elements can be identified within a risk analysis, (based on: {cite:t}`CUR1997`, {cite:t}`CIB2001`, {cite:t}`faber2003` and {cite:t}`jongejan2008`): - -1. System definition and setting the scope and objectives of the analysis; -2. Qualitative analysis of undesired events; -3. Quantitative analysis of the risk; -4. Risk evaluation (of the acceptability of the risk) - -Each of these steps is illustrated in {numref}`risk-steps` and described in more detail below, providing context for the following chapters in this book. In addition to the risk analysis of a given system, *risk management* also includes the element ‘risk reduction and control’. Depending on the outcome of the first four steps of the analysis, measures can be taken to reduce the risk, which will lead to changes in the system configuration and risk level. Steps 1--4 are often repeated several times with adjusted system specifications to obtain an optimal design. - -```{figure} ../figures/risk-steps.PNG ---- -width: 250px -name: risk-steps ---- -Schematic view of steps in risk analysis (risk assessment) and risk management. -``` - -## 1. System definition - -This step entails the definition and description of the system as well as the scope and objectives of the analysis. Usually a system is divided into components and subsystems, which can be schematised graphically. Further information on the decomposition and analysis of system is provided in the {ref}`rel_sys` Chapter of this book, and illustrated through the example exercises. - -A system can be represented in terms of physical components, organizations and users, and an external environment. In order to analyse failure and risks, not only physical components, but also organizations and operators and users need to be considered (see e.g. {cite:t}`bea1998`), as different groups of organizations and persons will be involved in different roles. Consider the aviation industry, where professionals may be responsible for operation and management of the system (e.g. the pilots and crew in an aircraft), but important roles are also played by the users of a system (passengers) and external parties (people living near the airport exposed to risk and noise). Each group has a different relationship and attitude towards the risk, which could affect its acceptability. For example, a higher risk might be acceptable for pilots and crews in an aircraft (who derive a direct benefit from flying) than for regular passengers. Finally, the external environment (e.g. wind or runway conditions) will determine the loads on the system and affect potential failure mechanisms. - -## 2. Qualitative analysis - -In this step, potential hazards, undesired events, failure mechanisms and scenarios are identified and described. An important goal of this phase is to gain insight, as complete as possible, into all possible undesired events and their consequences. For most systems, multiple undesired events can be distinguished. For example, two events with different impacts that can both lead to flooding of a polder are 1) the inflow of large amounts of water due to a dike failure; 2) the inflow of smaller amounts of water when a sluice gate is not closed. - -Failure occurs when a system no longer fulfils one or more desired functions, where the failed state can be reached through different failure mechanisms (or failure modes). For example, a dike can fail due to overtopping, but also due to geotechnical failure mechanisms such as instability or piping. A **limit state** is a condition of a structure beyond which it no longer fulfils the relevant design criteria {cite:p}`eurocode2001`, of which two types are distinguished in practice: serviceability and ultimate limit states (SLS and ULS, respectively). - -- **Ultimate limit state (ULS)**: failure or collapse of a system or structure occurs, for example, the breakwaters of a harbour entrance are destroyed as a result of extreme conditions. An example from structural engineering is the collapse of a roof of a building. -- **Serviceability limit state (SLS)**: exceedance leads to temporary and/or partial failure. For example, inability to use the harbour due to waves that are (temporarily) too high. Another example could be too much vibration of a structure, such that users experience discomfort. - -Further information on the use of the SLS and ULS concepts in civil engineering is included in the {ref}`rel_comp`. - -In a risk analysis, it is very important to get an overview of the various undesired events and failures before proceeding with a quantitative analysis, as many accidents in practice are caused by failing to identify failure modes. Unfortunately, creating a complete list of threats and failure modes is not an easy task. Support for this process can be found through are failure databases, literature studies, interviews, experiences with comparable systems, brainstorm sessions, et cetera. In addition, formal techniques for systematically identifying undesired events exist, such as Failure Modes and Effects Analysis. - -## 3. Quantitative Analysis - -The probabilities and consequences of the undesired events identified in step 2 are quantified in this step, and risk is quantified in as expected damage(s) or with a risk graph as described in the next Section. - -### Probability - -In simple cases the probability can be computed directly, but generally the undesired event must broken down into multiple steps or processes to facilitate the computation of probability, which are then recombined using integration or the total probability theorem. Such an approach results in systems of systems, each of which is composed of individual *components* (or elements), each of which is typically evaluated using the limit state concepts defined above. Often this the probability of a limit state being exceeded is referred to as the probability of failure, which of course reflects the component, not necessarily the system. Techniques for computing the probability of failure are covered in the {ref}`rel_comp` and {ref}`rel_sys` Chapters. - -Whereas the most critical aspect of the previous step is identifying the most important failure modes, in the quantitative analysis it is critical to precisely define the quantity of interest, as ambiguity can lead to misunderstandings and incorrect assessment of risk. Often such ambiguities have a direct relationship with the conditional terms used inthe probability computations, which imply specific statements about dependence (or independence). Consider the previous example of river level exceeding the dike height $P(h_w>h_{dike})$: the probability can be significantly different if a design lifetime of one year or fifty years is considered. In addition, the time of year may also play a role as different types of floods may occur. If the seasonal probability of flooding is binary and mutually exclusive with wet and dry season each lasting 6 months of the year, the following expression holds (all values computed an a *per year* basis): - -$$ -P(h_w>h_{dike}) = 0.5 \cdot P(h_w>h_{dike}|\mathrm{wet}) + 0.5 \cdot P(h_w>h_{dike}|\mathrm{dry}) -$$ - -Thus, if the risk analysis were only focusing on floods during the wet season, the probability of flooding would be overestimated by a factor on the order of 2 (assuming the probability is roughly equal in dry and wet seasons). - -### Consequences - -After failure has been defined, consequences of the events are quantified. First, physical effects associated with an undesired event are considered, sucha s heat and/or smoke from a fire, or inflow of water due to dike breach. Depending on the exposure of people or objects to the physical effects, damages, life loss or other impacts may occur. As an example, a specific consequence, $D$, of dike failure during a flood is considered as a sequence of three discrete events: - -- The probability that a dike fails, $P(E_{1})$ -- The conditional probability that water flows into the polder given a dike breach $P(E_{2}|E_{1})$ -- The probability of damage given dike breach and inflow into the polder $P(D|E_{1}\cap E_{2})$ - -The probability of damage can now be computed by combining these terms: - -$$P(D)=P(E_{1})P(E_{2}|E_{1})P(D|E_{1}\cap E_{2})$$ - -which is analagous to the hazard, vulnerability and exposure formulation of risk introduced in the previous Section. - -Multiple types of consequences can be caused by one disaster, which are illustrated in {numref}`risk_damage_types` for the failure of a flood protection system. The damage is divided into tangible and intangible damage, depending on whether or not the losses can be assessed in monetary values. Another distinction is made between the direct damage, caused by physical effects of the event, and damages occurring outside the directly exposed area. The latter occurs when companies outside an impacted area experience damages, due to loss of demand from customers in the flooded area. In a risk analysis it is desirable to take into account a complete set of impacts; unfortunately many of the items from the table cannot be easily quantified, if at all, thus the quantitative analysis and risk evaluation are often focused on economic damages and life loss. - -:::{list-table} General classification of damages, based on {cite:p}`vrouwenvelder1996` -:header-rows: 1 -:name: risk_damage_types - -* - - - Tangible - - Intangible -* - Direct - - - - -* - - - Residences - - Fatalities -* - - - Structure inventory - - Injuries -* - - - Vehicles - - Animals -* - - - Agriculture - - Utilities and communication -* - - - Infrastructure and other public facilities - - Historical and cultural losses -* - - - Business interruption - - Environmental losses -* - - - Evacuation and rescue operations - - -* - - - Reconstruction of flood defences - - -* - - - Clean up costs - - -* - Indirect - - - - -* - - - Damage for companies outside the exposed area - - Societal disruption -* - - - Substitution of production outside the area - - Damage to government -* - - - Temporary housing of evacuees - - -::: - -## 4. Risk Evaluation - -In the risk evaluation phase a decision is made whether the risk is acceptable or not and whether risk reduction measures should be implemented. In other words, a direct answer is sought to the question “how safe is safe enough?” {cite:p}`starr1967`. Results of the quantitative analysis provide input for risk evaluation and decision making, and different quantitative approaches can be used to support risk evaluation, which are outlined here and introduced formally in the {ref}`risk_eval` Chapter. - -**Decision Analysis**: Also called 'decision making under uncertainty,' this approach aids the decision-making process by recording different possible outcomes along with the associated risks, costs and benefits, leading to the optimal selection from a number of alternatives. Often visual tools are used such as a risk matrix or decision tree. - -**Cost Benefit Analysis**: costs and benefits of risk reduction measures are considered. When a large number of design choices are possible, an **economic optimization** can be applied to select an optimal system design, based on the costs and benefits of risk reduction. - -**Safety Standards**: risk is compared with predetermined safety standards to directly determin acceptability. Such standards are typically imposed by government organizations or standards of practice and often focus on loss of life as the primary risk metric. - -Given the nature of the key question "how safe is safe enough?", several political, psychological and social processes play a role in the evaluation of risk---in other words: risk evaluation is not purely a technical process, but involves many subjective elements and decisions. One difficulty facing regulators is that preferences and risk attitudes within society may diverge and that costs and benefits may not be distributed evenly, and that a single, collective decision has to be based on strongly divergent individual preferences. In practice, this implies that the establishment of collective decision making procedures is inevitably a political process. This ambiguity can also be found in the numerous interpretations of “the” precautionary principle, which is interpreted by some as a decision making criterion that requires proof of harmlessness (a scientific impossibility), whereas it is seen by others as a decision making procedure that puts emphasis on dialogue and stakeholder involvement, (e.g. {cite:t}`jongejan2008`). - -## 5. Risk Reduction and Risk Control - -If the risks evaluated in first four steps of a risk analysis are considered unacceptable, several forms of risk reduction can be implemented, such as changes to the engineered system, or changes to its organization and management. It can be helpful to determine how risk can be controlled, for example by monitoring, inspection or maintenance. - -Post-accident analysis indicates that human and organizational errors are still a major cause of failure in civil engineering systems, and it seems that the only suitable way to reduce human errors is by the incorporation of sufficient control in different phases of the construction process {cite:p}`taerwe1986`, and by a thorough education of all personnel involved. Therefore, an extensive interaction between the safety methodology and quality management is a necessity in order to guarantee the safety of infrastructure. \ No newline at end of file diff --git a/book/risk-evaluation/cost-benefit.md b/book/risk-evaluation/cost-benefit.md deleted file mode 100644 index cee0619..0000000 --- a/book/risk-evaluation/cost-benefit.md +++ /dev/null @@ -1,138 +0,0 @@ -(cost_benefit)= -# Cost Benefit Analysis - -This section deals with simplified cost benefit analysis for risk reduction interventions in the engineering domain. An important question in evaluating (engineering) projects is whether the benefits outweigh the costs. Cost benefit analysis (CBA) is generally used for appraisal of a wide range of effects of projects or interventions in order to support decision making. The cost benefit analysis starts with defining the system and existing situation. Then, a broad range of effects of the proposed project and intervention can be identified. - -{numref}`costs_and_benefits` below shows an overview of effects of the Delta works that were built after the 1953 flood disaster in the Netherlands. The main aim of the delta works was to provide flood protection to the Southwest of the Netherlands. However, other effects included the agricultural benefits to the region (benefits) and the effects on environmental quality in the estuaries in which dams were built (costs or negative effects). - -```{list-table} Costs and benefits of the delta works -:header-rows: 1 -:name: costs_and_benefits - -* - Costs - - Benefits -* - Construction and maintenance costs - - Reduction of flood risk (damage, loss of life) -* - Loss of environmental quality - - Improvement of infrastructure -* - - - Recreation -* - - - Agricultural benefits -* - - - Economic stimulus for the region -* - - - Economic stimulus for the water engineering sector -* - - - National Pride -``` - -A choice has to be made for which effects in the CBA are evaluated in monetary terms. For some items, such as construction costs or economic risk reduction (see below) this is straightforward. For other items such as environmental effects or reduction of risk to life, approaches for monetary evaluation exist, but they are not standardized or undisputed. - -## Risk Reduction via Probability - -When considering investments that primarily focus on risk reduction (e.g. dike reinforcement or reinforcing of buildings for earthquakes), the main benefits will consist of the reduction of expected economic damages. For a measure to be cost effective, the investments should be smaller than the risk reduction. - -$$ -I < \Delta E(D) -$$ (investment) - -where: - -- $I$ is investments -- $\Delta E(D)$ present value of risk reduction - -This formula can also be used to calculated the benefit/cost ratio, i.e. $\Delta E(D)/I$, which should be greater than 1 for cost effective projects. Note that all costs and the risk reduction are given in terms of present value with a unit of €. - -For investments that focus on prevention (i.e. reducing the failure probability of the system) {eq}`investment` can be formulated as follows. - -$$ - I < (P_{f,0} - P_{f, new}) D -$$ - -where: - -- $P_{f,0}$ the initial failure probability -- $P_{f,new}$ the failure probability after risk reduction investment - -```{admonition} Example: Drainage of a construction site - costs and benefits -The example from the previous section could also be formulated as a simplified cost-benefit analysis. The same values for the variables are used. The costs of the drainage are €150,000. The benefits are equal to the risk reduction, i.e. - -$$ - \Delta E(D) = (P_{f,0} - P_{f,d}) = (0.12 - 0.04)\text{€} 5,000,000 = \text{€} 400,000 -$$ - -This shows that costs are smaller than the risk reduction benefits, i.e. $I<\Delta E(D)$. The benefit/cost ratio equals €400,000/€ 150,000 = 2.66 - -One can easily show that the investment would just be acceptable if the benefits and costs are equal, i.e. when the benefit / cost ratio equals 1. This would still be the case if the probability of failure with drainage equals $P_{f,d} = 0.09$. -``` - -## Risk Reduction via Damages - -Other types of interventions do not affect the probability of an accident, but focus on reducing the damages. They are often indicated as mitigation. An example in the field of flood management concerns raising buildings instead of reinforcing the dikes. In this case the criterion becomes: - -$$ -I < P_{f,0}(D_0 - D_{new}) -$$ - -where: - -- $D_0$ the initial damage [€] -- $D_{new}$ the damage after investments in reducing the consequences [€] - -## Net Present Value - -The foregoing assumes that both the costs and benefits are expressed in the same unit, generally in the form of a present value [€]. The net present value (NPV) represents the sum of the present values of the benefit and cost cash flows over a period of time. In engineering we often deal with situations with larger initial investments, whereas the risk reduction benefits are spread out over a longer time period. For example, when a government invests this year in flood protection, the costs are made in year 0, but the benefits will be spread over the coming decades. - -For such situations the failure probability is generally expressed per unit of time, mostly per year. That means that the risk (reduction) is expressed in terms of € per year, whereas the initial investments have the unit of €. The net present value of cost or benefit values over a future range of years can be calculated with {eq}`npv`. To calculate the net present value NPV [€] a discount rate should be used. The discount rate represents a required return on an investment. - -$$ - NPV = \sum_{t=1}^{T} \frac{C_t}{(1+r)^t} -$$ (npv) - -where: - -- $C_t$ the costs in year $t$ [€] -- $T$ the reference period [years] - -```{admonition} Interest Rates -:class: tip, dropdown -The discount rate, $r$, is analagous to opportunity costs and interest rates that you may be familiar with from the field of economics. It provides a way to evaluate the true cost of investing in a particular project over a long time period, for example: if the value of a stock market increases with an annual interest rate of 4%, how does that compare to the expected earnings on the alternative investment under consideration? - -Although civil engineering projects are typically not associated with financial investments like stocks and bonds, the need to consider the time value of money is identical. In fact, many governments use the financial instruments like bonds to finance projects, which is easy to see the relationship to interest rates. -``` - -The contribution of costs in a certain year to the net present value depend on the discount rate and the reference year. Costs or benefits closest to the present will have the greatest contribution. {numref}`present-value` below shows the value of $1/(1+r)^t$ for a given year $t$ for different discount rates. The higher the discount rate, the smaller the contribution to the net present value of costs or benefits that are far away from the present. For an infinite time horizon it can be shown that $\sum 1/(1+r)^t \approx 1/r$. This approximation can be used in evaluating engineering projects with a long life time. - -```{figure} ../figures/present_value.svg ---- -width: 600 -name: present-value ---- -Normalized present value of a cost or benefit in year $t$ for different discount rates. -``` - -(value_human_life)= -## Valuation of Human Life - -The previous paragraphs have focussed on the evaluation of economic costs and benefits of risk reduction interventions. Many of these interventions also directly focus on reducing injuries and fatalities. Examples are regulations and investments in traffic safety which have introduced measures such as airbags and seat belts. - -In literature on risk management the economic valuation of human life is often depicted as a difficult problem as it raises numerous moral questions. Some claim it is unethical to put a price on human life because life is priceless. The actual expenditures on risk reducing prospects show however that the investment in the reduction of risks to humans is always finite. Different approaches are available for evaluating the costs of interventions in relation to the reduction of risk to human life, see {cite:t}`vrijling2000`; {cite:t}`jongejan2005` for a further discussion of the various approaches. One of the options is to add the economic value of human fatalities to the economic damages, i.e. $D+N \cdot d$. The value of the number of lives lost can be determined with different approaches. - -Several approaches are based on so-called stated preferences. A survey can reveal how much people are willing to pay, e.g. for safety measures. In these cases the value of statistical life (VoSL) is obtained from the willingness to pay expressed by respondents in surveys. For example, in the cost benefit analysis for the flood defences in the Netherlands a value of a statistical life of €6.7 million per fatality is used {cite:p}`jeuken2013`. The Value of a Statistical life lost in traffic accidents is estimated at €2.6 million {cite:p}`SWOV2012`. - -One alternative approach is based on so-called revealed preferences. The costs of saving and extra (statistical) life ($CSX$) for actual life-saving interventions that have been taken in the past can be determined. - -$$ - CSX = \frac{I}{\Delta E(N)} -$$ - -where: - -- $CSX$ the costs of saving an extra life [€/life year] -- $\Delta E(N)$ the reduction of the expected number of fatalities per year - -An extensive study on values in various sectors, see {cite:t}`tengs1995` showed that these vary widely across sectors and even within sectors. The highest $CSX$ values are found for risks for small probability – large consequence events, for example in the nuclear domain. For such cases the expected number of fatalities is already small and investments in incremental safety are large. - -One other approach is to base the value of a human life on macro-economic indicators. Several metrics have been proposed that relate this value to a person’s economic production. -Given the difficulties associated with economic valuation of human life and the associated risk reduction, it is decided in some domains to develop separate criteria for considering the risk to life. This topic is further elaborated in ⚠️section 3.5. \ No newline at end of file diff --git a/book/risk-evaluation/decision.md b/book/risk-evaluation/decision.md deleted file mode 100644 index 9dfda7e..0000000 --- a/book/risk-evaluation/decision.md +++ /dev/null @@ -1,202 +0,0 @@ -(decision)= -# Decision Analysis - -Decision analysis, or decision-making under uncertain conditions is part of everyday life: when choosing to buy a lottery ticket or choosing to take an umbrella during cloudy weather. In contrast to the rather intuitive decision making in everyday matters, a structured analysis of different alternatives with associated risks, costs and benefits is very useful for decisions in (civil) engineering. This chapter offers a very basic introduction into the decision theory with applications to decision problems in the civil engineering domain. Further reference is made to the work by other scholars for more rigorous and detailed treatment of this topic. See, for example {cite:t}`raiffa1961`; {cite:t}`benjamin1970`. - -## Introduction - -Making a decision is in fact choosing from alternatives. The decision theory is based on the classic “Homo Economicus” model assumes that the decision-maker: - - - has complete information about the decision situation; - - knows all the alternatives; - - knows the existing situation; - - knows which advantages and disadvantages each alternative provides, be it in the form of random variables; - - strives to maximise that advantage (formally called utility). - -The decision-making concept discussed in these lecture notes assumes this model, although decision-making in practice is often different since the above conditions are often not fulfilled. For example, there can be multiple decision makers and multiple objectives, and in reality the decision maker does not know all the alternatives or their outcomes. For many practical cases this has led to an extension of the decision model, but not to a fundamental adjustment of the classical model described here. - -Within a decision problem the following characteristics can be distinguished: - - - the set of all possible actions or decisions $a$, from which the decision maker can choose - - the set of all (natural) circumstances, $\theta$ that influence the outcomes* - - the set of the set of all possible results, $\omega$, which are functions of the actions and circumstances: $\omega = f(a,\theta)$. - -The actions, natural circumstances and the outcomes can be shown in a so-called decision tree (Figure {numref}`decision-tree-blank`). - -```{figure} ../figures/decision-tree-blank.png ---- -height: 300px -name: decision-tree-blank ---- -Decision tree. -``` - -Based on the possible results a choice is made for an action. To be able to assess the different results, a numerical value is assigned to each outcome, $\omega$, which can be used to establish the benefit of each outcome. This number can be a monetary value, a number on an arbitrary scale or utility--as long as the decision maker(s) can establish a consistent ranking of the outcomes with it. In the last two cases the benefit has no absolute value, but only gives the relative value of the different outcomes. - -Utility, $u$, is a concept used to rank the possible outcomes according to the preferences of the decision maker, with possible values $0\leq u \leq 1$ . A utility function can be used to characterize the relative utility of various outcomes. The elaborations below are based on the monetary values as a measure for the outcomes and assume a risk neutral decision maker. This is a decision maker who is indifferent between choices with equal expected outcomes, even if one choice is riskier than the other. For example, a risk neutral decision maker would have the same preference for a € 400 pay out, or a 50/50 bet with a coin toss with outcomes of € 0 (head) or € 800 (tail). Utility and risk aversion are further discussed in ater sections. - -## Decision rules - -Once a set of actions, circumstances and outcomes is known, various approaches can be used to come to a preferred decision. Various deterministic decisions rules are available which do not take into account the probabilities of the possible circumstances and outcomes. One example of such a decision rule is the minimax criterion: a decision maker wants to minimize maximum losses. This is in fact a risk-averse criterion. Another example is the maximax criterion: a decision maker chooses the option with the maximum income and is risk seeking. - -Although these decision rules are helpful in some cases, the probability of occurrence of certain circumstances is a key feature of the decision problem. Information on the probability of outcomes is needed for an optimal choice of action(s). For example, when making a decision to start a business in soup or ice cream, the decision maker would want to know what the probabilities of rainy or sunny weather are. Selling ice cream in Dutch winter will probably not make a good (expected) profit, but it would be a profitable business in a Mediterranean summer. - -Therefore it is necessary to include information on the probabilities of circumstances and outcomes, in order to determine a rational action with the highest expected value of the benefit. This theory is known as the Bayesian decision theory. In a probabilistic or Bayesian decision framework the optimal action $a*$ is defined as the one maximizing the expected utility. The following formula is found for the case with discrete outcomes. - -$$ -a^*: \max_a E(u(a, \theta))=\max _a \sum_\theta u(a, \theta_i) P(\theta_i) -$$ -In which $u(a, \theta)$ is the utility of action a under circumstance $\theta$ and $P(\theta)$ is the probability that circumstance $\theta_{i}$ occurs. - -A rational decision is choosing the action with the highest expected (utility) value or highest benefit if outcomes are expressed in monetary values. This is illustrated in the example below. Note that