From 00eab6a5808fe67ecc6ec6b46294485ab4edcbd8 Mon Sep 17 00:00:00 2001 From: Elizaveta Semenova Date: Thu, 14 Nov 2024 18:29:49 +0000 Subject: [PATCH] starts edits for Version 2 --- 01_intro.md | 22 +- 02_about.md | 22 +- 03_intro_epi.md | 59 +- 04_probability_distributions.ipynb | 3096 ++++++++++++++-------------- 06_Monte_Carlo.ipynb | 922 +++++---- 07_MCMC.ipynb | 1324 ++++++------ 6 files changed, 2721 insertions(+), 2724 deletions(-) diff --git a/01_intro.md b/01_intro.md index 1fe50b6..4490a73 100644 --- a/01_intro.md +++ b/01_intro.md @@ -1,12 +1,12 @@ -# Bayesian Modelling and Probabilistic Programming with Numpyro and examples from Epidemiology. +# Bayesian modelling with Numpyro and deep generative surrogates for epidemiology. -Welcome to the course! The course materials are a WORK IN PROGRESS. For the latest version, as the PDF may not render everything correctly, visit . +Welcome to the course! The course materials are a WORK IN PROGRESS. If you are using the PDF, please refer to the online content at for the latest updates, as the PDF may not render everything accurately. ## About the author -These lecture notes were written by Elizaveta (a.k.a. Liza) Semenova. I am a lecturer in Biostatistics, Computational Epidemiology and Machine Learning at Imperial College London. My work is centered around scalable and flexible methods for spatiotemporal statistics and Bayesian machine learning with applications in epidemiology. This course is meant to set you up well for doing similar research. +These lecture notes were written by Elizaveta Semenova (a.k.a. Liza). I am a lecturer in Biostatistics, Computational Epidemiology and Machine Learning at Imperial College London. My work is centered around scalable and flexible methods for spatiotemporal statistics and Bayesian machine learning using probabilsitic programming with applications in epidemiology. This course is meant to set you up well for doing similar research. -Most recently, my focus has been on using deep generative modelling to power MCMC inference in classical spatial statistics, as well as adaptive survey design. Even though this course does not touch these subjects, feel free to reach out to discuss. +Most recently, my focus has been on using deep generative models to power MCMC inference in classical spatial statistics. It turns out that the same method works for a much wider range of applications, including disease transmission modelling! In part, this course does touch on these subjects. Feel free to reach out to discuss the landscape. More details about my work are available [here](https://www.elizaveta-semenova.com/). @@ -27,12 +27,14 @@ Acknowledging here that learning does not always have to be enjoyable. - If you are creating a written document (a paper, report, book chapter) where you use what you've learnt here, please cite ``` -@book{semenova24, - author = {Semenova, Elizaveta}, - title = {Bayesian Modelling and Probabilistic Programming with Numpyro and examples from Epidemiology.}, - year = {2024}, - source = {https://elizavetasemenova.github.io/prob-epi}, - doi = {https://doi.org/10.5281/zenodo.11550659} +@software{Semenova_Bayesian_Modelling_and_2024, +author = {Semenova, Elizaveta}, +doi = {10.5281/zenodo.11550659}, +month = jun, +title = {{Bayesian Modelling and Probabilistic Programming with Numpyro and examples from Epidemiology.}}, +url = {https://github.com/elizavetasemenova/prob-epi}, +version = {v1.0.0}, +year = {2024} } ``` diff --git a/02_about.md b/02_about.md index 8e3ac88..27720d4 100644 --- a/02_about.md +++ b/02_about.md @@ -1,14 +1,26 @@ # About this course -This online book consists of lecture notes of the course which will I taught during three weeks from 25 March to 12 April 2024 to the inaugural MSc ["AI for Science"](https://ai.aims.ac.za/) cohort at the [African Institute for Mathematical Sciences (AIMS)](https://aims.ac.za/), South Africa. +This online book consists of lecture notes of the course which I taught during -## Content +- 25 March to 12 April 2024 to the inaugural cohort, +- 25 November to 13 December 2024 to the second cohort -In this course we will cover such topics as Bayesian inference, hierarchical modelling, Gaussian processes for spatial statistics, ordinary differential equations for disease transmission modelling. +of MSc ["AI for Science"](https://ai.aims.ac.za/) at the [African Institute for Mathematical Sciences (AIMS)](https://aims.ac.za/), South Africa. -We will build probabilistic models and perform inference using a probabilistic programming language `Numpyro` in a fully Bayesian manner to characterise uncertainty of the modelled quantities. -Although the course is primarily computational in nature, the models which we will examine are inspired by the typical modelling practices found in epidemiology. +The title of the course for the first cohort was "Bayesian Modelling and Probabilistic Programming with Numpyro and examples from Epidemiology''. + +The title of the course for the second cohort is "Bayesian Modelling with Numpyro and Deep Generative Surrogates for Epidemiology''. + +## Abstract + +In this course we will explore a range of topics in Bayesian modelling, such as Bayesian inference, hierarchical modelling, Gaussian processes for spatial statistics, ordinary differential equations and agent-based models for disease transmission modelling. + +Using the probabilistic programming language `Numpyro`, we will construct probabilistic models and perform Bayesian inference to quantify uncertainty in model predictions and parameter estimates. + +As the course progresses, we will introduce deep generative models as efficient surrogates for computationally demanding model components (yes, this is 'generative AI'!). These surrogates, implemented in `JAX`, will be integrated seamlessly into Numpyro programs, enabling fast and scalable MCMC inference. + +While the course emphasises computational techniques, the models and applications are rooted in real-world epidemiology, providing a practical framework for data-driven decision-making in health research. ## Prerequisites diff --git a/03_intro_epi.md b/03_intro_epi.md index 24282c0..9fb147f 100644 --- a/03_intro_epi.md +++ b/03_intro_epi.md @@ -1,4 +1,4 @@ -# Introduction to Modelling in epidemiology +# Introduction to modelling in epidemiology In this course we will consider a range of models used in epidemiology - from hierarchical modelling and spatial statistics to disease transmission modelling - and their probabilistic (Bayesian) formulation. In order to perform Bayesian inference we will use the probabilistic programing language (PPL) Numpyro. @@ -7,9 +7,9 @@ Let's uncover each of the three key terms of the course - **epidemiology**, **Ba (epidemiology)= ## Epidemiology -Epidemiology serves as the underlying rationale in this course, explaining WHY we develop the probabilistic models we'll be examining. Essentially, it addresses the question: 'What real-world phenomena are we aiming to analyze using these models?' +Epidemiology serves as the underlying rationale in this course, explaining WHY we develop the probabilistic models we'll be examining. Essentially, it addresses the question: 'What real-world phenomena are we aiming to analyse using these models?' -Epidemiology is the study of how diseases and health-related events are distributed within populations and the factors that influence these distributions. It is a branch of public health that focuses on understanding the patterns, causes, and effects of diseases and health conditions on a large scale. Epidemiologists collect and analyze *data* to investigate the occurrence of health outcomes, their risk factors, and the impact of various interventions or preventive measures. +Epidemiology studies human health. To be more specific, it is the study of how diseases and health-related events are distributed within populations and the factors that influence these distributions. It is a branch of public health that focuses on understanding the patterns, causes, and effects of diseases and health conditions on a large scale. Epidemiologists collect and analyse *data* to investigate the occurrence of health outcomes, their risk factors, and the impact of various interventions or preventive measures. Epidemiological studies are essential for understanding the health of populations, identifying health disparities, and guiding public health efforts to improve the well-being of communities and societies. @@ -19,20 +19,22 @@ Here is a few examples of epidemiological study types. ```{margin} If the surveillance tackles purely the temporal development of a health outcome, it suffices to construct temporal models. If space is also of interest, one needs to build spatial or spatiotemporal models. ``` -- **Disease Surveillance:** Epidemiologists monitor the occurrence of diseases and health-related events over time and across different geographic areas. This involves tracking the number of cases, identifying outbreaks, and assessing trends in disease incidence and prevalence. Disease surveillance can be conducted for both infectious and non-infectious diseases. +- **Disease Surveillance:** epidemiologists monitor the occurrence of diseases and health-related events over time and across different geographic areas. This involves tracking the number of cases, identifying outbreaks, and assessing trends in disease incidence and prevalence. Disease surveillance can be conducted for both infectious and non-infectious diseases. -- **Outbreak Investigation:** Epidemiologists are often involved in investigating disease outbreaks, such as foodborne illnesses, infectious disease outbreaks, or clusters of chronic diseases. They work to identify the source of the outbreak and implement measures to contain and prevent further spread. +- **Identifying Risk Factors:** epidemiological studies aim to identify the factors that are associated with increased likelihood of developing a particular disease. These risk factors can include genetic predisposition, environmental exposures, lifestyle choices, and social determinants of health. + +- **Disease Prevention and Control:** the insights gained from epidemiological research are crucial for designing and implementing public health interventions and policies aimed at preventing and controlling diseases. This may involve vaccination campaigns, health education programs, quarantine measures, and more. + +- **Outbreak Investigation:** epidemiologists are often involved in investigating disease outbreaks, such as foodborne illnesses, infectious disease outbreaks, or clusters of chronic diseases. They work to identify the source of the outbreak and implement measures to contain and prevent further spread. ```{margin} -It is important to distinguish associative studies with those where researchers try to oncover causal relationships between risk factors and outcomes. +It is important to distinguish associative studies with those where researchers try to uncover causal relationships between risk factors and outcomes. ``` -- **Identifying Risk Factors:** Epidemiological studies aim to identify the factors that are associated with increases likelihood of developing a particular disease. These risk factors can include genetic predisposition, environmental exposures, lifestyle choices, and social determinants of health. -- **Disease Prevention and Control:** The insights gained from epidemiological research are crucial for designing and implementing public health interventions and policies aimed at preventing and controlling diseases. This may involve vaccination campaigns, health education programs, quarantine measures, and more. +- **Public Health Planning:** epidemiological data and findings play a vital role in informing public health planning and resource allocation. This includes assessing healthcare needs, identifying at-risk populations, and developing strategies to improve overall health outcomes. -- **Public Health Planning:** Epidemiological data and findings play a vital role in informing public health planning and resource allocation. This includes assessing healthcare needs, identifying at-risk populations, and developing strategies to improve overall health outcomes. -- **Causality Assessment:** Epidemiologists use various study designs, including cohort studies, case-control studies, and randomized controlled trials, to determine if a specific factor or intervention causes a particular health outcome. +- **Causality Assessment:** epidemiologists use various study designs, including cohort studies, case-control studies, and randomized controlled trials, to determine if a specific factor or intervention causes a particular health outcome. Mathematical and statistical models are frequently used in epidemiology to simulate disease spread and estimate disease distribution. These models help in making informed decisions and planning interventions. @@ -43,7 +45,7 @@ Some models that we will build in this course are more relevant to generative AI and deep generative modelling (DGM). It is indeed the same 'generative' idea as we are talking here about. The difference is that DGM uses deep learning and neural network for the generative mechanism, and in traditional epidemiology it is more common to use statistical and mechanistic models for such generation. Having said that, we will touch DGMs in this course too. ``` -Bayesian modelling represents the fundamental focus of this course, addressing the question of "WHAT models can describe the generative process behind the observed data?" Throughout the course, we will use the terms "Bayesian" and "probabilistic" interchangeably. +Bayesian modelling represents the fundamental focus of this course, addressing the question of "WHAT models can describe the generative process behind the observed data?". Throughout the course, we will use the terms "Bayesian" and "probabilistic" interchangeably. Probabilistic modelling is a mathematical and statistical framework used to incorporate uncertainty and randomness into models to account for variability and its sources in real-world phenomena. It involves using probability theory to describe and quantify the uncertainty associated with different events, outcomes, or variables. The primary goal of probabilistic modelling is to make predictions, infer information, or make decisions in situations where there is inherent uncertainty. Probabilistic modelling is a powerful tool for dealing with real-world complexities in a quantitative manner. It plays a crucial role in data analysis, machine learning, and decision-making processes where probabilistic reasoning is necessary. @@ -51,48 +53,47 @@ Probabilistic modelling in epidemiology helps epidemiologists and public health Some key concepts and components of probabilistic modelling are as follows: -- **Random Variables:** In probabilistic modelling, random variables are used to represent uncertain quantities or events. These variables can take on different values with associated probabilities. +- **Random variables:** in probabilistic modelling, random variables are used to represent uncertain quantities or events. These variables can take on different values with associated probabilities. -- **Probability Distributions:** A probability distribution describes how the values of a random variable are distributed or spread out. +- **Probability distributions:** a probability distribution describes how the values of a random variable are distributed or spread out. -- **Parameters:** Probability distributions are often characterized by parameters that determine their shape and behavior. For example, the mean and standard deviation of a normal distribution are parameters that describe its central tendency and spread. +- **Parameters:** probability distributions are often characterized by parameters that determine their shape and behavior. For example, the mean and standard deviation of a normal distribution are parameters that describe its central tendency and spread. -- **Bayesian Inference:** Bayesian probabilistic modelling is a framework that uses Bayes' theorem to update the probability distribution of a random variable based on new evidence or data. It combines prior beliefs (prior distribution) with observed data to form a posterior distribution, which represents the updated beliefs. +- **Bayesian inference:** Bayesian probabilistic modelling is a framework that uses Bayes' theorem to update the probability distribution of a random variable based on new evidence or data. It combines prior beliefs (prior distribution) with observed data to form a posterior distribution, which represents the updated beliefs. -- **Monte Carlo Methods:** Monte Carlo methods are a class of computational techniques used to estimate complex probabilistic models through random sampling. They involve generating random samples from probability distributions to approximate quantities of interest. +- **Monte Carlo methods:** Monte Carlo methods are a class of computational techniques used to estimate complex probabilistic models through random sampling. They involve generating random samples from probability distributions to approximate quantities of interest. ## Probabilistic programming -Probabilistic programming is a specialized approach to building and analyzing probabilistic models that offers several advantages for epidemiology and the study of infectious disease dynamics: - -- **Flexibility:** Probabilistic programming languages(PPLs), such as Stan, Pyro, Numpyro, PyMC, Turing.jl and other, provide a flexible framework for defining and customizing probabilistic models. This flexibility is crucial in epidemiology, where the complexity of disease transmission models can vary widely depending on the specific disease and the population under study. +Probabilistic programming is a specialised approach to building and analysing probabilistic models that offers several advantages for epidemiology and the study of infectious disease dynamics: -- **Abstract modelling from inference:** Probabilistic programming languages abstract model formulation from inference. We can focus on the applied question, and do not need to write samplers by hand. Instead, we can use robus and tests in battle samples provided by the PPLs. +- **Flexibility:** probabilistic programming languages (PPLs), such as Stan, Pyro, Numpyro, PyMC, Turing.jl and other, provide a flexible framework for defining and customising probabilistic models. This flexibility is crucial in epidemiology, where the complexity of disease transmission models can vary widely depending on the specific disease and the population under study. -- **Uncertainty Quantification:** Probabilistic programming allows for the explicit representation and quantification of uncertainty. Epidemiological models often involve uncertain parameters and data, and probabilistic programming makes it easier to incorporate this uncertainty into the modelling process. +- **Abstract modelling from inference:** probabilistic programming languages abstract model formulation from inference. We can focus on the applied question, and do not need to write samplers by hand. Instead, we can use robus and tests in battle samples provided by the PPLs. +- **Uncertainty quantification:** probabilistic programming allows for the explicit representation and quantification of uncertainty. Epidemiological models often involve uncertain parameters and data, and probabilistic programming makes it easier to incorporate this uncertainty into the modelling process. -- **Model Validation:** Probabilistic programming facilitates model validation by enabling researchers to compare model predictions with observed data using techniques like posterior predictive checks. +- **Hierarchical modelling:** many epidemiological models involve hierarchical structures, where data at multiple levels (e.g., individuals, households, communities) are analysed simultaneously. Probabilistic programming makes it easier to specify and fit hierarchical models capturing such structure. -- **Hierarchical modelling:** Many epidemiological models involve hierarchical structures, where data at multiple levels (e.g., individuals, households, communities) are analyzed simultaneously. Probabilistic programming makes it easier to specify and fit hierarchical models capturing such structure. +- **Model validation:** probabilistic programming facilitates model validation by enabling researchers to compare model predictions with observed data using techniques like posterior predictive checks. -- **Data Integration:** Probabilistic programming facilitates the integration of various types of data. This integration can improve the accuracy and informativeness of epidemiological models. +- **Model selection and comparison:** epidemiologists often need to compare different model structures or assess the fit of alternative hypotheses. Probabilistic programming facilitates model selection and comparison through techniques like Bayesian model averaging and model evidence calculation. -- **Model Selection and Comparison:** Epidemiologists often need to compare different model structures or assess the fit of alternative hypotheses. Probabilistic programming facilitates model selection and comparison through techniques like Bayesian model averaging and model evidence calculation. +- **Data integration:** probabilistic programming can enable the integration of various types of data. This integration can improve the accuracy and informativeness of epidemiological models. -- **Transparent Communication:** Probabilistic programming encourages transparency in modelling and analysis. Researchers can clearly specify their assumptions, priors, and likelihood functions, making it easier to communicate and collaborate with other experts and stakeholders. +- **Transparent communication:** probabilistic programming encourages transparency in modelling and analysis. Researchers can clearly specify their assumptions, priors, and likelihood functions, making it easier to communicate and collaborate with other experts and stakeholders. -- **Extensible Libraries:** Probabilistic programming languages often come with extensive libraries and tools for model development, inference, and visualization, reducing the implementation and computation burden. +- **Extensible libraries:** probabilistic programming languages often come with extensive libraries and tools for model development, inference, and visualization, reducing the implementation and computation burden. `````{admonition} Task 01 :class: tip -Find a publication that applies Bayesian inference in the field of epidemiology, such as in spatial statistics or disease transmission modeling. +Find a publication that applies Bayesian inference in the field of epidemiology, such as in spatial statistics or disease transmission modelling. - Identify which Bayesian methods (such as MCMC, VI, ABC, etc) and models were employed in the paper. -- Determine the inference tools applied in the study, such as PPL usage, custom MCMC samplers, or specialized libraries. +- Determine the inference tools applied in the study, such as PPL usage, custom MCMC samplers, or specialised libraries. - Do you think the modelling part of the study could be improved or extended in some way? ````` \ No newline at end of file diff --git a/04_probability_distributions.ipynb b/04_probability_distributions.ipynb index 4238a25..3aacf22 100644 --- a/04_probability_distributions.ipynb +++ b/04_probability_distributions.ipynb @@ -1,1558 +1,1548 @@ { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Probability Distributions and Random Variables" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Throughout the course we will work with probability distributions. Hence, it is important to master the basic principles of probability distributions, and learn to manipulate probabilities in code.\n", - "\n", - "Probability distributions and random variables serve as tools for describing and performing calculations related to random events, specifically those whose outcomes are uncertain. \n", - "\n", - "An illustrative example of such an uncertain event would be the act of flipping a coin or rolling a dice. In the former case, the potential outcomes are heads or tails. \n", - "\n", - "An example of a random event from epidemiology, is the number of disease cases $y(t)$ on a given day $t$.\n", - "\n", - "In the context of epidemiological modelling, we will encounter data of different types and origin. It is crucial to grasp the suitability of different probability distributions for modeling specific types of data.\n", - "\n", - "Since the probabilistic programming language that we will be using for this course is Numpyro, also in this section we will use the implementations of distributions from this library avalable via `import numpyro.distributions as dist`" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "# uncomment this line on Colab\n", - "# !pip install numpyro" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "```{margin}\n", - "In all notebooks of this course, we will always import all necessary libraries in the first code cell.\n", - "```" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "/opt/anaconda3/envs/aims/lib/python3.9/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n", - " from .autonotebook import tqdm as notebook_tqdm\n" - ] - } - ], - "source": [ - "import jax\n", - "import jax.numpy as jnp\n", - "\n", - "# distributions\n", - "import numpyro.distributions as dist\n", - "\n", - "import matplotlib.pyplot as plt\n", - "\n", - "# Since we are using jax, we will need a random key:\n", - "rng = jax.random.PRNGKey(42)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Discrete Distributions\n", - "\n", - "Discrete probability distributions represent the probabilities of distinct outcomes in a finite or countably infinite sample space." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The Bernoulli distribution\n", - "\n", - "A Bernoulli distribution is used to describe random events with two possible outcomes e.g. when we have a random variable $X$ that takes on one of the two values $x \\in \\{0, 1\\}$ with probabilities $1-p$ and $p, 0 \\le p \\le 1$ respectively:\n", - "\n", - "\\begin{align*}\n", - "p(X = 1) &= p, \\\\\n", - "p(X = 0) &= 1 - p.\n", - "\\end{align*}\n", - "\n", - "Here $p$ is the probability of the 'positive' outcome. For example, in the case of a *fair* coin toss, $p = 0.5$ so that both outcomes have a 50\\% chance of occurring.\n", - "\n", - "We will be denoting this distribution as \n", - "\n", - "$$\n", - "X \\sim \\mathcal{Bern}(p).\n", - "$$\n", - "\n", - "or, equivalently, \n", - "\n", - "$$\n", - "\\mathcal{Bern}(X | p).\n", - "$$\n", - "\n", - "#### Probability mass function\n", - "A *discrete* probability distribution can be uniquely defined by its probability mass function (PMF).\n", - "\n", - "```{margin}\n", - "The term 'mass' is used to underline that the support of the distribution is discrete, and each possible value carries a certain `mass` (probability).\n", - "For continuous distributions, the analogous is probability density function (PDF), we will see those later.\n", - "```\n", - "For the Bernoulli distribution, we write the PMF as\n", - "\n", - "\\begin{align*}\n", - "p(X = x) = \\mathcal{Bern}(X\\mid p) &= \\begin{cases}\n", - "p\\, & \\text{if } x = 1 \\\\\n", - "1 - p\\, & \\text{if } x = 0\n", - "\\end{cases} \\\\\n", - "&= p^x(1-p)^{1-x}.\n", - "\\end{align*}\n", - "\n", - "`````{admonition} Task 02\n", - ":class: tip\n", - "Convince yourself that the two definitions of the Bernoulli distribution shown above are equivalent.\n", - "`````\n", - "\n", - "Now let's construct a Bernoulli distribution in code." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Drawing a sample\n", - "\n", - "We construct the distribution with a certain value of the parameter `p`:" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "p = jnp.array(0.5)\n", - "bernoulli = dist.Bernoulli(probs=p)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "```{margin}\n", - "We can think of a sample as a realisation of a random variable. \n", - "```\n", - "Now that we have constructed the distribution we can get a sample from it:" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "1\n" - ] - } - ], - "source": [ - "sample = bernoulli.sample(key=rng)\n", - "print(sample)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "And we can evaluate the probability of observing a sample.\n", - "\n", - "**Note:** the distribution objects in `numpyro` (and most other libraries for probability distributions) return log-probabilities rather than raw probabilities. This means that we need to take the exponent if we want to know the probability." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "log p(X = 1) = -0.6931471824645996\n", - "p(X = 1) = 0.5\n" - ] - } - ], - "source": [ - "log_prob = bernoulli.log_prob(sample)\n", - "print(f\"log p(X = {sample}) = {log_prob}\")\n", - "print(f\"p(X = {sample}) = {jnp.exp(log_prob)}\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As expected, we get a probability of 0.5." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Multiple samples\n", - "\n", - "We can also easily get multiple samples in one command by including `sample_shape`:\n", - "\n", - "```{margin}\n", - "Multiple samples are different realisations of the same random variable.\n", - "```" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[0 0 1 1 0 1 1]\n" - ] - } - ], - "source": [ - "n_samps = 7\n", - "samples = bernoulli.sample(key=rng, sample_shape=(n_samps,))\n", - "print(samples)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "What if we wanted to evaluate the probability of observing all of our samples?\n", - "\n", - "The `bernoulli` object we created earlier treats each sample individually and returns the probabilities of observing each sample on its own:" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[0.5 0.5 0.5 0.5 0.5 0.5 0.5]\n" - ] - } - ], - "source": [ - "individual_sample_probs = jnp.exp(bernoulli.log_prob(samples))\n", - "print(individual_sample_probs)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "But, we can use one of the laws of probability to compute the probability of observing all of the samples together, i.e. jointly:\n", - "\n", - "\\begin{align*}\n", - "p(X_1=x_1, X_2=x_2, \\dots, X_N=x_n) = \\prod_{n=1}^N p(X_n=x_n).\n", - "\\end{align*}\n", - "\n", - "This is called the product rule of probability, and it says that for independent random variables, the joint probability (i.e., the probability of observing them all together) is equal to the product of the individual probabilities.\n", - "\n", - "Now, let's calculate the joint probability of our samples.\n", - "\n", - "```{margin}\n", - "Working with log-probabilities is preferable due to numerical stability, computational efficiency, and ease of handling multiplicative operations.\n", - "```" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.0078125\n" - ] - } - ], - "source": [ - "joint_prob = jnp.prod(individual_sample_probs)\n", - "print(joint_prob)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Visualise PMF\n", - "\n", - "Now let's visualise the PMF:" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [], - "source": [ - "def Bernouilli_vis(rng, p, n_samps):\n", - "\n", - " # define distribution\n", - " bernoulli = dist.Bernoulli(probs=p)\n", - "\n", - " # collect samples\n", - " samples = bernoulli.sample(key=rng, sample_shape=(n_samps,))\n", - "\n", - " # how many ones\n", - " num_ones = (samples == 1.).sum()\n", - "\n", - " # how many zeros\n", - " num_zeros = (samples == 0.).sum()\n", - "\n", - " # plot\n", - " fig = plt.figure(dpi=100, figsize=(5, 3))\n", - " ax = fig.add_subplot(1, 1, 1)\n", - " ax.bar([0, 1], [num_zeros/n_samps, num_ones/n_samps], alpha=0.7, color='teal')\n", - " \n", - " ax.set_xticks([0, 1])\n", - " ax.set_xlabel('Outcome (x)')\n", - " ax.set_ylabel('Probability Mass p(X=x)')\n", - " ax.set_title(f'Bernoulli Distribution (p={p})')\n", - " ax.grid(True)\n", - " \n", - " plt.show()\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "Bernouilli_vis(rng, p=0.2, n_samps=10)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`````{admonition} Task 03\n", - ":class: tip\n", - "Recreate this plot using `bernoulli.log_prob(sample)` functionality (see examples below).\n", - "`````" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "Bernouilli_vis(rng, p=0.7, n_samps=100)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`````{admonition} Task 04\n", - ":class: tip\n", - "Plot a panel of histograms where you vary probability $p$ horizontally and number of samples $n$ vertically. What do you observe?\n", - "`````" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Common usage\n", - "\n", - "Bernoulli distribution is commonly used as a likelihood in models with binary outcomes, such as presence or absence of a disease." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The Binomial distribution\n", - "\n", - "A binomial distribution is a discrete probability distribution that models the number of successes $x$ in a fixed number $n$ of independent and identical Bernoulli trials, where each trial has only two possible outcomes: \"success\" (represented as \"1\") with probability $p$ or \"failure\" (represented as \"0\") with probability $1-p$.\n", - "\n", - "We will use the notation \n", - "\n", - "$$\n", - "X \\sim \\mathcal{Binom}(n,p)\n", - "$$\n", - "\n", - "#### Probability mass function\n", - "\n", - "The PMF of the Binomial distribution is\n", - "\n", - "$$P(X = x) = \\binom{n}{x} p^x (1 - p)^{n - x},$$\n", - "\n", - "where\n", - "\n", - "- $P(X = x)$ is the probability of getting exactly $x$ successes,\n", - "\n", - "- $\\binom{n}{x}$ is the binomial coefficient, representing the number of ways to choose $x$ successes out of $n$ trials,\n", - "\n", - "- $p$ is the probability of success on a single trial,\n", - "\n", - "- $1-p$ is the probability of failure on a single trial,\n", - "\n", - "- the number of successes $x$ ranges from $0$ to $n$ inclusive.\n", - "\n", - "`````{admonition} Task 05\n", - ":class: tip\n", - "Compute $\\sum_{x=0}^n P(X=x)$.\n", - "`````\n", - "\n", - "#### Drawing a sample" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As before, we begin by constructing the distribution:" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [], - "source": [ - "p = 0.3\n", - "n = 10\n", - "binomial = dist.Binomial(total_count=n, probs=p)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now we can draw a sample from this distribution:" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "4\n" - ] - } - ], - "source": [ - "sample = binomial.sample(key=rng)\n", - "print(sample)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`````{admonition} Task 06\n", - ":class: tip\n", - "Draw several samples from this distribution using different keys. And draw repeatedly several samples with the same key. What do you conclude about the role of `key` in reproducibility of numerical experiments?\n", - "`````" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "What is the probability to observe this sample?" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "log p(X = 4) = -1.608832836151123\n", - "p(X = 4) = 0.20012104511260986\n" - ] - } - ], - "source": [ - "log_prob = binomial.log_prob(sample)\n", - "print(f\"log p(X = {sample}) = {log_prob}\")\n", - "print(f\"p(X = {sample}) = {jnp.exp(log_prob)}\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Multiple samples" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let us generate several samples: " - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[3 6 1 3 2 4 5]\n" - ] - } - ], - "source": [ - "n_samps = 7\n", - "samples = binomial.sample(key=rng, sample_shape=(n_samps,))\n", - "print(samples)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Individual probabilities to observe the samples:" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[0.26682812 0.03675695 0.12106086 0.26682812 0.23347507 0.20012105\n", - " 0.10291947]\n" - ] - } - ], - "source": [ - "individual_sample_probs = jnp.exp(binomial.log_prob(samples))\n", - "print(individual_sample_probs)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Assuming that the samples are independent, what is the joint probability of observeing them?" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "1.5234818e-06\n" - ] - } - ], - "source": [ - "joint_prob = jnp.prod(individual_sample_probs)\n", - "print(joint_prob)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Visualise PMF" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [], - "source": [ - "def binomial_vis(rng, p, n, x_ticks=True):\n", - " \n", - " # Binomial distribution with n trials and probability of success p\n", - " binomial = dist.Binomial(total_count=n, probs=p)\n", - " \n", - " # Generate the possible outcomes (x values)\n", - " x_values = jnp.arange(0, n + 1)\n", - "\n", - " pmf_values = jnp.exp(binomial.log_prob(x_values))\n", - "\n", - " # Create a bar plot (PMF plot)\n", - " fig = plt.figure(dpi=100, figsize=(5, 3))\n", - " plt.bar(x_values, pmf_values, align='center', alpha=0.7, color='teal')\n", - " plt.xlabel('Number of Successes (x)')\n", - " plt.ylabel('Probability Mass p(X=x)')\n", - " plt.title(f'Binomial Distribution (n={n}, p={p})')\n", - " if x_ticks:\n", - " plt.xticks(x_values)\n", - " plt.grid( linestyle='--', alpha=0.7)\n", - "\n", - " plt.show()\n" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "binomial_vis(rng, p=0.2, n=100, x_ticks=False)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`````{admonition} Task 07\n", - ":class: tip\n", - "What is qualitatively different between the shapes of distributions `Bernoulli(p=0.2, n=6)` and `Bernoulli(p=0.2, n=100)`?\n", - "`````" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "#### Common usage\n", - "\n", - "Binomial distribution is commonly used as a likelihood in models with binary outcomes with multiple experiments. For example, to model disease prevalence." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The Categorical distribution\n", - "\n", - "A categorical distribution is used to model random events with multiple discrete unordered outcomes, such as the die-rolling event from above. \n", - "\n", - "We can characterise the categorical distribution with its PMF:" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "\\begin{align*}\n", - "p(X = x) = \\mathcal{Categorical}(X \\mid p) = \\prod_{k=1}^K p_k^{I_{x=k}},\n", - "\\end{align*}\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "where $K$ is the number of possible outcomes, $p_k$ is the probability of the $k$th outcome, and $I_{x=k}$ is the indicator function which evaluates to 1 if $x = k$ and 0 otherwise. All porbabilties $p_k$ form a vector" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "$$\n", - "p = \n", - "\\begin{pmatrix}\n", - "p_1\\\\ \n", - "p_2\\\\\n", - "\\dots \\\\ \n", - "p_K\n", - "\\end{pmatrix},\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "\n", - "such that \n", - "\n", - "$$\n", - "\\sum_k p_k = 1.\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`````{admonition} Task 08\n", - ":class: tip\n", - "Explain why a categorical distribution with $K = 2$ is equivalent to a Bernoulli distribution.\n", - "`````" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [], - "source": [ - "ps = jnp.array([0.1, 0.2, 0.3, 0.4])\n", - "categorical = dist.Categorical(probs=ps)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As before we can take some samples:" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[3 2 1 3 3 1 2 1 3 3]\n" - ] - } - ], - "source": [ - "samples = categorical.sample(key=rng, sample_shape=(10,))\n", - "print(samples)" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "p(X=0) = 0.1\n", - "p(X=1) = 0.2\n", - "p(X=2) = 0.3\n", - "p(X=3) = 0.4\n" - ] - } - ], - "source": [ - "print(f\"p(X=0) = {jnp.exp(categorical.log_prob(0)):.1f}\")\n", - "print(f\"p(X=1) = {jnp.exp(categorical.log_prob(1)):.1f}\")\n", - "print(f\"p(X=2) = {jnp.exp(categorical.log_prob(2)):.1f}\")\n", - "print(f\"p(X=3) = {jnp.exp(categorical.log_prob(3)):.1f}\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We can use an alternative way to represent the categorical distribution. Instead of specifying the probabilities $p_k$, we specify logits $l_k$. Each $p_k$ is then computed as\n", - "\n", - "$$\n", - "p_k = \\frac{\\exp(l_k)}{\\sum_{k'}\\exp(l_{k'})},\n", - "$$\n", - "\n", - "i.e., using the softmax function." - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "l_0 = 0.7 \n", - "l_1 = 0.3 \n", - "l_2 = 2 \n", - "l_3 = 1.6\n", - "\n", - "logits = jnp.array([l_0, l_1, l_2, l_3], dtype=jnp.float32)\n", - "categorical = dist.Categorical(logits=logits)\n", - "samples = categorical.sample(key=rng, sample_shape=(1000,))\n", - "\n", - "values =[0, 1, 2, 3]\n", - "num_bins = len(values)\n", - "\n", - "hist, _ = jnp.histogram(samples, bins=num_bins, density=True)\n", - "\n", - "fig = plt.figure(dpi=100, figsize=(5, 3))\n", - "plt.bar(values, hist, color='teal', alpha=0.7)\n", - "plt.xticks(values)\n", - "plt.xlabel('x')\n", - "plt.ylabel('p(X=x)')\n", - "plt.grid(linestyle='--', alpha=0.7)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The Ordinal distribution\n", - "\n", - "The ordinal distribution is a probability distribution used to model outcomes that are ranked or ordered, often encountered in scenarios where data points lack clear numerical interpretation but possess a defined order of precedence. It assigns probabilities to different rank orders, capturing the relative likelihood of each outcome's position within the ordered set." - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "metadata": {}, - "outputs": [], - "source": [ - "# Define study hours for each student\n", - "study_hours = jnp.array([5, 7, 3, 10, 8, 6, 4, 9, 2, 7])\n", - "\n", - "# Define cutpoints for the ordered categories\n", - "cutpoints = jnp.array([0., 5., 7., 10.]) # Ordered categories: (0, 5], (5, 7], (7, 10]\n", - "\n", - "# Sample logits (unnormalized probabilities) based on study hours\n", - "logits = 0.5 * study_hours\n", - "\n", - "ordinal = dist.OrderedLogistic(logits, cutpoints)" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "metadata": {}, - "outputs": [], - "source": [ - "# Sample from the OrderedLogistic distribution\n", - "ordinal = dist.OrderedLogistic(logits, cutpoints)\n", - "samples = ordinal.sample(rng, (1000,))\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Continuous Distributions\n", - "\n", - "Continuous probability distributions describe the probabilities of outcomes within a continuous range of values.\n", - "\n", - "### The Beta distribution\n", - "\n", - "The Beta distribution is a continuous distribution with support in $[0,1] \\subset \\mathbb{R}$.\n", - "The Beta distribution can be used to describe a continuous random variable between 0 and 1, for example, percentages and ratios. It has the following form\n", - "```{margin}\n", - "Note that in this distribution more than one parameter defines its shape.\n", - "```\n", - "\n", - "$$\n", - "p(X = x) = \\mathcal{Beta}(x|\\alpha,\\beta) = \\frac{1}{\\mathrm{B}(\\alpha,\\beta)}x^{\\alpha-1}(1 - x)^{\\beta - 1},\n", - "$$\n", - "\n", - "where $\\alpha > 0$ and $\\beta > 0$ are the two shape parameters of the distribution, and $\\mathrm{B}$ is called the beta function. \n", - "\n", - "Let's visualise the distribution.\n", - "\n", - "`````{admonition} Task 09\n", - ":class: tip\n", - "* Try making each parameter big or small while leaving the other at the same value.\n", - "* Then try make them both big or small.\n", - "`````" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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MYOmUKSyePJmyoiLGZGYO/ObxeKisrGT58uUDs6wYY2ju7mZPczNbGhrYVF9PS3c3T+zfzxP79zO/qIh3L1rE8mnTUtphpkOdiYZ466KOUlGUEdPR28vfdu7k4b178dgh+1PHjmVtWRmrZ81iUl5eRPsTESaOGcPEMWM4f8YMjDHsbGzkiX37eOnQIfa0tPCd559n7vjx3LRsGYsmTRqNYikKoI5SUZQR4PH5eHD3bv62cycnT50CoHziRK4rL+ec6dNxxai1JyIsmjSJRZMm8ZGeHu6vruaRvXvZd+IEt6xbx+qZM7lx6VImjBkTk+Mpij/qKKPE5XJRUlKi3SEBqC6hSTVt9jY387NXX6WutRWA2QUF3LBkCcumTo2oOzRSXQpycvjw0qVcV17O/732Go/v28fzr7/O5oYG/uPss1kze3bKdMemWp2JFfHWRYN5FEWJCI/Px33btvHvmhoMkJ+VxY1Ll/LmOXMccVD7W1r4xaZN7G1pAeCCGTP49DnnkJeVFXdblORC53odZbxeL9XV1Xi9XqdNSShUl9Ckgjb1HR18+ckn+ZftJNfMmsUv3/pWLiktjdpJjlSXsqIifnDppbz/rLNwi/DSoUN8/oknOGC3dJOZVKgzo0G8dVFHGSXGGNra2ki3FvlwqC6hSXZtXjh4kM8+/jj7TpwgPyuLW1et4ovnn09BTs6I9hsLXdwuF9cvWsQP165l0pgxNHR28qUnn+SFgwdHZJvTJHudGS3irYs6SkVRhsQYwx+2beOODRvo8XhYVFzMTy+/nHNLSpw27TTmFhXx48suY8nkyfR6vdyxYQP/2LVLHY0yItRRKooSku5Tp/j+Cy/wt127ALhu4UK+/+Y3MzGBo0vzs7O57eKLuXbhQgD+d9s2fr1lizpLJWocdZQicouIbBKRDhE5LiL/FpEFYWx3kYhsFpEeEakVkY/Hw15/XC4XpaWlGo0WgOoSmmTT5kR3N199+mleOXKETJeLL5x3Hh9eujRmQz76GQ1dXCLcuHQpH1m6FICH9uzhhxs24E2y5aqSrc7Ei3jr4mjUq4g8DvwF2IQ1VOX7wFnAGcaYkyG2mQPsAH4N/Aq4ALgbeI8x5p9hHFOjXhVlGI52dvLNZ5+lobOTwpwcbl21igUTJzptVlQ8f/Agd738Mh6fj1UzZ/LFlStxq+NRSJKoV2PMZcaYe40xO40x24APAzOBs4fY7OPA68aYzxljqo0xvwF+B3wpDiYP4PV62bZtm0ajBaC6hCZZtDnQ2spXnnqKhs5OJuflcccll4yqkxxtXVbPmsUtF15IhsvFC6+/zp0bNyZNyzJZ6ky8ibcuiTbhQIH9t2WIPCuBJwPSngBuEpFMY8wp/x9EJBvI9kvKB2t+SY/HA1jNeJfLhc/nG7Ridn+61+sd9H7D5XJhjKGrqwuPxzPwm9vtRkQG9tuP217xIPCkhkrPyMjAGDMoXURwu92n2RgqPZoyBUuPtEzBdEn2MsXqPAXTJtHKdLC9na8/8wydvb3MKizkW6tXD8x2M1rnyefz0d3dfVqdieV5WjFtGl867zzu2LCB5w4cQIAvnn8+xpiErnt6PQW33ev10t3dHdLGSOpeOCSMoxRrENadwIvGmB1DZJ0CHAtIO4ZVlolAQ8BvtwDfCtxJVVUVefb8k8XFxZSVlVFXV0djY+NAnpKSEkpKStizZw9tbW0D6aWlpRQVFdHR0cGWLVsGxo8tXLiQwsJCqqqqBp3sxYsXk5WVRWVl5SAbli9fTl9fH9u3bx9Ic7vdrFixgra2NmpqagbSc3NzqaiooKmpidra2oH0goICysvLqa+v5/DhwwPp0ZRp0qRJ7Nixg+7u7oH0SMu0dOlSfD7fIF2SvUyxOk/z5s2jp6dnkDaJVKajvb38tamJ1q4uJhjDOwoKqN25k4ZRPk+zZs0CYNeuXfT6rRgS6/PkbmjgyvHj+UNtLQ+99hoT8/K4Ytq0hK57ej0FL1N+fj4ADQ0NNDS8ccuPtEzFxcWEQ8LMzCMivwDeClxojDk8RL49wO+NMbf7pV0AvAhMNcYcDcgfrEV5uLm5eeAdZTRPVj6fj02bNrFs2bKBJyRtUVpPwJWVlYN0SfYyxbJFGVhnEqVMB1pb+cb69XSeOsX8oiK+tXr1wAofo32e+h3B0qVLB9WZ0TpPz9TV8dNNmxARblqyhCvnzYt5mfR6Gv0WZVVVFcuWLRsU0BNpmTo7Oxk/fjwkw3qUIvIz4BpgtTGmbpi8zwNVxpjP+qVdC/wNGBPY9Rpk+5gE8/QPeC0oKEiZeSVjgeoSmkTV5lBbG7esW0dbby/zior47sUXx3X6Nyd0+fvOndy3fTsC/OcFF3DBzJlxOW6kJGqdcZpY6ZIUwTxi8XPgOuBNwzlJm43ApQFpa4HK4ZxkLBERCgsLtfIGoLqEJhG1aerq4pvr19PW28vc8ePj7iTBGV3eccYZXDlvHga46+WXqT1xIm7HjoRErDOJQLx1cTpG+hfA+4H3Ah0iMsX+5PZnEJHbReQ+v23uAWaJyJ0iUi4iNwI3AT+Mp+Eej4dNmzad1t2Q7qguoUk0bTp6e/nms8/S1NVFSX4+33HASYIzuogIHz37bJZNmUKv18v3nn+etp6euB0/XBKtziQK8dbFaUd5M1ak63qsIJz+z/V+eaZiDRkBwG51XgGsAbYC3wA+E84YylijIdvBUV1Ckyja9Hm9fPf55znU3s6E3Fy+c/HF5GdnD7/hKOGELi4RvnzBBUwbO5bGri5uf/HFgUWnE4lEqTOJRjx1cXocpYT43OuX5wZjzJqA7Z4zxiwzxmQbY+YYY+6Jt+2Kkqz4jOGOl16iuqmJvMxMbluzhmI7AjzdGJuVxTcuuogxmZnsbGzk15s3O22SkoA43aJUFCXO3Lt168C0dLeuXs2swkKnTXKUknHj+NLKlQjw6L59vPj6606bpCQYCRH1Gk9iGfXa3d1Nbm6uvmj3Q3UJTSJos662lh+/8goAXz7/fFbbYxidJBF0AfjDtm38bdcucjMy+MlllzHVHqvnJImiTaIRK12SIuo12cnSFdSDorqExkltqhsb+fmmTQC8+8wzE8JJ9pMIdea9Z53FGRMn0u3x8D8vvcSpBHk3mAjaJCLx1EUdZZR4vV4qKyv1RXsAqktonNTm+MmTfP+FF/D4fJxfUsJ7zzor7jaEIlHqjNvl4ssXXEB+Vhb7T5zg91u3OmoPJI42iUa8dVFHqSgpTq/HYw1/6O2ltLCQz69cqd14IZg4ZgxfWLkSsJbm2tIQOCOmko6oo1SUFMYYwy8rK6lrbaUgO5tvXHQRORkJM8VzQrJ82jSumj8fgJ+88gqdfX0OW6Q4jTpKRUlhnty/n3V1dQNTtU20VwJRhuZDFRVMz8+npbubewIm9VbSD416jZL+yXv7JwRWLFSX0MRbm/0tLXz5qac45fPxoYoK3nHGGaN+zGhI1Dqzp7mZLz/1FD5j+M8LLuBCB+aDTVRtnCZWumjUaxzo0y6ZoKguoYmXNp19ffzXCy9wyufj3OnTeXt5eVyOGy2JWGfmT5jAu+yHi7s3baLVoSnuElGbRCCeuqijjBKv18v27ds1Gi0A1SU08dLGGMOdGzdyvKuLKXl5fP688xK6NZLIdeb6RYsoLSyko6+P/+fArD2JrI2TxFsXdZSKkmI8uHs3m+rryXS5uGXVKkcmOk8VMlwuPnPuubhEeOH119l05IjTJikOoI5SUVKI2hMnuHfbNgA+smwZpdaitMoIKCsq4poFCwC4u7KS7lNxW81PSRDUUY4A/xXHlTdQXUIzmtr0eDz84KWX8NjvJS+fO3fUjhVrEr3OvPess5iSl0dTVxd/2L49rsdOdG2cIp66aNSroqQIv3j1VR7fv5+i3Fx+dvnljHNw2axUZOvRo3zj2WcR4I5LL2XhxIlOm6SMEI16HWWMMbS2tpJuDxrDobqEZjS12XDoEI/v348AXzjvvKRykslSZ5ZMmcKb58zBYD2UeOOwdmWyaBNv4q2LOsoo8Xq91NTUaDRaAKpLaEZLm6auLn726qsAvL28nIopU2K6/9EmmerMjUuXMjYriwNtbTy+b9+oHy+ZtIkn8dZFHaWiJDHGGO7auJHOvj7mFRXxvsWLnTYppRmXnc0HbI3/sH07bQ6NrVTiizpKRUliHt27l+3Hj5PldvPFlSvJcOklPdpcNncupYWFnDx1ivvsCGMltdGrKkpERBdTDYLqEppYa9PQ0TGwFNQNFRVMT9LgtGSrMy4RPr58OQBP1dayp7l51I6VbNrEi3jrolGvipKE+IzhlqefZldTE4snTeJ7b3qT3kzjzF0bN/LMgQPMKyriR2vXqv5JiEa9jjI+n4/jx4/ji0PkWzKhuoQmlto8uHs3u5qayMnI4LMJPkXdcCRrnblhyRLGZGayt6WFZ+rqRuUYyarNaBNvXdRRRonP56O2tlYrcACqS2hipc3h9vaBQe83LV3KpLy8WJjnGMlaZ8bn5g5Mmv6H7dvp9Xhifoxk1Wa0ibcu6igVJYnw+nz8+OWX6fN6WTZlCm8pK3PapLTmqgULmDRmDM3d3fy7psZpc5RRQh2loiQR/6qpYXdzM3mZmXz63HOTuss1Fchyu/nQkiUA/KO6mhPd3c4apIwK6iijREQoKCjQG1UAqktoRqpNfUcHf3rtNQA+umwZE8eMiaV5jpHsdWbVzJksmDCBHo+H/7PPT6xIdm1Gi3jrolGvipIEGGP42rp17GhsZNmUKXx7zRq9eSYQ1Y2NfOXppxHgZ5dfzqzCQqdNUsJAo15HGZ/Px+HDh/UlewCqS2hGos1TtbXsaGwk2+3mk+eck1JOMhXqTHlxMRfMmIEBfldVFbP9poI2o0G8dVFHGSVagYOjuoQmWm1aursHbr4fWLw46aNcA0mVOvOhigoyXC62HD3K9mPHYrLPVNEm1qijVBRlEL+qrOTkqVPMKyriKnsBYSXxmJqfz2V2FPJ927bpih8phDpKRUlgNh46xIbDh3GL8OlzzsGVQl2uqci7zjyTbLeb3c3NbKqvd9ocJUaoo4wSl8tFcXExLp2EehCqS2gi1eZkXx/3bN4MWMtnzRk/fjTNc4xUqjPjc3O52m71/yEGrcpU0iaWxFsXVT9KXC4XZWVlWoEDUF1CE6k2927dSkt3N9Pz87l+0aJRts45Uq3OXFdeTl5mJgfa2nj+4MER7SvVtIkV8dZF1Y8Sn8/H/v379SV7AKpLaCLRpqapicf37wfgU+ecQ5bbPdrmOUaq1ZmxWVlcV14OwP+99hqeEZQr1bSJFfHWRR1llPh8PhobG7UCB6C6hCZcbbw+H3dv2gTApaWlLJo0KR7mOUYq1pmrFyygIDubhs5Onq6tjXo/qahNLIi3LuooFSXBeHjPHupaW8nPyuIGe3o0JbnIycjg+jPPBODPO3bQ5/U6bJEyEtRRKkoC0dzVxR/tadA+VFHBuOxshy1SouWyuXMpHjOGlu5uHt+3z2lzlBGgjjJKXC4XJSUl+pI9ANUlNOFo85stW+jxeFgwYQJr02RlkFStM5luN++yW5X/rK6OqlWZqtqMlHjr4qj6IrJaRB4SkXoRMSJyzTD519j5Aj8L42TyAFqBg6O6hGY4baoaGnjx0CEE+MSKFSk1Td1QpHKduaS0dKBV+UQUrcpU1mYkpJWjBPKAbcCnItxuATDV77M3xnYNi9frpbq6Gq++exiE6hKaobTp83r5ZWUlAFfNn09pio6ZDEYq15kMl4t32os7/yOKVmUqazMS4q2Lo47SGPOYMeZWY8z9EW563Bhz1O8T91pkjKGtrU2nqQpAdQnNUNrcX11NQ2cnRbm5vG/xYgesc45UrzOXlJYy0W5VPmUP+QmXVNcmWuKtS0ZcjhJ7qkQkB9gFfM8Y82yojCKSDfhHROQDeDwePB4PYDXjXS4XPp9vULhxf7rX6x10Qvqb+8aYQU80brcbERnYr386cNrTT6j0jIyM0/YtIrjd7tNsDJUeTZmCpUdaJmPMabYne5lidZ769fHP73K5OHbyJH/dsQPj8/HhxYvJEsHn8yVFmWJxnvrzBLMxWcvkny7GcN2CBfxq82b+sWsXa8vKkIAbvF5PkZWpP4/P5xt03Gjr3nAkm6NsAD4GbMZyfh8A1onIGmPM8yG2uQX4VmBiVVUVefYqDMXFxZSVlVFXV0djY+NAnpKSEkpKStizZw9tbW0D6aWlpRQVFdHR0cGWLVsGboILFy6ksLCQqqqqQSd78eLFZGVlUWl3rfWzfPly+vr62L59+0Ca2+1mxYoVtLW1UVNTM5Cem5tLRUUFTU1N1PqNyyooKKC8vJz6+noOHz48kB5NmSZNmsSOHTvo9lulPdIyLV26FJ/PN0iXZC9TrM7TvHnz6OnpGaTNxIkT+cOhQ7R1djIrO5vsY8eoPH48acoUi/M0a9YsAHbt2kVvb29KlCnwPBX6fPi6umjwenm6tpaJra16PY3gPOXn5wPQ0NBAQ0ND1GUqLi4mHBJm4WYRMcC1xph/R7jdQ4Axxlwd4vdgLcrDzc3NAws3R9uiPH78OEVFRQPfU+UJeCRPiyJCU1MT48ePH/SiPZnLFKvzJCKn1ZmXjxzhfzZswC3CT9auZXpAnUz0MsXiPAG0tLQwfvz4QQFMyVymYOkP79nDb7dupTgvj7svv5wMv+tDr6fIymSM4cSJExQVFQ3aR6Rl6uzsZLwVDzDkws2p4Ci/DrzfGFMeZv5xQFtbW9uAo1QUJ+jzern54Yc53tXFu844gw9UVDhtkjKK9Hm9fPShh2jp7uaTK1Zw2dy5TpuU9rS3t1NQUADDOEqno15jwVKsLtm44vV62bZtm0ajBaC6hCZQm3/X1HC8q4sJubm80x5vl46kS53Jcrt5uz0H7N937gxrDth00SZS4q2L0+Mox4rIEhFZYifNsb/PtH+/XUTu88v/ORG5RkTmiciZInI78Hbg5/G23RhDd3e3RqMFoLqExl+b5q4u/r5rFwA3LFlCTkayhQvEjnSqM5fNnUtBdjbHu7p4IYyVRdJJm0iIty5OtyiXA1X2B+BO+//v2N+nAjP98mcBPwS2Ay8AFwJvjWJ4iaI4yv9u20aPx8PCCRO4yA5mUVKfLLd7YL3Kf+zapQ4wSXD0MdYYsx4IOf2IMeaGgO93AHeMrlWKMrrsbm7m2QMHAPjY2WenzQw8isVb583jH7t28Xp7O5vq6zln+nSnTVKGwekWZdLidrtZuHDhQASXYqG6hMbtdrNgwQJ+u3UrAG+eM4d5EyY4a1QCkG51Ji8ri7fOmwdY7yqHalWmmzbhEm9d1FFGiYhQWFiorYEAVJfQiAhVra3sbWkhJyODD2qUK5CedebqBQvIdLmoaW5mp994v0DSUZtwiLcu6iijxOPxsGnTptPGDqU7qktoOrq7+dG6dRifj+vPPJOi3FynTUoI0rHOjM/N5ZLSUsB6VxmKdNQmHOKtizrKEaAh28FRXYLzj+pq2vr6mDJ2LG+zAzoUi3SsM9eVlyPA5oYGak+cCJkvHbUJh3jqoo5SUeJAQ0cHD+zeDcCHlywhU985pT1Txo5l1UwrqH+oVqXiPOooFSUO/K6qCo/Px7z8fM6ZNs1pc5QEoX+iiRdff52Gjg6HrVFCoY4yStxuN4sXL9ZotABUl9PZevQoLx85gtvl4quXXkpGGk8uEIx0rjOzCwtZMW0aBvhndfVpv6ezNkMRb13UUY6ArKwsp01ISFSXN/D6fPx682YArpg3j7KJEx22KDFJ5zrzDnth52fq6mjt6Tnt93TWZijiqYs6yijxer1UVlbqi/YAVJfBPL5vH6+3t5OflcW7ystVmyCke50pnziRBRMmcMrn45E9ewb9lu7ahCLeuqijVJRRoqO3lz++9hoA71+8mPzs7GG2UNIREeHahQsBeGTvXnp1KEjCoY5SUUaJP732Gp19fcwuKOAtZWVOm6MkMCtnzGByXh4dfX2sq6tz2hwlAHWUijIKHGxt5dF9+wD46Nln43bppaaExiXCNXar8t81Nfh0svSEYsQLN4tItjGmN0b2jDqxWri5fyXu/tW9FQvVxdLgG88+y7Zjxzi/pIRbVq0aSE93bYKhulj0eDx8+IEH6Ozr4+urVnFeSYlqE4JY6TJqCzeLyFtE5F4R2S8ip4AuEekQkedE5OsikjaDxPr6+pw2ISFJd11eOXKEbceOkely8eGlSwf9lu7ahEJ1gZyMDK6YOxeA+/2Giqg2wYmnLmE7SnvB5N3A/wI+4AfAdcBbgJuA54BLgFoRuUdEikfB3oTB6/Wyfft2jUYLIN116fN6+e2WLQBcu3AhU8aOHfgt3bUJheryBm+dP58Ml4vqpiZ2NzWpNiGIty6RtCi/BnwJmGaMudEYc48x5iFjzNPGmL8ZY75pjLkYKAPagQ+OhsGKksg8uHs3R0+epCg3d2DWFUUJl6LcXNbYC3n/q6bGYWuUfsKeIsQYc06Y+Y4AX4naIkVJUlq6u/nrzp0A3FBRQY7OwKNEwbXl5TxdV8eGQ4c4umiR0+YoRBn1KiIh1wcSkanRm5Nc6LRSwUlXXe7bto0ej4cFEyawZvbsoHnSVZvhUF3eYGZBAWdPnYoBHtqzR7UJQTx1iSrqVURqgPcaY7YEpL8D+KUxJmHfT8Yq6lVR/NnT3MwXn3wSgB+tXcv8CRMctkhJZrYdPcqtzz5LttvN79/2Np2sYpQYtahXm6eADSLyVbEYKyL3YgX6fCfKfSYVxhhaW1sZ6fCaVCMddTHG8P/s+VzfPGdOSCeZjtqEg+pyOosnT6a0sJBej4d/bt+u2gQQ7zoTlaM0xnwauAb4LPA8sA2oAFYYY34WM+sSGK/XS01NjUajBZCOuqw/cIDdzc3kZGTwwYqKkPnSUZtwUF1OR+wJCIwx/H3rVnpPnXLapIQi3nVmJNOFPAncD1wAzAC+aozR1UeVtKLH4+HebdsAuP7MMynKDfn6XlEi4sKZMynIyaHt1Ck2Hj7stDlpTbTBPGXARuBKrHGUdwAPiMgdIpIZQ/sUJaH5+86dtHR3MyUvj6sXLHDaHCWFyHS7ByYgeChgVRElvkTbotwK1AEVxpinjDG3Am/CmoDg1RjZltCICLm5uTqtVADppMvRzs6BsW43LVtG1jBReOmkTSSoLqG5fO5csjIy2NPSwu6mJqfNSRjiXWeidZSfMMa82xjT2p9gjNkALAW2hNwqhXC73VRUVGjodgDppMvvq6o45fNRMXky506fPmz+dNImElSX0BTl5fG2xYsRER7cvdtpcxKGeNeZaIN5/hAivcMYc9PITEoOfD4fx48fx+fzOW1KQpEuumw/dowNhw/jEuGjy5aF9WSbLtpEiuoSGp/Px/kTJ2KM4cVDh2jq6nLapIQg3nUm6mAeESkREVfg/+mCz+ejtrZWL+4A0kEXr8/Hr+3hIFfMncuswsKwtksHbaJBdQmNz+fD29TEouJifMbwiL6rBOJfZ0bi3HYBs4P8rygpzRP793OgrY38rCzee9ZZTpujpAFXzZ8PwOP799Pr8ThsTfoxEkcpIf5XlJSlo7eXP27fDsD7zjpLZ0xR4sKKadOYkpdHZ18fzx444LQ5aUdadZfGEhGhoKBAI/UCSHVd/rxjBx19fcwcN47L7ND9cEl1baJFdQlNvzZul4sr7Vblg7t3p/1MPfGuM+ooo8TtdlNeXq6RegGksi6H2tp4ZO9eAD529tm4XZFdPqmszUhQXULjr82lZWXkZmRwqL2drUePOm2ao8S7zqijjBKfz8fhw4c1ACGAVNWlfz5XnzGcN306FVOmRLyPVNVmpKguofHXZkxmJpeWlgLwQJoPFYl3nVFHGSV6cQcnVXV59cgRth47RobLxY1Ll0a1j1TVZqSoLqEJ1ObK+fMRYHNDA4fbQy52kfKoo1SUBOOU18tvq6oAuGbBAqbm5ztskZKuTM3P5xx7couH0rxVGU/UUSrKMDy4ezcNnZ0U5ebyrjPPdNocJc3pn1N4XV0dnX19DluTHozEUf4RaA/yf1rgcrkoLi7GFWFAR6qTarq0dHfzl507Afjg4sXkZkY/53+qaRMrVJfQBNPmrEmTmF1QQK/Xy5P79ztonXPEu85EfRRjzM3GmKbA/yNBRFaLyEMiUi8iRkSuCWObi0Rks4j0iEitiHw8CvNHjMvloqysTC/uAFJNl//dupUej4cFEybwpjlzRrSvVNMmVqguoQmmjYgMtCof2rMHbxq+2413nYnoKCKSE0aeeRHsMg9r0edPhXn8OcCjwAtYE7D/F/BTEXl7BMeMCT6fj/3792sAQgCppMvupiaesQd3f+zss0c8ZiuVtIklqktoQmlz0ezZFGRn09TVxctpuFZlvOtMpO54q4icG+pHEfkC1hJcYWGMecwYc6sx5v4wN/k48Lox5nPGmGpjzG+A3wFfCveYscLn89HY2KgXdwCpoosxhl/Z87m+ec4c5k+YMOJ9poo2sUZ1CU0obbLc7oEJL9JxVZF415lIHeXTwPMicrv/As0iMldEXgRuAT4SSwMDWAk8GZD2BLBcF4xWYskzdXXsbWkhNyODD1VUOG2OopzGFfPm4RZhV1MT+1tanDYnpcmIJLMx5lMicj9WK+5KEfkwsAr4PpbDersx5ljszRxgChC4/2NY5ZgINARuICLZgP+EnPkAHo8Hjz25sMvlwuVy4fP5Bj2h9Kd7vd5BU0b194sbY/B6vQPpbrcbERnYr386MCjvUOkZGRmn7VtEcLvdp9kYKj2aMgVLj7RMxpjTbE+2MnX09PC7qiqMz8e7ysspzMmJSZn69fHP79R5SqS6158nmI3JWqZ4XE/jc3I4v6SE5w8e5F/V1Xz+vPOSokyxOE/9eXw+36DjRlv3hiMiRwlgjHlGRM7CinR9BegCPmKM+VOk+4qSwEkOJUR6P7cA3wpMrKqqIi8vD4Di4mLKysqoq6ujsbFxIE9JSQklJSXs2bOHtra2gfTS0lIm2mvEVdnj6wAWLlxIYWEhVVVVg0724sWLycrKorKycpANy5cvp6+vj+32JNtgVaIVK1bQ1tZGTU3NQHpubi4VFRU0NTVRW1s7kF5QUEB5eTn19fUc9ntXEU2ZJk2axI4dO+ju7o66TMuWLWPy5MmDdEm2Mt3x6KMcPHaM4uxsprS34/V6Y3KeFixYQF5e3iBtnDpPiVT3Zs+eTUlJCdXV1fT09KREmeJ1Pc3u7eXBtjYe2r6dc7OyWLViRcKXKRbnady4cZSUlHD06FHq6+ujLlNxcTHhINFMrisiHwN+COwAzgb+D/isMaYj4p29sU8DXGuM+fcQeZ4Hqowxn/VLuxb4GzDGGHMqyDbBWpSHm5ubGTduHJDcT1ap+LToZJmOtLfzqUcfxePzceuqVSyfNi3pyxTMdi1T6pTpK08/zZ7mZt69aBHvr6hIiTINZ3usytTZ2cn48eMBCowxIYc4RtSiFJHpWN2uK4DPGGPuFZEK4H+BnSJykzHmqUj2GSEbgasC0tYClcGcJIAxphfo7f/e3wWWkZFBRsbg4veLGUiwiXe9Xi979uxh/vz5p/0euN9o0kUkaHooGyNNDzWZcKj0cG0fSpdkKNNvq6rwAiumT+e8mTOHzR9JmYbSJt7naaj0eJ8nr9dLdXU18+fPD3rcZCzTcOmxvJ6uKS/nBxs28Pj+/Vy/aBGZbndCl2mo9HDP03B1JtwyBcsTjEiDeXZgdXEuNsbcC2CM2YblOO8DHhGRX4a7MxEZKyJLRGSJnTTH/j7T/v12EbnPb5N7gFkicqeIlIvIjcBNWK3buGKMoa2tLe2XuwkkmXWprK+nsqGBDJeLjyxbFvP9J7M2o4nqEppwtDl/xgwm5ObS1tvLC6+/HkfrnCPedSZSR/k1Y8xlxphBA3eMMaeMMbcC52MF94TLcqDK/gDcaf//Hfv7VGDgsd4YUwdcAazBGobyDayW7T8jLIeiDMLj8/GbLVsAuHr+fKbb3fKKkuhkuFy8dZ41fF3XqhwdIo16HbK1aIypFJGwH8WNMet5Ixgn2O83BEl7Doj9476S1jy0ezdHOjoozMnh+kWLnDZHUSLisrlz+cvOnew/cYLqpibOCDNIRQmPsFuUIpIXTj5jTF8k+ZMVl8tFaWlp2H3c6UIy6nKiu5s/79gBwA0VFYwZwXyuQ5GM2sQD1SU04WqTn53NmlmzgPSYgCDedSaSo+wTka+JyLRQGcTiUhF5DPjMyM1LXFwuF5MmTdKLO4Bk1OV/t22j2+NhflHRiOdzHYpk1CYeqC6hiUSbq+z5XzccOsTxkydH2zRHiXedieQoa7DmV60TkVdE5Bci8nUR+aKIfM+eiKAe+C3wIHBH7M1NHLxeL9u2bTstxDndSTZddjc1sa6uDojNfK5DkWzaxAvVJTSRaDO7sJDFkyZhgEf27Bl94xwk3nUmbEdpjNltjHknUAb8BZgGvAP4KJYTPWL/P9sY80tjTErXemMM3d3d+uI8gGTSxWcMd2/aBMAlc+awYOLEUT1eMmkTT1SX0ESqzdsWLgTgif376QkY15hKxLvORDMzz2HgLvuD2I/gRmu5kmQ8tncvta2t5GVmcsOSJU6boygjZsW0aUwdO5aGzk6eravj8nmRLOakhCLqDl4RuUlEdgA9QI+I7BCR0ZwQXVFiRltPD3+wp9D6YEUFBTnDriCnKAmPiHDl/PmAtValtl9iQ1SOUkS+C/wEeAh4p/15CLhLRL4XO/MSF7fbzcKFC0POUpGuJIsuv9+6lZOnTlE2fvzAckWjTbJoE29Ul9BEo80lpaXkZmRwqL2drUePjqJ1zhHvOhNti/Jm4KPGmFuMMQ/an1uAj2GtGZnyiAiFhYWjGvyRjCSDLtWNjayrq0OAm5cvxxUnW5NBGydQXUITjTZjMjO5pLQUSN2hIvGuM9E6SjdQGSR9M1G890xGPB4PmzZtOm0i4HQn0XXx+nwDATxry8pGPYDHn0TXxilUl9BEq81V8+cjQGVDA0faQ871nbTEu85E6yj/iNWqDORjWCuJpAUazh6cRNbl0b17OdDWRn5WFh90YEHmRNbGSVSX0ESjzdT8fJZPs4a8P5SiQ0XiWWdGMlrzJjuA5zf2ZwfW8BCfPWn5nSJyZ4zsVJQR09LdzR9few2wAnjGZWcPs4WiJC9vsycgWFdXx8m+PoetSW6i7SZdBGyx/y+z/zbaH/+JMjXkSkkY7t26la5Tp5hfVMRbysqG30BRkpjFkyczq6CAg21tPFVbyzX2GEslcqJauDmZEZFxQFtbW9vAws3R0D/gNTc3V4MQ/EhUXXYcP84t69YhwI/WrmXehAlxtyFRtXEa1SU0I9XmiX37+PmmTUwaM4ZfX3113ALXRptY1Zn29nYKCgpgmIWbdXLFEZCVleW0CQlJouni8QvguWzuXEecZD+Jpk2ioLqEZiTarJk9m/ysLI53dfHqkSMxtMp54lln1FFGidfrpbKyUoMQAkhEXe6vruZQezsF2dl8YPFix+xIRG0SAdUlNCPVJjsjY+A1QyoNFYl3nVFHqaQ09R0d/MVeQuujy5aRrwE8Sprx1vnzcYnw2vHj1J444bQ5SYk6SiVlMfak56d8PpZOmcJqe70+RUknJo4ZwwUzZgDWAuVK5KijVFKW9QcOsO3YMbLcbm5evlwDRZS05Wp7qMhzBw/S1tPjsDXJh0a9RokxBq/Xi9vt1huwH4miS3tvLzc/8gjtvb18qKKCd5xxhmO29JMo2iQaqktoYqWNMYYvPvkke1taeP9ZZ3H9okXDb5TAxEoXjXqNA306iDcoiaDL76uqaO/tZVZBQUKNH0sEbRIR1SU0sdBGRAZalY/u24fH5xvxPp0mnnVGHWWUeL1etm/frpF6ASSCLq8dO8bTdXUAfOqcc8hwJUY1TwRtEhHVJTSx1ObCmTMpys2lpbubl15/PQbWOUe860xi3EEUJUb0eb38wh4zefncuSyM46TnipLIZLhcXG4vKffA7t26VmUEqKNUUoq/7dzJkY4Oxufk8CEHJj1XlETm8rlzyXC52NvSwu7mZqfNSRrUUY4AXWg2OE7pUnviBH/ftQuAjy9fTl4CzvaidSY4qktoYqlNQU4Oa+xhUsk+AUE864xGvSopgcfn4wtPPEFdaysXzJjBVy+80GmTFCUhqTtxgs88/jguEX579dVMHDPGaZMcQ6NeRxljDK2trdrPH4BTuvxz1y7qWlvJz8ri48uXx/XY4aJ1JjiqS2hGQ5s548ezqLgYnzE8undvzPYbT+JdZ9RRRonX66WmpkYj9QJwQpfX29r4y86dAPzH2WdTmJMTt2NHgtaZ4KguoRktbfqHijy+bx+9Hk9M9x0P4l1n1FEqSY3X5+PHL7+Mx+fjnGnTdJo6RQmDc0tKmJyXR0dfH+vsoVRKaNRRKknNA7t3s7elhbzMTD6xYoXO7KIoYeASGZiI41/V1fi023tI1FFGiYjoQrNBiKcuR9rb+eP27QDctHQpExI8KEHrTHBUl9CMpjaXlJaSn5XF0ZMn2XDoUMz3P5rEu85o1KuSlHh9Pr769NPUNDezdMoUbluzRm+0ihIh/7d9O3/ZuZN5RUX8aO3atLuGNOp1lPH5fBw/fhxfCsyZGEvipcs/q6upaW5mTGYmnzrnnKS4wLXOBEd1Cc1oa3Pl/Plkud3sbWlhZ2PjqBxjNIh3nVFHGSU+n4/a2lq9uAOIhy61J07wp9deA+Bjy5YxKS9v1I4VS7TOBEd1Cc1oa1OQk8Ob58wBrCFWyUK864w6SiWp6PN6+eGGDXiNYWVJCW+yL3JFUaLjmoULEaCyoYHX29qcNichUUepJBV/2LaNQ+3tFObk8EmNclWUETMtP5+VJSUA3F9d7bA1iYk6yigREQoKCvRGHcBo6vLasWM8YM9P+ZlzzqEgQScWCIXWmeCoLqGJlzbXlZcD8NzBgzR3dY3qsWJBvOuMRr0qScHJvj4+/dhjNHZ1sba0lE+fe67TJilKSvHVp59mZ2Mj1y1cyIeXLnXanLiQNFGvIvIJEakTkR4R2Swiq4bIu0ZETJBP3Jew9/l8HD58WAMQAhgtXX61eTONXV1MzsvjI8uWxXTf8ULrTHBUl9DEU5u3263Kx/fv52Rf36gfbyTEu8446ihF5Hrgx8D3gaXAC8BjIjJzmE0XAFP9PnGf2Vcv7uCMhi7P1NXx7IEDCPDFlSvJzcyM2b7jidaZ4KguoYmnNsunTWPGuHF0nTrFY/v2jfrxRkJaOUrgC8BvjTG/McZUG2M+BxwCbh5mu+PGmKN+H51NOUU50t7OLysrAXjvWWdRXlzssEWKkpqICO844wwA/l1Tk5STpY8WjjlKEckCzgaeDPjpSeD8YTavEpEGEVknIhePioGK45zyernjpZfo8Xg4a9Ik3nXmmU6bpCgpzepZs5icl0dbby9P7N/vtDkJQ4aDx54IuIFjAenHgCkhtmkAPgZsBrKBDwDrRGSNMeb5YBuISLadt598AI/Hg8d+YnK5XLhcLnw+36CmfH+61+sdtO5Zf/qECRPw+XwD+3G73YjIwPd++lfiDlwSJlR6RkYGxphB6SKC2+0+zcZQ6dGWKTA90jKJCBMnThykS7Rl+l1VFftbWsjPzuazK1aAMSAS9zLF6jy5XK7TtHHqPCVS3QMoLi7GGDPI/mQuUyJeT+GW6bqFC/nl5s38c9cuLp09m0zbtkSqe8YYiu3eJf/jRnqewu26ddJR9hMYditB0qyMxuwGdvslbRSRGcCXgKCOErgF+FZgYlVVFXn2jC7FxcWUlZVRV1dHo980TiUlJZSUlLBnzx7a/AbilpaWMmnSJLq6utiyZctA+sKFCyksLKSqqmrQyV68eDFZWVlU2l2I/Sxfvpy+vj622xN7g1WJVqxYQVtbGzU1NQPpubm5VFRU0NTURG1t7UB6QUEB5eXl1NfXc/jw4YH0aMu0Y8cOuru7R1SmadOmDdIlmjJ1jBvHP7Zvp7unh+vKyqjbtYtOB8sUq/OUk5MzSBsnz1Mi1b2ysjK2bduWUmVKpOspkjKVT5vGhNxcDh4/zj1PPslK2yElYt07fPjwiM5TcZivchwbHmJ3vXYB7zTG/Msv/SfAEmPMRWHu5+vA+40x5SF+D9aiPNzc3DwwPCSap0WA/fv3M2vWrIHv+gRs2VNXV8fMmTMHdIm0TM3d3Xz+ySdp7+3lynnz+Igdqp7srS8Roba2dpA2yV6mWLUoDx48yMyZMweNi0vmMiXS9RRNmR7eu5f/t3kzxWPG8MsrriDDzpsodc8Yw+uvv86sgPVnIz1PnZ2djB8/HoYZHuJYi9IY0ycim4FLgX/5/XQp8EAEu1qK1SUb6ji9QG//9/4LMSMjg4yMwcXvFzOQ/hPrj8fjobm5mTlz5py2n8Dv0aSLSND0UDZGmh6sTEOlh2u7x+OhqamJ2bNnn/ZbOGU65fXyg40b6ejro2z8eG5atoyMAJviXaah0iM5T0Npk6xliiY90HaPx0NjYyOzZs0KetxkLNNw6fG6nqJNf0tZGX/buZOm7m42HDkyaKrIRKh7w9WZcM9TsDzBcDrq9U7gIyJyo4iUi8hdwEzgHgARuV1E7uvPLCKfE5FrRGSeiJwpIrcDbwd+7oj1Ssz5bVUVu5ubycvM5JZVqwbejyiKEj+yMzIGFnb+286dab+ws6OO0hjzV+BzwDeBrcBq4ApjzEE7y1Qsx9lPFvBDYDvWmMsLgbcaY+6Pk8nKKLL+wAEe2WsNif3iypVMGTvWYYsUJX25Yt48xmZlcaSjI+kWdo41TrcoMcbcbYyZbYzJNsac7R+9aoy5wRizxu/7HcaYucaYXGNMkTFmlTHmUSfsdrlclJSUhN10Txei1eVAays/e/VVAN595pmsmD59NMxzFK0zwVFdQuOkNmMyM7l6/nwA/rpjx2nvlZ0k3rpozYwSvbiDE40uJ/v6uP2FF+jzelk6ZQrvOeusUbTQObTOBEd1CY3T2ly1YAFjMjM50NbGSwnUqlRHmSR4vV6qq6tPi9xKdyLVxWcMP9ywgfrOTorHjOHL55+PK0VXkdA6ExzVJTROazM2K4trFiwA4E+vvZYw7yrjrYs6yigxxtDW1pZQ3RGJQKS63Lt1K5UNDWS53Xxt1Srys7OH3yhJ0ToTHNUlNImgzdULFpCflcWh9naeO3DAMTv8ibcu6igVx1hXW8u/7MHFnz/vPOYWFTlskaIogeRlZQ2sV/nnHTvwpOHk9eooFUeobmzk55s2AVbwzoUzh1swRlEUp7hy/nwKsrNp6Ozkmbo6p82JO+ooo8TlclFaWqoBCAGEo8vxkyf5/gsv4PH5OL+khPemaPBOIFpngqO6hCZRtMnJyOCd9soif96xg1MOv0+Oty5aM6PE5XIxadIkxytwojGcLif7+rht/XraenspLSzk8ytXDpq2LJXROhMc1SU0iaTN5fPmMSE3l6auLp50eGWReOvivPpJitfrZdu2bRqpF8BQuvR5vXzv+ed5vb2dotxcbl29mpwQ01ulIlpngqO6hCaRtMlyu7neXuruLzt30n3qlGO2xFsXdZRRYoyhu7tbI/UCCKWLMYa7Nm5kR2MjuRkZfPuiiyi2V29JF7TOBEd1CU2iaXNpWRlTx46ltaeH+6urHbMj3rqoo1Tiwm+rqnjx0CEyXC6+vmoVc6wZ+xVFSSIyXC5uWLIEgPtramju6nLWoDihjlIZde6vruaB3dYyop8991wqpoRal1tRlERnZUkJ5RMn0uf18n+vvea0OXFBHWWUuN1uFi5cGHLJmXQlUJdH9+7l91u3AnBDRQVrZs92zjiH0ToTHNUlNImojYhwk71G7NO1tRxobY27DfHWRR1llIgIhYWFaROxGS7+uqyrreWX9urm7zzjDN5uh5enK1pngqO6hCZRtVkwcSIXzpiBAX5fVRX348dbF3WUUeLxeNi0adNpq3qnO/26rK+r4yevvALAVfPn84HFix22zHm0zgRHdQlNImvzoSVLyHC52HL0KJvr6+N67Hjroo5yBCRCyHYisr25mbtefhkDXFpaykeXLUu4J2Kn0DoTHNUlNImqzZSxY7nKXobrV5s3x30Sgnjqoo5SiSkvHjrEfXV1eH0+Vs+cyafOOUedpKKkKO9etIjxOTk0dHYOzNuciqijVGLGM3V1/GjjRrzGcNHs2Xxh5cqUXTJLURRrcecb7cCev+7cyfGTJx22aHSQRBnIGi9EZBzQ1tbWxrhx46LeT/+A19zcXG0xAY/v28fdmzZhjOGiGTP4/AUX4E6AabcSCa0zwVFdQpMM2hhj+Nq6dexobOT8khJuWbUqLseMhS7t7e0UFBQAFBhj2kPl0zvZCMjKynLaBMcxxvCPXbv4xaZNGKz5ID973nnakgyB1pngqC6hSXRtRISPL1+OS4QNhw/HLbAnnrqoo4wSr9dLZWVlwr5ojwc+Y7inspL/3bYNgGsXLuSjS5awefPmtNYlFFpngqO6hCZZtJlVWDgQ2HP3pk30jHI0arx1UUepREWf18vtL7zAo/v2IcBHli7lxqVLE7Z7SFGU0eX9ixczacwYjnd1cZ/98JwqqKNUIqa1p4evr1vHy0eOkOly8ZULLuBtCxc6bZaiKA6Sk5HBp889F4CH9+xhV2OjwxbFDnWUSkTsbW7mc48/Tk1zM2OzsvjuxRdz4cyZTpulKEoCsGTKFC4tLcUAP33lFfoSvMs4XDTqNUqMMXi9Xtxud9p0Nz5TV8fPX32VUz4f0/Pz+cbq1UwP0DAddQkX1SY4qktoklGbk319fOLRR2np7uaq+fP52Nlnx/wYsdJFo17jQF9fn9MmxIU+r5dfVVZy18svc8rn45xp0/jR2rWnOcmB/GmiSzSoNsFRXUKTbNrkZWXxmXPOAeChPXvYdOTIqBwnnrqoo4wSr9fL9u3bEz4abaQcaW/nS08+ycN79wLw7jPP5NbVq8kLEZqdLrpEg2oTHNUlNMmqzdnTpvG2BQsA+PErr9DS3R3T/cdbF3WUSlCMMTxdW8tnH3+cutZWCrKz+fZFF/G+xYuTpgtIURTn+FBFBXMKC2nv7eWujRtJ5td86iiV02jp7uZ7zz/PT155hV6vl4rJk/np5Zdz9rRpTpumKEqSkOl28+XzzyfL7WbrsWP8KYkXeVZHOQISaTHVWGCMYV1tLZ945BFera8nw+Xig4sX852LL6YoNzfs/aSaLrFEtQmO6hKaZNZmRkEBn1yxAoC/7NzJxkOHYrbveOqiUa8KAIfa2vjV5s1sO3YMgHlFRXz23HOZVVjorGGKoiQ9v968mQf37CEnI4MfrV3LTCvS1HE06nWUMcbQ2tqa1P3uYIVy/2bLFj712GNsO3aMTJeLD1VU8INLL43KSaaKLqOBahMc1SU0qaLNh5cuZfGkSfR4PHxr/XqaurpGtL9466KOMkq8Xi81NTVJF43WT5/XywM1NfzHww/zwO7d+IzhvOnTufutb+UdZ5wR9cofya7LaKLaBEd1CU2qaJPhcvGfF17I9Px8mrq6+Nazz9I5guEd8dYlIy5HURIGj8/H07W1/GXHDprtkO2S/Hw+dvbZLJ061WHrFEVJVcZlZ/Odiy/my089xevt7Xznuef4zsUXk5OR+G4o8S1UYsLJvj6e2L+fh/bsGej2mDhmDO9ZtIg3zZlDhq4dqSjKKDMpL4/b1qzhq08/TXVTE9945hm+vWZNyHHZiYI6yigRkYReTLWfQ21tPLF/P0/s3z+w9M34nBzeecYZXDZ3LpkxjhxLFl2cQLUJjuoSmlTUZnZhId+9+GK+uX49Nc3N3PrMM3zzoosYH0Fkfbx10ajXFORkXx8vHTrEk/v3s7u5eSB95rhxXFtezkWzZsXcQSqKokRC3YkT3Prss7T39jJxzBi+sXo1pePHx9WGcKNe1VFGic/no6mpiYkTJ+JKgG7Ltp4eXj1yhA2HDrH12DE8Ph8ALhFWTJvGFfPmsXTKlFF/Aks0XRIJ1SY4qktoUl2b+o4OvvPccxzp6CDb7eajy5axtqxs2PtUrHQJ11E63vUqIp8AvgxMBXYCnzPGvDBE/ouAO4EzgXrgDmPMPfGw1R+fz0dtbS1FRUWOVOA+r5eapia2HT3K9mPH2N3cjP8jT0l+PpeUlvKmOXMi6tIYKU7rksioNsFRXUKT6tpMy8/nR2vX8j8vvUTV0aP8fNMmXjlyhI8vX86kvLyQ28VbF0cdpYhcD/wY+ATwEvAfwGMicoYx5vUg+ecAjwK/Bt4PXADcLSKNxph/xs3wOHPK6+VQezv7W1rYZ3/qWls5Zbca+ykbP57zZ8xgZUkJMxJkQK+iKMpQ5GVlcduaNfy7pob7tm9nU309Wx9+mKsXLODahQspyMlx2kTHW5RfAH5rjPmN/f1zIvIW4GbgliD5Pw68boz5nP29WkSWA18CktJRGmPo7OujpbubEz09nOjuprWnh6OdndR3dFDf0UFjVxfBOsiLcnOpmDyZismTWTx5MsVDPIEpiqIkKiLCteXlLJs6lV9t3sxrx4/zz+pqHti9m1UzZ3LBjBlUTJni2FASxxyliGQBZwP/HfDTk8D5ITZbaf/uzxPATSKSaYw5FeQ42UC2X1I+gMfjwWNHgbpcLlwuFz6fD59fK60/3ev1DpoBwgfcvWkTR48d4/mXX0YAnzEYu1/d4/Va343BZwyI4DWGU14vXadO0X3qFD1eL70eDz0ez2mzS4jLBfb2/eRlZTG3qIjS8eMpKyykbPx4powdi8vlwu124/P5BsoTTZlCpfcvjOq/7/50IOiA33Hjxp1mT0ZGxsBiq37nZsB2fxtDpTtVplDpkZZJRE7TJtnLFIvzZIyhoKDgtDqTzGXS6ym68zSzoIDbVq+msqGBv+7cyb4TJ3j2wAGeqatDgKljxzIpL4+8zEw6TpxgXHMz8ydMiLpM/nmGwskW5UTADRwLSD8GTAmxzZQQ+TPs/TUE2eYW4FuBiVVVVeTZLbDi4mLKysqoq6ujsbFxIE9JSQklJSXs2bOHtra2gfQZs2ax7sAB2tva8NbXD6SPHTuWzMzM06ZWGjduHC4RWv32AVBYUIDPGNrb2xnjdpOfmUlBVhZnzprFGODUiRMUZ2czMTub4vx8lixZwvHjx6mtreXI8eMcAQoKCigvL6e+vp7Dhw8P7DvSMpWWljJp0iR27NhBt9/acQsXLqSwsJCqqqpBFXvx4sVkZWVRWVk5qEzLly9n9uzZbNmyZSDN7XazYsUK2traqKmpGUjPzc2loqKCpqYmamtrB9ITsUx9fX1s3759xGUaN27cIG1SoUyxOE/l5eVs27Ytpcqk11P050mAd48fz/Fx4ziak8Nz+/ZxsLmZE62t7AIyMzIYm5/P7sOHaa+ri7pMxcXFhINjUa8iMg04ApxvjNnol/514APGmIVBttkD/N4Yc7tf2gXAi8BUY8zRINsEa1Eebm5uHoh6jfQpBBHur66mpaWFCePHW/lEcLtcuF0ujM+HiOCyP277d5cIuRkZ5GRkkJuRwdjsbHIzM8lxuQYN10jmp0URob6+nsmTJw96yZ7MZYpli/LIkSODtEn2MsXiPAEcPXqUyZMnD4p2TOYy6fUU+/PUfPIkB9raaO3pob23l6aWFt5y5pmU+I1eiLRMnZ2djLeGpCRs1GsT4OX01uMkTm819nM0RH4P0Hx6djDG9AK9/d/7L8SMjAwyAvq7+8UMJNhyLtctXEhlZSXLy8tP208sEJGg+w1lY6TpoZaoCZUeqoyB6R6PhyNHjjB16tTTfkvWMg2VHkmZhtImWcsUTXqg7R6Ph8OHDzNlypSgx03GMg2XrtdT5OepOD+f4vx8wNKlsrKSknHjItIg0PZgeYLhWLyxMaYP2AxcGvDTpcCGEJttDJJ/LVAZ7P2koiiKoowUpwfm3Al8RERuFJFyEbkLmAncAyAit4vIfX757wFmiciddv4bgZuAH8bdckVRFCUtcHR4iDHmryIyAfgm1oQDO4ArjDEH7SxTsRxnf/46EbkCuAv4JNaEA59xYgyly+WiuLg47KZ7uqC6hEa1CY7qEhrVJjjx1kWnsFMURVHSknCnsNPHlCjx+Xzs378/7HE46YLqEhrVJjiqS2hUm+DEWxd1lFHi8/lobGzUChyA6hIa1SY4qktoVJvgxFsXdZSKoiiKMgROz/XqGO3tIbujw8Lj8XDy5Ena29tHZRxlsqK6hEa1CY7qEhrVJjix0iVcP5COwTzTgcPDZlQURVHShRJjzJFQP6ajoxRgGtAxwl3lYznckhjsK5VQXUKj2gRHdQmNahOcWOqSD9SbIZxh2rXlbTFCPjmEi9+clB1DhRWnG6pLaFSb4KguoVFtghNjXYbdXoN5FEVRFGUI1FEqiqIoyhCoo4yeXuA2/FYmUQDVZShUm+CoLqFRbYITV13SLphHURRFUSJBW5SKoiiKMgTqKBVFURRlCNRRKoqiKMoQqKNUFEVRlCFQRzkEIvIJEakTkR4R2Swiq4bJf5Gdr0dEakXk4/GyNZ5EoouIXCciT4lIo4i0i8hGEXlLPO2NJ5HWGb/tLhARj4hsHWUTHSGKaylbRL4vIgdFpFdE9ovIjfGyN55Eoc37RGSbiHSJSIOI/F5EJsTL3nggIqtF5CERqRcRIyLXhLHNqN1/1VGGQESuB34MfB9YCrwAPCYiM0PknwM8audbCvwX8FMReXtcDI4TkeoCrAaeAq4AzgaeBR4SkaWjb218iUKb/u0KgPuAdaNtoxNEqcvfgDcDNwELgPcANaNrafyJ4j5zIVZd+S1wJvBOYAXwm3jYG0fygG3Ap8LJPOr3X2OMfoJ8gFeAXwakVQO3h8j/P0B1QNo9wEany+KkLiH2sRP4ptNlSRRtgL8A3wW+DWx1uhxO6wJcBrQCRU7bnoDafAnYH5D2aeCQ02UZRY0McM0weUb1/qstyiCISBZW6+fJgJ+eBM4PsdnKIPmfAJaLSGZsLXSGKHUJ3IcLaxLiltha5yzRaiMiHwbKsAZPpxxR6nI1UAl8RUSOiMgeEfmhiOSOoqlxJ0ptNgAlInKFWEwG3gE8MnqWJgWjev9Nu0nRw2Qi4AaOBaQfA6aE2GZKiPwZ9v4aYmmgQ0SjSyBfxOpW+VsM7UoEItZGROYB/w2sMsZ4/CZ6TiWiqTOlwIVAD3CtvY+7gSIgld5TRqyNMWaDiLwP+CuQg3V/eRCrVZnOjOr9V1uUQxM4bZEESRsuf7D0ZCdSXaxMIu/B6l683hhzfBTsSgTC0kZE3MCfgG8ZY/bEwzCHiaTOuOzf3meMedUY8yjwBeCGVGtV2oStjYicAfwU+A5Wa/QyYA5WN2O6M2r3X21RBqcJ8HL6U90kTn9q6edoiPweoDmm1jlHNLoAA0ELvwXeaYx5enTMc5RItckHlgNLReTndpoLa8lUD7DWGPPMaBkbR6KpMw3AEWNMm19aNdaNrwTYG2sjHSIabW4BXjLG/MD+vl1ETgIviMitxphU6LmKhlG9/2qLMgjGmD5gM3BpwE+XYr0jCMbGIPnXApXGmFOxtdAZotSlvyV5L/BeY0xKvkuJQpt24Cxgid/nHmC3/f8ro2JonImyzrwETBORsX5p8wEf1mK9KUGU2ozB0sEfr/03Jfvuw2R0779ORzQl6ge4HujDeidSDtwFdAKz7N9vB+7zyz8HOAncaee/0d7+7U6XxWFd3gOcAj6B9cTX/ylwuixOaxNk+2+TmlGvkdaZscAh4O/AGVhDjPYAv3a6LAmgzQ329XQz1rvcC4BNwCtOlyXGuozljQdIA3ze/n9mCF1G9f7ruCCJ/LFv7gewlnLZDKz2++1eYH1A/ouALXb+OuDjTpfBaV2A9XZFD/zc63Q5nNYmyLYp6Sij0QVYiDX+tst2mj8Ccp0uR4Jo82msIVZdQD3wR2C60+WIsSZrhrpvxPv+q8tsKYqiKMoQ6DtKRVEURRkCdZSKoiiKMgTqKBVFURRlCNRRKoqiKMoQqKNUFEVRlCFQR6koiqIoQ6COUlEURVGGQB2loiiKogyBOkpFURRFGQJ1lIqiKIoyBOooFSVNEJFiETkqIl/zSztXRPpEZK2TtilKIqNzvSpKGiEiVwD/Bs4HaoAq4BFjzOccNEtREhp1lIqSZojIL4BLsJZnqgBWGGN6nLVKURIXdZSKkmaISC6wA5gBLDfGbHfYJEVJaPQdpaKkH6XANKzrf5bDtihKwqMtSkVJI0QkC3gV2Ir1jvILwFnGmGNO2qUoiYw6SkVJI0TkB8A7sN5NdgLPAh3GmCsdNUxREhjtelWUNEFE1gCfAz5gjGk3xviADwAXisjNDpqmKAmNtigVRVEUZQi0RakoiqIoQ6COUlEURVGGQB2loiiKogyBOkpFURRFGQJ1lIqiKIoyBOooFUVRFGUI1FEqiqIoyhCoo1QURVGUIVBHqSiKoihDoI5SURRFUYZAHaWiKIqiDIE6SkVRFEUZgv8P0pzD/AK0UuIAAAAASUVORK5CYII=", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "def beta_vis(a, b, x_ticks=True):\n", - " \n", - " beta = dist.Beta(a, b)\n", - " \n", - " x_values = jnp.linspace(0, 1, 1000)\n", - "\n", - " pmf_values = jnp.exp(beta.log_prob(x_values))\n", - "\n", - " fig = plt.figure(dpi=100, figsize=(5, 3))\n", - " plt.plot(x_values, pmf_values, alpha=0.7, color='teal')\n", - " plt.xlabel('x')\n", - " plt.ylabel('p(X=x)')\n", - " plt.title(f'Beta Distribution (a={a}, b={b})')\n", - " if x_ticks:\n", - " plt.xticks(x_values)\n", - " plt.grid( linestyle='--', alpha=0.7)\n", - "\n", - " plt.show()\n", - "\n", - "beta_vis(a=4.3, b=3.2, x_ticks=False)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The Gamma distribution\n", - "\n", - "The Gamma distribution is a continuous distribution with support in $\\mathbb{R}^+$.\n", - "Its PDF has the form \n", - "\n", - "$$p(X=x) = \\mathcal{Gamma}(x; \\alpha, \\beta) = \\frac{ \\beta^{\\alpha}}{\\Gamma(\\alpha)} x^{\\alpha - 1} e^{-\\beta x},$$\n", - "\n", - "where $\\alpha>0$ is the shape parameter, which determines the shape of the distribution, and $\\beta>0$ is the scale parameter. \n" - ] - }, - { - "cell_type": "code", - "execution_count": 28, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "def gamma_vis(a, b, x_ticks=True):\n", - " \n", - " gamma = dist.Gamma(a, b)\n", - " \n", - " x_values = jnp.linspace(0, 20, 1000)\n", - "\n", - " pmf_values = jnp.exp(gamma.log_prob(x_values))\n", - "\n", - " fig = plt.figure(dpi=100, figsize=(5, 3))\n", - " plt.plot(x_values, pmf_values, alpha=0.7, color='teal')\n", - " plt.xlabel('x')\n", - " plt.ylabel('p(X=x)')\n", - " plt.title(f'Gamma Distribution (a={a}, b={b})')\n", - " if x_ticks:\n", - " plt.xticks(x_values)\n", - " plt.grid( linestyle='--', alpha=0.7)\n", - "\n", - " plt.show()\n", - "\n", - "gamma_vis(a=2, b=0.5, x_ticks=False)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The Uniform distribution\n", - "\n", - "Perhaps, the simplest, but still a very important distribution among continuous distributions is the uniform distribution. Under this distribution, all possible values are equally likely. The uniform distribution has the following form\n", - "\n", - "$$\n", - "p(X = x) = \\mathrm{Uniform}(x\\mid a, b) = \\begin{cases}\n", - "\\frac{1}{b - a}\\, & \\text{if } a \\le x \\le b \\\\\n", - "0\\, & \\text{otherwise},\n", - "\\end{cases}\n", - "$$\n", - "\n", - "where $a$ and $b$ are the upper and lower bound parameters, respectively." - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "def uniform_vis(a, b, x_ticks=True):\n", - " \n", - " uniform = dist.Uniform(low=a, high=b)\n", - " x_values = jnp.linspace(-5, 5, 1000)\n", - "\n", - " pmf_values = jnp.exp(uniform.log_prob(x_values))\n", - "\n", - " fig = plt.figure(dpi=100, figsize=(5, 3))\n", - " plt.plot(x_values, pmf_values, alpha=0.7, color='teal')\n", - " plt.xlabel('x')\n", - " plt.ylabel('p(X=x)')\n", - " plt.title(f'Uniform Distribution (a={a}, b={b})')\n", - " if x_ticks:\n", - " plt.xticks(x_values)\n", - " plt.grid(axis='y', linestyle='--', alpha=0.7)\n", - " plt.grid(axis='x', linestyle='--', alpha=0.7)\n", - " plt.xlim(-5, 5)\n", - "\n", - " plt.show()\n", - "\n", - "uniform_vis(a=-1, b=3, x_ticks=False)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The Normal distribution\n", - "\n", - "The normal – also known as *Gaussian* – distribution is one of the most common distributions for modeling *continuous* random variables, i.e., corresponding to events with an uncountable number of outcomes. Its probability density function is\n", - "\n", - "$$\n", - "p(X = x) = \\mathcal{N}(x\\mid \\mu, \\sigma) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp\\left(-\\frac{(\\mu - x)^2}{2\\sigma^2}\\right),\n", - "$$\n", - "\n", - "where $\\mu$ and $\\sigma$ are the mean and standard deviation (also called the location, and scale or square-root of the variance $\\sigma^2$, respectively).\n", - "\n", - "`````{admonition} Task 10\n", - ":class: tip\n", - "How do the mean and standard deviation affect the samples?