{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Probabilistic Programming 1: Bayesian inference in conjugate models\n", "\n", "#### Goal \n", " - Practice forming factor graphs out of probabilistic models.\n", " - Familiarize yourself with message passing on factor graphs.\n", " - Practice specifying models and inference procedures in a probabilistic programming language.\n", "\n", "#### Materials \n", " - Mandatory\n", " - This notebook\n", " - Lecture notes on factor graphs\n", " - Lecture notes on continuous data\n", " - Lecture notes on discrete data\n", " - Optional\n", " - Chapters 2 and 3 of [Model-Based Machine Learning](http://www.mbmlbook.com/LearningSkills.html).\n", " - [Differences between Julia and Matlab / Python](https://docs.julialang.org/en/v1/manual/noteworthy-differences/index.html)." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "using Pkg; Pkg.activate(\"../../.\"); Pkg.instantiate();\n", "using IJulia; try IJulia.clear_output(); catch _ end" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "using CSV\n", "using Random\n", "using DataFrames\n", "using LinearAlgebra\n", "using SpecialFunctions\n", "using Distributions\n", "using ReactiveMP\n", "using RxInfer\n", "using Plots\n", "default(label=\"\", linewidth=4, margin=10Plots.pt)\n", "\n", "import CairoMakie: tricontourf\n", "import ReactiveMP: @call_rule, prod\n", "import BayesBase: ClosedProd" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem: A Job Interview\n", "\n", "Suppose you have graduated and applied for a job at a tech company. The company wants a talented and skilled employee, but measuring a person's skill is tricky; even a highly-skilled person makes mistakes and - vice versa - people with few skills can get lucky. They decide to approach this objectively and construct a statistical model of responses. \n", "\n", "In this session, we will look at estimating parameters in various distributions under the guise of assessing skills based on different types of interview questions. We will practice message passing on factor graphs using a probabilistic programming language developed at the TU/e: [RxInfer.jl](https://biaslab.github.io/rxinfer-website/)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1: Right or wrong\n", "\n", "To start, the company wants to test the applicants' programming skills and created a set of bug detection questions. We will first look at a single question, which we treat as an outcome variable $X_1$. Your answer is either right or wrong, which can be modelled with a Bernoulli likelihood function. The company assumes you have a skill level, denoted $\\theta$, and the higher the skill, the more likely you are to get the question right. Since the company doesn't know anything about you, they chose an uninformative prior distribution: the Beta(1,1). We can write the generative model for answering this question as follows:\n", "\n", "$$\\begin{aligned} p(X_1, \\theta) =&\\ p(X_1 \\mid \\theta) \\cdot p(\\theta) \\\\ =&\\ \\text{Bernoulli}(X_1 \\mid \\theta) \\cdot \\text{Beta}(\\theta \\mid \\alpha = 1, \\beta=1) \\, . \\end{aligned}$$\n", "\n", "The factor graph for this model is:\n", "\n", "\n", "\n", "We are now going to construct this factor graph / probabilistic model in RxInfer." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "@model function beta_bernoulli1(X)\n", " \"Beta-Bernoulli model with single observation\"\n", " \n", " # Prior distribution\n", " θ ~ Beta(1.0, 1.0)\n", " \n", " # Likelihood of data point\n", " X ~ Bernoulli(θ)\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we may define random variables using a tilde symbol, which should be read as \"[random variable] is distributed according to [probability distribution function]\". For example, $\\theta \\sim \\text{Beta}(1,1)$ should be read as \"$\\theta$ is distributed according to a Beta($\\theta$ | $a$=1, $b$=1) probability distribution\"." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Having defined the model, we can now call an inference procedure which will automatically compute the posterior distribution for the random variable:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Inference results:\n", " Posteriors | available for (θ)\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "results = infer(\n", " model = beta_bernoulli1(),\n", " data = (X = 1,),\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Under the hood, RxInfer is performing message passing. Each variable definition actually creates a factor node and each node will send a message. The collision of messages will automatically update the marginal distributions. \n", "\n", "We may inspect some of the message and marginal computations with the following commands:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "WARNING: both ExponentialFamily and ReactiveMP export \"MvNormalMeanScalePrecision\"; uses of it in module RxInfer must be qualified\n" ] }, { "data": { "text/plain": [ "Beta{Float64}(α=1.0, β=1.0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "message1 = @call_rule Beta(:out, Marginalisation) (m_a = PointMass(1.0), m_b = PointMass(1.0))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Beta{Float64}(α=2.0, β=1.0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "message2 = @call_rule Bernoulli(:p, Marginalisation) (m_out = PointMass(1),)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alright. So, they are both Beta distributions. Do they actually make sense? Where do these parameters come from?\n", "\n", "Recall from the lecture notes that the formula for messages sent by factor nodes is:\n", "\n", "$$\\underbrace{\\overrightarrow{\\mu}_{Y}(y)}_{\\text{outgoing message}} = \\sum_{x_1,\\ldots,x_n} \\underbrace{\\overrightarrow{\\mu}_{X_1}(x_1)\\cdots \\overrightarrow{\\mu}_{X_n}(x_n)}_{\\text{incoming messages}} \\cdot \\underbrace{f(y,x_1,\\ldots,x_n)}_{\\text{node function}} \\, ,$$\n", "\n", "visually represented by\n", "\n", "

\n", "\n", "The prior node is not connected to any other unknown variables and so does not receive incoming messages. Its outgoing message is\n", "\n", "$$\\begin{aligned} \\mu_1(\\theta) =&\\ f(\\theta) \\\\ =&\\ \\text{Beta}(\\theta \\mid \\alpha=1, \\beta=1) \\, . \\end{aligned}$$\n", "\n", "We can also derive the message from the likelihood node by hand. For this, we need to know that the message coming from the observation $\\overleftarrow{\\mu}(x)$ is a delta function, which, if you gave the right answer ($X_1 = 1$), has the form $\\delta(X_1 - 1)$. The \"node function\" is the Bernoulli likelihood $\\text{Bernoulli}(X_1 \\mid \\theta)$. Another thing to note is that this is essentially a convolution with respect to a delta function and that its [sifting property](https://en.wikipedia.org/wiki/Dirac_delta_function#Translation) holds: \n", "\n", "$$\\int_{X} \\delta(X - x) \\ f(X, \\theta) \\mathrm{d}X = f(x, \\theta) \\, .$$ \n", "\n", "The fact that $X_1$ is a discrete variable instead of a continuous one, does not negate this. Using these facts, we can perform the message computation by hand:\n", "\n", "$$\\begin{aligned} \\mu_2(\\theta) =&\\ \\sum_{X_1} \\mu(X_1) \\ f(X_1, \\theta) \\\\ =&\\ \\sum_{X_1} \\delta(X_1 - 1) \\ \\text{Bernoulli}(X_1 \\mid \\theta) \\\\ =&\\ \\sum_{X_1} \\delta(X_1 - 1) \\ \\theta^{X_1} (1 - \\theta)^{1-X_1} \\\\ =&\\ \\theta^{1} (1 - \\theta)^{1-1} \\, . \\end{aligned}$$\n", "\n", "Remember that the pdf of a Beta distribution is proportional to $\\theta^{\\alpha-1} (1 - \\theta)^{\\beta-1}$. So, if you read the second-to-last line above as $\\theta^{2-1} (1 - \\theta)^{1-1}$, then the outgoing message $\\overleftarrow{\\mu}(\\theta)$ is proportional to a Beta distribution with $\\alpha=2$ and $\\beta=1$. So, our manual derivation matches RxInfer's message 2.\n", "\n", "Let's now look at these messages visually." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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label=\"Likelihood-based message\", legend=:topleft, size=(800,400))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The marginal distribution for $\\theta$, representing the posterior $p(\\theta \\mid X_1)$, is obtained by taking the product (followed by normalization) of the two messages: $\\mu_1(\\theta) \\cdot \\mu_2(\\theta)$. Multiplying two Beta distributions produces another Beta distribution with parameter:\n", "\n", "$$\\begin{aligned} \\alpha \\leftarrow&\\ \\alpha_1 + \\alpha_2 - 1 \\\\ \\beta \\leftarrow&\\ \\beta_1 + \\beta_2 - 1 \\, , \\end{aligned}$$\n", "\n", "In our case, the new parameters would be $\\alpha = 1 + 2 - 1 = 2$ and $\\beta = 1 + 1 - 1 = 1$. \n", "\n", "Let's check with RxInfer. The product of the two Beta's can be computed with:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Beta{Float64}(α=1.0, β=1.0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "prod(ClosedProd(), Beta(1.,1.), Beta(1.,1.))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "Extra information:\n", "\n", "The `ClosedProd()` input indicates that julia should not use the generic `prod` function (e.g., for products of `Float64`'s or `Int64`'s), but that it should use the product operations defined by the RxInfer ecosystem for parametric probability distributions. It is an example of Julia's \"multiple dispatch\" feature, which is making waves in the programming languages world ([youtube](https://www.youtube.com/watch?v=HAEgGFqbVkA), [blog](https://medium.com/swlh/how-julia-uses-multiple-dispatch-to-beat-python-8fab888bb4d8)). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That matches our manual derivations as well as the posterior reported by the `inference` procedure:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Beta{Float64}(α=2.0, β=1.0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "posterior = results.posteriors[:θ]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's visualize the messages as well as the marginal posterior." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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legend=:topleft,size=(800,400))\n", "plot!(θ_range, x -> pdf.(posterior, x), color=\"purple\", label=\"Marginal posterior\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The pdf of the marginal distribution lies on top of the pdf of Message 2. That's not always going to be the case; the Beta(1,1) distribution is special in that when you multiply Beta(1,1) with a general Beta(a,b) the result will always be Beta(a,b), kinda like multiplying by $1$. We call prior distributions that have this special effect \"non-informative priors\"." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Multiple questions\n", "\n", "Of course, in practice you would be evaluated on multiple questions, which are essentially more samples from the underlying distribution that is your skill level. We are going to add question outcomes to the model. For now, we will still work with right-or-wrong questions (i.e., binary outcomes), denoted $X = (X_1, \\dots, X_N)$. The generative model becomes\n", "\n", "$$\\begin{aligned} p(X, \\theta) &= p(\\theta) \\prod_{i=1}^{N} p(X_i \\mid \\theta) \\\\ &= \\text{Beta}(\\theta) \\prod_{i=1}^{N} \\text{Bernoulli}(X_i \\mid \\theta) \\, , \\end{aligned}$$ \n", "\n", "The factor graph for this model is:\n", "\n", "\n", "\n", "Specified in code, this is:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "@model function beta_bernoulli(X,N)\n", " \"Beta-Bernoulli model with multiple observations\"\n", " \n", " # Prior distribution\n", " θ ~ Beta(3.0, 2.0)\n", " \n", " # Loop over data\n", " for i in 1:N\n", " \n", " # Likelihood of i-th data points\n", " X[i] ~ Bernoulli(θ)\n", " \n", " end\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You may have noticed that the prior distribution changed; the company now assumes that you must have _some_ skill if you applied for the position. This is reflected in the prior Beta distribution with $\\alpha = 3.0$ and $\\beta = 2.0$.\n", "\n", "Now suppose we have two outcomes, $X_1 = 1$ and $X_2 = 0$:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "X = [1; 0];\n", "N = length(X)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Running the inference procedure is nearly exactly the same, except now we have to provide the sample size parameter $N$:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Inference results:\n", " Posteriors | available for (θ)\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "results = infer(\n", " model = beta_bernoulli(N=N),\n", " data = (X = X,),\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now have two likelihood-based messages:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Beta{Float64}(α=2.0, β=1.0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "message1 = @call_rule Bernoulli(:p, Marginalisation) (m_out = PointMass(X[1]),)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Beta{Float64}(α=1.0, β=2.0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "message2 = @call_rule Bernoulli(:p, Marginalisation) (m_out = PointMass(X[2]),)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Taking their product gives us a total likelihood message, i.e., \n", "\n", "$$\\begin{aligned} \\mu_3(\\theta) &= \\mu_1(\\theta) \\cdot \\mu_2(\\theta) \\\\ &= \\sum_{X_1} \\delta(X_1 - 1) \\ \\text{Bernoulli}(X_1 \\mid \\theta) \\cdot \\sum_{X_2} \\delta(X_2 - 0) \\ \\text{Bernoulli}(X_2 \\mid \\theta) \\\\ &= \\text{Beta}(\\alpha = 2, \\beta = 1) \\cdot \\text{Beta}(\\alpha = 1, \\beta = 2) \\\\ &= \\text{Beta}(\\alpha = 2, \\beta = 2) \\end{aligned}$$\n", "\n", "Let's verify that manual calculation using RxInfer:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Beta{Float64}(α=2.0, β=2.0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "message3 = prod(ClosedProd(), message1, message2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This product of messages is the result of passing the two likelihood-based messages through an equality node (see [Bert's lecture](https://nbviewer.org/github/bertdv/BMLIP/blob/master/lessons/notebooks/Factor-Graphs.ipynb#Equality-Nodes-for-Branching-Points)):\n", "\n", "$$\\begin{aligned} \\mu_3(\\theta) &= \\int_{\\theta'} \\int_{\\theta''} \\overrightarrow{\\mu}(\\theta'')\\ f_{=}(\\theta, \\theta', \\theta'') \\ \\overleftarrow{\\mu}(\\theta') \\mathrm{d}\\theta' \\, \\mathrm{d}\\theta'' \\\\\n", " &= \\mu'(\\theta) \\cdot \\mu''(\\theta) \\, . \\end{aligned}$$\n", "\n", "You don't have to worry about explicitly managing equality nodes; most packages automatically perform these operations (or functionally similar ones) under the hood." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "#### Exercise\n", "\n", "What would be your likelihood-based message if your data was $X = [0 \\ \\ 0 \\ \\ 0]$?" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have a likelihood-based message, we can combine that with the message from the prior distribution, $\\mu_4(\\theta) = \\text{Beta}(\\alpha = 3, \\beta = 2)$, to get the marginal posterior for $\\theta$:\n", "\n", "$$\\begin{aligned} p(\\theta \\mid X_1, X_2) &= \\mu_3(\\theta) \\cdot \\mu_4(\\theta) \\\\ &= \\text{Beta}(\\alpha = 2, \\beta = 2) \\cdot \\text{Beta}(\\alpha = 3, \\beta = 2) \\\\ &= \\text{Beta}(\\alpha = 4, \\beta = 3) \\, . \\end{aligned}$$\n", "\n", "Let's check with RxInfer:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Beta{Float64}(α=4.0, β=3.0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "message4 = Beta(3.0, 2.0)\n", "posterior = prod(ClosedProd(), message3, message4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That should also be equal to the inferred posterior:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Beta{Float64}(α=4.0, β=3.0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "results.posteriors[:θ]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Great. That checks out.