other examples in these lecture notes will also be based on monetary values. - -````{admonition} Example: buying shares or bonds? - -Suppose a person has €1000 at his or her disposal and is given the choice to invest this money in bonds or in shares of a given company. It is known that, on a yearly basis, 3 % of the current market value is distributed as interest on the bonds. The dividend of the shares depends on the company’s profit. Suppose that the board of directors have made the following agreements: -- for a profit smaller than 5% of the shareholders capital, no dividend is paid; -for a profit larger than 5% of the shareholders capital, dividend is paid, the percentage of which corresponds to 3% of the current market value of the shares; -- for a profit larger than 10% of the shareholders capital, the dividend corresponds to 6% of the current market value of the shares. - -The set of actions A has two elements: $a_{1}$= investing in shares AND $a_{2}$= investing in bonds -The set or market circumstances N has three elements, namely: - $\theta_{1}$ = company profit ≤5 % - $\theta_{2}$= 5 % < company profit ≤ 10 % - $\theta_{3}$= company profit > 10 % - -Assume the inflation amounts to 2 %. The set of outcomes ω contains three possible outcomes for the shares: - $\omega_{1}$= return (0 % -2 %) = -2 % per annum - $\omega_{2}$= return (3 % -2 %) = 1 % per annum - $\omega_{3}$= return (6 % -2 %) = 4 % per annum - -Note that for the bonds the net outcome always yields $\omega_{2}$ =1% (i.e. 3% interest – 2% inflation). The outcomes can be illustrated using a decision tree (see {numref}`decision-tree-example`) or a table (see {numref}`ex_market_outcomes`). - -```{list-table} Outcomes given the decisions ($a_1$, $a_2$) and market conditions ($\theta_{1}$, $\theta_{2}$, $\theta_{3}$). -:header-rows: 1 -:name: ex_market_outcomes - -* - - - Market circumstances - - - - -* - Actions - - $\theta_{1}$ - - $\theta_{2}$ - - $\theta_{3}$ -* - $a_{1}$: buy shares - - $-$2 % - - 1 % - - 4 % -* - $a_{2}$: buy bonds - - 1 % - - 1 % - - 1 % -``` - -```{figure} ../figures/decision-tree-example.png ---- -height: 300px -name: decision-tree-example ---- -Decision tree for the example of buying shares ($a_{1}$) or bonds ($a_{2}$). -``` -The deterministic decision rules can be applied to this example. Minimax would result in investing in bonds ($a_{2}$), maximax would result in buying shares. -The optimal decision can be found by taking into account the probabilities of the market circumstances. These three circumstances are assumed to be exhaustive and mutually exclusive (i.e. outcomes cannot overlap and the sum of probabilities equals 1). The probabilities are estimated at $P(\theta_{1})$ = 0.2; $P(\theta_{2})$ = 0.3; $P(\theta_{3})$ = 0.5. These probabilities can now be included in the decision tree. The expected value of the return of the actions is as follows: - - Buying shares: 0.2(-2 %) + 0.3 (1 %) + 0.5 (4 %) = 1.9 %. - Buying bonds: 1% - -In this case the expected outcome is larger for buying shares than for buying bonds. So for a risk neutral decision maker buying shares (a1) would be the preferred action. Note that this action also includes a probability of 0.2 of a loss. This is also expressed by a higher standard deviation of the expected outcomes for buying shares. The above example can also be extended by applying different utility functions for various outcomes. - -```` - -In the previous example, the number of circumstances is limited and the probability distribution of the circumstances is discrete. For many decision problems this is not the case. The state of nature, for instance, can assume many values that cannot be made discrete. This, for example, would have been the case if the dividend in example 0 had been a percentage of the profit. In such cases a probability density function can be used to characterize the spectrum of outcomes. Using a continuous form of formula (3.5), the expected value of various actions, and the optimal action / decision can be identified. - -In taking decisions with uncertainties, it appears that probabilistic calculation techniques are a valuable aid to reach a rational choice. This is particularly the case if risks are dependent on the possible decisions. In such cases, Bayesian decision theory minimizes the total costs (i.e. investment costs plus risk in terms of potential losses). This can best be illustrated by means of an example from the civil engineering domain. - -````{admonition} Example: drainage of a construction site – decision tree - -In a river polder a basement has to be built in an excavated construction site. The construction site is made of sheet piling and the bottom is sealed off with a clay layer with a thickness of approximately 2.5 m. The thickness is not known exactly but measurements indicate that a normal distribution can be used with mean $\mu_d$= 2.5 m and a standard deviation of $\sigma_{d}$ = 0.2 m. - -The river cuts through the clay layer and the underlying sand layer is fed by the river, which causes high uplift pressures on the clay which is exposed in the excavation (see Figure {numref}`example-river-excavation`). If the pressure becomes too high the excavation base will push upward and water will enter the excavation in an uncontrolled way, damaging property and perhaps risking human life. - -```{figure} ../figures/example-river-excavation.png ---- -height: 300px -name: example-river-excavation ---- -Cross-section of excavation and river. -``` - -Measurements of the groundwater levels indicate the maximum upward pressure, $h$, under the sealing layer in the construction period has an a normal distribution with an expected value of $\mu_{h}$ = 4 m water column and a standard deviation of $\sigma_h=0.75 \mathrm{m}$ (see Figures {numref}`example-river-excavation-2`). Since $h$ is a hydraulic head (units of $[\mathrm{L}]$), pressure is calculated by multiplying the unit weight of water ($10\:\mathrm{kN/m^3}$). - -Failure occurs when the uplift pressure exceeds the weight of the clay layer, which can be described by a limit state function $Z = R - S$ with resistance $R$ and load $S$: - -$$ -Z=\rho_c\cdot d-\rho_w \cdot h -$$ -Where $\rho_c$ is the density of clay ($20\:\mathrm{kN/m^3}$), and is assumed here to be a deterministic value. The probability of failure is thus $P(Z<0)$, which for this situation can be found by calculating the mean and standard deviation of $Z$: - -$$ -\mu_Z=\rho_c \mu_d-\rho_w \mu_h=20(2.5)-10(4)= 10\:\mathrm{kN/m^2} -$$ - -$$ -\sigma_z=\sqrt{\rho_c^2 \sigma_c^2+\rho_w^2 \sigma_{\mathrm{h}}^2}=8.5\:\mathrm{kN/m}^2 -$$ -Since $Z$ also has the normal distribution, we find the failure probability: - -$$ -p_f=P(Z<0)=\Phi\left(-\mu_z / \sigma_z\right)=\Phi(-1.17)=0.12 -$$ - -```{figure} ../figures/example-river-excavation-2.png ---- -height: 300px -name: example-river-excavation-2 ---- -Cross-section of excavation near a river. Hashed area indicates the clay layer, which is underlain by sand. The water pressure is given by $h$ and is directly related to the river level (Figure {numref}`example-river-excavation`). -``` - -The effect of a drainage system in the construction site (see {numref}`example-river-excavation`) on the groundwater levels has been reviewed using groundwater flow calculations. It appears that it reduces the mean value of the maximum water levels to $\mu _{h}$ = 3.52m and the standard deviation remains the same. In this case the failure probability is reduced to 0.04. Such a drainage system costs €150,000. - -The flooding of the construction site will result in estimated damages of €5,000,000, and the designer of the construction site is faced with the choice whether drainage facility is a worthwhile investment. To provide insight, the decision problem is illustrated with a decision tree, but first the set of actions, circumstances and outcomes are defined: - -The set of actions A consists of: -- $\textit a_{1}$= excavation without drainage -- $\textit a_{2}$= excavation with drainage - -The set of circumstances N is formed by: -- $\theta_{1}$= the sealing layer remains intact -- $\theta_{2}$= the water pressure exceeds the weight of the sealing layer - -The set of outcomes $\Omega$ consists of: -- $\omega_{1}$ = nothing happens; loss = € 0 -- $\omega_{2}$ = the construction excavation is flooded: loss = €5,000,000 - -The previous analysis has shown that the probability of flooding of the excavation equals $p_{f}$ = 0.12 for a situation without drainage and $p_{fd}$ = 0.04 with drainage. - -Without drainage, the risk, defined as the expected value of the loss, is - -$$ -\textrm{risk, without drainage = }0.12 \cdot \euro{} 5,000,000 = \euro{} 600,000 -$$ -With drainage the risk is: - -$$ -\textrm{risk, with drainage = }0.04 · \euro{} 5,000,000 = \euro{} 200,000 -$$ -Costs and probabilities can also be shown in the decision tree (see Figure {numref}`example-river-excavation-3`). The expected values of the costs can be calculated for the different actions by adding the present values of the cost of actions and risk: -- $\textit a_{1}$ : expected value (additional) costs = risk =€ 600,000 -- $\textit a_{2}$ : expected value (additional) costs -= extra costs + risk = € 150,000 + € 200,000 = € 350,000 - -This implies that the construction of the drainage system is rationally speaking the best decision for a risk neutral decision maker. - -```{figure} ../figures/example-river-excavation-3.PNG ---- -height: 300px -name: example-river-excavation-3 ---- -Decision tree with probabilities and costs. -``` -```` \ No newline at end of file diff --git a/book/risk-evaluation/econ-optimization.md b/book/risk-evaluation/econ-optimization.md deleted file mode 100644 index 9ffdfc8..0000000 --- a/book/risk-evaluation/econ-optimization.md +++ /dev/null @@ -1,58 +0,0 @@ -(econ_optimization)= -# Economic Optimization - -The previous sections have focussed on decisions for which the number of actions was limited, e.g. excavation with or without drainage and the associated costs and benefits. However, there are several situations in which the number of actions is unlimited. This occurs when the failure probability level has to be decided for a system that is yet to be designed, with an infinite number of design options. An example of this type of decision problem is the heightening of dikes, as in theory an unlimited amount of values can be chosen for the elevation, e.g. 2m, 5m, 5.1m, 5.11m, 5.1111m 6m etc. - -For this situation an economic optimization that takes into account the costs of increasing the safety level and reducing the risks can be applied to derive an optimal level of safety (or the optimal “failure probability”). The economic optimization was developed and applied by {cite:t}`vandantzig1956`, to derive the optimal dike height for South Holland after the 1953 storm surge disaster, as will be further elaborated in the next section. -In the economic optimization the total costs ($C_{tot}$[€]) are determined, consisting of the investments $I$[€] in a safer system and the present value of the risk $R$[€]. - -$$ - C_{tot} = I + R -$$ - -The annual risk, or expected economic dagmage is found by: - -$$ - E(D) = P_f D -$$ - -where: - -- $E(D)$ the expected value of the risk [€/year] -- $P_f$ the failure probablity of the system per year [1/year] -- $D$ the damage in case of failure [€] - -In this approach it is thus assumed that all damages are expressed in monetary terms. Additional criteria for separately considering the loss of human life are included in the next section. - -The present value of the risk for an infinite time horizon can be found as follows: - -$$ - R = \frac{P_f D}{r} -$$ - -The risk can be reduced by constructing a safer system (a lower $P_f$), or limiting the damage (smaller $D$). In this case we assume prevention measures that focus on reducing the failure probability. The investments will become a function of the failure probability of the system, since increasing the safety will lead to an increase of costs. - -$$ - I = I(P_f) -$$ - -{numref}`economic_optimum` shows the costs and risks as a function of the accepted failure probability of a system. The economic optimum is found when the total costs are minimal. - -```{figure} ../figures/economic_opt.svg ---- -width: 600 -name: economic_optimum ---- -Economic optimization: costs, risks and total costs as a function of the -failure probability of the system. -``` - -For this situation the following is valid: - -$$ - \frac{d C_{tot}}{d P_f} = 0 -$$ - -This approach can be applied to various decisions problems, such as the optimal dike height (see next section) but also the dimensioning of other interventions such as sprinklers or ventilation in tunnels to reduce fire risks. In cases where no continuous functions are available to create a curve as in {numref}`economic_optimum`, the analyst can consider a limited number of design options (e.g. no, small, medium or large sprinklers in a tunnel) and determine investments, risks and total costs for these options. - -In addition to the determination of the optimal failure probability, the cost benefit criterion should still be verified. (It is possible that we find an economic optimum with higher total costs than in the current situation without interventions). It is checked whether the benefits of risk reduction are larger than the costs of the dike heightening, i.e. $(P_{f,0} - P_{f,opt}) D > I$. \ No newline at end of file diff --git a/book/risk-evaluation/example-dike-height.md b/book/risk-evaluation/example-dike-height.md deleted file mode 100644 index 8aea567..0000000 --- a/book/risk-evaluation/example-dike-height.md +++ /dev/null @@ -1,121 +0,0 @@ -(ex-dike-height)= -# Optimization Example - -Economic optimization is illustrated through the determination of an optimial dike height to protect against flooding. - -Before the major floods of 1953, dikes in the Netherlands were not designed for a specified safety level but mainly strengthened based on practical experience. One of the main questions after the disaster was the optimal dike height and the “acceptable” probability of flooding. Van Dantzig was a professor in mathematics and a member of the first Delta committee. He developed an econometric approach to determine the optimal probability of flooding (or protection level) and the corresponding dike height {cite:p}`vandantzig1956`. - -## Probability and Risk - -The approach only considers failure of the dikes due to overtopping. The probability distribution of water levels along the Dutch coast can be approximated by an exponential distribution. - -$$ - F(h) = 1 - e^{(-\frac{h-A}{B})} -$$ (prob_dist_water_levels) - -In which: -- $h$ the water level [m] -- $A,B$ constants of the exponential ditribution [m] - -Neglecting wave run-up, the probability of failure of the dikes - leading to flooding - can be approximated by the probability of exceedance of the dike height $h_d$, i.e. - -$$ - P_f = P(h>h_d) = e^{(-\frac{h_d - A}{B})} -$$ (exceedence_dike_height) - -It is assumed that there is total damage to all objects and infrastructures in the flooded area if the dikes fail. For the discount rate Van Dantzig applied a reduced interest rate $r^\prime$ = economic growth – inflation. The net present value of the expected damages (i.e., the risk) is found as follows, assuming an infinite time horizon: - -$$ - R = \frac{P_fD}{r^\prime} = \frac{e^{-\frac{h_d-A}{B}}D}{r^\prime} -$$ (dike_height_risk) - -## Costs and Benefits - -As the risk is dependent on height, the dikes can be heightened further to limit the failure probability and thus risks. Investments in dike heightening are determined by initial costs for mobilization and variable costs that are dependent on the level of dike heightening (see also {numref}`dike_heightening_schematic`): - -$$ - I = I_0 + I(h_d - h0) -$$ (dike_investments) - -```{figure} ../figures/dike_heightening_schematic.png ---- -height: 200px -name: dike_heightening_schematic ---- -Schematic view of dike heightening -``` - -Now, the total costs $C_{tot}$ are the sum of the investment costs and the risk. - -$$ - C_{tot} = I_0 + I(h_d - h_0) + \frac{e^{-\frac{h_d-A}{B}}D}{r^\prime} -$$ (total_costs) - -The optimal dike height is found when the total costs are minimal. This is the case when $dC_{tot}/dh_d=0$. - -$$ - \frac{dC_{tot}}{dh_d} = I - \frac{e^{-\frac{h_d-A}{B}}D}{Br^\prime} = 0 -$$ (optimal_dike_costs) - -Since the $P_f = e^{-(h_d-A)/B}$, we can find the optimal flooding probability $P_{f,opt}$: - -$$ - P_{f,opt} = \frac{IBr^\prime}{D} -$$ (optimal_flooding_prob) - -The larger the damage $D$, the smaller the optimal failure probability and thus the higher the level of protection. If incremental protection is expensive – i.e. for high values of $I$ – a higher optimal failure probability and thus a lower level of optimal safety will be found. The optimal failure probability is also dependent on the discount rate. Combination with {eq}`exceedence_dike_height` gives the optimal dike height $h_{d,opt}$: - -$$ - h_{d,opt} = A - B \cdot \ln(P_{f,opt}) -$$ (optimal_dike_height) - -## Verification - -In addition to the determination of the optimal dike height the cost benefit criterion should still be verified by checking whether the benefits of risk reduction are larger than the costs of dike heightening. - -$$ - I(h_{d,opt})<\frac{(P_{f,0} - P_{f,opt})D}{r^\prime} -$$ (risk_reduction_check) - -Where $P_{f,0}$ the flooding probability in the initial situation. It can be easily shown that this is equivalent to a check of whether the total costs in the optimal situation are smaller than those in the original situation. The first Delta committee used the following values for South Holland: - -- $D$ = fl 24.2$\cdot 10^9$ [unit is Dutch guilders] -- $r^\prime$ = 0.015 -- $I$ = 40.1$\cdot 10^6$ fl/m -- $A$ = 1.96 m -- $B$ = 0.33 m -- $h_0$ = 3.25 m -- $I_0$ = fl 110$\cdot 10^6$ - -Using these values, the following optimal dike height and optimal failure probability were derived: - -- $h_{d,opt}$ = 5.83 m -- $P_{f,opt}$ = $8 \cdot 10^{-6}$ per year - -## Discussion - -Although the optimal safety level was determined at a failure probability of $P_{f,opt}$ = 1/125,000 per year, in later political discussions a value of 1/10,000 per year was selected for the probability of exceedance of design water levels. This implied that the dikes of South Holland would need to be designed for hydraulic conditions (water levels and waves) with a probability of exceedance of---on average---1/10,000 per year. In later decision-making, safety standards were derived for other dike rings (see {numref}`dike_rings`), for example, flood defenses in the river system are designed for a safety standard of 1/1250 per year. - -```{figure} ../figures/dike_rings.jpg ---- -width: 400px -name: dike_rings ---- -Dike Rings in the Netherlands, showing probability of exceedance of the design water levels per dike ring. Note that dike rings along the River Meuse are not shown on this map. Most of these dike rings have a safety standard of 1/250 per year. This map defined design levels until the safety standards changed in 2017. -``` - -It was expected that the actual failure probability for dikes designed for this design load, would be smaller than 1/10,000 per year. Recent risk analysis in the project VNK have shown that this is not the case due to the geotechnical failure mechanisms. For most dike rings the estimated failure probabilities are larger than the probability of exceeding the design loads. For example, for riverine dike rings that have been designed for design levels with a probability of exceedance of 1/1250 per year, failure probabilities are often in the order of magnitude of 1/100 per year {cite:p}`vnk2014`. This is part of the reason for revising the safety standards and flood defence assessment criteria in the Netherlands, which since 2017 is based on an allowable probability of flooding rather than a load-based exceedance probability approach. - -Historic discussions and developments in the Netherlands illustrate how the risk analaysis and risk management for a given system can change over time. Several extensions and additions to the van Dantzig model have been proposed over the years. For example, the inclusion of sea level rise {cite:p}`vrijling1990`, modelling of the damage as dependent on the water depth in the polder {cite:p}`vandantzig1956`, the inclusion of the economic value of loss of life as part of the damage, and inclusion of risk aversion by giving quadratic weight to the damages {cite:p}`vangelder1997`. - -The model by van Dantzig was primarily focused on finding what the optimal safety at that time (when van Dantzig published his model in the 1960’s) should have been. However, a single optimal level is not always the best solution. While considering longer timescales and changing conditions, such as economic growth and sea level rise, the model needs to address the possibility of multiple interventions during the period considered. This leads to questions regarding the timing of interventions (when? At which intervals?), as well as the optimal strengthening or raising of the dikes (how much?). {cite:t}`Eijgenraam2006` developed an economic decision model that takes into account both questions. - -{numref}`periodic_investments` below depicts the “saw-tooth” curve that shows the periodic interventions: both the extent of the intervention (vertical) as well as the timing between interventions (horizontal). In between interventions, the safety will gradually decrease due to sea level rise and / or subsidence of the dike. Over a longer period of time, the dike heightening (or strengthening) should follow sea level rise. Additional dike heightening (lower the failure probability even further) could be considered in case of economic growth, which will lead to an increase of damages and increase of protection standards. The length of the optimal interval between interventions is largely dependent on the initial or mobilization costs. If these are high, for example in the case of structural interventions such as storm surge barriers, a long interval or life time of almost 100 years can be chosen. For regular dike reinforcements this interval will be more in the range of several decades (e.g. 50 years). For interventions with no or very small initial costs, such as nourishments along the coast, it is optimal to intervene more frequently. - -```{figure} ../figures/periodic_investments.png ---- -width: 400px -name: periodic_investments ---- -Periodic investments in dike reinforcement for a situation with sea level rise. -``` \ No newline at end of file diff --git a/book/risk-evaluation/overview.md b/book/risk-evaluation/overview.md deleted file mode 100644 index 372b495..0000000 --- a/book/risk-evaluation/overview.md +++ /dev/null @@ -1,8 +0,0 @@ -(risk_eval)= -# Risk Evaluation - -This chapter focuses on the evaluation of risk (Step 4) by applying several different techniques. While the Sections may seem long, the methods are relatively simple and a lot of examples and explanations are provided to illustrate how they can be applied in practice. After this chapter, you will be ready to try all of the practice problems in the Exercise Chapter. - ---- - -_The primary author for this chapter is Bas Jonkman. Robert Lanzafame contributed through rearrangement of the topics and formatting._ \ No newline at end of file diff --git a/book/risk-evaluation/safety-standards.md b/book/risk-evaluation/safety-standards.md deleted file mode 100644 index 312d6d0..0000000 --- a/book/risk-evaluation/safety-standards.md +++ /dev/null @@ -1,371 +0,0 @@ -(safety_standards)= -# Safety Standards - -When answering the question “how safe is safe enough” a merely economic treatment with cost benefit analysis or economic optimization is often not sufficient for activities with risks to people. Therefore, criteria have been developed that focus on risks to human life. This section focuses on safety standards and criteria for evaluating the risk to life. - -Two aspects are typically considered when evaluating and regulating risks to the public: the total or population-wide effects, and the distribution of effects within the affected population. {numref}`risk_evaluation` summarizes these perspectives. The societal perspective is concerned with ‘total effect’ and the effects of large-scale accidents on the society, in terms of economic damages and life loss. The individual perspective is concerned with distributive justice (‘equity’), i.e. the distribution of harm over the population. - -As risk is often the by-product of an otherwise legitimate and advantageous activity, such as production or transportation, regulating risks is essentially a balancing act between economic and social activities on the hand and a sufficiently safe society on the other hand (e.g. {cite:t}`jongejan2008`): just as too lenient regulations are suboptimal, too stringent ones are too. - -```{list-table} Overview of perspectives on risk evaluation -:header-rows: 1 -:name: risk_evaluation - -* - Aspect - - Relevant risk metric - - Rationale -* - Equity ('distributive justice') - - Individual risk - - Regulation is to prevent that individuals are exposed to disproportionally large risks -* - Total effect - - Societal and economic risk - - Regulation is to limit large-scale accidents and optimize the costs and benefits of risk reduction -``` - -## Three Types of Risk - -Based on the general concepts described above, it has been proposed to evaluate risks based on three criteria {cite:p}`TAW1985,vrijling1995,vrijling1998`: -- limit the **invidual risk** to prevent that certain people are exposed to disproportionally large risks; -- limit the **societal risk** to limit the risks of large scale accidents with many fatalities; -- **Economic optimization** to balance investments in risk reduction from an economic point of view. - -### Societal and Economic Risk - -Two of these criteria have already been discussed elsewhere in this book. **Societal risk** refers to the probability of an accident with multiple fatalities and is often graphically represented by an FN-curve ({ref}`risk_curve` Section). **Economic optimization** has already been discussed in the {ref}`econ_optimization` Section. - -### Individual Risk - -**Individual risk** concerns the probability of death of a person due to an accident. Various related definitions exist. The “average individual risk” for a certain activity can be calculated, e.g. the individual risk due to smoking or the risk of an airplane crash for a frequent flyer. {numref}`death_probability` compares the probability of various types of fatal accidents. - -```{list-table} Average probability of death due to several activities. (statistics based on various sources for the Netherlands and Europe) -:header-rows: 1 -:name: death_probability - -* - Activity - - Probability (per year) -* - Mountain climbing - - $10^{-2}$ -* - Traffic (young men) - - $10^{-4}$ -* - Accidents at home - - $10^{-4}$ -* - Structural failures - - $10^{-7}$ -``` - -The individual risk due to an accident can be calculated with: - -$$ - IR = P_f P_{d|f} -$$ - -where: -- $IR$ the individual risk [1/year] -- $P_{f}$ the probability of an accident [1/year] -- $P_{d|f}$ the conditional probability of death given an accident - -Both the individual risk and $P_{d|f}$ can be formulated as a function of a location near a risk source. If it is assumed that a person is permanently present at that location, the individual risk becomes a property of that location and it can be used for zoning and land use planning. This is applied in the industrial safety policy in the Netherlands (see next section). - -```{admonition} Example: Difference between individual and societal risk. -To illustrate the difference between the individual and societal perspective, consider a fairly safe car that has a probability of 10$^{-5}$ per year of causing a fatality due to technical failure. This may well be acceptable to an individual. Such a probability is in the same range as the average death rate in traffic (650 fatalities / 17 million people which is about 4.10$^{-5}$ per year). If only 1000 cars are sold in the Netherlands, the number of fatal accidents with this car is rare, i.e. 0.01 fatalities per year. However, when the car becomes popular and 10 million cars are sold, the average number of fatalities due to technical failure becomes 100 per year. This may well lead to public concerns and indignation. From a societal point of view this may no longer be acceptable, whereas the individual risk has not changed. -``` - -## Limits for Individual and Societal Risk - -Safety standards can be used to set limits to the individual and societal risk. A **limit** value can be set for **individual risks**. Such a limit value is to avoid disproportionate exposures by laying down a minimum safety level for all individuals. In various fields of applications limit values in the range of 10$^{-4}$ to 10$^{-6}$ per year are used (see below for more information). To put the stringency of the individual risk criteria into perspective, one could consider the effect of the probability of an accident on life expectancy. When an average person would be constantly exposed to a maximum allowable level of risk of 10-6 per year, the decrease of his or her life expectancy would be only 1 day as shown in {numref}`individual-risk-life-expectancy`. - -```{list-table} Relationship between the additional risk and life expectancy -:header-rows: 1 -:name: individual-risk-life-expectancy - -* - Additional probability of death in a year - - Life expectancy in years - - Decrease of life expectancy in years - - Decrease of life expectancy in days -* - $10^{-3}$ - - 74.97 - - 3.16 - - 1153 -* - $10^{-4}$ - - 77.81 - - 0.32 - - 117 -* - $10^{-5}$ - - 78.10 - - 0.03 - - 11 -* - $10^{-6}$ - - 78.13 - - 0.00 - - 1 -* - $10^{-7}$ - - 78.13 - - 0.00 - - 0 -``` - -Societal risk can be evaluated by means of an FN limit line. The calculated FN curve of the system should, in principle, not exceed the limit line. An FN-criterion is defined by three variables: - -1. A base point: the exceedance probability of 1 fatality (i.e. $C$), -2. A slope, $\alpha$, and -3. Probability and/or consequence cut-offs ($A$ and $B$). - -{numref}`limit_line` schematically illustrates the different criterion that could make up an FN limit line. - -```{figure} ../figures/fn_limit00.svg ---- -height: 600px -name: limit_line ---- -Schematic FN curve illustrating limit line formulation with horizontal and vertical cut-offs. -``` - -The general formulation for such a limit line without horizontal of vertical cut-off equals: - -$$ - 1 - F_N(n) \leq \frac{C}{n^\alpha} -$$ (limit_line) - -where: -- $C$ a constant that determines the vertical position of the limit line -- $\alpha$ a coefficient that determines the steepness of the limit line - -The limit line is called *risk neutral*[^neutral] if $\alpha=1$, since it places equal weight on exceedance probabilities and numbers of fatalities. If $\alpha = 2$, the limit is *risk averse.