\n", - "`````" - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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cGU/zeplyfZ8mJydpb2+Pa+amMg0PD7NgwQK4xPQQJx1lMTACvM0Y83BC+peBjcaY25LyVwPngUR1A4DYaa8yxvx6Btd17TzKcDhMS0sLzc3Nnl3BwglUt9ScHx3lb596iiPnzgFw64oV/P769dRXVEzRbDwa5edHjvD9l15iPBKhoriYj998M+uXLHG4BO5D61rmuFkz18+jNMZMADuBu5I+ugt4NsUhg8A1wMaE14PAIfv/53NiqKJ4kN6REe771a84cu4cFcXFfPq22/joTTdRX1FxUd6y4mLedtVVfO11r2PtwoUMTUzw6W3b2NnV5YDliuI+nI56vR/4gIi8T0SaROQBYAWWA0REPi8i3wYwxkSNMfsSX0A3MGa/v+BYKRTFRQyNj/PJX/+azqEhaubP53+96lU019df8riasjK+8MpXsrWhgXA0yueefpq9Z5NDCBSl8HDUURpjvg/cC3wK2A3cCtxtjGm3syzFcpwFQSAQoKGhIR5dp8wM1e1lwtEon3/mGTqHhlg8fz5feOUrWZqiFTmdZsXBIB+96SZuWLaMyWiULzzzDKeHdOvWGFrXMscPmular4riIx5qbeXHhw5RGgrxxbvuYlV19azOMxGJ8Ilf/YpDfX0sr6zk/le/mnkuG19SlLni+jFK5WIikQgHDhy4KBpMSY/qZrGzq4sfHzoEwF/eeGNaJ3kpzYqDQT5xyy0sLC3l1OAg39y1Kxcmew6ta5njB83UUboIYwwDAwMUWit/rqhuMDA2xgPbtwPw+rVrub6hIW3+mWi2sLSUv7jhBgB+fvQoLRrco3VtFvhBM3WUiuIDHmptZWB8nJVVVbx306asnXdjXR2/c/nlAPx/zz/PhYmJrJ1bUbyCOkpF8Th7zpxhW3s7Anzo+usptid0Z4s/2LiRZRUVnB8b499efDGr51YUL6CO0kUEAgEaGxs9HR3mBIWs20Qkwj/v2AHA69auZe2iRTM6LhPNioNB/qS5GYBHDh+m7fz52RvscQq5rs0WP2jmXct9SCAQoLa21tMVygkKWbefHT5M1/AwC0tLedf69TM+LlPNNtbVcfPy5RjgwZYWT483zYVCrmuzxQ+aeddyHxKJRNizZ4+no8OcoFB1G56Y4D/27wfgv69fT1lx8YyPnY1m79+8meJgkP29vbzQ2ZmxvX6gUOvaXPCDZuooXYQxhtHR0YJ9Wp8tharbD156ieGJCVZVVXHH6tUZHTsbzRbPn8/vXnEFAN/es4dogekNhVvX5oIfNFNHqSgepHdkhEcOHwbgPRs3EpjZlnNz5i1NTZQXF3NycJAn29ryck1FcRp1lIriQX504ACT0ShX19SweenSvF23rLiYtzY1AfBvL75IeIYb3yqKl1FH6SKCwSDr1q2L79emzIxC0+386CiPHTsGwDuuuWbKHpwzZS6aveGKK6gqKaF7ZISn2tsvfYCPKLS6lg38oJk6ShchIlRXV8/qh6+QKTTd/uvgQSYiEdYtWsQ1tbWzOsdcNCsOBnnjOmtf9f/cv9/TY0+ZUmh1LRv4QTN1lC4iHA6zY8eOi3YKV9JTSLoNjY/z86NHAXj71VfP+sdnrprdvXYtZUVFnBocZHtHx6zO4UUKqa5lCz9opo7SZXg5hNpJCkW3Rw4fZiwcprG6mmvnODY5F83mFxXxurVrAfhBgbUqC6WuZROva6aOUlE8wkQkws+PHAHgbVdd5XhX1u9ccQXFwSBHzp3jxe5uR21RlFyijlJRPMLT7e0MjI+zeP58brzE7iD5oGrePF5pz9/8ib29l6L4EXWULiIYDLJ+/XpPR4c5QSHoZoyJ7zX5+rVrCc5xObBsafZ6e2eRFzo7OTs8PKdzeYFCqGvZxg+aqaN0GcUZLEOmvIzfddvX3U1bfz8lwSCvWrMmK+fMhmbLq6rYVFeHAX5mdwv7Hb/XtVzgdc3UUbqISCRCS0uL5we+800h6Bbr2nzF6tVUlJTM+XzZ1OwNdqvy8WPHGPNwZONMKIS6lm38oJk6SkVxOb0jIzxvL0Iec0puorm+nqXl5VyYnGTbiRNOm6MoWUcdpaK4nCeOH8cAV9fUsLyqymlzLkJE4lNFHi2Q7lelsFBHqSguJmoMj9vL1b36sssctmZ6XrF6NaFAgOP9/Rw7d85pcxQlq6ijdBHBYJDm5mZPR4c5gZ9123X6ND0jI5QXF7N1+fKsnTfbmlWUlLDVnrISW4fWj/i5ruUKP2imjtJlTExMOG2CJ/Grbr+wl6u7c/VqirP8Q5NtzWIt3m0nTvg6qMevdS2XeF0zdZQuIhKJsHfvXk9HhzmBX3U7NzrKC11dALw6S1NCYuRCs2tqa1laXs5oOMxvT57M2nndhF/rWi7xg2bqKBXFpTxx/DhRY7hy8WJXBvEkIyLc1dgI+Lv7VSk81FEqigsxxvDrtjaArC0wkA/ubGwkIMKB3l5ODQw4bY6iZAV1lC7DywPeTuI33Q739dE5NERJMJjVIJ5EcqHZwtJSttTXA8Qdvd/wW13LB17XTB2liwiFQmzZsoVQKOS0KZ7Cj7rFnMzW5cspLSrK+vlzqdkdq1YBsK293Xfbb/mxruUaP2imjtJFGGPo7+/33Y9LrvGbbuFolKftYJiY08k2udRsy7JllBUV0Tsy4rvtt/xW1/KBHzRTR+kiIpEIBw8e9HR0mBP4TbeWri6GJiZYWFrKhrq6nFwjl5oVB4PcZHcX+21JO7/VtXzgB83UUSqKy4h1u96+ciUBhzdnni132PtU/vbUKSY8/AOpKKCOUlFcxdD4ODvsuZOvsJ2NF7mqpoba+fMZmZzk+Y4Op81RlDmhjtJFiAilpaWIR1sRTuEn3Z4+eZJwNEpjdTUrq6tzdp1cayYi3G6Prz7po+5XP9W1fOEHzdRRuohgMMiGDRs8H0qdb/ykW2xM744ctybzoVmsRbzz9GkGxsZydp184qe6li/8oJk6ShcRjUbp7u4mGo06bYqn8ItuvSMjHOjtRYBbV67M6bXyodmyykrWLlxI1Bie8cmSdn6pa/nED5qpo3QR0WiU48ePe7pCOYFfdHu6vR2wxvcWlpbm9Fr50uw22+E/7SNH6Ye6lk/8oJk6SkVxCTFnckuOW5P55KYVKwDY39ND38iIw9YoyuxQR6koLuDM8DBHzp1DIGdL1jnB4vnzaVq8GAO+6X5VCg91lC5CRKiqqvJ0dJgT+EG3mBNZv2QJ1fPm5fx6+dTsFrtV6YfuVz/UtXzjB80cd5Qi8kERaRORMRHZKSK3pMl7s4j8VkT6RGRURA6KyF/k095cEgwGaWpq8nR0mBP4QbfY+GTMqeSafGp204oVCHCor4/uCxdyfr1c4oe6lm/8oJmjjlJE3g58CfgcsAl4GnhURKb7tbgA/G/gVqAJ+Dvg70Tkj3Jvbe6JRqN0dHR4etDbCbyuW+fgIMf7+wmK5K3bNZ+aLSwt5aqaGgDPb+js9brmBH7QzOkW5YeBbxhjHjLGHDDG3AucAu5JldkYs8sY8z1jzEvGmBPGmO8AjwHTtkK9hB8qlBN4XbdYl+TGujoqSkrycs18a3aLT6JfvV7XnMAPmjnmKEWkGLgWeDzpo8eBrTM8xyY772+ya52i5I98d7s6wU3LlyPAkXPnOD005LQ5ipIRTm4QthgIAmeT0s8CabdMEJEOoAbL/s8YYx5Kk7cESHxMrwAIh8OEw2EAAoEAgUCAaDQ65aknlh6JRKZsETNdejAYRETi501MBy5aPT85PfF8xpgp+UWEYDB4kY3TpbulTDFCoVDOyhT7P/maXihTx9AQJwcHCYrQXFd3UZ3M1X0yxlxke7bKlOo+lYVCXFNby97ubp46cYK3NDVlvUz5qnuJ5/Lj9ykXZUq01U1lmmkr1w07aSZvUiYp0pK5BSgHbgC+ICJHjTHfmybvfcCnkxN37dpFWVkZADU1NaxZs4a2tjZ6enrieRoaGmhoaODw4cMMDAzE0xsbG6mtrWXfvn2Mjo7G09etW0d1dTW7du2acrPXr19PcXExLS0tU2xobm5mYmKCvXv3xtPGxsYIBAIMDAxw8ODBeHppaSkbNmygt7eX48ePx9Orqqpoamqiq6uLjoTFp91UpmAwyJYtW3JWpvr6empqajh27BiDg4OeKtOzw8MArC4p4UDC+XN9nzZv3hzPn+0yTXefmsrK2Av89MUXWZkQ1OOF+xQr08mTJxkdHY3r5sfvU7bLtGvXrimaualMNfbY+aUQpzbTtLteR4C3GWMeTkj/MrDRGHPbDM/zSeDdxpgrpvk8VYuyo6+vj8rKSqCwWl9aJneV6UOPPcbJwUHuvf56bkvoevVymaa7T8OTk/zBj39MJBrlwbvvpq683PNl8uN9KqQyDQ8Ps2DBAoAqY8zLT9lJONaiNMZMiMhO4C7g4YSP7gJ+nMGphKmOMPk648B4PLM9lycUChEKTS1+TMxkpgtrni49+bwzTY9Go7S1tbF69WoCgUDK/NPZmGl6vsqUiIjkpEzRaJRjx46xevXqlPa7tUyn7W7XgAjXNzSkPE+u7lNyXctWmdKlV4dCXF1Tw97ubnacPs2bErpfs1GmdOnZKhNAe3v7Rbr56fsUI1tlCgQCKeuaG8o03T2+6HwzypU77gc+ICLvE5EmEXkAWAE8CCAinxeRb8cyi8ifisgbRGSt/Xov8BHgO45Yn2Wi0Sg9PT2ejg5zAq/qtt3uMrqmtpby4uK8XtspzWLTX549dSqv180WXq1rTuIHzRwdozTGfF9EFgGfApYC+4C7jTHtdpalWI4zRgD4PLAaCAPHgI8DX8+b0YqSJZ6zHeWNDQ0OW5I/bmho4MGdOznY18e50dGcL/6uKNnA8WAeY8w/A/88zWfvSXr/FeAreTBLUXLK+dFRDvb2AnB9ATnKRfPnc8WiRRzq62N7Rwd3r13rtEmKckmc7npVEggEAjQ0NMy431yx8KJuz3d2YoC1CxeyeP78vF/fSc1u8nD3qxfrmtP4QTPvWu5D/FChnMCLum13uNvVSc1usMv8Ync3Q+Pjl8jtLrxY15zGD5p513IfEolEOHDgwEVh00p6vKbbyOQke85a62zc4JCjdFKzpRUVrK6uJmoML3R25v36c8Frdc0N+EEzdZQuwhjDwMDAlHk+yqXxmm4tXV2Eo1GWVVSwvKrKERuc1syr0a9O6+ZF/KCZOkpFyTNOd7u6gVjZd505w+jkpMPWKEp61FEqSh6ZjERo6eoCnOt2dQMrqqqoLy9nMhqN66EobkUdpYsIBAI0NjZ6etDbCbyk256zZxkNh1lYWsrlixY5ZofTmknC3pte6n51Wjcv4gfNvGu5DwkEAtTW1nq6QjmBl3SLdbvesGxZfDlFJ3CDZjFH2XL6NBMeCfRwg25eww+aeddyHxKJRNizZ4+no8OcwCu6RY15eXzSdhJO4QbNLrPnkI6Fw+w+c8YxOzLBDbp5DT9opo7SRRhjGB0d9XR0mBN4RbdDvb0MjI9TVlTE1bW1jtriBs1EJB7U45XuVzfo5jX8oJk6SkXJE7G1XbfU1xPycDdUNok5yhc6O4l4eNFsxd/ot1VR8oAxhufsVpPT3a5u4sqaGiqKixmamOClhI12FcVNqKN0EcFgkHXr1k2735uSGi/o1j4wwJkLFygOBtm8dKnT5rhGs2AgwPXLlgEvBzq5Gbfo5iX8oJk6ShchIlRXVzsaDelFvKBbzAlsXLKEedNscJtP3KRZrIX9XEeH68ex3KSbV/CDZuooXUQ4HGbHjh2Ew2GnTfEUXtDNbd2ubtJsY10d80IhekdGOHrunNPmpMVNunkFP2imjtJleDmE2kncrFv3hQsc7+9HsAJ53IJbNCsOBrnW7o72QverW3TzEl7XTB2louSYWGvyqpoaqubNc9gadxKLfn3OA45SKTzUUSpKjnHLIgNuptmeMnNqcJDOwUGnzVGUKaijdBHBYJD169d7OjrMCdys28DYWHzag5sWQXebZmXFxay3F2Fwc6vSbbp5AT9opo7SZRQXFzttgidxq247urowQGN1NbVlZU6bMwW3aRaPfnX5Kj1u080LeF0zdZQuIhKJ0NLS4vmB73zjZt3cFu0aw42aXb9sGQIcPneOvpERp81JiRt1czt+0EwdpaLkiLFwmF32Yt9u6nZ1KwtKS1m3eDHgjehXpXBQR6koOaL19Gkmo1GWlpezsqrKaXM8gUa/Km5EHaWi5IhYt+sNDQ2eXpUkn8Ra3i92dzM0Pu6wNYpiMWdHKSIl2TBEsaLDmpubPR0d5gRu1C0cjbKjqwt4uZXkJtyoGcDSigpWVVURNSaun5twq25uxg+aZewoReTVIvItETkmIpPAiIgMichvROSvRcQ9S494kImJCadN8CRu021fdzcXJiepnjePK+xxN7fhNs1ixFqVbo1+datubsbrms3YUYrIG0XkEPD/gCjwj8CbgVcD7wd+A7wSOC4iD4pITQ7s9TWRSIS9e/d6OjrMCdyoW+xH/vplywi4sNvVjZrFiEUIt545w7jL1gd1s25uxQ+aZbKNwSeAjwA/M8ak2mH1PwBEZBnwIeC/A/9rzhYqiscwxrC9sxNwZ7er21ldXU3t/Pl0j4zQevq066bWKIXHjFuUxpjrjDGPTOMkE/N1GmM+ZoxRJ6kUJIf7+jg3OkppKMT6JUucNsdziMiUrbcUxWlmFcwjIqVpPnN+V1oP4+UBbydxk26xOYDN9fUUuciuZNykWTKxlvgLnZ2Eo2mfzfOOm3VzK17XbLZRr7tEZHNyooi8Fdg7N5MKl1AoxJYtWwi5YGNfL+E23WKtIDd3u7pNs2SaamqoKinhwuQk+7q7nTYnjtt1cyN+0Gy2jvKXwLMi8nGxKBeRb2EF+vxN1qwrMIwx9Pf3u36Xd7fhJt1ODQzQOTREKBDgWhftPZmMmzRLRUCE65ctA9wV/ep23dyIHzSblaM0xvwP4I1YQTtPAXuADcAWY8xXsmZdgRGJRDh48KCno8OcwE26xbpdNyxZwvyiIoetmR43aTYdsXHK7Z2drvmR9YJubsMPms1lwYHHgR8BNwHLgY8bY/ZnxSpF8She6Hb1ChuWLGFeKMS50VEO9/U5bY5SwMw2mGcN8Bzweqx5lF8EfiwiXxQR9z5GK0oO6R0Z4ci5cwhwnd1tqMyeomCQ5qVWbKAukq44yWxblLuBNmCDMeaXxphPAq/AWoDghSzZVnCICKWlpbouaIa4RbfYj3nT4sUsKJ02MNwVuEWzS5E4TcQN3a9e0c1N+EGz2TrKDxpjfs8Y0x9LMMY8C2wCWrNhWCESDAbZsGGD50Op841bdHPr3pOpcItml6K5vp5QIEDn0BAdg4NOm+MZ3dyEHzSbbTDPv06TPmSMef/cTCpcotEo3d3dRF02b8ztuEG3wfFx9vX0AN4Yn3SDZjNhflERG+xFG9yw+IBXdHMTftBs1sE8ItIgIoHk/5XZE41GOX78uKcrlBO4QbcXOjuJGkNjdTVLyssds2OmuEGzmRJ78HDDOKWXdHMLftBsLs5tP7Aqxf+KUnB4qdvVa1zf0IAAR86do3dkxGlzlAJkLo5SpvlfUQqK0clJdp05A3ij29VrVM+bR5O9VZmbFh9QCgfHu0tF5IMi0iYiYyKyU0RuSZP3zSLySxHpEZFBEXlORF6dT3tziYhQVVXl6egwJ3Bat52nTzMZjbK0vJwVVVWO2JApTmuWKfHFBxzufvWabm7AD5o56ihF5O3Al4DPYUXMPg08KiIrpjnkVqzl8+4GrgWeBB4RkU25tzb3BINBmpqaPB0d5gRO6xbvdm1o8MyPgdOaZUqspb6vp4eh8XHH7PCabm7AD5o53aL8MPANY8xDxpgDxph7gVPAPakyG2PuNcZ80RizwxhzxBjzCeAI8Ib8mZw7otEoHR0dnh70dgIndZuMRNjR1QXAVg+NT3qtri0pL2d1dTVRY3jB3uvTCbymmxvwg2aOLecuIsVYrcIvJH30OLB1hucIABXAuTR5SoCShKQKgHA4TNjePT0QCBAIBIhGo1NuZiw9EolMmew8XXowGERE4udNTAcuWuswOT0SiXDq1Cnq6uoQkSn5RYRgMHiRjdOlu6VMMUKhEMaYnJQp9kWsqamZ8tSajzLtOXOGkYkJFpSW0lhVRSQS8cR9MsZw6tSpizTL5X2aa5muq6/n+LlzPHvqFK9YvdqRuhcOh6fo5sfvU7bLNDk5OUUzN5Vpps7byX1PFgNB4GxS+lmgbobn+EugDPiPNHnuAz6dnLhr1y7KysoAqKmpYc2aNbS1tdFjz4UDaGhooKGhgcOHDzMwMBBPb2xspLa2ln379jE6OhpPX7duHdXV1ezatWvKzV6/fj3FxcW0tLRMsaG5uZmJiQn27rV2JjPGxK8zMDDAwYMH43lLS0vZsGEDvb29HD9+PJ5eVVVFU1MTXV1ddCSM37ilTGB9YbZs2ZKzMi21lzk7evQoQ0NDeS3Tr48coX9ggCuLiti5c6dn7tOmTZuIRqO0trbGu4tzfZ/mWqay0VH6BwbYKcKF8XH27d494/uUrTK1t7fT398f182P36dsl6m1tXWKZm4qU01NDTNBZrsslIgMYS1hdzzx/wyOrwc6ga3GmOcS0v8aeLcxZt0ljn8H8BDwu8aYJ9LkS9Wi7Ojr66OyshJwT+srEonQ2trKli1bCAaDnnhadMMTcOwHf9OmTXltUQaCQf77ww/TPzrKZ267jY12T4AX7pMxhpaWFjZv3uyZFqUxhj/5+c/pvnCBj998M9cnbWOWj7o3MTHBzp0747r58fuU7TJNTEzQ2toa18xNZRoeHmbBggUAVcaYaZd+mkuL8jvAYIr/Z0ovEOHi1mMtF7cyp2AHAX0DeFs6JwlgjBkH4qP/safnUCh00UaiMTGTmW4Qerr06TYovVR6IBCgtraWQCCAiKTMP52Nmabnq0yJ5KpM0WiUmpoaioqKMirrXMu0r7ubgfFxKubNY6O91Fq2ynQp2+dapmg0Sm1tbUrN3Fz3blqxgocPHmR7Rwc3rUgd85fLuhcKhVLq5qfvU4xslamoqCilZm4oU6o8qZh1MI8x5h5jTG/y/xkcPwHsBO5K+ugu4NnpjrNbkt8C3mmM+VlGRrucQCDAmjVrZnzzFAundItNVbguyUl6Aa/WtVj0646uLsIOBId4VTcn8YNmGVkuIvNmkGdtBqe8H/iAiLxPRJpE5AFgBfCgfa7Pi8i3E879DuDbWGOT20Wkzn55Y/LaJYhGoxw7dszT0WFO4IRuxhhPr8bj1bq2bvFiqufN48LkJC+eTdvxlBO8qpuT+EGzTF38bhG5froPReTDWFtwzQhjzPeBe4FP2cfdCtxtjGm3syzFcpwx/hiru/irwOmE15dnek03E41G6enp8XSFcgIndDt+/jzdIyOUBINsqptp7Jl78GpdExFusPf6dGKRdK/q5iR+0CxTR/kE8JTd0otv0Cwil4nIM1gRph/I5ITGmH82xqwyxpQYY641xjyV8Nl7jDG3J7y/3RgjKV7vybAcijInnrVbk9cuXUrJNGMzSm64we5+fb6z0xV7VCr+JyNHaYz5M+C1wDuAVhFpFpG/APYCPcDVxpjvZd9MRXEPxhiePnkSYNqAEiV3bKirY35REedGRznU1+e0OUoBkPHoqjHm18A1wHHgeeBvgA8YY95kjMn/oIGPCAQCNDQ0eHrQ2wnyrVtbfz+nh4cpDga5zu4G9BpermuhQIBme+5svhdJ97JuTuEHzWZr+TuAO7AcZTHwShGpyJpVBYofKpQT5Fu3Z+zWZPPSpczzaLer1+taLIDquY6OvHa/el03J/CDZplGvS4Tkcewlp37c2PMVuA6YDPwkogkT/VQMiASiXDgwIGLJuIq6cmnbsaYuKP0crer1+tac309RYEAp4eHOZmw0kqu8bpuTuAHzTJ18fsAA6w3xnwLwBizB9iCNW3jZyLytaxaWEDElrDTAIXMyKdufuh2Be/XtXmhEBvtaON8Rr96XTcn8INmmTrKTxhjXmOMmVIzjTGTxphPYi1mPu1+koridfzQ7eoXYosP6GbOSq7JNOo1bWvRGNOC1Q2rKL4jsdv1Zg93u/qF6xsaEOB4fz+nExbDV5RsM2NHKSJlM8lnL0034/zKywQCARobGz096O0E+dItsdt1i4e7XcEfda2ypIQNS5YAxKfr5Bo/6JZv/KBZJpYfFZFP2Lt+pEQs7hKRR4E/n7t5hUXioujKzMmXbk+3WwtG+aHb1S917daVK4GX702u8Ytu+cQPmmVi+e3AJqBNRJ4Xka+KyF+LyF+KyN+JyI+ALqxdPX4CfDH75vqbSCTCnj17PB0d5gT50M0Yw2/tsTA/dLv6pa7duHw5oUCAEwMDeYl+9Ytu+cQPms3YURpjDhlj3gasAf4dqAfeCvwhlhPttP9fZYz5mjHGu6o4hDGG0dFRT0eHOUE+dDt+/rxvul3BP3WtvLiYa+3FB/LRqvSLbvnED5pl3H9kR7w+YL8Qe4NH42UVFOUSaLSre7l15Uqe7+zkqfZ23nnNNfE9ZxUlW8y601hE3i8i+4AxYExE9olIRguiK4oXMMbwlN1aucUeE1Pcw3XLllEcDNI1PMzx8+edNkfxIbNylCLyt1hbWz0CvM1+PQI8ICJ/lz3zCotgMMi6deum3UFcSU2udTvY20v3yAjzQiG21E8by+Yp/FTX5oVCXGffl6dy3P3qJ93yhR80m22L8h7gD40x9xljfmK/7gP+CPiT7JlXWIgI1dXV2nWUIbnWbduJEwBsbWjwzZZafqtr8ejXkydzOhbmN93ygR80m62jDAItKdJ3MotxT8UiHA6zY8cOwuGw06Z4ilzqFo5GecaOdr1t1aqsn98p/FbXrq2vpzQUomdkhIO9vTm7jt90ywd+0Gy2jvI7WK3KZP4I+O7szVG8HELtJLnSbfeZMwyOj1OVMLndL/iprhUHg/El7XLd/eon3fKF1zWbywzQ99sBPA/Zr31Y00OiInJ/7JUlOxXFEWLdrreuXEnQwxOmC4HE7tdINOqwNYqfmG036dVAq/3/Gvtvj/26OiGfThlRPMtYOMx2e2eK2zTa1fVsqKujqqSEgfFxdp05Q7NPAq8U55mVozTG3JFtQxQrOmz9+vWejg5zglzp9nxHB+ORCEvLy7l80aKsnttp/FjXQoEAt65cySOHD/NkW1tOHKUfdcs1ftBM+5JcRnFxsdMmeJJc6PYbe6zrtpUrPR2xNx1+rGuvWL0agO2dnVyYmMjJNfyoW67xumbqKF1EJBKhpaXF8wPf+SYXug2Oj9N6+jQAt/so2jWGX+vamgULWF5ZyUQkwrM52KfSr7rlEj9opo5SUVKw7cQJIsawduFCllVWOm2OMkNEJN6q/HVbm8PWKH5BHaWipOCJ48cBeGVjo8OWKJly+6pVCLCvp4ezw8NOm6P4AHWUipLE8fPnaevvJxQIcIsPttQqNBbPn896e87rk/b0HkWZC+ooXUQwGKS5udnT0WFOkG3dYq3JG5Yto6KkJCvndBt+r2ux7tcn29qyuqSd33XLBX7QTB2ly5jIUaSe38mWbuFoNL7IgN+7Xf1c17YuX06JvaPIob6+rJ7bz7rlCq9rpo7SRUQiEfbu3evp6DAnyKZuL3R2MjQxwcLSUjbZGwL7Eb/XtXmhEFuXLwfgl8eOZe28ftctF/hBM3WUipJArNv1FatWEfDh3MlC4lVrrEXDnjp5ktHJSYetUbyMOkpFsTk/OspOe+6k37tdC4GrampYVlHBWDjM0ydPOm2O4mHUUboMLw94O0k2dHvyxAmixrBu0aKCmDvp97omIvFW5WNHj2btvH7XLRd4XTN1lC4iFAqxZcsWQj7ZHDhfZEM3Y0z8x/TOAmhNFkpdu3P1akKBAIfPneNEf/+cz1coumUTP2imjtJFGGPo7+/P6Q7tfiQbur3Y3U3X8DCloVBB7BRSKHWtat48rl+2DMhOq7JQdMsmftBMHaWLiEQiHDx40NPRYU6QDd0ePXIEgDtWraK0qChbprmWQqprr7a7X588cYKJOZa3kHTLFn7QTB2lUvCcHx3lOXvfyddcdpnD1ijZZmNdHbXz53NhcpLfalCPMgvUUSoFzy+PHydiB/GsXrDAaXOULCMi3BUL6sninEqlcFBH6SJEhNLSUl/ufZhL5qJbNCGI57Vr12bbNNdSaHXtrsZGAiK81NMzp6CeQtMtG/hBM3WULiIYDLJhwwbPh1Lnm7no1nr6NN0jI5QXF3NzAS2AXmh1bdH8+WxtaADgp4cPz/o8haZbNvCDZuooXUQ0GqW7u5toNOq0KZ5iLrr93A7iuXP1aoo9/EXOlEKsa6+//HLACuoZGh+f1TkKUbe54gfN1FG6iGg0yvHjxz1doZxgtrp1DQ3R0tUFwGsLLIinEOvalTU1rK6uZiISiS9VmCmFqNtc8YNmjjtKEfmgiLSJyJiI7BSRW9LkXSoi/yYih0QkKiJfyqOpis945NAhDLClvr4gVuIpdEQk3qr86eHDRD08r0/JL446ShF5O/Al4HPAJuBp4FERmW6wqATosfPvyYeNij+5MDHBE21tAPzOFVc4bI2SL25buZLy4mK6R0bY0dnptDmKR3C6Rflh4BvGmIeMMQeMMfcCp4B7UmU2xpwwxnzIGPNtYCCPduYFEaGqqsrT0WFOMBvdHj92jLFwmJVVVWxYsiSH1rmTQq1rJaEQr7KXKJxNUE+h6jYX/KCZY45SRIqBa4HHkz56HNiaf4ucJxgM0tTU5OnoMCfIVLdINMoj9o/k715xhae/wLOlkOva6y6/HAF2nz2b8VSRQtZttvhBMydXqV0MBIGzSelngbpsXURESrC6bGNUAITDYcLhMACBQIBAIEA0Gp0y4BxLj0QiU9YpnC49GAwiIvHzJqYDFy3hlJwejUY5c+YMDQ0NiMiU/CJCMBi8yMbp0t1SphihUAhjTE7KBHDmzBmWLFkyxelNV6btnZ30jIxQXlTETQ0N8bK5qUy5vk8iQldXF0uWLCEQePl52ctlmul9WlhSwo0NDTzb0cEP9+/nQ9ddN+MyhcNhurq6qKuri6e5oUzpbHf6Pk1OTnLmzJm4Zm4q00wDjNywnHvyiLqkSJsL9wGfTk7ctWsXZWVlANTU1LBmzRra2tro6emJ52loaKChoYHDhw8zMPByT29jYyO1tbXs27eP0dHRePq6deuorq5m165dU272+vXrKS4upqWlZYoNzc3NTExMsHfvXsBaPHhgYID6+nqGh4c5ePBgPG9paSkbNmygt7eX4wkRe1VVVTQ1NdHV1UWHvQybm8oE1hdmy5YtDAwM5KRMS5cu5fTp0wwMDDA0NJS2TMYYvt/bC8CVoRB7d+1yZZlyfZ82bdrEyZMn6ejoiD9ceL1MmdynqwMBngV+eeQITZOTLCwpmXGZjh49SmdnJyLiqjK59T7t3LmT/v7+uGZuKlNNTQ0zQZxa0d3ueh0B3maMeTgh/cvARmPMbZc4fhuw2x7XTJcvVYuyo6+vj0o70tEtT8CRSITW1la2bNlCMBj0xNOiG56Ao9Eora2tbNq0aUr3Tqoy7evu5n9u20ZRMMiDd9/NwtJSV5Yp1/fJGENLSwubN2+eopmXy5Tpffr0b37D7jNneP3atXxg06YZlWliYoKdO3fGdXNbmdx4nyYmJmhtbY1r5qYyDQ8Ps8BatrLKGDPINDjWojTGTIjITuAu4OGEj+4CfpzF64wD8dnFsafnUCh00f5oMTGTma5vfbr06fZdm0l6zD4RSZl/OhszTc9nmWLkqkyJXaepzp9YpocPHQIRXtnYSG1FxYxtny7dq/cpHA7Hf2ySP/NqmdKlpyrTW6+8kj1nz/JEWxu/v349FSUvP0+nK1Mq3dxSpkvZ7sR9ijnSZM3cUKZUeVLhdNTr/cAHROR9ItIkIg8AK4AHAUTk8yLy7cQDRGSjiGwEyoEa+/2V+TY8FwQCAWpqamZ88xSLmep29Nw5Ws+cISDCm5ua8mSdO9G6BhuWLKGxuprxSISf2Ss0XQrVLXP8oJmjlhtjvg/cC3wK2A3cCtxtjGm3syzFcpyJ7LJf1wLvtP//eR7MzTmBQIA1a9Z4ukI5wUx1+8FLLwHWXLq68vJ8mOZatK5ZrZe3XGk9Yz9y+DDjSV2HqVDdMscPmjluuTHmn40xq4wxJcaYa40xTyV89h5jzO1J+SXFa1W+7c4F0WiUY8eOeXqpJyeYiW6nBgbie06+9UpfdEDMCa1rFjctX05dWRmD4+PxdX/Tobpljh80c9xRKi8TjUbp6enxdIVygpno9oP9+zHADcuWsaKqKn/GuRStaxbBQIC3X301AD88cICxS7QqVbfM8YNm6igV33NqYIBtJ04AxH8UFSXGHatWsbS8nIHxcX42hy24FP+ijlLxPd998UUMsLWhgcsWLnTaHMVlBAMB3n7VVQD86ODBS7YqlcJDHaWLCAQCNDQ0eHrQ2wnS6Xb8/Hl+e+oUArzzmmvyb5xL0bo2ldtXraK+vJzB8fG0a8CqbpnjB828a7kP8UOFcoJ0un3HXv3j1pUrWVldnWfL3IvWtakEAwF+z+6W/8/9+6fd2Fl1yxw/aOZdy31IJBLhwIEDF61YoaRnOt0O9PSwo6uLgAjv0LHJKWhdu5jbVq1iZVUVFyYn+cH+/SnzqG6Z4wfN1FG6iNhar04tK+hVUulmjOGh1lYAXrl6tW7MnITWtYsJiPDejRsBa17l2eHhi/KobpnjB83UUSq+5Kn2dg6fO8e8UIh3rV/vtDmKR9i8dCkbliwhHI3y7T26N7xioY5S8R0TkQjfsn/k3nbllSxIWPhcUdIhIrxv0yYEeOrkSY709TltkuIC1FG6iEAgQGNjo6cHvZ0gWbf/OniQ3pERaubP543r1jlsnTvRujY9jQsWcPuqVQB8fefOi3bQUN0yww+aeddyHxIIBKitrfV0hXKCRN16R0bigRjv2biRYg/vqp5LtK6l5w82bGBeKMShvj6eSNgHUXXLHD9o5l3LfUgkEmHPnj2ejg5zgkTdvt7Swlg4TNPixdyyInk9fSWG1rX0LJo/n9+3591+c/fu+HQR1S1z/KCZOkoXYYxhdHTU09FhThDTbXtHB9s7OwmK8GfXXRff21O5GK1rl+b1l1/OispKhiYm4oE9qlvm+EEzdZSKLxiPRPg/9nSQN61bpwufK3MmFAhwz5YtADx27BgHe3sdtkhxCnWUii947PRp+kZGWFJWFl9hRVHmytW1tdy5ejUG+NL27Ux4uPtQmT3qKF1EMBhk3bp1BDUAJSMO9PWxa2QEEeGe5mZKQiGnTXI9Wtdmzgc2b2ZhaSmdQ0N876WXVLcM8UNdU0fpIkSE6upqHVvLgNHJSb60fTuhoiLuWrOGa+vrnTbJE2hdmznlxcX8md0F++NDhzgTDqtuGeCHuqaO0kWEw2F27NhBWLf5mTEPtbZydngYGRnhPboCz4zRupYZW5Yt4xWrVhGNRvnET37C8NiY0yZ5Bj/UNXWULsPLIdT55vmODh4/fhwR4e0rVjC/qMhpkzyF1rXM+MNrr2Xh/Pl0j43x4M6dTpvjKbxe19RRKp7kzPAwD2zfDsDvXH45ayoqHLZI8TvlxcX85Q03IMC2Eyf4VcJCBIq/UUepeI6JSIQvPPMMFyYnuWLRIt6tXa5KnriqpoZXL10KwNdaWjg1MOCwRUo+UEfpIoLBIOvXr/d0dFg+eKi1lWPnz1NRXMzHb76ZkqIi1S1DtK7NjmAwyL2vehUb6uoYj0T43NNPc2FiwmmzXI0f6po6SpdRXFzstAmu5udHjvDo0aMI8JGtW1k8fz6gus0G1Wx2zCspide9zqEhvvjb3xKJRp02y9V4va6po3QRkUiElpYWzw9854qdXV082NICwLvWr2ez3QWmumWOajY7YrpVFBXxP2+9leJgkNYzZ/jm7t1Om+Za/FDX1FEqnuBEfz9f+O1vMcCdq1fztiuvdNokpcBpXLCAv7jhBsCaX/nTw4cdtkjJFeooFddzemiIT2/bxlg4zPraWl3wXHENN69YEd9l5Os7d7LtxAlnDVJygjpKxdX0XLjAX//615wbHWVFZSX33XILIQ/va6f4j7dfdRVvuPxyAB7Yvp0XOjsdtkjJNuLlrU9mg4hUAgMDAwNUVlY6bc4UjDFEIhGCwaC2mIBzo6N8/IknOD08zLKKCj5/550sKC29KJ/qljmq2eyYTjdjDA9s386TJ05QFAjw8Ztv5rplyxy01D24ua4NDg5SZe00VGWMGZwunz6au4wJDTUHoGtoiI8+/jinh4dZUlbG373iFSmdZAzVLXNUs9mRSjcR4c+vv54bGxqYjEb5+6ef5qn2dgescyder2vqKF1EJBJh7969no4OywbHzp3jY7/8Jd0jIywtL+fv77wzPg0kFapb5qhmsyOdbqFAgI/ddBO3r1xJxBj+6dln+cXRow5Y6S78UNfUUSqu4oXOTu771a8YGB+nsbqaL951F7VlZU6bpSgzIhQI8OEbb+S1l12GAb66YwcPtbYSLbAhLr+hG/cprsAYw/dfeonvvvgiAOtra/nrW2/Vhc4VzxHbF3VhaSnfffFFfnzoEB2Dg3x061bKPD7xvlDRFqXL8PIyT7NlcHyczz39dNxJ3n3ZZXz2jjsycpKFqNtcUc1mx0x0ExF+7+qr+aubbqI4GGTn6dP8+aOPcqi3Nw8Wug+v1zWNelUcZWdXF19+/nnOj40RCgT4YHMzd61Z47RZipI1jp47x+effprukRECIvz+NdfwlqYmgjrNyXFmGvWqjtJFGGMYGBigqqrKdWHU2WZofJxv7d7N4/ZWRcsrK/nI1q00LliQ8bkKSbdsoZrNjtnqdmFigq/u2MHTJ08CsGbBAv7suuu4bOHCXJnqGtxc13R6iAeJRCIcPHjQ09FhlyJqDI8dPcof//SncSf5hssv50uvec2snCQUhm7ZRjWbHbPVray4mI9u3cq9119PWVERx86f58OPPcb/2bmTwfHxHFnrDvxQ1zSYR8kLxhie6+jgO3v3cmrQenBbVVXFPVu2cGVNjcPWKUruERHubGxk89KlPNTaylMnT/LI4cP8qq2NtzQ18TtXXMG8kP4kuxG9K0pOCUejbO/o4D/37+fY+fMAlBUV8Y6rr+b1l1+u4zRKwbGgtJSP3nQTd61Zwzd37eJ4fz//uncvPzl0iDdcfjl3r11LRUmJ02YqCaijdBEiQmlpqev68WdD/9gYTxw/zs+OHKF3ZASAeaEQb7ziCt64bl1Ww+T9pFu+UM1mRzZ121hXx5de8xp+097Ov+7ZQ/fICN958UV+sH8/d65ezV1r1rBmwQLP3yM/1DUN5lGyxujkJM91dPCbEyfYffZsfJJ1VUkJr73sMl5/+eVUzZvnsJWK4j7C0SjPnDzJwwcOcLy/P56+qqqKV6xezY3Ll1NXXu6cgT5Fo16nwc2OMhqN0tvby+LFiwl4oEvSGEPn0BA7u7po6epiX08P4YSd3i9fuJC7167llpUrKc7hPCqv6eYGVLPZkWvdjDG82N3NY0eP8lxHB5MJ36eVVVVcv2wZm5cu5fJFiyjyyNxEN9e1mTpKx7teReSDwEeBpcBLwL3GmKfT5L8NuB+4CugCvmiMeTAftuaaaDTK8ePHWbhwoesqFMDI5CTt/f0c7O3lgP3qHxubkmdZRQW3r1rFrStXUl9RkRe73K6bG1HNZkeudRMR1i9ZwvolSxiemOCp9nZ+e/Ik+3p6aB8YoH1ggP/Yv5+iQIArFi3i6tpa1i5aROOCBSxyafemH+qao45SRN4OfAn4IPBb4I+BR0XkSmPMyRT5VwM/B/4FeBdwE/DPItJjjPlh3gz3MZORCD0jI3RfuED3hQt0DQ1xcmCA9v5+uu2xxkRCgQBX19TQXF9Pc3099RUVrvyyKorXKC8u5u61a7l77VqGxsdp6erihc5OXuzuZmB8nH09Pezr6ZmSf3V1NcsrK1laUcHS8nLq7FeJRtPOCafV+zDwDWPMQ/b7e0Xk1cA9wH0p8v8JcNIYc6/9/oCINAMfAdRR2hhjGI9EGAuHGZ2cZCwctv63/w5PTDAwNsbA+DiD4+Px/8+PjXFudDTtuReWlnLFokWsW7yYpsWLWbNwYU67VRVFgYqSEu5YvZo7Vq/GGEPX0BD7urvZ39PD8fPnOTU4yPDEBC92d/Nid/dFx5cVFbFg3jwWlJbG/1aWlDC/qIiyoiLrb3Fx/H1JKERRIEBxMEgoECj4h1/HHKWIFAPXAl9I+uhxYOs0h91of57IY8D7RaTIGDOZ4jolQGKsdQXAV55/nnn2rhRiZcQYYwWgxMZt7coRS0sczRURosZg7BeA2N0K0WjUSk/Ia+z0GMYYJBCYcnw0GqXv3Dl+euGCZY+dP2oMYft8k5EIk5EI4WiUiDFEolEiQNhOjxhDOBrFxK6bWB67TJdKLwkGqZk/n9qyMuoqKlhVXc2y8nJWVFbGw9ZjazdGIhHC4XD8NInpiYRCofgGrokaBoNBotHoFG2mSw8EAgQCgYvSjTFUVVURjUan2BLLH4lESByLj20gm5g3ne1OlGk627NVJoDKysqLNPNymfJxn4wxVFRUxHVzqkzLKiupr6jgzlWrAOt3oWNoiPbBQToGBjg9NMSZCxc4MzzMhclJLkxOMjwxwamBgZdPMoPfAoxBRCynGQpREgoREiEoQjAQIGD/DQUCYEz8fcC2PSgCxnD+3Dl+OTaGiMS7X000GnfAYmtmIG5L7Hc5YOcxxsTT4vnt38/YeQJ2/vhveex+2GWK/WbHmEjRS5YKJ1uUi4EgcDYp/SxQN80xddPkD9nnO53imPuATycnPrJ3LyF7I+Di4mLKysq4cOHClA1GS+fNY15pKcNDQ0wmVOz58+dTUlLC4MAAkYQvU3l5OUVFRfT390+5GZWVlQRE6E+spEB1VRVRYxgcfHkMWUSojkSYnJxkeHg4nh4MBKisqmJ8fJyRhJtbFApRXlHB2OgoownjhbEyRcbHIRymJBCgJBBgUVUVdYsWMdbfTyAcpjwUoiwU4vKVK2lcupSzbW0EJyfjFW/d2rVUV1ezY8cODiV8WdevX09xcTEtLS1TytTc3MzExAR79+592fZgkC1btjAwMMDBgwdf1re0lA0bNtDb28txe5UegKqqKpqamujq6qKjoyOeXlNTw5o1a2hra6MnocupoaGBpqYmDhw4wECCxo2NjdTW1rJv3z5GE1rK69ato7q6ml27dk35AXJbmRoaGjh8+HDOyrRq1SpaW1t9VaZc36eTJ08yNDQU181tZXrlhg10d3dbZSouhgULKCoro3bFCg62t3O0o4OhcJihyUkC8+ZRWlVFx9mznBsaYjQSYSwSQUpKCBYXc2F4OLu/e3ZLd9rfverqrP3uzfS3vHiGLWXHol5FpB7oBLYaY55LSP9r4N3GmHUpjjkMfNMY8/mEtJuAZ4ClxpgzKY5J1aLs+L/PPktZRQWC/RQZCFhPG/ZTjmC1EGNPJ/GnGTs9aD8xk/g0Y+ef8oRqp0tCC5GEa4LVkhT7uPPnz1NTU4Pw8hOUiBCyn+gCItbTmp1WFAxSUlSEGEMA4mnzi4spLSqynqx89lSfnA5w5swZlixZMqWLyMtlyvV9EhG6urpYsmTJlAALL5cpH/cpHA7T1dVFXV1dPM3rZUqVLiKMT04yHg4zEYkwGY0Stnu2RicmmIhEiNqttliP2Xg4HE+L9ahFjWEiHKa3r49qe05orL4l97zFWogxWxLTY7/NBuItyFh6yvz2uRM1SJU+euEC773xRnBx1GsvEOHi1mMtF7caY5yZJn8Y6Et1gDFmHIgvphj7IX3LVVe5bnpIOBympaWF5hUrCGVp8D2xYiYy3bY306VPZ08m6SKSMj32hZ1tejgcpqOjg7q6upTn92KZYuTqPoXDYTo7O1m6dOlFn3m1TOnSs1UmgK6uLurr66ecz8tlmi59XnEx87KwMEg4HKbl/Hma167N2u9athgcHOS9M8jnWKyuMWYC2AnclfTRXcCz0xz2XIr8rwJaUo1PKoqiKMpccXpSy/3AB0TkfSLSJCIPACuABwFE5PMi8u2E/A8CK0Xkfjv/+4D3A/+Ud8sVRVGUgsDRdrAx5vsisgj4FNaCA/uAu40x7XaWpViOM5a/TUTuBh4A/hRrwYE/98scykAgQE1NjWcn5TqF6pY5qtnsUN0yxw+a6RJ2iqIoSkGiGzd7kGg0yrFjxy6K6FTSo7pljmo2O1S3zPGDZuooXUQ0GqWnp8fTFcoJVLfMUc1mh+qWOX7QTB2loiiKoqTBXZNa8kjiqhBuIRwOc+HCBQYHB10338jNqG6Zo5rNDtUtc9ys2Uz9QCEG8ywDOi6ZUVEURSkUGowxndN9WIiOUoB6YMhpW1JQgeXEG3CnfW5Fdcsc1Wx2qG6Z43bNKoAuk8YZuqsdnAdsMaZ9cnCShHVKh9KFKitTUd0yRzWbHapb5nhAs0vapME8iqIoipIGdZSKoiiKkgZ1lO5iHPgsCbudKDNCdcsc1Wx2qG6Z43nNCi6YR1EURVEyQVuUiqIoipIGdZSKoiiKkgZ1lIqiKIqSBnWUiqIoipIGdZQuR0RKRGS3iBgR2ei0PW5GRFaJyDdEpE1ERkXkmIh8VkSKnbbNbYjIB22dxkRkp4jc4rRNbkVE7hORHSIyJCLdIvJfInKF03Z5CVtDIyJfctqW2aCO0v18Eehy2giPsA6rTv8xcBXwF8CfAH/vpFFuQ0TeDnwJ+BywCXgaeFREVjhpl4u5DfgqcANwF9aKZo+LSJmjVnkEEdkC/BGw12lbZotOD3ExIvJa4H7gLcBLwCZjzG5HjfIYIvJR4B5jTKPTtrgFEXkeaDXG3JOQdgD4L2PMfc5Z5g1EpAboBm4zxjzltD1uRkTKgVbgg8Angd3GmHsdNWoWaIvSpYjIEuBfgHcDIw6b42WqgHNOG+EW7G7oa4HHkz56HNiaf4s8SZX9V+vVpfkq8DNjzBNOGzIXCm5RdC9g73DyLeBBY0yLiKxy1iJvIiJrgP8B/KXTtriIxUAQOJuUfhaoy7853sL+bt4PPGOM2ee0PW5GRH4P2AxscdqWuaItyjwiIp+xB7TTvZqxftwrgc87bLIryEC3xGPqgV8APzDGPOSM5a4mecxFUqQpF/O/gfXAO5w2xM2IyHLgy8C7jDFjTtszV3SMMo+IyGKsJ/p0nAD+HXgDU3+4gkAE+K4x5g9yYqBLmalusS+k7SSfBJ4H3mOMiebYRM9gd72OAG8zxjyckP5lYKMx5jbHjHM5IvIV4I3ArcaYNofNcTUi8kbgYazfrBhBrN+0KFBijImkONSVqKN0IXb0YWVCUj3wGPBW4HljTIcjhnkAEVmG5SR3Yj3NeubLmC/sYJ6dxpgPJqTtB36swTwXY3e3fgV4E3C7MeaIwya5HhGpAFYmJX8TOAj8g9e6rXWM0oUYY04mvheRYfvfY+okp8duSW4DTgIfAWpim8YaY844Z5nruB/4VxFpAZ7DCt1fATzoqFXu5avAO4HfBYZEJDaWO2CMGXXOLPdijBkCpjhDEbkA9HnNSYI6SsVfvAq4zH4lP1DIxdkLE2PM90VkEfApYCnWD9rdxph2Zy1zLbFpNNuS0t+LFXSn+BztelUURVGUNGjUq6IoiqKkQR2loiiKoqRBHaWiKIqipEEdpaIoiqKkQR2loiiKoqRBHaWiKIqipEEdpaIoiqKkQR2loiiKoqRBHaWiKIqipEEdpaIoiqKkQR2lohQIIlIjImdE5BMJadeLyISIvMpJ2xTFzehar4pSQIjI3cB/AVuxtjzaBfzMGHOvg2YpiqtRR6koBYaIfBV4JbAD2ABs8cMu9IqSK9RRKkqBISKlWFtrLQeajTF7HTZJUVyNjlEqSuHRCNRjff+Td6FXFCUJbVEqSgEhIsXAC8BurDHKDwPXGGPOOmmXorgZdZSKUkCIyD8Cb8UamxwGngSGjDGvd9QwRXEx2vWqKAWCiNwO3Au82xgzaIyJAu8GbhaRexw0TVFcjbYoFUVRFCUN2qJUFEVRlDSoo1QURVGUNKijVBRFUZQ0qKNUFEVRlDSoo1QURVGUNKijVBRFUZQ0qKNUFEVRlDSoo1QURVGUNKijVBRFUZQ0qKNUFEVRlDSoo1QURVGUNKijVBRFUZQ0/P/LvVYyDhud/wAAAABJRU5ErkJggg==", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "def norm_vis(mu, sigma, x_ticks=False):\n", - " \n", - " normal = dist.Normal(loc=mu, scale=sigma)\n", - " \n", - " x_values = jnp.linspace(-5, 5, 1000)\n", - "\n", - " pmf_values = jnp.exp(normal.log_prob(x_values))\n", - "\n", - " fig = plt.figure(dpi=100, figsize=(5, 3))\n", - " plt.plot(x_values, pmf_values, alpha=0.7, color='teal')\n", - " plt.xlabel('x')\n", - " plt.ylabel('p(X=x)')\n", - " plt.title(f'Normal Distribution ($\\mu$={mu}, $\\sigma$={sigma})')\n", - " if x_ticks:\n", - " plt.xticks(x_values)\n", - " plt.grid(axis='y', linestyle='--', alpha=0.7)\n", - " plt.grid(axis='x', linestyle='--', alpha=0.7)\n", - " plt.xlim(-5, 5)\n", - "\n", - " plt.show()\n", - "\n", - "norm_vis(mu = 0, sigma = 1 )" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "`````{admonition} Task 11\n", - ":class: tip\n", - "Implement the PDF of the Normal distribution and test it using the function provided below.\n", - "`````" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "metadata": {}, - "outputs": [], - "source": [ - "def test_normal_pdf(pdf_fn, run=False):\n", - " if not run:\n", - " return\n", - " assert pdf_fn(0, 1, 0) == jnp.exp(dist.Normal(loc=0, scale=1).log_prob(0)), \"Normal(X=0|0, 1) is incorrect.\"\n", - " assert pdf_fn(0, 2, 0) == jnp.exp(dist.Normal(loc=0, scale=2).log_prob(0)), \"Normal(X=0|0, 2) is incorrect.\"\n", - " assert pdf_fn(0, 1, 1) == jnp.exp(dist.Normal(loc=0, scale=1).log_prob(1)), \"Normal(X=0|1, 1) is incorrect.\"\n", - " assert pdf_fn(2, 3, 1) == jnp.exp(dist.Normal(loc=2, scale=3).log_prob(1)), \"Normal(X=1|2, 3) is incorrect.\"\n", - " print(\"Nice! Your answer looks correct.\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### The Multivariate Normal distribution\n", - "\n", - "```{margin}\n", - "This distribution will be very useful in chapters where we will talk about Gaussian Processes and spatial modelling.\n", - "```\n", - "\n", - "The *multivariate normal distribution* is a generalization of the *univariate normal distribution* to consider multiple random variables that have a jointly normal distribution. In other words, it lets us model variables that are not independent – if we know the value of one variable, that tells us something about the other variables!\n", - "More concretely, the multivariate normal distribution lets us consider multiple random variables such that when we condition on some of these variables the remaining variables have a normal distribution. These variables are distributed in a kind of stretched fuzzy ball in higher dimensional space.\n", - "\n", - "As a rule of thumb, the more one variable tells us about another, the larger the *covariance* or *correlation* between the two. \n", - "\n", - "We will be using the same notation for multivatiate and univariate normals $\\mathcal{N}$. Which one to use, should be clear from the context throughout this course.\n", - "\n", - "The PDF for an $D$-dimensional random variable $X$:\n", - "\n", - "$$\n", - "p(X = x) = \\mathcal{N}(x\\mid \\mu, \\Sigma) = \\frac{1}{\\sqrt{(2\\pi)^D|\\Sigma|}}\\exp\\left(-\\frac{1}{2}(x - \\mu)^\\intercal\\Sigma^{-1}(x - \\mu)\\right),\n", - "$$\n", - "\n", - "where $x$ and $\\mu$ are now vectors of numbers rather than single numbers, $\\Sigma$ is a covariance matrix that replaces $\\sigma$ from our univariate definition above, and $|\\Sigma|$ is its determinant. The covariance matrix looks like this:\n", - "\\begin{equation*}\n", - "\\Sigma = \\begin{bmatrix}\\sigma_1^2 & \\rho_{12} \\sigma_1 \\sigma_2 & \\cdots & \\rho_{1D} \\sigma_1 \\sigma_D \\\\\n", - " \\rho_{21} \\sigma_2\\sigma_1 & \\sigma_2^2 & \\cdots & \\rho_{2D} \\sigma_2 \\sigma_D \\\\\n", - " \\vdots & \\vdots & \\ddots & \\vdots \\\\\n", - " \\rho_{D1} \\sigma_D \\sigma_1 & \\rho_{D2} \\sigma_D \\sigma_2 & \\cdots & \\sigma_D^2 \\end{bmatrix}\n", - "\\end{equation*}\n", - "\n", - "where $\\sigma_i^2$ is the variance for the $i$-th dimension, and $\\rho_{ij} = \\rho_{ji}$ is the *correlation* between the $i$-th and $j$-th dimensions. The covariance matrix tells us how the \"ball\" of random variables is stretched and rotated in space.\n", - "\n", - "`````{admonition} Task 12\n", - ":class: tip\n", - "Show that the equation above is equivalent to the univariate case when $D = 1$\n", - "`````" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "\n", - "Now let's look at how the equation above simplifies in the two-dimensional case\n", - "\n", - "$$\n", - "\\begin{align*}\n", - "&p(X_1 = x_1, X_2 = x_2) = \\\\\n", - "&\\mathcal{N}\\left( \\begin{bmatrix} x_1 \\\\ x_2 \\end{bmatrix} \\middle| \\begin{bmatrix} \\mu_1 \\\\ \\mu_2 \\end{bmatrix}, \\begin{bmatrix} \\sigma_1^2 & \\rho \\sigma_1 \\sigma_2 \\\\ \\rho \\sigma_1 \\sigma_2 &\\sigma_2^2 \\end{bmatrix}\\right)= \\\\\n", - "&\\frac{1}{2\\pi\\sigma_1\\sigma_2\\sqrt{1 - \\rho^2}}\\exp\\left(-\\frac{1}{2(1 - \\rho^2)}\\left[\\left(\\frac{x_1 - \\mu_1}{\\sigma_1}\\right)^2 -2\\rho\\left(\\frac{x_1 - \\mu_1}{\\sigma_1}\\right)\\left(\\frac{x_2 - \\mu_2}{\\sigma_2}\\right) + \\left(\\frac{x_2 - \\mu_2}{\\sigma_2}\\right)^2 \\right] \\right)\n", - "\\end{align*}\n", - "$$\n", - "\n", - "**Group task:** Try to understand what this equation means. Discuss the following questions with your neighbors. \n", - "\n", - "1. If $\\rho = 0$, how does this two-dimensional case relate to the one-dimensional case above?\n", - "2. Now, think about what happens as $\\rho$ becomes larger? What if it becomes negative?\n", - "\n", - "We will come back to this distribution later in the course." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Batch and event shapes\n", - "\n", - "All distributions in `numpyro` have an `event_shape` which describes how many dimensions the random variable is, e.g., for a 2-dimensional normal distribution this would be 2, and a `batch_shape` which describes how many sets of parameters the distribution has – it is probably easier to show what this means with the following examples rather than tell.\n", - "\n", - "Let's first look at a simple univariate normal $\\mathcal{N}(x|0, 1)$. We will evaluate the probabilities of $X = 1$ and $X = 2$:" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "event_shape = ()\n", - "batch_shape = ()\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "p(X = [1. 2.]) = [0.24197073 0.05399096]\n" - ] - } - ], - "source": [ - "values = jnp.array([1., 2.])\n", - "normal = dist.Normal(0., 1.)\n", - "print(f\"event_shape = {normal.event_shape}\")\n", - "print(f\"batch_shape = {normal.batch_shape}\")\n", - "print(f\"p(X = {values}) = {jnp.exp(normal.log_prob(values))}\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We see that this distribution has an empty event shape, which you can think of as being the same as an event shape of 1 (like how a scalar is the same as a vector of length 1). The batch shape is also empty, since we only specified one set of parameters ($\\mu = 0, \\sigma = 1$). \n", - "\n", - "Now since we tried to evaluate the probability of two values at once, and neither the event shape nor the batch shape are 2, this is equivalent to calling `dist.log_prob(1.)` and `dist.log_prob(2.)` separately. `numpyro` is just making our lives easier by *broadcasting* the `log_prob` calculation to do both $p(X=1) = \\mathcal{N}(X=1|0, 1)$ and $p(X=2) = \\mathcal{N}(X=2|0, 1)$ at the same time.\n", - "\n", - "We could also specify a *batch* of two sets of parameters so that we are essentially working with $\\mathcal{N}(x|0, 1)$ and $\\mathcal{N}(x|1, 2)$ at the same time:" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "event_shape = ()\n", - "batch_shape = (2,)\n", - "[p(X_1 = 1.0), p(X_2 = 2.0)] = [0.24197073 0.17603266]\n", - "p(X_1 = 1.0, X_2 = 2.0) = 0.042594753205776215\n" - ] - } - ], - "source": [ - "batch_normal = dist.Normal(jnp.array([0., 1.]), jnp.array([1., 2.]))\n", - "print(f\"event_shape = {batch_normal.event_shape}\")\n", - "print(f\"batch_shape = {batch_normal.batch_shape}\")\n", - "print(f\"[p(X_1 = {values[0]}), p(X_2 = {values[1]})] = {jnp.exp(batch_normal.log_prob(values))}\")\n", - "print(f\"p(X_1 = {values[0]}, X_2 = {values[1]}) = {jnp.prod(jnp.exp(batch_normal.log_prob(values)))}\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now, notice that while the event shape is empty (as expected since we are still working with a univariate normal), the batch size is 2!\n", - "\n", - "As a result, the calculation we are doing is equivalent to separately calculating $p(X_1=1) = \\mathcal{N}(X_1=1|0, 1)$ and $p(X_2=2) = \\mathcal{N}(X_2=2|1, 2)$! Again, this is just `numpyro` making our lives easier.\n", - "\n", - "If we want to calculate $p(X_1=1,X_2=2)$, i.e., the joint probability that $X_1 = 1$ and $X_2 = 2$, then we either need to manually multiply the probabilities (assuming that $X_1$ and $X_2$ are independent) – as we've in the cell above – or we need to work with a multivariate normal.\n", - "\n", - "Let's look at the case when the $X_1$ and $X_2$ are independent:" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "event_shape = (2,)\n", - "batch_shape = ()\n", - "p(X_1 = 1.0, X_2 = 2.0) = 0.055732980370521545\n" - ] - } - ], - "source": [ - "multivariate_full_normal = dist.MultivariateNormal(jnp.array([0., 1.]), jnp.array([[1., 1.], [1., 2.**2]]))\n", - "print(f\"event_shape = {multivariate_full_normal.event_shape}\")\n", - "print(f\"batch_shape = {multivariate_full_normal.batch_shape}\")\n", - "print(f\"p(X_1 = {values[0]}, X_2 = {values[1]}) = {jnp.exp(multivariate_full_normal.log_prob(values))}\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "This results in a slightly different value for the joint probability, but otherwise everything looks the same." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Measuring distances between distributions\n", - "\n", - "There are several ways to measure distances between two probability distributions with PDFs $p(x)$ and $q(x)$, each with its own characteristics and applications. \n", - "\n", - "- Total variation distance (TVD): This metric quantifies the difference between two probability distributions by measuring the total absolute difference between their probability mass functions (for discrete distributions) or probability density functions (for continuous distributions).\n", - "\n", - "$$\n", - "\\text{TVD}(p, q) = \\frac{1}{2} \\int |p(x) - q(x)| \\, dx\n", - "$$\n", - "\n", - "- Kullback-Leibler Divergence (KLD): Also known as relative entropy, measures the information lost when one probability distribution is used to approximate another. It is asymmetric, and, hence is not a 'distance' but a 'deviance'\n", - "\n", - "$$\n", - "\\text{KLD}(p \\parallel q) = \\int p(x) \\log \\left( \\frac{p(x)}{q(x)} \\right) \\, dx\n", - "$$\n", - "\n", - "- Jensen-Shannon Divergence (JSD): JSD is a symmetrized version of KLD. It measures the similarity between two probability distributions by averaging their KLD values.\n", - "\n", - "$$\n", - "\\text{JSD}(p, q) = \\frac{1}{2} \\text{KLD}(p \\parallel m) + \\frac{1}{2} \\text{KLD}(q \\parallel m),\\\\\n", - "m = \\frac{p+q}{2}\n", - "$$\n", - "\n", - "- Hellinger Distance: This distance metric is used to measure the similarity between two probability distributions. It is based on the square root of the total variation distance and ranges between 0 and 1.\n", - "\n", - "$$\n", - "\\text{Hellinger}(p, q) = \\sqrt{1 - \\int \\sqrt{p(x)q(x)} \\, dx}\n", - "$$\n", - "\n", - "- Wasserstein Distance (Earth Mover's Distance): This metric measures the minimum amount of \"work\" needed to transform one distribution into another. It considers the underlying structure of the distributions and is often used in optimal transport theory. $\\Gamma(p, q)$ represents the set of all joint distributions with marginals $p$ and $q$. The Wasserstein distance is defined as the minimum \"cost\" required to transform one distribution into another.\n", - "\n", - "$$\n", - "\\text{Wasserstein}_m(p, q) = \\left( \\inf_{\\gamma \\in \\Gamma(p, q)} \\int_{\\mathcal{X} \\times \\mathcal{X}} d(x, y)^m \\, d\\gamma(x, y) \\right)^{\\frac{1}{m}}\n", - "$$\n", - "\n", - "- Maximum Mean Discrepancy (MMD) between two distributions can be defined using the kernel trick. Let $\\phi(x)$ be a feature map $\\phi(x)$, and $\\mathbb{E}_{x \\sim P}[ \\phi(x) ]$ the expected value of the feature map $\\phi(x)$ computed over samples drawn from distribution $p$. In the same way, $\\mathbb{E}_{y \\sim Q}[ \\phi(y) ]$ is the expected value of the feature map $\\phi(y)$ computed over samples drawn from distribution $q$, $\\| \\cdot \\|$ is the Euclidean norm. The feature map $\\phi$ is usually chosen to be a reproducing kernel Hilbert space (RKHS) kernel function, such as the Gaussian kernel $k(x, y) = \\exp \\left( -\\frac{\\| x - y \\|^2}{2\\sigma^2} \\right)$.\n", - "\n", - "$$\n", - "MMD(p, q) = \\left\\| \\mathbb{E}_{x \\sim p}[ \\phi(x) ] - \\mathbb{E}_{y \\sim q}[ \\phi(y) ] \\right\\|^2\n", - "$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "```{margin}\n", - "For all implementations, use `jax` or `numpyro` functionality. For instance, `import jax.numpy as jnp` instead of `import numpy as np`. And `import numpyro.distributions as dist` for access to distributions.\n", - "````" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`````{admonition} Task 13\n", - ":class: tip\n", - "1. Implement numeric evaluation of the KL divergence:\n", - "\n", - "```\n", - "def kl_divergence(p: dist.Distribution, q: dist.Distribution, n: int = 10_000):\n", - " \"\"\"\n", - " add your code here\n", - " \"\"\" \n", - " pass\n", - "```\n", - "\n", - "2. Calculate the following KL divergence. What do we see?\n", - " - $\\mathrm{KLD}\\left[\\mathrm{Uniform}(0, 1) \\mid\\mid \\mathrm{Uniform}(0, 1)\\right]$\n", - " - $\\mathrm{KLD}\\left[\\mathrm{Beta}(5, 2) \\mid\\mid \\mathrm{Beta}(5, 2)\\right]$\n", - " \n", - "3. Calculate the following KL divergences. What can we say about the relationship between the beta and uniform distributions?\n", - " - What is $\\mathrm{KLD}\\left[\\mathrm{Uniform}(0, 1) \\mid\\mid \\mathrm{Beta}(5, 2)\\right]$?\n", - " - What is $\\mathrm{KLD}\\left[\\mathrm{Uniform}(0, 1) \\mid\\mid \\mathrm{Beta}(2, 2)\\right]$?\n", - " - What is $\\mathrm{KLD}\\left[\\mathrm{Uniform}(0, 1) \\mid\\mid \\mathrm{Beta}(1, 1)\\right]$?\n", - " \n", - "4. What is $\\mathrm{KLD}\\left[ \\mathrm{Beta}(5, 2) \\mid\\mid \\mathrm{Uniform}(0, 1)\\right]$. How does it compare to $D_\\mathrm{KL}\\left[\\mathrm{Uniform}(0, 1) \\mid\\mid \\mathrm{Beta}(5, 2)\\right]$ from above?\n", - "\n", - "5. Compare $\\mathrm{KLD}\\left[\\mathrm{Uniform}(-1, 1) \\mid\\mid \\mathcal{N}(0, 1)\\right]$ and $D_\\mathrm{KL}\\left[\\mathcal{N}(0, 1) \\mid\\mid \\mathrm{Uniform}(-1, 1) \\right]$.\n", - "`````" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "```{margin}\n", - "You can tackle this task during week 2, as we have not looked at kernels yet.\n", - "```" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`````{admonition} Task 14 (week 2)\n", - ":class: tip\n", - "\n", - "1. Implement numeric evaluation of MMD taking as inputs two distributions `p` and `q` of type `dist.Distributions`, number of samples `n`. Use RBF gaussian as a default kernel. \n", - "\n", - "2. Modify the MMD computation code to accept different kernel functions besides the RBF kernel: linear, polynomial, and exponential kernels.\n", - "\n", - "\n", - "`````" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Probability distributions and random variables" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Throughout the course we will work with probability distributions. Hence, it is important to master the basic principles of probability distributions, and learn to manipulate probabilities in code.\n", + "\n", + "Probability distributions and random variables serve as tools for describing and performing calculations related to random events, specifically those whose outcomes are uncertain. \n", + "\n", + "An illustrative example of such an uncertain event would be the act of flipping a coin or rolling a dice. In the former case, the potential outcomes are heads or tails. \n", + "\n", + "An example of a random event from epidemiology, is the number of disease cases $y(t)$ on a given day $t$.\n", + "\n", + "In the context of epidemiological modelling, we will encounter data of different types and origin. It is crucial to grasp the suitability of different probability distributions for modeling specific types of data.\n", + "\n", + "Since the probabilistic programming language that we will be using for this course is Numpyro, also in this section we will use the implementations of distributions from this library avalable via `import numpyro.distributions as dist`" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# uncomment this line on Colab\n", + "# !pip install numpyro" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{margin}\n", + "In all notebooks of this course, we will always import all necessary libraries in the first code cell.\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import jax\n", + "import jax.numpy as jnp\n", + "\n", + "# distributions\n", + "import numpyro.distributions as dist\n", + "\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# since we are using jax, we will need a random key:\n", + "rng = jax.random.PRNGKey(42)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Discrete distributions\n", + "\n", + "Discrete probability distributions represent the probabilities of distinct outcomes in a finite or countably infinite sample space." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Bernoulli distribution\n", + "\n", + "A Bernoulli distribution is used to describe random events with two possible outcomes e.g. when we have a random variable $X$ that takes on one of the two values $x \\in \\{0, 1\\}$ with probabilities $1-p$ and $p, 0 \\le p \\le 1$ respectively:\n", + "\n", + "\\begin{align*}\n", + "p(X = 1) &= p, \\\\\n", + "p(X = 0) &= 1 - p.\n", + "\\end{align*}\n", + "\n", + "Here $p$ is the probability of the 'positive' outcome. For example, in the case of a *fair* coin toss, $p = 0.5$ so that both outcomes have a 50\\% chance of occurring.\n", + "\n", + "We will be denoting this distribution as \n", + "\n", + "$$\n", + "X \\sim \\mathcal{Bern}(p).\n", + "$$\n", + "\n", + "or, equivalently, \n", + "\n", + "$$\n", + "\\mathcal{Bern}(X | p).\n", + "$$\n", + "\n", + "#### Probability mass function\n", + "A *discrete* probability distribution can be uniquely defined by its probability mass function (PMF).\n", + "\n", + "```{margin}\n", + "The term 'mass' is used to underline that the support of the distribution is discrete, and each possible value carries a certain `mass` (probability).\n", + "For continuous distributions, the analogous is probability density function (PDF), we will see those later.\n", + "```\n", + "For the Bernoulli distribution, we write the PMF as\n", + "\n", + "\\begin{align*}\n", + "p(X = x) = \\mathcal{Bern}(X\\mid p) &= \\begin{cases}\n", + "p\\, & \\text{if } x = 1 \\\\\n", + "1 - p\\, & \\text{if } x = 0\n", + "\\end{cases} \\\\\n", + "&= p^x(1-p)^{1-x}.\n", + "\\end{align*}\n", + "\n", + "`````{admonition} Task 02\n", + ":class: tip\n", + "Convince yourself that the two definitions of the Bernoulli distribution shown above are equivalent.\n", + "`````\n", + "\n", + "Now let's construct a Bernoulli distribution in code." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Drawing a sample\n", + "\n", + "We construct the distribution with a certain value of the parameter `p`:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "p = jnp.array(0.5)\n", + "bernoulli = dist.Bernoulli(probs=p)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{margin}\n", + "We can think of a sample as a realisation of a random variable. \n", + "```\n", + "Now that we have constructed the distribution we can get a sample from it:" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1\n" + ] } - ], - "metadata": { - "colab": { - "provenance": [] - }, - "kernelspec": { - "display_name": "Python 3", - "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" + ], + "source": [ + "sample = bernoulli.sample(key=rng)\n", + "print(sample)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And we can evaluate the probability of observing a sample.\n", + "\n", + "**Note:** the distribution objects in `numpyro` (and most other libraries for probability distributions) return log-probabilities rather than raw probabilities. This means that we need to take the exponent if we want to know the probability." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "log p(X = 1) = -0.6931471824645996\n", + "p(X = 1) = 0.5\n" + ] + } + ], + "source": [ + "log_prob = bernoulli.log_prob(sample)\n", + "print(f\"log p(X = {sample}) = {log_prob}\")\n", + "print(f\"p(X = {sample}) = {jnp.exp(log_prob)}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As expected, we get a probability of 0.5." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Multiple samples\n", + "\n", + "We can also easily get multiple samples in one command by including `sample_shape`:\n", + "\n", + "```{margin}\n", + "Multiple samples are different realisations of the same random variable.\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0 0 1 1 0 1 1]\n" + ] + } + ], + "source": [ + "n_samps = 7\n", + "samples = bernoulli.sample(key=rng, sample_shape=(n_samps,))\n", + "print(samples)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What if we wanted to evaluate the probability of observing all of our samples?\n", + "\n", + "The `bernoulli` object we created earlier treats each sample individually and returns the probabilities of observing each sample on its own:" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.5 0.5 0.5 0.5 0.5 0.5 0.5]\n" + ] + } + ], + "source": [ + "individual_sample_probs = jnp.exp(bernoulli.log_prob(samples))\n", + "print(individual_sample_probs)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "But, we can use one of the laws of probability to compute the probability of observing all of the samples together, i.e. jointly:\n", + "\n", + "\\begin{align*}\n", + "p(X_1=x_1, X_2=x_2, \\dots, X_N=x_n) = \\prod_{n=1}^N p(X_n=x_n).\n", + "\\end{align*}\n", + "\n", + "This is called the product rule of probability, and it says that for independent random variables, the joint probability (i.e., the probability of observing them all together) is equal to the product of the individual probabilities.\n", + "\n", + "Now, let's calculate the joint probability of our samples.\n", + "\n", + "```{margin}\n", + "Working with log-probabilities is preferable due to numerical stability, computational efficiency, and ease of handling multiplicative operations.\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.0078125\n" + ] + } + ], + "source": [ + "joint_prob = jnp.prod(individual_sample_probs)\n", + "print(joint_prob)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Visualise PMF\n", + "\n", + "Now let's visualise the PMF:" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "def Bernouilli_vis(rng, p, n_samps):\n", + "\n", + " # define distribution\n", + " bernoulli = dist.Bernoulli(probs=p)\n", + "\n", + " # collect samples\n", + " samples = bernoulli.sample(key=rng, sample_shape=(n_samps,))\n", + "\n", + " # how many ones\n", + " num_ones = (samples == 1.).sum()\n", + "\n", + " # how many zeros\n", + " num_zeros = (samples == 0.).sum()\n", + "\n", + " # plot\n", + " fig = plt.figure(dpi=100, figsize=(5, 3))\n", + " ax = fig.add_subplot(1, 1, 1)\n", + " ax.bar([0, 1], [num_zeros/n_samps, num_ones/n_samps], alpha=0.7, color='teal')\n", + " \n", + " ax.set_xticks([0, 1])\n", + " ax.set_xlabel('Outcome (x)')\n", + " ax.set_ylabel('Probability Mass p(X=x)')\n", + " ax.set_title(f'Bernoulli Distribution (p={p})')\n", + " ax.grid(True)\n", + " \n", + " plt.show()\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "Bernouilli_vis(rng, p=0.2, n_samps=10)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`````{admonition} Task 03\n", + ":class: tip\n", + "Recreate this plot using `bernoulli.log_prob(sample)` functionality (see examples below).\n", + "`````" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "Bernouilli_vis(rng, p=0.7, n_samps=100)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`````{admonition} Task 04\n", + ":class: tip\n", + "Plot a panel of histograms where you vary probability $p$ horizontally and number of samples $n$ vertically. What do you observe?\n", + "`````" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Common usage\n", + "\n", + "Bernoulli distribution is commonly used as a likelihood in models with binary outcomes, such as presence or absence of a disease." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Binomial distribution\n", + "\n", + "A binomial distribution is a discrete probability distribution that models the number of successes $x$ in a fixed number $n$ of independent and identical Bernoulli trials, where each trial has only two possible outcomes: \"success\" (represented as \"1\") with probability $p$ or \"failure\" (represented as \"0\") with probability $1-p$.\n", + "\n", + "We will use the notation \n", + "\n", + "$$\n", + "X \\sim \\mathcal{Binom}(n,p)\n", + "$$\n", + "\n", + "#### Probability mass function\n", + "\n", + "The PMF of the Binomial distribution is\n", + "\n", + "$$P(X = x) = \\binom{n}{x} p^x (1 - p)^{n - x},$$\n", + "\n", + "where\n", + "\n", + "- $P(X = x)$ is the probability of getting exactly $x$ successes,\n", + "\n", + "- $\\binom{n}{x}$ is the binomial coefficient, representing the number of ways to choose $x$ successes out of $n$ trials,\n", + "\n", + "- $p$ is the probability of success on a single trial,\n", + "\n", + "- $1-p$ is the probability of failure on a single trial,\n", + "\n", + "- the number of successes $x$ ranges from $0$ to $n$ inclusive.\n", + "\n", + "`````{admonition} Task 05\n", + ":class: tip\n", + "Compute $\\sum_{x=0}^n P(X=x)$.\n", + "`````\n", + "\n", + "#### Drawing a sample" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As before, we begin by constructing the distribution:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "p = 0.3\n", + "n = 10\n", + "binomial = dist.Binomial(total_count=n, probs=p)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we can draw a sample from this distribution:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "4\n" + ] + } + ], + "source": [ + "sample = binomial.sample(key=rng)\n", + "print(sample)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`````{admonition} Task 06\n", + ":class: tip\n", + "Draw several samples from this distribution using different keys. And draw repeatedly several samples with the same key. What do you conclude about the role of `key` in reproducibility of numerical experiments?\n", + "`````" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "What is the probability to observe this sample?" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "log p(X = 4) = -1.608832836151123\n", + "p(X = 4) = 0.20012104511260986\n" + ] } + ], + "source": [ + "log_prob = binomial.log_prob(sample)\n", + "print(f\"log p(X = {sample}) = {log_prob}\")\n", + "print(f\"p(X = {sample}) = {jnp.exp(log_prob)}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Multiple samples" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let us generate several samples: " + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[3 6 1 3 2 4 5]\n" + ] + } + ], + "source": [ + "n_samps = 7\n", + "samples = binomial.sample(key=rng, sample_shape=(n_samps,))\n", + "print(samples)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Individual probabilities to observe the samples:" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.26682812 0.03675695 0.12106086 0.26682812 0.23347507 0.20012105\n", + " 0.10291947]\n" + ] + } + ], + "source": [ + "individual_sample_probs = jnp.exp(binomial.log_prob(samples))\n", + "print(individual_sample_probs)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Assuming that the samples are independent, what is the joint probability of observeing them?" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.5234818e-06\n" + ] + } + ], + "source": [ + "joint_prob = jnp.prod(individual_sample_probs)\n", + "print(joint_prob)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Visualise PMF" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "def binomial_vis(rng, p, n, x_ticks=True):\n", + " \n", + " # Binomial distribution with `n` trials and probability of success `p``\n", + " binomial = dist.Binomial(total_count=n, probs=p)\n", + " \n", + " # generate the possible outcomes (x values)\n", + " x_values = jnp.arange(0, n + 1)\n", + "\n", + " pmf_values = jnp.exp(binomial.log_prob(x_values))\n", + "\n", + " # create a bar plot (PMF plot)\n", + " fig = plt.figure(dpi=100, figsize=(5, 3))\n", + " plt.bar(x_values, pmf_values, align='center', alpha=0.7, color='teal')\n", + " plt.xlabel('Number of successes (x)')\n", + " plt.ylabel('Probability mass p(X=x)')\n", + " plt.title(f'Binomial distribution (n={n}, p={p})')\n", + " if x_ticks:\n", + " plt.xticks(x_values)\n", + " plt.grid( linestyle='--', alpha=0.7)\n", + "\n", + " plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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cYwp8FPiemV1uZivM7CzCotNnxjKb2f1m9mEz+xFhrb0YZxEW6r3QzFaa2YXAzYndcRzHcZpObuFfklqBQ4EvZpJ+Bxzej10fBlycsd1IH42ppNGEXm+FXSFEhHV1dQFQKBQoFAqUy+UedzsVe6lUIv38OWsvlUoAFItFJHXvt0KxWATozrc9e0tLS4/9JuWgWCz28rGavb9lSvtYb5kqC+qm04Z6mWL2essE9Mo/1MvUjPNUyRPzcaiWqRnnqbKtmfXKP1TL1Je91jKlj9+surc98oyl3gMoAo9l7I8Be/Zjv3s2sM/zgPOzxiVLljB27FgAJk2axIwZM1izZg3r16/vzjNlyhSmTJnCfffdR3v7c53l6dOnM3nyZFasWMGWLVtYsmQJADNnzmTChAksWbKkR4WYPXs2ra2ttLW19fBh/vz5dHZ2snTp0m5bsVhkwYIFtLe3s3Llym77mDFjmDNnDhs2bGD16tXd9vHjxzNr1izWrVvH2rXPzUXRaJmWLVvGli1buu2NlKmjo6OHLsOhTM04TwceeCCtra3dugyHMjXjPO2///5MmjSJFStWsHXr1mFRpmadpz322IOOjg6WLVs2bMrUjPNkZhQKhX6XadKkSdRCbtG8kvYmzCZxuJndkbJ/Ani7mc3czva3AHclQ8NpeyfwTjNbmLK9lTCcvFOVfcV6pms3btzYHc07VO/Q+rJ7mbxMXiYvk5epb983b97MxIkTYTvRvHn2TDcAJXr3GCfTu2dZD4/Wu08z6wA6Kr8rw20tLS29XvitCJ6lcvKzSOL+++9n2rRpPbar9iJxPXZJUXs1H+u1VytTNXs9vr9+4UJmtbSwoquLX556ard9KJepmr2eMpXLZdasWdOrvlTL35fvg6VMjdizvpfLZVatWsW0adOi5RqKZdqevRbfy+Uyq1evZtq0acOmTNuz11Km7P9Rf8oUyxMjtwAkM+sEFgHHZpKOBW7vx67viOzzuH7us2HK5TLr16/3aLsMAvYpFvFXzXvi9SWO6xLHdYmThy55zz91EXCFpDZCI/geYD/gMgBJFwL7mNk7KhtIOiT5ugswKfndaWb3JvavAX+WdC7wS+D1wCuBlw54aRzHcZwRSa6NqZldJWl34FPAXsAy4HgzeyDJshehcU2zJPX9UOAtwAPA/sk+b5d0CvA54LPAKuBkM/vbQJXD2T4nLOx+hM2vUsO6juM4w4G8e6aY2aXApVXSTovYtjsyaGbXANf027kmUCgUmDJlSs3j7iOFMrCqqwsfnOqJ15c4rksc1yVOHrrk3pgOdyon1emJAasykXqO15dquC5xXJc4eejitzMDTKlUYsWKFb1CvEc6RWDeqFHEY/5GLl5f4rgucVyXOHno4o3pAGNmtLe393hvyQns4UNTvfD6Esd1ieO6xMlDF7+aOY7jOE4/8cbUcRzHcfqJByANMIVCgenTp3u0XYYysHzbNsr4azNpvL7EcV3iuC5x8tDFG9MBplAoMHny5LzdGHQY8LDP2tILry9xXJc4rkucPHTx25kBplQqcffdd3u0XYYicLhH8/bC60sc1yWO6xInD128MR1gzIwtW7Z4tF2EXXxoqhdeX+K4LnFclzh56OJXM8dxHMfpJ96YOo7jOE4/8cZ0gCkWi8ycObPq+n4jlTKwqLPT5+bN4PUljusSx3WJk4cuHs07wEhiwoQJebsx6DBgoz/n6YXXlziuSxzXJU4eunjPdIDp6urizjvvpKurK29XdjgnLFzY/clSBI5ubfVo3gwjub70hesSx3WJk4cu3pjuADxsPU6Ltrua3ojE60sc1yWO6xJnR+vijanjOI7j9JO6nplKEnAk8DJgf2BnYD2wBLjJzB5qtoOO4ziOM9ipqWcqaYykjwMPATcArwUmACXgecCngTWSrpf0kgHydUhSLBaZPXu2R9tlKAG3dXbiA1Q98foSx3WJ47rEyUOXWnum9wF/A84AbjSzbdkMkqYCbwGukvQ5M/tu89wc2rS2tubtwqBkq0fzRvH6Esd1ieO6xNnRutT6zPQ1ZvZmM/t1rCEFMLMHzOxC4ADglmY5ONQplUq0tbV5kECGInDM6NEezZvB60sc1yWO6xInD11q6pma2bJad2hmncD/17BHjuM4jjPEqDuaV9JnJfXqUEgaL6n3C4WO4ziOM8xp5NWYdwC3SZpRMUg6CriHEOHrOI7jOCOKRhrT2cD9wF2S3i3pK8DvgB8AL22ea8ODYrHI/PnzPdouQwm4uaPDo3kzeH2J47rEcV3i5KFL3XPzmlk7cIqkzwPfBroIAUo3N9u54UJnZydjxozJ241Bx04Sz3hEby+8vsRxXeK4LnF2tC4NzYAk6YPAR4CFwGrg65LmNNOx4UKpVGLp0qUebZehCBzhc/P2wutLHNcljusSJw9d6u6ZSroBWAC8w8yukTQGuAj4q6TzzezLzXbSGVmkJ8b/1amn5uiJ4zhObTTSM20BZpvZNQBmtsXMzgTeTOitOo7jOM6IopFnpsdWsf9G0gv779Lww4MD4nT589IoXl/iuC5xXJc4O1qXpi4ObmYbmrm/4UBLSwsLFizI241BRwn4Q2dn3m4MOry+xHFd4rgucfLQpdEApN9I2iv73emNmbFp0ybMe2E9ELC7hK9o2hOvL3FclziuS5w8dGl0PdOXA2Mi350MpVKJlStXerRdhgJwaGurL6ibwetLHNcljusSJw9d/FrmOI7jOP0k98ZU0vskrZG0VdIiSS/bTv4jk3xbJa2WdEYkz1mS/iFpi6SHJF0saaeBK4XjOI4zksm1MZV0MnAJ8HlgLnArcIOk/arknwZcn+SbC3yBMGHEm1J53gp8kbBg+SzgdOBk4MIBK0gfSGLMmDFI/nQwy+ZyOW8XBh1eX+K4LnFclzh56NLUaN4G+CjwPTO7PPl9lqRXAWcC50XynwE8aGZnJb9XSJoPnA38LLEdBtxmZj9Jft+frGbzooEowPYoFovMmeOTQ2UpAbdviy6NO6Lx+hLHdYnjusTJQ5fcGlNJrcChhF5kmt8Bh1fZ7LAkPc2NwOmSRiULl/8FeJukF5nZ3yVNB44HftiHL6OB0SnTrgBdXV10dXUBUCgUKBQKlMtlyqkeVcVeKpV6RI5V7Nu2bWPDhg3svvvuFAoFisUikrr3W6HyTlT2gXk1e0tLC2bWwy6JYrHYy8dq9kbLlLVXK1N3eua3mSFgSqHAI+UylT2VkrR0/lKpNKjKNNDnSRKPP/44u+22G4VCYViUqRnnCeCJJ55g4sSJPXobQ7lMzThP5XKZJ598kj322KOXXkO1TH3Zay1TuVzmiSeeYPLkyd2/Gy1TOk9fNNqYWpXv9bAH4Tr7WMb+GLBnlW32rJK/JdnfI2Z2paRJwF8U/utagG+ZWbbRTnMecH7WuGTJEsaOHQvApEmTmDFjBmvWrGH9+vXdeaZMmcKUKVO47777aG9v77ZPnz6dyZMns2zZMh599FEmTJiAJGbOnMmECRNYsmRJjwoxe/ZsWltbaWtr6+HD/Pnz6ezsZOnSpd22YrHIggULaG9vZ+XKld32MWPGMGfOHDZs2MDq1au77ePHj2fWrFmsW7eOtWvXdtv7U6YtW7Z026uVaazEVjOOGZ2+Twn/ILtKvHz0aNYnFbXLjD90dtLe3t4j/7JlywZVmQb6PB1wwAGsWLGCnXbaqbvRGOplasZ5mjp1Kg888ACjR4+mo6NjWJSpGeepctHfeeedWb58+bAoE/T/PJkZzzzzDEcddRSPPvpov8o0adIkakGNvIcj6WlgjpmtTn+vcx97Aw8Dh5vZHSn7J4C3m9nMyDb3Af9rZhembEcQeqN7mdmjydqqVwL/D/gb8Dzga8B3zeyzVXyJ9UzXbty4kXHjxgGN36F1dHSwePFi5s2bR7FYHFF30idefXVIpyfXnnIKJ155Ja8cPZo/ppZhKwHXJWkVfvZv/zaoyjTQ58nMuPPOO7vry3AoUzPOU7lcZvHixcydO7fHzDZDuUzNOE+lUonFixczf/78Xs8Hh2qZ+rLXWqaKLgsWLOj2v9Eybd68mYkTJwKMN7OnqEJDPVMz2zX2vU42EK6f2V7oZHr3Pis8WiV/F7Ax+f1Z4IrUc9h7JI0FviPp82bWq89uZh1A9+1upVK2tLTQ0tJToorgWapNXVWpRMVisce+svttxC4paq/mY732vsoUo9J4Qs8J6rNvelX0tSStlElL/842KLX63qwy7ejz1NXVFa0v1fL35ftgKVMj9qzvlYtwTJd6fa9mH2z/T7X6Xnk8MJzK1Je91jJVrjP9LVMsT4zconnNrBNYBGTn+j0WuL3KZndE8h8HtCXPSwF2BrINZokw6c4OD3mTxPjx4z3aLsIGj+bthdeXOK5LHNclTh661NyYSvqMpKo9WUn7Sfp9nce/CPgPSe+SNEvSxcB+wGXJPi+U9KNU/suAqZIuSvK/i/Dqy1dTeX4FnCnpFEnTJB1L6K1eZ2Y7fJqQYrHIrFmzfDLqDCVg8bZtvXqtIx2vL3FclziuS5w8dKmnZ3oacKciK8NIeg+wjDDcWjNmdhVwFvAp4C7C1ITHm9kDSZa9CI1rJf8aQmTuUUn+TwIfMrPKazEAnwP+O/l7L/A9QsTve+vxrVmUy2XWrl1bc0TYSEHAjGLR5+bN4PUljusSx3WJk4cu9TSmBwP3EBrU8yQVkt7oTcCXgY+a2WvqdcDMLjWz/c1stJkdamZ/TqWdZmZHZfL/yczmJfmnmdllmfQuM/u0mT3PzMaY2X5m9n4z21Svb83AK3ucAjCjpSX/KbgGGV5f4rgucVyXOHnoUnMAUhLF9A5JPwO+TZhVaBrhOeYLzeyhgXHRcRzHcQY3jXQM/kbooc5Otv+yN6SO4zjOSKauxlTSqcDyZLtZwLcIc+l+TZIvwxahUCgwadKkmsOrRwoGPFwqNTzjx3DF60sc1yWO6xInD13qiea9BvgOcIGZHWNm/zCzcwjBQK8G7pZ02MC4OXQpFArMmDHDK3uGMrC8q6vXO0wjHa8vcVyXOK5LnDx0qedIewFzzewbaWMye9Ec4AbgT030bVhQLpdZtWqVBwhkKAAHeQBSL7y+xHFd4rgucfLQpZ5r2cvM7J+xBDPbamYfBl7ZHLeGD+VymfXr13tlzyBgH381phdeX+K4LnFclzh56FJzYxqbhi+S58/by+M4juM4w42aGlNJl0nat8a8Jyss0O04juM4I4Ja3zNdDyyTdDtwHdAGrAO2AhOBFwAvBU4hrATznua7OjQpFApMmTLFAwQylIFVHoDUC68vcVyXOK5LnDx0qakxNbNPSvoGYR7cMwizIaV5GrgJ+A8zyy7ePaKpnFSnJwasKvnMvFm8vsRxXeK4LnHy0KWeZ6aPm9mFZjYH2B2YBxwBHAhMNLM3e0Pam1KpxIoVK3qtyzfSKQLzRo3qtdZplhMWLuz+jAS8vsRxXeK4LnHy0KXR9Uw3AZua6skwxcxob2/vsdisE9jDh6Z64fUljusSx3WJk4cuDTWmkiYShnxnEUbsVgLfN7Mnmuib4ziO4wwJ6u4aSDoSWAN8iBB8tBvwQWBNkuY4juM4I4pGeqbfBH4KnFlZbFtSEbg0ScsGJ41oCoUC06dP92i7DGVg+bZtHs2bwetLHNcljusSJw9dGmlMZwBvqjSkAGZWknQR8I6meTZMKBQKTJ48OW83Bh0GPOyztvTC60sc1yWO6xInD10aabYXE56VZpkF3NUvb4YhpVKJu+++26PtMhSBw2uI5h1peH2J47rEcV3i5KFLIz3TrwNfk/Q84K+J7SXA+4GPSZpdyWhmS/vv4tDGzNiyZYtH20XYxYemeuH1JY7rEsd1iZOHLo00ppUX/r5cJc0I85gbeMfDcRzHGf400phOa7oXjuM4jjOEqbsxNbMHBsKR4UqxWGTmzJkUi95JT1MGFnV2ejRvBq8vcVyXOK5LnDx0aWjSBqd2JDFhwoS83Rh0GLDRn/P0wutLHNcljusSJw9dPAJkgOnq6uLOO++kq6srb1cGFUXg6NZWf6iewetLHNcljusSJw9dvDHdAXjYepwWKW8XBiVeX+K4LnFclzg7WhdvTB3HcRynnzQyN+++kqakfr9I0iWSfEFwx3EcZ0TSSM/0J8ArACTtCfweeBHwBUmfaqJvw4Jiscjs2bM92i5DCbitsxMfoOqJ15c4rksc1yVOHro00pgeDPw9+f5vwDIzOxx4C3Bak/waVrS2tubtwqBkq0fzRvH6Esd1ieO6xNnRujTSmI4COpLvrwSuS76vBPZqhlPDiVKpRFtb27ANEjhh4cLuTz0UgWNGj/Zo3gzDvb40iusSx3WJk4cujTSmy4EzJL0MOBb4bWLfG9jYLMccx3EcZ6jQSGN6LvBe4BZgoZndndhfx3PDv47jOI4zYmhkOsFbJO0BjDOzJ1NJ3wGebZpnjuM4jjNEaOTVmDHA6EpDKmmqpLOAA83s8Qb29z5JayRtlbQoGT7uK/+RSb6tklZLOiOSZ4Kkb0p6JMm3QtLx9frWDIrFIvPnz/douwwl4OaODo/mzeD1JY7rEsd1iZOHLo0M8/4SeAeERgv4G/CfwC8knVnPjiSdDFwCfB6YC9wK3CBpvyr5pwHXJ/nmAl8Avi7pTak8rYTXdfYH3gwcCLwbeLge35pJZ2dnXoce1OzkMyBF8foSx3WJ47rE2dG6NNKYziM0ZhAaq8eAqYQG9kN17uujwPfM7HIzW2FmZwEPAdUa5TOAB83srCT/5cD3gbNTed4F7Aa8wcxuM7MHzOwvqWe7O5RSqcTSpUs92i5DETjC5+bthdeXOK5LHNclTh66NLJqzM7A08n344Cfm1lZ0l8JjWpNJD3IQ4EvZpJ+BxxeZbPDkvQ0NwKnSxplZtsIgVB3AN+U9HpgPWGiiS+ZWVRZSaOB0SnTrhAmS65MlFwoFCgUCpTLZcrl5xYOq9hLpVKPVd2z9spJLRaLSOo1AXNlOCJ78qvZW1paeuw3KQfFYrGXj9Xs/S0ThEaxTO+V4NPlyzaYlW2VSSsladn8pSRvep8DWSbI7zxV9EnnH+plasZ5quSJ+ThUy9SM81TZ1sx65R+qZerLXmuZ0sdvVt3bHo00pv8E3iDpWuBVwMWJfTLwVB372YNwLX0sY38M2LPKNntWyd+S7O8RYDpwNPB/wPHAAcA3kzyfqbLf84Dzs8YlS5YwduxYACZNmsSMGTNYs2YN69ev784zZcoUpkyZwn333Ud7e3u3ffr06UyePJl7772XTZs2sXjxYiQxc+ZMJkyYwJIlS3pUiNmzZ9Pa2kpbW1sPH+bPn09nZydLly7tthWLRRYsWEB7ezsrV67sto8ZM4Y5c+awYcMGVq9e3W0fP348s2bNYt26daxdu7bb3miZli1bxpYtW4Dwruiizk42mnFka2v35PVtbW2MldhqxjGj0/cpoaKPldijUOCoJK3LjD90dtLe3t4j/+Zymdu3bWPvQqGHNgNZJiC383TAAQewdevW7voyHMrUjPM0dWq4T7/33nvp6Ojotg/lMjXjPFUu+lu3bmX58uXDokzQ//NkZjzzzDMA/S7TpEmTqAVZnbPQSHozoadXBG42s+MS+3nAy83sNTXuZ2/Cc8zDzeyOlP0TwNvNbGZkm/uA/zWzC1O2I4C/AHuZ2aNJnp2AaZWeqKSPAv9lZtFJJar0TNdu3LiRcePGAY3foXV0dHDXXXdxyCGHUCwWh92d9JuvvjraM73mpJM48eqrQxnoybWnnMKJV17JUa2t3JqaUrAEXJekpan0TH9+0kk7pEyQX4/HzFi8eDFz5szp3udQL1OzeqZ33313rynihnKZmtUzvfvuu5k7d273zddQL1Nf9np6pnfffTfz5s3r9r/RMm3evJmJEycCjDezqh3GRl6NuUbSXwizHaWfQ94MXFvHrjYQrpPZXuhkevc+KzxaJX8Xz00Y8QiwLTOkuwLYU1KrmfV6Km1mHTw3q1N3pWxpaaGlpadEFcGzVIsaGz16NC9+8Yt72bP7bcQuKWqv5mO99mplStvTIqe/p/3Kjq1LCtG8kQCBSloWI67BQJQpTR7n6UUvelF030O5TM04TwsWLIj6V83Heu2D4f9pez5m7S0tLVXrCwzNMm3PXkuZsrr0p0yxPDEaWoLNzB41syVmVk7Z/m5mK/vaLrOPTmARYRalNMcCt1fZ7I5I/uOAtuR5KcBtwPMkpcv2fOCRWEM60JgZmzZt6nGn44Se5u4SHs/bE68vcVyXOK5LnDx0aagxlbRA0pclXSnp5+lPnbu6CPgPSe+SNEvSxcB+wGXJcS6U9KNU/suAqZIuSvK/Czgd+Goqz7eA3YGvSXq+pNcCHyc8N93hlEolVq5c6dF2GQrAoa2tvqBuBq8vcVyXOK5LnDx0qXuYV9IpwI8IUbXHJn8PIAy/1jPMi5ldJWl34FOEYeNlwPFm9kCSZS9C41rJvyaZfOFi4P3AOuBDZvazVJ6HJB2X5FlKeC77NeBL9ZbVGXykJ9T/1amn5uiJ4zjOczQSzftx4CNm9k1JTwMfBtYA3yY8r6wLM7sUuLRK2mkR258I77r2tc87gJfU64vjOI7jNEIjo2wzgN8k3zuAsRYGpi8G3tMsx4YLkhgzZkyvSDsnvPbi9MTrSxzXJY7rEicPXRrpmT5BMqkBYQj1YOAeYAJhQgcnRbFYZM6cOXm7MegoAbdv27bdfCMNry9xXJc4rkucPHRppGd6K89F1P6UEOjzXWAh4fUYJ0W5XObxxx+veRaNkYKAfQoFj+bN4PUljusSx3WJk4cujTSmHwAqb9VfSIik/Rfg54TIWidFuVxm9erVXtkzFICDRo3yaN4MXl/iuC5xXJc4eejSyKQNT6S+l4EvJx/HcRzHGZF4x8BxHMdx+knNPVNJNb39ama+qlYKSYwfP96j7SJs8KGpXnh9ieO6xHFd4uShSz3DvAIeAH4ILBkYd4YfxWKRWbNm5e3GoKMELPZo3l54fYnjusRxXeLkoUs9w7wvBn5LmKThfGBf4M9m9sv0ZyCcHMqUy2XWrl3rAQIZBMwoFj2aN4PXlziuSxzXJU4eutTcmJrZnWZ2JmGKv4uAE4G1yfy82cnnnQSv7HEKwIyWFn9on8HrSxzXJY7rEmdQN6YVzGyrmf3YzI4hTNgwGfitpN2a7p3jOI7jDAEamQEJSVOA05LPGOArQNVFUx3HcRxnOFNPNG8rYWj3dOBlwA3AWcD16XVNnZ4UCgUmTZpU8wKzIwUDHi6V8FUYe+L1JY7rEsd1iZOHLvX0TB8BniZE874PeDyx75IOPzYz76GmKBQKzJgxI283Bh1lYHlXV95uDDq8vsRxXeK4LnHy0KWeZnsiYW3RTwL/AJ7MfDYlf50U5XKZVatWeYBAhgJwkAcg9cLrSxzXJY7rEicPXerpmb5iwLwYxpTLZdavX8/UqVN9KCaFgH2KRVZ677QHXl/iuC5xXJc4eehSc2OaLMrtOI7jOE4Gv5VxHMdxnH7ijekAUygUmDJlig/BZCgDq7q68Cc9PfH6Esd1ieO6xMlDl4beM3Vqp3JShwsnLFzY/f1Xp57a8H4MWFWqae2EEcVwqy/NwnWJ47rEyUMXv50ZYEqlEitWrKDkDUcPisC8UaPwJYZ64vUljusSx3WJk4cudTemkk6TtPNAODMcMTPa29sx8+kJsuzhQ1O98PoSx3WJ47rEyUOXRq5mFwKPSvqepMOb7ZDjOI7jDDUaaUynAG8jTOLwR0krJZ0rac/muuY4juM4Q4NGVo0pmdl1ZvZGwpqm3wHeCjwo6TpJr5fk43cJhUKB6dOne7RdhjKwfNs2j+bN4PUljusSx3WJk4cu/TqSmT0O3AbcQbg+vhD4AbBK0lH99G1YUCgUmDx5slf2DAY8XC77RPcZvL7EcV3iuC5x8tCloSNJ+hdJZ0taDtwCjAP+1cymAXsDPydMiD/iKZVK3H333R5tl6EIHO7RvL3w+hLHdYnjusTJQ5e63zOV9CvgVcB9wHeBH5nZE5V0M9si6b+BjzTNyyGMmbFlyxaPtouwi99N98LrSxzXJY7rEicPXRqZtOFx4Egzu6OPPI8A0xpzyXFqo1kTSDiO4/SXRroGfwIWZ42SWiW9A8ACD/TXOcdxHMcZCjTSmP4vMD5i3zVJc1IUi0VmzpxJsehPB9OUgUWdnR7Nm8HrSxzXJY7rEicPXRoZ5hVEgzCnAO39c2f4IYkJEybk7cagw4CN/pynF15f4rgucVyXOHnoUnPPVNISSYsJ18GbJS1Ofe4GbgVuqtcBSe+TtEbSVkmLJL1sO/mPTPJtlbRa0hl95D1Fkkn6Rb1+NYuuri7uvPNOunwR7B4UgaNbWz2aN4PXlziuSxzXJU4eutTTM/1F8vcQ4EZgcyqtE7gf+Fk9B5d0MnAJ8D7C+6rvBW6Q9AIzezCSfxpwPSGK+G3AEcClktab2c8yeacCXyU08rniYetxWqS8XRiUeH2J47rEcV3i7Ghdam5MzezTAJLuB64ys61NOP5Hge+Z2eXJ77MkvQo4Ezgvkv8M4EEzOyv5vULSfOBsUg25pCLwf8D5wMuACU3w1XEcx3GiNDKd4A+b0ZBKagUOBX6XSfodUG0C/cMi+W8E5ksalbJ9ClhvZt/rr5+O4ziOsz1q6plKegJ4vpltkPQk8QAkAMxstxqPvQfh0dljGftjQLVJ8/eskr8l2d8jko4ATicMR9eEpNHA6JRpVwjj7pUx90KhQKFQoFwuUy4/F4NasZdKpR4vCFfsAAcddBBmRldXF8ViEUm9xvIrUWfZoYlq9paWFsysh10SxWKxl4/V7I2UCeh+ztnV1UWREJlrKXslrbsM9MTMKAF/7ezskV5K0rL5S4Sot8rxsvZC6niNnqesPc/zdPDBB3fXl+FSpv7WPUnMnj0byNStIVymZpwnM+OFL3whhUKhV/6hWqa+7LWWycw46KCDmlKmdJ6+qHWY9yPA06nvzQzDzO6rWrRwX/kBTNKuwI+Bd5vZhjp8OI8wJNyDJUuWMHbsWAAmTZrEjBkzWLNmDevXr+/OM2XKFKZMmcJ9991He/tzwczTp09n8uTJLF++nGeffRYlzwdnzpzJhAkTWLJkSY8KMXv2bFpbW2lra+vhw/z58+ns7GTp0qXdtmKxyIIFC2hvb2flypXd9jFjxjBnzhw2bNjA6tWru+3jx49n1qxZrFu3jrVr13bbGykTwItHjWKXQoG2tjaOGT2aRZ2dbDTjyNbW7uegbW1tjJXYasYxo9P3KeEfZKzES1pbu21dZvyhs5P29vYe+TeXy9y+bRt7p44HsKFcZvG2bUwvFpnR0tKtW6PnadmyZWzZsqXbntd5mjlzJhs3buSRRx7p13kaTGVqRt2bNm0au+++O8uXLx82ZWrWeZo7dy5btmzhnnvuGTZlasZ52nXXXXnBC17Q7zJNmjSJWlBe01Alw7zPAieZ2bUp+9eAQ8zsyMg2fwaWmNmHU7YTgZ8COwMHAUsInZYKlaHsMnCgma2K7DfWM127ceNGxo0bF3bS4B1aR0cHixcvZt68eRSLxSF/J/36q67q7h1ec9JJvPnqq6M902tOOokTr746lIGeXHvKKZx45ZW8cvRo/tjR0X2ySsB1SVqaSg/058nxsvZCcrxGyzQY7qQrdjPjzjvv7K4vw6FMzeodLF68mLlz5/Z4d3Aol6kZ56lUKrF48WLmz5/ffcM+1MvUl73WMlV0WbBgQbf/jZZp8+bNTJw4EWC8mT1FFWod5h1XSz6Avg6WydcpaRFwLHBtKulY4JdVNrsDOCFjOw5oM7NtklYSVq5J8zlC4/hh4KEqvnQAHZXflUrZ0tJCS0tPidLDt2mqvRxcqUTFYrHHvrL7bcQuKWqv5mO99mplqlTjlpaWHnct6e9pv7IxdRV9LUkrZdJiMXgWOV56H804TzF29Hnq6uqK1pdq+fvyfbCUqRF71vfKRTimS72+V7Pn9f/U3/MkqarvQ7VMfdlrLVPlOtPfMtW68kytw7yb2P7QbmV4tp5XBy8CrpDURmgo3wPsB1wGIOlCYB8ze0eS/zLgA5IuIrwecxjh+eipAElg1LIeTkmbkrQedsdxHMdpFrU2pq8YiIOb2VWSdidE3+5FaAiPT83ruxehca3kXyPpeOBi4P3AOuBD2XdMHcdxHGdHUlNjamZ/GigHzOxS4NIqaadV8WVeHfvvtY8dSbFYZP78+T53ZoYScHPqeakT8PoSx3WJ47rEyUOXWp+ZzgaWmVk5+V4VM1vaV/pIpLOzkzFjxuTtxqBjJ4lnfH7eXnh9ieO6xHFd4uxoXWqdtOEuwnucle9Lkr/Zz5KmeTZMKJVKLF261Kf8ylAEjvC5eXvh9SWO6xLHdYmThy61PjOdBqxPfXccx3EcJ6HWZ6YPxL47juM4jtPYeqZIOhD4IDCL8DrMSuAbZvaPJvo2bPDggDhd/rw0iteXOK5LHNclzo7Wpe6J7iW9mfAKy6HA3cBSQnTtMkknNde9oU9LSwsLFiyo+lLySKUE/KGz06N5M3h9ieO6xHFd4uShS92NKfBl4EIzO8zMPpp8Dge+AHypue4NfcyMTZs29ZieygkzfOwuoe3mHFl4fYnjusRxXeLkoUsjjemewI8i9h9TfbWXEUupVGLlypUebZehABza2tpQBRzOeH2J47rEcV3i5KFLI33gWwgLbv8zY38pcGt/HXIGHycsXJi3C47jOIOaWidteF3q53XAlyQdCvw1sb0EOInIMmaO4ziOM9yptWf6i4jtfcknzTdJJql3ApIYM2ZMr+WRnLBWqdMTry9xXJc4rkucPHSp9T1Tf7TVIMVikTlz5uTtxqCjBNy+bVvebgw6vL7EcV3iuC5x8tDFG8kBplwu8/jjj/dYhNYJ0bz7FApNjeY9YeHC7s9QxetLHNcljusSJw9dGp20YSxwJGF5tNZ0mpl9vQl+DRvK5TKrV69mt912q3mR2ZFAATho1Cge9ZVjeuD1JY7rEsd1iZOHLnU3ppLmAtcDOwNjgScIk+A/CzwOeGPqOI7jjCgaabIvBn4F7AZsIUTyTgUWAWc3zzXHcRzHGRo00pgeAvy3mZUIcSSjzewh4BzCLEhOCkmMHz/eo+0ibPDnPL3w+hLHdYnjusTJQ5dGnpluI0xuD/AY4bnpCqA9+e6kKBaLzJo1K283Bh0lYLFH8/bC60sc1yWO6xInD10a6ZkuAeYn3/8IfEbSW4FLgHua5NewoVwus3btWo+2yyBgRrHoc/Nm8PoSx3WJ47rEyUOXRhrTjwOPJN8/CWwEvgVMBt7TJL+GDV7Z4xSAGS0t/m5WBq8vcVyXOK5LnDx0qXuY18zaUt/XA8c31SPHcRzHGWI0vNibpMnAgYTnp/9IGlbHcRzHGXE0sjj4OElXAA8DfwL+DKyT9GNJ45vt4FCnUCgwadIkf6E6gwEPl0r4Kow98foSx3WJ47rEyUOXRo50OfBi4F+BCcD45Pt84LtN82yYUCgUmDFjhlf2DGVgeVcX/qSnJ15f4rgucVyXOHno0siRXgu8y8xuNLOnzOxpM7sReHeS5qQol8usWrXKAwQyFICDPACpF15f4rgucVyXOHno0si1bCPhndIs7cCT/XNn+FEul1m/fr1X9gwC9vFXY3rh9SWO6xLHdYmThy6NNKafAy6StFfFIGlP4CvAZ5vlmOM4juMMFWqK5pW0BHrEihwAPCDpweT3fkAHMAn4dlM9dBzHcZxBTq2vxvxiIJ0YzhQKBaZMmeIBAhnKwCoPQOqF15c4rksc1yVOHrrU1Jia2acH2pHhSuWkOj0xYFXJVzLN4vUljusSx3WJk4cuDTfbkg6V9DZJb03WOHUilEolVqxYQckbjh4UgXmjRlHM25FBhteXOK5LHNclTh66NLI4+GTgSuAoYBMhMHO8pD8Cp/hMSD0xM9rb2zHz6Qmy7OFDU73w+hLHdYnjusTJQ5dGrmbfAMYBB5nZbmY2ETg4sX29mc45juM4zlCgkcb01cCZZraiYjCze4H3A6+pd2eS3idpjaStkhZJetl28h+Z5NsqabWkMzLp75Z0q6Qnk89Nkl5Ur1+O4ziOUyuNTHRfICwQnmUbdTbOkk4mrIP6PuA24L3ADZJeYGYPRvJPA64nTFv4NuAI4FJJ683sZ0m2o4CFwO3AVuAc4HeSDjKzh+vxrxkUCgWmT58+pKLtTli4sPv7r049dUCOUQaWb9s2YNG8O6IMA8FQrC87AtcljusSJw9dGjnSH4CvSdq7YpC0D3AxcHOd+/oo8D0zu9zMVpjZWcBDwJlV8p8BPGhmZyX5Lwe+D5xdyWBmbzWzS83sLjNbSZjmsAAcU6dvTaFQKDB58mSv7BkMeLhc9onuM3h9ieO6xHFd4uShSyM90w8AvwTul/QQ4bq4H3APobdYE5JagUOBL2aSfgccXmWzw5L0NDcCp0saZWaxHvPOwCjgiT58GQ2MTpl2Bejq6qKrqwsIJ6dQKFAul3tMUVWxl0qlHg+7K/bOzk6WL1/OQQcdRKFQoFgsIql7vxWKxRDXmo0+q2ZvaWnBzHrYJVEsFnv5WM1erUwinNRiokEl4racspNKy9orad1loCdmRhF4yahR3LltG5USlFJpaUqJT2lf0vZCKs0SfwpJWsWX7Z2nrD2v8wRwzz338IIXvKD7QtBo3RssZaqn7lXz3cy49957mTVrVo8L5FAuUzPOU7lc5t577+Xggw8my1AtU1/2WstULpdZvnw5s2fPRlK/ylTrlISNLA7+EDBP0rHATMI1614zu6nOXe1BuM4+lrE/BuxZZZs9q+RvSfb3SGSbLxKWi+vLv/OA87PGJUuWMHbsWAAmTZrEjBkzWLNmDevXPxewPGXKFKZMmcJ9991He/tzUxZPnz6dyZMns3z5ch599FG2bt2KJGbOnMmECRNYsmRJjwoxe/ZsWltbaWtrI838+fPp7Oxk6dKl3bZisciCBQtob29n5cqV3fYxY8YwZ84cNmzYwOrVq7vt48ePZ9asWaxbt461a9d226uVaXqxyKpSiTmjRtHW1sYxo8N9xvJt23i4XObFo0axS6HQnbaos5ONZhzZ2kpL0iC0tbUxVmKrWff2FUqlEmMl9m9pYWxyYewy4w+dnbS3t/fIv7lc5vZt29g7dTyADeUyi7dtY3qxyIyWlu60h0sllnd1MaulhX2Sf8i2trbtnqdly5axZcuWbnte5+mAAw7gySefZNGiRd2Na6N1b7CUqZ66V61MU6dOZcuWLSxfvpyOjo5hUaZmnKfKRb+izXAoE/T/PJkZzzzzDGbGI4880q8yTZo0iVpQPaHDkloIzyEPMbNlNW8Y39fehEbucDO7I2X/BPB2M5sZ2eY+4H/N7MKU7QjgL8BeZvZoJv85wMeAo8xsKVWo0jNdu3HjRsaNGwc0fofW0dHB4sWLmTdvHsVicUjcSb/x6qu7e5rXnHQSb776aqB3D7SSFuuZXnPSSZyYbJftaV57yimceOWVvHL0aP7Y0dGjZ3pdkpam0gP9ecqXtL2Q8iXWM73mpJMG/Z10xW5m3Hnnnd31Je3jUOsd9GVvpHewePFi5s6d2+3XUC9TM85TqVRi8eLFzJ8/v/vma6iXqS97rWWq6LJgwYJu/xst0+bNm5k4cSLAeDN7iirU1TM1sy5JD9D7+tgIGwjXw2wvdDK9e58VHq2Sv4uwmk03ks4GPg68sq+GFMDMOghzC1e2BcKJa2npKVFF8Czpf/CsvXKy0/vK7rcRu6SovZqPtdor1aiUHDf72nPldzYt/T3tV3b7ir6WpJUyabHXrK2KL5V9ZNPSAzNpX/o6TzF29Hnq6uqK1pdq+fvyfbCUqRF71vfKRTimS72+V7Pv6DJtz16r75Kq+j5Uy9SXvdYyVa4z/S1Trc9dG1015kJJuzWwbTdm1gksAo7NJB1LiMSNcUck/3FAW/p5qaT/Aj4JvNrM2siRYrHIzJkzq1aukUoZWNTZ6XPzZvD6Esd1ieO6xMlDl0YCkD4EPA9Yl/RSn0knmtm8OvZ1EXCFpDZCQ/keQjDTZQCSLgT2MbN3JPkvAz4g6SLC6zGHAacD3e8+JEO7nwXeQgiSqvRkN5vZ5noK2gwkMWHChB192EGPARt91pZeeH2J47rEcV3i5KFLIz3TXwJfBS4EfpL8Tn9qxsyuAs4CPgXcBbwcON7MHkiy7EVoXCv51wDHE94lvYvQ+/xQ6h1TCO+stgLXEAKSKp+zyYGuri7uvPPOXs8KRjpF4OjWVp+bN4PXlziuSxzXJU4eujQSzXtBMx0ws0uBS6uknRax/Qmo2vs1s/2b5Vuz8Emo47RkAiacgNeXOK5LHNclzo7WpeaeqaSdJX1T0sOSHpf0E0l7DKRzjuM4jjMUqGeY99PAacBvCKvGHAt8awB8chzHcZwhRT3DvG8ETjezKwEk/Ri4TVLRzHycoQrFYpHZs2d7tF2GEnBbZ2f0NZiRjNeXOK5LHNclTh661NMz3Re4tfLDzP5OeL9z76pbOAC0trbm7cKgZKtH80bx+hLHdYnjusTZ0brU05gWgc6MrYvGXq8ZMZRKJdra2jxIIEMROGb0aI/mzeD1JY7rEsd1iZOHLvU0hAJ+IKkjZdsJuExS97umZvbGZjnnOI7jOEOBehrTH0ZsP26WI44zkAzV9U0dxxka1NyYmtm/D6QjjuM4jjNU8RVlB5hiscj8+fM92i5DCbg5tWKME/D6Esd1ieO6xMlDFw8e2gF0dnYyZsyYvN3ok/Qw6I5iJ4lnPKK3F0OhvuSB6xLHdYmzo3XxnukAUyqVWLp0qUfbZSgCR/jcvL3w+hLHdYnjusTJQxdvTB3HcRynn3hj6jiO4zj9xBvTHYAHB8Tp8uelUby+xHFd4rgucXa0Lh6ANMC0tLSwYMGCvN0YdJSAP3RmJ9RyvL7EcV3iuC5x8tDFe6YDjJmxadMmzHthPRCwu4SvaNoTry9xXJc4rkucPHTxxnSAKZVKrFy50qPtMhSAQ1tbvQJm8PoSx3WJ47rEyUMXv5Y5juM4Tj/xZ6bOiMPn6XUcp9l4z3SAkcSYMWOQ/Olgls3lct4uDDq8vsRxXeK4LnHy0MV7pgNMsVhkzpw5ebsx6CgBt2/blrcbgw6vL3FclziuS5w8dPGe6QBTLpd5/PHHKXsvrAcC9ikUPJo3g9eXOK5LHNclTh66eGM6wJTLZVavXj3oKvsJCxd2f/KgABw0apRXwAyDtb7kjesSx3WJk4cufi1zHMdxnH7ijanjOI7j9BMPQBpgJDF+/HiPtouwYZAMTQ2mV2W8vsRxXeK4LnHy0MUb0wGmWCwya9asvN0YdJSAxR7N2wuvL3FclziuS5w8dPFh3gGmXC6zdu1aDxDIIGBGsejRvBm8vsRxXeK4LnHy0MUb0wHGK3ucAjCjpcUrYAavL3FclziuS5w8dPFh3hFEXq/BOI7jDHe8MXWcFIMpGMlxnKGDj7INMIVCgUmTJlEouNRpDHi4VMJXYeyJ15c4rksc1yVOHrrkfgYkvU/SGklbJS2S9LLt5D8yybdV0mpJZ0TyvEnSvZI6kr8nDlwJ+qZQKDBjxgyv7BnKwPKuLvxJT0+8vsRxXeK4LnHy0CXXMyDpZOAS4PPAXOBW4AZJ+1XJPw24Psk3F/gC8HVJb0rlOQy4CrgCmJP8/amkFw9cSapTLpdZtWqVBwhkKAAHDYEApB097aLXlziuSxzXJU4euuR9Lfso8D0zu9zMVpjZWcBDwJlV8p8BPGhmZyX5Lwe+D5ydynMW8Hszu9DMVprZhcDNiX2HUy6XWb9+fS6VPe/5d/tCwD7+akwv8qwvgxnXJY7rEicPXXILQJLUChwKfDGT9Dvg8CqbHZakp7kROF3SKDPbluS5OJLnrH45PEQYjA3ncMGDkxzHqUae0bx7AEXgsYz9MWDPKtvsWSV/S7K/R/rIU22fSBoNjE6ZdgV44okn6OrqAsIYfKFQoFwu97jbqdhLpRJm1sve0dHB5s2befLJJykWixSLRSR177dCsVgEoFQq1WRvaWnBzHjLNdd02378xjey7dlnEb2HHJ566im6nn22h90Izy43bdpE+dlnu+3lJK2YaFBJS9tJpWXtlbRtyXZpO0B7ezvbnn2WraUS5Y6O7uempSQt7UvFrowvaXshlVYpUyFJq/jSlaRlfdm0aRPbnn22l72caBbzpbLPt197bS97EbjixOce0VfOU/r8SaJYLPaqS5Iwsx71BRqve1l7s+terWWK2estU7lc5plnnumhy1AvUzPOU6lUYvPmzbS3t/eaOm+olqkve61lqujy1FNPdfvfaJk2b95MTZhZLh9gb8I1+LCM/RPAyirb3Aecl7Edkexnz+R3J3BqJs9bga19+HJBsg//+Mc//vGPf2Kfffpq0/LsmW4g3NBne4yT6d2zrPBolfxdwMbt5Km2T4ALgYsytt2AJ/rYplZ2BdYCU4Cnm7C/4YLrEsd1ieO6xHFd4jRbl12BdX1lyK0xNbNOSYuAY4FrU0nHAr+sstkdwAkZ23FAW/K8tJLnWHo+Nz0OuL0PXzqAjoz5qT4LUCOpoZenzawp+xwOuC5xXJc4rksc1yXOAOiy3X3kPQPSRcAVktoIjeB7gP2AywAkXUjoWr8jyX8Z8AFJFwHfJQQbnQ6ko0G+BvxZ0rmERvn1wCuBlw58cRzHcZyRSK6NqZldJWl34FPAXsAy4HgzeyDJshehca3kXyPpeEKv8/2EbveHzOxnqTy3SzoF+BzwWWAVcLKZ/W1HlMlxHMcZeeTdM8XMLgUurZJ2WsT2J2DedvZ5DXBNX3l2IB3Ap+k9jDzScV3iuC5xXJc4rkucHa6L0iHAjuM4juPUT94zIDmO4zjOkMcbU8dxHMfpJ96YOo7jOE4/8cbUcRzHcfqJN6YDTL3rtQ4nJJ0n6U5JT0t6XNIvJB2YySNJF0haJ2mLpFskHZSXz3mQ6GSSLknZRqQukvaR9GNJGyU9K+kuSYem0kecLpJaJH0uuY5sSdZx/pSkQirPsNdF0ssl/Sopo0l6QyZ9uxpIGi3pG5I2SHpG0nWSpjTDP29MB5B612sdhhwJfBN4CWFWqhbgd5LGpvKcQ1iK7wPAAsJ0kL+XtOsO9jUXJC0gTFayNJM04nSRNBG4DdgGvAZ4AfCfwKZUthGnC3AuYfnJDwCzCBr8F/DBVJ6RoMtY4G5CGWPUosElwInAKYSJfHYBfi0pu9ZF/eQ10f1I+AB/A76Vsa0ALszbt5z0mESYMPrlyW8RVvo5N5VnNOHi+d68/d0BeuxCWLzhlcAtwCUjWRfCcoy39pE+UnX5NWHd57TtZ8AVI1WX5DryhnrqBjCesBDKyak8exPmiH9Vf33ynukAkVqvNbv+al/rtQ53xid/KwsITCMsStCtkYV5kv/EyNDom8BvzOymjH2k6vI6oE3S1cljgSWS3p1KH6m6/AU4RtLzASTNIfSqrk/SR6ouaWrR4FBgVCbPOsLMe/3WKfcZkIYxjazXOmxRmHn6IuAvZrYsMVd0iGk0dUf5lgfJlJfzCMNRWUaqLtOBMwn15AvAi4CvS+owsx8xcnX5EuFGdKWkEuG68gkzq6xWP1J1SVOLBnsCnWb2ZCRPv6/J3pgOPNkpphSxjQT+B5hNfMGBEaWRpH0JCzIcZ2Zb+8g6onQhxHC0mdnHk99LkgCSM4EfpfKNNF1OBt4GvAVYDhwCXCJpnZn9MJVvpOkSoxENmqKTD/MOHI2s1zoskfQNwhDeK8xsbSrp0eTvSNPoUEIZF0nqktRFCNb6UPK9UvaRpssjwL0Z2wqeW+xipNaXrwBfNLMrzeweM7uCsNjHeUn6SNUlTS0aPAq0JoFu1fI0jDemA4SZdQKV9VrTHEsfa6sOJ5JQ9f8B3ggcbWZrMlnWECr4saltWgkNy3DW6GbghYQeRuXTBvxf8n01I1OX24ADM7bnA5VVpEZqfdkZKGdsJZ67fo9UXdLUosEiQqR4Os9ewME0Q6e8o7KG84cwPNMJvIsQ0n4xsBmYmrdvO6j8lxKi6Y4k3DFWPmNSec5N8pyYVOqfEJbW2zVv/3ewVreQRPOOVF0Iz4+3AR8HnkcY1nwGeOsI1+UHwFrgtcD+SdnXA18aSboQot8PST4GfCT5vl+tGgDfAh4CjiG8rngzcBdQ7Ld/eQs03D/A+4D7CUsBLSJ5LWQkfJIKH/uclsoj4ALCEN9WQvTdwXn7noNW2cZ0ROoC/CtwT1LmFcC7M+kjThdgV8L7kQ8AWwhrNH8OaB1JugBHVbme/KBWDYCdgG8AG4FngV8B+zbDP1+CzXEcx3H6iT8zdRzHcZx+4o2p4ziO4/QTb0wdx3Ecp594Y+o4juM4/cQbU8dxHMfpJ96YOo7jOE4/8cbUcRzHcfqJN6aO4ziO00+8MXWcJiFpf0km6ZC8fakgaaakv0raKumuvP0ZLkj6rKTv1JH/A5KuG0ifnHzxxtQZNkj6QdKYfSxjf4OkkTrV16cJ89seSJiPtBeSJkv6tqQHJXVIelTSjZIO26GeDhEk/QvwYcKaq7XyXWCBpNgShM4wwBtTZ7ixFTg3sszSkCVZ/aJRZhAWZH/AzDZWyfMzYA7wTsIqLa8jzBW8Wz+OO5w5HbjDzO6vdQMz6yBMvP7BgXLKyRdvTJ3hxk2EpZjOq5ZB0gXZIU9JZ0m6P/X7B5J+Ienjkh6TtEnS+ZJaJH1F0hOS1kp6V+QQMyXdngytLpd0VOZYL5B0vaTNyb6vkLRHKv0WSf8j6SJJG4DfVylHQdKnEj86JN0l6dWpdCOsnfqppMd+QWQfEwgLtp9rZn9MGt2/m9mFZvabJE+v4WtJExLbUSnbQZJ+I+kpSU9LulXSjFT6uxI9OiQ9kizPV0kbL+k7kh5Ptv+DpDmp9DmS/pjs9ylJiyTNT9KmSvqVpCclPZMc4/g69H6zpHskbZG0UdJNksbGNE84Bbgutf2kpDf/8ZTtxZI6JR2X2u464A2SxvSxb2eI4o2pM9woEZbw+qCkKf3c19HA3sDLgY8SVqT4NfAk8GLgMuAySftmtvsK8N+EJZ5uB66TtDt0r5/4J8KyT/OBVwP/Avw0s493Al3AEcB7q/j3YeA/gbOB2cCNybEOSNL3ApYnvuwFfDWyj83J5w2SRlcTYntI2gf4M2Fk4GhCI/59oCVJPxP4JvAdwlqurwP+maQJ+A1heb7jk20XAzdLqvSO/4+wDNmCJP2LhOXaSPY7mnCeXkhYimtzsu8+9U7SFya+ziKsTPJzwgoksXJOJCzv1Vaxmdl6wjKLF0iaL2kX4MfApWb2u9TmbcAo4EV9q+kMSfJeVsc//mnWh7Du4y+S73cA30u+vyFU9e58FwB3ZbY9C7g/s6/7gULKthL4c+p3kXDRPiX5vT9hSahzU3laCOsnnpP8/gxwY+bYU5Ltnp/8vgVYUkN5HwY+nrH9Hfhm6vddwAXb2c+bgCcIy3vdRngWODuVXinXISnbhMR2VPL7C4RFzUf14evnqqQdDbQDozP2fwLvSb4/BbyzyvZLgfOrpPWpNzAv+T61xjp2SJK/17JdhEb9H4SG9B5gp0ieJ6qVwz9D++M9U2e4ci7wTkkv6Mc+lptZOfX7McJFEgAzKxHWRZyc2e6OVJ4uQo9kVmI6FHhFMuS4WdJmQiMN4flmhTb6QNI4Qq/5tkzSbalj1YSZ/SzZ1+sIvdujgMWSTqtjN4cAt5rZtmyCpMnJ/m+usu2hhIWfN2Z0mcZzmlwEXJ4MwX4sPXwMfB34f5Juk/RpSbMz++5L77sTv+6RdLWkd6vv5+2VIdqtkbSzCTdP/0ZY0DyWZwuwcx/7d4Yo3pg6wxIz+zOhYYhFXJbpPYw3KpIv2zBYFVst/0eVaOICYUHiQzKfAwjDpBWeqWGf6f1WUMS2/Z2YbTWz35vZZ8zscELP/NNJcuWGIq1ZVq8tfey+rzQImjxCb00OJAyZY2YXAAcRhoOPBu6VdGKSdjkwHbiCMMzbJumDqX1X1Tu5IToWeA1wLyFA6B+SplXxdUPyN9bgTifcNBSAqVW23w1YXyXNGcJ4Y+oMZz4GnAAcnrGvB/ZMntVVOKSJx31J5YukFkLvqNIbWkxoFO43s39mPrU2oJjZU8A6QvBQmsOBFf3yPnAvUAnCqVz890qlH5LJvxR4maReNyVm9jRhyDz6ag5Bkz2BrogmG1L7uc/MLjaz4wjPNf89lfaQmV1mZm8kPCN+d2rffeptgdvM7HzCc+5O4MQqvq4iDDn3GPFQiLj+P+Aq4P8B31N4hSadZwawE7Ckyr6dIYw3ps6wxczuIVzgsq8j3AJMAs6RNEPS+wk9k2bxfkknSppJeI42kRDgQvJ7N2ChpBdJmi7pOEnfl1Ss8zhfIbwGdLKkAyV9kdDIfa3WHUjaPYmcfZuk2ZKmSToJOAf4JYCZbQH+CnwsiYx9OfC5zK7+BxgHXJkE4Rwg6e2SDkzSLwD+U9KHkrR5qd7jTYSh8V9IepVC9PDhkj6X7GuMQnTzUUnk7hGEQKQVSRkuSbabJmkeoedauaHoU+8k6vbjyXH2A95IqBvRG5Jk2P8met/EfB4YD3wI+HKy/fcyeV4GrDazVdXPiDNkyfuhrX/806wPqQCklG0q4fmWZexnAA8SAoh+SIgAvn87+7oFuCRjux84K/m+P2GI9VRC49NB6OEdndnmAELP6kngWcKF92JA1Y5TpbwF4FOEKNdOQrDRqzN57qKPACRCFOyFwCJgE2F4eSXwWWBMKt8sQoP3LKFndSypAKQkTyWi+BlC7+3PwPRU+nuTfXcSetVfT6XtSnj2+XCS/iAhkGdfoJUQcftgounDwDdIAnyS7/9MzvPjwI+A3WvROynXb5PtthICiD6wHd1flWheSH4fRRj+f2kqz36JnmembDcCH8v7/8Q/A/Op/PM6juM4NZA8Hvgr4YZnYY3bHEwIdHq+mbUPpH9OPvgwr+M4Th1Y6IG8h+Qd2hrZG3iHN6TDF++ZOo7jOE4/8Z6p4ziO4/QTb0wdx3Ecp594Y+o4juM4/cQbU8dxHMfpJ96YOo7jOE4/8cbUcRzHcfqJN6aO4ziO00+8MXUcx3GcfuKNqeM4juP0k/8fFahtg+VDdlUAAAAASUVORK5CYII=", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "binomial_vis(rng, p=0.2, n=100, x_ticks=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`````{admonition} Task 07\n", + ":class: tip\n", + "What is qualitatively different between the shapes of distributions `Bernoulli(p=0.2, n=6)` and `Bernoulli(p=0.2, n=100)`?\n", + "`````" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "#### Common usage\n", + "\n", + "Binomial distribution is commonly used as a likelihood in models with binary outcomes with multiple experiments. For example, to model disease prevalence." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Categorical distribution\n", + "\n", + "A categorical distribution is used to model random events with multiple discrete unordered outcomes, such as the die-rolling event from above. \n", + "\n", + "We can characterise the categorical distribution with its PMF:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "\\begin{align*}\n", + "p(X = x) = \\mathcal{Categorical}(X \\mid p) = \\prod_{k=1}^K p_k^{I_{x=k}},\n", + "\\end{align*}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "where $K$ is the number of possible outcomes, $p_k$ is the probability of the $k$th outcome, and $I_{x=k}$ is the indicator function which evaluates to 1 if $x = k$ and 0 otherwise. All porbabilties $p_k$ form a vector" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\n", + "p = \n", + "\\begin{pmatrix}\n", + "p_1\\\\ \n", + "p_2\\\\\n", + "\\dots \\\\ \n", + "p_K\n", + "\\end{pmatrix},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "\n", + "such that \n", + "\n", + "$$\n", + "\\sum_k p_k = 1.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`````{admonition} Task 08\n", + ":class: tip\n", + "Explain why a categorical distribution with $K = 2$ is equivalent to a Bernoulli distribution.\n", + "`````" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + "ps = jnp.array([0.1, 0.2, 0.3, 0.4])\n", + "categorical = dist.Categorical(probs=ps)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As before we can take some samples:" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[3 2 1 3 3 1 2 1 3 3]\n" + ] + } + ], + "source": [ + "samples = categorical.sample(key=rng, sample_shape=(10,))\n", + "print(samples)" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "p(X=0) = 0.1\n", + "p(X=1) = 0.2\n", + "p(X=2) = 0.3\n", + "p(X=3) = 0.4\n" + ] + } + ], + "source": [ + "print(f\"p(X=0) = {jnp.exp(categorical.log_prob(0)):.1f}\")\n", + "print(f\"p(X=1) = {jnp.exp(categorical.log_prob(1)):.1f}\")\n", + "print(f\"p(X=2) = {jnp.exp(categorical.log_prob(2)):.1f}\")\n", + "print(f\"p(X=3) = {jnp.exp(categorical.log_prob(3)):.1f}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use an alternative way to represent the categorical distribution. Instead of specifying the probabilities $p_k$, we specify logits $l_k$. Each $p_k$ is then computed as\n", + "\n", + "$$\n", + "p_k = \\frac{\\exp(l_k)}{\\sum_{k'}\\exp(l_{k'})},\n", + "$$\n", + "\n", + "i.e., using the softmax function." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "l_0 = 0.7 \n", + "l_1 = 0.3 \n", + "l_2 = 2 \n", + "l_3 = 1.6\n", + "\n", + "logits = jnp.array([l_0, l_1, l_2, l_3], dtype=jnp.float32)\n", + "categorical = dist.Categorical(logits=logits)\n", + "samples = categorical.sample(key=rng, sample_shape=(1000,))\n", + "\n", + "values =[0, 1, 2, 3]\n", + "num_bins = len(values)\n", + "\n", + "hist, _ = jnp.histogram(samples, bins=num_bins, density=True)\n", + "\n", + "fig = plt.figure(dpi=100, figsize=(5, 3))\n", + "plt.bar(values, hist, color='teal', alpha=0.7)\n", + "plt.xticks(values)\n", + "plt.xlabel('x')\n", + "plt.ylabel('p(X=x)')\n", + "plt.grid(linestyle='--', alpha=0.7)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Ordinal distribution\n", + "\n", + "The ordinal distribution is a probability distribution used to model outcomes that are ranked or ordered, often encountered in scenarios where data points lack clear numerical interpretation but possess a defined order of precedence. It assigns probabilities to different rank orders, capturing the relative likelihood of each outcome's position within the ordered set." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# define study hours for each student\n", + "study_hours = jnp.array([5, 7, 3, 10, 8, 6, 4, 9, 2, 7])\n", + "\n", + "# define cutpoints for the ordered categories\n", + "cutpoints = jnp.array([0., 5., 7., 10.]) # Ordered categories: (0, 5], (5, 7], (7, 10]\n", + "\n", + "# sample logits (unnormalized probabilities) based on study hours\n", + "logits = 0.5 * study_hours\n", + "\n", + "ordinal = dist.OrderedLogistic(logits, cutpoints)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# sample from the OrderedLogistic distribution\n", + "ordinal = dist.OrderedLogistic(logits, cutpoints)\n", + "samples = ordinal.sample(rng, (1000,))\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Continuous distributions\n", + "\n", + "Continuous probability distributions describe the probabilities of outcomes within a continuous range of values.\n", + "\n", + "### The Beta distribution\n", + "\n", + "The Beta distribution is a continuous distribution with support in $[0,1] \\subset \\mathbb{R}$.\n", + "The Beta distribution can be used to describe a continuous random variable between 0 and 1, for example, percentages and ratios. It has the following form\n", + "```{margin}\n", + "Note that in this distribution more than one parameter defines its shape.\n", + "```\n", + "\n", + "$$\n", + "p(X = x) = \\mathcal{Beta}(x|\\alpha,\\beta) = \\frac{1}{\\mathrm{B}(\\alpha,\\beta)}x^{\\alpha-1}(1 - x)^{\\beta - 1},\n", + "$$\n", + "\n", + "where $\\alpha > 0$ and $\\beta > 0$ are the two shape parameters of the distribution, and $\\mathrm{B}$ is called the beta function. \n", + "\n", + "Let's visualise the distribution.\n", + "\n", + "`````{admonition} Task 09\n", + ":class: tip\n", + "* Try making each parameter big or small while leaving the other at the same value.\n", + "* Then try make them both big or small.\n", + "`````" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def beta_vis(a, b, x_ticks=True):\n", + " \n", + " beta = dist.Beta(a, b)\n", + " \n", + " x_values = jnp.linspace(0, 1, 1000)\n", + "\n", + " pmf_values = jnp.exp(beta.log_prob(x_values))\n", + "\n", + " fig = plt.figure(dpi=100, figsize=(5, 3))\n", + " plt.plot(x_values, pmf_values, alpha=0.7, color='teal')\n", + " plt.xlabel('x')\n", + " plt.ylabel('p(X=x)')\n", + " plt.title(f'Beta distribution (a={a}, b={b})')\n", + " if x_ticks:\n", + " plt.xticks(x_values)\n", + " plt.grid( linestyle='--', alpha=0.7)\n", + "\n", + " plt.show()\n", + "\n", + "beta_vis(a=4.3, b=3.2, x_ticks=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Gamma distribution\n", + "\n", + "The Gamma distribution is a continuous distribution with support in $\\mathbb{R}^+$.\n", + "Its PDF has the form \n", + "\n", + "$$p(X=x) = \\mathcal{Gamma}(x; \\alpha, \\beta) = \\frac{ \\beta^{\\alpha}}{\\Gamma(\\alpha)} x^{\\alpha - 1} e^{-\\beta x},$$\n", + "\n", + "where $\\alpha>0$ is the shape parameter, which determines the shape of the distribution, and $\\beta>0$ is the scale parameter. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def gamma_vis(a, b, x_ticks=True):\n", + " \n", + " gamma = dist.Gamma(a, b)\n", + " \n", + " x_values = jnp.linspace(0, 20, 1000)\n", + "\n", + " pmf_values = jnp.exp(gamma.log_prob(x_values))\n", + "\n", + " fig = plt.figure(dpi=100, figsize=(5, 3))\n", + " plt.plot(x_values, pmf_values, alpha=0.7, color='teal')\n", + " plt.xlabel('x')\n", + " plt.ylabel('p(X=x)')\n", + " plt.title(f'Gamma distribution (a={a}, b={b})')\n", + " if x_ticks:\n", + " plt.xticks(x_values)\n", + " plt.grid( linestyle='--', alpha=0.7)\n", + "\n", + " plt.show()\n", + "\n", + "gamma_vis(a=2, b=0.5, x_ticks=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Uniform distribution\n", + "\n", + "Perhaps, the simplest, but still a very important distribution among continuous distributions is the uniform distribution. Under this distribution, all possible values are equally likely. The uniform distribution has the following form\n", + "\n", + "$$\n", + "p(X = x) = \\mathrm{Uniform}(x\\mid a, b) = \\begin{cases}\n", + "\\frac{1}{b - a}\\, & \\text{if } a \\le x \\le b \\\\\n", + "0\\, & \\text{otherwise},\n", + "\\end{cases}\n", + "$$\n", + "\n", + "where $a$ and $b$ are the upper and lower bound parameters, respectively." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def uniform_vis(a, b, x_ticks=True):\n", + " \n", + " uniform = dist.Uniform(low=a, high=b)\n", + " x_values = jnp.linspace(-5, 5, 1000)\n", + "\n", + " pmf_values = jnp.exp(uniform.log_prob(x_values))\n", + "\n", + " fig = plt.figure(dpi=100, figsize=(5, 3))\n", + " plt.plot(x_values, pmf_values, alpha=0.7, color='teal')\n", + " plt.xlabel('x')\n", + " plt.ylabel('p(X=x)')\n", + " plt.title(f'Uniform distribution (a={a}, b={b})')\n", + " if x_ticks:\n", + " plt.xticks(x_values)\n", + " plt.grid(axis='y', linestyle='--', alpha=0.7)\n", + " plt.grid(axis='x', linestyle='--', alpha=0.7)\n", + " plt.xlim(-5, 5)\n", + "\n", + " plt.show()\n", + "\n", + "uniform_vis(a=-1, b=3, x_ticks=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Normal distribution\n", + "\n", + "The normal – also known as *Gaussian* – distribution is one of the most common distributions for modeling *continuous* random variables, i.e., corresponding to events with an uncountable number of outcomes. Its probability density function is\n", + "\n", + "$$\n", + "p(X = x) = \\mathcal{N}(x\\mid \\mu, \\sigma) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp\\left(-\\frac{(\\mu - x)^2}{2\\sigma^2}\\right),\n", + "$$\n", + "\n", + "where $\\mu$ and $\\sigma$ are the mean and standard deviation (also called the location, and scale or square-root of the variance $\\sigma^2$, respectively).\n", + "\n", + "`````{admonition} Task 10\n", + ":class: tip\n", + "How do the mean and standard deviation affect the samples?