\n", "\n", "Let's also visualize the messages and the resulting marginal:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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label=\"Total likelihood message\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Message 1 and message 2 are direct opposites: the first increases the estimate and the second decreases the estimate of your skill level. The total likelihood message ends up being centered on the average, i.e., $0.5$. If we plot the prior- and likelihood-based messages as well as the marginal, we can see that Bayes' rule is really a weighted average. " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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label=\"Likelihood\", size=(800,400))\n", "\n", "# Plot marginal posterior\n", "plot!(θ_range, x -> pdf(posterior, x), color=\"purple\", linewidth=4, linestyle=:dash, label=\"Posterior\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2. Score questions\n", "\n", "Suppose you are not tested on a right-or-wrong question, but on a score question. For instance, you have to complete a piece of code for which you get a score. If all of it was wrong you get a score of $0$, if some of it was correct you get a score of $1$ and if all of it was correct you get a score $2$. That means we have a likelihood with three outcomes: $X_1 = \\{ 0,1,2\\}$. Suppose we once again ask two questions, $X_1$ and $X_2$. The order in which we ask these questions does not matter, so that means we choose Categorical distributions for these likelihood functions: $X_1, X_2 \\sim \\text{Categorical}(\\theta)$. The parameter $\\theta$ is no longer a single parameter, indicating the probability of getting the question right, but a vector of three parameters: $\\theta = (\\theta_1, \\theta_2, \\theta_3)$. Each $\\theta_k$ indicates the probability of getting the $k$-th outcome. In other words, $\\theta_1$ indicates the probability of getting $0$ points, $\\theta_2$ of getting $1$ point and $\\theta_3$ of getting $2$ points. A highly-skilled applicant mights have a parameter vector of $(0.05, 0.1, 0.85)$, for example. The prior distribution conjugate to the Categorical distribution is the Dirichlet distribution. \n", "\n", "Let's look at the generative model:\n", "\n", "$$p(X_1, X_2, \\theta) = p(X_1 \\mid \\theta) p(X_2 \\mid \\theta) p(\\theta) \\, .$$ \n", "\n", "It's the same as before. The only difference is the parameterization of the distributions:\n", "\n", "$$\\begin{aligned} p(X_1 \\mid \\theta) =&\\ \\text{Categorical}(X_1 \\mid \\theta) \\\\ p(X_2 \\mid \\theta) =&\\ \\text{Categorical}(X_2 \\mid \\theta) \\\\ p(\\theta) =&\\ \\text{Dirichlet}(\\theta \\mid \\alpha) \\, , \\end{aligned}$$\n", "\n", "where $\\alpha$ are the concentration parameters of the Dirichlet. This model can be written directly in RxInfer:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "@model function dirichlet_categorical(X, N, α)\n", " \n", " # Prior distribution\n", " θ ~ Dirichlet(α)\n", " \n", " # Likelihood\n", " for i in 1:N\n", "\n", " X[i] ~ Categorical(θ)\n", " \n", " end\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose you got a score of $1$ on the first question, a score of $2$ on the second question and a score of $2$ on the third question. In a one-hot encoding, this is represented as:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "X = [[0, 1, 0],\n", " [0, 0, 1],\n", " [0, 0, 1]];\n", "\n", "N = length(X);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "#### Exercise\n", "\n", "Compute the likelihood-based message towards $\\theta$. I've given the three messages below:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "message1 = @call_rule Categorical(:p, Marginalisation) (q_out = PointMass(X[1]),);\n", "message2 = @call_rule Categorical(:p, Marginalisation) (q_out = PointMass(X[2]),);\n", "message3 = @call_rule Categorical(:p, Marginalisation) (q_out = PointMass(X[3]),);" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The company thinks that applicants are more likely to get the answer partially correct than entirely wrong or entirely right. This is reflected in their prior concentration parameters:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "# Prior concentration parameters\n", "α0 = [1.0, 2.0, 1.0];" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The inferrred posterior is a Dirichlet distribution with higher concentrations for scores $1$ and $2$: " ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Inference results:\n", " Posteriors | available for (θ)\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "results = infer(\n", " model = dirichlet_categorical(α=α0, N=N),\n", " data = (X = X,),\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Visualizing a Dirichlet distribution is a bit tricky. In the special case of $3$ parameters, we can plot the probabilities on a simplex. As a reminder, a [simplex](https://en.wikipedia.org/wiki/Simplex) in 3-dimensions is the triangle between the coordinates $[0,0,1]$, $[0,1,0]$ and $[1,0,0]$:\n", "\n", "

\n", "\n", "Every point on that triangle is 3D vector that sums to 1. Since the triangle is a 2-dimensional subspace, we can map the 3D simplex to a 2D triangular surface and plot the Dirichlet's probability density over it." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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x7c+vVRRoRacAALgMBxZCSZKeeuopT0/PsrKyn/3sZ7ZbedXV1WlpaWvXrpUk6de//nWPpUFvvvnmpKSkpKQknU5nG/H29t6yZYskSdnZ2XPnzj148KBWq21ubj558uQvf/nLxx9/XJKk66677j/+4z8c+gcBALgK2SqvuWtjW4v9Na5HPWOrcc1d6VaLVXQQAIBrUDn6YYPNmzc/+OCDtk8JCQlpaGiwjV911VVHjx7tse1jcnJydna2JElarTYiIqJr/G9/+9vq1au7bht2N3fu3MOHD3c/eQhs204o6rkLjUZjsViioqLYdgIABuWtfx58+a9uenuwy73P/ucvHrlVdAoAcCUWi0Wj0ajV6qioKNFZLnJCT3HsHUJJkh544IGPPvpoyZIlKpXK1gajo6OffvrpY8eO9WiDkiTNmzdv2bJly5Yt6/HW008/ffr06ZUrV3YVP39//zlz5mzfvv3bb78dZhsEAIwapTkVrz3V18azbmLn3/cUnysVnQIA4AIcfoewi8Fg0Gq1QUFB48aNG851Ghsb9Xr9xIkTbXV5RHCHEABGAbPJ8tvFfy3MKBYdRBGmpk7e+O2znt6eooMAgGvgDqHDBQQExMbGDrMNSpIUHBwcHR09gm0QADA67HpyD22wS/HZC6/9Y6/oFAAApXNeIQQAwHEKM4r3rjkkOoWyvL36UN63haJTAAAUjUIIAHB5He2m1XduMJvsrD3mzixmS9qqdGOrUXQQAIByUQgBAC7vpUdeK82pEJ1CicrzK1/+65uiUwAAlItCCABwbWc+zTqUflR0CuU6uOGD7z48IzoFAEChKIQAABfW2ty29p5NilomWmlkWX7+vi0tDQbRQQAASkQhBAC4sI2/f6W6VCc6hdLpKuq2PLxTdAoAgBJRCAEAruqbw98de/W46BSu4cMdn331zreiUwAAFIdCCABwSU21+hd+tVV0Cley7oFtjTVNolMAAJSFQggAcEkbHtpeX9UoOoUradI1r/ufbaJTAACUhUIIAHA9n7751ed7vhadwvWcOHjys91fiU4BAFAQCiEAwMXUVTak//Zl0Slc1foHt+vK60SnAAAoBYUQAOBKZFl+7t5N+voW0UFcVUuj4YVfbWGjDgCADYUQAOBKjmz7+NRRtlkfllNHz7z/0ieiUwAAFIFCCABwGdri6m1/2iU6hUL5jw3wUA/0P+tbH96pLa52aB4AgEugEAIAXINsldfes6mtpV10EIWaes3lM25dolKpBnJyW0v76jvTrRaro1MBABSOQggAcA37nj987vMc0SkUasb1l+dmV+ZkVabe9pMB/kj2ibx31h1xaCoAgPJRCAEALqAsV7PzibdFp1CokAmhmoYO2+vMzMpZP108wB985bHdJZllDssFAHABFEIAgNJZzJa0VenGtg7RQRQqYv50fVNb12FWri7lxvkD+UGT0ZS2Kt1ssjgsGgBA6SiEAACle/3/9uWfKhKdQqFm3rywIFfbfUSW5YLSpoRlKQP58aLTJW8+vd8x0QAALoBCCABQtMLvi9969oDoFAoVPmX8+Qr9peNms6W80Tx1fvxALvLmM+/knaRvA4CbohACAJTLZDSlrdrInEa7VB6q4OTY9laj3XeN7aZ6yScycWK/12FGLgC4MwohAEC5XvnbmxeyWPXEvpkrFxUX9LWXoL6pzRIeHhg2pt9LledpXn1898hFAwC4DAohAEChMr/I2c++CL2ITJxYUNLQ72l1NfrJS2cP5IL71x3J/IJdPQDA7VAIAQBK1G4wrr13s2yVRQdRIrWXp9/U6I5200BOzs2unHXbkn5Pk63y6lXprfq2fs8EAIwmFEIAgBJt/uOrlUVVolMoVMrKhaXndQM/Pyu7OuXGef2eVn1Bt/XhXcPIBQBwPRRCAIDiZBw7+8H2T0SnUKiY1Km5eYNog1LnRhTNCUuT+z3z/Zc+/vbI90ONBgBwPRRCAICytDQanrt3sywzWdQOL19veVy42TzoZVfNZkuFXo5OndLvmc/fv6W5zs5WFgCAUYlCCABQlhcf2KarqBOdQqFmrFhYWTbEv5z2VmNbwNjQSeP6Pq1e25D+m5eH9hEAAJdDIQQAKMiJAyePv/216BQKNWV+QnbOsJ6rbKhr8YudFBjaz0YUn711gn8KAOAmKIQAAKWo1zY8f/8W0SkUyjfQt91/jNViHeZ1tBUNkYtmevl6930a92kBwE1QCAEASsHTa31IuGFBjbZxRC5VXFidcNMilUrVxzk8yQkAboJCCABQhA9e/pT1LXuTsDQlO6tyBC+Ym6WZ9dMr+j4n49jZo698NoIfCgBQIAohAEC86gu6Lf/7qugUChVw2ZgGq+eI36zLzquZPCe273M2/f6VyvPVI/u5AABFoRACAASTrfKauze2NreJDqJQU6+aU6cb+Zm0FovVHBLi7dfXw4TtBuPz922WrUwcBYBRi0IIABDsnRePnD2eLTqFQiUtn52TpXHQxbUVDXE3Luz7YcKzx7MPrH/fQQEAAMJRCAEAIpXnaXY8tlt0CoUKGhdc3TLcZUX7lpdVOetnS/o+Z/ujb1zILndoDACAKBRCAIAwFrNl9Z3pxrYO0UEUauIVKU0NBkd/SmZ2VfKN8/o4wWQ0rb17k8VscXQSAIDzUQgBAMLsfuZA/qki0SkUKuWm+fk5Wid8kCzLhaXNsVdM7+Oc/FNFu5894IQwAAAnoxACAMQoOl3yxjP7RadQqNDo8NLqVqd9nNls0XWoI+Oj+jjn9X/so70DwOhDIQQACGAymtJWpZs7zKKDKJFKpQqfk2jQtzvzQ1ua26TIiKBxwb2dYDFb0lald7SbnJkKAOBoFEIAgAA7Hn+rJLNMdAqFSl25qDDPGZNFe6ipaho3b7qXb68bUZTlanY+8ZYzIwEAHI1CCABwtqyv8vY9f1h0CoWKjI8quNAg6tNLimqSVizq44S9zx3O+irPaXkAAI5GIQQAOFW7wbj2nk3sdW6X2svTb1qMUei0zOxMzYzrL+/tXdkqr75zQ6u+zZmRAACOQyEEADjV1od3agoFzId0CSk3Lywt1olOIZXXtodGh/f2blVJzUuPvO7MPAAAx6EQAgCcJ+Ojc0e2fSw6hUJNTJmSWyC+DUqSZGgxhs9JUKlUvZ1wZOtHJz847cxIAAAHoRACAJykpcGw9u6NssxkUTu8fL09IsPNJqVs/l6YVzXz1l4fJpRl+YX7t7Q0GJwZCQDgCBRCAICTbPjN9lpNvegUCjXjpoWaUmX95WTn6ZKuTu3t3VpNffpvX3ZmHgCAI1AIAQDO8OX+bz598yvRKRRq6vz47Nwq0Sl6kq1yWYM5asak3k745I0vv9z/jTMjAQBGHIUQAOBwTbrm9Q9uF51CoXwCfdsDgqwWq+ggdrS3Gs2hoWPH97pb/YsPbKuvanRmJADAyKIQAgAcbt0D2xprmkSnUKjEG+ZXVyq3U9VWN4fP7XW3+qZa/Qu/2urkSACAEUQhBAA41oc7PvvqnW9Fp1CouCUzsrOUvglHSVFN0k29LjDzzeHvjr163IlxAAAjiUIIAHAgXUXdlod3ik6hUP7BAU2Sj0ssu5qdpZn1syW9vbvx969UlypiwwwAwGBRCAEAjiLLctqqdDYn6E3sNXPrdM2iUwxUVm71tEWJdt9qbW5be88ml2i2AIAeKIQAAEc5uOGDM59miU6hUElXz8rO0ohOMQiyVW7x8vcP8rf77plPsw6lH3VyJADA8FEIAQAOUXm+esdju0WnUKig8KDqVte7n1Zb3Rx33bze3t3+6Bvl+ZXOzAMAGD4KIQBg5FnMlmf/68W2lnbRQRQq5iezmlxzJm1Wpibxypl23zK2Gp/9rxfNJouTIwEAhoNCCAAYeXvSDuV9Wyg6hUIl3zgvN9uF76TpjKqQCaF23yrMKN675pCT8wAAhoNCCAAYYcVnL+x6aq/oFAoVOjGsrKZNdIphaaw3BM+M8/H3sfvurif3FGYUOzkSAGDIKIQAgJFkMppW35lu7jCLDqJEKpUqbE6SQe/yM2nLSmoTblxg9y2zybL2nk0mo8nJkQAAQ0MhBACMpJ1/31N8rlR0CoWauXJhUb7St6EfoOzMytSfLrb7VvG50l1P7nFyHgDA0FAIAQAjJudfBXvXvis6hUKNmxp5vrRJdIqRlJ2nS7zK/gIzb6cdyvwy18l5AABDQCEEAIwMY6txzV3pVotVdBAlUnmogpKmtLV1iA4ykmSrXNFkmTA92u5ba+7ayDKzAKB8FEIAwMjY9sjrFQWjZD7kiEu9dXFJUY3oFCOvzWBURUT4jw249C1tcfX2R99wfiQAwKBQCAEAI+D0J5mHN30oOoVCTZgenV9UJzqFo1RpGmKvnWv3rcObPjx19IyT8wAABoVCCAAYLkNT69p7NsmyLDqIEnl6q31iojqMo3nZ1exMzfTlsy8dl2X5+fs2tzQYnB8JADBAFEIAwHCl//blmrJa0SkUKnnlFWUlo/8vR6u3jB0ffOl4raZ+0x92OD8PAGCAKIQAgGH5+tCpj1/7QnQKhZoyNy47p0p0CmdobmyNWpxi962Pdn3+xb5vnJwHADBAFEIAwNA16Zpf+NVW0SkUyifQ1zhmrPssu5qfo02+cZ7dtzY8tL1J1+zkPACAgaAQAgCGbv2DLzXWjKq99UZQ0g0LqisbRadwqvMV+pjZ0y4db6xpev7+Lc7PAwDoF4UQADBEH7/2BVMBexN7xfSsrErRKZytw2huDwwKGmfnYUKmFgOAMlEIAQBDUaup3/j7V0SnUCjfMX7NHj7uuexqXY1+3PwZnj5el77F4kMAoEAUQgDAoLGdQN9irkytq9GLTiFMSWF18s2LLx1nexIAUCAKIQBg0NhwvA9Trkg6X+Du98EyMzUzVyy4dPz0J5mHNx9zfh4AQG8ohACAwaksqnrpL6+LTqFQQeFBDSZP0SkUoaC0KSZ16qXjLz3yWmWRW2zFAQAugUIIABgE2SqvvWdTu8EoOohCRS+dpW9qE51CEUwdZmtYmLefd4/xdoNx9Z0b3Gc3DgBQOAohAGAQ3k47lPllrugUCpV8w9w891tZtA/aivrpNy28dDznXwV7177r/DwAgEtRCAEAA1WaU/HaU3tEp1CokKjQ8jpunPaUla2NXZR06fjOv+8pPlfq/DwAgB4ohACAATGbLKvv3NDRbhIdRIlUKlXEvOktzUwW7Um2yi3efv5B/j3GTUbT6jvTzR1mIakAAF0ohACAAXntqT2FGcWiUyjUzBXzC3K1olMolK6qOe76uZeOF5+98No/9jo/DwCgOwohAKB/hRnFe9IOiU6hUOFTI4oqWkSnULSsc5UpN867dPzt1Yfyvi10fh4AQBcKIQCgH8ZW47P/9aLZZBEdRIlUHqrg6dPaW3l6sB9FFfqY2dN6DFrMlmf/68W2lnYhkQAAEoUQANCvl//6Znk+i2faN/OWxcWF1aJTuIAOo9k4ZmxQeFCP8crz1Tse2y0kEgBAohACAPp25tOsgxs+EJ1CoSITJxacrxOdwmXUVjdHLpqp9vLsMX5wwwfffXhGSCQAAIUQANCr1ua2tfdskmVZdBAlUnupvSdFdRhZJ9MOlcoj8cqES8eL8qtSblncY1CW5efv29LSYHBKNADAj1AIAQC92vSHHdWlOtEpFGrmysUVF7g9aF/istjTZTWJV9vphJmZlUlXp/YY1FXUbXl4p1OiAQB+hEIIALDvm8PffbjjM9EpFCpm1rScvBrRKRQqdGJIXk2TJEmZFbWTZkVfekKVQR47PrjH4Ic7PvvqnW+dkQ8A0A2FEABgR1Ot/oVfbRWdQqG8fL3lsFCzmWVX7VGrfOPCW9s7JEkym61ayRoSObbHKc2NrVGLUy790XUPbGusaXJGSADADyiEAAA71j/4Un1Vo+gUCjVjxcLK8nrRKRRq+lWJRd2mGTc1t/rEh3v5ePU4LT9Hm3zD5T0Gm3TN6/5nm8MjAgC6oRACAHr65I0vv9j7L9EpFNlSE6YAACAASURBVGragoSsbK3oFAo1fmpYVkVtj8GS8rrJV8VdenKZrj10UniPwRMHT3765leOygcAuASFEADwI3WVDRt/94roFArlG+hr8AmQrSy7aoda7SFFBxs77Cy7eq5Am3hlfI9BQ4tx3JxElUrVY3zDQ9t15azWAwBOQiEEAFwky/Lz923W17eIDqJQ8TfM11U3i06hUAnLEy/0XuRyqhqikiJ6DBbkaGfe2nMXipZGw3P3stkJADgJhRAAcNGRrR+d/OC06BQKFbc0OSeLyaL2RSVEnC2p7uMEY4e5aYz3mMv8e4zn5Ovilib3GMz46NyRbR+PcEQAgD0UQgBAJ21x9bY/vyY6hUKNCR9bb1Zz28oub18vY7i/2Wzt+zRdrT541kSV+kffPawWa63R49KHCbf9aZe2uK+GCQAYERRCAIAkSZJsldfes6mtpV10EIWa9JPUxjqD6BQKNe3KuPLKhoGcWXBBl7g8scdgc2NrYOI0H3+f7oNtLe2rf7nBaumnZAIAholCCACQJEna+9zhc5/niE6hUMk3XJ6bXSk6hUJNSp14prBq4OefKaqKWzClx2DFhdqkm3s+TJj9df7+F94bbj4AQJ8ohAAAqSxXs/OJt0SnUKiQCaEV9R2iUyiUr79Po6/aOpiZtFZZLtK3RkzrOUc080z5jOt77ky44/G3SjLLhpsSANA7CiEAuDuL2ZK2Kr2j3SQ6iEJFzJ+ub2oTnUKhJi2NrdINetnV1vaO9nGBfmN8e4yX17aHRv+oKJqMprRV6WZ7W1kAAEYEhRAA3N3r/9iXf6pIdAqFmnnzwoJcVha1b+rlk88WDnEmrba6MXLhZJXqR99DDC3G8DkJPXYmLDpd8sYz+4eeEgDQJwohALi1wu+L3/rnAdEpFCp8yvjzFXrRKRQqYKxftco8nFVXs89XJ12T0GOwMK8q5ab5PQZ3P3Mg7yS/swAAh6AQAoD7MhlNaXemm00W0UGUSOWhCk6ObW81ig6iUJGLptTWD3fZ1TOlNVPmxPQYLNa0jI+d0H3ENqvZ2MaTnAAw8iiEAOC+tj/6xoXsctEpFGrmykXFBeyDZ1/cwqmZBSMwk9ZisWola0BwQPfBtlbjmITJHj/errA8T7Pjsd3D/0QAQA8UQgBwU+c+zzmw/n3RKRQqMjG6oGRAG+u5obHhgaXtI7ZfZUOjYfz8mB4PE5YU1cy8ZVGPM9958Qg7owDAiKMQAoA7ajcYn7t3k2wdxhNgo5fay9Nv6kSWXe1N6OzopuaRXHY1u6gqcXnPhwmzcmsSliZ3H5Gtctpd6a0j+tEAAAohALijTX/YUXme+ZD2paxcWHpeJzqFQiUui88uGsQ29AN0pqR68uzo7iOyVa4xeoRO+tEuFNUXdFse3jninw4A7oxCCABuJ+PY2aMvfyo6hULFpE7NzaMN2hcSObawftC7Dg6E1SprZUtI5Njug82NrWNnxHr5encf/GD7J98e+d4RGQDAPVEIAcC9NNfp0+7aKA9nu4DRy9vPWw4PM5tZdtUOlcojcHpEi8FRy642Nrf5xoervdXdB0vP65JW9HyY8Pn7tzTXsR0IAIwMCiEAuJcND22v17Jcin3Tb1pYWV4vOoVCJV6TUFBS49CPKC6vi7s6scdgdqZm+rVzuo/Uaxuev3+LQ5MAgPugEAKAG/nsrRPH3/5adAqFmjI/ITtn5J+OGx3GTQnLrqh1wgedLqhMWNZzgZnKJvPYyJDuIycOnOTfZAAYERRCAHAX9dqG9N+8LDqFQvkG+rb7j7FarKKDKJFa7eERE2zsMDvn43Kq66OSIrqP6JtaoxYm9zjtxQe26SrqnBMJAEYxCiEAuAuevOpDwg0LarSNolMoVPw1SSXlzqteHR3mpjHeYy7z7z6Yn6NNvnFe95GWRsNz927maVgAGCYKIQC4hfdf+pi1GXsTt2RGdlal6BQKFZUQkXnB2TuU6Gr1YZfH9Bgsq24NmzSu+wjr5QLA8FEIAWD0q76g2/rwLtEpFCrgsjFNkjc3muzy8vEyhvubRCy7mnO+OunK+O4jhhbjZTPjVCpV98FNf9hR6YB9EQHAfVAIAWCUk61y2l3prfo20UEUaupVc+p0zKS1L/bK+PJKYWvS5tU0jZsc1n3kfEF16sof7ULRbjA+d99m2UqfB4AhohACwCi3f92Rc5/niE6hUEnLZ+dkaUSnUKiYlKgz57UCA7S2d1iigrz9vLoP5hbVTZn/o2VIz32e886LR5wbDQBGDwohAIxmZbmaVx/fLTqFQo2NDNE2swe9fT7+3k3+nlbRd94qtA3RP4ntPmI2Wwze/kHjgrsP7nhsd1kuxR4AhoJCCACjlsVsWXNXurGtQ3QQhZq4KFnf1Co6hUJNXhpXpWsWnUKSJCmrqCrxx7vV1+n0EQtmeKgvfocxtnX887/Xm03UewAYNAohAIxau585kHeySHQKhUq5aX5etsj5kEo29fJJZwsVtOxqlqZ24vTI7iPnC6pTf3pF95HC74vfevaAc3MBwGhAIQSA0anodMkbT+8TnUKhQqPDS6sMolMolH+Qb7XKqqhVV00mS4O/OjA0sPtgZnZV7KKk7iOv/9++/FP8BgQABodCCACjkMloSluVzgw6u1QqVficBEOLUXQQhYpaPLW2vkV0ip5q6w0hs6I81OquEdkqt3j7+Qdd3L/eYrakrWKONAAMDoUQAEahVx7bXZJZJjqFQs1cubAwj53r7ItdNPVcgUJn0haU1CQs/9HDhLqq5tjr5nUfKcvV7HzibefmAgDXRiEEgNEm++v8d9axCr99kQlRBRcaRadQqDGhAWVtir5xeqZIO23+5O4jOVmViVfO7D6y7/nD7LMCAANHIQSAUaXdYFxz10arxSo6iBKpvTz9psZ0tJtEB1Go8DnRTc2KXnbVKstlRuPY8DFdI7Is13Z4BIZ1G7HKa+7e2KpvExEQAFwPhRAARpWtD+/UFCp0yp9wM29eWFqsE51CoRKXxWefrxadon/N+vbgmRNUqotfYBrqWiYvm939nKqSmpceed3p0QDAJVEIAWD0+O7DM0e2fSw6hUJFp07JKaAN2ndZZHBBXZPoFAOVV1KTsCyu+0huVuWM6+Z0Hzmy9aPvPjzj3FwA4JIohAAwSrQ0Gp6/f4usqO0CFMPL11s1PpxlV+1SqTwCZ4w3tLrS4pzZVfVRCRHdRy7ojJGJ0V2HsiyvvWeTXnnLpQKA0lAIAWCUSP/Ny7ryOtEpFCp5xUJNab3oFAqVcFV8fnGN6BSD09Fh1of4+Af5do20txq9YiJ9Ai+O1FU2bPzdKyLSAYAroRACwGhw4uDJT974UnQKhZoyLz4rh30m7AuLuSyvukF0iqGormkev2By94cJNaX18dcv6H7OJ298+cXefzk9GgC4EgohALi8huqmF+7fIjqFQvkE+hoDg1h21S6Vp4fPtLA2l93JPed8ddI1CT8aydLMXPGjTrj+wZcaql3m8UgAcD4KIQC4vPUPvtRUqxedQqES/21BdSUbD9qXdHViUalrL7RztqxmUmp095HzFfqI+Kiuw6Za/fP8ugQAekchBADX9uGOz75651vRKRQqbsmM7MxK0SkUavy0cZllrt0GJUkym61alXXs+Iv7ELa3dQTETvJQX/yG883h7469elxAOABwBRRCAHBhuoq6LQ/vFJ1CofyDA5okH5ZdtcvT01OaENTRYRYdZAQ0NbcGTo9Ud2uAF87XzLxlUfdzNv7+lWoXvxcKAA5CIQQAVyXL8vP3bWlpMIgOolCxy+fW6ZpFp1CouGsSLmhGz5q0RaW6hGuTuo/kFdZFp0zuOmxtblt7zyZ+OwAAl6IQAoCrOrjhA7be7k3S1bOyMzWiUyhUVFLkuZLRtuzq6ULtlNkXHyY0dZg9Isd7+nh1jZz5NOtQ+lER0QBA0SiEAOCSKs9X73hst+gUChUUHlTdyr0g+7z9vFqDfczm0bbsqlWWdV4qvzEX9yGsKK1LuXlh93O2P/pGeT7PlALAj1AIAcD1WMyWf/73+raWdtFBFGrikllNzKTtxdRl8ZWjdBsGXa0+5oqp3Ueyc6onz43rOjS2GtfctdFitjg9GgAoF4UQAFzP26sP5X5TIDqFQiXfOC8/h7tA9k2ZE3OmcDT/5Zwp0CYsvdgALRZrq1/gmPCxXSO53xTsSTskIhoAKBSFEABcTPHZC6/9Y6/oFAoVOjGsrKZNdAqF8hvjW6Me/euq5Nc1R0wL7zqsq9FPvGKmSqXqGtn15J7CjGIR0QBAiSiEAOBKTEbT6jvTzaNit4ARp1KpwuYkGfTMpLUvevHU2roW0Skcrq2toyMi0MfPu2ukIFeb+tMrug7NJsvaezaZjCYR6QBAcSiEAOBKdj25p/hcqegUCjVz5cKifK3oFAoVt3DK2UJ3+cvRaBujlkzrPpKTVzNtYWLXYfG50l1P7nF6LgBQIgohALiMnH8V7FnzrugUCjVuWmTRhdG5VsrwBYYGlrZ3iE7hVNnnq5KujO86tFisLd4BgSFjukbeTjuU+WWuiGgAoCwUQgBwDcZW45q70q2W0bZbwIhQeaiCEqe0u1nnGbjxl0c3NbeKTuFsWVUNUUkRXYe11U1Tr5nddShb5TV3bWSpXgCgEAKAa9j259cqCtxlyt9gpd66uKSoRnQKhUr4SVxW0Wjbhn4gOjrMjYFeAcEBXSPZmZXTl8/qOtQWV29/9A0R0QBAQSiEAOACTn+SeXjzMdEpFCoqKTqvsE50CoUKjhhb1KgXnUKY2rqW8fOiu49Ut0pjx4d0HR7e9OGpo2ecngsAFMSphbCpqclsHoGV8fR6vdXKpCkA7sLQ1Lr2nk2jf7uAIfH0VntPijKx7Ko9KpXH2OTIFoNRdBCRss9XJ3Z7mLCxriVqcUrXoSzLz9+3uaXBICIaACiCMwphRkbGbbfdFhAQEBwc7OPjM2vWrE2bhvLNJiMj44477hg7dmxQUFBAQMDll1++a9cuRwQGAEVJ/+3LNWW1olMoVPLKK8pK+MuxL+Gq+LziatEpxMvXNYVGBV88zKmccf3lXYe1mvpNf9ghIhcAKILK0b9y3r1795133mky9dztZ8WKFQcOHPD09BzgdTZv3vzb3/720huMK1euPHjwYPcNZ4fA9uOK+u27RqOxWCxRUVFqtVp0FgAifX3o1BM/TROdQqFiZk+t7vAymy2igyhRWHRI3RjvVhbakSRJkuKnjCs/XiBZOv9DHxDo41VTU1eu6zrh8T3/u/TnCwWlA6AIFotFo9Go1eqoqCjRWS5yQk9x7B3C7Ozsu+++22QyRUZGrl+/PjMzc//+/TfccIMkSe+9997jjz8+wOu8//77Dz30kNlsTk1N3bZtW25u7vHjx1esWCFJ0rvvvvvPf/7TgX8GABCnSdf8wq+2ik6hUD6BvpaQUNqgfWqVd2wYbbBLQUnN9Ksv7kNoaDGGzU5QeVz8bfKGh7Y36ZpFRAMAwRx7h/D222/ft2+fn5/fF198MXfuXNtgR0fH8uXLv/zySz8/v5KSkvHjx/d9EbPZnJiYeP78+ZSUlOPHj1922WW2cVmWb7zxxqNHjwYHB9fU1Hh5eQ05J3cIASjTP/79uS/2fSM6hULN+vmyzEyN6BQKlXRt0vfn3XFl0T6o1R5x/v6lZ8u7RlKSI8/s/7LrcPEt85488GcR0QAoAncIR15jY+PBgwclSfrd737X1QYlSfL29t6wYYMkSW1tbW+//Xa/13nnnXfOnz8vSdL27du72qAkSSqV6m9/+5vtg7788stefx4AXNPHr31BG+xN7BXTs7IqRadQqMjYcVnlPFfZk8VirfKwBoVd3Js+K6cq/iczug6/PnTq49e+EBENAERyYCH86KOPbI/83X777T3eSk1NjYmJkSTp6NGj/V7nwIEDkiTFx8fPnz+/x1tLlizR6XQ6nW7x4sUjExoAlEFXUbfxd6+ITqFQ/sEBzSpfRU3rUA5PT7U1KqiDZVftaWxqHZMSqVJ3fvmRrXKtyTMkKrTrhI2/e0VXwRYmANyLAwvh2bNnJUny9fVNTU299N3rr79ekqRz5871e53jx49LknTrrbfafTcsLCwsLMzX13c4UQFAUWRZfuH+LS2NLIVvX+zyuXU87tWLuGsSL5RTaXpVVKpLvObiw4RNDYbx86Z3LU3X0mhYc9dGftcAwK04sBAWFhZKkhQdHW33Kbhp06ZJklRZWdna2trHRRobG6uqqiRJst1RLCoqeuGFF/74xz+uWbPm2LFjer37brYLYBRjs+w+JF6Vms2jg72ISoo4V8Kjg/04c75q2tzJXYeFudqUFQu6Dk9/knl48zEBsQBAkIHu+jAE9fX1kiSNGzfO7ru2cVmW6+vr/f39e7vIhQsXbC9CQ0MfeOCBrVu3dv+9XWRk5ObNm2+55ZZ+w6xevbrfc5qbFfT7Zr1eb7Vam5ubWVQGcDfVF3Qv/eV10SkUKihsTHUbd2/s8/TxagnyNuvcehv63nRflcEqy2UmY/D4oMbqzv/uF5U1jYuNqCnq7NJb/7QrfuHUCbH9LHoHYJSxWCwtLS0eHh6KKgVO4MBCaDAYJEnqbTKnn59f99N60/XP46mnnsrNzfXz87v88ssnT55cVFSUkZGh1WpvvfXWl1566d577+07zF/+8pd+Azc2NvZ7jtM0NzdbrVY/Pz8KIeBWZKu87v5t7Qa+09s3fsH04iLmQ9oXvSgmp6xedAqFmjJ7nOThUfyd1nbYrG8PjrtMqtXbdiY0tpvCp0Z7lNRYLVZJkjraOtbdv/Uvex/yUDt2dy4AimKxWJqbmz08PPq4WTUqObAQ2n4P19uW8V03+i7da767rgmlubm5V1999Y4dO2xzRyVJOnv27O23315YWPjwww/fdNNNkZGRfVznkUce6eNd2/3DoKCgPs5xMoPBYLFYgoKCKISAWzm47mjByWLRKRQq8dpZhbTBXkxMjswrbxCdQqHCI4NyGpvMFuuMpPDS3M7N6Msqm2YujSv8rMB2WFHaMOPGeZmHv7Udnv++9PjOf936+38TkxiACBaLxWAwqNVqRZUCJ3BgIQwICJAkqb293e67RqOx+2m96dpdMCIiYt++fSEhIV1vpaam7tixY8mSJU1NTa+88optC4re9L15va0QBgcH93GOk9kKYXBwMIUQcB+lORV7094VnUKhQqJCtY3sQW+fr79Pc4CXtdX+f3DdnNrTQ4r276hqkySpQmUMDgtorO2cmpRbWR8dN15bWG07LLzQNDF5UkVWqe1wz+rDS3+2eOrMSUJiA3C+rkKoqFLgBA6cC2H7q7Q9SXip2tra7qf1JjAw0PbiF7/4Rfc2aHPFFVfExcVJA1utFACUzGyyrL5zQ0e7SXQQJVKpVBHzprc0t4kOolAxS2OrdayyZl/8wpjzVZ03lhta2vxig9SenV9+TCaLaXyA2rvzF6+mDrN6QoSnT+dvok1G0+o7081s4AFgtHNgIbRVtbKyMrvLN5eXl0uSFBYW1nchnDhxou1FYmKi3RNsn1JQUDDMtAAg1mtP7SnMYLKofTNXzC/I1YpOoVDTFkw5W1ApOoVCRU0Ny9D86N+c/Mra+IUxXYfllQ3xVyd0HVaU1iXfvKjrsPjshdf+sdcJOQFAIAcWwpSUFEmSWlpa7La1jIwMSZKSk5P7vkhUVNTYsWMlSdJq7X8VqKurk37YlAIAXFRhRvGetEOiUyhU+NSIoooW0SkUasxl/hoTd5Xt8/RWt4aozBZrj/FT5ZXTkid0HZ4prJo2b3LXYVaWNunqi/snv736UN63hQ5OCgAiObAQXnvttR4eHpIkvffeez3e0ul0J0+elCTpxhtv7Pc6V199tfTD9vQ9NDc3Z2VlSZI0c+bMYecFADGMbR3P/teLZhMPyNmh8lCNTZra3sqyq/aNnzepobGvxbrdWeyC6FKdnfXDrbJcYtEHhwV0HZYa20MiO+crybKsbZFDJ4XbDi1mS9qqdGNbh3MyA4DzObAQhoeH33DDDZIkrV+/vsfeEmvXrjWZTN7e3nfccUf38ZKSkry8vLy8PIvl4hej//f//p8kSV988cWbb77Z4yMeeeQRg8GgUqlWrFjhqD8GADjYy4++UZ7PlD/7Zt6yuKSoRnQKhYpfEptZyDb09k1KGPddea//s2o0tHtPHeP5w8OE+hajT3xY1ypu+qbW4OQ4tVfnwnvl+ZUvP/qGowMDgCiO3WDnqaee8vT0LCsr+9nPfnbmzBlJkqqrq9PS0tauXStJ0q9//evo6Oju5998881JSUlJSUk6na5r8Lbbbps7d64kSb/85S//8pe/ZGZmtrS0fPvttz//+c+3bNkiSdKDDz64YMECh/5BAMBBznyadXDDB6JTKFRk0sSC8+wzYd/YcWOKm7k3aJ+vn3etn8VqtbOEQZeiqrq4RRefNykpr4u/9uJqBReKapJXLuw6PLjhg+8+POOIqAAgnMruii8jaPPmzQ8++KDtU0JCQhoaOndJuuqqq44ePert7d395OTk5OzsbEmStFptRERE13hpaemSJUsqKiouvf4tt9zy+uuvdy1GOjS2zRId/VcxKBqNxmKxREVFse0EMIq1Nrfdn/q/1aW6/k91P2ovz5jl88qK+cuxb/LyxNziatEpFCr+J5O+K+3/rrtKJc0JGVd4RtN1mBIeUvhN59pOarXHBF/rhe+LbIfhE0O3nX0uMKSvvbIAuDSLxaLRaNRqdVRUlOgsFzmhpzj2DqEkSQ888MBHH320ZMkSlUpla4PR0dFPP/30sWPHerRBSZLmzZu3bNmyZcuW9Xhr0qRJZ8+e/c1vfhMWFmYbCQgIWLhw4e7duw8ePDjMNggAomz8/Su0wd7MXLmINtibpCvjaYO9mZockVE2oDnYsiwVtDWFRgR1HRYbWsOiO/e4slis5pDLfPx9bIe6irotD+90RGAAEMvhdwi7GAwGrVYbFBQ0bty4IV/EarXW1NS0t7fHxMTYVqwZEdwhBOB83xz+7vFbVotOoVAxs6ZWdXhaLlkfEpIkhU4MqQ/ybm1nmRM7Asb4mCb51Q5mMm1sRGj99zVmc+e/bFOjQ6u/KrH+sJZBSsqEM/u+6Dr5iX0PL/kZT6kAoxN3CB0uICAgNjZ2OG1QkiQPD4+IiIjJkyePYBsEAOdrqtW/8KutolMolJevtxwWRhu0T63yjQunDfYmYtb4QbVByfYw4eKLDxMWl9clXHNxZ8KsbG3soqSuw3UPbGusaRp+TgBQDmoVAAiw/sGX6qvsLIgPSZJmrFhYWV4vOoVCTb8qsYhpxr2Imx11utT+rsV9O1mqiZs9sesw80LNhITxtteyVW7x9vMP8rcdNuma1/3PtuFHBQDloBACgLN98saXX+z9l+gUCjVtQUJW9lC+07uD8VPDsipqRadQqKCQgKL25qH9rCxL+YbGsPFjbIcms8UUHujl27nthK6qOe66eV0nnzh48tM3vxpmWgBQDgohADhVraY+/bcvi06hUP5B/gbfALnP3QLcllrtIUUHGzvMooMoVMj0y5oM7UP+8ZZ2o+eUQA8Ple2wrLI+dtnFiaPZWZWJV87sOtzwm+21Gm5iAxglKIQA4DyyLL9w/5aWBraPsy/2urm6qiHe5Bn1EpYnXihnV0b7EhfEZJZXDfMiBZW1CYsndR2eKdJOnTfZ9lqWZa1BDp/cOY+0pcGw9u6NilqLDgCGjEIIAM5zZNvHJz84LTqFQiVeOTMni8mi9kUlRpwtYZ8J+0LCx+Q2jsz9ulPlldOSJ9heW2W5wtQRHDHWdtjS3DY2OVbt1TmPNOOjc0e2fTwiHwoAYlEIAcBJtMXV2/60S3QKhQoMG6PrcN5OSK7F29fLGObftS8CulOppMC4IH2bcUSuZpXlEos+OKxz9/mm5jafhPCu/Z9KCqtTVi7uOnnbn3Zp2Q0SgOujEAKAM8hWee09m9pahv6M0+g2eensxjpm0to37cq48soG0SkUKnHhpOyKmhG8YKOh3S82SO3Z+QXpQnldwrWJXe9m5WhjF0+3vW5raV/9yw1W9kcB4OIohADgDHufO3zu8xzRKRQq+YbLc7MrRadQqEmp0WcKh/t03Gg1bmLwWd1ItkGb/Mra+EUXdyY8XaidNn+y7bVslfWevv5jO3ehyP46f/8L7414AABwJgohADhcWa5m5xNviU6hUCETQivq2WbdPl9/nwY/Dyszae1Re3pIUb7tjll29WSZJm7WxYcJS9vbQ6OCbYe11c2x117chWLH42+VZJY5IgMAOAeFEAAcy2K2pK1K72g3iQ6iUBHzp+ub2kSnUKhJS2Ora1h21b74hTFFWkctuyrLUpFRHxLeuTOhvsXoGz9OUnduSpGdqUm8qnMXCpPRlLYq3cx2IABcFoUQABzr9X/syz9VJDqFQs28eWFBLiuL2jf18slnC5lJa1/U5NDvKx07k7bJ0O41JcDzh4cJi0p106+6+DChzqgaE965AGnR6ZI3ntnv0DAA4DgUQgBwoMLvi9/65wHRKRQqfMr48xV60SkUKmCsX7XKzFxRuzy91a2hHiazxdEfVFRVF9vtYcJz5brIuHG21411huglqV1v7X7mQN5Jfu8DwCVRCAHAUUxGU9qd6WaTw7+2uiKVhyo4Oba9dWR2Cxh9IhdNqa1n2VX7YhdEl+oanfNZp8o001Iiba9NJot1QpCnZ+cuFPk5lTOuv9z22jYz3NjG07AAXA+FEAAc5ZW/vXkhu1x0CoWauXJRcQF7uNkXv3haZgEzae2blDDuu3LnzaSVZanM2hYY5Gs7vFBeF39NQte7moaOkAmhttfleZpXH9/ttGAAMFIohADgEFlf5e1fd0R0CoWKTIwuKGFjPfvGhAaUtrLKjn0+vl51fhar1alTaev0hsuSw1SdC8pIp89XTZnTOY9U39QWNifRQ935bWr/uiNnj2c7fhVnjgAAIABJREFUMxsADB+FEABGXrvBuOaudNm5X1tdhdrL02/qRJZd7U345TGNzRRC+ybNi6qsF7DsalZFdeKiSbbXVqtcKVvG/rAAaXFhdeqtV9hey1Z5zd0bW/nHB8ClUAgBYORt/uOrleeZD2lfysqFped1olMoVOKy+OwitqG3b+qMiIwyjahPz9BWTUr4YUWZptaxqRO6dqHIzKmKWzLD9rr6gm7rn3aJiQgAQ0IhBIARlnHs7AfbPxGdQqFiUqfm5tEG7QuJHFso4vaXS/AP9NGo2wUuu2q2WKu8TYFj/WyH+cU106/p3IVCtsr1Vs+uXSjef+njb498LyYlAAwehRAARlJLo+G5ezfLbBdgj5evtzUszOz43QJckUrlETg9osXAsqv2TZg1XtcoeNlVXVPLZTNCux4mPFNSMyl1ou11Y51h0tKLu1A8f/+W5jq2VAHgGiiEADCSXnxgm66iTnQKhZqxYqG2ol50CoVKvCa+oKRGdAqFipsV9X2ZIpZd7f4wocVi1XlKgaGBtsPcrMoZ182xva7XNjx//xYxEQFgkCiEADBiPnvrxPG3vxadQqGmLEjIylbEd3oFCp8cmqOhKtsXFOJX3KGgu23fV1XHxIXbXtc1GMLnRHe9pWk0hUy4zPb6xIGT/L8BAJdAIQSAkVGvbUj/zcuiUyiUb6Bvu98Yll21S632UE8KaTey7Kp9l80Ib2hR0LqdJrOl2u/iw4Q556sSlnXuTKhvahs/b4bqh0mlzBcA4BIohAAwMnhqqA8JNyyo0TaKTqFQCcsTS8qpDfYlzos5p4zJot3pGg2h3XYmLKhtDI0Ktr0uzNMm3zjP9ponigG4BAohAIwA1hXsQ/xPZmRnVYpOoVATEsaf49HBXoSMC8xpUuhM2szyqsSFk22vW9s6/BPHq1Sd36lKNC3jp0XYXmccO3v05U+FJASAAaIQAsBwVV/QbX2YncfsC7hsTKPszU0Su7x8vDrCA0wsu2qPSiUFxgW3tCt32dWzuupxP9wYLCipSbymc+JoW1vHmKRpKo/OG4ib/rCjkr0lASgYhRAAhkW2ymvu3tiqV9AzTooy5arZdTpm0toXe2V8eWWD6BQKlbhwcnZ5tegUfWnvMFsn+Hh6q22HWRW1UQmdNwZLCqtTb13ceZrBmHbXRqvFKiYlAPSHQggAw7J/3ZGzx7NFp1CopOWzc5ks2ouYlKgz5xX3dJxChEWOzax1gZm0xdX10xZ2rjLa0WFuCfbxDfS1Hebk6abM77xnmH0i78D698VEBID+UAgBYOjKcjWvPr5bdAqFGhsZom1mMqR9Pv7ezQFeVpZdtUelUnlN8m91kWVXvyvVxM2Ksr2u0jVHLZpie22xWA3eAYFhY2yHOx7bXZarERMRAPpEIQSAIbKYLWvuSje2dYgOolATFyXrm1pFp1CoyUvjtDVNolMoVNLimPzKWtEpBkqWpfzWprDxncUvq9suFHW65pils22vjW0d//zv9WYTvyIBoDgUQgAYojeffifvZJHoFAo186b5eWxD34upl086W8hMWvuiplz2fZULTBbtrqXdqJrkr/bs/E6VV9MQMW2c7XV+dmXyDXNtrwu/L37r2QNiIgJA7yiEADAURadL3nz2HdEpFCo0OvxCNfcG7fMP8q1WWVl11S5PT4/2MK8Ok1l0kEE7X1Uft7jzYcJ2o8kUEeDt52U7LNW1hU4Kt71+/f/25Z/it0gAlIVCCACDZjKa0lalmztc72urE6hUqtBZ8QZ9u+ggChW1eGptfYvoFAoVtzCmpFqhGw/261RpZWzqBNvrCm3jlGXxttetLcbw2YkqlUqSJIvZkrYqvaPdNR6PBOAmKIQAMGg7Hn+rJLNMdAqFSl256HyBoncLECh20dRzBcyktS8mPvxUhQvPpJVlqbC9OfSHhwnPFlZOmz/Z9rowV5uyYoHtdVmuZucTbwlJCAB2UQgBYHCyv87f/8J7olMoVGRCVMEFNtazLzA0sKxNudusi+Xj69Xgb3X1ZVf1bUb15ABPTw9JkmRZqjSbA4IDbG+dL28eH9d5/3Dvc4fPfZ4jLCUA/BiFEAAGod1gXMMe071Qe3n6TY0xMh2uF+GzJzY182ilfZPnRWnqm0WnGAFF2rq4hTG21/WNhgkLJtlet7d1BMZP9lB7SJIkW+U1d29s1bcJSwkA3VAIAWAQtj68U1PIlD/7Um5eWFqsE51CoRKXxuUUM5PWvikzIr8rGz179H1XoY2O7VxF5lyhNn5JrO31haKamSsX2V5XldS89MjrYvIBwI9RCAFgoL778MyRbR+LTqFQ0alTcgtog/ZdFhlcMCpufzmCf4C31qN9NC27arFaG4NkH9/OVUZL9IbgiLG213lFddGpnTvXH9n60f9n7z7DIz3Lu+Gf9/QZlZE0M5JGI436aFS3eqVdcFnbEB5jTI48R5I3vJDYFIMJBBKcEHj9hPpgsjZurM163XDFeMFex7GNGzYGA9u02lXvGknTe+9zvx+0lMCldZN039L8f59upLH2f8yhXa5zrvM6r5MvDAkTEQDgj6AgBAB4S2Kh+C3XHuK30rp17chVCq7GgEu3mThOUtpdE09khA4iUqadRk94q41dtfvCpguMK8+RaKqks0YilRJRNpPLVeo02hIi4nn+5k/cFcXIWQAQGgpCAIC35ODn7/Mu+YVOIVI9Vw7YbZv1toD11rHfMjm3yW5a3zBt20ynbJt4suh5DNmc1gvOHSacsXmtl3esPHucodbLz11V73cE7/zC/cLkAwD4HRSEAABv7vWf/PaVR38pdAqRatljGRlzCZ1CpKqbdBNujF1lK9Oq57NbeX9sOOSrbahceT4942reea4+HBux91xxwcrzK4/+8vWf/FaYfAAARISCEADgTYW9ke9/7l6hU4iUslSV0pRj7CqTRCqVNlUlk2gWZTP0GoKxrTx2NZnOpgxShVJGRAWed/B5raF05VuL7oS+sXrl+Y7PHg64QoKlBICih4IQAOBN3Hbd4ZAnLHQKkbJ+YI/bibUsW8dlHXOLPqFTiFTH7oahxa0/sHfRF27qr195DoUTZb11K4cJ47F0VV87x3FEFPZFb/303UKmBIDihoIQAOB8Xnjg1V89eUzoFCLV/t7u0ZGtv6Z/Z2paDMM2HB1kq9CXTESLpZP25ILdsutcTTi94O241LLyPDvl7rtqYOX5t8+cfPGHrwkSDwAABSEAwKq8y/5D1z8odAqR0lSUhEmJsatMUqmUTNosxq6ycByVWSqiybTQQTbOWCRQU1+x8jy86DW216w8Ty+EjBbTyvOdX7zfbcPFLQAgABSEAABsPM/f8qlDsWBc6CAi1XrZLr8Xd+uxNV7YtGDHTFq2jn7z6HJx7Z0m0tmcUSlTSIkom83na0tlchkRpVNZTVujRCohokQkefMn7sInLACw8VAQAgCwHf3+87g2ejWdl24fG9matwW8e7WW6vHlYumHfLv0NWUjgWIslefdgfb+hpVnmz3Q/rvG0YVZT9+H9648D/185OmDPxMmHwAUMRSEAAAMS5OO+776mNApRKrcUO5OYB+DTaGWx7WKQgHvDwPHcfLmskSqSMeunlh0NFlrV57PzLkbeupWniem/Q29TSvP93z5YdvYsiDxAKBooSAEAPhT+Vz+wNUH04kiOuP0ttS/d3sYnbSraLnY4vHjzWHr3GeedBTvMbkCz3tUWZVGQUT5fCFWplCo5USUzeQkxhq5SkFEmVT25k/clc/h9CkAbBwUhAAAf+rH//n0xLFpoVOIVO8VeybH0CzK1rzTPDSNN4ettqFy0FVcRwf/nCsQqdt5bpPQ4Q43XXyucXTZ5u++8lzj6MSx6ScOPC1MPgAoSigIAQD+h9mhhYe/dUToFCKlazTY3Nj+YlOXqTxSzARhk8ok+VpFJpsTOojwhhadnXvMK89nphyWC9tWnoeH7V2Xb195fuibR2aHFgSJBwBFCAUhAMAfZNPZA1cfzGWwbGXgOE6/rSMeQyctW8O+Fp8/JnQKkWofMM+6A0KnEIvTfq+pSbfyPOWPGhr1K8/LoZyuwUBEuUzuwNUHs+msYBEBoJigIAQA+IMHv/7E3Fmb0ClEqu+qgZlJl9ApRKq9v/nMtFPoFCLV0GYYtOPN+YNMNherkihVciJKpjJk1sqVciKKR1OGXVaO44ho7qztoW88IXBQACgOKAgBAM4Z+83UkZv/S+gUIlXdYpy1hYVOIVKlutLFTJFOznxTMoU0Uk65fEHoIOKy5AuZLzg3ZXTRHmjZ377yPD3u7L2yf+X5xweeHv7luDD5AKCYoCAEACAiSifSN11zsIBlKwsn4co7m5NJ1DxsNbsaQuGE0ClEqq2/YckXEjqFGJ2yOTouOHcz4dCUs7W/eeV5ZjFc015HRHyBv+maO5OxlGARAaA4oCAEACAiOvxvDy9PoauNbdtf7pufKfb5kKuxXtQ+MoNOWrbmrpqTixi7uqrRcKC6rmLl2ZHNllaWEFE6lS1tb5JIJUTknHPf+5VHhYwIAEUABSEAAJ1+ZfiZH7wodAqRMnWZJ2f8QqcQqYra8ulgVOgUIqXSKNzybAFzV1eXSGXydUqZQkpEgVC89oLGla8vzHr6Prxv5fmZu1448bMhwSICQBFAQQgAxS4eTtz8ibtwXQCTTCFVmOsyaYxdZeA4ibanLhbH2FU28+46F6rlVbS2nJssOu8JtPefaxwdnnFa3nPuFoqJaV99TyMR8Tx/y6d+EAviuhcAWC8oCAGg2B38p/s8iz6hU4hUz1XvWZzHm8PWsd8yMecWOoVItfQaT9nsQqcQKXN95Xgu2NNzbqjMiUVHk/XcbfUz4WilUUtE2UxOWlcrU8qJyGcP3PXPDwiVFgC2PBSEAFDU3jh6/OWHXxc6hUg17W4fG8PpODa9uWrCHRQ6hUiVlqsWCwlsujPJFdJEBZ/N54fjvhpDOREVeN6rzKo0CiKKJzLabiPHSYho2ebv+dDelf/qpYd+8cbR4wLGBoAtDAUhABSvsC96+3WHhU4hUgq1IqetyGPsKpOUU7XpMXZ1NdXbqgNRjF1ls/YZbcEQESUyGYlRppBLicgZjNTvMq68YHzObb3MsvI8Mupsf2/3yvOt1x4KunH1CwCsPRSEAFC8bv00Flir6rxywLmMHTC2zkut0wteoVOIVPt205ANA3vZmpv1J1x/6KSd8Qc6tp2rAwdtDuvvbqE4u+g1dRqJiC/wQV5eXl1BKx9gfRYfYAHA2kNBCABF6uWHX3/jKbRgsbW9p2t0GGt6NmNb9cgSzlWyVehKplP4kIVNrZKH1Jn8/2ylPeZc7uo8d4BwOOSvra8kolyuECmXq0pVRBT0xUz7elde8MZTaHEHgLWHghAAipHPHrjzi/cLnUKkNNqSiESJsatMUqmkYCrPZDB2la28ozKSwNhVtpae6uVw5E++yBNNpoN6XSkRJdPZdI1MqZQRkccbNe07d1X91Liz78r+lWcMwQKANYeCEACKDsa4n1/b+3b7PbgtgM1yuXVhCbcysln7zSPLGLvKZmmvPuFkj12NpNOKeqVMJiEimzfU1G9a+frIjMt6ybnDhHP2WE2rkXBNDgCsAxSEAFB0cNHzeVj3bxsdxm0BbKbO2rPzKHjYdLXlI0GUymwlGqVdkjhPDTft83dt/90tFAuOjl3nDhOOu0OGJh0RJRPpss4WiVRCRKdfGX7mBy+ud2YAKB4oCAGguDjn3Pd+5VGhU4hUuaHckxI6hFjJlPJEhSqXw9hVBo7jlM0liRTGrrI1dOk8sdj5X3PMZW9vM6w8j0eDutpyIkqls/KmKolUSkTz0+7eDw2svODwvz28PIVTvgCwNlAQAkAR4Qv8TdfcmYyh6GFruGh7OIBOWrb2/RYHZtKuwrrXPGHHwTa2nu66U07Hm76swPM2LlahVRNRLJWWmjVSmYSIZhd91ss6Vl4zORswdTcSUTqRvumagwXcCgMAawEFIQAUkR8feHr4l+NCpxCpng/snhh582VrcWrcVj80jQ0ZtpqGyiG3R+gUIlWhVU+mA2/xxcFEsrK1TMJxRDTj8lv6zStfP2vzGC01RJTN5OT1tTKFlIjGfjN15Ob/Wp/UAFBcUBACQLGwjS0//M0nhE4hUpUm3ZIfwyHZVBplUCUpYIwHi1QmKRiV6SzGrrIZ2rSh5NtoSRhxe3p2nhsqc9LubGg3EFE2m89Vl0gVUiJaWvD3fGjvygse/PoTc2dtax0ZAIoOCkIAKAq5TO7Gj96eSWWFDiJGHMfVXNAZiySFDiJSjRe1ur0Yu8pm6TfPujBLhq23zzTkcr3d/+q4x9HcqCOifKEQKSOFQkZEi46gZb915QXjE17z9lYiyqazB64+mMMlKADw7qAgBICi8NA3j8wOLQidQqR6r+yfHn/by9Yi0bq76QyaRVdhatGdcuDNYdNVlYzG3sm5ynyhENBkNRoFES35Qs0D9StfH5pxNu80E1Eul89WVGrKNUQ0O7Tw8LeOrF1qAChGKAgBYOubPjV35KanhU4hUoaW2tllbH+xlWjVTj6HXlEmmUKaqJTkMNeERcJxpY0l0fQ7bMN2RCINnbqV5xML9vbtJiIq8LyLK5TqSonI4wy1vf+ClRf8+D+fnjg2vRapAaBIoSAEgC0unUjf+NHbc9m80EHEiJNw2q7WVAKnB9mMA03+IMausrX1N9i8IaFTiFTPdtOY510N2hl0OXu2nTtMOJkIr9xCEQjGq3bUc5yEiEaH7T0f2E1E+Vz+wNUH0/hbDADvFApCANji7v3Ko0uTGJ7Jtu3D++ancdM6m+XCtuFpdNKyNXZUn1zCXyu2ulrt6cAa/OYMhdwNpkpauYWiUSOTSYhocs5tvdSy8gKbN6lrrCaipUnHfV997N3/iQBQnFAQAsBWNvTzkacP/kzoFCJl7KyfnMU4EDZtddlcGHuDbCq1wqfOFwpopWWQSiRUI0vl1mDQSzqXS1bySqWMiGacfsvexpWvDy/5TJ1GIkrE0obtFo7jiOjo958/+cLQu/9DAaAIoSAEgC0rEUne/Im7eJwAY5HKpQqzKZPGfEK2yj5TNPY2bgsoKubdRmcgInQKkerZUTftW7PPWWzBUFtvzcrz8UV7c3ctEWVz+bhWqVDLiWh6wtV7ZT8R8Tx/y6cOxdDhDABvHwpCANiy7vzi/W6bV+gUItV71b7lBWwPsnXu7xifQyctW2tP3alFNIuymesrT3jXeOzqcae9s6uWiAo8v8gnyyvVROT0hJsvbl95wcxiuKa9joi8y/5D1z+4tn86ABQDFIQAsDX99pmTL/7wNaFTiJR5e+v4xLuaeLGF6eorJ9yYlcJWUqZcogQ23ZkUcmmygs/m135+1UQyWG0oI6JgLKHt0nEcEdGZaWfrBU1ElE5lS9ubJFIJEb3wwKu/evLYmgcAgK0NBSEAbEFhX/TWT98tdAqRkqsUvF6Xy2HsKouUU7UbEqmM0DlEqnZ7rS+CpkQ26zbjQnBdPkqIZdIyo2JlqMzoktva30hEPE+OQk6jVRPRwqyn78P7Vl5823WHQ57wesQAgK0KBSEAbEF3/OM9ARc2edi6rxxwLAWETiFSXfutM2gzXkX7DtNpG5pF2Zqb9Mdd9vX7+dN+f+f2upXnMz5PtamCiALBeP3e5pUvTkz7GnqbiCjsjdz2mcPrlwQAth4UhACw1bzy6C9fP/IboVOIVGt/x8joGp9x2jJqWvQjyz6hU4hUeaV6JoVBMmxqlTykyeTXuZX2mHPZ0l5NRKlMjqtXSyQcEZ2ZcrbvayOibCYnMdbIlHIieuPo8Z8/9qt1DQMAWwkKQgDYUnz2wMF/uk/oFCKlKdfEVSU8bgtgkUolfL02ncHYVbbKLl04jrGrbC291cvhda+WeaJlSbysVEVE005fx75zt1AsJhLa6jIiWrb5e67cu/LF73/+Xp8djQAA8JagIASArYPn+VuvxeD1VbW9/wKvC5s8bB2XW23LWECzWfvNw0sYu8rW3lZ9wrGOzaJ/zBuLV1u0nISI6MSyo7mrhohCkWRpt1EilRLRyJiz/aIeIooF4zd//E5cugMAbwUKQgDYOp49/PLx508LnUKkrJf0jY3gABibyVp7Zh4FD1uloWwsiFKZTaNROGXxjay6zrrdvdvqiahQ4B3SdKlWTUQzNq/1sg4i4gu8PyPVGiuJ6NRLZ589/PIGRgOAzQoFIQBsEa55zz3/9rDQKUSqpKrMn5Niu4BJrpSndJpcriB0EDHiOE7TWhZLpYUOIlJNXXp3dKNbEk75nY3mKiLyhuNV3eduoRiadzf21RNROBg3DfSsvPLu6x+0T+PMMAC8CRSEALAV8AX+po/fmYgmhQ4iUs37dwa8UaFTiFTbJZZlZ1DoFCJlHTCPOzB2lc3aWXvCKcCueyafD5fmNGoFEY0su60DjUSUzxd8Cm7lForJMWfvFRcQUSqevumaOwt5fNgBAOeDghAAtoIj33vm7C/GhE4hUtZLt42PbNAZp02ncVv90Ay2UNhq6iuGPB6hU4hUeZlqPifYdX/2cKShS7/yfNrtrmuuIiJfIFY30LTyxQV3QtdYTUSjv5786a3/LVBMANgcUBACwKa3OG5/8GuPC51CpCrrdK4Y9gfYlBpFQCUpoJOWRSqT8CZVOouxq2zGjspAQsiWhEGXo6e3jogyuXy0glNpFEQ0PO2yXNhGRIlYWr/NwnEcET3wfx6fH14UMCoAiBwKQgDY3PK5/IGrD2ZSWaGDiFTtnq5oGJ20bM0Xt3vQSbsKS3/DjNMvdAqR6umpG3QKv7F8Nuo11pYTkd0fadhlXPniXDhWadQS0cykq++qASLKprMHrj6Yw5UqALAKFIQAsLk98q2fTJ6YETqFSPVd2T81LvyyVZxadjUNTWHsKpupSTfoxNhVNl1lyXhCFKVyMpvN6iUKhYyITtkclp31RBSNpcu6azlOQkTTCyGjxUREM6fnH/3OT4VNCwCihYIQADax6cG5x7/7lNApRMrQXDPniAmdQqRKtGo3l0OvKJNMIU3oJNlcXuggYsRJqLy5NJIWy9hVWzBk6atZeZ5NRcorNUQ0OefpuLidiNKprLqtUSKVENGPvvPUxHF8dgYADCgIAWCzyqazB/7hYC6LZSsDJ+EqetqScbEsW8XGONDsC2z0bQGbRXt/g80bEjqFSPX0mUbc4to7Pe60d1hqiCgYS+q6dStfHPcEDeYqIrLNevo+vI9+112fTmYEjAoA4oSCEAA2q/u++tjC6JLQKUSq76q9c1PiWraKR/u+tmFczraKxo7qE0vopGWrMZSfCYlu7CpPtEix8jIVEZ1ZdFn3NBBRKpWVt+okUikRjU95zdtbiWhpwv7ADT8SNi0AiBAKQgDYlEZ+NfHk7c8KnUKkjNaGqXlcrMdWpitZTCSETiFSSpU8oM4XCmilZZBwnMKkTGbFOL/KF4/r27WchIhoOOivra8kolmbr+OyDiLKZfPZikqNtoSInrz92TOvjQoaFgBEBwUhAGw+iWjyu39/B49lK4tULlM112Ps6mqqdzeGIhi7yta0x2QPRIROIVI9O00TXq/QKVY17Hb3bqsnomQ6m66RKZUyIhqadTVurycijzPUdvluIuIL/E0fvzMRxV8BAPgDFIQAsPkc+pcfuhfEuzITVu9Vexfn8OawWS/pGEGz6CpaumtP2uxCpxCpujrtoM8ldIo3ccLnaG7UEZHNG2raU09EBZ73SKlUV0pEoyP27vftJCL3gvfQlx4UNioAiAoKQgDYZE69eOZn978qdAqRMm9rGZ8Q3RknkdCZKiYxK2UVJaVKuzSFsatMMpmE10vTObHf45crFAKarEatIKKTi/b2bXVEFAjG9TsbVm6hsIdzFXVVRPT8va8ce3ZQ2LQAIB4oCAFgM4mF4t/75A94rFtZ5CpFQa/P4bYAFo6TaKw1CYxYXEXtjhpvCGNX2bq21834A0KneEsckUhDl56IeJ6mUpFKQykRjc+6rPstRBQNJ+r6u1deecu1hyL+qIBRAUA8UBACwGZy+3WHvcuiuBJahLqvHHAub45l68azXtYxNY+9U7b27abTNnTSspkbqk64N9PY1UGXo6e3joiiybSqtUwi4YhozBkwNOmIaHLM2XvFBUQUcAZvufaQsFEBQCRQEALApvHq42+89uNfC51CpFr2WEbHxH7GSSjVzfoxOz5HYCuvVM9lsFPEplTKomW5XKEgdJC352zUa6wpJ6JJh69jbyMRpdJZRXPVyi0U866EoamGiN546jj+RQUAQkEIAJtFwBk8+Pn7hE4hUqpSVaqkvJDfZMvWjSGVSiTmilQaY1fZdN36YAwzJ9nae2uWw5tv7Goym80aJHKFlIhO2p0NbQYimrH5rJd1EFEynq7qa+c4jtBzAQBEhIIQADYLnHg5D8sH+t0OjEth67jcOr+EJS+bdU/DmUVsLLNZ2qqPOzfr2FVbMGTtMxJRvlCIlJNSISOiszaP0VJDRDOTrr6rBginsgGAiFAQAsCm8Nw9L2Mm3mosF3aPjWymM04bqa6j5iyODq6iQl8yHg4KnUKkNGqFQ5bY1HXSMedyh6WGiJZ8oeb+eiLKZvPZ6hKpQkpE0wsho8VEK3Ob7/u5sFEBQFgoCAFA7Fzznruvf0joFCJVqisLFOT4gJ9JrpRnDCVZjF1l4TgqtVREk2mhg4hUU7fBHY0JneJd4YmWuFh5qZKITi46mrtqiGjJEbTstxJROpVVtzVK5TIiOvSlB1343ASgiKEgBABR4wv8zZ+4KxHFGSe25kt2Bn2be9m6ftousSw5sAPGZh1oGltGDcBm7aw9sWmbRf+YNxav7qjkJFTgeYc0XapVE9HQjLN5p5mIbLOevg/vJaJENPndv/8+DiEDFC0UhAAgak/e/uyZ10aFTiFSXe/bOTayFZat66Gxr35oFldIHBtpAAAgAElEQVQpsOmN2mEfqkG28jLVQn7zDZJZzRmXq6fPRETecLyqW8dxVOB5F1co1ZUS0fCoq/293UQ0+sbEU3c8J3BWABAICkIAEK+lCfsDN/xI6BQiVV5d4YqiGZJNoZaHNbJCAZ20DBzHyRs1CYxdXYXRUumPJ4ROsZZOB90N9ZVENLLstg40ElEgGNftqOc4CV/ggwV5qb6MiO776mMLI4sCZwUAIaAgBACRyufyB64+mE5mhA4iUg3v7Q0H40KnEKnmiy1OT1joFCLVua9x0uETOoVIdffWDbq22sZyOpdLaHmlUkZEp91uU4uOiCbm3NbLLEQU9MeaL9lJRNl09sDVd+ay+JgJoOigIAQAkXrs/z45cXxG6BQi1ffB/onRrbZsXSstuxrPTGPsKpupqWrQ5RY6hUhVVWgmElvzhpLFUKitt4aIMrl8uJxXqOVENLzkM7bXENHYsL37/buIaHpw7vEbnxI2KgBsPBSEACBGM6fnH/vOT4VOIVK6BsOCC4Nk2DTlKjdXwNRVJplMkjLIM9mc0EHEiJNQRUtZJLVlx64ed9q7e+qIyBGINu2uI6JsNp+rOXcLhT2UrayrIqJHvv2TyRP4JA6guKAgBADRyaazB64+iM4lJk7C6bZb4rEtu2x9l0z7WnwBVMts7Xsb590BoVOIVE+vadi9xfdOx+L+akMZEZ20OSy76olo8Xe3UETDCWN/N6FXH6AooSAEANG5/4YfzQ9jtgFb34cGZqe2+LL1HWvb23J2Cp20bA2t+lPL6KRlqzaUnY14hU6x7mKZtLROLpdJiWgiGqqsLiWiM3Ouhm4TEU2OOXuv2ENEi+P2B7/2Y2GjAsBGQkEIAOIy+sbEk7c9K3QKkTJ2mKYWQkKnEKkyXckirllfhVIlD5XzOVw0xyLhOIVJlcgUxZ7YjC/Qud1IRLFUuqy9guMony+ES6WqEgURLbjjusZqIvrJLc+c/cWYwFkBYKOgIAQAEUnF0weuuRP3IzNJ5TJ1izmTwm0BbIZd5nBkS90WsIaa9pjs/q1zt97a6tlhmvRu/e3B3zvmsre1GIhoZMnd0W8mIrc32nRhOxElYmn9NgvHcXyBv+njdyaiSYGzAsCGQEEIACJy9/UPOmZcQqcQqd4PDdjmimjZ+rZYL2ofxW/OKpq7jSdtdqFTiJTJWDHoL67fnALPe5QptUpORCN+n96oJaIz087mnWYimpl09V01QESuec89//awsFEBYGOgIAQAsTj10tlnD78sdAqRqu9tHp9CNchWUaudDkaFTiFSmhKFU5LC2FUmqURSqJakc0U3dtUZiTb1GIgokc5y9SqZTFrgeRdXKNWVEtHUfLC+t5mInj388vHnBgXOCgDrDwUhAIhCLBT/3ifv4rFuZZGrFBKjAWNXmThOUt5TG4vj9CCbaafRE8bYVbbunXUzviIdu3rS6ejpqSOiWXegbW8DEQWCcf3Oeo6TZNI5qtYrS1U8z99y7aEoxvYCbHUoCAFAFO74x3u9S1vzSuh3r/uDA3ZbkS5b35T1UsvknEfoFCLVts10yobJomyN5qoT7qJ+c4bjXmNNORGdXHS09NQS0fis23qphYicy8HOD/QTkd8RPPhP9wmbEwDWGwpCABDeG0ePv/qjXwmdQqSaL7CMjhfXGae3Tm+uGncFhU4hUmVa9XwWeztsCrk0Xl7IFYp6flUik6UamVwmLfC8jU9oqzRENLzsM3XUEtHIiKPjol4i+vljv/rFE78WOCsArCcUhAAgsLA3cttnDgudQqSUpap0STnGrjJJpFJ5iy6JG7RXYeg1BGMYu8rWsc1oC+IGF5rxB6zbjUQUjCbLrJUcR9lsPlGlkqsVPM+HeHlJVSkRff9z9wZceLsAtiwUhAAgsNuuOxzyhIVOIVLWD+xxO7EOY7NeZplb9AmdQqQ6djcMLTqFTiFSrS364y6MXT3nmHPZaq0lorFlj3VvIxE53OG2i9uIyOeJtF66k4jCvuitn75b2JwAsH5QEAKAkH52/89/9eQxoVOIVPt7u0dHsKZnq2k1nLVh7Cpbhb5kIopOWjaNWuFTZgqYX/U7PNFcPlyh1RDRoMttatET0dC0q2mHmYhGhx1d79tBRL995uQLD7wqbFQAWCcoCAFAMN5l/93XPyR0CpHSVJSESYmxq0wymYzqtFmMXWXhOCqzVESTGLvK1txtcEQiQqcQl2AiqW0plXBcNpePakmhkBV43icndZmKiJyRvNZYSUR3/fMDbnwKA7AVoSAEAGHwBf7APxyMheJCBxGp1st2+b1YtrK1X25ZsGMmLZu13zy6jLGrbNaO2uNONIsyjHk8PTtMRLTsD7f01xOR1xc1v6eFiCKhhGlvLxElIsn//Pvv8wV8SgWw1aAgBABhHP3+80OvjgidQqQ6L90+NlLUA/HPw9RpPDvnFjqFSOlryoYDKJXZSjTKRYoKnUK8Tngd5oYqIjq56GjuqiGioSlna38zEU2OOno+sJuIhn85fvTg88LmBIA1h4IQAASwNOm476uPCp1CpMoN5e4EPoNnU6jliQplLoexqwwcx8mbyxIpjF1lq+/UeWNoSVhVrlCIlxfkCmmB593yrEqjICJ7NltWpSEimzepa6wmonv//ZGF0SWBswLAmkJBCAAbLZ/LH7j6YBq3BazCfOH2cBDLVrbmi9sdbsykZevcZ5504IgXW3d33aALu+5s7Q26XT11RLQYCln7jETkCkYbdhuJKBiKG3aZiSgRS1f1tkukkkwqe+Dqgzmc4AXYQlAQAsBGe/y7RyeOTQudQqR6rrhgfBTLVrbmneYz0xi7ylbbUDnowtFBtsoKzWQKnbRsKoU8pE4eDy+11+voj26hOLXg6NjdQESjs27rpVYimpt29314HxFNn5p74sDTgqYGgLWEghAANtTs0MIj3/6J0ClEStdgWHTjJnE2dbnaI8XUVTapTJKvVWSyOaGDiFRVS1k4hbGrbFarbjkezhUKXlWsXKNcuYWiskJDRGORoL6mjIhGHf7atmoiGpvwNO1sI6KHv3VkdmhB0OAAsGZQEALAxsmmsweuPpjLYNnKwHGcYVdHPIZlK1vDvmafPyZ0CpFqHzDPugNCpxCpvm2ms25MIWLrbDIc9587EOhOxhpatUQUTCQrWkolHBdPpTmzRiaTZDK5bE2JQi3P5wvZykqlRpnL5G786O2ZVFbQ+ACwNlAQAsDGefBrP547axM6hUj1XTUwPe4SOoVIte1tOTOFZlG2+lb9oB1vDlu1vvRMBOcq2crUSqcs8seb7oMB+06rkYhG3OduoZh1B9r3molo2RlqudhCRK7lYOcV/URkG1t+6BtPCBEcANYYCkIA2CBjv5k68r1nhE4hUtUtxlkbZqWwlepKl9DvtwqZQhrVcrk8xq4ySDhOXa9OZDC/iq2pXetO/umu+5mks95QTkQnvI7mJh0RnVh0tHTXEtHQtKN1TxMRjYw62/Z1EtETNz09/PrYBscGgDWHghAANkI6kT5w9cEClq0snIQr72xOYuzqKmp2NYTCOFrJ1j7QsOQLCZ1CpHp21I15sT3I1tNWfdJv//OvJ3LZvK6glMtyhUJAndWoFQWeX6JUqVbN8+TM50oqNHyBj8rUGm0JX+Bv+vhdyVhq4/MDwBpCQQgAG+Huf33IjvmQq9j2l/vmZzAfkq3jwvaRGXTSsjV2VJ+wYSYtm9GoPe3H0UE2bYlqrrDqodOFaLCr00BEjkikoVtHRP5o3NCrJyJ/MF430EREPnek7X27icg557733x/ZmNgAsE5QEALAuht8+ex/H3pJ6BQiZeoyT85gID5bRW35bDgqdAqRUqjlXlWugLmrLFKJhDdIUznMr2JraC0PppPnecEx/2J3i4GIBp3Ont46Ijqz6OrY1UBEZ6ecln2tRDQ6bLfu7yOiZ37w4vHnT29EbgBYHygIAWB9xcOJ733yB7gugEmmkCrMdZk0lq0MHCfR9tRFMXZ1FY0X1LmCqJbZunfUzfoxdpVth9V4itUs+sd4opmCv6ayhIhG4j69rpSIxqPBSkMZEc3HE1pDKRF501yZQcvz/K3XHooF4+ufHQDWBQpCAFhf3//8fZ5Fn9ApRKrnqvcszuPNYevYb5mYQ8sfW0uvcRDNoqswN1Sd8ODNYauuKB1OvaUe7Eg2XWZSSjguns6UNmo4CcVS6ZL2co6jSDRVtb2eiEL+eMN7txGRzx6484v3r290AFg3KAgBYB298dTxVx55XegUItW0u31sDKfj2PTmqgl3UOgUIlWqVS8WEth0Z5IrpAltIVfA/CoGCcdp6xXx7FudXzUadO/oqiWiUbend1s9EY0te6z9jUQ0Nuu2XmIhoskxR88HdhPRyw+//sZTx9crOgCsJxSEALBewt7I7Z89LHQKkVKWqrLlFXmMXWWScqo2Pcaurqa6zxCIYuwqm7XPaAti7Crbjk7jSPDt7bofjyy3maqI6JTfaa6vJKLTXk9dcxURjXtCNS16IlpwJYwWExHd+ulDQTeuzwHYfFAQAsB6ufXTd2NxsBrr/9rjsmMHjK3zUuv0Am4LYOvY1TBkw8BettZm/QnXm5yOK1omfflg7G2/OblCIViSLFEpMvl8pDyvUcsz2Vy8UqpUylKpbM5YJlfKksmMutUslcvCvujt1+FDQIDNBwUhAKyLFx987Y2jaB9ia3tP1+gw1vRsta2GkSWcq2Sr0JVMxvE5AptaJferM3m00rJIJBJ5NZfKv5P5VY54pNlSQUT2cKS5u5qIlnyhpv56Ilp2htr2W4jINuft+9AAEb1x9PhLD/1iLaMDwPpDQQgAa89nD/zgX34odAqR0lSURDgVxq4yyWQyvk6byWDsKlt5R2UkgbGrbC291fZwROgUIrWjq3Yy/M4/Zznlt2/vqCWi4057d08dEZ1YsLfvMBHR6Wln654mIhqb8jbubCOiO79wPwaJAWwuKAgBYI3xPH/Lp36AEeSrabt8l9+LZSub5fKOBTtuZWSz9ptHljF2lc3SXn3CgWZRtqbaihPh5Xf5Q4ZTLpO+nIjG4v5qQxkRTSXCupoynid7LldWpcll8/nKSoVaEQ8nbv7EXfjMC2AT2aCCMJfLnThx4umnn3711Ve93rU5GfL8888//vjjyeT5blYFgI33X3e+cOJnQ0KnEKnOS7eNDmMgPpvJWjs0i7GrbPqaspEgSmW20hKVXZJA/cGkkEqzFblsIf8uf04il5UYSC6TxjJpiVEulUqiybSiuYzjuGAoXnNBExE5l4NdV/QT0elXhp+564V3Hx4ANsZGFIQHDx40mUx79uz5y7/8y0svvbSuru5v/uZv3mVZePTo0SuuuOLv/u7v/H78HySAiDjn3Pd99VGhU4hUuaHcjY+wViFXylM6NcauMnEcp2gpTaQwdpWt3lrpicWETiFSPd01c9G1OXc6E/H3dtUQ0aw/0L2jjogmHd7OfWYiGp52Wt7TRkQjY67WvVYiOvzlR5ancFIaYHNY94Lwi1/84uc//3mPx0NEer1eIpHkcrkjR47s2bPnHdeEdrv9E5/4xJrGBIA1wBf4m665MxlLCR1EpBou2h4OoJOWrXW/ZdmJ2wLYrHsbJ+w4lMXW1WU85ULhwWYx6Y4HFtfwB/7Wb+ts1hPRMZe9rdVARIMuT11TFRHNRePa6jK+wMcVGk25Jp1I33TNwQI+4gHYDNa3IHzuueduv/12Itq3b9/Zs2e9Xq/b7f7GN75BRAsLC5/+9Kffwc8sFAof/ehHA4HAGmcFgHft8f88OvzLcaFTiFTPB3ZPjKBZlK1xW/2Zaazp2WoaKofcODrIVqHVTGcwdpVNpZAFS5JrO3aVJ7JxocpSVYHnXfKkRqPIZHMZg1wuk0ZjKW1fHcdJvK5I+19cQERjv5l64qb/WsM/HQDWyfoWhN/85jeJyGw2Hz16tLe3l4j0ev1//Md/fPaznyWio0ePjoyMvN2feeONN7722mscx615WgB4NxZGlx751hGhU4hUpUm35MdwSDaVRhlUSQoYQcEilUkKRmU6i7GrbPrW8lASLQlsnR365fja3wQbTCerm0o4Inc01tRlIKI5d6BtbwMRTc55Oi5uI6LRYUfHxb1E9ODXfzx31rbmGQBgba1jQWiz2Y4dO0ZEX/rSlwwGwx9/6ytf+QoR8Tx/5MjbWz4eO3bs61//ulwu/8IXvrCGUQHgXcplcjd+9I5MKit0EDHiOK5md1csguODbI0Xtbq9UaFTiJSl3zzrwlF5tt4+0xk3phCxdTYZjgWW1umHnw26dnTVEdEJp72rs5aITi45G9oMRDTpDesbKnmeD+RlpfqyXCb3n/9wMIeLZADEbR0Lwpdeemnl4corr/yTb9XX12/fvp2IXn755bf+AyORyEc+8pFcLvftb397165da5UTAN69h77xxNyZBaFTiFTvlf3TE+iHZGvd3YRm0dWYWnSnHHhz2HRVJaMxnKtkK1UpnLLIuu65n4otN9VWENFkOqjXleYLhUBJXlOiSCQz0hadTCYLeKPmC3cQ0dyZhYe+ieYRAFFbx4JwbGyMiLRabUtLy59/d//+/UQ0MTHx1n/gddddNzc3t3///uuvv36tQgLAuzf+WxwUWVV1i3FuCbcOspVVljhpbY84bR0yhTRRKclhJgcLJ6HyppJoGm3YbM2WSndyfceuZvL5VEVWpZBG0mlNg4qTcs5gtHZHLREtLPktl3UQ0eSYo+9D/UT0xIGnx387ta55AODdWMeCcG5ujojMZjPzu42NjUQUCARCobc0Vu6hhx567LHHqqqqHn74YYlkg65PBIA3lU6kD1x9MJ97t5dcbUmchNN2tSSTuC2ArWaP2R/AbQFsbf0NNi/GrrL1bqsfcXuETiFSPa3VJ/3v9hr6t8IWDVmtBiIa9/r6tpuIaGjRab2ggYhOzzibd5qJaHYpWtNel8/lv/uxOzCAGkC0ZOv3oyORCBFVVFQwv/v7r4fD4dVe83szMzOf+9zniOiee+4xmUzvIMxbmWgqqsmloVAon8+r1WqpVCp0FoDzuf/ff4TLplbT/cE941OYD8nW0t80PI0DYGwN7fqTS5hJy1ZjKB30498cNq1GOcdv3GLmmH9pR7NxbN53zOOwmCsXF4PDQV9NbWnAFXPwOY1WkwgnqtvMkjmXY9Z915fuv+bG/2fDsgG8A/l8PhQKSaVStVotdJYNtY4FYSKRICKVSsX87u/f6Hj8TW7lymazH/nIR6LR6Kc+9am/+qu/emdhDh8+/KaviYnpWtt4PF4oFGKxGApCELOJX8+8eN8vhE4hUoa22pkF7PCwlek0C3FM2WFTqGReZbaQRistg1QiKRgk6TBaEtgMDcrR2IZOIZoq+HRlan806VEnNRp5IpHN1aqlXkkonLTsMCZem12c81nev3Pi+ZMv3Pta53vbei62bmQ8gLcln88nEgmJRCKqomADrGNBKJPJiCifZ/+rnc2em0b4phdI3HDDDSdOnOjo6LjtttvecZi77777PN9d2T+sqqp6xz9/zaVSqXw+X1VVhYIQRCsRSf7wy0/wOAHGIpXLNK3mwIKI+g5EpXJbvWfBK3QKkTLvMg4uYe+UzdpbfdyHN4etr736RMy+wX9oPJetr9eGJlL+ZKrPUj075FkORHf310/9enFqMdC7t2XmN3MLSzFTV4N9bOmhr/zk9t9+u6RCs8EhAd6ifD6fSqWkUqmoioINsI4FYUlJCRGlUuyW8d9/vbS09Dw/5JVXXrnpppvkcvmjjz6q0bzzf0Guvfba83x3pSA8f5INVlJSks/nS0tLURCCaP3g8w96lzAQn633qr3DI+hqY+vc3zG4gANgbK29xtPLKHjYGuorTwfxOQKbXlsymRVm7OpkxLevx3xq2HnW6xnoMw2ftQ/aXd0d1bZJz0I8WWnUBp1hWZNJNuvyO4IP/ceRf73/HwXJCfCm8vl8SUmJVCoVVVGwAdaxIFy5e9DtZp+fcblcRMRxnE6nO88P+d73vsfzfG9v70svvfT7eyyIaGhoaOXhrrvuKi8vJ6IvfelLcrl8rcIDwPn95r9Ovvjga0KnECnz9tbxCRQ8bLr6ygk3OmnZNKWKJT6JTXcmhVyaquCzQTSLMnBEBrPaHhDsb9Zvg0td9TXTy/4zEY+pptzpjvjUebVGEY2l6rprQ67o8oKv78qB0z/95Ys/fG3gg7su/N8DQkUFgD+3jgVhR0cHES0tLWWz2T8v1ebn54mooaHh/Pt+hUKBiAYHBwcHB5kvuPHGG1cePve5z6EgBNgYYV/0ts+crw27mMlVCl6vyy2hWZRFyqnaDQkbNnnYjDuMp22YJcNm3Wb8jXMjhmduRjs6jb8JLAoYoMDzHnWsTK2MJtOSWq3UK3EGIrt31029bpuc8+y4uH3itcnRcXfTzraFwZnbP3tP74WdFdVaAQMDwB9bx4Jw5e74TCZz+vTpPXv2/Ml3jx07RkQ7d+48/w/p6+tjNp263e6VOwwHBgaUSiURobUSYMPc8Y/3BFzY5GHrvnJgeBhrerau/dZTc+iHZGvfYTqFanAVzc26466NPh23WdTpys4khG9Q9yRjO9tMo8OeKZ9v3476M6eWT9kcO/qMM2ed455gtbnKuxjIVlYqNcqwN3LbZw5//cl/FToyAJyzjgXh/v371Wp1Mpl84okn/qQgHB8fHxkZIaKrrrrq/D/kwIEDzK8/8sgjH/vYx4joyJEj9fX1axQZAN7cK4/+8vUjvxE6hUi17e0cGRV+ZSZOta2GkWVhzjiJX3llyUwqInQKkVKr5EF1Np9BKy2DlOOUtdJEKCt0ECKiwYC9v6NhaNJ1wutsq69cXA4uFpKl5apYJKVsM5A96FoO9l7RP/ST1984evyVR3952f97odCRAYBoXS+mV6vVV199NREdOnRo5ZL6FTzPf/nLXyYig8Hw13/913/8nzzxxBOHDh06dOhQMolx5ABi5HcE7/zC/UKnEClVqSqmLOELWLYySKUSMmnTmZzQQURK110VjuPabrbWnhp7GNUy2/Zu40RIRD3YI2l3nb4sm89Hy/NqldwXiRv6DEQ0veDtvKyTiEZGnNb9fUR08PP3YSwZgEisY0FIRDfccIPBYIjH45dccsltt9125syZJ5544sorr3zmmWeI6Dvf+c6fzPD55je/ed1111133XXhcHhdgwHAO8Dz/M2fuCsaKK7Led46ywf6vU500rJZLrPOL2Pxx2btN59ZRCctm6W9+jiODq6ioVp7KiKuTtp4NiOr5uQy6XI40tJTTURnFl3WATMRnZl3N/SaeJ73pDhtTUUsFL/l2kO4uAhADNa3IKyrqzt69KjBYFhaWvrnf/7n7du3/+3f/u1zzz3HcdwNN9zwyU9+cl3/dABYW8/e/dLJF4aETiFS7Rf1jI3gABibqaP27AJ74jRUGsrGghhBxKbRKBzSOCoGJplEQjo+nRfdrvt02N/XWU1Ex5327u46Ihryeo2NVfl8IayWacpV4UDctK+XiE6+MPTs4ZcFjgsA63qGcMW+ffuGh4cPHjz4wgsvOByO8vLyXbt2feYzn3nPe97z5y/+7Gc/6/F46C1cCdjX1/e1r32NiFbunACA9eaa99zz5UeETiFSJVVlgawUH3UzKVSylF6dc6aFDiJGHEel7eW2ZVxSwtbYrT/pwOcsbNu6a34t6GTR8/htcKmv0Thu844n/dX6Uo8vltRLFC6Z2xfp3dsy88LY5Jiz54oLRp47cff1D+64tMfUbhQ6MkBR47CCISKO44hIVG+F3W7P5/MmkwnTU0EM+AJ//WVfP/uLMaGDiFTPX100PoplK1vnX3QPTuPNYevc23jMjjeHzdpZeyqCTlq2lrrKaakvVygIHWRVVSqN0i0NxFIdBoN92Mfn+QuaTJOvLxDRtjrd1K9mSkqVCp/XZ/N07+u45RfflEjXt2cN4K3I5/N2u10qlZpMJqGz/MEG1Cn46wcAb+7I955BNbia7r/YhWpwNY199UMzGLvKVlNfccaLvUG2inL1fA7TBNhUCmmsLC3mapCIAqmEobmUI5r0enu3m4jopM3etq2OiOYi8UqjNh5LV/W1cxw3+uvJn97630LnBShqKAgB4E0sjtsf/NrjQqcQqco6nT2YETqFSCk1iqBKUhBT84V4SGUSvk6VwtjVVdRYKgMJzBtn6+wwLMU2QbV8NuDc0VVHRMfc9pYWA8/TfDZeplVHY6nK3jqO42an3H1XDRDRA//n8flhkba/AhQDFIQAcD75XP7A1QczKVFcciVCtXu6omEsW9kaL2pz+6JCpxApS3/DjAtjV9l6eusGndh1Z7M26o8FloRO8Vadii031mgLPO9RJEo0ymAssXILxeiMq+PidiKaXggZLaZsOnvg6oM5fD4CIBAUhABwPo986yeTJ2aETiFSfR8amBpHPyRby66ms9N4c9hMLbpBJ8ausumrSsbiKJXZSlQKtyK6ifbcM/l8ujKnUkjd0Xhjl46IhmzOjt0NRDTuCRnMunQqq2lrlEglM6fnH/3OT4XOC1CkUBACwKqmB+ce/+5TQqcQKUNzzewytr/YSrRqN5dDryiTTCFNVEqyubzQQcSIk1BpoyaaxkxatjZLlSuxyW6CtUVDnVYDEZ1wOrq7jUQ0HglWVpemUll5axVJuYVZT9+H9xLRj77z1MRxfP4IIAAUhADAlk5mvvuxO3JZLFsZOAlX0d2WSmDZymYcaPYF4kKnEKn2/gabNyR0CpHq7asf9XiFTiFSPS3Vx/2bpln0jx3zL3U3GYhoOhPSlqtjqXRpewXH0azN13lJBxFNTPsbepvyufxN1xxMJ3EqG2CjoSAEALb7/7/HFsftQqcQqW0f3js3jZY/tvaBlmE0i66i0VJ9Ygmn49hq9GVnwvhrxaYtUS1wQaFTvEM80bwkqCvXBBNJXVs5J6HRJZg4vR8AACAASURBVLd1oJGIhpd9dR012UyOaqqVGuXiuP2BG34kdF6AooOCEAAYzv5i7Kk7nhM6hUgZrfWTswGhU4iUVl+6mE4JnUKklCq5X5MvFNBKyyDhOEW9KpHB/Cq2hpYyfyohdIp3LphO6s1qjmjY7e7dVk9Ep91uU5Mum82ndGq5Wu5YCliv6CeiJ29/FrccAWwwFIQA8KcS0eSBaw7yWLaySOUyVVNDJo1peGz6XeYQxq6uovECkyMQETqFSPXuME140SzKtt1Seyqw6TeWzwZdO7vqiOiU32mur8zk8rEqiVIlt7vCLRdbiGh0xNlxUS9f4A9cczARxT8jABsHBSEA/KlD//JD9wJWZmy9Vw0szuPNYbNeYhlBs+gqWnuMpxbRg81WV6c95XcJnUKkdOWaiaxH6BRr42Rsubm2IpPPx7W8Uilb8oUa99QR0dCUo32ghed5f05api93L3gPfelBocMCFBEUhADwP5x68czP7n9V6BQiZd7WMj6BapCtqq5i0oftL7aSUuWyJImxq0wymYTXS9M57LozcET6Rk04s0XmV2Xy+Vh5Rq2ULYZCbb01RHRywdG2vY6IbKmU1lAa9MeaLt5BRM/f+8qxZwcFjgtQNFAQAsAfxELx733yBzzWrSxylYKvNuRwWwALx0k0HdUJjF1dhXFHrTeEsatsndvqZvw4lMu2o9N4NrCldt2X4+GODj0RHXfaO7tqiGgmFak0lIUjSd2OBiIaG7F3v38nEd1y7aGIH1f7AGwEFIQA8Ae3X3fYu4wrodm6rxxwLOLNYbNe1jFtw94pW/sO06Bt0x8AWyfNTbqTHrw5bLWVZWeSW7CT9ph/qc9SS0STqaCuqiSSSJe0lXMcjc64Oi62EJE9lKusqwo4g7dce0josABFAQUhAJzz6uNvvPbjXwudQqRa9lhGx7bgymxNGMy6cSd2eNhKtaq5NHY52JRKWUiTzRUKQgcRIwnHlZpkiezWvJRvIuOuriiJpjMlZrWE48bsHuuAmYim/JGquopoOGHs7yaiN546jv9XAtgAKAgBgIgo4Awe/Px9QqcQKVWpKlVSXshj2coglUqkzZVJ3CW9Cn2PIRjDvEQ2S2/tchjnTtl2dNaOBrfILJk/F81mSk0KKceNe309O0xEdNbnqzZpE4l0SWcNx0kmx5y9H9xD6FsB2BAoCAGACKc1zsvygX63IyR0CpHquNw6v4TlGpv1goazS9hYZrO0VR93Yewqm7laeyq2xTtpx0Oe7d21RDTodzWYKpPpLNWrJRJuat5jvdRCRPPOuKGpBifbATYACkIAoOfueRnz3FZjubB7bGSLr8zesbqOmrPzW3YT412q0JeMR4JCpxApjVrhkCUKWOWzSCQSTk/p/NYfu3o8vNxSV5nO5TJVnFwmnXH6O/Y2EtGYI2Bo0iXjaW13KyfhTr145mf3/VzosABbGQpCgGLnXvDeff1DQqcQqVJdWaAgx4fTTHKlPGMoyWLsKgvHUamlIprE2FW2pm6DOxoTOoVI7eiumQr7hE6xEXKFQrw8o1JI5wKBzu1GIjrtdJladKl0VmqulMlk8zOebR/eS0SHvvQgbscFWD8oCAGKGl/gb/r4nYkozjixNV+yM+jDspWt7RLLkgM7YGxNO2rHlrF3ymbtrD3hRLMoW7Ox8nhoWegUG2cxGrJaDUR0zGW3tFVncvlwOak0ivllv+XyDiKamAmYt7UkoskbP3YHDnIDrBMUhABF7cnbnz3z2qjQKUSq6307x0awbGVr7Ksfmt1S16OtoUpDyWQYh07ZystUC3kMkmFTSKWp8qIbu3rMv9TXXlvg+WVJvKxU5QhEzLuMRHR62tm0w5zN5Ap6nUKtGH1j4qk7nhM6LMDWhIIQoHgtTdgfuOFHQqcQqfKaCkd465/heWdUGmVILS0U0EnLwEk4qVmdyqKTls1oqfTHE0KnEKme7uqFWDHuuk9kPdUVpd54vLajkohO2hxtO+oKPO+WFMqqNM7lYOcHB4jovq8+tjCyKHRYgC0IBSFAkcrn8geuPpjGbQGrMO3tiYaxbGVruqjN5cUmD5t1b+OcNyx0CpHq7q0bdGFjma29XncssCR0CmFEs+kyk1zKcUMuZ982ExFNxcNV1aWBYLx6dyMRjY462/Z1ZtPZA1ffmcOnLQBrDQUhQJF67P8+OXF8RugUItX7wT1T47gtgK15p3loGmNX2YyNVaed+M1h01VqJhK4oYRNpZAHNUU9dnUs5NnebSSiwZC7rq4ilsooW8okEm5kxtVxYTtf4KMytaZcMz049/iNTwkdFmCrQUEIUIxmTs8/9p2fCp1CpHQNBpsrLnQKkdJo1W5JMa9az0cmk6YNsgzGrrJwEtI2l0VSGLvK1mHV2ePFvut+PLzUXq9L53KZSpIrZJMO38otFLPhaJVR63NH2t+/m4ge+fZPJk/g00yAtYSCEKDoZNPZA1cfRNcNE8dxhp0d8RiWrWymvc3+AKplNste84KnGA+AvRW9vaZht1voFCLV01xzwl+kzaJ/LFcoeFXRUrXCFgpZ+2qJ6LTTVddcFY2lS7pqOU4yMuyw7u/DeQeANYeCEKDo3H/Dj+aHcS6fre+qgekJtPyxte1tOTuFA2BsDa36k8vopGWrNpSdieASObbyEqVNGsSm+wp3Mt7UpiWiY85li6Umk8undDKZTDo177Hubycib5orM2gXx+0Pfu3HQocF2DpQEAIUl9E3Jp687VmhU4iUscM0tYDbAtjKdCWLuGZ9FUqVPFTO53BJGouE4xQmVSKD/Ry2xlatL4ld9z84FXBs76jliexcXKNRLHiC7QMNRDTmClY36UP+uPnCPiL6yS3PnP3FmNBhAbYIFIQARSQVTx+45k7c7csklcvULeZMKit0EJEy7DKHIxi7yta0x2T3F/sBsNX07DBNerE9yLatvfakH5ed/qnRjKemssQTizV26Yno5LLT3G5IpbLSpkqJVDox6uz+i118gb/p43cmokmhwwJsBSgIAYrI3f/6kGMG/ZBsvR8asM1h2cpmvah9FL85q2juNp60YU3PZjJWDPrxm8NWVaaezHmETiFGsUy63KSUcNxJp6Ory5gvFIKlBaVKPrfos15qISJ7MKOr17vmPfd8+RGhwwJsBSgIAYrFqZfOPnv3S0KnEKmGbc3jU6gG2SpqtdPBqNApREpTonBIkxi7yiSVSPIGSTqXEzqISFU3acIZtGGzjQTdO7qNRDSZCuh1pXZ/xHxBHRGdsXkauk3RcLJqe4dEKnn27peOP39a6LAAmx4KQoCiEAvGb/74nTzWrSxylYKrMWDsKhPHSbS9xlgcy1Y2006jN4QDYGzdO+tm/QGhU4jUjk7jmQD2Ttnqy0uI6Hh4qc1UFUmn1Q1qTsqdsjk6djXkcoVwqUxVopybdvddtZfn+VuvPRQL4u8gwLuCghCgKHz/8/f67FiZsXV/sN9uw5vDZt1vmZjFbQFsbdtMp2yYLMrWaK464cabw1ZTVXI2iWqQrVyp0FZF39NoyBUKoZJkiUox4fX2bTcR0Xg0qKspc3sj5gtbiWhixl/f0+izBw7+031CpwbY3FAQAmx9bxw9/vPHfiV0CpFqvqB9dBwFD5vBXDXmQqnMVqZVz2djQqcQKYVcGi8v5AqYX8Ug4bhSozKRxdhVtl2NJb50xMUv1ZeX2OORNkslER3zOJqb9LFUWt5cKpFwZ6ac7ftas5mcrN4oU8peefSXrx/5jdDBATYxFIQAW1zYG7ntM4eFTiFSylJVulSLsatMnFQia9alMHZ1