* This means that given an arbitrary point, the exceedance probability of 10 times as many fatalities should be 100 times lower. This has been motivated by public aversion to large numbers of fatalities. For example, the loss of 1000 people in one accident (e.g. a major explosion) could be valued differently than 1000 losses of 1 person in separate accidents (e.g. in traffic). - -For different applications limit lines have been developed with varying constants and steepness. Examples of application areas include industrial risks in the Netherlands (next section), dams in the United States and Canada, and chemical risks in Hongkong and the UK {cite:p}`jonkman2003`. - - -````{admonition} Exaple: Risk Matrix -Risk matrices are often used in various industries for risk evaluation and decision support, for example, to quickly prioritize actions, especially in time-sensitive situations. For a given undesired event the extent of probability and consequences are estimated on a qualitative or semi-quantitative scale, see {numref}`risk_matrix` for an example. Ranges of failure probabilities or consequences can be assigned to the qualitative terms on the axes in the example. The combination of probability and consequence determines the level of risk, and depending on the application, whether it is acceptable or whether it requires more attention and risk reduction efforts. However, unlike the FN curve, the cumulative effects of multiple possible events are generally not considered in a risk matrix. - -```{figure} ../figures/risk_matrix.png ---- -width: 500px -name: risk_matrix ---- -Example of a risk matrix used by various engineering and military branches of the United States Army Corps of Engineers. Source: [this USACE document](https://home.army.mil/lee/application/files/7815/3809/1878/Tables.pdf) (opens a PDF); general explanation can be found via Engineering Manual EM-385-1-1 {cite:p}`usace14`, or online at USACE [Risk Management Center](https://www.rmc.usace.army.mil/) or [Risk Analysis Gateway](https://www.iwr.usace.army.mil/Missions/Risk-Analysis-Gateway/Risk-Assessment/). -% Note: real source is a PDF [here](https://home.army.mil/lee/application/files/7815/3809/1878/Tables.pdf) -% Formal definition is in this: Manual EM 385-1-1 https://www.publications.usace.army.mil/portals/76/publications/engineermanuals/em_385-1-1.pdf -``` -```` - - - -## Case Study: Industrial Hazards - -The Dutch major hazards policy deals with the risks to those living in the vicinity of major industrial hazards such as chemical plants and LPG-fuelling stations. The development of the Dutch major hazards policy was strongly incident driven, as were European efforts aimed at the prevention of major industrial accidents. After a number of severe industrial accidents, including the Bhopal accident in 1984 which killed an estimated 3000 people and severely injured over 200.000, a European directive was drafted concerning the prevention of major accidents: the 1982 Seveso Directive. This was later replaced by the Seveso II Directive. -The cornerstones of the Dutch major hazards policy are a) the use of quantitative risk analysis (QRA); b) comparison of QRA outcomes with limits to individual and societal risks {cite:p}`bottelberghs2000`. - -Within the Dutch major hazards policy, individual risk is defined as the probability of death of an average, unprotected person that is constantly present at a certain location. It is thereby a property of location and iso-risk contours can be plotted on a map (see {numref}`risk_contour`). Individual risk is therefore also named local risk (“plaatsgebonden risico”) in the Netherlands. The shape of the risk contours for other applications will look different. For airports the contours will follow the shape of the runway and flight paths, for polders and flooding the risk contours will be highest in the deepest part of the polder. - -```{figure} ../figures/risk_contour.png ---- -height: 400px -name: risk_contour ---- -Example of a schematic individual risk contour (circles) for a chemical installation. -``` - -```{list-table} Individual risk criteria used in the Netherlands. -:header-rows: 1 -:name: individual-risk-criteria - -* - - - - - Individual (or local) risk criterion -* - **Existing situations** - - Vulnerable - - $10^{-6}$ per year -* - - - Limitedly vulnerable - - $10^{-5}$ per year, strive for $10^{-6}$ per year -* - **New situations** - - Vulnerable - - $10^{-6}$ per year -* - - - Limitedly Vulnerable - - $10^{-6}$ per year -``` - -A distinction is made between vulnerable objects such as schools and houses and limitedly vulnerable objects such as small offices. The following criteria apply. For new situations a limit of $10^{-6}$ per year applies. A comparison with {numref}`individual-risk-criteria` shows that this individual risk value has a negligible effect on life expectancy. - -The criterion for societal risk that is used in the Netherlands for evaluating the third party risks posed by major industrial hazards is shown in {numref}`fn_limit` below. It serves as a reference in the broader assessment of third party risks by competent authorities. Exceedances of the criterion line also have to be motivated by competent authorities. When the criterion line is not exceeded, the acceptability of the third party risk still has to be motivated. The limit line is characterized by $C=10^{-3}$ and a steepness of $\alpha = 2$, making it a risk averse criterion. The criterion is used to assess the acceptability of the risks of individual facilities. - -```{figure} ../figures/fn_limit01.svg ---- -width: 600 -name: fn_limit ---- -FN limit line used for installations in the Netherlands, with hypothetical risk curve. -``` - -## Case Study: Flood Protection - -For systems for which no regulations are available the question 'how safe is safe enough?' can be difficult to resolve. A general model has been developed by the Technical Advice Committee for Water defences (TAW)[^taw] in the process of deriving safety standards for flood protection in the Netherlands, which, in a formal sense, has been an ongoing process since the 1950's. This approach is derived on the basis of accident statistics {cite:p}`TAW1985,vrijling1995,vrijling1998`, where underlying assumption of the model is that accident statistics are the result of a process of societal optimisation and that they thereby reflect what is apparently considered acceptable by society at large. Such an approach is commonly referred to as a 'revealed preference' approach, and was already introduced in a a general sense in the Chapter on Risk Analysis, Section {ref}`risk_curve_famous` ({numref}`risk-curve-baecher`). - -### Individual risk - -Accident statistics reveal that the extent to which participation in the activity is voluntary strongly influences the level of risk that is accepted by individuals. Relatively high individual risks are accepted for activities that are voluntary and have a (personal) benefit, such as mountain climbing. Much smaller individual risk values are accepted for involuntary activities for which the risks are imposed by others, e.g. for chemical and nuclear industry. A policy factor ($\beta$) is therefore introduced to account for voluntariness of exposure. This factor is set at $\beta=1$ for an individual risk value of $10^{-4}$ per year. This represents the “baseline” individual risk for the group young men[^men] who are most at risk of dying in a traffic accident. - - -:::{list-table} Accident statistics and proposed policy factor and characteristics of the activity {cite:p}`CUR1997,vrijling1998,vrijling2001`. -:header-rows: 1 -:name: accident_statistics - -* - Prob. of death(per year) - - Exmaple/application - - $\beta$ - - Voluntariness - - Benefit -* - $10^{-2}$ - - Mountain climbing - - 100 - - Voluntary - - Direct benefit -* - $10^{-3}$ - - Driving a motor cycle - - 10 - - Voluntary - - Direct benefit -* - $10^{-4}$ - - Driving a car - - 1 - - Neutral - - Direct benefit -* - $10^{-5}$ - - Flooding - - 0.1 - - Involuntary - - Some benefit -* - $10^{-6}$ - - Factory/LPG station - - 0.01 - - Involuntary - - No benefit -::: - -The proposed individual risk limit becomes: - -$$ - IR < \beta \cdot 10^{-4} -$$ (individual_risk) - -An appropriate value for the policy factor $\beta$ can be chosen depending on the characteristics of the activity. If the conditional probability of death due to an accident $P(d|f)$ is known, the acceptable failure probability can be computed: - -$$ - P_f \leq \frac{\beta \cdot 10^{-4}}{P_{d|f}} -$$ (acceptable_failure_prob) - -Note that the Dutch individual risk criterion for hazardous installations would be obtained for $\beta = 0.01$ and a conditional probability of death of 1 ($P_{d|f} = 1$). - -### Societal risk - -The societal risk criterion proposed by the TAW is based on the thought that societal risk should be evaluated primarily at a national level as local developments may lead to a situation that is considered unacceptable by society as a whole {cite:p}`vrijling1995`. The societal risk criterion at a national scale proposed by the TAW is: - -$$ - E(N) + k \sigma(N) \leq \beta \cdot 100 -$$ (societal_risk_criterion) - -where: - -- $E(N)$ the expected number of fatalities per year -- $k$ the risk aversion index (proposed value, $k=3$) -- $\sigma(N)$ the standard deviation of the number of fatalities per year -- $\beta$ the policy factor - -A risk aversion index $k$ has been introduced to account for risk aversion. For accidents with small probabilities and large consequences the standard deviation $\sigma(N)$ is large relative to $E(N)$, see example below. The total risk takes a risk aversion index $k$ [-] into account. For $k>1$, the “cost of risk bearing” exceed expected loss, implying a risk averse attitude. - -````{admonition} Expected value and standard deviation for two systems - -We consider two sytems - -1. This sytem has a high failure probability of 0.01 per year and 1 fatality -2. The second system has a smaller failure probability of 0.0001 per year but a higher number of 100 fatalities. - -For both systems a binomical distribution of the number of fatalities is applied meaning that the number of fatalities in case of failure is exactly known. The expected value and standard deviation of the number of fatalities are found as follows: - -$$ - E(N) = P_fN \;\;\;\; \sigma^2(N) = P_f(1-P_f)N -$$ (binomial_moments) - -The resulting expected value and standard deviation are shown in {numref}`exp_val_std_dev_two_activities` below. Although both systems have the same expected value, the standard deviation for the “small probability – large consequence” event for system 2 is higher. Taking into account the standard deviation in the TAW criterion thus accounts for risk aversion against accidents with large numbers of fatalities. - -```{list-table} Calculation of expected value and standard deviation for two activities. -:header-rows: 1 -:name: exp_val_std_dev_two_activities - -* - - - $P_f$ - - $N$ - - $E(N)$ - - $\sigma(N)$ -* - 1 - - $10^{-2}$ - - 1 - - $10^{-2}$ - - 0.0099 -* - 2 - - $10^{-4}$ - - 100 - - $10^{-2}$ - - 0.995 -``` - -The next step would be to distribute this maximum allowable level of societal risk over individual installations. After all, locally imposed societal risk criteria are necessary for achieving the desired national level of societal risk. The translation of the nationally acceptable level of risk to a criterion for a single local installation depends on the type of probability distribution of the number of fatalities. In {cite:t}`vrijling1998` a formulation of the risk acceptance at a local level is presented conform {eq}`limit_line`:️ - -$$ - 1 - F_n(n) \leq \frac{C}{n^\alpha} -$$ - -For a binomial distribution this yields: - -$$ - C = \left( \frac{\beta \cdot 100}{k \sqrt{N_a}} \right)^2 -$$ - -in which $N_a$ is the number of independent locations where the activity takes place. This requirement corresponds to the requirement set for the chemical installations if $\beta=0.03$, $N_a=1000$ and $k=3$. -```` - -### Combination of Risk Types - -According to the approach by TAW the three approaches (individual, societal and economic risk) lead to three acceptable failure probabilities. The most stringent of the three criteria can be chosen to determine the acceptable probability of failure of the system and to make sure that all three conditions are fulfilled. This can best be illustrated with an example (see below). The principles of this approach have been applied to derive the proposed new safety standards for flood defences in the Netherland by the {cite:t}`delta2014`. - -````{admonition} Example: Combination of individual, societal and economic risk for a dike ring area - -We consider application of the three criteria to the case of dike rings in the Netherlands. There are about 100 dike rings in the Netherlands of different sizes. A dike ring is a flood prone area protected from flooding by flood defences and high grounds. The conditional probability of death given flooding depends on the depth of the polder and flood characteristics. Research on loss of life due to floods shows that a conservative estimate would lead to $P_{d|f} = 0.1$. - -First, we consider the individual risk. A value of $\beta = 0.1$ is proposed as being exposed is considered as an involuntary activity with some benefit (i.e. living in a prosperous delta). This leads to an acceptable individual risk value of $10^{-5}$ per year. This limit has also been proposed by the Dutch government in the year 2014 (“basisveiligheid”). The acceptable flooding probability according to the individual risk becomes: - -$$ - P_f \leq \frac{\beta \cdot 10^{-4}}{P_{d|f}} = \frac{0.1 \cdot 10^{-4}}{0.1} = 10^{-4}\text{ per year} -$$ (acceptable_flooding_probability) - -The societal risk criterion can be determined according to {eq}`limit_line`. Assuming a risk averse criterion $\alpha=2$. We can determine the constant $C$ of the limit line for $N_a = 100$ installations and $\beta=0.1$. - -$$ - C = \left( \frac{\beta \cdot 100}{k \sqrt{N_a}} \right)^2 = \left( \frac{0.1 \cdot 1000}{3 \sqrt{100}} \right)^2 = 0.11 -$$ - -The limit line for societal risk becomes $1 - F_N(n) \leq 0.11/n^2$. Both the individual and societal risk criteria are plotted in below. As a third criterion the economic optimization can be added. The optimal or acceptable probability of failure depends on the damage and investment costs. A relationship with the graph below can be established by assuming that the number of fatalities is related to the economic damages. A dike ring with many inhabitants and potential fatalities will generally also represent a large economic value. For the sake of the example we assume that every fatality corresponds to an economic damage of €$5 \cdot 10^7$ (note: this is not equal to the value of a human life). To calculate the economic optimum for the example we assume arbitrary values of $r=0.025$ and €$5 \cdot 10^6$ $B=0.33$. {numref}`combined_risk_criteria` below shows the combination for the three criteria. - -For a given number of fatalities in a dike ring the acceptable failure probability according to the three criteria can be derived. The individual risk criterion is independent on the number of fatalities. The economic criterion shows a linear relation between the failure probability and damage or number of fatalities. The societal criterion is risk averse so shows a decreasing quadratic relationship between acceptable failure probability and consequences. - -For a given number of inhabitants and potential fatalities for a dike ring, the acceptable failure probability can be determined. For dike rings with between 1 and 10 fatalities – generally small areas-the individual risk criterion is the most stringent. For dike rings with large numbers of fatalities, the risk averse societal risk criterion becomes dominant. - -Several extensions of this model are possible. One can consider to add the economic value of life loss or consider a different distribution of the nationally acceptable societal risk over dike rings with different sizes. - -```{figure} ../figures/risk_types.svg ---- -width: 600 -name: combined_risk_criteria ---- -Combination of individual, societal and economic risk criteria for a -hypothetical example. -``` -```` - -One field of application where these concepts have been applied concerns the flood protection standards in the Netherlands. Since 2017 new safety standards have been in place for primary flood defences in the Netherlands that have been derived based on a risk assessment, with standards been formulated as a (tolerable) probability of failure of the flood defences. - -[^neutral]: It should be noted that the usage of the term “risk neutral” to describe the FN-curve limit line for $\alpha = 1$ is widespread but, strictly speaking, incorrect in the context of decision theory (see {ref}`decision` Section). This is because the cost of risk bearing to a risk neutral decision maker equals expected loss (i.e. the product of probabilities and damages). The FN-curve shows cumulative probabilities, however. Also, an individual crossing of the limit line would not necessarily disturb a risk neutral decision maker, provided the other accident scenarios have relatively small probabilities. -[^taw]: TAW is nowadays called ENW: Extertise Network on Flood Protection. -[^men]: The group 'young men' is used as a baseline because this was the only information available at the time the study was completed. \ No newline at end of file diff --git a/book/some_content/overview.md b/book/some_content/overview.md new file mode 100644 index 0000000..5adab4e --- /dev/null +++ b/book/some_content/overview.md @@ -0,0 +1,3 @@ +# Overview + +Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum. \ No newline at end of file diff --git a/book/some_content/text_and_code.ipynb b/book/some_content/text_and_code.ipynb new file mode 100644 index 0000000..9abffd6 --- /dev/null +++ b/book/some_content/text_and_code.ipynb @@ -0,0 +1,51 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Text and code\n", + "\n", + "Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "hello world\n" + ] + } + ], + "source": [ + "print('hello world')" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "base", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.18" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/figures/cover.ipynb b/figures/cover.ipynb deleted file mode 100644 index bb44b64..0000000 --- a/figures/cover.ipynb +++ /dev/null @@ -1,341 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "a4d8be0c", - "metadata": {}, - "source": [ - "Took code from Week 1.8 Project and axle data. helper and solution file are included here, but I did not clean out the unnecessary code. bivariate plotting function included here but other aspects (marginal, copula) are still included in `helper.py`. `solution.py` is not needed, but the model definition code uses a dictionary that is set up there. \n", - "\n", - "Not sure why the figure in this notebook is not rendered with transparent background, but the svg is transparent, so i ignored it.\n", - "\n", - "`pyvinecopulib` was added to virtual env using pip without any issue. not included in requirements file to avoid build issues on the server." - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "7eeb37e0-aca0-4759-866f-f5ad09ea8d0b", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "import scipy.stats as st\n", - "\n", - "from helper import plot_contour\n", - "from helper import Bivariate\n", - "from solution import *\n", - "\n", - "from matplotlib import rcParams\n", - "rcParams.update({'font.size': 16})\n", - "# TUDelft colors palette\n", - "colors = [\"#0C2340\",\"#00B8C8\",\"#0076C2\",\"#6F1D77\",\"#EF60A3\",\"#A50034\",\"#E03C31\",\"#EC6842\",\"#FFB81C\",\"#6CC24A\",\"#009B77\"]" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "2152bd99-12cb-44a2-afee-7b36fb4b4780", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Length of the dataset: 992\n", - "Mean and standard deviation: (38.216, 10.020).\n", - "Mean and standard deviation: (55.941, 18.914).\n" - ] - } - ], - "source": [ - "X1 = univariate_RV_dict(\"Heaviest axle\", \"$AX_{max}$\", \"kN\")\n", - "X2 = univariate_RV_dict(\"Lightest Axle\", \"$AX_{min}$\", \"kN\")\n", - "X1[\"data\"], X2[\"data\"] = np.genfromtxt('./data_axle.csv',\n", - " delimiter=\",\", unpack = True)\n", - "\n", - "print(f'Length of the dataset: {X1[\"data\"].size}')\n", - "print(f'Mean and standard deviation:',\n", - " f'({X1[\"data\"].mean():.3f}, {X1[\"data\"].std():.3f}).')\n", - "print(f'Mean and standard deviation:',\n", - " f'({X2[\"data\"].mean():.3f}, {X2[\"data\"].std():.3f}).')" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "2ccfbc68-6705-4adf-83f8-9ebff6c1015d", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "dist_parameters = st.lognorm.fit(X1[\"data\"], floc = 0)\n", - "dist_object = st.lognorm(*dist_parameters)\n", - "X1[\"LN\"] = univariate_model_dict(\"Lognormal\",\n", - " dist_parameters, dist_object)\n", - "\n", - "dist_parameters = st.gumbel_r.fit(X1[\"data\"])\n", - "dist_object = st.gumbel_r(*dist_parameters)\n", - "X1[\"Gum\"] = univariate_model_dict(\"Gumbel (right)\",\n", - " dist_parameters, dist_object)\n", - "\n", - "dist_parameters = st.lognorm.fit(X2[\"data\"], floc = 0)\n", - "dist_object = st.lognorm(*dist_parameters)\n", - "X2[\"LN\"] = univariate_model_dict(\"Lognormal\",\n", - " dist_parameters, dist_object)\n", - "\n", - "dist_parameters = st.gumbel_r.fit(X2[\"data\"])\n", - "dist_object = st.gumbel_r(*dist_parameters)\n", - "X2[\"Gum\"] = univariate_model_dict(\"Gumbel (right)\",\n", - " dist_parameters, dist_object)" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "8f6a77dd-71c1-49e0-9e30-28269efc6d98", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# -----------------------------------------------------------------\n", - "plot_title = \"\"\n", - "font = \"Arial\"\n", - "x_label = \"Random Variable $X_1$\"\n", - "y_label = \"Random Variable $X_2$\"\n", - "legend = False\n", - "grid = False\n", - "save_svg = True\n", - "remove_ticks = False\n", - "remove_ticks_labels = True\n", - "file_name = \"../book/figures/cover_bi\"\n", - "# -----------------------------------------------------------------\n", - "\n", - "M2 = bivariate_model_dict(\"Model 2\", \"Gum\", X1, \"Gum\", X2, 0.54)\n", - "\n", - "M = M2\n", - "\n", - "rvs_temp = M[\"X1X2\"].rvs(1000).T\n", - "\n", - "import matplotlib.cm as cm\n", - "def plot_contour(bivar, xy_lim, data=None,\n", - " design_case=None, design_region=None,\n", - " nb_points=100):\n", - " \n", - " f = plt.figure(figsize=(6,6))\n", - " ax = f.add_subplot() # axes_class=AxesZero)\n", - " plt.setp(ax.spines.values(), linewidth=2)\n", - "\n", - " xlim = [xy_lim[0], xy_lim[1]]\n", - " ylim = [xy_lim[2], xy_lim[3]]\n", - "\n", - " x = np.linspace(xlim[0], xlim[1], nb_points)\n", - " y = np.linspace(ylim[0], ylim[1], nb_points)\n", - " X,Y = np.meshgrid(x,y)\n", - " pdf = np.zeros(X.shape)\n", - " for i in range(X.shape[0]):\n", - " for j in range(X.shape[1]):\n", - " # if X[i,j]>0 and Y[i,j]>0:\n", - " pdf[i,j] = bivar.pdf([X[i,j], Y[i,j]])\n", - " \n", - " ax.contour(X, Y, pdf, levels=8, cmap=cm.winter)\n", - " \n", - " if isinstance(data, np.ndarray):\n", - " ax.scatter(data[0,:], data[1,:], s=10.0,\n", - " facecolors='none', edgecolors='dimgray',\n", - " label='Data')\n", - " \n", - " if isinstance(design_region, np.ndarray):\n", - " ax.plot(design_region[0,:], design_region[1,:],\n", - " label='Design Boundary', color='k')\n", - " ax.fill_between(design_region[0,:], design_region[1,:],\n", - " ylim[1], label='Design Region', color='grey')\n", - " \n", - " if design_case:\n", - " ax.plot(design_case[0], design_case[1], 'ro',\n", - " label='Design Case')\n", - " \n", - " ax.set_aspect(\"equal\")\n", - " ax.set_xlim(xlim)\n", - " ax.set_ylim(ylim)\n", - " # ax.set_xlabel(r\"$X_1$\", fontsize=14)\n", - " # ax.set_ylabel(r\"$X_2$\", fontsize=14)\n", - " if isinstance(design_region, np.ndarray) or design_case:\n", - " ax.legend()\n", - " return f, ax \n", - "\n", - "fig, ax = plot_contour(M[\"X1X2\"], [0, 150, 0, 150],\n", - " data=rvs_temp, nb_points=100)\n", - "\n", - "ax.set_xlabel(x_label, fontfamily=font)\n", - "ax.set_ylabel(y_label, fontfamily=font)\n", - "\n", - "fig.patch.set_alpha(0.)\n", - "ax.patch.set_alpha(0.)\n", - "\n", - "if grid: ax.grid()\n", - "if legend: ax.legend(prop={\"family\":font})\n", - "if remove_ticks: ax.set_xticks([]); ax.set_yticks([])\n", - "if remove_ticks_labels: ax.set_xticklabels([]); ax.set_yticklabels([])\n", - "if save_svg: plt.savefig(file_name + '.svg', bbox_inches=0, transparent=True)" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# -----------------------------------------------------------------\n", - "plot_title = \"\"\n", - "font = \"Arial\"\n", - "x_label = \"Consequences\"\n", - "y_label = \"Probability\"\n", - "legend = False\n", - "grid = False\n", - "save_svg = True\n", - "remove_ticks = True\n", - "remove_ticks_labels = True\n", - "file_name = \"../book/figures/cover_fn\"\n", - "# -----------------------------------------------------------------\n", - "\n", - "fig2 = plt.figure(figsize=(6,6))\n", - "ax2 = fig2.add_subplot() # axes_class=AxesZero)\n", - "ax2.set_title(plot_title, fontfamily=font)\n", - "\n", - "\n", - "plt.setp(ax2.spines.values(), linewidth=2)\n", - "\n", - "right = 500\n", - "top = .5e-5\n", - "\n", - "u = np.array([1, 2, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 120, 150, 180, 200, 220, 250, 275, 300, 350, 400, 450, 475])\n", - "v = 1e-8 + top*(np.log(right) - np.log(u))**3/np.log(right)\n", - "\n", - "\n", - "C = 10**-3\n", - "alpha = 1\n", - "\n", - "limit_line_N = np.array([1, 1000])\n", - "limit_line_P = C/limit_line_N**alpha\n", - "\n", - "# Visualize\n", - "\n", - "# plotting\n", - "# ax2.plot(limit_line_N, limit_line_P, '--', label='Limit Line', color=colors[0], linewidth=4)\n", - "ax2.plot(u, v, label='Risk Curve', color=colors[1], linewidth=4)\n", - "ax2.plot(limit_line_N, limit_line_P, '--', label='Limit Line', color=colors[0], linewidth=4)\n", - "\n", - "ax2.set_xscale('log')\n", - "ax2.set_yscale('log')\n", - "\n", - "ax2.set_xlim(1, 1000)\n", - "ax2.set_ylim(10**(-7),.001)\n", - "# ax2.set_yticks([10**(-7),10**(-5),10**(-3),10**(-1)])\n", - "\n", - "ax2.tick_params(axis='x', labelsize=13, width=2, length=8)\n", - "ax2.tick_params(axis='y', labelsize=13, width=2, length=8)\n", - "\n", - "ax2.set_xlabel(x_label, fontfamily=font)\n", - "ax2.set_ylabel(y_label, fontfamily=font)\n", - "\n", - "fig2.patch.set_alpha(0.)\n", - "ax2.patch.set_alpha(0.)