\n", + "`````" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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cGU/zeplyfZ8mJydpb2+Pa+amMg0PD7NgwQK4xPQQJx1lMTACvM0Y83BC+peBjcaY25LyVwPngUR1A4DYaa8yxvx6Btd17TzKcDhMS0sLzc3Nnl3BwglUt9ScHx3lb596iiPnzgFw64oV/P769dRXVEzRbDwa5edHjvD9l15iPBKhoriYj998M+uXLHG4BO5D61rmuFkz18+jNMZMADuBu5I+ugt4NsUhg8A1wMaE14PAIfv/53NiqKJ4kN6REe771a84cu4cFcXFfPq22/joTTdRX1FxUd6y4mLedtVVfO11r2PtwoUMTUzw6W3b2NnV5YDliuI+nI56vR/4gIi8T0SaROQBYAWWA0REPi8i3wYwxkSNMfsSX0A3MGa/v+BYKRTFRQyNj/PJX/+azqEhaubP53+96lU019df8riasjK+8MpXsrWhgXA0yueefpq9Z5NDCBSl8HDUURpjvg/cC3wK2A3cCtxtjGm3syzFcpwFQSAQoKGhIR5dp8wM1e1lwtEon3/mGTqHhlg8fz5feOUrWZqiFTmdZsXBIB+96SZuWLaMyWiULzzzDKeHdOvWGFrXMscPmular4riIx5qbeXHhw5RGgrxxbvuYlV19azOMxGJ8Ilf/YpDfX0sr6zk/le/mnkuG19SlLni+jFK5WIikQgHDhy4KBpMSY/qZrGzq4sfHzoEwF/eeGNaJ3kpzYqDQT5xyy0sLC3l1OAg39y1Kxcmew6ta5njB83UUboIYwwDAwMUWit/rqhuMDA2xgPbtwPw+rVrub6hIW3+mWi2sLSUv7jhBgB+fvQoLRrco3VtFvhBM3WUiuIDHmptZWB8nJVVVbx306asnXdjXR2/c/nlAPx/zz/PhYmJrJ1bUbyCOkpF8Th7zpxhW3s7Anzo+usptid0Z4s/2LiRZRUVnB8b499efDGr51YUL6CO0kUEAgEaGxs9HR3mBIWs20Qkwj/v2AHA69auZe2iRTM6LhPNioNB/qS5GYBHDh+m7fz52RvscQq5rs0WP2jmXct9SCAQoLa21tMVygkKWbefHT5M1/AwC0tLedf69TM+LlPNNtbVcfPy5RjgwZYWT483zYVCrmuzxQ+aeddyHxKJRNizZ4+no8OcoFB1G56Y4D/27wfgv69fT1lx8YyPnY1m79+8meJgkP29vbzQ2ZmxvX6gUOvaXPCDZuooXYQxhtHR0YJ9Wp8tharbD156ieGJCVZVVXHH6tUZHTsbzRbPn8/vXnEFAN/es4dogekNhVvX5oIfNFNHqSgepHdkhEcOHwbgPRs3EpjZlnNz5i1NTZQXF3NycJAn29ryck1FcRp1lIriQX504ACT0ShX19SweenSvF23rLiYtzY1AfBvL75IeIYb3yqKl1FH6SKCwSDr1q2L79emzIxC0+386CiPHTsGwDuuuWbKHpwzZS6aveGKK6gqKaF7ZISn2tsvfYCPKLS6lg38oJk6ShchIlRXV8/qh6+QKTTd/uvgQSYiEdYtWsQ1tbWzOsdcNCsOBnnjOmtf9f/cv9/TY0+ZUmh1LRv4QTN1lC4iHA6zY8eOi3YKV9JTSLoNjY/z86NHAXj71VfP+sdnrprdvXYtZUVFnBocZHtHx6zO4UUKqa5lCz9opo7SZXg5hNpJCkW3Rw4fZiwcprG6mmvnODY5F83mFxXxurVrAfhBgbUqC6WuZROva6aOUlE8wkQkws+PHAHgbVdd5XhX1u9ccQXFwSBHzp3jxe5uR21RlFyijlJRPMLT7e0MjI+zeP58brzE7iD5oGrePF5pz9/8ib29l6L4EXWULiIYDLJ+/XpPR4c5QSHoZoyJ7zX5+rVrCc5xObBsafZ6e2eRFzo7OTs8PKdzeYFCqGvZxg+aqaN0GcUZLEOmvIzfddvX3U1bfz8lwSCvWrMmK+fMhmbLq6rYVFeHAX5mdwv7Hb/XtVzgdc3UUbqISCRCS0uL5we+800h6Bbr2nzF6tVUlJTM+XzZ1OwNdqvy8WPHGPNwZONMKIS6lm38oJk6SkVxOb0jIzxvL0Iec0puorm+nqXl5VyYnGTbiRNOm6MoWUcdpaK4nCeOH8cAV9fUsLyqymlzLkJE4lNFHi2Q7lelsFBHqSguJmoMj9vL1b36sssctmZ6XrF6NaFAgOP9/Rw7d85pcxQlq6ijdBHBYJDm5mZPR4c5gZ9123X6ND0jI5QXF7N1+fKsnTfbmlWUlLDVnrISW4fWj/i5ruUKP2imjtJlTExMOG2CJ/Grbr+wl6u7c/VqirP8Q5NtzWIt3m0nTvg6qMevdS2XeF0zdZQuIhKJsHfvXk9HhzmBX3U7NzrKC11dALw6S1NCYuRCs2tqa1laXs5oOMxvT57M2nndhF/rWi7xg2bqKBXFpTxx/DhRY7hy8WJXBvEkIyLc1dgI+Lv7VSk81FEqigsxxvDrtjaArC0wkA/ubGwkIMKB3l5ODQw4bY6iZAV1lC7DywPeTuI33Q739dE5NERJMJjVIJ5EcqHZwtJSttTXA8Qdvd/wW13LB17XTB2liwiFQmzZsoVQKOS0KZ7Cj7rFnMzW5cspLSrK+vlzqdkdq1YBsK293Xfbb/mxruUaP2imjtJFGGPo7+/33Y9LrvGbbuFolKftYJiY08k2udRsy7JllBUV0Tsy4rvtt/xW1/KBHzRTR+kiIpEIBw8e9HR0mBP4TbeWri6GJiZYWFrKhrq6nFwjl5oVB4PcZHcX+21JO7/VtXzgB83UUSqKy4h1u96+ciUBhzdnni132PtU/vbUKSY8/AOpKKCOUlFcxdD4ODvsuZOvsJ2NF7mqpoba+fMZmZzk+Y4Op81RlDmhjtJFiAilpaWIR1sRTuEn3Z4+eZJwNEpjdTUrq6tzdp1cayYi3G6Prz7po+5XP9W1fOEHzdRRuohgMMiGDRs8H0qdb/ykW2xM744ctybzoVmsRbzz9GkGxsZydp184qe6li/8oJk6ShcRjUbp7u4mGo06bYqn8ItuvSMjHOjtRYBbV67M6bXyodmyykrWLlxI1Bie8cmSdn6pa/nED5qpo3QR0WiU48ePe7pCOYFfdHu6vR2wxvcWlpbm9Fr50uw22+E/7SNH6Ye6lk/8oJk6SkVxCTFnckuOW5P55KYVKwDY39ND38iIw9YoyuxQR6koLuDM8DBHzp1DIGdL1jnB4vnzaVq8GAO+6X5VCg91lC5CRKiqqvJ0dJgT+EG3mBNZv2QJ1fPm5fx6+dTsFrtV6YfuVz/UtXzjB80cd5Qi8kERaRORMRHZKSK3pMl7s4j8VkT6RGRURA6KyF/k095cEgwGaWpq8nR0mBP4QbfY+GTMqeSafGp204oVCHCor4/uCxdyfr1c4oe6lm/8oJmjjlJE3g58CfgcsAl4GnhURKb7tbgA/G/gVqAJ+Dvg70Tkj3Jvbe6JRqN0dHR4etDbCbyuW+fgIMf7+wmK5K3bNZ+aLSwt5aqaGgDPb+js9brmBH7QzOkW5YeBbxhjHjLGHDDG3AucAu5JldkYs8sY8z1jzEvGmBPGmO8AjwHTtkK9hB8qlBN4XbdYl+TGujoqSkrycs18a3aLT6JfvV7XnMAPmjnmKEWkGLgWeDzpo8eBrTM8xyY772+ya52i5I98d7s6wU3LlyPAkXPnOD005LQ5ipIRTm4QthgIAmeT0s8CabdMEJEOoAbL/s8YYx5Kk7cESHxMrwAIh8OEw2EAAoEAgUCAaDQ65aknlh6JRKZsETNdejAYRETi501MBy5aPT85PfF8xpgp+UWEYDB4kY3TpbulTDFCoVDOyhT7P/maXihTx9AQJwcHCYrQXFd3UZ3M1X0yxlxke7bKlOo+lYVCXFNby97ubp46cYK3NDVlvUz5qnuJ5/Lj9ykXZUq01U1lmmkr1w07aSZvUiYp0pK5BSgHbgC+ICJHjTHfmybvfcCnkxN37dpFWVkZADU1NaxZs4a2tjZ6enrieRoaGmhoaODw4cMMDAzE0xsbG6mtrWXfvn2Mjo7G09etW0d1dTW7du2acrPXr19PcXExLS0tU2xobm5mYmKCvXv3xtPGxsYIBAIMDAxw8ODBeHppaSkbNmygt7eX48ePx9Orqqpoamqiq6uLjoTFp91UpmAwyJYtW3JWpvr6empqajh27BiDg4OeKtOzw8MArC4p4UDC+XN9nzZv3hzPn+0yTXefmsrK2Av89MUXWZkQ1OOF+xQr08mTJxkdHY3r5sfvU7bLtGvXrimaualMNfbY+aUQpzbTtLteR4C3GWMeTkj/MrDRGHPbDM/zSeDdxpgrpvk8VYuyo6+vj8rKSqCwWl9aJneV6UOPPcbJwUHuvf56bkvoevVymaa7T8OTk/zBj39MJBrlwbvvpq683PNl8uN9KqQyDQ8Ps2DBAoAqY8zLT9lJONaiNMZMiMhO4C7g4YSP7gJ+nMGphKmOMPk648B4PLM9lycUChEKTS1+TMxkpgtrni49+bwzTY9Go7S1tbF69WoCgUDK/NPZmGl6vsqUiIjkpEzRaJRjx46xevXqlPa7tUyn7W7XgAjXNzSkPE+u7lNyXctWmdKlV4dCXF1Tw97ubnacPs2bErpfs1GmdOnZKhNAe3v7Rbr56fsUI1tlCgQCKeuaG8o03T2+6HwzypU77gc+ICLvE5EmEXkAWAE8CCAinxeRb8cyi8ifisgbRGSt/Xov8BHgO45Yn2Wi0Sg9PT2ejg5zAq/qtt3uMrqmtpby4uK8XtspzWLTX549dSqv180WXq1rTuIHzRwdozTGfF9EFgGfApYC+4C7jTHtdpalWI4zRgD4PLAaCAPHgI8DX8+b0YqSJZ6zHeWNDQ0OW5I/bmho4MGdOznY18e50dGcL/6uKNnA8WAeY8w/A/88zWfvSXr/FeAreTBLUXLK+dFRDvb2AnB9ATnKRfPnc8WiRRzq62N7Rwd3r13rtEmKckmc7npVEggEAjQ0NMy431yx8KJuz3d2YoC1CxeyeP78vF/fSc1u8nD3qxfrmtP4QTPvWu5D/FChnMCLum13uNvVSc1usMv8Ync3Q+Pjl8jtLrxY15zGD5p513IfEolEOHDgwEVh00p6vKbbyOQke85a62zc4JCjdFKzpRUVrK6uJmoML3R25v36c8Frdc0N+EEzdZQuwhjDwMDAlHk+yqXxmm4tXV2Eo1GWVVSwvKrKERuc1syr0a9O6+ZF/KCZOkpFyTNOd7u6gVjZd505w+jkpMPWKEp61FEqSh6ZjERo6eoCnOt2dQMrqqqoLy9nMhqN66EobkUdpYsIBAI0NjZ6etDbCbyk256zZxkNh1lYWsrlixY5ZofTmknC3pte6n51Wjcv4gfNvGu5DwkEAtTW1nq6QjmBl3SLdbvesGxZfDlFJ3CDZjFH2XL6NBMeCfRwg25eww+aeddyHxKJRNizZ4+no8OcwCu6RY15eXzSdhJO4QbNLrPnkI6Fw+w+c8YxOzLBDbp5DT9opo7SRRhjGB0d9XR0mBN4RbdDvb0MjI9TVlTE1bW1jtriBs1EJB7U45XuVzfo5jX8oJk6SkXJE7G1XbfU1xPycDdUNok5yhc6O4l4eNFsxd/ot1VR8oAxhufsVpPT3a5u4sqaGiqKixmamOClhI12FcVNqKN0EcFgkHXr1k2735uSGi/o1j4wwJkLFygOBtm8dKnT5rhGs2AgwPXLlgEvBzq5Gbfo5iX8oJk6ShchIlRXVzsaDelFvKBbzAlsXLKEedNscJtP3KRZrIX9XEeH68ex3KSbV/CDZuooXUQ4HGbHjh2Ew2GnTfEUXtDNbd2ubtJsY10d80IhekdGOHrunNPmpMVNunkFP2imjtJleDmE2kncrFv3hQsc7+9HsAJ53IJbNCsOBrnW7o72QverW3TzEl7XTB2louSYWGvyqpoaqubNc9gadxKLfn3OA45SKTzUUSpKjnHLIgNuptmeMnNqcJDOwUGnzVGUKaijdBHBYJD169d7OjrMCdys28DYWHzag5sWQXebZmXFxay3F2Fwc6vSbbp5AT9opo7SZRQXFzttgidxq247urowQGN1NbVlZU6bMwW3aRaPfnX5Kj1u080LeF0zdZQuIhKJ0NLS4vmB73zjZt3cFu0aw42aXb9sGQIcPneOvpERp81JiRt1czt+0EwdpaLkiLFwmF32Yt9u6nZ1KwtKS1m3eDHgjehXpXBQR6koOaL19Gkmo1GWlpezsqrKaXM8gUa/Km5EHaWi5IhYt+sNDQ2eXpUkn8Ra3i92dzM0Pu6wNYpiMWdHKSIl2TBEsaLDmpubPR0d5gRu1C0cjbKjqwt4uZXkJtyoGcDSigpWVVURNSaun5twq25uxg+aZewoReTVIvItETkmIpPAiIgMichvROSvRcQ9S494kImJCadN8CRu021fdzcXJiepnjePK+xxN7fhNs1ixFqVbo1+datubsbrms3YUYrIG0XkEPD/gCjwj8CbgVcD7wd+A7wSOC4iD4pITQ7s9TWRSIS9e/d6OjrMCdyoW+xH/vplywi4sNvVjZrFiEUIt545w7jL1gd1s25uxQ+aZbKNwSeAjwA/M8ak2mH1PwBEZBnwIeC/A/9rzhYqiscwxrC9sxNwZ7er21ldXU3t/Pl0j4zQevq066bWKIXHjFuUxpjrjDGPTOMkE/N1GmM+ZoxRJ6kUJIf7+jg3OkppKMT6JUucNsdziMiUrbcUxWlmFcwjIqVpPnN+V1oP4+UBbydxk26xOYDN9fUUuciuZNykWTKxlvgLnZ2Eo2mfzfOOm3VzK17XbLZRr7tEZHNyooi8Fdg7N5MKl1AoxJYtWwi5YGNfL+E23WKtIDd3u7pNs2SaamqoKinhwuQk+7q7nTYnjtt1cyN+0Gy2jvKXwLMi8nGxKBeRb2EF+vxN1qwrMIwx9Pf3u36Xd7fhJt1ODQzQOTREKBDgWhftPZmMmzRLRUCE65ctA9wV/ep23dyIHzSblaM0xvwP4I1YQTtPAXuADcAWY8xXsmZdgRGJRDh48KCno8OcwE26xbpdNyxZwvyiIoetmR43aTYdsXHK7Z2drvmR9YJubsMPms1lwYHHgR8BNwHLgY8bY/ZnxSpF8She6Hb1ChuWLGFeKMS50VEO9/U5bY5SwMw2mGcN8Bzweqx5lF8EfiwiXxQR9z5GK0oO6R0Z4ci5cwhwnd1tqMyeomCQ5qVWbKAukq44yWxblLuBNmCDMeaXxphPAq/AWoDghSzZVnCICKWlpbouaIa4RbfYj3nT4sUsKJ02MNwVuEWzS5E4TcQN3a9e0c1N+EGz2TrKDxpjfs8Y0x9LMMY8C2wCWrNhWCESDAbZsGGD50Op841bdHPr3pOpcItml6K5vp5QIEDn0BAdg4NOm+MZ3dyEHzSbbTDPv06TPmSMef/cTCpcotEo3d3dRF02b8ztuEG3wfFx9vX0AN4Yn3SDZjNhflERG+xFG9yw+IBXdHMTftBs1sE8ItIgIoHk/5XZE41GOX78uKcrlBO4QbcXOjuJGkNjdTVLyssds2OmuEGzmRJ78HDDOKWXdHMLftBsLs5tP7Aqxf+KUnB4qdvVa1zf0IAAR86do3dkxGlzlAJkLo5SpvlfUQqK0clJdp05A3ij29VrVM+bR5O9VZmbFh9QCgfHu0tF5IMi0iYiYyKyU0RuSZP3zSLySxHpEZFBEXlORF6dT3tziYhQVVXl6egwJ3Bat52nTzMZjbK0vJwVVVWO2JApTmuWKfHFBxzufvWabm7AD5o56ihF5O3Al4DPYUXMPg08KiIrpjnkVqzl8+4GrgWeBB4RkU25tzb3BINBmpqaPB0d5gRO6xbvdm1o8MyPgdOaZUqspb6vp4eh8XHH7PCabm7AD5o53aL8MPANY8xDxpgDxph7gVPAPakyG2PuNcZ80RizwxhzxBjzCeAI8Ib8mZw7otEoHR0dnh70dgIndZuMRNjR1QXAVg+NT3qtri0pL2d1dTVRY3jB3uvTCbymmxvwg2aOLecuIsVYrcIvJH30OLB1hucIABXAuTR5SoCShKQKgHA4TNjePT0QCBAIBIhGo1NuZiw9EolMmew8XXowGERE4udNTAcuWuswOT0SiXDq1Cnq6uoQkSn5RYRgMHiRjdOlu6VMMUKhEMaYnJQp9kWsqamZ8tSajzLtOXOGkYkJFpSW0lhVRSQS8cR9MsZw6tSpizTL5X2aa5muq6/n+LlzPHvqFK9YvdqRuhcOh6fo5sfvU7bLNDk5OUUzN5Vpps7byX1PFgNB4GxS+lmgbobn+EugDPiPNHnuAz6dnLhr1y7KysoAqKmpYc2aNbS1tdFjz4UDaGhooKGhgcOHDzMwMBBPb2xspLa2ln379jE6OhpPX7duHdXV1ezatWvKzV6/fj3FxcW0tLRMsaG5uZmJiQn27rV2JjPGxK8zMDDAwYMH43lLS0vZsGEDvb29HD9+PJ5eVVVFU1MTXV1ddCSM37ilTGB9YbZs2ZKzMi21lzk7evQoQ0NDeS3Tr48coX9ggCuLiti5c6dn7tOmTZuIRqO0trbGu4tzfZ/mWqay0VH6BwbYKcKF8XH27d494/uUrTK1t7fT398f182P36dsl6m1tXWKZm4qU01NDTNBZrsslIgMYS1hdzzx/wyOrwc6ga3GmOcS0v8aeLcxZt0ljn8H8BDwu8aYJ9LkS9Wi7Ojr66OyshJwT+srEonQ2trKli1bCAaDnnhadMMTcOwHf9OmTXltUQaCQf77ww/TPzrKZ267jY12T4AX7pMxhpaWFjZv3uyZFqUxhj/5+c/pvnCBj998M9cnbWOWj7o3MTHBzp0747r58fuU7TJNTEzQ2toa18xNZRoeHmbBggUAVcaYaZd+mkuL8jvAYIr/Z0ovEOHi1mMtF7cyp2AHAX0DeFs6JwlgjBkH4qP/safnUCh00UaiMTGTmW4Qerr06TYovVR6IBCgtraWQCCAiKTMP52Nmabnq0yJ5KpM0WiUmpoaioqKMirrXMu0r7ubgfFxKubNY6O91Fq2ynQp2+dapmg0Sm1tbUrN3Fz3blqxgocPHmR7Rwc3rUgd85fLuhcKhVLq5qfvU4xslamoqCilZm4oU6o8qZh1MI8x5h5jTG/y/xkcPwHsBO5K+ugu4NnpjrNbkt8C3mmM+VlGRrucQCDAmjVrZnzzFAundItNVbguyUl6Aa/WtVj0646uLsIOBId4VTcn8YNmGVkuIvNmkGdtBqe8H/iAiLxPRJpE5AFgBfCgfa7Pi8i3E879DuDbWGOT20Wkzn55Y/LaJYhGoxw7dszT0WFO4IRuxhhPr8bj1bq2bvFiqufN48LkJC+eTdvxlBO8qpuT+EGzTF38bhG5froPReTDWFtwzQhjzPeBe4FP2cfdCtxtjGm3syzFcpwx/hiru/irwOmE15dnek03E41G6enp8XSFcgIndDt+/jzdIyOUBINsqptp7Jl78GpdExFusPf6dGKRdK/q5iR+0CxTR/kE8JTd0otv0Cwil4nIM1gRph/I5ITGmH82xqwyxpQYY641xjyV8Nl7jDG3J7y/3RgjKV7vybAcijInnrVbk9cuXUrJNGMzSm64we5+fb6z0xV7VCr+JyNHaYz5M+C1wDuAVhFpFpG/APYCPcDVxpjvZd9MRXEPxhiePnkSYNqAEiV3bKirY35REedGRznU1+e0OUoBkPHoqjHm18A1wHHgeeBvgA8YY95kjMn/oIGPCAQCNDQ0eHrQ2wnyrVtbfz+nh4cpDga5zu4G9BpermuhQIBme+5svhdJ97JuTuEHzWZr+TuAO7AcZTHwShGpyJpVBYofKpQT5Fu3Z+zWZPPSpczzaLer1+taLIDquY6OvHa/el03J/CDZplGvS4Tkcewlp37c2PMVuA6YDPwkogkT/VQMiASiXDgwIGLJuIq6cmnbsaYuKP0crer1+tac309RYEAp4eHOZmw0kqu8bpuTuAHzTJ18fsAA6w3xnwLwBizB9iCNW3jZyLytaxaWEDElrDTAIXMyKdufuh2Be/XtXmhEBvtaON8Rr96XTcn8INmmTrKTxhjXmOMmVIzjTGTxphPYi1mPu1+koridfzQ7eoXYosP6GbOSq7JNOo1bWvRGNOC1Q2rKL4jsdv1Zg93u/qF6xsaEOB4fz+nExbDV5RsM2NHKSJlM8lnL0034/zKywQCARobGz096O0E+dItsdt1i4e7XcEfda2ypIQNS5YAxKfr5Bo/6JZv/KBZJpYfFZFP2Lt+pEQs7hKRR4E/n7t5hUXioujKzMmXbk+3WwtG+aHb1S917daVK4GX702u8Ytu+cQPmmVi+e3AJqBNRJ4Xka+KyF+LyF+KyN+JyI+ALqxdPX4CfDH75vqbSCTCnj17PB0d5gT50M0Yw2/tsTA/dLv6pa7duHw5oUCAEwMDeYl+9Ytu+cQPms3YURpjDhlj3gasAf4dqAfeCvwhlhPttP9fZYz5mjHGu6o4hDGG0dFRT0eHOUE+dDt+/rxvul3BP3WtvLiYa+3FB/LRqvSLbvnED5pl3H9kR7w+YL8Qe4NH42UVFOUSaLSre7l15Uqe7+zkqfZ23nnNNfE9ZxUlW8y601hE3i8i+4AxYExE9olIRguiK4oXMMbwlN1aucUeE1Pcw3XLllEcDNI1PMzx8+edNkfxIbNylCLyt1hbWz0CvM1+PQI8ICJ/lz3zCotgMMi6deum3UFcSU2udTvY20v3yAjzQiG21E8by+Yp/FTX5oVCXGffl6dy3P3qJ93yhR80m22L8h7gD40x9xljfmK/7gP+CPiT7JlXWIgI1dXV2nWUIbnWbduJEwBsbWjwzZZafqtr8ejXkydzOhbmN93ygR80m62jDAItKdJ3MotxT8UiHA6zY8cOwuGw06Z4ilzqFo5GecaOdr1t1aqsn98p/FbXrq2vpzQUomdkhIO9vTm7jt90ywd+0Gy2jvI7WK3KZP4I+O7szVG8HELtJLnSbfeZMwyOj1OVMLndL/iprhUHg/El7XLd/eon3fKF1zWbywzQ99sBPA/Zr31Y00OiInJ/7JUlOxXFEWLdrreuXEnQwxOmC4HE7tdINOqwNYqfmG036dVAq/3/Gvtvj/26OiGfThlRPMtYOMx2e2eK2zTa1fVsqKujqqSEgfFxdp05Q7NPAq8U55mVozTG3JFtQxQrOmz9+vWejg5zglzp9nxHB+ORCEvLy7l80aKsnttp/FjXQoEAt65cySOHD/NkW1tOHKUfdcs1ftBM+5JcRnFxsdMmeJJc6PYbe6zrtpUrPR2xNx1+rGuvWL0agO2dnVyYmMjJNfyoW67xumbqKF1EJBKhpaXF8wPf+SYXug2Oj9N6+jQAt/so2jWGX+vamgULWF5ZyUQkwrM52KfSr7rlEj9opo5SUVKw7cQJIsawduFCllVWOm2OMkNEJN6q/HVbm8PWKH5BHaWipOCJ48cBeGVjo8OWKJly+6pVCLCvp4ezw8NOm6P4AHWUipLE8fPnaevvJxQIcIsPttQqNBbPn896e87rk/b0HkWZC+ooXUQwGKS5udnT0WFOkG3dYq3JG5Yto6KkJCvndBt+r2ux7tcn29qyuqSd33XLBX7QTB2ly5jIUaSe38mWbuFoNL7IgN+7Xf1c17YuX06JvaPIob6+rJ7bz7rlCq9rpo7SRUQiEfbu3evp6DAnyKZuL3R2MjQxwcLSUjbZGwL7Eb/XtXmhEFuXLwfgl8eOZe28ftctF/hBM3WUipJArNv1FatWEfDh3MlC4lVrrEXDnjp5ktHJSYetUbyMOkpFsTk/OspOe+6k37tdC4GrampYVlHBWDjM0ydPOm2O4mHUUboMLw94O0k2dHvyxAmixrBu0aKCmDvp97omIvFW5WNHj2btvH7XLRd4XTN1lC4iFAqxZcsWQj7ZHDhfZEM3Y0z8x/TOAmhNFkpdu3P1akKBAIfPneNEf/+cz1coumUTP2imjtJFGGPo7+/P6Q7tfiQbur3Y3U3X8DCloVBB7BRSKHWtat48rl+2DMhOq7JQdMsmftBMHaWLiEQiHDx40NPRYU6QDd0ePXIEgDtWraK0qChbprmWQqprr7a7X588cYKJOZa3kHTLFn7QTB2lUvCcHx3lOXvfyddcdpnD1ijZZmNdHbXz53NhcpLfalCPMgvUUSoFzy+PHydiB/GsXrDAaXOULCMi3BUL6sninEqlcFBH6SJEhNLSUl/ufZhL5qJbNCGI57Vr12bbNNdSaHXtrsZGAiK81NMzp6CeQtMtG/hBM3WULiIYDLJhwwbPh1Lnm7no1nr6NN0jI5QXF3NzAS2AXmh1bdH8+WxtaADgp4cPz/o8haZbNvCDZuooXUQ0GqW7u5toNOq0KZ5iLrr93A7iuXP1aoo9/EXOlEKsa6+//HLACuoZGh+f1TkKUbe54gfN1FG6iGg0yvHjxz1doZxgtrp1DQ3R0tUFwGsLLIinEOvalTU1rK6uZiISiS9VmCmFqNtc8YNmjjtKEfmgiLSJyJiI7BSRW9LkXSoi/yYih0QkKiJfyqOpis945NAhDLClvr4gVuIpdEQk3qr86eHDRD08r0/JL446ShF5O/Al4HPAJuBp4FERmW6wqATosfPvyYeNij+5MDHBE21tAPzOFVc4bI2SL25buZLy4mK6R0bY0dnptDmKR3C6Rflh4BvGmIeMMQeMMfcCp4B7UmU2xpwwxnzIGPNtYCCPduYFEaGqqsrT0WFOMBvdHj92jLFwmJVVVWxYsiSH1rmTQq1rJaEQr7KXKJxNUE+h6jYX/KCZY45SRIqBa4HHkz56HNiaf4ucJxgM0tTU5OnoMCfIVLdINMoj9o/k715xhae/wLOlkOva6y6/HAF2nz2b8VSRQtZttvhBMydXqV0MBIGzSelngbpsXURESrC6bGNUAITDYcLhMACBQIBAIEA0Gp0y4BxLj0QiU9YpnC49GAwiIvHzJqYDFy3hlJwejUY5c+YMDQ0NiMiU/CJCMBi8yMbp0t1SphihUAhjTE7KBHDmzBmWLFkyxelNV6btnZ30jIxQXlTETQ0N8bK5qUy5vk8iQldXF0uWLCEQePl52ctlmul9WlhSwo0NDTzb0cEP9+/nQ9ddN+MyhcNhurq6qKuri6e5oUzpbHf6Pk1OTnLmzJm4Zm4q00wDjNywnHvyiLqkSJsL9wGfTk7ctWsXZWVlANTU1LBmzRra2tro6emJ52loaKChoYHDhw8zMPByT29jYyO1tbXs27eP0dHRePq6deuorq5m165dU272+vXrKS4upqWlZYoNzc3NTExMsHfvXsBaPHhgYID6+nqGh4c5ePBgPG9paSkbNmygt7eX4wkRe1VVVTQ1NdHV1UWHvQybm8oE1hdmy5YtDAwM5KRMS5cu5fTp0wwMDDA0NJS2TMYYvt/bC8CVoRB7d+1yZZlyfZ82bdrEyZMn6ejoiD9ceL1MmdynqwMBngV+eeQITZOTLCwpmXGZjh49SmdnJyLiqjK59T7t3LmT/v7+uGZuKlNNTQ0zQZxa0d3ueh0B3maMeTgh/cvARmPMbZc4fhuw2x7XTJcvVYuyo6+vj0o70tEtT8CRSITW1la2bNlCMBj0xNOiG56Ao9Eora2tbNq0aUr3Tqoy7evu5n9u20ZRMMiDd9/NwtJSV5Yp1/fJGENLSwubN2+eopmXy5Tpffr0b37D7jNneP3atXxg06YZlWliYoKdO3fGdXNbmdx4nyYmJmhtbY1r5qYyDQ8Ps8BatrLKGDPINDjWojTGTIjITuAu4OGEj+4CfpzF64wD8dnFsafnUCh00f5oMTGTma5vfbr06fZdm0l6zD4RSZl/OhszTc9nmWLkqkyJXaepzp9YpocPHQIRXtnYSG1FxYxtny7dq/cpHA7Hf2ySP/NqmdKlpyrTW6+8kj1nz/JEWxu/v349FSUvP0+nK1Mq3dxSpkvZ7sR9ijnSZM3cUKZUeVLhdNTr/cAHROR9ItIkIg8AK4AHAUTk8yLy7cQDRGSjiGwEyoEa+/2V+TY8FwQCAWpqamZ88xSLmep29Nw5Ws+cISDCm5ua8mSdO9G6BhuWLKGxuprxSISf2Ss0XQrVLXP8oJmjlhtjvg/cC3wK2A3cCtxtjGm3syzFcpyJ7LJf1wLvtP//eR7MzTmBQIA1a9Z4ukI5wUx1+8FLLwHWXLq68vJ8mOZatK5ZrZe3XGk9Yz9y+DDjSV2HqVDdMscPmjluuTHmn40xq4wxJcaYa40xTyV89h5jzO1J+SXFa1W+7c4F0WiUY8eOeXqpJyeYiW6nBgbie06+9UpfdEDMCa1rFjctX05dWRmD4+PxdX/Tobpljh80c9xRKi8TjUbp6enxdIVygpno9oP9+zHADcuWsaKqKn/GuRStaxbBQIC3X301AD88cICxS7QqVbfM8YNm6igV33NqYIBtJ04AxH8UFSXGHatWsbS8nIHxcX42hy24FP+ijlLxPd998UUMsLWhgcsWLnTaHMVlBAMB3n7VVQD86ODBS7YqlcJDHaWLCAQCNDQ0eHrQ2wnS6Xb8/Hl+e+oUArzzmmvyb5xL0bo2ldtXraK+vJzB8fG0a8CqbpnjB828a7kP8UOFcoJ0un3HXv3j1pUrWVldnWfL3IvWtakEAwF+z+6W/8/9+6fd2Fl1yxw/aOZdy31IJBLhwIEDF61YoaRnOt0O9PSwo6uLgAjv0LHJKWhdu5jbVq1iZVUVFyYn+cH+/SnzqG6Z4wfN1FG6iNhar04tK+hVUulmjOGh1lYAXrl6tW7MnITWtYsJiPDejRsBa17l2eHhi/KobpnjB83UUSq+5Kn2dg6fO8e8UIh3rV/vtDmKR9i8dCkbliwhHI3y7T26N7xioY5S8R0TkQjfsn/k3nbllSxIWPhcUdIhIrxv0yYEeOrkSY709TltkuIC1FG6iEAgQGNjo6cHvZ0gWbf/OniQ3pERaubP543r1jlsnTvRujY9jQsWcPuqVQB8fefOi3bQUN0yww+aeddyHxIIBKitrfV0hXKCRN16R0bigRjv2biRYg/vqp5LtK6l5w82bGBeKMShvj6eSNgHUXXLHD9o5l3LfUgkEmHPnj2ejg5zgkTdvt7Swlg4TNPixdyyInk9fSWG1rX0LJo/n9+3591+c/fu+HQR1S1z/KCZOkoXYYxhdHTU09FhThDTbXtHB9s7OwmK8GfXXRff21O5GK1rl+b1l1/OispKhiYm4oE9qlvm+EEzdZSKLxiPRPg/9nSQN61bpwufK3MmFAhwz5YtADx27BgHe3sdtkhxCnWUii947PRp+kZGWFJWFl9hRVHmytW1tdy5ejUG+NL27Ux4uPtQmT3qKF1EMBhk3bp1BDUAJSMO9PWxa2QEEeGe5mZKQiGnTXI9Wtdmzgc2b2ZhaSmdQ0N876WXVLcM8UNdU0fpIkSE6upqHVvLgNHJSb60fTuhoiLuWrOGa+vrnTbJE2hdmznlxcX8md0F++NDhzgTDqtuGeCHuqaO0kWEw2F27NhBWLf5mTEPtbZydngYGRnhPboCz4zRupYZW5Yt4xWrVhGNRvnET37C8NiY0yZ5Bj/UNXWULsPLIdT55vmODh4/fhwR4e0rVjC/qMhpkzyF1rXM+MNrr2Xh/Pl0j43x4M6dTpvjKbxe19RRKp7kzPAwD2zfDsDvXH45ayoqHLZI8TvlxcX85Q03IMC2Eyf4VcJCBIq/UUepeI6JSIQvPPMMFyYnuWLRIt6tXa5KnriqpoZXL10KwNdaWjg1MOCwRUo+UEfpIoLBIOvXr/d0dFg+eKi1lWPnz1NRXMzHb76ZkqIi1S1DtK7NjmAwyL2vehUb6uoYj0T43NNPc2FiwmmzXI0f6po6SpdRXFzstAmu5udHjvDo0aMI8JGtW1k8fz6gus0G1Wx2zCspide9zqEhvvjb3xKJRp02y9V4va6po3QRkUiElpYWzw9854qdXV082NICwLvWr2ez3QWmumWOajY7YrpVFBXxP2+9leJgkNYzZ/jm7t1Om+Za/FDX1FEqnuBEfz9f+O1vMcCdq1fztiuvdNokpcBpXLCAv7jhBsCaX/nTw4cdtkjJFeooFddzemiIT2/bxlg4zPraWl3wXHENN69YEd9l5Os7d7LtxAlnDVJygjpKxdX0XLjAX//615wbHWVFZSX33XILIQ/va6f4j7dfdRVvuPxyAB7Yvp0XOjsdtkjJNuLlrU9mg4hUAgMDAwNUVlY6bc4UjDFEIhGCwaC2mIBzo6N8/IknOD08zLKKCj5/550sKC29KJ/qljmq2eyYTjdjDA9s386TJ05QFAjw8Ztv5rplyxy01D24ua4NDg5SZe00VGWMGZwunz6au4wJDTUHoGtoiI8+/jinh4dZUlbG373iFSmdZAzVLXNUs9mRSjcR4c+vv54bGxqYjEb5+6ef5qn2dgescyder2vqKF1EJBJh7969no4OywbHzp3jY7/8Jd0jIywtL+fv77wzPg0kFapb5qhmsyOdbqFAgI/ddBO3r1xJxBj+6dln+cXRow5Y6S78UNfUUSqu4oXOTu771a8YGB+nsbqaL951F7VlZU6bpSgzIhQI8OEbb+S1l12GAb66YwcPtbYSLbAhLr+hG/cprsAYw/dfeonvvvgiAOtra/nrW2/Vhc4VzxHbF3VhaSnfffFFfnzoEB2Dg3x061bKPD7xvlDRFqXL8PIyT7NlcHyczz39dNxJ3n3ZZXz2jjsycpKFqNtcUc1mx0x0ExF+7+qr+aubbqI4GGTn6dP8+aOPcqi3Nw8Wug+v1zWNelUcZWdXF19+/nnOj40RCgT4YHMzd61Z47RZipI1jp47x+effprukRECIvz+NdfwlqYmgjrNyXFmGvWqjtJFGGMYGBigqqrKdWHU2WZofJxv7d7N4/ZWRcsrK/nI1q00LliQ8bkKSbdsoZrNjtnqdmFigq/u2MHTJ08CsGbBAv7suuu4bOHCXJnqGtxc13R6iAeJRCIcPHjQ09FhlyJqDI8dPcof//SncSf5hssv50uvec2snCQUhm7ZRjWbHbPVray4mI9u3cq9119PWVERx86f58OPPcb/2bmTwfHxHFnrDvxQ1zSYR8kLxhie6+jgO3v3cmrQenBbVVXFPVu2cGVNjcPWKUruERHubGxk89KlPNTaylMnT/LI4cP8qq2NtzQ18TtXXMG8kP4kuxG9K0pOCUejbO/o4D/37+fY+fMAlBUV8Y6rr+b1l1+u4zRKwbGgtJSP3nQTd61Zwzd37eJ4fz//uncvPzl0iDdcfjl3r11LRUmJ02YqCaijdBEiQmlpqev68WdD/9gYTxw/zs+OHKF3ZASAeaEQb7ziCt64bl1Ww+T9pFu+UM1mRzZ121hXx5de8xp+097Ov+7ZQ/fICN958UV+sH8/d65ezV1r1rBmwQLP3yM/1DUN5lGyxujkJM91dPCbEyfYffZsfJJ1VUkJr73sMl5/+eVUzZvnsJWK4j7C0SjPnDzJwwcOcLy/P56+qqqKV6xezY3Ll1NXXu6cgT5Fo16nwc2OMhqN0tvby+LFiwl4oEvSGEPn0BA7u7po6epiX08P4YSd3i9fuJC7167llpUrKc7hPCqv6eYGVLPZkWvdjDG82N3NY0eP8lxHB5MJ36eVVVVcv2wZm5cu5fJFiyjyyNxEN9e1mTpKx7teReSDwEeBpcBLwL3GmKfT5L8NuB+4CugCvmiMeTAftuaaaDTK8ePHWbhwoesqFMDI5CTt/f0c7O3lgP3qHxubkmdZRQW3r1rFrStXUl9RkRe73K6bG1HNZkeudRMR1i9ZwvolSxiemOCp9nZ+e/Ik+3p6aB8YoH1ggP/Yv5+iQIArFi3i6tpa1i5aROOCBSxyafemH+qao45SRN4OfAn4IPBb4I+BR0XkSmPMyRT5VwM/B/4FeBdwE/DPItJjjPlh3gz3MZORCD0jI3RfuED3hQt0DQ1xcmCA9v5+uu2xxkRCgQBX19TQXF9Pc3099RUVrvyyKorXKC8u5u61a7l77VqGxsdp6erihc5OXuzuZmB8nH09Pezr6ZmSf3V1NcsrK1laUcHS8nLq7FeJRtPOCafV+zDwDWPMQ/b7e0Xk1cA9wH0p8v8JcNIYc6/9/oCINAMfAdRR2hhjGI9EGAuHGZ2cZCwctv63/w5PTDAwNsbA+DiD4+Px/8+PjXFudDTtuReWlnLFokWsW7yYpsWLWbNwYU67VRVFgYqSEu5YvZo7Vq/GGEPX0BD7urvZ39PD8fPnOTU4yPDEBC92d/Nid/dFx5cVFbFg3jwWlJbG/1aWlDC/qIiyoiLrb3Fx/H1JKERRIEBxMEgoECj4h1/HHKWIFAPXAl9I+uhxYOs0h91of57IY8D7RaTIGDOZ4jolQGKsdQXAV55/nnn2rhRiZcQYYwWgxMZt7coRS0sczRURosZg7BeA2N0K0WjUSk/Ia+z0GMYYJBCYcnw0GqXv3Dl+euGCZY+dP2oMYft8k5EIk5EI4WiUiDFEolEiQNhOjxhDOBrFxK6bWB67TJdKLwkGqZk/n9qyMuoqKlhVXc2y8nJWVFbGw9ZjazdGIhHC4XD8NInpiYRCofgGrokaBoNBotHoFG2mSw8EAgQCgYvSjTFUVVURjUan2BLLH4lESByLj20gm5g3ne1OlGk627NVJoDKysqLNPNymfJxn4wxVFRUxHVzqkzLKiupr6jgzlWrAOt3oWNoiPbBQToGBjg9NMSZCxc4MzzMhclJLkxOMjwxwamBgZdPMoPfAoxBRCynGQpREgoREiEoQjAQIGD/DQUCYEz8fcC2PSgCxnD+3Dl+OTaGiMS7X000GnfAYmtmIG5L7Hc5YOcxxsTT4vnt38/YeQJ2/vhveex+2GWK/WbHmEjRS5YKJ1uUi4EgcDYp/SxQN80xddPkD9nnO53imPuATycnPrJ3LyF7I+Di4mLKysq4cOHClA1GS+fNY15pKcNDQ0wmVOz58+dTUlLC4MAAkYQvU3l5OUVFRfT390+5GZWVlQRE6E+spEB1VRVRYxgcfHkMWUSojkSYnJxkeHg4nh4MBKisqmJ8fJyRhJtbFApRXlHB2OgoownjhbEyRcbHIRymJBCgJBBgUVUVdYsWMdbfTyAcpjwUoiwU4vKVK2lcupSzbW0EJyfjFW/d2rVUV1ezY8cODiV8WdevX09xcTEtLS1TytTc3MzExAR79+592fZgkC1btjAwMMDBgwdf1re0lA0bNtDb28txe5UegKqqKpqamujq6qKjoyOeXlNTw5o1a2hra6MnocupoaGBpqYmDhw4wECCxo2NjdTW1rJv3z5GE1rK69ato7q6ml27dk35AXJbmRoaGjh8+HDOyrRq1SpaW1t9VaZc36eTJ08yNDQU181tZXrlhg10d3dbZSouhgULKCoro3bFCg62t3O0o4OhcJihyUkC8+ZRWlVFx9mznBsaYjQSYSwSQUpKCBYXc2F4OLu/e3ZLd9rfverqrP3uzfS3vHiGLWXHol5FpB7oBLYaY55LSP9r4N3GmHUpjjkMfNMY8/mEtJuAZ4ClxpgzKY5J1aLs+L/PPktZRQWC/RQZCFhPG/ZTjmC1EGNPJ/GnGTs9aD8xk/g0Y+ef8oRqp0tCC5GEa4LVkhT7uPPnz1NTU4Pw8hOUiBCyn+gCItbTmp1WFAxSUlSEGEMA4mnzi4spLSqynqx89lSfnA5w5swZlixZMqWLyMtlyvV9EhG6urpYsmTJlAALL5cpH/cpHA7T1dVFXV1dPM3rZUqVLiKMT04yHg4zEYkwGY0Stnu2RicmmIhEiNqttliP2Xg4HE+L9ahFjWEiHKa3r49qe05orL4l97zFWogxWxLTY7/NBuItyFh6yvz2uRM1SJU+euEC773xRnBx1GsvEOHi1mMtF7caY5yZJn8Y6Et1gDFmHIgvphj7IX3LVVe5bnpIOBympaWF5hUrCGVp8D2xYiYy3bY306VPZ08m6SKSMj32hZ1tejgcpqOjg7q6upTn92KZYuTqPoXDYTo7O1m6dOlFn3m1TOnSs1UmgK6uLurr66ecz8tlmi59XnEx87KwMEg4HKbl/Hma167N2u9athgcHOS9M8jnWKyuMWYC2AnclfTRXcCz0xz2XIr8rwJaUo1PKoqiKMpccXpSy/3AB0TkfSLSJCIPACuABwFE5PMi8u2E/A8CK0Xkfjv/+4D3A/+Ud8sVRVGUgsDRdrAx5vsisgj4FNaCA/uAu40x7XaWpViOM5a/TUTuBh4A/hRrwYE/98scykAgQE1NjWcn5TqF6pY5qtnsUN0yxw+a6RJ2iqIoSkGiGzd7kGg0yrFjxy6K6FTSo7pljmo2O1S3zPGDZuooXUQ0GqWnp8fTFcoJVLfMUc1mh+qWOX7QTB2loiiKoqTBXZNa8kjiqhBuIRwOc+HCBQYHB10338jNqG6Zo5rNDtUtc9ys2Uz9QCEG8ywDOi6ZUVEURSkUGowxndN9WIiOUoB6YMhpW1JQgeXEG3CnfW5Fdcsc1Wx2qG6Z43bNKoAuk8YZuqsdnAdsMaZ9cnCShHVKh9KFKitTUd0yRzWbHapb5nhAs0vapME8iqIoipIGdZSKoiiKkgZ1lO5iHPgsCbudKDNCdcsc1Wx2qG6Z43nNCi6YR1EURVEyQVuUiqIoipIGdZSKoiiKkgZ1lIqiKIqSBnWUiqIoipIGdZQuR0RKRGS3iBgR2ei0PW5GRFaJyDdEpE1ERkXkmIh8VkSKnbbNbYjIB22dxkRkp4jc4rRNbkVE7hORHSIyJCLdIvJfInKF03Z5CVtDIyJfctqW2aCO0v18Eehy2giPsA6rTv8xcBXwF8CfAH/vpFFuQ0TeDnwJ+BywCXgaeFREVjhpl4u5DfgqcANwF9aKZo+LSJmjVnkEEdkC/BGw12lbZotOD3ExIvJa4H7gLcBLwCZjzG5HjfIYIvJR4B5jTKPTtrgFEXkeaDXG3JOQdgD4L2PMfc5Z5g1EpAboBm4zxjzltD1uRkTKgVbgg8Angd3GmHsdNWoWaIvSpYjIEuBfgHcDIw6b42WqgHNOG+EW7G7oa4HHkz56HNiaf4s8SZX9V+vVpfkq8DNjzBNOGzIXCm5RdC9g73DyLeBBY0yLiKxy1iJvIiJrgP8B/KXTtriIxUAQOJuUfhaoy7853sL+bt4PPGOM2ee0PW5GRH4P2AxscdqWuaItyjwiIp+xB7TTvZqxftwrgc87bLIryEC3xGPqgV8APzDGPOSM5a4mecxFUqQpF/O/gfXAO5w2xM2IyHLgy8C7jDFjTtszV3SMMo+IyGKsJ/p0nAD+HXgDU3+4gkAE+K4x5g9yYqBLmalusS+k7SSfBJ4H3mOMiebYRM9gd72OAG8zxjyckP5lYKMx5jbHjHM5IvIV4I3ArcaYNofNcTUi8kbgYazfrBhBrN+0KFBijImkONSVqKN0IXb0YWVCUj3wGPBW4HljTIcjhnkAEVmG5SR3Yj3NeubLmC/sYJ6dxpgPJqTtB36swTwXY3e3fgV4E3C7MeaIwya5HhGpAFYmJX8TOAj8g9e6rXWM0oUYY04mvheRYfvfY+okp8duSW4DTgIfAWpim8YaY844Z5nruB/4VxFpAZ7DCt1fATzoqFXu5avAO4HfBYZEJDaWO2CMGXXOLPdijBkCpjhDEbkA9HnNSYI6SsVfvAq4zH4lP1DIxdkLE2PM90VkEfApYCnWD9rdxph2Zy1zLbFpNNuS0t+LFXSn+BztelUURVGUNGjUq6IoiqKkQR2loiiKoqRBHaWiKIqipEEdpaIoiqKkQR2loiiKoqRBHaWiKIqipEEdpaIoiqKkQR2loiiKoqRBHaWiKIqipEEdpaIoiqKkQR2lohQIIlIjImdE5BMJadeLyISIvMpJ2xTFzehar4pSQIjI3cB/AVuxtjzaBfzMGHOvg2YpiqtRR6koBYaIfBV4JbAD2ABs8cMu9IqSK9RRKkqBISKlWFtrLQeajTF7HTZJUVyNjlEqSuHRCNRjff+Td6FXFCUJbVEqSgEhIsXAC8BurDHKDwPXGGPOOmmXorgZdZSKUkCIyD8Cb8UamxwGngSGjDGvd9QwRXEx2vWqKAWCiNwO3Au82xgzaIyJAu8GbhaRexw0TVFcjbYoFUVRFCUN2qJUFEVRlDSoo1QURVGUNKijVBRFUZQ0qKNUFEVRlDSoo1QURVGUNKijVBRFUZQ0qKNUFEVRlDSoo1QURVGUNKijVBRFUZQ0qKNUFEVRlDSoo1QURVGUNKijVBRFUZQ0/P/LvVYyDhud/wAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def norm_vis(mu, sigma, x_ticks=False):\n", + " \n", + " normal = dist.Normal(loc=mu, scale=sigma)\n", + " \n", + " x_values = jnp.linspace(-5, 5, 1000)\n", + "\n", + " pmf_values = jnp.exp(normal.log_prob(x_values))\n", + "\n", + " fig = plt.figure(dpi=100, figsize=(5, 3))\n", + " plt.plot(x_values, pmf_values, alpha=0.7, color='teal')\n", + " plt.xlabel('x')\n", + " plt.ylabel('p(X=x)')\n", + " plt.title(f'Normal distribution ($\\mu$={mu}, $\\sigma$={sigma})')\n", + " if x_ticks:\n", + " plt.xticks(x_values)\n", + " plt.grid(axis='y', linestyle='--', alpha=0.7)\n", + " plt.grid(axis='x', linestyle='--', alpha=0.7)\n", + " plt.xlim(-5, 5)\n", + "\n", + " plt.show()\n", + "\n", + "norm_vis(mu = 0, sigma = 1 )" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "`````{admonition} Task 11\n", + ":class: tip\n", + "Implement the PDF of the Normal distribution and test it using the function provided below.\n", + "`````" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [], + "source": [ + "def test_normal_pdf(pdf_fn, run=False):\n", + " if not run:\n", + " return\n", + " assert pdf_fn(0, 1, 0) == jnp.exp(dist.Normal(loc=0, scale=1).log_prob(0)), \"Normal(X=0|0, 1) is incorrect.\"\n", + " assert pdf_fn(0, 2, 0) == jnp.exp(dist.Normal(loc=0, scale=2).log_prob(0)), \"Normal(X=0|0, 2) is incorrect.\"\n", + " assert pdf_fn(0, 1, 1) == jnp.exp(dist.Normal(loc=0, scale=1).log_prob(1)), \"Normal(X=0|1, 1) is incorrect.\"\n", + " assert pdf_fn(2, 3, 1) == jnp.exp(dist.Normal(loc=2, scale=3).log_prob(1)), \"Normal(X=1|2, 3) is incorrect.\"\n", + " print(\"Nice! Your answer looks correct.\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### The Multivariate Normal distribution\n", + "\n", + "```{margin}\n", + "This distribution will be very useful in chapters where we will talk about Gaussian Processes and spatial modelling.\n", + "```\n", + "\n", + "The *multivariate normal distribution* is a generalisation of the *univariate normal distribution* to consider multiple random variables that have a jointly normal distribution. In other words, it lets us model variables that are not independent – if we know the value of one variable, that tells us something about the other variables!\n", + "More concretely, the multivariate normal distribution lets us consider multiple random variables such that when we condition on some of these variables the remaining variables have a normal distribution. These variables are distributed in a kind of stretched fuzzy ball in higher dimensional space.\n", + "\n", + "As a rule of thumb, the more one variable tells us about another, the larger the *covariance* or *correlation* between the two. \n", + "\n", + "We will be using the same notation for multivatiate and univariate normals $\\mathcal{N}$. Which one to use, should be clear from the context throughout this course.\n", + "\n", + "The PDF for an $D$-dimensional random variable $X$:\n", + "\n", + "$$\n", + "p(X = x) = \\mathcal{N}(x\\mid \\mu, \\Sigma) = \\frac{1}{\\sqrt{(2\\pi)^D|\\Sigma|}}\\exp\\left(-\\frac{1}{2}(x - \\mu)^\\intercal\\Sigma^{-1}(x - \\mu)\\right),\n", + "$$\n", + "\n", + "where $x$ and $\\mu$ are now vectors of numbers rather than single numbers, $\\Sigma$ is a covariance matrix that replaces $\\sigma$ from our univariate definition above, and $|\\Sigma|$ is its determinant. The covariance matrix looks like this:\n", + "\\begin{equation*}\n", + "\\Sigma = \\begin{bmatrix}\\sigma_1^2 & \\rho_{12} \\sigma_1 \\sigma_2 & \\cdots & \\rho_{1D} \\sigma_1 \\sigma_D \\\\\n", + " \\rho_{21} \\sigma_2\\sigma_1 & \\sigma_2^2 & \\cdots & \\rho_{2D} \\sigma_2 \\sigma_D \\\\\n", + " \\vdots & \\vdots & \\ddots & \\vdots \\\\\n", + " \\rho_{D1} \\sigma_D \\sigma_1 & \\rho_{D2} \\sigma_D \\sigma_2 & \\cdots & \\sigma_D^2 \\end{bmatrix}\n", + "\\end{equation*}\n", + "\n", + "where $\\sigma_i^2$ is the variance for the $i$-th dimension, and $\\rho_{ij} = \\rho_{ji}$ is the *correlation* between the $i$-th and $j$-th dimensions. The covariance matrix tells us how the \"ball\" of random variables is stretched and rotated in space.\n", + "\n", + "`````{admonition} Task 12\n", + ":class: tip\n", + "Show that the equation above is equivalent to the univariate case when $D = 1$\n", + "`````" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "Now let's look at how the equation above simplifies in the two-dimensional case\n", + "\n", + "$$\n", + "\\begin{align*}\n", + "&p(X_1 = x_1, X_2 = x_2) = \\\\\n", + "&\\mathcal{N}\\left( \\begin{bmatrix} x_1 \\\\ x_2 \\end{bmatrix} \\middle| \\begin{bmatrix} \\mu_1 \\\\ \\mu_2 \\end{bmatrix}, \\begin{bmatrix} \\sigma_1^2 & \\rho \\sigma_1 \\sigma_2 \\\\ \\rho \\sigma_1 \\sigma_2 &\\sigma_2^2 \\end{bmatrix}\\right)= \\\\\n", + "&\\frac{1}{2\\pi\\sigma_1\\sigma_2\\sqrt{1 - \\rho^2}}\\exp\\left(-\\frac{1}{2(1 - \\rho^2)}\\left[\\left(\\frac{x_1 - \\mu_1}{\\sigma_1}\\right)^2 -2\\rho\\left(\\frac{x_1 - \\mu_1}{\\sigma_1}\\right)\\left(\\frac{x_2 - \\mu_2}{\\sigma_2}\\right) + \\left(\\frac{x_2 - \\mu_2}{\\sigma_2}\\right)^2 \\right] \\right)\n", + "\\end{align*}\n", + "$$\n", + "\n", + "**Group task:** Try to understand what this equation means. Discuss the following questions with your neighbors. \n", + "\n", + "1. If $\\rho = 0$, how does this two-dimensional case relate to the one-dimensional case above?\n", + "2. Now, think about what happens as $\\rho$ becomes larger? What if it becomes negative?\n", + "\n", + "We will come back to this distribution later in the course." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Batch and event shapes\n", + "\n", + "All distributions in `numpyro` have an `event_shape` which describes how many dimensions the random variable is, e.g., for a 2-dimensional normal distribution this would be 2, and a `batch_shape` which describes how many sets of parameters the distribution has – it is probably easier to show what this means with the following examples rather than tell.\n", + "\n", + "Let's first look at a simple univariate normal $\\mathcal{N}(x|0, 1)$. We will evaluate the probabilities of $X = 1$ and $X = 2$:" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "event_shape = ()\n", + "batch_shape = ()\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "p(X = [1. 2.]) = [0.24197073 0.05399096]\n" + ] + } + ], + "source": [ + "values = jnp.array([1., 2.])\n", + "normal = dist.Normal(0., 1.)\n", + "print(f\"event_shape = {normal.event_shape}\")\n", + "print(f\"batch_shape = {normal.batch_shape}\")\n", + "print(f\"p(X = {values}) = {jnp.exp(normal.log_prob(values))}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We see that this distribution has an empty event shape, which you can think of as being the same as an event shape of 1 (like how a scalar is the same as a vector of length 1). The batch shape is also empty, since we only specified one set of parameters ($\\mu = 0, \\sigma = 1$). \n", + "\n", + "Now since we tried to evaluate the probability of two values at once, and neither the event shape nor the batch shape are 2, this is equivalent to calling `dist.log_prob(1.)` and `dist.log_prob(2.)` separately. `numpyro` is just making our lives easier by *broadcasting* the `log_prob` calculation to do both $p(X=1) = \\mathcal{N}(X=1|0, 1)$ and $p(X=2) = \\mathcal{N}(X=2|0, 1)$ at the same time.\n", + "\n", + "We could also specify a *batch* of two sets of parameters so that we are essentially working with $\\mathcal{N}(x|0, 1)$ and $\\mathcal{N}(x|1, 2)$ at the same time:" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "event_shape = ()\n", + "batch_shape = (2,)\n", + "[p(X_1 = 1.0), p(X_2 = 2.0)] = [0.24197073 0.17603266]\n", + "p(X_1 = 1.0, X_2 = 2.0) = 0.042594753205776215\n" + ] + } + ], + "source": [ + "batch_normal = dist.Normal(jnp.array([0., 1.]), jnp.array([1., 2.]))\n", + "print(f\"event_shape = {batch_normal.event_shape}\")\n", + "print(f\"batch_shape = {batch_normal.batch_shape}\")\n", + "print(f\"[p(X_1 = {values[0]}), p(X_2 = {values[1]})] = {jnp.exp(batch_normal.log_prob(values))}\")\n", + "print(f\"p(X_1 = {values[0]}, X_2 = {values[1]}) = {jnp.prod(jnp.exp(batch_normal.log_prob(values)))}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now, notice that while the event shape is empty (as expected since we are still working with a univariate normal), the batch size is 2!\n", + "\n", + "As a result, the calculation we are doing is equivalent to separately calculating $p(X_1=1) = \\mathcal{N}(X_1=1|0, 1)$ and $p(X_2=2) = \\mathcal{N}(X_2=2|1, 2)$! Again, this is just `numpyro` making our lives easier.\n", + "\n", + "If we want to calculate $p(X_1=1,X_2=2)$, i.e., the joint probability that $X_1 = 1$ and $X_2 = 2$, then we either need to manually multiply the probabilities (assuming that $X_1$ and $X_2$ are independent) – as we've in the cell above – or we need to work with a multivariate normal.\n", + "\n", + "Let's look at the case when the $X_1$ and $X_2$ are independent:" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "event_shape = (2,)\n", + "batch_shape = ()\n", + "p(X_1 = 1.0, X_2 = 2.0) = 0.055732980370521545\n" + ] + } + ], + "source": [ + "multivariate_full_normal = dist.MultivariateNormal(jnp.array([0., 1.]), jnp.array([[1., 1.], [1., 2.**2]]))\n", + "print(f\"event_shape = {multivariate_full_normal.event_shape}\")\n", + "print(f\"batch_shape = {multivariate_full_normal.batch_shape}\")\n", + "print(f\"p(X_1 = {values[0]}, X_2 = {values[1]}) = {jnp.exp(multivariate_full_normal.log_prob(values))}\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This results in a slightly different value for the joint probability, but otherwise everything looks the same." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Measuring distances between distributions\n", + "\n", + "There are several ways to measure distances between two probability distributions with PDFs $p(x)$ and $q(x)$, each with its own characteristics and applications. \n", + "\n", + "- Total variation distance (TVD): This metric quantifies the difference between two probability distributions by measuring the total absolute difference between their probability mass functions (for discrete distributions) or probability density functions (for continuous distributions).\n", + "\n", + "$$\n", + "\\text{TVD}(p, q) = \\frac{1}{2} \\int |p(x) - q(x)| \\, dx\n", + "$$\n", + "\n", + "- Kullback-Leibler Divergence (KLD): Also known as relative entropy, measures the information lost when one probability distribution is used to approximate another. It is asymmetric, and, hence is not a 'distance' but a 'deviance'\n", + "\n", + "$$\n", + "\\text{KLD}(p \\parallel q) = \\int p(x) \\log \\left( \\frac{p(x)}{q(x)} \\right) \\, dx\n", + "$$\n", + "\n", + "- Jensen-Shannon Divergence (JSD): JSD is a symmetrized version of KLD. It measures the similarity between two probability distributions by averaging their KLD values.\n", + "\n", + "$$\n", + "\\text{JSD}(p, q) = \\frac{1}{2} \\text{KLD}(p \\parallel m) + \\frac{1}{2} \\text{KLD}(q \\parallel m),\\\\\n", + "m = \\frac{p+q}{2}\n", + "$$\n", + "\n", + "- Hellinger Distance: This distance metric is used to measure the similarity between two probability distributions. It is based on the square root of the total variation distance and ranges between 0 and 1.\n", + "\n", + "$$\n", + "\\text{Hellinger}(p, q) = \\sqrt{1 - \\int \\sqrt{p(x)q(x)} \\, dx}\n", + "$$\n", + "\n", + "- Wasserstein Distance (Earth Mover's Distance): This metric measures the minimum amount of \"work\" needed to transform one distribution into another. It considers the underlying structure of the distributions and is often used in optimal transport theory. $\\Gamma(p, q)$ represents the set of all joint distributions with marginals $p$ and $q$. The Wasserstein distance is defined as the minimum \"cost\" required to transform one distribution into another.\n", + "\n", + "$$\n", + "\\text{Wasserstein}_m(p, q) = \\left( \\inf_{\\gamma \\in \\Gamma(p, q)} \\int_{\\mathcal{X} \\times \\mathcal{X}} d(x, y)^m \\, d\\gamma(x, y) \\right)^{\\frac{1}{m}}\n", + "$$\n", + "\n", + "- Maximum Mean Discrepancy (MMD) between two distributions can be defined using the kernel trick. Let $\\phi(x)$ be a feature map $\\phi(x)$, and $\\mathbb{E}_{x \\sim P}[ \\phi(x) ]$ the expected value of the feature map $\\phi(x)$ computed over samples drawn from distribution $p$. In the same way, $\\mathbb{E}_{y \\sim Q}[ \\phi(y) ]$ is the expected value of the feature map $\\phi(y)$ computed over samples drawn from distribution $q$, $\\| \\cdot \\|$ is the Euclidean norm. The feature map $\\phi$ is usually chosen to be a reproducing kernel Hilbert space (RKHS) kernel function, such as the Gaussian kernel $k(x, y) = \\exp \\left( -\\frac{\\| x - y \\|^2}{2\\sigma^2} \\right)$.\n", + "\n", + "$$\n", + "MMD(p, q) = \\left\\| \\mathbb{E}_{x \\sim p}[ \\phi(x) ] - \\mathbb{E}_{y \\sim q}[ \\phi(y) ] \\right\\|^2\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{margin}\n", + "For all implementations, use `jax` or `numpyro` functionality. For instance, `import jax.numpy as jnp` instead of `import numpy as np`. And `import numpyro.distributions as dist` for access to distributions.\n", + "````" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`````{admonition} Task 13\n", + ":class: tip\n", + "1. Implement numeric evaluation of the KL divergence:\n", + "\n", + "```\n", + "def kl_divergence(p: dist.Distribution, q: dist.Distribution, n: int = 10_000):\n", + " \"\"\"\n", + " add your code here\n", + " \"\"\" \n", + " pass\n", + "```\n", + "\n", + "2. Calculate the following KL divergence. What do we see?\n", + " - $\\mathrm{KLD}\\left[\\mathrm{Uniform}(0, 1) \\mid\\mid \\mathrm{Uniform}(0, 1)\\right]$\n", + " - $\\mathrm{KLD}\\left[\\mathrm{Beta}(5, 2) \\mid\\mid \\mathrm{Beta}(5, 2)\\right]$\n", + " \n", + "3. Calculate the following KL divergences. What can we say about the relationship between the beta and uniform distributions?\n", + " - What is $\\mathrm{KLD}\\left[\\mathrm{Uniform}(0, 1) \\mid\\mid \\mathrm{Beta}(5, 2)\\right]$?\n", + " - What is $\\mathrm{KLD}\\left[\\mathrm{Uniform}(0, 1) \\mid\\mid \\mathrm{Beta}(2, 2)\\right]$?\n", + " - What is $\\mathrm{KLD}\\left[\\mathrm{Uniform}(0, 1) \\mid\\mid \\mathrm{Beta}(1, 1)\\right]$?\n", + " \n", + "4. What is $\\mathrm{KLD}\\left[ \\mathrm{Beta}(5, 2) \\mid\\mid \\mathrm{Uniform}(0, 1)\\right]$. How does it compare to $D_\\mathrm{KL}\\left[\\mathrm{Uniform}(0, 1) \\mid\\mid \\mathrm{Beta}(5, 2)\\right]$ from above?\n", + "`````" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "```{margin}\n", + "You can tackle this task during week 2, as we have not looked at kernels yet.\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`````{admonition} Task 14 (week 2)\n", + ":class: tip\n", + "\n", + "1. Implement numeric evaluation of MMD taking as inputs two distributions `p` and `q` of type `dist.Distributions`, number of samples `n`. Use RBF gaussian as a default kernel. \n", + "\n", + "2. Modify the MMD computation code to accept different kernel functions besides the RBF kernel: linear, polynomial, and exponential kernels.\n", + "\n", + "\n", + "`````" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "aims", + "language": "python", + "name": "python3" }, - "nbformat": 4, - "nbformat_minor": 0 + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.19" + } + }, + "nbformat": 4, + "nbformat_minor": 0 } diff --git a/06_Monte_Carlo.ipynb b/06_Monte_Carlo.ipynb index 9147364..44c0ca5 100644 --- a/06_Monte_Carlo.ipynb +++ b/06_Monte_Carlo.ipynb @@ -1,485 +1,481 @@ { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# The Monte Carlo method\n", - "\n", - "The Monte Carlo method is a computational technique that uses random sampling to estimate complex mathematical outcomes or solve problems that might be deterministic in nature.\n", - "\n", - "The name “Monte Carlo” for the Monte Carlo methods has an origin that ties back to the famous Monte Carlo Casino located in Monaco. This name was not chosen because of any direct association with the mathematical principles behind these methods, but rather for its metaphorical connection to randomness and chance, which are central elements in both gambling and Monte Carlo simulations.\n", - "\n", - "Let us consider the example of computing of an integral of a function. This is a deterministic problem, but we will solve it using random sampling. Assume we want to find value of the integral\n", - "\n", - "$$\\int_a^b f(x)dx. $$\n", - "\n", - "Monte Carlo integration estimates this integral by finding the fraction of random points that fall below $f(x)$.\n", - "\n", - "The convergence of Monte Carlo integration is $\\mathcal{O}(n^{1/2})$ and is independent of the dimensionality. Hence, Monte Carlo integration generally beats numerical intergration for moderate- and high-dimensional integration since numerical integration (quadrature) converges as $\\mathcal{O}(n^d)$!\n", - "\n", - "## Computing the integral $\\int_0^1 e^x dx$\n", - "\n", - "Estimate the integral $\\int_0^1 e^x dx$ using Monte Carlo integration." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`````{admonition} Group Task\n", - ":class: tip\n", - "Compute this integral before we proceed to see how Monte Carlo solves it.\n", - "`````" - ] - }, - { - "cell_type": "code", - "execution_count": 50, - "metadata": {}, - "outputs": [], - "source": [ - "import random\n", - "import math\n", - "import numpy as np\n", - "import jax.numpy as jnp\n", - "import scipy.stats as stats\n", - "\n", - "import matplotlib.pyplot as plt\n", - "import matplotlib.patches as patches" - ] - }, - { - "cell_type": "code", - "execution_count": 51, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "1.630969\n", - "1.5222379\n", - "1.5657302\n", - "1.8136375\n", - "1.7423098\n", - "1.7120391\n", - "1.7192066\n", - "1.7177035\n", - "1.718586\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "1.717916\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "fig, axs = plt.subplots(1, 2, figsize=(10, 4), dpi=100)\n", - "\n", - "# Plot function and Monte Carlo samples\n", - "x = jnp.linspace(0, 1, 100)\n", - "axs[0].plot(x, jnp.exp(x), color='teal')\n", - "pts = np.random.uniform(0, 1, (100, 2))\n", - "pts[:, 1] *= jnp.e\n", - "cols = ['teal'] * 100\n", - "for i in range(100):\n", - " if pts[i, 1] > jnp.exp(pts[i, 0]): # acceptance / rejection step\n", - " cols[i] = 'orangered'\n", - "axs[0].scatter(pts[:, 0], pts[:, 1], c=cols)\n", - "axs[0].set_xlim([0, 1])\n", - "axs[0].set_ylim([0, jnp.e])\n", - "axs[0].grid(True)\n", - "axs[0].set_xlabel('x')\n", - "axs[0].set_ylabel('f(x)')\n", - "axs[0].set_title('Monte Carlo approximation of $\\int_0^1 e^x dx$')\n", - "\n", - "# Monte Carlo approximation\n", - "n_values = 5**np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])\n", - "results = []\n", - "for n in n_values:\n", - " pts = np.random.uniform(0, 1, (n, 2))\n", - " pts[:, 1] *= jnp.e\n", - " count = jnp.sum(pts[:, 1] < jnp.exp(pts[:, 0]))\n", - " volume = jnp.e * 1 # volume of region\n", - " sol = (volume * count) / n\n", - " print(sol)\n", - " results.append(sol)\n", - "\n", - "# Convergence plot\n", - "axs[1].plot(np.log10(n_values), results, marker='o', color='steelblue')\n", - "axs[1].axhline(y=jnp.exp(1) - jnp.exp(0), color='red', linestyle='--')\n", - "axs[1].set_xlabel('log(number of samples)')\n", - "axs[1].set_ylabel('Approximation value')\n", - "axs[1].grid(True)\n", - "axs[1].set_title('Convergence of Monte Carlo approximation')\n", - "axs[1].legend(['Monte Carlo Approximation', 'True Value'], loc='lower right')\n", - "\n", - "plt.tight_layout()\n", - "plt.show()\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "`````{admonition} Group Task\n", - ":class: tip\n", - "Rerun the experiemnt above several times. Do you always get the same path for the Monte Carlo approximation?\n", - "`````" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## The Monte Carlo method - computing $\\pi$\n", - "\n", - "We can also use Monte Carlo to estimate the value of π!" - ] - }, - { - "cell_type": "code", - "execution_count": 52, - "metadata": {}, - "outputs": [], - "source": [ - "def in_circle(x, y, r):\n", - " # is point (x,y) within circle of radius r?\n", - " return jnp.sqrt(x**2 + y**2) <= r\n", - "\n", - "def approx_pi(r, n):\n", - " xs, ys, cols = [], [], []\n", - "\n", - " count = 0\n", - "\n", - " for i in range(n):\n", - " x = np.random.uniform(0, r, 1)\n", - " y = np.random.uniform(0, r, 1)\n", - " xs.append(x)\n", - " ys.append(y)\n", - "\n", - " if in_circle(x, y, r):\n", - " count += 1\n", - " cols.append(\"orangered\")\n", - " else:\n", - " cols.append(\"teal\")\n", - "\n", - " pi_appr = round(4 * count / n, 3)\n", - "\n", - " plt.figure(figsize=(6, 4))\n", - " plt.scatter(xs, ys, c=cols, s=20, alpha=0.5)\n", - " plt.title(\"Monte Carlo approximation of π = \" + str(pi_appr))\n", - " plt.annotate(f\"Points inside circle: {count}/{n}\", xy=(0.5, 0.9), xycoords='axes fraction', ha='center')\n", - " plt.annotate(f\"Approximated π ≈ {pi_appr}\", xy=(0.5, 0.85), xycoords='axes fraction', ha='center')\n", - " plt.xlabel(\"x\")\n", - " plt.ylabel(\"y\")\n", - " plt.grid(True)\n", - " plt.axis('equal')\n", - " plt.show()\n", - "\n", - " return pi_appr" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let us iterate $n$ through values $5*10^1, 5*10^2, 5*10^3$ and run the function approximating $\\pi$. How does the result change?" - ] - }, + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# The Monte Carlo method\n", + "\n", + "The Monte Carlo method is a computational technique that uses random sampling to estimate complex mathematical outcomes or solve problems that might be deterministic in nature.\n", + "\n", + "The name “Monte Carlo” for the Monte Carlo methods has an origin that ties back to the famous Monte Carlo Casino located in Monaco. This name was not chosen because of any direct association with the mathematical principles behind these methods, but rather for its metaphorical connection to randomness and chance, which are central elements in both gambling and Monte Carlo simulations.\n", + "\n", + "Let us consider the example of computing of an integral of a function. This is a deterministic problem, but we will solve it using random sampling. Assume we want to find value of the integral\n", + "\n", + "$$\\int_a^b f(x)dx. $$\n", + "\n", + "Monte Carlo integration estimates this integral by finding the fraction of random points that fall below $f(x)$.\n", + "\n", + "The convergence of Monte Carlo integration is $\\mathcal{O}(n^{1/2})$ and is independent of the dimensionality. Hence, Monte Carlo integration generally beats numerical intergration for moderate- and high-dimensional integration since numerical integration (quadrature) converges as $\\mathcal{O}(n^d)$!\n", + "\n", + "## Computing the integral $\\int_0^1 e^x dx$\n", + "\n", + "Estimate the integral $\\int_0^1 e^x dx$ using Monte Carlo integration." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`````{admonition} Group Task\n", + ":class: tip\n", + "Compute this integral before we proceed to see how Monte Carlo solves it.\n", + "`````" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [], + "source": [ + "import random\n", + "import math\n", + "import numpy as np\n", + "import jax.numpy as jnp\n", + "import scipy.stats as stats\n", + "\n", + "import matplotlib.pyplot as plt\n", + "import matplotlib.patches as patches" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ { - "cell_type": "code", - "execution_count": 53, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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", 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wCfAPwLN/hKEeCA5Bx05IxiHiBwHklcDyL8NXrwX9R3910orCb95+m5f3NmE2mjihoYHBaJTBWAyjXs+zTU1cPn8+M8rK/qXhphSF2zdsYEt/P4coCne3tDCvooIN3d10h0JcOHMmiUyGeCaD22x+38tw18AAjf39WA0GltXWUmCzve/YbX4/f9u2jQqXC5NeT184zF8aG/nZkiUfGIeqqp/40uoMBlnZ1kYyk6E/EqHF58NiNBJLp3li1y7i6TR6nQ6jXs/3DzmE8YWF/9K9+WeQyWZ5ubmZLf39FNhsnD5xIiUOB6qqcv+WLbzb2YnLbGZDTw97hob44cKFH0osnwavt7by0NatADT292PW65lSXMykwkJ2DQ1RYLVi1Ot5bMcODDodR9fXf6rjRlIp7ti4EYfJhMNkIpxM8scNG7jlqKOwGo0j20VTKe7fsoVNvb3YjEYumDGDuRUVI+tf2ruXPUND1LjdAGzu7+eN1laOGzfuQ8/bH4nQ5veTb7UyxuPB+BnJfjgW4zdvv83YUIinBweZUVbGE7t2kVYUiu12ouk04wsLGePxoGSz3LpuHYORCGUOB9u9Xu5tbGRaSQnVbjcr2tqwG42cMXnyyPGVbJbfr1tHNJWixu0mnEzyh/XrueGII0hkMjyxaxdDsRhTS0o4saHhn7qOrmCQG9esIZZKoagqy2tr+cr06e/7n8iqKvF0GqvR+E9NzHL4ZAj1P+hW0Uj8BVVVp3zIuheA61VVfVf7ewVwpaqqH+huIoS4BLgEoKSkZPZjjz32mccUiURwOByfef/PEz71tSoZSdoRPwgBVgdEAnI5gKoCqkbcAlwF4PSAyfqhh+sLBRmKRjGgoiLI6vQYDQZcZrM8nWYFlTudpBSFtKKMENh+V5/VaMT8CS8SbzTKcCyGTggK9HoGMxnMBgMWg4FUJkO+zUYgkQBVxajXU2izYdDpSGQyDESj6IRAhZGx6Ee9XKLpNIPRKGbN6lRVlXQ2O/JyB0kIA9EoiqriMpspstsR2r6+eBxVVUdIpS8SGTlOJJXCpNeTyWZRkSSab7Vi0OlQtGVVLtfHXvtHPdt4Ok00nUYnBC6z+VN5I3zxOMFkEr0QJBUFVVUpcziwmUx0BYOY9HqEEKiqSkpRKHc6/ynLNKu5efU6HV3BIHqdjlg6La9fu0dxbcw2kwmdECjZLHqdjjKH41N9j9OKQm8k8r5x7R+rcdQ9GIrFCKdSKNksaUUBIahxu7FpRO+NRkkpCnohyGSzJDIZ9DodVoMBnRAjk0GVA88/k80ihMBhMuE0mTDodDi06/i06I9ECKdS5AmBN50euS8pRcFkMLD/SMV2Oya9np5wGJNeT1ZV8cXjI/9DArAajdiMRiqczpHjK6pKdyj0gftTbLMxHI+jqCp6IUhns7jMZgqs8n87lk6TVJSRaxp9RYp2bl88jgDs2vqUolDqcIx4bFKKIu+Tdo5iu33kfzv3Pv70OOywwzapqjrn4OX/zS5mH/YN/9AZhaqqdwN3A8yZM0f9VzrB/J/umuMfgL594OsDdxFUTwSbC/56FYSGYc8GMBjBZIGBLoiFIZsGBGQVuTyrSJf6mOkw/3g49GxJ/BqS6TRH3XId4VQal8kIWYXedAazu4jTZ0jZQyyZRD/cTVV4H48Es4i8EpKxMB5vK+NJsrdsIhGHh8sXL2VGWRmBRIIndu2iJxRifEEBJ0+YwFavl9+/8gqxdBohBBfk5XGfz4fJYEDJZgnE41hMJo4cMwaX2cybmhU8taSEYDJJpdOJxWjEpNfTFQxyfk0Ny8aMGbmO5uFh/vH221RpxD8QjVLsdPLVZctQVZWHt2/nx6+/DqqK22JBUVW+MXs2JzQ0cMWrr5JVVUx6Pd1eLwBGnY6lNTVkVZXHWlvJZLOMKyggkkzS7PNxTH09k4uLAegIBLhz8eKPdVvvf7aJTIaXmptp9ftJZDLsDIXwWCwk02nswDXLlqEXgp5wGLvRSLXb/T4LSVVVvv788xTY7azp6iKcSpHIZBjj8XD+9OmsCoWodjhGSLwzGOSnM2Zg1OkwGwyUaev88TjD8TgFVitWo5HNfX0jE4rn9+5FyWZxmEz0p1I0FBTwRmsrep2OSCrF+IICVnd2kgVK7HZmlJZiMxoZ4/HwpYULP/R/9mDvRySV4opXXyXPbMZmNBJJpYimUvxuyZL3WeKXvfACu/x+gskkdpOJwWiUGarK/aecgs1o5Nk9e3hp924E0lPg0wiuwuGgzOlkm9dLhdNJkd3OzoEBzAYDhTYbA9Eo3miUaSUl1LjdlOn1/GLpUhwm0yf+n2ZVlQuffZa+aJRjjEaubG4emcQUWK18ffZsdEIQTiYRqsqvFi/muy+/TCKZ5O2ODvoiERRVxaTTodfpMOv1nDR+PH8ddc9SisKlL7xAMpnEpNfjsVgYTqVY5PHw3MAANqORnnAYARRYrTx99NE8tXs3zzU1YTUaSWQyzHQ6+dKUKYRSKfLMZm7fuJHudJpNg4Ooqkq+1cqSmhq6gkEubmhgUXU1KUXhytdfJ6XXYzEYCKdSGBMJbjrqKGxG4//t9/G/Cf9NEu8Gqkb9XQn0/pfG8sVHcyM8dSvs2wKJGBRXSxI/9iJphRdVyji40MkYeF4JhH2g00E6KYlaSYPRAiW1UFwL770Ks44C14H4thjswhoewqe3oqoZMFnJkqVQlZatRacjsHs9V+x6gd+7xlOWTWI2W4joTWxTjBw3sIkZrWt5oWYBT+pVJp50BjetWUN/OEyexcLL+/bRH42iZLOUOZ20+Hy4NaunNxzGbDDgsViodLvxRiK82dZGOpulJxTCoNORZ7Gwz+9n+8AADu3lLoD7t2yhOxTi6Pp6AokEAjhh/Hhe2rt3xKr9+iw5CXmjtZVb164lmkphMxoJJpMUWK08tWcPCUVhz9AQbouFnlAIRVVxms0Y9XrWdneztLoavU5HUlFIKQqpbBar0YgvkQCkRVbpcn2iFwLky//OjRvZ0t9PnsXCyvZ28sxmxuXnoxOCVr+fl5qbeau9nT1DQ/jicaYUFXHzUUdRnZc3chyDTsegZqHmWSwEEgnKHA5WtLYyr7yctd3duEwmvNEoQgh+vmIFBp0Oi8HA0poaJhcX85dNm1A0i9uo15PMZEgpCo19fSyprqbK7cYXjxNOpWjz+7EZjXSHQrjNZvYOD2M3mbAaDISTSd5oa2NhZSVnT57M6s5OEpnMCGn74nHuaWxkz9AQJXY750+fPuJNuXjmTO7dvJlhLWzzrblz30fgAA6zmYFoFIfJRGcwSDSVYvfgIHuHhphRVsYx9fV0BIP8+b330AmBw2jEbDDQGw7TFQqRyEjvVFJRCCWTOAEhBJF0GjRLs87jodXvZ2t/P4uqqwHY7vWyqqMDg07HUWPHMsbjGRmTTrNO13Z1oRYWSsueA16bNr+fsfn5mA0GgokEdpOJJTU1/PrttwmnUuiQ1o+qfScAEpkMiUwGi8GAqqqs7eqi0++n2e/HqNNh0OmYUVrKi1oYJZZOU+fxYBCCPcPDbOnr4+WWFmry8jDodKiqyqstLazp6sJlNhPPZIimUswsK6MnHMYbieCPx/HH46hAueYF8GuWek84zFAsBoDNaKQ/EnnfPcjhs+O/SeLPAd8WQjyGFLQFc/HwfxPiEdjwEgSAja/AtEPhpbshHgWdHgoqpOs8FobNK6W7XFFg/DzYuVpuN2YGFJVBV5OMkZsskMlIAq+eBHo9ICTBJ2KwdyMEBjCte4GvhLzc7JpIf1ZHliSlQuXm5ct4M6oQ8XZxlncz1fosGaMFUzQEsQAms4OspZBhRxEVkT7K0hF69zbSEziCvsE+qnUqkMZhd7O1aQdHmtLUY0XJy6MjGETncEj3eTxOSlFwms20BwL0RSLSZa+5PNd0dZHWrJxat5vBWIxQKoUvkWBDdze/X7eOKSUl6IWgoaCAaw87jKyqUmy30x+JsLGnhyd27cJpMqEXApNeT0JRSGQyeIRgU28vZoNBuuGFIJvN4jSb0QuBNxqlMxSi2G4nnEyiqirjCwqoycsjlcnQGQxS6nDw7XnzPjbGHkunSWQybOzpYYvXS21eHkJz9fricaKpFE6zGQE839REfzRKJJXCY7Gw1evl5ytX8qfjjsNtsSCE4MxJk/jd2rXE0mlUwGM2U2iz4YvHuWjmTKrdbh7fuZPGvj4CiQSKqlLpcjGjtJR/7NyJbtcuJhcXYzMa2efzsbqzkzMmTSKUTGLU6dg7PEyV202+1Uqx3c4x9fVs93rZPjCAXgje6+1lTF4esXRa3jNFoTcc5o8bNuAwmTgUeGjrVs6bNo0/rl9PdyhEpcuFNxLhy088wdiCAkx6PeMLCvj18uXE02nyrVacWvhmP1QtXvvo9u30aeEUt8VCNJ3mmaYmZpSVjQjitnm9GITgjdZW+gKBEbe6UafDbjQS1/6Oaa7vZDqNUa8f0VYIpIsfYFt/P7esXYvDZEJRVd7r7eWqpUupGTWRumTWLP66ZcuIK1InBFajkazm/Sh1OOgLhzlh/HgAql0uZhQXs3t4mN5wmEQmg0B6fKaXlGAzmWRoRvMa3b1pE33hME6TSYZqhKAzGOTwujp2DgwQz2ToC4cpstup93jY6vWiapMSgHgmw75AgMPr6ih1OBiIRtnU28vk4mJmlJayrrubnlCIQCLBxbNnU6cRtNNspjMYZCgeJ99ikULUaJRt/f05Ev834T9G4kKIR4FlQKEQohu4GjACqKr6Z+Al4DigBYgBX/tPjeX/FNIpePwWGGiHmuWw8hHob5fLBZLEdTppWQuddI8vOBFWPyOXVY6HqUtg4clQWCHV6ukUtG+Hl+6BTFKeZ6hbrrfY4e83QH+bnBh07uZLNZMpH97MGmMBHiXBWad8hcJp85gtBDRthA1J1Mgw47Jt7DPlUZaNEciqFKSiWJUUSWAII4cRxrBnA9nmzahCQagKWUUBnYXDdf1UDw7ywtQTsBWWY9Xrqfd46NTpcJrNNA8PMxiNktJizEL7ZLJZsqpKidXKcDxOLJ3GYTDgMBoJp1IMB4PMKS+n3OmkaWiIHQMDHDtuHC/u3cvju3ahE4KNPT2Uae74/bHdhE7Hl6ZMYXN/P/lWK/5EgpSiIIRgYmEhxXY77/X2Umi1UmyzEU+nGYzFUIGjx47ligUL0H+KWOpQLMaPX3+duek0lz/9NOlslvLJkzEbDNTn5/NORwe+eJxQMjkSaw4kEuSZzQghsBmNBBIJOoNBpmoq+ENraugJhfjzpk3ohWBiURG94TCnTpyISTvuUDyO3WQikcmgqCr94TCvRaPYTSbSmQxlTic2o3HkpR9JpWj1+xmMRgmnUsTSadKKgtts5sxJkzhnyhTSisI3X3iBQCLB2p4esqpKkc1GgdWKNxrFpNczubgYUzjMa+3tzK2ooD0QGCG/vnCY7nCYhKJgMRjY5/MxEImQUBSsRiPnTZvGIZWVgCTwf+zaxUvNzZQ4HPgGBymy23EYjdTk5dHu95PJZoml03gjEaYVF/OH9esZiEZJatds1OtJKoq0RBUFj8XCUDzOjsFBLHo9RXY7pXY7vaEQZoNhRPn9RlubjDNrBN8dCrGmq+t9JG41Gql0uRCAQQgQgkQmQ7nDgUEIXt+3D71ORziVYktfHw0FBdhMJmaWlJBSFPrCYVSg0G6n0G5nTlkZNqORwViMFa2tuMxmYuk0NqMRbzRKucNBRlUx6PXU5+ezz+dDJwQLKyuJZzIU2GzMKivjvd5eCmw2uoNBbFroAKDIZqPE4aBleBin2Uyl08l5U6fylenTR3QkIK3uiUVFrGpvJ5RMEk2lUDVh3nA8zoEAVg6fFf9JdfqXPmG9CnzrP3X+/7MY6JAEbs+DVAIGO2F1v0wRS0SkWC0eltZ3JgET5sP0ZdK6Dg7KWHllw4E4t04HZguMnwtlY2Hl36CvDcZMg8O/Al17wNsGZWNkrL1tO7o96zgsr5jDYn1Q0QCHnXXgeMU1YDAiwsN8KxzgBddYmix5lKRjXDG4hbg9j5DZwXKbjsMKXbDhGWbZi9ioGLEmosTDXk4ot1FSOA6HI4/SwG5alx2Pf88eak0mPFYrOwcH6Q+HyWhxwrRG5KqqghAYdDrybTaGNBFTOpulNxIhrSgjYjehWUKDsRi+eJwnd++mwunEqAnS1nR1MaO0lKahIQRw7rRpLKmpIc9iIZJMUuFyYdHcn3otZnzp7Nm809lJv+aWdpnNuEwmxhcW0jQ8zFiPZ0T891G4e9Mm1nR1Ma+0FI/FQrPfz4vNzSyurkbJZjllwgRq8/JwmEwcU1/P/Vu2sG1gAMVkQtUmMFbNRQzS/fqXxkbWdndTm5c3ImT72owZLKurA8CfSKCqqhSeaeGDSCqF22LBYTSS0etZ193NyePHj4jfVrW3k9FCBSlF4eXmZhZWVfGjRYtGlO0vNzfzelsbJr2eqOYF6NfI22owjFiyIInvpjVr2Ob1otfpqHS5aA8GSWmkajEY2DM0RCSV4vRJk0hkMtyxcSOqqjI2P59EOs3Lzc1Uu1w4jEaCWvhifmUleZo13urzceu6daQUhaahIcx6PU6TiUKbjVAyiU4I9DodQ/H4yIRjWW0tgWSSVp8Pu9HI883N5JnNzCkvH3G9C94v9lFVFd1BgsNIKsXU4mKM6TRZgFGix/ZQCKNORzKZJJ5OY9Lp6AqHqXS5WNXeTjydxmIwUGS3c0RdHYfW1nLS+PEIIUhmMuiEoNLppFN7tvsFlUVWKxFNo9AWCFBitxPLZCi22zm0thaLwUCx3U7T8DBjPB7s2qTQqXl8ZpeVcfaUKQxGo5Q7ncwsK/vQCeihtbX44nH0QrDF60WvqlS5XLzd0YHn/6N0ys8r/pvu9Bz+IxCSvNvegfkN0rUe8sGyL8mYdzwK/n7pLl92lnS1CwFV4+Xn4+DKh1O++/5lmZS06EGq2pMxyGbAYJZWvlCly92sKdk9xXD4edC8Cbd/gHOHtmkELyCvCHQpyIYh3gtHXAZP3MI3i4xMi2cJh71UD29jauUCwI7d4aI+HqY+NcTT6SSJSIhxFTWU2O3s8/koczoJJ5NkU6kRZaxRr6cuL29EWZwFUFUiySR6TRiUb7WSyWaJai+4aColXZVanHqMx0M4keCwMWO4cOZM+kIh3uzoYLvXS4HVyvENDWzs6aHEZmNicTGVTidlTicTi4q4ac0arAYD+doLdNvAAH/bto0yhwOTXs8VCxawa2iIrf39FNlsnD5pEqWjFK3bvd4RK78zFCLPbMZqMDCrtJQqt5vD6urep0D+xpw57Bse5q3OTgxCMMbjYUl19Uiefqvfz7qeHuo0l3y1240/HmdZXd3IC7nEbsemuXatRiM+zYNg1NTjBr2ebf39rOnsZCAWo87jYVt/P2aDgTnl5Zj1ejqCQeaWl1M7yvps8ftJKwqZbHYko0AVgrhG6CpS5FemKLT5/RRYrRTZbKxqb2dmaSmxdBq7yYTZYCCWyRBOpXCYzYSTSSwGA9u8Xq5ZtYoyh4N6jwcB6HU6Cm02GgoK2DM0hD+RYMfgIJMLC7n81Vepz8+nxOGgMxgkGQ6PuOXzLRYSikKZ08kZEyfS6veTymZxm820BQIMxmJ4VRWb0YjdZMKo13PrunXccMQRHFNfz42rV4/UTTDo9SyuGi0HgjKnE4NOh04IphcXE0wmyaqq1ClYrURTKcKpFE6TiVAqxRi7HUVRKHM4mFFaSp7ZjDcaZUFVFWeOSi0rcTgo0hTo00pK2Or14jSb+d78+RTa7Ty8fTspReE78+YxvqAAi8HAjLKykcnk2VMOJBbtGhjgd+vWsb6nB1VVOXfaNGaUln5i3YATGxroDARY0dpKMpNhYmEhY/LzSSsKUS1OnsNnR47Ev2goqZHx7d59ksw7doO7ELavgh/eLwnVaH6fonwEnbthxd8k8U9cAItPA+MnqGsrxoHBJMVxmZQk8vwyyCuWn0xaxt7No9LRysaA1SnHlxz1T6wzgLsYxkyVY1j7PBTXYhxoZ9lgN3jbITAAzQaYulR6DoQO/vYrXJNOo6C5kfZEhGxBBVajkTyzmXKrGd9gPyElQ0leAUabgynFxbze2kqeRtb7RVj5ZjPVeXls83oJJBLMr6hgfEEBVqMRl9nMYDQ6okQeV1jIN+fMYffQELesWUM0nUYvBHt9PnojkZGUsTVdXSytrqba7WZddzcus5loKoUunaYrGCSYSJDJZqlwuQgkEvxsxQpsRiPFdjt94TDNPh/XHnbYyEs1lEoRS6UQQiCAwXic2eXlXDx79oc+nnyrlXtOPpntXi8D0Sh5ViszSktHCDqujXt/DN6suYz3F0wBqPN4OG/aNK58/XUpbgNKHQ6qXC76olEGIxHimQxdoRAGvZ4pRUUEtdh5VyhEVlVJZjK82NICQnDRzJkjYYb9IQ69ZuUCIARTCgsZSiRY09XF9KIiwqkUTcPDqKqKx2plcXU18ysreWbPHgYiEQZjMZkipSi83dExMkma63KRZ7HwbleXzCQwm3FbLJQ6HJQ7nURSKery8rCbTOwdHpZiNpOJQCLBQDyOJ5slqZHv4XV1nDB+PKs7O9nQ20uexcLEwkL6tNS2pKJQZLePeF+afT5+/MYb5JnNHN/QgF9LxTpq7Fii6TTvdnZSaLMxvqAAh8nEaZMm0bp5M6lslmpNI5DW7p9Jr0fVSH2M5t3YL4jbP8nLs1ho8/vpCYVIZ7NE02ke3LqV7lCIaCpFucvFpbNnc960aeRpFvDs8vKP//8ehbH5+RTb7SQ1d/v67m4y2Szf+RANhz8eZ1NvL+92duJLJChxODhnyhReamlhQkEBOiGIpFL/ckGmHHIk/sVDLAypuFSSCzQSVqUqPRKQ+d0fhqEeeOJmsDghmYDn74DmTfDln4Mj76PP5ymBc34Cb/1dEnnFOKiZBDa3PJ/RBPYDudV07IaX/iLJO5UAhNxG6A6o4cfPBWcB9OyFs38Cj98sY+6eUph4CLRtg9Zt0u3/3qsgQD8+xdV9a9itDKIu/TVTHBYe37uPs/a8wZhQHzq7i/m2StzHfZthewFKy2a8wsB2gw2nVhyk3OlkWkkJsVSKMXl5hFMp/ufdd7lm2TJ+uHAht2/cSIcmMppaXDyS2jUQi1HpdCKEIKhVprts7tyRFKrfr1/PlKIidDrdiOhq58AAKS2vvT8SYZvXy/iCApqGhzl1wgT8iQTeaBR/PM6Gnh6O0NLf8q1WSh0OlGyWWCaD3WjkxIaGj/1KCCGYVlr6oeuq3W6sBgNDsRgus5m+cJhpJSXvi2uCjMXPr6ykxOHArNezobubvT4fRp0OBRhfWEh3KES+0cj2gQHGFxayvrubWDpNsd3OGI+HKUVFvKuJ3vIsFo4cO5YvTZnC3Y2N0k1sMFDucDAuPx+31crE4mLsJhO6gQEyioJRpxtRtZc6HBw3bhxNQ0O0BQIgBOPy8xFCEE6lGIzFqNXS6Va0tY0I+1r8fgptNurz81leV8c9mzZR5XbTpqXo7a8q6IvFMOt0KFqZ0tMnTuSEhgYe3rGDYrud+vx83mpvJ6koRFIpXFoGQlpRUIF9Ph9vd3ayuqMDk14v9ykowGOxsLG3l2gqhUHL8z6hoQFfPM7ari4WauGfarebDd3dIznfsXSamKY43+b1MrmoiItmzuTJ3bvJqioCRtT/P1+5kkw2y87BQeZXVFDtdkvrORTihIYG7Acp9j8tukMh+iMRxmpeHJfJxMvNzfRHIngsFo4dN45tXi+NfX1s6u0d0X04zWZmlpbSHggwoaBAClE1UWj+QUWWcvjnkSPxLxr626TYzGwDoZdWdzwiY+K+vo8m8Z5myCiyQlvTOunLXP8ioMK5vwT7xxQfKRsDX/qp/L1jFzz7J4h2gsUBp14OJi3Om83KyYHVCfUzYdcaSfSqKl3wQi/j9TvegSlLIRKUJWAnLwS9DjxahTeHR463u0la4yYLqCoOq525bRvguRuZgWBmKEF+2kd67GQml5TgzCThhTuo1Bu4vL+TTt8wL5ZO55m8sajAnIoKmSOdnz9iIXQEAqzr7mZVezu94TBWg4G+SIS+cBi9Tkd7IEAmm5XFMoCkplreb1XuHR4mpSiUOBx0h0L44nEGo1FsJhMFdjtpRcFpMtERCOAymSjRhFHv9fdjEIJQMsk9WjWuYrudCqeTo+vryUulOGbsWIZiMfQ6HcOx2Aeqzu3HcCzGS83NBJNJppeWsriqasRyclss/HjRIh7YsoVWv59qt5tTJkwY2TelubL3p7HtL4risVoptNnQ63TENWW0zWgkm80STCaZW17OYH4+oUSCyUVFlGuiLSHESBpUXziMTggO1XKLnWYzY/Pz+er06Ty8fTs2o3EkXxohCGphBIfJxJj8fHYMDhLLZKhyufBrlv/c8nKG43HUbJb+SISndu2SXxmzmUmFhSjAz5csYVxBAXuHh8kCOwcGeLOjAzWbJZJOs7a7G5NOJwVwiQQZRWGL18uWgQHqPZ6RAj6LqqqwGo3MKi2l2ecjlkqxe3iYQquVtd3dqNksLrudaCrFXp8Pj8XChIICnti9m8lFRcwsK0PJZnlo61YsRiOTCgtxaF6ctzs6yLdYCKVS+ONxbEYj5Q4HM0tKsBiNpLNZimw2Dq2pYXVXFwiBXUtVHF9QwEA0SjSVojMYpMXnYygWozcc5uFt2+gKBrlk9ux/qjSqqqoYdDqyqjqS7tfm97NnaAidViTmke3bGePxkNSyC4LJJGPy8kgqCsPxOPlWK0eOHYvLbCapKNTl5bFz48ZPPYYcPhw5Ev+iwWiSn4JymQZmc8m/XQXy94+CyQpqFrp2g1FzfdtdskDMvs0ydv5pUDMJvvl7ScY2lyweM9gtJxdCQDQoSb+oGoybQG+UbngEkJVpbN3N0qovKIOHroHhXrlf1QQorJRu/0wSqifD3vek9yGdlO72dBKsTkxOD0cmmyA+AOVL5Hl0OnjvFaiexLSSEkLo+WrPejxWC2OXn8GlC5dw6QsvMLqKoQo8sn07Bq2y15b+fvYMDXHaxImYtcIyvaEQoWQSAVgMBqaVlNAVDFJos9Gn5be3BQK0BwLkWSwYdDqGYjGWVVejAJv7+khnsxxdX0+RzcZPV6wgoyig01HldmPS69nQ08MJDQ1cNHMmN69ZA8DuoSG8kQi/fPNNblyzhmsPO+wDVnk4meS6d96hNxTCl0jw6PbtXDhrFhfNnHngkeXlsaCqirZAgN5wmN+8/TaXzJ7N1OJiblm7lj1DQzT29hJKJjm0poax+fkEkklZqUtzizZr4iejTofJYCChKBxaU8Obra282d6OzWjEYjBw1uTJeCwWUooyIiKbXV4+kpJ0wxFHYDUa2TM0xLqeHqq0Snp5ZjNTSkoQyAnEuPx8/tLYSL7Viqu0lNVa6mCb309NXh4TCwt5eNs2sjBSCc+o1yNUlajWHKUuLw+zXs/fW1pQNRHeOE2p7TTLkJMeiCgKHcEg6WyWeCo1oio36vUsrKriK9Omsam3l7ZAQIomrVbOfvxxTHo9OiGkWFJViWUyZFQVi16PXxPW6XU6Upq6PpPNEkmlGIhEGI7FyLdaObyujoFolLXd3eRbrcQUhfrCQoKJBHt8Pi6aNYtTJk5E0cSWL+zdi9C0H0Ztkrlf/GfS6xnj8bCup4ezp0wZcamPfNc/pHywX8vL3z00RLHdTpXLRWsggNVgoLG/n5SisHNwEL0QDESjlNjtmAwGnGYz/kSCeCaDUa8npVUCtBmNTP8Ir1AOnw05Ev+ioWqCVJqHhrVyqVlZ2GWBljL2URg7Q7qnWzZBVpWcWjlbuua7myEwBI2vyRS16YdBPAToJNF37ZEW/4KT5DGMJjAWyOO27YAnfydV8dmsJGSzBfQmqaBPxCCdkO50ISC/GIZ6ZVy9YS5sfVO63fPLZHrang2QXyoFeuyU6W/7y8Om4tINv9/bUFghr8fvlbH2jp3yvnQ3Y0rFOSwWxPDEAFOK2nnl7r+zcv5izvzFVTyvpQTFNNf3UCxGpcdDy6o36dm5A7F4KZFUCrMmUFtSI5vCxDMZKhWFimAQfXk5rX4/M7WKcy0+n3Tbp1LMKC1li9dLeyhEmcNB7113cdf993PMlCm83tKC2WAgoMURx3o80tLXuqjVeTzMKS8n2d7O3jVrsAcCVJx2Gr5YjBvefZeZpaVUulw4tHKlu4eG6AqFaPP7yaoqiqpy8+rVLK2uZlyBfEbDsRiP7dgxor5PZDLcu3kzee3tPPfuuyQOOYS0opDMZFjZ3k5/NEqpw8Hyujp6w2G6jUY5SWlvJ/bgg3z17rsx6nTsHBigJxIZEa4V2GxkRhVtCSYSVLndZFWVUDLJK7fcwrOXX47LbKa+vp6JX/86b7a1cbJOx+D99/PK8DAuu53777sPt8VCwufjyZ/9jFQwiAI4Fyyg7ktf4srFiznljDMY6OwkmU4TiUbR22x4b7iBIi0WPnv2bP7w+OM885OfkBoYAKORDKD//vdlmVNFofvee0l0daGz2XB84xtkXC46gkGefOQROp5/Hp1Ox5SrruIxnY6VbW0khoZ477bbSEejJFwu9KefTlwIOSFDltK1GY0YNFLb4fUyHI/jNJkw6fW0BQJUZLPodDpcWp7/3uFhmZalquiQ3ovOQICMqtIXDjOjpGQkrl3pctHq99MWCJBnNhNPpwkmk6SyWXzx+IgHRtXc7/uRyWZ5fOdO3mhtxRePM7+igtMmTWJcfj63jcrLDyQSpDIZzp40iXAqxQ6vl85gcCT/PanVOlhSU0O7349dq5yX1aq5jc3PZ4pWlTCHfx9yJP5Fg8EIp18hhV+tXrjkFqkSB2jZDM58aVkbTFK8tr/amskMZ/5ILn/hz2AwwNZVkhgDAzKmbs+T9dNXPgIzDpPH7dglz2W2yXzxc6+C0toD43nlPmkhh/2aZ8AphXeJgIyBZ9KS0JWM9AT4BuR5qidI6xuku9xdJAlYb5CpbnvWw95GKZjT6QAhC9GgSiveoRF5/Wy5byIsJybl4+R5fX2ITAqrDrZedT7EQpz7tpeulSu55Mwz2TUwQL7VymF1dfx85UoqmtdzUmQjifI0W/a8QFPReYT0pQzFYnx99mwWayUm1737Ljf/9a+8cPHFgCz48ej27dywejUpRWFaSQkVTieJTIbD6+oodjj48auvMqGwkOvfeYdHduygOxQinkoRSaUYisWYVFTEHO1F/fzevbzT0cFSITBNmoTQ60dU2rF0Wk44RtVdF8gqcFmtvnsmmyWQzfJKS8sIie/3IuxX31sMBrLZLL6qKvpmzCARiaAXAp1OxySPhyqHg0klJWzo7WU4HiedzWIzGJhRXk6jycRAJEJ3KMSM0lLsWogglk4zt7ycNZ2dvNrSMqJST6TT7BwcpC0QwHniicweM4Yl1dWsvuceXn74YVILFvDqK6+gLytjzve/T302y02//CXHrljBUfX1NF54IY6aGroHB1l/9dUs/NrXqM/P5zs33cSm3l48ViuP3HwzMb0eVQi+NXcuscFBKioq2DI0hEGvZ8Ill9Cn3bN+wG40Yt+2DdXjIXjWWeh27KDjiScwnn02tkyG5qef5mt33MEPFi5k8SGHsPS662iorOSJW26haPly7rjySq74znfYsmULunnzMBsMVLndOM1muoJBxng87Bkc5D2tuEqB1cqUoiJWtreTtVgodzoZiEZlHnwohBCCqcXFRNNpesJhhrXvRJXbzR83bOCXhx5KbV4eT+3eza6hIWLpNNlsFrNezwnjxrFtcJBoKsU+vx+XxcKS6ur3pTK+1NzM83v30h0KMRyLsX1ggLXd3Vx+yCG0BwKUOBxs6u2V/QCAr82cyQnjx3NPY6OsI6/1FciqKh3BIKqWOlbscFCXl4dJryeUTBJKJlnd2clhdXW5Lmf/RuRI/IsIowkmLYDOF+H1+6Q7u2ysFJPFQtKdnVVkm9Fzr3o/kXuKZapZIgq9LdKq9XZI8sykpIIcVR7T5pQEG/ZJa3+wS5Z3HU3i+xplipvDI+PeA11w/Ddg3nFwx/dgzTOShBW9nIDodNIrkE5J615rUrE/7k0kAP2tcjxqVn6KauR6JS33aXxdThjqpkthXp2WJnPXDyC/HNY9LycNWlENupuhoIwls6aybd8+vuZwcMt3v0trayu32Gz84IpvUbbtVR5sDbG3P8iNR03muZt/S6B2CpH2di7w+7nxxhs544wz+MlPfsLu3buZMm0aDcuXo6uvZ93tt2NCuiYbfvQjWlSVfJuN8YWFTCwqYtbEifz9tdf48xtv0HfXXYjqajIdHQTcbsZ8//uUOhw8+cAD/PnPf2YokSC/uprDv/99Mo2NxLu7iZ17Lmmfj76//pWv3nUXJx1//Mjtn1BYyOBrr9G+Zg06RcE5fTrzzj33ff2ki+12BrZu5fkHH0SnqhgcDs668Uaeeewx4rt3YzrxRFJPPknWYmHn4CCJyZOZdfHFvPzLX4KWpmc85xx0tfK5200moqkUG//6V5o2bkRks+QvXcoKIQin0zyybRsGg4HDamt5sbmZPUND2IxGFowbR11eHht7etjR04MxP1+6nXt6UOfPpyMQIO5w4G1rw+v1Mm/CBH5XUsJVb76JMJvJr6rikTVrKBszhjMmTWKfVmzGv2kTl952G9edcQZWo5E777yTY445BpvJRFZVmV1WxlupFF6tnK/FYCCwYQNTzjwTj8tF/5QpDD/7LI5slvTevTTMnUtEr8cHVMyYQWTXLnSVlbRv3kz+uedy53vv8b1LL+W3v/41lxxxhIwF19XRE4nwt23bWNvVNaKdsBgM2IxGusJhbj3mGDauXs2kwkIGo9ER4WIik8FpNjOnooIX9u7FqNOxrLYWq2bp7hkcBOCFvXupc7sx6vUEEwla/X4avV70mg5BAGdOmsRx48a9j0Q39fWh0zQHRXY7oaQs6PT0nj3odTre6egglslgMxgYjEb527ZtTC0uptjhoMThYCASGelh4LZYqHG70et03H3iiQQSCW5YvXqkhe99W7ZgNBhYopWjzeFfR47Ev6jY8iYEvDJ+bLZJpXcsLF3L0aBUeYf90qKdd+yB/frboahKiuPiYSk2S/RqueCqJM39DVF0es1lr0HNSiIeDb1RLk/GpAgtHoGWRmktBwbk9hXjZSGawICcYPzgXpnq1rpNTixsmrpdSR2I80dDUjWv14PRIMcT9kuXviNPXqfeABWjWllOmA+vPah1YLNAaAhIw0AnmfwKXn5vB8eceDJXX301M2fO5JlnnmHlypVccdk3WPPVeWwKmIjGVCaPn0rpGztx6nT8feNG9uzZw0knncQZZ5zB9ddfzw3XXs13FlUyPLSdW+5/DWX2LKqPOJI/L1hAJJnkxbY2+sNhfrFyJQatjnqLz4cKpAYHsZ15Js4zziD88MNYm5uxjxnD9ddfT1tbG3947z32dndj1Omozctjb1cX/kSC6BNPcOb55/Ojyy7j5UceGbnktatWMUmvp+Saa8gqCi133EGqtZXDli8f2SYWDPLeXXdx4m9/S9btxpXN8q25c3nliScw6/VoQRnw+Si97DL+5/jj+e7ppzPzxBPJnzWLUDRKVyAgO8YBiqLApk0Is5mlv/kNewcG6L/tNgzjxnH8vHk88d3vctYf/0hrIMDPlyzhF2++SZ3bTRZ47De/oWPTJgqqq1l63nm0dXZSUV3Nvh07SNbX07ZjB8OdnXR3d1NSUkJEU0Bn/X58ra1MnDGDp3bv5uj6en61bBlPvvwy71VWcuM556Bqleaee/FF/viHP+AoKeHnQvD0DTcQUxTUCRNQly4lkcmQ9fvpyGapNhop93jwWyxYUimywSDC7WZjby+/eftt/EYjam8vLT09qBYLg4kEq9rbWREI4GtvZ3ldHdVa57v9MepKp5Odg4OkFIVdg4P44nFKHA52DQ6SyWZ5cvdu0tksc8vLmVdRQWNfH7sGB3GazRi01Lz9NeEzo7qdZbSqcvsr/6W1WgeVLheKFo9eVF39gTajHotF1kLQiF3JZrFr4rmTJ0xgVXs7dpOJSCrF5OJi1vf0cNTf/kYinSaeSslzKgoOraKb0WCgyGZjMBZjm9eLdVQHw3yrlfXd3TkS/zciR+JfVDS+Bo6JkqysTuhtliSKkBXWfH0webGMR4Mk47XPwfZ3ZNW3fE18kghLkm1pBNUgyV3NStGZ1Sm3NZrkT5tLegBGY9ICGdfu2iNJ3+qAVf+AqongKpTLOndKS71mElxxj0xbO/0K6Q0A6N4r3fr+M6TQLRaS8e5EVE5IijVLfOJ8mZsOciIy2CUt9/3XsuhUed0v/Fk2ePGUEFfWMOOpZnD7WXLcKVx00UXMnz+fJ598EoDly5czHAqTTiu4TbI9qgj5wGLnlFNOkS7mSZPwat3KCA6j9LaQCphJ6fQc405z32svsysS5WWTieMPOYRQMkl7MIiitbr0xeMEtCpgOo+HbEkJgUQCQ3k5vr4+jhk7lt3TpnHuueey+MgjUfPzR8RKk4uKuPOsszjs2mtJT5rEjatX46iuHqkQ9tprr9H47rtYt24lnEySicVYYLO9L+Vs3bp1LF+2jHvOP3+kaYbQUrZ69XpqPB5aDAb0M2Zw0ezZLC0tJTg4yKGLF1OTl4eqqqzv7mawt5e0ojC3shL/8DCNW7bQt2GDTA1Lp6lVFAptNr5xzz3E0mmiqRSTiotZXFXFc3v3SjI++WQmn3km9jfeYO/bb2Orr+ewk05ixZ/+RP8tt2AqK6Ny/HgMWgrcS83NNPX2MnD77RSddhrbAgFq8/LIaqS15uWXueArX6EnFOInb7zBpq4uOrdt44adO7mutJRXn3qK327Zwks7dxJ66CHE1q1kZ8yQOdnpNC1+P+dOnUqzVhfdr9PJGLFez4TCQrosFgZiMeK9vaijWq4qQDKb5cbVq/nt4YfjMptHcrutBgNJrZqboso+292hEH9cv55znE6cZjPDsRj9kQjRdJoJhYUU2mx8dfp0lGnTeHznTtoDAVRVZYymkegIBim0WumLRCiwWglojVLKHA6SikKN202BVuOg8KAshjMnTWJ7fz/btfK4BTYbKrIc7+KqKmaWleEwGrEajWzt72f34CDVbjc6zcK3aO1/C202WX0vlSLfYsFtNmPXctr3I6l5F3L49yFH4l9U7K+RbnFI0gv7pStcpwOzHaIBaYVXjZdiOFWFd5+UTVBMFmm5W+xQXi/J1mSVhG91wqmHa8fSwwnfkFa10SwJ2134/nEcc5GcANjcYLXL/cN+WRrW2yZT2pSsjG2XN0jXvFIrxWzxiCT3cbJ7GJm0rOHe1yqvKzgg4+AzDpfNXvo98nhmqxTM6Q3vV+QbjHDyd+TPVx+Arj1YdbDlawtkuGFMA5hM71OnA6A3IOYdDzv/LMdkNEJFA+bhbrjtmxAYQM2k5IRhuAehqoRMNtLpDFOmNvDLch+/TZl44Ac/IO/qq/Ab9GSVLG6rFbP2Mt/n92M1GtEbjXisVlKZDDqLhSmFhRw1dixHvPgib7/9Ns899xyrXnyRk2+7jSPGjMGrKCQ14VtNXh56g4G2/n4y2Sxb+/vpDga55Hvf42ff//5HflX2q5L3l5rdj+PGjcPb3IzebMZpMnHW3Ln8dMkSIuEwFq0/e5vfLyu95eXxtbo6fvnXv/K9+fN5x2Dgr3ffzdFHHw1AZzDINW+9hT8ex2ww0BcOc+bkyeiE4MTx43l+717K7HY8VqssqTp7NqnXX2fc/PlYLRZqzz8fo8HAmLw83r7iClS3m0e2b+f+TZvovfdeXLNmUTpv3kgnOoNORyaT4amnnmL9xo389p132Nrfj7GnB09DA+92dvK7tWu5/ogjsO7cidlmwzB9OumuLpgxA1wu1GAQS3Exm7q7Eckk5SUlDDudZFtbmV1Wxqa+Pnq6u3E0NDClro7WZBKb1uazOxDA6vEQSiToCgaZXFxMhcuFx2qlLxQi32KhNxIZCekMaHXo9UJQ5nAQTiYZjsfZrdV4/9bcuczX6sBPKymheXgYk17PpKIi/rZ9O2u6uih3OhmMxYin04zLz2dWWRmlDgduLRugT6tAdzAsBgOFdju1eXkyDzwvj9MnT+bEhgb0QnD6pEm80NREOBpln9+Px2KhUCP6WDqNSa9nUVUVm/r6GIzFGJOXx3ENDSPlf2/fsIG32tuxGgzMLitjbH4+r+/bR8n/kT7i/2nkSPyLigUnw9ZdUD5W5lPrdODIl67mkFZdzV0kiefvN8r66UIn3dcNcySxp+LwndsPEONnEaOU1MCxX5cFXkpqpdt79dPSgjYYpZDOrJPu702vwnCXPPdQjxTECSFj6Ed8RRPt/QA2vixLx1pmS8X5qr/D2KNladm3HoWQKicYJ34TLAflTut0B2LonhLQRSEWBFWBtu2QSbN06VIefvhhrrrqKt566y0KCwtxHXMe7PPBpvfgy1fBo0fCE29CmUHe10wa7v0ZztKZxNMKRXYHzcND9PuDuNwOpsw5kmJfJ4kXHsIxay4moWeXu5JgSoqQwqkUk4uKGDAaWVZbS5HNxprdu6lyuVBVla6uLg477DAWL17MI488gi6Toc7jYVhLVyudOJHtK1agmzGDdc8+S1rr46xUVHDrnXcy/9hjOXzCBHp6ejAajRRrKuFQMkn15Mm8tWoVbW1t1NXV4fP5cOfljZRN/dNFF3HBO++wtKZGtmV1uaiqqmJWMEjdggVs6+nhrbY2nuzrG0mHmrNkCb+6+WaMY8Ywv6aGhNfLt6ZP57n2dmKpFGdMmsTx48YBUh09xuPBGY2SX1KCqqrsW7+eI2bM4BvHH8+rL7/MhPx88h0OfKtX42po4Odr1rB7YIDuBx/EUV6OafFiUopChcvFpMJC2gMBdqxeTW19PQGTib5IBLPBwNDOnRRNn47eYGDPwAB9Xi/jCwvZ2tuLb+9e0DINxPjx6LZt44ijjqLxjTcomTKFiYWFfPfyyznv2GPZ3NZGMJXCt3MnxqOOwmkyUTJ5Mr5Nm0jMnEnvO+/gmTiRdT09tPh8I13ertRy8jf09mIzGqnV8qgjySQRLRat1+ko1krdzq+s5JwpU5hQKCfHfeEwgUSCCYWFFNhsNPb18U5HB2M8HoQQ5Fut1Hk8/HjRIpqHh7l13To6g0Hi6TRnTp5MiRabHo2/NDZK9Xp1NYlMhv5IhDllZSO1Es6aNIkJBQU0as/XF4/Le4Rs1nJIZSUmLbVyemkpp4wfT502nt+vW8e+QAABBJNJVnd3j7TfVbJZTrPZPjS1LYdPjxyJf1ExYR50+sA6T1qtBpNUkit2mepldcKkQ6TlrKSleC2bPRDrToRlRzMhpPXZ1yoFcAUfU6YxI1tJote+Vk3vweqnZGzdYJTH8bbJCYTeILdPp2TKmcEIFqv0Eqx5Ro7X4pDj+ceNsurb4lOlNb/0DGnN3/dT2d+8sFJa7k0b4JKbpTXvKnh/pbjR6G2RQryYpn43muWkoKwedHquufpqvnbhhUybNg2bzcZf//pXuZ3VIc/z5+/LY+QroDrkZAcBXbuYdsRXMVrtXPmXFzluYhmDsQQvtjdT8OQ6hFHhthMms94p+H5QRyoSwOMqIKJZYrVuNwIpNPPH47JTmsGAoiicd955BINBVFXl+9//Pg6HgyGt4cd7vb04Tj6ZlfffT+aRR7BNny4vMxJh6bx5ZL1eTjvqKAptNtwuF48/+ijFxcWs7uri/s2bUVWVGRdfzPEnnwyqStxkYsaPfkTX+vXk+/2ENXIZjYceeohLL72UgWuvxRuPc+ovf4nN5cKg03Hz6tVYKyuJuN2cfsQRGHU6JtbU8Nyzz/Kr2lpmzJjBTVu2jByrzOnEIARP/Pa3KPE4aUWhctw4fnX11VgdDgJeL+/eeit6vR5bWRmlX/4yQlUx9faS3ryZUGkp8ZYWfEDlKafwdF4eT+zezbu33UbZ1Kn8bs0aWQs9kyGwZw+VJ5/McCqFPxxmwbJlGIDhaBRLbS2ZefNQgJrDD0d96ime/fa3KSsq4sXHH2dCQwM6ITjrG9/gr9ddB4Bt+XLsLhc7Bge5/oYbuOLrX6ft+eexVlVRsHAhZXl5PL93L4fV1eEymym22/nxokXoheCFvXvJqirlTieVLpes4qfpI4psNpbW1PD1WbN4uaWFR3fsIJFO0xsOY9LrEZrS3hePo9fp3le8py8cBmBcQQHfP+QQfvjaa3gjEX6/bh33NzZS6nRySGUlZ06ejNNkomloiCotbm8xGBBAXyQysqxHK9xSn5/P7LIy1vf0MByPk8xkKLXb+c3y5SP9w0eTcVaL71c4HJi0hjZbvV76IxEmFxeTb7EQDIfxxeMfWagoh09GjsS/yDCYZA31/lZp6aoqBLROZdUT5E+Q5F1aK0Vgja9LInYXwRHnw47V8NDVkjSNZjjt+3Dome8/j5KRaWdb35T7zj9B5qo/+0eZt220StIuHyvFdgtPlYQ70A6ppCRzk01uo6SllW40Sze+3iBJedNrksT3Y6hbTgA8WmzXYITWJhknt7s/vrBNQZk8bmEVka8hr83ikDH5P15Gflbh2SvOk7Xj94uAslkuKExwQVEvrNnGA+NT8r4JHSRjRC6YCIDRZGLFU/+QVr0rH0rHwLO3gc8rY/SZGMubVnJ02SKiZOksaODIBx4gk81y8SGHMP/FF+kMBllcVcUJJ5440lzi3Xfffd8lvPXWWxx/5pmsLypix8AAcYeD5Fe/Sp7ZTH1BAZFjj0UnhCyneuihFE6YwMKqKvQ6HT0GA+5YjPsaGymy27EYDLjmz6d6zhyMOh294bCsNDd5MnEhuHbVKm6/+27sWqghmk5TWVvLypUr8UYi/HTFCiwmE5F0mi/fcQerOjqYVVbGad/+NiCbrFw6ezZujRS2jCJwkGKnHy5ahP2WWwgkEtTn5/PNOXNway/2xXPmUP3ii3SHQjhMJrb299MVChEsLqb21ltJKwp5FgvhZJL6oiIqXC5afD4yJ51E0m6nxefDoteT9PvJWq14tepupfn5TLjxRtJaz/euQIACmw1vJEJrIMDcH/6QY8eN47SJE99X4/vyyy7jTY+HQqsVs9EIqiqbj0ydytZNm/j2Sy/h0BqzlNjtdIVC+ONxXGYzqqry+K5dvLh3Lx3BIIurqylzOHi9tZVyhwOzFls+cfx4Lj/kEG5dt46+cBijTsfrra1Uu90sqa4mkkrxu7Vr+eacOSOd4wxaFbVpJSUj7VMvf+UVmoaHMep0dGvCOY/Vysq2Njb19XHjkUdS6nQSSCTIt1pRtFSx/YVgdni9/G7dOrLa8uq8PM6cNImdg4N4o1HsRiPXrlrFudOmsVTzYuxHi8+HPx4nmU6Tb7MRS6dJKgrtmghyjMfDOKuV5KiYeQ7/PHIk/kVGKi4FZX2tMrbsLpTWcOUEaf0OdUti1xtgxnIpFpt5hCTaXWtlidRV/5Db2FxSYf63X0krv2TUP+ym16QozmSRpPb245LEDaYD5VoLK7W66PNkwReDEawuUHzS2tYboGSM9BbsJ3ZvuxSl6fUyPj8aFrt0gWez8rhZBbqa4P6fA0KO8diL5XkURaaVbX1LivDmnyBV8CDP6ymBWUfB2mfkONNJePwm6RFYcBIsPEUK97a8KQnfbJWfsE/mrput0kKvnQLrnpOTJnTScl9yhjy/ySJDBKgYsgrnJFbROPkoKquqULJZukIhiux2vjx16qd+vDsHBtg7OMgWrxeh5XGHUimpWh8eJpRKkcpk2D4wQJ3Hw9j8fJKZDA9t28b35s+Xt1GbJLgtFnYNDmLSSNymxeaDiQTtgQDbvF5mlJZy96ZNbOnvRwjBCQ0NHFdfL13oXV2YNWsrnsngHpWHrNN6Y38cxhcWcuvRR5PRKqsBtPn93LVpExMiEbxGI9+aNw+dEFz07LN0h0Koqoo/HieTzYJWxKTZ5yOiVWQLp1LkaW1K/fE4SyZN4qzbb+e1lhYSikKpwyFj1OEw67q6OKa+HiEEFS4XRXY7lx9yCFNLSj4w1jKHg0qXi2AySTqZREV2tjMbDLgtlgMTI63ZjVGr4gbwt23buGbVKiw6HWlF4fmmJhZUVZFvsbCwqgpXLMYJDQ0jOds9oRDVbje+eByH0YgvHmcoFmNLf78UAqoqEwsL2evzsbqzk+F4nI29vewcGOCiWbPoDoUo0gRt6WyWtKIQS6VIZjKs7uxku9fLpbNnc/OaNXQFgyiqyrHjxjFOq4/+t+3bR5rGqKpKWyDAKRMm4LJYeLu9nRotHHBvYyNlDgdWrc67ks1yy9q1lDoctAUCsvOelrvuMptxmEzsHBjgNC10lMNnR47Ev6hIpyTJtG+XRDPQKV3RzgLptj75O7L+uBAwedGBam52Fzz9e2m56/TSevSUSBIyWWC4RxLtaBLf9racLOgNkvCFThZsUdIHtkklJKkdejz88TLpYncXQs1EeayQH4a6pBVdPUGK7qJBSdDjZsPSg6z/0jqYvhw2rwBfLzR45BiyWZi5XNZlLxsDc46Wk4x3npTXmEnDK/fCWT/WJh1CKtlXPix/370OOmW9bXQ62PCSvI+TFsrrMRilSC8alK5/AVRPhKMuhKJKePPRAxMEvxe2rJSTKF8vJKOgKOjNVirzPCT6dvG3wDIyCE5qaHhfy9FPAwHsGR5GrzUGMQhBIJlkc38/EwsL8cXjGPR6iux25lXI56sXgoFIhL1DQ8QzGeLpNFajkUAiQYHVSjyTGXnZxtJpvNEooVSK+zdvZk55OY39/dS63SiqytO7d+PWWqE6tEIyVqMRl8lEXzg8kj5n0OlGYrofez1auVCQsfqb16xBr9Nh0utp9fu5bf16rj700JG650V2O1lVZTgWk2JEVcWXSBBKJim221FVVbYF1Vp87hocJJXNkm+z0R4I8EZrK0a9fiRcENYamWRVlYyqYjUYSCnK+1q7AhTabJw6cSJvtbVh1OvJAgsrKymx29HrdHxn3jz+uGEDwUQCo17PZXPnyjKuSFJ0Go3kWa0UAT2hEBVOJ8qoHuP6/VXVNPW3qqrYjUb0Ot1IA5RAIoEAuoJBWZDFbmcoFpM54vE4zzU1samvj5j2jLOqSlpREEJg0drKtgUC3Lt5M2dPnsz/HH44fZEINqORCq2ZDzDS3GX/89EBCW1iWKptp0N2w7t9wwb8iQR6nY7+cBiX2cxJ48ezvqeH5uFhIqkUp06YQFc4TCAeJ99mo8Bq/UDKWw7/HHIk/kVF0wbp5tYbtbKkOkjEwRCWJFs39YDqezS8HeDrlzHjrGZBhnzSbZ1JS2Lf74YHaZlufFlamXa3LI8aGJC52BmHrJkOkvxcBbJa3JRFWn33StlDPBaS6vDaSXKMNqeMT+/dKNPGjrlYEjtI8uxvk3niUxaDzQH3/QLGIycRPXtlUZkJ82XOO0hizis+MBGJBqXVvuS0A9dhdUoVfVaVBdOzihQAFh0h7+XCU6QosDslr03NAi6Zb//D++T1rXn2/XnyVockbyUta8IbzVLE5y6iavZyPL1tOGfOIM/pZqznIxrT7MdgtxTwhXzac8tnWmkpep2OWDpNAkhr/a3r8vK46tBDmVRURDKT4WcrVhBKJnGZTLzR1kZKUXh2714iqRStfj8usxmL0cjcigrWdXURTaXoTyaJaFZkQFF4o62Nl/ftY3pxMeFkknyrFZNezz6fD5fZzDFjx44QXncoxNKaGnYPDVFgtTLG4+HWdetwm818eerUkS5Yqqqyrrubdzs7sRoMnDB+PKUOB7sHB9nn843EYUUkQrnW4zuSSuHROrk5TSZq8vL427ZtWPR6Kl0uesJhhmIxskCN2008k8Efj2PR6rnXuN14tFr2+7QubAa9HqvBwKqODqaVlJDVuoj9bMUKeiIR6txufnP44SNV5vbHo8d6PLRqtdqPra8nnc3yj507aR4e5pDKSg6pqCCeyWA3mUgriqzdjpZzryGRTrO5rw9FVWn1+xmbn097IMAhlZWM8XiYX1HBmq4uLAYDFS4X8XSa1kCARDqNUa8nmk7LOupDQzK7QEtfS2nV+ypcLnpCITkREQK9EGSyWcLJJEo2y+v79vFmezvfnDOHHy5c+IGv3Zzycp7evZtiux2TXo9Bq79eZLPRFQzSHI2yUYuRG3U6DqmqYm55OX3hMHuGh5lQVMTCqqqRmvSKqjKrtBR/IoFJr//EXuQ5fDJyd/CLiM7d8OLdULZAuqLdxTJHPJuRBD7j8A8WZdkPnV6rhKYpvCccAjvelsIvvQHmHANjpslts1l4+g9yW5NFuup7W6TFO2aGLCLTslmq2xtfk655nRb33u8GjwYh4ofDvizj2a/dL8+fScn0t1MvlxYuyPj+I9dB83syhaygQrrblbQcm04vXfgDXbKG+/797G55/WZtjPGQ9EqMRt1UObZMUh7PbJNpdbGwphEohPOuhkevk6GGvGJ5b8760YF7Wdkg9w8Ny/17W+R9Cw7JSYvFIScyWQUGu3CMn82cmrpPfp5hP/z9eumWt2jCv0mn8GZ7O5UuF9v7+1GRRToyWuxyIBplRmkpJr2eHy1axD2NjWz3esmqKkePHYvVaMRjsaAXgh8uXMhLzc282dZGnsWCRadjMJ0mpSiks1nGFxRgN5lo7OtjTVcXdR4PTYODoNORZ7EQ1wijyG7HG4kQSCR4u6MDhCBqMLB3eJhKl4uBaJQbVq/m14cdRonDwbtdXdz93nt4rFbSikKj1inNF48TTaXYMTBAoeaGTmQyGHQ6BqNRtvb30xkMyg5kg4OY9XpMer2M95rN6IAzJk2iKxhkfU8PqWwWNZNBKAr9kQgVLhcuk2lEzV3icEhLWFWZW1bGPr+fl5qbiabT2I1GNvT08NWnn+aZc87Bo43HbDBw8kHd3r738su81tqKDjmhKrDZmFJcjA6oz8/nigULuHDGDH62YgVKNks8ncafTGLTaqf3hMOk3W6Ob2jg5PHj0QnB12fPZmpJCf3hMNVuN5OLizn24YfZ3NuLyWAYmVCpqko8kyGTzZJSFLJa5bmjx45lfU8PHi33PJJK4deU8PlWKzV5eaQ1d/gls2bhGtUUJZ5O0+7340sk2Ds8jMdq5dajj8ZmNJJRFF7ftw9vNIpOCNxar4Hdg4PkW62MLyykIxikKxhEr4UOfnXYYazt7qZpeJhyh4MLZ86kubHxk7//OXwsciT+RUNfG/zjpgO1yEPD8neLXVqSqioLnnwUSmule7hjlyQxuwvO/qm0mAvKZTczo0luGw1KN/2YabK2ut4o3eTFNVI8NtglybF3n3Qrx0IH4sNVE6T6PRaEecdL0vf3wdxjpTVttMjlo5u2vHiX9BToDHIs0YB0USdjcpnFptVbF1A7Vcb3Qeavr35KurUNJmnp7xf67VfTugrldeiMsvhMLCRj84F+OFxLbyurk8VoUkl5TptL3t/n7pCThKJqeX2Nb8h4vT0PaqZAaovWM13IyYnFLrUBBeVw9w/lfVt0qozjq6ps9LJlpZyYzD9BVrNLROV9BTBZ8MdiPLV7N/MqKkhrnaRK7XYW19RQ6XLx2I4dLKqqwm4yUe12c+1hh/FuZyf3NDaO5ILb97vRbTZWtLXhsVjwRiKE02mS2mRAyWYZ0rqVGYTAoJHloFacJpBIkFQUQskkSa2YiV6no0JrPfrw9u0UWq0MRKM4tUYZe4eHKXE4eKO1lSK7fcRdu7ari3a/n6W1taiqii8eZ013NzOLi/FGIlwyezZvtrfjMJk4vqGBHq0zW4XTSUcgQFZrwqGoKru1Smh2o5G55eUU2e10BAJs0jrGxTMZHJolr9fpCCeThNJp1mg90Nu0vP1iux27yURvOMyW/n4Oq5OTrqx2jrBWEc0Xj/NWezvFNhtmg4GeUIiW4WHmaLnae30+VrS1cdaUKViMRp7YtYtWn49UNkuR3Y4AhrXUrbMmTx75yht0OhaPqm62vrsbt8lEKpslnkyCqpLJZim224mFQqQUBSWblbn7bjd2k4mxHg/LamupdLl4fOdOdgwMMKxlP+yvma9ogsXRJL6irY22YJDDtWvuCgbZNTjIKy0tdAaDNBQWyip9mo6gPRAglc0yHIthMxo5a/JkJhYVkVYUZpWWUuxwMLOs7H3hieaPe5fl8KmQI/EvGlo2S7KoHCcV3yarJJi8Ykke7kIZ1/4o6A1w6vdg2yrpFi+vl67pUercEZgsoBNQWCUnDH2tkrzqpsLL90ovgN4giXigUytAo9fIPAMLT5Lk39si4/CuAklo6YT82dUkXcfHfV2Sb0DzJhjNB7qe5ZXKYylpMJilq3vyYjmeJ2+RddhXPyPPadDatE5cIGPp4+dJN31PsxStWewylFDRIMV9Y2fCsrPlMd533Wb5iUekhRyPSHf86j9Iq//Qs6QG4N0n5YRh/Fxo3iRd6jOWw0W/lSVlX71Phh/iUbjnSimuK6qQMXxXgZwQ/ONGWHK69FzsRyZNRNVR6XRi0UppBmJRFjlN1CYCYJMv4v2uXCWbJZZOy5rWWo9ym9FIVyjE8ro6Gnt7ea+3F6vBgC8exxePj/TxTioKfaEQSjaLQa+n1u1mrFYxzqTXU6rVzx6Oxbjz+OO5f+tW3uvpwaDTEUmlCCUSBBMJhBAoWmz32aYmFlZVYRBipDsbyG5qQ7EYwWSSKrebyUVFqECR0cg1c+dSk5fHlv5+DFqXL1dREb3hMMlMBqvRyEA0SjyTYXltLdV5eewaGKAzGKTc6cRsMFCbl0eR3c6pEyYwuaiI+zZvpj8SwaTF/8ucTmrcbvyJBAa9nmQmQyydRi8EZoNhpN58VlW5b/Nm3u7oQK9NApfV1pLR7rM/kSCcSo14R4TW67s/HB6psnb6xIk8vWcP/dHoiPLdqLVM/TjE0mm6Nb2BThtPLJNBLwRHjR1LZzBIIp0eEZe1+f2Ekkle27cPi8GANxrFbDRi1Olo8/spcjjQa9X5Dq7kNhiNYh3l7naazbQFAnRrYrtMNovDbCaUSIxY46FUipSiUO1285158/BYrewaGOCPGzaQ1HrBf2/+/JGQSg7/OnIk/kWDSWsagpDW7LjZMg7tKpQu5LKxH1R678eeDfDaA5IQDzkZlp/74eS9H2arLLDyxkOSWCsboH6WbIJSXCNJPBqCzStlPN1ikiQudJJU33sdKsZJS72nWR4jvxS2vy2V3mNnSNf5uwWw/Mvy+AOdkAzIyYOqyuv90k+hLyYFcmOmSfV7QDaFYP11ssSq3iAt5VRMrncXScFaTzM8+j8HlObppCwSM3mRHNvHFaHoa5WhgOKaAzXkIwFAlffG5oLBThgzXYrw/H1w3lWSoPeslyJDoYctK6TXonOXfG61U+RzEkJqDUI+OZbuJjkRyaTReWaT7NyDxWLBbnVhCA0RGvChpPx4rfmUzTsSj8XC3uFh/rh+PdF0mgKrlS9NmcLLLS2sam8HVWW7zcYb+/YxsbCQtkAAobllHUYjbs21nVQUqQAHBuNx8uNxUorC2Px8jJplrmhejSKbjbimRO8JhbAZjfgTCUkGQmDURE+7Bgc5afx4frd2LfFMhmAigS+RwGQwjMTaB6NRzp4yhWGvl2veeoupJSUsqKxkXXc3Pu17ud3rpchmY3pJCX2RCOu6u0eabZQ5nWzu75e9uW02+iMRzpg0iWAiwXavF5vRKCuQmc1cOGuWvH7tGurz89nu9eKLxzHr9cwoKWGaplRv9ft5p6OD2rw8dEIQS6d5Y98+kopCVzA40vLVoNeTUVViqRSdwSDzKip4ubmZx3bulCQaCBBPp/HF4+iEIKUoOEap+j8MbrOZnlBITiz0eiLpNHqkKC+uTTgMWpx/ZlkZy+vqeLapaSSev667e6QWQWcwSGcwyJyyMu464YQPCMzGFxaysq2NTDaLTgiG43EWVVXRHQqR1oi63uNhi9fLQCyG02Ti9EmTuPyQQyh1OEZ6zd+2YQNWgwF/IsGm3l7e7ujg1qOPHvFq5PCvIUfiXzRMWiitzP42qKmVVm5WkW7rRETGV39w/wf3270Obv4aoHX2am6U8udDTpCWbiImhVoHk/qsI6TVvPJvkshiEUnS+18INqdsa+r0gDBIS9rqkFa80SyPl4zIGHJEy0U3WaSbXAhwFUHnLp5++mlO+/LP2P3bS5mQjEJwWBLb7KOl+7p8sRTj7XwXimsP9BQ3mqQnwlkgiVropEtbzUrVfeMbMm491C0t+VgI3noMlp71AQLv7e3lu9/9Lk888YRcIIR0y8e13HSLXV4DQt6zinEyV3ygU977gnJ45wlYcBLPbN1HgxpkUrJPpqTpDNL9Hg9LMq+fKY+XVWSY4Mwfwu51OBYcS+Tlh8jvixLo7yKgZlESMY5NhnCoGfqMDuqDPVy08xniRx7LrevWYTUYqLbZGI7FeKmlBVVV6QmHsRgMPL17N0lF4bypUymw2djn8+GNxcju2UP/67JmgCoEs7/9bSbOns12rxd/IsHkoiIKbTbe+sc/2PT000T6+7l+cJDD6+rY1NdHRyDAYCyG0eslctNNeC68EMfMmTgTCVZccw3varW9T/nyl5l44om0+HykIhHW/+EPdPT2Ql4eBeefz2OqyjeLi2l7/nmeePFFLCYT19xwA+GiIlRVxez1su7ee3k3mWTs/Pnoli+nPRDA2tPDi3/6E8NtbUz62c+wLVrEqRMnMq2khBMuvJC2DRtIKwoFxxyDY/58Wnw+HN3d3HHrrbLtqsnEvEsuobiigs1vvcXLN93E9J/9jBKXi+9dfTV6TfGeiER44aab6GhuRgXUE04gW1mJXqfDqtfz4gMPMPTssyz4wx9Y2drK2rffJvzii6iKgjAYsBx7LPkzZ2IzGtl8/fX8OBDghl/8ApB174uLi+ns7OSrX/0qgz4ffaEQpqOOIlFZSTaTwW4woNNS2LYPDOA0mUYmBSs1EWMslcKg0xHXdAXd4TBmnQ6XVo51UPN+VB70SlhQWUl/JMILe/eiqipH1NVxyoQJmA0Gnti1Cx1Q6nDwk/p65paXU+p0Msbjed9kYDgWI60oRFIpdg0O4jKbCSaT3LFxYy617N+EHIl/0eD0yPaiu9dB24B09TrzNSFYpXSnjxZ1KRnY8S488Au5bdkYqc4ODkp3cGmdzBdPxqUFeer3DgjGQFqvbz2qubILoG2rtHTNVkngET9MWiTd+k0bJInml0qXd8Qv3cT2PBnzLaqQ3oNUXB4rEYONL4Gi8GjjwyyeP5fHEiVcc/3rcj+TWZKiirRQC8rlpMXbLq12kKK+4R6ZRhbxyzh6URUcehaZRByDr19OeFwFkkjVrBSzde2W5WdHoby8/ACBqyrsXC0t5XhEegYc+dIVP9Ql1x92DhxyErRsgtu/By1b5MTotQd4pruYEyx+JmVbtHarmsjP6TmQEmixycnNlMVyYjN9mfRktGzC6prM1aU2mtJg2/Eec4KdWIurIQVkwuD10THYSyqTGSm1uZ+kV3d1UeZwyFhoNsv2gQGahoeZUVaGzWikNxzGMGMG+vnzZcpZby/r77yTuQ8+yNyKCgajUX57+OE829SEa+5cvnbWWVx9wQWAbEP6s8WL2ef30xsMcv7NN+OZMgVFVdELQbnbTdmFF3LX17+OTVWZPXs2z5x6Kg3jxvH4739Pw5w5JA45hLbnnyfzzjsMHn88Lfv2seHVVxn3858THh7m+p/+lKamJkwGA7+/6CKO/N73qJ82jYd/8hNKu7txVlcTsNk4+corCaxcyTnTp3PGMccA8Ke//Y3upiYc3/kOIptl+M47Ydw4siUlPH3LLdx0110EXS62Pv88wfXrsY4ZwzFHHYXrtNPoCYfxhEL89kc/Yvktt+CPx3nzttvInzqVuZdfzq7+fvb295PndErhms9HtKkJe2Ehi2tqMDudvGkysfDKK5lWX89AWxsP/PCH3HjJJYzxeLj8rrv4yre/zaWXXvq+791vfvMbzjrrLEzz5/PK2rW8eu21lP3kJ/RGImRUlQqbjdnl5bzb2YnNaMRhMhHX0gPfbG0lrap0h0LUejz0h8MEEwn0QuDSGpQI4K9bt3L25MlkVZUJhYU4zWaE1jFNyWaxm0wsq63FqNdzYkMD4/Lz6QuHKbDZmFZS8pFlU/MsFnRC0BEIYNNS20w6HU6zmZ2Dg3wwCz+HfxY5Ev8iwumRyu42r/zd6pRE6euVaVNP3irjrLOOlI1Atq+CoT5phQ73SjJUs5BKwTO3SVW1u0iqrJ/+A1x0/QFLu69VuqCLtcppxTWwb6us3qYoMHaazKHuaZZitkRMTiKOvVgKuHa+K70DqgqdTWDugPJxkqzeehTiYSKeClY37+PNsws56aEHuOb0w6GokreaOvnl5b+mgCSbAy9zzLhS7lhUhs7Xh+Pi33DpgvG82TqAp7yaxy6rp6huKsuuf5CFnkpWn38ZJ40rZka+mR8+10xG187cEjt3Lq5gW8bFRSd+iQ1bt6MoCvPmzePvf/87DoeDE044gR3btvHAH2/hmT/dgJJOs2M4xg/mVJMyRHmovwWzychLT/yd/LoG/vKXv3D3dVeRCvmpL3Dx0LET2LKvk+fe3M0qm4Xf6BSenGEBjHzrbR+DKR82h4O/HNbAhLpq2oqn8uXjTiGTyXCMRkRkUiAEtUaoNcJ317SwbEsPUwu8KKpKkz/BdYdN5CKrbFKxP34dS6cRyDzk/a/c/W0rm/1+Nvf3YzUaOXXiRELJJKFkEo/Fwr5YjA1at62+SIQj6uoosNm4cOZMmDkTgKu143UGg7zR2komm6X95Ze57Ktf5cU330Sfl0dJQQFj8/P52owZI80vJk6cSE9PD4eOH89AYyNVP/0pPbEYJYsW0f6HP1B80klsWruWgnnzsFmt6EpLaXc4OPV3v6OwrAyRSmGorqYzGKRs4UIye/Zwp1YS1ajXc86qVXQFgzIf2+WivbkZ45gxWEwmMtkshrIyEnv2kBg3Dr1Ox5S8PObPn8//vPUWTYWFqKpKnlZprsLlonHPHoQQnDN5Mn9vbKRt61Z+c+21skTq88+jt9nIaEVV4i+8QPHJJ+O///6Re10zYQLDQhBNpcgUFKCm0yyvqqJQK1n7YRBCEAqFsKbTqIkE7qIijm9o4PmmJipcLuZXVEhRmfac8yyWkVCG2WhESaVo9vloDQQAKWhMKgqxTIYyp5OMovB2ezsDWkOWfKuVny1ZQtPQEHdt2oRJryetKKzr7uZnS5ZgMRiYWFTExKKiDx3vaOi05jivt7aiZLMU2WzM01LvnJ8QOsjh0yFH4l9UpFOAgJrJ0L5DvviHe6BumlScr3xYEurO1VBSJ4m0ab0kar3m9t5fNMXmPJBGtr+9p7tAnsdollbxfqV3S6Ps773oDJluNdQrC6bY3QesY3+/JPBjL5Kx50d+DQtPljHfnmYZO64aL49ZVM0zLUGOqcunIdJBfipN4703M6vSA4Vz2NDczq7vn0Tb9OO5/qc/5CmlizMWzSKa3sOsymJueeI1rr3zXn61sZc//elP8MdnCTRvZ9VSJ4lgD+OeHGDFURU0uE2cvzHMnd2Cy0+dzUmeufziF78gHo9z3nnnMWXKFNrb26Uq/bZvwstvsaPPz+avzCGhQP0D73HDEZPZ/O5Kvn/NdTz47EtcfnkDp512Gl8Pb4Sd7/CLnTHu3dHPd8blcdI4hROWLuSMCWXgbefwu17hz1NNjJsxl/WuCVz2u3tY+Y1j+N7Pb+Gbl13B+Rdfwu233y7v34zl0ssSDUE6wW3nHct9Ox9gy8k1DPmDzHnFy4/mVcPu1VyR7OGNNi8t5ZMZ8IcxNjai6+hgX3U1hZMmMdzeTjgUwjRtGka9Hp0Q7BwY4Jj6ego7O/nVD35Av9fLWdddh6KqHFdfz2mTJn3oV64nFOJPO3cigLjPx+uPPsprb7xBy/btnLBgAWecccb7tm9vb2fz5s3Mnz9fEkUoxHePOILbN2xgYmEht4dCFNvtBHw+RFkZSa28quJwYIxEMEajCLeb82fMQKgqLdksz+7dO+LO3dzXJ5t27N3LtpUrOXPyZObOmsX9jz2G64gj6AkESO3bh7WsjAqXi3v+8heOPuYYFIMBvcXCN+68k/ZEgqyq0vTuu7x+993EAgGW//zn3NXYSLSzk/KSEjb/+c88sHUrtupq3AsXEldVxN69OAsLOXXZMv5y331kFGVE8DW9pIRQMkl6xw7mzp5NoetAieAbbriBO++8k9NPP51f/OIXCCG45pprOOqoo/D+/vcEw2HOvP56LAYD4wsLQVV5taWFrKpSZLPRH40S04q7FNvt9EcilDmdFGhtb406HcUOB1v6+8mqKglNpe8wm6nVahV0h0I839TEVq+XUocDm5bN0BYIsHNggNnlH9M/YRSSmQw3a3XrF1ZVsa67G7PBQDyTocLlYkl1NZt6PkZkm8OnwseolnL4XKOo6kD/7vpZ0lVcWAXTD5OWuatIiqsEknzHzpBqbLNNKqYvvB4OOVFa5ImIrKn+zhOSfF+4U04AQKaj1UySaWH7NsvypGNny1i3ySot9kRYEn0qKV3GqZRcL4RWUMYqPQRD3ZBfDggpdov4wdfHo7v7OceTgESUc+ZO5NHmIfCUwaZXmTd3HmO+/T/oLTa+NNbFu2oRTJiPTgjOnloFmRTnnXfegdrjqsrZ5gEY6KApkKTOpqNBH4Mx0/nq2afzdtgA5/yMX/76N7z++uu89957/PjHP5b7ejvkZMfhAZ2Ow4qMOIO9FFn1uE06TpxcDc58pk6dKgkf2LFjB0seeIepT+3j4V397PQG5EQgrwQa5kIsQMSWzxqfwpm7TMx4fA+X3vEIfbE0ODys3r2PLw2tgUev5yueqHwec4+V7n9nnpwYffnnMgWupE56TUwWGU+/83KmbH2FSyOtXNO3huLt27j4nHO48bvfxdPdzd5bb8W3Zg2ZwkJ6wmF6NVdrIJGgsa+PM047jT179vDcs8/S+tRT3HzUUZwzdeoHKpjtx4aeHlStoUfj/fez+KKLWNnR8aHbdgwMcMIpp3DdjTfiGkVix9bXc/KECXijUemC1+nQC0Gl283hdXWEkkmMej1mg2GkeIqqqiyrqyORydAVCvH07t0E4vERK7LQZqPc6eTxnTtZsnw5Cw47jN4//AHLs89SPH48M8rLuW75cn57001UXXYZpVddhXnOHO767W/xxeNs93pRxo/nxNtuo+bSS1l1//3sGhiQ7vOdO2HOHF5YtYpZNTVMaWnhyKoqsm+/zcVXXIFA5ow/29TErsFBLpgxgx8vWsSXS0t5+957uf+ee0au/eGHH+a+++7jnXfe4Z133uGhhx4C4NFHH+WCCy7A29vLrQ8+yCs33YRFr+e65cuZVV7OrPJyThg/njKHA4MQmHQ68qxWkpkMRXY7aUXBZbGQb7WSQcaxjx03jgKbjanFxcwtLyebzXJfYyN/2bSJrf39bOrrozMYJDOqrrkORgSOnwYdmnCuJi+PhoICTp84kXyrla/Pns0vli7NWeL/JuQs8S8qrHYZexbjZV747CPAP3igw1gqDiaTjJf3NMufICuQnfZ9mLxQEu3Ss+CO78rUK4NRxtT3bJC1yJedLYm4vF7WTs+kZSnSrt1aWVYhY+kgxXbJmLTIjSa5L8i/s4r0ABjM0mNgNMvjmm0Mx1OsHEixI5iWaUrmnQgBN551BCgZqT2rqIe9nZBfhgiOaqag00RsGBHpJLx8Dwz1YLeEQJ9CjWfk5CKdlErymafBlj5w5ePr7ycSiZBOp0kkEtgtFulRSMVh73sAmG32kSIzOp0O89ip0L0XnRBkNIX2BRdcwDNPP830fW/ywJ1/5K2esKz+pvTKvPP5J5Hd8jZ59sfZctmRMpzh90py3rYKslnE+uegZSPUzJD3uGOnHO/ib8mqdI1vyOUDHXLSpKRl45pUHLr3YrU6sCppvuMZz2333IFPmKmcOZM555/PK6tXM9zdjW7CBIwg1dgGA5OKitBr7t2lS5eyb98+hoaGKPyY8qmj+7D3NjXRdcMNrNTpSIXDvPTSSxgMBk455RTebGnhK2eeScWsWbxjtzPD62VqSQklJSX09fVx/rRppAIBnnI65Yu+sJDNWlUwg06HMRolr7gYZ2Eh0eFh8iwW/rFzJ/9YuxbF4eDZpiaea2pi5+AgwUSCWCo14mWIpFI8dfvtrGxrozMY5NFrruHy444jFgyydds2Kk48kXKbjYLFi9ly8830hkKUO53YTCZ6QiGSlZUoPh+RQIAhgwG92020uJjr332X4046iT/deivfHDuWl/1+/njhhWRVlZTfT+dNN6H/0Y8ITp1KT08Pp556Kr/43e/YkU4z0NXFvIoKysvL2dXUxFAmw5lnn82GDRs4//zzuffee3nllVcQQnDZaadx8w9/yCUTJ7IrFmP7wADFVistw8N0hEIjZVptJhNHjxlDu1aWdYpWaW9jby8ZVcWi1/PLpUs5b9o0bl23jke2bx+xuLd6vfjjccq1zmrLamsRQmAzGhlXUPCZX0kWg4Fiu5255eWYc5Xa/m3I3ckvMvQGOOMK+Xs0CA//RmvOIWRLUFeRtNSDAzDcLUuOFlXJoiq+PtmtzFMiidnhlnnnFru0mL3tkEzA778OG1+RAjl3oUyNGu6RJVPzy6TlmM1K0tHppIt8/Hx453E50TCYZBW4l/4i3fQ2p5xIdO6C2ik8sXOI8yf0c9cR4yGTgAmHcOifnuPdDe9BaR0bHniAtrY2sir8fe8wl0wtg0SUrKryRPMQ5xRV8cjPr2RxnirJNxqASAgKTExwKLTHFFr8ceqNJh667z4OLXfCP27iktv+wa+v/iVtXd1ceeWV/Onco6TnQlWl0j8elr878uS1qaqWrnYd9BtAkVZGOBymrLyc9ORv8/Adz1MxqxQuvgHn9u8RDoehajwuTwl1eT/n8d4MZ9bVo4b9bHtvA9Mri1mUr+Ox1jDnZTM8vDciz3P3j2DuBXDXX+VkZ9caudzpwSBipDIZea8MRumN8XaAxc49u3ZwxpRammccx++ee5Ut//gH8fx8jIceigIoWuGQdDbLMq0QCEBjYyOpVIqCT3iBz6usZGMgQF84zJfuuYdYOs0PFyzg5iuv5Pjjj6dk9mx++sYb/OWqqyiprOTY888nmEhww7vv8uvly1ly5JGc8fOfU33ccax6+GFq5s9nYmEh7gULePOmmzjvf/4Hqqo41etFKStjWAjyXC4ira28MjhI/+rVzD/tNIw6HStaW7EYjYSTSXYNDVEeDmPQ6ym0WAgHAhxTX8+2bdu4ra2N4449FoBkNEp6YAC1thb/zp0YiovxJRLMMJkYW1XFKy0tRDs6UNJp/EJgdrtJ5OXhCIWIms08s2IFkyZNYuGcOWxrbeUXK1awc3CQLT/9KXOuvpqIwcDfNmzg6ltu4eTLLmOlomBqaiKlKGzq7oZEAkcoxMMrV7LmgQe4WAs/VFdXs2LFCi644AJ2795NIpHggb17aQsESGUyvNPVhU4I0opCNJWiMC+PgWiU19vauObQQ7Eajazr7qbW7ebyQw7BbDBgNxqpcbvxahXw3BbLiHvdqNORzmaZV1HBin372NDTw/ENDXxjzpyRRi6fBrV5eXisVtZ2dWE3mbDo9ZzQ0JAj8H8zcnfz/wrsbqla37cZuvdKd3j1xAMpY/s2yxahQkhB2saXZAevoW4ID0v1eEaRkwGLTVrad35PWuDZrLSuoyGpqq6fDWOmSDHcir9JhbvRBO46SYAGI+xZJ4V0ZptUol9yI7z5mFR7p+IyBBDw8ui+Fn5y7DIos8DcY6BvH6dPreGRtghnn3wSCxY08ZOf/IT169dzzJFHcOqZi6GrCbvFxM688cxetAR3Msjfz10m678bjPKcQsEiVO6fqufMrQqZpkeZW1nAN85czIMvvo4hMMCXnUGUK69k4aJFrDQNMKaiAQybpHWfTkvyPu9qeP2vMiRQWAV9u2DDZlDcsPoZfn3ttcyfP5+amhqmTp0qiVun45xzzuHrX/86t912G0/ccycPn72Ibz69ht+EYqTTGc4pUZluTfGH8YIvb83wh44IpxdH5ERrzzqoPwbeewWWnKl1dFOhoAJ3vIkik+CSLQnunpsnn1tCVrW7qaoA8lSqy22svvRS8i0WXm5uZiAWQ1EUrEYjZoOB4xsa6N6wgSnf/jZGoxGr1crf//73EQXycccdxz333EN5eTm33XYbN954I/39/Ry3eDFLjjiCIy+/HCWbZUl1NZOKiwHZlvK5jRsZ3rOH4XXriFZU8McLLySZyeA+7jh+kE6zo6qK7nvvZcPzz5N1uUiffz4r29r4VlUVtYsWcc7y5ZiNRm783e9YtHgxZr2eb/31r3zta1+ja2iI8YccQv38+bzd0YHa20vHffeRCIcJ79jBoy++yMbNm7Hp9UxftIhAIoFqNnPWj3/MUCJBqcPBj6+/npuvu44OVcVgs+E66ywKrP+Pvf+Okuuu7//xx73T2872XqRV7122XOVubIPppvfeQkiBBAgktECAEEpCCb2DwRhccLcsW7as3utqe2/T+8z9/fG8syO5EBI+nPP7Gr3O2bPa3Zlb3nf0fr7K8/V8+Rh98knu/dSnyFgWKSD0yleSLBQwLIs1b3gD9/zbv5HOZlm/bBm3/uQnAATdbmYzGc7MzlIolRiKxQjX1tJ/3330njnDd/7jP3Da5YDXfO5z3H38ODs+8QlCpRIZoGn1ako2afALX/gCb33rW/n3f/931ci/9CV2RKPMr6mhMxzG73KxY3CQkmXRFQ4zk8mQtjXVv7VvH9fMn09jIEAynyddKLC+pQWAnx85wj2nT3NgfJxELseSujqi2SzjiQRO02R7fz/ZUomAy8VwLPaMc+X/kJ2cmmIymSRXLBKJxVhSX88Lliz50/ax8/Y0M85Ogf1/wTZu3Gjt3r37//z+hx9+mK1bt/6/u6D/P7ZnvdcjO+Cub0LTPP08OwH775d+OQiUpwbhPV+TkMuvviiSWial1HPLAnjdv8BX36V2LMuSQpnHrzpt5woBvdsDx3aqTxxDUX8uo5ry7Bhc8hJlCyYHYe0VEo6ZHtbx6tvUkvXor5QeXnOFasFnMXgffvhhPv/5z3PH7bfz8MMPsXXdCug/DhN9BF/0LhLTU4r2f/avSlOHalXT3nmHUveJGbXC1TSJD3DgQbjg+RUxnIkBeMcXxfD/3kfUD+6v0vvG+uDm94iY99X3qke995DY+gZSucum4CUfUM/3H7JEFD78PPECPAFF+TXNMHpa/IFCVuterkcGq3n4ho+y9a5P6LwtC+SEdSyTw1WeGd80H3bfpeMFqpX1yKWxXv5BfrD8Bh7s7WUykWDP2Bgeh4Owz8f65mY+vnUr8/+HgSz5YpHHBgcZjcfpqq7mwvZ2zD8gjPPxhx7i9OwsdT4fjw4MkLcFRHKFAhlbKnQ4HsdtmpSAgj0wZHFdHe9saOBb09PMr67GaZo4TJMPX3rpnIMA8IMDB7ivp4dqr5cdg4M4TJNrFyzABM5EIrx8xQpesGQJhVKJjz70ENOp1Nzkr4DbzaeuvBKHYXDXqVPcdeoUqUKB5fX1HJqYoKu6Gpdp8mBvL0OxGFUeDzF7QMzyhgY6q6tZ2dDAB7ZsmSPVTadSvPbXv+bJkREsy8IC2quq2NTayocuuYRPb99OZzg85xjtHBrC73Lx0kCAE8EguWKReDbLV264Ye4eLctix+Agtx0/zo7BQba0t88NsZlIJolns7hMk/FUiqDbTcjtZlNrKzuHh7m0q4uAPcr0TevW0RwM8plHH6UrHCaayfDzI0ckNuN2E8vlWN3YKEcHKbVlbEW779x8M83BICXL4qCddve7XJpAZ5osb2iYi7Q//MADpPJ5wraU65nZWd61aRMXtldaVM/vx3+8GYaxx7KsjU/9/flI/C/Ryn3e2XRFWKWxU2DqrxIQLL/Y7vUOSnEsMq6IzheE9dfB3d+SsEs6AZTAMkSAq22S7OrMiJwEh0sMeNOp/menS33Z4QbVcUHOwY7blU5fd3VlYtmSjfr6Q1YsKIXt7IB3v0GCLqYpZ+H9l8Dz3ggrL4W7vqEMQyEv0LOKUMxJjGXJZrHqZydg3/3qLV+0QccvOw2XvVytecmomPvzV6nX3euH1gUqL0Q1FATTIYehWNTv/ycQHzyutj5vQGtQ3w6NHYClvnevX/dVyGkd/VVyFIpFSbkGa6RGNzOqY6y6VMTAbAI5TyF7SIsFGBixaV43c5SrvXkmVmwgVNfCTCaDa2KA+ce2UX3XYSnMrbjoGRXrSpbFN/bsYefwMD6bbdwzM8NrVq+eA6ViqcTjQ0MMx2LEsll+39NDNJvF63TSVVXF8elpUvm8iFhOJzn7uGX99XJ62EJp/pZQiNlMRgpyhQIfeuABbrvllrm6/atWraIxEODE1BRtoRC7R0Z4qLdXIO1y0bh5MyBwnUgk6LDbxpqCQQajUY5PTXHr0aMMx+OMJRIEXC4mUimW1ddzdHKSmUyGaDbL/OpqVjQ2SrY2GiXs9fLqVavY3N5+jsjJYCxGcyjES5cv58nhYbKFAtlCgXdu2sTC2lqWNTRwbHKSer+f2UyGjnCYVC43xysYTyRY09x8zro/1NvLd/fvJ+B2k8hm+fWxYzqnZdEYDBL2eonY89VT+TyWPRmtWCrRHAyKT+BwcO+ZMzx/8WIcts49hkFXOMxALMZFHR1cOX8+vzt5UrKrLhfpXA6nw8FkMqnSxxVX8IujR3m4r49UPs+hiQk6q6poDYVYUFvL3198MV6nk2Q+f86UMhNNbTtv/2/tPIj/JVpjJ9z4dkmsRrJil7/hExq6MT0Cqy/T8BHDgGUXwd4HVO82HUqHt3bDE7cr0s6loAhg14c/+CMY7YE9EzpXQ4ei1WxGdffZcTkRUyPwyC91zNkxe+jKETi5B17xIbWY/Q+2detWtiZPqlbd2CRyHIBlkbjWreElO+8CDHjp38Lh7YpGX/Y38NhtcN8PVAI4tUcA2L5E0fNEv1L6171RgAmSc33NRzUYxuPXsJKyaM4L3q0Z5f1HxQFYcanOk88KaO/4upj5qy4VoJ8NjAcehl//O/Qd0fCZ9Vfr7/EZHfenn9Y1OZzKHpRs9TwMqGlU7duy4JIXyxEpZ1eCNbZDNiuWv2kDTHQSju/ESMdpK+Zp690Hr/2Yru+Bb8kJcDjhzq/r9Ssvftq6j8bj7B4Zobu6WmTDUokHe3t5wZIlhL1eLMviu/v3s62vD6dp8ujgIK3BIF6Hg2KxyNHJSS7p6qK7uppbjx3D63AQyWQw0ZjOgmVhIi3x+dXVVHk89E9OErX71sNeL6dnZnhiaIiLOzuZTCb5+u7d9EUidNfU8Ob165lOpxlLJlnW0EC9z8d39+1jUW0tPpcLC+ZGg5anvv3gwAG2DwyQyOWYTqWo8fkoWha/Gx8n7PGQsLXnT8/MMJFM4rEniL18xQoueAqAA/hdLvKlEi7TZG1TE0XLImePii2USrx70yZ+ceQIJ2dmWN/Swi0rVrBzeJjJo0fF6A6Hed2aNecc856eHpqDQQJuN9cvWsRPDx2SzpGtU1/WeW8LhRRBu92cnp2l2utlMBqdq2f7XC6ag0EsIJLJ8NjAAJlCgWX19XidTgzD4D9vvJGPPvggTw4PE3K7yRSLbGxtJZrN8qQtnTqvuponhoYIOJ2MJRLMq65m1/Awn3zkEYnIWBb9kQid9khYp8PB4j9irvx5+9/ZeRD/S7RSSTXtV35YEaMvIOC49g1Pf23LfGmTPynlNNZeqci9qUupY19I7HIM9aD//tsitKViirxNh6LLbLoyZzwZU3Q5OSjQqGlS5FzIKzNw4OE/CsQBOQyhOnt2ulnpWTcdOmZVnSRkn//OygjVe78n4tyFNykt3n9EU8+6VytLEBlXq1tdq8Z+zlslBnxLt+r7PftVZnB75dyc2KVzvuojYpTHJhWxty1S3ToZVdZi5x3w2o9XgHGkB+75ro47PSoCWnRSWY1F6yWh+4Fvy7maGtJM8eiEPY3NpUEuF78ILn4h7L5HzsjZZpqSa/32hwT+xaIckPmrtOag+z252wZ6U+sFup9D22DeCpVMwvXKzKDI2DSMuai7nEYvnhVF/vLIERymidM08TqdRLNZLmxvZzAa5fTMDFVuNxd1drJrZIRjU1Nz40TLgiUlwONwEM/lIBBgKBrFNE3S+Txup5OFNTX89969/O7kSRHOcjn8Lhd9kQgTySQz6TRXzZ8/d40D0SiDsRhrm5t56fLl/PzwYUzDoGRZ3LBoEZ/avh2nYRC1h5ek8nmyhQLVXi+TqRT1fj/xbJYl9fVsHxigKRBgbVMTfZEIvz1xgpc8pXd+vj3i876BAUBguaqxkU9v3z43lvSN687N0NywaBEPDg3x6U2beGxggK/v3k1rKMTNtnNk2rPAQZmOXLFINpuda8PzOZ2MJBJc1909N1luJp0mUyjw2OAgDsNgaX09H738crpranjN6tV8+YkniOVytAaDbG5rw+1w8OTwMG9dv54PXXIJb/jNb/C7XKyqqdG0uGgUCwkGmYZBOp+fq/n/5vhxYtksjw8OcsMizR1wmCaFUok6n493b9pEayj0x/2/Pm9/tJ0H8b80y2Xht19T/dZAEfDN753boAHN445OakNv6hIYveivKn+fHBIYNM8TIJeKIs6NnFaavAzqwbDaxRo64MwBibg4XErJTw1rHnhdS2VoyOl9ioBHTknydLGd0o5MaspY3yG9d8vNlZR7fbvU4ebNU7bYUsqYUlHnLkfS5lmR0ondep/TrSxEMqrJaYapVDvomh76qaLSHb+Bm9+n69l9D9z6ed1/sSAgXnOFfn7ox7BgPXhtkps3CMd2CKBNhxyZH3wMPnWXiH5Tw7pWT0CM/MOPwWS/0v9Olyakve6f5USBzjU1JOdkqgjX3qBnYBhK/z/xOzknhQJQgiv+URmDmmYBciAMw6crw1pAwF20J8OVzmrPK+b1OfjG3+hnb0D1/eZ5tASDdIbDDESjc/O/VzU2UmPXPm89dkyDRbxessUis/ZwDMuy6I9GcTkcZItFvrd/P29dv567Tp8mZkuBDsVi1Pv9uO3hHqlcjmgmQ1tVFZOplKZ3ASOJBNVeL2OJBD2zs7TY6eTJVIqT09M0BAKkCwUsyyJlT/Uqt1Bd3tVFyOMhWyjQUVWF1+nEYRgk83kSdko7Wyoxk04TdLkwDQOfy0Uyl6Pd5aIpEJgb7ZnK59k1MvI0ED8xPY3L4eD6BQs4NjWFy+EgUyjQGQ7PjSW9afHip/33NA2D244d4/GhIWp9Pk5NT3NqepqPXHYZL1iyhP/avZtkPs+u4WGqvV6m7DUZTybxO53ki0W29fezpL6eep9P3IDubqbTaaKZDI2BABttsZaru7sJezx84fHHWVxbi2lH9AG7xr2soYFPXHklPzp4kJJl0RuJcEF7Oxe0tXHnyZMMRKP4XS4OjI0BthKgnZnZPz7O8xYuZCKZ5IOXXEJj4FmGLp23P9nOg/hz3SxLm3O5P3zf/QLUctq17wjsulvpWFAUfO/3lM6NTCpqfNnfVSI3UDr85vfCbV+GE0+o9Wz0TEXRLbRa51y6BS68UdFp70Glq8spZ0oC5M4VcGS7DXSm6tGN8+D2r4j5PXAUbv+q2rd8Qc0dHzwBr/knXdPMiMCt84oKCFkl9Uu73HD4EXj+u3UvoRqBY7BaZK+gW+sTbtA9TfQLyH1BHaN5vo6Xiin1X98G3/8nvdfpFvg7nOIK1DSprW74tByQ0V45LCNnVHfPpHR9s+PqDpi/sjLl7MwBwLJHvy4SBwGUJeg7Uln71gX6Anj4YWVJyjY9orT76f1S5KttUZkCYPmF+io/399/W5F5PqdrXLBG91P+bGBUshrtS7WO8Rk9h7f9Gy6Hgw9s2cKvjx1jMBplc2srNy9dimEYZAsFdo2M0F5VRSSTIeByETNNfC4XJ6enKVkWV3d3U+vzEclk2D8+zueuuYa9IyP80AaLWp+P8WSSgMvFquZmTHuUaXdNDelCgel0mmqPhzXNzWzv78djmkQzGVqCQUwqAPr44CD5YhGnPTJ1Np3m4Pg4/7lrl35vmrxz0yZqfD4W1tXx2MAADtOkWCjMjW9N5HKsb23l2NQUDsMgkc/jMs05GdtkLkenXV8/29J2vb8xGOT07KxmgNvCKX47/fxMVrIsnhwZYb5dqqj2eumPRBiMxVjd1MSi2lp2Dg2RLhS4Yv58DoyNcWxykmyxSK5QoM7vp9bn4/DEBE7TpLOqioZAgMZgcG60ar5Y5OT0NPlSie6aGtY0NbF7dBSf04nLNHnvBRfMXc813d10VFUxEI1S4/OxvqWFkmXRHgpxnz25DcNQ+cPhwG9nacbice7t6SHo8ZCzp7t9e98+RuNxltbX88Z166g+a3b5efu/23kQfy5bNg1fe69Y1d2rpVc+MSCQKtdl/VWKuEAktft/aBOy+kWievTXGpBS26L08qUv1SCORevh/d8QyPz0k4rqHW6xy0dO6xwP/BCWXaAo8cm79bemLp3npncoldt/VuTYtkxa68EaKcDd8XXN1k7F5CA43WJsty9RitwfUjR7wY0CU19QrV4Bu2+7Y6nq0r/+d437bJonIZtrXge//LyOWyrCwrXwwvcp/X9oG+ywI1p/WADqdAsg7/2+Te4L2VPXIjaxz9LfZ8eV2Qg3aPTr4DFFtCM9cgosS9c8OSAQN02NGU3MyunI2b3dc2ZVnK9nMsvS+fsOSwOg75DuH5RReOw28RHKKXKA1Zfrnu/8ptjwS+0NO2Dfa/9R/ewLKTvjcuvnUK3NFciAx0eVx8Mb1q6tfM4KWbsLwR5+197O8akpIpkMjcEgb123jplMhsMTE3O12WKphNM0mUml+Pv772cmncYqlRguFBR1GwZ3nzrFuo4OMoUCq5uayJdK1Hq9JG0d+Bqfj6DHQzybZTadZjgepy0UYlFtLccmJ/E6nVzc2Umdz8c39uzBtIEx6HaTzOX4r127+OzVV3NFVxcHRkdJ22SsGq9XM7lRfXteOExXdTW1Ph8TiQT39vRgAAttItdTrau6Gpdd66/xeumZnWVxbS0lyyKRyz2raIphP9eSPTDm7O6hrz75JGdmZ1nW0MBMJsPjg4NYQMKWWTXtKLi8Lk7DYCKV4sDYGEsbGhiOxdja1cVrbruNY5OTBN1umoNBPA4HhWKRWLHIuzZunGtBA+Yi8rJOeiyb5cMPPMDdp0/jd7noDIfxOBycmZ2lyjTJGQbxXA6PTWzzOJ386uhRemyCXUMgwJGJCb6ycycfueyyZ/9sn7c/2s6D+HPVpkcU2bl99nSxg4qw2xfDsccFMiAgK0d0maS+j/cJpEDANjuur5kx/eyvEhDc/d86x+m9iuiik/q90600eT4Ld3wDXv1hePVHVLPNZQR0jZ1yEIZPwaJ1qkvHpzXFLDYNhx5Vaj2XEZAZpiLhQk7pX6db4Of02Kn5JqWsS0VdU8HWjo+MC4AMh0oJt38V3vwZEfnG+nSNvoCcm8lBeOJOOQHFotL0Ky7WvUfGBbi5tK6ztk2Am03ZteopgXI5UgY7Tb5FEa6/Wo6IacLue3Wte++HdEyAWcwr7R2d1P0U81Dd+OzM9kIOPvlyOWAT/XZGwG4BzGd0L04XTA7r+p1uZRYcDmUC3Pas+fgs/Pyz0gQYPCHGvWEoszJwTFkRt0fPJNyg95WtVIJHblXd37JgyUY817+Fizs6uP/MGdrtaV5TqRR3nDpFybJEYDMM3Dap7PmLF/PvTzwxB3ZDsRiTySQFy6LG652r/QbdbrrCYQyUSj8+NUVfJMI8m/jWHgoRcLspAjctXkzK1gQH8Did+N1u0rEYhmHQXlWlEZ32pK9/2baN2UyGhkCAiVSKgNNJplDA73LJIairw2Ga5IpFfnviBE2BAOtbW8kVi2RsZb6nWmMgwN9edBHf2bePKo+Hi+y2qqFYjBsWL+bSzs5nfJ9hGFy3cCF3njxJwO0mlc+zqrGRKo+HE1NTc21pl3V1ccfx45ycncW07zFbKDCTyeCxywNej4cVDQ0MxWLMr63lxsWLeaS/n13DwzTZfePb+vpY2djIFfPnk8zl+M2JE1w2b95c6eFsS+ZyvPeuu3iwr49MPk/Y7WYimaRQKuEwTWLZLIVSCbfDwbL6epY1NNBeVcW2/n7CHo8G7UxP4zJNTk5Pi+9w3v5kOw/iz1WbGACsSs9zfbtSpTe+XSNBn7hDkWTnMm3u2bQ28VRc4OgNirFdKmrj9lcJwFIxpajPHNKmnpjVccqR3NSQLXdaUCp5+JQIZAvWKAo82w4+ot5mj0/R95N3y9noPaTroFwKcChEmRpSfT1Yo/anyUG1pp3aAxetscettsiBKQ9sKbe2GYbIWRP9ArqaJp3jl/8mQl155nrjPKXb110lJbSZMUXOuWwlrewLCmRNU+vncusYC9Yqui3kdazuNfb0t0mBrsev74e2KRV/8GEdt75dTsrMiGrjG67Ra1ddqsi9WFS0nUmolaxWQ1M4c0DPKW6zz4PVivijU3D0cQiE4N9eb1+jSyI8N7xVsrlN8+akbZkYELA7nJUMTW2LrjU2aWcQqlRCOZtZf8KW322aB6aJdexJ7ir4ecysIWITxKbTaSzLYiAapWRZhNxu1rW00BQIsKmtjZDbzcHxcXLFIsenpqQYZ7PT83akDrCptZWXr1jBRx58EI/TybL6ekbicdqrqnj/hRcS9niwgM8+9hglFD07DIOUPUN7Jp2m1ucjXyoxkUiwb2yMeDbLZDrNYDTKDYsW0RgIcHhighKqTY/E4wzH4xyamGB+dTXPW7QI0zCYsFnvraEQA9Eo0+k0XdXVgAh0vzx6lFg2y2Zbk73cBndyaorv7NvHrUeOcHB8nHds2DD3vrPt5StW0FFVRc/sLM2BAJfPm0euWMSyiXgOw8DjcNAYDDIUj1OwpVYNwyBbLDKRTM4NNTk9M0N7VRX/ft11xLJZ/nvvXqrcbjxOJxZK38eyWUqWRcCeRR7NZJ4RxH9w4ACHJyao83oZzucZisfnyiJrm5vZ0NLCSCzGzpERLu/qwu92ky0U8DqdjMXj9MViOO3sgsOO/s/bn27nQfy5ar5QhehlWao5u33arE/tFbBgKuL68SeVCp0dt4Vb7EElpaKiSatUEWrJJCuiIx6fwD/caAunBBSRmw6BejYFwToNTHnnfyiiO9scDrs+joB54TqR6E7uttnlKUXQmbTaqVxeePnf2wNAalXjbmhXyh0qAFa+tlxGjofpEKAn7OElLvs6fv/fWpPaFt3Trrv0c7BaX53LdZ7opCLZ8nUW8tKld7h0zQ6ngHaiHzZcD/EpjWTdeJ0Acv+DElsp5GHP72H5JSorhOsVdcdnBI6ZNISbKusAOu6dX7eH1ZiqY6+/Wt9rWuRMeH2QTumeUzGdp6ZZPf6xaTljqy5TzX7xJj3rska9ZalnvmmeMjT5rO51dgwuuEEqfuWZ9E99fqM9cgLs9qoT/np+3jdIx5pO9R1Ho+yx67tee5b0SDzOIjsq7JmZ4aMPPcRMOs1EMjmXyjaQz+Y0DBbW1uI0TZbU1/Pd/fs5MT1N0OOhWCrRGAjgczrnpmpNJJNsam3lu/v3g60fHrJT7bU+H3+zZQuJXI633XEHs+k0QY+HFtNkMpnk8aEh5ldXE3C7MYDpdHouRZ0pFOiZneWJoSGNGC0UyNh935Y9LQxgKpXiM9u3A3Iifnb4MNlikRcvW8ZoPM4H77+fwxMT+FwuDk1McHRigv+66aanMbZNw+Dizk4uPita9zidXLdgAXeePInH6SSRy7GgtpbDExPk8nlMw5AQjmXhdjhoCYVw2/Pii5ZFzuYAVHk8jCcSFEolkrkciVyO0Xich3p7WdnYiMfpfNZa9f6xMbprajg5PU1LMMhgLEYkk8HrdLKxpYUqr5eA201PJEJ/NErAHvf6ypUr+cA99zCZSmHaGuzL6+s5MT39jOc5b/87Ow/iz1XrXAYHjkHPSbVAxWxi16ld2ryDNdrAk1GBenJWEaFlSbClbTF4vIraCgVpjmczak9af42i5WJBqWi3W++tqle0mE7YxLFqWLJJIJiOPx0EttwMt31JtXSnQ8DmtoEln7HHqQKcFQle8cqKAIthKAuweKMAzmEzwL1+WHOV9OE9frXEHXlM1/LGT+t9liXAr7Xrf6YpIIvPioGez+p6Fm/U+vUfVXq6kNM9r75ChLx8ViDucOj72iuUDShb+2J40fvh8dvlRLQuFqMcVLeOzai00HdY1zAzDD/5FLz0b7TWwyelTZ+KK6WfzUh29fL3yaHyBhSN57KajOavgkCNiGxHH5NjlYzYnAWnMgRbXwn3fldOSCEvp2HDtfpcPPxT/W7xRnDbanf+EFz2Mjtjk6pMp6tplpNkj6EdSWUwgy1zPdN1Ph+GYZC2BVxS+TzZfJ4He3sZTyY5OjGBx+Hgqu5uxhOJOSGQxkCAmVSKVD7PiakpisEgJ6eneaSvj1g2iwXU+3wMRKM47XM9OjDAN3bvZt/Y2BzZLOR28/aNG7l83jwCLtdcRLylvZ2kzcK+/cQJIpkMPTMzjMbjmKjOPTU0hNvpxIQ55vrxqSlqfT5m7ddbwBvXrqXdnsJ2YmqKdD4/N9LT7XDwYG8vL162jD2jo/RFo/hcLqZTKbLFIntHR3msv5+XrVz5R/2XvmXFChbV1rJ7ZIT7enrIl9vxsllcLhcuh4NF1dWMJhLEslmKlsWi2lrabIU1v8vFq1au5Jt793JmdpbxRIKOqiqx+pNJdo+M8IMXvQjfM0ThoDq72+EgXSgwFItR4/PxipUrqfP52D8+TqpQIJLJsKKhQZG908lr165l/9gYboeD+dXVYv7bZMP/zUS08/bsdh7En6tmmor0AtUSBOlYqk27/7CivWxSUVwhB6mkojZfUFFrOf38rq+IHPXknQKRtVfC1a/Vpn7Ji1XTdnoEnImIUrz+sJwFtw9WXibQ8FcpMi9bMgp3fwee+K1S4sFqOQQzYzbJzhKQGIYdqRsCrCOPCkCvek0lrWtZSncv9QjEMkmBTSln165blMp3OMBXVan/G4b6v88cUIo+l1ak73CCaaeZHS69LhlRJJ/P2g5GXtcyOai6caAailloW6J7eaotXKuvYgF+9C+KvsP1AuD2xSpjZFPKaEQnNZjm3u/D2/5Nxx84pig7MqlrMOz77j+sezYdSuUvWqd133MfHNquqDwZlUOXzyuqb+rSz3UtIhYGawTYDofmx5eJb0/eBdt/pbLDZFSys4FwZeLbla/Suaob9dxNB3XVrRRDTZSOPo4ZnyXuqWJpuJGUBadnZ8kXCuQti8MTE8RzOXYOD3NJRwdBt5u1zc3sHh3F73IJLEyTsMdDwOOhzuejNxJhKB4n4HYzm04zm8lQ7/VyTXc3sWyW7+7fj2EYOA2Dtqoq4rkcG1pbuaenh+ctWsRUKoXP5aLK42FdczP39vSQyufFqLbTy+UZ3GGvF4dhULQsfLb4CTZJy+9ycdPixThNky9ddx3Bs8Zpuuz+9rJlCgVyxSLjiQQmkCsUGIhGKdrp70Q2y12nTvHSFSvm+tn/kBmGwYbWVn5+5AitVVXU+nw8f8kSbj9xggU1NcyrrmYskWDMVqnzOJ2cmZ1lY2vrnHLaS5YvZ151NQ/29vJQXx+b2too2rPGJ5JJFtbWPuv537RuHf+2YwcNPhEbN7a28lcXXEDJsnikv5/BaJRHBwYoWBbNgQAz6TR3njxJtlhkUV0dZ2ZnCbhcZItFCqUSS+rrOdrb+z/e93n7w3YexJ/rNjUAofoKa9lfrc09lxZgFfL2zPAkDJ2qANq8ldrYL3upvp5qW14gudL9DwrAB48res4kwVWtNPKBBxVlvvHT57Ku7/yGIvzYtNK0sSn9e3JI9eVUTK9z2aNJvXZKv2m+znfBTXIUADbfIAIaloC3sVMAWSxU+qEdLoFN/Cnpu+veKMnWY08oJR2shb4TEq1p6NDa9B5U3T6TrNTnB08ond7YKW33fE5gnElImvUF76qAeSquYxQLOs6L/xoe/LEAtNza5fIICB0uOLlX+vO+kPrUkxE7A5DXMQo5gbZh2l8oin7Xl+HQI3DHfypix1QpoFRUFiQ6IVZ+5zJdV+eyyr/PNodDXwe3qRvB49PX/gf0+vYl6kj49KvUeWA6oLkbrnwVq+raufq7n+OhSArT7aU2HeHLzhhvdi2g3u8nksnQ4vUynkyysrGRWq+XIxMTXNTZSUsohGNsbK6v+9oFC8iWSsyvrsZhi7cE3G6CbjfFUonJVIoSMJZI0BTQABi3wzEnRJIuFDg1PY3DMPjogw8ynhRp8yXLlvHiZcuIZDLcfuIE+WKRK+bNoy0UmiOzvWjZMnLFIjvt+ejFUommYJCXLV9OwO53H0kk8NvEubKtamykMxzmzOwslmVxYHycrnCYD91/P6ubmnDZYjUu06Rg17DvPH2aLz7+OO/YuJGAfTzLsphOp8kXizQEAnO8ANA874lkkq6zZGM3tbZS4/MR9njwOBx0hsNMpVIkcjkaAgFag8G59xuGwca2NuoDAY7aHASnaVK0LJpsadazLZbNcmh8HAtY0dDAp6+8kn67P3yJTfhzAFd1dzORTPLIwIAIiIZBwO1mIBpleUMD1R4PS2prOT07C8DbN2ygMRDg6NM/geftf2nnQfy5bo1dqoMHqwVqDgd0rasQvDJJsdeTEUWdkwOwaKM2/P/JapsFLMFqAViZmR6z69LhBmUETu6uRMCFPPQfUwRomnar1izqTXbqehORinqbYYic5g1W0uhlzXVQfXjJBcoILNkkUOk9BC0LK+c4vN3uSV8OA8crQjGn9yn6r6oVySyTVn14pEdZh9aFuqZVl8HpPSKVnTmgawqEK4ztYK3WdmJI/e1P3A7Xv1VKar/4nN2vbQoMX/kPGpwCes8X3qw0/sSA1h5L4Ny9Vmn9xRuha4VAv5jXWth61xLjma/n2HtAE+O8QUX0lCSmc8ENEuR5z1f+cLva2ZbL2J+NlEoqubT9PHxymEZ79Zrh08rwHHkMwvWY0Uled/werll0IZlAgBZHkNLUICvr1tDS2MzjQ0Okcjlydl25Mxymwe8nak/7WtPUREsoRDKfx+lw4LR7sUHAXOPz4XU4GI7HqfJ42NDSwi+OHCFfLBLNZskWCpQsi9Ozs6RyObL5PKZpMmWrtxVKJX5x9CiL6up49+bNPG/hQj65fTt+W4o1ms1y4+LFbOno4Ne33MKPDx7kwPg49X4/fdEow/E4XpsFvrG1lSMTE7SGQtT5/UwkkxwcHyfkcuE0DHoiEbrCYTa0tjKeSPD13bspWRYuhwOPw4HDsvA7nbhNkydHRojv2MHrbZnVHx44wIN9fZi2pvlfb9lClR3xO01zLuJuDgbnHI+bbGLeselpnhwaYp3dJjYYjVLn9z/tEXdUVdEUCPDLI0cwUEvc12644ZyMwOnpad7yu98xaRPlVjU18eZ166j3+5lXXT1XniibyzTnyHIOm4RXsixevGwZU8kkt584QaFUoiUY5ODEhFTdztufbOdB/Llq5cliizYq9Ts1CBiSD33HF9U7HZ9VBF0qib1s2q1cr/u4UuSjvYpgyxrhz2S1LXbq27QFRJKKFoM1ApFQrcRkNj9PQOpwqmZdFmYpt4JZBbsvuZwWTyhNHZ9Rert7jUh4Xp8i29IKpYR9QXj9P8Njj+uY4QYND2nthkwMjj5h1/s75GD8/F8lXtOxBB78keRVR06q1uxy6/pyWUWiHh9c+0apnpUK0HPAToEvsa+5JIBzumyp1YjuKZvWlLjeA5CMK1IFgfljt1XU7wxDI1dP7xEr/dFfCygXbVTae3JQjsfJXaptuzyK7B1OwO4RH++TE9R7SA6av0aTJlwBpdJnx9Xm9scC+MyYGPvTw4q469sVkfuC+lt8VpF9qai2wMiEnItfnIBVl2Eko7Qe3SYVO18QyyrREAwSy2ZZVFvLYwMDFC2LWCZDyOPhby++GJdp8pKf/xwLyBaLLKmrYzge58aFC7nz9GmylkWNz0cylyOSyeAyTTrDYebX1LB/bIzPPPoos5nM3LCTaDbLyoYGGgIBjtvjMGPZLGGvFwMR4BbX1dFdW8s/Xnopvzp6lFShwLULFnDNArUI+lwu3rJBioG5YpF/2baNu0+fZjadlkrb8DC/PHqU7poa3rR2LbceO8bJqSn67KEo+UKBZD5PLJNh18gILtOkKRgkmsmQsnvcM8UiXdXVHJuc5OjEBH2RCNc7ndw7M0N3TQ2mYTAQjfLzw4d5q30t2UKBBTU17BgcpGdmhjqfj1ypxO9OnsQCfE4nboeDXjvirfP7uX7hQjKFAm6HY04id8fQECPxODcuXkyuUGAmnaY/Gp3TNs8Vi/ztffcxEo/TGAgQz2a58+RJjk1OsriujgU1NXzgoovOYbFXe71cM38+d50+jceW0L1q/nzmV1fPtQzW+f0srqujd3ZW0+b+uE/lefsDdh7En6u25z6xkocfExD4g3Dpy2H5FtW0b/mgeqbLqV63zyavpeBr71P/8rxVUN0guc2W7mc+z+rLpSV+cpfS6aWSouF8VuASrgcsnQMEXNe/Weeub4fhE/o+NSRHYHZMIP/i9wsgMymgpJR1/xEoVcH9PxLg3vLBiopZwyDc/A0B6jc+IMGZsT7dayFfGUgSqFJ/dusCW27ULWfHKunaaxslXJKK6b4XrNU1v/j9er3pEBHwkV8qGl96oer4qZgckpYFeo3LrTa8s/vG3T5bHOYsu+6NOn7PPpEJaxqVmk9GdT2jPTpO/xE7nW9vmqWiPWUupHt+5JfKYHQsUyvZ8SeU5ViwVhyCP9bu+a7WfME6lRT6j6jd7oa3wVffLaegWLS12AvKungDctYikzrf4Uc1Zz5ch3HFq3nfZVv59+3bSEWmWOp1sahjHssaG7m6u5s6n49Pbd/OSCJByO1mLJEglslQ6/OxtqWFCzo6OLBzJ6+cN49bjx7lzOws2UKB6VSK20+cYDAWo8brpd7no97nI1Mo4LHJV/3RKIlcjmQ+z1AsRtBOhdf7/Vj2KM3DExMsra9nWX099YHAM45TfXxwkN7ZWapcLoajUaZTKSIOB6ZpkikU+KeHH2ZVYyPxXI62UIh4LofPrt0PxeMUSiVM05TiXD7P3rExDCBgmowmEtT6fLSGQnRUVRGbnZ0b0wpQ6/NxJhLRI7cs/mv3bvaNjrKwtpbpVArLsqjz+WizyXWD0SiXdHWxrL4eA2gOhfiv3bs5PTODz+nkLevXs6G1lb0jI0Tt1rKmYJBGh4Mdg4PMr6mhORikPxLRmrlcOO0e+VQ+P5euPzUzw309Pdy8dOncOhmGwStWrWJJfT1DsRitoRAbWlvZPTLCvT09AKRjMcZtJyqWzVLzx38yz9uz2HkQfy5asQiP/EJSpA0ddqq3X9Gd325naelWRN6+RFrgWAKh6malbhs6FAnWNAlw3/6FZxxLicstsHO6VA+uaVFN1uFSJOdyqcZ8NrFt0Xp44ydVA3d7lULvP6rIuFCAS16kOu/IaUXiNc2KwmfHlD4eOqHo9XOvh7d8RlrjUGG/v+A98KW3y6ko5qGqRuefHa2M8XR5VPfv2Q+RKUXPRlbncHvVxvZUoZVyNLt4Q0XXPZdVBP3br2lKW1m9bP4aOQaFXCV6jk5JXe5s8wU0nCU+o9LGbV9WnT2X1hruvFNZCbD7zPP2wBpTEX64TtHw6BllRQ5vh+YuWH+tnkvTM4uKPKtNDmmtJgbkSBRLuo/lF8LGa+VAOZy6vmxaQO4NVPgLHr+uLVwvR+OOr9N+eg//WigSLUEgMoZvvAle/y9QVUXv7Cz90SgXtrWxd3QUCzg6Ocl7L7iA+XY0etrl4pHJSZbYAiJ3nzpFbyRCtdeL19ZhT+RytFZVKb3sdjMSjxOyW5xA7VFBt5vnL17Mkro6Hu7rm2tF2zs2hsM0Wd3YyEuWL+fmJUvOSSvPpNOk83kG43Ei2azIa7aITUdVFTPpNC6HQ3xDlPpvDQYpFItEMxmSuRwrGhtpDYV4cniYBTU1NAUCTKZS9Eej1Pv9rGpqmhtkkrLLAqZhMJNOc2F7O/like/u389/791Lo/36er+f35w4QZ3Px/JcjsV1dWKrW9bczO7PPfYYfXZqP10o8LVdu/jgxRfzYG8vR23VtmOTk3icTpwOhxyfbJZ8qcRwLKZ1tfkCAK1VVRh2qvzu06dxGAZbOjrmUvamTb4rt/0B/OrYMUzDYDQel55+oTAnvzo+Pv6/+3yet6fZeRB/LppVEpAbRoWcNXSykkruOmtYQ+dSRZMut8aAlhnhvqAic19IqdV8rgKSxYLqtf1HBfJbXqD06aFHtIG3LxYgzYzC6q1w+S0VByBtt3ulYrqO8rWs2KIvkNPxyK2a+mWa+rltsdL9Y2ckier26Tru/KbS7mdb8zxF+4/+SiB3crfuxWXLp264Vtdz49vhux8WCDbNU5RcyELDYnj7F/+4tXZ74MpXqhXs9q+qZczj172//O/FG3j013ImrniFau0gB2f/A1JUO7FLoFjTpNetvETp8URUAG5ZeiaGYX/ZZY9Vl6lUMHhCpYvVl4vdHhnX4JRg+OnXW1ai6z2ktbng+RWSIMh5e/BHen7xGT33VEQyvOuvlUhQ3NYEMB36nIRqlWavaYYz++U0BauVfne54fhuXMU89V6/zbvoh/96P7z7K+CtxiqViOdylFC62ON08oqVK8+JisuT0/wuF93V1UQzGZY1NDCWSJDO54nmcgTtnuWQx8NkIkEinyfgdtPgdGKYJp+88sq5iPVXx47REgyye2QEp93+lszn+dXRoyyrr2fJWSMzF9bWksrnmUmncRgGBWzyXD5PPJdjRUMDkXSarnCYw1NTFG0Fs2u6u3nXpk3sHxvj9pMnGYjFSBcKbO3q0nz0dJp7z5yhq6pKGvPZLE6HgxsWLuTJ4WEMuyZ+y8qV/OLIEe6zo9l4LsdDfX2qsdt69QfHx0nn81R5vWyw55CXLIujk5NzRDO/ywWWxT2nTxN0u2kLhYhms0ykUsxmMiysqWEsHqc3EiFXKJC0p7mdnpnB73LRFQ4zv7qa8USCHUNDLKmt5VfHjnHfmTP80+WXP2PtvVgqsXNoiFyhoOeSSmGaJm9Yt45lDQ2ch/A/3c6D+HPRnC5FTokcnHxSG7A/rPTszz4Db/03gQuImOT1qQWpZLcheYOqe3r82rDr2yoa2gAP/Fgp6araSgvUDW8VcCWj6vvGErgv3iiwD1Rp0//9d1Sfd3qUcr3x7XrNgz/Wdc5bKanTJ+8UkczhEJCcOaCU+NgZHT+X0Wvddo3cbBOoP/RT2PegCGqGode1LBDIbLweLnqBnAwQEE6PSPzE6xeYda/V2gSq/vj1LrfXXfcmqa6l7fa95VtUjli6Wa/LZbSeU8PiJORzYttn06rjp2JyJGqaBaLhOmVQigXAUDkA/ZNAGAb2CWBNU2nsVFzP3h+WbvvDP9OxO5eq/S1UqzXeeYfute8w9B7WoBlfQPfRf0RrkklWouyJQdh7n9joa67Qs/eH5GAUioq6r3uT0ugnd2vdIxPQvECvMSzIp3WdtS3MTZnb/Xs6bnw7PqeTR3pOUVvM4LRMqmrqeLC3l1evXj23xNctWMD3DxyQ6ppl4XO5WN3UxLzqarb19VHj9WIYBquamri4s5OBaJQqj0fT0HI5Am73OUSsMit7PJFgOp0mWyxyaHycGp+PsUTiHBBf2djILStX8sTwMA7TxGXXewFSuRwfvvRSYrkc99kDP9rDYdY1N3PV/PmEvV7m1dRwYUcHs+k0v62r49jUFNlikaJlcVFHB02BAP12Lb05EODajRt5+YoV5Esl6v3+uZnsi2priWWzjCUSzKbT5IpFFtXW0hUOc2p2ltFEgr+/+GLW2CBuGgZ1Pt8cH6BkWRQtC4c9HvbSri4GolEe7O3F53AQ9nrpjUSIZbNzw2uCHg+JbJawx8O1CxYwFItxeGKC7upqNra1YRoGfZEIjw8NPeNUtvFkEp8d5Qc9HqpsVbjJZJLP79jBimeRrT1vf7ydB/HnosWm7U3YISZ4Y5cizN6DAokHfywxEVD0d8uHYNsvBDyzdvQ03i/w84eUni5HRfmcmNzN87UpB2sENAcfESENQ8DhcIn93XNAwJvP2mIqMwJTp0u114d/Bnd9QwBgOrW5b7hWgG8LeeByC0yufQN8/6OQnBAxrXWBUv6+MGRRdmDPvTpPqaQU85orFe23L660fVmWAHPfAzYD26eMQzal9Pq6D/zv1juf1X17fJVRppMDFdAFtdTd/d+qJY/3Q127eujBZoDbo1AzCUXzTrfWsa5NjlFiRusQrJXD1NQF135W6/nbrykLkkvr+Sxar9/VNENmRuIxDpvhbwAXv0TXWgb1kVNyAp68S85bfbtq8Yap63A4dE2Tw2plu/XzsO3nWuO6FvXfP/hjRfemA7B0b8WSrrO+XYpzXlsj3irp3PkcTtNki5nhTGoKl8NJLQXqZqKcHumEs0D86u5uvC4Xu4aHWVpXR380yngyiQE8b9Ei3rt5M/Ps9PtkMsmdJ08ybafBy/rq7vLnCU3nKs+/Lqfg6/1+xpNJptPpcx6vYRi8ds0anhwe5sD4OGdmZpi1CXZ+t5sPP/ggv3r5y7l2wQKezZqDQZqDQeZVV/Ozw4c5ODGhSNoe//m8hQt5ybJlPLp9O/lSiYd6e5lMpVjX0sIFbW34nU5ypRKb2to4NjnJtv5+LMsilssxZivV1QcC56i8Abxj40Y+//jjxOz+9GsWLOCi9nZ2j4wQtxn9DsOYA/mg203vzAwlwHK5MICgx4PX7WZZQwOvXbOGTz/yCPFcbi5T4jCMOafmqeYwDBoDAdpCIYbicdK2vvtsJkOmUKA+l+PQ+Dirmpqe/f/XefuDdh7En2uWz2lC1/ApWHSD0r0T/bYMZ5Vqzge3wcUvqpDVWrrhFR/Sv5OxShReKgr4EhEBYnWjap+ZJJzardc3dKgQGJ/W3xestYVIjmqWttOjVLZpt1hlUgKNzuWKgEdHFGW7vHqdZalFa/ONSg2H6lTLrm8TyFY3Kl08eEw/L9kMay6HJ/cosgzVCUhMh9LJBpVIGJRpeOCHGsk51qe6ecdSrVc+J+ekpklDQTw+pZvPHvn5TBabFgif2qNe6mREDk11o/4+OyFHJVSvYw73yKEqZzhSccjZA1RKJaXm2xerbNDSrch60XpNPuteI7b4tm0iwdU06ve9B3W+6kbV5h1u8QeO7dA1mE5FwWcOaJ2WbLIv3m5pA5HUqhsrJEOKtrhLo17X2CmH4+IX6fnWtcoZOrhNz8rttYfCpAFTxMaW+TYBcLNKOglbGTCfhdWXATB/8BCNbhfdLhMjMsFAOsvqx38FS+fBvBWAgPTSzs65wSH5YpHTMzMULWtOLrVs9X4/z1+yhPt6enA5HOSLRZ63cOHcvHOAFy5dSsDt1ojRVIqg2026UGB+dTV19pS1s81pmvzT5ZfzlZ07OTI5SZ3PR2d1NR6Hg/5IhG39/eeQvCaTSbb19ZEpFtnU2joX2ftcLl67Zg2/O3GCr+/eTUc4TNDt5o6TJ/G7XASBV916K/vsOr3TMPiHSy/lVatW8ZUnn8RA+uzlGvx0KjUHqO/ZvPlp172oro5/veoqhuNxArbYTTKf55UrVnB3Tw8+p1OqblVV7BoepjcapWTXvGfSaYJuNz6nk3gmQzybxe1wcM3ChXxz924smOMcnD357GxrDAS4sKODHYODdIbDHLJ759tCIQzDwMzn2dbffx7E/wT7s4K4YRjXA/8BOID/tizrX5/y9zDwI6DTvpbPW5b13T/nNT3nbXZMYDI7DvMyYBnanANhRUH1dttXdOqZGefFvKLj8T6BQEO7ZD8NQ0B79auVmh7vEwANnVCtdMkFimKLRYHRRJ/+7bF1y8syp1V1Ss/Wt2vj714tze50XIBPSY7E2ivU0z01LB3xra+AH39C/27utqeKTUtYpUzWCzcIjMsRdzZdmdZWtsPbFYE3zbfVze5V+nzj9XJ25q/SvO1grZyVQ4/CSz8gcl5kQhmB6gYdK5eF3Xcri2FQacG6+IXKGpimnJbIhBwdjw0OC9Zo2IvLq0g3l9F3AxHmgrWw9RatDeg6B44KXF3ec2e7g9Zh4foKeTAVs4eu5CsRvvMsTfvxPkXIubQ+D2Wd9vmrVZ9ffhHEIyoNePwqt3QtrwywScfV9nd8p5y3yIRA2eODkkPnNww5EsOnVfZ4z1fh8GPwk09ojZxutTAuWMsWn8nhZJadkQRmrkinleMlZlolhzd++mkf0ZJlsWd0lNMzMzQFAiyyVcbi2Sy/PXFiTp/93Zs2MZVO0xoKsba5+RyymmEYbGxt5RUrV3LnyZM4DUPpXo+Hec8wlGT7wAA/OXhQ+u4OB13V1RoiYou25M+SEJ1OpfjEI4+QzCnTcF9PDx/YsoU1zc0USyU+99hj/PTQIaZSKQZjMba0t9MUDLJrZIT12Sz7xsZoC4UwTZNoNstXn3ySR974Rj52+eUcHB9nz+godT4fIbebqVRqzsE5uwRwttX4fNT4fNxz+jQ/O3yYfWNj9NnEwO6aGi5sa6M/GiVTLOIyTVY2NJDK5+mdnSVp67KvbW5m79gYd506xY2LFjGRTPLjgwcxgTesXfuMa1Ze57esX88ym7Fe7/czlkic8yxcZ2VIztv/3v5sIG4YhgP4GnANMATsMgzjt5ZlnS3S827gqGVZzzcMowE4YRjGjy3LOj+j7v9qliV2eXWToq+6Fg3kqG3WZu1w2RPOnsEKebj1CwL9qnoxwO/9nlTR3F5F5D/9jFK8DR3awEslHXvlxaql7r5bgNW5vJIWLsZ0Xd6Aol5/VWVS2JILpeCWjoMVV6o1UA2WKQZzWd/9ybsEPr6gUvhN8+zUrSGHJZ2o9I1P9Ot9rQsqRLKyjffpOkzTzhysk155uEFR98AxyZ6C5nPHZ+AbfyOAaugELLjohWL1//arqg+7ferz3nyDjr/5Bjk3937fHpbSpD70Qk7rYTq0Xqsvh5UXwbZf6nylkkA/m9Zr2hfrd7/5Chx8SBF7saBIuHZt5Z5aFijK9VdV1jlcL0Ki0621bZonp8Tj10z4hg5xGtZfU3EuVl2mSPnJu2DVJRXWeV2r2tTKegENHWKxJyPSaZ8dqwzKic/qmt1e8QzyWTk5Y73KBi2/yHYoi5LdXbQe54U38o5bv8gLBw9S8AVodhi4Wi7X53Dy3M/qSDzOe++6iwPj47SHQnSEw+wbG+M9mzfzhccfZyASIeTxcGhigi3t7bxj48anSZpmCgX+a9cuDoyPc2h8nOl0Go8NJC9dvpzOcJjReJzTMzN4nU68Tiff2rOHlmCQhkCAsMdD7+wsLTZru9rn45KOjrnj7x4ZIZbNMq+6ek529dZjx1jT3MyTw8P88MABcsXiXKvczuFhLu3spCkYpJBOYxoGJWDYbpErAT2zsyxvaCBfKtEUCDCeTOJyOHAYBsPxOI8ODPC5xx7jPZs3z41gPdsGolF+evgwyVyO/kgEr9NJoVhkMBql1ufjnRs3MhyP43e5CLjdBNxusvao1VeuXEnA7SZTKHBfTw/JXI6PPPggxVKJhbW1/OLoUdqrqlj7LNG40zS5fN48QKNYP/HIIwxGoxiGwXzg2u5naV89b3+U/Tkj8c3AacuyzgAYhvEz4GY4R2nPAkKG/pcFgRngPNPhT7FQrTbL2JStqnVSPzd2qn48dFIR+B1f1wa76lL9bqxPUfj0iDZ8UK0zl9bv8drKbCl9b5ynY8ZtoDYM2PpyjR0tFRWNffGtih7Lg0OqGzRC9KZ3njuXet4qMdatvD4RubTkYkGOwJffqRT87Liuc/01AuHypLSffBJatsChB+V83PgOReetC88l5IEckGyqIskaqFJL25Wv0j38+JOQLKq+WypVyH2Ros3UH4EjO7SmC9YKwN1e9cmvv0bgO9EPD/9cr3F5tAaBKkXqhqHfveojEt4BnefObyhijk0prX/bfyhr0bZQ8rVjfZVpaXd9A275UuWetrxAz7b/iNZv3VUacnJyl4ReHvihnnGpKOb+xuv0HJ5qpikHYcvN+mw89BNJ0s6Mau3LZMj6NkX+++6XBn/zAjlagSqVDlJRZRPScbtH3ynQ7zuqNrVMQg6HacoRCNVilEq0pGcgGxWBzuPT9XoDgFrsplMpXvqLX3BofByPw8F0Oq25LqbJzqEh+iORudGe1V4vTw4P85rVqwmdpW8OcNepU+wfG6PW56NQKlHl8bCmsZF5NTUMxePsHhnhG3v2UCiVKNlTAA3DmBsM8rxFi3hiaIig202D389HLr8cDINHBwZwOxwkbTGXoxMTbB8YIFcsUuX18uKlS3l8aIhCqURrKEShVCKRyzGWSFC0LF6+fDlHdu3C5XDQMz1N0bLmyG3/uWsXn7nqKjwOB83BID6nkxPT04wnEtT5/WxsbeXE1BS/OHKEN617SmskapMzDYNIJkO+VCJnt8o1mianpqe5qKODhbW1YvpnMjjsHviWYHCuVFEslRhPJvnAPfeQtOVj94yOcoFp8vuenmcF8bOtvaqKD118MV/fvZvxZJKA203LU6a4nbf/nf05QbwNGDzr5yHggqe85qvAb4ERIATcYlnl2ZTn7f9kvqCkSO/9njZJfxVgCHCO7VS0GahSKvje7yl1/cgvBC7ZtCZ/1bapv7ust14WaolMKq1ayAuYHC6NC73uTZXze+02E38I3vwZjftMxuQ4NNjRysk9Ym6Xa8ChakXCZZ1wy4J9DylS/t1/qf4aqtV1R6akQHfJi8Vsf+hnAk6nR2n2sV5Fk8ue+lGzbfXlArue/brn5vlw0c0V4t6WF8CvvggRWyo1OSvHpVQU+JQzAKM9KjU0tCuzYVkCqmBYGRCMiqNS26rjvfVziqarG/Scyta6QNmF0R45HXVtcnru+75aAicGBPwevz1WdliOCOhZ7H9Q17d4k/rQGzvVY//QT/T3Qh7a7TLE6X3wqVvgileJB3F2e1nZTFPEtYPblH3IpuVUvO6fxaIHkQ+jU/rZMJV5uOiFIsF9/QOVuepYerYYAvzd9yhjUihIVa+6CX7xWf3uoheqtNJzUM7Kog1aF7sR6d6eHsZszXKvPWbzyNQUndXVc4NHyuntku2kPZN4y5nZ2blxm4Zh4DIMItns3Gt/ceQIAXsQC8ATg4MYttxpOXX+0uXL+duLLsIwDHpmZvinhx4iVyiQKRap8ng4MzPDE8PDc+fwOBy87+67efXKlThNk2yxSFsoxEgiQXsoxKeuvJKGQIBel4u/u+gi/v6++zAMg/aqKp63cCHT6TS9kQhL6uq4rKuLRwYG5hyBizo6cDudNAQCnHqW8Z4NtsBNrlgkVyzicjhwGQaztrCOz+Xi3Zs28aUnnuDM7CzxbJbrFiwgUyjMtZiVB7pYMJehSOXznJiZ4dKurqedszy2Neh2z62tZVn87uRJxhIJqjweErkc/7lrF++/8MJnfFbn7X82wypHJP+vD2wYLwOusyzrLfbPrwU2W5b13rNe81LgYuADwALgPmCNZVmxpxzrbcDbAJqamjb87Gc/+z9fVyKRIHjWQIDnpKUTMDVIwl9PMDVdIamV2cZgDz1JVFKf5Rnb6cRTmOFeMduLBW28Xr8dHVl26jZ4blRdtlxG6Xfs12SSIpEZZoUwF7QBZNJWPCuV5sZa4nLrtYVcZUhLmYDlDVTquDOjUCyScPkJFrN6fSD8zNPEzrZCThGv6dC9n60Dnc/quOlE5XqLhUoUbVm6L9MhJymb0rFCNcoElIpKMTvdlfc6XeIBPJOl4hpQkkkqksbSez1+e9pYn62b7phbh0RVC8FwWPXwVExReqmk89S2iEsAdrQbta+jiD1kXnPaQ7VyQp7JJgcrQ1ZAn4Gq+nOdj/iMPazGkIPl8SvbUCrqXgr5Sp8/9j5jOirDcFxeZQYmBmw+BGoNzGhYic5vkAg0EAyHmUmlGI3HwTA0QATVxxsCAVqCQSZTKdJ2DbdoWYQ9HmqfgaQ2m8kQzWTm2s9yxSI+pxOHaeK3p2yZhjEHKtlCAcMwsM5yDFpCIVz2Z2bUns9dLJVIFwpzEXzRVl4zDAPDft+86momkklyxeKcoEtbVRUhO9pNJBIEgkEGolEc9vkLpZLU0pzOuZngHjvij2Yy+O1Z7fGcqpBOu4Ws2uudOy5AIpdjJB4nmc9z9r7vd7lYVFuLwx6Eks7nmUqnwbL0abHXMuB2M2FL2JadpJLdsrawpuacEaapfJ6pVAoLaao32mp4U6kUU6mUpse5XPhKJWKWRVtV1dx6PlftT8WeK664Yo9lWRuf+vs/ZyQ+BHSc9XM7irjPtjcC/2rpE3XaMIxeYCnw5Nkvsizrm8A3ATZu3Ght3br1/3xRDz/8MH/K+/8/YTt+Cz//Ig9f+ddsfeCL2uA7lioSNgzVL3f/XhtzqSTA6FyufuKJfqVTA2FFwl3LYfAk/Oif9Tu3V1HW1a9TxH9qr4h0/irYcI1SwKNnRELz2lrpY2fUh75kk85fLMLQEPzVN2wxkF3w0Zsqs7ldHmUB5q9U+vrMwYpjUbKgYzF8+QmBwe574IEf8fCC69k6uQcS03aq+g8MVygWFOGf2q3jegPw8g+eC2jJGHzoOsgldc50AmIT4AkKrNNJKOZUCmiZL1nSMuPbspTluPcbun6HUwpur/6wiHOgNYhOVkDt4y+C03uV3TBNXdPqrfCir8NBS2n+cr27oY2HW1/J1ou2wH+8XdFyeQMcHIANH4Dd31droWGobj94Qs/bsiopbn8VfPb+c8V/yvadf5SDUFVvP8Neab6XlerKls/pHE4X3PM9GHlcjodpwc5fSZu/HGGVinJkVlys6DwVgRd/E354r1Lv4Qat6/ZfCOA9fijmefjSd7N1fg1j++/gvZMWqRL0VLczbjnY2NLC57du5cT0NIZl4bUs0oUC3bW1XNLR8bQhHSCA+fLOnZyYmqJgGDjt9qkldXVcv3Ahtx07xp2nT9NRVaX0crHIRy69lJQdiXbX1MxF8gAfvO8+otksT4yMELKBbiadJpHLUefz4XQ4iGUy+N1ufrJ5M0Yux4O9vQTdbq5dsICLOjrmnIS777+fsbo6ZjweHunv5+D4OJFMhhKwpqmJC9vbGYrFeO/mzVzX2sq39+3jrr4+9o6NUSpJEOjstq53bd7MRWfV6+8+dYovPPYYfdEoGAZTySSGYbCisZGvPO95rGtp4Qs7dtCTz9MYEAfizOwslzY2ciab5Uwmw91lgRzbYfnopZfyvAsvnFvbIxMTfPOJJ+ioqsLncjEaj9NimrgdDrbPztJjR/YBj4d3NzSwrVjkM5s30/wcD67+XNjz5wTxXcAiwzDmA8PAK4BXPeU1A8BVwHbDMJqAJcCZP+M1/WXY6b2KcgsFRUuFvNLbF79IrUj9hxWJrr9WtdLJQRg6rs3aQOIrZwPa4FERjAYSgCFn4NAjAuC7v63oLJ+FE0/Caz8mwQ/TIUAHtUj1HoDiOm325U29XDmpqlUL1WiPju90K2p3eZRqHjopAMoXbILdrKaFXfMGSa4WCzA4qzrq1X8lAM9lYfutYlsHw3DVays16J79+n3z/Iowyf0/1ISxsgWqNLSlPO+87zAcmtC5poZ1HRuu1fpuedFZLVvomKu3SjK1c5nIX8W8eAjv/orS07/5DzHpLUtkr5ZuAfTwKbtFzrAJhR6dxxcSs77c9naiv6LgZpWAsyJep1vs80Pb5aQZqD+9PGzGNPWZiE3Df/01/N33BLxli83IiTnwsD0Cdp5EXlIxkd7aFlWcpLM5B4bBXMRdzqZ4/fZ57ec9Mwonduoe2xbpdS98r5jokwOQzcrBCVfZI2gtgf/P/5Xm9iV8dl6A741GWBzrpfnyl3DtyjV8evt2nLYIS8jt5p8uv5wGG4Ceyfx2yno8mZS+eSxGoVRiTVMTHqeTFy9fTglppgfcbj6wbh3dtbVEMhn2jIywM5lktT1xDWBzWxvf2bePkmUxnUoxkUyCndJP5PPks1nyxSILamv5wL334jRNnEDWVnZbWFtLUzDIHSdPMpVM8nhfH9lCgb5IRLrrdiR/anqa7poa/C4XB8bHWdbQwFvWrWNxbS3/uXs3qXyesUSCgMvFbCbD0vp6dg4NnQPiV3d388ujR+mNRJhIJimUSmq1m5zk7++7j6/ecMPctLayJbJZfnLkCCsbGnA5HCyuq8Nji8PcsmIFNy1ezEg8zi+OHOGOkycB6I9EMA2DhbW1NAeDHJmY4OjUFE4gVSgQzWapLhRI19Swurl5zmE4b/97+7OBuGVZBcMw3gPcg1rMvmNZ1hHDMN5h//3rwCeA7xmGcQhtNR+0LGvqz3VNfzGWz6i/thzRFfKKag4+DO/7ugDs7m8JnFq6NYFr3CaSdSyFn34aXva3lRa0MwcVUdZ3aCPu2af65uBxAbrfVjcb6xXYub2VKWW5tGrakQlFWJ0rBJCrLquk4Q1TJLByjzWmgK5jsc4RqoZUQuzoqnpt7L//LjzxOzkQl74U6rvgpWcN+tj2c0Wgda1iTP/yc/D6T6g9KxmtjPMEXX9kQut05oDS283z4fo3wY/+RcA1MypHqGRJSa1YUIuVwwm//gJ0LTu3nzyTUOaixiaDWW6x+Qs52HGbwLqhU/dyeLvq6M3zVQcu5OU8tNtAaRgiop1NRjvRL5Dc+DzY+TtlPbIpPec7vylHanLQLpOUpAPff1QRbz6n5+j26Xnd+gV4++crx77nO3KaLny+sgWxaaX77/munbYvwk3vEK/hbFuzVaI90yN21t4ujVjIeSsW7El3OWV9AmHV8zc/D978r+JK3PVNfbbGzogbUE7fl4oQCNMN/Mu8epgcIL6oixfffz9DsRgep5NOW1J1x+DgOT3boLTvI319/PbECZwOB5d1ddFdXc0H77+fE1PacpqCQT6xdStXdHfzqlWreNWqVXPvn0mn+eQjjzCdSmEg2dZ/vPRS5lVXc/PSpYwnk3xxxw6iuRzzwmHylsVYIkHQ7SZfLLKlo4OQ282u4WFm0mmqfT5cpsnvT58mmsnwsa1b+c3x41zlcNAaCmFZFnecPElLKITX6SSayZAuFBiLx5lKpzk6McF9PT1c093N1vnz8btcFO2UfjlNny8Wn0bqczkcvG7NGvoiEabSaY2CzWYpWhaPDgxw889+Nje17CqbNT6aSDCvunpOVnVhbS2rGht55yY5rqPxOP/y8MM8NjiIZVmUEA/g0Pg4DfZ7ItksuXyeuqoqwj4fA/ZQl2qvl9ds2nS+Hv4n2J+1T9yyrLuAu57yu6+f9e8R4No/5zX8Rdryi+Cub0FtSSBqIXZxPqeNdNF62NkiMB48rjnapmkzuhcIMO/8BrzlszqeZSmyT0ZU505GlV6eHhW5adWlZ9WOi0qX7vo9HNpm13MLih6nhgVeV7wCrnx1pXfcMNRONXjcFoRJwoU3wmUvE0Gr54Aci3Id2rJg5KgEXwD2PgCv+7rOXa7lH90hB8PpkrMw3qc0f02TiF+WpbavyAT07BUAf/sf9LNh6B4vfL7IYPEZu32rpFp3NiWg94VsgRM3/ObL8LbPV85f16o1TcXtMZ4jAmmXR85OoKYSSbv9cgKGTkqStlQUQM5bxR+0dEJZE3/IZpCPwn0/0jpFJkWgW7ReztjEIHSvgwd/qKyJNwRut0oD+x/QZ6McVfcdVp06PiMn0OnWM1h6ge43k5K87VNBvKkLXv0RuOu/RT6sqhPhzWF/NkwnOL3qR1+6WWtdrt0bpoh4/pBa5gaO6dnXtcoxqW9XJsBfZQ+rMfn18Diz6TRVHg9ep5O+aBQLpXQf7utjNp1mYW0tS+rq+NfHHuOHBw7gcjio9Xrps3ug+yIRmoPBuWEjX9u9m41tbU8Dv+39/cym08yvEY9jPJHgtydO8L4LLsBpmrxr0yZM4IuPPw6GQcjl4qpVq+batuZXV3NiehrTMMgUiwRcrrkWsdlMhoFodK7OXLayvGudz0cil6NgT2abSqVoDgaJT0/TF43SEgqxua2Nh/v6yBaLxOJxFtTU4HE6ufEZZnZf1NHBqsZG9oyMEMvlyJdKEnQpFnEAIbcbEw2NWVxbS0MgwJHJSY5PTRFwu6nyeFjd1MSekRGS+TxHJydJFwo4TJOg281oLEY8n2cknyeazdIaDLKkvh4TOQQOw8DtdLK5rY06nw+P888KQ895O796z0XbfKPY4xN5MF3qUy6nJXNp9RC/8h/h829QNOgJKPJJxuxWolYY65EkZ1W9Nueu5Xr/0ScUIbUu1MZ7dIcEPUZPQ3RaoHXD2wRwhmkLvvgkzpKKCUCO7ADnl8VMPviwwK6qXszqbEqb+IqL9fvOZZUI/cDDAtXffrVSizXMytjTbT+DC18gIPAGbBEVm+1uWZXIv22RouxffaEyM9vhVoS84XoB9cgpyYv6qwT8XSsqc72nR2x2uKGoOZtWtF+OvkEA9qL3K4U+0a97esG7bEZ8N4za+uOWJYb/wvUSiJkY0HW2LjyXbPdUy2fhW3+ndcCCK16tcaRlKdzpEQE3aLJcOiGn6MROMcCzSYErqJUwkxSIW5Yi+JlRCDfqmY0eBH+1HLh5K5Rej02pBHFqrxyBq14rR8iy5Igs2az7GD6lYwSr5cylE1rPUklZgXK2J5vW5y0yoci/pklOhC8kIL/479QvnxzUPd7wNk6NJFhcX8+RiQlABLBEPs/+sTHuPHVK7GkbpHbYQzg6q6pI5PPEs1n6olE8Dkelbm63YI0mEk8D8VQ+f44oicdmZp9tz1u0iEcGBqj3+6nyeIhmMiysraXK46FnZoagy0XKljl1mSbJXI7umpo5udOLOzrIDQ4Sy2aJZ7OsaGggXSiQKRRoDARYWFs7xy6v8fmwLIuxZJIHenv5wrXXsrmtjaFYjHgmQ53fz/KGBhoDAR7q7eXg+Di1Ph83Ll5Mrc/Hx7Zu5dTMDPtGRzHRHPcqt5uQx0Min2ddSwtjiQQHJyaIZbP0RSIYKHJ2Oxxs7+9nx6A+X6dnZqjxegm4XPTMzJCzWellG4rFiGSzFIrFuTa0WCbDW9evp9TX9+yf8fP2R9l5EH8umsOhdp377pHqVyYh0tDZzOJAlYhPWGo9GzujjbWcWp4ehR/+szbU6gaBiz+kaNQfUs+wNygiWXwGZicFbEd2wNHHYP5aRegggDu1Txu526fzHn5UG/fyLYqupwYVtb/sb58ZvK56jaLjMwds4KIyGrRYkoNx25dh/0MCw6teq7ao+LT+1rlcQFy21ZerhcpC9wGVKWkzo3afcwJaFkpoZcnmSkRb16prD9XIWYhOqHfa+5S63rwV8O4vy1HY8RvJ4a68RBH+xIAibyxYdbmcFofjf2bVg8AwMgEunxyhfBbu/Loct1wappJynvIZAfL931dW4uefVfbC7VNaO50QMK+9qqJ6l8vIAUknNFN+ZkT35Q/Zc8/3C/Cr6lSuqG1R1P+Lz8IbPqnzQUVAZu2V4k+0L66UWEoFvW7N1jnpVY7vFOBPDcuZcHnkLHQs0Weucym87d903yd3wZ57uCGa5mfhRVxe5SF1+gBmOsHGpgb+c3Yay6MZ25ZlsXd0lJDHQzafZziRoMWe3tVWVcVoPE4ylyNTKDAYi5ErFPjcY4/x/gsuYOVZUqAbWlv5/enTRDIZnKbJdCrFi5ctO+exdNmp9V8dPUo0k6Ha6+VdmzYR9nj44cGDHJ+c5JLOTnpnZxmKx2nw+/G5XGxua6MzHOZ1a9dy1+QkNV4vS+vr+ehll3HHqVPsGx0lUyjQH4nQMztLplDAZZrU+/2ULAunaeIwTTa2trK2uZkfHDjAL48elUig00kim6XW5yOVz3NwfJyPbd1Krc/H1264gY88+CCPDg5S4/GQt9n1LaEQB8bGmE6nKZRKZAoFnKZJvc9H0bJY29zM4YkJts6bx87hYWbTaY5NTrKioYFssUjeTul7HA5G43GqPB78bjfza2o4PD7OBe3t3LJiBZd0dfHIeRD/k+08iD9XrbpJachaWzM9GVW0VyabgSLcn39WURWmppid3itW+oUvUAQ1fFKp6KUXiIXu9gq0d9+rDXbhBruOHFPUW8oLAI4+qo2/e41APR2TM+ELwcARtRTlswLw+IzStUef0Cb9ovcp5Q06Vj4rFbeX/Z0AtveQ0rTlti/LAgw5B1X1mpT25s/A6z6uFLrHr5rw2SSsZFSR/dSQousy8SuTEmikYlDfCtODOvbgcV3rze8V4FiWSIKZhMCppgm+9leq21/1GjlPY33q9X7it7q2lm71tZdKGlMam6oQAJ9aEyyVBJIndur5XfziSo92Jqm/lyetlfu0E7MqjZRr/qZTgJ1NCUSP77SFVsI6bz6re33pByoOkdOt1rP6NjkCe+/Xc120QcSz2Qk5NMOn9IxMhz4TE/0qE5QdvXI93BdUzXvDdfrbks32czft2e7283vkF3KsHv21XepIQYsdzWOvjdevLMKTd0FVAxvTMbwDR4ilkxRMN+GaemKndvBSfwv3Lr+OoViMaCZDwO3G43Dgc7lI5HJMJBTBf+aqq7j16FF+e/IkI7EYneEwV3d34zBNvrZrF1+6/vq5VO/iujr++sIL+c2JE+SLRd64du2cjnvZ7u3p4Z7Tp3GbJoZh8M5Nm+gMKzNztq55vljk0MQEE8kkdT4f61taMA0Dt8NBtdfLRy+/fO6179q0ibF4nOt//GNyxSJeh4N4NstwPE4JCLrd3HzW9LBtfX081NvL/JoaLMviZ0eOsK65mTq/nzqgLxLh5PQ061tamF9Tww9f/GJ+dvgw9/T0cGp6mryd6h+MxVjT1MShiQmcpkkkncbvduOy783pcPDk8DCWZc2xyuO5HF3hMFUeDwfGx/Ha5QCnaRLNZNiyciVNwSBfuv56wmex+8/bn2bnQfy5ag6HwHjLC6QVHpsSK/2RWyWUMnRCqfBkVNGXw245KuS0gQarBVL+sN2aVNJr56/WsaeGBSYv+1v47GsFgkVTjHiHS8DWdxCwIFhna5gbYkFnkhAbFPANnRDRLptWz3AuDd//GNz8HtVE99yjaLmpSy1ONU1KC//2awJ/qyQmt9OllLXLXWGQL1qv95VtelQksmJRbPFgtdL0JUvvCVQL7A8+LCCralCpoG2h2OapuDThV16sqW0rLhZwzowpfd3SrbX89Zfg+e8UL2F6RI7BwDFFvVV1Ujrb8vyna6CfbU/epRqxN6i1HTguGdrqBv2u7PyEagWg2bSu8fS+ynS0toVa/4lBpb0L+Uq7XLn9rLGz4jCVPzfXvwV+95/62elUFqehQ1H39LDU7W79vO4V5CjNjskhuvAFyq4ce0K96G6vHJbmeZVzlAWBzrZiQWn/tVfIKSzYzmAqps/ub/9T593/oK7d4cQdqGJtdIKc6YaF65lIJhhIpmmIzXByaooikMjn2dDcTL3fPxfFBtxuFtTUEMtm+derr+Z1a9bw2UcfZX5NzZxE60w6TTyb5fGhIe4+dQrTNHn+4sV8/FlahIZiMX566BCtoRAuh4OZdJpv793L56655mmyry6H41kHhpxtlmVxZnaWnxw+TCSToSscps7nowSk83k6qqp407p1XHKW0MrpmRmqPB5Mw1Ak7nAwnUqdc9yzr8Y0DF61ahXPX7yYvB1FF0sl/nnbNoJu99yccwxNh1vR0IDH4WBeOMyxyUnq/H4i2SyL6uqo8/kIuN30RyK4HQ7SxeJc73mN18t4IkF7VRVVTylVnLc/zc6D+HPZDEO11R2/Efjm0hoZCQLHbFqgUMzbKWpDm3gmqY3Z4dR73LbASdEW4mhbBB3LlAL3hQSqBx9Wbdcq6X2hGjGzB4+rBm9ZNsvcrouXz7fzTv0cqhXIHXlMgNB7UAC78Xl6/8SAWNen9qpdrapeoFsqqPUM4MQT6kcfOiHS3pab1fLmdAnAf/QvclIMU9mFQBWs2qqUcT4rJ+Dtn5fy2t3/rcxDIAxLL6wIvWRTStX7QmLtt3SL9V1VpyjW6Ra47n9I5wrXq74en1VpIlSnkZ69hwRWFkqxnw1yAI/fLgeiaEvRhuu1ltUNAkvTVFrZH9Z6ty/Rs65u1NjSbEYAmoxWovzGTq2xVVRGo2NJpU5/ti3ZCPWflCOUS8Njv9E5LQuueKUco6tfJ2W7nv0C3Kp6ZRmOP6nPVU2zhsosXPc/lwjKLXm77xGQt2d03S637tsw9SxiNgmyWJjLHJiGA6/TAocDt8NJ0Srx+9pFeFyuOVJYPJdjQV0dbbaIy9auLtxOJ9/Zt49MocDG1lZ8LhfJfJ6g2z1Hljs2NcW39+6VpnmhwNd378bndNJp67X3RyJM2RPQyqzwct281uejPxIhVyz+n4lbt584wW3HjnFmdpZYNstIPC7JVbuO//IVK7igvf0cJ6E1FGLH4CD1Niu8ORAgWyoxkUySzudptklmT7WQx3POPbxk+XJ+eOAA3bW1DEYiNIdCXNTeTkswyEWdnXgdDl57223Es1m6qqtZXFvLTCbD327ZwsN9fUQyGTwOB16nk+PT09T5/VR5vbx38+anOTXn7U+z8yD+XLf+wxV29uBxbY77HtBm6K+qtKCV7BqqvwrabdGX8ljLhkWqYSZn7ZTqmMBt840Ck62vgAMPwY7bBYa+oFrIBo5B22Klcvfep97tlZcIvEyHpltFp8Sq9gZ1DQOn7Vr7rICvZ6/62asb1DaWiorNHZ1Sir66GS56vjb1viMCkNoWpZEf+omu5RUfUl22kKtIv+YyAtfaVhH1ohPq9R44pvt+3ccVYX//nypa64PH5NB87yOq97/+X+T0fP9jAscyca5YlCNwfKfWNx7RGrvclcEg3/r7ioLbgYfgVR8+d6pc/1GtZbBG6zJ6RqWG2Qn42Weg5SJYvFmR/qpLYM99cioa2qF1kbIGZRAP1mg93V7do9N2Rt7y2WeXp61r1RdoQl18WvdSJu4t2SSQjs3IOahpUpQ8dFLa7IlZ2HmHBsOULRHRdSajKjcs2SSH58A2AfPSzfq55Uo5Tnf8p56NYWitxvvU5fDYr/V881kJAgWq4cwBGg2DkAH9oWZqfT5Mw+Dizk4mk0levXIl9545Q63PR5XXSyqf59jUFP+8bRtrm5vZ2tXF9oEBZtNpQh4Pf3XBBfz2xAmqvd65gSLT6TQffeghYtnsXK13NpOhyRZW6bWZ7j6Xi8lkkuZg8JwZ5v8bm0gmuf34ccJeL8l8nmKpxGAsNqf2FnS7+bcdO7j79GneuXEj19izzK9ZsIBD4+OSqE0mqfV6eeXKlXhcLmq9Xq5duJDpVIrbBwawgEs6O+moquKuU6e47fhxiqUSl3R28vzFi/md18v+sTGCbjdXzp/P0clJhmIxdo+O8s6NG/nRi1/Ml554gow9I/z1a9bQXVtLd20tl3Z18b39+5nJZLhpyRJeuHQpfqeTeC5HMpc7Z3TsefvT7DyIP9ctWKONdrSnEiWWCoCpHuBMXMBdzCu6dDj1+4tfBC/+azGIB44pNbz0AoFJJqmospATqNQ0wnv/Ey56Edz3A/0+GbUj/UbVicvs7qkhReML1ys6Tswo0podUxRfshTpmaaAerxPf8vZ0XuhAJOn7Ha2vKLFfL7ikHj8FfDxV6l96pYP6p4NU7XkQk712dWXC5RyGQgv13jQPffqdS94Nyxcq/f++ks6TmQSulcBliaPmQ4x6q96Nfzy32A8ahP/ghXHJJe2p5e5dM/tS5RNME3VnUHOwp774Ka36+eynG1kojL5zOvXs3nkF0qPt9vZjmJB/dvN81WTnhxUKaKmSUS6jiVyDvY/WBHPyWXgeW+B5Ree+1mZnZCKnWWpBl4eeGKVlCHpP6rU+vxVco4C1SqP1LfpmMmIShBurxypyQE5Ga0LlBr/6aftueM+tR9e9CKVN5IRdQfk0vDC9ykTcGynonqHEy7tsDMIaLhLS7c+k8FqOYsuN/Tsx0zFWRWop2vPEep8Pmr9fgwUZZ6emWHPyAhDsRhD0Sg5m7C1oKaGGq+XB/r6+Pjll+NzuQh7PLgcDoJuN9mzWNaHxscJeTzEbKLYqZkZFtbUkC4UaKuq0vjOSISg202Nz8d7/oSoM5rJMGuLy5iGwaK6OnpmZiiWSrQEg7RVVZEtFplNp/nZ4cNs6egg6HbjdTpZ0djI7pERljc24nM62TU6yocvvZQl9fX0RyJ88pFHGIhGGYiq7PKy5cs5MztLV3U1DtNkW38/2/v7MU2TK+fPZyqV4pt79nD9woXU+f2k8nm+uXcvX77+ej53zTVMpVJUeTxzWvMA86qr+djWrXNOzN7RUQ09icfpi8VY0dDAi5cu5ek5gfP2v7XzIP5ct1U2WehMovI7wxQoOpyq1xpO1U+jUzYQ+iT+EptWpNPSDbd9Sc6AZQmE3X6Jc0Q/Aa/9uNLJW56vSV4/+7R6jX0hbdaLNwpkCnm47o3a3A89qu9OF2AIMCYGlHL3+LXpF/LqWd97v4C9bZFAtpwSB0mf9h6EtkvsGndUUeDsuEhcmYTqyW2L1UN97HE5AFYJ3vQZ8QNmJ+DbHxQYOV1yUn73NdVyo1OKahs65ERMDMo5qG8XsF1wozINr/+EPcDEqwi877DNZrdbxnIZMeSLeZ377DnnpllhbgOc3i8+QDoufkGwRqS2bb/QvQ2egGVxrcPwKb2ne42+Jgf0/Mr98OV69+bna7Tsqq1yRMqzyss2Myap3IzUxnjid5KvrWsVy3/7rWpBjIzrelZcquyI6VBqPhHROrp9OlZ1oxymsib/wDE9k+b5+tlfBff/QE5U+XfJqMoIncs0ea2+TQ5csQD77tMAlkCV5rEvWHPu9S/eCEjb+Q1FF7cdP65Z28CWjg629fWxqbWVTKHAUDxOwiZhLa6rk+Z3KkU0m6XDJqIB3LBoEXtHR+mdncWy5Vwv6exkW3//nM534aze7qZQiA9ceCGNgQC1Pt//eU52sVTiN8ePc2RykolEAq/TSb3fT2soRDKXw+ty4TBNnJZF0T5/2i4FgABzfk0NQbebRC4nIt34OEvq63mor4/xZJL+aJR4Nks6n+erTz7JhrY2FtaJ9Frn87Gtr4+blizBMAy14BnGXNuY3+ViKpUils1iGAb1fv85k86+vns39/f24nc6uX7hQm5avJj/2r0bgP5YDJdpcnxykl8Brziv1PYn23kQf66bLyA50chEZRrZeJ/YLQ4nlAxFpU3zBJJun6KtyLgiu/krBfSpuCKhQq4yFKWhTRt7z35FSKD68sSArSm+QEB3co+iyRvfJtLToe0QOKRe5fp2gbbLo+swHYrMJoe1wW+4VuAcn1H6dc89gKHr9/htwl1EBKz3/Rd88c2VWrLDIWflS2+za9OnBerN8wVOD/5EIFfuaS8P5nA44cRu+MHHK/3tbUsqCniTgwLhs2u9tc0CzkREc8jzWXA3KvL2BlQLd3vsMaQfFiCXhWWyKRG6QED3lXdVlM5SMYFbKiogX7DOFu7Ji8SWmJUTUTanRw5QefhKmSVuoIj4qlc9vQYOItvls5UxtNMjsOtuESN336PnbpX07BOzKj9YRdj0PDkvp/dJ7S86qWN1LJWDVM42lK9jzgx7KM9ZvzMd+oxGJ5XFWbbFnlXu1zquupw/xm5eupS1zc1EMhmag0G29ffjdTrxu91cPm8eZ2ZmODQxwYbWVkIeD/likaJlPW1Yitvh4LVr1jAaj1Pr81Fz7Bgle1jHgE3emk6laAoGmU2n6a6tZUl9/f85hQ565J/evp1fHDnC/HCYRDZLrlgklstx1bx5PDIwgMMwiGYyFEol2sNhmoJBanw+opkMD/b2csJmmacLBUbicRLZLD6Xi+ctWkShWGQ6lWImncZlD0rJFoscHh/nwrY2HKZJMp+nPhAgmslQ4/PhczoxEaseYDKZxO9y8cXHH2c8mcQAXrVqFVfOn88/P/ww39m/H5dp4rEHzJQsi2Q2S7qoz2PQ7dax7VLBefvT7DyI/yVYywJ4xT+IrDUxqI3TdGpTrmmuiK2UCvp5ekSRU8tCpZzzWUVHs+MaqVmyyWv9RyqTyMpWyM9Nn8IbUA/yyCl4y+eUgv3pp+REWEi1rL5NqfZkVMe85MUiye24XZHraI82dJdbc8gbOpWSd3t1jnwWbnir0rfLLoTNN4nIVybt5bIqAbh9SnOH6+WQZHsE6D/9jOr0pkO/94fEli8VBHoYqvPWtinCnRkVqGRTcPnLK/edTorRXa5lJ2b1O5fdsvXC99ra9IayFi3dyipYJVh3tdYX4PBjFUEUf1iiO06vItfBk5rJ7QsCJR3ngpvg2I5K21k2qVR4xxJxDnoPVqRSb3jrMwN4OgH9x2CsX+tV22Lr12d1/6ko5HJypNIJAe2R7frMzFspR2z+anEUnE45GPNWql+/fL6OpfqsTA3pWSRmtX5HHlPk7vKotHLdm2x525LOU76Wp05Q+x+sq7qaMme7KxwmUyhQLJXwOBwE3G7etG4dvZEIx6emOD0zQ2c4zD2nT3PLypX4XS52DQ/zjT17sOxJXm9cu5b3X3ghX3j8cRp8PtL5/Jx+eq3PR3d1NTctWfInAXixVGIgGuUbPT1zbWTtoRCmPWwEw+DvL7qI49PT7Boexu9ycXFHB2/fsIFMocCntm9nMpnEYZo82t9PCaj3+WgJhcgXi9x+4gSXdnXxrb17yRYKuNxuSkBDIEAmn+fUzAw+p5Nav59PXnkl39m3j8FolIJl8fq1axmNx+mPRmmyo+eZdJrOcJhcscgPDx7EYZr87MgRUvk8bodD9e/RUUqlEidtEZiMTfRzmuacPOx5+9PsPIj/pdjyLdC9Vqn1H/+LrS5WXZmi9aL3wh3fUF/y0Cn1mQ8dUx3zFf8olTGXR+ndw48oIpsZU6TkC1XO09gpcJkaFvDEpiQDW9OotqNTexWBYvd2p+ICoIZ2MZ6HTuq4xYKIUf6qii74gYfglr9X/Tk2LYehtknkp7KF6wWA2ZTel7bLCF4/xE05LJFxAY8vKAenZ7/01/fcA+MzIvgt2SwwmujXMQ4/IjB0ugVGHUv13rJtvxUGjirtfnqf2OcNbYrAs2n4h2v1vapOzsYrPyxgf6oV83I+YtMiyBkOtdCVo3Knyx4NW1Ta3umyMyM5OTY3vL2San7RX4nVnYzKaTg7Yi/bWJ8m1B3cppp/IGw/Z6eeTcdSfUamh7UuxYKem9Oj6zn0iKLx03sUbTtcyowkI+eK9ri9OtZjv5aTd83r4PJb5CQ+cYc+A5e/TG17hiFp3od+pntvnw/XveGZW9NAZZ7jO7UGC9ed2zIHbGpr4/qFC7n/zBkAltbX866NG4lms/zDgw+ysqGBpmCQbX19xHM53rJ+Pd/au5c6e852z8wM77zjDi5sb+fyefPY1NpK2OudG4CSKRQ4OTXFf+/dy0w6TUdVFS9dvvycGvHZlikUmEwmCbjd50T/h8bHVW/3eikUixiGwVA8ziUdHWxobeUdGzeSKxaJHDrElo4O1jQ18bIVK/A6newcGmI8kThHFrZ3dpYL2ttpDATmJGZftWoVH9+6lTf95jdqevB6CXk8bGht5e+2bMEwDJqDQRoCARbV1jIUi+F3ueiuqcFCaXsTeP5Pf4ppGMym0yyqq8MwDE5MTRHP5eYifMuymEgmGU8mJQwzNEQ0FmMwFmNzayuWZVHrf5Znet7+aDsP4n9J9sTvYNddArnxtKLNhg7VqZu7Vdv+yrtgnd0TbJhKqQ+fgBe/X3XK4VPQ1C2w9AUFsv1HxSzOpMSQdvvgzDZtqqsvh+vfrI358HYBucdO2efScgIWb1CaODqlEZ7BWgF0PiugKORgxSVKh7/kA4ChGr1V0kCVnXfAypfqHi+6WQS60/uU6jdNlRRqW3TfZZZ6IS8Cldev40UnYdlFAjPTqR762lbVpets4lY+LZBpXyKQ7jtcqS0PnRRgH9pW6cmeGacy1QsBcmxa6fhTe+AffirAefjnYt6DIvJsSteYTgjUl2/R8ctzz8t1WMPUUJrxXli8Ca5+TeVZl2wy2nFbLKY8AvWpdsd/iUkfqFbkPzlg33O7rvPb/2hzANpUpihbLquMRP9RnSs2o2l0pYKcp/jMuVr2D/9M17NgnQD7wMPKQDR2qs3tqbbxOmVo4jPQO6F1fyaLzah1MDGrtX7it3DLh84ZRVvuhb5p8WIKySg1236K+ZXvkHa4aa9eiWv+SkDR+97RUaaSSZK5HFl72tap6WlM08TjdHJvTw81Ph832QIrsWyWzz76KA/09jIci1GwLAIuFz85dIhvveAFLDir9xxgMBrlC48/TjybxUKksuctWkS2UOBbe/ey0G4Hw55DXiyV2Njayt9efDG5YpF/2bYNC+mb39fTQ18kwkuXL5cE7FnnaQwEGIxGqbFZ+pFMhi32NLPnLVrEV264ge8dOIBpGIQ9Ht6xaRM+l4uv7dpFPJulIRDgfRdcwNL6erJ2Gr2sL/9vO3bMSdZOpFJMpdO0hUJ0hsP4nU5F3IUC+WIRl8NBd00NLaEQNy5ezGA0Sq3fz0uXL2dxXR1Hd+165ud63v5oOw/ifymWScHuuwXWrQuVMh/r1QY6MQgffb5AtVQUYJaJY4ahTTpUI+ZweRhGWahkalgbdZl9fHqvACdQrTGhcTtKqm6Ee78vgMpn9PuyWpmF+tdbupV+nh0RGPhC9vCLNqVhF22QA9C1HBasrdRvc1lFm6Bo822fl6LcyGlt5g0digCz6Ur6P5tUL3UiotaxdNxO3Sdhka2udWa/nI3OZQK0QqBSxzVtRn2PpfuobdbQl9P7BFJl8J4zE6wC5CytYSKiPutVl6vEgF0b3/+gIml/WPd/wU06XkGCG4Qb5LwYhv5+cpfWe+99qrNf/jK47OVi0z/0UzkWY71qv3v9P8v5KluxqBKJ012Zqx7zy3maHFDGIp/VM5m/Rg5IOq57MQw9x7oWm29wUs6OxyeHqZwBKdu++2153jGtlWGqzFHd8Oyf2YZ2ffU/JEfD7X26ut3RHcoSjPfb2YIcjPbBR35euddCHmO8j3B0Cm7/Gkz2w7xVOIoW1+y/nZ2NbaQDNXPqYoVSicMTE2QLBTLFIrFsls5wmLDXi9fpZNfIyByI33HyJIOxmAaUlEqqRQN7Rke5/oc/pKO6mmX19Vw5bx4vXLaMr+/eTaFUoiMcJl8s8vMjR1je0EDP7CwzmQwOe0AKdr/2ptZWPnTJJbidTk5MTZEuFOgMhymWSowmEuwYGqJndpagraY2Eovhc7lI5XL4XC5uO3YMp2ly89KlXDN/PrtHRiiUSlzZ3c2mtjYmkkl6Z2fZNzLCXadO0V1TQ1d1NVOpFH9z770EXS5KlsXC2loW19Xx1SefZN/Y2Nx41JZQiIFolFeuXMm1CxZw/cKF3HfmDF77+ueFwzgdDixbHhbDYENLC/Orq6k5r9r2/8TOg/hfipWKwpXyCM76Nv1u8CT8/r+1mZdrzImINK8zKaVXO5fqGIW8ouTRHo0vDYQVXa7eKs30qWGlU0N1gCXJ1vYlqsumEwIpX0DSoIU8GEXV4H1BKDXAaK/q7MmoNvzycJPYtICkHNFDJRrVD+du7I2dcMNbzr3/NVs1mc0wBDKn9sDJJxXt1TSLvT7aUykjbL6p0orWulAOzvApAWcuIwDb9gutYSGv1HPPPq3Z0wDcvkbLAsNWs6uqFzg/9muBaU0TTCSUHo9NC4gn+mHjtdA0XwDVd0QZg4JNBqqqUzo8MSvnZOyMWt+wpFVf22prmFcLyHsPqVbtcClN7QupJJCyme4Z5LAlowJ0X1Cfl3TS1g1oUjq9kBNYhusVIVfVicyHvbaJWbH2y1F4MqasRXkk7syo7t9tM9dP71eWqJjX8yi3FK66tOJw/uCHaj/cdL1q6eXnnUqIJ5CM2M6NqWv5+b/Cy/5eDtpDP1NZp/ewXUrpgKOPEV5yIQ0+L/GhHoabFlKyLF6/Zg3b+vtZVl9PbzRKOh6nUCrR4PfjNE1643E8qRS3HjnCxrY2xhIJQva40ZJN3otmsxhoYpfTNAm5XNx+4gSGYTAcj9NlM+BdDgemYTCVSjGZTOIyTVymiWVZ5Gy98s9fey1uWyzG43RStCwsy2IwFmMkHqfa66UrHGY0kWBhTQ11fj9TqRRDsRiXdnTgt0lk08kk//rYY4wnEhiGQcDl4h8uuYSD4+M81NfHiN3/vX98nHXNzcyvrmbvyAjXL1jAZCrFL48cYTqdxu9y4XM6cZkm2VIJl2mysrGR6xcu5NTMDK9atYoFNTUaD+twYJom+8fGuHt6GgtwGQbZQoGH+vroqKrisj9u9zpvf8DOg/hfivmCqhee3iOQjc2I6HXUJhaVdaxLlja8cr11zRU2yaioKVI9+xQlTo9IVOT57xJr+vhOe2O1HQFvQN/LwzKSMUV7hl2XdjhsALRT27mM3WZlKeIyTQF/IKz6/eobFRHvvFMp+9i0PbAlpOiw9aLKvVqW0uZHH5czMH+1WpAmBgSWbo963uvbVPs+tVv36nDqmKWSQKpU1H2OnrElWdcLKBIzItglZuUwHH1CUb/DLXAslVPeZ6W9y/ruWALc7tW6Z29QLG/Q2udtAtnQSXsCG3KGshllMwpFqK6tjDfN28psda1aL7cXjj0p8C63raViyiTc+nl7jGuPwHvJJimw5dI6zvSIQPnJu+w2xLStje7RtWcSYoxX1Ukdb/FmRdWWBQ1dAuGjjytT0rak8jyGbWLg1KCt144+Fx3L1P73809DIi4n757v6lk1dIoo6A9D0yb9XCzq+XetkGMZnVIKP59WpsLltfv0w0r9f/tDeuZjvZXPlOnQearqMIdOsKyxk5dv2MxooJ4un5ulHV18efduqn0+QqkUCbebeDbL8clJ+qNRJlMpqj0eZjIZ7jp9mi3t7cSyWeZVV7NzeJhMPk/RsnDYsqeJXI5INsuS+np2j47SGQ4zmUrRGAiQKxaxLItGmyjWOzvLBaEQ86urmU6n8TgcfOmJJ/j4Vg0smUgmcZsme0dHSeZy5IrFOcW2Ko+HVKHAhzZsYDyR4PTMDHX2cX0uF48PDjKbzbKysRGAsUSCHx86xPGpKYJuN2PJJD6nk0KxSO/sLNFMBtMw6IvFGIhEsCyL2UyGnD2jPJ7NYpVKRDMZ1re08NsTJ3hyeBiH7Yi8dPlyfnzoECG3m0w+r3p9dTUDsRgOh4PLu7oYisWYdbn+DJvdX5adB/HnqpUlUh/8qTb4lRerxWvH7apLTw0oUjtzUEBaJk8ZptLOC9ZWtLK/9xEd78ijIsfNW640dXSiIqziC6oH23RoJKlhQlOnNviN1wtE7vueANIbUPTncAggH7tNNfXaFkVoxbyua/C4hpPMXymg/v4/iRQXrFa/cC4jktiCdTAckWBKQ7s27vu+rza1ySGNzAw3aKBJIKzflVnWm65XRBqdEDgc3aHXntgpQFh7ja0VPygi1qbrlX7+xWftMaSZyjWZJqQiyjQYVORBTYfOW9MESZsBv/8h1X23PF9cgYjd157P6ljlsaeZpFLRZea8NyTQd3lg6y1w5HGVGgxDvzcMOWcXvkCZh7FeydQmY4qCiwU5LzMjyiw89mtNH0tG9Xe3Bz52s+r63oCA0rLk9MyO2ap37bD6gyICHt+pZ5OM2T3wlkRafvwv6jNfvEGfhXAdtHZLhQ/kZLjcsO9BOH0QXHZ/fioGUyPqeTdNPY+WLRWRnkJOn9+7/1vXXM4OpZOVufdOt+6vXI4J1crpw7JHnM5CWuIy5lWvZrXbYvXd/671Czdy8ZZb+PXRSSZTKUJuN0YoxGw2y0QiQbZYZLpU4tD4OFfMn890Os013d080NtLZzhMbySCo1RSj7jdW26ABGF8Pt6wdi1ffOIJBm2hldeuWUNHOEx7VRUtwSD5YpGe2VmKlkW118uJ6Wled9ttJPN5RuJxwl4v9T4fKxobCXk8tASDcwSyGxYuBCRu4zBN0vk8PpeLrF2fDtiAaVkWPqeTaDYLwKztMDQFAgzF4xSBqVSK7poaBqJRqr1eErkcAZeLbLFIi9uNaRik83k2tbVx1bx5fHXXLuZVV2PYZLf/eOIJ2qqqCHu9TGcyNAYCRHM5wrYDEM1kqPX5yNrXcN7+73YexJ+LZlnwwI8gUoLRxxVRDR6FG9+hVOTJ3dC1UptboaCWrEREmx92dFvTJEBwemD372HpFsBQatzp1BCKYkGgs+NuTUPzBOQMhOuU9nW5lea87/tiSr/xM/DND9gpZ8Bji6CkosoMLN6oNHdDp0C2VNC5JvoVZU0MKs1vmrr28X71kR94COIukdJKJYFhsFaRcsm+xnwWBk7omv1B3Ve4XiDx4g+IXR6Z1AQ1Xwhu/6pStQcfkkNT3ShALI/Y7F4jslZ1k60Hn4OuZTBvtWrpwRrVexdvFtPa7ZGTdPe3BHg1zXrf0cfhr76hqPPEk3JIXC5F5QPHBFjl9UrG9G+HQ47W5uth5IzAODala/H6pe0+b4Xu45t/I/JfWQt/ol/OSbEoEDz4iFr3DEPOQKgW3vll+Pr7lV0wHXKU2hbqa6JPdfCDD8vJyqT0bFJR+3PTLFBPx9VnvniDWOm1LXICvAE9n0teojV74nYBrsdfYbMnZvS9VNQ6puNw73ftNrqisiwenzgRizbZrY8T+qyl41qHjqW6F6ezoosQm5Ez1LoIqmpEupwckib/vFVyOmfHWL/ndlY3X8BjAwO4HA42tLby2xMnSOXzOE1zrh49Go+zoKaG161dyy0rV1KyLF7y85+zd2yMdKGgGrtl4bHJXresXElLKMSnr7ySmXSagNs9J9CC/ufhsieZFUol0vk8iVyO/kiEbLGonu5CgVyhQJXHw5vXr+fOU6coWRYXtrfzQns0qt/l4q3r1/ONPXsopVKM24Ixjw8NcWxykmyxSDqf52UrVrCupYW7Tp0iXSjgcTpZYjPNfU4ntT4fx6fkxHls4ZZt/f1EMhnCHg9Xd3fz0csuozcSUY3cLnGE7KxAsVSau7eiZeF3uYjZEb6FZGw95yPxP9nOg/hz0RIRsX+7r1GkXI6OtrxQqdDopD1LHPUTL1hTGZRR3WgTguya43ifNumGdlssJSlGcjKqTXDH7Yrm4rPanK2S1NzyOUU/yZg2zpWXwNaXa4P+wccEQumkXh+bVj26327RmuhXZOwNavO3EMA0tDGXoi7XxGfHBMTd12pTL+RVX+1eXXEynC5t+uXxm6suhURUG/6ZQ5VpbKDr+q/3a31GTgsUe/YrfbvqrArexuu0zr//jhwOw1RrnsulNq8rXwXBsIRlyvXbkR5dd9dy+x5qdI4XvBve+1X45t/KgTEMgVLvAXvKWsl+HiXdf3noyQ//WY5HKqbjur1w5WsE4KDz1LfpmLFp9XGD1j0ybg+38cLX3lsRuzEMcQ8+9GNlVu74hgDRMLS20WlJoro8ek8gfNZI2VkBaKEgfsNYv8o3l75M9elDD2vN5q3Uez7+Iq1tqSRwztlciWJeTodpKgtTLNgjX0v6WzYtByU2pT56LCn6Va3T+9KJSuTdslCZjbFee569LVS07mrxONIxOSCn98jRqm7CGO/j2s2vIJLJML+6mpJlkbKj2rJCWqlYZDge5/J58wDVqy3LwjRNwh4P7aEQqUKBRDbLa1av5roFC2iyR3a6HI65f5etZFkEXS78hkHRsiiUSgRcLkYTCUp2HbxQKuFwOjENg95IhKu6u3nBkiUULQvvU4asbGpro7umhof7+vjp4cMkcznimYxkYV0utrS30xuJcGlXF22hEN/dv594NkvJsphKpVjV1YUFzKupwet00hIIULAsrunuxmNzHW5eupTGQIBHBwY4OjnJhD3lbCKV4prubgZjMYZjMcIeD8OxGMvq6xlEI0sTuRwLa2qoPQvoz9v/zc6D+HPRioVz5w0CcwpZTpc29uikADufk6jKi9+vyKW6Ufrce+9XxFfMSfTE7YUVF6nPPD5tS7P2K3IO1goUsFnb8Vlt8sFabf7jfYqil10oIKxuqqSzTYc9djKmWuWWm+VEZJK2Mpi9Gde3aKLZ4DFt4JmkHJBwvR3B2TfscKpGn7N7mrMpRX/FgiLI8X67Ttpnz9pOwk8+JScjWK36ebGg+ns6YSu2xXUv666uLKfDqXT2vvtVCji+U3XYTE7XuP9BOT6ZZKW9y+lWBFwq6ZqLBQGhy6P1XbheQjOBsACqVJLP4nTZU9/s5xhuEJjte6AiQetwaY0f+QWsuVzX53CIB3Fqr74f3q7zRCb0PVQjTsDe+1WfXrhW6/b772ia2+rLpVy3+15IzuhZLttir63d0lSe922VpMM/fFLHL0uuZpMi5MVm4OZ36z3DpyTxWsjJSZvor3RDuDyKvmdG4DUf0xCboBfqOwXkyYjuNR3XOiWjek4NHRIicrrFX5gcFLcgl9W1rbhYzks6qmPc9Q1btMgmEtbanw2nC2qauHbRIvpiMXaPjAASREnn87gNg0w+j8fp5MZFi7jYbtsCyBWL1Hi9rG5qEunM56OmoYGwx8Mvjx6lZFlc3d3N8gYx8mfTaR7p7yeVz7OhtZV1LS0URkYIud2MJ5OkCwW8DoeEUexzlEVran0+Qm63atDPsg2USW4Ow2AkHqfK650D/GyxSL3fz9HJST6wZQs3L13K6elpPvLQQ2zp6MBvR8i5QoHL583DYZrEMhkeGxoi7PViAD84cIB9o6Mcmpigq7qawxMT9EcivHb1aq7s7mYwGuWBvj5yxSLVPh/5YpH3XHABl3R04HQ4qPP52P7II3/Ehnbe/pCdB/HnooVqtRFmkopwHU5FhLXN2kRf8G61N00OavN83pvO1aK+6jXarNNxRcN3fl3M5+iUNsmLXijAmx6Gkd7K/OpiQcpeGOCwmeWZlDb9skRpbbPSrg5nRcqzDOSJiDbxpi7JuB7ZIdZ4JiVN9Re8W8S6oZPadNdfXamDFvMi6J3cJXDecKFAcfutAvJwgwh9xZKIaOXRogvXq/6ds4VYDj4igJ0Z0/Wm4gKJ5Cz85BNyMjw+icVU1VWIYoMnFLU7XarF3/l1tdjtvBOufLV6uU/s0mCU+HTlvVtfUUnR3/h2e5DJGd1/NqPUcTFrEwHR+9oW2cNgchUCnVVU9mJySJGq3xbgue7N6nvv2adjbr4Bdt4lJ66+rcJ0L2cL3N7K7PhAWG1/Jnqty6d1MRCfwkLPrHm+nmfTPJUHDNPmWFh6dm4f7LhNJLpwndar3F4YnVLb49SwjrFwA6zYYg9jsUmYGGBYSrnHpvW8TVPr6AtJsnb4lJ6VN6R2N49fhDenSxmJngN6xomIsjA2uY32RfrcTo+I3GlZcNM7cTscvHvTJmbSaQDuPHmST23fPjdBrLumhn+45JJzesDdDgctoRDpfJ4VjY3kikVOTE3xk0OHqLOHsewdHeWDF19MSyjEJx55hNl0GpfDwe9Pn+aFS5cyPjSk8aUOBw7DwGEYdNfX0zMzQyqfx2WaNASDvG3DBmmaP4Mlcjlm0mmqbSGXRC6HASoFWBZee0b4ZCqlYSZ79nBRezsrGhtpDATOUVGzgHUtLaxtbubbe/dS7fHMlQDCHg+/OXGCrfPm4XY4WFZfT18kgsPh4CtPPslMOs32gQFCLpdS89PTjMbjtFZVUTgfgf8/s/Mg/ly0R3+tzTZot3ctuwhe9P65GczUtWr4R3xWhLSnKmEZhuqfZXvNx5T2PPAw+KoqgByoVm1xolfHdnvBDGuDdHrkQJTstp/ffFnf114hZbb//ns5CIWsXmuYipTLqmLXvkHH7z2kdO7WW5SeXrNVX2fby/8eHnxA15eMyGnoOyQS3t99X6n4kdP6eyauzdsX1OY9MaBorKquMu5y4Qa459sChfhsRap1ZkxR68L1ihRDtWJXTw3ajHabpFPTqOOH7R7on/+r0vONHUqFj5/RGNf5q5RNKJvLDRfeVPk5OqnvsWnV9nMZ9WJPDcN8h4CwzOgv2an2stxt2XyBp4upuNyqAxcLdqvfWe9JxStSseP9IvDlsyIcdixTlN22SGnr5nlK5TfNU/Q/M64xs2Vlt2Ie0oXKxLmffQZe+Y9yDooFMeTj03I8vH5NQFu6GTAEwsmohIi2P6qfI5Nio/uCyh7NXwXXvF7cg9u+rLJKcVROSF2bIvemLj3/RERObS6tkofl1ed0etRucayBN35KmQmf1sIoleg9cYB7B4cwAjX83UUXMZpIUOfz8erVq6l6Sp+zYRi8Z/NmvrBjB4PRKBYwv7qaRD4/x0C3kkke6utjaX0906nUnMJaNJPhrlOn2GwYBD2eOanU0zMzNAUC1Hq9jCeTbOno4JoFC7hp0SKeyQ6Pj/PFJ55gPKE+/detXk2938/xqSk8Dgcuh4NYNksmn2cqlWJLezv7Rkd5dGCAv77wQl62fDnf2bdvjhA3r6aGpfb88aDHQ84WfgHIFgq4z3Ik8qUSRycnebivj9ZQiEyxiAMNtewJowABAABJREFUiQnazsRdp05R5fFwf28vWBYvDwSwLOv8jPE/wc6D+HPN4rNqEWruFjhhKu36+O2KsMv/WZwugc0fY4EqAf/IafVWz4xqs4tOSFIVQzXHbNJmnrttARGnHXXWKnr+zZfV0jbeJ1BIRtR6FKxSRNXYKdbxqstUC73iFfr6n6ymyR6eYgjs/CGBRP8R+O1X4M2fVdp7dlQRrFVS5FXIqX4brhdoQYXlvWCtorIzBwS8Iz0V7XPDVBajPMDE5REYng2ETXX6famgyLpUVNq4bZGck8aOSv/9s9llL5OTMTWsa16yWc9w+60QMbRm8RkUL5UETpe+5Fy502eyxZvh6E6R05wuEeGGTuj6PH64+X16pr/8vAh2noDA+tgT0GxnSV7yAQFzuTURBKTFvCLvTKLS4maYYv4nZpUev+Ftqov3H1WEX92icsmTdynl37VS5ZV1V6qU09AH7/maQLixS8TEMuPfMCoOQ0u3pu8lZnQvy7bomXgDsOk6jZr1BsHnVzklWKNI3+OFC59fGUIDUCxw6Huf4SdnBnB4vGTdAY7PW8WHrrqWZQ3PLlDTGQ7zWXs8Z9Dt5jfHj7NjcHDu7yXLwmELypwNW6ZdC8+XSvgcDtwOB4VSibaqKi7q6OCijg6W1NfT/JRa+tmWzuf50s6dHBofJ2cPdfnYtm1886abWN3UxF0nTxLP5Yhms+TtSH8kkWBBbS3ubJZbjx7l8q4uLu7owGGadIbDXNrVNVdvv3r+fB4fHOTM7OzciNc3r1/PvT09VHk87B0bI57LzY1wHYrFwDCwLGuurj+TTvPd/fuJZbNYlsXF9fVs6+tj6/z5f/gze96e1c6D+HPNchmbaTwIza3a6K2SGOjN85Ti/d9aMgq3fqFSQz29T6Mhr34NdK8Taa6xXanMxKxSuPsfgpETkEvBhGQkcTgVWW+4RlFvNvX/Y++/o+S6quxxfL/36lVOnXNUzjlakuWI5QjGYDCYnHMYGMIQZpgBBoZsMsaYZGycc5CDJCvnboWWOudcOdcL3z/2rX4tSzYMDL/f+pi+a2mpu6vqhftu3X3OPvucQ+BtWkLKeqSHm/OZ/cDrP31+u8xXGqYpjidSukwTUAzGYjuPEXRtTiA9QlBJhGnk2J0E4N6TvCZFJYB3HCXYmiDYQ/wfLGfstZCupdr5N0+ABsHkII2eyibe00AbwSwdJ+PQtp/GisP98vdSGN4gcNGNVGbnszSknB7S0o8/zNBEKkaqXXXSmJGVVz6mrlMJ391C4Os7TcOvrBZYcSWLzKh2Gi3ZJNXlZ/ZzzkLDzCBoXnbhOuaLL6IxlIiKqnXg9bj9BEx/CeP2io1q8MEOACZDFfse5XkjY0B0B3DTp5iaWDjG3FUvf08tO4Ajz1LEVjufc5yKCjahh8dZsgXoOE6GJiS0IckowwJrrwau/cC5x3z8V5Bf+CNusjlhU2zYV70UHQNt2NM3/xVBHACcNhtq/X4AwCWNjdjd14fBWGyqjOoVzc1wqyrus9kwKgrCHBgcRNDhwEqnE33RKCp9PtgVBfNLS7GisnJKQPdKI5bNYiAWY2xe1GQfTSTwZGcnvn7ZZYhlsxhMJFAfCCCcyWAkkcBIIoGJVAqaYWD/4CAGxHV6VBXXzp07FRsHGGP/6tataBkZgWGaWFJRgWKXC7OKi9EyMoJT4+O4uKEBj7W3I53PI6tpMAEoqoqEKGNb6/ejJxpFmds9pVK/8/jxGRD/O8YMiL/aRrCM3s3R7UDleiCb4CYaKGNlqwuBuGkSyArq5JeOiSF6fP5iAlD1bHo6nmICjCIDQwP0aG/8FIuI7LoHiIXFZi6818g46fO2AzxXRSOP6w4Asso4N0D6+Mgz/zsQd3p4n8l+Gi2QSJN6gwS6zmP0ELWcqE4nk3L1FZFq1XWKv9ZsI1gWeoIXVxDQKhrpEdsdNAziYQJ1aS3z533FQG0zsGAtcM0HgSNP897KG3hdA2dJM+fS9AYbFv3lexrtBR76ET/vCQK77sNUsRjFxtztmrn0vB1uGiTZ1Csfc7yfOfjFVTSoiivJiMxfx5ztNVcDqqCsDQMoLmdp2IlBHvuWLxLATZPMTCzEY1Q0EJjXXsO5G3cwvSuTpIE3eJbXt2A9maHn/8h0tDMHmZJX2SyMEQfXV918q+LbK43jO1iEaKwbiI7SoFp1JQ2PQCmw4Fo+02yKIaJEmCVl9TxfL68jyHsCvKfIGFma3fcjZ3dj0u5DdTaG1598DN3eMpQmO4GKr164mQww1Q40ms1ieUUFllVW4ksXX4ydvb3IahpWVlWhIRCAIsv4/ObNePjMGRweHkbA6cS6mhoEEgk4VBV2WUZzURHqAwFsrK//y/MANjORgal4c05UkesKhXBwcBB9sRicNhsUoaAfFTXiJ1MpDCUSqPB4puj9wVgMT3V24h3Ll59zjqDTiS3CoMjpOrZ3dWEgFsP8sjIsrajA/sFBlLndiGWziGQycNtsmFdWhiKnEzcvXoxdvb3oCIcJ4KYJCZjKV58Zf9uYAfFX21BswI2ftHpqpxIiPigqp00fpklB0OO/ZPy1pJrisUIP6MI49SJFRi4Py6w2L+V5WnYADi+9WFkm9Xt6N2Pb5Y1MM5Jkq0pbXlQA07KiEluSADB49txOZKZpiaZkhd7ieD83/QXrrNj+9CErwIdvA379eUtl3LAAuPlfgb2PiMpoBkE9Mk5jJR0nU2CzAyuvsLyxgpo6kyQwvfmLPOe93yHtnEnRM3b7ecz568hQlFRTbOcromAKAJ68nSlZKy7l/cRDwNptVqGb7b/j32avZNzfPi3O2t8GgnaQvxdXMOUrWA40XEIRXy5L4HW66HWGRoBvv8OiyZdOS4sDrNrvusZj53MEuFyaf89RyIWiCjaT2fOQSCXzA6//BIHPNGlQ7HvEashy5TuoVXjzF4F7vsVGOxVNfH24yxIxjnSz4UvBuEqEOf+5tMidF2pzm4q/OE7sBn74QaFsl0j9jw8KRb8o+LLvEa5nSeY6yyRpKJTVi5oBPhq8TUvYfKd1F69hvB/Nkg2Dhg5/fBzQckh4y7C8qAi473vAe/6bczJtJHK5qXagDpsND7W1sSVqIACXqLm+u78fNX4/PrFuHRqDQbx/1Sr8586dyObz6AqHUQvqCBOiW9gHVq+G3+H4y3MBMgCfWL8eH3vySYynUshqGtL5PMZSKbzvkUcwFI9DApDK5aYU5llNw3AigXnFxXCoKnTDQEbTIEsSkrncy57LME385OBBHBkehkdV8Vx3N2YVFWEylYJHVeERYja7LOP1CxbgvStXTinSn+nqQjidhiRJkHw+bJym8J8Z//sxA+KvxuEJAPXzAMNG8Ok7zRSc5Zfx9XiYorMX7qZ6WpYZP0xGqVp/1zdIbQIUHZ3YTVHT4FkAJmOjt34VuP/79FokAbq5DHDsBVKupkGjwdDo5Zo644+KSvV0MspzFDwuXT+3mUp0HLjtI8xVTsUZQ6+exfzs6z504bjvsouBT/4SOPQU73vl5YxB59L0LIc6CNy6JsDHAPI6gXDVlRS+HXqKxWMaFrHu+8QA7zE8SmBrWkLQGu5kXHfpxVQ/ewLWdYz1Ma3LprKwyKO/sJTUs1bwXNEJFsix2Xltx54j0F39Xus4dhfnpTASEaa8VTYK0FUIhIeepCAsUM64cibJeW/ZCbzvO8CGaWK50loaWeODXAeJMK/ryDPA/PWc58LY+FpS5/EQAbasln8PjwIHHiMQKiL3/pnfck5O7uG81swhY1CoAlfWAEwOWCGGdJKGW3yCLIqWIyOQigPzqzi3rzSGu5kmpthoECQilrjSyNP4KtSnf+QnvP7JIYZbDIPhpmC5aGajkBE49jzZlVwZ0HMCAY8XW3JxmPkENLcfm5ashNfttfQQLwHxk2NjU+1Ao5kMusJhdIbDWFFZiRf7+rC5vh6NRUUYisfxqyNH8P7Vq/HRJ57A9s5OTKbTcNpsWN3UhGgmg2WVlfA5HLirtRVf3LLlglMwtSxyORwbGUEil8NgPI5LGhvREQphMBbDiro6jCaT6ItGp4qvpDQNiVwOxU4nrp47F6os48zkJLLxOPalUsjqOnK6jk2vAK7D8TiOjYygSVRpKzNN9ESjuGLWLAzFYhhLpRDLZBAzDDzT2QmHzYZ3Ll+Oixsb8an16/FoeztkUS72jS/x9mfG/27MgPircUTH6Y02zqEnZpoEzbEeYLiDnnfXcQKCZKOHd/Ygq6EVvMXiSh4rFeOGGxriZqdrTIl68lfctJNRUeDFxc00Okrvfs3V9FoVlbFid5Ab+tu+xnadI930ZLUccN3HueEee040E4mS8p0cokesqFbXqxfuJmCuu5Ye7/Rx4kXgN1/iBg2JZUFf/ynS86M9BJuCihugB1pWT5r17AFu4rkMwa3rOOvGl9TQaCmpsrxDSeL9ljewTej0MdgO/OmbnHM9T8o6lyGoRseB2Bip9+4W0Q+9irHmkW5S/uUN1AxIEru2HX6K54+N87KDFUxnK17O+YNJQ2HrmxjayGU4l5JEw+HJX1meP0BAfcNnWEo3kxDhE5PHUu1WU5LCfVY189/0kU2J3HRxTNVBw+VQgjXTDZ3gWdHAbIbVV1JUViyMB5efhlw+Q1DV8ox5h0Zo0CTj9Oav//C5Xdemj/F+ADLDHAVBXiZBur4wB4DozDbJUFLjUq7JQuqbJ0AmYs02sh6qncad001mpecE/NWNQGQYKCqhMFJt4HqfbrQBU6KtZD4P3TAwFI/DBL1jmyzDoSjoj8XQWFSECo8H7aEQfrBvH17o7kZeiNySuRwM02RRGcNAhdeLrnD4ZdXb7ZOTuPfUKTzZ0QGXzYZIJoPJTAab6+pQ6/djLJnE7OJi7Orrg0NRYCgKqr1ehDIZNAaD2FhXB7t4hgGHA0O5HGySBK/LhTq/Hzt6e3H13LkouUDPb+Ml1ySJfx9ZswY/2L8fJ8fH4VFVrKiqQlNREXb29uL1CxYg4HTi3StX4vr585HVNHQcPXrB48+Mv37MgPircRSEXZJED2S8ny1C7/5vUsXz1gqRlqCyA4Jmj00QMF3TFLDFVQSmQjW3tEi1ik0wLth7kptuLiMqamkE4Ne8m7T79t9SsFZWy9SyeatZLvTMQYJB7VwLJK58O////X8QoNuPECAg8fiJMM//4gPA2cPAW7/MOD3Acz/yE15XcTWBZHyAFKkujIjJIWtenF4yCNWzCBRnj1gduApit0JNdLefWoJHf0rwKqRMzVtz/tzvfYSfD5TxWicGRFpeMUGr8zhTofwlPE50gjFkWaSMbf8dwWTZVoYvlmxhwZWyBv69q4XztsSgseMvpdra0EWYwbSAuVCERdfOjS/nsxSYFVfxOlIxYVDlrUI0rzQKneeiEzRIwiOimE41z6MojOFXz+a17LqfQkG7g+93eQCpggaSJJHhWPUa4MX7CMqeAAWCD/2IjM+FhssLwCAzYlNpBJVUkc6/93+sWvO5LOdGlgBvCVByMY20oU6C95Y30ohLJ/idMHRRvc7OWvm9J4BFmwn+bftp+L7hs+e0UDVNE/ecOoWH2tpwanwcHaEQyt1uJHM5LC4vh0tVp4q1AEAonUat349dfX1ICOBWZJlPTJJQ4fVOVU5rEJ7uS0dvJIJv7t6NsUQCo8kkbKJWel7X8Wx3NxaUlUGVZezt70csmwVME267HS5VhS2Xg99upzfucsEUqni33Y7NDQ1T5+iPRjGRSqHE7T7HkDg0NIS7WltxamwMPeEwllRUIJrJYEVVFRaUleEzF12EqDAUnKo6FfsWpjMkSZpKuet85ZU2M/6K8Re+rTPj/8kRKKVHks/RA23dyRh1ufAiek/Qcyl4FIkIN7FUnDTy128BPnsZPcqJASAoPLtkhJunS6T4yDYCpiy+otkUEA0RfO/4AhuSxMMEwkCpFSd2uMgQrLnqfC8PIOWbioniKXaCXzpGb9ZfRvo6GSF1WxiFlqCKzapgJssE/87jLABi6EL0ZlJ5LSnclLe+mTnohk6A8pdwPsKj9CgvfQs97mvex3spqgBu+jSvPRZiadnCyGcE+5BjGCMVp2Ex3kfQK6QA1i8gAHW1WDF2j5/z/fyfrLKyJ3ezjGr9AuY0ZzNWCVSXTxRasVNR/5p38e/hEXqfNhuNgOnedT7HTmGDZ4F4hJoJl4/rpHHRhQFc18gSnNxt5XTf9C80tCYGeA3rr7FqvAO8n2SYhWUCpbzXeMiqpOb2c76Hu2gsHX2Ga9Ib5P0VVzNdLJu+8BpvXkYtwsQAn92C9cAnfwVUNQHXf4TPd7yPrIyuEcyPv8D69LLCsrhv/CwBPJvmvY32shlP53E+24ZFfJZNiwn4S7aQaVh95TmXcnJ8HI+dPYtZRUW4es4c+B0OmKZJALfZkNM0VHg88Dkc6I9GoSoK3rNyJXTDgGEYUwpwQ4BdKJWCqihw2Wx4z8qVF7z9g4ODBGZVhVtV4bTZMCaqvJkAxhIJhDMZRLJZBBwO6KaJVC6H1rExpPJ5zC8rm6rL3hONormoCIZhoGV0FBlNm1KWR7NZfH77drzn4Yfx3b17cWR4GD/avx950YHt4NAQ7jx2DKcnJpDIZjGZTqMxGMSi8nKMJpMIp9PojkRQ6fXimY4ObO/qQjqfv/AznRl/05jxxF+NQ5KAbe8Bnn4CkBaw+tXc1SI2bdAzrpnDGLGhAUVVwEWv4yZ1+2cBKATDe75F+lq1EwxXXMafj7/A1xNh/h0yc3dh0sty+wiyj/yEjS5cHm6Qz991firPhcbm19OziocFGBUTVIureA2KjWATHePfXV7+zVdstbmUQCD1Fk3rpW7j/ZomPfya2Wz+sfpKAtJDtwFqgkKo4irg8lvJJhQ6tS3ebKn7MynqB7paefx1V5PSXrIFePRnwJFjVinadBzICqPH7iS1m0myKYwkU5cQn6QxoOX4/j0PEagKdcUnhzinHh8B0e3lsRoWAhuuJ9NRVktNwBO/4vGXXwZc8bZz5/b5P1JnUBAb9p8WQq9a4Kr3nP8sdJ3z0nFEpK9JvO5Zy4B3fM1iNsJjLOYy1su/Vc8i+3FmP5+jTRSQKakG5q9h1byRLhbkqV9Iw3K0m2K4Qkczu1MwMRcYisJnt/IKrsHyeksA6PKwi5uWo5HQe4rrvaqRxXkWbWR1PMVGAP/OuwjuTi+NRC3P52zoljFlU2nU6Rqw92Eq2oVuZDyZhCxJiOdyaJ+chCrLKHK58INt27Cjpwc5w8CnN25EwOnEaCKBHb29uO3AATZAcTiQyufZixzMF19QVoaPrlmDhqIiPNXRgZyu46K6OiyuqJi6fVVRYJgmKrxenJmcRE7TIInOYnZFQc4wYJgmFpSWYmNdHR5sa8N4KgVN01Dn82Fvfz+8djuumTMHNX4/HjpzBg6bDSfHxtA+OYnllZV40+LFuOPoUdgVBTV+P06OjeHY8DBkScL27m70hMMwTBN5SUJ/JIIT4+P43r59+PetW/GpDRvwyJkz6I/FUOJy4czkJMZTKeR0HXv6+/Gp9etnCrz8H40ZEH+1DsVGD+ui95AOL1Qxy6bp5Z7Zz421vEGkfe2z6NSiCqshSmQM2HwTy2Y+/wfmOtfMFR6SSQ/H7rDaZhZX0SM/e4TAdOxZ1q32l5LC/GuGJwC85UsUuiXCBJLBM8DBJ60Sme1H6OWeeBHYdCMgeelZ3fV1Ao6msYDH2msYU/YITzuf5fU5XATcS97Mc85bA9z8OXqcBYGUrr28J/jifTRmQsN8X3cL73HVFVTtH3iMoGB3kRqGxKIiniCNDy0PeFTgqneRph3tITCrbMKB33yJYrV0wmr6kU0JIKxhXvjslcDrP3nudS3ZzH/5HLvVndhFr7J2Lp/tsectBmFyiGvAX0KxXE8ra8hPH32nOZ8VTTSMhjqBX30OeONn+N6CALKoHHj7f1AnISuM03/nHZwft5j7iX6rDa2h832qkwAaGuLfDz/BYi+qnd7vQ7cBOT/wo3v5jLa8wcpRl+VzU72GOhmq2P8o590wyEpUz+LzGOrk84+H+U+xkd1oP0xD1tSBvpNkNu7+JtdtoIzGbt9pfifmr2WxnfF+CiwF/Z3I5XB8ZASKLCOVzyOWzaI7EsGbliyZujzNMPDjAwewZ2AAmXweyXweQacT80pLcXZiAiVuN4pdLiwIBvGnU6emisHYZBl7+vvxyfXrsbyKaZgb6+rwTFcX4tksmoNBnBwfB0wTXrsdiiRBM4ypwjCnxsdR5nYjk8+jyOXCeDqNnGHApijY1dcH0zRR6fOhMRjE/NJSnJmYwOvmz0djMIicrk81a6n1+7FvYAAT6TQ6RcEXzTThVBRkDAN5XcdwPI5wOo0yjwc3L6Y48UOPPYa6QGCqaMyOnh4cGBxEicuFbaIE7F+rwJ8Z548ZEH+1D38JsO29wEM/JIWaTdPrKlDo0TEqxCMT9NA0jZ/ThccqK0D3MYKPLPJ445Okb4e7gAovN+RsSsTLh/lem40bqWqnaK5hIRXu+Zy18b/SUO2kRtFEEI+M0RBpP0TjonoW6U4tD+z8M7D8zfzbJ35BY8LpobeWmZYfnE3x/bJitVvVNQBiA2lYQDD70zcIqrKNzMUNH7WKjWh50uGP/pyeY0ktjaXwCEu1rr6Sc1tczblPRjnHkkR1viTi1IUKcd4g07MSYauV6OGnea9dLYy9+kpocOzNCtAyCUZ18y4cw9bywP3fY567YuP8Xf5WwOnns5BFBkAhrrtwI++h4wiByzStY+bSnAeAOoaBdp7/qTsIfq//pJXy5/ZxXQBkUBJRwFNk9QHPJFnDve8k71W1s4JfYZ3MWUmGoHkp0LQMePQnFAZu/TjfF53gPL3u45zHTIqaDC1P73jXfRQA2p3Aiit47X2neN1anvNu6DS4JodohAy18ziuNI+v5bjGS2to1Gy6SdTlH+bc+Io5P2cOAZdGAW8QC0pLMbe4GMdGRuBRVQQdDiytrMQznZ1T6VM5Xce9J0/ij62tME0TZaJGeVbTML+kBDldx5rqaiiaBp/djmMjI6gPBNAYDAIAQrKMJzs7p0C8zOPBly++GC/29SGv62ibmMDu/n6MJhKQBCuwtLwcTlXF8dFR6IYBSZbhUVWEM5kpwV1TMIgnOjpQI4rT2BUFfocDdpsNbtG1zTBNyJKEjKYh4HRiKBYDBPUPALphQBUxfQDoDofxzd27Ec1ksKqqCmlNQ6kswzAMPHr2LFrHxuC12zG/tBRbS0tx57Fj+Oi6dX95T5gZFxwzIP7PMBasAwL/Afzk4/QgHC6CC0xumtkMN+DyeoL8xIAoZakRfMMjVipOJsFNz9AZTy2v42cTYYvOhMlyqlWz6WElo/xzPse2l1e9W9TI/ivH9t8yR7vAFCTCwEWv5WuFAjW6MD4U5dzUH6eb/brv/BJrygOMe9vd9Eq9RcC2d1vv724lgFeKWH0qDuy4mxR2IkyDoW0/u7ul41QslzeICmAxIaLz01uOjAD5vJDuyny/JHGeTQNTkpSFG5gmlkky5hyb4HvsTj6LXAbY/A16tIefJluwdjbQspusynUfOtcwGjhL8Kps5vM6sRv40YcJxpVNZAa0PL3ROSuZfhgaZse4H3+U1zF3NXDlO3lvskzWobuF9+L200DpPckwSfWs85+Zzc7r9/qtWgIF6t3lsxqf5MY5FwWjLBXjOtv7AJ9FPMTXI2M0AjuPc42aBo2t8QG+dmoP11syQnbo4ONkhdwBsg4F483l5TOVZDHPDaTJR7pp5Ok6GZSBs/x7eAS48t2Cri/i2h5q5zO480vAxTdDWnQRNtXXY8/AACZSKaQ0DcdHRlDazDWUzOXwsSeewLNdXRhMJKCKEqt1gQDiuRyumj0bWV2nuM00MRCLoc7vP6cRyYWGQ1GQyucxkkigJxrF3JISzC4uRjybRTKfx+bGRlwzZw68djv2DQyg2utFXywGzTCgGQYWlZfDpiio9HoxFI9jJJFAOp+HQ1WxtKICdX4/LmlsxHPd3ZCFUXfTggV4RFGgmyZ6o1E4TBM5w4CqKFBlGZc1NeHnhw8j4HSiyuvFvsFBSCL97NToKI6PjcE0TWQ0DSfGx5EvKsLpiYlXvM+Z8cpjBsT/GUbbAYJPdIJx2qIqbrCpuABGDZi7noVP3vhZ0sGKjZ5w32l63FWNrMA23MkN2ummx9l/msrpYAW9oOJqgkJRBYVKp/bQ60lECP5FlcBjP2f6UVHF+ddqmizGkkvzdcUGvHCPEDvRC0EqSiDdVGuJ1S5UAKYwgmVkI4Y6meblCdLjiozSMzyyndfXsJD/h0ZpLATL6ZWFR1hEJjrBLl0LN5DKHu3lHEYneG118wgUa7fRS/WXktmITTIDQHUS7H1FBIlCX3FvELjl3wjQR7YTLNxBHktSaATd8y3+P9LN67Y7qOTuOMIKaGu3Wfer5TBlIJzeL9TpQvAXGSUtHQtRMa6opJ8BaiVmLaeSvu0gn/PV72W64KkvEcx9JQTC7haev2A8ATTSultodFQ1s9jMAz9gXnghLU2WRZMVJwCT1LliA6qbhRguQkDfcTfv0Wbn5zJpMkCltZzDo89aorp4iOtmrJfrWcvyuooq6OUHy/ncbSrXZCrOc0fHhWGaojhOdVhNYSKjoqNeM0V3JdU07pIR6iBq5zK09NjPAZcPRa5iDCcScCoKZEnCRCo1lZf9ZEcHdvf3o8rrRTiTQVbXMZFKwS4AdE5JCT6+bh1+ceQIcrqOuaWluH7ePHx//34MxmIYisfRG41iS0MD2iYmML+0FBlNw7f27EFfJIJQOo3OUAiaaWJdTQ28djskScLKykoUuVz4ytatuPvECbzY348yrxeRdBouVUWx0znVOvTpri4cGxmBTZbRGAwilslACgTwtmXLsLamBrFsFjV+Pzyqih8dOIC8YaDI5UIsk0Gl2425JSUwTBODsRh005yix+v9fgyJ3PVHz5yBJFTuhmkir+vICtHfzPjbxwyIv9pHXxvw8G0sBFLZRAFR4jS9qerZ9KIrG6nmNcG8ZFkhMK7ZRhVyyw7gmTuZLw6Jm+5oL2OH+RzBGxCFRGoo8Nr3CHNvJ4a4kcYnmQfed4IAWCieMn2YJrDzXtLVskQwu/GTLN5R6DcN8O+mSTobEkVGshOvOPQ8gcM0rDBBJsX5Sf2OG/yL9wLZLIFyrJcAV9VM79PhZk65/aho63k5sPAigmh1M+/9+g/TCNh5LxkB0wAq6pn6VFRBg8PtJ0AU6rEXRrCMiunYhGgyMySyAGSgtI4gaJrARB+QTtHrH+3k8cb7zz1WZRONrIlBAr8s05MMj1nzUCHYg1SM8WstC3Sf4GftTt7zgcetfPz6BWRw4mEeLzzKVMXyep4znyNb0tMqmBcJeOO/Ah/+IfCzTzClLSoKu8RDgJThOZZuYenUg0/yOKtew38P/pCgmU0SWA3BDG2+ybpuxX7uesimRGMdoaNIxiiETCWoYdA0Ph+7kwyFogimIw3oXmDOCn4HTu7m55sX8P7G+iwB3VN3CLp/KechnQA6jyI9ewuWV1TAME1ohoEytxspocIejschSxJUUVN9IMZshgqPB6+ZPRuzi4uhKgp+tG0bXtixA+/YRF3Cv23ejO/u3YvxVAqrq6pgk2V8e/dufGXrVqTyefRHo+iPxRDOZBDNZDCWSmE4kUCR04n/vOQSLCwvB0CK/NZly3DrsmUAWBzmyfZ2jKdSWFBWxlzxri7cuGABAJaOvevECfxXRQUkIbQrjH0DA6jweuGy2ZDI5xFzOCDJMjbV10MzDOzo7YUEoCEQgCRJSObzKHa5sLG2luAtvue6EPJJkoR3rVjxyt/dmfGKYwbEX+2ju4UeQzpBkZPNTlA1DW6EizexR7aWFXm6TfR6U3FuWB/4Lrs7VTWzAtjOe0i7ZhLc6OwOHq9psagvPsD48aor6KWc2g/sf1j0rZYI6vk8veGXjv42YP8j9OwVhUCx/bdUGj/wA9GMJEsQaFhMEJ63jl7ShHb+8TIpUseqg20vS6uBVIRVwnIZsgfeIgIXQBVz/2mmvvWeIn3u9vK8kTHm2CsqDZKxPqqgN93IzmJVzfSon/w1wapxCeen7wTzxOMhGjjJKA2Cisbzr3ffo/SKo5OktBMhXrfbR2agp5XUdDLO59dxhGBS0cBz7riHrEHDIho/O/8MdBzieWetICi27ef1e4tYTGaok0ZGaJjzP9JFujg0wnm788tUjx/dzvvR8mQW1l3D2HQ2zTW172Eq6hNhq07BTz8G/Nufmd44exUNu8gYQXTuKuAdX6dYsnkZU8S0HOdprJfnstkBr4Pr0eGiCn/FZZyrxsWcr3Sca8Xto4GRSdCwWbIV6D7OeLjDwzTBigYaMm4vq/LFQrxHj052Z2yAhkllM9kAw6AA1DBoBM9aynk6e9DSDGhZoO8MilsPwpHxorGuCXLdPIwkElNx5oVlZQg6nQhnMvA5HAg4nSh1u/HJ9etxzbx5UEUOf7fwqn/f0oItDQ2oDwTgVFVc3NAAj+jhHc9mcWp8HM1FRUiI+uSSaSKSzcKhKPDYbPA7HPhtSwvevnz5BRXgmmGg0udDuceDJRUVOD4yck6uscNmQ/Jl0sDi2Sx8djsWCwPh6c5OZIUyXhXMgmma6IlEIMsyFEnCp9avR/vkJDJCbyOBPJEBoMztRl0gcMFzzYy/bsyA+Kt9uHxW0w9ds3KYC72ox3qBk7uo4pYVqwGK00NvsBDHrGigOKqsFvjZJ/lNbFhAr/zMQR5flukVF8pZFlcDyZDVvtPU2ehEexlxW2zy3Epg/hKC5Ud/QsDc+WdS+7OWE5RaXiAlfHYlMPdaxkcLpUFDI4KCjnATXrQJeNPnaYQMd7MNaMMi4Nnf8/25LAVoqTjnadFFNHycHir3x/oJ0qbO+5m1nKAYHQce/jELg6y6giBaaIXadoDzGyhjrnQuw3m85JZp+gExTBN47vfA5AjDEWM9NEJUB8EpMs7Pp2JWmtz4AD3E+euBP36NnqfLRw86HgLe/Hl26Hr4Nj5Lxcae2fPX0WPd/yipboBMgb+U85bPUs1fELk98H3AlJgDbxpARgMUB/CDD9BIKuglJgboDdud1ETk08Du+zkvT91BL1jLcg2uv5556cmoZdDYnfy95yS1Fk4PjSlINBRP7qaa/PJbSWdvew8rz0XGyFYoKkMF1bNJtwfKaKhpQhB44yd4re1HuK6yaQrVdJ1rMpsiE3LrV4E/fZ1zKCt8dv2nWdlw2SWs5jfSzWvOZ4HhDiytnoNLkzJe6G2HbEgoqm7C24Xne3FjI96/ahXuOHoUoUwGG+vq8I3LLptqNgIAHaEQvrFrFzaZJn62fz/+Z88evG/VKtgVBclcDgXCWRdq8KZgEHWBAFrGxqAZxhSFLcsy3DYbeiIRjCWTJBbGxqDKMlZUVSGr6/jPnTsRTjPrwmO3Y1ZREU5NTGAkkcCC8nJMJJO4bt48ns8wMCaKyZS63WguKoIJIJXPwyFi44W+6qaIj79z2TKUeTxI5fNoCAaR1TTcefw4HIoCUzAVLmFs2G0zEPT3jpkZfLWPxZtIh/efJmgbIn4sK4KqraV34fRQ+JSM8ufxPsavn7oDgAks3kKV9/JLuBkee45eu5YjHXnRjRRJFWpemyaw8jJg30M8r8PFcwbLrK5pLx1FFed2VIuMcfOVZYrhLrsV+P77KEbqbyOF6/ZZSu9d95JudftZy7tQVtUwWOp1zkrG/AsjHgZ2Pwi0vsj5SUa4yR99lvFqp4eA238acEcIYpLEmuqF6nSyjQbM3f/NNKv6hUD//bz28DCNlZrZNFDcPqrMR3ussqRHn6VmoHo2NQeFhiKSQo89l+F1tx2kl6vlgOq5BPfyelYhCw3Rqyyv53HzOVL6TjdB0BNgbfyFG6ycd4CAdGIXr0eSmKVQ0cA4euMiK36ciPJeC/HpfBbYeRfB1+2nUZSO89oNQ8S2YzTC+tqAy98B/PbLpPIlGwAJ+O1XuQ6D5WQR/CVWsZjiKr6naYnVOc7tZ/GXjqPUZcxeASzdymtYdgmvv7uVRl6h+l15k6Vej/yBoYHaOcwZ9xWL0rQCqBdsoBHx5i/QSKqdy/cU0tB+9kkyNmV1DBflMgwpte0D8lnIuQzeHvDjCjOPjCeL6ksugUsUcVFkGW9fvhxvWrx4qhTrS8eTHR2IZjJIy/JUL/A/trTgmrlzkczlEEqlEM1mp7xnVVHw1a1bMZpIoHVsDKoASJskoSMUgttux8effBI5TcN4KoVQOo1SjwfXzp6NeDaLpqIimKaJpzo7cXx0FPNLStA6NobEwAA+tn49Xjd/PhK5HH64fz/aJydhAthUV4d3rliBD6xejd+3tCCUTuOWxYvRF41O1WZfVlGBTQ0NU+VcAeCB06fhVlU0BYPojkSgSBIgSWguLj6n1enM+NvGDIi/2ofbx5zruauYFjXWR2/RpnKj9pcB4SFuTjd9Gnjq1/RIXX52Qjv0FMHQ+SMWyLjm/SxVmYpTvKXYgNd+nF26DIOU6oHH+ZlllwDv/AY339FuUesbjIlPK1s5Napns5PXrnsBSASc17yTm7tp0hDwFdPQ0PJWExO7iHXvuEcoqGV6rJVCNS3L3KjjoXPP5ysiLXzsOdKpqoP/DINg8PavsYnKi/exDOp042K0h0bAaDdjs4kw47gf+TG9uWfuJJg2LrJadvaeJJvQvJQhDllm7N/hIZi6vfSMc0LgZbPzORgmGYYF64Dn/kiQkWVS0DL4DEyDQNq6k5+PTwK//xqfi8NDurtpybn3X1QOvPUrpNjzORorHceYipjPcl5HexhDz07wf0MHYBLU7U7RpCUv8t79onqdSQGc000mom0vuVObnUyBJPEZHnwCeNu/k8l48T6ec8VlDE3MWcW0snScz6NQGz2T4hpOxqw5LLBHdfNoeN78WeC/b6VIsPB6Og488UsaZU/ezmdUWss14XDTYFst0tJGe7j+vEU0sI5u5/1l0qxb/+APAIcPGBFCSdMEQsOQFm9GTWQQcDuZrjl/7Tld6RwvAW9TxIUN08Su3l4cGh7GpspKjCaTKHG5UOx2oyMcxkfXrcN/7dyJvK4jo2n44YED+OzGjShyufCrG27AI2fO4PajR9E2Po6oyLm+du5cnJ2cRNvEBMo8HgSdTozE4/htSwvW1pKtymgaIpkMmoJBNBcXo6moCH3RKDbW1UFVFPz2+HEcGRpC0OlETtdxz8mTKPd4cN28eVhXUwMAUwVmHjt7Fg+0taF1dBQ/PXgQ71m5cioEkBGd0lZUVcHrcKA7HEaJ241vXXEFMh0df80uNjNeYcyA+D/DcHlYJGPOauD4c8DxnQSionIW4Fh3DQHNXwy891vcNH/wfiEesjGmmggTnOevo2f42o8SLBSbRX+37iQAF8prnt7LNK4Pfp+NOEKjjL++/lPc0AtUfWFIEunfxZvp6bj9VCkff57vXbSJaukHf8T3p6KMPSs2q9Vq4bgTA/SSa+YIYZTBTXv60DV6dqFhgljBi7TZgVkXCUo9TmDZcfc0D7qRBkLfKSr9ZYmUbWScm/629/D1J2/nOVJxy8N2iqI4lRU0kDbdSOPEX8r63KqLQKI6GItPRWkouESaliRZ8eJ8lsxIZRMZkL0PExztTpHPLDQIc1cLAdYxepixEI2MoU5671e+g6GJnlYaTpLErmYFxkYVRkI2abWWBYRIzMW/o8BMiNf8RTQa7C7OrWSKtDoQ9BWF9104x+JNvObYBCv93fJFguBTv6YnrueFV+60usgVwDadIBBPDLKrXEHsV0jpUxSmmp09RG+9rJYFi8b7aQhdfivv5aHbgEd+ypoJWpb3NTbAeS6toZGSCAP9Zyn0U1Sur8F2shVHnhG93Z2smte6k8zPS0JHpmnima4u3HfqFAzTRHNxMVKi0poEIK/rGE+lsKGuDjZZxpGhIfgdDiwScejucBi/FGlcfocD2+bMwRsWLcLj7e345eHDWFBWBreq4szkJNKipel4KoVENguXqqIvEkGx04mMpiGv66jy+aauLZbN4sDAAM44nfjVkSMYjccRzuWgAMjqOroiEXSEw3j/qlXoCIWQyudhk2U82t6OGr8fLpsNR0dG8Nvjx/HBNWuwu7cX/7VrFwZiMZimiRq/H5c0NeELmzdjfmkpXpgB8b97zID4P9OoagKq3k1P+v7vM32sZg5bY04HU9MkUGTiYpNOWark3lMEceDcmtwAc3i1vKhnXUzPbaiD3uNrP06AME0CyNmDBLQr3sGmKNOH2yf6PD/HjbFCCM8OPEZh2lXv5uuDHfSiR3qAhibGKccHABjM9S2uYMEUQ2PMum6edY5clp7z03fQw4Nk1SSPjQO9rcC3buU9qHaeo6iShs1wNwE7OsGNXLUTgOJhMhGX3sK2qOFh4LFfEJRL6+gd2+w0UGSZugJjmiAvPAL2Dy+mJ1tUToNo5ZW8z4bFfK39MI+x7b00bCQJeO3HeN1nj1CYNdpNg0IXYQs9T6DTNRaCCY9Y1cju+i8add0nANsZGgJuH8G6vIFGRzourlux8t7Do6KLnUnGwFfEOQCoMPcW8ZlUNQNXv48hh0SYoFo7j4K3QlvPmjmcm+Jqeu+hEV7//PVA2iOK99h4b7LMeU9GaUw++3uGFBZtZAW+KYW8GJrG3/vbOAeTQ6TjyxvoWRdVMvzQdZwGgb+EGQSjvfy5qJJsBkBNBAyr45mikv4vrWUIasVllmhzsJ2Gl6wwzu8NAku24Gg4it8dP45avx+KLOP57m4YpolLGhuhpNOwKQrcNhsymob3rFyJ/QMD8NotQyCcyeCekyextLISWU3D3oEBvH/VKpS63Qg6nVMlXH2qCk3kc2c0DbppwpXPo6moCJFMBnldx5aGBmQ1DaOJBNonJxHNZvHQmTM4NjKCvKYhKjqbxXM5OBQFkUwGvzh8GI+fPYsqnw+KLGM8mYQqUtMAoMbnQ8vYGJK5HL74/POQACwqK8NEKoVIOo111dWYV1JywS1qZvzvxwyI/7MNw2B3qJEuehcTA6wB/tYvW602FYUeXu9JejeRMXpSuTQ97eWX8LMvHf5iejSFPtejvSyKMjnAjXPVFfRqWl7gxqjYSKW+7auMxb50DLYTHGSZ9HZ/G6+nq5XxzXXXUD1sdxB8Q8Pc5G12Aozqolek2FhMxeVjSVJ/MXUCPa0EmtAIY826LmplyxTg9Z5mPLlxMdPrSm00aEqFyrxxiVXWs+MIz3t0O4Hx1q8SzGvmcH6LKpkzH59kSl86wevpaqEXns/QY7epNAgKArbauTzGwScIMl3HLVFi+2ECl2IjqFzxTt6L3cFKciPdBJmRLsaeF28S5VYHqRXQ8gTMgbM8n8MjBHhZMgCBMv5fEKt5ipjuV2h1WtnMZ1JaK3L1VdEvPkXQT0YpQOxu4fvmr2VhoZIqYO5aerZP3cHKcqO9fN0TACAB932Hn1dUoHy1MJYcotOeTaTEtRLAb/gon0HBEJ0YFqyH2ypapOUoRpwYJKvR1UKP3VvE9RUZ5doNlPL8bh//b1jIa46OMcQhKzSq0gkeNzZpFZGpaKDxWBiyzFDFSVGVLp8FTu3BmSXXwa2qU/R6jc+H46OjWF1djWIAyyoqMKuoCB9dtw7zS0uRzOXQMjoKv8MBwzTRHgphZWXlVFnV3X19+MSTT6LS60Uyl0N3OIxELoehWAw2WUYql4MsqrU5bTbkRIW3Wp8PdtFAZUFZGbojEVza1ASXqqJ1bAyaLEORZWREbXfdNGEzTWQ1DUdGRnC5y4WF5eXQDQOHh4exrLJyqlpcqcuFUDqNRC4Hj90OVVFQ6nZjMpXCb1tacDYUwgdWv8R4nxl/05gB8X+2EQ8RHMvqRUtOD2OMoREqggvjkjcz1nvbh+h9OLzciM4eBH76CVKQa68+t8jKumsZh+w9yQ2xIIYyTILU0WcJcKkYr8HuEkrsPiv33OkhaCoKN/tDT4oKZCf5/vo6XvvBx7lJD3cTTCSVxxjvp8dfVsec+FkreM8ndhH0Fm4ALn0rwdfu5vsmh0idKnYR//dYldJyKb7HZiOATKezF1/EYw53AroB+ANkAlIxKtM3XEu19PUfofHTuIheoaoCo/0ExkSE3mlFA/O1w8O8HtUODHUxTz+TZAbA5KAlTDRNnqO7lV4lQMX9jZ+i6jxQynNnEvx5w2statmEVVt9tBvIawTI6BhzrCWZAJ+ICh2BYCk8AcDmE1S/SeOikGKo5entZ5LsClc/n+C2815g+28I9A2LaRBe9lbS0Xd+Caidz+P3nWLYpHk5wynthxgmGOkWPeZjgpmI0IBRHaTCJZnMwnu/bdVU9/isbmiZpKiZn6foUFFF/nmKRsKbPs/PzFpOTYUmahLERa5532l62KZBz/2Wf6Mx9Pxd7NLXe4rnq1/A70/LDiriM0nxfTlEdsHhogGx7xEY/WPY5ZkDt9ePOcXF8KgqLm9qQjidRk7XceWsWXjfqlVT3vcVs2YhnE5je3c3ZEnCnOJi1AgKPJXPozsSwYbaWtQFAih1u7FvYAC90ShM06TYTVHgUlXU+nyYSKVwcmwMNkVBMp/H2upqpDQN9YEAqn2+KTFescuFvkgETcEg+mMxaOk0VNEXXZYkeFQVPdEoFpaXoz4QQFc4jM5wGMPxODKahncuXw63qqLE7WbnNllGTzSKvGjKYpNlfG/fPtzsnWb0zIy/acyA+D/bsKncxE2DHrNhADAtL7wwFBsp4comsWk6RZwxIcqP3sufL73F+oyvCPjIbcAXtwHtR0UM1ADsdip8A6X0kL3F3HBTMYL65BA9skIhljmrWDildh430ETU2oxdPgKRJFuUaV8bUFfGTddfwk22EBPvOckGG3YnN1Kbk17e2qsJcDVzCdYdRwQ46qK2up+glM/xdV8Rr63ggc1fT++yspFx5/J6Ht80CbapGH/uOUFv9tJbKOgzdOAPX2MZ04LXNnslPzPay+uUZZ53xRUEtNs+TCHgxACflaHxOCNdnM+n7qDxUDsX2HgDO4ztuh/Y+6Ao95qgCt8vQhwNi4Adf2JMPJe16HFdzG9JNT1MXQcCxTRuHC565qEhXtvs5Xw2xVUE08EOzt28dRQDyjJDCYefYmw+NEyDpXEJY/+KjSGKVIyhBkjAse00itoPExArm3iOyvUE7UUX0bONTQDLL7WyEsb7eb0FEF+8maDc3cr8bi1HTzmb5PlVO8MVb/8PGgYAayV0HCWQSzI/UzuPxw2W04uubGJIZ+nFwJVvp/fucJFRGOnm81x3LY9TXs9zPfpTi/o/cwDhvIY9iRzGjSjymQzOTkxgQ20tvnH55Shxu7Fjxw68Y8OGc7+ysoxbli7FzYsXQ5IkPNXRgT+0tqLY5cJYIgG7oqBagHo6n8eRkREoAGRZRlbXoek6NMNA1G5HQuR/lzgcsMsyjo2OYmlFBVL5PBqDQfRFIqjwelHr86E7HMZ4MglN16l+BxB0uVDkdCKSyUyVbx2MxXDLkiXoiUYRzWbRXFSEnX19yOg6/mPrVvzr9u3oj0aRyGaxsa5uqkd6gdKfGX/fmAHxV+PQ8tyMxrPAf98ObHwdsPF6bpyeAJt07HuUG3guA6x+jVU9zTC42aoOAntJjSg3GWVerWJjjepAKeO0l7z53Hh6LsMNs7KRwJtNszhJ0LA2xskh0rj5LEH3xC5uyC4vga/9MD2g/jY2wnB5mPaUSdBrd7oJsvPXsrjKxADQeKmlek6EGYP/1WdoAGRT/KzLB5zew+uShacfHuYmvWQzN9uek7xfLcdrMXX2Mt90I6u0dRyhWK/3JCldgECUz4EAK4yApiUsbrLjz5xHLU/jYv5aMgtuP8VWWp7HcrpoXE0O0ZixqQQyTRgR6YQQlMmAIsRj4/0UG2aSPNbBxwmWV7yd5y6r57UceYY0/oYbeE+tOy3aeOAMafRcBpCzfCayzCIz0TGuHcXGwjOSzJ7lfSJtq+MIjYj9jxHAbvmCFWbJkTpGRSPV7i4/n01kFFCWUxcRGiEgD7ZT9Fh4JskYRXhFlUKUqDOu7nABZTWW919Yb8C59fLzOVYbLBh+66/j78/fRWNp/jrqKnxF1mdUO/Cur1PkN9hB8K1sElkDAR7T5eNziId43MF2grUkMQ7edxK46p1sv/vIT2goZeI0ZLxBQM+jX/Vhn6sclXoaEzARs7nQHg7DLjzcad+k84YiRINXzZ4Nt92Ow0NDmFNSAqeqIqfrcKkq9g8OQpEkKKJhiSxJU+leWVFsxWWzYTyZhCn6kUfSadhkGa+bPx/bu7pwNhRC0OXCiqoqNAaDsCsKxpNJtIyOoi4QgN/hwGQqBa/djrFkEhvq6nBZczP+a+dOrBSUummaODQ0hDcvXoxH3vxmjCQS+MaLL6LE5YIkSdBFbvtfqg8/M/7ymAHxV9swDAqInrkTuOQTwNnDBCXTALbcxPdsfB37Ofe0kDoePEPwcPko9hruAmACG19L8Nr5ZwKGLJO6La6wlOkvHXqeoJhJERAMnRt+eR0Bv6Bez6rc/Gx2ekxLLubnC4VDcmnBDoh0pWVb2XY0mwCKK7kJl9YwBzuX4ueWX8oNfvMbuemX1tEbT4QZH08LatnlpdcanaB62FfM9pqFuHw2RXDy+AHJJXqLvx0oqWSq3vz1wD3fJNABfG9ohGCoZVmApaoZeOB73ORjk8IbfoBzY3fRmEpGeV2pGA0TCQSW6CSB7NGfEZTPHCSTYQrWRBPeS3kd4+iF63b7GDOPjgvRlY3gk01Zoja33+rUtWgjjSlD47n9JYDTR+q76zg/e+AxVjHrO00vPhHhGnN5mfNdVkf2YHKY6vjrPshrkWX+q2jk9STCon5+GZmRXJYe+9mDopBNimEU2cbnkY7xWiuaRBlYieuyuAq48l3si17IbnjNO0UsXaz/h2+jAdi4RJw3yufxtq/+5e9P7VzS3607OQdanrFwh5tzlhcFd574FXByD1A5TK/fVhCeSTRudt3L71ZlM9M42w8DxVU4WLsOI0kFdgAp2KCbJobjcXx91y7856WX/uXrA9O6Lm5owMUNfO4doRB+tH8/eqNRGKaJ1VVVODo6Cs0wAEmC02bDmqoqtIyNwaEo8Nrt8KgqRhMJ1AYCiIkyrI+3t+Py5mZ8Yv167Onvx6+OHJmi9EvcbhS5XJhVVISA04l/2bBhqqwrAAzF4+dfp/jfY7ej0uvFh9eswU8PHcJkOg3DNHH1nDmwj4//Vfc8M15+zID4q21MDFBI43DTswyUciM7+pwF4u2H6Vkt3sJNcHKIXorDTVqwrI5g/OCPSOM6XKSfo+Pc2CeGCNBXvv18VbvqpFgoesjK7a5fAHzyV8yDDo+SEnV6ufHOW0NwHu1mzDGdIF1e3sB/R56h9y0rVJe/8bM8XmySMUktB9TMo7dUv4AbvUfkIrt9BIb569jJa+C0oMLX8vyxkAAkH9PETIPAPNTJmLk3yJi6qgKHniBYANzIC4VPANK3p/cAy7ZwzlMxNkwZ7RPtMk8RUOOTwD3/zdddwhOPjjEFbO4a4N7/IWBks2QAJgZ4j6bOz9tUzqndSYBYcTnjrAUwMwx688FyUYp2gAaQluf7p3p5Gzymzc75GeygIeAtpghxsB1oXsGmLd0tjL0HSoXIK0Uj7PBTBNmxbpZULYRHCsOm0gjc+WfO6Vgfz+srYuphIkJjZ/VVDAUceVq0qXXSu7Y5qLtYshl4djswr4He8qwVNK5mLbOKxEyvORAPUXFe0Hy4fTRUwqM0+ka6rXa8BeCfPo7vBH7yEcbuDYNzFiilV56MMCzy8I+5jioaGA5KhLgGF11E4+uBH/A75Qny3hoX0RDyBrExOQm7VoGobIPLyMMGA5LdhfZQCD2RyN/0lZ9dXIzvXXUV4tks7j15Es/29GCFJOHw0BBgmphbXIyjIyNI5vOo9noRTqfhFq1A55SUoFQAtGGaeKazE2uqq1Hl88EEW6jaZBnPCQV9OJPBUDyO+aWl54B4hceDReXlaB0dhc/hQCybxfraWsSzWXx91y6EBHBf0dwMr8OBcDoNr6rS0JgZf9eYAfFX2yh0rCqMQpvObJKbdWUTY7SKSm/3zEGC86m93HhVB4HH4eSGFyglmA52kGpU7dwo6xdYxUPGB/je488TAPtOE+SLqwRN7mFlq1VXUNl+YifBxaZy066ZzVhqTys3+es+aMUq3/Ilgnw+R/CtnsX614Uyo5kkRVG1m0U6UxNjt7sfoPESnaA3XDuXx/SJlKF4mPdSVsvrW3kFaeGCaKxhEf8my4wDH3mGQFA3j/n2slDgO70E4k03Ecge+D4Fc3XzSRX3n6ZRlMuIIixh3kdfG42GzTeRXt/zIN+TSVmGkSwDiUmCa0kVjxMVqW12F3DNJ1l7/Owh/p5L09jyBlk7fftvOSfrrqVR0nuKMfqyeqrtO4/R6yytYdikson3/dSveS6AQH9qD0F4rI9Mx8QA1fuyDYDEbIOSGgLV9LH+Ov59qIPXOFFKA0GSaAwcfpoFgex2iv/u/y7j/IqdhW1O7RVd8+qAVZefe+yCvuK5PxCUV11JlqRQ+Ga6YVNoufvEr7iWFIUMyBs/w7BPYQycBb77Ls6x3clnDNAIqagnK+AJcs2V1QkDopxM15yVwM67ma6XitFAMME10X4EuOHDwMVvQmPbAbzjsQfxeEZFXrGhQktjrR5D16xmGKaJRC6H9z3yCCQAb1u2DBfV17/i1z2WyeCZri4cHxmhgt3pZHU2lwsNgQAimQzaJidhmCaKnU5EslnU+/3IaBpWVFUhnsshIMqmypIEWZIQzWaxtqYGty5dij+eOIFoJkPBXXMz3HY7NNEX/Nq5c6eoekWW8dG1a/F0Zyf6olE0FRVhU10dvvzCC9ANg9cxMYE9/f1QZBkLSksRcDpxqSRhIBZDrd//Src5M15hzID4q22U1nIjHu+nNz0qYs+JMPDH/6TntepKvnZyNzdAwyB9qYv0ob6T3KAVG+nwfY9wwzyxE7jhI8AbPmvliHccIwU/McgNunYOvW/Vzmupn0+vJDrB95fUsqtU2wEe3+4CrvkAcO37Lnw/RRXA5tef+7djz4mCKU383eGi8XHDR7h53vMtkb9bzY3ZV8xjzFrOcqy9Jwn02z5m1TBftIl08Hg/N3mXj/Oma6RNyxtImfed4lzc+EnG4ycH+dpYP2PSpsn76m4RQC7U3W6fiJfbeOzmZcDJF6daWUJ1iD7ZwtPW8gShfN5KgbIJ9bwkkba//3vMD29aymurbCTrAFDEduMnrDmLhYCffIwGRO8p3mc2TT3Ex38mYuTgcUxR9CYVZ7lam93q011abQkjZZnzq+VozBx+mmC3eDOPJUkE1rmreKzuFqaoeYtolGl5pqLd/DX2el96MdX7Y30E71yG4YTNHwb2JFiyNpviWkqEgcd/yfclosBTt1MHcf2HGVY58gwNxHyGzzY6DrTu4pqRJDI5T9/BinGFsfdhiwUwQWM3ERYagjIyCN0tVmEgWayTeAj48//wfvwlDIdExigMLKpg+Oc17wZcHrjWXY33PP071MQSGDMkeGFgnhZHkZlEVyiE3kgEO8fGAAA7enrws2uvxdampvO+FpOpFH584AAeaGtjDrhhQJFlzCstxdySEvREIqj2+9EfiyGv6yj4uwqA4UQClV4vPnvRRbjv9GmcnZxEjc/HBiWSNCWSu6y5GRfV16N1dBQ/OXgQbkGtyyLmrRsGIMq9vtjfj919fTBMEwGHA386cQI/P3wYXeEwVlZWoiscRqnbjVPj49BNE8lcDm9ZsgRmKoUnOjrw3pUrL/z9nxl/ccyA+KttqHbgTSK+m3JRSFaglU2T+bFzVpEW/Okn6DV6/EyhMkxRnnSSdKe/hCCdDBO0HV7g2T+wSMcVt/J4T/1aFDqZpBc90s3ftRw90UJt9UKhldN7uaEHyoVHZGfVuCPbGbesan7l+9N1elOn99GrrF8oUp9UUvM77uEGXBDq2VRSoukEAbOoEnjXN1kYZWKAQNawkIr14U5uyIoNgMk0p7E+AkfTUp7HE+C5L7sV+MB3CGJ3/zfQdYxsRzpBw0BWOIezljP2nUsTSErrCCA9rTQAFJUGibeIXpuh0WssFNnRBJimYpzbfFZoBjIspaooBCJJOr8CXmGI4h9QbDS0RrotA+rsIeC3XwE+9EMeq7gSuPKd1FQMtPNcSy+mmC8VFfntXp4/m+K6cHoI6m4fsP33bNFaqNxWGMsuptecjAPjQ7xPb5DGS6Cc1+Ut5nooALNuWFX0fvpxruVCGKbvNJ+dJJFhScVZVGjJFqawBUp5b8EKllrtPn5uiVa3n4zO9GEYotrbAMMNpmlV+9PzNNZGe2iY9p/hWmw/DJTXinKzBteyLAG6+KwE4PWfJtsDAKaBGo8HN5bWom1iHAndQJOmYsPSxfhgays2StJU/vdoIoE7jx+fAnHDNBHLZuFUFNx24ABOjo9P1WLvi0ZR4nLhxb4+zC4qwnA8jgqvF0GnE6qiIJrJYDyVgiLLsMkyav1+dIXDGIrF0BkKIZROo8ztxvtXrTrHK3babFhcXo4KrxcDsdiUqG19be1UOtqOnh7cfvQonKqKPb29GE4mEXQ6EXA4EEql8NCZM6yXDiCazUIBVfT3nT6NLzU0IP0yHdNmxl83ZkD81Ti8QVLSL7zA9J90gn+XJJEPPAFseh3FZG4/vY0zB7mJ+0roHVU10eMY76cnpjq5wadiBLcrbuXrkXHS1bLC92aS3ND0POAJE7gueTMFcekkC81M9IuN36RnWvCAYbKC20g3N/WKBjabmN7x68gz3EhlkR7Xtp/AP3sbX5dtwJTfAb6n8xhpbV8JY+b7HmW4wGbn6ysuZZGW0Ag/b+pkFuatJWvRupMGg91llSUtgNSzf6AwLzIh7kcm82Cz8RypGNOknF6eb7SHrT4hUQiXzxDscxkhbCumGCoV49xVz+J706V8blqW2gXTpHf9yE+ZT64oPHfdApZ99Yv0q9AIy4lODLCi3lCHABcBaIFSGiqpmKXWXrqFxsf234lCJeLZ6zlSy8Fy0v8SPTZqKDTeg57nWsql+fdqIf6rmQPc+hXgm28VxkIF7yuXYS/x9sM0KOMhGo1aTjAO4n9Z5ZrwlzGMMzlEZX3NXIgcOdGsZJCG2wM/ogjSU8SY+KVv4XXkMvwOhIZpzE4fyy9h2Cc0DGSyXI9OL+eyu1WEO5Ls+Lfhev5Nz/E+BzuArMhO8AS41ouraEwW2qcCvMbGxSh+6nZsNIUOo3kp0LAA+sm+cy7HBDAYi+F7e/fCo6o4PTGBaDYLwzQxmkxiTnEx2icn4VZV5DQNE6kUbIqCtKZhPJ1GVtfhczggSxIM04Qk6PIarxeHh4dx8733osLjgW4YCGcyeNfy5VhWUXHeduJSVXz2ootw/+nTGI7HcVFdHa6dO3fq9e3d3Sj3eNAdiUAW9LrXbkcyl0M6n0dqWrEYl0hVs8kyxlMpZDQNF9XVnXfOmfHXj38oiEuSdBWAH4Aszq9M0/zmBd6zFcD3AagAJkzTvPgfeU3/dKNhIWlel5cbbT7DjVWxsRTmIz+xSn+6/dzwXF52dXK66T3JCgG1kHJVWkNK+b7vsmVm6w5WtUpGwK0HVrOS93+PXogkAZ1H6T05XBR1xSboddXOE2ItLwVhdQsILmcOEUynV5M79hw3el0HcjEC2pxVNAoAKq6PPkPQkoTKvZDaJss8T8sOUq7FVdx0Dz9DEJYVkett0LMLjxEkfMX0uFt3UG191bt4nLOH2WpT0whsI10i3chPw8Y0Gc4oa6AXC3B+vEGqwKPjpKgLDUUkmXR301IAEgG3tJZgVaDRTVO8XyegOFwsapPPUiQ21E519lu+RAPl/u9b7T5Hekn5mgZgEyxIOsHn7HCdu26cHgJyxxHg7AE+L3eAhoc3yHi3YiOQmSBNHp0gQD98m9VT/Or3WPT6sq1C/BXlvdvsTP3b8yCfeU8rfzdEDDsRsXLYbQqgSwwrHH1W/F0io+IWArVAKent2z5iVWZLxgi0S7ey7v4zv+V6qF8AXPG2c+957mrg5s9Rl9DfRqNG00TL2UmmH6p2ztfrPkGG4vDTnJP5a3ldukbjtm4+jaFU7NzyxKZJJb/LT8PVNGhYxsN48+LF6G9pwXgyCd00MZJIIJ7NoisSQSKXg1dVcc3cuXDabNjb348a4WlPpslIaKYJr82GiVQKLpsNOdFG1GGzTVWHm1NSAp/djsHBwakqbuPpNEbCYXx1xw682N+Pz23ahKCIkxdGscuF97wM5a0qCmLZLELpNPKaNkW1p/L5qb7kLpsNiXweOcNAqdsNu6Igkcsh4HBgZVXVBY87M/668Q8DcUmSFAA/BnAFgAEAByVJetg0zVPT3hME8BMAV5mm2SdJUvkFDzYz/vax8QbSt2cPcjPc8garwte81UDZ1+l52FR61fd8i3R5cQU3nFkrppVelSnquvxtpKaTUXr6/WcYU4fJeKKuc5Nq2w/86IPcxK98B4GmqILnGu8Ttb1FHvCpPazeFQsxdUqSz68ml4zymMkIvepMnEAwby0g0oVRXAm85csEai3H1/78LZGeJYsWqCZpbIBgY7OLWOYYjZyCYjY8wutKRPi702OB0457WPIzESFzkS+xKrBVNZNS7jrOe1QEtR6fFAwECFaKQuU7ZHpzs1cCXj+LkAA8x75HKGobauf77W4CuqkLr1Ll+V0+/l9aS1A48ATBsXUnNRKBUoJJeR1BJh3jvDs91BLYz920cXI3veO119C7jYwBF7+R9doLsfB7v0PWYLAdCFbSmOpvExX0hJe9/ffAgo3AoaeB/Y9wTmMhyyAJj9LI2/haqrwVG+eqkJsOiWshWMl8cy3P9ZWO8ZmVN5KdCJQBa7fxc7FJGl6qg2tgfIDGyuormR6o58+933SShqEnYInZEmH+zTR4ftXOcIHdCaRTwAM/ZLe0VVdSqe/yktkyNOoYgqU0VF7zrnOFprkMMN7L/8vquA5DQ8Azv8H1b/kSHu7pwVzTxGA0iqzoD17mdiOcyUA3TZydnMS62lrMKylBVziMaCaDaCYDn90Or92OMo8HoXQaJS4XyjwejCaTmEylsKC0FMPxOBQwHSyn6zA1DafHxyHLMiSQ4m4ZGcH9p0/jxgULEE6nUeJ2w+94SY+El4xr5szBBx99FCOJBCKZDI8lOqTlDQNOmw1eux1ZXYduGChxuWAAqPb5UOx2Q5rJFf+7xj/SE18LoMM0zS4AkCTpTwBuAHBq2ntuAXC/aZp9AGCa5th5R5kZf9+wO4HrP0QPWFasjkqmKTwdmZ7ftP6/ePoOeglajhTjZbdSDObyMPfW5SXlXVonlO5C4JNN8fi5jKjMFqQ6+eSLTAOav46vVzTyugqbrc1ueeqBcnpiCs6vJjfWR7FaLgMkQyImKpP6PdlhXX9JFXDJm/hzPsdY64v30vutqOd1Fzz0QkWuGz5KsJdtvCePnyK8XJpGQ1kdld8F+l91WClLuQxTswqGR1kd6XmHmx55f5tVXU51EmjDw7w2RaVh43TzXsumqZEveh0B6+RuGgWBMhoCR7bzXIFSwQD08LriIbIHHUeotC8IDPvbCCT+EgLu+uvooYYGGXYpeMrTx2iPyI22k0IvrhJ6AbFO6uYB7/4GAdLpIbvTcwK473tW3Fm1ky148X7grv/kvWhZeqIl1YDNT3X62UM0PEpq+L9hADVNQCLAkrA2kY8en+C6yaYIuCU17IhXUiWap1RS0e4rJsMjSUKgqTDNC+DP09d6XxuFmXlRuCcRooFVPZsG5ng/zyVJfG7JKP/1tAB3/BvXwOVv5z20HwbsPj6TFZcD1c0MI0wfqsNqG2tT+RwdbmCoE6l8Hhldh0dVMZRIIJnLQQKQ0jR2ERNNTHTDgFNVYQBMD0uncWZiAlldx3A8jlAmgyXl5dhQVwdZktAfjeLLF1+Mf3n6aTzb1QXdNJEXOgld12HqOhRRQW0gFsPhkRH8oaUFDcEgVFnGh9aswbLKygvvL2LU+P0ocjoxGIshpWmQxN+6w2HkNQ1jmgZVlmHKMvK6joXl5fjS5s2It7e/4nFnxl8eUqGn7f/5gSXpJtDDfo/4/VYA60zT/Mi093wfpNEXAfAB+IFpmr+9wLHeB+B9AFBRUbHqT3/60998XYlEAt5/knq9r3iv8ZDI6xVx8qJyK+85l7EEVE7P+WKpTJJ0tWEwTpyKviRXWcSGHW5uVIbBzbe0hseNh+nxajkh4EpbHo+/hNclyZZYyi+U0/ksWQNJomdVWLu+YiTsPnintVScGtEJekS6LmhkmxVzLrQd9ZdYHmAiZFWmc7hFH+kkf3YIoM2lLQ8+ERHV3YRaWVb4vulCs2xKzKfNep9p8H2yLIriGHwOJdXC2HJcWKSWywATA0i4iuCNj/F6tDyfozyNaZBEnNgURpAsxHKFmD8kwBuwOm69dKRiVvU4gJ8LlFqlTi80DF18RtDhhVagmhAuqXa+lk1zXbnE2sxnmFam50VlOnEvsg1QHUg4A/D6heBMVqx50XIUrk0PBegawxCFCnqmSeOz+iVgaprWelJsPJehiz7uqvXs8jlrPRdYGJicP4/fEr8BfGaF63L7X2auTNYPmGIZJNHP3I1JdzGQzSIOIJHLIW8YImpANbgiSXCpKmyyDLuiIKfrsCsKotksJHFVLpsN8WwWkqjUZpNl+BwOlLndmEilMJlKIaVpU53OCkOCVRHOME2osgyv3Q6bLMMwTdQFAi9bTS6Ry2EkkUBO16euNW8Y8NvtiGaz0MW5ZFF4xmWzodrnI6U+sx//1eOSSy45bJrm6pf+/R/piV/omb/UYrABWAXgMgAuAHslSdpnmubZcz5kmr8A8AsAWL16tbl169a/+aJeeOEF/D2f/39m6DpeeOF5bF23xlLGFsbp/cC++0W6jQz094l60O/4y8ftOArcdzsB4dQeeiV+QR2qdm7QLq+l0M6mCWLFVcAnf2mp1BMR4M4vcyN1uBkfX389sOVGnmO8n0ryuastz8kwWMXsiV/yuKqDhUZGNbyw9A3Wc81laaQ4PcBXXysoWx8359Aw8LqPk+Z0us8FytadwL130KtKxqgYn7+WMemKBlK3ySiFcGcO8Hi9p+j1ZdP0lFUHPUJvEbD1Znraf/4270/X6CmnE3zv/LVAwwLSuZNDFHQFK3lNxZXAzf9qFSTRdeCxnzE1r+s4XtjwXmwNHScgD3cRbHwlLBNaaERSAOySWir3YyFAz1Ic9pYvnd8Cdvp47o/Ajh8RiGUbn+kHvwes2Mrn0LKDc+AJUuRVIuKaY32MOx/dzmtaugV4/k809KpF+mHfabIPS7ZwLhoXs3GLoQMv/IlMR0kNn9lgH15Y+kZsveRSPp/Hf2WVsa2dyyyL6f26QyPA3l9Q05DPkrmx2YCrruOcAny2f/42axqcPUgvf+EGwbI8yGubGCRLk01znVTN4jr2FfMeF6y3MiladvAYhd9TcSDjBa6blr5WGCd2A3ue5joMD5F6LyoH/uU3+MzpXixXFDyTy+Hk5CRi2Sw0w0BO11HiduNH27ah1u+H1+FAVyiEXxw5gnq3G3/s7ERK02CXZZR5PGgPheCw2WCYJio8Hnx240asbmzE6Y4O/PHECXSGQgin01OK8ZwwFnwOBxXl6TRq/X7U+v1YV1uLnkgE6zwenBgbg1tV8ZYlS7B8Why7NxLBl/70J0iSBJ/djkgmg4lUCl5VhSTL6AmHoZsmgk4n3r58OcLpNN7Y0ACf243c6dP/HPsx/nHY848E8QEA02WHtQCGLvCeCdM0kwCSkiTtBLAMwFnMjL99xCYpaHLNZm7wljcAa66yXp8YPLeYRUG1XRh9p7nBeYOMKU/fJE/v5ybVe4qAVqArP/ADYLidAqB5qxgDbdlBT7qokkKfF+8D3vwFHscb5M8v3s/446or2INaklg4o9CzHKD3+cLdVD27fdxQZYXH9RVZ1cAA/nzvdxkzNUEAzmUIorKNQPr4LwlSssKY5vUfplf19J3A+KCIVQ6znvexZ5l/3LiIceH6hTR4ll5MgwKgsGr5paRT4yFu9OX1FFMVVNqzV7AJiU2l3qBhCdB5hGEGu4sg7nBbJVTH+wlml9/K33taOfeVTWQOJJkgOmsFvdGzhwjcubTwDIVvZoKx/tN7CXz5LOe4/wzwjSesXPvCSCcYi7/vuzTM/CWijkCcSvjwKA2V3Q/wteFOXtvb/oMq7kLY4fgLFB4eeMIqvRubpEHpL6Guwu0jWK+6wqK5N99EgOtvIxuwZIvlsS/ZQuNn4CyNmwXrz12bgMWE1M6n92wU0r6mUej7HuF3oGoWvfbQMLvhldVS+V5SIxgfcB02LuZav/7DPOb93+d7AF6jt4j3WPDeU1HWS7jgd3OCWQuLN/G5pOJkOOrmoXowDH10FOUeD04CsNts2FBVBUmS8MZFi6CZJnb29qIuEMDamhpU+3zY0dODuFCBe+12tI6NwaOqmF1UhN5IBP2xGH7X0oIHz5zBRXV1yOTzcNtsiEgS8oYBu+hMVuX1QpVl2ITgLJROQzdNqsoNA3ldR0MwiKym4fv79uHNS5bA53CgxudDQzCI1TU1ODg4iFguh7pAAGVuN05NTKDc45kqJlPp8yGWzWIwHscdx47BrarYYpp4tqsLlzU3X3i+ZsZfHP9IED8IYI4kSU0ABgG8CYyBTx8PAbhNkiQbADuAdQC+9w+8pn+O8eSvudn6FhLonr+LMb6a2Xy9pMqicGWZIFq/gK8dfwF48naCRHScVare8m+WpzXUTsFWKi7aWmYB3xzg0dvoBRk6FduVjYxVl1Rzwy3kFU8fxZWM17/SyKRYpKZlJwHO0EXZUh+9umSMlK/dxfd+9z2kXd1eglsySs+8QINKEpuNhEaoWh7qJJh+8nYxJxqQShOwCyrw48/RENryBuu6qpqB936L3uaOu1nWtnY+jZVVV/DenW4aS2W1BGW7U+Tkq0DTYhoarTuFENBzbo92p5fPsDDSCSvP2e3nv6alwLXvZxy6IMryl1KIVqD2C+GQeJhzV8iBD49ynbzja9Y5DIPpaH2nRQaARpZAVgg+yQiV/ANnWEDF6QZQRF1Afxtjwbd/jnn0kXErHFJWL4RoxWQB1l8LXPuB83PJAR7zDZ+xlO6+YmDHDuv1+gXWWr3QCJQCCzeSkXB4mLu/aJNVzAYgQBe64c1fx0qD431cM6//FIE7l+aaKlD1hVz9VVdQR3DPt6nhyKWpV6iezcwOSeY8bHnj+deWjFnr1NC5PrNpfg9++Vm8ZXwUT8/ZhqiWR1NREfK6jhq/H1saGtATiWD/wAB8Dgd29vXh7OQkPrFuHR5ua4NLVWGYJqlrw0DeMDAqFO6qJGE0kcBgPI6BaBRlbjcymoZqnw/pXA4OVcWHVq9GsduN248cgW6aKHI6MZpMwudwoC8ahctmw/LKStgVBaosY9/gIP5nzx7U+v0wAbxv1SrcunQp0vk8ipxO5A0DWU2Do0Dt+3xI5vOIZTIYjMWQ1TQ0BAJwqSrUeBx/bG3FmpqavyigmxkXHv8wEDdNU5Mk6SMAngJlSr82TfOkJEkfEK//zDTN05IkPQmgBUzu/ZVpmif+Udf0TzOGOriRAFY8NDJqgfi8tUyXObmbG3x5PeuqmyYB31dMzy0Zp8cWmyBgVTTQm3K4hVBL5Gr7ipm/XVLDjanQ4al+oaVSDo/Q+/rfjEQU+MH76TlBYq53eSNQOwuYtZJAZHcy3ac/BPzmixRXlTfwvGcOEiBlBYAhenGr/JzbD0Al9dx2kF5t3TzmlI/1WnNndwKTI8xlLoijAM7VcBfBdc025rMXPjN9KAqv74nbgdYX+bfZqwhwsXF60pXNvO72wxRPqQ7GTNe8xjpOeT3nIJMisOQz/P3gkwBMAlV3Cz3VggFis/N5jPfR2Jgq52qjwGy6kQAwxNHdSi81m+Y5MimuH6eHxtB4Pw2gdNxq/Vn47O/+XXj8ORpDpkngN3SmkF33AabcjXQDT/8GuPjm80M9AM/nLyYTcXo/ULKcediF9XuhMdTJ9EPTZL312rlkZcrr6fVOD5vUL2DRo0KRIJePf7vkLVbmRmUTjRmHS+g8DKtGe3E1hX82B+e77zSv+dZ/p5ddaAozfZzaS+PYNGjQ9LfRoKtoZIhksAPlpoHq6jX43MB+2N/1ddRX1UKWJIwnk7j31Ck0FxVBkiSUud04MjyMErcbNllGUNQqL4yMpmEkHifoKgryhoGg0wmP3Y7m4mIsqaxEVtPQNjGBxmAQlzU3Y0VVFW5etAgHh4bwnT17cN08hr2cNhsebW/HeDoNr8OBSCaDkXgcWxoa0BAMIqNp+M2xY/jJ1VdDlWXs7u+HS1Vx7Zw5+MG+fbjj2LGpPPGAwwGHLONsPI5kTw8WlpVhljDkkrncDIj/jeMfmidumubjAB5/yd9+9pLfvw3g2//I6/inG6W1pGf9IIgZOinzwlAUYNu7gQ3X0dsqqqCHpgsv98QubtQ2uxCm6Wxk8YZ/ASARdJIxerSFGuyAAEZYKvhVl4t2p2nSwisv/9/dx93fIDMgujEhlyVA2VTg5s9bG248DBw4RKDMZwms9QuFmEwC7B5uqskIrzeb4rG0LH/PZ8kevPfbPNZjv+BxHR7OZTZJsC8M02R62dHtzEUvAPV0kJ8+PAGmdzUs5Obd8jznsKiS/4/20FDK51j5rbiaddsrGgmM6Tjz9q95P/Ds70hhN1dxngfbWcRlWTFzsHfdy/NlkgTh0R7qEWIiJ71A+/qKz1dO20RBFS1LDzqUFIJDGz3R/jb+nk3T6Jm7mtdcVEGjY7hDCM9kSxBXSDmUJHq8qpNx9NadBP7Xf/LCAr4X76fxVlzFNXrPfwNv/5oV154+hruAu77OZymBTMCbP8+89AuNVVfSqDz6nMiIKKNBc/u/sl3r6z/Fqm/3/g8NIMPk2m1ays+ffJFrulD4R1EpVrOp588pQC3Ck7eTJbE7AXeQz+bd3+QaOvTkVFMbWbFhbu9RoPc4UM1oZGc4jMNDQ2gZHYXHbkcym8VEOj1Vc/zM5CSS+TxkAG5VhctmQzSbhcduZ/30bBZpTcOi8nJ47XacHBtDsduN1dXVyGgafrh/P76ydSsag0GsrKpCqdsNl6pOlVdtCgah6Tp6IxFMptMIOp2oEVXdcpqG8VQKo6Il6QZRuCWradjV1wfNMOB3OJARKWfRXA6KJKFtYgLjiQTW1NYiYhgocbvPn7eZ8VeNfyiIz4z/P43L3gL815sA33xg+x1s21kQlGlCAez2WaVJC0NRuMnHIwT1grJalgmAQ53cqIe7BcU6yQ1QkkmTjnQzDzmXpTe5/HJg9vK/7R4MAzixh8exO0U1sBwB1VfEOGVhPPZzIOelEZFNEXD6ToL51w2MPWo5Mgi+UubpZhKiEp2dFGdknOd4538xjHDmMBtzFCqGrbvWOt9QJ9O8yhs4N6k48PgvgA9+/8KA1HeKrEChmIyW44ZfVEumo/0w46j5LDCssFVsdyvj0pVNBIY9D1J89Zp3EahtKnPES6vpLQ+1ExSzadLyTi/nYrSHIRFvEe87m+E91807X8jo9tEACI/wOAVv0u5iyEXL0xjxl/KcdfMZVli21WJLPAEakNN1rXanKCcrEZQBzl1PK49zIW/85G4K8uwOMgf5PA2MC4H48Re4XguvhUVBmAsBKsC5u+rdZHWe/DXXwmg318uzv+exXv8pxvnDIyJ7o8J6toXCQoXwhKHRWHxpwZzCiIcshXsySkMmGaFxYnfxudtd/F7mszznoz8FmhZjwl+O248eRdDpxHA8jlOi1GqRw4HBeBx5XYfTZoMhDF0ZQMDpRFNxMX541VV4sK0NT3Z2YmFpKaq9XvTFYjBME9U+H1RFgSLLODQ0hI898QRmFxfj5kWLsLWxEdu7uuCx25HK57G0ogKXNDYilc/Dpaq4SzRFGUsmsXdgADZZxtsffBD/fvHFuEi0RwVYo91ts8ElmqYosoyBWAyKLMNls0EHK7epkoR0Pj/VTGVm/O/GBYJSM+P/6WGaFHZFxukhONzArvtIu3afAH7+KeDnnwZ+9ilSlC8dJdUsuZpNC+W4l8dqXgb87JMUe9ld3KMrm7mJ59JAvTASxvoJEjd/ju0idZ3n/tM32UUqMv7X34cnQCDKpkCRlkFB3A0fOZe2HusVHmKKTIJpEHAqGwn289ZRHOUJUq3dvJwbqdNDcFuwnoaBoXMjfutXgIXraBSUVAIf/Qlj2IUx0sW8+UNPsPiMYiMzYegXvpdMiuKq4Q5St24/vdpllxDI4pO85nKRI37Xf9K7jodJ+04MsHLYg7dRVf3UHfS02/aRNfEF6Tl+7CdW3r1i4/25/QSZeWuA2gV8vhuuBz5z57ktPAtj0UWklr1FZAIqGlkWVFFI/xZVEtBcXtLWG28QLWXX8n+nxwKzgh5g4UYWCTLFczVN3n/7Ya6L7lYhnktaaYOqk891pFtQ88a0nt1/xdAN5s+P9nINXmjYHQAMnsdTxPCA20fR5uQgX69ooHEw3ThbejHQuJRgOzlIFmX2KquSIMD1N9jBf24/DawDj7Pj276Hya54/KwwWDObcfqRTs5RoIzivwd+gL7QJDRdx8WNjbApChRJglNRMKekBDaRRhbLZuF3OuG12+FQFKTyeVxUV4dV1dX4xuWX48fbtkGSJJyamMDamhqsqqlBMpcDAJyZmEB/LIYipxOyJOEnBw9iXU0N3rtqFTbW1WFWURG6wmH89vhxPNDWhjK3G5/ftAmKLGNXXx8SIr1tMBbDhx5/HKEUdS8Omw2NgQAyus4GLEIkp8oybJKECq8XVzY3w+9wwKOqSM3UT/+bx4wn/mobqTg39uJKbrzZLBXXv/kSN8L56wgWiQjbZr7vf86N31U0UlleUk1vIRmmaKe4kjHGAjWcy9ATH+/na6ZJMFRswLu+wUIXALDrzyw84hNK5t5TbNjhvkBO9/ShKPTw2g/REMmlSW+XN1LFPn0UVwMZQROrDm6gngAFSs1LaWxAojHj9nGDVB30vuavJUUfGSPlefHN9FI/+Uur2cf0ilvZNLDrfoKo28+NPDIKbHr9ue+bPiobCciKKtiNDDdqXxGwcD1w7AX+bnfymlIJEVvOEsxadgovuUiooYNCjS9z81edBBZ/MXDRa3kfio0MSdUsCrEGzrDQzfLL6NG/XJWsq95NQ6GigZ5voIzzanfxmPkc56CqCWg/SlZi9grGoG/6NGltT5DPrGYOPW+Xl8V0Wl7gfYVHqduYtYJgdudXOJeyRC3H9R8ha3F6L89XuooG2qxlF77mZVuBU7sZApLA59Z3ikaOrDCMcf2H+fP0EqiNi2mojvcDtlEaIAs38hiv1Oc6UAp84mfA7oeAjsNsNTpwBvj1F4DV24DXvIPfrZFuvt9mp14hNsn79BZxPabiXAOf+CXwh68xhGB3sPhOSTUw1gevxlrpiiQh6HBgUuSJy5I0ldI1v6QE1X4/Dg8PI5HLQZFlfGbjRkykUvjzyZN4urMTI4kESlwu7BsYwHtXrsQfWlvRE4ng1Pg4nDYb2iYm0DYxgbxh4Nt79uB1Cxbgoro6PNfdjfpAADZZRjybxU8PHcIPt23DRXV1uPP4cciShLFUasq4uPvkSTQVFSHodOK7r3kN3nTffZhMJqcKwAwlEvDZ7VhcXo4qnw/5eBzFbvcMnf53jBkQfzWOQsvKbJqVxGCSSlWdIv+6goU+ulq5cdTO40Ysy9zYZJneT6BMdI7y0EtSFAKxYuOGmEkQQD0Bxg2HO0mxekVus2latLNiI/iM9XIDt7so5nJ5KTwqpBFNH8svYW1qQIDCbNHS9CXlBpZeDBxtJXgXGlAEywmKDg+9RS3PuLe/hAC2cAONmniEXvTcNTz2n78FvPWrDAtMb7xSuJ/9j1HNHigTnatM3tslt5AqzaSEkTDNayyqYEy10EK1rJag7PKxReWJF0V6WIagVaD6JZnGi2nwPMu20oP1FpGJ8AZ5TcFyoOcUr6lmDoGpkFK3eDOw6cYLK8ELo1AQx1vE+37X18kE/OaLzGuXwEp9A2cAJFiYJTRMytumAgefAK77MJ/nnJW8r2SMhpHLQ0MiUMKY/tzVTNEqrqLBqOWA/lOsUT97Ja/j9/8husEViaqCErUCQ50X1h1UNQNv+gJj7vkcY92nn+S6rZtH4+H485yn2nnMiPAE6Knnc2QvUjHS24kwDd2y2pefL4BAvu1dwBf+TKGaliPL9PSvaYiN9oiwQ4LP3TD43UiEadS5fSIdsYj/3vR5PltJJvMCAHYXZtfUY/14GPsGBuC02aAqCtw2G8ZTKeR0HTcuWICheBwmgE11dRiKx3HFrFlwqyq+/PzzGIjFcGhoCOl8HmNOJ5yRCGyyjG9dcQU6QyF8O5tF6+goFEnCQDyOcDqNIqcT95w8iaDTiZaREZwYG0OZ241llZUIpdOIZjL4fUsL8roOzTBgk2VkdB1ZTcNPDx7EqupqaIaBFVVVePhNb8I1f/wjvIaBap9vqvTq3JISDMRiWGiz4dMbNsxQ6X/HmAHxV9tw+9ih7N7vWCKmQreuVIzxYYA0bc8JUogHnyBALNgAPPELsbmUWKrkZITU5+QIN8J0QtCBAW5IoRGrmUbjknMrVRW6jRW+o6ZJZfyRp4XoKUeR0y3/dq7aGWA8uKrZUhBPDtJ7e6kCvKwOcHTSQ+87SVD1BGl4zBUFTWwqjzc5SMNDz/NeBs4QfPc/QjGcv4RUeXkdzhutO1mMJBUH7KIc6IINNJh6WpkHLkm8/5s+fW789rUfE2IzkdpXM4cUt6wA136QsdhC7FmSBa0s8XiBcoLe0ef4DLU8sFrm38dEfH/n3RTMHXySsWS3l0bc6b1UT7+c6O7MIRaRMU1e1+W30nh64S6riYisANFRGnhNS/j39sN8XsFyAu3zf+S1VQoGJjTC8EFlEwHtrm+wJvz8tfSox/p5b5kkQwWFojaBMqYwjvbyPA7BACgqWZ2XZgj0neb5S2vYve2Z37JhSyYlOupF+d7aeTQmhzpYJ+DGT7BPwFC7KC/roI4gUMZe8S/HqkwfiSjvsaiKzyw7Cgz38ryxSSvHPhEV/eQNfq/G+mgEqE568YCg/TWuy742/v2i10HuasH7Vq7Epvp6RDIZnBgbw6HhYeiGgRvnz8e18+ahLxrFH1tbEU6nce3cubhx4UK0jo4ils0iq2lI5nJw2+3IitSyA4ODKHa5UC7o8o5QCOFsFolsFh5VhdduR43Ph/tOn4YEIOh0YiSRwERXF66YNQu/PHwYbZOT8NhsGE+nYZomZElidTcADcEgTNPE8dFRzCspgV1R0FRUBABwmyaGEwm8YdEibKitxY4dO6Zar86Mv23MgPirbUgScNO/0GMsFL7wBkWrS0XECrsJVIs2k2I1DMZZf/cfBHAtzw2luIo50rUL6HnB5OYYKOVmGh2neltWuPHYnUBsDPjee0kbXvF2gtyue+mVSCDgnj0kvKwwRXC9JxkXXbCO95BN89hOL/DGzwKP/5yVtbxFvF5dO3eTrWoCAifIABRX0ZNxuKm+LyjYAVKqD/6QwCfbaKRkkzRIINFjsqlAJk3PPDBN0R8eY+WxIpFCN9xF0Oo/zdryu+4nkNhU0uuP/ZytNwujogF4x38SRHpP09j41edYDzybZo65nqOBAPDYskIPz+Wlujw2yWdVKPPaf5rzWqBtVQc/V1XK+3G4aYCFhi8M4rkMBXm+Yr43nwOe+z2B88whPkOXj0ZCdBIobyLYRsfPLaeq2KxGNoZBWny4k8/PGxRhAsHAzFnJ0MPd/01wz4qUuaAQWUbHCXLD3dQvyAoNH6fHOh9AAN/+OzI9hUIu24TozzBFa1aFynDVbsW1S2oY0ml9kevA7uY9paKCyt50YaHdhYYpQDkZEYbOBI0Np4f3kYpTQxAdo8FlGlTxO1xcMw/+QKQDgobtgg2c70IhpsgocPc3oay8HEtmLQdmLcfmacKxwmgMBvGFzZvP+ZsiywilUmibnERG16Fls1Akialcdjvyug6bLKMhGMSKykpkNA1HDQMORYFbVRHLZmGaJpZVVuLI8DAM04RbVXFpUxN+39KCRaWlaB0bY8zbMFDsdMJhs8EteoxLksQysTYb7DYbkrkcPHY7ckIzUO3zzTQ++T8aMyD+ahyqnXnDNpVFWsKjBIpCtbONN9DiL3ib2RQ9Gm+RoLUlUoROL0G9eQnfMznM9y+6iBvSvLX8/+Rulo5U7MDeR2gcAKwWFywnWI71AJvewHjhLz9D0C4AVTJKkF6wTlRc+45VG33TjbyOkmpucC8+wPjyFW+j91OgiV0+Utr3fYcUanSStOxYP8Hb7qDx8bZ/p6eUiFAnIKu8hkTEEqad2Q/88APAp26nt9myg33DO45QuLR4E0FhuJu90usXkLJNhK32oCM9VgWvwgiUEsx23sP7nBzi+0trgfr5jCv3nuLGL8ucA7uTnbeOP0eWwzQJvqZJwIiOs6ELAEz0WcDlDdJAUWyWSjsZ5flcfsaMJwYJQCXV1rqBxGI5wXI+s3zOMpgUmSDtcPNvWs7qznbFO9iN6/DTwjhKAfWLpuktTAtsa2YDb/sqgcvu4PPc+xDno/OoyHYI0pvXcqLIjXxuo5bxfhpdFY18PZehF56KU+iXy/BnQycrUVZnzYHdKTQCjeyMloyIGvkpYPVL9BYAQwP7HqExVL+AKWqFcMbsFVyT+QwN0to5NPQKjVIMnQCuyFyXpgG88V/5fYuO8xoAlhoe6gBKllmNf3SNIYSRHqBxIdfJtvfQUH05JbwYC0pLMZnJQJEkuFUV6VwOss0GzTCm2pkCwGvnz8fp8XEYpgmf3Y6MpsFjt2MkkYDXbkd7KAS/w8GuZwBUEY9fVF4OSBL2Dwwgls2i2OVCKp+H325HOp9HLJuF127HqupqvHflSvzi8GGERI/zbbNnwzFDn/+fjRkQfzWOoU5rc4+McSMprQFWXkkP5cSLBIzOFlJ+iTAAibG5TEo0oBAiIH8JQdTlo8fbe4qbWUUjcN2HmC88OUyx3P5H6RmO99ErnhikEM3u5AZ3/Fng2vcRVA49Se9Ly9Pjaz/Kzevhn/D/sjq+9tQd9OzqF1nVyp68nRu4wwVsfgOraKViwEPfono+EeKmb+jAn77BWOPHf8bNPh4SueYO/m6zCe9yknOnqPRMW3cC//MOUp7RcdLyc9dQQNW6E5i/hnHTgTP0/tqPENxcHhpMzUsvLB47/BQ35Vza6uMem2SqmaxwXj1+oKyGNPPcVTzP8WctoyAR5gafivKzhbxvp1d0BTtMr9DhYlvWigbS7Dvv4dyOdBFYHG4CqQmKv5JRK/3MGwQ8y4TQLklF+6wVjE17AsCHfkgmIJNk+GbJFl5H0xIajQsvAlp3EZjzWYZd6uZb81Bac26FuvlrKTyESeNlcohd5zIJrk3T4LqtaKTBk0mda8SpDs7JnFVcW5BotAYryMhM9PNvg+0E2b299HQXbuQchkeBza8/95oArts/f1uEFnwMQ4WGaZA9/yeGFSoa+b0a7eUcFFfxO1g7j951ZJQhivoFoiNcJQ1fuwgfaTlWtZsc4L0XdCfRcVL1gVI+21338vxldTRMp2dMvGQ4bDYsLi9HJJNBLJvFWDKJWDaLq+bMwSfWr5/ygmv9fvz7JZegbWICmq6zSUomg+ZgEL86fBjHRkfhUlXopgkJwO1HjsAmyxgWIO9WVThsNlT5fLApCnyqCt0w0FxUhFuWLIHDZsNH167F0ooKfHfvXhiGgZym4SsvvIDPb9r0CpvYzPhrxwyIv9pGNg3c/z3RRamIm2n/aapme1pJHacSjMeGR4DBMwT72jncxL1BbvKmQS9r5RWiBWglNyd/CXDDx2gEOIVHVijsYXfR+3H7uHGbBmOG6QTfN9AG/O6rFA5VzxKxUD9QMw/Ipy1PrLiaYGrqBDptmpBtoI0e2uLN3MSfuoPXF5VYRCM2SW85n2RNc6eH1eRadhB8HvmJFf+ds4reT/sRTFU4A7hh63nOSz5LQ6WymRv8koupJVi4iWGBQ0+LHtkT/Gx5AwFVkukR+6fpAwCrfnlsUsRANavbV9sBqstv+ChjtZ4gBXjxEPDQj3le0xQUtJuA2dXC390B9rBe/RrgrV+moeIvEYxBFyvxBSvIJvScBIITZDnsTgKRxCnAa97J417xNn6mZo5oYyvRa11yMWPaFQ3szz19SBLLzQK8znlr6XH6i8kMDbbTACmqFBkNBtepJJENKKnhfRVXESi1vFUaeMFGrqN7/4dsSqFcbucxoGExPeOqWTRG9j0sQg4mQfrWr9Bzf/4u1l03wfWXinIuKhrYW+CKt5//fRrrJe2vawRjd5CtesOjoi79OL83q66kkdK2n+zFki2iq1yOdRvWbDvXqGtaSiCPjVNEWCjzappkwwod8qJjNADOHLAMTKcHePg24H3fmaL+h+Jx9EYi8NjtWFRWBkWWsbGuDtu7urC8shLpfB4Toq/4XSdOYHF5OTbU1kKSJJS63dhUX3/erR8cHIRqsyGjacxPN02MpVII2O3QTROnJyYQz2ZR5vGgzOPBrKIi9EWj+OymTZAlCT8+cADdkQh8djsWlJai1OVCo4iNjyWTeLCtDSvOO+vM+N+OGRB/tY1EWNRjriaY+fmlwZl94E4tkdrrPMq+0g43QXvjaymu6mkh3briUlKquTTzgftOUaR0+a0W/Qowrezw09zsiivFRtdEitQT4EbkLyHw5rJsrtHfRtV4ZQU3rbEebtJ/+Bq9+r42Al2ghBvigg30clxeAkHNHKsf+ZGnKcy79ivcbAsxY4Abby7N+fjdVylaqmzm692tBIBLbuY5htpJwaoOGiLVs2nQ5LM0QELDDE3ICu957krWdI+Oi7ahspWfPW8Nj3dyF7DiinMFe6uv4gZsGpZnLUlkDWrn0sMMlp/rZck2siBaToCJyLWvaqbxEBohUM5aDqy4jO/L5zjPsUmCjCQxHWqgnd7zcCefxfrr+TwVlf9e+BOPedlbCYBHnqEH7ynmmtn/GAVupbXAzZ+1Gra8dEgSC/3MXm7Fr49u5/ob6gA0ncVqmpYCN36cIGvqNJ6yadYlGOm2mBpJGEPJCKntE7tpJHS3AG17gXXXAFe/j4r6NduEBkTi/4VY9cEnuB5zGa6VxsUE/avfJ7ruXUDBbxrUMOh5Hi9yjEZVsIxzkEnSiDr8FI0k0wSu/RCw9C94mYs2ktX549dpILmDFGICNAZSMSFuFEZMNm21zXV5+T1PhAGXB62jo/j+vn1TDUvWVFfjQ2vW4OZF1EHsGxiABEBVFOwRZVFf6OnBgYEBrKmpweziYlRcQFy2takJpycmEBO54A6bDfNKShDNZrGvvx/1gQAymga/qAJXK6q4SQBuO3AAQ/E4GgIBJHI53N/WhipxDtM0p/LZZ8bfP2ZA/NU23H5++Vt3AMsqudklo6SLHaL4RqBMxEcTtOpVJ0HgEz8H7v4mK3wVNrSxPtKM3neffy7TpLf41i+T6sxn2bzC0Am6faeAZ34n+n/H6aVqWdKBoWF6qkNnScHvf4Se1LKtbCiSzxL0564mQM5aTgOhYRGm+p7veZCbnVNsQEPtjB9PDgHZHKBkCQy+Ym583S3caNv2i17RGWDHvdzU113He42HuNHPWcX3qA4aDZLE1/0lrJr2x69ZfcqRtY6XzwKHnqKRsePPwOkDpD6DZfQW568li3DmIAEgk+RzqZ3PTmgTA6I7nEwjSLGxznhXC5+VofM42RTzx2vmkLa98RP8v+ckS5R2HOV7vUVWjDY6wWs0IYRTY8CRpzg/DSJ+bRisdrZki5Ur7iul1zrWR6No4Czp46d/c6547+VGVwtDIJ4gd/ixPt53RQNw4BFew/wNBDNZpVaj5ySf2Xi/5VUX+tUPdXBuAqU0Vsf6uab1PJ+Ht8g693g/1/npfZy/VNwS6w2e5dp+KVsyfdjsBHJd4/PW8ryWRJTHKSonyBdKzfqKgDs+x0yJeIiG7UsNX4D30nOS7E6glM9kuNPKSvCXcP3XNLOugGIjA1IoqVtI2QTwa1HRzedwwDRNHBoexumJCSwuL8e22bOxu78fR4aGMBSPY2tjI2r8frSOjuLg0BAuGhmB3WbDv150EWYVnzsPG2qZZveDffsQyWSwtqYGQacT+wYHMZlOwyNi6N3RKHx2O7rCYVza1AS3qqIvGkV9gBkHPocDPrsdZ0MhHB4eRk7XIQN43+rVMEXRmZnxt48ZEH+1DZeXdPWRZ4BFeXrEugbuEhI3vOJKbsY2URgln6HnGSynx6LnAdlBoA2NsIdzRQNp1noR1zy1l0KifJZAsugiHrd6NlN4Hvs5N/50jJunrwjQMuyX7Q6w1rQsAetvIGAdeIwgvHAjQT2XERXDmrjJxya4yckKN7fRHl6b3UnDpSCUGTxDjzk6QYBXnYwvNy0lW9B3mhR9ga4E+L6WHeztXboEWLwFGGwj2JgGAe26D3FeXD7SoOk4N9/ImFUYRHXSYyqvo3hLyzOO2XmUXvP1H+H8XftBEd8PEGzTcVaRG+ulh3rPt2h8uHz03Ft38j4lmdS9228pwrMp4MM/5LVk0yzXOdormqiEWTEsNgm43EB4mCEMWTAyuTSV3GX1fD/AZyErVsc5t5+fi0wAkRGKFw2dQD7dcy3Q3pkUjavBdtGO9RIKFSeH6GlGRoBEjHX3HR4acomoBcqjvaTNM0nAFQDKJN5X11EaAbVzuc5O7+N5R3vZ1364QxRtETnsNjtBUssBYwM0Youred/hEa6v+oXnCtl0nXUTjj3Lz2+5ieuvcRG1FqkYqf5EiMbA5BDLDTtcVN2Hx/h9GOvla2uvof7h118EFqy1ivJUNXO+8hkaZIUmPZLEORzq4Pe4di6Nq7Fe3vtoL9+n2LiGXF6YpolYNjtVy7ygCk8LL/cLzz6LF3p6oMgyUvk8nuzowMLSUoymUvDZ7WgIBhFKp3HXiRP4ty1bztlKJEnC3JISrKqqQnckgjMTE6jweDCWSMBjt2MilUKR04lwOo16vx/vXbEClzQ3Q5YkOKcp0jP5PDpCIYTSaaTyeWR0HX67HXe1tqKmpmaq49nM+NvGzMy9Gkd5HWPNqp0bYzLCjVHPA5AY8128xQLZLW+kylaSWE/7mTvpqXS1cNN45Mfc1JqXknqsamZucbCS3smTvyIIV80i1fz0b7hJldTSUBjpIhhUNJBqToQJuqrTAoKq2azOFhmnytk0rXStfI4g7vTw2hWVAGt3kmoGeF+KyngrJKBEUNz5LM+h2NhJK5+j8E61c448QXqiVbMIpjd9ilRuJiVS0RS+bohcZkN4ZU4fN3TFRiAydG7QgRLmOXe3MDRgmmQRFDvT2977bVLeep7ivGVbrRKqWo4/1y0Qnn3WUqvnMyLtyhSZBn7GcTNJq81m2wF652O9/LyuU5xocwCNy4Bcjp6+ixs+bEJ3UD2LivRClT7VwZ8L9b67WwlQyQTrydudNAAiE0zxOvgEjcWGhfz7YCe92xMvAkeeFWxICedIdQHaGGAvJpAmQryWySHOnU0FTu3jc7epNKJmKzRy1l3DuUxGeU19pxnjdwdouOoaX3N6SPsbBs/51evJJkgS119JDZCJA2/+4rnVCg89yXh6WT2fz+O/ZLpmwyIafIWa6Q1LKIjsa6PRmRaA7vSQadANitbik2QIjj3L75NXzMmbPk8jb95adgoMDXN9F1rsrriMhkEqRiNQy3HtaVngotcBV71rqjiSJElYVV2NA4ODqPX7kRQNRhqCQRiGgRf7+1HmdkOWJIwkEohlszg1Po6cYWCdiIm7VBXRTOa8bSSZy+GbL76IaCaDZRUVaJuYgCzLcNvtMHQd4WwWsXgcQacTW5ua8GRnJ86EQnj7smX4wKpV+OGBA5hMp9Efi8Fus6HM40EonYaqafA7HNBNExlNw/HRUaytqTnv/DPjrxszIP5qHDVz6GFJArzSSbGhGaRuq5qBRRuA132cHuvu+4E7v8QUpo2vZazw4R8DQ11CKasCqohV7rhb9NWWCIRdx+k550W89uk7CbSVTdy4YhMEheal3Oi6Wxjze+3HWEs9l+VxHC5g6VZuymW1ImYqvKrZqwjsuQy9W4fbyqeNTohUHo3ndHpJ46t2sH+4DIz0AuV9wOabGC/93VcJjsOd9DgrGgluhbxfSbIqjT3xS6q9M0neT6CMoK4opMDtTm7Y66+l4OqnH6eX5g1iSlWdTdFgGI9wY3fVA2uv5j/TBH7xLwQsLU+waBU0uc1OYZPqAOauo8Fxai+fn2IjC1AQkoVGaDylYgReXeO5czkCkq+ILICsEHRyWSCX4jm7jhOARrroPW97r9XI5MRuepRHt/M+8nmeyzR4rB99iB5t8zKg4xiFh2uvsTIJTu5hpsKijSwHnI7xmUQnRX1/GzUafadEUxcHjctCwR7TtFL/TuwkC7J2G3DrV2k4DneI8NFOPvvxflLR3mIaPpNDXJuRUQouu1spNFt/Hdfk9NF+mM/XpoprEalor/s45+WpO/gdKq2hgfXxnxJwBzuAb9zClD5VpDLKQsQ20m0p1n3FonvaswTxbe+hodVxlCmWm26kuK1unqUzKaT4FcrtHnkauPq9lvZDdeAdy5dDliQcGR5GkdOJT2/ciHKPB6ZpwqkoyOo6ZEmCKstQFQUVXi9SmoaxZBJZTcNwPI7Xzp+Pl47OcBiTqRQagkEAQKXXi1Pj44AQuBUKvCRyOdx5/DhURUFO07Crtxe/e93r8I3LLsNwIoEdPT3Y1duLM5OT0EWFt1Q+D7edQtKMpv0fbHr/vGMGxF+No2YO43BZIYKaEnrlAE3hxuDycaO/9zvcnF0+borJCMtjRif4z2anN5dKcPMOlBFEDd0q8CFJpGzzWQJ9NkXaXhFxQtVBYVbVLBoI13/Iim8++ztuZDWzGTv+2ae4SUYnCFKSTBDyBpmGJYHXY+oEsEL5VpuDdHjvKbHpC2rS7mAs8davMs1Jkgi2h56iEaHlRDlRkzH7u/6LrxdV0DM7uZutOLtbCHj+EqvrlL+EhkBJNe+z77RIXVPo2eYzBPjIGL1/SbYqkxVGPksjQdcItOP9PFYmCRR5OdelNUB4iKA4b7UQ7GXIbFzxNh5nvJ/3ViSKiqQTgJ7mtXj8NFLmrmZq2XAXwQ8Sz9NzkiA1ewXw5i9YJXAzSc6hy8v7tdnE85atkrAON8Gmbh7DFm37OU+qXaS+FfHnkR4hKhNzV6DrKxvp6Q53cp7e/U1mVwx3EYB1EYM+e4D0smEAd38LuOWLnNtElM8hk+SzL6snWJ49TOFcNkVAVlQ+G0O7MIADjKVPDFotdbWcqAPvAi69hZ87/jzvo2mJZUDVzAbe/x0yLd4izvVQJ681PMb51zU+66k0AHAt3PxZzsltH7YK3pgmGS5fCRAa5Pcnm2YoRLGzx/rOezj/VbPgvv7D+MDq1efdjiRJePfKlbjtwAHkdR05XUeNz4fr5s1DOJ3G3oEBxLNZXDtvHq4X/cOnD0WSzilwbJgm8oaBnK6jxO2GZhjQTRMj8Tjq/H74nU4Ypokjw8PYOzCAixsbUSaMif2Dg6j2+RBOpzGeSkGRZThsNqTyeeivVKd+ZvzFMQPir9bxxs8C9/+RXoGiWOlMTi8Bec1V9BKSEYIXwA351D4Kt/xFojiHRGGNZHLTaFpMyvzsIaq7JYkCHtVJr9RmZw710WcBXQYgM784WMmSp96AlWqz7GJ6aIWKXJLEvOg9DzFmHh0jICQjwvsU9xGP8Fo7jtIomLWUIF9Uyc270ODF4eKeedmtNCIKw+1jvHPBeuBrb+A5iit5rNgkU35WX8lKcgNnCQQRkVI02ksB2lAHMJHmZt5zkgU/9j3KY2k5K5WsIF4LjQLXvf98EC/Eok0QaFxeXkMuxePUL2T60sINZEae/Z1QXkP0E+8gEBZEb0VVBIHSGoJDdIIAEA/RUFt3Nb3njDh+SS3nruDZ956i+A6wiorEQ6K4iMy503UCuk3kZpt23q8s07AY7xNNazIMMay7BvjJJxgDV8JiXZlCaT/GNq/BMhGOWUcNwsBZsjhaXpQiPWUJxXylLHE72sP5H+sjG6MoZHGqZ9OwS0Rp0BgSy/5qWZ735SqFbX49DbrRHs5heT21HtPXzYbrL/zZJZsJ/qf2kGKvaua62f0AvwuFaoD1C5jLP33YHWTAXvgT4J3H83sC1HEcHCMDZAjRXFktsP1Osl+BMr73sZ8Db/rcOYfsi0bxXHc3bLKM969ahbaJCRwdGcHCsjJIkoSsruMja9fi/RcA/8lUakqAVu7xoDsSgVOoyV8zaxb6olHa0oqCRC4HWZKmYtoFEyU2TbC2tKIC71i2DPecOgVZdFPz2e0ocjrhUVX8+dQpbKirmypAMzP+d2Nm1l6tQ1EICgs3UhTk9FpNLuoXkHruP3NuqpOh8XOSTLXw6QME0MiYyLldD1zzAW5Ga6/h5r9wI6nW488TeOatpRho5RXApbdyw1EUbjZuP/9eGJ3HaQw43ELso/Pzz/yW5UhVB1PC8llu+AvW0wvJJLmhlVQTaJdu5fVNDHLjrGoW8cYoY+arrrzwHE0OkQJ1evi5Ey9yXgoiuUyKx3B4RD9znYBdUs0qXoUmMoNneK3JGOD2WCBhgp6TohDgTh+w8ugLQ5JYxe6ubwBJiNahBuPiZbU8d0E0+PCPrd7Wug489WsaLcEy4PWfJtAf38HQQyrGMruzlnLeTPC9p/exLehoN2PayQg91gJLYU7zilxexoQf+zk7qDmcBJd4mPfj9vE96QQND0kG3vIlvjY5RKNq8UU0EBZu4LoZ76MHbWhC3JUlcPpLWJQFIEV919f5OYcbFKONcg2fPcTP9Z0SBuQkUxALcXJfEdfl3DWilWkXn2MubcXkDz3F74YsM5RSaFZTUg28/WsU5RW6n12oMtpoL5kPl4+GX2G9zFp2bqe19iNcV6uvEkVz4ozH153v9WLdNQTroSS/p0u2MJS08CIaJIqNRpUk0UAtGN4lNUwl1PWp6xiIxfCfO3dyG5AkpDUN/7JhA7wOB37f0oLJVAqXNjXh5sWLz7uMsWQSX9u5E7FMZiot7fKmJkiShPmlpaj1+bBnYACJbBYZTUON34/JdBpnJibgsdvhUlUUu1xYUl4+bYlLuHzWLFzW3IyeSAT/uXMn6oRy3ZFIIKNpiGYycM7UUP+bxgyIvxqHlqdHYIgCFSU1pLd1nRb89R/mZlAzm1Rm9wl60IXCFIrCAhO9J1kgpm4eK6/d9CnGik+8SNGPJBHgh7u4uatObjiFPNoX7qKXMXctzzVrOd8/2E7R175HCKBDHaQgZ62gKa86mYPrCfJ+cmnSsdVz+PfwCMVxNpUbWn8bUCYKt5jgRh8aIWvwxn8lnXmhsf9Rerqn9/EcWo73N2sFX29eBux7jOVMFTsgifDBgccJsj0tBHdF0MzZJNkI1c4Nt1A21e7ktQ60cVO3O7nBJ6NkCC57K5/Z4ad5rLlrWDpUdVL4VmikMtZPw2usF3jN5/heXzHv+c5/Y03yK99GwHV5Se/6S8FGKgAgUqPmruL9plMEDEXEf3MZKzd7zirmt1c2suZ75zGGFl68j+spNkGDY9mlrJgXGqHA7Zk7uRZe93F+tjDWbgO6j4s1My7axtr5/JdsIXAXQjzJKMG7ejbj97JM4J4YoFGWTfC+SqsIpkeeIaNTVEFDYqyX5/7oT7h+v/9+0UimhPqKZ/9AIaHTx1r8b/iMFULwFVlMxIXG6f3MANB1freqmoHXfpyhnJeOZJTGQKCU//JZK4xQeD0Z42vRcWD/40Dleq7HEy8yZfC1H2UBnj0P8t4i4xSc+kvJtqTiXAPTMgX29Pcjns2ixO2G126Hksvh6a4ufGrDhvMU6C8dz3V1IZXLTTUs6Q6HMRiL4RMbNkx5ym9buhR/OnECiiShLxbD4rIyDMbjiGQyyGgaPrtxIxpFHH36kCQJJW43FFmeUq7rhgGXzYaA03ne+2fGXzdmQPzVNnSdHlv7YaDxcoKd3UkF8vx1wKVv4WY31EkQuOFjrBUeD3HTbBTWuWrnRjw5aIl5bCp/3v47glQmSc+voMLV8gSfeJixyfJ6blpnD5KGPPwM48ySRBCrnkWAio6LhiQizWZyiKAo2wQ/Z4i82CICSyouCmQEAHec8VQtL1TvMhCsA2CK/PeSl58rU4QIVLuVVqXrBA5/MWPINbMJzm4/ldSFLmTpODfgXEbk2jvoeaaiAMQGb+rcXE2T12930Dt+4AfciGFQKHb9hyhWKlQMm97GdPq19p5kbrNi5zWM9tIImRwkILgDpJ5v/CQNmHmrKSwDeL50nM8kMsbiOpXNpOOXbCZ9HR0H7vwy565hCfDe/+aaeOIXwMm9BJGSKuZAL95E+luWaRg8dBuNv+IqAvH93wfe922r41zTEuCWL9ErPvY858zpJgCNdrP/NiRe36W3cK4KJYMLMdNCJTwJImc7y7UcHgGKa4CP/YxsTMcReu77HyZLs3gT169io24hnWDYwV9Chuip35BlClZcuHvd9Gfw9G8Yq24/xHU+0k0D5uZ/JdswfZTVWpUPB9v5nOau4Zo5vY/fI4DzMGslr610pZWX3nOCKvtLb+EclNfyGmITLNxjGlybq7fx+z5rOaDYcHh4GIeHh+FRVSiyjPklJTCDQcSzWfREIlAVBbOLi2G7QHGbtKZBFR59++QkjgwPo21iAiPJJD69YQPqAgG8ZvZsLK2oQCSTwQ/270fQ6cRGRUFG0zAUi6HS5zvvuIXhdzjwwdWr8XNRS70ZwEfXrp2h0v+OMTNzr7Yx3k+aurKZ3vWKy/m3D/2QXmZ0AvjxR62UrblrgOs+eH57T9MkJetwn2vp6xqFcaqDbS5VuwWweo7gPdrLgi6SxHPEJqmAPvw0N2lNeFvHnhfVu4QQqvck2QPTII1ZKANbPUukSzkJKp3HCIapKMvF9rbxusJjvBZ/qVXOs/0QN+bIOOOT0XHGGtduI825+37eazzE94eGGcO86l08d+Miem0w2fN64Cyvy1dMwAwN82e78GT9JaTATZPzJMkUm/mK6dmHR0j7SiJ1S9eAn3wc+K8nCJAvN+Jh0f61SNQTNzlXp/bw53lrCVSJCAurrNnGZxF+gDnwumZdYybJa3O4gA98l8/yji/QePIV0zMf7qSxccNHCDiVTVYFtNP7aHAUPOSHbiNwurxMu5q/VvTmjpCRKYz6+eyrXshzt9m5Hk/to0ZDVrhWDzxBD7dll3WvNqHQDlZQGBcdF93nBrlGhzt5vMgYn5+3iH/rOMr1M9hBsOxqEWI5YRhEx4Htv+X1mwZw5Tup1Zg+dI1ruO80q/DpBq+rvJGGiyfA6nfTQXxyiHOz4QY24smlaThkk8B93+M6Kq608vn3P0KQN00adoW5PfEiex5k03yf08t0zNJaZnmcPchQ1tHtwJxVGLjk7egKheBWVciShLyu4/DwMN65fDm+9PzziGWzMEwTC0pL8ckL9PFeU12N53t60BeN4ujwMGyyjCUVFdAMAz89dAhfv+wyAECVz4cqnw9+hwN5XYdTdDBTZBnKy2gOcrqOP7W2YldfH1RZxusXLoRrYADzy8ou+P6Z8deNGRB/tQ1ds0p5AqJDVxS4/XPcBNsPi1KWPm6mWp4W/NJpNJuukxZt3UWvp34hKXinm2A7ezlTnSJjlpesCWX6+CCBYKKfcbtCrq5iExW5FKDjAI8jSdywxnu5ATu99KyKK7nxDneLVKxrqA4/up3XFijjNRdXUuyVioh0OpWGxHAXPX/ToDcfC7GkazZNoNlxD2PBl70VKG0Ajj6NqZS5dIICtc03sXlKbJJCtrb9BKV8lkaCYrMKsKTjjKcGyxmPTifpkZrg57NpwK3R29bzVK33n7E6xk0MMMXvg9+3aN2XjgLoeYIWrVxgLgydXh9Ar7b7BD1EXeO8qU7A57EarkgSadpZy2gc/PijBL581uoYpyi8j+gkDabCelIdfJ+Wp7c82E7K2uXlZ02Ddb7nreUaM02+p1AopXq2qJ7mBYw8GQtfQUQJerlHnuY6mLuK1LjNQQNorNdKM9TzVktaQ2dBndEeMj0l1SKWLuZj42tpkD11h/XdOLmb3m/vKaryy+r4nB7+Ed9bv4DrIR6mWr6/jU16VJX3Xyj24gta6vid9wLHX2AjEy1PZiaTpEFSv9DqBte2T4SfhKjR5RXlcFOcP02o2CWJ8/bEL2mQqE4xpwYNyid+xXlasoXz13kUkVnr4Xc4sLWxEV3hMHTDgF1RcHR0FOl8HvWBAEzTxImxMezt78fFjY3I6Tqe7uxERyiEWp8P71u1Cr89fhyqzYZVVVWoEZ51bzQK3TCgTPPgb1q4ED8+cACxbBY5XUeVz4elFRUXXMK/P34cfz51CpVeL1w2G+4+cQJv8b9MqGtm/NVjBsRfbaOsjl/siQHANZubT3QUqG6m1xEdYyzQEySQKSq9w+nj1B5a9xVNVnnIvQ8Dl7yJr6+4nBtWPMRNtXo2vYyB09z8tRy9v/qF3PTq5nND8wRJPYZH6a2Wu2hgOL3cnKIT3NCaltCD0vPcmB/6IXDLv9HQyKSAiSHghT9yIw0P87h2BzffyCg3wbZ9jH+Gx4DvvJObdf0CAr/dycYlyy8HRrsIUjYbDYRUnOftbuV8FQRExTWs8X7xG9hEJR4iQHuLGGt1uKnM7m4RRswQXwcYxrA7qbq/4SPM4c9l6FGOdPEZHH+BrVFv+aJVvGX6cHpoWGz/LQ0NmHzWq69iTLiQL3/8Bc7HWB9BI58TxozMVLl8jht+gUF59Kekbe1OAk82RW+4YQG1BPXz6bFHJ/h7aJhMhl0AUDYl6OAV9AoLRsvizVSQn9hF8V90jIA2b43QbOzl2vIERDEdcY1xIZBz+niNLh8NyWyKhkt0guezuzGVqiWBczjeT0DPZ61CQiZ4/cXVNATKanm/vadYhCWfYWgpFhJx7hGWHq6dD7zhX9hPYHKIz8rp4nUWldNwTMeoHYmOc33veYiG8cBZXmtlM42YrhbWYJAkGh4Ot0jRyxDI9z/Oaw+W82YMg+8tGCI9rVxbqTjZJ5efhvRYL7/DI91MK5UVVNgkSJIEu6JgZVUVRhMJFLvdiGQy8Dn4zCShJg+l0zBNE7cfOYK9AwMIOBw4NjKCOcXF+PymTfj3HTtQ6fUinMng6PAwNNPE57dvx+ziYlw5axai2SyG43G8ZtYsSJKEoNOJTfX18NjPDwdNplL48aFDyGoahuJxuFUVjcHgTI74/8H4iyAuSdJHAPzBNM3w/w+uZ2b8vcPuYHrZrnuBtCJyqZ3cXDIpNlpIRiwPOh2nZ7n7AYLArBUUkTncFoXuE9RkYey42/I0EmECRrCCQJOOc4OyO7n5VTRQxHbv/1CZPtoDnDYJNNWzGBv3Bhl/7jzOjX60h4ZA3Tx6bxMD9N4uei03vfr5wJwVPPfJPcDv/926d7uD566aTUA48BivbaSH/+IhbrqZJHDH57lxewT1LskEi2SMIYG8lSYDWSIY3PAx3ufuB0mNltYJhfBpUV0ra7UHLTABZw6wEcpgO+f19Z8EbvsIr091MHfb7iRFu/dhUvmFYZoMQ+y6l2GI1VdZoLv5JoLWrKVA/WIKy/xlNFQUhYCrKASy+CTBweZgLLuikYBSUGJXzSIoxEP8vaSGBXkCpYz3Pv0bGkTz1wMXv9HygsvqeI82RbATLlLvhYyFyJjVxc6m0kBUnaSIAyWc64l+K8+9kON+4DHR07xfNKgprD+J1DRMzoGucS35Swlm3S0EaKeXa7+8njqP8QHBXMg0QmSFbIi9XKQO9lgGac0cevCHniKr4y8VXeok3kf1HAobxweA4gqq/c8cpPGcEQVfTHCd1c4Fejz8/jjcNDAuvplhhqfu4HvCI5xHfwkNF5vK6/cEWFlO10T54CKq+wv3UVrD6niJCI0b1YGy+rn4UHE9fnH4/2Pvr+PkuM70D/SpZhpmnhGzZNmSbZlkZogdJw4zwwY2m91kN7i72SSbZIMbZnDiOHbMINsyybIli5lGw0w9PdPcdf/4nlJJMsRJNvfenzPn89FH0kx31alzTr3Pi8/7rIanp1UdjeoDq1fr0Y4O3X3ggCJ+v3KFgtK5nOZWVCieTuuZnh61lZbKsiyVh8M6NDoqj2XpjcuX63ubN2trfz9EdLat2/fv1+KqKt26d69igYBKQyFl8nmtamjQq5cskecFXOn3HTokSYr4/YoYhrjOeFxek6U+M/7y8VIs8VpJmyzL2iLpx5Lut23b/ttOa2b8VaOoDNft+vUImF/9OwK8pFLqN27rxDgC55xXSpvuwW3qD+JWnbfKuPbMNk+Nww3tjINbAJyiCgToSA8Cp+cAwt+yEM59R4jNOmxk2x6W3vM1GN9+/xUEY2oSi72qEUF1YJOOJTi1LjVJZAkUh2fv5z7XvJ+Es6IyYoNHtrsNKiIlUMo2zeNZ7IKbrT3UjeVrWfxs68MAQqwM5SObcWlan74LwS6bayYnSZLa8gCJZTXNKBeBMHH3xBjPaIn67Fi5yUS2AdNHfoWy8uTt1CO/+fO468eHANr5q1ySj+PHkR1Yg5VNAMjgUZi+JgNSfz8KxWv+1dRLH6WGvv8wlqzlIS6enkbR8nkhZKlrc+vyo6Wmrj1jKgKMmzcQku76rnT+a7B8PV7W8OCzZh+KpdVXwTJ24z9KN/8X92maj8KYTJiM/yyAZtuAWGLccMwnJH89CYTZlPSW/4A29uFfkhkfCOMiz2d5bsvDfP0hFK9Mmjl7/axfm1Fixs0ZmBoHWGevQDFqXggoO+s9MQwI1s/hPtkUitqiM4wnIIpXp6bFUN/W4TEY7EDZLa0mcS8YZr16DqJEOOEQw6am8UGU11Mu4rzXzeZdsixT/XCn2wsgMWruHcETUlLNvccHjIJjEiT9JrGxdSnu/lAE78BFb5SKyrQyZuubl16q6e2PqmjLA/K0P6jrVl2ueHOzNnR1yefx6I3Ll2txVZUmTT23LVPAIEkW1vwFbW3qicfl9Xg0mEgonsmQU5hOq9tkpVdEItra16fvbNqknnj8GFvcyWM8ldLiqirtGRrSeCqlZDarppISRfz+53x2Zvx540+CuG3b/2pZ1r9JukTSWyR9y7Ks30n6kW3bh1/82zPj/+ejfg7lO1sfInO73Li1Q6b+uGk+8e/SGgRUahqhtuhMF1DrZsPZ7IxwkSEySbj9lI/udElR0ikDahmsjOJKft9zUPr6eyBSuf5DfP7R32GxD3Xz+bd9gZjmr/8T0O89RFywuoU4dy4r3fpVmL2ObJM23UfstqKc5ymtxsq0bVz5YwNY1XYB1302zfxzaYDcLhgrO+Iy1/UecluMllRjIe3bKN3yZcOeNY3FH4xKhzZzf9tYhsEIcf6SSoAhn8XCi4b53cY7UD5WX4HkvP0beCSCUdb/+IYcEjXU/pCbsV5cBVg0nSdd/X0UJMf6mb8az0StsaqjJdI7viTd/X2uG4qynwMdxko3nphkgn2TSURsWohlmM1IN/+nyzS3Yz3rWVJNnPfJ27BEl5xDGOCXn2PtO/Zg0WfTLqmMLJ43EDRJZWbOo31Y7vf+kM57fe3cd/5peBlGe7m3z2/K94IoFMEg9521HPa1onJIbIJRlMtACOv3wGbW68BmEjh3PYEbPFaK52esHwUoFDOVHBHuOx2nxGv2cun3X4U5raqJxLxl56GoPPhTlJJCgc8W8igJFfWGmtZmLq/4IFb6ySMco8RTMu/OIOeyot5wIOyhvNEyCX/hGM887zQS8SwPCtRZr3C9Zrselx7+jfxD3SqZHCGUY3kUvP9HescrPqTrLr5Yg1NTKjau9aJAQGc1N+uxo0dVFAwqkcloUVXVsTh4LBBQyOuVx1zfsd5s25Yl6amuLk1nswp6veoYH9dXNmzQ5y+44DkJc6fU1Wljd7fWNDVpPJnUaCqlj555puyjR/+EAJsZf2q8pJi4bdu2ZVn9kvol5SSVSfq9ZVkP2rb9T3/LCc6Mv3JYFhSsi85EWFc0IFzu/DYgvekeYm1HdiJ0LQ/W6o0fw8oq5BFATlJOPg+oJcaNi9ID8MVHcS9PTcj0uuR3G/6IhTcxiJAc6ADIWpdI7/oqNcj7n8GiqJ8NwYZk2lTeDWh7fYDqlnUwjo1O8u8NtwOU7bukkkU8R2LcpXRddDZZv4Wc66q1zHxlS/Eh4pZv/CzC77HfG5awjMv45hDCZLNk909P4sGIFJlyqrzUvg3LN5eRJqYBGdsGKFJTWPrl9a7Vv/sJYuYbbufaWx7k91e+k5rr44dD8+oQ8qQmyW+QnluKdsmbSX47sg0X+8VvQmFzkgYda8758+TtBmjK3eSs6Uk8KtkkVnzfYUkmdp2a5lrpacA3FJU69wMstW2csV2PSx273MqGfFbHRH96irU/9VL2Z7ATLN98P2BaWgP49h5GCQpHXUu7uAKQC4RQ1KoaaYHbvJB5j/UD/oU86zzSaxLBigHf/nbW8YYPS7d9g71pWYz3YvcGrOWWKyDE8XgIWyw9l3u/4dPc2+FFtyzplv9mPaqaWcPOPdLFb+bM+PyAugTwPl+fcme0LmENIsWGUCdCKCgxjpJc1YRSHC2BtOjtX2ROmbTxTBx3Bjr3SXf/gGuND7AmAzWED9LTOrhzo75yoE/ZfF5529YVc+fqxkWL9OYVK9RSUqIjY2OqLyrSBW1tuvPAAT3a0aF8Pq+xVEphr1dHUyl5LEtNxcVK5XLK2LbGUikFvV7FAgHNLi9XfyKhwampY73FnXFmY6MSmYzuOnBApeGwXrdsmc5tadGjMyD+V4+XEhP/oKQ3SRqW9ENJH7NtO2tZlkfSQUkzIP7/z8MR/g1z3Z/d+jWEXHULQn7dzxEKwRBJV7OXA6A3fuzEa/UclH7+GUrLQlEEtOUx9KALiQWP9COsi0opwek96PZJLtgInXyOrPI/fA2Gr9o2rGjHopyawM0oIfQnR4gHO61R7QIJe5GYtHc3As62cUn6fFhKF73RxOs7cP2mk9x/sAPr0+sHWxrmUCf9xK0oDk7DlmxasoMmkShmmOx8pn3msI71j66og8QlkyQ27PWZLmBO+dA4Vml6ihBBfIRSuk33maS+CAAyNQGoeE96JRefBcFIz37uGSuTzrlR2r7nuXsdDEuXv+3En+VyKBsHn8W6y2VINCyvM0lkMuxrJXgMMkmUEI+JX+eM8jLaZzLDMwD5sV7l1dzH46HDXWWDFB/DK7DzMVOF4AE08zkIWj74Hb7TvpN6cjvPunbvdzvtHfARYlh9pRTPAXbjg4BoJsN5DhdR1z7Sy7pFillbj9eUdNXgBUonmbtTb961F6WpuhlPVMculMSDSdblyndxTv7nHSgIp10GR72zN9OTlJs53eAsy6WSXbzmRV/H5wzbxlXftpzvh4s4nw5ve7TU5ahPT7nscE5i4fGj5yAKVscu2PiScZSS5kWysxl9ezSrZGVWEb9fRYGA7jl4UKfV12tWWZkunj372GXuPnBAt+7Zo4pIRJv7+tSXSKg2GtXalha1lpaqobhYa5qb9XB7u77zzDOqika1rKZGlmWpICn8PDXflmXpktmzdclx95kZ/zfjpVjilZKut2274/gf2rZdsCzrqr/NtGbGXz2SCVx7X3sHwvayt7m9wHsOYEk6gtnyAACRYoRufBTLU8JV/MivEQaHnjUEK8UIn/Q0VvZwt441xLCMoCwUEIDl9Vwvk+TnjpWay3DNb76Pn6+8iAx0r5dYusfEQQt5wLaQwbrb9QRNOrY9jNt/pA/AXWZKjmJlJH5lkiQPWWLO0TKEcN1s6FLHBlBE3vAZA9I+rLveQy7Na3k9VszEEBzjI72SLOaWGAP000linJ37sfg9XlPuZUkrLsQa2r4e5SJWisehot61NrMprMSSakBKYn12b+D5osUwdiXGmFNtm6FtfR4QP3nkc9Jvv0BseMok9F38Jq7n9UpzVlIFkMuyHvFhN1SSGDWx/VJCMD2HmKvldc9X1iTxPXUnlQPREuK0ZTUA5EAnsWlfEI/H9AShBNsGqIa7XWrVo7vd0jWn7G7OKabpyB7plbeQH/CbL0gBCyv+y2/Ce1PdTAJcfBhil4khUwYW5/lGerjPjkdxRZfXc/ZLq/l5Xzt5IDWt7MGvPofHaHwI5eTQVt6Ta97LHO74tqn6GCL/oqzG5as/tvZ58iq2PYzSc84r4YU/eXi9hA72beJc5HOSbCkYQ1lw8lIyKdZlsJN37vms+2gxQO4PcgZ7DgDkB59Vqn6enswFlOnvl8fjUcDjUWtpqcafpwXpU93dqonFtHtwUMlsViXBoEpCIT3T2yvLslQbi6l9dFRLq6v1b+eeqzsPHNDg1JRs29Y18+erIhLRVCajLYZ/fWFVlepfhABmZvx146XExD/1Ir/b+387nZnxfzbu/7GULnbpP2/9ivSW/wTYfEFp0/0AdmoKi7KkypTzWAjmJedwnft+iBDz+blOaorPFFUiJKcmUAAGjwJQjoXqWM6zlrlkHNkUQOcPEfubGnddpg/+DCC75j38v34Wgt5xufqDgGVxFbHZXAY343Tc7VqWTpr5eRCK598krbpSevhXzKllESCfSgDO17zP5bE+5SJ6pPuMp6CykVjpK/4BEN7yAK7T0R6y5FuXIbQb50qP3kKilC3A2qEv3bcRoPjX36JYTMWJbfYcBBzHBkyNfRb39bMPmKz3abeuOpuiPvmNn3lu85Q/NTbfL637palnF56IoS6XD3zlxYDWoa1uW9DkJIA2OYoXoWkBYJpNA1wO37nl4bt7nmL+ux7Hq1LVBEHOkR3mfE1LVgolIFaCi/q7H0bJmoobEpoIf+eygFYowlxG+qSn/ihF5vL/res4v6XVfH73k4QCfAHJaTtb00oc2C4QcklPSa2LcFH3HXaz/3/3JdZiahxvQr2xEEur2evRAUDV40Vpe/BnKEB3fgcldtl5KFq7HuN+57+WtXLGlgepKPAFpSMbCCtd+HrpVR97Lh/7JW/hc88+KLU0EfpwKjS697mhmfFBPA9zVj4/QdOC01FIExOccds+Vov+0KpXqv/JTbJtW9WxmFK53DH3+ckjFghoPJXS8PS0YoGARpJJHRodld/jUdfEhNa1t6u1pEQNxcVqKy3VR9es0UQqpcpIRAsqK5XIZPTvjz2m3snJYy1QP3722ZpTXv7nnd+Z8ZLGS4qJz4z/x0ahgGBuu9i0oiwBbAc7EYLZFII9m3YtqjITj5yaQNCmpw0JyMOGRzuKQCgUiE9ODJGlvfICaeWlWHzJhCn3qTA10gXKupoW4Hbu2APQO01XclmAt7wUN+qme6Sr3w2wzj7FlHwlAf7Zp2BFde4BcOadBsg4HNaWhXUSH8H62fW49Ievopg4TTF8fqyp6hYEqWPNxEdx/TpCXRbZzq//FFboha8zOQWTWHGOC9kZDXNRMB7+FRZcMgFBTFkN17ztm4Za1sP6ZlKGf3wEsCyrYV0nRynb2/U4a920QPJVUu7Usee5tJ5/ajzxB8AyUoRSNTkMgY9Tk+3QpC5eg0s3aXINDm9lHws5rNiGuQCrAwpeH+djcpTscn+IPIr2nVzr2g9w77u/S8euiWHWdc4prEeoCKUxNII3xmlra1kocIU8Lnafj3uYcmlNjprkPJn8gGnyOooqXJKUyWHO+2g/SZ3BMM8ocd2+wwBwtIx51c5yu7H5/Jw3xzXuENBY5n7jA5xZZw7Lz8OKf92/ocwdP/Y/g3JyYBNKhtfHmqQSJGj2HsLTUdsqLT6b/JN9T6MgzD2V3x3eircmn0ORaJzH+hzYJO1eBq/+8SMQkq56N30NMkkUmkJeqUBYj637gwKxVqVyObWPjakiHNby5mbVPk/TkVctXqz/euIJ5Wxbg1NT8liWprNZFUwb0pJgUMlcTrPKynR4ZET9iYRW1derNBSSZVl6pqdHvZOTmmX414enp/X73bv1z+ecc+weQ1NT6ksklMnnSZJ7oc5yM+NPjhkQfzkOyzIub+Patm0EmCOIsxm6I+14BGHqD+LCblliuKbPotSnrA5BemgLnbDq56AcNMwBbM5/DW7wYFjacBsCJjON5Z2a4v9nXA2A9rVLN34U4N38IBZS72FchpYQeE6cz+eXXvlRYu8NcwCHmjZc09Fil8M9ViZFIlKozW3gcsz6sHDfxkcQgrOW8Z0Hfy69/b9OXK/t61EOAmGpqY659x4G2M97FevpWGrPNwIhrPPTr6TX9XCPC/S5nLR3A2Dm9QESA+0oEpX15A1MDsORXdXEswXDfG56glI1h73rzxn7NwEKUxOGUtYoLL4ALS9PuRD62n1PowgFw/wJR9mHhWdiSe/fBJi3LZMObTNc5nn3nI2PkEuRzRhXsPBC9B5i/x2egkKBmHcu53ZxK6oAmIorUH5SU4BkIW+S70T2+ZR5prmnYtGW16NcOPXU+SyhjkgxFv90gmYwlQ2Ego6VSk4QW7/ly6xvTSveEI+H6zlr9MqPSr/4HCDv9fJsy9eiDARCeBCixYSaguHnp8uNlrBedsHQ8/Yy13t+QAKlCigPzQtRrM690U28zOekzt1ued10nJyBiSGUv0CYeT/fOO/VeEE23sV70LZMfdmCZg/1KlY+T7WxmDL5vJK5nC6eNet5L9FWWqrPnX++nujo0K937dKzvb1KZDKqikQ0YWhbm0Mh5QsFHRgb09eeekq1sZjOaGzUW085RdPZ7Am87CGfTwknPCdpa1+fvr1pkwq2rXNN7fkrFix4vqnMjJcwZkD85TgsC87m3QehoSyuoGdz43y3PvWZe7A0QlEE1dzTEK5v+Q8y1yMlhonrVEDo6B6pYTaZ7quvQPg/eRvgfdrlxi1tk9gWN7W4y9YiCPc/g9Bsmk/stPsAADzah+COj0izmhC8DlgFggjOpecSyzywGSF95jUA3o5HEeK2RRKd09HL8Sb4AiY5rcC8pidxlcaHub5tA2KjfVi52TTfsSyTxGYRf4+WAjTHd+SybUDppDIa+fyA453fkeI+wGyoi3V1rLpAiJr87n2sydP3UCc/2ocyseJ8rMOt60h+83gR9E0LX/r+Fwrwp7csAmhG+1iDWBlW6IbbKTks5E1lwg6AKRgi9j5rBa5kCW/ARW+Q1v8OwPL6AJ/JUQB39xM65srOpmHC+95HTB9zs7erLsP7UFbtJpkFQljSMuGbonLWKZ0EtPJ5rNYj26XqVcxlyTnSw7+WnrodYK1q4meb7uVsFJVRuz7UgUegcZ4pL9vE9+tmkyy350lCIxKx48FOckbG+omvzzsNJfXnn0Hx8Hi5xnc/jCv78Hb21R/A6/B8VLlnXc/5mZ7Ec1TISTmTZ+Bk6VeVst5DXaZhjs15HepibYJhlLhUghyFQsHUyCfJjXi+4Q9Ia1/Ns9S0SR6PAkf3KRIr0oraWu0cHFQ6n1dTcbGumDtXv9qxQ4fHxtRSUqLzWlt1865dOjAyorpYTO889VQ1FBfrv554Qn2mZWi+UNBwMqm1LS3a1t+vkelprWlsVFEwqCe7utRaWgoZzJ49Gk+lFPB61Z9I6LVLl0qScoWCvvTkk0obi97v9eqP+/ZpdX29GmYoWP+iMQPiL8cxMUxjj8pTie1m0wCBox1f9lYydPsOoa0vOB1BlZrCIg1GcblLkJqkJqGhPOs6LKstD5K5nJrGAtrxKAIynQL4556KUD6yw1hIRVx79+PMo5BH6J5zI4CcMuVIRRUmYS6JSzwxhkBdcT5/nHHpW3B3j/bhPgxFpT2HcbkPHDVEIymXmzqXxR3ZuRfB3rWfbO1N92ItTgxzr0LBxIWnpJwpXZuOS7KIjTcvhDlu/W+4ft1s7n98k4+Fp0Nk8vPPIMBrWoglO3zinYa8Y+HpKCapBBSe81ahGB3YTOy6ot503vIjmAeOSrHlL23/c4a0pnEBoJFKoJTMX8Xetu8A4Gva2J9cGpDKpljL9p1uomMoBpAXlUnzT8cr49TJF1cCzKEonoVHfwdhy0iPcYsXWPOSKqm2hZ7niTGs0Wya53L4ySUsb6ckbvlaQLprnxQ2XpD7f8w9V1+BInh4u4md97gc/U6SZXyEfR3u5u+aFunSt5rcgIIbUshlCCM88BO8BBNDeH/Ofy3KVGk1+Qy5HI1aEuNYzUvOxtoOhJ5/D6qbpPd9U/rxv6AA+YOcS8vj0qo6JXNO8uXFb5T2dbA/+RxZ+BNDfD6X4+dJ42WYv+rE+9k2DYU23cu1KxsNu5tHZTWN2l21Sj6PR6vr65XIZvW+Vav0wy1btG94WGXhsNpHR/WTbds0p7xcjcXFGksm9d8bNuj1y5apLBTS4upq9U5OaiqTUd/kpMrCYfVNTemMxsZjbUSLAgEdGRvTpXPm6J0rV+p/n31WqWxWV8+fr0tNVvoj7e16prdXxYGACratM6urJa9X8XRaDZoZf8mYAfGX4ziyAwDxh3AfTk+S5OTE0CJFkKX4g1it6Wlik7WzYFIrrcba6m/n81VN0g0fctt6duyhRnxsAAGZmkTzn7ea5KWzrsf9/ulrsUBSUwBSVRMuwoVnAGrDvQiws1+JQL3tf6gn33gXYOYwdL3rKxDEOMPr5RrHj0O9botVy4NQC8dcF7WTeBeKSD//NHNfcjbKS2UjgtLO4QqPFEmKEVbweFm/+37EdTbdo2MEOD4/ZC3XfRClY2oCS628gTiyw7te2QSRSUkV32lbYpKxhPLi0LEWCrhsoyXMPWzczsPdPNfslwjigRANMnoPsf+jfTzX0V2Q7hQKgJptA4SRIlzQdbNN3L+OOZ3/GmntTez7krMpwwtF2VMn3jzcw1raNvMe6eXs+Pzsw9QEAO4kVQ50GECbZB4TIyZByzaW+xDlVtXGUi6pRmHK5wFuf4j2t7bNWTqy3YRizD4e3kqGfLRU+tG/0GbX5ydTe2JI+qdfkMS45QH3nOSynPWufSSF7XyMzPKiChQYu0BIaHoCb8bep2Dd+1OjvFa6+r1Y5CO9LleBLaNcJaU6ExJomEt+Qc8dKMAVdZyzsT6UurmncZb9fmnlhc8Nr+zdiCJSVsu6jvShFDTOU6S8Th/JZLXO9Apf1dCg+qIifX/LFjWXlMgyyWdPdHdrZV2d4um0dg8NaSCRUE00qsbiYnXF4wr5fMr7fPq3887TpXPm6A979+qO/fvlEHgmMhk1lZQonk7rtv370U0CAT3e2amzm5vVWlqq2/ftU3UkokyhoGK/X9lCQYlc7nlj8zPjpY0ZEP97GZaFwH3yNqzL+atJyNn1ONZwyyKXPar/KK06q5r4f+sSYoAS19j+iKGqTMtt2OAFLOrayB4vq8aKHupGIMVKEeCxUoBh5cXSH79JQpDjuk5OSr/+DyyUpoVYWZOjdCA7HsRPHg7zlscrzVspZXN4G4rKEIil1dJ3Pig1LzZkICkscacXuMcjlVdDPBOMAtSP36pjrGKBIJZqeS3xyHAxLtjyOoT/Lz5j+pKHTOvIC11qK4l5tJpEuYkh6Y7vsGZ1s1CIchmpMgSYZtOA4/QkIF7Is277nqYG2rJQiPzNL77f17xXuvdHAHe0jJyHXBaXef0c1qykhrOQSwN0Xh9rUdOCm/nC16MYxUfh+Q7HiEeHIqzd7g0uFehgF2AdDOLJSMYBn0IOBaGoHOD66ScBr6pGnm33k25YIpOmtLFzDzkMxRUkxFX6+UxJFSEHfxALPps0zVbO5pxNx7n3Wdcx130b2av0tJTLE3vu2EWi4uwVeAWKKqQvvZ5ndDwCloe9H+okscy2Tbzf5Ca8kPXtjGwGxcZJBLULXGd8CMWjUGDelsX5XnA6AC7x85ZFKCQdu3kXalqlxWdyvvuPomwsPuvEe+57xmVilEwPgo5j5EHV/sAxl7YkjSaTkm0fo1v1eTyyBBBv7etTwbblsSxtHxzUWU1NOqu5WaPJpBZVVWlFba0k6fI5c7R/eFjb+/tlS1pZV6eLZs3SI+3tGkgk1GYS2wanpnTbvn368BlnKJXLqS4W08aeHmXyeRUiEd24eLHKwidl7M+MlzxmQPzlOGavIFady5gGFJPSeTdJv/oPsn4DYemBn0lrU1A2du0nm9cZTub68cQVtk2izq//nf/n8/zxWK6Qs/MIKqeGNpkgiSsQwCKrbCCG6fHg1m5ZDA97zx63eYY3IGW7AcVwkUv28mJj072St8GlthzsxIV86kX83+nw1b7T9JKW+7nSaq5fN4t73f09vADtO1BKFpyBdyBaSllddreUHQLExvrcZKj6OfwdiuLVqGzg+sEILmivDwrT8gZAfdtD/K6yQZKFopCelnoPYLXlc3yvUEDK7nocYHAs6BWvkR7sBQBGe1m72Su4zsEt0rpfsAaOJ8bhph/rA9jL611+83yOv7NpgNIWIBgrA9x+8RmUiLCJWS9aQz6Bz8/cp+PMabgbRenIdtbC45FKalESjmwnkXLPU1ynz4Q/Cjms73yBsxQrJ5lyy4MAbCYJxexIL6GLTffxuWyKcEH3AYC7YS4ELSsuJNN7oAOlZWIIC9/ysB6P/p77ti1hjmMDLh+BZLrw5VyKV2eMD5BTkp6WznnXC5/F+AhsbmMDgHdtGx4uhyBoqNugpp+z4jD2LTuPvfV4UAJq2/BsDHZxz74j5owdlzV//IjEWBOHBz+T5GcvMMpCIZ3X0qKH2tsV8vmUyuV09bx5OjgyovFUSlG/XwsqK1Ubjer3e/bodUuX6oK2Ns2vrJRExvkDhw9r79CQRlMpFQeD6pqY0ObeXg1OTcl/XL5IyOdTIpM5VmN+14EDCng8ivr9sixL0Rn+9L9qzID4y3EUl0uv/TfpiSdwwc5aAdXptnUI5pYlgMeWdcTWymoAuHARQJyeIv57/Nh4J8DfvsPQeEaxJHJZhGouLfW2Y6mX1xM/rWo29cYT1A5f+la+lxgnYSib5vMjfYZBrYAFkU3xs9oAwm/OqS/+vM/bj+e4n4WLEfDpJMAwHUcQFvJ4FcIxXN9P3806NM4HzHY9LvUfks5/HVbbsw+YLmfjCHp7N+7So7vce1kerv2qfyJ5cN8zWNYLz3QJR1JT3CM1RfjB8uL6tjzSyICU7QSUKhu49ulX446vqEdBKipHGXnwFkIQLYsBhoZ5ZNPf/k2s2NIa7jcxwnL0HHCfOzVJVvysFdx7asK0OLW49vWfwNp98FYy1B3K1kCQOLddMO1LcydWQdS2SlNjJByGIriB8xnc84e2cf68fsBq5+MoEOESchD8Qc5R2zKUjZIKqX6eIa35IkmXN3yIDPWKBlzLwTBNX3Y9wbqM9sFAWNPGeh3ezjztHK75gXbOXxFWorw+1i2XA4BzWRSiXBZQfceXUTR6DzPv1sUofC801v2C61Q3s86HtnL/Uy7CW/TMvaxzaTVnNDGB4jvUzf2ipax1xx68XU4m//5nUAzmrgTMew8f10XOA7PdM/fgqbBtvnfDR19wmpZlaU1Tkx5ub9e2gQHVRqN668qVKhQK+spTT2lWaal8Ho8eOXpU2UJB2/v79XRPjz62Zo3qior0+Ucf1cHRUR0aGVHA59Po9LS29fdrx8CAWsrKlM7lNJFKye/1amhqSpfPmSPbttU+NiaPZSkvKV8oyGNZ2j8yoqteeEVnxp8YMyD+ch1l1Qi1tdeTcHRwi2ke4aPrVssiBMyG27EKoiUIK3lwiQ9148YrrcLSefI2BHTfEQTnaD/u5JEe07LTNklJhjBkzwZjHXViVUyOU0teVsd9u/cjjIorUDpyWazbkkr+TiXwIrQuJSb+YuO0S6UtO1x3pc+PheqMbIr2keMDKBXRYpctrXE+z/T4rbh2nb7PxRXU71bWExYIxfhMJo3LvXUWz19UzvWcVpPpaenCN6AYlFQCRtNx/kSK3U5r9bMRtj0HUZomR8lATk1x/f521x07PcFzOGvkkPJMjWFxlVS6fay3rGMvPB72YLCTezplfxLCf+GZxPFjpcfaWCpSBEgEw0ax2yU9cjPz8gex+GNlKF/XfoD2skMHTWmUZTrFdbFuuRxAlp7G01FUDgjOX20AaZT9iJaigKTzktckFpZV05501gpTz+7nTA11QacbihEDjhSh4Dz0S8B1ahyl55efx4sUKUJJ8gUB0sVrTmwvKzGvlReZ+ReR8Onx4Ll4y39yXYmKDmc4yZdOT/bjx0AH17QLpk1qCZ3jhnuNaz3Pz/JZfp9NM+c7vgXo+/zS1e+j6Uq4mATIiSFpqMfwoQ9In72BEFUgRBLpVe9m/r4gCZL+AGv20C+kti+67n27QMw8GNLG7m59/MEH1ROPH+v//eMtW/SJc87RxbNmaWtfn45OTGg6m9W5LS2qLSrS8PS0HjxyREurqzWeSink86koGNR0NquuqSnNKiuT11jYAY9H+4aHlcnndd3ChbqgrU1x0/2sJhZTqUmGKxiX/sz4y8cMiP89jENbKO+ajrtNLp65F7eb07d4Oo6QiUTpG73xDly+r/uUywwVigH+R3djUceHSSqSTPwzL0XKsUTS08Q2fX6E+fiA4VyPATjFFSaGPos/I/1u+9PVV3CthrnSDR95bqOPk8fclVL7gBRejKW48mK3REpirmU1KCSxUoD4wCYpmZQmO+mx7g8CeKEwoCgb4dq1D0s1X0AQRorcTmY+P0I5XOzSl66+ClDYsg4hKgtra9fj0uJzENqOFejEV0+/CsDMFyRvkPnZBawxj4UC5vQs93hNf27jyvb4dCx27/G4lvbejbigJ03WfXwYPvTSSvZ7qIfPWR6+5wuSVe+AdHwEz0NVI14IjxcvRjgmveZfsJZ/+XmeX5LkZf5D3TS2OfgsFnykSLruH1AMH/41fAGxUsPmZ9zp4wM8QjYNyPQdAiQ33oFHZEWTSdQ0CXNrX80fiXVLJdir1BR7FAgTtiitRkGpm2VKtSZR7mKl7tmwLJjYGucTDiitkuau4pqP/EZa9zOU0DkrWa9wjHdn2yNSZgoL+MZ/or5eQjnb9gjxdKchy0VvIEEumcA7svEOFNRs2lVsalrJO1j6Suk7n8VrMh03ylzAJSEKx/AkZFMQCu17hjBKrAzly8ljkfA+DXbCT79nA8pAcaVyV79XP8lUKJHJqCBc40PT0zqtrk4dExP6wOmna2tfn27ft08HR0fVdFzPb9u2lTfkLCXBoLKFgrKFgqazWR0YGVFNNKrqaFR7h4fVUFSknnhcX9+4UU8cPSq/16vuyUnERaEgj8cjKxrVBa2tL/5+z4wXHTMg/vcwQkVS9yEExdSENLkDQecQiziMZ88+QJ1z2zK+N9iBm/Ks61wXXlUTgns6QeKNw5pmCcGSnAQknLKulsUIrIEO8zkLdq+iciOc4lgzi9cgRJ2M7sEOQPxPAbgzAmHpkve6/58cQ3Bl0jCFXfdBGq44ndfOu0m653uSL2RirGnuHatA8E1PYOUuOZea7v2bSaQqrpCCZS4l7PgwFuqKCxHYPfuJF29/hHKokV7irEPdxIUb5hkX8BjXqKiHO9up1/f4SAqzbe4XLQVEg2H2YGxQyk4bznFTnuT1sQ8eL16J8UG8ColxQh9FZaZXtRclqpDHOp61wu1I5rUBaX8QYI2YRMZwEYljXftRLFZfAYHPp687MSdABVzhNS3SgtX8cSxECS/J1DhrmU0DcC0L8UAMmoz15kUoD8VVzGXnY4DYgmtwRXuNMrl/E/SphQIVBP1HTdJe2MT3p1nrOaew3muuJWxTP5tOYCdndnu9XMcZyYT02/9CaRrulcZ/x3eWnsN8EuN4S7xeaG3TSemtX+D/p18FGGfT7EtlA5UhKy7g3F35Dqhabds0dKkyiYpBzuFYP3OtbuX+iXGuU8jz/SPbWadsGiVvbEB69LfSVe8xpWgZ9jwxBrCvvxkFMzGOkjMxrMz/fljpJa9WJlKrSW9Y4UBAU9ms9gwPK+zzyefxaFVDg2piMX3+0UfVZ+hTHYKY6lhMt+3dq1yhoMpwWM+Ojytv24r4/Qp4vXq0o0MtJSXqmZxUVTSqkelpPdzRodX19VpWXa3tAwMK+XyqikZVHg5rmUmUmxl/2ZgB8Zf72P4o2dZHdwIQ0WIERmWz1LXHgJWJRwYjxDsrGwFZjw+3n8eD+/SRX+P+nbcad3h8BKUgVsrfhTyCYu6pxIT9IYhPju4ycfQw9ysUsJA8Fi7StiXEy+/9AfXQEnM49Xky0scGqYGfGMLF2bIYoZeeRoB7fQDkrz4PQHh8tCO98WP01p4cBaCCEengJqymfBa3a0UDSVHL12L9PvwrrMKhTgAiZ7LxJb5f0wpYB0IoKF37AKoHfooi074DxcchnBnqhDo1Mc6zrzgfUp7kJLkLTvOZ1BSNZGJlrFUyAej1bUdZsQtYipe+jec9sBmL96p3E/K48R/xNBzdjQcik2K9i4oBjHyOCoFMEi9NabXUvt3lB7jiHZyTUy/BZR4IA841LdLlb0cx6d5nmtkU8MLYJgHvtEvdfTgeLNf/jnyDaClK4Gg/9w6EUHaixWRcP34r301NkVORSaLg1M9FKZtaTFVDUQUKxMO/4RmnJpiXnZdsD+d4rB8rdayfKoiVFz+Xb/z5Rv9RFMrhPpdxTQIw0ynANxhxP394Kz+rqANcZy3jmfI5wHTnY9Kd30VR7drHuS2uJM8hNUWnv0ixIXPJkUvg87P/iXHyGfwBlLBcBl53yyJvJJcht2Hf0+QBHNzCPEIxuA1+/1XDUz/BfuWyCvssNcYH9KSnRFWelEYLxZLHq6JA4FgfcUlqLinRJ889Vw8dOaJcoaBzW1q0sKpKkvTJc8/VPQcPqq2sTJZlaXhqSt2Tk5rOZhXwehXweJSxLHk9HqXzeQW9Xo2nUrpw1iwFfT5NZbN6z2mnKdLbewK728z488cMiL+cRy4j3fVj3HJNi7HGoiUIgJhxkTmdkoIRMmQPPktGrEOe4ZBKRIsBCQnA+urbAB6nljwUQdCWVknv/SbsbhLuv2+/H4vG45dSYwiocBGWpD9A97KKOkreeg/zvYY53Oeu72JJxMog2bjnB1i+4SJp55NYraXV0oKrabF6w4ex1OIjLqvV5Cix/9d8Ast3ckzq3kb/Z28AhSAQBDROvQRAbJzHd4d78GRkM1I6wNzLa92M91wGIZxOAaD+IIrOknOo18/nsNBS0ybruwhlYWocqy1azBrNPoU1H+okG95vwG1ikP1KjLoJfPVzJHlQEq54J0BV2+a6dINh1vR/3mXc6MZqT0ywX80LUFYiRSSJde+HGW/xGq5TQgay2pZIr/44CWheH16a6iZAzhc8jh7VKCkeP4rD775EGOT4Uqw9j6PIOU1cEnE8Gc6Ys8JlzDuWRBdi7Xx+N0xwcDMhHOc6+SzAXVRuuPuLAdtwjD2aGKLP9v5nsPivfPdzLfGThz/AWo3181zpaRSGyTFDLZyky5jfxOqHe93ufD2H8FoUDTKPwU4Uoz9+U9r+EK59p2vgwjPIS4iP4dU4/zXS0SGAPRB2s+ODIZfu1evjzKWmWJeiMuYVH+VcRItRVtZcxzvpdOxLJsx+2LJ8Pr1nfK/ujzYpY1lqtQqaX10r1dQoFgyesBStpaV628qVx/6fKxT0THe3BqamtKq+XgsrK/XA4cMqSFpcVaWCbatzYoL6b5OR7rEs+SxLsUBAHstSaSiks5qbdeW8eVrf2/viezEz/uSYAfGX88hlXRayQBCLJZXAeh3twzVseQDwaAl/muZJ5TUA0ulXPX8mrtdLjK/7AJ2+BjslFWOpnX29C+ASPyuvw3oo5CXZCMk6U0JTXu9yTwfDbumPRMvHPRuII6anpR9/Ass4XITAnBg0NJbT0qy0tPn3xKNzmRNbNXp9fE7CrX/zFxCIlkhku/ytCOeGuS7w1LRIl7xZ+u5HsKaiJazVWB8x8OJyLKqciR/HRwH1+jnkH4z2YkEGwljd40M8fzrp9vI+uguPQ3ktHdW2rsOC9AUMoHexh6U1Li+5xwCQJbwIk6Omq1y5dNO/uAC8YLX0id/g3di/iedadh6g3nuYePbbvuDGll9oNC88sVJhoAML0uc3yVQB0yZTLuB27adxztJzOFteLwqJbJII81lDjLOCKobt6+mZns9SvpbPGQtzFG+HoygsPstwvWfd+Qx183cgiLJaViudeR1naeNdhH8CIZSXe38oldbiXn8x669uNgCYTXNdJ28gMYrSm89JE6YOPFbG2SipJBz16M0A68Etpn+AT6qby36lkrRnDUaw3D1ezt+Fr3drxSfWoZT1HGRtG+bgtSjk+X0oKi1cwx6U16FEpKdRMm1xnnoOMv+eQ1J/BwrNWL+hI/ZLoZgapob1mfguPRSq1nRRi6ZH+nTRslNVE42+4LIUbFvff/ZZPdXVpaApS7t+4UI1FhdraGpK8UxGtm2rraxMl82erYePHlV/IqGFlZWayGRUFg6rc2JCJcGgXr148Yufu5nxkscMiL+ch8eLteAPk9RjW7zoVc0A+KzlgMSeDVgeA+3EdpedKz30K+mWL9HK86xrn5uFe+W7pLv+17SSDAMaS8/DgnWSkDIpUysdhjym27BmxUeIG1sWWdJOk5KxAVzz1c0I7g13mHj9HoB7pA9hFi1FqHcfQCGIFCNkR/spY1p5EZb3xBCCMD5MHFeS7v6+dGCLAQKb76y4gMSlk0fDXLwNOx9HIEZLKHeraJCObDVlVmHKqKbj1JRXNxPzn4rz3IWCFIjyWa8PoZ9LA6R3fBuhHIqiNIz24+6+7h9owVlWi2eksoEchPFBwDAxhgt7etxUCdRyv8duwVp2uqE1LyCz/54f4roe7CBJzxZJhr//b4D/peYd9ByWvv0+FDKnT7gl9iQQxh1/aCu5Bbd9nVac0WLyEVZeTD2/k5Gdz5FPYBcgJOncC3Pf6it4voEO6dl1UvdezsmrPsYahaLE+/dvlvoPY20vOZt1rTDJbHYBTvdUAnf0gc3ufdffzL6fff0LP6fXy3swOeZSyE6Ocv48XvbRFspBeY1h/vMQp69oQAnI50i6C4TxeGSSnLlghGfZ8iCepsvehjJz7N4+6SM/4gx5vOzjLz5jePi7eV+nRnkWp995Js05L64AzB2r/Q//w/uz5FzO5s71KJFeFLAr+rZrTUmNEonDmqybowXNtS/aTaw7HtczPT2aZVzouUJBdx04oNPq65XN5xUNBBT0etU/Oamne3tVV1SkklBIZaGQ/nftWk1mMsoVCmotLVUs8BLP3Mz4k2MGxF/OIxCSVl1BNmzvYcDjjKtxOT95G+Bd1Yzrt/uAdPnbAImvvh0Q9XiNSziDq+/4UVSGezo5RfwwPgLwPDhsLIccVna0BEshnUL4On2O7QKMYYkx6s87dvOd/g5Aq3UxSkWsDEGYjBNPrzTZ0o5S4Qvi8s6m+fmWdViXr/5ngDyTJDFv6bl8fs+TboZ4IY+S0bGbUp7jh20jBAc6DVhZCEwne9vjY80c0Gicj5Du2ouFPWs5dcl9h7lXw1yu6STE+QL8zPJgwe1+klrijj08zxs/K63/LWufGMeyOudGyGA8fsDT4zXg0ovnZPt6stI9HpSHi98IqDcvxG3bcwiFJxnHkzJwlD9O6OBPjTu+xTkqKmdPNIZbuawWBSNcBLD0HQbMGuYAdrd+ldKw+jn8frSPn08MEi9etIZ1XL6W5wyG4SXoO4jCls/Ta7thHhbv2TdIv/68JIvEsP52LO7GuezVwc2EIyobqZP3etk3h3hly7oXB3GJssKDm3m2IztcDn3bZn6ZaUk2oOr1S9//mNSxV5p7iqQQ9+o6gBKdGANcY6WcM6eBSqzsxEx5Z/j8vJfREu6x8Ayy1SdHufdQt1GSp3nuzDTzTCYo8TztUuk3/4nyMjXB3sxfLS2/APKfmlbpux+SFYiorKRSZdNxqXenqV1/4ZHN5+WxrGNA7zV/n9fSoofb29UzOanSUEgBj0fVsZg8knonJ3V4dFQ379ypj6xZM9Ny9G8wZkD85T4ueC1u1PQ08WCn49L5r0EodO5D6F/zXqygL72J35fVAk79R6Vffg436HmvRjA7I5vBGj+6C/DJJBHIQ118t34uoJ1KYvnlMoCW1weoO8k2m+8jU7pjN3OaGELA2zafGe5GkAdCuKpt29CFZrnn5BggW16HQHv6LkhPbvzH566H16dj/cwLBX52PDPXsWdLM+f4iEnSMpb+7ieJM2YzWFDREu674gLA+em7AJL62YB0URnzvuTNJPxNTWB1PnErz+6EA7x+tx3oYCfr2b4DBjSnD7nXK73/ftzjew4RG/YHUQjadwLki85222c+/Gs8HYvX4N4/uFlKeQHD2jb26c8ZXfuZ81A3cehC3lC2VvCsTj/2YJjEqj1PsS7JSRNGqDVNcuImxyBFPPnobukNn3ZDAZOjuNdNFy75A3gSxge5xqGtUsN8Ub43bpSxLta6uMIFqnxO2vEYSkXrEkJD2cxzvUrPNxav4Yz98rMkZMbKCYFkUtJ03oQ1TChqcoTaf4+HRNKFZ3A2F6yCyKb/MO/eWdfBl7DpXsOx0EcW/Jv/nXkXTMLitz/IM5XXooBtfoD38cCzxNdjpVJFLR6RV38cpSqX4R1pWyp1HyS3Yt5peCRsm0THOSt5x3MZLPOuvfyxLNb6WKXBicMhZWkoLlZ1NKqeeFyloZCGpqc1t7xcP9++XWWhkGJ+v1L5vEpDIaWzWW0bGFDQ61W2UNDt+/fr3NZWrWpo+PPO3Mz4k2MGxF/uw7Ko9T15hGNkkCcTaP5OLDiVcIWck30ejgJgv/0ivZZr24gV7t1IyUvtLASxxweYeDy47lNTWArTkwjoYAT3ZyYFkCYTzK+6BQtisIMEsFQCqy6bZm6RYreEqGUxoF7ZACvd7V9HqHv9pktXBFf9Wa8wddzGZZ6eRnAuO1969n6IUrI5rI/ns0S9fly66aRbm53PAlLZFP3Y+9ulf/iey7AVH2ENHFeh5cEarJtFO06JxD9HiciZzP9MUqom6/eYlyKX4b5O7DZS7GbJx0rYo9YlZDvnc1y3uhkAL+SJ344PYqU3zCEpMDWFGzdaJh3ajMv1nh9KZ1yJp+JPWUkNc6R9T6E0eEz8u2422djJBCAfLWXfxvoB1fEh9rZtKfHfnY+zTv6gVFYvjfdh3f/2iyg3Z1yFlW+Zs5tJS74kCsEt/y2df5NbctUwF6Uqk2I/K+rIqRjpMXvoY26ymev4IOfgsre9tPdmxfl4l7pMJr7TLlQ5KS+Ui+k4mfI+P8B/YBPKVGk1/eWdpkHO3v7PO80++djLgQ7CIIe3oZC0nG8qRcKEge79EbHw3sOGYCaE98vvN8+7zFWs83kqKtbfjJeodTHx896D7P3CMwx962zOcCbJu5fP4uXa/aR0+hXHpjuWTOp7zz6rfcPDKg+H9e7TTtM/nXWWbt61Sz3xuC5oa1NjcbF+tm3bMZ706WxWR0ZH1Tc1Jdvwr3s9HrWWlurRjo4ZEP8bjBkQ/3seluXSOjpj5SUIjMkRwM/jkWavBOR3Pip990MA0yVvBpAdV3O0BAs6lzEWrnE7JsawilIJatXDRVhvBQ+u0IWnm9hjrxGSxm2dnEQ4e7zcO1pCU5RwkfQP33Xnm56S7vsxIJdOolhUNxNHvP4jAPb635KQFghLr/gQSsCO9W4C3FN3UHvrZHdLCO5AyLVwVDBMXk1cZ3IUAW0XpCduJ2QhCzBLjAHmHi/zM00ojo3GeXhCHvsdbuW5p7mu/fQ09931BEpCtJQ9Gu7h3z/+BNZk2VKE/cLTAeOzXoHVNdpP+ddILwL/91+WXvNJ1uTC1xPi2LoOIJhzCvO/94fs46IzXvy8XPh68hQKWeZd24Zn5Kr3UsZ4aAtWYTZNGGJiCHC48R8Bous+SM7CjvWGAc7kOCTjJKx17cXt/8p/BPAPbCL2fc57WIt7fiA9c7d0+TuMV8fC2zM5Kp37StbA6wOMhrpQNtJTWLrTkyhgbUsNsP+Jkc8R158YAvwdEhnLwssQjqFIDvcwN6fffHk9z+nkGUyOAcbRUhStYMStIbdtlK1n7oYKebiXM/zAT8klqG7mZ+3b2R+Ph/ORmpSCNbx/v/gszYHW3kRoYsuDhErGBnDvy+NSJO99irXJZQhVDfVIgWGAfPHZNIwxIG7btr7+9NNqN73GJzMZfWXDBn3hoov0zlNP1cbubvVPTurI6OgJjGuWpMaSEs2tqNCdBw7Ia9qf+jwehY7jU58Z/3djBsRfjqNQwDqdmiAuNmfli2fjHj8ueRM808/cC4g2LyLWuPMxNPeKRuLm9/1IWvsaBFIuSwLYpvuwvoLmtc6kiHFe/R54yQ/9B4LU8knzlyM8Minc0ruewAr3eGjd6TXEJHNPQWkIxRDWJ7tCl69F6YinpCPbAJYFpyN4b/kyFvJgB0IwPiL96nPSqZfxHB6T1d13BEY1x1qWWLuWxfxuagLFwy4YUhYfwv2SNwEOT99NDNPrM/XiexGkgRAWrkPd6dRP2zaW2spLuP+ytZDE9LdLT92JZZRNc6/9TxNLDkVxw+ayrNNlLVius5dLV76T+yw8Q/rpv7o83LNOgR/gP19L8tXamxD4g53Mu6jC3acDz7w4iBcKJrM842bYz1uNW722BeVq7mk8eyGP4tE0X/rg/7rVB/6AdOZVnKPew5J3iDUqFAy/uSkre/CnsL79oh9QsixTM59jL569Tzr/9TROqWriucvr3Brw1/2btPUh7jP/9BMrHl7qGOxEkWtZgqdp5+Osa2UDisFUXOo0YYHdj1Mr3ryIGnsHwA9tgyfBKcW7+E0oQnd8G2Av5I0b3otl3LVXaj3f9CTIEIvPZUxjIFNmF/Aa/v8JQwvcSE5FuAilKFLMn6XnEj7JZUxfeh9nLpWQnvgD3eJ8ftbeIQoyCr1t2/rt7t361Y4divj9Gpia0ql1dZowtKlPdHbqqa4uhXw+TaTTiqfTCni9Cvt8Gk4m9erFi3VmY6MmMxklMhnlTejqynkvMfdiZvxZYwbEX27DtnGpbX5AartIuu33ZAZf9IY/7S6VsJ4vfguuzv2bsIY69xIbr2qkTM3pXhUrlS54DQQdhTwZ66suQ4hkMwim8jq+v3cj1nt8GNAbOEpZVj7HtVsWIaAzGayVxnkI7WgJ1m3KJBKddinz7D+KJTsdR1ArB4g0LTAlVxVk+I70AKwhnxQs5/7bHsLSD0axpCwvJDLHj6pGnm/J2QD2vqdJ1goX4SpetpZkrcSY4fc2r5LXixV13qt4tuEeyq22rANQJamiCfdvKGKsoqMI/0ix9OTteC4kYuiDHfR+/+5HAM/UFH/yeeLcDXMMOYwJm5zzSvampoV8h+FuhHMuQ7OU138KheD4Mi2HfvfFxpZ1JKiFY+a5uiG6+fAP8EjMW8lZaZxPeVUhz1qlEideZ9UVZG2P9Ji6cI/kNefWto1HZZr1bFnM/tviDNgFqTAp7X6K/S+vR8HZeLc03o8idfpV0qpLyQU5eYz2o8iVVLod715oFAo61no0FCW3YOpe5hgfIbnQzrMeLUvwvJRVueczk5bu/i7zD0VRytb9HMKh13/KJBkWGcv7JygFxBBMqGnKsLT5TIlohOfNTKO0pFPssUQC5eFtKDo9B9mf8lrWZtXlhphplM+mpkzNuMmnmJpAYdn56DEeiC19fbpz/34VB4MKer3qSyS0Z2hIJaGQEpnMCRnqtYWCDo6MaGVdnbb09iqeSul3u3frNzt3qr6oSBWhkE5vbNSa5mY1Fhe/+JrPjL9o/E1B3LKsyyR9XbymP7Rt+79e4HOrJG2U9Grbtn//t5zTy35MjgIata0IyZo26olXX+E2F9myDndr/WzA6Hg3VyZNss329QDQxBBJPfks1z64mRaQBUOwsWA1BCn5PMLmiT9IWx9E+JxzA3HL3oMAsy8AqEdLEFQti/nZ/k0I77pZJChNx7nWxW/E9bnrCa6/6Eyea2yQWm+PiSs++jvIXpyGIV6vm5A22GloRo1L01EKLC9AOjUJvemzD+CSDUVYh+pmlJIHfoKgPvM6PBTZjHTeK2lyEgjyu7IaQKm4kvuW1iBMH/gp8zm4CXrXfI4/Ox/HajvlAkBszwZiwQ4Dmm27hCeyWLvEGIqHLL5jiecIRlCKDm7Buq5pRvlJTRNDl421GinmGl37KcHbt9El6pHN2m17hLyCcAyh7ygdbcv4fCpBA5uyWjwq4SLXyl58NiVjP/8U4LRoDUrQbV+X3vkV1kpCwXndv7KXt30dJWVsAKBuWYT16w9K9/8YhcAbYH65jKmVd8C+FOWnex9hlpEeLN89TxJWeNt/nXiutz+KhW9Z3Ouyt6KgvdCoanLbyUaKOfuXvwOWw95aPBIjfZwnf0BqXYYi4SjKqYRRjkyIxkmeTIzz3jn8C5k0RDR7jkv8rGjgvfN43EYqE4MoDbFylJX9T0t2C/dLJQyl7YHjqgMaiemvvoLzeO8PuHbGeM5Ki6SJpCHU8XF2N98nzV6ujokJhf1+nVZfr2d6e5UvFHR4bEz/dNZZqovFTshQ91iWwn6/llZX66muLi2rqdGGri71Tk5qIp1WbSymoxMTeuVxTHAz4/92/M1A3LIsr6RvS7pYUrekTZZl3WHb9p7n+dwXJd3/t5rL39XIZU05lBFgHo/rnsvnpdu/QTZ5KIYLeaBDuvQtrvDpP4LVnBg1PYmLpMSIcdf1G8uxQ7rpnxFGEkLA68MFv/EOhEwhT+lYUQVc2JmkAScxj4Y5xD3HBriGnacGu6gCQXfTP5OZa1lYtccPp41pTZ17/6wpn3vmHuN+LcXtufBMBHsmLeWGCC3kMrgeO03cOFINQG6880Tyk0VnUpqTM7W3DrBaFhbU7d8kDpzLAXypKeZ8/mukn/0bYJfL0tRkqBNXv78YopDEOF6Bslr2KJcFOOasdFnJ0lN4USJFgOTuDYBHNuOyt430ETpYsBq3656NzGGsD8Wroh7vhMy6h6LEZm/8GOA/3IOnZMs69mDz/bjn//A1Yx3KtYYnR/m7qFySxZo458yyaEQzf/WJTTiGupjLcA/WZdN8LMhVlwOQd3+PRLuiUp4rl2H+B59F4XCsTYfsRhb7PTXGfzNpQCubdi3YDbeTVLZ8LZ+ZmsAKLqs1pVlpFKxZy5+bE+KMQJA1euqPKLwrzmfOT94m5e41TYMeJcwSKeEZnXV21ixSwpoVlaNgeX3kgZx8n1d+FK/JY7eg7GWS7EVZveFQKEheEw8vriBs1HcYRTFaiiLl8fNO1c/mnqP9eHfCMXgf7ILh8y/HG7L7cc6tP4gl37QABSqbUVUkonQ+r1mlpbqwrU2HR0d1Sl2dXrd0qbKFguqKitQ1MaGycFjD09NaUl2tkelpBbxepXI5xdNpVUWjmspk1FJSon3DwxpLJlURiTz/Ws+Mv2r8LS3x1ZIO2bZ9RJIsy7pZ0rWS9pz0uQ9IulXSqr/hXP5+Rkklgm+wU4rMQYhWNxMPG+4m2aWmzbTbrATIz73RFWYDHWSYZ5II1UgRAOOQksw7DcBz3NbHj71Pmb7Ue7hfICR17qau9+Cz1LrKQtiEooCeXUAwOV3ULAHggZCJ9cVwKx9P4enE8pyRy2JlnHcjVmY2DUje8mXKqaqbsfim4tTI73iUDlXl9WROh2Ks26Z7iT3OXekmKnm9kjfs3st55kd/xzNVt3D/4S6IU1oWASR5IyAdl6xtA4CWheKQSxlruRvvRHkdYH71e8g/GO4B9Bet4Tuv+CBlaZ17jCVu8Zy9B7lncblpxZpDyfnYT4k7/+5LbslfbSv7NzUh/fFbhAUOb2OOp16MVd93hASydNKlrT2wiSQqb4Brjfa5ZXWO619CcXIUnGDYrT6454ecR4+Hud/wYenITuZg2+yxx0uc94yr8c5IJHSlEuxJSZUbE/cHuHYmZdjKUoBYKOy6+/dscEF8epK/HWs4EDQ1+4kXBnEJr8FFbzjxZ2dcjQega59hTIuTW1HVdGLWu9cnXf8h19sQiMBlHn0el7LPL81aSux+3YPSP/4URaRrH88YLSaB79AW1j+f532xbeL1+YKUjrshnZIq9sB5R5xM+xXnu+vxg4+TUBcphhQoWnKMYe6MxkZt7e/Xlr4+eSxL8ysr9b5Vq/RUd7fuPXhQmVxOVZGI/F6vLmxr0w2LFmlbX58y+bwsccxTuZxqYzHZIsbuPS4nx7Ztbevv177hYUXTaU1ns4r4/S+8DzPjRYdlOxr9//WFLeuVki6zbfvt5v9vkHS6bdvvP+4zDZJ+LekCST+SdNfzudMty3qnpHdKUk1Nzak333zzXzyvRCKhWOxPxP/+Xx+FgpQYVSLvUcxTINnM48XKGek1QtK8brkMAsjhph7qRlA6rkvJpdf0mHhvLgtIH98Ewi4AGtm0sc5shG9ptUta4ViQPj+CJD2FSzxWauqGpwFVhyFLZgqBIFaUA6B2wfUKyJLyWSUiFYqFAoaExMx7uMdQZnrdGLDlAQzSSZ4xGHFLhbx+I+ht7ne84iDxneSkcWFOGeYrI5xyGdbZ6f413A1Ie73sRyZpeME9LkgFw/w7EOLnjmvzhYbDBZ7PKlFUq9hkP9/zB93kKMcFX1lviFLMs6an+J0/yFonxphbPueucSCCZWl5dMzilbB6vX7WKpMyz1rO3p6syKWmSThzFJZwzACvWctC3lVAsinTStXm5/k8Z8Fj7mvmnAiVKjbWbeZV4G/bxKx9fpde2GPW1mMU1HCM7HC7gPXtD3DtgrHqKxtfWp7I841jNLheQ4z0IomjTgcyWXzPie+Hos/hKDgmn2ybd2BylDOdy3BGnfyLbMa8OyVcN5UwCXDm+Tw+vDAv9nzjQ3zPOcNO9rwZmXyeo+H1Kp5Oa3BqSn6PRz6PR7lCQdXR6AngOzQ9ralMRqlcTnnbVtTvly2pOBhURdhVhOPptIanp2VZloolZXw+1cZi+gt34v+Z8ddiz/nnn/+sbdunnfzzv6Ul/nx7crLG8D+SPm7bdv7FmHxs2/6+pO9L0mmnnWavXbv2L57U+vXr9dd8//+l8Zxnzeekm/9L6jqMe3xqHJfx+Rfwsnfulbb8ClKJ4S7jgk4DLrFSLOJoKZb++TedCHIHNktPPIjVkU0bcpYgWcZHdxqL+jRK1zbdx/1Ov4r7p6ZhmBrq4ucHNhMXTCUQWpFi6Y2fk+adyr1sG8tu/zO4mPvatX7xK7T20R/w+/o5uKVXnU/51FScuLU/gPu+vA5X4tYHAaJMClBrXQrhTDKB2/dffm3YuVLSr/9TWv8bBF5VI8BU00Z/7kya/1/5TqlnNyVUe5/G9e3xEpO85r3Qlk5PUNq15jrW79f/YRjMbNamZQnre9Z1J/ZEl4jr3vYrqe+w1p/1bq29+/PsowNqkSLWb94qaWiT9O6voUD98Zu4gSdHAPTEGHMKx3DFFwrEaNuWApxnXis99nvWzLYhsFlwumuZ97dLp76LuujnG1MTgOfYgHTrVww5yzwy6Qs2JVKToyS4ZbNScgJQqqgjTyJSzBnyB6QtD2n9RR/V2oe+ggJV3YwXKFwEOFY1SQNHcBX7glRSVNRLC18r3f9TPCyBEHSzlsftZX/dB1xX/fGjcy9JZ7FSnvl4StrJMc5mIU+uxsn786dGfISSsFQCkM1lpOs/zLqYsf6hdVrbWGJyLVZJX38Xse6pMZS40hreq4FO9vaiN7gNUZoWwNcQjkhrXsG79WJKoW0TskhOotA4+Q3JhGly45fqZ+uRzi59Yd06jafTCnq9mltRoapIRAuKihT2+7VjYEBhn0/RcFh7p6bUFY8r7POpIhzWZXPmqLaqShGfT4uqquS1LF34859rLJWS17L0nqoqrc/l9C+rVmlpzZ9INvx/fPytsOdvCeLdko4LjqlRUu9JnzlN0s0GwCslXWFZVs627dv/hvP6+x1eH0LjmbuxuBvnndhf2ek17bFgCkubrPDmhdTghotMfPYstzToWK3vFGrbwjOxqDMpXKbfeA9Cxmka4vOTiCRJd/4vmv/UOKDsJPvseJQkpfpZCJTew9QPz13JPR/4ibTzCWm0G2rL2acAYlNxN0xw8FmE0ru/xlyCYen7/0gGr4TF37QA92h6mlrxw1vJWI8UAVTrbyZf4Kk7AIlwEX8mhgx/+jY3Nh0pln76b6zHxBBgVVFLXNTrl9b9gnhloQBBSmkVysxon6Ho3AfT1rRJUurcI73hM8wtl0XILjmLtdn3DM/kZKnLJgmsYQ7PHitFIcqmAZ57f0jCoNfHtbJpKRhnLYrKWLfyOhSac2/kXESKyS/weKRL3wzgJsbcPInj47/OiI+iKBSVY2He833mEoqRa5HPAkJnXk2448h2Muw9xlsSKyf/IZOmc9cDP+M7uZwpPWxAwbjpn1mH9b/lew1zWY/KOpS30ho62vUd4cwtOAO3czgGw1kw/PwW6vb1JNR5/ZzZ3U8Sr/b5eTanva1l0Q73pk+4YZfjh22jXO5Yj2fgzGtQCh0aVEcZSoxxthwQP7qb9+D2T3JOmuajeFfUoRBmsuxTYow5VTdhnU+OUr7WOA8lZHJMuu+H5LZc/6EXbr9qWbjSjx+j/SS2TselQl6Z5kW6OTBHldGoMoWCYoGADo2Oyu/x6PZ9+xRPp1UZiagvkVAym5XP45FlWRqzbR0eG9Mj7e0KBwIK+XxqLCrSW1euVM/k5LEEuVyhoM7JScrQZsZfNP6WIL5J0lzLstok9Ui6SdIJdR+2bbc5/7Ys66fCnX7733BOf18jmyZTvaoJAW9ZEJqcnCjmjKpGGpX0HnTJUdqWGsF7DQLfGbksbUIPPovQ7dxjyq28MIk5XcI8Xrf15kgPoD1/NddIT5OZXtngJkhJCD47bogyTJz38VuJv5ZWI8BzWcgqpiYA31kXu9eYmsDy+sP/oASsvYlnb5yPYKtqcsMFLYsQ7ut/AxAETGJR61ITLxbXchLXLAshnxgH6BacDjh27iNjuLzODUdMjgGUfYchZalqNnSov8Kr4LDlSQBOtASwKq8D9G7+giln8rAHN36MePJ9P8SqDEXdREa7wNoGI6xzRT3X/9W/Y1l6/VIowDMWCnCeZ9OUKq24AAKd413Cy9e6MeVCgTU/sJlnPvMaXOFOv/KSSvbx7u8bN7dItCsUWOslZxvA7ifDO5siZp1OosyU17rekXRSuvB10v0/ISO7pApr2OtD+amoYy9WXkxi15Ht+PcWr5GufT/P94N/Mq1uwyhT+zai6JXXutUHJw/bNnkSDW7MvGsfVnD9bIBt52PkQDQtMAD8R+LcJ489T1FeVlTBOfjtF6ldd3I3nGF5Xbe8bUNvXH8WeSn+ILkNKy9BMWlbLj11O2Ear4/nmX8az3vuK8kF+c0XXAZE26bO/OCW5/YFeLGx/mb2oKpZsm3Zh7erpayg2KyVGkgkNJFKaSqbVefEhLrjcdXGYuqKxzU0NaWAqQawJI0kkwp6vcrk88pJivj96pmc1Nc3blRtLKZ4Oq2wccXnCwXNLit74TnNjBcdfzMQt207Z1nW+0XWuVfSj23b3m1Z1rvN77/7t7r3zBCZ0+OW9LMv86K3LqXk6/QrAdXnY0+yLPjRmxdTE3xws9TXjnv25LHzcdzZNW3S47cQf44UIbi79rtMbMPdfN4XADCOZRnLLcFpXsibnxhHeEWK+Pz4gCuMa5phBVt4Ol3ZOvYgJJMJhKNtk+1d1QT4JhNY9tvXoyxc8z6yxp0yK0vSeTcBLI/dAlg6jUZmr+D+wTDXrWpkTuODWCjJhFRSgTv2WNMIJ3HNJJ0V8vx42sTQ62a7n+vYLX39PVwzPoq1btu4spvm87HxQWKW81fz/eFu6uKvejfzsW231WVBWGVN80m6alksnXENbG3jA8bbMUGNsWWxR9kU5C6WB8v2xWK6Hs+JiVHP3Cs9aqxgy5IufRvekaIyN26++QGjjNm4r+eeylwjRdLDd0jVrVLtbGnwKOdi/yaeZ2wA0O9vx3reuo5zEh8FkK79AHPwB2BGGx/kHmU1zHOo21CyzsHKTyZMA56pF296kkqafa1y3wXLw73v+i7KXzaNcpUYQ1FNJ5//WjvWczad5iZD3Si7i9eY/u0HeNaRXjLHj+6G4GjX41LtGW7SWiFHqKBtCWGtTJp3paYVL9CWdRAJbTAVIZOmisSZv8/Hvr/QSE5xz6kJlNk2Uy3i5HVYlgLBkFq8BbWn0zq3pUX7h4c1mU5rIpNRvlDQaDIp27Y1mcnIa1mybVvZQkGWpLRtK2vbKvZ4lMnnVRIMyrIslYRCaigq0uDUlDyWpdcuXaqik/qYz4yXPv6Wlrhs275H0j0n/ex5wdu27Tf/LefydzW69hEHPf/DWH75PGQlPQfRtE+/ipjgyYlbtk2N7d0/QGgVcpI/Jz30C9y+b/l3t4HKSK8LDuOD/NwXQEEYH4Sqde+TJuvYJLGVVODudeqToyUAQ/tOBEf3frc+e8ejxJWdrlaFPOBb0eh2QrPkJkJ5PICYL8BzVtQTt/QFoO7M5wCQV/2TaZUa4Bl//hmALzEG+GRT0sQI7tzWZXBXn3OD1NtueNj7sOiv+4D04M8A/nCRUT5iuNKzaZM8ZTH/OStct/vOxxDS1S2AiyVcxjWtCOFgmPkEwqyJ4/aNlroK0ZxT+V6k2PCsZ8kcf+VH3b08tJV5VDfTGS6ZYA39AamkFNCbcwqx0+rjo14ybGSmiKR5oUlMNGO0n8z8iga8CKkpmuB4vG5SVCBEAmRtG6EQx11+w0dw0cfKUSJbF5Mv0X/UeG183Pd/3imd+yqALxQzyYB+5v6b/8Srs+Y6/l9e684tMY4LvGM3e7zwTEr70knpTZ9//hi4ROjm7u+y7oe20gfd8VoVldN1rG0Z74YvyB4Pd0trn8ejlUnj9TheWbXznI/SGtjtHvktuSP+oPRsBpd6y2LXO+Q1yX7prDQ2BLCO9OAhaF2Cp8gp/6ts4tze8wNi4FvXoSBl0ygggx14SOrn0AjJUd7TSbwLgx0kHT59F9n1bUupF69pk/JZWbmcrjr3UvWOpHVgZEQloZB6JyfVE49rOpvV4PQ0TU7yeQUDAeVtW3ae5EWfx6N0LqfRZFIFSWGfTy2lpVpdX6+Do6NqLS1Vqc+nq0455fn3ZWa8pPE3BfGZ8f+jMdiFG1FCyDsWRXEFMe6OXQjTky2T7euJnx7Z7jKRldUCNn2HUQ7mmeTImhZ4yZ3s6EwaoLEshNbSc6Syakpleg4S07363fQcb98hycLi3fU4lnBxJWDiD8A6tvoK3KJTE4DeEZMc13fQzZTuPgjYNswDaP7tDzT2+OO3AR+vDwHnD5xYz+yU+WxZ54JupBhh5lCerrwIoNr5GHHP134CxcXjRUHweLDC7/sRJB+nXQZxzm1fo6tXUTnWd1Ujcdg7vsUaTk1Ii88x9cXFuNuveAcgvucpYtmlNczxnu8j2D1ekppWXsi811wn7TrgNgqpaTFNLCbdkil/EOWtsprypZFuFImGeQj7yTFA7mQAj4+SbDc5zP9j5dJrP4nL/BhbmccNAzi83H4TYoiVAjCBsHTdhwyITjPHshq8N537sNonBo/LqJfbEGbvRukdX5a2P+xyHoSirFcmST1/NgVjnjMGOqT//TBlaZk0Z66ogkS3y99xYstP536WxfPe8W1+v/x8yukOb+MM1rRIv/8KP5t7qtv5a3qc96LnMMpYdbNpJvM9rGonXyGTNAmHxax5+w5p3yYUgGyadZmeJPdjuNudVz6LV8cX4B2Zv0pKLqSE0xfgDNkFzqtlFMX4EPkd2Yz7uUgJREmhKO/ZUCesiRKx8849KCV2irV64lbpincRNjm8jT1feZFKvB59bEGbUiWn68Kf/1yZQkFhQ7nq9XgU9Hrl83jUUFSkvG0rVyhoPJ1WPp+Xz7HK83llCwVdMnu23nXqqRpLpZQrFLRv8+aZ3uJ/5ZgB8ZfjqGygZrZQQBhkTCmP18vLHS5G6J08tqwDQPxBPm/nseCez9W6aA0W9eb7XUHu9eLCnLMSEJ13KoJp833c9+l7sBJOuRBw6txHu8yKOhQAlRoWrv1QS77vG9TZPnoLAnX2KVh57TsQXOV1WK7paQRarBgl4cgOrDin/OeKtz9/IpMvANAVCpLPuMGdsiifn+cOx4hXr7zouZZcwxzpbV9w/7/7SRSk6hbWZrCTpCOPBwaxVFL67HWQz3j9PENVE9e//ZtYyl4frv+2pSgYT9/FtWctpd5eIhHqUA+KUvt27mOLtpmv+SQA2TgPMpPDW1kzJ5muqsXlwV/3C+5fVE4oIhihNn9qDEtMAlyeuYdkxju/gyei+wCWf3mNaQ9aRy/6P34Lyy4UJVYcK5ZiS05cszOuIRTSdxh+80LBZanz+Nxysa59JI794tPM33HxVjWxvjsfhzXP2dcHfso6ltaYWvkD1MGnpqTf/zfu/Vd9DEv72fv53prrUJ6cci8JxWawA/Bc9wsUtSrj6p6zErDPJNmr3U8S23/dv0kbboODobqF2vHew4BvRQMAXlKJRd++3XDoG66DfA5FYlYjc/V4pUAUz1U4Rub40nPYP68Pj1o+i1LeupQ5t+9k3Z78A9z4l72V9/uXn+P5nGTPHY+inIRjeLUOb8eLZBd4j6IlcCs470AwIm15iPBAwVbnOa/RdCajWCAgjygVyxQKmltRoWQuJ9u2dWptrZ7o6lJLcbFGkknNrajQyro6JdJpDUxP67LZs+X1eFRpiF/2PfetnBl/5pgB8ZfjaF4oXfN+aSRn3Lq2YcTK4oqdjruZ4McPxz3atACLa3IUgR4t4/N1s8kI3rMB4bb2JgThYAfW9JEdbrenH3wM0Nm6Dreqx4sL794fEH+749sA3tGdCNzlaw0zmO0m/xRXSJe/Heu0qtnEhnsAaAnBG47CZpaachuMXPt+twFMTeuJPdCPH+e9SnrmLqzOxKihcTUKSaSYuYz1A5Kb70fAPx9ZhzPqZiOcD20BxPM5AO7X/ym96bOAstcoB7LdxK2Nd2GRhyII7R/8o1Qzi/9f+AaUoeNd6yWVuJH3JVnXBWfgLh3ugjr1nOtZh+s+gEXltMvccDtJdeEiacWFCP7ffIF9T4wxp2CEnIPhHpj9kpMoH7s3AKb1c6VcHirZ1iU833UfRBF711ewLB0lSMIq7m9n7rVtZIu/4TOEe/Y9TXikfQfntGDczuGY1HeU9b7y3dL+ToCzZRFrPDHoxuOdER9269679rsMgQ6RUGIMSljJJG0VWIvzX8fnshnDFzDJGnTs4jyGY+SEOPMKRqCeddz4w90AfPsu1qJjFxUT4wN4bi57m1sLXlxObwB/EMVaJiSUy7B/pdXGI+SViptQHpoXSHd+V3rXfxNmWnK22xZ3wx8558PdKB17n+bPGz7N/U7WW225BDDt23l/PB5Y4sb6WYM5pxoynTix9lWXs4aZlLxP/kGNNWepIz6pnLG4LUlNxcXK27bKQiFVRqP6wOrVCnu9+sO+fTqlrk7JbFZ7R0Y0kU7rs48+qreecorOa2194fdoZvxZYwbEX47DsnDRPrxO+u/HsI6fvhOKzvgQgtDJED9+rLmWJhnBCAJzfEBqWkTyzdk3kO199/cQkB4vgPHxX2A11s2WvvdR/o4UIQzv/YFLRBIfwWKID1Gr3ncYwSUPSsHuJ/l/UTkxZ2dU1FNC1HWA6+55AmGfSQJCTslO8SL3O14fVtCfGs0LpI/9nHnv2+jWpM9ZRlLZ5CixyEgxHoOtD2F1vRDLV3kt1t4X34BnoLGFdRzqxLK0bQC4cZ5L3OH0Vneypkf7seIa5rNuD/zUeCpKTryXL0CSX0WdoUEVrtFk/LjP+E9ch3wON2pVk9sOc/sjhEiqmljPw1tR9sZ6UWgkacjEb5ecw/9bFjLft/wH93fA1Os7sYJhKg5j3HAP/69ro81oKMJazDuN+HW0mH30+HjObJrww7YH4emffxU8+vufQREp5Imn733azbxuWwqQduwmVCGxfqkplA+fH8bA+auPCwXEpNEeOos99Et+VshLV71L6thngFbsU3EFGfFjA4Z50BmmMqCkCmW0+wAxe6c64ZFfo0id/xrO8ezlhAucEE82jdcjmTClmzXSKZdw7p2clcEOtyfA8W1Ul57Lu9S5h2dyON73PMW7XNuGAhUuItSx+MwTz+6iNVw7k0TZ9frctcnlTsykD4TUUsjo3Ppa3Z3L69neXuVtW0WBgA6Njel9q1frLStWyGPOgm3bCvh8eqi9XVv6+mTbtlbV16u+qEg/3bZN8ysrVftyJ936/9KYAfGX63BKodoW82fFBdId34Rbe6RX+u+34NZecQH115ZFotNNnyArPRjBNV1sAKKvndKmxDjCJJsGfJ/4g3Tt+7B0chm3O1SkSJrwI+CGe9y2iNEygDiXR6hVNyOgOnfhmvV4SLi54SOAk8eLAvHzT0mHD0vTU27tdTaNkD66W1pyw4sTWzijUCBBqX0n1umC1cz5yncjwDJpYtyv/hcStmpaXJDsP4KVvey8F75+4zzcn7bcJEDJ1EGXSbKxgKIl7EPTAnIYkgk+399O+Zc/yJpOTZC53Wxq6+MjELckY1hOo/2upZeeIuTgNMHwB0mY8gdwnd72PwDI1nUI6HyWcMJck+fg82MN+gOAm2VJs1Ywrz0bXE9HOslnSypfnBHs6bt4RicM0XuE1qJrrsWz07mX/ICegygPJVUuU184aghHglLtkHTtB6UvvwnwrmzE23PvD0lmjJViUU9PEYpxmNkcEhyHta5+DqEXZz+zKf59ygWUkd3xbeZ79w9QyA5v46yUVAG+Ky9ivQ9vMTS6JhSw+GwA8WvvdLuElVRw1vs7UJ6dfIFX/qN07/elzv2Eq1ZdTsletBSF75GHDZDarO1Ij2kEc1I1ScdelJqn7sQz4SR/OpTKPr90w0fZg+EeaeVcOqw5+7X0XBTT5kVufL6kCqu+rIbnCIY5H7YtjQ/KV1at151ymr65baey+bwCXq+yhYKKg0GNJZPHAFySLMvSm1as0IKqKn3mkUc0u7xcVcaF7rEsjUxPz4D4/9GYAfG/l9G9nxKdmjZishPDuBPbd2LlrLyIzzXNd8ucjh/jg1JiAiIYrx8hmZnGJXrt+xBCHg9WpEO5GowQ3/3Nf7gZ2Q53945HEaz+IL8LRKi59vkByy++HvdkOAaYFVdh5Y/2kcVd08bfloUF45C4HD8695H5O9yNNdK2FEVi8/10QhvqROBXNqFMSGQAWx4syoBJDnOG5ZGGe2G0Kyon4e14EBvpIymo1CRwxcq4X2kN946PuHz1ZbUA2ZXvAhju+DbPaXmwWHc/gSU4PUmpkMMp/pv/ZL0azqHkLJ8j2aptqXT1e1GefvqvbkOQpoXSFe8knu20kU1Oosz4Q1x756OQqPhNffTStZR9OSGX8SEy7Ie7TWctMe/j2cyeb4z2n6jIhCJuw5szriZM0bEbitjla/H87N3IGZocA5Tad6CgOZ3tbJv51LTwfJNjgGM4Kr3ywySdDXThPRjo4LMV9dKCVWS83/4N8i4kfr7CJAvufIzP1s3mfD52CwpQKIqrfvYpKC0lldKN/0Sc2OPFOncIXy56A8qmQzyUSpr4chGWbipBKOgjP+IsREtOTLiT3JyIe3/AfGpbWevjx6FtJFBm0oSakpNuB7yRPjwJEmtyfEMfZ9g2iZiWh3NWXCmdewPn9Pav46YvFPDiWMJar2mRrn6vHuzoUDqfV1k4rKDPp0w+rz2Dg7p09uzn3MZjWSoPhTSSTOrwoUPK27bCfr+CXq8KM+Qu/2djBsT/HkahQJZqfzvgnRhH605O4g594g9Y5Zbl9sDeuxFLxB/EcioulwIBstvzOZP17kUgfvsDgEWsTNp+m47xsl/zAdx/13+EpCen61kuC5jHh5lDbQvlWY4F0ncUt/uCMyAq2f+0dMpFXHfuSmnHY3y2phXQOv8maTh34jP3tePKTU0Rqy/kiB8OdaJMTAwAavFhQLCkEvfjxBCu01gpnoiHf4V1Oh3n+wc2sXYVjZBsnHUd9xvskn7971jHMnH92SuIvy47l3X/9X/wu+pmytiSk2Q/r7zIxJPjCPqvvRMhH4wYt2oEC7ZhHklQNS0AfHyEvVh8Folm1S2AVNd+wLm8HpDc9Rif8wXcdpcej6mDL3A+ek3W/+wV3LO6mUQxjwe37hs/h/CfGkcBqaijzviJWwHd2lY8JsfnDDQvxMKOlvLd5KSrIAbDeFucbPeicnID9m4EvANhN4HL4fQ/uguQ8/iYb+tS9ur4cdV74Dgo5HEJLz+ffTrtUp7zxo9xLa8XL4gTxuhvZ88HjnKf6Tj3b5wnZVqo2HBG62L+nDx6D3IuCjZhjfQ070Rdm2E4zPPzcOxE5ebkMe9U9iGbfn52uY13YuX7k1JxGdf0B9zkvw1/5LlPDvsMdVPxMNTNu3jFO6VVl7m/TyfZjwVnsK7jgygg7/oK85CUOtylsM+nVD6vTD6vQqGgTKGgC2c9N8dmNJnUV556SosqK3X/oUNK5/NK5XI6tb5eX3/6aX3ynHNeeA1mxkseMyD+9zDW/9a1Pod7sLI8HkOQ4XOJSVLTuFx3PWFqsuvJcP7NFwCyogpclpYpWwv4AbTUNLHKiSHqjvNZLIP2bQiG2Sso9ek5aFzeFl2zdjxm4pL9CDxHOZgYwGUqkXA2PojlHivhWk3zIAKxLOm0y3FlPvbYic988FnmOD7gxpOzKUC27wig4TQjqWjg/oMdxIaXn4+w8/qxWLr3A+DTcayWyTF+t+F2Mo/LasjAt23XdTzcDaCdeRX/f+x3LhtbfIR4biFH/fEDP8Wqqm5CaVp+AWQe0VLWo2u/9Lv/pmRv4CiAUFRmGsqYTO7icmKjWx4ERAo53NfltS5o57OAv+XBo+IPsne1bWSNb3sIdrru/VLdHDqqSYQ9SipPXN9CAYXBqfEf7MCyfu0n3bDGqRdzJrY9zP9Pv9KNq0umTK/K/f+y8/BIhKKGX9xrGu1ESUBctAaAzWexdJec/dxEw/Ja6Q2flb76NqzxkR7i/ue/hj2eHOU8XPuBE9nbqlvwkIz0uw1reo+QvJfLvjjoOusx1EN4qvcQSuTUOOesugVAHh/AG/BShtcreSPP/7t8zuWBLxi3e3EFim2x2aepiRNBPJ0kS9+h8B3spN3smz7Hfg12QTm76wk8EMUVnOuhLpPsB4if19qqbz3zjPy5nFK5nFKFgq6aN0+r6uufM83ueFw98bjax8eVsW0Vh0IKer3qn5zU/uFhDU1N6Y0lJbJtWy/WO2NmvPiYAfGX+0hNS1seIN4WK4WGNTFKf+LZK7FM11yHINh0LwlkWVNTnowTb+vaB/Cc/UoE/Vg/Vs1lEVAAAPUKSURBVKHHi5DuOww4jA3wO4dfOhBEaESL+e66XwCkK87HWiipApCm48RHh7oQ7P6QmyE/3GOafEiaHMdSe+83uPbkOExuz1s+5ifm6PT/duK5VUaATU/w/1AUgLrqPQDy0d0It1DUuNIL0oIz4Zt3urBFS3nu8lrin2U1COnjOaq9fpQlZzj13hIhAa+X53TCBb/+PN6MQh6A9htSkb0bXa7syVGqDDbfK62db6xrP0rOYKe0bT3lg32HENrZNEmNXQeo/73ne+xFPmeAKoXLdcUFZFWX17tg5cTU565059+5j2vWtrGvz9zD3lmW2zFtbIASR8mlSt31hNukI5dl755vRIulV31cuuVLAFS4iGcOhlByiivg+s8kyU3Y8iBKzdk34O53Rvt2whmVTax5Jkmi3LmvBlAT4+zx27/kAvnZ15O0acl4MeqY85EdKLOXv/2587VtN+HM4+FsHdqKQpPPEW6qWmbmkKL/wOorXLY9y/PCNLAvNk69mLnGylBoR3rZl7JalC+f97keirEBwNjp9V5ex7ufGOcZfvMfrFM6iQJcyONFktzyO0kLKiv1vauu0heffFIThsXtk+ec87wg/NjRo3q8s1MBj0epbFZey9KYoWMdT6d1ZGxMfV6vfr1zp163bNlzvj8zXtqYAfGX+yjkXTrQiSFDaepHYPYflm74R+n0K/jsUDe/9wew8LwBgDSTNN2gggihwU7oP3/0cTT+WJkUSCNMnr0fYTI5AgjsfhKX5K1fMa07RWMLjwX4FfIucNS1Ub5z/uvI6h0fJFlr4RncP51ECeg7TGa8x4MAOv8mSScJwwVnwDTn8K9Hy0hsihRRGrfu5wjX8nosjwUma/nZB7DUnOSnfRsprxrsxAKMj5jWrR5TbmRKjRafRWMSrwkJpKdRCpyx9FwAeWLYbWpSY4Tk0V2moUUzAr7/CGGIP37LpaaNFKF81c3Ce+ALsE9OlnmsBGDz+VxaVVm44u/7gXTGVdI7v4LH4PFbmWNyWmqai1v7ux+C2GWwC+GenAQg565krrd9Havbca8vXOP2CC/k3cTG45MLew6iOJTVcRZ2PIqb/ILXvvB5XbGWZh8b/kgoxS5wxpye6BUNuO+Hu3HXJxN4j177STwGEp93WtDKnP183gVMp0FMfFgKmT2IFGHpJyddBr5DW+klsOa655Li7HpceujXgGDjPOLhV7xT+sSleLzS0+zRvo1Y/cuMByKbId6992nehVMu4jw+Hw3yC43FZ+FB27OBNbj6/dItX8RzMNorXf2+57Q4VTDi1qU7rUwl9uPAJrd/fCbDPh/aynt/5rXPmdua5mb9sbn5hJ/Zti1bOpbc1jUxofsPHVJJMKhMoSBfoaDJdFo+j0f9iYQqIhFVRCLyWJZu3rVLF82apZqZRLe/aMyA+Mt9hGM0StjzFG4+XwAtfOm5uBobZrsvacMctPCGubi4pycQfD6/23Yxl+XvxnkkwnTuMz2PQ65beqTXUIp64AhfdSlCx6mtTSawzjr3MR+vl5/VtJGMNNIrvf5TxCEf/BnWhi/IfKsaAYOaVgAkl5Ue/7208vUIqaO7AO59T3P/inrAJZtCiVl1KUxfZ18PGPgDZOg61qFlucxZEhnS6SReg+k4ADHQzrPPPsUFhjmnUJe9+T6sRl9Q+uE/ITxXXyGd/1oyk599gESukkpcwtOTrNWcs937e7xY5TUtAO1YH4qYxwfI1M8B2H1B/vb6uL/lAZgKecIUHg9KSnqaxK2r3kVtfMtiXPSxEoArGILX+8FfssZO//UnbzfUpV3shRPCmBgmQz6flZJGicimUH6OccnLUK56j7liVVZHlvyLgbhlEb+uqId4pLqF54wWc5/yWkq8lp4rlZh7JSdh9AuEAfdAGLKj+DCVDBPDgLQD6k7C4Pgg++rM75wb6KxnS8qPEPe+5M3PjS13H5Du+SGu7K69gOD2R2Dmi5VzfiPFbv39H7/hgvjm+1AKa1ol2fy/qvG5FQ+2DfnSnf/Le7j8fJStUIQ1WnQGfyQU2qIK6cwlnOd9G+FbP+GaNsxwuzdw9jxeFI9w1KyLOfNN83kXju6S5IHFsXMveQWb7ucdaluK4mHO/q6BAf1w61ZNpNNaUVOjt55yioamp+X3elUaCimTyymfz6vg9arI71cmn1c8ndZkJqNCJKKI36/h6ekZEP8LxwyIv9yHZUmXvR1h1bUPAG9ZYrKMCyd2Dzv1EqywvU8D5BV1xJynxnGdTo0jXM57tSHb8ADAgZDb9KOkEkuyuALwVJ7Y98Lj6tIHO1whl8sSoz7jSlz8MhZQZaM0/1TITn73RcCzrEY663oarjgsck7Gsm0TW972MPfdvwlrsX42Fl0ug5t6yzrW4LRLsch6DhIDrmkFKFZdRuwwnzMxehsgLq0yNbUpPA+nX0lmbzbtxlnPuYFWr9//R+4TjEgyrlOvF+WhbQnznpqgWiCfI++gfYdLOmLb1LC3LpGefZC1HO3DmvR6UaDsgqv8zF7BfvUeIobfZWqVQyV4MooqELgjfaYEK8hzHu/KPe8m6YnbDGd7EZ6AqQnm5fGeSK4SjhGz9oek4mpa1uZCKA5O+EJiTZw1tCzAtqqZZzr4LL9bvhZKUwdInTExLMlyz2dxFX3Ib/pnFL/eQ+5nczm8Ak/fyf8LBSzIXU8Qh25bwto/cxfA3rkX9/+d32FtXvVP7O+iM7HC27fzLMvXcsa7zJpVN3Pu+o6gBOzbyP1CMRS3x3/vWrxeH88XjKKYFgp8t2s/59A5v6EYys7JIL73aenHn2D/fEG6uo0P0lr3ZKv96E48R45HK1IMK55zzb52OuJl0ryrHh8Jfq2L+P2s5Sil/UdRAkZ6UcZaFnG+nr6Ld6u0Gq/YzsfY/+s+qP5EQl/buFGloZCai4u1rb9fP9m2TQsrK7VneFjjqZQmUimFfD4VBQKqCofVPjEhTz4vj1kDW1JF5C8IK8wMSTMg/vcxAkEsMH+Q0pnJEcCobhYgNNCBgPL5qZc+31hKx7OEzTsNwVpaxff2Ps3nl56LYMplEdqpKYR2LivJlNcUCpTbjPbjQpwYNjXoFbjsnM5O2QzW7kgvQj4cxbpvmEfiVjqJMhGKEXuPlhGzr5/D9279IuCWnmYeWx5gvpMmA/roTshD9m4kDnzb1/mZ5eVeN/0LVsar/xkA6D1MQt7+TVIhy/yCYa5ZVIZb//HfQyAyMYSgPONq3JqhGEpCOgnH+53f5T5rrkXYOs1fJNyj9/0Q5cXnh8K0cR4x2/xH8aJESxHAsXLi8+e8n2vtfJx5hGNkrm9Zx56lk27jjdpZ0N3++BP8TAJMb/oXnltCeM9ajuXrlD0lxlBQympNrfU0wD3aRy389CRZ3Y4bPWcS5xzlYO6pKCIde4wbPsK63fdjFKL4MO0/T70Ez8vxRDFlNZJst5HIxCDXkogt3/wF3P12AQA6st0kwYU5b4Od0kd+iIvYOcNLzsYTMj2JN8KyeJb1v4F1TgLwmxfyXiTG8QZMT3DNRWtgYJMF0OcyPNPkCM9veahEaN9+nOLjIdnMmUNFPUpErMztXHd8Exdn7FiP0lNWw/28XsoXxwdcr5gzwsbbEC1x6/idBDeJd/54b1p/O1UL6Snez6b5hCN2Pg5oD/fg7bBtFJVs2siRMCGbFReZBjsZdU1MyJaOdSFrKinRxu5u7RwY0JKqKm0bGFAik5Hf69V18+drU2+v2kpLFfD5lDfscec0N8/UjP8VYwbEX+7DsQAkSCUq6rE+CwXi1bf9D/9evhZrxeN5LjuYhEXrlIgdPyLFgKjHxGVnrZB++RkTG/UQZy8qN41K5nDtYNTEDP0IukgJwF1eZ4DeAgyCYUhi6ucAYtFSXLtXvNM0dOg2jSlOlzZvY+7xcUk21lomSc2wz4ewKqrAEp17GuC78zGINAY6EFq/+Jz0gW8jxEf7+X39PCzgA5tdas6GuVx/qIvkwEgRf/rb+eOUyhVMpv3UBErI1nX8/qZ/PjF2HIoAIlkDhs5+RYulj/yAe9/yFamuFauza4/btGXlxXhYispMTDxArXRlIxnq6RTu3i+/yd3b2acAcvufcRUJyWXsmxgyMeMRFIOyatZgfIhrLDmLDPrHfo+yFIqwtsUVgKRTducP4ALu2g/g1bRKP/5nU989imWYHiM88tgt0pXvdOfSvBCwfuBn0pxG3OROvXQowplq30ES3SVvxnviMJw5XdNS0ycmPZZWsWbREvfnkWI8FM448Cwx60wKToCqRjdXYdfjKLPRYs7ilAmF+IOm41+ABMLD2wwvfN50dCuS9j5DGOXMa1BYBzswQVsWo1CePHx+0yAlzvtSMF6Yk7lU23dKux6VOndDQlM7i/d0+XH7Oh0HgJ2RGKf6oqqJ6y5fyxqeeTW/3/s01zr4rOF9MPMJGE6HxLjk9alvOqnf7d6tp7u7NTo9rcXV1UrmcvJ5PCrYtpbU1CgWDOrpnh75PR5VRqOyLEuxQEAXtLVpOptVJJnUipPi6zPjzxszIP5yHU4y1lffjpvwojcgUOav4s/PPoWgq2pGmN73Y9y7C04nkcex0F5oNC/AZbv7SV7wqQniuKdfSfOLdT8HCMrrSZxLJwGpK94BYP/2S/y+kKc71+FtLgWp5QGAkz7m5mQ8Fwoma7ZRuvEfAZX7fyz97F+l+dcwr0IeYZPNYEFODGP1eL2AUi4LIOx4lF7Nh7e7FsyuxykFO/81/Lu4inUIRd02kMkEwi2TItxQVn3iutTPZq6TI3gLJkawEBeczjz6jgAa1U0A5Pb1uCbnnvr8tccS8w6EcKt6/VjjuTTA0rWX+OXEMM9QVitZPpL5UtOmtCznMoYVlaEYNc5jjY8fc06RLnkrSlg2zZ4NdQG+viBzfvU/c72f/htKVnm9ZOeYX20bMfXjh8/vhhAcXvz4CPP1BwHTxJj09N0mTGDjDSmpBJBCEQCoppW+3pFimNqSk/B8x4fIm6ifA+BUNpBr4AtwTk4eNS2cgVyW9RofgrFNkgY6pdu+4dL69h4g1l/d7OYqTI5iHTcvAoCP7sSytyWdc6NUVoUylJoC6As53pHdG3iOM66S3vhZXOOWxbUzaUP+Uso8pidRLLNpQkFeL+Gws653GRGdz/3xWyhY5fWEGI7uQpm67WswthWXo7Q++DMsfl8ARXbJOe47tX09/3d6DMw5BY9L10a3Vt3rk8aHOXeJEU1e/i7914YNSufzaigu1s7BQfUnElpSU6M3LFumX+3cqXyhoOaSEnVPTKhrclK98bgWVFaqYNvqSySULxQUCwS0rOa4Z5oZf/aYAfGX4+g5RAnKrEuwyHY9jpC96A38PjWNtu2xcBWO9LmW8NZ1WAmv+rgbe8vniTUf3QUgnX4lsb9QFItpuNuwR3UiYBecTv/mR3+L+9qyEAojvVyvop7e5MM9bhbtt97P753+2MGI20d68CjJZLksNJXldfz71q8iVIurjKViSrym45RazT+dORdyCNXUFMIwPYULsf8QwlPCi1DbKt3xHTwVXft5vvYdAGXSuI5rW0noKqmAbvPpO3HnhiIIxaXnkXPw+K3c++hOadFZWG8OVWd/O5SuWx4ElOpmse7XvJ8s+ePHSB+c4ANHEcjhItYvn5ce+hnWmtNXfDqOxesLMF9bGG5O3oBDCWp5+F7TQvc+uSwJUo/dwvcbm9hTvx9wmLMSy9TjkUaHXA7+9E4pWosS54Q2XmhYFkD0s08xT4+Xc+EPoMTd9yOUr0gx9cvbHkZh8QVIYtv9pPSVt5GlP/90zmdZLYrGZW8j1NKxmzN6+T88lw1NQkE471V0/LJtStPOvJaY8xN/IHQSCLHW2Syu76XnmXLFAu9T/WwUk6O7OE9TE3h0Hvw5oBcfNd6jErgEUlM8R2mV9NQfAeI113GOt6xDcbSFZdx0LgrmdJx8kMPbSWxccDqxe8dLM9JLmKL7gNvGdHKUvQ0XoSQ89Eu8Ins3oCj17MeDUT/bda0f81pMsfYP/ZIy1APPGJ75IO9AapKudadcJJ13ozr9JZrsfkrNJSWqiUY1p6xMXfG4Pn3eeWosLtZEKqW7Dh6Ux7LUWlamD59xhlrKytRcUqJ0Lqej4+MK+Xwa2btXvufrkjgzXvKYAfGX43CYthySj/J6hORFb3DBLzFmyog60OiLKxEq0RJA7PjY22O/Q0DGyhBc7TtJjPEFAKDD2wCKQkEqraVeeefjuHmnJnGxH9wEKN7/E4RmcTlAmknD6jUVNxSVxcwrn8Xia15AhnZ6mns89Ue+d+a1WOjVzab7VcA00bAk2wL8j+7EVbnvaYRXcYWpEZ80MdwcYDIxhLWRGKc8yCkDO7zVJUfxGm/Dgc38v/sAgFDdzOeX3yituRqGt6FurMr3fUNafzOZy+lplIeGeSQJTY2jTGXTAFRFHQL/eBB3WODSKSzDp+/CAuw9LC16BZ6BA5u4hpOlnklLeVMZcAzF5SpShbzk90mXv5OSPgkAuO+HWIuj/SgMqWkdCwkUCpyH2Sv4fCBMZnZ1M2Az0IHVvuQ8mP9OHtkM5y1cRI3z+BB18dk0sXzLYp6DnYa1blr61b+Tj2AXzJk+jHLZOM8kBW4GbAMhQPzQNjKmy2tfnM/dsrCGV17M+QpFYEDb9jDfzaZ53qJy3ofhLkIt4Zh0wes5jxIJjDsfJ2Z+6qUAcy5L0uXqKzkn/gDPYsskOYozd++PsIYzKfa2eSHndaRHKh6WlAM8wzFCF1MTKABOBcUz90iP/o692rPBJJZ6UFZ9ARTT2lZyQjbczjkqq5ZWXeFWL/S385yJMa5b2cD52r4eZaJ9B+/6ojUksw0cJW6+hCqKwMiIktmsjo6NyevxqCIcVk0spvqiIlmWpRsWLdLqxkbF02nVxWInJq4Fg6qK4ulbv3fvC+/VzHhJYwbEX44jWmKISkzZSHLSJeDob0eALFsrHXpWGjUx29alfM4hLHGygvM5somrW7F8isrdMrCmBdIDPzE9x30A4pYHaV9aZyyyPU9iHRUbC2DXk1g3b/gM97jly/x+rA+htfQclIhsGjaz8UEpPoYr17EY7vsxgtJJfPL6iBtm04CYxwPIlNfz/VnLEVw+v7GUhgGEygY+H44BNIOdWB9F5Sgs8RFJFq7dA5u5ltPAxDLx/nmrsM6GuygHat+BkvDsA6zzKz4MFed4P5/Lpk0iWpEhm4nBLFbVeCJPu2RY4ATY1rayTv4A4On1uY1g0kmUqf52k+VtY4WODRg2PstQm5YSD19zrRv/lLDg9j6N+7qogvUZH+Q+/e3MrbYNjn2JvVxzDSVoTlb0mdfC030ygPa1E2dPJjg/l79DWvsqaaQbZdDymLhrgnWLlLDPB57B43NkB3XjXftQHpoWcL4PbCaZbXKMfdx8n7T1QRILY2Wsx/O5052RTbE/wQhJWsWVbiew5CThkJIqkg7f8Gks6+O54p1+8w6JjUO8I4u4eTrJeyMZJWiQZ06nCJ1UNQOSPfvdzmQl1ZyPluXSpvu4hsfLu1ZUIT3+B+Lqj92CB8Jhy0smUEbSGZ7D6+N3PQf5eSiCwnBkBwpweS3eue6Dbtne1odYY4cPomk+4bVtD5vzVI53auGZUv8RlWy4S6md7XrEV6Ypf0glwaC+fcUV8hqr2rIsNZecmFsznkqpfWxMAa9X8ysrZyzw/6MxA+IvxzF3JQCYywBWgTDtFvc9A1PV/k3EBueehtB4/Bapex+lYZJ0yRuPq/d1hLJ93A1sBNiC1VgFhQKC32NhsdkFWMMa5wMmfYcpIXPqegc7+FkygUXbMA/X+uQof1oWoyjMPw2Qvfu7CHqnz3esFOFz1itwW3s8Um09wlSSPJKSE1LHTpp5bH3IlP7kSbBbfZX08C8B+kVnAoR9h/ldiym7sW2EuD+AZZKexmIvqmAO44MsTXpKClZi0fS34/72+Xm2O76NoI6UYKEuX4tL2Mmo9vlNLX6ULOlL33LiPmbTJOVJrPFwj8kVSEgLJvEsFJWzno6iVlyJsK1qQFEY7sGrcdnbpHNvNODWdCLYDvcCWuEirrf4HCz8ZedKb/1PEvkixa4rV8Id3LyIfS+p4jOWhSdj52PETueeRhzbcRWnpmidecmbKfFbtpbnyaSk//0Q98hmOLeVDSgk139IemYLz+wPsIeN8wDhUBFA17qI9dl8P/XizQuZ6w0fcePxx4+n7pR+9Xn2LBQlT6CigT2prEeZq58LuNXNdgF8Ko4naKSXOXfu40wMd+MNaJyPglFWI130etz29/9E+vG/wH7oOEYcCtuSKhSIXNbUlI9KpQFA/bK34d6fHCWcMdhBDwGPj2uU1bJOJVVu/od3mOsmE3jj7AKegMlRlDCnK17zQuYYCPO5yTEat6x5BecoUkyopXs/c569Ava77etZr2cf0P6+fl0fn9Q5wWLd0bpGhyTtGBjQtQsWPGe5e+JxfX/LFt194IBKgkHVFxVpaU2NPnTGGc/dm5nxZ48ZEH85Dp9fuuFD0kPrpJUf4AVOTxOHrWiQKvsAyaFurJ9Cjhc7XGQs1uBxPaK90ulXQe4RKULoVjcj2JKTXHvZebQ1zKZN44mMSU5LuW0R42MuiNvi96kp4/a3iPnt2YD1O+80Ax5ziFE717M8uBBbFwM2Z1yNK/GxW3iGfEaSx20/KYs5VTUiyLxeLPazX4F7cs8G1iNp4n3VxjoKRhB+a67lOR/5tSuc/UFD6VqgZGy0Tzq4Fcul11jYo30mBDBF7e3qywGY6massMpG1r52Fhb8ojXELhefDeje9yNAIRg1CWt+fj4+gBu4/yjPt/cpvAznv5Z8hFgZCtytX+WZnNrmshpizCdTcUpY4Hd9F/A9ugcXdkk1a3TDR1mzfA5K3kNbUGLOvh6Aa5ovab57rbFB6Vef46x5fNLT97DHs1egFA0cxXp+4Mes05rruJZt81y7HpdCAcIvsgG7LeskqwzQ3/oQexEuxtV9+irOsSxDKxrneWtbAauHfym97b9OfN7uA9Ifvwn4V9Rz/qcnpel9hF3sgpsUt+w85ufzS9MJmtUMdTH3TfdSLbDyEhSeoS5IiV75UTdL3h8gOa64AvbDXIY9nBgCaLv2kczmlMcVlZFrYVkofPNOo2Www4o4YDw244Moa/FR9x0q5FGq3v5FzoU/gCUeKUaJG+qmfHDJ2eQBbHsEpTNaylonxlBAi8vd/uWl1VzTYS8MhtkPf0Dd3rASYUuzs9O6cvygflq3SodGRyVJ9x48qG8984ymczmd39Ki3kRCW/v7lcxmlc7lVBIMaufAgDb39v5l8m1mnDBmQPzlOrw+hInDfd1zkL/DMdi5dj5OwlZlC0ByaCsv7JxTEGrHj7Ouk0orsTxKKgGio7sA40ySRJh8FpCftwprMz5E1nW0FKsmMUa2djoF8DfMdeOh03HitXWzICu54LWuEjHUCVjv38S9/GGadQSCWESP/g6LwvJI+YIUDLqhgGAYYbboLDfrfaQbkLnsrQDzoa0809rXoDTsfJzr1rYCrh6PS596cAttPqfiZPh7A1hhDXMMLew0gtXrdTO2pyZMN6gY1v6yc6XXfJKYbsbEQ502qOmkdMt/o3iU1iLwwzGE6OSI1LoM8CqrYb2c3IHiMun6fwC0u/bx+5C5n22jVBzZ/txSplyW7P5oCWGE4W6E/VnXkz/hJDY+/nuyx4ur+H33fpQCpxSx97D0y8+TQ5DLovSFIoDVQLvJFvcxt1CYPcyk4dJfcQGelTd8mmcfHzStMi/Bsv39V0jQjJXxZ3oSS7W0BqVDBWnMQ8XAaJ/hKkiw91MTfH77IyhxrUsBvfQ0Z2limHOUTvK+LDuPdQ2GOa/n3ghw3v1dlKj+o3ScC4SN92QAb8OKC1BQrny3G7ZyxviwaeRirO9sirk8cw/7NXsF8119Oev21NPudzv2YJ2HY9zPHwRoF6zi3Dpsig6L26s/jnfsyA5A3uNjrwJh3rfXfcqEikrxOqVT/C41jcfB65Fe8wm3/8HOx2mq49S0Z1Kse3JSNdGYBqemZNu2cratVD6vRVVVevToUX34/vvl93jk83j0vS1bVBEOayyZVDqflyVpOpvV2U1NGk8mTyZLnhl/wZgB8b+XESl2k5R8AV7K8nopl5JUQND0H8FaeP2nTvyuxwOpy9Jzcb/d/AWApvsgAqi4wmXn8vmxDrv3YWlGigD9eaukJ35P8pg/CCjseJR2lvFRLOJVV0DvaFlYKmMDAGUoRvenTIaysJpW5tW1n3sWV3DNcMzUl/uZh9PPu2svCkp6WpIp6wmEUA4GjgJCt3yJOPs5N7gKhG0jLHsPY7kvPFP67B8Bp0AYABzsdC2Vuadi3YeixoLNI2CTU4CGY6GFo89l6Oo9jPKzfT2AEo4h4Kcm6Nc+PuiueyYphZKGWtXLd2SxFrufRIgPd/OzQECac5p0/08BxeNBJpPCghztFyESH2u79FyXQc22sYCrW5hXtBhLreeg6Q0fl77yVgR/Ju0C1NnX40GYvxrgGhvjftESYvuWByVk2yNY/SWVKAZjA6xTSSX3DoQMeVCGs1ZUhjVaVMHcT78K5rVs2rC6TcEQ2DCHXuE3fwGlLBCStjyE98BhtHMSP6MlrI3jzvd4uedgB4RA4SK8J0d3EZJavpYcjY7d7G12hGvUzX7ue9e2lHM6PuQ2tzntCpRTJwQxPck5O/fG534/Vo4XKz1FUtzEEHOZMl6HYBhlur8dL9bR3SiYu5/Eqo+cxrM2LcDD4/FyPi97G+9yIU+yXiiKEu3kfzx6M0pK7yHWr6ZVWnwm/AC/+5LOiQVUGMlpLJXWI8WtOru5We9ZtUqfe/RRvP3hsHKFgmJ+v46MjakyEpGVz8vn8Wg8ldJ4Oq3Z5eXqm7HG/+oxA+J/L6NpPnHZbQ/zInt9uMviw8S7hrsRdKEo2bYvNNb9HOFcVI6mPjmKJVNWK4UjLgVo8yKaMTiMUI/eAoBXNtJm84GfwNTVMIfs2dWXu8lWfe00TEknEfTTCRc4wkW4plsWGZINk73sC0hVLVJmSopVcO+WRcSjO/e4z/uKf3Cz7tffDHg6pBdP3cHcZy/n90/fTZmcPwQQ7d9EVrIDhP6AyygmEZ885SLyASKlCM/4MLHMogrpmXsB/zXXnhiT3voQ5UmHt2M9l9fx8x3rmWvHHjLRL3kL7uTuA9LiNqzwoztZg752PlvIm8Q7yzCGeRHwqQRW3PEgnk6asj4BQtNxlK/j24NK7LeTQCiRS9C5Hy/I1oew9kprAIDUFIL/kd9g7b3531mT0V6s9X0bcddnktxn0z14eizLJO01ufe1LOniN0s793E+U9O4sP0hFL9sGhd2VSNek/gIiYUTwy5b3M7H8PxIUiQJkUt6ynQgy0g5m+ebGMJFHggBlnNXYqnmcyhUhQLna6Adq9y2AbaBdsrvrnr3c9uiSuz15vtQTiyTVxIKiaTMPJ6hoW6+m0yc+N2mBW7XsYEO4/4u5r1LjOH1aF2CEnDwWbw1zz5IaOiqd5nwgI2CvPFOl71ufAhGwo/9lFLU+Aj3uuIdzHP9b/l7tJe1HuyULngdndwsS3rNJ+TfsV7nLzxd3W0rdUpNq5qKixX0+RTy+ZTIZtU3MKB8oSBbNEeJ+v0q2LYSmYyifr8umjVL8ysr1ffcFZsZf+aYAfG/l2FZuEiXnougDYalX3wGweAPutb5+BCA+XzsbBIvfDiGoBwfNAqBH5BIJbCMRvulb76Hl7+kSnr9pwGkqmYTT7Zd91xxBeB6YDMgns+TCDQ2iJCvaQW0kglixpUNuJnv+l8ailQ3Y1G0tkqtCxHe29cT23WeoZCD733VZSeCZ89B5mdZAJTXR5nP7OUIyCdvO3HOR3exXg4pxmqTPe2Q1gSjKCyDHYQofD4svIp6rmMXKPmZtdwt78qkyCcorZFko+SMD2DJjw2Sn3D397ASX/tJ6U3/Ln3x9e6eJqcAIG8A12u0FIvaSUj0h3iu+IhOTE4UQNCymLmO9nMmGuadyCZnWViI9/8EgHPIP56+C4UjMeaWkOWzJsdBPHNpNUrjqZegHK25lprlsT6AZf5qlECnnefzjUVnSL1xafG7sAIf/qW04TYUiVBUuut7htbVyxouW4uVe+6rWMfj93tskHXwh9nPvMh/KCpHwSyp4Of+gOvJGewkFGFZeK6aFmCxjvSQL2ELBWOwk2cprT6x93oohkI35xSuGS6WHruVtdrxmNsNzz9b+u0XpZYL2Iu9T/GMl7yZEs6HfolXp6Sa984XQEnsO8JnM0mjXJg969qHwirh8XJyTyTO0lAX3pV3/veJrI5d+7mWQ2tsWSS+7XiUMJad5x287G3ydu1Xy76npYGDeCfKanTV3Ln66lNPKVcoyDInriwUUktJiYqCQZWGQkrmcrqgre3593tm/NljBsT/noZlEet1xnu/Kf3ys2jeyQSWmST991txcUaKEcDHl+rMPsVkAW8H6AopQMvnA4B/8kks31wG625sQPrBxwCHSAmCzB8E9CwjONLTrgX22O+gAy0qB5R6DvJ3wUZ5qGygG1bfEYTtaz5BYlH3hPTWL/B8yQRC2RmOYD5eoKdTrtXYvBi3fz7rZuUXDLmHA2iWZeLux1ne9bNRUA5uBjijxdQAn3IxVm18CKKWhWeae5vkvMSYpONA3C5gtTolZ5ZQLiZHUYyO7mLN7vgOlvOBzdKcyykj8gWIM9c2S4PdrjvaZ4A8m0L417Si8DhMZZYF2BTyeDoCYeYybhSH48fytexH1z72dOAo7tpcVipvwCrOJLlXPs+9lp0LsA51uXN65h6UDdtmf/oOowj9qTacvgAJWZWNeEdai/GKTI5i8Xt9KHpF5VibZ1zJmY2WmDyB/SRsde9DaRwbJAnStrDuy2sBsXmrqaf2+gDloS6UllyGtezcI732X815bUZpsCws3u99lKx5y5KueR8W8sO/xgI+upPQQ/0ckvdyGeLoG+9i753fDXZINQnpF591+cq9PpLl1v2cMxGOSbJRohesxvPVf8Rw1seYcyYF6LYuRXmobDRKc5ozvuVBFKBvvV+69K1uN7SMiddPTxrGvmnepWBEGhuSvvMBFNVIjJDAY79lffM5adfjyr/239SbSKgyEpFHUkFSaSikqUxG1dHosYYoq+vrVWPqxGfGXz9mQPzvcTiWcHISQXDvD41FEMJyO7wVgVFcjoB6zScQBF4vLvk//I9hiSog/PMZKZVFMBzYhIAJxxCQ+SyCYeXFWHxeP5ZxVSMgOnAUwbBsLWU/636BZZDLIvi792NdBiMIfa+PuRRXmvhehPjy6HpXQTnzWumnnwBcJFz7c091nz8+Kv3X6wClxDiWzvzVxHHnmETAQIg4/r6NxFqTpqTLSUJzRnWTq4DseoK/Dz1L2ZZMUtnTdxqQL0FJ8AWke36AtdO0kOcZMe7//c/gAs+k2KNIMWs2OYLreWrSZOsLwMimTbvVPBZyLmNCDBagVtUESM0+hRh+1wHW7Ip34nEoqUYhC4SYX0klll3LYhKgHOVn9nI3zLD+t6b+3KassKoJKzCXkSJRzlL7ToCsUOBcbHuY7666DMUmPsT9lp7D+jsJey82Dj4r9R5EKXByDBJjtLCVOE8jvSS8de1H+Zma4KyO9OJy37YOz0F8hORDXxAOhP4jKJi+AHtW2wZoty11+QVyWaz7PRtMK9cy9qzvCEpqVRNn/u7vEY/fug5wHmhH8cqkCN+UVPJehKNuX/ipCUA2NcXvnHM22g/oxsqg8E1Pc+4zKcB/pJf7du4xrH2TfMfj4T099WJIcJacRWldX7vbO733sPS9j6AknHIR/PPD3bznI73snT/EHvceoiw1HCMZ89f/Ls095VijldH+Tn397j9qi69IE6mUGoqLVR2NKpXNKpnLaWhqSn2JhIJerx49elQ33nKLPnXeeSczwc+Mv2DMgPjf07Bt4r4b7wQQC3le+EzalB9ZvMT5PMIyXopF+eW3QEtaP4eXOxjBrZiIQ1TiD0pWATezkzA0Psg1C3mu8cw9NH+YjiMMT7uU5iFFpcS5v/V+BGTSZLTHh7muXeBzfp+hmdyPgnHODWTFF1cgVI4fmSQWX7QUAVTIIdwcGs4/fgtq2upmAHSsH4F1yZtPrIW+7G1cv2MPVvd5rzqxfefJo7IRBWawg+8lJty1iJUjqKua4LFOjOFa3XgHHOBF5TzbqiuwOnsOAvSWcUpaFvsy2qsT+p1bwgKTDSg2zDXWWTuCf6QH1/VgB0DbMBcQ+OM3pLf8J8B/2mX8LBCm8cXvvoRiEC0hB+D4OLWEFbnrCRQMh/IzWkxCVSBCzkPHbgT+ea8iLJLLmmY3xVRH9LdLHXulL7wWJaO0RrrqPSiO8VGA1LJcPvmBDkoJE+OmP3wa74wsPmvbhC68Hu772y/i+q2fy1kdHzA87BGeK5dxyVT6j+B6bt+JBV7ZIF39XhSPTMr1zgx2Svs3u96k1BRhIole3RL3iA+jCBdXoWgsPhs+g11PMKf+uOv5murlmZIJzl7rBTrW1jeb5t92gfcllyV0kk7Corb2JrcDYNNC5j8xiNK68AzWxslZGOjAE5aZ5ncHNrmKwx3fhrgnk2S9HWbGUJTzMdjJukZL+UznPuaQz7P2o/36cbZIvcVTWj5vjjrHx9U+Pq5ULievZenitjY9dPSoWkpKNJZMajyV0vaBAX1pwwa9raxMtm3LejGWvZnxomMGxP+exvZHpN9/lRdxpMftdx2JASrREoSW1+uWs4z1IRQmBhESTptDO49wjg/y2aApgfEFcUn2TvLZVMKwm3WiQNh5YsJbHsLie883SGIb6cUqTE1jJRWVITwDYallIRa4P0zcsmkB5CDTcX5+yoXQkDpj20NYUg5oD3bi8naajnTuhRPc6VcdjrEmx4OjRPnR2le/9PWtbQWA1x1hbpGoVKgAoBedxVw792BN2cJaj5ZgYX74By6tpoTisP0R5mvniceWVEIBihnu5jFUNUg9h3m++jm4VLev5/nL63CtDnYYZrlu3PsFm4SqWcsIj9S0AiZd+3GfVzayD7d/Q3rHl57bDeyNn6HjV99hhPmWdZwTy0Lh6zsi3fhP0qylfGfhGeyLQ2m78zEUp7JqU3tdLH3/I3hoju7BNT9rBSCy7NXUqIeiWMZ7NuCdyCZNmWOKtR3rx/oPF7FOJVWuq76oAmXq2vdDOBMtpXoik+TvutmUEk7FAcTSKoDz4LN4iySeK5PE6i6rpeRsYhjFwylrnBhCgatsJOM8WkyinD+Ax2hiCKt8chRFKZVA8XXqxDMpWA0nRyHM8QWkZd+Qzrmez3TuZU/XXMvanHkN63dgk6GRjaKgHN2FcnvwWfa/qBwCqFg5LIr+oKE47uXda9+Jt6h9B2tjeVA4a1qZ00gvxESOu726ifDESJ/k8ehg6UrVjHbLl1uoK+bO1ZNdXVpYWakbFi5Uwbb1cEeH8oWCRpJJhbxeZQoF1cdiSmQy6kskVF9U9NLfs5lxwpgB8ZfzKOTJ/C6p5IW/90fQf3r9JvM2j/CpnYXLL1IMiDoJPqmE6V40iMDJpvlZMoFrLZtCu69sMOVKnbiCfQFA1B/EygkXSTIlO6EYgiUQ5v8/+jgCIxQBm6pbcLsHwlgaY/0Iy+Qkv191GaUy+SyCNDFGRm7TeeaZTaZ2x24AsnmRjpVPPXUHFscxZrUgQm8qTuvGPxWbfSlj9eXcu7IRIbzxLpSl+LBLWNOxl3k7hDEVdVhhtk0J0+Gt7MXpV7FWloe1XHMNINu9j3t5/Vh6qy6XrPsR8L2H3I5YlQ14WpKTbjMZjw/3df0c9m/h6Qjn/ZvZ16b5zF0yXPMdnImTu9oVV1DLLWEhJkYN7WvU5aL/w9c4e1e+Cy/Nqz5OaGHv0wBsJsXnPT5IURIT7L/EuRofIAyQGJNKSzjPs09hnoMdprtb0PTQTgFedbNQVNqWATwOG9r4IN6UhWeYXuGjXGfJ2YDwQ79028B6/dKrPobX4vWfJuwiG/D+4cddRTZWzpm/8A0k2w128FxXvRvg7j3IzyaGjdLQxjkoq8UKrm7hdx6Pu+Yeo/CGi1gDy2Id11wLYJ95zYn7EIrgDv/xJzjLfUc4z90HTCe0FGcpGOFctS5Fec7nTYZ+3uRfjKGgFHKcqfiIlLdZu0yaOTteF6ehTvsurPaaFjWWN6ovnVH1+KB8lY1qLS3VB04/XUuqq9UTj6u1tFQHR0aUyeeVsm3Vx2KqicVkJRLKnEw3PDP+rDED4i/Xsfl+aahf+sWvsTSveZ/pGhZGwPqGEWZ1sxGW/iB9j+eulGQB1vkMAsHrM7Sjw1jL8SH+NC2QXvevdO06uke6/4cIxvI6XHgjvQhou2Bcup0I5PJahEo+h+D2+RGQjrC0PAjRC16LAPn9V2jmEAgB4OMDhsWs2xB3pBA6I32AnsOINR1HiC4+m3jrHd92Y8SZlEsOsvQcuNydUShgRQ118izzViF0tzzIusxZicv6eOs0MU4Gd8duwKT/CApLXRuu+7521mHJOcwvM42yk80ARMkE1uYDP8VCchSkGz4M0Fc1cr/5p+F6DoYBn2CUZKnOPQhjGeUrY6z9QMi1DkcHmIPHA0Dd/X2UuMoG6S3/wXP85BOmb7qfvYmWuDXjLzR8ftjdNt3Lnifj7E9lI+v2+/+GOc3rYy16DwOi6RQJeF6fm0DlJDv6g2Te+wLMeeGZKGvDXXg8/AH2tKLB/cyR7Tzr/FUoDrs3QCkssY8Xv0n63ZdRYIJhk2dxBCXH4+N7TmvUu78PbWtxhTTvuHyKK97BOXIaiZx2Ka1Ml681rua9uPJzWWLPF7yOZ3ngJ6apjLCcI8WckfSUSVYT70OhwNo1zjc3tFnToS4qLo4f+Zzp5x7Dmi+vNyQ4u/Ae2AVi8wc2ofTaBdcbcXQXCl7vYZ5FYh5TE+x7wxypqhYZsfx81j1rlC5LhKsk9s8u6G3F0pc7J9XReVjto5MaykuvuuUWLaio0KfXrtU3L79cX3vqKT3c3q6gz6dzWlo0NDWlxR6P6mKxFz9fM+NFxwyIvxzHYCdZu7MuAbTiI9LdPwAIshkEfCgG2ITCUtokq0Ribvcqy5IiZfw/EMb16vUZged1WdLOuNqUZ3ldNjcJq+OJW/mZQ3bi8yGksmn+FJXhtmxagOVQPxsr5/Sr6OktIZS3PICl4PG4gB0M81nLlOh4vNR0D3Vhfde2obTER5mjA15OtvkZV2PRNs7H3fjRc1Fgrnk/YLBlHc+YTcOQ1deOxeoL4qq+4h2U60lYJXd+B4FYXs/3chmY2X71eerw7QKgdfBZfldWhzB0mNcS4yQelde7oDlw1I1/OuPV/4wiEwjhXl16nmH1KuLZ/UG3O9tQFwBbKKAMRYsBDY8PBWbB6bhRdz2O6/7yd0inXy395j8Q5g543voVSvROTuqT2ItkAgXi3FdyXg5tdeubY6XMY8ejJFB27JZSSRSsQBBPkcMYV8gbjnYvCmNlAwBWvwaF5fWfwpWezbC///sPxN/9QSzLVZdKb/0vN29h9eVY2pkUZ216EoB2zmjnXta+qgnAdZSy8SGs1slRvnfDR/GWSJyRt/wH84oUc2Yti/OfSUFhW1zBmZwYQpk+79Xs067HDf1pM5/3+nDdp6cMOY+MN8imt7nTq97jPbFsTSJn4vZvmhySEuLvo328423LmENxBfu++Cy6vE1NkOA2eznPl4yjEHu8KASTo8bNXsSzXPIWl5TowLMQ5xSVmQ5tQf7t8UoDnarv79B/ZjO6w16jn02MqyxWrkJlo/YOD+vjDz6o7119tb5z1VVKZDL67a5dOjAyogWVlapNJBT0zcDQXzNmVu/lOOIjJkHLCKVYGYBwxjW4/XIZBOGcU/nI5AgxQwkXXHwYITvUiYByhMnEkHG/t3GNqQmsnWXnuveybZdopHE+bvp8RkoksYbOuh6ALDGxYifRrayGGtkFq1EoHIHa3w4YlxmXcyCCUhCIAuzBCHHXQFiKdxjrNs21i8qxdkqNu/Dgs8Sa62Zh3R7eJu3dyJzLaqQ9T0k7n+DZymuxuNPTdE0rqSZmms8xtydvd0E8NY1QrWrmd8UVAFdi1GTiNyNgD23levkcOQZVza47s6hMz6njlv3cOH1tq/Tmz0sPP0RmdDAs5WKmJCiJ9VvIA5SJcbwrzQtdxaduNlbZaC9hiv529t7jJXGs7xD7YYu4ecduFIbv/6N0zitZuzkr2Ysnb8f7ILG3r/kX7h8I8pzBiGEJzFMTbXmN4mUzF4+PiohP/hZrd9fjVCfUtZnGJkukJedKKePKLy6njaiEwlPd4pbiWUIBOjnxMFLEHwl3s23z7I6nKZcF0Dw+1sGyIedpnA+4jw/CSfCmz7nXLK/lz8nDoYx12o4WV9CNbLgb0JPYi4a5nFMJT9GFb2CNDm2V7KDrlZoc4Ro3/qM5H3LP263/43a0mxyTJoyXZedjKOjXfZDQyO++iLVePwvF+PSrpJ9/mnXrO8LzZxPuWbNtY2kbN3omhUIVKyMbfveTpgQtQ6fCQh6vWyqhcGmNRpJTKvF4VaWcOmpaVBQMaiyV0r7hYbWUlioWCOhtK1cee5T169c/dx1nxp81ZkD85ThKqswLWUBQH9hkwLjWJKokEcTnvRrX4MSw+92JQbT7ykZDkWqSpxacTiauL2A4zINk/g52Iqirm1zhE4qh5ZfXIjjzOahPpyYA0svfjoIwPcE9EmNcY8ejWE7Hu6k9PoRW7wGXs7qkgoS4279hqCeNa75tGSD1x28QBshnEezRUumeHxL77ztMTNayEFaFvHHrjzPnQBgBNj4IQPmDpsRrDGE41AG4FVdS6lRWY+KypgwpEHKBK1Liehl6Dpqkr1Ksqr7DCMmKWlyu0RJqptf9nPlmU8Rcna5qJw+Pl+c9vA1BX1KFBZmeNnSilpTNAoJT4zzfyovduumhLvbaF+BeJRXMaXIC4e+At0SYomc/+1BUhnW2aI30s0+ZuXg4B7d8WXrfN6XL3o5nQmZ9T70Ed38oaurWY4asJYKF6yQgLjlHWriGfQuEqD5Y/xup/izavF76FndOTomZQ+iTGNex3uPPN2wbqzgxKh3eQTjI8vA+REtQXjv34FIurSH27rxLgx1Y+n8qZ8LhGHfi8AMdAF79XNYoPkxmd2oKIM9lcE/PWcEebn1IKmvAg9C6hJj62tdK17znxPvEh1lHh1kvVipte5azWNngVjGsvJAKhMFO1qpuFufFsvAIjA+aGnizh/4wa9g4z3TA65J+8E94mHoPumcsnzUx9JQA/4JUUqWdZa36Y7BF+ws+FdlSNJdTNp9XNBBQxO9/8bWbGX/x8Pzpj8yM/+dGVSN0ldm0tPsJXuBwjLjcfT+i3GvD7YD76Vci+J24mwT4OhzShQIvbi5DUkz9bFyfC86QOndDA/rN90EZev2HqNFOT9H4oX0H1x7sAGhj5VjmD/4UwRYrx4IrKgfYfH7cpceP/U+bPs4egHmkB+DZ+xTJPqkEP4vESPAa7MDNHI7x+9d+Emszl8bqlyiXmXLKfFIoClMTptY6giAe6uI7mWmeJ5+jx3V8FCE61EH7Rgm36CVvIglvoIM5rLgAq/mq95CNn0yY+ffyGcuLZXnTv1DaZlnU9F79XtbfqQfe9jCgIAH6I73MVSKBatXlgND5N9Ga1SnjymWxLLv3EwO2LMPhPQgYnXktezw1ztpX1POdUBgh7Q8AQEPd1K7bIv5c00ap1KO/A0iLyk02s0WDmHyOuP1b/l265r2s/wWvhQdABeaWTnKPkiqsXQeYJeYWCEEtetv/ACy+AB6Tx291PzfnFK7hlGdNjqBYvND4/7D311F2XMf+B1p9mM8ws5gZLduSmTGO7diJfYMO801yk5vcMHPiMJljx8wsW5Ys5hGMNMw8Zw5jvz8+u90zsuzQL++tJ89eS0vSzDndu/feXd+Cb1X1tdLIpW4B6+z0ch9/AWDuDTDvW34MiBljfAiFtq+VePodX6Pe+4keEhEUkg3X43UZ7ASsa+cAkJExPD3jQ6x76wH25fovmN3lbDbljNFUN7Z62qyeOLyK8JZKqjkO845WzDRbp+59EaD1BmjHWjHN5B3ksnwnokImuq5Y/oqn0deOQrf7Oe4x0oPiZfR0TybwbuSXiqy8SMRilSHNLj+zlEpFJiopi02O2/2yp7dXxhIJWVtdLcsrKt54b6bGvzWmLPFTdSw6U6RzFBeYw0XRFk1TBLY8XvrnbhP56K8QtEe2Yk0WV9O1KabidEbe9oGXAYyiKhjQh7ZAwJqxHI38kV8iuHVlhc5aDmgc2YrgCJaIjLRCiEmniJcnIgCDMYw2kMbIZrmvkecsDgRNcTXWRXcThLSCcpFNm8i/Prod5SA2TknU1ZcieNoO8nwuL5ZxJqVId1mRhAMil8uDFTbYwWd1nc+Lpip8iWpO4jeZ5++PAXzzTjOLtniDZkjAGxC58mMIzQd/AvCJBYFtpBQZFp6m8b0X7jTJTq88iNBccDotRqMhEdFF5lyJS3rDdeZ6dRwR+d67UIa8QYA5GQecG+bTCMXjx6sybTFzffjnEN4iIX5XO4+1yuVQXgJFWOCJiMkrsFjYG6OCndXG304X9xbh3oUVZqe5TJoc+NAQCp9mITzjC3KtiePQVsCyv419Ll6qCFsHzM9UziCHfcuDeBzOu/n1TWUmjvHhyT0DCsuxMBNR9tJfgGJZXk9WxEt/VeAeRBn863fgL9gcKMK6DqHtxLH8PNUJUBFC7/m2akxykHepahYEut4W3s2J1RDXXimy96DJqg8Us08nDm+Q5zVCGckYioeRoqhpeGKM6oKJGCGB1oP8rrAcz5DhUdM0swdBLqMUrBrc+wtONwE+k+J90XMofpkU56OwQnrsQcnYndIkDqmwiRQXFMlwOi0zCgrkQ8uXi3vKEv+PjSkQP5WHzc6fRFSVSM3yf6td9f1O8yJWTJtcK72nmbhZeIT/R0Z4WXc+TVz4ovdTlaqoSjFWFRFrqJsXP78MoeAJ4uobHVClPq1o76kE9+s6arrSJYdAmSiIe5tx6xou/MgYgnhsALAZ7OD3xVVco2kXlqLhtu5vw31YWI4gymb4TjYDgFuslN6UnMiF78FKO/AycWG7E+XDZufeWU2BY55IImyC49euRInIKxW56L1m21KRyTWpW/ZyT4dbEYmygNhI7+Q92/k0VpTdgaXasEhk3wtYbqkEa55NY3kOdE4uxFJWD2nJX6hi8LtRAEZ7IVCND+EyHuxkH4qrRG76OkApwlpte4wQQCZFeKSgDIEfj6hsA415rbwQL8loP9/NZnCjTxzDPYCxUeil66jyCqnYdEEpVuPDP6d//CsP4FI+/KpIYZUKn/hY6/FB9mfiqF+A4pVKYLm+WcGQvBLAJ51ibacvRnmyqDDT7NVmF7EVF6DoJKI8697n2a8iRS7TNEJLJwNxEdzchqv77Z9DWY6H8cxMX8zPrTbK3U4cs5aLtA+JFG/guRacYbZ7PXHMX4en5KW/ithcIo4Miq6/kLNRMd208Df9jfNTUqvSTttFLn4/HdoSMUVoc6G0zV0L8U8TlN3BHlVCeAirfKibufe3c54PvSpSMU2CDcsl3Twg4axdCopKJWmxidPlkqpAQCLp9Bvvy9T4t8cUiJ/Kw+mBqXxku2o0kUVgxUIIp+rZk12Zxug6AjB7gwjS8DBCyJ8PuD13uypXuge2ti8IkLn9ZoWz7iblso5BgCkoxTJORGH42hy4Vs95p8qVtWLNTiQMNW7Gcmncwv2N+FvbAWKZ6SRlRH35KudazNzrZBzvgwFQsZDqX25F+Bgs4KwgyP2FWDerLqZc5RO/BSyN2OvZ76TrWWRUWfFW1qi9ESXF5QWkPvUHrJnHfyPS08J6XPAeiGaeABaN3cU6hEcQtsYYG0Qoi7D248OEPGrnUaAjGsI6rJ4lMm0mSsBEEHc4eYYnf8/8yqdh2S89V+TVh+i3XlKLQL7/R9SaN/qNR0OA4uyV/HvHkxSQKSwnlnrgJbwHtfNxjwcKyU9++T5AdNXFNB2ZOA5sAsCLq1mzAy+rtrV5eCiiIc7T+BDX2fEkFrGui4x0s17xCArCsV24tJ+7nXWfv47PNr7CPfJKIfyV1p78XSitZQ+f/TP/LygX+frjZi3743sA2+rZpFT5800ymdU+Od6eTZtEtb83yuvpld6wECVF180QRSzMe3LezYRWRDhr66//+9ftPApfIK+U+fU2o/A4XSJ1Z6CQGB6ejsOTG/3YHCjY59yEwmSxqDa9FhQNQxmqmcO5TSf4v9snIhrvlseveCF9IovOlJqrPyqXHzokuzdulMF0VuwWXYIul+zq7ZUnjx2T6kBAgq6TyJqp8W+PKRA/lUcyxgu68iKs19b9gFLFNJEVF4tc8O7J1ouuo313HDXLsRpWvNWOwMsrITaWTqpGGTpu95JawMXjF/nJLVhhbp9IqYrtVc3kz5FtWId9rapH8ToV8z7JyKQROJpmxqr1LMpI0w5FOrNSjW3a+VRFO/ASVszu51E+kgmR6ChztdiUWzxHIQujEYi/CEHXvAfCn80BoI0N8NnaeQBEeT0568k4LvtkjPUcH+EZ2g5QzKTjiIpTDvC8O58E/DTBohvv5vlK6ibHcYe7Abf8EjOlbqiLkMCBlxHwDreqS362ygs/Ycw7jXUd6UW5KW9gL54N8f3hHsBvfIjPPH8npEOjpv1FH6As6kgfylNoQPU2X0LzDyPVSoQc6WXn8e+J58jIsz+2E2WvuEqBoMZ9RFAoNI3f+4IoePllylL3E6sPFJhFcHz5eIhi4/x74z2mZ0azKJJiTuQLd5z8LKWSKFy6jlJQPZv1y2YIBQ12ECc/so19W3c1iqM3iPt7x5OcWSt50XLxB15/j1xOZNczqqe8j9LAhodr9aW8MzufIUWrdj7XfuK3hE/Oegcpfv/o6DhkhodE8NC4vSJXfoJn2PMCbv2Sata/ea/Jzs+k8MSsvoRnCw0QssqkUT6Npi/5pbjT/3iYM5PTucdwN6ERo/Vtb4toIvK2WTOlXE/Lzw4ckqNjIekJh2VxWZkcGRqSH736qnzpjDPE/v+ioNLUmDSmQPxUHpkU4Jdfyp+yegBuYrrMxPHqIyKbH8CdHAtBKrJY5DULeO5aEdFUFy6N4hNOD5aly4NQLqoUWXOJKsZRgrYeC2NtR8YA0t5mAP20K6jTPT5MM4Uz3m56Bga7IDO1HVRlSpV7Pq8EC9QbhLldXGM+a3EVgvDoDpFND2B1R4ZxoeZyxBc9fuKR3U14KZxu0m9iYcA4HgE4F67nupqG+3mkl7Qdm4PUqvJpCPZ4ViQ/oFp+OvB6pBKKLNjNfKNjZmGdw1tMMA4Pijz8U1yuIgh+XURmr+G70RCCd6QXITvax5yzGVz72Qz3OtGbUlQ5uW+4xYqCkU6j9OgqxeuXH0Uhq5sPqGWzAErPcdzaDhdgHhtnXn/5X6zG+evMaxs13TXNBNznbuP7yQRhhHgY17zXDwExWCjScoBnc7hELv8oLt+BDn42ZzXK0LHdpqLV08w+GqQ9o6hNoFjVDIjR3CQefX11ORHCBMd3sQe6Tl58xXT2Z7DDrBTnz8cbsm8jSo07QF31G7+M6zidUK1kG15/jx1PUhXRyAzpOIS3o7Cc51h/HTUMHvwJSuCrj/KejQ3gichkRMpWvf66o/2cy/xS9nLTffAxeprxanj8qpf6Psh/Njv7ufUR6gqsv051ZVOZJHPW4HGx2qiV/renqFjnCRAO0iz8br7iYeSVmA2JhrpRdoIlzM3IyBgdEO2BH8m6oR6pSqbls/lLpX7WIvE4nTISj8vL7e1y+/79csXs2VLgdr/+GafGvzymQPxUHkb6kBGbDY+8ccpSeJRmCkXVgNnYAMLDagfMXX6szr4x4siD7ao3sxMLvGYWwmv3cyJP/xlwKKwgrhcJYQ17ArjS7U5+f9c3yP92+xQTNkVcWQSSmsOFF+HYbixvi5XnqV+AtRkeFcm14Rp1asT3VlyA90BEcP0lsb7TSdXCcwku/FiYexilZoe6sdxtDlJrmnbBYi+fBrC4vIDJBe9BoB3fA7knEWFto2M8b1Eluelj/Sp22AaIZVK4PoPF/O1QLvVXHzNBvGIadeD3PG8Wz8krARyMhinlDaqLV1Lkrq+jJF3zWTMGe7LReQTQGB8CjAc72deRPs5EKslazlnDffa+wHWHurhXJknMOJcFpErrUJiGe0Wev539cftgvM9cLrLvJbgJFgtgdvAV7rPsfPau9QAx7/oF7JfFyr/bDrImui5SXIvSaRRSyWbZx5ziMmTS7K+mqfKhOdY7ETk5iHcfM/tjaxr72dfC36EhlMtgEcDdcYTvjA2ancv++zZ4AG82Xrmf+xjWem8z5WzXXsoZ23gPa9Gyj9TH8UGUObvKq9/2qMjlCsRTCdZ3/0bW02Dt55Vy3cIqQHzHE9SY7zqiOt4p8t5Au0j9IhTzt31K5F1f5Yzb7FjtFpWh8e13iLQ14gEKFPK+zFiCV+qpP6BMzlqp3uExzu+Mpbz/VhvrvnC9yFev5Kykk5JnsYm3MCvOngPSv+Bs2RJOSDydlqebm+VAf798+cwzJX8KyP+fjSkQPxVHLAwjOKpyljsPoz2X11Ow42QjFTdjZr58rDx3wIxR+/PR0rc9gfDxFyDgjKYIZ78TYPvTFxGkBWUIjW2PQ7bqa1W5s21o+EbRE6MSVUkd8bkL3o2AGe3DyrA7EBojvSKiAWKX3kLecNdRPAFOt8i6GaaC4nBCbOtrF8lNINXEwwDF2z6l6l+rZ9B1rPTuY6SR6cr7kMtBDjvrBgBahPmc9Q5AZ+dTsMfjEay6wgrcsKN9In/5Cs+sC0qGlsOVbVSYE+H5J8ZWNQ0FY+4a9rC/ndryNifzzWWZjycA+BTXkP7z/B2UZ32z81Bay5yHu1X9+7BKK0vx77EBwH7uGizWg5uI/Yb6aQwdGuTzmsbzDXVjmfcqICytY+9La/EgFFWKhMew6o3KckOKUDc+RPhixxMi93yLvS+tZS/mLMPSf/k+gNvhVs1vHMwnHkYh8fjNUE88zF7Z7IQdTn/b60luxdWcF18e+52Mcb5fuAsrteMwikhBhar534pb32pDgWzeA5i92ehpAUQNMtpgh0hfM/9+4re4tPNLue6xnay9zcFaaVZT+RwbJOe+vw0FqWYOYZ7wsMjL99IyV7Ootq4HRBas453JpPCa2F3UPMimVDaETM6pN8bffoB3weZQRV+SisDYxf9Tcf5/cDNu9foFkDrf9VXWJzbOWXzid2bOeHRMgiJyrqtHnrI1yKGmRknmV8js0jKZXVgobWNjsqOnR86bdsJcpsa/PKZA/FQb2Sys074WkeoNNNvIJAHSZeehcZ9seIII+70vIMgyaUhYo30I0qIK8stjIbOwSWElFuDMZYDxpgf4fX6ZiGhmLWZdcO/1taoKWXv5nVFIRtOwsO0u7nFkq8hgN4KpahYEKU2DoJXL0omtaqaqP92K8HN6RWpm8yyldQh5fULqksWqUr6UgHW6cW0aVklMEed2PyfiC4iU16lypXGeTdeJNe59AWUjNAywGVXdElGRSz/IHGpmi9zyI6wci5X0tWAJ7uTOI1i4FivW2hUfm7wPmkb6lK7D2rY5FBksCNC6vIQxNDXngU6RY3v43KL1KDInAlj1LADQakf5ymZRJIyUwoEO1mDp2SJn3Sjy3RvN/umahWoS/e2AcS5LPPvWj2PtWW0i7iAEs7wSFJPhXmrAGzXhq2Yzb6sNF6/VZnbu6jgskmnimQrLAaVzbyJL4cW78dT43ADIqktQZpJRQgC9LYBdNo3nYMUFuKirZ/P5iWPNZSgU/e2s+/QlKuNhFFJe93H2pWombH6LTfEEUvx9fJ/qgz4MSW3JOa8v/lIxnbNrlKx1KkUrlcD6Lqllbxaeyd9DXRP6Egyi7I0PUyEwOoYy7faxzoUVnKF0Cs+JUfHOX4AH5eh2rOihbtzyusr2OOddhJc23s3azT+D8rixMNXkXF721GLBG5PNmF39vHkoF+EhlJi8YpErPj65Yt2x3fwdKERBzOmiaSLXjx+TmXZdvu8JiNXnlBllZaJpmlg0TTJTDU/+n44pED/VRngE4VZcTatGiwZYevPQmEtrTavSGLou8vxt/DudxPIQXaSgUqSgBKHQdQywrppNXNfpIW6tiYjFgRD0+BH6GSNmmzXjr1UzVYexFoTWf30Tq6n1gJmGVTNbZONfsVYChfz++G7l6l1tpswc3qo+P4c/Q12TyXGHXlWNNAww01R97QwKRW8r3bvcPpQUm51YqssDI96oiz1nDcIwUIzrfcfTIi17EJ7xMApA9zEIXqN9kwuATFsMqBq55g4PjOuP/1Zkz3OswcqLVcnak4xclnX0BLiXw82eVM9S9dCzIgdf5tlzOWKXrz5Mo5u1l0++VtVMrNP7fwyoFlaKSM6cc+UMiFcX3wIwrbyIs9LXyrOmErhrC8qY821fhiQmOnH2eEQttYYy4XAAtHaXyj8PsMeJKL8Pj6iynspKtNjM0p59bVitc9fhnj+6HYXnPd9+PTCLUDwok8HNa7GYfdNP/KzHL3L9/5jekMIKWPwON3Oqncu5q2jApb7nef7WrIQGdirmvMsLCS8SEll/Ahv/jLcBxkYPeIMUN9QNONuc3EOEcMTctZzv9kYAev4Z7PWe50jzyiovkuE5GB8Smbuac5TJoqTOWc07qWsih15hL/Qc7783H6Vl3wucYV8B3g+7g7i+N6haoY6rTIyEmZdu5I1LjtS+vBKRD/709YqLN8hZrF/AeYmERDRNLN58WaFH5EPaiPwgJ/JMc7Oks1kp8/lkYWnpyc/81PiXxhSIn2rDZjcZuFoGayA+bubTDve8HsTDIyKHtwOItXOJuW19DCWgvxOCWmkdwi6/hK5ebY1Y3XoVLuij20TOfDvxuaYdXNdqw3qOjauyqAvwBJx1AyA6Yyku+Ng4bvIHf4Zr0ei8lU7Biu4+quKzdWbqT38bgscTUIVGlIs6GUcIzl7Jcw334mY0ek77glgmTTtI5QkPq8pjhSKbHwS4Gzfz8/0bsf4KSqkdbrECWkWlqmSlIlilFO9gYt1uq1Vk7RWwfR0ugCO/FPZysAiC2InpUNksAj0ZJ9Wnbp6I5HCvjo8AVDd9nfBISz9rpAsWYE5HgG95iBSpiR6X8WHyzytnkoI00mf20rZaRRZuEFk2wbJcfj4EN2/QTPMKFlP33p8PKdDlBXD0rEoVc/A7t585ldSKLD2HUrrHdyu2fB7PfdtXzNasqRjrY7HSJS4ZBySfvQ3vT90Cvrf1MUIoFdOwLg0OQPl0KgdaLKq5Tgo+w/6NzHnD9Zz3sUEs8U6VPlk9h/PYuJlnNLqXTVtMjwGjwp7DAfhmM2a7ULefpjxnXjPZ67HsPP5/8BUV4rmad+mZP6Mc73mWa2gWlJhAIT/Xhedx+8yaCKFBPtuwCLa7UQr5bZ+m3HDHYRTTQBHrm8uw56mEOafyetz2mpX96WriPXr4FyLv/S5Ar1lELL0oWIFClImuI8S3ExHTG7DuqpOXnS1vQOnb/iS59UZdCsmK+AulYsZCyWh+sSST4nc4xKJp8lJHh6yqrJTaYPCkImxq/HNjCsRPteENIkx2PCFSVgnYVM9CUOrZkxePMJoeiKDxt+wXER3QSyUB61krSFfpPIrlVFBKTHnmClUCMiGy9VGRj92KFTPSi5Cctw6LetPfEDSrLzPTkmx2wLanGcb38d1YezVzFAvWJRLIF3EvwSJrP4QS4fTgfj+6Hdf9u78j0qfiibkcz+MvglR3ZDsCsayB705fwnxbD4j86mMiNfOoepZfqhqsuLCOxwYBmgvfh+WZSqiQQ0hk1IrAi4UQgmMDrE/lTHNNdzwFy9npQXGKhczqddVziM2/66umWzKbQbge36Oqolm5t66LWI9iLV/8AdzOVTNERh+hdvpAh3L7Js2QQSKGsE5EKYLSfQxLN68E67i0jvX70E9OfobKGxDwBit62mIUlHSCa1psZoMdw+MSLGZNoqOs1bzTAPmhLtVW1c9nDm0BGIZ7VHtMndCEYdkvPVt1yXIRU49FAN+Nf0Bx6G9nb276GsB09g241LuOcl+bnX/nl/Hcf/0uIYLHf00Yx2jZWVorsvwCLN6j25nf+us4rxYLINdxmOtpFpQxY+RyrPWJw2JBAVp+Pv/vbBL58xfZ87JpnMHDr2LRV81EoQspZWaom3DN6vmqiYxb8UhsMNwXbUCZefqP7Mmc1Si/Wx8RWbCeNUwlWBPNigLbeZS5tB3EOzXYaTZHuvVjZIPY1LucVuTP8nq8EW0HUV4Wncn+G530uprgS1istDktqUZ5n7tGMejLVOfB50Qio9Jv9cs0u0uKq6slmcnIC62t8sMtW2RRaalMLyiQtScrXzs1/qkxBeKn2tA0QKl6lsihZqw5X1BkoAt27cTiIsbwF6DxN++BIZ6M4n6PhxEw4yNc9/KPYoHHw7zwmx8ytX67E8D3+HErThxLzhJZvMGcnwjgs+MpLOXm3bjui6oQZHFFvHK4EAo2O9eeuwYrMhk1m7z0tU4uxOHy4KY8+ApgMXsl7uMVFxBrTMQQbo2bEHqj/aQmnftfWETxiGrakkZIDXYgsIx4ZbCY7xRVieQVwQCumEZK0uO/RUm68L3cv7CSubUfgoBWUqOawRwhrtp20ATxtkYAvLSONYqGKA7yvu8iYG32yVafy8v1+tpQIiwWBHBhpcirD1K6VLPw8/wyk0FusZD3bnSmy2ZJv9q3EevxjLeLiK5CJRYsw84jAFBhBUJcdNIFXT74FuVVeGAWbWBOe58nbLL3RdastA7PRmEFYN3XovgQOZP1789XmRAu9sWl4rJdR0QCc8zqgoOdgOLYAC7pYBFu6Kf/yLM070MRcHn4M9ABt0AEt29hJWsbHRe582vUFrDZiHGvvIj9t9rMtEwRs1Jefxvgmohg4b9ZhbjhHpG7v0EPAU9AZPRVLNVshvKu2Qy/SydZi/FhQHnhON6IuLKCr/vcZM9ZbzPv2MFNuK4TEUI1sZAqnDPC2bVYWa9LPyhy+/8B4tExeAoltapl7G4q5dmdFNN56V5FkEurBi1pvm8Mo1e63cXeNW4RueF/AfKJbWp3PCmy62kRX77UjYfkHN0tB896tzQNj0gomZSaQEAq/X5pGhmR+VMs9X97TIH4qTg0DVd197jIZ/6IQHH5EHonEzwWC406djxBh6/BTgRdSQ1CxugBPjZIIRARhPjOpxGmsTCFZIoqAIvZJ2HxahqpO9sfR9B0HFI9kHtwD/uLVP1nF96Ac2/GLT7cxffL6ymNesfXcGeKMK/BTizYOZcxv7xiul0VlAE4BSshNSXj3OvwqyLDfbBsXR6lrESIJ3/oZ9xzcBgr1xPAddl5BBJcf7vqdObCqi2toVDG5gcBHKPN5R+/ALiX1iKYNQ2hN9AhIhqfzaToImeMRNRMfxJRqU+D/PtkxXAsVpEbvwLQ734W4CmpBiCfux3BbLNz3/ERVawjI5LT8Ah8XFmWO58SeflvZp31B38CMNYtoHPVaJ9INEJGQdt+zse0Jcryi+NtmbMGr8WSs9mnxRtQmCJjZq3+bAZgD6m0LSM9KTrO89mcWOxGGCU9AnntwCaRObrqQZ/Ayiyq5Lq6jqflsV/hCk9E+XvHU7jcrTbVljViZkFoin/RdZRrBItZoy0PKwWjlT1YcRHKaDoFKDndXKNiOmTGWSvMvThZh7M9z/NsvjwzC6F1P9ex2jj/sTHmY3egMISGOFvTl3CNgQ5auG64jr3Z9jgKqOFK9+apZiZD9DB4/jZ+7ssHrI069pd+CIWx47BqYBIzFbxcjnsXlKMUdDzNM2fTvMfbnyCtbfoSPAcur1lkaLCLcETJdeZzH94qcsdXAXqtQ0rqF0hlX5/saDskHVm3pDMZ6Y9G5bFjx8RptUpyqjHKvz2mQPxUH97g613o2ay85i43hsNJ/Hfe6SJF5SIP/lwkqiE0Z60AjEb7EKBON8Lp2s+L3PMd4m7FNcQnH/65iOOzWJoTR08zhV2cyjrqOESnL18e1l53k0gmAThUziDeOG8t37PaAOsX7kTYD3eRltS0k2uV1SOY7vk2LupcltzV1ZeaoDg+jCJjCEvNoohougmewUKRD/0Uwbb9CSyTiulY/3ufBwgLK0V8hVjo9fMBjkQEIWsIt2hIpO+4SPUMSpf2tQJARlW0bJZrPn8HzxgsIgZutbLOTq/KN7aI/PlLKBDrrnp9UZe8YmpgG8zrx39NNsLYgAkcVjsKiyfAupRPBzyObgfwDm9jTZwu9jUawtNgcA9Ges1iK6N9hAwsFhSUXU9joUbHSI0rr2deNjshkYJy9ru/VQH2GOcpWIRiqWdRRhwu1uj8m1EcvQGRzmNm2VuLBRC3WEUyMc6jv4AGIFsfhd+QzeAtKK7mWk07AJ+GhXy/eS/rEVaWajoJoO1+hjknoqz9tMXMdesjzKVpBxwKbx4KnDcPBVnT2MNHb+UM5pfRta2kxozp97cD0BYr5yO/lK51j/+G/bLYTAUvMsY1rHYRIyvS6QGgcznu07JfJK+MkIQuhMDKG4iL18xmbrFxVUJVV73WR1kXIyUvGRcJKeD2Bvk7o9j98XG+b9Qw2PeSYrrr8BtyOTHjbmLO3RjJOGTBbEYk0ieSjImz97gsqZ0nuYZ6yWbccm9jo3jsdrFZLNIbiUg8k3kz6TU1/oExBeJvpZHLYXG++qj5Yq6/FpBsa6T8ZCqBwN/wDgS9Px/tP52g+MPLfxN5+2cB85JqWi1qmmnp5LJo4w0LuYeRtnJoC8IsWAR42Oy4gmtmI1DbDpKiYsRbb/2kSFzFnIf7sNYNy2HmUkC9v5X4dUkN1dLGh0Tu/jYpQrrwu3PeBThGRgkr1C/g85v+xn0jIRHRUAQCRcpjcBg2up5jnos2cL/CCiyewQ6RYQvC0u5U7SNFVS9TzHyjGEfvcWKMfW24MK1WkdIqlKZkFOvmrHdw7Ss/AQlquIv5FlVR9Wzn0yghl39kgidFp/vY7mdRMEb78XRYbchZmwNrP5vm3xYrCoSReXBsJ8852Mk+RccU8a8A5efFu5i/24dl5/JgSeo5lKGiSizyqz8JsE8k9Ylwboy2qW4//w6WiaRjkPBsdrPVrS+Pz8w/HSt+/fUi9/8QUpyuq2IuWcCmsFzkkg+h9O1/CYXv8DYRi46SUVDOWtYtFFl3BZyNdBJwyaQB3urZkOGGe4mPpxMi4U7uYRSXcbhF2g/iZjZCHL48vAlD3dzj/h/hhSqpRTn42w9Fbv4GnoHKGQBzNg24NSykbG3DQs75SB/XS8ZZo0SE72TTZuvZ6JjqK35c5MV7VI/6AM/WexwPSKBYZKDNrPFQXAMIp2LsbaAQYHb5yJZoP8w5sDtJ5RvqwtsUGhQZ6oH9bnOq99XCO+H2UeHuvP+iAp+eU4Cuw30wRizMs6RTeCFEJJfLyvGhIdnU0izWuoVS7PW+BtwLS0pE13VJZ7NT5Vj/jTEF4m+lcehV3K9Gvuqrj6i4dDdWQ8NC3MiRUWJsN38NK2TrYwiTtv286FsfRdAvOhNhkE6a98ikEOjZLNW89r0EqKRSIjb1ohZWkDcbHibvOplQ9a8tFJUY6cVCWnc16WwHNuG+Lq7mWi0HRH70isifPo+1JSLEcVUYoGExgn/vC4DzovVYObogNMunkZbTeZjPuT0iS84F3H/3WbOAi82O1T7/dLNxhy9PhRj2q3imcq0PqXsbuehrLyOHu34RFu6RbQCov4A5x8OkABk9zkVQMD7wQ8D43u+ZcUaXlzBFMs7aDnYBJL/4JcA6dy1r2nZQ8RnyUZ505W0prEDhiIwCEt489qV+oUg0TEjAE4B3kIyrEIYCz3RCxFdPbvj4MPPQLKzDaVeJVM4CbLIZrL2uJuax8W7VK9xNcaBgEcpAWMX7rXaR/EK8DMXVqkFPDmA9vNWMw7fsVzHzQqzaQBHx/MEOQMbpQZFs3seeWayc1aVnc52n/0Ro5cL3UT7VYuF69/2QgjLxcRSIqplm+ELXVcZCEWCbiLH/gSLVYMfC+o4PM3cRfj/YiVWeSrJ3C84gvBEaBDAbFlKrfutjrLkvH8CzWjmTdfO493A3+3b61RDt/vQ/rFleqVnRzhtESUgl2ccdT7EHoz14ihxOaiyM9eOxGh8SmbaUdyOX47z68mj2Y7WLlDaItDaKHN/Ley0ir7UuNtrPltWLXPPfMP8tNgiqEzMsfHlc2whZ6Fk57syTDotLuno6pNldKr2RiKyurJSG/HzJ6rpYEwmxGSmmU+NfGv9RENc07QIR+amIWEXk97quf+eE398gIp9T/42IyAd1Xd/3n5zTW3LoOoUz7v4WGvKclVhPzfsQsHklCNHWAwj40lqEZFkDVtOhVwGgTBohkk4ASuNDFK4wKrHpOoJ86bkI0N3Pm6Uzu46KDPXz8ueyuKltDqynqplYOJqFeYRHER4dh3CNigBCAx0iZbUI0lRMZN3bqLjlcIk460j/Guk1yVQWC4pKJg0L+eIP4E0YaMeVe9H7EdIdh0We+7NI12GeK1jCOvS38lwePwK5q4na8k6vyBUfVaVA0yKf+ROx9O1PMJc5q+EY/O2HKAEuD27avhYAIRYGeCwa8zpxGKQvoxBONsOzWG1mEZjAfISm3YVCtHA9lnvbQfYznVD90nOEAAyyU3hEAGjBZZ9Nk2Jms6kiLCFKhU5bSu68JwDgDLTBqjcAN5XAarvtf9kvEVy7nUdRMAaUUjhjKZbkzqc4TxYLz11cQ0GdQBHnKB4WeeEOrpOIoXRlkoQMLFYRj1ekdoFZIKi4SkQ0PltSR50Cq5WwxOKziJUPdfLskVGqk7372+ylCB6g6lmmQtvdhFI20KGKwSzFWo+E+J1mhQOx/AKUIiOVK53krBqV//JKUBpG+1W/ggbc2vNOY592PUMap8OtCsOMc/7nrMbitdqx2MvVWkVDKAHVs5ibzY7StP46PDO5HFXvjLBZoAhLu2YOJZTv/Abv1egg53P+OlWAZ4Yq9xoXKVZetNmraCBkpI/6C3nv+ltQUP78JZHK6dQTMIiRJ57b8/+Lwj+5jKQdHjnuLpJ2m08OJrPSOzIiqUxGtnR2yrGREVlSVibFPp9ob0YQnBp/d/zHQFzTNKuI/FJEzhWRLhHZoWnaI7quH5rwsVYROVPX9VFN0y4Ukd+KyKr/1JzeckPXAeadT4k88iuEUzxMh6PwGH3C3QHV1WqY3430YjXZHCKiYS2P9quyrFaElS8fIRYs5oV/5/8RcxSBABMbp3WmRTMLuRRWAACBQlzARhvD4hpcs4NdEwpPpJhDXytgOtiFsMqmcf+VT+d6JTW4T7ubRMZt3C8cQZgd3YHCUT2bZ9v2GEzaj/yCNXnkl6xP11E+H4+geKSSIkGriN3HtV0+2jqODiDQK6YpV2UXaU5Ot2oqsYpCK9kM62m14sq/97t4OZJRkdOvAbQPbmJdlp3POgz3qNKsGpbx1kdxv3c2iVRNZ55nvB0hmYwT8863MTeLBaUoneBZS2vNOgGVM9T6HAPci6t5zkiIs5BNo3S4POyBrvM7m530wdq5MOsTEc7DzOWqHeU0lLyX7mVvi6v5zFN/wppMxrhWTzMgFh7Fm2C490f6AVPfUgq6HH6VPfIGsMDbGtnf2nmEUnJZwDoREVlyKWtbWMF63/0tXLz5ZQC7y4cFuutZ1sNiMa3koW6zqt+Sc1De2g4yr2CJyLJzIUd6AxR4efAnAHF0FG/R+Ajrdf+PWJv11+Nt0jSU3fVvV1XNPoaLur+dOu5XfYLwwlEVyhABDH15KH/zTuMa7Y0i9eXMs3I6n7O7UGJq53KuwiOA64XvRVkY7lXepQY+b9Sfr5xhphW6vOyvce6Wnw+PQtdVvD6GRyNQqOpB2PEA9LUCyHYX+5pfxjo++BOR67+EAWB3skYGEK+4UGTRWSJbH5VINiezYv3S5/DKsG6V0URCSjwemVtSItF0Wt4+b564urv/E5LvLTX+k5b4ShE5rut6i4iIpmn3iMjlIvIaiOu6vmXC57eKSNV/cD5vrRGPAsg7/4JbOTZuppdFRrFy7U5T+88vBZiSMbT/FReJfPlSrIBEBCEWKFSNOYoV0znL9/NLRJafB5g98ycYtaFB2M2eAEInMgoIHN9DXNnpxkI4vgvBN30JKS9VM7B69zyH0DOITakYc8ubCYvcYN5OX8yfxx7C3agLQBUL8705q01i3N4XIcxVKitksMss+er2qY5hPfxJxFSzlUXExG/7P4hbhrAa7MDVu/tZsz74JR80yV0i/PvmbxIjbdrJdZtyIu/4onLp/kDkpXtYt3nrYKt/61osfptDgVclaUYzlmH5730BYC1dxR7UzRM5sgOgrJyBy9jgJ0wcfW0iP72F9bQ5CEs4PWQUGA0zcjnK8+o5PBD5Kv2tYgaKTtsB5m20Ax3pn1yPOzbGuXJ5sRaTUcIv6QRuXIcTRclfyNr4CyDHifCdA5vMGP5wj0h/h4g/j/l589j/064y7zdzGVZscTWAmIiSYTHUSSpWbJyzlkmhfE6M2zucIld9ktjvY7/G0/CrT/AelDeoBimtXMNiw+0+0oP7ef5phDEWn0XxnbEB3o2yOq5dUEZFwmRcFbKxoFQd3UbNhMPbWbf8MpGl5zHfln0oxg3nijz1e+XRWcU8z76RsIBmYc2WX2C6sT0BE4jLGxRxc1Dk6k+L/P6/zdr8VhsK1Vk3TM4eueh9pEaO9OKe13PICX8B52j7EyKpATPsYzRiiY6h8OZypJCefaPJJ1hyjmQObpK9tgKJWh1SmE7K6eEOuSNQJjarVaYVFEj3+Lh47PbX6CRT418f/0kQrxSRzgn/75I3t7LfIyJP/gfn89Yae19EeGlWQC0RwyIra0AY1M4RsToRzENdvLxzVsPurpxB3e/ICBZPIopVkV+CIBwfxsqJhenqZYyOw5CNSupwU6aS/H/mCu47dy0xVV2HNBcLm67jQKHILT+BrZ1Jowh4AlSNy2VVVTY3Qvulv2KpGGzt8WGUBKNnckkNQsv4I4Kikozyb2+AJih/+hLeh/wyZfm3qXh3FuHkLwSsBruw8g3SmmHpPn+7aoFag+C89/vkdacSPHcqQby1q4l4t8UKOD1/B/MaH+K7uRyfH+7ms0ajkfAonhDDSt/1NJ2w6hao3tXP4qa/6atcp7DCLE174iirQ4D3tUyucFc+DcDpbQY8a+YA9C//DU/JnNVYbSKQATsOE3Nefx0W2fgQSl08ajYhcfuVG3tEZMFpuKZfuJPrOT38qZmNNT44Bmgc3sJ9PUGUlelLRY5tp8yrv4A5DHZyFicqKcY9RfCwZNIoc/llvAPdTZz30rrXyFavDauVcEuwGFd1oJAzqevwGUZ6cHuPDih+gVXlzR+FQ7H/JQigJdXmNbNZ1ULWM1lp2PWMKhesEZ4Y7WXvPnc78wyPqo55PrwCWx4CxEXgdJTUArT+fN49Q5l0exUQ/8asgnfxByBxzj+dM5NfrvoLuF7fBGXWCp7/rm/w7nQfYy7z1zFfA2WHulB0i6qpoOj240EwzmH9QhRANSdL3QIZHx4Xr54T3eOTeVpKHBaLLCgpkbaxMRlLJCSVzYr95Kd1avwTQ9P/QxVzNE27RkTO13X9ver/7xSRlbquf/Qkn90gIreKyDpd14dP8vv3i8j7RURKS0uX3XPPPf/yvCKRiPh8vn/5+/9/M8aHJZIV8YUHTIKSiFnyMVikukApbdrtx+VmsfL5jsN81qiqpWcRsH5FxrHZ+I7NYd4zEQXMbEr7F111CytE0NqdCINUwqwzrucQIkaTEYsVkBnqUgI1B6gax9TmAPiNWKnVJhILS0Rs4osMqc/mTEa2YYnkMgj2iWlauk6oIDoGGFusIqLxfbff7NntdJs1vzWLam7hVjXDNZPYpwuWbSysCD7qd5pGHN14XiPWbeyHCPcXwethtTEPgy1dMZ2fDXVzE80qEatTfPExBG86odZHEZ58+Sc/E4kYRCfNwv10HRAorDQ/k4rjUjZIcXklqjtW2GRoG2uaSbN+uaypaGma2VDDakOhMyzR2LjKhXaSTWDsVWGF6p8+zjNYbOxxOiniDUrE5hFfJs41iqsmV0uLh7mmOgeiaar5ja7i/8LvjPMQLFZ7bWGPjfachqWZTplZELraQ4Oslcty7g1iXzYDqFmtnP3wiKpop8A+WAgoi7BORrU0Y2/1HAqNsX6egESsLp5VdDgO2Yx6dzXTe3WyYay/1WauTy7LPdNJntFfMPl9NYZRaMbuMqvyWW3m9XSddRExaw9YbWYoRxeyBrx5ak8iIqEhSVqsEk+nxZbLSNzukpg7KJlcTpKZjDhtNrFqmuRZLJIXCJz8mU6x8e9iz4YNG3bpur78xJ//Jy3xLhGZoKJKlYj0nPghTdMWisjvReTCkwG4iIiu678V4uWyfPlyff369f/ypDZu3Cj/zvf//2IM94r88X9kY9FSWf/415QVMqZePBvW9rZHSa+x2QHqzl6Ri38MCOi6yOe/hZWui2oQEuE6pbXES3M5rJDl6837DnbRnjJYjAXTvBfroWYuL37DQnLQ7/iW6mplh0xz5FG+HwtTAvLmb4rsv5fYsK5DskmnVNetKlXNKg+FwuYQyeVk47pbZH2qDUu355hIxUwAKp1CwKy+TGTW684/8dcvXWymPDmcWJXz17Fe4RGY+OfdjKXX3w5IHtsl8tTPVO6zxeQViA44TFtsNoVoO0gOvtXGGk1fzPo0vqIs8Szu7NmrRDbfwWfSSRSPlZeIXHgp82h6nOfx58tG7yxZ3/Eia1E+DSspmxXp6CRWP7GCljHiEZFffwqrMJNCKatfQMx23lpivn/4HD93+3ATHw/zTB4//IHwKG1nL/4A65tKKsXNIfLIL5i7N8h8Z60Q2bCBNWs7KJIfEKkrxhORTQMaV3wMq3y4V+RLFzFHpwdwnnuaiMsjG8vXyvruTTDMDevUGLrOOh7eJtK7l/kkIpA2QwMqJKCUSbuDZ5t/OufRlwcnofM4IHZ0O/tpsZkFUQzCmsG9Mhq8lNSjeBZXc25Cgyi+qRh7O3OViN0m8q6vYak/9DOR534M6GuaagkbxcPg9pOXXlonG5e9U9Y3P03efU0DKZPJGPcuKCcUY5Dz0imULrff5J4Yo7cVMp9R13/dVSLzV6AcOz243scGaIrTuBkrfs5a3q/2A7jWjRRDXZiD1YpC2XWUuRdXoxSPDVDo5yO/VL3fMyKP/1b0w6/KWMcxGUxnJDTvTJl5yc3yyYMtUlFYKDaLRXK6Lg2hkKxatkzK/f43k2inxPhPYc9/EsR3iMgMTdPqRaRbRK4TkXdM/ICmaTUi8oCIvFPX9ab/4FzeOiObFXngx4CRw6U6UB3FJWfku05fLPLsn3lJ9ZxiwlpNVrjDRbzwW9eZLSxr52LxOD0ATyZFPHf2SoShCALg0g9RrWtsAFCbvQpL3CDZ1czBvZ6nXPPRMGAfKMBabWsU+cWHRd7zXeKEnUchDWkaLu3xYeVBSKkCFjHuZbCEXT7cn8U1CKBMig5eJxafMcazt5lNG3JZ08uw9wVVI9sCSOayXKNhIev21B5isruexeUfHhYxaonnsqy51Yagq5qF0NYUK/vsG/nd2ADuS10XWXulyOpLAKSBDoDAnw8QfedGQCKVwMVfO0ekpk5xAHRFNhMEqGYx3ca5HJZmNs16P/wLLELNYha+sTuJ2c9dg5Wey5nXyyuBrT9zBQAVCXGtrY/w9zWf5ZwVKyrL2z6DG3ioCyVo1SXs5/0/ZG0yaZS0G75CDramTQ6J1M5Tfa0TimGfxtW/fbfIxT8wz9nEoWmA8vzTUQB+8VHK+GbTgFt0jPNrc8DrMMoJ18whtLDsPPa7rZHfpZTHyu3jnYiGUDhj4/w+kxKpnotrf8lZ3GPPc4RBjAI7iWGR3mMor2P9KMO7nlWVDffh8RIhXOTNw8KefzqKj80OaW3hmbQUFiHDQ0QRzTZTQrhxMzUFslmuN5ELoesUh7Go85fN8NmN97De2QzX72tlfWrnQXo7uo3fO9wipXk8/9gAAB4ewR3fcxxlKDLGmuRycF0yKeSDkY520ftFa9op+aFeyfcERBqflUSoUwIzLharsrwtmiaapklyqjXpvzX+YyCu63pG07SPiMjTQorZH3Vdb9Q07Rb1+1+LyJdFpFBEblVpBpmTuQumxj8xoiFepuiYSDBJA5HwGMAzPox1tO9Fs2KUy0vsK1BEow+LFRJSRyOx8fAogiWvnOsa3bEM9rphFRtj1gpIWOmUyC8/Yv5O00yLdeZySGxxJ8JQ01ShFQsCbaADgL7p6+RtD3UBTDnlJtcjSrlwAPzREBbY5ocgV+WVETO3qOO998WTg7iuY4FkM1zfqkIJGRHxOBH28YRqfqGJvPc7CKikItuVNwBiRjqXxSqvldJKREmbc7qxNuvnM0eDHCgicu3nVGlSB6CRTrHe0xZjzRZUoig5nDyT0wsonHEVYH7pV0hjG+7huqkEcxjsJH7dvFdEcqytVbmMC8qw+uNRyFnhYb53dKdIcaVZVMXwvthdKBBdTVxD0/DgHN+DYJ8Yn/YG2Nu+FlK8HC4sZE8Aj0zLfubQuFWkrMZ07V78AcXot6EwiTAvo0iJ3cE5GulDsTOUukQUK3fGMuUe95HSZrURCx/qJeddT6lc8zyzGhmHkv05+52sl9MDIDtcKILZjIhFxfhzStlNJfDEdByGiFdWz7k1+m8bzVFCw8qdPSLyhy9wrvJLeQdTKZViaFGNiXQzA8FShsItoqr3uc31tTnYk8Euite4/CJjHcxlpFfkk78zUxJDg8TRRdR6HAOsi6uZ494XuFbDIrwMs1dCJI2OkZ/+6qN4Z4a6qcNvdOLzBERmraLfgNNNwSibg3f09q/SDjWno+A2biYkoNrOOjoPy8Jp62Xz+LiUeL0yHI/LDItFyt8K4c3/4PhPWuKi6/oTIvLECT/79YR/v1dE3vufnMNbbri8ZsnE6jNFkklTgM9YLiIaqUBFVQjryBgveTwsUlyLENj+OBr+4rNg78bGRXqOAupGudLxYdWZSgnxVBJwMupVb3sUhnPjZpjn/gKAoXwa+cYlNVh53jzT2raq6zjdCJ0/fkFp/GFcyxanKr9pYR6xMFZUKs59nW7ISD3HAL65a5mL9Q2Ouabh+h8f5vNG/N9mV72uVYw5ESU/fOGZkLV6mnH/vqZEhKkYJjr/9+WxFvmlIpd+GBewpol4T7i/xYIHQoT7PvUHyHUOl2q9OqCKreSrmGdaKQoqnuvxw2j/6fsBOJuDtKcX78Yy6jyCZVhSy7WM7l6hIQXQKue6tBbPzEd+QUeql+9jfS1WrMLffQZFyZinrvPdtkazMIgIc7/rG6yBN6jIbP2cs5Z9gEsmTcw9FcfzkEpQHe9DP8Pb07wX5WdskDSv331WZMaFIj0tIvd9j+91Nqlsh2WsxYoLqHqnaea50oW90nMiukUVlalCuSh3qp7xioB397dYL7tLNVfpV0xru4g9x7r7C1D4AkVY024fiptRx9zgZyTUOkkO0Nz9HJaswTuw2kU8Pljpmx+AeFbWQEhhzaUi23aa6zlrpSo17DAbwNQvgCCYTou0b4fTYrWjqG57QmS1Cg2V1PIc+WWsWSphZhsYfAUji8CXz/xm6JAkCysoHpNKcq6sNp7R7mAPm7ardqlDsNfr5hGm2PkERNpsGiXAalMKpIjYnaKFhqSusEhu6xuVnT09sqKyUkp9PnHa/qMwdMqPqdU71YbDiVWWzYiIZqZ9GDFAb5C/h3sU61ing1UuZ1qI7gCFTlxe0qtG+wGWaz9HT+eBdlUr+sPc4/HfUBDGYiX2FgvTFMQow7j9CTT+G75C28iBdoRf1SwEXDJGNbhAEcJi2Xk0e4hHYJQbikE2LaK5JxCrEiJWr0kOGukjZNDbDLtYtopUNpitIU82yurNXG+XD3CMjZupWAZJy+YgPzibNpWCQeUx8AZ41kSUP0bziHd/GyVhpBdBOdGqMkY0hLWWywAw89cRb9cFi9YTUOStARSrXIZnK1kBmG68B4CafwZCfuvDrHUmjVvUYsGacgfY82ScfUrFmXt5A2zz4V6edeVFgM/RHez/nucBZc2q4v8CgM5fR1W2BaebxLUHfswzuH0qDTGLxyc8wn2NbIFshvM12sc5GusnLLLyItZjsFtkwZm4pHc8JRKYK/L0d7AiC8pFUvs4j+kUTO3dz4msuphzvfx8zs5wF14Hp9fcQ4ebYiRON+/BqktQNONhzo0I6VvtjXhyRvvwOrj9AFhsnM5j/kKesbvJ9OY43DyD3Q1I+/LxePW1mhkPBmlzrB9P1Mxl7I0vT+Tyj2PZj4wR9lh3FUWT0kkA2u7gfaueRWGbyAjvjb+AvQwWiex6ChAXoY77/T9WrWptKDqxkNlzXNepu//yfar0bg4L3EhdO+8mkSd+h9U/2EnoKzLGOybCdWavYl4V01CsouM8n/HHCFOl4iLJmIQKKuS2sC6rKitF0zTpHh+XxFTt9H97TIH4qTiCxbzsVivWx3AvAq+vRSRWRCw1Ng7YhUdx/Xl8CFqnW8Tl5jMD7VibmSQWWXGVyLu/CUDEI1iLrz4MIaikDkG18R7AJB422ynaHFh2j92KEM6ksbzbDpg56tksnztXkaZ+9kE+p1lVPFxp+PFxfuZ0i8w5TcRu555Gl7J0nLkXlMFgv/5Lk3O3TxxuL9XOepsVEziJi/DIdoSt0yviyUNR6DxCmp3FhoVcXC3y6T+ixIz2sx7BYkhwS85GgN7zbRUrdVHlzSg2IgJQPv5bVYEuyZpNW8xnjZj6/DNobKLrAFdZvQL0DHs60G5WHbPZFdiGFA8hK5JR4NF5GMALFqsSpxniwg2LmHfDQrN//PN3cH/Nwt7abCJ5NSJ9GaXseIiTD3awXk43rVfbD6vOcEGVXTBOjnkuq7q85UQ8+SgBujDPTApL9K6v8/OuJhHRUBgMD0wmTf55bwvPP9gFKPvyRWospgtZxKyYl4yz/24f4JJfSs3/E70yAx1mpsRwD8+bSbE23nzmMdQFwXDxBs7A83cwj+IqvDJNO00yX2xMFUHp4V6ZtHL1B1iPRARlNa9EpUzOYh1fvAuv17TzRToPcp+bvi6y9nL+TBwV04ihP/UH0/s1famY7Dvhef/rm2a6WzpJPnx7o0iXims/8XuRFefjHvcGJ1dhm3ca/I3ffw6FoaQGORINERt3+9mv2atpkuJ0mb0BjA51hmckmxEpKJVHl75dPAkRt53EsjyXS2Lp9D8i0abGm4wpED8Vx+yVCGGbcpeKDgh1NYnkDptEmM0PEdu02gHAsQEEYFkDjRyO7yZ2On0JLjNj9LfDfM2kaaSRX45Qi0ZUcZgYL/vYgOo8lVQWSQqrb6ADYTs8DNhabCIFhVgWe57H9Vs+DcskGVNpZhlAxebE3edwiYx0A7T+AnmtE1loWMUKlSvx75V0nLdOZO9GirpkEigX138RgfybTyPE80pwF4aHEcaahmAe7CJv/cYvM28R1VO7mud/7NeEC1weBPjDP+ezo/2KwfsbrDqnGwA/0IT1a7TsdHlEXvmbaiupXLY1s5XnIWfGimPjCOFsRqUJKjD2F7IOr/XHLjN7U+cVs08jvQDAeTfz8+a91G438onHBikP6vSgIOhZkdr5nJeyepOY1t/Gc48NYClmUuxZ/XzmHwszp2zWrA4mOi7jyBgKX3ENNdoPvqzaYWZVuMfKswz3cF5zyiNxfA9rsPBMzoAxyhuwgl0+EdEAmwWnnzysUjcfxbLjEIx2q426+psfROHJLyW007yXyocXvoc1NlqWJmMoOZ6g2Xo1GVNKleI6REZVyMcKZ6BXEdQWbeBzuk6efF4x/zcU6K6m17PxRfjMZR/mM2ODKDOJGKEQY4RHOYPBYkVWc0FE/OXHOBMev+npKqmhyNKJo6QaYyAR4ZzEw5Atc0rhTsZQftddRRz/lQc4gwZ3Ja+Y0rCzVop4g2I/fFgSzc2vXT6eyYhVAfrU+NfHFIifimP5+bzU/XEsrfxSBO9wNwzd7qNYEwdfARjK6xGYY/1o1hd/AMFruNbGBilT2rwXq6+/HbDJL0M77zmGUOhuEolFAL2BDiWwXQCfiLLIEma7SIMNbs0h9Ie7RIpWqm5TvRB9Nt2HVZVOYf1WTEeQRMcRjpEQHcPsTgT9+BCgVjofV/Rfv4NCcmIVM12nEcWmvyGkCspF6lciWKtm8pnvv4A7WIRnvv2rJts5GaM7mcWKNd3XCrAfeEnkbZ/F5d15hLUoq2MuHYdEfv95WPaxMG7KOWsRym4/lnJxJVZzUTXNLMaHWQ97WkQ0PASrLwU4RCjt+uitiimcFTnnRqzk43sAjbr5APxAJ4rX2ABC1hMQed/3Jzew6G9H0Ti8FcCcscxst6rneG6Hg/UvqhK57COmklRcw57lsiokEULpGuyiTv9oH2fF4QYYLr5FZN2V7OtXr0KxcXuJ+RoFhiIjKDgW5YZ3edhvA+xSCcDq0g9NTrGafzpKhdF8Z/oS3O0nG26vyPX/g+t4pBd3eHcT9zaKCOWV4gHy+Ck09L4fspe5DN6H+3/I70XYI9FUkaWwSZYUIVzQfgiga92v3oUqfv7iXSiC59aKbLyNdXizzl7eAOGaXc8A1tOXoCCI4H5//nZzPpd9mN+3HkAhCxSiSCVjnMGOI1RJFEFuxCMqfdOOR6K3mZDNi3exHp6gmW2xaD28DNGRNYOdeJJsDpSdYJFkfXnydHOz7OrpkeaREQklEuJzOKTQ45HgFIj/22MKxE/FYbVRXnTjRpF1XxS565sIwMoZAEsqYRLNMimEVV4p33P7AHBjjA/jUmvcrApevMT3V12srKdqSlYe24WALm/Amo+MIdANL4AvH+XCAMWiKjNeGyii9KS/CFBxuFV+9sUib/9vvApN20UeuZXrRccRFmV1uNi7DossE2VdRkVWXQSoaBrA1NvyehDf8wI57TmV3jLcS9c0A8BFIO7seR6ArJ5NDLOvXdXaLqS05fE9xHeN2tWRUWLDsXHc3pFRFJqZywH66ctJs4qMce2xIcChpAaBvvoykaY9AHg8ghtUz4mkdP4e7oEANSYw09saAZN56yCKGelLRtqXMeqDcBr2bWSfl5wDWBqFZ+IRysBabViwYwPUvy9rQKk77QqA+JFb8RIMdgFk89dx/QWnizz4Y+bicIpoQaxPoyLguTeJnHEdPdKdHjPL4eW/stcGYfHgZuLRV32CuT79J/aocgagGCjES2O0Ty2pQbmYdP6t3O+0K81Wp2/mkfEGiBnveprz4s+Hla5nOANGFTxPkGe3WrGQM2n2X7NMsLYVcS0e46wa65mKE7t3elBGc1lVja8MwBvpQ1nVRDUj2j+hQ5+o31kmv5v+fFoJi3AuDPLgc7dR9a11P9b64VfxvFXONIsUiaD4hgZRNEV4x5/+s8mfufpT8GY6j0KwGx8iDGKxQoTTc+TuuxVj8xO/Ffn1JznbvgLe32mL5bGmJvnboUNS4vXKzMJCGYrF5Lr58+W0mhrZ/eqrb7wvU+MfGlMgfqqP4moFtB1YX/1tCG+DnBMaFEnERcJDvOCzVk7+ftMuLG2XV7WrTKCF736W7xsVmyqmI1zzihE2ZXUI2vJpCBY9A4PY4cbqeu42irDMPQ1Nv69VpGEBv9cVYDncCLzeZqz5yz8CSW50gOsvv5DmFFseMnN05601+4Ib17E7zOfpbUVYP/VHhE1pLfMf7aO4zOINfC40BGtZhHm8+gix8jmrCTHMXgkw731hcgUxu4s1m7mMePaxXQrI24kPB/L5XMchnslmY45dR+mqFh2joUc2jUDXdcGyE1E/gH0+/ULim0bMsXEzgGqA+MlGzRwE+cZ7RL73TjPF6MYvc59kDIKX043VNj4MGJ5+NWv41B/Noj+pBDHZ8gbOk80uMnuN6fbuOS7i8IqUVqu84lGR4gpzLgbxsnEL8zaKs4RHlRXoFLn285Q3PXAEJXDRBuLGYwMAqdNHLH9iedPeVpSPXI79KqyQ1424Ih96gyqeniVPemzQ7IJns4ukM1imbY28F2P9eBEMguKzf4EJXzWLYjbZLHNPxrmHUd2vagb36Ws1K7AVVgDoBeUQ8Yx3xWoD2B0enrOgTOS525mfCKTPM69lfVv2815qFlIRNQ2SZCquWsr24E6PhAgZOdwoz31tnLN4FOVo6bkoEU/+AUB3qLTCh34u8h7F6ZizxnzXExE8RgYR1Rg2B+fR4xcRi0jNPBGrTTa2t0uF3y9uu138Tqekcznx2O0ScDplavz7YwrET/UxPgxgHN7GC7fkbFx/difdhrY/IaLpaM43/C/u04lDz8kkwoymAd6xcQSI3SlSWafydiMiqYDK363BWm/ZB7Ctvdx03dodk3sxZzNYH11Nqt67BuBYbSI/ei+/zy9BSHzgR7g7tz6OIA8UYUH78kS+9RTxy0d/KRKyYBUGS3Av7n4OYbvlIYCo+5iKXSryn65j3b9yv8hAF0DQfhgGbn4pcz6+R+RDP8UC6z4G0BVWmpaY3UWsuEj9rLCC+fUcJ14ZGYHFX1xj5twvOANQGO0HxPa+wLqM9SN8rTYAR0TFWL24RKvO4NkMQpvViqI2kbtwsrHjSch2RknaoztFbv8/kXf8r+oUl8UCnBfE8jr3Jp49k2Z9jNxjh4t7j/abQLl4A+7mkAppiE5HOocLcF18NoD94j10lRsbwBU8bTHFZtoPQRIb7hV56Ke4xS96n0h/TOTq32Opb39S5Jk/EhZaeCa/N6zs1gMiv/okniFdaFbymT+ZNb11nZrwO55kbjVzccV3N6FMLD4L/kZcMaoDRSLaCN9r288av//7ypWfJBxVWs+8aucCxjYH5z+vhH0JlgB+hZViutotZk3+xldY22hIle/VOEduH8rJrmfwSJTWMY/tTxCKObRZ5V8nsLiXnovFn8kSDnG4ma/FynV8eXz20g9ibUdGAfRpS0Se/gNKk54zOQ7BYhTPdBIFd6RHZZLEOSeGAlhSw/8jY1Sl8+VzRjIpkRduF/H4pCwyJAPeAhG7XXRdF13Xxf5moYKp8U+NKRA/1ceP3yfSdQRgiYdxrV18C+5pEfJC11938vQnEQRscTUWZSbFH18+VmXDQjNtZnwQId20E6G+4Xos993PIlxb9nOv0jrAwehLPqTcgOkErmxNw+pxekVu/TgCxO1XFb3mQC5auB5hm1WpQ7FxrBp/PhZyoBDgTERFXn3MzCN/9RHlQhzCCkvFcPXGx5UVMyzyxB8IORSUIXybdpjlVyOjIi/dR3pcbzP39gYhhe1+lvutvQIB+OTvzLxofz5sX08AIXh8L8BYXINbPqlc5iO9PMeMpQC1UXQkETGFsjfI9S0WrCmn8lxkMifvXnbi2Psif/vyuWdkFIt+oIPY7PbHRMQiIjokLsN9a7Upq26UUEwmrSzPCYQyPcdZ8QZRclIJzovbB4g9fwfCf8tDplUaHhHZ+TQlcVsP0rM7r5S1eO52M85rtWIVZ1JY59WzAPnxYbganiAFUIZ7SAvTLChCd31T5Et/ZX+P76HanFHPvb0RpS1YhDJitWNx7n2e85W2Y6larKpefwncAqdX1SrQlJJrUa18x0VmrGCOTjcgmFWZHKsvZQ8Pb+Vd6W3hXBu9DLJZM6wQHUN5qpqFYuDLN2P+Lp/IlgepteBRCvPhrezLUA9k1FiYa+jC/jUsgm+y+hKUxrlrUVQe+LFI4yaeZ6QXpaqwQvUJGAX8tzyM8tbWiMISGhKJDJOnfs1/c/+7v4V1f3Qbe+IJsLfH94jc+315r8UuD6accnfeLOkXm+TlF0mxZ4L3ZGr8W2MKxE/lkc3gpjWEmt2JkCupEbng3SKiT24IcrJRUCbynu9QDKRlP1r2ovXklxrx1NAAMeP119J7O5XACvnODXQtc/uJq+1/Efe51cY8ju2C2OT2YsnUzqfQzPgIQrSrCWvVE1BM2DaY1DOWiqy6FEAXnXv78805V0zjz6YHIJEZMT+3It+5vAir8SERPQ3IO1wIqYF2hHo8wr3Hh+lWlUly76f+gMBbfSnPMdILiNz0Ne5hFEMx0q6cbnosF5bD2vYGsUarZ8HmfXoXxK3yBp4jncJjMf8MQGb6UnJww8OsQ/UspbAUqC5gHVhC89eqNKO/M7wB1iw8goKUiPHnyd8S43/HlxDgBeWTu3NpGlbr/T9CqIeGANa7v4W34qx3cJ1gEYQ4tw+FMZVg/RsWcr+W/Sgluq7SD+08f16ZSHUGd3zTdizDWAhresVNKA1/+4GqgufFgj20hf/ryoPQ324WAhIBeKNjrKnDyd7anCZhLFCEZ+TwVpHe4ypLolykbBoKby5rss39BXh2nvqDYqTbcX93HWU+/a3MYbibeYuQ6RCP8L2uJs7LjCUoevf/AKXIE0ChKa0hJOUNYh1f9hGepaAcD4U/3wx52J0mD8Dh4tlG+nin4mFVxKYcZTSb5fr5JaTMiTCP0IA668UA//gIynD3MRW3T+E42PGkiM1lpnD68kXmruY+T/4OBczhRtnqPkpYZ+VF7HMmLVI5XQKjA3JkOCyV2TZZ6LBJLOiSW3fskG+fc87fP69T4++OKRA/lYfFolK8UqooxQgCJjY+mSBz4hgdEHnxTkhnVbOwqm/4X6y143u45qqLeYGNbkvn/RcC9aGf41pzuJRVXolg03V+vv9lBIrRGWl8EJdrfweWQywsMrOCOfrzVWW4gIoRW3AbaprI+reLrLwQRcUbFHn55cnPkIiJ7N9IzLK/HRDJLyVXfnxYRIbltRaVHj9CquuIKp2ZVczuBZDPQoN8rqgSV29vM+voL0QxCA3yPLuepQpXLiuy7HzKrRqA0XkUprzVQXhjtB/Aszq4f/Vs4qqGUBdBsbn+i6zF/T9S6TtZlALxkEc81IXlVFz9+iYYJxvrr8O6az+ocpiteAOKq4mVf/DHb/zd8noUupZ9sNgLKlBS9m/k3ovPUrXbQ6RpdR9DITGKmujCd9sOc24sNp4prxSLt7xe5Pk7cScbNfsHO3n+vlYFdnXMxZ9P3fsVF7L/uazal7DyKmmcr5o5JicirxQgajvAfV0+kUQYj0z5NJSMoU7msngDruzhbkJNBaUAcUktYJtOohCuvUIV7BkGzKJj3Lu7SdWg11Xv+k6s1K5jkBcXnsneJyJ4qnJZMxUsUGhmH6y+FDDub+f/VbNIM3zlAVz16QSg73DDMs9mUE6yGX4WKEQ5LqkW2fMsyp4x9ByKViKG1Z2MAeBGuKvzCM9aPx8lJZPk/etrRWEYaFdppBZK2s5dJ7L7Gbxg40N41GwOGek4KiOeWdLgdon48yU42CadwVIZiEb//nmdGn93TIH4qTw0i8gF7xV5+Ge420QDyHY9jdv5xN7CIsRhf/1JxVothewTHkFY3fs9wCqXRTi866sIHV8+Qu22HwEKpbVo4kaRmVRC5UrnsAL6WrEwclkEdTqJNXl8N5aSvxBrufMoAtobxKK59INmfFMEIXnoVepde2YiDOsX8Lun/gBQGnWdR3upCb/sPFyosShWSiaDsGnZzxrVLQAM7C6RI6/iJXB5uc6hV1EG9BzPlcth0cy5DI/Dc7ebrPstDwPORrW4HU9BVgoWUlDE6WZegUIqlO15jv25+pO4P3M5gD1QgFX1nu8gON0+PCkvvcQ1KlV+b2gIj0EyTv366lknPxOldYCl00Up07wykVya7+m5v3+m3F7TQjW6aRVVEVs/72YYzRvvBhiu+ayKp/ahwNkcgPhoL9bpaJ9qt5nGq1Jai6cgHmUvXF7Ab3wYQubEkc2aQJrJ0AK2YgYFgPY8qxqjnCFy3RfMmHmwSLULjaBAGHXjfXkAujfIGlfPhs09d43pqg4WEwcvqzcbt2gW3qfpS/EMrFIpZOFRAPHsG9kTu1PlySfMMMjFt5ANsH8jCo7FSsZE1Rm4vQ2FzPAIxEIoWue+Cy+S2w8AewLMd9czqlSwxjMYLYXdPlIhczkz1U0EZSSvFC6ANx9FqWYOJFajN/1gJ+9wQTlhhqPbUFgKy1UBoFLOQyJG0RtPEMLpNf+NAtD4ikgmJd50UjQRSdmd4rBYJKNromfT4p1KL/t/MqZA/FQd2Swv/1UfF+lr5iU3cnTDo6QKrb0cARMsAtCP7QbAj+82AaekFmGV/ivfN+KufW2A5soL+X93B0QdoyJYbzMgEx1D2CZjWGIjPYDFQJrCId58hLXLLWIrxbqIjiJUS2uwDOrmiyw8gzSqiePIdgqqBApFnGlSrq7/H4Dq2C6Vd11tWgxLz8Olf9Y7+dlRxQuw2bGy6xfgNr3kgwiqZ/4CaHccxoLPZETGRxFo2QxCbuGZpOFsvIfncDhVMQw7AnzpuWbfZaMgjZ5TCk4SJclqFXFVA6Q7n4F9fGLHLn/+5JDBxDE+InLn1xH4FhsgduUn6Vb3unOhLLRZqxC+mkaBleEeur0Zw/jdybgSTg/C/NhuwNhqR+hns1ht9d+c/Pm+NnLsjW5YwSKziUxoUCQ4G0uv4wgky4JKVY/cJuLzcP0j2wGXgXbOxkgf8+tpBsgGOlBO3vtdkes+x329wcm51l1Nyir38ww1cygoFA2Z5VlzWZ7lL/9r9oU/8xpcxLf9H8pSsIif53Lcw2LBde7yEVqIR0S2KE9PoJAzb/Sp13VAsWomf/Y8x7lLxJQbXhdZrNzMqQRnOpVEuRzrxwNy8zdElp3Ln7ZGasq37ONe4WERZx7fDRZjuaeSXHtiMRi7Q+Rtn6ZYk1XF+4uq8ab5C3gul4cUyLYD7Mf660Wu+TRhoid+x3rGwuxFOoXSXFaHN+rKj3PP1gPik6xcr4XkjmyxWMbGJGN3ytLKajk6PCyZ3D+gOE6NNx1TIH4qjoEOkQd+KpK/QOT7N6tSlgJo7H4OLb37GCVTa+bw0i45B2b0SB8AbrFiEQ12qZaeaYDJGFYrrjwRYpN/+TKC1u5A+HqUxVhYiVs9FlatR1OAeSalanirghcLN+DK3PAOmMuNr4iIRvx42XlYl7rOvI389IObzHrwFhuW3pHtuEZtduXmHFKlXctESpSV7HAiQIPFIoc3I6DWXI4gs2hYwm4fZDVdF6lfCPD1tlCm8qx3AAJ6zqwC5stjPVJJLKSRHoT9I78UueQWsgJa9gmM7TSfDRZhheWE9ameLeILonCcrO3mG42mnXhQyur4f2SUdLmTgbjLg4v00BYIXgNt7Pfpb4PTkM3g0t6/kc8vXK9ap04AQ7ePeY/2oRDqOeLgt39VtcQsnHxPox93Msa/jcYiBWUA/ECn2fY1GRexKeKjLa4UF53zcs1nCQWM9mG1axpKQESRsESjE186ifJ5xUcBtv52eAvP3ibS34n1HBnDs7L8fOLaHYf5/ulv4x3IZDhjmbTIxnthsl/wbrxRg52A/aL11JnXdZSX5n2ci0SEvPPRXuY/0kuYJhoiNGXUIhju5uy6/fwx+CntjTxfVrHWjXmM9uMZ8BeQnx0oULwLj4iu4cFyuDjrwWKR06/iO6kERZwKKwD9klrez/xSChM98yf2ZqCNZ4qM8f1Zq6hcl4iheLTshZS49FwU1l3PqN4Beax5sJia9yO9xNKv/hTvaudROecXH5YZfUelx+GVjRVLZHf/gOwdGZMNmibHR0ZkesEEguTU+KfGFIifaiOThgyUSvLvI9sQelllHaaTys0WRYiODQBar9wPuBls58gYQGO1AvDVs3BRi4ZwiYVVvvftsL5H+1W3rF5cc9ExmO1VMwFrI46sB3BVx8dVa0uVijXSjYU71IWFN9KHcDqwCfCcdxouurFBBKPVitWeUelXoivGe5L/rriQLmjZLL/LL8d161eWkTcfy3Xd20TOfzfdtyJjAIPLJ3LDl3APP/l785lr5wBeBzahWEws47ngTATeqw8huIoqqcZ2dDuehMUbsHz2b8TlWreAdbbYAIT6+YD4cC+C/Z8ZuQzKhzGMjIGTjeN7cEEnoqx13XyRD/6U/H4RPAF7njdjz3ueY3+WnWte4+AmSIB9bWZo4dCrAOX+F0Vu+sbk7mbFVShWBuDHwwj+ZEzVa08ACvEw+zfYydnML0Xhi0cIoxzeiuVosVKExunGE5LNoqwd3ESKndMDQD76K3Lc7/0+56R5L2uViHDfZBxP0nu+zbo73YSGfvQeM5XOZke5GB+CvPVf3+LaDrepSIiIXP5RPC8jvbjc566lNv7hrSioC89QhYwmEEkrZogceFlVdrPjDUklRb7/LhHRRE67nPdsuAfldXyIM9NxCGXiXf/H/LJZ1mq0j/cpm6aozozlKDEdh0n92/ww/BOXR+SDP2NO8YhZh9/lFbn8Y2QoNO/lPS5vIJZvNLnZ+iiNYzZcj3fKl48COdavUiGVC39sgLXxKLd/JiO1sUEpG+mQGb1HZGdqRLad9yGxhCNy54ED8pUzJ5yXqfFPjSkQP9VGNASA5nJmC8WxARGrBmDYhRcyFSP+nIwgFG0OXkaLlZcvUEiMbd463LtGha39L5klPo/uQLB0HAKYA4Vcu7dZRKwA7vYnIGgZ3Zc0qyIfqTzYZeeKXPQBrp9OUoIzHkaoWKz8u3U/VkJsHKsxfw3fHe5GeTiyTWTVu8mFz2YRpAXlyoJ2MTddR8i//b9RPIa7Kdyy4XoEUyIK8I4PA/KbH6QTVGkdoPv0HwGHeETkhbuwDI3GFLoOWz+VAHREmH/HITMjQATXfMNCPtO6H6XCGwTYMyk8JufciED+Z8a0JcTgR/sR6pExKqydOIx2p3mlgKCuEwNtPQD5zBsE4D0BMybrUT+bCOK6wOYWXcVasyZzuq1R5A+fF/nK/Wb+uM2OVbbjSe5xaCux1MIKkWUNWIKhAa4lAtCPj/DvQuVaH+pCodKsWKA9zezHQAe/H2jH8+P08L2CCjgVj97K2hZVc8Yyiv2fX4aFWVrPOSuuMgG5tBZypy+ftRnq4txXzuQaxrswcdgdk9coOo5b2XD7H9upQj215mfOuRES2IGXeWfSKdZSs0IUe/Y2VfI1YnJU5q5mzoMdKJRLzkapDBTikRgfgSdx8QdRdu/9Hp6a/Rt5x8unsU+//bTIx35Fy+CaeSjFYwOc87NvQHFPxUVu/xpg7Q1C8DPCCGX1vGMF5dyzrxlPli6EHIzQl67j8Ws/KJLNiE1E3JpV1h14SganrxBLyVwZTyT+sXM+NU46pkD8VBtuH1p9qE+kVCPeZbOj4RvEJY8SZmN9xMxCgwB+Kg4AJMJYGqsvQ8D9+hMAy2Ufxt123/e5XrAIi6rtIFaNI0ZMzuHCBVhaj2BZeREC8K/fASRTMbqNWTWsm2mLiMP/9TuqK5YXQZGIAoxWK/fJ5hCWR7ch6IzCKi71+VwG4GzZQ/y0fBoWnQiCJRnD4nzbpyavWSLG2uzbqKpdJVAYzr6B6/ccR+HJK2HdQgMid3wND8FZN3DfxlewrOIRXNUGESsySnOV43sApPwSkXPeibdksAMhd/rVEMN6Woi7dh9nrU+MR48N4uKPR0RsVWaKX2E5ALHtMfZh3dWAWePmyWuQTqHwDPdCTKqcgSs7EcMVetH7ALdju0SkiOsnongxJo5F60Ue+CH/NjIfRFR6nXCeDr3KcxnD5eH/p18NQBpkMauVnPjmPYqMlRPRbPztVOxqqw3FybhOeIR5nX0jIBIPY1Fvut9s+RkaxE2eTmJBDnWhuDTvxVWeSRGiadopcs+3uPbqS3EVn3YVBXFeuZ/zUFRNfv1QNwTDiRUATxypBMrUoVdVI58GtXcDMMqv/qT52UAhxWN++VE8M/te5FxHRiAeJuO8q3PXKk6L0yz6ksvx+62P8Kwdh3hn84pZt+dvx7PVdRRrWLOgxI8NcKZH+1EcNKsZKrFacZeP9pk1DnqbWSurzaz/4HDCdj/vv0Sevw0+QP1C1mWoEy/M6ku4ZvcxDAvVDlYTTSy6iK5npa55hzQXzpIVFRVvvJ5T4++OKRA/1YbDRa3rO77Oi5MIEwNtPcDv3X4EQO18VckpnzhseATtOZVAcIVHAPZcFtdieASSzXu+o5qWqKPj8QPQI72AWiLCNWevwWIa7sGFvehM4qaf3WB2dxKhk1cyjlXffhhANPovp5LM0eh73dvCZ40mKnpO1bYuUkVfQlgMnjxA1GY3041iIdzbuRy/S6e4htF044EfYz0FCmjy4XArktk1KidX58/R7YCg2497/77vkQGgaQi/yNhka9ztBwyGOhCkV34ct/lF7wWMLTaR770LcNF13OIP/Zw1uvJj5r6GR3H5xyPMo2SlyA/eLbLkLEA7kyZ84fYT3tj3InvmcIm857u4Th/9JWtosfD5/S8j0KtmstZ//AIxYpudNdI0yGIn9mOvnC5yzk3E+y1Wkax6YIv1taJkJ+0YZoz8EjPNsPsYSl7HYdU2VVe9uSOq0E1MZNk72fOBDrN+uMONl+kMRcbTdc7GjidV+KZFdRlTZ9lIn6qbR8/w2rmswbN/MV3nT/0RMqPVBrgbNf8HO4irH3yZ673/B2a9cGP0NHOt3c+Z5YmtdtPlbneZNcsnDpuDeZQ3cLaMMruJGL/3F6BAz1zOnPrb2f9ZK0X2vYACPdxDCGiwE8DNL2MOG+82Mz00je9lM3jC3H44EXqO79gcKH3eAO/F+IjIjscpDmOkpmoaKYrGWHQmilAiqrgLirw3kTsTj2C1tx4UyabEolnFqYlErXYZ1C3idzrl0rlz3/isTI2/O6ZA/FQcM5aKfOr3IhtfwNpq3ktnK5cH4TLUDfnI6YGxvew8kd99lpfPZgc0DddcrXrBAoUIs9AggPD473ipM2msZLuLe2RUutAr90POKijDVSvCCx0dNet9ZzNYtZsfIg0mvxQBnIhwv3QSsGjZJ3JsD+AQDyMowsN8PzqOpp/NYFVYrMT9CivMOvC6jrCftgj3atNOwMAbpNHG9icB91QcZcSoUhcZ5fsNiwC7ziby2Z1u3OIF5QBLLgt4tx0wU58KyqjjfvAVBJxmoU3qbf8HiI/0cM+8Yr6nabiFs2nVfGSLyMXvN2OoLfu4R3E1ndKKluPmFx13bDoFOI8OwPTWrChK8YjIbz4l8u1neM6iKgAtNi4iGkLbYhNpegWFqPWAWXd8/umAkM3OdY0e5/ULWbfu4xTniY5h3VqUtVcxgzX7e2Pro1jPRvhHMpD84uM8t8fP/RMRs5WtQZBzpcw69yKs35lvx2pNRETu/IZqk1uq5t/H2bzlx2b63QM/NQvO5LKqUU6x+cwjw1zX6I1tc8IReOlekQv+y7z3cA9epON7mWMiQme91gNYt+UNuNXnrjG9J8awWFCyBztYc6O9qdPF3Euq+JwvH0BddQlna84qkVs/wXobBMtcjnM20M75HOw0WeqzVuEtcgqff/vncM3HQjyPKC/KnDXqnVHX0jQUn0SU8zdx9LZQbz00gFFw/n+9PtRQVIVCMX3Ja21kx+1u2eevkNvKl8vlyaR0j49LfX7+3z8vU+OkYwrET9URLOTl/eBPsLDK6nkpm/coK8tKfPmxXxFPjShQLK5SaUDFZj1nu9NMIXnwZ4DYvLXEw21OyEU7nkDotB/GSsqkcNXb7Aiz0lq+5/Ti2oyNK5ddCuEaGTVTfKw2gPSyj8Cw3vsiz1A+XaRiJgJ9fAgBMdyNAiE6381msF4KymHen/l2U2ge2Y47uazBtJwf+hku/tkrcSMn48SrY2Gqz4mY7Sr3vYTAqpzJs+ZyCDuLFYWoqFp5MFSMeLhHuXOzKp3NwrP3tzHfbBbhmMuqZhm6qRg172VvznmX2UVLBCUmHkH422y4ul/5G6EPj59ymAdeUqmBmtkH3ahUl8uybpk09cAtDhSzaAgBXFRFOOGZP5M7X1oDae/x3wAIIjz7dV8Qecf/4DnJZvFKjPbB1r7xyyZT/o1GeFTklQdRSuJhPj+u0rLGhzhvyThKmhFSsbjN/vJWh0liNIammVXmdJ0zrmmch8gIysEjvwQIl51LOKh1v4gohTEV57ODXZx1wyOkaZxJXx4Wa9vByfdtPch65rJ4tdIJ3rNYmHj13hdYV5ud87nhuslAfsktIg/+FOXaG8BzMms55+rpP2F9F5ZTPMgIjYigqI71q7LHw9x3rJ/nCA3xzq+5jHOkZ2G0r74UhbmkhmssP1954OIiz96OQun2887bHPAKXn0Ez4Dhdr/iY6Sk3vd9vA15ZazjY7+iU97EkV8icuUnRB78iUg8Kv2ZjHwnME92Vi+RuCtPYum0fOXFF+XPV14pljfrNDc13nBMgfipPgorsPx6mnE7dxwmdaz9ENbg+DAvq9Ui4i2gElt5PbWbO49CdAkNEz+32ESqsny/cQtkpemLITO98gDkn57jgIzbr/JfI9xz9SWq5eOFIo/8QllVGn+i42bTh3QSS/9jvzLdciU1AHKxsuDDw7DgNYHAVFKD4lAzx7QyI6MIncFO8r7dXgDWajMFqCeI5W210ZWpeY+qOa0YtgdfYS5Gi9bVF3PPjX9FsOYyWKsGMzg8oqpX5RMfrF+AkjLYZZZytVpxIeeVyGstQDXlhs6o+K3FggLUfhhm9bu+yrU8fqx0owlFxQyzUM5YP3/aDwJ6/a0oTAGlzFltlFX96ftRgqJj7GcsBKEum8FzYbVjlYeHEOQdh0W2PIpHp7iGNKPGzQD8JbdAFNz6GCARLCJj4NAWLPGJ3cVOHMkYz2lYkA4XQFU5A6XSIFhGQ1j5hiLpDarYexZL/oqPTb7u6ADno3I6QBweRlHKZkWK61C2nv0zNfFjYfbGYMl7Alx7VKWE6SMoNCIoaC6PUhSqzPvFo1i+48Ocb6NueTTEmU4nzdLEXUchu9XNw1I2RrCIPY6HRbbvFtkwwcMwbTH76XRjzR/fw9zK6kTOu0nknl6U00SE85zL8AxDXXgdWvah8BSUM4fe45MzB0R4N9xekQvfTf2IrqOcg7NvpFd6VinWVhux+UyK2Hg6ZbZL9QZ5X1ZeRMbDREAOFKLsT1skQ0ODsjjULy1er4QcDrFqmhweGpJYOi0+x5twDabGGw7L/68nMDX+w8NioTpUxXRc2bkcQsMTAHQMwPIVIrhTcchQu57BajWskVwOYBwdQFi5ffxeRJW2tKMoGD2wExHcvLGwybbWNOKR7gDKRXmDEs4JBOloL+C3+rLJcbWSGuY/0I5Lr6yevN3qOSIrLzBzqssaEFaj/SKlDTxHeyOFWIzrGNZ/Lod1Wlihqsi1IawKKvAszF2LxTw2YM5D12Ho5pUootY1Ihe8RwnuEL+3u5WFLiI3foXUIxFVRraA76cSrFM8wr9L6xCaOUVYmraYP4UVCN7hHgTh+usVn8CPMmC1IaytNsh+BzejnFkdAF90DHCZdxoW8sLTRT5/B9Zv/UIs0pIaSIYzl7Muwz3sw/QlAGtBBfuu51A+Bjq4v8eHKzwewaq1WOE8lNXhedn0tzc/lwF1Bkd6CVUkVLy45QBrYXOoMMWoUowKzXXNZQnddByZfM0Dm2DG3/cDFBNfELD0BlnjyunE0we7UAAyaSxbuwMi4af+wDuSSfHdpedSStaXJxLqRyH05ZtFccZH6AC3/yUY3KMDnP1IyIzda6JSKTVALzTEn5O9p0Zr1BN/7vIA1H/6IsVe7vgqBLSiSjgqqy8jn3/ZeXie5p8Oa32kh0yMkhqev7QeoDWyJU4c3qDIdZ8X+fAvcNfvfYE5i44Xx+1XHocchDdDLgz3UIK5/bDIX79LnQGjh0BvK3PuPiISj4glNCQVoR45Z+/DYg0NSU7XxWWziWeqetu/PKYs8VN9xKNYvv1tqvOUIo4ZgtlmQ+CEhyE3HXiJPG2HC7db42Ze/sJKAKPjMOCbSZmWlsWC+9blAWxG+7B+2g4CRmsv576HtxFDzWVVL2I7gtFiwY2fiGBtbH9M5PguLI6F64mpX/VJmNkjfVhrpbV4CZr3YXWWr+HvgjLmMNQuMm0hlmHnYeZZMwfr4qV7FZEqjTKiC9+zOVQlrVnyWi9yiw2l4NVH6R7V2yJSOUuksBQ2+KzlWLO18wDywU4UE1+QdV5yNoU/YuMA+EifSfoyFKhclrmN9LEPfa1Y1cEShKTdwXyf/D0W2bTFgObMZSJGr/HwKOutaXze6mY/cxlAx+lmDwoq6G8tGvFdQxDnl5mxz8rpKEoiSukrBHi6jqCw2B1YYJkMKWpOD5ZWNsN+jA+iPKy7+vUEMBF+9/AvUDha96vysbMAju1PACaJqFkr3u6AH/Dor/C4VM1gbQIF5jWjIYhleaWAp9H3/rx3c6b7WpU7O43iUL8Iz4ZLhXd8+cTKL/4AzHSjmYk3D49HWT337jkm8sP38DO7g72vmM75bdpFul9xFeTEdMLsXWD34O3K5cyGPMa8jToLtfNExH3iagGkT/8Bj4qxj1seVgVcykWWnkVoorSO9RrsJNf/yFYs8VwWz4jFgrK89XG8CbNXm2sYGkIpz2aY8/6XeO+P7Wb+iZiIS5+Q1+9DWdj/EiTKeIT59bWiIM07jbTLZ/9i1hOwWKUhm5VOb4V0Z0RaBvokU1opH1+1asqV/m+MKRA/1cfOp83GEe2HVYMGkddoxLkcbrxUQpUE1YhJ+vJVx6kY4FA9B7CPhcwiD0sn5MWWNYiILpKMmkBidygCnZdY+nO34TpPRADWYAmC1V9otvo0CrxYrAiZ1v1Ys7NWmHnZxrj0QyJ//KLZmjOdRPM3eqDnciKdhxA4u57Fwl5+PoB993dU20WbGVu96uMiu59HyKcTxILHh0X+8iXAKRpCkPc1i7g9CNc9L2CtWW0oAdk0P08n6fJ01SdErv28yIt3Y+HOP80sumO0s8ykVYGYKoT0YCfCccZy5lxQDoEomxbxl6vwh13E61F1v714JixW+kxnUiKeIp4pUES81e1lPwvLYdcPdgDyVjvzPb5HMYnr8JT0NKPI5XJ4APY8jxckk2aOfe2sUWiA5xlTaU5GPDuVgA3/ts+8vjHLY78mVDM2gHKYTWHZV8/mzDz6a+6dTauysIorsfZy5m618f/zJpDLouMoRUZjH4eLdaqZTSGdu7+lcrGT/DxQgKUZDfH50BAgPjqgCF05rjk6gDVfMQ1QHxvg2jOW8W6V1YsUC67ziukiNbNEzr2Z+T30UzN+7/KKxCKsZfVs7plKYLmO9nNGW/aJzL3i9e9wKo7CZKQcWm1mDQUpF1l5Mee0cTPnXrOgaLv9rFfbQRSHWAhlcKSfVDCHi+I1c9fiURjuEhEL1/UXcI3piyGCphKIDH8+IbO9L+C9WXcl/66Ybhbs6TmuSrP+lnmKqHdMl5TNKzNSIXnEWyCzshHxWCwSz2ROLrumxj80pkD8VB+jvapbUxTilq7R8MLpNfOrjRKo5dOwILtUdSgjRSenrJLyBgqkrL0cBvzE/tVnXgtIG1a8vxDB0d1MDvi+FxGyxdWA7kAbAFo1G8u6rwUL1uj6pIsqTVqCkJi1YvJzRUMIivg4VpxmRdCl4qqUpU/kwEaE86wVWARNOwCV0BBKhGGhl9dTwe3sdyJgBzoAlzmrIdTFIypPXaXn5LKK0Z4hNW7RBqztO74KKAaLIcq1HYTBXTMbBUEEV+7t/6fAQ1PFWUaxVgy3cTrJ2l35MSy7Vx7AOxEL49KeuxaWseiAt2gAbEm1yHGXSDyGsmazU4e8cTPg6HRzH7dfdZpzi0hOeU96RdxBVZ+8E2ty/jrY8y4/zOaz34mSkIjCHwgWwvjXLLjB+9Uz2F0oDfteIv1uosWczbAmVpu8Vt0rFuIsHtlGSdtdz5qx/lhYpaId599rL+e8lNRMriUfKOS8tuxTNewVx8KXD7Cvuljk7m8TSy8oQylxOPG0uHxkU8xaIdK6T2TZBaRmGm5jo7zwSD/P5/RwRktqeOaaOWYluvIZhBIioyKXfRTPQGejyMEtKFzdx/GMXfZhlOuRXjPFzRvkGdOpybnobj/K12gf14uG+H2+IrnZHSIXvhcSpJ4T+ekHVa9yjVruBmlvRJHgmnayDrmcyC8+jNLR+Iq81sLVSDGtno1F7QnyrtsdyIZpi1nf5n18J6+Ed8KoQBgd4/k1UW1nFXs+mxZLLiUDzmIpslulKDUiLqtF2kOhf0iUTY2TjykQP9VH9WzY3f1tIrExLGWXF3d0Okm82u7i5R7uxuqxWPicLirVREOAzFsj8oEfnLwphttD+c4f3sz3fPm87OERlATRTCKbkT4zcwXNHJ79C/HpgMppbT/IPIJFWAQn5hwPdIrc+12spJZ9WEwr52NZ61mRd3xZxOsHLOeuA+gPbwMkelsAymRMxF9EbLllPy5nqxXgnrPavFd4BBAfbFelOmOqfKxupiYZqVcNixHshqVtVM2bOIqraOu653ms2oVnYHn/4iPEY0VD0Vl1MaDSfYyqWtOWMH+jxer6xbCKS2shGL58L/c9/z3kO1s0QLl1r9lZzRNEwHoCPLvDpZrUhNgzp0uxshNY6os38Fy9rer3bsIb4RHIa7NWAhaxcYBdz4k4vCiEVjsAeOLeWawoiiP9ZsjC6LDlC2LZVk5HcRjpQfG0OwAKmwPFy8gNnzgSUdaz8whr7vSIfPw3AHVbo8gvP2ayzJ0e9qewnDWZtojnHh/m3KZinDtdZ098+Zyb+Djei/kLuGew0ARXI4e6o5FSq8FiwiMjPexR1Qz2Qdd5pkNbAGRd53Mt+7B2T7tFZYRMAHGLReSKj8P+7mtDKbriM2bHty0PoQSX1lKopmY2Cm4ywVoUlHM2D29jT/Qc4Q+bnb18+T7OXWE590snUfAGu3iuGUshED75e0DbeP/dPt6H6lmKRDjCdZadw890nTloFvL/dZtYROSAs1By4VHRPD7JaNapuun/5pgC8VN9LFyPJdeyT9WrjvNiDncT8wqWwCZt3Q/YRkdhnu54EsKKJ4jVER/HQjgZgBujbh4WecdhhLtRbzoeJcY72s89UgnFVl2M4Lj2c1j5f/0ubtZkHCu9+zjxVU+QZ1h5EcDzwp2qYM1cRerajvVQOZ365KW1xIi9QRHRAT+bHYsrmyUWPHs1Aj8VQ3k40dI3hp5j7TIqPptTTGmrHQ5AIoqgziuGDNZ2EEGbiDK3k5GYSmtppmGM6tmQ4F65n+9UTKdueyxsuncLyrGKDGZ5QblZwrN+Pn9ESA1beIaZIpVNqXg17szXmN3TFvEs0XFVAc6Bx2R8EHJeaQ1V5a76BBZ+1QzIYi4vzzZzhVkBcKADq8vlRRHKZbl/9Sx+NnFoGtkC936fZx3uJqfaZqf5TbAIFv0Tv1NhnTxANyYqbewNuLh7X+Dep18DcIWGIdjNXYNbV9cBVl1HQYmMioSUApJK8LwuL+t+/4/M3PVZq/AmtB0gFW/b4wBXfxvgfv3/mF6AdErkpx8gdJWMMY/Oo6yxJ2g+v93Fvs5Zw3e3PKJ6FmRZx5fvm3w+REjVeudXUFSMDItsFtJY11E8Sb2tIsf2sqaHtqAwBYpQZHY9jaJuVNfLpEQ0p6mI2hymbMjleD/e+WWeKVCo8t3reRd8+VwnHkGRq53LM5TWoSBe8xmUruUXiDx3B/PVLSK+QnEmwlLgD8rmwumi2Z0yV7Jy2axZJ9/TqfEPjSkQP9WH1YpLLZVA8Lc3AmpOL8J5yVm44Zr3IHiLqyDBfOPtCCKjnKm/8I0F6MR7XfExFICBToDZ4aIGdO08rMi+VjT4ygrKnHqDgMHu5xCywz1YGpUzyJsdH4F41N4o8vL9IqdfCWh4AtyzaqaI6FhOV33HbODiy+M5DryslIKMWXym8wj3XHGhainaQSjhZKPzqHKlK1ZubBxlIBlDOKeTpIa1NRI7NVp4ltYRR33hTtLDgkWAYF8r15ux1GTgaxolXlddrBQcO1ZX60Huk0qQixssRojPX/fGpT/TKT5Xp0C9vZG9cAZYT7uTUME7vshcepshRek5iFli4d8zV+ChaNnPXK/6JBkLwz0oGZ6AyJ+/ZBIEXT72IJVQlpwLUE4nRZ65GyUxUCiy6lJcrGe8DcCMjOIWr5hu5kDXzBa55YdYqHd8nT0a6YNFfyK4GSMZA4gsFhGLE+BKRPmdoaQYpC0DVO12VRylDcXVGxDxzsU71N+OklYzV3loVnGtRet5Zl1H+ZpY3MRq5frjI/SiN7gOiRjP5vKgXIz2ovTZHYRitj2hwhtOpZTufOPnnJi1MT4EgBfXqGI0dmr+Z9OqcYuNtfUEWH9fPsTJWFheKytotYksPVtkqId55rLwItZc+vpOeisu4iwd38P/568zvTXz1qkSvaWmon/Lj7nWjqcV6a1ZLBa7XLn4NDlbs0g2NCz7rSLuKWb6vzWmQPytMOasxlIZ6+dFnrmCog9zVgGuFsvrLdGLbyHmZXciIHxBlIE3Gl1NCJBUAtbqlVfyvT9+Ea3c4zerUc1biwxp2mG694KlKBUjvfJaH+vQoLxmSRtu4FwGgRfIJxZuEJVcXoTrs39BcM5eKXLWjQD2gZcRmKkETGBN41pDnaR1LTv/jSuM5bIoPwYTv+0gc7DZzaIrFhtKR4+K66+6xPy+UeWu45DZwCOXwT1+5ccnt/g0hObffkzudTLB2qQSrJ8nSFrRRe8X2XPw5POddxpx6/AI/3d6KMoSGUN4T1uMsmFUQ6tfQMy8WK29zaHSisRkM4uwHwaxsLeVErBFFXg8xofN0EdPi0hinLU/9100XDmynVBHb6vI995JnXC7HXfyO774xm1XC8pEbvxfkc1bOKtz1gDwJxuzVsK7iIbY38ioWX1sxjKUgOEepYxlRBaeB+AkY3x2YtvWgrLJRVUmDrfvjb02Vhu14f/yZbxPdgeKbLCY7+16hrUqqcHaHh8W+duPTHa8v0AkESd0Ew39/W52VpsKeelmTn14mD3UBUu9+ziKud2N16lyJu9JOom3bNWFIu/6Oor33uc5vysuglB54nA4ae8aHkH58eWZKXF5xQLDb8KwO+CgLD4bsttwj8iR7aLpWQnqWZH4qOJlTI1/Z0yB+FthVM1EoD3xW/5fMV1VrCoGiAyAnTiWno019PSfIMM1LIA8I4KFsfcFtPKSGizOe79LBTibne+IYOVbLKbbNaPYxnqO9CJfHsLA5sAFWDUDsBwbAtxTCYRgZMxkKBdVIbyCRaqDlUPkwveI9CdIW/Ln80yP3AojPFhMadndz4rEe834oMUq8o4vKcUgh3Xh8pBeNpFNvfpSwDebR+wznQCIrTZcmIXlIqLjtrRZRXJOUwCnkwhTbx6u6YIKLFRdh0DV3QQp6sSx73msGp+KFQ53i1TNEbnm08x3IvCfOOrmiVz1KVK1Og6rXOw+kXVXsWa6DrGpu0kkUIxC5S8QGRnArd17HOA3SngaqWYTx6b7ITDmMkqRsWLFxcMoV4vPwoI9uFmk8VX20GJBmcmksV4LynFJ73tR5LQr3/h5CspUjfQrWNd4xKy7L8LztOwjfrvkHIhX7Qewup/5E9yOtVdA3Brq5swtPpuwkUNxQQKFJ3/OgQ6Ax5tnlmrNZnCpt+xjPU9/G8pAaAgvzfzTUXb7O4iZF1ez/mX1/H7hepTptkZAM78cAI+HRdpHRBYrr8OfvkhWQ3GVOZ/uY7xz3iDKmL9AZME6PFoON+fEYsXTMtiBB8roQ/6eb8MRGRtA4fXn4zK/6lPIhb5WzvWSs2Gcaxr3e/k+FJJ5a3GPG8RFh+v1MuNkw4ipz1jKmXr1YZHtT0hSF8msvVIk5/v715gabzqmQPytMAY6IdssvwCQHR8SufVjCA/RiI9e/IHXx7tXX4qValiCRrzssV/Dyna6yZV2eYkRFxWqL2qQr5acRdnHh3+O8Og6aroXs1mRbBSXpK8AayQ8ikLgCaoUNTeWk1GcxeFGgIftpNXUL0BQFZSJdL0gIjrgdGw3ANpzDNA30spyOdx7NbMhk9kcyhr6oZmTPGc1a2EA+bWfxzp54S7c5oFiVbt9VFmQygqKhQD4tVfggo6N87tzb8JKSaew2Ac7FREsxtxPHKmEKvqSVQqPztomowjeREzk6btEIk6R274Cs7j8BACatoiyrR2H2O+mHaz9u76G8vXyvShc6TjnwhMU2fGUyv/1EFpwukUu+QCW/8SRiFEbP6Ms2tg4z5VJoQC4A/SP3vYI3o32RsDOl6fSlCwm2c3uVK7dvzNyOWqTdx4F+B0envHsG7n+1sfMHHBfAWekpI4z9tQfcfXbnSILTkcRKG9gLY/v4VycfePk0rYieCee+B17kEqaFctGegHKqpkAfFcTVuvWx4hni0XE5cZazStmvTIpPBGdR1TYqg+LOzSAImizc6aMVMfCCp75hTvNMqb7NlIXQbOoc7qGinnn3ox1PdjBtWLf4f3Opjk73oDJY/jIL0R++1kUu4oG9uPPX8JTVlzNPbc9gWKZVyLy1++pVr5OQmIdh4nljw/yLl70/skejImjt5U0SRHWp7xexGIRfe0V8kTxPHng8GHJjYpcaItKLJ2eKvbyb4wpEH8rjPCwGTMT4eVtOyhyxrX87PgeikdsuO713zXyvY0RGoQAVVCOsI6F0fTzS3CHW6wIEKNxx6wV5PPe8VUEeVEVGr6m0qnK6rFC5qxWjFYRufxj3OeFuxFuRr/oylkoAzYHZLKNd3Mdl1ek7myEdvM+/ra7EEqj/TChrXYRSSPADHexx09RDpfXLOe570XioRYLceV1V0HUCRRSBCS/zKzLHRsD5DQNMlv1bBjAFdOJ+eaXmelVs1ZQySo6ZjKyD2+BDGdYNAc3iTxzG4A92q9YvVauMVe5hp/5k8iRHSLTziX2eu93yfU9MY1r30aALJNinUd6Ybk/9Uf2wHAX730eS/O0q8wGMNd8BkvvZGNsAAAcHxYZGwHA0wm+6/SabSvHh1izgnKUicIK0+0bCZnu39EBXO4Ni/l811E8ATOXm0plZESlmI2rKoPDWLl//S73q5ypCHU5wHT2ChN0jeyBReu5lr8ABefDP8Pdb4xcDu/F7meZW28L3gSHiz3tOYabebDTPDtuH8rn03+iAp6ew2WejOOhOvwq+3vlJ1BktjxE3rY/nxr3Lh/PZqTRWazseWgIIA0Nmvv5zJ9FomHW2l9IIZfl56P0LjjdfI54mPrwsbBIvo+iNHXzyFC58D0oMEbddI9OJztfvrlfNjvKyfgw73GgEs9A52HeDX+ByNzTeGce+QVnL79k8hnpbRG565ucDRGRxk0i139RJK9Uuh/+tdi3vyDXFpTKgQUXSCyty32NjXLT4jc4b1Pj744pEH8rjGCxqenbnVjmbr8JzoEiBN0/Moye0Z1HEBjeAFZZMkbsuriazyw7j4IhRgpS2QThUVoLcBgks9I6hPzu5wDPR26lBeiSswC2unmUV7W7uN60xbi4i6sVYAxj4c9YgrsumxERHcskEVHs8RIIRRYbf5/9ToA7PAzQiCC02g4C8pUzsDhb94uIhhUYC0Mw0yxwBIqrRD77F5G/fps1tjkQwC/ejcVVO5eyrKV1kOgevRUFypdH0ZemXXw+rxh38FN/5PoF5WaN+Ko5KDirL0U5adpldic7so04ZecRlITXiHIWrMKm7SgDIigGoUEzNzk8gjUbCZGlYLGY+dU9LZNBPJczc6aHe7jP3DX0zB4bELEHze5yFkXuMnKrjW5uRZUwlftaqHxntWOpOxvZ180PkQFQWGZmEFz7eYDc6MTV3siexVU6W1YRDQ2vicXCehhFUEQ4mzaHqUAYoZ0TSZp7X6AmflElCkl7I2fSXorl7PYp9rgFt7yRqZGMU+DFZgfgsxneq5nL8BTpOfgZIlSwu+vr6n2oJWvg+G4K3ViCSvl08C4NK/Lbrz6B1XtkG89hd6qskYDZkGbiOPPtzOGpP6he8uUmWdKXr9Ytw3sz0MFaHdlq9iLPK+WP0Wgmm8GTY9SyDxSKNO/GQ6fnWJsTQXzvC1zfeK9G+kipTERFP/iKpB0uKQ4Py7pt90jzqnfJ/qGTZHBMjX94TIH4W2EUVWINP3ebmY/r9k0mxBiEoVyOdK62g2jtJ5bOzCsBnF64i/9HxiA4FZQjsOeuBaCf+hOCXM8Ra32tybaoyloukUs/yP/DoyK//pTZ6SmTJu76wR/DGtY007IXIaZrsZpuWX8BAHzBzVjWoSHlLk7wvYveDyh5/ABxsMh0E09bQsvK4hqEYyaN8HN5yVV++T4Y1eX1CLO+FkA4k0bYdR01XeWJGC7ErEoD2vIwRLol5zBfA8CzadyNwSKlcAjCUDSz4tiis7D+PvhTPmexmHnVBzeJrJtPJbCeZpFffhRLcO4a3PcOJ2u59wWumU7iTm1YhnXZ10rYwe5kPhbN3Jd0CitXBFB5+V6syy71+dJaFIBUApDqOITl3HkEkHG6URJcPpQGm5Pnbz+kGsyE2JNUnHrvdfM4U8f3YFUbLPDeFizmuWu4bmSU+6eSrIHLxzx8eaxBUQX/n71S9Yxv53PVswkRdBw2XeNrLnt9OdimnQCU4T72FvBMQUXW0gXgtNhQiKIWzpfTS3GdZJz1SyXZL6sNpSQzoU7AuqsA7WgIQB3ooBLiUCdeJl8engPRAdHND7Ke6TSWckE5Smwux/+NuRkjnWLOkVGU1yNbUdB8eZStLatjDq88wHnqOoKCONrPe9Hbipt++hKep6iK8x0b533w5Zltf6Mq/XH/S+zzvHXm2dVlcrzcSL9r3itSWivJnl6JenwSHIcjUe6biov/O2MKxN8qY9GZWAdGh7Gn/oBA0SyA7+lvQwj9/nO85Eb+aOMrIh/6ufmCWiwil38Ea3bfy1SoKp9GycaF6yHX3PcDgDVYjJu5aTd5uEYRkFRM5PwJKTSJKEBis5nlXzUBFAtPwtDNK53sWRjrR1iHh1RjjEauqXmJYS+/EGA6GSHsvJuwsFSvY6mebRKnhntELHYlvC2wzvtaEGDZFKS2F+9CsHcfRyj2tZj1qy1W5rfnOeZaVIU73eGheceZ1yhWryDUjVaqVhufK62bbOVoGj2lD77C848PsGfZDNdu3Iyluv5as+yoUSY1EVU9q8/md0ZmQHE1oJ7NsgdFFVhlo/2syfYn4CbExhHOZfW4r3NZ+kcHigDx7U8Q3hju5fl8Qchbp12JB2bP8wh9Iy6eyzG3pl3ETHOZEwS/xYwRBwrN89S6n797WwCrmtkmwXHmcpS+7mNY9sd2wfD3+BU7P4RiZnANJt7PE8Db0teq2uJm+NlAB16OaAiLckxZ5Z48gDY0yLtx8GUUQZebNRzo4PfnTHDZuzy0cH35XpSMeJgQlDeIglNUJdJwjsgnfyfysw+jDDi9zHtsQPWbz6CAFFdNJvjFwpAnD21B4XL76LwWHWOf5q/jc2sug3gXj1COd7Sf8+YvoHLcvNM460b73cYtcFrEItLTpBj+WZHdz3D+W/fDj2naSRqizY6sObTZ9AKlE3jVWvZJpdslPQG/9I6HxZ5MiMVikXcsWPD693Jq/MNjCsTfSsPtM1/8yz8C0KQSCOt7v4eQfvk+rFSrsoj3v4Q2PrF1otNNLOyJ30EiG+uDkbzrGYTd+BDWWDaNlZWIIBjnnYbQn7cWa94YwWIIUXueNzuC2RwiD/+S9p9zVk8WuCXVCP7Hf8Oc6+erfPS/EKNcuB6QSKdFug6L/O4zCO3yBtjnM5eZbGO3j9z2XA5gevCnKrXOQcy7pHoyW33OGshVRr9uw8IY7QfIUwnl7o6acU49h8t/2QUAaXhUpKAU60gESzKXhay34wmzP/klt7x+D2cuV25oD1bWUDf7YbWy1i37AXEjr72kVhXmCKv+5ikIek6PyJJzec7eZpG6uSKaDdb1478WEQ1w8RXwXcPzYViEEwv5dBwCTD9yKwzopeeYbT27j1G3/JiyQC1WEYfdJF51H6XEqVG+08iLt9lUDQDhO+/6KmdqsFPk+btEdj9NzL+gAoZ3Mi5y0fs4yw//HE9SIoYCYLGw/msuB2R2PAXfYdoic13XXEqL0tCw6bnQcwDztZ9jnZr3qSYwEc5bdAywN+LhDYuYwx1fM0MA/hMIc3nFlFxt2kW9+eJqMrPK6lXhm0qzS11Ouf7dftUq1YeCZaRlPvFbiG0v3YPS0nPcLF0cjwKetfOYZ387YGu14i2rmMa6Nu3knUwnRUa6JxP83D6R5efx2a9dDQ+kuIpz17KPuH1BOWd32+NcP1CItX/t5/EE6TrnoWqmyNk3iOWpP8oKm0jUIxJbeIGk8gqk2HuCV2Rq/FNjCsTfqsNiAawfuZU86tI6BGRklBfTKorxm0MYREMIsVwWAZhXjCIQC+Ma3fY4wrxuvmkppeIIokRURHQExn/f9vo+0w4nrtl9G806z1YbAvPRdhSKWcvNz7c1wn6vXwQY9BwXKRsBbBwuhMf0pQC62w/BbP9GiGTTlgAAV34Ct+HE9bBYAPSj2xH6eSV4JfpaRMRCWdKl54o89Xvlmk3gqWg/pMp5ulifeBTrXldraChO4WHW2Rdk7nmleC06j+J5KKoi7U3TmPPJOoDVzsXFnBUs53RcpH4tv4uNq1rqQvrQlkdMlnzlLFUIJ6esZ7/pXQkWi/R14CEprATk9RzKSVkdezLUjRWoWVC45q6haMrd31KhAMHlmk2x5iKKINbKGamZAws+MiKvVY6zO1W9/nzAZd3VgH6wiBKmhRWTz0hpLXyD0ADu9FgI78PiDWbf8FceUCRF4RxHRlWRF5vqtKVc3aN9IjIBxC02CIlFVVR6K62BQZ6Iijz5W5Gbvo7SUjkLd3rrQbMKXF4Jz9LdxLmftVKVJI3j8aqZbebCp1Ncv+0gCstAJ+c8k+ad0jRS1kpqCQFkM3yutEZk/hkQ72avhmNyfA/8hdiYGSPvb1MZAFaUo7wSzsCdX5fX2oPueo78+2Qc7odhjRfUKXf+CaO0DkUlGuL6/W3mey/CMw93c/b8BSLP34FVboTLjLHwTJHCSrEMdIjfGxT/tMVyeNOm199vavxTYwrE36ojHhV58CfEyW1OhFXdfCy0kV5e/mgId643X+TWj5vVytxe2KbFVQid+39MvfOeZiyZ6UvMFz0RVaDhxfW46xmahVisr68+tWg9gDnUA6hl0yLecgT1RBDfv5HrGS0dj2wVER2rsWGRqoteAJAWVOJuTycBEYuVz21+cDKIG8PuwPWYzVJ+89gu1UHrSppz+PNxj/e3QUYb6gUcA0UAUDZDy8ms4gDoguW2aANlYwc7IbWtvhTGcMchLMp4GBf7wU24P99oWG0UiXn+WZFrPivyykOED/rbAMT11/K5WSvwYIwNMM+xATwgl30Yi/yxX/GMbQdQQlxuvB+tB+S1LnB5xSJigVTl9iO0xwdF9Bkwu195gM8XV1G+d6yfOPBgJ+vUtBOA8q5g3Rvm463w+JlPsBgPjsvLd+auMb0TJxtjA4QBknHi354AezPQAfC5/WZZXIvFjEc7VDjA7jDrDRjNQ4xhs/Me2F3Mx2IXEWXJD3aLHNqKRVs5Hc9U3TzCURUz+Lwxn8iYiLsU5TUaYu07jojMXU28/P4fqoqBOtZsImqGUtJBFI1AISD71++hiFZME3nX/9FkJjRoKjeBQtZ49iozRdNguOdyeCJCQ/xtc5jvy2AHnQIdTjxsdhfv8UD7yasyWiys3bGd6t4WPCVtjYoU28S7FShQvAgPZ2rG0tdfq3I6f6bG/7MxBeJvlaHruPDaDyI0QkNYsJ6gWcPa6L5lFNWomyfyts+K/OZTCB6nisU5nPQMrpmLldJ5FOALj6LVtx5AoDrGFBEoBrjVzyeG/OrDCIvT3wagaxpuxc6jWN25LEDicANOeg4FoWIaz2KxmSxjEVEJunz/yFYUguEemPMjfRDrjNix0616PKflTcedX8c97w3y2Wf/LLJkA0rN2z4tsvEe6n9nErjtczm8AImo6gGurNyCMiy4Kz9uEq1q5vDZ0T4EaNMOFKdMCkt13VVvXK0rHhXZdJ9IxCEycAwL1JdnlhQ17uv2EzLY+TQKwrSlWIf3fpd88dmrcMH2NqPw1C2ANV5QBsBFRvFGXPQBgKOoAtdwNg1QHd5GOCM0BIAEizgPDYu4z7N/MZ9/qJs9nb6cM1JWr/rVzwQAjXz5iX22Txy9reSK79vI/71BzprNhuV76YewPhefzRmrmgnIiobVardzriOjIqsumhweEgEQF56B98JoplI5A+AODZBZYLGiJMxcblbPC49ATLM58Uw9/At+1rRTlWfNifz4PSLv+z7r13GY+XQcMt+zwgrVGcxploqtXyDy2T/z7ri8AOnYIIrUREJqUSUKisONcm0QB4069kvORkGZ2IjGYsNjsu4q1aPeo5ohlame5hOGrpMa2XNcJJUS6Wxizf0FeOiSMc5XJg1XY/ZKPAITUx6nxn90TIH4W2Xselbkid8gMA0X3bTFCO9jO3Hz9TZTEOaazyIAbHbcvfEIVobLh9Xj9AIAf/lfXmw9A9gGixEGkVFccDY71qnNjibfeRTNvXoOYPDi3YB3/XwINz3H0eBTcbOMajKOgLrz6/QVn7mManNNOwAH0XH56jrPER1DwOaX4xYeHYCElE4geNw+LMbz3sTazWZFtj7C8ziV63+om1iqAVJG/+/QoIhoIsOdfM7uVHnneQjkeWshMz3yS7MUan6ZyPVfwH374l0iw30oVrEQys2m+19fO3t8BLb7pvvYqxU3EcLIZUlfs9ogER7eKrLyQnKSj+5AsBeUQkSsnI41ONwD6B3dgfWVywJ4Lh/COBri2QvK2TdvEEtb0yB+dR5m/cdHzbSj0X72ee3lcA/aDkJoG+7Bku9rY+/Pfzd/YmP0mB/sAFQuej/WtDEyaZj9x3aJ5C8Uuft2ntubB2jEQoC+Ufzkjq+TYnjufwFiR7bhAp6+FHd2YQVKic2Bl8Bgqu94Egu/YREktJo5KD7HdvE5m5N1Kas3v9N2kA5p576LM2vkhfvzUdZ+82k+43DDqchkRO78BnFii5U17zrKO5XNcN6TMTOBY+tjPJOvgOd0egDH+etQkI/vBtQLK0XOeScKxvgQz+bLZy6pOPux9BzO58M/4+9clndv1iqUYm8e1/QG4JKcGMLpb8fzVDEDhdgouerysR7tjXyvea9Z4e60K/nZ1Pj/ypgC8bfC0HXc5j3HRUQxc0NDWL2zV5Me0nFI5LQrqFY2MZ1rpBeh3LRTVU7LUpmr+zju6qxKo0nGRRIJEacTi6O/lRSooipe/PAowKBpxPWCRQicvlZA3O0D7IZ7+Oy+FxFm0xerXPMw1u/MZcznhv8lHi0WCHM7dgES2QwC22oHxKcvRjjb7MQx0wlyaeef/mYLxtyzaf4dHgH4Nz8IQF/wHgTfnNW4RIe6EIa18/i5Px+B7FApUQc2YS2V1nH5gXZy4k+7EoWmv50ucSU1PNtQ1+TpxKPUKh/oQMmJjYvMudxkLHc1cY3xQUB3wRlmNbJju/ldOsnPKhrY33hYVT9zMfdUHALi9KWAYSKGojLvNPb+0BbOzkA7xKiOw1w/NIjllc2IzFmLe3y4BwtU19mLBWegIF7xMTwAAx0oGR4/wLTsvNdXC3z5PgA2v4w1PLiZuXgDZBoYFn33MZQzp0f1sndDLlu84fXbOrEeeioh8qP38VyaBjC9/bN8d85qfp+Ms3YP/9wkVtodZkc7m90k3xmjcrrI6ksIUxRVKZZ9CpAOFim3dSeKizWLFyWdQjFyeFFYHvi86hwYIeTjDYo8+iuIeEUVdHlz+7DC7Q6Rd36VM3BsFxUUh7pRZK/7AhwQqxUFeM/zKHurLjZd2tMWTSb4nTgSUVXKtYL3d2yAnzvdlEk+vE1kYbGZDZFOIFvGh0RcNa+/Xlsj83R5zQI8U+PfGlMg/lYZPc2wSz0BQHegg58NdWHJnnUDsdgT07CqZyPoZi4H6EWwALqP4Ta2OSe4pnOQtTIpBK9LsayNBiWxEKQxqw0QCBSKXPg+8142O+Sl0lrIQy37TJKU3QHwjI8g8EQjf9voIuVugvRl1OiOhRGY0xYjLBwuXIsif9+VbrVRve7RW1WDj0HmMfc0rFd/AQpDIopSUbcAi/K0K0Q23iuv9WAvrAAcIyOmRS8C0IRHmetZ70DgFdWIOByAhtG4wxg7n8LqtlhRqrx5AGQuhxI00IFCZXOS+nPbl02mejbNXmTTEK/K6oidj/TgBclmsbxFx/L2BQEBm0Pk8g8DZqN9gEpaEd4ChTxbzzHCAXVzAaVz3mkSJueshstgpLld+F68EsM9VL6z2rjmy/cBSMbeGGP/S5C7rDbOhaap4kJ5hBBEAygzGaz82rkw1Vv3T75ObyulRftacY+/66uswb6NVFQrrFC13yOUE153Na5gh4s/FitEzNF+3p3hHub0289w77p5vCNzVpuEzYbFqrVnArCLhVBGGhZCqPzLV3DB18zFwm1vVDXuFRcknWKfrXb2sGEhnxGd5+g4IvLO/+OdOLyNKn7pJM/30V/y+11Pw3l55BcoAXPW8G4mwiLth1nbEwmmJxtFlax/NISXYqiLZzGUNbs6s5ERlJRMin19/k68TRPH0R0oRA63cr9vEpl16d+fw9R40zEF4m+FkctiFfa1qNrlERHRsLjKGhAYC04/eR71hut5gdsbETpnXEOlrmM70biN+LUILtc8RXAKFgHGNqdqajJA3N3mUJaPhuvbiOGeOCpm8LvQoEm2W3CGyO1fgRUtAvHq+i9i+VptxCT/8hVV2MOK5ZtKQC6qnA5wPvZr3Pour8iltxB7PNm4/CM8y7O3iYz4EVoePyDV1ojFds+3yU3XrFh+S84hLphU4YDQEClyeaWsWV8rFq5Fo2KcCPHc1ZeK7HwGAT59sdktTMT0QFjt7KHdCSjoOdV8xCYiOmBqd5CjfWiLyPt/iAdABNCNhfn9kW2A2mUfwUqsngUZsesIgLVoA+EKm5N1ff4OwGraEvZspBeL3qjPPj5EnPjC9wCOInzuwvdh1Y/242EwYtCtBwCpVALAzekoPieCuN3J56w2zmr1bLwbpbXcb2xApRGmcPcmongxJrrkY2GR776TM+Txw5f4xUdEvnCXcgtrPLMIzxsfNxnXxvAGcIM/f4c6i26UiXCOinh7niXTYP9GLF+nG+t53ZUiz93JnpbUiLz/Bygr0xaJfOEOUjoHOlEQpy2C8W/wKfQcz210kWtvRIl0ulFU+ppRogOFpAMGS1SlvWbO5Egf70BOKWi+PPYqlxGZu05E240ifO3nJsfKTzZ8eXQie+K3NI2Ztph7DXaiPLr9qqiQzlrOXKkqIY5Mvo6ui7x0H58PFrGnfa1ml7yp8S+PKRA/1YeuU87TILdEQ7i8CirQxr1BYthjA2bu9MTh9olc8XE0+8gYL/WKi6jDHR7GkhOVnpWKAzAWK3HP3maKfzTtxFKMhBC0druIaHw/9QYvcX4JwvOlvzLn069mjqmk2XFqoB0BcvrV/H/aYuYbLEbgef0InKPbAPHHfk08cbATAX90q8jn7jx5e0urDSu5pAYCl9G/PBYSqZ0PAKVUClLVbFqpPnqrImdpCOKl51DfOhHH8jD4AcFiVYN7DUBSPk2R3ZzUMJ/oWh4fRiEIFvL8VsXotzuxmnM+pRhYAaFcL/uZSZNn/uivCCsM96JUaJrIy38V2fkkxUCaduKe9+Xjrt71DK5+h4s9HWiHne1wqaIxMSzgpp0iopNHvehMmNNtB02lyGo1y42euK5dh1VuvG4Wxjm6Y3KLzw3Xs18Wq0hVHcB42UdREO/6JmEFw+sTGaXYytiAyNrLeM5gkWo20o+1bVT9M0rHzliG4hMZ5cyMD6IoBIpeP+eiSrMRyc8/wvnbt5GsjVSMc9bfzvPPWEYK4kAXRLlkDC/XjCWT36nrv6jyvXVi01sexjNgFDHSLIQofPmceXcAgN/xJHyCh37GWRExz0thJRkDNbOVByDM9WwOyHmFVaxRJqlc2n4U2TfqTW+Myuki7/uembfeul/knu+glHuDhA16W1i//BLCdlWzyL6omYPn6uk/4FHKZblewyJVdOfNbz01/v6YAvFTfURDCIfZqyF7dTURCy0sx6JKKGvO9gYvciQk8pP3wWw32hyecwOW1p1fB1QM68TuFCmbxkt63k0IqN/9Ny935QyRF+4gVl5aB/jnlwNg8YiZ2lQ9x2S2lteLXPd5cy5/+xGCODwCeCbjyhWsxvE9AKXbp8pyjiIAV10CqLUeQNhY7Qjr0T6Ku3zs1jduqzh7FQDTsg9Q8+WTivfMn0gNG+qCbf/qw+SQZ9JY2jd9XVkcguXkzxc581qEWFsjFlMyTv7v038yW5d2HCGdyLAo/fnMd/pSrOCOwwCPw4VbsnYelndoAI+ALnx34z0wopt2iLz6KGuWy7LvA51Ya7pmKnduL2SrbIZ9WHsF9+o4jPWUjAE6gUJc2mkFCg4nVb1qZuOGfyPPhjHKGiDy5bKAqGF1brwHEDcIbUe3w62onS2iFYmcfR3r8Ogv4WTo2cnrkM2QojbYRWOUd33V9PrksqoZis79RvqoKDZ9qcjxXYRo6heK3PJjM3f+jYbLi5s8m8F613XeH6MC3VAX5MLyBu6dSRMKWXnRZOXM4Zxc8KhmDi72OuF9cLiZUzyCIqlnAV6LzWzHu/URlTKX42xGQwDyQAd/ckrBNvLksxn22J/PvPe/iALyZimNE4dFXWvLwyL7XuKd72tTtRD8cE6sdpTCnuP8zuHAOm98FSW7eS+ZLtks4ZwTuRBT458eUyB+qg9dqbqZtKrQFke4dR4BOGx2rMx9L2I5nQhmT/0BcDRyU8PDCKVLbiHW7M1T37Hwu2v/Gy3c7sRyT8XNntmnXQWr3WIlVe3t/w3g3v5VLCzRmMv1/6P6dJ8wZi2HuDOiQCCdnGy9DXVjJfUcR5Bk03gdFpxhuifTSQSOUb99bADr8mSFVURYnys+pkqTprE89zzHGnYcBqDHh5h7xyHi5gPt/O617lKauQ9GbrieE7nzazzvovVmSllfK4Ju+fn83xvEdf/E7whLzFktcvo1IsMZWku+eBdA1xQFYPNLWfdtj/LsN3wZkt5jvxKx5LAYsxmEbW8LCoexlvEoYO8v4DyIhf0trSN8kkmh9Dk8gFlkWCSscZ/IGIQpY/S2ModkHBLhXOV1cLqxPHtb+bfHj0JmlFjddD/nq6Cc+zXtElnQwJz/9kMImi4f1eWyGZTMbEpkxnKz2lhvMx6X2nn8Ob4b0MxmYGX/4sMqJdBJhsCVHz85Ee5k45wbqYvg8tAzvLACq9nhUilpIbMBzUiv6gHeDmP9tCvxzpxMYdz8IIq2L580ud7jeAAu/wjnd+M9eCaKqjjjNjvK+MzluPLtLs5KzVyKGrk87Ek6zv6WVKM8ORysQ34pSkTjZpHzbn5jJfbEMdyLgiU5FaZzK8Jrhj0c6GD988vwOBVVQmIsb1BFfWym7HnHF0Uaj/9j950abzimQPxUH748XHwv3InAs9tNVvG0xbxkTo9q5JE0mendx/iz/yWzeIZoZpyuYhpWldGXO50UuexDXLP1IAInESGeZ3eT5uT0AGxXf1qkeib32vwgIFjWwH1HerDELvnA65+lYTFAOj4kIjouxu1P0vRDRLFn+01Q8gZxtRv1x8+9WeTIhxBumo5ADBZNZuOfbFitkwtU5JUA/P2tgNxoP8A2Pkyc34gPGqNqJuvceYT1sNlE8qtwh7cfYi8m5YWfIFBnryTUER4FqDx+kY0bRZasZ727m2j84ssjPWp8hHsc2ESO/6qLecbIKPFtm03lzWdFMjmAfEylylmtzH+wEwGtWVA0bA7+Hyg289tTCT6vaYDhvpcobRoNidzzLdPD89ivEPILzmCPZi6noI/NjsvXZoMXIMKcS6oVGdIDUKWT9NJuPcAcbHYVttD5fkE9pDnj3B7dpjp8qfNaWM6ZPfNauAl6DhAzKpztevofB/H6BVj5XU2468eH2ZMzroGj4fbx/4ObUZLGh1j77uPkzjvdZh1zwzuUiqOA+gtUdcIVlFhde4VZy3zhmYQ6ChXRLDauvDoHAcZUDC7FjqdEFpxplj1Op1CgaucRRtjyEEpZ5XTOgv3vnP0Th0Wx7T1B1j6rmPqJKD8b6jLr7OcyqgJkKVa7L1/1Lc+yXsVVIjIF4v/umALxU3roZg/jRBQhX1yFK3n3s7xMLh/Wks1hxlsPbqawRiKGi89IM3F6cO/NWgkAzFqB4MkvJWZZOxeh9tBPeaGDRVz76DbARs/B4G5YYGr+sTBuSWMY1bVONlIJwEaz8GzpBFZ351F+P9qPgDFctKn4ZMLU0rPplb3tMUDMagN0JhL6UkmVax54Y1ffrBW42Zt2IKzySlnLZNwk0Z1Ya/7az4s8dzsWbmHlBFa9D0Hv9mPReAMw3k8c3iB/QkMij90pkgqKbHqAdKY5q3mev34Xt7rbj8fAYDdbrSJnvB2LreOQiCiLODqOi9lfRJw0lTBbuxou2lmryDHXdVy1uSxrY1TFc7ohvRmpceFRQg/ZDM8pwtnZ+6LyiFgpLRsoonZBNgWwb35QhVR09sAI7+g68z2+B0s3HkbB0HMokqdfzfdfvg+wP7KdM55fDlPfXwCApRJ4R4yyvn0tqh681ewkd7IRj+AdaNsvUlwnctb1KBkl1ZynE4fTTQ7+t67jjPvzRQqr2ZfiKjwL89cB4A/8BH6BxcoZtjtFVs0XOfCSqoEgENDqFpiKbm+z2StdF97fwgqut+MpqgV68iAA6jpKynk3824aWRkdhwD0XI6U0n/ECtd1znegCKWytxlvTHRMhSxynAmPX1nnCc7f2CCepOEexQEQFJRDWwjzla15fTOaqfFPjSkQP5VHeFSk8UFA1puPxTf/dASkkSLV3y4iusjFtyDQdJ0GDu2NvJS5LC9YsMQsXnLmdcR0NQ0BWDULzVpEubpzZr3wmjkqT/UjzMNoAWqMhkUoFIaiYAiX330O6/PMt5vX6j6mKrgJ1pvdJaLHVe9qK/HNuWvNOGhkDFCdMQEUN7wDS+m523Gnvnwvn11zKdbVQz9TSo2dEqUni/FabSJXfBQAOvQqrt+RXpWa9g4Uh4kdpkQA3/52PjPUJWKp4T6FlSI3fAVh7fTAgp/YhGLiiEdZ91hYpOoMFLTICOlbc9eQ0tO8j1xiq93sCd3bKiIWXP3G/X0FCNvZK3n+oS6RjqMqfmwXkbTgEciJ5FUAMsFigKCkGpdvVxPWVV4xYGe1m5kCRvhAxKzHvflB4ucev8jqywDkrY+y57581c4zx88jI5yt8unK7R7g9zOWcXZ7WziHZ9+AslFSizcim2EuB17iHHUfM6ugZTNcJzyGwmSUlz0xpS+bQfHNpuFM7HoaZSeTRjH41B9e30N74vAGVeORcYDLZhNJaezfULfIC3ejTLTsR/npacZijUf4e7CD5jT5ZTTE2f+yio+Pk9K29kqe42cf4vMWCy52iwXS6fYnWL9cjv2tUoRVm13k6k+hfMbGUYoqZ7zxcxgjERO573t4STQLnq/LPyLy2G8U+S6P9XQH8AjklynFL0ff9DWXo5wOdePxe+4OEauT9zQ0iOJltKCdGv/0mALxU3UYnatKaxGq89bAbO08hBC8+P3EERMRgLWkhu/FwpRmTafN2HF4hLSjKz7GZ3/zaa4xEVzbDlIr2ahnbbTUNFqf+vJP7rauX4CmvuVhkXhcpQ2p/NqDm7BArvksgPz4b1RVsRTXTyeZh90pIkpAh4bM8p1hxewWwUJ/+o94GRo3wc4vrBAZbCbnt2U/cUhvvkhxEfN+5JdUEutqAvDrFqjwgxvF5KpPQnLrPIq7c9XFrwdvEdzL932f9Vh3NcA12k9q0c3fRAFIxRVpLPDGe9rXyl6U1KLwlNYR0zz3Jp4vFoEo19+Gmz8yCrD68lFweptpI1o5A2VhxxOEAQwvSy6HEqBpZn5++2Fiv7oOfyBQhLv+/JsR7g//QoVU7LRWbdyC1etwER+12tivsjo8B4VlWNzP/EUpCzqKTGyc+QaLCHsY5UZnrRDZspUCOw/+VOWIC+z1c25UTVk01i4ywrN6AmQRGM1A7MMAjaF0ipipaw4XhDEjwyEeFXngx8oVPoIF7s0zz3VXEx6Ec254433y5bHGrcoLMtTN+RnpFpEc1utgO1kLeSVmKWSXV2UBeAHCeAQFxJvH84VHRJ76E+dt1ireOz3Hd/raUJgXnIEiO9DO9WpU7YSjO3mfHC4q/OWVIA92PEkoZOm5k3sZTByP3Eret8ODi/zOr4t84rc0OOk+TuZE+yE8MDYHe1lcrQq6bECxs1g4A3uf5x0xzrnVBhFwCsT/5TEF4qfqMKpQpZO4nAfa6Ui2/CKRM95mVo86cbQeUMValDUquiqb6lQxLFGu1AnWombhOyJ8Zu3lgLLFiqDXNCqO5XI06FhxAcL0pft4qQ1wK6snllpYqSpiOSDCOT0AlsUC8IaHVdw7hUu1cqbI0CG8Afd826y3XlxjWlnbnyB1aqgb4Tw2CIHMamN+z/2F5zBis26faqP5Tdz9LQrcZq4g9j9rBeuy8iL+vNkY6mYfDOXitCupnuXNF/njF3i+gnLciy/fhxVXWksp2olKgWHhGlZuLssaJxPURB/sxEqOhYldaxZct/4ClLSuoyhzF7yXePPCM3HvZ1J4aI7vEfnRe5mPZjFzpvUcQJKM8sx187HkS+tEPvBDFKzwCCCbSTE/txdFwWKFkPjYr+FijPTDDUgrhnc8zDPaHACovxAOwcTqaiKEJ27+BoqBywuf4befwWPkDYqsvIQ51s/HbT6m0ulcHs7J2AB8jJE+5ZkKsp6xsBmO6WsT+fUncTeX1rMnsXHVBjRg1jdIRE6+z6mESZy84qMiL90LGFssKIC7nuasGu/dK/fzPIkIylHVLNY3FTfDQpk02RqDnSjKBhH1qd/zrhlNhjJp1qzxFRTduWvMs3N4G4qJza7aj+5CKRjrZ65Hd+Cxuuh9J5cJO58SEY00vFyO0Mum+0XWX8O13D7e3VSSdrodB/l5PAK/JRUXWXY+iozVbsoK42z9I0VnpsYbjikQP5WHP59ypH0dlEN1B2CuLj9Pdag6YRx6FWHr8mPVxUKqlWfpZLfyvHUIpIIKBIjdQaqYCELgtCux8qMhrGdNA0gyaVi2tXNRFrY+AhhoFkg/Z92IkEglaI/acRiX5vM5cprTCWLrLfv5dy6n3PQlInII4Lvp6xC9LDYEvxHXbnwFyyg0qKx4o5CIsuCtdp6lt4VnTcbNEqPNewEOI576+G8QWkYK2d8bLq8iAOVEREeZGO1lbsPddFqrmc3z9hw33cA9x2HqGwU5KqaRrtdxSMTVgNt1/XV0MRvowDUrQs66xQKweoOsf0kN4LrgTFNoFldRZc0YlTPYn8bNIjarSH4dbvboGOumaXhGFpyOxyOTYg2cbpEX7mINjSyGvlbO36qLibG3NTLvVILfGwQ1gxhod2KBLjlrcsGW3lbu+dhvYPHPWcXefecGwMcgUw124SWpmIEV+MoDuOI1zax1n4wznyf/wFlMJ5l7WR1n9d7vMxd30Ox8581DSXF5mXteMRwEY8QjhAOO7kAxE2Efrvjo5Pr3va2caSPU09ZopmPFI1x7zlpVgGe2apWaQ2GyO3G5p5NYzd4goaREFEUpk+J6O54yK/stOEPkgz9BmXrhTpQdI47uDUDKnHca6/D/ae9co6O6rjv+3zOakYTeQi+MBMiuYvBy7AQRsJ2UCIpjHnWIHeI6eGEXu00dl9bOJ7yStOkrjZMPTtIndRwnTldbWsdeDs0ithMn1CaEGOPwNIkhgHkJCST0QhLSSLsf/mc8QoykK2ke3NH+raWlmbl3Zvaec+/e5+xzzt65+bz3G+6NHwkKZtGB5+RT5r4edmoffpJ2YtePqNfdjzLs/4+vUh9xUwjffxJ45bvsHM58Hxcanj3G47OvHbsTbIxKUp24iCwH8E2wOvXTqvrEsOPijq8E0A3gD1X1rWTKNKXIyedNk1PAG7+8hsbh3bdjFcGG8vJ3GNqtnEND091O57toFXvYUT56Dw3wO28yPLpk7ZWdgooaIFLFkVbFbL6WFaJz6WjhPN+JX7uTlSOwjhYayJe+4xYh9cYqmU2/JrYlbvY8OvdVn71ycVFxefwOypkjXIyX5ZxFa6Or+S3sjECBGW7F8rmTNDC1N7m55R63j7uPI0ZVOjWvTrxiFufJ3/oJM6Od/DWdwoUmGrmO83Tav/0Vzz+6l3O/Z4/RQUSnOrJCDOEf3A6c7uD85nUfYJa4QCD2fdHRXP3tNOr5pRztFZXRCYyECOd7n/86Owgd57lbIJRNQ97fx2nynT+k0Q8EudVw+YOcCx2aNCTL/W5dbcC//xX16+6kIwoE+Ve3gKHkojKGcz9yN6dkoqPBpncZCaleDDTuYaRi1Z8wgrP7FY7swjluxXwjF01GR9V5hcDv1FPvaJ7/j94DNHyaa0UOv8m2LKlkMZxzp3i9lVUzYhHNOlbrOoKtZ9lZvHNDLNd480lOk7SeYRRj9g3AtR9ku73yLHDXn8d+j7KZ7DSdO+mK1RyjbNl5vLa7OziPP2cp8LlvuamsQV5/u19hhblwtivvKYzqtJ/j3+Agp0t6Ot06EQV+/gJQv4wRrt+8wU7ttCLe103HGe06uMPt9ED8JDdRbv04f/u+XgBKmXs6ga+7qM3ST8dqEbQ0UiYd5Pc1n6R8EmRk48xhRloWreLr7YEr18kY4yJpTlxEggD+GcDtAE4B2CUiW1T17SGnrQBQ5/4WAfhX999IFFW1NJhFzrEN9Mdfdd14lCtGg1k0HHlFdPQfW0/jNzQJRijMsHi0dvVIZIXYcWg/R6PTd4kLhIorODKIhph1kIbl0kUmkXntOSA7h9vhctwoqukEHfY9G12VrTIukPJK6QzW/u5u56g4J4/7p0WAvovsLMysc5WmApyjPLTTldQcpEEPhfl6Tyc7N14R4Yh3WiEdWm5erD53MIuffWQPjVpBCb/j6D6OzofXdw5ns0PQvi1WDz26L7/tHNu2rYnRkFtX87OO7efvdcvHR94PH6WwlMlmLrZxGuAb0TUBOTHj3dnKdhuIcBdD7fu5aO7lZ3itDUT4d90H2CG50OwKl5TTaXS2UE4BnffaL8TPC3DgdXDbW4jOtu0c94pnhWJ5zbsuxCIL1y8Efv+zvF5azzIxTDiXzvWGW1gIJxAA1n+Z0ZW+Xo6ay6t5/Q9G2MnpbucWuIE+VoS748H4KYlf+rbb4VEAZOfzGi2rYQg92pmIEgozfen25xnejvRRtnC2W9VdyOQzpZWxaEaUD3+CI+vNf+8y/YGJkP5gI/UICJ129jR+pip/l/3bgQUrgOIqoPk42y5a4je6zzy/hJ2X3m52mq6Ns5Bz0SpOj3W2Xt4RL6/m2pmt3+LC15rreV0UVzLCFMph5y4YdNNWbj99W5OrrgZulTQmRTJH4gsBHFHVowAgIpsBrAYw1ImvBvA9VVUAO0WkWERmqGpjEuWaWiz+FA3t2eNunrj68nBglAPbaYBaT7vMTAN0+AtXjJ3FajTufAR4/snY6Hb5g+x555dwq8nFNp43rYAGNOh67M0naXT6L3EU1dfNMqmFpROrVXzjYq4Wrq7j3GJvN/cr5xUD/d1MtHHr6sudSf3tNL6/2MKc42XVLCCxbN3lIV8viOC9IiPdHfx+VbZJ7U00pPlFHL329XKUNuO6Kw16PKIpal9/jp+9+B6GKINBJo2JJo7xSjDIOdNwLncPdLQw5DowQENeOD1W0KWnk7/NnY/Qce/9Gdv1jvXcanf+lCtgEqDTLa6gwyoq4+K0mxu8RzQAfn/dfK53aDpGmVqbmNb0htvYXtMK2I7rvxybQ6+ZG4tWhMJXpoStquVocv/rbKOCUnZg628feftTayM7JjoY29rf10sZy2uuPD+vkL/LtCIXedkTq6WeFWJUKzCCSS4sZdGTE4f4fNY8tsnchQyJ//fX2E7BUKyWQUkFda+uY5v0dPH3yitkJ7JgOu+vglL+Ni2n4zvxytlcxLbjRbbh4d3stAWygOws/j99mE48GAQe+Gt2/rrb2dbRwjXRYjyzb4yvozEhRIduBUnkB4usAbBcVf/IPV8HYJGqbhhyzg8BPKGq293zVwFsVNU3h33WZwB8BgAqKyvrN2/ePGG5urq6kJ8fZwVxBvKergOR2BxVdu6VozuAhqe7E4DGFidNK7pygdGEUBqPQCD23ReaOBKVQMyZTZ9JA3uxjWE5HXTbk4ROM7owbDRdRxRBY9t4AkFXqWqEfeBx3z/I5BjB4OWJXMZDTxf3C/f3c9Q3OMgRSlWtKyQyGFvMBOFc7QgFKlJ2HQ9E6Ky6O9l+kX7+D4Zcwpj+WKdspPe3nHEGvNftN8+mo4y3kn8okT6gpRFd4Xzk91+M5QGP9PN3iWZ6yytkCth4o+Xx0tcbKzM6UiriKG3Nse2Il7r53uxpfF5aFcu7MJyeTjpcVbeNUxl1qpyDrkv9E2vXljNcpxBNRh7MckWE3O91oWnIdtFyytDXw2gUlL9jSeXl1faGM9DPa7Sz1bVBKPbe4nJGzaJE+l3WxAj/91+K7Xoom/nePTQl7fEEWbJkyW5VXTD89WSOxON1X4f3GLycA1V9CsBTALBgwQJtaGiYsFDbtm3DZN7vJ8ala/MJbh1RuOIL/dx37GUf6UTocKuZoyP0pWtjiVkGIgxj/+pVAMJwXsOay+d9h+GLdu3v4z70Y29R/+xc1kWvm8/Iw4vf5OvhbI5sR8lDnnJ9BwdpiA/8HNj0mOvogSH9Nf/GbVUj0XKGc/NtbRyd37w0/rqFeJw9jm1v7EZDuJer6UurmCSl+V06vw+t4Na2dCQL6Wrj3vQTR9mBqP8YQ+LTrxl9xfWlHo6czx5zJWTDvA6q5ky8Xft6ueBy7zaOrD/5OS6KizIQYSQqJ4/X14Vmzud3tLBzNO9WYNkd3jpC5065ZFAXeV3UzOX9O1LEbnCQ0xuBADsQQ77DF/dtgkiWrsl04qcADI0pVQM4M4FzjFRQMYuZtPZu4039/sXxF78lisJSYN2XOL8drZAVJZjFfcFL7wP38k4inH81EQoDdz/G+ddIPxcQRueoK2qAh77KUUtu/sh7dtNFIMA2ql8G/MVznH7JL+Hq6NEcOECntvKPJ/a9VXOAwuNAwydjr639Ip1PKDz2dyeT/GLgvi8yShHOGbsaWJTsXBb2OfE2r4OZdVwLMRnCOcwBf9ej8Y8Hsy6fhiqpAB74G657CIUZ/vfaESqv5i6QxqN8b83c0a/XQIAJiIykkEwnvgtAnYjUAjgN4F4Aa4edswXABjdfvghAu82Hp5HK2aw+lioCgdGN11g5zf1IMIurc+MeC07emKeCWfNiRW3SQTA4esa0VCIyeoKekQhnxxYmpovs3MtrAoyHghKgoD6x8hgTImlOXFUjIrIBwMvgFrNnVPWgiDzsjm8CsBXcXnYE3GK2PlnyGIZhGEamkdR94qq6FXTUQ1/bNOSxAvjTZMpgGIZhGJnKyCuFDMMwDMO4qjEnbhiGYRg+xZy4YRiGYfgUc+KGYRiG4VPMiRuGYRiGTzEnbhiGYRg+xZy4YRiGYfgUc+KGYRiG4VPMiRuGYRiGT0laKdJkISLnALw7iY8oA3A+QeJc7ZiumctU0td0zVymkr6T1XW2ql5R/s93TnyyiMib8WqyZiKma+YylfQ1XTOXqaRvsnS1cLphGIZh+BRz4oZhGIbhU6aiE38q3QKkENM1c5lK+pqumctU0jcpuk65OXHDMAzDyBSm4kjcMAzDMDKCjHfiIlIqIj8WkcPuf0mcc2pE5GcickhEDorIo+mQdaKIyHIR+Y2IHBGRx+McFxH5B3d8n4jMT4ecicCDrvc5HfeJyA4RuTkdciaCsXQdct6HRGRARNakUr5E40VfEWkQkT3uPv2/VMuYKDxcx0Ui8r8istfpuj4dciYCEXlGRJpF5MAIxzPJPo2la+Ltk6pm9B+ArwF43D1+HMBX45wzA8B897gAwDsAbki37B71CwL4LYBrAYQB7B0uO4CVAH4EQADcAuCX6ZY7ibreBqDEPV6RyboOOe+nALYCWJNuuZPctsUA3gYwyz2vSLfcSdT181FbBaAcQCuAcLpln6C+iwHMB3BghOMZYZ886ppw+5TxI3EAqwE86x4/C+ATw09Q1UZVfcs97gRwCMDMVAk4SRYCOKKqR1W1D8BmUOehrAbwPSU7ARSLyIxUC5oAxtRVVXeo6gX3dCeA6hTLmCi8tCsA/BmA5wE0p1K4JOBF37UAXlDVEwCgqn7V2YuuCqBARARAPujEI6kVMzGo6mug/CORKfZpTF2TYZ+mghOvVNVGgM4aQMVoJ4vIHAAfBPDL5IuWEGYCODnk+Slc2QHxco4fGK8eD4E9fD8ypq4iMhPAXQA2pVCuZOGlbd8HoEREtonIbhG5P2XSJRYvuv4TgHkAzgDYD+BRVR1MjXgpJ1Ps03hJiH3KSoAgaUdEfgKgKs6hL4zzc/LBUc1jqtqRCNlSgMR5bfiWAy/n+AHPeojIEvAm+UhSJUoeXnT9BoCNqjrAAZuv8aJvFoB6AL8HIBfAL0Rkp6q+k2zhEowXXe8AsAfAUgDXAfixiLzuI7s0HjLFPnkmkfYpI5y4qi4b6ZiINInIDFVtdCGauCE4EQmBDvw/VPWFJImaDE4BqBnyvBrsvY/3HD/gSQ8RuQnA0wBWqGpLimRLNF50XQBgs3PgZQBWikhEVV9MiYSJxet1fF5VLwK4KCKvAbgZXMPiJ7zouh7AE8rJ0yMicgzAXABvpEbElJIp9skTibZPUyGcvgXAA+7xAwB+MPwEN+/0bQCHVPXJFMqWCHYBqBORWhEJA7gX1HkoWwDc71aB3gKgPTrF4DPG1FVEZgF4AcA6H47QhjKmrqpaq6pzVHUOgO8DeMSnDhzwdh3/AMDvikiWiEwDsAhcv+I3vOh6Aow4QEQqAVwP4GhKpUwdmWKfxiQZ9ikjRuJj8ASA/xGRh8Ab41MAICLXAHhaVVcC+DCAdQD2i8ge977Pq+rWNMg7LlQ1IiIbALwMrnp9RlUPisjD7vgmcOXySgBHAHSDvXzf4VHXvwQwHcC/uBFqRH1YYMGjrhmDF31V9ZCIvARgH4BB8P6Nu5XnasZj2/4tgO+KyH4w3LxRVX1Z7UtE/gtAA4AyETkF4EsAQkBm2SfAk64Jt0+Wsc0wDMMwfMpUCKcbhmEYRkZiTtwwDMMwfIo5ccMwDMPwKebEDcMwDMOnmBM3DMMwDJ9iTtwwDMMwfIo5ccMwDMPwKebEDcMYFVevfJ+I5IhInqtvfWO65TIMw5K9GIbhARH5OwA5YOGRU6r6lTSLZBgGzIkbhuEBl+N7F4BeALep6kCaRTIMAxZONwzDG6UA8gEUgCNywzCuAmwkbhjGmIjIFgCbAdQCmKGqG9IskmEYmBpVzAzDmAQicj9Ybek/RSQIYIeILFXVn6ZbNsOY6thI3DAMwzB8is2JG4ZhGIZPMSduGIZhGD7FnLhhGIZh+BRz4oZhGIbhU8yJG4ZhGIZPMSduGIZhGD7FnLhhGIZh+BRz4oZhGIbhU/4fhVdPOkF2d70AAAAASUVORK5CYII=", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "r = 1\n", - "\n", - "for n in 5 * 10**jnp.array([1, 2, 3]):\n", - " approx_pi(r, n)\n" - ] + "name": "stdout", + "output_type": "stream", + "text": [ + "1.630969\n", + "1.5222379\n", + "1.5657302\n", + "1.8136375\n", + "1.7423098\n", + "1.7120391\n", + "1.7192066\n", + "1.7177035\n", + "1.718586\n" + ] }, { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Buffon's needle problem\n", - "\n", - "Here is another interesting example where random number generation can help us solve an analytical problem.\n", - "\n", - "Buffon's Needle is a classic probability problem that involves randomly dropping a needle of a certain length onto a floor with parallel lines drawn at regular intervals. The goal is to estimate the probability that the needle will intersect one of the lines. The probability can be calculated using the following formula:\n", - "\n", - "$$\n", - "P = \\frac{2L}{\\pi d}\n", - "$$\n", - "\n", - "Where $P$ is the estimated probability of the needle intersecting a line, $L$ is the length of the needle, $d$ is the distance between the lines on the floor." - ] + "name": "stdout", + "output_type": "stream", + "text": [ + "1.717916\n" + ] }, { - "cell_type": "code", - "execution_count": 54, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# Visualise Buffon's needle problem\n", - "num_lines = 10 # Number of parallel lines\n", - "line_spacing = 1.0 # Distance between lines\n", - "needle_length = 0.8 # Length of the needle\n", - "num_needles = 20 # Number of needles to drop\n", - "\n", - "# Create a figure and axis for visualization\n", - "fig = plt.figure(dpi=100, figsize=(6, 4))\n", - "\n", - "# Draw the parallel lines vertically\n", - "for i in range(num_lines):\n", - " line_x = i * line_spacing\n", - " plt.axvline(x=line_x, color='black', linewidth=1, linestyle='--')\n", - "\n", - "# Simulate dropping needles and visualize them\n", - "for _ in range(num_needles):\n", - " # Randomly choose a midpoint and an angle for the needle\n", - " mid_point_x = random.uniform(0, num_lines * line_spacing)\n", - " mid_point_y = random.uniform(0, num_lines * line_spacing)\n", - " angle = random.uniform(0, math.pi / 2)\n", - "\n", - " # Calculate the endpoints of the needle\n", - " x0 = mid_point_x - (needle_length / 2) * math.cos(angle)\n", - " x1 = mid_point_x + (needle_length / 2) * math.cos(angle)\n", - " y0 = mid_point_y - (needle_length / 2) * math.sin(angle)\n", - " y1 = mid_point_y + (needle_length / 2) * math.sin(angle)\n", - "\n", - " # Plot the needle as a line segment\n", - " plt.plot([x0, x1], [y0, y1], color='teal')\n", - "\n", - "# Set plot limits and labels\n", - "plt.xlim([0, num_lines * line_spacing])\n", - "plt.ylim([0, num_lines * line_spacing])\n", - "plt.xlabel('x')\n", - "plt.ylabel('y')\n", - "plt.title(\"Buffon's Needle problem\")\n", - "\n", - "# Show the plot\n", - "plt.show()" + "data": { + "image/png": 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", + "text/plain": [ + "
" ] - }, + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, axs = plt.subplots(1, 2, figsize=(10, 4), dpi=100)\n", + "\n", + "# plot function and Monte Carlo samples\n", + "x = jnp.linspace(0, 1, 100)\n", + "axs[0].plot(x, jnp.exp(x), color='teal')\n", + "pts = np.random.uniform(0, 1, (100, 2))\n", + "pts[:, 1] *= jnp.e\n", + "cols = ['teal'] * 100\n", + "for i in range(100):\n", + " if pts[i, 1] > jnp.exp(pts[i, 0]): # acceptance / rejection step\n", + " cols[i] = 'orangered'\n", + "axs[0].scatter(pts[:, 0], pts[:, 1], c=cols)\n", + "axs[0].set_xlim([0, 1])\n", + "axs[0].set_ylim([0, jnp.e])\n", + "axs[0].grid(True)\n", + "axs[0].set_xlabel('x')\n", + "axs[0].set_ylabel('f(x)')\n", + "axs[0].set_title('Monte Carlo approximation of $\\int_0^1 e^x dx$')\n", + "\n", + "# Monte Carlo approximation\n", + "n_values = 5**np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10])\n", + "results = []\n", + "for n in n_values:\n", + " pts = np.random.uniform(0, 1, (n, 2))\n", + " pts[:, 1] *= jnp.e\n", + " count = jnp.sum(pts[:, 1] < jnp.exp(pts[:, 0]))\n", + " volume = jnp.e * 1 # volume of region\n", + " sol = (volume * count) / n\n", + " print(sol)\n", + " results.append(sol)\n", + "\n", + "# convergence plot\n", + "axs[1].plot(np.log10(n_values), results, marker='o', color='steelblue')\n", + "axs[1].axhline(y=jnp.exp(1) - jnp.exp(0), color='red', linestyle='--')\n", + "axs[1].set_xlabel('log(number of samples)')\n", + "axs[1].set_ylabel('Approximation value')\n", + "axs[1].grid(True)\n", + "axs[1].set_title('Convergence of Monte Carlo approximation')\n", + "axs[1].legend(['Monte Carlo approximation', 'True value'], loc='lower right')\n", + "\n", + "plt.tight_layout()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`````{admonition} Group Task\n", + ":class: tip\n", + "Rerun the experiemnt above several times. Do you always get the same path for the Monte Carlo approximation?\n", + "`````" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Monte Carlo method - computing $\\pi$\n", + "\n", + "We can also use Monte Carlo to estimate the value of π!" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": {}, + "outputs": [], + "source": [ + "def in_circle(x, y, r):\n", + " # is point (x,y) within circle of radius r?\n", + " return jnp.sqrt(x**2 + y**2) <= r\n", + "\n", + "def approx_pi(r, n):\n", + " xs, ys, cols = [], [], []\n", + "\n", + " count = 0\n", + "\n", + " for i in range(n):\n", + " x = np.random.uniform(0, r, 1)\n", + " y = np.random.uniform(0, r, 1)\n", + " xs.append(x)\n", + " ys.append(y)\n", + "\n", + " if in_circle(x, y, r):\n", + " count += 1\n", + " cols.append(\"orangered\")\n", + " else:\n", + " cols.append(\"teal\")\n", + "\n", + " pi_appr = round(4 * count / n, 3)\n", + "\n", + " plt.figure(figsize=(6, 4))\n", + " plt.scatter(xs, ys, c=cols, s=20, alpha=0.5)\n", + " plt.title(\"Monte Carlo approximation of π = \" + str(pi_appr))\n", + " plt.annotate(f\"Points inside circle: {count}/{n}\", xy=(0.5, 0.9), xycoords='axes fraction', ha='center')\n", + " plt.annotate(f\"Approximated π ≈ {pi_appr}\", xy=(0.5, 0.85), xycoords='axes fraction', ha='center')\n", + " plt.xlabel(\"x\")\n", + " plt.ylabel(\"y\")\n", + " plt.grid(True)\n", + " plt.axis('equal')\n", + " plt.show()\n", + "\n", + " return pi_appr" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let us iterate $n$ through values $5*10^1, 5*10^2, 5*10^3$ and run the function approximating $\\pi$. How does the result change?" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [ { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's write Python code to simulate Buffon's Needle experiment and estimate the probability.\n", - "\n", - "This code simulates the dropping of needles and calculates the estimated probability of the needle intersecting one of the lines. The more needles you drop, the closer the estimated probability will be to the actual value of $\\frac{2L}{\\pi d}$." + "data": { + "image/png": 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GDx7M0qVLAXj++ee5+eabARg/fjy33norQ4cOpWPHjsyYMQOAu+66iy+++ILevXvz2GOPsXz5cgYOHEjv3r1JT09n7dq1Rx23ffv27Nmzh40bN9KtWzeuu+46evTowRlnnMGhQ4cAePzxx+nevTvp6emMHTv2qHg2bNjAkCFDGDBgAHffffcR+586dSoDBgwgPT2de++9t8Kyf/DBB/Tt25eMjAxOO+20Csv7q1/9ihEjRnDnnXeybt06fvGLX5CRkUHfvn1Zv379EfsrLS3ljjvuYMqUKaSnp/Pvf/+72ve/adOmgDMa2KFDh7wD0/iaPn06l1/+8yMrVq5cSZcuXQiton/HO++8w9ixY4mMjKRDhw506tSJBQsWVBtPZQ4WF/PQ/Pn8ed48/jxvHg/Nn8/B4uJj3p+ILyVxOVpUExj7Ozh9PAw9H664G7r0czuqBqWkpIT333+fXr16ce+999KnTx+WLl3K3/72N6655poKt9m+fTtffvkl7777rrfG+sADDzBs2DAWL17M7bffztNPP81tt93G4sWL+e6772jTpk2Vcaxdu5abbrqJ5cuXk5CQwJtvvund7w8//MDSpUsrbC247bbbuOGGG1i4cCEtWrTwzv/oo49Yu3YtCxYsYPHixSxatIjPP//8iG13797Nddddx5tvvsmSJUt44403KoxtzZo1fPLJJzzyyCNceeWV3HTTTSxZsoSvvvqKli2PHHV42rRpxMfH8/TTT7Nw4UL+85//sGHDBgB69+5dafknTJhAixYtWLVqFbfccssRyw4ePMgHH3zARRdd5J33/vvvM3r0aO/0E088QXp6OhMnTiTbM6zs1q1baevzBLU2bdqwdevWSmOozofr17Nm717S4uNJi49n7b59fLBu3THvT8SXkrhULDoG+oyEIedA605uR9NgHDp0iN69e9O/f3/S0tK49tpr+fLLL7n66qsBGDlyJHv37iU3N/eobc8//3xCQkLo3r07O3furHD/Q4YM4W9/+xsPPvggmzZtIrqaZ2p36NDBm+T69evHxo0bAUhPT+fKK6/k5ZdfJqyCh4nMnz/fW0M9HDs4Sfyjjz6iT58+9O3bl1WrVh3VGvDNN99wyimn0KFDB4Ajmqp9XXLJJYSGhnLgwAG2bt3KBRdcAEBUVBRNmjQ5Yt2PPvqIF198kUmTJjFo0CD27t3rPe7ixYsrLf9///tftm3bRrdu3XjttdeOWPa///2Pk0466Yj4PvzwQ28Sv+GGG1i/fj2LFy+mZcuW/PrXvwYqHue7olp+TW3bv5/YiAiMMRhjiIuIIGv//mPen4gv9U4XqYXD18R91fRHP9Iz4EVl2wBcccUVDBo0iPfee49Ro0bx7LPPEhJS+bm27z5DQ0O9zenvvfcen3/+ObNmzeK+++5j+fLlNYrRWsvvfvc7rr/++kqPaa2tUVKL8TxjvrKylt/nP//5TyIjI2s9fGNoaCiXXXYZU6dOZcKEn4dgyMzMPKIp/eDBg+Tk5NCqVSsAUlNTvcuuu+46zj77bMCpeW/ZssW7LCsry7vNsejcrBnfZmWR5DkhyykspHMlJz4itaWauMhxOuWUU3jllVcAZwzh5s2be6/XVicuLo4DBw54p3/66Sc6duzIrbfeyrnnnuu9vl4bZWVlbNmyhREjRvDQQw+Rk5Pj7bl92EknnURmZiaAN3aAUaNG8dxzz3nX37p1K7t27Tpi2yFDhjBv3jxvc7dvz++KNG3alDZt2jBz5kwACgsLj+rVP2rUKJ566ilvJ7g1a9aQn59f6T6ttazzNElba/nf//7HiSee6F2em5vLvHnzOO+887zzPvvsM0aMGOGd3r7950ET3377bW9P+XPPPZfMzEwKCwvZsGEDa9euZeDAgVWWsSojO3Tg1Pbt2bJ/P1tyczk1LY3TTzjhmPcn4ks1cZHj9Mc//pEJEyaQnp5OkyZNeOGFF2q8bXp6OmFhYWRkZDB+/HgKCgp4+eWXCQ8Pp0WLFtxzzz21TuSlpaVcddVV5ObmYq3l9ttvP6o3+z/+8Q+uuOIK/vGPfxxxzfiMM85g5cqVDBkyBHBuPXv55ZdJSUnxrpOcnMwzzzzDhRdeSFlZGSkpKXz88cdVxvTSSy9x/fXXc8899xAeHs4bb7xxRAvDpEmT2LhxI5MnT6ZJkyYkJyd7k37v3r0rbP0YN24c+/fvx1pLRkYGTz31lHf522+/zRlnnOFtDQDnevjFF1/snf7tb3/L4sWLMcbQvn17b2e6Hj16cOmll9K9e3fCwsJ48sknq+wIV52wkBAm9unDZT17Yq31Nq2L1AVTk6auhqR///72u+++q3a9uXPn1rpZLlA1prKCyltfDv821GfC8WdZ+/bty7fffkt4eLhf9n8s9F0OXnVdVmPMImtt//LzVRMXkSNYa5m3cSOvr1hBcWkpI9q359KePQmr4tp8IPj+++/dDkGkzgX2/0oRqXPLd+9m2g8/0DQyktTYWN5ft47ZFdyvLiLuUxIXkSOs2r2bqLAwosLCCAsJISUmhh98OoGJSMOhJC4iR0iIjqbI59GgeUVFJJW7r1tEGgYlcRE5wklt29IxMZGNOTlsyskhMiyMi7t1czssEamAOraJyBGiw8O56+STWbVnDyVlZXRKSiI+SgPg1NSG7Gx25efTrEkTTkhM1O1k4ldK4iJylMiwMDJ8nqkuNfPx+vW8vHQpISEhlFnLBSeeyPk+D6ERqWtqTpcG6+2338YYw6pVq+r3wDm7Yf7bMO91tv3wzREPCDkeM2fOZMWKFbXe7swzz6yT41fnlVdeIT09nfT0dIYOHcqSJUsqXG/OnDn07duXnj17Mm7cuCOGGp07dy69e/emR48enHrqqd75H3zwAV27dqVTp05HjDm+b98+Tj/9dDp37szpp59+xNPrKhvTe9GiRfTq1YtOnTpx6623eu9nLyws5LLLLqNTp04MGjTI+xz5TZs20a9fP29cvgPCfPrpp/Tt25fevXtz8skne58Ct2rVKoYMGUJkZCQPP/zwUe9BaWkpffr08T6qFZy+A/c88ADv3nor7912G2umT+edVavYlpPDhAkT6NWrFxkZGcydOxeAAwcOMGnSJO945s2bN+eXv/wlAI8++qh3FLrTTjuNTZs2Ac5T5w6v361XLyIiI7nj8cfZWe6JfNKIWGsD6tWvXz9bE5999lmN1gsGwVrWSy65xJ588sn23nvvPWL+8ZS3uLi46hWyd1n7z5usnTre2keutXbqBGs3rzrm4/kaN26cfeONN2q9XVRUVJ0cvzrz58+3+/bts9ZaO3v2bDtw4MCj1iktLbVt2rSxq1evttZae/fdd9tnn33WWmttdna27datm920aZO11tqdO3daa60tKSmxHTt2tOvXr7eFhYU2PT3dLl++3Fpr7R133GHvv/9+a621999/vx07dqy11trly5fb9PR0W1BQYH/66SfbsWNHW1JSYq21dsCAAfarr76yZWVldvTo0Xb27NnWWmuffPJJe/3111trrZ0+fbq99NJLrbXWFhYW2oKCAmuttQcOHLDt2rWzW7dutdZa27lzZ7tixQrv9uPGjfPGvmDBAvv73//eTp069aj34ZFHHrGXX365Peuss7zz3nzvPdsyPd3+4cMP7b2ffWZ/89ZbduLMmfbPU6fa8ePHe/fbt29fW1paaq098rvct29fO2/ePGuttXPmzLH5+fnWWmv/9a9/ecty2Ipdu+zlL75oI2Nj7dWvvWZvfPdduzMv76g4G5pg/a2qSF2XFfjOVpATVROXBikvL4/58+czbdo07zO+wanp3XbbbVxwwQV0796dKVOmUFZWBjiPCP31r39N3759Oe2009i9ezcAw4cP5/e//z2nnnoq//jHP/j000/p06cPvXr1YuLEiRQWFrJw4ULS09Mp+GEu+ftz6PHYeywriGBjXgk9TzoVSkt4/pmnOf/88znnnHPo0KEDTzzxBI8++ih9+vRh8ODB3meI/+c//2HAgAFkZGRw0UUXcfDgQb766itmzZrFHXfcQe/evVm/fj3r169n9OjR9OvXj2HDhnlbHKoa6/uwW2+9ldDQUHr37k2vXr2IiIhg6tSpx/WeDx06lMTERAAGDx5MVlbWUevs3buXyMhIunTpAsDpp5/uHf701Vdf5cILLyQtLQ3A+6jWBQsW0KlTJzp27EhERARjx47lnXfeAZyxu8eNGwfAuHHjmD9/vnd+RWN6b9++nf379zNkyBCMMVxzzTXex7P67uviiy/m008/xVpLRESEd6CYwsJC7/cFnKfR7feMKJabm+sd6CQlJYUBAwZU+HS3rKws3nvvPSZNmnTE/On//S+nXnkluwsLKbOW/IgImkZGsnX9eu+Y6ykpKSQkJFD+qZNr165l165dDBs2DIARI0Z4R3qr6LN4d80ati9YQJdBg+iYksLB4mK+9hm0RRoPJXFpkGbOnMno0aPp0qULSUlJRzxta+XKlTzyyCP8+OOPrF+/nrfeeguA/Px8+vbty/fff8+pp57Kn/70J+82OTk5zJs3j5tuuonx48fz2muv8eOPP1JSUsJTTz3FgAEDOPfcc/m/p1/kt+99z1VDe9GzTQqEhkJxEfzzJvj0ZZZ9/QWv/vtJFixYwB/+8AeaNGnCDz/8wJAhQ3jxxRcBuPDCC1m4cCFLliyhW7duTJs2jaFDh3LuuecydepUFi9ezAknnMDkyZP55z//yaJFi3j44Ye58cYbgcrH+vb1+OOPe0dU++yzz2jVqhV33HHHUeutW7eO3/zmN9x4442899575Ofn8/XXX/P+++9X+f5Pmzatwmb85s2bU1xc7E1CM2bM8I74tWbNGrKzsxk+fDj9+vXzvh9Vjc+9c+dO79jiLVu2rHZM761btx4xxrrvvny3CQsLIz4+nr179wKwZcsW0tPTadu2LXfeeac3WT/77LOMGTOGNm3a8NJLL3nHea/KL3/5Sx566KGjRpdbu3YtrbOzmX3nnTxzyy0Ubd7Mb4YOpW+fPrzzzjuUlJSwYcMGFi1adMQoaQDTp0/nsssuq7ATXEWfRUlZGes+/5yenpODEGMoDbBHaEvdUBKXmisphvkz4ZX74N1/Q+4evx1q+vTpjB07FoCxY8cyffp077Ju3brRsWNHQkNDufzyy/nyyy8BCAkJ4bLLLgPgqquu8s4HvPNXr15Nhw4dvDXJcePG8fnnnwNwzz338PGydXy3ZTe/PbkL5GXD3u1QWgwxCRDXjBEdmhP3RSbJycnEx8dzzjnnANCrVy/vNdhly5YxbNgwevXqxSuvvFLhMKB5eXl89dVXXHLJJfTu3Zvrr7/eO6pWZWN9H4t///vfnHXWWVx00UXMnj2bESNG8Nxzz5GRkVHpNp999hnTpk3jwQcfPGqZMYbMzExuv/12Bg4cSFxcnHe88pKSEhYtWsR7773Hhx9+yH333ceaNWuOaXzuyrapal9VLWvbti1Lly5l3bp1vPDCC97x3B977DFmz55NVlYWEyZM4Fe/+lWVcb377rukpKTQr1+/o5aVlJRQlJ/P5uXLeWfaND596CFaxcUxceJE2rRpQ//+/fnlL3/J0KFDjxrjvfywqYe9/PLLfPfdd0edoGXExLB740YSe/ZkV34+xhj6H8dwqRK41Dtdam7Oq/DDJ9A0GXZtga1r4Jo/QXRsnR5m7969zJkzh2XLlmGMobS0FGMMDz30UIXrV5YQfOfXZGzrffv2kVdQRHFUPAXN0ogJM9C7FWR+C5HRYAyRMU1hyyqwlpCQEG8zbUhIiLeD1/jx45k5cyYZGRk8//zz3o5MvsrKykhISDhqdK7qylRbkyZN4vHHHyc/P58LLriABx98kCVLlrBw4cIjhuk8bOnSpUyaNIn333+fZs2aVbjPIUOG8MUXXwDw0UcfsWbNGsCpFTdv3pyYmBhiYmI45ZRTWLJkSZXjc6emprJ9+3ZatmzJ9u3bvc35lW3Tpk2bI5qWffd1eJs2bdpQUlJCbm4uSeXG7W7VqhU9evTgiy++4NRTT2XJkiUMGjQIcE70Ro8eXeX7OX/+fGbNmsXs2bMpKChg//79XHXVVbz88su0adOGCy+8EGMMgwYNIiQkhD179pCcnMxjjz3m3cfQoUPp3Lmzd3rJkiWUlJQcdWLwySef8Ne//pV58+YdMW48wJrPP+fMs8+mQ7NmRISGclbnzqTFx1cZuwQn1cSlZkpLYMlcSO0AMU2hWSs4sA92bKjzQ82YMYNrrrmGTZs2sXHjRrZs2UKHDh28NetVq1axYcMGysrKeO211zj55JMBJzHOmDEDcK7PHp7v68QTT2Tjxo3eXsgvvfSStxf15MmTue+++7hy3ATu/GYrjL0LungGDTp8HbWkCBJSoIoke+DAAVq2bElxcfERY3X7jh3etGlTOnTowBtvvAE4JxeHe4NXNtZ3ZcLCwigqKqpw2bPPPsvFF1/M1VdfzQcffMCIESOYNm0aAwYMOGrdzZs3c+GFF/LSSy95Wyoqcnh88cLCQh588EGmTJkCwHnnnccXX3xBSUkJBw8e5Ntvv6Vbt24MGDCAtWvXsmHDBoqKisjMzOTcc88FnLG7Dw/d+sILLzB06FDv/IrG9G7ZsiVxcXF88803WGt58cUXvScjvvuaMWMGI0eOxBhDVlYWhw4dAiA7O5v58+fTtWtXEhMTyc3N9Z6EfPzxx3Sr5qE2999/P1lZWWzcuJHMzExGjhzJyy+/DMD555/PnDlzAOfSQlFREc2bN+fgwYPesdE//vhjwsLC6N69u3ef06dPP6oW/sMPP3D99dcza9asI4aBPSwzM5NbJ03iN0OHcuugQZxQ7mRFGg/VxKVmTIhzfbisFEJCwFrnFXLs4yxXZvr06Uddm7zooot49dVXueyyy+jRowd33XUXP/74I6eccgoXXHAB4NS2ly9fTr9+/YiPj+e11147at9RUVH897//5ZJLLqGkpIQBAwYwZcoUXnzxRcLCwrjiiisoLS1l6NChzJkzh44dOjotDbs3OycttgzOmlxl/Pfddx+DBg2iXbt29OrVy5u4x44dy3XXXcfjjz/OjBkzeOWVV7jhhhv4y1/+QnFxMWPHjiUjI6PSsb4rEx8fT3JyMpMnT+aZZ545YplvZ7fDnasq8+c//5m9e/d6r82HhYV5r32PGTOGZ599llatWjF16lTeffddysrKuOGGGxg5ciTgXOYYPXo06enphISEMGnSJHr27AnAE088wahRoygtLWXixIn06NEDgLvuuotLL72UadOmkZaWxm233QZUPab3U089xfjx4zl06BBnnnmm93rxtddey9VXX02nTp1ISkryngitXLmSX//6197m+N/85jf06tULcDohXnTRRYSEhJCYmMhzzz0HwI4dO+jfvz/79+8nJCSEv//976xYsYKmTZtW+v5NnDiRiRMn0rNnTyIiInjhhRcwxrBr1y5GjRpFSEgIrVu35qWXXjpiu9dff53Zs2cfMe+OO+4gLy+PSy65BIC0tDRmzZoF4D2x9b2FTxovjSceBOqtrAtmw2fTISIaiguhdWe49LcQHuH/Y3vMnTuX3/3ud3z99ddHLYuNjSXPH/fLWgu7t0BBvtMCEVO/zZb6LgcvlTd4aTxxaXgGnAmJLWDLamjaDHoNq9cE7hpjICXN7ShERI6iJC41Zwx07uu8XDJ8+HDuv//+Cpf5pRYuItKAqWObiIhIgFISFxERCVBK4iIiIgFK18RFRKRa1lpW7tnDvkOHaBkbq3vTGwglcRERqZK1lsxly3h/3TpCjMECV/XqxeknnOB2aI2emtNFRKRKO/Ly+Gj9etrFx9M+IYHWcXFkLlvGoeJit0Nr9JTERUSkSodKSggxhlDPyG0RoaFYaznkGS9A3KMkLiIiVWoZG0vTyEh25edTUlbG1v37aRsfT0JUlNuhNXpK4iIiUqXo8HDuOOkkWsbGsufgQbolJ3Pb4MGE1NFoe3Ls1LFNRESq1Soujrs16EqDo5q4iIhIgFISFxERCVBqTheRoPVTdjY/ZWcTFxFB35YtCfeMSS4SLJTERSQoLdi6lX8tXAjWUmYtvVJT+eXgwUrkElSUxEUk6FhreWnJElJiYmgSHo61lmW7drFyzx7SU1PdDk+kzuiauIgEpUMlJUR6at3GGEKMoVAPJ5EgoyQuIkHHGMPgNm3YnJtLQUkJew4eJDIsjI6JiW6HJlKn1JwuIkHpqvR0IkND+X7HDlrExnJlr140a9LE7bBE6pRfk7gxZjTwDyAUeNZa+0C55fHAy0CaJ5aHrbX/9WdMItI4RIWFcXVGBldnZLgdiojf+K053RgTCjwJnAl0By43xnQvt9pNwAprbQYwHHjEGBPhr5hERESCiT9r4gOBddbanwCMMZnAecAKn3UsEGeMMUAssA9QzxMRqTcFJSUs27WLotJSOiclkRwT43ZIIjXmzyTeGtjiM50FDCq3zhPALGAbEAdcZq0t82NMIiJeh4qLeWj+fH7KzsYAUeHh3HXyybRPSHA7NJEaMdZa/+zYmEuAUdbaSZ7pq4GB1tpbfNa5GDgJ+BVwAvAxkGGt3V9uX5OByQCpqan9MjMzqz1+Xl4esbGxdVSahq0xlRVU3mBW32XNKyry9lwHKC4tJSI0lBb1FENj+myhcZW3rss6YsSIRdba/uXn+7MmngW09Zlug1Pj9jUBeMA6ZxLrjDEbgBOBBb4rWWufAZ4B6N+/vx0+fHi1B587dy41WS8YNKaygsobzOq7rO+uWcPnK1eS5vmxzS8qIiw0lLH1FENj+myhcZW3vsrqz/vEFwKdjTEdPJ3VxuI0nfvaDJwGYIxJBboCP/kxJhERrxObN6e0rIy8oiKKSkvZkZfHgFat3A5LpMb8lsSttSXAzcCHwErgdWvtcmPMFGPMFM9q9wFDjTE/Ap8Cd1pr9/grJhERX52Skrh54ECsteQWFHB2166c27Wr22GJ1Jhf7xO31s4GZpeb97TP39uAM/wZg4hIVQa0bs2A1q3dDkPkmOixqyIiIgFKj10VEXGRtZacggIskBgVhfPYDJGaURIXEXHRf77/nq+3OI/U6NOyJdf36+e95U2kOmpOFxFxyYHCQr7YvJm28fGkxcezaNs2Pli3zu2wJIDodE9EpBLFpaX8b80aFm7bRkJkJJf17FmnT3MrLC0lLiKCEE8TenxUFOuzs+ts/xL8VBMXEanEmytX8vbKlZSUlrI5N5cHvvySPQcP1tn+I0JDyS8qwlqLtZb9BQWkNW1aZ/uX4KeauAS2/FyY+xrs2AAtO8Kpl0GMfgSlbszbtIm0+HjCQ0OJiYhgY04Oa/fupXkdjUseFxlJRtOm/LhzJwAnJiczpkuXOtm3NA5K4hK4SkvgzUdhdxbEJcGKr2HfDrj89xAa6nZ0EgSiw8IoLC0l3PN9stYSUYffLQP8cvBgth84gAVaxsYSGqIGUqk5fVskcOXsgt1bILktRMU4/+7YAPv10D+pG2N79mT3wYNszs1lfXY2HRMT6ZGSUqfHCDGG1k2b0qZpUyVwqTXVxCVwhYaDtVBWBiEhYMuc6dBwtyOTIDGwdWuSoqNZtWcPcRERDGzdmijd/iUNiL6NErjim0P6cPjhEwiLgOIi6D8K4hLdjkyCSKekJDolJbkdhkiFlMQlcBkDv7ga2nWHvdugeWvo1NeZLyLSCCiJS2ALCYGuA9yOQkTEFepFISIiEqCUxEVERAKUkrg4vbvzc6Go0O1IRESkFnRNvLE7kA0zH4edm5zry6ddDRmnuh2ViIjUgGrijd0H05wHpqSkQXwyfPRf2LHR7ahERKQGlMQbu6zVkNjS+Ts8EjCwb7urIYmISM0oiTd2Sa0gzzP0YVmp89Sz2ARXQxIRkZpREm/szpzkXAvfvcV59R8FbU90OyoREakBdWxr7FLawsT7Yd82iGwCzVrpiWciIgFCSVwgOgZad3Y7ChERqSU1p4uIiAQo1cRFRFxSai3vrFpFXlERvVu0qPOxyiX4KYmLiLhgf2Eh2w8c4JPcXCJCQ/lw/XpuGjCAQW3auB2aBBA1p4uIuGDpzp2UlJXRPiGBVnFxJDdpwsxVq9wOSwKMkriIiAtKy8qOmA4NCaG43DyR6iiJi4i4oHtyMiHGsCMvj5yCArYfOMDpHTu6HZYEGF0TFxFxQXJMDC3j4ugVF8eBwkLO79qVU9q3dzssCTBK4iIiLgkPCeGmAQPcDkMCmJrTRUREApSSuIiISIBSEhcREQlQSuIiIiIBSklcREQkQCmJi4iIBCglcRERkQClJC4iIhKglMRFREQClJ7YJvWnrAzWLoJ9O6BZK+jcF4xxOyoRkYClJC71w1r4+AVYPAfCIqCkCAacCSMuVyIXETlGak6X+pGzC5bOg9QOkNwWUtvDoo8hP9ftyEREApaSuNSPkmIICXFeACYEQgwUF7kbl4hIAFNzutSPxFRo1hp2b4G4ZrB/D7TsCE2buR2ZiEjAUk1c6kdYOFz8a+g6AEJDoPsQOP9WCA11OzIRkYClmrjUn9gEOHuK21FIY1JUAF++BRuWQnyK05GyWUu3oxKpM6qJi0jw+vgF+O4DKC2DrWvhtQcgf7/bUYnUGSVxEQlOpSWw4htIaQ9RTZx+GQcPwM6NbkcmUmeUxEUkOJkQCAuD0mJn2lqwpc5zCkSChJK4iASnkBAYfjnsyYJdm2HHT9CuF7Tu5HZkInXGrx3bjDGjgX8AocCz1toHKlhnOPB3IBzYY6091Z8xiUgj0mek05Ft23qITYQTB0Ko+vNK8PDbt9kYEwo8CZwOZAELjTGzrLUrfNZJAP4FjLbWbjbGpPgrHhFppNK6OS+RIOTP5vSBwDpr7U/W2iIgEziv3DpXAG9ZazcDWGt3+TEeERGRoOLPJN4a2OIzneWZ56sLkGiMmWuMWWSMucaP8YiIiAQVY631z46NuQQYZa2d5Jm+Ghhorb3FZ50ngP7AaUA08DVwlrV2Tbl9TQYmA6SmpvbLzMys9vh5eXnExsbWUWkatsZUVlB5g1ljKiuovMGsrss6YsSIRdba/uXn+7OHRxbQ1me6DbCtgnX2WGvzgXxjzOdABnBEErfWPgM8A9C/f387fPjwag8+d+5carJeMGhMZQWVN5g1prKCyhvM6qus/mxOXwh0NsZ0MMZEAGOBWeXWeQcYZowJM8Y0AQYBK/0Yk4iISNDwW03cWltijLkZ+BDnFrPnrLXLjTFTPMufttauNMZ8ACwFynBuQ1vmr5hERESCiV9vmLTWzgZml5v3dLnpqcBUf8YhIiISjPTENhERkQClJC4iIhKglMRFREQClJK4iIhIgNJIACIiclxKy8rYeuAAZdbSOi6O8NBQt0NqNJTERaRx27sN9myF2ARo1QmMcTuigFJUWsoTCxawdOdOQoyhXXw8vxoyhLjISLdDaxSUxEUkeBzIhu0/QXgEtD0RwsKrXn/lt/De04CBslLoPxpGjFUir4W5GzaweMcOOiQkYIxhU04O76xezVXp6W6H1igoiYtIcNi1GTIfhKKDUFYG7brDhbc7Cb0ipSXw4XMQnwKR0c42iz6EnidBSlr9xh7AtuXl0SQ8HOM58WkaFUXW/v0uR9V4qGObiASHOa8CFlLaQWp72LgM1nxX+fpFhVBS5CRwgJAQCAmFgvz6iDZodExMJL+oiDJrsdaSfegQXZKS3A6r0VBNXESCw/69EB3n/G0MhIbBwSpqhFFNnGS/JwuSWkF+LoRFQLNW9RJusDipbVs25uTw2caNAPRv1YqzunRxN6hGRElcRIJDp76w8H1IbQfFRU7zeKsTKl/fGDjvFpj9DGxZDQnJcP4tEBNffzEHgdCQEK7JyOCCE0+kzFqaRkZ6m9bF/5TERSQ4nHwhFB2C5fMhIgrOuh5ad656m6ZJMPYuJ+GH6Ori8VBvdHcoiYtIcIiIhNET4YzxTi27NrVBJXAJUPrmikhwCQnx/y1ixUWQu8f5V8RFqomLiNTGltUw85/OrWwR0c519bQT3Y5KGinVxEVEaqrwEMx83OnFnpwG4ZHOdMFBtyOTRkpJXESkpvKyoagAYpo6002aQnEhHNjnblzSaCmJi4jUVJN45/7zQk/Nu/CQcw1et6WJS5TERURqKjrGuXUtLxt2b3Fq4GMmQ5M4tyOTRkod20REaqNzX5j8sPOEuLgkZ/QzEZcoiYuI1FZMvJrQpUFQc7qIiEiAqjaJG2NuNsYk1kcwIiIiUnM1qYm3ABYaY143xow2erK9iIhIg1BtErfW/h/QGZgGjAfWGmP+ZoypYnggERER8bcaXRO31lpgh+dVAiQCM4wxD/kxNhEREalCtb3TjTG3AuOAPcCzwB3W2mJjTAiwFvitf0MUERGRitTkFrPmwIXW2k2+M621ZcaYs/0TlojIcSotgb3bwIRAs1YablSCUrVJ3Fp7TxXLVtZtOCIideBQHrz1d9i+HqyFjhlw7k0QHuF2ZCJ1SqemIhJ8vnnXSeDJaZDSDtb9AEs+czsqkTqnJ7aJSPDZvcUZYezwHbFRMU7TukiQUU1cRIJPqxMgL8dpSi8rg4I8aNHB7ahE6pxq4iISfAaeBbuznGZ0gIwR0HOYuzGJ+IGSuIgEn4hIOP8WpzYeEnJk07pIEFESF5HgZAzEadgHCW66Ji4iIhKglMRFREQClJK4iIhIgFISF3FLUaHTg3r/XrcjEZEApY5tIm7YtwNmPAwHssGWwZDzYOh56kEtIrWimriIG2b/Bw7lQ3JbaNYa5r8NW9e6HZWIBBglcRE37N4MTZs7f4eGOTXw3D3uxiTBx1ooLnL+laCk5nQRN7ToADs3QVJLKCl2fmQTUtyOSoLJvh0w60nnOfJxSc4obq1OcDsqqWOqiYu4YfQkiE10fmD3bYfhl0HrTm5HJcGitNQZijV3jzOKW1kZzHjUGaJVgopq4iJuSEyB8fc5PdMjm0BMU7cjkmCSnws5uyAlzZmOTXBOGLN3QnSsq6FJ3VISF3FLWDgktXA7CglGUU2cvhaFhyAyGkpLnNp4dJzbkUkdU3O6iDROxUVOcgtGEVEwaiLk7oZdm2FPFpxysdMCJEFFNXERaVyKCuHj52HlN84IZydfBAPODL579LsPhhbtnSb0uMSfm9YlqCiJi0jj8vU7sPwrT4evUpgz3blX/4QMtyOre0ktdMkmyKk5XUQal43LID7ZqYWHhTtjj29b73ZUIsdESVxEGpfEVDiY6/x9+GEoTZPcjUnkGPk1iRtjRhtjVhtj1hlj7qpivQHGmFJjzMX+jEdEGqiyMuee5rJS/z9dbNgl0KSp0+Fr10bo0BO6D/XvMUX8xG/XxI0xocCTwOlAFrDQGDPLWruigvUeBD70Vywi0oAdyod3/glZa6DtKfDpyzDySqe52x8SU+CaP8POjc5tWK1OcP4VCUD+rIkPBNZZa3+y1hYBmcB5Fax3C/AmsMuPsYhIQ/Xlm5C12hkMJiwCFn0Eqxf695jRMdC+B7TtqgQuAc1YPzVdeZrGR1trJ3mmrwYGWWtv9lmnNfAqMBKYBrxrrZ1Rwb4mA5MBUlNT+2VmZlZ7/Ly8PGJjG8eTiRpTWUHlDTp7tznN6SGh5IVGElt4wHmCXWyi25H5XdB/tuU0pvLWdVlHjBixyFrbv/x8f56CVnTTZfkzhr8Dd1prS00V92haa58BngHo37+/HT58eLUHnzt3LjVZLxg0prKCyht0PngOls+H5LbMjenC8I2fwFnXQ8+T3Y7M74L+sy2nMZW3vsrqzySeBbT1mW4DbCu3Tn8g05PAmwNjjDEl1tqZfoxLRBqSYRd7OplthrbtocfJ0G2I21GJBAR/JvGFQGdjTAdgKzAWuMJ3BWtth8N/G2Oex2lOn+nHmESkoYlpClf8wXmy2NJVMPK04Ht6mr9l74Q9W6FJHLTqpPevEfFbErfWlhhjbsbpdR4KPGetXW6MmeJZ/rS/ji0iASYsHJLbQOi6xpuADh6AHz6BA/sgrTt0G1yz92LdDzDrCSizzi16fX8Bp13VeN/HRsav3TKttbOB2eXmVZi8rbXj/RmLiEiDVVQArz3oDFQSEQ2L5zrD1A4+u+rtyspg9n8gNgmiYpzp7z+BHidBy46Vb3coH3Zvdu4GSG0PoaF1WRqpR7q3QkTEbVlrnASe2t6ZjktynvE+cEzV98uXFEPhQecxsuCsGxIKh/Iq3yZ7p3PCkJ/j1Nw79YNzb9StdgFKj10VEXGbtRxxQ48xTq26OhGR0KYL7N3q7CN/v5OMm7eufJvPXoWCfEhOg5T2sGYhrPnueEsgLlESFxFxW6tOEN8cdm9xronv3AT9RtXsqXVn3+Bsv2sTYOGiX0HTZpWvv3cHxMQ7fxsDoeHOMSUgqf1ERMRt0TEw9nfwzf8gdzcMPgd6j6zZtnGJMPYuKC11kn51Hdra94AfPnWa7kuLobTEGZZVApKSuIhIQ9A0Cc4Yd+zb17Rz2rCLIS8b1i92rp+PvALadT/244qrlMRFRBqTqCZwwW1QeMi5fh4W7nZEchyUxEVEGqPIaLcjkDqgjm0iIiIBSklcREQkQCmJi4iIBCglcRERkQClJC4iIhKglMRFREQClJK4iIhIgNJ94iIS+IoKYOk8Z4Su1p3hxEE1e+64SIBTEheRwFZaAm/9HTavgIgmznjae7fBsIvcjkzE73SqKiKBbccG2LIaUjtAUgtISYNv34XiIrcjE/E7JXERCWxlZc5Q3IdH7zKen7WyUtdC8psD2bBtvfOvCGpOF5FAl9oOklo6Y3E3aQr790KvYcH3bPBVC2D2M2Ctc6Jy1mToOsDtqMRlSuIiEtgiouDS38L8t2HfDkg/BQae5XZUdetQHrz/H4hr5pycFB6C2f+BtG4QHet2dOIiJXERCXyxCTBqgttR+E9+rnPZ4HDrQmQ07N8DB/criTdyuiYuItLQxSZCeBTk73em83OdRB6b6G5c4jolcRGRhi6qCVxwK5QUwe7NUFoM598afNf9pdbUnC4iEgjadoUpj8KhA04HvrBwtyOSBkBJXEQkUIRHQHgzt6OQBkTN6SIiIgFKSVxERCRAKYmLiIgEKCVxERGRAKUkLiIiEqCUxEVERAKUkriIiEiAUhIXEREJUHrYi0gwyc+FOa/CtnWQ3BZOuwrim7sdlYj4iWri4rAWVi+Eua/BD3OguMjtiKS2Skvh7cdhzXcQGg6bV8AbD0NRoduRiYifqCYuji/fgq9mQkQ0FBXA+sVwwW0QGup2ZFJTedmwcwM0bwvGQFIrZ7CM7B2Q2s7t6ETED5TExUna374HKe0gNMyplW9YCrs2Q8sObkcnNRUeCRYoK3U+x7Iy5xUW4XZkIuInSuLiNMPaMgjx1LqNARMCZSV1s39rnSbeJXOdkZcGnQWtO9fNvuVnTeJg8Nkwf6bzWZaVQp/TIKmF25GJiJ8oiYszVnGX/rB6ATRtDvn7ITHV6RhVF1YvhHf+CbGJzgnDhgfgyruhRfu62b/87KQLnBOkvdsgIQU6ZjgnZSISlJTExfmRP/M650d/yypo1x1Ovggioupm/0s+g9gkiEt0pvdkOScMNU3ieTmw4msoLoCOvesmpmBlDHTo5bxEJOgpiYsjIhJOvdQ/+w4Nd5p2DysrdZrVayI/F165D3L3ONd5v54F6Zf5J04RkQCjW8zE/wadBYUHYc9Wp7NcZBPoflLNtl290EngLTo4zfvRTZ1e2CIiopq41IO2XeHK/3MScmg49DwJElNqtm1JkdPJ7rCwcKejnIiIKIlLPWnZ0XnVVod05x723D3OrVK5u6FtXN3HJyISgNScLg1bchu47E7nYSWx8TBqgnMrlYiIqCYudaDgIHzyEqz9zrmNbNQESOtWd/tv3RkuvePn6blz627fIiIBTDVxOX6fvOjcApaQCiXFMOMRyN7pdlTS0K1fAq/8BV76Eyybr74OIsdANXE5PoefxpbS1nlKWEw85OfAjo3OA2NEKrJ5Fbz1KMQkOB0X3/u3cwuhiNSKauJyfIxxEnfBQWfaWud53VFN3I1LGrbVCyA8yrn8EhPvvJbPdzsqkYCjJC7H74zxcDAHdm6CnRuhcz9I6+5yUNKgRURBafHP0yXFEBntXjwiAcqv7VfGmNHAP4BQ4Flr7QPlll8J3OmZzANusNYu8WdM4gcdesG4vzgJPLIJtO+pIUwDSVEhrFkIB/c7nQjrY3Ca9OGw7AvnO4Nx7v8fOAZWbvD/sQPNhmWw+FMICYP+Z2jwIDmC35K4MSYUeBI4HcgCFhpjZllrV/istgE41VqbbYw5E3gGGOSvmMSPmrV0XhJYiovgzUdg88qfhy89ewp0H+Lf4yamwFX3Og8AKiuFzn2hWSsl8fI2LIMZD0NUjHOpau0iuOIP0OqE2u3HWqefSkE+NG/98zgGEvD8WRMfCKyz1v4EYIzJBM4DvEncWvuVz/rfAG38GI+IlLd5JWSthhYdnf4NhQfhs1f9n8QB4pvDwDP9f5xAtmSOk8Djk53pvducvgO1SeLWwqcvww+fOp1PQ8Pgkt+oRh8k/HlNvDWwxWc6yzOvMtcC7/sxHhEpr7TY6R1+eLjSsEgoKtDtXg2FCT3ys7AWQmr5s711LXz/CSSnOeMPRDZx7gaQoGCsn/6zGmMuAUZZayd5pq8GBlprb6lg3RHAv4CTrbV7K1g+GZgMkJqa2i8zM7Pa4+fl5REbG3t8hQgQjamsoPLWqbJSZ2AacGppJUXQpCk0beaf41VDn205xYWwbwcYwOL8m9Sq5qMAgtO6krPbeWwxODsqKYLU9scc97FqTJ9vXZd1xIgRi6y1/cvP92dzehbQ1me6DbCt/ErGmHTgWeDMihI4gLX2GZzr5fTv398OHz682oPPnTuXmqwXDBpTWUHlrXO7NsNn0yF7n3Nt+qRzIDyi+u38QJ9tBbb/BMu+dGrg6cOdRxHXxt7t8N8/QNPmzh0Ae7dC6y4wfPwxRn3sGtPnW19l9WcSXwh0NsZ0ALYCY4ErfFcwxqQBbwFXW2vX+DEWEalMSprzfHppmI518KDDmrWEc2+C95+F/buh5Qkw5rq6i09c5bckbq0tMcbcDHyIc4vZc9ba5caYKZ7lTwP3AM2AfxnnmlxJRc0FIiJyHLr0g059nOb5iKif+0BIwPPrfeLW2tnA7HLznvb5exIwyZ8xiIgITnO8HqgTdPTENhERkQClJC4iIhKgNGyQHJuc3bB5hXNbUscMaBLndkQiIo2OkrjU3u4smP5XKDgEtswZcvSKP0BsgtuRiYg0KmpOl9r7aiaUWWjR3rn1JXcP/Pi521GJiDQ6SuJSe4fynNtUDgsLh0MH3ItHJNgVF0H2LueRuCI+1JwutXfiIPhgmvNUr9JSKC6Ajr3djkokOG3/Cd76uzMCWWgYnH0DdOrtdlTSQKgmLrWXfiqMvNJ57nZYOJxzE7Tv4XZUIsGnpNhJ4CbEGbykSVP4378gP9ftyKSBUBKX2sveCWu+c5rV4xJrP7axiNTMwf1QkPdzp9GoGOfkOXePq2FJw6EkLrVTVAAzHnbGNY5Phu3r4a3HoLTE7chEgk90HIRHwUFPn5OiAueRqbGJ7sYlDYaSuNRO9k7Iy3FuKwsNc4ZF3LsdDmS7HZlI8AmPgPNuhsJ82L0F9u+B0ROhaZLbkUkDoY5tUjsR0VBW5nRoCw11rtkZ9EzmQFVaAmsWwYG9kJzm9G3Q4BgNS7vucN1U2L/XaVbX8xjEh5K41E5CMgw6C76Z5XS2sRZGXA7RsW5HJrVVVgbv/RtWfgOh4U5CHzEWBo5xOzIpr0mcnoooFVISl9oxBoZdBO17OrW3hFRo3cntqORY7NwEqxdCi47O51pSDF+8CX1+4TTjikiDpyQutWcMpJ3odhRyvEqLndaUw83noWHOY3RLipXERQKEkrhIY9W8jXOL4L7tEBMPObugQy+IauJ2ZCJSQ+qdLtJYRTWBS+/0tKoY5yE+Z9+gjm0iAUQ1cZHGLDEFLrzd7ShE5BipJi4iIhKglMRFREQClJK4iIhIgFISFxERCVBK4iIiIgFKSVxERCRAKYmLiIgEKCVxERGRAKUkLiIiEqCUxEVERAKUkriIiEiA0rPTRYJZfi7Mex12bYKWJ8Apl0B0rNtRiUgdUU1cJFiVFMOMR2HlN1BYAD9+DjMfh7IytyMTkTqimrhIsMreCbu3QEqaMx0VA1vXwv69kJDsbmwiUidUExcJVqFhgP255m3LwAJh4W5GJSJ1SDVxkWCVmArdT4Kl8yAiEooLof9oiIl3OzIRqSNK4iLByhgYNQHa94B926F5G+jS35kvIkFBSVwkmIWGQvchbkchwaC4CKx1WnWkwVASFxGRypWVwfy34dt3nSTe6xT4xdXqW9FAqGObiIhUbsXXMH8mNGsNyWmwZC4s/MDtqMRDSVxERCq3dQ1Exzh3O4SEQFwSbF7hdlTioSQuIiKVS0iBwkNOUzrAwf2Q2MLdmMRL18RFRKRyvUfC+sXOg4Iw0KwlDD3P7ajEQ0lcREQqFxkNl/4WdmxwOrm1aA8RUW5HJR5K4iIiUrWwcGjTxe0opAK6Ji4iIhKglMRFREQClJK4iIhIgFISFxERCVBK4iIiIgFKSVxERCRAKYmLiIgEKN0nLtKY5e93RqfK3glp3aDvL5xnZItIQPBrTdwYM9oYs9oYs84Yc1cFy40x5nHP8qXGmL7+jEdEfBQVwOsPwfefOE/jmvMKfDbd7ahEpBb8lsSNMaHAk8CZQHfgcmNM93KrnQl09rwmA0/5Kx4RKWfHBtizFVLSnJGpUtvDD3OguMjtyESkhvxZEx8IrLPW/mStLQIygfJPzT8PeNE6vgESjDEt/RiTiHiZIyetZ5YxFa0sIg2QP5N4a2CLz3SWZ15t1xERf2jZ0al979wIObtg10bof6bznGwRCQjGHh4jtq53bMwlwChr7STP9NXAQGvtLT7rvAfcb6390jP9KfBba+2icvuajNPcTmpqar/MzMxqj5+Xl0dsbGxdFadBa0xlBZW3TtkyZ3zokhJnZKpod99XfbbBrTGVt67LOmLEiEXW2v7l5/uzG2oW0NZnug2w7RjWwVr7DPAMQP/+/e3w4cOrPfjcuXOpyXrBoDGVFVTeYNaYygoqbzCrr7L6szl9IdDZGNPBGBMBjAVmlVtnFnCNp5f6YCDXWrvdjzGJiIgEDb/VxK21JcaYm4EPgVDgOWvtcmPMFM/yp4HZwBhgHXAQmOCveERERIKNX5/qYK2djZOofec97fO3BW7yZwwiIiLBSo9dFRERCVBK4iIiIgFKSVxERCRAKYmLiIgEKCVxERGRAKUkLiIiEqCUxEVERAKUkriIiEiA8tsAKP5ijNkNbKrBqs2BPX4Op6FoTGUFlTeYNaaygsobzOq6rO2stcnlZwZcEq8pY8x3FY34EowaU1lB5Q1mjamsoPIGs/oqq5rTRUREApSSuIiISIAK5iT+jNsB1KPGVFZQeYNZYyorqLzBrF7KGrTXxEVERIJdMNfERUREglrQJHFjTJIx5mNjzFrPv4kVrNPWGPOZMWalMWa5MeY2N2I9VsaY0caY1caYdcaYuypYbowxj3uWLzXG9HUjzrpSg/Je6SnnUmPMV8aYDDfirAvVldVnvQHGmFJjzMX1GV9dq0l5jTHDjTGLPf9X59V3jHWpBt/leGPM/4wxSzzlneBGnHXBGPOcMWaXMWZZJcuD7XequvL693fKWhsUL+Ah4C7P33cBD1awTkugr+fvOGAN0N3t2GtYvlBgPdARiACWlI8dGAO8DxhgMPCt23H7ubxDgUTP32cGanlrUlaf9eYAs4GL3Y7bz59tArACSPNMp7gdt5/L+/vDv1lAMrAPiHA79mMs7ylAX2BZJcuD5neqhuX16+9U0NTEgfOAFzx/vwCcX34Fa+12a+33nr8PACuB1vUV4HEaCKyz1v5krS0CMnHK7Os84EXr+AZIMMa0rO9A60i15bXWfmWtzfZMfgO0qecY60pNPluAW4A3gV31GZwf1KS8VwBvWWs3A1hrA7nMNSmvBeKMMQaIxUniJfUbZt2w1n6OE39lgul3qtry+vt3KpiSeKq1djs4yRpIqWplY0x7oA/wrf9DqxOtgS0+01kcfQJSk3UCRW3Lci3O2X0gqrasxpjWwAXA0/UYl7/U5LPtAiQaY+YaYxYZY66pt+jqXk3K+wTQDdgG/AjcZq0tq5/w6l0w/U7VVp3/ToXV5c78zRjzCdCigkV/qOV+YnFqNL+01u6vi9jqgalgXvlbC2qyTqCocVmMMSNw/nOc7NeI/KcmZf07cKe1ttSprAW0mpQ3DOgHnAZEA18bY76x1q7xd3B+UJPyjgIWAyOBE4CPjTFfBNDvU20E0+9Ujfnrdyqgkri19heVLTPG7DTGtLTWbvc0zVTY/GaMCcdJ4K9Ya9/yU6j+kAW09Zlug3PWXtt1AkWNymKMSQeeBc601u6tp9jqWk3K2h/I9CTw5sAYY0yJtXZmvURYt2r6Xd5jrc0H8o0xnwMZOP1YAk1NyjsBeMA6F07XGWM2ACcCC+onxHoVTL9TNeLP36lgak6fBYzz/D0OeKf8Cp7rTdOAldbaR+sxtrqwEOhsjOlgjIkAxuKU2dcs4BpP78/BQO7hSwwBqNryGmPSgLeAqwO0hnZYtWW11naw1ra31rYHZgA3BmgCh5p9l98BhhljwowxTYBBOH1YAlFNyrsZp9UBY0wq0BX4qV6jrD/B9DtVLX//TgVUTbwaDwCvG2OuxfkPcQmAMaYV8Ky1dgxwEnA18KMxZrFnu99ba2e7EG+tWGtLjDE3Ax/i9HZ9zlq73BgzxbP8aZxey2OAdcBBnLP7gFTD8t4DNAP+5amhltgAHFyhhmUNGjUpr7V2pTHmA2ApUIbzf7jCW3gauhp+vvcBzxtjfsRpbr7TWhuQo30ZY6YDw4Hmxpgs4F4gHILvdwpqVF6//k7piW0iIiIBKpia00VERBoVJXEREZEApSQuIiISoJTERUREApSSuIiISIBSEhcREQlQSuIiIiIBSklcRKrkGcN8qTEmyhgT4xnvuqfbcYmIHvYiIjVgjPkLEIUzGEmWtfZ+l0MSEZTERaQGPM/8XggUAEOttaUuhyQiqDldRGomCYgF4nBq5CLSAKgmLiLVMsbMAjKBDkBLa+3NLockIgTXKGYi4gfGmGtwRl561RgTCnxljBlprZ3jdmwijZ1q4iIiIgFK18RFREQClJK4iIhIgFISFxERCVBK4iIiIgFKSVxERCRAKYmLiIgEKCVxERGRAKUkLiIiEqD+H5KkTcB0zB2uAAAAAElFTkSuQmCC", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "def buffon_needle_simulation(num_needles, needle_length, line_spacing):\n", - " intersected = 0\n", - "\n", - " for _ in range(num_needles):\n", - " # Generate a random angle between 0 and 180 degrees (in radians)\n", - " angle = random.uniform(0, math.pi / 2)\n", - "\n", - " # Generate a random position for the midpoint of the needle\n", - " mid_point = random.uniform(0, line_spacing / 2)\n", - "\n", - " # Check if the needle intersects a line\n", - " if mid_point <= (needle_length / 2) * math.sin(angle):\n", - " intersected += 1\n", - "\n", - " # Estimate the probability\n", - " if intersected == 0:\n", - " estimated_probability = 0\n", - " else:\n", - " estimated_probability = intersected / num_needles\n", - "\n", - " return estimated_probability\n", - "\n", - "def compute_true_value(needle_length, line_spacing):\n", - " true_value = (2 * needle_length) / (math.pi * line_spacing)\n", - " return true_value\n", - "\n", - "\n", - "# Input parameters\n", - "needle_length = 1.0 # Length of the needle\n", - "line_spacing = 2.0 # Distance between the lines\n", - "max_num_needles = 500 # maximum number of needles to drop \n", - "\n", - "estimates = []\n", - "\n", - "for num_needles in range(max_num_needles):\n", - " estimated_probability = buffon_needle_simulation(num_needles, needle_length, line_spacing)\n", - " estimates.append(estimated_probability)\n", - "\n", - "# Compute the true value\n", - "true_value = compute_true_value(needle_length, line_spacing)\n", - "\n", - "\n", - "# Create a plot\n", - "plt.figure(figsize=(10, 6))\n", - "plt.plot(range(max_num_needles), estimates, color='teal')\n", - "plt.xlabel('Number of Iterations')\n", - "plt.ylabel('Estimated probability')\n", - "plt.axhline(y=true_value, color='red', linestyle='--', label='True Value')\n", - "plt.title('Dependence of the estimated probability on the number of iterations')\n", - "plt.grid(True)\n", - "\n", - "# Show the plot\n", - "plt.show()" + "data": { + "image/png": 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", + "text/plain": [ + "
" ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" }, { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "You can read more on the analytical solution of the version of this problem over a grid [here](https://mathworld.wolfram.com/Buffon-LaplaceNeedleProblem.html)." + "data": { + "image/png": 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", + "text/plain": [ + "
" ] - }, + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "r = 1\n", + "\n", + "for n in 5 * 10**jnp.array([1, 2, 3]):\n", + " approx_pi(r, n)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Buffon's needle problem\n", + "\n", + "Here is another interesting example where random number generation can help us solve an analytical problem.\n", + "\n", + "Buffon's Needle is a classic probability problem that involves randomly dropping a needle of a certain length onto a floor with parallel lines drawn at regular intervals. The goal is to estimate the probability that the needle will intersect one of the lines. The probability can be calculated using the following formula:\n", + "\n", + "$$\n", + "P = \\frac{2L}{\\pi d}\n", + "$$\n", + "\n", + "Where $P$ is the estimated probability of the needle intersecting a line, $L$ is the length of the needle, $d$ is the distance between the lines on the floor." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Monte Carlo Tree Search\n", - "\n", - "Monte Carlo Tree Search (MCTS) is a heuristic search algorithm used mainly in decision processes involving uncertainty and in particular in games. It's a popular algorithm for game-playing AI, especially in environments where the full breadth of possible moves can't be exhaustively explored due to computational constraints. Some remarkable recent applications of MCTS are [AlphaGo](https://blog.research.google/2016/01/alphago-mastering-ancient-game-of-go.html) and [AlphaZero](https://arxiv.org/pdf/1712.01815.pdf), where MCTS is combined with neural networks to determine the best next action." + "data": { + "image/png": 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2LS1SU3n2jDNIEvE7yRhjjFEvYQaO9PT0Az5nWUEBt336KQD3n3gifdq0iXLV/qWnp3PEEUfUqT2exHN3eWUlv3r/fRbm59f68Xhu3x+t3aC3XWs36G3X2g26271ip8WGVAYCHPXMM3y/YQMn9e/PBxdfjNjWjUYlr6SEs197jW/Wr2dAu3ZkXXedXaLeGGP2w8vTYu0e6yF/+/prvt+wgdZpafxr8mQbNhqZb9ev56xXXyVvxw7aNG3Ko5Mm2bBhjDExlDC7VDIzM/f5sYX5+dw5axYAj0yaRI8ILxAWLfPmzUNEmDdvnt8pEYm37mfmz+eY554jb8cOhnbsyA+/+AUnDRhQ63Pjrb2utHaD3nat3aC3XWs36G73SsJv4dhdVcXl06dTEQgwedAgLj30UL+TjEcqqqq46cMPefSHHwA4c/Bgnp8yhZZpaT6XGWNM4kn4geOvX3xB5qZNtGvWjCdPO812pTQSm3fu5NzXX+eLNWsA+POxx3Lb0UfbWUfGGOOThB445m7cyF+//BKAx085hS4tWvhcZLwwLy+PKf/5D+u2b6dlaiovn3UWpw8a5HeWMcYktIQdOMoqK7ls+nSqnOO8oUM5/5BD/E4yHnh54UJ+PmMGZZWVHNS+PW9fcAGDO3TwO8sYYxJewpwWm5+fT6dOnfY8fsvHH/O3OXPolJ5O1nXX0aF5c/8i96GsrIz169fTo0cPmjZt6ndOnfnRXRkI8MdPPuH+b74B4NSBA3n5rLNoHeHnt3Uee1rbtXaD3nat3aC33cvTYhNm4Ai/Dsc369Yx7tlnCTjH9PPP54zBg/2NNA1SWFrKBW+8wcerVwPwp6OP5q4JE3y54Z4xxjQmdnv6eqi+Q9+uigounz6dgHNceuihcT1s5OTkcMkll5CTk+N3SkRi2b0oP5/Dnn6aj1evJj0lhdfPPZe/HHdcvYcNW+exp7VdazfobdfaDbrbvZIwA0dxcTEQPKBwY0kJ3Vq25OGTT/Y36gCKiop4+eWXKSoq8jslIrHqfmPJEsZOncrqoiL6tmnDN1ddxTkHH9ygZdo6jz2t7Vq7QW+71m7Q3e6VhDtodFyvXiy89lo27dhB22bN/M4x9RBwjv/97DPu/uorACb268er55xDO/v7NMaYuJVwAwdAv7Zt6de2rd8Zph62lZVx8bRpvJedDcDvxo7l3okTaWLHaxhjTFxLyIHD6LSsoIAz/vMfVmzdStMmTfjX6adzsV0Z1hhjVEiYgaNLly5+J0Ssa9eu3HHHHXTt2tXvlIhEo3vG8uVcPG0aJbt307NVK6ZfcAEjo7BebJ3HntZ2rd2gt11rN+hu90pCnhZr9Ag4x1+/+ILbQzfXG9+7N6+fey6d0tP9DTPGmARgp8XWw/btDVpPvti+fTsffvihunavukvKyzn39df3DBs3HHYYn1x6aVSHjURf537Q2q61G/S2a+0G3e1eSZiBY3XoolCarFy5kpNPPpmVK1f6nRIRL7pXFhYydupUpi1dSmpyMlMnT+Yfp5xCSnKyh6W1fN4EXud+0dqutRv0tmvtBt3tXkmYYziMHh+uXMkFb75JcVkZXVu0YNr553NEjx5+ZxljjGkAGzhMXKmoquLXM2dSXFbG2B49ePO88+jasqXfWcYYYxrIBg4TV1KSk3nzvPN48scf+fuJJ5LWxL5FjTGmMUiYf83T0tL8TohYWloa/fv3V9fe0O5DOnXiH6ec4nFV3STqOveT1nat3aC3XWs36G73ip0Wa4wxxpha2WmxxhhjjFElYQaOxYsX+50QsYULF9KxY0cWLlzod0pEtHaD3nat3aC3XWs36G3X2g26272SMANHZWWl3wkRq6yspKCgQF271m7Q2661G/S2a+0Gve1au0F3u1cSZuAwxhhjjH9s4DDGGGNM1NnAYYwxxpioS5jTYjds2EC3bt38zonIjh07WLRoEcOGDaNFixZ+59SZ1m7Q2661G/S2a+0Gve1au0Fvu5enxSbMwGHX4TDGGGMiY9fhqIcNGzb4nRCx9evXc9NNN7F+/Xq/UyKitRv0tmvtBr3tWrtBb7vWbtDd7pWEGTi2bNnid0LENm/ezIMPPsjmzZv9TomI1m7Q2661G/S2a+0Gve1au0F3u1fieuAQkSYi8hcRyRGRUhFZLSK3i0hcdxtjjDFmb/F+87ZbgGuAy4EsYDTwLLANeNjHLmOMMcZEIN4HjrHA286590Lv54rIhQQHD2OMMcYoEe+7Jr4CjheRgwBEZDgwDnh/Xy8QkTQRaVX9BrQEaN++fSx6PdWhQweuu+46OnTo4HdKRLR2g952rd2gt11rN+ht19oNutu9EtenxYqIAHcT3LVSBSQDf3LO3bOf19wJ3FHzcTst1hhjjIlMIp0Wez5wCXARMJLgsRy/F5HL9/Oae4DWYW89AHbt2hXd0ijYtWsX8+bNU9eutRv0tmvtBr3tWrtBb7vWbtDd7pV4Hzj+D7jXOfcf59wi59yLwIPArft6gXOu3Dm3vfoNKAFYsWJFbIo9tGzZMkaNGsWyZcv8TomI1m7Q2661G/S2a+0Gve1au0F3u1fifeBoDgRqPFZF/HcbY4wxJky8n6UyA/iTiKwleFrsCOAm4Blfq4wxxhgTkXgfOH4F/Bl4HOgEbASeBP6fn1HGGGOMiUxcDxzOuRLgt6G3BklK0rcXJikpiZYtW6pr19oNetu1doPedq3doLddazfobvdKXJ8W6wW7W6wxxhhTP4l0WqwxxhhjGoGEGTg0noq0ZMkShg4dypIlS/xOiYjWbtDbrrUb9LZr7Qa97Vq7QXe7VxJm4CgrK/M7IWJlZWUsWbJEXbvWbtDbrrUb9LZr7Qa97Vq7QXe7VxJm4DDGGGOMf2zgMMYYY0zU2cBhjDHGmKhLmIGjT58+fidErF+/frz99tv069fP75SIaO0Gve1au0Fvu9Zu0NuutRt0t3vFrsNhjDHGmFrZdTjqIT8/3++EiG3atIl77rmHTZs2+Z0SEa3doLddazfobdfaDXrbtXaD7navJMzAkZeX53dCxDZu3Mhtt93Gxo0b/U6JiNZu0NuutRv0tmvtBr3tWrtBd7tXEmbgMMYYY4x/bOAwxhhjTNTZwGGMMcaYqEuYgSN0lK0qbdq04ZxzzqFNmzZ+p0REazfobdfaDXrbtXaD3nat3aC73St2WqwxxhhjamWnxdbD7t27/U6I2O7du1m/fr26dq3doLddazfobdfaDXrbtXaD7navJMzAofGWwIsXL6Znz54sXrzY75SIaO0Gve1au0Fvu9Zu0NuutRt0t3slYQYOY4wxxvjHBg5jjDHGRJ0NHMYYY4yJOhs4jDHGGBN1CXNabFFRkbrznwOBABUVFaSkpJCUpGc21NoNetu1doPedq3doLddazfobffytNiEGTiidR0O5xwi4vlyjTHGGL/ZdTjqYeXKlZ4uL2vzZn47cyYHPfooZZWVni672ooVK5gwYQIrVqyIyvKjRWs36G3X2g1627V2g952rd2gu90rTfwOiJUdO3Y0eBmlFRW8vmQJT82dy9fr1u15/J3lyzlv6NAGL7+mHTt2MHv2bE/aY0lrN8SufVtZGa9mZVFaUcFvjjiiwcuzdR57WrtBb7vWbtDd7pWEGTgaYlF+Pk/Pm8eLCxdSXFYGQLIIkwcN4upRozihXz+fC40GAef4LCeHZzMzmbZ0KWWVlbRr1oxrRo8mrYn9r2iMadzsX7l92Ll7N69lZfHUvHl8u379nsf7tGnDL0aO5MqMDLq2bOljodFiVWEhz2Vm8vyCBazb/t9doEM7duTKjAwqAwHSfOwzxphYsIGjhgWbNvHU3Lm8tGgR28vLAWiSlMSUwYP5xciRTOzXjyQ7SNQcwI7du3k9K4tnMzP5cu3aPY+3adqUiw45hCsyMhjdrZsdcGyMSRgJM3D07Nlznx/bsXs3ry5ezFPz5vH9hg17Hu/fti2/GDmSKzIy6NyiRSwy99KrVy+efvppevXqFfPP3RBau6Fh7c45vlizhmczM3ljyRJ2VlQAIMCJ/ftzZUYGZwweTNMo7D5J1HXuJ63doLddazfobvdKQp8WOy8vj6fmzuWVRYsoCd3BLyUpiTOHDOHqkSM5tm9f25phDmhNcTEvLFjAcwsWsLqoaM/jA9u148qMDC4dPpweUTgl2xhtqgIBVmzdyty8PH7cuJG5eXmcPWQIv/XgwGkTHV6eFpswWzi2bt1Kq1atKCkv59+LF/PU3LnMzcvb8/EB7dpx9ciRXJ6RQaf0dB9L/6ugoIDp06czZcoUOnTo4HdOnWnthrq376qo4K2lS3k2M5PPcnKoHttbpqZy/tChXDliBGN79IjZLpNEWOfxRms3xKY94FxwuAgNFj9u3Mj8TZvYUeP27J3S0+s8cNg61y1hBo6PFy/mx8WLeWXRoj2bulOTkzl7yBCuHjWKY3r3jrv96WvXruUXv/gFI0eOVPUNqrUb9t/unOPb9et5NjOTV7Oy9hzjA3Bc375cMXw4Zw0ZQnpqaqyzG+06j2dau8H79oBzrCwsDG612LiRH/PymJ+Xt2fLcbjmKSmM6NKFUV27MrpbN8b06OFbdyxpbvdKwgwcv5wzB5o2BWBQ+/ZcPWoUlw0fTofmzX0uM/FuY0lJcJdJZibLt27d83ifNm24YvhwLs/IoI+yy+YbU18B51hVWLjXbpF5eXl7DeDVmjVpQkaXLozu1m3PgDG4QweSFV3a23gnYQaOlKQkzhs2jKtHjeLoXr3ibmuGiS/lVVW8lpXFc5mZfLhqFYHQsU7NU1I45+CDuTIjg/G9e9sxPqZRc86xqqgouNUibLjYVstw0bR6uOjalVHduu0ZLprYcGFCEmbgmHbccZx2/PF+Z5g45pxjSXExnHIKJ3/8MdtDu94AxvXqxZUZGZx78MG0TLOrZpjGxzlHTnHxXrtF5uXl7bnYYbimTZowvHPnvbZcDOnY0YYLs18JM3B0a9vW74SItWjRgmOOOYYWPpyS2xDauvN37ODlRYt4NjOTxZs3w+GHs72igh6tWnH58OFckZHBgHbt/M7cL23rPJzWdq3dAOnp6Rx+0kl8WVjIa598wty8POZu3EhRLcNFWnIyw8O2XIzq2pWDO3YkJTk55t2a17nmdq8k9GmxJnFVVFXxXnY2z2Zm8n52NpWBABD8x/WsIUO4IiOD4/v2tX3NptEoKi3lb19/HRwu8vIoLC39yXNSk5MZ3rnznq0Wo7p1Y6hPw4WJD3ZabD0EQj9QNAkEAlRUVJCSkkKSoh98Grof+OYb/vjpp3veH9O9O1dkZHDewQeTnpwc1+210bDO90Vru7butCZN+L85c6gK/ZKZmpzMoZ067TneYlTXrgzt1InUOB4utK3zcJrbvZIwX/XChQv9TohYZmYmTZs2JTMz0++UiGjovnDYMLq1bMnNRx5J1nXX8e3Pf841o0eTu2xZ3LfXRsM63xet7dq6m6ek8L/jx/Pkaafx0tFHs/vOO3ly9GieOO00fj5yJCO6do3rYQP0rfNwmtu9kjBbOIwJ16t1a9bdeKOdZWISyh0TJgAwb948qKryN8YknITZwmFMTTZsGGNM7NjAYYwxxpios4HDGGOMMVGXMKfFbtmyRd3163fv3s3mzZvp1KkTqT7cn6O+tHaD3nat3aC3XWs36G3X2g162708LTZhBg67DocxxhgTGS8HjoTZpZKTk+N3QsRWr17Nueeey+rVq/1OiYjWbtDbrrUb9LZr7Qa97Vq7QXe7VxJm4Ni2bZvfCRErLi7mjTfeoLi42O+UiGjtBr3tWrtBb7vWbtDbrrUbdLd7JWEGDmOMMcb4xwYOY4wxxkRd3A8cItJdRF4Ska0isktEMkVklN9dJr6tLiqiwq6kaIwxcSOuL20uIm2Br4HPgUnAZqA/UBzpsrp27eppWyx069aNu+++m27duvmdEhG/u51znP7vf7OtrIxp55/P4d271/m1frfXl9Zu0NuutRv0tmvtBt3tXonr02JF5F7gKOfc0Q1Yhp0Wm2BmrlzJpJdfpmVqKutuvJHWTZv6nWSMMSol0mmxk4EfReR1EdksIvNF5Bf7e4GIpIlIq+o3oCWg8sjg4uJi3nnnHXXtfnff/803APx85MiIhw2/2+tLazfobdfaDXrbtXaD7navxPvA0Q+4FsgGTgKeAB4Rkcv285pbgW1hb+sBcnNzoxoaDatXr+aMM85Qd962n90L8/P5ZPVqkkT49ZgxEb/e1nnsaW3X2g1627V2g+52r8T7wJEEzHPO3eacm++cexJ4muAQsi/3AK3D3npEP9PEiwdCWzfOOfhg+rRp42+MMcaYPeL6oFEgD1hS47GlwNn7eoFzrhwor35f7BbkCSOvpIRXFi0C4KYjjvC5xhhjTLh438LxNTCoxmMHAWt8aDFx7tHvv6ciEOConj0Z08M2bBljTDyJ94HjQeAIEblNRAaIyEXA1cBjkS6oqcIzFZo2bcrBBx+srt2P7p27d/PE3LkA3DR2bL2XY+s89rS2a+0Gve1au0F3u1fi+rRYABE5jeBxGQOBHOAB59zTEbzeTotNAI//8APXv/8+/du2ZfkNN5CcFO+ztDHGxD8vT4uN92M4cM69C7zrd4eJXwHnePDbbwH47RFH2LBhjDFxKGH+ZV64cKHfCRHLzMykVatWZGZm+p0SkVh3z1i+nJWFhbRp2pQrMjIatCxb57GntV1rN+ht19oNutu9kjADRyAQ8DshYoFAgJKSEnXtse5+ILR145pRo2iRmtqgZdk6jz2t7Vq7QW+71m7Q3e6VhBk4TOP048aNfLFmDU2Skrjh8MP9zjHGGLMPNnAY1aov9HXhIYfQ3Q4KNsaYuGUDh1Fr7bZtvJaVBTTsVFhjjDHRF/enxTZU9WmxeXl5dOnSxe+ciOzatYtly5YxePBgmjdv7ndOncWq+/cffcT933zDcX378ull+7u9Tt3ZOo89re1au0Fvu9Zu0Nvu5WmxCTNw2HU4Gpft5eX0fPBBtpeX895FF3HKwIF+JxljTKOTSLen98y6dev8TojY2rVruf7661m7dq3fKRGJRffUefPYXl7O4A4dOHnAAM+Wa+s89rS2a+0Gve1au0F3u1cSZuDYunWr3wkRKygo4PHHH6egoMDvlIhEu7syEODh774DgjdpS/LwBn22zmNPa7vWbtDbrrUbdLd7JWEGDtN4TFu6lDXbttGxeXMuOfRQv3OMMcbUgQ0cRhXnHPeHToW97rDDaJaS4nORMcaYurCBw6gyZ906vt+wgbTkZK477DC/c4zBOcfWXbv8zjAm7iXMwNGxY0e/EyLWqVMnbrzxRjp16uR3SkQ6derEb2+8kfYdOrC7qorSigp27N6NF2dEVV/G/NJDD6VTenqDl1eT5nWusRv0tTvnWLplCx9u3cpBt93GpE8/5eSXX/Y7KyLa1nk1rd2gu90rdlpsI5JTVMTf58yhyjmqAgEqQ39W1fJnZSCwz49VBQLBj9fz9ZWBAIFavq+KbrmFNk2b1vvrW1VYyMB//AMHZF13HQcrHCKNPs45lhYUMCs3l9lr1jArN5fNO3fu9Zz0lBS23Hyz7eIzjU5C3Z7eKzt27FA3cOzYsYNFixYxbNgwWrRoccDnb9m1i8d//DEGZfVT2xASiRcXLsQBkwYMiNqwEek6jxdauyH+2p1zLNmyZa8BY0uNXSZNmzRhTLduHJSSwtmjRzNhwADSmuj55zTe1nldae0G3e1e0fN/SAOtXLmSbt26+Z0RkRUrVnDkkUcyd+5cRo4cecDnd2/Zkv8dP55kEZokJZGclESySK1/NtnPxw70+gMte2lWFiefeCKffPwxIzMy9nyseQN/+7v9mGMY3a0bnaOwK6VapOs8XmjtBv/bAzUGjNm1DBjNmjThyJ49mdCnDxP69OGwbt3IWriQUaNGcc3cuaqGDfB/ndeX1m7Q3e4VXf+XmP3q3qoV/+/YY/3OoKBpU9i5k7ZpabRt1syz5SaJcNpBB3m2PJOYAs6RtXnzfweMNWsoqGXAOKpXLyb07h0cMLp3JzU52adiYxoHGziMMY1awDkWhw8YublsLS3d6znNU1I4KrQF45jeveN+wFixdSsHtW/vd4YxEbGBwxjTqAScY1F+/l5bMAprGTDGhbZgHNOnD6O7dYvrASPcG0uWcP4bb3D7+PHcMWGC3znG1FnCDBxNlO1jhWBzhw4d1LVr7Qa97Vq7oeHtAedYGD5g5OZSVFa213PSqweM0BaM0d26kdLAAcOPdb6qsJCr3nmHgHOUVlbWezlav1+0doPudq9EfFqsiDwHPOOc+yIqRR5LpNNijUkEAedYsGnTngHjizVrah0wju7dm2NCx2CM6tq1wQOG38orKznqmWeYm5fHkT17Muvyy9V/TSb++X1abEvgIxFZBzwLPO+c29CQCGOMqavyykqOmDqV3VVVex5rkZrK0b167RkwRjaCAaOmP3z8MXPz8mjXrBn/OfvsRvf1mcYv4iuNOufOBroDjwLnArki8oGInCMicXvVm6VLl/qdELGsrCwGDBhAVlaW3ykR0doNetu1dkPk7c1SUjixf38mDRjAfRMn8t3Pf07RLbfw/sUXc8u4cYzp0SMmP4xjuc7fWrqUR77/HoDnp0yhZ/A3znrT+v2itRt0t3ulXjuTnHNbgYeBh0VkBPAz4EVgh4i8BDzunMv2LrPhysvL/U6IWHl5OatWrVLXrrUb9LZr7Yb6tc+48MIoFtVNrNZ5bnExP3vnHQB+N3asJ6eGa/1+0doNutu90qB7qYhIV+DE0FsV8D4wFFgiIjc2PM8YYxLX7qoqzn/jDYrLyhjTvTv3HH+830nG1FvEA4eIpIjI2SLyLrCG4G6VB4GuzrnLnXMnApcCt3ubaowxieW2Tz/l+w0baNO0Kf855xw7bsOoVp9dKnkEB5V/A4c75zJrec6HQHH9s4wxJrG9u2IF93/zDQDPnnEGfdq08TfImAaqz8BxI/C6c65sX09wzhUBfetdFQX9+vXzOyFiAwYMYObMmQwYMMDvlIho7Qa97Vq7QW97NLvXbdvG5dOnA/CbMWOYMniwp8u3dR57mtu9YrenN8aYOFJRVcWE559nzrp1jO7Wja9/9jM1V0E1jY+X1+Fo0EGjmmzatMnvhIjl5eVx5513kpeX53dKRLR2g952rd2gtz1a3f/7+efMWbeOVmlpvHrOOVEZNmydx57mdq/YwBHH8vLyuOuuu9R9g2rtBr3tWrtBb3s0uj/Izua+r78G4JnJk+nXtq1nyw5n6zz2NLd7JWEGDmOMiWcbtm/nstBxG9cfdhhnH3ywv0HGeMwGDmOM8VllIMCFb75Jwa5djOjShb+feKLfScZ4zgYOY4zx2Z2zZvHl2rW0SE3l1XPOoWkC31HUNF4JM3C0UXgOe9u2bbn44otpG6X9uNGitRv0tmvtBr3tXnV/vGoVd3/5JQBPn346A9u39yJvvxJ9nftBc7tX7LRYY4zxSV5JCRlPPsnmnTu5euRInjz9dL+TjNmLnRZbD2Vl+7xOWdwqKytj5cqV6tq1doPedq3doLe9od1VgQAXT5vG5p07ObRzZx46+WSPC/ctUde5nzS3eyVhBo5ly5b5nRCxJUuWMHDgQJYsWeJ3SkS0doPedq3doLe9od1/+eILPs/NJT0lhdfOOYdmKSkeF+5boq5zP2lu90rCDBzGGBMvPs/J4a7ZswF44rTTGNShg89FxkSfDRzGGBND+Tt2cNG0aTjgZxkZXHLooX4nGRMTNnAYY0yMBJzj0rfeYtOOHQzt2JF/nHKK30kmwRSVlvLo999z2NNPs2F7g44BjZid7G2MMTHinGNM9+58s349r517Ls1jeNyGSVwB5/gsJ4ep8+fz1tKllFdVAfD8ggXcdvTRMeuw02KNMSbGNu/cSaf0dL8zTCO3priY5zIzeTYzkzXbtu15/NDOnblqxAguHjaM9s2b73cZXp4Wa1s4jDEmxmzYMNFSVlnJ9GXLeGb+fD5ZvZrqTQqt09K4eNgwfjZiBCO7dkVEYt6WMMdwZGdn+50QseXLlzN27FiWL1/ud0pEtHaD3nat3aC3XWs36G3X2g3Rb8/ctIlfvf8+3e6/nwvffJOPQ8PGcX378vJZZ5H3u9/x2KmnMqpbN1+GDUigLRw7d+70OyFiO3fu5Ntvv1XXrrUb9LZr7Qa97Vq7QW+71m6ITntRaSmvLFrE1Pnzmb9p057He7RqxZUZGVyZkUHfOLqUesIMHMYYY4x21QeAPjN/PtPCDgBNTU5myuDB/Cwjg4n9+pGcFH87MGzgMMYYY+KcFweA+s0GDmOMMfvknGNDSQnLCgr2vN19/PG0SkvzO63RK6us5O1ly5haywGgFw0bxlU+HgBaH6oGDhG5FbgbeNg599tIXturV6+oNEVTnz59ePHFF+nTp4/fKRHR2g1627V2g952rd1Qe3t5ZSUrCwv/O1hs3crSLVtYvnUrO3bv3uv1lx56KGN69IhxdeNb5/uSuWkTz8yfz0sLF1IUdrO34/r25WcZGZw1ZEhM773jFTXX4RCRw4DXgO3A53UdOOw6HMYY81+FpaV7hoqlW7awbOtWlhUUsLqoiMA+fh40SUpiQLt2DO7QgcHt23PVyJEMaNcuxuWN24EOAL0iI4N+PhwAmnDX4RCRFsDLwC+A/6nPMgoKCtQNHFu2bOG1117jvPPOo2PHjn7n1JnWbtDbrrUb9LbHc3dVIMDabduCQ0XYrpBlBQVs2bVrn69rlZbGkA4dgoNF2Fv/tm1JSU6O4VdQu3he5wdSW/u+DgBNSUpiyuDBXDViRNweAFofKgYO4DHgPefcJyKy34FDRNKA8J2LLQHWr19Pv379opjovXXr1nHDDTcwduxYVf9zae0Gve1au0Fvezx076qoYHn4QBHaWrFi61bKKiv3+bouzZqxadEiLjjhBMYPGbJnsOjSokVcHw8QD+u8vsLbS1NTeXb+/J8cADqsU6fgAaCHHkqHOD8AtD7ifuAQkQuAkcBhdXzJrcAd0SsyxpjYcc6xeefOn2ypWFZQsNcPq5rSkpM5qH37n2ytGNS+PcsXL2bULbdw8403MnLkyBh+NcY5xzHPPUducTHw3wNAfzZiBKMUHQBaH3E9cIhIT+Bh4ETnXNmBnh9yD/BA2PstgfVetxljTDTllZRw1muvsayggOKyff/z175ZM4Z07MjgGsNFnzZtGs2m+MZERLh8+HC+WLOGq0aM4MwhQxLmJn5xPXAAo4BOwNywqS8ZGC8iNwBpzrmq8Bc458qB8ur3G/O0aIxpvNo3b84PGzZQ5RxJIvRt0+YnWysGd+jQKDe9N3Z3HHNMQv5siveB41NgWI3HngWWAffVHDb2p2XLll52xUTLli058cQT1bVr7Qa97Vq7IbL2TTt20LF587j4zT3a6zw1OZm3L7iAXq1bM7B9e5o28e6fa63fL1q7Ye/2RBw2QNFpsdVEZBaQaafFGpNY3l62jJ+98w6/GzuW244+2u8cYxKCl6fF+v9rQoxUVdV5Y0jcqKqqYvv27eratXaD3nat3XDg9tKKCm54/32mvPoqhaWlzFixgspAIMaVP9WY13m80toNutu9om7gcM5NiPQqowCLFi2KQk10LViwgNatW7NgwQK/UyKitRv0tmvthv23L9myhTH/+heP/fADAL8fO5bZV1xBkzjYpdJY13k809oNutu9Eu/HcBhjEpBzjqfnzeO3M2dSWllJp/R0XpgyhZMGDPA7zRhTTzZwGGPiSlFpKVe/+y5vLFkCwIn9+/P8lCl0adHC5zJjTEPYwGGMiRtz1q3jwjffZO22bTRJSuKe44/nprFjSUrQo/qNaUxs4DDG+E+Ef61YwVPvvkuVc/Rv25Z/n302h3Xv7neZMcYj6k6LjVT1abEFBQW0b9/e75yIVFRUUFxcTJs2bUhRdCU6rd2gt11rN0DO1q1cMm0aczZuBODiYcN4/NRTaZWWdoBX+kvzOtfarrUb9LZ7eVpswgwcdh0OY+JP9bU1CktLSU9J4Z+nnsqlw4f7nWWMCbHrcNTD6tWr/U6I2KpVq5g8eTKrVq3yOyUiWrtBb7u27rLKSn4Vdm2N1jt38vakSaqGDW3rPJzWdq3doLvdKwkzcGzf3qDBzBfbtm1jxowZbNvPHSHjkdZu0NuuqXtp6Noaj4aurXFxv35se+AB2irb2qppndektV1rN+hu94odNGqMiQnnHFPnz+fXH3xAaWUlHZs35/kpU+hcUsLLCXz1RWMShQ0cxpioKy4r4+oZM3g9dG2NE/r144Uzz6RLixbMmzfP5zpjTCzYwGFq9Y/vvqNX69ZM7NeP9NRUv3OMYnPWreOiN99kTejaGn897jh+f+SRdm0NYxJMwgwc3bp18zshYt27d+f++++ne4yvRVBaUcHNH39MeVUVS6+/nsEdOkT0er+6vRAP7dvKymiekkJKcnKdXxMP3TVVBQLc+9VX3DFrFlXO0S90bY3DazTGY3tdaO0Gve1au0F3u1fstFjzE5+sXs0JL75I95YtWXfjjYj9JhoT5ZWVPP7DD/zlyy+55/jjuXrUKL+T6m3D9u1c+tZbfJ6bC8CFhxzCE6edFvfX1jDG7M1Oi62HoqIivxMiVlRUxOuvvx7z9k9CpxBP7NevXsOGX91e8KO9KhDghQULGPToo9z00UcUlpbyalZWRMuIp3U+Y/lyhj/xBJ/n5pKeksJzZ5zBy2edtc9hI57aI6G1G/S2a+0G3e1eSZiBY82aNX4nRCwnJ4fzzjuPnJycmH7e8IGjPvzq9kIs251zvJ+dzYgnn+Ty6dNZs20b3Vu25F+nn86Hl1wS0bLiYZ2XVVby6w8+YPJ//sPW0lJGdOnCvF/+ksszMvY7uMZDe31o7Qa97Vq7QXe7VxLmGA5TN1t37WJeXh4Ax/ft63NN4/Xd+vXc8sknzA4Nwq3T0rh13Dh+NWYMzRVd9rja8oICzn/jDRbk5wNw4xFHcM/xx5PWxP6JMcYE2b8GZi+f5+bigKEdO9K1ZUu/cxqd5QUF3PbZZ0xbuhSAtORkfj1mDH8cN452zZr5XFd/uyoqWFpQQMfmzXluyhROGTjQ7yRjTJyxgcPspaG7U0ztNpaUcNesWUydP58q50gS4fLhw7lrwgR6Bg/IUm1E16785+yzOaJHDxtUjTG1SpiBo5nC3x6bNWvGiBEjYtruxcDhR7dXvG4vLivjb19/zUPffktpZSUAkwcN4u7jjmNop06efA6Ij3V+5pAh9XpdPLTXh9Zu0NuutRt0t3vFTos1e+QUFdHvkUdIFqHolltoaacw1ltZ6BTXv375JYWlpQAc2bMn902cyLhevXyuM8aYuvHytNiE2cJhDuzT0NHTR/ToYcNGPVUFAry0cCG3z5rF2tBNmg7u2JF7jj+e0w86yK5pYoxJWAlzWuyCBQv8TojY/PnzSUtLY/78+TH5fF4dvxHrbi/Vt905x3srVpDx5JNc8fbbrN22jR6tWjF18mQWXHMNkwcNiuqwkYjr3G9au0Fvu9Zu0N3ulYTZwqFx15Fzjt27d8ekPeDcni0cDR04Ytnttfq0f7NuHbd88glfrl0LQJumTblt3DhuOPxwmsXoFNdEW+fxQGs36G3X2g26272SMAOH2b8FmzZRsGsXLVJTGZPA1/qPxLKCAm779FPeWrYMgKZNmvCbMWO45aijaJvAB4YZY0xtbOAwwH93pxzTu3dENw1LRBu2b+eu2bOZOn8+gdAprldmZHDnhAn0sAOTjTGmVjZwGAA+8Wh3SmNWXFbGfV99xUPffUdZ6BTXKYMHc/dxxzGkY0ef64wxJr4lzGmxmzZtonPnzn7nRKS0tJTVq1fTr1+/qJ67XVZZSbv77qO0spJF117LIQ28PkSsuqOhtvayykoe+/57/vrllxSVlQEwrlcv7ps4kSN79vQzd4/Gts410NoNetu1doPedi9Pi02YgcOuw7Fvn+fkcNwLL9A5PZ283/3OTt0MqQoEeHHhQm7//HPWbQ/+fzY0dIrraXaKqzEmAdjt6ethbegMAk3WrFnDz3/+86jf6baht6OvKVbd0RDe/llODle+/Tbrtm+nZ6tWPHvGGSy45hpOj/IprvXRWNa5Jlq7QW+71m7Q3e6VhBk4CgsL/U6I2NatW5k6dSpbt26N6ufx+viNWHVHQ3j7xH79OGPQIP5+wgms+NWvuCIjg+Sk+PxfprGsc020doPedq3doLvdK3bQaIIrKi3lx40bAbsdfU0iwvQLLvA7wxhjGoX4/HXNxMys3FwCzjGofftGcddSY4wx8ckGjgRnt6M3xhgTCwkzcHTy8FbgsdK5c2f++Mc/RvV03mhcfyMW3dGitV1rN+ht19oNetu1doPudq/YabEJbO22bfR+6CGSRNj6hz/QpmlTv5OMMcbEkeyNGzkoeLsLOy22rkpKSvxOiFhJSQmzZs2KWvunod0ph3Xr5umwEe3uaNLarrUb9LZr7Qa97Vq7QV97VSDA4z/8wOinnvJsmQkzcKxatcrvhIhlZ2dz7LHHkp2dHZXlH9mzJ3859lh+OWqUp8uNdnc0aW3X2g1627V2g952rd2gq31eXh5jp07l+vffZ3t5uWfLTZiBw/zUoA4d+NP48Vw5YoTfKcYYY3y2vbyc386cyWFPP80PGzfSKi2N/zvhBM+Wb9fhMMYYYxKYc443ly7lNzNnsjG0y+fCQw7h/hNPJN05bvbo89jAYYwxxiSo1UVFXP/++8xcuRKAAe3a8fgpp3BC//5A8F4qXkmYgSMlJcXvhIilpKTQvXt3de1au0Fvu9Zu0NuutRv0tmvthvhrL6+s5O9z5vCXL7+krLKS1ORkbh03jj+OG0fTJtEZDey0WGOMMSaBzMrN5dr33mNZQQEQvK3F46eeykHt2//kuV7eLTZhtnAYY4wxiWzzzp3c/PHHvLBgAQCd0tN58KSTuPCQQ2JyB+yEOUslKyvL74SILVq0iB49erBo0SK/UyKitRv0tmvtBr3tWrtBb7vWbvC3PeAcT8+dy+BHH+WFBQsQ4NrRo1l2/fVcNGxYTIYNSKAtHBUVFX4nRKyiooINGzaoa9faDXrbtXaD3nat3aC3XWs3+Ne+KD+fX777Lt+sXw9ARpcuPHHqqYzp0SOmHZBAA4cxxhiTaBbk5/PN+vW0SE3lz8ceyw2HH06TJH92btjAYYwxxjRSFw8bxqrCQq4aOZIePp84YQOHMcYY00iJCHdMmOB3BpBAp8WuX7+e7sE73qlRUlLC3LlzGTVqFC1btvQ7p860doPedq3doLddazfobdfaDXrbvTwtNq4HDhG5FTgLGAyUAnOAW5xzyyNYhl2HwxhjjKkHLweOeD8t9hjgMeAI4ASCu4A+EpH0SBe0ceNGj9Oib8OGDdx6661s2LDB75SIaO0Gve1au0Fvu9Zu0NuutRt0t3slrgcO59zJzrnnnHNZzrkFwJVALyDi+6lv3rzZ875oy8/P59577yU/P9/vlIho7Qa97Vq7QW+71m7Q2661G3S3e0XbQaOtQ38W7usJIpIGpIU9pGdnmTHGGNNIxfUWjnASvBTaA8BXzrnF+3nqrcC2sLf1McgzxhhjzH6oGTiAR4FDgQsP8Lx7CG4JqX6L/eXUjDHGGLMXFbtUROQfwGRgvHNuv1ssnHPlQHnYawFo165dNBOjon379lx11VW0r+UOfvFMazfobdfaDXrbtXaD3nat3aC73SvxflqsAP8AzgQmOOey67EMOy3WGGOMqYdEOi32MeAS4CKgRES6hN6aRbqg0tJSz+OirbS0lKysLHXtWrtBb7vWbtDbrrUb9LZr7Qbd7V6J94HjWoLHYcwC8sLezo90QcuX1/laYXFj6dKlHHLIISxdutTvlIho7Qa97Vq7QW+71m7Q2661G3S3eyWuj+FwzonfDcYYY4xpuHjfwmGMMcaYRsAGDmOMMcZEXcIMHNWnx2oiIqSmpqpr19oNetu1doPedq3doLddazfobvdKXJ8W6wU7LdYYY4ypn0Q6LTZuNPbBzBhjjImmhBk46ntabMA5nvzxR0555RWqAgGPq/Zv6dKljBw5Ut1pVFq7QW+71m7Q2661G/S2a+0G3e1eievTYr1Un4utLNmyhatnzODrdesAeDUri4uGDfM6bZ9KS0uZP3++ugvFaO0Gve1au0Fvu9Zu0NuutRt0t3slYQaOSJRVVnL3l19y71dfUREIkJ6Swl+PO47zhw71O80YY4xRyQaOGmbn5nL1u++yYutWAE476CAeO+UUegUPmjHGGGNMPdjAEVJYWsofPv6YqfPnA9ClRQv+MWkSZw8ZktCnMWmxu6qKOevW8UF2Nt9v3Minl11Gkv29GWNM3EiYgaN37961Pu6c49WsLH4zcyabd+4E4JejRnHvxIm0ado0lok/0bdvX1577TX69u3ra0ekYtW9bts2Pli5kg9WruTT1asp2b17z8fm5eUxulu3iJdp6zz2tLZr7Qa97Vq7QXe7VxL6Ohy5xcVc+957zFy5EoAhHTrw1OmnM65XLx9KzYGUV1by1dq1e4aMJVu27PXxjs2bc/KAAUwaMIBTBg6ktc8DozHGaOfldTgSZgvH5s2b9wwclYEAD3/7LbfPmsWuigpSk5P5n6OP5g9HHUVak/hZJfn5+bz88stcfPHFdO7c2e+cOvOyO7e4mJlhWzF2VlTs+ViSCEf06MGkAQM4ecAARnbt2uDdKLbOY09ru9Zu0NuutRt0t3slYbZwzJ49m/HjxzN340Z+MWMG8zdtAmB87948ddppDOrQwd/QWsybN49Ro0Yxd+5cRo4c6XdOnTWku6yyki/XrNmzFWNZQcFeH++cnr5nK8YJ/fvTrlkzL9Mb3Tq//fPPyS0u5tdjxtRrF1MsNLZ1roHWdq3doLfdtnDUQ2llJTd9+CEPf/cdAedo07Qpfz/hBK4cMcIOLvTZ6qIiPsjO5oOVK/k8N5ddYVsxkkUY27Mnk0JDxvAuXezvq46cczy/YAFrt23j7CFD4nbgMMYkhoQZOC776is2h7bmXHjIITx40kl0btHC56rEVFpRwew1a/ggO5uZq1btOQW5WtcWLYIDxsCBTOzXz/eDd7VakJ/P2m3baNakCSf07+93jjEmwSXMwLG5tJTenTvzz1NPZdLAgX7nJJzsrVv5YOVKZoa2YpRVVu75WJOkJI4KbcU4ecAADu3c2U5F9sD0ZcsAOLF/f5qnpPhcY4xJdAkzcFw2aBCPX3QR6ampfqfUWevWrTn99NOr95+p0bp1ayZNnsz8HTt49v33+WDlSlYVFe31nO4tW+7ZinF8375xc0aJ5nVes/vt0P2Dpgwe7FdWnTSmda6F1nat3aC73SsJc9Co3Z4+upxzrAhtxfhg5Upm5+ZSXlW15+MpSUmM69Vrz5AxtGNH24oRRbnFxfR9+GGSRMj//e/p0Ly530nGGIXsoNF6qAg7EFGLiooKiouLadOmDSlxvEl8dVERE194gZzi4r0e79WqFZMGDmTSgAEc17cvLdPS/AmMgJZ1XlPN7ndCWzfG9eoV98NGY1nnmmht19oNutu9kjC3p8/KyvI7IWKLFi2iU6dOLFq0yO+U/erZqhVbS0tJTU5mYr9+3HjwwfDYY0wbP54nTjuNMwYPVjFsgJ51XlPN7urjN84YNMjPrDppLOtcE63tWrtBd7tXEmYLh4melORkPr3sMgZ36ECL1FTmzZvHg1u22C4TnxSWlvLFmjWAjoHDGJMYbOAwnrBrPMSP91asoMo5DunUif7t2vmdYxJAZSBAk6SE2WBu6sm+Q4xpZPacnWJbN0yMXPDGG/R/5BFmhL73jKmNbeEwphEpr6raczPCM+L8dFjTeMzNyyO3uFjNsVrGHwlzWmxhYSFt27b1OyciVVVV7Ny5k/T0dJKTk/3OqTOt3aC3vbp71saNnPHqq3Rv2ZJ1N96o4jga7etcWzd4215YWkr7v/0NgKJbbonqlYFtnceenRZbD5r+gqslJyervHaI1m7Q217dPWPWLCB4sKiGYQP0r3M/Oefq9ffsZfv8vDwA+rdtG/XbEMTDOq8vze1eSZhjOFatWuV3QsSys7M56aSTyM7O9jslIlq7QW97dnY2J550Em8tXQrE/9VFw2le5352f5CdzbHPP8/O3bsjfq2X7fNCA8fIrl0bvKwD8XudN4Tmdq8kzMBRUlLid0LESkpK+Oijj9S1a+0Gve0lJSV8vHQpW8vKaJ2WxjF9+vidVGea17kf3ZWBALd+8gmnvPIKs9es4e9z5kS8DC/b523aBMRm4ND6vQK6272SMLtUjGn0QmelnDJwIKkKdyGaA1u/fTsXvvkmX61dC8D1hx3GH8eN87Uplls4jG42cBjTWIR2o2janWLqbubKlVz61lsU7NpFy9RUpk6ezLlDh/ratL28nBVbtwIwoksXX1tM/LOBw5hGIKekBDp0oIkIJw8Y4HeO8VBlIMAdn3/O3V99BQR/sL927rkMiIOLui0I7U7p2aoVHdPTfa4x8S5hBo4ePXr4nRCxnj178uijj9KzZ0+/UyKitRv0tmeWlQEwvmdPWim7FoLWdR6L7g2hXShfhnahXDt6NA+cdBJNmzTsn26v2mO9O0Xr9wrobvdKwlyHw25PbxqzsVOn8u369fzz1FO5ZvRov3OMBz5atYpLpk1jS2gXytOnn875hxzid9ZeLp8+nRcWLOCuCRO4/Zhj/M4xUeDldTgS5iyVwsJCvxMiVlhYyEsvvaSuXWs36GzPKynh2/XrATi6UyefayKncZ1D9LorAwH+57PPOPmll9iyaxcZXbow9+qrPR02vGqP9RYOrd8roLvdKwkzcKwNbZLUJDc3l0svvZTc3Fy/UyKitRt0ts9YsSL4H+vXU15Q4G9MPWhc5xCd7o0lJUx84QX++uWXOOCaUaP45qqrGNi+vWefA7xp31VRwZItW4DYDRxav1dAd7tXEuYYDmMaq+nLlgX/o/pPo9LHq1ZxcWgXSovQLpQL4mwXSrhF+fkEnKNzejpdW7TwO8coYAOHMYqVlJfzaU5O8B27U6dKVYEAd82ezV+++AIHHNq5M6+fey4HebxVw2vhu1O0XEbf+MsGDmMUm5eXR8A5eqWnsza0edvokVdSwkXTpjErtJn96pEjeejkk2mWkuJvWB3YBb9MpBJm4EhXeI54eno6RxxxhLp2rd2gr/2YPn0ouPlmZmVmcq+i7nDa1nm1hnZ/uno1F02bxuadO0lPSeGp00/nomHDPK6snRfrPJaXNK+m9XsFdLd7xU6LNcaYGKoKBPjzF1/w/2bPxgHDOnXi9XPPZVCHDn6n1dnuqipa3H03FYEAOb/5DX3atPE7yUSJ3Z7eGGMU2rRjBxdPm8ZnoeNufj5iBI9MmqRiF0q4rM2bqQgEaNu0Kb2DP4yMOaCEOS02MzPT74SIzZs3DxFh3rx5fqdERGs36G3X2g162yPt/iwnh4wnnuCznBzSU1J48cwzeXryZF+GjYauc78OGNX6vQK6271iWziMMSaKqgIB/vLFF9wV2oVySGgXymBFu1Bqqh447IZtJhI2cBhjTJTkh3ahVJ+6fFVoF0pzZbtQavLjgFGjnw0cxhgTBZ/n5HDRtGls2rGD5ikp/PPUU7ls+HC/sxqsMhDYc5dYGzhMJGzgMMYYj32ek8PEF18k4BxDO3bk9XPPZUjHjn5neWJ5QQGllZW0SE31/JLrpnFLmNNi8/Pz6aTsxlZlZWWsX7+eHj160LRpU79z6kxrN+ht19oNetv3110ZCHD8Cy/Qv21b/jFpEumpqT5V1q4h6/zFBQu4bPp0xvXqxZdXXhmlwtpp/V4Bve1enhabMAOHXYfDGBNLpRUV6k53rYvfffghD3z7Lb8+/HAenjTJ7xwTZXZ7+nrQeIe+nJwcLrnkEnKq75WhhNZu0NuutRv0th+oO56HjYas87+dcAJZ113Hr8eMiULZ/mn9XgHd7V5RMXCIyHUikiMiZSIyV0SOjnQZxcXFUSiLrqKiIl5++WWKior8TomI1m7Q2661G/S2a+2GhrUnJyVxcMeO9G/XLgpl+5eo67yxiPuBQ0TOBx4C/gqMAL4EPhCRXn52GWOMMabu4n7gAG4Cpjrn/uWcW+qc+y2wDrjW3yxjjDHG1FVcnxYrIqnAKODeGh/6CDhyH69JA9LCHmoJsHPnTrZvb9DxLjG3Y8eOPX9qatfaDXrbtXaD3nat3aC3XWs36G33sjWuz1IRkW7ABuAo59ycsMdvAy53zg2q5TV3AnfELNIYY4xp/Po653IbsoC43sIRpuZUJLU8Vu0e4IGw91sC64EeQIn3aaYWts5jz9Z57Nk6jz1b57FXvc4LG7qgeB84CoAqoOYdgjoB+bW9wDlXDpRXvx92J8OShp5DbOrG1nns2TqPPVvnsWfrPPa8vBtwXB806pzbDcwFTqjxoROAOT99hTHGGGPiUbxv4YDg7pEXReRH4BvgaqAX8ISvVcYYY4yps7gfOJxzr4pIe+B2oCuwGDjFObemjosoB+4ibDeLiTpb57Fn6zz2bJ3Hnq3z2PNsncf1WSrGGGOMaRzi+hgOY4wxxjQONnAYY4wxJups4DDGGGNM1NnAYYwxxpioa9QDhxe3tTd1JyK3isgPIlIiIptFZLqI/OTy8yY6QuvfichDfrc0diLSXUReEpGtIrJLRDJFZJTfXY2ViDQRkb+E/j0vFZHVInK7iDTqn2GxJCLjRWSGiGwM/TsypcbHRUTuDH28VERmicjQSD5Ho/3Lstva++IY4DHgCIIXZ2sCfCQi6b5WJQAROYzgNWoW+t3S2IlIW+BroAKYBBwM/A4o9jGrsbsFuAa4ARgC/AG4GfiVn1GNTDqwgOA6rs0fCN69/QbgMGAT8LGItKzrJ2i0p8WKyHfAPOfctWGPLQWmO+du9a8scYhIR2AzcIxz7gu/exorEWkBzAOuA/4HyHTO/dbXqEZMRO4leENJ22IaIyLyLpDvnLsq7LE3gV3OuUv9K2ucRMQBZzrnpofeF2Aj8JBz7r7QY2kEbzFyi3Puybost1Fu4Qi7rf1HNT60z9vam6hoHfqzwTf9Mfv1GPCec+4Tv0MSxGTgRxF5PbTrcL6I/MLvqEbuK+B4ETkIQESGA+OA932tShx9Cd7TbM/P1NB9y2YTwc/UuL/SaD11AJL56Q3e8vnpjeBMFIQm4geAr5xzi/3uaaxE5AJgJMFNnCY2+gHXEvz+vhs4HHhERMqdcy/4WtZ43UfwF5hlIlJF8N/3Pznn/u1vVsKo/rlZ28/U3nVdSGMdOKpFclt7461HgUMJ/hZiokBEegIPAyc658r87kkgScCPzrnbQu/PDx08dy1gA0d0nA9cAlwEZAEZwEMistE597yfYQmmQT9TG+vAEfFt7Y13ROQfBDc7j3fOrfe7pxEbRfB7em7YLaSTgfEicgOQ5pyr8iuuEcsDltR4bClwtg8tieL/gHudc/8Jvb9IRHoDtwI2cETfptCfXQh+/1eL6GdqozyGw25r74/QaVOPAmcBxznncvxuauQ+BYYR/G2v+u1H4GUgw4aNqPkaqHm690FAXW8oaSLXHAjUeKyKRvozLA7lEBw69vxMDR0reQwR/ExtrFs4wG5r74fHCG7yPAMoEZHqLUzbnHOl/mU1Ts65EoJ3T95DRHYCW+24mah6EJgjIrcBrxE8huPq0JuJjhnAn0RkLcFdKiMInqL5jK9VjUjobLcBYQ/1FZEMoNA5tzZ0fZ/bRCQbyAZuA3YBr9T5czTW02IheOEvgucOV9/W/kY7PTN6QqdS1eZK59xzsWxJVCIyCzstNupE5DTgHmAgwd/+HnDOPe1vVeMVutbDn4EzCW7G3wj8G/h/oS3apoFEZALweS0fet45d0XoRIA7gF8CbYHvgOsj+eWmUQ8cxhhjjIkPtv/LGGOMMVFnA4cxxhhjos4GDmOMMcZEnQ0cxhhjjIk6GziMMcYYE3U2cBhjjDEm6mzgMMYYY0zU2cBhjDHGmKizgcMYY4wxUWcDhzHGGGOizgYOY4wxxkSdDRzGmJgTkY4isil0x9Xqx8aIyG4ROdHPNmNMdNjN24wxvhCRU4DpwJHAMmA+8J7d6daYxskGDmOMb0TkMWAi8AMwHDjMOVfmb5UxJhps4DDG+EZEmgGLgZ7AaOfcQp+TjDFRYsdwGGP81A/oRvDfot4+txhjosi2cBhjfCEiqcD3QCbBYzhuAoY55/L97DLGRIcNHMYYX4jI/wHnEDx2YwfwOVDinDvN1zBjTFTYLhVjTMyJyATgt8ClzrntzrkAcCkwTkSu9THNGBMltoXDGGOMMVFnWziMMcYYE3U2cBhjjDEm6mzgMMYYY0zU2cBhjDHGmKizgcMYY4wxUWcDhzHGGGOizgYOY4wxxkSdDRzGGGOMiTobOIwxxhgTdTZwGGOMMSbqbOAwxhhjTNT9fyKYsAx4RD9GAAAAAElFTkSuQmCC", + "text/plain": [ + "
" ] - }, + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# visualise Buffon's needle problem\n", + "num_lines = 10 # number of parallel lines\n", + "line_spacing = 1.0 # distance between lines\n", + "needle_length = 0.8 # length of the needle\n", + "num_needles = 20 # mumber of needles to drop\n", + "\n", + "# create a figure and axis for visualization\n", + "fig = plt.figure(dpi=100, figsize=(6, 4))\n", + "\n", + "# draw the parallel lines vertically\n", + "for i in range(num_lines):\n", + " line_x = i * line_spacing\n", + " plt.axvline(x=line_x, color='black', linewidth=1, linestyle='--')\n", + "\n", + "# simulate dropping needles and visualize them\n", + "for _ in range(num_needles):\n", + " # randomly choose a midpoint and an angle for the needle\n", + " mid_point_x = random.uniform(0, num_lines * line_spacing)\n", + " mid_point_y = random.uniform(0, num_lines * line_spacing)\n", + " angle = random.uniform(0, math.pi / 2)\n", + "\n", + " # calculate the endpoints of the needle\n", + " x0 = mid_point_x - (needle_length / 2) * math.cos(angle)\n", + " x1 = mid_point_x + (needle_length / 2) * math.cos(angle)\n", + " y0 = mid_point_y - (needle_length / 2) * math.sin(angle)\n", + " y1 = mid_point_y + (needle_length / 2) * math.sin(angle)\n", + "\n", + " # plot the needle as a line segment\n", + " plt.plot([x0, x1], [y0, y1], color='teal')\n", + "\n", + "# set plot limits and labels\n", + "plt.xlim([0, num_lines * line_spacing])\n", + "plt.ylim([0, num_lines * line_spacing])\n", + "plt.xlabel('x')\n", + "plt.ylabel('y')\n", + "plt.title(\"Buffon's Needle problem\")\n", + "\n", + "# show the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's write Python code to simulate Buffon's Needle experiment and estimate the probability.\n", + "\n", + "This code simulates the dropping of needles and calculates the estimated probability of the needle intersecting one of the lines. The more needles you drop, the closer the estimated probability will be to the actual value of $\\frac{2L}{\\pi d}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Monte Carlo Integration\n", - "\n", - "Assume that we are able to generate independent samples $\\theta^{(1)}, ..., \\theta^{(M)}$ from the posterior distribution $p(\\theta|x)$ of interest. A Monte Carlo estimate of the posterior mean\n", - "\n", - "$$\n", - "\\mathbb{E}(\\theta |x) = \\int \\theta p(\\theta|x)d\\theta\n", - "$$\n", - "\n", - "is given by \n", - "\n", - "$$\n", - "\\hat{\\mathbb{E}} (\\theta |x) = \\frac{1}{M} \\sum_{m=1}^M \\theta^{(m)}, \\quad \\theta^{(m)} \\sim p(\\theta|x).\n", - "$$\n", - "\n", - "This approach is called Monte Carlo integration and avoids the analytical integration. More generally, for any sortable function $g$,\n", - "\n", - "$$\n", - "\\hat{\\mathbb{E}} (g(\\theta |x)) = \\frac{1}{M} \\sum_{m=1}^M g(\\theta^{(m)}), \\quad \\theta^{(m)} \\sim p(\\theta|x).\n", - "$$" + "data": { + "image/png": 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" ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [] - } - ], - "metadata": { - "colab": { - "provenance": [] - }, - "kernelspec": { - "display_name": "Python 3", - "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" + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" } + ], + "source": [ + "def buffon_needle_simulation(num_needles, needle_length, line_spacing):\n", + " intersected = 0\n", + "\n", + " for _ in range(num_needles):\n", + " # generate a random angle between 0 and 180 degrees (in radians)\n", + " angle = random.uniform(0, math.pi / 2)\n", + "\n", + " # generate a random position for the midpoint of the needle\n", + " mid_point = random.uniform(0, line_spacing / 2)\n", + "\n", + " # check if the needle intersects a line\n", + " if mid_point <= (needle_length / 2) * math.sin(angle):\n", + " intersected += 1\n", + "\n", + " # estimate the probability\n", + " if intersected == 0:\n", + " estimated_probability = 0\n", + " else:\n", + " estimated_probability = intersected / num_needles\n", + "\n", + " return estimated_probability\n", + "\n", + "def compute_true_value(needle_length, line_spacing):\n", + " true_value = (2 * needle_length) / (math.pi * line_spacing)\n", + " return true_value\n", + "\n", + "\n", + "# input parameters\n", + "needle_length = 1.0 # length of the needle\n", + "line_spacing = 2.0 # distance between the lines\n", + "max_num_needles = 500 # maximum number of needles to drop \n", + "\n", + "estimates = []\n", + "\n", + "for num_needles in range(max_num_needles):\n", + " estimated_probability = buffon_needle_simulation(num_needles, needle_length, line_spacing)\n", + " estimates.append(estimated_probability)\n", + "\n", + "# compute the true value\n", + "true_value = compute_true_value(needle_length, line_spacing)\n", + "\n", + "plt.figure(figsize=(10, 6))\n", + "plt.plot(range(max_num_needles), estimates, color='teal')\n", + "plt.xlabel('Number of Iterations')\n", + "plt.ylabel('Estimated probability')\n", + "plt.axhline(y=true_value, color='red', linestyle='--', label='True Value')\n", + "plt.title('Dependence of the estimated probability on the number of iterations')\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can read more on the analytical solution of the version of this problem over a grid [here](https://mathworld.wolfram.com/Buffon-LaplaceNeedleProblem.html)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Monte Carlo Tree Search\n", + "\n", + "Monte Carlo Tree Search (MCTS) is a heuristic search algorithm used mainly in decision processes involving uncertainty and in particular in games. It's a popular algorithm for game-playing AI, especially in environments where the full breadth of possible moves can't be exhaustively explored due to computational constraints. Some remarkable recent applications of MCTS are [AlphaGo](https://blog.research.google/2016/01/alphago-mastering-ancient-game-of-go.html) and [AlphaZero](https://arxiv.org/pdf/1712.01815.pdf), where MCTS is combined with neural networks to determine the best next action." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Monte Carlo Integration\n", + "\n", + "Assume that we are able to generate independent samples $\\theta^{(1)}, ..., \\theta^{(M)}$ from the posterior distribution $p(\\theta|x)$ of interest. A Monte Carlo estimate of the posterior mean\n", + "\n", + "$$\n", + "\\mathbb{E}(\\theta |x) = \\int \\theta p(\\theta|x)d\\theta\n", + "$$\n", + "\n", + "is given by \n", + "\n", + "$$\n", + "\\hat{\\mathbb{E}} (\\theta |x) = \\frac{1}{M} \\sum_{m=1}^M \\theta^{(m)}, \\quad \\theta^{(m)} \\sim p(\\theta|x).\n", + "$$\n", + "\n", + "This approach is called Monte Carlo integration and avoids the analytical integration. More generally, for any sortable function $g$,\n", + "\n", + "$$\n", + "\\hat{\\mathbb{E}} (g(\\theta |x)) = \\frac{1}{M} \\sum_{m=1}^M g(\\theta^{(m)}), \\quad \\theta^{(m)} \\sim p(\\theta|x).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + } + ], + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3", + "name": "python3" }, - "nbformat": 4, - "nbformat_minor": 0 + "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": 0 } diff --git a/07_MCMC.ipynb b/07_MCMC.ipynb index 22d5f3d..2aa12ce 100644 --- a/07_MCMC.ipynb +++ b/07_MCMC.ipynb @@ -1,684 +1,680 @@ { - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Markov Chain Monte Carlo \n", - "\n", - "We want to estimate the posterior distribution, but this is often intractable.\n", - "\n", - "Markov Chain Monte Carlo (MCMC) is a computational technique used to approximate complex probability distributions by generating a sequence of (correlated) samples, where each sample is obtained by iteratively transitioning through a Markov chain with carefully designed transition probabilities.\n", - "\n", - "The MCMC simulation method is the modern way of approximating complex posterior distributions. The idea is analogous to treating the posterior distribution as the population, and then repeatedly draw samples from it. When we draw a large enough sample (say 1000), the sample distribution should be very close to the population distribution.\n", - "\n", - "One tweak of MCMC from the above analogy is that the samples drawn are correlated, so that if the first sample is high, the next one is more likely to be high too. This is needed because we don’t have a direct way to draw samples from the posterior distribution, which usually has a very complex form; instead we have some algorithms that can indirectly get us to the posterior. The correlation among samples usually is not a big problem, except that we need to draw more samples to compensate for it. \n", - "\n", - "An overview of how an MCMC works is as follows:\n", - "\n", - "- Draw samples from a (simple) proposal distribution so that each draw depends only on the state of the previous draw (i.e. the samples form a Markov chain).\n", - "- Under certain conditions, the Markov chain will have a unique stationary distribution.\n", - "\n", - "- We set up an acceptance criteria for each draw based on comparing successive states with respect to a target distribution that ensure that the stationary distribution is the posterior distribution we are searching for.\n", - "\n", - "- There is no need to evaluate the potentially intractable marginal likelihood.\n", - "\n", - "- After sufficient number of iterations, the Markov chain of accepted draws will converge to the stationary distribution, and we can use those samples as (correlated) draws from the posterior distribution, and find functions of the posterior distribution.\n", - "\n", - "Some examples of MCMC algorithms are\n", - "\n", - "1. The Metropolis algorithm,\n", - "3. The Metropolis-Hastings algorithm,\n", - "4. The Gibbs sampler,\n", - "5. Hamiltonian Monte Carlo,\n", - "6. No U-turn sampler (and several variants).\n", - "\n", - "Let us take a closer look at some of these algorithms." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Metropolis-Hastings algorithm\n", - "\n", - "The Metropolis-Hastings algorithm is particularly useful when direct sampling from the distribution is difficult or impossible, but evaluating the probability density function (PDF) up to a constant of proportionality is feasible. It's useful for sampling from high-dimensional, complex distributions. The algorithm iteratively generates samples from a target distribution by constructing a Markov chain.\n", - "\n", - "Let $\\pi(x)$ be the target probability density function (pdf) from which we want to sample. The steps of the Metropolis-Hastings algorithm are as follows:\n", - "\n", - "1. **Initialization**: Start with an initial state $x_0$ from the sample space.\n", - "\n", - "2. **Proposal Generation**: At each iteration $t$, propose a new state $x'$ based on some proposal distribution $q(x' | x_t)$, which defines the probability of transitioning from state $x_t$ to $x'$.\n", - "\n", - "3. **Acceptance Probability**: Calculate the acceptance probability $\\alpha$ as follows:\n", - "\n", - "$$\n", - "\\alpha = \\min \\left(1, \\frac{\\pi(x')}{\\pi(x_t)} \\times \\frac{q(x_t | x')}{q(x' | x_t)} \\right)\n", - "$$\n", - "\n", - "where $\\pi(x)$ is the target probability density function and $q(x' | x_t)$ is the proposal distribution.\n", - "\n", - "4. **Acceptance or Rejection**: Generate a uniform random number $u$ from the interval [0, 1]. If $u < \\alpha$, accept the proposed state $x'$ as the next state: $x_{t+1} = x'$; otherwise, stay at the current state: $x_{t+1} = x_t$.\n", - "\n", - "5. **Iteration**: Repeat steps 2-4 for a sufficient number of iterations.\n", - "\n", - "The resulting sequence of samples $x_1, x_2, ..., x_n$ forms a Markov chain that converges to the target distribution $\\pi(x)$ as $n$ approaches infinity. Proper choice of the proposal distribution is crucial for efficient sampling, and tuning its parameters can significantly impact the algorithm's performance.\n", - "\n", - "The Metropolis algorithm is a special case of the Metropolis-Hastings algorithm where the proposal distribution is symmetric, meaning $q(x' | x_t) = q(x_t | x')$, leading to simplifications in the acceptance probability calculation.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Metropolis-Hastings by hand\n", - "\n", - "Let us implement the Metropolis-Hastings algorithm for sampling from the normal distribution $\\mathcal{N}(5,1)$. As the proposal distribution we will use $\\mathcal{N}(0,1)$, making the proposal a random walk process. Note that this proposal is symmetric, hence, we don't need to account for it in the acceptance ratio." - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "\n", - "import scipy.stats as stats\n", - "\n", - "import matplotlib.pyplot as plt\n", - "from matplotlib.colors import LinearSegmentedColormap" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "# Target distribution: Univariate normal distribution with mean = 5, variance = 1\n", - "def target_distribution(x):\n", - " return np.exp(-(x - 5)**2 / 2) / np.sqrt(2 * np.pi)\n", - "\n", - "# Proposal distribution: Normal distribution with mean = 0 and variance = 1\n", - "def proposal_distribution(x, sigma=1):\n", - " return np.random.normal(x, sigma)\n", - "\n", - "# Metropolis-Hastings algorithm\n", - "def metropolis_hastings(num_samples, initial_state, proposal_sigma):\n", - " samples = [initial_state]\n", - " current_state = initial_state\n", - "\n", - " for _ in range(num_samples):\n", - " # Propose a new state\n", - " proposed_state = proposal_distribution(current_state, proposal_sigma)\n", - " \n", - " # Calculate acceptance ratio\n", - " acceptance_ratio = min(1, target_distribution(proposed_state) / target_distribution(current_state))\n", - " \n", - " # Accept or reject the proposed state\n", - " if np.random.uniform(0, 1) < acceptance_ratio:\n", - " current_state = proposed_state\n", - " samples.append(current_state)\n", - "\n", - " return samples" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [], - "source": [ - "# Parameters\n", - "num_samples = 1000\n", - "initial_state = -3 # Initial state\n", - "proposal_sigma = 0.2 # Standard deviation for the proposal distribution\n", - "\n", - "# Generate samples using Metropolis-Hastings algorithm\n", - "samples = metropolis_hastings(num_samples, initial_state, proposal_sigma)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now when we have collected samples, we can plot them to make a traceplot, and we can also plot the sampling distribution we obtained:" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# Traceplot\n", - "plt.figure(figsize=(6, 4))\n", - "plt.plot(samples, color='teal')\n", - "plt.xlabel('Iteration')\n", - "plt.ylabel('Sample Value')\n", - "plt.title('Metropolis-Hastings: traceplot')\n", - "plt.grid(True)\n", - "plt.show()\n", - "\n", - "# Plot posterior\n", - "plt.figure(figsize=(6, 4))\n", - "plt.hist(samples, bins=50, color='teal', density=True)\n", - "\n", - "x = np.linspace(-5, 15, 1000)\n", - "plt.plot(x, target_distribution(x), color='black', linestyle='--', label='True Distribution')\n", - "plt.xlabel('Sample Value')\n", - "plt.ylabel('Probability Density')\n", - "plt.title('Posterior of Metropolis-Hastings')\n", - "plt.grid(True)\n", - "plt.show()\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Warm-up\n", - "\n", - "We can notice on the traceplot, that the initial value we started with wasn't great. For this reason, it is common to use a warm-up period. \n", - "\n", - "A warm-up, also known as a burn-in period, refers to an initial phase where the algorithm runs to reach a state of convergence or equilibrium. During this phase, the algorithm explores the parameter space and adjusts its state transition probabilities, aiming to approach the target distribution.\n", - "\n", - "The initial part of the chain may have not reached convergence yet. Furthermore, it may also include phase for adapting algorithm parameters. So the initial part of the chain may be non-representative. This initial burn-in part must be thrown away.\n", - "\n", - "\n", - "The samples generated during the warm-up period are typically discarded as they may not accurately represent the target distribution. Once the warm-up phase is complete, the samples generated by the MCMC algorithm are considered to be from the stationary distribution and are used for inference or analysis.\n", - "\n", - "The length of the warm-up period can vary depending on factors such as the complexity of the target distribution and the effectiveness of the MCMC algorithm in exploring the parameter space. A longer warm-up period may be required for more complex distributions or when starting from a distant initial state." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Chains" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We have ran the simulation forward once. In fact, we could run several simulation fowards in parallel, each with its own initial values, to see whether they converge to the same distribution.\n", - "\n", - "Chains refer to the sequences of samples generated by the algorithm as it iterates through the parameter space. Each chain represents a trajectory of parameter values explored by the algorithm over multiple iterations. Multiple chains can be run simultaneously, each starting from different initial parameter values, to improve convergence diagnostics and assess the mixing properties of the algorithm. \n", - "\n", - "Running several chains from different initial values can help convergence diagnostics, for example, because visual inspection of the chains is straightforward.\n", - "\n", - "Let us return the same experiment as above, but now by using three chains." - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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OJnWF2RIfC6x091XuvheYBZxVYRkH2pqZAZnAVkADx4qIJLlED0W6bds2vvWtb3Hrrbdy7LHH1nk7qS7MJN4DWBczXRDMi/UH4EjgM2AxcJW77w8xJhERqQelQ5G+/PLL9O3bl8GDB5OXl1d2s1llYociPfvssw9qKNI//OEPrFy5kptvvpmcnBxycnLYuHFjnbeXqqz0zsB637DZecCp7n5pMH0hMNbdfxqzzLnAscA1QF/gZWC4u++osK3JwGSArKysUaWPM6SDwsJCMjMzEx1GSlBdxU91daDCDYUAZHYrXy+pWlft27enX79+Dba/kpISMjIyGmx/qexg62rlypVs37693Lzx48fPd/fRFZcN8znxAqBXzHRPoi3uWD8EbvPofxIrzWw1cATwfuxC7j4dmA4wevRoz03AuLlhiUQipNPxhEl1FT/V1YFKn6POnZRbfn6K1tWyZcto27Ztg+1v586dDbq/VHawddWyZUtGjBgR17Jhnk6fC/Q3sz7BzWrnA89UWGYt8A0AM8sCBgKrQoxJREQkbYTWEnf3YjObCrwIZAB/cfelZjYlKJ8G3AzMMLPFgAHXuvvmsGISERFJJ6F2u+rus4HZFeZNi3n/GXBKmDGIiIikK/XYJiIikqKUxEVERFKUkriIiNRJIociff/998ueDx8+fDhPPvlkbcNPCxqKVEQkHczMq9/tXVT99hI9FOmQIUOYN28eTZs2ZcOGDQwfPpwJEybQtGnjSmtqiYuISK0leijS1q1blyXsoqIior13Nz5K4iIiUmvJMBTpe++9x+DBgxk6dCjTpk1rdK1wUBIXEZEQNMRQpOPGjWPp0qXMnTuXW2+9tcoR0dKZkriIiNRaMgxFWurII4+kTZs2LFmypA5HktqUxEVEpNYSPRTp6tWry5L7mjVrWLFiBdnZ2XXeXqpSEhcRkVpL9FCkb731FsOHDycnJ4eJEydy33330blz5zpvL1WFNhRpWEaPHu3z5s1LdBj1JlVHUEoE1VX8VFcHKhvFLC+3/PwUratly5Zx5JFHNtj+NIpZ/A62rir73ZpZpUORqiUuIiKSopTERUREUpSSuIiISIpSEhcREUlRSuIi0qhE8iJlN7mJpDolcRERkRSlJC4iIrW2ZcuWsqFADz30UHr06FE2vXfv3nrZR25uLgMHDmTYsGEcccQRTJ06lW3btpWVH3PMMdWu/5vf/Kba8jPOOINt27aRn5/PkCFDahVbJBLhnXfeKZueNm0aM2fOrNU26oOSuIiI1FqnTp1YuHAhCxcuZMqUKfznf/5n2XTz5s1r7Co1Xg8//DCLFi1i0aJFtGjRgrPOOqusLDaJVqaqJO7u7N+/n9mzZ9OhQ4c6xVUxiU+ZMoWLLrqoTts6GEriIiJSLy655BKuueYaxo8fz7XXXkteXl65EciGDBlSNpjJ3/72N8aOHUtOTg6XX345JSUl1W67efPm/Pa3v2Xt2rV8+OGHAGRmZgKwYcMGTjjhBHJychgyZAhvvvkm1113HV999RU5OTlccMEF5Ofnc+SRR3LllVcycuRI1q1bR3Z2Nps3bwaguLiYiy++mGHDhnHuueeye/dugHLLzJs3j9zcXPLz85k2bRp33303OTk5vPnmm+WOddGiRRx11FEMGzaMiRMn8uWXXwLRMwvXXnstY8eOZcCAAbz55psHXedK4iIiaSA3N/eA13333QfA7t27Ky2fMWMGAJs3bz6grK4+/vhjXnnlFe68884ql1m2bBmPPvoob7/9NgsXLiQjI4OHH364xm1nZGQwfPjwA8YX//vf/86pp57KwoUL+fDDD8nJyeG2226jVatWLFy4sGzbK1as4KKLLuKDDz6gd+/e5baxYsUKJk+ezKJFi2jXrl1Z3VUmOzu73NmH0jHUS11++eXcfvvtLFq0iKFDh3LjjTeWlRUXF/P+++9zzz33lJtfV0riIiJSb8477zwyMjKqXebVV19l/vz5jBkzhpycHF599VVWrVoV1/Yr6yp8zJgx/PWvfyUvL4/FixdX2eVp7969Oeqooyot69WrF8ceeywAP/jBD3jrrbfiiqei7du3s337dk488UQALr74YubMmVNWHs8Qq7XR+EZQFxFJQ5FIpMqy1q1bV1veuXPnastro02bNmXvmzZtyv79+8umS0cxc3cuvvhibr311lptu6SkhMWLFx/Qr/gJJ5zAnDlzeP7557nwwgv5+c9/Xun16djYKjKzSqdjj6E+xiuvzRCr8VBLXEREQpGdnc2CBQsAWLBgAatXrwbgG9/4Bo8//jgbN24EYOvWraxZs6babe3bt49f/vKX9OrVi2HDhpUrW7NmDV27duWyyy7jxz/+cdk+mzVrxr59++KKde3atbz77rsAPPLIIxx33HFlx1A6bvoTTzxRtnzbtm3ZuXPnAdtp3749HTp0KLve/dBDD5W1ysOgJC4iIqH4zne+w9atW8nJyeGPf/wjAwYMAGDQoEHccsstnHLKKQwbNoyTTz6ZDRs2VLqNCy64gGHDhjFkyBB27drF008/fcAykUiEnJwcRowYwRNPPMFVV10FwOTJkxk2bBgXXHBBjbEeeeSRPPjggwwbNoytW7dyxRVXAHDDDTdw1VVXcfzxx5e7TDBhwgSefPLJshvbYk2bNo2f//znDBs2jIULF3L99dfHV2F1oKFIEyxVh0FMBNVV/FRXB6rYS1vpkKSpWlcaijR5aShSERERqZGSuIiISIoKNYmb2WlmtsLMVprZdZWU/9zMFgavJWZWYmYdw4xJREQkXYSWxM0sA7gXOB0YBEwys0Gxy7j7/7p7jrvnAL8E3nD3rWHFJCKSTlLtniapWW1/p2G2xMcCK919lbvvBWYBZ1Wz/CTgkRDjERFJGy1btmTLli1K5GnE3dmyZQstW7aMe50wO3vpAayLmS4AxlW2oJm1Bk4DpoYYj4hI2ujZsycFBQVs2rSpQfZXVFRUq+TSmB1MXbVs2ZKePXvGvXyYSdwqmVfVv4wTgLerOpVuZpOByQBZWVn11rNQMigsLEyr4wmT6ip+qqsDFQ4sLDddWj+qq/gUFhaWDTgi1TvYuqqp45tYYSbxAqBXzHRP4LMqlj2fak6lu/t0YDpEnxNPxWc6q5Kqz6gmguoqfqqrAx3wnPik3Oh81VVcVE/xa8i6CvOa+Fygv5n1MbPmRBP1MxUXMrP2wInAgd3wiIiISJVCa4m7e7GZTQVeBDKAv7j7UjObEpRPCxadCLzk7rvCikVERCQdhTqKmbvPBmZXmDetwvQMYEaYcYiIiKQj9dgmIiKSopTERUREUpSSuIiISIpSEhcREUlRSuIiIiIpSklcREQkRSmJi4iIpCglcRERkRSlJC4iIpKilMRFRERSlJK4iIhIilISFxERSVFK4iIiIilKSVxERCRFKYmLiIikKCVxERGRFNU00QGIiCRCJC8SfZObyChEDo5a4iIiIilKSVxERCRFKYmLiIikKCVxERGRFKUkLiIikqKUxEVERFKUkriIiEiKUhIXERFJUUriIiIiKUpJXEREJEUpiYuIiKSoUJO4mZ1mZivMbKWZXVfFMrlmttDMlprZG2HGIyIikk5CGwDFzDKAe4GTgQJgrpk94+4fxSzTAbgPOM3d15pZ17DiERERSTdhtsTHAivdfZW77wVmAWdVWOb7wD/dfS2Au28MMR4REZG0Yu4ezobNziXawr40mL4QGOfuU2OWuQdoBgwG2gK/c/eZlWxrMjAZICsra9SsWbNCiTkRCgsLyczMTHQYKUF1FT/V1YEKNxRWXtAW1VUc9JmKXxh1NX78+PnuPrri/DDHE7dK5lX8j6EpMAr4BtAKeNfM/u3uH5dbyX06MB1g9OjRnpubW//RJkgkEiGdjidMqqv4qa4OVDZ+eEW5qK7ioM9U/BqyrsJM4gVAr5jpnsBnlSyz2d13AbvMbA4wHPgYERERqVaY18TnAv3NrI+ZNQfOB56psMzTwPFm1tTMWgPjgGUhxiQiIpI2QmuJu3uxmU0FXgQygL+4+1IzmxKUT3P3ZWb2ArAI2A/8yd2XhBWTiIhIOgnzdDruPhuYXWHetArT/wv8b5hxiIiIpCP12CYiIpKilMRFRERSlJK4iIhIilISFxERSVFK4iIiIilKSVxERCRF1ZjEzewOMxvcEMGIiIhI/OJpiS8HppvZe2Y2xczahx2UiIiI1KzGJO7uf3L3Y4GLgGxgkZn93czGhx2ciIiIVC2ua+JmlgEcEbw2Ax8C15hZ+owJKiIikmJq7HbVzO4CJgCvAb9x9/eDotvNbEWYwYmIiEjV4uk7fQnw3+6+u5KysfUcj4iIiMQpntPpF1RM4Gb2KoC7bw8lKhGRehLJixDJi1RZXrihsNpykWRWZUvczFoCrYHOZnYIYEFRO6B7A8QmIiIi1ajudPrlwNVEE/aCmPk7gHtDjElEJLFm5kV/XpQX33yRBKkyibv774DfmdlP3f33DRiTiIiIxKG60+knuftrwHozO6diubv/M9TIREREpFrVnU4/kehjZRMqKXNASVxERCSBqjudfkPw84cNF46IiIjEK54BUK4ys3YW9SczW2BmpzREcCIiIlK1eJ4T/5G77wBOAboCPwRuCzUqEZE60PPe0tjEk8RLnw8/A/iru38YM09EREQSJJ4kPt/MXiKaxF80s7bA/nDDEhERkZrE03f6j4EcYJW77zazTkRPqYuIiEgC1ZjE3X2/mX0BDDKzeJK+iIiINIB4hiK9Hfge8BFQEsx2YE6IcYmIiEgN4mlZnw0MdPc9IcciIiIitRDPjW2rgGZhByIiIiK1E08S3w0sNLP7zez/Sl/xbNzMTjOzFWa20syuq6Q818y2m9nC4HV9bQ9ARKQ+6BlzSUXxnE5/JnjVipllEB2y9GSgAJhrZs+4+0cVFn3T3c+s7fZFRBrMzLxERyBSqXjuTn/QzFoBh7n7ilpseyyw0t1XAZjZLOAsojfIiYiIyEEyd69+AbMJwB1Ac3fvY2Y5wE3u/u0a1jsXOM3dLw2mLwTGufvUmGVygSeIttQ/A37m7ksr2dZkYDJAVlbWqFmzZsV7fEmvsLCQzMzMRIeRElRX8WusdVW4oZDMbpkHzKtOSYsSMvZkAHy97pYN0Z+dupWfLlU6vxFprJ+pugijrsaPHz/f3UdXnB/P6fQ8oq3qCIC7LzSzPnGsV1nXrBX/Y1gA9Hb3QjM7A3gK6H/ASu7TgekAo0eP9tzc3Dh2nxoikQjpdDxhUl3Fr7HWVSQvQu6k3APmVadwYCGZK6JfuGXrzsyL/vzOpPLTpUrnNyKN9TNVFw1ZV/Hc2Fbs7tsrzKu++R5VAPSKme5JtLX99Ubcd7h7YfB+NtDMzDrHsW0REZFGL54kvsTMvg9kmFl/M/s98E4c680F+ptZHzNrDpxPhRvkzOxQM7Pg/dggni21OgIREZFGKp4k/lNgMLAHeATYAVxd00ruXgxMBV4ElgH/cPelZjbFzKYEi51L9J+ED4H/A873mi7Si4iICBDf3em7gf8XvGolOEU+u8K8aTHv/wD8obbbFRERkRpa4mZ2sZktMLNdwWuemV3UUMGJiISt+d7NZK+dkegwROqkypZ4kKyvBq4hehe5ASOB/zUz3H1mg0QoIiIilaquJX4lMNHdX3f37e6+zd1fA74TlImIiEgCVZfE27l7fsWZwbx2YQUkIiIi8akuiX9VxzIRERFpANXdnX6kmS2qZL4Bh4cUj4iIiMSp2iTeYFGIiIhIrVWZxN19TUMGIiIiIrUTT49tIiIpqabBT0RSnZK4iIhIiqoxiZvZmWamZC8iIpJk4knO5wOfmNlvzUw3u4mIiCSJGpO4u/8AGAF8CvzVzN41s8lm1jb06ERE6kjXw6UxiOs0ubvvAJ4AZgHdgInAAjP7aYixiYiISDXiuSb+bTN7EngNaAaMdffTgeHAz0KOT0RERKpQ43jiwLnA3e4+J3amu+82sx+FE5aIiIjUJJ4kvqFiAjez2939Wnd/NaS4RETqRNfCpTGJ55r4yZXMO72+AxEREZHaqbIlbmZXEB03vG+FgVDaAm+HHZiIiIhUr7rT6X8H/gXcClwXM3+nu28NNSoRERGpUXVJ3N0938x+UrHAzDoqkYuIiCRWTS3xM4H5gBMdR7yUozHFRUREEqq6oUjPDH72abhwREREJF7V3dg2sroV3X1B/YcjIiIi8arudPqd1ZQ5cFI9xyIiklgz8xIdgUitVHc6fXxDBiIiIiK1U93p9JPc/TUzO6eycnf/Z3hhiYg0rOy1M+Dw7ESHIVIr1fXYdmLwc0IlrzPj2biZnWZmK8xspZldV81yY8ysxMzOjTNuERGRRq+60+k3BD9/WJcNm1kGcC/RblsLgLlm9oy7f1TJcrcDL9ZlPyIiIo1VPEORdjKz/zOzBWY238x+Z2ad4tj2WGClu69y971ExyI/q5Llfkp0rPKNtYpcRKQWstfOiJ4yF0kj8QyAMgvYBHyH6LCkm4BH41ivB7AuZrogmFfGzHoAE4Fp8QQrIlJftu/enugQRA5aPEORdnT3m2OmbzGzs+NYzyqZ5xWm7wGudfcSs8oWDzZkNhmYDJCVlUUkEolj96mhsLAwrY4nTKqr+DXWuiocWFhl2cd9cgHY27yQWf+cxUuRl7j/rvvJaN2Whw/pxOihQ8hv07L8SqV12GZg5fMbkcb6maqLhqyreJL462Z2PvCPYPpc4Pk41isAesVM9wQ+q7DMaGBWkMA7A2eYWbG7PxW7kLtPB6YDjB492nNzc+PYfWqIRCKk0/GESXUVv8ZaV9WNJZ699nEAXl67lodffZ2Th51MmxVtmL/nJf77rrv49dFH8aspp5Zf6TuToj9n5lU+vxFprJ+pumjIuqrydLqZ7TSzHcDlRPtR3xu8ZgH/Gce25wL9zayPmTUHzgeeiV3A3fu4e7a7ZwOPA1dWTOAiIvWlqLiY6999j0EdO/KzCT+jedPmjBw8mGO6Hcpt8+bzxfaqW/IiyajKJO7ubd29XfCzibs3DV5N3L1dTRt292JgKtG7zpcB/3D3pWY2xcym1N8hiIjE5+EVK/h8927+e+xomjdtDoCZcdPRR1G4bx/3vPjvBEcoUjvxnE7HzA4B+gNlF4zcfU5N67n7bGB2hXmV3sTm7pfEE4uISG3E3pG+YOMmxmZlcXS3buTHLNO3fXvOyM7mvtfm8f++fQKZLaMJXt2wSrKrMYmb2aXAVUSvaS8EjgLeRX2ni0iKuXd8Lrv27au07IeDjmRJ4Zes/GIrOb0PbdjAROoonkfMrgLGAGuC/tRHEH3MTEQkZRTv3w9Am2bNKi0f2bULq/73KiVwSSnxJPEidy8CMLMW7r4cGFjDOiIiSaOouJijHn2Mh5evKJtXsfMXM6NJE6O4ZD9Fe4sTEKVI7cWTxAvMrAPwFPCymT3NgY+KiYgkrTnrP2NLURGHtW1b7XIbtu0k66d3MOOthQ0TmMhBqjGJu/tEd9/m7nnA/wB/Bs4OOS4RkXrzwpo1dGjRgqO6VX+q/ND2mXTMbMXTC1ZUu5xIsoinJY6ZjTSz/wCGAQVBX+giIklvvztz1n/GiT160KxJ9V95ZsZZIwby2rLV7PhqT9ULzszTneuSFOIZAOV64EGgE9Fe1f5qZv8ddmAiIvVhxZdfsqWoiOO7d4tr+TNzBrC3uIQ3lueHG5hIPYinJT4JGOPuNwTDkx4FXBBuWCIi9aN98xZclTOc43p0j2v5o/v1pGWzprz20eqQIxM5ePF09pJPtJOXomC6BfBpWAGJiNSn7pltuHpETtzLt2jWlP/7wWkM6dk1vKBE6kmVSdzMfk901LE9wFIzezmYPhl4q2HCExGpu73Fe3mjYD1jsrrSuornwytzWe6oEKMSqT/VtcTnBT/nA0/GzI+EFo2ISD1avn45V738CvefNJ5Teh8W93rFJft58+M1dG3bhsFqkUsSqzKJu/uDpe+DUcgGBJMr3L3yfgtFRJLIknVLABidVbtE7O6cedcjXHriCH73g9PDCE2kXsTTd3ou0bvT8wEDepnZxfEMgCIikkhLC5bSp107OrZsWfPCMZo1zWDM4d15Z2VBSJGJ1I947k6/EzjF3U909xOAU4G7ww1LROTguDtL1y1lVNcudVr/mH69WLj2c3bv0YlHSV7xJPFm7l7WfZG7fwzEf4eIiEgCrN+6nu27tzOia92uaR/TvxfFJfuZt1q9TEvyiieJzzezP5tZbvB6gOjNbiIiSavbId144PIHOLUWN7TFOqpvTwDe/XRdfYYlUq/ieU58CvAT4D+IXhOfA9wXZlAiIgcro0kG/Q7tR6e9dXsitnPb1iy4aTKDe+judEle1SZxM2sCzHf3IcBdDROSiMjBe+StRxjQfQDZ8TRVqjCid3xdtYokSrWn0919P/ChmdXtfJSISALsLd7Ln1//MwtWLTio7azYsJn/euRFPt9WWE+RidSveK6JdyPaY9urZvZM6SvswERE6mr1xtWU7C+hf7f+B7WdzTt3c9cL/+b9VevrKTKR+hXPiaYbQ49CRKQefbzhYwAGdB8AO/PrvJ2c3ofSxIwFazbw7ZED6yk6kfpTXd/pLYne1NYPWAz82d2LGyowEZG6+mTDJ7Rp0YZuHbrBzrpvp02L5hzRrTPz8zfUX3Ai9ai60+kPAqOJJvDTiXb6IiKS9DZu38iAbgMws4Pe1sjsbszP17PikpyqO50+yN2HApjZn4H3GyYkEZGDc9sFt1G0r6jmBeMwKrsbLy5eybZdRXRoU7vuW0XCVl0SL+tr0N2L6+M/WhGRhtKyWf0k3KnfHMtVp4yrl1a9SH2r7nT6cDPbEbx2AsNK35vZjoYKUESkNt5a/hY3Pn4jhUX181hY04wmSuCStKpM4u6e4e7tgldbd28a875dQwYpIlKTSF4EgAWrF/DeJ+/RukXrWm8jP5Jf6fxrH32Zq/72r4OITiQc8TwnLiKSMj7Z8An9Du1HE6u/r7fVm7bx3MJP6m17IvUl1CRuZqeZ2QozW2lm11VSfpaZLTKzhWY2z8yOCzMeEUlv7s6qL1bRL6sf2WtnkL12Rr1sd1ivLFZt+pLCor31sj2R+hJaEjezDOBeoo+nDQImmdmgCou9Cgx39xzgR8CfwopHRNLfF9u/YPfe3fTJ6lOv2x3aKzoIypKCjfW6XZGDFWZLfCyw0t1XufteYBZwVuwC7l7o7h5MtgEcEZE6KiwqpH+3/vTN6hv3OnuLS8jftq3sFcnPP2CZYb2yAFi07ov6ClWkXoSZxHsAsQPxFgTzyjGziWa2HHieaGtcRKRO+h3aj+mTpzOoZ8WTfgend6cOHNOvFy2bHcSQaCIhsK8bwvW8YbPzgFPd/dJg+kJgrLv/tIrlTwCud/dvVlI2GZgMkJWVNWrWrFmhxJwIhYWFZGZmJjqMlKC6il9jrKvCDeUfKWu+d3Nc633VJpOM7du/ntE6g8zmLeLbaafGM1RpY/xM1VUYdTV+/Pj57j664vww/60sAHrFTPcEquy70N3nmFlfM+vs7psrlE0HpgOMHj3ac3NzQwg3MSKRCOl0PGFSXcWvsdRVXiTy9cSLm5nxwm1075TNb867juy1j8e1jSXHHk/m889+PSOnA7nZ2ZUuW9roKXtu/DuT6hB1amosn6n60JB1Febp9LlAfzPrY2bNgfOBckOYmlk/C/4azGwk0BzYEmJMIpKm9u8voWDTpxy279NK70qPve4d+4rXk/OW0fHK31KwVX1dSfIIrSUedNU6FXgRyAD+4u5LzWxKUD4N+A5wkZntA74Cvudhnd8XkbS2dedGSvYXc3i7cPqi6tKuDdt2F7Fo3Rf06tQ+lH2I1Faod2m4+2xgdoV502Le3w7cHmYMItI4bPyyAIA+7dqGsv2hPaOPmS0u2Mi3cgaEsg+R2lKPbSKSFr7YVoCZcVjbcJJ4+9Yt6d25ffnHzGbmRV8iCaIkLiJpoXO7QxnR/wRaZGSEto9hPbP0rLgkFT30KCJpYejhRzP08KNhx1Oh7eO8sYP4+HPdeyvJQ0lcRFLe/pIS9u37ihbNWoW6nwuPHR7q9kVqS0lcRFLeF59+yvS/X8n5J11Fbntq9ehYbe3as5c9+0romBnuPwwi8dA1cRFJeRtXrwagU7usUPdTXLKfTj/5Lb+d/Xao+xGJl5K4iKS8jatXk9GkKR3bdg11P00zmjAgq5NGM5OkoSQuIilvY34+ndt3o0mT8O5MLzWkZ1cWK4lLklASF5GUt3H1aroecsAgiaEY2rMra7dsZ/vuogbZn0h1lMRFJKW5O8eefz7DDj+mQfY3JOi5ben6TQ2yP5Hq6O50EUlp9uAaxjIC6rEhHsnPj75ZuA1yOpTNz83OZlzfnvz+B6fTW/2nSxJQEheRlPblzk3s319Cx3ZZXw8RGqKu7dow9eSxoe9HJB46nS4iKe3dj15k+nM3Nug+127Zzpsr1jToPkUqoyQuIilt45cFdD2kR4O0wkvd8vQcJv7fo2jkZEk0JXERSVnuzsZt6+nSoWHuTC81pGdXthR+xefbCxt0vyIVKYmLSMra9eWXfLWnkKxDejbofof2it6hrk5fJNGUxEUkZZV2t9q1oVviPaJJXJ2+SKIpiYtIyjq0Xz++N/6ndOuU3aD77dKuDVnt27B4nZK4JJYeMRORlNW6fXuOOGxkQvb92E/Oo1dHPSsuiaUkLiIpa8lrr9FpSwbdOvVu8H0fP7Dh9ylSkU6ni0hK2r9/P8/ecQcLP30rIfvfsG0n977yPhu27UzI/kVASVxEUtSaNWvY+9VXdO3QsHeml1q3ZQdTH/oX7326PiH7FwElcRFJUUuWLAGga4fuCdn/4J5dAFhc8EVC9i8CSuIikqK+TuKJaYm3adGcw7scwpICjWYmiaMkLiIpafHixbTPyqJF81YJi2For65qiUtCKYmLSEqaPn06F95xR0JjGNKjK598sZW9e/cmNA5pvJTERSQlZWZm0qlnYk6ll7rmtKPZeu8vaN68eXTGzLxEhiONkJ4TF5GUs3r1au6//36KcnLokMA4OmYm7lS+CITcEjez08xshZmtNLPrKim/wMwWBa93zGx4mPGISHp47733uP3229mza1eiQyHvyQgzZ85MdBjSSIWWxM0sA7gXOB0YBEwys0EVFlsNnOjuw4CbgelhxSMi6WPx4sVkZGTQqVevRIfCP+ct49FHH010GNJIhdkSHwusdPdV7r4XmAWcFbuAu7/j7l8Gk/8GEnuBS0RSwpIlSxgwYABNS69Fh2HhtrgWG9orq+xxN5GGFuY18R7AupjpAmBcNcv/GPhXZQVmNhmYDJCVlUUkEqmnEBOvsLAwrY4nTKqr+KV7Xc2dO5eBAwcysLAQctuWKyssmVCrbZW0b0/ht2LWaZ0R/dmjpPw0EGne4oD1W/cZxNp3H+W5554js81ASNN6T/fPVH1qyLoKM4lbJfO80gXNxhNN4sdVVu7u0wlOtY8ePdpzc3PrKcTEi0QipNPxhEl1Fb90rqs9e/awZ88eTjrpJFZkZsLjm8uV5+54tlbbK/zWBDKfj1knp0P0Z2lLvHQayM3OPnD9rCb8CejYsSPHrJwH35lUq/2ninT+TNW3hqyrMJN4ARB7waon8FnFhcxsGPAn4HR33xJiPCKSBlq0aMHmzZvZt28fv3nnnUSHw5AeXWnfvj0bN2pscWl4YSbxuUB/M+sDrAfOB74fu4CZHQb8E7jQ3T8OMRYRSSNm9vWz2QnWu3N7vvzyS8wMZi5MdDjSyIR2Y5u7FwNTgReBZcA/3H2pmU0xsynBYtcDnYD7zGyhmc0LKx4RSQ933XUXU6ZMqXnBBmJm0QQukgChdvbi7rOB2RXmTYt5fylwaZgxiEh6mT17Njt27Eh0GOX89a9/5aGHHuLVi4+v9GYgkbCo21URSSmLFy9myJAhiQ6jnMLCQl5//XU+316Y6FCkkVESF5GUsXHjRjZu3MjQoUMTHUo5Qz6LXglcUqCb26Rhqe90EUl6eZEIzMhn9bCtACwoKYnOawiVPGpW0ZAeXQFYXLCRk8OPSKSMWuIikjKK9+2jS3Y2h/btm+hQyunSrg1Z7duoJS4NTi1xEUkZ/ceNo/+46jp+TJxv5wykS7vWiQ5DGhklcRGRejD9R7Xr7lWkPuh0uoikhOKSfdx57rl8MHt2zQsnkHulvUuLhEItcRFJCRu3radwyxZatGlTaXnujqdCjyGSn3/gfoP+1Fds2MwJv5nB/e1yOPvss0OPRQTUEheRFPH5ljUAHNqvX4IjqVzPju3YuGMXixcvTnQo0ogoiYtISvh861qat27NId26JTqUSrVp0ZzDuxyiscWlQSmJi0hK+PzLdRzaty/WJEFfW6XPi1djaK+uLFq0KPxYRAJK4iKSEg7vNojB48cnOoxqjezdjRUrVrBz585EhyKNhG5sE5GUkJtzNkzMTnQY1Tp5yOFsyx5BUVERbdu2TXQ40ggoiYtI0isqLCSjeC/NEh1IDY7u14ujL8pLdBjSiOh0uogkvbdnzeL2R35Cyb594e9s4ba4rn9XZc+ePeRX8iiaSBjUEheRpLfh44/p3L4bGc2SvS0O5x+Tw7INm1j+2eZEhyKNgFriIpLU3J31y5fTvXOfRIcSlxG9D+Xjz7fo5jZpEEriIpLUPv30U4p27qRH58MTHUpcRmV3wx0++OCDRIcijYCSuIgktffffx+AHsnYEq/k2vmo7O4AzJv2a5iZ16DhSOOja+IiktTGjBnDyVdcQdfCHokOJS6HdsikxyFtmZ+/IdGhSCOgJC4iSa1///4c893vwoz8RIcSt99dcBo9DmmX6DCkEVASF5GktW/fPp5//nl2m9E60cHUwnfGDEp0CNJI6Jq4iCStJUuWMHHiRFbNn//1zBn5iWuVx/n8+J59xcz+8BNWbCj/mFkkL1L/MUmjpiQuIklr7ty5APQ44ogER1I7+0r2M+HuR/jbOxoMRcKlJC4iSev999+nU6dOdEjS4UerktmyOcMPy+LdlQWJDkXSnJK4iCStd999l3HjxmFmiQ6l1o7p14v3Vq2nuLg40aFIGlMSF5GktGXLFj766COOP/74RIdSJ8f070Vh0V6WLFkC6Hq4hENJXESSUseOHVmxYgUXX3xxokOpk2P69QKiZxNEwhJqEjez08xshZmtNLPrKik/wszeNbM9ZvazMGMRkdRiZgwYMIBuKXY9vFTvzu1Z8usrmDx5cqJDkTQWWhI3swzgXuB0YBAwycwqPjy5FfgP4I6w4hCR1HTTTTcxe/bsRIdRZ2bG4J5dycjISHQoksbCbImPBVa6+yp33wvMAs6KXcDdN7r7XKABBgkWkVSxa9cubr75Zt5+++1Eh3JQln+2mcm5o/jsd/+V6FAkTYXZY1sPYF3MdAEwri4bMrPJwGSArKwsIpHIQQeXLAoLC9PqeMKkuopfqtfVggULKC4upl27dkQiEQYWFkJuWyj9CZC/JfozmC4smVCnfZW0b0/ht2qxbuugZb27BHpApE35vuT2Fu4BoHlmCz7JaMEDbyygy/CjOPqoQoCU/b2k+meqITVkXYWZxCt7JsTrsiF3nw5MBxg9erTn5uYeRFjJJRKJkE7HEybVVfxSva4ikQhmxuWXX06HDh3Ii0Tg8c1wSafoz0rk7ni2Tvsq/NYEMp+vxbo5HaI/g97bcs/OKVec/0Y+ANm52ZzQxbmuTSs2fPAOmYecF11+Um6d4ky0VP9MNaSGrKswT6cXAL1ipnsCn4W4PxFJE6+88gqjRo2iQ4cOiQ7loDRpYow/MptXP1qNe53aMCLVCjOJzwX6m1kfM2sOnA88E+L+RCQNFBcXs2PHDk4++eREh1IvThrUh7VbtrNhm4YmlfoX2ul0dy82s6nAi0AG8Bd3X2pmU4LyaWZ2KDAPaAfsN7OrgUHuviOsuEQkuTVt2pRFixZRUlKS6FAOSn4kn+zcbE46sg+HdWrPxu0b6X5I97JOX3LzchMan6SHUIcidffZwOwK86bFvP+c6Gl2EZFyavNoVu6Op8IL5CAN7NaJ/Duv4o3VOYkORdKQemwTkaRy1FFH8Zvf/CbRYdQbM8PM2O/72e/7Ex2OpBklcRFJGmvXruW9996jdevWNS+cQt7/dD3n3nkuHxV8lOhQJM0oiYtI0njhhRcAym5qO2DQkBn5DRtQLeRH8qssG3BoJ7bv3s67H3/dj7oGRJH6oCQuIknj6aef5vDDD2fQoIo9NKe2Dm1aMqz3MP798b8THYqkGSVxEUkKO3fu5JVXXuHss89OyfHDa3L0gKNZtXEVn2/7PNGhSBpREheRpLBnzx6uvvpqzj///ESHEoqjBxwNUO6UekLNzIu+JKWF+oiZiEi8OnfuzO23337A/EheBPLzGzye+lJ6rbzXYbl8/7jvM6hnel0qkMRSS1xEEu6rr77ixRdfpLi4ONGhhOqyb1zGwO4DEx2GpBElcRFJuOeee47TTjuNOXPmxLV87o6nkrqDl+osX7+cD9d8GN/CM/N0yluqpdPpIkksr5LhDPNScCSpmo7j4Ycfplu3bpx44okNF1SC3PHsHTRv2pz7Lr0v0aFIGlASF5FqVZaA4eD/mSjd7lc7dvDs888zduJEbn7zTXKD3aVK3+Kxz4dX96x4qW8M+QbTX53O+q3rwwtKGg2dTheRhFr86qvsLy5mWJqMWlaTk4efTBNrwnPzn0t0KJIG1BIXkYT6+N136X7EEXTr3x+ASHAneiQSSYm70vO3bat0fnYVY6F3btuZYwYewwsLX2Dv3r00b948vOAk7SmJi0hCff/WWyncujXRYTSoCaMm8MHqD1iyZAkjR46seYWZedGfF+XFN7++zcyDNrqrPhnpdLqIJExJcTFNMjJo16XLgYXJ2k/6wm3R10EY3Xc0j13zGCNHjlQf6nJQlMRFJCG2rFvHPd/7HvkLFyY6lAbXxJrQqnkr3J0dX+1IdDiSwnQ6XSSNhXVneX148+GHKdq1iy69eyc6lAaRvXYGAPmHXVI279RTT2XvRx/x7cELyp8Snxnz/mCVbivsU+6SEGqJi0iD+/Kzz1j08suMnjCBNocckuhwEuakk07ijfXreXflukSHIilKLfEqJHMLRiTVvXz//TRt3pxj0nSwk3gN3zGcrq1acc3fX+KdGz0tR2+TcCmJi0i9qeqf31hffPopy+bMYfyPf0zbTp3CDypJlZ5e/9moEfzirXeYNWsWkyZNCn/HM/PiK9fp95Sg0+ki0qCy+vblorvu4pjvfjfRoSSFc/r2ZWTvbvz5z39OdCiSgtQST0Hpcqo/XY5D4rdj0ybadelCnxEjEh1K0sho0oSnrvoeXa+8LdGhSApSEk9i8ZyabIj9JUNSzYtEGFhYeECM9RFbugwykuyWv/UWj914I9+/9Vb6jh5dL9tM1ZHMKurVqT20aMH27dt58803ObOmFWbm1d/OS7el0+cpSUk8jTTGZNQYjzlZ1OafzM9WrOCfv/41h/brR+9hw8ILKsnEMyBK6XL5qyL8/l+/56m5T/HCz77PyUP6hhucpAUlcWk0GvrMRkOLPb7KzlokyoaPP+bha6+ldfv2TPr1r2mqvsKr9KOTfsQH+R9w1u9m8ezVk/jG4MMTHZIkOSVxqVF9tHaTJaEkq9rUTyrVZeHWrTx4zTW0zMzkwjvuILNjx0SHlNTatGjDoyeN4YdvFnLm3Y/wwA8n8INjY85czMyLf2MVl63NupIylMTrQbJfS650fj2NBV3f261u2w21vhy8kuJiMpo2JbNjR4674AKGfuMbtO/aNdFhpYQurVrx+nUXc969j3Hj02/wnTFH0qp5s0SHJUkq1CRuZqcBvwMygD+5+20Vyi0oPwPYDVzi7gvCjEkkHvXxT0pjvF6/r6iID196iTcffphJwTXw4xri2ec0s2vBJh4YdwIth3eiVfNmbNtVxJ/nLODSE0fSvnXLRIcnSSS0JG5mGcC9wMlAATDXzJ5x949iFjsd6B+8xgF/DH42mETfAV567TJdvtzTvRV8sIk5Hetnf0kJK99/n+Vvv82yOXMo2rmTHkcckeiwklZpJy81zW/WpEn0rnXg+Q8/5mezXibvqTf49oiBnDPqCE48IpvObVtHF56ZF/15MHeYl26jpnmSVMJsiY8FVrr7KgAzmwWcBcQm8bOAme7uwL/NrIOZdXP3DSHGdVDS5dplMseWairWZfTj/DUzw/fvP2A+gDVpgpmxv6Tk6/KY5TKaRU+j7i8pYX9JyQHrl94kVrx3L75/f9n+i4qK2Ne0Kc1aRltt+/bsKVf+y9mzMTOat2oFwN6vvuLaY44pt+2MjAwyMzMB+GLVKnZv386eXbvYsWkT27/4gnZduzLunHMAeOLmm8GMAUcdxeizzuKwoUPVhWg9uuCYYRzZvQv3vTqXpxYs5+/vLsYMtv3xOtq1asHTC5azdst2urd5gg4dOtChQwc6bdpGdpcOAOzesw+AZhlNaJrRRL+bNBJmEu8BxPbqX8CBrezKlukBJG0SD4uSavU+W7GC266+mv0V5p917bUMzs0lf+FCHr722gPW++5NN9F/3DhWvPMOj+XlAeWT7EV33knvYcNY/MorPHXbbQeUXzZtGt3692feM8/w/D33HLD9qTNn0qlnT96eNYtX7r//gPL/euIJMjt2JDJjBnMeeuiA8l/Onk3zVq14ado03nv88fKFZtzw2msAPHfXXXwwe3a54uatW/PL558H4KnbbmPp66+XK2/buTPXPPYYAI/dcAOfvPdeufJOvXoxdeZMAB6+7jpuXbSoXHmPI4/k0vvuA+DJX/+aL1atKivLaNaMI447jnHnnEOTjAwuvvtusg4/vOyfDql/I7O78acff5tpl5zJO5+sY9mGTbRr1QKAv72zmMfnfgR/e6Fs+R6HtKXgnmsA+M7v/8ELi1eWlWU0MQb36MqHt0wBYPytD/JOzCAsZjDmgVd587JvADDuxj/xYcEmMppeGpQb48eP59lnnwVg6NCh5Ofnl4v3zDPP5JFHHgGgT58+bN68uVz5pEmTmD59OgBdunShqKioXPmll17K3XffTXFxMYdUMkjO1Vdfzc0338yXX37JYYcddkD5//zP//CLX/yCdevWMWjQoAPKb7/9dq688kqWL1/OmDFjDii/9957ueiii5g7dy4nnXTSAeUPPvgg55xzDq+//jrf/va3y5X96le/IreBzq5aZa2Detmw2XnAqe5+aTB9ITDW3X8as8zzwK3u/lYw/SrwC3efX2Fbk4HJweRAYEUoQSdGZ2BzjUsJqK5qQ3UVP9VVfFRP8Qujrnq7e5eKM8NsiRcAvWKmewKf1WEZ3H06ML2+A0wGZjbP3eun+6o0p7qKn+oqfqqr+Kie4teQdRXmAChzgf5m1sfMmgPnA89UWOYZ4CKLOgrYnszXw0VERJJJaC1xdy82s6nAi0QfMfuLuy81sylB+TRgNtHHy1YSfcTsh2HFIyIikm5CfU7c3WcTTdSx86bFvHfgJ2HGkALS8jJBSFRX8VNdxU91FR/VU/warK5Cu7FNREREwhXmNXEREREJkZJ4ApjZeWa21Mz2m9noCmW/NLOVZrbCzE5NVIzJyszyzGy9mS0MXmckOqZkYmanBZ+dlWZ2XaLjSWZmlm9mi4PP0bxEx5NMzOwvZrbRzJbEzOtoZi+b2SfBzwMf3m6EqqirBvueUhJPjCXAOcCc2JlmNojoXfyDgdOA+4Lua6W8u909J3jNrnnxxiGmq+PTgUHApOAzJVUbH3yO9OhUeTOIfgfFug541d37A68G01J5XUEDfU8piSeAuy9z98o6rDkLmOXue9x9NdG79sc2bHSSwsq6Onb3vUBpV8citeLuc4CtFWafBTwYvH8QOLshY0pWVdRVg1ESTy5VdUMr5U01s0XBaSyd0vuaPj+148BLZjY/6BVSqpdV2o9H8FNjy1avQb6nlMRDYmavmNmSSl7VtYwqG5Wg0T0+UEPd/RHoC+QQ7WP/zkTGmmT0+amdY919JNHLDz8xsxMSHZCkjQb7ngr1OfHGzN2/WYfV4uqGNt3FW3dm9gDwXMjhpBJ9fmrB3T8Lfm40syeJXo6YU/1ajdoXpaNMmlk3YGOiA0pW7v5F6fuwv6fUEk8uzwDnm1kLM+tDdJz19xMcU1IJvjxKTSR6k6BExdPVsQBm1sbM2pa+B05Bn6WaPANcHLy/GHg6gbEktYb8nlJLPAHMbCLwe6AL8LyZLXT3U4Nuaf9BdMz1YuAn7n7gINKN22/NLIfoaeJ84PKERpNEqurqOMFhJass4MlgXO2mwN/d/YXqV2k8zOwRIBfobGYFwA3AbcA/zOzHwFrgvMRFmDyqqKvchvqeUo9tIiIiKUqn00VERFKUkriIiEiKUhIXERFJUUriIiIiKUpJXEREJEUpiYukADP7f8HId4uCUZHGhby/SMUR9qpZ9pLgMZvYeZ3NbJOZtahmnT/UR6wijZmeExdJcmZ2NHAmMNLd95hZZ6B5gsOK9U/gDjNr7e67g3nnAs+4+54ExiWS9tQSF0l+3YDNpQnR3TeXdhlqZteb2dygb/npFvReErSk7zazOWa2zMzGmNk/g7GgbwmWyTaz5Wb2YNDCf9zMWlfcuZmdYmbvmtkCM3vMzDJjy919B9HuSifEzD4feMTMJpjZe2b2QdAnflYl259hZufGTBfGvP95cHyLzOzGg6hDkbSkJC6S/F4CepnZx2Z2n5mdGFP2B3cf4+5DgFZEW+yl9rr7CcA0ol1k/gQYAlxiZp2CZQYC0919GLADuDJ2x0Gr/7+BbwaDhcwDrqkkxkeIJm7MrDswAHgdeAs4yt1HEB0a9RfxHrSZnUK06+GxRAeSGKVBSkTKUxIXSXLuXgiMAiYDm4BHzeySoHh80NJdDJwEDI5ZtbTf9MXAUnffELTmV/H1QCnr3P3t4P3fgOMq7P4oYBDwtpktJNpndu9KwnwOOM7M2gHfBR4PugzuCbwYxPfzCvHV5JTg9QGwADiCaFIXkYCuiYukgCAhRoBIkBAvNrNZwH3AaHdfZ2Z5QMuY1UqvR++PeV86Xfq3X7Hf5YrTBrzs7pNqiO8rM3uB6GAP5wP/GRT9HrjL3Z8xs1wgr5LViwkaFMHlgNLr/Qbc6u73V7dvkcZMLXGRJGdmA80stgWaA6zh64S9ObhOfW7FdeNwWHDjHMAkoqe/Y/0bONbM+gWxtDazAVVs6xGip9qzgvUA2gPrg/cXV7YS0QEiRgXvzwKaBe9fBH5Ueg3ezHqYWdd4DkqksVASF0l+mcCDZvaRmS0ieno7z923AQ8QPV3+FNGhSGtrGdFW/SKgI/DH2EJ33wRcQvQmtUVEk/MRVWzrJaA78Kh/PbJSHvCYmb0JbK5ivQeAE83sfWAcsCvY90vA34F3g7MPjwNt63CMImlLo5iJNFJmlg08F9wUJyIpSC1xERGRFKWWuIiISIpSS1xERCRFKYmLiIikKCVxERGRFKUkLiIikqKUxEVERFKUkriIiEiK+v+6C//OEuk6QwAAAABJRU5ErkJggg==", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# Parameters\n", - "num_samples = 1000\n", - "initial_states = [-12, 5, 10] # Initial states for each chain\n", - "proposal_sigma = 0.2 # Standard deviation for the proposal distribution\n", - "\n", - "# Generate samples using Metropolis-Hastings algorithm for each chain\n", - "chains_samples = []\n", - "\n", - "for initial_state in initial_states:\n", - " samples = metropolis_hastings(num_samples, initial_state, proposal_sigma)\n", - " chains_samples.append(samples)\n", - "\n", - "# Plot all chains on one plot\n", - "plt.figure(figsize=(6, 4))\n", - "colors = ['teal', 'purple', 'orangered'] # Define colors for each chain\n", - "for idx, samples in enumerate(chains_samples):\n", - " plt.plot(samples, color=colors[idx], alpha=0.8, label=f'Chain {idx+1}')\n", - "\n", - "plt.xlabel('Iteration')\n", - "plt.ylabel('Sample Value')\n", - "plt.title('Traceplot of Metropolis-Hastings Chains')\n", - "plt.legend()\n", - "plt.grid(True)\n", - "plt.show()\n", - "\n", - "# Plot posteriors for each chain\n", - "plt.figure(figsize=(6, 4))\n", - "for idx, samples in enumerate(chains_samples):\n", - " plt.hist(samples, bins=50, color=colors[idx], alpha=0.5, density=True, label=f'Chain {idx+1}')\n", - "\n", - "x = np.linspace(-5, 15, 1000)\n", - "plt.plot(x, target_distribution(x), color='black', linestyle='--', label='True Distribution')\n", - "plt.xlabel('Sample Value')\n", - "plt.ylabel('Probability Density')\n", - "plt.title('Posteriors of Metropolis-Hastings Chains')\n", - "plt.legend()\n", - "plt.grid(True)\n", - "plt.show()\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Convergence diagnostics\n", - "\n", - "Assessing MCMC convergence involves evaluating whether the chains generated by the algorithm have reached a stationary distribution and are sampling effectively from the target distribution. \n", - "\n", - "Reaching convergence on the sample is essential, otherwise, the samples do not come from the posterior distribution and subsequent analysis are meaningless.\n", - "\n", - "\n", - "\n", - "\n", - "A few common methods for assessing MCMC convergence are:\n", - "\n", - "- Visual Inspection: traceplots: Plotting traceplots of the chains can provide visual cues about convergence. Traceplots show the parameter values sampled at each iteration for each chain. Flat, stable traces suggest convergence, while erratic or trending traces indicate potential issues.\n", - "\n", - "- Visual Inspection: density plots: Density plots of samples from different chains overlaid with the target distribution can visually assess convergence. As chains converge, their density plots should match the target distribution.\n", - "\n", - "- Auto-correlation Plots: Auto-correlation plots show how each sample in the chain is correlated with previous samples. Rapid decay in auto-correlation suggests convergence, while slow decay may indicate lack of convergence.\n", - "\n", - "- Effective Sample Size (ESS): ESS estimates the number of *independent* samples obtained from the MCMC chains. It quantifies the amount of information each chain provides about the target distribution. Higher ESS values indicate more reliable estimates.\n", - "\n", - "- Gelman-Rubin Diagnostic (R-hat): This diagnostic compares the variance between chains to the variance within chains. An R-hat value close to 1 indicates convergence. Values significantly greater than 1 suggest that more iterations are needed.\n", - "\n", - "We have already performed visual diagnostics. Let's use the more quantitative measures to assess convergence.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Autocorrelation plots" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# Compute autocorrelation function (ACF) for a given chain\n", - "def autocorr(chain):\n", - " n = len(chain)\n", - " mean = np.mean(chain)\n", - " c0 = np.sum((chain - mean) ** 2) / n\n", - " autocorr = np.correlate(chain - mean, chain - mean, mode='full') / (n * c0)\n", - " return autocorr[len(autocorr)//2:]\n", - "\n", - "# Compute autocorrelation for each chain\n", - "autocorr_values = []\n", - "for chain in chains_samples:\n", - " autocorr_values.append(autocorr(chain))\n", - "\n", - "colors = ['teal', 'purple', 'orangered'] # Define colors for each chain\n", - "\n", - "# Plot autocorrelation for each chain\n", - "plt.figure(figsize=(6, 4))\n", - "for idx, acf in enumerate(autocorr_values):\n", - " plt.plot(acf, label=f'Chain {idx + 1}', color=colors[idx])\n", - "\n", - "plt.xlabel('Lag')\n", - "plt.ylabel('Autocorrelation')\n", - "plt.title('Autocorrelation Plot of Metropolis-Hastings Chains')\n", - "plt.legend()\n", - "plt.grid(True)\n", - "plt.show()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Since neigbouring samples will contain similar information adn are auto-correlated, one can decide to save only every second, or fifth, or tenth sample. This is called thinning.\n", - "\n", - "`````{admonition} Group Task\n", - ":class: tip\n", - "- Increase the number of iterations in the algorithm above and create an ACF plot. What do you conclude?\n", - "- Experiment with the values of parameter `proposal_sigma`. What do you observe?\n", - "`````" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Computing effective sample size (ESS)\n", - "\n", - "The effective sample size describes the efficiency of dependent sample in terms of independent draws from the same distribution, is descriptive of the effectiveness of the sampling and of the autocorrelation of the chain.\n", - "\n", - "The formula for estimating the Effective Sample Size (ESS) of a Markov chain is:\n", - "\n", - "$$\\text{ESS} = \\frac{N}{1 + 2 \\sum_{t=1}^{T} \\rho_t}$$\n", - "\n", - "Where:\n", - "\n", - "- $N$ is the total number of samples in the chain,\n", - "\n", - "- $T$ is the lag, which represents the maximum number of auto-correlation terms considered, \n", - "\n", - "- $\\rho_t$ s the auto-correlation at lag $t$, i.e., the correlation between two consecutive samples separated by $t$ iterations.\n", - "\n", - "In practice, $T$ is often chosen such that $\\rho_T$ is small, indicating that the auto-correlation has decayed sufficiently. The sum $\\sum_{t=1}^T \\rho_t$ is then approximately truncating at $T$. \n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Chain 1 - ESS: 5.432800285507235\n", - "Chain 2 - ESS: 12.250567042041817\n", - "Chain 3 - ESS: 9.336800817741272\n" - ] - } - ], - "source": [ - "# Compute auto-correlation function (ACF) for each chain\n", - "def autocorr(x, t=1):\n", - " return np.corrcoef(np.array([x[:-t], x[t:]]))\n", - "\n", - "acf_values = []\n", - "for chain in chains_samples:\n", - " acf_values.append([autocorr(chain, t)[0, 1] for t in range(1, len(chain)//5)])\n", - "\n", - "# Estimate Effective Sample Size (ESS) for each chain\n", - "ess_values = []\n", - "for acf in acf_values:\n", - " T = 100 # Truncate at lag T\n", - " ess_values.append(num_samples / (1 + 2 * sum(acf[:T])))\n", - "\n", - "# Print ESS values for each chain\n", - "for idx, ess in enumerate(ess_values):\n", - " print(f'Chain {idx + 1} - ESS: {ess}')" - ] - }, + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Markov Chain Monte Carlo \n", + "\n", + "We want to estimate the posterior distribution, but this is often intractable.\n", + "\n", + "Markov Chain Monte Carlo (MCMC) is a computational technique used to approximate complex probability distributions by generating a sequence of (correlated) samples, where each sample is obtained by iteratively transitioning through a Markov chain with carefully designed transition probabilities.\n", + "\n", + "The MCMC simulation method is the modern way of approximating complex posterior distributions. The idea is analogous to treating the posterior distribution as the population, and then repeatedly draw samples from it. When we draw a large enough sample (say 1000), the sample distribution should be very close to the population distribution.\n", + "\n", + "One tweak of MCMC from the above analogy is that the samples drawn are correlated, so that if the first sample is high, the next one is more likely to be high too. This is needed because we don’t have a direct way to draw samples from the posterior distribution, which usually has a very complex form; instead we have some algorithms that can indirectly get us to the posterior. The correlation among samples usually is not a big problem, except that we need to draw more samples to compensate for it. \n", + "\n", + "An overview of how an MCMC works is as follows:\n", + "\n", + "- Draw samples from a (simple) proposal distribution so that each draw depends only on the state of the previous draw (i.e. the samples form a Markov chain).\n", + "- Under certain conditions, the Markov chain will have a unique stationary distribution.\n", + "\n", + "- We set up an acceptance criteria for each draw based on comparing successive states with respect to a target distribution that ensure that the stationary distribution is the posterior distribution we are searching for.\n", + "\n", + "- There is no need to evaluate the potentially intractable marginal likelihood.\n", + "\n", + "- After sufficient number of iterations, the Markov chain of accepted draws will converge to the stationary distribution, and we can use those samples as (correlated) draws from the posterior distribution, and find functions of the posterior distribution.\n", + "\n", + "Some examples of MCMC algorithms are\n", + "\n", + "1. The Metropolis algorithm,\n", + "3. The Metropolis-Hastings algorithm,\n", + "4. The Gibbs sampler,\n", + "5. Hamiltonian Monte Carlo,\n", + "6. No U-turn sampler (and several variants).\n", + "\n", + "Let us take a closer look at some of these algorithms." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Metropolis-Hastings algorithm\n", + "\n", + "The Metropolis-Hastings algorithm is particularly useful when direct sampling from the distribution is difficult or impossible, but evaluating the probability density function (PDF) up to a constant of proportionality is feasible. It's useful for sampling from high-dimensional, complex distributions. The algorithm iteratively generates samples from a target distribution by constructing a Markov chain.\n", + "\n", + "Let $\\pi(x)$ be the target probability density function (pdf) from which we want to sample. The steps of the Metropolis-Hastings algorithm are as follows:\n", + "\n", + "1. **Initialization**: Start with an initial state $x_0$ from the sample space.\n", + "\n", + "2. **Proposal Generation**: At each iteration $t$, propose a new state $x'$ based on some proposal distribution $q(x' | x_t)$, which defines the probability of transitioning from state $x_t$ to $x'$.\n", + "\n", + "3. **Acceptance Probability**: Calculate the acceptance probability $\\alpha$ as follows:\n", + "\n", + "$$\n", + "\\alpha = \\min \\left(1, \\frac{\\pi(x')}{\\pi(x_t)} \\times \\frac{q(x_t | x')}{q(x' | x_t)} \\right)\n", + "$$\n", + "\n", + "where $\\pi(x)$ is the target probability density function and $q(x' | x_t)$ is the proposal distribution.\n", + "\n", + "4. **Acceptance or Rejection**: Generate a uniform random number $u$ from the interval [0, 1]. If $u < \\alpha$, accept the proposed state $x'$ as the next state: $x_{t+1} = x'$; otherwise, stay at the current state: $x_{t+1} = x_t$.\n", + "\n", + "5. **Iteration**: Repeat steps 2-4 for a sufficient number of iterations.\n", + "\n", + "The resulting sequence of samples $x_1, x_2, ..., x_n$ forms a Markov chain that converges to the target distribution $\\pi(x)$ as $n$ approaches infinity. Proper choice of the proposal distribution is crucial for efficient sampling, and tuning its parameters can significantly impact the algorithm's performance.\n", + "\n", + "The Metropolis algorithm is a special case of the Metropolis-Hastings algorithm where the proposal distribution is symmetric, meaning $q(x' | x_t) = q(x_t | x')$, leading to simplifications in the acceptance probability calculation.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Metropolis-Hastings by hand\n", + "\n", + "Let us implement the Metropolis-Hastings algorithm for sampling from the normal distribution $\\mathcal{N}(5,1)$. As the proposal distribution we will use $\\mathcal{N}(0,1)$, making the proposal a random walk process. Note that this proposal is symmetric, hence, we don't need to account for it in the acceptance ratio." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "\n", + "import scipy.stats as stats\n", + "\n", + "import matplotlib.pyplot as plt\n", + "from matplotlib.colors import LinearSegmentedColormap" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# target distribution: Univariate normal distribution with mean = 5, variance = 1\n", + "def target_distribution(x):\n", + " return np.exp(-(x - 5)**2 / 2) / np.sqrt(2 * np.pi)\n", + "\n", + "# proposal distribution: Normal distribution with mean = 0 and variance = 1\n", + "def proposal_distribution(x, sigma=1):\n", + " return np.random.normal(x, sigma)\n", + "\n", + "# Metropolis-Hastings algorithm\n", + "def metropolis_hastings(num_samples, initial_state, proposal_sigma):\n", + " samples = [initial_state]\n", + " current_state = initial_state\n", + "\n", + " for _ in range(num_samples):\n", + " # propose a new state\n", + " proposed_state = proposal_distribution(current_state, proposal_sigma)\n", + " \n", + " # calculate acceptance ratio\n", + " acceptance_ratio = min(1, target_distribution(proposed_state) / target_distribution(current_state))\n", + " \n", + " # accept or reject the proposed state\n", + " if np.random.uniform(0, 1) < acceptance_ratio:\n", + " current_state = proposed_state\n", + " samples.append(current_state)\n", + "\n", + " return samples" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# parameters\n", + "num_samples = 1000\n", + "initial_state = -3 # initial state\n", + "proposal_sigma = 0.2 # standard deviation for the proposal distribution\n", + "\n", + "# generate samples using Metropolis-Hastings algorithm\n", + "samples = metropolis_hastings(num_samples, initial_state, proposal_sigma)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now when we have collected samples, we can plot them to make a traceplot, and we can also plot the sampling distribution we obtained:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Computing the Gelman-Rubin Statistic ($\\hat{R}$)\n", - "\n", - "To compute the Gelman-Rubin statistic (often denoted as $\\hat{R}$), we need to run multiple chains and compare their variability within each chain to their variability between chains. Here's the algorithm to compute $\\hat{R}$:\n", - "\n", - "\n", - "1. Run $m$ Markov chains of length $n$, where $m$ is typically greater than 1.\n", - "2. For each scalar parameter $\\theta$, compute the within-chain variance $W$ and the between-chain variance $B$.\n", - "3. Calculate the pooled within-chain variance $\\hat{V}$ as the weighted average of the within-chain variances.\n", - "4. Calculate the potential scale reduction factor $\\hat{R}$ as the square root of the ratio of the pooled within-chain variance to the within-chain variance:\n", - " \n", - " $$\\hat{R} = \\sqrt{\\frac{\\hat{V}}{W}}$$\n", - " \n", - "5. If $\\hat{R}$ is close to 1, it indicates convergence of the chains.\n", - "\n", - "The Gelman-Rubin statistic $\\hat{R}$ is a measure of convergence for the Markov chains. It quantifies the degree to which multiple chains agree with each other, providing a diagnostic tool for assessing convergence in Markov Chain Monte Carlo (MCMC) simulations.\n" + "data": { + "image/png": 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", + "text/plain": [ + "
" ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" }, { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "R-hat for each parameter: [1.00069545]\n" - ] - } - ], - "source": [ - "import numpy as np\n", - "\n", - "# Function to compute Gelman-Rubin statistic (R-hat)\n", - "def gelman_rubin(chains):\n", - " num_chains = len(chains)\n", - " num_samples = len(chains[0])\n", - " num_parameters = len(chains[0][0])\n", - "\n", - " # Calculate means and variances for each chain and parameter\n", - " chain_means = np.mean(chains, axis=1)\n", - " chain_vars = np.var(chains, axis=1, ddof=1)\n", - "\n", - " # Calculate within-chain variance (W) and between-chain variance (B)\n", - " W = np.mean(chain_vars, axis=0)\n", - " B = num_samples / (num_chains - 1) * np.sum((chain_means - np.mean(chain_means, axis=0))**2, axis=0)\n", - "\n", - " # Calculate pooled within-chain variance\n", - " V_hat = (num_samples - 1) / num_samples * W + 1 / num_samples * B\n", - "\n", - " # Calculate potential scale reduction factor (R-hat)\n", - " R_hat = np.sqrt(V_hat / W)\n", - " return R_hat\n", - "\n", - "# Example usage\n", - "chains = np.random.normal(loc=0, scale=1, size=(3, 1000, 1)) # Three chains with 1000 samples each\n", - "R_hat = gelman_rubin(chains)\n", - "print(\"R-hat for each parameter:\", R_hat)\n" + "data": { + "image/png": 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", + "text/plain": [ + "
" ] - }, + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# traceplot\n", + "plt.figure(figsize=(6, 4))\n", + "plt.plot(samples, color='teal')\n", + "plt.xlabel('Iteration')\n", + "plt.ylabel('Sample value')\n", + "plt.title('Metropolis-Hastings: traceplot')\n", + "plt.grid(True)\n", + "plt.show()\n", + "\n", + "# plot posterior\n", + "plt.figure(figsize=(6, 4))\n", + "plt.hist(samples, bins=50, color='teal', density=True)\n", + "\n", + "x = np.linspace(-5, 15, 1000)\n", + "plt.plot(x, target_distribution(x), color='black', linestyle='--', label='True distribution')\n", + "plt.xlabel('Sample value')\n", + "plt.ylabel('Probability density')\n", + "plt.title('Posterior of Metropolis-Hastings')\n", + "plt.grid(True)\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Warm-up\n", + "\n", + "We can notice on the traceplot, that the initial value we started with wasn't great. For this reason, it is common to use a warm-up period. \n", + "\n", + "A warm-up, also known as a burn-in period, refers to an initial phase where the algorithm runs to reach a state of convergence or equilibrium. During this phase, the algorithm explores the parameter space and adjusts its state transition probabilities, aiming to approach the target distribution.\n", + "\n", + "The initial part of the chain may have not reached convergence yet. Furthermore, it may also include phase for adapting algorithm parameters. So the initial part of the chain may be non-representative. This initial burn-in part must be thrown away.\n", + "\n", + "\n", + "The samples generated during the warm-up period are typically discarded as they may not accurately represent the target distribution. Once the warm-up phase is complete, the samples generated by the MCMC algorithm are considered to be from the stationary distribution and are used for inference or analysis.\n", + "\n", + "The length of the warm-up period can vary depending on factors such as the complexity of the target distribution and the effectiveness of the MCMC algorithm in exploring the parameter space. A longer warm-up period may be required for more complex distributions or when starting from a distant initial state." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Chains" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have ran the simulation forward once. In fact, we could run several simulation fowards in parallel, each with its own initial values, to see whether they converge to the same distribution.\n", + "\n", + "Chains refer to the sequences of samples generated by the algorithm as it iterates through the parameter space. Each chain represents a trajectory of parameter values explored by the algorithm over multiple iterations. Multiple chains can be run simultaneously, each starting from different initial parameter values, to improve convergence diagnostics and assess the mixing properties of the algorithm. \n", + "\n", + "Running several chains from different initial values can help convergence diagnostics, for example, because visual inspection of the chains is straightforward.\n", + "\n", + "Let us return the same experiment as above, but now by using three chains." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Gibbs sampling\n", - "\n", - "Another simple example of MCMC is the Gibbs sampling algorithm.\n", - "\n", - "In Gibbs sampling, you iteratively sample from the conditional distributions of each variable given the current values of all other variables. This assumes that you have a joint distribution of multiple variables and want to sample from the posterior distribution of one variable while keeping the others fixed.\n", - "\n", - "Here's a simplified outline of the Gibbs sampling algorithm:\n", - "\n", - "1. Start with initial values for all variables.\n", - "2. Choose one variable to update.\n", - "3. Sample a new value for the chosen variable from its conditional distribution given the current values of all other variables.\n", - "4. Repeat steps 2-3 for each variable in the model.\n", - "5. Repeat the process for a sufficient number of iterations.\n", - "\n", - "Each iteration of Gibbs sampling updates one variable at a time, conditional on the current values of the other variables. Over iterations, the samples generated by Gibbs sampling converge to samples from the joint posterior distribution of all variables.\n", - "\n", - "Gibbs sampling is used where it's difficult or computationally expensive to sample directly from the joint posterior distribution. It's relatively simple to implement." + "data": { + "image/png": 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", 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", 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "# Define the mean and covariance matrix of the bivariate normal distribution\n", - "mu = np.array([0, 0])\n", - "covariance = np.array([[1, 0.8], [0.8, 1]])\n", - "\n", - "# Function to sample from the conditional distribution of x given y\n", - "def sample_x_given_y(y, mu, covariance):\n", - " mu_x_given_y = mu[0] + covariance[0, 1] / covariance[1, 1] * (y - mu[1])\n", - " sigma_x_given_y = np.sqrt(1 - covariance[0, 1]**2 / covariance[1, 1]**2)\n", - " return np.random.normal(mu_x_given_y, sigma_x_given_y)\n", - "\n", - "# Function to sample from the conditional distribution of y given x\n", - "def sample_y_given_x(x, mu, covariance):\n", - " mu_y_given_x = mu[1] + covariance[0, 1] / covariance[0, 0] * (x - mu[0])\n", - " sigma_y_given_x = np.sqrt(1 - covariance[0, 1]**2 / covariance[0, 0]**2)\n", - " return np.random.normal(mu_y_given_x, sigma_y_given_x)\n", - "\n", - "# Initialize variables\n", - "num_samples = 1000\n", - "x_samples = np.zeros(num_samples)\n", - "y_samples = np.zeros(num_samples)\n", - "\n", - "# Initial guess\n", - "x_samples[0] = np.random.normal(0, 1)\n", - "y_samples[0] = np.random.normal(0, 1)\n", - "\n", - "# Run Gibbs sampling\n", - "for i in range(1, num_samples):\n", - " x_samples[i] = sample_x_given_y(y_samples[i-1], mu, covariance)\n", - " y_samples[i] = sample_y_given_x(x_samples[i], mu, covariance)\n", - "\n", - "# Create a color gradient for the samples\n", - "colors = np.linspace(0, 1, num_samples)\n", - "cmap = LinearSegmentedColormap.from_list(\"my_cmap\", [(0, 'blue'), (0.5, 'yellow'), (1, 'red')])\n", - "\n", - "# Plot the samples\n", - "plt.figure(figsize=(6, 4))\n", - "sc = plt.scatter(x_samples, y_samples, c=colors, cmap=cmap, alpha=0.9)\n", - "plt.colorbar(sc, label='Sampling order')\n", - "plt.xlabel('X')\n", - "plt.ylabel('Y')\n", - "plt.title('Gibbs Sampling')\n", - "plt.grid(True)\n", - "plt.show()\n" + "data": { + "image/png": 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OJnWF2RIfC6x091XuvheYBZxVYRkH2pqZAZnAVkADx4qIJLlED0W6bds2vvWtb3Hrrbdy7LHH1nk7qS7MJN4DWBczXRDMi/UH4EjgM2AxcJW77w8xJhERqQelQ5G+/PLL9O3bl8GDB5OXl1d2s1llYociPfvssw9qKNI//OEPrFy5kptvvpmcnBxycnLYuHFjnbeXqqz0zsB637DZecCp7n5pMH0hMNbdfxqzzLnAscA1QF/gZWC4u++osK3JwGSArKysUaWPM6SDwsJCMjMzEx1GSlBdxU91daDCDYUAZHYrXy+pWlft27enX79+Dba/kpISMjIyGmx/qexg62rlypVs37693Lzx48fPd/fRFZcN8znxAqBXzHRPoi3uWD8EbvPofxIrzWw1cATwfuxC7j4dmA4wevRoz03AuLlhiUQipNPxhEl1FT/V1YFKn6POnZRbfn6K1tWyZcto27Ztg+1v586dDbq/VHawddWyZUtGjBgR17Jhnk6fC/Q3sz7BzWrnA89UWGYt8A0AM8sCBgKrQoxJREQkbYTWEnf3YjObCrwIZAB/cfelZjYlKJ8G3AzMMLPFgAHXuvvmsGISERFJJ6F2u+rus4HZFeZNi3n/GXBKmDGIiIikK/XYJiIikqKUxEVERFKUkriIiNRJIociff/998ueDx8+fDhPPvlkbcNPCxqKVEQkHczMq9/tXVT99hI9FOmQIUOYN28eTZs2ZcOGDQwfPpwJEybQtGnjSmtqiYuISK0leijS1q1blyXsoqIior13Nz5K4iIiUmvJMBTpe++9x+DBgxk6dCjTpk1rdK1wUBIXEZEQNMRQpOPGjWPp0qXMnTuXW2+9tcoR0dKZkriIiNRaMgxFWurII4+kTZs2LFmypA5HktqUxEVEpNYSPRTp6tWry5L7mjVrWLFiBdnZ2XXeXqpSEhcRkVpL9FCkb731FsOHDycnJ4eJEydy33330blz5zpvL1WFNhRpWEaPHu3z5s1LdBj1JlVHUEoE1VX8VFcHKhvFLC+3/PwUratly5Zx5JFHNtj+NIpZ/A62rir73ZpZpUORqiUuIiKSopTERUREUpSSuIiISIpSEhcREUlRSuIi0qhE8iJlN7mJpDolcRERkRSlJC4iIrW2ZcuWsqFADz30UHr06FE2vXfv3nrZR25uLgMHDmTYsGEcccQRTJ06lW3btpWVH3PMMdWu/5vf/Kba8jPOOINt27aRn5/PkCFDahVbJBLhnXfeKZueNm0aM2fOrNU26oOSuIiI1FqnTp1YuHAhCxcuZMqUKfznf/5n2XTz5s1r7Co1Xg8//DCLFi1i0aJFtGjRgrPOOqusLDaJVqaqJO7u7N+/n9mzZ9OhQ4c6xVUxiU+ZMoWLLrqoTts6GEriIiJSLy655BKuueYaxo8fz7XXXkteXl65EciGDBlSNpjJ3/72N8aOHUtOTg6XX345JSUl1W67efPm/Pa3v2Xt2rV8+OGHAGRmZgKwYcMGTjjhBHJychgyZAhvvvkm1113HV999RU5OTlccMEF5Ofnc+SRR3LllVcycuRI1q1bR3Z2Nps3bwaguLiYiy++mGHDhnHuueeye/dugHLLzJs3j9zcXPLz85k2bRp33303OTk5vPnmm+WOddGiRRx11FEMGzaMiRMn8uWXXwLRMwvXXnstY8eOZcCAAbz55psHXedK4iIiaSA3N/eA13333QfA7t27Ky2fMWMGAJs3bz6grK4+/vhjXnnlFe68884ql1m2bBmPPvoob7/9NgsXLiQjI4OHH364xm1nZGQwfPjwA8YX//vf/86pp57KwoUL+fDDD8nJyeG2226jVatWLFy4sGzbK1as4KKLLuKDDz6gd+/e5baxYsUKJk+ezKJFi2jXrl1Z3VUmOzu73NmH0jHUS11++eXcfvvtLFq0iKFDh3LjjTeWlRUXF/P+++9zzz33lJtfV0riIiJSb8477zwyMjKqXebVV19l/vz5jBkzhpycHF599VVWrVoV1/Yr6yp8zJgx/PWvfyUvL4/FixdX2eVp7969Oeqooyot69WrF8ceeywAP/jBD3jrrbfiiqei7du3s337dk488UQALr74YubMmVNWHs8Qq7XR+EZQFxFJQ5FIpMqy1q1bV1veuXPnastro02bNmXvmzZtyv79+8umS0cxc3cuvvhibr311lptu6SkhMWLFx/Qr/gJJ5zAnDlzeP7557nwwgv5+c9/Xun16djYKjKzSqdjj6E+xiuvzRCr8VBLXEREQpGdnc2CBQsAWLBgAatXrwbgG9/4Bo8//jgbN24EYOvWraxZs6babe3bt49f/vKX9OrVi2HDhpUrW7NmDV27duWyyy7jxz/+cdk+mzVrxr59++KKde3atbz77rsAPPLIIxx33HFlx1A6bvoTTzxRtnzbtm3ZuXPnAdtp3749HTp0KLve/dBDD5W1ysOgJC4iIqH4zne+w9atW8nJyeGPf/wjAwYMAGDQoEHccsstnHLKKQwbNoyTTz6ZDRs2VLqNCy64gGHDhjFkyBB27drF008/fcAykUiEnJwcRowYwRNPPMFVV10FwOTJkxk2bBgXXHBBjbEeeeSRPPjggwwbNoytW7dyxRVXAHDDDTdw1VVXcfzxx5e7TDBhwgSefPLJshvbYk2bNo2f//znDBs2jIULF3L99dfHV2F1oKFIEyxVh0FMBNVV/FRXB6rYS1vpkKSpWlcaijR5aShSERERqZGSuIiISIoKNYmb2WlmtsLMVprZdZWU/9zMFgavJWZWYmYdw4xJREQkXYSWxM0sA7gXOB0YBEwys0Gxy7j7/7p7jrvnAL8E3nD3rWHFJCKSTlLtniapWW1/p2G2xMcCK919lbvvBWYBZ1Wz/CTgkRDjERFJGy1btmTLli1K5GnE3dmyZQstW7aMe50wO3vpAayLmS4AxlW2oJm1Bk4DpoYYj4hI2ujZsycFBQVs2rSpQfZXVFRUq+TSmB1MXbVs2ZKePXvGvXyYSdwqmVfVv4wTgLerOpVuZpOByQBZWVn11rNQMigsLEyr4wmT6ip+qqsDFQ4sLDddWj+qq/gUFhaWDTgi1TvYuqqp45tYYSbxAqBXzHRP4LMqlj2fak6lu/t0YDpEnxNPxWc6q5Kqz6gmguoqfqqrAx3wnPik3Oh81VVcVE/xa8i6CvOa+Fygv5n1MbPmRBP1MxUXMrP2wInAgd3wiIiISJVCa4m7e7GZTQVeBDKAv7j7UjObEpRPCxadCLzk7rvCikVERCQdhTqKmbvPBmZXmDetwvQMYEaYcYiIiKQj9dgmIiKSopTERUREUpSSuIiISIpSEhcREUlRSuIiIiIpSklcREQkRSmJi4iIpCglcRERkRSlJC4iIpKilMRFRERSlJK4iIhIilISFxERSVFK4iIiIilKSVxERCRFKYmLiIikKCVxERGRFNU00QGIiCRCJC8SfZObyChEDo5a4iIiIilKSVxERCRFKYmLiIikKCVxERGRFKUkLiIikqKUxEVERFKUkriIiEiKUhIXERFJUUriIiIiKUpJXEREJEUpiYuIiKSoUJO4mZ1mZivMbKWZXVfFMrlmttDMlprZG2HGIyIikk5CGwDFzDKAe4GTgQJgrpk94+4fxSzTAbgPOM3d15pZ17DiERERSTdhtsTHAivdfZW77wVmAWdVWOb7wD/dfS2Au28MMR4REZG0Yu4ezobNziXawr40mL4QGOfuU2OWuQdoBgwG2gK/c/eZlWxrMjAZICsra9SsWbNCiTkRCgsLyczMTHQYKUF1FT/V1YEKNxRWXtAW1VUc9JmKXxh1NX78+PnuPrri/DDHE7dK5lX8j6EpMAr4BtAKeNfM/u3uH5dbyX06MB1g9OjRnpubW//RJkgkEiGdjidMqqv4qa4OVDZ+eEW5qK7ioM9U/BqyrsJM4gVAr5jpnsBnlSyz2d13AbvMbA4wHPgYERERqVaY18TnAv3NrI+ZNQfOB56psMzTwPFm1tTMWgPjgGUhxiQiIpI2QmuJu3uxmU0FXgQygL+4+1IzmxKUT3P3ZWb2ArAI2A/8yd2XhBWTiIhIOgnzdDruPhuYXWHetArT/wv8b5hxiIiIpCP12CYiIpKilMRFRERSlJK4iIhIilISFxERSVFK4iIiIilKSVxERCRF1ZjEzewOMxvcEMGIiIhI/OJpiS8HppvZe2Y2xczahx2UiIiI1KzGJO7uf3L3Y4GLgGxgkZn93czGhx2ciIiIVC2ua+JmlgEcEbw2Ax8C15hZ+owJKiIikmJq7HbVzO4CJgCvAb9x9/eDotvNbEWYwYmIiEjV4uk7fQnw3+6+u5KysfUcj4iIiMQpntPpF1RM4Gb2KoC7bw8lKhGRehLJixDJi1RZXrihsNpykWRWZUvczFoCrYHOZnYIYEFRO6B7A8QmIiIi1ajudPrlwNVEE/aCmPk7gHtDjElEJLFm5kV/XpQX33yRBKkyibv774DfmdlP3f33DRiTiIiIxKG60+knuftrwHozO6diubv/M9TIREREpFrVnU4/kehjZRMqKXNASVxERCSBqjudfkPw84cNF46IiIjEK54BUK4ys3YW9SczW2BmpzREcCIiIlK1eJ4T/5G77wBOAboCPwRuCzUqEZE60PPe0tjEk8RLnw8/A/iru38YM09EREQSJJ4kPt/MXiKaxF80s7bA/nDDEhERkZrE03f6j4EcYJW77zazTkRPqYuIiEgC1ZjE3X2/mX0BDDKzeJK+iIiINIB4hiK9Hfge8BFQEsx2YE6IcYmIiEgN4mlZnw0MdPc9IcciIiIitRDPjW2rgGZhByIiIiK1E08S3w0sNLP7zez/Sl/xbNzMTjOzFWa20syuq6Q818y2m9nC4HV9bQ9ARKQ+6BlzSUXxnE5/JnjVipllEB2y9GSgAJhrZs+4+0cVFn3T3c+s7fZFRBrMzLxERyBSqXjuTn/QzFoBh7n7ilpseyyw0t1XAZjZLOAsojfIiYiIyEEyd69+AbMJwB1Ac3fvY2Y5wE3u/u0a1jsXOM3dLw2mLwTGufvUmGVygSeIttQ/A37m7ksr2dZkYDJAVlbWqFmzZsV7fEmvsLCQzMzMRIeRElRX8WusdVW4oZDMbpkHzKtOSYsSMvZkAHy97pYN0Z+dupWfLlU6vxFprJ+pugijrsaPHz/f3UdXnB/P6fQ8oq3qCIC7LzSzPnGsV1nXrBX/Y1gA9Hb3QjM7A3gK6H/ASu7TgekAo0eP9tzc3Dh2nxoikQjpdDxhUl3Fr7HWVSQvQu6k3APmVadwYCGZK6JfuGXrzsyL/vzOpPLTpUrnNyKN9TNVFw1ZV/Hc2Fbs7tsrzKu++R5VAPSKme5JtLX99Ubcd7h7YfB+NtDMzDrHsW0REZFGL54kvsTMvg9kmFl/M/s98E4c680F+ptZHzNrDpxPhRvkzOxQM7Pg/dggni21OgIREZFGKp4k/lNgMLAHeATYAVxd00ruXgxMBV4ElgH/cPelZjbFzKYEi51L9J+ED4H/A873mi7Si4iICBDf3em7gf8XvGolOEU+u8K8aTHv/wD8obbbFRERkRpa4mZ2sZktMLNdwWuemV3UUMGJiISt+d7NZK+dkegwROqkypZ4kKyvBq4hehe5ASOB/zUz3H1mg0QoIiIilaquJX4lMNHdX3f37e6+zd1fA74TlImIiEgCVZfE27l7fsWZwbx2YQUkIiIi8akuiX9VxzIRERFpANXdnX6kmS2qZL4Bh4cUj4iIiMSp2iTeYFGIiIhIrVWZxN19TUMGIiIiIrUTT49tIiIpqabBT0RSnZK4iIhIiqoxiZvZmWamZC8iIpJk4knO5wOfmNlvzUw3u4mIiCSJGpO4u/8AGAF8CvzVzN41s8lm1jb06ERE6kjXw6UxiOs0ubvvAJ4AZgHdgInAAjP7aYixiYiISDXiuSb+bTN7EngNaAaMdffTgeHAz0KOT0RERKpQ43jiwLnA3e4+J3amu+82sx+FE5aIiIjUJJ4kvqFiAjez2939Wnd/NaS4RETqRNfCpTGJ55r4yZXMO72+AxEREZHaqbIlbmZXEB03vG+FgVDaAm+HHZiIiIhUr7rT6X8H/gXcClwXM3+nu28NNSoRERGpUXVJ3N0938x+UrHAzDoqkYuIiCRWTS3xM4H5gBMdR7yUozHFRUREEqq6oUjPDH72abhwREREJF7V3dg2sroV3X1B/YcjIiIi8arudPqd1ZQ5cFI9xyIiklgz8xIdgUitVHc6fXxDBiIiIiK1U93p9JPc/TUzO6eycnf/Z3hhiYg0rOy1M+Dw7ESHIVIr1fXYdmLwc0IlrzPj2biZnWZmK8xspZldV81yY8ysxMzOjTNuERGRRq+60+k3BD9/WJcNm1kGcC/RblsLgLlm9oy7f1TJcrcDL9ZlPyIiIo1VPEORdjKz/zOzBWY238x+Z2ad4tj2WGClu69y971ExyI/q5Llfkp0rPKNtYpcRKQWstfOiJ4yF0kj8QyAMgvYBHyH6LCkm4BH41ivB7AuZrogmFfGzHoAE4Fp8QQrIlJftu/enugQRA5aPEORdnT3m2OmbzGzs+NYzyqZ5xWm7wGudfcSs8oWDzZkNhmYDJCVlUUkEolj96mhsLAwrY4nTKqr+DXWuiocWFhl2cd9cgHY27yQWf+cxUuRl7j/rvvJaN2Whw/pxOihQ8hv07L8SqV12GZg5fMbkcb6maqLhqyreJL462Z2PvCPYPpc4Pk41isAesVM9wQ+q7DMaGBWkMA7A2eYWbG7PxW7kLtPB6YDjB492nNzc+PYfWqIRCKk0/GESXUVv8ZaV9WNJZ699nEAXl67lodffZ2Th51MmxVtmL/nJf77rrv49dFH8aspp5Zf6TuToj9n5lU+vxFprJ+pumjIuqrydLqZ7TSzHcDlRPtR3xu8ZgH/Gce25wL9zayPmTUHzgeeiV3A3fu4e7a7ZwOPA1dWTOAiIvWlqLiY6999j0EdO/KzCT+jedPmjBw8mGO6Hcpt8+bzxfaqW/IiyajKJO7ubd29XfCzibs3DV5N3L1dTRt292JgKtG7zpcB/3D3pWY2xcym1N8hiIjE5+EVK/h8927+e+xomjdtDoCZcdPRR1G4bx/3vPjvBEcoUjvxnE7HzA4B+gNlF4zcfU5N67n7bGB2hXmV3sTm7pfEE4uISG3E3pG+YOMmxmZlcXS3buTHLNO3fXvOyM7mvtfm8f++fQKZLaMJXt2wSrKrMYmb2aXAVUSvaS8EjgLeRX2ni0iKuXd8Lrv27au07IeDjmRJ4Zes/GIrOb0PbdjAROoonkfMrgLGAGuC/tRHEH3MTEQkZRTv3w9Am2bNKi0f2bULq/73KiVwSSnxJPEidy8CMLMW7r4cGFjDOiIiSaOouJijHn2Mh5evKJtXsfMXM6NJE6O4ZD9Fe4sTEKVI7cWTxAvMrAPwFPCymT3NgY+KiYgkrTnrP2NLURGHtW1b7XIbtu0k66d3MOOthQ0TmMhBqjGJu/tEd9/m7nnA/wB/Bs4OOS4RkXrzwpo1dGjRgqO6VX+q/ND2mXTMbMXTC1ZUu5xIsoinJY6ZjTSz/wCGAQVBX+giIklvvztz1n/GiT160KxJ9V95ZsZZIwby2rLV7PhqT9ULzszTneuSFOIZAOV64EGgE9Fe1f5qZv8ddmAiIvVhxZdfsqWoiOO7d4tr+TNzBrC3uIQ3lueHG5hIPYinJT4JGOPuNwTDkx4FXBBuWCIi9aN98xZclTOc43p0j2v5o/v1pGWzprz20eqQIxM5ePF09pJPtJOXomC6BfBpWAGJiNSn7pltuHpETtzLt2jWlP/7wWkM6dk1vKBE6kmVSdzMfk901LE9wFIzezmYPhl4q2HCExGpu73Fe3mjYD1jsrrSuornwytzWe6oEKMSqT/VtcTnBT/nA0/GzI+EFo2ISD1avn45V738CvefNJ5Teh8W93rFJft58+M1dG3bhsFqkUsSqzKJu/uDpe+DUcgGBJMr3L3yfgtFRJLIknVLABidVbtE7O6cedcjXHriCH73g9PDCE2kXsTTd3ou0bvT8wEDepnZxfEMgCIikkhLC5bSp107OrZsWfPCMZo1zWDM4d15Z2VBSJGJ1I947k6/EzjF3U909xOAU4G7ww1LROTguDtL1y1lVNcudVr/mH69WLj2c3bv0YlHSV7xJPFm7l7WfZG7fwzEf4eIiEgCrN+6nu27tzOia92uaR/TvxfFJfuZt1q9TEvyiieJzzezP5tZbvB6gOjNbiIiSavbId144PIHOLUWN7TFOqpvTwDe/XRdfYYlUq/ieU58CvAT4D+IXhOfA9wXZlAiIgcro0kG/Q7tR6e9dXsitnPb1iy4aTKDe+judEle1SZxM2sCzHf3IcBdDROSiMjBe+StRxjQfQDZ8TRVqjCid3xdtYokSrWn0919P/ChmdXtfJSISALsLd7Ln1//MwtWLTio7azYsJn/euRFPt9WWE+RidSveK6JdyPaY9urZvZM6SvswERE6mr1xtWU7C+hf7f+B7WdzTt3c9cL/+b9VevrKTKR+hXPiaYbQ49CRKQefbzhYwAGdB8AO/PrvJ2c3ofSxIwFazbw7ZED6yk6kfpTXd/pLYne1NYPWAz82d2LGyowEZG6+mTDJ7Rp0YZuHbrBzrpvp02L5hzRrTPz8zfUX3Ai9ai60+kPAqOJJvDTiXb6IiKS9DZu38iAbgMws4Pe1sjsbszP17PikpyqO50+yN2HApjZn4H3GyYkEZGDc9sFt1G0r6jmBeMwKrsbLy5eybZdRXRoU7vuW0XCVl0SL+tr0N2L6+M/WhGRhtKyWf0k3KnfHMtVp4yrl1a9SH2r7nT6cDPbEbx2AsNK35vZjoYKUESkNt5a/hY3Pn4jhUX181hY04wmSuCStKpM4u6e4e7tgldbd28a875dQwYpIlKTSF4EgAWrF/DeJ+/RukXrWm8jP5Jf6fxrH32Zq/72r4OITiQc8TwnLiKSMj7Z8An9Du1HE6u/r7fVm7bx3MJP6m17IvUl1CRuZqeZ2QozW2lm11VSfpaZLTKzhWY2z8yOCzMeEUlv7s6qL1bRL6sf2WtnkL12Rr1sd1ivLFZt+pLCor31sj2R+hJaEjezDOBeoo+nDQImmdmgCou9Cgx39xzgR8CfwopHRNLfF9u/YPfe3fTJ6lOv2x3aKzoIypKCjfW6XZGDFWZLfCyw0t1XufteYBZwVuwC7l7o7h5MtgEcEZE6KiwqpH+3/vTN6hv3OnuLS8jftq3sFcnPP2CZYb2yAFi07ov6ClWkXoSZxHsAsQPxFgTzyjGziWa2HHieaGtcRKRO+h3aj+mTpzOoZ8WTfgend6cOHNOvFy2bHcSQaCIhsK8bwvW8YbPzgFPd/dJg+kJgrLv/tIrlTwCud/dvVlI2GZgMkJWVNWrWrFmhxJwIhYWFZGZmJjqMlKC6il9jrKvCDeUfKWu+d3Nc633VJpOM7du/ntE6g8zmLeLbaafGM1RpY/xM1VUYdTV+/Pj57j664vww/60sAHrFTPcEquy70N3nmFlfM+vs7psrlE0HpgOMHj3ac3NzQwg3MSKRCOl0PGFSXcWvsdRVXiTy9cSLm5nxwm1075TNb867juy1j8e1jSXHHk/m889+PSOnA7nZ2ZUuW9roKXtu/DuT6hB1amosn6n60JB1Febp9LlAfzPrY2bNgfOBckOYmlk/C/4azGwk0BzYEmJMIpKm9u8voWDTpxy279NK70qPve4d+4rXk/OW0fHK31KwVX1dSfIIrSUedNU6FXgRyAD+4u5LzWxKUD4N+A5wkZntA74Cvudhnd8XkbS2dedGSvYXc3i7cPqi6tKuDdt2F7Fo3Rf06tQ+lH2I1Faod2m4+2xgdoV502Le3w7cHmYMItI4bPyyAIA+7dqGsv2hPaOPmS0u2Mi3cgaEsg+R2lKPbSKSFr7YVoCZcVjbcJJ4+9Yt6d25ffnHzGbmRV8iCaIkLiJpoXO7QxnR/wRaZGSEto9hPbP0rLgkFT30KCJpYejhRzP08KNhx1Oh7eO8sYP4+HPdeyvJQ0lcRFLe/pIS9u37ihbNWoW6nwuPHR7q9kVqS0lcRFLeF59+yvS/X8n5J11Fbntq9ehYbe3as5c9+0romBnuPwwi8dA1cRFJeRtXrwagU7usUPdTXLKfTj/5Lb+d/Xao+xGJl5K4iKS8jatXk9GkKR3bdg11P00zmjAgq5NGM5OkoSQuIilvY34+ndt3o0mT8O5MLzWkZ1cWK4lLklASF5GUt3H1aroecsAgiaEY2rMra7dsZ/vuogbZn0h1lMRFJKW5O8eefz7DDj+mQfY3JOi5ben6TQ2yP5Hq6O50EUlp9uAaxjIC6rEhHsnPj75ZuA1yOpTNz83OZlzfnvz+B6fTW/2nSxJQEheRlPblzk3s319Cx3ZZXw8RGqKu7dow9eSxoe9HJB46nS4iKe3dj15k+nM3Nug+127Zzpsr1jToPkUqoyQuIilt45cFdD2kR4O0wkvd8vQcJv7fo2jkZEk0JXERSVnuzsZt6+nSoWHuTC81pGdXthR+xefbCxt0vyIVKYmLSMra9eWXfLWnkKxDejbofof2it6hrk5fJNGUxEUkZZV2t9q1oVviPaJJXJ2+SKIpiYtIyjq0Xz++N/6ndOuU3aD77dKuDVnt27B4nZK4JJYeMRORlNW6fXuOOGxkQvb92E/Oo1dHPSsuiaUkLiIpa8lrr9FpSwbdOvVu8H0fP7Dh9ylSkU6ni0hK2r9/P8/ecQcLP30rIfvfsG0n977yPhu27UzI/kVASVxEUtSaNWvY+9VXdO3QsHeml1q3ZQdTH/oX7326PiH7FwElcRFJUUuWLAGga4fuCdn/4J5dAFhc8EVC9i8CSuIikqK+TuKJaYm3adGcw7scwpICjWYmiaMkLiIpafHixbTPyqJF81YJi2For65qiUtCKYmLSEqaPn06F95xR0JjGNKjK598sZW9e/cmNA5pvJTERSQlZWZm0qlnYk6ll7rmtKPZeu8vaN68eXTGzLxEhiONkJ4TF5GUs3r1au6//36KcnLokMA4OmYm7lS+CITcEjez08xshZmtNLPrKim/wMwWBa93zGx4mPGISHp47733uP3229mza1eiQyHvyQgzZ85MdBjSSIWWxM0sA7gXOB0YBEwys0EVFlsNnOjuw4CbgelhxSMi6WPx4sVkZGTQqVevRIfCP+ct49FHH010GNJIhdkSHwusdPdV7r4XmAWcFbuAu7/j7l8Gk/8GEnuBS0RSwpIlSxgwYABNS69Fh2HhtrgWG9orq+xxN5GGFuY18R7AupjpAmBcNcv/GPhXZQVmNhmYDJCVlUUkEqmnEBOvsLAwrY4nTKqr+KV7Xc2dO5eBAwcysLAQctuWKyssmVCrbZW0b0/ht2LWaZ0R/dmjpPw0EGne4oD1W/cZxNp3H+W5554js81ASNN6T/fPVH1qyLoKM4lbJfO80gXNxhNN4sdVVu7u0wlOtY8ePdpzc3PrKcTEi0QipNPxhEl1Fb90rqs9e/awZ88eTjrpJFZkZsLjm8uV5+54tlbbK/zWBDKfj1knp0P0Z2lLvHQayM3OPnD9rCb8CejYsSPHrJwH35lUq/2ninT+TNW3hqyrMJN4ARB7waon8FnFhcxsGPAn4HR33xJiPCKSBlq0aMHmzZvZt28fv3nnnUSHw5AeXWnfvj0bN2pscWl4YSbxuUB/M+sDrAfOB74fu4CZHQb8E7jQ3T8OMRYRSSNm9vWz2QnWu3N7vvzyS8wMZi5MdDjSyIR2Y5u7FwNTgReBZcA/3H2pmU0xsynBYtcDnYD7zGyhmc0LKx4RSQ933XUXU6ZMqXnBBmJm0QQukgChdvbi7rOB2RXmTYt5fylwaZgxiEh6mT17Njt27Eh0GOX89a9/5aGHHuLVi4+v9GYgkbCo21URSSmLFy9myJAhiQ6jnMLCQl5//XU+316Y6FCkkVESF5GUsXHjRjZu3MjQoUMTHUo5Qz6LXglcUqCb26Rhqe90EUl6eZEIzMhn9bCtACwoKYnOawiVPGpW0ZAeXQFYXLCRk8OPSKSMWuIikjKK9+2jS3Y2h/btm+hQyunSrg1Z7duoJS4NTi1xEUkZ/ceNo/+46jp+TJxv5wykS7vWiQ5DGhklcRGRejD9R7Xr7lWkPuh0uoikhOKSfdx57rl8MHt2zQsnkHulvUuLhEItcRFJCRu3radwyxZatGlTaXnujqdCjyGSn3/gfoP+1Fds2MwJv5nB/e1yOPvss0OPRQTUEheRFPH5ljUAHNqvX4IjqVzPju3YuGMXixcvTnQo0ogoiYtISvh861qat27NId26JTqUSrVp0ZzDuxyiscWlQSmJi0hK+PzLdRzaty/WJEFfW6XPi1djaK+uLFq0KPxYRAJK4iKSEg7vNojB48cnOoxqjezdjRUrVrBz585EhyKNhG5sE5GUkJtzNkzMTnQY1Tp5yOFsyx5BUVERbdu2TXQ40ggoiYtI0isqLCSjeC/NEh1IDY7u14ujL8pLdBjSiOh0uogkvbdnzeL2R35Cyb594e9s4ba4rn9XZc+ePeRX8iiaSBjUEheRpLfh44/p3L4bGc2SvS0O5x+Tw7INm1j+2eZEhyKNgFriIpLU3J31y5fTvXOfRIcSlxG9D+Xjz7fo5jZpEEriIpLUPv30U4p27qRH58MTHUpcRmV3wx0++OCDRIcijYCSuIgktffffx+AHsnYEq/k2vmo7O4AzJv2a5iZ16DhSOOja+IiktTGjBnDyVdcQdfCHokOJS6HdsikxyFtmZ+/IdGhSCOgJC4iSa1///4c893vwoz8RIcSt99dcBo9DmmX6DCkEVASF5GktW/fPp5//nl2m9E60cHUwnfGDEp0CNJI6Jq4iCStJUuWMHHiRFbNn//1zBn5iWuVx/n8+J59xcz+8BNWbCj/mFkkL1L/MUmjpiQuIklr7ty5APQ44ogER1I7+0r2M+HuR/jbOxoMRcKlJC4iSev999+nU6dOdEjS4UerktmyOcMPy+LdlQWJDkXSnJK4iCStd999l3HjxmFmiQ6l1o7p14v3Vq2nuLg40aFIGlMSF5GktGXLFj766COOP/74RIdSJ8f070Vh0V6WLFkC6Hq4hENJXESSUseOHVmxYgUXX3xxokOpk2P69QKiZxNEwhJqEjez08xshZmtNLPrKik/wszeNbM9ZvazMGMRkdRiZgwYMIBuKXY9vFTvzu1Z8usrmDx5cqJDkTQWWhI3swzgXuB0YBAwycwqPjy5FfgP4I6w4hCR1HTTTTcxe/bsRIdRZ2bG4J5dycjISHQoksbCbImPBVa6+yp33wvMAs6KXcDdN7r7XKABBgkWkVSxa9cubr75Zt5+++1Eh3JQln+2mcm5o/jsd/+V6FAkTYXZY1sPYF3MdAEwri4bMrPJwGSArKwsIpHIQQeXLAoLC9PqeMKkuopfqtfVggULKC4upl27dkQiEQYWFkJuWyj9CZC/JfozmC4smVCnfZW0b0/ht2qxbuugZb27BHpApE35vuT2Fu4BoHlmCz7JaMEDbyygy/CjOPqoQoCU/b2k+meqITVkXYWZxCt7JsTrsiF3nw5MBxg9erTn5uYeRFjJJRKJkE7HEybVVfxSva4ikQhmxuWXX06HDh3Ii0Tg8c1wSafoz0rk7ni2Tvsq/NYEMp+vxbo5HaI/g97bcs/OKVec/0Y+ANm52ZzQxbmuTSs2fPAOmYecF11+Um6d4ky0VP9MNaSGrKswT6cXAL1ipnsCn4W4PxFJE6+88gqjRo2iQ4cOiQ7loDRpYow/MptXP1qNe53aMCLVCjOJzwX6m1kfM2sOnA88E+L+RCQNFBcXs2PHDk4++eREh1IvThrUh7VbtrNhm4YmlfoX2ul0dy82s6nAi0AG8Bd3X2pmU4LyaWZ2KDAPaAfsN7OrgUHuviOsuEQkuTVt2pRFixZRUlKS6FAOSn4kn+zcbE46sg+HdWrPxu0b6X5I97JOX3LzchMan6SHUIcidffZwOwK86bFvP+c6Gl2EZFyavNoVu6Op8IL5CAN7NaJ/Duv4o3VOYkORdKQemwTkaRy1FFH8Zvf/CbRYdQbM8PM2O/72e/7Ex2OpBklcRFJGmvXruW9996jdevWNS+cQt7/dD3n3nkuHxV8lOhQJM0oiYtI0njhhRcAym5qO2DQkBn5DRtQLeRH8qssG3BoJ7bv3s67H3/dj7oGRJH6oCQuIknj6aef5vDDD2fQoIo9NKe2Dm1aMqz3MP798b8THYqkGSVxEUkKO3fu5JVXXuHss89OyfHDa3L0gKNZtXEVn2/7PNGhSBpREheRpLBnzx6uvvpqzj///ESHEoqjBxwNUO6UekLNzIu+JKWF+oiZiEi8OnfuzO23337A/EheBPLzGzye+lJ6rbzXYbl8/7jvM6hnel0qkMRSS1xEEu6rr77ixRdfpLi4ONGhhOqyb1zGwO4DEx2GpBElcRFJuOeee47TTjuNOXPmxLV87o6nkrqDl+osX7+cD9d8GN/CM/N0yluqpdPpIkksr5LhDPNScCSpmo7j4Ycfplu3bpx44okNF1SC3PHsHTRv2pz7Lr0v0aFIGlASF5FqVZaA4eD/mSjd7lc7dvDs888zduJEbn7zTXKD3aVK3+Kxz4dX96x4qW8M+QbTX53O+q3rwwtKGg2dTheRhFr86qvsLy5mWJqMWlaTk4efTBNrwnPzn0t0KJIG1BIXkYT6+N136X7EEXTr3x+ASHAneiQSSYm70vO3bat0fnYVY6F3btuZYwYewwsLX2Dv3r00b948vOAk7SmJi0hCff/WWyncujXRYTSoCaMm8MHqD1iyZAkjR46seYWZedGfF+XFN7++zcyDNrqrPhnpdLqIJExJcTFNMjJo16XLgYXJ2k/6wm3R10EY3Xc0j13zGCNHjlQf6nJQlMRFJCG2rFvHPd/7HvkLFyY6lAbXxJrQqnkr3J0dX+1IdDiSwnQ6XSSNhXVneX148+GHKdq1iy69eyc6lAaRvXYGAPmHXVI279RTT2XvRx/x7cELyp8Snxnz/mCVbivsU+6SEGqJi0iD+/Kzz1j08suMnjCBNocckuhwEuakk07ijfXreXflukSHIilKLfEqJHMLRiTVvXz//TRt3pxj0nSwk3gN3zGcrq1acc3fX+KdGz0tR2+TcCmJi0i9qeqf31hffPopy+bMYfyPf0zbTp3CDypJlZ5e/9moEfzirXeYNWsWkyZNCn/HM/PiK9fp95Sg0+ki0qCy+vblorvu4pjvfjfRoSSFc/r2ZWTvbvz5z39OdCiSgtQST0Hpcqo/XY5D4rdj0ybadelCnxEjEh1K0sho0oSnrvoeXa+8LdGhSApSEk9i8ZyabIj9JUNSzYtEGFhYeECM9RFbugwykuyWv/UWj914I9+/9Vb6jh5dL9tM1ZHMKurVqT20aMH27dt58803ObOmFWbm1d/OS7el0+cpSUk8jTTGZNQYjzlZ1OafzM9WrOCfv/41h/brR+9hw8ILKsnEMyBK6XL5qyL8/l+/56m5T/HCz77PyUP6hhucpAUlcWk0GvrMRkOLPb7KzlokyoaPP+bha6+ldfv2TPr1r2mqvsKr9KOTfsQH+R9w1u9m8ezVk/jG4MMTHZIkOSVxqVF9tHaTJaEkq9rUTyrVZeHWrTx4zTW0zMzkwjvuILNjx0SHlNTatGjDoyeN4YdvFnLm3Y/wwA8n8INjY85czMyLf2MVl63NupIylMTrQbJfS650fj2NBV3f261u2w21vhy8kuJiMpo2JbNjR4674AKGfuMbtO/aNdFhpYQurVrx+nUXc969j3Hj02/wnTFH0qp5s0SHJUkq1CRuZqcBvwMygD+5+20Vyi0oPwPYDVzi7gvCjEkkHvXxT0pjvF6/r6iID196iTcffphJwTXw4xri2ec0s2vBJh4YdwIth3eiVfNmbNtVxJ/nLODSE0fSvnXLRIcnSSS0JG5mGcC9wMlAATDXzJ5x949iFjsd6B+8xgF/DH42mETfAV567TJdvtzTvRV8sIk5Hetnf0kJK99/n+Vvv82yOXMo2rmTHkcckeiwklZpJy81zW/WpEn0rnXg+Q8/5mezXibvqTf49oiBnDPqCE48IpvObVtHF56ZF/15MHeYl26jpnmSVMJsiY8FVrr7KgAzmwWcBcQm8bOAme7uwL/NrIOZdXP3DSHGdVDS5dplMseWairWZfTj/DUzw/fvP2A+gDVpgpmxv6Tk6/KY5TKaRU+j7i8pYX9JyQHrl94kVrx3L75/f9n+i4qK2Ne0Kc1aRltt+/bsKVf+y9mzMTOat2oFwN6vvuLaY44pt+2MjAwyMzMB+GLVKnZv386eXbvYsWkT27/4gnZduzLunHMAeOLmm8GMAUcdxeizzuKwoUPVhWg9uuCYYRzZvQv3vTqXpxYs5+/vLsYMtv3xOtq1asHTC5azdst2urd5gg4dOtChQwc6bdpGdpcOAOzesw+AZhlNaJrRRL+bNBJmEu8BxPbqX8CBrezKlukBJG0SD4uSavU+W7GC266+mv0V5p917bUMzs0lf+FCHr722gPW++5NN9F/3DhWvPMOj+XlAeWT7EV33knvYcNY/MorPHXbbQeUXzZtGt3692feM8/w/D33HLD9qTNn0qlnT96eNYtX7r//gPL/euIJMjt2JDJjBnMeeuiA8l/Onk3zVq14ado03nv88fKFZtzw2msAPHfXXXwwe3a54uatW/PL558H4KnbbmPp66+XK2/buTPXPPYYAI/dcAOfvPdeufJOvXoxdeZMAB6+7jpuXbSoXHmPI4/k0vvuA+DJX/+aL1atKivLaNaMI447jnHnnEOTjAwuvvtusg4/vOyfDql/I7O78acff5tpl5zJO5+sY9mGTbRr1QKAv72zmMfnfgR/e6Fs+R6HtKXgnmsA+M7v/8ELi1eWlWU0MQb36MqHt0wBYPytD/JOzCAsZjDmgVd587JvADDuxj/xYcEmMppeGpQb48eP59lnnwVg6NCh5Ofnl4v3zDPP5JFHHgGgT58+bN68uVz5pEmTmD59OgBdunShqKioXPmll17K3XffTXFxMYdUMkjO1Vdfzc0338yXX37JYYcddkD5//zP//CLX/yCdevWMWjQoAPKb7/9dq688kqWL1/OmDFjDii/9957ueiii5g7dy4nnXTSAeUPPvgg55xzDq+//jrf/va3y5X96le/IreBzq5aZa2Detmw2XnAqe5+aTB9ITDW3X8as8zzwK3u/lYw/SrwC3efX2Fbk4HJweRAYEUoQSdGZ2BzjUsJqK5qQ3UVP9VVfFRP8Qujrnq7e5eKM8NsiRcAvWKmewKf1WEZ3H06ML2+A0wGZjbP3eun+6o0p7qKn+oqfqqr+Kie4teQdRXmAChzgf5m1sfMmgPnA89UWOYZ4CKLOgrYnszXw0VERJJJaC1xdy82s6nAi0QfMfuLuy81sylB+TRgNtHHy1YSfcTsh2HFIyIikm5CfU7c3WcTTdSx86bFvHfgJ2HGkALS8jJBSFRX8VNdxU91FR/VU/warK5Cu7FNREREwhXmNXEREREJkZJ4ApjZeWa21Mz2m9noCmW/NLOVZrbCzE5NVIzJyszyzGy9mS0MXmckOqZkYmanBZ+dlWZ2XaLjSWZmlm9mi4PP0bxEx5NMzOwvZrbRzJbEzOtoZi+b2SfBzwMf3m6EqqirBvueUhJPjCXAOcCc2JlmNojoXfyDgdOA+4Lua6W8u909J3jNrnnxxiGmq+PTgUHApOAzJVUbH3yO9OhUeTOIfgfFug541d37A68G01J5XUEDfU8piSeAuy9z98o6rDkLmOXue9x9NdG79sc2bHSSwsq6Onb3vUBpV8citeLuc4CtFWafBTwYvH8QOLshY0pWVdRVg1ESTy5VdUMr5U01s0XBaSyd0vuaPj+148BLZjY/6BVSqpdV2o9H8FNjy1avQb6nlMRDYmavmNmSSl7VtYwqG5Wg0T0+UEPd/RHoC+QQ7WP/zkTGmmT0+amdY919JNHLDz8xsxMSHZCkjQb7ngr1OfHGzN2/WYfV4uqGNt3FW3dm9gDwXMjhpBJ9fmrB3T8Lfm40syeJXo6YU/1ajdoXpaNMmlk3YGOiA0pW7v5F6fuwv6fUEk8uzwDnm1kLM+tDdJz19xMcU1IJvjxKTSR6k6BExdPVsQBm1sbM2pa+B05Bn6WaPANcHLy/GHg6gbEktYb8nlJLPAHMbCLwe6AL8LyZLXT3U4Nuaf9BdMz1YuAn7n7gINKN22/NLIfoaeJ84PKERpNEqurqOMFhJass4MlgXO2mwN/d/YXqV2k8zOwRIBfobGYFwA3AbcA/zOzHwFrgvMRFmDyqqKvchvqeUo9tIiIiKUqn00VERFKUkriIiEiKUhIXERFJUUriIiIiKUpJXEREJEUpiYukADP7f8HId4uCUZHGhby/SMUR9qpZ9pLgMZvYeZ3NbJOZtahmnT/UR6wijZmeExdJcmZ2NHAmMNLd95hZZ6B5gsOK9U/gDjNr7e67g3nnAs+4+54ExiWS9tQSF0l+3YDNpQnR3TeXdhlqZteb2dygb/npFvReErSk7zazOWa2zMzGmNk/g7GgbwmWyTaz5Wb2YNDCf9zMWlfcuZmdYmbvmtkCM3vMzDJjy919B9HuSifEzD4feMTMJpjZe2b2QdAnflYl259hZufGTBfGvP95cHyLzOzGg6hDkbSkJC6S/F4CepnZx2Z2n5mdGFP2B3cf4+5DgFZEW+yl9rr7CcA0ol1k/gQYAlxiZp2CZQYC0919GLADuDJ2x0Gr/7+BbwaDhcwDrqkkxkeIJm7MrDswAHgdeAs4yt1HEB0a9RfxHrSZnUK06+GxRAeSGKVBSkTKUxIXSXLuXgiMAiYDm4BHzeySoHh80NJdDJwEDI5ZtbTf9MXAUnffELTmV/H1QCnr3P3t4P3fgOMq7P4oYBDwtpktJNpndu9KwnwOOM7M2gHfBR4PugzuCbwYxPfzCvHV5JTg9QGwADiCaFIXkYCuiYukgCAhRoBIkBAvNrNZwH3AaHdfZ2Z5QMuY1UqvR++PeV86Xfq3X7Hf5YrTBrzs7pNqiO8rM3uB6GAP5wP/GRT9HrjL3Z8xs1wgr5LViwkaFMHlgNLr/Qbc6u73V7dvkcZMLXGRJGdmA80stgWaA6zh64S9ObhOfW7FdeNwWHDjHMAkoqe/Y/0bONbM+gWxtDazAVVs6xGip9qzgvUA2gPrg/cXV7YS0QEiRgXvzwKaBe9fBH5Ueg3ezHqYWdd4DkqksVASF0l+mcCDZvaRmS0ieno7z923AQ8QPV3+FNGhSGtrGdFW/SKgI/DH2EJ33wRcQvQmtUVEk/MRVWzrJaA78Kh/PbJSHvCYmb0JbK5ivQeAE83sfWAcsCvY90vA34F3g7MPjwNt63CMImlLo5iJNFJmlg08F9wUJyIpSC1xERGRFKWWuIiISIpSS1xERCRFKYmLiIikKCVxERGRFKUkLiIikqKUxEVERFKUkriIiEiK+v+6C//OEuk6QwAAAABJRU5ErkJggg==", + "text/plain": [ + "
" ] - }, + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# parameters\n", + "num_samples = 1000\n", + "initial_states = [-12, 5, 10] # initial states for each chain\n", + "proposal_sigma = 0.2 # standard deviation for the proposal distribution\n", + "\n", + "# generate samples using Metropolis-Hastings algorithm for each chain\n", + "chains_samples = []\n", + "\n", + "for initial_state in initial_states:\n", + " samples = metropolis_hastings(num_samples, initial_state, proposal_sigma)\n", + " chains_samples.append(samples)\n", + "\n", + "# plot all chains on one plot\n", + "plt.figure(figsize=(6, 4))\n", + "colors = ['teal', 'purple', 'orangered'] \n", + "for idx, samples in enumerate(chains_samples):\n", + " plt.plot(samples, color=colors[idx], alpha=0.8, label=f'Chain {idx+1}')\n", + "\n", + "plt.xlabel('Iteration')\n", + "plt.ylabel('Sample value')\n", + "plt.title('Traceplot of Metropolis-Hastings chains')\n", + "plt.legend()\n", + "plt.grid(True)\n", + "plt.show()\n", + "\n", + "# plot posteriors for each chain\n", + "plt.figure(figsize=(6, 4))\n", + "for idx, samples in enumerate(chains_samples):\n", + " plt.hist(samples, bins=50, color=colors[idx], alpha=0.5, density=True, label=f'Chain {idx+1}')\n", + "\n", + "x = np.linspace(-5, 15, 1000)\n", + "plt.plot(x, target_distribution(x), color='black', linestyle='--', label='True Distribution')\n", + "plt.xlabel('Sample Value')\n", + "plt.ylabel('Probability Density')\n", + "plt.title('Posteriors of Metropolis-Hastings Chains')\n", + "plt.legend()\n", + "plt.grid(True)\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Convergence diagnostics\n", + "\n", + "Assessing MCMC convergence involves evaluating whether the chains generated by the algorithm have reached a stationary distribution and are sampling effectively from the target distribution. \n", + "\n", + "Reaching convergence on the sample is essential, otherwise, the samples do not come from the posterior distribution and subsequent analysis are meaningless.\n", + "\n", + "\n", + "\n", + "\n", + "A few common methods for assessing MCMC convergence are:\n", + "\n", + "- Visual Inspection: traceplots: Plotting traceplots of the chains can provide visual cues about convergence. Traceplots show the parameter values sampled at each iteration for each chain. Flat, stable traces suggest convergence, while erratic or trending traces indicate potential issues.\n", + "\n", + "- Visual Inspection: density plots: Density plots of samples from different chains overlaid with the target distribution can visually assess convergence. As chains converge, their density plots should match the target distribution.\n", + "\n", + "- Auto-correlation Plots: Auto-correlation plots show how each sample in the chain is correlated with previous samples. Rapid decay in auto-correlation suggests convergence, while slow decay may indicate lack of convergence.\n", + "\n", + "- Effective Sample Size (ESS): ESS estimates the number of *independent* samples obtained from the MCMC chains. It quantifies the amount of information each chain provides about the target distribution. Higher ESS values indicate more reliable estimates.\n", + "\n", + "- Gelman-Rubin Diagnostic (R-hat): This diagnostic compares the variance between chains to the variance within chains. An R-hat value close to 1 indicates convergence. Values significantly greater than 1 suggest that more iterations are needed.\n", + "\n", + "We have already performed visual diagnostics. Let's use the more quantitative measures to assess convergence.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Autocorrelation plots" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Hamiltonian Monte Carlo\n", - "\n", - "Hamiltonian Monte Carlo algorithm introduces gradient information in improving efficiency on the proposals and reduce random walk behavior of the sampling. The gradients help the algorithm to find high probability states. HMC can potentially improve sampling efficiently, but the gradients of the distribution need to be tractable. Additional parameters need to be tuned, which makes its implementation more difficult than other MCMC methods. However, methods have been developed for automatic adaptation of the parameters, such as no-U-turn sampler (NUTS)." + "data": { + "image/png": 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9+3IHKHR1daVz5844OTlZtF3lvUexCBhnikkbClwyxYAuFTIcquGRfJLf9u1jcNOmpVWNRqMpA15cuZKI2IJMoEUnuGZNPu+b//ybPXv20LZt23zPb9++nb179+Lr60unTp1Yu3YtnTt3Zty4cbz++usAjBo1isWLFzNo0KBc+b29vdm2bRvffvstH3/8MT/++GPJG2UG1p4e+yuwHmgiIlEi8oCIjBWRLHW8BDiCEWv4B4yYs6VGhqMn7raJLNq/n9SMUo1VrtFobkDat29P7dq1sbGxITg4mGPHjgFGTyQ0NJSWLVuyYsUK9u7dm2f+YcOGAdC2bdurecsCq/YolFJ3FnJeAY+VkThkuHrhmpzIpaREwo8d4+aAgLKqWqPRWJgPuncvcxtFYGDg1aGivHB0dLz63dbWlvT0dJKTk3n00UfZsmULderUYfz48fmuc8jKn5W3rCjvNooyRblXx0YyqZOZzvyICGuLo9FoKhg9evQgJSWFH3744eqxzZs3s2rVqnzzZCkFb29vEhISClQ01kIrimyIZw0AhntW4/f9+8nIzLSyRBqNpiIhIixYsIDly5cTEBBAYGAg48ePx9fXN988Hh4ePPTQQ7Rs2ZIhQ4bQrl27Esng7+/PM888w5QpU6hduzYRFnjpLe/G7DLFxrsmAL2dnPjk/AXWnjxJ13r1rCyVRqOpSPj6+jJnzpxcxxs1anTdFOWvv/766vd33nmHd955J1eeKVOmXP2e3SYREhKS7zqI0rBd6B5FNuxqGlq/BQpHW1t+u8E8T2o0Gk1eaEWRDQc/PwDsYqO5OSCA+ZGRZKo81/dpNBrNDYNWFNlwrGMoisyYswxv3pyo+Hg2RkVZWSqNRqOxLlpRZMOlRlUSU52RuGhuadIEB1tb5uQzn1mj0WhuFLSiyIaDmwNX0lyRhAu4OznRt2FD5kZE6OEnjUZzQ6MVRTZEhKTMKtglGcv+RwQGcuryZdafPFlITo1Go6m8aEWRgyTcsE+7CMCgxo1x1MNPGo2mCJw9e5Y77riDgIAAmjdvTv/+/Tlw4ADh4eEMHDiwSGW9/vrr/PPPP2anX7FiBW3btqVly5a0bduWFStWFFX8PNHrKHKQbFsVh4wjALg5OtK/USPmRkTwWd++2OjIWRqNpgCUUgwdOpTRo0cza9YswHAzfu7cuWKV99ZbbxUpvZeXF3/88Qe+vr7s2bOHPn36cOrUqWLVnR3do8hBin1VnOQKZBh+VG4PDORMQgJrT5ywsmQajaa8Y20340FBQVdXgQcGBpKcnExKSkqJ26V7FDlIcXSHTODSBahWk4GNG+NkZ8fsvXvpoldpazQVhpUvriQ2wrJuxmsG16Tv5xXDzfj8+fNp3br1dY4Ii4vuUeQgzcUTAHXR6CpWcXBgQKNGzIuI0L6fNBpNiSgrN+N79+7lxRdf5Pvvv7eI3LpHkYO0Kh6QAOlnT2MfEAQYw0/zIyP578QJwvz9rSqfRqMxj+4f3JhuxqOiohg6dCjTpk0jwEKhEnSPIgfpHtUASD11bUX2gEaNcLG317OfNBpNgVjbzXhcXBwDBgzg/fffp1OnTsUuJydaUeQgzas6AOmnrq2dcHVwYGDjxsyPjCRdDz9pNJp8sLab8UmTJnHo0CHefvttgoODCQ4O5vz588Uu7ypKqUq3tW3bVhWX379coJK7O6iLL9xz3fF5e/cqxo9X/x45UuyyyysrV660tghlzo3W5hulvREREVe/x8fHW1ES62Bum7NfpyyALSqfZ6ruUeTA3sOB+OSqSMz1c4/7NWqEq709s/fssZJkGo1GYx20osiBvYc98SlVsb105rrjLvb2DG7alLkRESSXYaxajUajsTZaUeTAztWO+BR37BNzr6QcHRTExeRk/ti/3wqSaTQajXXQiiIHYiMk23jhkBYL6WnXnetZvz61q1Zlys6dVpJOo9Foyh6rKgoR6Ssi+0XkkIi8lMd5dxH5Q0R2isheEbmvLORKcayOoCD2+uEnWxsb7mnViqWHDnH68uWyEEWj0WisjtUUhYjYAt8A/YDmwJ0i0jxHsseACKVUEBAGfCIiDqUtW1qVmsaX6NzR7e4NDiZTKWbs2lXaYmg0Gk25wJo9ivbAIaXUEaVUKjALGJwjjQLcRESAKkAsUOqW5EwP05znC7kVRSMvLzrVqcPkHTuuOu7SaDSaLKzpZnzLli1X108EBQWxYMGCooqfJ9Z04eEHZI8IFAWE5kjzNbAIOA24ASOUUqW/4s27Nlwhzx4FwP2tW/PAokWsO3mSTnXrlro4Go2mYqCs7Ga8efPmbNmyBTs7O86cOUNQUBCDBg3Czq5kj3prKoq8gjvkfEXvA+wAegABwHIR+U8pFZ+rMJExwBgAHx8fwsPDiyVUQkIC0UmJpGbYc27bOg57t8mVplZGBi62try9ZAkvNW1arHrKEwkJCcW+XhWVG63NN0p73d3duWyyH2ZkZFz9XlasWrUKGxsbRo4cebXuLH9L//33H5cuXWLIkCFEREQQHBzMjz/+iIgwYcIE/vrrL5KTkwkNDeWLL75ARBg7dix9+/ZlyJAhtGjRgjvvvJOlS5eSlpbGtGnTaNy48XX1Ozo6kpSUBMCFCxcAuHz5ci5FkZycXKTfgzUVRRRQJ9t+bYyeQ3buAyaYVg0eEpGjQFNgU87ClFKTgEkAISEhKiwsrFhChYeH4x3izaU57vjapFMnn3JGJSUxbedOZt10Ex5OTsWqq7wQHh5Oca9XReVGa/ON0t7IyMirjgBTv3gUh5MRlq0gIBge+Tzf00eOHKF9+/Z5OiN0cXFh165d17kZ37VrF507d+bZZ5/l3XffBQw346tWrWLQoEHY29vj7OyMm5sbIoKfnx87duzg22+/5bvvvsvlZvzy5ctERERw//33c/z4caZPn46np2cuWZycnGjdurXZzbamjWIz0EhE6psM1HdgDDNl5wTQE0BEfIAmwJHSFszF24VLye6os8fzTfNQmzYkpafzy+7dpS2ORqOpJJSFm/HQ0FD27t3L5s2bef/99/P1RFsUrNajUEqli8g44G/AFvhZKbVXRMaazk8E3gamiMhujKGqF5VSF0pbNpfqhqKQmPyj2rX19aV1zZr8sG0bj4SEIDpMqkZTrki5/wMcbkA341k0a9YMV1dX9uzZQ0hISDFacw2rrqNQSi1RSjVWSgUopd41HZtoUhIopU4rpW5WSrVUSrVQSs0oC7myehS2Vy5ASlK+6R5s04YdZ8+y9cyZfNNoNJobB2u7GT927NhVBXL8+HH279+PvwVi6OiV2XlgKAoPYyf6ZL7pRrZsibOdHT9s3Vo2gmk0mnKNtd2Mr1+/nqCgIIKDgxk6dCjffvst3t7exS7vKvm5la3IW0ncjK9cuVKlJKSoyZ73KtUbpbYsKzD96AULVJX33lOXU1KKXae1uVFcUGfnRmvzjdJe7WZcuxkvMxxcHUhQXsbO+fztFGAYtRNSU7X7cY1GU2nRiiIfMtxqohCILlhRdKxTh2be3vywbVsZSabRaDRli1YU+eDk7UYSnnAu/ymyYIxJPtSmDRtPnWJ3MVdfajQay6G0a50CKc710YoiH1y8Xbic7lno0BPAqKAgHGxt+VH3KjQaq+Lk5ERMTIxWFvmglCImJganIi4StubK7HKNi7cLccfc8TlfcI8CwNvFhaFNmzJ91y4+6N0bpxL6VdFoNMWjdu3aREVFER0dTXJycpEfiBUdc9rs5ORE7dq1i1SufqLlg0t1F2J3uUH0bsjMBJuCO18PtWnD7L17mR8RwchWrcpISo1Gkx17e3vq168PGG5LiuKmojJQWm3WQ0/54OLtQuwlVyPKXWzhC+q6169PA09PbdTWaDSVDq0o8sHF24WLSdWMndOHC01vI8KDrVuz6vhxDsTElLJ0Go1GU3ZoRZEPLt4uxCRmKYpDZuW5NzgYWxFt1NZoNJUKrSjywcXL5EHWxs5sRVHLzY1BTZowZccOUgpx2KXRaDQVBa0o8sHZyxmlbEl184NTB83O90hICNGJicyNsLAffI1Go7ESWlHkg4uXCwDJzn5m9ygAejVoQGMvL77ZvLm0RNNoNJoyRSuKfHD2cgYgwbaWoSjMXMBjI8Jj7dqxISqKLadzBuzTaDSaiodWFPlg72yPnZMd8coHkhIg7rzZeUcHBeFqb697FRqNplKgFUUBOHs5E5di8iJbBDuFu5MTo1q14tfdu4lJTCwl6TQajaZs0IqiAFy8XIhJMAUmL4KiAHisfXtSMjL4afv2UpBMo9Foyg6tKArA2cuZ6IuuYGNbZEXRokYNutWrx7ebN5ORmVlKEmo0Gk3poxVFAbh4uZAYkwa1GhRZUQCMa9+e45cuseRg0fNqNBpNeUErigJwquZEUmwS+DWCUweKnH9wkyb4ubnxtTZqazSaCoxWFAXg4uVCUmwSyrchnDJ/imwW9ra2PNy2LcsOH9b+nzQaTYVFK4oCcPZyJjM9k3TvBpCSCDFFXxfxUNu22NvY8K3uVWg0mgqKVRWFiPQVkf0ickhEXsonTZiI7BCRvSKyqizlu7o626WOcSCq6MNPNatUYXhgIJN37CAhNdWS4mk0Gk2ZYDVFISK2wDdAP6A5cKeINM+RxgP4FrhFKRUIDC9LGbNWZ19x8DMOFMOgDfBYu3bEp6Qwc9cuS4mm0Wg0ZYY1exTtgUNKqSNKqVRgFjA4R5q7gN+UUicAlFLmL4+2AM7VTG48Mj3B3rHYiqJD7dq0rlmTrzdv1rF8NRpNhcOaoVD9gJPZ9qOA0BxpGgP2IhIOuAFfKKWm5VWYiIwBxgD4+PgQHh5eLKESEhKu5k08Yayq3rpmO7Xca5K0az17illuz6pV+fjAAb5YuJBgD49ilVFaZG/zjcKN1uYbrb2g22xJClUUItIJGA/UM6UXQCmlGpSwbsnjWM7XbTugLdATcAbWi8gGpVQuY4FSahIwCSAkJESFhYUVS6jw8HCy8l6JvsJmNuPv44+rXWtco/ZT3HLbp6Xx06efsi4tjaeKWUZpkb3NNwo3WptvtPaCbrMlMWfo6SfgU6Az0A4IMX2WlCigTrb92kDOaUVRwFKl1BWl1AVgNRBkgbrNwtnTGHpKijGtpThzGDIyilWWi709D7RuzW+RkZyKj7ekmBqNRlOqmKMoLiml/lJKnVdKxWRtFqh7M9BIROqLiANwB7AoR5qFQBcRsRMRF4yhqUgL1G0WNnY2OHk4kRiTCLUbQ1oqnD9R7PIeadeOTKX4futWC0qp0Wg0pYs5imKliHwkIh1EpE3WVtKKlVLpwDjgb4yH/xyl1F4RGSsiY01pIoGlwC5gE/CjUmpPSesuCs7VnEmOTYbaTYwDUfuLXVYDT0/6N2rEpK1bSS1mz0Sj0WjKGnOM2VkG5pBsxxTQo6SVK6WWAEtyHJuYY/8j4KOS1lVcnL2cTT2KbIqiXd9ilzeufXv6zZzJ/IgI7mzZ0kJSajQaTelRqKJQSnUvC0HKKy5eLiReSASP6uDmCSf3lai8mwMCaFitGl9v3qwVhUajqRAUOvQkIu4i8qmIbDFtn4iIe1kIVx642qMQgTpNS6wobER4NCSEdSdPsv3MGQtJqdFoNKWHOTaKn4HLwO2mLR6YXJpClSecvZyNWU9gEUUBcG9wMC46VKpGo6kgmKMoApRSb5hWUB9RSr0JlHQNRYXBuZozKfEpZKRlGIoi9iwkxJWoTE9nZ0a2bMkvu3cTm5RkGUE1Go2mlDBHUSSJSOesHdMCvBvm6XbVMeDFZKhrckV1PKLE5T7Wrh1J6elM1qFSNRpNOcccRfEI8I2IHBOR48DXwNjSFav8kOUYMDEmEeoFGgePlXyGblDNmnSpW5dvt2whU/t/0mg05ZhCFYVSaodSKghoBbRUSrVWSu0sfdHKB1k9iqSYJPCpB06ucHyvRcp+rF07jly8yNJDhyxSnkaj0ZQG+U6PFZG7lVIzROSZHMcBUEp9WsqylQuu61HY2EC95hZTFEObNaNWlSp8vWkT/Rs1skiZGo1GY2kK6lG4mj7d8tiqlLJc5QbX6sZlSIw2PMni38IiQ08ADra2jGnblr8OHeJQbKxFytRoNBpLk6+iUEp9b/r6j1Lqzewb8G/ZiGd9XKobQ09Xoq8YB+oFwsVzcOmCRcof07YtdjY2fKenymo0mnKKOcbsr8w8Vimxd7bHoYoDV85nUxRgseEnXzc3bm3WjJ937OCKDpWq0WjKIfkqCpMTwGeB6iLyTLZtPGBbZhKWA1xruF4/9ARwzDKKAgyjdlxyMr/s3m2xMjUajcZSFNSjcMCwRdhxvX0iHrit9EUrP7hUd7nWo/D2A5eqFutRAHSuW5dWPj58o0OlajSacki+s56UUquAVSIyRSl1vAxlKne41nDl0olLxo6IRQ3aRpHCuHbtGLN4MWtPnqRz3boWK1uj0WhKijk2ikRTPIolIrIiayt1ycoR1w09gWGnOL4XLPj2f1fLlrg7OvL1pk0WK1Oj0WgsgTmKYiawD6gPvAkcw4hOd8OQNfR0dVjIPxDiY4zZTxbC1cGB+1u3Zn5kJGcuX7ZYuRqNRlNSzFEUXkqpn4A0pdQqpdT9wE2lLFe5wrWGK5npmSTHJRsHsgzaFrRTADzarh3pmZlM0qFSNRpNOcIcRZFm+jwjIgNEpDVQuxRlKnfkWnRnQeeA2WlYrRp9Gzbk+61bSdOhUjUaTTnBHEXxjilQ0bPAc8CPwNOlKlU5w7WGoSiuznyqVhOqeMAJyyoKgHHt2nEmIYEF+0oe90Kj0WgsgTmhUBebvl4CbsiwqLkUhYjRq7BwjwKgb8OGNPD05OtNm7g9MNDi5Ws0Gk1RKcgp4FdAvtN6lFJPlIpE5ZBcbjzAmPm0boHF67K1seGRkBCeX76cXefO0crHx+J1aDQaTVEoaOhpC7C1gO2GIctGcbVHAYYX2UsX4OJ5i9d3f+vWONnZ8Y2eKqvRaMoBBS24m5p9X0RclVJX8ktfHESkL/AFhkuQH5VSE/JJ1w7YAIxQSs2zpAzmYOtgi5OH0/WKon4r4/PoLvDsZdH6qjk7c1eLFszYvZsPevfGw8nJouVrNBpNUSjUmG3y+RQBRJr2g0Tk25JWLCK2wDdAP6A5cKeINM8n3QfA3yWtsyS4VHe5ftFdQJDxeXhHqdT3WPv2JKalMWVH6ZSv0Wg05mLOrKfPgT5ADIApul1XC9TdHjiklDqilEoFZgGD80j3ODAfsPwYTxFwreF6fY+iqhd41y41RdGmVi061qnDV5s2kZGZWSp1aDQajTkUOusJQCl1MiuynQlLTPL3A05m248CQrMnEBE/YCjQA2hXUGEiMgYYA+Dj40N4eHixhEpISMgzb5JNEknHkq4718KjDk6717GlmHUVxs1ubow/eZJ358+na/XqpVIH5N/mysyN1uYbrb2g22xJzFEUJ0WkI6BExAF4AtMwVAmRPI7lnGX1OfCiUiojh6LKnVGpScAkgJCQEBUWFlYsocLDw8kr7+Vml9m/f//15471hFnvE9bxJnCwvB2hS2Ym086cYWl8PK8PH27x8rPIr82VmRutzTdae0G32ZKYM/Q0FngMowcQBQSb9ktKFFAn235t4HSONCHALBE5huHa/FsRGWKBuouMaw1XEi8kojKz6bIGQZCZYdHYFNmxtbHh6ZtuYn1UFOtOniw8g0aj0ZQCBSoKkyH5c6XUSKWUj1KqhlLqbqVUjAXq3gw0EpH6pp7KHcCi7AmUUvWVUv5KKX9gHvCoUup3C9RdZFxruKIyFUmxSdcONmpjfB4oPR+J9wUH4+nkxCfr15daHRqNRlMQBSoKpVQGRoQ7B0tXrJRKB8ZhzGaKBOYopfaKyFgRGWvp+kpKnmspataHarVg93+lV6+DA4+EhLAgMpJDsbGlVo9Go9Hkhzk2imPAWhFZBFx9SiqlPi1p5UqpJcCSHMcm5pP23pLWVxKyu/Go3txkWBaBFp1h9yojNkUhdpTiMq59ez5ev57PN2zg6/79S6UOjUajyQ9zbBSngcWmtNlDot5QXFUU0TnWHN40CC6cgj1rSq3uWm5ujGzZkp+3bycmMbHwDBqNRmNBzLFRNFJKvZlzKyP5yg1X/T2dz6EoOg0D5yqwbEqp1v9shw4kpaczccuWUq1Ho9FocmI1G0VFw8XLBSQPReHsCl1ug79/hqc6wlu3Gj0MCxNYowZ9Gzbkq02bSE5Pt3j5Go1Gkx/mDD0dw7BR/E9EnsnaSlmucoeNnQ0uXjnceGRxy2NgYwsn98OmJfB4ezhzxOIyPNehA+euXOGX3bstXrZGo9Hkh7ZRFIGs2Nm5aBwCUw7Br6fg83WQfAVe7AWfPgjhsy1Wf4/69Qny8eGT9euvxe/WaDSaUsacwEVvAoiIm7GrEkpdqnKKaw1XrpzLx4FuTX/js2FreHsxfPM4LP3J2GxsoettJa5fRHiuY0dGLVjA0kOH6NeoUYnL1Gg0msIwx3tsCxHZDuwB9orIVhG5IUOvVfWryuXTlwtP2KIzfLcdlqRCk3bw0WhY+7tFZBgRGIifmxsfrVtnkfI0Go2mMMwZepoEPKOUqqeUqocRO/uH0hWrfOLm50b8qXjzh33s7OHNReDfAt4aBqvnllgGe1tbnunQgZXHjrH2xIkSl6fRaDSFYY6icFVKrczaUUqFA66lJlE5pmrtqmSkZJAUk1R44iyq1YSPw6FpKHz2EJw7XmI5Hm7bluouLry1enWJy9JoNJrCMEdRHDHNePI3ba8BR0tbsPKIm59hw48/FV+0jI7O8MJ0SE+Dh1vCmpLF2nZ1cOD5jh1ZdvgwG6KiSlSWRqPRFIY5iuJ+oDrwm2nzBu4rTaHKK1X9qgIQH1VERQHg1xA+Xwt1msE7w+FEyTy1P9KuHd4uLry5alWJytFoNJrCKFRRKKUuKqWeUEq1MW1PKaUuloVw5Q33uu4AXDpxqXgFBAQbM6LsHWDuRyWSpYqDA8926MDSQ4fYdMryC/w0Go0mC3NmPS0XEY9s+54iYtX41daiSs0q2DnZcfFwCfSkR3XoMRJWzYGkfKbamslj7dpRzdmZt3SvQqPRlCLmDD15K6XisnZMvYkapSZROUZsBI/6Hlw8UsIOVc9RxqK89QtLVIyboyPPdujAnwcPsuV0zphPGo1GYxnMURSZIlI3a0dE6pE7ZOkNQ7WAaiXrUYCxzqJ6HVhV8lXb49q3x8vZmWeXLdOrtTUaTalgjqJ4FVgjItNFZDqwGni5dMUqv3gGeBJ7OLZkD2UbGwgdCNv/hdSUEslT1dGR93v2ZPXx49oHlEajKRXMMWYvBdoAs01bW6XUDWmjAPBs4EnalbS8nQMWhXb9jOGnvSWPY/FAmza09/Pj2WXLuJhUhDUeGo1GYwbm9CgAOgJhpu2m0hKmIuAZ4AlA7OEShiUN7mHMftr8V4llshFh4oABXEhM5MmlS0tcnkaj0WTHnFlPE4AngQjT9qSIvF/agpVXqgVUAyi5ncLZFQI7w7blFpAKWteqxStdujB91y7+2L/fImVqNBoNmNej6A/0Vkr9rJT6GegLDChdscovHv4eIJR85hNAm95wZBfEni15WcBrXbvSyseHhxcvJlYPQWk0Ggth7tCTR7bv7qUgR4XBzsmOqn5VS96jAENRAGz7p+RlAQ62tkwdMoQLiYk8tmSJRcrUaDQacxTF+8B2EZkiIlOBraZjNyyeDTxLbqMAI3ZFVS+LDT8BBNesyRvdujFrzx5m7dljsXI1Gs2Nizmznn7FMGBn+XrqYDpWYkSkr4jsF5FDIvJSHudHisgu07ZORIIsUW9J8QzwtMzQk40NtO5pKAoLroF4sXNnQv38ePTPPzl92Yz4GRqNRlMA5hiz/1VKnVFKLVJKLVRKnRWRf0tasYjYAt8A/YDmwJ0i0jxHsqNAN6VUK+BtjNgYVsczwJOEMwmkJaaVvLA2vSH2DByPKHlZJuxsbJg2dCjJ6ek8sGiRXoin0WhKRL6KQkScRKQa4G3y71TNtPkDvhaouz1wSCl1RCmVCswCBmdPoJRal80B4QagtgXqLTGeDSw0RRay2SksN/wE0NjLi49692bpoUNM2rrVomVrNJobi4J6FA9j2COaAttM37cCCzF6AiXFDziZbT/KdCw/HgBKvujAAvi09AHg3M5zFiisHtRuAv9Mh8zMkpeXjUfataN3gwY8s2wZh2ItoNQ0Gs0NiRQ2LCEijyulvrJ4xSLDgT5KqQdN+6OA9kqpx/NI2x34FuislIrJp7wxwBgAHx+ftrNmzSqWXAkJCVSpUqXANCpDsWbAGmoNqkXDxxoWq57s1NiznOaL3uN060Ec6PsUiLmT0QonOiWF+zZvJqBKFT4LCsJGJFcac9pc2bjR2nyjtRd0m4tK9+7dtyqlQvI6Z2dG/ksick/Og0qpacWS5hpRQJ1s+7WBXC5QRaQV8CPQLz8lYZJnEiYbRkhIiAoLCyuWUOHh4ZiT90jrI9ietzUrbaF06wa2V/Bd8AW+AY1hzMclLzMbl2vU4IFFizjq7s4DbdrkOm9umysTN1qbb7T2gm6zJTHn1bVdtq0LMB64xQJ1bwYaiUh9EXEA7gAWZU9g8lr7GzBKKXXAAnVajFpta3Fm+xlUpgUMxSIw9jO45TGY9wk8cRNEbiw4T2oy/Pa5MWRVSK/wvuBgutarx/PLl3P+SsliYGg0mhuPQnsUOYeCRMQdmF7SipVS6SIyDvgbsAV+VkrtFZGxpvMTgdcBL+BbMYZM0vPrGpU1tdrUYvM3m4k9FItXY6+SFygCj3xuDDst+R5eHwj3vAWnD4GNLayZD541oU5TuHgWju2B8yeMvE6u0HlYAUUbvqCCJk7kqaVL+eXWW0sur0ajuWEozmB4ItDYEpUrpZYopRorpQKUUu+ajk00KQmUUg8qpTyVUsGmrVwoCTB6FACnt1owYJCtHTz2JUzaYyiMrx6F+Z8aYVNFIDEeNv1pTKetFwjv/gXu1WHFL4UW3ax6dV7t0oVf9+xhkfYFpdFoikChPQoR+YNrgYpsgWbAnNIUqiJQvXl1bB1tObPtDC3vbGnZwv0awfe74EQkNA4BOwfD02xedB0Oy6YYcS0cHAss9uUuXZgfGcnYxYvpWq8eHk5OlpVbo9FUSszpUXwMfGLa3gPuAdxKU6iKgK29LT6tfDiz9UzpVODpA0Fh4FwlfyUBENIHUhIhcn2hRTrY2jJ58GDOX7nCM3/fsCFFNBpNETHHhccq4BKGx9iZGCukI0tZrgpBrTa1OLPtDJkZll3/UCRahRk2DDMX7LX19eX5jh2ZvGOHdkeu0WjMoqCV2Y1F5HURiQS+xlgcJ0qp7kqpr8tMwnJM/Z71SbmUwpF/jlhPCNeq0OymIq3sHh8WRpCPDw/+8YeeBaXRaAqloB7FPqAnMEgp1dm06C6jbMSqGDS5pQnOXs5s+2GbdQVp0xsObIF481ZfO9rZMWPYMC4lJ/Og9gWl0WgKoSBFcStwFlgpIj+ISE8g97LeGxg7RzuCRgexf+F+Es4lWE+QNr2NtRQ7zPfV2KJGDSb06sUfBw7w51nLBE7SaDSVk3wVhVJqgVJqBIavp3DgacBHRL4TkZvLSL5yT9sxbclMz2TFqyus92betD24VIWtRXMs+ERoKD3r1+ebQ4eIiI4uJeGukXwpmaSLOvKeRlPRMMeYfUUpNVMpNRDDzcYOIFfsiBsV7ybe3PT0TWz/aTt7ZlkpUJCtHQT3KHJcCxsRpg8dirOtLbfOmcPllJRSE3H75O18UusTPqn1CZu/21xq9Wg0GstTpAV3SqlYpdT3SqkepSVQReTmj2/Gp5UPa95fYz0h2vSGc8fg9OEiZavl5sbrzZtzICaGB//4o1R6RZfPXOavcX/hG+JLnY51WP7cchJjEi1ej0ajKR0s56b0BkZshOD7gzm/+zwX9l+wjhBtix/XItjDg/d69GDO3r18tWmThQWDiHkRpCWmMfD7gfT7qh9piWls/LIQX1aVjMz0TNKT0wGIOx5HRqqeF6KpOGhFYSGa32YE59s7Z691BPBtaMS2KGYApBc6dWJwkyY8u2wZ606eLDxDEdi/cD/eTb2p3qw6NQJr0GRwEzZ9tYmUy6U31FWeyEjLYGLwRL5p/g3LX1zOF/5f8I7jO6x+d7W1RdNozEIrCgtR1a8qdbvUZe9sKykKEWP4accKyEgvNHnSxSQi5kVcna0lIkwZMoR67u7cPneuxdZXJMclc3zVcZoMbnL1WOeXO5N8MZntP2+3SB3lnSPLjxC9N5q4o3Gs+3AdngGeBNwcwMrXVrL+s8JX1Gs01kYrCgsSOCKQ6L3RnN9z3joCtL0ZrlyC/QUbi1OvpDKtxzTmDp/L98HfkxJtvNl7ODkx7/bbiUlK4q7588mwQMS9g38dJDM98zpFUTu0Nt5NvTn6z9ESl18ROPLPEWwdbXlo80N0G9+Nh7c9zJ1/3EmTwU1Y9swyDvxZrjzoazS50IrCgjS/rTliI+yZbaXZT8E9jJ5FIcNPO6fu5OyOs3R+pTMp8SkcmXhtZXlwzZp8278//x49ysv//lti4/b+hftxreFK7dDrw537hfpxatOpG2Kx37GVx6jbqS6+Ib6EvRGGY1VHbB1sufXXW6nRogZLHlty1X5RYchIh6Tyuar/8unLbP95OwmHrbi2qZKhFYUFqeJTBf/u/uydtdc6D8CqXtCobYGKQinF5m834xviS893exL6VCjnV5znzPZrzg3va92aR0JC+GjdOp5dtozMYrYlPTmdg38epMngJojN9Ws1/UL9uHL+CpeOXypW2RWFxJhEzu44i393/1zn7J3t6fNZHy4dv8SuGbvKXriikp4GaxbA5FdhdAAMdYcJd0NS8R/ISim2/7yd2UNn80P7H5jcdTIbv9pI4oXizYqLPRzLN82/YdEDi9j64FYmBk20nt2wEqEVhYUJHBFI7KFYzu06Zx0B2vSGyA2QeDnP0yf+O0H03mhCHjFCe3R6oRN2Ve349+XrV3V/3b8/T4aG8tmGDdy3cCFpGUWfpXN42WFSE1JpdmuzXOf82vsBcGrTqSKXW5E4Fn4MgPo96ud5vn7P+ng39WbPr1bqhZpLRga8dye8NQxmfwDetY2IjOG/wlu3GkqkiCScTWBmv5ksemAR5/ecx7maM0mxSSx9Yik/tP+BuGNxRSovMz2TBaMWAHDPinsIGBeAUop5I+bxz0v/FFk+zTW0orAwjfo3AgwDplVo09sYFti5Ms/TEfMisHO2o8UdLQBwcnei7si6HP77MEdXXrMZ2IjwWZ8+vN29O9N27uTWOXNITi/a8Mjmbzbj5OFE/e65H5I+rXywdbTl1ObKrSiOrjiKvas9vu188zwvIjS7tRnHVh3L9RatlOLsjrMcW3XMeh6KlYI/voPH2xlRFh/8ABYlwOdr4dEv4KkfYOsyWPRNkYpNS0xjRp8ZHF99nP7f9mfcgXHcvfRuHt3zKPf9dx/JF5P5MfRHDi45aHaZ6z5ZR9T6KAZ8N4D63etT+9bajNkyhqB7glj7wVoOLy/aGiPNNbSisDBV/ari3czbeh5lm3cEFzdYvyjP04f/Pox/mD/2LvZXj/kN8cO1hitbvt1yXVoR4bWuXfm2f38WHzjAoF9/JTHNvDfHuONxHF52mNCnQrF1sM113tbeFp+WPpzdXrn9TB1fdZy6netia5/7GmTRbFgzVIZi57SdV4/FHYtjStcpfN/6e6aGTeWbZt+w4YsNJF9Kvprm3K5zLLx/Icf/O156DVi/yIi0iMCT38PtL4BDtoBXfe+HoO4w632zbRYZaRksvH8h53afY8SCEbR7pB2mUMcA1O1clwfWP4BLdRd+GfALSx5fUuhQbtyxOFa/tZqmQ5peF0jM1sGWgZMGUrV2VesuiK3gFBrhTlN0GvRqwPaftpOeko6dYxlfYgdH6DAY1v4Gj397XdCjuGNxxByIIeTR6yPK2jjY0HRoU3bN2EVaUhr2zvbXnX+kXTtc7O25f9Ei+s2cyZ933UUVhwKCKQHHVxsPr2bDcg87ZVGzTU0i5kaglLruQVFZSIlPIToimsDbAwtMV7N1TQL6BLDyfytx9nLGu6k3vw76lZT4FPp+2ReHKg5sm7SNv5/6m5WvraT9E+1BwaavNpGakMqu6bvwauKF2CiaDQygbs/GuNVyw7updy7bUJFZ9A3UqAtfbTRcxeTFvW/D053hj2/h9ucLLE4pxcL7FrJ39l56vNuDhn0a5pnOu6k3Y7aOYfkLy9n05SZsHWwJGx+Go1vuKI6JMYnMv2s+Yiv0+bxPrvN2jnaEPhnK8ueXc3rraXzb5t270+SP7lGUAg16NSAtMY2o9VHWEaDLbXD5Iuz577rDh5cZXe+AmwNyZWk2rBlpV9LyHTIbHRzMzGHDWHviBENmzSp0GOrUplPYu9pTvXn1fNP4hviSfDGZmAMxhbWoQnJ662lQ1+wx+SEiDP55MJ4Bniy8dyE/3fQTdo52PLjhQUIfD6X1fa25f939jPpnFH6hfqx5bw1r3l9DtYbVeHTvowTeHohNRhJD3CbQaeMgTox5gO9afMXn9T7nwOISTL09fwK2/wM335e/kgAI7GRMzZ73sRGStwB2TtvJ7pm7CXszjM4vdy4wrZ2jHX0/60ubh9qw4dMN/Nzp51xemi8evciPoT9yevNpBn4/EI96HnmW1XZMWxyrOrLuo3UF1qnJG92jKAX8w/yxc7Jjz+w9+If5l70AbXqDozOs+x1a97x6+PDfh6lapyreTb1zZfEP88fR3ZF9C/bR5JYmuc4D3NGiBakZGYz+/XfumDePucOHY2+b95DK6c3Gm5uNbf7vIlnX5tjKY3g3yS1TRSfLUJ+ffSI7br5ujN05lsN/H+bcrnO0uLMF7nXcr54XERr0bECDng2Ij4onPSUdj3oe2NjZMGz6EPjsIdSyU2Q06kCYbTiNb23For99+XXQr7R5qA1OA4oRH33ZVMNG0Xt04WmHPQ2v9jPsGD3uyjNJclwy/770L74hvnT9X1ezepFiIwyaNIjGgxozb8Q8ZvadScfnO5JyOYVzu86x55c9IHDff/dR+6ba+ZbjWNWRtmPbsv7j9US/EU31Zvm/wGhyo3sUpYBjVUda3NmCXdN3WcdNhZMLhA6Elb9CqjGmnZmeyZF/jxDQJyDPP6itgy2NBzZm/x/7yUzP33B6T1AQX/frx8L9+7l34cI8F+VlpGZwdvtZfNsX/ICs1rAabn5uHFt5rGjtqyCc3nSaag2r4eLlYlZ6EaFh34Z0eqHTdUoiJ1VrV6VaQDVs7Ex/3x+eh79/Ru54Gbuv10Knofju/pYHpzSj4wsd2fbjNrY8uIWk2CK4eM/MhOVTjLU5tfKesXUdbW8Gv0awKO/gl0oplj61lCvRVxj4/cAiDzU2GdSE4XOHc+nEJX4b+Rt/jv2THT/voG7nujy44cFrSiI12fjdb1qSy5Nyx2c74ujuyB8P/YHKrPzrdyyJVhSlRJsH25B2JY2IeRHWEaDfQxAfA2t+AyBqYxQpl1LyHRMGaDq0KUkxSYUaRx9r3573evTgl9276TtzJmcTrh8OOL3lNBmpGbkW2eVERKjfvT7Hwo9VyoV3pzadKnTYqcQc3Aa/fQYDHoZ73zGOPTcZatTF7qOR9G6/h3tX3k3qhdSiuXffsQLOHDGGnczBxsaYLhuxHg5sve6UylT89fhf7Jy6k84vd6ZWm1rmy5GNxgMa83TU09y/7n4e3vEwL116iTv/uBOvxl5Ggv2bYZQ/vH8XvDaAxks/u05ZuNZwpe/nfTm59iSbvrG888vKjFUVhYj0FZH9InJIRHLFuBCDL03nd4lIG2vIWRxqd6iNVxMvdkzeYR0BWvc03vDmfgSZmRxedhixEer3zP/tsGHfhtg52bFvwb5Ci3+5SxcmDRzI2hMnaPndd8yLuKYQD/x5ALEtuK4s/Lv7c+X8FaIjSj9wUlmScDaB+Kh4aoUU76FoNpNfgSqexrTVrLd0V3d4dbaxAPP7Z6h3fBqe7T3Z9NUm81aAK2XMYqpWE7reZr4svUeDkyv8cW2qrFKKPx/7k83fbKbDcx3o/lb3Ijbweuyd7anToQ41g2peP5tOKfjmcRAbeH0+3PYcvtv/gCmvXacsWo1qRcO+Dfn35X/ztY0lXkgk/M1wJnedzE8dfmLZc8uImBdBxPwINn2ziTUT1rDitRUkxyXnmb8yYjVFISK2wDdAP6A5cKeINM+RrB/QyLSNAb4rUyFLgIjQ8q6WnPjvBFfOW8HVgY0NjPwfHN4Baxdw+O/D+LX3w9nTOd8sDq4OBNwcQMS8CLP+BA+1bcvWMWPw9/Bg+Ny53Dl/PtGXE9g7ey91O9ctsK4s6nauC8CpjZVrPUXWSvfivj2bxY6VsOVvuPMVQzlkp3EITNwJYXfAnA9pMLQaV85dYfU7ZnisXfOb0aMY8fL1U2EL4e83NrLteCAZy2aw/n+/sXjsYmYPnc3WiVvp+EJHen/Yu/Rmt23/F/ZthFHjofMweOhDTgcPgF/fg1kTriYTEQZ+PxB7Z3um9ZpG1MYooiOjSU9J5/ze80T+Fsl3rb5j1fhVZKZnkpaUxuZvNjN3+Fzm3jaXv8b9xb8v/8t/7/7HtJ7TSL2SWnLZr8QXa8FiWWJNY3Z74JBS6giAiMwCBgPZx2oGA9OUMS6xQUQ8RKSWUupM7uLKHw37NST8jXAOLz9Mq5Gtyl6A7nfBr++ROfl/nNl8O13+F1Zolg7PdmBar2nMu2Medy+9u9D0zapXZ/0DDzBhzRreWrWK03MP0ONwKr0/7G2WiNUaVsPe1Z6zOyrXeoqs9SE1g2uWTgUXz8PnY66tkM6P256D8Fk0cthGxr3d+O/d/0hLSqP1fa2p0aJG3nkWT4RaDQouNwent55mw6cb8KvVlZbe26i77HHCt45GOVahy6td6P5299KdAv3LO+Dtd83wLsKBfs/g6+4K098AN0+4+V5wcMK9rjt3/303P3f6mZ9u+slIbiNX7RauNVx5aMtDV6fRZqRmcHbHWWwdbHH2csbB1YGT604ya/Asfh/9O8PnDC/+NORNf8GbQ8C9Ojz0MXS/o8hFnF6xG756BO+ErTRIrwEd9xdJwZuDWGtsWERuA/oqpR407Y8CQpVS47KlWQxMUEqtMe3/C7yolNqSR3ljMHod+Pj4tJ01a1ax5EpISKBKlSrFypsTlalYf9t63Fu5Ezi+4Ln0pUX1yHACF7zJb7uHYf/Wvbg1csuVJmebT84+yZGJR2gzsQ1uTXKnz4+DsfEcuncHsVUVZ1+ryeONG+FgU3indfu47YitEPxFsNl1lRRL3ue8iBgfweWDlwmdGWrxsiU9ldYznsL1/BF23vUJ8bUL+G0pRciPD5Bm48D20d+y//39nF9xHlsXW9r+0BZn3+t7fQ6XL9Dhq9s53nkUx7qaZ59QSrHruV0kHEogdGYoHrv+o82qd4ir1YLIXs+SVrtuSZpbKO4ndtF6xpMc7D2OU+1uvXo8ISEBD9tMWs55BfdTe4mv1ZS9t76J+8ldXKzXhvjLzlw5fIW0+DSSTibhUtcFRx9H3Jq6YedS+Dv0yTknOfLdEar3qE7AowE4euVe45GdjKQM4nbFkXg8EVtnW2wSr3DL0RdQLk5kuHlQ9cw+okKGcqj349eGEQsgJSaFU9MPMuj8m3i6XGTD5ZYk2juSPv4dXOyK3gfo3r37VqVUSF7nrNmjyOtK5NRa5qQxDio1CZgEEBISosLCwoolVHh4OMXNmxdJdyWx/aftdGjbIc/FQqXN5UatOTfje3q03ITHg/Py/AHmbHNycDKfzfiMK39dYdDDg8yqJzMjE8cvN3L6ssLmleb8eC6CkyjmDh9OIy+vAvNe6XaFXdN30a1rt5IvEDMTS9/nnERciKBeSL3SqeOf6XA6El6dTZtutxee/sKj8MPz9Ghamx7/9uDcrnNM7jKZs9+dZfjc4VSpmU1hzvsEUPjf/yr+tRubJc7euXuJ2xZH3y/7EjowFAb2gtDGVPvsQTrNuB/GfAzDnipWU83ilQngUYNGj39AI6drM8zCw8PpHBYGfQfB6rlUnTCSDl+PME7a2EBwTxj+/LXokEVEdVOsqrGKNe+v4fK2ywz6cRDNb71+9Dw+Kp71n60n9mAsx8KPkXr52lBVWMAKXBrE8cO/D0LDNvTw/4uALQuoFdobm0FjSTiXgGNVR+xd7Lmw7wIxB2JwqOLA6S2n2ffbPk5tOkW3gJVUb3CBWxqP4mCzUN5q2JDhvXoVqz0FYU1jdhRQJ9t+beB0MdKUa1rc2YL05HT2L9xvsTJPrD3BzH4ziTlY+EK1tR+tZ9PJUDyIgr1rzSrfycOJTi92Yv/C/YU67Tu57iQbv9zID+1+YNkzy/Bt58t7L9zG4jvv5GR8PG0nTWLO3oK9d9YMrknq5dQiO4Err2SkZRBzIAbv5qWwNkQpWDIJfAOg63Dz8vS4CyU2sNCYuurTyod+X/fj5PqTfBnwJYsfWXxtIdu/M6BJOyhESSilOLz8MFN7TGXe7fOoGVyTkLHZXkZ7joSpR4xpsxOfNjzOWiC+SS72bzbsNLc+Y0wLzwsR6HY7vLnQ+Hz8WxjxEkTth5dvhg/vyTWV1hxEhLDxYTyy+xG8m3ozd/hctv207er5mIMx/NzpZzZ+sZG4o3E0GdSEu5fdzfMXnueZ3XfQtdkW0m+6lRbj78fO1YkF/3Xi0IUA+PoJZga+zKe+n/KB5we85/Ie3zb/ltlDZjO913T+felfVKbi5tcC6dhwPbO9ArHp3J/1DzxAdcfSeRm1Zo9iM9BIROoDp4A7gJwrdRYB40z2i1DgUkWxT2RRp0Md3Ou6s2PyDlrdXXI7xdkdZ5k9dDaJ0YlM7zWdR3Y/gmPVvH8cSiki50dSt90wUOHGA6ZFwathswh9MpSNX25k6VNLGTptKFVqVuHcrnPU7lAblDGmm3Qxiandp5KRmoGtgy39vu5H24faIjbCgMaN2f7ww9wxbx4j5s3j3yNH+Pjmm3HL44ecNY5/dsdZPBt4FvvalBdiD8WSmZZZ4Kr0YrPxT9izBh790qzhCQC8fDkdPBC/hV9BQDD0vZ+gUUHUvqk2q8avYtsP2zj450FGTw6h2uEd8MgXBRYXtSGKBaMWEHsoliq1qtDh2Q50e6Nbbn9WXrXgjQXwzTjDqHzlEozLe51FsfnlHcP+MPCRwtO2729sWYz8H0x7A+Z8aPQubjZjYWEeeDX24p4V9zBn2Bz+ePAP/n76bzwbeBJ7MBZ7F3se2vRQ7kkNX70EGWnYjf2ADr4BdHi6g6F853QhZVJfhtT+gRO3v42KOoJL0nGo3xKnvreRfiEGD/ckMnyrsfvDh8kgk5O3v8pvQ0ZgU4o2IKspCqVUuoiMA/4GbIGflVJ7RWSs6fxEYAnQHzgEJAJmTuouP4iNEPpUKMueWcaK/62g0/Od8n2wF8aF/ReYNdiwvdzy0y0semARG7/cSNfXuuaZ/sg/R4iPiqfR+z0h+nZY+Qs8/h04uxZal6ObI70/7M3C+xbyVaOvrh538nAi+VIyPd7pwfnd58lIzeDWX2+lQa8GuHhf/0ZX192dVffey/9WruTDtWtZfuQIv40YQXDN6w28NVrUQGyEszvOFugbqqKQNdXX4ooiPQ0mPWe87Q8cW6Ssh24eh59NsmEAt3OAXnfj1ciLYTOH0eG5DvzS/xciH3uNDnVs2LK3Pu2G5O1/a8fUHfz5yJ+41XJj8JTBNL+1OQ5VCvD75eAIT00yZmXN+wTqBcIgMx7q5rBnjeG08J63wLVq0fM7OMH97xs97S/HGuuOwkYYRvEiYu9sz4jfR7D5283EHY0jZn8MtTvUpuNzHakWUO36xHvXGV4TRr9t9AxNiAgNR3SEtqvg5Ztpvt40mcDGFi7Mg81vXFdMF2B7/yd5buidRZa3qFjVhYdSagmGMsh+bGK27wowf+pFOaX9Y+3Z8+se/nvnP2L2xzB8jplDBiZSr6Sy9oO1rH5nNQ6uDowOH41vW1/2L9rPuo/X0e6xdnlORd389WZca7jSfHhz2H83/PUDrF+Yr4uFnATfG4xnA0/O7jxLdEQ0NnY2pCenE7MvhhWvrgCM+NdZLsvzwt7Wlgm9ejGwcWPunD+fTj//zMxhwxjStOm1NM72eDf1rjQzn6IjokGwvJuIP783hkveXAR29oWnz4aytYfX5sLzYfDhKPj9C3jwQwjuTq3WtXhg7X04PPYBp5Kb8df/tuHSqD4tRlx/X4+uOMqi+xfh286XOxbeQRUfMycDiMADH8DJffDtE+DjD+37FUn+XKQkwacPQM36xrBTcbGxMXo9L98Mk56FX9+FF6df3/MwEztHOzo83aHwhNPeAHdvw+1JXjRsDVMOG6vLazc29nevJjNyI8ujL/LNkVPUs8lk7MDbaB02pMhyFge9MrsMsHWw5f619xPyaAgRcyOKFM1MKcWCUQtY/fZqmgxqwrj9465O2+v+VndSLqWw6avcq0wvnbjE/j/202ZMG8ODbYvOUL0OrJhZJNnrda1H6OOhDPxuIP2/6s8tP9zCbXNuw9HdEe9m3vn2ZnLSuW5dNj34IC1q1GDo7NmMDw+/zv1HzdY1K42iOLfzHJ4NPK9z5X4dcdGGm4kr8eYXevmi8YAJ7gE3DSyeYK5V4atN8NBHxtvz27dCtOG40uPyLlwyovF75QVqtq7J8ueXX7dG4PKZy8y/a74xzPLPPeYriSxsbeHFGVC/JbxxC/w3v2j5lTICcv36Hnz2EHwwCqIOwNM/mNVDLhCP6vDNVvhoJVSvDa8NuGrPsTjb/zUcLd7xSsFyu1Y1pso2agMinPJvTbfE6vSNcULa9+f1N78nsIyUBGhFUWbY2tvS+4Pe+LbzZcGoBRxbdcysfBHzIti3YB9d/9eVOxbegZvvtemqPq18qNu5LpHzI3O5wIiYHwEKWt/X2jhgYwM9RhqGv4vni96AzMyrnkHdarnxxOEneGD9A/k/DPOglpsb4aNHc09QEG+uWkW/mTM5fdmIxFczuCbxJ+NJjCleCMzyxNntZ/NfaJcQB890NtxMvNLH/IVWv7wDCRfh4U/Nt03kha0dDH8O3v8b0lLho9HGvV36E7hUxabLbfT9oi/xJ+OZ0WcGy55fRuSCSCZ3mUxKfArD5w0veKipIKp4GA/jJu3gg7uNh6Y5RuSYMzCmJTzZwTCK//Wj4Xzwjpevc3pZImxsICgMvtgANw2C754yXJhYksxM+Pll44WtCMNvK44epc2kSWw/c4bpQ4fy+4gRVHctoXIsIlpRlCEOVRy4N/xeqtauyvLnlxfo3yg9OZ0ZfWcwb8Q8arauSbfXu+WZrsVdLTi361wul+YHFh2gRssa1xuHe4yEzAxYNbtogqemwMt9YGhV+GcGAC5eLji5F31Rj7O9PVMGD2bSwIGsMbn/mLFrF9UDjWGaiu7KIzkumYtHLlKzdT4L7X55F04dNBazRW4w/DQVxqlDsPAr6HM/BARZRlC/RvDI58YK7B+eh//mGb8PJxfqdalH2JthREdEs+GzDcwZNoeMlAxGLR9FjcB8FumZi6s7jF8IXr7wYi+4zRsebWvYXvIKfJQQB6/2hbNH4Ynv4NfTsCQVFl6G+98rmSx54egMT040ekBzPrRs2bMnGLO07nvXrAVxSik+WruW3tOn4+XszOaHHuLuVq2sErtFK4oyxt7Fnu5vd+f05tNs+2Fbvuk2fb2Jw38fplH/RoxcMvKap9ActLijBQjXhXnMSMsgakMUDXo1uD5x/RbQIOj64adD22n6xwRDAayaA0fyGBb79V2ju+zkCp89AGeO5k5TBESEh9q2ZcfYsTSsVo1RCxYwZrdh8zi7x0qxxi1E1vBZrdZ59ChSkmDJ9xB2pzH7p+MQmD7ecLNSED+9aBigR79tWWH7PmDIMP9Tw0dStrUO3V7vxouxLzJu/zgGThrI2J1jqdvJQgvnPKrDt9vgiYlG7BQRQ4ah7jCkqqE83hhs9HzfHAYnImH874YB36uWYZ9xLr3Fknj5Qq/RsHyqMURnCT55wOgNdbsdehbu8eBiUhJ3L1jAC//8w63NmrHpoYdoVt16rtF1PAor0GpUK3ZM2cHK11fSalSrXBHlMtMzWfvBWgL6BHDX4oINz86ezviG+HL0n6OEvREGGCEy05PT8QvNY/ZGr3sMo93i78GjBnz2IDUvx8Luv43zNjZw/4RrkcoiNxpvQt3vMhzP3d8YJj5l/HFL+GbT2MuLdfffz7SdO3nl33/p4ADvTf8blxonGda0Kf0aNSo0kl55IysGeJ49ik1LIPEy9DFN3nv0S3iqg9Fb+2K94TYjO5cuGGP5a34zlISXhf1GicCzP0OjtobdI4+1E9UCquWetWMJXN1h4MPX9neGGzOBAOLOG0NLI3yM/eenFntRXLEZPM6Y/LFsCtz2bMnK2rQE/v7ZMF4/MKHA/018Sgpfb9rEh2vXcjk1lXe6d+eVLl2sHgFSKworYGNrQ9j4MKZ2n8qOyTto92i7685HbYwi8UIibR40z1lu/R71Wf/petIS07B3sb+6SC5PN9+Dx8HGxcZ0QAD/Fmy64xPaezmAs5sRg+CnF42uceue8N4dxhvWuK+N+eqj3oQfXzA8dXr5Qdw54404KQGa3QRHdkK7/sY4uBkzc2xtbLivdWtuDwzkm6kTaZ6Uzo9HjjBrzx4cbW25OSCAoU2bckuTJni5mBfXwZocWHQAn1Y+eRt7V/4Knj5GjGmAGnXgg3/hqY7wSl/4eJWhDHatggVfwKY/DTuCf4uSzewpCDdPGPla6ZRdFILCjC2LXath2WSjxxE6oOzladDKmACy+DvjAW+GK5o8SUs1FhzWbmIoCfu8X3zOJSTwwdq1TNq6lStpaQxq3Jh3evSglY9PCRphObSisBL1utWjdofarJmwhuD7gq/rVRxcchCxldxDR/ngH+bP2g/WcnLdSRr0asCpjadwqe6Ce708gt/YO8CE5UZMbRtbaN+fxHUbIMvVROue8M5wYxojGG8/n6w2HihgPLAO7zBiKYPxB6peF84dg4NbDSd1k1+BfRuM6Zj5/DFy4urgQOM2dTny7xHOPvssa0+e5LfISBbs28cfBw5gK0Lfhg3p7u9PVUdHXB0c8PfwIMDTkxqurlZ/4wK4fPoyJ9aeIOzNsNwnr8QbD/5+Dxrj31nUaQJvLTLG68eFGFMhs4LudLnNWEjW7Kb8Vx1XVlp1NTZrMugxeP9OY61GpyHFK2PB58bsrHeW5PlfUEoxY9cunli6lMspKdzVsiVPhIYS4lu+4nprRWElRISe7/VkaveprP90PV1e6UJidCKnt55m7Qdr8e/mj5OHecbiup3r4ljVkfWfrKd+z/ocW3mMup3q5v/wtLXN3/2Dkwu89Ydh3IyPMVbyNu9wfd4XpsEtj0KdpuBWzVAmUQfgeAR0uMV4C/t6nDGz5eVfCo63nA3v5t7snLaTtMupdK1Xj6716vFZnz5sP3uW2Xv28MuePfx58GCufC729tT38KC6qyvujo40r16dEF9fejdokOdK8NIickEkKGh+W05v+RjrV1KTDftETgI7wadr4L0RcGCL4V7izldKdxxeUzidh0G95vDFw8awYIMielY4utuY0nzToFzrRpRSLD9yhI/WreOfI0foVKcOP95yC029y2dIYK0orIh/mD9NhzZl9durObH6BIeXGQZpe1d7uo3Pe5ZTXjhUcaDb+G4se2YZ6z5ex6UTl+jyapfiC2ZjYxjd8sPW1ni4Zad242tj3Lc8ZsyUmvSsYRyv19zwr1OtYJfbWSuZL0ReuBraUkRoU6sWbWrVYkKvXsSnpJCQmkp8SgpH4+I4HBvLkYsXORoXR2xSEgdjY/nz4EHSMzNxsLWlf6NGjA4Kon+jRjjkE987F+lpxlvkiUhjJpA5oUCByPmReDXzxr1xHmP64bOgRl2jd5AXjdvClEPmyacpG+wd4H/z4aVexpTmz9eDfxG8QP/yrjEJ4alJ1x1efOAAr69cyfazZ6lZpQqf3HwzT4aGYlvc4a0yQCsKK9P7o97sW7CPw8sO03RoU1rc0YJG/RsVea56+3Ht2TZpG/+88A82djY06t+olCQ2k9ueMXoayyYbQymvDTCC6PQcadg88iBLUURHRF+LgZwNEcHdyQl3Jyf8IN9ZICnp6Ww8dYrf9+3jl927+X3fPnxcXXmgdWvGhoRQxz3/eNQoBR/fd21m2JwP4OstxhBRHuy/cIFfdu9m/R+76RB+kdVd4cl336WuuzsNq1WjoacnnT1cuWvrMqQkY90a61C3qaEgHmsLnz9k9PzMuYdnjsB/c414IKYXpMS0NJ5eupRJ27bR2MuLn265hZEtW+JYDJfgZU35l7CSUy2gGnf9acxsKsnD3dbelttm38aa99fQsH9DqtYuhu8bS3Pr08a2ao5hFD+0zRjS+nzd9eP0Jjz8PbBzsivxWgpHO7urQ1cf9u7N0kOH+H7rViasXcuEtWu5pUkTGmRk4H3+PM2rV7/emVr4bFgxkwvDnmNLoy70+nQER797kfUj3sTDyYnYpCQOxMRwMDaWyOho9kZHU+cU3Pcz4OtEv+fb09UFDl28yMGYGGbt3UvGsTWMzEjnvnhnWq1fz/2tW+PuZNnAMppSpEYdw1X6R6ONIdXHvix8OHX+p4YNcOiTAERGRzN87lz2RkfzQseOvN2jh/k93HKAVhTlAEu9/fu08uHWX28tPGFZ0+12IzTn2gXGwqrNf+XphsLG1obqgdUt6srDzsaGgY0bM7BxY47FxTFxyxam7NjB71eu8OnBg7g7OuJkZ0dccjIjkk7y1Y7pnHHw4dtXXdgQup2D1Vvx8NY/CCOA045Vr5ZZ38ODRl5e3Nu4BU7P7CHVJ5lH9zyay66klCLhyUVcqFaHHa61mLJsGW+EhzMiMJCOderQzs+PZt7e+Q47JKWlcSwujtSMDDycnPBwcsLN0bFUPYVq8qDXKMPmMO9jOHvEmKjhkk9Qr+RE+GeaYY/y8uW/48e5ZdYsHGxt+fvuu7k5ICDvfOUYrSg0ZUOtBjDkCeOP9uf3+for8mvvx+6Zu1GZKncQo6QrhlG401BjBe3mpcbQVlB36D+m0CEBfw8PJvTqxfs9e/LL0qVk+Pqy/uRJbJMTGLlxOqE7/+K4Zx0W7R1JtVgbBq60pdeST7CfEMbqc1Gcf2EC3t5V8ffwwN7Wlj2z9rBkxBJiYpMYPnd4npMP5MwR3Patw+2eN9l+91i2nznDJ+vXMzcigh+3bwfA1d6ewBo1rnvDjEtO5sSlS8SnpOQqM0v5vd61K61rlWJMbs01RGDMR4Yd7stH4PVBhjPBrNmA2dnwh7Fe5uZ7mb1nD6N//x1/Dw+W3n03/h4eZS66JdCKQlN22NlDnwdg9vtw/oRh3M2BX3s/tny3xQj80zTbDJBLF+DZroaBuUUXeG4yvH0bZKQZQ1vnT5jt0kFE8HN2JiwoiHtatYL37oSdS6DPfVyQe0ics4qur3dl4+cbWTxiPek1m9M47Xd+b9cYW08v/Nr74Rfqx/IXluPb1pdbZ91KQO983hKXTDKGIPo+AEDrWrWYMWwYmUpxMCaGTadOsfn0aSIvXCAzm0uXAE9PwurVo2aVKvh7eOBkZ8ellJSrCmTazp203bePu1u14p0ePahbkN1FYzn6P2R4KPjwHmMa+fvLcr+gLJuM8vbjw8u2vLRiPp3r1uX3ESMqxDqg/NCKQlO29H8IZr1nOHYb/Vau037tjdXkURuj8K7nBP/OhMsxsHqu4WK792gjrsa9DY23vEl7YO5HxtbnPsOHUVHYscLwfXXfu3DnK2xu8S11OtUhbHwYTQY14Y8xf3Ckyq20tBvP0F7bWR1zG/v/2E/EvAiq1KrCPSvuyT/EbWoK/D3ZmDKcI8aBjQhNvL1p4u3NqKCi+28aHxbGhDVr+HzDBubs3cuzHTrwYufOVC3D6cA3LD3ugpREw4vtn99f7+DvyC7Y8jeLOtzNSytWMiIwkClDhuBUAQzWBaGnYGjKFp96ENLX8FaakZ7rtFcTLxzcHIzV5Z+PMVaQT37ViI72ymx4forR5ffyNdYb1GtuBJ+xd4QZuRVPoayea7wh3voM0ZHRRO+NJnBEICKCb4gvD297mMGr34AhT9Ag4U/u/cSXZ6KeoePzHRm5ZGTBcdDXLoBL0TCgaEGGzMHDyYkJvXpx4PHHGR4YyHtr1lDv8895Y+VKYhIrvgfeck/fB4zFqT+9BBdM4YKVIv3nV0i0c+LeTD9e7NSJX269tcIrCdCKQmMNBo6FmNPGQzoHNrY2+LXzI3PbKsPlxe0vwOIkmHoYut5mJAodAL+eujbUVK2mseJ51WzDJbW5ZGQY/oVCB4CDE9t+3IaNnQ2Bw/OYK//ABEMpfXwvLk6p9P6w99UQrvny50TDNtPG8sHus6jr7s70oUPZ8tBDhPn789bq1dT7/HOeX7aMMyYX7ppSQMRwapieetWLwcnFP2G36U/eqN2V9wffxoRevSrNpAOtKDRlT+hAIyTmjLeMh3UOaod40cX+B1QNfxj5uuF3qrA/3ODHDX//s4rgejpyPVw8B52GkZqQyo6fd9BsWDOq1MxjRbSjs+GcLvbMNfclBXEi0vDZNODhMlk70dbXlwUjRrD7kUcY3LQpn27YQP0vvuC+hQvZfqZChZmvOPg1hLvfgDW/sWVcN6p98yg7q/gS9sznjA0JsbZ0FkUrCk3ZY2MDo94wQmPmERujufMaPJziuNB/gvnRy3wDjOGAP7833w36wq/A0QXa92fXjF0kxyUT+lRo/ukbh0C7fobDvuRChneWTTHm2ve+1zxZLESLGjWYOWwYB8aNY3RQEPMjImj3ww/8cOQIaXkoZU3xycjM5Ms6nZnrE0TIgdXEeNelzmcrGdC04sd9z4lWFBrr0PlWIyxmzl5FShI19k7maKw/Ry74F63Mu183ZhhN/V+hSX12/23MlhrxIri4sWfWHrybeVOnQ52CM454ybA7/P1z/mkyMoyV3SF9wbOEgX6KSUC1anw/aBAnnn6a0UFB/HLyJJ0nT+ZAjIXiK9zgHI6NpfvUqTz5z7/81Oc59k+MpO7UfVSrl9tVe2VAKwqNdbCxMR66UfuNIZosFk/E5tI5NsX359TGU0Ur09vPWAm7Yib8/EreaTIy4KN7afbHBMOt9YiXSDibwPHVxwm83Qw/Pi27GO6nJz0HGxYbw10R6w1jexZblhoGzl6jiiZ/KeDh5MRPgwczvnlzDsTE0Pybb7hnwQK2nj5dYIRFTd4opZi4ZQtBEyey69w5pg4Zwl8jR9KkQVOznV9WRCpvyzTln05DjdWtsycYcRqO7YGZb0FwD3DtejWuRpEY9aYR+GbW+4YdpOfI68/PfAuWTyWq7VBqj58J9g5EzN9heH0dnofX15yIwKtz4H8DjHUc9QIN1yT1msOXGyEtBb561DBidxxSdPlLiW7Vq/Nwv358tHYtE7duZfquXQRWr859wcGMDg7GuwLP8S8rdp49y2NLlrD25El6N2jAT7fcUrDfsEqEVXoUIlJNRJaLyEHTZ67ljSJSR0RWikikiOwVkSetIaumFHF0hkGPwrblMKaF4Q/KvTo88xO+7X2JPRRL0sWkopXp4GjMRmnRxfDNs/Brw9EfwJoFxlBX79Ecuvlxo34gYk4E1ZtXNz8etFctY6FV4xA4usuI/nc8Aqa/adR58Sy8OtvsWBxlRc0qVfikTx+inn6aiQMG4OboyHPLl+P36afcOX++NnrnQ0ZmJh+uXUu7H37gYGwsPw4axN93333DKAmwXo/iJeBfpdQEEXnJtP9ijjTpwLNKqW0i4gZsFZHlSqmIshZWU4rc+y607WOsrPZraITldHDCr10mAKe3nM5/1XN+2DvAO38a8Za/edyILta6J0x9Deo2gycnwroNAJxYc4Ljq4/T490eRavD3Rs+/c8waju7Gmsx5n1snHvkC0OJlFM8nZ15OCSEh0NC2HP+PD9s3crUnTuZtWcPtwcG8lZYGE3KaVyEsuZ4XBz3/P47q48fZ1izZnw/cOAN2fuylqIYDISZvk8FwsmhKJRSZ4Azpu+XRSQS8AO0oqhM2NpCcPdch31DDFfkpzcXQ1GAMaT19mK4NwBmvg3JV4y3/pdmGtNtgeRLycy7Yx6eDTxpP6590esQuTYr67GvjN6Mm5cRbraC0KJGDb7o1483u3fn0/Xr+XT9euZFRDA6KIg3unWjXgX1TVRSjl68yDebN/Pt5s3Y2dgwefBgRgcFlYtIitZArGHQEpE4pZRHtv2LSqk8vGtdPe8PrAZaKKXi80kzBhgD4OPj03bWrFnFki0hIYEqVW6syGLltc2b7tmES10XWrzTokj50hPT2f/hflJjUrl5+FEC13wFQJKnL5senoaysSUhIYHoOdGcmH6C4K+DcQ+s3MMI5t7ji6mp/HLiBAtPn0YBQ3x9ub9+fZwrkEvsLMxpc6ZSnEhM5HhiIseuXOFQQgIHExI4l5KCDdCjRg0eqF+fmhXELXxJ/svdu3ffqpTKsytcaj0KEfkHyGvp6qtFLKcKMB94Kj8lAaCUmgRMAggJCVFhWTGgi0h4eDjFzVtRKa9tju0ay7GVx4ok28UjF5nRdwaxB2MBWO/akqajn8F2zVycX5tDN1OEuT++/4MTM07Q6u5WDH5scGmIX64oyj0eCkTFx/NmeDg/bt/O9sREfh48mK716pWqjJYmvzYrpVh1/DhTduzgr0OHOH/lCgACNPbyonujRrSpWZM7W7akdtVyENelCJTWf7nUFIVSKl+/BSJyTkRqKaXOiEgt4Hw+6ewxlMRMpdRvpSSqppzi286X3TN3E38qnqp+hf9h05LSmN57OslxyYxcOpLUhFTm3jaX6U4tueefj7CxM+ZuKKU49M0hXLxd6Pd1v0JKvTGpXbUqP9xyC6OCgrhv4UK6TZnC4+3b837Pnrg6lC8jvblkKsXiAwd4f80aNkRF4eHkRN+GDekTEECQjw9NvL1xsbe3tpjlEmvZKBYBo4EJps+FOROIMRj4ExCplPq0bMXTlAeyPMme3nz6qqKIOxZHlVpVsHPM/dPdMXkHF49cZNTyUTTo1QCAgd8PZPHDi/m+9fc0vqUxXV/ryt7Ze4nfHc/ASQNxcq8YQwrWomu9euwaO5ZX/v2XLzdt4s+DB/n5llvo5u9vbdHMJiMzk9l79/L+mjXsOX8efw8Pvu3fn3uDg3HWisEsrKUoJgBzROQB4AQwHEBEfIEflVL9gU7AKGC3iOww5XtFKbXECvJqrEDN4JrY2NkQOT+SfQv2EXMghqgNUbQc2ZJhM4ZdlzYjNYN1H62j9k21qd+z/tXjbce0JT05nT2/7mHNe2tIu5LG/oX7cWvmRuv7W5d1kyokrg4OfNGvH7c2b879CxcSNnUq49q14/1evahSjnsXSil+i4zkfytXEhEdTfPq1Zk+dCgjAgOxr4A2F2tiFUWhlIoBeuZx/DTQ3/R9DcawoeYGxd7Znjqd6rBrxi5s7GzwC/XD0d2R3b/spvtb3fFscG3+w6ZvNhF3LI4BEwfkmpkS+kQooU+EsujBRWz8YiMAgW8HYmOrHRMUha716rFz7FheXbGCLzdu5M+DB/m6f3/6NWxYrmYDKaX4+/Bhnty2jQMJCTTx8mL2bbdxW/Pmlcaba1mjV2ZryjW9P+rNytdW0uW1LtTrUo/4U/F8Uf8LVv5vJcNmGr2KxJhEVr+1moA+ATTs0zDfsnq+15Mjy4/gUd8Dr45eZdWESoWrgwOf9+3Lrc2acf+iRQz45ReaV6/O2LZt6VinDrWrVqWGq6tVFIdSimWHDzN+1So2REXh4+jI5MGDubtVK+zKwINvZUYrCk25xq+dH3f/fffV/ap+Ven4fEfWvLeGTi91onrz6ix/fjkp8Snc/PHNBZblWsOVxw89jtgIq/9bXdqiV2q61KvHnkceYfbevXy2YQNPLF169Zy3iwuta9akdc2a1K5alZPx8bja29PA05PGXl408fbGw0LTTZVSbIiK4pfdu5kXGcnZhATqurvz/cCB1L90id7BwRap50ZHKwpNhaPjsx3Z9NUm/hr3Fw5uDhz88yAdX+hIjRaFu+Cwtddj05bC0c6Oe4KCGNWqFYcvXmTP+fOcuHSJXefOsf3sWT7bsIG0zEwcbG1JzeHi3MnODk8nJ6o5O+Pp7Ew1Z2fqe3gQ5ONDUM2aBFavjqOdHWkZGZy7coWo+Hh2nztHRHQ0cSkpZGRmcvzSJSKio7mQmIiTnR0DGzdmUOPG3NGiBQ62toSHh1vnwlRCtKLQVDicqznT/e3u/P3U3wD0/aIv7R8vxspqjUUQERpWq0bDatWuO56WkUFccjJeLi6kZWRwNC6O/RcucCAmhujERGKTkriYnExsUhLH4uL458gREtPSALCzscHDyYmYxESyLwl2sbfHy9kZGxH8qlZlcJMmdKlbl6HNmul44aWIVhSaCknoE6G413XH0c3x6lRYTfnC3taW6q6GixNHOzuaenvTtAAfUhmZmRyKjWXnuXPsPHuWC4mJ1HJzo1aVKvi6uRFYowb+Hh7aIG0FtKLQVEhEhGZDK18ksRsZWxsbmnh708Tbm9sDzYgNoikz9FQAjUaj0RSIVhQajUajKRCtKDQajUZTIFpRaDQajaZAtKLQaDQaTYFoRaHRaDSaAtGKQqPRaDQFohWFRqPRaArEKjGzSxsRiQaOFzO7N3DBguJUBHSbKz83WntBt7mo1FNKVc/rRKVUFCVBRLbkF2C8sqLbXPm50doLus2WRA89aTQajaZAtKLQaDQaTYFoRZGbSdYWwAroNld+brT2gm6zxdA2Co1Go9EUiO5RaDQajaZAtKLQaDQaTYFoRWFCRPqKyH4ROSQiL1lbHkshInVEZKWIRIrIXhF50nS8mogsF5GDpk/PbHleNl2H/SLSx3rSFx8RsRWR7SKy2LRfqdsLICIeIjJPRPaZ7neHytxuEXna9JveIyK/iohTZWyviPwsIudFZE+2Y0Vup4i0FZHdpnNfihQhVKBS6obfAFvgMNAAcAB2As2tLZeF2lYLaGP67gYcAJoDHwIvmY6/BHxg+t7c1H5HoL7puthaux3FaPczwC/AYtN+pW6vqS1TgQdN3x0Aj8rabsAPOAo4m/bnAPdWxvYCXYE2wJ5sx4rcTmAT0AEQ4C+gn7ky6B6FQXvgkFLqiFIqFZgFDLayTBZBKXVGKbXN9P0yEInxJxuM8WDB9DnE9H0wMEsplaKUOgocwrg+FQYRqQ0MAH7MdrjSthdARKpiPFB+AlBKpSql4qjc7bYDnEXEDnABTlMJ26uUWg3E5jhcpHaKSC2gqlJqvTK0xrRseQpFKwoDP+Bktv0o07FKhYj4A62BjYCPUuoMGMoEqGFKVhmuxefAC0BmtmOVub1g9IajgcmmIbcfRcSVStpupdQp4GPgBHAGuKSUWkYlbW8eFLWdfqbvOY+bhVYUBnmN1VWqecMiUgWYDzyllIovKGkexyrMtRCRgcB5pdRWc7PkcazCtDcbdhjDE98ppVoDVzCGJPKjQrfbNCY/GGN4xRdwFZG7C8qSx7EK094ikF87S9R+rSgMooA62fZrY3RjKwUiYo+hJGYqpX4zHT5n6o5i+jxvOl7Rr0Un4BYROYYxhNhDRGZQedubRRQQpZTaaNqfh6E4Kmu7ewFHlVLRSqk04DegI5W3vTkpajujTN9zHjcLrSgMNgONRKS+iDgAdwCLrCyTRTDNbPgJiFRKfZrt1CJgtOn7aGBhtuN3iIijiNQHGmEYwSoESqmXlVK1lVL+GPdxhVLqbippe7NQSp0FTopIE9OhnkAElbfdJ4CbRMTF9BvviWF/q6ztzUmR2mkanrosIjeZrtc92fIUjrUt+uVlA/pjzAg6DLxqbXks2K7OGF3MXcAO09Yf8AL+BQ6aPqtly/Oq6TrspwgzI8rbBoRxbdbTjdDeYGCL6V7/DnhW5nYDbwL7gD3AdIyZPpWuvcCvGHaYNIyewQPFaScQYrpWh4GvMXnmMGfTLjw0Go1GUyB66Emj0Wg0BaIVhUaj0WgKRCsKjUaj0RSIVhQajUajKRCtKDQajUZTIFpRaDQWREQSrC2DRmNptKLQaDQaTYFoRaHRlDIiMkhENpqc9f0jIj6m49VNsQS2icj3InJcRLytLa9GkxOtKDSa0mcNcJMynPXNwvBsC/AGhouRNsACoK6V5NNoCsTO2gJoNDcAtYHZJudtDhgBd8BwrzIUQCm1VEQuWkk+jaZAdI9Coyl9vgK+Vkq1BB4GnEzHzQ9FqdFYEa0oNJrSxx04Zfo+OtvxNcDtACJyM4YTP42m3KGdAmo0FkREMrnez/+nGN46P8NQFhuAdkqpMBGpgeEZ1BNYBYwA6iulUspWao2mYLSi0GishIg4AhlKqXQR6YARnS7YymJpNLnQxmyNxnrUBeaIiA2QCjxkZXk0mjzRPQqNRqPRFIg2Zms0Go2mQLSi0Gg0Gk2BaEWh0Wg0mgLRikKj0Wg0BaIVhUaj0WgK5P9XZATSp9SL+AAAAABJRU5ErkJggg==", + "text/plain": [ + "
" ] - }, + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# compute autocorrelation function (ACF) for a given chain\n", + "def autocorr(chain):\n", + " n = len(chain)\n", + " mean = np.mean(chain)\n", + " c0 = np.sum((chain - mean) ** 2) / n\n", + " autocorr = np.correlate(chain - mean, chain - mean, mode='full') / (n * c0)\n", + " return autocorr[len(autocorr)//2:]\n", + "\n", + "# compute autocorrelation for each chain\n", + "autocorr_values = []\n", + "for chain in chains_samples:\n", + " autocorr_values.append(autocorr(chain))\n", + "\n", + "colors = ['teal', 'purple', 'orangered'] \n", + "\n", + "# plot autocorrelation for each chain\n", + "plt.figure(figsize=(6, 4))\n", + "for idx, acf in enumerate(autocorr_values):\n", + " plt.plot(acf, label=f'Chain {idx + 1}', color=colors[idx])\n", + "\n", + "plt.xlabel('Lag')\n", + "plt.ylabel('Autocorrelation')\n", + "plt.title('Autocorrelation Plot of Metropolis-Hastings Chains')\n", + "plt.legend()\n", + "plt.grid(True)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Since neigbouring samples will contain similar information adn are auto-correlated, one can decide to save only every second, or fifth, or tenth sample. This is called thinning.\n", + "\n", + "`````{admonition} Group Task\n", + ":class: tip\n", + "- Increase the number of iterations in the algorithm above and create an ACF plot. What do you conclude?\n", + "- Experiment with the values of parameter `proposal_sigma`. What do you observe?\n", + "`````" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Computing effective sample size (ESS)\n", + "\n", + "The effective sample size describes the efficiency of dependent sample in terms of independent draws from the same distribution, is descriptive of the effectiveness of the sampling and of the autocorrelation of the chain.\n", + "\n", + "The formula for estimating the Effective Sample Size (ESS) of a Markov chain is:\n", + "\n", + "$$\\text{ESS} = \\frac{N}{1 + 2 \\sum_{t=1}^{T} \\rho_t}$$\n", + "\n", + "Where:\n", + "\n", + "- $N$ is the total number of samples in the chain,\n", + "\n", + "- $T$ is the lag, which represents the maximum number of auto-correlation terms considered, \n", + "\n", + "- $\\rho_t$ s the auto-correlation at lag $t$, i.e., the correlation between two consecutive samples separated by $t$ iterations.\n", + "\n", + "In practice, $T$ is often chosen such that $\\rho_T$ is small, indicating that the auto-correlation has decayed sufficiently. The sum $\\sum_{t=1}^T \\rho_t$ is then approximately truncating at $T$. \n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## More MCMC algorithms\n", - "\n", - "To watch some MCMC algorithms in action, check out [this](https://chi-feng.github.io/mcmc-demo/app.html?algorithm=RandomWalkMH&target=banana) online resourse.\n", - "\n", - "`````{admonition} Group Task\n", - ":class: tip\n", - "Which algorithm, in your opinion, is the most efficient?\n", - "`````" - ] - }, + "name": "stdout", + "output_type": "stream", + "text": [ + "Chain 1 - ESS: 5.432800285507235\n", + "Chain 2 - ESS: 12.250567042041817\n", + "Chain 3 - ESS: 9.336800817741272\n" + ] + } + ], + "source": [ + "# compute auto-correlation function (ACF) for each chain\n", + "def autocorr(x, t=1):\n", + " return np.corrcoef(np.array([x[:-t], x[t:]]))\n", + "\n", + "acf_values = []\n", + "for chain in chains_samples:\n", + " acf_values.append([autocorr(chain, t)[0, 1] for t in range(1, len(chain)//5)])\n", + "\n", + "# estimate Effective Sample Size (ESS) for each chain\n", + "ess_values = []\n", + "for acf in acf_values:\n", + " T = 100 # truncate at lag T\n", + " ess_values.append(num_samples / (1 + 2 * sum(acf[:T])))\n", + "\n", + "# print ESS values for each chain\n", + "for idx, ess in enumerate(ess_values):\n", + " print(f'Chain {idx + 1} - ESS: {ess}')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Computing the Gelman-Rubin Statistic ($\\hat{R}$)\n", + "\n", + "To compute the Gelman-Rubin statistic (often denoted as $\\hat{R}$), we need to run multiple chains and compare their variability within each chain to their variability between chains. Here's the algorithm to compute $\\hat{R}$:\n", + "\n", + "\n", + "1. Run $m$ Markov chains of length $n$, where $m$ is typically greater than 1.\n", + "2. For each scalar parameter $\\theta$, compute the within-chain variance $W$ and the between-chain variance $B$.\n", + "3. Calculate the pooled within-chain variance $\\hat{V}$ as the weighted average of the within-chain variances.\n", + "4. Calculate the potential scale reduction factor $\\hat{R}$ as the square root of the ratio of the pooled within-chain variance to the within-chain variance:\n", + " \n", + " $$\\hat{R} = \\sqrt{\\frac{\\hat{V}}{W}}$$\n", + " \n", + "5. If $\\hat{R}$ is close to 1, it indicates convergence of the chains.\n", + "\n", + "The Gelman-Rubin statistic $\\hat{R}$ is a measure of convergence for the Markov chains. It quantifies the degree to which multiple chains agree with each other, providing a diagnostic tool for assessing convergence in Markov Chain Monte Carlo (MCMC) simulations.\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Enough of hand-crafted MCMCs!" - ] - }, + "name": "stdout", + "output_type": "stream", + "text": [ + "R-hat for each parameter: [1.00069545]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "\n", + "# function to compute Gelman-Rubin statistic (R-hat)\n", + "def gelman_rubin(chains):\n", + " num_chains = len(chains)\n", + " num_samples = len(chains[0])\n", + " num_parameters = len(chains[0][0])\n", + "\n", + " # calculate means and variances for each chain and parameter\n", + " chain_means = np.mean(chains, axis=1)\n", + " chain_vars = np.var(chains, axis=1, ddof=1)\n", + "\n", + " # calculate within-chain variance (W) and between-chain variance (B)\n", + " W = np.mean(chain_vars, axis=0)\n", + " B = num_samples / (num_chains - 1) * np.sum((chain_means - np.mean(chain_means, axis=0))**2, axis=0)\n", + "\n", + " # calculate pooled within-chain variance\n", + " V_hat = (num_samples - 1) / num_samples * W + 1 / num_samples * B\n", + "\n", + " # calculate potential scale reduction factor (R-hat)\n", + " R_hat = np.sqrt(V_hat / W)\n", + " return R_hat\n", + "\n", + "chains = np.random.normal(loc=0, scale=1, size=(3, 1000, 1)) # three chains with 1000 samples each\n", + "R_hat = gelman_rubin(chains)\n", + "print(\"R-hat for each parameter:\", R_hat)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Gibbs sampling\n", + "\n", + "Another simple example of MCMC is the Gibbs sampling algorithm.\n", + "\n", + "In Gibbs sampling, you iteratively sample from the conditional distributions of each variable given the current values of all other variables. This assumes that you have a joint distribution of multiple variables and want to sample from the posterior distribution of one variable while keeping the others fixed.\n", + "\n", + "Here's a simplified outline of the Gibbs sampling algorithm:\n", + "\n", + "1. Start with initial values for all variables.\n", + "2. Choose one variable to update.\n", + "3. Sample a new value for the chosen variable from its conditional distribution given the current values of all other variables.\n", + "4. Repeat steps 2-3 for each variable in the model.\n", + "5. Repeat the process for a sufficient number of iterations.\n", + "\n", + "Each iteration of Gibbs sampling updates one variable at a time, conditional on the current values of the other variables. Over iterations, the samples generated by Gibbs sampling converge to samples from the joint posterior distribution of all variables.\n", + "\n", + "Gibbs sampling is used where it's difficult or computationally expensive to sample directly from the joint posterior distribution. It's relatively simple to implement." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Was it very painful to write a sampler by hand?\n", - "\n", - "If not, bare in mind that we only wrote the simplest one possible! Sampling algorithms can get very complicated." + "data": { + "image/png": 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", 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" ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [] - } - ], - "metadata": { - "colab": { - "provenance": [] - }, - "kernelspec": { - "display_name": "Python 3", - "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" + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" } + ], + "source": [ + "# define the mean and covariance matrix of the bivariate normal distribution\n", + "mu = np.array([0, 0])\n", + "covariance = np.array([[1, 0.8], [0.8, 1]])\n", + "\n", + "# function to sample from the conditional distribution of x given y\n", + "def sample_x_given_y(y, mu, covariance):\n", + " mu_x_given_y = mu[0] + covariance[0, 1] / covariance[1, 1] * (y - mu[1])\n", + " sigma_x_given_y = np.sqrt(1 - covariance[0, 1]**2 / covariance[1, 1]**2)\n", + " return np.random.normal(mu_x_given_y, sigma_x_given_y)\n", + "\n", + "# function to sample from the conditional distribution of y given x\n", + "def sample_y_given_x(x, mu, covariance):\n", + " mu_y_given_x = mu[1] + covariance[0, 1] / covariance[0, 0] * (x - mu[0])\n", + " sigma_y_given_x = np.sqrt(1 - covariance[0, 1]**2 / covariance[0, 0]**2)\n", + " return np.random.normal(mu_y_given_x, sigma_y_given_x)\n", + "\n", + "# initialize variables\n", + "num_samples = 1000\n", + "x_samples = np.zeros(num_samples)\n", + "y_samples = np.zeros(num_samples)\n", + "\n", + "# initial guess\n", + "x_samples[0] = np.random.normal(0, 1)\n", + "y_samples[0] = np.random.normal(0, 1)\n", + "\n", + "# Gibbs sampling\n", + "for i in range(1, num_samples):\n", + " x_samples[i] = sample_x_given_y(y_samples[i-1], mu, covariance)\n", + " y_samples[i] = sample_y_given_x(x_samples[i], mu, covariance)\n", + "\n", + "colors = np.linspace(0, 1, num_samples)\n", + "cmap = LinearSegmentedColormap.from_list(\"my_cmap\", [(0, 'blue'), (0.5, 'yellow'), (1, 'red')])\n", + "plt.figure(figsize=(6, 4))\n", + "sc = plt.scatter(x_samples, y_samples, c=colors, cmap=cmap, alpha=0.9)\n", + "plt.colorbar(sc, label='Sampling order')\n", + "plt.xlabel('X')\n", + "plt.ylabel('Y')\n", + "plt.title('Gibbs sampling')\n", + "plt.grid(True)\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Hamiltonian Monte Carlo\n", + "\n", + "Hamiltonian Monte Carlo algorithm introduces gradient information in improving efficiency on the proposals and reduce random walk behavior of the sampling. The gradients help the algorithm to find high probability states. HMC can potentially improve sampling efficiently, but the gradients of the distribution need to be tractable. Additional parameters need to be tuned, which makes its implementation more difficult than other MCMC methods. However, methods have been developed for automatic adaptation of the parameters, such as no-U-turn sampler (NUTS)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## More MCMC algorithms\n", + "\n", + "To watch some MCMC algorithms in action, check out [this](https://chi-feng.github.io/mcmc-demo/app.html?algorithm=RandomWalkMH&target=banana) online resourse.\n", + "\n", + "`````{admonition} Group Task\n", + ":class: tip\n", + "Which algorithm, in your opinion, is the most efficient?\n", + "`````" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Enough of hand-crafted MCMCs!" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Was it very painful to write a sampler by hand?\n", + "\n", + "If not, bare in mind that we only wrote the simplest one possible! Sampling algorithms can get very complicated." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] + } + ], + "metadata": { + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3", + "name": "python3" }, - "nbformat": 4, - "nbformat_minor": 0 + "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": 0 }