FfpefTCGsatsHduMtiBucGHb3mUcC+FDKLaBev1YdJ6IYtmUuaYg4+i4f3m7pTZfKPjVaY1aMeXwWfc1EpEtkSzXly3N+3qu3EtEd/zjPQEXfuUA3iEUhABb3G3XHQ55wkKnECnr/+p3O7CGYOu8rGNuySd0CpHq2N1wZhEtf2ytLfrjLoxdZavXl5+O4s1h06lVAYnz9/9zNua8uNVARKNZT21lmTMSbejWEdGJZWdDmyEcSep2mIhobNzdtLs97Ive+um7hUoOsNmhIATYyl544NVfPXlM6BQiZbmwe3QYZ5zYaloNZ20Yu8pWoS+ZiAaFTiFSGrXco0wVML+KRSKRSKu5VB5jV9n6GpTh7P8YDzOWmPn/2bvT6DjOMm/4VdX7vu/danW31N3aF2+ys9jOAiGEkDPnMF/meYcEwjLMwADhhZOBZ4Aw70CchSVOYpyEkHUgCRBPnkBCCDshlrxoa+1bS73ve1d3VXe9H8xh8oRbduxIqpJ8/T7lWHLr745k31fd931dfWZtqV4TWnAeQZyJRru7rY1mM69ghEL+1GLcd9DbaDQplVokFb350qlf/vC3LGUHYHuDghCAHSsZSh/7whNsp+AoqVqWY0TQdhWJz+djVhUFbVdRcBxTeNXFKrRdRXN1GWMFuFqJNtBlmsvDrjvaVa2GqWLwbb/YZBhanNKIRfP5dH+XCcOwQDmt18lD6bx7yI5h2Fy6oLWqY6Fsx437MAx78LM/iMOTLAAuHhSEAOxMDMPc/zFoxr0uz3W708kC2yk4qv0670o4zXYKjvLvcwZCMEwcze8zD0fhPCSay6IZzoXYTsFRVrk00lxDfihVK/S3iDEMO5lda7frSvWavEWKE9ipYMTVaa5UarIOE44Tk4Fo24HOSqF670cfgid9AFwsKAgB2JlefOAXp14dZTsFR3Vc0z81ActWtJZu2+gC3I5D05sUExnY4UGTSUWrWJHtFBwl5PFqKgrariLhGOOxEiWKXO8TporBq13GBsOkpWWZSBBIJHp67U2GifFrUplwbjnhv8bLNJkiXyxVyUZ/PXni6CtbmR+AHQAKQgB2oNBc9LF/e5btFBylMqnjFXh+jCaUCIoKQbMJ7w8CjuN8l7xCwrQANHunLlmCIwlo3V3GZbh3uo5DHtNc8QJ7p6vUSotaHi0X2306DMNGc3GLSRnPlWyDFgzDpiIZQ6suFS+0Xb8Lw7BH73wmNBc9/wsCAN4KCkIAdpoG3bj7ww/UKnDHCc1xRW8eTtKuw3WwPRKHnrRo/gPOuQhsD6J1dVnPRKFFE1q7QzecQZ+HBK0axWJt+YKfVm3Uzbq6gOCdTK/1tZuqFIWZ+AI+73Qw4t1lJ2sU7lDzhLzARKTrvbtqldp//sN3aLgFDcA7BgUhADvNc0dOzJycZzsFR3XfuGc6AMtWNNdgy9g8PFZHMzs0Z2MwOw5No5bOknDpFE0s5GcllQbcakPhE4RZR9Ua72jYabCSONimxTBsjk4Z1bKFdKaj34Jh2EwxpzMqguGM9xo/hmFr6ZrOrp8/vfT8PSc2NTwAOwkUhADsKEtjK0/e9TzbKThKZ9evJqpsp+AoiUKc4EEvBjQen2iYhXUKpgWgad2KPAlHEtD8fn24DP2r0A669cvli7ixHCgtDFp0uTqpsAt5OH4yFva2G0tkTeiWEwQ+Oh9172otF0n9oB/H8Se//tz86aXNCw/ATgIFIQA7B1Wj7v7wUboOy1YEHMf1g/5ycd2+BZc5+xWeVBqmBaC1D7UsxjNsp+Co3j7beBz2TtE6Wg3DaTgsiubVqWarixf1W5oMUxUltBLRVDbR32VpMkwQK6pVktlIynfA2WSYKEPL1LKF2VjPTftoqnH3hx+ok+9o+xGAyxwUhADsHE987bml8bfPcQLn9N48tDALzTPR2va7x+fgJC2ao91wOgQnadGMevlYAca+oSkkoii/AJvuSEI+oVSXqeZFX/PL1Io9DiGOMcP5tTabNlOpatwKnMBOh6Mt7YZMrmzZ58QwbHGtYG63BqdCT9313CbEB2CngYIQgB1i6s9zz9/732yn4Cij27IYhF4paHKdfA3O+62DL+QVFFgDpgWgEDgusUsqdWi7itbaropXYdcd7WqXbq1yiS2aZoprB90mutnMyqoysXAykejutdGNZlraEEuFE/NR7xVtZLUu87YSPOLHR05M/GF6Y8MDsPNAQQjATlCr1O657WizActWBJzAlR2uahWWrWimXY5cvsJ2Co5qG3KspXJsp+Co7n7bVBK2B9H62s2n0jDsFK3bpAmUL+6w6Nss1pa8WmWkXGjzajAMG83GbRZ1NFt07rJgGLZULKuNipWFRO/N+5kmc89tD1ZLcFkAgPOBghCAneD4F5+CsUvr6bvlwPJCgu0UHOW7qn0SxtCvw+kzngrCSVo0i0V1NgPfOWgqmXi+ARNK0CQCPk+aazLv6vFlvUkr1BUJjzecDvV7zSRN03pcwOedWo14eizFEqnsteI4MbOQtnc7o0vxR+98ZqPyA7AjQUEIwLZ39vWJlx7+JdspOMrW2TK7AA3x0dRm5WK+yHYKjhJKBEkx3YS+qyg8gsCMPJKG/lVoNrc8W4OGxmgHXMoYmX33rxOqpq70aDAMC1AJk1a2lMl29FsYBgtjpFwhml1K+A62UXWaZzXzRYKXHnp15JXRd/9FAdipoCAEYHsr5yv3fvQhGBeAxBfyhC3Weg2WrQg4Tqi6rcUS3B5Ec+6xxrJQLaN1DVgXUtB2FW3AbzmbgfMaaINWbaB44TH079BEcXGv3VCq12QWIYHjw/GIy6lL5EvmfjOGYdOJnKFFFwqmu28aYhjm/o89XMqWN+pLA7DDQEEIwPb24L/+ILEKZ5PQum++YnUZ3hw03+H2mSWYFoDW1ms5vQKHRdGcLdqRBLw5aCaNbLIGP1ZoSpGwJkwx2IY9vmQwJkdE9FLRdC4x0GFpNJsFOS0U8s8EI+0DNpKkhB4dxsOnpuOtg22pcOahzz2+UV8agB0GCkIAtrE3Toy89uTv2E7BUS0D7ulpWJmh6R2a2Rj0SkGTKkRrDJz3QxMKeGVlk4a2qyg4hqntolIddt3R9jilqVphY18zT5W77AIcY06VQq1m9Wou395nwjBsgSxo9LKFYLLzGn+j0SSVaqlS+tqTv/v9C29ubAAAdgYoCAHYrvLJwrc/8X22U3CUSC5uaHQ0fdFDri4LPFzcbqiQ0HYVzdxvSubhaBmar88SzMKjBLTBTut4Bh5Coe1z6CeLK5vxyjPF0EGPqd5okGpKJOAPR8L+DnO+TIrbVDiOjwUTtk5rMppre88eDMMe+JdH88kNLkoB2AGgIARgu/rePz+SS8BsPbSOG/bFwhvQt2BH6rjGP78C0wLQfLsco0G4AIbmcelHYjBKAc2mV54pwZuDppOIc/gm/lgtkktevSpYzHV2GDAMW6RyWrV0NpLsONBC082igi+WiwMT4c7rBnKJ/P0fP7Z5SQDYpqAgBGBbgqMv59F2RefkJNxxQjN7jJNrcK8STa2TzZbhOQKaRCxIS+oN6F+FQhCEwIiTDehfhdbrEOeoTdx1rzdpubIk4fHeTK92e4y5Kil3yQgcPxWJ2dz6eLLYcqUHw7B4qakyqd84MfKrp36/eWEA2I6gIARg+4HL8echVckKhAjariLx+fymVVGvw7IVTenTFCpwAQzN3WMM5+GsHdpAp3k2D89Z0K5uNU5tzmHRtwpX0+emUCwxaZ1SOp1Idg/Y6EYzp2iKpMKxuYhnnyuXLbdc1Yth2NHPPAbN2AB4KygIAdhmoH32+bVdvzudgGkBaN7rfMEwTAtA8+9rmQzBBTA0b7txJALnIdFazeqRfIjtFBxllknCzdWt+VoTxcV9dn22RmocIgLHR5IRl1MXzRadu60YhoVqNYVeMTUR6b5hF4xrAuBtoCAEYJuBAbvn4T/cF5iAZSuazW8eXYyxnYKjdGblZDbNdgqOkstEIbwMa2ckIY9HqWmqCf2rEHCM8Vr5JYrcmi/HYEyWiBjlkkAuMdBpoZvNrIySiAWng2FPjyVXqJp2OzAMW02SOqfh7OsTLz38y60JBgD3QUEIwHYSXYo/euczbKfgKKVBmdiihcf2IxAJSJ2k0YBpAQg4jotcMmi7uh67X5ssw5EEtO4u01IR7p2iHfSYZktrW/kV81TFa8EJHB8urHls2nC+4Ok2MQy22qzKleKJuaj3qrZyqabv8+M4fvyLT4XmoIMUABgGBSEA2wjTZO657cFqCYoeNMfV/fkMLFvRPIe9oShMC0Dz73fOhOFCEVpnp+V0DBbNaO123XBmi85DbjutKnmwtrL1X3e+FDnkNtDNZlFGioW84WjI225KF8umc/MJs0WNRbUwG+29aW+tUrvntqNNeEwGABSEAGwjPz5yYuIP02yn4KjuG3bPQGfRdTj77GPzsKZHM9s1o3G4OoimUkgWKHiOgCYW8nLSKrRdRSJw3GpoVBrs7LrPVhc7jZq1cr7Db2QwbA0vKeWis8GId9BertTlnWYcJxbWiqZ269Sf556/979ZCQkAp0BBCMD2EJwKPXXXc2yn4CiNTbeWhuaQaGKpKCsmmrBsReHxiYZVVKOg7Sqa0avKVqpsp+CoTr8hVIZJsGiHPYbFMmsPoWimIZLnJDzeyfRqt8uYKpdtHToMw+YqOZVWOrec8B9sI6t1ubeV4BFPfO25pfEgW1EB4AgoCAHYBmiqcfeHH6iTFNtBuAjHcfOezlIBlq1oLVe3xZPQdhXNO9SyGINeMmg9vbbRGHQhQutwGt5Mb+ntuG3Eo1XMVZfYzRCpZq/0qBkMW+PllDLRqUikq9taqNSUfg2OY1OJnNGlX1lI9H5wP1Wj7v7wURqG8YDLGxSEAGwDT3/j+fnTLP/7ylm9N+2dm4bzkGhte13j83CSFs3m1p0Ow3cOmk4rC5TgXiWaXCyMCgqw547E5+E6Ta3eZL++Gi8u7nPoE9Wy3aPEMGy6kjbq5YFQwj/kJEkKs6t4At70bKp1sG1pbOXp/3iB7bwAsAkKQgC4bubk/I++9SLbKTjK6LYsrsH2F5pcI4s0aTgrisQX8ioagoZ+Eig4gSlbZcUaHMNG83g18WqJ7RQcddBtCFYSbKf4iyweMcolZ9ORgQ5zsVYT2iU4Dz8bj9tadcFwxnetn6YblEYjkop+9K0XZ07Os50XANZAQQgAp9VJ6t6PPtSgYcgVAk7gig5XtQrTAtDMe5zpDCxb0Tz7HMEktEtB6+mzT8a5sqbnmm6PcTgNY+jROgzqmfIi2yn+x1+nUIxXYna9cjaZ7Om31elGSUsIRfyz81HXgCMWyna8f6hBN47cerRWgYcg4DIFBSEAnPbIl54KTsHiA63vgwdWFmDZiua9sm1iAc5Dojn9ptNrcJIWzWpWnc3A1UE0lUy8jMHUQTSJgC9W5GmGW48vz02hqNAUbsAEfN5wIuJy6ddSOdc+e5NhkgJcohBPTkbaDnSuzUYe+7dn2c4LADugIASAu0Z/PXni6Ctsp+Aoi98+uwjtQNBURsVSAUYyoomlwpSIajbhKC0CjyAwE5+k2b8Axk12jyJDVthOwVFXuNSRKher5XNTKBYK6Z5OU6PZTItqUqnwVDDc1mdNpoqOKzxMk8kTIplW8eIDvzj16ijbeQFgARSEAHBUpVC996MPMXADDIUn4ItdjnoNlq1oml5bsUSynYKjWnZbo1m4d4rWPWCdT8FzFrQ+n/lMGjaW0QYsuskihw6LvhXNNASynFwoeDMd9LcaosWis1PPMNgKXZarJGNzEe8BTyZZ9FwzyDDM/R87VsrC0zRw2YGCEACOevCzP4gHk2yn4Kiem/evLsGbg9ZxyDu9BJPW0dzd5tPBMNspOKrFrhlJwjFjNL1KNlODA+poCqGAFicZjLuPL2NkdsilODeFQisXn4pGurotmWLF0KPHMCxYqSr0isBEuPO6gWQofewLT7CdF4CtBgUhAFz05kunfvnD37KdgqNa+j3TM7AyQ9PZNTMJGJaNJlWIwngNNt2RhAJeRc1QDW5dAOMIHMO0DnGBgo4jaHtb5QmywHaKC5goLA05dBmyYnbJMQybrWb0WtnYasy7y54rVA0DNgzDosWGyqR+9fHf/PGnJ9nOC8CWgoIQAM7Jp4rf/sT32U7BUQKxkNHraGi7isTDxe2GCgltV9Es/aZkHtquovn7LMEstF1FG+iwTGSh0Q7aXrthsrjMdop3JImHLQrp2Ux0wG/JkzVFqwwnsJliTmNQBBbj3qvaCrmK7UAPhmHf+afjOXiyBi4nUBACwDnf++dHMjFYmaF13TQUWcuwnYKjOg/7F+CY8TraB2xng3AeEs3Vqh+OwUlaNJNOPlaB7xw0rUSUJ7bNvcoSRXosOIHjE2TMqlVMxhNdPbYSWZO1KXEcW8gWNRbV7FS0+4bd+WThO588znZeALYOFIQAcMuvn/3j75//M9spOKptf8dkAFZmaGaPYSKUYjsFRyk1sgXOH2lji0QsyEnrDThKi8LDcamZX6EptoNwVL9DnKO2UwuW+WL4oNtQpupSC5+H4xOFpMmomAonfPtaypW6stOM48RqitQ5DX96cfjXz/6R7bwAbBEoCAHgkHQke/Qzj7GdgqOkSmlJKGFgWgAKj0dgdlW9Dm1X0XRd2nwZ2q6ieXqMoTxUy2j9neaZHOy6o13pNASKQbZTXLQFcsmrUwVyif4uS6Vex80CPp8YTSYtTu3McsJ/jbdcJLU9XpzAj37msXSEi4M0ANhwUBACwBUMw9x3+0PFDNxxQmt/z+5kDJataN5r/ctrMC0Azb+vZWwVLoChtbcZhyNwWBTNblCdKsKbg2aWSaLMGtspLkW9SctUJYmAP5xfa7PpFtOZzj5rnaKrep5QyJ8Ipaw+89J8vO+DB4qZ0n23w/AncFmAghAArnj5+K9GXoGRuGjtV3UHJuGwKJqtwzy+AnMm0HRGxVQWLp2iSaXCKL8Mq10kPkHgeqYObVdRcIzx2Xglarvuukeq6QMuFd1sZmUVmVh4Mh5u8xhWkznPkJ2iGqROLJAIZxfT9m7nyCujP3/kdbbzArDpoCAEgBNiy4lHvvgU2yk4SqaVZ2gePKZFEor5pFZC0022g3ARjGnapgAAIABJREFUjmPSNmWJhGkBaK2d+nhxO10A20p9XaaFAuy6ox10m2aKIbZTvCuTxcUDLfpIudDm1TQZJsKvKOWi4WDY3WMJx/Keg+31Gs23W/gi/rE7fhhZgCMGYIeDghAA9jFN5p6PPFgpVtkOwlGuQ4O5DCxb0TyHfKEo9KRF8w85AyEYWYnW2WkZiW6b/pBbzG3VDOe2d8Gzeewq2Qq1/a4O/q04FrIopMPpUL/XnCyVzT4tw2CrzYpcJRmbj7oGHWvLqe6b9pPl2pHbHmw24KEb2MmgIASAfS/c/9L476bYTsFRndf1Twdg2Yrm7LWNzsNJWjSTXT2WhGoQTaWULFDwHAFNLOSVFDW6CQUAAoHjTiNTpXfCrnuJIt1mjI9jASph0srOxqI9vbZMsWLsMTQZJsnHJQrx1HS8dbAt8KeZn37nZbbzArCJoCAEgGWr0+EnvvpjtlNwlMaqixTgDg+aWCrKSvlNOEmLwuMTjE1MQtvVdZi96mwFjiSgdfgMayUYSo52yGNYKO2cJ3QLpchBj7FUr0nNAh6OjxUSJoNydDXq2+VIpoqOKzyNRpPSaERS0Q++8l/LE6ts5wVgs0BBCACbGnTjyK1Ha9U620E4yry3s5iHZStay9WeeALarqJ5h1oWonABDK2nx3omChvLaH6n/mRmWzbP3AJtGuV8dYntFBtsprLo16tm8sn+LkuVosR2MUHg08WsxqAYm4t49rlioWzHjfuoGnXk1qM0BQ8owc4EBSEAbHr6P16YHVlgOwVH9d60b24alq1o7l2t43BYdB02t+5MBJpAoOm1skAZSmU0uVgUFxZhzx2JTxA6Xa3e3Gm77jTTECkKcqFgOL/msmqmEomefluJrCl9ahzHQrWaQq+YDETbDnQsnF1+9v/7Cdt5AdgUUBACwJr5M0s/+ubP2E7BUQaXaSkCIxnRZCpJHKfhrCgSX8iraAiKhgf5CDiBqVrlxdpOuAC2Gdq8mlgF/tpBO+TRrZR35nibGJkdalXSzWZVWRcLeKdSUbtNNbEa8+1tyRWqhgEb02SKfIlUJXv2P386MwzPcMEOBAUhAOyok9S3/p/vwfkTJJzA1d1t1TIsW9Es+10paLu6jrZ9jmAS2qWg9fTax+M7c03/7nW7TSfTcFgUrdOgniovsp1iE00Wl/ba9cFirrPDWG80aB2Pzycms2m9RRVYjPuuak/FC23X727QjXtuO1onKbbzArDBoCAEgB0/+PKzq9NhtlNwVO/N+5fmYNmK1j7knpiDw6JoTq/x1NrO6XixsUx6xVgefqzQVDLxCp5hOwVHCfmERFFqMDu57SqDMTkiYpCK30yvdrmNi+lMZ7+1QtZxu5jPJ+ayRZ1dE5gId7131+p0+PGvPMt2XgA2GBSEALBg/HdTP/0u9LBGs/jtc8tZtlNwlEovX62RbKfgKJFYkJE2mk04SotA4LjQLq7UYWcDze5WpMkK2yk46qBbG6qm2E6x6fJUpdPOxzBmlchp5OKTsbC3zbgYz7QNtVQqNVGbnuDxQpm6xqr7yXdehklRYIeBghCArUaWa/d97GEGlq0oPAFf7HLAgZz1aAfsOWi7ug7nHms4A21X0boHbTPJJNspOKrfaz6TgY1ltB6TZrK0kw+LvtVMMXTIY0pVy0aXnGGYEFFWyMWn1iItfuPiasp/nb9UqJr3dWIMduS2o5Ui/FUMdg4oCAHYag997vHIArRAROu5eWh1CZataP5D3qlFOPKH5u4yn16FNT2a1ao6k4K/c9B0SukMlWA7BUdJBXxCmr2shp0ukEtevWo8Ex3otCTLZbNP02SYmKAmlYvGlmO2DsvcVLT7/XvjK8nvf+FJtsMCsGGgIARgS53+5dgrj/2a7RQc1dLnnp6FahBNY1HPJmFYNppUIQoTtctp1XoRBAIeo+fX6J02LWBD4Bimd0rzdehfhbbfpYyRl1eLpnqTlitLEgH/TCnSYlSPxqK9fbZUvmIZMNF0s6oRCcWCpVDR1G79+SO/OvnyGbbzArAxoCAEYOuUcuX7bn+YgXUrikAsZIwGaLuKxsNlHcZKtc52Do6yDpiTeZgWgNbRZ1lIw+BBtIEOy3gGWjSh7bbqAsVltlOwIFxNX+FS1xp0XUMLBfzRfMJqVp0NRn277OFY3nOonazWFd5Wgkfc//FjhXSR7bwAbAAoCAHYOt/9p+PJEKzM0LpuGoqswpuD1nnYP78Ce6do7QO2MytwWBTN1aobjkE3YzSzRjFWhZO0aEqRsCJMMthl+vhyoriwz64PlrLdfkOVopoGgscjZss5lVY6Oh9rHXAsLyR6PjCUiWaPfvoxtsMCsAGgIARgi/zpZ8O//fEbbKfgKPdeb2AKVmZoRpd+MrTzW/xdGoVKslSHJ/RoIhE/J6UacCQBhcBxqZVfoWDXHW13qzRdu6xbNGWJiFEueTOz2ukyLmayXQPWQqWm8GkYjEnzcbFcPLuYsXU5f/OjP8G/7GAHgIIQgK2QiWbv//gxtlNwlFguJmXKZmMnD7m6ZDweQbSoa3W4AIam69ZnodffOrw95lD+sl7Tn8dAp2U6B71k0K5oMQYKK2ynYFmeqvgsBI7ja7ycQioaiUecLdqpcMK/pyWRLrZc6abqtMBu5gt5cPYH7ABQEAKwFeCmwXl4b9gXj1xefQveOe+1HctrsNRA8+9xjK/BxjKat814MhpiOwVH2Y3K00U4SYtmlEsSzBrbKThhrhQ+6DakquXWNjXdbJYUDaGQP55NGSzKsbmoZ49rbSXd/YH90B0A7ABQEAKw6X7x6OvQi2w9vqu7pybhAhiazWeeWIE5E2gao3wqn2U7BUdJpcIIvwzrUyQ+QeA6rNaAXXe0Dgu/QMOu+18s1pZdGuWpdKi33byay/t6zdUaJWiV4TgeaVAytWx6Jtky4Ib+4WC7g4IQgM0VX0ke+8ITbKfgKJlWkW0K4MEqkkAkqBmkFA1tVxFwHJO3q0skTAtAa+0yxItltlNwVF+XeaEAu+5oB1uNMyXYHvwftQZl0FYFBG+GSpg0suFYuL3NOBNO+Q84M7myaY+DphuUSitWSB/63OMRmBMLti0oCAHYREyTuecjD1YK8LQVzX14MJ2Ek7RonkPtaxHYAUPzDzkDa7D2QvN3mEcicB4SrdWiHs5BwYNmV8mCjSDbKTgnWEkeatMUqZrCKsIxLEyUFXLx6Ui0pd0QWIz7D/kS0Zzvht1kuXb/xx5mmvB8E2xLUBACsIl++t2Xx34bYDsFR/mvGZiahGUrWkuvfWwRbsehGW2qiRQM4UBTKsQrDWgkgybk8WpKmm5C/yoEAsdbjUyVhl13hMnS4qBVG8jF+zvNyXLZ7FPTjWZa2hBKBNOJrNGlD0xE/Yd6x34b+Nn3fs52WAAuBRSEAGyWtZnw41/5L7ZTcJTSqE5UYFmGJpQIClJ+E540o+A4znNIKzWK7SAcZfFq0uUK2yk4qrvLuFKCXXe0Q27DfAmuc6M1GYYUJLUS0XAh5LFpR2Ox3j5bNFt07rGSJIXZVTweL1Un5HrFo3c+sxKALWiw/UBBCMCmaNCNI7cerVVhyBWabX93Pgt3nNDcB73RRJ7tFBzVccA5G4GpjGhd3ZYzsSjbKTiq3a47mYGVOppbrZgnl9hOwVFGsfgGmy5dL/Y7xI1mMy+rykSC0XzcYlGdXom0D9iD4Uz7Nd5suuQ6OEjVqCMfPkpTcPcbbDNQEAKwKf7rP382M7zAdgqO6nn/3rkZOA+J5hpsGZ2H5/Ro5hbNmRhcHUTTqqUz1QzbKThKLBRkpZUm9K9C4ROEUV+vN6HtKtoVZibfGO3TqAPF4NUuY7hcaPNpqxTN6HkCPm+BzKu00rHluKPTOjUZ7nrP4PyZpR9962dspwbg4kBBCMDGWzi7/Mx//oTtFBylcxiCMdgbRJOqJHECVq1ofD6vbhTUKVi2IuAEpnYrCtB2dR0+vy5chquVaAfduuUyPGdBe49VF6nONpmGWR5SCARL9aV2rXI4Her1mhczmY5+S75Mqjt1jUazohEJxYJwjtZYtU9/44XZEXgiDLYTKAgB2GBUjTpy61G6DstWBJzAdf3ecgmWrWi2/a50BqpltPYhx0oCLoCh9fTYJ+KwpkfrchmH03BYFM2vV81U4LAomlUqrWFT5/47V09dZxXWm7RSXRbxebP1hEEtG46F29yGidWYf09LKJrzHPIW8xXLvq5zd0bqJFx1BtsGFIQAbLDH//ePlidW2U7BUb0fGFqcg2UrWtt+9/gcXABDs7n1p0Lw5qCZjIqxAvxYoSllolVeju0UHCXkE3JVmWbgwhsCj8D36Ktk43+mRkXIwGGzLlRNX+XWFKia2iZqMkxaXJOIBYF8RmdUjM5HW/sds1PRnvfvXZ0OP/HVH7GYH4CLAgUhABsp8MbsT779f9hOwVEWn21uBVZmaHKdfLUKG6doIrGgoGIaMC0AhcBxkVVUqcNeBJrTo0pVYdcd7aBbu1aBFk1o77FqY7Xlt/1ik5iyS6WTxcVBi24yFx/osITyBXePsUzWxB4FgzFpAS6Wi5ejZUOr6fn7Xhr/3RQr4QG4WFAQArBhqiXyyIcfaDZg2YrAE/Al7hY4QrMe46A9X4BpAWite2zhNFwAQ+sesE0nYU2P1ttuPpWGYadofWbtZGmR7RQc5VHIi42Jv/11slHdZajgOF4XJRUi4WglatUpRiJhb7txOpz0DzkT6aLzSk+1XNP2tmMYdt/tD1VL5JbHB+CiQUEIwIY5/v8+GVmEg1tovR8YCi7BMHE0/9XtAfjOWYery3JqFdb0aFaz6kwaGvaiaRWSeRr+zkGTCviYJAsNrJD4ON6lLVBN9NSoGLnyfrs6WSvsdkqrNMUz4nw+L4SXFXLx2UTC4tSOzUfa97kWZmO9H9wfWYwf/+JTW5wfgEsABSEAG+PUq6MvH/8V2yk4ytHnmpqDlRmaxqKezxbZTsFRUpkwSpCwakXiEQRj4tVo6F+FZmyV5eqwOYN2wKWKkdCiCe1GuyZOnq8RQIoa69Oop4orVzoNC4V0b4cxWS6bfZo6RVf1PIGAHyRrSoNidiHj6HO9/P3XTr06umXhAbg0UBACsAFK2fJ9tz/MwLoVRSAW4iYDDOpFwnFC2W0uleH2IJpt0JLIl9hOwVFdg9aFFAweRBv0W8cy0IUIbbdNN1mEzqJoHWpliho//+f8dQpFpLlmV8lOZtf8TsNoLNrTa1tN5txD9nyxqu610lQTNxn4IsF9tz9cysJFVsBpUBACsAEe+PSjqTCszNC63j8UDsKbg+Y/7J2Bw6LraOuznQ5G2E7BUc4W7Ugc3hw0k1Y2RkI1iKYUCauCJIPB40sEEY/nUaYazIV33c9NoSjTpN1A4wQWFRQUUtFYIWGxqEaC4bZey+xywn/YGw5mum8aSoUzRz/z2BbkB+CSQUEIwLv1pxeHf/3sH9lOwVGuPe2BabjjhGZo0U7FoFRGU6gkyzScpEUTCvllZZOGtqsoBI7LLaIKhb4ABnY7ZakatGhCu8GmSNbe6XOWCBk4ZNYtl+OH3IZEtdTSpqxSFKMn+DzeSqOiUEmmYhljq35yKuYZ8r/+zB9+//yfNzU8AO8GFIQAvCv5ZOE7nzzOdgqOEsnFNbkK2q6i8XCBR0dC29V1GHoM2WL1wp93WfL1moNZmOCC1t9pmcrBrjvakF0fKL59lAI4p0+rTtQvcFj0bRhiyiGTBsrz/WbtmXSk32dZzGQ7+i2ZYkXXrSNJiudUYxheEcnECun3/vmRTAx+bAFHQUEIwLvynX86nkvk2U7BUf4b9sYj8O8fWue1HYtBmBaA5tvtGF2FI39obW7DcAzarqI5DMqzRXhz0HQScYaAHys0KZ9nlUaazMU9viQb1UF9GcNwSpxSi4QTZNSil5+MhdvchvG1uG+3Y2kt7b/Wm4jlfe/dk08Vv/2J729SfgDeJSgIAbh0rz7+mz/+9CTbKTiq/cquwCQsPtBMHuPEKrRdRdPoZbMl6H+IJhYL4kISpgUgEQSBGzCyAW1X0fpaRHkKWpug3WCTZqjEJfzGGBl8v12dqhX6WiQVmhIaeRiOJ0SkVCKYLmQ1Rvn4StLiNQUmI76re9586dQvf/jbjc4OwAaAghCAS5QMpY994Qm2U3CUVC3LYyJou4rE5/Mxq7Jeh2UrAo5jcq+6UIG2q2iebmOsCFcr0QY6TfP5NNspOOqqVkOgEGQ7BUft1Wsj5OQl//YUNdanVc+Uglc6DXP51ECnOVootnYbS2RN3q6mGw3aKCMERLrBk+sUD372B/EgPA0EnAMFIQCXgmGY+z92DBpJr8dz7a50EvoWoLVf510Jw7IVzb/PGQhdynP6y4G33TQShfOQaC6LZjgfYjsFR1kVslDjfIP1LmcqoUAlXnk3bVebTMMsCykEgnBz1aqQDefXPFbtSCTs95kDa3HfvpbVSNZ72J9NldyHBiuF6r0ffQielgKugYIQgEvx4gO/gFGz6+m4pn9qEhrio9k6LONL0PECTW9STGTgXiWaTCoKESVYRSIJebyaioK2q0gEjrstWIWGXXe0a63CAvVuuz3n6qnrrcIKXfNY8CbDlJQ1kYC/whQUcvFEOmW0qseWYo4uW2Ay3Hn94OivJ08cfWVDwgOwUaAgBOCiheaij/3bs2yn4CiVSR2vwKoVTSgRVNQimoZlKwKO43yXvELCtAA0e4cuWYIjCWjdXablItw7RTvoNsxDo511XGXShauBDXmpMBk4aNbPFUMH3YbVYq6rw5AuV6x+TbVGEQ4JhmNFhUAsFUULtMaqffTOZ0JzcMcecAgUhABcnAbdOHLr0RrccVqH7UBvHk7SrsN1dXskDj1p0ToOtMxFYHsQravLeiYGu+5o7Q7dcAbOQ6K1ahSLNZgzgaYXiQS8+Y18RSJgl0oXyCWvTvVmerXLbTwTjfb02uaiKe9QSzSRd17dVshVTHu66tX6kVuPNujGRn51AN4FKAgBuDjPHTkx/eYc2yk4qvvGPbNTsGxFcw22jC3AI2E0s0NzJgZXB9E0auksCZdO0cRCfkZSacCNLBQ+QZh19VoDhp2iXW3By42NvOtONqqDhgrNNOSqkpjHWyVyGrl4rJCwmlWnQlGnzzg6F2nb75mfifbePDT95txzR05s4FcH4N2AghCAi7A0tvLkXc+znYKjtHb9arzCdgqOkirFCQL6CKDxBUTDIqxT0HYVTetW5Ek4koDm9+sjZehfhXbIrVsuw41ltGutunB1ZsNfNk6u3GjXhKvpKzyaVLVsdMlJimKMPILAk2JaKhOulMsqo2IhmDd7bU9+/bn500sbngGASwAFIQDvFFWj7v7wURqmBaDgOG4Y9JdLsGxFsx9wpzIltlNwVPtQy2Ls3TZ12Kl6eq3jcVjTo3W0GobTa2yn4CivXjVThWIDzSqR0tjUJr14hhrr1qgmi4v77IbxTHSgw7KQzvj7LbFs0TJoLpZqmj5bjaTlXmezydz94QfqJGzhAvZBQQjAO/XE155bGoc5Tmi9Nw8tzMbYTsFRbfvdY9A/YB02t/50CN4cNKNePl6Ee5VoCokoyi/ApjuSkE8oVWWqCVfUEHAM32esk43qJr1+g2nY5BE5n58lwka55Ew50mJSDcfC3jbj2WDUO2ibXoz7DrYvzyd6P7g/OBV66q7nNikJAO8cFIQAvCNTf557/t7/ZjsFRxndlsUg9EpBk+vkq1XYOEUTivhFFUY3oO0qAoHjYoekUoe2q2it7ap4FXbd0a5269Yq8CgB7QabLkIubOqXyNWT19tEearis/LqDYrS0HweHuZVpFLhQrWg1MhmkzmDUzczn3b0tP74yImJP0xvah4ALggKQgAurFap3XPb0SYsW1FwAld2uKpVWLaimXY58gW4Wonm3msPpeFRAlrPgG06kWQ7BUf1tplOpWGUAlqPSRMoLbKdgqNaZLJyc3ILvlCYnDxk1s0VQ4c8ppVirqfDlCiVnJ36XJnUdGoq1brApW00GMJi4gn499z2YLVEbkEqANYDBSEAF3b8i0/ByKD19N1yYHkB+kOi+a5un1yAk7RoTp/x1Cr0pEWzWFRn0vCdg6aSiRea0HYVTSLg82S5JgOPLxF4BD6gL9eaW1R6McTUX6ZQ6FVvZtf8LfpT0Uhnp2ViLe7f61hcTfkOe0PBdPcH9keX4o/e+czWpAIACQpCAC7g7OsTLz38S7ZTcJSts2V2AVZmaGqzcjFXZDsFRwklgqSYbkLfVRQeQTAGHklD/yo0m1uerW3WBbDt7kqXKlrNsp2Co95n08TIlS37cmSjustQoZmGQlnm8/CEqCQTCRaonEohCeSyOpNiYi1paTdOTcVad7e/9NCrI6+Mblk2AN4GCkIAzqecr9z70YdgXAASX8gTtljrNVi2IuA4oeq2FqHt6jqce6yxLFTLaF0D1sU0tF1F6/dZzmbgvAbagEU7UYTOomg+pTJLTWzxF42RK++za0PV1EGXNloptvt02UrV2K4qkzWxW0HTjYZZgeMEpVQLJcL7P/ZwKVve4oQAnAMFIQDn8+C//iCxClfz0XpuPrC6DG8Omu9w+8wSTAtAa+uznl6Bw6JozhbtSALeHDSTRhaow48VmlIkrItSDAaPLxFEPKJdlaIZFgY8ZKmxTrVqsrzYZ9aeTK91u42j8Vh3j3U6nPQPOYPhTPu1vlg423HjUCqceehzj299QgAwKAgBOI8/vTj82pO/YzsFR7Xubg9MwcoMzdCinY3l2E7BUXKVZIWGp+BoQgGvrGzSTbgAhoBjmNomLtVh1x1tj1OWqhXYTsFRN9iUyTo7z1kaDN2qiIl5