\n", - "\n", - "if grid: ax2.grid()\n", - "if legend: ax2.legend(prop={\"family\":font})\n", - "if remove_ticks: ax2.set_xticks([]); ax2.set_yticks([])\n", - "if remove_ticks_labels: ax2.set_xticklabels([]); ax2.set_yticklabels([])\n", - "if save_svg: plt.savefig(file_name + '.svg', bbox_inches=0, transparent=True)" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "2ea36977", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# combine ax and ax2 in one figure and overlay them offset to each other\n", - "fig3 = plt.figure(figsize=(6,6))\n", - "ax_bi = fig3.add_subplot() # axes_class=AxesZero)\n", - "\n", - "# add \n" - ] - } - ], - "metadata": { - "colab": { - "collapsed_sections": [], - "provenance": [] - }, - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.11.7" - }, - "widgets": { - "application/vnd.jupyter.widget-state+json": { - "state": {}, - "version_major": 2, - "version_minor": 0 - } - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/figures/data_axle.csv b/figures/data_axle.csv deleted file mode 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a/figures/economics.ipynb +++ /dev/null @@ -1,200 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 2, - "id": "65cbe2ec-de72-44d4-8af9-a969b06134a9", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from matplotlib import rcParams\n", - "rcParams.update({'font.size': 16})\n", - "# TUDelft colors palette\n", - "colors = [\"#0C2340\",\"#00B8C8\",\"#0076C2\",\"#6F1D77\",\"#EF60A3\",\"#A50034\",\"#E03C31\",\"#EC6842\",\"#FFB81C\",\"#6CC24A\",\"#009B77\"]" - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "id": "fc2eb45c-9f4e-4fbd-91c3-dc0ff10b4c46", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "image/png": 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lchjet5PC45Zv3Itrtx5kcXRERERE2oPJci6l7O7yvk8RmOHZH+VKOcn1yWQyDBy3EJHfo7M6PCIiIiKtwGQ5l+pka6nw4u4JiYCBvh42LZsMPV1duf7A4FCMm+WT9QESERERaQEmy7mUjb4uGlqaybXf/x6LlzFxKF+6GKZ79lN47J6jZ3Hk1KUsjpCIiIgo52OynIsp2qAEAPaGRAAARvTthLqulRWOGTXNi7v7ERERUZ7HZDkXa2+TH7oK9l7f8ykCMpkMIpEI6xdPRD5TY7kxXyO/Y8iExdzdj4iIiPI0Jsu5mIWuDppb5ZNrfxkTj4ffYwEADnYF4DVrtMLjL1y/g/U7j2RliEREREQ5GpPlXE7Z9td7/n8pBgB0btMYHVs1VDhu2qL13N2PiIiI8iwmy7lcG2sLGInlL/Pe/1+K8ZPXrNHc3Y+IiIgyLCEhARUqVIAgCHjz5k2qvrCwMHTu3BlmZmawsbFBz549ERoaqvA8U6ZMgampqdL+7MJkOZcz1hGjjbWFXPuH+ET4fvtfPWWLfKZYt3iCwnM8ev4Gc5ZvybIYiYiISHtNnjwZjx8/VtjXo0cPHDhwAOXKlUP58uWxZ88edOzYEUlJSanGBQcHY/ny5fD09ISNjY0mwk43Jst5QNeC+RW27wgOT/V1/ZpVMaxPR4Vjl2/YiwvX7qg9NiIiItJeFy5cgLe3t8K+x48f49y5c+jcuTN8fX1x/vx5jB07Fk+ePME///yTauyMGTNgYmKCsWPHaiLsDGGynAc0szKHuY5Yrn3vpwjEJaeudjFz7ACULemo8DwDxs7H54ivWRIjERERaZdv376hd+/eKFGiBGxtbeX6X758CQCoV69eStvP/3716lVK2/Pnz7F161ZMmzYNJiYmWRx1xjFZzgP0RSKFD/pFJiXjWFjq5Det3f3Cwr9i0LiFLCdHREREGDp0KIKDg7Fjxw7o6+vL9ZubmwMA4uLiUtqio38sAf13Ujxx4kQULVoUgwYNytqAM0knuwMgzehtZ411gWFy7duCPssl0s5limPuxEEYP2eV3PizV25j1ZaDGNm/c5bFSkRElNMMePIOT6Ljfj0wBytvYoiN5Z3Ucq49e/Zgz549mDp1KmrUqKFwTIUKFWBgYIBNmzahffv2MDIywqpVqyAIAlxdXQEA165dw19//YW9e/dCV8GNupyAyXIe4ZLPGKWNDfAiJj5V+9mISATFJ8LeQC9V++Be7rhw7S7+vugrd66Zyzaido2KqOJcKktjJiIiyimeRMfhZmT0rwfmAYGBgRg6dCiqVKmC6dOnKx1XoEABzJo1CxMmTECxYsVS2ocPHw5nZ2cAwPjx41GtWjV07pxzb8JxGUYeIQgCetvJl4aTAtj5nwf9fo5fu2gCCtpYyfVJJEnoO3oOvkfHZkWoRERElEPJZDL88ccfiIuLw44dO355N3j8+PG4ePEiPD09MWbMGJw8eRJz5swBABw+fBi+vr5YuHAhhP/fcVgikeDbt29Z/W1kCJPlPKSnnZXCC74t+HOqmss/WeXPh01LJ6f8AP/b24AgeM5crv4giYiIKMfy8vLCxYsXMW/ePJQrVy5dx9SvXx9Lly6Fl5cXmjVrBgBISkrCpEmT0LRpUzRq1AgSiQSDBg2CqakpLCwsUKJECbmKGdmFyXIeYm+ghyZKtr++peSjpbq/VcbYIT0U9u05ehZ7jpxRa4xERESUMz1+/BhTpkxB3bp1MWbMGJXOtWnTJrx+/RoLFy4EACxcuBAbNmzAwIEDsXfvXpiYmMDd3R0fPnxQR+gq4ZrlPKa3nTX+Do+Ua98WFA5Xc1OFx0we2RuXfe/j9v2ncn0eM5ejeuWyKF7UQe2xEhER5RTlTQyzOwSVqfo9TJo0CQkJCRCJROjVq1eqvvDwH0s6x44dCxMTE0yZMgVlypRReJ6YmBjMmTMH3bt3R6VKlQAAK1euhLOzM3x8fAAAxYsXR7Vq1bB27VosWLBApbhVxWQ5j2lbwAL5dMSITEpO1b73UwS8SxeBoYKtsXV0xNjiPRW1WvdH5PeYVH3RMXHoO3oOzu1fBT29nPkUKxERkarUVUVCm/0s+3bp0iWlY44dOwYA6N+/v9JkefXq1fjy5Qvmzp0LAIiIiMDnz5/RoEGDlDE/l3j8rNWcnbgMI48xEIvQLZ01l/+tiIMtVs0fp7Dv/pNXmLlsk9piJCIiopzn0qVLkMlkCv8VKVIEAPD69WvIZDLUr19f4TnCwsKwatUqDBkyBEWLFgWAlP0bEhMTU8bFxv4oIiAWy2+qpmlMlvMgRVUxgB81l9PSrnk99OnaSmHfys37cebyLZVjIyIiotzrZyWMKVOmpLRZW1vDxsYG165dQ1RUFADg9OnTAJDuhwizEpPlPOhnzeX/+llzOS0LpwxD6eJFFPYNGrcQn8Ii1BIjERER5S5v3rzBxo0bMXLkSFhapv6Ue9SoUQgPD0eFChXQunVr9OvXD+bm5hg2bFg2Rfs/TJbzoIzWXP43I0MDbFsxHfoK1ieHf/mGgeMWcDtsIiIikjN58mRYWVlh6NChcn0TJ07E3LlzIZFIcObMGVSvXh3nzp2DtbXiT8M1iclyHpXRmsv/Vq6UExZMlv9BB4CL1+9i+cZ9aoiQiIiItMX79+8hk8lQvHhxpWP279+Pjx8/wsjISK5PEARMmTIFQUFBSEhIwNWrV1G1atWsDDndmCznUZmpufxv/Xu0RSu32gr75nhvxs17T1SOkYiIiCi7MVnOw5Q/6Jf2UgzgxzvA1QvGwd5W/hxJScnoPXI2wr/I13MmIiIi0iZMlvOwnzWX/2vvpwjEJf963XF+czNs9p4KkUj+xyjo02cM8JzH9ctERESk1Zgs52GZrbn8b7WqV8CkEb0U9p276odl6/5UKUYiIiKi7MRkOY/LbM3lfxs3tCca1FK8CH/u8q244ns/U7ERERERZTcmy3mcKjWXfxKLxdjsNQUFbazk+qRSKfqMmcP6y0RERKSVmCzncarUXP43a0sLbF0+DWKx/I9UWPhX9Bk9B0lJyaqESkRERKRxTJYJv6tQc/nfalWvgBme/RX2Xbv9EPNWbM1khERERJqTkb99lHNk1XVjskywM9BDUxVqLv/bqP5d0LxhTYV9S9fuxpnLtzIVIxERUVYTi39UiJJIJNkcCWVGQkICAEBHR0et52WyTACA3vaZr7n8byKRCOsWT0BhexuF/f095yMwODTD8REREWU1XV1d6OvrIzIykneXtUxycjK+fPkCY2NjtSfL6j0baa021hYw1xHj23/WFe/9FAHv0kVgqGAtsjL5zc2w3WcGmnQdCYkkKVXf129R+GPkbPz953Lo6emqJXYiIiJ1sbKyQlBQED5+/Ih8+fJBV1cXgiBkd1i5hlQqRWJiIuLj4xXu05ARMpkMycnJiIuLQ2RkJKRSKQoWLKimSP+HyTIB+F/N5bWBYanaf9Zc7qqgHnNaqlUsgwWThmLsbB+5Pr8HzzB98QYsnDpMpZiJiIjUzczMDAAQHh6OoKCgbI4m95HJZIiLi4OhoaHa3oSIxWIYGRmhQIEC0NPTU8s5/43JMqXobWctlywDP2ouZzRZBoCBv7fDdb+HOHL6slzf6m0H8Vt1Z7RtWjdTsRIREWUVMzMzmJmZQSKRIDmZlZzUSSKR4MqVK6hbty50dVX/hFkkEmX53X8my5Siej5jlDE2wPOY+FTtP2su2xtk7N2aIAhYNX8cHj1/i7fvP8r1D52wGM6li8GpiL1KcRMREWUFXV1dtSR09D9isRhJSUkwMDDQmv9v+YAfpRAEQeGDfhmtufxvZqbG2LlyBgz05RPtqOgY9BoxC/EJ6dv8hIiIiEjTmCxTKj0LKq65vCUoYzWX/825THEsnTFSYd/DZ68xdpb8umYiIiKinIDJMqWirOby69h4XPoSlenz9urUAt3aN1HYt33/SWzdeyLT5yYiIiLKKhles1y3rvoeyBIEAZcvyz/8Rdmrj701TodHyrWv+xiGBpbyiXR6CIIA71mj8eDJKzx//V6uf+wsH5Qv7YTqlcpm6vxEREREWSHDyfK1a9fUNjnrFuZMbQtYwEZPF6GJqXcwOhz6FZ8SEmGrYP1xehgbGWLHypmo7z4YMbGpHyJMlEjQc9gMXD22HgWs8mc6diIiIiJ1ylQ1DDc3N0yePFmliefNm4fz58+rdA7KGnoiEfo5WGP+u+BU7UkyGbYEfcZkp8xXryhdvAjWLZqI30fMlOsLDg3HHyNn46/tS6Gry0ItRERElP0ylZHY2NigXr16Kk28adMmlY6nrDXAoQAWvAvGfx/p2xAYhgmOdhCr8KlAu+b1MHpgVyzfsFeu79rth5i2eD0WTuGGJURERJT9MvyA3x9//KGWdct169ZFr169VD4PZY2ihvpobmUu1x4Qn4h/FKxnzqgZHv3RoFZVhX2rtx7E/r/OqTwHERERkaoynCxv3boV/fv3V3niAQMGYOvWrSqfh7LO4EIFFLavCwxV+dw6OmJs8Z6GwvY2CvuHT16KJy/eqjwPERERkSpYOo6UamFtjkIKdu07+fkbPsQlqHx+q/z5sHv1bIUblsTFJ6D7kOn48i3z5eqIiIiIVKX2ZPnGjRs4c+aMuk9L2UAsCBjgIH93WQpg08fPapmjUvmSWD5njMI+/8Bg9PeYh+TkZLXMRURERJRRak+W+/XrhxYtWqj7tJRN+tlbQ6zgWb5NQWGQSKVqmaOHezMM7NlOYd/ZK7exYOV2tcxDRERElFFZsgwjs9siU85jZ6CHttYWcu0hCRL8FfZNbfMsmDwUrlXLK+xbtGonTpxVX31vIiIiovTimmX6pSGFFT+Et+6j6g/6/aSnp4udK2fCtoClwv6BYxfg1bsPapuPiIiIKD2YLNMvNcxvhuJG+nLt5yKi8DomXsERmWNbwBI7V81UuCHJ95hYdB8yHd+jY9U2HxEREdGvMFmmXxIJAgY5KL67vOFjmFrncq1SHouUbEjy8m0AhkxYxGU+REREpDFMlildettbQU/Brn1bgz4jPlk9D/r91L9HW/To0Exh37F/rmDx6p1qnY+IiIhIGSbLlC5WerroZJtfrj1CkoRDoV/UOpcgCPCeNRqVypVQ2D93+VYc++eKWuckIiIiUoTJMqXb4EJKHvQLVO9SDAAwNNDH7jWzkd/CTGH/wLEL8Pj5G7XPS0RERPRvWpUsS6VSeHt7o3Tp0jAwMEChQoXg6emJmJiYdB0fHR2N+fPnw9nZGaamprCyskLNmjWxbds2roNNh1rmJihnYijXfu3bdzz+rv4H7wrb22KHzwyIxfI/prFx8egyaCo+R3xV+7xEREREP2lVsjxmzBh4eHigbNmyWLlyJTp16gQfHx+0bt0a0l9skCGVStG8eXNMmzYN1atXx7JlyzB16lQkJyejT58+mDhxooa+C+0lCAIGK9jRDwDWZ8HdZQCo91sVLJ46XGFfYHAoegybgcRESZbMTURERKQ1yfLTp0+xcuVKuLu74/DhwxgwYAC8vLzg5eWFixcvYu/evWkef+vWLVy7dg0jR47Eli1bMHDgQIwePRpXr16Fo6Mj1q9fr6HvRLv9bmcFIwV3encEf0Z0UtZsSz2gZzv07dZaYZ/vncfwmLmCnwwQERFRltCaZHnPnj2QyWQYPXp0qvYBAwbAyMgIu3btSvP4qKgoAICdnV2qdj09PVhZWcHY2Fit8eZW+XR10M1WfuOQ78lS7P0UkSVzCoKApdNHorZLRYX92/efxLodh7NkbiIiIsrb5Hd/yKH8/PwgEong4uKSqt3AwACVKlWCn59fmse7uLjA3NwcixcvRtGiRVGjRg3ExsZi+/btuHv3LtatW5fm8T/vYv9KSEhIyn9LJFm/PODnHJqY66f+BfNjc9Bnufa1H0Lxh4381tjqsnX5VDTuPAIBHz/J9U2ctwbFitijQa2qWTZ/VsiO60fqwWun3Xj9tBuvn/bSxmsnyNT8+fX48eMREhKCnTvVWwvX2dkZYWFhCA2V32K5c+fOOHDgABISEqCnp6f0HFevXkX//v3x6tWrlDZTU1Ps2LED7dq1S3P+mTNnYtasWemO19LSEps3b073eG0zVs8Sb0S6cu1LE8JRXJaUZfMGhoRj1sp9iE+Qf5EZGepj1qiuKGiddQk7ERERab9+/fohIiIC9vb2+PjxY5pj1X5nefHixeo+JQAgNjYW+vryWy4DP+4u/xyTVrJsYmKC8uXLo02bNqhZsya+fPmC1atXo3v37jh27Bjc3NyUHmtmZgZ7e/tfxhkSEgKpVAoDAwO0aNHil+NVJZFIcPbsWbi5uUFXVz55zSqhweEY9OKDXPvToqUwskyRLJ27UNHi+H3ELLl1yrFxCdiw7zzO7PVBPjOTLI1BXbLr+pHqeO20G6+fduP101455dr9zB3TQ2uWYRgZGSEsTHHFhfj4+JQxyjx+/Bg1a9aEt7c3Bg8enNLerVs3lC9fHgMGDMDbt28hFosVHu/h4QEPD49fxung4ICgoCAA0OgPga6urkbn62FfAOPeBCHqPw/17Qv7Cq8yRWGum3U/Wm2b1cO0MX0x20v+zv1r/48YOG4hDmycr/Ra5kSavn6kPrx22o3XT7vx+mkvbbp2GX7Ar0qVKpg2bZrKE0+dOhVVq6Z/famdnR3Cw8ORkJAg1xcUFAQrK6s07yp7e3sjPj4enTp1StVuZGSEli1bIiAgAO/fv093PHmdsY4Yveys5Npjk6XYGRye5fOPHdIDnVo3VNh39sptTF3E6iZERESkugwnyw8ePEBAQIDKEwcEBODBgwfpHl+9enVIpVLcvn07VXt8fDwePHiAatWqpXn8z7u9ycny5c2SkpJS/S+lzyAlNZfXBYZleSk3QRCwesF4VHEupbB/1ZYD2HXo7yyNgYiIiHK/TH1W/vDhQ0yfPl2liR8+fJih8V26dMH8+fOxfPly1KlTJ6V948aNiI2NRY8ePVLa3r59C4lEgtKlS6e0lS1bFmfOnMG2bdswfvz4lPZv377h2LFjsLCwQPHixVX4jvKe8qZGqG1uimvfvqdqfxYTh6tfv6NufsVbVauLoYE+9qydg3ruQ/ApTL5s3aipXihW1B6/VXXO0jiIiIgo98pUsvz48WM8fvw405MKggCZTAZBENJ9jLOzM4YNG4ZVq1bB3d0dLVq0wPPnz+Hj44N69eqhe/fuKWMbNWqEgICAVHc3R48ejR07dmDixIl4/PgxatWqhS9fvmDjxo0ICQnB6tWrtWqNa04xuFABuWQZAFYEfMryZBkA7GytsWftHDTrNgoJ/9nJL1EiQbfB03Dx0Bo4FrZTcgYiIiIi5TKcLM+YMSMr4kiX5cuXo2jRotiwYQNOnjwJKysrjBgxArNnz4ZIlPaKkiJFiuD27duYPXs2zp8/j71798LQ0BCVKlXCsmXL4O7urqHvInfpYJMfo14EIEKSegnL0bCv8I+Nh6NR+p82zaxqFctg9YJx6O85X64v4mskOvSfiPMHVsMin2mWx0JERES5i1Yly2KxGJ6envD09ExznLIH9YoVK4bt27dnQWR5l4FYhEGFCmD+u+BU7VIAPh9C4V06a8vI/dSlrRuevvSH94Y9cn2v3wWix9DpOLp1MfT0tOPJWyIiIsoZtGa7a8q5hhWyga6CJTWbP4YhSoMPTc7w7IcWjWoq7Lt66wFGTvPK8gcPiYiIKHdhskwqszPQQxfb/HLt35Ol2PxRflvsrCIWi7HFeyoqlSuhsH/3ob+xdO1ujcVDRERE2o/JMqnFmKIFFbb7fAhFsgbv5hobGWL/hvmwt7VW2D/bazMOHD+vsXiIiIhIuzFZJrWoYmaMuhbyD9C9j0vAsbCvGo2loI0VDm5aABNjQ4X9QyYsgu/dzFdzISIioryDyTKpzZgitgrbvd9/0nAkQPnSxbDDZybEYvkf8YRECboOnoq374M0HhcRERFpFybLpDatC1jAyVBfrv3at++4Exmt8Xjc6rlg6fSRCvu+fI1CxwGT8OVblIajIiIiIm2i1mQ5JCQE+/fvx7Jly3Ds2DEAwJ07dyCRSH5xJOUGYkHASGV3lwM0f3cZAPr3aIvhfTsp7Hvj/6OkXGIifz6JiIhIMbUky5GRkejVqxeKFCmCbt26Yfz48Th06BAAYNSoUXB0dMStW7fUMRXlcH3trWGmI78T4v5PXxAUn5gNEQFzJwxCK7faCvuu3X6I4VOWsqQcERERKaRyshwbG4uGDRti165dsLS0RMeOHVMlHnp6eggODoabmxvevXun6nSUw5nqiNHfXr4SRZJMhlUfsufuslgsxqZlk1G5fEmF/XuOnMHi1Ts1HBURERFpA5WT5SVLluD+/fvo3bs3/P39sW/fvlT9Fy9exKRJkxAdHY1FixapOh1pgRFFbBX+YK0PDENscrLG4wH+V1LOoWABhf1zl2/F/r/OaTgqIiIiyulUTpb37dsHe3t7rF+/HgYGBgrHzJ07F05OTrh06ZKq05EWKGqoD3cb+U1KviYlY0dweDZE9INtAUsc3LQApsZGCvuHTFiMK773NRwVERER5WQqJ8v+/v5wdXWFrq6u0jGCIKBixYoIDAxUdTrSEsrKyC0P+ARpNq4PLlfKCTtWzlBYUi5RIkG3IdPw5MXbbIiMiIiIciKVk2VjY2N8+vTrtajBwcEwMlJ8R49yn9/MTeCSz1iu/WVMPP4Oj8yGiP6ncV0XeM0cpbAvKjoG7v0mIjA4VMNRERERUU6kcrLs4uICPz8/PH36VOmYBw8e4O7du3BxcVF1OtISgiBgtNIyciEajkZe325tMLJ/F4V9IaHhaN9nAmswExERkerJsoeHBxITE9GyZUscO3YMkZH/u2sokUhw4sQJtGvXDsnJyRg2bJiq05EW6WiTHw4GenLt5yKi8Ph7bDZElNqc8QPRsVVDhX0v3wagy6ApiItP0HBURERElJOonCw3btwY8+fPR2BgINzd3ZE/f34IgoCDBw/CyMgIbdu2xYcPHzB27Fi0bNlSHTGTltAViTC8kI3CvuXZtEnJv4lEIqxbNAF1XSsr7L959wn6jpmL5Gyq4EFERETZTy2bkkycOBHnzp1DkyZNYGhoCJlMhvj4eIhEItSpUwdHjhxh2bg8amChAjBS8DDd7pBwhCVk/855+vp6+HPtbJQv7aSw/8TZaxg7y4eblhAREeVRatvuukGDBjh9+jSioqIQGhqK4OBgREdH49KlS2jbtq26piEtY6Grg952VnLtCVIZ1gXmjIfo8pma4PDmRShsr/gu+KY//8LStbs1HBURERHlBGpLllNOKBLB2toatra2aZaTo7xjlJIH/dYEhiFBKtVwNIoVtLHC4S2LYWFuprB/ttdm7Dx4WsNRERERUXZTe7JM9F8ljQ3Rytpcrj00UYI9IRGaD0iJUsUKY/+GeTDQl38oEQBGTFmKfy7d1HBURERElJ10VD1B3bp10z1WEARcvnxZ1SlJC40pYosTn7/JtXu//4Q/7KwgCILmg1LAtUp5bF0+DT2GzYD0P3e9k5Ol6DViFk7t9kbVCqWzKUIiIiLSJJWT5WvXrv1yjCAIkMlkOSYhIs1rkN8MFUyM8Cg6dcm4R9GxuPglCg0t82VTZPJaudWG96xRGDXNW64vNi4eHftPwrn9q1CsqH02REdERESapHKyfPHiRYXtycnJ+PbtG3x9fbFu3Tp06tQJa9asUXU60lKCIGB0UVv0ffJOrs8r4FOOSpaBH5uWBIeGY9GqnXJ94V++oX2f8Th3YCUKWOXPhuiIiIhIU1ROluvVq5dmv7u7O9q0aYMGDRrA1dUVAwcOVHVK0lLdbC0x8dUHhCUmpWo/+fkbHn+PhbNpztoOfcqoPggJjcCOA6fk+vwDg9G+zwSc3O0NczOTbIiOiIiINEEjD/jVqVMHrq6uWL16tSamoxzKQCzCUCWblCx4F6zhaH5NEASsmOOBpg1cFfY/ev4GnQdORmxcvIYjIyIiIk3RWDUMGxsbvH79WlPTUQ41rLCNwk1K9n2KwJuYnJd06uiIsX3FdFSrqPiBPt87j/H78JlITMz+DVaIiIhI/TSSLEdGRuLq1aswNzfXxHSUg1np6WKQQwG5dimARf457+4yABgbGWL/hgUo7lhIYf+Zy7cwaPxCbotNRESUC6m8ZnnLli1K+5KTkxEWFobt27cjIiICffr0UXU6ygU8ixbE6g+hSPzPFtLbg8Mxo7g9HAz0syky5awtzXFs22I06TISQZ8+y/UfPHEB+cxM4D1rNKu+EBER5SIqJ8v9+/f/ZXIgk8lQpEgRzJkzR9XpKBewN9BDb3trbPgYlqpdIpNhqf8nLC9TJJsiS1the1sc274UTbuORMTXSLn+zX/+BXMzE8wcOyAboiMiIqKsoHKy3KtXL6XJskgkgomJCSpWrIguXbrA2NhY1ekolxjvWBCbPobhv5tdb/gYhinF7GCtlzO3Si9VrDCObF2Elj088D0mVq5/2bo/YZ7PFKMHdM2G6IiIiEjdVE6Wt23bpoYwKK8pZmSAbgUtsfs/213HSaVYEfAJc0soXh+cE1QuXwr7N8xDuz7jkaDgwb5pi9bD3MwUvbu0zIboiIiISJ00Vg2D6L8mOtopbF/1IRSRkiSFfTlF7RqVsGPlTIgVVPYAgFHTvHD0NLd2JyIi0nYZvrOc1gN96dG3b1+Vjqfco7ypEdoWsMCxsK+p2iOTkrEmMBSTnHL2dtItGtXE+sUT0d9zvlyfVCpFX4+5MDUxQqM61bMhOiIiIlKHDCfL6XmgLy1MlunfJjvaySXLAOAd8AmjitjCSCzOhqjSr0tbN0RGRcNzlo9cn0SShO5Dp+Ov7UtRo0q5bIiOiIiIVJXhZDmtB/qIMsrF3ASNLc1wLiIqVfvnxCRs+vgZI4vYZlNk6Tfw9/b4FhWNOd7yn7rExsWjY/+JOP3ncpQvXSwboiMiIiJVZDhZ5gN9pG6THe3kkmUAWPI+BIMLFYCeKOcvrR83tCe+fIvC6q0H5fq+RUWjbe9x+HvPCpRQsrEJERER5UwazULu37+vyelIS9TPb4bfzE3k2j/GJ2JncHg2RJRxgiBgweSh6NmxmcL+sPCvaNXTA/4fcuYuhURERKSYyqXjAODevXtYv349/P39kZCQANm/dmaTSqWIj49HaGgoQkJCkJSUs6sckOYJgoDJjnZoff+VXN9C/2D0treGWAuW/giCgJVzxyIyKgbHz1yV6w8ODUer3z1w+s/lKGyf85eXEBERkRqS5Tt37qBOnTpITExMSZIFQUiVMP/82tnZWdXpKJdqaW2OCiZGeBSdeqOPN7EJOPjpC7oUtMymyDJGR0eMLd5T0WnAJFy6cU+u/0NQKFr/7onTfy6Hna11NkRIREREGaHyMoxFixYhISEBbdq0wdGjRzF48GAIgoBjx47h8OHDGDRoEARBQLly5eDn56eOmCkXEgQBk50U112e/y441ZuvnM5AXw971s6Fa9XyCvvffQhGq16eCAv/ouHIiIiIKKNUTpavX78OW1tb7Nu3D23atEG3bt0glUohCALatWuHtWvXYtWqVXj27Bl8fOTLaxH91NE2P0oYGci1P4qOxcnP3zQfkApMjA1xaNNCVKtYWmH/63eBaN1rLCK+Rmo4MiIiIsoIlZPliIgIVK1aFXp6egCQstTizp07KWMGDx6MQoUKYe/evapOR7mYWBAw0bGgwr55WnZ3GQDMTI1xeMtiVChTXGH/s1f+6NBvEmJi4zUcGREREaWXysmyoaFhSqIMAObm5rCwsMCLFy9SjatSpQpev36t6nSUy/W0s0IhAz259puR0bj0Rb68XE5nkc8Ux7YvRZkSRRX2P3r+Bos3HkFUdIxmAyMiIqJ0UTlZLlGiBB4+fJiqrWTJkrh7926qtvj4eFbCoF/SE4kwrqjiu8vz/bWz7JpV/nw4sXMZSjgprrH89kMougyaiuiYOA1HRkRERL+icrLcsmVL+Pv7Y/To0YiM/LH+slatWnj37h2OHz8OAHj16hUuXboER0dHVaejPKCfgzWs9eQLtZyLiMLtb9HZEJHqCljlx4kdy+BUWPFDjLfuPUXngZMRG8clGURERDmJysny6NGj4ejoiJUrV6J79+4AgGHDhkEsFqNDhw6oWrUqqlSpgoSEBHTr1k3lgCn3MxKLMUbJNtfaencZAOxsrXFilxcK29so7L966wG6D5mG+IREDUdGREREyqicLJubm8PX1xfDhg2Di4sLAMDR0RHbt2+HgYEB7t+/j9jYWLRu3Rpjx45VOWDKG4YWskE+HbFc+7Gwr3j8PVbBEdqhkJ0Nju9YBjsbK4X956/dwe/DZyIxUaLhyIiIiEgRtWx3bW1tDR8fH8yYMSOlrVu3bggJCYGvry/evHmDo0ePQl9fXx3TUR6QT1cHwwsrvgM7481HDUejXk5F7HF85zIUsLJQ2P/3RV/0GjmLCTMREVEOkOFkeeHChfj06VO6xhobG6NGjRpwcnLKcGBEo4vYwkgs/yN6JOwr7kRq59rln0o6FcaJHctgaZFPYf/Jc9fRc/hMJHBJBhERUbbKcLI8efJkFC5cGO3bt8fJkychlUqzIi4iWOnpYmghxXeXp2n53WUAKFPSEYc3L4SxoeJPXE5fuIEew2dwDTMREVE2ynCy3KFDB4jFYhw7dgxt2rRB4cKFMXXqVLx79y4r4qM8boJjQZgouLv8d3gkrn39ng0RqZdzmWKYMMgdpiZGCvv/uXgTPYZOZ8JMRESUTTKcLB84cAAhISFYs2YNXFxcEBwcjPnz56NkyZJo3Lgx9uzZg8RE/mEn9bDS08WYIorrLk95Hah1u/op4lTIBoc2LYCZibHC/jOXb6Hb4KmIi0/QcGRERESUqQf8zM3NMXjwYPj6+uLly5eYPHkyChUqhAsXLqBnz54oWLAgRo0ahUePHqk7XsqDPIvawkJBZYwrX7/jXIT27eqnSLWKZXBs+xLkM1WcMJ+76oeug6ayDjMREZGGqWUHv7lz58Lf3x8XLlxAr169IJFIsHLlSlSuXBkuLi7YsGEDvn/X/o/MKXvk09XBeEfFm3nklrvLwI+E+a8dy2BuZqKw/8L1O9y4hIiISMPUUjrup/r162Pr1q0IDQ3Fjh070KhRI9y/fx+DBw+GnZ0d+vbtq87pKA8ZUdgGBRTs6ucXFYO/Pn/NhoiyRhXnUji+Yxks8pkq7L/sex+dBkxGTCy3xiYiItIEtSbLPxkaGqJnz544c+YMPn36hKlTpyIxMRHbt2/PiukoDzDWEWOyk73CvmmvP0KaS+4uA0Cl8iVxYqcXLMzNFPZfuXkfHftPQnQME2YiIqKsliXJMgAEBQVh6dKlaNmyJebNmweJRIICBQpk1XSUBwxyKAAHAz259sfRcdj/6Us2RJR1KpQtjpM7lyG/heKE+drth+jQfyK+R2vvboZERETaQK3JcmRkJDZv3oyGDRuiSJEiGD9+PO7evYuWLVviyJEj+PhR+2vjUvYxEIswTcnd5RlvPiJJmnvuLgOAc5niOLXLG1b5zRX23/B7BPd+ExD1PUazgREREeUhKifLiYmJOHz4MDp06ABbW1sMHDgQly5dQrFixbBgwQIEBgbir7/+Qtu2bSEWy1c0IMqIPvZWKKZgE49XsfHYEfw5GyLKWuVKOeHULi9YWyreGvvm3Sdo12c8vkVp946GREREOVWmk+WLFy+if//+sLGxQadOnXDkyBGIxWL8/vvvuHz5Ml6+fIkJEybA1tZWnfFSHqcrEmFmcQeFfbPeBiEhF+4oWaakI07t8kIBK8UJs9+DZ2jV0wOfI75pNjAiIqI8IMPJ8rhx41CoUCE0btwYW7ZsQWRkJKpXr47169cjJCQE27ZtQ506dbIiViIAQLeClihrbCjX/iE+EZs+hmVDRFmvdImiOLV7OWys8yvsf/jsNZp3H42Q0HANR0ZERJS7ZThZXrZsGYKCgmBpaYkxY8bg8ePHuHnzJgYMGABTU8XlrojUSSwImK3k7vLct8GITU7WcESaUapYYZza7Q3bApYK+1++DUDTrqMQ8PGThiMjIiLKvTKcLDdr1gwHDhxAUFAQli1bhnLlymVFXERpcrexQGVTI7n2T4kSrPmQO+8uA0BJp8I4/edyOBRUXFnGPzAYTbqMwKt3HzQcGRERUe6U4WT51KlT6NChA3R1dbMiHqJ0EQQBc0sUUti30D8YUUlJGo5Ic4oXdcA/e1fAqbDiXQ2DQ8PRrNtoPH7+RsORERER5T5ZVmeZKKs1t8qHmubyW0NHSJKw/H3uXopQ2N4W/+z1QZkSRRX2f474ihY9xsDvwTPNBkZERJTLMFkmrSUIAuYpubu8LOATviTm3rvLAGBbwBKndi9H5fIlFfZ/i4pGmz/G4urNB5oNjIiIKBdhskxarX5+MzTKL7/LXVRSMpa8D86GiDTLKn8+HN+5DL9Vc1bYHx0TB/d+E3Dm8i0NR0ZERJQ7MFkmrTe3hOLKGD4fQvEpIVHD0WhePlMTHNmyCA1rVVPYH5+QiK6Dp+LY35c1HBkREZH2Y7JMWs/V3BStrM3l2mOTpVjwLvffXQYAYyND7NswDy0b11LYL5EkodfI2fjzyD8ajoyIiEi7qZwsN2zYEAsWLPjlOA8PD5QqVUrV6YgUmqOk7vLawDC8iYnXcDTZw0BfDztXzkTnNo0U9kulUgwatxDrdhzWcGRERETaS+Vk+dKlS3j+/Pkvxz169AgBAQGqTkekUCUzY3S2ld/dTiKTYcKrvFNzWFdXBxuWTELvLi2Vjhk3eyXmeG+BTCbTYGRERETaSSejB3Tr1g1BQUGp2s6cOYO6desqPSYyMhJPnjyBo6NjxiP8F6lUihUrVmD9+vV4//49rK2t0blzZ8yePRvGxsbpOseXL18wf/58HD16FB8/foSpqSnKly+P2bNnc5tuLTe7uAMOhX5B8n9ywMNhX3HlSxTqKngQMDcSi8XwmesJYyNDrN56UOGYxat34nPEV3jPGg2xWKzhCImIiLRHhpPlNm3aoEePHilfC4KAsLAwhIWlvWuaWCzGjBkzMh7hv4wZMwY+Pj5o3749PD098fz5c/j4+OD+/fs4d+4cRKK0b5QHBASgfv36iI6ORr9+/VCyZElERkbi0aNHcm8ASPuUMjbEkEI2WPUhVK7P4+UH3HYtB5EgZENkmicIAhZMHgpTYyMsXLVD4Zite08g4mskNntNhYG+noYjJCIi0g6ZurPs4OAAqVQKmUyGhg0bws3NDZMnT1Y4XhAEGBgYwNHREdbW1pkO9OnTp1i5ciXc3d1x6NChlHZHR0eMHDkSe/fuRffu3dM8R8+ePZGUlIRHjx6hYMGCmY6Fcq4ZxeyxMzgckUnJqdrvRsVgd0g4frfL/M+gthEEAVNG94GpiTGmLFyrcMxf/1yFe98J2LNuDvKZym/wQkRElNdlOFkGkGq5wh9//IFatWqhXr16agtKkT179kAmk2H06NGp2gcMGICJEydi165daSbLV65cwbVr1+Dj44OCBQtCIpFAIpHAyMgoS+MmzbLS08W0YvYY+1J+nfKkV4HoYJMfRnls2cHI/p1hZZkPQycuRnKyVK7/6q0HaNF9DA5vWQQba/l130RERHmZyg/4bd26Ff3791dHLGny8/ODSCSCi4tLqnYDAwNUqlQJfn5+aR5/6tQpAEDhwoXRunVrGBoawtjYGCVLlsSuXbuyLG7SvOGFbeBkqC/XHpQgwbJcvg22Mt3bN8XedXNhaCD//wsAPHr+Bm6dR+BdAJcjERER/Vum7ixnh+DgYFhZWUFfX/6Pvb29PW7cuIHExETo6Slee/ny5UsAP+5ElyhRAtu3b0diYiKWLVuG33//HRKJBH369FE6v5eXF7y8vH4ZZ0hISMp/SySSX45X1c85NDGXthABmF/MDl2f+Mv1LfIPxh82Fiior6v5wBTQ5PVrVLsaDm9ZiG5DpuNb5He5fv/AYLh1GYEDG+bDuUyxLI9H2/G1p914/bQbr5/20sZrJ8jUUD/q9u3bWLZsGZ48eYKYmBhIpfIf9QI/1lBmtnxcsWLFIJFI8OGD/MfrvXr1ws6dO/H161eYm5srPL5x48Y4f/48nJyc8Pz585Sk+uvXr3BycoKBgQGCgoKUPiQ4c+ZMzJo1K93xWlpaYvPmzekeT+olAzBZLz+ei+TfPDVOisXwpCjNB5VDfPwUgUUbjuBrZLTCfkMDPYzp0xplixfScGRERESa0a9fP0RERMDe3h4fP35Mc6zKd5Zv3LiBhg0bQiKR/LJuq6BCJQIjIyOlFTfi4+NTxihjaGgI4McDiv+++2xhYYE2bdpgx44dePnyJcqUKaPweDMzM9jb2/8yzpCQEEilUhgYGKBFixa/HK8qiUSCs2fPws3NDbq6OeNuaU5hExWDmndeyrWf1zHCgt+qoKJp9q9Xz67r17xpE3QcMAmv/eV/QcTFJ2LZ5r+wcekktHKrrbGYtA1fe9qN10+78fppr5xy7QwMDNI9VuVkefbs2UhMTESnTp0wfPhw2NnZQUdH/as77Ozs8OzZMyQkJMgtxQgKCoKVlZXSJRgA4ODwY4c3W1tbub6flTG+fv2q9HgPDw94eHj8Mk4HB4eUMnSa/CHQ1dXlL4z/+M3SHD0KWmJ3SESqdhmACW+Dca5aaZXewKmTpq+fU1EHnNm3Ch37T8TdRy/k+hMSJeg9ei6Wzx6DPl1baSwubcTXnnbj9dNuvH7aS5uuncoP+Pn6+qJkyZLYt28f6tSpg2LFiqFIkSJK/2VW9erVIZVKcfv27VTt8fHxePDgAapVq5bm8T8fDFR0q/1nW4ECBTIdH+VM80sUgoFIPiG+8CUKJz9/03xAOYhV/nw4sdMLDWspfu1IpVKMnLqMu/0REVGepnKyLJPJUL58eXXEkqYuXbpAEAQsX748VfvGjRsRGxubaqOUt2/f4sWL1HfL2rVrB1NTU+zatQvR0f9bqxkSEoKjR4+iZMmSKF68eJZ+D6R5hQ314VlUcU3tca8+QKJkfX1eYWJsiAMb56Njq4ZKxyxevRODxi1AYqL2PIxBRESkLiony5UrV8bTp0/VEUuanJ2dMWzYMBw+fBju7u7YtGkTPD094eHhgXr16qWqsdyoUSO5tccWFhZYunQpgoKC4OrqCi8vLyxcuBCurq5ITEzEypUrs/x7oOwxwdEONnryH/W8iInHho9p7zyZF+jp6WKz1xQM7tVe6Zg9R8/Cvd8EfItS/FAgERFRbqVysjxx4kS8fPkSK1asUEc8aVq+fDmWLl2Kp0+fYtiwYdi7dy9GjBiBEydO/HKrawAYOHAgDh06BBMTE0ybNg3z5s1DqVKlcPHiRTRp0iTL46fsYaojxtwSDgr7ZrwJwjdJkoYjynlEIhEWTxuB6R79lI657HsfTbqMwMdgvsEgIqK8Q+Un8SQSCdq3bw8PDw/s3LkTrq6usLCwUPjglCAIGSq/9l9isRienp7w9PRMc9z79++V9rm7u8Pd3T3TMZB26mNvDZ+AT3gcHZeqPUKShHnvgrGkVOFsiiznEAQB44b2REEbK4yYshRJ/9kyHACev36Php2G4eDGBahQlsuWiIgo91M5WW7Xrh0EQYBMJsO9e/dw7949uTE/+1VNlokySywIWFaqCJrcla/84BPwCYMLFUAxo/SXkcnNenZoBjsbK/QcNgPfY2Ll+kNCw9G020jsXDkTjeu6KDgDERFR7qFysjx9+vQcU36LKC1uVvnQwsocp8K/pWpPlMkw8VUgDlQqkT2B5UANa1fDmX0+6NBvIoJDw+X6o2Pi0HHAJKyY44E/OrfMhgiJiIg0Q+VkeebMmWoIg0gzlpQqhH8iviH5P5XQDoZ+wfWv31HLwjR7AsuBypcuhgsH16BD/4l4+vKdXH9yshTDJy9FYHAopozqwzfNRESUK6n8gN+/hYSEYP/+/Vi2bBmOHTsGALhz545W7f9NuVtZEyMMclBcT9vjZQCkrCecin1Ba/yzdwUa1KqqdMyiVTsxaPxClpYjIqJcSS3JcmRkJHr16oUiRYqgW7duGD9+PA4dOgQAGDVqFBwdHXHr1i11TEWkspnFHWCmI5Zrvx0Zgx3B8ksO8rp8piY4uHEBurs3VTpmz5EzLC1HRES5ksrJcmxsLBo2bIhdu3bB0tISHTt2TLXbl56eHoKDg+Hm5oZ37+Q/yiXSNGs9XUx1slPYN/7VB3xJZCm5/9LT08W6RRMwcXgvpWMu+95H407D8S4gSIORERERZS2Vk+UlS5bg/v376N27N/z9/bFv375U/RcvXsSkSZMQHR2NRYsWqTodkVqMLGILR0N9ufbPiUmY8iYwGyLK+QRBwJTRfbB6wTjoKLgzDwAv3wagQcehuO73SMPRERERZQ2Vk+V9+/bB3t4e69evh4GB4tJbc+fOhZOTEy5duqTqdERqoS8SYXnpIgr71geG4fY3LidQplenFji4cQFMjA0V9n/5GoXWvTyx69DfGo6MiIhI/VROlv39/eHq6gpdXfnthH8SBAEVK1ZEYCDv2FHO0aaABVpbm8u1ywAMee6PZD7sp1SjOtXxzx4fFLSxUtgvkSRhyIRFmL54A6RSqYajIyIiUh+Vk2VjY2N8+vTpl+OCg4NhZGSk6nREarWidBEYKtgq/V5ULNYFhmZDRNqjQtniuHhwDSqWVV6f2nvDHvQYNgMxsXFKxxAREeVkKifLLi4u8PPzw9OnT5WOefDgAe7evQsXF+72RTmLo5EBphZT/LDflNcf8SkhUcMRaZefpeVaN6mjdMyJs9fQtOsoBIV81mBkRERE6qFysuzh4YHExES0bNkSx44dQ2RkZEqfRCLBiRMn0K5dOyQnJ2PYsGGqTkekdp5FC6KUsfx6+8ikZIx7+SEbItIuxkaG2LVqJjwHd1c65uGz16jfYQjuPpLfbpyIiCgnUzlZbty4MebPn4/AwEC4u7sjf/78EAQBBw8ehJGREdq2bYsPHz5g7NixaNmS2+JSzqMvEmF1maIK+3aFRODSlyjNBqSFRCIRZo4dgHWLJ0BXV/HGoJ/CItCs2ygcOXVJs8ERERGpQC2bkkycOBHnzp1DkyZNYGhoCJlMhvj4eIhEItSpUwdHjhxh2TjK0RpZ5kM3W0uFfUOf+SORD6mlSw/3Zjix0wuWFvkU9scnJKLXyFlYvHpnqnrsREREOZXatrtu0KABTp8+jaioKISGhiI4OBjR0dG4dOkS2rZtq65piLLMstKFYSqWf0k8j4mH9/tfP8RKP9Ss5oyLh9agdHHFpfkAYI73FvT3nIe4+AQNRkZERJRxakuWU04oEsHa2hq2trYIDQ3FrVu38P37d3VPQ6R2BfX1MKdEIYV9s98FISCOiV16ORa2w7kDq+BWV/lDvfv/Oo8mXUYgMJhVR4iIKOdSS7L87Nkz9O3bF9euXUtpGzduHIoWLYqaNWvC3t4eGzduVMdURFlqWCEbVDSVL3EYmyzF6BcB2RCR9spnaoL9G+ZjyB/uSsc8ePoaddsNxrXbDzUYGRERUfqpnCy/ePECrq6u2L59Ox49+rHF7aVLl7Bs2TIAQMWKFSGRSDB48GBcvnxZ1emIspSOSMDaskUV9h0N+4oTYV81G5CW09ERY/G0EfCeNRpiBUtcACD8yze07uWJDTuPcB0zERHlOConywsXLkR0dDRGjhyJzp07AwC2bNkCQRCwYMEC3Lt3D9euXYNIJIK3t7fKARNltd/MTdHf3lph34gXAYhNTtZwRNqvf4+2OLx5EczNTBT2JyUlw3OWD4ZPXooE1rYmIqIcROVk+eLFiyhTpgy8vb1hZWUFmUyGU6dOQRAE9OnTBwBQtWpV1K5dGzdv3lQ5YCJNWFiyECwVlEB7H5eABe+CsyEi7dewdjVcOrwuzQf/dhw4heY9xiAkNFyDkRERESmncrIcGhqKcuXKpXx9584dfPnyBc7OzrCyskppt7a2xtev/AibtIOlni4WlVT8sN9i/xC8jOH2zZlRrKg9Lhxcg1ZutZWO8XvwDHXbD8bt+880GBkREZFiKifLVlZW+PbtW8rXp0+fBvBjs5J/e/fuHczNzVWdjkhj+thb4zdz+WUDiTIZhj9/z/W1mWRqYoTdq2dh8sjeSsd8CotA8+6jsePAKc0FRkREpIDKyXL58uVx9epVvHz5ElFRUdixYwcEQUCbNm1Sxhw6dAj37t1D9erVVZ2OSGNEgoC1ZYoqfJGci4jCvk9fNB5TbiESiTBp5B/Ys3YOTIwNFY5JlEgwbNISjJ3lA4kkScMREhER/aBysjxq1CgkJiaiQoUKsLOzw7t371C1alXUqVMHANCyZUt06dIFIpEIY8aMUTlgIk2qaGaMkUVsFfaNevEeEYkSDUeUu7Ryq42LB9egWBF7pWPW7zyCNn+MRVg435wQEZHmqZwsN2/eHNu2bYODgwNkMhmaNm2KI0eOpPQHBgbCwsICBw4cQKNGjVSdjkjjZhW3R0F9Xbn2sMQkjGLtZZWVLlEUFw+vTXMDk2u3H6J220G4ee+JBiMjIiJS06Ykv//+O96+fYuYmBicPn0a9vb/u0u0b98+fPr0Ce3bt1fHVEQaZ6ajA+9Siis47A6JwHHWXlaZRT5THNg4H2MGdlM6JiQ0HM27j8ba7Ye4XpyIiDRG7dtd/1eZMmUgFouzehqiLNXZNj9aWZsr7Bv0zB9fuaZWZWKxGLPHD8S2FdNgaKCvcExSUjLGz1mFvmPmIpoVSYiISAPUmiyHhIRg//79WLZsGY4dOwbgRyk5iYTrOkm7CYKAdWUdkU9H/o1fSIIEHlyOoTYdWjbEuf2rUNjeRumYgycuoL77ELx8+0GDkRERUV6klmQ5MjISvXr1QpEiRdCtWzeMHz8ehw4dAvDjAUBHR0fcunVLHVMRZRt7Az14l1a8HGNbcDhOf/6m2YBysQpli+PykfVoVLua0jEv3wagvvtgHDl1SXOBERFRnqNyshwbG4uGDRti165dsLS0RMeOHVOtJ9TT00NwcDDc3Nzw7t07Vacjyla97azQ1DKfwr4BT98hkssx1MYqfz4c2rwQE4f3UjomOiYOvUbOwsR5q1lejoiIsoTKyfKSJUtw//599O7dG/7+/ti3b1+q/osXL2LSpEmIjo7GokWLVJ2OKFsJgoCN5RxhKpZ/6QQlSDD2JZcFqJNYLMaU0X1wcNMCWOQzVTpu9daDaNGT22QTEZH6qZws79u3D/b29li/fj0MDAwUjpk7dy6cnJxw6dIlVacjynaFDPWxVEl1jE1Bn3E2PFLDEeV+Teu74uqxDahcvqTSMTfvPkHttgNx7dYDzQVGRES5nsrJsr+/P1xdXaGrK1+H9idBEFCxYkUEBgaqOh1RjjDAwRqN8psp7Ov/9B2+JyVrOKLcr4iDLc7sW4k+XVspHRMW/hWtennCe8MeSKVSDUZHRES5lcrJsrGxMT59+vTLccHBwTAyMlJ1OqIcQRAEbCrvBGMFyzE+xCdiwisux8gKBvp68JnribWLJsBAX0/hmORkKaYv3oBOAybjc8Q3zQZIRES5jsrJsouLC/z8/PD06VOlYx48eIC7d+/CxUX5Dl1E2qaooT4WlSyksG9tYBguRnA5Rlbp2aEZzh9YDcdCdkrHnLl8C7XaDMC12w81GBkREeU2KifLHh4eSExMRMuWLXHs2DFERv4vQZBIJDhx4gTatWuH5ORkDBs2TNXpiHKUIYVsUM9C8YNn/Z/6I4bLMbJMhbLFcfnoOjRvWFPpmJDQcLTs6YHFq3ciOZnXgoiIMk7lZLlx48aYP38+AgMD4e7ujvz580MQBBw8eBBGRkZo27YtPnz4gLFjx6Jly5bqiJkoxxAJAjaVc4KhSP6l9C4uAZNfc51+VrLIZ4q96+Zghmd/iBRcAwCQSqWY470F7ftOQFj4Fw1HSERE2k4tm5JMnDgR586dQ5MmTWBoaAiZTIb4+HiIRCLUqVMHR44cYdk4yrWKGxtggZLlGCs/hOLa1+8ajihvEYlEGDukB07sWAbbApZKx128fhe/teqPSzfuajA6IiLSdionyxMmTMC2bdvQoEEDnD59GlFRUQgNDUVwcDCio6Nx6dIltG3bVh2xEuVYIwrboJa5iVy7DEDfJ+8QyyUAWa6OayXcOL4RjetUVzomLPwr2vwxDnOXb0ESl8gQEVE6qJwsb9y4ET4+Pv87oUgEa2tr2NrapllOjig3EQkCtpR3goFIkOt7HRuP6W8+ZkNUeY+1pQUObV6ImWMHQKygUgkAyGQyLFq1E61+90Dwp88ajpCIiLSNysmyRCJBkSKKN2ggyktKGhtiTnHFyzG83n/C1a9RGo4obxKJRPAc3B2n/1wOh4IFlI677vcINVsPwNnLtzUYHRERaRuVk+Vu3brhzJkzuHuX6wCJxhS1RY18xnLtMgA9H73FN0mS5oPKo36r6oxrf21Is1pGxNdIuPebgEnz1yAhIVGD0RERkbbQUfUEbm5uuHLlCmrUqIEaNWqgYsWKyJ8/v8In0wVBwKxZs1SdkijHEv//cozKN54gUSZL1fchPhGDn/ljT4XiEAT55RqkfpYW+bBv/Vys3noQ05dsgETJm5VVWw7giu99bPaeitLF+UkZERH9j8rJcpcuXSAIAmQyGXx9feHr6ys35mc/k2XKC8qaGGFOCQdMeCVfNm7fpy9obhWOP+ytsyGyvEkQBAzv2wmuVcuj96jZCPioeMfRR8/foE7bgVgweSj6dW/DNzRERARADcny9OnT+UeF6D/GFi2Iv8MjcfGL/DrlYc/fo5a5KYobG2RDZHlXtYplcO2vjRg+aQmO/XNF4Zj4hESMmbEcZ6/cxqr542Btaa7ZIImIKMdROVmeOXOmGsIgyl1EgoAdzk6oeOMJvvzno/+YZCm6P3qD6zXKZlN0eZe5mQl2rpqJTbuPYfKCtYhXsk751Pkb+K1VP2xYMgkNa1fTcJRERJSTqGVTEiKS52Cgj03lHBX2+UXFYObbIA1HRMCPZRkDerbDlSPrUK6Uk9JxoZ+/oG3vcXz4j4goj8tUspycnIwVK1agXr16KFOmDJo2bYodO3aoOzYirdfeJj8GOChen7zgXTAuc3e/bFOmpCMuHV6Lob07pDlu1ZYDaNBxKF68fq+ZwIiIKEfJcLKcmJiIRo0awcPDA1evXsXLly9x9uxZ9OnTB507d86KGIm0mnepIiilYH2yDECfZ+/xHVzzn10M9PWwaOpwHN68CAWsLJSOe/z8Leq0G4RNu49B9p8qJ0RElLtlOFles2YNrly5Ajs7O6xYsQInT57EwoULYW5ujkOHDmHXrl1ZESeR1jLWEWNPheLQVfAg7McECdbq5mMCls3c6rng5snNaNrAVemYnw//dR44BaGfv2gwOiIiyk4ZTpYPHjwIQ0NDXL9+HSNGjEDz5s0xfvx4XLx4EQCwZ88etQdJpO0qmxljfgnFu/vdEBtgW0iEhiOi/7K2tMCBDfOxbMZIGOjrKR3390VfuLToo7SiBhER5S4ZTpZfvHiBunXronDhwqnaK1SogKpVq+Lhw4dqC44oN/EoaovGlmYK+8a8+ohXMXEajoj+SxAEDPy9/S8f/vvyNQp9Rs/Fmt1/41sk150TEeVmGU6Wv3//DgsLxWv7HB0dERHBO2REiogEAdvLF4OlrnzFxlipFN0fvUWiVJoNkdF/pffhvxv3XqBW20E4f9VPQ5EREZGmZThZlkgk0NFRXJ5ZT08PiYkssUSkjJ2BHraUV3zH8m5UDKa9/qjhiEiZ9D78FxIajnZ9xmPMdG/ExPLTASKi3IZ1lok0rE0BCwwpVEBh35L3IbgQEanhiCgtbvVccOvUVrRrVi/NcZv+/As1W/XHzXtPNBQZERFpApNlomywtFRhlFFSTu73x28RkSjRfFCklFX+fNixcgY2e02BuZmJ0nHvPgSjaddRmLFkIzcyISLKJZgsE2UDI/GPcnJ6CsrJBSdI0PvJO0hZTi5HEQQBnds0xq1TW9C4TnWl46RSKbzW/4n6HYbg8fM3GoyQiIiyguLFx79w9OhRODnJr7sMDw8HAIV9wI8/Nm/fvs3MlES5TkUzY8wvbo+xCtYpn/j8DQv9gzHZyT4bIqO02Nla4/CWRdi46ygmL1iDhMQkheOevHiHeu5DMH5oT3gO7gFdBQ92EhFRzpep397R0dGIjo5W2v/+/XuF7YKCu2hEedlwB2vsfvEW98X6cn3TXn+ESz4TNLbMlw2RUVoEQUCfrq0gS4zC/r9v4/b9ZwrHSSRJmLdiG/46cxVrFoxHpfIlNRwpERGpKsPJ8s/NR4hIdSJBwEhJJCYa2iH0P3copQC6PXyDe7+VRyFD+WSasp+tlTlO7lyGNduPYN7yrUiUKF5r/vj5W9TvMAQeg7pjwrDfoZ/GpidERJSzZDhZrlcv7SfCiShjLCDF7nKOaPrgNZL/s0w5XJKEjg9f44pLWeiL+IhBTiQWi+ExqBua1HPBgLHz8eTFO4XjkpOlWLJmF46fuYo1C8ejeqWyGo6UiIgyg399iXKAuhamWFiisMK+25Ex8HgRoOGIKKPKly6Gy4fXYeyQHhCLlf9qffEmAI07j8CUhesQF5+gwQiJiCgzmCwT5RCeRW3hXkDx5hdrAsOwKzhcwxFRRunp6WKGZ39cOLgmze2ypVIpfDbtw2+t+uO63yMNRkhERBnFZJkohxAEAVudnVDSSL7+MgAMfOqPR99jNRwVZUYV51K4cmQdJo34Azo6YqXj3r7/iObdR2PcbB9Ex3D3PyKinIjJMlEOYqajg8OVS8BIwcf4cVIpOjx4hW8SxaXKKGfR09PF5FG9ceXIOlQsW0LpOJlMhnU7juC3Vv1w8fpdDUZIRETpwWSZKIcpZ2KEjWUdFfa9iU1A7yfvIOOGJVrDuUxxXDy0BjM8+0NPV1fpuPeBIWjzx1gMHLcA4V+45TkRUU7BZJkoB+puZ4XhhW0U9h0L+4rF/iEajohUoaurg7FDeuD6XxtQrWKZNMfuOXIGVZv2wp9H/uGbIiKiHIDJMlEOtaxUYfxmbqKwb/LrQFyI4N1HbVO6RFGc278S8yYOgUEatZa/fI3CoHEL0eaPsXj7PkiDERIR0X9luM5yw4YNMz2ZIAg4f/58po8nykv0RCLsr1gcVXyf4LOCDUu6PvqxYYmDATcs0SZisRgj+3dGi8Y1MWzSEtxIoxrGpRv34NqyLyYM74VR/btwy2wiomyQ4d+8ly5dUtguCILSjwx/9nG7a6KMcTDQx94KxeF25wWk/+n7nJiEzg/f4FL1MtDjhiVap3hRB5ze7Y1Nu49h5tJN+B6juNJJfEIiZi3bhIMnLsBnridcKnMzEyIiTcrwX9izZ8+m+vf333+jbNmy0NHRwYgRI3D+/Hm8e/cOHz58wM2bNzF16lQYGhqiZs2aePHiRVZ8D0S5WkPLfJhXopDCPt9v0Rj78oOGIyJ1EYlEGPh7e9z5ZxtaN6mT5tinL9+hcefh8Jy5AlHfYzQUIRERZfjOcqNGjVJ9vXjxYrx48QInT55E06ZNU/U5ODjAxcUFTZo0QYMGDbBt2zbMmzdPtYiJ8qAJjgVxMzIax8K+yvWt/BCKiqZG6OdQIBsiI3Wws7XGn2tm468zVzF2lg9CQhVvQCOTybBh11GcOHsNS2aMRGu32vzEjogoi6n82e2GDRtQu3ZtuUT532rXro369etj586dKs0llUrh7e2N0qVLw8DAAIUKFYKnpydiYjJ+lyU2NhZOTk4QBAHDhw9XKS6irCYIAraXd0JxI8Xrkwc/e49LX6I0HBWpW5smdXDn720Y2LNdmklwcGg4egydjk4DJ8P/Q7AGIyQiyntUTpZDQkJgbW39y3EmJib48uWLSnONGTMGHh4eKFu2LFauXIlOnTrBx8cHrVu3hlT63xWdaZs+fTo+f/6sUjxEmpRPVweHKpWEoYL1yUkyGTo8eI3XMfHZEBmpk5mpMZbNHIVz+1ehbEnF9bZ/+ufiTbg074NFq3YgISFRQxESEeUtKifLRYsWxeXLl/H9+3elY0JCQnD+/HmUKlUq0/M8ffoUK1euhLu7Ow4fPowBAwbAy8sLXl5euHjxIvbu3Zvuc927dw/Lly/HrFmzMh0PUXaoYGqETeUUJ1BfJElode8lvnKHv1zBpXJZXDu2ATM8+6dZZi4+IRFzl29FjZb9cP6qnwYjJCLKG1ROlnv16oXw8HA0a9YMT58+lev39fWFm5sbYmJiMHjw4EzPs2fPHshkMowePTpV+4ABA2BkZIRdu3al6zzJyckYMGAAmjVrBnd390zHQ5RduttZYYqTncK+V7Hx6PTgNSQZ/KSFcqafm5ncPLkF9WtWSXPs2/cf0a7PePw+fCaCQvipGRGRuqhctNPDwwNnzpzBxYsXUaFCBdjZ2cHe3h4AEBAQgLCwMMhkMnTv3h0DBgzI9Dx+fn4QiURwcXFJ1W5gYIBKlSrBzy99d1S8vb3x4sULHDp0KEPz/7yL/SshIf/bWU0ikWRojsz4OYcm5iL1y+z1m1bEBs+/x+Lw529yfee/RGHYU3+sKlWID39lIU2+9grbF8ChTQuw79g5TFu8ARFflW9Ic/Tvyzh75RbGD/sdg39vz9rMSvB3p3bj9dNe2njtBJka9lNNSkrCihUrsG7dOrx9+zZVX9myZTFmzBj069dPpTmcnZ0RFhaG0NBQub7OnTvjwIEDSEhIgJ6e8o8r/f39Ub58eUyfPh0TJkzA+/fv4ejoiGHDhmHVqlVpzj9z5swMLduwtLTE5s2b0z2eKKMSAEzRs8Qbka7C/n6SKLROVly7l7RXdGw8Dpy6jgs3H+NXv70dbC3R270BShdz0ExwRERaol+/foiIiIC9vT0+fvyY5li13HLQ0dGBp6cnPD09ERwcjODgYAiCAHt7e9ja2qpjCsTGxkJfX3ElAAMDg5QxaSXLgwcPhpOTEzw8PDI8v5mZWcod87SEhIRAKpXCwMAALVq0yPA8GSWRSHD27Fm4ublBV1dx0kQ5l6rXr0ZCImrdeYmgBPl36Ft1zdCmamU0t8qnjlDpP7Lztde5ozvuPX6JcbNX4v6TV0rHffwUgblrDqJLm8aYNW4AClhZaDDKnI2/O7Ubr5/2yinX7mfumB5q/3zOzs4OdnaK11OqwsjICGFhYQr74uPjU8Yos2vXLpw9exZXrlzJ1MXx8PBIV5Lt4OCAoKAgANDoD4Guri5/YWixzF6/Irq6OF6lFGrffobY5NTrlKUAej71x/Ua5eBsqvy1QarJrtdejSrlcfHQGmzbdxIzl27Et6hopWP3/XUOp87fwIQRvTCklzv09Pi74if+7tRuvH7aS5uunVr3yA0JCcH+/fuxbNkyHDt2DABw584dtaxLsbOzQ3h4OBISEuT6goKCYGVlpfSuckJCAjw8PNCiRQvY2trizZs3ePPmDQICAgAAkZGRePPmDb59+6ZynESaVtnMGLudi0HR6uTvyVK0vvcSYQruPJP2E4vF6Ne9De6d3YEeHZqlOfZ7TCymLlyHGi374Z9LNzUUIRGR9lNLshwZGYlevXqhSJEi6NatG8aPH5/yAN2oUaPg6OiIW7duqTRH9erVIZVKcfv27VTt8fHxePDgAapVq6b02Li4OHz+/BknT55EiRIlUv7Vr18fwI+7ziVKlMCmTZtUipEou7SzyY8FSrbEDohPRLsHrxCfzAoZuZW1pQXWLZqAf/b6oHxppzTHvvEPRMf+k9Ch/0S89g/UUIRERNpL5WQ5NjYWDRs2xK5du2BpaYmOHTvi388M6unpITg4GG5ubnj37l2m5+nSpQsEQcDy5ctTtW/cuBGxsbHo0aNHStvbt2/x4sWLlK+NjY1x4MABuX9r1qwBADRr1gwHDhxAmzZtMh0fUXYb71gQve2sFPb5fotGv6fvoIbneSkHq1nNGVePbsDCKcNgapz20pszl26hRou+mLpoHaK+Z3wXVCKivELlZHnJkiW4f/8+evfuDX9/f+zbty9V/8WLFzFp0iRER0dj0aJFmZ7H2dkZw4YNw+HDh+Hu7o5NmzbB09MTHh4eqFevHrp3754ytlGjRihTpkzK17q6uujYsaPcv+bNmwMAihUrho4dO6JkyZKZjo8ouwmCgPXlHFHHwlRh/58hEZj3jlsj53Y6OmIM69MRd89sR+c2jdIcK5EkYcXGfajs9jt2Hfo7wzuhEhHlBSony/v27YO9vT3Wr1+v9MnCuXPnwsnJCZcuXVJpruXLl2Pp0qV4+vQphg0bhr1792LEiBE4ceIERAq2ACbKa/REIhyuVAJOhoorx0x78xF7QyI0HBVlh4I2VtjsNRX/7PVBxbIl0hwbFv4VQyYsQqNOw+D34JmGIiQi0g4qZ5j+/v5wdXVN84lGQRBQsWJFBAaqtj5OLBbD09MTL1++REJCAoKCguDl5QUTE5NU496/f5+uj5uLFi0KmUz2yxrLRNrESk8XJ6qUQj4dscL+Xo/f4lyE8k0tKHepWc0Zl4+shc9cT1hapF1G8M7DF2jYcRgGjp3PXQCJiP6fysmysbExPn369MtxwcHBaZZ2IyL1KWNiiP0Vi0OsoESGRCZDu/uvcCdSeakxyl3EYjH6dG2FB+d3YVjvjhCL0/7Vv+foWVR2+x1zl29BdEychqIkIsqZVE6WXVxc4Ofnh6dPnyod8+DBA9y9e1duq2oiyjpNrMzhU7qowr6YZCma332JV0yE8hRzMxMsnDoMN09sRsNayisIAUBcfAIWrdqJSo17Ytu+k0hOTtZQlEREOYvKybKHhwcSExPRsmVLHDt2DJGR//t4VyKR4MSJE2jXrh2Sk5MxbNgwVacjogwYWtgGnkUV76IZLklCkzsvEBSfqOGoKLuVLlEUR7ctxp61c+BYKO1NpEI/f8GIKUtRq81AnL/qp6EIiYhyDpWT5caNG2P+/PkIDAyEu7s78ufPD0EQcPDgQRgZGaFt27b48OEDxo4di5YtW6ojZiLKgMUlC+N3JSXlAuIT0ezuC3yVJGk4KspugiCglVtt3P57K2Z49oexUdpbvz59+Q7t+oyHe98JeP7KX0NREhFlP7WUkJg4cSLOnTuHJk2awNDQEDKZDPHx8RCJRKhTpw6OHDmiUtk4Iso8kSBgczlHtLAyV9j/JDoOre+9RCw/Zs+TDPT1MHZID9w782MXQEFQtBfk/5y9chuurfpj1DQvhIV/0VCURETZR2311ho0aIDTp08jKioKoaGhCA4ORnR0NC5duoS2bduqaxoiygRdkQgHKhVHTXMThf3Xv0Wjy8M3kLDObp5lZ2uNdYsm4OrR9aj3W+U0x0qlUmzZcxwVG/XEkjW7EBefoKEoiYg0T+Vk+cqVK/jw4cP/TigSwdraGra2tqnKyW3cuBF9+/ZVdToiyiQjsRjHK5dCORNDhf0nPn/DgKf+3OUvj6tYrgSO71iGfevnoYST4i3Uf4qOicNsr82o1OjHQ4BJSfx0gohyH5WT5fr168PZ2RmHDx9Oc9yVK1ewfft2VacjIhXk19PB31VLobCBnsL+7cHhmPBKtXropP0EQUCLRjVx6+QWLJsx8pf1mYNDwzFiylLUaNkXf525yjdcRJSrqGUZxvfv39GpUydMnz5dHacjoizkYKCPM9VKw0pXR2H/kvchWOofouGoKCfS1dXBwN/b4+GFXRg9sCv00th8CgBevf2AHkOno1Gn4bh264FmgiQiymJqSZZdXV1RqFAhzJs3D23btsX379/VcVoiyiKljA1xqmopGCvZnGLcqw/YHsQd3OiHfKYmmDN+EO6d3YGOrRr+crzfg2do3mMMOvSfiCcv3mogQiKirKOWZLl48eK4ffs2XFxccPz4cdSoUQOvX79Wx6mJKItUz2eCI5VKQldJ9YN+T9/hRNhXDUdFOVkRB1tsXT4NFw6uhmvV8r8cf+bSLdRsPQADPOcj4OOvd3olIsqJ1FYNo0CBArh8+TK6d++OFy9eoEaNGjh16lRK/6/KERGR5rlZ5cMO52JQ9OpMlgGdHr7GuYhIBb2Ul1WvVBZn9vpg77q5KF28SJpjZTIZ9h47iypuvTBh7ip8jvimmSCJiNREbckyAOjp6WHXrl2YM2cOIiMj0aZNGyxYsAAAoK+vr86piEhNuha0xIrSihOeeKkMbe69wgUmzPQfgiCgZeNauHlyM9YsHA97W+s0xydKJFiz7RAqNOyOucu34FtUtIYiJSJSjVqT5Z+mTJmC/fv3w8DAAFOnTkWPHj0gEmXJVESkBiOK2GKak73CvjipFK3uvcKlL1Eajoq0gVgsxu8dm+P+uZ2YO3EwLPKZpjk+OiYOi1bthHP9bliyZheiY+I0FCkRUeZkWQbboUMHXLlyBQULFsTevXuxdevWrJqKiNRgVnF7DHIooLAvTipFy3svcYUJMylhaKCPUf274NHFP+ExqDsMDdL+NPFbVDRme21G+frdsHLzfm5sQkQ5Vpbe7q1SpQr8/PxQtWpVJCUlZeVURKQiQRCwumxR9LKzUtgfmyxFi3svce0rq92QcuZmJpg1bgAent+FPl1bQayk4spPEV8jMXnBWlRo2AMbdh5BQkKihiIlIkoflZNlf39/eHt7K+0vWLAgrly5grFjx6JXr16qTkdEWUgsCNhS3gk9C1oq7I9JlqL53Re4zoSZfqGgjRV85nri9umtaNu07i/HfwqLgOcsH1R264Xt+09CIuENFiLKGVROlosUKQJLS8V/WH8yMDDA4sWLuRSDSAuIBQHbnIuhu5KEOfr/E+ab35gw06+VdCqMXatn4fKRdWhSr8YvxwcGh2L45KWo3qw39h07i+RkbqFNRNlL8RZeaZg+fToEQcCoUaOQP3/+DO3aJwgCZs2aldEpiUjDxIKA7eWLQSoD9n6KkOv/nixF07svcaZqadQwN8mGCEnbVHEuhUObF8L37mPM9d6KKzfvpzn+bUAQ+nvOx+I1uzB+aE90aNkQOjpiDUVLRPQ/GU6W586dC0EQ0KNHD+TPnz/la5lMpvSYn/1Mlom0h45IwE7nYpBChv2fvsj1RyUlo8ndFzhXrTSq52PCTOnzW1VnnNzlhcu+9zDbawtu33+a5vhXbz+gv+d8LFi5A+OH9UTn1o2ZNBORRmX6zrKVlVWqr4ko99ERCdjlXAzJMhkOhcrv5heVlAy3Oz8S5mpMmCkD6v1WBef2V8bZK7cxx2szHjxNe9fXt+8/YtC4hVi0cgfGDu2Jrm3doKub4T9hREQZluHfNDNnzkzzayLKXXRFIuypUBxdHr7BEQXbX0f+f8J8vnoZVDEzzoYISVsJgoAm9WrAra4Ljp+9hrneW/D89fs0j3n3IRhDJy7G4tU74Tm4B7q3bwI9PV3NBExEeRJ3CiGiX9IVibC3YnG0LWChsP9bUjIa+z3HvagYDUdGuYEgCGjTpA58T2zCFu+pKO5Y6JfHvA8MwYgpS1HZ7Xds2fMXEhMlGoiUiPKiDN9Z3rJli0oT9u3bV6XjiSh76IlE2F+xODo+eI3jn7/J9X9NSkYDv+c4Xrkk6uY303yApPXEYjE6tW6E9s3r4+CJC1i8ZidevwtM85gPQaEYNc0bS9bshsegbujZsfkvN0QhIsqIDCfL/fv3V2mNMpNlIu2lJxLhQKUS6PDgNU4qSJijkpLR9O4LHKxUAi2tFd+FJvoVHR0xurZzQ6fWDXH41CUsWrUTL98GpHnMx5AweMxcgYWrdmB4307o160NzEy5LIiIVJfhZLlXr158oI8oD9MXiXCoUgm0v/8Kp8Mj5frjpTK0u/8aO5yd0K2g4t0AidLj551m9xb1cfTvy1i0aucv1zSHhX/F9MUb4LXuTwz8vT0G93KHtaW5RuIlotwpw8nytm3bsiAMItIm+iIRDlcqCfcHihPmJJkMPR69xTdJMoYUtsmGCCk3EYvF6NCyIdo3r4+//rmKhat24OnLd2ke8y0qGotX78TKzfvRp2srjOjbGQ52BTQUMRHlJhp9wO/+/bSL0BOR9jAQi3C0ckl0ts2vsF8GYOjz95j/LijNOuxE6SUSidCueT3cOL4Ru9fMRoUyxX95TFx8AtZsO4QKjXpg6MTFeO2f9hpoIqL/UkuRynv37mH9+vXw9/dHQkJCqj+MUqkU8fHxCA0NRUhICJKSktQxJRHlAHoiEf6sUBzmOu+x4WOYwjFTXn/EV0kyFpcsxCVcpBYikQhtmtRBa7faOHX+Bhav3ol7j1+meYxEkoSdB09j16G/0a5ZXYzq30VD0RKRtlM5Wb5z5w7q1KmDxMTElCT5vzv6/fza2dlZ1emIKIcRCwLWlS0KC10xFvmHKByz9H0IvkqSsL6cI8RMmElNBEFAy8a10KJRTVy6cQ9L1+7+5TbaMpkMR05fxpHTl1G+ZGEY5rOBW70afCNHREqpvAxj0aJFSEhIQJs2bXD06FEMHjwYgiDg2LFjOHz4MAYNGgRBEFCuXDn4+fmpI2YiymEEQcDCkoWxsITy+ribgz6j68M3SJBKNRgZ5QWCIKBBrao4ucsL5w+sRotGNdN13JNXH9Ch/yTUajMAe4+ehUTCTz6JSJ7KyfL169dha2uLffv2oU2bNujWrRukUikEQUC7du2wdu1arFq1Cs+ePYOPj486YiaiHGqCkx3Wl3WEsnt0B0O/oM29V4hJStZoXJR3uFQui33r5+HWqS3o2tYNYvGv/8w9fv4WA8bOh3OD7vDZtB9R37m5DhH9j8rJckREBKpWrQo9PT0ASFlqcefOnZQxgwcPRqFChbB3715VpyOiHG5goQLYU6E4dJV8rH0mIhJud1/gK+/iURYqW9IRG5dNxoNzu9C/exvop2NL7KBPnzFl4VqUqdMF0xavR/CnzxqIlIhyOpWTZUNDw5REGQDMzc1hYWGBFy9epBpXpUoVvH79WtXpiEgLdCloib8ql4ShSPGvGN9v0ah7+xk+xCVoODLKa4oWKgjv2WPw5NIejB7YFSbGhr88Jio6Bss37EX5Bt0xaPzCX5apI6LcTeVkuUSJEnj48GGqtpIlS+Lu3bup2uLj41kJgygPaWZtjjPVSiOfjlhh/5PoONS4+RR3I/mRN2U92wKWmDN+EJ5d2YeZYwfAxkpxycN/k0iS8Ofhf+Dash/a9xmPc1duswwiUR6kcrLcsmVL+Pv7Y/To0YiM/LE5Qa1atfDu3TscP34cAPDq1StcunQJjo6Oqk5HRFqktoUpLlUvgwJ6igvvfEqUoK7fMxwL+6LhyCivsshnCs/B3fHg/A4M6OyGksUKp+u4c1f90L7vBFRv1gdb9vyF2Lj4LI6UiHIKlZPl0aNHw9HREStXrkT37t0BAMOGDfux41KHDqhatSqqVKmChIQEdOvWTeWAiUi7VDIzxlWXsihsoKewPzZZivb3X2NFwCfetSON0dfTQ70a5XDjrw04sHE+artUTNdxL98GYNQ0b5Su0wUzlmxEUAjXNRPldiony+bm5vD19cWwYcPg4uICAHB0dMT27dthYGCA+/fvIzY2Fq1bt8bYsWNVDpiItE9JY0Ncr1EWziaK14vKAIx+EYCRLwKQJGXCTJojEonQrMFvOP3nclw6vBbuLepDpGSt/b99/RYFr/V/olz9rugzeg78HjzTQLRElB3Ust21tbU1fHx8MGPGjJS2bt26ISQkBL6+vnjz5g2OHj0KfX19dUxHRFrIwUAf12qURRPLfErHrPoQinYPXiGapeUoG1StUBrbfWbgwbmdGNyrPYwMDX55THKyFAdPXEDDjsPQsOMwHDp5gfWaiXIZtSTLyhgbG6NGjRpwcnLKymmISEuY6ejgRJWSGORQQOmYk5+/oc7tZwiKT9RgZET/41jYDkumj8SzK3sx3aMfCtpYpes4vwfP0HvUHDg36I4la3bhc8TXLI6UiDRBrclyWFgYPnz4kOY/IsrbdEUirC1bFEtKFla6ecmD77GocfMJHkSxUgZlH0uLfBg3tCeeXPwTm72moIpzqXQdF/TpM2Z7bUbp2l0wwHM+/B4843p8Ii2m+BH1DEhKSsLEiROxefNmREVFpTlWEASWjyMiCIKAsY4F4Wioj56P3yBewTrloAQJat9+hv0VS6CFtbnmgyT6f3p6uujcpjE6tW6EW/efYs3Wgzj2z1VIf7F1e6JEgr3HzmLvsbOoXL4kBv7eHh1aNoChAZckEmkTlZPlhQsXwsvLC8CPZRf58uWDoGTnLiKif+tgmx8OBmXR5v5LhCXKv5GOSZai9b2XWFmmKIYWtsmGCIn+RxAEuFYpD9cq5fEh6BM27DqK7ftO4ltU9C+Pvf/kFYZMWITJC9bij84t0L97WxRxsNVA1ESkKpWXYezcuRP6+vr4+++/8f37d3z8+BGBgYFK/xER/VsNcxPcci2Pskp2VpMCGPb8PYY880fiL+7kEWlKYXtbzJ0wGM+v7ofXzFEo7lgoXcd9/RaF5Rv2wrlBd3QeOAXnr/r98g41EWUvlZPljx8/ws3NDU2aNFFHPESUBxU11Mf1GmXRKL+Z0jHrAsNQ3+85gvngH+UgJsaGGNCzHe7+sw0HNy1Ak3o10nWcTCbD6Qs30K7PeFRx64XlG/fic8S3rA2WiDJF5WS5ePHiKTv3ERFllrmuDk5XLYV+9tZKx/h+i0ZV3ye49vW7BiMj+jWRSISm9V1xaPNC3D+3E8P6dIS5mUm6jn0bEIRpi9ajdO3O6DtmDq7desAHAolyEJWT5ZEjR+L69eu4evWqOuIhojxMVyTCxnKOmF/CQemYT4kSNPB7jtUfuOMf5UzFizpg4ZRheHFtP3zmesK5TLF0HZcokeDA8Qto3mMMqjXrjdVbD+LLt7QfnCeirKfyA379+vXDmzdv0KhRI3Tt2hUVKlRA/vz5lY7v27evqlMSUS4mCAImOdmjhJEBej95h5hk+fWcSTIZhj8PgF9kDNaWdYShOEtLxhNlirGRIfp0bYXeXVrC9+4TbNx1FEf/voykdGy68+rtB0yctxozl25E++b10Kdba7hWKc8H6ImygcrJcnh4OM6dO4ekpCTs3r0bu3fvTnM8k2UiSo+OtpYobWyI9g9e4U1sgsIx24PD8Tg6FocrlUQRQ5bjopxJEATUrOaMmtWcsSBsKLbuPYEte4/jU1jEL4+NT0jEnqNnsefoWZQt6Yi+XVujc9vGsMhnqoHIiQhQQ7Ls4eGBu3fvwsjICPXq1YO1tTXf+RKRWpQ3NYKfa3n0fPwWJz9/UzjmXlQsqvo+wb6KxdEoja20iXIC2wKWmDTyD4wd0gMnzl7Dlr3HcenGvXQd++yVP8bO9sHURevQpmkd9OrUAnVqVIJIxE9WiLKSysny33//DWtra9y/fx92dnbqiImIKIW5rg7+qlwSs98GYdbbIIVjIiRJaHLnBRaWLISxRQvyDTvleLq6Omjfoj7at6iPN+8/Ytu+E9h18G9EfP31A/PxCYnY/9d57P/rPBwL2aFnx2bo4d4M9gWVPxxLRJmn8tvR2NhY1KpVi4kyEWUZkSBgZnEHHKtcEmY6YoVjpADGvwpE10dvEJ2ONaFEOUXxog6YO2EwXl7bjy3eU1HbpWK6j/UPDMYc7y0oW68rOvSfiGP/XEFioiQLoyXKe1ROlitWrIiAgAB1xEJElKY2BSxw27UcyhgbKB2z/9MXuNx8gsffYzUYGZHq9PX10Kl1I5z+czn8/t6GYb07pnttslQqxZlLt9Bz2AyUqt0ZkxesxYs3/NtMpA4qJ8uTJk3C/fv3sXbtWnXEQ0SUplLGhrjlWh4dbCyUjnkeEw+Xm0+w9kMoy8uRVipdvAgWTh2Gl9cPYMOSSXCtWj7dx4Z/+YaVm/ejerPeaNhxGDb/+Re+RrI2OVFmqbxmWSQSoVWrVhg+fDjWrVsHV1dX5M+fH7q6unJjBUHArFmzVJ2SiPI4Ux0xDlQsgUX+IZjyOhCKNguOl8ow9Pl7nIuIxKbyTrDQVfnXHZHGGRroo1v7JujWvglevAnAzoOn8efhfxD+5Vu6jvd78Ax+D55hwtxVaNm4Frq7N0Wj2tWho2Q5ExHJU/mvR6tWrSAIAmQyGR4/fozHjx/LjfnZz2SZiNRFEARMdLJDFTMjdHv0Fl8kSQrHHQ77ijs3HuPPCsVRy4Lltkh7lS5eBPMmDsYMj344fdEXOw6cwrkrfpBKFb1dTC0hUYLDpy7h8KlLsLHOj85tGqOHe1OUK+WkgciJtJvKyfKMGTPUEQcRUaY0sTLHHddy6PTwDe5GxSgc8yE+EfX8nmFmMQdMcrKDmNUySIvp6emibdO6aNu0LoI/fcbuw/9g54HT8A8MTtfxoZ+/YOXm/Vi5eT8qli2B7u5N0Kl1Y1hbmmdt4ERaSuVkOTY2FmXKlMEff/zBck1ElC0cjQxwo0ZZTHoVCK+ATwrHJMuAaW8+4sKXKOxyLgY7Az0NR0mkfna21hg3tCc8B3fHtVsPsePAKRz75wriExLTdfzDZ6/x8NlrTFm4Dk3ru6JrWzc0a/gbDPT5+iD6SeUH/DZu3AgfHx8mykSUrfREIiwrXQQnq5SCVRrrky9+iULFG49x8vNXDUZHlLVEIhHq/lYZm7ym4LXvIXjPGo1qFcuk+/ikpGScPHcdv4+YiWI13DF04mJc9r2H5GSWYSRSOVmWSCQoUqSIOmIhIlJZC2tzPKzpjIb5zZSOCZckodW9V/B4EYCEdKz3JNIm5mYm6N+jLS4eWoM7/2yHx6DusLOxSvfxUdEx2HnwNFr97omydbtiysJ1ePTsDSvLUJ6lcrLcrVs3nDlzBnfv3lVHPEREKrMz0MOZaqUxr4QDxGl86OUd8Ak1bz3F8+g4zQVHpEGlihXGrHED8OzKXhzbtgRd2jSGoYF+uo8PDg2Hz6Z9qNVmAGq06Iula3fjQ5DipU5EuZXKa5bd3Nxw5coV1KhRAzVq1EDFihWRP39+hXvVsxoGEWmKWBAw2cke9S3M0O3RG3yIV7yG815ULCr7Psac4g7wKFqQD/9RriQWi9GwdjU0rF0NUd9jcOT0Jfx55Axu+D1K9zmev36PWcs2YdayTahZvQI6t26ENk3r8sFAyvVUTpa7dOmSUhrO19cXvr6+cmNYOo6IsktNC1M8qOmMAU/f4VCo4nXKCVIZxr8KxNGwr9hWvhhKpLFDIJG2MzM1xh+dW+KPzi3h/yEYe46cwd6jZ9NdTQMAbvg9wg2/R/CctQINalaFe8sGaN2kDszNTLIwcqLsoXKyPH36dD7cR0Q5moWuDg5ULIENH8Mw+kUA4qWK117e+BaNijceY0HJQhhR2AYi/m6jXM6xsB0mj+qNSSP/gN+D59j/1zkcPHEBEV8j03V8crIU56764dxVP4ye5o3GdaujQ8sGaNGoFkyMDbM4eiLNUDlZnjlzphrCICLKWoIgYFAhG9QyN0XXR2/wVMk65TipFKNfBOBw6BdsLe8EJyPeZabcTxAEuFQuC5fKZbFg8lBcuH4H+/86hxNnryM2Lj5d50iUSHDq/A2cOn8Dhgb6aNbAFR1aNkCT+q4ZWidNlNOodf/Xd+/e4fLlywgJCYG+vj5sbGxQr149FCpUSJ3TEBFlWnlTI/i5lsfU14HwDvgEZc/3X/n6HRVuPMaSkoUxuFABfoJGeYaurg6a1ndF0/quiI6Jw8lz17Dv2DlcuH4Hycnpqx4TF5+AI6cv48jpyzAxNkTLRrXQrnk9NK7rwhrOpHXUkix//foVAwcOxOHDhxX2t2nTBhs3boSVVfpL1xARZRVD8Y+azO1t8qP347d4G5egcFxMshRDn7/H4bAv2FzOCYUNeXeM8hYTY0N0aeuGLm3dEBb+BYdPXcK+Y+dw5+HzdJ8jOiYO+/46h31/nYOJsSGaN/wNbZvVg1tdFxgZ8pMbyvlUTpbj4uLQsGFDPHz4EPny5UPz5s3h6OiI5ORkvHv3DmfOnMGxY8cQEBCAmzdvQk+P7yiJKGeobWGKhzWdMfF1IFZ9CFU67lxEFMpffwTv0kXQ196ad5kpTypglR+De7ljcC93vA8MwaGTF3H45EU8ev4m3eeIjonDgeMXcOD4BRgZGqBp/Rpo16wemjZwhbER1zhTzqRysuzt7Y2HDx+iVatW2LVrF8zMUm8EEBUVhR49euDUqVNYtWoVPDw8VJ2SiEhtjHXEWFmmKNwLWKDPk3cIUFJi7nuyFP2f+mPfpwisLeuIwrpiDUdKlHMULVQQnoO7w3Nwd7x8+wGHT17EwZMX8Orth3SfIzYuPmWphqGBPtzquaBds3po1uA3mJoYZWH0RBmj8qYke/fuhZWVFfbs2SOXKAOAmZkZ9u7dC0tLS+zevVvV6YiIskQDy3x4XKsCBjoUSHPc2f+/y7zgfQgkGoqNKCcrVawwJo38A3f+3gbfE5vgObg7ihYqmKFzxMUn4K9/rqLvmLlwdGmHzgOnYOfB0wj/kr6qHERZSeU7y2/evEGLFi1gbGysdIyxsTHq1KmDs2fPqjodEVGWMdURY305R7jbWKDfk3cISlCcDsdLZZjxLgQOelaw/BaNBtYWGo6UKOcRBAHlSxdD+dLFMMOzP+49fokDx8/j2N9X8DEkLN3nSUiU4PSFGzh94QZEIhFqVnNG6ya10cqtNgrb22bhd0CkmMp3lnV1dREdHf3LcTExMVznR0RaoamVOZ7UqoDedmk/lPxRpIOG916h35N3iEjkfWainwRBQNUKpbFwyjA8vbwHFw6uxsj+XVDEIWPJrlQqxbXbDzFh7mqUq9cNddoOxOLVO/HslT9kMmW1bIjUS+VkuWLFirhy5QoCAgKUjvH398fly5dRsWJFleaSSqXw9vZG6dKlYWBggEKFCsHT0xMxMTG/PPbVq1eYPn06XF1dYW1tDVNTU1SqVAnz5s1L1/FElLeY6+pgq3MxHK9cEgX1ddMcuyXoM0pfe4QdQZ/5B5zoP0QiEapXKot5Ewfj8cU/ceXoOowZ2A1Ohe0yfK4HT19jjvcW1G47CGMXbseMJRtx695TSKXpK2lHlBkqJ8uDBw9GfHw8mjZtimvXrsn1X716Fc2aNUNiYiL69++v0lxjxoyBh4cHypYti5UrV6JTp07w8fFB69atf/lC2bJlC7y9vVGsWDFMnz4dS5YsQalSpTB16lTUrFkTcXGKNyggorytVQELPK9VAcMK2SCtz8bCJUn448k7NLrzAi9j+PuESBFBEFC5fCnMHj8QD87vwvW/NmLc0J4o7pjx/RhCw79h5ZYDaNx5OIr/1hFDJy7G8bPXEBPL1x+pl8prlrt3747Tp09j9+7dqFevHqytrVGkSBEAwPv37xEeHg6ZTIYuXbqgV69emZ7n6dOnWLlyJdzd3XHo0KGUdkdHR4wcORJ79+5F9+7dlR7fsWNHTJo0Cfny5UtpGzx4MEqUKIF58+Zh8+bNGD58eKbjI6LcK5+uDlaVLYpedlYY+MwfD7/HKh178UsUKlx/jElOdpjoaAcDscr3JIhyJUEQUKFscVQoWxzTxvTF89fvceTUJRw/ew1PX77L0Lk+R3zFzoOnsfPgaejr6aJezSpo2agmmjX4DXa21ln0HVBeoZbf4jt37sSKFStQpEgRhIWFwc/PD35+fvj8+TMKFy6M5cuX488//1Rpjj179kAmk2H06NGp2gcMGAAjIyPs2rUrzeOrVauWKlH+qUuXLgCAJ0+eqBQfEeV+LuYmuONaHstKFYZxGklwokyGWW+DUOHGY5wI+8qlGUS/IAgCypZ0xJTRfXDz5GY8PL8L8yYOgWvV8hl+3ikhUYIzl25h1DRvlKrdGXXbDcLCldvx8OlrvhYpU9S23fWIESMwYsQIfPz4EcHBwZDJZLCzs1PbVtd+fn4QiURwcXFJ1W5gYIBKlSrBz88vU+f9+PEjAMDGxibNcV5eXvDy8vrl+UJCQlL+WyLJ+gd+fs6hiblI/Xj9tNMIeyu0NDNEr5sPcVusfAey17HxaH3/Fdzym2JJCQeUNeamCzkFX3s5WyG7AhjyR3sM+aM9Qj9/wemLvjh57jqu3HwAiSQpQ+e6/+QV7j95hXkrtsG+oDWa1K2BJvVcULtGRW6Ekg208bUnyLTkbZazszPCwsIQGiq/y1bnzp1x4MABJCQkZGiHwOTkZNSpUwd+fn548uQJSpUqpXTszJkzMWvWrHSf29LSEps3b073eCLSTjdF+tioa4YIIe1NSkQyGZolx6JrUjTMoBW/dolynNj4BDx8/h53Hr/BwxfvEa+kvGN66OqIUaa4AyqVdkTFMkVhY2WuvkApx+vXrx8iIiJgb2+fcuNUmQzfWb5w4UKmAwOAhg0bZuq42NhY6OvrK+wzMDBIGZORZHn06NHw9fXF/Pnz00yUgR+bq9jb2//ynCEhIZBKpTAwMECLFi3SHUtmSSQSnD17Fm5ubtDVTfuJfcp5eP20189rN61RXYwTRJjtH4KVgWFQ9qixVBBwSscYvgZmmO5YEAPtraErYjnN7MLXnvbqiB/X7+Sp0zAwtca5q344ffEmQkLDM3QeSVIyHr0IwKMXAcBRoISjAxrXdUGTejXwW9Xy0NPjz0VWyCmvvZ+5Y3pkOFlu3LhxpuslC4KApKSMfXzyk5GREcLCFBc1j4+PTxmTXtOmTcOqVaswcOBATJo06ZfjPTw80rVVt4ODA4KCggBAoz8Eurq6/IWvxXj9tJeuri6MdHWxvKwjejkUwKCn/rgTpbwc5dekZIx5/REbgsPhVaoImlmbay5YksPXnvbS09VBs4a/oXXTulguk+HRszc4df4GTp2/jgdPX2f4fK/9P+K1/0es3X4YJsaGaFCrGprUq4HGdarDwS7tnT0p47TptZfhZLlu3boZSpZfvHiRsnRCJMr884R2dnZ49uwZEhIS5O4wBwUFwcrKKt13lWfOnIm5c+eiT58+WLduXaZjIiL6typmxrjpWg5bgz5jyutAhCUqvznwPCYeze+9RAsrc3iVLoxSXM9MlGmCIKBiuRKoWK4EJo38A0Ehn/H3RV+cunADl2/cQ0IGNw2KjonD8TNXcfzMVQBA6eJF0LiuC9zquqBm9Qow0E//p9ik/TKcLF+6dCld4xISEjBt2jRcvfrjB61kyZLYsmVLRqdLUb16dZw5cwa3b99GnTp1Utrj4+Px4MED1K1bN13n+bn2+I8//sCmTZu4qyARqZVYENDfoQA62eTHvHfBWB7wCZI0Hg05Ff4NZ65HYnhhG0xzskd+PbU9d02UZ9kXtEa/7m3Qr3sbxMTG4cL1uzh1/jrOXLqFsPCvGT7fizcBePEmAKu2HIChgT7q1KiERnWqoXFdF5RwLMRcIpfLkgKgt27dQuXKlbFs2TIAP5YwPHjwADVr1sz0Obt06QJBELB8+fJU7Rs3bkRsbCx69OiR0vb27Vu8ePFC7hyzZ8/GrFmz8Pvvv2PLli0q3ekmIkpLPl0dLC5VGM9qVUDbAhZpjk2SybA84BOcrj7AgndBiElK1lCURLmfsZEhWrvVxtqFE/D6xkFcOboOU0f3QbWKZTKV5MbFJ+DM5VuYMHc1qjb5A+Xrd8OoaV7468xVRH6PzoLvgLKbWm9hJCQkYOrUqVi+fDmSk5NRqlQpbN26Fa6uriqf29nZ+f/au+/4Ksu7f+Cf++yZnGwySEKAsEmAJGxZ4kChokULVlBaR0UsBK3V/lxY6VNbQRGq4p5gKX1aFB6VFmSPEIGEESCBBLLI3jn7+v2R5EAMJyRkHvJ5v17ndcJ1j3PdfjH5cOe6rwuLFi3CmjVrcPfdd2PGjBk4deoUVq9ejUmTJjVakGTatGnIyspqNJ/i2rVr8eKLLyI8PBw333xzk3mfg4KCMH369Db3k4joSv30GvxrRDT+W1yOJWlZOF7lfnWxcrsDz53NxuqsS3i+byh+HRYAFf9RT9RuZDIZRgwdgBFDB+CZJ+ajsLgM/9l1CN/vPIj/7DqEsorWh90LOZfw4fqv8eH6ryGXyzBq+CBMHT8Kk8ePQkLsYCiV/G2Rp2u3Cu7fvx8LFy7EmTNnIJPJ8PTTT2P58uVuZ7C4Hm+88QYiIyOxbt06bNmyBf7+/li8eDGWL19+zbvEDfMwX7hwAQsWLGiyfdKkSQzLRNRhpvl548jYYXg/pwD/72w2ipuZKzbfasOiU5l4PTMPy/uFYW6wH2T8NS9RuwvwM2Hu7Fswd/YtsNsdOHT0JL7/4QC+++EAjqe1bhVBAHA4nDh05AQOHTmB/1nzKQx6LcYnxGDq+FGYOj4OA/pFcMiGB2pzWLZYLHjuueewevVqOBwODBo0CB999FGTxUPag1wux7Jly7Bs2bJm98vMzGzS9vHHH+Pjjz9u9z4REbWUQibhsd5B+EUvPyzPyMFbFy7B3sx45nO1FvwyNQOvnc/Dq/3DcEeAiT9oiTqIQiHHuLhhGBc3DC899TBy8grx3z1J+O/uJOzYm4zS8spWn7Oquhbf7TiA73YcAAAEB/lj8riRmDJuFKaMH4VegX7tfRnUAdoUlvft24eHHnoI6enpkMlkeOaZZ/Dyyy+3aq5jIqKexqRUYOXACDzaOxBPn76ArwvLmt0/paoGM4+cwXiTAX+K7o2JPl6d01GiHiw0OADz58zA/Dkz4HA4kJxyGv/dnYRtuw4hOSUNTqe7WdXdy7tUhPX/+z3W/+/3AIABfSMwaewI3DR2BCYkxMDPx7u9L4PawXWFZbPZjGeffRZr1qyBw+HAkCFD8NFHHyEuLq69+0dEdMMaoNdi88gB2Ftaid+fuYg9Zc3fudpbVoWbDp3CDH8TXu0fhlgvfSf1lKhnk8vlSBgxGAkjBuPZJxegpKwCP+xNxn92J+E/u5NavSBKg9MZWTidkYV1n/8LkiRh+KB+mDgmFpPGjsC4uOHwMvL/8e6g1WF5z549WLhwITIyMqBQKPD73/8eL7zwgsdMLE1E1N2M9zFiV8Ig/F9ROZ47exHHKmua3X9rURm2FpVhVoAJz/cNRZy3oZN6SkQA4Gvywt13TMHdd0yBEAKnzmZi+57D2LE3GXsOHUNNrbnV5xRC4NjJszh28izWfLgRcrkMI4cNxKSxIzBp7AiMHjkUWk37PQdGLdfqsDxp0iTX1/7+/ti5cyemTZvWomMlScLOnTtb+5FERDc8SZIwI8CE2/y98VV+MZ4/m42MWkuzx2wuLMPmwjLc5u+N56NCMc7H2Em9JaIGkiRhcHQfDI7ugycWzoHVasOhIyewfW8yduw9jB9Tz1zXkA2Hw4mkoyeRdPQk/vr2F1AqFRg1fCAmjo7FhIQYjB45BHodFzPqDK0Oy1dOx5aXl4e8vLwWH8sHU4iImieTJMwN9sfPg3zxQU4hlmfkIM/S/Opj3xaV49uickz19cLzfUMxycfI77dEXUSlUmLC6FhMGB2LFxJ/hdLySuw6cAQ79ibjh73JyMjKua7z2mx2HEg+jgPJx/GXv30OhUKOEUMHuMLzmFFDYTTo2vlqCLiOsLxjx46O6AcREV1BKZPhsd5BmB/ij7eyLuF/zuei7BqLlWwvqcD2kgpMMBnxfN8QTPfzZmgm6mI+3kb87Nab8LNb61YazsrOx469ydh98Ah27j+CS4Ul13Veu93huvO88t0vIZfLEDskGhNGx9SH52EweXGIVnto0zAMIiLqWDq5HM9EheCR3oH4y/k8vHkhHzWO5n+lu6esErcmn0aCtx7PR4VyyjmibiQirBcevO8OPHjfHRBC4HTGBeza/yN2HjiC3QePobSs4rrO63A4kZyShuSUNLz53leu4SHj4oZhXPxwjIsbhpBeAe18NT0Dl5UhIvIAPkoFVkT3RmJkL6zKysdbWfmovEZoPlRejZlHzmCEUYdn+oTgniBfKGQMzUTdhSRJGNgvAgP7ReCRB2bD6XTieNo57KwPz3sPHUNVtftVP5sjhMCJ0+dw4vQ5vPfFvwHUBfVxccMwNm44xsUPR3RUb/5DugUYlomIPIi/SolX+/fGU5HBWJ2Vjzey8q85PONIZQ1+kZKOCI0Kv43ohV+HBcKokHdSj4mopWQyGYYP7ofhg/th8a/uhc1mx5HjZ7Dn0DHsOXgU+5NTrzs8A3VDQLKy87H+X9sAAH4+3hgbNwxjRw3D6JFDEDukP9RqrpXxUwzLREQeyEepwIv9wrA0shfWXriElZn5KGpmCW0AyDJbkXj6Al7KyMGjYYF4MiIIYZyKiqjbUioVrvmdEx+dC7vdgWMnz2L3waPYc+gY9ieloqKq+rrPX1xajm+27cE32/YAAFRKJUYMi8aYUUMxeuRQjB4xGIH+vu11OR6LYZmIyIN5KRR4NioUT4b3wjvZBfjL+TxcsjY/e0aF3YG/ZOZhVVY+7uvli2WRwRjBBU6Iuj2FQo5Rwwdi1PCBWPLwL+BwOJB6KuNyeD6cel3Lcjew2mw4+OMJHPzxBICvAABR4SEYPWooxowcgtEjh2JQ/0jIZLJ2uiLPwLBMRHQD0CvkWBYZjMd7B+H97AL8+Xwucq4x5ZxdCHyRV4wv8oox1dcLT0UG4zZ/zqBB5Cnkcjlih0Yjdmg0Fv/qXjidTpw4fQ77D6diX/3relcXbHDuQi7OXch1LdHtZdAjLmYQ4kcMQnzsYMTFDLrhl+lmWCYiuoFo5TIsjuiFR3oH4pOcIryemYczNddeTaxh2rnBei2WRvbCvGA/6OQc10zkSWQyGYYN6odhg/rhkQdmQwiBrOx87Ducgn1Jqdh3OAVnz11s02dUVFVj+97D2L73sKutb2QYEmLrwnN87GAMGRAFpfLGiZg3zpUQEZGLWibDI70D8euwAHxTWIbXM/Owq/Tav549WV2Lh0+cx9OnL+DB0AD8pncgovVcJYzIE0mShMjewYjsHYx5s28FABQWl2F/cir2JaVg/+FUHDt5Fo5rzKxzLRmZ2cjIzHY9OKjVqDFi2ADExw5C3PBBGBUzEGHBgR77WyuGZSKiG5hMkjAr0AezAn2QVF6F1zPz8I9LJXCI5o8rszvwRv1sG9P9vPB47yDcGeDDqeeIPFyAnwmzbpmIWbdMBABU19TiSOpp7E8+joNHTuDQjyfaNO4ZAGrNFuxLSsG+pBRXW6C/D0YOG4gRQ/vDYa7A2HEVCAzwa9PndBaGZSKiHiLe24ANMf2RVWvBm1n5eC+7AFUtuKO0rbgC24or0FujwqNhgfh1WCCC1MpO6DERdTS9TutanhsAnE4nzp7PxoHk1LqH/Y6cwJmMC23+nIKiUny7Yz++3bEfAPDae/9CVHgIRsUMxKjhgzBy+ADEDO4PnVbT5s9qbwzLREQ9TIRWjZUDI/BC31C8l12AN7Pyr/kwIABcNFvx/9Kz8XJGDu4J8sXj4YGYYDJ67K9WiagpmUyGAX3DMaBvOBbcewcAoKikHElHT+Lgj8dx+NgpJKektWm+5wYNDw9u/Ho7AEAul2FIdBRGDh+A//nDIuh13WMIGMMyEVEPZVIq8HSfEPw2ohf+nl+CN7LykVxx7TlbbUJgQ34xNuQXY5hBi1+HBeL+YD/4qXi3mehG5O/rjdunjsXtU8cCABwOB9LSs3DoyEkkHa17paVntflzHA4nUk6l42LuJaz+47I2n6+9MCwTEfVwKpkMvwzxx/3Bfkgqr8bai5fwVX4xLM5rDGwGkFpVi9+mZeHp0xfws0Af/CosADf7eUPOu81ENyy5XI4hA6IwZEAUHvrFnQCAsooq/JiShqSjJ3Ho6EkkHT2F0rKK6zr/yGEDutVvrBiWiYgIQN2T8wkmAxJMBrw+IBwf5RTi7YsFOF9rueaxViGw8VIJNl4qQZhGhQdD/PFgaAD66rrf+EMian8mLwOmTojD1AlxAAAhBM5fyEVyShqSj6XhcMopHDtxFmaL9ZrnGhUzqKO72yoMy0RE1IS/Somn+4RgWWQwvi0qx98uXsLWwjJc+14zkG224o/ncvHHc7mY7GPEwrAA3BPky3mbiXoQSZIQFRGKqIhQzJk5DQBgs9mReiodn3z5D1iFEkdPnMHJM5lwOhs/aDxq+MCu6LJbDMtEROSWTJIwI8CEGQEmnK8x452LBfggpxDFNnuLjv+htBI/lFZi0clMzA32x4IQf4w1GbrVr1iJqHMolQoMG9QXU8cOw4wZM6BUKlFdU4ujJ84i+VgafkxNw+FjpxiWiYjIM/XRafDnAeF4uV8YNl4qxvvZhS1a6AQAKh1OrMsuwLrsAvTRqjEv2A/zgv0w2KDr4F4TUXem12kxPn44xscP7+quuCXr6g4QEZFn0chleCAkADsTBuPMhBg8FxWCkFbMu3y+1oJXz+ViyN5UxO5LxV/O5+JiC8ZFExF1BYZlIiK6bv31GrzavzeybhqBLSMH4J4gHyhbMcTiWGUNfnfmIiJ2HcXkQyex7mIBSqwtG+JBRNQZOAyDiIjaTCG7PLa50GrDF7lF+CCnEMerWrZwgQCws7QSO0sr8cSpTNzu7415wf64I8AEg4IPBhJR12FYJiKidhWgUmJJZDB+G9ELyRXV+DCnEF/mFaPc7mjR8TYhsLmwDJsLy6CRSbjN34SfB/nizgATvJX8sUVEnYvfdYiIqENIkoQ4bwPivA1YOSAC/1dUhi/yivBNYVmLFjwBALNT4F8FpfhXQSlUkoTp/t64J8gXPwvwga+KP8KIqOPxOw0REXU4jVyG2UG+mB3ki3KbHf9bUIov8oqwvbgCzmsfDqBu4ZMthWXYUlgGhSRhiq8RPw/yw12BPghsxQOGREStwbBMRESdylupwIOhAXgwNAB5Fiu+yivGl3nFSKqobvE57EJgW3EFthVX4Dcnz+MmHyPuCvLFzAATorhqIBG1I4ZlIiLqMsFqFZZEBmNJZDDOVNdifV4xvsgrxtkac4vP4cTlxU+WpGVhiEGLOwNMmBnggzEmA+RcAIWI2oBhmYiIuoVovRYv9gvDC31DcayyBpsuleAfl0qQVt3y4AwAJ6pqcaKqFn8+nwd/pQIzAkyYGWDCLf7e8FLwxx4RtQ6/axARUbciSRJivfSI9dLjlf69cbKqBv/IL8GmS6VIqapp1bmKbHZ8mluET3OLoJQkTPY14s4AH9zmY+ig3hPRjYZhmYiIurXBBh1e6KfDC/3CcLbajE2XSrDpUgkOt2KMM1A3JV3DOGcACFH5Y/aZi7g90AeTfLw4nzMRXRXDMhEReYz+eg1+HxWC30eFILPWgn/WB+f9ZVVo2WR0l+XKFFibXYi12YVQShIm+Bhxq583bvX3RoxRB4ljnYkIDMtEROShIrVqJEYGIzEyGIVWG7YWluHrwlJ8V1SOKkdLJ6SrYxMCO0oqsKOkAr8/exFBKiVu8ffGrX7emO7nzanpiHowhmUiIvJ4ASolFoQGYEFoACxOJ3aWVODrwjJ8XVCKLLO11ee7ZLXhs9wifJZbBACIMeow1dcLU329MNHHyJUEiXoQ/t9OREQ3FLVMhlv8TbjF34TVAyNwoqoWXxeW4uvCMhy4juEaAHCssgbHKmuwKisfMgBx3npMqQ/P401G6DnemeiGxbBMREQ3LEmSMNSow1CjDs9GhaLAYsN3xWX4v4JSbM0vQrnU+pDrBHCovBqHyqvx5/N5UEoSRnsb6sKznxfGeBugkcva/2KIqEswLBMRUY8RqFbigZAA/CLAhG+yTiF04mT8t6wK3xWVY29ZFeyi9fedbUJgT1kl9pRV4pVzOVDLJMR7GTDRx4gJPkaMMxlg4rANIo/F/3uJiKhHkgEYYdQhwdcbz0aFotLuwI6SCnxXVIbvisqRUWu5rvNanJfDM84DEoBhBh0m+BgwwceIiT5GhGnU7XotRNRxGJaJiIgAGBVyzAr0waxAHwBARo0Z3xWVY3tJOXaUVKLEZr+u8woAKVU1SKmqwd8uFgAAIjQqTHDdeTZiiEHLZbmJuimGZSIioqvoq9Pg8XANHg8PglMIpFbWYEdJBbaXVGBnaSUq7I7rPneW2YqsvGJ8kVcMADDIZYjz0mOMyYAxJgNGexvQS61qr0shojZgWCYiIroGmSQhxkuPGC89lkQGw+4UOFJZXReeiyuwp6wS1a2c2/lKVQ4nfiitxA+lla62CI2qLjx7GzDaZMAIo54PDhJ1AYZlIiKiVlLIJMR7GxDvbcDv+oTA6nQiqbwaO0srsKe0EnvLqtp05xmov/ucX4Kv8ksAAEpJQqxRh1HeesR56THKS48hBi2UMgZooo7EsExERNRGKpkM432MGO9jBAA4hMDxyhrsKavE7tK6V67F1qbPsAmBpIpqJFVUu9rUMgkxRh1GeV0O0IMZoInaFcMyERFRO5NfMWxjUXgvCCGQZbZid2kF9pRWYU9pJU5W17b5cyxO4ZrzuYHmigA9wkuPGKMOQw06aDmEg+i6MCwTERF1MEmSEKlVI1IbgAdCAgAAxVYbDpZX40BZFQ6UV+JQeTXK2zh0AwDMToGD5dU4eEWAlgEYoNcgxqhHrFGHGKMOsV46PkRI1AIMy0RERF3AT6XEjAATZgSYAABOIXC62owD5VV1AbqsCseranD9jw1e5gRwqtqMU9VmbMgvdrUHqhR1wdmox3CjDkMNWgzUa/kgIdEVGJaJiIi6AZkkYZBBi0EGLR4Krbv7XGV34HBF3d3ng+VVSK6oxkWztd0+s8Bqx7biCmwrrrjcDwD99RoM0Wvrlgo3aDHEoEV/nYZjoalHYlgmIiLqpgwKOSb7emGyr5errcBiQ3JFtet1uKIa2e0YoJ0ATlebcbrajH8WlLralZKEgXoNhhjqAvQggxaD9Fr01amhYoimGxjDMhERkQcJVCtxe4AJt9cP3wAuB+jDDQG6vAo5bZx946dsQiC1qhapVY0fTJRLQF+tBgP1GgyqH8YxUK/BQL0WJiVjBnk+/i0mIiLycFcL0EVWG45V1uBoZQ2OVdbgWEUNTlbXwi5Eu362QwBnasw4U2PG5sKyRtt6qZQYqNdggF6LaL0G/XV1ryjejSYPwrBMRER0A/JXKTHNzxvT/LxdbRanE6eqahuH6MoalNjsHdKHfKsN+VZbo5UJgbpx0RFaNaJ1GvS/IkRH6zWI0KihkEkd0h+i68GwTERE1EOoZTLEeukR66XHgvo2IQRyLFacqKrF8apaHK+swYmqWpyorkVNG5bwbo4TwPlaC87XWvBdcXmjbQpJQqRWhSht3R3ovvXvUVo1onRqeCkYXahz8W8cERFRDyZJEsI0aoRp1LjV3+RqdwqBzFpLfYiuwfGqWpyoqsWpqlpY23kox5XsQiC9xoL0GgtQ3HS7v1KBPloVNEpv7M/IQX+DDhFaNSI1avTWqqDm8A5qZwzLRERE1IRMkhCl0yBKp8HMQB9Xu90pcL7WglPVtUirrkVatRmnqmpxqrq2XRZVuZYimx1FNjsg12J31qVG2yQAwWolIrVqRGjU9QvBqBGhVSFSq0a4Rs2VDKnVGJaJiIioxRQyqW6csV6DWbgcooUQKLDaL4foKjPSqutC9EWzFR13L/oyASDXYkOuxYZ9qLrqPgEqBXprVOitUde/173C6/8colZxzDQ1wrBMREREbSZJEoLUSgSplY3mhQYAs8OJjFozzlbXzZpxttqMszV1r9x2nuLuWgqtdhRa7fixouaq22WouzvdW6NGmEaFULUKoRpl/bvK9c471D0HwzIRERF1KI1chiEGHYYYdE22VdkdSK+5HJ4zaiw4V2NGRq0F2Z10R/pKTgA5FlvdPNXl7vfzUcgRckV4DlUrEaxWIVitrH+p0Eut5BjqGwDDMhEREXUZg0LumqHjpyxOJ7JqLThXY0FGrRnnaiw4V2tBRo0ZZyurYZa6LoiW2h0orX/osTk+CnmTEB2sVqKXWolAlRJBqrq78X5KBWQSh390RwzLRERE1C2pZTJE67WI1msbtdtsNmzZuhXxN09Hrt2JzFoLMmstyKq1ItNscf25uoOmvmuNUrsDpfZanKxuPlTLJSBAWRecGwJ0UH2YDlQpEKhSIkClRIBKgQCVksNAOhHDMhEREXkcCUCgSolQvRLx3oYm24UQKLHZkVlrRZa5bk7nC7UWXDRbXa9L1s4dL90ch7i8iEtL6OWyuvCsVDQK0Q3vfkoF/JUK+Knq3n145/q6MSwTERHRDUeSJPiplPBTKTHKu+kQD6BumEe2Kzw3DtIXa63IsVhR3EGrG7ZVtcOJ6vo76C0hAfBVKupCtKrhvS5U+ykV8FUq4KuUw7c+WPvWvwxyGaQeHrIZlomIiKhHUstk6KvToK9O43Yfs8OJXEtdcM4x2+rfra73XIsNOWZrhy7U0h4EgGKbHcU2O85cfSKQq1JIkitENwRpH4UcJqUCPgoFTEo5fJQKmBRN370U8hsiaDMsExEREbmhkctci7O40zDkI89iq39ZkW+9/PWV7VXdYBx1a9jr588usLb+DrsMgJdCDu/6cO2tkMMol6Fa6Y3vz1yEj0pZt02hgLdS7vo6qH5hme6CYZmIiIioDa4c8jHU2Py+VXYH8i02XLLWv672df27pwXrn3ICKLM7UGZ3IMtsvbxBrsUP2YVuj5vsY8SOhMEd38EWYlgmIiIi6iQGhRz9FHL007u/U92gxuFAgdWOSxYbCq02FNrsde/Wn7zXt3eH2T/ag7eye8XT7tUbIiIiIgIA6ORyRGrlLR6SUONwoNBaNy652GpHkc1W/17XVmS1o9hmq3+ve3XHgG1SyLu6C40wLBMRERHdAHRyOSK0ckS0Yryv2eFEqd2OEtuVL8dP/nz5VWpzoMxmR5nd0WGrK3ozLBMRERFRd6CRyxAsVyFYrWrVcU4hUFE/HrnUZkeZzY5Su8P1XtfmQLndjvL6/crr/1xUa0aNJHMbtr0V3Suedq/eXIPT6cSbb76Jd999F5mZmQgICMC9996L5cuXQ6+/+hyK7Xk8EREREQEySYJJqYBJqWjVzBU2mw1bt27FbbffDotMhnJbfZC21wdrmwODDdprn6gTeVRYXrp0KVavXo3Zs2dj2bJlOHXqFFavXo0jR47gP//5D2Sy5pd+bOvxRERERNR2MkmCl0IBL4UCvbu6M9fgMWH5xIkTeOutt3D33Xdj06ZNrvY+ffrgySefxIYNGzBv3rwOO56IiIiIeh6PuZW6fv16CCGwZMmSRu0PP/wwdDodPv/88w49noiIiIh6Ho8Jy0lJSZDJZEhISGjUrtFoEBsbi6SkpA49noiIiIh6Ho8ZhpGbmwt/f3+o1U0HkYeGhmLfvn2wWq1Qqa7+NGdbj1+5ciVWrlx5zX7m5eW5vrbZbNfcv60aPqMzPovaH+vnuVg7z8b6eTbWz3N5Yu08JizX1NRcNegCdXeHG/ZxF3bbenxFRQVycnJa3F+z2YytW7e2eP+22rZtW6d9FrU/1s9zsXaejfXzbKyf5+rq2pnN5hbv6zFhWafToaCg4KrbGi5Yp9N12PFeXl4IDQ29Zj/z8vLgdDqh0WgwY8aMa+7fVjabDdu2bcP06dOhVCo7/POofbF+nou182ysn2dj/TxXd6ldw43SlvCYsBwSEoKTJ0/CYrE0uUOck5MDf39/t3eF2+P4xMREJCYmXrOfYWFhrjvQnfmXQKlU8huGB2P9PBdr59lYP8/G+nkuT6qdxzzgFx8fD6fTiUOHDjVqN5vNOHr0KOLi4jr0eCIiIiLqeTwmLN93332QJAlvvPFGo/b33nsPNTU1uP/++11tGRkZSEtLu+7jiYiIiIgADxqGMWzYMCxatAhr1qzB3XffjRkzZrhW4Js0aVKjBUWmTZuGrKwsCCGu63giIiIiIsCDwjIAvPHGG4iMjMS6deuwZcsW+Pv7Y/HixVi+fHmLlqpu6/FERERE1LN4VFiWy+VYtmwZli1b1ux+mZmZbTqeiIiIiAjwoDHLRERERESdjWGZiIiIiMgNhmUiIiIiIjckceWUEdRmKpUKNpsNMpkMwcHBnfKZZrO5VSvRUPfC+nku1s6zsX6ejfXzXN2hdg0rLiuVSlit1mb3ZVhuZ3K5HE6ns6u7QURERETXIJPJ4HA4mt3Ho2bD8AQajQZmsxlyuRyBgYEd/nkN/zLqzDvZ1H5YP8/F2nk21s+zsX6eq7vUrqCgAA6Ho0V3uBmW21l1dXWnfl5YWBhycnIQHByM7OzsTv1sajvWz3Oxdp6N9fNsrJ/n8sTa8QE/IiIiIiI3GJaJiIiIiNxgWCYiIiIicoNhmYiIiIjIDYZlIiIiIiI3GJaJiIiIiNxgWCYiIiIicoNhmYiIiIjIDS5K4uESExNRUVEBLy+vru4KXQfWz3Oxdp6N9fNsrJ/n8sTaSUII0dWdICIiIiLqjjgMg4iIiIjIDYZlIiIiIiI3GJaJiIiIiNxgWCYiIiIicoNhmYiIiIjIDYZlD+V0OrFq1SoMHDgQGo0GvXv3xrJly1BdXd3VXaN6Z86cwQsvvIAxY8YgICAARqMRsbGxePXVV69ap9OnT+Ouu+6Cj48P9Ho9Jk6ciO3bt3dBz+lqampqEBUVBUmS8MQTTzTZzvp1PyUlJXjqqafQr18/aDQaBAQEYMqUKdi9e3ej/Q4ePIibb74ZRqMRXl5euO2223D06NGu6TQBAKqqqrBixQoMGzYMRqMR/v7+GDduHD7++GP8dBIv1q9r/OlPf8KcOXNc3xcjIyOb3b81dcrNzcX8+fMREBAArVaLuLg4bNy4sf0voqUEeaQnn3xSABCzZ88W69atE0uXLhUKhUJMmTJFOByOru4eCSGeeeYZYTAYxLx588Tq1avF22+/Le69914BQAwfPlzU1NS49k1PTxe+vr4iMDBQrFixQqxdu1bExsYKhUIhtm3b1oVXQQ2WLVsmDAaDACAWLVrUaBvr1/1kZmaKyMhI4e/vL5555hnxwQcfiJUrV4oHH3xQrF+/3rXf/v37hVqtFlFRUWLlypVi5cqVIioqShgMBpGSktKFV9BzORwOMWHCBCGTycRDDz0k3n33XbFq1SqRkJAgAIjf/e53rn1Zv64DQPj6+oqbb75Z+Pj4iIiICLf7tqZOxcXFok+fPkKv14vnn39evPvuu2LSpEkCgPjwww87+KqujmHZAx0/flxIkiTuvvvuRu2rV68WAMQXX3zRRT2jKyUlJYmysrIm7X/4wx8EAPHWW2+52ubMmSNkMpk4cuSIq62yslKEh4eL6Oho4XQ6O6PL5EZycrKQy+Xi9ddfv2pYZv26nwkTJoiwsDCRm5vb7H7x8fHCaDSK7OxsV1t2drYwGo1i+vTpHd1Nuop9+/YJAGLJkiWN2i0Wi+jTp4/w9vZ2tbF+XScjI8P19ZAhQ5oNy62p09NPPy0AiM2bN7va7Ha7iI+PF76+vqKysrL9LqKFGJY9UEPY2rVrV6P22tpaodPpxO23395FPaOWSElJEQDEo48+KoQQoqqqSqjVajF16tQm+y5fvlwAEAcPHuzsblI9u90uRo4cKe644w5x/vz5JmGZ9et+du7cKQCI1atXCyGEsFqtorq6usl+Z8+eFQDEwoULm2xbuHChkCRJ5OXldXh/qbFvv/1WABCvvfZak23x8fEiJCRECMH6dSfNheXW1ik0NFT07du3yb6ffvqpACC++uqrdut3S3HMsgdKSkqCTCZDQkJCo3aNRoPY2FgkJSV1Uc+oJbKzswEAQUFBAICUlBRYLBaMHTu2yb5jxowBANa0C61atQppaWlYs2bNVbezft3P1q1bAQDh4eGYOXMmtFot9Ho9oqOj8fnnn7v2a6iLu9oJIZCcnNw5nSaXhIQEmEwmvPbaa9i4cSMuXLiAtLQ0PPvss0hOTsZLL70EgPXzFK2pU15eHnJyclzfO3+675Xn60wMyx4oNzcX/v7+UKvVTbaFhoaiqKgIVqu1C3pG1+JwOPDKK69AoVBg3rx5AOrqCdTV7qca2nJycjqvk+Ry/vx5vPjii3jhhRfcPrzC+nU/p0+fBgA8/PDDKCkpwSeffIIPP/wQKpUKDzzwAD766CMArF135ePjg82bN8PX1xf33nsvIiIiMGjQIKxduxabNm3Cww8/DID18xStqVN3rami0z+R2qympuaqQRmou7vcsI9KperMblELLFmyBPv378eKFSswYMAAAHW1AnDVml5ZT+p8jz32GKKiopCYmOh2H9av+6msrAQAGI1G7Nixw/W98K677kJUVBSee+45LFiwgLXrxgwGA4YOHYpZs2Zh3LhxKCkpwdq1azFv3jz8+9//xvTp01k/D9GaOnXXmjIseyCdToeCgoKrbjObza59qHt5/vnnsWbNGjzyyCN49tlnXe0NtbJYLE2OYT27zueff45t27Zh165dUCqVbvdj/bofrVYLAJg7d26jmwY+Pj6YNWsWPv30U5w+fZq166ZSU1Mxbtw4rFq1Co899pirfe7cuRg6dCgefvhhZGRksH4eojV16q415TAMDxQSEoKioqKr/mXKycmBv78/7yp3My+99BL++Mc/4qGHHsI777zTaFtISAiAq/9qqaHtar+Soo5jsViQmJiIGTNmoFevXkhPT0d6ejqysrIAAOXl5UhPT0dZWRnr1w2FhYUBAHr16tVkW3BwMACgtLSUteumVq1aBbPZjDlz5jRq1+l0uOOOO5CVlYXMzEzWz0O0pk7dtaYMyx4oPj4eTqcThw4datRuNptx9OhRxMXFdVHP6GpeeuklvPzyy1iwYAHef/99SJLUaPuwYcOgVquxf//+JsceOHAAAFjTTlZbW4vCwkJs2bIF/fv3d70mT54MoO6uc//+/fH++++zft1Qw8PPDQ/TXqmhLTAwEPHx8QDgtnaSJGHUqFEd2FO6moZQ5HA4mmyz2+2ud9bPM7SmTsHBwQgNDXV97/zpvkAXfT/t9Pk3qM1SUlKanWf5s88+66Ke0U+9/PLLAoB44IEHml0s5uc//7mQyWTi6NGjrraGeXr79+/PeXo7mdVqFRs3bmzy+tvf/iYAiNtuu01s3LhRnD59WgjB+nU3JSUlwmg0itDQ0EZzsubm5gq9Xi+io6NdbXFxccJoNIqcnBxXW05OjjAajWLatGmd2m+qs2TJEgFA/PnPf27UXlpaKoKDg4WPj4+w2+1CCNavu7jWPMutqdNTTz3ldp5lk8kkKioq2r3/1yIJ8ZN1I8kjLF68GGvWrMHs2bMxY8YMnDp1CqtXr8b48eOxfft2yGT8pUFXW7t2LZ544gmEh4fjlVdeaVKToKAgTJ8+HQCQnp6OhIQEKJVKLF26FF5eXnjvvfeQmpqKLVu24NZbb+2KS6CfyMzMRJ8+fbBo0aJGU8mxft3PunXr8Oijj2LIkCFYuHAhrFYr3n77beTl5eGbb77BLbfcAgDYt28fpkyZgrCwMCxevBgA8NZbb+HSpUvYu3cvYmJiuvIyeqSsrCyMHDkSpaWluP/++zF+/HiUlJTgvffeQ2ZmJtauXYvHH38cAOvXlT777DPX0LS33noLVqsVy5YtAwBERETggQcecO3bmjoVFxdj1KhRKC4uRmJiIkJDQ7F+/Xr88MMPeP/99/GrX/2qE6+yXqfHc2oXdrtd/PWvfxXR0dFCpVKJkJAQsXTp0i5Z2YaubsGCBQKA29ekSZMa7X/y5Ekxa9Ys4e3tLbRarRg/fjyXSu5mrrYoSQPWr/vZtGmTGD16tNDpdMJgMIjp06eLPXv2NNlv3759YurUqUKv1wuDwSBuueUWkZyc3AU9pgbp6eli/vz5IjQ0VCgUCmE0GsXEiRPFpk2bmuzL+nWNhiWoW/LzTYjW1Sk7O1v88pe/FH5+fkKtVosRI0aIDRs2dPAVucc7y0REREREbvB39UREREREbjAsExERERG5wbBMREREROQGwzIRERERkRsMy0REREREbjAsExERERG5wbBMREREROQGwzIRERERkRsMy0REREREbjAsExHdQJYuXQpJkhAYGIiioqJm983JyYHJZIIkSfjggw86qYdERJ6Fy10TEd1AamtrERMTg7Nnz2Lu3Ln48ssv3e575513YsuWLZg5cyY2b97cib0kIvIcDMtERDeYPXv2YNKkSXA6ndi8eTNmzpzZZJ/PPvsM8+fPh7+/P44fP46goKAu6CkRUffHYRhERDeYCRMm4MknnwQAPPbYYygvL2+0PT8/H0uWLAEArFu3jkGZiKgZDMtERDegFStWoF+/fsjNzcWyZcsabVu0aBFKSkowf/58zJ4929X+97//HZMnT4a3tzd0Oh1iY2PxxhtvwGazNTm/3W7HBx98gGnTpsHf3x9KpRK+vr6YMmUKNmzY0GT/yMhImEwmHD9+HKNGjYJarUZERAR2797d/hdPRNSOOAyDiOgG1TAcQwiBPXv2YNy4cfjnP/+Je+65B+Hh4UhJSYG3tzeAujvQ7777LrRaLRISEmAymbB7926UlJRg+vTp+Oabb6BSqQAAQgjcdddd2Lx5M3x8fDBmzBhoNBqcPHkSp0+fBgC8+eabrrvbQF1YLigocAXr4cOH48iRI0hNTYXRaOz8/zhERC0liIjohvXb3/5WABCxsbGitLRUhISECEmSxPbt2137fPTRRwKAGD58uDh//ryrvby8XNx6660CgPjDH/7gat+0aZMAIBISEkRlZWWjz/vTn/4kAIh+/fo1ao+IiBAAxMiRI4XZbBZCCOFwODrgiomI2hfvLBMR3cBqamoQExOD9PR0DBkyBCdOnMCSJUuwatUq1z6DBg1CWloakpOTMXLkyEbH5+XlITIyElqtFpcuXYJarcaGDRuwfv16LF26FJMnT260f3l5OUwmE+RyOex2u6s9MjISWVlZeOedd/Doo4926DUTEbUnhmUiohvc7t27XcMxBg0ahB9//BEajQZA3cN+wcHB8Pb2RllZ2VWPT0hIQFJSEvbv348xY8ZcdZ/a2lqkpaVh3759eOKJJwDUjWuWy+UALofl5s5BRNQdKbq6A0RE1LEmTpyIcePGYe/evUhMTHQFZQC4cOECgLo7wpIkNXueixcvuoJuRUUF1q1bh2+//RanTp1CXl4ehBCNznG1ezG+vr7tcUlERJ2GYZmIqAdQKBSN3hs4HA4AgJ+fH2677bZmz9GrVy8AwIkTJzB16lTXA3sJCQmYO3cuYmJiMHnyZISHh7s9h0zGSZiIyLMwLBMR9WDBwcEAAI1Gg88//7xFxzzxxBMoKCjA7373O6xYscI11AIASktLO6SfRERdhf/EJyLqwSIjIxEeHo6cnBwcO3asyfaGBwRvuukmZGZmAgD2798PAHjuuecaBWUA+P77711fO53Ojus4EVEnYVgmIurhli5dCgCYP38+MjIyXO1WqxW/+c1vkJKSgqqqKkRGRgIAAgICAACbN29udJ5du3Zh8eLFrj+bzeYO7jkRUcdjWCYi6uGefPJJ3HfffUhJScHQoUNx0003Yfbs2ejTpw8+/fRTBAYGNlqVLzExEUBduJ4wYQLmzJmDESNGYNKkSXA6na6xzfn5+V1yPURE7YlhmYioh5PJZFi/fj0++eQTxMfH49ixY/juu+/g7e2NxMREHD16FNHR0a79ly5dii+//BLx8fFITU3F119/jerqaixevBjHjh3DnDlzAABff/11V10SEVG74TzLRERERERu8M4yEREREZEbDMtERERERG4wLBMRERERucGwTERERETkBsMyEREREZEbDMtERERERG4wLBMRERERucGwTERERETkBsMyEREREZEbDMtERERERG4wLBMRERERucGwTERERETkxv8HYUO1GzZIiwoAAAAASUVORK5CYII=", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# -----------------------------------------------------------------\n", - "plot_title = \"\"\n", - "font = \"Arial\"\n", - "x_label = \"Year\"\n", - "y_label = \"Normalized Present Value [$-$]\"\n", - "legend = True\n", - "grid = True\n", - "save_svg = True\n", - "remove_ticks = False\n", - "remove_ticks_labels = False\n", - "file_name = \"../book/figures/present_value\"\n", - "# -----------------------------------------------------------------\n", - "\n", - "fig = plt.figure(figsize=(8,6))\n", - "ax = fig.add_subplot() # axes_class=AxesZero)\n", - "ax.set_title(plot_title, fontfamily=font)\n", - "ax.set_xlabel(x_label, fontfamily=font)\n", - "ax.set_ylabel(y_label, fontfamily=font)\n", - "\n", - "plt.setp(ax.spines.values(), linewidth=2)\n", - "# ax.spines[\"left\"].set_position((\"data\", 0))\n", - "# ax.spines[\"bottom\"].set_position((\"data\", 0))\n", - "# ax.spines[\"top\"].set_position((\"data\", 1))\n", - "# ax.spines[\"right\"].set_position((\"data\", 100))\n", - "\n", - "# not a permanent solution (removed the part below 0)\n", - "# ---> find a better way to auto set upper bound\n", - "# ax.spines.bottom.set_bounds(0, 