BCVOacSiZSyjVUgmSkmzSXk2Hre16kYXoo4e++RkxHew57Unf/enF4dZyQkuc1AQAoCWS+S/88njbKfgKJFcXFeoGtB2FYmHi9r0FRLarqIZew2ZIrRdRfP1WYJZeJSANthpHc9Cox20IYd+srjMdgqO6tNokvWtPiz6Vul6/AabNF0rDDglmVrV0Cqt1inczG9iTElLCIS8nJgQy0UpilAYVN/55PFcAnovg60GBSEAaA/8y6Pwl/J6Ot63Lx6BZStaxzX++RWYFoDm22UfDcIFMDSPSz8Sg1EKaDa98mwZTtKi6STiLA4/VmhSPs8qCzeYBrsxwuTElUZdoLByldM4nokNdloXUpmufutaKte6z55IF+1XuHPpsuvgQC6R//Ynvs9uWnAZgoIQAITXnvzd7194k+0UHNV2RefkBKzM0Mwe4+Qa3KtEU+tks2V4joAmEQvSknoD+lehEAQhMOJVmoULYNtCt0OYo+AYNtp7bfIMxYnBSELBnFksWWsGnSrFqVKo1ax+MxZ2uXSnguG2Xsv4XLT9gCcwEep67643Toz86qnfs50XXF6gIATg7eBi93lIVbICIYK2q0g8HsHYlfU6tF1FU/o0hQpcAENz9xjDebgAhjbQaZ7Nw3MWtKtbjTPFVbZTcNQevTZKjrOd4i/KdHHIVCfputlQb2JNUk0J+LyEsCaTipbpslIjWSlXVAb5WorUOQxHP/MYNLQDWwkKQgD+LwzDQOvn82i7fnc6AdMC0HzXd6yswVRGtI4h52QIuhCheb2mkQgcFkVrNatH8iG2U3CUWSYJN6EaRFMKBGrxCqfarkbJxRvtmpVy/JBbHyzmOjsMiVKppUOXLVUNPcZCkdT228ulmmHQVylUYeQV2EpQEALwf4HhsOfhP9wXmIBlK5rNbx5dhI4XaDqzciIDT7vR5DJRCCvBug9JyONRappqsnwBjJtwjPHZ+CWKZDsIR11nFRYozs3zzNETHWpVoLzQY9acTK92uYwj0Uhnp+XsSsS3yzG1GPdf3T4/E+t5/96zr0+89PAv2c4LLhdQEALwP6JL8UfvfIbtFBylNCgTsPBYh0AkIHUSaLuKhOO4yCWDtqvrsXfokmU4koDW3WlcKmbZTsFRBz2mmeIa2yk46kqjNkwG2E6BQDOUSxETEbymOK0SCVfwjEYhma9n1SrpdDGrMShmM0WtVb0YKprarce/+FRoDtoFga0ABSEAf8E0mXtue7BagqIHzXF1fz4Dy1a0tsPtoSi0S0Hz73fOhGF7EK2z03I6Ci2a0NrtuuEsFDxorWrFSm2F7RQcpROJRYJFtlOsK12Pv88uTdUKu5zSTK1qcylyVdLQpiyRNaVPXa3WZB2mGkkrvK11sn7PbUeb8KgRbD4oCAH4ix8fOTHxh2m2U3BU9w27ZyZh2Yrm7LWPLsBhUTSzXTMah6uDaCqFZIGC5whoYiEvL61C21UkHo5Z9FS1AbvuaFeb8RLN6alREXLigEE3WVw50GI4nQ73tZtHY7HuHuvEasy/t2VuOeE/7F1eSPTevH/qz3PP3/vfbOcFOx8UhABgGIYtT6w++fXn2E7BURqbbi0NzSHRxHJxRkQ0m7BsReDxiYZFWKOg7Sqa0avKVqpsp+CoDr9xrczpNT2LDrkNS2V4CIV22KKLkFx/tstgjES4oBeJUlhYL5PM0gm9ShYopfU6+UQ2rbeopmIZY6t+bjlr8duf+NpzyxPQOghsLigIAcBoqnHPRx6kajDkCgHHcdOejlIBlq1ozivdiTS0XUXz7mtZjHOuqQNH9PTaRmOwpkfztxpOpmEFjObRKubIZbZTcJRZImHwGbZTvCMlOn+luVmgqh1WXqFOqu3CClWXOCRVisLtYppu4A51o9nk2604gX/rHx+gYaAR2ExQEAKAPXXXc/Onl9hOwVG9N+2dn4ZlK1rbXtfYPNz4R7O5dWei8J2DptPKpkpwrxJNLhbF+AXYc0cSEDyNhqw3oTZAwDF8v5GuNrbNXfcoOf8em3auFDrkMQVyiYFO80wy2dtvW4xn2odaVsJp7zW+yFqm88Z9S2MrT33jebbzgp0MCkJwuZs/vfTckRNsp+Aog8u8uAYTDrSlAAAgAElEQVTbX2gKrTREU3DFCUkg4le0BEXDtAAEnMBUrbJCDY5ho7m96ni1xHYKjjro0a5Vkmyn4Kj32LQRcp7tFBen3Bz3KZUL5JJXrxouhNxWzclExNWqG1mLOH2G0flYa78jMB33DHX8+O4TMye32Z8ObCNbVBDSND0yMnLixInf/OY3yeSl/11WKBROnTr10ksvTU9P0zQ8IQPvVq1S++b/+i5NwbIVASdwdZenWoW+BWimPc5sbts8it5inr32YALapaD19Nkn4gm2U3BUt8c4koYx9GjdRk2gzN3mmexqkckqTS7OmTg/qkm1q9I43pQrSwIcLyvrAj6ekVAiET8pbohlwrQQF0qEZZFEJBV98399Fxqhg02yFQXh0aNHbTbb3r17b7nllmuuucZqtf793//9xZaFp0+fHhoaUqlUe/bsufnmmzs7O2Uy2e23355KwakbcOkevfOZtVlononW98EDS/PQHxLNe0XbxDych0Rr9RtPrcGPFZrVrBrNwncOmkomXsZg6iCaRMDny3NNBiYQIPAIfEBfrje3ZbGUrIffZ1OGq+krPJrVYq7Db4wUCq4eQyxbtA2YE6liy5WeZKzQ/t49kcX441/5L7bzgp1p0wvCz372s5/+9KcTiQSGYXq9niAImqaff/75vXv3vvOa8LHHHtu7d+/JkycxDJPL5R6Ph8fj1ev1xx57zOfzjY2NbeIfAOxco7+ePHH0FbZTcJTFb59dTLOdgqNURsVSEfYG0UQSQULUgLarSDyCwEz8KrRdXYfDo8iQFbZTcNSVLnW0CtUy2vtsmhi5wnaKSxerje3VayeLi3vt+jfTq90e40gk0tlpOR2M+AbtY3MRzz5XYCLiO9jz4gO/OPXqKNt5wQ60uQXhz3/+8+9+97sYhh04cGB8fDyZTMbj8a9//esYhq2srHziE594Jy8Sj8fvuOOOZrPpcDhee+21QqGwsLBQLBa/9a1vicXiTCbzD//wDyS5LR8LARZVCtV7P/oQAzfAUHgCvtjlqNdg2Yqm6bUV4dzOOpx7rLFsge0UHNU9YJ1PwXMWtH6f+XQaNpbRBiy6iSIcFkXzKBU5eoLtFO8KgzFK0ZJGKMwRUZ1EtMxktArJQj2rVkkWagWlRhqmKJlamqZ4Mp38/o8dK2XhiSTYYJtbEN51110YhrW0tLz44os9PT0Yhun1+n//93//1Kc+hWHYiy++ODk5ecEX+cY3vpHP5zEMe+GFF6677jocxzEMk0gkX/rSl7797W9jGBYIBJ5++ulN/YOAnefBz/4gHoSr+Wg9N+9fXYI3B63jkHd6CU7Sorm7zaeDsKZHc9g1I0noSYumV8mma3CvEk0hElKiJIPB40sEPo53qrNUc9tPjSrSuYMWLE+Vu+zCbK1iaJXkqqTeo8oWq5ouXTZXNu52ZNMl16HBZCh97AtPsJ0X7DSbWBAGg8FzhzzvuOMOg8Hw1g/deeedGIYxDPP88xfuovvKK69gGHbdddft3bv3bR/65Cc/qdVqMQwbGRnZqNjgcvDmS6d++cPfsp2Co1r6PdMzsDJD09k1MwkYlo0mlQtDGAmb7khCAY9UM1QD+lch4BimdYgKFLRdRdvrlCVrsOuOdqNDnajtkC5EEXL2PTbdbGntoNs0non3d1jG4rGeHuvEasy32xFYjHuvaJuaCHddP/jq47/5409Psp0X7CibWBC+9tpr5/7jpptuetuH7HZ7f38/hmG/+tWvzv8iFEUtLS1hGLZr1y7kJ3R2dmIYNjs7+y7TgstHPlX89ie+z3YKjhKIhYxeR8O0ACQeLm43VEhou4pmGTCnCnCQCc3fZ1nJQttVtIFO60QWdt3R9tn1k0UYQ4/WrVEl6+Nsp9hI1eakRyFfqa+0qhXjlahFp5gop/Q6+VQhqzHKF/JFjUUVztMaq/Y7/3Q8B08nwcbZxIJwamoKwzCVSuV2u//2o4cPH8YwbGZm5vwvUqvVPv/5z99xxx233HIL8hNWV1cxDLPb7e82LrhsfO9TxzMxWJmhdd00FFnLsJ2CozoO+xfgmPE6vIP2s0E4D4nmcumHY2G2U3CUVacYK8MxYzSdRJwj4McKTcLjO+SxJrOjHl/Wm7UubYFqUhY9VW9QUgu/WqfkLdJqrS5vU1WqdVWXpVQgLUPd+WThgX95lO28YOfYxILw3M5eS0sL8qNOpxPDsEwmk8udb2kul8vvvffee++9d2ho6G8/+rOf/excQXjo0KF3HxhcDl5/5g+/f+FNtlNwlGefbzIAiw80k1sfCMGQGzSlRrpIwpE2NJGIn5PUG3CUFoXAcYmZX6G3/QWwTdLrEOco2HVHu8Euy9R34MZynFy90a5ZKscOeoxT2cRAlyWQSPQM2AKhhH+fc3op7j/snQ1Eem/a9/sX3vz1s39kOy/YIfib99KFQgHDMLVajfzoX389n8+v9znnNzw8/JGPfATDMKfT+Y//+I/n/+Trr7/+gi94bjYGR6RSqWazKRAIeDwe21l2jkw098Cn4YkamkQhKQgkTLPEdhAu4vGIhkVei8L5HDSlTxmKQPNMtFa/9kyKQ/+4cEqXV38qB9uDaPus6qniCtspOKpHqYiSO+qw6Fsl6mf71d0T+QW/znYyu+YxaUaSkVaL8kw81upQTYRTZqd2Ya2gd5u+9y+PWLuMWsulrKIBUqPRSKfTBEEIBAK2s2ypTSwIK5UKhmFisRj5UYlEcu4/yuWLfvpVqVTuvvvub37zmxRFqdXqEydOCIXC8/+WC15WxDCMU7MrarVas9kkSRIKwo3CMMzxzz1VzsGQK7SWQ30Lc7ADhua80hWAk7TraO0zjUM1uI5Wp/osVIPrsGhk45UduMOzIfQSYZKIYDvqOOSGkfF4JlmouHOHnTIYoxOvSop6niwrzosKcpKfIcrSBp7GS3Ici2MNq5yK5GRtLZnXTx/7zBOfe/Lj5zrwg3ev0WjUajWCIDhVFGyBTSwI+Xw+hmGNdZqqUdRfjohc1DcxwzBPP/30nXfeGQ6HMQzr6Oh4+umn+/r6Lvgb/9rhBunc/qHRaHznSTYbTdONRsNoNEJBuFF+8cjrE7+9wJ3Vy1bblV2L87CmR7N4jbNRuHSKptbLl6qwq4wmlQqTYoqBtweFTxA8E1EvQsWDgGNMh00wV4b+VWjXWUWxepbtFJurxOSvs1lfXC3tbdX/ZiG3x2cbn0zs7rZMn4nu2mOb/9Nq/2Hv7C9nuj+wb/zFP595KfC+269hO/IO0Wg0aJrm8XicKgq2wCYWhDKZDFt/2+2vvy6Xy9/hC05OTn7iE5944403MAyTSqV33HHHl7/8ZZFI9E5+73XXXXfBz1lvM5MVIpGo0WiIxWIoCDdEbDnxw6/8mO0UHCXTKrINPsNAz3cEoZhfN8hoKAhRcBxTeFWrIdgBQ3N26U9F4DwkWl+X6Y3MKtspOOqg2zRdnmM7BUcdMGpj9TNsp9gK0dr0Ycuu30RXrmzx/nE1vKfdcXo+OthhPjMT7e0yj0/H27ttc3NxR0/rD+58du97B2ztFrYj7wSNRkMkEvF4PE4VBVtgE5vKnJs9GI+jD4TEYjEMw3Ac1+l07+TVHn300d27d7/xxhs8Hu9jH/vY/Pz8XXfd9Q6rQXCZY5rMPR95sFKssh2Eo1yHBnIZ6FuA5jnkDUE1uI6O/c4AVIPr8Hi0UA2up82mPZldYzsFR9lVshUqyHYKjtIKRRLBItsptk4Tn3bIZFFs1aKQzlIJjUq6ROdVSkmUqEnkopyMxxMQhMVE0817bnuw2WiynRdsY5tYEPp8PgzD1tbW/no69K2Wl5cxDHM4HFKp9IIv9eSTT3784x+v1Wr9/f0jIyPHjx+3Wq0bHhjsVM/f99L476bYTsFRXe/dNR2AZSuas9c2Oh9jOwVHmezqUS414uIUhUwYxOAhC5pYyCvISWi7ikTgeKuRqdJwXgPtoIUo0ZdRcy+yURnQlSp03WViynRN7xDnq6TBo0rkS5Y+UzxZdF7VFgqmuz+wP/DG7E++/X/Yzgu2sU0sCM+Nkq/X62fPnv3bj548eRLDsMHBwQu+zp///OePfvSjDMN86EMfOnny5MDAwIZHBTvY6nT4ia/+iO0UHKWx6sJZuKaCJpaKslJ+E5atKDw+wdjEZJ1mOwhH6dzyPAlrerQOn2GtdBmt6S/KIY9hvgRP6NAOm3URcprtFFstXgveZFcvlqOH3IaJbLy/wzIaj3X3WM8EI95B+9h81L2ndWoq1rq7/fH//aPlCTiGDS7RJhaEhw8fPtdK9Lnnnnvbh6anpycnJzEMu/nmmy/4OkeOHKFpuq+v79lnn71gN1EA3qpBN47cerROwpArNPPezmIeTtKitVztiSdgth6ab8ixEIUuRGjdPdZABnrSovmd+pMZOCyK1qZVzleX2E7BUWaxBONdpm3hktRYr1Y1Sy759OqzpbBNrwyU0nqdfJEsKNTSaJMWyUWUUk3wiCO3HqXhOR24JJtYEEokkltvvRXDsGPHjp0bUn8OwzBf+tKXMAwzGAwf+tCH3vpbnnvuuWPHjh07dqxa/csiNRwOv/TSSxiG/eu//uu5tqUAvHNPf+OF2ZEFtlNwVO8HhuamYQw9mntX6/g8vDloNrfudASmBaDpNLLpMpTKaDKxMC4swp47Ep+HazXVehNW82j7TY0KfZkew24yDYssIiJwhbLE4AxhwEiakrVIcpWqpkuXyZbt+12xcLbj/UMLZ5ef+c+fsJ0XbEs4s5kHoiKRSH9/fzKZdDgcn//85w8fPjw7O/vEE0/8/Oc/xzDskUceuf3229/6+d3d3YFAAMOwaDRqNpsxDHv55ZdvuukmDMNUKtV5CsK/+7u/O378+CXnPDf6YlPfiosVDocbjYbNZoMuo5ds/szSZ/b/G01BW3MEg8tUUevJCpxqQ5CpJFi7LgWNdlD4Qp6iRxtMQqMdBJzA3P2m8XVaqYG+XtNwOsR2Co66rs04AZ1F1/Eemy5Pn2Y7Bcts4u6fBku98rbX5lMHNM7Tk5H9Bvv4aGivyTwzstZr1i28udiqESwPz37nj//h39vGdt7tqtFohMNhHo9ns9nYzvI/tqBO2dw9N6vV+uKLL95yyy1ra2uf+9zn/vrrOI5/+ctffls1iPTXrcV8/nxXDgoFONkF/i9UjTry4aNQDSLhBK7ubsvMwbIVzTLkmoDtwXW073OcDIbZTsFRPb32P8eh4EHrdhuhGlyPT6+erlxGzTMvikMmqzYDbKdgX5icvNI4+EZyccDiHo6veW2GM/GYy6YOpLNGszJYqSh18jyGSdTSI7ceffj0EZEE7liBi7DphzAPHDgwMTFx9OjRV199NRKJKJXKXbt2ffKTn7ziiiv+9pM/9alPJRIJ7C3DCTs7O7/61a9e8Kt0d3dvbGyw3T32b8+uBOCmClrvzfsnp6EaRPNd0TYK1eA6nF7jyBp0vEAz6RVjefixQlPJxCv4Dp8kfsmEfEKuLOWq8PgSgUfgg7pKrIaeaH25EQrmjSJ7jUkqhJICj+Tz8LqSqMdpgVOTHYmZe61rv573HxyY/MnvH//Kf33yvg+znRdsJ5t7ZHS7gCOjO8z476a+cO3XmCaH/odyh8XvyInk0GgHSWWQV6yKQhEWHwgiiUDgU0YycBwDgcBxW59+JplkOwhHdfUYzmTgUQLa9V79eBHuuqPdaNelqcv9sOhbmcVt/x1sdCicv5nL7dM6RidiQxb7xKnQvhbb9B9XBt3m6V9N+53KqV+dvff1r/Ue7GQ77/Zz2R4Z3cSmMgCwgizX7rv9IagGkXgCvsRth2pwPboBB1SD63HutkE1uJ7uQRtUg+vp95qhGlxPj0kzWYLDomgepaLQmGA7BbfEyIX32bVTxZWrW40nM2u97ebhWLi9zXgqFG3xGiZDKbPHGM5RarP2yG1HKwXoIg7eKSgIwU7z0Gd/EFmEg1tovR/cH1yEZSua/5A3sABj6NHc3ebTq3B1EM1hU59JwXcOmk4pnaESbKfgKJmAz0gyMOwUiY/jneos1YRJuW9XaIz7lIrVRrBVpZylEjqVNEyUpVJhRtrECRyzKyulmnWoKxFMHfvCE2yHBdsGFIRgRzn9y7FXfvAbtlNwVEufe2oGVmZoGotqLgXDstEkClEYJ2HViiTg8+pavEbDtAAEHMP0Tmm+Dt2M0YZcymQN/tpBu9GuSdSgCxEC1aQ8qiTGNEwGstKsa+zidKVi9qkjmULrHuvyWtp7bcdMINJ9455fPPr6yZfPsJ0XbA9QEIKdo5Qr33f7w5y6C8odArGQMRqg7SoSjhMyv6lcgUfRaLZ+czIPQzjQOvotSxlol4I20GEZz0CLJrR9dkOguMx2Co7qUqtS1BjbKThKzhem67H32qQr5cRht34iG+vvtIzGYl091lOrEXeXeWIl7ui0LodLJo/5/o8fK6SLbEcG2wAUhGDn+O4/HU+GYCQ0WtdNQ5FVeHPQ/Nf+/+zd95Nc53Un/L63cw63c/f0TPeE7skBYWaQQQJgkCj7D9gqUZItOa9d9qstuezy+vWuvQKVCVIkTYmWqEhFmksrWYkiKGIwACbnPNM559t90/7wul6v5TOMAO6dwfn8RhaA+VYXZvCc5znPebpWt7GTFtY55Lu5jRfAYIEW2/Ukfjgwt9U4XcdOWphJrSorkoIMty8Barm8zZTiBNy+BJAy4pK1ccLqTDRmTzhtc9W1IbftRnkv4LQsVLKUzbBH0CqtompRcQJv7G7PJwuf+vBTYqdGBwAWhOiQ+Pk3rv7im6+JnUKiQse75hdwZQZzBu0L0ZzYKSTKYNZsNHF3GaZWK8pGluV5sYNIEUkQOq+ixuCpO+xomy7bwBFNsId8hkwDD5Zh5yl7jZm1Ea+71XqNYpVSq1hNVi0neYqnWcbYqs9Wqp4hdzRRbD8b3lxNDjwydvV7E7g6Qm8KC0J0GOTi+St//AWxU0iUxqCh9Saew2UrQC4nyYCFbuDYVZij35Gv4Jw6WGe/a6+Ia3rYcI9nsYA3lmEnA4750pbYKSRqxGZJNGbETiFRAY1Zw78qk8lYvjJmytf5yimXkG4Uj7cZ10vZgV7XXDLZN+C7uR3rGvFPrcXbhlpWNvO+3gD2T6E3hQUhOgywS/4NdD04mowVxE4hUeELkc1d/GcSFjnWMr2DB8uwrg7nRBzHrsL8DtONMn44MKdBmxJwVgpMr1A69XvYSQuSE/IjxiQn/NuIpjqzeNFmi9ErF732ufLGWIv9emGv3WebLiQ9LtNqvWiw6HIqklSQSr+HrtE4YQG9MSwI0YGHc7TeQPhM38Ic3nGCecOumU08xIBZHcaFIs5Kgem0qpiihmsrkIIkCbusweHYVVi3R1Fi8dQddsmnyTczYqeQqIuUpc6s/N//h+R/FdbbaGGuzaAvkAmzWlU20AJByN3KSr1p7bUlM6XW0527W9m+R07c+PH0D7/wM7HCI+nDghAdbMmt9FN/ji/twAyUMcspcFMQpFQrmw49w+LcAgBByAxd5gqNrwXA2vocyXJF7BQSNdjrXivhqTvsbNCxVNkVO4VEjdptcXpO7BQS1aG3kNyrv/E/BYHt1q4qZFy/rVhh6n0tir1KIRKhljPZ3mHv7E4iMhaYWol1jAUXFpPBo51P/fmXkls4Pg3BsCBEB5jAC4998IlaGXdbYcFzI/kMLlthHee6dmN4AgYLj7bO7ybFTiFRkW739Rj2Q8LaPJaJAhY8ML9Zv83uiJ1CoiwqtVmzic2iIBUh79fu8gJw151moxcoTaqx95DfvFTeOxtyXcvuDnZ6JlKxYNA+k0m7/ZYdumGg9A2jmROExz74hMDjh4wAWBCiA+y7n315+hfzYqeQqO4LwwtzuGyFBfp9U+s4xQ5m95jnsriLDDMZNVscDpKBqeTyhgnHrsJIgmh1CnUWT91h5z3yIoM7dLBLlLHO7vtkZZO5Om5xpJq3jlLW9cZGB2Va5VJmvTqrbpBykvWoqrWmqd+bipe6Hxyd/sX89z73L3czPDoosCBEB9XuUvS5v/q62CkkyuSyxEvYDAnT6NRFnYLHXVIISRLygK6GY1f34emyZas1sVNIVF+vc6uCa3rYuXbHWgWvc8POuqkYvSB2ConqNtg59jebRX8DRU7YVVpKu6OWE5SlXmEYe6suUS639jk2kvmO8ZaVzVTkbMfcXCxyrv/Zj311ax6P8dFvwoIQHUgcy11+9Eqjjo9cwVpO9peLuGyFtZ7pSKTxkAcWOdG6GsehDrDePu/NBK7pYZGA/VoOV5mwoNW0Ru97wnOPs6vVCnLlzX/dPUkrV4Y1K4LsTU7dWb58ylwtMtmLPtVWLX223TabT4z0eidj0d5e7+RuLBhxLaQK9hZrhpGrDZrL77/CMrhljP4DLAjRgfT1v//e0sSa2Ckkqv89x5fmsR8SFhwJTK/imh7mabXdjOE7EzDKqluq46wUmEalzGiqPM6vgihI0kU1GhyeusNOuYUKh69GwS5SGpp9S4+U1JnZ+yl7tD5/n5uar66NeKjJ8l6b27JYz5hN2rSGFWQydae9UKiFzg+v3tz4xv/63p0Ojw4WLAjRwbN2a/Orf/8dsVNIFNXi2E7i2SBMZ9KkSJy6ClMoyKZT2cSxqxCClJmDxhKOXd1HOEJFq3jqDjsbojarOKIJdtFjj9N4PAgbMtmbzdfe+q9X8a926C0cuejT6erqlF6loC1Mk+csIWO8UGo75l3dTHefC8/PxnouDn/l7769fB131dG/w4IQHTBMg7n86BW2iY9cAQiCcIxEqmVa7CAS5TsRyuRw7CqscyywmcyJnUKi+vp9s0lc08MirfaJLDaLwsJ2y1JtQ+wUEuXX6RkCrw7CjAp1q3Je9nbGrvJCs0+7LciYEXul0KwOtWi3y4XeiHMumezv803uxNr7PTO7aU+nM17iDA7T5UevNGk8uEb/BgtCdMA899ff2JzFyd2wwfeNry5hsyisYzw0s4IfDswXsk/u4YcDc9mNM6WU2CkkyqzTJFTY7wdTK+R6U5kV8NQdQMiIo456ncN+Fth9VrLBve1NKJrdfsCmTdDb7/FbFspbp1qd1/K7HT7bdDntsBujMlqlVXJuY63S9I337yxGv/Q337gT4dFBhAUhOkjmX1v+zqf/t9gpJMoT9q1s4Yg/mIEy7NSx3w+m1ihLZoHD1wIgJEGoWzS1Ju6jwwIdpmQNT91hp4PWKN473cdDflucxrNT2HGLo8Fce2e/t8lcPWp2ZJjpPqs5Luy4Ddq8vi4QvMqnTleqnkHXdjTXdX94eT7W9+DRb33ypZlf4iEtksmwIEQHSL1CX37/4zyHy1aAXKnQtrc2sP1jH84Rf7GEW9GwtmO+aBYvgMH6hn2LKXyVETbQ6Z7M4mOnsEG3bb66LnYKiQoZDWVuTuwUEkUptS75zXfxBwhexS2rQhUwpBiO6XDL49ViJOxYTmf6B3w3t2OdQ77pzYSv27OTrtta7J/8nSfrFbxmgrAgRAfHMx99PraO13hg/Y+Mba9jVxssfLpzHv/m7CPY65ncwTU9zOs238zi2FWYzahdZbFUhumUCpk2j2NXQQqC6LOVmjy2bMDOWDmGe1fNPk0ud8ZC55uJh1sMy5XdcyHXtexOX8h5IxsP+K0r9aLRpiubVCwvsw10xTdTz3z0+dsVHh1cWBCig2HyR1MvP/0TsVNIVMtgcHEFV2Ywq8eyVsA7TjCdXhUnaVy1guQkKbjkDRbnV8GcbfpCEw8WYCeC5gSNDfywh/zWJI2DAGCnbc56c/Ld/zl1ZvqszR6nZ8Yd1rXGRjtl2pDljDpV1cw3eU7Xbk5lyq1n2jdWkoO/Nf7y0z+Z/NHUu/+i6EDDghAdAJVC9VMffgqfCwApNSqZ04mPzIIIgjT0uCpV3IqG+UY8qSJeAIP1jnjXMjh2FTbc7ZnO4RQi2IiXmivj7ThYt8WcZWbETiFRTrXBLHuHVwf/M63walBn1inXLCqF2Vyj2aa9VbdbKHYMuBajqch4YHol3jkaXF7P+XoDn/jQk2UcwX1vw4IQHQCP/9Gz6V28mg/rfe9YbAc/HFjkfNfKJnbSwjqHvDe2Y2KnkKi2Vup6Ej8cmMumn6ljJy3MrFbWVSnh7bwWcO9Qy+XtpjQn4Kk7gJQRp0w1lr9t/Sy80BjURWm+dtLF79UzJ9utM/nEcI/3eiwaDrtuJZK+Nmqn2VQZNKoWbzFTeuK/fvF2fWl0EGFBiKTu6vcnfva1V8VOIVHBY13zC7gyg9kDtsUkdm3BjGbtRhP3g2EqlaJsYFkcuwohCcLgUdeYpthBJGqk1ZBrYI867CG/Md3AfRbYOcpeY25z32adXX/AbozRKw/4qLny+lEfdaOy53eaN/mSTq+qUWS13nQeadneSPc9cuKnX/3VK9/69e0NgA4QLAiRpBXTpc/83jNip5AotUHTMJhw7CpMTqjaqXodl60wR78jX6mLnUKiwgPunUJR7BQSNdTjWSjgiCbYmN++UN4UO4VEDdosyQY2i8J8WqNOuCPFGM+8Omi0V/mZLpOhJE+YNCrWytWYpr3dvJ0utI/659cS4dOdC4vJtpGOz/3hP+YShTsRA0kfFoRI0j7z+88UUrgyg0UeGk3G8Gc3rOf+7vXtjNgpJCp8tGVqBy+AwTpCjokEjl2F+R2mW2X8cGB2nTZH4rcVTKdQePR7vIDblwA5SY4aMix/Rx5GEmR8q3JGR8o7LXmar3d7ya1KrrfbOZ1M9A/4JndjgS7HWqFsdppYq42uNT/9kafvRAwkfVgQIun60XM/f/W7t+2C9SHTdbp3fhZ7b2CudufsDo5dhVnt+uUKdtLCtBplWt3A1wJAJEmSDoLm8AIYrM+vLDJVsVNI1AM+bb6JO3SwC1ZrjVm+c39+k8/cZ2XTjb2H/OaVSvRs0HkttxsO2GcraZtVn9VyrHpw1V0AACAASURBVCDoe1yJaKH74dHXX5r88T/94s6FQZKFBSGSqPRe9qm/+JLYKSRKZ9EXBDWOXQUpFAqZ19Rs4rIVQBAyfZelVMOxq7BgvzNWKomdQqKGe1yrRVzTw84EnYtlfEoBNmq3xWl8hh4W0lnl/Gt3+qvUmZtnbM4EPXXMbtthtgMmfVpTEWSCPqBNFMutR7wrm6nw+c65+XjHePcTf/rF5DbuqN5zsCBEUiQIwqd+96lKHndbYe0XjmbTuGyFdV0Ib0Vx7CosMtq6sIdjV2Fdna7JGPZDwoJuy0RxT+wUEuUx6KIcVoMwk1Jp0mzh2FWQkiAH9Xu8cDd26IzC1RaN0aLeVMllHgebrpW7wtRCKt0/6J/cibb3exYTeUeAqqi0MhnxiQ89iTvO9xosCJEUvXjlh/hM6n56LgwtzOKyFRbo802t49hVmN1jns3ivi/MaNDsEGVcAYHUSjltxrGrMEImtHuJCkOLHUSiLvhUJQbf84RdspvrzPrd+VqcUD9iTFW50n0e5UY1cSbknMju9rY5pvIJj8u8R9RJJakIWrPpauelY1M/m3vxyg/vTjAkEVgQIsnZW4k/+7Gvip1CoswuS6KCq1aYSqssGZQcjl2FEAShbNXXGozYQSTKG7Zlq3dkqMMh0Nvt3MJ7p/s41+5axUE7+zjlpKL1ebFTSFS3wcYzv7qbX7HOrFyiLFF6/pybWqU3OinzJpnXqhW8Q16o0K5B5/p2JnJ/eG422n3f4LMf++reCg5JuodgQYikhWO5y49eaeAdp334TgwUsZN2H6GznXGcSbuP7hOB5RgeD8J6e703EziiCdbpt13L7YqdQqLarMaNBr4zAbOrNSrFqtgpJEorV4Y1a4Lsrm9fsr/sM9oFcsGuURrMFZptekLGjVwuMuSZ3kmEj7ZMbSZ9vd5EVdAYtZcfvcKx3N1OiESCBSGSlm9+/MXF11fETiFR/Q8fW17AZSssOBKYWsXtTJi31XYzgVcHYVaLbpnGS6cwjUpZ0NE4dhWkIEk3xdAcnrrDznhkVQ7vusMu2rQ0K8KlXEHGd6gWFAR3zFGP0/lT7dab2dhwt2ciEe3qcC6U8haHoWpU0Q3Gf3Jg8fWVFy6/ePdDIlFgQYgkZGN66/m/+5bYKSSK8tu3U/iSOExr1KRIvAMPUyjIplPRZHDsKswWMhZpbEmARSLUXhVP3WFnQ/bNKt5Yht3vpaL1JbFTSNSg0d5kror11WkuccGqSNBbD/sts+X14377VC3upYx78ioplylb9clMKXi2c2k+1vfwsS//7QurNzbEioruJiwIkVQwDebj77/C4msBEIIg7CORahnnFsD8J9szuYrYKSSqczywkcQLYLD+Ad9MMil2ConqDTonstgsCuuizMv1uzQO5MDxanWsbFHsFBJlVKjbVPMyUceu0szrJyyOHDPTYzYWybhRLSccsgJNeyPUSjwTHg9Mr8aDI4HtZM3ipT7+/sebNB6DH35YECKp+NJ/f2FjZlvsFBI18L6xtWXcioZ1jgZnVrCTFuYL2W/sYSctzGk3zJTxXiXMqFVH5UU8dAepFKTJUmV4vF4FIGTEqLNJcziiCXafVdHgxN+EspHXnCpNqynZFOiIV7leyvR3O28mYr193lvxpKfNliB4mZy0DXTuLEaf/39fEDsvuuOwIESSsPDrlW994p/FTiFRzpBnfRu7tmAGyrDdaIqdQqLUakXZLGNx7CqEJAhNi7bWxL88sLYOS7KOp+6w00Fqt5YRO4VEPeizxeg1sVNI1DGzo8H8WuwUMplMxvKVcVMh10w+4NMvV3bPhlzX8rvhgH2pljUaNTSlKJVp31hwfSU58L6xb15+cfZXeOR7yGFBiMTXqDUe+8AVHpetEIIkTN3Beh2XrTDXkZZiCbeiYcHj/r0sbiXA+od9iyk8HoT1tjsnc/gMPazfZVuoYrMorE1vqPL4zgTMqtR4FLfETvHvaszCJYqK0TMnnbaN5mabxZDRVDiCNwUN25l851jLzGq880TH6lbB3eF97ANP1Ct4aeUww4IQie+Zjz6Pz93sZ/C3T2yu4XxIWPh059wadtLCWiPOyR3spIV53eabWfybA7MaNFsCviQO0yoVpC7PC7h9CSAJcoAqNXgsG2DnrEKTk9Z3Fsm/0qW3qJWrZqXcQTVS9WpnFzWXTPb3+yb34oFOx3atpjGqdR2tye00PhB9uGFBiER266ezL33+x2KnkChfT2B5DQfiwyxu03qxLHYKiVJrlGkNh68FgOQkKXMqaBbnV8E8QWOugQONYSdD5gSNI5pgD/stycaO2Ckk6pTVWW9eFzvFbxIErke7LvD0STe3VU2dDVHXsru9QedUMeVwGPIGnm4wtqGWrfXUwG+Nv/Tkj67/cErsyOhOwYIQialarD32wSfwuQCQQq1U+D3NBi5bAQRBmvo85Qq+FgALHPMmcvgCGKx3xLuaxX0W2FDYcyuHB8uwES81V8IR/LCw2ZRnZsVOIVFOtcFCXBM7BYxmoxcpday+eslLLdU2uh2WHXlBqSKVHnU8V24b9S+sJ8JnOpdWs/6+1k9/5KlqEe9oHE5YECIxXfmTL6R3cWUG63tkfG8bPxxY+HzX8gZ20sJC/Z6b2Cy6j4Dfej2JHw7MbtYtNMSffyhNRrWqqUoLor4WIFlKQt5pzrECPk4AIGXESVOV5aXbz9Jgfn3U7KCF+Ra9VmMsV9mGv920lE73jfgmt6MdA96VXNnkMMhczlK28sR//aLYedEdgQUhEs3V70/86/OviJ1CotqOdi4s4B0nmCNgW05g1xZMZ1RHZXU8dAeplPKaRWB5vAAGIAnC0qIpM3jqDjveqks38NQd9nCLKd3AKUSwszZ7nZkWO8UbEzyKG0YF2WcrpOnCyZD5VjY2FPZMpGJtAWqbq8mVpKrLkYgVIw+P/uTLv7z6/QmxA6PbDwtCJI5iuvSZ33tG7BQSpdapGZOFw7GrIDmhbKdqNI5dhbmHXOliVewUEhUe9GznC2KnkKjhbs98Ho8HYWMt9rnyltgpJGrQakk1JV7wiMarMeplr4ud4s0xXOG0uZ5pRB/ym+dKG8f9jrlGwmU15PVMjWlSfdTGdiZyf9f8fLx9PPKZ33ummMbNkcMGC0Ikjs/94T8WUjgQH9b98FgiiidgsO77I+vb+AIYrOuIf2obB/bCOkKO64mo2Ckkymc33azghwOjtJo8gd9WMJ1C7tXHcOwqiJDJRo15lj8YO3R1Zvo8ZU8z04M2c4GM6tVyhUuWLFdC/a6Z3WT3aGBmK+3pdFWUuibNfOrDT4mdF91mWBAiEfzky7985dsHYM9MFB0ne+bm8Y4TzN3unNvBahBmofQrVTz+gmk1yoymwWErLYQkSaWToDmcXwXrb1EXmIOxpr/7LvkMOQavc8MuUPY6syB2irdBzb/aqjG49Hu8jOn2KtaKmcFe90Rsr6fXM5PLWBx6xqHL56udl46+9uJ1vPJzyGBBiO62TDT35J89J3YKidKZ9SVSLfC4bAXI5aTgNzWbuGyFmcLWUg0vgMFC/c5oEXucYMM97uUi7rPAzrQ5F8vbYqeQqGN2W4KeETuFRLXpzEr+qtgp3h5eaAwZduts/qJXtVTePRdyvZ7fCQfsq428WqOUB/R7iUL4vsjcbCxyfuDKn3whhfuzhwgWhOiuEgThU7/7+Uoed1thHRePZlPSnUUmrvCFyBbOpN1H92hgbg8vgMG6ulzXY9gPCWtzW64XcRwIzGvQRfldsVNIlFGptGq2cOwqSEmQw7o4Lxy8Hbo6s3WRMkbp+fNuaq2xEbIa0+oKw3OOdtNKPBMZD9xaiwcHW9INglQpP/GhJ/HZsEMDC0J0V+HDpm8gcn5wfhaXrTBft3t6EwseGOU2zeawVIbpdeooUcU1C0gllzctLMNzYgeRIkImtHuIClMXO4hEXfCqikxO7BQSdZGy1Nk1sVO8Qxzz6qDRzpMLDo3SYq1lm9XOMDWVTPT1e2/Gk64WS1ZN0jTTembo1k9nX/r8j8XOi24PLAjR3RPfSD77sa+KnUKiTA5TihY7hFQp1UrapmVZnFsAIAhCHdTXGjh2FdbSQ6UqFbFTSFRfj3OzjPOrYGdDrhUctLOPU05bjJ4XO4VEhQ02gXtV7BTvnCDjW5UzKoI/aqdjdPZMiLqW3e0NOucrWZNJw7hU2UKl7XTn4ly094Ejz3z0+b0VHLl0GGBBiO4SgRce+8AT9QoWPbCWM0PFHHbSwtrPd+3FcVwKLDIeWIriRQ5YT7f7RhxHNME6fdREHvshYS0mw1ZzS+wUEkWpNWrlutgpJEpFyHu0m4JwsO+6N/nM/VYu0dh80Gedr6wNum078gKplBla9ZupXOdYYGo11n6sbTdDGyjTYx+4wuMrWQcfFoToLvnm5Rdnf7UodgqJ6nvw6NIcLlthrYP+6VXcgIS5/dapJI74g5mN2jUW37aBaVTygr6OY1dBJEG0OLk6h6fusDNuWQW/s/ZxyW6oM4dhClGduXnG5iiys50mk6DN1bmmv900n0r1D/gn9+L+DkeMZwU56RgJL76++q1P/LPYedG7hQUhuhs2Z3e+/LcviJ1Coii/fSeDB6cwjUGTU5E8LlshcgXJeVQN5mBvRd85zi5zvoYXwGDdYcdeFdf0sPMh+3oVN6Fg5z1UjF4SO4VE9RntHHPAJou+AZPsml2p7jRlCkxprM10Kxsb6nJPFRIup7FoEKr1pm8suLqU6H/v8S/99xc2Z3fEzoveFSwI0R3HNtmPv/9xpsGIHUSKCIJwHI1Uy1gQwgInQ6ksjl2FdY0F1pM41AHWP+CbSiTETiFR3a2OazlsFoW1W40r9KbYKSTKrdUKBFaDMK1c2a5eEmSHp3mS5StjplyOjT/kN82V10f99nkmZTKqeYc8Way0HfPOrMa7TnWu75ZtAcfH3/84i49CHWRYEKI77vm/+9b61JbYKSSq/72jq4u4bIW1Hwtis+h+/CHqRhQ/HBhl089X8F4lzKBRx5QlPHMHKUm5jaKbPK5rAYSMGHeydQ7vusMuUaoGe9iuftSZpYs2a4KePkpZ82RMqyAMHtVWPt895JnciXUMeNcKJZ1VZ+hs25zdef7vviV2XvTOYUGI7qzVGxsvXH5R7BQS5Qi51/fw+AumM2mjHJ4qw1QqRdlCsniPH0IQMkOrvtw4eC+A3R3BLkuqjmNXYWfbbTvVtNgpJOqSzxajV8VOIVFDJkej+brYKe4IgnslYrBaNVskyUb8isVCcqjXcy0RbQ85NtmKXK3Ud7u2NzIDvzX+zY+/uHQN/4YcVFgQojuoUWv8w3/5LMvgI1cAgiRM3SG6hstWmHcsmC/gVjQsOOrfzeDYVVj/kH8hhYN2YH3tzsksPkMP63VYF6o4PBPWZtDXeXxnAmZWagPKGZnscJ67CwLXpV5m+cp5N7lS3jsXck0Ud4Nea0xR42S8tce6spmK3B9eXMl4uwP/8F8+i8PkDygsCNEd9OzHvrq7fNg6KG6Xwd8+ubWGy1ZY54n22TXsh4QFws4bO/htBfO6zVN57MGGWQyaTRm+OgjTKhVKY4ET8NQdICeJQarW4HGhD7vPwje5w3yw3ODiF+2qKL10v5daa2yELIaivl5pNr1h2+xuMjIaWIhmbX6r4LRnYvnn/urrYudF7wQWhOhOmfrZ3ItXfih2Cony9QSW1/COE8zsNG5WamKnkCiNTpXVsDh2FSQnSZlLUcexq/vwBY05Gr+zYCfbzPE6Vsuwh3y2BA7a2ce41Vlnroud4o5rNH89ZnE0hXmvVmOwVDONajhC3UjEe3o9c7ms3qKRt1nTiXLPe8a+//gPJn80JXZe9LZhQYjuiFqp/okPPSngshUiVypUAV+zgctWmHXAV8aek30Ejnjiebx3Cusb9q5msmKnkKihsPtmDg+WYcMeaq6yIXYKieoymQrsjNgpJMqu0tmJw18N/n/s5IRVqeinCkk6fzpkncju9oWcK3ROrVWogobNnWzXfV1z8/HQaPhTv/tUJY83Pg4YLAjRHfHEn34xuX2YOyjejf7fOrGziR8OrPtc1+JGUuwUEhXqc2Oz6H4Cfuv1NLYZw+xm/WIDG9RhRrWKUaeFQ3oB7F1SEvIuS47hcb4XgJARpy00w98r73myfPmEKZ9u7D3cYp6vrA96bNtkQZDLLCHDSiITGQtMbyW9YXdNrS8X60/9xZfEzoveHiwI0e33+kuTP/6nX4idQqICQ+2Li1jwwCi/dSl1r/zj+nbpDKo9GY2H7iCVUl6zCAyH86sAhExmb9GUGJxfBTveZkg3SmKnkKiHWkzpBk4hgp2xOerNe6s3ss4sXqDs6eZMn8XMqrMNrukLGueSqd5+33Q65fBZ6lZ1oVCNPHDsR8/9/NXvXhM7L3obsCBEt1kxU/70R54WO4VEqbQqwU6xLC5bIXJC0+mo0U2xc0iUZ9idKWETDiwy6NnO49hV2HCPdxoH7exj1G+fK2GzKKzXYkw3sVkU5tUYjbJfi51CBEr+1aDW5DPEK2z1eJtxKh8f6HTPFFNmi7bpVCYz5faz4bm5WPhM/2d+/5kC7vAeHFgQotvsc3/wTC6BKzNYz3vGYrs5sVNIVPf5yBq2Ge+ja8R/axv7IWHBoH0iERU7hUR5KeN0FduMYTatukDitxVMK1e0GlO8gNuXAEImGzPmWf5e3KHjheaAbqfCZB706+fKG8f9jlU2rdMq1T7NdirfORaYWo8H+n15XslywuN/9KzYedFbhQUhup1+9rVXX/n24Xyb9d3rGO+em8fFB8zd7pjfw7GrMJNVt05jSxtMrVYUtE0OW2khJEFo3YoaixfAYIMt2gJzL67p34oH/fpsE283wC5Q9hqzIHYK0dTZzUt2Q5yeOeG0FcioUiGjAtrldKZv2De5F/d32HNqskY3g+eHX/n26z/72qti50VvCRaE6LbJRHOP/zHuBsF0Jl1FpRV4XLYC5HJS8JsbTRy7CrP3UflKXewUEtU54NorYrUMG+71LBRwlgzsVKtjobwldgqJOkLZ4jQ2i8ICWrOKvyp2CpFxzNUBI6VRrKrkXI9fOZePD/W4r6djgRZrRssX6w3/ydDiXKz30sjjf/xsJoqNUQcAFoTo9hAE4dMfxkHD++q4dDSdwGUrLHwhsrWLrwXAIqOBqW28AAbr7HBOxLBZFNbiNN8o4YcDcxm0CWFX7BQSpVco7bpdHLsKkhPyI4YkJ9zrI5oEGd+qnFGQzZMufrm8dzbkvlGO+p2mvJ4p1uuBI56ZlXjXqY5ogVFqNZ/44BP4CJn0YUGIbo+Xn/7JxA9uiZ1CojpP9y3MYbMozNftnt7ExiQY5TLO5bBUhul1qriiiqsMkIIkZZTQ4PDUHUDIhC6PvMzgY6ewSz5NoYnXuWGXKHOdWRE7hSQ0+cx9Fi5Or17y2jaaG61mA21hMrVae5/rxnasc8i7VamRKrl3rPfmv86+/My/ip0XvQksCNFtkNhM/eN/+4rYKSRKbzMWBCVuj4GUaiVt07EsL3YQKSIIQhMy1ho4dhUW6HEky9iSABvoda2VcCsBdjboWqngUwqwUYctTs+JnUKiOvVWGYc34v5dnbl5xuqoCXMtOo3JUk3WKz3djon4XiTs3mQqgoK0DfmX5mP97zn+9F98KbqK2+KShgUhercEXnjsg0/UynjHCRY8N5xLl8VOIVEd5zv34nmxU0hUZCywGMV9elh3t3syjv2QsHaf7XoBCx5YwGzYYrfFTiFRFpXKpNrAZlGQipD3arcFAU/d/wOj7DW3Sh2x5tPN3OmQ9Vp2pzvo2BJKPEFYe2wL68nI2a71vbLZbX3sA0/wHG7+ShcWhOjd+tYnX5r55b07buuN9T5wZHEeZ77DWgd8U6t4Ow7m8lumUjgOBGYxaTdYfN4KplHJywaa5XHhBSAJosXJ1dl7/QLYfs575CUWX42CXbIbaHZL7BSSwwn1I8Z0rhl/0Geaq6wNe6iovMjIOKrdNLuTCB9tWc6WdFadsbt94fWV73z6f4udF+0LC0L0ruwsRr/0N98QO4VEWb1UNI/9fjCNTp3XKXjspIXIFaTg0zQY3IqGubosuRq2JMC6I87dClbLsPPtjrUK9q3BzrupGL0odgqJ6jVQHHOvTxbdT51ZvkRZko3pEcpSV6eaPNMassykEr293oVSXm1Q6rtdW2vpgfeNP/fX39ic3RE7L4JhQYjeOY7lLj96pUnjI1cw9/GechGXrbDAmfZkCseuwsJjLWtxvAAG6+333ozjmh4WabVfy+J6C9ZuNa7UN8ROIVFujVYmXxI7hURpSUWHekmQ4ak7gCTk3bp+GfdKr8FuVW/yQmOkTT+Z2+vvcC3RWZVGbuw0r26lIveHl9dzzg7P5UevsPjElCRhQYjeua/83beXr6+JnUKiBh4ZW1nEZSssdKRtBu+X78MXom7EcOwqjLLql6pYKsMMGlVCWcYzd5CCJO1Uo8njShQ27mJrLI5ogl2ktA0O/8GCHdMPBIVbfnVru3qB5avnPar50uZ4i2OdzyhVckvIOB9NRcYCC9Gs1WdR+j1b8ztf/fvviJ0aAbAgRO/QyuT61//he2KnkChH0LW+h4NkYDqzNi5jsVcUpFDJa1aSYTmxg0gRQcpMQUOpgRfAYO1dtmS9InYKiTrXTm1V8VIu7JKPitGrYqeQqCNmR5N5TewUEuVRtVL8DZmM65WXZELxIqWO0XOnnLYsEZPLBWerfi6Z7O/3zWQyRruObLXEdvP9j5z4+t9/b2VyXezs6DdhQYjeiUa9+fH3P87hshVCkISlr4Ou4bIV5hlty+VxKxrWOdqyncahDrD+Af9cEs9OYX0h10QWX1qHhe2WxSo2i8ICen2dnxc7hUQZFWqfYkaGY1chCkI1oGJkAiOTyUg+OqbvaDCvjVmcKuWqWs71+FTTuehwt2eqmLJadYJXsxvLhy9E5heTLUOhj7//8UYdJyxICxaE6J147q++vrOIM99hA+8b31jBZSssfLJjbg0ni8Jau5zXd3EmLcxlN04X8dsKZtZrNomc2CkkSqNQ6ExlVsDtS4CcJIbttSZPix1Eou63EU0O3/6BHTf0yrnN//8/9ez1Hl2/Qz6pJbkTLmalsnc26JqpxW1mreCU72aLneOBqY2kr8fTNJqTu9nn/urrIoZH/xkWhOhtm3t16buffVnsFBLlibSsbOLDejAjpd+q1sROIVFqjTKn43get6IBJEGo/JpaE+dXwVpCxhyN31mw0yFLrI73TmEPeG0JevPNf9096bjFQTcnxE4hUQFNu4W9/hv/s41YMRCK0+Zqkt540EetNze8Zi3pkG0Xi91Dnus7sUDYUdAqisVa94Oj3/3sy9O/wKNpCcGCEL09dLXx2AeuCLhshciVCm3Ij2NX92MbbimUcOwqrO2YN5rDsauwvmHvUhr36WFDXe4bOTxYhvW7rHMVvK0E6zAaS9ys2CkkyqrUueQ3xU4hUSpC3SMvymT/6dSdLx3VWuvM3HnKUeangwadzUJvVwoD3c5riWhb0J5SMsUa3Xq6c24u1nWq97EPPlHDJYFkYEGI3p4n//SLsXVs3IL1v298ex2XrbDIufDSBv7NgYV63ZM7uKaHtfisNzLYZgyzm3RLDM5KgemUClKXx8dOQQqC6LYWGB7vccHOWRmGw2Yf2KghQvLwpSElO3dEP6TmXwloDO3mdILOnu2wvZ7f7fDb0up6kW4EjnqnV2OhY61ZTlEt00/9xZfucni0HywI0dtw48fTP/ziz8VOIVGBwdDiEq7MYFaPeSWDs1JgOoM6Kqdx1QpSyEnaKmtyeAEMQMhkVEBbbOL8KthY0JSg8ccO7OEWS6qBU4hgZ2zOevOG2Ckkql0bMf6nZtH/m0u46VJ5BvRbFS7zkN84X1kbcFvTmkql2Wzrs09uRdv7PTGWbbJC6PzID5796bWX8SRWErAgRG9VpVD95O98XsB1K0SpUQlOB4tjVyEESRp63NUabkXDvMPudAHHrsK6h71bedynhw13e2byeHYKO+qjFsp4Ow7WazZlmjNip5Aoj9pgkr0udgqJ0soNXfLEm4xdFZqDSppl4xdtukRj+ghlYdQZmmu2d1mvx2LhiGubqzd5zjvWOj8b7bk4/KkPP1XK4jNd4sOCEL1Vn/39Z9J7eDUf1vvesdgOfjiwyH3hlU08O4V1DvlubmOzKCzYRl1P4DRjmNtqnK5jNQgzqVU1ZVrA1wIgarm8zZzmcOwqhJDJxk1Flsf3PGGj+iDBvfnVD5LbGTX0sMyrI2a7Rb3FC42RVt1Edm+g3b3JFlmCdw06Z1biXac64iWOk8k+9eGn7kJ49MawIERvyc+/cfUX38S3WWHB4+H5BVyZwZxB+/xeRuwUEmUwazaauDMKU6sVeR3DYUsChCQIg09RY/DUHXa0TZdt4Igm2EM+Y6YRFzuFRN1HOWsMjr6ERbS9OmbyLf5iEzvRoY345NMEUTvrIefLWycCzjUhI5CCu9NyazsePuLfLFcJpdw33n/1exO4whQdFoTozeXi+St//AWxU0iUxqChdUae48UOIkVyOUkGLI0mK3YQiXL0O/IVnLEG6xxwR4u4pocN93jm83jqDjsZcM6XtsROIVFDNkuiMS12CokKaMwa/lWxU0iUQW4Jkltv53cIneS2imTOW/kYvXjeTWVkewq54A2ZbibivX3e5WqBUJK2Id/yfKzvwaPYgyY6LAjRm8MO7zfQ9eBoKo5zC2DhC5HNXfwRD4sca5newYNlWFeHcyK2J3YKiQo4zTfK2EkLcxq0KQFnpcAMCoVLv4edtCA5IT9iTHICLXYQiTqu9xB87m39FoLPH9d56eaNkxaHQC5pFUKvX3UrFxsKu5fqWYVKbum2LawnI2e7djK02qD97O8/c4fCo7cCC0L0JnAG1BsIn+lfmMMLekq7ewAAIABJREFUYDBf2D2DVwf3YbHrF0s4KwWm06liiiouWkEkSRJ2WYPDU3dYt0dRYvHUHXbJpyk0sYEfdpGy1JkVsVNI1IB+UMNMvYPfqGGmBg2DFvJ1i4IYczaXyrtn25zzzZRWpzCHjHPRZGQssJQuas1a+0hk4ge3fvDsT297ePQWYUGI3khyK/3Un+MrMTC9zZjnFTh2FaRUKxsOHYNjVyEEITOGreU6vhYAa+t1JMs4dhU23OteKeKaHna2zblUweNB2KjdFqPxdhysQ28hOWwWhZnllF+29I5/u4+ftcnN46Z8qrn5kN+2zW7Z9SqdW7mYSvUP+mcyaZNdp+qwb6ylBx4Ze/LPnoutYeOMOLAgRPsSeOGxDz5RK+NuKyx030g2jZ20sI5zXbsxPAGDhUdb53fffFDbvSnS7b4ew35IWNBjnShgwQPzm/Tb3LbYKSTKolKZNJvYLApSEfJ+7S4vMGIHkSbimI6S8e/iOrdQH9HIaW71gtVaZGcCBo3T1lgv54Z6PTeycYfTyHpUW7Fc5P7wylaBanVd/sATOJRBFFgQon195zMvT/8CNxRh3ReGF2Zx2QoL9Pum1nGKHczptcxm02KnkCiTUbPF4SAZmEoup00My+NSCUASRJtLqLN46g4771GUGNyhg12kTHUWn6yEjRiGVOzsu/xD5OzacX0/yb/SoTO2m1KpRu5MOzVR3G1xm2tmYS9f7hoLzGylnCG7ssWzfH31e5/7l9sSHr0tWBAi2O5S9J/++utip5Aok8sSL2EzJEyjUxd1Cp7HrWgASRJEi7bewK1omCdszVZrYqeQqN5e51YF1/SwcyHnagWvc8POuqkYvSB2ConqNth59ldip5AoSul28zO35Y+ysRNt6vaIdqXGZh706xeqa31Oa1FfT9eqkQH39b2YJ2SjbdpEvNT/3vEv/OXXtuZ2bsvXRW8dFoQIwLHc5UevNOr4yBWs5WR/uYjLVljrmY5EGg95YJHx1tU4XgCD9fV5b8bxYBkWDtgnctgsCgvZTGuNDbFTSJRdrVaQOCsFppUrw5oVQYan7gBSRh7RaGXC7Vrq8BF5RiYUL1LaOD0z6rAymlSZrYcj1EQi2tnuzOj4dKHaca5rfinl6QlcfvQJlsFt97sKC0IE+Nr//O7SxJrYKSSq/z3Hl+Zx2QoLjrROr+I+PczTarsZx+vyMMqqW6zjCyUwrUqZ1lR4nF8FUZCkw0Y3ODx1h512CxUO77rDLti0NIvP28COGgcV7DufJfOfEXx8TB9qMlePmu165bogY462Ga5ld7vbHLtkuVinW496p9bjLf0+3mbbXtz7xj987zZ+dfSmsCBEv2nt1ubX/v47YqeQKKrFsZ3Es0GYzqRJkbhqhSkUZNOpbOLYVQhBysxBY4nGC2CwrggVr+KaHnY2RG1V8Xkb2CUvFaPxeBA2aLQzzFWxU0iUS+W3c7du+x+rYyZ79QNuxQ012TzjFuZLmycCjh15oSFwwT775HY02OPJqch8vtrz8OhX/se3l6/jycTdgwUh+g+YBnP50St4Ug8iCMIxEqmW8eFamO9EKJOriJ1CorrGWzeTb+9V33tHf79vNoljV2F9Qdf1LDaLwsJ2y1INm0VhLXodLcOrgzCjQt2mmpPh2FWIglAOqXiZcEd26FplSwZCcdpcT9Arl7xUWtgjSd4bMl6PxcJhd5SsVxuNttOdcwuJtmOdeHfpbsKCEP0HX/yrr2/O4l1e2OD7xleXsFkU1jEemlnBDwfW0m6f3MNOWpjTYZwu4dhVmFGr3pUXcNEKUilIo7nCCrh9CSBkxIi93uDw1SjY/VZ5g8ODZdgxfZ+cu2NjV/nyUa2hwcyco+y0bMGsJsI++UwuNtDp3mALDZ7zDLmnVmOhI61VlS4TzX/pb755p5Kg/wgLQvTv5q8uffczL4udQqJc7e617YLYKSTKQBl28Jn1fahUipKZYPFhJQhJEBq/ptbEPWBYW6c5VcdTd9iZoG23hiOaYA/5bQkan1KAHbc4aOZ1sVNIVIum3cpdv6NfQskuHzUMa/mrLqXyiJ1er0bPBF1LTEquIp2d5hvbsc5hX4xnq3Wm84Fj3/7USzO/xIPuuwELQvRv6GoD3wPdj1yp0HcF69i6sA/X0UCxhFcrYcEx/24GtxJgfcO+xRQeD8IGutyTWXzsFNbvtM5XsVkU1m40lLh3+3bcYWVV6tzy23877nBQEepeRUkmu+On7nb+hlPpOmJMZBpbD3ht28wWpVdRAc10ItHb712rlzhC8I0F52dj4bP9j33wiVoZz7rvOCwI0b95+v/5cmwNRyDC+h8Z297AZSssfLpzbhWbRWHBXs/kNq7pYV63+WYWf+bAbEbtKoM/c2A6pYLUF3gBty8BCoLotZUYHrcvYWetTJPD69yw44ZukrsrY1eF5qCK5tidC5SlyM60GjQue3OhmBru8S5UsiqtwtRtm12Ld55sTzeIaqXxj//tK3cj1b0NC0Ikk8lkkz+aevnpn4idQqJaBoOLK7gyg1k95tU8vjoI0+lVcZLGsasgOUkKLnmDZcUOIlHONn2hifOrYCeC5gSdFzuFRD3ktyZpHAQAO21z0s0bYqeQqKA2bGIn7tqXI7md44YeGftKxGAOmpKJeuZs0H6rEqWsWpVfsxBLdY8F1gplUqVsPTP48tM/mfzR1F3Ldm/CghDJKoXqpz78lIDrVohSoyJcDhy7CiII0tDtrtZwKxrmG/GkingBDNY77F3L4D49bLjbM53DU3fYiJeaK2OzKCxiNmWZGbFTSJRTbTDLromdQqI0cn1EnrzLY1dN7ESnLtKhWmjy+YdaDIu19Q67sWlhtwr5gSHfVDpttOn1Pa6l+UTPpZFPfOjJMo4xv5OwIESyz/3hs+ldfBIa1vfeseg2LlthkfNdK1s4qA3WMei7sY2TRWFtAdtECj8cmNtmmKljJy3MrFbVlSkBXwuAqOXyDnOGE/DUHUDKiFOmGsvje56wMX07wd39t3+EdmJLSdAXrIo4PXPUbpHr8ulmpbfbOZGKud1mzqNa381E7uvayzVlcvmVP/nCXU94D8GC8F539fsTP//6q2KnkKjgsa65BVyZwewB22ISu7ZgRrN2k8G9TJhSKS8ZOY7HC2AAkiAMHmWNwVN32EirLtfENT3sIZ8x3cB9Ftg5yl5jsOcQFtb16pg7O1l0PwSfH9W6aObauNWhV66xssZ40Hgtt9vZQpUM7G6+FB4LLMRyWpvOPtz9869f/eULr4mS816ABeE9rZgufeb3nhE7hUSpDZqGwYRjV0GEnFQGKRy7uh97vz1fwbGrsMigZ7dQFDuFRA31eOYLeOoOG/PbF8pbYqeQqCGbJdnEZlGYX2PS8lhIwPRyc4jYFjGAip0Z0g/aiGsGBX/GLcyWNsYC9piyWGTorgHXZDRO+cyKVuvGWqr/vaOP/9GzuQRO7b4jsCC8p33m958ppHBlBos8eDwZw587sO77wxu7+AIYLHy0ZXoHD5Zh7SH7RALHrsL8dtPNMn44MIdOkyPx+AumVyjc+iiOXQURMtlxY5YT8N0C2KjOR/AiXxryCjNWuemkKZ9orFzy2tP8nkzOt3VYridibW1U2SzbSxYj93et75Y0VuOnP/K0uGkPKywI710//OLPXv0uXrCGdZ7qnZ/DoQ4wV7tzdgerQZiF0i+VsZMWptMq06oGj/OrICRJKlxEg8MLYLBuv7LI4Kk77JJPl2/iKGzYJYqqMYtip5CoPt2ghpXAq4xCfURD0tzq/VYbLczZNGSvVzmZ3esJOZKqeq5WD436Z7bS1harsatt4l9u/ui5n4ud+BDCgvAeld7LPv0XXxY7hUTpLPqiTI1jV0EKhULmNTWbuGwFEITMGLaU6w2xg0hUsNcZL+MFMNhwr2u5gPsssNNtjuXyrtgpJOq43Ran8Rl6WLvOKuevip1CoswKKkAsiZ3i38jZtVHdgIL/VYtWM2CrLFX2zgSdG0K2ybPBXsfkTszfZW86dNG93MD7xp78s+eS27gDcpthQXgvEgThk7/z+UqhKnYQiWq//0g2jW/rwTovdG1FcSYtLDLaOr+HF8BgXZ2u63Hsh4QF3ZaJwl15D/oA8hh0MR6rQZhJqTRrtnDsKkhBkAO6XV7Au+4g4piWkvESWupYuYmAOtiv2ykwew/7LdvMllGjcAcNE/FopNuVVDKZYq39XNfSWs7a4vzEh54UePxrfzthQXgv+v7jP7jx42mxU0hUz4WhhTm8qQJr6fVNr9/9ydQHg8Njms3iniXMaNDsEGX81xukVsppM8vi2FUISRAhj6zC0GIHkagLPlWJwYeRYJcoc53FJythw/pBFSu1g2WuW54W+PQFyphnZgMGTYuTn84nhsKeDbZUZ9nAEc/UWsITcSv97rmry9+/8gOxAx8qWBDec3aXY1/4y6+JnUKizC5LooKrVphKq6yYlByOXYUQBKFoNdQajNhBJMobtmWreAEM1tvt3KrgvVPY2ZBjrYI7dLBTTipanxc7hUR1G2wC+yuxU0iUTenyCFKrBmUymYzgE2P6EM+82mswt5uS0XrqfLtjlo6rNXKq03RjN9Yx5MuryXSm2vfI+Bf+8mu7y/jD4bbBgvDewrHc5UevNGp4xwnmOzFQzGMnLSx0tiuWxJm0sMh4YDmGx4Ow3l7vzQT+sw3raKGu5bAfEtZmNW40NsVOIVF2tUalWBU7hURp5cqwZk2Q4fYlgJSRRzR6mSDRHTodM9mj721VzrB88UG/frm+3mrVq93yhXS6v8+3Wi82BC5wKjS/kPD2tl5+9ArHcmJHPiSwILy3fON/fX/pGv4TAut7+NjyAi5bYcGRwNQqfjgwT6vtVhKvDsKsFt0yjZdOYRqVsqit49hVkIIk3RRDc3jqDjvjkVU5CV0Ak5SLNi3N4qVc2BHDkJKV9NjVVtmyniTO27g4PXPUblEZiru1wlCPe6qU1BvVpoh1ZjXeMRakdcatheg3P/6i2HkPCSwI7yHrU1tf+R/fFjuFRNla7DtJiW6YiU5r1KTkOHUVplCQjFPRZHDsKswWMhZpbEmARSLUXhVP3WHnQtRmFd/zhN3vpaJ1qcyHlJpBo73J4GRRmFPpd/A3xU7xZvjyMa2h2bx5yurQKdcYoT7WZpoo7vqcZt4pX05kIqOtW1W6zrCRB459+W9fWJlcFzvxYYAF4b2CaTCXH73C4msBEIIgnEci1QouW2EtJ0OZbEXsFBLVMRbYSOIFMNjAoG8miVOIYN1tjoksNovCuuzmpTqOA4G5dVpOJukTHhEZFeo21bwMx65CSEI+rCFlwgFY6ijYpSOGYTPxmkXBn3Hz8+WNI15bXl9LVMq9g96ZbFptUNlHAnNzsY4TPZcfvdKksZXg3cKC8F7xpb/55sbMttgpJGrgfWOri7gVDesYC02vxMVOIVH+dvuNPfxwYC67cbqE9yphRq06rijhohWkUpAmc5Xh8WoQgJARo45GncN+Fth9VkWDw00o2HHDgJw9MJeGHNx1l9JxzJhNNtcueKk8GWOEZmeYupaKuVxGMqBd3Eh2nW7PcvJssvjlv31B7LwHHhaE94SFX69865MviZ1Copwhz/o2dm3BDJRht3EAdhNFoVDJy2aCw9cCICRBaPyaWhNfAIO1dVqSdTx1h50JUru1jNgpJOpBny1B49kp7JjZ0WB+LXYKifKp2mzspNgp3ha2X0lz7OZFm5UWZm1qssenmsjudrfZSwZuK1PoHm9dyVUIpSJ0fviFx16cfWVB7MAHGxaEh1+j1rj86BUeXwuAECRh6g7W67hshbmOtBSKuBUN6xht2c0UxE4hUf3DvoU0Hg/C+jqck1mceAHrc1nnq3gjCBY0GCr8nNgpJMqq1HgUU2KnkCgFoepX0TLZAbs0RHI7o4ZugnslpNP1U6W16u6ZoHObLBRZOjzgvplImB16fY9zYS7Rff/QYx98sl7BB0vfOSwID79nPvp8dBW72mCDv31icw3nQ8LCpzvn1rCTFtYacU7u4NhVmNdtvpnFvzkwq0GzyeNL4jCtUqHQF3gBty8BJEH02cpNHls2YGetXJPDgcawUUMPyR3IS0NGdqJDG45o1ktM/GG/dZvZ0qmI1pBlIhENtNoYp2JzNxc+3xUvcbV689mPfVXsvAcYFoSH3K2fzr70+R+LnUKifD2B5TX89wNmcZvWi2WxU0iUWqNMazh8LQAkJ0mZU0GzB2wr+q7xBI25Rl3sFBJ1MmiJ13FEE+xhvzXVOJBr+rvglNVJN2+InUKigpouM3td7BTvmNBBbCuE8kVKk2am203aFid3Mx/t63AlVfVEqdox3rKYyGksOt94/0tP/uj6D/GU+B3CgvAwqxSqj33wCXwuAKRQKxV+T7OBy1YAQZDmXk8Zx67uI3DMm8jhC2Cw3hHvahb3WWBDYc+tHB4sw0a81FwZm0VhYbMpz8yKnUKinGqDhbgmdgqJ0sh1EXlaJjvAp+4Enzuu9zWbrw0Yba3G1G4tdTbkWGXTjIwP9jomd+MOv0XRZl1dSvY+dPTTH3mqUqiKHflAwoLwMHvyT59L7+LKDNb/yNjeNn44sPD5rqVN7KSFhfo9N7FZdB8Bv3UyhQ3qMLtZt9jA+Ycwo1rVVKUFfC0AoiTkneYcK+BgfQApI06aqiyP/SywUV0HwR/4Bn4Nc2vQMBBQTDN87qEW4xq94TSoqID2ejwa7nZlDXw0U4pcCG8lajKF4sk/fU7svAcSFoSH1tXvTfzky78UO4VEtR3tnF/AlRnMHrAt4cN6+zCYtTt8DQ/dQSqlvGYRGA5fCwAQMpnZrykxeOoOO9amTzfw1B32cIsp3cApRLAzlKPOTIudQqI6tN36AzZZdF8+ftYsV91v4RP09LDNYLLWlsup4R7PaiPf4NnAUe/0ZtIepCx9Hf/6lVeufm9C7LwHDxaEh1MxU/7sHzwjdgqJUmlVnMXK4dhVkJxQtlM4dnU/zgFHroxjV2Fdg57tPI5dhQ33eBcKuAkFG22xz5c2xU4hUYNWS6qJBQ/MqzEaBHxnAqYnzZ3kruzQnLoL9RGNnOamT9scRvVWlS2fDdluVKImo8YcMt7YiQb7PRWjenc3P/C+8U9/5Kl8Ep8Te3uwIDycPvcHz+A3w3563jse28Upf7Du+yIb2/gCGCx8xD+1jf2QsPagfTIRFTuFRPnspqkqthnDKJ0qT+C3FUynkHv1MRy7CiJksjFjnuXxwhhsVO8n+EN1L0bOrh3X9xuFqxYFe9Yrm6usD3psjJVdy2X6B/1rdKnKNNrPdqxs5g1O62d+72mx8x4wWBAeQj/58i9f+fbrYqeQqI6TPXNzuDKDudsdc7tYDcIslH65isdfMK1GmdU2OWylhZAkqXQSdRYvgMEG/doig2t62AM+fY7B69ywi5S9xuBb5LBe/YCGvSl2itvPxk4E1C1Hjak0vXrBY6vKE0Wu1hdx3sjGjRa1pds+vZrw9XiULZ6JH9z81+dfETvvQYIF4WGTieae/DO8UAvTmfUlUi3wuGwFyOWk4Dc3mzh2FWYKW0s1vAAGax9wRYt4AQw23ONeLuI+C+x0q3O+jE8pwI7ZbXEaJ4vC2nRmBX9V7BQSZVLYWmXLYqe4Q/iIPCPw8QuUtS7MmdXCYIvm9fxuyG/lKMViLNV1tCVJ8Ll8rf+RE1f+5AupHfzZ+1ZhQXioCILwqd/9fCWPu62wjotHsimcRQYLX4hs4UzafXSPBub28AIYLNzpnIjixAtYm9tyvYgfDsxr1MWEHbFTSJRJqbRotnDsKkhJkMO6OC/gDh2IOK51yPhDu0NH8PExfbuMe6VDZ+i1llYrO6faHAllJVWr9Ax754s5Xkn4xoPzi0lHu/cTH3oSn157i7AgPFTwUc43EDk/OD+LzaIwX7d7ehMLHhjlNs3msVSG6XXqPbKG/96CVHI5Y2EZHseuAgiZ0O4mKgwtdhCJut+rKjF41x12gbLU2TWxU0jUkH5Qxc6IneLO0jHXe3Q9nerFKht/2G/dY3fkSi7YaZ1IxhxOg67dNLMaD40GWatt/rXllz7/Y7HzHgxYEB4e8Y3ksx/7qtgpJMrkMKVw4bEPpVpJ27Qsi3MLAARBqNoMNRrHrsICPVSqUhE7hUT19jg3yviCC+xsu2ulglOIYKecthg9L3YKiQrrrTLuV2KnkCib0uUV7ok241bZioZgL9hUaWY6ZNSE3MT17E530F4xcWvpXGSsdbtWr9BMz3vGnvno83srOLbqzWFBeEgIvPDYB56oV7DogbWcGSrmsJMW1n6+ay+O41JgkfHAciwtdgqJ6ul2T8bx1B3W6jRez++KnUKiWkyGrcaW2CkkilJr1Mp1sVNIlIpUdGs3BAFP3QGkjDyi0cuEe+NhJL50XGthmGvHzXa/Ib5XS54LuTaFXJmhIwOe6XRKbVQ7Rvxz8/GWwdBjH7jC40tjbwYLwkPim5dfnP3VotgpJKrvwSNLOFl0H61DLdOruHkGc7dYp5I44g9mMWtXGdxHgKmVirKxgWNXQQpC5neydQ5P3WFn3ESFxVejYJcoPc3iPgtsxDCoZO+hdaCSnR82DDrlNwSh/KBfv9HcNGkUnpBxIhH1+60yv2ZxI9l1sqOi1m/M7b3w2D+LnVfqsCA8DDZmtr/8ty+InUKiKL99J4NXz2FagyavJnlctkLkCpLzqBsMjl2FOTrMhTq2JMDaQ8Y4jS0JsLPtjo1qQuwUEnWfxx6j76E1/dvSa6T+T3v3HiZFdecN/HfOqaq+zB3mwmUY7rfIVRAMqECMEUFAfNzF9U027pqsxJgEE3mJifExaxITs4+7JkjIq4mrxo1I3IWIiJF4g7hBjCAo9zsMzDAMDDNM36rqnPePmunpmanuaWBmusf6fh7/aKpqjmeqe6rPt86lbBMri7or1ctLpeeWkCiTH/bWcmYWhqujO8cW5ZYWR3eeqx43ouyUHq6qvzBq2sD95+ptohE3XvXcD186tAMLGqeCQNjjWTHrsTuXm1E85MoFY6xk8qjGBjRb3VVcM6S65lO7FtllGnF1xcEqrCXjbuy4/tur0KZ3N2pQ8fYL6Fh2N6JX/r7w4UzXIkv1CQYkQxp0F+T6MN9eRRj454IzMdHPSXmvqaNi43XTtHZf26t3oe9wvVV33dDeO6PVuo9VjO699cSpXv3yA6NKd+0+NXTaZx67c7mFB2slh0DY4z33r6sPbj+S6VpkqbE3T92/G81Wd0MnD8Jg0WT6D+n9t0qcHHe9e+V8cgEPd3KX6zeqtAb0ubvSBCssisQk2mQuGLGrS6ywjY5ldzcU61ELUz/cTckdJ6z9ma5FZnD76NTcK3LkXwo1NbMf29W4f3jvXKOP+LDq1KjP9KnNVSdqzo+eObI6pM6cqnv+kdWZrm/2QiDs2fb/7dDqn6/NdC2yVMmQPgdP4KmD7nIKAqeUhbGirjRDhIq4hTnobhin/EE5DVEMw3Y3eERRdRjLrrqbOaT4aAh9p+6+0L/XqYhH2/QdurKgOBrbkulaZKl+xqBe1geZrkUmFVjvD/QPnJR38nTkwKy+vSz/marw+QlX9NkdqrWYrJjcb8fxmpySvP7Txq762do9W/BX5g6BsAeLhqKPfvEJy8RyWy4YZwWjh0RCaLa663v1oNpzuBXtbtjUAUdrsFyKu7Hjyz/GQjtJjB1a9kEtHkPvbkxp0a5GLJ7priInJyzxnAl3BbqvXNtOhPuXLjRmjDOiRB7vdZcjxSlun/lCcYFJu4KafeXA4PvnT5QV5+RUBD48erJiVKnsk3dwX83oz0989ItPYEF+VwiEPdjTD7xwfC9GULgbv2Da4QNotrobce2wnfsxktbdwJGlHxzHn5W7fn0Ktp/DJ8ddUV7goMKkU3cBXdNy62yFXncXgrOJxaGoRCPV3axCFbPPZroWWWpq7hXcPpLpWmQes2um5vRT5rsjgzkTel/YfeHYlPLe53Mih+rqxkzof0yGzzQ0Dr9+5LGacNSSzzz4+0zXNxshEPZU29/8eO3yDZmuRZbqO6p870G0zNwVlOYdOo++QXf+oHHGb0mJW9EuBOdUpoWx7GoSfQblnIuGM12LLDV9cOGp8LlM1yJLze5fVBXBQjvuphWVRkxPj4dMYaB/eIG1NdO1yBZ+a/uYnLGDjV0hu2pueWE1HbeZOXpU8Ydnq4wcUTaudMfhqt4Di4vHj1qz/LUPXvfciqwdQiDskUL14X+7a4XCDDA3Qtf8gwfEomi2uisa178B4yWSqJjU99Q5zDt1N2Ziv/1ncJ/F3YSRfbafxSpE7ib27f1xAwaLuhuen3/e2pnpWmSpYiPYi72f6VpkKYMFRotzRJg01GKA+jhPsOuL+BnzoyG5vuH9+Ptnjw0d0ItKtZ0nq4eM61efbxw9Vjt27pTHv7ryAmbNtIZA2CM9ueS31UdrMl2LLDV2/mePHcLJcTd65ojdh6ozXYssNXhM378dw2BRdxXlRVtrEHjclRTm7o7imuMuz2eYvhqFCWBuNMZHFp41JZ4a5e7awogl8WAkd1fnDeeyMtO1yDIqdKXhi5nvTy3s3T+36lio6rrBpSdEXXX4whXj++0Pnw+ZsaEzhh883sADvpX3P5vp6mYXBMKe56+vfPCn/3w707XIUhUThu7eg6mD7nqXF+05fT7TtchSwTzfSRZBp7srQxfhQmXauBXtghH1KvfVm+h1dzdlUG5NFG16d3MGFNREsQqRu5m9SsMxjOtzNywwOhcjad1o9t4puRN7s/cFXZhdnnM4djjH4EOGFW05fbKod7BwdK+P9p/qO6osb8SgN557Z/N/Y+naFgiEPcz5Mw2P/8vKTNciS3HBtX5lloVmq7uiK/pK3KdPomJC30jM9OlapiuSjUZd0bcuEsn3+fwazk9bY4eVVUUa8nVfvu7zCZyfVsaW9Todrc3V/c6r8JaJAAAgAElEQVR/Bsf5aTEoN9eUlbkiLyCCzn+CiUxXKlsU6f4iftAQJRrPi//HGD4/REQaM4ZoEcX7EM9v9R/h80NE1MveWqIVXVMYPhXZ8ZnCvH6l1vu1J0YPKm7Ml7sqa0ZMHnBGY5WV58bOu/oXX3/q/BlMEmnCMA+NiBhjRJRVp6KystK27f79+wvR6i/8kUWPv7v6fzNVqx7BCBqFfXsX9O1l5AW4YSghYjHZGIqdq22MRmKZrl3mCcH9eYFAvs+XYxh+Xfh1TRdM48QYCU6c2aSkUqatTNs2TTsasxvD0XDEtD3zXD5/0NA07s/xEVEgqBNjuk9wjXPBuMaJMy4YESnOFCOplCTlLENjKWlLZUrblioSsxSpxkjMlioU/VR98DhjwaBBRH6/LhgTBteE4IwZPkFEms6JMc4Y58w5uunGIyciUkSSKUVkS0lEppJSKamkKZs+XTHbNqUkRY2xGBFFLCvWA3smfbqmC8Y59xma4IyI/IbmnBAhuMY5EQnBuOBExDkxzoiIc0aMiEixli8jRUoxIiJbKUWSiCySUikiMpW0mk6jHT+BipRz6oiowYxm0bdaAo1RrmE4r4OGJhhvfi04Y0Skca43f/UZzvki4oyJ5pvYjDHRfJYYZ9RyxuLnQSbe/5Jky+av+JiKOS8lqVjzcE1TWjHVMvPcljJsZ/LPNiA0X/Nv6+fCaH6tC+5vOh+kcebjLbf1fYI5Z4+INK4ENb0WXPGml8RJCdbqSs5Zwnx7ZlPzWZJkJ85PU6Rs1TK01VTR+HMgLGkm7iKimIzaqmv/bDmxXM2I/1NjIqC1NJb8TBPNp4KIDM60hH/6OWfNlRfENNHqr0QnYvGPllJawuliTPHWc/YYWTzxADJbnTQVbTPHTylTJZwrRVGZ8E9bhZXqtOUPDObTmB7/p+C6wXyJB/iYP+GskMEMzlr1EhlMT9hPgjHRqhuJGYk/7xyTcPaIiJPiCf9kSol2T8jgZLPWZ4lT+weGKS5DrbfEGLUea908uljxok1RI0zjN56LHD4/pFCUbTpQXxEpLBbB/R9WfcYo8JvsxFv7h5X69ryzc/otUx7+76WJxdi2XVlZKYTo379/u2pkTDfklG4KhDt37tywYcPJkyfz8/MnTpw4Z84cwzA6/rHWQqHQ2rVrP/nkk1AoVFFRcfPNNw8bNqxTqtdTAuGfX9j00y/9IoO16ulye+cFC3KJyF8QCBbmGTl+7tMV46akaMRqqA+frwvhuY7J6AHDn+PzBXUi4oLrft0XNLghhCa4zpkmiDNFyiaypbKksmxpWU3flJaUpmmHItFozI7FvLjej6ZxX0DXdKH7mr6hfT6NC6b5BGNMGBpjSuhCMeKCKSLFGSOyGSW0z5RUZCtlSWkradrSsqVl26Yto6ZlSRmOfmpnIjFOOQEfERm60JubfVww3dCISDeEE7o0QxAR46ypLaglNFYYNWUtIskUEUmlnIQQU1IppZSKyVZ/+xHLspWKR1NLyVCsp57hHJ8uBCciQxeaaGnStcRUzp3tnJHQBRExUlxr1TpknDU3/5oyKjWfTCKySanWT5UwlXSmDtqk4qk+ZDedw6httRmEbCkZsrLxDAeE8DV/6gKGpiU0mgVjAaNpl+DMEPE81nLyBOOct2pdcM44uaZZ1eZpe6opmBERMVJmQsqKyrZ5VZKMSav5B2UoIdBeyNyQZp2JHL2lGZOn620yREAT8bQmGPkT2jyJEdfBSBm8ZYvGVeJ+jdltAwojnpBAFCnWKuXaqt2iLIqknZDKpDLthGMsO2q7reMStkPtN14+RpSntUpxeXrbxjNTLNh6bEKAtzptBnfpehaMaQkfS0EkWNs2cJs8TESC2YkfUcZs7nY2mJLEWn8+VUSRyz1lpaKq1b0DaSv3M2nLRtcSXPm1QetriwJ8wvZa6/BJY1yw7+HDdb4qNbqo99EPTxWdjfQrzvlo9TvOwd99/pvX/59rW/5HCIRdpK6u7itf+crLL7+cuLG8vPyFF1647rrr0i9nzZo1d91119mzrZ5F89WvfvUXv/iF3++/zEr2iEB4pvLsV8d9G8sidbX8kvy80qJg7zxfboA3t5wY51zTJGOmTTHTDodiDedDjRfw1PtLIlgw1+8P+jS/pvt1I+B0UQrhS/zOYkzjxEgRs5mSRFIq07YtS5q2jMXsSMyyW7cmG0PRbPoLzjBNE76AJjRh+HVGyh80iEj3a0TkhE+nqzPxR5jTlmWMGElGSilFZCslidrPHoxZliQyLduW0lIyErWIqDESkx54DwxDM3RBzR2kibt8fo2Y09cnicgwfJrByenO4m1bqvG8qnhTV47Td0pElmo7uFsRxfNq1LaISCmKx6dGty7okGlasqf26uf4DdHcoeprjhPx+BqnFPmNpqawEJzH85hgqt35Tgi0LX2wjMhu1w6mhP5YRcxsjgdSqah0af5aUsZUy7sT/3sJ25bpdnyWKPS1RIvEoOvTuc7bzidijPkT7rAYouWt4IwL7nIOE3MvMUrsfGKkXNcZkkwmtsSsJN1lNtmWbJWNVcuPyPZR2WFKO2p3xx0HRqzA0Ntv58RyE2YlCMaCCb2abcJwooDWfEOLiIh8QlH7z3frrmBy6w1uqSFrE4yJJXm0vWJKte7+lWTJhFs/imxLJT2rMRlOfENtZcdk5zScdMYDotVJDghda/79681Ynl6x9qhVKgebEe3IrroJuWXhs9GG7bVj+vY+u6+67oOPI83LrecW5Ty14/Hi/r2aKolA2BVM07zhhhveeecdIiopKbnuuuv27du3c+dOIgoEAps2bZo0aVI65bz++utz5861bZtzPnny5D59+rz99tv19fVE9Pd///erVq26zHpmfyBUSn1/7k+2bsAE6yyi+fSCkoJg77xgQa7ma3Vh4obGDZ1xLhm3pIpFrXDEDF2INtSHFZ5x12U0TTNydH/QJ3Ru5Pg0QwhNaD6tTfLhnDGNk+CMMcWYcgKnIkUUs9p/KbJYzLaVjMXsmGWbpuWp0bOXwOfXNb1ta9IfNBjnmsZ1Q1A8muqctYtJjHOmMaKmnlLnDj85rXZFksg1czqDdYkoYllE5PSduhwmZSRmEVHEtEzPTDb2+TSnW1XXhaG5tDgNv+Z8Ceo6dzoSibH2byK1SbbxeNB8oEroMGzDUsrp65ZKmUkeT+90fVPrrBuz7WTvlCntHvpUTJ8u4tOVNcGN5sRraELT3Fd2MAwtfmp1Tbiu/9CmUzc+ApmIiCVt3yhG8WymiFIM9Yx3+RKRKaXV/D5KUhE76RthSjtqxfstqcHMlhupuYautRvx6AjompYQieMjmdvTONNFyy6dc+H+BhIRJR5JRJpglPC2dDSBtNVfjWsvZcuhyk6xXoBKGCntSEzU7dlKRlpn7JAV7Yp7fzmarid8I7TJz21wxnJaX80MwfWEt2l/w4Vyo+J/D9cX1+cM8BUc2F41RAULuXH0zb3luezw+3sTf/aq2RN+/Or3nMsgAmGXWL58+Te+8Q0iWrx48YoVK5zf55133vnCF74Qi8UmTpz44YcfdlhINBodOnRoZWVlYWHhe++9N3r0aCIyTfPWW29dt24dEa1Zs2bBggWXU8/sD4Trfv3GE1/7f5muFFwuxlhecZ4/L6fNdmEIf36OL8evBQxh6EwIxbhUZNq2a9spGjUjETPUGGtswNqGmREsCAiN+3J87XdpuiYMofk0IbjwaYwzoXHFOU/S1CPOlCLJSJFyUk2yWXNSkmVJJ53aUkaippQqFP5UTVDsZsE8HyNyulJdDzD8QnBOzSGWMS4M96ZhPMoyYlErSkS+QNPoFUnJm+NEdlNSkmbyu0WWbJ4uaNnO9MuolTQpOXtjPTMsXZpgwIhP0Yz3GbYX78IVnOnNQz25xnn7/ttmIrFvV0t6GFHLsGQikq0ngrYRn0NLRLZSVpKE7IjZdjyGhS0r3hCPWFbqO1Nhq+2g3OyX6zfi74XGmZH8rSSigK+l/S8YT5almw7QWeIEOZHyrWTxERNNlFuHXKsfSAxgipT7N3cCs90Q6zaUoohs9Scc6qh7UynVaLb6OsjULOI8o9XoCV3w1AuSMUY5rd9rjZOeIlsTEbXqsnb14cm6icF+lSca5NHYuOKSyp3Vgcr6irK87S9van/wt371LzfffQMhEHYFpdSgQYOOHTv22c9+9t1339USPg1PPvnkvffeS0RvvPHG5z//+dTl/Pa3v73rrruI6NVXX50zZ058+4ULF8aNG3f48OHp06dv3rz5cqqa5YHw1KHquyfcH8bDxMFNTq+8YEHQnx/05fhdb04yzjW/oRka0zXiQhFJYrYtbdv9Ay+lMk0rGrHCYTMSjpmenPLXwwgWzE06cj6Y7yfGjIDOONd9WrI72Iwx4deIiDtrfDDGnHFgSW6NExExpzeBOa1bSyqZvInjpFkiCsdipJjT3Zrid0JPbKfQDOHzaZQy9Dp8Ac3pBuG6ECJVS0vzxadxCmddQ0as4wUOmxv6zoDkFAcm9gNHO4o0UslY8+ckZloddlw0RptWlLGlDH16p922oRsi9RLKnLNAwjgXf1BPfSKFxvWUAYyItIRx6e6jpltTzasrNdcp9eFEKTulE1myZXKmJGWmMZTaUspOGJXaNKO4Ix2mdEfUbuk1zbj4BOMUdE0kvt2MsYCv4xVfO0zpTYclDPZu3pLQuZ0c5ym/noiUrbbvqRrvL1GNsmZr1ZjSXo3Hz1Zt3m66rS8YyPX/evu/9R1ShkDY+T788ENnROiLL764aNGixF319fXFxcWmad57772//OUvU5czf/78V155ZdSoUbt3726za9myZY899hjnvKqqqqSk5JKrms2BkDP+7ZkPfbx5T6ZrBB6l+fRAfjCQF0x2gNC5HvT5cwNC14WhcV3w1A9vYJwYU8RspaQi20r19Wnb0rLsaMSKmZYZtTBv02ucYcBE5M/xJe1iJSIi3adzjXPG9ECq2ENEwllWl0g09REx1lGrJb5yhUwYX5eMVBSJRIhIaHqHD3qxbeXcmolZVrJ7NC3VUCoUiTkvGkPoGe5ynLNATtNEu8QVoZKJz9clIsaZZnSYkolrgqfxsIDESb+Mp9VcduYDd0ixVvMYrI4/4EQddWgnindudyhmWbK5zPjM5HQ0hD+d3wvx9Zyb/0kBf1rLMQqNa3oanyoiXeMijcxG7TrS00n4LTrqykso1nV2pDvZYc8tkTDZ/t3V/RuNPjmBw3/eW6aZxz46lOzgMdeMevztf5VKejMQduFDXd59913nxec+97k2u/Lz82fMmLFx48b4MSls2rSJiK6//vr2u+bPn//YY49JKTdv3rxw4cLLrnI2+sPjryANQgZZUbOh5nxDTc94on0wP6j5NH9ejh4wREetMSPoF0JoPp3pItXMDyIi4lyQYMQFKZIs5W1JImru5bBtqSSZpt3hdVwpFY1YUqlwOg19pTySjS3Lss5bRBQ6H850XbJLII1juBD+XIOIGOOBfJfhze35cgxKI0Zohua0I5lgIuW4vpbKaC5TRl0xwZtu/LM0en+IiEi1HrOXung77bV2bKXiB0dN22WlmvYiyhnUTeSydn575sUM7jVNO+qZIRtp5wLKT/tI1xnOyQSSD7togzPmC6TbnGaCpZnWKOUYdfea6M1PG0ljsDBjjCxKspqMC8XS+OZL4Ez8dn40reNJKXUR77tK+PNMRhKNLSyuOVNbubPqM6NKt7kNFo37ePOePzz+yq33zU27Cp8qXRgI9+7dS0RlZWWufXdTpkzZuHHjgQMHlFIpPmLV1dV1dXVENGbMmPZ7r7rqKsaYUmrfvn2dV/EscnTXif986MVM1wKgxwjVh4iovqY+0xXpJrm989I5zJfrF0LTA3qabXd/boCINJ/OWFqNJ+HT0/waZ5rGGBHj6bb3GKXfQog/EDIdlimJSEplpb26jGXJNB9LY9mWtJVpXsSQ166YDyxtOx6kG+uwQnWPx9O7EeAQgvty07oL4OiwE75VTTjvsCu+VWU0rqV38Ykfz9JOTWlK/5ZEs47HDrShOHXcw6WILqp3P3ZRK9U2z03tmuXrTCkvtpPKlsq2uqQytkzrgnyOqA/X7OLcHX/s+CHe//nQi5NuHK8VXNTn5FOiCwPh8ePHiai8vNx1r7M9FAqdOXMmxWhPp5Bk5RiGUVJScvr06WPHjnVCjbOMbcmf37kiFvHKJAcAuFgXahs68TDoKXS/4bqgUTLOHYHOrYMzVjz94znjxsXUmYg0n3FxXRLpYYJ1MKy9naYBAl2AEVPp3Xa5BGnlk0tlXVQwUIouasZmegMglFQdDrSOu4QZyekM7ugekXC2NAXDYVNmx/NspFThxrQ+KBG/Xhi9YKfRFR+LmD+/88n/u/oekeQRIJ9iXRgIL1y4QES5ubmue+PbGxoaUgRCp5DU5Zw+fbqhoYPmTq9evTqs8IkTJzo8pttUVVX9aeW7B7YdznRFAAAgu5iRmOu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"text/html": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Load pre-generated triangular mesh\n", "mesh = Matrix(DataFrame(CSV.File(\"../datasets/trimesh.csv\")))\n", "\n", "# Compute probabilities on trimesh of simplex\n", "pvals = [pdf(Dirichlet(α0), mesh[n,3:5]) for n in 1:size(mesh,1)]\n", "\n", "# Generate filled contour plot\n", "tricontourf(mesh[:,1], mesh[:,2], pvals)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The yellow spot is the area of high probability, with the contour lines indicating regions of decreasing probability. These prior concentration parameters clearly indicate a higher density in one corner of the simplex. Let's inspect the posterior concentration parameters." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/html": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Extract parameters \n", "αN = params(results.posteriors[:θ])[1]\n", "\n", "# Compute probabilities on trimesh of simplex\n", "pvals = [pdf(Dirichlet(αN), mesh[n,3:5]) for n in 1:size(mesh,1)]\n", "\n", "# Generate filled contour plot\n", "tricontourf(mesh[:,1], mesh[:,2], pvals)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The distribution has shifted to the upper right edge and has concentrated more (i.e., the probability contours drop off more rapidly). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "#### Exercise\n", "\n", "Add some more data to the model. What scores lead to a yellow blob in the exact middle of the simplex?" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3. Continuous-valued score\n", "\n", "Suppose the company wants to know how fast applicants respond to questions. The interview conductor also has a stopwatch and measures your response time per question. Each applicant is assumed to have some underlying response speed $\\theta$. Each measurement $X_i$ is a noisy observation of that response speed, where the noise is assumed to be symmetric, i.e., the applicant might a bit as faster as often as they are a bit slower than usual. The Gaussian, or Normal, distribution is a symmetric continuous-valued distribution and will characterize the assumption well. The likelihood is therefore:\n", "\n", "$$p(X \\mid \\theta) = \\mathcal{N}(X \\mid \\theta, \\sigma^2) \\, ,$$ \n", "\n", "where $\\sigma$ is the standard deviation. The conjugate prior to the mean in a Gaussian likelihood is another Gaussian distribution: \n", "\n", "$$p(\\theta) = \\mathcal{N}(\\theta \\mid m_0, v_0)$$ \n", "\n", "with $m_0, v_0$ as prior mean and variance. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "#### Exercise\n", "\n", "Write down the full generative model using the above prior distribution and the likelihood of $N$ observations.\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In code, the model is:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "@model function normal_normal(X, m0, v0, σ, N)\n", " \n", " # Prior distribution\n", " θ ~ Normal(mean = m0, variance = v0)\n", " \n", " # Likelihood\n", " for i = 1:N\n", "\n", " X[i] ~ Normal(mean = θ, variance = σ^2)\n", " \n", " end \n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The interview conductor cannot stop immediately after you have responded. From previous interviews, the company knows that the conductor in front of you is typically off by roughly $2$ seconds. That translates to a likelihood variance of $\\sigma^2 = 4$. " ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "σ = 2.0;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Your response times on the questions are:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "X = [ 52.390036995147426\n", " 74.49846899398719\n", " 50.92640384934159\n", " 39.548361884989717]; \n", "\n", "N = length(X);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The company designed the questions such that they think it may take the average participant 60 seconds to respond, $\\pm$ 20 seconds. That translates to the following values for the prior parameters:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "m0 = 60;\n", "v0 = 20;" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(54.61030279130141, 0.9523809523809523)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "results = infer(\n", " model = normal_normal(m0=m0, v0=v0, σ=σ, N=N),\n", " data = (X = X,),\n", ")\n", "\n", "posterior = results.posteriors[:θ]\n", "mean_var(posterior)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ah! It seems that you are a bit faster than the average participant.\n", "\n", "Let's visualize the prior message, the total likelihood message and the posterior again. First, we want to get the likelihood message:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(54.34081793086648, 0.5625)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "message = @call_rule NormalMeanVariance(:μ, Marginalisation) (m_out=PointMass(X[1]), m_v=PointMass(1.5^2))\n", "for i in 2:N\n", " message_i = @call_rule NormalMeanVariance(:μ, Marginalisation) (m_out=PointMass(X[i]), m_v=PointMass(1.5^2))\n", " message = prod(ClosedProd(), message, message_i)\n", "end\n", "mean_var(message)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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"plot!(θ_range, x -> pdf(message, x), color=\"blue\", label=\"Likelihood\")\n", "\n", "# Posterior\n", "plot!(θ_range, x -> pdf(posterior, x), color=\"purple\", linestyle=:dash, label=\"Posterior\", size=(800,300))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The prior is quite wide, indicating the company has a lot of uncertainty about participants' response speeds. The likelihood is sharply peaked, even after only 4 questions. Note that the posterior is a weighted average of the prior- and likelihood-based messages. In this case, it is closer to the likelihood because the likelihood variance, $4$, is much smaller than the prior variance $20$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "#### Exercise\n", "\n", "Suppose each question was timed by a different interviewer, and that the interviewers differ vastly in how precise they record response times. How can we incorporate this knowledge into the model?" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] } ], "metadata": { "@webio": { "lastCommId": null, "lastKernelId": null }, "kernelspec": { "display_name": "Julia 1.10.5", "language": "julia", "name": "julia-1.10" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.10.5" } }, "nbformat": 4, "nbformat_minor": 4 }