100)\n", - "# ax.spines.left.set_bounds(0, 1.0)\n", - "# ax.spines.top.set_bounds(0, 100)\n", - "# ax.spines.right.set_bounds(0, 1.0)\n", - "\n", - "t = np.linspace(0,101)\n", - "y_2 = 1 / (1 + 0.02)**t\n", - "y_4 = 1 / (1 + 0.04)**t\n", - "\n", - "# plotting\n", - "ax.plot(t, y_2, label='2%', color=colors[0], linewidth=4)\n", - "ax.plot(t, y_4, label='4%', color=colors[1], linewidth=4)\n", - "# ax.plot(1, 0, \">k\", transform=ax.get_yaxis_transform(), clip_on=False)\n", - "# ax.plot(0, 1, \"^k\", transform=ax.get_xaxis_transform(), clip_on=False)\n", - "\n", - "\n", - "\n", - "ax.tick_params(axis='x', labelsize=13, width=2, length=8)\n", - "ax.tick_params(axis='y', labelsize=13, width=2, length=8)\n", - "\n", - "if grid: ax.grid()\n", - "if legend: ax.legend(prop={\"family\":font})\n", - "if remove_ticks: ax.set_xticks([]); ax.set_yticks([])\n", - "if remove_ticks_labels: ax.set_xticklabels([]); ax.set_yticklabels([])\n", - "if save_svg: plt.savefig(file_name + '.svg')" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "id": "a19d456c-b5d3-43d6-8b51-1441f902985d", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# -----------------------------------------------------------------\n", - "plot_title = \"\"\n", - "font = \"Arial\"\n", - "x_label = \"Safety, $-\\ln p_f$ [$-$]\"\n", - "y_label = \"Present Value [€]\"\n", - "legend = True\n", - "grid = False\n", - "save_svg = True\n", - "remove_ticks = True\n", - "remove_ticks_labels = True\n", - "file_name = \"../book/figures/economic_opt\"\n", - "# -----------------------------------------------------------------\n", - "\n", - "fig = plt.figure(figsize=(8,6))\n", - "ax = fig.add_subplot() # axes_class=AxesZero)\n", - "ax.set_title(plot_title, fontfamily=font)\n", - "ax.set_xlabel(x_label, fontfamily=font)\n", - "ax.set_ylabel(y_label, fontfamily=font)\n", - "\n", - "plt.setp(ax.spines.values(), linewidth=2)\n", - "# ax.spines[\"left\"].set_position((\"data\", 0))\n", - "# ax.spines[\"bottom\"].set_position((\"data\", 0))\n", - "# ax.spines[\"top\"].set_position((\"data\", 1))\n", - "# ax.spines[\"right\"].set_position((\"data\", 100))\n", - "\n", - "# not a permanent solution (removed the part below 0)\n", - "# ---> find a better way to auto set upper bound\n", - "# ax.spines.bottom.set_bounds(0, 100)\n", - "# ax.spines.left.set_bounds(0, 1.0)\n", - "# ax.spines.top.set_bounds(0, 100)\n", - "# ax.spines.right.set_bounds(0, 1.0)\n", - "\n", - "t = np.linspace(0,101)\n", - "risk = 1 / (1 + 0.08)**t\n", - "inv = 0 + 0.005*t\n", - "tot = risk + inv\n", - "scale = 0.9\n", - "\n", - "# plotting\n", - "ax.plot(t, scale*risk, '--', label='Risk', color=colors[2], linewidth=4)\n", - "ax.plot(t, 1.05*inv, '-.', label='Investment', color=colors[1], linewidth=4)\n", - "ax.plot(t, tot+.05, label='Total', color=colors[0], linewidth=4)\n", - "# ax.plot(1, 0, \">k\", transform=ax.get_yaxis_transform(), clip_on=False)\n", - "# ax.plot(0, 1, \"^k\", transform=ax.get_xaxis_transform(), clip_on=False)\n", - "\n", - "\n", - "\n", - "ax.tick_params(axis='x', labelsize=13, width=2, length=8)\n", - "ax.tick_params(axis='y', labelsize=13, width=2, length=8)\n", - "\n", - "if grid: ax.grid()\n", - "if legend: ax.legend(prop={\"family\":font})\n", - "if remove_ticks: ax.set_xticks([]); ax.set_yticks([])\n", - "if remove_ticks_labels: ax.set_xticklabels([]); ax.set_yticklabels([])\n", - "if save_svg: plt.savefig(file_name + '.svg')" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.11.7" - }, - "widgets": { - "application/vnd.jupyter.widget-state+json": { - "state": {}, - "version_major": 2, - "version_minor": 0 - } - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/figures/figures-template.ipynb b/figures/figures-template.ipynb deleted file mode 100644 index e05b9ac..0000000 --- a/figures/figures-template.ipynb +++ /dev/null @@ -1,266 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 3, - "id": "65cbe2ec-de72-44d4-8af9-a969b06134a9", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from matplotlib import rcParams\n", - "rcParams.update({'font.size': 16})\n", - "# TUDelft colors palette\n", - "colors = [\"#0C2340\",\"#00B8C8\",\"#0076C2\",\"#6F1D77\",\"#EF60A3\",\"#A50034\",\"#E03C31\",\"#EC6842\",\"#FFB81C\",\"#6CC24A\",\"#009B77\"]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## **Template #1**" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# -----------------------------------------------------------------\n", - "plot_title = \"this is the title\"\n", - "font = \"Arial\"\n", - "x_label = \"xlabel [$x-units$]\"\n", - "y_label = \"ylabel [$y-units$]\"\n", - "legend = False\n", - "grid = False\n", - "save_svg = True\n", - "remove_ticks = True\n", - "remove_ticks_labels = True\n", - "file_name = \"template_blank\"\n", - "# -----------------------------------------------------------------\n", - "\n", - "fig = plt.figure(figsize=(8,6))\n", - "ax = fig.add_subplot() # axes_class=AxesZero)\n", - "ax.set_title(plot_title, fontfamily=font)\n", - "\n", - "ax.set_xlabel(x_label, fontfamily=font)\n", - "ax.set_ylabel(y_label, fontfamily=font)\n", - "\n", - "plt.setp(ax.spines.values(), linewidth=2)\n", - "ax.spines[\"left\"].set_position((\"data\", 0))\n", - "ax.spines[\"bottom\"].set_position((\"data\", 0))\n", - "ax.spines[\"top\"].set_visible(False)\n", - "ax.spines[\"right\"].set_visible(False)\n", - "\n", - "ax.tick_params(axis='x', labelsize=13, width=2, length=8)\n", - "ax.tick_params(axis='y', labelsize=13, width=2, length=8)\n", - "\n", - "if grid: ax.grid()\n", - "if legend: ax.legend(prop={\"family\":font})\n", - "if remove_ticks: ax.set_xticks([]); ax.set_yticks([])\n", - "if remove_ticks_labels: ax.set_xticklabels([]); ax.set_yticklabels([])\n", - "if save_svg: plt.savefig(file_name + '.svg')\n" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "id": "fc2eb45c-9f4e-4fbd-91c3-dc0ff10b4c46", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "image/png": 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/374vKBSSn1Zch/ZujwY1FZfrGjtrJct1ERERkUKJiYkoV64cBEHA+/fvU/V9+/YNHTt2hLm5ORwcHNCtWzd8+fJF4XumTJkCMzMzfP36VRNhZxmTWQ0z0hGhrYO1XPuXJDEuhEam/P57ua4JsLaSr4AQG5eA3iNnIzExKVtjJSIiIu0zefJkPHv2TGFft27dcPDgQZQpUwZly5bFX3/9hSZNmiA5OTnVuMDAQKxYsQJjxoyBg4ODJsLOMiazOUDZVoNtAcGpfl/AwRZr5ysu1/X4xTtMW7xB7bERERGR9rp06RKWL1+usO/Zs2e4cOECOnbsiFu3buHixYsYN24cnjx5grNnU29hnDFjBkxNTTF27FhNhK0SJrM5oIG1BZwM5A94HfkajrCk1N8ZtWhYC326tFT4nnU7DuP4uevZEiMRERFpl4iICPTq1QvFihWDo6OjXP+bN28AAHXr1k1pq1evXqo+AHj16hW2bduGadOmwdTUNHuDVgMmszlAVySgp5OdXHuSTIa/gkLk2hdMHoJSxdwUvmvoxMXw+6x4rwsRERHlH0OGDEFgYCB27twJAwMDuX5LS0sAQHx8fEpbTEwMAMDMzCylbeLEiXBzc8PAgQOzN2A10c3pAPKr3s52WOAbKNe+NSAYw1xTfzdlbGSInatmoE6bQYhPSEzVFxEVg14jZ+PcvlXQ0+MfJxER5X39n/vgeUx8+gNzubKmRthUtrBa3rV3717s3bsXU6dORdWqVRWOKVeuHAwNDbF582a0adMGxsbGWLVqFQRBQLVq1QAAN27cwPHjx7Fv3z7oKSgTmhsx+8khxUwMUcvSDDciUl+C8Cg6Do+iYlHB3CRVe8liblg6cySGTFws9677T15h1rLNmDthULbGTERElBs8j4nH7ciYnA4j1/D398eQIUNQsWJFTJ8+Xek4e3t7zJo1CxMmTECRIkVS2seOHQsPDw8AwPjx41G5cmV07Ngx2+NWFyazOaiPi51cMgt8Pwj232QWALq3a4Jrtx5h37Hzcn0rN+1HLS9PNKlfPVtiJSIiotxHJpOhZ8+eiI+Px86dO9NdTR0/fjy8vLxw8uRJSKVSNGrUCE2aNAEAHD58GLdu3cKFCxcg/O/GUrFYjNjY2JQtCrkR98zmoA4O1jBRUHN2d2AIEiRSuXZBELBs1igUdS+o8H0Dxy9EQFCwwj4iIiLKe5YtW4bLly9j3rx5KFOmTIaeqVevHv744w8sW7YsJZFNTk7GpEmT0LhxY/zyyy8Qi8UYOHAgzMzMYGVlhWLFislVPMgtmMzmIFNdHXRylC/TFZ4swfHgcIXPmJkaY+eq6TDQl//OKyw8Cn285yI5WaL2WImIiCh3efbsGaZMmYI6depg9OjRKr1r8+bNePfuHRYuXAgAWLhwITZu3IgBAwZg3759MDU1Rdu2bfHp0yd1hK5W3GaQw/o422FrgPxq6tbPweioINEFAI9SRbFo6jCMmi5fR+7mvadYsHoHpo3uo/ZYiYiIcoOypkY5HYJaqPpxTJo0CYmJiRCJROjRo0eqvpCQ79WRxo4dC1NTU0yZMgWlSpVS+J7Y2FjMmjULXbt2Rfny5QEAq1evhoeHB1atWgUAKFq0KCpXrox169ZhwYIFKsWtbkxmc1gNS1MUNzbE27iEVO3nQiPhH5+IgkbypTUAoE+Xlrh66yGOnL4q17fkz92o5eWJ+jUrZUvMREREOUldFQC03Y+yWleuXFE65tixYwCAfv36KU1mly5dirCwMMydOxcAEBoaiuDgYNSvXz9lzI8tDD/Xo80tuM0ghwmCgD7O8jVnZQB2BsrXnP35udXzx8KtYAH5Z2Uy9PWeh6/BYeoMlYiIiHKRK1euQCaTKfzl6uoKAHj37h1kMlnK5Qj/9e3bN/zxxx8YMmQI3NzcAABS6fdzO0lJSSnj4uLiAAA6OjrZ9wFlEZPZXKCHsy10BPn2rQHBkMpkSp+zMDPF9pXTFdaXDQ4NR1/vuZBIuH+WiIiIFJs9ezYEQcDUqVNT2uzs7ODg4IAbN24gKioKAHD69GkAyPAhM01iMpsLFDDQR1NbS7l2n/hEXA+XL931s0rlSmLOeMU3dFy99QhL1/+ljhCJiIgoj3n//j02btyI8ePHw8Ym9TmdkSNHIiQkBOXKlUPLli3Rt29fWFpaYujQoTkUrXJMZnOJ3gq2GgBQeDjsv4b0aodmv9RQ2Ddv5XbcuPNYldCIiIgoD5o8eTJsbW0VVkKYOHEi5s6dC7FYjHPnzqFKlSq4cOEC7OwU5ys5SZDJ0vg5NmWai4sLAgIC4OzsjM+fP2f4uSSpFM5XHiFEnJyq3Ugkwpf6FWCum/ZZvbCIKNRs2R+fg77J9Tna2+Df4xthb2ud4XiIiIhyWkJCAnx9feHu7g5DQ8OcDocySVN/flyZzSX0RSL87mQr1x4vlWJ/UPoHuawtzbFt5TToKLiE4cu3UPQexfqzRERElPcwmc1FFFU1ADK21QAAqlUsi+ne/RT2Xbv9CHOWb81ybERERES5EZPZXKSsmTGqmJvItd+OjMHLmLgMvWNU/05oWMdLYd+yDX/h5PkbKsVIRERElJswmc1l+rgoXp3dFqC85uzPRCIRNi2djIJODgr7B45biA8fA7IcHxEREVFuwmQ2l+nsaANDkXzR2V2BIRD/r4hxemysLLBrzUzo6+nJ9UXFxKL7sOmIi09Q8CQRERGRdmEym8tY6uminYN81YGvSWKcDonM8HsqlSuJJdOHKex7/toHo6YvBwtZEBERkbZjMpsLqXoQ7IfenVuiS5tGCvv2HjmHbftPZjo2IiIiotyEyWwuVM/aHG5GBnLtJ4PD8SUxScETigmCgBWzR6NsycIK+8fNWo2Hz95kOU4iIiJN4E8StZOm/tyYzOZCIkFALwU1ZyUyYHdgaKbeZWxkiN1rZsPcVL5KQpJYjN+HzUBoeMa3LxAREWmKjo4OAEAsFudwJJQViYmJAADddC5+UhWT2Vyql7Md5I+BAVsDvmX6O50ibs7YsGSiwr5PAV/Rf8x8SDN4uIyIiEhT9PT0YGBggMjISK7OahmJRIKwsDCYmJhkezLL62zVLKvX2SrS8P4rXAiNkmu/VbU0qlmaZfp90xdvxPKNexX2TRnZCxOH98z0O4mIiLJTVFQUAgICYGpqCgsLC+jp6UEQFC33UE6TyWSQSCSIj49HZGQkpFIpChYsCCMjo2ydN3tTZVJJH2c7hcns1oDgrCWz3n1x/8krXL/zWK5v/qodqOxZCr8quXCBiIgoJ5ibmwMAQkJCEBDAOunaQEdHB8bGxrC3t4e+vn62z8eVWTVT58psvEQKpysPEZEsSdVupiNCUL2KMNHVyfQ7v4WEoVbrgQj6Kn8Jg5WlOW4c24BCzo5ZjpmIiCi7iMViSCSS9AdSjhGJRBpfPWcyq2bqTGYBYOhLX/zp/02ufadHYfzupLiEV3puPXiGZt1GIzlZ/h+Eih4lcG7fKhgYZP93UkRERESq4gGwXK6Ps73C9o3+mas5+7PqlTwwb+IghX0Pn72B98yV3GhPREREWoHJbC5X0dwY5UyN5dpvRETjWXRclt87uGc7tG1WT2HfzoP/YMtfx7P8biIiIiJNYTKbywmCgH4uircT/On/VaX3rpk/DsWLFFLYP27Oaty4+yTL7yciIiLShEzvma1Tp476JhcEXL16VW3vyw3UvWcWACLFyXC6+ghxktS1YE10RAisVwHmKtRve/3eD/XbDUZMbLxcn621Ja4f3QAXJ8VbHYiIiIhyWqaTWZFIfYu5giDkuVOJ2ZHMAsDAF77Y+Fn+INiaUq4YWki16gMnzt9A18HTFPaVL1MM5/avhpGh/PW6RERERDktS8lsw4YNMXnyZJUmnjdvHi5evMhkNoMeR8Wiwq3ncu2lTYzwvKaHyiUw5q/cjgWrdyjs69y6ITb+MYlFqomIiCjXydLPpx0cHFC3bl2VJt68ebNKz+c35c1NUMPSFDcjYlK1v4yNx7XwaNS1Nlfp/ROH98DTV+9x6sK/cn37jp2HZ5liGNang0pzEBEREalbpvcM9OzZUy37ZuvUqYMePXqo/J78ZEhBB4XtqhwE+0EkEmHjkkkoUcRVYf+Uhetx+d8HKs9DREREpE68NEHNsmubAQAkSqUoePURgpOSU7XrCgI+1S2PAmq46OCdrz/qtx2MyOhYuT4rS3NcPbwO7oWcVJ6HiIiISB1YmkuLGIhE6KfgEoVkmQybP2f9EoWfFXMviK0rpincHxseEYUug6cprHxARERElBPUnszevHkT586dU/dr6X8GFrSHomNYG/y/IlmqnkX2RnWrYsaYfgr7XrzxweAJi3hDGBEREeUKak9m+/bti2bNmqn7tfQ/rkYGaGFnKdcekCjG8eBwtc3jPbCL0hvCjp65ij/W7VHbXERERERZlS3bDLhql72UHgT7pPpBsB8EQcCfC8ejbMnCCvvnLN+KM5dvqW0+IiIioqzgnlkt1MjWAoWN5C8xuBgWhdcx6tvPamJshL3r5sLaSr7sl0wmQ9/R8/DW55Pa5iMiIiLKLCazWkgkCBisZHV2vb/8LWGqcCtYADtWToeOjvxflaiYWHQeNBURUTEKniQiIiLKfkxmtVRvZ1sYiOSPgm0PDEZssnpvVatXoxLmTRyssO+djz96Dp+FZDXPSURERJQRTGa1lI2+Hjo72si1RyZLsPdLqNrnG9KrHbr81lBh36V/72P8nNVqn5OIiIgoPVqVzEqlUixfvhwlS5aEoaEhChYsiDFjxiA2Vr7AvyIxMTGYP38+PDw8YGZmBltbW9SoUQPbt2/XykNrQwsp3mqw9tNXtX88giBg5dwxqOhRQmH/pj3HsGHnEbXOSURERJQerUpmR48eDW9vb5QuXRqrV69Ghw4dsGrVKrRs2RJSqTTNZ6VSKZo2bYpp06ahSpUqWLp0KaZOnQqJRILevXtj4sSJGvoo1KeKhSkqm5vItT+OjsOdSPXvYzUyNMDedXNQwMFWYf/4uWtw4dpdtc9LREREpIzar7MtVaoU3r59C4lEvXsoX7x4AQ8PD7Rp0waHDh1KaV+9ejVGjBiBPXv2oGvXrkqfv3XrFmrUqIFRo0Zh+fLlKe1JSUkoWbIkwsLCEBERoXKc2XmdrSLbAoLR57mPXHv3AjbYVa5otsz56PkbNO48EvEJiXJ95qYmuHhwDUoWc8uWuYmIiIh+pjUrs3v37oVMJsOoUaNStffv3x/GxsbYvXt3ms9HRUUBAJycnFK16+vrw9bWFiYm8iuc2qCTozWsdHXk2g98CUNwkjhb5qxQtgQ2LZ2ssC8qJhYdB0xBSFhktsxNRERE9DOtSWbv3bsHkUgELy+vVO2GhoYoX7487t27l+bzXl5esLS0xOLFi3Hw4EF8+vQJr1+/xqRJk/DgwQPMnDkzzeeXLVsGFxeXdH8FBQWp+qFmirGODno728m1J8lk2Po5ONvmbd24DqZ791XY5+sfiG5DpyMxMSnb5iciIiICAN2cDiCjAgMDYWtrCwMD+csCnJ2dcfPmTSQlJUFfX1/h81ZWVjh+/Dj69euHjh07prSbmZnh0KFD+O2339KcPyoqCgEBASp9DNllUEEHLPP7Ite+/vM3jHUvAB1BvoSXOowd3A3vfD5h79Hzcn037z3FyOnLsW7heAjZND8RERGR1iSzcXFxChNZ4Pvq7I8xypJZADA1NUXZsmXRqlUr1KhRA2FhYVi7di26du2KY8eOoWFDxaWnAMDc3BzOzs7pxhkUFJTuYTR1K2ZiiEY2FjgXmvpH+x/jE3EmJALN7ayyZV5BELB63lj4fArEnYcv5Pr3HDqDEkUKYfSALtkyPxEREZHaD4CNHz8eQUFB2LVrlzpfCw8PD3z79g1fv36V6+vYsSMOHjyIxMREpcnss2fP4OXlheXLl2PQoEEp7XFxcShbtiykUik+fPgAHR35/aeZoekDYD8c+xaG3x69k2tvZmuJU5UUl9NSl+DQcNRvNwR+n+VXhwVBwJ4/Z6Nlw1rZGgMRERHlT2rfM7t48WK1J7LA94NbISEhSEyUP0EfEBAAW1vbNFdlly9fjoSEBHTo0CFVu7GxMZo3bw4/Pz98/PhR3WFrTHNbKxQ0lP/4T4dEwCcuIVvntrOxwoGN82FmYizXJ5PJ0H/MPDx9+T5bYyAiIqL8SWsOgFWpUgVSqRR376auY5qQkIDHjx+jcuXKaT7/Y7+ropJhycnJqf6rjXRFAgYVtJdrlwHY4P8t2+cvXdwd21ZOg0gk/1cqNi4BnQZOwdfgsGyPg4iIiPKXTCezFStWxLRp01SeeOrUqahUqVKGx3fq1AmCIGDFihWp2jdt2oS4uDh069Ytpe3Dhw94/fp1qnGlS5cGAGzfvj1Ve0REBI4dOwYrKysULZo9dVk1pa+zPfQUHLbaEhCMeEn27+NtXK8a5k8arLDvc9A3dB40RWFtWiIiIqKsynQy+/jxY/j5+ak8sZ+fHx4/fpzh8R4eHhg6dCgOHz6Mtm3bYvPmzRgzZgy8vb1Rt27dVBcm/PLLLyhVqlSq50eNGgVra2tMnDgRv//+O9avX4/58+ejQoUKCAoKwty5c1XeL5vTHAz00N7BWq49VJyMPUEhGolhSK926N25hcK++09eo/+Y+Ro/IEdERER5V6YPgIlEInh4eKB169YqTXz06FG8ePEiUzeFSSQSrFixAhs3bsTHjx9ha2uLTp06Yfbs2TA1NU0Z5+bmBj8/P/z3Q/vw4QNmz56Nixcv4uvXrzAyMkL58uUxatQotG3bVqWP54ecOgD2w43waNS++1KuvZSJIZ7XLAeRBspkicXJaNNnPK7eeqSwf1ifDlgweUi2x0FERER5X5aSWZUnFQTIZDIIgqD2a29zWk4nszKZDJVvP8fDqDi5vlMVS6CZnaVG4giLiEKD9kPx4aPi/weLpw3D4J7tNBILERER5V2ZrjM7Y8aM7IiD1EQQBHi7FkD3Zx/k+pZ+DNJYMmttaY6Dm+bjlw7DEB4RJdc/Ye5auDg5sGQXERERqUTtdWbzu5xemQUAsVSKwtef4HOC/HWyD6uXRQVzE43FcvP+M7TqMQaJSWK5PkMDfZzavRxeFUprLB4iIiLKW7SmNBdlnJ5IhBGFHBT2Lf0YpNFYalT2wMYlkxT2JSQmoeOAyfDxy53XBBMREVHux2Q2j+rvYg9THfk/3v1fwvBZw+Wx2javj7kTBynsCw2PRNu+ExESFqmwn4iIiCgtTGbzKEs9XfRzkb9EIVkmwyo/+SuBs9uIvh0xoPtvCvs+fPzMGrRERESUJUxm87CRro4K/4A3fv6G6GTNVpEQBAGLpw1D0wY1FPbfefgC/cfMz3PVLYiIiCh7MZnNw9yMDNDeUf4ShchkCbZ8zv4rbv9LR0cH21ZMRaVyJRX2Hzt7DVMWrtdwVERERKTNmMzmcWNcCyhsX+H3BclSzReyMDE2woGN8+BWUHFca7f9jT+3/63hqIiIiEhbqTWZDQoKwoEDB7B06VIcO3YMAHD//n2IxfJlmUgzvCxNUcvSTK7dLyEJh7+F5UBEgL2tNQ5tWQgrS3OF/RPn/Ynj565rOCoiIiLSRmpJZiMjI9GjRw+4urqiS5cuGD9+PA4dOgQAGDlyJNzd3XHnzh11TEVZMNbdUWH70o9Bclf+akrxwoWwb/1cGOjryfXJZDL0HT0Xdx/JX8tLRERE9DOVk9m4uDg0aNAAu3fvho2NDdq3b58qQdLX10dgYCAaNmwIHx8fVaejLGhpZ4VixoZy7XcjY/FvREwORPRdejVoOwyYhDcfPmk4KiIiItImKiezS5YswaNHj9CrVy/4+vpi//79qfovX76MSZMmISYmBosWLVJ1OsoCkSBgtKvy1dmclFYN2rDwKLTpPR4BQcEajoqIiIi0hcrJ7P79++Hs7IwNGzbA0FB+9Q8A5s6di8KFC+PKlSuqTkdZ1NPZFjZ6unLtx76F411sQg5E9P/SqkHrH/gVbfqMR1hElGaDIiIiIq2gcjLr6+uLatWqQU9Pfu/jD4IgwNPTE/7+/qpOR1lkrKODwQXlL1GQAVjhl7Orsz9q0Db7RXEN2lfvPqLjgMmIi8/ZpJuIiIhyH5WTWRMTE3z58iXdcYGBgTA2NlZ1OlLB0EIO0BcEufZtASEITcrZihPfa9BOQ7VKZRX233n4Aj1GzIJYnKzhyIiIiCg3UzmZ9fLywr179/DixQulYx4/fowHDx7Ay8tL1elIBY4G+ujuZCvXHi+VYr2/5i9R+C9jI0Mc2DgfpYu7K+w/e/k2hk35I8cqMBAREVHuo3Iy6+3tjaSkJDRv3hzHjh1DZGRkSp9YLMbJkyfx22+/QSKRYOjQoapORyrydlN8EGz1p69IlEo1HI08KwszHNm6CIWcHRT2/3X4LKYt3qDhqIiIiCi3EmRqWOZauHAhpkyZkqrNwMAAYrEYUqkUMpkM48aNyxfVDFxcXBAQEABnZ2d8/vw5p8NRqOmD1zgTEinXvqWMO/q4yO+rzQlvfT6hUacRCA2XjxMA5k4chJH9Omk4KiIiIspt1HJpwsSJE3HhwgU0atQIRkZGkMlkSEhIgEgkQu3atXHkyJF8kchqizFuiq+SXeb3Jdf8CL944UI4tGUhTBTUxwWAqQvX468jZzUcFREREeU2almZ/ZlUKkVoaCgkEglsbGzSrHKQF2nDyqxMJkP5m8/xNCZOru90xRJoYmep+aCUuHTjPtr3n6Tw4JeOjgj71s9Fk/rVcyAyIiIiyg3UsjKb6oUiEezs7ODo6JjvElltIQgCxijZO7s0h8t0/VeDWpWxcckkCAqqMEgkUvQYPgu3Hz7PgciIiIgoN1B7MkvaoXMBGzgZyH+zcSE0Ck+iYnMgIuXat2iAxdOGKeyLT0hEx/6T8eqtr4ajIiIiotxA/kqoTKpTp06GxwqCgKtXr6o6JamBvkiE4YUcMemd/EUWf3wMwq5yRXMgKuUG9WiLbyHhWPLnbrm+8Mho/NZ7PM4fWI1CzopXnImIiChvUnnPrEiU/uKuIAiQyWQQBAESiUSV6XI9bdgz+0O4OBkFrz5CrCR1SS4dAXhTyxNFlBy+yikymQwjpi7F9v2nFPYXLuSEs/tWwdHeRsORERERUU5ROZlVttIqkUgQERGBW7duYf369ejQoQP+/PNPGBrmrgRJ3bQpmQWAka8+YtWnr3LtfZ3tsLls4RyIKG0SiQS/D5+FE+euK+wvVcwN/+xZAVtrCw1HRkRERDlB7dUMFLl+/Trq16+PP//8EwMGDMju6XKUtiWz/vGJKHL9CcT/+WugKwh4X9sTrkYGORSZcgmJSWjTezxu3H2isL9C2eI4sWspLMxMNRwZERERaZpGDoDVrl0b1apVw9q1azUxHWVCQSMD9HKWv+I2WSbDYt/AHIgofYYG+ti3YS48SxdT2P/o+Vt06D8ZsXHxGo6MiIiINE1j1QwcHBzw7t07TU1HmTDR3Qk68pWvsCUgGIEJSZoPKAMszExxZNtilCjiqrD/1v1n6Dp4OhITc2f8REREpB4aSWYjIyNx/fp1WFpaamI6yqTCxoboXkB+dTZRKsOSj7mr7uzP7GwscXzHErgVVHyj2aV/76PXqDkKL1wgIiKivEHlPbNbt25V2ieRSPDt2zfs2LEDHz58QO/evbF582ZVpsv1tG3P7A9vY+NR8sZT/Pcvg5FIhI91ysNeQU3a3OKjfxAadx6BwK8hCvs7tfoVG/+YlKHKG0RERKRd1FKaS9HtTD+TyWRwdXXFzZs3UaCA4lW0vEJbk1kA6PLkPfZ9CZVrn+BeAAuLF8qBiDLuzYdPaNJlJELCIhT29+nSEitmj0737yoRERFpF5WT2V69eilNEEQiEUxNTeHp6YlOnTrBxMRElam0gjYns8+j4+Bx85lcu6nO99VZG/3cuzoLAE9fvkfz7qMRERWjsH9Ev06YO2EgE1oiIqI8RCOlufITbU5mAaDdo7c4/C1crn1aYWfMLuaSAxFlzt1HL9Gq5xjExiUo7J8yshcmDu+p4aiIiIgou3ATIaUytYizwvZVn74gUgsOUnlVKI39G+bBQMkq8ryV27Fm60ENR0VERETZJdMrs2kd+MqIPn36qPR8bqftK7MA0OLhG5wKjpBrn1vUBVOUJLu5zZnLt9Bl8DQkJyu+PnnlXG/06dxSw1ERERGRumU6mc3Iga+0SCSKk4u8Ii8ks3ciYlDtzgu5dhs9XXysUx6mujo5EFXmHT51Gb1Hz4VUKlXYv3bBOPTo0EzDUREREZE66Wb2gR49evAATR5X1dIUDW3McT40KlV7qDgZ6/y/Ypy7Uw5Fljltm9dHbHwChkxcrLB/2OQ/oKMjQre2TTQcGREREakLD4CpWV5YmQWA6+FRqHP3lVy7vb4ufOuUh7GOdqzOAsD6nYcxbvZqhX2CIGDD4ono0qaRhqMiIiIiddDoAbBHjx5pcjpSQW0rc9S1MpNr/5aUjM2fg3Mgoqwb1KMtZo7tr7BPJpNh0IRFOHD8goajIiIiInXI9DYDRR4+fIgNGzbA19cXiYmJ+HmxVyqVIiEhAV+/fkVQUBCSk3P/iXj6bmoRZ1y9/1qufbFvIAYWtIeBFt2oNWZQVyQnJ2Puim1yfVKpFP3HLoBIJEL7Fg1yIDoiIiLKKpWT2fv376N27dpISkpKSWIFQUiV0P74vYeHh6rTkQb9Ym2OahamuB2Z+hKCgEQxtgUEY1BBhxyKLGsmDOsBqVSG+au2y/VJpVL0GzMPOiIR2jSrp/HYiIiIKGtUXlpbtGgREhMT0apVKxw9ehSDBg2CIAg4duwYDh8+jIEDv9+4VKZMGdy7d08dMZOGCIKAaUpKcS30CYRYSZWA3GzSiJ6YMOx3hX0SiRS9R8/BsTNXNRwVERERZZXKyey///4LR0dH7N+/H61atUKXLl0glUohCAJ+++03rFu3DmvWrMHLly+xatUqdcRMGtTU1gIVzY3l2v0SkrA7KDQHIlLdlJG9MXZwN4V9EokUvUbNwfFz1zUcFREREWWFyslsaGgoKlWqBH19fQBI2Upw//79lDGDBg1CwYIFsW/fPlWnIw0TBAFTCytenZ3vE4BkqfYVwxAEAdO9+2L0gC4K+5OTJeg5YhZOnr+h4ciIiIgos1ROZo2MjFISWQCwtLSElZUVXr9OfXCoYsWKePfunarTUQ5obW+FsqZGcu3v4xKx/4t2rs4KgoBZ4/pjRL9OCvuTkyXoMWIW/rl4U8ORERERUWaonMwWK1YMT548SdVWvHhxPHjwIFVbQkICKxloKVEaq7PzfAIg0dJSxYIgYO6EgRjau73CfrE4Gb8Pm4mzV25rODIiIiLKKJWT2ebNm8PX1xejRo1CZGQkAKBmzZrw8fHBiRMnAABv377FlStX4O7urup0lEPaO1qjhImhXPur2ATs09K9s8D3hHbB5CEY0qudwv4ksRhdB0/Hmcu3NBwZERERZYTKyeyoUaPg7u6O1atXo2vXrgCAoUOHQkdHB+3atUOlSpVQsWJFJCYmoksXxXsUKffTEQRMVnKN7fT3n5GkhZUNfhAEAQunDMWgHm0U9ieJxeg6ZDoPhREREeVCKiezlpaWuHXrFoYOHQovLy8AgLu7O3bs2AFDQ0M8evQIcXFxaNmyJcaOHatywJRzuhawRVFjA7l2n/hEbNGyW8H+SxAELJ42HP27tVbYLxYno8fwmTh06pKGIyMiIqK0CDJZ9m14jI2NxfPnz2FnZ4fChQtn1zS5iouLCwICAuDs7IzPnz/ndDhqty8oFF2evpdrd9TXw/vanjDR1cmBqNRHKpVi9IwV2Lr3hMJ+kUiE9YsmoEubRhqOjIiIiBTJ9MrswoUL8eXLlwyNNTExQdWqVfNNIpsfdHS0Rnkz+bqzX5LEWP3paw5EpF4ikQjLZ41C366tFPZLpVIMHL8Q2/ef0nBkREREpEimk9nJkyejUKFCaNOmDU6dOgWpFu+VpMwTCQLmFSuosG+RbyDCxdpfseJHQqvsUJhMJsPwKX9g464jGo6MiIiI/ivTyWy7du2go6ODY8eOoVWrVihUqBCmTp0KHx+f7IiPcqGmthaoZWkm1x6RLMES36AciEj9fhwKGzWgs9IxY2atwpqtBzUYFREREf1XppPZgwcPIigoCH/++Se8vLwQGBiI+fPno3jx4vj111+xd+9eJCUlZUeslEsIgoAFxRWvzq789AVBiXnjz18QBMweNwATh/VQOmbS/D/xx7o9GoyKiIiIfqbyAbB3795hx44d2LNnD/z8/CAIAiwtLdG9e3f07dsX5cqVU1esWiGvHwD7WYuHb3AqOEKufUhBe6wtnbdqCi/5czdmL9uitH/S8J6YNKInBEHQYFRERESk1moGV65cwY4dO3Do0CHExMRAEARUqlQJ/fr1Q5cuXWBmJv+j6bwmPyWzT6JiUf7Wc7l2XUHAm1rlUNhY/pIFbbZq8wFMWbhOab/3wK6YObYfE1oiIiINypbSXPHx8Th06BB27tyJy5cvQyKRwMTEBB06dMDWrVvVPV2ukp+SWQDo+uQ99n6RvwGsewEb7CpXNAciyl4bdx3BmFmrlPYP7dUeC6YMYUJLRESkIdlaZxYAQkNDsXLlSixatAjJycmQSCTZOV2Oy2/J7PvYBJT69ymS//PXSADwpIYHPBSU8dJ22/adxMhpy6DsU6dv11ZYNnMkRCKV7yQhIiKidGTbV9uAgAD88ccfaN68OebNmwexWAx7e/vsmo5ySFETQ/RzsZNrlwGY8s5f8wFpQO/OLbBu0XilyeqWv46j35h5EOeBMmVERES5nVqT2cjISGzZsgUNGjSAq6srxo8fjwcPHqB58+Y4cuRIvlipzI+mFXaGkYLE7kRwBG6GR+dARNmvW9sm2LJsCnR0FH8KHTxxCZ0HT0VcfIKGIyMiIspfVN5mkJSUhJMnT2LPnj34559/kJSUBJlMhmLFiqFPnz7o2bMnHB0d1RVvrpffthn8MOHNJyz+KF9jtq6VGS5XKZVn95AeO3sNvUfNUboKW6NKORzYOA8WZqYajoyIiCh/yHIye/nyZezZsweHDh1CVFQUZDIZjI2N0b59e/Tt2xe1a9dWd6xaIb8ms2FJySh8/TEik+X3RJ+pVAKNbS01H5SGnLl8C78Pm4kEJfV1PUsXw5Fti2FnY6nZwIiIiPKBTCez48aNw759+xAYGJhyAMbLywt9+/ZF586d80X5rbTk12QWAOZ9CMDU9/Ifc0VzY9yrVhaiPLo6CwA37jxGxwFTEB0bp7C/WOGCOLZ9CQo6OWg4MiIiorwt08nsj0Mvtra2+P3339GnTx+UKVMmW4LTRvk5mY1JlqDo9Sf4miSW69vvWRQdHW1yICrNefT8Ddr0noDQ8EiF/S4F7HFsxxIUL1xIw5ERERHlXZk+ANakSRMcPHgQAQEBWLp0KRNZSmGqq4OphZ0U9k179xnJ0mytApfjKpQtgbP7VsHZUb66AwB8DvqGxp1H4smLdxqOjIiIKO/K9jqz+U1+XpkFgCSpFCVuPMXH+ES5vk1l3NHPJe+XZ/sU8AWteo7Dh4+K//zNTU1wYNN81KySv656JiIiyg6s6k5qpS8SYVYRZ4V9sz4EIEEi1XBEmlfI2RHn9q2ER6kiCvujYmLxW69xOHvltoYjIyIiynuYzJLadXOyRRlTI7n2zwlJWPPpaw5EpHn2ttb4Z88KVKtUVmF/QmISOg+air9PXtJwZERERHkLk1lSOx1BwLxiLgr75voEIFjBAbG8yNLcFMe2L0HDOl4K+5OTJegzei7W7zys4ciIiIjyDiazlC1a2VmhmoX8RQGRyRJMV1C+K68yNjLEvvVz0bZZPYX9MpkM42avxvTFG8Ht60RERJmnVcmsVCrF8uXLUbJkSRgaGqJgwYIYM2YMYmNjM/yOsLAwjB07FkWLFoWhoSHs7OxQv359XL9+PRsjz38EQcCi4gUV9m30/4an0YrrseZF+vp62Lp8Knp3bqF0zPKNezFw3AKlN4kRERGRYionsw0aNMCCBQvSHeft7Y0SJUqoNNfo0aPh7e2N0qVLY/Xq1ejQoQNWrVqFli1bQipN/2CRn58fKlWqhB07dqB9+/b4888/MXnyZLi5uSEgIECl2EheHWtztHewlmuXAhj92i9frUTq6Ohg5RxvjB7QRemYvUfPo0P/SYiOyT+JPhERkap0VX3BlStX4OKieH/kz54+fQo/P78sz/PixQusXr0abdu2xaFDh1La3d3dMWLECOzbtw9du3ZN8x3du3dHcnIynj59igIFCmQ5Fsq4xcUL4kRwOBL/U2P2UlgUjgeHo7W9fLKbVwmCgNnjB8DG2gJTF65XOObijfto3n00/t68APa2+ef/DRERUVZlus5sly5dUq1i3rhxA/b29ihevLjSZyIjI/H8+XO4u7vj/fv3WQp06tSpmDdvHq5du4batWuntCckJMDGxgZ169bFP//8o/T5a9euoW7duli1ahWGDx8OsVgMsVgMY2PjLMWjTH6vM6vI5Lf+WOAbKNdexMgAL2qVg4FIq3a7qMX+Y+cxeOJipdsK3As64ci2xSjiprjMGREREX2X6ZXZVq1aoVu3bim/FwQB3759w7dv39J8TkdHBzNmzMh8hP9z7949iEQieHmlPhluaGiI8uXL4969e2k+/yPRLVSoEFq2bInTp09DIpGgWLFimD59Orp3757m88uWLcOyZcvSjTMoKCjdMfnNpMJO2BYQjC//qWLwIT4Rq/y+YJy74lvD8rJOrRvC3tYaXYdMQ0xsvFy/r38gfu04DH9vXoBK5UrmQIRERETaIdPJbJcuXeDi4gKpVAqZTIYGDRqgYcOGmDx5ssLxgiDA0NAQ7u7usLNTfM1nRgQGBsLW1hYGBgZyfc7Ozrh58yaSkpKgr6+v8Pk3b94AAPr3749ixYphx44dSEpKwtKlS/H7779DLBajd+/eSuePiorivtosMtPVwfziBdHnuY9c35wPAejhZAcHA70ciCxn1a9ZCWf+Wom2fSfgW0i4XH9IWASadRuNXWtmolHdqjkQIRERUe6XpT2zP/+Yv2fPnqhZsybq1q2rtqAUiYuLU5jIAt9XZ3+MUZbMRkdHAwDMzMxw+fLllHG//fYbChcujMmTJ6Nnz54QKfmRt7m5OZyd0/+Rb1BQUIYOo+U3PZ1ssfbTVzyISl15IloixbT3/thYpnAORZazPMsUw8WDa/Fb7/EKr7+Ni09AxwGTsWb+OHRv1yQHIiQiIsrdVN6suG3bNvTr108dsaTJ2NgYiYmJCvsSEhJSxihjZPT9RqouXbqkSnitrKzQqlUrfPnyJWX1VhFvb298/vw53V88WKaYSBCwoqSrwr7Nn4PxOCrj5dXyGreCBXDhwBpU9iylsF8ikWLwhEVY8ufufFUBgoiIKCO05uSNk5MTQkJCFCa0AQEBsLW1VboqCyCl4oKjo6Nc348ENDxc/ke9pD61rMzQ0VH+hL4MwKh8Vqrrv2ytLXBy11I0rl9N6ZjZy7Zg9IwVSE6WaDAyIiKi3E0tyezdu3fRqVMnlClTBm5ubihUqJDCX66uilfmMqJKlSqQSqW4e/duqvaEhAQ8fvwYlStXTvP5HwfHFFUY+NFmb2+f5fgoYxYXLwRDkSDXfjU8Gke+5e9vJkyMjbBv3Vz83r6p0jFb/jqOjgMmIyo6/65kExER/SzTpbn+6+bNm2jQoAHEYnG6K2uCIEAiydqq0rNnz+Dp6Yk2bdqkqjO7evVqjBgxArt27UqpSPDhwweIxWKULPn/p8DDw8Ph6uoKc3NzvH79Gqam369aDQoKQrFixeDs7JzmNoOMYmmu9E1754+5PvKlutyNDPCyZjkY6mjNDwyyhUwmw7yV27BozS6lY8qWLIyDGxfAxYnfgBERUf6mcjLbpEkTnDt3Dh06dMCwYcPg5OQEXV3l58pUWZ0dPnw41qxZgzZt2qBZs2Z49eoVVq1ahZo1a+LSpUsph7fc3Nzg5yf/Y+uNGzdi4MCBKFOmDPr06YOkpCSsW7cOQUFBOHnyJBo1apTl2H5gMpu+mGQJit94gqBEsVzfwmIFMaFw/ivVpcjWvccxesZKpQcKHe1tcHDjfJQvq7zGMxERUV6ncjJrYWGBAgUK4PXr1+qKSSmJRIIVK1Zg48aN+PjxI2xtbdGpUyfMnj07ZaUVUJ7MAsDhw4exePFiPHv2DCKRCNWrV8eMGTNQs2ZNtcTIZDZjdgYEo6eCUl2mOiK8q+0JRwPl+5/zk5Pnb6DP6LmIT1B8+NHYyBDbVkxDs19qaDgyIiKi3EHlZNbc3ByNGjXC33//ra6YtBqT2YyRymSodvsF7imoYtDH2Q5byubPUl2KPHj6Gh0HTFZYixb4vn1n0dShGNyznYYjIyIiynkqb06sUKECXrx4oY5YKB9Jq1TXtoBgPMzHpbr+q1K5krh86E+UKuamsF8mk2H8nDUYO2sVKx0QEVG+o3IyO3HiRLx58wYrV65URzyUj9SwMkMXRxu5dpbqklfI2RHnD6xGg5rKq3Zs2HUEnQdPVXg9LhERUV6l8jaD48ePY8eOHTh69CgqVKiAatWqwcrKCoIgX35JEATMmjVLlelyPW4zyJxP8YkoeeMp4hUccjrgWRQdFCS7+ZlYnAzvmSuwff8ppWPKlSqKg5vmw8kx69dHExERaQuVk1mRSARBENJcRfvRr0ppLm3BZDbzZrz/jNkfAuTaXQ318bJWORjr6ORAVLmXTCbDys37MW3RBqVjnBxscXDTApQrXVSDkREREWme8hpaGTR9+nSFq7BEGTXerQC2fP6GgP+U6vJLSMLcD4GYX7xgDkWWOwmCgFH9O8PNpQD6j52PhMQkuTGBX0PQqPNwbF46BS0a1sqBKImIiDRD5ZVZSo0rs1mzOzAEvz/7INeuKwh4XKMsypga50BUud+9xy/RaeBUBIcqvz1tundfjB3cjd90EhFRnqTWq5aCgoJw4MABLF26FMeOHQMA3L9/H2KxfHF8op91LWCD6pamcu3JMhkGvfgIKb/nUqhK+dK49PdalCii/DKS2cu2oK+38lq1RERE2kwtyWxkZCR69OgBV1dXdOnSBePHj0+5cnbkyJFwd3fHnTt31DEV5VEiQcD60u7QUbB4eCMiGtsCgjUflJZwK1gAFw6uQd3qFZSOOXjiEpp0GYnAL/z/SEREeYvKyWxcXBwaNGiA3bt3w8bGBu3bt091GExfXx+BgYFo2LAhfHzkb3wi+qGcmTG8XQso7Bv/1h/BSVzhV8bS3BSHtyxCz47NlY55+OwN6rYdjPtPXmkwMiIiouylcjK7ZMkSPHr0CL169YKvry/279+fqv/y5cuYNGkSYmJisGjRIlWnozxuRhFnuBrKX2UbJk7G2DefciAi7aGvr4fV88Zg8bRhEIkUf2p/+RaKJl1GYv+x8xqOjoiIKHuonMzu378fzs7O2LBhAwwNDRWOmTt3LgoXLowrV66oOh3lcSa6OlhTyk1h387AEFwOjdRsQFpGEAQM7tkOR7YugqW5/B5kAEhMEqPfmPmYsWQTpArq+xIREWkTlZNZX19fVKtWDXp6ekrHCIIAT09P+Pv7qzod5QMt7K3Q1t5KYd+glx+RyAQsXQ1qVcalQ3+iWGHlZc2WbfgLnQdNQ3RMnAYjIyIiUi+Vk1kTExN8+fIl3XGBgYEwNmZ5JcqYlaVcYaoj/9fzbVwCFvkE5kBE2qeYe0Fc+vtP/Fq7itIxpy/dxC8dhsL3E/+fEhGRdlI5mfXy8sK9e/fw4sULpWMeP36MBw8ewMvLS9XpKJ9wMTTA3GKKVxXn+wbiXWyChiPSTpbmpji4aQGG9emgdMyrdx9Rr91gXLv1SIORERERqYfKyay3tzeSkpLQvHlzHDt2DJGR/7+nUSwW4+TJk/jtt98gkUgwdOhQVaejfGRYIQdUNJdfzU+UyjD4pW+aVyjT/9PV1cGCyUPw58Lx0NNTfOlfWHgUWvUaizVbD/L/KxERaRW13AC2cOFCTJkyJVWbgYEBxGIxpFIpZDIZxo0bly+qGfAGMPW6HxmDqrdfQNEu2d0eRdDNyVbjMWmzWw+eoduQGWneGNahZQOsnjcWJsZGGoyMiIgoa9RyacLEiRNx4cIFNGrUCEZGRpDJZEhISIBIJELt2rVx5MiRfJHIkvpVtjDF0EIOCvu83/ghXJys4Yi0W/VKHrh6ZB08ShVROubgiUv4pcMw+PgFaDAyIiKirFHLyuzPpFIpQkNDIZFIYGNjk2aVg7yIK7PqF5WcjFI3niIwUf7ShIEu9lhfxj0HotJusXHxGDhuIY6dvaZ0jKW5KbYsn4pGdatqMDIiIqLMUcvKbKoXikSws7ODo6Mjvn79ijt37iA6Olrd01A+Yq6ri5UlXRX2bfj8Dbci+Pcrs0yMjbBz9QxM9+4LQVBwhzCAiKgYtO83CYvX7mI9WiIiyrXUksy+fPkSffr0wY0bN1Laxo0bBzc3N9SoUQPOzs7YtGmTOqaifKqdgzWa2Voq7Bv4whdiJluZJhKJMG5IdxzavBBWFmYKx8hkMsxZvhVdh0xHZHSMhiMkIiJKn8rJ7OvXr1GtWjXs2LEDT58+BQBcuXIFS5cuBQB4enpCLBZj0KBBuHr1qqrTUT4lCALWlnaDkYJrWp/FxGOFX/q1jkmxhnW9cPXI+jT30Z668C/qtR2C1+8+ai4wIiKiDFA5mV24cCFiYmIwYsQIdOzYEQCwdetWCIKABQsW4OHDh7hx4wZEIhGWL1+ucsCUf7kZGWBGEWeFfTM/BOBjfKKGI8o73As54cKBNejY6helY977+qN++yE4dobflBIRUe6h8gEwV1dXmJqaplyaIJPJYGdnh4iICHz58gW2tt9LJ9WvXx+vXr3K0G1h2owHwLKXWCpFxVvP8TwmXq6voY05zlYqqXQPKKVPJpPhz+2HMGXhOkgkyrdueA/simmj+0BXV0eD0REREclTeWX269evKFOmTMrv79+/j7CwMHh4eKQksgBgZ2eH8HDltS2JMkJPJMKG0oqrF5wPjcKmz8EajihvEQQBQ3u3x8mdS2FnY6V03LINf6FVz7H4GhymweiIiIjkqZzM2traIiIiIuX3p0+fBgD8+uuvqcb5+PjA0tJS1emIUMPKDP1d7BT2jXnjx+0GalCranlcP7oBlT1LKh1z/c5j1GjZD9dvP9ZcYERERP+hcjJbtmxZXL9+HW/evEFUVBR27twJQRDQqlWrlDGHDh3Cw4cPUaVKFVWnIwIALC5eCM4G8jWMYyRS9HnuAymvZFWZcwE7nPlrJXp1aq50zLeQcLToMQZL/tzN8l1ERJQjVE5mR44ciaSkJJQrVw5OTk7w8fFBpUqVULt2bQBA8+bN0alTJ4hEIowePVrlgIkAwFJPF5vLFFbYdzksCuv8v2o4orzJwEAfq+eNxaq5Y6Cv5AIUqVSK2cu2oEP/yQgNj9RwhERElN+pnMw2bdoU27dvh4uLC2QyGRo3bowjR46k9Pv7+8PKygoHDx7EL78oPylNlFlN7CzRz1nxdoPxb/3xPjZBwxHlXb07t8C5/atQyFnx1cIAcO7qHdRqNQB3Hr7QYGRERJTfqf062/969eoVihcvDh2d/HHqmdUMNCsqORke/z7Dp4Qkub5alma46lUKIlY3UJuwiCgMHLcQZy7fUjpGV1cHcycMwpBe7VhZgoiIsp3ar7P9r1KlSuWbRJY0z1xXF1vKKt5ucCMiGit5mYJaWVuaY/+GuZg9fgB0dBT/85GcLMHEeWvRfdgM3hpGRETZTq3JbFBQEA4cOIClS5fi2LFjAL6X6hKLxeqchiiVX20sMLigvcK+ye/88SZWviYtZZ1IJMLoAV1wctcyONrbKB13/Ox11Gk9EE9evNNgdERElN+oJZmNjIxEjx494Orqii5dumD8+PE4dOgQgO8HxNzd3XHnzh11TEWk0OLiheBuZCDXniCVodczH0hY3UDtanl54uaJTahXo6LSMT6fAvFLh6HY8tdxZPOOJiIiyqdUTmbj4uLQoEED7N69GzY2Nmjfvn2qL1r6+voIDAxEw4YN4ePjo+p0RAqZ6upgm5LtBrcjY7D0Y5CGI8of7GyscHTbYkwc1kPp/tjEJDFGTV+O34fNRHhktIYjJCKivE7lZHbJkiV49OgRevXqBV9fX+zfvz9V/+XLlzFp0iTExMRg0aJFqk5HpFRda3OMKKT4tP20d5/xMiZOwxHlDzo6OpgyqjeObF0EGysLpeOOnb2GGi364eb9ZxqMjoiI8jqVk9n9+/fD2dkZGzZsgKGhocIxc+fOReHChXHlyhVVpyNK0/xiBVHUWH67QZJMhp7PfJAs5Y+6s8svtavg3+ObULViGaVjPgd9Q9Ouo7BozU5IJBINRkdERHmVysmsr68vqlWrBj0lBdWB7/e9e3p6wt/fX9XpiNJkoquD7WWLQNEPvO9HxWKRb6DGY8pPnAvY4fSeFRjet6PSMVKpFHNXbEPLHmMR+CVYg9EREVFepHIya2Jigi9f0i9/FBgYCGNjY1WnI0pXTSszeLs5Kuyb9SEAT6O53SA76enpYv6kwTi4aX6a2w6u33mMai364dSFfzUYHRER5TUqJ7NeXl64d+8eXrxQfuvP48eP8eDBA3h5eak6HVGGzClaECVN5Le9iGUy9Hz2AUlSaQ5Elb80qV8dt05uRt3qFZSOCY+IQudBUzFu9iokJMpffEFERJQelZNZb29vJCUloXnz5jh27BgiI///bnaxWIyTJ0/it99+g0QiwdChQ1WdjihDjHRE2F62iMK/4I+j4zDPh9sNNKGAgy2ObV+C6d59lV6yAADrdx5Bg/ZD8ObDJw1GR0REeYFarrNduHAhpkyZkqrNwMAAYrEYUqkUMpkM48aNyxfVDHidbe4y6e0nLPSVL8ulIwDXvUqjuqVZDkSVP915+AJ9Rs/Bp4CvSscYGxliyfTh+L19U16FS0REGaKWSxMmTpyICxcuoFGjRjAyMoJMJkNCQgJEIhFq166NI0eO5ItElnKfmUVdUMbUSK5dIgO6PHmPCHFyDkSVP1WtWAb/ntiMNk3rKh0TF5+AoZOWoPuwGQgJi1Q6joiI6AeVV2YnTJiAUqVKoVevXgC+n1QODQ2FRCKBjY1NmlUO8iKuzOY+DyJjUfXOc0gU/E3v4GCN/Z5FuQqoQTKZDNv3n8KEuWsQn5CodJyDnTXWL5qAX+twrz0RESmncjJrbW0NNzc3PHz4UF0xaTUms7nTnA8BmP5e8Z/HxtLu6F/QXsMR0et3H9Fr1By8eJP2zYADf2+D2eMHwNhIcR1rIiLK31TeZiAWi+Hq6qqOWIiyzeTCTqhrpXh/7MjXfrwdLAeULOaGy4f+RP9urdMct2HXEdT+bSAeP3+rociIiEibqJzMdunSBefOncODBw/UEQ9RttARBOwuVwTWerpyffFSKTo/eY94Cct1aZqRoQGWzRqFvevmpFmT9u2HT6jffgj+WLeHN4cREVEqKm8zOHjwIKZNm4b379+jatWq8PT0hLW1NUQi+TxZEATMmjVLlelyPW4zyN2OfwtH60eKV/iGFLTH2tLuGo6IfvgaHIYhExfj3NU7aY6rXtkDG5dMglvBAhqKjIiIcjOVk1mRSARBEJDWa370C4KQ51dVmMzmfiNefcTqT4rLQx0uXwxtHKw1HBH9IJPJsOWv45i8YF2ah8PMTIyxZMZwdG3TmIf3iIjyOZWT2ZkzZ2bqi8mMGTNUmS7XYzKb+yVIpKh25wWeKLjW1kpXB49reKCQkUEOREY/vPX5hH7e8/AonX2yrRvXwcq53mluUSAiorxNLZcm0P9jMqsd3sTGo+Kt54hTsE+2lqUZLlcpBV0RV/xyklicjIVrduKPdXsgTeP6YXtbK6yaOwbNf62pweiIiCi3UMulCUTapoSJEdaUclPYdyMiGnN8AjQbEMnR09PFtNF9cHbfyjT3x34LCUfnQVMxYOx8hEdGazBCIiLKDbKUzEokEqxcuRJ169ZFqVKl0LhxY+zcuVPdsRFlq15OtujiaKOwb+6HAFwNi9JwRKRItYplcfPEZvzevmma4/YePY+qzfrgzOVbGoqMiIhyg0xvM0hKSkKjRo1w/fr1VIe+BEFAu3btcODAAbUHqU24zUC7RCUno8LN5/CJlz9s5Gyghyc1PGCjn79uscvNjp+7juFT/kBYeNrfaHRv3wQLpwyFhZmphiIjIqKckumV2T///BPXrl2Dk5MTVq5ciVOnTmHhwoWwtLTEoUOHsHv37uyIkyhbmOvqYm+5otBVcIgxIFGMPs990qzUQZrVqlFt3Dm1FY3rV0tz3O6/z6Bq0z64eP2ehiIjIqKckumV2Vq1auHRo0d49eoVChUqlNL+9OlTVKhQAU2aNMGpU6fUHqi24MqsdlrsG4gJb/0V9q0u6Yphro4ajojSIpPJsOfwWUyYswZRMbFpju3duQXmTRwMM1NjDUVHRESalOmV2devX6NOnTqpElkAKFeuHCpVqoQnT56oLTgiTRnrVgCNbBSXdxr79hMeR6WdMJFmCYKA7u2a4O7pbfi1dpU0x27bdxLVmvfBlZu8pZCIKC/KdDIbHR0NKysrhX3u7u4IDQ1VOSgiTRMJAnZ4FIa9vvx1t4lSGdo+foewpOQciIzS4lzADoe3LsLqeWNhZqJ85fVTwFe07DEWo6cvR3SMfH1hIiLSXplOZsViMXR15b/gA4C+vj6SkpJUDoooJzga6GOXRxGFfb7xiej69D0k3D+b6wiCgF6dmuP2P1tQr0bFNMdu/us4vJr2xtkrtzUUHRERZTfWmSX6SSNbS4xzU1zT9GxoJGa85z7o3KqQsyOO7/gDK2aPhomxodJxn4O+oX2/SejnPQ8hYZEajJCIiLIDk1mi/5hXzAW1rcwU9/kE4ujXMA1HRBklCAL6dm2F26e2onbV8mmO3X/8Aio37okDxy+wYgURkRZjMkv0H3oiEQ54FoWTgeL6sj2efcDrmHgNR0WZ4VawAE7uWoo/po+AsZHyVdrQ8Ej09Z6HDgMm43PgNw1GSERE6pLp0lwikQimpqawtbWV6wsJCUFsbCxcXV0VTyYI+PDhQ9Yi1RIszZV33IqIRt27ryBW8ClS0sQQd6qVgbmS/eOUe/j4BWD4lKW4dvtRmuPMTIwxe/wA9OnSEiIRv88nItIWWUpmszyZIEAikWT5eW3AZDZvWe//FYNfflTY18beCn+XLwaRggsXKHeRyWTYceAfTF24DpHRaZdZq1GlHFbPG4PihQulOY6IiHKHTCezV69eVWnCunXrqvR8bsdkNm+RyWTo98IXWwOCFfbPL+aCSYWdNRwVZVXQ1xB4z1yJk+dvpDnOQF8PE4b1wKj+naGnx9V3IqLcLNPJLKWNyWzekyCRovbdl7iv4OIEAcDpSiXQ2NZS43FR1shkMhw7cw1jZq3Et5DwNMeWLu6OlXO9Ua1iWQ1FR0REmcWNYUTpMNQR4VD5YrBVsEInA9DlyXv4xCVoPjDKEkEQ8FvTurh3Zju6tWuS5tiXb33RsONwDJ/yB8IiojQUIRERZQaTWaIMKGRkgAOeRaGjYHtseLIEbR+/Q1we3w+e11hbmmP9ogk4tn0JXF0c0xy7ff8pVGrUE3uPnGMZLyKiXIbJLFEG1bexwOLiig8FPYmOw4AXvkx0tFCDWpVx55+tGNq7PYQ0DvOFhEVgwLgFaPH7GLz1+aTBCImIKC1MZokyYbSrIzo72ijs2xMUitWfvmo4IlIHE2MjLJwyFBcPrkGZEoXTHHvt9iNUb94P81ZsQ0Iir+8mIsppTGaJMkEQBGwu4w4PUyOF/d5v/HAtjHsrtVWV8qVx/egGzJkwMM3LFpLEYixcsxPVmvXB5X8faDBCIiL6LyazRJlkoquDIxWKw1JXR65PIgPaP3nHA2FaTE9PF6P6d8a9M9vQtEGNNMd+8AtAq55j0dd7Lr4G85pjIqKcoFXJrFQqxfLly1GyZEkYGhqiYMGCGDNmDGJj0y6CrkhcXBwKFy4MQRAwbNiwbIiW8rIixobYU64oFO2wDE5KRvOHbxAuTtZ4XKQ+hZwdsX/DXPy1bg6cHe3SHHvg+EVUatQD63YcQnIyDwISEWlSpquBN2jQIMuTCYKAixcvZvn50aNHY9WqVWjTpg3GjBmDV69eYdWqVXj06BEuXLiQqdvJpk+fjuBgxYXwiTKimZ0lZhV1wfT38vWEX8cmoP3jdzhdqQT0eTWq1hIEAS0b1kK96hUxb+U2rNtxGFKpVOHYyOhYjJ+zBjsO/IM/ZoxALS9PDUdLRJQ/qe06W0EQlJ7k/tGnynW2L168gIeHB9q0aYNDhw6ltK9evRojRozAnj170LVr1wy96+HDh/Dy8sLixYsxZswYDB06FGvWrMlSXP/FSxPyF6lMhraP3+HYN8XF9/s422FzGfc0T8mT9njy4h1GTV+G+09epzu2Y6tfMHfCIBRwsNVAZERE+Veml4zOnz+f6teZM2dQunRp6OrqYvjw4bh48SJ8fHzw6dMn3L59G1OnToWRkRFq1KiB16/T/wKgzN69eyGTyTBq1KhU7f3794exsTF2796dofdIJBL0798fTZo0Qdu2bbMcDxEAiAQBuz2KoIKZscL+rQHBWOgbqOGoKLt4limGCwfWYPmsUbAwM0lz7IHjF1GxUQ+s3LwfSUliDUVIRJT/qHyd7eLFizF58mScOnUKjRs3Vjjmxo0bqF+/PsaPH4958+ZlaZ7GjRvjwoULiIuLg4GBQaq+mjVr4u3btxnaNvDHH39gxowZePHiBQDA3d09Qyuzy5Ytw7Jly9J9f1BQEKRSKVdm85nAhCRUvfMCnxMUl2raV64oOhVQXNKLtNPX4DBMnLcWf5+8lO7Y4kUK4Y/pI1C/ZiUNREZElL+ovJlv48aNqFWrltJEFgBq1aqFevXqYdeuXVmeJzAwELa2tnKJLAA4OzsjJCQESUlp13z09fXFjBkzMH36dLi5uWVq/qioKAQEBKT7S9l+OsrbnAz1cbJCcZjqKP6U6vn8A25FRGs4KspODnbW2LZiGk7tWoaSRV3THPv2wye06jkW3YfOgH8gaxETEamTyslsUFAQ7OzSPukLAKampggLy3rpGkUrsj8YGhqmjEnLoEGDULhwYXh7e2d6fnNzczg7O6f7KzOH0Chv8TQ3wX7PYgo/qRKlMrR6+JYlu/KgOtUr4OaJzVg4ZSjMTdPeenDs7DVUatQTS/7czQsXiIjUROXMy83NDVevXkV0tPJVp6CgIFy8eBElSpTI8jzGxsZITExU2JeQkJAyRpndu3fj/PnzWLduHfT09DI9v7e3Nz5//pzurwIFCmT63ZR3NLOzxOpSbgr7QsTJaMaSXXmSnp4uhvZuj4fnd6JLm0Zpjo1PSMTsZVtQuXFPHD19lVcgExGpSOVktkePHggJCUGTJk1S9qH+7NatW2jYsCFiY2MxaNCgLM/j5OSEkJAQhQltQEAAbG1toa+vr/DZxMREeHt7o1mzZnB0dMT79+/x/v17+Pn5AQAiIyPx/v17REREZDk+oh+GFHLAKFdHhX1vYhPQ7vE7JHE7Sp7kYGeNjUsm4dz+VShXqmiaY/0+f8Hvw2eiaddRePz8rYYiJCLKe1Q+ACYWi9GkSRNcvnwZgiDAyckJzs7OAAA/Pz98+/YNMpkMXbt2zXDFAUWmTp2KefPm4dq1a6hdu3ZKe0JCAmxsbFCnTh2cPn1a4bMRERGwsrJKd44lS5Zg7NixWY4RYGku+k4ik6Hto7c4HhyhsL+Xky22li3Mkl15mEQiwda9JzB72RZERMWkOVYQBHRv1wQzxvSDg521hiIkIsobVE5mASA5ORkrV67E+vXr8eHDh1R9pUuXxujRo9G3b1+V5nj27Bk8PT2V1pndtWsXunfvDgD48OEDxGIxSpYsCeB7wn3s2DG5dwYHB2PIkCFo0qQJ+vbti3LlyqF48eIqxclkln6ITZagzr2XeBileC/33KIumFLEWcNRkaYFh0Zg1tLN2Hnwn3S3FJiaGGHMoG4Y1qcDDA0U/6SJiIhSU0sy+7PAwEAEBgZCEAQ4OzvD0VHxj1uzYvjw4VizZg3atGmDZs2apdwAVrNmTVy6dCnl8JWbmxv8/PzS/cLx8ePHDJfmyigms/Sz9Ep27S1XFJ1ZsitfuP/kFcbNXpWhCxdcXRwxd8IgtG5Sh6v3RETpUPvReycnJ1SuXBmVKlVSayILACtWrMAff/yBFy9eYOjQodi3bx+GDx+OkydPsooA5UpOhvo4VbGE0pJdvZ5/wLWwKA1HRTmhsmcpXDy4Fpv+mAyndG4F435aIqKMU+vKbFBQEK5fvw5/f38ULVoUrVu3xv379+Hp6ZmlCgLaiCuzpMiZ4Ai0ePQGEgWfbea6OrhSpRQqmKdd1onyjti4eKzYuA8rNu1Lt0SXIAjo2rYxpo3qA+cC6ZdBJCLKb9SynBkZGYkePXrA1dUVXbp0wfjx41P2tY4cORLu7u64c+eOOqYi0kpN7CyxuqSbwr6oZAkaP3iNN7Hxmg2KcoyJsRGmjOqNh+d3omOrX9IcK5PJsOfQGVRo+DtmLd2MyOi0D5MREeU3KiezcXFxaNCgAXbv3g0bGxu0b98+1V5VfX19BAYGomHDhvDx8VF1OiKtNbiQA7yVlOwKTkpGw/uv4R+vuJYy5U0FnRywZdlUXDiwBpU9S6Y5Nj4hEX+s2wPPBt2xfudhJCWJNRQlEVHupnIyu2TJEjx69Ai9evWCr68v9u/fn6r/8uXLmDRpEmJiYrBo0SJVpyPSaotLFEInR8Wll/wTktDwwWsEM0nJd6pWLJPh/bSh4ZEYN3s1vJr25qULRERQw57Z0qVLIzo6Gj4+Pin7YkUiEbp3746dO3cC+P5jsmLFikFHRwdv3rxRPepcjHtmKT1JUilaP3qLMyGRCvsrmhvjcpVSMNfV1XBklBvExsVj5ab9WLFpH+IT0l+pr1K+NOZNGoTqlTw0EB0RUe6j8sqsr68vqlWrluYBL0EQ4OnpCX9/f1WnI9J6+iIRDpUvhpqWpgr7H0bFodXDt4iX8Jaw/MjE2AiTR/bCw3M70bVt43RLc917/BKNOo1A1yHT8dbnk4aiJCLKPVROZk1MTPDly5d0xwUGBsLY2FjV6YjyBGMdHZysWAKeZoo/J66GR6PTk3cQ89rbfMvFyR4bFk/Ev8c34tfaVdIdf+LcdXg17Y3R05fja3CYBiIkIsodVE5mvby8cO/ePbx48ULpmMePH+PBgwfw8vJSdTqiPMNSTxdnK5VEUWMDhf0ngiPQ57kPpNwTma95lCqKI9sW49j2JfAoVSTNsRKJFJv/Oo5yDbph5h+bEB4ZraEoiYhyjsrJrLe3N5KSktC8eXMcO3YMkZH/vw9QLBbj5MmT+O233yCRSDB06FBVpyPKUxwM9HC+cik4GyjeprM7KBQjX6d/mx3lfQ1qVcaNYxuxcckkuBSwT3NsXHwClq7/C+Xqd8Uf6/YgNo5l34go71LLpQkLFy7ElClTUrUZGBhALBZDKpVCJpNh3Lhx+aKaAQ+AUVa8jIlDnbuvECpOVtg/vYgzZhV10XBUlFvFJyRi/c7DWLpuDyKjY9Mdb29rhQlDf0evTi2gr58/LrAhovxDbTeAXb58GYsXL8b169cRFxcHANDT00P16tUxevRotG7dWh3T5HpMZimr7kXGoMG9V4hRcvBreYlCGOVWQMNRUW4WGh6JJWt3Y+OeoxAr+UboZ64ujpg8shc6tfoVOjo6GoiQiCj7qfU6WwCQSqUIDQ2FRCKBjY1NvrnG9gcms6SKy6GRaPrwDRKlij8tt5UtjF7OvNKUUvP9FIg5y7fg4IlLGRpfqpgbpnn3RYtfa6ZbLYGIKLdTec/stWvX8OnT/5eDEYlEsLOzg6OjY6pEdtOmTejTp4+q0xHlafVtLLDfsyh0lOQXfZ77YEdAsGaDolzPvZATti6fhpsnNqFx/Wrpjn/17iO6Dp6GBu2H4PK/D7gnm4i0msrJbL169eDh4YHDhw+nOe7atWvYsWOHqtMR5Xmt7a2xtUxhhX0yAL2f+2AbE1pSwKNUUfy9aQHO7luFGlXKpTv+/pPXaNVzLJp0HYXrtx9nf4BERNlA5WQWAKKjo9GhQwdMnz5dHa8jyvd6ONthZUlXhX0yAH2f+2DL52+aDYq0Ro3KHjjz1woc3rIInqWLpTv+5r2naNZ9NJp1G40bd59oIEIiIvVRSzJbrVo1FCxYEPPmzUPr1q0RHc3ahkSqGuHqiFlFnBX2yQD0e+GLTf5MaEkxQRDQsK4Xrh1djx0rp6Ooe8F0n7l+5zGadh2Flj3G4NaDZxqIkohIdWpJZosWLYq7d+/Cy8sLJ06cQNWqVfHu3Tt1vJooX5te1AUzlSS0ADDgpS82+H/VYESkbUQiEdo2r497p7dhzfyxcHZM/wDhlZsP0ajTCLTuOQ53Hiq/EIeIKDdQSzILAPb29rh69Sq6du2K169fo2rVqvjnn39S+nlilihrZhR1wew0aswOevkR6z4xoaW06erqoGfH5nh8cTcWTB4CW2vLdJ+59O99/NpxGNr2mYD7T15lf5BERFmgtmQWAPT19bF7927MmTMHkZGRaNWqFRYsWADg+yUKRJQ104o4Y24aCe2QVx+x9tMXDUZE2srQQB/D+nTA8yt/Yfb4AbCxskj3mfPX7qJ+uyFo338Sk1oiynXUmsz+MGXKFBw4cACGhoaYOnUqunXrBpEoW6YiyjemFHHG/GLKE9phr/yw2o8JLWWMibERRg/ogudX9mLm2P6wsjRP95mzl2+jfrshaN1zHA+KEVGuofKlCSKRCN27d8fOnTvl+h4+fIhWrVohKCgIOjo6kEgkkEgkqkyX6/HSBMpui3wCMfGdv9J+3hRGWREVHYsNu45g9ZYDCI/M2CHeGlXKYcLQ31G/ZiVuJSOiHJOty6UVK1bEvXv3UKlSJSQnp3/VIhGlb0JhJywurvxk+ug3n7D8Y5AGI6K8wNzMBOOGdMezK39hyshesDAzSfeZm/eeonWvcWjQfgj+uXiTly8QUY5QeWXWz88PpqamsLGxUTomISEB06dPR3BwMLZt26bKdLkeV2ZJU5Z9DMKYN5+U9v9RohDGcIWWsigiKgZ/bvsba7f9jaiY2Aw941GqCMYP+R2tGtfm1jIi0hiVk1lKjcksadKKj0EYnUZCO6OIM2YUceaPgCnLwiOjsXbbQazfcRiR0RlLaksUccXYwd3QvkUD6OrqZHOERJTfZTqZnT59OgRBwMiRI2FtbZ2pW78EQcCsWbMyHaQ2YTJLmrbK7wtGvvZT2j+koD1WlXKDDhNaUkFkdAw27jqKNdsOIiw8KkPPuBUsgBF9O6J7+6YwMmRFGyLKHplOZkUiEQRBwKtXr1C8ePGU36f1mh/9giDwABhRNljj9wXD00hoOzpaY6dHERjwR7+kopjYeGzdewIrN+/Dt5DwDD1ja22JwT3bon/332BlYZbNERJRfpPpZHbmzJkQBAHDhw+HtbV1yu8zasaMGZkOUpswmaWcsvbTFwx7pTyh/dXGHIfLF4cZf+xLahCfkIhdB//B8o378DkoY9cqmxgbonfnlhjWuwOcC6R/ExkRUUZwz6yaMZmlnLQtIBj9X/hAouSzurK5Cf6pVAJ2+nqaDYzyrKQkMf46cg7L1v8FX//ADD2jp6eLjq1+xaj+nVGyqGs2R0hEeR2TWTVjMks57fi3cHR68g4JUsWf2iVMDHG2Ukm4GnEPI6lPcrIEf5+8hCXrduPtB+WHEv+r+a81MXpAF1StWCYboyOivCzTyezWrVtVmrBPnz4qPZ/bMZml3OBaWBRaPXqLyGTFe9SdDfRwtnJJlDE11nBklNdJJBKcvPAvVmzci/tPXmf4uRpVymFE345o2qA6y3oRUaZk+QBYVvEAGJFmPImKRZMHb/AlSayw30pXB6cqlUB1Sx7IIfWTyWS4fvsxlm/ciwvX72X4uSJuLhjWuz26tm0MYyPDbIyQiPKKTCezvXr1UimZ5aUJRJrjE5eARvdf40N8osJ+I5EIh8oXQ1M7S80GRvnK05fvsWLTXhw6dQVSqTRDz1hZmqNf11YY0P03ONorv5SHiIh7ZtWMySzlNl8TxWjy4DUeR8cp7NcVBGwrWxjdnWw1HBnlNx/9g7B6ywHsPPgPEhKTMvSMvp4eOrT6BcN6t0fZkkWyOUIi0kYaTWYfPXqEChUqaGq6HMFklnKjSHEyWj96i6vh0UrHLCleCGPcHHlbGGW74NBwrN95BJt2H0V4pPK/k/9Vv2YlDO/TEb/WqcK/p0SUQi3J7MOHD7Fhwwb4+voiMTEx1QUKUqkUCQkJ+Pr1K4KCgpCcnKzqdLkak1nKrRIkUnR5+h5HvykvdN/fxQ5rS7lBjwdwSANiYuOxff9JrNtxCJ8Cvmb4uZJFXTGkV3t0av0r99USkerJ7P3791G7dm0kJSWlJLH/vRHsx+89PDzw5MkT1SLO5ZjMUm6WLJVh8EtfbA4IVjqmgbU5DnoWg7W+rgYjo/wsOVmC42evYfXWA5mqgGBlaY6eHZuhf7fWKOTsmI0RElFupnIy26FDBxw6dAitW7dG7969cebMGWzcuBFHjhyBRCLB2bNnsWnTJpQqVQoPHjyAvr6+umLPlZjMUm4nk8kw9f1nzPdRXuC+uLEhTlYsgWImXPUizZHJZLj98DnWbD2IE+dupHlN+s9EIhFaNKyJwT3aoqaXJ7cgEOUzKiezTk5OAICPHz9CX18f169fR926dXH8+HG0aNECALB+/XoMHToUixYtwtixY1WPOhdjMkvaYqXfF4x+7Qdl/wBY6ergcIXiqGdtrtG4iADAxy8A63Ycwq6/TyM2LiHDz5UtWRiDerRFx1a/wsiQF4MQ5QcqJ7MGBgZo1KgRTpw4AQCIiIiAtbU1pk+fjpkzZ6aMc3Nzg62tLe7fv69SwLkdk1nSJse/haPr0/eIlSgul6QrCFhf2g19Xew1HBnRd+GR0di27yTW7zyMoK8hGX7OytIcvTu1QL9urVDQySEbIySinKbyKQ8jI6NUWwcsLS1hZWWF169T73uqWLEi3r17p+p0RKRGreytcMOrNFwMFW//SZbJ0O+FL8a9+QQJq/hRDrCyMIP3wC54fvkvbFwyCeXLFMvQc+ERUVi24S941O+K7kNn4NqtRxnetkBE2kXlZLZYsWJyh7qKFy+OBw8epGpLSEjI85UMiLRReXMT3K1WBlXMTZSO+eNjENo+eosYJdfjEmU3fX09dGnTCNeObsD5A6vRrnl96Oik/yVMIpHi2NlraP67Nyo36YV1Ow4hIipGAxETkaaonMw2b94cvr6+GDVqFCIjIwEANWvWhI+PT8rWg7dv3+LKlStwd3dXdToiygYFDPRxxasUOjhYKx1zPDgCte6+hL+S28SINEEQBFSrWBbbV07Hiyv7MG5Id9haW2bo2bcfPmH8nDUoUbMDhk5agsfP32ZvsESkESrvmY2IiEDlypXh6+uLJk2a4NSpU/D19UWJEiUAAB4eHnjz5g3i4+Mxe/ZsTJkyRS2B51bcM0vaTCqTYeb7AMzxCVA6xlFfD8crFkcVC1MNRkakXEJiEg6duoR12w/jycvMbWer7FkS/bq1Rttm9XlgjEhLqeXShODgYMyZMwc2NjaYMWMGAGDv3r0YOHAgYmK+/zinVatW2L9/PwwM8vY/FkxmKS/YExiCPs99kKTknwdDkYD1pd3R09lOw5ERKfejtNf6HYdx7Ow1SJQcbFTEytIc3ds1Qd8urVDEzTkboyQidcvW62xjY2Px/Plz2NnZoXDhwtk1Ta7CZJbyin/Do9Hm8VsEJynf6z7QxR4rS7nCgDeGUS4TEBSMzX8dw44D/yA4VPmtd4rUr1kJvTo2R4uGtaCvr5dNERKRumRrMpsfMZmlvORjfCJaPHyDFzHxSsdUMTfB3+WLoZBR3v6pC2mnpCQxjp+7jk17juHmvaeZetbW2hJd2zZGz47NULxwoWyKkIhUpdZk9tu3b0hISLu4daFCefsfBCazlNdEJSej85P3OB0SqXSMjZ4u/ipXBI1sLTUXGFEmvXzriy1/HcfeI+cQHRuXqWdrVimH3p1boHWTujA0yNs3WRJpG5WT2eTkZEycOBFbtmxBVFRU2pMJQp4vz8VklvKiZKkME95+wjK/L0rHCABmF3XB5MJOEPE6UcrFomPicPDEBWzacwzPX/tk6lkrCzN0/q0henVqgdLFWaGHKDdQOZmdO3cupk+fDgAwMTGBhYVFmvdi+/v7qzJdrsdklvKyA19C0ee5j9IbwwCghZ0ldnoUgZWergYjI8o8mUyGO49eYPPuYzhy+iqSxOJMPV+lfGn06tQcbZvVh6mJUTZFSUTpUTmZLVGiBD59+oRjx46hUaNG6opLazGZpbzuZUwc2j1+h9exyrcUFTYywKHyxVA+jYsYiHKT4NAI7Dl8Btv3n8KHj5n7t9vE2BBtmtVD93ZNUaOyR5oLOkSkfionsyYmJvjll19w/PhxdcWk1ZjMUn4QnSxBn+c++PtrmNIxhiIB60q7oxfLd5EWkclk+PfuE2zffwpHz1xFYlLmVmuLuDqjW7sm6NqmMZwL8O8+kSaonMx6enrC0tISV69eVVdMWo3JLOUXMpkMy/2+YPzbT5Ck8a/IABd7rGL5LtJCYRFR2Hf0HLbvP4VX7z5m6lmRSIQGNSuhe/smaP5rLR4aI8pGKiezW7ZswcCBA3H58mXUrl1bXXFpLSazlN9cC4tCxyfv8TWNFazyZsbYW64oSppyXyFpH5lMhruPXmLb/pM4fOoy4hMyd6WzlYUZOrT8Bd3bN0H5MsW5DYFIzdRSmmvSpElYunQpOnfujHLlysHaWvn97n369FF1ulyNySzlR4EJSej45B3+jYhROsZIJMKKkq7o72LHL+aktSKjY3Dw+EVs338q01fnAkCpYm7o0qYROrX6FU6O3IZApA4qJ7MhISFo2rQpHjx4kKEvUBKJRJXpcj0ms5RfiaVSjH/rjxVplO8CgDb2VthUxh02vFmJtNzTl++x+9Bp7D9+AWHhaZem/C9BEFC3egV0adMIrRrVYTUEIhWonMz26NEDu3fvhrGxMerWrQs7u7RXXbZt26bKdLkek1nK7/YHhaLvi7TLdzkb6GGnRxE0sLHQYGRE2SMxMQmnL93CrkOnceHaPUilyv/uK2JsZIiWDWuhS5tGqFejInR0dLIpUqK8SeVk1t7eHoIg4NGjR3ByclJXXFqLySzR9/JdnZ68x/M0rsEVAIx3L4DZRV2gz8NhlEcEfQ3BX0fOYfehM3jvm/m66o72NujQ8hd0bdMIZUsWyYYIifIelZNZU1NTNGrUCIcPH1ZXTFqNySzRd/ESKca//YQ1n76mOa6yuQn+KlcUxUwMNRQZUfb7cSHD7r/P4PCpy5m+PhcAypYsjA4tf0X7FvVRyNkxG6IkyhtUTmZr1qyJhIQEPHjwQF0xaTUms0SpnfwWjt7PfRAiVn6VtYmOCGtKuaGnky0Ph1GeExsXj+Nnr2Pf0fO4cuthprchAEC1SmXRseUv+K1pPdjZWKo/SCItpnIye/LkSbRq1Qpr167F4MGD1RWX1mIySyQvKDEJvZ754FxoZJrjOjpaY0Npd1jyKlzKo4K+huDAiYvYe+QcXrzxyfTzOjoiNKhZGR1a/oIWDWvBzNQ4G6Ik0i4qJ7P//PMP1q9fj1OnTqFs2bKoVq0arK2toacnf1JZEATMmjVLlelyPSazRIpJZTKs8PuCiW/9IU7jn52ChvrYXMYdjWwtNRccUQ549uo99h49jwPHL+BrsPLb9JQxNNBH0wbV0b7lL2hUtyovZqB8S+VkViQSQRAEpPWaH/2CILA0F1E+9ygqFl2evseb2IQ0x/V1tsPSEoVgwVVayuOSkyW4cvMB9h09jxPnbyAuPu3PDUUszEzQolFttG1WD/WqV4Q+S99RPqJyMpvZldYZM2aoMl2ux2SWKH2xyRJ4v/mEjZ+/pTnO2UAPG8sURjM7S80ERpTDomPicOL8dRw8fhGXbz6AJI0Sd8pYWZihRcNaaNusHupWrwg9fkNIeZzKyeyECRNQqlQp9OzZkwc3wGSWKDOOfA1Dvxe+CEvjcBgA9HSyxfKSrrDiF2XKR76FhOHIP1dx8ORF3Hn4IkvvsLI0R6v/rdjWqVYBurqsYUt5j8rJrLW1Ndzc3PDw4UN1xaTVmMwSZc7nhET0fOaDS2Fp36BUwEAPG0q7o6W9lYYiI8o9/D5/wd8nL+HgiYtZOjgGADZWFmjV+HtiW8urPBNbyjNUTmbNzMzw66+/4siRI+qKSasxmSXKPKlMhvX+3zD+7ac0bw4DgG4FbLCypCuvw6V86+VbXxw8cREHT1yE3+e0r49WxsbKAi0a1kKrxrW5x5a0nsrJ7IABA7Bnzx5cu3YNlSpVUldcWovJLFHWfYxPRL/nPriYziqtg74e1pd2w28O1hqKjCj3kclkuPvoJf4+eRFHz1zDl2+hWXqPhZkJmjaogZaNa+PX2lVgbMQLTEi7qJzMHjx4ENOmTcP79+9RtWpVeHp6wtraGiIF11OyNBcRpUcmk2HT52CMfeOH6HRWaTs72mBVKVfYcVWJ8jmpVIpbD57jyD9XcPTM1SyV+gIAYyNDNKzjhdZN6qBxvWowNzNRc6RE6sfSXGrGZJZIPT7FJ2LAC1+cTeeiBStdHSwoXhD9Xewh4iFUIkgkEty6/wyH/7mCo2euITg0PEvv0dfTQ/1aldC6cR00bVADttYWao6USD1UTmZnzpyZqSoGLM1FRBklk8mwLSAY3m8+ITI57W+EvSxMsK60OyqacyWJ6AeJRIJ/7z7F4dNXcOzMNYSERWTpPSKRCNUrlUXzX2ui+a81UdjVWb2BEqlA5WSWUmMyS6R+AQlJGPjSF6eCI9IcJwIwtJAD5hR14WULRP+RnCzB9TuPcezsNZw4dx3fQrK2YgsApYu7pyS2FT1KsDQn5Si1JrM+Pj64evUqgoKCYGBgAAcHB9StWxcFCxZUy/ulUilWrlyJDRs24OPHj7Czs0PHjh0xe/ZsmJikvRrz9u1b7N69G+fOncOHDx+QkJCAIkWKoEOHDhg1alS6z2cUk1mi7CGTybArMAQjX/shIp1VWgd9PSwrUQhdCtjwiyyRAhKJBHcevcTxM9dw/Nx1+Ad+zfK7nBxs0eyXGmj+a03UqVaBlRFI49SSzIaHh2PAgAE4fPiwwv5WrVph06ZNsLW1VWmekSNHYtWqVWjTpg2aNm2KV69eYfXq1ahduzYuXLig8NDZDxMnTsTatWvRqlUrVKtWDXp6erh8+TIOHDiAcuXK4fbt2zAyMlIpPoDJLFF2C0pMwohXfvj7a/oHXBpYm2NtKTeUNFX9c5sor5LJZHj0/C2On72GY2ev472vf5bfZW5qgoZ1vdCkfnU0rOsFGyvus6Xsp3IyGx8fjxo1auDJkyewsLBA06ZN4e7uDolEAh8fH5w7dw5RUVEoX748bt++DX19/SzN8+LFC3h4eKBNmzY4dOhQSvvq1asxYsQI7NmzB127dlX6/P3791GsWDFYWKT+xJo6dSrmzZuH1atXY9iwYVmK7WdMZok040xwBIa9+ogP8YlpjtMTBIxzL4AphZ1grMMi8URpkclkeP3uI46d/b5i++zVhyy/SyQSwatCaTRtUANN61dDyWJu/EkJZQuVk9n58+dj6tSpaNGiBXbv3g1zc/NU/VFRUejWrRv++ecfLFmyBN7e3lma50fSee3aNdSuXTulPSEhATY2Nqhbty7++eefTL/32bNnKFeuHAYOHIj169dnKbafMZkl0pwEiRQLfQOx0DcQidK0/ylzNdTHqlJuaGlnyS+oRBnk+ykQpy78i5Pnb+DWg+eQStMul5cWVxdHNKlfHU3qV0OtquVhaJC1xS2i/1I5mS1Xrhy+fPkCX19fpftOY2Nj4e7ujoIFC+LBgwdZmqdx48a4cOEC4uLiYGBgkKqvZs2aePv2LYKDgzP93tOnT6NZs2aYPn16mjVwly1bhmXLlqX7vqCgIEilUiazRBr0LjYBw199TLeMFwD8Ym2OpSUKwZNVD4gyJSQsEmcu38KpC//i4vV7iE9I+6ciaTExNkT9mpXRpH41NKpbFQUcVNuGSPmbysmssbExmjVrhr///jvNce3atcP58+cRFZX2zT7KeHh44Nu3b/j6VX6TeseOHXHw4EEkJiZmahuDRCJB7dq1ce/ePTx//hwlSpRQOnbmzJmZuvCBySyRZslkMhz6GoZRr/0QkChOc6wAoI+zHeYUc0EBrg4RZVpcfAIu//sApy78i9OXbmW55NcPHqWKoGGdqmhY1wtVK5SBHquRUCao/LdFT08PMTEx6Y6LjY1V6Ud7ilZkfzA0NEwZk5lkdtSoUbh16xbmz5+fZiILAObm5nB2Tr+u3o+VWSLSLEEQ0N7RBo1tLTHrw2es8PsCiZJv1WUAtgQEY9+XUEx0d4K3myP30xJlgrGRYUpprh+VEb4ntjfxzifzB8ievfqAZ68+YNmGv2BuaoL6NSuhYV0vNKzjBSdHu2z4CCgvUXlltk6dOrh//z5evXoFV1dXhWN8fX1RunRpVKlSBdeuXcvSPOpemZ02bRrmzp2LAQMGYMOGDVmKSRHumSXKHZ5Fx2HwS1/8G5H+N9suhvpYWKwguhSw4S1iRCp6//Ezzl6+jTOXb+HG3SdITqeUXnrKliyMhnWqolFdL1StWJartiRH5WT2r7/+Qvfu3VG8eHFs3rwZtWrVStV//fp19OvXD+/fv8e2bdvQo0ePLM2jzj2zP7YM9O7dG1u2bFHrYRAms0S5h1Qmw47AEEx664+vSWlvPQCAKuYmWFbSFbWszDQQHVHeFxkdg8s3HuD05Vs4e/k2QsPT39eeFjMTY9SpXgG/1KqMX2pX4U1kBEBNdWZ///137NmzB4IgwM7OLmWF9uPHjwgJCYFMJkOnTp2wd+/eLM+RXjWDOnXq4PTp0+m+50ci27NnT2zdujXN2rRZwWSWKPeJTpZgsW8g/vgYhIR0qh4AQHsHaywqXhCFjQ01EB1R/iCRSPDg6RucuXwLZy7fUqns1w/uBZ3QoHZlNKhVGXWrV4CFmakaIiVto7YbwFavXo3ly5fj48ePqdpdXV0xevRoDB8+XKUV0GfPnsHT01Npndldu3ahe/fuAIAPHz5ALBajZMmSqd4xe/ZszJgxA7///ju2b9+u9kQWYDJLlJv5xydi0jt/7AkKTXesviBgYEF7TC7sBEceEiNSu8+B33D+2l2cv3YXV/59gOjYOJXep6MjQmXPUvi1dhU0qFUFFT1KQFeXe+HzA7VeZwsAnz9/RmBgIGQyGZycnNR2lS0ADB8+HGvWrEGbNm3QrFkzvHr1CqtWrULNmjVx6dKllOTUzc0Nfn5++PlDW7t2LYYNG4ZChQphzpw5comsg4MDGjZsqHKMTGaJcr+7ETHwfuOXof20xjoiDC/kgPFuTrDW5149ouyQlCTG7QfPce7aHZy/ehcv3/qq/E5Lc1PUrlYB9apXQL2alVDMvSBrTOdRak9ms5NEIsGKFSuwceNGfPz4Eba2tujUqRNmz54NU9P//9GComS2V69e2LFjh9J3161bF1euXFE5RiazRNrhRymv8W/94ZvOLWIAYK6rgzGujhjl5ghzXSa1RNlJ3au2AODkYIu6NSqiXo2KqFe9Iqsk5CGZTmYvXbqk0oQNGjRQ6fncjskskXZJlEqx2u8r5vgEICoDp65t9HQx0d0JQws5wEhH/VuViCi1pCQx7jx8gQvX7+HSjXt4/OKdWt5bvEgh1KteEfVqVkLtquVhac79ttoq08msSCTK8jK9IAhITk7O0rPagskskXYKThJj5vvP2PD5m9L6tD8rYKCHqYWd0c/FDvrZsP+eiBQLDg3HlZsPcfHGfVy6cR9BX0NUfqdIJEL5MsVQu1p51KlWAdUrecDM1FgN0ZImZDqZrVevXqaS2devX6fUhtXR0YFYnH55HG3GZJZIu72NjceM9wHY9yX9Q2IA4GqojxlFXfB7AVvoirgfj0iTZDIZXr37iIvX7+HSjfu4cfcJEhKTVH6vjo4IFcqWQJ1qFVCnWnlUq1QWJsZGaoiYskO27ZlNTEzEtGnTsGzZMkilUhQvXhxbt25FjRo1smO6XIPJLFHe8DQ6DtPe+eN4cESGxhc1NsBEdyf87mTLlVqiHJKQmIRb95/h4o17uHrzIZ68fA91pDm6ujqoVK4kalf9vnJbtWIZGBuxdF9ukS3J7J07d9C7d2+8efMGgiBg1KhRmDt3bsq1s3kZk1mivOVORAymvvfHhdCoDI13MdTHOLcC6OdixytyiXJYaHgkrt9+jCu3HuLKvw/wwS9ALe/V09NFpXIlUbNKOdSs4omqFcvA3MxELe+mzFNrMpuYmIipU6dixYoVkEgkKFGiBLZt24Zq1aqpa4pcj8ksUd50JSwKU97542YGynkBgJ2+LrxdC2BwQXtY8PpNolzBP/Arrtx8iCs3H+DKzYf4FhKulveKRCJ4li6KGlXKoaaXJ6pX8oCttYVa3k3pU1sye+vWLfTp0wdv376FSCSCt7c3Zs+eLXf1bF7HZJYo75LJZDgdEomp7/zxKDpjpYIsdHUwvJADRro6wlZfL5sjJKKMkslkeP3uIy7ffIBrtx/j37tPEBGVsW9WM6JUMbfvK7denqhR2YOlwLKRyslsYmIiJk+ejFWrVkEikaBUqVLYtm0bvLy81BWjVmEyS5T3SWUyHP4ahunvP+NVbEKGnjHWEWGgiz3GuBWAsyFvFCPKbSQSCZ69+oDrdx7j2u3HuHnvKaJiYtX2flcXR1Sv5IFqlcqiemUPlCzqmi03keZHKiWzN2/eRO/evfH+/XuIRCKMHTsWs2bNgr5+/v2HmsksUf4hkcnw95cwzPcJxNOYjK3U6gsCejnbwdvNESVMeDqaKLdKTpbg6av3uHb7Ea7ffoyb958iJjZebe+3NDeFV8UyKQlupXIlYWSYv36arS5ZSmYTEhIwadIkrFmzBhKJBGXKlMG2bdtQuXLl7IhRqzCZJcp/ZDIZTgVHYJ5PIG5HZvzHlM3tLDHa1RENrM15zSZRLpecLMGj529SVm1v3X+mlpvJftDT00X5MsVRvbIHqlYsg6oVysDBzlpt78/LMp3M3rhxA3369MGHDx+gq6uL8ePHY/r06dDT414wgMksUX4mk8lwOSwK830CcTEsY9UPAKCcqTFGuTmii6MNDHmrGJFW+LEt4d97T//36wnCwjP+eZ8Rri6O8KpQGl4VysCrQhl4lCwCPR4olZPpZFbnp1Izjo6OKFKkSMYnEwRcvXo1M9NpHSazRAQAtyOiscAnMMN1agHAXl8XQwo6YHBBB9gbcIGASJvIZDK8ee+XktjeuPtULbeT/czI0AAVPUr8L7ktjaoVy8DOxkqtc2ijLF1nm+XJBAESSfp3n2szJrNE9LOn0XFY6BOI/V9CIc3gMwYiAd0K2GK0qyPKmvFKTSJtJJPJ8NE/CDfvP8XtB89x6/5zvPngp/Z53As6oZJnSVT2LIXKnqXgWaYYDA3y19mlTCezqq6s1q1bV6Xnczsms0SkyLvYBCz5GIidgSFIlGb8n91fbcwxopAjmtlZQof7aom0Wmh4JO48fIFbD57h1v1nePTsLZLEYrXOoaenC4+SRVKS28rlS6Gom0ue3pefbdfZ5ldMZokoLcFJYqz3/4a1n77ia1LGv4gVMtTHABd79HWxg2M+W3UhyqsSEpPw8Nmb/63cPsOdh88RHhmt9nmsLMxQ0aMEKpcvhUrlSqGiR4k8dbiMyayaMZklooxIlEqxLygUy/2+4EkGL2AAAF1BwG/2VhhU0J5VEIjyGKlUine+n3H30Yv//XqJV+8+IjtSNWdHO1QsVxIVyhZHpXIlUcGjBKwszNQ+jyYwmVUzJrNElBkymQxXwqKwzO8LTmbisBgAFDc2xMCC9ujpZAsb3i5GlCdFRsfg/uNXuPvoJe4+eoF7j18iMlp9lzn8rIirMyp4lEBFjxKoWK4kPEsXg6kW1MNmMqtmTGaJKKvexsZjpd8XbA8MQZwko8fFvh8Y6+Rog0EF7VHNwpSrtUR5mFQqxZv3frjz6CXuPX6J+09eZdvqrUgkQokihVC/ZiUsmjpM7e9XFyazasZklohUFZaUjE2fv+FP/6/4lJCUqWc9TI3Qx9kO3ZxsYcfVWqJ8ITomDo+fv8W9J69w/3+/1FkWrF6Nijixc6na3qduTGbVjMksEamLRCbDmZAIrPf/hlPBEcjMP9a6goAWdpbo5WyLZraW0OMd8ET5SkBQMO4/eYn7T1/j/uNXePT8DWLjErL0Lu+BXTFrXH81R6g+TGbVjMksEWUHv/hEbPr8DZs/B2eqCgIA2OnrolsBW/R2tkM51q0lypckEgnefPiEB09f49GzN3j47A2evfqQodJgu9fOQuvGdTQQZdYwmVUzJrNElJ2SpFIc+xaO9f7fcCkTV+b+UMHMGL2c7dC1gA1suQ2BKF9LShLjxVsfPHz65nuS+/wNXr37CMl/9uy/urYfLk72ORRl+pjMqhmTWSLSlDex8djo/w3bAoIRnpy52xX1/rcN4XcnWzS1tYShDrchEBEQF5+AJy/ffV+9ffoGHz8H4fz+1bn6YCmTWTVjMktEmhYvkeLvr6HY+jkYV8IzX3DdXFcHbeyt0KWADX6xtoCuKPd+0SIi+i8ms2rGZJaIcpJvXAJ2BoZge2AIPsYnZvp5Wz1ddHC0RpcCNqhpaQZRLl6NISICmMyqHZNZIsoNpDIZroVHY3tAMA5+DctU3dofXAz10cnRGl0cbVHR3DhX/5iRiPIvJrNqxmSWiHKb6GQJDn0Nw/aAYFzNwjYEAChmbIhOjtZo52ANTzMmtkSUezCZVTMms0SUm/n8bxvCzsAQ+GZhGwIAuBsZoK2DFdraW6OapSm3IhBRjmIyq2ZMZolIG8hkMtyNjMXeoFDs/xKKL5msXfuDo74e2jhYoa2DNepamfFyBiLSOCazasZkloi0jUQmw9WwKOz7Eoq/v4RluszXD1a6Omhpb4W2DlZoZGMJI5b7IiINYDKrZkxmiUibJUmlOBcSib1fQnHsWzhis3BwDACMdURoZGOB5naWaGZrCSdDfTVHSkT0HZNZNWMyS0R5RZxEgpPBEdgbFIozIRFIkGb9y0VFc2M0t7VCCztLVLYw4T5bIlIbJrNqxmSWiPKimGQJzoRE4PDXcJwMDkd0FldsAcBeXxfNbC3R3M4SjWwtYK6rq8ZIiSi/YTKrZkxmiSivS5RKcSk0Coe/huHot3CEiJOz/C5dQUAdKzM0s7NEIxsLlDU1YtkvIsoUJrNqxmSWiPKTZKkM/0ZE4/DXMBz+Fo7PCUkqva+AgR4a2ligoY0FfrUxh6MB99oSUdqYzKoZk1kiyq9kMhkeRMXiyLdwnAqOwJPoOJXfWc7UGI1sLdDIxgK1rMxYIYGI5DCZVTMms0RE3/nHJ+KfkAicDI7AxdAoxEuzvs8WAAxFAmpbmaGhjQV+sbGAp5kxdLglgSjfYzKrZkxmiYjkxUukuBwWhVPB4TgZHIFPKm5HAAALXR3UsTJDPWtz1Lc2Rzkmt0T5EpNZNWMyS0SUNplMhhcx8TgZHIGTweG4HRkDiRq+ElkqSG5ZAowo72Myq2ZMZomIMidSnIzLYVE4FxqJcyGR+BCfqJb3WunqoI61OepamaGmpRkqmBvzul2iPIjJrJoxmSUiUo1PXALOh0bifGgkLoZGISKL1+v+l5FIhKoWJqj5v+S2uqUpLPVY45ZI2zGZVTMms0RE6pMs/V4h4ceq7e3IGCSr6cuWAKCsqVFKclvT0hRuRgasc0ukZZjMqhmTWSKi7BOdLMG/4dG4Eh6FK2FRuB8Vq5b9tj8UMNBDNQtTVLUwhZeFCSpbmMJMV0d9ExCR2jGZVTMms0REmhOdLMGN8GhcCYvClfCo/2vvzoOqOu83gD9337hsAsoStiiJcSMgxLrEfampjtpiRlO1sWO1dalgmkySSX5GWzLNtGJcmrgljdpo69iZktgxzYxpXWsYjOKGDUZQAVd2Lnd/f39cuOEKCOi93Hv0+cww59z3vOfynnwz8Pjy3nNQ6OVwKwPwTJAOz7UKuAOD9FDKOXtLFCgYZr2MYZaIyH/q7HYcq27AV1V1+KqqDt/UezfcAoBeIUd6sAGZIQZkhgQhzWhAsl7DOycQ+QnDrJcxzBIRBY4GuwMnaxtwrLoex2oacKKmHvWOh3t4Q3tClAo8a9QjLdiAtGAD0oMN6GfQ8r63RD2AYdbLGGaJiAKXQwicrTfhWE09jlU34FhNvVce4NAeg0KOVKMe6c0BNy3YgKcNWt4ejMjLGGa9jGGWiEharjVZcKzGFWxP1jTgdL0JNh/9alTLZHgmSIfBRj2GGPXubaRa5ZPvR/Q4YJj1MoZZIiJpszidOF1nwsnaBnxd24CTtQ0oMXnnQQ4d6aNWeYTbwUY9Z3GJuohh1ssYZomIHj13rTYU1DbiZHO4/bq2EXdtdp9+T6VMhhS9FgOCdK2+9Oir1zDkErXCMOtlDLNERI8+IQRKmyw4VWdCYV0jTtU1orCuEXd8HHABQCWTIcXQHHINroA7IEiHJxly6THFMOtlDLNERI8nIQSum604Vd+IwlpT87YRN6y2Hvn+SpkMT+o1eEqvxdMGHZ4yfL/txTW59AhjmPUyhlkiImqt0mJFYW0jihpMOFNvQlG9Cf9rNMP7NwjrWIRKiacMWjxl0OFpgxYpBi366bVI1mmhVXA2l6SNYdbLGGaJiKgzJocDFxqa3OG2qN4VdKvtjh4dhwxAnFaNfnot+uq1zVsN+hlcQVfHoEsSwDDrZQyzRET0IIQQKLdYcabehLP1TTjfYML5hiZcbGyC2emfX9UtQTdZp0GSToNkvQbJOi2SdBpEqpWQ8aEQFAAYZr2MYZaIiLzJIQSumCw43+gKtxcamtwh1+KnkAu4HgqRpNMgWadBsl7r3k/UaZCg08CoVPhtbPR4YZj1MoZZIiLqCQ4h8J3JgvMNJhQ3mnGpsQnFjWYUNzahpoeXK7QnTKlAQnOwTdCqm7caJOhc+xEqzuySdyj9PQAiIiLqPoVMhn4GLfoZtB7tQgjcttpR3NiES83h9pLJjOKGJlxpsvTYB8+q7Q5U15twut7U7nG9Qo54rRpPaNV4QqtBXPN+nEaNJ3SubYiKMYU6x/9LiIiIHiEymQxRGhWiNCo8Hx7scczidOKyyYwSkwXfmswoMZnxbaNre9VsRU/+qdbkcDbPJJs77GNUyD2CbqxWjViNGjEaFWKa9yPVSsg5w/tYY5glIiJ6TGjkcjwTpMczQfo2xyxOJ74zWVwBtyXomsz4zmTBVbMVdj+sSqx3OHGhsQkXGps67KOUyRCtUbkCrsYVeFv2ozUq9Gne9lIx9D6qGGaJiIgIGrkc/YN06B+ka3PM7hS4brHiO5MZV5os+K7Jgu9MFlxpMuO7JgtuW33/5LOO2IXANbMV18xWAI0d9lPIgN5qFaI1avTRqNBHrWoOu6623moVotQq9NYoYVQouJ5XQhhmiYiI6L6UchkSm+9U0J4Gu6M55JpR1mRFWZMFZWaLa9/s37DbwiGACosNFZbOn8imkctahdvmrVqJqOa2KLUKkWolItUqRKiV0PAxwn7FMEtEREQPJUipwCCjHoOMbZcvAK6HRFxtDrZl7q3FPaN63WyFLYBurmRxClw1W3HVbO1Sf6NC7g62kWoVIlVKRLQKvL1USvRSKRGhdm3DVEooOPPrNQyzRERE5FN6hQJPB+nwdDtLGADA2XwHhmtmizvctt5eM1tQbrH5Zd1uV9Q7nKhvXn7RFTIAoUoFejWH214qlTvotoTdcJUS4SqFez9MqUSISsEQ3A6GWSIiIvIruUyG3hrXn/SHhrTfxykE7ljtKLdYUWGxosJs+37fYkO52bV/KwCWNHRGoPnWZXYHStC1AAx8H4LdAbc57IYqXfuhSiVCm7etX4c1b9WP6HIIhlkiIiIKePJWtxx7FoYO+1mdTlRabLhhseGG1fr9vsWGG1YbKi1W92trgM70dqR1CO7qLHBrOrkcIUoFQlQK11apQIhS2WpfgRDVPa+VSsRp1eitUXn/gryEYZaIiIgeGWq53P3ksfsRQqDa5sANqyvc3rTacMtqx02LDbesLa9tuNl8zOzHRwd7S5PTiSarEzesnX8IrrVfx/fB+v4JPhrVw2OYJSIioseOTCZDuFqJcLUSzwTdv68QAo0OJ242h9vbNhtuW+24Y7XjttWG2zY77lhdbbetNtyx2dHo6KlnrfleiErh7yHcF8MsERER0X3IZDIEKRUIUirwpF7b+QkAmhxOV8C12XHXasddmx13bTbcce+3bnd91dkdPr6SBxOiZJglIiIieqzoFHI8odPgiU6WO7RmdTpRY3OgymZHlc2OanvztnWbzY4qm8N9rMbmQLXN7tP1vwyzRERERNQptVyOKI0cUd38sJUQAmanQI3dFW5r7K4AXGOzo8bu+brW7mj+ar3vgOk+yyIYZr3I6XTi/fffx5YtW1BaWorIyEjMnj0ba9asgcHQ8ScbvXU+ERERUaCRyWTQKWTQKdSI7vpEsAeb04l6u7NNyK2125EZ0smi4gdksVigVqsf+tHBkrrhWHZ2NnJycvDMM89g48aNyMrKwoYNGzBt2jQ4nZ0vtH7Y84mIiIgeRSq5HOFqJZL0WqQGGzA6PBjTo8IwLyYS8d1YKtFV165dQ0JCAp577jl88cUXEA+xTEIyM7Pnz5/Hxo0bMWvWLOzfv9/dnpSUhBUrVmDv3r2YO3euz84nIiIiIu+4ffs2bt68idu3b2PKlCnIyMjA2rVrMWnSpG7P1EpmZnbPnj0QQmDlypUe7YsWLYJer8fu3bt9ej4REREReVfLX8ZPnTqFKVOmPNBMrWRmZgsKCiCXy5GZmenRrtVqkZqaioKCAp+ev27dOqxbt67TcZaXlwMAKisrERcX12l/IiIiosdNcHCwx2uHw3VbspZQm5GRgdzcXEyYMKHT95JMmK2oqEBERAQ0mrbrNmJjY3H8+HFYrVao1WqfnF9XV+cOql3hdDq71Z+IiIjocWGztf8UspZQW1BQgBUrVuDChQudvpdkwqzJZGo3iAKu2dWWPh2F0Yc9Pzg4GLGxsZ2Os3WA7Up/CiyVlZVwOp2Qy+WIjo7293CoG1g7aWP9pIu1kzZ/1S84OBi3bt1q065QKOBwONwzs10hmTCr1+vbvWgAMJvN7j6+Oj8nJwc5OTmdjjMuLg7l5eWIjY3F9evXO+1PgaWlftHR0ayfxLB20sb6SRdrJ23+qt+pU6eQnp7uft0SYtPS0rr9QTDJfAAsJiYGd+7cgcViaXOsvLwcERERHc6qeuN8IiIiIvIuudwVRdPS0nDw4EGcPHkSkydP7tYdDSQTZjMyMuB0OvH11197tJvNZpw+fRpDhw716flERERE5B1RUVHo06cP0tPTHzjEtpBMmH3xxRchk8mwfv16j/Zt27bBZDLhpZdecrddvnwZxcXFD3w+EREREflOXFwcSktLHyrEtpDMmtlBgwZh6dKl2LRpE2bNmoWpU6fi4sWL2LBhA0aPHu3xwIPx48ejrKzM4x5l3TmfiIiIiHyrow/md5dkwiwArF+/HomJidi6dSsOHDiAiIgILF++HGvWrHGvufDl+UREREQUWCQVZhUKBVatWoVVq1bdt19paelDnU9ERERE0sDpSCIiIiKSLIZZIiIiIpIsSS0zkIKcnBzU1dW1eeYwSQPrJ12snbSxftLF2knbo1A/mWj9kX8iIiIiIgnhMgMiIiIikiyGWSIiIiKSLIZZIiIiIpIshlkiIiIikiyGWSIiIiKSLIZZL3E6ncjLy8PTTz8NrVaLJ554AqtWrUJjY6O/h0bN/ve//+Htt9/GsGHDEBkZCaPRiNTUVPzud79rt06XLl3CjBkzEBYWBoPBgFGjRuHQoUN+GDm1x2QyITk5GTKZDMuWLWtznPULPFVVVXjllVfQt29faLVaREZGYuzYsThy5IhHv5MnT2LChAkwGo0IDg7GlClTcPr0af8MmtDQ0IDc3FwMGjQIRqMRERERGD58OP785z/j3hsisXb+8+677yIrK8v9czExMfG+/btTq4qKCsyfPx+RkZHQ6XQYOnQo9u3b5/2LeFCCvGLFihUCgJg5c6bYunWryM7OFkqlUowdO1Y4HA5/D4+EEK+99poICgoSc+fOFRs2bBAffPCBmD17tgAgBg8eLEwmk7tvSUmJCA8PF1FRUSI3N1ds3rxZpKamCqVSKb788ks/XgW1WLVqlQgKChIAxNKlSz2OsX6Bp7S0VCQmJoqIiAjx2muviR07doh169aJn/3sZ2LPnj3ufidOnBAajUYkJyeLdevWiXXr1onk5GQRFBQkioqK/HgFjyeHwyFGjhwp5HK5ePnll8WWLVtEXl6eyMzMFADEq6++6u7L2vkXABEeHi4mTJggwsLCREJCQod9u1Oru3fviqSkJGEwGMRbb70ltmzZIkaPHi0AiI8++sjHV9U1DLNecO7cOSGTycSsWbM82jds2CAAiL/85S9+Ghm1VlBQIGpqatq0v/nmmwKA2Lhxo7stKytLyOVy8c0337jb6uvrRXx8vEhJSRFOp7MnhkwdKCwsFAqFQvzxj39sN8yyfoFn5MiRIi4uTlRUVNy3X0ZGhjAajeL69evutuvXrwuj0SgmTpzo62HSPY4fPy4AiJUrV3q0WywWkZSUJEJCQtxtrJ1/Xb582b0/YMCA+4bZ7tTqN7/5jQAg8vPz3W12u11kZGSI8PBwUV9f772LeEAMs17QEoYOHz7s0d7U1CT0er344Q9/6KeRUVcUFRUJAGLx4sVCCCEaGhqERqMR48aNa9N3zZo1AoA4efJkTw+TmtntdpGWliZeeOEFceXKlTZhlvULPP/5z38EALFhwwYhhBBWq1U0Nja26fftt98KAGLhwoVtji1cuFDIZDJRWVnp8/HS9w4ePCgAiPfee6/NsYyMDBETEyOEYO0Czf3CbHdrFRsbK5588sk2fXfu3CkAiL/+9a9eG/eD4ppZLygoKIBcLkdmZqZHu1arRWpqKgoKCvw0MuqK69evAwB69+4NACgqKoLFYsEPfvCDNn2HDRsGAKypH+Xl5aG4uBibNm1q9zjrF3j++c9/AgDi4+Mxbdo06HQ6GAwGpKSkYPfu3e5+LXXpqHZCCBQWFvbMoAkAkJmZidDQULz33nvYt28frl69iuLiYrz++usoLCzE6tWrAbB2UtKdWlVWVqK8vNz9s/Pevq3fz58YZr2goqICERER0Gg0bY7Fxsbizp07sFqtfhgZdcbhcGDt2rVQKpWYO3cuAFc9AVft7tXSVl5e3nODJLcrV67g//7v//D22293+OEG1i/wXLp0CQCwaNEiVFVV4ZNPPsFHH30EtVqNefPm4eOPPwbA2gWisLAw5OfnIzw8HLNnz0ZCQgL69++PzZs3Y//+/Vi0aBEA1k5KulMrqdRV6e8BPApMJlO7QRZwzc629FGr1T05LOqClStX4sSJE8jNzcVTTz0FwFUrAO3WtHU9qectWbIEycnJyMnJ6bAP6xd46uvrAQBGoxFfffWV+2fhjBkzkJycjDfeeAMLFixg7QJUUFAQBg4ciOnTp2P48OGoqqrC5s2bMXfuXPzjH//AxIkTWTsJ6U6tpFJXhlkv0Ov1uHXrVrvHzGazuw8FlrfeegubNm3CL37xC7z++uvu9pZaWSyWNuewnv6ze/dufPnllzh8+DBUKlWH/Vi/wKPT6QAAc+bM8fhHfVhYGKZPn46dO3fi0qVLrF0AOnv2LIYPH468vDwsWbLE3T5nzhwMHDgQixYtwuXLl1k7CelOraRSVy4z8IKYmBjcuXOn3WKXl5cjIiKCs7IBZvXq1fjtb3+Ll19+GR9++KHHsZiYGADt/+mkpa29P7mQ71gsFuTk5GDq1Kno06cPSkpKUFJSgrKyMgBAbW0tSkpKUFNTw/oFoLi4OABAnz592hyLjo4GAFRXV7N2ASgvLw9msxlZWVke7Xq9Hi+88ALKyspQWlrK2klId2ollboyzHpBRkYGnE4nvv76a492s9mM06dPY+jQoX4aGbVn9erVeOedd7BgwQJs374dMpnM4/igQYOg0Whw4sSJNuf+97//BQDWtIc1NTXh9u3bOHDgAPr16+f+GjNmDADXrG2/fv2wfft21i8AtXw4tuXDlq21tEVFRSEjIwMAOqydTCZDenq6D0dK92oJLA6Ho80xu93u3rJ20tGdWkVHRyM2Ntb9s/PevkCA/Dz1890UHglFRUX3vc/srl27/DQyutc777wjAIh58+bd92EWP/nJT4RcLhenT592t7Xcp7Rfv368T2kPs1qtYt++fW2+/vSnPwkAYsqUKWLfvn3i0qVLQgjWL9BUVVUJo9EoYmNjPe5JWVFRIQwGg0hJSXG3DR06VBiNRlFeXu5uKy8vF0ajUYwfP75Hx01CrFy5UgAQv//97z3aq6urRXR0tAgLCxN2u10IwdoFks7uM9udWr3yyisd3mc2NDRU1NXVeX383SUT4p5n0dEDWb58OTZt2oSZM2di6tSpuHjxIjZs2IARI0bg0KFDkMs5Ce5vmzdvxrJlyxAfH4+1a9e2qUnv3r0xceJEAEBJSQkyMzOhUqmQnZ2N4OBgbNu2DWfPnsWBAwcwefJkf1wC3aO0tBRJSUlYunSpx626WL/As3XrVixevBgDBgzAwoULYbVa8cEHH6CyshKff/45Jk2aBAA4fvw4xo4di7i4OCxfvhwAsHHjRty8eRPHjh3DkCFD/HkZj52ysjKkpaWhuroaL730EkaMGIGqqips27YNpaWl2Lx5M371q18BYO38bdeuXe6lVxs3boTVasWqVasAAAkJCZg3b567b3dqdffuXaSnp+Pu3bvIyclBbGws9uzZg3//+9/Yvn07fv7zn/fgVXbA32n6UWG328Uf/vAHkZKSItRqtYiJiRHZ2dkB8WQMclmwYIEA0OHX6NGjPfpfuHBBTJ8+XYSEhAidTidGjBjBR6EGmPYemtCC9Qs8+/fvF88995zQ6/UiKChITJw4URw9erRNv+PHj4tx48YJg8EggoKCxKRJk0RhYaEfRkxCuB4PPX/+fBEbGyuUSqUwGo1i1KhRYv/+/W36snb+0/KI2a78fhOie7W6fv26+OlPfyp69eolNBqNePbZZ8XevXt9fEVdx5lZIiIiIpIs/u2biIiIiCSLYZaIiIiIJIthloiIiIgki2GWiIiIiCSLYZaIiIiIJIthloiIiIgki2GWiIiIiCSLYZaIiIiIJIthloiIiIgki2GWiMhHsrOzIZPJEBUVhTt37ty3b3l5OUJDQyGTybBjx44eGiERkfTxcbZERD7S1NSEIUOG4Ntvv8WcOXPw6aefdtj3Rz/6EQ4cOIBp06YhPz+/B0dJRCRtDLNERD509OhRjB49Gk6nE/n5+Zg2bVqbPrt27cL8+fMRERGBc+fOoXfv3n4YKRGRNHGZARGRD40cORIrVqwAACxZsgS1tbUex2/cuIGVK1cCALZu3cogS0TUTQyzREQ+lpubi759+6KiogKrVq3yOLZ06VJUVVVh/vz5mDlzprv9b3/7G8aMGYOQkBDo9XqkpqZi/fr1sNlsbd7fbrdjx44dGD9+PCIiIqBSqRAeHo6xY8di7969bfonJiYiNDQU586dQ3p6OjQaDRISEnDkyBHvXzwRkY9xmQERUQ9oWW4ghMDRo0cxfPhw/P3vf8ePf/xjxMfHo6ioCCEhIQBcM7hbtmyBTqdDZmYmQkNDceTIEVRVVWHixIn4/PPPoVarAQBCCMyYMQP5+fkICwvDsGHDoNVqceHCBVy6dAkA8P7777tnhwFXmL1165Y7+A4ePBjffPMNzp49C6PR2PP/cYiIHoYgIqIe8etf/1oAEKmpqaK6ulrExMQImUwmDh065O7z8ccfCwBi8ODB4sqVK+722tpaMXnyZAFAvPnmm+72/fv3CwAiMzNT1NfXe3y/d999VwAQffv29WhPSEgQAERaWpowm81CCCEcDocPrpiIyPc4M0tE1ENMJhOGDBmCkpISDBgwAOfPn8fKlSuRl5fn7tO/f38UFxejsLAQaWlpHudXVlYiMTEROp0ON2/ehEajwd69e7Fnzx5kZ2djzJgxHv1ra2sRGhoKhUIBu93ubk9MTERZWRk+/PBDLF682KfXTETkawyzREQ96MiRI+7lBv3798epU6eg1WoBuD4MFh0djZCQENTU1LR7fmZmJgoKCnDixAkMGzas3T5NTU0oLi7G8ePHsWzZMgCudbUKhQLA92H2fu9BRCQVSn8PgIjocTJq1CgMHz4cx44dQ05OjjvIAsDVq1cBuGZUZTLZfd/n2rVr7iBaV1eHrVu34uDBg7h48SIqKyshhPB4j/bmLcLDw71xSUREfsUwS0TUw5RKpce2hcPhAAD06tULU6ZMue979OnTBwBw/vx5jBs3zv2BrszMTMyZMwdDhgzBmDFjEB8f3+F7yOW8oQ0RSR/DLBFRgIiOjgYAaLVa7N69u0vnLFu2DLdu3cKrr76K3Nxc91ICAKiurvbJOImIAgn/WU5EFCASExMRHx+P8vJynDlzps3xlg+QPf/88ygtLQUAnDhxAgDwxhtveARZAPjXv/7l3nc6nb4bOBGRHzHMEhEFkOzsbADA/PnzcfnyZXe71WrFL3/5SxQVFaGhoQGJiYkAgMjISABAfn6+x/scPnwYy5cvd782m80+HjkRkX8wzBIRBZAVK1bgxRdfRFFREQYOHIjnn38eM2fORFJSEnbu3ImoqCiPp3rl5OQAcIXfkSNHIisrC88++yxGjx4Np9PpXlt748YNv1wPEZGvMcwSEQUQuVyOPXv24JNPPkFGRgbOnDmDL774AiEhIcjJycHp06eRkpLi7p+dnY1PP/0UGRkZOHv2LD777DM0NjZi+fLlOHPmDLKysgAAn332mb8uiYjIp3ifWSIiIiKSLM7MEhEREZFkMcwSERERkWQxzBIRERGRZDHMEhEREZFkMcwSERERkWQxzBIRERGRZDHMEhEREZFkMcwSERERkWQxzBIRERGRZDHMEhEREZFkMcwSERERkWQxzBIRERGRZP0/MNyy0QKsxlEAAAAASUVORK5CYII=", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# -----------------------------------------------------------------\n", - "plot_title = \"\"\n", - "font = \"Arial\"\n", - "x_label = \"Year\"\n", - "y_label = \"Normalized Present Value [$-$]\"\n", - "legend = True\n", - "grid = False\n", - "save_svg = True\n", - "remove_ticks = False\n", - "remove_ticks_labels = False\n", - "file_name = \"template_exp_decay\"\n", - "# -----------------------------------------------------------------\n", - "\n", - "fig = plt.figure(figsize=(8,6))\n", - "ax = fig.add_subplot() # axes_class=AxesZero)\n", - "ax.set_title(plot_title, fontfamily=font)\n", - "ax.set_xlabel(x_label, fontfamily=font)\n", - "ax.set_ylabel(y_label, fontfamily=font)\n", - "\n", - "plt.setp(ax.spines.values(), linewidth=2)\n", - "ax.spines[\"left\"].set_position((\"data\", 0))\n", - "ax.spines[\"bottom\"].set_position((\"data\", 0))\n", - "ax.spines[\"top\"].set_visible(False)\n", - "ax.spines[\"right\"].set_visible(False)\n", - "\n", - "t = np.linspace(0,101)\n", - "y_2 = 1 / (1 + 0.02)**t\n", - "y_4 = 1 / (1 + 0.04)**t\n", - "\n", - "# plotting\n", - "ax.plot(t, y_2, label='2%', color=colors[0], linewidth=4)\n", - "ax.plot(t, y_4, label='4%', color=colors[1], linewidth=4)\n", - "ax.plot(1, 0, \">k\", transform=ax.get_yaxis_transform(), clip_on=False)\n", - "ax.plot(0, 1, \"^k\", transform=ax.get_xaxis_transform(), clip_on=False)\n", - "\n", - "# not a permanent solution (removed the part below 0)\n", - "# ---> find a better way to auto set upper bound\n", - "ax.spines.bottom.set_bounds(0, 105)\n", - "ax.spines.left.set_bounds(0, 1.05)\n", - "\n", - "ax.tick_params(axis='x', labelsize=13, width=2, length=8)\n", - "ax.tick_params(axis='y', labelsize=13, width=2, length=8)\n", - "\n", - "if grid: ax.grid()\n", - "if legend: ax.legend(prop={\"family\":font})\n", - "if remove_ticks: ax.set_xticks([]); ax.set_yticks([])\n", - "if remove_ticks_labels: ax.set_xticklabels([]); ax.set_yticklabels([])\n", - "if save_svg: plt.savefig(file_name + '.svg')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## **Template #3**" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "id": "a19d456c-b5d3-43d6-8b51-1441f902985d", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# -----------------------------------------------------------------\n", - "plot_title = \"Cumulative distribution function, $F_{N}(n) = P(N \\leq n)$\"\n", - "font = \"Arial\"\n", - "x_label = \"Fatalities [$-$]\"\n", - "y_label = \"Probability [$-$]\"\n", - "legend = False\n", - "grid = False\n", - "save_svg = True\n", - "remove_ticks = False\n", - "remove_ticks_labels = False\n", - "file_name = \"template_cdf\"\n", - "# -----------------------------------------------------------------\n", - "\n", - "fig = plt.figure(figsize=(8,6))\n", - "ax = fig.add_subplot() # axes_class=AxesZero)\n", - "plt.setp(ax.spines.values(), linewidth=2.0)\n", - "\n", - "ax.set_title(plot_title, fontfamily=font, x=0.55, y=1.0)\n", - "ax.set_xlabel(x_label, fontfamily=font)\n", - "ax.set_ylabel(y_label, fontfamily=font)\n", - "\n", - "# data\n", - "N_fatalities = ['0', '10', '100', '']\n", - "N_fatalities_loc = [0.03, 0.33, 0.76, 0.95]\n", - "pdf = ['0', '0.989', '0.999', '1']\n", - "pdf_loc = [0.03, 0.66, 0.86, 0.99]\n", - "\n", - "# plotting\n", - "ax.step(N_fatalities_loc, pdf_loc, color=colors[0], linewidth=4)\n", - "\n", - "# ticks\n", - "ax.set_xticks(N_fatalities_loc)\n", - "ax.set_xticklabels(N_fatalities)\n", - "ax.set_yticks(pdf_loc)\n", - "ax.set_yticklabels(pdf)\n", - "ax.tick_params(axis='x', labelsize=13, width=2, length=8)\n", - "ax.tick_params(axis='y', labelsize=13, width=2, length=8)\n", - "\n", - "# add text\n", - "ax.text(0.8, 0.9, r'} $10^{-3}$', fontsize=16, fontfamily=font)\n", - "ax.text(0.37, 0.725, r'} $10^{-2}$', fontsize=16, fontfamily=font)\n", - "\n", - "current_values = plt.gca().get_yticks()\n", - "plt.gca().set_yticklabels(['{:,.3f}'.format(x) for x in current_values])\n", - "\n", - "if grid: ax.grid()\n", - "if legend: ax.legend(prop={\"family\":font})\n", - "if remove_ticks: ax.set_xticks([]); ax.set_yticks([])\n", - "if remove_ticks_labels: ax.set_xticklabels([]); ax.set_yticklabels([])\n", - "if save_svg: plt.savefig(file_name + '.svg')" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "629e2cf8", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.11.7" - }, - "widgets": { - "application/vnd.jupyter.widget-state+json": { - "state": {}, - "version_major": 2, - "version_minor": 0 - } - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/figures/helper.py b/figures/helper.py deleted file mode 100644 index b9714c0..0000000 --- a/figures/helper.py +++ /dev/null @@ -1,109 +0,0 @@ -import numpy as np -import matplotlib.pyplot as plt -import matplotlib.cm as cm -import pyvinecopulib as cop - -class Bivariate: - """Bivariate dependent distribution, design to function in the - same way as an instance of the scipy.stats.rv_continuous class, - specifically, with methods: cdf, pdf, rvs. - """ - - def __init__(self, X1, X2, rho): - """Constructor to initialize Bivariate object. - - Arguments: - --- - X1: scipy.stats.rv_continuous object. Marginal distribution - X2: scipy.stats.rv_continuous object. Marginal distribution - rho: float. Pearson correlation coefficient. - """ - self.X1 = X1 - self.X2 = X2 - self.rho = rho - self.copula_uv = cop.Bicop(family=cop.BicopFamily.gaussian, parameters = [rho]) - - def cdf(self, x): - """Compute cdf with array or list as argument: [x1, x2].""" - x1 = x[0] - x2 = x[1] - u = self.X1.cdf(x1) - v = self.X2.cdf(x2) - return self.copula_uv.cdf(np.array([[u, v]]))[0] - - def pdf(self, x): - """Compute pdf with array or list as argument: [x1, x2].""" - x1 = x[0] - x2 = x[1] - u = self.X1.cdf(x1) - v = self.X2.cdf(x2) - return self.copula_uv.pdf(np.array([[u, v]]))[0]*self.X1.pdf(x1)*self.X2.pdf(x2) - - def rvs(self, size=1): - """Create random sample with keyword argument size.""" - sample = self.copula_uv.simulate(size) - sample_X1 = self.X1.ppf(sample[:,0]) - sample_X2 = self.X2.ppf(sample[:,1]) - return np.vstack([sample_X1.T, sample_X2.T]).T - -def plot_contour(bivar, xy_lim, data=None, - design_case=None, design_region=None, - nb_points=100): - """Contour plot of PDF in the bivariate plane (X,Y). - - bivar: bivariate distribution, defined by - scipy.stats.multivariate_normal. - xy_lim: list. 1x4 list of xlim and ylim (in order) for plot limits. - - Optional arguments: - - data: array. A 2xN array of points. - design_case: list. Typically a 1x2 list defining a key - calculation point; plots as a red dot(s) - design_region: array. A 2xN array of points that define the - boundary of a region that will be shaded in gray between - the boundary and the max y-axis value (ylim[1]). - nb_points: int. Size of the grid (default: 200). - - returns: matplotlib.pyplot Figure and Axis objects. - """ - - f, ax = plt.subplots(1) - - xlim = [xy_lim[0], xy_lim[1]] - ylim = [xy_lim[2], xy_lim[3]] - - x = np.linspace(xlim[0], xlim[1], nb_points) - y = np.linspace(ylim[0], ylim[1], nb_points) - X,Y = np.meshgrid(x,y) - pdf = np.zeros(X.shape) - for i in range(X.shape[0]): - for j in range(X.shape[1]): - # if X[i,j]>0 and Y[i,j]>0: - pdf[i,j] = bivar.pdf([X[i,j], Y[i,j]]) - - ax.contour(X, Y, pdf, levels=8, cmap=cm.Blues) - - if isinstance(data, np.ndarray): - ax.scatter(data[0,:], data[1,:], s=10.0, - facecolors='none', edgecolors='darkgray', - label='Data') - - if isinstance(design_region, np.ndarray): - ax.plot(design_region[0,:], design_region[1,:], - label='Design Boundary', color='k') - ax.fill_between(design_region[0,:], design_region[1,:], - ylim[1], label='Design Region', color='grey') - - if design_case: - ax.plot(design_case[0], design_case[1], 'ro', - label='Design Case') - - ax.set_aspect("equal") - ax.set_xlim(xlim) - ax.set_ylim(ylim) - ax.set_xlabel(r"$X_1$", fontsize=14) - ax.set_ylabel(r"$X_2$", fontsize=14) - if isinstance(design_region, np.ndarray) or design_case: - ax.legend() - return f, ax \ No newline at end of file diff --git a/figures/risk_curve.ipynb b/figures/risk_curve.ipynb deleted file mode 100644 index 821ad75..0000000 --- a/figures/risk_curve.ipynb +++ /dev/null @@ -1,411 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 2, - "id": "65cbe2ec-de72-44d4-8af9-a969b06134a9", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from matplotlib import rcParams\n", - "from scipy.interpolate import make_interp_spline\n", - "rcParams.update({'font.size': 16})\n", - "# TUDelft colors palette\n", - "colors = [\"#0C2340\",\"#00B8C8\",\"#0076C2\",\"#6F1D77\",\"#EF60A3\",\"#A50034\",\"#E03C31\",\"#EC6842\",\"#FFB81C\",\"#6CC24A\",\"#009B77\"]" - ] - }, - { - "cell_type": "code", - "execution_count": 191, - "id": "ba992138", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[0. 0.33333333 0.56632333 0.66666667 0.89965667 1. ]\n", - "[1.00100000e-04 6.67666667e-05 4.34676665e-05 3.34333333e-05\n", - " 1.01343332e-05 1.00000000e-07]\n" - ] - } - ], - "source": [ - "print(np.log(x)/np.log(1000))\n", - "\n", - "print(y)" - ] - }, - { - "cell_type": "code", - "execution_count": 285, - "id": "1c820b9d", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "(1e-07, 0.001)" - ] - }, - "execution_count": 285, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "right = 500\n", - "top = .5e-5\n", - "\n", - "u = np.array([1, 2, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 120, 150, 180, 200, 220, 250, 275, 300, 350, 400, 450, 475])\n", - "v = 1e-8 + top*(np.log(right) - np.log(u))**3/np.log(right)\n", - "\n", - "fig, ax = plt.subplots()\n", - "ax.loglog(u, v, color=colors[0], label=\"Ellipse\")\n", - "ax.set_xlim(1, 1000)\n", - "ax.set_ylim(1e-7, 1e-3)" - ] - }, - { - "cell_type": "code", - "execution_count": 340, - "id": "f7c03e2f", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[ 1.00e-04 6.00e-05 3.00e-05 1.00e-05 3.98e-06 1.98e-06 9.80e-07\n", - " 6.00e-08 -8.50e-07]\n" - ] - } - ], - "source": [ - "right = 500\n", - "top = .5e-5\n", - "\n", - "u = np.array([1, 2, 5, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 120, 150, 180, 200, 220, 250, 275, 300, 350, 400, 450, 475])\n", - "v = 1e-8 + top*(np.log(right) - np.log(u))**3/np.log(right)\n", - "\n", - "# fig, ax = plt.subplots()\n", - "# ax.loglog(u, v, color=colors[0], label=\"Ellipse\")\n", - "# ax.set_xlim(1, 1000)\n", - "# ax.set_ylim(1e-7, 1e-3)\n", - "\n", - "C = 10**-3\n", - "alpha = 2\n", - "\n", - "limit_line_N = np.array([1, 1000])\n", - "limit_line_P = C/limit_line_N**alpha\n", - "\n", - "N = np.array([1, 7, 20, 40, 60, 100, 160, 200, 300])\n", - "N_pmf = np.array([0.9999,\n", - " 0.00004,\n", - " 0.00003,\n", - " 0.00002,\n", - " 0.00000602,\n", - " 0.000002,\n", - " 0.000001,\n", - " 0.00000092,\n", - " 0.00000091])\n", - "N_cdf = np.cumsum(N_pmf)\n", - "N_exc = 1 - N_cdf\n", - "print(N_exc)" - ] - }, - { - "cell_type": "code", - "execution_count": 341, - "id": "2c5ef408", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# -----------------------------------------------------------------\n", - "plot_title = \"\"\n", - "font = \"Arial\"\n", - "x_label = \"Fatalities, N [$-$]\"\n", - "y_label = \"Probability of Exceedance, $1-F_N(n)$ [$-$]\"\n", - "legend = True\n", - "grid = True\n", - "save_svg = True\n", - "remove_ticks = False\n", - "remove_ticks_labels = False\n", - "file_name = \"../book/figures/fn_simple01\"\n", - "# -----------------------------------------------------------------\n", - "\n", - "fig = plt.figure(figsize=(8,6))\n", - "ax = fig.add_subplot() # axes_class=AxesZero)\n", - "ax.set_title(plot_title, fontfamily=font)\n", - "ax.set_xlabel(x_label, fontfamily=font)\n", - "ax.set_ylabel(y_label, fontfamily=font)\n", - "\n", - "plt.setp(ax.spines.values(), linewidth=2)\n", - "\n", - "# Visualize\n", - "\n", - "# plotting\n", - "# ax.plot(limit_line_N, limit_line_P, '--', label='Limit Line', color=colors[0], linewidth=4)\n", - "ax.plot(u, v, label='Risk Curve', color=colors[1], linewidth=4)\n", - "\n", - "# ax.plot(1, 0, \">k\", transform=ax.get_yaxis_transform(), clip_on=False)\n", - "# ax.plot(0, 1, \"^k\", transform=ax.get_xaxis_transform(), clip_on=False)\n", - "\n", - "ax.set_xscale('log')\n", - "ax.set_yscale('log')\n", - "\n", - "ax.set_xlim(1, 1000)\n", - "ax.set_ylim(10**(-7),.001)\n", - "# ax.set_yticks([10**(-7),10**(-5),10**(-3),10**(-1)])\n", - "\n", - "ax.tick_params(axis='x', labelsize=13, width=2, length=8)\n", - "ax.tick_params(axis='y', labelsize=13, width=2, length=8)\n", - "\n", - "if grid: ax.grid()\n", - "if legend: ax.legend(prop={\"family\":font})\n", - "if remove_ticks: ax.set_xticks([]); ax.set_yticks([])\n", - "if remove_ticks_labels: ax.set_xticklabels([]); ax.set_yticklabels([])\n", - "if save_svg: plt.savefig(file_name + '.svg')" - ] - }, - { - "cell_type": "code", - "execution_count": 343, - "id": "fc2eb45c-9f4e-4fbd-91c3-dc0ff10b4c46", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# -----------------------------------------------------------------\n", - "plot_title = \"\"\n", - "font = \"Arial\"\n", - "x_label = \"Fatalities, N [$-$]\"\n", - "y_label = \"Probability of Exceedance, $1-F_N(n)$ [$-$]\"\n", - "legend = True\n", - "grid = True\n", - "save_svg = True\n", - "remove_ticks = False\n", - "remove_ticks_labels = False\n", - "file_name = \"../book/figures/fn_limit01\"\n", - "# -----------------------------------------------------------------\n", - "\n", - "fig = plt.figure(figsize=(8,6))\n", - "ax = fig.add_subplot() # axes_class=AxesZero)\n", - "ax.set_title(plot_title, fontfamily=font)\n", - "ax.set_xlabel(x_label, fontfamily=font)\n", - "ax.set_ylabel(y_label, fontfamily=font)\n", - "\n", - "plt.setp(ax.spines.values(), linewidth=2)\n", - "# ax.spines[\"left\"].set_position((\"data\", 0))\n", - "# ax.spines[\"bottom\"].set_position((\"data\", 0))\n", - "# ax.spines[\"top\"].set_position((\"data\", 1))\n", - "# ax.spines[\"right\"].set_position((\"data\", 100))\n", - "\n", - "# not a permanent solution (removed the part below 0)\n", - "# ---> find a better way to auto set upper bound\n", - "# ax.spines.bottom.set_bounds(0, 100)\n", - "# ax.spines.left.set_bounds(0, 1.0)\n", - "# ax.spines.top.set_bounds(0, 100)\n", - "# ax.spines.right.set_bounds(0, 1.0)\n", - "\n", - "# Visualize\n", - "\n", - "# plotting\n", - "ax.step(N, N_exc, where='post', label='Risk Curve', color=colors[1], linewidth=4)\n", - "ax.plot(limit_line_N, limit_line_P, '--', label='Limit Line', color=colors[0], linewidth=4)\n", - "# ax.plot(u, v, label='Risk Curve 2', color=colors[2], linewidth=4)\n", - "\n", - "# ax.plot(1, 0, \">k\", transform=ax.get_yaxis_transform(), clip_on=False)\n", - "# ax.plot(0, 1, \"^k\", transform=ax.get_xaxis_transform(), clip_on=False)\n", - "\n", - "ax.set_xscale('log')\n", - "ax.set_yscale('log')\n", - "\n", - "ax.set_xlim(1, 1000)\n", - "ax.set_ylim(10**(-9),.001)\n", - "# ax.set_yticks([10**(-7),10**(-5),10**(-3),10**(-1)])\n", - "\n", - "ax.tick_params(axis='x', labelsize=13, width=2, length=8)\n", - "ax.tick_params(axis='y', labelsize=13, width=2, length=8)\n", - "\n", - "if grid: ax.grid()\n", - "if legend: ax.legend(prop={\"family\":font})\n", - "if remove_ticks: ax.set_xticks([]); ax.set_yticks([])\n", - "if remove_ticks_labels: ax.set_xticklabels([]); ax.set_yticklabels([])\n", - "if save_svg: plt.savefig(file_name + '.svg')" - ] - }, - { - "cell_type": "code", - "execution_count": 350, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "array([5.e-04, 1.e-06])" - ] - }, - "execution_count": 350, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "limit_line_P" - ] - }, - { - "cell_type": "code", - "execution_count": 368, - "id": "59293d62", - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# -----------------------------------------------------------------\n", - "plot_title = \"\"\n", - "font = \"Arial\"\n", - "x_label = \"Fatalities, N [$-$]\"\n", - "y_label = \"Probability of Exceedance, $1-F_N(n)$ [$-$]\"\n", - "legend = True\n", - "grid = True\n", - "save_svg = True\n", - "remove_ticks = True\n", - "remove_ticks_labels = True\n", - "file_name = \"../book/figures/fn_limit00\"\n", - "# -----------------------------------------------------------------\n", - "\n", - "fig = plt.figure(figsize=(8,6))\n", - "ax = fig.add_subplot() # axes_class=AxesZero)\n", - "ax.set_title(plot_title, fontfamily=font)\n", - "ax.set_xlabel(x_label, fontfamily=font)\n", - "ax.set_ylabel(y_label, fontfamily=font)\n", - "\n", - "plt.setp(ax.spines.values(), linewidth=2)\n", - "# ax.spines[\"left\"].set_position((\"data\", 0))\n", - "# ax.spines[\"bottom\"].set_position((\"data\", 0))\n", - "# ax.spines[\"top\"].set_position((\"data\", 1))\n", - "# ax.spines[\"right\"].set_position((\"data\", 100))\n", - "\n", - "# not a permanent solution (removed the part below 0)\n", - "# ---> find a better way to auto set upper bound\n", - "# ax.spines.bottom.set_bounds(0, 100)\n", - "# ax.spines.left.set_bounds(0, 1.0)\n", - "# ax.spines.top.set_bounds(0, 100)\n", - "# ax.spines.right.set_bounds(0, 1.0)\n", - "\n", - "C = 0.003302\n", - "alpha = 1.173\n", - "\n", - "limit_line_N = np.array([1, 10000])\n", - "limit_line_P = C/limit_line_N**alpha\n", - "\n", - "limit_line_N_trim = [1, 5, 1000, 1000]\n", - "limit_line_P_trim = [5e-4, 5e-4, 1e-6, 1e-7]\n", - "\n", - "\n", - "\n", - "# Visualize\n", - "\n", - "# plotting\n", - "ax.step(N, N_exc, where='post', label='Risk Curve', color=colors[1], linewidth=4)\n", - "ax.plot(limit_line_N, limit_line_P, ':', label='Limit Line', color=colors[0], linewidth=4)\n", - "ax.plot(limit_line_N_trim, limit_line_P_trim, '-', label='Limit Line with Cutoffs', color=colors[0], linewidth=4)\n", - "# ax.plot(u, v, label='Risk Curve 2', color=colors[2], linewidth=4)\n", - "\n", - "# ax.plot(1, 0, \">k\", transform=ax.get_yaxis_transform(), clip_on=False)\n", - "# ax.plot(0, 1, \"^k\", transform=ax.get_xaxis_transform(), clip_on=False)\n", - "\n", - "\n", - "\n", - "ax.set_xscale('log')\n", - "ax.set_yscale('log')\n", - "\n", - "ax.set_xlim(1, 10000)\n", - "ax.set_ylim(10**(-7),.01)\n", - "\n", - "if grid: ax.grid()\n", - "if legend: ax.legend(prop={\"family\":font})\n", - "if remove_ticks: ax.set_xticks([]); ax.set_yticks([])\n", - "if remove_ticks_labels: ax.set_xticklabels([]); ax.set_yticklabels([])\n", - "if save_svg: plt.savefig(file_name + '.svg')" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.11.7" - }, - "widgets": { - "application/vnd.jupyter.widget-state+json": { - "state": {}, - "version_major": 2, - "version_minor": 0 - } - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/figures/risk_types.ipynb b/figures/risk_types.ipynb deleted file mode 100644 index a662a11..0000000 --- a/figures/risk_types.ipynb +++ /dev/null @@ -1,167 +0,0 @@ -{ - "cells": [ - { - "cell_type": "code", - "execution_count": 1, - "id": "65cbe2ec-de72-44d4-8af9-a969b06134a9", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "import numpy as np\n", - "import matplotlib.pyplot as plt\n", - "from matplotlib import rcParams\n", - "rcParams.update({'font.size': 16})\n", - "# TUDelft colors palette\n", - "colors = [\"#0C2340\",\"#00B8C8\",\"#0076C2\",\"#6F1D77\",\"#EF60A3\",\"#A50034\",\"#E03C31\",\"#EC6842\",\"#FFB81C\",\"#6CC24A\",\"#009B77\"]" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "fc2eb45c-9f4e-4fbd-91c3-dc0ff10b4c46", - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "# -----------------------------------------------------------------\n", - "plot_title = \"\"\n", - "font = \"Arial\"\n", - "x_label = \"Fatalities, N [$-$]\"\n", - "y_label = \"Probability of Exceedance, $1-F_N(n)$ [$-$]\"\n", - "legend = True\n", - "grid = True\n", - "save_svg = True\n", - "remove_ticks = False\n", - "remove_ticks_labels = False\n", - "file_name = \"../book/figures/risk_types\"\n", - "# -----------------------------------------------------------------\n", - "\n", - "fig = plt.figure(figsize=(8,6))\n", - "ax = fig.add_subplot() # axes_class=AxesZero)\n", - "ax.set_title(plot_title, fontfamily=font)\n", - "ax.set_xlabel(x_label, fontfamily=font)\n", - "ax.set_ylabel(y_label, fontfamily=font)\n", - "\n", - "plt.setp(ax.spines.values(), linewidth=2)\n", - "# ax.spines[\"left\"].set_position((\"data\", 0))\n", - "# ax.spines[\"bottom\"].set_position((\"data\", 0))\n", - "# ax.spines[\"top\"].set_position((\"data\", 1))\n", - "# ax.spines[\"right\"].set_position((\"data\", 100))\n", - "\n", - "# not a permanent solution (removed the part below 0)\n", - "# ---> find a better way to auto set upper bound\n", - "# ax.spines.bottom.set_bounds(0, 100)\n", - "# ax.spines.left.set_bounds(0, 1.0)\n", - "# ax.spines.top.set_bounds(0, 100)\n", - "# ax.spines.right.set_bounds(0, 1.0)\n", - "\n", - "# Given Parameters\n", - "\n", - "N_fatalities = np.linspace(1,1000,1000) # fatalities\n", - "\n", - "P_df = 0.1; beta = 0.1\n", - "\n", - "alpha = 2\n", - "k = 3\n", - "N_A = 100\n", - "\n", - "r= 0.025\n", - "I = 5*10**6\n", - "B = 0.33\n", - "\n", - "# Individual Risk\n", - "\n", - "Pf_ind_risk = (beta*(10**-4))/P_df # per year\n", - "\n", - "# print('Acceptable Failure Probability: ', Pf_ind_risk)\n", - "\n", - "# Societal Risk\n", - "\n", - "C = ((beta*100)/(k*np.sqrt(N_A)))**2 # binomial distribution\n", - "\n", - "Pf_SR = (C/(N_fatalities**alpha))\n", - "\n", - "# Economic Risk\n", - "\n", - "D_damage = (5*10**7)*N_fatalities\n", - "\n", - "Pf_ER = (I*B*r)/(D_damage)\n", - "\n", - "# Visualize\n", - "\n", - "# plotting\n", - "ax.plot(N_fatalities, Pf_SR, label='Societal Risk', color=colors[0], linewidth=4)\n", - "ax.plot(N_fatalities,Pf_ER, label='Economic Risk', color=colors[1], linewidth=4)\n", - "ax.axhline(Pf_ind_risk, label='Individual Risk', color=colors[2], linewidth=4)\n", - "\n", - "# ax.plot(1, 0, \">k\", transform=ax.get_yaxis_transform(), clip_on=False)\n", - "# ax.plot(0, 1, \"^k\", transform=ax.get_xaxis_transform(), clip_on=False)\n", - "\n", - "ax.set_xscale('log')\n", - "ax.set_yscale('log')\n", - "\n", - "ax.set_ylim(10**(-7),.1)\n", - "# ax.set_yticks([10**(-7),10**(-5),10**(-3),10**(-1)])\n", - "\n", - "ax.tick_params(axis='x', labelsize=13, width=2, length=8)\n", - "ax.tick_params(axis='y', labelsize=13, width=2, length=8)\n", - "\n", - "if grid: ax.grid()\n", - "if legend: ax.legend(prop={\"family\":font})\n", - "if remove_ticks: ax.set_xticks([]); ax.set_yticks([])\n", - "if remove_ticks_labels: ax.set_xticklabels([]); ax.set_yticklabels([])\n", - "if save_svg: plt.savefig(file_name + '.svg')" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "59293d62", - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3 (ipykernel)", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.11.7" - }, - "widgets": { - "application/vnd.jupyter.widget-state+json": { - "state": {}, - "version_major": 2, - "version_minor": 0 - } - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/figures/solution.py b/figures/solution.py deleted file mode 100644 index 271f531..0000000 --- a/figures/solution.py +++ /dev/null @@ -1,264 +0,0 @@ -"""Set of helper functions for Week 8 part of Project 4, 2023. - -Primary purpose is: - 1) define dictionaries to track information about bivariate - and univariate probability models, as well as a few - important characteristics, - 2) print and plot results, - 3) perform simple calculations (e.g., covariance, ecdf etc). - -Organized in order used in solution notebooks. -""" - -import numpy as np -import matplotlib.pyplot as plt -import scipy.stats as st - -from helper import plot_contour -from helper import Bivariate - -def univariate_RV_dict(name, symbol, unit): - """Create a dictionary to track a random variable.""" - d = {"name":name, "symbol":symbol, "unit":unit} - d = create_plot_label(d) - return d - -def create_plot_label(univariate_dict): - """Combine RV name, symbol, unit into key xlabel.""" - univariate_dict["label"] = (univariate_dict["name"] + ", " - + univariate_dict["symbol"] + " [" - + univariate_dict["unit"] + "]") - return univariate_dict - -def univariate_model_dict(dist_type, parameters, - distribution, empirical=False, note=None): - """Create a dictionary to track a distribution model. - - dist_type: string, - parameters: tuple, from scipy.stats rv_continuous - distribution: frozen instance of scipy.stats.rv_continuous - empirical: boolean. Set to True if distribution is a sample - (array). This is just a placeholder to support other functions - that will be used for printing results - (e.g., compare_univar_prob). - note: string (optional) - """ - model = {"type":dist_type} - model["parameters"] = parameters - model["distribution"] = distribution - model["empirical"] = empirical - model["note"] = note - - if empirical: - model["N"] = len(distribution) - model["sample"] = distribution - - return model - -def print_dist_model_summary(RV, model_key): - """Prints info about a model.""" - print(f'Random variable {RV["name"]}, model \"{model_key}\" is:\n' - f' distribution: {RV[model_key]["type"]}\n' - f' parameters: {[f"{i:.3f}" for i in RV[model_key]["parameters"]]}\n' - f' (μ,σ) dist: ' - f'({RV[model_key]["distribution"].mean():.3f}, ' - f'{RV[model_key]["distribution"].std():.3f})\n' - f' (μ,σ) data: ' - f'({RV["data"].mean():.3f}, {RV["data"].std():.3f})\n') - -def calculate_covariance(X1, X2): - """Covariance of X1 and X2 (numpy arrays).""" - mean_x1 = X1.mean() - mean_x2 = X2.mean() - diff_x1 = X1 - mean_x1 - diff_x2 = X2 - mean_x2 - product = diff_x1 * diff_x2 - covariance = product.mean() - return covariance - -def pearson_correlation(X1, X2): - """Pearson correlation of X1 and X2 (numpy arrays).""" - covariance = calculate_covariance(X1, X2) - correl_coeff = covariance/(X1.std()*X2.std()) - return correl_coeff - -def bivariate_model_dict(model_name, - X1_key, X1, X2_key, X2, rho): - """Create dictionary to track the bivariate model. - - model_name: string. Arg is root name, which has - marginal info added; used for plot title. - X1, X2: dict.from univariate_RV_dict() - X1_key, X2_key: string. Name of model of X1, X2 - rho: correlation coefficient - - returns: dictionary - """ - - d = {"X1_key":X1_key, "X1":X1[X1_key], - "X2_key":X2_key, "X2":X2[X2_key], - "rho":rho} - - d["title"] = (model_name + ": " - + r"$X_1 \sim$" + X1_key + ", " - + r"$X_2 \sim$" + X2_key + ", " - + r"$\rho$ = " + f"{rho:.2f}") - - d["xlabel"], d["ylabel"] = X1["label"], X2["label"] - d["X1X2"] = Bivariate(d["X1"]["distribution"], - d["X2"]["distribution"], - d["rho"]) - d["data"] = np.array([X1["data"], X2["data"]]) - d["data_X1"], d["data_X2"] = X1["data"], X2["data"] - - return d - -def compare_bivar_prob(point, model): - """Compare probabilities at a given point (bivariate). - - point: array or list; size = 2. - model: dictionary defining bivariate distribution. - - returns: none, except printed output. - """ - - data_X1 = model["data_X1"] - data_X2 = model["data_X2"] - N = data_X1.size - - left_emp = sum(data_X1 < point[0])/N - bottom_emp = sum(data_X2 < point[1])/N - lower_left_emp = sum((data_X1 < point[0])*(data_X2 < point[1]))/N - - union_emp = 1 - lower_left_emp - intersection_emp = 1 - (left_emp + bottom_emp - lower_left_emp) - - lower_left = model["X1X2"].cdf(point) - union = 1 - lower_left - - left = model["X1"]["distribution"].cdf(point[0]) - bottom = model["X2"]["distribution"].cdf(point[1]) - intersection = 1 - (left + bottom - lower_left) - - print(f'-------------------------------------------------') - print(f' Comparison, Empirical Values in ( )') - print(f'-------------------------------------------------') - print(f'Lower left, P[X1x1 or X2>x2] = {union:.5f}', - f'({union_emp:.5f})') - print(f'Case 2: P[X1>x1 and X2>x2] = {intersection:.5f}', - f'({intersection_emp:.5f})') - print(f'-------------------------------------------------') - -def compare_univar_prob(point, model, dist_key): - """Compare probabilities at a given point (univariate). - - point: float - model: dictionary defining univariate distribution - dist_key: specify which distribution model to use - - returns: none, except printed output. - """ - - data = model["data"] - N = data.size - p_data = sum(data < point)/N - if model[dist_key]["empirical"]: - N_model = model[dist_key]["N"] - n_eval = sum(model[dist_key]["sample"]x] = {1 - p_model:.5f} ({1 - p_data:.5f})') - print(f'There are {N} points in the data set.') - if model[dist_key]["empirical"]: - print(f'This distribution is from MCS:') - print(f' number of smaples = {N_model}') - print(f'---------------------------------------') - -def ecdf(var): - """Empirical cdf from list or array. Returns [F(x), x].""" - x = np.sort(var) - n = x.size - y = np.arange(1, n+1) / (n + 1) - return [y, x] - -def ecdf_inverse(p, data, exceedance=False): - """Compute x = F^-1(p) for an empirical distribution.""" - N = len(data) - if exceedance: - p = 1 - p - index = int(np.floor(p*(N + 1))) - x = np.sort(data)[index - 1] - return x - -def semi_log_plots(dist_1, dist_2, exceedance=True): - """Helper function for plot_univariate_comparison. - - dist_1, dist_2: ndarray, list. Empirical distributions. - exceedance: bool. Default (True) plots exceedance, 1 - F(x) - - returns: matplotlib objects fig, ax - """ - fig, ax = plt.subplots(1, 1, figsize=(8, 5)) - - e_dist_1 = ecdf(dist_1) - e_dist_2 = ecdf(dist_2) - if exceedance: - e_dist_1[0] = 1 - e_dist_1[0] - e_dist_2[0] = 1 - e_dist_2[0] - - ax.step(e_dist_1[1], e_dist_1[0], - color='k', label='Data') - ax.step(e_dist_2[1], e_dist_2[0], - color='r', label='MCS Sample') - ax.set_xlabel('$Z(X_1,X_2)$') - ax.set_yscale('log') - ax.legend() - ax.grid() - return fig, ax - -def plot_univariate_comparison(rv_dictionary, dist_key, plot_values): - """Compare univariate plots. - - Assumes model is an empirical distribution (MCS - - rv_dictionary: dict. Created from univariate_RV_dict() - dist_key: str. Name of probability model - plot_values: array, list (size 4). Limits of X and Y, respectively. - returns: none, except printed output. - """ - - data = rv_dictionary["data"] - model = rv_dictionary[dist_key]["sample"] - - fig, ax = plt.subplots(1) - ax.hist([data, model], - bins=plot_values, - density=True, - edgecolor='black'); - ax.legend(['Data', 'MCS Sample']) - ax.set_xlabel('$Z(X_1,X_2)$') - ax.set_ylabel('Empirical Density [--]') - ax.set_title('Comparison of Distributions of $Z$'); - - fig, ax = semi_log_plots(data, model, exceedance=False) - ax.set_ylabel('CDF, $\mathrm{P}[Z < z]$') - ax.set_title('Comparison: CDF (log scale expands lower tail)') - - fig, ax = semi_log_plots(data, model, exceedance=True) - ax.set_ylabel('CDF, $\mathrm{P}[Z < z]$') - ax.set_title('Comparison: CDF (log scale expands lower tail)') \ No newline at end of file diff --git a/figures/template_blank.svg b/figures/template_blank.svg deleted file mode 100644 index 39783aa..0000000 --- a/figures/template_blank.svg +++ /dev/null @@ -1,534 +0,0 @@ - - - - - - - - 2024-02-18T07:45:46.054013 - image/svg+xml - - - Matplotlib v3.8.2, https://matplotlib.org/ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/figures/template_cdf.svg b/figures/template_cdf.svg deleted file mode 100644 index e127582..0000000 --- a/figures/template_cdf.svg +++ /dev/null @@ -1,1191 +0,0 @@ - - - - - - - - 2024-02-18T07:44:25.882057 - image/svg+xml - - - Matplotlib v3.8.2, https://matplotlib.org/ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - diff --git a/figures/template_exp_decay.svg b/figures/template_exp_decay.svg deleted file mode 100644 index e9de5b6..0000000 --- a/figures/template_exp_decay.svg +++ /dev/null @@ -1,1119 +0,0 @@ - - - - - - - - 2024-02-18T07:45:46.459979 - image/svg+xml - - - Matplotlib v3.8.2, https://matplotlib.org/ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -