diff --git a/Chapter2_MorePyMC/Ch2_MorePyMC_TFP.ipynb b/Chapter2_MorePyMC/Ch2_MorePyMC_TFP.ipynb index 3ee81d43..851a101b 100644 --- a/Chapter2_MorePyMC/Ch2_MorePyMC_TFP.ipynb +++ b/Chapter2_MorePyMC/Ch2_MorePyMC_TFP.ipynb @@ -1,4317 +1,4302 @@ { - "cells": [ - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "phBEJ8iLIAwF" - }, - "source": [ - "# Probabilistic Programming and Bayesian Methods for Hackers Chapter 2\n", - "\n", - "\n", - " \n", - " \n", - "
\n", - " Run in Google Colab\n", - " \n", - " View source on GitHub\n", - "
\n", - "
\n", - "
\n", - "
\n", - "\n", - "Original content ([this Jupyter notebook](https://nbviewer.jupyter.org/github/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/blob/master/Chapter2_MorePyMC/Ch2_MorePyMC_PyMC2.ipynb)) created by Cam Davidson-Pilon ([`@Cmrn_DP`](https://twitter.com/Cmrn_DP))\n", - "\n", - "Ported to [Tensorflow Probability](https://www.tensorflow.org/probability/) by Matthew McAteer ([`@MatthewMcAteer0`](https://twitter.com/MatthewMcAteer0)), with help from Bryan Seybold, Mike Shwe ([`@mikeshwe`](https://twitter.com/mikeshwe)), Josh Dillon, and the rest of the TFP team at Google ([`tfprobability@tensorflow.org`](mailto:tfprobability@tensorflow.org)).\n", - "\n", - "Welcome to Bayesian Methods for Hackers. The full Github repository is available at [github/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers). The other chapters can be found on the project's [homepage](https://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/). We hope you enjoy the book, and we encourage any contributions!\n", - "___\n", - "### Table of Contents\n", - "\n", - "- Dependencies & Prerequisites\n", - "- A little more on TFP\n", - " - TFP Variables\n", - " - Initializing Stochastic Variables\n", - " - Deterministic variables\n", - " - Combining with Tensorflow Core\n", - " - Including observations in the Model\n", - "- Modeling approaches\n", - " - Same story; different ending\n", - " - Example: Bayesian A/B testing\n", - " - A Simple Case\n", - " - Execute the TF graph to sample from the posterior\n", - " - A and B together\n", - " - Execute the TF graph to sample from the posterior\n", - "- An algorithm for human deceit\n", - " - The Binomial Distribution\n", - " - Example: Cheating among students\n", - " - Execute the TF graph to sample from the posterior\n", - " - Alternative TFP Model\n", - " - Execute the TF graph to sample from the posterior\n", - " - More TFP Tricks\n", - " - Example: Challenger Space Shuttle Disaster\n", - " - Normal Distributions\n", - " - Execute the TF graph to sample from the posterior\n", - " - What about the day of the Challenger disaster?\n", - " - Is our model appropriate?\n", - " - Execute the TF graph to sample from the posterior\n", - " - Exercises\n", - " - References\n", - "___\n", - "\n", - "This chapter introduces more TFP syntax and variables and ways to think about how to model a system from a Bayesian perspective. It also contains tips and data visualization techniques for assessing goodness-of-fit for your Bayesian model." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "AIIO6GhdH89m" - }, - "source": [ - "### Dependencies & Prerequisites\n", - "\n", - "
\n", - " Tensorflow Probability is part of the colab default runtime, so you don't need to install Tensorflow or Tensorflow Probability if you're running this in the colab. \n", - "
\n", - " If you're running this notebook in Jupyter on your own machine (and you have already installed Tensorflow), you can use the following\n", - "
\n", - " \n", - "Again, if you are running this in a Colab, Tensorflow and TFP are already installed\n", - "
" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "jFKYjxy1IAwG" - }, - "outputs": [], - "source": [ - "#@title Imports and Global Variables (run this cell first) { display-mode: \"form\" }\n", - "\"\"\"\n", - "The book uses a custom matplotlibrc file, which provides the unique styles for\n", - "matplotlib plots. If executing this book, and you wish to use the book's\n", - "styling, provided are two options:\n", - " 1. Overwrite your own matplotlibrc file with the rc-file provided in the\n", - " book's styles/ dir. See http://matplotlib.org/users/customizing.html\n", - " 2. Also in the styles is bmh_matplotlibrc.json file. This can be used to\n", - " update the styles in only this notebook. Try running the following code:\n", - "\n", - " import json\n", - " s = json.load(open(\"../styles/bmh_matplotlibrc.json\"))\n", - " matplotlib.rcParams.update(s)\n", - "\"\"\"\n", - "!pip3 install -q wget\n", - "from __future__ import absolute_import, division, print_function\n", - "#@markdown This sets the warning status (default is `ignore`, since this notebook runs correctly)\n", - "warning_status = \"ignore\" #@param [\"ignore\", \"always\", \"module\", \"once\", \"default\", \"error\"]\n", - "import warnings\n", - "warnings.filterwarnings(warning_status)\n", - "with warnings.catch_warnings():\n", - " warnings.filterwarnings(warning_status, category=DeprecationWarning)\n", - " warnings.filterwarnings(warning_status, category=UserWarning)\n", - "\n", - "import numpy as np\n", - "import os\n", - "#@markdown This sets the styles of the plotting (default is styled like plots from [FiveThirtyeight.com](https://fivethirtyeight.com/))\n", - "matplotlib_style = 'fivethirtyeight' #@param ['fivethirtyeight', 'bmh', 'ggplot', 'seaborn', 'default', 'Solarize_Light2', 'classic', 'dark_background', 'seaborn-colorblind', 'seaborn-notebook']\n", - "import matplotlib.pyplot as plt; plt.style.use(matplotlib_style)\n", - "import matplotlib.axes as axes;\n", - "from matplotlib.patches import Ellipse\n", - "%matplotlib inline\n", - "import seaborn as sns; sns.set_context('notebook')\n", - "from IPython.core.pylabtools import figsize\n", - "#@markdown This sets the resolution of the plot outputs (`retina` is the highest resolution)\n", - "notebook_screen_res = 'retina' #@param ['retina', 'png', 'jpeg', 'svg', 'pdf']\n", - "%config InlineBackend.figure_format = notebook_screen_res\n", - "\n", - "import tensorflow as tf\n", - "tfe = tf.contrib.eager\n", - "\n", - "# Eager Execution\n", - "#@markdown Check the box below if you want to use [Eager Execution](https://www.tensorflow.org/guide/eager)\n", - "#@markdown Eager execution provides An intuitive interface, Easier debugging, and a control flow comparable to Numpy. You can read more about it on the [Google AI Blog](https://ai.googleblog.com/2017/10/eager-execution-imperative-define-by.html)\n", - "use_tf_eager = False #@param {type:\"boolean\"}\n", - "\n", - "# Use try/except so we can easily re-execute the whole notebook.\n", - "if use_tf_eager:\n", - " try:\n", - " tf.enable_eager_execution()\n", - " except:\n", - " pass\n", - "\n", - "import tensorflow_probability as tfp\n", - "tfd = tfp.distributions\n", - "tfb = tfp.bijectors\n", - "\n", - " \n", - "def evaluate(tensors):\n", - " \"\"\"Evaluates Tensor or EagerTensor to Numpy `ndarray`s.\n", - " Args:\n", - " tensors: Object of `Tensor` or EagerTensor`s; can be `list`, `tuple`,\n", - " `namedtuple` or combinations thereof.\n", - "\n", - " Returns:\n", - " ndarrays: Object with same structure as `tensors` except with `Tensor` or\n", - " `EagerTensor`s replaced by Numpy `ndarray`s.\n", - " \"\"\"\n", - " if tf.executing_eagerly():\n", - " return tf.contrib.framework.nest.pack_sequence_as(\n", - " tensors,\n", - " [t.numpy() if tf.contrib.framework.is_tensor(t) else t\n", - " for t in tf.contrib.framework.nest.flatten(tensors)])\n", - " return sess.run(tensors)\n", - "\n", - "class _TFColor(object):\n", - " \"\"\"Enum of colors used in TF docs.\"\"\"\n", - " red = '#F15854'\n", - " blue = '#5DA5DA'\n", - " orange = '#FAA43A'\n", - " green = '#60BD68'\n", - " pink = '#F17CB0'\n", - " brown = '#B2912F'\n", - " purple = '#B276B2'\n", - " yellow = '#DECF3F'\n", - " gray = '#4D4D4D'\n", - " def __getitem__(self, i):\n", - " return [\n", - " self.red,\n", - " self.orange,\n", - " self.green,\n", - " self.blue,\n", - " self.pink,\n", - " self.brown,\n", - " self.purple,\n", - " self.yellow,\n", - " self.gray,\n", - " ][i % 9]\n", - "TFColor = _TFColor()\n", - "\n", - "def session_options(enable_gpu_ram_resizing=True, enable_xla=True):\n", - " \"\"\"\n", - " Allowing the notebook to make use of GPUs if they're available.\n", - " \n", - " XLA (Accelerated Linear Algebra) is a domain-specific compiler for linear \n", - " algebra that optimizes TensorFlow computations.\n", - " \"\"\"\n", - " config = tf.ConfigProto()\n", - " config.log_device_placement = True\n", - " if enable_gpu_ram_resizing:\n", - " # `allow_growth=True` makes it possible to connect multiple colabs to your\n", - " # GPU. Otherwise the colab malloc's all GPU ram.\n", - " config.gpu_options.allow_growth = True\n", - " if enable_xla:\n", - " # Enable on XLA. https://www.tensorflow.org/performance/xla/.\n", - " config.graph_options.optimizer_options.global_jit_level = (\n", - " tf.OptimizerOptions.ON_1)\n", - " return config\n", - "\n", - "\n", - "def reset_sess(config=None):\n", - " \"\"\"\n", - " Convenience function to create the TF graph & session or reset them.\n", - " \"\"\"\n", - " if config is None:\n", - " config = session_options()\n", - " global sess\n", - " tf.reset_default_graph()\n", - " try:\n", - " sess.close()\n", - " except:\n", - " pass\n", - " sess = tf.InteractiveSession(config=config)\n", - "\n", - "reset_sess()" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "24368dz9IAwM" - }, - "source": [ - "## A little more on TensorFlow and TensorFlow Probability\n", - "\n", - "To explain TensorFlow Probability, it's worth going into the various methods of working with Tensorflow tensors. Here, we introduce the notion of Tensorflow graphs and how we can use certain coding patterns to make our tensor-processing workflows much faster and more elegant. " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "tOj8bjBmNuxm" - }, - "source": [ - "### TensorFlow Graph and Eager Modes\n", - "\n", - "TFP accomplishes most of its heavy lifting via the main `tensorflow` library. The `tensorflow` library also contains many of the familiar computational elements of NumPy and uses similar notation. While NumPy directly executes computations (e.g. when you run `a + b`), `tensorflow` in graph mode instead builds up a \"compute graph\" that tracks that you want to perform the `+` operation on the elements `a` and `b`. Only when you evaluate a `tensorflow` expression does the computation take place--`tensorflow` is lazy evaluated. The benefit of using Tensorflow over NumPy is that the graph enables mathematical optimizations (e.g. simplifications), gradient calculations via automatic differentiation, compiling the entire graph to C to run at machine speed, and also compiling it to run on a GPU or TPU. \n", - "\n", - "Fundamentally, TensorFlow uses [graphs](https://www.tensorflow.org/guide/graphs) for computation, wherein the graphs represent computation as dependencies among individual operations. In the programming paradigm for Tensorflow graphs, we first define the dataflow graph, and then create a TensorFlow session to run parts of the graph. A Tensorflow [`tf.Session()`](https://www.tensorflow.org/api_docs/python/tf/Session) object runs the graph to get the variables we want to model. In the example below, we are using a global session object `sess`, which we created above in the \"Imports and Global Variables\" section. \n", - "\n", - "To avoid the sometimes confusing aspects of lazy evaluation, Tensorflow's eager mode does immediate evaluation of results to give an even more similar feel to working with NumPy. With Tensorflow [eager](https://www.tensorflow.org/guide/eager) mode, you can evaluate operations immediately, without explicitly building graphs: operations return concrete values instead of constructing a computational graph to run later. If we're in eager mode, we are presented with tensors that can be converted to numpy array equivalents immediately. Eager mode makes it easy to get started with TensorFlow and debug models.\n", - "\n", - "\n", - "TFP is essentially:\n", - "\n", - "* a collection of tensorflow symbolic expressions for various probability distributions that are combined into one big compute graph, and\n", - "* a collection of inference algorithms that use that graph to compute probabilities and gradients.\n", - "\n", - "For practical purposes, what this means is that in order to build certain models we sometimes have to use core Tensorflow. This simple example for Poisson sampling is how we might work with both graph and eager modes:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 34 - }, - "colab_type": "code", - "id": "CmiGas0kXiEw", - "outputId": "6ecefef8-ec11-4048-e840-15c875565a8f" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Value of sample from data generator: 1.0\n" - ] - } - ], - "source": [ - "parameter = tfd.Exponential(rate=1., name=\"poisson_param\").sample()\n", - "data_generator = tfd.Poisson(parameter, name=\"data_generator\")\n", - "data_generator_samples = data_generator.sample()\n", - "\n", - "if tf.executing_eagerly():\n", - " data_gen_samps_ = tf.contrib.framework.nest.pack_sequence_as(\n", - " data_generator_samples,\n", - " [t.numpy() if tf.contrib.framework.is_tensor(t) else t\n", - " for t in tf.contrib.framework.nest.flatten(data_generator_samples)])\n", - "else:\n", - " data_gen_samps_ = sess.run(data_generator_samples)\n", - " \n", - "print(\"Value of sample from data generator:\", data_gen_samps_)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "9kArT4GTIAwT" - }, - "source": [ - "In graph mode, Tensorflow will automatically assign any variables to a graph; they can then be evaluated in a session or made available in eager mode. If you try to define a variable when the session is already closed or in a finalized state, you will get an error. In the \"Imports and Global Variables\" section, we defined a particular type of session, called [`InteractiveSession`](https:///www.tensorflow.org/api_docs/python/tf/InteractiveSession). \n", - "This defnition of a global `InteractiveSession` allows us to access our session variables interactively via a shell or notebook." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "4IEk40NbIAwX" - }, - "source": [ - "Using the pattern of a global session, we can incrementally build a graph and run subsets of it to get the results.\n", - "\n", - "Eager execution further simplifies our code, eliminating the need to call session functions explicitly. In fact, if you try to run graph mode semantics in eager mode, you will get an error message like this:\n", - "\n", - "```\n", - "AttributeError: Tensor.graph is meaningless when eager execution is enabled.\n", - "```\n", - "\n", - "As mentioned in the previous chapter, we have a nifty tool that allows us to create code that's usable in both graph mode and eager mode. The custom `evaluate()` function allows us to evaluate tensors whether we are operating in TF graph or eager mode. The function looks like the following:\n", - "\n", - "```python\n", - "\n", - "def evaluate(tensors):\n", - " if tf.executing_eagerly():\n", - " return tf.contrib.framework.nest.pack_sequence_as(\n", - " tensors,\n", - " [t.numpy() if tf.contrib.framework.is_tensor(t) else t\n", - " for t in tf.contrib.framework.nest.flatten(tensors)])\n", - " with tf.Session() as sess:\n", - " return sess.run(tensors)\n", - "\n", - "```\n", - "\n", - "Each of the tensors corresponds to a NumPy-like output. To distinguish the tensors from their NumPy-like counterparts, we will use the convention of appending an underscore to the version of the tensor that one can use NumPy-like arrays on. In other words, the output of `evaluate()` gets named as `variable` + `_` = `variable_` . Now, we can do our Poisson sampling using both the `evaluate()` function and this new convention for naming Python variables in TFP." - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 51 - }, - "colab_type": "code", - "id": "Bk-vyPB9IAwX", - "outputId": "2b934b1e-c0a5-4b92-e6d2-a959b281c354" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Sample from exponential distribution before evaluation: Tensor(\"poisson_param_1/sample/Reshape:0\", shape=(), dtype=float32)\n", - "Evaluated sample from exponential distribution: 1.2240193\n" - ] - } - ], - "source": [ - "# Defining our Assumptions\n", - "parameter = tfd.Exponential(rate=1., name=\"poisson_param\").sample()\n", - "\n", - "# Converting our TF to Numpy\n", - "[ parameter_ ] = evaluate([ parameter ])\n", - "\n", - "print(\"Sample from exponential distribution before evaluation: \", parameter)\n", - "print(\"Evaluated sample from exponential distribution: \", parameter_)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "ZlGWIiPLIAwo" - }, - "source": [ - "More generally, we can use our `evaluate()` function to convert between the Tensfflow `tensor` data type and one that we can run operations on:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 51 - }, - "colab_type": "code", - "id": "1tzQmnsFIAwp", - "outputId": "c7c87627-826f-445d-e000-843894eecc16" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "'parameter_' evaluated Tensor : 0.18858196\n", - "'data_generator_' sample evaluated Tensor : 1.0\n" - ] - } - ], - "source": [ - "[ \n", - " parameter_,\n", - " data_generator_sample_,\n", - "] = evaluate([ \n", - " parameter, \n", - " data_generator.sample(),\n", - "])\n", - "\n", - "print(\"'parameter_' evaluated Tensor :\", parameter_)\n", - "print(\"'data_generator_' sample evaluated Tensor :\", data_generator_sample_)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "m0PLxpCIc--r" - }, - "source": [ - "\n", - "A general rule of thumb for programming in TensorFlow is that if you need to do any array-like calculations that would require NumPy functions, you should use their equivalents in TensorFlow. This practice is necessary because NumPy can produce only constant values but TensorFlow tensors are a dynamic part of the computation graph. If you mix and match these the wrong way, you will typically get an error about incompatible types." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "wqkS8vztNoyh" - }, - "source": [ - "### TFP Distributions\n", - "\n", - "Let's look into how [`tfp.distributions`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions) work.\n", - "\n", - "TFP uses distribution subclasses to represent *stochastic*, random variables. A variable is stochastic when the following is true: even if you knew all the values of the variable's parameters and components, it would still be random. Included in this category are instances of classes [`Poisson`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Poisson), [`Uniform`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Uniform), and [`Exponential`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Exponential).\n", - "\n", - "You can draw random samples from a stochastic variable. When you draw samples, those samples become [`tensorflow.Tensors`](https://www.tensorflow.org/api_docs/python/tf/Tensor) that behave deterministically from that point on. A quick mental check to determine if something is *deterministic* is: *If I knew all of the inputs for creating the variable `foo`, I could calculate the value of `foo`.* You can add, subtract, and otherwise manipulate the tensors in a variety of ways discussed below. These operations are almost always deterministic.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "NdKiqWtWIAwy" - }, - "source": [ - "#### Initializing a Distribution\n", - "\n", - "Initializing a stochastic, or random, variable requires a few class-specific parameters that describe the Distribution's shape, such as the location and scale. For example:\n", - "\n", - "```python\n", - "some_distribution = tfd.Uniform(0., 4.)\n", - "```\n", - "\n", - "initializes a stochastic, or random, [`Uniform`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Uniform) distribution with the lower bound at 0 and upper bound at 4. Calling `sample()` on the distribution returns a tensor that will behave deterministically from that point on:\n", - "\n", - "```python\n", - "sampled_tensor = some_distribution.sample()\n", - "```\n", - "\n", - "The next example demonstrates what we mean when we say that distributions are stochastic but tensors are deterministic:\n", - "\n", - "```\n", - "derived_tensor_1 = 1 + sampled_tensor\n", - "derived_tensor_2 = 1 + sampled_tensor # equal to 1\n", - "\n", - "derived_tensor_3 = 1 + some_distribution.sample()\n", - "derived_tensor_4 = 1 + some_distribution.sample() # different from 3\n", - "```\n", - "\n", - "The first two lines produce the same value because they refer to the same sampled tensor. The last two lines likely produce different values because they refer to independent samples drawn from the same distribution.\n", - "\n", - "To define a multiviariate distribution, just pass in arguments with the shape you want the output to be when creating the distribution. For example:\n", - "\n", - "```python\n", - "betas = tfd.Uniform([0., 0.], [1., 1.])\n", - "```\n", - "\n", - "Creates a Distribution with batch_shape (2,). Now, when you call betas.sample(),\n", - "two values will be returned instead of one. You can read more about TFP shape semantics in the [TFP docs](https://github.com/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/Understanding_TensorFlow_Distributions_Shapes.ipynb), but most uses in this book should be self-explanatory." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "UPt9k8YrIAwz" - }, - "source": [ - "#### Deterministic variables\n", - "\n", - "We can create a deterministic distribution similarly to how we create a stochastic distribution. We simply call up the [`Deterministic`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Deterministic) class from Tensorflow Distributions and pass in the deterministic value that we desire\n", - "```python\n", - "deterministic_variable = tfd.Deterministic(name=\"deterministic_variable\", loc=some_function_of_variables)\n", - "```\n", - "\n", - "Calling `tfd.Deterministic` is useful for creating distributions that always have the same value. However, the much more common pattern for working with deterministic variables in TFP is to create a tensor or sample from a distribution:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "feDM_HX6IAw0" - }, - "outputs": [], - "source": [ - "lambda_1 = tfd.Exponential(rate=1., name=\"lambda_1\") #stochastic variable\n", - "lambda_2 = tfd.Exponential(rate=1., name=\"lambda_2\") #stochastic variable\n", - "tau = tfd.Uniform(name=\"tau\", low=0., high=10.) #stochastic variable\n", - "\n", - "# deterministic variable since we are getting results of lambda's after sampling \n", - "new_deterministic_variable = tfd.Deterministic(name=\"deterministic_variable\", \n", - " loc=(lambda_1.sample() + lambda_2.sample()))\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "cRzLJmAJIAw3" - }, - "source": [ - "The use of the deterministic variable was seen in the previous chapter's text-message example. Recall the model for $\\lambda$ looked like: \n", - "\n", - "$$\n", - "\\lambda = \n", - "\\begin{cases}\\lambda_1 & \\text{if } t \\lt \\tau \\cr\n", - "\\lambda_2 & \\text{if } t \\ge \\tau\n", - "\\end{cases}\n", - "$$\n", - "\n", - "And in TFP code:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { + "nbformat": 4, + "nbformat_minor": 0, + "metadata": { "colab": { - "base_uri": "https://localhost:8080/", - "height": 51 - }, - "colab_type": "code", - "id": "IXdTQeqrIAw3", - "outputId": "6ab97e74-6a36-4b27-fe7f-c1d4e6ea30be" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "5 samples from our deterministic lambda model: \n", - " [0.24760574 0.24760574 0.15390001 0.15390001 0.15390001]\n" - ] - } - ], - "source": [ - "n_data_points = 5 # in CH1 we had ~70 data points\n", - "idx = np.arange(n_data_points)\n", - "\n", - "lambda_deterministic = tfd.Deterministic(tf.gather([lambda_1.sample(), lambda_2.sample()],\n", - " indices=tf.to_int32(\n", - " tau.sample() >= idx)))\n", - "[lambda_deterministic_] = evaluate([lambda_deterministic.sample()])\n", - "\n", - "print(\"{} samples from our deterministic lambda model: \\n\".format(n_data_points), lambda_deterministic_ )" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "EFgJwLATIAw8" - }, - "source": [ - "Clearly, if $\\tau, \\lambda_1$ and $\\lambda_2$ are known, then $\\lambda$ is known completely, hence it is a deterministic variable. We use indexing here to switch from $\\lambda_1$ to $\\lambda_2$ at the appropriate time. " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "IMNdtRTtIAxB" - }, - "source": [ - "### Including observations in the model\n", - "\n", - "At this point, it may not look like it, but we have fully specified our priors. For example, we can ask and answer questions like \"What does my prior distribution of $\\lambda_1$ look like?\" \n", - "\n", - "To do this, we will sample from the distribution. The method `.sample()` has a very simple role: get data points from the given distribution. We can then evaluate the resulting tensor to get a NumPy array-like object. " - ] + "name": "Ch2_MorePyMC_TFP.ipynb", + "version": "0.3.2", + "provenance": [], + "collapsed_sections": [], + "toc_visible": true + }, + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "accelerator": "GPU" }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 336 - }, - "colab_type": "code", - "id": "VNdQVTSFIAxC", - "outputId": "c73c52bd-11cf-4d81-946d-f947eb9c0d59" - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" + "cells": [ + { + "metadata": { + "id": "phBEJ8iLIAwF", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "# Probabilistic Programming and Bayesian Methods for Hackers Chapter 2\n", + "\n", + "\n", + " \n", + " \n", + "
\n", + " Run in Google Colab\n", + " \n", + " View source on GitHub\n", + "
\n", + "
\n", + "
\n", + "
\n", + "\n", + "Original content ([this Jupyter notebook](https://nbviewer.jupyter.org/github/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/blob/master/Chapter2_MorePyMC/Ch2_MorePyMC_PyMC2.ipynb)) created by Cam Davidson-Pilon ([`@Cmrn_DP`](https://twitter.com/Cmrn_DP))\n", + "\n", + "Ported to [Tensorflow Probability](https://www.tensorflow.org/probability/) by Matthew McAteer ([`@MatthewMcAteer0`](https://twitter.com/MatthewMcAteer0)), with help from Bryan Seybold, Mike Shwe ([`@mikeshwe`](https://twitter.com/mikeshwe)), Josh Dillon, and the rest of the TFP team at Google ([`tfprobability@tensorflow.org`](mailto:tfprobability@tensorflow.org)).\n", + "\n", + "Welcome to Bayesian Methods for Hackers. The full Github repository is available at [github/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers). The other chapters can be found on the project's [homepage](https://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/). We hope you enjoy the book, and we encourage any contributions!\n", + "___\n", + "\n", + "### Table of Contents\n", + "\n", + "- Dependencies & Prerequisites\n", + "- A little more on TFP\n", + " - TFP Variables\n", + " - Initializing Stochastic Variables\n", + " - Deterministic variables\n", + " - Combining with Tensorflow Core\n", + " - Including observations in the Model\n", + "- Modeling approaches\n", + " - Same story; different ending\n", + " - Example: Bayesian A/B testing\n", + " - A Simple Case\n", + " - Execute the TF graph to sample from the posterior\n", + " - A and B together\n", + " - Execute the TF graph to sample from the posterior\n", + "- An algorithm for human deceit\n", + " - The Binomial Distribution\n", + " - Example: Cheating among students\n", + " - Execute the TF graph to sample from the posterior\n", + " - Alternative TFP Model\n", + " - Execute the TF graph to sample from the posterior\n", + " - More TFP Tricks\n", + " - Example: Challenger Space Shuttle Disaster\n", + " - Normal Distributions\n", + " - Execute the TF graph to sample from the posterior\n", + " - What about the day of the Challenger disaster?\n", + " - Is our model appropriate?\n", + " - Execute the TF graph to sample from the posterior\n", + " - Exercises\n", + " - References\n", + "___\n", + "\n", + "This chapter introduces more TFP syntax and variables and ways to think about how to model a system from a Bayesian perspective. It also contains tips and data visualization techniques for assessing goodness-of-fit for your Bayesian model." ] - }, - "metadata": { - "image/png": { - "height": 319, - "width": 821 - }, - "tags": [] - }, - "output_type": "display_data" - } - ], - "source": [ - "# Define our observed samples\n", - "lambda_1 = tfd.Exponential(rate=1., name=\"lambda_1\")\n", - "samples = lambda_1.sample(sample_shape=20000)\n", - " \n", - "# Execute graph, convert TF to NumPy\n", - "[ samples_ ] = evaluate([ samples ])\n", - "\n", - "# Visualize our stepwise prior distribution\n", - "plt.figure(figsize(12.5, 5))\n", - "plt.hist(samples_, bins=70, normed=True, histtype=\"stepfilled\")\n", - "plt.title(r\"Prior distribution for $\\lambda_1$\")\n", - "plt.xlim(0, 8);" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "9nOs9Gq3IAxH" - }, - "source": [ - "To frame this in the notation of the first chapter, though this is a slight abuse of notation, we have specified $P(A)$. Our next goal is to include data/evidence/observations $X$ into our model. \n", - "\n", - "Sometimes we may want to match a property of our distribution to a property of observed data. To do so, we get the parameters for our distribution fom the data itself. In this example, the Poisson rate (average number of events) is explicitly set to one over the average of the data:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 136 - }, - "colab_type": "code", - "id": "qtHXSR6QIAxH", - "outputId": "cad9361a-f6ee-4750-8e24-b46656babcb1" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "two predetermined data points: [10. 5.]\n", - "\n", - " mean of our data: 7.5\n", - "\n", - " random sample from poisson distribution \n", - " with the mean as the poisson's rate: \n", - " 1.0\n" - ] - } - ], - "source": [ - "data = tf.constant([10., 5.], dtype=tf.float32)\n", - "poisson = tfd.Poisson(rate=1./tf.reduce_mean(data))\n", - "\n", - "\n", - "# Execute graph\n", - "[ data_, poisson_sample_, ] = evaluate([ data, poisson.sample() ])\n", - "\n", - "print(\"two predetermined data points: \", data_)\n", - "print(\"\\n mean of our data: \", np.mean(data_))\n", - "\n", - "\n", - "print(\"\\n random sample from poisson distribution \\n with the mean as the poisson's rate: \\n\", poisson_sample_)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "8oxo5VcbIAxP" - }, - "source": [ - "## Modeling approaches\n", - "\n", - "A good starting thought to Bayesian modeling is to think about *how your data might have been generated*. Position yourself in an omniscient position, and try to imagine how *you* would recreate the dataset. \n", - "\n", - "In the last chapter we investigated text message data. We begin by asking how our observations may have been generated:\n", - "\n", - "1. We started by thinking \"what is the best random variable to describe this count data?\" A Poisson random variable is a good candidate because it can represent count data. So we model the number of sms's received as sampled from a Poisson distribution.\n", - "\n", - "2. Next, we think, \"Ok, assuming sms's are Poisson-distributed, what do I need for the Poisson distribution?\" Well, the Poisson distribution has a parameter $\\lambda$. \n", - "\n", - "3. Do we know $\\lambda$? No. In fact, we have a suspicion that there are *two* $\\lambda$ values, one for the earlier behaviour and one for the later behaviour. We don't know when the behaviour switches though, but call the switchpoint $\\tau$.\n", - "\n", - "4. What is a good distribution for the two $\\lambda$s? The exponential is good, as it assigns probabilities to positive real numbers. Well the exponential distribution has a parameter too, call it $\\alpha$.\n", - "\n", - "5. Do we know what the parameter $\\alpha$ might be? No. At this point, we could continue and assign a distribution to $\\alpha$, but it's better to stop once we reach a set level of ignorance: whereas we have a prior belief about $\\lambda$, (\"it probably changes over time\", \"it's likely between 10 and 30\", etc.), we don't really have any strong beliefs about $\\alpha$. So it's best to stop here. \n", - "\n", - " What is a good value for $\\alpha$ then? We think that the $\\lambda$s are between 10-30, so if we set $\\alpha$ really low (which corresponds to larger probability on high values) we are not reflecting our prior well. Similar, a too-high alpha misses our prior belief as well. A good idea for $\\alpha$ as to reflect our belief is to set the value so that the mean of $\\lambda$, given $\\alpha$, is equal to our observed mean. This was shown in the last chapter.\n", - "\n", - "6. We have no expert opinion of when $\\tau$ might have occurred. So we will suppose $\\tau$ is from a discrete uniform distribution over the entire timespan.\n", - "\n", - "\n", - "Below we give a graphical visualization of this, where arrows denote `parent-child` relationships. (provided by the [Daft Python library](http://daft-pgm.org/) )\n", - "\n", - "\n", - "\n", - "\n", - "TFP and other probabilistic programming languages have been designed to tell these data-generation *stories*. More generally, B. Cronin writes [2]:\n", - "\n", - "> Probabilistic programming will unlock narrative explanations of data, one of the holy grails of business analytics and the unsung hero of scientific persuasion. People think in terms of stories - thus the unreasonable power of the anecdote to drive decision-making, well-founded or not. But existing analytics largely fails to provide this kind of story; instead, numbers seemingly appear out of thin air, with little of the causal context that humans prefer when weighing their options." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "3RJEK_yjIAxR" - }, - "source": [ - "### Same story; different ending.\n", - "\n", - "Interestingly, we can create *new datasets* by retelling the story.\n", - "For example, if we reverse the above steps, we can simulate a possible realization of the dataset.\n", - "\n", - "1\\. Specify when the user's behaviour switches by sampling from $\\text{DiscreteUniform}(0, 80)$:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 34 - }, - "colab_type": "code", - "id": "Ma56S7r1IAxS", - "outputId": "68ec7a14-3090-472f-dfcf-0bf6445a233c" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Value of Tau (randomly taken from DiscreteUniform(0, 80)): 48\n" - ] - } - ], - "source": [ - "tau = tf.random_uniform(shape=[1], minval=0, maxval=80, dtype=tf.int32)[0]\n", - "\n", - "[ tau_ ] = evaluate([ tau ])\n", - "\n", - "print(\"Value of Tau (randomly taken from DiscreteUniform(0, 80)):\", tau_)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "Xt_6sYG6IAxW" - }, - "source": [ - "2\\. Draw $\\lambda_1$ and $\\lambda_2$ from a $\\text{Gamma}(\\alpha)$ distribution:\n", - "\n", - "Note: A gamma distribution is a generalization of the exponential distribution. A gamma distribution with shape parameter $α = 1$ and scale parameter $β$ is an exponential ($β$) distribution. Here, we use a gamma distribution to have more flexibility than we would have had were we to model with an exponential. Rather than returning values between $0$ and $1$, we can return values much larger than $1$ (i.e., the kinds of numbers one would expect to show up in a daily SMS count)." - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 51 - }, - "colab_type": "code", - "id": "l2QX3nEbofZr", - "outputId": "1c78f1b5-4847-49b0-a9a6-2155285e5d03" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Lambda 1 (randomly taken from Gamma(α) distribution): 50.1973\n", - "Lambda 2 (randomly taken from Gamma(α) distribution): 26.417625\n" - ] - } - ], - "source": [ - "alpha = 1./8.\n", - "\n", - "lambdas = tfd.Gamma(concentration=1/alpha, rate=0.3).sample(sample_shape=[2]) \n", - "[ lambda_1_, lambda_2_ ] = evaluate( lambdas )\n", - "print(\"Lambda 1 (randomly taken from Gamma(α) distribution): \", lambda_1_)\n", - "print(\"Lambda 2 (randomly taken from Gamma(α) distribution): \", lambda_2_)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "uIoKaO4bIAxb" - }, - "source": [ - "3\\. For days before $\\tau$, represent the user's received SMS count by sampling from $\\text{Poi}(\\lambda_1)$, and sample from $\\text{Poi}(\\lambda_2)$ for days after $\\tau$. For example:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 119 - }, - "colab_type": "code", - "id": "6xxOtwxvpk_P", - "outputId": "83a9c98c-df27-411a-b9b2-c59e1f33765f" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Artificial day-by-day user SMS count created by sampling: \n", - " [64. 48. 41. 37. 60. 47. 53. 53. 59. 58. 55. 56. 76. 55. 42. 44. 51. 44.\n", - " 54. 35. 43. 51. 41. 58. 49. 51. 42. 64. 49. 60. 51. 51. 50. 60. 48. 49.\n", - " 43. 56. 56. 51. 48. 55. 44. 53. 49. 54. 47. 52. 23. 27. 27. 23. 33. 25.\n", - " 22. 22. 28. 23. 22. 23. 29. 24. 21. 27. 24. 33. 21. 22. 20. 27. 32. 20.\n", - " 20. 27. 28. 29. 30. 33. 22. 20.]\n" - ] - } - ], - "source": [ - "data = tf.concat([tfd.Poisson(rate=lambda_1_).sample(sample_shape=tau_),\n", - " tfd.Poisson(rate=lambda_2_).sample(sample_shape= (80 - tau_))], axis=0)\n", - "days_range = tf.range(80)\n", - "[ data_, days_range_ ] = evaluate([ data, days_range ])\n", - "print(\"Artificial day-by-day user SMS count created by sampling: \\n\", data_)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "5PWuas1oIAxg" - }, - "source": [ - "4\\. Plot the artificial dataset:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 348 - }, - "colab_type": "code", - "id": "vrGXdyZyIAxh", - "outputId": "e4987d94-1fa3-44c3-c7f5-edd18c727c01" - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" + }, + { + "metadata": { + "id": "AIIO6GhdH89m", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "### Dependencies & Prerequisites\n", + "\n", + "
\n", + " Tensorflow Probability is part of the colab default runtime, so you don't need to install Tensorflow or Tensorflow Probability if you're running this in the colab. \n", + "
\n", + " If you're running this notebook in Jupyter on your own machine (and you have already installed Tensorflow), you can use the following\n", + "
\n", + "
    \n", + "
  • For the most recent nightly installation: pip3 install -q tfp-nightly
    • \n", + "
  • For the most recent stable TFP release: pip3 install -q --upgrade tensorflow-probability
    • \n", + "
  • For the most recent stable GPU-connected version of TFP: pip3 install -q --upgrade tensorflow-probability-gpu
    • \n", + "
  • For the most recent nightly GPU-connected version of TFP: pip3 install -q tfp-nightly-gpu
    • \n", + "
\n", + "Again, if you are running this in a Colab, Tensorflow and TFP are already installed\n", + "
" ] - }, - "metadata": { - "image/png": { - "height": 331, - "width": 835 - }, - "tags": [] - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.bar(days_range_, data_, color=TFColor[3])\n", - "plt.bar(tau_ - 1, data_[tau_ - 1], color=\"r\", label=\"user behaviour changed\")\n", - "plt.xlabel(\"Time (days)\")\n", - "plt.ylabel(\"count of text-msgs received\")\n", - "plt.title(\"Artificial dataset\")\n", - "plt.xlim(0, 80)\n", - "plt.legend();" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "ulb46iQIIAxn" - }, - "source": [ - "It is okay that our fictional dataset does not look like our observed dataset: the probability is incredibly small it indeed would. TFP's engine is designed to find good parameters, $\\lambda_i, \\tau$, that maximize this probability. \n", - "\n", - "\n", - "The ability to generate an artificial dataset is an interesting side effect of our modeling, and we will see that this ability is a very important method of Bayesian inference. We produce a few more datasets below:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 319 - }, - "colab_type": "code", - "id": "vrLFYvVzIAxp", - "outputId": "1feb58e1-242f-433f-8cd4-035a588ae7ea" - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" + }, + { + "metadata": { + "id": "jFKYjxy1IAwG", + "colab_type": "code", + "colab": {} + }, + "cell_type": "code", + "source": [ + "#@title Imports and Global Variables (run this cell first) { display-mode: \"form\" }\n", + "\"\"\"\n", + "The book uses a custom matplotlibrc file, which provides the unique styles for\n", + "matplotlib plots. If executing this book, and you wish to use the book's\n", + "styling, provided are two options:\n", + " 1. Overwrite your own matplotlibrc file with the rc-file provided in the\n", + " book's styles/ dir. See http://matplotlib.org/users/customizing.html\n", + " 2. Also in the styles is bmh_matplotlibrc.json file. This can be used to\n", + " update the styles in only this notebook. Try running the following code:\n", + "\n", + " import json\n", + " s = json.load(open(\"../styles/bmh_matplotlibrc.json\"))\n", + " matplotlib.rcParams.update(s)\n", + "\"\"\"\n", + "!pip3 install -q wget\n", + "from __future__ import absolute_import, division, print_function\n", + "#@markdown This sets the warning status (default is `ignore`, since this notebook runs correctly)\n", + "warning_status = \"ignore\" #@param [\"ignore\", \"always\", \"module\", \"once\", \"default\", \"error\"]\n", + "import warnings\n", + "warnings.filterwarnings(warning_status)\n", + "with warnings.catch_warnings():\n", + " warnings.filterwarnings(warning_status, category=DeprecationWarning)\n", + " warnings.filterwarnings(warning_status, category=UserWarning)\n", + "\n", + "import numpy as np\n", + "import os\n", + "#@markdown This sets the styles of the plotting (default is styled like plots from [FiveThirtyeight.com](https://fivethirtyeight.com/))\n", + "matplotlib_style = 'fivethirtyeight' #@param ['fivethirtyeight', 'bmh', 'ggplot', 'seaborn', 'default', 'Solarize_Light2', 'classic', 'dark_background', 'seaborn-colorblind', 'seaborn-notebook']\n", + "import matplotlib.pyplot as plt; plt.style.use(matplotlib_style)\n", + "import matplotlib.axes as axes;\n", + "from matplotlib.patches import Ellipse\n", + "%matplotlib inline\n", + "import seaborn as sns; sns.set_context('notebook')\n", + "from IPython.core.pylabtools import figsize\n", + "#@markdown This sets the resolution of the plot outputs (`retina` is the highest resolution)\n", + "notebook_screen_res = 'retina' #@param ['retina', 'png', 'jpeg', 'svg', 'pdf']\n", + "%config InlineBackend.figure_format = notebook_screen_res\n", + "\n", + "import tensorflow as tf\n", + "tfe = tf.contrib.eager\n", + "\n", + "# Eager Execution\n", + "#@markdown Check the box below if you want to use [Eager Execution](https://www.tensorflow.org/guide/eager)\n", + "#@markdown Eager execution provides An intuitive interface, Easier debugging, and a control flow comparable to Numpy. You can read more about it on the [Google AI Blog](https://ai.googleblog.com/2017/10/eager-execution-imperative-define-by.html)\n", + "use_tf_eager = False #@param {type:\"boolean\"}\n", + "\n", + "# Use try/except so we can easily re-execute the whole notebook.\n", + "if use_tf_eager:\n", + " try:\n", + " tf.enable_eager_execution()\n", + " except:\n", + " pass\n", + "\n", + "import tensorflow_probability as tfp\n", + "tfd = tfp.distributions\n", + "tfb = tfp.bijectors\n", + "\n", + " \n", + "def evaluate(tensors):\n", + " \"\"\"Evaluates Tensor or EagerTensor to Numpy `ndarray`s.\n", + " Args:\n", + " tensors: Object of `Tensor` or EagerTensor`s; can be `list`, `tuple`,\n", + " `namedtuple` or combinations thereof.\n", + "\n", + " Returns:\n", + " ndarrays: Object with same structure as `tensors` except with `Tensor` or\n", + " `EagerTensor`s replaced by Numpy `ndarray`s.\n", + " \"\"\"\n", + " if tf.executing_eagerly():\n", + " return tf.contrib.framework.nest.pack_sequence_as(\n", + " tensors,\n", + " [t.numpy() if tf.contrib.framework.is_tensor(t) else t\n", + " for t in tf.contrib.framework.nest.flatten(tensors)])\n", + " return sess.run(tensors)\n", + "\n", + "class _TFColor(object):\n", + " \"\"\"Enum of colors used in TF docs.\"\"\"\n", + " red = '#F15854'\n", + " blue = '#5DA5DA'\n", + " orange = '#FAA43A'\n", + " green = '#60BD68'\n", + " pink = '#F17CB0'\n", + " brown = '#B2912F'\n", + " purple = '#B276B2'\n", + " yellow = '#DECF3F'\n", + " gray = '#4D4D4D'\n", + " def __getitem__(self, i):\n", + " return [\n", + " self.red,\n", + " self.orange,\n", + " self.green,\n", + " self.blue,\n", + " self.pink,\n", + " self.brown,\n", + " self.purple,\n", + " self.yellow,\n", + " self.gray,\n", + " ][i % 9]\n", + "TFColor = _TFColor()\n", + "\n", + "def session_options(enable_gpu_ram_resizing=True, enable_xla=True):\n", + " \"\"\"\n", + " Allowing the notebook to make use of GPUs if they're available.\n", + " \n", + " XLA (Accelerated Linear Algebra) is a domain-specific compiler for linear \n", + " algebra that optimizes TensorFlow computations.\n", + " \"\"\"\n", + " config = tf.ConfigProto()\n", + " config.log_device_placement = True\n", + " if enable_gpu_ram_resizing:\n", + " # `allow_growth=True` makes it possible to connect multiple colabs to your\n", + " # GPU. Otherwise the colab malloc's all GPU ram.\n", + " config.gpu_options.allow_growth = True\n", + " if enable_xla:\n", + " # Enable on XLA. https://www.tensorflow.org/performance/xla/.\n", + " config.graph_options.optimizer_options.global_jit_level = (\n", + " tf.OptimizerOptions.ON_1)\n", + " return config\n", + "\n", + "\n", + "def reset_sess(config=None):\n", + " \"\"\"\n", + " Convenience function to create the TF graph & session or reset them.\n", + " \"\"\"\n", + " if config is None:\n", + " config = session_options()\n", + " global sess\n", + " tf.reset_default_graph()\n", + " try:\n", + " sess.close()\n", + " except:\n", + " pass\n", + " sess = tf.InteractiveSession(config=config)\n", + "\n", + "reset_sess()" + ], + "execution_count": 0, + "outputs": [] + }, + { + "metadata": { + "id": "24368dz9IAwM", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "## A little more on TensorFlow and TensorFlow Probability\n", + "\n", + "To explain TensorFlow Probability, it's worth going into the various methods of working with Tensorflow tensors. Here, we introduce the notion of Tensorflow graphs and how we can use certain coding patterns to make our tensor-processing workflows much faster and more elegant. " ] - }, - "metadata": { - "image/png": { - "height": 302, - "width": 821 - }, - "tags": [] - }, - "output_type": "display_data" - } - ], - "source": [ - "def plot_artificial_sms_dataset(): \n", - " tau = tf.random_uniform(shape=[1], \n", - " minval=0, \n", - " maxval=80,\n", - " dtype=tf.int32)[0]\n", - " alpha = 1./8.\n", - " lambdas = tfd.Gamma(concentration=1/alpha, rate=0.3).sample(sample_shape=[2]) \n", - " [ lambda_1_, lambda_2_ ] = evaluate( lambdas )\n", - " data = tf.concat([tfd.Poisson(rate=lambda_1_).sample(sample_shape=tau),\n", - " tfd.Poisson(rate=lambda_2_).sample(sample_shape= (80 - tau))], axis=0)\n", - " days_range = tf.range(80)\n", - " \n", - " [ \n", - " tau_,\n", - " data_,\n", - " days_range_,\n", - " ] = evaluate([ \n", - " tau,\n", - " data,\n", - " days_range,\n", - " ])\n", - " \n", - " plt.bar(days_range_, data_, color=TFColor[3])\n", - " plt.bar(tau_ - 1, data_[tau_ - 1], color=\"r\", label=\"user behaviour changed\")\n", - " plt.xlim(0, 80);\n", - "\n", - "\n", - "plt.figure(figsize(12.5, 5))\n", - "plt.title(\"More example of artificial datasets\")\n", - "for i in range(4):\n", - " plt.subplot(4, 1, i+1)\n", - " plot_artificial_sms_dataset()\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "V8QMiJXOIAxv" - }, - "source": [ - "Later we will see how we use this to make predictions and test the appropriateness of our models." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "2lU8C4C-IAxw" - }, - "source": [ - "### Example: Bayesian A/B testing\n", - "\n", - "A/B testing is a statistical design pattern for determining the difference of effectiveness between two different treatments. For example, a pharmaceutical company is interested in the effectiveness of drug A vs drug B. The company will test drug A on some fraction of their trials, and drug B on the other fraction (this fraction is often 1/2, but we will relax this assumption). After performing enough trials, the in-house statisticians sift through the data to determine which drug yielded better results. \n", - "\n", - "Similarly, front-end web developers are interested in which design of their website yields more sales or some other metric of interest. They will route some fraction of visitors to site A, and the other fraction to site B, and record if the visit yielded a sale or not. The data is recorded (in real-time), and analyzed afterwards. \n", - "\n", - "Often, the post-experiment analysis is done using something called a hypothesis test like *difference of means test* or *difference of proportions test*. This involves often misunderstood quantities like a \"Z-score\" and even more confusing \"p-values\" (please don't ask). If you have taken a statistics course, you have probably been taught this technique (though not necessarily *learned* this technique). And if you were like me, you may have felt uncomfortable with their derivation -- good: the Bayesian approach to this problem is much more natural. \n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "AFcmkQEyDgyK" - }, - "source": [ - "### A Simple Case\n", - "\n", - "As this is a hacker book, we'll continue with the web-dev example. For the moment, we will focus on the analysis of site A only. Assume that there is some true $0 \\lt p_A \\lt 1$ probability that users who, upon shown site A, eventually purchase from the site. This is the true effectiveness of site A. Currently, this quantity is unknown to us. \n", - "\n", - "Suppose site A was shown to $N$ people, and $n$ people purchased from the site. One might conclude hastily that $p_A = \\frac{n}{N}$. Unfortunately, the *observed frequency* $\\frac{n}{N}$ does not necessarily equal $p_A$ -- there is a difference between the *observed frequency* and the *true frequency* of an event. The true frequency can be interpreted as the probability of an event occurring. For example, the true frequency of rolling a 1 on a 6-sided die is $\\frac{1}{6}$. Knowing the true frequency of events like:\n", - "\n", - "- fraction of users who make purchases, \n", - "- frequency of social attributes, \n", - "- percent of internet users with cats etc. \n", - "\n", - "are common requests we ask of Nature. Unfortunately, often Nature hides the true frequency from us and we must *infer* it from observed data.\n", - "\n", - "The *observed frequency* is then the frequency we observe: say rolling the die 100 times you may observe 20 rolls of 1. The observed frequency, 0.2, differs from the true frequency, $\\frac{1}{6}$. We can use Bayesian statistics to infer probable values of the true frequency using an appropriate prior and observed data.\n", - "\n", - "\n", - "With respect to our A/B example, we are interested in using what we know, $N$ (the total trials administered) and $n$ (the number of conversions), to estimate what $p_A$, the true frequency of buyers, might be. \n", - "\n", - "To setup a Bayesian model, we need to assign prior distributions to our unknown quantities. *A priori*, what do we think $p_A$ might be? For this example, we have no strong conviction about $p_A$, so for now, let's assume $p_A$ is uniform over [0,1]:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "blTLKyo2IAxy" - }, - "outputs": [], - "source": [ - "reset_sess()\n", - "\n", - "# The parameters are the bounds of the Uniform.\n", - "p = tfd.Uniform(low=0., high=1., name='p')\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "f0XLF9h3IAx2" - }, - "source": [ - "Had we had stronger beliefs, we could have expressed them in the prior above.\n", - "\n", - "For this example, consider $p_A = 0.05$, and $N = 1500$ users shown site A, and we will simulate whether the user made a purchase or not. To simulate this from $N$ trials, we will use a *Bernoulli* distribution: if $X\\ \\sim \\text{Ber}(p)$, then $X$ is 1 with probability $p$ and 0 with probability $1 - p$. Of course, in practice we do not know $p_A$, but we will use it here to simulate the data. We can assume then that we can use the following generative model:\n", - "\n", - "$$\\begin{align*}\n", - "p &\\sim \\text{Uniform}[\\text{low}=0,\\text{high}=1) \\\\\n", - "X\\ &\\sim \\text{Bernoulli}(\\text{prob}=p) \\\\\n", - "\\text{for } i &= 1\\ldots N:\\text{# Users} \\\\\n", - " X_i\\ &\\sim \\text{Bernoulli}(p_i)\n", - "\\end{align*}$$" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 68 - }, - "colab_type": "code", - "id": "riLrk5KTIAx4", - "outputId": "6c8cf3ef-cdef-4340-f941-9f6ea1c7454e" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Array of 1500 Occurences: [0 0 0 ... 0 0 0]\n", - "(Remember: Python treats True == 1, and False == 0)\n", - "Sum of (True == 1) Occurences: 76\n" - ] - } - ], - "source": [ - "reset_sess()\n", - "\n", - "#set constants\n", - "prob_true = 0.05 # remember, this is unknown.\n", - "N = 1500\n", - "\n", - "# sample N Bernoulli random variables from Ber(0.05).\n", - "# each random variable has a 0.05 chance of being a 1.\n", - "# this is the data-generation step\n", - "\n", - "occurrences = tfd.Bernoulli(probs=prob_true).sample(sample_shape=N, seed=6.45)\n", - "\n", - "[ \n", - " occurrences_,\n", - " occurrences_sum_,\n", - " occurrences_mean_,\n", - "] = evaluate([ \n", - " occurrences, \n", - " tf.reduce_sum(occurrences),\n", - " tf.reduce_mean(tf.to_float(occurrences))\n", - "])\n", - "\n", - "print(\"Array of {} Occurences:\".format(N), occurrences_) \n", - "print(\"(Remember: Python treats True == 1, and False == 0)\")\n", - "print(\"Sum of (True == 1) Occurences:\", occurrences_sum_)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "UpJrMifMIAx7" - }, - "source": [ - "The observed frequency is:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 51 - }, - "colab_type": "code", - "id": "trjtemdNIAx7", - "outputId": "d528af9d-8d7c-49bc-c191-ca58fca5b6bb" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "What is the observed frequency in Group A? 0.0507\n", - "Does this equal the true frequency? False\n" - ] - } - ], - "source": [ - "# Occurrences.mean is equal to n/N.\n", - "print(\"What is the observed frequency in Group A? %.4f\" % occurrences_mean_)\n", - "print(\"Does this equal the true frequency? %s\" % (occurrences_mean_ == prob_true))" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "Gue-SRTYIAyA" - }, - "source": [ - "We combine our Bernoulli distribution and our observed occurrences into a log probability function based on the two." - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "Ct9o0w7lGaZb" - }, - "outputs": [], - "source": [ - "def joint_log_prob(occurrences, prob_A):\n", - " \"\"\"\n", - " Joint log probability optimization function.\n", - " \n", - " Args:\n", - " occurrences: An array of binary values (0 & 1), representing \n", - " the observed frequency\n", - " prob_A: scalar estimate of the probability of a 1 appearing \n", - " Returns: \n", - " Joint log probability optimization function.\n", - " \"\"\" \n", - " \n", - " rv_prob_A = tfd.Uniform(low=0., high=1.)\n", - " \n", - " rv_occurrences = tfd.Bernoulli(probs=prob_A)\n", - " \n", - " return (\n", - " rv_prob_A.log_prob(prob_A)\n", - " + tf.reduce_sum(rv_occurrences.log_prob(occurrences))\n", - " )" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "UN7Mh5U-uFye" - }, - "source": [ - "The goal of probabilistic inference is to find model parameters that may explain\n", - "data you have observed. TFP performs probabilistic inference by evaluating the\n", - "model parameters using a `joint_log_prob` function. The arguments to `joint_log_prob` are data and model parameters—for the model defined in the `joint_log_prob` function itself. The function returns the log of the joint probability that the model parameterized as such generated the observed data per the input arguments.\n", - "\n", - "All `joint_log_prob` functions have a common structure:\n", - "\n", - "1. The function takes a set of **inputs** to evaluate. Each input is either an\n", - "observed value or a model parameter.\n", - "\n", - "1. The `joint_log_prob` function uses probability distributions to define a **model** for evaluating the inputs. These distributions measure the likelihood of the input values. (By convention, the distribution that measures the likelihood of the variable `foo` will be named `rv_foo` to note that it is a random variable.) We use two types of distributions in `joint_log_prob` functions:\n", - "\n", - " a. **Prior distributions** measure the likelihood of input values.\n", - "A prior distribution never depends on an input value each prior distribution measures the\n", - "likelihood of a single input value. Each unknown variable—one that has not been\n", - "observed directly—needs a corresponding prior. Beliefs about which values could\n", - "be reasonable determine the prior distribution. Choosing a prior can be tricky,\n", - "so we will cover it in depth in Chapter 6.\n", - "\n", - " b. **Conditional distributions** measure the likelihood of an input value given\n", - "other input values. Typically, the conditional\n", - "distributions return the likelihood of observed data given the current guess of parameters in the model, p(observed_data | model_parameters).\n", - "\n", - "1. Finally, we calculate and return the **joint log probability** of the inputs.\n", - "The joint log probability is the sum of the log probabilities from all of the\n", - "prior and conditional distributions. (We take the sum of log probabilities\n", - "instead of multiplying the probabilities directly for reasons of numerical\n", - "stability: floating point numbers in computers cannot represent the very small\n", - "values necessary to calculate the joint log probability unless they are in \n", - "log space.) The sum of probabilities is actually an unnormalized density; although the total sum of probabilities over all possible inputs might not sum to one, the sum of probabilities is proportional to the true probability density. This proportional distribution is sufficient to estimate the distribution of likely inputs.\n", - "\n", - "Let's map these terms onto the code above. In this example, the input values\n", - "are the observed values in `occurrences` and the unknown value for `prob_A`. The `joint_log_prob` takes the current guess for `prob_A`\n", - "and answers, how likely is the data if `prob_A` is the probability of\n", - "`occurrences`. The answer depends on two distributions:\n", - "1. The prior distribution, `rv_prob_A`, indicates how likely the current value of `prob_A` is by itself.\n", - "2. The conditional distribution, `rv_occurrences`, indicates the likelihood of `occurrences` if `prob_A` were the probability for the Bernoulli distribution.\n", - "\n", - "The sum of the log of these probabilities is the\n", - "joint log probability. \n", - "\n", - "The `joint_log_prob` is particularly useful in conjunction with the [`tfp.mcmc`](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc)\n", - "module. Markov chain Monte Carlo (MCMC) algorithms proceed by making educated guesses about the unknown\n", - "input values and\n", - "computing what the likelihood of this set of arguments is. (We’ll talk about how it makes those guesses in Chapter 3.) By repeating this process\n", - "many times, MCMC builds a distribution of likely parameters. Constructing this\n", - "distribution is the goal of probabilistic inference." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "rzm3amOgDAGg" - }, - "source": [ - "Then we run our inference algorithm:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "g9XHX0h8IAyB" - }, - "outputs": [], - "source": [ - "number_of_steps = 48000 #@param {type:\"slider\", min:2000, max:50000, step:100}\n", - "#@markdown (Default is 18000).\n", - "burnin = 25000 #@param {type:\"slider\", min:0, max:30000, step:100}\n", - "#@markdown (Default is 1000).\n", - "leapfrog_steps=2 #@param {type:\"slider\", min:1, max:9, step:1}\n", - "#@markdown (Default is 6).\n", - "\n", - "# Set the chain's start state.\n", - "initial_chain_state = [\n", - " tf.reduce_mean(tf.to_float(occurrences)) \n", - " * tf.ones([], dtype=tf.float32, name=\"init_prob_A\")\n", - "]\n", - "\n", - "# Since HMC operates over unconstrained space, we need to transform the\n", - "# samples so they live in real-space.\n", - "unconstraining_bijectors = [\n", - " tfp.bijectors.Identity() # Maps R to R. \n", - "]\n", - "\n", - "# Define a closure over our joint_log_prob.\n", - "# The closure makes it so the HMC doesn't try to change the `occurrences` but\n", - "# instead determines the distributions of other parameters that might generate\n", - "# the `occurrences` we observed.\n", - "unnormalized_posterior_log_prob = lambda *args: joint_log_prob(occurrences, *args)\n", - "\n", - "# Initialize the step_size. (It will be automatically adapted.)\n", - "with tf.variable_scope(tf.get_variable_scope(), reuse=tf.AUTO_REUSE):\n", - " step_size = tf.get_variable(\n", - " name='step_size',\n", - " initializer=tf.constant(0.5, dtype=tf.float32),\n", - " trainable=False,\n", - " use_resource=True\n", - " )\n", - "\n", - "# Defining the HMC\n", - "hmc = tfp.mcmc.TransformedTransitionKernel(\n", - " inner_kernel=tfp.mcmc.HamiltonianMonteCarlo(\n", - " target_log_prob_fn=unnormalized_posterior_log_prob,\n", - " num_leapfrog_steps=leapfrog_steps,\n", - " step_size=step_size,\n", - " step_size_update_fn=tfp.mcmc.make_simple_step_size_update_policy(),\n", - " state_gradients_are_stopped=True),\n", - " bijector=unconstraining_bijectors)\n", - "\n", - "# Sampling from the chain.\n", - "[\n", - " posterior_prob_A\n", - "], kernel_results = tfp.mcmc.sample_chain(\n", - " num_results=number_of_steps,\n", - " num_burnin_steps=burnin,\n", - " current_state=initial_chain_state,\n", - " kernel=hmc)\n", - "\n", - "# Initialize any created variables.\n", - "init_g = tf.global_variables_initializer()\n", - "init_l = tf.local_variables_initializer()" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "yUVnbqhDVfAx" - }, - "source": [ - "#### Execute the TF graph to sample from the posterior" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 34 - }, - "colab_type": "code", - "id": "Q3By4GWdEtQN", - "outputId": "b40ec87c-cb5e-49c1-e6ff-44ecd1dc7cf3" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "acceptance rate: 0.6088958333333333\n" - ] - } - ], - "source": [ - "evaluate(init_g)\n", - "evaluate(init_l)\n", - "[\n", - " posterior_prob_A_,\n", - " kernel_results_,\n", - "] = evaluate([\n", - " posterior_prob_A,\n", - " kernel_results,\n", - "])\n", - "\n", - " \n", - "print(\"acceptance rate: {}\".format(\n", - " kernel_results_.inner_results.is_accepted.mean()))\n", - "\n", - "burned_prob_A_trace_ = posterior_prob_A_[burnin:]" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "MQUWTY7-LgGv" - }, - "source": [ - "We plot the posterior distribution of the unknown $p_A$ below:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 280 - }, - "colab_type": "code", - "id": "w_P52-CRFJPs", - "outputId": "bbf9109c-d7a8-47e4-814c-bf27aa79afe0" - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" + }, + { + "metadata": { + "id": "tOj8bjBmNuxm", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "### TensorFlow Graph and Eager Modes\n", + "\n", + "TFP accomplishes most of its heavy lifting via the main `tensorflow` library. The `tensorflow` library also contains many of the familiar computational elements of NumPy and uses similar notation. While NumPy directly executes computations (e.g. when you run `a + b`), `tensorflow` in graph mode instead builds up a \"compute graph\" that tracks that you want to perform the `+` operation on the elements `a` and `b`. Only when you evaluate a `tensorflow` expression does the computation take place--`tensorflow` is lazy evaluated. The benefit of using Tensorflow over NumPy is that the graph enables mathematical optimizations (e.g. simplifications), gradient calculations via automatic differentiation, compiling the entire graph to C to run at machine speed, and also compiling it to run on a GPU or TPU. \n", + "\n", + "Fundamentally, TensorFlow uses [graphs](https://www.tensorflow.org/guide/graphs) for computation, wherein the graphs represent computation as dependencies among individual operations. In the programming paradigm for Tensorflow graphs, we first define the dataflow graph, and then create a TensorFlow session to run parts of the graph. A Tensorflow [`tf.Session()`](https://www.tensorflow.org/api_docs/python/tf/Session) object runs the graph to get the variables we want to model. In the example below, we are using a global session object `sess`, which we created above in the \"Imports and Global Variables\" section. \n", + "\n", + "To avoid the sometimes confusing aspects of lazy evaluation, Tensorflow's eager mode does immediate evaluation of results to give an even more similar feel to working with NumPy. With Tensorflow [eager](https://www.tensorflow.org/guide/eager) mode, you can evaluate operations immediately, without explicitly building graphs: operations return concrete values instead of constructing a computational graph to run later. If we're in eager mode, we are presented with tensors that can be converted to numpy array equivalents immediately. Eager mode makes it easy to get started with TensorFlow and debug models.\n", + "\n", + "\n", + "TFP is essentially:\n", + "\n", + "* a collection of tensorflow symbolic expressions for various probability distributions that are combined into one big compute graph, and\n", + "* a collection of inference algorithms that use that graph to compute probabilities and gradients.\n", + "\n", + "For practical purposes, what this means is that in order to build certain models we sometimes have to use core Tensorflow. This simple example for Poisson sampling is how we might work with both graph and eager modes:" + ] + }, + { + "metadata": { + "id": "CmiGas0kXiEw", + "colab_type": "code", + "outputId": "6ecefef8-ec11-4048-e840-15c875565a8f", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + } + }, + "cell_type": "code", + "source": [ + "parameter = tfd.Exponential(rate=1., name=\"poisson_param\").sample()\n", + "data_generator = tfd.Poisson(parameter, name=\"data_generator\")\n", + "data_generator_samples = data_generator.sample()\n", + "\n", + "if tf.executing_eagerly():\n", + " data_gen_samps_ = tf.contrib.framework.nest.pack_sequence_as(\n", + " data_generator_samples,\n", + " [t.numpy() if tf.contrib.framework.is_tensor(t) else t\n", + " for t in tf.contrib.framework.nest.flatten(data_generator_samples)])\n", + "else:\n", + " data_gen_samps_ = sess.run(data_generator_samples)\n", + " \n", + "print(\"Value of sample from data generator:\", data_gen_samps_)" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Value of sample from data generator: 1.0\n" + ], + "name": "stdout" + } + ] + }, + { + "metadata": { + "id": "9kArT4GTIAwT", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "In graph mode, Tensorflow will automatically assign any variables to a graph; they can then be evaluated in a session or made available in eager mode. If you try to define a variable when the session is already closed or in a finalized state, you will get an error. In the \"Imports and Global Variables\" section, we defined a particular type of session, called [`InteractiveSession`](https:///www.tensorflow.org/api_docs/python/tf/InteractiveSession). \n", + "This defnition of a global `InteractiveSession` allows us to access our session variables interactively via a shell or notebook." + ] + }, + { + "metadata": { + "id": "4IEk40NbIAwX", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "Using the pattern of a global session, we can incrementally build a graph and run subsets of it to get the results.\n", + "\n", + "Eager execution further simplifies our code, eliminating the need to call session functions explicitly. In fact, if you try to run graph mode semantics in eager mode, you will get an error message like this:\n", + "\n", + "```\n", + "AttributeError: Tensor.graph is meaningless when eager execution is enabled.\n", + "```\n", + "\n", + "As mentioned in the previous chapter, we have a nifty tool that allows us to create code that's usable in both graph mode and eager mode. The custom `evaluate()` function allows us to evaluate tensors whether we are operating in TF graph or eager mode. The function looks like the following:\n", + "\n", + "```python\n", + "\n", + "def evaluate(tensors):\n", + " if tf.executing_eagerly():\n", + " return tf.contrib.framework.nest.pack_sequence_as(\n", + " tensors,\n", + " [t.numpy() if tf.contrib.framework.is_tensor(t) else t\n", + " for t in tf.contrib.framework.nest.flatten(tensors)])\n", + " with tf.Session() as sess:\n", + " return sess.run(tensors)\n", + "\n", + "```\n", + "\n", + "Each of the tensors corresponds to a NumPy-like output. To distinguish the tensors from their NumPy-like counterparts, we will use the convention of appending an underscore to the version of the tensor that one can use NumPy-like arrays on. In other words, the output of `evaluate()` gets named as `variable` + `_` = `variable_` . Now, we can do our Poisson sampling using both the `evaluate()` function and this new convention for naming Python variables in TFP." + ] + }, + { + "metadata": { + "id": "Bk-vyPB9IAwX", + "colab_type": "code", + "outputId": "2b934b1e-c0a5-4b92-e6d2-a959b281c354", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + } + }, + "cell_type": "code", + "source": [ + "# Defining our Assumptions\n", + "parameter = tfd.Exponential(rate=1., name=\"poisson_param\").sample()\n", + "\n", + "# Converting our TF to Numpy\n", + "[ parameter_ ] = evaluate([ parameter ])\n", + "\n", + "print(\"Sample from exponential distribution before evaluation: \", parameter)\n", + "print(\"Evaluated sample from exponential distribution: \", parameter_)" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Sample from exponential distribution before evaluation: Tensor(\"poisson_param_1/sample/Reshape:0\", shape=(), dtype=float32)\n", + "Evaluated sample from exponential distribution: 1.2240193\n" + ], + "name": "stdout" + } + ] + }, + { + "metadata": { + "id": "ZlGWIiPLIAwo", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "More generally, we can use our `evaluate()` function to convert between the Tensfflow `tensor` data type and one that we can run operations on:" + ] + }, + { + "metadata": { + "id": "1tzQmnsFIAwp", + "colab_type": "code", + "outputId": "c7c87627-826f-445d-e000-843894eecc16", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + } + }, + "cell_type": "code", + "source": [ + "[ \n", + " parameter_,\n", + " data_generator_sample_,\n", + "] = evaluate([ \n", + " parameter, \n", + " data_generator.sample(),\n", + "])\n", + "\n", + "print(\"'parameter_' evaluated Tensor :\", parameter_)\n", + "print(\"'data_generator_' sample evaluated Tensor :\", data_generator_sample_)\n" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "'parameter_' evaluated Tensor : 0.18858196\n", + "'data_generator_' sample evaluated Tensor : 1.0\n" + ], + "name": "stdout" + } + ] + }, + { + "metadata": { + "id": "m0PLxpCIc--r", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "\n", + "A general rule of thumb for programming in TensorFlow is that if you need to do any array-like calculations that would require NumPy functions, you should use their equivalents in TensorFlow. This practice is necessary because NumPy can produce only constant values but TensorFlow tensors are a dynamic part of the computation graph. If you mix and match these the wrong way, you will typically get an error about incompatible types." + ] + }, + { + "metadata": { + "id": "wqkS8vztNoyh", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "### TFP Distributions\n", + "\n", + "Let's look into how [`tfp.distributions`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions) work.\n", + "\n", + "TFP uses distribution subclasses to represent *stochastic*, random variables. A variable is stochastic when the following is true: even if you knew all the values of the variable's parameters and components, it would still be random. Included in this category are instances of classes [`Poisson`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Poisson), [`Uniform`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Uniform), and [`Exponential`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Exponential).\n", + "\n", + "You can draw random samples from a stochastic variable. When you draw samples, those samples become [`tensorflow.Tensors`](https://www.tensorflow.org/api_docs/python/tf/Tensor) that behave deterministically from that point on. A quick mental check to determine if something is *deterministic* is: *If I knew all of the inputs for creating the variable `foo`, I could calculate the value of `foo`.* You can add, subtract, and otherwise manipulate the tensors in a variety of ways discussed below. These operations are almost always deterministic.\n" + ] + }, + { + "metadata": { + "id": "NdKiqWtWIAwy", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "#### Initializing a Distribution\n", + "\n", + "Initializing a stochastic, or random, variable requires a few class-specific parameters that describe the Distribution's shape, such as the location and scale. For example:\n", + "\n", + "```python\n", + "some_distribution = tfd.Uniform(0., 4.)\n", + "```\n", + "\n", + "initializes a stochastic, or random, [`Uniform`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Uniform) distribution with the lower bound at 0 and upper bound at 4. Calling `sample()` on the distribution returns a tensor that will behave deterministically from that point on:\n", + "\n", + "```python\n", + "sampled_tensor = some_distribution.sample()\n", + "```\n", + "\n", + "The next example demonstrates what we mean when we say that distributions are stochastic but tensors are deterministic:\n", + "\n", + "```\n", + "derived_tensor_1 = 1 + sampled_tensor\n", + "derived_tensor_2 = 1 + sampled_tensor # equal to 1\n", + "\n", + "derived_tensor_3 = 1 + some_distribution.sample()\n", + "derived_tensor_4 = 1 + some_distribution.sample() # different from 3\n", + "```\n", + "\n", + "The first two lines produce the same value because they refer to the same sampled tensor. The last two lines likely produce different values because they refer to independent samples drawn from the same distribution.\n", + "\n", + "To define a multiviariate distribution, just pass in arguments with the shape you want the output to be when creating the distribution. For example:\n", + "\n", + "```python\n", + "betas = tfd.Uniform([0., 0.], [1., 1.])\n", + "```\n", + "\n", + "Creates a Distribution with batch_shape (2,). Now, when you call betas.sample(),\n", + "two values will be returned instead of one. You can read more about TFP shape semantics in the [TFP docs](https://github.com/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/Understanding_TensorFlow_Distributions_Shapes.ipynb), but most uses in this book should be self-explanatory." + ] + }, + { + "metadata": { + "id": "UPt9k8YrIAwz", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "#### Deterministic variables\n", + "\n", + "We can create a deterministic distribution similarly to how we create a stochastic distribution. We simply call up the [`Deterministic`](https://www.tensorflow.org/probability/api_docs/python/tfp/distributions/Deterministic) class from Tensorflow Distributions and pass in the deterministic value that we desire\n", + "```python\n", + "deterministic_variable = tfd.Deterministic(name=\"deterministic_variable\", loc=some_function_of_variables)\n", + "```\n", + "\n", + "Calling `tfd.Deterministic` is useful for creating distributions that always have the same value. However, the much more common pattern for working with deterministic variables in TFP is to create a tensor or sample from a distribution:" + ] + }, + { + "metadata": { + "id": "feDM_HX6IAw0", + "colab_type": "code", + "colab": {} + }, + "cell_type": "code", + "source": [ + "lambda_1 = tfd.Exponential(rate=1., name=\"lambda_1\") #stochastic variable\n", + "lambda_2 = tfd.Exponential(rate=1., name=\"lambda_2\") #stochastic variable\n", + "tau = tfd.Uniform(name=\"tau\", low=0., high=10.) #stochastic variable\n", + "\n", + "# deterministic variable since we are getting results of lambda's after sampling \n", + "new_deterministic_variable = tfd.Deterministic(name=\"deterministic_variable\", \n", + " loc=(lambda_1.sample() + lambda_2.sample()))\n" + ], + "execution_count": 0, + "outputs": [] + }, + { + "metadata": { + "id": "cRzLJmAJIAw3", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "The use of the deterministic variable was seen in the previous chapter's text-message example. Recall the model for $\\lambda$ looked like: \n", + "\n", + "$$\n", + "\\lambda = \n", + "\\begin{cases}\\lambda_1 & \\text{if } t \\lt \\tau \\cr\n", + "\\lambda_2 & \\text{if } t \\ge \\tau\n", + "\\end{cases}\n", + "$$\n", + "\n", + "And in TFP code:" + ] + }, + { + "metadata": { + "id": "IXdTQeqrIAw3", + "colab_type": "code", + "outputId": "6ab97e74-6a36-4b27-fe7f-c1d4e6ea30be", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + } + }, + "cell_type": "code", + "source": [ + "n_data_points = 5 # in CH1 we had ~70 data points\n", + "idx = np.arange(n_data_points)\n", + "\n", + "lambda_deterministic = tfd.Deterministic(tf.gather([lambda_1.sample(), lambda_2.sample()],\n", + " indices=tf.to_int32(\n", + " tau.sample() >= idx)))\n", + "[lambda_deterministic_] = evaluate([lambda_deterministic.sample()])\n", + "\n", + "print(\"{} samples from our deterministic lambda model: \\n\".format(n_data_points), lambda_deterministic_ )" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "5 samples from our deterministic lambda model: \n", + " [0.24760574 0.24760574 0.15390001 0.15390001 0.15390001]\n" + ], + "name": "stdout" + } + ] + }, + { + "metadata": { + "id": "EFgJwLATIAw8", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "Clearly, if $\\tau, \\lambda_1$ and $\\lambda_2$ are known, then $\\lambda$ is known completely, hence it is a deterministic variable. We use indexing here to switch from $\\lambda_1$ to $\\lambda_2$ at the appropriate time. " + ] + }, + { + "metadata": { + "id": "IMNdtRTtIAxB", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "### Including observations in the model\n", + "\n", + "At this point, it may not look like it, but we have fully specified our priors. For example, we can ask and answer questions like \"What does my prior distribution of $\\lambda_1$ look like?\" \n", + "\n", + "To do this, we will sample from the distribution. The method `.sample()` has a very simple role: get data points from the given distribution. We can then evaluate the resulting tensor to get a NumPy array-like object. " + ] + }, + { + "metadata": { + "id": "VNdQVTSFIAxC", + "colab_type": "code", + "outputId": "c73c52bd-11cf-4d81-946d-f947eb9c0d59", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 336 + } + }, + "cell_type": "code", + "source": [ + "# Define our observed samples\n", + "lambda_1 = tfd.Exponential(rate=1., name=\"lambda_1\")\n", + "samples = lambda_1.sample(sample_shape=20000)\n", + " \n", + "# Execute graph, convert TF to NumPy\n", + "[ samples_ ] = evaluate([ samples ])\n", + "\n", + "# Visualize our stepwise prior distribution\n", + "plt.figure(figsize(12.5, 5))\n", + "plt.hist(samples_, bins=70, normed=True, histtype=\"stepfilled\")\n", + "plt.title(r\"Prior distribution for $\\lambda_1$\")\n", + "plt.xlim(0, 8);" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [], + "image/png": { + "width": 821, + "height": 319 + } + } + } + ] + }, + { + "metadata": { + "id": "9nOs9Gq3IAxH", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "To frame this in the notation of the first chapter, though this is a slight abuse of notation, we have specified $P(A)$. Our next goal is to include data/evidence/observations $X$ into our model. \n", + "\n", + "Sometimes we may want to match a property of our distribution to a property of observed data. To do so, we get the parameters for our distribution fom the data itself. In this example, the Poisson rate (average number of events) is explicitly set to one over the average of the data:" + ] + }, + { + "metadata": { + "id": "qtHXSR6QIAxH", + "colab_type": "code", + "outputId": "cad9361a-f6ee-4750-8e24-b46656babcb1", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 136 + } + }, + "cell_type": "code", + "source": [ + "data = tf.constant([10., 5.], dtype=tf.float32)\n", + "poisson = tfd.Poisson(rate=1./tf.reduce_mean(data))\n", + "\n", + "\n", + "# Execute graph\n", + "[ data_, poisson_sample_, ] = evaluate([ data, poisson.sample() ])\n", + "\n", + "print(\"two predetermined data points: \", data_)\n", + "print(\"\\n mean of our data: \", np.mean(data_))\n", + "\n", + "\n", + "print(\"\\n random sample from poisson distribution \\n with the mean as the poisson's rate: \\n\", poisson_sample_)" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "two predetermined data points: [10. 5.]\n", + "\n", + " mean of our data: 7.5\n", + "\n", + " random sample from poisson distribution \n", + " with the mean as the poisson's rate: \n", + " 1.0\n" + ], + "name": "stdout" + } + ] + }, + { + "metadata": { + "id": "8oxo5VcbIAxP", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "## Modeling approaches\n", + "\n", + "A good starting thought to Bayesian modeling is to think about *how your data might have been generated*. Position yourself in an omniscient position, and try to imagine how *you* would recreate the dataset. \n", + "\n", + "In the last chapter we investigated text message data. We begin by asking how our observations may have been generated:\n", + "\n", + "1. We started by thinking \"what is the best random variable to describe this count data?\" A Poisson random variable is a good candidate because it can represent count data. So we model the number of sms's received as sampled from a Poisson distribution.\n", + "\n", + "2. Next, we think, \"Ok, assuming sms's are Poisson-distributed, what do I need for the Poisson distribution?\" Well, the Poisson distribution has a parameter $\\lambda$. \n", + "\n", + "3. Do we know $\\lambda$? No. In fact, we have a suspicion that there are *two* $\\lambda$ values, one for the earlier behaviour and one for the later behaviour. We don't know when the behaviour switches though, but call the switchpoint $\\tau$.\n", + "\n", + "4. What is a good distribution for the two $\\lambda$s? The exponential is good, as it assigns probabilities to positive real numbers. Well the exponential distribution has a parameter too, call it $\\alpha$.\n", + "\n", + "5. Do we know what the parameter $\\alpha$ might be? No. At this point, we could continue and assign a distribution to $\\alpha$, but it's better to stop once we reach a set level of ignorance: whereas we have a prior belief about $\\lambda$, (\"it probably changes over time\", \"it's likely between 10 and 30\", etc.), we don't really have any strong beliefs about $\\alpha$. So it's best to stop here. \n", + "\n", + " What is a good value for $\\alpha$ then? We think that the $\\lambda$s are between 10-30, so if we set $\\alpha$ really low (which corresponds to larger probability on high values) we are not reflecting our prior well. Similar, a too-high alpha misses our prior belief as well. A good idea for $\\alpha$ as to reflect our belief is to set the value so that the mean of $\\lambda$, given $\\alpha$, is equal to our observed mean. This was shown in the last chapter.\n", + "\n", + "6. We have no expert opinion of when $\\tau$ might have occurred. So we will suppose $\\tau$ is from a discrete uniform distribution over the entire timespan.\n", + "\n", + "\n", + "Below we give a graphical visualization of this, where arrows denote `parent-child` relationships. (provided by the [Daft Python library](http://daft-pgm.org/) )\n", + "\n", + "\n", + "\n", + "\n", + "TFP and other probabilistic programming languages have been designed to tell these data-generation *stories*. More generally, B. Cronin writes [2]:\n", + "\n", + "> Probabilistic programming will unlock narrative explanations of data, one of the holy grails of business analytics and the unsung hero of scientific persuasion. People think in terms of stories - thus the unreasonable power of the anecdote to drive decision-making, well-founded or not. But existing analytics largely fails to provide this kind of story; instead, numbers seemingly appear out of thin air, with little of the causal context that humans prefer when weighing their options." + ] + }, + { + "metadata": { + "id": "3RJEK_yjIAxR", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "### Same story; different ending.\n", + "\n", + "Interestingly, we can create *new datasets* by retelling the story.\n", + "For example, if we reverse the above steps, we can simulate a possible realization of the dataset.\n", + "\n", + "1\\. Specify when the user's behaviour switches by sampling from $\\text{DiscreteUniform}(0, 80)$:" + ] + }, + { + "metadata": { + "id": "Ma56S7r1IAxS", + "colab_type": "code", + "outputId": "68ec7a14-3090-472f-dfcf-0bf6445a233c", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + } + }, + "cell_type": "code", + "source": [ + "tau = tf.random_uniform(shape=[1], minval=0, maxval=80, dtype=tf.int32)[0]\n", + "\n", + "[ tau_ ] = evaluate([ tau ])\n", + "\n", + "print(\"Value of Tau (randomly taken from DiscreteUniform(0, 80)):\", tau_)" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Value of Tau (randomly taken from DiscreteUniform(0, 80)): 48\n" + ], + "name": "stdout" + } + ] + }, + { + "metadata": { + "id": "Xt_6sYG6IAxW", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "2\\. Draw $\\lambda_1$ and $\\lambda_2$ from a $\\text{Gamma}(\\alpha)$ distribution:\n", + "\n", + "Note: A gamma distribution is a generalization of the exponential distribution. A gamma distribution with shape parameter $α = 1$ and scale parameter $β$ is an exponential ($β$) distribution. Here, we use a gamma distribution to have more flexibility than we would have had were we to model with an exponential. Rather than returning values between $0$ and $1$, we can return values much larger than $1$ (i.e., the kinds of numbers one would expect to show up in a daily SMS count)." + ] + }, + { + "metadata": { + "id": "l2QX3nEbofZr", + "colab_type": "code", + "outputId": "1c78f1b5-4847-49b0-a9a6-2155285e5d03", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + } + }, + "cell_type": "code", + "source": [ + "alpha = 1./8.\n", + "\n", + "lambdas = tfd.Gamma(concentration=1/alpha, rate=0.3).sample(sample_shape=[2]) \n", + "[ lambda_1_, lambda_2_ ] = evaluate( lambdas )\n", + "print(\"Lambda 1 (randomly taken from Gamma(α) distribution): \", lambda_1_)\n", + "print(\"Lambda 2 (randomly taken from Gamma(α) distribution): \", lambda_2_)" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Lambda 1 (randomly taken from Gamma(α) distribution): 50.1973\n", + "Lambda 2 (randomly taken from Gamma(α) distribution): 26.417625\n" + ], + "name": "stdout" + } + ] + }, + { + "metadata": { + "id": "uIoKaO4bIAxb", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "3\\. For days before $\\tau$, represent the user's received SMS count by sampling from $\\text{Poi}(\\lambda_1)$, and sample from $\\text{Poi}(\\lambda_2)$ for days after $\\tau$. For example:" + ] + }, + { + "metadata": { + "id": "6xxOtwxvpk_P", + "colab_type": "code", + "outputId": "83a9c98c-df27-411a-b9b2-c59e1f33765f", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 119 + } + }, + "cell_type": "code", + "source": [ + "data = tf.concat([tfd.Poisson(rate=lambda_1_).sample(sample_shape=tau_),\n", + " tfd.Poisson(rate=lambda_2_).sample(sample_shape= (80 - tau_))], axis=0)\n", + "days_range = tf.range(80)\n", + "[ data_, days_range_ ] = evaluate([ data, days_range ])\n", + "print(\"Artificial day-by-day user SMS count created by sampling: \\n\", data_)" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Artificial day-by-day user SMS count created by sampling: \n", + " [64. 48. 41. 37. 60. 47. 53. 53. 59. 58. 55. 56. 76. 55. 42. 44. 51. 44.\n", + " 54. 35. 43. 51. 41. 58. 49. 51. 42. 64. 49. 60. 51. 51. 50. 60. 48. 49.\n", + " 43. 56. 56. 51. 48. 55. 44. 53. 49. 54. 47. 52. 23. 27. 27. 23. 33. 25.\n", + " 22. 22. 28. 23. 22. 23. 29. 24. 21. 27. 24. 33. 21. 22. 20. 27. 32. 20.\n", + " 20. 27. 28. 29. 30. 33. 22. 20.]\n" + ], + "name": "stdout" + } + ] + }, + { + "metadata": { + "id": "5PWuas1oIAxg", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "4\\. Plot the artificial dataset:" + ] + }, + { + "metadata": { + "id": "vrGXdyZyIAxh", + "colab_type": "code", + "outputId": "e4987d94-1fa3-44c3-c7f5-edd18c727c01", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 348 + } + }, + "cell_type": "code", + "source": [ + "plt.bar(days_range_, data_, color=TFColor[3])\n", + "plt.bar(tau_ - 1, data_[tau_ - 1], color=\"r\", label=\"user behaviour changed\")\n", + "plt.xlabel(\"Time (days)\")\n", + "plt.ylabel(\"count of text-msgs received\")\n", + "plt.title(\"Artificial dataset\")\n", + "plt.xlim(0, 80)\n", + "plt.legend();" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [], + "image/png": { + "width": 835, + "height": 331 + } + } + } + ] + }, + { + "metadata": { + "id": "ulb46iQIIAxn", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "It is okay that our fictional dataset does not look like our observed dataset: the probability is incredibly small it indeed would. TFP's engine is designed to find good parameters, $\\lambda_i, \\tau$, that maximize this probability. \n", + "\n", + "\n", + "The ability to generate an artificial dataset is an interesting side effect of our modeling, and we will see that this ability is a very important method of Bayesian inference. We produce a few more datasets below:" + ] + }, + { + "metadata": { + "id": "vrLFYvVzIAxp", + "colab_type": "code", + "outputId": "1feb58e1-242f-433f-8cd4-035a588ae7ea", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 319 + } + }, + "cell_type": "code", + "source": [ + "def plot_artificial_sms_dataset(): \n", + " tau = tf.random_uniform(shape=[1], \n", + " minval=0, \n", + " maxval=80,\n", + " dtype=tf.int32)[0]\n", + " alpha = 1./8.\n", + " lambdas = tfd.Gamma(concentration=1/alpha, rate=0.3).sample(sample_shape=[2]) \n", + " [ lambda_1_, lambda_2_ ] = evaluate( lambdas )\n", + " data = tf.concat([tfd.Poisson(rate=lambda_1_).sample(sample_shape=tau),\n", + " tfd.Poisson(rate=lambda_2_).sample(sample_shape= (80 - tau))], axis=0)\n", + " days_range = tf.range(80)\n", + " \n", + " [ \n", + " tau_,\n", + " data_,\n", + " days_range_,\n", + " ] = evaluate([ \n", + " tau,\n", + " data,\n", + " days_range,\n", + " ])\n", + " \n", + " plt.bar(days_range_, data_, color=TFColor[3])\n", + " plt.bar(tau_ - 1, data_[tau_ - 1], color=\"r\", label=\"user behaviour changed\")\n", + " plt.xlim(0, 80);\n", + "\n", + "\n", + "plt.figure(figsize(12.5, 5))\n", + "plt.title(\"More example of artificial datasets\")\n", + "for i in range(4):\n", + " plt.subplot(4, 1, i+1)\n", + " plot_artificial_sms_dataset()\n" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [], + "image/png": { + "width": 821, + "height": 302 + } + } + } + ] + }, + { + "metadata": { + "id": "V8QMiJXOIAxv", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "Later we will see how we use this to make predictions and test the appropriateness of our models." + ] + }, + { + "metadata": { + "id": "2lU8C4C-IAxw", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "### Example: Bayesian A/B testing\n", + "\n", + "A/B testing is a statistical design pattern for determining the difference of effectiveness between two different treatments. For example, a pharmaceutical company is interested in the effectiveness of drug A vs drug B. The company will test drug A on some fraction of their trials, and drug B on the other fraction (this fraction is often 1/2, but we will relax this assumption). After performing enough trials, the in-house statisticians sift through the data to determine which drug yielded better results. \n", + "\n", + "Similarly, front-end web developers are interested in which design of their website yields more sales or some other metric of interest. They will route some fraction of visitors to site A, and the other fraction to site B, and record if the visit yielded a sale or not. The data is recorded (in real-time), and analyzed afterwards. \n", + "\n", + "Often, the post-experiment analysis is done using something called a hypothesis test like *difference of means test* or *difference of proportions test*. This involves often misunderstood quantities like a \"Z-score\" and even more confusing \"p-values\" (please don't ask). If you have taken a statistics course, you have probably been taught this technique (though not necessarily *learned* this technique). And if you were like me, you may have felt uncomfortable with their derivation -- good: the Bayesian approach to this problem is much more natural. \n" + ] + }, + { + "metadata": { + "id": "AFcmkQEyDgyK", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "### A Simple Case\n", + "\n", + "As this is a hacker book, we'll continue with the web-dev example. For the moment, we will focus on the analysis of site A only. Assume that there is some true $0 \\lt p_A \\lt 1$ probability that users who, upon shown site A, eventually purchase from the site. This is the true effectiveness of site A. Currently, this quantity is unknown to us. \n", + "\n", + "Suppose site A was shown to $N$ people, and $n$ people purchased from the site. One might conclude hastily that $p_A = \\frac{n}{N}$. Unfortunately, the *observed frequency* $\\frac{n}{N}$ does not necessarily equal $p_A$ -- there is a difference between the *observed frequency* and the *true frequency* of an event. The true frequency can be interpreted as the probability of an event occurring. For example, the true frequency of rolling a 1 on a 6-sided die is $\\frac{1}{6}$. Knowing the true frequency of events like:\n", + "\n", + "- fraction of users who make purchases, \n", + "- frequency of social attributes, \n", + "- percent of internet users with cats etc. \n", + "\n", + "are common requests we ask of Nature. Unfortunately, often Nature hides the true frequency from us and we must *infer* it from observed data.\n", + "\n", + "The *observed frequency* is then the frequency we observe: say rolling the die 100 times you may observe 20 rolls of 1. The observed frequency, 0.2, differs from the true frequency, $\\frac{1}{6}$. We can use Bayesian statistics to infer probable values of the true frequency using an appropriate prior and observed data.\n", + "\n", + "\n", + "With respect to our A/B example, we are interested in using what we know, $N$ (the total trials administered) and $n$ (the number of conversions), to estimate what $p_A$, the true frequency of buyers, might be. \n", + "\n", + "To setup a Bayesian model, we need to assign prior distributions to our unknown quantities. *A priori*, what do we think $p_A$ might be? For this example, we have no strong conviction about $p_A$, so for now, let's assume $p_A$ is uniform over $[0,1]$:" + ] + }, + { + "metadata": { + "id": "blTLKyo2IAxy", + "colab_type": "code", + "colab": {} + }, + "cell_type": "code", + "source": [ + "reset_sess()\n", + "\n", + "# The parameters are the bounds of the Uniform.\n", + "p = tfd.Uniform(low=0., high=1., name='p')\n" + ], + "execution_count": 0, + "outputs": [] + }, + { + "metadata": { + "id": "f0XLF9h3IAx2", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "Had we had stronger beliefs, we could have expressed them in the prior above.\n", + "\n", + "For this example, consider $p_A = 0.05$, and $N = 1500$ users shown site A, and we will simulate whether the user made a purchase or not. To simulate this from $N$ trials, we will use a *Bernoulli* distribution: if $X\\ \\sim \\text{Ber}(p)$, then $X$ is 1 with probability $p$ and 0 with probability $1 - p$. Of course, in practice we do not know $p_A$, but we will use it here to simulate the data. We can assume then that we can use the following generative model:\n", + "\n", + "$$\\begin{align*}\n", + "p &\\sim \\text{Uniform}[\\text{low}=0,\\text{high}=1) \\\\\n", + "X\\ &\\sim \\text{Bernoulli}(\\text{prob}=p) \\\\\n", + "\\text{for } i &= 1\\ldots N:\\text{# Users} \\\\\n", + " X_i\\ &\\sim \\text{Bernoulli}(p_i)\n", + "\\end{align*}$$" + ] + }, + { + "metadata": { + "id": "riLrk5KTIAx4", + "colab_type": "code", + "outputId": "6c8cf3ef-cdef-4340-f941-9f6ea1c7454e", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 68 + } + }, + "cell_type": "code", + "source": [ + "reset_sess()\n", + "\n", + "#set constants\n", + "prob_true = 0.05 # remember, this is unknown.\n", + "N = 1500\n", + "\n", + "# sample N Bernoulli random variables from Ber(0.05).\n", + "# each random variable has a 0.05 chance of being a 1.\n", + "# this is the data-generation step\n", + "\n", + "occurrences = tfd.Bernoulli(probs=prob_true).sample(sample_shape=N, seed=6.45)\n", + "\n", + "[ \n", + " occurrences_,\n", + " occurrences_sum_,\n", + " occurrences_mean_,\n", + "] = evaluate([ \n", + " occurrences, \n", + " tf.reduce_sum(occurrences),\n", + " tf.reduce_mean(tf.to_float(occurrences))\n", + "])\n", + "\n", + "print(\"Array of {} Occurences:\".format(N), occurrences_) \n", + "print(\"(Remember: Python treats True == 1, and False == 0)\")\n", + "print(\"Sum of (True == 1) Occurences:\", occurrences_sum_)" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Array of 1500 Occurences: [0 0 0 ... 0 0 0]\n", + "(Remember: Python treats True == 1, and False == 0)\n", + "Sum of (True == 1) Occurences: 76\n" + ], + "name": "stdout" + } + ] + }, + { + "metadata": { + "id": "UpJrMifMIAx7", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "The observed frequency is:" + ] + }, + { + "metadata": { + "id": "trjtemdNIAx7", + "colab_type": "code", + "outputId": "d528af9d-8d7c-49bc-c191-ca58fca5b6bb", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + } + }, + "cell_type": "code", + "source": [ + "# Occurrences.mean is equal to n/N.\n", + "print(\"What is the observed frequency in Group A? %.4f\" % occurrences_mean_)\n", + "print(\"Does this equal the true frequency? %s\" % (occurrences_mean_ == prob_true))" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "What is the observed frequency in Group A? 0.0507\n", + "Does this equal the true frequency? False\n" + ], + "name": "stdout" + } + ] + }, + { + "metadata": { + "id": "Gue-SRTYIAyA", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "We combine our Bernoulli distribution and our observed occurrences into a log probability function based on the two." + ] + }, + { + "metadata": { + "id": "Ct9o0w7lGaZb", + "colab_type": "code", + "colab": {} + }, + "cell_type": "code", + "source": [ + "def joint_log_prob(occurrences, prob_A):\n", + " \"\"\"\n", + " Joint log probability optimization function.\n", + " \n", + " Args:\n", + " occurrences: An array of binary values (0 & 1), representing \n", + " the observed frequency\n", + " prob_A: scalar estimate of the probability of a 1 appearing \n", + " Returns: \n", + " Joint log probability optimization function.\n", + " \"\"\" \n", + " \n", + " rv_prob_A = tfd.Uniform(low=0., high=1.)\n", + " \n", + " rv_occurrences = tfd.Bernoulli(probs=prob_A)\n", + " \n", + " return (\n", + " rv_prob_A.log_prob(prob_A)\n", + " + tf.reduce_sum(rv_occurrences.log_prob(occurrences))\n", + " )" + ], + "execution_count": 0, + "outputs": [] + }, + { + "metadata": { + "id": "UN7Mh5U-uFye", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "The goal of probabilistic inference is to find model parameters that may explain\n", + "data you have observed. TFP performs probabilistic inference by evaluating the\n", + "model parameters using a `joint_log_prob` function. The arguments to `joint_log_prob` are data and model parameters—for the model defined in the `joint_log_prob` function itself. The function returns the log of the joint probability that the model parameterized as such generated the observed data per the input arguments.\n", + "\n", + "All `joint_log_prob` functions have a common structure:\n", + "\n", + "1. The function takes a set of **inputs** to evaluate. Each input is either an\n", + "observed value or a model parameter.\n", + "\n", + "1. The `joint_log_prob` function uses probability distributions to define a **model** for evaluating the inputs. These distributions measure the likelihood of the input values. (By convention, the distribution that measures the likelihood of the variable `foo` will be named `rv_foo` to note that it is a random variable.) We use two types of distributions in `joint_log_prob` functions:\n", + "\n", + " a. **Prior distributions** measure the likelihood of input values.\n", + "A prior distribution never depends on an input value each prior distribution measures the\n", + "likelihood of a single input value. Each unknown variable—one that has not been\n", + "observed directly—needs a corresponding prior. Beliefs about which values could\n", + "be reasonable determine the prior distribution. Choosing a prior can be tricky,\n", + "so we will cover it in depth in Chapter 6.\n", + "\n", + " b. **Conditional distributions** measure the likelihood of an input value given\n", + "other input values. Typically, the conditional\n", + "distributions return the likelihood of observed data given the current guess of parameters in the model, p(observed_data | model_parameters).\n", + "\n", + "1. Finally, we calculate and return the **joint log probability** of the inputs.\n", + "The joint log probability is the sum of the log probabilities from all of the\n", + "prior and conditional distributions. (We take the sum of log probabilities\n", + "instead of multiplying the probabilities directly for reasons of numerical\n", + "stability: floating point numbers in computers cannot represent the very small\n", + "values necessary to calculate the joint log probability unless they are in \n", + "log space.) The sum of probabilities is actually an unnormalized density; although the total sum of probabilities over all possible inputs might not sum to one, the sum of probabilities is proportional to the true probability density. This proportional distribution is sufficient to estimate the distribution of likely inputs.\n", + "\n", + "Let's map these terms onto the code above. In this example, the input values\n", + "are the observed values in `occurrences` and the unknown value for `prob_A`. The `joint_log_prob` takes the current guess for `prob_A`\n", + "and answers, how likely is the data if `prob_A` is the probability of\n", + "`occurrences`. The answer depends on two distributions:\n", + "1. The prior distribution, `rv_prob_A`, indicates how likely the current value of `prob_A` is by itself.\n", + "2. The conditional distribution, `rv_occurrences`, indicates the likelihood of `occurrences` if `prob_A` were the probability for the Bernoulli distribution.\n", + "\n", + "The sum of the log of these probabilities is the\n", + "joint log probability. \n", + "\n", + "The `joint_log_prob` is particularly useful in conjunction with the [`tfp.mcmc`](https://www.tensorflow.org/probability/api_docs/python/tfp/mcmc)\n", + "module. Markov chain Monte Carlo (MCMC) algorithms proceed by making educated guesses about the unknown\n", + "input values and\n", + "computing what the likelihood of this set of arguments is. (We’ll talk about how it makes those guesses in Chapter 3.) By repeating this process\n", + "many times, MCMC builds a distribution of likely parameters. Constructing this\n", + "distribution is the goal of probabilistic inference." + ] + }, + { + "metadata": { + "id": "rzm3amOgDAGg", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "Then we run our inference algorithm:" + ] + }, + { + "metadata": { + "id": "g9XHX0h8IAyB", + "colab_type": "code", + "colab": {} + }, + "cell_type": "code", + "source": [ + "number_of_steps = 48000 #@param {type:\"slider\", min:2000, max:50000, step:100}\n", + "#@markdown (Default is 18000).\n", + "burnin = 25000 #@param {type:\"slider\", min:0, max:30000, step:100}\n", + "#@markdown (Default is 1000).\n", + "leapfrog_steps=2 #@param {type:\"slider\", min:1, max:9, step:1}\n", + "#@markdown (Default is 6).\n", + "\n", + "# Set the chain's start state.\n", + "initial_chain_state = [\n", + " tf.reduce_mean(tf.to_float(occurrences)) \n", + " * tf.ones([], dtype=tf.float32, name=\"init_prob_A\")\n", + "]\n", + "\n", + "# Since HMC operates over unconstrained space, we need to transform the\n", + "# samples so they live in real-space.\n", + "unconstraining_bijectors = [\n", + " tfp.bijectors.Identity() # Maps R to R. \n", + "]\n", + "\n", + "# Define a closure over our joint_log_prob.\n", + "# The closure makes it so the HMC doesn't try to change the `occurrences` but\n", + "# instead determines the distributions of other parameters that might generate\n", + "# the `occurrences` we observed.\n", + "unnormalized_posterior_log_prob = lambda *args: joint_log_prob(occurrences, *args)\n", + "\n", + "# Initialize the step_size. (It will be automatically adapted.)\n", + "with tf.variable_scope(tf.get_variable_scope(), reuse=tf.AUTO_REUSE):\n", + " step_size = tf.get_variable(\n", + " name='step_size',\n", + " initializer=tf.constant(0.5, dtype=tf.float32),\n", + " trainable=False,\n", + " use_resource=True\n", + " )\n", + "\n", + "# Defining the HMC\n", + "hmc = tfp.mcmc.TransformedTransitionKernel(\n", + " inner_kernel=tfp.mcmc.HamiltonianMonteCarlo(\n", + " target_log_prob_fn=unnormalized_posterior_log_prob,\n", + " num_leapfrog_steps=leapfrog_steps,\n", + " step_size=step_size,\n", + " step_size_update_fn=tfp.mcmc.make_simple_step_size_update_policy(),\n", + " state_gradients_are_stopped=True),\n", + " bijector=unconstraining_bijectors)\n", + "\n", + "# Sampling from the chain.\n", + "[\n", + " posterior_prob_A\n", + "], kernel_results = tfp.mcmc.sample_chain(\n", + " num_results=number_of_steps,\n", + " num_burnin_steps=burnin,\n", + " current_state=initial_chain_state,\n", + " kernel=hmc)\n", + "\n", + "# Initialize any created variables.\n", + "init_g = tf.global_variables_initializer()\n", + "init_l = tf.local_variables_initializer()" + ], + "execution_count": 0, + "outputs": [] + }, + { + "metadata": { + "id": "yUVnbqhDVfAx", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "#### Execute the TF graph to sample from the posterior" + ] + }, + { + "metadata": { + "id": "Q3By4GWdEtQN", + "colab_type": "code", + "outputId": "b40ec87c-cb5e-49c1-e6ff-44ecd1dc7cf3", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + } + }, + "cell_type": "code", + "source": [ + "evaluate(init_g)\n", + "evaluate(init_l)\n", + "[\n", + " posterior_prob_A_,\n", + " kernel_results_,\n", + "] = evaluate([\n", + " posterior_prob_A,\n", + " kernel_results,\n", + "])\n", + "\n", + " \n", + "print(\"acceptance rate: {}\".format(\n", + " kernel_results_.inner_results.is_accepted.mean()))\n", + "\n", + "burned_prob_A_trace_ = posterior_prob_A_[burnin:]" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "acceptance rate: 0.6088958333333333\n" + ], + "name": "stdout" + } + ] + }, + { + "metadata": { + "id": "MQUWTY7-LgGv", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "We plot the posterior distribution of the unknown $p_A$ below:" + ] + }, + { + "metadata": { + "id": "w_P52-CRFJPs", + "colab_type": "code", + "outputId": "bbf9109c-d7a8-47e4-814c-bf27aa79afe0", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 280 + } + }, + "cell_type": "code", + "source": [ + "plt.figure(figsize(12.5, 4))\n", + "plt.title(\"Posterior distribution of $p_A$, the true effectiveness of site A\")\n", + "plt.vlines(prob_true, 0, 90, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n", + "plt.hist(burned_prob_A_trace_, bins=25, histtype=\"stepfilled\", normed=True)\n", + "plt.legend();" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [], + "image/png": { + "width": 815, + "height": 263 + } + } + } + ] + }, + { + "metadata": { + "id": "LdLJ2iriIAyI", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "Our posterior distribution puts most weight near the true value of $p_A$, but also some weights in the tails. This is a measure of how uncertain we should be, given our observations. Try changing the number of observations, `N`, and observe how the posterior distribution changes.\n", + "\n", + "### *A* and *B* Together\n", + "\n", + "A similar anaylsis can be done for site B's response data to determine the analogous $p_B$. But what we are really interested in is the *difference* between $p_A$ and $p_B$. Let's infer $p_A$, $p_B$, *and* $\\text{delta} = p_A - p_B$, all at once. We can do this using TFP's deterministic variables. (We'll assume for this exercise that $p_B = 0.04$, so $\\text{delta} = 0.01$, $N_B = 750$ (signifcantly less than $N_A$) and we will simulate site B's data like we did for site A's data ). Our model now looks like the following:\n", + "\n", + "$$\\begin{align*}\n", + "p_A &\\sim \\text{Uniform}[\\text{low}=0,\\text{high}=1) \\\\\n", + "p_B &\\sim \\text{Uniform}[\\text{low}=0,\\text{high}=1) \\\\\n", + "X\\ &\\sim \\text{Bernoulli}(\\text{prob}=p) \\\\\n", + "\\text{for } i &= 1\\ldots N: \\\\\n", + " X_i\\ &\\sim \\text{Bernoulli}(p_i)\n", + "\\end{align*}$$" + ] + }, + { + "metadata": { + "id": "yPDLHl6RIAyJ", + "colab_type": "code", + "outputId": "f04783fe-3111-41b5-cfb9-7166b6f4827d", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 85 + } + }, + "cell_type": "code", + "source": [ + "reset_sess()\n", + "\n", + "#these two quantities are unknown to us.\n", + "true_prob_A_ = 0.05\n", + "true_prob_B_ = 0.04\n", + "\n", + "#notice the unequal sample sizes -- no problem in Bayesian analysis.\n", + "N_A_ = 1500\n", + "N_B_ = 750\n", + "\n", + "#generate some observations\n", + "observations_A = tfd.Bernoulli(name=\"obs_A\", \n", + " probs=true_prob_A_).sample(sample_shape=N_A_, seed=6.45)\n", + "observations_B = tfd.Bernoulli(name=\"obs_B\", \n", + " probs=true_prob_B_).sample(sample_shape=N_B_, seed=6.45)\n", + "[ \n", + " observations_A_,\n", + " observations_B_,\n", + "] = evaluate([ \n", + " observations_A, \n", + " observations_B, \n", + "])\n", + "\n", + "print(\"Obs from Site A: \", observations_A_[:30], \"...\")\n", + "print(\"Observed Prob_A: \", np.mean(observations_A_), \"...\")\n", + "print(\"Obs from Site B: \", observations_B_[:30], \"...\")\n", + "print(\"Observed Prob_B: \", np.mean(observations_B_))" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Obs from Site A: [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] ...\n", + "Observed Prob_A: 0.050666666666666665 ...\n", + "Obs from Site B: [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] ...\n", + "Observed Prob_B: 0.04\n" + ], + "name": "stdout" + } + ] + }, + { + "metadata": { + "id": "LDzYsDVgMgsz", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "Below we run inference over the new model:" + ] + }, + { + "metadata": { + "id": "7ghHBEdXYtxV", + "colab_type": "code", + "colab": {} + }, + "cell_type": "code", + "source": [ + "def delta(prob_A, prob_B):\n", + " \"\"\"\n", + " Defining the deterministic delta function. This is our unknown of interest.\n", + " \n", + " Args:\n", + " prob_A: scalar estimate of the probability of a 1 appearing in \n", + " observation set A\n", + " prob_B: scalar estimate of the probability of a 1 appearing in \n", + " observation set B\n", + " Returns: \n", + " Difference between prob_A and prob_B\n", + " \"\"\"\n", + " return prob_A - prob_B\n", + "\n", + " \n", + "def double_joint_log_prob(observations_A_, observations_B_, \n", + " prob_A, prob_B):\n", + " \"\"\"\n", + " Joint log probability optimization function.\n", + " \n", + " Args:\n", + " observations_A: An array of binary values representing the set of \n", + " observations for site A\n", + " observations_B: An array of binary values representing the set of \n", + " observations for site B \n", + " prob_A: scalar estimate of the probability of a 1 appearing in \n", + " observation set A\n", + " prob_B: scalar estimate of the probability of a 1 appearing in \n", + " observation set B \n", + " Returns: \n", + " Joint log probability optimization function.\n", + " \"\"\"\n", + " tfd = tfp.distributions\n", + " \n", + " rv_prob_A = tfd.Uniform(low=0., high=1.)\n", + " rv_prob_B = tfd.Uniform(low=0., high=1.)\n", + " \n", + " rv_obs_A = tfd.Bernoulli(probs=prob_A)\n", + " rv_obs_B = tfd.Bernoulli(probs=prob_B)\n", + " \n", + " return (\n", + " rv_prob_A.log_prob(prob_A)\n", + " + rv_prob_B.log_prob(prob_B)\n", + " + tf.reduce_sum(rv_obs_A.log_prob(observations_A_))\n", + " + tf.reduce_sum(rv_obs_B.log_prob(observations_B_))\n", + " )\n" + ], + "execution_count": 0, + "outputs": [] + }, + { + "metadata": { + "id": "h0TDeF3IIAyQ", + "colab_type": "code", + "colab": {} + }, + "cell_type": "code", + "source": [ + "number_of_steps = 37200 #@param {type:\"slider\", min:2000, max:50000, step:100}\n", + "#@markdown (Default is 18000).\n", + "burnin = 1000 #@param {type:\"slider\", min:0, max:30000, step:100}\n", + "#@markdown (Default is 1000).\n", + "leapfrog_steps=3 #@param {type:\"slider\", min:1, max:9, step:1}\n", + "#@markdown (Default is 6).\n", + "\n", + "\n", + "# Set the chain's start state.\n", + "initial_chain_state = [ \n", + " tf.reduce_mean(tf.to_float(observations_A)) * tf.ones([], dtype=tf.float32, name=\"init_prob_A\"),\n", + " tf.reduce_mean(tf.to_float(observations_B)) * tf.ones([], dtype=tf.float32, name=\"init_prob_B\")\n", + "]\n", + "\n", + "# Since HMC operates over unconstrained space, we need to transform the\n", + "# samples so they live in real-space.\n", + "unconstraining_bijectors = [\n", + " tfp.bijectors.Identity(), # Maps R to R.\n", + " tfp.bijectors.Identity() # Maps R to R.\n", + "]\n", + "\n", + "# Define a closure over our joint_log_prob.\n", + "unnormalized_posterior_log_prob = lambda *args: double_joint_log_prob(observations_A_, observations_B_, *args)\n", + "\n", + "# Initialize the step_size. (It will be automatically adapted.)\n", + "with tf.variable_scope(tf.get_variable_scope(), reuse=tf.AUTO_REUSE):\n", + " step_size = tf.get_variable(\n", + " name='step_size',\n", + " initializer=tf.constant(0.5, dtype=tf.float32),\n", + " trainable=False,\n", + " use_resource=True\n", + " )\n", + "\n", + "# Defining the HMC\n", + "hmc=tfp.mcmc.TransformedTransitionKernel(\n", + " inner_kernel=tfp.mcmc.HamiltonianMonteCarlo(\n", + " target_log_prob_fn=unnormalized_posterior_log_prob,\n", + " num_leapfrog_steps=3,\n", + " step_size=step_size,\n", + " step_size_update_fn=tfp.mcmc.make_simple_step_size_update_policy(),\n", + " state_gradients_are_stopped=True),\n", + " bijector=unconstraining_bijectors)\n", + "\n", + "# Sample from the chain.\n", + "[\n", + " posterior_prob_A,\n", + " posterior_prob_B\n", + "], kernel_results = tfp.mcmc.sample_chain(\n", + " num_results=number_of_steps,\n", + " num_burnin_steps=burnin,\n", + " current_state=initial_chain_state,\n", + " kernel=hmc)\n", + "\n", + "# Initialize any created variables.\n", + "init_g = tf.global_variables_initializer()\n", + "init_l = tf.local_variables_initializer()" + ], + "execution_count": 0, + "outputs": [] + }, + { + "metadata": { + "id": "beUUmGMbdrRr", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "#### Execute the TF graph to sample from the posterior" + ] + }, + { + "metadata": { + "id": "HTYITb9fdqIe", + "colab_type": "code", + "outputId": "8bcb70ee-4c1c-4347-b0b8-6bdb6e6d2aa6", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + } + }, + "cell_type": "code", + "source": [ + "evaluate(init_g)\n", + "evaluate(init_l)\n", + "[\n", + " posterior_prob_A_,\n", + " posterior_prob_B_,\n", + " kernel_results_\n", + "] = evaluate([\n", + " posterior_prob_A,\n", + " posterior_prob_B,\n", + " kernel_results\n", + "])\n", + " \n", + "print(\"acceptance rate: {}\".format(\n", + " kernel_results_.inner_results.is_accepted.mean()))\n", + "\n", + "burned_prob_A_trace_ = posterior_prob_A_[burnin:]\n", + "burned_prob_B_trace_ = posterior_prob_B_[burnin:]\n", + "burned_delta_trace_ = (posterior_prob_A_ - posterior_prob_B_)[burnin:]\n" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "acceptance rate: 0.6161\n" + ], + "name": "stdout" + } + ] + }, + { + "metadata": { + "id": "YaD67cOkIAyT", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "Below we plot the posterior distributions for the three unknowns: " + ] + }, + { + "metadata": { + "id": "PpBXqVKELHRO", + "colab_type": "code", + "outputId": "2296d675-b1c4-409b-e314-c5e4d8b53321", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 742 + } + }, + "cell_type": "code", + "source": [ + "plt.figure(figsize(12.5, 12.5))\n", + "\n", + "#histogram of posteriors\n", + "\n", + "ax = plt.subplot(311)\n", + "\n", + "plt.xlim(0, .1)\n", + "plt.hist(burned_prob_A_trace_, histtype='stepfilled', bins=25, alpha=0.85,\n", + " label=\"posterior of $p_A$\", color=TFColor[0], normed=True)\n", + "plt.vlines(true_prob_A_, 0, 80, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n", + "plt.legend(loc=\"upper right\")\n", + "plt.title(\"Posterior distributions of $p_A$, $p_B$, and delta unknowns\")\n", + "\n", + "ax = plt.subplot(312)\n", + "\n", + "plt.xlim(0, .1)\n", + "plt.hist(burned_prob_B_trace_, histtype='stepfilled', bins=25, alpha=0.85,\n", + " label=\"posterior of $p_B$\", color=TFColor[2], normed=True)\n", + "plt.vlines(true_prob_B_, 0, 80, linestyle=\"--\", label=\"true $p_B$ (unknown)\")\n", + "plt.legend(loc=\"upper right\")\n", + "\n", + "ax = plt.subplot(313)\n", + "plt.hist(burned_delta_trace_, histtype='stepfilled', bins=30, alpha=0.85,\n", + " label=\"posterior of delta\", color=TFColor[6], normed=True)\n", + "plt.vlines(true_prob_A_ - true_prob_B_, 0, 60, linestyle=\"--\",\n", + " label=\"true delta (unknown)\")\n", + "plt.vlines(0, 0, 60, color=\"black\", alpha=0.2)\n", + "plt.legend(loc=\"upper right\");" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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9iqYMa9OmDQCffvopK1asYPHixXTs2JFGjRqVK9uhQwcA5s6dC8AZZ5zBihUr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\n5vPPP6d9+/Y1qnPVqlVA5Z/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OURz59XnwIuB4ZGf5HwOdCCSLCzAhhc6lcn6WAXr/dyK4IgeILI7+U+DYJg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\ntWvXBuD7778v9nVp75TG1GpEp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+ "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [], + "image/png": { + "width": 825, + "height": 725 + } + } + } + ] + }, + { + "metadata": { + "id": "Hn-G0eFwIAyh", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "Notice that as a result of `N_B < N_A`, i.e. we have less data from site B, our posterior distribution of $p_B$ is fatter, implying we are less certain about the true value of $p_B$ than we are of $p_A$. \n", + "\n", + "With respect to the posterior distribution of $\\text{delta}$, we can see that the majority of the distribution is above $\\text{delta}=0$, implying there site A's response is likely better than site B's response. The probability this inference is incorrect is easily computable:" + ] + }, + { + "metadata": { + "id": "nZxDurxyIAyh", + "colab_type": "code", + "outputId": "7cb41824-d97a-4b53-e12b-169d009251e7", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + } + }, + "cell_type": "code", + "source": [ + "# Count the number of samples less than 0, i.e. the area under the curve\n", + "# before 0, represent the probability that site A is worse than site B.\n", + "print(\"Probability site A is WORSE than site B: %.3f\" % \\\n", + " np.mean(burned_delta_trace_ < 0))\n", + "\n", + "print(\"Probability site A is BETTER than site B: %.3f\" % \\\n", + " np.mean(burned_delta_trace_ > 0))" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Probability site A is WORSE than site B: 0.145\n", + "Probability site A is BETTER than site B: 0.855\n" + ], + "name": "stdout" + } + ] + }, + { + "metadata": { + "id": "Q8cAEzbUIAyl", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "If this probability is too high for comfortable decision-making, we can perform more trials on site B (as site B has less samples to begin with, each additional data point for site B contributes more inferential \"power\" than each additional data point for site A). \n", + "\n", + "Try playing with the parameters `true_prob_A`, `true_prob_B`, `N_A`, and `N_B`, to see what the posterior of $\\text{delta}$ looks like. Notice in all this, the difference in sample sizes between site A and site B was never mentioned: it naturally fits into Bayesian analysis.\n", + "\n", + "I hope the readers feel this style of A/B testing is more natural than hypothesis testing, which has probably confused more than helped practitioners. Later in this book, we will see two extensions of this model: the first to help dynamically adjust for bad sites, and the second will improve the speed of this computation by reducing the analysis to a single equation. " + ] + }, + { + "metadata": { + "id": "f-jxOi70IAyl", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "## An algorithm for human deceit\n", + "\n", + "Social data has an additional layer of interest as people are not always honest with responses, which adds a further complication into inference. For example, simply asking individuals \"Have you ever cheated on a test?\" will surely contain some rate of dishonesty. What you can say for certain is that the true rate is less than your observed rate (assuming individuals lie *only* about *not cheating*; I cannot imagine one who would admit \"Yes\" to cheating when in fact they hadn't cheated). \n", + "\n", + "To present an elegant solution to circumventing this dishonesty problem, and to demonstrate Bayesian modeling, we first need to introduce the binomial distribution.\n" + ] + }, + { + "metadata": { + "id": "qzCqZqzBDpMa", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "## The Binomial Distribution\n", + "\n", + "The binomial distribution is one of the most popular distributions, mostly because of its simplicity and usefulness. Unlike the other distributions we have encountered thus far in the book, the binomial distribution has 2 parameters: $N$, a positive integer representing $N$ trials or number of instances of potential events, and $p$, the probability of an event occurring in a single trial. Like the Poisson distribution, it is a discrete distribution, but unlike the Poisson distribution, it only weighs integers from $0$ to $N$. The mass distribution looks like:\n", + "\n", + "$$P( X = k ) = {{N}\\choose{k}} p^k(1-p)^{N-k}$$\n", + "\n", + "If $X$ is a binomial random variable with parameters $p$ and $N$, denoted $X \\sim \\text{Bin}(N,p)$, then $X$ is the number of events that occurred in the $N$ trials (obviously $0 \\le X \\le N$). The larger $p$ is (while still remaining between 0 and 1), the more events are likely to occur. The expected value of a binomial is equal to $Np$. Below we plot the mass probability distribution for varying parameters. " + ] + }, + { + "metadata": { + "id": "9I53Ta3maWgJ", + "colab_type": "code", + "outputId": "e097f79a-2032-4e1a-949a-2b26a1004a78", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 294 + } + }, + "cell_type": "code", + "source": [ + "k_values = tf.range(start=0, limit=(N + 1), dtype=tf.float32)\n", + "random_var_probs_1 = tfd.Binomial(total_count=10., probs=.4).prob(k_values)\n", + "random_var_probs_2 = tfd.Binomial(total_count=10., probs=.9).prob(k_values)\n", + "\n", + "# Execute graph\n", + "[\n", + " k_values_,\n", + " random_var_probs_1_,\n", + " random_var_probs_2_,\n", + "] = evaluate([\n", + " k_values,\n", + " random_var_probs_1,\n", + " random_var_probs_2,\n", + "])\n", + "\n", + "# Display results\n", + "plt.figure(figsize=(12.5, 4))\n", + "colors = [TFColor[3], TFColor[0]] \n", + "\n", + "plt.bar(k_values_ - 0.5, random_var_probs_1_, color=colors[0],\n", + " edgecolor=colors[0],\n", + " alpha=0.6,\n", + " label=\"$N$: %d, $p$: %.1f\" % (10., .4),\n", + " linewidth=3)\n", + "plt.bar(k_values_ - 0.5, random_var_probs_2_, color=colors[1],\n", + " edgecolor=colors[1],\n", + " alpha=0.6,\n", + " label=\"$N$: %d, $p$: %.1f\" % (10., .9),\n", + " linewidth=3)\n", + "\n", + "plt.legend(loc=\"upper left\")\n", + "plt.xlim(0, 10.5)\n", + "plt.xlabel(\"$k$\")\n", + "plt.ylabel(\"$P(X = k)$\")\n", + "plt.title(\"Probability mass distributions of binomial random variables\");" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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jG6Tn7jHS/FbfJAWS7iMFj2o1tFOMcRLwb6TG/3akZ2tIdqyXgK/HGAt7I/0H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\n9OnTp5lLIknFWU9JaumspyS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+ "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [], + "image/png": { + "width": 839, + "height": 277 + } + } + } + ] + }, + { + "metadata": { + "id": "xT-q-ZI0IAys", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "The special case when $N = 1$ corresponds to the Bernoulli distribution. There is another connection between Bernoulli and Binomial random variables. If we have $X_1, X_2, ... , X_N$ Bernoulli random variables with the same $p$, then $Z = X_1 + X_2 + ... + X_N \\sim \\text{Binomial}(N, p )$.\n", + "\n", + "The expected value of a Bernoulli random variable is $p$. This can be seen by noting the more general Binomial random variable has expected value $Np$ and setting $N=1$." + ] + }, + { + "metadata": { + "id": "9HmW-50PIAyv", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "## Example: Cheating among students\n", + "\n", + "We will use the binomial distribution to determine the frequency of students cheating during an exam. If we let $N$ be the total number of students who took the exam, and assuming each student is interviewed post-exam (answering without consequence), we will receive integer $X$ \"Yes I did cheat\" answers. We then find the posterior distribution of $p$, given $N$, some specified prior on $p$, and observed data $X$. \n", + "\n", + "This is a completely absurd model. No student, even with a free-pass against punishment, would admit to cheating. What we need is a better *algorithm* to ask students if they had cheated. Ideally the algorithm should encourage individuals to be honest while preserving privacy. The following proposed algorithm is a solution I greatly admire for its ingenuity and effectiveness:\n", + "\n", + "> In the interview process for each student, the student flips a coin, hidden from the interviewer. The student agrees to answer honestly if the coin comes up heads. Otherwise, if the coin comes up tails, the student (secretly) flips the coin again, and answers \"Yes, I did cheat\" if the coin flip lands heads, and \"No, I did not cheat\", if the coin flip lands tails. This way, the interviewer does not know if a \"Yes\" was the result of a guilty plea, or a Heads on a second coin toss. Thus privacy is preserved and the researchers receive honest answers. \n", + "\n", + "I call this the Privacy Algorithm. One could of course argue that the interviewers are still receiving false data since some *Yes*'s are not confessions but instead randomness, but an alternative perspective is that the researchers are discarding approximately half of their original dataset since half of the responses will be noise. But they have gained a systematic data generation process that can be modeled. Furthermore, they do not have to incorporate (perhaps somewhat naively) the possibility of deceitful answers. We can use TFP to dig through this noisy model, and find a posterior distribution for the true frequency of liars. " + ] + }, + { + "metadata": { + "id": "gPcqaqxMIAyw", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "Suppose 100 students are being surveyed for cheating, and we wish to find $p$, the proportion of cheaters. There are a few ways we can model this in TFP. I'll demonstrate the most explicit way, and later show a simplified version. Both versions arrive at the same inference. In our data-generation model, we sample $p$, the true proportion of cheaters, from a prior. Since we are quite ignorant about $p$, we will assign it a $\\text{Uniform}(0,1)$ prior." + ] + }, + { + "metadata": { + "id": "LIg-xs2LIAyw", + "colab_type": "code", + "colab": {} + }, + "cell_type": "code", + "source": [ + "reset_sess()\n", + "\n", + "N = 100\n", + "p = tfd.Uniform(name=\"freq_cheating\", low=0., high=1.)" + ], + "execution_count": 0, + "outputs": [] + }, + { + "metadata": { + "id": "7L0nMGmrIAy0", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "Again, thinking of our data-generation model, we assign Bernoulli random variables to the 100 students: 1 implies they cheated and 0 implies they did not. " + ] + }, + { + "metadata": { + "id": "aXxhrJdtIAy0", + "colab_type": "code", + "outputId": "57d6feb0-f99d-460e-ea0f-c6ea67392c16", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 68 + } + }, + "cell_type": "code", + "source": [ + "N = 100\n", + "reset_sess()\n", + "p = tfd.Uniform(name=\"freq_cheating\", low=0., high=1.)\n", + "true_answers = tfd.Bernoulli(name=\"truths\", \n", + " probs=p.sample()).sample(sample_shape=N, \n", + " seed=5)\n", + "# Execute graph\n", + "[\n", + " true_answers_,\n", + "] = evaluate([\n", + " true_answers,\n", + "])\n", + "\n", + "print(true_answers_)" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0\n", + " 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n", + " 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n" + ], + "name": "stdout" + } + ] + }, + { + "metadata": { + "id": "vNB9WGYcIAy4", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "If we carry out the algorithm, the next step that occurs is the first coin-flip each student makes. This can be modeled again by sampling 100 Bernoulli random variables with $p=1/2$: denote a 1 as a *Heads* and 0 a *Tails*." + ] + }, + { + "metadata": { + "id": "68t8O39EIAy4", + "colab_type": "code", + "outputId": "8c2114dd-6c5b-4db6-a10d-23c73c0ede87", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 68 + } + }, + "cell_type": "code", + "source": [ + "N = 100\n", + "first_coin_flips = tfd.Bernoulli(name=\"first_flips\", \n", + " probs=0.5).sample(sample_shape=N, \n", + " seed=5)\n", + "# Execute graph\n", + "[\n", + " first_coin_flips_,\n", + "] = evaluate([\n", + " first_coin_flips,\n", + "])\n", + "\n", + "print(first_coin_flips_)" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "[1 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 1\n", + " 0 1 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0\n", + " 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1]\n" + ], + "name": "stdout" + } + ] + }, + { + "metadata": { + "id": "8-ZnScpWIAzA", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "Although *not everyone* flips a second time, we can still model the possible realization of second coin-flips:" + ] + }, + { + "metadata": { + "id": "acP-4TAfIAzB", + "colab_type": "code", + "outputId": "f4c3e132-3dee-4eb9-afd7-6c22fd128b37", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 68 + } + }, + "cell_type": "code", + "source": [ + "N = 100\n", + "second_coin_flips = tfd.Bernoulli(name=\"second_flips\", \n", + " probs=0.5).sample(sample_shape=N, \n", + " seed=5)\n", + "# Execute graph\n", + "[\n", + " second_coin_flips_,\n", + "] = evaluate([\n", + " second_coin_flips,\n", + "])\n", + "\n", + "print(second_coin_flips_)" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "[1 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 1\n", + " 0 1 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0\n", + " 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1]\n" + ], + "name": "stdout" + } + ] + }, + { + "metadata": { + "id": "uiVbAjoTIAzI", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "Using these variables, we can return a possible realization of the *observed proportion* of \"Yes\" responses. " + ] + }, + { + "metadata": { + "id": "BJxN0jmBIAzJ", + "colab_type": "code", + "colab": {} + }, + "cell_type": "code", + "source": [ + "def observed_proportion_calc(t_a = true_answers, \n", + " fc = first_coin_flips,\n", + " sc = second_coin_flips):\n", + " \"\"\"\n", + " Unnormalized log posterior distribution function\n", + " \n", + " Args:\n", + " t_a: array of binary variables representing the true answers\n", + " fc: array of binary variables representing the simulated first flips \n", + " sc: array of binary variables representing the simulated second flips\n", + " Returns: \n", + " Observed proportion of coin flips\n", + " Closure over: N\n", + " \"\"\"\n", + " observed = fc * t_a + (1 - fc) * sc\n", + " observed_proportion = tf.to_float(tf.reduce_sum(observed)) / tf.to_float(N)\n", + " \n", + " return tf.to_float(observed_proportion)\n" + ], + "execution_count": 0, + "outputs": [] + }, + { + "metadata": { + "id": "OoIWHbsNIAzL", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "The line `fc*t_a + (1-fc)*sc` contains the heart of the Privacy algorithm. Elements in this array are 1 *if and only if* i) the first toss is heads and the student cheated or ii) the first toss is tails, and the second is heads, and are 0 else. Finally, the last line sums this vector and divides by `float(N)`, producing a proportion. " + ] + }, + { + "metadata": { + "id": "ma5VwRSNIAzM", + "colab_type": "code", + "outputId": "92449808-a8fe-4bd4-973b-73e22bb27eb5", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + } + }, + "cell_type": "code", + "source": [ + "observed_proportion_val = observed_proportion_calc(t_a=true_answers_,\n", + " fc=first_coin_flips_,\n", + " sc=second_coin_flips_)\n", + "# Execute graph\n", + "[\n", + " observed_proportion_val_,\n", + "] = evaluate([\n", + " observed_proportion_val,\n", + "])\n", + "\n", + "print(observed_proportion_val_)" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "0.01\n" + ], + "name": "stdout" + } + ] + }, + { + "metadata": { + "id": "HNoBM39rIAzQ", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "Next we need a dataset. After performing our coin-flipped interviews the researchers received 35 \"Yes\" responses. To put this into a relative perspective, if there truly were no cheaters, we should expect to see on average 1/4 of all responses being a \"Yes\" (half chance of having first coin land Tails, and another half chance of having second coin land Heads), so about 25 responses in a cheat-free world. On the other hand, if *all students cheated*, we should expected to see approximately 3/4 of all responses be \"Yes\". \n", + "\n", + "The researchers observe a Binomial random variable, with `N = 100` and `total_yes = 35`: " + ] + }, + { + "metadata": { + "id": "SLcH6ZPsIAzR", + "colab_type": "code", + "colab": {} + }, + "cell_type": "code", + "source": [ + "total_count = 100\n", + "total_yes = 35" + ], + "execution_count": 0, + "outputs": [] + }, + { + "metadata": { + "id": "-kWZd1ygofav", + "colab_type": "code", + "colab": {} + }, + "cell_type": "code", + "source": [ + "def coin_joint_log_prob(total_yes, total_count, lies_prob):\n", + " \"\"\"\n", + " Joint log probability optimization function.\n", + " \n", + " Args:\n", + " headsflips: Integer for total number of observed heads flips\n", + " N: Integer for number of total observation\n", + " lies_prob: Test probability of a heads flip (1) for a Binomial distribution\n", + " Returns: \n", + " Joint log probability optimization function.\n", + " \"\"\"\n", + " \n", + " rv_lies_prob = tfd.Uniform(name=\"rv_lies_prob\",low=0., high=1.)\n", + "\n", + " cheated = tfd.Bernoulli(probs=tf.to_float(lies_prob)).sample(total_count)\n", + " first_flips = tfd.Bernoulli(probs=0.5).sample(total_count)\n", + " second_flips = tfd.Bernoulli(probs=0.5).sample(total_count)\n", + " observed_probability = tf.reduce_sum(tf.to_float(\n", + " cheated * first_flips + (1 - first_flips) * second_flips)) / total_count\n", + "\n", + " rv_yeses = tfd.Binomial(name=\"rv_yeses\",\n", + " total_count=float(total_count),\n", + " probs=observed_probability)\n", + " \n", + " return (\n", + " rv_lies_prob.log_prob(lies_prob)\n", + " + tf.reduce_sum(rv_yeses.log_prob(tf.to_float(total_yes)))\n", + " )" + ], + "execution_count": 0, + "outputs": [] + }, + { + "metadata": { + "id": "QZC4TITlIAzV", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "Below we add all the variables of interest to our Metropolis-Hastings sampler and run our black-box algorithm over the model. It's important to note that we're using a Metropolis-Hastings MCMC instead of a Hamiltonian since we're sampling inside." + ] + }, + { + "metadata": { + "id": "Awl3GmgjIAzV", + "colab_type": "code", + "colab": {} + }, + "cell_type": "code", + "source": [ + "burnin = 15000\n", + "num_of_steps = 40000\n", + "total_count=100\n", + "\n", + "# Set the chain's start state.\n", + "initial_chain_state = [\n", + " 0.4 * tf.ones([], dtype=tf.float32, name=\"init_prob\")\n", + "]\n", + "\n", + "# Define a closure over our joint_log_prob.\n", + "unnormalized_posterior_log_prob = lambda *args: coin_joint_log_prob(total_yes, total_count, *args)\n", + "\n", + "# Defining the Metropolis-Hastings\n", + "# We use a Metropolis-Hastings method here instead of Hamiltonian method\n", + "# because the coin flips in the above example are non-differentiable and cannot\n", + "# bue used with HMC.\n", + "metropolis=tfp.mcmc.RandomWalkMetropolis(\n", + " target_log_prob_fn=unnormalized_posterior_log_prob,\n", + " seed=54)\n", + "\n", + "# Sample from the chain.\n", + "[\n", + " posterior_p\n", + "], kernel_results = tfp.mcmc.sample_chain(\n", + " num_results=num_of_steps,\n", + " num_burnin_steps=burnin,\n", + " current_state=initial_chain_state,\n", + " kernel=metropolis,\n", + " parallel_iterations=1,\n", + " name='Metropolis-Hastings_coin-flips')" + ], + "execution_count": 0, + "outputs": [] + }, + { + "metadata": { + "id": "Lq0OtJDCufOu", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "##### Executing the TF graph to sample from the posterior" + ] + }, + { + "metadata": { + "id": "x--bCsBrr91E", + "colab_type": "code", + "outputId": "cfab9154-992d-418d-ba2e-d16f1cae1e65", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + } + }, + "cell_type": "code", + "source": [ + "# Content Warning: This cell can take up to 5 minutes in Graph Mode\n", + "[\n", + " posterior_p_,\n", + " kernel_results_\n", + "] = evaluate([\n", + " posterior_p,\n", + " kernel_results,\n", + "])\n", + " \n", + "print(\"acceptance rate: {}\".format(\n", + " kernel_results_.is_accepted.mean()))\n", + "# print(\"prob_p trace: \", posterior_p_)\n", + "# print(\"prob_p burned trace: \", posterior_p_[burnin:])\n", + "burned_cheating_freq_samples_ = posterior_p_[burnin:]" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "acceptance rate: 0.105625\n" + ], + "name": "stdout" + } + ] + }, + { + "metadata": { + "id": "QhCgk98ynq5s", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "And finally we can plot the results." + ] + }, + { + "metadata": { + "id": "JoKNmLpxB1yt", + "colab_type": "code", + "outputId": "b793d81e-288a-4d80-8a37-f34f19e50aab", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 374 + } + }, + "cell_type": "code", + "source": [ + "plt.figure(figsize(12.5, 6))\n", + "p_trace_ = burned_cheating_freq_samples_\n", + "plt.hist(p_trace_, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30, \n", + " label=\"posterior distribution\", color=TFColor[3])\n", + "plt.vlines([.1, .40], [0, 0], [5, 5], alpha=0.3)\n", + "plt.xlim(0, 1)\n", + "plt.legend();" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [], + "image/png": { + "width": 816, + "height": 357 + } + } + } + ] + }, + { + "metadata": { + "id": "tqDMt8xyIAzd", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "With regards to the above plot, we are still pretty uncertain about what the true frequency of cheaters might be, but we have narrowed it down to a range between 0.1 to 0.4 (marked by the solid lines). This is pretty good, as *a priori* we had no idea how many students might have cheated (hence the uniform distribution for our prior). On the other hand, it is also pretty bad since there is a .3 length window the true value most likely lives in. Have we even gained anything, or are we still too uncertain about the true frequency? \n", + "\n", + "I would argue, yes, we have discovered something. It is implausible, according to our posterior, that there are *no cheaters*, i.e. the posterior assigns low probability to $p=0$. Since we started with an uniform prior, treating all values of $p$ as equally plausible, but the data ruled out $p=0$ as a possibility, we can be confident that there were cheaters. \n", + "\n", + "This kind of algorithm can be used to gather private information from users and be *reasonably* confident that the data, though noisy, is truthful. \n", + "\n" + ] + }, + { + "metadata": { + "id": "Y0bK5tMAIAze", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "### Alternative TFP Model\n", + "\n", + "Given a value for $p$ (which from our god-like position we know), we can find the probability the student will answer yes: \n", + "$$\n", + "\\begin{align}\n", + "P(\\text{\"Yes\"}) &= P( \\text{Heads on first coin} )P( \\text{cheater} ) + P( \\text{Tails on first coin} )P( \\text{Heads on second coin} ) \\\\\n", + "&= \\frac{1}{2}p + \\frac{1}{2}\\frac{1}{2}\\\\\n", + "&= \\frac{p}{2} + \\frac{1}{4}\n", + "\\end{align}\n", + "$$\n", + "Thus, knowing $p$ we know the probability a student will respond \"Yes\". In TFP, we can create a deterministic function to evaluate the probability of responding \"Yes\", given $p$:" + ] + }, + { + "metadata": { + "id": "wBps82qhIAzf", + "colab_type": "code", + "colab": {} + }, + "cell_type": "code", + "source": [ + "reset_sess()\n", + "\n", + "p_new = tfd.Uniform(name=\"new_freq_cheating\", \n", + " low=0., \n", + " high=1.)\n", + "p_new_skewed = tfd.Deterministic(name=\"p_skewed\", \n", + " loc=(0.5 * p_new.sample(seed=0.5) + 0.25)).sample(seed=0.5)" + ], + "execution_count": 0, + "outputs": [] + }, + { + "metadata": { + "id": "m_kgk64TIAzh", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "I could have typed `p_skewed = 0.5 * p + 0.25` instead for a one-liner, as the elementary operations of addition and scalar multiplication will implicitly create a deterministic variable, but I wanted to make the determinism explicit for clarity's sake. \n", + "\n", + "If we know the probability of respondents saying \"Yes\", which is `p_skewed`, and we have $N=100$ students, the number of \"Yes\" responses is a binomial random variable with parameters `N` and `p_skewed`.\n", + "\n", + "This is where we include our observed 35 \"Yes\" responses out of a total of 100 which are passed to the `joint_log_prob`." + ] + }, + { + "metadata": { + "id": "GJ2jFKI7ofa9", + "colab_type": "code", + "colab": {} + }, + "cell_type": "code", + "source": [ + "N = 100.\n", + "total_yes = 35.\n", + "\n", + "def alt_joint_log_prob(yes_responses, N, prob_cheating):\n", + " \"\"\"\n", + " Alternative joint log probability optimization function.\n", + " \n", + " Args:\n", + " yes_responses: Integer for total number of affirmative responses\n", + " N: Integer for number of total observation\n", + " prob_cheating: Test probability of a student actually cheating\n", + " Returns: \n", + " Joint log probability optimization function.\n", + " \"\"\"\n", + " tfd = tfp.distributions\n", + " \n", + " rv_prob = tfd.Uniform(name=\"rv_new_freq_cheating\", low=0., high=1.)\n", + " prob_skewed = 0.5 * prob_cheating + 0.25\n", + " rv_yes_responses = tfd.Binomial(name=\"rv_yes_responses\",\n", + " total_count=tf.to_float(N), \n", + " probs=prob_skewed)\n", + "\n", + " return (\n", + " rv_prob.log_prob(prob_cheating)\n", + " + tf.reduce_sum(rv_yes_responses.log_prob(tf.to_float(yes_responses)))\n", + " )" + ], + "execution_count": 0, + "outputs": [] + }, + { + "metadata": { + "id": "0clIAcyHIAzj", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "\n", + "Below we add all the variables of interest to our HMC component-defining cell and run our black-box algorithm over the model. " + ] + }, + { + "metadata": { + "id": "C5QLZ17e5u6t", + "colab_type": "code", + "colab": {} + }, + "cell_type": "code", + "source": [ + "number_of_steps = 25000\n", + "burnin = 2500\n", + "\n", + "# Set the chain's start state.\n", + "initial_chain_state = [\n", + " 0.2 * tf.ones([], dtype=tf.float32, name=\"init_skewed_p\")\n", + "]\n", + "\n", + "# Since HMC operates over unconstrained space, we need to transform the\n", + "# samples so they live in real-space.\n", + "unconstraining_bijectors = [\n", + " tfp.bijectors.Sigmoid(), # Maps [0,1] to R.\n", + "]\n", + "\n", + "# Define a closure over our joint_log_prob.\n", + "# unnormalized_posterior_log_prob = lambda *args: alt_joint_log_prob(headsflips, total_yes, N, *args)\n", + "unnormalized_posterior_log_prob = lambda *args: alt_joint_log_prob(total_yes, N, *args)\n", + "\n", + "# Initialize the step_size. (It will be automatically adapted.)\n", + "with tf.variable_scope(tf.get_variable_scope(), reuse=tf.AUTO_REUSE):\n", + " step_size = tf.get_variable(\n", + " name='skewed_step_size',\n", + " initializer=tf.constant(0.5, dtype=tf.float32),\n", + " trainable=False,\n", + " use_resource=True\n", + " ) \n", + "\n", + "# Defining the HMC\n", + "hmc=tfp.mcmc.TransformedTransitionKernel(\n", + " inner_kernel=tfp.mcmc.HamiltonianMonteCarlo(\n", + " target_log_prob_fn=unnormalized_posterior_log_prob,\n", + " num_leapfrog_steps=2,\n", + " step_size=step_size,\n", + " step_size_update_fn=tfp.mcmc.make_simple_step_size_update_policy(),\n", + " state_gradients_are_stopped=True),\n", + " bijector=unconstraining_bijectors)\n", + "\n", + "# Sample from the chain.\n", + "[\n", + " posterior_skewed_p\n", + "], kernel_results = tfp.mcmc.sample_chain(\n", + " num_results=number_of_steps,\n", + " num_burnin_steps=burnin,\n", + " current_state=initial_chain_state,\n", + " kernel=hmc)\n", + "\n", + "# Initialize any created variables.\n", + "# This prevents a FailedPreconditionError\n", + "init_g = tf.global_variables_initializer()\n", + "init_l = tf.local_variables_initializer()" + ], + "execution_count": 0, + "outputs": [] + }, + { + "metadata": { + "id": "eJYLS8EysHqj", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "#### Execute the TF graph to sample from the posterior" + ] + }, + { + "metadata": { + "id": "ALvEN1yQkTIx", + "colab_type": "code", + "outputId": "2bedf661-d0d3-45d2-fbba-c1ca8c85bb6b", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + } + }, + "cell_type": "code", + "source": [ + "# This cell may take 5 minutes in Graph Mode\n", + "evaluate(init_g)\n", + "evaluate(init_l)\n", + "[\n", + " posterior_skewed_p_,\n", + " kernel_results_\n", + "] = evaluate([\n", + " posterior_skewed_p,\n", + " kernel_results\n", + "])\n", + "\n", + " \n", + "print(\"acceptance rate: {}\".format(\n", + " kernel_results_.inner_results.is_accepted.mean()))\n", + "# print(\"final step size: {}\".format(\n", + "# kernel_results_.inner_results.extra.step_size_assign[-100:].mean()))\n", + "\n", + "# print(\"p_skewed trace: \", posterior_skewed_p_)\n", + "# print(\"p_skewed burned trace: \", posterior_skewed_p_[burnin:])\n", + "freq_cheating_samples_ = posterior_skewed_p_[burnin:]\n" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "acceptance rate: 0.6052\n" + ], + "name": "stdout" + } + ] + }, + { + "metadata": { + "id": "Ye0uC_c-xrWf", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "Now we can plot our results" + ] + }, + { + "metadata": { + "id": "_P5Z_uySgi-S", + "colab_type": "code", + "outputId": "0b085693-c710-449f-c25a-730abbde9a92", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 374 + } + }, + "cell_type": "code", + "source": [ + "plt.figure(figsize(12.5, 6))\n", + "p_trace_ = freq_cheating_samples_\n", + "plt.hist(p_trace_, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30, \n", + " label=\"posterior distribution\", color=TFColor[3])\n", + "plt.vlines([.1, .40], [0, 0], [5, 5], alpha=0.2)\n", + "plt.xlim(0, 1)\n", + "plt.legend();" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [], + "image/png": { + "width": 816, + "height": 357 + } + } + } + ] + }, + { + "metadata": { + "id": "Lxt6fSRvIAzy", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "The remainder of this chapter examines some practical examples of TFP and TFP modeling:" + ] + }, + { + "metadata": { + "id": "KMoiodMmIAzy", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "## Example: Challenger Space Shuttle Disaster \n", + "\n", + "On January 28, 1986, the twenty-fifth flight of the U.S. space shuttle program ended in disaster when one of the rocket boosters of the Shuttle Challenger exploded shortly after lift-off, killing all seven crew members. The presidential commission on the accident concluded that it was caused by the failure of an O-ring in a field joint on the rocket booster, and that this failure was due to a faulty design that made the O-ring unacceptably sensitive to a number of factors including outside temperature. Of the previous 24 flights, data were available on failures of O-rings on 23, (one was lost at sea), and these data were discussed on the evening preceding the Challenger launch, but unfortunately only the data corresponding to the 7 flights on which there was a damage incident were considered important and these were thought to show no obvious trend. The data are shown below (see [1]):\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "metadata": { + "id": "tlPZvBWkg5g-", + "colab_type": "code", + "outputId": "c1d98c8c-e923-468b-85ff-c70e8628ee70", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 34 + } + }, + "cell_type": "code", + "source": [ + "reset_sess()\n", + "\n", + "import wget\n", + "url = 'https://raw.githubusercontent.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter2_MorePyMC/data/challenger_data.csv'\n", + "filename = wget.download(url)\n", + "filename" + ], + "execution_count": 2, + "outputs": [ + { + "output_type": "execute_result", + "data": { + "text/plain": [ + "'challenger_data.csv'" + ] + }, + "metadata": { + "tags": [] + }, + "execution_count": 2 + } + ] + }, + { + "metadata": { + "id": "BNOqG_9zIAzz", + "colab_type": "code", + "outputId": "639d0193-a43f-4c1e-b79f-2b1d0cf0853d", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 675 + } + }, + "cell_type": "code", + "source": [ + "plt.figure(figsize(12.5, 3.5))\n", + "np.set_printoptions(precision=3, suppress=True)\n", + "challenger_data_ = np.genfromtxt(\"challenger_data.csv\", skip_header=1,\n", + " usecols=[1, 2], missing_values=\"NA\",\n", + " delimiter=\",\")\n", + "#drop the NA values\n", + "challenger_data_ = challenger_data_[~np.isnan(challenger_data_[:, 1])]\n", + "\n", + "#plot it, as a function of tempature (the first column)\n", + "print(\"Temp (F), O-Ring failure?\")\n", + "print(challenger_data_)\n", + "\n", + "plt.scatter(challenger_data_[:, 0], challenger_data_[:, 1], s=75, color=\"k\",\n", + " alpha=0.5)\n", + "plt.yticks([0, 1])\n", + "plt.ylabel(\"Damage Incident?\")\n", + "plt.xlabel(\"Outside temperature (Fahrenheit)\")\n", + "plt.title(\"Defects of the Space Shuttle O-Rings vs temperature\");\n" + ], + "execution_count": 3, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Temp (F), O-Ring failure?\n", + "[[66. 0.]\n", + " [70. 1.]\n", + " [69. 0.]\n", + " [68. 0.]\n", + " [67. 0.]\n", + " [72. 0.]\n", + " [73. 0.]\n", + " [70. 0.]\n", + " [57. 1.]\n", + " [63. 1.]\n", + " [70. 1.]\n", + " [78. 0.]\n", + " [67. 0.]\n", + " [53. 1.]\n", + " [67. 0.]\n", + " [75. 0.]\n", + " [70. 0.]\n", + " [81. 0.]\n", + " [76. 0.]\n", + " [79. 0.]\n", + " [75. 1.]\n", + " [76. 0.]\n", + " [58. 1.]]\n" + ], + "name": "stdout" + }, + { + "output_type": "display_data", + "data": { + "image/png": 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JJ466LHPnzuWkk05i5cqV45zD6akpbawp5Wia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\nir/1wee9OnAINWnq+m253KaidJLq4Zd0fz7/rlxuk5n3U3S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+ "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [], + "image/png": { + "width": 824, + "height": 250 + } + } + } + ] + }, + { + "metadata": { + "id": "El9Z_4ulIAz3", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "It looks clear that *the probability* of damage incidents occurring increases as the outside temperature decreases. We are interested in modeling the probability here because it does not look like there is a strict cutoff point between temperature and a damage incident occurring. The best we can do is ask \"At temperature $t$, what is the probability of a damage incident?\". The goal of this example is to answer that question.\n", + "\n", + "We need a function of temperature, call it $p(t)$, that is bounded between 0 and 1 (so as to model a probability) and changes from 1 to 0 as we increase temperature. There are actually many such functions, but the most popular choice is the *logistic function.*\n", + "\n", + "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t } } $$\n", + "\n", + "In this model, $\\beta$ is the variable we are uncertain about. Below is the function plotted for $\\beta = 1, 3, -5$." + ] + }, + { + "metadata": { + "id": "U4kW2QIddYEs", + "colab_type": "code", + "outputId": "9035341f-411e-47b9-a89a-7d03e3b8934b", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 210 + } + }, + "cell_type": "code", + "source": [ + "def logistic(x, beta):\n", + " \"\"\"\n", + " Logistic Function\n", + " \n", + " Args:\n", + " x: independent variable\n", + " beta: beta term\n", + " Returns: \n", + " Logistic function\n", + " \"\"\"\n", + " return 1.0 / (1.0 + tf.exp(beta * x))\n", + "\n", + "x_vals = tf.linspace(start=-4., stop=4., num=100)\n", + "log_beta_1 = logistic(x_vals, 1.)\n", + "log_beta_3 = logistic(x_vals, 3.)\n", + "log_beta_m5 = logistic(x_vals, -5.)\n", + "\n", + "[\n", + " x_vals_,\n", + " log_beta_1_,\n", + " log_beta_3_,\n", + " log_beta_m5_,\n", + "] = evaluate([\n", + " x_vals,\n", + " log_beta_1,\n", + " log_beta_3,\n", + " log_beta_m5,\n", + "])\n", + "\n", + "plt.figure(figsize(12.5, 3))\n", + "plt.plot(x_vals_, log_beta_1_, label=r\"$\\beta = 1$\", color=TFColor[0])\n", + "plt.plot(x_vals_, log_beta_3_, label=r\"$\\beta = 3$\", color=TFColor[3])\n", + "plt.plot(x_vals_, log_beta_m5_, label=r\"$\\beta = -5$\", color=TFColor[6])\n", + "plt.legend();" + ], + "execution_count": 4, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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FMiIiIlNxHKivt2Xb9rJTJjZaEtIUwxpnYOD2t81m4coVW4A14/f8ot+uS7N6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\njTHeP04hO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+ "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [], + "image/png": { + "width": 818, + "height": 193 + } + } + } + ] + }, + { + "metadata": { + "id": "H_rdEcFIIAz7", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "But something is missing. In the plot of the logistic function, the probability changes only near zero, but in our data above the probability changes around 65 to 70. We need to add a *bias* term to our logistic function:\n", + "\n", + "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t + \\alpha } } $$\n", + "\n", + "Some plots are below, with differing $\\alpha$." + ] + }, + { + "metadata": { + "id": "T0iZj_eCIAz8", + "colab_type": "code", + "outputId": "fe88b350-5b63-49bd-9de4-d3d18df432f0", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 210 + } + }, + "cell_type": "code", + "source": [ + "def logistic(x, beta, alpha=0):\n", + " \"\"\"\n", + " Logistic Function with offset\n", + " \n", + " Args:\n", + " x: independent variable\n", + " beta: beta term \n", + " alpha: alpha term\n", + " Returns: \n", + " Logistic function\n", + " \"\"\"\n", + " return 1.0 / (1.0 + tf.exp((beta * x) + alpha))\n", + "\n", + "x_vals = tf.linspace(start=-4., stop=4., num=100)\n", + "log_beta_1_alpha_1 = logistic(x_vals, 1, 1)\n", + "log_beta_3_alpha_m2 = logistic(x_vals, 3, -2)\n", + "log_beta_m5_alpha_7 = logistic(x_vals, -5, 7)\n", + "\n", + "[\n", + " x_vals_,\n", + " log_beta_1_alpha_1_,\n", + " log_beta_3_alpha_m2_,\n", + " log_beta_m5_alpha_7_,\n", + "] = evaluate([\n", + " x_vals,\n", + " log_beta_1_alpha_1,\n", + " log_beta_3_alpha_m2,\n", + " log_beta_m5_alpha_7,\n", + "])\n", + "\n", + "plt.figure(figsize(12.5, 3))\n", + "plt.plot(x_vals_, log_beta_1_, label=r\"$\\beta = 1$\", ls=\"--\", lw=1, color=TFColor[0])\n", + "plt.plot(x_vals_, log_beta_3_, label=r\"$\\beta = 3$\", ls=\"--\", lw=1, color=TFColor[3])\n", + "plt.plot(x_vals_, log_beta_m5_, label=r\"$\\beta = -5$\", ls=\"--\", lw=1, color=TFColor[6])\n", + "plt.plot(x_vals_, log_beta_1_alpha_1_, label=r\"$\\beta = 1, \\alpha = 1$\", color=TFColor[0])\n", + "plt.plot(x_vals_, log_beta_3_alpha_m2_, label=r\"$\\beta = 3, \\alpha = -2$\", color=TFColor[3])\n", + "plt.plot(x_vals_, log_beta_m5_alpha_7_, label=r\"$\\beta = -5, \\alpha = 7$\", color=TFColor[6])\n", + "plt.legend(loc=\"lower left\");" + ], + "execution_count": 5, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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4qwPHWx0AVOP+XKKAsUgOE5E8uit6aowt5/GNy4nyfZ/Vi3ZnHouOFPoabGjg\nPCVbQtcEmtwWNLktuL3FbIBO5gxMFsOZUkgzHcvjWiOfpfMSlxZyuLSgetJoAujwWdBbb0VvQPWi\n8Tt41THdevl0HtOvT2Pq1SlkohkIXSB4KAiL3QKhCRz9yFG4Glyw2PlVl2gnycazmL+o5oRZ2ctt\nJVejC8HDQTQdboIz4LxmXSIiou2Gn1L3MD1Vu7uvyGaBpSVV1kEKoRq/vb5iUONTYU0psPGuKC43\nA5zdQAg1HFuJvw44fsf6HvuJT0JmsyqwSSaAeNy8XTm0mpSQ/QeKdRJAIq7m0FkOrwpycOY0xPee\nrvl0sq0N+NRvmyv+8rMqpPF4q4NFjxcIBNQ2IqI9TtcEWr0WtHotuKejepvfoeGRHifGo3mMR/KI\n5jREczZcfDMGAPjPP9QAX7GxPp414LYKBjRbyGXV0N9gQ3+D2Qs6b0jMxguYiObKYc14JI9UvnZK\nY0hgLJLHWCSPZ0bUZ8hGl4aeehv2B6zYH7Ci2a3zfaZNkwqnMPnKJGbemCnPCWP329E40AgjbwDF\nDNLX5rvGXohou4nPxjH23BgWLi8A17hQwFHnKIcw7ib3rTtAIiKiDcZAZg9bK5B5q4SUqkE9fu2u\nxCVS0wGvR01c7/Wppc+/4r7PDHgY3uw+Qqjhzux2FYCspakZ+JV/b96XUgU58TiQiCNTec4dGFDh\nYHEbEnEz6KnsnZPLQbz4wppPKX/8XwEPPqTunH4NeOYpFdqUzslS4OjzqeHV2PBERHtQq9eCHzms\nelgaUuLFc0OYTFmwrPkRyxjlMAYAPv18GJmCRF/Air7iPDQtHjbcbzWLJtDus6DdZ34dMKTETLyA\noaUchsJZDC3lsHiN4c4WkgYWkmm8MpkGoOYcOtJkx+GgCn/sFr7HtDEysQxe+R+vlBtr67rr0H6y\nHYG+AP+WEO1Q8Zk4Rp8bxeLlxTXr2Dw2BA8HETwchLfVy993IiLaFRjI7GFzb/8heD/0kWLDdcwM\nVcolZjZux+MQ6fSGPK8wCkAkosp1SCGKPWt8gN+vght/qdSpRvHSbTvHht71KoOchgbIwUFz210n\nVKmlUKi6K3/6f1fnd6xYSrfjcaCu3qw4OwNxOVRzl9JuB/7ov5sr/ujTan4dXymw8ZtBY0cn0Nx8\no6+aiGhb04RAk8NAkyOL/v66qm2pnIFU3kA8K3F6OoPT02p+Eo9NYH/Ahod7nOV5aWjraUKgzWtB\nm9eCU91qCJjldCmgyWFoSc1Ls9YFzEspA8+OpvDsaAoWDehvsOFw0IYjTTYE3fzaQetnFAwsXV1C\nQ38DhBCwe+1o6G+AxWFB+93KA2ipAAAgAElEQVTt8DR7rr8TItqWYtMxjD03hsXB2kGMxWmBrdUG\nR5cDR+47whCGiIh2HX4z2sMMpxNoa1t3fZnLqd4GpaAmFq1u0I5WNmzHIJLJmz5GISUQjaoyOXHt\n43M4qkOb0rKuTgU2dfXqNoej2nsqh1azWoF77l3f4+57ALKnV53rpfMwFlP3V/bcGhuDSNTuJSaf\neDfwnvepO5cuAp//XPEcregdVjpnDx5Sx0hEtAs4rRp+9x2NmI0XcGUph8GlLK4s5hDNGHhjJoMH\nusz/yeMRNVdJh8/CxpdtpM6h4842HXe2qfcqnTcwspwv96IZCeeRqTEZTd4ALs5ncXE+iy9dAIJu\nHUeCNhxusqEvYINV53tMq+WSOUydnsL0a9PIJrK4/V/dDn+nHwBw+AOH+beBaAeLTcUw+twolq7U\nHhrd3+1H5z2dqOupw9WhqwDA33kiItqVGMjQ+lmtKtCoq7t+XQAyn18d3MSiKxq3o0BEbRdG4fo7\nvQaRTgPpNDA7e+3jcjhWhDR+M6wprfP71KT3tLe9hfMd/+HXIEuBTTQKRCPmsrPTrLe0BDE/B8zP\n1dyN/MM/NgOZz/6ZOp/9deo89deZ52lzMxBsuskXSES0+YQQaPFa0FLsdSGlxHyygCuLuareMd8a\nTOLN2QzqHBqONdtxrJkN99uRw6LhYKMNBxttANwoGBKT0Twuzmdxfj6LkXCuZg+a+UQBzyRSeGYk\nBZsOHGhQ4czhoB0NLr3GI2gvScwnMPnKJObOzan5YAC4gi4YBXPIPDbMEu1M0ckoRp8bRfhquOb2\nun116D7VDX+X/xYfGRER0dZgizNtHotl/Q3ahgGZTJohTWVgU27cLg5zFo2qnjM3SKTTwMyMKmso\nD5VWVw/UB4BAvbodCJjr6urUayQCVDiynoDkxAnI3v0V53QUiC6rZSIOOJxm3YkJiKnJmruR958C\nfvKn1J3ZGeAvPmsGi/X1qtRVnLc6G7uIaHsQQqDJbUHTiiGsGlwafHYNy2lz2Cu7LnAoaMMDXU4c\nDHJos+1I1wS66qzoqrPi0X43ElkDF+ezuDCfwcX5LOLZ1Z/ZsgXg3FwW5+ayAOLo8ltwot2Bu1rt\nVfMP0e4npcSFL12omkMisD+A9pPtqNtXxxCGaAeLTEQw9uwYwsO1g5j6nnp0PdgFfweDGCIi2lvY\nmkzbg6YBHo8quM4waoYBGYuZAU0kAkSWy2ENIsvlbSKXu6HDqRoqbWy0Zh0V2vjMxu/6QPWyoUH1\nZFg5tBXtbTY70NKiyvX8wi9BLofVOb1cOs+L53pXl1lvcRFieGjN3chP/RbQ1q7uPP1dYHrKDGsq\nz1/Ow0REW+j9h7143yEPJiJ5nJ3N4OxcFpPRPF6fyaCn3loOZJbTBWTzEk0efozdjtw2DSfaHTjR\n7oAhJcYieVyYy+D8XBZjkXzNx4xF8hiLxPHlC3EMNFpxot2B25rtcFr5GWq3E0LA1ehCeCiM5mPN\naL+7Ha5G11YfFhHdhMh4BKPPjmJ5ZLnm9vr99eg+1Q1fu+8WHxkREdH2wG+ytPNomppvw+8HOq9R\nT0rIVKrYmL0MLIdVQ3Y4XLFOhTfCMK6xo9pUaFPs5TA6UvsQNF01dgcCQKBBhTT1AbUMNKieNzY2\ngtMaAgFVrqenF/KTv6rO8eVldY6Hw8X7YRW8lJx9E+LC+Zq7kcfvAD728+pOJgN872n1/PXF42DA\nSESbTBNmb4snB4ClZAHn5jI42mT+r3xuNIVvX0miu86CezocuKvNARcb7rclTQjsq7NiX50VTxwA\nohkDF+czuDCn5pZJ5at7z0gAlxZyuLSQg1WL4WizHXe3O3AoaINFY0+J3SI8HIY0JAL71Wecrge6\n0HGyA1YX59Aj2slS4RQGvzm4ZhAT6Aug61QXfG0MYoiIaG9jIEO7lxCAy6VK6zV63RgGZCxqBjSl\nsCa8ZDZqh8MQmcxbPwSjACwuqLIG6fVWhzQNDUBjI9AQVLcdjjUfSwQAcDqBvv711X3XY5DHbiuf\n11Xhjctt1ltcgPiHL1Y9VGqaOQTaR38M6CgmovPzQKGg1ts4pBARbZyAS8fb9lVfLS8AOCwCo8t5\njC7H8Q8X4jjWbMc9HQ4cbLRBZ8P9tuWza7inw4l7OpwoGBIjyzmcmc7g9FQasRVDm+UM4Mx0Bmem\nM3BZBe5oteNEuwO99VZoHMZqR8omshj67hDmzs3B5rbhxP9xAhaHBbpVh27lUHVEO5WUEjNvzODq\nd67CyK2+0LGhvwFdp7rgbfVuwdERERFtPwxkiDRNXfnvrwO616hT6m1TCmlWLdVtkc2+5acXsZia\nCH6todE8HqChUZXGYindb2gwJ4AnWo+Dh1RZyTCAfMUQfzY75CPvUOf40pI6v6NRYGkRWFpU4UzJ\nt/4J4vnnAADS5zPPzYYGoLMLOHFyk18UEe0lTw548M4+N96cyeCliRRCC7lyw/2pLic+cowNPjuB\nrgnsD9iwP2DDjxzyILSQxatTabwxk0W2UB3OJHMSz4+l8fxYGgGnhrva1JBobV5+ldkJSo21w08P\nI5/KQ7NoaLu7DRp7thHteNlEFoPfGMTi4OKqbQ0HGtB9qhueFs8WHBkREdH2xW8xROtR2dumvaN2\nHSkhk0mzAXtpsXq5uKiGR5OrJ7e95lPH40A8vvawaH6/agAPBoHGYHFy+aAqXp86dqLr0bTq4fMa\nG4EPf7SqiszlzPM72GRucLkhG4PAUjG0iUaB4pw28vARM5BJpYBP/VpFuBisWAbV8H46r5Alouuz\n6aI8T0k4VcDLk2m8PJHG7a3m37HBxSymY3nc1eaA28aG3+1M1wQON9lxuMmOTF7i7GwGr06lcXE+\nC2PFx6allIHvXE3iO1eT6PRZ8FCPE3e2OmDV+XlnO0ouJHH5m5cRHY8CUJN49z3WB2e9c4uPjIhu\n1uLgIi7/02XkktXztnrbvOh/vB+eZgYxREREtTCQIdooQgButyoda0xuk89DhsPlXgblwGbRvC3y\ntSe8XfNpIxE1N87Q1VXbpN1eDGkqgppSaBMIsPGb3hqrFWhqVqXSBz6kimFARpbV+by4oJaVc+As\nLZo9wkaGV+1e/sIvAUePqTtn3wSmp8ywJtgIODnJLxGtVu/U8WifG+/aX/034unhJM7OZvHli3Ec\nbVJDmh0Kckiz7c5uMcO2eNbA6ak0Xp3KYDicW1V3PJrHX78Rw1cuJXCqy4FTXU74HPxss11IKXHh\nSxeQXEzC6rJi/zv3I3g4CMGLhYh2tEK2gKv/chUzr89UbxBA94Pd6Lq/C4L/a4mIiNbEQIboVrJY\nzN4rtRgGZDQKLMybDdoLxTloFhbUsFHG6nF51yIyGWByQpUVpKYDDQEVzjQ3mw3tTU1qLhuGNfRW\naZqaD6k+UHtOm9Y2yN/7fXNepYUFNf/Mwry63Vjxe3H6VYgXX6h6uHS7VZ3+A8AHP2xuiMcAt4e9\nwYj2uJWNvHe3O5A3gEvzWbw+k8HrMxl47Rru73TgoX0ueO3sNbPdeWwa3rbPhbftc2EhWcBrk2m8\nOpXGTLxQVS+WMfDNwST++UoSd7Y58HCPE11+Dum6VaSUEEJACIHed/Zi4dICet7eA6uT7wnRThed\niOLSVy8hvZyuWu8MOHHwPQfhbeOwoURERNfDQIZoO9E0oK5OlVoN2oWC6mFT2aBd0bAtopF1P5Uw\nCqoxfH4euHC+apvUddXw3bQyrGlWx6axEYtugKapYcnq62uf35Vuux3S6VLn9oIKbUQiASQSal6l\nkmQS4pOfgHQ6VbjY1FS97OgEHI7NfV1EtC3d0erAHa0OLKcLeGUyjZfG05hNFPDtK0loQuCJA+6t\nPkR6CxpdOh7td+NdfS5MRPN4cTyNlybSVfPNFCTwymQar0ym0VtvxcM9TtzWbGevqFskm8hi6LtD\nsNgt6Hu0DwAQ6A0g0Bu4ziOJaLszCgbGnhvD2AtjwIqhJNvuakPPIz3Qrbygj4iIaD0YyBDtJLpe\nnHOjseZmmcmoxuv5eWB+zux9MD8HLC6pEGYdRKEAzM6ocnbFc1itZq+a5hagpcVcckgp2ih33KVK\niZSQsSgwN1fdeyuyDOl0QqRSwNioKhXkv/1l4MhRdefMaWBiXJ2vpfOXYQ3Rrlfn0PHO/W68o9eF\nq+EcvjecwoPd5vwVZ2czcFsFegO2LTxKWi8hBDr9VnT6rXj3gBsvjqfx/ZEkllLVPYiHwjkMhXOo\nd2p4W7cT93c54eIk8ptm4dICLn/jMvLpPDSrhq5TXbC5+TtFtBskF5K49NVLiM/Eq9bbPDYcePcB\nhq5ERERvEQMZot3EbgfaO1RZqVCAXFpaEdgUy9wcRG712Oy1iFwOmJpUZQXp91eENK1q2dKqekSw\nVw3dDCEAn1+VSq1twKf/GDIRV2HN3BwwN1s+r9HcYtY98xrEyy9VPVz661Q4c2AAePd7zA2GwXOW\naJcRQqAvYENfRfBSMCT+/lwM4bSBnjoLfmi/G8eabdA4BOKO4LJq+KFeFx7e58TZ2Qy+N5LClaXq\nzzPhlIGvXErgm4MJnGx34qF9TrR4+RVoo0gpMfGDCQw/reaGq++pR99jfQxjiHYBKSWmXpvC8FPD\nMPLVoXfjwUb0P9YPq4tDERIREb1V/DZCtFfoujl/zaEV2wwDcnlZNWTPzQFzMxUN2/Oqx8w6iEgE\niESAy6Gq9dJqU43epd40ra2qIb2pWU0UT3QzhAA8XlV6969d7+57IAMNZu+vuTmIyLLqZWO3m/US\nceBXP1ndE6y1TZ237FVDtKvkDeBkhwPPjqYwvJzH/3wtgqBbxyM9LpzscMCmM5jZCXRN4HirA8db\nHZiI5PDMSAqvTaVR2X6YLQDPjaXw3FgKh4I2PNbnRm+An0FuhjQkrnz7CqbPTAMAet7eg457O1bN\n50REO08mlsHlr19GeDhctV636+h7tA9NR5r4u05ERHSDGMgQkeoJEAiocnBFWlPqWTM3a5bZ4nJx\nEULK2vusIHJZNVTUxHjVeqlpqtG7ra3Y4F3R6M2ghjbasdtUKTEMyKVFdT7bKq7kXViAyOeB6SlV\nVpCf+CQwcFDdGRsDshnVE6xybhsi2hHsFoF3D3jwzv1u/GA8haeGk5hPFPB352L4p8tx/NJ99Wjx\n8OPyTtLht+InbrfivQc9eH4shWdHU4hmqq/svjifxcX5LI402fDuATc6fPzMcSNGnx3F9JlpCF3g\n4HsOIngouNWHREQbYOnqEi595RLy6XzVen+XHwM/PACHnxcnERER3Qx+wySia6vsWVOai6Mkm4Wc\nnwNmZoCZabWcnQZmZyEymevuWhiG2VvhzOnyeimEmpS9tSKoaWtjUEMbS9OAxqAqlbr3QX7mT1Qv\nsdnSuT0NTE+rILKpyaz7nW9BvPIyAEB6vSqYKZ2z3d3X7rFDRNuG3SLwUI8Lp7qdeGMmg+8OJZHK\nSTS5zTmrElkDbhuHMtwpvHYNj/W78Y79LpyZyuCZkSTGItWNi+fnsjg/l8VdbXY8ccC9RUe6c7Wf\nbEdkLIKet/fA1+Hb6sMhog0wd2EOoa+GIA3zojuhC/Q83IP2k+3sFUNERLQBGMgQ0Y2z2WrPWSMl\n5HK4GNQUG7SLwYsIh2vvq4KQUvVamJ0FXj9j7lbTVGN4WwfQ3g630JANBjnfB208hwPo6lKlUqFQ\nfa4FmyC7utW5HYsBsRgweBkAIG8/Dnz8F1S9ZBL46j8Cbe0qXGxrB1yuW/RiiGi9dE3gzjYH7mi1\nI5aV5blkIukCfvuZRdzT4cTj/W547fyfs1NYNIG7Oxw40W7HcDiP7w4l8OZstqrOa1MZnJnO4JDP\niZOB9BYd6c6QXEjCUe+ApmuwOq247SduYwMt0S4x88YMLn/jMlAxAIK7yY2D7zkIdxNDayIioo3C\nQIaINp4QQH1AlUOHqzbJdLo4FNS0OSTU1BTE0uL1d2sYZshz+lW0l/b5139ZbOhuB9rbiyFRu5pT\nhGgj6Xr1/fe8TxXDgAyHiz1piuf3vh6z3uQExDNPVT1U1tcDbe1odLoQvuvuW3DwRLReQgj47GYj\n89WlHHIF4NnRFF6ZTOMd+114e4+Lc8zsIEII9Aas6A3UYXQ5h6+H4ri0kCtvNyRwPmLDpagVI4jh\nXX1ueNgjqsrilUVc/PJFNB1pQv/j/RBCMIwh2iUmX5nE1e9crVoXPBLEwJMD0Cz8W0hERLSRGMgQ\n0a3lcAA9vapUkOl0dWN2MawRCwvX3aXIZIDhIVUq9+nzmwFNRyfQ2Qm0tAA6//TRBtM0oKFBlZVD\n+wFAQwPk+z8ETE2qMj2leouFwwgA1YHMF78ALMyrc7ajE+joABoaVdBJRFvizjYHWrwWfOViHBfm\ns/h6KIHnRlN48oAbJzsc5Z40tDN011nx8/fU4/JCFl8LxTGybA5lVpACTw+n8MJYGo/0OvH2Hhec\nVjZGTr02hSv/fAWQgJEz1BX0PO2JdoWxF8Yw8sxI1bqW4y3of6wfQuMvOhER0UZjqyQRbQ8Oh+pR\nUNmrAIDMZMygZrLYmD05CbG8jqHPohEgGgEuXjD3Z7GoIaM6ulRAU2rwdnL4KNpEgQbgXY+a9w0D\ncn4emJrEwvlzKLgrhoG4cB5iarJ6uD6HU52n99wLPPjQLTxwIipp81rw8ZN1CC1k8Y8X45iI5vH5\nN2MYWc7ho8c4f8ZOdKDRhn/XUI9zc1l8PRTHVKxQ3pYpSHxzMInvj6Twzj43Hux27skeUdKQGHpq\nCJMvTwIAuh7oQvfbutkzhmgXkFJi5HsjGH9hvGp9+93t6H1HL3/PiYiINgkDGSLa3ux2oHufKhVk\nIo6Jl16CfWEewVy2HNaI9LXHfhf5PDA2pkrl/hqDZkBTWtYH2CuBNoemAc3NQHMzwiuH1vuZn4Wc\nGAcmJoCJcWBiXM1Pc2UQ8sCAWe/qFeCv/hxoL4aKpR419fU8b4k20UCjDf/nqXq8NpnB1y/H8UCX\ns7ytYEjovJp4RxFC4FizHUeabPjG6VH8YNGOSM4cnjKRk/jHi3E8M5zEY/1u3Nvh2DPvcSFXwKWv\nXMLi5UUITaD/iX603Nay1YdFRBtASomhfxnC5CuTVesZuhIREW0+BjJEtDO5PUh1diHV2YVgf79a\nJyXk4iIwNaECmslJYHJCTbhuGNfcnViYV8NEnTldXiddLqCzC+jqBrq71TLYxMZu2lztHarcY66S\nkYg6lwMBc+X4GMTsLDA7C5x+1azr8ahz9ec+rnqeEdGG04SaKP7ONntV4/yfvRaB26rh3QNu1Dv1\na+yBthtNCAz4cujz5rBg78C3BhOIZMzPDstpA397NoZnhpP46DEv9gdsW3i0t8bos6NYvLwI3a7j\n8AcOo35f/VYfEhFtAGlIDH5rEDOvz1St73l7Dzrv69yioyIiIto7GMgQ0e4hBNDYqMptx831uRzk\n9BQwPg5MjBWX49fvTZNMAqFLqhRJp7N2SKNxfHnaRH6/KpUeeBCyt0/1opms6E0Tj0OOjqreZSV/\n8F/U70fp3O3qAppbAJ0NxkQ3ozKMmU/kcWk+i4IEzkyn8XCPC+/cz/lHdhpdAKe6nTjZ4cCzIyn8\n89UEkjlZ3j4TL+AzLy7jvk4H3nfIA9cufn+7HuhCaimFfQ/tgzvovv4DiGjbMwoGQl8LYf7CfNX6\nvnf1oe1E2xYdFRER0d7CQIaIdj+rtdgI3W2uMwzVm6YioMH4OER46Zq7EqkUcDmkSpF0ONUwZ93d\nQNc+9TxNDGlok1mtKljp6jLXSQm5tASEl8yeXLkcMHRV9RIbvGxWtdrUUGePPg4cv+MWHzzR7hN0\nW/B/PdyAr12K4/R0Bt+5msSL4yk81ufGqW7nnhnmarew6QI/tN+F+7sceGo4iaeHUsgUzGDmxfE0\nzs1m8P7DXtzVZt81w/tEp6LwNHmgWTRY7BYc+eCRrT4kItogRt7AxX+8iMXLi+ZKARx48gCHIyQi\nIrqFGMgQ0d6kaUAwqModd5VXy3i83NMA42PA6Kga8kzKNXcl0inV0F3Z2O1wqHlv9u0D9vUA3T2c\n24M2nxBAQ4MqJVYr8Hv/FXJsTJ3T42oOJbG4AAwPQRbMSazxwnPAs99X521p7qbmFoaLROvU6NLx\n03f68fblHP7xYhxXl3L44oU4XplK4xP31TOU2YGcVg1PHvDgwW4XvnwhhlenMuVtsazEX74excuT\nNnz4qBeNrp3d6zAyEcGbn38TwYNBDLxnYNeETESk5oQ6/8XzWB5eLq8TmsDB9x5E8FBwC4+MiIho\n72EgQ0RUyeMBDh5SpSSdVpOsj42aZXr6OiFNevVwZz6/CmfKIc0+wM0hQOgW8NcBx+qAY7eVV8lE\nXPUO66gYK/zKFYjhIWB4yKzncKheXwMHgSd/+FYeNdGOta/Oil+6tw5nZ7P40oUYDjTYGMbscD67\nhn99hx8nOzL4u7MxLKbM+WUuzmfxu99bxOMH3Hikx7Uj3+vUUgoX/v4CZEFC28XDsBHtRflMHue+\ncA7R8Wh5ndAFDr//MBr6G67xSCIiItoMDGSIiK7H4QD6+lUpyWTMkGa0FNJMXTukiUaAN19XpUg2\nNxdDmmLp6FQ9Gog2m9tTHTwCwAc+BHn3SWB0BBgZBkZHIMJh4HIIUggzkMnngf/3T9WcNPv2Aft6\nAZ/vVr8Com1NCIHbWuwYaLRCq+hpcGkhC4cusK+ef+t3okNBO37tIRu+OZjAU0NJGMV/+zkD+Oql\nBF6dTOOjx3zo2UHvby6Zw7kvnEMulUP9/nr0P9bP3jFEu0QumcPZvzuL+HS8vE6zajjywSOo76nf\nwiMjIiLauxjIEBHdCLsd2N+nSkk2AzkxocKZkRHVoH294c5mZ4HZWeClHwAApK6rUKZ3v1kCAQ51\nRreG2w0cOqxKkYxEVEBjqfjIMDkBcfZN4OybZr3GINDTA/T0AidOMqAhKrJbzN4GyZyBz70eRSxj\n4O09Tjw54IFN59/3ncamC7z3oAcn2hz427NRjCzny9umYgX84QthPNDlxHsOuuHc5r1NjLyB8188\nj9RSCu5mNw697xDEDuzhQ0SrZeNZvPm/3kRyPllep9t1HP3IUfg7/Ft4ZERERHsbAxkioo1is5sh\nSkkqCTk6Wu5tgJFh1eNgDaJQUPVGR4CnvwsAkH6/2mfPfqC3Vw11xl40dKv4/cBtt1evCzZB/uzH\nzJ40I8MQC/PAwjzwysuQh4+agcyZ14BCQZ2/DBdpj7NoAifbHfjuUBJPDadwdjaLH7vNi74G21Yf\nGt2Adp8Fn7i/Hs+NpvC1UALpvLoAQwJ4biyFN2cz+OARD4632LdljxMpJUJfCyE6EYXNa8PRDx+F\nxc6vh0S7QS6Zwxt//QZSS6nyOovTgmM/egzeFu8WHhkRERHxEzcR0WZyulbNSSOXl8uN2OVhoVKp\nNXchIhHgzGlVUOxF09lVDH961bKeDd10C7lcwF0nVAGAQgFyegoYGgLGx4CmJrPut74JMToCoDiP\nUk+v2ZNmX4/qbUa0R9h0gfce8uB4qx2ffzOK6VgBf/SDZTzYrXpTOCzbuzcFraYJgbftc+H2Fju+\neD6O12cy5W3RjIHPno7iSJMNHz7iRcClb+GRrmbkDGQTWeg2dcW83cu/x0S7gTQkLn7lYlUYY/PY\ncOxHj8Ed5PyVREREW42BDBHRrVZXBxy/QxUAMAzIuTkVzgwPAcNXgYkJCMOo+XBRKJhhzlNqnfTX\nAfv3A/v7gb4+NeyZvr0afmgXKw2119G5etsdd0J6PKoXTTQCvHFGFQDy4UeAj/6YqpdKApms+v0g\n2uW666z496cC+OcrCXz7ShLPjqYwHcvjl+7jeP47ld+h42fu8uPcbAZfOB9DOGX+Dz8/l8V/XlzC\nh496cE+HcwuPsppu03Hso8eQXEzC0+TZ6sMhog0y8r0RLA8vl+/bvDbc/uO3wxnYPn9/iIiI9jIG\nMkREW03TgJYWVe69T63LZCBHR4Chq6rXwfBViFhszV2IyDJw+jVVAEh7cfi0vn41z01PL3si0NZ4\n7AlVpFTB4/CQKkNXgf4DZr0zpyH+6i8gGxqL4WJxjqa2dvU7QrTLWDSBJw54cHuLA3/zZhSP9vGq\n5d3gaLMd/Q1W/NPlBJ4ZTqE0i1y2IPHXb8QQWsjhI0c9VXML3WrxuTjcjW4ITUCzaPA0M4wh2i3m\nL85j/MXx8n3NouHoh44yjCEiItpGGMgQEW1HdjtwYEAVQDVmL8ybAc3QVTWx+lq9aDIZ4OIFVQBI\nTQe6ulTvmf3FkIaTrtOtJATQ3KxKKXislExCOhwQiwvA4gLw8ksAAOlwAgMHgY/9Gw7LR7tSu8+C\nX3mgHlrF+f2twQTavBbc1sIgfSeyWzS8/7AXd7c78L/OxjAeyZe3vTKZxuhyDj99hw8d/ls/H1x8\nNo43PvcGfB0+HP7AYehW9qYl2i0ScwmEvh6qWtf/RD88LQxdiYiIthMGMkREO4EQQLBJlXsqetGU\nhjkbugpcvQKRSNR+uFExzNm/fAcAIJubiz1o+lVPhcZGNnjT1nnHu4BH3gE5OQFcvQJcLZ7TS4uQ\nibh5bhoG8Jn/BnR1q/O2rw9ws6GBdrbKMGY8ksM3LicgAdzd7sBHjnpht/Bv807U6bfiV+6vx7eu\nJPDtwWS5t8xcooD/9kIYP3LIgwe7nRC36H9vJprBuS+cQyFbgMVhgcY5i4h2jVwqh/NfOg8jZ16s\n1X53O5qPNm/hUREREVEtDGSIiHYqu131HBg4qO4bBuTMDHB1ELhyBbg6CLGwsObDxewsMDsLPP8c\nAEDWB4ADB1SvnP4DKvxhQEO3kqYBnV2qPPwIAECGl4Bk0qwzMQ5xOQRcDgH/8s+QQqhhzfoPqHL4\nCODksBy0c7X7LHj/YQ++Forjlck0xiM5/MxdfrR4+LF9J9I1gScPeNAXsOGvXo8imlGNpXkD+Pvz\ncVxezOHHbvPCZd3ccDrB5PEAACAASURBVCSfyePcF84hG8vC1+nDwLsHblkQRESbSxoSl756Celw\nurzO3+VHzyM9W3hUREREtBZ+syMi2i00DWhrU+XBhwAAMhyuCmgwMQEhZc2Hi/AS8NIPVAEg/XXF\nYdOKIU1TMwMauvXqA6qUtLRA/uIngCuDKpQZGYaYnAAmJ4BnnoL89d8E2jtU3bExwOMGAg1bcuhE\nN0ITAg/3uDDQaMNnT0cwEy/g958L48du8+KuNsdWHx7doIFGG/7DgwF87o0oLs5ny+vfmMlgPJLD\nT93hR0/95gxhZhQMXPzyRSTmEnAGnDjygSPsHUO0i4w+O4rw1XD5vt1nx6EfOQRN5+85ERHRdsRA\nhohoN6uvB06cVAUAUknIoSHVmH1lUDVm53I1Hyoiy8ArL6kCQPr81T1oWloZ0NCtZ7OrXjCHj6j7\nuZwaum/wMjA6ArS2mXX/9vMQQ1chAw3qnD1wADhwkMPz0Y7Q6rXgkw/U42/OxnB6KoO/OBNFKidx\nqps9wHYqr13Dx+7246mhJL4WSsAoXh+xlDLwmRfD+OEBNx7pdVUNYXezpJS48u0rCA+FYXVacfQj\nR2F13fq5a4hocyyEFjD2/Fj5vtAFDn/gMGxu2xYeFREREV3LhgQyAwMDAQC/AeB9AFoBLAD4BoBf\nD4VC0+t4/E8A+BiA2wHYAIwB+DqA3wmFQosbcYxERATA6QKOHFUFAPJ5yNER1dNg8DL+f/buOz6u\nu8r7+OfOqLdRdbeaLY/kLlvuJc2kh/RCIAEWCCXwbCCBhW08sJuFB1jYXfrSQkshJKSTkOpuy7Ll\nKmskW9WSbEu2ep+Z3/PHlVVsucWyRuX7fr3uS7l37p05iq+kmXvuOYdDxVhdXYMeajU1Qt4OewFM\ndLSdnMnMspfEJF3kluEXHNzXrqw/Y8DlwoSHY508Adu32gtg4uPhpg/CqtUBCFjkwoUGOfjYwhhm\nxLXzTkkbCyaFBjokuUQOy2LdjEhmxIfwRH4jJ9vtFmZ+Ay8WtlJ0opsHFsQQHTo0d7Ybn6GzqRNH\nkIM5d88hPE4JPZGxoq2uDc/LngHbMm7IIHpydIAiEhERkQtxyQkZt9sdDrwHZAI/AvKADOAx4Gq3\n273Y4/HUn+P4/wC+BuQC/wi0ACuBLwA39xzfdKlxiojIIIKCYMZMe7nhJvB5MeXldnKmyGMnaDo7\nBz3Uam6GnXn2Qs9F7swscGdBZia4YofzOxEZyLLg05+zZytVV9nnc0/i0Tp5EhPk7Nt3/z7Yk29X\nz7jdEOMKXNwip7Esi7WpEayYHk6w0056+/yG8gYv6fGqdBit0uKC+Yc18Ty5t5k9R/v+zh6s7eLb\nG0/y4MIY3ImXfof7qURM67FWoqfoIq3IWOHt8HLgzwfwdfl6t01ZPIVJ8ycFMCoRERG5EENRIfMI\nMA942OPx/OTURrfbvQf4C/AvwJcGO7CnsubLQBmw1uPxnPo08hu3210HfBX4OPDfQxCniIicjzMI\n0mfYy3U3gM+HqehJ0BQXQXExVkf7oIdaJ0/Cls32AphJk3sSNJl2JU1k5HB+JyI2hwOmTbeXq9fZ\nCZqqI5CQ2LfPnnysjRtg4wYAzOQp9nnrdkOGG6KiAhS8SJ9TyRiAV4paeftwG9dlRHBDRuSQtriS\n4RMR7OATi2LYWN7OXw624LWLZWjq9PPj7Q1cNzOC6zMicTou/t+3ra6NsLgwHE4HDqdDyRiRMcQY\ng+dlD+0n+96Tx0yPIX1degCjEhERkQs1FAmZB4FW4FenbX8ROAJ8xO12P+rxeAabIp3cE0Nuv2TM\nKRuwEzKpQxCjiIi8H04npKXby7XX2xezKyvs5Iyn0K426OgY9FDraA0crbEHrVsWJKfYF7kzs+yK\nnFC13pEAcDhgevLAbVdchUlM6jmni7FqqqGm2j53U9Pgq/9k72cMdHfZc2xEAiisJznzenEbZfXd\nPLjQNWQtrmR4naqASo8L5jf5TRxvte92N8Drh9ooPtnNx7JjiA1znvuJ+mmvb2f373cTmRTJnLvn\nEBSqsaEiY0nFpgpOFPd1dg+JCmH27bNxOPV3QEREZDS4pHfnbrc7BrtV2cbTEyoej8e43e5c4A4g\nDSgZ5ClKgU7sFmenS+35uv9SYhQRkSHkcEBKqr2su9auoCkvg8KD9sXsw4ewvN4zDrOMsQeul5fB\n317HnGqVNnsOZM2BadPs5xYJhFMVNNfdYM9VKiu1z2dP4cDZNDU18B/ftM/drNn2Mj1Z564Mu+sy\nIkmJC+a3+Y0U1nXznU0n+Xi2Sy3MRrFprmC+sjqOZ/a3sKOq70aHwye7+e6mej69xEWy6/z/vsZv\n3znvbffiDHbiDL7wRI6IjHwnik9QvrG8d91yWsy+czYhUZfe4lBERESGh2XMYIUrF8btds8D9gJP\neTye+wd5/AfYLc0+4PF43jrLc/wT8O/Y82f+C2gGlgI/A2qBFR6PZ/Dbr8+isbFx0G+quLj4Yp5G\nREQuktXdTVh1FREV5URUlhN29KidjDkPb3gEbSmptKWm0pqSii9KrVVk5Ik+eIBJr71C/+ZBvrAw\n2pJTaEtJpWn2XDvZKDJMWrot/loTQU1HEA4Mq5I6WBjbhTqYjW4HG4N593g4XtP3DxlkGa6b3MaM\nqDNveuivxdNC895mHGEOkq5LwhGihLHIWOFt9lL3Vh3G2/fe2rXYRUR6RACjEhERGV8yMgarKwGX\ny3XBn8Iu9arBqStmbWd5vPW0/c7g8Xged7vdx4AfAp/v99ArwIMXm4wREZHAMcHBtKek0p6SygnA\n0dlJeGVFb4ImtK5u0OOC2tuIKSwgprAAgM7ERFpT0mhLTaV96nRMsO76lsBrzppDa2q6fT6XlxFZ\nXkZwUyPRRR4iykppnDOvd9/wI5V0JibhDwsLYMQy1kUFG+6Y3sqWujDy60Mpbw1iQWwXyseMblmu\nbiaG+3itOoKTXXaFi9dYvFodweqkDrLPknTrbuqmeX8zAK4cl5IxImOIv9tP/eb6AcmYiPQIJWNE\nRERGoYDfxul2uz8L/A/wN+Ap7KqYZcBXgNfcbvcNHo+nYShe62wZrPHoVLWQ/p/IaKbzeJSYO7f3\nP01To90G6mABFBRgNdQPekhoXR2hdXXE79xhVxzMzLDbm82eA1OnMZZu/9Z5PArNn29/NQZTexwO\nFuBobycjM9Pe3t0N//N98HohNc0+b+fOs1v9jdH2ZjqPAytzFuw92kl6fDBRugj/vo2083jeLD+/\n2WW3pbNZbKoNx4THcfecaJyOvr+Ffp+f3b/bDX6YtGASs9bOGvxJZcwbaeexXDpjDAXPFeBt7quQ\ni5kaw/y75uMIGpu/83Uey1ig81jGAp3Hl8elJmSaer5GnuXxqNP2G8DtdruxkzFvezyem/o99Ibb\n7d4DvAD8I3ZyRkRERrsYFyxZZi/GYGpq4OABKDgARUVY3V1nHGJ5vfaMmsKD8PyfMS4XzJkLc+bZ\nMzwidGegBIhlwYSJ9tJfU5OdiCk5jFVaAqUl8OrLmMhIe2bSzbfApMmBiVnGrPmTQnv/2+c3/GFP\nE1ekRZAaqwrD0Soi2MFnlsTy7IFmNlf0NQ3YXNHBiTY/f7cohvBg+2LssX3HaKlpITQmlPR16YEK\nWUQug8otlZwoOtG7HhIZQtYdWWM2GSMiIjLWXWpCphQwwLSzPJ7S8/Vsw1uu7onh+UEe+2vPc191\nKQGKiMgIZVkwZYq9XPMB6O7GHD7Uk6ApwKqsGPywxkbYshm2bMY4HJA+w64+mDPXHsw+hqpnZJRK\nSIBHvwIdHZgiDxzYDwf2Y9XVQl4u5tbb+/bdtxdCQ2HGDHAGvHBZxogN5e3kVXey52gnH1/kYt7E\n0PMfJCOS02Fx79xokiKCeLGwhVPNigrruvjBlno+vSSWhAgnk+ZPwtfpI3JiJEGh+l0iMlbUl9ZT\ntr6sd91yWGTdkUVotH6vi4iIjFaX9G7d4/G0ut3uvcAit9sd1n/ei9vtdgIrgUqPxzP4VbW+yprB\nGqyHAtZZHhMRkbEmOBgys+zldjBNTXZVTMEBOHjATsScxvL74VCxvbzwPMYV21M9Mxdmz4ZwVc9I\nAIWFwfwF9gKY48fsczUpqW+fvzyHVV2FCQsDd1bf+ZuQEKCgZSxYmxJOdZOXbUc6+EVeI/fMjWZ1\nSnigw5L3ybIsrpkRQWKkk9/mN9Ltt7fXtPj4z80neSgnltS4YKYtO9s9ciIyGvm6fBS9WjRg24xr\nZ+Ca7gpQRCIiIjIUhuL2qV9htx37NPDf/bZ/BJgAfP3UBrfbnQl0ejye0p5NW3q+3ut2u3/o8XhM\nv+PvPm0fEREZT2JiYOkyezEGU10FBw7AgX1wqBjL5zvjEKuxAbZsgi2bMA6nXXUwZ65dQTPGZs/I\nKHR6ezO/H2bPxhiDVVMNe/LtBTCTJsEtt8HinAAFK6OZ02Fx//xo4sId/LW4jWf2N1Pf7uNmdySW\nfg+OWgsmhfLIijh+ntdIU6edlWnuMvz3tnoeXBhD9mTdxyYylpStL6OzqbN3feL8iUzOVstTERGR\n0W4oEjI/Az4MfM/tdqcAecAc4EvAPuB7/fY9CHiATACPx7PF7XY/i5182eR2u/8E1AJLgIeBY8Dj\nQxCjiIiMZpZlJ1SmToNrr7NbQRUetJMz+/dh1defeYjfB8VF9vLC85jYOJg3365WcGdCSEgAvhGR\nfhwOuOteuAvMyRN2wrFgPxw8iHX0KCa439u0Ig+cqLNnJ8XEBC5mGTUsy+LGWVHEhTl5en8zfzvc\nRn2Hn/vnRxPkUFJmtEqODebRVXH8fEcD1c32jQleP/x6VxMfzPSxLj1CSTeRMaCpuomqHVW96yFR\nIcxYN0M/3yIiImPAJSdkPB5Pt9vtvhb4v8CdwOeB48Avga97PJ628zzFh4ANwMewky8hQDXwa+Df\nPB5P1dkPFRGRcSksDBZm24sxmOrq3uQMhw7ZyZjTWA31sHE9bFyPCQ6BrCyYt8BO0sTGBuCbEOkn\nPgHWrLUXnxdz+DCkpvY9vv5drJ15GMuC1DT7vJ07H6ZrbpKc24rkcGLCHPx6VxOtXX50tox+8eFO\n/s+SGH74ajVV4X2t6F4qbKW21cc9c5V0ExnN/D4/xa8NHMM787qZBIVpPpSIiMhYMCR/0T0eTxN2\nRcyXzrPfGZ8MPB6PD/hRzyIiInJxLAumTrWXa6+H9na7emb/PnuQesMg1TPdXbB3j70AJjnFrpyZ\nNx+SU3SBWwLLGQSz3AO3zZ6LaW+HIg9WaQmUlsBLL9iVX9esgw9cF5hYZVSYMyGUL62MIzHCgVMX\n6seEmo3lLC+qZv+MqXiionu3b63s4ESbj08sdhER7AhghCLyfh3ZfoTW46296wmzEkh0JwYwIhER\nERlKusVCRETGlvBwyF5kL6dmz+zbay8lh7GMOeMQq6IcKsrhlZcwrtie1mbzITMLQkID8E2InGbV\nans51a5v/z7YtxeroR7Tf57S0RooPAjzF0J8fODilRFnakzf2/5un+HJvU1cOzOSydH6ODDaNJQ1\nUJ1XjdNh8eDaJHZ1BPF8QQun/roVnejm+5vr+czSWBIjnAGNVUQuTvvJdio2VfSuO0OdzLxuZgAj\nEhERkaGmT2AiIjJ29Z89c/2N0NKM2b/frowpOIDV0X7mIY0NsGkDbNqACQ62kzILFtoVNDGuAHwT\nIv2c3q6vsnLgTJm8HVivvARPP4mZnmyfuwsWwjS1NpM+b5W0kVfdyYHjXXwqx0VGgmZqjRbeTi+e\nVz0AJK9KJmZyDFcCCRFOnshvostnp2WOtfr4z80neXhZLNNiggMXsIhcMGMMxa8X4/f6e7elXZlG\naLRuDhIRERlLlJAREZHxIyoalq+wF68Xc6jYTs7s24NVW3vG7lZ3d291jbEsSEu3L4QvyIaJEwPw\nDYj0Y1mQnDxwW2oaJnuRnXCsrIDKCrvyKz4elq+ED94WmFhlRLkmPYIjjV72HuvkJ7kNfGRBDIun\nhAU6LLkAjeWNdDZ1EjUpiukrp/dunzcxlEdWxPLzHY00dtoXc1u6DD/c1sDDS2NJjlVSRmSkO7bv\nGA1lDb3rMdNimLxocgAjEhERkctBCRkRERmfgoLs6pfMLLj7XszRGjv5sncPHD50RmszyxgoOWwv\nz/8ZM3mKXXmwMNueO+NQr34ZAebOs5fubru12d7dsGcP1smTmBMn+vbr6IB9e2DOPIiICFy8EhAh\nTotPLI7h+YIW1pe180R+Ew3tfq5OD8dSJdWIljArgeyPZuMMceJwDvy7M90VzGOr4/j5jkaONHkB\naOs2/HB7A59dEkt6vJIyIiNVV2sXJW+X9K5bDouMGzL0O1lERGQMUkJGRETEsmDyFHu59npobbFb\nm+3bA/v3D97arKYaaqrh9dfsweqnWkPNctvJHpFACg62ZyHNmw8f8mPKyyCkX1uqA/uxfvULjMMJ\ns2b1nb/xCQELWYaXw7K4c3YUceFOXjjYwguFLdR3+LhjdhQOXQAc0aKnRJ/1sdgwJ19YHstPcxso\na7CTMh1ew49zG/jMErWnExmpDr91GG+7t3d9+orpRCZFBjAiERERuVx0xUhEROR0kVGwbLm9eL2Y\nIg/szoc9+ViNjWfsbjXUw/p3Yf27mPBwmDvfvrg9d54980MkkBwOu91ef2FhmIxZcKgYq/AgFB6E\nZ57CJKdA9iK47gZVfY0DlmVxTXoEsWEO/rCnicYO//kPkoA4/OZhYlNiSZh1/qRpRLCDh5fF8rMd\njRw+2Q1Al8/w09wGHsqJJTNJSRmRkeTk4ZPUHuhrnRseH07yquRzHCEiIiKjmRIyIiIi5xIUBLPn\n2Mt999uVBnt2w+58rKM1Z+xutbfDju2wYzsmKAhmz4VFi2DeAojUnY4yQsyZay8tLZj9++xzumA/\nVkU5BgM33NS375FKmDrNriSTMWnxlDASIpxMiQ5SdcwIVFtYS9WOKmp217D0c0sJiTx/QiUsyMFn\nl8Tyv3kNFJ2wkzLdfvh5XgOfWORi7kQNCRcZCXxdPopfLx6wLePGDBxBuilCRERkrFJCRkRE5EKd\nqjRIS4fb7sAcO9qbnKG05My5M16vPcNj7267NVRmJmQvtufORJ+95YzIsImKguUr7KWrC3OwAPpf\nj6+pxvr3b2DiE+zKmexFkD5D1TNjUGq/oe9dPsN7pW1ckx6B06EETSB1tXZx6K+HAEi/Kv2CkjGn\nhAZZfHpJLL/a2UhBbRcAXj/8cmcjH8uOYeFkVXCKBFrZhjI6Gzt71yctnERscmwAIxIREZHLTQkZ\nERGR92viJHvmzLXXQ2MjZu8e2JMPhQftZEw/lt8HBQeg4ADmyd9DxizIXkyQKxavkjMyEoSE2K32\n+jtxAhPjwjp5At5+E95+ExMdbScVFy6CzCxwOgMTr1w2v81vYu+xTqqavDy4MEZJmQAxxlD812K6\n27uJTY1l8uLJF/0cIU6LTy528Zv8RvYds5MyPgO/yW/iQWNXR4lIYDTXNFO1o6p3PSQyhPSr089x\nhIiIiIwFSsiIiIgMBZcL1qy1l44Ouw1U/k7Yvw+rs3PArpYxUOSBIg/pQPvkKbBylV09k5gYmPhF\nBjN3Hnz7u5jSEsjfBbt3YdXVwcYNmB258N0f9CVk/Jo/MlasmxFB0YkudtV0Ymjio0rKBMTxA8c5\nUXQCZ4iTWTfNwnqf7eSCnRafWOTit7ubyK+x/x75jZ148/oNy6aFD2XYInIBjN9Q/Fox9CuunnHt\nDILCdIlGRERkrNNfexERkaEWFgY5S+ylqwtTcMBOzuzdY8+YOU14TTU89yw89ywmORkW5cCixTBh\nYgCCFzmNwwEzZtrLnXdjjlTabfp8Pgi221xZ3d2k/ep/YfZs+/ydM9euuJFRKS0umM8tjeUnuQ09\nF/CVlBlu3g4vJW+VADDjAzMIc11aJYvTYfHRhTEEOZrZUdUB2NeB/7CnGa8fViUrKSMynI7kHqHl\nWEvvenxGPImZuilHRERkPFBCRkRE5HIKCelp75QNXi+m8CDs2gl7dmO1tpyxu1VRARUV8MLzdnJm\n8RL7AndSUgCCFzmNZcH0ZHvpJ7zqCEGtLbAjF3bkYkJDYd4CWLwY5sxTcmYUSosL5uGlsfy4Jylj\nTBMfy1ZSZrh0NHTgCHIQMy2GifOHJjnvdFh8ZEE0QQ7YWtnRu/3pfc10+wxXpkUMyeuIyLm117dT\nvqG8d90Z4mTmdTPfdxWciIiIjC5KyIiIiAyXoCC7BdTceeDzYYqLaHz3HaIOFRHU2nrG7r3Jmb88\nh0lJtZMzi3MgIWH4Yxc5h7bUNEo/8WlST9bBzjysinLIy4W8nuTMv/0HxLgCHaZcpNR+SZndRztZ\nX9bO1em6aD8coiZFkfPpHLrbu4f0Iq3DsrhvXjTBDosN5X0Vm88VtOD1G9bNiByy1xKRMxljKH69\nGL+3r81n6hWphMVonpOIiMh4oYSMiIhIIDidkJnFcWcQx69eR4bTYVfO5O/Cqj95xu5WeRmUl8Hz\nz2LS0u3EzKIciI8f9tBFBtMdGwtLlsB1N2Bqa2FXnn1O+3wDkzHPPQtp6TB3LoSEBi5guSCpccE8\nvCyWjeXtXJGqtlbDyRnsxBnsHPLndVgWd82JIsgB75T2JWVeLGzF64frZkboTn2Ry+T4geM0lDb0\nrkdPiWbK4ikBjEhERESGmxIyIiIigeZwwMwMe7nrHkxZKeTtgF07sRrqz9jdKi2B0hL4858w6TN6\n2pothri4AAQvMoikJLjuBnvp7OzbfuwY1ptvAPS0NZsPOUvtmTM982hk5EmNDSY1tu/fp8tncFqo\nfdll0FjZyImiEySvSr6sw70ty+K2rCiCnRZvHGrr3f5qUSvdPsPN7kglZUSGWHdbNyVvlvSuWw6L\nWTfOwtLvUhERkXFFCRkREZGRxOGA9Bn2ctc9mJLDsDMPduVhNTaesbtVchhKDmP+/Iw9dD2nZ+ZM\nTEwAghcZRGi/KpjICMwdd9vn86nEY94OTFi4PWfp9jvBpdZmI1mXz/CzHQ2EBzn4+KIYgnQhccgY\nYyh5q4TmmmacoU5SVqdc1tezLIub3VEEOSxeLeprm/m3w3aC5pbMqMv6+iLjzeG3DtPd3t27Pm35\nNCInqE2giIjIeKOEjIiIyEjVv3Lm7nsxhw/ZF7Dzd2I1NQ3Y1TIGDhXDoWLMn56GzCy78iA7G8I1\n80FGiKhouPY6uPY6TF2d3dZsRy5WZQUmfyfc/+G+fY8ehQkT7J8DGTHq2nwcafTS7jX8ZlcjH1/k\nUlJmiBw/cJzmmmZCokKYtnTasL3u9RmRBDssXihs6d32t8NtRAQ7uGaG/n6IDIX60nqO7z/eux4W\nF0byquQARiQiIiKBooSMiIjIaOBwQMYse7n3Q5jiIrtyJn8nVnPzgF0tvx8KDkDBAcyTv+9rCzVv\nPoSEBOgbEDlNYiJcez1cez3m6FGoruqbKdPdDd9+HEJD7JZ8OUvsuTNqoRRwU6KD+PzyWH60rYG9\nx7r49a5G/k5JmUvm6/ZR+m4pYA/4doYM/eyYc7lmRgRBDvhzQV9S5oXCFsKDLVYma3aQyKXwe/0U\nv148YNusG2ZdlhlRIiIiMvIpISMiIjLaOBzgzrSX3uTMDti1C6u1ZcCultcL+bsgfxcmLAwWZMOS\npZCVBU69DZARYtIkezmlrhaiIrHq6uCdt+CdtzAJiZCTYycXp01XciaAkl3BfGF5LD/a3sA+JWWG\nRFVuFV3NXUROjGTivIkBieGKtAg6fYaXPX3ty57e10x4sEX25LCAxCQyFtTk19BR39G7PnHBRGJT\nYwMYkYiIiASSrsSIiIiMZk6n3Z4sMwvuux9TUAB5ubA7H6v/MHXA6uiA7Vth+1ZMVBQsWgxLltmz\nZ9QWSkaSyVPg376F6TdnxjpRB2+8Dm+8jvm//waTJgc6ynFtuiuYzy8bmJT5xCIXTiVlLlpnSycV\nWyoAmHHNjIAO+P7AjAjaug1vl9hzZAzw2/wmwoIsspJCz32wiJzB2+mlYlNF77oz1En6VekBjEhE\nREQCTQkZERGRscIZZLclmzcfujoxe/fCjlw4sM+ulOnHammBDethw3pMXJxddbBsuV15IDISWJbd\npiwtHe68G3Oo2E42Hjs2MBnzh9/B1Gl2W7Po6MDFOw71T8pYWPgNqAHPxas7WIe/20/CrISA3zVv\nWRa3ZkbS1u1na6V9R7/PwC93NvLw0jjS44MDGp/IaHNk+xG627t716evmE5whH6ORERExjMlZERE\nRMaikFD7AnXOEmhrw+zeZSdnCg9iGTNgV6u+Ht58A958AzN1KixdDkuXQVx8gIIXOY3DAbPc9tLf\nsWNYmzYAYJ59GrJm2+fvgoUQphZLw2G6K5hHV8WRGOHEoTZy78vUJVOJSIwgzDUyzlnLsrhvXjQd\nXkN+jV1p2eWDn+1o4O9XxDE1Rh8hRS5EV0sXR7Yf6V0PiQph6pKpAYxIRERERgK9mxYRERnrIiJg\n5Wp7aWrE7MyDHblYJYfP2NWqqoK/PId54Xn74vfS5bBoEYRHBCBwkfOIi8V84lOQux0OHMA6sB8O\n7MeEhNjzku64C+LiAh3lmDchsu8jRZfPcLC2iwWT1N7qYsSljazz1GFZPLAghvbuRgrrugBo9xp+\nnNvAF1fEkhSpj5Ei51O+qRx/t793PWVNCs5g1RGKiIiMd3onLSIiMp7EuOCqa+CqazB1dXYLqNzt\nWNVVA3azjAFPIXgKMU/9AeYvtFuazZkLQXr7ICNESKg9B2nJMmhpxuTlQe42rJLDmD358OEH+vat\nq4WERLsVmlwWPr/hx9sbKKnv5oEF0SydFh7okEa0xspGHEEOoiePzFZ7wU6LTy528ePt9ZQ22G0v\nmzv9/Gh7A19cGUdsmC4si5xN+8l2ju4+2rseHh/OpAWTAhiRiIiIjBS6oiIiIjJeJSbC9TfC9Tdi\njlTC9m12cqax3Z9JLQAAIABJREFUYcBultcLu/JgVx4mMhIWL7GTM+kzdHFbRo6oaLjyKrjyKkxd\nLVRW9rUt6+6G//g3u1ps6XJYtgImTgxsvGOQ02GxYFIoJfXd/HFvM5EhDuZMUKXMYPw+P0WvFtF+\nsp25980lPn1ktogMDbL4zNJY/ntrA9XNdlLmZLufH29v4JEVcUSGOAIcocjIVLa+DOPvaxGbdmUa\nlkPvmUREREQJGREREQGYNt1ebr8TU+SB3G2waydWR8eA3azWVtjwHmx4D5OYZM+a0cVtGWkSk+zl\nlNrjEByCVVcHr70Cr72CSZ9hJxZzlkBkVOBiHWOuTo+gpcvPm4fb+NXORr6wPI60OA2wPl3Nrhra\nT7YTHh9ObEpsoMM5p4hgBw8vdfGDrQ3UtfkAONri4ye5DXxheSxhQUrKiPTXXNNM7cHa3vXoKdEk\nuBMCGJGIiIiMJHr3LCIiIn0cDsjMggc/Dt/5PuaTn8bMX4BxnNmaxqqrxXrtFayv/xN851uwYT20\ntQUgaJHzmDIVvvUdzCOPYpavxISGYpUcxnrqj/APj9ntzGTI3OKOZPm0MLr99iD4mp7KCrF1t3dT\nvqkcgPRr0nE4R/5HspgwJ59fFosrtC/WikYvv8hrpNtnznGkyPhijKH0ndIB29KuSsNSRbGIiIj0\nUIWMiIiIDC4kxK4eyFlyxnyO01klh6HkMOZPT8GChbB8JcyeA07NGJAR4lSyMTMLPvRhzO582L4V\nmprs2TKnvPkGzMyA1DS15HufLMvivnnRtHb72Xesi5/kNvDYqjhcmjkCQMXmCrztXmJTYomfOTJb\nlQ0mIcLJw8ti+a+t9bR120mYohPdPJHfyN8tcuFUOyYR6kvraSjva/0aPzN+xFfBiYiIyPBSQkZE\nRETOr/98juPHYEcubNuKVXt8wG6W1ws782BnHiYmxh62vmKl3Q5NZKQIDbXblS1bbs+XOZV4qT2O\n9dyzAJiJE+12fMtWQIJazVwsp8PiY9kufry9gbhwh2aN9Gg/2U51XjUA6evSR91d85Ojg/jc0lh+\nuK2Bzp7KmL3HunhyXzMfnh+NY5R9PyJDyRhD6bunVcdcmRagaERERGSkUkJGRERELs6EiXDTLXDj\nzZjSEti6BXbuwDqtXZnV1ARvvwlvv4mZNh2Wr7BnzsS4AhS4yCCC+803CQrCrPsA5OZiHTsGL70A\nL72AyZhlV30tWWpXjskFCXFafG6pi2CnpQv1Pco22IO+Jy6YSNTE0Tm7KCU2mIdyXPx0RwNev70t\n90gHEUEWd8yOGnVJJpGhUltQS+ux1t71ifMmEjkhMoARiYiIyEikhIyIiIi8P5YF6TPs5Z77MHv3\nwLYtcGA/lt8/cNcjlfDnSszzf4Y5c+2qgwULB14MFwm0uHi46164/S5M4UH7fN6dj1VchCkrhUWL\nACVkLkZov4HvHV4/b5e0cf3MyHHb3ip9XTpBoUEkr0kOdCiXZFZiCB/PdvGrXY34e0bIvFfWTkSI\ngxsydAFaxh+/z0/Z+rLedctpkbI2JXABiYiIyIilhIyIiIhcuuBgWJxjL02NmNztsH0rVmXlgN0s\nvx/27YV9ezEREXZLs5WrIDlF8zpk5HA67cThnLnQ3o7ZtROaGiE8wn7c64XvfhvmzrMrZ5KSAhvv\nKPGbXU0U1HZR1+rjgYUx47JqJjQqlIwbMgIdxpCYPymU++dH84c9zb3bXitqJT7cwbJp4QGMTGT4\n1eyqoaOho3d9yuIphLnCAhiRiIiIjFRKyIiIiMjQinHBumth3bWYI5V2lUHudruFWT9WWxusfxfW\nv4uZMtVOzCxdDjExAQpcZBDh4bBq9cBtBQewysugvAxefdluabZiFSxaDGG6AHc2N82K5PDJbvKq\nO4kKbeGOrPHT3qrtRBvhceFYY6wyaNm0cNq7Dc8VtPRue2pvM3FhTmYlqppMxgdvp5eKTRW9685Q\nJ8krR3cVnIiIiFw+mq4pIiIil8+06XYLqG99F/Pw/8EszsEEnXk/iFVdhfXnP8FXvww//RHs2Q0+\nbwACFrkAc+dhHnkUs2wFJjgEq7gI63e/gX94FJ74NXR2BjrCESk5NphP5rhwWvBeaTtvHm47/0Fj\ngK/Lx94/7mXnL3fS2Tz2zo0r0yJYNyOid91n4Jc7GznarN/hMj4c2X6E7vbu3vXpK6YTHKGWrCIi\nIjI4VciIiIjI5ed0wrz59tLWhsnbAVs2YZWVDtjN8vvsZMye3ZjoaHvWzMpVMGVqgAIXGYTDAZlZ\n9nLf/ZhdebB1C9ahYkxZCYT0qwxobASXK3CxjjCZiSE8uDCGJ/KbeNnTSnSogxXTx3Z7q8ptlXS1\ndBEaHUpI1NisGrnFHcmJNh/5NXbCqd1r+OmOBh5dFU9MqO4BlLGrq6WLI9uP9K6HRIUwdYnes4iI\niMjZKSEjIiIiwysiAtZeAWuvwFRXwdYt9ryZ01uaNTfDW3+Dt/6GSUm1EzNLltnHi4wU4eGwag2s\nWoM5fsxOwJxqw1VXB//yNZjlhpWrIXvRwGTNOLVoShgtXX6ePdDCU3ubmRjpJD1+bP5/6Wzu5Mg2\n+2Jt+rr0MduizWFZfGRBDA3t9ZQ22JUxJ9v9/CKvgS8sjyPEOTa/b5HyTeX4u/296ylrUnAGOwMY\nkYiIiIx0SsiIiIhI4EyZCnfeDbfdjjmwHzZvhn177UqZfk7N6zDPPmNf1F61xr7I7dCd1zKCTJho\nL6dUlkNQEJanEDyFmKfD7aTiqtWQnNKXuBmH1qZG0Nzpp6nTT0rs2G3tU7m1Er/XT6I7Edf0sV0p\nFeK0+FROLN/fcpK6NvsCdVmDl9/vbuLji2JwjOPzXcam9pPtHN19tHc9PD6cSQsmBTAiERERGQ2U\nkBEREZHAcwbB/IX20tSEyd0GWzdjVVUN2M3yemFHLuzIxSQm2lUHK1ZCXHyAAhc5h+zF8P+yMHm5\nsHmTnVjc8B5seA+TmgZf+dq4TireOCsSYMxWjXQ2d1KTXwPYd82PB9GhDj6zJJbvb6mnrdsAsPto\nJy8VtnJbVlSAoxMZWmXryzB+07uedlUalmNs/j4TERGRoaOEjIiIiIwsMTGw7lq45gOYinLYshl2\nbMdqGzgA3Kqrg5dewLz8IsyeA6vXwLwFEKS3NzKCRETA2ith7ZWYI5X2+bx9GyQm9iVjfD7wFNoz\nacZRgqZ/Iqat289fi1q5JTNqzLS3qtxaifEZEjMTiZwQGehwhs3EqCA+udjFj7c34Ou5Vv12SRuJ\nEU5Wp4zteUEyfjTXNFN7sLZ3PXpqNAmzEgIYkYiIiIwWumIhIiIiI5NlQUqqvdx1D2ZPvn0x+2AB\nlum7I9UyBg7shwP7MdHRsHyl3RJq0uSAhS4yqGnT4Z774PY7ob1fgvHAPqyf/AgTF29XfK1cBYlJ\ngYszAH6b30RBbRcNHf4x094qMimSkOgQUlaPj+qY/jISQvjw/Bh+t6dvNtizB5qJD3cwe0JoACMT\nuXTGGErfKR2wLe2qtDFb7SciIiJDSwkZOauuri6efPJJ3njjDY4csYeRJicnc88993DrrbcGODoR\nERlXgoMhZ6m9nDiB2boZtmzCOnlywG5WczO8+Qa8+QYmfYZdNbMoB8LCAhS4yCCCgyG43zyRbi8m\nMdGu+nrtFXjtFYw70z5/Fy6y9x/jbsuKoqS+nt1HO3nF08oHM0d/e6vJ2ZOZtGDSuG1htGRaGLVt\nPv5a3AqA38CvdzXxyMpYpsWM/XNaxq760noayht61+NnxhObHBvAiERERGQ0UUJGBtXd3c0XvvAF\n8vPzmTVrFrfffjudnZ387W9/4/HHH2fChAmsWLFi2OJ5++232bVrF0VFRRw6dIjW1lauv/56vvnN\nbw5bDCIiMkIkJMDNH4Qbb8YUHoTNG2HPbnu+TD9WyWEoOYx55ik7kbN6DaSmjetB6jJCLc6B7EWY\n4iL7fM7fheUpBE8hJiUVvvbPgY7wspscHcQnFrn46Y4G3jzcxoRIJ8unj/72VuM1GXPKDRkRnGjz\nkVvVAUCnz/DzHY08uiqO2DBngKMTuXjGGErfPa065sq0AEUjIiIio5ESMjKop59+mvz8fG6//Xa+\n+tWv9pZfZ2dn86//+q/s2bNnWBMyv/71rykuLiYiIoIJEybQ2to6bK8tIiIjlMNhz46ZPQdamjHb\nt9mD06urBuxmdXbaF7k3b8RMmWonZpatgMjxM9NBRgGHA9yZ9tLWhtmxHTZthIXZffs0NMCBfbB4\nyZis+spMCuHuOdE8s7+Zp/c1kxDhJCMhJNBhXbTS90qxLItpy6YRFDa+P25ZlsWH5kdT3+6j+GQ3\nAA0dfn6+o5FHVsQSGjR+ZibJ2FBbUEvrsb7PohPnTRxXM6JERETk0o3vTwhyVs8//zxhYWE88sgj\nA3rhOp32nWwul+tsh14WX/ziF5kwYQLTp09n165dfPaznx3W1xcRkREuKhqu+QBcvQ5TVgqbN8GO\n7XYyph+rugr+9DTmL8/BosWwei3MzFDVjIwsERFwxVX24vP1bd+yCeulFzB/ehqWLoNVa+wZS2Po\n/F2dEs7xVi/vlrbzy52N/MOaeOLDR08lRWdTJ0e2H8H4DElZSeM+IQMQ5LD4ZI6L/9xcz/FW+3w+\n0uTlN/lNfGqxC+c4ryKS0cPv81O2vqx33XJapKwdfzOiRERE5NIMyScEt9sdD3wduA2YDNQBrwH/\n4vF4ai7g+FDgq8BHgOk9x78K/JPH46kbihjlwtXU1FBVVcWaNWsIDx/YKuLtt98GICcnZ1hjGu7X\nExGRUcqyIC3dXu6+F7MzDzZvxDp8aOBu3d2wfRts34aZOMmumlm+EqKjAxS4yFk4+yUjJk/BpM+w\n2/Ft3AAbN2CmTbfP36XL7UTOGHBbVhS1rT4SI53Eho2uCorKrZW9yRjdNd8nItjBZ5fG8p+bT9LS\nZQA4cLyL5wpauHtOlIahy6hwdPdROho6eten5kwlzDX2qhVFRETk8rrkhIzb7Q4H3gMygR8BeUAG\n8BhwtdvtXuzxeOrPcXwQdvLlip7jdwI5wOeB1W63O9vj8XRdapxy4Q4ePAjAnDlzercZY3jmmWd4\n5513WLp0KRkZGYEKT0RE5MKEhsLKVbByFeZojd3+adsWrJaWAbtZx47Cc89iXnjebg+1eq3dNsox\nui4EyziQvcieNVNdbbfh27YV60glPP0kpsgDD42NCmKHZfHJUVg50dnUSc1u+1605NXJAY5m5EmM\ncPJQTiw/3FZPt9/etrG8naRIJ1eljY1kooxdfp+fyq2VvevOUCfTV0wPYEQiIiIyWg1FhcwjwDzg\nYY/H85NTG91u9x7gL8C/AF86x/GfAa4BPurxeH7Xs+0Pbre7Dvg7YBmwcQjivCTWZz551sfMhx+A\nNVfYKxvXY/3x92ff92e/7Fv5j29iVVQMvt/qtfCRB+2V8jKsb/372Z/za/9st6sYIoWFhQBkZWWR\nl5fHG2+8we7duykvLycjI4NvfOMb5zz+qaeeorm5+YJfb9asWVx55ZWXErKIiMi5TZoMd90Dt96O\n2ZMPmzZiFR4csIvl88HOPNiZh0lMsqsOVqwEV2yAghY5iylT4O574bY7es9nVqzqe/zwISgtgeUr\n7HZ+o1D/ZExzp5/tR9q5Jj1iRFdSDKiOSVJ1zGDS4oJ5YGEMv97V1LvtLwUtxIc7WTApNICRiZzb\nsb3H6Gzqa4M6dclUgiOCAxiRiIiIjFZDkZB5EGgFfnXa9heBI8BH3G73ox6Px5zl+IeBYmBAFsPj\n8fw7cPYshFw2pypksrKy+O53v8ubb77Z+1hqaip+v/+cxz/99NPU1Jy3U12vm266SQkZEREZHsHB\nkLMUcpZiao/bF7K3bsZqahqwm1VXCy88j3npBZi3ANashdlzVDUjI0u/83mAt9/E2rXTrvrKXmyf\nvxmzRuWsGb8x/Gh7PdXNPvwGrp05MhMdHU0dqo65QNmTw7g108eLhfZgdAP8Nr+RR1bGkezSBW4Z\nec6ojglxMnXJ1ABGJCIiIqPZJSVk3G53DHarso0ej2fA1FyPx2PcbncucAeQBpQMcvy0nuN/fCph\n43a7w4DOcyRwAmJAZcu5rLkCc6pa5nz+8V+5oG8yJfXCX38IFBYWMnnyZGJjY/nmN7/Jl7/8ZUpK\nSvjTn/7Em2++SWlpKU8++eRZj3/xxReHLVYREZH3LWkC3H4nfPBWzN69sGkDFBzAMn1/nS2/H/bk\nw558THyCXTWzarWqZmRkW74S09lpn887tsOO7faspDVrR13VjMOyuCEjkl/tauJlTytJkU6yJ4+8\nmQ21BbV2dcxsVcdciGvSI6hr87G5wp7H0e2HX+Q18uVVccSEOc9ztMjwOn7g+IDZMVNyphAcruSh\niIiIvD+WMe8/7+F2u+cBe4GnPB7P/YM8/gPslmYf8Hg8bw3y+DrgTeyWZn7gi0AK0Am8Djzm8XgO\nnX7c+TQ2Ng76TRUXF1/sU407tbW1PPLIIyxZsoRHHnnkjMe/9rWvUVFRwQ9+8AMmTJgQgAihoKCA\nxx9/nFWrVvG5z30uIDGIiMjYFNTUiGvfXmL27yX4tFkzpxiHg5YZM2mcv5C2lNRRWXUg44N9Pu/B\ntW8fQa32+Xxi+UpOrFoT4Mgu3s6TIWyuC8dpGe6a3srEMF+gQxrAGEPX8S6cEU6CooeiCcHY5zfw\nUlUEFW19F7YnhXm5Y1orQSpGlBHC+A21b9Tia7F/51hOi6SbknCGKnEoIiIyHp1trrrL5brgCwOX\n+mnh1O11bWd5vPW0/U4X3/P1o0AI8DhwDHumzOeBFW63e6HH47nw/ldyScrKygBIT08f9PHISPuO\nv7Cws9+Z+Ne//pW2trOdEmdKSUkhJyfnwoMUERG5TLwxLk6sWsOJFauILC3BtW8PkSWHz6iaiS4u\nIrq4iC5XLI3zFtA0dx6+SN0VLyOLfT6v5cSK1USWHMa1dzeN8xb0Ph5dsB9nWxtNs+fijxjZQ9UX\nxXVR3+WkoCmEl6siuDe5hejgkVNQb1kWoRM1A+ViOCy4YXIbz1RE0dBtX9w+2hHEu8fDWTexXblu\nGRE6Kjt6kzEAETMilIwRERGRSxLo27dCer5OBOZ6PJ4TPesvud3uY9gJmkeBx4bixc6WwRqPTlUL\nnf7/5NS8mNWrV5/xWGNjI8XFxcycOZPFixef9bkfe+yxi54h86EPfeiC92/q6fMfHR2tf9Nx7mzn\nschoovN4BHO74foboL4es2UTbNqAVV8/YJeQxgaSNq0ncesmWJANa6+AWe5xN2tG5/Eo4HbDDTeS\ndmrdGPjDE1jHjpG0eSNkL4I1V4zoWTPpMw0/yW2g+EQ3b9TF8aWV8YQGDV2s7+c87mzuxNvhVZuy\nS5A0zct/bq6n3Wsn2A42hZA1LZ6r0kZ2knCk0u/joWP8hrx38nrXHUEO5l0/j5CokHMcJUNB57GM\nBTqPZSzQeXx5XGpC5tQE3LN9Aok6bb/TneoF8lK/ZMwpv8JOyFz5vqOTi1ZYWAjYiZmlS5di9Xwg\n7+7u5lvf+hZer5f77z+jO90AmiEjIiJjSlwc3HQL3HATZv8+2Lge9u8bWDXj88GuPNiVh0maYM/q\nWLEKokfPrA4ZZ4yB2+/CbNoAB/Zj7ciFHbn2rJm1V9izZiKjzv88wyjIYfGJRS6+v6WeORNCCR4B\nN6lXbKqgJr+GmdfOZErOlECHMypNjArio9kx/HxHY+98zb8UtDApyklWkqqOJHDqCutoP9Heuz45\ne7KSMSIiInLJLjUhUwoYYNpZHk/p+Xq24S1lPV8H+zhV1/PcMe83OLl4pxIyL730EkVFReTk5NDW\n1sb27dupqqri5ptv5uabbx72uN577z3Wr18PwIkTdu5u3759fOMb3wAgNjaWv//7vx/2uEREZBxx\nOGD+Ans5eQKzeRNs2ojV2DBgN6v2ODz/Z8xLL8DCRfbF7RFcdSDjlMMBC7Pt5cQJzOaNsHkj1rGj\n8OwzmLh4WHT2iuhAiQxx8JXVcYSOgCEjHY0dHN1zFIDY1NgARzO6zZkQyq1ZUbxw0L5fzwC/2dXE\nY6vjmBAZ6KYOMh4ZYyjfXN67bjktpi0/22UPERERkQt3Se9uPR5Pq9vt3gsscrvdYR6Pp+PUY263\n2wmsBCo9Hk/FWZ6iAGgEFg7y2HTAAo5cSoxy4Y4ePUpDQwPLli0jKiqKvLw8nnrqKSIjI8nMzOTh\nhx9m3bp1AYmtqKiIV199dcC2qqoqqqqqAJg8ebISMiIiMnziE+CWW+HGmzH79tpVMwUHBlbNeL2Q\nlwt5uZhJk3uqDlbCCJ/VIeNQQgJ88Da46WbM3r2wMw8W9M2a4dWX7WqvpcvhHHMEh0v/ZExTh4/q\nFh+ZicN/13rllkqM35A0J4mIRP1cX6qr08KpbvKSW2V/pGz3Gv53RyOProojPDjwCTgZX04UnaCt\ntm8u6qQFkwiNVsWWiIiIXLqhuN3oV8D/AJ8G/rvf9o8AE4Cvn9rgdrszgU6Px1MK4PF4utxu95PA\nZ91u9y0ej+flfsd/vudr/21yGR08eBCApUuX8sADDwQ4moEeeughHnrooUCHISIiMpDT2VdlUFfX\nU2WwCaupccBu1tEa+NPTmL88D0uW2smZ1LSzPKlIgDiD7Fky2Yv6trW2wF9fxfJ6Mc89C0uXwZor\nITk5YGGe0tTp57ub62nr9vPFlXFMiwkettfuXx2TsirlPHvLhbAsi/vmRXO81UtZgxeAY60+nshv\n4tNLXDhUZSjDxBhD+aZ+1TEOi+krpgcwIhERERlLhiIh8zPgw8D33G53CpAHzAG+BOwDvtdv34OA\nB8jst+3rwHXAs263+9vYbcyuBh4Advc8vwyDU+3K3G53gCMREREZhRIT4dbb4eZbMHv3wIb1WAcL\nBuxidXfBlk2wZRMmOcVOzCxZBqG661ZGqNAw+OjfYTa8h1VcBBs3wMYNmNQ0+/zNWQIhgTl/o0Ms\nZiWGkHukg1/kNfLl1fFEhQxPJUXF5gpVx1wGwU6LTy528d1N9TR2+gEoqO3i5cJWbs0aWTONZOw6\neegkrcdae9cnzp9ImCvw1YEiIiIyNlzyJxaPx9MNXAv8ELgTeAL4KPBL4EqPx9N29qPB4/HUAsuB\n3wIPAf8LXAF8v+f49nMcLkNICRkREZEh4AyC7MXw91/CfPNxzAeuwwwyHN2qKMf6w+/gHx6Dp5+E\n6qoABCtyHkFBdlXXo1/BfP2bmKvXYSIisMpKsX73BNQ3nPcpLhfLsrhvbjQpsUGcbPfz652N+Pzm\n/Adeoo7GDo7tPQaWqmMuB1eYk0/luOg/JuitkjZ2HOk4+0EiQ8QYQ8Wmfh3XLZi+UtUxIiIiMnSG\nZEKix+Npwq6I+dJ59hu0zrwnKfPpnkUCpLCwkMmTJ+NyuQIdioiIyNgwYSLceTd88DbMrp2wcT3W\noeIBu1gd7fDeO/DeO5iZGbD2SrtlVPDwtV8SuSCTp8A998Ftt2Py8uBIJUycaD9mDPzx95CZCQsX\n2YmcYRDstPjUYhff2VRP8clunito4Z650Zf1NS2HxYS5E8Cg6pjLJCU2mPvnx/C73U29257c10RS\nlJPUWP1ulMunvqSe5prm3vWJ8yYSHhsewIhERERkrBmeT0oyKrzxxhuBDkFERGRsCg6GZcth2XJM\nVRVseA+2b8XqGHjHt3WoGA4VY6KiYOVqWHMFJCUFJmaRswkJhZWrBm4rLcHatAE2bcDExPSdvwkJ\nlz0cV5iTTy528T/b6tlY3s7UmCBWJV++C6ih0aG4b3ZjzOWvxhnPlkwNo7rZy1uH7YYLXj/8Mq+R\nL6+OwxXmDHB0MhYNVh2TvDLw87JERERkbBmeJssiIiIiYps6FT70Yfj29zAfeRAzyHB0q6UF62+v\nw7/+I/zwv2DvbvD7AxCsyAWaPAVz34cxU6ZiNTVhvf4a/PNX4cf/A/v2XvbzNy0umHt7KmNauobn\nZ8XSkPnL7hZ3JHMmhPSuN3b6+cXORrp9SobJ0Gsoa6Cpqq8qa8KcCYTHqzpGREREhpYqZEREREQC\nISwMVq+FVWsw5WWwYT3syMXq7urdxTIGDuyHA/sx8QmwZi2sWg0xai8qI0x4OFx5FVxxJebwIVj/\nHuTvxNq3F1NyGL79PXBc3nvBlk8PJ9kVzJSYy/MRp6Ohg4MvHiR5ZTIJGZe/8kfAYVl8dGEM399S\nz9EWHwDlDV6e2tfMAwuilRSTITWgOgZVx4iIiMjloYSMiIiISCBZFqSm2cudd2O2bYWN72EdPTpw\nt5Mn4MW/YF55CbIXwxVXwswM+3iRkcKy7PNyZgY03YvZuhksR99MpI4OePpJWL0GZswc8vO3fzKm\nscNHeLCDEOfQvEbFlgqaq5qpPVirhMwwCg928FCOi+9trqet266M2VHVwdToIK6ZoRk+MjQayhto\nrGzsXU/KStKMKBEREbkslJARERERGSkiI+GadXD1NZgij11lsDsfy+/r3cXy+SAvF/JyMVOmwNor\nYdkKu0JBZCSJiYHrbhi4LXcb1rYtsG0LZsrUnvN3+ZCfv2X13fxiZyOzEoJ5cGHMJVdStDe0c2zv\nMXumxCrdNT/ckiKD+Hi2i5/kNnCqWdmLhS1MinYyZ0JoQGOTsaFi82nVMfo5FxERkctEM2RERERE\nRhrLAncmPPQZ+Nb/w9xyKyY27szdqquxnn4SvvoY/PH3cKQyAMGKXIS58zDX34iJjsaqrsJ6+o/2\n+fvkH6DqyJC9TEiQRafXkFfdydslbZf8fJVbKjF+w4S5E4hI0F3zgZCZFMIds6N61w3wRH4TR1u8\ngQtKxoTGI400lDX0rie6E4mcEBnAiERERGQsU0JGREREZCRzxcJNt8Dj38Z85mFM1uwzdrE6O7E2\nrsf692/Ad74F27dBd3cAghU5j/gEuO0O+NZ3MZ/8NGaW2z5/N7wHf/jdkL3MlOggHlgYA8BLha0U\nHO9838/bc9xwAAAgAElEQVTV0dRhV8egmRKBdkVqOMunhfWud3gNv8hrpL3bH8CoZLQ7Y3bMav2c\ni4iIyOWjlmUiIiIio4HTCQuzYWE25tgx2PgebNmM1Tbw7n+r5DCUHMb8+RlYtQbWXAEJmnchI0xQ\nEOQsgZwlmOoq2LAeMmb1PV5VBTu2w9or7CTO+7BgUig3zorktaJWnshv4rFVcUyIuviPP0e2HcH4\njT1TQtUxAWVZFvfMjeZYq4/SejvpfLzVx+92N/GpHBcOzdSSi9RU3UR9SX3vekJGAlETo85xhIiI\niMil+f/s3Xd4VOeZ9/HvmVFvo4KEEEiiSQLT1SgCg2uwTWJjx8YldrxeO4nXr994k3iTTd51yq43\n2dib7G52HSdOcYoB47XjFtsYN5pAQiAJMEiIIoSERJM06mVmzvvHgZEEAlMkjcrvc13ngnPmmTP3\niEdcc+Y+93OrQkZERERkqBk9Gr64An7yLOaX/wZz/IRzhhiNjRjvvQP/7zvw3C/g093g0V3kMggl\njIW774WMzK5j6z+y5u/3vgPP/fdlz9/PTQ5hVnwgrS6TX19GJYXH7eFk6UkAEnMSL/n1pe/52w0e\nznAQGdR1Kbv7eAfv7mv2YVQyVJ3TO0bVMSIiItLPVCEjIiIiMlQFBMD8HJifg3m4HNZ/AtvyMTo7\nvEMM04SdxbCzGDM2FhYtgQU5EKY7gGUQm7cAs7UNdhRg7CyCnUXW/L16iTV/Qy9u/toMg/tnhXO8\n2UVNo5vSkx3MHhP02U8883y7jcyvZFJ3sI6wOP3ODBYRgTb+NsPBf26pw3U6x/be/hbGOfyZFR/o\n2+BkyGiqaaK2rNa7HzUpivAx4T6MSEREREYCJWREREREhoPk8fDAg3DHnZhbc2H9JxjHj/UYYpw4\nAa+9gvnW69ZyUYuvgV6qa0R8buIka7tzBWbuJtjwiTV/X30F88QJuPdLF32qQD8bX8mM5FiTi2lx\nl/5lvV+gH7FTYy/5edK/xkf6s2J6OC/tbPQe+1NRA3E5UYwJ12WufLazq2OSc5J9FImIiIiMJPqk\nKiIiIjKchIbCdTfANddhlpbAJx/DziKrUuY0o7MTtuTCllzM5PGweAlkZlsVNyKDSUQELL0ZblyK\nuXunVQV29eKuxz/dDU6nlWC8wPwdFWJnVIjdu+/2mNhtF+430lDVQGhcKHZ/+wXHie/MSwzmiNPF\nhsOtALS7TV7Y7uRbOVGE+Gt1bjm/5uPN3uUIASLHRxIxLsKHEYmIiMhIoYSMiIiIyHBks8HUq6yt\nthZz0wbYtAGjoaHHMONwOfzxRcz/XQMLFlpfdseN9k3MIudjs8HM2dbW3dtvYhw6iPlqt/kbG3fB\nU5Wd6uDPxQ18NTOShIjeL4dc7S52r9mNgUH6w+kEhmsZrMHq9qvCONroYn9tJwAnmt38obCBr2Y5\nsBkXTrrJyHVOdcxCVceIiIjIwNBtQyIiIiLDXXQ0fOE2+NefYj78FcyU1HOGGC0tGB+8j/HU9+AX\n/wE7iy6ribrIgDFNWLQYM3k8RnMzxrq1GP/03dPzt/i88ze/so3aVg8vbK+nuaP3MdWF1bhaXQTH\nBBMQpsqxwcxuM3go3UFkUNel7Z4THfy1tNmHUclg1nKyhRN7T3j3HUkOHEkOH0YkIiIiI4kqZOS8\nOjo6WLlyJWvXrqWyshKApKQk7rrrLm699VYfRyciIiKXzM/PWposMxuzqgo2fAJbczHa23sMMz7d\nDZ/uxowZZVUcLFgI4Wp0LIOMYcCCHFiQg1l+CNZ/DNvyu+bv/Q9CzsJznnbn9HCqGl0ccbp4sbCB\nR7N7VlK4O91U5p3+7JuThKEqi0EvPNDGIxkOfr6lDtfpHNv7B1pIdPgxe0yQb4OTQefs6pikhUk+\nikRERERGIiVkpFednZ08/vjjFBYWkpqayvLly2lvb+f999/n6aefJi4ujvnz5w9YPL/4xS/Yu3cv\nFRUVOJ1OAgMDiY+PZ/Hixdx5551ERkYOWCwiIiLDwtixcM99sPwOzK1bYP3HGNVHewwxTp2Ev7yK\n+dYbkJFl9ZqZMNH6IlxkMBk/wdruuAszdzNs2woZmV2PF+RDdAxMmEiA3eDhDAfPbKql5GQHb5U0\nc+vUMO/QmuIaOps7CYsPI2pilA/ejFyOpEh/7p4Rzp+LG73H/lTcSFyYHwnhuuwVS2tdK8f3HPfu\nR4yLIDJZ15IiIiIycPTJVHq1evVqCgsLWb58Od/5zne8dwbOmTOHp556iuLi4gFNyKxatYopU6Yw\nd+5coqKiaG1tZffu3bzwwgu8/vrr/O53v2P0aK13LyIicsmCgmDJNbB4CWbZPvjkYygqxPC4vUMM\nlwvytkDeFsykJFh8DWRlQ4D6asggExYGN37O2s7o6IBVL2E0N2MmJsGSa4jOyuahdAf/nVfPBwdb\nGOfwIwIwPSaVW63qmMQFiaqOGWLmjgvmiNPF+vJWADrcJi8UOHlyYRQh/lqtW+DIliNgdu2rCk5E\nREQGmhIy0qvXXnuNoKAgnnjiiR4fUO12OwAOx8Cusfvxxx8TGHjulz7PPfccL774Ii+++CLf/va3\nBzQmERGRYcUwIDXN2urrMTdtgI0bMJz1PYdVVMCf/oD56ivWclFXL/FNvCIXy+WChYswN23CONI1\nf1Pm57A8bQmvHjFYvauRB5LBU9FKe0M7ITEhjEob5evI5TIsnxrG0QYXZbWdAJxscfNiYQNfy+q5\nNJ2MPG3ONo7tPObdVxWciIiI+IJuE5JzVFdXU1VVRVZWFsHBwT0e+/DDDwHIzMzs7an9prdkDMD1\n118PwJEjRwYyHBERkeEtMhKWfQH+9SeYj3wNM23KOUOMlhaMD9ZhPPU9xr66htD9Zedtoi7iUyEh\nsPyL8JNnMB98CHPCRGv+friOJc99jyWxbh7OcBBkB1uwjdC4UBJzVB0zVNltBn+T7iAquOtSd++J\nDt4ubfZhVDIYVG6txPR0lceoOkZERER8QRUyco69e/cCMG3aNO8x0zR5+eWX+eijj8jOziYlJcVX\n4fWwceNGACZPnuzjSERERIYhu5/VhyMjE/PoUdjwCWzNxWhr6zEstPwQoeWHMDeuh6sXQ84iCA/3\nTcwi5+PvD/MWwLwFmIfLYf0nUFPNHVnxYBiU1UFs3UFG33WN5u8QFx5o45EMBz/PraPzdJ543YEW\nxkX4kZ4Q5NvgxCc6mjqoLqr27ofEhhCTGuPDiERERGSkUkLmIj3+1+PnfezuGeHkJFmVJJsrWlm9\nq/G8Y39xS5z37z/dWMuRBlev4xYkBnHPzAgAKpydPLOp7rznfHJhFEkO/wvGfylKSkoAmDp1KgUF\nBaxdu5aioiIOHz5MSkoKP/zhDy/4/FWrVtHYeP6fwdlSU1NZsmTJRY3985//TEtLC01NTezdu5fi\n4mImT57Ml7/85Yt+PREREbkMCQlw971w2+2Y+Vvhk48xjlb1GGLUnoLXX8N8+00rkbP4Gpgw0VoO\nTWQwSR4PDzxoVXWdnp/+tbXU5++l6EALSyObNX+HuESHP/fMiOCPxQ3eYy/tbGB0mB9jI3QZPNJU\n5lViurtVxyxQdYyIiIj4hj6JyjnOVMhMnTqVZ555hnXr1nkfGz9+PJ7PWI5k9erVVFdXX3BMd7fc\ncsslJWRqa2u9+/Pnz+epp54iKkpr/4qIiAyIoCCrb8yixZj7y2D9x7BjO0a3zweGywV5WyFvq7eJ\nOlnZEND7EqQiPmOzlrU6VXaKY3s6eXPOPTQEBRO7fTWZP/2x5u8QlzUuiCMNnXx8qBWADje8UFDP\nkwujCQ3Q6t0jRWdLJ0d3HPXuB0cHEzs11ocRiYiIyEhmmKb52aOGGKfTOfzeVB8rKysD6HXpsRtu\nuIGQkBDeeOMN3G43jY2NHDx4kDVr1vDRRx8xefJkVq5cOdAh93Dq1Cl27tzJ//zP/9DS0sLPfvYz\npkw5d317Gd4uNI9FhgrNYxkODhYW4thVTMyeTzHqe6/qNUNCYH6OlcwZPXpgAxS5ANM0KXyxkKbq\nJhpTo3gveDT+pptvbPs9iccOWmMiHPD0T6xlz2RIcXtMnsuvZ9+pTu+xKaP8+VpWJHbb8KuQ0OeK\nc5WvL6dic4V3P3VZKvEz430YkXwWzWMZDjSPZTjQPL54Dofjoj9Y6rYg6aG6uhqn08nUqVMBsNvt\nREZGkp6ezk9+8hNSUlLYv38/VVVVn3Gm/hUTE8M111zDL37xC5xOJz/4wQ98Go+IiMhI5g4Lo3Z+\nDjz9Y8yvPIqZdu5NEmeaqBvf/x7818+huMhaLkrEx+oO1dFU3YQt0MbkqwKZOy6ITsPOC1d/haYH\nHsGcMBGuuqorGeN2wc4icLt9G7hcFLvN4G/SHUQHd136lpzs5K3SZh9GJQPF1eaiqqDr2jXQEUjc\ntLgLPENERESkf2nJMumhe/+Y3kREWH1tQkJCznuO/uwhc7YxY8YwYcIE9u3bR319PZGRkZd1HhER\nEekDdj9Iz4D0DMzqo7DhE9iyBaOttccwY8+nsOdTzOhoq2JmwUI4/RlDZKAd2XwEgNDUUGz+BivS\nwqludFHhdPG70FT+7sls7O5ufR+LizF+/UvMqGi4ejHkLIQIh4+il4sRFmDj4QwHP8+to/N0HvjD\ngy2Mi/Ajc2yQb4OTfnV0+1Hc7V3J08R5idjsui9VREREfEcJGenhTP+Y3pb/cjqdFBcXM3ny5Av2\nbOnPHjK9OXnyJAA2mz5Yi4iIDBpjEmDFvXDr7Zj5W+GTjzGO9qywNWpr4fXXMN9+00rkLL4GJk5S\nE3UZMM4KJ84jTvyC/AiZZN1w5G83eDjDwTObatl3yqqkuG1qWNeTDDBj4zBOHIc3/nJ6/mbC4iUw\nabLm7yCV6PDn3pkR/KGowXts5c4GRofZSXRoKbrhyN3hpjK/0rsfEBZA/CwtVSYiIiK+pYSM9HCm\nQmbdunVkZ2djnL6g7Ozs5Mc//jEul4t77733gud44403+jSmw4cPExMTQ1hYWI/jHo+H559/ntra\nWmbOnOmt3hEREZFBJCjIqoJZtBhzfxms/xh27MDwdN2xbLhckJ8H+XmY4xKtL7az5lrPFelHFblW\nX4mEzAQ6/bt6jEQF23kow8EfChuYHhfQ80lzMmDWHMy9e2D9J7CrGGNbHmzLw5yTDl/9uwF8B3Ip\nMscGUdng4sODLQB0euCF7U6ezIkmPFA3dw031YXVuFq7qtvGzRuHzU//ziIiIuJbSshID2cSMm++\n+Sb79u0jMzOTlpYW8vLyqKqqYtmyZSxbtmxAY8rNzeW5555j1qxZJCQk4HA4qK2tZceOHVRVVRET\nE8N3v/vdAY1JRERELpFhQEqqtTmdmJs2wKYNGHV1PYdVHoGX/oT56v/C/AVWciZ+jG9ilmGttbaV\nuoN12PxtjM0cS3lVeY/HJ0cH8NSSGPztvVS82Gwwbbq1nTqFuXE9bN5oVcic0dAALc2av4PMF6aE\nUtXgouRkBwB1rR5+t8PJ/5kbid2m6qbhwuPyULm1qzrGP9ifMbP1uygiIiK+p4SMeNXU1FBfX8/c\nuXMJCwujoKCAVatWERoaypQpU3jssce4/vrrBzyu7OxsKisrKSoqorS0lKamJoKCgkhKSuKmm25i\nxYoVOBxat1tERGTIcDjgls/D0psxdxbD+o8xSvb2GGK0tcLHH8LHH2KmTYEl18DM2WC3+yhoGW6C\no4NJfzidlhMt+If0vmRV92TM3hPtJDr8CQs46w77mBi47XZrTpueruOffITxztuYU6ZaiUXN30HB\nZhg8OCeCZzfXcrLF+vfaX9vJa3uauHN6uI+jk75SU1xDR3OHd3/s3LHYA/T7JyIiIr6nhIx4nekf\nk52dzf333+/jaLpMmjSJJ5980tdhiIiISF+z22FOOsxJx6yphg3rYctmjNbWHsOM0hIoLcGMjIJF\nV8PCReCI9FHQMpyExYURFhf2mePyKlt5qbiRyTH+PJZ9nkoK/7OSOh4PZkCAlWws2av5O4iEBth4\nJDOSf99cR4fbBGDD4VbGOfyYnxjs4+jkSnncHo5sOeLd9wvyIyEjwYcRiYiIiHTRAqridWa5srS0\nNB9HIiIiIiNO/Bi46274ybOY9z1g9ZI5i1Ffh/HWG/CP34ZfPw+lJWCaPghWhrqWUy2XND5tVADh\ngTbKTnXyl71NF/ek22635vOdKzBHj+45fz94/zKilr6UEO7HA7N79qBcs7uRQ3Wd53mGDBXHdx+n\nvaHdu5+QkYBfoO5FFRERkcFBCRnxUkJGREREfC4w0Koi+N5TmP/wj5hz52H69fwizfC4MXYUYPz8\nWfjhU9bSZq2X9gW7jFytta0U/LqAnS/txPRcXEIvMsjOwxkO/GywvryVLUdaP/tJACEhcN0N8IN/\nwXzim5hz0gETuiccT57U/PWRWfGBLE0J8e67PPCb7U6cbW4fRiVXwvSYVORWePdt/jbGZo31YUQi\nIiIiPek2EfEqKSlhzJgx6sciIiIivmcYMHGStd1xF2buJtiwHqP2VM9hNdXw8irMv7wKc+fB1Usg\nMck3McuQcGTLETAhKDII4xKauE+I8mfF9HBe2tnIy7saGR3qx8To3nvPnMMwYMpUa6urg8huS5at\nWQ2leyF7ntVrppfqMOk/N6WEUtXgYtcxq99IQ7uH32x38n/nRfXoISRDw4m9J2ira/PuJ2QknLdH\nlIiIiIgvKCEjXmvXrvV1CCIiIiLnioiApTfDjUsxd++E9Z/Ank8xui1XZnR0wMYNsHED5sRJ1hfb\n6Znn9vWQEa3N2caxXcfAgMT5l574mJcYTGWDi/Xlrfxmh5Mnc6KICr7ERuFRUV1/d7uhox2jvR02\nroeN6zEnTYbF11j9lTR/+53NMLh/VgQ/y62jpsmqjCmvd7FmdyP3zgzHMJSUGSpM06Ric7fqGD8b\n47LH+TAiERERkXMpISMiIiIiQ4PNBjNnW9uJ45gb1kPuJozm5h7DjIMH4OABzDUvQ85CWLQYYmN9\nFLQMJpVbKzE9JrFXxRIcfXnN25dPDaO60UVNk5umDs+lJ2S6s9vhiW9iHj0KGz+BLVswDuyHA/sx\nw8Phb79iVdVIvwr2t/FIhoNnN9fR6rISvVsr2xjn8GPx+JDPeLYMFqf2naLlZNfyf/Gz4wkIC/Bh\nRCIiIiLnUkJGRERERIae2Di44074wm2Y2wtg/ccYhw72GGI0N8H772GuWwvTplvLmU2fYSV2ZMRp\nb2qnprgGgKQFl7+snd1m8FC6A5fHxBF0BcmY7hISYMW9cOvtmNvyrCqwo0chfkzXmJMnIDpG87ef\nxIX58eCcCJ7f5uRM7d1re5pICPcjJUZf6g92Z1fHGDaDcfNUHSMiIiKDjxIyIiIiIjJ0+fvDvPkw\nbz5mRQVs+ATyt1pLmJ1mmCbs3gW7d2FGx8Ciq2HBQlDfvBHlSO4RPC4Po9JGERoXekXnCg3omRQ5\n0ewiNrQPLq2CgqyKroVXw/FjXb1mPB74j38Hj2nN35yFEKH529euigvk81NCebPEqrrzmPC7HU6e\nzIkmOqSPkm/SL+oO1tFU0+TdHz1zNEERQT6MSERERKR3ur1KRERERIaHpCT40gPwk2cxV9yDGR9/\nzhCj9hTGG3+Bf/wHeOF5KC2Bbr1oZPjyD/bHHmAnadHlV8f05p19TfzL+lr2nmjvu5MaBozuNn/r\n6qzD3efvb34F+0o1f/vY9RNDSB8T6N1v6jB5YbuTDrd+zoPV2dUxl9sjSkRERGQgqEJGRERERIaX\nkBC45jpYci3mvlJr+aeiQgyP2zvE8LhhewFsL7ASN4uWwPwF1nNlWEpelMy4ueOwB/RtpYOJVUnx\n+x0NfGthFHF9USlztpgY+NG/Yu7dY83nXcUYBdugYBvmmAT4P1+3xsgVMwyDe2dGcKy5jqoGFwCV\nDS5e2tnAg7MjMAzDxxHK2ZwVThoqG7z7cdPiCI66vB5RIiIiIv1NCRkRERERGZ4MA9KmWFt9Pebm\njbBpA8bpagPvsJoaeGU15uuvQVaW1Wtm/ATfxCz9qq+TMQA3pYRS1eBi17EOXihw8o0FUQT798NC\nBDab1Qtp2nSoPYW5aSNs2ghtbRAV1TWu9pTVa0YuW6CfwSMZDp7dXEtTh1UZs+NoO4kRLVw/6cqW\nu5O+16M6BlXHiIiIyOCmhIyIiIiIDH+RkXDL52HpzZi7dsLG9bDnU6u/zGlGZwfkbobczZhJyXD1\nYsiaC4GBFzixDHYVmyvwC/YjflY8NnvfJ0pshsEDsyP42eY6qpvc/LGogUcyHdj6s5IiOga+cBvc\nsgxOnLCSNQANDfBP34Uz8zcjCwLUkP5yxITYeSjdwX/n1eM5/d/EmyXNJIT7cVWc/k8YLBoqG6gv\nr/fuj5oyitBYJc1ERERk8FIPGREREREZOex2mD0HHn/CWgLqc0sxw8LOGWZUHMb48x/h29+C1Svh\n6FEfBCtXqr2xncObDrP/vf20nmrtt9cJ8rPxSKaDEH+D3cc7eGdfc7+9Vg92P4gf07VfVQkBARiH\nDmL84ffwnW/BmtVQUz0w8QwzKTEB3D616/8HE3ixsIHjTS7fBSU9VOT2rI5JyunbHlEiIiIifU0J\nGREREREZmWJjYfkX4cfPYD70CObklHOGGG2tGJ98hPGjp+DZf4O8rdDZ6YNg5XIcyT2C6Tatu+bj\n+veu+dhQP/5mjgMDyK9so7XT06+v16upV8FPnsW8/8uYyeMxWlowPvoA4wf/BD9/FlxKJFyqq8cH\nM3dckHe/1WXyqwInLb7495UemmqaqN1f692PnhxN2OhzE+wiIiIig4mWLBMRERGRkc3fH7LnQvZc\nzKoqazmzrVsw2npWVBj7y2B/Geaa1TB/ASy6GkbH+yho+Sztje1UF1mVIckLkwfkNafEBvDgnAgm\nxwT0Tx+ZixEYCDmLIGcR5uFy2LgBtuWBn5+1AZgmnDoFo0b5JsYhxDAMVkwP51iTi/J6K6F1vNnN\n73Y4eTQrErutH5emkws6u3eMqmNERERkKFBCRkRERETkjLFj4e574bbbMbflw4ZPMI70/NLPaG6C\nD96HD97HTJsCixZby6D56aP1YHKmOiZ2amy/V8d0l54Q1GPf7TF996V98nhru+NOaG7qOr6/DOPf\nf4p51TS4egnMmGkt5ye98rcbPJzh4NnNddS3WZUxpSc7eXVPE3dND/dxdCNT8/FmTpae9O5Hjo8k\nYmyEDyMSERERuTh9ctWYlpYWDXwfuA0YA5wE3gH+qbS09JIWLE5LSwsCioFU4JrS0tJP+iJGERER\nEZGLFhRkVcAsXIRZfuh0lUE+RmdHj2FGaQmUlmCGh8OChbDwamspNPGp9oau6pikhb65a95jmrxV\n0szh+k4em+vjSorgYGs7o/oopr8/xp5PYc+nmI5IWLjI2qKifRfnIOYIsvOVTAf/saWODrd1bOPh\nVkaH2Vk8PsS3wY1A5RvKe+yrOkZERESGiiuuo09LSwsGPgEeBV4FHgR+BawANqelpUVd4in/CSsZ\nIyIiIiLiW4YBEybCAw/Cvz2LueJezISx5w5rbMRY+y489V34r59D4Q5wuwc+XgGgurC6qzomduCq\nY7pr7jDJr2qjrNaqpBhUrl4CP3kG884VmKPjMZz1GH99C777bfjTH3wd3aCV6PDn/lk9qzBe/bSJ\nvSfafRTRyNRY3cipfae8+45kB5HJkT6MSEREROTi9UWFzBPADOCx0tLS584cTEtLKwb+gpVg+cbF\nnCgtLW0G8CRQCMzpg9jkCnR0dLBy5UrWrl1LZWUlAElJSdx1113ceuutPo5OREREZICFhMA118KS\nazAPHoAN62H7NoxujdIN04TuVQc5C62qg+gYHwY+8iQvSiYoKoiIBN8tYRQeaOPhDAf/tbXOqqQI\ntbN4wiCqpAgNg+tugGuvx9xXavVOKtwBYd2aore2Qlurqma6mT0miM+nuXmrtBkAE/j9jga+sSCK\n+HAtWzgQyteX99gff/V4n8QhIiIicjn64hPjA0Az8Nuzjr8BVAJfSktL+2Zpaal5oZOkpaXZgBeA\nw1gVNs/3QWxymTo7O3n88ccpLCwkNTWV5cuX097ezvvvv8/TTz9NXFwc8+fP93WYfebWW2+lurr3\n1fWio6N57733BjgiERERGbQMAyZNtra7VmBu3QIb1mMcq+k5zFkP77yN+e5fYdp0azmzGTPAri9t\n+5thM4ifGe/rMJgQ5c+9MyP4Y1EDr+5pYlSonWlxgb4OqyfDgLQp1tbgBKPbIgpbc2HNapgxy1rC\nb9p0sF3xIgtD3g2TQqhpcrOtqg2AVpfJrwqcfCsnitAA/Xz6k/OIk7qDdd79qElROBIdPoxIRERE\n5NIYpnnBPMkFpaWlRQBOYGNpaenVvTz+KnA7MKm0tPTgZ5zr/wL/CVwPJAK/5zJ7yDidzl7fVFlZ\n2aWeasR6++23WbVqFddeey0PPfQQhmGteb1582aee+45brvtNu68804fR9l3vv71r9PS0sLSpUvP\neSwoKIhbbrnFB1GJiIjIkGGaBFcewVFcRHhZKYbH0+swV2gYzukzcM6YicuhJXb6mrvNWibOHjS4\nGtRvPRlIfm0Q/obJnUlNjArsfX4MNqM2rieqIN87nzvDw3HOmEXD9Jm4wkd2M3uXB/5SGUp1W1eC\ndWywi9vGNWP3Ybug4cw0TWrX19JxoquX16jrR+Ef5e/DqERERGQkSUlJ6fW4w+G46E+AV3p7XvLp\nPyvP83jF6T8nAudNyKSlpSUCTwN/Ki0t/TAtLe3BK4xLrtCHH35IYGAg9913nzcZA2C3Wxe3Yd2X\nMhgmQkJCuOOOO3wdhoiIiAxFhkFrYhKtiUmcaGkh4tNdOHYWEVBf32OYX3MTMXlbiM7bQkvyeJwz\nZ9M0aTLYB1cCYahq2tNES3kLkZmRBCcFf/YTBsjcmHbqO23sawxgw/Fgbk9s9nVIF+XkosXUpWee\nntWgqHAAACAASURBVM/FBDjrGZW7iZgtm6mdO59TOYt8HaLP+NngloQWXq4Io9FlVcVUtfrx8bFg\nrhvdiqGkTJ/rON7RIxkTNDZIyRgREREZcq40IXPmtqiW8zzefNa48/kl0AF88wrjuaDzZbBGojPV\nQr39TKqrqzl+/DiLFi1ixowZPR777W+tleluuummYfXz9Pe3PsgPp/c0ElxoHosMFZrHMhxoHvdi\n1iy4+96u3hxFhRhut/dhAwg9XE7o4XLMiAiYn2P1momN813MQ1ybs42aQzXggcmzJhMy6tL6tfT3\nPJ4wyeSNkiaWpoQSNtSWtZo9G+65D7O0BDZugKJCoqdNJ/rMz6r2lLX02QjsNRM71sXPcutod1uL\nNOxpCCBtbDTXTvRNv6Dh+v+xaZoUbS7qcWzazdMIjQ31UUTSn4brPJaRRfNYhgPN4/7h8wWs09LS\n7gZuAR4qLS094et4BPbu3QvAtGnTvMdM0+Tll1/mo48+Ijs7e1j+InZ0dPDuu+9SU1NDcHAwkydP\nZs6cOd6qIBEREZFLYrPBlKnW1tiIuSUXNm3AOH6sxzCjoQHWvgtr38WcMtXqNTNrNvjrzu9LcST3\nCKbHJPaq2EtOxgwEf7vBF6f1vE/NNM0e1eiDms0GU6+ytgYnBHf7Gb/9FmzZDNNnWPN3+owRU/WV\nEOHHg3Mi+HWBkzPrZr++t4m4UDvTRw+yfkFDWO3+WhqPNnr346bFKRkjIiIiQ9KVJmQaTv95vk9C\nYWeN6yEtLS0aq2/M+tLS0t9fYSz9asO/bjjvYyk3pTBmzhgAqgurKXv3/L1qrv5uV6udHb/bQVNN\nU6/j4mfHk3pzKgCN1Y0U/r7wvOec8zdzCB/Td2s4l5SUADB16lQKCgpYu3YtRUVFHD58mJSUFH74\nwx9e8PmrVq2isbHxgmO6S01NZcmSJVcScp84deoU3//+93scS0hI4KmnniI9Pd1HUYmIiMiwEB4O\nN34ObrjRqprZtAEKd2C4XD2GGSV7oWQvZliYVTWTsxDix/go6KGjzdlGTXENAMkLkz9jtO+5PSav\n7WkiyM/g81OG4FLAEWc1UTc9YLNh7NoJu3ZiOhyn5+8iiI31TYwDaProQG6dGsbre61rOxN4sbCB\nbyyIIiHC5/dADnmmaVK+vrzrgAHJiwb/77mIiIhIb6700+EhrM+b487z+JlPSefLUDwDRAI/SEtL\n636OqNN/xp4+fqK0tLT9CmOVi3SmQmbq1Kk888wzrFu3zvvY+PHj8ZynSe0Zq1evprq6+qJf75Zb\nbvF5QmbZsmXMnj2biRMnEhoaSlVVFWvWrOH111/n61//Or/97W9JTU31aYwiIiIyDBgGpE2xtqZG\nzK1brKqZmpqew5qaYN1aWLcWc3KKlZhJz4RA3XHfG291zLTBWR1ztsoGF5sqWvGYEBdmZ+64wdPv\n5rJ8+SFY/kVrPm/egHHsGLz3Drz3Dubd98KSa30dYb+7dkIwx5pcbDnSBkC72+RXBfV8Kyea8MAh\ntkTdIHOy5CTNx7v6LsXPjCc4eoj/zoiIiMiIZZim+dmjLiAtLa0ISAFiSktL27odtwNHgfbS0tKk\n8zy3nK6kzYVcU1pa+snFxuR0Oq/sTY0AF1oD8IYbbiAkJIQ33ngDt9tNY2MjBw8eZM2aNXz00UdM\nnjyZlStXDnTIPdx6662XlPRZunQpP/rRjy75df7zP/+Tl156icWLF/PMM89c8vOlf2ktSxkONI9l\nONA8vkKmCfvLrKqZ7QXnVM14hwUFQ1a21WsmKRl1Dbe0OdvY9sttmKZJ5iOZl52QGeh5vOlwKy/v\nbsRuwGNzI0mJCRiQ1+133vm8EXYUwD/+EyQkWI8d2G8tdXZmf5hxeUz+J6+e/bWd3mMTovx5fG4k\n/vaB+X0dbv8fmx6TghcKaD3VCoBhM8h6NIsgR5CPI5P+NNzmsYxMmscyHGgeXzyHw3HRH/b6on76\nt8B/AV/FWn7sjC8BcYB3Dai0tLQpWAmaQ6cPPQT0dsV0HfAE8F1g1+lNBkB1dTVOp5OMjAwA7HY7\nkZGRpKenk56ezn333UdZWRlVVVWMHTvWZ3GOHTuWgICLv2gdNWrUZb3O7bffzksvvURh4fmXjBMR\nERG5IoYBKanWdtfdmHlbraqZo0d7DmtrhY3rYeN6zHGJ1nJQ2XMhdGT3UfC4PEQmR+If4j8kqmPO\nWJgczLFmF58cauU32518MyeKuNBhsLxV9/l8z30Q1O2L8zWrMQ6XY06cZPWayRheVV9+NoOHMxw8\nu7mOky1uAA7VdbJqVyP3zwofOv2CBpHjnx73JmMAxswZo2SMiIiIDGl98Yn/eeA+4Nm0tLRkoACY\nBnwDK5HybLexe4FSYApAaWnpR72dMC0t7cy351supTJGrlz3/jG9iYiIACAk5PwXuwPRQ+a55567\npPGXKyrKWj2vra3tM0aKiIiI9IHQMLj2erjmOszyQ1aVQUE+RnvP1XuNyiPw8krMV9dAeoaVnElN\nG5FVMyExIcy4ZwYe94WX1R2Mlk8N42Szm93HO/jVNiffWBBFaMAwWt6qezLG5YKkJMyaaoyDB+Dg\nAcw1qyE725q/w6TqKzTAxlczHfx7bh1tLmvhhm1VbcSH2blx8shOnl4qj9vD4Y2Hvfs2PxuJOYk+\njEhERETkyl1xQqa0tLQzLS3tRuAHwB3A/wGOA78Bvl9aWtpypa8hA+dM/5gpU6ac85jT6aS4uJjJ\nkyd7ExW9GYo9ZM5n1y6rOMuX1UAiIiIyAhkGTJhobXeuwNy+DTZtxDh0sOcwlwvy8yA/DzM2zuo1\nM38BOCJ9FLjv2OxDL5FhMwwenBPBz7fUU9Xg4s2SJu6ZGeHrsPqHnx/c9wDccRfm9gLYvNFKzGxY\nDxvWY371UZiT4eso+0R8uB8PpUfwy3wnZ9bSfqu0mdFhfsyKHz4VQf3t2M5jtNV33RiXkJFAYJh+\nfiIiIjK09UlNfGlpaQNWRcw3PmPcRd3yVFpa+iLw4hUHJpfsTIXMunXryM7O9pbVd3Z28uMf/xiX\ny8W99957wXO88cYb/R5nXzp06BDx8fEEB/dsDHn06FGefdYq8Fq6dKkvQhMRERGxqgxyFkHOIsyj\nVbB5E2zdgtHc1GOYceI4vP4a5puvw/QZMD8HZsy0vggfhtrq2zjwwQGScpIIHxPu63AuW6CfVVHx\nVmkTt00N83U4/S8oyEoc5izErKqCzRthZxFcNb1rzOaNEBkFU68C29BLtAFMjQ3kjmlh/O+nXb+n\nfyh08vi8KCZE+fswsqHB4/JweFNXdYw9wE7ifFXHiIiIyNA3PK/O5LKdSci8+eab7Nu3j8zMTFpa\nWsjLy6Oqqoply5axbNkyH0fZt9atW8fKlSuZM2cO8fHxhISEUFVVxebNm2lvbycnJ4cvfelLvg5T\nREREBBLGwp0r4LbbMYuLrCqDvXt6DDE8HthZDDuLMcPDYe48mL8QhlnFb0VuBaf2ncLub2fKredW\ndw8lUcF2Hpjt8HUYA2/sWLjrbmtOn1murKMdXlmD0daKGRUNC3Ksqq9Rsb6N9TJcnRxMTaObTRVW\nD5RODzy/rZ5vLIhidJguxS+kekc1HY0d3v2xWWPxD1EiS0RERIY+fQoUr5qaGurr65k7dy5hYWEU\nFBSwatUqQkNDmTJlCo899hjXX3+9r8Psc5mZmVRUVFBaWkpxcTGtra2Eh4cza9YsbrrpJm6++WY1\n4BQREZHBxd8fMrMgMwvz5AnI3QxbNmPU1fUYZjQ2wgfr4IN1mMnjrcqEzGy4QD/AoaC1vpVjO4+B\nAUkLk3wdTp9yeUzW7G7kqtgAZo8ZIc3Lu3/Wdnvgxs9h5m7COHkS/voW/PUtzClTYcFCmD0HAgJ8\nF+slMAyDL04Lo7bVzZ4TVnKhpdPkuXwrKeMIsvs4wsHJ3eGmIrfCu+8X5Me4ueN8GJGIiIhI31FC\nRrzO9I/Jzs7m/vvv93E0Ayc9PZ309HRfhyEiIiJyeUbFwhdug2VfwPx0N2zZDMVFGG53j2HG4XI4\nXI75ysswO91KzqSmDckloY7kHsH0mMRNjyMkZmgnl85WWN3OliNtFFS1ER1sJylyhFUFBAfDzctg\n6c2YZfus5csKd2CU7IWSvZjfewoSh04Szm4zeCjdwX9traPC6QKgttXDL7c5+fq8SIL9h97vX387\nuv0onS2d3v1xc8fhF6SvLkRERGR40Kca8TqzXFlaWpqPIxERERGRS2azWT1jZsyEpkbMvDzI3YRR\nVdljmNHZCdvyYFseZnSMtRzU/BwYNcpHgV+a1rpu1TE5Q+eL+YuVmRDIvpNBbK1s41cFTr6xIIqY\nkBFYSWGzQdoUa2tpwdyWB4cO9kzG/OlFaxm/7HkQPnj7CAX6GXwtK5Kf59ZxosVKlFY1uPjNdieP\nZkfiZ1M1/hmuNhdHthzx7vuH+DM2a3gttygiIiIjmxIy4qWEjIiIiMgwERYO110P116HeaQCNm+C\nbXkYLS09hhm1p7qWhEqbYvXrmJ0OgYE+CvyzlX9SjukxGT1j9LCrjgFrmasVM8I51eKmrLaT5/Lr\neWJ+FOGBI7iSIiQEFl9jbWdUH8XYvAkA89X/tRKR8xfAjBlgH3yXueGBNh7NdvDz3DoaO0wA9p3q\n5KXiBu6fHYFNSyQDUJlfiavN5d1PXJCIPWAEJiRFRERk2BrBn+rlbCUlJYwZMwaHYwQ2FBUREREZ\njgwDkpLhnvvg3/4d8+GvYF41DbOXL3+N0hKM3/8W/uEb8MffQ9k+8Hh8EPT5tTe2c2r/KWx+NpIX\nJ/s6nH7jZzN4JNPB2Ag/jje7eX5bPe2uwfVv4XOjYjEf+RrmjJlgejCKCzGe/x/4zpPwysvQ1Ojr\nCM8RG+rH17IiCbB3/f4VHG3nzZJmH0Y1eHS2dFKVX+XdDwgLYMycMT6MSERERKTvDb5bh8Rn1q5d\n6+sQRERERKS/+PtDZra11Z7C3LoFcjdjnDzRY5jR3g65myF3M+aoUTB3PsxbALGxPgq8S2B4IFlf\nzaLxaCNBEcO74X2wv41Hs6yKigqni3f2NbP8qsG7LNeA8/eHjExrc9ZbS/Rt2YxRfRRz43r4/K1d\nYzs7rfGDQFKkP3+bHsGvCpx4rEIZPjzYgiPIxjUThl/F16U4svUI7o6u3ldJC5Ow+6s6RkRERIYX\nJWREREREREaa6JiejdNzN0PhdoyOjh7DjJMnu5Y0S0m1EjMZmRDku2RIYEQggRGDd0m1vuQIsvPY\n3EjeLWvh5tQwX4czeDki4cbPwQ03YlYchuqjXXO0sxO+922YOMlakm/adJ8vaXZVXCD3zgznz8Vd\nVTyv7WkiItBGRsLwTjSeT0dTB0cLjnr3Ax2BxM+K92FEIiIiIv1DCRkRERERkZGqe+P0e+7D3FEA\nW3IxyvadM9Qo2wdl+zBXr4T0dCs5kzbFOkc/c3e6OVlykrhpcRgjrAF6bKgfD8yO8O57TBMDq9eM\nnMUwIHm8tZ1RfggaGzGKCqGoEDM8HObOs+bvuERfRcrcccE42zy8Vdq1XNmfixsID7CROirAZ3H5\nSkVuBZ5uy/IlL0rGZtcK6yIiIjL8KCEjIiIiIiJWRcGChbBgIebJE7B1C2zdcu6SZp0dkLcV8rZi\nRkV1LWkW3393s1flV1G+vpy6g3VMuXVKv73OYNfpNvljUQNjI/xYmhLq63CGhpRU+PEzmHlbrCXN\namrgg3XwwTrMcYnw99+EUN9UH90wKYT6Ng8bD7cC4PLAC9udPDE/irERI+dSva2hjerCau9+cHQw\no6eP9mFEIiIiIv1n5HzKExERERGRizMqFpZ9AW75POb+MtiSCzsKMNraegwz6urgvXfgvXcwx0+w\nKg8ysyG873qddDR1UJFbATDilzA6WNdJcU07RTXthAfayEkK9nVIQ0NkJHzuJrhxKWb5IWs+F+SD\nxwMh3RJbu3dBaioEDMySeIZh8MVpYTS0eyiuaQegzWXyy/x6vpETRXTwyOifUrGpAtNteveTr04e\ncZVwIiIiMnIoISMiIiIiIr0zDKvCICUV7r4Hs7AQtuZCyV4M0+w5tPwQlB/CfGUNTJtmVc7MnAUB\nV7b8UvmGcjydHmJSY4gcH3lF5xrq0kYFcNf0cF7e3cjLuxoJ9TeYPWZk9hy5LIYBEyZa250roK7W\nOgZw/BjGf/8nZlAQpGdY8zcltd+X5LMZBg/MjuB/8uo5WNcJgLPdwy/z63lifhShAcN72a7WulZq\nimu8+6GxocROjfVhRCIiIiL9SwkZERERERH5bAGBVgXM3HlQW4uZv9XqN3Ospscww+OGXTth107M\noODTX27Pu6wvt5uONVFTVINhM5hwzYS+fDdD1sLkYBo7PLyzr5k/FDUQGmAjJWbk9Ry5Yv7+ENdt\nWazmZswJEzEOHYTczZC7GTM6GrLnwbz5ED+m30IJsBt8NcvBz3PrqGlyA1DT5ObXBU4emxtJgH34\nVosc+ugQdMvtJi9OVn8kERERGdaG9+02IiIiIiLS96KjYenN8IN/xvz2dzEXX4PZSx8Oo60VI3cT\nxs+fhe99B/7yKhw9elEvYZomBz84CEBCRgIhMSF9+haGsqWTQ1iUHIzLA78ucFLp7PR1SEPfhInw\n7e9i/uBfMG9ehhkdg1Fbi/HeO/D0P0N7e7++fIi/jUezI4kM6rpEP1jXyR8KnXjOqkYbLmoP1nKy\n9KR3PzwhnJiUGB9GJCIiItL/VCEjIiIiIiKXp/sSUHetwPx0N2zdCjuLMFyunkPramHtu7D2Xcyk\nJKvyIGsuOBy9nrruUB31h+vxC/IjaWHSQLybIeNM75GmDg+F1e28f6CFh9J7/znKJYqPhy/cBsu+\nYPVPytsCNjsEnu4r43LB738Ds+fAzNldx/tAdLCdR7Mi+Y8tdbS6rCTMzmMdvLK7ibumhw2ryhGP\n28OB9w/0ODbphknD6j2KiIiI9EYJGRERERERuXJ2P+sL6pmzobUFc8d22LoFo2zfOUONigqoqMB8\n9RWYehVkZcPsdAjualIfmRzJ5M9NxrAb+Af7D+Q7GRJshsH9syJICG/huomqHupzNhukpllbd7t3\nYWwvgO0FmIGBMGu2lVycehXY7Vf8sgkRfjyS6eC5/HpcHuvYpopWgvwNvpAWOmwSFlX5VbTWtnr3\nR88aTcTYCB9GJCIiIjIwlJAREREREZG+FRwCOYsgZxHmqVOwLc9KztRU9xhmmCbs+RT2fIr50p9g\n5iyramb6DGz+/iRkJPjoDQwN/naDpSmh3n23x8TlMQn008rU/WbyZMy774W8rVa/mfw8yM/DDA+H\njCy4406rP80VSIkJ4P5ZEbxY2OBtr/LBgRb8bHBL6rlLAw417Y3tHN502LtvD7QzYYl6RImIiMjI\noISMiIiIiIj0n5gYq9/M527CrDgMeVthWx5GY2OPYYbLBTu2w47tmEHBkJ5uJWfSpljVCnJBHW6T\n3+9w0u4yeTQ7Ev9h3Ajep8LCYcm1sORazBPHvQkZ41gNZsle8Ot2iX3qlDX/L0N6QhBNHR5e+bTJ\ne+y9shbsRs8k3FB08MODeDo93v3xV48nIDTAhxGJiIiIDBwlZEREREREpP8ZBiSPt7Y77sTcu8eq\nnCkqxDirYbrR1gq5myF3M2aEAzKzrGXNxk+wziPnaOrwUOF00dDu4Q9FDTyUHoFNP6v+FRsHt3we\nbl5mJRubm7vm58kTGP/vHzGTkiF7rjV/HZGXdPqrx4fgNuG1PV1Jmb/ua8ZugxsmDc2kTP3hek7s\nOeHdD40LVSWciIiIjChKyIiIiIiIyMCy22H6DGvraMfcWQz5+fDpLgy3u8dQo8EJH30AH32AGRtr\nVc1kZcMYfYnbXXSwnceyrYbwxTXtrNzZyL0zw5WUGQhnko3dHa3CDArCqDgMFYetfkmpaZCZDXPS\nIezilh67ZkIIbo/JGyXN3mNvljRjNwyuHWK9gzxuD/vf39/j2OQbJ2PYNEdFRERk5FBCRs6ro6OD\nlStXsnbtWiorKwFISkrirrvu4tZbb/VxdCIiIiIyLAQEWl9SZ2ZTsmo7tl2FjDOqCKmttHrMdGOc\nOAHvvA3vvI05LtGqnMnIgthYHwU/uCRE+PHVLKshfF5lG4CSMr4yczb89GeYu3Zay5p9ugujtARK\nS6zkzDM/u+heM9dPCsXtgbf3dSVl/rK3CT+bVUUzVFRvr6blRIt3P25aHI4khw8jEhERERl4SshI\nrzo7O3n88ccpLCwkNTWV5cuX097ezvvvv8/TTz9NXFwc8+fPH7B4PvzwQ3bs2MG+ffvYv38/zc3N\nLF26lB/96EcDFsNAG4nvWUREREau+vJ6jh9qxhY1heSv3Q+uFszt26z+HBWHzxlvVB6ByiPw+muY\nyeOtxExmJkRfXs+O4WJSdABfy4rk+W1WUsYE7lNSxjcCAiAj09paWjCLCqEgH0JCu5IxLhf88fcw\naw7MmGElKHvxuZRQ3KbJu2VdCY1XPm3CbjPISQoeiHdzRTqaOijfWO7dtwfYmXDtBN8FJCIiIuIj\nSshIr1avXk1hYSHLly/nO9/5DsbpC7g5c+bw1FNPUVxcPKAJmd/97neUlZUREhJCXFwczc3Nn/2k\nIW4kvmcREREZmUyPyYEPDwCQOD+RwPBAIBCuvxGuvxGzpsbqN7MtH+P4sXOebxwuh8Pl8NormBMn\nWcmZjEyIvLSeHcNFSkxXUqap3YPbAza7r6Ma4UJCYEGOtXm6Gtqzdw9Gfh7k52EGBlqVNVlZMHXa\nORU0N6WE4vLAugNdSZnVuxqxGTA/cXAnZQ59fAh3e9dyhMmLkk//nouIiIiMLErISK9ee+01goKC\neOKJJ7zJGAC73bqSczgGtrT87//+74mLiyMxMZEdO3bw6KOPDujr+8JIfM8iIiIyMh3bfYzmY80E\nhAcwbu64cwfEx8Pnb4VlX7Cap2/Lg+0FGHV15ww1Dh6Agwcw//dlmJxiJWbSMyBiZC2NlBITwBPz\no4gP88PfruqYQcVm6/p7cjLmnSugYBvGoYOnE495mCEhMDsd7r7HWzVjGAafTwvF7TH56FCr9xSr\ndjbiZxhkjQsa6HdyUZyVTo7t6kqkhsSEkJCpHlAiIiIyMikhI+eorq6mqqqKRYsWERzc806rDz/8\nEIDMzMwBjam/X8/lcvHKK6/w9ttvU1FRgcPh4Nprr+Xxxx/H7XZz2223kZWVxT//8z/3axzdDfTP\nWERERMRXQmNDiRgXwZj0Mdj9L1DKcaZ5evJ4uP1OzIMHYPs22L4do8HZc6hpQtk+KNuH+fKq0w3V\ns043VA/v1/czWCQ6uiosOt0mGw+3smRCsJYvG0wiHHDdDXDdDZgnTljzeVs+RlUl5oH94B/QNfbg\nAYzk8dw2NQy3CevLraSMCfypuAGbDSJ88y7Oy/SYHFh7oMexSTdOwma3necZIiIiIsObEjIX699/\n6usILuyb/9Bnp9q7dy8A06ZN8x4zTZOXX36Zjz76iOzsbFJSUvrs9XzN6XTy9a9/nT179rBw4ULm\nzZvHpk2bWL16NXFxcRiGgdPp5Ctf+YqvQxUREREZlsLHhDPr/lmX9iSbzaqAmZwCd96Nub8MCrZB\n4XaMxsYeQw3ThDMN1Ve9BGlTrKqZWXMgYrB9hd0//lTcQGF1O5UNnXxpVoSSMoNRbCwsvRmW3ox5\n9Cg0NlhJSIBTpzB++mPMsDCM2encMScDd+I4Nh1pB6ykzB+LGlga78fkcJfv3sNZqguraTrW5N0f\nNWUUUROifBiRiIiIiG8pIXORjLJ9vg7hgsw+PFdJSQkAU6dOpaCggLVr11JUVMThw4dJSUnhhz/8\n4QWfv2rVKhrPugi+kNTUVJYsWXIlIV+R733ve+zZs4dvfvObrFixAoD777+fZcuWkZuby6FDh1i2\nbBmJiYnnPcdQe88iIiIig4HH7fHeKW9cSYLAZrMqYFLTYMU9mPtKreRM0Q6Ms/rwGR4P7N0De/dg\nrvwzpKRCegZ2RxTusLAreTuD2uLxwew53sG2qnZMs4H7ZyspM6glJADdlvWqq8UcHY9xrAY2bcDY\ntIE7Q8NwL7ifLUHWdYrHhPeqQ7jZaGEw3D7X2dJJ+fpy777N38bE6yb6LiARERGRQUAJGTnHmQqZ\nqVOn8swzz7Bu3TrvY+PHj8fTvQllL1avXk11dfVFv94tt9zis+REfn4++fn5zJ49m7vuust7PDIy\nkjFjxlBQUEBAQAAPP/zwBc8zlN6ziIiIyGCx76/7cHe4mXT9JIIi+6j/hd0OU6+ytnvvw9y710rO\nFBditLb2GGqYJuwrhX2lTARax46DBQutZc2io/smnkFiUnQAf5ft4Ll8JwVH24EGvjQrArtNSZkh\nYXIK/OCfMY9WwfYC2FGAvaaGe9Y9j3vOF8kfNwcADwbvHA1h3Nh2psUF+jTkQ58cwtXWVa2TtCCJ\nIMfg7HMjIiIiMlCUkLlIZkqqr0MYMCUlJYwZM4bIyEh+9KMf8eSTT3Lw4EHWrFnDunXrOHToECtX\nrjzv8994440BjPbKvPPOOwDcc88959yVGRBgrde8fPlyRo8efcHzDKX3LCIiIjIYNB5t5Pju4xh2\no//umrf7wfQZ1tbZibn3U9ixHYqLzk3OACFVlfDKanhlNeaEidayZnMyYNSo/olvgE08Kylj0sD9\nSsoMHYYBY8dZ2+dvxTx6FGNHAfe11uFJCDydaLOSMr/Jr+Ur8Y1MnT0R/Ab+sr/xaCM1RTXe/aCo\nIMbNHTfgcYiIiIgMNkrIXKw+7NEymFVXV+N0OsnIyADAbrcTGRlJeno66enp3HfffZSVlVFVVcXY\nsWN9HO2VKywsxM/Pj/nz5/f6eFBQEA8++ODABiUiIiIyzHncHsrWlgEwNmsswVHB/f+i/v4wc7a1\nuVyYJXtPJ2cKz1nWDMA4dBAOHYRXX8FMHm8lZ2anw/9n777D4yrPhP9/zxTNaDTSqPdiyZJGDwxl\n6wAAIABJREFUltwrxjbFGEIxGBNCAgmbsll2k1Cyyab8su9LINm87L5pu5uQcmWTZa83wYAJEAIE\n42BjMAaMe5E0Vu9do1EZaer5/XFGGsmSbRlb1ffnup5rNOc855nn2MfyzLnnfu4LfFFnttOCMrH8\n8sMeDjd7yLYNsjnPMtPTEhdLUSAjAzIy0AGfCaoEVK1OEIBf0fOb5igeeO0/KcqI1rK+ShaDaeqz\nZlRVpfKNyjHb8m/KR2fQTflrCyGEEELMdhKQEWOMrh8zkZhQ0VOL5dwf2uZKPZWhoSFaW1vJzMzE\nbB6bOt/U1ERdXR1LliwhISHhgmPNlXMWQgghhJgNGt5roL+lH1OMiewN2dM/AcOozJnAZ1DPnMG1\ndw/WijMYBt3juit1tVBXCy/+ETUtHZav0Fp2Trjo+hySF2/ky2tjeavWzaacaQiGiSmn1yl8dnkM\nrt5mqgeMAPj0Rn614lN89shOVn74S1SjER77F5jE55tL0Xq8lb7m8GejhIIE4hfOryUAhRBCCCE+\nKgnIiDGG68cUFRWN2+dyuTh+/Dj5+fnExcWdc4y5Uk/F4/GgquqEBWR/+tOf4vV6MUwyvX+unLMQ\nQgghxEzrb+unfn89AIW3FWIwzfBHEr0BFhXTbjDSfsONFKBqmTNHj6D0usZ1V1qaoaUZ/vIqalw8\nLF8Oy1ZAQaFWv2aOyI0zkhtnG3nuC6joFGT5sjlMr1O4Jd3Nq80WakNBmYDOwH+v/hR9zdlcU//h\n2NpIzz0DqWmwbDnYbOcY9eL4Bn3U7q0dea7oFfK2TNGShEIIIYQQc5AEZMQYwxkyu3fvZu3atSPB\nCp/PxxNPPIHf7+e+++477xizpZ7K448/zquvvsqjjz7K1q1bx+2PiYnBYrHQ2NhIRUUFBQUFADz/\n/PO8/fbbAJPOepkt5yyEEEIIMZsF/UEcLztQgyrpq9KJyz33l3xmhE4HBQVgL4JP3otaXRUKzhxG\ncTrHdVec3bB3D+zdgxoVBUuWaZkzxcUQMbMF1S+GL6Dym8MuzAYty0KCMnOXXoFb09y8N5A8snyZ\nisLO9A30bdzMrWj1knA6Ufb8Vdu/4/ewMD+U+bXykmom1b1dh2/QN/I8a33W9CxJKIQQQggxR0hA\nRowxHJB5+eWXOXPmDKtXr8btdvPBBx/Q1NTE1q1bJwxuTLW33nqLffv2AdDV1QXAyZMnefzxxwGI\njY3lkUceGXNMMBgEtDo4E1EUhdtuu42dO3fy4IMPcsMNN9DV1cVbb73FNddcw8DAAIcPH+aJJ55g\n27ZtFBcXT9XpTeijnLMQQgghxKymQHxBPMFgkNzrc2d6Nuen00F+gdbuvge1rhaOHYVjR1HaWsd1\nVwYG4P0D8P4BVGMEFJfAihWwZClEWad//hehYyBAjdPHkF8lqPby2eUxGPUSlJmrDDr43IoYrBH9\nvFM3OLL99WoP/f5+PrHYii4yEvVvPgdHj0BZKUplBVRWwPPPoWZlw+e/COnpF/W6/W39NB9pHnlu\nspnIWp91uU5LCCGEEGJekICMGNHa2kpPTw/r1q3DarVy6NAhduzYQVRUFEVFRXzlK19hy5YtMzK3\nM2fO8Oqrr47Z1tTURFNTEwBpaWnjghNVVVVERUWxYcOGc4778MMPExERwe7du3nxxReJiYnh3nvv\n5cEHH8ThcPDYY4/x4osvsnnz5st/UhfwUc5ZCCGEEGI20+l15F6XS87GnLlV4Fung9w8rW3/OGpr\nixacOXpEqy9zFsXnheNH4fhRVJ1OW85s6TJYuhySkqZ//heQHmPgK2tjefJgD8dbPfziYA9/t9qG\nxTiH/o7EGDpF4RMlVqwROv5SMTCyfX/9IP3eIH+zPAbj1Rvh6o0wNIR66iQcOwInT0BzE8TFhgf7\n4H2IiYHCQm2JvwmoqkrlrkpQw9sWblmI3jh3lvETQgghhJgOiqqqF+41x7hcrvl3UpdZRUUFwMgy\nXQB79+7lW9/6Fg899BD333//TE3tsujr6+PGG2/kvvvu4+GHH57p6YgpMtF1LMRcI9exmA/kOhYX\nEvAFCPqCGC3GmZ7KOX3k69jZDcePaQGaMw6UUJb2uajp6drSZsuWw4JcLdgzSzT2+vjVQRcuT5BU\nq54vrY0lPlJuqM8lE13H79S52Xmqf3SshMIEI19cZSPy7KCbzwcN9ZC3UHseDMI3v4bS348aGQkl\nS7Rrt2QxWCwjh7WdasPxsmPkeVxeHIs/uXjCep1CXIi8rxDzgVzHYj6Q63jybDbbpN/0SIaMGDG8\nXJndbp/hmVy6Y8eOYTAYLljvRgghhBBCTL3at2rpKO3Avs1O3IJZVjfmUsXFw3WbtTbQj3oylGlw\n+rSWKXMWpbkZmpth119Qo6O1Jc2WLINFxWA2z8AJhGXGGPnahjh+ebCH1v4AP37XydeujiPBIkGZ\nuWxTjgVrhI7/OdpLIBSVOdPl42fv9/APa2OJMY0KyhiN4WAMgNcLG69BPXFMu3YPHYRDB1F1ei1j\n5o478SRlUr27euQQRaew8MaFEowRQgghhJiABGTEiPkUkNm0aRP79++f6WkIIYQQQlzxemp7aPqw\nCUWnYDDN848fUVa4ar3WvB7U0lItc+bUCZT+/nHdlb4+OPAuHHgX1WAAe5GWfbBkqRbomQHxkXr+\n8eo4fnPIhdmgEGuePRk84qNbkWbGYtTxm0MuPKGoTEOvn38/4OTL62JJPFfQzWyGO++CO+9C7WjX\nssGOH4PKCpTyMoLb7qL85XJ8g76RQzLXZmBJsEw8nhBCCCHEFW6efyISF6O8vJy0tDRsNttMT0UI\nIYQQQswDfo8fx6vaMkbZG7KJToue4RlNowgTLF+htWAQtaYaThyDEydQWprHdVf8fjh9SmuAmp2t\nZc4sWQrZOdO6tJnFqOPLa2NRAb1Oy3IIBNWRn8XcZE+M4OH1sfzyYA/9Xi0o0+EO8NMDTr68NpaM\nmAvcHkhKhi03aa2/H7XsNA1NOlx1rpEuUV4n2bv+DE0lsHjprMj8EkIIIYSYTSQgI0bs2rVrpqcg\nhBBCCCHmkeo3q/G4PFhTrWRdnTXT05k5Oh0szNfa9ru1TIMTx7VWUYESDIw7RKmvh/p6ePXP2tJm\nJYth8RJYVAJRUVM+ZaM+HHzxBVR+/kEPxUkR3JRvkaWo5rBsm5F/XB/Hkwd76B7U6h31eoL8x3tO\nHlhtIz8hYnIDWa24Uouo/f3xkU06JUiR7xgGlxPe3Q/v7tcyvwoK4YYbtetXCCGEEOIKJwEZIYQQ\nQgghxGXXXdVN67FWFL2C/XY7Or0sfTUiKVm7QX3DjeB2o54+pQVnTp9EcbvHdVf6+uD99+D991B1\nOq3Gx+IlWsvIhCkOkJzp8lLj9FHt9OEcCvCJkmjJlpnDkq0Gvna1FpRp6dOCgYN+lScP9vD5FTaW\nppouOIZv0Ef5n8pBDW9beLOdqOXXojY1wskTWqupRikrRV13VbhjUxP090F+PujlloQQQgghrizy\n7kcIIYQQQghxWQX9Qc68dgaABdcuICpp6jM65iyLBdas1VrAj1pZOZI9o3S0j+uuBINQWaG1l15A\njY0LB2eKFk3J8lAlySb+dpWN/znq4t36IXqGgnx+hQ2TQYIyc5XNrOer6+P49Ycuqp1a/Rd/EP7r\nsIt7l0azPivynMeqqkrFaxV4ej0j2xKLEkldnqoFBzOztHbLbdDfpwUcSxaHB3hrD8o7+1DNkVBc\nAkuWQMkSiImZsvMVQgghhJgtJCAjhBBCCCGEuKx0Bh32rXZaj7WSuTZzpqczd+gNYC/S2t33oLa3\nwamTWqs4o9WZOYvS44T9b8P+t1H1em15qMVLtBvgqWmXLXtmWaqJB9fF8etDPZxu9/Kf7zv5hzWx\nRJsk82mushh1fGVdLP99xMWpdi+gJbw8faIP11CQj51jebqWoy10OjpHnptsJgpvLZx4KTtrNKxb\nP3ZbYiJqahpKawscOQRHDqEqilYracNGuOa6y3iWQgghhBCziwRkhBBCCCGEEJddXG4ccblxMz2N\nuUtRICVVazfcCENDqI7yUIDmBIrTOf6QQADKy7T2/HOocfFQXAzFi7XsmUusPZMXb+RrV8fxy4M9\n1Lv8/ORAN/+4Po4Ys/6SxhUzJ0Kv8MVVNnac7OODxqGR7a+eGaCp189nlkVjMoSDbgPtA1T/tTo8\ngAKLti3CYL6IWwsfuwU+dgtqZwecPAknj8MZB0pdLWpRUbhfdzeUlWpZNHHyu0QIIYQQ88NlCcjY\n7fZ44LvAnUAa0Am8Bvxvh8PRMonjN4aOXwuYgQbgj8D3HQ5H/+WYoxBCCCGEEGJqeQe8uLvcxGbH\nzvRU5h+zGZYt15qqojY3w6kTWoCmqlJbyuwsirM7XFxdUWBBrnZzu2Qx5CwA/cUHUlJC9Ud+dchF\nokWPVTJk5jy9TuHTS6OJjtDx1+pwDaNjrR7a+v383WobSVEGAr4AZS+VEfSHr7UF1y4gJvMjLjWW\nmATXb9aa14NaUQEJieH9x4+iPLsDADUjQwssliyGhflgNH601xRCCCGEmGGXHJCx2+2RwFtAEfBz\n4BBQAPwTsNlut69yOBzjv74VPv7TwO8BB1pQphfYCnwT2GS32zc6HI7xny6EEEIIIYQQs4aqqlT8\npYKuM10U3FJA2oq0mZ7S/KUokJGhtY/dAm43almpFqA5fQqlt3f8IaoKNdVae/XPqBYL2BeFAjQl\nEJ8w6ZePMet55KpYdIqCLrRMVSCootdJTZm5SlEUti2yEhep44+l/QRVbXtLf4Af7nfyN8tjiDhc\nh7szHLCJXRBL1vqsyzOBCNPYOjMAiUmoS5eDowylqQmammD3LlSTCZYsgy8+cHleWwghhBBiGl2O\nDJmvAkuArzgcjl8Mb7Tb7ceBF4H/DXxtogPtdrsJ+CVaRsw6h8PhCu36nd1ufxEt4+ZmtGwbIYQQ\nQgghxCzVfrqdrjNd6CP0xOXJ8kLTymKBVau1FgyiNjZA6Wk4fQqqqlCCgXGHKG43HD2sNUBNTdUy\nEBYVa3VozObzvuToZaw8fpWff+BkSYqJLQstI0EaMfdcs8BCeoyB3x120efVojKDfpVX/9rA+rrW\nkX5GixH7HfaJ68ZcLkuWas3vR62q1K7n0ydRmppQPeHl1fD54PnnQvWX7BBlnbo5CSGEEEJcossR\nkPkbYAD47Vnb/wQ0Ap+x2+1fdzgc6gTHpgIvAB+MCsYMew0tILMUCcgIIYQQQggxa3l6PVTuqgRg\n4Y0LMdvOfzNfTCGdTiuOnp0DN98arj1TehpKT6N0tE94mNLaCq2tsOevqDo95OVpdWeKFkFuLujP\n/dHxdLuH2h4/tT1+apw+7l8eg8UoS5nNVfnxEXxzUzy/PeyitsePxetlVUPrmD722+2YrKbpmZDB\nEAq2FMFdd6M6nTA0GN5fVYmyby/s26stzZedowUWFxVD3kJZ3kwIIYQQs4qiqhPFSSbHbrfHAC7g\nHYfDcc0E+/8I3AUsdDgc1Wfvv8DY/wT8kLMybybD5XJNeFIVFRUXM4wQQgghhBDiAlRVxfmOE0+b\nB1OaibgNcVP7rXlxSYw9PVhqa4iqrSGyoQ6913vBY4LGCNxZWbizc3BnL8CbmKgtmzZKTb+BN1oj\n8QR1xBiC3JLuJsU8PjNHzB3+IOxrNZNytIUEdzgjpS4llsKrooiPmB0rixtcLmLKTmOpqyWyuWlM\nPaWgwUjN3z5AwCpZM0IIIYS4dAUFBRNut9lsk/4AdKkZMjmhx8Zz7K8PPeYBkw7I2O32COALgBt4\n6SPPTgghhBBCCDGlBmsG8bR5UIwKtlU2CcbMcr7YWFzLV+BavgICASJbmkcCNKa2Vib629P5vFir\nq7BWVwHgt1hCwZkc3DkL8MfYyLX6uTenn9eaLbR7DOxsiOLapCEW27xnx27EHGHQwZqudgZGBWO6\nI818mJzC0Xq4KdXNQqt/Bmeo8dtsdF91Nd1XXY3i9RLZ1EBUXS2WuloUn49AVNRI34znnyVgseDO\nWYA7ewH+6OgZnLkQQgghrkSXGpAZfvfiPsf+gbP6XZDdbtcBvwEWAV93OBzNH316Y50rgnUlGs4W\nkj8TMZfJdSzmA7mOxXwg1/GVSw2qHH5Lq0Fiv9VOcknyDM/oo7tir+OiovDP/X2oDgeUl0JZGUpn\nx4SHGNxuYsrLiCkvA0BNSoKiYrDbWboqiRcadeyvH2RveyTFuWkUJUZMx5kILu917Kxx0lLeMvLc\nr9Pxfk46qk7BF4RXm6O4Od/CLYVRs6tuUElJ+GePhwJTaGm1XhdKXS0AMWWlAKgpKVAYWg5t0SKp\nPzNLXLG/j8W8ItexmA/kOp4al6OGzGVjt9sjgafRasc86XA4fjLDUxJCCCGEEEKcg6JTWHrvUlqP\nt5JUnDTT0xGXyhoNq1ZrDVA7O6C8DMrLwVGG0tc34WFKRwd07IN39hEBfDI1jesz8qlIyMVuXAZI\nQGau8Q54cbzsGLMt72P5JA+aqHH6Rra9XummodfP38zWukGmUXVuomNQH30cysq0oOMZB0pbG7S1\nwTv7UL/0ICxbrvXt6gKzGUZl1wghhBBCXA6XGpDpDT2e612K9ax+52S325OAl4GrgO87HI5HL3Fu\nQgghhBBCiCkQDATR6bWbrxHWCLI3ZM/wjMSUSEyCjUmw8RoIBlGbm7QATVkpVFageDwTHqa0tpDS\n2kIK78AboKalM5hbQGv6QnLXLoaYmGk+EXExVFXF8YoD70C4vlDK0hQWrEjl4aDKH0/3s79+cGTf\n6XYvP3rXyd+tspEWPau+8zmWokB6htZu2AIBP2pdHZxxgKMcCgrDfV/8Ixz+EDKztOwZexHkF0Bk\n5MzNXwghhBDzwqW+W6oBVCDzHPuHa8xUnG8Qu92eArwD5AKfdzgcT13ivMRl4PV6efrpp9m1axeN\njVqZoOzsbO655x62bds2w7MTQgghhBAzIRgIcvq500SlRJF7fa7UjLlS6HTazenMLNhyE/j9qDXV\noQyaMqipQQkGJjxUaWnG0tJMHvvgeS1AQ6E93KSOx6zSdLAJZ5Vz5HlkfCT5N+UDYNApfHJJNNmx\nBp471Yc/qPXpGAjwo3edfGZZNCvSzDMx7YunN0DeQq3dfOvYfcEg6PUoDfXQUA9/fQNVp4OcBbDp\nWrh6w4xMWQghhBBz3yUFZBwOx4Ddbj8BrLTb7WaHwzFS7c9ut+uBq4EGh8NRf64x7HZ7DPA6kA3c\n4XA4/nIpcxKXh8/n46GHHuLo0aMUFhayfft2PB4Pb7zxBj/4wQ9ITk5m/fr10zafn/3sZ5SVlVFf\nX4/L5cJkMpGamsq1117LJz7xCWJjY6dtLvNBT08Pb731Fu+++y5VVVV0dHRgMBjIz89n69at3H77\n7eh0s3DJASGEEELMKFVVqdxVibPGSX9bPxlrMjBFmy58oJh/DAYto6CgEG7fBh4PalWllm1wxgG1\ntecN0NDSDPv2AqEATX6B1goKID5hOs9EjNLX0kfN3pqR54peYdH2Regj9GP6rc+KJC3awG8Pu+gZ\n0qIy3oDK7470cnWWl+3FVsyGOfx54oF/AK8HtToUdDzjgNoalJpq1KXLwv0a6uH997R/B/kFYJUa\nNEIIIYQ4v8uRT/xb4D+Bvwf+Y9T2zwDJwHeHN9jt9iLA43A4akb1+w9gOXCXBGNmj2eeeYajR4+y\nfft2vv3tb49883HFihU8+uijHD9+fFoDMjt27KCoqIh169YRFxfH4OAgp06d4je/+Q0vvfQSv/vd\n70hJSZm2+cx1b775Jv/2b/9GYmIiq1atIjU1le7ubvbu3csPfvAD3nvvPZ544gn5xqsQQgghxmh4\nr4HWY63oDDpKPlEiwRgRZjJBcYnWAIaGxgZo6mpRgsEJDx0J0LyzDwA1Pj4UoAnd5E5L05abElPK\n5/ZR9lIZalAd2Za3OQ9rysRBhgWxRr6xMZ7/PuKisjtcV+ZAwxDlnV4+syyGgoQ5XD8owgRFi7QG\n2jVdWQGjP3eePoXy5m54czcAanpGKFBZoD3a5IuDQgghhBjrcgRkfgV8GviR3W7PAQ4BJcDXgJPA\nj0b1LQMcQBGA3W5fCnwWKAX0drv97gnG73A4HPsuwzzFRXjhhRcwm8189atfHXNTXq/Xvhlls9mm\ndT579+7FZBr/gf8Xv/gFTz31FE899RTf+ta3pnVOc1l2djY//vGP2bBhw5hMmC996Ut8/vOfZ8+e\nPezdu5fNmzfP4CyFEEIIMZu0n26n9q1aAIruKCImQ+qAiPMwm6FksdZgJEDjLSvHebyUpM5G9Oo5\nAjTd3XDwA60BapQV8vPDWTTZ2dpyU+Ky8Xv8nHz2JEPOkUUviC+IJ311+nmPizHpeHBdLC+V9fNW\nbbiuTPdgkJ+938N1uZFstVuJ0M+DgJrZDIuXjN1WXILq9ULFGaipRmluguYm2LcX1WaDf/1ROJjY\n0wOysoMQQghxxbvkd7EOh8Nnt9tvAh4DPg48CLQD/wV81+FwuM9z+EpAAYqBnefosw+47lLnKSav\npaWFpqYmNm3aRORZRQvffPNNAFavXj2tc5ooGAOwZcsWnnrqKRoaGi5pfL/fz86dO3nllVeor6/H\nZrOxefNmHnroIQKBAHfeeSdr1qzh+9///iW9zmyxZs2aCbcnJiZy11138ctf/pLDhw9LQEYIIYQQ\nALjqXThecQCQtyWPxKLEGZ6RmHNCAZqIksUkfVxl9+luqj8s43ZdI5ltNVoGTeAcS5wN9MPxY1oD\n1IgIre5HfoH2mJsnxdYvQcAX4NRzp+hv6R/ZFhEdgf02+6Qy5vU6hY+XRLMoKYKnT/Th8miBNhXY\nWzNIabuX+5fHkBNrnKpTmDnZOVoD8PlQ62q1jLDKCoiLCwdj3G74/76hBWQW5odbRibo9eccXggh\nhBDzz2X5WpHD4ehFy4j52gX6KWc9fwp46nLMYar9x3vOC3eaQY+sj7tsY5WVlQFQUlIysk1VVZ59\n9ln27NnD2rVrKSgouGyvdyneeecdAPLz8z/yGC6Xi0ceeYTS0lI2btzIVVddxf79+3nmmWdITk5G\nURRcLhcPPPDA5Zr2rGYwaL8W9PLBQAghhBBo7wOr91ajBlTSV6WTsSZjpqck5jidovCxxQk0ZV9F\nerReu2nt9dJ6uoLk5mqUqkqoqkTxeCY8XvF6tboe5drnFlVRID1DC84sDBVpT0qWZc4mIegPUvp8\nKb0NvSPbjJFGlt67FKPl4gIoxckmvnOtkZ2n+jjUHP67axsI8JMDTm5caOHmgigMunn692I0hrO4\nztbeBpGRKE4nHPpQa4BqMmkBxU99GlJTp3nCQgghhJgJkuc9SaPXxJ3vysvLAVi0aBGHDh1i165d\nHDt2jLq6OgoKCnj88cfPe/yOHTvo6+ub9OsVFhZy3XXXTarv73//e9xuN/39/ZSVlXH8+HHy8/P5\n7Gc/O+nXO9s///M/U1payte//nU++clPAnD//fezdetWDhw4QE1NDVu3biUrK+ucY0zlOU8nv9/P\na6+9BjCtNYKEEEIIMXspisLiTyym6cMmcjblSI05cdlkxIQ/jrb7dPxbaxIZsWnc9/lbSLMoqI0N\nWqZBqCnneL+tqCo0NWptuA5NdLQWmBluOQsgYg7XM5kCalCl7KUynDXhLx/qTXqW3LsES6LlI41p\nMer47Aoby1KHePZUH/1erR5NUIVdlW5Oh7Jl0qOvsFsRC3LhR/+O2toCoYAjVZUoHR1QXoYaFRXu\n+/JLMDAQzqKJj5fgohBCCDGPXGHvgsRkDGfILFq0iB/+8Ifs3r17ZN+CBQsInqMY57BnnnmGlpaW\nSb/ebbfddlEBme7u7pHn69ev59FHHyUu7qNlCB08eJCDBw+yfPly7rnnnpHtsbGxpKWlcejQISIi\nIvjiF7943nGm8pyn05NPPklVVRUbNmyQgIwQQghxhQsGgig6BUVRMFqMLLh2wUxPScxjvZ4gFqOO\n2h4//3d/NzcXRLElLwd9zgK44UZQVdS2Nqg8Ew7QdHaeczylr2/sMmc6vVZ7ZiRIkwdxV+6NblVV\ncbzioOtM18g2nVHH4k8uxppqveTxl6eZyYuP4JmTvZxs845sb+z188P93dxWGMXmPAu6K+nPX6fT\nMrnSM2DTtQCoLhc01EN0dLjfwfe1a3vfXq1PbFz4mi0u0Y4XQgghxJwlAZlJyo+fh+vdnkN5eTlp\naWnExsbyve99j2984xtUV1fz3HPPsXv3bmpqanj66afPefyf/vSnKZvb66+/DkBXVxcnTpzgySef\n5P777+cnP/kJRUVFFz3ecDbIvffeO+7bnhGhb9Bt376dlJSU844zlecMsG3btosK+Nx8881873vf\nu6jXePbZZ/nDH/7AggULeOyxxy5yhkIIIYSYT1RVpfylciKsESy8cSHKfF1iSMwa+fERfOfaeF4q\n6+e9hiFecQxwrMXDp5dGk2kzaoGT1FStbbwGANXVA9VVUFWlPdbXofj9E46vBANQW6O1PX/Vjo+x\naZkLubnaslE5ORD50TJD5hJVVal8vZL2U+0j2xS9QsndJdgybZftdWJMOv5ulY2DTUM8f7qfIb+W\nLeMPwp/KBzjR5uX+ZdEkRV3BtyVsNrAtCT9XVfjsF1BHZ9H0OOHIIThyCPX2beGATHsb1NRogZrE\npCs2uCiEEELMNVfwO5+LczlrtMxmLS0tuFwuVq1aBWh1RGJjY1m5ciUrV67k05/+NBUVFTQ1NZGR\nMXPfzElISOD666+nqKiIu+++m8cee4xnnnnmosc5evQoBoPhnNkgZrOZz33uc5c420uXkZExEiCa\njMTEiyu0+9xzz/HjH/+Y3NxcnnzySWy2y/dBTAghhBBzT82eGjodnehNejLWZhAZJwXTxdSzGHXc\ntzSGlelmdpzo1bIp3nXyqSXRrM+a4Bq0xcKKVVoDrah6Q712IzsUqFF6Xed8PaXXBSf+XU6HAAAg\nAElEQVSOaY1QLZqUVC1AsyAUpMnIAP38+disqio1e2poOTrqy14KFG8vJi738n/mVRSFdZmRFCZE\n8IcTvTg6w0uB1zh9/Os73WwrsrIxJ/LKypY5F0WBgkKtAQSDqK2tUFOttUXF4b7Hj6H8cScAqtWq\nXa/DbcGCKyK4KIQQQsxF8+edpbgsRtePmUhMTAwAFsu539xNZz2VtLQ0cnNzOXPmDD09PcTGxk76\n2KGhIVpbW8nMzMRsNo/Z19TURF1dHUuWLCEhIeGCY031Of/iF7+YdN+LtWPHDn7605+ycOFCnnzy\nSeLj46fstYQQQggx+zUfbqbxg0YUnULxXcUSjBHTrigxgu9cE8+fHQMcqB8kN26SqxUYjeElyUBb\n5qyrKxScqYSaKmhsRDnHEsyKqkJri9beO6ANYTRCVnboRncoUJOQOGezEerfrafxg8Yx24ruKCKh\n8MKfeS5FXKSeL6+NZX/dIH8q78cb0LZ7A7DzdD8n2jx8akkMiRb9lM5jztHpID1daxs2jt2XmIS6\ndDnUVGlL9J08oTVAtdngX38Uvk6bmiAlBQxyC0gIIYSYafK/sRhjuH7MRMt/uVwujh8/Tn5+/nlr\ntkx3PZXO0NrROp3uoo7zeDyoqjphYdqf/vSneL1eDJN8wzpXa8j8z//8D08++SSFhYX8/Oc/v6iA\nlhBCCCHmn67KLirfqASg4NaCKfnGvBCTYTLouLskmhsXWrCZtZv0qqryXsMQqzPMROgnERBRFEhM\n1Nraddq2oSHUutrw8mU1NdqSUOcawufTAjrVVSPb1KgoyM6BnAXhxzlQeL3xYCN1b9eN2VZwawHJ\nJcnT8vo6ReGaBRYWJUXw/473UeMMZ8s4On38YF8Xm3Mt3JRvwWS4uM92V6QVK7WmqqhdnaEsmhrt\ncXR9pKEh+JfHQK+HzCztes1ZoGXRpKZpQR8hhBBCTBsJyIgxhjNkdu/ezdq1a0eCFT6fjyeeeAK/\n389999133jEudz2Vuro6EhISsFrHFpcMBoP86le/oru7m6VLl45k7wx7/PHHefXVV3n00UfZunXr\nuHFjYmKwWCw0NjZSUVFBQUEBAM8//zxvv/02wKSzXqa6hsxU+O1vf8uvf/1rioqK+NnPfibLlAkh\nhBBXuL7WPspeLAMVsjdmk7o0daanJMRIMAbgUJOHHSf7+GuVm3uXRlOQMPklfUeYzWAv0lqI6nSG\nAjShG9p1tSgezzmHUAYGoKxUa8NjWK3h4MxwoCYubtYEaVqOtVD91+ox2/K25JG2PG3a55IUZeCr\n62PZU+3m1TMD+EMJS/4gvFHl5v3GIe4oimJNhlmWMZsMRdFqyCQmwZpQ4FFVw/t7nJCcgtLWGg5E\nhqgmEzz4SHiJNI8HIiJmzXUrhBBCzEcSkBFjDAdkXn75Zc6cOcPq1atxu9188MEHNDU1sXXr1gmD\nG1PpwIED/OIXv2DZsmWkp6djs9no7u7myJEjNDU1kZCQwHe+851xxwVDSxHo9ROnvSuKwm233cbO\nnTt58MEHueGGG+jq6uKtt97immuuYWBggMOHD/PEE0+wbds2iouLJxxnLnrllVf49a9/jV6vZ/ny\n5Tz77LPj+qSnp0/737UQQgghZk7N3hqCviDJi5PJ2ZQz09MRYpwUq560aD0tfQH+8/0eNmSbua3Q\nSrTpEr/hHxentRUrtefBIGpLixagCWXR0NSoLWl2Dkp/P5Se1lqIGh09NosmK3tGgjTtp9upeK1i\nzLacTTlkrs2c1nmMplMUtiyMojjZxB+O91Lv8o/s6/UE+f3xPt6uHeTukujJL1knwkZfY6lp8Pi/\noA66oa4O6mqhthbqalC6u1ETk8J9d/xeW/Zs+LrNytYeE+fuMn1CCCHEbCMBGTGitbWVnp4e1q1b\nh9Vq5dChQ+zYsYOoqCiKior4yle+wpYtW6Z9XmvXrqWxsZFjx47hcDjo7+/HbDaTnZ3NLbfcwic/\n+ckJszuqqqqIiopiw4YN5xz74YcfJiIigt27d/Piiy8SExPDvffey4MPPojD4eCxxx7jxRdfZPPm\nzVN5itOuubkZgEAgwDPPPDNhn5UrV0pARgghhLiCFG8vpuG9BnI25Uy4pKsQMy071sg3N8bzRqWb\nXZUDvFs/xOFmDzcutHBdrmVyy5hNhk4HGRla27BJ2+bxoNaHbmbX10FdnZZxcB5KXx+cOqm1EDXK\nCllZ2o3urGxtCanU1ClbNqrrTBflL5eP2Za5LpPsjdlT8noXKz3awNc3xPFh0xAvlw/Q6wnX96l3\n+fnJASer003cUWQlLlLqy1ySSAsULdJaiNrXB9HR4T6dnVoG2NnBxchIuOZa2H63tmG4DpMsdyaE\nEEJcNAnIiBHD9WPWrl3L/fffP8OzCVu4cCHf+MY3LuqYvr4+Kisrue+++8YtZTaayWTikUce4ZFH\nHhm3r6SkhJ07d170fOeCBx54gAceeGCmpyGEEEKIGdZT10NMZgw6vQ6D2UDu9bkzPSUhzsugU7i1\nMIoVaSZeKuuntMPLnx0DROgVrsu1TN0Lm0zask7DSzsB6uAgNNRrQZpQ5oHS0X7eYZSBfigv09rw\nOMYIyMzUgjNZ2VrAJiMDIkyXNGVnjZPSF0thVGJP2oo0cjfnzqqgq05RWJcZyfJUE29UutlT4x5Z\nxgzgULOH460etiyMYsvCyxh4E2ODMQBf/6a2hF9dDdTXa8HHhnqU3l5U3aiAWE01/MdPwtdsdjZk\n5UB6OkyyDqsQQghxpZL/KcWI4eXK7Hb7DM/k0h07dgyDwXDBejdCCCGEEFciVVVpOthE9ZvVpC5P\npeCWgll1g1aIC0mLNvCltbE4Or3sq3WzITtyZJ9zMDA92RSRkVBo11qI6naHMmhqw5k0nR3nHUbx\neUMF2cM1XlRF0ZaaysrSbnpnZGpBmxjbpJaOcjW6OP38adRAOBqTvDiZ/JvzZ+2/dZNBx+1FVtZn\nR/Knsn6OtYbr+PiC8JeKAd5vGGTbIisr00yz9jzmNEWB+HitrVg1sll19QCj/rzbWlG8Xqiu0tpw\nP70e0jPgH/8JLKEAqder1aURQgghBCABGTHKfArIbNq0if3798/0NIQQQgghZh01qFL5RiUtR1oA\nMMeaZ3hGQnx09sQI7Inhm70D3iBPvN1NTqyRbYuiyIyZ5vojlgmWhRroh4YGLZumoV77ubXl/DVp\nVBVamrV28IPwWFarFpwZbpmZkJY2JpvG2+nl1IFTBH3hNJOEwgTsW+1zIoiRaNHzt6tsVHR5+WNp\nP0294foyzqEgTx3t5e1aIx8vtpIdK/VlpoUtduzzqzeiLl0evqbr66GhDqWtDbWrUwtWDvu3H4Db\nPTawmJkFySmy5JkQQogrkgRkxIjy8nLS0tImrMcihBBCCCHmPr/HT9lLZTirnCh6BfvtdpKLk2d6\nWkJcNsM378s7vTje8bIm08zWwqiZrT8SZR0XpMHrRW1q1IIzjaEgTWOjli1zHkp/PzjKtRaiKgok\nJ6OmZ6IGUujqSWB0NkNcbhyL7lyEopv9wZjRChIi+ObGON5rGOIVRz/93nAAq9rp40fvOlmbaeZ2\nexQ2s9SXmXZWKywq1lqIOjQEXZ3hLK5AAJxOFLcbnE44eSLc1xgBd90N14fqtQ4OarVpoqKm8yyE\nEEKIaScBGTFi165dMz0FIYQQQggxRTx9Hk49e4qB9gEMkQZK7i7BliVfxBHzS2FiBI9en8CuigHe\nqRvkYOMQR5uHuC7Xwo0LLUQaZ8k38iMiIDdPa8MCAdT2tnHZNMpA/3mHUlSVQHsXZ/wFtEcljtkX\ng4tiTzW6vc3aUlJp6RAXN6llz2YDnaKwITuSlWkmXq8YYF/tIMOrsKnAB41DHGke4qqsSLbkWYi3\nSGBmRpnNWhbMML0efvTvqB3t0NgIjQ2h1oji7EaNtob7HnwfZccfUGPjyIiNxZOQCB3tWj2ls7LA\nhBBCiLlMAjJCCCGEEEJcAWrfrmWgfYDI+EgW37OYyPjICx8kxBxkjdDx8ZJorlkQyZ8dAxxt8bC7\nyk1jr58vr4298AAzRa/XAiZp6bB2nbZNVVF7XdrN7KZQa2zUljwLBABwG6IpTbyOgYi4McMluuuw\nd72Lod4/ZrtqjtRucKenh4M06Rlgm1x9mpkQadSxvTiaDTmRvFjaz6n2cCaRLwjv1A3ybv0gazLM\n3LjQQopVbnXMGjodpKRqbdXqkc3qwAAYRv09ud2oxgiUHidRPU6iamvg8IdaX6sVfvjT8PV58gQk\nJEBKCujl71oIIcTcIv9zCSGEEEIIcQXIvzEfnU7HgmsXYLRI3QUx/yVFGfjCShu1Th8vlvWzJc8y\nsq/PEyTSqGCY7ct4KYpWv8MWCyWLw9v9ftS2NjqP1uE45SUQHJX5owbJ6zlCZl8pE52dMjQINdVa\nG0W1WELBmXRITQu3uLhZU+sjOcrA36+JpazDwwul/bT2B0b2BVUtY+Zg4xDL00zcuNBClk1+181a\nZy9Ndstt8LFbUDs7aD50CFNXJwmeIWhugphRwUK/H375JEowgKrXa4Ge4Ws2LR3yC7TgohBCCDFL\nSUBGCCGEEEKIearT0Un8wnh0Bh36CD0FtxTM9JSEmHYL4ox8dX3smIL2O0/3Ud3t47rcSDZkR86e\npcwmSdXpqT3jpeGEHwjPXRehkLIwSKZtKbQkojY3Q0uzVsPjAhS3G6oqtTb6tSIitJveqaljAzXJ\nyWCcmYDHoiQT394UwdEWD29UDdDSFw7MqMDRFg9HWzwUJ0XwsXwLefERMzJPcZF0OkhOYaCgkIGC\nQhIKQv9nqeH6QQwOwuIlqM1NKJ0dWsCmuWlkt/rFv4fVa7QnJ09o13PaqOvWJEufCSGEmFkSkBFC\nCCGEEGKeUVWVmj01NH7QSFJJEkV3FI25GS3ElWb09e8LqHQMBHB5gvypfIBdlW7WZ5m5PtdCXOTs\nr0HiHfBS/qdyemp7xmyPyYjBvMIMkXooGBV8VVXUnh5oadZuXLc0w3CgZmjogq+neL3hmjajqIoC\niUlnBWpSITlFK/g+xb9z9DqF1RlmVqabON3uZVflAHU9Y5dnK+3wUtrhJT/eyE35FooSI+R34Vw0\n+u8sOhq+/CAA6tCQdj23tEBrqGVmhfuePIHy9ltjhlLjE7QATd5CuO32aZi8EEIIMZYEZIQQQggh\nhJhHAr4AjpcddDo6UXQKcQvi5AakEKMY9Qrf3BhHWYeXN6vdnOnysbdmkH21g6xKN3FboZWEWVoc\nvrepl9IXSvH2ecdsT1+VTt6WPKqqq8YfpCjasmNxcVBcEt6uqqhO58SBGo/ngnNRVFUrut7RrmUi\njKJaLFpgJiVl1GOqllVjNn+kcz8XnaKwJMXE4uQIznT5eKNygDNdvjF9Krt9VB50kW0zcFN+FEtS\nItDJ78W5z2yG3DytTWTVatToaO3abm2BtjaU7i7o7kL1esMBGZ8Pvv0NSEoK1btJCWeFJafMWCaY\nEEKI+UkCMkIIIYQQQswT3gEvp58/TV9TH3qTnuK7ionLjbvwgUJcYRRFoTjZRHGyiQaXjzer3Rxt\n8XC42cPWQutMT28cVVVpOdpC1RtVqMHw8k06g46CWwtIWZxy8YMqCsTHa210fZrhjJrWFmhtDWce\ntLaiuHrOPd7ood1uqK3R2tnnYosN3fBOGRu0SUi8pBvfiqJgT4zAnhhBjVMLzJxqHxu4qnf5+a/D\nLlKterYstLAyzYxRL4GZectepLVhAT9qR6cWoIkYtYxdRwfKQD8M9I+7ZlVFgS8/BEuWahsaG6Cv\nT7tmZ1F9JSGEEHOHBGSEEEIIIYSYB9pL26naXYVvwIfJZmLxPYuJSoq68IFCXOGybEY+t8LGHfYA\nFd1e4kPZMUFV5amjvSxJNrEy3YReNzM37gO+ABWvV9B+sn3MdnOcmeKPF2NNvswBpNEZNYuKx+xS\nB92jgjSjHjvaUYLByQ3v6gFXD5xxjB17+HWTkkMtSXtMTtaWRruIzJrcOCN/vyaWpl4/b1QNcLTZ\nw6gqJLT2B/j98T5eKO1nbYaZq7MjSYuW2yPznt4QWmIvdez2tDTU//tjaGvTrue24dYGnR2QkBDu\nu28vyjtvA6AaDNq1mRy6TrMXwNp103c+Qggh5iR5xyGEEEIIIcQ84Kp34RvwEZMVQ/H2YiKsUsRa\niIsRb9GzzhI58ryswztSHP5lh47rci1cnWUm0jh934gfdA5S+sdSBtoHxmxPKEjAfrsdg3maP9JH\nWiZeIsrvR+1o125gt7eNeVR6XZMaWlFV6O7WmqN83H41JiZ883t00CYx6Zw1azJiDHx+hY3bCv38\ntcrNwcYhAqMiM26fylu1g7xVO0hurIH12ZGsTDNjMkjWzBVFUSDGprWCwrH7An5QRv2bT0pBzS+A\n9nbt2h7OIAPUokXhgIzXA//nX8LX6+jHuHjQz85lEYUQQkw9CcgIIYQQQggxBwUDQTwuD5Hx2g3k\n3OtyiU6PJmVJitSMEeIyKEyI4L6l0eypdtPaH+Clsn5edfSzPM3EusxIChKMU1aHRFVVOso6qHy9\nEv/QqEL1Ciy4dgFZ67Nm179zgwHS0rV2FnVwUAvODAdqRgdrhgYn/RJKby/09sIEdXJUkwkSEyEh\nSXscbqHnyVEm7lsawy0FUeypdvNu/SC+sxJ6anr81PRoWTOr0k1cnRVJls0wu/6cxfTTn3Xb7KaP\naQ1Qh4a0GkrtoVpKsaOWCG1vRxkVrBlN1eng4X+EokXahuoqcDrDAUaLZarORgghxCwgARkhhBBC\nCCHmGFeDi4q/VBD0B1n1d6vQG/UYzAZSl6Ze+GAhxKQY9QrrsyJZl2mmtN3Lnho3FV0+PmzyUNnl\n47HNCRce5CPobeql+s1qeht7x84n0kjRnUVzry5UZCTkLNDaaKqK2terBWiGb2p3dozc3FYGLyJY\n4/FAU5PWJqBGR0NiEnEJiXw8MZFbEpI5ZEznPXcUjYNjAy5DfpV364d4t36IzBgD67PMrM4wY5nG\nzCgxR5jNkJWttbOlpKL+r++Gr++RwE0HSo8T1WYL993/DsqB/SNPVYtFC8wkJkFeHmy5KdzX79cC\noEIIIeYs+S0uhBBCCCHEHOEb9FGzt4bWY62AVkPC0+vBkiDfphViqugUhcUpJhanmOh0BzjYOIjF\nqBvJjun1BPnvIy7WZJhZkWb6yEuaDbmGqNlbQ0dpx7h90WnRLLprEWbb5OuozHrnWyZKVVEHBkI3\nsjvCN7RDPyu9vROPea6X6uvTCrHXVAMQBVwLXAM02NJ5N38Dh1NKGNKPXeqxsdfPztP9vFTWz4o0\nM1dnm8mLM0rWjLgwoxEys7R2FtXnG7tkWU4O6kC/FpDs7ERxu6G+DurrUIcGwwEZtxu+/gjYYrW6\nNgkJkJAYfszOgSipHSeEELOdBGSEEEIIIYSY5VRVpaO0g6rdVfjcPhSdQtb6LLKuzkJvlHXohZgu\niRY9txZax2w71DREZbePym4fz5/uY1mqtqRZYeLkljTzD/lpeK+BxoONqKMLnACKTiF9dTq51+Wi\nM1xBGRqKotWFsVrH16shtFRUZyhQ09kZah3Q1QldXSg+3+ReBsh2NZN9eCd36f/EkfTFHMheQ018\nzph+viAcbBriYNMQKcEBVhl6WRYXJC0xGiU+Hmw2qQkiJs9oHPv82uu1BqHMsb6R4AyR4bpW9PQA\noPQ4occJVZVjhlEf+iqULNaeHNgPZWXhwE18gla7Jj5ey+wRQggxYyQgI4QQQgghxCx35pUztJ1s\nAyAmM4aCWwqISpJvwQoxG2zINhMVofBBwxAV3T4ONXs41Owh1qzjqkwztxZGTZhRoQZVWo62UPdO\nHT73+ABCQmECudfnSgbcRMzmc2YfEAyi9vaGAzTDwZrOTu2504miquMOMwW8rG84wvqGIzRHp/Be\n9io+yFyJO2Lsn3+bLorXglG81gVJdZ0sb3mTpW2l5NCPEhcPcXHaje+4eIgf9XN0NOiuoKCa+GgU\nBWJitJa3cOy+9HT4+S9RnU7o6gq1zvBjcnK475kzKB9+MOFLqLl58K3vhJ6osHuXlnUTH68FbmJt\n42vnCCGEuGzkN6w4J6/Xy9NPP82uXbtobGwEIDs7m3vuuYdt27bN8OyEEEIIIa4c8fnxdFV0kbs5\nl9RlqbJcjhCziMmgY11mJOsyI+l0B/iwaYiDjYN0uoPUu/wj/14DQZWOgQDJUTqc1U5q3qzB3eUe\nN5411UreDXnE5sRO96nMDzodxMZqLb9g/H6/H7W7C7q7wzezu0M3t7u7wekkva+Nj59+jTvK3uB4\najEHctZwJnHhuKE6rInsLriW3QXXEjvYw7KWUpbVnmbhkSPo1eCYvqrBoN30Hp5bbNzEj2dnTwgx\nmt4Qri9zPjdsQbXbw9d1dxc4u6HbCZZRQUa3G+WF58ccqiqKdi3GxcO27WAv0nZ0tIPLpW232aSW\njRBCfETy21NMyOfz8dBDD3H06FEKCwvZvn07Ho+HN954gx/84AckJyezfv36mZ7mZbNt2zZaWlom\n3BcfH8/rr78+zTOaWq+88grf+973zttHp9Px/vvvT9OMhBBCCDGaq8HFQPsA6avSAUgsSiR2QSzG\nSLlRJ8RslmjRc0tBFDfnW6hy+jCMCp5Wdvv4f2+1sqatgzjXwLhjI6IjyL0ul+TFyRJ0nUoGAySn\naG0iwSBqTw90d2Ho6mJVdxeruivoqDvFe8Z0jsYupNMSP+6wnshY9uVdzb68q7F6BljSWsry1tMU\ndlZhDAZQ/P5QAKjzvNNTrdYJgjWxWjDHZtNadIxk24jzy8rW2tlUFXzeMc/VLTeFgpHd2mOvC8Xp\nBKcTNRAI9z3wLspfXtUOUxTtOowLXaOpqbD97nDfzg6wRsvyaEIIMQEJyIgJPfPMMxw9epTt27fz\n7W9/e+QDwYoVK3j00Uc5fvz4vArIAFitVj71qU+N226xzL8lAgoLC/niF7844b5jx45x6NCheff3\nK4QQQsx2alClq6KLpoNNuBpcKDoFW7aNqCRtuSMJxggxdyiKQn58uEC8p89D554qbqzs5OxQS1Cv\nw7w0jVU35GCMkI/oM06nCy3dFD8mwyYJuAO4PRikqb2f4w39HHeqtPjG/27uN0XxXs4a3stZg9k3\nREmbg+Wtp1nUfgZzwDuu/2hKfz/090Njwzn7qMPLWtlsoUDNqGDN6J9jYmTpKTGWokCEKfzcaoW7\n7xnbx+9H7dECMmRkhrfH2LTlzpxOcPWg9Lqg1wV1oHZkhAMyqgqPfxfF50U1m8dep7GxsHJVuDaU\n1wMoEBGBEEJcKeR/ZjGhF154AbPZzFe/+tUx387ShwoV2my2mZralImOjuaBBx6Y6WlMi8LCQgoL\nCyfc94UvfAGA7du3T+eUhBBCiCuW3+On7UQbTYeaGHIOAaCP0JOxJgNzrHyzVIi5bMg1RMvRFpo+\nbCLoC44JxqhATbyNU6lJRJsjWGcMF4V3DQWwmaVI/Gyk6HRkpsaQmRrDbUB7v5/jbR6Ot3qo6/GP\n6z9kNHM4cxmHM5ehU4PkDHZg766hsKmU3M4ajMHA+Be50BxUVVs6yuUC6s/ZT1UUiIqCGFu4LklM\nzKjno7ZbpcaNCDGcY1m06zdrDSAQQO11acEZp3PsteP1gs2G6upBGRqCoSFoaxvZraalhQMy7x1A\n2fEHVIslHEwcuTZtcONNWhAJYHBQy7iRDEIhxBwnARkxTktLC01NTWzatInIyMgx+958800AVq9e\nPRNTm7P8fj87d+7klVdeob6+HpvNxubNm3nooYcIBALceeedrFmzhu9///szOs/KykpOnTpFcnIy\nGzZsmNG5CCGEEFcCv8fPwScP4h/SbuKZY82kr04ndVkqBpO8VRdiLgoGgnRXdNNyrAVntXPCPnG5\nceTdkEeRxURWmxejnpEvwrmGAvyvN7vIiDGwODmCosQIcmKNGPVyE3I2SrYauNFq4MaFUTgHA5xo\n1YIzld0+1LP6BhUdNZYUaiwpvJ55FUYd5FmCFOoHKPR3kdXXgr6nB3qc0NMDPT0oA/0feW6KqmrZ\nNv390Nx03r7aElTR2jJUw8uiRUePajFjHyWj4cqm12u1ZOLGL9+HyQT/8oS2HNrgoHYtu0KtpwcW\n5IX7eryoej2K2w1uN7Q0j+xSLRa46WPhvv/ne9qSaqODibZY7XFRMRSEvnTq82ktMlKCN0KIWUk+\n5U3S8d8fn+kpnNeyzyy7bGOVlZUBUFJSMrJNVVWeffZZ9uzZw9q1aykomKA44hzn9Xr5y1/+Qmtr\nK5GRkeTn57NixYqRrKCPyuVy8cgjj1BaWsrGjRu56qqr2L9/P8888wzJydr60C6Xa1Zk57z44osA\n3HHHHZd83kIIIYSYWF9LH9ZUK4qiYDAZsGXb8Ll9ZK7NJKEwAUUnNw+EmIvcXW5aj7fSdqINn9s3\nYR9LooW8G/KIX6jdxIwCUqxjP5Y39/kx6RWaev009frZVenGoIMFsUbyE4xcn2vBYpRMhtkoLlLP\ntbkWrs210OcJcqrNw7FWD45OL4GzozOALwiOfh0OooFozBG5FCwyUpgQQWFCBGnReu3Gcm8oG6an\nJ/yzq2fMo9L/0QM3EAre9PZqranxgv1Vk+msQE3oZ6tV+9karf08/GgyXXBMMc8oClgsWktPn7jP\nTR+DG29CHegPBW5Cy6D19mpLn43m86MEAuGsnFFUgyEckDl9CuVXT2rbxgQUQ9fqbbeHa9t0dWnB\nJatVywwSQohpIL9tJslV75rpKUyb8vJyABYtWsShQ4fYtWsXx44do66ujoKCAh5//PHzHr9jxw76\n+vom/XqFhYVcd911lzLly6Krq4vvfve7Y7alp6fz6KOP/v/t3XmcZXV95//XuftSW1d1d/XeNHTz\npUEiNISWxQVQAkJEMEZBVGJcxsCIEU3GOKghmSHzw180MRodMSbjiBmNA2Z+bgR/VggAACAASURB\nVGlR3H8iyhaRQzXdQG/Va+1193Pmj++5W9W9tXVV36rm/eRx+J7zPd9z7vfee271vd/P+X6/bNu2\nbc7n/dCHPsSTTz7J7bffzhve8AYA3vzmN3PNNdfw05/+lN27d3PNNdewfv36puc4Ea9pNpvl29/+\nNuFwmGuvvXZWx4qIiMjUvJLHkaeOsO8X+xjZP8LZN5zNsk3LADjj2jMIR3UjhMhSVCqUOOIeof/R\n/il/Mya6Eqx7yTpWn7N62qDr1hVx7nrVcnYey/PrQ3n6jubZP1Ji57ECuwYKvPLUdKXsQ3sztMdD\nnLosSjyiIM1i0h4PceGGJBduSJIpeDx1JM/TRwo8fTTPobHGw5Rliz5PHMzzxEE7z0x7zGFLT4wt\nPW1sXN7Fmk2nEW5y/fjFYk2wpiZgMzIMQ8NBaredQuOA4Ww4uRzkcnDkyIzK+9FYEKAJAjbpcuCm\nrRq4SaehrY3w6AheIjn9SeXk4DhB4K4d1jVvF+Gv7sbP54PA4VA1HRqC0021XDB3jZPNNg7e/G5N\ne8cX7sHZ2WfzE0loD67F9nY460Xw8kttuWwWdvZVg43tbfVz8YiIzIICMjJJuYfM1q1bufvuu9mx\nY0dl3ymnnILneVMe/8///M8cOHBgxo939dVXtzwgc80113DOOedw6qmnkk6n2bdvH1/5yle4//77\nue222/j85z/fdM6VqTz00EM89NBDnHPOOfz+71cnyuvq6mL16tU8/PDDxGIx3v72t095nhPxmn73\nu99lZGSEiy++mN7e3lkdKyIiIo0VMgX6H+1n/y/3kxvOARBJRsiPVSd1VjBGZOkZPThK/6P9HPr1\nocqQgxM5YYflpy9n1Tmr6Dqlq25uzulEww5bV8TZusI2+I3lPXYeK3AsUyIesefxfJ+vPTnKeMEn\n5MD6zgg9ToK1ySLrCh5J9aJZNJLREOeuTnDuantX/kCmxNNH8zx9tMDTR/IMZhv/xh7J+/zqQI5f\nHbD/fkRDsK4jwoauKBs7o2zsirA8HSbkOPbu/u4eu0zF9/GzmWpvmImN2+W8kWEYGZmX4A2AU8jD\nwDG7TOO0clVjMRu4aUvbNB2kbTXr6XR1SaVtbwyN9nDyisVg+XK7NPPb2+G3t+PnczAyaq/rkRG7\njI3WD7eXSuF3dMDoKE42A9kMHD4MgN/VVS13sB/n7/6m7mGqQcY0vO0dsDroBfTvT8DhQ7SPjFJK\nJiEWrV638biGURMRBWRmqnPDyTeJfTNPPfUUq1evpqurizvvvJMPfOAD7Nq1i6985Svs2LGD3bt3\nc++99zY9/utf//qC1/Haa6+dVYDiyiuv5M4772y6/x3veEfd9mmnncYHP/hBUqkUX/rSl/jc5z7H\n3XffPet6fvOb3wTghhtumPQDLBZ8CbjuuuumDYCciNf0/vvvB+D6669f8McSERF5Idj94O7KRN4A\nye4kay9YS+/ZvQrCiCxBxVyRw08epv/RfkYONO+9nupJsercVfS+qJdoKjovj52OhXjxqvq7sQsl\nuHB9kp3H8uwZKvLcYJHniPOrgTj/3/4jvPXcDs5bYwMAY3mPaNghpnloFoVlyTDb1yXZvi6J7/sc\nHi9Ves/0Hc0zmm8wvhl2iLPdg0V2DxaBDADJiMP6zggbu6Js7IqyoTNCVyLUPADoOJBM2aV31dQV\n9X38XC5ozB6ekE5cH4HREZxpbuCcDSefh/zMgjh11U4kbWAmna5J05BOBUGbdP3+VPB6JJP1k9PL\n0haLQ08ceqYIUv7Rf7Sp5+Fnxm0AZzS4nrtr5scJh/G3nhnMyTQSBCurQUa/Ngj485/h/OIhVjd4\nOH/L6XD7n9iNYhHu+WzN9ZmuX1+3zvbGEZGTjgIyMzSfc7QsZgcOHGBoaIjzzjsPgHA4TFdXF9u2\nbWPbtm286U1voq+vj3379rF27dqW1XPt2rWVgMZMLJ/q7okpXH/99XzpS1/ikUcemdPxjzzyCJFI\nhAsvvLDh/kQiwc033zync8+nZ555hscff5yVK1dy0UUXtbo6IiIiS052MMvRvqP0bOkh0WUbQB3H\nwSt4dJ3SxboL1rHstGWzukNeRFrL933GD48zsHuAgd0DDD0/hFds3NgcioZYsXUFq85ZRcfajhPy\nWY9HHF67tQ2AbNFj90CBh3YeZN94hEO5CD2pagPhA7vG+e4z46xqC7OuM8r6zgjrOyOs64iQ0FBn\nLeU4DivTEVamI1yyMYnn+xwYKeEescGZnccKZIuNAzQAmaJve9ocrfZk6YiH2NgVYUNnlDXtEVa3\nh+lJBT1pZlc5O9dGIgErVkxf3vPwx8erjdYN09FqT4XRUTus1Dyr9HQ4dnRWx/nl55tM1QdqUslq\nECcZrCeTwXoKEsnqtgI6S1MoFPS4agMaBCrXrYfb3lfdLgcrR0fttVzbM+2sF+Gn0oz0HyCcyZDy\nveq1n6wZim9sDOfR5m1N/jvfDdts2xw7vmOXVKp6LZbXOzvhqqurB+7eBdFodb965YgsOgrISJ3a\n+WMa6ejoACCVSjU9x4mY7+TTn/70rMrP1bJldmz37By+JGazWfr7+1m3bh2J8oRxgX379vHcc89x\n9tln0zPV3RqBhX5Ny71jXvOa1xBW924REZFp+b7P6IFRjvYd5WjfUcYOjdl8z2fd9nUArN62mt7f\n6iW5TOPgiywV+dE8A88OMLBrgMFnB8mP5qcs37aqjVXnrGLlmSuJJFr38zoRCbF1RZzIYA7IsfHU\nzdR2hhkveDgOHBgtcWC0xC/22XwHeFFvjHeeb4fm8X2fTNEnpeHOWibkOKztiLC2I8Jlp6YoeT4H\nR0s8N1TgucECzw8W2TdSxGseo2E459XNRQN2uLPetgir2sKsbo+wut2uzylQ07TyoeqcMI0atRvw\nC4VqwGZsDEZHObR7N+Fshp5EwjZ2B/mMjdnt8XGciRO+zwPH9yGTscssgzllfjxe7W1TWSZuJ20Q\nJ5EI1hNBUCdIo1E1oC92tcHKiTcAv+QieMlF9PfZuWm2bNlS3VeqGeIymcB/17uD67pmGQ/SoD0K\ngOFhnPJwghP4y7rrAzKf/iROTfuRHwoHwcMkvOpKeNnL7Y69e+BnP62/RstBx2QK1q7V8H8iC0QB\nGalTnj/mjDPOmLRvaGiIxx57jM2bN1cCFY0sxTlkmnniiScA5tQbKJfL4ft+w7vjPv7xj5PP54lE\nZvYRXMjXNJfL8a1vfYtwOMy11147/QEiIiIvcLse2MWhXx+qa6gNx8J0n9ZNemV1su14uyZ7FVns\nSoUSQ3uGGNw9yMCuAcYOj017TDgepvdFvax68SraVrWdgFrO3sShyd54dgevO7Od/SNF9gwV2TNU\nYM9Qkf0jxbrgy0DG4yPfP0pHPMSqtjC9bRF602F622065VBYsiDCIYc1HRHWdES4cL0N8BdKPnuH\nizw/WAgCNUUOjZWmPE/Bg73DRfYOF4FcJf+EBGqmEo3ahueaNoahThsg7KltyK5V7olTDtaUG7HH\nx2u2x6sN2zX7nNLUr9PxcnI5yOVgcGD6wk3YBvREg6BNAuKJxuuJ+ITtYL96Rywu4Zo2oFgczj1v\nZse95rX4l7+qei1XlrHJQZM1a/FHRir7nXw++KyM2nl1yvbtw3lgB834f/23NkAD8Km/heefq/YG\nK/ckSyZg8xa46BJbLpu1c+gkk/XXbflaVg8yEUABGZmg3ENmx44dXHDBBZUv24VCgbvuuotisciN\nN9445TlOxHwn82n37t2sWrWKZLL+7tX9+/fzsY99DLBz0Ez053/+53zjG9/gwx/+MNdcc82k/R0d\nHaRSKfbu3UtfX1/lroh/+Zd/4Yc//CHAjHu9LORr+sADDzA8PMwll1wy7Vw2IiIiLyReyWP8yDgj\n+0foPbuXUDCsT3YwS340T6w9Rs+WHnpO76FrQ1dlv4gsXr7nM3po1AZgdg8wtGcIvzT9nfbRVJRl\nm5ax7LRlLDfLl+Q8UNGwU5lnBOxvn6Lnk6sZDuvweIloyPawGM55dcNgAbz/4mXB8fDUkTzZgkdv\nW4QV6TCRkBp9T5Ro2GHTsiibllXnKMoUPJ4fKtpeNEE6mJ1+PpdmgZqwA92pMMtTYXqSQZoKBWmY\nZCt7UdX1xJmF8jBTtcGaTKbayF1Zz0CmptE7WHdyuekfYx44XqkaWDpOvuPYoEw8Xg3QxONBwKZZ\n3oT8WCzYjtkgQjwOM7y5VOZJNApdXXaZzh+/v27TLxar13e6ZrSb9RvwX/f6oFfYeHDdB+uZjL0e\nyoaGcIaGYGho0sP5vl8NyBw9gnPPZ5tWzf/Af4LTNtuNHd+Bxx+rD9iUl+5uuPDi6oF9T9dfm4mE\nvS4V4JElSn9BpU45IPOv//qvPP3005x//vmMj4/z85//nH379nHNNdc0DD4sZTt27ODee+/l3HPP\nZdWqVaRSKfbt28dPfvITcrkcF198MTfddNOk47xgssJmQ3w5jsPVV1/NV7/6VW699VYuv/xyjh49\nyoMPPsjLXvYyxsbG+OUvf8ldd93Ftddey5lnnrmgz7OZ++67D4DrrruuJY8vIiKyGPi+T3Ygy8iB\nEUb2jzByYITR/tHKfBHxjjjdp9nJXTdcvIH1F6+nrbdNd4qLLGLFXJGxQ2OMHhxl7NAYYwfHGDs8\n1nQemFqhSIiO9R02CLNpGemV6ZPy8x4JOURi1edllsf42JUrOJbxODha5OBoyaZjNu1tq/72+d6u\ncX5z2PYUDDnQkwqzIhWmOxlmc0+U89bYxjw/GFrqZHz9FpNkNIRZHsMsr861Opr3ODBSpH+0yIGR\nEv3B+kh++iBkyYfDYyUON+l5k4469ATBmeUT0s54iGh4Eb7ftcNM1U7YPkN+qWgbqsfG7Rw1mUy1\nobvciJ3JNNhXzXOKxekfaB45vm97LWSzwOTG9LnyQ2HbKycWrw/UxGvzyku8ul4O8ERr1uNxux2r\nWSIR9eyZL5EIdHTYpdaaNXaZifd9AL/22s5mq9f18pr5paJR/HPPs5+H8nWXy0ImSOM1vccP7Mfp\ne7rhw/kbT6kGZDwP5//9fxqXi8fhDTfCRUHZxx+DB79XDSDGg8BNOYDzyiuq19XuXeD7E67ZuAI9\nckIoICMV/f39DA4Osn37dtra2nj44Yf58pe/TDqd5owzzuCWW27hla98ZaurOe/OP/98nn/+eVzX\n5bHHHiOTydDe3s6LX/xirrrqKl796lc3/PHwzDPPkE6nufjiixuc1XrPe95DLBZjx44d3HfffXR0\ndHDDDTdw66234rouH/3oR7nvvvu47LLLFvIpNrV7924ee+wxVq5cyUUXXdSSOoiIiLRCfjRPbiRH\n++p2AIqZIr/4zC8mlUssS9C+ur2u98tiHaJI5IXK931yQ7lK4KWcZgdnNw9kujddCcB0rOtYkr1g\n5kPIcVgeNK6ftbJ5uc3dUUIOHBwtcXS8VNd4X/T8SkDm4GiJu39yjO6kDdb0pMJ0J0NBGmZNe2Rx\nNt6fBNpiIbb0xNjSE6vLH8179I8UOVAO1IwW6R+ZWaCmbKzgMzZU5PmhxgGGdNShM2GHuetMhIK0\ndjtMOuosrUBdOAJt7XaZI79QqDZkVxq1s0FDd3ZCfm1eBrK5SgP3ieqt04zjlao9iBaA7zjV4Ew0\nWrM+Ia3dX5tGYxAL0on50Uj9/lgUQmEFgKZSDmTSfPoCAFb2wrve3XjfxHmfrroaf/uF9lrPZasB\nnEwGOjur5YpF/M1b7FCA2axNg8+Ak8vhh2uCJ4cP4Tz568YPH4nAq36nmvHFf8TZv79x2Usvhzfc\nYDf27oH/8YVqsKYcwInFbBDnVVdW69v3tJ1/amIgMhqzw7/NpIeTvCAoICMV5fljLrjgAt785je3\nuDYnzrZt29i2bdusjhkZGWHnzp3ceOONdEy8y6BGPB7ntttu47bbbpu076yzzuKrX/3qrOs7nzZt\n2sRDDz3U0jqIiIgspFKhRGYgQ+ZYhszRDKP9o4wcGCE3nCPeGWf7LdsBOxxRx9oOIqkI7avbaV/T\nTvuqdqKp6DSPICInSqlQIjeUIzuUJTuUZfzIeCX4UsrNfl6IWHusEoDpOqWLWDo2/UFSccXm6pxZ\nhZLP4bESRzM2OFPbk2YgWyJfgv7REv2jk9+nD76smzXttmni33aOsXe4SEfcNtrb1Pa46EyE6ua7\nkblri4XY3BNjc5NATf9oiSPjdjkapNnizIM1EARsCkX2TzFKdyQEHXEbnCm/322xEOODMZJhj9Cx\nPG2xEO3xEMnIEgveNBON2mWKdoSZ8D2vpoG6pjF74nZdI3auuq+yXc1zJjaYt5Dj+9X6nQC+49QE\nbKJB0CYKkWi1x075vasN7ESC7Uh5vZrXduQwfjgC+Vz1uEikpmzNdjRy8geFJj63FSvtMp1YDN7/\np5Oyfc+DfL5+Dp1zt+H3rqpeO/ma69yb0Dt23Xr8eKK+bD5vl9oh+UZHcZ5/vmn1/Je+ohqQ+eGD\nOL9o3Mbmbzkdbv8Tu5HLwe231QcPy4GbaBSueQ2csdWWffLX8NijDYKOURsc2n5h9UGee9YGviZd\nq8G6ev4sGgrISEV5uDJjTItrsvg9+uijRCKRaefTERERkYVXypfIDNqgS3YgS9cpXZWeLwd+dYBd\nD+yadEw4FibRlcArepXeL+e89ZwTWm8RqVcqlMgNBwGXwWw1+DJoAzCFscL0J2kiFA3R1ttGemWa\n9Mo0nes7SS1PnRwNvItANFydeH6irSvi/LcrlnMsU+LYuMexjA3cHBsvcTTj0Z2sNhD1HS3w1JF8\nw8fYuiLGH11g7y4eL3h8+fEROuK2sT4dc2iLhUhHbYP+8nSYmHrdzFo1UFOf7/s+4wV/UpCmnA5k\nPObSlF/04FjG41hm4jCCdo6jbx4YrOSEHFs/uzi0x0M12yGSUYdU1CEZDZGKOqSiNogTPlnnNgqF\nqhOnzwfft3ON5LK2J045UFNprM5X88rr+Rzk8vWN3rmaRu2aBu7FFOxpxPH9ar3nyQwHA6vwHacm\nYBMEbcrBmtrt8hIur4cn76uUKe+rScO1+yashyP1Zcrr4bC95hbTv5mhUP08NwDdPXaZibe9o3G+\n79cHb07ZhP/B/zzh+q659jtqesydthkfx5YpTPgc9NTUK5+3wxcWg2EQJ1ahtufZc8/i/OD7jaua\nStUHZD73GZwjRxqXveJKuP737Ebf0/APn6sGBmsDhtEo3PTWSpCp44nHGd1yeuPXSuZsXgIyxphu\n4CPAa4HVwBHgm8AdrusemMHxFwF3AC/B/sv7NPA54O9c113cf7VPIgrIzNxLX/pSfvzjH7e6GiIi\nIic93/cpZosUs0WSy5KVvL5v9ZE5miEzkCE/Wv/jedOlmyoBmVRPimR30i7LkqR703Ss6SDZk1RD\nrMgJ4Ps+pVyJwniB/Fiewnihfn2sQHY4S24wR35sfhrC4h1x0r1p2la2VdLEsoQ+8y2UitreLeum\n6RTwuybN9nUJhnMeQ9lSkHoM5TxWpKp3QQ9mPR7tb37n/K3buypzqTywa5xHD2RtwCZovE/HbIN9\nVyLEWSurcxqM5j0SEYfIydqIP0eO45COOaRjITZ2Te45WvL8INDmMTBeYjB4/waz9v0bzJYYncVw\naI14PgznPIZz088BVSsRcYJgjQ3QVII1QZqIOCQiDvEgTURCdj3skIg6xMMncVCnVqWHSPS4hmRr\nyPftUG0TgjSTgje5mkbsQiEoW6iWqds3IS+fxynMPWi/GDi+b5/bIn0evuPYwEx5KQdwwuEgcFMT\nvCkHeSYtzfKnWEKN8kLTHBOqOW7Cevmczb4TlJ9nWSIBG0+Z2Yv0isvsMp22NvxP/n39tV6+rgsF\nWF0TzjvzLPxEorqvkIdC0aaRCc36a9fjp9JQLNjPTm35aM3f7mwWZ2CgafV8r9qbte2ZnYydetrM\nnr/M2HEHZIwxSeBB4Azg74CHgS3A+4HLjDHnua7b9F02xlwGfAvYA3wUOAZcC/wtcBrw3uOto8zM\nU089xerVq+msHatRREREZAF4JY/CWIFwPEwkbr+SDj47yOHfHCY/lic/GixjefySTzQZ5cI/tneA\nOY7DwO4BckO2Mc4JOyS7kiS6EySXJWlfU21I6N7cTffm2U/cKyL1fM+nmCtSypdsmqtPi9liJcBS\nGC+QH89X1n1vYe6xc8IO6eVp0r2210u5B0w0qaEGl6oNXVE2NGjwn6grEeLmczsYznmM5jzGCh6j\neZ+xvMdo3qMjXu110z9S5NnBxvOcrOuIVAIyvu/zoe8ewfMhGqLS0yIZsb0uXn5KkjODsnuHC+w8\nWqg05MfDtjE/FjTo9yRDL6gAYDjksCIdYUW6eZlCya8E2gazXhCsKQdv7DKa92Y9NNp0skWfbNFn\nYFIvnJmLhgje62oAJxauX+IRh2gY4mGHaNhpmMbCtkw07BAN2fxIyM7bdFKrnQ+GhZuHz/d92+Og\ntuE6X26QrmnsbrSvWKyWKZbLFIOG7XKZIK8w+bjF3gNoPjjl17fY+O/pUjMpwFQJ4gRpKFQTzKnN\nK5cN1R9XKd/g+HL5icc3XMLQ32+PdYJztLUF53Hqz+c48NRv7DkdB37nysbndIL06FF7jtVr8P/s\nDiiV6pdiEbwSpKp/zIdedDZePD7FKylzMR89ZN4LnA3c4rrup8uZxpjHgPuwPV/eN8XxnwaywEtr\netN80RhzP/AeY8wXXNd9bB7qKdP4zne+0+oqiIiIyBLhlTxKuRKlQonCYAGv4HHEO0IxVyQcDbNi\n64pKuSe/9mSll0u54dYr2IYR87uG3rN7ARg7MsaBRyZ3rg7Hw0RSEXzPxwnuUt18xWZCkRDJ7iTx\n9nglX+SFyvd9/JKPV/TwSp5NCx6lYsmmBZt6xQbr5bKFEqV8aVKwpZS3+SecY3u7JDoTJLoSJDoT\nxDur2/rsv3CloiHOW5OYviDw6tPTXLg+GQRtvCBo4zNe8OhMVAM3BQ+SEYdM0afgQSHnMVzTCWfb\nmmqD1M6jBb725GjDxws58ImrVlS2P/GzAY6Ol2yDfE1DfjTkcHZvjJest70/BzIlfr43SzTsEAtT\nVy4adjilK0o8Yq/3kZxH0fODhn2IhBZ/L45o2KEnFaanpqdTI4WSzxPuM2RKDt2r1jGSs+/XaN4L\n1msXf94DOA3r5EEh7zOyQH8Hww7V9zJ4zyOhIHhTE7iJhKpp2HHsKFSOzQuHass4hGvKhx27PTm1\nx4UdCE0qawNF4RA4sDQCjLW9fE4k37c9CsoBnCBQ89zOnTilEhtWr64GgorFamCnvF4OcpSDQsVp\n9pVK1XOUivVlinbfCyFAdLxOtgDTQvBDIVY7Ds/+4btaXZWTznwEZN4CjAGfn5D/dWAvcJMx5vZG\nQ48ZY7YDBrinwdBmf4ftKXMToICMiIiISAOVRtiSh+9VG2TjnfHKj+fR/lEKmYJtdK1prPVLPoll\nCbpPtT1IcsM5nvvxc9WG2aDRtpS362defyZtvfbOxmf+7ZlJwZNjHAMgvSJdCcg4IYeBXQOT75B3\nIJaK1eV3bejitCtOI9YWs0vapuHo5Mabni0zHB/6JOTP5kf2FEWbnqdBdsOy/jRl/Fnuq83Dr277\njfMq237NeWrXG5SrWw/Kl9Pc4Rz4MBAZqDtfXeoFnznPr+Y3Wi+XK5ed6VKqntsv+XieV/181wRb\n6vKCdKF6oSykcCxMNBWtBF3infFK4CXRmSDWHiMU1gS0cnyWJcMsS04dBAAbAPmrK1bg+z75kp0z\nJVP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+ "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [], + "image/png": { + "width": 818, + "height": 193 + } + } + } + ] + }, + { + "metadata": { + "id": "W_B8n8wuIAz9", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "Adding a constant term $\\alpha$ amounts to shifting the curve left or right (hence why it is called a *bias*).\n", + "\n", + "Let's start modeling this in TFP. The $\\beta, \\alpha$ parameters have no reason to be positive, bounded or relatively large, so they are best modeled by a *Normal random variable*, introduced next." + ] + }, + { + "metadata": { + "id": "_52Ml-KhIAz9", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "### Normal distributions\n", + "\n", + "A Normal random variable, denoted $X \\sim N(\\mu, 1/\\tau)$, has a distribution with two parameters: the mean, $\\mu$, and the *precision*, $\\tau$. Those familiar with the Normal distribution already have probably seen $\\sigma^2$ instead of $\\tau^{-1}$. They are in fact reciprocals of each other. The change was motivated by simpler mathematical analysis and is an artifact of older Bayesian methods. Just remember: the smaller $\\tau$, the larger the spread of the distribution (i.e. we are more uncertain); the larger $\\tau$, the tighter the distribution (i.e. we are more certain). Regardless, $\\tau$ is always positive. \n", + "\n", + "The probability density function of a $N( \\mu, 1/\\tau)$ random variable is:\n", + "\n", + "$$ f(x | \\mu, \\tau) = \\sqrt{\\frac{\\tau}{2\\pi}} \\exp\\left( -\\frac{\\tau}{2} (x-\\mu)^2 \\right) $$\n", + "\n", + "We plot some different density functions below. " + ] + }, + { + "metadata": { + "id": "OLw3-8x2hxkm", + "colab_type": "code", + "outputId": "2ba9f921-56b7-4530-8de0-544dd320ff6c", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 239 + } + }, + "cell_type": "code", + "source": [ + "rand_x_vals = tf.linspace(start=-8., stop=7., num=150)\n", + "\n", + "density_func_1 = tfd.Normal(loc=float(-2.), scale=float(1./.7)).prob(rand_x_vals)\n", + "density_func_2 = tfd.Normal(loc=float(0.), scale=float(1./1)).prob(rand_x_vals)\n", + "density_func_3 = tfd.Normal(loc=float(3.), scale=float(1./2.8)).prob(rand_x_vals)\n", + "\n", + "[\n", + " rand_x_vals_,\n", + " density_func_1_,\n", + " density_func_2_,\n", + " density_func_3_,\n", + "] = evaluate([\n", + " rand_x_vals,\n", + " density_func_1,\n", + " density_func_2,\n", + " density_func_3,\n", + "])\n", + "\n", + "colors = [TFColor[3], TFColor[0], TFColor[6]]\n", + "\n", + "plt.figure(figsize(12.5, 3))\n", + "plt.plot(rand_x_vals_, density_func_1_,\n", + " label=r\"$\\mu = %d, \\tau = %.1f$\" % (-2., .7), color=TFColor[3])\n", + "plt.fill_between(rand_x_vals_, density_func_1_, color=TFColor[3], alpha=.33)\n", + "plt.plot(rand_x_vals_, density_func_2_, \n", + " label=r\"$\\mu = %d, \\tau = %.1f$\" % (0., 1), color=TFColor[0])\n", + "plt.fill_between(rand_x_vals_, density_func_2_, color=TFColor[0], alpha=.33)\n", + "plt.plot(rand_x_vals_, density_func_3_,\n", + " label=r\"$\\mu = %d, \\tau = %.1f$\" % (3., 2.8), color=TFColor[6])\n", + "plt.fill_between(rand_x_vals_, density_func_3_, color=TFColor[6], alpha=.33)\n", + "\n", + "plt.legend(loc=r\"upper right\")\n", + "plt.xlabel(r\"$x$\")\n", + "plt.ylabel(r\"density function at $x$\")\n", + "plt.title(r\"Probability distribution of three different Normal random variables\");" + ], + "execution_count": 6, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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tyBhc2ZUS1rWVtXYTLrGXMF7y4gfe5G2hCSEvhj/gkmzdgesibMK3sg3zbGgCwBM8lwcY\n132fb7zzKRjL/caYLjGsFuxK8Qtc14XVZeB1y3UHrvXQad51FK64noQQwJvBhJC3zSPUfD92Be4M\nK/e/ea/h3yUv4c7LH4QmhDyPeK8nGtctY1NFOx8OALfgktS1khDWdU0YrKw/N8p2YzofvFYrwd8S\nPwkmhLz9HMB1L5YWYftN/S3xSDAh5K1TRM09aXtogtZLjPyfN9ng976XiA12f3ZNhEWC1+VCa22Z\n93dTy3tJjAkhSP5vox/ifkP8NjQh5G1rJS6hCLXvNQO91zq/day1fwPOof6WWSIiIu2GkkIiIiLi\nO2NMF2PMpbjuqLKAl2zkPvYPAysivH+e91qnv3jPElzFQjcgUgVttPWCFQXV4xtZa1dZa/9grV0U\nvrBXAbjDm4xWWVlnX14SJFiRdHL4/AT4K7AfGGrc+EGhgt3PzG1oI15F8ineZJ2WDF5F3PIYY9qE\nqzg9xRjzP+Hd81hrN1hrP45QmdmQZXEuD3GcD82k3vPbWrsGN/ZSGq71QLg64zF4ld9fepOxVKwH\nY3jXWrs7wvYqcC0DwCWPEm15lGRfcNyWSMmxaPePYJd30T734LV+hlfZHLrOigitZvAqZYPl8dUo\n2w0VbEHybpRz/OUI7/npJFxXhIeIfs0EyyHS8fhZtqEijSUSOjaPr0khqE4A/wWXHK937BlP8Np4\nNUILCLzr5UNvMtK10dA9KlK3l8HKc2ut/TLKvFoJLWvtcmvtLBt5fJbQJKAfZRrxfLDWbrXWPuEl\nGSMJxhEthljPh6/guv88Qk23gqFxrKHm/heqqb8l6vusIsUe8bOqxzPea6RERfC7u7rFnQ/lHfP3\nZzJ/G3mtioL3pYbuNaH3r2Brqx8ZY+rc16y1b4Um+URERNozdR8nIiIiTbXC9RoUUQDX1U60p8Z3\n27ABkT3Bpz0j/ufdWltmjNmDq/QcgBuvI9SnUfYXrDDpG/qm1zXT7bgKvt64p7XDRRojo9hau7+e\nfQ0K31ciWGsPGmPm4Z6Kvhk3fgLek8/fwo2DEN6yJJJuuDEjoHalYqiYnjK21n5pjPk+MBu4F9dt\n3xu4sQ8W2bAB7uMQqeKvIXGdD82g3vPbs4Wa8zvc51HWqfReY3nwK9YYiBKD36KdV8FEUaRWANHu\nH/ne6zXGmEhJNXBPuWfgxmv5KGSd44wx0cZlCpZDpFZL4Y71Xpt0HTVBvvdaBcyMco8Odu0Z6Xj8\nLNtQdc5da21lSHyJemjxR7gWQLcZY57wkgjRxHptjCTytdHQPSq8BSbUXLt1ErQh8+p8BxljxgDf\nxY0Z1ZPIyYho4zvFI9r5gDGmD6711EW48747da/XaDHEej4Er6ed1trK8HU8n1E3edzU3xKN/axi\nPY9fwLVAHGGMGWqt3QhgjDkF1+JzJ278qWpNLO+4vj+T+NsoJ2Rf/2aMidSaNzhOZS9jTBdrbQmu\nS8xxuETRUmPM57jE38vAi/XEJCIi0u4oKSQiIiJNtQBXcRHqIG6w65e9rpKiKYvyfjAxUd+4KMGn\n77MizCtvYJ1gZQLGmCtxx5CB6xptCa7iJNg9zWTgmCjbi7afiPtKsMdxSaFrjTHft9aW4wZ17o4b\noyda5XSoTiF/R2vBE3PXbdbaOcaY93HdwFwS8u83xpgVuG5pPoh1e8DhCN2cxSLm86GZNPX8rtN6\nIQkx+C1aRW99ot0/gq3SvhllfqhgJXpwnWE03P1eLK0AguXb5OuokYLH0wlXqVufSMfjZ9mG8uPc\njZu1dqcx5qe4cbpmG2POidAVWlBTr41oZRdU3z0sWkx1GGO+hzueFFxF+0u4REVw+w197vGIeEze\n+Fhv4RIGh3Ct6T6n5p57MW6cuGhiPR8aup4g8jXV1M/Sl88qGmvtIWPM33APc1xDzZiAwVZCz4Qm\nwXwo74bOzWpJ/m0U2rL42w0G6+41Jd4DMpfiutL9DnCq9/dNwGFjzOO4McJiGXNPRESkTVNSSERE\nRJrqd9bad3zeZjnuP/md6lkmOC9SJUe0yobg+wegemDoP+AqPf4ITAtPOhhjriJ6xUd9lRq19pVo\n1tpVxpiPcN1GXYHrlibmruM8oRVuHaMsU99nEimulbhWBRm4gcC/BkzEPXn8ujFmuK07dpHfYjof\nYpTRxFigpsKssee3H1pCDIlShnvS/BJrbazdtAWPcZ61dkK9S8YmeC35ch01QvB4dlhr+/m83XjL\ntqWYjavIPhtXCf9ElOVa/LVhjOkJzMQlhH4G/G9oksvrCtTPpFA09+MSFKtx50StMeeMMU9Rf5Ii\nVg1dTxD582rqb4nm8DTufLyaukmhP4ct2yzl3QJ+G4V+FsZaG/PYg143t48CjxpjeuBaVF2J+130\nXVzrqliS2iIiIm2axhQSERGRlijY3degSDO9wadzvclI3cJE6+6qv/caTEIMp6a7mf+OUOnRCVcB\nE00Pb5lY9tUc/ui9XmeMyQKuAvYC9Q16HqqYmqeA+0RZJuJn0hBrbYW19jVr7X8DBvfUcWfcE7yJ\nFuv5AK67LYjcXRnUdJ/VFPWe355YurBKdAzBea1tDIZC7zWebu8as059guNt+HodxSF4PL2NMR0S\nsN3m6FLQV16Li9twLTzuM8bkRlm0NVwbZwEdcGPJ3Ruh1VOiz6+gMd7rL8MTFD7HEbyeenvjzUQy\nMMJ7Tf0t0RyW4Y7vFGPMIK9bxnxgrbX2w7Blm6u8k/rbyBvXLXh8jb7XWGt3W2vnWWuvBc7EJaKu\nMMbkNXabIiIibYWSQiIiItISLfdex0WZf6n3uh3YGGH+JVHWO8d7Xe29BltNV+Eq18Ldgqt4g8j9\n5qfgnkKtxatwyA/bl5+iVYo9jetC51JclytdgPnW2pi6qvIqTT/2Js8Jn+8lmsbGsi1jzAnGmGnG\nmGPD51lrD1CTqKozH3/GwAgV6/kAUOq91qnMN8b0op7BsT2xxL7ce70s0kxjzCjc+E6HiDCouk+C\nMZxujKlTuWeMyaTms14ePr8J/P5sI1nqvUYahwJjTJYxZrwxpnuEdUYZYyJWQhpjLjXGnBBjDMHK\n3DO8p+7DfS3G7TTWv3DdeqYSeRB7jDGnGmPO9cYei1VjyrapfDtnrLVvA3/CjSHziyiLLfdeLzLG\n1GmZYozph2uRCa77rmQIfmYlUcbYmRbydyKvuWAce8NnGGNG4Fpl+RHDWlwXk5m48ZPC93Um7p4Z\nbrn32tjfEgnnjdU035v8GjXXa6RxAJurvFvCb6OG7jW9jTFXGGOO8abTvXv0LZGW97qqDY5lGOl3\nh4iISLuipJCIiIi0RLNwyY1xxpgrQmd4gyzf603+Psq4EDcaY2pVHBljJuMGVj8APO+9vRFX0ZQK\nfD1s+StxY+Gs997qT11HgF+EVoB6TzH/3Jt8t4ExleIVTFgcF2mmtbYY+Duuy5dfe2//Kc59POe9\nft/rogioPq77iL3bq0m47poeDK8U96av9CZDn4Su9/ia4FJjTPjnewFwAa7Sa37IrGBS7MrQlgRe\nQmw20ce+CXZ3E0vsT+Kegj7JGPP9sLg6A7/zJucmamBsa+0aXKVbOvCQMaa6ZZT3Wf8aN9D3OuBV\nH3YZT/k01RzcGCIXGWNuCJ3hJUAexn3ms4PvW2v/BfwTVx6zvM87dL1LcfeNlaHXRT2W4FredQP+\nM2xbxnuvMeMoxcSraH7Qm/x5eKLLGDMI+BvwOhEqb+sRd9k2QaLuB3fiKtW/AxREmP8CsAGXOPpl\n6Azv3jUL952x2FprfY4tVsHK7TxjTK1EtTHmVlyyY5f3VqTvLr/jqJV0McYcD/wVeNuPGLyWI694\nkzPC7ledgQeoaeUaqqm/JZrL097rJbiyrMJ1ARuuWcqblvHb6He4Vn3fNsZcGBZDNq5b3IXAT7y3\nq3Ctpf9ojPlW+Ma8MjoRdz6sD58vIiLS3mhMIREREWlxrLWFxpjvAo8BfzfGvI6rpOsDnIcb0+If\nuDEVIrkXeNsY80/cIMyDcQMwA9xlrd3t7afUGDMb+HfgOWPM87jKwtNwlQdX4VpzFAC/MsacBfw0\nZD+bcYM+bzDGLMY9UXs2MALXyqNWhb8PVnmvY4wxb+MqNyZZa7eFLPM4cB2uldA6a+17ce7jYeBG\nXPcxa40xL3n7OQfXncyDwI9i2M79uLL7FvC5MWY5LhGSg/sM++NawcyNcHzf9iqxM6y158YZfyQz\nqH0e9fNiS8GNibUuZNnngHuAvsA6Y8yruErwC73XWcB/R9jHKlzLmueMMe8BK621d0cKxlq7zxgz\nCZfAe9AYMxH4CNeNUbCcVwL/1YRjjsVkXEuHa4BTjTErcGUyEtfF35fA9V6CoaliLp+mstZu9p4W\nfwp4yhgzDViDG/9iLO4p8S3AD8JWvQWXKBsHFBpjXsFVbp6Au64rgX+z1u6iAd6A5z/CXY+/MsZc\ngqvQ7YNrDfAAriuznCYdbP3ux3WZdAXwL+8etQt37V2Ee9L/cWvtS7FusAll2xix3O/iZq3dbYz5\nH1yCq04rOWttpTHmelwS4g5jzEVeLFm48jwOV2k+pSlxNIW19hNjzD+Ay3Fjsz2PK5/RuHPsQtx9\n7Ou4SvIl1tppUTfYePfhkot3eC1VNuC6MDsfl1D72ItpojEmgDvf3o62sQbcibs/XgZ87N3Ps3CJ\nlI3Ay4QlS3z4LdEsrLWrjTEWdywdgFejnOfNUt4t4beRtfZtY8yduAcU/mmMWeYdby7u/pULvI+X\n2LPWVnn3o+eAvxpjVnnlcQjXBd0FuDGp/iNRD1uIiIi0JmopJCIiIi2StfYJXOXG34BhuLFnzsVV\nQE4Grgzv5z7EU7iK7lxci5XzcJV6E6y1vw9b9ke4ipaduMGHx+EqNUdba18EfoV7+jYX9/R16O+n\nSuBWb5mTvRjzgZeAc621vnb9Za19Ddfl0W7gFFxyI7wMlnjxQ+2ES6z7KMeV12xchfgE4Bu4Fj1n\nEOO4C954B+fgKoq24Sopp+LKdxuu0nhsWNd2T+Oe9N2Pq3z1q8J8KTWtgq7HVcpbXIXXD8Pi3o8b\nt2EhrnJuPK6i7gXveMqJ7HvAe7jK8TOoGZsoImvtYuBU3GfUB5eIuwhXvnfgyqY06gZ8YK39DFfJ\n9ytchfK3cJV9AVwl6Qhr7cfRtxCXuMqnqay183DJrb/gkiC34Fqn7cZVlp9irS0KW2cbcDrwM1zy\n5GrcNT0A99T+mdbauXHE8ASuPN/GHfNNuHFP7rDW/hhX5gnj3R+vwg1ivwpXcTwFGIXrVusaa23c\niY3GlG0j44/lftdYj1KTdIq07/dx9/RZuC7Lrsfdu/bhksynNzU55YNvA4/g7knjcfePd4AzrLWr\ngbtwleLHUTMWja+stf8P9338Me7+eC1eeVlrp+MS38/gvkuuwF3/jd3XR7jfBM/jknk3e/t8CneP\nPhBlvab8lmhOT1PTJdufIy3QnOVNC/htZK39DS7Z/DwuOf8dXKKzEPfdPdpaWxKy/D9wyacnvLiu\n8dY5BXgRuMBa+yAiIiJCSiCQzFbSIiIiIuInr3ujzUB3oH+wVZSIiIiIiIiIiFoKiYiIiLQtN+O6\ncPqLEkIiIiIiIiIiEkpJIREREZE2whtw/H5c1zG/SnI4IiIiIiIiItLCpCc7ABERERFpGmPMw0Av\n3BgCHYDbrLWbkhuViIiIiIiIiLQ0SgqJiIiItH63ABmABX5hrX06yfGIiIiIiIiISAuUEggEkh2D\niIiIiIiIiIiIiIiIJJjGFBIREREREREREREREWkHlBQSERERERERERERERFpBzSmUILs379f/fKJ\niIiIiIiIiIiIiEhC5eTkpMS6rFoKiYiIiIiIiIiIiIiItANKComIiIiIiIiIiIiIiLQDSgqJiIiI\niIiIiIiIiIi0A0oKiYiIiIiIiIiIiIiItANKComIiIiIiIiIiIiIiLQDSgpJ0mzcuJGNGzcmOwyR\nZqXzXtojnffSHum8l/ZI5720Rzrvpb3ROS/tkc57aWuUFBIREREREREREREREWkHlBQSERERERER\nERERERFpB5QUEhERERERERERERERaQeUFBIREREREREREREREWkHlBQSERERERERERERERFpB5QU\nEhERERERERERERERaQeUFBIREREREREREREREWkHlBQSERERERERERERERFpB5QUEhERERERERER\nERERaQeUFBIRERERERERkRa16v7sAAAgAElEQVSt6mgVOz/aye71uwlUBZIdjoiISKuVnuwARERE\nRERERERE6rPhxQ18ufZLADr16MSgCweROyg3yVGJiIi0PmopJCIiIiIiIiIiLVZJUUl1QgjgwO4D\nrJ2/lrXPruXA7gNJjExERKT1UUshERERERERERFpkQKBAJ8u/TTivOLCYvZ+upd+p/VjwDkDyMjK\naOboREREWh+1FBIRERERERERkRZpz8Y9lBSVVE+nZ9V+vjlQFWDbe9t47w/vsW3VNqoqq5o7RBER\nkVZFSSEREREREREREWlxAlUBNi/bXPNGCgwYPYD8r+aT1T2r1rJHDx5l08ubWP3H1RRvKm7eQEVE\nRFoRJYVERERERERERKTF2blmJwf3HKye7prflY7HdCSraxbHnXscx55xLBmdancZd3DPQdYuWEvh\ny4XNHa6IiEiroKSQiIiIiIiIiIi0KJVHKvns9c+qp1PSUuhZ0LNmOiWFLsd2YdCFg+h5Qk9S02tX\ncW1ftZ39W/c3W7wiIiKtRXrDi4iIiIiIiIiIiDSfoneLOFJ+pHq6+9DupGfWrcZKTUulx7AedB3Q\nlV3/2sW+z/ZVz/ty3ZfkDMhplnhFRNqKffv2sXz5ct566y02bdrErl27SE9PZ8iQIYwbN47LL7+c\n1NS21dbkiy++4NFHH2XFihXs37+fHj16MGbMGKZMmUKXLl1i2sYLL7zAPffcU+8yqampvPPOO36E\n3CRKComIiIiIiIiISItxpPwIRe8UVU+ndUwjd0huveukZ6bT99S+HC47XN3l3K71uxh88WBS09pW\n5aWISCItWbKE++67jx49enDaaafRp08fiouLWbZsGffeey8rVqzgl7/8JSkpKckO1RdFRUVMmTKF\n4uJizjvvPPLz81m3bh3z589nxYoVPPbYY3Tt2rXB7QwbNowpU6ZEnPfhhx+yatUqzjrrLL/DbxQl\nhUREREREREREpMXY+uZWKo9UVk/3LOhJWkZaTOvm5OVUJ4WOHjzK3k/30n1o94TEKSLSFg0YMICZ\nM2cyevToWi2Cpk2bxs0338zSpUtZtmwZ559/fhKj9M99991HcXExP/jBDxg/fnz1+w888ADz5s1j\nzpw53HXXXQ1uZ9iwYQwbNizivMmTJwNw5ZVX+hN0E+lRCRERERERERERaREOFh9kxwc7qqc7ZHeg\na37DT2gHHXPsMRDy8PqX6770MzwRaWcWLFjAxIkTWb58eZ15ZWVljBo1imnTpjV/YAl0+umnc+65\n59bpIq5Hjx5cddVVAKxevbpR2963bx+jRo3ijDPOqPff6NGjOXz4cJOPpSFFRUWsXLmSvn37cs01\n19SaN3XqVLKysnjppZc4ePBgo/dRWFjI2rVr6dWrF6NHj25qyL5QSyEREREREREREWkRNi/fTKAq\nUD3d84SepKTG3kVResd0sntlU/5FOQB7Nu6h8kglaR1ia2kkIg17cMXeZIdQr9vP6ubbttavXw/A\nwIEDI84LBAIMHz7ct/21dOnpLp2Qlta4e+qBAwe45ZZbqqd37NjBokWLKCgo4Jxzzql+v1u3bnTs\n2LFpwcZg1apVAJx55pl1kmDZ2dmcdNJJrFy5ko8//pgzzjijUfv4+9//DsA3vvGNRpeb35QUEhER\nERERERGRpCvZVsLu9burp7Nyszim3zFxbyenf051Uqiqooo9G/fQ64RevsUp0t4VFlckO4RmY60l\nIyODvLy8OvOCCSNjTNT1582bR2lpacz7GzZsGGPHjo07zuZw9OhRXnzxRYBGj43Tr18/pk6dWj29\ncOFCFi1axMUXX8ykSZNi2oafZbp161bAdZkXyYABA1i5ciVbt25tVFLo0KFDLF68mLS0NK644oq4\n108UJYVERERERERERCSpAoEAny75tNZ7vU7s1aiBzI/pewwpaSkEKl2Loy/XfamkkIjE7fDhw2ze\nvJn8/PyILTyCSaGCgoKo25g/fz47duyIOj/cZZdd1mKTQrNmzWLTpk2MHj260UmhcBs3bgSIOhZP\nJH6WaVlZGeBaBUUSfD+4XLxeffVVSktLGT16NL17927UNhJBSSEREREREREREUmq4o3FlBSVVE93\n7tuZTt07NWpbqempHNP3mOrt7f10LxUHKsjolOFLrCLt3ZDc9nEtFRYWUllZGbHrOIBPPvmE7Ozs\nqK1MAJ5//vlEhVftiiuuiCtJcumll3LPPffEtY8FCxbw9NNPk5+fz4wZM+KMMLoNGzYAMHTo0JjX\naY4y9cvChQsBqsdiaimUFBIRERERERERkaQJVAX4dFlIK6EUmtyyp0tel+qkUKAqwK71u+h3ar8m\nbVNEHD/H7GnJ6htPqKysjKKiIk4++eRGtWj007HHHkuHDh1iXr5Hjx5xbf/ZZ59l5syZDBw4kFmz\nZpGTkxNviBEFAgEKCwvp2bMn3bol55zq3LkzAOXl5RHnB98PLhePTZs28dFHH9GrVy/OPvvsxgeZ\nAEoKiYiIiIiIiIhI0uxcs5ODew5WT3c9risdj2naAOOde3cmNSOVqooqwHUhp6SQiMTDWgtAfn5+\nnXlr1qwhEAjUO54QNM+YQrNnz45r+XjMmzePBx54gMGDBzNr1ixyc3N92/b27dspLy9nxIgRccfk\nV5kGW3kFxxYK19CYQ/UJthL6xje+EbH7wWRSUkhERERERERERJKi8kgln73+WfV0SloKPYf3bPJ2\nU1JT6HJsF/Zt2QdAyeclHNp/iMyczCZvW0Tah2BLoUiJkJdffhmA4cOH17uN1jym0JNPPsmsWbMY\nNmwYDz/8MF27dvV1+1u2bAFg0KBBca3nZ5mOHDkSgHfeeYeqqipSU1Or55WXl/PRRx+RmZnJV77y\nlbhiPHz4MC+99BJpaWlcccUVca3bHJQUEhERERERERGRpNi1fhdHyo9UT3cf2p30TH+qq7r0r0kK\nAez61y76n9Xfl22LSNt29OhRNm3aBLgWQ6effnr1vFdeeYXFixcDMHjw4Hq305rGvwn1+OOP88gj\nj1BQUMBDDz3UYJdxd999N4sWLWL69OmMGzcupn0Eu2bLzs6OKzY/yzQvL49Ro0axcuVKnnvuOcaP\nH18979FHH+XgwYNceeWVZGVl1VqvqKiIo0ePkpeXR3p63e+sJUuWUFJSwjnnnEPv3r19i9cvSgqJ\niIiIiIiIiEhS7N28t/rvlLQUcof41zVRp+6dSM9M5+iho4DrQk5JIRGJxaZNm6ioqCA3N5dZs2Yx\ncuRI8vLy2LhxIxs2bKBbt24UFxfz+OOPM2nSpLhbkrRkL7zwAo888ghpaWmcfPLJLFiwoM4y/fr1\nq5X8qapyXXXG001asEu2+fPnU1JSwvHHH88ll1zSxOjjd+eddzJlyhRmzpzJe++9x8CBA1m7di2r\nV69mwIABTJs2rc46t912Gzt27GDhwoX061e3a9K///3vAFx55ZUJj78xlBQSEREREREREZFmFwgE\n2L9lf/V0px6dSMvwb9yFlJQUuuR1obiwGIDyL8sp31VOds/4nkoXkfYn2HXclClTWLt2La+//jof\nfPABJ5xwArNnz+aDDz7gkUceYceOHfTp0yfJ0fpr+/btAFRWVjJ//vyIy5x66qm1kkKbNm0iOzub\n0aNHx7yfgoICbr31Vp577jnmz5/P9ddfn5SkUF5eHk8++SSPPPIIK1as4O2336ZHjx5cd911TJky\nhS5dusS1vc2bN7NmzRp69erF2WefnaCom0ZJIRERERERERERaXYHdh+o1XVcIpI1Of1zqpNC4FoL\nDRw70Pf9iEjbYq0F3JhBI0aMYOLEiQwdOrR6/vHHH8/EiROTFV5CTZ06lalTp8a8fGlpKYWFhUyY\nMCHuBMrkyZOZPHlyvCH6rnfv3kyfPj3m5evrwm7gwIG8++67foSVMKkNLyIiIiIiIiIiIuKv0PF+\nIDFJoY45HenQuUP19K5/7SIQCPi+HxFpW9avX09aWlqDYwYJfPjhh6SnpzNhwoRkhyIxUlJIRERE\nRERERESaXWhSKK1DGh1zOvq+j5SUFLr0r3ly/dC+Q5RuL/V9PyLSdlRWVlJYWMhxxx1HZmZmssNp\n8c4991zefPNNevTokexQJEZKComIiIiIiIiISLMKVAXYt7UmKdSpRydSUlISsq+cvJxa01+u+zIh\n+xGRtmHLli0cOnSIYcOGJTsUkYTQmEIiIiIiIiIiItKsSneUUnm4sno6u5f/XccFdejcgcxumRza\newhwXcgNvnAwKamJSUKJSOs2ePDgFj8mjEhTtKmkkDGmA/Bz4IfA69basXGsezbwU+BMIAvYADwG\nPGytVWezIiIiIiIiIiI+aY7xhELl5OVUJ4UqDlSwd8tecgflJnSfIiIiLVGb6T7OGGOAFcA0IK5H\nPYwx5wPLgKHADOA7uKTQ74EHfA1URERERERERKSdC00KpWelk5GdkdD9HZN3TK3pXet2JXR/IiIi\nLVWbSAoZY7oB7wNpwMhGbGI2cAg411r7oLX2z9baq4Hnge8bY0b4F62IiIiIiIiISPtVWVHJ/qL9\n1dPZPbMTNp5QUEZmRq3WSLvtbiorKutZQ0REpG1qE0khoAPwFHCmtdbGs6IxZhRggGettTvCZj+M\na3U0yZcoRURERERERETauZJtJQQqa3rqT3TXcUFd+nep/rvySCXFhcXNsl8REZGWpE2MKWSt/QLX\nbVxjnOG9rogwb6X3OqqR2xYRERERERERkRDh4wl16tmpWfZ7TL9j2PnhTgJVLiH15bov6Tm8Z7Ps\nW0REpKVoE0mhJsr3XovCZ1hrS40x+4BBfu1s48aNfm2qzVCZSHuk817aI5330h7pvJf2SOe9tEc6\n7+Oze/3u6r9Ts1LZvX837K9nBR+ld02norgCgD2Fe7DrLKkd2kpHOs1H57y0RzrvpSUYOnRok7eh\nbz0IjjR4IMr88pBlRERERERERESkkaoqqqqTMgDpOc37vHJGj4yQYODQtkPNun8REZFkU0uhZuZH\nJq+tCGbXVSbSnui8l/ZI5720RzrvpT3SeS/tkc77+O3ZsIcv+KJ6uudxPenSp0s9a/irqmcVGz/d\nSNXRKgBSi1MZerE+v1jpnJf2SOe9tDVqKQQl3mu0UQ07hywjIiIiIiIiIiKNtHfL3lrT2T2iVcck\nRmpaKp37dK6eLtlWQiAQaNYYREREkklJIfjUe80Ln2GMyQFyAHUYKSIiIiIiIiLSRPu27Kv+O7Nr\nJmkd0po9hqzuWdV/Vx6u5MCuaCMKiIiItD1KCsHb3uvoCPPO9V7fbKZYRERERERERETapCNlRziw\nuyYBk92zeVsJBWXlZtWaLtmmDmJERKT9aHdJIWNMgTFmYHDaWvsh8D5wjTEmL2S5FOAOoAJ4stkD\nFRERERERERFpQ/Z9tq/WdKdenZISR2aXTFLSUqqnlRQSEZH2JD3ZAfjBGHM8cHzY2z2NMVeHTL9o\nrT0AfAJYoCBk3neBZcDrxpjfAfuA64DzgZ9aazclLHgRERERERERkXYgdDyhlNQUOuUmJymUkppC\nVres6lZLSgqJiEh70iaSQsC1wM/C3jseeC5keiCwJdLK1tqVxpjzgHu8fx1xyaPJ1to/+R6tiIiI\niIiIiEg7EggEao0nlJWbRWp68jqwycqtSQod3HOQioMVZGRlJC0eEZF4fPHFFzz66KOsWLGC/fv3\n06NHD8aMGcOUKVPo0qVLssPz1ZIlS3j//ffZsGEDhYWFlJeXc+mll3LPPfc0anvtqeyiaRNJIWvt\nDGBGjMumRHl/FfB1/6ISERERERERERGAQ/sOcXj/4erpZI0nFBQ+rlDp9lJyB+cmKRoRkdgVFRUx\nZcoUiouLOe+888jPz2fdunXMnz+fFStW8Nhjj9G1a9dkh+mbJ554go0bN9KpUyd69epFeXl5o7fV\n3soumjaRFBIRERERERERkZYrtJUQQKeeyek6Lig8KVRSVKKkkIi0Cvfddx/FxcX84Ac/YPz48dXv\nP/DAA8ybN485c+Zw1113JTFCf91xxx306tWL/v378/777zNt2rRGb6u9lV00yWunKyIiIiIiIiIi\n7UJoUig1PZWsbln1LJ146R3Tyciu6S5O4wqJSCQLFixg4sSJLF++vM68srIyRo0a1aQkRbyKiopY\nuXIlffv25Zprrqk1b+rUqWRlZfHSSy9x8ODBuLe9b98+Ro0axRlnnFHvv9GjR3P48OGGN+iTkSNH\nMmDAAFJSInYAFrNEll1ro5ZCIiIiIiIiIiKSMOHjCXXq0YmU1KZV7vkhKzeLivIKwHUfF6gKtIi4\nRFq8mb9OdgT1+8F/+bap9evXAzBw4MCI8wKBAMOHD/dtfw1ZtWoVAGeeeSapqbXbe2RnZ3PSSSex\ncuVKPv74Y84444y4tn3gwAFuueWW6ukdO3awaNEiCgoKOOecc6rf79atGx07dmzCUSRHIsuutVFS\nSEREREREREREEqb8y3IqDlZUTyd7PKGgrNwsSj53LYQqj1RyYPcBsnu1jNhEWrKUjRuSHUK9Aj5u\ny1pLRkYGeXl5deYFE0bGmKjrz5s3j9LS0pj3N2zYMMaOHRt1/tatWwEYMGBAxPkDBgxg5cqVbN26\nNe7ERr9+/Zg6dWr19MKFC1m0aBEXX3wxkyZNimkbfh+vnxJZdq2NkkIiIiIiIiIiIpIwLW08oaBO\nubXjKNlWoqSQiFQ7fPgwmzdvJj8/n7S0tDrzg0mhgoKCqNuYP38+O3bsiHmfl112Wb1JkrKyMsC1\nbIkk+H5wuabYuHEj4BI3sfL7eP3UnGXX0ikpJCIiIiIiIiIiCbPvs5qkUFrHNDp2aRndDnXs0pGU\ntBQCla5dQcm2Evqe0jfJUYm0fIGhsScJWrPCwkIqKysjdh0H8Mknn5CdnR215QnA888/n6jwEm7D\nBtcibOjQoTGv05qPtz1RUkhERERERERERBKiqrKK/Vv3V09n98xu8mDhfklJTSGrWxYHdh8AoKSo\nJMkRibQSPo7Z05LVN55QWVkZRUVFnHzyyc16T+vcuTMA5eXlEecH3w8u11iBQIDCwkJ69uxJt27d\nmrStlqK5yq41UFJIREREREREREQSonRHKZVHKqunW0rXcUFZuTVJoYPFB6k4WEFGVkaSoxKRlsBa\nC0B+fn6deWvWrCEQCNQ7nhD4P8ZOsFVScHyccA2NmxOr7du3U15ezogRI+JaryWPKdRcZdcaKCkk\nIiIiIiIiIiIJET6eUHbPljVmT1ZuVq3p0m2l5A7JTVI0ItKSBFsK5ebWvSe8/PLLAAwfPrzebfg9\nxs7IkSMBeOedd6iqqiI1NbV6Xnl5OR999BGZmZl85StfiXmfkWzZsgWAQYMGxbVeSx5TqLnKrjVQ\nUkhERERERERERBIiNCmU0SmDDtkdkhhNXeFJoZJtJUoKiQhHjx5l06ZNgGsxdPrpp1fPe+WVV1i8\neDEAgwcPrnc7fo+xk5eXx6hRo1i5ciXPPfcc48ePr5736KOPcvDgQa688kqysmrf2+6++24WLVrE\n9OnTGTduXIP7CXallp0dXyK/JYwpVFRUxNGjR8nLyyM9vSb90diya4uUFBIREREREREREd9VVlRS\nsq1mnJ6W1koIIL1jOhnZGVSUVwDUildE2q9NmzZRUVFBbm4us2bNYuTIkeTl5bFx40Y2bNhAt27d\nKC4u5vHHH2fSpEnN2rrkzjvvZMqUKcycOZP33nuPgQMHsnbtWlavXs2AAQOYNm1anXWqqqoASEtL\ni2kfwS7U5s+fT0lJCccffzyXXHKJfwcRh+XLl/Paa68BsGfPHgA+/vhj7r77bgC6du3K7bffXr38\nbbfdxo4dO1i4cCH9+vWrta3GlF1blNrwIiIiIiIiIiIiIvHZ//l+ApWB6ulOvVrWeEJBnXJr4ird\nXkqgKlDP0iLSHgS7jpsyZQoXXXQRH3/8Mf/4xz9IS0tj9uzZ3HDDDWRmZrJjxw769OnTrLHl5eXx\n5JNPMm7cONatW8fTTz/Ntm3buO6663jiiSfo2rVrnXU2bdpEdnY2o0ePjmkfBQUF3HrrraSnpzN/\n/nw++eQTvw8jZhs2bGDRokUsWrSId955B4Bt27ZVv7d06dKYt9WYsmuLfG0pZIxJs9ZWNrykiIiI\niIiIiIi0ZXXGE+rR8loKgetCbv/n+wGoPFJJ+e5yOvfqnOSoRCSZrLWAGzNoxIgRTJw4kaFDh1bP\nP/7445k4cWKywqN3795Mnz49pmVLS0spLCxkwoQJdOnSJeZ9TJ48mcmTJzc2RN9MnTqVqVOnxrx8\nQ13YxVN2bZXfLYWeN8Z09HmbIiIiIiIiIiLSyoQmhTp26Uh6ZsscxaDOuEJF6kJOpL1bv349aWlp\nDY4Z1Bp8+OGHpKenM2HChGSHIi2E30mhrwMvGWP0OIWIiIiIiIiISDtVWVFJ2Rdl1dOderbMruPA\nJaxS0lKqp0u3lSYxGhFJtsrKSgoLCznuuOPIzMxMdjhNdu655/Lmm2/So0ePZIciLYTfSaF5wFhg\niTEmN9pCxpizjTFv+bxvERERERERERFpAcq/KIeQoXmyumVFXzjJUlJTasVXsk0thUTasy1btnDo\n0CGGDRuW7FBEEsLXdrvW2onGmL3Ad4HXjDEXWWt3BucbY4YAvwKu9HO/IiIiIiIiIiLScpTurN3a\nJrNry37aPis3iwO7DwBwsPggFQcqyOiUkeSoRCQZBg8ezLvvvpvsMEQSxvfOXK213zPGFAM/Ad40\nxlwIlAI/A/4NyAD2A/f5vW8REREREREREUm+sp01XcelpqfSoXOHJEbTsDrjCm0vofuQ7kmKRkRE\nJHH87j4OAGvtdOAOYCCwAigEvgdUAvcDg6y1v0rEvkVEREREREREJLnKdtQkhTK7ZpKSklLP0slX\nJylUpC7kRESkbfK9pVCIImAP0BvXi+z/Ad+z1hYlcJ8iIiIiIiIiIpJElRWVlO8ur55u6V3HAaR3\nTKdDdgeOlB8BoHRbaQNriIiItE6+J4WMMecDvwRGAinAv4DjgVOBTn7vT0REREREREREWo7yL8rd\n48Ge1pAUAtdaqDoptKOUQFWAlNSW3cJJREQkXr52H2eMeRl4BTgdsMAV1toTgf8AjgXeMMac4uc+\nRURERERERESk5SjdWbuVTatJCnWv6UKu8kgl5bvK61laRESkdfJ7TKELgd3AbcBXrLX/ALDW/h6Y\nDOQCS40x5/m8XxERERERERERaQHKdtaMJ5SankqHzh2SGE3s6owrtE3jComISNvjd1LoF8AQa+0c\na21l6Axr7ZPAtUAmsNgYM87nfYuIiIiIiIiISJKV7ahJCmV2zSQlpXV0wdaxS0dS02uqypQUEhGR\ntsjXpJC19ifW2qgj8Vlr/w5cDlQBf/Vz3yIiIiIiIiIiklyVFZWU767pdq21dB0HkJKSQma3mnhL\nt0Wt4hIREWm1/G4p1CBr7au4bubUMauIiIiIiIiISBtS/mU5BGqmW1NSCGp3IXew+CAVByqSGI2I\niIj/mj0pBGCtfQcYk4x9i4iIiIiIiIhIYoR2HQetOykE6kJORETanqQkhQCstWuTtW8RERERERER\nEfFf6c6aLtdS01Pp0LlDEqOJX1Y3JYVERKRtS1pSSERERERERERE2pbQlkKZXTNJSUlJYjTxS++Y\nXiuRpaSQiIi0NUoKiYiIiIiIiIhIk1VWVFK+u2YI6dbWdVxQaBdypdtLCVQF6llaRESkdUlPdgAi\nIiIiIiIiItL6lX9ZDiH5k9acFNq/dT8AVRVVlO8qp3PvzkmOSkTEeeihh/jkk0/YunUr+/fvp2PH\njvTp04cxY8ZwzTXX0LVr12SH6Jt9+/axfPly3nrrLTZt2sSuXbtIT09nyJAhjBs3jssvv5zU1Pja\nvbz55pssWLCAzZs3s3//frp3705BQQETJkzgpJNOStCRtCxKComIiIiIiIiISJOFdh0HrTspFKqk\nqERJIRFpMebNm0dBQQGjRo2iW7duHDx4kLVr1/LYY4+xcOFCnnjiCXr37p3sMH2xZMkS7rvvPnr0\n6MFpp51Gnz59KC4uZtmyZdx7772sWLGCX/7ylzF3VfrQQw/x5z//mZycHMaMGUPXrl0pKiri9ddf\nZ9myZcyYMYOvfe1rCT6q5PM1KWSMWQrMsdY+18ByfwTOstae4Of+RUREREREREQkOUp3llb/nZqe\nWmtsntakY5eOpKanUnW0CnDjCvU7rV+SoxIRcZYtW0bHjh3rvD979mzmzp3L3LlzufPOO5MQmf8G\nDBjAzJkzGT16dK0WQdOmTePmm29m6dKlLFu2jPPPP7/Bbe3evZunn36a3NxcnnnmGXJzc6vnrVq1\niu9+97s88sgjSgo1wljghRiWSwMG+bxvERERERERERFJkrKdNS2FMnMyY35yu6VJSUkhs1smB3Yd\nAFxSSETapwULFjBz5ky+853vMHTo0FrzysrKuOCCCzj11FOZM2dOs8UUKSEEcOGFFzJ37lw+//zz\nRm133759XHLJJQQC9Y+jlpGRwdKlS6PG4afTTz894vs9evTgqquuYs6cOaxevTqmpNDOnTupqqri\nxBNPrJUQAhg5ciTZ2dns27fPl7hbuiYnhYwxVwBXhLw13hhzYj2r9AAuAfY0dd8iIiIiIiIiIpJ8\nlRWVlO8qr55urV3HBWXlZlUnhQ7tPcSR8iN0yG6dLZ9E/LbmL2uSHUK9Rkwa4du21q9fD8DAgQMj\nzgsEAgwfPty3/TXFG2+8AcCQIUMatf6BAwe45ZZbqqd37NjBokWLKCgo4Jxzzql+v1u3bs2SEGpI\nerpLbaSlpcW0fP/+/cnIyGDdunXs27ev1thL77//PuXl5YwZMyYhsbY0frQU6gicBQzDDSd4uvev\nPkeAn/mwbxERERERERERSbLyL8tdrZAns1vrTgp1yu3EnpDnmUu3l9J9aPckRiTScuzfuj/ZITQb\nay0ZGRnk5eXVmRdMGCaB/FoAACAASURBVBljoq4/b948SktLo84PN2zYMMaOHRvTsn/5y184cOAA\nZWVlfPLJJ6xZs4YhQ4Zw4403xry/UP369WPq1KnV0wsXLmTRokVcfPHFTJo0KaZtJPJ4Qx09epQX\nX3wRgLPOOiumdXJycvje977H7373O8aPH8+YMWPIycmhqKiIN954g1GjRnHXXXfFHUtr1OSkkLX2\nWeBZY0w3XOufOcCz9axyCNhorS1u6r5FRERERERERCT5ynaU1Zpu7S2FwpNaZV+UKSkk0s4cPnyY\nzZs3k5+fH7E1SjApVFBQEHUb8+fPZ8eOHTHv87LLLosrKVRcXFPFftZZZzF9+nS6desW8/7qs3Hj\nRsAlbmKVyOMNNWvWLDZt2sTo0aNjTgoBXH/99fTt25ef//znLFy4sPr9/v37c9lll9XpVq6t8m1M\nIWvtXmPMk8Dz1trX/NquiIiIiIiIiIi0bKU7a54MT01PpUPn1t3VWnrHdNKz0jl68ChQe7wkkfYu\nZ0BOskNoFoWFhVRWVkbsOg7gk08+ITs7mwEDBkTdxvPPP5+o8Fi8eDEAe/bs4aOPPmLWrFnccMMN\n/Pa3v603URWrDRs2ANQZS6k+iTzeoAULFvD000+Tn5/PjBkz4lr3qaeeYs6cOVx77bVce+21dO/e\nnS1btjBr1iymT5/Ohg0b+P73v5+YwFsQ35JCANbam2NZzhjTD+hirV3v176NMbm4Lum+CfQFdgMv\nAj+11jaYnjTGTAJuBUYAHYCtwAvAz621Gv9IRERERERERCSK0KRJZk4mKSkpSYzGH5k5mZQddMdV\n9oWSQiJBfo7Z05LVN55QWVkZRUVFnHzyyUm/33Xv3p2vfvWrFBQUcPXVVzNjxgzmz5/fpG0GAgEK\nCwvp2bOnby2P/PDss88yc+ZMBg4cyKxZs8jJiT1BuXr1ah5++GHGjh3LHXfcUf1+QUEBv/nNb7j6\n6qt55pln+Na3vsWxxx6biPBbDF+TQnG4BZgK9PdjY8aYLGA5UAA8DKwChgI/BM43xpxmrd1bz/q/\nAO4C3gX+BygDzgb+HRjnrV/iR6wiIiIiIiIiIm1JZUUl5bvKq6dbe9dxQZldM6uTXYf3H+booaOk\nZyarKk1Empu1FoD8/Pw689asWUMgEKh3PCFovjF2APr27cvAgQPZsGED+/bto2vXro3aDsD27dsp\nLy9nxIj4EoCJPN558+bxwAMPMHjwYGbNmhV3V29vvvkmwP9n787D5LrrO9+/T1V3V/UmtVZLso1t\nCevnBRtjQ4CwOizGrAYCzAyEJeQONzFPhutM5iEwCUsgM3PD5IawBBgctkwgJgTMloAJ493BGNtg\nY+eHvMi2rH2xurt6rzr3j9NdXd1Sa+vTql7er+epp+rUOXV+3yqVuqX61Pf345JLLjlkX7lc5rzz\nzuP6668nxmgodCJCCC8DLgQO96+AFcBvAaUch3wPcAFwZYzx0w11/Bz4JvDHwFUz1LoS+ENgK/D8\nGOPw+K4vhBD2Au8F3gF8PMd6JUmSJEmSFoXK7gqkk9vT1+NZqMrLD11XqOeME/+QVdLCMtEpdLjw\n4Yc//CEA55577hHPcbLW2Jmwd+9eAAqFwgmfA2Dr1q0AbNy48bgeN1fP90tf+hKf+tSn2Lx5M5/8\n5CdPKPAaGRkB4Iknnjjs/gMHsp6S1tbW4z73QpNrKBRC6AJ+ADzrKIcmwOx62KZ6K1ABrp52/7XA\nNuAtIYQ/iDGmhzwSnkT2OtzeEAhNuJEsFDozx1olSZIkSZIWjenr7SymTqFGhkLS0jE2NsaDDz4I\nZB1Dz3jGM+r7rrvuuvp6Pps2bTriefJeY+eRRx5h1apVdHV1Tbm/Vqvxmc98hv3793PhhReybNmy\nKfs/9KEP8b3vfY8/+ZM/4ZWvfOVRx6lUsu7Pzs7O46pvLtYUuvrqq/nsZz/LOeecwyc+8YmjThm3\nbds2xsbGOO2002hpmYw/LrroIr7+9a/zzW9+k9e+9rWsXbu2vu/WW2/lF7/4BaVSiQsuuCD35zDf\n5N0p9MfAs8mCmB8BQ2Tr9PwjsBt4EdAJ/D7wrTwGDCEsI5s27qbpoU6MMQ0h3A68DjgLeOgwp3gY\nGCabbm66M8ev782jVkmSJEmSpMWmb+fkVEFJMaGtq62J1eSnpb2FQmuB2mgNODT8krR4Pfjgg4yO\njrJy5Uo+9alP8fSnP53TTjuNLVu28Ktf/YoVK1awf/9+rr76at7ylrectCDh1ltv5dOf/jRPfepT\n2bBhA8uXL2f//v3ceeedPP7446xatYr3ve99hzyuVst+jhWLxWMa50lPehKQdf709vZy3nnncdll\nl+X3RI7Rd7/7XT772c9SLBa56KKL+Pu///tDjtmwYcOUoOvKK69kx44dfOtb32LDhg31+1/0ohdx\n7bXXcvvtt/OmN72JF7zgBaxatYqtW7dy8803k6YpV1555aym3Vso8g6FrgD+Dbg4xjgUQjiDLBT6\ncozx2yGEFuAvgf8H+D5ZaDRbZ4xfb5th/6Pj1xs5TCgUYzwYQvhT4CMhhE+M19cH/BrwfuBu4H/n\nUCcAW7ZsyetUi4aviZYi3/dainzfaynyfa+lyPe9lqKl/r7ft3Vf/Xaho8DOXTubWE2+Cu2TodD+\nR/cv+T/rCb4OWuxuvPFGAF796leze/dubrzxRu688042bdrEH/3RH3H//ffzjW98g61btzI4OHjS\n/k6ccsopPP/5zyfGyH333cfAwAClUon169fzute9jssuu4xqtXpIPffddx/lcpn169cfU63FYpE3\nvOENXHfddXzta1/jZS972XFPJZeHe+/NejWq1Spf+9rhJx4799xzp6ztNDo6CmRT4E10PE248sor\n2bx5M7fddhs//vGPGRkZoauri6c+9alcdtllXHjhhfP+59vZZx+ut+X45B0KnQH8zxjj9LAnAYgx\njoUQ/hNZ0PJfxy+z1T1+PTDD/sq04w4RY/xoCGEX8Ang3Q27vgu89TDPR5IkSZIkaclLqyljvWP1\n7ZauOVm+ummKncX68xvrGyOtpiTFpMlVSZprDz/8MJCtqfOSl7yEN7/5zVP2b9y4kVe84hUnva7T\nTz+dt7/97cf1mEqlwqOPPsrLX/7y45oO7oorruCKK644zgrz9frXv57Xv/71x/WYj3/84zPua2lp\n4fLLL+fyyy+fbWkLWt6/qWvAYMP2xO36JIcxxmoI4VrgjeQTCs1aCOF3gb8Cfgh8FdgDPBP4L8D3\nQwiXxxgPvwLVccojyVssJlJXXxMtJb7vtRT5vtdS5PteS5Hvey1Fvu+h9/FedqaTnUGrTl3F8nVH\nXu9hITk4cpDtO7ZnGymsX7ae7g0zfu940fM9r6Vi586dFItFXvjCF/LYY48BC/d9f9NNN9Ha2sqV\nV17J6tWrm12O5oG8Q6FHgec2bO8FUuBipk7BNgacmtOYvePXM8WcXdOOmyJkvWV/BfxLjLEx3v1B\nCOHnZGsfvY8sIJIkSZIkSdK46evslHvKTapkbkx/Pv27+pd0KCQtBdVqlQceeIAzzjiDcnnh/0x7\n3vOex80339zsMjSPFHI+33eBl4QQvhVC2BxjrAG/BN4ZQng2QAhhPfAfgLwmmH2YLHg6bYb9E2sO\nzTQZ4G+QhWP/eJh9/zR+7ktnU6AkSZIkSdJi1Lezr347KSa0dbU1sZr8tXW1kRQmp4vr39V/hKMl\nLQZbt25laGiIzZs3N7sUaU7kHQp9lCx8eRWTYcxfAcuAm0MI+4DHgE0cPoQ5bjHGCvAL4OIQwpTo\nNoRQBH4deCzG+OgMp5joMDpc7FsiWw9p4UfCkiRJkiRJOevfMRmSlHvKJMniWm8nKSSUlpfq24ZC\n0uK3adMmbr/9dj784Q83uxRpTuQaCsUYD5BNFfdO4L7x+z4PfBDoB1aQTR33BeBPchz6aqADeNe0\n+98CrAU+P3FHCOGcEMJZDcfcOn79phDC9H+5vGHaMZIkSZIkSQJqYzUG9g7Ut9t72ptYzdwpL5/8\nrnBld4W0ljaxGkmSZifvNYWIMQ4AX5x234dDCB8FVgN7xqeVy9NngDcDHwshnAHcAZwPXAXcA3ys\n4dj7gQicM17brSGEr5MFQDeHEK4B9gDPAK4EdpF1QEmSJEmSJGlc/+7+KQHJYltPaELj86qN1hjc\nP0jH6o4mViRJ0onLPRSaSYyxShawzMW5R0MILyXrSHo98G5gN1mH0AfGg6oj+ffAjcDbyQKgNmA7\n8DfAn8YYH5+LuiVJkiRJkhaqxqnjYBGHQsunPq/+Xf2GQpKkBeukhUJzLcbYS9YZdNVRjjtkctvx\nwOqT4xdJkiRJkiQdRd/OvvrtpJjQ1t3WxGrmTmlZacp2/85+1p6/tknVSJI0O7muKSRJkiRJkqSl\nobFTqNxTJkkO+R7uolBoKUwJvPp39R/haEmS5jdDIUmSJEmSJB2X2liNgb2Ts/W397Q3sZq51zg1\nXv+uftI0PcLRkiTNX4ZCkiRJkiRJOi79u/tJa5PByGJdT2hC47pCY4NjDPcNN7EaSZJOnKGQJEmS\nJEmSjkvj1HGwBEKhac+vsrPSpEokSZodQyFJkiRJkiQdl/6dk6FQUkymrLmzGDV2CoHrCkmSFq6W\nvE8YQngN8DZgM9AOzLTKYBpj3JT3+JIkSZIkSZpbfTv76rfLPWWSZKaPfxaHYluRlvYWxgbHAEMh\nSdLClWsoFEJ4J/A5Zg6CGrkinyRJkiRJ0gJTG6sxsGegvr3Yp46bUO4p0z+YhUGNnVKSJC0keXcK\nvYcs7Hkv8EPgIIY/kiRJkiRJi0b/7n7S2uTHPe097U2s5uQpLy/X11Ia7h1mdHCU1vbWJlclSdLx\nyTsUOhv4Sozxz3M+ryRJkiRJkuaBiWBkwlLqFGrUv6ufFWeuaFI1kiSdmELO5+sFfpXzOSVJkiRJ\nkjRPNK6nkxQT2rrbmljNyVNePjUUquyqNKkSSZJOXN6h0C3A+TmfU5IkSZIkSfNEYyhUXl4mSY5l\naemFr6W9hWJbsb7tukKSpIUo71Do/cDLQwhvzvm8kiRJkiRJarK0llLZPdkhM717ZjFLkoTS8lJ9\nuzEckyRpoch7TaHnAlcDXwghXAX8DNg7w7FpjPH9OY8vSZIkSZKkOTKwd4C0mta3Sz2lIxy9+JSX\nlxnYMwDAwL4BqqNViq3FozxKkqT5I+9Q6DNACiTA08YvM0nJOoskSZIkSZK0APTvntods5Q6hQDK\nPQ3PN4XK7grLTl3WvIIkSTpOeYdCHyYLeyRJkiRJkrTITFlHJ4HSsqXXKdSof1e/oZAkaUHJNRSK\nMX4wz/NJkiRJkiRp/mhcR6fUXaJQzHu56vmtrbuNpJjUp9Cr7Koc5RGSJM0veXcK1YUQEmAjsBqo\nAXtijFvnajxJkiRJkiTNnTRNp4QgS23qOIAkSSgvKzN4YBCYGpJJkrQQ5B4KhRDWAB8F3gR0Tdu3\nD/gb4MMxxoG8x5YkSZIkSdLcGO4dZmxorL5d6llaU8dNKPWU6qFQZXeFtJaSFJImVyVJ0rHJtcc3\nhLAauA34HaAb2AbcBfwc2E7WNfSHwE0hhI48x5YkSZIkSdLcmd4VsxQ7hWDq866N1RjY5/eeJUkL\nR96dQu8lmzLuk8CfxRh3Nu4MIZwOfAD4beAq4CM5jy9JkiRJkqQ50L/TUAig3DP1effv6qdzTWeT\nqpEk6fjkvRrgq4DrYoy/Pz0QAogxPhZj/B3gZuCNOY8tSZIkSZKkOdK4nlBLewvFtmITq2me0rIS\nNMwWNz0skyRpPss7FDod+MkxHHczsCnnsSVJkiRJkjRHGqePm94ts5QUigVK3ZPrKTWGZZIkzXd5\nh0JV4FjWCioAac5jS5IkSZIkaQ6MDowy3Dtc316qU8dNaHz+/bv6SVM/5pIkLQx5h0K/Al4SQpjx\nvCGEIvDS8WMlSZIkSZI0z/Xvnrae0BLuFAIo9Ux2Co0NjU0JzCRJms/yDoX+HrgA+KcQwq+HEFom\ndoQQWkMIzwO+DzwV+N85jy1JkiRJkqQ5MH2KNDuFpj5/1xWSJC0ULUc/5Lj8JfBy4CXAi4FqCOEg\n2fJ7y4Di+O3rgI/nPLYkSZIkSZLmQGPoUWgt0NKe90dKC8shodCuflaH1U2qRpKkY5drp1CMcYQs\nDPrPwD1kAdAqYOX4IXcBvwdcHmMcy3NsSZIkSZIkzY3+XZOhULmnTJIkTaym+YptRVo7Wuvbja+P\nJEnzWe5f6xgPe/4C+IsQQhtZIJQC+2OMo3mPJ0mSJEmSpLlTHa0ysG+gvr3Up46bUF5eZnQg+6jL\n6eMkSQvFnPb6jncO7ZzLMSRJkiRJkjR3BvYMZF/3HVfuMRQCKPWU6NvRB8BI3wijA6NTuockSZqP\nZhUKhRDeCvw0xnh/w/YxizF+eTbjS5IkSZIkaW5NnxrNTqHM4dYVWnHWiiZVI0nSsZltp9AXydYP\nur9hO53p4AbJ+HGGQpIkSZIkSfNY49RoSSGhrautidXMH9M7pgyFJEkLwWxDoQ8BtzZsf5hjC4Uk\nSZIkSZK0APTvngyFSstLJIWkidXMHy3lFoptRaojVcB1hSRJC8OsQqEY44embX9wVtVIkiRJkiRp\n3khrKZXdlfq2U8dNSpKEck+5/vpMn2ZPkqT5qJDnyUIIPw4hvOEYjvt8COGXeY4tSZIkSZKkfA3u\nH6Q2WqtvT58ybalrDMkG9w3Wu4YkSZqvcg2FgBcCpx/DcUVgY85jS5IkSZIkKUfTu1/sFJrqcOsK\nSZI0n812TSFCCK8BXtNw15tCCE85wkNWA5cB+2Y7tiRJkiRJkubO9JCjtKzUpErmp0NCoZ39LD99\neZOqkSTp6GYdCgEl4NnAZiAFnjF+OZIR4AM5jC1JkiRJkqQ50hgKtXW3UWjJe9KZha21s5VCS4Ha\nWDbFnp1CkqT5btahUIzxGuCaEMIKsu6fvwauOcJDhoAtMcb9sx1bkiRJkiRJcyNNUyo7K/Vtp447\nVJIklHvKDOwdALJOIUmS5rM8OoUAiDEeCCF8Cbg2xnhDXueVJEmSJEnSyTfSN8Lo4Gh921Do8BpD\nocqeCrWxmh1VkqR5K7dQCCDG+A6AEEIJWBFj3Nm4P4RwAfBAjHEwz3HHz72SbEq6K4D1wF7g+8Af\nxxh3HMPjS8B7gbcAp48//nvA+2OMe/OuV5IkSZIkaT6bPhXa9PVzlJnyuqRQ2V2he0N38wqSJOkI\ncv/aQgjhjcBO4J2H2f1hYEcI4Q05j9kOXA/8LvAN4O3AZ4E3AbeMT213pMe3kAVA/xX4LvA7wD+Q\nPYcbQghtedYrSZIkSZI0300PhUrLS02qZH6b3kHVt7OvSZVIknR0uXYKhRCeA3yNbN2gA4c55CfA\npcBXQwj7Yow/zmno9wAXAFfGGD/dUM/PgW8CfwxcdYTH/9/Ai4C3xRi/PH7f34YQ9gK/DTwTuCmn\nWiVJkiRJkua9yq7J9YRa2ltoKeX6MdKi0dbdRlJMSKsp4LpCkqT5Le9OoQ+STbv2lMZwZkKM8b8D\nFwL7yKZqy8tbgQpw9bT7rwW2AW8JISRHePyVwBbgK413xhg/EmPcGGM0EJIkSZIkSUtKY6eQ6wnN\nLEmSKa+PoZAkaT5L0jTN7WQhhF7gf8UY/+Aox/0F8M4Y4/IcxlwGHARuijE+/zD7vwG8DtgUY3zo\nMPtPAx4DPhVjfPf4fWVgOMZ4wi/OwYMHD/vYLVu2nOgpJUmSJEmSToraSI1d1+6qb5dOLdH+pPYm\nVjS/DTw8wMjOkWyjAOteu46kcKTvJ0uSdPzOPvvsw96/fPnyY/6lk3enUIGsC+hoDgDFnMY8Y/x6\n2wz7Hx2/3jjD/nPGrx8MIfynEMJWYBAYDCF8K4Tw5FyqlCRJkiRJWiBGD45O2S525vUxzuI05fWp\nwVjvWPOKkSTpCPKeDHYL8BvAn810QAihALwSOKRr5wR1j18PzLC/Mu246VaOX78NaAM+CuwiW2Po\n3cCzQwgXxRh35FDrjEneUjTRNeVroqXE972WIt/3Wop832sp8n2vpWgxv++3HdjGfvbXt9efuZ62\nzrYmVjS/DbUP8fCDD9e3V7atZN3Z65pY0dxYzO95aSa+77XY5B0KfQX4WAjhb4CPxRjvm9gRQmgF\nLgWuAp4OvD/nsU/UxL9oTiFbC2mi0+nbIYRdZCHRHwD/uRnFSZIkSZIknWyVXZX67UJLgdaO1iZW\nM/+VukskhYS0lq0m0L+zH57a5KIkSTqMvEOhjwMvAd4OvC2EMEq23k+JyU6dBLge+J85jdk7ft05\nw/6uacdNN7H637cbAqEJV5OFQi884eokSZIkSZIWmP5d/fXb5Z4ySeL6OEeSFBJKy0oMPTEEjIdC\nkiTNQ7muKRRjrAIvB34fuIcsdFoDLAOqwN3Ae4CXxhhHZzrPcXoYSIHTZtg/sebQlhn2bx2/Ptzk\nuHvHz73sRIuTJEmSJElaSGpjNQb2Ts7SX15ebmI1C0e5Z/J16t/VX+8akiRpPsm7U4gYYwp8Evhk\nCKENWA3UgH05BkGN41VCCL8ALg4hlGOMQxP7QghF4NeBx2KMj85wivvIupkuOsy+08k6m7blXLYk\nSZIkSdK8VNlbmRJolJaXmljNwtEYCtXGagzsG6BzzUwT20iS1By5dgpNF2MciTFujzHunItAqMHV\nQAfwrmn3vwVYC3x+4o4QwjkhhLMaawT+DrgkhPCqaY9/9/j1d3KvWJIkSZIkaR6aPvVZY9ihmU1/\nnRqn4JMkab7IvVMohPAa4G3AZqCdrNPmcNIY46achv0M8GbgYyGEM4A7gPOBq8imsftYw7H3AxE4\np+G+DwCXAV8PIfx3sinlfgP4LbIp7z6TU52SJEmSJEnzWmVXpX47KSSUuu0UOhalZaXsU7DxJqv+\nHf2c8pRTmlqTJEnT5RoKhRDeCXyOmYOgRrlNrBpjHA0hvBT4IPB6sg6f3WQdQh+IMQ4c4eHEGPeE\nEJ4FfAT4j2RT3u0A/gL4cIxxMK9aJUmSJEmS5rPGDpfSshJJ4Vg+5lGhWKC0rMTwwWHg0I4rSZLm\ng7w7hd5DFva8F/gh2Vo9J2VVvRhjL1ln0FVHOe6w/5KJMe4hm35u+hR0kiRJkiRJS0KaplR2T3YK\nuZ7Q8SkvL0+GQrv6SdOUJDFUkyTNH3mHQmcDX4kx/nnO55UkSZIkSdIcGzowRHWkWt8uL3c9oeNR\n7ilz8NGDAFRHqgwdGKJ9ZXuTq5IkaVIh5/P1Ar/K+ZySJEmSJEk6CaZPeVbuMRQ6HtNfr76dfU2q\nRJKkw8s7FLoFOD/nc0qSJEmSJOkk6N89NRQqLXP6uOMxvbPKdYUkSfNN3qHQ+4GXhxDenPN5JUmS\nJEmSNMcaQ4zWzlaKrcUmVrPwFFoKtHW31bcNhSRJ803eawo9F7ga+EII4SrgZ8DeGY5NY4zvz3l8\nSZIkSZIknaD+XZMhhlPHnZhyT5mRvhEgez3TNCVJkiZXJUlSJu9Q6DNACiTA08YvM0nJOoskSZIk\nSZLUZMN9w4xWRuvb06dC07EpLy/T+1gvAGODYwz3DvtaSpLmjbxDoQ+ThT2SJEmSJElaQPp29E3Z\nLq8wyDgR0zus+nf0GwpJkuaNXEOhGOMH8zyfJEmSJEmSTo6+7VNDofae9iZVsrBND4X6dvax+pzV\nTapGkqSpCs0uQJIkSZIkSc3XGAq1dbVRbCs2sZqFq9hapLWztb7duE6TJEnNZigkSZIkSZK0xKVp\nOmX6OKeOm53GbqH+Hf2kqastSJLmh1ynjwsh3Hoch6cxxufkOb4kSZIkSZKO3+D+QarD1fp2+wqn\njpuNck+ZvsezkG10YJSR/hFK3aUmVyVJUs6hEPCsYzgmBZLxa0mSJEmSJDVZY5cQGArN1vR1hfp3\n9hsKSZLmhbxDoUuPsO8U4BLgncD/B/xtzmNLkiRJkiTpBDSuJ0QCpeUGGLNRXn5oKLTq7FVNqkaS\npEm5hkIxxhuOcsg1IYTPAbcDvwQeyXN8SZIkSZIkHb/GUKi8vEyh6DLUs9FSaqGlvYWxwTEA+nf1\nN7kiSZIyJ/03fIzxQeAa4H0ne2xJkiRJkiRNVavWpoQW5RXlIxytY9U4hVz/TkMhSdL80KyvfWwH\nzm3S2JIkSZIkSRpX2V0hrU4u/ex6QvloDIWGe4cZqYw0sRpJkjLNCoWe3aRxJUmSJEmS1GDKekIY\nCuWlMRQCp5CTJM0Pua4pFEJ461EO6QEuB14K3JLn2JIkSZIkSTp+fTsmQ6GkmNDW3dbEahaPQ0Kh\nnf2s3LiySdVIkpTJNRQCvgikRzkmAQaAP8p5bEmSJEmSJB2nxk6h9hXtJEnSxGoWj9ZyK8VSkepw\nFXBdIUnS/JB3KPRlZg6FUmAIeAj4+xjjYzmPLUmSJEmSpOMwNjzGwN6B+nZ5RfkIR+t4tfe016eN\nMxSSJM0HswqFQggbgP4YY+/4XX8C7I8x+ltOkiRJkiRpnpseVLieUL7KPeV6KDT0xBCjg6O0trc2\nuSpJ0lJWmOXj7wd+r2H7YeD/muU5JUmSJEmSdBI0Th0HhkJ5m76uUGVXpUmVSJKUmW0oVAY2N2wn\n4xdJkiRJkiTNc42hULFUpKU975UGlrbpodBE15AkSc0y29/09wNvCyFcAuwbv+93QwivPIbHpjHG\nF81yfEmSJEmSJJ2gvh2ToVD7inaSxO/65qmlvYViW5HqSBWAvp19R3mEJElza7ah0O8B1wAXjG+n\nwKbxy9GksxxbkiRJkiRJJ2ikf4Th3uH6dnlF+QhH60QkSUK5p0xldzZtXP8OO4UkSc01q1Aoxnhr\nCOF0YC3QDjwEfBT4fA61SZIkSZIkaY40dgmB6wnNlfLyyVBocP8gY8NjtJScpk+S1Byz/g0UY0yB\nXQAhhBuAX8QYH5nteSVJkiRJkjR3GtcTAkOhuTJ9XaHK7grLT1/epGokSUtdrl9LiDFemuf5JEmS\nJEmSNDcaO4Va6+ueJgAAIABJREFUO1spthWbWM3iNT0U6tvRZygkSWqaQrMLkCRJkiRJ0smVpumU\nTiG7hOZOa2crxdbJwK13W28Tq5EkLXWGQpIkSZIkSUvM0IEhxobG6tuGQnMnSRLaV02+vr3beknT\ntIkVSZKWMkMhSZIkSZKkJaZx6jiA8oryDEcqD+0rJ0Ohkf4Rhg4ONbEaSdJSZigkSZIkSZK0xDRO\nHUdy6Lo3ylfHqo4p204hJ0lqFkMhSZIkSZKkJaaxU6i0rESh6EdEc6m8ogzJ5LahkCSpWVryPFkI\n4afAl4Cvxhj35XluSZIkSZIkzV6tWqN/Z3992/WE5l6hWKDcU2boQDZtnKGQJKlZ8v4ayCXAx4Ht\nIYRvhRBeH0Joy3kMSZIkSZIknaCBPQPUxmr1bUOhk6NxCrnK7gpjQ2NNrEaStFTlHQo9iywU2gW8\nGrgG2BFC+OsQwq/nPJYkSZIkSZKOU+/2qV0q5RWuJ3QytK+cGr5N/3OQJOlkyDUUijHeHmO8Ksb4\nJOB5wKeAIeBdwE0hhAdCCH8SQjgrz3ElSZIkSZJ0bPp3TE4dlxQTSstKTaxm6WjsFALofcxQSJJ0\n8s3ZKoIxxltijL8PnAb8BnA1sBL4APBACOHGEMI7Qgh+HUWSJEmSJOkk6dveV79d7imTJEkTq1k6\nWsottHa21rddV0iS1Awtcz1AjDEFrg8h3AB8m2x6ubOA5wLPAT4WQvgU8N9ijIMnOk4IYSJwugJY\nD+wFvg/8cYxxx3Geqwz8HNgMXBpjvP5E65IkSZIkSZovqiNVKnsr9W3XEzq5OlZ2cLByEMimj0tr\nKUnBUE6SdPLMWafQhBDCJSGETwA7gGvJAqGDwOeA9wC7gf8K3B5CWHuCY7QD1wO/C3wDeDvwWeBN\nwC0hhBXHeco/JguEJEmSJEmSFo2+nX2QTm4bCp1c7asmX+/aaI3+Xf1HOFqSpPzNSafQeLjzW8Db\ngPOBBKgBPwK+AHwzxjg8fvgnQgjvAz5C1kX0709gyPcAFwBXxhg/3VDHz4FvkoU8Vx1j7RcAfwjc\nBTztBGqRJEmSJEmalxrXEwIor3BW/5PpkHWFtvXSvb67SdVIkpaiXEOhEMLryLp0Lhs/dwJsAb4I\nfDnG+PjhHhdj/LMQwq8BrzjBod8KVMjWLWp0LbANeEsI4Q/Gp7I7Uv0F4H8Bj5B1Gn3mBOuRJEmS\npMWrVoPh8e/5ja9FkoyOAAmMjNTvI0mgWJzcltR0jesJFduKtHa0HuFo5a2tu41Ca4HaaA3IQqFT\nn3Fqk6uSJC0leXcK/cP4dS9wDfDFGOOtx/jY24BXHu+AIYRlwDnATQ3dR0C2nlEI4XbgdWTT1j10\nlNO9G3gm8GLg9OOt5Vhs2bJlLk67oPmaaCnyfa+lyPe9liLf91qQqlVaKhVa+vto6eubct06sd3f\nT1KrTXnY2TOcrtbSyuiybsa6lzHWvYzRZcsY6+5mtHsZY8uWMdbVTdrqh9Ja2BbSz/v9j+yv3046\nEnbu2tnEapamQmeB2hPZz9B9W/ctqPfPhIVYszRbvu81H5x99kz/6j52eYdC/8Lk9HCDx/nYrwI3\nncCYZ4xfb5th/6Pj1xs5QigUQjgd+CjwlRjjv4QQ3n4CtUiSJEnSwpGmtB44QHnHdtp3bKe8Yzul\nvXsOCXxmozA2Smn/fkr79894zFhHB0OnrGNow6kMrt/A0Pr1pG2l3GqQlKkOV6kOVOvbLV1zsqqA\njqKlu4WxJ8YAqA3WqA5UKXYUm1yVJGmpyPu3fwswerRAKITweeDZMcbzJ+6LMT7KZIBzPCYmXh2Y\nYX9l2nEz+WtgBPiDE6jhmOWR5C0WE+m6r4mWEt/3Wop832sp8n2veavSD1u3wkMPwtaH4eGHSAZm\n+q/UydMyMEDXww/R9XD2Pb40SeDU02DjRtj45Ox6zVqnodO8s9B+3u9/YD+72V3fXnP6GrrWdTWx\noqWpUqzw6GOTH4GtbFnJ2rPXNrGiY7fQ3vNSHnzfa7HJOxR6AfCdYziuSNa5My+EEP4d2XpGvx1j\n3NPseiRJkiQpF2kK2x6Du+6En99F8vhhl3k9+mkKBejsgs7OyUt7O9kysimk0NfXC0B3V3f9PtIU\nhgahvz8LpPr7SYaGjjpeMlH3tsfgxhuyGrq74clnw0UXw4UXQnvHUc4iabre7b1Ttssryk2qZGlr\nX9Fe//EJ2bpCa89fGKGQJGnhm3UoFEJ4DfCahrveFEJ4yhEeshq4DNg327HHTfyLpnOG/V3Tjpsi\nhLAS+DhwQ4zxCznVJEmSJEnNUatlnUB33wV330myd+8xPSwtFGDVali7FnpWZCFQ13gAVCoftUun\nf+cOALrXrT/yOGOj0F+ph0RU+uHAAdi9i6S/f8bHJX19Wbh1152kLS1wzrlw8SVw4UXQZaeDdCz6\ndvTVb7d2tNJScvq4Zii0FCj3lBk6kIXkB7cdbHJFkqSlJI/f/iXg2cBmsu84PGP8ciQjwAdyGBvg\n4fFxT5th/8SaQzOtBPbnQA/wwRBC4zlWjF+vGb9/T4xxeLbFSpIkSVLuqmMQI9x9J9x9N0nv0T9g\nTLu7Ye0pWQi05hRYtQpaTsIHxC2t0NOTXabXVOmHXbtg967seob1jZKxMbj3Hrj3nizMCufA0y6B\niy6CZcvn/jlIC1CapvRtnwyF2le0N7EadazsqIdCld0VxobHDOkkSSfFrH/bxBivAa4JIawg6/75\na+CaIzxkCNgSY5x5ldHjG78SQvgFcHEIoRxjrM9FEEIoAr8OPDa+ZtHhvAhoA/7PDPsnnsulwPV5\n1CxJkiRJuXh8G9xwPdxx+1HXBkqXLYczz4R167P1eTrm4fRrnV2wsQs2bsq2x8ZI9+3NAqKdO2Db\nNpLq2JSHJLUa3H8f3H8f6Vf/Npti7pnPgl97JrSVmvAkpPlp6OAQY4OTf3+cOq652le1w4PjGyn0\nbe9jxVkrjvgYSZLykNtXEGKMB0IIXwKujTHekNd5j9HVwF8B7yKbCm7CW4C1NHQlhRDOAYZjjA+P\n3/XbwOH+N/Qi4D3A+4B7xi+SJEmS1Fyjo9k0ajdeT/LATBMiZNJVq+DMjXDmWbBixVGngJt3Wlrg\nlHXZ5cKnwugo6WOPwtaH4dFHSEZHpxyepCls+RVs+RXpP/4DPPs58IIXZh1R0hLX2CUEdgo1W/uq\nqa9/77ZeQyFJ0kmRa19qjPEdeZ7vOHwGeDPwsRDCGcAdwPnAVWRhzscajr0fiMA5ADHGHx/uhCGE\n1eM3b4sxXj83ZUuSJEnSMdq7F266AW69OVtf5zBSyAKUM8/KLsuWndQS51xra9ZFtHFT1kX0+DZ4\n+CF4ZCvJyMiUQ5OBAfiX6+BfriM973x44aXwlAuhUGhS8VJzTQ+Fyj12CjVTa7mV1o5WRgeycNt1\nhSRJJ8usQqEQwluBn8YY72/YPmYxxi/PZvyG84yGEF4KfBB4PfBuYDfweeADMcYjz6MgSZIkSfNR\nrQa/vBduvB7uvSfrhDmMdM0a2HxONj1cR+dJLbFpWlrgjDOzS7VKuv3xLCB66MFDO4ju+yXc90vS\nVavh+S+A5zwXurqbUrbULE888kT9dml5iUKLAWmzta9qr4dCfY/3kdZSksIC6+iUJC04s+0U+iLw\nn8m6bya2D/+/lKmS8eNyCYUAYoy9ZJ1BVx3luGP67Rpj/CLZ85EkSZKkk2tsDG67BX7wzyR79xz2\nkLRYhE1nw3nnZWsELWXFIpz+pOzyrF8nfWAL3HcvyYEDUw5L9u2Fb36D9DvXwtN/DS57Gazf0KSi\npZNnpDJCZVelvt25ZomEx/Ncx8oOeh/rBaA6UqWyp0LXKV1NrkqStNjNNhT6EHBrw/aHObZQSJIk\nSZI03ego3Hoz/PM/kRzYf9hD0uXL4dzzYXOAUukkF7gAtLXBeefDueeR7tyRdVpt3UqS1uqHJGNj\n8K+3kv7kNrjkGfDyV8IGwyEtXgcfmTo1maHQ/HDIukKP9RoKSZLm3KxCoRjjh6Ztf3BW1UiSJEnS\nUjQyArfclHUGPXHgkN1pkmRrBJ17Hmw4FRKnFzqqJMm6gNZvgEqF9N/ug3+7P1traOKQNIU7bif9\n2U/hkqePh0OnNrFoaW4c2NrwcyWBjtUdzStGdaVl2TR+tbEstD647SAbnm5ALUmaW7PtFDpmIYQu\n4Bzg8RjjjpM1riRJkiTNWyPDcOMN8MMfkPQeush42toK5z8l63zp9NvjJ6yzM+sIetrFpA8/nK3P\ntHtXfXcWDv2U9Gd3wMWXwMtfBacaDmnxeGLr5HpC7SvbXU9onkiShPaV7VR2Z1P79W7rbXJFkqSl\nIPdQKITwLuA/xhgvabjvHcBfAR1AGkL4XIzx9/IeW5IkSZIWhOFhuOF6uO6fSfr6DtmdtrbBBRfA\n+RdAuXzy61usCkXY9GTYuIl0++PwsztIdu2s707SFH52B/zsDtKLnw6vMBzSwjf4xCBDTwzVt506\nbn5pXzUZCg33DjPcO0xpmVODSpLmTq6hUAjhNcBfA3tCCIUYYy2EcA7wOaAKfAs4H3hXCOH2GOMX\n8xxfkiRJkua1Wg1uuwWu/dbhO4Pa2uCCC7MwyPWC5k6SwKmnwYZTDxsOASR33gF33kH69GfAFa+D\n1WuaVKw0O41dQgCdaw2F5pOOVVOn8ju47SBrz1vbpGokSUtB3p1CVwLbgYtijBOreL4LKABXxhg/\nF0IoAXcBbwe+mPP4kiRJkjQ/3X8f/MM1JI9vO2RXWirBBU/Npopra2tCcUvUlHBoO9x5B8nOqbOd\nJ3f8lPTuu+A3XgyXvxzaXYtFC0tjKJQUE9pXtDexGk3XvqIdEiDNtnu39RoKSZLmVN6h0FOAr8cY\n9zbc9wqgl/EAKMY4HEL4LvA7OY8tSZIkSfPP9u3wj18nufeeQ3alpTJc+NRszSDDoOZJkmyauFPH\nO4fuvINkx2Q4lIyNwQ//mfS2W+BVr4HnPA+KxSYWLB2bNE2nhEIdqztICkkTK9J0hZYC5eXl+hR/\nriskSZpreYdCq4H6v5xDCKcDTwa+FWMcaThuP2C/siRJkqTFq7cXvvttuPlGklptyq60WISnXgQX\nXgStrU0qUIe14dTJaeV+8q8ke/fUdyV9ffB3f0t6/Y/h9W/MOrukeayyp8LowGh926nj5qf2le31\nUKh/Vz/VkSrFNoNnSdLcyDsUOgisb9h+NVkD7D9NO24NcCDnsSVJkiSp+UZH4cc/gn/6PsnQ4JRd\nKcDZm+HpvwZdXU0pT8dow6lwxetIH9gCP/0JSaVS35Vs3w6f+EvS85+ShUMbNjSxUGlmh6wntMZQ\naD7qWNXBgYfGPyZLoXd7LyvOXNHcoiRJi1beodDdwBtDCJ8GqsAfAqPAtycOCCG0Aa8E7s95bEmS\nJElqnjSFn98N13yNZP++Q3ev3wDPejasXtOE4nRCkiQL8c46i/QXv4Cf35VNJTex+5f3kt5/Hzzv\nBdm0cgZ9mmcaQ6FiW5HSslITq9FM2ldNXeepd5uhkCRp7uQdCv0VcC1w3/h2AnwyxrgLIISwDvga\n2ZRy/yPnsSVJkiSpOfbugb//Ksk9vzhkV7psGTzz2XDGmVnIoIWnpRUuvgTCOaR33A6/ikz8SSa1\nGtzwf0jv+Cm8/jfh2c/xz1nzQq1a4+CjB+vbnWs7SXxvzkut7a20tLcwNpiFzq4rJEmaS7mGQjHG\n74QQ3gK8G+gBvgu8t+GQKvB84G9ijH+T59iSJEmSdNKNjcF1P4Dvf49kdGTKrrRUgoufDueeB0XX\nhlgUOjvhBZfC+U8h/ddbSXbUl9QlqfTDl79Ieust8B/ekk0/JzVR3/Y+qiPV+nbHmo4mVqOj6VjV\nUQ+Deh/vJa2lJAVDPElS/vLuFCLG+HfA382wb08I4YIY4y/zHleSJEmSTqr4b/DVvyXZuXPK3WmS\nwHnnwyXPgJJTNS1Kq9fAK15N+shW+MltJL2T3+pPHthC+pEPw0teCq94JbT5HlB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1UDmsH7+RpVXwd+C/hfgd9csP0XgGbgqzc2pNPp/UApk8n0LDjuN4GjwJclEBJCCCHE7dBa0zfj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\nGVlo4njEbw6P1E3zKldDAZOi9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+ "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [], + "image/png": { + "width": 834, + "height": 222 + } + } + } ] - }, - "metadata": { - "image/png": { - "height": 263, - "width": 815 - }, - "tags": [] - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize(12.5, 4))\n", - "plt.title(\"Posterior distribution of $p_A$, the true effectiveness of site A\")\n", - "plt.vlines(prob_true, 0, 90, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n", - "plt.hist(burned_prob_A_trace_, bins=25, histtype=\"stepfilled\", normed=True)\n", - "plt.legend();" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "LdLJ2iriIAyI" - }, - "source": [ - "Our posterior distribution puts most weight near the true value of $p_A$, but also some weights in the tails. This is a measure of how uncertain we should be, given our observations. Try changing the number of observations, `N`, and observe how the posterior distribution changes.\n", - "\n", - "### *A* and *B* Together\n", - "\n", - "A similar anaylsis can be done for site B's response data to determine the analogous $p_B$. But what we are really interested in is the *difference* between $p_A$ and $p_B$. Let's infer $p_A$, $p_B$, *and* $\\text{delta} = p_A - p_B$, all at once. We can do this using TFP's deterministic variables. (We'll assume for this exercise that $p_B = 0.04$, so $\\text{delta} = 0.01$, $N_B = 750$ (signifcantly less than $N_A$) and we will simulate site B's data like we did for site A's data ). Our model now looks like the following:\n", - "\n", - "$$\\begin{align*}\n", - "p_A &\\sim \\text{Uniform}[\\text{low}=0,\\text{high}=1) \\\\\n", - "p_B &\\sim \\text{Uniform}[\\text{low}=0,\\text{high}=1) \\\\\n", - "X\\ &\\sim \\text{Bernoulli}(\\text{prob}=p) \\\\\n", - "\\text{for } i &= 1\\ldots N: \\\\\n", - " X_i\\ &\\sim \\text{Bernoulli}(p_i)\n", - "\\end{align*}$$" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 85 - }, - "colab_type": "code", - "id": "yPDLHl6RIAyJ", - "outputId": "f04783fe-3111-41b5-cfb9-7166b6f4827d" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Obs from Site A: [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] ...\n", - "Observed Prob_A: 0.050666666666666665 ...\n", - "Obs from Site B: [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] ...\n", - "Observed Prob_B: 0.04\n" - ] - } - ], - "source": [ - "reset_sess()\n", - "\n", - "#these two quantities are unknown to us.\n", - "true_prob_A_ = 0.05\n", - "true_prob_B_ = 0.04\n", - "\n", - "#notice the unequal sample sizes -- no problem in Bayesian analysis.\n", - "N_A_ = 1500\n", - "N_B_ = 750\n", - "\n", - "#generate some observations\n", - "observations_A = tfd.Bernoulli(name=\"obs_A\", \n", - " probs=true_prob_A_).sample(sample_shape=N_A_, seed=6.45)\n", - "observations_B = tfd.Bernoulli(name=\"obs_B\", \n", - " probs=true_prob_B_).sample(sample_shape=N_B_, seed=6.45)\n", - "[ \n", - " observations_A_,\n", - " observations_B_,\n", - "] = evaluate([ \n", - " observations_A, \n", - " observations_B, \n", - "])\n", - "\n", - "print(\"Obs from Site A: \", observations_A_[:30], \"...\")\n", - "print(\"Observed Prob_A: \", np.mean(observations_A_), \"...\")\n", - "print(\"Obs from Site B: \", observations_B_[:30], \"...\")\n", - "print(\"Observed Prob_B: \", np.mean(observations_B_))" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "LDzYsDVgMgsz" - }, - "source": [ - "Below we run inference over the new model:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "7ghHBEdXYtxV" - }, - "outputs": [], - "source": [ - "def delta(prob_A, prob_B):\n", - " \"\"\"\n", - " Defining the deterministic delta function. This is our unknown of interest.\n", - " \n", - " Args:\n", - " prob_A: scalar estimate of the probability of a 1 appearing in \n", - " observation set A\n", - " prob_B: scalar estimate of the probability of a 1 appearing in \n", - " observation set B\n", - " Returns: \n", - " Difference between prob_A and prob_B\n", - " \"\"\"\n", - " return prob_A - prob_B\n", - "\n", - " \n", - "def double_joint_log_prob(observations_A_, observations_B_, \n", - " prob_A, prob_B):\n", - " \"\"\"\n", - " Joint log probability optimization function.\n", - " \n", - " Args:\n", - " observations_A: An array of binary values representing the set of \n", - " observations for site A\n", - " observations_B: An array of binary values representing the set of \n", - " observations for site B \n", - " prob_A: scalar estimate of the probability of a 1 appearing in \n", - " observation set A\n", - " prob_B: scalar estimate of the probability of a 1 appearing in \n", - " observation set B \n", - " Returns: \n", - " Joint log probability optimization function.\n", - " \"\"\"\n", - " tfd = tfp.distributions\n", - " \n", - " rv_prob_A = tfd.Uniform(low=0., high=1.)\n", - " rv_prob_B = tfd.Uniform(low=0., high=1.)\n", - " \n", - " rv_obs_A = tfd.Bernoulli(probs=prob_A)\n", - " rv_obs_B = tfd.Bernoulli(probs=prob_B)\n", - " \n", - " return (\n", - " rv_prob_A.log_prob(prob_A)\n", - " + rv_prob_B.log_prob(prob_B)\n", - " + tf.reduce_sum(rv_obs_A.log_prob(observations_A_))\n", - " + tf.reduce_sum(rv_obs_B.log_prob(observations_B_))\n", - " )\n" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "h0TDeF3IIAyQ" - }, - "outputs": [], - "source": [ - "number_of_steps = 37200 #@param {type:\"slider\", min:2000, max:50000, step:100}\n", - "#@markdown (Default is 18000).\n", - "burnin = 1000 #@param {type:\"slider\", min:0, max:30000, step:100}\n", - "#@markdown (Default is 1000).\n", - "leapfrog_steps=3 #@param {type:\"slider\", min:1, max:9, step:1}\n", - "#@markdown (Default is 6).\n", - "\n", - "\n", - "# Set the chain's start state.\n", - "initial_chain_state = [ \n", - " tf.reduce_mean(tf.to_float(observations_A)) * tf.ones([], dtype=tf.float32, name=\"init_prob_A\"),\n", - " tf.reduce_mean(tf.to_float(observations_B)) * tf.ones([], dtype=tf.float32, name=\"init_prob_B\")\n", - "]\n", - "\n", - "# Since HMC operates over unconstrained space, we need to transform the\n", - "# samples so they live in real-space.\n", - "unconstraining_bijectors = [\n", - " tfp.bijectors.Identity(), # Maps R to R.\n", - " tfp.bijectors.Identity() # Maps R to R.\n", - "]\n", - "\n", - "# Define a closure over our joint_log_prob.\n", - "unnormalized_posterior_log_prob = lambda *args: double_joint_log_prob(observations_A_, observations_B_, *args)\n", - "\n", - "# Initialize the step_size. (It will be automatically adapted.)\n", - "with tf.variable_scope(tf.get_variable_scope(), reuse=tf.AUTO_REUSE):\n", - " step_size = tf.get_variable(\n", - " name='step_size',\n", - " initializer=tf.constant(0.5, dtype=tf.float32),\n", - " trainable=False,\n", - " use_resource=True\n", - " )\n", - "\n", - "# Defining the HMC\n", - "hmc=tfp.mcmc.TransformedTransitionKernel(\n", - " inner_kernel=tfp.mcmc.HamiltonianMonteCarlo(\n", - " target_log_prob_fn=unnormalized_posterior_log_prob,\n", - " num_leapfrog_steps=3,\n", - " step_size=step_size,\n", - " step_size_update_fn=tfp.mcmc.make_simple_step_size_update_policy(),\n", - " state_gradients_are_stopped=True),\n", - " bijector=unconstraining_bijectors)\n", - "\n", - "# Sample from the chain.\n", - "[\n", - " posterior_prob_A,\n", - " posterior_prob_B\n", - "], kernel_results = tfp.mcmc.sample_chain(\n", - " num_results=number_of_steps,\n", - " num_burnin_steps=burnin,\n", - " current_state=initial_chain_state,\n", - " kernel=hmc)\n", - "\n", - "# Initialize any created variables.\n", - "init_g = tf.global_variables_initializer()\n", - "init_l = tf.local_variables_initializer()" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "beUUmGMbdrRr" - }, - "source": [ - "#### Execute the TF graph to sample from the posterior" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 34 - }, - "colab_type": "code", - "id": "HTYITb9fdqIe", - "outputId": "8bcb70ee-4c1c-4347-b0b8-6bdb6e6d2aa6" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "acceptance rate: 0.6161\n" - ] - } - ], - "source": [ - "evaluate(init_g)\n", - "evaluate(init_l)\n", - "[\n", - " posterior_prob_A_,\n", - " posterior_prob_B_,\n", - " kernel_results_\n", - "] = evaluate([\n", - " posterior_prob_A,\n", - " posterior_prob_B,\n", - " kernel_results\n", - "])\n", - " \n", - "print(\"acceptance rate: {}\".format(\n", - " kernel_results_.inner_results.is_accepted.mean()))\n", - "\n", - "burned_prob_A_trace_ = posterior_prob_A_[burnin:]\n", - "burned_prob_B_trace_ = posterior_prob_B_[burnin:]\n", - "burned_delta_trace_ = (posterior_prob_A_ - posterior_prob_B_)[burnin:]\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "YaD67cOkIAyT" - }, - "source": [ - "Below we plot the posterior distributions for the three unknowns: " - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 742 - }, - "colab_type": "code", - "id": "PpBXqVKELHRO", - "outputId": "2296d675-b1c4-409b-e314-c5e4d8b53321" - }, - "outputs": [ - { - "data": { - "image/png": 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9iqYMa9OmDQCffvopK1asYPHixXTs2JFGjRqVK9uhQwcA5s6dC8AZZ5zBihUr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\n5vPPP6d9+/Y1qnPVqlVA5Z/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OURz59XnwIuB4ZGf5HwOdCCSLCzAhhc6lcn6WAXr/dyK4IgeILI7+U+DYJg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\ntWvXBuD7778v9nVp75TG1GpEp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- "text/plain": [ - "" + }, + { + "metadata": { + "id": "HAxWLKGcIA0A", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "A Normal random variable can be take on any real number, but the variable is very likely to be relatively close to $\\mu$. In fact, the expected value of a Normal is equal to its $\\mu$ parameter:\n", + "\n", + "$$ E[ X | \\mu, \\tau] = \\mu$$\n", + "\n", + "and its variance is equal to the inverse of $\\tau$:\n", + "\n", + "$$\\text{Var}( X | \\mu, \\tau ) = \\frac{1}{\\tau}$$\n", + "\n", + "\n", + "\n", + "Below we continue our modeling of the Challenger space craft:" ] - }, - "metadata": { - "image/png": { - "height": 725, - "width": 825 - }, - "tags": [] - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize(12.5, 12.5))\n", - "\n", - "#histogram of posteriors\n", - "\n", - "ax = plt.subplot(311)\n", - "\n", - "plt.xlim(0, .1)\n", - "plt.hist(burned_prob_A_trace_, histtype='stepfilled', bins=25, alpha=0.85,\n", - " label=\"posterior of $p_A$\", color=TFColor[0], normed=True)\n", - "plt.vlines(true_prob_A_, 0, 80, linestyle=\"--\", label=\"true $p_A$ (unknown)\")\n", - "plt.legend(loc=\"upper right\")\n", - "plt.title(\"Posterior distributions of $p_A$, $p_B$, and delta unknowns\")\n", - "\n", - "ax = plt.subplot(312)\n", - "\n", - "plt.xlim(0, .1)\n", - "plt.hist(burned_prob_B_trace_, histtype='stepfilled', bins=25, alpha=0.85,\n", - " label=\"posterior of $p_B$\", color=TFColor[2], normed=True)\n", - "plt.vlines(true_prob_B_, 0, 80, linestyle=\"--\", label=\"true $p_B$ (unknown)\")\n", - "plt.legend(loc=\"upper right\")\n", - "\n", - "ax = plt.subplot(313)\n", - "plt.hist(burned_delta_trace_, histtype='stepfilled', bins=30, alpha=0.85,\n", - " label=\"posterior of delta\", color=TFColor[6], normed=True)\n", - "plt.vlines(true_prob_A_ - true_prob_B_, 0, 60, linestyle=\"--\",\n", - " label=\"true delta (unknown)\")\n", - "plt.vlines(0, 0, 60, color=\"black\", alpha=0.2)\n", - "plt.legend(loc=\"upper right\");" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "Hn-G0eFwIAyh" - }, - "source": [ - "Notice that as a result of `N_B < N_A`, i.e. we have less data from site B, our posterior distribution of $p_B$ is fatter, implying we are less certain about the true value of $p_B$ than we are of $p_A$. \n", - "\n", - "With respect to the posterior distribution of $\\text{delta}$, we can see that the majority of the distribution is above $\\text{delta}=0$, implying there site A's response is likely better than site B's response. The probability this inference is incorrect is easily computable:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 51 - }, - "colab_type": "code", - "id": "nZxDurxyIAyh", - "outputId": "7cb41824-d97a-4b53-e12b-169d009251e7" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Probability site A is WORSE than site B: 0.145\n", - "Probability site A is BETTER than site B: 0.855\n" - ] - } - ], - "source": [ - "# Count the number of samples less than 0, i.e. the area under the curve\n", - "# before 0, represent the probability that site A is worse than site B.\n", - "print(\"Probability site A is WORSE than site B: %.3f\" % \\\n", - " np.mean(burned_delta_trace_ < 0))\n", - "\n", - "print(\"Probability site A is BETTER than site B: %.3f\" % \\\n", - " np.mean(burned_delta_trace_ > 0))" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "Q8cAEzbUIAyl" - }, - "source": [ - "If this probability is too high for comfortable decision-making, we can perform more trials on site B (as site B has less samples to begin with, each additional data point for site B contributes more inferential \"power\" than each additional data point for site A). \n", - "\n", - "Try playing with the parameters `true_prob_A`, `true_prob_B`, `N_A`, and `N_B`, to see what the posterior of $\\text{delta}$ looks like. Notice in all this, the difference in sample sizes between site A and site B was never mentioned: it naturally fits into Bayesian analysis.\n", - "\n", - "I hope the readers feel this style of A/B testing is more natural than hypothesis testing, which has probably confused more than helped practitioners. Later in this book, we will see two extensions of this model: the first to help dynamically adjust for bad sites, and the second will improve the speed of this computation by reducing the analysis to a single equation. " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "f-jxOi70IAyl" - }, - "source": [ - "## An algorithm for human deceit\n", - "\n", - "Social data has an additional layer of interest as people are not always honest with responses, which adds a further complication into inference. For example, simply asking individuals \"Have you ever cheated on a test?\" will surely contain some rate of dishonesty. What you can say for certain is that the true rate is less than your observed rate (assuming individuals lie *only* about *not cheating*; I cannot imagine one who would admit \"Yes\" to cheating when in fact they hadn't cheated). \n", - "\n", - "To present an elegant solution to circumventing this dishonesty problem, and to demonstrate Bayesian modeling, we first need to introduce the binomial distribution.\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "qzCqZqzBDpMa" - }, - "source": [ - "## The Binomial Distribution\n", - "\n", - "The binomial distribution is one of the most popular distributions, mostly because of its simplicity and usefulness. Unlike the other distributions we have encountered thus far in the book, the binomial distribution has 2 parameters: $N$, a positive integer representing $N$ trials or number of instances of potential events, and $p$, the probability of an event occurring in a single trial. Like the Poisson distribution, it is a discrete distribution, but unlike the Poisson distribution, it only weighs integers from $0$ to $N$. The mass distribution looks like:\n", - "\n", - "$$P( X = k ) = {{N}\\choose{k}} p^k(1-p)^{N-k}$$\n", - "\n", - "If $X$ is a binomial random variable with parameters $p$ and $N$, denoted $X \\sim \\text{Bin}(N,p)$, then $X$ is the number of events that occurred in the $N$ trials (obviously $0 \\le X \\le N$). The larger $p$ is (while still remaining between 0 and 1), the more events are likely to occur. The expected value of a binomial is equal to $Np$. Below we plot the mass probability distribution for varying parameters. " - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 294 - }, - "colab_type": "code", - "id": "9I53Ta3maWgJ", - "outputId": "e097f79a-2032-4e1a-949a-2b26a1004a78" - }, - "outputs": [ - { - "data": { - "image/png": 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jG6Tn7jHS/FbfJAWS7iMFj2o1tFOMcRLwb6TG/3akZ2tIdqyXgK/HGAt7I/0H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\n9OnTp5lLIknFWU9JaumspyS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- "text/plain": [ - "" + }, + { + "metadata": { + "id": "F3DBYxvAIA0B", + "colab_type": "code", + "colab": {} + }, + "cell_type": "code", + "source": [ + "reset_sess()\n", + "\n", + "temperature_ = challenger_data_[:, 0]\n", + "temperature = tf.convert_to_tensor(temperature_, dtype=tf.float32)\n", + "D_ = challenger_data_[:, 1] # defect or not?\n", + "D = tf.convert_to_tensor(D_, dtype=tf.float32)\n", + "\n", + "beta = tfd.Normal(name=\"beta\", loc=0.3, scale=1000.).sample()\n", + "alpha = tfd.Normal(name=\"alpha\", loc=-15., scale=1000.).sample()\n", + "p_deterministic = tfd.Deterministic(name=\"p\", loc=1.0/(1. + tf.exp(beta * temperature_ + alpha))).sample()\n", + "\n", + "[\n", + " prior_alpha_,\n", + " prior_beta_,\n", + " p_deterministic_,\n", + " D_,\n", + "] = evaluate([\n", + " alpha,\n", + " beta,\n", + " p_deterministic,\n", + " D,\n", + "])\n" + ], + "execution_count": 0, + "outputs": [] + }, + { + "metadata": { + "id": "PxOWy25CIA0D", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "We have our probabilities, but how do we connect them to our observed data? A *Bernoulli* random variable with parameter $p$, denoted $\\text{Ber}(p)$, is a random variable that takes value 1 with probability $p$, and 0 else. Thus, our model can look like:\n", + "\n", + "$$ \\text{Defect Incident, }D_i \\sim \\text{Ber}( \\;p(t_i)\\; ), \\;\\; i=1..N$$\n", + "\n", + "where $p(t)$ is our logistic function and $t_i$ are the temperatures we have observations about. Notice in the code below we set the values of `beta` and `alpha` to 0 in `initial_chain_state`. The reason for this is that if `beta` and `alpha` are very large, they make `p` equal to 1 or 0. Unfortunately, `tfd.Bernoulli` does not like probabilities of exactly 0 or 1, though they are mathematically well-defined probabilities. So by setting the coefficient values to `0`, we set the variable `p` to be a reasonable starting value. This has no effect on our results, nor does it mean we are including any additional information in our prior. It is simply a computational caveat in TFP. " ] - }, - "metadata": { - "image/png": { - "height": 277, - "width": 839 - }, - "tags": [] - }, - "output_type": "display_data" - } - ], - "source": [ - "k_values = tf.range(start=0, limit=(N + 1), dtype=tf.float32)\n", - "random_var_probs_1 = tfd.Binomial(total_count=10., probs=.4).prob(k_values)\n", - "random_var_probs_2 = tfd.Binomial(total_count=10., probs=.9).prob(k_values)\n", - "\n", - "# Execute graph\n", - "[\n", - " k_values_,\n", - " random_var_probs_1_,\n", - " random_var_probs_2_,\n", - "] = evaluate([\n", - " k_values,\n", - " random_var_probs_1,\n", - " random_var_probs_2,\n", - "])\n", - "\n", - "# Display results\n", - "plt.figure(figsize=(12.5, 4))\n", - "colors = [TFColor[3], TFColor[0]] \n", - "\n", - "plt.bar(k_values_ - 0.5, random_var_probs_1_, color=colors[0],\n", - " edgecolor=colors[0],\n", - " alpha=0.6,\n", - " label=\"$N$: %d, $p$: %.1f\" % (10., .4),\n", - " linewidth=3)\n", - "plt.bar(k_values_ - 0.5, random_var_probs_2_, color=colors[1],\n", - " edgecolor=colors[1],\n", - " alpha=0.6,\n", - " label=\"$N$: %d, $p$: %.1f\" % (10., .9),\n", - " linewidth=3)\n", - "\n", - "plt.legend(loc=\"upper left\")\n", - "plt.xlim(0, 10.5)\n", - "plt.xlabel(\"$k$\")\n", - "plt.ylabel(\"$P(X = k)$\")\n", - "plt.title(\"Probability mass distributions of binomial random variables\");" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "xT-q-ZI0IAys" - }, - "source": [ - "The special case when $N = 1$ corresponds to the Bernoulli distribution. There is another connection between Bernoulli and Binomial random variables. If we have $X_1, X_2, ... , X_N$ Bernoulli random variables with the same $p$, then $Z = X_1 + X_2 + ... + X_N \\sim \\text{Binomial}(N, p )$.\n", - "\n", - "The expected value of a Bernoulli random variable is $p$. This can be seen by noting the more general Binomial random variable has expected value $Np$ and setting $N=1$." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "9HmW-50PIAyv" - }, - "source": [ - "## Example: Cheating among students\n", - "\n", - "We will use the binomial distribution to determine the frequency of students cheating during an exam. If we let $N$ be the total number of students who took the exam, and assuming each student is interviewed post-exam (answering without consequence), we will receive integer $X$ \"Yes I did cheat\" answers. We then find the posterior distribution of $p$, given $N$, some specified prior on $p$, and observed data $X$. \n", - "\n", - "This is a completely absurd model. No student, even with a free-pass against punishment, would admit to cheating. What we need is a better *algorithm* to ask students if they had cheated. Ideally the algorithm should encourage individuals to be honest while preserving privacy. The following proposed algorithm is a solution I greatly admire for its ingenuity and effectiveness:\n", - "\n", - "> In the interview process for each student, the student flips a coin, hidden from the interviewer. The student agrees to answer honestly if the coin comes up heads. Otherwise, if the coin comes up tails, the student (secretly) flips the coin again, and answers \"Yes, I did cheat\" if the coin flip lands heads, and \"No, I did not cheat\", if the coin flip lands tails. This way, the interviewer does not know if a \"Yes\" was the result of a guilty plea, or a Heads on a second coin toss. Thus privacy is preserved and the researchers receive honest answers. \n", - "\n", - "I call this the Privacy Algorithm. One could of course argue that the interviewers are still receiving false data since some *Yes*'s are not confessions but instead randomness, but an alternative perspective is that the researchers are discarding approximately half of their original dataset since half of the responses will be noise. But they have gained a systematic data generation process that can be modeled. Furthermore, they do not have to incorporate (perhaps somewhat naively) the possibility of deceitful answers. We can use TFP to dig through this noisy model, and find a posterior distribution for the true frequency of liars. " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "gPcqaqxMIAyw" - }, - "source": [ - "Suppose 100 students are being surveyed for cheating, and we wish to find $p$, the proportion of cheaters. There are a few ways we can model this in TFP. I'll demonstrate the most explicit way, and later show a simplified version. Both versions arrive at the same inference. In our data-generation model, we sample $p$, the true proportion of cheaters, from a prior. Since we are quite ignorant about $p$, we will assign it a $\\text{Uniform}(0,1)$ prior." - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "LIg-xs2LIAyw" - }, - "outputs": [], - "source": [ - "reset_sess()\n", - "\n", - "N = 100\n", - "p = tfd.Uniform(name=\"freq_cheating\", low=0., high=1.)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "7L0nMGmrIAy0" - }, - "source": [ - "Again, thinking of our data-generation model, we assign Bernoulli random variables to the 100 students: 1 implies they cheated and 0 implies they did not. " - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 68 - }, - "colab_type": "code", - "id": "aXxhrJdtIAy0", - "outputId": "57d6feb0-f99d-460e-ea0f-c6ea67392c16" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0\n", - " 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0\n", - " 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n" - ] - } - ], - "source": [ - "N = 100\n", - "reset_sess()\n", - "p = tfd.Uniform(name=\"freq_cheating\", low=0., high=1.)\n", - "true_answers = tfd.Bernoulli(name=\"truths\", \n", - " probs=p.sample()).sample(sample_shape=N, \n", - " seed=5)\n", - "# Execute graph\n", - "[\n", - " true_answers_,\n", - "] = evaluate([\n", - " true_answers,\n", - "])\n", - "\n", - "print(true_answers_)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "vNB9WGYcIAy4" - }, - "source": [ - "If we carry out the algorithm, the next step that occurs is the first coin-flip each student makes. This can be modeled again by sampling 100 Bernoulli random variables with $p=1/2$: denote a 1 as a *Heads* and 0 a *Tails*." - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 68 - }, - "colab_type": "code", - "id": "68t8O39EIAy4", - "outputId": "8c2114dd-6c5b-4db6-a10d-23c73c0ede87" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[1 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 1\n", - " 0 1 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0\n", - " 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1]\n" - ] - } - ], - "source": [ - "N = 100\n", - "first_coin_flips = tfd.Bernoulli(name=\"first_flips\", \n", - " probs=0.5).sample(sample_shape=N, \n", - " seed=5)\n", - "# Execute graph\n", - "[\n", - " first_coin_flips_,\n", - "] = evaluate([\n", - " first_coin_flips,\n", - "])\n", - "\n", - "print(first_coin_flips_)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "8-ZnScpWIAzA" - }, - "source": [ - "Although *not everyone* flips a second time, we can still model the possible realization of second coin-flips:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 68 - }, - "colab_type": "code", - "id": "acP-4TAfIAzB", - "outputId": "f4c3e132-3dee-4eb9-afd7-6c22fd128b37" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[1 0 1 0 0 1 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 1 1 1\n", - " 0 1 1 1 1 1 0 1 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0\n", - " 0 1 0 0 1 1 1 0 0 1 0 1 1 1 1 1 0 0 0 1 0 1 0 0 1 1]\n" - ] - } - ], - "source": [ - "N = 100\n", - "second_coin_flips = tfd.Bernoulli(name=\"second_flips\", \n", - " probs=0.5).sample(sample_shape=N, \n", - " seed=5)\n", - "# Execute graph\n", - "[\n", - " second_coin_flips_,\n", - "] = evaluate([\n", - " second_coin_flips,\n", - "])\n", - "\n", - "print(second_coin_flips_)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "uiVbAjoTIAzI" - }, - "source": [ - "Using these variables, we can return a possible realization of the *observed proportion* of \"Yes\" responses. " - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "BJxN0jmBIAzJ" - }, - "outputs": [], - "source": [ - "def observed_proportion_calc(t_a = true_answers, \n", - " fc = first_coin_flips,\n", - " sc = second_coin_flips):\n", - " \"\"\"\n", - " Unnormalized log posterior distribution function\n", - " \n", - " Args:\n", - " t_a: array of binary variables representing the true answers\n", - " fc: array of binary variables representing the simulated first flips \n", - " sc: array of binary variables representing the simulated second flips\n", - " Returns: \n", - " Observed proportion of coin flips\n", - " Closure over: N\n", - " \"\"\"\n", - " observed = fc * t_a + (1 - fc) * sc\n", - " observed_proportion = tf.to_float(tf.reduce_sum(observed)) / tf.to_float(N)\n", - " \n", - " return tf.to_float(observed_proportion)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "OoIWHbsNIAzL" - }, - "source": [ - "The line `fc * t_a + (1 - fc) * sc` contains the heart of the Privacy algorithm. Elements in this array are 1 *if and only if* i) the first toss is heads and the student cheated or ii) the first toss is tails, and the second is heads, and are 0 else. Finally, the last line sums this vector and divides by `float(N)`, producing a proportion. " - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 34 - }, - "colab_type": "code", - "id": "ma5VwRSNIAzM", - "outputId": "92449808-a8fe-4bd4-973b-73e22bb27eb5" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "0.01\n" - ] - } - ], - "source": [ - "observed_proportion_val = observed_proportion_calc(t_a=true_answers_,\n", - " fc=first_coin_flips_,\n", - " sc=second_coin_flips_)\n", - "# Execute graph\n", - "[\n", - " observed_proportion_val_,\n", - "] = evaluate([\n", - " observed_proportion_val,\n", - "])\n", - "\n", - "print(observed_proportion_val_)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "HNoBM39rIAzQ" - }, - "source": [ - "Next we need a dataset. After performing our coin-flipped interviews the researchers received 35 \"Yes\" responses. To put this into a relative perspective, if there truly were no cheaters, we should expect to see on average 1/4 of all responses being a \"Yes\" (half chance of having first coin land Tails, and another half chance of having second coin land Heads), so about 25 responses in a cheat-free world. On the other hand, if *all students cheated*, we should expected to see approximately 3/4 of all responses be \"Yes\". \n", - "\n", - "The researchers observe a Binomial random variable, with `N = 100` and `total_yes = 35`: " - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "SLcH6ZPsIAzR" - }, - "outputs": [], - "source": [ - "total_count = 100\n", - "total_yes = 35" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "-kWZd1ygofav" - }, - "outputs": [], - "source": [ - "def coin_joint_log_prob(total_yes, total_count, lies_prob):\n", - " \"\"\"\n", - " Joint log probability optimization function.\n", - " \n", - " Args:\n", - " headsflips: Integer for total number of observed heads flips\n", - " N: Integer for number of total observation\n", - " lies_prob: Test probability of a heads flip (1) for a Binomial distribution\n", - " Returns: \n", - " Joint log probability optimization function.\n", - " \"\"\"\n", - " \n", - " rv_lies_prob = tfd.Uniform(name=\"rv_lies_prob\",low=0., high=1.)\n", - "\n", - " cheated = tfd.Bernoulli(probs=tf.to_float(lies_prob)).sample(total_count)\n", - " first_flips = tfd.Bernoulli(probs=0.5).sample(total_count)\n", - " second_flips = tfd.Bernoulli(probs=0.5).sample(total_count)\n", - " observed_probability = tf.reduce_sum(tf.to_float(\n", - " cheated * first_flips + (1 - first_flips) * second_flips)) / total_count\n", - "\n", - " rv_yeses = tfd.Binomial(name=\"rv_yeses\",\n", - " total_count=float(total_count),\n", - " probs=observed_probability)\n", - " \n", - " return (\n", - " rv_lies_prob.log_prob(lies_prob)\n", - " + tf.reduce_sum(rv_yeses.log_prob(tf.to_float(total_yes)))\n", - " )" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "QZC4TITlIAzV" - }, - "source": [ - "Below we add all the variables of interest to our Metropolis-Hastings sampler and run our black-box algorithm over the model. It's important to note that we're using a Metropolis-Hastings MCMC instead of a Hamiltonian since we're sampling inside." - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "Awl3GmgjIAzV" - }, - "outputs": [], - "source": [ - "burnin = 15000\n", - "num_of_steps = 40000\n", - "total_count=100\n", - "\n", - "# Set the chain's start state.\n", - "initial_chain_state = [\n", - " 0.4 * tf.ones([], dtype=tf.float32, name=\"init_prob\")\n", - "]\n", - "\n", - "# Define a closure over our joint_log_prob.\n", - "unnormalized_posterior_log_prob = lambda *args: coin_joint_log_prob(total_yes, total_count, *args)\n", - "\n", - "# Defining the Metropolis-Hastings\n", - "# We use a Metropolis-Hastings method here instead of Hamiltonian method\n", - "# because the coin flips in the above example are non-differentiable and cannot\n", - "# bue used with HMC.\n", - "metropolis=tfp.mcmc.RandomWalkMetropolis(\n", - " target_log_prob_fn=unnormalized_posterior_log_prob,\n", - " seed=54)\n", - "\n", - "# Sample from the chain.\n", - "[\n", - " posterior_p\n", - "], kernel_results = tfp.mcmc.sample_chain(\n", - " num_results=num_of_steps,\n", - " num_burnin_steps=burnin,\n", - " current_state=initial_chain_state,\n", - " kernel=metropolis,\n", - " parallel_iterations=1,\n", - " name='Metropolis-Hastings_coin-flips')" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "Lq0OtJDCufOu" - }, - "source": [ - "##### Executing the TF graph to sample from the posterior" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 34 - }, - "colab_type": "code", - "id": "x--bCsBrr91E", - "outputId": "cfab9154-992d-418d-ba2e-d16f1cae1e65" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "acceptance rate: 0.105625\n" - ] - } - ], - "source": [ - "# Content Warning: This cell can take up to 5 minutes in Graph Mode\n", - "[\n", - " posterior_p_,\n", - " kernel_results_\n", - "] = evaluate([\n", - " posterior_p,\n", - " kernel_results,\n", - "])\n", - " \n", - "print(\"acceptance rate: {}\".format(\n", - " kernel_results_.is_accepted.mean()))\n", - "# print(\"prob_p trace: \", posterior_p_)\n", - "# print(\"prob_p burned trace: \", posterior_p_[burnin:])\n", - "burned_cheating_freq_samples_ = posterior_p_[burnin:]" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "QhCgk98ynq5s" - }, - "source": [ - "And finally we can plot the results." - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 374 - }, - "colab_type": "code", - "id": "JoKNmLpxB1yt", - "outputId": "b793d81e-288a-4d80-8a37-f34f19e50aab" - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" + }, + { + "metadata": { + "id": "vRqoyxqnofbT", + "colab_type": "code", + "colab": {} + }, + "cell_type": "code", + "source": [ + "def challenger_joint_log_prob(D, temperature_, alpha, beta):\n", + " \"\"\"\n", + " Joint log probability optimization function.\n", + " \n", + " Args:\n", + " D: The Data from the challenger disaster representing presence or \n", + " absence of defect\n", + " temperature_: The Data from the challenger disaster, specifically the temperature on \n", + " the days of the observation of the presence or absence of a defect\n", + " alpha: one of the inputs of the HMC\n", + " beta: one of the inputs of the HMC\n", + " Returns: \n", + " Joint log probability optimization function.\n", + " \"\"\"\n", + " rv_alpha = tfd.Normal(loc=0., scale=1000.)\n", + " rv_beta = tfd.Normal(loc=0., scale=1000.)\n", + " logistic_p = 1.0/(1. + tf.exp(beta * tf.to_float(temperature_) + alpha))\n", + " rv_observed = tfd.Bernoulli(probs=logistic_p)\n", + " \n", + " return (\n", + " rv_alpha.log_prob(alpha)\n", + " + rv_beta.log_prob(beta)\n", + " + tf.reduce_sum(rv_observed.log_prob(D))\n", + " )" + ], + "execution_count": 0, + "outputs": [] + }, + { + "metadata": { + "id": "oHU-MbPxs8iL", + "colab_type": "code", + "colab": {} + }, + "cell_type": "code", + "source": [ + "number_of_steps = 100000 #@param {type:\"slider\", min:25000, max:120000, step:1000}\n", + "burnin = 95000 #@param {type:\"slider\", min:20000, max:100000, step:1000}\n", + "\n", + "# Set the chain's start state.\n", + "initial_chain_state = [\n", + " 0. * tf.ones([], dtype=tf.float32, name=\"init_alpha\"),\n", + " 0. * tf.ones([], dtype=tf.float32, name=\"init_beta\")\n", + "]\n", + "\n", + "# Since HMC operates over unconstrained space, we need to transform the\n", + "# samples so they live in real-space.\n", + "unconstraining_bijectors = [\n", + " tfp.bijectors.Identity(),\n", + " tfp.bijectors.Identity()\n", + "]\n", + "\n", + "# Define a closure over our joint_log_prob.\n", + "unnormalized_posterior_log_prob = lambda *args: challenger_joint_log_prob(D, temperature_, *args)\n", + "\n", + "# Initialize the step_size. (It will be automatically adapted.)\n", + "with tf.variable_scope(tf.get_variable_scope(), reuse=tf.AUTO_REUSE):\n", + " step_size = tf.get_variable(\n", + " name='step_size',\n", + " initializer=tf.constant(0.5, dtype=tf.float32),\n", + " trainable=False,\n", + " use_resource=True\n", + " )\n", + "\n", + "# Defining the HMC\n", + "hmc=tfp.mcmc.TransformedTransitionKernel(\n", + " inner_kernel=tfp.mcmc.HamiltonianMonteCarlo(\n", + " target_log_prob_fn=unnormalized_posterior_log_prob,\n", + " num_leapfrog_steps=2,\n", + " step_size=step_size,\n", + " step_size_update_fn=tfp.mcmc.make_simple_step_size_update_policy(),\n", + " state_gradients_are_stopped=True),\n", + " bijector=unconstraining_bijectors)\n", + "\n", + "# Sampling from the chain.\n", + "[\n", + " posterior_alpha,\n", + " posterior_beta\n", + "], kernel_results = tfp.mcmc.sample_chain(\n", + " num_results = number_of_steps,\n", + " num_burnin_steps = burnin,\n", + " current_state=initial_chain_state,\n", + " kernel=hmc)\n", + "\n", + "# Initialize any created variables for preconditions\n", + "init_g = tf.global_variables_initializer()" + ], + "execution_count": 0, + "outputs": [] + }, + { + "metadata": { + "id": "eNkhSXDkthRs", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "#### Execute the TF graph to sample from the posterior" ] - }, - "metadata": { - "image/png": { - "height": 357, - "width": 816 - }, - "tags": [] - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize(12.5, 6))\n", - "p_trace_ = burned_cheating_freq_samples_\n", - "plt.hist(p_trace_, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30, \n", - " label=\"posterior distribution\", color=TFColor[3])\n", - "plt.vlines([.1, .40], [0, 0], [5, 5], alpha=0.3)\n", - "plt.xlim(0, 1)\n", - "plt.legend();" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "tqDMt8xyIAzd" - }, - "source": [ - "With regards to the above plot, we are still pretty uncertain about what the true frequency of cheaters might be, but we have narrowed it down to a range between 0.1 to 0.4 (marked by the solid lines). This is pretty good, as *a priori* we had no idea how many students might have cheated (hence the uniform distribution for our prior). On the other hand, it is also pretty bad since there is a .3 length window the true value most likely lives in. Have we even gained anything, or are we still too uncertain about the true frequency? \n", - "\n", - "I would argue, yes, we have discovered something. It is implausible, according to our posterior, that there are *no cheaters*, i.e. the posterior assigns low probability to $p=0$. Since we started with an uniform prior, treating all values of $p$ as equally plausible, but the data ruled out $p=0$ as a possibility, we can be confident that there were cheaters. \n", - "\n", - "This kind of algorithm can be used to gather private information from users and be *reasonably* confident that the data, though noisy, is truthful. \n", - "\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "Y0bK5tMAIAze" - }, - "source": [ - "### Alternative TFP Model\n", - "\n", - "Given a value for $p$ (which from our god-like position we know), we can find the probability the student will answer yes: \n", - "$$\n", - "\\begin{align}\n", - "P(\\text{\"Yes\"}) &= P(\\text{Heads on first coin} )P( \\text{cheater} ) + P( \\text{Tails on first coin} )P( \\text{Heads on second coin}) \\\\\n", - "&= \\frac{1}{2}p + \\frac{1}{2}\\frac{1}{2}\\\\\n", - "&= \\frac{p}{2} + \\frac{1}{4}\n", - "\\end{align}\n", - "$$\n", - "Thus, knowing $p$ we know the probability a student will respond \"Yes\". In TFP, we can create a deterministic function to evaluate the probability of responding \"Yes\", given $p$:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "wBps82qhIAzf" - }, - "outputs": [], - "source": [ - "reset_sess()\n", - "\n", - "p_new = tfd.Uniform(name=\"new_freq_cheating\", \n", - " low=0., \n", - " high=1.)\n", - "p_new_skewed = tfd.Deterministic(name=\"p_skewed\", \n", - " loc=(0.5 * p_new.sample(seed=0.5) + 0.25)).sample(seed=0.5)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "m_kgk64TIAzh" - }, - "source": [ - "I could have typed `p_skewed = 0.5 * p + 0.25` instead for a one-liner, as the elementary operations of addition and scalar multiplication will implicitly create a deterministic variable, but I wanted to make the determinism explicit for clarity's sake. \n", - "\n", - "If we know the probability of respondents saying \"Yes\", which is `p_skewed`, and we have $N=100$ students, the number of \"Yes\" responses is a binomial random variable with parameters `N` and `p_skewed`.\n", - "\n", - "This is where we include our observed 35 \"Yes\" responses out of a total of 100 which are passed to the `joint_log_prob`." - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "GJ2jFKI7ofa9" - }, - "outputs": [], - "source": [ - "N = 100.\n", - "total_yes = 35.\n", - "\n", - "def alt_joint_log_prob(yes_responses, N, prob_cheating):\n", - " \"\"\"\n", - " Alternative joint log probability optimization function.\n", - " \n", - " Args:\n", - " yes_responses: Integer for total number of affirmative responses\n", - " N: Integer for number of total observation\n", - " prob_cheating: Test probability of a student actually cheating\n", - " Returns: \n", - " Joint log probability optimization function.\n", - " \"\"\"\n", - " tfd = tfp.distributions\n", - " \n", - " rv_prob = tfd.Uniform(name=\"rv_new_freq_cheating\", low=0., high=1.)\n", - " prob_skewed = 0.5 * prob_cheating + 0.25\n", - " rv_yes_responses = tfd.Binomial(name=\"rv_yes_responses\",\n", - " total_count=tf.to_float(N), \n", - " probs=prob_skewed)\n", - "\n", - " return (\n", - " rv_prob.log_prob(prob_cheating)\n", - " + tf.reduce_sum(rv_yes_responses.log_prob(tf.to_float(yes_responses)))\n", - " )" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "0clIAcyHIAzj" - }, - "source": [ - "\n", - "Below we add all the variables of interest to our HMC component-defining cell and run our black-box algorithm over the model. " - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "C5QLZ17e5u6t" - }, - "outputs": [], - "source": [ - "number_of_steps = 25000\n", - "burnin = 2500\n", - "\n", - "# Set the chain's start state.\n", - "initial_chain_state = [\n", - " 0.2 * tf.ones([], dtype=tf.float32, name=\"init_skewed_p\")\n", - "]\n", - "\n", - "# Since HMC operates over unconstrained space, we need to transform the\n", - "# samples so they live in real-space.\n", - "unconstraining_bijectors = [\n", - " tfp.bijectors.Sigmoid(), # Maps [0,1] to R.\n", - "]\n", - "\n", - "# Define a closure over our joint_log_prob.\n", - "# unnormalized_posterior_log_prob = lambda *args: alt_joint_log_prob(headsflips, total_yes, N, *args)\n", - "unnormalized_posterior_log_prob = lambda *args: alt_joint_log_prob(total_yes, N, *args)\n", - "\n", - "# Initialize the step_size. (It will be automatically adapted.)\n", - "with tf.variable_scope(tf.get_variable_scope(), reuse=tf.AUTO_REUSE):\n", - " step_size = tf.get_variable(\n", - " name='skewed_step_size',\n", - " initializer=tf.constant(0.5, dtype=tf.float32),\n", - " trainable=False,\n", - " use_resource=True\n", - " ) \n", - "\n", - "# Defining the HMC\n", - "hmc=tfp.mcmc.TransformedTransitionKernel(\n", - " inner_kernel=tfp.mcmc.HamiltonianMonteCarlo(\n", - " target_log_prob_fn=unnormalized_posterior_log_prob,\n", - " num_leapfrog_steps=2,\n", - " step_size=step_size,\n", - " step_size_update_fn=tfp.mcmc.make_simple_step_size_update_policy(),\n", - " state_gradients_are_stopped=True),\n", - " bijector=unconstraining_bijectors)\n", - "\n", - "# Sample from the chain.\n", - "[\n", - " posterior_skewed_p\n", - "], kernel_results = tfp.mcmc.sample_chain(\n", - " num_results=number_of_steps,\n", - " num_burnin_steps=burnin,\n", - " current_state=initial_chain_state,\n", - " kernel=hmc)\n", - "\n", - "# Initialize any created variables.\n", - "# This prevents a FailedPreconditionError\n", - "init_g = tf.global_variables_initializer()\n", - "init_l = tf.local_variables_initializer()" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "eJYLS8EysHqj" - }, - "source": [ - "#### Execute the TF graph to sample from the posterior" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 34 - }, - "colab_type": "code", - "id": "ALvEN1yQkTIx", - "outputId": "2bedf661-d0d3-45d2-fbba-c1ca8c85bb6b" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "acceptance rate: 0.6052\n" - ] - } - ], - "source": [ - "# This cell may take 5 minutes in Graph Mode\n", - "evaluate(init_g)\n", - "evaluate(init_l)\n", - "[\n", - " posterior_skewed_p_,\n", - " kernel_results_\n", - "] = evaluate([\n", - " posterior_skewed_p,\n", - " kernel_results\n", - "])\n", - "\n", - " \n", - "print(\"acceptance rate: {}\".format(\n", - " kernel_results_.inner_results.is_accepted.mean()))\n", - "# print(\"final step size: {}\".format(\n", - "# kernel_results_.inner_results.extra.step_size_assign[-100:].mean()))\n", - "\n", - "# print(\"p_skewed trace: \", posterior_skewed_p_)\n", - "# print(\"p_skewed burned trace: \", posterior_skewed_p_[burnin:])\n", - "freq_cheating_samples_ = posterior_skewed_p_[burnin:]\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "Ye0uC_c-xrWf" - }, - "source": [ - "Now we can plot our results" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 374 - }, - "colab_type": "code", - "id": "_P5Z_uySgi-S", - "outputId": "0b085693-c710-449f-c25a-730abbde9a92" - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" + }, + { + "metadata": { + "id": "XJyZIwoyth2j", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + }, + "outputId": "66444d91-4c78-495b-ee3a-083c37c6fd81" + }, + "cell_type": "code", + "source": [ + "# In Graph Mode, this cell can take up to 36 Minutes\n", + "evaluate(init_g)\n", + "[\n", + " posterior_alpha_,\n", + " posterior_beta_,\n", + " kernel_results_\n", + "] = evaluate([\n", + " posterior_alpha,\n", + " posterior_beta,\n", + " kernel_results\n", + "])\n", + " \n", + "print(\"acceptance rate: {}\".format(\n", + " kernel_results_.inner_results.is_accepted.mean()))\n", + "print(\"final step size: {}\".format(\n", + " kernel_results_.inner_results.extra.step_size_assign[-100:].mean()))\n", + "\n", + "alpha_samples_ = posterior_alpha_[burnin::8]\n", + "beta_samples_ = posterior_beta_[burnin::8]" + ], + "execution_count": 10, + "outputs": [ + { + "output_type": "stream", + "text": [ + "acceptance rate: 0.62579\n", + "final step size: 0.014119372703135014\n" + ], + "name": "stdout" + } ] - }, - "metadata": { - "image/png": { - "height": 357, - "width": 816 - }, - "tags": [] - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize(12.5, 6))\n", - "p_trace_ = freq_cheating_samples_\n", - "plt.hist(p_trace_, histtype=\"stepfilled\", normed=True, alpha=0.85, bins=30, \n", - " label=\"posterior distribution\", color=TFColor[3])\n", - "plt.vlines([.1, .40], [0, 0], [5, 5], alpha=0.2)\n", - "plt.xlim(0, 1)\n", - "plt.legend();" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "Lxt6fSRvIAzy" - }, - "source": [ - "The remainder of this chapter examines some practical examples of TFP and TFP modeling:" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "KMoiodMmIAzy" - }, - "source": [ - "## Example: Challenger Space Shuttle Disaster \n", - "\n", - "On January 28, 1986, the twenty-fifth flight of the U.S. space shuttle program ended in disaster when one of the rocket boosters of the Shuttle Challenger exploded shortly after lift-off, killing all seven crew members. The presidential commission on the accident concluded that it was caused by the failure of an O-ring in a field joint on the rocket booster, and that this failure was due to a faulty design that made the O-ring unacceptably sensitive to a number of factors including outside temperature. Of the previous 24 flights, data were available on failures of O-rings on 23, (one was lost at sea), and these data were discussed on the evening preceding the Challenger launch, but unfortunately only the data corresponding to the 7 flights on which there was a damage incident were considered important and these were thought to show no obvious trend. The data are shown below (see [1]):\n", - "\n", - "\n", - "\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 34 - }, - "colab_type": "code", - "id": "tlPZvBWkg5g-", - "outputId": "d48fc2b4-441e-47b5-853d-91c7f37b6162" - }, - "outputs": [ - { - "data": { - "text/plain": [ - "'challenger_data.csv'" + }, + { + "metadata": { + "id": "xIGyBkilIA0G", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "We have trained our model on the observed data, now we can sample values from the posterior. Let's look at the posterior distributions for $\\alpha$ and $\\beta$:" ] - }, - "execution_count": 7, - "metadata": { - "tags": [] - }, - "output_type": "execute_result" - } - ], - "source": [ - "reset_sess()\n", - "\n", - "import wget\n", - "url = 'https://raw.githubusercontent.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter2_MorePyMC/data/challenger_data.csv'\n", - "filename = wget.download(url)\n", - "filename" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 675 - }, - "colab_type": "code", - "id": "BNOqG_9zIAzz", - "outputId": "2f884384-a913-4b04-f6b1-56cd315f6ce2" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Temp (F), O-Ring failure?\n", - "[[66. 0.]\n", - " [70. 1.]\n", - " [69. 0.]\n", - " [68. 0.]\n", - " [67. 0.]\n", - " [72. 0.]\n", - " [73. 0.]\n", - " [70. 0.]\n", - " [57. 1.]\n", - " [63. 1.]\n", - " [70. 1.]\n", - " [78. 0.]\n", - " [67. 0.]\n", - " [53. 1.]\n", - " [67. 0.]\n", - " [75. 0.]\n", - " [70. 0.]\n", - " [81. 0.]\n", - " [76. 0.]\n", - " [79. 0.]\n", - " [75. 1.]\n", - " [76. 0.]\n", - " [58. 1.]]\n" - ] - }, - { - "data": { - "image/png": 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JJ466LHPnzuWkk05i5cqV45zD6akpbawp5Wia\nJtWLn2H11JQ21pRyNI31MvGmZAAHeAPwl8AbMvNfMvNzmXkacATwF8A7JjV3kiRJ0jS2bNkyNmzY\nMOrJint6enjggQe47rrrxilno3fGGWewcePGzSrLxo0bOfPMM8cpZ6PTpDppUlkuvPDCMZXlM5/5\nzDjlbHprShtrSjmapkn14mdYPTWljTWlHE1jvUy8qRrAeQWwGvjEkPX/A9wBHB4RIxpDTpIkSVJ1\nBgcHWbp0KfPmzdus/efNm8c111xDHebq7O/vZ8mSJWy55Zabtf+WW27JFVdcQX9/f8U5G50m1UmT\nyjIwMMBll13G3LlzN2v/uXPncskllzAwMFBxzqa3prSxppSjaZpUL36G1VNT2lhTytE01svkmHIB\nnIjYBng8cENmrm/flpmDwHXAn1H0xJEkSZI0gVasWEFfX1/XsbA3ZcaMGfT19bFixYqKczZ6F198\nMWvWrBn1Nwxbenp6WLNmDRdffHHFORudJtVJk8qydOlS+vr6xtS++vr6WLp0acU5m96a0saaUo6m\naVK9+BlWT01pY00pR9NYL5Nj5mRnYDPsUi7v6LK91QJ2Bf5vrCe77bbbxnoIaULYVqXpx/temn6m\nwn1/4403smrVqjH1Olm9ejXXXnstDzzwQIU5G73LL7+c/v5+NmzYsNnH6O/v5/LLL+dJT3pShTkb\nnSbVSZPKsmTJEjZs2MDatWuHTTfc9g0bNrBkyRJ22GGHqrM3bTWljTWlHE0z0nq59957u26rS72M\n9DNsOH6GVa8p935TyjEa/p3fXLvvvvuY9p9yPXCArcvlmi7bVw9JJ0mSJGmCrFmzht7e3jEdo6en\npxYTnK5cuXKzv1nc0tPTw6pVqyrK0eZpUp00qSyrVq2qpCz3339/RTkSNKeNNaUcTdOkevEzrJ6a\n0saaUo6msV4mx1TsgTOhxhohk8ZbK0JvW5WmD+97afqZSvf9Pffcw6233srWW2/+96nuu+8+dttt\nt0kv72Me8xiuv/56Zs2atdnH2LBhAwsXLpzUsjSpTppUlt12241ly5YxZ86cjttb32rvth1g48aN\n7LrrrpNeliZpShtrSjmaZlP10up5s91223U9Rl3qZVOfYSPhZ1j1mnLvN6UcI+Hf+dqUqdgDp/X1\ntW6zJW01JJ0kSZKkCbLzzjuPeULigYEBdt5554pytPn22WefWh1nczWpTppUlj322KOSsuyxxx4V\n5UjQnDbWlHI0TZPqxc+wempKG2tKOZrGepkcUzGAczswCDyqy/bWHDn1HzhQkiRJapiFCxcyf/58\nBgcHN2v/wcFB5s+fz8KFCyvO2egtXryYuXPnbvZ/VAcGBpg7dy6LFy+uOGej06Q6aVJZFi1axPz5\n88fUvubPn8+iRYsqztn01pQ21pRyNE2T6sXPsHpqShtrSjmaxnqZHFMugJOZq4Gbgb0jYnb7tojo\nBQ4Afp2ZKyYjf5IkSdJ0NmPGDBYtWsTq1as3nbiD1atXc+CBBzJjxoyKczZ6vb29PPOZz2T9+vWb\ntf/69es5+OCDxzxW+Fg1qU6aVJaenh4OOeQQ1qzpNr3r8NasWcNhhx025nma9FBNaWNNKUfTNKle\n/Ayrp6a0saaUo2msl8kxVT8lPwHMBY4Zsv5wYAfg4xOeI0mSJEkA7L///syaNWvU38odGBhgiy22\nYN999x2nnI3eW9/6VmbOnLlZZZk5cyannHLKOOVsdJpUJ00qy5FHHjmmshx++OHjlLPprSltrCnl\naJom1YufYfXUlDbWlHI0jfUy8aZqAOc84FrgrIj4YET8Y0S8p1z/Y+CsSc2dJEmSNI3Nnj2bY445\nhtWrV4/4P3cDAwOsXr2ao48+mtmzZ296hwmy4447cu6557J+/fpRlWX9+vWce+657LjjjuOcw5Fp\nUp00qSwLFizgrLPOYs2aNaMqy5o1a3j/+9/PggULxjmH01NT2lhTytE0TaoXP8PqqSltrCnlaBrr\nZeJNyQBOZm4ADgHOAV4AXAAcSdHz5hmZuXn9NyVJkiRVYqedduK4445jw4YN3H///V3Hyh4cHOT+\n++9n48aNHHfccey0004TnNNNO/jggznvvPPo7+9n7dq1Xf+zOjAwwNq1a+nv7+e8887j4IMPnuCc\nDq9JddKksuy1116cffbZD5ZluPbVKsvZZ5/NXnvtNcE5nV6a0saaUo6maVK9+BlWT01pY00pR9NY\nLxNrxuZOOtQ0fX19XghNSbfddhsAu++++yTnRNJE8b6Xpp+pfN+vW7eO6667jmuuuYa+vj56enro\n7e2lv7+fgYEBFixYwAEHHMC+++5b+2/k3X333Zx55plcccUVD4753yoLwNy5czn44IM55ZRTatPz\nppMm1UmTyrJy5Uo+85nPcMkll9DX18eGDRvo6el5cJiSBQsWcOihh3L44Yf7rfUJ1JQ21pRyNM3Q\nelm1ahU9PT1ss802U65ehn6GdWpjfoZNvKbc+00pRyf+nT99zZ8/f0STARnAKRnA0VQ1lT/oJW0e\n73tp+mnCfT84OMiKFSu48847Wbt2LXPmzGHnnXdm4cKFU24i0/7+fi6++GKuv/56+vr6mD9/Pvvs\nsw+LFy+mt7d3srM3Yk2qkyaVZWBggKVLl7JkyRLuv/9+dt11V/bYYw8WLVrkZN+TqCltrCnlaJpW\nvVx77bWsW7eO3XbbbcrWS+szbPny5axatYptttnGz7AaaMq935RytPPv/OnLAM4oGcDRVNWED3pJ\no+N9L00/3vfS9ON9L00/3vfS9ON9P32NNIBj6FuSJEmSJEmSJKlmDOBIkiRJkiRJkiTVjAEcSZIk\nSZIkSZKkmjGAI0mSJEmSJEmSVDMGcCRJkiRJkiRJkmrGAI4kSZIkSZIkSVLNGMCRJEmSJEmSJEmq\nGQM4kiRJkiRJkiRJNWMAR5IkSZIkSZIkqWYM4EiSJEmSJEmSJNWMARxJkiRJkiRJkqSamTE4ODjZ\neaiFvr4+L4QkSZIkSZIkSRpX8+fPnzGSdPbAkSRJkiRJkiRJqhkDOJIkSZIkSZIkSTVjAEeSJEmS\nJEmSJKlmDOBIkiRJkiRJkiTVjAEcSZIkSZIkSZKkmpkxODg42XmQJEmSJEmSJElSG3vgSJIkSZIk\nSZIk1YwBHEmSJEmSJEmSpJoxgCNJkiRJkiRJklQzBnAkSZIkSZIkSZJqxgCOJEmSJEmSJElSzRjA\nkSRJkiRJkiRJqhkDOJIkSZIkSZIkSTVjAEeSJEmSJEmSJKlmDOBIkiRJkiRJkiTVjAEcSZIkSZIk\nSZKkmjGAI0mSJEmSJEmSVDMzJzsDkrqLiAuAI4dJ8sbM/PeIOBV45zDpzs7MN1SZN0njKyIOA94M\n7A1sBG4ETs/M/x2Sbg7wFuClwC7AKuB/gXdk5q0TmmlJYzKS+95nvtQMETE4gmR/kZm/LNP7vJem\nuNHc9z7vpWaJiD2AtwJ/A2wPrAS+D7w/M69uS+fzXg9jAEeaGl4H3NNh/U1Dfj8VWN4h3W1VZ0jS\n+ImIVwKfAL4LnABsDbwRuDQiDsnMq8p0M4D/AQ4GPgWcBvw5cCKwNCL2zcxfTHwJJI3WSO/7Nqfi\nM1+ayl40zLb3AvMp//73eS81xojv+zan4vNemtIi4snA1cADwLnArcCjgdcD34mIxZn5dZ/36sYA\njjQ1XNL69t0mfKfDCx5JU0hE7Ah8GLgCeHZmDpTrvw4sBZ4DXFUmfynwLIpv7ZzcdowrgR8A7wee\nP2GZl7RZRnnft/jMl6awzPxSp/URsRjYDTgqM1eXq33eSw0wyvu+xee9NPW9HZgL/ENmXtZaGRFf\nAX4KvAv4Oj7v1YVz4EiSVC9HAvOAU1svcQEy8/8y85GZeVJb2leUyw+3HyAzb6Dojv3ciFgw3hmW\nNGajue8lNVREbA2cA3wvMy9s2+TzXmqoYe57Sc3x2HL5vfaVmfkz4HfAY8pVPu/VkQEcaQqJiNkR\nscmecxGxRURsMRF5klS5ZwH3UXzrnojojYgtu6TdF/h1Zt7RYdu1wCyKuTQk1dto7vuH8JkvNco7\nKIZKef2Q9T7vpebqdt8/hM97aUr7abl8XPvKiJgPLABuKVf5vFdHBnCkqeH1EXE7sBZYHxHLIuJv\nO6R7cUQsB9aX6X4cEUdMaE4ljdXjgV8Ae0XEdyju53URcUtEvLSVqPy23nZApz/uAFaUy13HM7OS\nKjGi+34In/lSg0TEDhQvcC/KzB+3rfd5LzVUt/t+CJ/30tT3HuCPwEUR8bSI2D4i/pJinptB4B0+\n7zUcAzjS1PBs4AyKMfDfBuwOfKPDS53DgPPK5QkUkyBeFBGnTGBeJY3NdhTfwvkmcA2wGDiuXPdf\nEfGqMt3W5XJNl+OsHpJOUn2N9L5v5zNfapaTgdkUL3na+byXmqvbfd/O5700xWXmLcAioJdiGLV7\ngJuB/Sjmv7wKn/caxiaHYpI0qT4A/BdwVWauL9d9KyK+BtwEfCAi/hv4DLAMWJqZfWW6SyPi88DP\ngHdGxPmZuXKC8y9p9LagGAP35Zn5udbKiPgmRdfrMyLigsnJmqRxMqL7PjP78ZkvNU5EbAv8M/CN\nzPz5ZOdH0vgbwX3v815qiIgI4FvAlsAbKe7hHYA3AV+PiBcAyycvh6o7AzhSjZXdqB/WlTozfxIR\nV1GMmf+EzFwOPOyPvsz8XUR8CXgNcCDFN3sl1dv9FH/Yfb59ZWbeHhFLgEOBJwC/LDfN63Kcrcrl\nqnHIo6RqjfS+v6V8yeMzX2qWfwTmAp0mMG89x33eS80y3H2Pz3upUT4O7Ezx/u721sqI+CLFff4p\nir/1wee9OnAINWnq+m253KaidJLq4Zd0fz7/rlxuk5n3U3S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- "text/plain": [ - "" + }, + { + "metadata": { + "id": "Pdgjgw9RiluO", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 390 + }, + "outputId": "7693578e-7a8e-4531-a1d8-bff9c0f14297" + }, + "cell_type": "code", + "source": [ + "plt.figure(figsize(12.5, 6))\n", + "\n", + "#histogram of the samples:\n", + "plt.subplot(211)\n", + "plt.title(r\"Posterior distributions of the variables $\\alpha, \\beta$\")\n", + "plt.hist(beta_samples_, histtype='stepfilled', bins=35, alpha=0.85,\n", + " label=r\"posterior of $\\beta$\", color=TFColor[6], normed=True)\n", + "plt.legend()\n", + "\n", + "plt.subplot(212)\n", + "plt.hist(alpha_samples_, histtype='stepfilled', bins=35, alpha=0.85,\n", + " label=r\"posterior of $\\alpha$\", color=TFColor[0], normed=True)\n", + "plt.legend();" + ], + "execution_count": 11, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [], + "image/png": { + "width": 823, + "height": 373 + } + } + } ] - }, - "metadata": { - "image/png": { - "height": 250, - "width": 824 - }, - "tags": [] - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize(12.5, 3.5))\n", - "np.set_printoptions(precision=3, suppress=True)\n", - "challenger_data_ = np.genfromtxt(\"challenger_data.csv\", skip_header=1,\n", - " usecols=[1, 2], missing_values=\"NA\",\n", - " delimiter=\",\")\n", - "#drop the NA values\n", - "challenger_data_ = challenger_data_[~np.isnan(challenger_data_[:, 1])]\n", - "\n", - "#plot it, as a function of tempature (the first column)\n", - "print(\"Temp (F), O-Ring failure?\")\n", - "print(challenger_data_)\n", - "\n", - "plt.scatter(challenger_data_[:, 0], challenger_data_[:, 1], s=75, color=\"k\",\n", - " alpha=0.5)\n", - "plt.yticks([0, 1])\n", - "plt.ylabel(\"Damage Incident?\")\n", - "plt.xlabel(\"Outside temperature (Fahrenheit)\")\n", - "plt.title(\"Defects of the Space Shuttle O-Rings vs temperature\");\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "El9Z_4ulIAz3" - }, - "source": [ - "It looks clear that *the probability* of damage incidents occurring increases as the outside temperature decreases. We are interested in modeling the probability here because it does not look like there is a strict cutoff point between temperature and a damage incident occurring. The best we can do is ask \"At temperature $t$, what is the probability of a damage incident?\". The goal of this example is to answer that question.\n", - "\n", - "We need a function of temperature, call it $p(t)$, that is bounded between 0 and 1 (so as to model a probability) and changes from 1 to 0 as we increase temperature. There are actually many such functions, but the most popular choice is the *logistic function.*\n", - "\n", - "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t } } $$\n", - "\n", - "In this model, $\\beta$ is the variable we are uncertain about. Below is the function plotted for $\\beta = 1, 3, -5$." - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 210 - }, - "colab_type": "code", - "id": "U4kW2QIddYEs", - "outputId": "9706fbdc-9263-4903-ab32-c8c9062ff8ed" - }, - "outputs": [ - { - "data": { - "image/png": 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FMiIiIlNxHKivt2Xb9rJTJjZaEtIUwxpnYOD2t81m4coVW4A14/f8ot+uS7N6\nDaxeDW1rbamunu1nJiK3sKrGw8/tqeU94RA/6orzwqU48Uwxmekfy/KFwyNsqPfw/u3VbGrU1ISy\n9F09fJXz3ztvF1rKCzYF2fWRXQTrg5XrmIiIiIjIIqNARkRE5G6FqmFLuy0lTCJhpzu7dg2uXYGr\nV+HqVZyb/be9pZNMQlenLaX3rG+AtjYbzqxps/utKzWaRmSO1QXcvG9bNW/fUsXzXXG+f2GMREkw\n0zWU4Y9fGuK+Vj/v3RaitVpvq2XpMcbQ+WwnPa/0lNXXratjxwd34A16K9QzEREREZHFSZ8cRURE\nZksgAOs32FLCJBJ2urMrPfmQ5gpcvXJnU58NDcLQIJw8Ubyf12tH0owHNeNhTVXVLD8hEQl4XLxt\nS4hH1wX5l44YP74UJ1cySuD49SQnbyR5bF2Qd7aHqPErLJWlIZvOEvnnCP2R8h8VrNi1gq3v3orL\nrde6iIiIiMjdUiAjIiIy1wIB2LjJlhImGqXn0EH8/X20pNOFwMZJxG95OyedhktdtpTer7EJ1ubX\nw1m33m7r6mf5yYgsT9U+Fx/aWcMbNwT5ViTGkWvJwrmcgR9finPoSoInNlXx5k1V+NxaX0YWr1Qs\nxamnThG9Gi2rX//69ax73TqtnyQiIiIico8UyIiIiFRKTQ3xteuIr11HS3t++jNjMDdv2nCm5zL0\n2K3Td+O2t3MGbsLATTh2pFBnamvzIU0+oFm7Dpqa7Ro5InLXWkIePvFgHZ2Dab5xZpSLg+nCuUTG\n8O1zdhTNu8MhDrQFcOm/NVlkxvrHOPmVkySGEoU6x+Ww9d1bad3dWsGeiYiIiIgsfgpkREREFhLH\ngeZmW/bcX6g2iYSd6qzncjGoudJj15651e1GRuDUSVvG71VVVQxpxkfUrGjVujQid2Fjg5dPP1LP\n8esp/vnsKDdi2cK54WSOLx2P8sPOMd63rZodLT6NKJBFYejSEKe/dppMIlOo8wQ87PjgDurXa8Sl\niIiIiMhMKZARERFZDAIB2LTZlnG5HOZmfzGgudwNl7txBgdveStnbAwiZ23JM36/DWg2bIT162H9\nRhsK6UtkkWk5jsOelX52rfDxQnecpztijKaKC8xci2b57KFhdrT4+MjuGhqD7gr2VuTW+iP9nPn6\nGUzJIkmB+gC7PryLqmatUSYiIiIiMhsUyIiIiCxWLhe0rLDlgb2FahON2nCm+xJ050Oa20x55iST\n0HHOlvH7hKptOLNhYzGsqdcvpEUmcrsc3rChin1rAjxzcYxnL46RzhXPn+5L8V+eH+B926p5dJ2m\nMZOFZ+TKCGe/ebYsjKlZU8PCe7p0AAAgAElEQVTOD+3EF/JVsGciIiIiIkuLAhkREZGlpqYGduy0\nJc/Ex+DyZRvS5EfScO0ajjHT3saJjcLpU7aM36euHjZsgPX5smEDhKrn7KmILCZBr4v3hKt53fog\n34nEeKUnwfh/YYmM4cmTUV67muBj99XQEtLbcFkY4oNxTj11ilymmCI2h5sJvzeM26tRXSIiIiIi\ns0mfBEVERJaDYBVsDdsyLpXE9PTYkOZSly23C2mGh+DYUVvyzIpW2LjJlk2bYM0acOsthixf9QE3\nP7enljduCPKl41EujxTX4zg/kOa/PD/Ae8LVvGljUKNlpKLS8TQnnzxJeixdqGvc0sj292/Hcem1\nKSIiIiIy2/RtiYiIyHLl809elyaRwFzutuFMVxdc6rr9dGc3rsON6/DKSwAYr89OdTYe0mzcBA0N\nc/c8RBaotjov//6xBp65OMbTHTHGByCkc/D1M6McuZbgY/fVsqpGb8ll/uUyOU599RTxgXihrrq1\nmu0/rTBGRERERGSu6NOfiIiIFAUC0L7VljwTixVH0OSLMzg47S2cdArOd9gyfo+GBhvMbMiPolm3\nHnxal0CWPrfL4W1bQty30s+Xjo3QOVQcLdM1lOEPfzLAO9pDPLGpCre+BJd5Yowh8u0II5dHCnX+\nWj87P7wTt0/TlImIiIiIzBUFMiIiInJrodDkNWmGh+FSpx1Fc/ECdHXiJBLT3sIZHITB1+Dwa/Z6\nlxvWroXNW2zZsgXq6uf6mYhUzMpqD59+tIHnu+J8KzJKKmvrMzn4diTG0WtJfu6+GtrqvJXtqCwL\nXc910Xe6r3Ds9rvZ9eFd+Gv8FeyViIiIiMjSp0BGRERE7l5dHdx3vy0AuRym9xp0XoSLF6HrIly9\nOu16NE4uWxxx8+wPADDNzTac2bTZblevAZdrfp6PyDxwOQ5v2ljFrlY/Xzo+QsfN4rodPSMZ/uiF\nQd66uYq3bwnhdWu0jMyNa0evcfnFy4Vjx+Ww4wM7CK0IVbBXIiIiIiLLgwIZERERmTmXywYoq9fA\nY6+3dfE45lKXDWnyxYlGp72F098P/f3wyssAmEDQTm82Popm4ybw69fbsvg1V7n5twfqefFygm+c\nGSWRscFlzsD3zo9xrDfJx+6rZWODRsvI7Bq4OEDH0x1lde3vbKdho9b5EhERERGZDwpkREREZG4E\ng7Btuy0AxmBu9ttw5sIFuHAeei5PP4omEYfTp2wBjMsFbWthSzu0t8OWrVBTM1/PRmRWOY7DY+uC\n7Gjx8Y8nopzuSxXO9Y5m+eMXB3nTxiA/Fa7WaBmZFbEbMc780xko+ZO77rF1rNyzsnKdEhERERFZ\nZhTIiIiIyPxwHGhusWXfAVuXSGA6L9pw5sJ5O4pmmrVonFwOui/ZMj7N2arVNpxp32oDmgb9ylsW\nl4agm1/bV8ehKwm+dnqUsbT9ttwAP+yMc2EgzScerKOpSguty71LRpOcePIE2fHFi4CWnS2sf8P6\nCvZKRERERGT5USAjIiIilRMIwPYdtoBdi+ZKTzGguXAeZ2Bg2suda1fh2lV4/jkATEtLMZxp3wrN\nzTYIElnAHMdhf1uQbc0+njo1ytHeZOFc93CGP/zJAP9mTy27WjVln9y9TDLDya+cJBUtjsKqW1tH\n+N1hHP19FBERERGZVwpkREREZOFwuWDtOlve9DgAZnCgLKDh8i2mOevrg74+ePEFe21DQzGcaW+H\nlasU0MiCVRtw80t76zhyLcGXj0eJ59eWGUsb/ubVYd6+pYp3bQ3h0mtY7pDJGc5+4yyx67FCXbAx\nyI4P7cDlcVWwZyIiIiIiy5MCGREREVnYGhrhof22AMTHMBcuQMc5Wy514WSzU17qDA7CoVdsAUxt\nHWwNQ3gbhMPQskIBjSw4D6wKsLbOyxdeG+bySKZQ/73zY3QOpvmFB+qo9evLdLk1Ywznv3eegQvF\nUYbeKi+7PrILb9BbwZ6JiIiIiCxfsxLIhMPhRuB3gZ8GVgH9wHeB34lEItfu4PqPA78G7AF8QDfw\nbeD3I5HIzdnoo4iIiCwRwSrYtdsWgFQS09kJ5yJwvgMuXsBJp6e81BkZhlcP2gKYhkYbzGzdBtu2\nQWPTfD0LkVtqrnLzW4828LXTUV7oLq6rdO5mmj/88QC/+GAtmxt9FeyhLHQ9r/Rw7Ujxo5jL42Ln\nz+wk2BCsYK9ERERERJa3GQcy4XA4CPwI2Ab8BfAq0A78NvB4OBzeG4lEBm9x/f8F/K/AQeA/AaPA\no8C/Bd6Tv35kpv0UERGRJcrnz4942WaPMxnMpa7iCJoL53ESiSkvdQYH4OWXbAFMc0vxXuEw1NXP\n05MQmczrdvjo7lo2Nnh58kSUdM7WDydz/NnLQ7x3WzWPbwxqHRCZpO9MH53PdpbVbXvvNmrX1Fao\nRyIiIiIiArMzQubTwG7gNyKRyF+NV4bD4WPA14HfAT4z1YX5kTX/C9AFvCESiYyvYPr34XC4H/iP\nwC8CfzoL/RQREZHlwOOBzVtsece7IJvF9Fy2I2giZ6HjHE4yOeWlTn8f9PfBCz8GwKxcmR89s92G\nNKHQfD4TEQAOtAVZW+vl84eHuRGz0/PlDHzjzCgXB9J8fE8NQa+mMBNruGeYs/98tqxu0xObaN7W\nXKEeiYiIiIjIuNkIZH4eiAGfn1D/TaAH+Hg4HP73kUhkqtV31+X7cLAkjBn3PDaQ2TALfRQREZHl\nyu2G9RtseevbIZvBXLpkA5qzZ+DCBZx0aspLnd5e6O2F53+EcRx7j+07bECzeYsNf0TmwepaD7/9\nWANfOh7laG/xbfPx60n+6CcZPrG3lrZarQuy3KViKU5/9TQmW/zotXrvatbsW1PBXomIiIiIyLgZ\nfYsQDodrsVOV/XhioBKJREw4HD4IfADYCFyc4hadQBI7xdlEG/LbkzPpo4iIiEgZtwc2bbblHe+C\ndBrT1WlHz0TOQudFnExm0mWOMdDVacvT38H4fNC+1QY023fC6tWgqaNkDgW9Lj7xYC3PdcX5+plR\ncvnv3PvGsvy3Fwb58K4aHl6r9UGWK2MMHU93kB4rrqHV2N7I5rdu1rR2IiIiIiILhGPMVANX7kw4\nHN4NHAe+HIlEPjbF+T/GTmn21kgk8oNp7vG/Ab+PXX/mT4AosB/4LNAHPBKJRKae+H0aw8PDUz6p\njo6Ou7mNiIiILENOOk3w6hWCl7up6r5EoPeaDWNuIxMKMbZuA7H1Gxhbv55sdc089FaWq2txN09f\nq2I0Uz5V2Y7aFG9aEcejGcyWnbFLYwwfHC4cu2vcND/RjEsvBhERERGRWdHePtW4Eqirq7vjX0DN\ndJ6N8W8axqY5H5vQbpJIJPIH4XD4OvDnwG+WnPo28PN3G8aIiIiIzITxehlbv4Gx9Ru4CbiSSRvO\nXOoidKkL3+DAlNd5YjFqz5yi9swpAJJNzYyt30Bs40bia9ZivJpOSmbPqmCWj64b5Xu9QS6PFV9b\np0d83Ei6efeqGHW+e//hlSwu2XiWkSMjZXX1++sVxoiIiIiILDAVn/g8HA5/Cvgz4F+BL2NHxRwA\n/gPw3XA4/M5IJDI0G481XYK1HI2PFtK/iSxmeh3LUqDX8SKxa1dh1wwMwNnTcOY0nD2DE41OeYn/\nZj/+m/00HH7VhjFbw7BjF+zcBa2tS2p6M72OK2f3NsO/dMT4l44xxuOX/qSbr12t45P76tlQryDw\nTi3W17ExhpNPnsSkiwHc2kfXsvHAxgr2Siplsb6ORUrpdSxLgV7HshTodTw3ZhrIjP8MKzTN+eoJ\n7cqEw+EwNox5JhKJvLvk1PfC4fAx4BvAf8KGMyIiIiKV19gIj77OllwOc6UHzpyxIU3HOZx0etIl\nTjoNp07a8hSY5uZiOBPeBoFABZ6ILAUux+FdW6vZUO/lvx8dIZb/Un40Zfizlwb5xQfr2N3qr3Av\nZS71Hu1l8OJg4Ti0IsT616+vYI9ERERERGQ6Mw1kOgEDtE1zfvyTwHSLtzye78M/TXHu6fy93zyT\nDoqIiIjMGZcL1q6z5W1vh3Qac+G8HT1z5hROd/eUlzn9/fD8j+D5H2HcbtjSDjt22oBmTduSGj0j\n82PHCj//4fWNfO7VYXpGMgCkc/C5V4f58K4aXrc+WOEeylyID8W5+MzFwrHjcgj/VBiXW1OViYiI\niIgsRDMKZCKRSCwcDh8HHgyHw4HS9V7C4bAbeBS4HIlEpv42ojiyZqqfhfoBZ5pzIiIiIguP1wvb\nttvy/g9iRkbgzCk7Mub0KZzR0UmXONksRM7a8vWvYerqYedO2LnbhjRBfZEud6Yx6ObfPVLPFw6P\ncKYvBdhfNz15MspgPMt7wiEchX1LhjGGc98+RzaVLdStf/16qlurb3GViIiIiIhU0mysIfN57LRj\nnwT+tKT+48AK4HfHK8Lh8DYgGYlEOvNVL+a3HwmHw38eiURKVx79mQltRERERBaX2lo48IgtuRzm\ncndx6rKLF3DM5EXXneEhePEFePEFjMsN7e2w+z5bWldW4EnIYhLwuPjkQ3X844koL/cUfivFv14Y\nYzCR42P31eBxKZRZCq4euspw93DhuGZ1DWsfWVvBHomIiIiIyO3MRiDzWeDngP8aDofXA68CO4HP\nACeA/1rS9gwQAbYBRCKRF8Ph8FPY8OUn4XD4K0AfsA/4DeA68Aez0EcRERGRynK5YP0GW971HojF\nMGfPFAIaZ3ho0iVOrmT0zFe/gmlZYYOZXbuhfasdkSMygdvl8LH7amgIuni6Y6xQf+hKguFEll/e\nW0fQqymtFrOxm2N0/qizcOzyuAi/J4yjsE1EREREZEGbcSATiUTS4XD4bcDvAR8EfhO4Afwd8LuR\nSGTsFpcD/CzwPPA/YcMXH3AV+ALwf0YikSsz7aOIiIjIghMKwd6HbDEGc/VKcfTM+Q47ldkETt8N\nePYH8OwPMH4/bN9RDGjq6ivwJGShchyHd22tpiHg5h9PRsnlB2Odu5nmT14a4lP766gPuCvbSbkn\nJmeIfCtCLpMr1G140waqmqsq2CsREREREbkTszFChkgkMoIdEfOZ27Sb9JOtSCSSBf4iX0RERESW\nH8eBNW22vO0dEI9jzpyGk8fh5AmckZHJlySTcPSILYBZt96GM/ftgXXr7T1l2XtkXZDagIsvHB4h\nlbWpzNVohv/nhUE+tb+e1TWz8nFA5tHlly8TvRotHNetrWPNvjUV7JGIiIiIiNwpfQITERERWWiC\nQXhwry25HKb7EpzIhzOXuqa8xOm+BN2X4DvfwtTVw549sOcB2BrW1GbL3M4Vfv7dI/V89tAw0aQd\nVTGUyPEnLw7yKw/V0d7kq3AP5U6N3hjl0vOXCscur4ut79mKowBWRERERGRRUCAjIiIispC5XLBh\noy0/9T7M8BCcPGlHz5w+ZUfKTOAMD8Hzz8Hzz9mpzXbugj3326nNQtUVeBJSaevqvHzm0Qb++uAQ\nN2J2Orx4xvBXB4f4+J5a9q4OVLiHcju5bI7ItyKY8fnngE1v2USwIVjBXomIiIiIyN1QICMiIiKy\nmNTVw2OvsyWdxpzvsKNnThy3a8xM4CSTcPg1OPwaxuWCLe02nLnvfmhpqcATkEpprnLzmUcb+JtX\nh+kcTAOQycH/e2SEoXiOxzcFNdJiAev+STex67HCccPGBlY9sKqCPRIRERERkbulQEZERERksfJ6\nYfsOWz78UUxvLxw7AseOQudFHGPKmju5HJyL2PLUk5jVa/LhzB5Yv8GOxpElLeRz8ZsH6vmHIyMc\nv14cXfWNs6MMJrJ8YEc1LoUyC070apTuF7sLx26/m63v1lRlIiIiIiKLjQIZERERkaVi5UpY+U54\n+zthZARz4rgNZ86cxkmnJjV3rl6Bq1fg6e/YdWfufwAeeBDa28Gtt4lLlc/t8Et7a/mn06M81xUv\n1D/XFWcokeMX7q/F69YX/QtFNp0l8q0IlOSrW962BX+tv3KdEhERERGRe6JP2iIiIiJLUW1tcWqz\nVBJz5owNZ04cw4lGJzV3hofguR/Ccz/EhEKwe48NZ7bvAJ8WfV9qXI7DB3dU0xB0840zo4X6Y71J\nvnB4mE88WKdQZoG49Pwlxm6OFY6btjaxYteKCvZIRERERETulQIZERERkaXO57dTk+25H3I5TOdF\nG84cP4rT2zupuROLwcsvwssvYvx+2LnbhjO7dkNQC4gvFY7j8JZNVdQHXHzx2AiZnK0/eSPF5w8P\n80sKZSpuuHuYnld6CsfeoJf2d7RrqjIRERERkUVKgYyIiIjIcuJyweYttnzgQ5jrvTacOXoE5+KF\nSc2dZBIOvwqHX8V4PHbEzP0Pwp49UF1TgScgs23v6gAhr4u/fXWIdD6UOaVQpuKyqSyRb0fK6ra8\nYwu+ao1YExERERFZrBTIiIiIiCxnrSvhbe+At70DMzQEx47AkcNwLoKTy5U1dTIZOHEcThzHfNGB\n9q3wwIN46hrI1CicWcy2tfj41X31/O2h8lDm714b5pf3KpSphIvPXiQxlCgct+xsoWV7SwV7JCIi\nIiIiM6VARkRERESs+np445ttGR3FnDgGR47A6ZM2jCnhGAPnInAuwiYgvnqNXa/mwb3Q0FiZ/suM\nbGueHMqc7lMoUwlDXUNcO3ytcOyr9rHlbVsq2CMREREREZkNCmREREREZLLqanjkMVsSCcypk3bk\nzMnjOInEpObBq1fgqSfhqScxmzbbYObBh6BR4cxisq3Zxyf31fM3E0KZz702zK8olJkXJme48P3y\n6QO3vmsr3qC3Qj0SEREREZHZokBGRERERG4tEIC9D9mSTmPOnoGjh+HoUZzY6KTmzsULcPECfPUr\nmI2b7HUP7oXGpgp0Xu5WeIpQ5oxCmXnTe7yXWF+scLxi1woatyjYFBERERFZChTIiIiIiMid83ph\n9322fCyL6TjH8A+fobrjHJ6xsUnNnc6L0HmxGM6Mj5xpUjizkCmUqYxMMkPXc12FY5fXxcY3b6xc\nh0REREREZFYpkBERERGRe+N2w7bt3HB7uPH4W2nHwGuvwpHXcKLRSc0L4czXnsJs2JgfdbNP05ot\nUOFmH7+2r57PTghl/vbVYX7loTp8CmVm3eWXLpOOpQvHax9ei7/GX8EeiYiIiIjIbFIgIyIiIiIz\n53JBezuEt8FHP4bpOAeHX7PhzMjIpOZOVyd0ddpwZks7PLTPjp6pratA52U6W5t9fGq/DWVSWVt3\ntj/F514d4lceqlcoM4sSwwl6XukpHPuqfbQdaKtgj0REREREZLYpkBERERGR2eVy2WAmvA0+8rOY\n8x35kTOHcUaGJzV3znfA+Q7Mk1+21+zbD/c/CKFQBTovE7U3FUfKFEOZtEKZWdb5w05M1hSON7xp\nA26fu4I9EhERERGR2aZARkRERETmjssFW8O2fORnMRfO23Dm8GuTwhnHGDh7Bs6ewXzpi7BzFzy0\nH+7bA4FAhZ6AwPShzN++OsSvKpSZsZErI/Sd7iscV6+spnV3awV7JCIiIiIic0GBjIiIiIjMD5cL\n2rfa8uGP2mnNXj1ow5lYrKypk83C8WNw/BjG64Pd98G+fbBzN/h8FXoCy1t7k49P7avnrw8Nk8qP\n5Ij0p/mbQ0N8cp9CmXtljOHiDy6W1W16YhOOo39PEREREZGlRoGMiIiIiMy/0mnNPvoxzJkzNpw5\negQnkShr6qRTcPhVOPwqJhCAPQ/Yac227wC3pnSaT1uafHxqfx1/fbAYypy7qVBmJvrO9DFypbjO\nUnO4mfp19RXskYiIiIiIzBUFMiIiIiJSWW4P7NptSzqNOXnChjPHj9swpoSTSMArL8ErL2FqamDv\nPth/ADZuAo0omBdbGqcOZT7/2jC/+lAdbpf+d7hTuUyOzh92Fo4dl8PGN2+sYI9ERERERGQuKZAR\nERERkYXD64UHHrQlkcCcOAaHDsGpE3YasxJONAo/ehZ+9CympQX2HYD9D8PKlRXq/PKxpdHHr+dD\nmWQ+lDndl+L/Oz7Cx/fU4lI4dkd6DvaQHE4Wjlc/tJpgY7CCPRIRERERkbmkQEZEREREFqZAwIYs\n+w5ALIY5dgQOHYSzZ3CMKWvq9PXBd78N3/02Zt16O2pm336o09RPc2VzfqTMX74yRDpn6w5dSVLt\nG+X926u1BsptpEZTXH7xcuHYE/Sw/nXrK9gjERERERGZawpkRERERGThC4Xg0dfZMjyMefUQHHwZ\n51LXpKZO9yXovoT52lN2jZr9D8MDD0Cwav77vcRtbvTxiQfr+Nxrw+TyGdkPO+PU+l08sTlU2c4t\ncF3Pd5FNFUd9rX/9ejwBfTwTEREREVnK9I5fRERERBaXujp4yxPwlicw13vh4Ctw8BWcvhtlzRxj\n4OwZOHsG86X/AfftseHMrt3g0dvg2bKr1c/H7qvhi8eihbpvno1R7XPx8FpNvzWV2I0Yvcd6C8fB\npiCrHlhVwR6JiIiIiMh80CdREREREVm8WlfCT70P3vNeTFenDWdePWjXlynhZDJw+DU4/BomVG2n\nMzvwMGzYCJpaa8YOtAWJJnN882ysUPflE1FCPhe7W/0V7NnCY4zhwjMXoGTWvU1v2YTL7apcp0RE\nREREZF4okBERERGRxc9xYOMmWz70YczZMzacOXoYJ5ksbxobhR89Cz96FtO6Eh5+xIYzjU0V6vzS\n8MTmENFkjmc74wDkDPz94WF+40A9mxt9Fe7dwjF4YZChzqHCcf2Geho3N1awRyIiIiIiMl8UyIiI\niIjI0uJ2w85dtqQ+jjl+zIYzJ0/i5LJlTZ3rvfDNr8M3v47ZGrbhzAN7Iaiptu7F+7ZXM5oyHLyS\nACCdg785NMynH2lgda0+euSyOTs6ZpwDm5/YjKNRWiIiIiIiy4I+FYmIiIjI0uXzw0P7bRmNYg4d\ngldewunqnNTUOReBcxHMl78E998PDz8K27bbgEfuiMtx+Nh9NcTSOU7dSAEQzxj+8uAQn3m0gaaq\n5f1v2Xukl/jNeOF45Z6VhFaEKtgjERERERGZTwpkRERERGR5qK6BNz8Ob34c03sNXn4JXnkZZ3Cg\nrJmTTsGhg3DoIKa2Dvbvt+FM29oKdXxxcbscPvFgHX/x8iCdQxkARpI5/urgEJ9+pIEa//JcKyWT\nyND1467CsdvnZsMbNlSsPyIiIiIiMv+W56chEREREVneVq6Cn/4A/MH/jfmt38Y8+hjGP3nxeWdk\nGOcH38f5/f8Mf/Cf4ZkfQDRagQ4vLj63wyf31bOyujgi5kYsy2cPDZHI5CrYs8rpfqGbTDxTOF77\n6Fp81VpbR0RERERkOVEgIyIiIiLLl8sF4W3w878If/TfML/0K5iduzBTrOnhXL6M89Q/wn/8bfjs\nX8Kxo5DNTHFTAQj5XPz6/noaAsWPHN3DGf7utWHSWVPBns2/+GCcK4euFI79tX7W7FtTwR6JiIiI\niEglaMoyERERERGw683sO2DL8BDm4Ct2SrOey2XNnGwWjh6Bo0cwNTWw/2F49DFY01ahji9cDUE3\nv36gnj95cZBY2oYwkf40Xzw2wi88UItrmSxm3/lsJyZXDKE2vnkjbu/yXk9HRERERGQ5UiAjIiIi\nIjJRXT289e3w1rdjei7DSy/CwZdxJkxX5kSj8Mz34ZnvY9atg0ceg3377Xo1AsDKag+/tr+eP395\niFR+ZMzha0mqfaN8aGc1zhIPZYa6h+iP9BeOa9bU0LKjpYI9EhERERGRSlEgIyIiIiJyK21r4Wc+\nAu//IObkCRvOnDiOk8uWNXO6u6G7G/PVr8B998Mjj8LOXeDWSIgN9V5+eW8tnz00zPhAkecvxanx\nu3hHe6iynZtDxhgu/uBiWd3mt2xe8iGUiIiIiIhMTYGMiIiIiMid8Hjg/gdsiUbtlGYvvTD1lGZH\nXoMjr2Fqa+HAI3ZKs1WrK9TxhWF7i59/s6eWfzg6Uqj7zrkYNX4Xj60LVrBnc+fGyRuM9o4Wjlt2\ntFDbVlvBHomIiIiISCUpkBERERERuVs1NfCWJ+AtT2AudxenNBsdLWvmjIzA978H3/8eZtNmeOx1\nsHcfBAIV6nhlPbQmwGgqx9dOF/+dvnIySkPAxY4V/gr2bPblsjm6nusqHDtuh41v2li5DomIiIiI\nSMUpkBERERERmYm162z5wIfyU5q9ACdOTJ7S7OIFuHgB85V/hL0PwaOvg81bYJlNX/WmjVVEkzn+\n9cIYADkDf39khN96tIHVNUvn40nvsV6SI8nCcdv+NgL1yzOIExERERERa+l84hERERERqaTSKc1G\nRjAHX4YXX8C5eqWsmZNMwosvwIsvYFpbbTDz8KNQV1ehjs+//5+9O4+O4jzzvv+tbu1bCwFiEWKH\nFmbVyr44JoljkxC8x0s2x04yHj9xnPiNJ3PiJH7iN5nBSSaTGccT4sQTx4CXeI1jY2KbTQKE0AIY\nqRFIgBASILRLaGl1PX8UaqlBYEBLa/l9zqnT566+q+pqXOZ0cfV1X6uc4VQ1edhT2gRAk9vkf/ZU\n873FMUQF2/wcXfd53B5KMjqWsrMH2xm3YJwfIxIRERERkf5ACRkRERERkZ4WFQUrPwM3fBrz2FFI\n3wF7MjGazvlMM06dgtf/ivnm6zBrjtVrZvZssA/ur+mGYfCl2ZFUnmvjSGUrAJXnPKzLqubhBcMI\nsg/sqqHyfb7VMXEpcQSGBvoxIhEREREZalpaWli/fj2bNm3ixIkTAIwfP5477riD1atX+zm6oWtw\nP+mJiIiIiPiTYcDESdZ2+x2Y2dmQsQPjkMt3mscD+3JhXy5mVBTMX2j1mxk9xk+B975Au8E3kh38\nMr2KikZrebej1W5ezKvlK4lR2AboUm4et4fj6ce9Y3uwnbi0OD9GJCIiIiJDTWtrKw8//DA5OTlM\nnz6dNWvW0NzczPvvv89TTz1FbGwsCxcu7LN4PvjgA7Kzszl06BCHDx+moaGBG2+8kSeffLLPYugv\nlJAREREREekLQcGwYOmGgUIAACAASURBVCEsWIh5+pS1bNnODIyaap9pRm0tbN4EmzdhTp0GS5ZC\nUrJ1/CATEWTjW6lWUuac2wQgu6yZ2PAGbnZG+Dm6a1OeV05LXYt3HJeq6hgRERER6VsbN24kJyeH\nNWvW8Pjjj2Oc/7FTYmIiTzzxBHl5eX2akPnjH/9IYWEhYWFhxMbG0tDQ0GfX7m+UkBERERER6Wux\no+CLt8DnV2Me/BgydkBeHoanzWeacbgQDhdivrQB0hZYyZn48X4KuneMigjg/mQHz2RW47FyMrx3\nuJGR4XbSxoX6N7ir5HF7OJ5xQXVMqqpjRERERKRvvfbaa4SEhPDII494kzEAdrsdAEcf96/87ne/\nS2xsLPHx8WRnZ/Ptb3+7T6/fnyghIyIiIiLiL3Y7zJ5jbXV1mLt3QvoOjLKTPtOMc+dg60ew9SPM\n8RNgyTJITYPQgZWwuBTniCDunBXJhv113n0b9tcxPMzOlJggP0Z2dVQdIyIiIiL+VlZWRmlpKUuX\nLiX0gueFDz74AICUlJQ+jamvr9efKSEjIiIiItIfREbCys/ADZ/GLC6C9O2QtQejudlnmnH8GKx/\nAfPVlyAl1UrOTJps9asZwBaND+V0QxsfFDUC4PbAuqwavrd4GCPD+/9jS1fVMePSxvkxIhERERHx\n+uW/+zuCy/ve/9djp8rPzwdg5syZ3n2mafLSSy/x4YcfkpaWxrRp03rsenJ1euTJxul0xgA/Br4I\njAEqgL8DP3K5XGVXcHww8DhwLxB//vh3gH91uVwVPRGjiIiIiMiAYBgweYq13X4X5p5M2LEN49hR\n32ktLVYfmox0zLFjYfFSmL8QIgZm7xWALySEc6bBzb5TVpVJQ6vJs3uspExYoM3P0V1eee7F1TEB\nIf0/kSQiIiIyFBiFh/wdwmWZPXiugoICAGbMmEFWVhabNm0iNzeXY8eOMW3aNH76059e9vgNGzZQ\nV1dHZWUlADExMZedP336dFasWNEjsQ8F3X5CcDqdocAWIAH4LyALmAZ8H/iU0+lMdrlcVZc5PgAr\n+bL8/PF7gRTgn4ElTqcz0eVytVzqeBERERGRQSskBJYug6XLME+UwI7tkLkLo7HRZ5px8iS88hLm\n63+FeUnWMdOdA65qxmYYfHmeg9/srKKk1g3A6YY2nttbwz+lRWO39c/P43F7OL5T1TEiIiIi4n/t\nFTIzZsxg7dq1bN682fvexIkT8Xg8lz1+48aNlJV9Yo2F180336yEzFXoiZ9sPQLMBh5yuVzPtO90\nOp15wOvAj4BHL3P8t4AbgK+4XK4/n9/3F6fTWQF8HZgPbO+BOEVEREREBq5x8XDX3XDLbZg5e2HH\n9ot+6We43ZCVCVmZmLGjrOXMFi2CiEg/BX31ggMMvpnq4On0KqqbrIfFQ2dbeelAHV+aHenTlLS/\nKMst86mOGZc2TtUxIiIiIv2IOW26v0PoMwUFBYwZM4bo6GiefPJJHnvsMYqKinj55ZfZvHkzxcXF\nrF+//pLHv/nmmwAUFhYCaHmzHtYTTwlfBhqA5y7Y/yZwArjX6XR+z+VyXary6iGgEHih806Xy/Uz\n4Gc9EJ+IiIiIyOARFGQtTTZ/IWZ5udVrZlcGRl2dzzTj9Cl47RXMt14fcFUzjhA7D6Y4+I+dVbS0\nWft2ljQxKjyAG6aE+Te4C3jcHkoySrxje7CduNQ4P0YkIiIiIhfpwR4t/VlZWRk1NTUkJycDYLfb\niY6OJikpiaSkJO655x4KCwspLS0lLk7fWf2hWwkZp9MZhbVU2XaXy+XTbdTlcplOpzMTuAWYBBR1\ncfy488f/d3vCxul0hgDNl0ngiIiIiIgIwOjRcOvtsHoN5r482LEN8g9imB1fpbusmlm4CCL7d9VM\nvCOQryY6WJdV411T+82CekaE25k7OtivsXVWlltGS72qY0RERETE/zr3j+lKVFQUAGFhl/6Rk3rI\n9K7uPilMOP964hLvty+kPJkuEjJYyRiAI06n8zvAd8+fs9npdL4HfN/lch3uZoxe7WVW0kF/JjIY\n6D6WwUD3sQwGuo/9LDIKPreKgEVLcOzfh+PAPgIaGnymtFfNeN58jfqp06mZM5dz8eP7bdVMCLB4\nZBA7zoQCVrPT57OruS2+ntiQy699fa2u5j4220xObzvtHRuBBk3Dm/T/gvid7kEZDHQfy2Cg+1j6\nWkZGBgCRkZEX3X/19fXk5uYSHx9PRUUFFRUVXZ7jhRdeuOR7XVm6dOlVVducOGGlEurq6gbc/yM9\nsXxbdxMy7T+ra7zE+w0XzLtQe3rtK0AQ8BRwCqunzD8DC51O5zyXy3XlXYRERERERIYwtyOas0uW\ncXbhYiKKjuDYl0vY0WI6p1xsbW1EufKJcuXTMmwYNbPnUjtzNm2X+aWcvyRGt1DdYuNAjVUV4zYN\n3i4N587x9UQE+reovrGoEU9TR2IofHo4tkCbHyMSERERkaGsuLgYgF27djFr1ixv/0W3281zzz1H\nW1sbN91002XP8Zvf/KbX4xzK/F1LH3T+dRQwy+VynT0/fsvpdJ7CStB8D/h+T1xMDYg6qCmTDAa6\nj2Uw0H0sg4Hu434sIQFuuhkqzmDu2A4Z6Ri1NT5TgqqqGLltCyPSt0NiMixbDtOm96uqmSlTTZ7d\nU01BRSsADW023j8bwyMLhxEc0DNxXu197HF7yHw30zsOCAlgzmfnaLky8Sv9fSyDge5jGQx0H4u/\nHD9uLVi1ZcsWysvLSUlJobGxkd27d1NaWsqqVau4//77r+hcPXkfb9myha1btwJw9qyVAjh69Cjr\n168HIDo6mu985zvdvs5A0N2nhdrzr+GXeD/ignkXqj//+lanZEy757ASMiuuOToREREREYERI+GL\nt8Dnv4C5b5/Va+bgx769ZtraOnrNjB4NS1fAgoUQfqmv+n3HbjP4WpKDX2dUUV7fBsCJWjd/yavl\n60lR3l/+9aWyHN/eMXFpcUrGiIiIiIjflJeXU11dzfz584mIiCArK4sNGzYQHh5OQkICDz30ECtX\nrvRLbIcOHeKdd97x2VdaWkppaSkAY8aMUULmChVjLeU87hLvt/eYudRicEfPv9q7eK/i/LmjrjU4\nERERERHpxB4AiUnWVnEGM30HpO+4qGrGKC+HVzZivvFXSE61qmYmTfZr1UxYoI1vpkbzy/RK6lus\nRFJueTPvH27ks9P6NmnU1tpGyc4S7zggJIC4lCtfN1tEREREpKfl5+cDkJaWxn333efnaHw9+OCD\nPPjgg/4Oo1/o1gLHLperAdgHJDmdzpDO7zmdTjuwCChxuVzHL3GKg0ANMK+L9+IBAzjRnRhFRERE\nRKQLI0bC6jXw83/D/OY/YV4386IpRmsrxq4MjH//OTz1JGzbAk1NfR/reSPC7Nyf5MDWKS/0t0MN\n7D/V3KdxlOeUqzpGRERERPqVgoICAJxOp58jkcvpiY6TzwFhwDcv2H8vEAv8oX2H0+lMcDqdk9rH\nLperBVgPJDudzs9fcPw/n399uwdiFBERERGRrrRXzfyf72L+3/8f87M3YkZGXjTNOFGCsf4v8IPv\nwYsvQMmlfnPVu6YOD+L2mb7x/Tm3lrI6d59cv8vqmFRVx4iIiIiIfykhMzD0xM+4ngXuAZ52Op0T\ngCxgJvAosB94utPcfMAFJHTa92Pgs8ArTqfzF1jLmH0KuA/IPX9+ERERERHpbSNjYc1tsGo1Zm4O\nbN+KccjlM8VobobtW2H7VsxJk2HpckhJgaDgPgtzyYRQSmvd7Dh+DoAmt8m6rBq+v2QYYYE98Zuz\nSyvPKaeloaM6Ztz8cQQEqzpGRERERPyroKCAMWPG4HA4/B2KXEa3nxxcLler0+n8DPAT4FasypbT\nWJUxP3a5XI2fcPwZp9O5APgZ8CAwAigDfgU86XK5znU3RhERERERuQqBgZCaBqlpmGUnYfs22JWB\n0ej71d4oLoLiIsxXX4IFi6xeM6PH9EmIt86MoKzezZHKVgDONLbxp+wavpUajd3WO71uLqqOCQ1g\nbMrYXrmWiIiIiMjV2LRpk79DkCvQIz/lcrlctVgVMY9+wrwun4xcLtcZrCXPLlz2TERERERE/GnM\nWLjjLvjiLZh798C2rVYiphOjsRE+/Ad8+A9MZwIsWwHz5lnLofWSAJvB/UkO1u6opKrJA0BBRStv\nFdSz5rqLl1zrCWU5Zb7VMWmqjhERERERkSunpwcREREREflkQUGwcDEsXIxZctxatmz3LmsJs04M\nVwG4CjCjHLBkKSxZBjExvRJSZLCNB1Ic/DqjilYrJ8OHxeeIiwogbVxoj15L1TEiIiIiItJdvbvA\nsoiIiIiIDD7x4+Hu++Dffol5932Y4+IvmmLU1mD8/W/wrz+AZ/4LPj4AHk/Ph+II5J65UT77Nuyv\n41h1a49epyynjNaGjnOqOkZERERERK6WniBEREREROTahIRYfWOWLsMsLoKtW2DvHgy32zvFME3Y\nlwv7cjFHjLTmL1oMET23rFjy2BBKa91sPmL1uHF7YF1WDY8tGYYjxN7t86s6RkREREREeoIqZERE\nREREpHsMAyZPga/dD79Yi3nLbVby5cJpFWcwXnsVHn8M/rgODheCafZICKuc4Vw3Msg7rmn28Nze\nGlrbun/+suwLqmPmqzpGRERERESunhIyIiIiIiLScyIi4TM3wpNPYT78CObceZiG4TPFcLsxMndj\nPP1v8NSTVj+apqZuXdZmGHw1MYrY8I6KmOJqN698XIfZjaRPl9UxyaqOERERERGRq6efdYmIiIiI\nSM+z2WDmLGurrMTcsQ12bMeorfGZZpwogRdfwPzrq7BgISxbAWOvLeERGmjjwRQHv0yv4pzbSsLs\nLGkiLiqA5RPDrumc5TnltDaqOkZERERERLpPTxIiIiIiItK7YmLgC1+Em1dh5ubCti0YrgKfKUbT\nOdjyIWz5EHO6E5ZfD/Pmgf3qHllGRQTwlcQo/mdPDe11Ma8drGdMRADTRwRd9tgLedweSnapOkZE\nRERERHqGEjIiIiIiItI37AGQnALJKZjlZbBtK+xMxzh3zmeaccgFh1yYDgcsWQZLlsKwmCu+zMzY\nYL6QEM6bBQ0AeEz4Y3YN318Sw4gw+ycc3eHU/lO01Ld4x3GpcaqOERERERGRa6YeMiIiIiIi0vdG\nj4E77oJfPI1575cx4+MvmmLU1GC88zb86+PwP89AQT5cYT+YGyaHkTw22DtuaDVZl1VNs9tzRceb\nHtOnd4w9yK7qGBERERER6Rb9vEtERERERPwnONiqglm8FLO4CLZugb17MNxu7xTD44GcbMjJxhw1\n2uozs3ARhF26L4xhGNw9J4rT9VWU1FrnOlnXxl/y6vhaUhQ2w7hsWKcPnqapusk7HpsylsDQwG59\nVBERERERGdpUISMiIiIiIv5nGDB5CnztfvjFWsxbbsMcMeLiaafKMV7ZCD/4Przwv1By/JKnDLIb\nfCPFQWRQR/Ilt7yZ9w83XjYU0zQpSe+ojrEF2IhLjbuGDyUiIiIiItJBFTIiIiIiItK/RETCZ26E\nlZ/BPPgxbP0IDuzH6LRcmdHaAunbIX075uQpsPx6SEqGQN8qlphQO/cnO/jtrmrazh/+90MNjIsK\nYNaoYLpS4aqg8WxH0mZM4hiCwoN6/nOKiIiIiMiQooSMiIiIiIj0TzYbzJptbRVnMLdvg/TtGPX1\nPtOMoiNQdATz1Zdg0RJrSbPhw73vT4kJ4vZZkWzcXweACfxvbi3fXzyMURG+j0QXVscYNoNx88f1\n2kcUEREREekNLS0trF+/nk2bNnHixAkAxo8fzx133MHq1av9HN3QpYSMiIiIiIj0fyNGwppbYdUX\nMLOzYOsWKxHTiVFXB5vexXz/PZg9x6qamXEd2GwsHh9KSU0r6cetvjBNbpN1WTV8b/EwQgM7VnKu\nOlJF/amOhM+oOaMIjuq6kkZEREREpD9qbW3l4YcfJicnh+nTp7NmzRqam5t5//33eeqpp4iNjWXh\nwoV9Fs9vf/tb8vPzOX78ODU1NQQHBzN69GiWL1/O7bffTnR0dJ/F4m9KyIiIiIiIyMARGAjzF8L8\nhZjHj1vLmWXutpYwO88wTdiXB/vyMEfGwvIVsHARt14Xycm6NoqrWgE41dDGC3m1fCPZAVjVMcd3\ndupJY0D8wvi+/HQiIiIiIt22ceNGcnJyWLNmDY8//jiGYfVUTExM5IknniAvL69PEzIbNmwgISGB\n+fPnM2zYMM6dO8eBAwdYt24db7zxBn/84x8ZNWpUn8XjT0rIiIiIiIjIwDR+PNz3Fbj1dsydGbDt\nI4xTp3ymGGdOw6svY775OoGp87l/0QrWNkZQ0+wBYP+pFt4rbGSaAS1nWqg9Ues9NnZmLKHDQvv0\nI4mIiIiIdNdrr71GSEgIjzzyiDcZA2C32wFwOBx9Gs9HH31EcPDFVefPPPMMzz//PM8//zw/+MEP\n+jQmf7F98hQREREREZF+LCwMblgJP/6/mN95FHNuImanB08Ao7UVI2MH0U//jPs/fp0ATO977xY2\nUFQfQH2+b28aVceIiIiIyEBTVlZGaWkpqamphIb6/rjogw8+ACAlJaVPY+oqGQOwcuVKAEpKSrp8\nfzBShYyIiIiIiAwONpvVM2bGdVBZibljG+zYhlFb6zNtcv5u7mhoY/3cW7z7Mo8YLD/dsezZCOcI\nwkeG91noIiIiItJ7frOzyt8hXNZ3Fg7rsXPl5+cDMHPmTO8+0zR56aWX+PDDD0lLS2PatGk9dr3u\n2L59OwBTp071cyR9RwkZEREREREZfGJi4AtfhJtWYeZkw9aPMA4Xet9edDyL4444dkycD8C08kqf\nw8cvHt+n4YqIiIhI7zlc2ervEPpMQUEBADNmzCArK4tNmzaRm5vLsWPHmDZtGj/96U8ve/yGDRuo\nq6ujstL6fhwTE3PZ+dOnT2fFihVXFNtf/vIXGhsbqa+vJz8/n7y8PKZOncpXvvKVKzp+MFBCRkRE\nREREBq+AAEhNg9Q0zBMlsHULZO7CaG7mtgN/42TUKM6GjmZsbcdyZcOi2oiI9F/IIiIiIiLXqr1C\nZsaMGaxdu5bNmzd735s4cSIej+eyx2/cuJGysrIrvt7NN998VQmZ9kQPwMKFC3niiScYNqznKoT6\nOyVkRERERERkaBgXD/fcB7fcirlrJ/atH/GNrPW8O+Vun2mlTZXMfvwxK5Gz/HqYMNE/8YqIiIhI\nj5gaE+jvEPpMQUEBY8aMITo6mieffJLHHnuMoqIiXn75ZTZv3kxxcTHr16+/5PFvvvkmAIWFVnV5\nTy5v9t577wFw9uxZ9u3bx3//939z33338atf/YqEhIQeu05/poSMiIiIiIgMLaFhcP0NsOJT2LMO\nMHpzJWAAcDo8jK1TlzK2/ihzM9IhIx1z4iRYvgJS0iBw6DzMi4iIiAwWPdmjpT8rKyujpqaG5ORk\nAOx2O9HR0SQlJZGUlMQ999xDYWEhpaWlxMXF+S3O4cOHc/3115OQkMBtt93GT37yEzZu3Oi3ePqS\nEjIiIiIiIjI0GQYl5UG0J2MA8kcNB+DPiXfw2PZnGF1/BuNoMRwtxnz1FVi8BJYthxEj/RS0iIiI\niEjXOveP6UpUVBQAYWFhlzxHb/aQudCYMWOYNGkShw4dorq6mujo6Gs6z0CihIyIiIiIiAxJTdVN\nnDpwyjs+FxnM6Qjr4bQ5IJjfp97LY9ufIdTdDIDRUA/vv4e5eRPMnGUtZzZzFthsfolfRERERKSz\n9v4xXS3/VVNTQ15eHlOnTr1sz5be7CHTlYqKCgBsQ+Q7tRIyIiIiIiIyJJXsKgGzYzx6dhiTg4Io\nqmoF4HTESP535bd54KPfYW9u9s4zTBMO7IcD+zFHjIBlK2DREoiI6ONPICIiIiLSob1CZvPmzaSl\npWEYViV4a2srP//5z3G73dx9992XO0WP95A5duwYw4cPJ+KC78oej4dnn32WyspK5syZ463eGeyU\nkBERERERkSGnua6Z8rxy7zjAEUDo2GDuHx/F2vQqqps8ABwIjOXdB3/GzadzYOtHGOW+vxY0Kirg\ntVcx33rD6jGzfAVMmtyXH0VEREREBOhIyLz11lscOnSIlJQUGhsb2b17N6WlpaxatYpVq1b1aUwZ\nGRk888wzzJ07l7Fjx+JwOKisrCQ7O5vS0lKGDx/OD3/4wz6NyZ+UkBERERERkSHnxO4TmG0d5TER\nMyIwDIOoEDv3Jzn4za4q3FZOhveOtjIueTFzV1yPecgFWz6CvBwMj8d7vOF2w64M2JWBOWGilZhJ\nSYOgoL79YCIiIiIyJJWXl1NdXc38+fOJiIggKyuLDRs2EB4eTkJCAg899BArV67s87jS0tI4ceIE\nubm5uFwu6uvrCQkJYfz48Xzuc5/jzjvvxOFw9Hlc/qKEjIiIiIiIDCmtja2U5XRUuoTGhBIyLsQ7\nnjgskDtnRfLivjrvvhdya4ldPIwxzgRwJkBVFeaObbB9G0Ztjc/5jWNH4c/PY776srWU2fIVMDK2\ntz+WiIiIiAxh7f1j0tLSuO+++/wcTYcpU6bw2GOP+TuMfmNodMoRERERERE570TmCTytHdUt8Yvi\nvetrt1sQH8rSCaHecXObybqsGhrbjxs2DD6/Gn7+b5gPfAtz2vSLrmM0NmL8432MH/0QfvsfsC8X\nOlXViIiIiIj0lPblypxOp58jkctRhYyIiIiIiAwZ7iY3J/ee9I6DHcHEzoylrqjuorm3XhfByTo3\nRypbATjT2MbzObV8K9WBrT2BYw+A5BRITsE8WQpbt8CuDIzmZp9zGR8fgI8PYMbEwLIVVuXMEGlc\nKiIiIiK9TwmZgUEVMiIiIiIiMmSc3HuStuY27zh+QTw2e9ePRXabwdeTHESHdLyff6aFtwoauj75\n2Dj40j3wb7/EvOsezLFjL5piVFZivPEa/Mtj8Nw6OFwIptnFyURERERErlxBQQFjxowZUv1YBiJV\nyIiIiIiIyJDQ1tLGicwT3nFQRBCj546+7DFRwTYeSHbwHzuraF+t7IOiRuKiAkiNC+n6oJAQWHE9\nLF+BWXgItm2B7GwMT0ciyGhrgz27Yc9uzLhxVp+ZtAXWsSIiIiIiV2nTpk3+DkGugBIyIiIiIiIy\nJJTlluE+5/aOx80fhy3gkxcNGB8dyJfmRPHn3Frvvg37ahkVbmd8dOClDzQMmO60tpoazPTtsH0r\nRlWV77TSE7D+L5ivvQrzF1rJmbFxV/35RERERESkf1NCRkREREREBj2P28OJXR3VMQGhAYxJHHPF\nx6fGhVBa6+aDokYAWj2wbm8Njy0eRlSI/ZNP4HDATavgs5/D3L8Ptn6EkX/QZ4rR1ARbP4KtH2FO\nmw7Lr4d5iRCgxzYRERERkcFA3+xFRERERGTQK99XTkt9i3c8Lm0c9qArSKR08oWEcE7Wuck/Y52n\nusnDH7JreXh+NIF248pOYrdbSZZ5iZinymHbVtiZjtHY6DPNKDwEhYcwo6Jg8VJYugxihl9VvCIi\nIiIi0r98cn2+iIiIiIjIAOZp81CSUeId24PtjE0ee9XnsRkGX02MYmR4RyKnuKqVVz6uwzTNqw9s\n1Gi4/U74xVrM+76KOX78RVOM2lqMd9+Bf30cnvktHNgPHs/VX0tERERERPxOFTIiIiIiIjKoleeV\n01zb7B2PTR5LQMi1PQqFBdp4MMXBL9OraHJbSZidJU2Miwpg2cSwawswKBgWL4FFizGPFsPWLZCV\nieHu6HdjmCbsy4N9eZgjRsDS5bBoCURGXts1RURERESkz6lCRkREREREBi2P++LqmHHzx3XrnKMj\nAvjKvCg6L1L214P1FJ5tueQxV8QwYNJk+OrX4RdPY956O+bI2IunVVRgvP5X+JfH4I/r4HAhXEuF\njoiIiIiI9ClVyIiIiIiIyKBVvs+3OiYuJY7A0MBun3fWqGBWOcN529UAgMeE5/bW8NiSGIaHXV1v\nmi5FRMCnPws3fBqzIB+2bYF9eRidlisz3G7I3A2ZuzHj4mDZCpi/EEJCun99ERERERHpcUrIiIiI\niIjIoORxezieftw7tgfbiUuL67Hzf3pKGKW1brLLrIRPQ6vJ77NqeHTRMIIDjE84+grZbHDdTGur\nqsTcsR12bMOoqfGZZpSWwoYXMV97FeYvsJIz4+J7JgYREREREekRSsiIiIiIiMigVJ5XTktdxzJi\nPVUd084wDO6ZG8XphipO1Fr9Xk7WuflLXi1fT4rCMHooKdNuWAx8fjXcdDNmXh5s24JRkO8bU3Mz\nbNsK27ZiTp4Cy5ZDUgoEBfVsLCIiIiIictWUkBERERERkUHH4/ZwPKP3qmPaBdkNHkhxsHZHJfUt\nVh+X3PJm3j/cyGenhff49QCwB0BSMiQlY54qtxIwO9MxGht9phlFR6DoCObLG2HBIis5M3pM78Qk\nIiIiIiKfyObvAERERERERHraRdUxqT1bHdNZTKid+5Mc2DoVxPztUAP7TzVf+qCeMmo03H4n/OJp\nzC9/DXPipIumGI2NGB/+A+MnP4JfrYWsTHC7ez82ERERERHxoQoZEREREREZVLqqjhmXNq5Xrzl1\neBC3z4zkpQN13n1/zq3l0UXDGBPZB49dQUGwaDEsWox5/Bhs3wqZu60lzDoxDrngkAszMhIWLYEl\ny2DkyN6PT0REREREVCEjIiIiIiKDS1fVMQEhvZ8UWTIhlMXjQ7zjJrfJuqwaGls9vX5tH+MnwD1f\ntqpmvnQPZtzFS7UZdXUYm96FJ34I//lryM2Btra+jVNEREREZIjpkacSp9MZA/wY+CIwBqgA/g78\nyOVylV3luUKAPGA6cL3L5drSEzGKiIiIiMjg54/qmM5umxlJeX0bRypbATjT2Mafsmv5VqoDe+c1\nzfpCaCgsvx6WrcAsLoJtW2BvFkZrq3eKYZpw8GM4+DFm9DBYvAQWL4WYmL6NVURERER6VEtLC+vX\nr2fTpk2cOHECSSp84gAAIABJREFUgPHjx3PHHXewevVqP0c3dHU7IeN0OkOBLUAC8F9AFjAN+D7w\nKafTmexyuaqu4pQ/wkrGiIiIiIiIXJXyXN/qmHFp4/qkOqZdgM3g/iQHa3dUUtVkVcYUVLTwRn49\nt86M7LM4fBgGTJ5ibbffiblrJ2zbinGq3HdadRW88zbm3/8Gs2bD0mUwczbY7f6JW0RERESuSWtr\nKw8//DA5OTlMnz6dNWvW0NzczPvvv89TTz1FbGwsCxcu9HeYPWb16tWUlXVdFxITE8N7773XxxFd\nWk88mTwCzAYecrlcz7TvdDqdecDrWAmWR6/kRE6nczbwGJADJPZAbCIiIiIiMkR0VR0Tl3rxcl29\nLTLYxgMpDn6dUUX7amVbjp5jZLidZRPD+jweH+ERcMOn4VMrMQ+5rF4zOdkYnZYrM0wT9u+D/fsw\nhw2zes2oakZERERkwNi4cSM5OTmsWbOGxx9/HMOwKrUTExN54oknyMvLG1QJGYCIiAjuuuuui/aH\nhfn5+/cFeiIh82WgAXjugv1vAieAe51O5/dcLpd5uZM4nU4bsA44BvwP8GwPxCYiIiIiIkNEWW4Z\nLfX+q47pLN4RyL1zo/hTTq13318P1jMy3M6MkcF+icmHYYAzwdpqazF3psP2rRgVFb7Tqi6smllu\nvdrUjlRERESkv3rttdcICQnhkUce8SZjAOznK58dDoe/Qus1kZGRPPjgg/4O4xN16+nE6XRGYS1V\ntt3lcjV3fs/lcplOpzMTuAWYBBR9wun+GZgPrATiuxPXpRQWFvbGaQc0/ZnIYKD7WAYD3ccyGOg+\nFn8y20xObzvtHRuBBk0xTVd9X/bkfRwJLBgezK6zIQB4TPhDVjW3x9czPNjTY9fpEZOnwqQphB07\nimNfLhFHDmN4OmLsXDXTGhFJzew51M6agzsqyo9By6Xo72MZDHQfy2Cg+1j84cyZM5SWlpKUlOTt\nHdPujTfeACA2NvaK78+BcB+3nu+R2NuxTps2rdvn6O7PxSacfz1xiffb1wuYzGUSMk6nMx54CnjB\n5XJ94HQ6v9rNuEREREREZAhpLGrE09SRQAifHo4tyP9VHKkxzVS32CioCwKgxWPwdmk4d4yvJyzg\nsosI9D3DoHHiJBonTsLeUE/Ugf049ucRVFPjMy2wvo4RO9MZviuDhkmTqZkzj4ZJk1U1IyIiIv3W\n2S1n/R3CZQ1fMbzHzlVcXAzAlClTvPtM02TTpk3s2bOHWbNmMX78+B67Xn/hdrvZsWMHZ8+eJTg4\nmPj4eGbMmIGtn31H7W5Cpr0rZeMl3m+4YN6l/A5oAb7XzXguqycyWINFe7ZQfyYykOk+lsFA97EM\nBrqPxd88bg+Z72Z6xwEhAcz57JyrWq6sN+/jSVNM/mt3NUVV1i/3at02/lEZw8MLhhFkNz7haD+a\nlwgeD2ZBPmzfBnm5GB7fXjMRRUeIKDrS0Wtm0RIY3nP/oCBXR38fy2Cg+1gGA93H/U/ZK103fO8v\nevJe2bx5MwBLliyhpqaGTZs2kZuby7Fjx5g2bRpr165l+GW+r23YsIG6ujoqKysBiPmEPoLTp09n\nxYoVPRb/tQgMDKSiooLf/e53PvvHjh3LE088QVJSkp8iu5h/FlTuxOl03gXcDHzd5XKd8Xc8IiIi\nIiIysJTl+PaOiUuL81vvmK4E2g0eSHHwy/QqKhqthMbRajcv7qvlq/OifNb17ndsNrhuprXV1Fi9\nZnZsx6jwfXTz6TVz3UxYvBTmzIWA/vPfQURERGQoyM/PB2DGjBmsXbvWm6ABmDhxIh7P5ZfO3bhx\nI2VlV57Auvnmm/2ekFm1ahXz5s1j8uTJhIeHU1payssvv8wbb7zBd77zHZ577jmmT5/u1xjbdffb\ncXuHyvBLvB9xwTwfTqczBvgNsNXlcv2pm7GIiIiIiMgQ09baRsnOEu84ICSAuJQ4P0bUtYggG99M\ndfCr9CrOua2lyrJPNhMb3sDN0yM+4eh+wuGAG2+Cz9xoVc3s2Aa5F1fN8PEB+PgAZmQkLFgES5bC\nqNF+DFxERESGOsf4wdfE/lIKCgoYM2YM0dHRPPnkkzz22GMUFRXx8ssvs3nzZoqLi1m/fv0lj3/z\nzTeB3q30Wr169VUlfW688UaefPLJS77/wAMP+IynTJnCv/zLvxAWFsaLL77IunXrWLt27TXH25O6\nm5ApBkxg3CXeb+8xc6luOmuBaOAnTqez8zmGnX8deX7/GZfL1dzNWEVEREREZJApzy3v19UxnY2O\nCOD+ZAfPZFbjOd8+5r3CRmLDA0iNC/FvcFejq6qZ9O0YZy6omqmrg82bYPMmzGnTrcRMYjIEBfkp\ncBERERmq5t47198h9ImysjJqampITk4GwG63Ex0dTVJSEklJSdxzzz0UFhZSWlpKXJz/fsQUFxdH\n0FV8JxwxYsQ1XeeWW27hxRdfJCcn55qO7w3delJxuVwNTqdzH5DkdDpDXC5XU/t7TqfTDiwCSlwu\n1/FLnOIGIAj46BLvv3z+9XpgS3diFRERERGRwaWttY2SjAuqY1L7X3VMZ84RQdw5K5IN++u8+9bv\nqyUm1MaUmAGYqOhcNXPIBTu2Q242htvtM80oPASFhzBf2gBpC6zkzLh4PwUtIiIiMjgVFBQA1nJl\nXYmKigIgLCzskufoix4yzzzzzFXNv1bDhll1H01NTZ8ws+/0xE/HngP+E/gm1vJj7e4FYoEft+9w\nOp0JQLPL5So+v+vrQFf/9W8AHgF+COw/v4mIiIiIiHiV55TT0tBRHTNu/jgCgvtndUxni8aHcrqh\njQ+KGgFwe+APe2v43uIYRoTZ/RzdNbLZIGGGtdXXY+7eafWaKTvpM81obIQtH8KWDzEnTrJ6zaSm\nQcgAqhASERER6afa+8ckJCRc9F5NTQ15eXlMnTrVm6joykDsIXMp+/dbaQV/VgNdqCeeVp4F7gGe\ndjqdE4AsYCbwKFYi5elOc/MBF5AA4HK5PuzqhE6ns70GaafL5drSAzGKiIiIiMgg0lXvmLEpY/0Y\n0dX5QkI4Zxrc7DtlJZTqW0yezazm0cXDCAu0+Tm6boqIgBs+DZ9aiVlcZPWaydqD0dLiM804WgxH\nizFffQmSU2DREpgyFQzDT4GLiIiIDGztFTKbN28mLS0N4/z3qtbWVn7+85/jdru5++67L3uOvugh\n05OKi4sZPXo0oaGhPvtPnjzJ009bqYkbb7zRH6F1qdsJGZfL1ep0Oj8D/AS4Ffhn4DTwB+DHLper\nsbvXEBERERER6awsp2xAVse0sxkGX57n4Dc7qyiptZb3OtXQxnN7a/intGjstkGQlDAMmDzF2m6/\nC3NPJuzYhnH8mO+05mbISIeMdMxRo6zEzIJF1nJoIiIiInLF2hMyb731FocOHSIlJYXGxkZ2795N\naWkpq1atYtWqVX6Osmdt3ryZ9evXk5iYyOjRowkLC6O0tJT09HSam5tZvHgx9957r7/D9OqRJxaX\ny1WLVRHz6CfMu6KnCpfL9TzwfLcDExERERGRQaettY0TO094xwGhA6s6pl1wgMGDqQ6e3lFFTbMH\ngENnW3nl4zrunBXp/UXjoBAaCsuWw7LlmMePQ/p2yNyFce6czzTj1Cl4/a+Yb74Os+bAosUwezbY\nB06yTURERMQfysvLqa6uZv78+URERJCVlcWGDRsIDw8nISGBhx56iJUrV/o7zB6XkpLC8ePHcblc\n5OXlce7cOSIjI5k7dy6f+9znuOmmm/rV92p9qxURERERkQHlouqYtIFVHdNZdIidb6Y6+I+dVbS0\nWfvSjzcRGx7ApyZfutnqgDZ+PIy/B269DTM7GzJ2YBxy+UwxPB7Ylwv7cjGjomD+Qli8BEaP8VPQ\nIiIiIv1be/+YtLQ07rvvPj9H03eSkpJISkrydxhXbGA+tYiIiIiIyJB0Ue+YAVod01m8I5CvJjpY\nl1WDeX7fG/n1jAizM2d0sF9j61VBwbBgISxYiHn6lLVs2c4MjJpqn2lGbS1s3gSbN2FOngKLl1o9\nZ0JC/BS4iIiISP/TvlyZ0+n0cyRyOQO8W6SIiIiIiAwlZTlltDa0escDrXfMpcweFczqGRHesQn8\nb24NJTWtlz5oMIkdBV+8BX7+75gP/R/MxGRMu/2iaUbREYwXnocffA/+/DwcLgTTvGieiIiIyFCj\nhMzAMPCfXEREREREZEhwN7spybigOiZ5YFfHdPapSaGcaXCTfrwJgJY2eHZPDd9dNIwRYRcnJwYl\nmw1mz7G2ujrM3TutJc1OnvSZZjQ3Q8YOyNiBOXIkLFxsVdvEDPdT4CIiIiL+VVBQwJgxY3A4HP4O\nRS5DCRkRERERERkQSnaW0No4+Kpj2hmGwe0zI6lobMNVYX3O2mYPz+yu5ruLhhEZPMQWOIiMhJWf\ngRs+jXm02ErA7MnEaGrymWacOQNvvYH59pvgTLCSM4mJ1pJoIiIiIkPEpk2b/B2CXIHB8/QiIiIi\nIiKDVlNNEyd2n/COgyKCiEuJ82NEvcNuM/h6koP/2FlFWV0bAGca2/hdZjUPL4gmNHCIJWUADAMm\nTba22+7EzNkL6TswCg/5TjNNKMiHgnzMDSGQnAoLF8GUqdY5RERERET8TAkZERERERHp94o/KsZs\n6+gVMnHFROxBg3MZr7BAGw+lRfOrjCoqz3kAKKl184e9NXwrNZpA+xBOLgQHw4JFsGAR5pnTsGsn\n7MzAqDzrM81oaoL07ZC+HTN2lJWYmb8QYmL8FLiIiIiICAzBn1eJiIiIiMhAUltay5mDZ7zjiNER\njJo9yo8R9T5HiJ2H0qKJCOpIvhw628oLebV41MTeMjIWPr8afvZzzO9+H3P+QszAoIumGadPYbz5\nOvzrD+A3v4I9u6GlxQ8Bi4iIiMhQpwoZERERERHpt0zT5Mg/jvjsm3zDZIwhsARVbEQA306N5j93\nVdN8vjoop6yZiKB6bp8ZMST+DK6IzWb1jnEmwF13Y2bvhZ3pGIcLfaYZpgn5ByH/IGZIKCQnW1Uz\nU6dZ5xARERER6WVKyIiIiIiISL91Jv8MdaV13vHw6cOJnhDtx4j61vjoQL6R4uDZzGraV2zbfuwc\nEUE2bpoe7t/g+qPQUFi8BBYvwTx9ylrSbFcGRmWlzzSj6Ryk74D0HZgxw2H+Ais5M3q0nwIXERER\nkaFACRkREREREemXPG4PxR8Ve8eGzWDypyb7MSL/SBgRxJfnRfF8Ti3ti5W9W9hAZLDB0glhfo2t\nX4sdBV/4Iqz6AuYhF+xMh+xsjFbf5cqMyrPw7jvw7juYkyZbiZmUVIiI8FPgIiIiIjJYKSEjIiIi\nIiL90onMEzTXNHvHY1PGEhoT6seI/CdpbAj1LR5e+bjeu++VA/VEBNlIHBPix8gGAJsNEmZY213n\nrCXNdmVgFB66aKpRXATFRZivbIRZc2DBAus1MNAPgYuIiIjIYKOEjIiIiIiI9Dst9S2UZJR4xwGh\nAUxYMsGPEfnfsolh1DV7eO9wIwAm8OfcWsICbThHXNzMXrrQeUmzigrI3AW7d2KcOuUzzWhrg7wc\nyMvBDAuDlDRYsBAmTQb17hERERGRa6SEjIiIiIiI9DtHtx2lraXNO56wdAIBIXp8uWl6OHUtHtKP\nNwHg9sC6rBr+z8JoxjtUxXFVRoyAm1bB527GPFps9ZvJysRoaPCZZjQ2wrYtsG0L5shYSJsPaQtg\n1Cj/xC0iIiIiA5aeaEREREREpF9pON1AeV65dxw6PJQxiWP8GFH/YRgGd8yKpKHFJLfcWs6tuc3k\nd5nVfHfRMGLD9Yh31QzDqnyZNBluvxPzwH7YlQH791mVMp2nnjkN77wN77yNOWGilZhJSQWHwz+x\ni4iIiMiAom/rIiIiIiLSb5imyZEPjuDtXg9MvmEyNrvNf0H1MzbD4MvzomjIrKawshWA+haT/95d\nzaOLhuEIsfs5wgEsIADmJVpbfT3m3j2wa6fVW+YCxrGjcOwo5qsvWf1p5i+AeUkQop4+IiIiItI1\nJWRERERERKTfqDpSRXVxtXccPTGamCkxfoyofwq0GzyQ4uA/d1VzotYNQOU5D89k1vCdhdGEBSqB\n1W0REbD8elh+Peapcti9CzJ3Y1Sc8ZlmmCbkH4T8g5iBL8CcuVblzMxZVoJHREREROQ8fTsUERER\nEZF+wdPmsapj2hkweeVkDDVR71JooI1vp0Xz64wqKhqtpbVO1rn5fVYN/5QWTZBdf249ZtRo+MIX\n4fOrMYuLIHM37N2DUVfnM81obYW9WbA3CzM8HJJSrJ4zU6aCTUkyERERkaFOCRkREREREekXynPK\nOXf2nHc8eu5oImIj/BhR/xcVbOOh+dH8KqOKumYPAEcqW3k+p4b7kxzYbUrK9CjDgMlTrO32OzDz\n8yFzF+TlYjQ3+05taIDtW2H7VsyYGEhJs7b4eOs8IiIiIjLkKCEjIiIiIiJ+525yc3T7Ue/YHmRn\n4rKJfotnIBkRZuefUh38Zlc1TW6r+c7+Uy08n1PLVxOjlJTpLfYAmDXb2pqbMfflWpUzH3+M4Wnz\nmWpUVsL778H772GOGg0pqdY2ZqyfghcRERERf1BCRkRERERE/O54+nHc59zecfzCeIIigvwY0cAy\nzhHIgykOnsmsxm0VypBb3qykTF8JDobU+dZWV4e5Nwsyd2EUHbloqnGqHN55G955G3NcfEdyZsRI\nPwQuIiIiIn1JCRkREREREfGrc1XnKN1T6h0HRwUTlxbnx4gGpmnDg7g/ycFz2TU+SZk/5dTyNSVl\n+k5kJKy4HlZcj1lxxqqaydqDcbL0oqnGiRI4UQJvvIY5abKVmElKgWHD/BC4iIiIiPQ2JWRERERE\nRMSvij8sxvSY3vGk6ydhD7T7MaKBa9ao4IuSMnnlzfwxu5avJUURoKRM3xoxEm5aBTetwiwthb17\nYM9ujDNnLppqFBdBcRHmqy/D1GmQmgaJyVaCR0REREQGBSVkRERERETEb6qPV1PhqvCOI+MiGXmd\nlm7qjlmjgvlGsoM/7O1Iyuw71cyfsmv4WpJDSRl/iYuzts+vxjx+DPZkwt49GFVVPtMM04TCQ1B4\nCHPjekiYAUnJMC8JIiL8FLyIiIiI9AQlZERERERExC9M06ToH0U++6bcMAXDUMKgu2bGdpWUaeGP\n2TV8XUkZ/zIMmDDR2m65DbPoiJWcyc7CqKvznerxwMGP4eDHmOv/As4Ea0mzxESIUOWMiIiIyECj\nhIyIiIiIiPjF6QOnqS+v945HzhhJ1LgoP0Y0uMyMDeaBZAfrOiVl9isp07/YbNbyZFOnwR13YR5y\nQVYm5GRjNDb6TDU8Hsg/CPkHMTf8BaY7ITnFqpzRsmYiIiIiA4ISMiIiIiIi0ufaWtoo3lLsHRt2\ng0nXT/JjRIPTdbHBPJji4PdZSsr0e3Y7zLjO2r50L+bBj62eM3l5GE3nfKYaHg8U5ENBPuaGF63k\nTFIKdkc0bWFhfvoAIiIiIvJJlJAREREREZE+d2L3CVrqWrzjcWnjCIkO8WNEg9eMkV0nZZ7bayVl\nAu1KyvQ7AQEwZ661tbZi5n8Me/dCXu5lkzOTDYNz8eNhyVKrciZKFWciIiIi/YkSMiIiIiIi0qea\na5sp2VXiHQeGBRK/KN6PEQ1+7UmZdVk1tJ5Pyhw43VEpo6RMPxYYCHPmWVtrK2b+QcjOspIz5y5I\nzpgmYcePwfpjVuXM1GmQmGQlZ2Ji/PQBRERERKSdEjIiIiIiItJnTNPk0LuH8LRnBYCJyycSEKxH\nk95mJWWi+X1WtU9S5rnsGu5XUmZgCAz0rZwpyIe9WZCX02VyhsJD1vbyRswJEzuSM6NH+yd+ERER\nkSFOTz0iIiIiItJnyvPKqTpS5R2Hx4Yzeq7+cbivJIwM4sHUaH6/pyMp87GSMgNTYCDMnmNtbjdm\n/kFqt3xIxOFC7M3NF003jh2FY0fhjdcwx4ztSM7Ex4Oh/+4iIiIifUEJGRERERER6RNN1U0U/aPI\nOzZsBs7POzHUWL5PJYzoOinzh701fCNZSZkBKSAAZs/hVEgop9ramOZuhZxsq3Kmvv6i6UbZSSg7\nCX//G+bwEZCYaCVnJk8Bm80PH0BERERkaFBCRkREREREep1pmrj+5qKtpc27b8LSCUSMivBjVENX\nwoggvpkazf90SsocPNPCur01PKCkzMBmt0NCAsyaDffch3m40ErO5OZgVFVeNN04WwH/2Az/2IwZ\nFQVzE2FeIkx3WlU4IiIiItJjlJAREREREZFedzLrJDXHa7zjyDGRxC+M92NE4uwiKZN/poVnMqt5\nIMVBWKAqJQY8m81KrEx3wh13YR4/ZiVncvZinDp10XSjtha2b4XtWzFDQuC6WTB3rpXcCVfyVERE\nRKS7lJAREREREZFe1Xi2keKPir1jW4BNS5X1E10lZQ5XtvLrjCq+nRZNTKjdvwFKzzEMmDDR2lav\nwSwrg9xsyMnGKDl+8fSmJsjOguwsTJsNpk2HOXNh7jwYMbLPwxcREREZDJSQERERERGRXmN6rKXK\nPG6Pd9/EFRMJGxHmx6ikM+eIIL6dFs3vs2pocpsAlNe38cv0Kr6d6mCcQ8tWDTqGAWPHWttNqzAr\nzkBujlU9U3QEwzR9p3s84CqwtldewoyLgznzrOTM+AnqOyMiIiJyhZSQERERERGRXlOyq4S60jrv\n2BHvIC41zo8RSVemDQ/iOwujeTazhppmK3lW2+zhN7uquT/JQcLIID9HKL1qxEhY+Rlrq63B3L8f\n8nIh/yBGa8tF043SUigthXffwXREd1TOOBPUd0ZERETkMpSQERERERGRXtFwuoFj2455x7ZAG9NX\nTccwtFRZfzQuKpBHFw/jd5nVlNe3AdDkNvndnmrunhPJ/HGhfo5Q+kSUAxYvsbaWZsz8fCs5sz8P\no67uoulGTXVH35ngYEi4DmbPhllzIDraDx9AREREpP9SQkZERERERHqcp81DwdsFmJ6OpY8m3zCZ\n0GH6R/3+LCbUzncXDWNdVg2HK1v/X3v3HSbZVdh5/3srV3XumenJeXrOaIJQQgKRJRsLY4NMcuLF\nhH2d4Fmz4PC+uw+G1/hdP7vm8TrbrMGLF8y+YEBgWIKNEApgCQU00mhmrnqmJ3X39ITOXVVd8b5/\nnFuhp6tnOleH38fP8b333NCnxFWr+v7uOQeAogefOzrGcLrI6/clFKitJZGo7fnyklugWMQ7023D\nmaPP4lzqn3K4k8nA0R/bAng7dthg5sjNdu4aDW0mIiIia5wCGRERERERWXDnHztP8lKyvN22u43N\nt26uY4tkphLhAL95Zyufe26UZ/oy5fpvvJhkaKLA2w81EQwolFlzAgHYu8+Wt7wNr78fnrPhTK15\nZwCc8+fh/Hn45jfwmprg0BEbzhw8BHGFsyIiIrL2KJAREREREZEFNdY3xvkfni9vB6NB9r9RQ5Wt\nJOGgw6/c0kxbLMmD3aly/Q/OTzAyUeTdt7YQDel/zzVt0ybYdB+8/j4YHcU79hw8/zyceAFnYmLK\n4c7YGDz+Q3j8h3iBIHR22nDmyM2wcVMdPoCIiIjI0lMgIyIiIiIiC6aQK+B+3YWql+X3vX4f0eZo\n/RolcxJwHO6/qZG2WIAvHx8v/0967HKWP398iF9/aStNUQ1BJUBzM9z9SlvyebxTXfD8c3DsOZxL\nl6Yc7hQL4J605UtfxNvQAYcPw8HDYIwdKk1ERERkFVIgIyIiIiIiC+bcI+dIDVR6VKzbv46Owx11\nbJHM12t2J2iJBfifz46SK9q68yN5/uSHg/zGna10NOjPSqkSCsGBm2x5+8/jXboEx56zAU3XiziF\nwpRTnCuX4aHvwUPfwwuFoHM/HPIDms2bQb3rREREZJXQN2cREREREVkQI+dH6Hmip7wdjofpvK9T\nQ5WtArdsjtEcDfDJp0ZI5WxfmaupIn/ygyF+7aWt7G4L17mFsmxt3AgbfxLu/UlIp/FOHLcBzbHn\ncUZHpxzu5PNw4rgtfBGvrd2GM4cO2ZAnnlj6zyAiIiKyQBYkkDHGtAMfBe4HNgNXgW8CH3Fd9+IM\nzn+lf/6dQAy4AHwZ+LjruuML0UYREREREVk8hWwB9xvupLp99+0j0hipU4tkoe1pj/Chu9v46x8N\nM5i2XWWSOY+/eHyId9/aws2bNMyU3EA8DrfdbkuxiHf+nO0588IxOHcWx/OmnOIMDcJjj8Bjj9i5\nZ/burfSe2bYNAho2T0RERFaOeQcyxpg48H3gAPCXwFNAJ/DbwD3GmNtd1x26zvm/DHwOcLGhzCjw\nM8DvAq8yxrzSdd3ifNspIiIiIiKLp/t73UwMVyby3nBwAxtu2lDHFsli2NgY4sN3t/G3T41wYSQP\nQK4In3p6hLccbOQ1u+LqESUzEwjArt22/OybYXzM9p554Ri8cAxnbGzKKU6xAF0v2vLVr+A1N8NN\nB205cBBaW+vwQURERERmbiF6yHwQOAK833Xdvy5VGmOOAg8AHwE+VOtEY0wU+Btsj5i7XNcd8Xf9\nvTHmAWyPm/uwvW1ERERERGQZGjozxMVnKh3jIw0R9v3Uvjq2SBZTcyzIb72slb9/ZpTjV7IAeMCX\nj49zdjjHLx5pIhpSrwWZpcYmeOldthSLeD09cNyGM5w+hVOc+p6mMzoKTzxuC+Bt3lIJaDr3Qyy2\n1J9CRERE5LoWIpB5F5AEPn1N/deAHuCdxpgPu647te8xbAK+AjxRFcaUfBMbyNyMAhkRERERkWUp\nP5GfMlRZ5xs7Ccc1p8hqFg0F+NU7WvjCsTH+7UKlZ9TTfRl6R/O877YWNjVpylKZo0AAduyw5b6f\nhnQK7+RJG9AcO2aHMavBudgHF/vge9+1w5vt2VMJaHbugmBwaT+HiIiIyDUcr8YYrTNljGkGRoBH\nXdd9dY39XwbeAux1Xbd7ltf+beCPuabnzUyMjIzU/FBdXV2zuYyIiIiIiNzA8JPDpM+my9vx3XFa\n79CwQWuSBEc6AAAgAElEQVSF58EzQxF+eDWGR2WosrDjcc/GNKY5V8fWyarkeUQGB0ic6abh7Bni\nvT0E8vkbnlaIRklv30Fy5y5SO3aRa2sDDa8nIiIis9DZ2VmzvqWlZcZfKub7ytJOf9kzzf7z/nIP\nMONAxhgTAd4LpICvzrl1IiIiIiKyaCZ6JyaFMcFEkOaXNNexRbLUHAdub8+yMVbg2xcTpAp2qLKc\n5/Cd/gR96Qyv2jCBRjCTBeM4ZNetJ7tuPcN33ImTzxPr66Xh3FkS584SvdRPrSciwUyGxlNdNJ6y\nL2rmmppJ7dhBavtO0tt3kG/W7y4RERFZfPMNZJr8ZWqa/clrjrshY0wA+DvgJuDDruv2zb15k02X\nYK1Fpd5C+mciK5nuY1kNdB/LaqD7eG0avzTO0a8dnVR38P6DtO1qq1OL5kf38fx0AreZAp/58Sin\nBiu9Yp4fiTLqNPDeW1toT2i4qMW2Zu/jm26qrI+P47kn4cRxOHEcZ+BqzVPCY6O0vHCMlheOAeBt\n6ABzwJb9BlpalqLlUsOavY9lVdF9LKuB7uPFsawG9TXGxIHPY+eO+SvXdf+kzk0SEREREZFrZEYz\nHPviMQrZQrluyx1bVmwYIwujJRbkA3e18o0Xk3z3dOWdvXPDef7LY4O865ZmDnVE69hCWRMaG+H2\nO2zxPLyrV8rhDO5JnFTt90mdK5fhymV47BEAvE2bJwc0jY1L+SlERERklZpvIDPqLxum2d94zXHT\nMsZsAP4ZeBnwcdd1f3+ebRMRERERkQWWz+Q59sVjZMey5bqWHS3suXdPHVsly0Uw4PDmA43saQvz\n2WdHSeft9J6pnMcnnxzhp/YleMP+BgKau0OWguPAhg5bXv1aKBbxzp214cyLLpw+hZOrPc+R038R\n+i/Cww/hOQ5s3eYHNAb27YdEYkk/ioiIiKwO8w1kzgAesG2a/aU5ZrqudxFjzEbgUWA38B7XdT8z\nz3aJiIiIiMgCKxaKnHjgBMnLyXJdfF2cg289SCCoSUKk4sjGKL/7qnY+/fQIPaN2wnUP+PapFGeG\nc/zKLS00RXXPyBILBGD3Hlt++mcgl8M70w3uSVvOdOMUClNOczwPei7Y8uC/VgKazv227OsEzUEj\nIiIiMzCvQMZ13aQx5jngNmNMzHXdidI+Y0wQuBu44Lru+emuYYxpBr4N7ADe5Lrut+bTJhERERER\nWXie53HqO6cY6h4q14UTYQ7//GHC8XAdWybL1fpEkA/d3caXXhjjhxfKfyriXs3xXx8b5D23trCn\nXfeO1FE4bIcj22/gZ98M2QzeqVO294x7Es6dxSkWp5w2KaB56EEAvE2boNP4IU0ntLUv9acRERGR\nFWAh5pD5NPDnwK8Bf1ZV/06gA/hoqcIYcwDIuK57puq4PwNuAd6iMEZEREREZHnqebyH/mf7y9uB\nUIBD7zhEvDVex1bJchcOOvzizc3saQ/zhefHyPnPtocnivzZ40O8+UAjr9sdx9EQZrIcRKJw8JAt\nAOk03qkuG868eBIuXLBhTA1Ofz/098OjDwPgrV9vhzbb7/eiWb/BDqEmIiIia9pCBDJ/C/wy8Alj\nzE7gKeAQ8CHgeeATVceeAFzgAIAx5mbgV4DjQNAY87Ya17/iuu7DC9BOERERERGZg8vHL3PmoTOT\n6g68+QDNWzREj8zMXdvibG8O86lnRriStENCFT144MQ43UM5fuFIE40RDWEmy0w8DkdutgUgOW57\n0HS9aMv5c9MHNFevwtWr8PgPAfBaWmHfPtjrl23bIRhcqk8iIiIiy8S8AxnXdXPGmNcDHwPeCnwA\nuAx8Cvio67qp65x+G+AAB4F/muaYh4HXzredIiIiIiIyeyMXRnC/7k6q2/sTe1lv1tepRbJSbWkO\n8TuvaOPzz43xbH+mXH+0P8PpwSzvONzELZui6i0jy1dDI7zkFlsAJibwTvsBzakuOHsGJ5+veaoz\nMgxPP2UL4EWjsGt3JaDZswfiiaX6JCIiIlInC9FDBtd1R7E9Yj50g+Oca7Y/A3xmIdogIiIiIiIL\nKz2Y5oUvvYBXqLwBvuWOLWy9c2sdWyUrWTwc4L23NfP9s2m+emKcon9rjWc9/v6ZUW7eGOUdhxtp\nianngKwAsRgcOmwLQDaLd6bbhjNdL8Lp0zi5bM1TnUzGDoXmngTAcxzYsrUS0OzdB+vWaZgzERGR\nVWZBAhkREREREVldssksz3/hefLpytve6zrXsfcn9taxVbIaOI7D63Yn2NUa5rNHR8tDmAE8dylD\n10CWtx5q5M6tMfWWkZUlEgFzwBaAfB7v/LnKEGfdp3FStQcRcTwPentseeT7gD/MWXUPmm3bIRxe\nog8jIiIii0GBjIiIiIiITFLIFTj+peNMDE2U6xo3N3LgzQdwAnpALgtjd1uY/+tV7XzzxSTf605R\n6oeVznt87ugYT/dl+IUjTbTH1VtGVqhQCPbsteWn3gDFIl7/RTh9qlycK1emPd0ZGYZnnrIF8EIh\n2L4Ddu+pFPWiERERWVEUyIiIiIiISJnnebhfdxntHS3XRVuiHH77YYIRPRiXhRUJOtx/UyO3bo7y\nj0dHuThe6S1z4kqW//zwIPff1MjdO2IE9NBZVrpAwA5LtmUrvOo1AHijI1UBzWk4fw6nUKh5upPP\nw5luW3xec/PkgGbnLjuUmoiIiCxLCmRERERERKTszENnuHryank7GA1y+B2HiTRG6tgqWe12tob5\nnVe28y+nk/zLqVR5bplMweMLx8Z4um+CX7q5iQ0N+hNWVpnmFrj1dlvAzkNz7mwlpOk+jZNMTnu6\nMzoKR5+1haq5aPaUAprdsHmzDYNERESk7vRtVkREREREAOh7po+ex3vK207A4eBbD9KwoaGOrZK1\nIhx0eOP+Rl6yKcrnj45xYbQyf9GpwRx/9MggP2Maee3uuHrLyOoViUDnflsAPA/v8iXbK6bb7x3T\n24NTLNY8fdJcNI8+Yi8RjdqhznbtsgHNzp2woUNDnYmIiNSBAhkREREREWHw1CCnvnNqUt3+N+6n\nbVdbnVoka9W25jAffkUbD3an+FZXkrz/3DlXhAdOjPPjixP80s3NbG7Sn7OyBjgObNxky8vutnXZ\nDN65c5Xhy7pP44yMTH+JTAZOddni8xIJO7zZzl2wyw9pWtsU0oiIiCwyfYMVEREREVnjxvvHOf7A\nccqzqgM7X7WTjUc21q9RsqYFAw6v39fAzZuifP65Mc4M5cr7zg7n+a+PDXLfvgbu3ZsgFNADZFlj\nItGpvWiGhioBzZluOxdNLjftJZxUCk4ct8XnNbf4vWj8sn0HtLQs6kcRERFZaxTIiIiIiIisYWN9\nYxz74jGKucrwNx1HOtjxyh11bJWItakxxAdf3sojZ9N83R0n6891ni/CN15M8kTPBG860MBLNkVx\n9Ga/rFWOA+3tttx+h63L5/F6e+DcWVvOnoWLfdMOdQbgjI7Ac0dt8XktLbBjpw1ntu+w6+3t6kkj\nIiIyRwpkRERERETWqKvuVU5+7STFfOUBXcvOFvb/9H493JZlI+A4vHZ3gsMbo/yv50Z5caDy1v+V\nVIFPPzPK7tYQ99/UxJ72cB1bKrKMhEKVni4l2Qze+fOVkObcWZxLl657GWdkBJ5/zhaf19AwOaDZ\nvgM6OiAQWIxPIiIisqookBERERERWWM8z6P3yV66v9s9qb6ho4FDbz1EIKiHarL8rE8E+cBdrfzw\nwgRfPTHORL4yxt6Z4Tz/7d+GeMmmKG8yDXQ06k9dkSkiUdjXaYvPS6Xg/LlKL5pzZ3AGB697GSeZ\nhJMnbCldJxr1Q5rtsM0vm7dAJLJIH0ZERGRl0rdUEREREZE1xCt6nP7X0/Q93Tepvm1PGzf93E2E\novoTQZYvx3F4xY44N2+M8p1TSR49l6ZYNffR0f4Mz1/K8Iodcd7Q2UBTVOGiyHUlEnDgJlt83ugo\nXDhvy/lzcP48ztUr172Mk8nAqS5bStcJBKBjox/QbKsENS0tGvJMRETWLP21JSIiIiKyRhSyBU58\n9QSDpya//bzplk3s+6l96hkjK0ZTNMDbDjXx6l1xvn4yybP9mfK+ogePnkvzZO8EP7Enwev2JIgE\n9fBXZMaam+HQYVt8Xio1JaThUj+O5017GadYhP6Ltjz1o8q1GhunhjSbNtth1kRERFY5/ddORERE\nRGQNyIxleOGLLzB+aXxS/e57drPtrm2aM0ZWpI6GEO+7vYUzQzkeODHOmaHK/DITeY9vvJjksfNp\n3ri/gTu3xQjoPheZm0QCzAFbSjIZvN6eSkBz4Rz09eEUCte9lDM+PnXIs2AQNm6CLVtpj0bJrN8A\nra2wbp3mphERkVVFgYyIiIiIyCo3fnmcY184RnYsW65zgg4H3nSADTdtqGPLRBbG7rYw/+HlrRzt\nz/DPbpIrycoD4eGJIv/43BgPnUnx5gON3LQhogBSZCFEo7Bnry0l+Txe/0Xo6YGeC7b09uCMjV33\nUk6hAH290NfL+lLl176CF4nYuWi2boUtVUXDnomIyAqlQEZEREREZBUb7B7kxFdOUMhWHlCH42EO\nvf0Qzdua69gykYXlOA63bI5xZGOUH5xP862uJOPZynBKfWMF/ubJEcz6MD9rGtnZGq5ja0VWqVCo\nMgwZLy9XeyMjlYCmpwd6L0B/vx3W7DqcbBbOnbWlipdIVAU0W2xos2mzHW5NQY2IiCxjCmRERERE\nRFapiz++SNe3u6BqiP94e5zDP3+YeFu8fg0TWUTBgMOrdyV46dYY3z2d4qEzKXJVz3zdqzncq0N0\ntoe5d2+CmzZENJSZyGJrabGlal4acjm8ixcrQc3FPujtxRkdueHlnFQKTnXZUsVLJGwws3kLbN5c\nWW9r09BnIiKyLCiQERERERFZZTzP48xDZ+h5vGdSfcv2Fg6+7SDhuHoGyOoXDwf42QONvHJnnP/9\nYpIf9UxUZ5N0DeboGhxhU2OQe/ckuH1LjHBQwYzIkgmHYccOW6qcOnqU6MBVtgUcfxizPjvsWTp9\nw0s6qRR0n7aliheJ+OFMVUizaTNsWA9BPRoTEZGlo//qiIiIiIisIoVcAffrLldPXp1U33Gog/1v\n3E8gpDeEZW1piwd550uaed3uBF87Oc6JK9lJ+/vHC/zjc2N83U3y2t1xXrEjTiKsf09E6qWYSJBO\n7IDOzkql5+END5fnmaGvF3p74eJFnFx2+ov5nGwWzp+zpYoXCNpQZuMmv2ysLJs0/JmIiCw8BTIi\nIiIiIqtENpnl+JeOM9o7Oql+xyt3sPNVOzWRuaxpW5tD/OadrZwfyfFgd4pnL2YoVnWZGc0U+eeT\nSb7TleLuHTFeuztBezxYvwaLSIXj2GHH2tomD3tWLOINDED/RTvkWf9FuGiLMzGDHjXFAly6ZAtH\nJ+3z4vHaQU3HRohEFvgDiojIWqFARkRERERkFRg5P4L7DZeJ4YlynRNw6PzpTjbdvKmOLRNZXna0\nhHnPrS0MmAIPnUnxbxcmyBYqyUym4PHQmTQPn01z2+Yo9+5JsK1Fw/yJLEuBAGzYYMuRmyv1noc3\nMnJNSGPXnbGxGV3aSafh7BlbqnilcKhjI2zogI6Oycuwfl+IiMj0FMiIiIiIiKxguXSOMw+dof/Z\n/kn1wWiQg289SNuutjq1TGR5W5cI8rZDTbyhs4HHztsAZixTLO8vevBUX4an+jKY9WHu3ZPgwPqI\nepqJrASOA62tttx0cNIub3zchjT9F/3eMf22XLlqe8zc6NKeB4ODtpw8MfnajgOtbTac6eiADRsr\n6+s3qGeNiIgokBERERERWYk8z+PyC5fp/m43uVRu0r5oS5QjP3+ExPpEnVonsnI0RAL81L4G7tmd\n4KneCR7sTnEpOfmhrHs1h3t1hM1NQV6+Pc4dW2I0RTXPjMiK1NgI+zptqVbI4125WgloLvWXA5sZ\n96rxPBgatMU9OWmfVwqJ1vs9etaXynq7bGrSnDUiImuAAhkRERERkRUmPZim69tdDJ8dnrJvw8EN\n7P3JvUQa9BauyGyEgw4v3xHnru0xXric5XvdKU4NTg47L44V+Mrxcb56YpxDHRHu2hbnUEeEUEAP\nUUVWvGAINm2y5RpeMgmX/d40/f1w5bItly/jTEzUuNhUNqwZsqXrxak/IxqthDPVYc2GDbBuvYZC\nExFZJRTIiIiIiIisEMVCkZ7Hezj32Dm8qjkvAGKtMfbdt4/2Pe11ap3I6hBwHI5sjHJkY5SzQzke\n7E5xtD9D9b9xRQ+ev5Tl+UtZGsIOd2yNcde2GNuaQxrSTGQ1amiA3XtsqeZ5eGNjNqy5chmuXLHr\nl0thTXrGP8LJZKC315YavJYWG8ysWzd12b5OgY2IyAqhQEZEREREZAUYOT9C17e6SA2kJtU7AYdt\nL9vGjlfsIBgO1ql1IqvTrrYw77u9hSvJPI+eS/Nk7wTj2clhaDLn8fBZOwfNlqYgd22Lc8fWGM0a\n0kxk9XMcaG625doh0DzPzldz5XIlpLlyBa7aMtNh0Mo/amQERkag+3TN/V5Liw1mpoQ266CtHaLR\nuX5KERFZQApkRERERESWsVw6x5mHztD/bP+Ufc3bmum8r5OGjoY6tExk7djQEOItB5t484FGjl/J\n8kTPBMcuZbimoxp9YwUeODHO106Oc3BDhLu2xTjUESUcVK8ZkTXHcey8ME1NsGfvlN3exIQfzly1\ny3JYcxUGruLk87P7caXA5kx3zf1eQyO0t0HbOmhvr5Q2f9nSCgEFySIii02BjIiIiIjIMuR5Hpdf\nuEz3d7vJpSbPYxGKhdj9ut1sumWThkcSWULBQGU4s/Fskad7J3iid4ILI5MfnBY9OHY5y7HLWRJh\nh9u3xLh1c5Q9bWGCmm9GRABiMdi23ZZrFYt4I8M2nCkFNQMDMHDVLoeH7Jw0s+AkxyE5Dhcu1Nzv\nBQLQ2jY5pGlrs3WlZVOTQhsRkXlSICMiIiIissykB9N0fbuL4bPDU/ZtOLiBvT+xl0hjpA4tE5GS\nxkiA1+xO8JrdCfpG8zzRk+bJvgxjmeKk41I5j0fPpXn0XJpE2OFQR4QjG6McWB8hHtaDTRGpIRCw\noUhbO3Tun7o/n8cbGoLBqpCmejk0h8CmWLTXGxyY9hgvGLQ9adqqQprWVr+t/nZLCwQ1hKqIyHQU\nyIiIiIiILBPpwTS9T/Vy8ccX8a4ZCynWGmPfffto39Nep9aJyHS2NIf4uYNNvOlAIydKQ5pdzpCf\nnM2Qynk82Zvhyd4MQQc614U5vDHKkY4o7Qk9wBSRGQqFYMMGW2op+IHNgB+wDA3B4KAfuAzC0CBO\nJjPrH+sUCjcObRwHmpqhtcWGN62tdlle9+vV20ZE1igFMiIiIiIideR5HiPnR+j9US8DXVMfcDgB\nh20v28aOV+wgGNYDW5HlLBhwOLwxyuGNUZLZIk/3TfBEzwTnR6bOBVHw4OTVHCev5vjSC+NsbQ5x\npCPC4Y1RtreECGg4QhGZq2AI1m+wpRbPw0sl/aDGD2n8oKa8Podh0QB7zuiILZyf9jgvEIDmFhvQ\nlEObFr+u2W43N9twJ6THlyKyeug3moiIiIhIHRQLRa4cv0Lvj3oZvzRe85jmbc10vqGThg0NS9w6\nEZmvhkiAV+9K8OpdCYbSBZ6/lOHY5SxdA9kpPWcAekfz9I7m+fapFM3RAEc2RjjcEWX/+giRoMIZ\nEVlAjgMNjbbUmsMGoFDAGx2F4SFbhvxSWh8etqFNfmrgPKMmFIuVa5+7/rFeQ6MNaUoBTnOLDWvK\n2822JBrU60ZElj0FMiIiIiIiSyiXytH3TB8Xn75INpmteUxDRwPb7tpGx+EOHL0lL7LitcWD5XBm\nIl/k5JUsz1/K8sLlDMnc1DfQRzNFfnB+gh+cnyDowI7WMPvaw3SuC7OnLUw0pAeOIrLIgsHKXDHT\n8Ty88fFKUFMKa0aGbWAzMgzDIzjJ2i+ezJSTHIfkOPT1Xfc4LxCAxiY7HFpzc9WyVKq3myAcnle7\nRETmQoGMiIiIiMgSSF5J0vtkL5ePXaZY6/V4oH1fO1vv3ErrzlYFMSKrVCwU4JbNMW7ZHKNQ9Dgz\nnOPYpSzPX8pwOVmYcnzBgzNDOc4M5fjX0xBwYHtLiH3tEfa1h9nTHiYRVkAjInXgODbYaGqCHTum\nPczL5WB09Jqgpno5YnvbpNPza06xWBkurffGx3vxeCXAaWyCpsZrtpugsbGyHYnMq30iIqBARkRE\nRERk0Xiex1D3EL0/6mXozFDNYwLhABuPbGTrS7eSWJdY4haKSD0FA44frES4/6ZGLo3nbThzOUP3\nYI5aszcUPTg3nOfccJ4Hu8EBtjaH2LcuTEMmxJb41FBHRKSuwmFYt86W6/CyWRvcjI5UliMjk+tG\nhmF0dM5DpVVz0mlIp+HK5Rkd70WjNphpbPRLEzQ0VLYbSssGguNjFGPxebdRRFYfBTIiIiIiIgss\nPZRmoGuA/h/3kxpI1Twm0hRh6x1b2XTLJsJxDZkhIrCxMcTGxhD37k2QzBY5cSXLqcEspwZyXKrR\newbAA3pG8/SM5gE739TmywPsbYuwoyXE9pYQm5pChALqdSciy1wkAuvX23I9noeXSk0ObkbHYGzU\nltFRGBvzl6M4udyCNM/JZCCTgYGrNzx2b6mp0agf1DRUApwGG9qQaPC3GyZvJxJ2yDgRWZUUyIiI\niIiIzJPneYz1jTHQNcDAiwOkrtYOYQCatjSx9aVbWX9gPYGghhkSkdoaIgHu2Brjjq0xwM4rc9oP\nZ04NZukbm74nzMWxAhfHKkP/hAKwpcmGM9tbwmxvDrG5KUQ4qJBGRFYgx6mEGJu3XP9Yz8PLZGoG\nNYyOwvgYjI/ben/dKdYeWnZOTS2FOIMDszrPi8VtiFMd2iQSdjuRgHjCLhuu2Y7HIaDvlyLLmQIZ\nEREREZE5KOQKDJ8dZqBrgMGuQbLJ7PQHO7DerGfrnVtp3tqs+WFEZNaaowFu3Rzj1s02oElmi5wa\ntOHM6YEcPaP5mkOcAeSLcH4kz/mRPDAB2LloSiHNtuYQO1rCbGkOEVFIIyKrieNALGbLho4bH18s\n4qVTMDZuA5pSUDPmBzfVAU5yHJJJG7osdLMn0jCRBm7cG6ea5zg2lCkFNKUQJx6HhF8fj9v6WLxy\nTGk9FlOgI7LIFMiIiIiIiMxQNpll8NQgA10DDJ0Zopi7/huU4USYjsMdbL1jK7HW2BK1UkTWgoZI\ngJdsivKSTVEA0rkijx47R286xKDXQM9onvx1fkUVveqhzqyAAxsbg2xuDLGxMegPoRako0FBjYis\nEYGAP6RYI7BpRqd4uZwNaZLj/jLJ5e5ughNp1kWjlfrSMakUTmr63tTz4XgepFK2zK5TTpkXi08O\ncGIxu12qj8X8YCdWqSvVl7bDGo5XZDoKZEREREREpuEVPVJXUwyetiHMaM/oDc9JrEuwbv861nWu\no2lLE47mbRCRJRAPB9jdmGd3Y57Ozu0Uih4Xx/NcGCmVHL2jea6XIxe90nBnk4dDc4D2eKAc0JSX\nDSGaonqTWkTWuHAY2tps8Y00twCwrrOz5ileoQDpFCSTlZKabj1lw5xUCtKpBR1SrZZy75yhuV/D\nC4UgGrOhTdQPdKJRfxmr9FoqhTjV29EYxKKV4yIR29NJZJVQICMiIiIigp0HJjOaYaxvjLGLY4z1\njTHeP04hO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- "text/plain": [ - "" + }, + { + "metadata": { + "id": "gp0QmuZvIA0L", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "All samples of $\\beta$ are greater than 0. If instead the posterior was centered around 0, we may suspect that $\\beta = 0$, implying that temperature has no effect on the probability of defect. \n", + "\n", + "Similarly, all $\\alpha$ posterior values are negative and far away from 0, implying that it is correct to believe that $\\alpha$ is significantly less than 0. \n", + "\n", + "Regarding the spread of the data, we are very uncertain about what the true parameters might be (though considering the low sample size and the large overlap of defects-to-nondefects this behaviour is perhaps expected). \n", + "\n", + "Next, let's look at the *expected probability* for a specific value of the temperature. That is, we average over all samples from the posterior to get a likely value for $p(t_i)$." ] - }, - "metadata": { - "image/png": { - "height": 193, - "width": 818 - }, - "tags": [] - }, - "output_type": "display_data" - } - ], - "source": [ - "def logistic(x, beta):\n", - " \"\"\"\n", - " Logistic Function\n", - " \n", - " Args:\n", - " x: independent variable\n", - " beta: beta term\n", - " Returns: \n", - " Logistic function\n", - " \"\"\"\n", - " return 1.0 / (1.0 + tf.exp(beta * x))\n", - "\n", - "x_vals = tf.linspace(start=-4., stop=4., num=100)\n", - "log_beta_1 = logistic(x_vals, 1.)\n", - "log_beta_3 = logistic(x_vals, 3.)\n", - "log_beta_m5 = logistic(x_vals, -5.)\n", - "\n", - "[\n", - " x_vals_,\n", - " log_beta_1_,\n", - " log_beta_3_,\n", - " log_beta_m5_,\n", - "] = evaluate([\n", - " x_vals,\n", - " log_beta_1,\n", - " log_beta_3,\n", - " log_beta_m5,\n", - "])\n", - "\n", - "plt.figure(figsize(12.5, 3))\n", - "plt.plot(x_vals_, log_beta_1_, label=r\"$\\beta = 1$\", color=TFColor[0])\n", - "plt.plot(x_vals_, log_beta_3_, label=r\"$\\beta = 3$\", color=TFColor[3])\n", - "plt.plot(x_vals_, log_beta_m5_, label=r\"$\\beta = -5$\", color=TFColor[6])\n", - "plt.legend();" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "H_rdEcFIIAz7" - }, - "source": [ - "But something is missing. In the plot of the logistic function, the probability changes only near zero, but in our data above the probability changes around 65 to 70. We need to add a *bias* term to our logistic function:\n", - "\n", - "$$p(t) = \\frac{1}{ 1 + e^{ \\;\\beta t + \\alpha } } $$\n", - "\n", - "Some plots are below, with differing $\\alpha$." - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 210 - }, - "colab_type": "code", - "id": "T0iZj_eCIAz8", - "outputId": "b2aed49b-9ef8-49d1-bb5a-7c943ff3b629" - }, - "outputs": [ - { - "data": { - "image/png": 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4qwPHWx0AVOP+XKKAsUgOE5E8uit6aowt5/GNy4nyfZ/Vi3ZnHouOFPoabGjg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\nJVP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- "text/plain": [ - "" + }, + { + "metadata": { + "id": "EIzyJL_3IA0P", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 51 + }, + "outputId": "b8250999-8613-4e18-8a6f-3d47fc845b4b" + }, + "cell_type": "code", + "source": [ + "alpha_samples_1d_ = alpha_samples_[:, None] # best to make them 1d\n", + "beta_samples_1d_ = beta_samples_[:, None]\n", + "\n", + "\n", + "beta_mean = tf.reduce_mean(beta_samples_1d_.T[0])\n", + "alpha_mean = tf.reduce_mean(alpha_samples_1d_.T[0])\n", + "[ beta_mean_, alpha_mean_ ] = evaluate([ beta_mean, alpha_mean ])\n", + "\n", + "\n", + "print(\"beta mean:\", beta_mean_)\n", + "print(\"alpha mean:\", alpha_mean_)\n", + "def logistic(x, beta, alpha=0):\n", + " \"\"\"\n", + " Logistic function with alpha and beta.\n", + " \n", + " Args:\n", + " x: independent variable\n", + " beta: beta term \n", + " alpha: alpha term\n", + " Returns: \n", + " Logistic function\n", + " \"\"\"\n", + " return 1.0 / (1.0 + tf.exp((beta * x) + alpha))\n", + "\n", + "t_ = np.linspace(temperature_.min() - 5, temperature_.max() + 5, 2500)[:, None]\n", + "p_t = logistic(t_.T, beta_samples_1d_, alpha_samples_1d_)\n", + "mean_prob_t = logistic(t_.T, beta_mean_, alpha_mean_)\n", + "[ \n", + " p_t_, mean_prob_t_\n", + "] = evaluate([ \n", + " p_t, mean_prob_t\n", + "])" + ], + "execution_count": 12, + "outputs": [ + { + "output_type": "stream", + "text": [ + "beta mean: 0.19450754\n", + "alpha mean: -12.415545\n" + ], + "name": "stdout" + } ] - }, - "metadata": { - "image/png": { - "height": 193, - "width": 818 - }, - "tags": [] - }, - "output_type": "display_data" - } - ], - "source": [ - "def logistic(x, beta, alpha=0):\n", - " \"\"\"\n", - " Logistic Function with offset\n", - " \n", - " Args:\n", - " x: independent variable\n", - " beta: beta term \n", - " alpha: alpha term\n", - " Returns: \n", - " Logistic function\n", - " \"\"\"\n", - " return 1.0 / (1.0 + tf.exp((beta * x) + alpha))\n", - "\n", - "x_vals = tf.linspace(start=-4., stop=4., num=100)\n", - "log_beta_1_alpha_1 = logistic(x_vals, 1, 1)\n", - "log_beta_3_alpha_m2 = logistic(x_vals, 3, -2)\n", - "log_beta_m5_alpha_7 = logistic(x_vals, -5, 7)\n", - "\n", - "[\n", - " x_vals_,\n", - " log_beta_1_alpha_1_,\n", - " log_beta_3_alpha_m2_,\n", - " log_beta_m5_alpha_7_,\n", - "] = evaluate([\n", - " x_vals,\n", - " log_beta_1_alpha_1,\n", - " log_beta_3_alpha_m2,\n", - " log_beta_m5_alpha_7,\n", - "])\n", - "\n", - "plt.figure(figsize(12.5, 3))\n", - "plt.plot(x_vals_, log_beta_1_, label=r\"$\\beta = 1$\", ls=\"--\", lw=1, color=TFColor[0])\n", - "plt.plot(x_vals_, log_beta_3_, label=r\"$\\beta = 3$\", ls=\"--\", lw=1, color=TFColor[3])\n", - "plt.plot(x_vals_, log_beta_m5_, label=r\"$\\beta = -5$\", ls=\"--\", lw=1, color=TFColor[6])\n", - "plt.plot(x_vals_, log_beta_1_alpha_1_, label=r\"$\\beta = 1, \\alpha = 1$\", color=TFColor[0])\n", - "plt.plot(x_vals_, log_beta_3_alpha_m2_, label=r\"$\\beta = 3, \\alpha = -2$\", color=TFColor[3])\n", - "plt.plot(x_vals_, log_beta_m5_alpha_7_, label=r\"$\\beta = -5, \\alpha = 7$\", color=TFColor[6])\n", - "plt.legend(loc=\"lower left\");" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "W_B8n8wuIAz9" - }, - "source": [ - "Adding a constant term $\\alpha$ amounts to shifting the curve left or right (hence why it is called a *bias*).\n", - "\n", - "Let's start modeling this in TFP. The $\\beta, \\alpha$ parameters have no reason to be positive, bounded or relatively large, so they are best modeled by a *Normal random variable*, introduced next." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "_52Ml-KhIAz9" - }, - "source": [ - "### Normal distributions\n", - "\n", - "A Normal random variable, denoted $X \\sim N(\\mu, 1/\\tau)$, has a distribution with two parameters: the mean, $\\mu$, and the *precision*, $\\tau$. Those familiar with the Normal distribution already have probably seen $\\sigma^2$ instead of $\\tau^{-1}$. They are in fact reciprocals of each other. The change was motivated by simpler mathematical analysis and is an artifact of older Bayesian methods. Just remember: the smaller $\\tau$, the larger the spread of the distribution (i.e. we are more uncertain); the larger $\\tau$, the tighter the distribution (i.e. we are more certain). Regardless, $\\tau$ is always positive. \n", - "\n", - "The probability density function of a $N( \\mu, 1/\\tau)$ random variable is:\n", - "\n", - "$$ f(x | \\mu, \\tau) = \\sqrt{\\frac{\\tau}{2\\pi}} \\exp\\left( -\\frac{\\tau}{2} (x-\\mu)^2 \\right) $$\n", - "\n", - "We plot some different density functions below. " - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 239 - }, - "colab_type": "code", - "id": "OLw3-8x2hxkm", - "outputId": "d361ad2b-ff47-4fb6-e5a9-71c7cf685ec2" - }, - "outputs": [ - { - "data": { - "image/png": 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K7lxci5XzcJV6E6y1vw9b9ke4ipaduMGHx+EqNUdba18EfoV7+jYX9/R16O+n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1UDmsH7+RpVXwd+C/hfgd9csP0XgGbgqzc2pNPp/UApk8n0LDjuN4GjwJclEBJCCCHE7dBa0zfj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\nGVlo4njEbw6P1E3zKldDAZOi9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- "text/plain": [ - "" + }, + { + "metadata": { + "id": "Ri4BriJHPJNg", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 294 + }, + "outputId": "92de9456-2fb0-42c8-f718-3eb9c515387b" + }, + "cell_type": "code", + "source": [ + "plt.figure(figsize(12.5, 4))\n", + "\n", + "plt.plot(t_, mean_prob_t_.T, lw=3, label=\"average posterior \\nprobability \\\n", + "#of defect\")\n", + "plt.plot(t_, p_t_.T[:, 0], ls=\"--\", label=\"realization from posterior\")\n", + "plt.plot(t_, p_t_.T[:, -8], ls=\"--\", label=\"realization from posterior\")\n", + "plt.scatter(temperature_, D_, color=\"k\", s=50, alpha=0.5)\n", + "plt.title(\"Posterior expected value of probability of defect; \\\n", + "plus realizations\")\n", + "plt.legend(loc=\"lower left\")\n", + "plt.ylim(-0.1, 1.1)\n", + "plt.xlim(t_.min(), t_.max())\n", + "plt.ylabel(\"probability\")\n", + "plt.xlabel(\"temperature\");" + ], + "execution_count": 13, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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eFxypx1XGfI7R+wLwQr/fp4wx9+Deuj0C13VdCniHtXZjEY4F8GVctyevBp4w\nxtyOqyxe5NNQCvzAWvv7rG2+jzvnn7XWxhVvWGv/Zoy5BngPvYO7Z7sPV+m51hhzJ65y5XRgpf+O\nH8pZ/yLc2+2vBJ7x23QBR+HORRp4p7W2KWubG3DX9y3Av4wxt+KCFaf641jgg1nrP4yrDFoKPGyM\naQI+6gMsIzn+Z3BvZ5/gz+eduMrh03FBsB+RE1QZop/i8t9luLep+1WIW2sPGGOuxZ3/m40xv8Gd\n12fh8vXrcJWJhwNfMMachOvKr5Crca1fLjDGHIELmNbhWoB9EddCo0/lurX2Z8aYFwCXAg8aY+7A\ndXM2F9d6qAo3jlG+lgX9WGtvNG7A8guAR33Z2+6PeyqugvrDIxhnbCBfAn7py97TuLfAX44779/w\nFedDYq39kzHmU8CVwF+MMX/Eje+xGDgNNw7Kt6y1+QJLXbjuFdcYY34P7ASOw12TDPCeuNLWWvuk\nMea3uGvzJ3/tO/268T3v0/57fN8Y8wdrbXbroHv89Jk8ZXM3LhBTTHGriPN88DlprX1hzjo/wN2b\npgG3WWu3MwzjnHfeB9wKXGyMeRbu+9XhWjLcinv29Kn4L/ZzxVq7wT/rfgT8yBjzLlyZrcHltQW4\nSvorcja9EBfofyuuRdBf/LFfAVQAV1lrswMwD+HuiR/x95AWa21cif4j3Ln9CO5ZNlQR7nqvMcbc\nhnsGHYvLvxEur+cLpGW7GxcIOgZ4yJeZvbgXPmbggnFfjFe21mb8OboZ+IUx5iG/fQeufL4YN87T\n+3wr01EZ4b3xv3EtP19njHkAlx/m4/LHL3AvFjyIC3zdBNxkrf3dUNJj3Pg3cUDwaVywtNDqN1lr\nH8QFEi8FnoMrU3/F5ZWX4PLFW3HduS3396ObrbU/ore8n2qMuQ93f3nrAMkb899B4339RUREJju1\nBBIREZFxYa39Ia5C6BbgMFzF3gtxlVwXAq/NfovVV1g8F1dJUoKrmP8PXIXQX4HXW2tzWwl9DPiD\nX/8kssYWsNb+N64i7Te4IMA7cBWqz+BaWDzfd/ky2u/Zjat8uxQXsDgT18XKYlxrkOdaa39SeA/D\nPl4KFxx4G66i5nRckOJEXMXwG6y1PUELY8x/4LqoegpXqZbro8Bm4KW+BUKul+PecD8Z16plOq4y\n67nW2nU5aduGq2z6JK5S8PW4674YN07O86y11+dsEwHn+n0/iquEPRdXkfgFf5ymrPXX4wIrDbgK\nppX4t/ZHePwGXN75Ma4C9XxcBdn/+e/cnOecDMrv9x5cpVTk95/PB3AVnTtwef6VuIrf51trb/Pn\n4D5cxd1ZDPB73lr7P7iKuocSmOjzAAAgAElEQVRxFdhvxlWgX2KtvXKA7d6NG1j7j7hK/P8AXoTr\nuuwdwCtzxjIazIW4oN6DuHvA23Bl8H+BF1lrvzjAtiPxR1wFYAr4d1x+fxqXT9473J1Zaz+Fy4d3\n4AJyF+Ly1T3A66y1lxTYNG2t/bw/7jJcXjoeV2F/lrX2Vznrnwd8Bzew+htx946/4fL8P3AV82tw\nb+OfmrNtChcIvgF3jzwfF8S4GTjJl5Ni+gmusnsfLo/kttIA1+Iqbn103QiPMy55x1p7By7P3AUY\nf5zjcGXxPFyld77tivpcsdb+FNdS8Me4QP5FuLK4CxcEXO27rczeZr1P61eApE/vWbjnwTnW2v+X\nc5irgF/i7pMn4wKZuTJ55g0k8PeUy3AB+XN9mv6My+u3DLYD34LkJbgAeSfufv1vuMDJ83D3+Nxt\nfuu/ww9x98Q34K7BauA24MXW2nyt9EZkuPdGa+1DuPv4A7ig2JtxY3S9Dzjfv6xwFa4cvYLeMeGG\noprea3cq7t5W6N+RPj1bcOf4btx1ejPu99jngJdZazfjXubYhfstscRvdy+udfYu3LmdzwCtYsfr\nd9B4X38REZHJLIii3DFHRURERER6GWMuwFXi3mutPW1iUyOSnzFmI67S8kXW2nsmNDGCcWPUbMUF\nTpcOM3AoE8QY8w/gu9ba7wxh3aXABgBrbbHHGBIRERGRIlFLIBERERERESm2K3AtFa5VAGhy8OO3\nHAM8NtFpEREREZHiURBIREREREREisYY8xJc14a7gGsmODkydB/GdWV3/0QnRERERESKp2SiEyAi\nIiIiIiKTm+/+7ZO48Y9ejhv76iJr7d4JTZgMmbX2ClwLLhERERGZQhQEEhERERERkdGqBC72fz8M\nfNRae8cEpkdERERERIAgiqKJToOIiIiIiIiIiIiIiIgUmcYEEhERERERERERERERmYIUBBIRERER\nEREREREREZmCFAQSERERERERERERERGZgkomOgFTxb59+zS4koiIiIiIiIiIiIiIjKna2tpgqOuq\nJZCIiIiIiIiIiIiIiMgUpCCQiIiIiIiIiIiIiIjIFKQgkIiIiIiIiIiIiIiIyBSkIJCIiIiIiIiI\niIiIiMgUpCCQiIiIiIiIiIiIiIjIFKQgkBy01q5dy9q1ayc6GSKTisqNyPCp3IgMn8qNyPCp3IgM\nn8qNyPCp3IgM31QvNwoCiYiIiIiIiIiIiIiITEEKAomIiIiIiIiIiIiIiExBCgKJiIiIiIiIiIiI\niIhMQQoCiYiIiIiIiIiIiIiITEEKAomIiIiIiIiIiIiIiExBCgKJiIiIiIiIiIiIiIhMQQoCiYiI\niIiIiIiIiIiITEEKAomIiIiIiIiIiIiIiExBCgKJiIiIiIiIiIiIiIhMQQoCiYiIiIiIiIiIiIiI\nTEEKAomIiIiIiIiIiIiIiExBCgKJiIiIiIiIiIiIiIhMQQoCiYiIiIiIiIiIiIiITEEKAomIiIiI\niIiIiIiIiExBCgKJiIiIiIiIiIiIiIhMQQoCiYiIiIiIiIiIiIiITEEKAomIiIiIiIiIiIiIiExB\nCgKJiIiIiIiIiIiIiIhMQQoCiYiIiIiIiIiIiIiITEEKAomIiIiIiIiIiIiIiExBCgKJiIiIiIiI\niIiIiIhMQQoCiYiIiIiIiIiIiIiITEEKAomIiIiIiIiIiIiIiExBCgKJiIiIiIiIiIiIiIhMQQoC\niYiIiIiIiIiIiIiITEElE50AETl0NTc3c+edd7JlyxZSqRQlJSUsXryYM844g/r6+olOnhyCJkOe\nnAxpFDnYqNyIyERat24d11xzDY899hipVIqamhpWrlzJJZdcwooVKyY6eSIHpfjZ/cgjj5BKpZgz\nZ46e3SIiIiMURFE00WkYMWNMKfBZ4P3An6y1pw1j25OBjwPPAyqAp4HvAd+01g77pOzbt2/ynsiD\n1Nq1awFYtWrVBKdEiq29vZ0bb7yRDRs2UFZWRllZWc+yzs5OOjs7WbZsGeeeey4VFRUTmNLJR+Vm\nZCZDnpwMaZysVG6mLpWbsaNyIzK45uZmLr/8cjZs2EAymST+v3dFRQUdHR10d3ezbNkyrrrqKlVq\ni3i5z+7W1lYA6uvr9ewWGSL9ThMZvslYbmpra4Ohrjtpu4MzxhjgfuBdwJC/sN/2dOBuYBVwJfAO\nXBDoauCqoiZURPpob2/n6quvZtu2bUybNq1PhRxAWVkZ06ZNY9u2bVx99dW0t7dPUErlUDEZ8uRk\nSKPIwUblRkQmUnNzM+effz5bt26lpqaG8vLyPsvLy8upqalh69atnH/++TQ3N09QSkUOHnp2i4iI\njI1JGQQyxtQB/wQSwLNHsItrgQ7ghdbar1trb7TWvh74DXCZMea44qVWRLLdeOONtLW19fuPcK7y\n8nLa2tq48cYbxyllcqiaDHlyMqRR5GCjciMiE+nyyy8f1j3o8ssvH6eUiRy89OwWEREZG5MyCASU\nAj8CnmettcPZ0BhzImCA/7HWbs9Z/E1cq6K3FiWVItJHc3MzGzZsGPRHfay8vJwNGzbozUgZM5Mh\nT06GNIocbFRuRGQirVu3bkT3oHXr1o1xykQOXnp2i4iIjJ1JGQSy1jZaa99lre0YwebP9dP78yx7\nwE9PHFnKRGQgd955Z78m/YMpKyvjrrvuGqMUyaFuMuTJyZBGkYONyo2ITKRrrrmGZDI5rG2SySTX\nXnvtGKVI5OCnZ7eIiMjYKZnoBEyApX66NXeBtfaAMWYvsLxYB4sHlZKR0zmcOh555BFSqVTP4J5D\n9fDDD7N69eoxStXUpHIzNJMhT06GNE4VKjdTh8rN+FG5EenvscceI4qiguOVFJq/Zs0alSk5ZA32\n7C7U4kfPbpHC9EwRGb6DsdysWrVq1PuYlC2BRqnGT9sKLG/NWkdEiiiVSo3rdiKDmQx5cjKkUeRg\no3IjIhNJ9yCR4VO5ERERGTuHYkugcVWMSN2hKo686hxOHXPmzKG7u3vY2yWTSeWDIVK5GZ7JkCcn\nQxonO5WbqUflZuyp3IgUVlNTk7diOm4BVFFRkXe7kpISlSk5ZBV6dsctgOrr6/Nup2e3SH/6nSYy\nfFO93ByKLYH2+2lVgeXVWeuISBEtWrSIzs7OYW3T2dnJ4sWLxyhFcqibDHlyMqRR5GCjciMiE2nF\nihV0dAxv+NqOjg5Wrlw5RikSOfjp2S0iIjJ2DsUg0Ho/XZi7wBhTC9QCB1/nfyJTwJlnnjmiH/Zn\nnHHGGKVIDnWTIU9OhjSKHGxUbkRkIl166aXDbo3Y3d3NJZdcMkYpEjn46dktIiIydg7FINB9fvr8\nPMte6Kd/Gae0iBxS6uvrWbZs2ZDfjOzo6GDZsmUFm/6LjNZkyJOTIY0iBxuVGxGZSCtWrBjRPWjF\nihVjnDKRg5ee3SIiImNnygeBjDGHG2OWxZ+ttY8A/wTeYIxZmLVeAFwOdAM3jHtCRQ4R5557LpWV\nlYP+uO/o6KCyspJzzz13nFImh6rJkCcnQxpFDjYqNyIyka666qph3YOuuuqqcUqZyMFLz24REZGx\nMSmDQMaYI40xr4//+dmzsucZYyr9/CeB3+fs4hIgAfzJGHOZMeY84FbgdODT1tp14/JFRA5BFRUV\nXHbZZSxYsID9+/f3a/Lf2dnJ/v37WbBgAZdddlnBgXNFimUy5MnJkEaRg43KjYhMpPr6em644QYW\nLlzIgQMH+lVqd3R0cODAARYuXMgNN9yg1gwi6NktIiIyVoIoiiY6DcNmjLkS+OQgqy2z1m40xkSA\ntdYenrOPZwOfBk4GynDBom9Ya68bSZr27ds3+U7kQW7tWjc006pVqyY4JTJWmpubueuuu9i8eTOp\nVIqSkhIWL17MGWecof8Ij5DKzehMhjw5GdI42ajcTH0qN8WnciMydOvWrePaa69lzZo1pFIpampq\nWLlyJZdccom6gBMpIH52P/zww6RSKebMmaNnt8gQ6XeayPBNxnJTW1sbDHXdSRkEOhgpCFR8k7Hw\niUw0lRuR4VO5ERk+lRuR4VO5ERk+lRuR4VO5ERm+yVhuhhMEmpTdwYmIiIiIiIiIiIiIiMjAFAQS\nERERERERERERERGZghQEEhERERERERERERERmYIUBBIREREREREREREREZmCSiY6AVPdcTfvoL48\nZEZZSH1ZSH25m87wUzcv4eaVhZSXDHk8JxERERERERERERERkYIUBBpjm1rSbGpJD3n9ypKgJzjU\nEyiKA0f+7xllIXV++czyBBUKHImIiIiIiIiIiIiISA4FgQ4ybamItlSara1DDxxVlwTMKA+ZVeGC\nQjPLQ2aVh8ysSLip/zerIsGMspDShIJGIiIiIiIiIiIiIiJTnYJAY+yxB97PrtJp7ExOoylZQ1Np\nLU3JGnaWTmNX0s3fWTqN3ckaMsHIhmhqSUW09LQ46h50/drSgFnlCWZVuFZFAwWP6stCEqGCRiIi\nIiIiIiIiIiIik42CQGPs8Pbt0L590PVeccwH+b8Zx/WZN727lcu23k5TaQ07k7XsStbQ5ANKzcnq\nEQeN9nVF7OtK8cz+wdcNA5hRFjK7ImRORYLZFSFzKxPMrkgwpyLsM60tDQgCBYxERERERERERERE\nRA4GCgIdJHaWTus3b3HnLj6x6Zd5108T0JScxo7SWhpLp/dMH6tayE1zX1C0dGUiaOrI0NSR4fE9\nqQHXLUuQNzg0x/89p9IFkWaXJyjXOEYiIiIiIiIiIiIiImNKQaAx1vSKRQQtacIDXZTs7aBiXyth\ne0TYDkHUu16mejqJANJZ82Z3FW6qkyBibvc+5nbvg9bNPfP/MP2ovEGgrzxzIyftW0tjaW2fwNGO\n0uk0ltb2zG9LlI/4u3amYUtLmi1D6JautjToaVk0rzLB3MoE8yoTzKsM/TRBVwZKR9bYSURERERE\nRERERETkkKcg0BjLzGyCmRCHRdop80sCgrCSIKogzJTzx9UhQd189ndFNHdmaO7MUP53yDwJQTcM\ntd3MjtLpeecf3bKF5x5YN+j2BxLlPUGi9608j0dqlvZZnsikKYu6RxUsgt4u6Z7eN9BalUwviVjw\neCPz40BRVcL/3RssmlkeEqobOhERERERERERERGRPhQEmjARUaaViFYyAZQkIAwCppcFTC8LWQ5k\nTj2KpvJyCEoJEtMIg0qCdBlhKknYEZBozRDu6yRobifcuZ+SPXtZvXIOXzmplqb2DLs63L+mjjSL\n0kMYAAioSXdQ097BqvZGojzLj27dwj/+8Z/sS1TQUFZHQ2kdDWV1bC+tY1tZ3793lE6nOxxdFtub\nCti7JzVgV3QlAb4lUW+rojhoNL8qwUIfOFIXdCIiIiIiIiIiIiJyKFEQaKyVVEOqZdDVgtL6fvOi\nrub4D6LULtLxghCo9P9mZW0Q1jC7fj8XHV7db1+J5iPo3FlHYvcBgr17SBzYO2ia9tfM6Ddvfpfb\nrjbdTm1bO0e0NQy4j53Jafx65rO5xFzUf1+dzbSFZewtqYRRtORJRbC1Nc3W1oG7oZtZHrLAB4Wy\np/G/eZUJSkIFikRERERERERERERkalAQaIxVnfILonQXUVczUdceN+3c0/u5s5moq5mgtK7ftlHX\nnuEdLNNRsN+41qM7SO9+GggISqcTlC50rYuiSsLuUsLOkLA1InGgm0RzG+G+Fh4+/zA6MgFNHWl2\ntmdobE8z8/5OWDP0JM3u3k95Jn9g5ronv82L9z5OS1jGlvIZbC2rZ0vZDLb56dbyGWzxf7eUVAzv\nXOQRt4x6dHf+9IQBzK0IfVCopE+QKP57VoW6nhMRERERERERERGRyUFBoHEQJEoJKuZCxdxhbRdW\nLyO54iIfOGruEzgi3Zb/WGX9W+8ARJ274798MMoFmNLZK1X4f7OBRCXlresor1nFouoSFvnGRUHa\n0Fb1RhLN7ST2NBPs3U2wd5ebZjJ5jz197mxevKCMxvYMO9vTNLVniICFna6lU3WmkyPaGgZsVbQ3\nUcnWsnpee8wVbKiY3WdZaaabRJShPVFWYOuhyUTQ0JahoS3D35vyB4pKQ5hXmWBRdYLF1SV+6v5e\nXO0CRWpNJCIiIiIiIiIiIiIHAwWBDmJh1RJKq5bkXRal2ok6dxF17ibjp1HXbhJ1x+VdP9O5a3gH\nT7cRJGv7zU5NT9FR+RuohGB5HUHZLILy4wjKZhBGNYTdSRIdIeH+NIm9bYR7d3Pm6mdx+uqZvfvI\nROxuT7P0r81DTs70dBvT29rYl6dF0Bl7HuN/13yZ3SXVbCqfyabymWwun8nG8llsKnOfN5bPYl+y\nanjnII+uDGxqSbOpJQ109VseBjC/Mg4MJVjkg0OLq0tYUuPGJipNKEgkIiIiIiIiIiIiImNPQaBJ\nKiipIChZBFWLSAxh/bIjLifq2JUVONpN1OX+JtWaZ4uQoLR/q6JMR1PP3z0tig48nf+gdSUEc2dS\nUjuHUk7umV0SBsypCOi68ArCPbsJmncSNu8k2N1EsKeJcH/+bvC6S8o4b/VcGtoz7GjLsL0tzY62\nNAs7XCunGakWZrS0cELLxrzb70tU+CDRLG6Z9Vx+PPeF+dM9Cpms8Ynua+y/PMAHiWoSLKryLYhq\nelsTLaxSkEhEREREREREREREikNBoENEycznFVwWpTt6gkNR5y4yHbsg3UoQ9g8vRZ1NefZQaMcp\noo4dROn2/svCBC3J3xHV7iaYO4egfA5h+So3Lakn7Eyyw24heWA/85IhYfNOyGS48jnT++/r512w\ndvDk1KbbObZ1C8e2buHxqoV51/n1mi9TEqXZWD6LzWWuBdHGilmsL5/NrmQNjHI8oAjY1pZmW1ua\n+/MsDwNYWJVgaU0Jy2riaQlL/d/Ty8JRHV9EREREREREREREDh0KAglBopygciFU5g+MZCuZeRJB\n6XSijiaijiYynW4adTZBpn/3aABh2cy88zMdO6B7P1HXbtj3RN/xiYCaREBmxjT2Vy8gWD6HsHwO\nyVQ7QU6XcOHxJ9JZXka4u5FgV6Ob7t5B0J1/XB+Ao80i3r6iii2taba1ptnWmmJPR4bT9zxOZYHv\nsT9Rzvry2WyomM2G8tms99O76o4mnSdgNhKZCDa3pNnckuZP2/svn14asGxaCUurS1g2zQWGlvi/\nF1QmSGg8IhERERERERERERHxFASSYQmrlxJWL+03P4oi6N7XGxTqaCLq3EmmYxdhzcr+66faoHv/\ngMcKiEik95HZt88HiUKSy97Sb73u2RHt6Z0Ex84nrHgWQcU8wrI5BO0Zwt0+KLRrB+GuRoLdjQRN\nO3jxCSs47ci+rYrampupvDd/AAhgWrqD41s3c3zr5p55nUEJ1adc12/dY1s2cUTrNtZXzGF9+Wx2\nJ6tH3YoIYG9XxMO7unl4V/8AVzKExdW9rYeW1CRYXlPCilr3uUzdzImIiIiIiIiIiIgcUhQEkqII\nggBKp5MonQ41qwbfIMqQXPpmoo5GMu2NRB2NRJ27cB2mFThG2QyCMNlvfnrfk6R23NV/g0QlYcVc\ngsp5hGYewfGHEVacSlAxj6BsNrkhkaooRWr1813AaPcOgrZ8YyX1tbd2Dq9aWsnmljRbWtLs7swA\n8Lqmv/OxTb/qWS+7FdH6ijk8UzGHZyrmsrZiLtvK6oiC0Xfz1p2BdfvTrNufBjr7LIu7mVsxrYSV\n00pYPq2EFf7f4poESbUgEhEREREREREREZlyFASSCREkqyldfl6feVGm241N1N5IpqOR3Q1Pkkjt\npjrZTtTRSFAxN+++ovYd+Q+SbiPTsh5a1vfrai654kJKl5zTdz8zZtP2jv9wAaKSCmhrIdy1g2Dn\ndsKmBoKm7YQ7GwibthM0bSdIp5ixeCE/On1Gzz5aujNsaUkz57q9sKl33/laEcXawyTryufwseXn\n8LuZzyp80kYhu5u5uxv6BohKAlhSk+gJCvX8qy1hYVWCsAgtmERERERERERERERk/CkIJAeNIEwS\nVMyDinkkgAOtywGYtcq1LIqiTP4NE2UEpXVEXXuGfKywYl6/eVG6i/YHLgYigtI6gooFhJULCGYt\nIFyykLDiRIKK+QSJUsikCfbsgpxxh6qTIUfUhVS07hxyWioy3RzdtpWa0v7jClWn2rn34U+7lkOV\nruVQ3IKosbS2KF3MpaLCLYjKErCsxrUcWjmthJW1JRzm/9WXF2ccJBEREREREREREREZGwoCyaQR\nFOgyreywd8Fh7yJKdxC1byfTvr3/tKMRot72QEG+IFBHI3F3dFHXHqKuPWT2PZabCoLyWT0BorB6\nBUkW9ttX+/u/5FoM7dxOuHObbz3UQLhzO8Gu7QTp3LZJ8O1zjuFLM+ex8UCajQdSbNyfIr2xkeNa\nN3NcnhZE+xPlPQGhpyvn8VTlfGzlfJ6unEtbonyAMzl0nWl4am+Kp/am+i2bURZy2PQSVvUEhpIc\nNr2ERVUJEupeTkRERERERERERGTCKQgkU0aQKCeoXkZYvazfsiiTJupsImpvINO+g7Cyf+Am094w\nhKNERB07iTp2ktnzMOE0Q3LBy/qtlWr5F1GimXD5AoKjX+zGM4qDWOkUwa5GwsathI3bCPw0mjWP\nmpKQY+pDjql3Yx+VtO0rmJJp6Q5OaNnICS0b+8z/67TDOPWET/ZbvyrVQWuirCithwB2d2a4v7GL\n+xu7+swvS8CKaSWY2iSrprsA0apa15KoKjn6sY9EREREREREREREZGgUBJJDQhAm3JhCFXMp1IlZ\nWLOSsiM/6FsQNZBp20ambSukWgrvt2JB3vmphttJ734ga+dlrmu5ykWEVYsIKxcTLl9IcNRq171c\nAVFFJamjnk3YuJVg906CQl3iZZm9YhmfeNY01u9PsW5/ivX7UzS2Z7j58a/xvP1rsZXze1oNPVU5\nn6cr5/FMxRy6wuSg+x6KzjQ8sSfFE3v6tx5aWJXA9LQeSnL49BKOqEtSV6bgkIiIiIiIiIiIiEix\nKQgk4oVlMwjnnt5vftS9n0zbVjJtDURtW8m0NxD5AFFYmT8IlGnfmjOjk0zLemhZT9+O4AKC8rmE\nVYsoXXUxYeX8PkvTx55I+tgT3YfuLoKm7YQ7tvpWRFsJGrcR7thC2NzUs83iw5bx/46t6bOfA90Z\n6h5tpDzdwXMOrOc5B9b3PQ4B6ytm9wSGHq9ayBOVC3m0ejGpsHi3ia2taba2pvnDtr5jD82pCDl8\nepIj6ko4YroLDh1el6S2VMEhERERERERERERkZFSEEhkEEFyGonaI0nUHtlnfhRFEHX3Wz+K0kQd\nu4a494ioYzvpju1w+Hv7Lc20bKB7628Jqxa7VkT1i8jMO5kgt0u3jjYXHNq+mfSSVf32U5PppHzP\nzoKpSBCxqr2RVe2NvHL3wz3z5518LU2ltX3WrUx3EBHQnigb4nccXGN7hsb2Tu7d3jc4NL8y5Ii6\nJIdP7201ZKaXUKNu5UREREREREREREQGpSCQyAgFQQBB/67cgiBB5Sm/JOrcSaZtW0+roUzbFqK2\nrUSdeQJEiUqC0vp+s9P7LamG23LWLSesXEhQuZiweilh1RLCqiVES1aSWXpY/sRmIjr//VLC7ZsJ\nt28m2L6ZcP+eAb9fpqaW+84zrNuf4pn9KdbtS/H0vhQnPHI3H//XD9hQPosnqhbyRNUCHq9cyBNV\nC3mqcj4dA3RvN1wNbRka2jr7tRxaVJ3giOklPcGhI+uSHDa9hMoSBYdEREREREREREREYgoCiYwB\nNwbRPMKKeTDj2X2WRalWFxRq3ULUtplM61YIk/1b9wCZ1i39d57uIHPgGTjwDOnGrPmJcsLKxZQs\n/DeS887ou01FJd1nvaHvvJb9riu5BhcYCndsJmzYTNC4jSDKEC1YyqyKBLMqEjxvTm+rn9KG3YRE\nrOjYyYqOnbxq9z9700vA+vLZPFG1gCeqFvJ41ULWVC3CVs6nu4jdym1pSbOlJc0dW3uDQ2EAK6aV\ncFRdkqPqSji6PslR9UkWVSXynlsRERERERERERGRqU5BIJFxFpRUkZhmSEwzg68cpSFRDumOwddN\nd5A58DSk2/Mu7lz7XcLyOT2th4Lq6WRWHkVm5VF9V+zqJNyxBdKpvPsJt20smISQiJUdjazsaOTf\nsoJDHzv6Qr4w88X9N4giKFKAJhPB2n0p1u5L8eusJE4rDTiqLsnRdS4odHR9kiOml1ClLuVERERE\nRERERERkilMQSOQgVnbYxZSueidR5y6iti1kWjf7VkSbyLRuhu59/bYJq5b0mxd17SW15Zd9ZyZr\nCauWEla77uTC6mWEVcsISivILF5ZME3dLzmbzMqjCLdtINy2kWBnA0EUDfg9PvqaE3j30nk844M0\ndl+K7Q1NXPWb9/FI5WLWVC/iX1WLWVO9mCcqFxS1S7n9XRH3N3Zxf2NXz7wAWFaT6AkKHVXnpour\nE4RqNSQiIiIiIiIiIiJThIJAIge5IAgIymdB+SwS9Sf0WRZ17SXTstEHhdw0XxAo07qp/46795HZ\n+yiZvY9mH811Y1e9jMT0Y0guek2/zdInvID0CS/ondHV6bqT2+qCQvG/YNf2nuBQZuFyqpMhx88s\n5fiZLsCTKHuaiq4DnN71OKfvfbx3/0HIxqq5/KNiEWuqF7OmajH/ql7E5rKZRWs1FAHrD6RZfyDN\nbzf1trKqSQYcWZfkmPokx85Icmx9kiPqkpQlFBgSERERERERERGRyUdBIJFJLCidTqL+eBL1xw+4\nXtS1b4jdykVE7Q2k2xuIUm35g0B7H4MgdK2GSiqgtIzMklVklqzqu2JnB2HDRsLGbVBR2W8/4Zb1\neVOQiDKsaGlgRUsD5zQ90DO/JVnJTxe9iHctfvMg32HkDnRHPLCziwd29rYaSoZw+HQXFDrOB4eO\nrk9Sre7kRERERERERERE5CCnIJDIIaBkzikkZr+AqGOnazXkWw9FrZvItG2GTHe/bcLq5Xn31bXu\nOjL7XMsd12pouetKrgiusF8AACAASURBVHo5YfVygvI5BEEAZeVklh1OZtnhefeTmbeE7pPPJNyy\nnrBhE0GBMYhi1d1tnH94Da983Tye3pviyb3dPLknxVN7uznloVtoyJTzcM1S1lQtoj1RNswzVFh3\nBtY0d7OmuZuf+HkBsLK2hON8a6G41VB9eaJoxxUREREREREREREZLQWBRA4RQRASVMwlrJgLM0/s\nmR9l0kTtDWRaNpBpWd8zDauX9dtHFEVkWjb0fm7fTrp9O+mmv/aulKgkrFlBWLOSsHoFiZqVBFWL\nCIK+AZL0cSeSPs6nI9VNuH0L4ZZ1LigUT/fu6rNNZvEqapIhz5pVyrNm+XGDMhmqbvk1QUe7+xiE\nbK9dwKM1S/hz2WIeqlrKw9VL2ZusGs3p63segLV+fKNfrG/vmb+wKuECQz4otHpmKXMrFRgSERER\nERERERGRiaEgkMghLggTBFWLCKsWwZxTeuZHfjyfbFFHI6TbBt5huo3M3jVk9q7pmVV5yi1QMkAQ\npiRJZtFyMotyWh8d2Eti6wbCzc8Qbn6G9Ioj+qd/Z0NPAAggjDIs2LuFBXu38PKs9ZprZvPU9KXc\nX7GEu8uWcnv9cUUbYyi2tTXN1tY0t27u7XZvXmXI6pmlrJ6R5IRZbqoWQyIiIiIiIiIiIjIeFAQS\nkbyCPAGSoHwWFSd+r0+LoUzLBqLOpsL7qZhHkCcA1L31f0k13O5aDPlWQ2H1cjfOUKxmOukjVpM+\nYnXB/Ye7dxCVlhN0DTzeUf2BnZx8YCcn8yDvnTmPu956Bo83d/P4nm4eb+7miT0pOlNpMkFxx/rZ\n3pZh++YObssKDC2pTnDCzFJWz3SthY6bkWRaqcYYEhERERERERERkeJSEEhEhiwIslsNndozP+o+\n0BsYOrCOTMszZFo3QZQhrFmZd1+Z/dZvsx623xEfgaByIWGN60YurFlFWLMybxAplj7q2bR+51aC\nHVtJbFpL6P8lNj1D0Lo/7zbR8sN5wdwyXjC3d+ygdCYi9e3/Irn2MdbNWMED1cv5fckS7i1bTEt2\nYKoINrWk2dTSzq82tvtvDatqS3qCQifMTHJMfSkVJcVtqSQiIiIiIiIiIiKHFgWBRGTUgmQNibrj\nSNQd1zMvSneRad0IQf6uz9IHnskzNyJq20K6bQvpxnt691+5kLDmMEqXnENYvbT/ZmGCaP4SUvOX\nwEln+F1FBM07fUBoLeGmZwg3PU3Y3ERmmem3i0QYUL3laRLNDaxubmA1f+ZiIAoC9s9cyPqZK/n/\n7N13lNxnYe//97dM211t1VaVVVuNeu+yZclVuGNsbIxxIDc3EAK/e29Ici8kQEiAA5fkXjr8KCFg\nYqoL4CZ3NatbVtdo1dtWrbZP+5b7x6wlr2ck71qyLdmf1zk6u/N96sw5X+94PvM8z8aCMawI1PK0\nNYKEFRzw6/NGfGBfh8O+DoffHMgEQ5YBE0sCzBoaYNbQIHPKg0wstrFMBUMiIiIiIiIiIiIyMAqB\nROQtYVhBrMLxOct838cqnYNnD8msBHqDc4b83uO4vcfxR96ZXeb04MUbMPNHYZiv+U+aYeCXVeKW\nVeLOuuLs5Y42fCtHMJXoxWw4kv08fJ+ilmPMbDnGTF7g44BvmnRWjuJAeR3fmXIv67rD7O90zvsc\nBsv1YWdbmp1taX6xL/P6FNgGM4cGmFuRCYXmlAepiOh8IREREREREREREclNIZCIvO0MwyBU918B\n8H0PP96A17Ufr+sAbtd+vO79kH7dVm5mCDO/Nqsv9/R2kju+BGYgc65Q4XjMIeOxCsdj5A3HeN0Z\nP35Rae5JOQ7pmz+MeTiGdTB2zq3kAAzPo6jhIDNbj/Gd//a3YAfoSnvsbEuz/VSag8db2Xk6zbp4\nHp4/uNfmfLodn9WNKVY3ps5cqy2wzoRCc8uDRDwI6HghERERERERERERQSGQiLzDDMPEyBuGmTfs\nzDlDvu/jJ5rxuurxuvbhdu7DMAMYZvaqF68z1vdLGq9zL17n3rOFVl7mfKHCKGbhBMyiiZihstwT\nKSgkdedf0DcBjNZGzEMxrEOxTDB0KIYR7+k/du14sAMADAmYLKwMsbAyRDD2O4JP/BynvJqWYRPY\nVVbHi3lj+YM/nD3dF/Z6vd6r5wv9/mBmG7mgESFa4HFFWztzy4PMqQgyIt/CMLSNnIiIiIiIiIiI\nyHuNQiARueQYhoERqcSMVELFFeet63XtO3eh24vXvgOvfcfZvkPlBMf+OXbVsvNNAL+8Gre8Gnfe\n0r6BPIzmE5lQ6OBerEN7caPTczY3D+wBwG5poLqlgWpe4FrgX+wAqZF1nKiO8krxOFaEx7AiXszx\nXu+8z3EwUr7Bji6LHbt7+AGZ0KoyYjKnPMj8isy/GUODhCyFQiIiIiIiIiIiIu92CoFE5LIWrPs4\nbsdevK59eJ378LoPgX/u83n8ZAvYkezrnovbvAqzaAJGuCp75Yxp4leNwKkaAQuvPfeEfB/r4J6c\nRYaTJnRwN2MO7mYMcAfgFZUQHzOFtUvuZ5VRydZTaba2pmiOX7xgqCnu8fjRBI8fTQAQsmBmWV8o\nVJn5WRbW2UIiIiIiIiIiIiLvNgqBROSyZubX9p0VdAMAvpfC6z6UCYQ69+F27cPvOQqcPZzHKpyQ\n1Y/Xc4Tk7q9nHgSKsIomYBZOxCqcgFk4HsPOG9iEfI/Ex/8B68AezAO7sQ7uweg99x5wZsdp8reu\nZvFHPs2issJMF77PiR6XHSc72NHUy6ruMFtb0/Q4F+eAoaQL65tTrG9Owc7MtfFF9plQaEFFkLGF\ntraQExERERERERERucwpBBKRdxXDDGIVRrEKo2eu+U5PJhDq3Isfb8AIFme18zpfs3on3YHbugG3\ndQNpAEyM/JFYRRMxiyZhFU3GiFTnDklMC3f6AtzpC/o69jAaj2Ed3IO1fzfmwT2Yxw5geGdX+nil\nFfhlFWefg2EwvMBmVNNG7vrJ1/GqR5IeN4VjwyayrjDKs95QNrekiXWce8XTYO3rcNjX4fBAfS8A\nQ8Mm8ysygdD8yiDTy7SFnIiIiIiIiIiIyOVGIZCIvOsZdj5W6Uys0pnnrON17D1PDx5+z2GcnsNw\n8slMn8ESAiPvIjDyjvMPbpr4NbU4NbU4VyzPXEsmMA/vwzqwG6t+B15Jec6mVn1mmY7ZcJRQw1HG\n8QTjgPuGFOGOm0L36MnsLI/yXLCW9W2wqSVFe+rirBZqTWRvITdraCYUWlQVYn5FkMKgeVHGEhER\nERERERERkbeGQiARESAY/RR2zXK8zr24HXvwOvfiJ1vPWd9PnQYj9zk67untmAVjMAIFuRuHwnjR\naXjRaaS555xjvBoCvZ7R1YG9dS3FW9dyBbDYDuCNmYAzfhqrhk9io13NMbOUTS0pdralcS9CLpR0\nYV1TinVNKf7vjm5MA6aVBlhcFWJRZSYYKgkpFBIREREREREREbmUKAQSEQEMK4RVPBmreDKBvmte\nogWvM4bXuScTDHXVg5c+08YsnpTVj5/uIrH17wEDI78202fRJMyiyRjhykGds5O8+xNY9Tux6ndi\nHtyDkU7lnruTxtq3A2vfDmrv/zuG1lRQV5fZ8q7X8djammZj3xlAG5qSF2W1kOfDK6fSvHIqzfd2\nZa5NKrFZXBVicWWIRVVBKiK5QzIRERERERERERF5eygEEhE5BzNcjhkuh4orAPC9FF7Xftz2XXhd\n+zDzx2S1cTt29/3mn9lCzjnxOABGsBSzeDJW0WTM4imYBaMxzrGaCMCdsRB3xsLMAyeNeaT+bChU\nvxOzo61ffT8QoLdmdL9rebbJlR0xrv3NN3EnTMcZP4191ZNYGy84Ewod7HLf5CvU3+7TDrtPO/x4\nTw8AdUU2i/tWCS2uCjEsX6GQiIiIiIiIiIjI20khkIjIABlmEKtoElZR9gqgV3kdu85Z5qfacJtX\n4zavzlyw87GKJmNXLsWuuvr8g9sBvLGT8MZOIr38g+D7GC0NmVBo3w6s2Db8ohJ8O5DV1Nr7Ctbx\ng1jHDxJ89hFmANOqRvCX0Wm40ek0LZzCS04J65tSbGhOsu1UmrQ3kFfk/Oo7HOo7HP5jXy8AtQVW\nZvu4qiBXVoWoHaI/QSIiIiIiIiIiIm8lfQInInIRBUZ8ALNwIl7Hrr4VQ/XgO7krOz24pzZi5I3I\nGQL5vodhnOOcHcPAr6jBqajBWXx95lo6BYePZFW1YtuzrpmNxzAbjxFY+Ti1wIihldwZnYE7cQY9\nc2ey2S9hQ3OK9U1JNjSn6LgIW8gd6XY5sr+XB/efDYWWVIdYUh3iyuoQVXlaKSQiIiIiIiIiInIx\nKQQSEbmIjGARdvlCKM9s4+a7Sbyu+kwg1LEbt2MXON392ljFU7L68X2P+Ev3Y0RqsIqnYhVPxSya\ngGGFzz14IJjzsjduMm68B/NwDMPLvcTHbG3CbF1BYO0KwsBVn/wCi+dfDQzB831i7Q7rmlK81JRk\nbWOSht4LXyp0pNvlgfpeHqjPhELji+wzgdCVVUFKwwqFRERERERERERELoRCIBGRt5BhhbCKp5wJ\nenzfw+85itu+A7d9B177ztwhUM9h/GQrfrIVr307aQDDxiwcnwmEiqdiFU3CsPPecA6pOz4Gd3wM\nEr1Y+3djxbZh7d2GeXAPhpPO2cYde3bLO9MwmFgSYKLVw3/t2oFz43QO+wWsaUzyUlOKtY1JjnZf\n+LlC+zoc9nU4/GRvDwYwpTRwZqXQwsoghcFzrIoSERERERERERGRnBQCiYi8jQzDxCgYhVkwisDw\nW/B9H8Mwsuq57TuzG/sOXsduvI7dcOQ3YJiYQ8ZjlczAKpmOeZ6zigAI5+FOmYM7ZU7mcSqJeXBv\nJhSKbcOq34mRSuKV1+APrcpqbu/YSPhHXwVg0sixRCfO4qMTZ+LeNI1jXpiXmlK81JhkbWOK/Z3n\n2AJvgHxgR1uaHW1pvrerG8uAWUPPhkLzKkJE7OzXTURERERERERERM5SCCQi8g7KFQABmPmjsKuv\nx23fgR9vyN3Y9/A69+J17iV95NdY5YshfM/ABw+G8CZMx5swPbPSKJ3CPLgXo6crZ3Vrz9azvx89\ngHX0AKz4Hb5hMn50lLETZ3DvxFm4c6bS5Ab6to7LBEO72y8sFHJ92NSSZlNLmn/b3k3QhLkVQZbV\nhLm6JsT0sgCWqVBIRERERERERETktS7bECgajZYCXwRuB6qBVuAJ4POxWOwcn5j2a38f8AlgOhAE\njgKPAV+OxWKn3qp5i4gMhFUyDatkGgBeshXv9A7cjp24p3fg9x7N3aZ4GiSyr6cbnsbMH4U5ZCyG\ncZ5zdgJBvOi0c89p3/ac1w3fwzq4B+vgHnj8V/h2gNq6KQyfPIc7Fl2Lv7CSUwmXdX1bx61uTLGz\nLfc2dAOV8mBtY4q1jSm+/DKUhAyuqg6zrCbE0poQtUMu2z9vIiIiIiIiIiIiF81l+SlZNBqNAC8C\nE4DvApuBOuBvgauj0ejsWCx2+jztvwp8FtgIfA7oBhYBnwZu7mvf+ZY+CRGRATJDQzGrlmFXLQPA\nT7VnzhQ6vQ339Db83mMAWCXToaF/uOKnu0jt+SbggZ2PVTwNq2Q6Vsl0jPxaDGPg5+z0fulHWLHt\nWHu2Yu3Zinl0P4bvZ9UznDT2nq3Ye7bijZ2IW1ZJWdji5toIN9dGADiVcFnTmGJVQ5JVDUnqOy5s\npdDppM+jh+M8ejgOwNhCi2U1mVDoyuqQzhMSEREREREREZH3pMsyBAL+OzAV+OtYLPb9Vy9Go9Ft\nwCPA54G/ydWwbwXR3wGHgSWxWCzZV/SzaDTaCvwv4GPAt96y2YuIXAAjWIxdcSV2xZUAeMlTeO07\nMPJrgf396mbOFvIyD5we3NZ1uK3rMo8DRX2B0Eys0pmYkexzgPqJ5OPOWIg7Y2HmcXcn1t5tWHte\nzgRDJw73q+4HQ7h1U7K6MY/up/rFx7hj8mxumz4TFhZzssdldWPyTCh0rNsd5KvS34FOlwOdPfxk\nbw+WAXPLgyytCXH1sBCzhgaxtXWciIiIiIiIiIi8B1yuIdD9QA/w09dd/wNwHLgvGo1+JhaLZX9F\nHUaSed4bXxMAvWoVmRBo1MWdrojIW8cMlWFWLs1Z5nXuOXfDdAdu8yrc5lUAGJEarNJZ2BVXZlYV\nvZGCQtw5V+LOyYRRRkcb1u6tWLs2Y+3ajDdsFASCWc2srS8RfO5ReO5RfNPEGzORUZPnMHzKbO5e\nMAnsEg53OaxqSLK6LxRqintvPJ9zcH1Y35xifXOKr73SRWHQ4MqqTCC0rCbM6CHWOc9mEhERERER\nERERuZwZfo6tfC5l0Wi0EOgAVsdisSU5yh8C7gDGxmKxgznKi4AmYHcsFpv1urK/Ar4P/EUsFnt9\nwHReHR0dOV/I+vr6wXQjInJx+T6200QwsY9Qsp5Qch+m13veJt0FS+ks+cAFj2umEnihSFbRuF98\ngyFH9+Vs5gbDdNdG6Rw7mc6xU0iVlOP7cDhusKndYnOHyZYOi07n4oU2w8IeC0tcFpW4zCnyiJzn\n2CQREREREREREZG3S11dXc7rRUVFA/5w7HJcCVTb9/P4OcpfPTF9DJAVAsVisY5oNPovwJej0eh3\ngG8CXcA84B+AV4D/vKgzFhF5pxgGTqAKJ1BF75Al4HvY6ZOEkvsIJfYRTO7H9PsvikyGo9n9+D7F\nbQ+QCtaSDE/EtcvhfKtnDCNnAISfWdHjGyaGn726x0olKKrfRlH9NgASpRV0jp1CaP51jK4Zygdr\nwPMh1mOw4bTFhnaLbZ0maf/Nh0InEia/bzD5fUOAoOEzs8hjUV8oVBvxz/s0RURERERERERELmWX\nYwg0pO/nub7K3vO6ellisdhXotFoE/Ad4FOvKXoMuD8WiyUueJZ9zpXUyRt7dRWVXkORgRvYfRMF\nlgHgew5e517ctq24bVvwug8yYtJyDLt/gON1HyR+fBN5vZsAMEIVWKUzsUpnYZXMwAgWDXyS//Ij\nenq7M+cI7dqCvXMzZlPuXD/c1ky47XnyP/gX+BU1/Z7BrX2/96Q91jWleP5kghdPJNnd7gx8Lq+T\n8g02tGfCpf97CEYWWFw3PMw1w0IsqQ5REDDfdN9y6dLfG5HB030jMni6b0QGT/eNyODpvhEZvHf7\nfXM5hkAXrG/bt28DTwO/AlqA+cDfA09Eo9H3xWKx9ndwiiIibwvDtLGKp2AVT4ExH8F3ExhWOKue\n27a132M/2YzTsAKnYQVgYA4Zh1U6G6tsLmbhBAzzDfZUyyvAnX0l7uwrSQFGSwPWri2ZUGjXFoye\nzjNVvaoR/QKgV1nbN2C/vAZr2nyunTiLa4cXA9DQ6/LiySQvnEzw4skkzRdwntDRbpef7u3hp3t7\nCJqwsDLEtcNDXDc8TLTI1llCIiIiIiIiIiJySbscQ6BXPxnMP0d5wevq9RONRqNkAqDnYrHYTa8p\nWhGNRrcBjwKfIxMIiYi8p+QKgAB8Lw12ATjduUrxuurxuupJH/k12AVYpTOxq5djl80e0Lh+eTXO\n0ptxlt5M0nMxD+7F3r4Ra8dG3LopOdvYG18ksPpJAi/8Cd+yccdPxZ06j2HT5vOhsaP50Lg8fN9n\n12mHF04keOFkkpeakiTcgb4a/aU8WNmQZGVDks9v6mR4vsV1w0NcMyzMVTUhhmiVkIiIiIiIiIiI\nXGIuxxDoEOADw89R/uqZQfXnKL+azPN+OEfZk319L7uQCYqIvNsER91DoPYuvK79fVvHvYzXsRv8\nHFuvOd24zauxiibDAEOgfkwLb9xkUuMmwx0fA9/PruP7WDs2nnlouA72nq3Ye7bCb/9/vJKhuNMW\n4MxYyJTJs5gydQifnjqEhOOzvjnJ8yeSPH8yyc629ODn1+d4j8vPYr38LNZLwITFVSFuGB7mfSPD\njBpyOf55FRERERERERGRd5vL7lOqWCzWE41GtwOzotFo+LXn90SjUQtYBByLxWJHz9HFqyuIcn3d\nPQQY5ygTEXlPMwwLqzCKVRiFUffgO3Hc9h24p7fintqM33usX32rNDsA8p1eknv+rW/ruDmY4YqB\nDJx9racTv7wav+M0hp+93Zt5uhVz5WMEVj6GHwjgTpiJO2MhXHEDS2vyWFoT5p+Bxl6XZ08kePZ4\nZvu4jlSOwGkA0h68eDLJiyeTfHZjB9Eim+UjwtwwIsy8iiC2qW3jRERERERERETk7XfZhUB9fkpm\nS7ePA996zfX7gArgi69eiEajE4BkLBY71Hfppb6fd0ej0e/EYrHXfuJ31+vqiIjIORh2BHvoPOyh\n86Du43jxRty2LbinNuPFGzDyshdsuqe34basxW1Zm+kjfyRW6RzssjmYxVMwzODABi8oIv6P34We\nrsw5Qts3YO3YiNl+Knue6TT2jo1Ye18hfeX7+pVV5VncV5fPfXX5OJ7P5pYUzx5P8syJBNtOvflV\nQrEOh1hHN9/a2U1JyOC6YZlA6JphYYpD2jZORERERERERETeHpdrCPRD4MPAv0aj0VpgMzAZ+Btg\nB/Cvr6m7B4gBEwBisdhL0Wj0d2QCnzXRaPS3QAswF/hroAn4ytv0PERE3jXMSBXmsJsIDLsJ3/cx\ncqzgcU9t6vfY7zmK03MU59jDYIawSmdilc3HGjoXMzT0jQfNH4I7bynuvKXg+5jHDmLt2IC9bQNm\n/Q4M7+wqIXfiTAhlL/S0tq3HiPfA1HksqBzCgsoQ/zi7kKZel+dOJHj2RJLnTyRof5OrhE4nfX57\nMM5vD8axDFhYGeSGEWHeNyLMuKLAm+pTRERERERERERkIC7LECgWi6Wj0ej1wD8BHwA+BTQDPwG+\nGIvFet+giw8Bq4CPkgl8gsBJ4N+Bf4nFYifempmLiLw35AqAADBtsPLAzfGfaS+J27oet3U9xMAs\nGIs1dD521TWYecMGMijeyLF4I8eSvule6O7E3rEJa9s67O0bcWYszNks8MSvsfe+gm+aeHVTcWYs\nxJm+gMqaWu6ty+fevlVCL7emeOZ4kmdPJNja+uZWCbk+rGlMsaYxxec3dTK20OKGEWGWj4iwsDJI\nQNvGiYiIiIiIiIjIRWT4uQ7clkHr6OjQC3mR1dfXA1BXV/cOz0Tk8nE53De+5+B17sU9tSmzdVz3\ngfPWD039Anb5ogsb1HXAdSEY6n+9p4v8T93Wb8XQq7zyapyZi3BnXYE7fipYZ7830RJ3ee5EJhB6\n7kSC08kL/xNQGDS4dliYm0aGuXZ4mKKgto17u1wO943IpUb3jcjg6b4RGTzdNyKDp/tGZPAux/um\nqKhowN8kvixXAomIyOXLMG2s4ilYxVNg7Mfwkqdw217GPbUR99SW/quEjABWycysPrx4I27reqyy\neZh5NW88qGX3C3FeZR47AJYFOUIgs6WB4NMPwdMP4ecX4kxfgDNrMe7UuZRH8rhnXOaf4/lsaknx\n1NEEK44n2NvuDOr1eFVnyufhQ3EePhQnYMKS6hA3jYzwvpFhqvOsN9WniIiIiIiIiIi8tykEEhGR\nd5QZKsOsvo5A9XWZVUIdu3BaN+Ce2oAZrsKwI1lt3JaXSO3/EdT/ECNvBFbZPOyh8zCLJmOYA//T\n5k2YQc/3/oi162XsV9ZhbVuP2d6aVc/o6STw0tMEXnoar3IYvf/7P8+U2abBwsoQCytDfGluEYe7\nHJ46lmDFsQRrGpOks/OlN5T24LkTSZ47keRv1sHsoQFuqo1w08gw44vsc2+3JyIiIiIiIiIi8hoK\ngURE5JJhmDZWyXSskulQ95f4biJnPefUxjO/+73HcHqP4Rx7COx8rNI52EMXYJXNxQgUvPGgoQju\nrMW4sxaD72Me3Y+19SXsrWuxDu/LHnvK3Nz9dHdAfiGjhth8YlIBn5hUQGfK44WTSVYcS/D08QSt\niTeRCAFbWtNsaU3zz1s6GVdoc9PIMDeODDO3IoipQEhERERERERERM5BIZCIiFyyDCucdc33HPze\n47kbOD24zStxm1eCYWEWT8UeuhCrfCFmuGIAAxp4tXV4tXWkb/8zjLbmTCC0ZQ3W3q0Yros764rs\ndr5P3hc/DnYAZ9ZinJmL8cZNojBocduoCLeNiuB6Pi+3pllxLMGTx+LsOv3mto3b3+nwrZ3dfGtn\nNxURk/eNCHPTyAhLqkOEbQVCIiIiIiIiIiJylkIgERG5rBimTWTRL/A69+Ge2oDbuhGv+0B2Rd/F\nO/0KqdOvQP0PiMz7IWbBqEGN5ZdW4FxzO841t0NvN/b2DbgTpmfVM48dxGxtBCD4xK8JPvFrvMIS\n3BkLcWZfgTtpNlYwxNyKIHMrgvzj7EKOdTs8fTzBU0cTrGpMknQH/1o0xz1+vq+Xn+/rpcA2uGZ4\n5hyh64eHKQ6Zg+9QRERERERERETeVRQCiYjIZccwTKyiCVhFE2DMn+ElWnBPbcJt3YB7eit4qf71\nQ+UY+bVZ/fjpbrDCAztHKK8AZ8E1OYusrWuzrpmdpzFXPUFg1RP44Tyc6Qtw5i7BnToPwnmMKLD5\nLxMK+C8TCuhOezx/IskTR+M8dSxBe8of2AvxGt2Ozx8OJ/jD4QQBE5ZWh7hlVOYcobKwNej+RERE\nRERERETk8qcQSERELntmuBxz2I0Eht2I7yZw27bgtqzLnB2U7sQaugAjx9k5qUO/xGl8FqtsLnb5\nQqzS2Rh2/qDHd2dfScp1sF5ei3Use1WSkeglsOF5Ahuexw8EcafOI73sFtxp8wEoCJjcOirCraMi\npD2fdU0pHj8S5/GjCY73DH6JUNqDZ04keeZEkv/xEiyuCnHbqDA3j4xQmadASERERERERETkvUIh\nkIiIvKsYVhi7fDF2+WKCnovXsRsjWJxVz/d93NZ14HTjNr2A2/QCGAGskmlYr54jFCob0Jje8NGk\nho+GO/4co6UB++U1mUBo33YMz+s/v3QK++U1uOMmnQmBXitgGiypDrGkOsTX5vtsb0vzxNEEjx9N\nsLMtPejXw/VhCMrxDwAAIABJREFUVUOSVQ1J/nZdBwsqg9xSG+GW2jAjCvQ2QERERERERETk3Uyf\n/oiIyLuWYVpYJVNzlvk9h/ATTa+7mM6sImrbAvu+i1k0Cbt8MVb5YsxI1YDG9MurSd9wF+kb7oKu\nduyt67A3r8TatQXDORviOHOWZDdOJQmsfBxn9hX4pRUYhsH0siDTy4J8dmYhh7ucvkAozrqmFN4g\nd43zgXVNKdY1pfjcxg5mDw1kViDVRhhdqLcEIiIiIiIiIiLvNvrER0RE3pOMUDnB6KdxW9bhnt4G\nfvYqG69jN6mO3bD/x5gFY7EqriRQe3fOreVyGlKMs+R9OEveB/Ee7FfWY29eidF+Cr9yeFZ1a9cW\nQr/8NqFffht37EScOVfhzL4Sv3IYAKOG2HxycgGfnFzAqYTLimOZFULPn0gSdwd/jtCW1jRbWtN8\ncXMnU0oD3FYb5tZREaLFgUH3JSIiIiIiIiIilx6FQCIi8p5kBIYQGHYTgWE34Ts9uKe24LSuwz21\nEZyerPpe9wGwQgRH3fPmBozk4yy8BmfhNeDnDmzszSvP/G4d2IN1YA+h3/wQd+RYnLlLceYtw6/K\nhEdlYYt76/K5ty6fXsfjhRNJ/nQkzpPHEnSkBh8I7WxLs7MtzVe2dhEtsrl1VIT3j44wqUSBkIiI\niIiIiIjI5UohkIiIvOcZdj525RLsyiX4noPXvh2n5SXclrX4qdNn6tnli3O2Tzc8jRkZhlk0EcMw\nBzBgjpVEvo+1f3fO6tbRA1hHDxB66Ke4I8fhzFuGM++qM6uJ8myTm2oj3FQbIeX6rG5M8sfDcR4/\nmqA14eXs83xiHQ7f2NbFN7Z1MaHY5vZREe4YHWG8VgiJiIiIiIiIiFxWFAKJiIi8hmHaWKWzsEpn\n4Y//K7yOvTgta3Bb1mLlCIF8N0Eq9j3wkhjBUqzyRdjlizGLp2GY1iAGNuj96s+w9u3A2rQSe8sa\nzPbWrGrW0f1YR/cT+v2PcWvHk/j45/CHjTpTHrQMrhkW5pphYf5toc9LTSn+dDjOn47EaYwPPhDa\n2+7wtVe6+NorXUwusXn/6DzuGB1hjM4QEhERERERERG55OkTHBERkXMwDAureDJW8WT8cX+Z8ywg\n99Rm8JIA+Kk2nBOP4Zx4DOwh2OULscoXY5XOwjAHsIrGsnEnzsSdOJPUff8f5sE92JtWYm9eidna\nlFXdPHkIv7T8nN3ZpsGS6hBLqkN8fUERm5pT/PFIgj8eiXOs2x34C9Fn12mHXac7+fLLnUwrDXDH\n6Ai3j44waojeToiIiIiIiIiIXIr0qY2IiMgA5AqAALyu+twNnC6chqdxGp4GOx976EKsiiVYpTMH\nFgiZJt64yaTGTSZ1z19hHtyLvfEF7I0vYrY1A+BOnQeR/Kym1pbVmM0nceYtxS+rzHRnGMyvDDG/\nMsSX5xbyyqk0fzwc549H4hzoHHwgtL0tzfa2NP+0pZNZQwO8f3SE20dFGFGgtxYiIiIiIiIiIpcK\nfVIjIiJyAYJjP4Zdsxy35SWc5jV4nXuyKzk9OI3P4jQ+C3YBwTEfJTD85oEPYhh4YyeSGjuR1N2f\nyKwQ2vgi7sSZOasHnnkYe89WQr/+Ae7YSZkzhOZehV9W0dedwcyhQWYODfKF2YXsPu3whyNx/nQ4\nzp52Z9CvwcutaV5uTfP5TZ3MKw/y/tERbhsVoSZ/ENvhiYiIiIiIiIjIRacQSERE5AKZkWrMkR8g\nMPIDeMlTmUCoZS1e+3bwX3cOj9ONESy6gMHOrhDKxWg/hbV325nH1oHdWAd2E/rV93DHTcFZcDXO\n/GX4hSWZ+obB5NIAk0sDfG5mIfva0zx6OM4jh95cILSxJcXGlhSf29jBgsog7x8V4f2jI5RHFAiJ\niIiIiIiIiLzdFAKJiIhcRGaoDHP4LQSG34KfasdpeQmneTXe6W2AB2YIq2xuVjsv2Ur64C8yW8aV\nzMAw39yfaKPpBH5hMUZHW1aZtX8n1v6dBB/8Lu6k2ZlAaPaVkFdwps744gB/PyPA388oZM/pNI/0\nBUL1HYMLhHxgXVOKdU0pPruxg6U1Ie4ck8dNI8MUBs039dxERERERERERGRwFAKJiIi8RYxgMYFh\nNxIYdmNfILQWP92JYYWz6rrNa15zhtAQ7PJFWBVXDjoQ8qLT6P3m7zD37cDe+CL2ppWYnaf7z8vz\nsHduwt65Cf/n/wdn8XKSH/tMVl8TSwJMLAnw2RlD2HXa4ZFDvTx8KM6hrsGdIeT68NyJJM+dSBK2\nYPmICHeOiXDd8DAhK/dZSyIiIiIiIiIicuEUAomIiLwNMoHQTecsd5pXveZBF07DCpyGFX2B0GLs\nyiWYxdMxzAFsq2ZaeBNmkJowg9R9n8aKbcfe8Dz2ppUY3Z3955VOg3n+lTmGYTClNMCU0iL+cVYh\n205ltox7+FCco92DC4QSLjx6OM6jh+MUBg1uq41w55g8rqgKYpkKhERERERERERELiaFQCIiIu8w\n30uDGQRM4PVnCHXhNDyF0/AUBIqxK67ErrwKs2gShjGAbdVMC3fiTNyJM0ne99+wdm3GXv8c9pbV\nGMkEAOkF1+SYlE/w0f/AmTwbb9yUM0GRYRjMGBpkxtAgX5xdyMutaR45lAl1jvcMLhDqTPk8UN/L\nA/W9VEVM7hgT4a4xecwoC2AYCoRERERERERERC6UQiAREZF3mGEGiMz8Gl6yDbdlbeYMofYdZE7W\neY10O86JP+Gc+BNGqILwrG9gRioHPpBt405fgDt9AclkAvuVdVg7N+HVTcmqah47QPDRnxN89Od4\npRU4C67BWXA13shx0BfQGIbB7PIgs8uD/PPcQjY1p3jkcJw/HI7T0Otl9Xk+jXGP7+/q4fu7ehhb\naHHnmDzuHBOhrigwqH5EREREREREROQshUAiIiKXCDNUijn8FgLDb+kLhNb0BUI7yQqE8DDC5W9+\nsFAYZ/4ynPnLchbb6587O6+2ZoJP/IrgE7/Cq6klveAanIXX4lfUnK1jGMyvDDG/MsRX5xWxrinF\nw4fiPHIoTltycIHQgU6Xr7/Sxddf6WJGWYA7x0S4Y3QeNfkD2ApPRERERERERETOUAgkIiJyCcoE\nQrcSGH4rXvIUbvNqnKYX8Tr3AmBXXpVzO7j08cfAS2BVXIV5ASGR0dKYe14njxB6+N8JPfzvuHVT\nSC+6DmfeMigoPFvHMFhcFWJxVYivzS/ihRNJfn+wl8ePJuhxXh9mnd8rp9K8cirN5zd1cmV1iLvH\nRrh1VIQhgQFshSciIiIiIiIi8h6nEEhEROQSZ4bKMEfcTmDE7XjxBpymldhDF2TV832f9NHf4iea\nYf9PMIumYFdehV1xJUaweFBjJv/6i6Q++JfY65/HXv8s1vFDWXWs+p1Y9Tvxf/kd3OkLSH3gz/GG\nj+lXJ2AaXD8izPUjwvSkPZ46luB3B+M8ezzBYPIgH1jVkGRVQ5K/XdfBzbVh7h6bx9KaELap84NE\nRERERERERHJRCCQiInIZMSPVBEfdk7PM69yTCYBefdyxk1THTlL1P8AqmYlVuRS7fBGGnT+gsfzy\natK3fJj0LR/GPHYQe/1z2Oufw2ztv0rIcB3sl9eQ/OBfnre//IDJB8bk8YExebQlXP54JMHvDvay\ntjE1oPm8Ku76/O5gnN8djFMRMblzTIS7x+YxrTSAYSgQEhERERERERF5lUIgERGRdwk/2YYRLMVP\ntb2uwMNt24LbtoVU7NtYZfOwq67GKpuLYQYH1Lc3YgypEWNI3fkXmPU7CLz0DPaGFzB6uwFwR0/A\nrx6Z1c5oOg6el1VWGrb4aDSfj0bzOd7t8MihTKizvS09qOfcHPf4/q4evr+rh0nFNnePy+POMXkM\n0/lBIiIiIiIiIiIKgURERN4t7IorsMoX4rXvxGl6Ead5NTjd/St5adyWtbgta8EuIDDyLoKj7h74\nIIaBN34ayfHTSH7401jb1hN46RmcqXNzVg/+8ZcE1jyFO3oCzuLrceYvwy8s6VdneIHNp6cO4dNT\nhxBrT/P7g3F+f7CXQ13uoJ7/7naHL27u5J82d7Kk7/ygW3R+kIiIiIiIiIi8hykEEhEReRcxDAur\nZDpWyXSC4z+J2/YyTtOLuK3rwE30r+x0Y5gX8FYgEMSdswR3zpLc5ckE9uaVAFiH9mId2kvwwe/i\nTp2Hs+g6nJmLIRTu1yRaHOAfZgX43MwhvNya5ncHe3noYJyWhDfgafnAyoYkKxuSfEbnB4mIiIiI\niIjIe5hCIBERkXcpwwxgD52PPXQ+vpvAbd2I0/QC7qlN4DuAgVW5NKud76VwTjyBVbEEM1T6pse3\ndmzCSMT7z8nzsLetx962Hj+chzP3KtJXLMcbPxXMsyt2DMNgdnmQ2eVBvjy3iBdOJvnNgV4eOxIn\nMYgFQq89P6gyYnLnmDzuHhthWtnAtsETEREREREREbmcKQQSERF5DzCsMHblEuzKJfjpLpzmVXi9\nJzBDZVl13daNpOp/CPU/wiqdmTk/aOgiDDsyqDHd2VfQ+4UfYL/0NIENz2N0dfSfU6KXwOonCax+\nEq+8hvQVN+Asvh6/vLpfPds0uG54mOuGh+lMefzxSJzf7O9lTWMKfxDzaYp7fG9XN9/b1c2U0gD3\njsvjg2MH95xERERERERERC4nCoFERETeY4zAEALDbjpnudP0Qt9vHm7bFty2LWCGsMoXYVddg1Uy\nE8O0BjCQgTd2IqmxE0l96K+xdm7EXvsM9ta1GOlUv6pmy0lCj/wMq34nib/7xjm7LAya3FeXz311\n+RzvdvjdwTi/OdDL3nZnIE/9jJ1taT63sYMvbOrgipIgN1e6jBrrE9B2cSIiIiIiIiLyLqIQSERE\nRM7wPQevsz67wEviNr2A2/QCBIqxK6/Crroac8h4DGMAwYlt485YhDtjEcnebuzNqwisXYG1d1u/\nas4Vy88xMR9eN87wApv/MW0I/31qAdtOpfn1gcGfH+T48GKbzYttNl871MgHx0a4d1w+U0oDA+5D\nRERERERERORSpRBIREREzjBMm8jCn+Ge3orT+Dxuy1rwkv0rpdtxjv8B5/gfMPKGY1ddQ2DYLRiB\ngoENkleAs+RGnCU3YrQ0YK9ZQWDtCozuTpzZV2TX72on78ufxllwNenFN+BX1PSfs2EwY2iQGUOD\n/MvcIl44kTk/6PGjgzs/qDXh8f1dPXx/Vw/TSgN8uC6PO8dEKAsPYNWTiIiIiIiIiMglSCGQiIiI\n9GOYFnbZHOyyOfhOHLd1XSYQansZ6L/Kxu89TvrwrwgMv/VNjeWXV5N+/0dJ33Y/RstJCIay6gTW\nP4/ZeIzgoz8n+OjPcaPTSV+xHGfuVRDJ61/XNLh+RJjrR4TpSHn88XBmu7g1jamsfs9ne1ua7Rs6\n+MdNHSwfEebecXlcOzys7eJERERERERE5LKiEEhERETOybAj2FVXY1ddjZdsw21ehdP4HF7X2S3j\nrPJFGHZ+Vls/1Q6BQgzDfOOBTBO/cnjOInv1U/0eW7FtWLFt+A98C2fuVThXLseNTgez/zhFQZOP\njM/nI+PzOdbt8NsDcX61v5f9nQM/PyjtwZ+OJPjTkQQVEZMPjsnj3ro8JpVouzgRERERERERufQp\nBBIREZEBMUOlmCNuJzDidryeYziNz+E0Po9ddW3O+omdX8FPNGFXXYNddS1m3rDBD+q5OLOvwOjt\nxmw52a/ISCUIrM1sJecNrcRZfAPpK5ZnbRcHMKLA5jPTh/A30wrY1JLiwfpeHj4UpzPtD3gqzXGP\n7+7q5ru7upk5NMC94/K4c0weJaEBhFwiIiIiIiIiIu8Aw/cH/uGHnFtHR4deyIusvj7zLfO6urp3\neCYilw/dN/J28/3M9nCvX+3jxRuJr/tov2tm0STsqmuxK5YM/PygswNh7ttBYM1T2BtfwEjEz1nV\nmTiT5Mf/Ab9k6Hm77HU8Hj+S4CfbW9nYbuIz+K3egibcODLC/ePzWFoTwjS0XZy8N+jvjcjg6b4R\nGTzdNyKDp/tGZPAux/umqKhowB9AaCWQiIiIvGnn2urNaXw265rXsZtUx25S9T/AGroIu/parJJZ\nGKY1kIHwotNIRqeRvO/T2JtXY695CmvPVozXfaHFbDiKX1j8hl3m2SZ3jc1jhpekMWGwwavkwfoe\nDna5bzyfPikPHj0c59HDcYbnW3y4Lo8P1+UxskBvsURERERERETknadPKEREROSis6uvB8PCaXgW\nP36if6GXxm1eidu8EiNY0nfm0HWYBaMG1nkogrP4epzF12O0NmKvfZrAmqcwmzPbxTmLbwAr+y2O\neSiGV14NBYVZZVVhn7+tG8JnphWwvjmzXdwjh+J0OwNf6Hu8x+Xrr3Txv1/pYllNiI+Mz+PGkRFC\nllYHiYiIiIiIiMg7QyGQiIiIXHRmuILgqA8RqL0Hr3MPTsOzOM0rwenpV89PnSZ99CHSRx8iMOaj\nBEfdM6hx/KFVpG+7n/StH8GMbSew6gnSS27MUdEn/IN/xmhrxpl1Jc5VN+JOnAVm/5VMhmGwsDLE\nwsoQX5tfxJ+OJHhwfy+rGpIDnxPw/Mkkz59MUhrq4O6xET4yPp9JJYFBPTcRERERERERkQulEEhE\nRETeMoZhYBVNwiqaRLDuE7it63Ean8Ft2wJ95wm9yiqdeSED4U2YTnLC9JzFZmw7ZlNmRVJgw/ME\nNjyPN7SS9BXvIzBiAumisqw2+QGTe8blcc+4PI50Ofz6QC8P1vdypHvg28W1JT1+sLuHH+zuYfbQ\nAPePz+f9oyMUBnNvoyciIiIiIiIicjEpBBIREZG3hWEFsSuXYFcuwUu24Ta9QLrhGfyewxh5IzGH\njM9q43Ufxml6Ebv6esy8mjc9dmD9c1nXzNYmQo/+B5Mx6BozEXv5XTizFkMgmFW3dojN/5xRyN9N\nH8K6phQP7u/l0UNxegaxXdyW1jRbWtv57MYObh8V4f7xecyvCGIY2i5ORERERERERN4aCoFERETk\nbWeGSjFHfgB7xB143Qcg3ZUzDEk3rMA59gjpI7/GLJqCXXM9dvmVGHZkUOMlP/wpnMmzCKx8Amvn\nJgz/bHhj4FN4cDd8/0v4+YWkF12Hs+RGvJFjs+dtGCyuCrG4KrNd3COH4jywr4dNLekBz6XX8Xlw\nfy8P7u+lrsjmI3WZ1UYVEWtQz0lERERERERE5I0oBBIREZF3jGEYWEPG5SzzvTRO49kVPF7HTlId\nO0nt+wF2xRLsmhswCycObCVNIIg7dynu3KUYp5qx1zxFYNUTmK2N/efT00nwmYcIPvMQiY9+BmfZ\nLefsckjA5P7x+dw/Pp89p9M8UN/Db/bHOZX0ztnm9eo7HL6wuZN/3tLJ8hFhPjI+n2uGhbBNrQ4S\nERERERERkQunEEhEREQuSX6iGSNQiJ/u7F/gxnEaVuA0rMDIG45dfQN21dWYoexzfXL2W1ZB+rb7\nSd9yH9aercQf/w3Fe1/GdJ2zdQwTd/r8Ac91YkmAr84r5p9mF/HksQS/2NfD8yeSDHSzOMeHx44m\neOxogpo8k3vr8rl/fB4jC/RWTURERERERETePH2yICIiIpckM28Ykfk/xuvcg3NyBU7zKnDj/er4\nvcdJH/gp6YM/wyqdi11zPdbQRQNbHWSauJNncyRYyPF4D9HmQ9irnsA6Uo87dS5+aUV2k/27MI/U\n4yy8FvIKssqDlsFtoyLcNirCsW6HB/f38sv6Xo51uwN+3id7Pf51Wxf/tq2La4eF+LNoPjeMCBPQ\n6iARERERERERGSSFQCIiInLJMgwDq2gSVtEkgnWfwGlZg9PwNF77jv4VfQ/31Ab8dCd2+eJBj+NG\n8klf+37S174f80g9+LnX8ASf+i32ppX4v/4hzvxlpJfejDd2EuQInUYU2PzPGYX83fQhrDyZ5IH6\nXh47Eic1wN3ifOCZE0meOZGkKmJyX10+HxmfR+0QvX0TERERERERkYHRpwgiIiJyWTDsCIHq6whU\nX4fXewKn4RmchmfwU6fO1LFrrs/Z1vccDHNgb3u82rrc43e0Yb28JvN7KkFg9ZMEVj+JO3w0ztJb\nSC+6DvKHZLUzDYNlw8IsGxamLeHymwNxHqjvYfdpJ6vuuTTGPf51exf/tr2La/pWBy3X6iARERER\nEREReQMKgUREROSyY+YNIzj2owTGfAS37WWchqdx27ZiVyzJquu7CeLrPoZVOhu7Zjlm0eSBbRf3\n+jGPH4JwHvR09btuHT+E9ctvE/zND3Hm9a0OqpuSc3VQadjiryYX8IlJ+WxtTfOLfT08dChOV3pg\npwf5wLMnkjyr1UEiIiIiIiIiMgD6xEBEREQuW4ZhYZfNxS6bi+8mMaxQVh2naRV+6jRO47M4jc9i\n5I0gULMcu+oajGDxgMdyJ8+m55u/x968isCLj2HFtvWfSzpFYO0KAmtX4NXUkl56M+nF10NBUY55\nG8wqDzKrPMhX5hXxh8NxHqjvZV1TasDzee3qoKuHhfiz8fm8b6RWB4mIiIiIiIjIWQqBRERE5F0h\nVwAE4DQ81e+x33uM1P4fkzrwM6zyhYT8aSRD4wc2SDCEs+g6nEXXYZw8QmDl4wTWPIXR3dmvmnny\nCKEHv4dVv5PEp7503i7zAyb31uVzb10+sfY0P9/Xw6/293I6OfDVQc+dSPLciSQVEZP76vK4f3w+\no7Q6SEREREREROQ9z7yYnUWj0Yvan4iIiMiF8H2fwLBbMIun5yh0cJtXU9byPSoavkTq0IN4iZaB\n911TS+pDn6Tnm78n8ckv4EyalVUnveTGQc03Whzgq/OK2fPBan68pIRFlcFBtW+Oe/yf7d3M+H0T\nd6xo5Q+H46S9gYVJIiIiIiIiIvLuc7G/Ino8Go0+CDwQi71ujxQRERGRt5lhGNhVy7CrluH1nsRp\neAqn4Rn81Ol+9Wy3jfShX5A+9EussrkEo5/CDJcPbJBAEGf+1Tjzr8ZoPE5g5ePYq5+EUAh3ypzs\nObWfIvjrH5Bedive+Kk5zw4K2wZ3jc3jrrF57GtP8/N9vfxqfy9tSW/Az/35k0meP6nVQSIiIiIi\nIiLvZYbvX7xvh0ajURcwyOxMsgN4APjPWCzWeNEGuUR1dHToa7YXWX19PQB1dXXv8ExELh+6b0Te\nmO85uKc24px8EvfUFuB1wYpdQN7i/zzn9nID4qQxmk/i19RmFQX+8AtCD/87AO6wUTjLbs2cHZRX\ncN4uE47PY0fj/EeshzWNAz876LWurgnx5xPyWT4ijK2zg+QC6O+NyODpvhEZPN03IoOn+0Zk8C7H\n+6aoqGjA/1N/sb8OOgz4IHA3sAD4BvC1aDT6LPAL4NFYLBa/yGOKiIiIDJhh2tjli7DLF+ElWmja\n+SvyetZhu5nVQXbV1TkDIK/3JEZ4KIY5gC3a7EDOAAjXIfDin848tE4cxvrltwn+9kc4C6/JrA4a\nHc3ZZdg2uHNMHneOyaO+I83PY708+CZXB9Xkmdw/Pp8/i+ZTnWcNuL2IiIiIiIiIXF4uagjUt+Ln\n28C3o9HocM4GQjcA1wPd0Wj0ITLbxb1wMccWERERGSwzXE530fvoLryB0WVdOCefIlCzPGfd5M6v\n4CVbsKuuIVCzHDM/R8jzBoyuDrzqkZht/c8eMlIJAisfJ7DycdzRE0hffSvO/KshFM7ZT11RgC/P\nK+Lzswt57EhmddDqQawOOtnr8bVXuvjGti5uHBnmv0zIZ0l1CDPH1nQiIiIiIiIicvm6qNvBnUs0\nGq0FPtz3byKZ7eKOA/8B/CgWi514E32WAl8EbgeqgVbgCeDzsVisYQDtQ8D/Au4DRvS1fxz4h1gs\n1jrY+Wg7uIvvclyGJ/JO030jMngDuW/crnoSmz7d75pZNAm7Zjl2xRIMK3dYcy5G43ECL/yRwOqn\nMHo6c9bx8/JJL15Oetkt+MP+H3v3HSVFne5//F1dVd0z3RPIGcnUoChBBQVUUMAAGDDntOi66e7q\n3t/eDV7vet3s3b3u3l1dFTG75kAwgIIRBRVEBYohwwxhSBO6Z7q7uuv3x4zKMD3QI40Kfl7ncJqu\neur5fttz6tDtU9/n23OfOVdWJnlwRYxHSmNsb8HqoM/0KTK5yolwad8wbfK0Okj2Tv/eiLSc7huR\nltN9I9Jyum9EWu5gvG9a0g4ucCAn8hnXddcBdwL/C6yhft+g7sDNwBrHcR50HKdjtvkcx8kH5gE3\nAE8DVwH/pH7V0duO47Tex/UW9QWfXwEzgO8ATwHXAq87jpNFnxcRERH5tvDKX25yLF25lMSyPxN7\n6xLi7t9J16zJOp/fqRuJi79H9H+fpO66X5DqN7BJjBGLEpz9NPl/+QVk8dBO32KbW48tZumFnZg2\nujUndm7ZnkarqlLcvLCKAU9s5vo3drBga5yv4mEhERERERERETlwcr0nUCOO49jAmdQXacYBNvUF\nIBd4APgU+AH1q3FOcRznRNd1V2WR+sfAkcD3Xdf9x27jfQQ8S31x6ca9XP9d4BTgStd1H2w49rDj\nONuAa4DhwJtZfkwRERE5xAV7X0kgchhe+YtNiz2pGF7ZdLyy6QSKBmB1PaNhdVAWRZhgCG/keLyR\n4wmsX4U1bzr2269g1MU+D0mOmQQtaNMWMg3O6RXmnF5hVlV6PLAi2qLVQfEUPL6qlsdX1TKwjc21\nToTz+uRTaH8lzw6JiIiIiIiISA4dkHZwjuMMBa4GLgLaUF/4qQSeAKa5rvvuHvGXUl8UesV13TOy\nyL+M+pVEbV3Xje923ADWAyGgo+u6GT9cw/Um4DQX01JqB5d7B+MyPJGvm+4bkZZryX3j+z7p6hV4\n5S/hbZkHqdrMgVYBoQE3YrUf0fIJ1cWw5r+K/drzBMrXEf3Lk1DUqnFMyiN07x/wjh1NatBwMPf+\nXE885fP82lqmuVHmb8l+76DPFNoGF/QJc40T4Yg2douvl0OP/r0RaTndNyItp/tGpOV034i03MF4\n37SkHVztBFICAAAgAElEQVROVwI5jnMjcCUwkPrCTxp4FZgGPOu6bl2m61zXfcRxnNOAyVmMUQSU\nAG/uXgBqyOM7jrOgIU8vYHWG67s1XP/3zwpAjuPkAfFcFYRERETk0GQYBmaRg1nkEOx7Hd7WeXhl\ns0hXlzYO9GoIhLt/uUHywnhjJuGNnohRsalpAQgwP3oX+53Z2O/MJt2mPcnRk/BOPAO/dbuMKUNm\nfRHngj5hPt2RZJob5fFVMaqT2X31qU76TF0eZeryKMM7BLmmJMJZPfLJs7JfoSQiIiIiIiIiX72c\nrgRyHOezPiMrgfuBB13X3ZjltT8DbnVdd6+9UxzHORJYAjzmuu4lGc7/hfp2ceNc152T4fxYYDb1\n7eLSwE+AHkAceAn4qeu6K7OZ8+6aWwn0WRVRREREDl12YgPhmrfJjy0k4CeIh/qyvcO/NYkzvQoM\nP4Vnd9qv8fo8+r8Urf600THfCLDLGcy2o0dT07Nkny3kYil4qcLk6U02K6Itb/VWbPmc2dFjcieP\nbvl6jkZEREREREQk15pbnfS1rQQCplLf7u2dL3HtXcAjWcQVNrzGmjkf3SNuT20aXq8EgsBvgC3U\n7xH0A+B4x3EGu667KYu5iIiIiJAMdqeyzUVUtTqb/Nj7pMy2GeMKq14hHH2XeKgvschIasODwGhh\ne7V0ilReGD9gYqRTnx82/DStl39I6+UfUtuuM9uOHs2Oo44nHcrPmCZswuROKc7pmOKT6gBPb7aY\nXWGS8LP7HlnpGTxUZvNQmc1xrVKc29ljVJsUWhwkIiIiIiIi8s2R6yJQH6DrvoIcx7kXON513SM+\nO+a6biX1+wYdaMGG147AQNd1tze8f8FxnC3UF4VuAn6ai8EOpj6C3zQHYy9Gka+b7huRlsv9fXNk\nxqN+soZY2SIAQvGVhOIraV1djN15LFaXMwiE9/kV6gs/+xOxXdux3nwRe950Atu2NDqdv20T3V9+\njG7znsUbMZ7k2LNJd+vdbLr+1PfS3RlP80hplGlulFVVqWbj9/TuLpN3d5l0i5hc5US4sn+Y9vlm\n9p9HDjr690ak5XTfiLSc7huRltN9I9Jyh/p90/LeH3s3GsimAb4JNP9/IvauquE10sz5gj3i9lTT\n8PrCbgWgz0xteB395aYmIiIikpm37V1IxxsfTFaSXP80te9eS+2i/8Db8gZ+OplVPr9VW5KTLiP2\np0epvfH3eIOOw9+jBZwRr8Oe+wL5t1wP0ep95mwdCvCDgYUsnNyR505ty5k98jBbsLJnYzTFbR9W\ncfgTm5ny+g7e2xInl62HRURERERERKRl9nslkOM4ZwFn7XboQsdxBu7lknbAqcCeBZhsrQF8oFsz\n53s0vDa3Gc/ahtdMj6dua8hd9CXnJiIiIpKR1ekUAuEueGWz8La+AelEo/PpnYuJ71wMdivsLuOx\nupxOIL/zvhMHTFKDjiM16DiMik3Yr72A/cZMjJovnofxjj0JIs11ys2Q0jAY3SWP0V3y2BRL8eCK\nKA+4Ucpj6X1fDCTT8OTqWp5cXcuRbWymDIhwXu98wlaunz8SERERERERkb3JRTu4EHA89Z1EfODY\nhj97kwBu+TKDua4bdRxnCTDUcZw813XrPjvnOI4JjAA2uK67vpkUS6lvOzc4w7nugAFs/DJzExER\nEWmOYRiYxYdjFh9OsN/1eJtfJVk+Cz+6x1eW5C6S654gue4J7B4XEuxzddZj+O07k7jwehLnXIW1\nYC72q89jrl5Gcuw5GePt6Q+T7nM4qQFDwMi85Kdz2ORng4u46ahCXt5Qx31ulFfL4hljM/l4R5If\nvb2LmxdWcmm/MN8pKaB3Ua47EouIiIiIiIhIJvv9C9x13SeAJxzHaU396p47gSf2ckkdUOq67o79\nGHYq8FfgeuCO3Y5fBnRgtwKT4zglQNx13TUN8004jvMocIPjOJNc152+2/U/aHjd/ZiIiIhIThl2\nIXb3s7G6nUW68lOSZTNJVbwFe7SCCxT2+XIDBEN4o07DG3UagfWrSHdv2oXX2FJG8OmpGL5PuksP\nkiefRXLUqZCfueOuFTCY0COfCT3yWVPlMc2N8nBpjB3x7FYHVSZ8/vFplH98GmVs1xDXlkQY3y0P\nM9CCfnMiIiIiIiIi0iI5ewzTdd2djuM8ADzvuu7rucrbjLuAS4HbHcfpAbwPHAHcCHwM3L5b7DLA\nBUp2O3YL9S3pnnQc5/fUt4g7GbgcWNyQX0REROSAMgwDs9VAzFYD8ZM34G2aXb86KFYGdivMdsc3\nucZP1pCqWo7ZZiiGse/2aunDMheS7Neex2jYrydQvo7Qw38l+OTdeCPGkxx7NuluzW/f2KvI4tZj\ni/nFkCKeX1fL1GVRFlQkmo3f05yyOHPK4hxWYHJtSYTL+oVpm5epU6+IiIiIiIiI7I+c9uJwXTf7\nfiX7N07ScZzxwH8B51K/gmcrcC9wi+u6sX1cX+E4znHAbcB11O9TtAn4M3Cr67q1B3D6IiIiIk0Y\ndhH2YedidZ9MetcS/MQujIDdJM7bPIdE6V0Y+Z2xupyB3Xk8RrC45eNV7cQ3jM8LQQBGvA577gvY\nc18g5QwiecrZeEefAFbmr4x5lsGFfcJc2CfM4m0J7l0e5anVMepS2c1hfU2KW96v4reLqpjcK8yU\nkghD2wdb/FlEREREREREJDPD3+2Hf0s5jvOfwCuu67672/ts+a7r/veXHvwbprKy8sv/h5SMSktL\nAejXr9/XPBORg4fuG5GWO5juG9/3qX1vCn5st+0LAzZm+xOwu00kUDQAo5m9fTIxtpbXF31en4UR\nrcoYky5ugzd6EsnRE/HbtN9nzp3xNA+XRrlveZQ11VlWg3YztJ3Nd0oiTO4VJs9Sq7hvqoPpvhH5\nptB9I9Jyum9EWk73jUjLHYz3TXFxcdY/mPd3JdB/ATXAu7u994FsJuADh0wRSERERORA86Nr8GPl\njQ+mk6S2vEZqy2sECnpjdZ2A1fFkDCt/3/k6dCFx4XdJnHM11nuvYb/6HOYat1FMoHIHwecfwJ7+\nELHfTMPv0mOvOVuHAvxwYCHfP6KAV8vi3Lushlc2xsn2aZkPtyX53lu7+NXCKi7vF+bqkgg9C3O6\neF1ERERERETkW2N/f1FfDSzc472IiIiIHACBgt7kj3gAr/xFvPIX8RM7G51P16wm4f6NxMqpWJ1O\nxu46kUBBz30nDobwTjgd74TTCaxejv3qs1jvvYaRTH6Ru0tP/M6HZT9Xw2BctzzGdctjbbXHfcuj\nPFQaZWc8u3LQjniaOz6p4a+f1DC+ex5TSiKc3DVEoAUrnURERERERES+7farCOS67gN7ey8iIiIi\nuRXIa0+w9xXYPS8hte0dkhtnkt71UeOgVAyvbAZe2QzM9qPIO/JXWedP9y4h3vvnxC+6AfvNl7Bf\ne55AxSaSY8+GDAUYc/F80p2643fq1mzOnoUWtx5bzM+HFPHMmhj3Lo+yaFuy2fjd+cDLG+p4eUMd\nvQtNrimJcFm/CK1Cgaw/k4iIiIiIiMi3lXpriIiIiByEjICF1eFErA4nko5uIFk2E2/zbPCijeIC\n4eaLM3tV2IrkGReRPO18zCULSJUMahqTiJN37+8xqivxjhxGctxkUkcOg0DmAk2+ZXBpvwiX9ovw\nQUWCe5bV8OzaWuJZbh20ujrFrxZW8ZsPqzm/Tz5TBhRwZBv7y30+ERERERERkW+B/SoCOY5z335c\n7ruue+3+jC8iIiIiEIh0J9T/uwT7XIW3ZR5e2UzS1aVAAKvrGU3ifd8nvXMRgdaDMAxzH8lNUoOP\nz3jKWjAPo7qy/u8fL8D6eAHpDl1InnIOyRNOg0hhs2mPbh/k6PZt+M2wFA+tiDHVjbKhJrtqUG3K\n58EVMR5cEeP4jkGuH1DAhB552AG1ihMRERERERHZ3f6uBLpqP671ARWBRERERHLEMPOwu5yG3eU0\nUlUu6cplBPI6NIlL7/yIusW/wMjrgNXlDOwup2EEW7V4PPPT95scC2wtJ/TY3wk+PRVv5DiSY88h\n3a13szna5pn8+KhCfjiwgFc21nHv8iivlsWznsP8LQnmb9lBl3CAa0oKuLJ/mPb5+yhsiYiIiIiI\niHxL7G8RaExOZiEiIiIiOWUWOZhFTsZzybIZAPh1W0muvp/kmocx24/E7jaJQPERGBn2/skkft0v\nSJ40keCcZzA/eBMjnf78nJGow547HXvudLwBQ0iOPYfUkBFgZv76aQYMTj8sn9MPy2dVpcdUt4ZH\nSmNUJvys5lIeS3Pbh1X8cXEV5/TK5/oBBQxtH8zqWhEREREREZFD1X4VgVzXfT1XExERERGRA8/3\noqS2L9jzIKmtr5Pa+jpGpAd21wlYnU7BsCJ7T2YYpEsGUVcyCGPHVuzXXsCaN4NA9a5GYdayRVjL\nFpFu25G6H/6adK+SvabtU2zx22Gt+NXQIp5aXcs9y6J8vCOZ1edLpOHxVbU8vqqWY9rbXDeggLN7\n5hM01SpOREREREREvn0y79orIiIiIockw4qQf/w07F6XY4TaNTnvR9eRWPEPYm9fSnz5HaSqV2eV\n12/TgcR53yH258epm/JzUr2arkIyolWkO3XPeq5hK8AV/SO8cWZ7Xj6jHef3zsduwbfX9yuSXPfG\nTgY+uZnfLqpiUyy7PYdEREREREREDhX7tRLIcZzXgDtd131yt/fZ8l3XPWV/xhcRERGRlguE2hLs\ndSl2j4tIbX+X5MaZpHd+2DgoVYdX/iJe+YsEigeSN+T3GIEsvjoGQ3ijTsUbdSqBVUuxZz+DtWAe\nRsojOfJUyG+6usjYvhW/uDVYdsaUhmEwvGOI4R1D3HZsivtXRJm2PMrm2nTG+D1trU3zx8XV/Pmj\nas7smc91AyIM7xDMuu2diIiIiIiIyMFqf/cEGg3M2ON9trJr8C4iIiIiB4QRMLHaj8RqP5J0rIxk\n2Sy8TS+DV9M4zo5kVwDaQ7rP4cT7HE7i4u9hzZuBd+xJGePy7rwVY2s5yTFn4o2ZhN+qbbM5O4ZN\nfja4iJ8cWcj0dfWt4t7dmshqPp4Pz6yp5Zk1tRzVxua6wyOc2ytMvqVikIiIiIiIiBya9rcI1AvY\nscd7ERERETnIBMJdCfWbQrD3FXhb38Arm0m6ajkAVtdJGa9J16zFiPTY54oav7gNybOuyDzuulLM\n0k8ACD13P8HpD+MdexLJcZNJ9zkcmskdNA3O7R3m3N5hFm9LcM/yKE+tjhHPsuPbkh1JfvDWLv5z\nYRVX9A9zbUmE7gX7+9VYRERERERE5Jtlv37puq67bm/vRUREROTgYpgh7M7jsDuPI1VdSmrL65ht\nhjaJS8e3U7vw+xj5nbG7TsTqNBbDLmjxeParzzceP+Vhv/sq9ruvkurZn+TYc/CGnwzBULM5BrcL\n8vdRQW49pogHV8SYujzKxmh21aAd8TT/+3ENf/2khjO653Hd4QWc0Emt4kREREREROTQcEAed3Qc\nxwZGACVAa+pbv+0APgXedV03uwbuIiIiIvK1MQv7YRb2y3jOK38J/BR+bCOJ0rtIrJqG1elk7G6T\nCBT0znqM+AVTSHfsiv3acwS2bWk8/toVmPf+Af/xu0ieNJHkyWfht+3QbK62eSY/OaqQHw4s4MUN\nddy9tIY3N2fXKi7tw4z1dcxYX8fhrSymDCjggj75ROxA1p9FRERERERE5Jsm50Ugx3F+APwaaNVM\nyFbHcf7Ddd0Hcj22iIiIiBx4vp+uLwLtLh3HK38Rr/xFAsWHY3edhNlhFEbA3nuygmKSEy4mefoF\nmIvnY89+Bmvph41CjOpKgjMewZ75GKmjR5E452rS3ZrvQmwFDCb1yGdSj3yW7kxyz7IaHl9VS8zL\nbkvKpbs8fjJ/F7d8UMll/cJMKSmgV5FaxYmIiIiIiMjBJ6ePNjqOMwX4K/Wrfz4A7gf+DPwFeABY\nDHQE7nMc55Jcji0iIiIiXw3DCJA39E/Yh10AdlGT8+nKpcSX/oHY25eTWHU/6bqKfScNmKSGjqLu\nZ38m+tv761f9hPIaj+unsd5/A1Je1nM9vLXNX0a0ZukFnfjNsGJ6FppZX1uV8PnHp1GGPr2FC2dv\nY87GOtJ+doUkERERERERkW+CXD/S+EOgCjjddd35mQIcxxkFzAR+Cjya4/FFRERE5CsQyO9EsO81\n2L0uw9v6Bl7ZDNJVyxsHJXeRXPcvkuuewGx/HKGSH2NkKBrtye/ak/iVPyF+/hTst17CnvMsgS1l\nAKT6H0m6R4YWdb4Pe9nHp1UowPePKOCGwyPM3hjn7mU1vFoWz+qz+sDLG+O8vDFO3yKL7wyIcEnf\nMEVBtYoTERERERGRb7ZcF4H6Af9srgAE4LruW47jPA5cluOxRUREROQrZphB7M5jsTuPJVVVilc2\nHW/LPEjvvhdPmnT1arAiLUseLiA5/jySYydjfrIQe86zJE84LWNo8JG/EajYTHLcZFJHHN1sQShg\nGJzaPY9Tu+dRWpnknmVRHlsZozqZ3QqflVUe//FeJbd9UMXFfcNMGRChf6t9tLwTERERERER+Zrk\nughUA2zZZxSUNcSKiIiIyCHCLOqHWXQjwb5T8Da9QrJsBn7tJgCsrhMwjKat2PxkNYZduPfEgQCp\no4aTOmp45vOxGuw3ZmHE67AWv0O682Ekx55DcuSpkB9uNm2/Yps/HteKm48u4rHSGPcsj1JamV2r\nuRrP557lUe5ZHmVMlxDXDYgwvlseZqD51UgiIiIiIiIiX7VcF4HmAcOyiBsEvJHjsUVERETkG8Cw\nC7EPOxer+zmkdnyIVz4Lu8upTeL8dIraBd/DyOuA3W0SZvuRGIGWr6qx33oJI173+fvApvWEHrqD\n4FP3khx1Gsmx5+B36tbs9YV2gOsOL2DKgAjzyuP8c1mUlzfUke3uP3PL48wtj9OjwOQ7JREu7x+h\nVUit4kREREREROTrl+si0L8DbzqOcyNwh+u6qd1POo5jAN8DjgVOzPHYIiIiIvINYhgBrLbHYLU9\nJuP51PYF+PEK/HgF8cpPMYKtsbqchtXlDAJ57bMeJ9V7AN7QUZiL3sHw01+MXxslOPtpgrOfxjtq\nOMmxk0kdeSwEMhdoDMNgTNc8xnTNY221x9TlUR5cEaUykV05aF1Nipvfr+K3i6q5oE8+1w0o4Ig2\nahUnIiIiIiIiX5/9KgI5jnNfhsMfAH8CfuU4zvvAViANtAOObnh9Hvg+8NP9GV9EREREDl7JjdMb\nvfcTO0mufYzkuscx2x2H3XUSgdaDMZrZ3+cz6b5HUPdvt2FUbMJ+7Xns12diRKsbxVhL3sNa8h7p\njt1Ijj2b5KjTIFzQbM6ehRb/fWwxPx9SyJOravnnshqW7syuVVxtyueBFTEeWBFjZKcg1w0oYMJh\neVhqFSciIiIiIiJfsf1dCXTVXs61AsY2c+5swEdFIBEREZFvrWCfq/HK2uFtmQfpxBcn/DSpindI\nVbyDEe6G3XUiVudxGFZkr/n89p1JXPhdEmdfhTV/DvacZzE3rGoUE9iykdAj/4cfLsQb1bRF3Z7C\nVoArnQhX9A/z9pYEdy+tYeb6OlJZ9op7e3OCtzfvoFvE5JqSCFf2D9M2r+neSCIiIiIiIiIHwv4W\nga7OySxERERE5FvHLOqHWXQjwb5T8Da9QrJsBn7tpkYxfmwjidK7SKyahtXpZOxelxEItd174lAe\n3uiJeCdNIOAuITjnGcwP3sRI17eKSxe2whs+pkVzNQyDUZ1CjOoUYmONxzQ3yv1ujO3x9L4vBjZG\nU9z6QRV/WFzFub3CXDcgwuB2wRbNQURERERERKSl9qsI5LruA1/mOsdxwoAapIuIiIgIhl2Ifdi5\nWN3PIbXjQ7yN00ltX0D9wvEG6TjepjkEe1/ZgsQG6ZJB1JUMwti+FXvuC9jzpuONngh20wKMuWAe\ngW2bSZ40ASKFzabtVmBx89HF/PugIp5ZE+PuZVEWb09mNaV4Ch5dGePRlTGGdwgyZUCEM3vkEzTV\nKk5ERERERERyb39XAn1ZP6G+lVy/r2l8EREREfmGMYwAVttjsNoeQ7p2M17ZLJKbXoJkFQBmh1EY\nwVZNrvP9FIax9xZrftsOJM77DokzL4dUhr19fJ/gc/djlq0l+Ow0vOPHkRw3mXT33s3mzLMMLukX\n4eK+YRZWJLh7WZTn1tTiZdkq7r2tCd7bmqBTfiVXORGudiJ0DKtVnIiIiIiIiOTOASkCOY5TAhwF\n5GU43Rq4Fuh4IMYWERERkYNfIL8Twb7XYPe6DG/rG3hlM7C7TcoYG19yKwRM7K6TCLQejGHsZVVN\nMASEmhw2ly/GLFsLgJGIY78+A/v1GXglg0mOm0xqyAgwM391NgyDYR1CDOsQ4rZjUw2t4qJsqc2u\nVdzm2jS/X1zN/yyp5uye+Vw3oIBj2tt7/xwiIiIiIiIiWchpEchxHBt4CDh/H6EG8EouxxYRERGR\nQ49hBrE7j8XuPDbj+XSsnNT29wBIVbyDEe6G3XUiVudxGFYk+3GqdpEubk2gcmej49byxVjLF5Nu\n04HkKWfVt4orbLoa6TOdwiY/H1LETUcV8sK6Wu5eGmVBRSKrOSTT8OTqWp5cXcuQdjbXDShgcq98\nQmoVJyIiIiIiIl9SIMf5bgIuAGLA68BM6gs+bwMvA7uATcC/NcSJiIiIiHxpybIZjd77sY0kSu8i\n9valxJf/lXTN6qzyeMPHEPvzE9Rd/0tSfQY0OR/YsZXQk/cQ+cn5hO79A4F1pXvNFzQNzusd5pWJ\n7Zk7qT0X9w0TbME370Xbktzw5k6OeGIzt31QRVk0lf3FIiIiIiIiIg1yXQS6BCgD+rmuezLwo4bj\nt7uuewbQB3gPGAVU53hsEREREfmWsdoOw2w7nPrnjnaTqsMrn0Xtgu9R+8GNeJvn4qf3sSLHsvFG\njKP2P+8kdstdJEeMx7fsRiFGMon95ouE/3MK9itPZzXHIe2C3HlCa5Ze2ImbhxbRtQX7/myrS3P7\nkmqOenIzV83dwTub4/h+lpsOiYiIiIiIyLderotAfYFHXdfd3PC+0S9U13V3AVcAx1K/akhERERE\n5Esz2wwmb9CvyT9+GvZhF4Bd1CQmXbmU+NI/EHv7ChKr7icd377PvOneJcSv/wWxvzxBfPI1pFu1\na3TeNwy8wce3aK7t8kxuGlTIR+d35IExbRjRMZj1tSkfnltbyxkvbuOEFyp4cEWUWk/FIBERERER\nEdm7XBeBAkDlbu/jDa+fN2R3XTcKPAVcleOxRURERORbKpDfiWDfawiPeJjggJ8SKCppGpTcRXLd\nv/BrNzc91wy/qDXJs64g9j//ou57t5DqfyQAqUHH4Xfo0iTeKF9HYPXyvea0AgZn9cxn1hntefOs\nDlzRP0x+C/b9+WRHkh+9vYvDn9jELQsrWVftZX2tiIiIiIiIfLtYOc5XDgze7f22htfD94irBnrm\neGwRERER+ZYzzCB257HYnceSqirFK5uBt2UepOufTQoU9CJQvOdX0yxYFt7wMXjDx9TvB2RkfpYq\n+MJD2PPnkOozgOTYyXjDRsMeLeV2d2Qbm7+ObM2vjynmoRVR7l0eZX1Ndvv/7Iz73PFJDX/7tIbT\nuudx/YAIJ3YOYRjZF5RERERERETk0JbrlUBzgHMdx7nDcZyurut6wCrgWsdxegI4jpMPnAXsyPHY\nIiIiIiKfM4v6ERrwE8IjHybY9zqM/C5YXSdmLJIkVj9EfNmfSVWV7jNvukc/0of1aXLc2LUda8G8\n+rFXLSPvn78hfOMFBJ+ZhrFzW5P43bUOBfjRkYUsOrcjj5zchtFdQtl9SCDtw6z1dZz18naOf24r\nU5fXUJNMZ329iIiIiIiIHLpyvRLoVuoLPD8AXgTKgHuA3wNLHcdZBvQAWgPTcjy2iIiIiEgThl2I\nfdhkrO5ng9+0OOKnEiTLpkOyCm/TKwSKSrC6TsTqcCKGmf2+PeaSBRipxq3ZApU7CT7/APaMh/GO\nOYnkuMmk+x4BzazWMQMGE3rkM6FHPu6uJPcsi/LYyhjRLPf/Wb7L46b5lfz6gyou7RtmyoACehfl\n+iu/iIiIiIiIHCxyuhLIdd2N1LeD+29gRcPh24H7gRAwBGgDvAb8v1yOLSIiIiKyN4YRwAg0LYh4\nW9+AZNXn79NVy0ksu53YO5eRWHkv6dpNWeX3Tjyd2G33kRw9CT/YeCWPkUphv/ca4dt+QP4t12O9\n+SIk4s1kque0srn9+FYsvbATvxtWTO9CM6t5AFQlfO5cGuXop7dwwextzNlYR9rPrpAkIiIiIiIi\nhw7D/4p+DDqO04n6VUBlDcWiQ0plZaV+VedYaWl9O5Z+/fp9zTMROXjovhFpOd03ktrxIYk1D5Ou\nXNpMhIHZ9hisrhMx2x6DYWRRjIlWY78xC/vV5whUZC4i+YXFxC+6AW/UaVnNM+37vFoW5+6lNcwu\n23sBKZM+RSZTBhRwSd8wRcH9exZM941Iy+m+EWk53TciLaf7RqTlDsb7pri4OOvNYL+y3hCu624G\nNn9V44mIiIiIZMNsM5T8NkNJVa/GK5uBt+U1SNXtFuGT2r6Q1PaFGHmdsLpOwO48HiNY3HzSSCHJ\n0y8keep5mIvfxZ7zDNanHzQKMaor8cOFWc8zYBiM65bHuG55rKr0uGd5DY+WxqhKZvcs0qqqFP/x\nXiW3fVDFxX3DTBkQoX8rO+vxRURERERE5OCT8yKQ4zgFwHeBCUAJ9fv/+MAO4FPgeeBe13Vb/vii\niIiIiMgBYhb2xiz5EcG+1+JtmkOybAZ+bEOjGL9uM8lVUzHMPOxuk/adNGCSGjqS1NCRGOXrsOc8\ni/3WSxjxOtLtO5MafFzTa+K1gAGhvGbT9im2+P3wVvxyaBGPr4xxz7IobqXXbPzuajyfe5ZHuWd5\nlDFdQlw3IML4bnmYgawfJBMREREREZGDRE6LQI7jdAdep77t256/Ijs3/DkF+J7jOCe7rrsll+OL\niMq7y6gAACAASURBVIiIiOwvw4pgdz8Lq9uZpHctIblxOqlt74Cfrg8ww1idTmlxXr9LDxJX/JjE\ned/Bfuul+lVAgaat5ew5zxKc+RjJkyaQPPks/Padm81ZaAf4zoACri2J8PqmOP9cGuWlDXVk26d4\nbnmcueVxehSYfKckwuX9I7QK5XTbUBEREREREfka5Xol0B+BnsDLwN+Aj6lfAWQAbYBBwI+oLwT9\nAbgqx+OLiIiIiOSEYRiYrQdhth5EOr4Nr+xFvPIXMduPxLDCTeK9rW+RqvwUu+tEAuGuzScOF5Ac\nf17mcykP+9XnMaLVBGf9C/vFJ0gNOZ7k2MmkDh8KRubVOoZhMLpLHqO75LG22mPq8igPrYiyK5Fd\nOWhdTYqb36/it4uquaBPPtcNKOCINmoVJyIiIiIicrDLdRFoLPCW67qnZzhXA6wHpjuO8w5wRo7H\nFhERERE5IAKhdgR7X47d8+I99gv6QnL906SrluFteBazzVCsrpMw2w3DMJqu9mmOuWg+ge1fLJY3\n/DTWh29jffg2qS49SY47B2/EOMhrWoT6TM9Ci/8+tpifDynkqdW1/HNpDZ/uzK5VXG3K54EVMR5Y\nEWNkpyDXDShgwmF5WGoVJyIiIiIiclDKda+HCPBSFnFzgIIcjy0iIiIickAZAQvDbvo1NlW9knTV\nsi/e7/iQ+Me/pvadq0ms/Rd+YmdW+VNHHE3dFT8m3fmwJufM8rXkPfAXIj85n+Cjf8fYUrbXXGEr\nwBX9I7x1Vgdmnt6Os3rmYbaglvP25gRXzt3B4Ke28Ocl1WyvS2V/sYiIiIiIiHwj5Hol0CqgVRZx\nxQ2xIiIiIiIHPy+KEemJH13b6LAf30py9f0k1zyM2eGE+lZxxYdjNNPWjfww3iln4518FuanH2DP\nfgbzo/kY/hdt3YxYlODLT2K/8hSpo4aTOOMi0iWDm52aYRiM7BRiZKcQG2s8prlR7ndjbI+ns/po\nG6Mpbv2gij8sruLcXmGuGxAhktWVIiIiIiIi8nXL9UqgO4ELHcdpthDkOE4RMBG4K8dji4iIiIh8\nLczWg8gfdid5Q2/H7HAS7NkCzvdIbZlL3Yc3UbfweyTLZuJ7tc0nNAxSA4+h7ie/JfbHR0icdgF+\nuPEKJMP3sT56F9NdkvU8uxVY3Hx0MZ9e0Il/jGrF4LbZ7/sTT8GjK2OMnl7BtR+FeKXCJJnObs8h\nERERERER+Xrs10ogx3H27FMxAxgILHIc5/+A+cBWIA20A4YBPwJeBh7an7FFRERERL5JDMPAbDUQ\ns9VA0vEdeOUv4ZXPwo9vaxSXrllDwv0b6eg6Qv2/t8+8focuJC7+HonJV2O9Mwd7zjOYG9fUn7Ns\nvDGTWjzXPMvgkn4RLu4bZmFFgruXRXluTS1eljWdJdUmS1yTv63fzNUlEa7qH6FjOPu9j0RERERE\nROSrsb/t4NYCmX4qGsAf93JdH+C6HIwvIiIiIvKNEwi1IdjrEuweF5La/i7JjTNI71zUKMbucnrL\nkoby8cZMwhs9EXP5YuzZz+CHC/CLWjcJNZe8h/3KUyTHTiZ11HAIZG4AYBgGwzqEGNYhxG3Hphpa\nxUXZUptdq7jNtWl+t6ia2z+q5uye+Vx/eAHHtA+27HOJiIiIiIjIAbO/RZj1ZC4CiYiIiIh86xkB\nE6v9SKz2I0lHN5Asn4W36RUCkV4ECno1iU/XrMWreAury+kEQm2bSWqQGjCE1IAhkM5crLFnP4P1\n8UKsjxeS7tCF5CnnkDzhNIgUNjvXTmGTnw8p4qajCnlhXS13L42yoCKR1edMpuHJ1bU8ubqWoe1s\npgwoYHKvfEJmM3sfiYiIiIiIyFdiv4pAruv2zNE8REREREQOaYFId0L9rifY+0r8+I6MMcmNL+CV\nzyK59jHM9iOwu04k0OooDKOZYkqGFT7G5o1YS977ImRrOaHH/k7w6al4I8eTHHsO6W5NC1CfCZoG\n5/UOc17vMIu21beKe3p1jER2i4P4cFuSG97cyc0LK7myf5irnAjdC9QAQERERERE5OuQuS+EiIiI\niIgcEIaZRyDcpclx34vibXmt4U2K1NY3qVv0M2rfm0Jyw7P4yeosR/BJDhuDv0eByEjUYc99gfAv\nrybvDzdifvAmpFN7zTSkXZA7T2jN0gs7cfPQIrq2YN+fbXVp/mdJDYOe2sIlr25nblkdaV9NBERE\nRERERL5KB+SRPMdxegDnA4OAdkAaqAAWAv9yXXf7gRhXRERERORglY6VY9hF+Km6Rsf92EYSpf8k\nsWoaVocTsbpOIFBU0uzqIL9Td+Lfv4XEjgrsuS9gzZ1OoHpXoxhr6YdYSz8k3a4jyZPPJnnSGVBQ\n3Ozc2uWZ3DSokH87soCZ6+v43w8qWFSVXUEo7cOs9XXMWl9H3yKLa0oiXNI3TKuQnkcTERERERE5\n0Aw/x0/jOY5zE/Bb6gtMe/4y9YEYcIPrug/ndOCvWWVlpR5rzLHS0lIA+vXr9zXPROTgoftGpOV0\n38g3ie+nSG1/H69sBqnt79Pc9puBgt5YXSdgdRyDYYX3njSZwFowD3v2M5hrlmcOOe4U4jfcnPU8\nS0tLWVFj8HKsLU+uqqU21bKvwvmmwfl98rm2JMKgtsEWXStysNK/NyItp/tGpOV034i03MF43xQX\nF2e9AWtOVwI5jjMJ+BNQDTwKLKB+BVAAaA+MAC4EpjmOs8p13fm5HF9ERERE5GBmGCZWu+FY7YaT\nrt2EV/4iyfKXIVnZKC5ds5qE+zdSFe+QN/g3e09qB/FGjscbOZ7AqqXYs5/BWjAPI+V9HpI8+awW\nz7V/gc+EIa359THFPLQiyr3Lo6yv2Xt7uc/UpnweXBHjwRUxhrUPcu2ACGf3zCdkZv07RkRERERE\nRLKQ63ZwPwS2AsNc112f4fxUx3H+CMwH/h2YnOPxRUREREQOCYH8zgT7XIPd63JSFe+QLJtJeteS\nRjFWp7EtypnuczjxPoeTuOgGrHkzsF97Hr+4Nen+RzaJNSo2Yb39Ct7oifit2jabs3UowI+OLOT7\nRxTw8sY67l4WZV55POs5LahIsKAiwS/eq+SK/mGuLolwWMEB6VotIiIiIiLyrZPrX1dDgcebKQAB\n4Lqu6zjO08CZOR5bREREROSQYwRsrI4nYXU8iXR0PcmyWXib54BhYnYY2STe96Ik1jyK3eU0ApHu\nGXP6rdqSPPtKkhMvwdi5DTLsL2TPfYHgzMcIvvAg3tEnkjzlLNLOoIyxAGbA4IzD8jnjsHxW7Eoy\ndXmUx1bGqEpm1ypuezzNXz6u4Y5PahjfLY8pAyKM6RIi0Mx4IiIiIiIism+5LgIVApuziFsPtMrx\n2CIiIiIih7RA5DBC/b9LsM9VpKPrMQJN99PxNr+Kt+FpvA1PE2g9GLvrGZjtjscI2E0TWjZ++85N\njyfi2G/MAsBIpbAXzMVeMJdUl554p5xFoFMf0qH8ZufZv5XNH45rxc1HF/HU6lruWVbDpzu9ZuN3\nl/bhpQ11vLShjt6FJteURLi0X4TWoUBW14uIiIiIiMgXcl0E2g44WcT1aYgVEREREZEWMsw8zKL+\nTY77vk+ybNbn79M7FxPfuRgj2Bqr86lYXU4jkN9pn/kDW8vxQ3kY1Y33IjLL12I+dAcD7RA7jjyO\nwOQrSXfv3WyeAjvAVU6EK/uHeW9rgqnLozy3tpZkOrvPubo6xa8WVnHbh1Wc1zvMd0oiDG7XtPAl\nIiIiIiIimeX6cbq3gMmO44xuLqDh3AXAmzkeW0RERETk2y1ZmfGwn9hJct2/qJ1/NXUf3Yy37V18\nP9VsmnS3XsT+9Ci1P/4t3pHDmpw3k3Haf/g64V9dQ/5vfoT17qvgJZvNZxgGx3UMcc9Jbfj0gk7c\nPLSIbhEz649Vl4KHS2OMnl7BKdO38tjKGHVedm3mREREREREvs1yvRLod9Tv9TPHcZzXgPnAVsAA\nOgAjgZOABPDb/RnIcZw2wC3A2UBnYBswC7jZdd1NLcyVB3wE9AfGuK47b3/mJiIiIiLydTCCrcgf\ndifpqmV4ZTPxtr4B6d2LMz6p7QtJbV+IEWqP1eW0+tVBobZNkwVMUkNGkBoyAmNLGfbcF7DfeBEj\nWtUozFyxBHPFErwBQ6j7j7/sc44d8k1uGlTIvx1ZwMsb6pi6PMpr5fGsP+MH25J88OZOfrmgksv7\nhbm6JELPwlz/rBERERERETk05PTXkuu6ixzHORe4DxgLnLLb6c92dC0DrnZd96MvO47jOPnAPKAE\n+D/gfaAf8FPgZMdxjnZdd2cLUt5MfQFIREREROSgZhgGZvHhmMWHE+x3Pd6m2STLZuHXljWK8+MV\nJNc8hFc2k/yRD2EYza/M8Tt2JXHRDSQmX4O1YC6pmY8TKV/TKMY79qQWzdMKGEzokc+EHvmsrEwy\ndXmUR1bGqEpkt8JnRzzNHZ/U8NdPahjfLcS1JQWM7RYiYBj7vlhERERERORbIuePzLmuO9NxnMOA\n04BjgPaAT/2KoIXAS67rZrcrbPN+DBwJfN913X98dtBxnI+AZ6kv6tyYTSLHcY4E/h1YBAzZz3mJ\niIiIiHxjGHYR9mHnYnWfTHrnRyTLZpDaNh92awVndRq71wJQI8EQ3qjTKO3Yh/zytfRZuQhr/hww\nTbwR45rGJxPYc18gOWI8FBQ1m7Zvsc3vhrfiV0OLeHpNLfcui7JkR/Pt5XbnAy9vjPPyxjg9Ckyu\nciJc1i9M+/zs282JiIiIiIgcqnJaBHIcpytQ47puJfB8w58D4QogCkzd4/jzwEbgMsdxbnJdd6+P\nETqOEwDuAdYB/wTuOgBzFRERERH5WhmGgdlmMGabwaTj2/E2vYJX9iJ+vAKr6+lN4n3fJ1H6T6x2\nwwm0HoRhNN1KtLZLT+InjSN+4Xcx15VCfqRJjPX+G4Qe+T+CT9yNN/xkkqecTbp3SbPzjNgBrugf\n4fJ+Yd6vSHLP8hqeW1NLIp3d51xXk+LXH1Tx20VVTOqRzzUlEUZ2DGJodZCIiIiIiHxLGb6fuw1V\nHcepBX7tuu7vc5a06RhFQCXwpuu6J2Y4/zQwGejjuu7qfeT6EXAH9a3rugPT+JJ7AlVWVmb8D1la\nWtrSVCIiIiIiB56fxk6sIxnq1eRUsG4l7SruAMCz2hGLHE8schxps/nVPJn0u/8PFGxc2ehYtHMP\nth09hp1HHItvB/eZY2cSnt9s8cxmi03xpsWofemZn2ZyJ48JHT2KtHWQiIiIiIgcRPr165fxeHFx\ncdZPurX8V9TelQLdcpxzTz0aXjc2c359w2vvvSVxHKc78BvgIdd1X83R3EREREREDg5GIGMBCCAc\nffvzv1veNooqp9Ox/GZab5tKqHYZ+PtemmPGqgnt3NrkeGTTOnrMuJ+Bd/w7XWc/QXBH05jdtbbh\nqu4ezx5Tx/8MiHN869Re4/e0tjbAn9cEOWNBPv+1IsjHVQFy+ByciIiIiIjIN1qun4W7AfiX4zgr\ngAdd192V4/wAhQ2vsWbOR/eIa86dQAK4KReTak5zlTrZt89WUem/oUj2dN+ItJzuG5HGfN8nXhck\nFTOo33GnnkGa/NrF5NcuxjPbECsYQceBFxMItW02V/yvT5N6/w3sV5/HXLGk0TmrLkaH92bT4b3Z\neEccQ/LkM0kNHgFW8z9RSoBrgdVVHvctj/JwaZRdiewqOvG0wcytFjO3WgxsY3ONE+H8PvkU2rl+\nLk4kM/17I9Jyum9EWk73jUjLHer3Ta6LQN8H3gd+B9zuOM46YAeQ6XE933XdkTkePyuO41wETACu\ncV234uuYg4iIiIjIN5FhGOQd+Z+ka7fgbXoZb9Mr+PFtjWKs1A6KKmdQ+84szLbDsbqcjtn2aAzD\nbJzMsvGOOwXvuFMIbFiN/drzWO+8glFX2zjs0/exPn2fdKfuxH73AAT2XpjpXWRx27Bifjm0iKfX\nxJi6PMqibcmsP+MnO5LcOH8X/7mwkvP75HO1E+GotvtuTSciIiIiInKwyXUR6KI93vdp+JPJl23C\nUNXw2nTn2XoFe8Q14jhOG+r3AXrddd1pX3IOIiIiIiKHtEB+R4K9r8DueSmpHQvxyl4ktX0hsFsr\nOD9Natt8UtveJX/EAxh5HZrNl+7em/iVPyF+wXVY78zGnvMcZvnaRjGpAUP2WQDaXb5lcFm/CJf1\ni7B4W4JpbpQnV9cS87L7qVHj+UxzY0xzYxzT3uZqJ8I5vfIJW1odJCIiIiIih4ZcF4HG5DhfJmuo\nLyA1t/fQZ3sGlTZz/k9AK+C/HMfZPUfrhtf2DccrXNeN7+9kRUREREQOZkbAxGp3HFa740jXVeBt\neoXa9TOwUjs/jzHbHkNgLwWgRvIjeKecjXfyWQTcj7DnTsd6/w0ML0ny5DMzXmLNm0HqqOH4bdo3\nm3ZwuyB3tAty67HFPLkqxn1ulKU7vaw/5/sVSd6v2MUvFlRycd8wVzsRnFZ21teLiIiIiIh8E+W0\nCOS67uuf/d1xnJ7Ut+1uBdQBW4B1ruuW7+cYUcdxlgBDHcfJc123brcxTWAEsMF13fXNpDgFCAJz\nmzn/RMPrGGDe/sxVRERERORQEshrT7DXpaxLHkOobhkdWEJq+7tYXc7IGB9f8Q8MqxCry6lNi0SG\nQbpkMPGSwcSrdmEteZf0YX2bjrl+JXnTbscPBEgNHkFyzCRSA49tdsVQcTDAdwYUcG1JhAVbE9zn\nRnlubS3xTA2qM6hM+Ny1NMpdS6OM7BTkGifCxB75hEwjuwQiIiIiIiLfILleCYTjOGcCfwQy7qLk\nOM5HwM9c1529H8NMBf4KXE99a7fPXAZ0AG7ZbbwSIO667pqGQ9cA4Qw5TwF+DPwC+Ljhj4iIiIiI\n7MkIEM8/grx+Z5OOb8ewWzUJ8RM78cpmgp8iufZRzLbHNOwdNAwjsMfPkKJWeKNOyziUPXd6/ZDp\nNNaHb2F9+Bbp9p1JnjQR78TT8YvbZJ6iYTC8Y4jhHUP8bliKR1fGuN+NsbIq+9VBb29O8PbmBO3y\nKrm0b5irnAi9inL+E0pEREREROSAyekvGMdxJgLPAAFgM+ACOxvet6J+ZdBgYJbjOGfsRyHoLuBS\n4HbHcXoA7wNHADdSX7y5fbfYZQ3zKAFwXfe1ZuberuGv813Xnfcl5yUiIiIi8q0SCLXNeDy5aQ74\nny2/8UltX0hq+0KMYBuszuOxOo8nEO6y9+S+T2BF02ezAhWbCD11D8Fn78MbegLemEl73U+oTZ7J\nDwYW8v0jCnhzc4Jpy6NMX1dLllsHsa0uzR2f1HDHJzWc2DnEVf3DTNDqIBEREREROQjk+jG2XwJJ\n4HLXdZ/a86TjOAZwETCN+tU6X6oI5Lpu0nGc8cB/AecCPwC2AvcCt7iuG/tSsxcRERERkZww7CKM\nvM74dZsaHfcTO0iu+xfJdf8i0Ooo7C6nYrYfhWGGMiQxqP3vezA/fh977guYi+dj+OkvTqdS2Avn\nYS+cR7pjN5KjJ5I84TQobLoyqT6dwYmdQ5zYOcSWWIpHVsaY5kbZUJNlrzjgjU1x3tgUp02ofu+g\nK/uH6a+9g0RERERE5BvK8P0sH3/LguM4NcDDrut+dx9xdwOXuK5bkLPBv2aVlZW5+w8pAJSWlgLQ\nr1/GzoIikoHuG5GW030j0nLZ3je+nya9czHJ8pdIVbwDfjOt2KwIVscx2N3PJhDu1mw+Y/tW7Ddm\nYr0+k8DObZnHtG1if3wUv037rD5LKu3zWnmc+5ZHeXljHekv8a3++I5Bruwf4aye+eRbWh0kmenf\nG5GW030j0nK6b0Ra7mC8b4qLi7P+4ZHrlUAesCGLuA1AIsdji4iIiIjIN4hhBDDbDMVsMxQ/sQtv\n8xySZS/i15Y1DvSieGUzsNqPgL0Ugfy2HUicczWJMy/H/Ohd7LnTMT9egLHbg23pHk7WBSAAM2Aw\nrlse47rlsbHG48HSGA+6UTbXpvd9cYP5WxLM35LgZ+/t4oI+Ya7sH2FgG60OEhERERGRr1+ui0Af\nAAP/P3t3Hh9Veff//3WWmUwmJIEQErawJIRB1rAvAqLs1K2uxaV6t1bq19bW+m3t3d61t97fttaf\nt+3derfWtipVK6LigiKyb7KIyCZoEvZ9CSRkmcxyzpzfH4FAnKAEsYq+n48HD51zPtd1rjNyJMN7\nrus6g7qewIpzfG0REREREfmCMvzN8XW4BjvvahLHNuHsm41zaCkkonXnU3IwWxQltfPcKJg+DOOU\n/X4sG7ffcNx+wzEO78e3+A3sJW9gHisnfsnljV7fXvQ6Xm473FCf0+4d1L6Zzc/6ZvDjPunM3h3h\nyQ9rWLAvesb3eCzm8dcPavjrBzUMaOXjm13TuKpzKs18jV9PRERERETks3auQ6CfAXNDodANxcXF\n/2ysIBQKXQ2MBS45x9cWEREREZEvOMMwsJr3xGreE3/XO3AOLsbZ/xZW1oCGQc9x8Z3TcQ7MxW4z\nDrvNOMxAToPzXqs2xK65jdiVt2KtXYbbZ2jyRWtrSHn2UYxYhEROW+IXfQ1n+AS85i0bHaPPNLis\nYyqXdUxle6XDP0pqeHZLmENNmB307uE47x6u4GerjnFNfiq3htIoyvafcXsREREREZFz4VyHQCOA\nV4CnQ6HQfwIrgUNAAsgGBgEXAC8A14VCoes+0t4rLi7++Tkek4iIiIiIfAEZdhq+dpPwtZuE57lJ\n5z3Pxdk/Fy96iPj2Z4hvfxYrqy92mwlYrYZgmKeEKraNO3BUo9exV87HiEUAMA/tI+WFv+J/6e+4\nRcOIj7oUt9dAMK1G23bOsPnlgEx+1i+DN3dF+EdJDfP3RjnTrYOqHY+nSsI8VRKmd5aPW0JBrskP\nkunX7CAREREREfnsnesQ6CHAAwygy/Ffjbn2eM1HeYBCIBERERGRrxjDSA5h3KPr8KKHTjni4R59\nD/foe+DLwM69BF/b8ZjNOn9s3+a+XXiG0WDvICORwH5vGfZ7y0hktcIZMYn4yIl42a0b7cNnGlze\nKZXLO6Wyq9rh6ZIwz5bWsC985rODNhyNc8+KY/xidSVXdkrllq5BBuX4MYwz3tNVRERERESkSc51\nCPQAnPGX4kRERERERE7LbNYJX+ebcfbPwYscbHgyXomz5xWcPa9gpnfFbjseO3cUhp2W1E/sxu8R\nH3c1vqVvYi+ZhVle1vA6Rw/jf3Uqvtf+gdtzIPGLvobb90KwG/+41KGZzc/7ZXBvUTrz9kaYWhxm\nzp4I7hl+Ego7Hv/cEuafW8Jc0Nzmpq5pXF+QSnag8dlIIiIiIiIiZ8vwPGU258KxY8f0Rp5jpaWl\nABQWFn7OIxE5f+i5EWk6PTciTfevfm48L0GifB3xfW/hli2HRLzxQjMFX4dr8OfffPrOXAdr4zv4\nFr+BtW4FRqLxmTy13/vP0y4v15h9NS7Pltbwj9Iwu6uTl7b7JD4TJuYFuKkwjdHtUrBMzQ76stGf\nNyJNp+dGpOn03Ig03fn43GRmZp7xB4ZzPRNIRERERETknDIMEyurH1ZWP7x4Fc6BBTj73yJRva1h\nYSKKYQc/vjPLxi0ahls0DKO8DHvZbHyL38A8vL++xEvPxC0a1qQxtk2z+HFRBvf0SWfRvihPFdcw\na1cE5wy/KhZPwGs7I7y2M0LboMnkLkFuLEwjP0Mf2URERERE5OzpE4WIiIiIiJw3DF86vrwrsNtf\nTqJqC87+t3AOLgSnBgwTu/UlSW28RAzn4BLsVhdi2Kknj7fIJn7ZTcS/dgPWB2uxF7+OvWYZ8QvH\ng8+f1I+9+A3M3VtxRn6NRIeCRsdnGgaXtAtwSbsAh2pdntsSZmpxDduqznx20L5wgv/eUM1/b6hm\nWK6fmwqDXNEplTSfecZ9iIiIiIiIgEIgERERERE5DxmGgZVRiJVRiL/Ld3APLyMR3ofhb5FU65a9\nQ+yDh4mVPIrdajh2m7GYzXthGMdDFdPE7dEft0d/olUVGI0tme15+N56AWvvDvxzZ+B26oozYiLx\noWMgLb3RMeakWvygVzp39WzGsgMxppbU8NqOWmKNr0DXqOUHYyw/GOPeVce4qnMqNxWmMaCVD8PQ\ncnEiIiIiIvLJFAKJiIiIiMh5zbBSsFuPPu15Z//cun9xIzgH5uEcmIcRaI3dZgx26zGYqa1PFqc3\np7EV3Mytm7H27qh/be0owdpRgn/an3D6jcAZMRG3Rz8wreTxGQYj2qQwok0KRwe7TNtayz9Kaviw\nwjnje6yKe0wtCTO1JEy35jY3Fga5viBITmry9URERERERE5QCCQiIiIiIl9anhvBPbYp+XjkAPHt\nzxDf/gxm897YbcZitxreYLm4UxnxGG7Hrlg7Sz5yPI5v1QJ8qxaQyMrBGTGB+PAJeDltG+0nK2Dx\nf3o0447uabx7OM7TpTXM2FZL9ZluHgR8WOHwi9WV3P9uJePzAtxUGGRs+wC2qdlBIiIiIiLSkEIg\nERERERH50jKsAMFhT+Mcfhtn/1wSFeuTahIVG4hVbCBW8r/YrUYcXy6u58nl4gD3gr7UPvA45s5S\n7KWz8S2fi1FT2aAf8+gh/K/+A/+r/8DpVkR8/DW4/YY3Pi7DYGCOn4E5fn4zKJNXd9TyTGmY5Qdj\nZ3xvjgdv7Irwxq4Iuakmk7sEubEwSGGm74z7EBERERGRLzeFQCIiIiIi8qVm2Kn42ozB12YMidoD\nOAfm4+yfixc50LDQjeAcmItzaAnB4f8EOy2pr0THQmIdC4ldPwVr3XJ8S97E2rgaw2u40Y/94ToS\nod6nDYFOleYzuaEwjRsK09h6zOHZLTX8szTMgdoz3zzoYG2C32+s5vcbqxmS42dylyBXdk4l029+\ncmMREREREfnSUggkIiIiIiJfGWZqa/ydb8TXaTKJik31oQ9upL7GzhmO0UgA5HkehnF8yTWfH3fg\nKNyBozCOHsZ+ew6+pbMwD+6tr48Pn5A8gEQCo7Icr3nLRsdXkGlzX/9MftY3gwV7ozxTWsObqija\n2gAAIABJREFUuyPEzzwPYuWhGCsPxbh3VQWXdkxlcpcgo9qkYGm5OBERERGRrxyFQCIiIiIi8pVj\nGCZWi15YLXrhL7yjwXJxduuxjbaJrP0phj8Tu/VorKz+GGbdxykvqxXxy24kfukNmCUb8S2ZhVFd\n2ei+QNYHawk8/GPc3kOIj5yI22co2Mkfy2zTYFxegHF5AcoiLs9vreWZkho+qHDO+B4jLry4rZYX\nt9XSJmhyXX6QyYVBujXXcnEiIiIiIl8VCoFEREREROQr7aPLxRmBnKSaRHhv/X5C7qEl4MvEzr0I\nu/VozPSudTOEDINEqDfRUG/wvEavZS99EyORwF63HHvdchIZLXCGjsEZPp5Ehy6NtskOWNzZoxn/\np3saa8viPF1aw0vbaqmMN36NxuwPJ/if96v5n/er6ZvtY3JBkGvyU8kKWGfch4iIiIiInH8UAomI\niIiIiBxnprZu9LhzYEHDA/FjOHtew9nzGkYwD7v1aOzcizFTc+vOG40svVZThf3u4obXqyzH/9YL\n+N96AbdDAc6F43GGjG50uTjDMOjXyk+/Vn5+NSiTmTsjPFNSw9IDsSbd49qyOGvLjvHz1ceYkBdg\ncpcgY9sH8Gm5OBERERGRLx2FQCIiIiIiIp/AzOyG1XIQ7tF3wWu4QY8X3k1821PEtz2F2bxXXSCU\nMyJ5X6FAKpHv/xe+JbOw1i7HcBsu7Wbt2oq160/4n38Mt9cgnAvH4fS9EPwpSeMJ2ibXFwS5viDI\njiqHZ0vD/LM0zN6we8b3FE/AzJ0RZu6MkB0wuSa/bv+g3lm+k3sfiYiIiIjIeU0hkIiIiIiIyCew\nWw7EbjkQL1aBc3ARzoH5JKpKk+oSFRuJVWwkVvIn/KG78LUZc/KkZeP2GYLbZwhUVeBbPhd72Wys\nXVsb9GEkEtjrV2KvX0kivTnhR55vNAg6oVO6zc/7ZfDTonSWHojyzy1hZu6IUOue+XJxZZEEj22u\n4bHNNXRvYTO5S5Dr8oPkBrVcnIiIiIjI+UwhkIiIiIiIyBky/M3x5V2JL+9KEjW7cA7MxzmwAC96\nuGFhIobZrPPpO0pvTnz8tcTHX4u5awv223OwV8zFPFbesJvCnh8bAJ3KMg1GtQ0wqm2AyiEJXt1R\ny3Nbwiw/2LTl4jaXO/xidSX/+W4lo9ul8I2CIBM7pJJqa3aQiIiIiMj5RiGQiIiIiIjIWTDTOuAv\n+Dd8+beQqNhYFwgdWgZuGCOtE2az/KQ2bmUJ7pF3sXNHYQbbApDo0IVYhy7Errsd6/13sZe9hb12\nGUY8TvzC8Y1e2z/9LyRa5+EMvAhS05LOZ/hNbu6axs1d09hR5TBtS5jntoTZWX3my8W5HszZE2XO\nnijpvgou65jK9QWpDG+dgqX9g0REREREzgsKgURERERERD4FwzCxWvTBatEHf9f/g1u2Cgyr0X11\nnP1v4ex9g/j2f2BmdMPOHYWVMxIzJavBcnHRmirs1Ytxi4YkX6+8DN+s5zG8BN7T/4PTfwTOheNx\ne/QDM3n5tk7pNj/tm8FPitJZcTDGc1vCvLqjlqr4mS8XVxX3+OeWMP/cEqZN0OSa/CDXFQTp2cLW\n/kEiIiIiIl9gCoFERERERETOEcMKYOde1Og5LxHHObik/nWi8kNilR9C6eOYLYqwW4/CbnUhhp0G\naek4oy5ttB97xTwML1F3vVgU34p5+FbMI9E8G2fYGJyhY0l0KEhqZxoGF7ZO4cLWKTw0JJPXd0Z4\nbkuYRfuinHkcBPvDCf74fjV/fL+a7s1trisIck1+Ku2b6eOliIiIiMgXjX5KFxERERER+RfwIgcx\n7CCeU/WRMwkS5e8RK3+PWPEfsVoOrpsh1HIQhuVP7igewwsEMSLhBofNijL8s6bhnzUNt31nnGFj\ncYaMxmuZm9RF0Da5rqBuNs/eGpfpW+uWiys55jTpnjZXOPznmkruX1PJha39XFcQ5PKOqTRPMZvU\nj4iIiIiIfDYMz2vKd77kdI4dO6Y38hwrLS0FoLCw8HMeicj5Q8+NSNPpuRFpOj03Z8/zPBKVH+Ac\nWIhzaAnEj52+2Api5wzH3+2HGMZHQpVoBPu9Zdhvv4X1/pr6mUGNcUN9iF79bRKh3p84tjVlcZ7b\nEualbWEqYmf3ESfFggl5Aa7NDzK2fYAUS8vFgZ4bkbOh50ak6fTciDTd+fjcZGZmnvEP2ZoJJCIi\nIiIi8i9iGAZWZneszO74C6fglq/DPbgQ5/BycGsbFrthEpFDyQEQQEoAZ+gYnKFjMMrLsFfMw142\nG2vvjqRSq3g9nMFHRMMwGNDKz4BWfn49KJPZuyO8sDXMW3sixE+fMSWJuvDqjgiv7ojQ3G/w9c6p\nXFcQZHCOH1P7B4mIiIiI/EspBBIREREREfkcGKaN3XIAdssB+N0Ibtk7OAcX4h5ZDV7dsmx27sWN\ntnUOLMRML8BM64DXIpv4pG8Qn3g95u6tdYHQinmY5WUAJLJbk+jSM/n6h/ZhHt6Pe0ERmFaDcymW\nwRWdUrmiUyrl0QSv7qjl+a1hVhyMNekeK2IeTxaHebI4TIdmFtfkp3JV5yA9WtgYCoRERERERD5z\nCoFEREREREQ+Z4YVwM4diZ07Ei9ehXN4Gc7BpditLkyq9eLVRD94BLw4ZrN8rJyR2DkjMYNtSXTo\nQqxDF2LX3o5VvB57+VwSrduDmTybyLfwNfyzppFono0z5BKcYWNJdOgCHwlnWqSY3BpK49ZQGruq\nHV7cVsvzW8IUN3H/oF3VLo9sqOaRDdV0a25zVedUrskPkp+hj6UiIiIiIp8V/bQtIiIiIiLyBWL4\n0vG1nYiv7cRGzzuH3wYvDkCiehuJ6m3Etz2FmV54MhBKzcW9oC/uBX0bv0gigb1yPgBmRRn+2dPx\nz56O27YTzrAxOENG47Vqk9SsQzObH/VO5+5ezdhwNM70rbW8uC3MwdomrBcHfFjh8Ou1Vfx6bRV9\ns31c1bluhlC7NOuTG4uIiIiIyBlTCCQiIiIiInIeSVRsbPx4VSmJqlLiW/+OmdENO2ckVs4IzECr\npFpz91aM48vFncratwPrxb+R8uLfcAt74gy+BGfQKLzMrAZ1hmHQp6WfPi39PDAgg6UHojy/tZaZ\nO2qpdrwm3c/asjhry+Lct7qSobl+rs6vW4YuO6BASERERETk01IIJCIiIiIich7xX3APdvsrcA4u\nwj20BC96OKkmUfkhscoPYcvjmJnd8Xe+GSvr5KygRMdCwo88j71yAfaKuVi7tib1YZW+j1X6Pv5n\nH8W9oAhnyGickZOSlouzTINRbQOMahvgv4dm8uauCNO3hpm3N4rbhDzIA5YfjLH8YIyfrDzGqLYp\nXN05la91TCXTn7ycnYiIiIiIfDKFQCIiIiIiIucRwzCwMgqxMgrxunybROWHOAeX4B5aihc7klSf\nOLYZz3OTjntZOcQnfYP4pG9g7tmGvXwe9op5mEcPNbyel8De/B5GLIpz0dc+dmxB2+Tq/CBX5wc5\nXOvy8vZapm8L8+7heJPu0fVg/t4o8/dGSVlRwdh2Aa7OT2V8XoCgrUBIRERERORMKQQSERERERE5\nTxmGiZXZHSuzO17h7SQqNuEcWoxzaBnEK+qKfBlYLYqS2iZqD+AeXYudcyGJ9vnErrud2DW3YZZs\nxLdiHva7izGqK+vrncGXNDoGc8smEnkFkBJocLxVqsXt3Ztxe/dmbK90mLG9lpe2hdlc4TTpHqMu\nvL4rwuu7IjSzDSZ1CPD1zqlc0i5AimV8cgciIiIiIl9hCoFERERERES+BAzDxGrRC6tFL/yFd5Co\n2IhzaDGGnY5hJn/0cw7MJ779aWIlj2K16IuVMwK71VAS3foQ7daH6M0/wNq8BnvVQuy1b+MMGpV8\n0Wgtqb+9Bwxw+g3HGXwJbs8B4PM3KOucYXNPn3Tu6ZPO5vI4L20L89L2WnZUJc9Q+jjVjsf0bbVM\n31ZLhs9gQocAV3ZK5ZK2AQK2AiERERERkY9SCCQiIiIiIvIlY5gWVlYRVlbyDKATnENL6v7Fc3GP\nvot79F1ixf+D2bwPds5w7FbDcHsPxu09mKjrgJX88dFetxIjFgHAt2IevhXz8ILNcAaMrAuELihK\nate9hY/u/TP5j34ZvFcW58VtYV7eXsuB2kST7rEy7jF9ay3Tt9aS7jOYqEBIRERERCSJQiARERER\nEZGvmET0CF7kcPIJL0GifC2x8rXEih/FbN4Tu9VwrJwLMa3spHJ79aKkY0a4Gt+SWfiWzCKR3hx3\n4EU4g0bhdu3VIBAyDIP+rfz0b+Xn/w3MZPnBGDO2h3l1R4Sj0aYFQlUfDYTyAlzZWYGQiIiIiIhC\nIBERERERka8YM6UlweHTcI+uwTm0GLdsFbi1H6nySFRsJFaxEUr/jJnRjUDRrzHsYH1F5Fs/xi4a\nir1yAdamdzESDcMbs6oCc8Gr+Ba8WhcIDRhB/JIrSXQoaFBnmQYj2qQwok0KDw3xWLg3ykvbw7yx\nM0K14zXp3qriJ5eMOxEIXdEpldHtFAiJiIiIyFePQiAREREREZGvIMPyY7cait1qKJ4bwy1/D/fQ\nMpyyleBUJ9V7bqRBAARAsBnO8Ak4wydAVQX2u0uwVy3E+nAdhtcwvDGrKjAXzsTpOQg+EgKdymca\njMsLMC4vQK3jMWdPhJe2hXlrT4Ro07YQUiAkIiIiIl95CoFERERERES+4gzLj509BDt7CP5EHLd8\n/fFAaDnEKwGwc4Y32ja2/dm6860uJD7qMpyLL8coL8NevRh71QKsLZvqa72UAG7vQcnXrziCuXML\nbo9+YPvqj6faBld0SuWKTqlUxhK8uTvCK9trmb83QqxpK8YlBUITjgdCl7RLIWibTetMREREROQ8\noRBIRERERERE6hmmD7vlAOyWA/Anvk+iYiPO4WXYOSOTar2EQ3z3K+BUEd/+NEawfd0eQq2Gkhh7\nFfFxV2McPVQ3Q2j1YhJZOeBPSerHXjGPlGl/xgs2w+l3Ic7AUbg9+oPPX1+T4Te5viDI9QVBjsUS\nzP6UgdAL22p5YVstqZbBmPYpXNYxlXHtAzRPUSAkIiIiIl8eCoFERERERESkUYZpYWUVYWUVNXo+\nUbEBnKr61154D/Gd04jvnIaRko2VPQS71TASY64kPu4aSDS+npu9elHd9cLV+Ja9hW/ZW3jBNJyi\nC3EGHQ+ETgmPMk8JhCqPB0Ivn2UgVOt6zNwZYebOCD4TRrapC4QmdQiQk2o1rTMRERERkS8YhUAi\nIiIiIiJyVjwnjBFogxfZn3wuWoaz93Wcva+DnYbVchB2q2FYWQMw7NSThZUVmNuLk9ob4Rp8y+fg\nWz4HLxDEKRqK039E3XJygZN7E2X4Ta4rCHLdKYHQKzvqAqGm7iEUT8D8vVHm741y93IYkuvnso6p\nXNoxQIdm+vgsIiIiIucf/RQrIiIiIiIiZ8XOGY7V6kIS1Vvr9hA6/DZeeHdyoVODe3Ah7sGFWK0u\nJNDrFyfPZTQn/PsXsd5bhr16MdYHazESDafzGJEwvpXz8a2cj+fz4fYYQOS7v4DUYIO6cxkIecCK\ngzFWHIzxs3eO0aelj8s6pnJZxwCh5r5PbC8iIiIi8kWgEEhERERERETOmmEYWOldsNK74C+4lUTN\nbpyyFbiHl5Oo/DCp3soeknTMy8wiNmwYzsWXQ2UF9olAaPOa5EAoHsfctxMCqUn9nOqjgdBbxwOh\neWcRCAGsPxJn/ZE4/++9Srpm2lzaMcBlHVMpaunDMIymdygiIiIi8i+gEEhERERERETOGTMtD39a\nHnS8jkT0CG7ZStzDK3DL14GXwM4enNTGi1VQ+/bNGGkdsVsNxe0/jPhFX8OoqcReswx7zVKsTWsw\nnDgATv8R0Ejw4ps1DeIxnAEj8dp2rK/J8JtcWxDk2uOB0Jw9EV7fGWHungg1jtfkeyw55vDIhmoe\n2VBN+zSLiXkBJnUIcGHrFPyWAiERERER+eJQCCQiIiIiIiKfCTOlJWa7r+Fr9zU8p4ZEZTGGLyOp\nzilbCXh4NTuI1+wgvuM5jJRsrOzBOD0GYw1/ACMWx16/EmvNMpyBo5Ivlkjge+sFzIojpMx4gkTr\nPJz+w3H6jyDRuRuYJlAXCF2TH+Sa/CC1jsfCfRFm7ozw5q5aKmJND4T21Lj89cMa/vphDRk+gzHt\nA0zMCzC2fYDmKWaT+xMREREROZcUAomIiIiIiMhnzrDTsLL6NXrOPbwi6ZgXLcPZ+wbO3jfATMHK\n6ofVYTBW3+9jpmQl1ZvbPsCsOHLy9YHd+N94Dv8bz5Fono3Tfzhu/+G4oSKw6z4Kp9oGkzqkMqlD\nKvFEc5YfiDJzZ4TXd9ZyoDaRdI1PUhn3mLG9lhnba7ENGNY6hUkd6kIhEREREZHPg0IgERERERER\n+Vz5Ot+A2awjzuHleOE9yQWJKG7ZCtyyurDITO+Kv+DfsLL61pcYVcdItMzFPHIwqblZUYZ//isw\n/xW8YBpOr8G4fYfh9B4Mael1YzANLmob4KK2AR4aksm7h2PM3Blh5s5adlQ1fRMhx4Ml+6Ms2R/l\np6uO0SUYYGRLl5uaxyjK9mFqHyERERER+RdQCCQiIiIiIiKfKysjhJURwl/wLRI1u3HKVuCWrSRx\n7EMgeUZOoqoETF+DY27fYYSLhmLuLK3bQ2jNUqy9O5LaGuEafKsW4Fu1AKfXICL/96GkGtMwGJST\nwqCcFB4YkMGmcoeZO2uZubOWzeXOWd3jlrDJlrDJE7sP0yZoMiEvwMS8VEa2SSFgKxASERERkc+G\nQiARERERERH5wjDT8vCn5UHH6/Bix3COrMYtW4l79D1ww3VFdjpmxgVJbd2qEiKV07CGDsa69BGs\n8jD2mqV1odDWzUn1Tt9hjY9hz3YSbTuAaWEYBj2zfPTM8vHvfTPYVunw+s5aXttZy7uH42d1j/vD\nCZ4sDvNkcZg02+CSdilMOL6PUE6qdVZ9ioiIiIg0RiGQiIiIiIiIfCEZ/kx8bcbgazMGLxEnUbER\np2wVhpmCYSaHJe7hFUnLxlndB2GN+AGW0wJ7wzvYa9/G2rQGIx7DLWokBApXk3rfbXjBdNw+Q3D6\nXojbsz8EggDkZ9jc1Sudu3qlcyDs8tbuCLN2R1i0L0K06avGUeN4x5ediwDQL9vHuPYBxucF6NNS\ny8aJiIiIyKejEEhERERERES+8AzTh5XVDyur32lrnLKVDV4nqkpIVJUQ3/4M+DKxWvXHnjwOq9kP\nsXfuwWuZk9SHvfEdDNfFqKrAXDYb37LZeD4f7gX9cPoOwy0aipdV16510OKWUBq3hNKoiSdYuC/K\nrF0R3tod4Ug0eRm7M/FeWZz3yuI8uK6KnFSTse0DjGsf4OK2KWT4zbPqU0RERES+uhQCiYiIiIiI\nyHnPS8Qwg+1xI4dOLht3qvgx3IMLcA8uAEzMjK5Y2z/E1+5rGP7m9WXW2uVJTY14HHvDKuwNq2Dq\n73A7dKmbJdRnCImCC8C0SPOZXNoxlUs7puImPFYfjjFrV4Q3d0coPXZ2+wgdqk3wbGmYZ0vD2AYM\nzfUzLi/A+PYBCjNtDM0SEhEREZFPoBBIREREREREznuG6SfQ6z8aLBvnHnkHr3Z/I9UJEpUfkqj8\nELvtBE6NUmJXf5tE/gVYa9/GKl6P4Sav8Wbt2oK1awv+mc/gpWUQveFOnOHjT543DYbkpjAkN4UH\nBmZSeizO0+/tYclRi/WVFt5Z3J/jwdIDMZYeiPGL1ZV0Srfql427MDeFgK1ASERERESSKQQSkS+c\n+++/nzfeeINXXnmFtm3bft7DEREREZHzSMNl4+4gEd6Le2R13a+KDZCI19ea6V0wU1o2aO+1akNt\n/44kusaw0m7Fv/Uw9roV2OtXYoSrk69XU4mXmZU8EM+r+2WaFGb6uLm9w83tHVrk5fPW7ghv7oqw\nYF+UsHM2kRDsqHJ5/IMaHv+ghqBtMLJNCuPbBxjdPoUOzfRRX0RERETq6CdDETkrW7du5Z133mHy\n5MnnvO9rr72W4cOHk5XVyIdpEREREZEmMIPtMIPt8OVdiedGcMvX14dCVtaARts4++fgHlpCHIj6\nW2CN7I91+d34jvrxbdyIvX4l5v5dAHj+AG6od/J1d20h8N/34vYejNNnMGagBYlAkOyAxY2FadxY\nmEat47Fkf5Q5e+r2EdpTkzzr6EyEHY/ZuyPM3h0BoDDTZnS7FEa3C3Bhaz9BW3sJiYiIiHxVnbch\nUCgUygJ+CVwJtAHKgFnAL4qLixub7//R9sOPtx8EBIDdwEvAfxUXFyd/vUtEGpg/fz5vvPHGZxIC\nde/ene7du5/zfkVERETkq82wAtjZg7GzB+N5HnjJe/V4CRf36HsnX8fKcQ7MwzkwjyhgdumCNWgU\nltGJlG1HMaprwJ+S1I+1YRXmsaOYS9/Et/RNepsW1e0L8A25GLfPYBLtOpNqG4zPq1vS7eEhHh9U\nOMzZHeGtPRHeORTDPbtJQpQecyg95vDY5hpSLBiWm1IfCnVrrr2ERERERL5KzssQKBQKpQKLgG7A\no8C7QCHwf4FLQqFQ/+Li4vKPaX8j8AxQTF0QVAlcCvwEGBEKhYYXFxcnPtObEDnPbd68+fMegoiI\niIjIWTMMAwxf0nEvegjDCuI5jX83MFG1hUTVFuJAxBfA6twba/cr2G0nYlgnwyB7/cqG10u4pO8q\ngV0lMP0vJLJycHsNxOk1ELd7f4y0dLq38NG9hY8f9k6nIppgwd66QGjenihHomf3ETXqwsJ9URbu\ni/IfqytpF7S45HggNKptCs1TNEtIRERE5MvsvAyBgB8CvYA7i4uL/3TiYCgUWg+8DPwC+FFjDUOh\nUArwZ+pm/gwuLi4+dvzUE6FQ6GXqZhZNoG5WkfwLbN68mX/84x+89957VFdXk52dTY8ePZgwYUL9\nfjCPPfYYTzzxBP/1X//F+PHjk/q4+uqrOXz4MLNnzyYYDOK6Ls899xyzZs1i165d+Hw+CgoKuOaa\na5gwYUJ9uzVr1nDHHXcwZcoU/H4/zz77LEVFRTz44IMA7Ny5k6eeeopVq1ZRXl5OixYtCIVCfOc7\n30maqXLkyBH+8Ic/sHz5cqLRKD169OCuu+5i8eLFPPHEE/z5z3+mf//+9fVr165l6tSpbNy4kWg0\nSk5ODqNGjeLWW28lIyPjY9+z119/nQceeICf/OQnNGvWjKlTp7J7927S0tK4+OKL+d73vkezZs3q\n6xOJBC+88AIzZ85k586dAOTl5TFp0iS+8Y1vYNsn/1dQUlLCU089xcaNGykvLyc9PZ0LLriAW265\nhT59+rBv3z6uvPLK+vpBgwbRr18/HnvsMQAikQhPPvkk8+bN48CBAwQCAbp168ZNN93E0KFDk+7h\n/vvv54MPPmDWrFlcfvnl3HXXXafdE2j27Nm88MILbN26FcdxaNOmDZdccgm33norqampDcY0cOBA\nbrrpJh5++GFqamqYPXv2x76nIiIiIiIAZmobUodNxQvvwj3yLs6R1SQqNoEXTy52I7hH3sE9thm7\n/WUNTjmDRuH5/FjFGzDc5BlH5tFDmIvfwLf4DTzDJFFwAdGbvk+iczcAmqeYXJUf5Kr8IG7C472y\nOG/tiTBnd4QNRxsZyxnaG3Z5ujTM06VhTAMGZPu5pF0KY9oH6NvSh2VqlpCIiIjIl8n5GgJ9E6gB\n/v6R468Ce4CbQqHQPcXFxY1Nnm8NzABWnRIAnTCLuhCoNwqB/iVKSkqYMmUKzZs355ZbbqFly5bs\n2bOHadOmsWLFCh588EEKCwsZN24cTzzxBAsXLkwKgUpKSti9ezfjxo0jGAzieR4///nPWbRoERMm\nTOCGG24gHA4zZ84c7rvvPvbu3cu3v/3tBn1s2rSJffv28b3vfY/c3FwADh06xHe+8x0SiQQ33ngj\nbdq04fDhwzz//PPcdttt/O1vf6sPglzX5a677qK0tJRLL72UoqIitm3bxg9+8AN6905eH3zRokX8\n+7//OwUFBdx+++2kpaWxceNGpk2bxsqVK3niiScIBAKf+P4tXryY3bt3c/XVV5Odnc3SpUuZMWMG\nBw8e5He/+1193a9+9StmzpzJ0KFDueKKK7Asi+XLl/OHP/yBkpISHnjgAQD27t3LbbfdRkZGBtdd\ndx25ubmUlZXx8ssvc+edd/L444+Tn5/Pb37zGx566CEAfvKTn9CiRQsA4vE4d955JyUlJVx++eX0\n6NGDiooKXnvtNX74wx/yy1/+kkmTJjW4h7lz51JVVcU999xDXl7eae/173//O3/5y1/o2bMnU6ZM\nIRgMsm7dOp588knWrVvHn//8Z0zz5LcYI5EIDz30ENdff732FhIRERGRJjEMAyOtI2ZaR3wdrq7b\nS6jifdyja3CPrsGr2dWg3mpRhGFYDY7Fx11DuEcqXnV3fOVBIis2kbl1E/6qiuTreQmsLZvwmmUm\nD8bzsEyDgTl+Bub4+Y9+GewPu8w9vo/Qon1RapyzWzcu4cE7h2O8czjGg+uqaJFiMKpNgEvapTCq\nbQp5zc7XvzIQERERkRPOu5/oQqFQBnXLwC0tLi6OnnquuLjYC4VC7wBXAZ2BbR9tX1xcvBO49TTd\nn/iJu/KcDVg+1tatW+nRowe33347/fr1qz+elZXFgw8+yJIlSxgyZAj5+fl06dKF5cuXE4lEGgQk\n8+bNA2DixIkALF26lAULFvD973+fm2++ub7u6quv5jvf+Q5///vf+frXv94gGFixYgUzZsygTZs2\n9ce2bdtGly5duOKKKxoET126dOEHP/gBM2bMqA+BlixZQmlpKZMmTeK+++6rr+3WrVuD1wCxWIzf\n/va3FBYW8te//pWUlLolIy699FIKCgp4+OGHmTFjBjfccMMnvn/r1q1j+vTp9eOeOHEi5eXlvP32\n25SUlNC1a1fef/99Zs6cyZAhQ/j9739fv/73VVddxd13383s2bO57rrr6NmzJ4sXLybOelyoAAAg\nAElEQVQSifDLX/6S0aNH119nwoQJ3HfffWzfvp3u3bszevRo/vCHPwA0qJsxYwYbN27k17/+NWPG\njKk/fuWVVzJ58mR+//vfM27cuAYzj95//31mzJjRYObSRx06dIi//e1vFBQU8Je//AWfr27Zjiuu\nuILU1FRefPFF5s+fz9ixYxv0e//99zeY+SUiIiIicjYMK4DdcgB2ywEAJCKHcY+urQuFytdiZfVv\ntJ2zdxaJ6q3EgURRgP2Du5DZLIR/VwT/hlKsLZswXLeuz9z2eK3aJPVhv7MQ/8tP4vQchNtrIG63\nPrQJpvLNrml8s2saUddjxcEoc/ZEWLA3yocVybOOzlR51OPlHbW8vKMWgIIMi1FtA1zUJoWRbbR0\nnIiIiMj56LwLgYCOx/+55zTnT3wlK59GQqDTCYVCfuBbQBh45axH9xGlpaXnqqsvpS5dunDPPfcA\nde9VbW0tiUSibpNWoKysrP49HDBgAFu2bOGll15i0KBB9X3Mnj2bjIwMWrZsSWlpKTNmzACgoKCA\ndevWNbhez549ef/995k9ezYDBw5kz56630b5+flUV1c3+O/VsmVL7r777vqxRSIRXNclGq3LHrdu\n3VpfP3/+fAB69erVoI/8/HxatmzJkSNH2LNnDxkZGWzcuJEjR44wevRoPvjggwbjy8vLwzAMlixZ\nwsCBA0/7vh04cACAHj16JI27Z8+erFmzhjlz5mAYBi+//DIAQ4YMYcuWLQ36GTBgAG+//TavvfYa\nKSkpHD16FKibYdShQ4cGtT/84Q/r3wuom/Vz6muA1157jdTUVLKzsxt97+fOncvChQvp1KlT/T1c\ncMEF7N+/v0FtZWVdDrtjxw5qamqYN28erusydOhQduzY0aC2qKiIF198kVmzZtGpU6f646Zp0q5d\nu6/sM/hVvW+RT0PPjUjT6bmRr7bOkNIZcq+CmgR85Hkw3SpaV289+dqLEIi8TzTyPtEguMPSiV00\nEKOqGanbq3ECrTnYyDPV4e35BPbvxr9/N8x9iYRlU5PXhcr8HlQV9KA2px3tDJN/awH/1gIORA1W\nlpusLLdYVWFR7Z798m5bK122Vtbw9w9rMPDo1izBoOYJBjV36ZORQJmQ/KvozxuRptNzI9J0X8Tn\nprCw8FP3cT6GQOnH/xk+zfmaj9R9olAoZAJ/BS4A7ikuLt539sOTpvA8j3nz5rFgwQL2799fHyyc\n4B7/VhzUhRjPP/8877zzTn0ItGPHDg4cOMC4ceOwrLrlF/bu3QucDC0ac+TIkQavW7Vq1WjdypUr\nefPNN9m9e3d9+HNCInFyY9bDhw8D1C8ld4JhGBQUFDS43onxTZ8+nenTp5/R+E6nffv2ScdOLM1W\nVlYGwL59db+dG1tq7cQMohMhzLBhw5gzZw6zZ89m/fr19O3blx49etC9e3f8fv8njmfv3r3U1tZy\n++23n7amrKysQViTk5Pzif2eGF9j93viHk6ESidkZGSc0ZJ6IiIiIiKfimECyWmI5ZYTt3PwOYca\nbWYlqkiNrgM/eCHwrJZkHq3iWIvrjvcJeB7p2zY1aGe6Duk7PiR9x4ew4CXiwXSqO3WjqlM3qjpf\nQOsWrbiytcuVrV0cDzZV1QVCK8pNNlebeJxdKORh8EG1xQfVFlP3+EgxPfpk1AVCg5q7dE3zsLSd\nkIiIiMgXzvkYAp1ToVAoFfgndXsB/W9xcfEj57L/c5HUfZk99thjPPXUU3Tu3Jkf/vCHtG/fHr/f\nz/bt2+v3nDnxHhYWFtK7d282bNhAx44d8fv9zJ07F4DJkyfX17mui2EYPProow32iDlV27ZtadOm\nTf2Mk9zc3KT/Vq+++ip//OMfyc3NZcqUKXTu3JlAIEBlZSX33nsvqamp9W1OBFDdunUjOzu7QT+t\nW7cG6gKMwsJClixZAsA3v/lNhg4d2uj4UlJSPvb3TnFxMQDt2rVLqisvLwcgLS2NwsLC+vegW7du\nSWFXamoqALZt1/fz9NNPM23aNObMmcOsWbOYNWsWaWlp3HjjjXzrW9+q7+/EkmynXj8ajZKVlcWv\nfvWr0469U6dOtGzZsv4eTrwvp8rIyKivbdu2bX0A1aVLl6TaE0Gh53kNzmVkZHwln78T31j4Kt67\nyNnScyPSdHpuRM5EITCaRO1B3KPvcWzXEvzRUqxEdaPVtnsEv3mInK6hkwdjURh1Kc7772DtKMXw\nkvf+8YWraLF5NS02rwYgkd2a2h8/jNe67gtUFwDXHK89GnFZtC/KvL1RFuyNcKA2kdTfmYomDN6p\nsHinou6zUIsUg5FtUhjVJsBFbVPonG7VL0Utcrb0541I0+m5EWm6L/tzcz6GQCf260k7zflmH6k7\nrVAo1Ap4DRgC/FdxcfF9n9BEziHHcXj++efJyMjgL3/5C82bN68/F4vFGm0zbtw41q9fz6pVqxgx\nYgTz58+nQ4cO9OjRo74mGAzieR4FBQUN9v1pqmeffRbLsnj00Ufp2LFj/fGdO3cm1Z4IKT46Wwig\npqamweu0tLrfuhkZGfTv3/ja4WcqEokkHauurvtQeeL9PBH0hMPJk+dqa2sbjAkgMzOTKVOmMGXK\nFHbv3s2yZcuYPn06jz/+OIZh8O1vf/u04wkGg9TU1Hzq+2qs30+6hxM1IiIiIiJfJGZqLma7iZSH\nu4CXIL+Nj0T5Wtzy9bgVG8Gtra+1WhQ1bOxPIXbNbUS6HcSr8eOLZuPfVUvKe1uwTrN6gFFZjtey\nkdn2NVVkmRZX5Qe5Kr/uM9OmcocFeyPM3xtlxcEosbPPhCiPery6I8KrO+o+o+Q1sxjROoURbVIY\n3tpPXrPz8a8fRERERM5/5+MKvtsBD0heF6rOib+t/9gF/EKhUC7wNjAA+DcFQP96FRUV1NTUUFhY\n2CAAAli7dm2jbcaMGYNlWSxevJiSkhJ2797NhAkTGtTk5+cDsH79+qT2VVVVOM6ZbZS6b98+cnJy\nGgRApxvbiRk2H12SzPM8Nm1quHzDifFt2LCh0etWVFSc0fiApP1xToz71DGduN7WrVuTardv3w7Q\nYHm2U+Xl5TF58mSefPJJbNtm4cKFHzue/Px8otFo/SyfU1VUVNTv9dRUnTt3Bj7+Hk7UiIiIiIh8\nYRkmVno+vg5XE+jzAMERLxDo/wi+zjdjNu+FlZX8ZSrPc3GPriVRs4Wos5KqtuspuyxK2ZQeVNw0\nmPDwHiTSTi6D7IZ6gy95KWffvJdJu/MyUv/f9/DPeBKreAM9M+CuXum8OiGb7Te04fkxLbmjexrd\nm3/6wGZ3tcs/t4S5Y2k5vV44SNGLB/jesnKe3xpmb437yR2IiIiIyDlx3oVAxcXFNcAGoF8oFGqw\n4UcoFLKAYcDu4uLiXafrIxQKZQCzgQ7A5cXFxU99diOW02nevDmWZXHgwIEG4cCWLVuYPXs2kDwj\nqEWLFgwcOJCVK1eyaNEiACZOnNigZsyYMQBMmzatwb49nudx3333cemll9bPlvk4WVlZVFRUNJht\nc/Dgwfp9fE6d9dO7d28A5s2b16CP2bNnJwVDffv2JSsri7fffjspxJk7dy4TJ06sv/9PsnLlyvr9\niE44EdQUFdV9i/CSSy4B4OWXX27wPnuexyuvvALAxRdfDMBvfvMbbrzxxqQZTYFAAMuyGuwLZJpm\nUt2J9/7ZZ59tcDwWi/H973+fyZMnN/hvcqZGjBiBz+fjtddeS9o36uWXX25wDyIiIiIi5wvDtLEy\nu+PvfCOp/f4/rKyipJpE1VZwPvL5xXNwI1uJWuupKtjK4WstDn+nGxXf6Eft0G54Tm1SP/amNRiu\ni1X6Pv5XpxL8zQ9Iu+MyAg//BN+saaTvLmF8W5vfDG7O8q/n8uH1rXl8ZAtu6BKkbfDT/9XBjiqX\nZ0rDTFlSTo/pB+j34gHuerucF7aG2R9WKCQiIiLyWTlf52P/HfgDMAX4n1OO3wTkAL88cSAUCnUD\nosXFxdtPqfsfoAi4qri4+M3PfrjSGNu2GTVqFPPnz+e+++5j2LBh7N69mxdffJEHHniAu+++m02b\nNvH6668zYsQIMjMzARg/fjz3338/M2bMoFevXrRr165BvyNHjmTUqFEsWrSIO++8k0mTJuE4DnPm\nzGHNmjV861vfolmzZo0NqYExY8bwzDPPcO+99zJ+/HgOHz7M888/z913383vf/97SkpKeOmllxg+\nfDhjx47l8ccfZ8aMGRiGQffu3dm6dStz585l5MiR9fsAQd1eOvfeey8/+9nP+O53v8sNN9xAdnY2\nH3zwAS+//DIdOnRg+PDhZ/Qe9ujRgylTpnDFFVfQqlUrFi9ezMaNGxk9enT97J5u3bpxzTXX8OKL\nL/KjH/2IkSNH4rouixcv5t133+WGG26goKAAgAEDBvDKK6/w7W9/m0mTJtGyZUsqKyt58803iUaj\nXHvttfXXbtu2LatXr+Z3v/sdrVu3ZvLkyVx11VXMnj2b2bNnE41Gueiii6iurmbmzJkUFxfzs5/9\n7LT7NH2c7Oxsvvvd7/LHP/6RO+64g/Hjx+Pz+Vi9ejVz587l4osvPuP3TERERETkfGJYqdjtLsMt\nX48XPs13HT2XRGwH0RQguhlj1SJSh/3j5J480VrMLZuSmhmxCPbGd7A3vlPXTSCI27UXbrci2nYr\n4rpOhVxXULd03JZKh0X7oizaF2XpgSiVsbOb5X/CtiqXbVVh/lFSt+Rzlwyb4a39jGiTwoWtU2gd\ntD5V/yIiIiJS53wNgR4DbgQeDoVCHYF3gR7Aj4CNwMOn1H4AFAPdAEKhUG/gFmAzYIVCoWtIdri4\nuHjxZzd8OeHee+/F7/ezatUqli1bRrdu3XjooYcoKiri61//Oq+//jp//OMf6dOnT30INGrUKB58\n8EGOHj3Kbbfd1mi/v/71r3nuueeYNWsWDz30EFC3VNnPf/5zrrjiijMa2+23304sFmPRokX89re/\npaCggJ/+9KeMHDmS2tpa/vCHP/CnP/2Jzp07k5uby6OPPsojjzzCG2+8wZw5c+jduzePPvoozz33\nHECD8OPiiy/mf//3f5k6dSpTp04lHA7TqlUrrrjiCm677bYzCqkABg8eTNu2bZk6dSo7duygWbNm\nXH/99dx5550N6n784x/TqVMnXnnlFR555BEMw2j0/Rg7dixpaWk899xzTJ06lcrKStLS0ujWrRuP\nPPJIg6BlypQp7N+/nxdffJEuXbowefJkfD5f/X3NmzePZcuW4fP5CIVC/Pa3v/1Us3VuvvlmcnNz\nmTZtGo8++iiJRIK8vLz6GUYiIiIiIl9GZloeKaG6n+8T0SMkyjfgVmzErdiAF97TeJvM7icDIADD\nJHLHf5DYNhtz51ZSSg5jxpPbGZEw9oZV2BtWAVDz+xfxWmRjGAaFmT4KM31854JmOAmPdUfix0Oh\nCO8cin2q/YQAtlQ6bKl0eOp4KNQ102Z46xQubO1naG4KbdMUComIiIicDeNs9+j4vB1f0u0/gauB\nNsAh4GXgl8XFxUdPqfOA4uLi4hMh0K3Ak5/Q/eLi4uJRTRnPsWPHzs838gustLRuW6fCwsLPeSSf\nzr333svChQt5/vnnz9m+Na+//joPPPAAd955J7fccss56VO+HL4sz43Iv5KeG5Gm03Mj0nSfxXOT\niB4hUfE+bsUG3PKN9TOF/KHv42v3taT68Krv4tXsAAwsWmGX26SUluHfXokV+UjfrfMI//bppD6s\n99/F3FmC262IRMeuYNvUxBOsPBSrnym08WgjCdOn1CndYmhuCkNz/QzL9VOQYTcMuuRLSX/eiDSd\nnhuRpjsfn5vMzMwz/kHofJ0JRHFxcSV1M39+9Al1xkdePwU89ZkNTL6SDh06xCOPPEJeXl6DWThH\njhxh1apVtGjRgg4dOnyOIxQRERERkS8bM6UlZu5F2LkXAeDFynHLN2JmXpBU68WOHQ+AADxcDuG2\ngOggYFAAk0zsYyn4t1WQsqOKRLc+jV7TXj4X39tv1fUSSMUt7ImvWxFjuxUxum9XGJjJkYjL2wdi\nLD0Q5e39UTZXOJ/6XndUueyoCvPclrqZQjmpJkNy/PXBUK8sH5apUEhERETko87bEEjki6RVq1Yc\nOXKEBQsWcPToUfr3709VVRXTp08nHA7zve99D8vS8gUiIiIiIvLZMfwtsHNHNnrOrdrysW0THCOW\nCbG+UN03BcNahfn+b0jp8dOTM248D+vDdSevF6nF3rgae+PqutP+FNz8C2gT6s3XC3txeZ8eMKQ5\nh2tdlh+MsWx/3X5CH56DUOhQbYLXdkZ4bWfdFKZ0n8GgHD/DjodC/bL9BGyFQiIiIiIKgb7Amj+5\n9/Mewseq+Ld2n/cQvjAMw+B3v/sdTz31FAsXLmTOnDlYlkWXLl347ne/y9ixYz/vIYqIiIiIyFeY\n3bI/1vDn/3/27ju+iir///hrZm5L7yEJEEgBpJdIBEGk6KqIAiqrwiq6BuwVFct+9YcrsLKuqygW\nBBZQRKW4gijKqqgURaqgoQUSSiC93+S2md8fN7nkkoRmFNTP8/HI4+bOnDlzZm7ygNz3/ZyDp2wH\nnpLt6GU/oldkAY0v5mN4KjAcBf5TrlWVg8eDJ0hBcRiox2U5itOBaedWqA2KDEVFT0wl9oHJDG8b\nw/C2AQDkV3tYe9TBmqNOvjniYHfZzw+FKlwGnx928PlhBwAWFdJiLPRt4a0W6h1jIdyqnqQXIYQQ\nQojfHwmBhGgmwcHB3HPPPdxzzz2/+LmGDRvGsGHDfvHzCCGEEEIIIX4/FEsYpph+mGL6AWC47ejl\nO/GU/oin7Ef0skzQHb72WlgX/w6Cw7C/uIia7x/GU/kTWk0g5lwnlkNVWAoM1EqD+rU3iqGj5h3E\nCIvw6yY2QOOa0EquCXBg9GlFXrXOmqOO2i8ne5ohFHLqsD7Pyfo8J1AJQMdwE71jLaTHWrgg1kKq\nrCskhBBCiD8ACYGEEEIIIYQQQog/IMUUiBbZCy2yFwCG7kavzEIv3YGn9Ee0yB4NjjHQ8VTvBww8\ntio8yVCTbPH257ZgLgLLwSrMBTrmIgNPahfQGr71YP78v1hWvIMeGkGb9l1p1a4rozp0Rb8glSMO\nhTVHHLUhjoPMZpg+DiCz1E1mqZv5u73rCkVaVW8oFOMNhnpFmwkyS7WQEEIIIX5fJAQSQgghhBBC\nCCEEimpCC+2AFtoBc+K1jbbRK7PBY290n2Fy4mwBzhbm2g0KmpKHsvtVLKnjUdRjb0Foe7YDoJaX\noG78GtPGr72HWGwkJ3egTUpnbkjtjGdIZ4ot0b6qnvV5DrYVuXAbP/96ix06nx6s4dOD3nWFNAW6\nRppJr60WSo+10DpIk2ohIYQQQvymyUdcxB/OpEmTSE9PJzc3t1n73bRpE+np6cycOfOkbXNzc0lP\nT2fSpElNjquxNr81hw4d4q9//SsXXnghN9544xn1MXPmTNLT09m0adMZHa/rOv/6178YNGgQ/fv3\n54cffjijfoQQQgghhBCgBsRh7fIkplbDUUPag6I13Vgx8JCPp/A7vwAIpwN13050GxjHHa44a9B2\nbsOy4h0CXnqS4HtH0Or/buKalS8wOaWGz6+KJWdMPB9eFsXEHiEMiLcSoDVPSOMxYGuRi5mZVWR8\nVUK3RXl0ev8oY78s4pUdFWzId1DTHOmTEEIIIcSvSCqBhDgLIiMjmTp1KvHx8afdZvbs2VxxxRUk\nJCQ0+7j+9Kc/MXPmTNq2bQvAhg0beOmll1iwYMEZ9Tdjxgx27NjBTTfdRNeuXZtxpKdu/fr1vPfe\ne3Tv3p2RI0f+IvetzjfffIPH42HgwIG/2DmEEEIIIYQ4mxRTEKbYizDFXgSA4XGgV+zBU5aJXp6J\nXpaJ4SzxO0YN6+jficlE9RMv4dj3Gk5lL6ZSMOe5MBfqmAsNtHL/tYXU/FzU/FwcY+4FIMiscnGC\njYsTbFBVgdttYqszkPVHHayrrRYqdTZPWHPErvNhdg0fZnurhUwKdIk0c36Md/q482MspIaZUKVa\nSAghhBDnKAmBzmGlt7Y820MQvxCbzcaQIUNOu83hw4d544036NGjR7OHGYcOHcLtdtOmTRvfth07\ndtClS5cTHHVie/fuJTw8nHvvvbc5hnjGYwAYO3Ys/fv3/0XP9fbbb5OQkCAhkBBCCCGE+MNQNCta\neBe0cO/fDYZhYNTkoZdl4qkNhbSw4/6mUDX0lE64CmrAbuCOBHekieq6Pl0K5gI3pkKjNhjSUcIT\nITi0wfnN61YR/PZ0BrRoRb/UznhSO+G+qDM/BbVifYGbb/OcfJfv5EClp1mu111bLbS1yOXbFmpR\n6BVtIS3aTFqMhbRoCy0CT1AhJYQQQgjxK5IQSIjfkJ9++ukX63vHjh107NjRb77rH3/88WcFGk6n\nk4CAgGYY3ZlzOBwAv/g4dF1n165dv2ilkRBCCCGEEOc6RVFQAuJQA+IwxQ1qsp3hqsCwH2x8n9nA\nmaDhrPdfa8VThvrDM1jPuw/FEu7brmZ5/0ZS8w6h5h3CvPZTAHpbbaS1ac+dyeehJ3fkaEJ71rkj\n2FDgYkO+k61FTpx6M1wwUO40WJ3rYHWuw7etVZBGWoyZ86Mt9Iqx0CPKTJBZZuQXQgghxK9PQiBx\nVk2aNIkVK1bw9ttv88UXX/Dxxx9TVFREbGwsF198MUOHDvW1nTlzJrNmzWLGjBksW7aMNWvWcNdd\ndzFq1CgAsrOzmTVrFhs3bqSsrIywsDB69OhBRkYGqampDc7tcrl45ZVXWLlyJSUlJbRo0YJrr72W\nMWPG+LXLyclh7ty5fPfdd5SUlBAREUGHDh0YN24cnTp1avS6vvnmG2bNmsW+ffuwWq307duX+++/\nn+joaMC73s+IESO48sorefrppxvt4/g2d9xxB5s3bwbgzjvvBODRRx9l2rRpjBo1ikceeaRBH//4\nxz9YunQpr7/+Or169Trha/Hjjz/SuXPnBtvuvvtuv20Oh4O33nqLVatWkZubi6ZpJCUlMWLECIYP\nHw7ARx99xDPPPOM7Jj09nfj4eD788MMmz19SUsKLL77I2rVrcTgcJCcnk5GR0WT7LVu2MG/ePLZv\n347D4SA2NpaBAwdyyy23EBoa6jtvnbp79tprr5GWlobH42HhwoV8/PHHHDhwALPZTEpKCtdddx2X\nX36537kMw2DJkiV8+OGHZGdnY7Va6dOnD7fffjutW7f2u94VK1awYsUKMjIyGD9+fJPjF0IIIYQQ\n4g9NNWPt9GjtNHI70Sv3g+FusrmhOfAUbwJTsN92be+PuIMVDBuYig2U2mBHcdSg7f4Bbbd3TdC2\nQGJIOH9OPg/ntbdR3SqVbUXeKqENtV951c2UCgGHqjwcqvL4ppFTFegYbuL8GAs9oiz0jDbTMcKM\ntZnWMxJCCCGEaIqEQOKc8PLLL+Nyubj55psxm80sXbqUd955B4D27dv7tV24cCGqqjJx4kTatWsH\nQFZWFhkZGWiaxrXXXktiYiK5ubksXryY2267jTfffLNBPy+++CIul4uxY8fi8XhYsWIFL730Eoqi\nMHr0aADy8/MZN24cuq4zZswY4uPjKSgo4L333iMjI4NZs2Y1CIJ27NjB8uXLGT58ONdeey3btm1j\n+fLlZGdnM2/ePFT1zD79NX78eBYtWsTnn3/OuHHjSE5O5sILL2Tu3Ll89tlnPPDAA5jNZl97j8fD\nl19+ScuWLenZs2ejfa5cuZJp06YBUFNTg6ZpLF682Le/srLSF8S88847xMbGMmHCBDZs2MCf/vQn\nbrzxRpxOJ59//jmTJ08mNzeXO++8k7S0NKZOnerr+9FHHz1hJY6u6zzwwANkZmZy5ZVX0qtXL/Lz\n85k2bRqtWrVq0H716tU8/vjjpKSkMH78eIKCgti+fTvvvvsu3377LXPmzMFmszF16lT+97//+d2z\n5ORkDMPgySefZPXq1Vx++eWMHj0au93OZ599xlNPPcXhw4e57bbbfOd7/vnnWbRoEUOHDmX06NHk\n5+ezYMECNmzYwH/+8x/S0tJ8gVxaWhrXXXcdSUlJp/HqCiGEEEII8ceiaDZMcYMxxQ0GwNCd6JX7\n0ct3oZfvwlO+C8N+yO8YNSQFRa33NoZh4PjLfTgPv0dNwE7wgKlUx1ykYyoyvI8lx4IhtaIUddu3\nOP98O1ZNIT3WSnqs1dtVZQUFe7NYY0tkfYnKd/lOdpS40JtnaSF0A34scfNjiZt52AEwq9ApwkzP\nKDM9or3VQp0izFgkGBJCCCFEM5IQSJwTCgsLeeuttzCZvD+SQ4YMYdiwYSxbtoz77rvPLzg5fPgw\nCxYs8LUFmD59OlVVVcyaNYtu3br5tvfr149bbrmFGTNm8NJLL/mds7q6mldffdXX9xVXXMGIESOY\nP38+N9xwA6qqsm/fPlJTUxk+fDiXXXaZ79jU1FTuv/9+li5d2iAE2rhxIwsXLvStrXP11Vfjdrv5\n5JNPWLdu3RmvS9OrVy82btzo+z4tLQ2AK6+8kv/85z988803DB482Nd+06ZNlJSUMGrUKL8p3uob\nMGAA3bp1w+PxcP311/Pyyy8TGxsLwNq1a/n444+ZPHkyANHR0Xz++eds2LCBkSNH8vjjj/v6ueaa\naxg7dizz58/n2muvJT4+nvj4eKZPnw5w0vWP1qxZQ2ZmJldccYVfZdSll17qC+TqOJ1OnnvuOdq1\na8ebb76J1er9o23YsGGkpKTw/PPPs3TpUkaPHs2QIUPIyspqcM++/vprvvjiC+69915uuukmX9/X\nXnst48aNY/bs2YwcOZLIyEh2797NokWLGlRtdejQgfvuu4/58+fz+OOPc+GFFwIQFxd30usVQggh\nhBBC+FNUC1poB7TQDr5thqsSvWI3nvLd6OW7UUPbHXeQgqdHX1wsh2JAA3eUijuq3gfvdANTqYGp\nSMdcZGCqNONp0YLj/0Iy7dxC8stPkaSqjGmVhJ7UEXub9mwPS+YLJZ7vSmBTgQiRxVwAACAASURB\nVJPCmuarFnLpsK3IxbYiF+z2BkOW2mCoR5SZntEWukswJIQQQoifSSakFeeEq666yi/UCQ4OpnPn\nzlRWVrJv3z6/thdffLFf2+rqar777jtSU1P9AiCATp06kZKSwoYNG3xrw9QZMWKEX7gUFhZGeno6\nxcXF7N+/H4A+ffrw6quv+gKg6upqKioqiIuLA+DIkSMNrqVXr16+AKjOJZdcAniDmeZ29dVXoygK\nH330kd/2//3vfyiKwpVXXtnksYGBgSQkJFBdXU1gYCA9evQgISGBhIQE8vPz6dKli++5yWRi9erV\ngDf0qc9kMjF06FA8Hg/r168/7Wv4/vvvAfyCNoDExER69+7tt23Lli0UFRUxaNAgnE4nFRUVvq8B\nAwagqqpv2rymrFq1CvCGU/WPt9vtDBw4ELfbzbZt2wDvfQRvSFhfeno6r7/+ul+IJIQQQgghhGg+\nijkYLbIXlrY3YOv2FJa2NzZoYxgGnvLdTXeiKrgjVWramajoY6bkErCvuQ5PyXa/Ztq+TO85dR3t\nQBbmrz4ibP4L9H/5Hv5vxvUs+/pxDlS/zYEWG/gwtYD7O1joE2vBpjXrJePUYWuRi7m77dy/rpSB\nywto9XYug5bn8+C6EubtqmJbkROnp5lKlIQQQgjxuyeVQOKckJyc3GBbREQE4A1a6q/pk5CQ4Nfu\n4MGD6LpOSkpKo323adOGrKwscnNz/aboauycLVu29J2zrr9Vq1axcOFCsrKyqK6u9mvv8XhO6Vrq\nxtxYaPRztWzZkrS0NNavX09RURFRUVG43W5Wr15NWloa8fHxJ+1j586dDSqadu7c2SD4yM7OBhq/\nxsTERAAOHDhw2tdw+PBhAFq3bt1gX9u2bVm7dq3veV1A99prr/Haa6812t/Ro0dPeL66PkaMGNFk\nm7y8PABfJVHdz0YdVVVPus6SEEIIIYQQ4pcXkPZvPOW70Ct2o1fsRa/IAt3R9AGGjhrk/7eHun8X\n7nCFqi4m7zRyxTqmYgPVBYrHjZazGy1nNwlAAjBU03Dc/CDVV1zJTyUuNhe42FjoZHOBk52lbpoz\nonHqsKXQxZZCF+BfMdQ1svYrykznCDOhFvmsrxBCCCH8SQgkzgmBgYENttWtIeNyuU7Y1m63+7U/\nXt10YccHOEFBQU22rasa+vDDD5k8eTItWrRg3LhxJCUlYbPZKC8vZ+LEiY2er7F+bTabX7/Nbfjw\n4WzcuJGVK1cyZswYNm7cSGlpKcOGDTvhcZWVlRiGwY4dO0hJSaGiosK3LzMzk3HjxlFRUYHZbMZm\ns1FdXY3JZPJbe6hO3b2rqak57fHXHVN3nxrrt05VVRUAN998M3379m20v+OPOZ7dbkdRFF555ZUm\n12iqC+7qXrPGrlkIIYQQQghxdimKghLU2hvqxHtnYDAMD4b9EJ7yPbWh0F70yizweP8mVKzRKJZw\nv34ctz6Me9dCalyrqEk5Vt6jVuiYSwxMxQamYh1zsYFaZaB4PBhRsZhVhe5RFrpHWbiVIHA6UOf+\nm/1RyWwIbMtKpSXrylSO2JtvGjk4VjG0tcj/7+WkEI2ukWa6RVl8AVF8oNrkFOFCCCGE+P2TEEic\nExoLDupCm/Dw8Ab76qsLherCoKb6OT6caeycx4cRCxYsQNM0XnnlFb8p3nJycpocz6n029wGDhxI\naGgon376KWPGjGHVqlUEBQX5rRHUmDFjxvhVJy1YsMBvf0ZGBoBvPZyAgADcbjcul6tBKFJ3jY0F\neidTF9o4nc4G+45/Xetex9DQUN8aP6crMDAQwzBISUkhMjLyhG3rKtIqKip86yUJIYQQQgghzl2K\noqEEtUENalMvGNIx7IfRK/Zi6A3/7jBiE3AXmyDXf7seouIIAUdivf6d3lDIUNZhKgtGCzs2q4J6\ncB+Ba1fSGegM3KKo6PGJVCUkkxXRlk2BiXymtmK1PYhiR/MGQwD7Kzzsr/CwLOfY36VRVpWuUfWq\nhiLNtAszYVIlGBJCCCH+CCQEEueE/fv3k56e7rctPz8fgOjo6BMem5iYiKZpvmm7GuvbYrE0mEZu\n//79DaaQO3jwIHBs6q/c3FxiY2MbrPGzZcuWJsdTN2Xaifptblarlcsvv5z333+fffv28eWXXzJk\nyJCThk7PPvssNTU13H///Tz77LOEhYUB3rWLVq9ezYQJEwCIiooCICkpiT179rB37146duzo11fd\nFGtt27Y97fHXTVl3+PDhBvfo+DWh6qai++GHHxrtq7S09KTBYXJyMrt372bbtm0MGjTIb19FRQUB\nAQG+dafqxrZv374GPy8rV64kICCAiy+++ITnE0IIIYQQQpxdiqIeqxhqspEGpmBwV56wL8Oi4IpT\nIH8lamQH/xAoezcG4IxTMZfoqA4dLTeb0NxsegI9gQxAD4vEnpBMTlQSa2O6sjigE1uKnJQ4mn+t\nnyKHzupcB6tzj81MYdOOTSfXOcJMp9rHCKtMJyeEEEL83si/7uKc8PHHH/utr1NWVkZmZibh4eGN\nrhNTn81mo1+/fmRlZbF161a/fZs3byYnJ4f+/fs3qFxZtmwZhnHsP9glJSVs3LjRL/SJjIyktLTU\nr7onLy+P999/H2h8erfvv//et8ZNnVWrVgHQu3fvE17LyWiad1qCxipmrr76agCmTJlCZWUlV111\n1Un769q1K+Hh4YSGhjJ48GDS0tJIS0vD6XTSu3dv3/O6YGfIkCEALF261K8fp9PJihUrsFqt9OvX\n77Svq2fPngB8/vnnfttzcnLYvHlzg7aRkZGsXbu2QeC2atUqrrjiClauXHnC811yiffTgO+++y66\nfuzTd4Zh8NRTTzFs2DAqK71/+NUFPMuWLfPr46effuKpp57i66+/Bk782gghhBBCCCHOfdYO9xB4\n0SIC+v4Ha9f/w9x2DFp0XxRb0zMCqMH+66UqNXY84QGUXmah4AYbBaOslFxipuJ8E9UpKq5IBUMD\ntayY4MyNdF6ziFvKN7P0smj23RjPtutaMG9QJA92DeaWwHxaaac/3fapqPHA5kIX83bbefS7MoZ9\nUkjSO0fo+N4Rrv2skKe+L+PdvXZ+KHLi8DR/MCWEEEKIX49UAolzQlBQEPfccw+DBw/GbDazePFi\nHA4HN9544ynNXXzvvfeyZcsWHn74Ya6//noSEhI4ePAgixcvJjw8nHvvvbfBMYqi8OCDD9K/f39c\nLhfLli3Dbrdz3333+c55ySWX8PbbbzNx4kQuu+wyCgoKeO+993jwwQd58cUX2b17N0uWLKF///6+\nfnv27Mldd93F8OHDiY6OZtOmTaxatYquXbs2qHY6XXXVTHPmzGHfvn3069fPF9C0b9+e8847jx9+\n+IHWrVvTvXv3U+rzxx9/pEuXLn7bfvjhB2644YYGbQcOHEi/fv348MMPcTqdpKWlYbfb+eyzz8jO\nzmbChAknrcJpzKBBg0hKSuK///0vhmHQtWtX8vPz+eCDD0hPT2fdunW+tmazmYkTJ/LEE09wxx13\nMHr0aKKjo8nMzOSDDz4gMTHR7/VozIABAxg4cCCrV6/m7rvvZujQobjdbj777DM2bdrEX//6V4KD\ngwHo3LkzV199NcuWLePhhx9m8ODBFBYWsnDhQkJDQxk3bhzgrZayWq2sX7+euXPn0rp1a19oJoQQ\nQgghhPhtUBQFJSAeNSAeYo59wM1wVaBX7kev3IdekeV9tB9CDWrrd7zryhupTk+G7U8DoAcqOAM1\nnPUnPNANtAoDU6mBqcTAaGVg2HNRAxNoE2KiTYiJ4W0DCJz3DGp5CY7oBPJiksgMTWSdpRWf6HFs\nNcWiK83/ud4jdp0jdgefHz72gUdNgdRQE50izHSK8D52jjSTGKyhylpDQgghxDlPQiBxTrj99tv5\n/vvvefvttyksLCQuLo6xY8dy6aWXntLxbdq0Yc6cOcycOZMlS5ZQVlZGREQEF110ERkZGY1Ow/bU\nU0+xYMEC5s6dS0lJCXFxcTzyyCNcc801vjbjx4/H6XSyevVqnnvuOVJSUnjssccYMGAA1dXVTJ8+\nnVdffZWkpCTfMRdeeCGjRo1i1qxZ7N+/H6vVytChQ3nggQd+9mKcgwcPZtWqVXz//ffk5OTQuXNn\nv/3Dhg1j586dDBs27JT73LFjB127dvU9d7vdZGZm0q1btwZtFUVh2rRpzJ8/n5UrV/K///0Pi8VC\n+/btmTZtGgMHDjyj6zKZTEyfPp2XXnqJzz//nE8++YSkpCQeeeQR8vPz/UIg8IZGM2bMYN68ecyb\nNw+73U5MTAzDhw8nIyPDF+CcyJQpU1i4cCEff/wx06ZNA7zTxD355JMMHz7cr+3jjz9OcnIyy5Yt\nY8qUKVgsFvr06cPdd99NXFyc7xoeeOABXn/9dWbPns3IkSMlBBJCCCGEEOJ3QjGHoEV0Q4s49neS\noXtQVK1BW71q/4k7UxU8YQqeMHC0AfgUbW85tm5PHztfaRFqeQm6GSyFuSQW5pLIWi4DJgG62Upp\nTCLZ4YlsDWjFalMCX6otOWKNaJbrrc9jwK4yN7vK3HyQfWx7sEnhvIi6cMg7nVzHCBPRtob3RAgh\nhBBnj1J/Oixx5srKyuRGnoFJkyaxYsUKZs+e7RdEAOzZsweAdu3anY2h/SZNnTqVFStWsGzZMiIj\nI8/2cMRZIL83Qpw++b0R4vTJ740Qp09+b/44DGcpnvJdxyqHqrIx7IfA0Js8xtz2RizJY33PtR++\nI+BfEykaZsETrHirhkr12kcDrVRHrYH6HzN0R8ay6tG32F7s8n3tLHGh6/ovUjXUlCirSodwE+eF\nm2sfTXQIN9MiQD3tD0bK740Qp09+b4Q4fb/F35uwsLBT/kdVKoGE+J3YvXs3H330EcOGDZMASAgh\nhBBCCCHOEsUSjin6Aoi+wLfN0J0Y9kPoldneryrvo+HIB2gwrZynbQfsdz2Fu/J5UHRcLRRcLfyD\nHMVhYCrzBkKmMgMlMpp+4aX0j4v1hS0Oj4H79X8QuHMzOeGJ/BDYiq9MLdlkbcmuwHiqNWuzX3+R\nQ2ddnpN1ef7rpYZbFF8w1CHc7AuHEgJPPxwSQgghxKmTEEiI37hvvvmGnJwc3nrrLUJCQrjzzjvP\n9pCEEEIIIYQQQtSjqBaU4GTU4GS/7Ya7Cr0qBzWwlf8BoeG4u7SD75quHjKsCq5YBVdsXTi0D77L\nIPDi/wLeKdmsmkJ4QQ6qvYDOFQV0MTYxuu54RaEkJJZ9oa3Yao3nW1MCmYEJZAa1pNwU2DwXXk+p\n0+DbfCff5vuHQyFm5VgwFOZ97BBuonWwTCsnhBBCNAcJgYT4jZs+fTqHDx+mS5cuTJw4kfDw8LM9\nJCGEEEIIIYQQp0AxBaGFdWp8nzkYS+o49Koc79RyVQdAd5ywPzWwFYpSLzzRddTD2VR1MVHVRfNW\nDpUZmMq8U8uFlOeTdiSP8z2QUa+fZ298hS+J46cSFwU13iBKMXQMFGjmqp0Kl8HGAhcbC1x+2wM0\nhVY2G20CdHpWlNMuzET7MBMpYSZCzL/e9HZCCCHEb52EQOKsevrpp3n66adP3lA0adGiRWd7CEII\nIYQQQgghmpliicCceK3vuWHoGDX56FU5GPaD6FUHfF947N5jAhP9O3G7cA69AZfyKWgluCMV3JHg\nwL/KRq00MJXraOUGWjnc06uK+yNsKOZoCqo9/FTiwvXtVwxZ+QpZwS3ZYo1ne0BLdga1JDMwgUPW\nSIxmXneo2mOwp0plT5XK/wor/PbFB6qkhppoF2YmNcxEu9qv1kEamipTywkhhBD1SQgkhBBCCCGE\nEEIIcY5TFBUlIA41IA6ot96QYWA4izCqDoApyP8gixXXyFtwfbsO7CVN9q0HKziDNUio3bDjaazd\nJ2OKSiMmQOPiAA2zlofFXUEnZRfdCnei1pvVrcZkJTswju22OHYHxLMrIJ49gfFkBiZQaQpovptQ\n64hd54jdyTdH/aeWs2qQHGLyBUOpoSbah5tJDTURbpXqISGEEH9MEgIJIYQQQgghhBBC/EYpioJi\njQZrdJNtzInX1E4pdxDDfgDDUXjSfo9fp0jNzcEVoVBypdV73moDU7mBVq5jKnfTtuwgqRUH0IoM\nFI/3mLfPv4lprYaxp9yNq97yRin2oxywReNSm/dtKYcHMkvdZJa6G+yLtKqkhGokhZpIDjGRHGoi\nJdT7GCEBkRBCiN8xCYGEEEIIIYQQQgghfsfMCZf7PTfcVej2Qxj2Q+j2w37foztAtaDYYvyO8XRN\nxx1RBOz09hGg4ApQcLVoGKCoVQZahcHQxN0Ma7cLYi5if4WbnaVu9hVU8uTLE3ArKtm2GF/V0K7A\nePYExLE7MJ4jlvBmn16u2KFTXKDz/XFrDwGEWxSSawOhZF9IpJEcaiLKqqI08zpIQgghxK9JQiAh\nhBBCCCGEEEKIPxDFFIQW2gFCO/htNwwdw1GE4ShAOS6Ecfe/DGfWEcjZedL+9SAFPUgB5zZMZW2w\nthhAuzAz7cLMqEouADVdFeIopGVFAX+q2IaWb/immKtWzWTZWpAV0IJ9AbFsCW7LO3H9m+fiG1Hq\nNNhc6GJzYcOAKNSi+CqHkkNMJNWGQ21DTLQIUFElIBJCCHGOkxBICCGEEEIIIYQQQnjXHbLFwHFV\nQHVMCZejhqTWqxzyfuGubLJPNSDB77ly9CAA9o4mDJt/gKI4vBVEpnKDthVHSak4glapc7CmHfkt\nB7G7TOdgpQejtv2o/PXEOcvICmhBlq0F+wNicKrmM78BjSh3GmwtcrG1qGFAZNMgMdhE2xCNNsEm\n2oRotAnxBkRtgjVCLTLNnBBCiLNPQiAhhBBCCCGEEEIIcVJqQBxqQFyD7YazDL36MLo9F6P6CHp1\nLkZ1Lro9F+W4EEhPPo/qW+/D0Gc27Meq4LYquI9b3iiYA8xTxxF47VJqdJV95W72lrvpM3sNSUe3\nggKKAwwUDlij2BfQgr0BxyqJsm0x7LPFUmYOatb7UeOB3WVudpe5AUeD/ZFWlTYhGm1rA6K6cKht\niIlWwRpmVaqIhBBC/PIkBBJCCCGEEEIIIYQQZ0yxhKFZwtDCOjXYZxiG//PoOFy9e6NsWYThLDn1\nc5jDUFSNABU6R5rpHGkm0H4UeweNql5mFJeBVmkQXlFG78pS+lTuRK000Iq921U3lJgCuajn/2Nn\nUEu/vi26C83QqdasZ3YDmlDs0Cl26GxpZJo5VYGWQZovFEoM1mgdbKJ1sEbrII2EIAmJhBBCNA8J\ngYQQQgghhBBCCCHEL0JpZM0cNag1gf0XYrir0auPeKuGqnMx7Lm+KiLDUejfT0AL/048bpTKMjzB\n3v4Ns4I7QsEd0cQ4agy0Sjdz4z/ic20oX1elklXuIafSzSVFO1i2/XmOmsPIDohhvy2GbFus9zEg\nhv22WA5aI3Grzfc2mm7AwUoPBys9rDnqbLBfVSA+QPOGQnVfQd4KorqgKMgs080JIYQ4OQmBhBBC\nCCGEEEIIIcSvTjEFoIUkQ0hyg32Gx0H2rg1o7iLiIzUUc6h/A81E1esf4/p+AlT+dNJzGTYFt02h\ntWsDt593GXfHeOecc+sG9o/Xo2eC+YpqOlTl0Kkq21s9VGWglRhoVQZGtcJhSyTZtliybdEsi07j\nw5jezXIfGqMbcNju4bDdw7f5jbeJtKq0CqofFJloXe95lFVtNIQTQgjxxyIhkPjDmTlzJrNmzeK1\n114jLS0NgPT0dHr16sXrr7/+q4/njjvuYPPmzWzYsOFXP3ed9evX849//IP8/HxGjhzJo48+etbG\nIiA3N5cRI0Zw5ZVX8vTTT5/t4QghhBBCCCHEr07RrLjNcbjNcZhbtWuikYIpZQxaVTZ69VGMmqO1\nj3mgN6yu8R1mi/V9b1IVoivy0YMU3BEqNFFJhG4QaK+ka2UFPar2Em8uxgjQWWa/wK/Zku0voCsK\nB2zRHLBGc8AW5XssMIdCM4YyddPN/VDccLo5gABNISFIpWWQiYRAlZa108y1DNJICPQ+RkpQJIQQ\nv3sSAgkBTJ06lYiIpv6n13y++eYbPB4PAwcO9G0bP348JSWnPg9yc9N1nUmTJuFwOHjooYdo3779\nWRvLb837779Pjx49mv2eRUZGMnXqVOLj45u1XyGEEEIIIYT4vTFFpUFUmt82w9AxnCUYNXkY1Ue9\nU87V5PkCItUa69fe06MvzuBS4OumT6Qq6MGgByu4gO5k8UqojfvaDCOnwk12hYcDFU6Gfr0N53kG\nnjAF1W6gVYFaYqDZDZzVJg6qURy0RXPAGlUbFEXxVtxFGErzT+1W7THIKveQVe5pso1Ng4RAbziU\nEKTRqjYgSqh9bCUVRUII8ZsnIZAQwJAhQ36V87z99tskJCT4hUC9evX6Vc7dlOLiYoqLixk8eDCj\nRo06q2P5LXE6nbz44os88cQTzR4C2Wy2X+1nUgghhBBCCCF+bxRFRbFGgTUKwjqdtL2nY0888Wa0\nnBr0mnyMmnzw2E96nCUglvNjLJwfY/Get7QIs+6msqUZZ4LW6DERrhKi7MWkVRmodnBVaxghBp/Y\ne1Koh/naDSvcxNCireRaIzhkjeSwNdL3WK4FNFtFUY0H9lV42FfRdFBk1SA+sDYUCtKID9SIC6x7\nVIkL1IgL0LCZJCgSQohzkYRAQvxKdF1n165dJCQknO2h+HE6vSXyAQEBZ3kkvy179uzB7Xaf7WEI\nIYQQQgghhGgGWngXtPAuvueGuwqjJt8XCvl97yjAcBSh2lr4d+Jy4u6chid0J9B4qGKYFTxhCp5j\neQ//4C1SWnZiY7WNg1UeDlZ6uKhsF3+t/JKqVBOq3UCtNtDKvY/VNVZy9QhytUi/gOjLiM7sCWz+\nGSUcHsiu8JB9gqAIINyi+AKiFgGq73tvSKT6vrdqEhYJIcSvSUIgcVZNmjSJFStW8M477/Dyyy+z\nZcsWpkyZQv/+/QE4cOAAs2fPZvPmzVRWVhIVFcWFF17IbbfdRmysf/n2d999x4IFC/jpp5+orq4m\nNjaWtLQ0br/9dmJiYk44juPXBEpPTz9h+/rr9+Tk5DB37ly+++47SkpKiIiIoEOHDowbN45Onbyf\nOProo4945plnAFixYgUrVqwgIyOD8ePHN7omkK7rLFq0iOXLl5OTkwNA69atGTp0KDfccAMmk/dX\nt27tmKuvvpobb7yR6dOns337dlwuFx07duTBBx+kY8eOJ73/9cdVtw5Neno6vXv35i9/+QvPP/88\nVVVVrFy58ozHN2LECP7973+ze/duQkJCGDFiBOPGjSMzM5OXXnqJnTt3EhISQv/+/ZkwYQJms/mE\nr8Hw4cOpqanh3Xff5YUXXuDbb7+lpqaGpKQk7rjjDi688EK/9tnZ2cyaNYuNGzdSVlZGWFgYPXr0\nICMjg9TUVF87t9vN+++/z8cff0xubi4ej4e4uDiGDBnCLbfcgsVi8btvzzzzDM8884zfGlNbtmxh\n3rx5bN++HYfDQWxsLAMHDuSWW24hNDTU7xo0TWPy5Mk8++yz5OTksHLlSsrLyxtdEyg/P59Zs2ax\nfv16ioqKCAwMpEuXLowdO5aePXv62i1ZsoSlS5cyY8YMli1bxpo1a7jrrruk0ksIIYQQQgghTpFi\nCkIJTkINTmp0v6G7QPf/YKARE0/No//C2PQw2A+Aq/yUz3f/+UkolnDfc21GNR5doSa58YqiSEqI\nchbTvdrwTjtXDZ/ZuvKW+WI+tp9/rB/dw/zMVzlqDeeIxft11BLBEWs4uZYISk2BzVZVVOo0KHW6\nySw98QcmI6wK8QH1AqJAlbiAY9/HBmjEBqgEmpp/ijwhhPgjkhBInBNeffVVoqOjefLJJ0lOTgZg\n7969TJ48mRYtWvCXv/yF6Oho9u7dy5IlS1i7di1z584lOjoagLVr1zJhwgTatm3L+PHjCQ0NZc+e\nPbz//vts2LCBd999l8DAwFMez9SpUxtsO3DgAK+99ppfYJCfn8+4cePQdZ0xY8YQHx9PQUEB7733\nHhkZGcyaNYtOnTqRlpbGo48+yrRp00hLS+O6664jKanx/0gCTJ48meXLl9O3b19fULBu3TqmT5/O\n7t27fYFSncLCQu69914uvfRSLr30UrKysnj33Xd56KGH+PDDD7FYLI2eZ9SoUXTu3NlvXPXXoamp\nqWHatGlcf/31REZGnvH48vPzefLJJxk5ciRXXXUV7733HrNmzULTND744ANGjhzJlVdeyfLly1m6\ndCktW7bkpptuOvGLhLeKqe51v++++6ioqGD+/PlMmDCBN954g27dugGQlZVFRkYGmqZx7bXXkpiY\nSG5uLosXL+a2227jzTff9E3p9vzzz7N06VL+9Kc/cf3116NpGps3b2b27Nns3buXadOmMWrUKAID\nA1m0aBGjRo2iV69evp/b1atX8/jjj5OSksL48eMJCgpi+/btvPvuu3z77bfMmTMHm83muwbDMHj2\n2We55JJLiIuLw2q1NnqthYWF3HrrrZSXl3PNNdfQrl07ioqK+OCDD7jrrrt44YUX6Nu3r98xCxcu\nRFVVJk6cSLt2TSykKoQQQgghhBDitCmqGdTGP7wYkPY8AIbHieEswqgpxHAUojsKa6uICr3bagow\nXKWgmMAc5teHyWrFFRkINB2oGBYFj8VbVeQCBvAT6FHsMffhYKWbGg+0cJVxfcG3lPUz4wlW0Gqr\nilS7gVpo4KnRKPSEkKeHc4hIjlgj2RMQx4xWlzXXrWqgxGFQ4nDz00nCohCzQoztWCgUG6ARE6DS\nIkBrsD1ApqITQogmSQh0DguYev9ptTfMVmoentZgu+m7LzB/8eFp9eXqfznui65osN328lMolWUA\nVD/+0mn1ecLzuVz83//9n9+2//znP4SEhDB79mzCw499GqZnz55MmDCBefPmMWHCBMBb5dG1a1f+\n9re/0aZNGwAuv/xyVFVl3rx5fPXVV1xxRcPracrx67HU1NQwa9YsgoKCf+t3vQAAIABJREFUeO65\n53zb9+3bR2pqKsOHD+eyy479Byk1NZX777+fpUuX0qlTJ+Lj432VKXVVJU3ZsWMHy5cvp0+fPrz4\n4ou+xRevueYaHnzwQVauXMmf//xnunQ5Vqa+bt06pkyZwiWXXOLbVl5ezvLly9m2bRu9e/du9Fyd\nOnXy3dvGxrVjxw4mTZrE5Zdf/rPG9+233/L666/71j9q3749t9xyC2+88QbTp0+nT58+AFx44YUM\nGzaMb7755pRCoKqqKtq3b89jjz3m23beeedxxx138NZbb/HPf/4TgOnTp1NVVcWsWbN8wRBAv379\nuOWWW5gxYwYvveT9ef70009JTk7m2Wef9bUbOnQorVu35scff6S6uppOnTqxb98+ADp27Oi7b06n\nk+eee4527drx5ptv+gKdYcOGkZKS4guYRo8e7es7NzeX22+/nVtvvfWE1zpr1iwKCgr4+9//7vez\ndtlllzFq1Cj+/e9/NwiBDh8+zIIFC3yVWUIIIYQQQgghfj2KZkEJiIeApqdoM3Q3hqvM97d1HUfG\nRFyHu6Fkv4PhLAbjxFOx1RmSFM8VKS0wDINih05ZZjGsB1eMgidMxdXIMQHYaYudtvph1BqocZi5\nwJbJhMJbKai3TtHfspdyZelm8m2hHFSjOGqJ4KglnDxLKAXmMPIsYeRZQrFrtkbOcvoqXAYVrhOv\nV1QnxKwcC4pstUFRwHEBkk0CIyHEH5O8M3gO03ZuO632hq3xNV2U4oLT7stzXo9Gt6t7f0QtLTqt\nvk7F4MGD/Z4fOHCA7OxsBg8ejKZpVFRU+Pb16NGD0NBQNm3a5Ns2ZswYxowZA3grK6qqqjAMg5Yt\nWwLeN9p/jqlTp5KVlcVzzz1H69atfdv79OnjCzAAqqurcbvdxMXFAXDkyJHTPtfq1asBGDlyZIP/\nBF511VWsXbuWNWvW+IUssbGxfgEQeAOe5cuXU1R05q+XqqpcfPHFP3t88fHxvgAI8FWlREdH+92/\n6OhoIiMjT2vMI0eO9Hveq1cvwsLC2LJlC+B9Tb777jtSU1P9AiDw3qOUlBQ2bNiAw+HAarWiaRoF\nBQXk5ub6rd80duzYk45ly5YtFBUV8ec//xmn0+lbbwlgwIABvPDCC2zevNkvBDIM44ShYJ3Vq1cT\nGhra4HWOi4ujd+/erFmzhkOHDvntu/jiiyUAEkIIIYQQQohzmKKaUKxRje4zt7wCc8srMAwdXBUY\nzmJ0RxGGoxjDWYzhKPI+1hRi1BRhuEtRLN6+FEUhyqYRE2SgxyagBxaffDCqgh4IlkA3Q9hOq1Ab\nVZUKdrcBQOeqQ3QNzaFskIXzdQO1Bm9VUY2BWo33scLA5TBR6g6iyBPCpLjr+DS4Ox6OTWun6R6S\na/LJs4RRrgU0y3R0dYFRVvnJA6Mgk0KUTSXa96X5vo+q97yuTZBJafD+hxBC/JbIu4PinFD/zXaA\n/fv3A/DFF1/wxRdfNHqMYRi+791uN/PmzePTTz/l8OHDuFz+n23xeE7tEzONWbp0KZ988gljxoxh\n0KBBDfavWrWKhQsXkpWVRXV19c8+b3Z2NgApKSkN9tVVOR04cMBve6tWrRq0ratCcbtPXF59IpGR\nkQQE+IeLZzK+41/fuvV+6sKy4/edzpgbm1YvJiaGvXv3YrfbOXToELquNzreujFnZWWRm5tLUlIS\n48aN41//+hd//vOf6du3L+np6fTp08cv/GtK3c/ta6+9xmuvvdZom6NHjzbYdvz9OV5FRQXFxcV0\n69YNTWs4H3SbNm1Ys2YNBw4c8Fv/6mT9CiGEEEIIIYQ49ymKCpYwFEtYk2sUQe37JMdVDOntu1H1\n3HzUH6fWhkWFGK4yTjTNnPekZr4Y4T1XmdMg1+4heX8luq02DKkNjPTAxsORAOy0ws6bzGB+xUAe\nLz4220eio4jMDQ9j76Dh0jQq3AGUeIIo8IRy1AjnENEcMUeQbw6lwBJKgTmUo5YwCixhjZ7rdFW5\nDaoqPRyoPLX3bGwaRNs0omwqMU0ERXVhUpRNJdQsoZEQ4twiIdA5zHNe99Nqb5gbX0vEiIw57b70\n6IZvzgPoqZ0xaqeDa07Hr9djt9sBuOiii/yqJuqr/w/q3//+dz755BO6dOnCo48+SlxcHCaTiY0b\nNzJ79uwzHtfOnTt54YUX6N69O3fffXeD/R9++KFv3aJx48aRlJSEzWajvLyciRMnntE564Kk48MX\nOBbsHB82NbXmz8/V2DpKZzK+utDneD933CaTqdE+goKCAO/0bHU/S42NFxqO+frrr6dt27a+NXy+\n+uorALp3787EiRP91oQ6XlVVFQA333xzg6nZjj9fHYvF0uT9qXO611DndNbBEkIIIYQQQgjx26Yo\nind9oeO3qyZsXY9NwW8YBrgrayuJSjCcpf6PjmJQVd/7LuFWhXCriqVzV2pc5UDBaY0rPCicbpg5\nWu2hoFqnhdP7vlJVFxN6sIIZB7E4iKWYznVjdhqoDgOlxlthVKiH8Hb4AF4sG0aVcexv47FHvuI8\n+2EKzKEUmkMotHgfC8yhFJhDqNRsP7vSqMYDh6o8HKo6tdDIrEKkVSXSqhJx3GOkrd73dc8t3kez\nKsGREOKXISHQOay51txxXzAY9wWDT97wFNTc+0yz9HMydW9eW61W0tLSTti2sLCQlStXkpiYyKuv\nvorNdmzu2ZycnDMeQ0VFBY899hjBwcFMmTKl0Wm1FixYgKZpvPLKK74qmJ973ro3+uve+K+v7k3+\nupDjbDiXxud2u3G73Q1em8rKSjRNIzQ01Pez1Nh4ofExX3DBBVxwwQXU1NSwZcsWVq5cycqVK7nr\nrrtYsmQJISEhjfZV10doaOhJf25Px6leg4Q+QgghhBBCCCFORlEUMIegmEOAtqd8nPP6OzDKB2Ep\n+8kbFlUXYVQXeqenc5dh6JWA3uC46zrEc2PrWABcuoF9/V7YAvoJlg4yLAoeiwK1f36HYucuVvKv\nsuF+7YYXbuTS0K2UX2hGdeANjmofVYeBXq1id1mo8ARQpgdRqIfwWvSlrLOeR5l+7H0Ak+4m1lVO\nsSmYGu3nfWDVpUNetU5edcN7cSIhZqXRgCjCVm9bvX3hFpVQi4IqVUdCiJOQEEick5KTkwHYvXt3\no/tLSkqIiIgAvOvuGIZBt27d/AIgwLcuzOkyDINJkyaRl5fH9OnT/abYqi83N5fY2Fi/AOjnnBe8\n1/7111+TlZXVoN+66cbatm17xv3/XOfa+LKzs/2qc9xuN3l5eURGRqKqKomJiWiaRlZWVqPH79+/\nH4vF0ujUaTabjb59+9K3b1/Cw8NZuHAhmzdvbrBOUp26n9sffvih0f2lpaWEh4ef7iUSEhJCdHQ0\n2dnZeDyeBlPC1d33pKQkv/WzhBBCCCGEEEKI5qSFdkAL7dDoPl+FkbPEr7JIizi2Pq9ZVQg/ryPV\nGQ+DcwZgNNpXY1yKlds7R5JX7aGgRie/WifBU4FhVUBreno6DTfhVBBOBW04yiz2MLP8UiaV3OBr\nc549l60bH6fifBMuk0aNy4zdbaW8Njwq0kMo0EM5SjhHlAiKTCEcsEWzJaTp6flOV926Rqc6TR2A\nqkCYRSHM4g2Fwq0qJqeFEJNBYmkZ4da67QrhFtXbzqoSXnuMJtVHQvwhSAgkzkmtW7emTZs25OTk\nsGHDBtLT0337duzYQUZGBnfeeSdjx44lMjIS8IZB9W3YsIFvv/0WAIfDcVrnnz9/Pl9//TV33nkn\nvXv3brJdZGQkpaWl1NTU+AKovLw83n///QbnrXvj3ul0nvDcgwcPZu7cuXzwwQcMGjTIV35tGAb/\n/e9/ARpdm+jXcq6Nb9myZTz00EO+599//z2VlZW+6dhsNhv9+vXj66+/ZuvWrfTo0cPXdvPmzeTk\n5DB48GDMZjOZmZn87W9/46abbmLEiBF+56mr8qmbfk5VVcD/Ne7ZsyeRkZGsXbuW7OxsvzBs1apV\nPPXUUzz99NNcfvnlp32dQ4YM4b333mPVqlV+xx84cIBNmzbRsWNH4uLiJAQSQgghhBBCCHFW+FUY\nBSU22c6IisVz0TACjSvAVYnhKsNwlnkfXWUYjhIMeyFUF2I4SjHc5RhKDRZrCJN6+68LFLDdij2w\n4dq5J1PiCfZ7Hun2Tu9ek6yhByhouAnBTQhVtKTwuAswUFzgcJnZbY5n5NHHsBvHPpT8933v09+d\niR5jUKwHU2yEUGCEcVQJ4wgRFGkhlJiCKDUFUWIOokKzYSjqaV8DgG5AicOgxOEB6sKj2rd7j1ae\n9PhQs0JovWCoLkjyhkpKvRBJJczibRtq9lYgBZlk7SMhfiskBBLnrFtvvZUpU6YwceJEbrzxRlq3\nbs3+/ftZvHgxkZGRvjfCExIS6Ny5M5s2beL555+nc+fO7Nq1i08++YSnn36ahx56iC+//JLU1FQu\nueSSk573p59+4vXXX6dFixa0bt2azz//vEGbTp06ER8fzyWXXMLbb7/NxIkTueyyyygoKOC9997j\nwQcf5MUXX2T37t0sWbKE/v37ExUVhdVqZf369cydO5fWrVszZMiQBn2fd955XHfddSxevJiHHnqI\nAQMG4PF4+Oqrr9i4cSOjR48mJSXl59/gM3Qujc9isZCZmckzzzxDjx49qKioYP78+ZjNZm6++WZf\nu3vvvZctW7bw8MMPc/3115OQkMDBgwdZvHgx4eHh3HvvvQC0a9cOq9XKtGnT2LNnDx07dkTTNPbs\n2cP7779PcnKyb5q3usqhRYsWUVNTQ/fu3enSpQsTJ07kiSee4I477mD06NFER0eTmZnJBx98QGJi\nIv379z+ja73tttv46quvmDx5Mnv27CE5OZm8vDyWLl2Kpmk88sgjP/NuCiGEEEIIIYQQvx5F0cAS\nhmIJg1OYVd4wGlYNVf/tFTyFGzEXfI9RXQSOEgxXOYa7CsOwY+AApeFxt3eP44qQaAprdIpqdKK3\n6xhbQT+VmeAUBcMCFoubLhykxvA/qFfFfs6PyqK8RxPr/7oNVGfdukeA0+CLoK6847mIZfZjH4KO\ncZbxyIGPMEJ0StRg8pUw8pQwik0hlJoCvSGSKYga1XzG6x6VuwzKXae+3lF9quKdws4bDNU+1v/e\nt02pDY7UY+1rt4WYFalGEuJXICGQOGe1a9eOSZMmsWrVKhYvXkxFRQUREREMGDCA8ePH06JFC8D7\nSZMpU6bw/PPP+9Zu6d69O6+++iopKSmMHDmSTz75hBkzZjBw4MCTnnffvn14PB7y8vJ44oknGm3z\n1FNPMWzYMMaPH4/T6WT16tU899xzpKSk8NhjjzFgwACqq6uZPn06r776KklJSbRo0YIHHniA119/\nndmzZzNy5MhGQyCARx55hLZt2/Lf//6XF154AUVRSE5O5sknn2T48OGNHvNrOpfG989//pOXXnqJ\nV155herqalJTU7nrrrvo0OFYeXqbNm2YM2cOM2fOZMmSJZSVlREREcFFF11ERkYGLVu2BMBkMjFz\n5kzmzJnDV199xUcffYTb7SYuLo7rrruOW2+91VcJ1KNHD6666ipWrVrFnDlzeOyxx+jSpQuDBg1i\nxowZzJs3j3nz5mG324mJiWH48OFkZGQQHBzc6HWcTHh4OHPmzOGNN97g008/paioiJCQEHr16sVt\nt91Gu3btfv7NFEIIIYQQQgghzlFNVZ2Yos+H6PMb3WcYBniqvcGQqwLcFRiucuJD2tMy0Hqs78iu\n1ETeh6ovxNBrMBQXnEI2UU0gg1oG+MKkwhoPke7KE4dJJgXdBAQqvtqdi/iJrWVt/UKgVo5iHjr0\nMYXXWPCEHKsUUlzeSiTF6Q2TDDe4XCacHhOHlCiWRvz/9u48Torq3v//q7eZYVgGRxRE2cGjuKFe\nERU0Iip69UtcQCMuISgqXhfACFdFRFGucQ0/JWrciCYaoiZGEzEkBiKuETGK4hFGEBFkG5bZeq/f\nH73QPdMD08Aw3c37+XjMo7qrTlV9+tQczlCfPqf688TWM6lztn2+wZsW0yW0nmCRl/WUscHTjq3e\nVmzxlLLV24qQO/tbxFEHtgQdtgSzTyClauuLJ4SSyaL0JFIbn4s2vtiybcrrNvEkUhufizZeN8We\nxn9HRPZ2rkxZdMneli1bVJG72dKlSwF0c1syGjZsGBs3bmTBggUtHUpOUbsRyZ7ajUj21G5Esqd2\nI5I9tRtpKY4TgXBNPHkUSyA5oa1QWxkbceTfjOMKQmk7ig8dn7Kfg+eZBwl4PibYdXNW57xn0wXM\n3Hp28v3gTYv523+ms+7i4thzj7LQZ+VjaVPU/WHxwwxt+wlbT45npyKxRJI7GFs6IReRkJtgxEsg\n7MMfKeL1smP5K8fwfuCQ5HFah/2cs/EToiUuNrlas9ZdxhZvKVs8pVR5WxHdyWntdgevC1r7XLRN\nJoniCSOvK55ASk8oNUgkJRNNsaVPI5T2KvnY35SVlTX5l1QjgURERERERERERETiXC4P+Nrh8rXL\ncj8X0dE34w1V4wluwglXxUYg1Vbi1MaSR/g3x5NK1RCtwYn6ibYu4pbjuvGzsv2pDETZFHBo83kR\nwS+KcRqZVa4xEcdFbcooIICycB2OL+V+sceF44FISeo9ZIciQhQRoi21/Ix/EN3qSksCHRSo5LdL\nHmPDsCIi7eMJn5CDOxwboRQNu4mGXYTDXkIRD8GIlx9c7flr2dE8ufUMqpzS5LEGbv6K3qEf8JSE\nqaQtG1yxn63xhFK1pySrpFJ4N41MSij2QGuvm1Jv7PlHrX2u5OtSr7veexetfe7k69J44qk0sX9K\n2VZeF26NWJI9TEkgERERERERERERkd3E5WuDy5fddPClQPvUFV1OJXDWyRSv+Rf4N+HUboLAFgjE\nEkhOpAYnXEc0WodDEFwhol6HsMvHLb1CFJV1YHMgyuZglC6f+7NOJgFUR0vS3pdFagFwvClJDJ+L\nqA9oFVvnwsFHCB+h+Geq5hBW8VzVYEiZR+mq1W9zQfH7bPmv9LnzktPdhRyciIto2E044iYU8fJx\naS/+GO3P72sGbau3iJ//WfU39infStjrZqtTylZK2ewqpZK2VNKGja42bPWUUuMuJtDEZygFIhCI\nRKkMZFdnTZFIFLVOJJHiCaPUZFOpNzbNXat44qjU66LEk/66NL6tVXx9Yp3PranxJJ2SQCIiIiIi\nIiIiIiI5xuXy4O18alb7LP36K4a7wvTp03bbyiMfJFL5BcVbvoTAVpxgNdFQNZFwDdFIHU40AATA\nFcLlCYMnissFh+zblh/v04rNwShbg1EO8QcBdiqhVFNvdFLbSF3G4zg+V3x9Ionh4CWClwiD+JKV\nVfumJYH2DVVz7/Lfs7FvEeEO2xk5FHVwhcEVhkDEiy3uzFXrr2NleL9kkZ+umcd/133Cvl03Uxct\npjZaTA3F1DglVDklVLtasZVWbKWULZSy2dWaZUUdWetuT5CmV0pt2KE27LChyXtkx+MimRhKTRI1\n+tqz/URTSbxM4nWJx0WxJ7YsUsIpLygJJCJ56bXXXmvpEEREREREREREcovL03Bdu/a4252Em5Oa\ndAjHiULEz/kuNxd4UkYDBQZRM2wWRev+QcS/hXCgikiwhmi4FiJ+iPqBIC5XCJcrjMsTwfECHjip\nc1uqgrA1FEsolUUD6VPUNVFdg2SSPxbzju5yu104ReAUgY8Ih/Md9R/wfvzWZZzNIjb3Ksp4iMbM\nqe3H6PXXJ9+3igT48qObcY4N4yqPEol4CEc9hKIeQlEvwaiXQNRLIFqEHx910SI2u0r5W9lR/LPu\nCCqj2xJ4B/o30jm8CZ8vzGZXLPG01dWKOncxEXeGaw1EHKgOO1SH98wj7Es8JJNCiZ/i5JLk+1be\n1PWuhvt5G9nP0/h+Hj27qUmUBBIRERERERERERERAFwuN3hLG24oLsHp3A1v55/hBYoblsjIcaK8\nUu/5Pq6zphHauBS2fE2wbivhQDXRUA1OqAYiflxRPy4ngJsQblcItytMTWkp7VqX099bRHUoSlXY\n4YC62HxtaVPUNVFtNP0TtI4EcJr6oVLUT0yVRoJ0CVRS2cZHaF8PEG7Scc7hY85ZcxuVwW1JoKtX\n/4OfV/2Zyv+Xcg7HgQi4IuBEXDhRcCJuolEXkaibb30deNs5grs3X5R2/HsrXqLL/uto3dqP3/HF\nfiiizimiliJqKaaW2OinalpRTQmLW3Xhh0h7/NupGH8E/BGHLQ3Sas3P6yKZXCpyQ5HHRbHbFVt6\nwOeObSuObytKbEt5X+yBqs1eitxwQLA6ua04fiyfO5Z0yrTfttex8xd7XHhzMDGlJJCIiIiIiIiI\niIiINAuXq+E0bU67ffC0609r+tO6icdpD4yK/2w7UEeqR8/BvfFrgtWVBOqqCPurCPurcUI1OKE6\nnHAtrkgdrmgAtxMg6POysW17Bh7Unk0hH9WhKNUhh7rSMtYWlVFCXVafz19vXrtW0fi0eTuRmKpz\n0kchtYoGG45ycrnAu230kwtwEcUNeIlwMGtYW9c+fR/H4ebv3mBrTy+B7plHEDXminU38Pe6o5Lv\nr1v1FtNXv0jVuR6IQDTqwom4iURdRKNuIo6bSNRN2ImNgAo7Hr4p2o/3fYfwyJZz04596Q/v0LvN\nGvZpVYUfH36niAA+6iiiLp6YqsNHDSXUuoqooZhVvn3Z5LTF7xQRdqAq5FAV2tUEVLzeV2zZxeOA\n20VaQqrYk5JIcrsoiienityxxJHPU/91ynYP3HFs2S7HpCSQiIiIiIgUjMrKSubOnct3331HOBzG\n6/XStWtXhgwZQnl5eUuHB8DChQuZOnUqK1euJBKJ4PF46NatG3fccQfHHntsS4cH5Ec9Qn7EWVFR\nwWOPPcbixYsJh8O0bduW3r17M3bsWHr16tXS4eWNfLjWkD9x5rpEPX766aeEw2E6duyYc/WYaNsV\nFRXJa622vXPyod3kQ4z5oFnq0eWC4hKKOx/Z5JFJAL2A/vVXnj8RgGg0TF3QT62/Dn9dFcHarYTr\nqojUVREJ1ECwGidYC+FaNrbrgG//XozZv3XyWT/eqjb8tcepdPUvo9WGWjzuCG53BLcnitvj4HY7\nuLxOxjvzGZNAnuyTSYF6iSmfE8GNg5Nd/gfInOQq8oRj88ABbhwgwvYO3ZmNlAerGySB/q/iRUqP\nqaGuZ3ZpinEbRjG7ZmDy/YXrPmDmsqcInefgRGOjo6JRN07UlRwhFU0mp9xEoh6+95WzsLgHUzZd\nknbsK9bM5/BW39KpbBNBvAQcL0G8+Cki4PgIuHwEHC8BfLHEFUUsLenE8mhH1kXaE3Vio6NCoTCR\naIioN8AmigjhJYQHh+08uyoDJYFERERERESAuro6nn/+eZYvX05xcTHFxbHbAKFQiC+//JJFixbR\no0cPLrvsMlq1atUiMa5evZoRI0bwww8/4PF4KCqK/Sc/Eonw1VdfcdFFF9GpUydmz55N586dWyTG\nfKjHfImzsrKScePGsXz5cnw+H44T+4ZqOBzm008/ZdSoUfTo0YOHH35YNxC3Ix+udT7Fmevq12M4\nHJtCKZfqsX7bLimJPS9FbTt7+dBu8iHGfJBv9eh2e2ld0obWJW2g/X47cYRyOHdKxi2RqENNPFlU\nG4pSGwrGEk3+WmpxuK3rflSHPdSEo9SGHao7D+PFzYfSqXIp3qgfT9SPxwnidYJ4COF1QnhcYbzx\nH48rwupW+2Aj6X9LFkXDVLuLcdzZj5ipnwQqiYbYbsanEcEMD24qiYbIMicCNExytY4EaB+tY31J\nCS4cXICbyHaPsT+b6Rze2CAJdNOqv9Kj9xpquvsa2TOzuzcN5/GtQ5PvB2/+gjc/u491PynGKUpJ\n5EVjP04UcIgnrVw4jotqVzGrfeWcuWZKfGzX7uFK/CGab4wx5cAU4MfAAcAG4K/AZGvtmibsfyIw\nGRgAtAK+Bn4NPGqtzbpStmzZkp8VmcOWLl0KQJ8+fVo4EpH8oXYjkj21G5Hs5Vq7qaurY8aMGdTW\n1iZvxmXi9/spLS3lhhtu2OM3GFavXs3QoUMJBALJ5E8mwWCQ4uJi5syZs8cTQflQj5AfcVZWVnLF\nFVekxVhXF5taJjWWRIyzZs3SzeIM8uFaQ/7Emesy1WNlZSVAWvvItbadidr2juVDu8mHGDPR32kS\nisaSTHVhB38k9tofdqiNxNYF/AHCgRqi/mqigRqcUG1sZFOoDle4Dne4DnfET9SJ8E37A/kweARr\nI22Tx+u/9jOGbP03h3WpwEcYnzuMzx3B647gdUXwuKN43FHcLge3O4rL7VBdVMK/w725fP1NabFW\n/eunBE8Ef6/sskpXrb+Wv9b+V/L9mO//zqMrn2X9xY3/jmWyKlzO8d/fn7buiw9v5sBD1lNzZHbj\nZ6ZUXsxTVacn35+9cRF//vwB1o4sjj28qIkijouuK59Kvt886sCM5crKypp80LwcCWSMaQXMAw4B\nHgU+BvoANwODjTHHWms3bWf/wcCbwHfAnUAlMAyYQWw04E2N7SsiIiIiIrnl+eef3+GNBYCSkhJq\na2t5/vnnGTNmzB6KLmbEiBE7TAABFBUVEQgEuOiii3jnnXf2UHQx+VCPkB9xjhs3LqsYx40bx6xZ\ns/ZQdPkjH6415E+cuS4f6lFte/fJh+udDzHmA9XjnudzuygrclHW6J+dJcCuTDHWCTgDiI1sCkQd\nAhHwR2JJorqwQyD+OrYk+XrGwbGEVGL7A72fxhPcgjtYjSvsT/54In7c0SCeSABPNIg3GsDtBPE4\nIT5q35ul4e64gMSojC9ad+GJjoPpt/KbWELKFf9xR/E0lpjylbDa1TBRX+SEcXZiEE6o3lx7vmhs\nNGu2A3oyjZjaVXmZBCKWpDkCuM5aOzOx0hjzH+CPxEb4jN/O/jMBPzAoZdTQ88aYPwE3GGOetdb+\np3lCFxERERGR3aWyspLly5fTrl27JpUvKSlh+fLlVFZW7rFvZy+zH3e7AAAgAElEQVRcuJAffvih\nyd9qLSoqYs2aNSxcuHCPPSMoH+oR8iPOiooKli9fTtu2bZtUPhFjRUWFniOSIh+uNeRPnLkuH+pR\nbXv3yYfrnQ8x5gPVY+HzuF2Uul2U7nSWoWm/G6mGx5eO4xCKJpJPnQhGTiYYhUDEoTriEIw6BKMQ\njCegEtuCUYdgZNvr2zo7rNlQSSgKpe3ac1/vx3CFArhCdbhCdbjDAdwRP55wAG/EjysSwhMN4o4G\n8EZDeKIhPinrzuLQgWmJqS9bH8TEnhfzX98sxUcEnyuML5GcIhJ/HY2NnoonqjYWt2VJq8wjf3ZF\nviaBLgdqgKfrrX8NWAVcaoyZkGlaN2PM8YABnsowbdyjxEYEXQooCSQiIiIikuPmzp2bnFe+qYqL\ni/n73//OiBEjmimqdFOnTsXjyW6KC4/Hw1133cVrr73WTFGly4d6hPyI87HHHsPny24OeZ/Px8yZ\nM3nwwQebKar8kw/XGvInzlyXD/Wotr375MP1zocY84HqUZqTy+WiyANFHtdOpJLSLV26FoA+fdrv\nclzhaCLpdACByNHxpFNstFQw6sSm64tCKJ6YCkad9NdRh+k9Y9P6BaO7HA6Qh0kgY0w7YtPAvWOt\nDaRus9Y6xpiPgPOBHsA3GQ7RP758P8O2D+PL43dTuMl5OGXnqQ5Fsqd2I5I9tRuR7OVCu/n0008J\nh8PU1NRktd+iRYs4+uijmymqdBUVFbhcLkKhUJP3cblcLFu2bI/VcT7UI+RHnIsXL8ZxnOQzgOpr\nbP3nn3+eE20qV+TDtYb8iTPX7ageE88Gqi+X2nZj1LYbyod2kw8x7kgu/N4VQj3K3qU5201R/Ge7\nXIAn/pPUtBGo27MTs9u1uG7x5apGtq+ML3s2sr17Y/tba6uAzdvZVwrAK6+8wsiRI/nyyy+T60aO\nHMm0adNaJJ5p06YxcuTIFjl3wn/+8x9uuukmLr/8cp599tkWjUVg/fr1jBw5kscff7ylQxEREcl5\n4XB4j+63M6LRnfsK387utzPyoR535Xx7Ms58iDEf5Es95kucuS4f6jEfYswX+VCX+RBjPlA9iuSG\nvBsJxLbUV20j22vqlduZ/Xc9vRbXp0+f3XWovU4i87q76zAxp+hBBx2UPPb06dPZZ599mv16vfPO\nO0QiEX70ox8l1914441s2rSpxX5XotEo119/PYFAgPHjx3PwwQfr97aJZs+eTb9+/Tj44IN363G7\ndOnC9OnTOeCAA7K+Fs3VbkQKmdqNSPZyqd107NgxqxE2CT6fb4/FX1xcTCQSyXo/j8ezx2LMh3qE\n/Iizbdu2GW9eJUYPNPZsKK/XmxNtKlfkw7WG/Ikz1zVWj4kRQI09GyQX2vaOqG03lA/tJh9ibIz+\nThPJXi61m+aQjyOBRHa70047jWOOOabZz/PCCy8wf/78tHXHHHMMp512WrOfuzGVlZVUVlZy/PHH\nM3z4cI466qgWiyWfBINBHnnkEb7++uvdfuySkhJOO+00+vbtu9uPLSIiUmi6dOlCIBDYccEUgUCA\nrl27NlNEDXXt2pVgMJjVPsFgkG7duu244G6SD/UI+RFnr1698Pv9We3j9/vp3bt3M0WUn/LhWkP+\nxJnr8qEe1bZ3n3y43vkQYz5QPYrkhnxMAm2NL1s3sr1NvXI7s39j+4rstGg0irW2pcNoIHFDorFv\nJEpmS5cu1fBkERGRHHD66afv1M2FIUOGNFNEDU2ZMiXrkUCRSIQ77rijmSJqKB/qEfIjzuuuuy7r\nbz2HQiHGjh3bTBHlp3y41pA/cea6fKhHte3dJx+udz7EmA9UjyK5IR+TQMsBBzioke2Jr8s19hSn\nb+LLBvsbY8qAsu3sK7vZ1KlT6d+/P8uWLePGG2/k5JNPZsGCBcntK1euZNKkSZxxxhmceOKJnHvu\nuUyfPp1169Y1ONaHH37IDTfcwJAhQzjppJM477zzmDZtGuvXr99hHP379+eaa65Je7+9n1Tffvst\nU6dO5eyzz+aEE07g7LPPZty4cWnPHHrjjTcYMGAAtbW1/OUvf6F///48+eSTAFxzzTUNjhmNRvn9\n73/PpZdeyqBBgxg0aBCXXHIJL7zwQlriYfXq1fTv359p06ZRUVHBjTfeyODBgxk0aBBjxoxhyZIl\nO6z/H//4xwDJuKZOnZqsg+uuu47333+fCy64gKFDh+5SfIsXL2b06NEMGjSIs88+myeffBLHcfjy\nyy+5+uqrOeWUUzjnnHP4v//7vyb9YT1s2DDOPPNMNm3axOTJkzn99NMZNGgQl19+Oe+9916D8itW\nrOD2229n6NChnHDCCQwdOpRJkyaxbNmytHLhcJjf/e53XHrppQwePJhTTjmFiy66iCeffDKZMJs6\ndSqjRo0C4K677qJ///4sXLgweYxFixZx0003cdpppzFw4EDOP/98ZsyYwdat6fnlYcOGcf7557Nk\nyRJGjhzJwIEDqa6uTtZb4lokrFu3jnvvvZdzzz2XE088kSFDhnDTTTexaNGitHKvvPIK/fv359//\n/jeTJ0/m1FNP5Q9/+MMO61RERCQflZeX06NHjyZ/O9vv99OjR49GpxZqDsceeyydOnVq8migYDBI\np06dOPbYY5s5sm3yoR4hP+Ls1avXTsXYq1evZo4sv+TDtYb8iTPX5UM9qm3vPvlwvfMhxnygehTJ\nDXmXBLLW1gCfAccYY0pStxljPMCJwHfW2pWNHCJxd/ikDNsGxZcLMmyTZjRz5kw6dOjAbbfdRs+e\nPQFYtmwZU6ZMYenSpVx66aXcfvvtnH766cyZM4ef/exnbNiwIbn/u+++y4033si6desYM2YMkydP\nZvDgwbz11luMHj2a2trGHgGV2fTp0xv8XHvttQBpQ7nXrVvHVVddxTvvvMPw4cOZMmUKP/nJT1i6\ndClXXnllMhF07LHHcssttyRfT58+fbvfarjnnnt48MEH2XfffbnhhhsYN24cnTt3ZsaMGdx1110N\nym/YsIHrr7+e7t27M378eC688EI+//xzxo8fv92bDcOHD28Q1/Dhw5Pb/X4/v/jFLxg+fDjjx4/f\n6fjWrVvHbbfdxqBBg5gwYQJlZWU89dRTPPPMM9xyyy3079+fCRMmcMABB/Dqq6/y0ksvNRpzqmAw\nyIQJE/D5fNxwww1ce+21rFu3jgkTJvDZZ58ly1VUVDBq1Cg++OADhg0bxu23384FF1zAokWLGD16\ndNqUbg888ACPPPII3bt3Z9y4cUycOJEjjjiCp59+mttvvz1Zb4l6Gj58ONOnT0/+3s6bN4+xY8ey\nYcMGxowZw6RJkzjuuON46aWXuOaaaxr84eM4DtOmTWPIkCHcdtttFBcXZ/ysGzZsYNSoUbz55psM\nHjyYW2+9lcsuu4wVK1YwduxY3n///Qb7vPjii9TV1TFx4sQ9Mt2hiIhIS7nssssoLS3d4Q0Gv99P\naWkpl1122R6KbJvZs2dTXFy8w0RQMBikuLiY2bNn76HItsmHeoT8iPPhhx/OKsaHH354D0WWX/Lh\nWkP+xJnr8qEe1bZ3n3y43vkQYz5QPYq0PG9LB7CTngZmAFcDv0xZfymwPzAlscIYcwgQsNYuB7DW\nfmqM+QQYboy5w1q7Kl7OBYwDQsCsPfIpdqDuk59nVd7lLqak37QG68Nr5xP6/o2sjuU94HR8B5zR\nYL3/87txQrHRDK2OuT+rY25PKBRi8uTJaeueffZZ2rZty9NPP0379u2T648++mgmTJjArFmzmDBh\nAhAb5XHEEUdw++23J+dOHzp0KG63m1mzZjF//nzOOuusJsdT/xk9fr+fp556itatW3Pfffcl13/z\nzTf07t07OSoloXfv3tx44428+uqr9O3blwMOOIATTzwRgE6dOm33GUCLFy/m9ddfZ8CAATzyyCO4\nXC4Azj//fMaNG8ecOXMYMWIEhx9+eHKf9957j3vvvTctsbR161Zef/11/vOf/3DcccdlPFffvn2T\ndZsprsWLFzN16tS0UUA7E98HH3zA448/nkxEHHzwwfz0pz/liSeeYMaMGQwYMACAE088kXPOOYd3\n3nmnSZ1+TU0NBx98MJMmTUquO+SQQ7jmmmt4/vnnuf/+2O/ojBkzqKmp4amnnuLII49Mlj3ppJP4\n6U9/ymOPPcYvfxn7p+Stt96iZ8+eTJu2rS2dffbZdOnShS+++IK6ujr69u3LN9/EBhUeeuihyXoL\nBoPcd9999OnTh1//+tfJhM4555xDr169eOCBB3j11Ve55JJLksdevXo1V199dXJkUWOeeuop1q9f\nz9133532u3bmmWcyfPhwHn74YU444YS0fb7//nt++9vf4vXm6z/1IiIiTdOqVStuuOEGnn/+eZYv\nX05xcXHaFysCgQCBQIAePXpw2WWXtcg0uJ07d2bOnDlcdNFFrFmzBo/HQ1FRUXJ7MBgkEonQqVMn\nZs+eTefOnfd4jPlQj/kSZ3l5ObNmzWLcuHEsX74cn8+Xtt3v9xMKhejRowcPP/ywvvHciHy41vkU\nZ67LVI+pcqEeM7XtkpJt309W2266fGg3+RBjPlA9irS8fL0z+DgwEnjAGNMN+Bg4DBgPfA48kFJ2\nCWCBQ1LWjQX+CfzLGPMIsBm4GBgMTLbWVjT7J2iC6ObPs9vBk/kfSSewIetjOe2PzLg+umUJTrAy\nu7iaYPDgwWnvV65cyYoVKxg8eDAej4eqqqrktn79+tGuXbu06bdGjhzJyJEjY7E7DjU1NTiOw4EH\nHgjEbrTviunTp1NRUcF9991Hly5dkusHDBiQTGAA1NXVEQ6H6dSpEwBr1qzJ+lzz5s0D4Lzzzksm\nWBLOPfdc3n33XRYsWJCWZNl///0bjCzq27cvr7/+Ohs3bsw6hgS3280pp5yyy/EdcMABaSNR+vTp\nA0CHDh3S6q9Dhw6Ul5dnFfN5552X9v6YY46hrKwsOUVaXV0dH374Ib17905LAEGsjnr16sVHH31E\nIBCguLgYj8fD+vXrWb16ddrNlyuuuGKHsSxatIiNGzcyYsQIgsFg2jd9Tz75ZB566CE++eSTtCSQ\n4zjbTQomzJs3j3bt2jW4zp06deK4445jwYIFrFq1Km3bKaecogSQiIjsNVq1asWYMWOorKzk73//\nOytXriQcDuP1eunVqxdDhgxp8ZtxnTt35p133mHhwoXcddddfPvtt0QiETweD4cccgh33HHHHp0C\nLpN8qMd8iTNxs7iiooKZM2fy+eefJ2Ps168fY8eO1TRRTZAP1zqf4sx19etx0aJFhMNhfD5fztRj\n/ba9bNkyte2dlA/tJh9izAeqR5GWlZd3B621IWPMGcCdwAXA/wDrgKeAKdba7c79Za390BhzMnBX\n/KeYWLLoZ9baZ5szdsms/jcdly9fDsDbb7/N22+/nXEfx3GSr8PhMLNmzeKtt97i+++/b/BMmWwf\nxJvq1Vdf5c0332TkyJGceuqpDbbPnTuXF198kYqKCurq6nb5vCtWrADI+EdjYpTTypXpsx0edFDD\nR2QlvlWR+oyebJWXlzf4BsbOxFf/+ia+CZlIltXflk3MPXr0aLBuv/32Y9myZdTW1rJq1Sqi0Wij\nf4R369aNiooKVq9eTY8ePbjqqqt48MEHGTFiBCeccAL9+/dnwIABacm/xiR+b3/1q1/xq1/9KmOZ\nH374ocG6HX3Tt6qqisrKSo488kg8Hk/Gz7BgwQJWrlzJfvvt1+TjioiIFKLy8nJGjBjR0mFs17HH\nHstrr73W0mFsVz7UI+RHnL169eLBBx9k6dLYo2cTX4iS7OTDtYb8iTPXJerx6KOPBnKz3STatuy6\nfGg3+RBjPlA9irSMvEwCAVhrtxIb+TN+B+Vcjaz/GDi7GULbbdztj8iqvMud+VkiruIO2R+rVcfM\nMZUdmpwObncqLS1Ne594hs+gQYPSRk2kSh2Fcvfdd/Pmm29y+OGHc8stt9CpUye8Xi8ff/wxTz/9\n9E7H9dVXX/HQQw9x1FFHcd111zXY/tprr3HPPffQsWNHrrrqKnr06EFJSQlbt25l4sSJO3XORCIp\n0/DXRGKnfrIpdSqR3an+dUk9dzbx1Z/+ImFX4/Z6vRmP0bp1ayA2rUrid6mx4cT1Y77ooovo3r07\nL730Eh988AHz588H4KijjmLixIlpz4Sqr6amBoDLL7+8wdRs9c+XUFRU1Gj9JGT7GRIyXT8RERER\nERERERHZe+RtEmhvsLueuePteArejqfsuGATlBwxeceFdoPEzevi4uIdTomxYcMG5syZQ9euXZk5\nc2bafLzffvvtTsdQVVXFpEmTaNOmDffee2/GabV++9vf4vF4ePTRR5OjYHb1vIkb/Ykb/6kSN/kT\nSY6WkEvxhcPh5PDhVNXV1Xg8Htq1a5f8XcoUL2SO+fjjj+f444/H7/ezaNEi5syZw5w5cxg7diyv\nvPIKbdu2zXisxDHatWu3W6dyaepnUNJHREREREREREREUrlbOgCRTHr27AnA119/nXH7pk2bkq/X\nrFmD4zgceeSRaQkgIPlcmGw5jsPUqVNZu3Ytd999d9oUW6lWr17N/vvvn5YA2pXzwrbPXlHR8NFU\nienGunfvvtPH31W5Fl9ierqEcDjM2rVrKS8vx+1207VrVzweT8Z4IRZzUVFRxqnTSkpKOOGEE5g6\ndSoXX3wxmzdv5pNPPmk0lkTdfPbZZxm3b968uYmfKl3btm3p0KEDK1asyDjFYKLeM02NJyIiIiIi\nIiIiInsvJYEkJ3Xp0oVu3bqxcuVKPvroo7Rtixcv5qyzzmLWrFkAyQfHrVmzJq3cRx99xAcffABA\nIBDI6vy/+c1v+Ne//sWYMWM47rjjGi1XXl7O5s2b8fv9yXVr165l9uzZDc6beJZLMBjc7rkHDx4M\nwB//+Me05x45jsOf/vQngIzPJtpTci2+P//5z2nv//3vf1NdXU2/fv2AWCLnpJNOoqKigk8//TSt\n7CeffMK3337LwIED8fl8LFmyhAsuuCD5OVIlRvkkpp9zu2P/fKZe46OPPpry8nLefffdBsmpuXPn\nctZZZzFnzpyd+pynnXYaVVVVzJ07N239ypUrWbhwIYceemjGZyyJiIiIiIiIiIjI3kvTwUnOGjVq\nFPfeey8TJ07kJz/5CV26dGH58uW8/PLLlJeXM3ToUAA6d+7MYYcdxsKFC3nggQc47LDDsNby5ptv\nMmXKFMaPH88///lPevfuzZAhQ3Z43i+//JLHH3+cjh070qVLF/7xj380KNO3b18OOOAAhgwZwgsv\nvMDEiRM588wzWb9+Pb///e8ZN24cjzzyCF9//TWvvPIKAwcOZN9996W4uJj333+f5557ji5dunDa\naac1OPYhhxzChRdeyMsvv8z48eM5+eSTiUQizJ8/n48//phLLrmEXr167XoF76Rciq+oqIglS5Zw\n11130a9fP6qqqvjNb36Dz+fj8ssvT5a7/vrrWbRoETfffDMXXXQRnTt35rvvvuPll1+mffv2XH/9\n9UDsYaPFxcX84he/YOnSpRx66KF4PB6WLl3K7Nmz6dmzZ3Kat8TIoT/84Q/4/X6OOuooDj/8cCZO\nnMitt97KNddcwyWXXEKHDh1YsmQJf/zjH+natSsDBw7cqc86evRo5s+fzz333MPSpUvp2bMna9eu\n5dVXX8Xj8fDzn/98F2tTRERERERERERECo2SQJKz+vTpw9SpU5k7dy4vv/wyVVVV7LPPPpx88smM\nGTOGjh07AuByubj33nt54IEHks9uOeqoo5g5cya9evXivPPO48033+Sxxx7jRz/60Q7P+8033xCJ\nRFi7di233nprxjJ33HEH55xzDmPGjCEYDDJv3jzuu+8+evXqxaRJkzj55JOpq6tjxowZzJw5kx49\netCxY0duuukmHn/8cZ5++mnOO++8jEkggJ///Od0796dP/3pTzz00EO4XC569uzJbbfdxrBhw3a6\nTneXXIrv/vvv55e//CWPPvoodXV19O7dm7Fjx2KMSZbp1q0bzzzzDE8++SSvvPIKW7ZsYZ999mHQ\noEFceeWVHHjggQB4vV6efPJJnnnmGebPn88bb7xBOBymU6dOXHjhhYwaNSo5Eqhfv36ce+65zJ07\nl2eeeYZJkyZx+OGHc+qpp/LYY48xa9YsZs2aRW1tLfvttx/Dhg3jyiuvpE2bNjv1Odu3b88zzzzD\nE088wVtvvcXGjRtp27YtxxxzDKNHj6ZPnz67XpkiIiIiIiIiIiJSUFyp0znJztuyZYsqcjdbunQp\ngG5uS0bDhg1j48aNLFiwoKVDySlqNyLZU7sRyZ7ajUj21G5Esqd2I5I9tRuR7OVjuykrK3M1taye\nCSQiIiIiIiIiIiIiIlKAlAQSEREREREREREREREpQEoCiYiIiIiIiIiIiIiIFCBvSwcgIrIzXnvt\ntZYOQURERERERERERCSnaSSQiIiIiIiIiIiIiIhIAVISSEREREREREREREREpAApCSQiIiIiIiIi\nIiIiIlKAlAQSEREREREREREREREpQEoCiYiIiIiIiIiIiIiIFCAlgURERERERERERERERAqQkkAi\nIiIiIiIiIiIiIiIFSEkgERERERERERERERGRAqQkkIiIiIiIiIiIiIiISAFSEkhERERERERERERE\nRKQAKQkkIiIiIiIiIiIiIiJSgJQEEhERERERERERERERKUBKAomIiIiIiIiIiIiIiBQgJYFERERE\nREREREREREQKkMtxnJaOoSBs2bJFFSkiIiIiIiIiIiIiIs2qrKzM1dSyGgkkIiIiIiIiIiIiIiJS\ngJQEEhERERERERERERERKUBKAomIiIiIiIiIiIiIiBQgJYFEREREREREREREREQKkJJAIiIiIiIi\nIiIiIiIiBcjlOE5LxyAiIiIiIiIiIiIiIiK7mUYCiYiIiIiIiIiIiIiIFCAlgURERERERERERERE\nRAqQkkAiIiIiIiIiIiIiIiIFSEkgERERERERERERERGRAqQkkIiIiIiIiIiIiIiISAFSEkhERERE\nRERERERERKQAKQkkIiIiIiIiIiIiIiJSgJQEEhERERERERERERERKUBKAomIiIiIiIiIiIiIiBQg\nJYFEREREREREREREREQKkJJAIiIiIiIiIiIiIiIiBcjb0gHI3skY8xxwxXaKjLPWPhIv2wr4X+Bi\noBuwFXgbmGyt/bqZQxXJGU1tN8aYO4Ep2yn3S2vtTbszNpFcZ4w5C5gEHAOEgUXANGvt2/XKqc8R\niWtKu1GfIxJjjHGaUKyHtXZFvLz6G9nrZdNu1N+IpDPGHAbcCgwGOgCbgfeA+621C1LKqb8RiWtK\nuynU/kZJIGlpY4H1GdZ/CmCMcQGvAUOAZ4GpQGfgZuB9Y0x/a23FHopVJFdst92kuBP4IkO5pbs7\nIJFcZoz5GfA08C/gRqAtMA6YY4w5w1o7L15OfY5IXFPbTYo7UZ8je7fh29k2HSgj/veb+huRpCa3\nmxR3ov5G9nLGmKOBBUAQeBT4GugCXAfMN8b82Fr7uvobkW2a2m5SdrmTAupvlASSlvZm4ttwjbgY\nOJ1YRvaWxEpjzD+Aj4H7gfObNUKR3LOjdpMwP8NNOpG9ijGmEzAD+DtwprU2Gl//OvA+8N/AvHhx\n9TkiZN1uEtTnyF7NWvtypvXGmB8DvYGfWmtr4qvV34iQdbtJUH8jArcDpcB51tq/JVYaY14FlgB3\nAa+j/kYkVVPbTUJB9Td6JpDkusvjyxmpK621nxAbrneOMab9Ho9KRETyxRVAa+DOxI1sAGvtN9ba\njtban6eUVZ8jEpNNuxGRRhhj2gL/H/COtXZWyib1NyKN2E67EZFtesWX76SutNZ+BawDusdXqb8R\n2aap7aYgKQkkOcEYU2KMyTQyrT/wnbV2VYZtHwI+YvPUi+x1ttNu6pcrMsYU7YmYRHLQ6UAVsdEL\nGGM8xpjiRsqqzxGJyabdpFGfI5JmMrFpd66rt179jUjjGms3adTfyF5uSXx5cOpKY0wZ0B5YHF+l\n/kZkm6a2G+ptL4j+RkkgaWnXGWOWA3VAwBjzgTHmbEh+A6gcyNRZAayML3s2f5giOaXRdlPPCGPM\nF0AgXu5zY8xlezRSkZZ3CFAB9DPGzCfWHvzGmMXGmIsThdTniKRpUrupR32OSApjzP7EbmL/xlr7\necp69TcijWis3dSj/kYE7gE2Ab8xxgw0xnQwxhxB7Lk/DjBZ/Y1IAztsN/XKF1R/oySQtLQzgXuJ\nzS1/G9AHeCN+g6FtvExtI/sm5gZu28h2kUK1vXaT6izg8fjyRmIPVv2NMWbiHoxVpKWVE/tWz1+A\nd4EfA9fH171ojBkdL6c+R2SbprabVOpzRNLdApQQu+GQSv2NSOMaazep1N/IXs9auxg4AfAQm9pq\nPfAZcDyx5znOQ/2NSJomtptUBdXf7HAaIZFm8iDwIjDPWhuIr/urMebPwKfx7ce1VHAiOWqH7cYY\nMxt4AfgAeN9auyVebo4x5iXgK2CKMeYJa+3mPRy/SEsoIja370hr7e8SK40xfyE2HPxeY8xzLROa\nSM5qUrux1kZQnyPSgDFmH+Ba4A1r7bKWjkckHzSh3ai/EYkzxhjgr0AxMI5YG9gfmAC8boy5APii\n5SIUyT1NaTfW2rkUaH+jJJC0iPjQ7gbDu621Xxpj5hGbi36/+OrWjRymTXy5dbcHKJKDmthuDrXW\nfgE0+I+TtXadMeZl4CrgJGLf8BYpdNXE/sh7KXWltXa5MeafwFDgUGBFfJP6HJGmt5vF8Rt16nNE\n0l0ClAKZHmqf6EfU34ik2167Qf2NSJqngAOJ/f9/eWKlMeYPxNrJs8T+VgP1NyIJO2w3xpgehdrf\naDo4yUVr48tSYkPzDmqkXLf4cmmzRySS+xLtpt1uKidSKFbQ+N876+LLdtbaatTniCSsoAntpgnH\nUZ8je6vhxOaPf7P+BvU3Io1qtN00gfob2WsYY1oTuwH9SXEfGZMAAAskSURBVOqNbABrbR0wj9iN\n7q6ovxEBsmo3B+/gUHnb3ygJJHucMaadMWakMWZoY0Xiy++A94CDjDFdM5QbBNQBnzRDmCI5JYt2\ns8oYc5ExZvgOyq1sZLtIoXmf2NRWfTNsS/zHJ/GwVPU5IjFNajfGGJ/6HJF0xpg2wInEphCpa6SY\n+huRFDtqN+pvRNK0AlzEnp+VSUnKUv2NSExT202bQu1vlASSlhAEHgOeM8Z0SN1gjBlC7FlAH1lr\nVwFPxzeNq1fuFOBY4KX4t+lECl1T2813wFRiD6vrU69cX2IP914FfLRHohZpec/Fl1OMMa7ESmPM\nkcT+4/OZtTbxB5z6HJGY5+LL7bYba20I9Tki9R0J+IDF2ymj/kYk3XbbjfobkW2stRuIjd45Mv77\nn2SMKQcGE5vibTHqb0SArNrNpxRof+NyHKelY5C9kDHmCmI3GJYDjwM/AEcTexCkH/iRtfbTeNlX\ngPOBZ4C3iX0D9WagBjjOWvvDno5fpCU0td0YY04D5gCVxBJHy4l9W+F6Ys94+LG1ds4e/wAiLcQY\nM4PY7/8bwGxi/cg4YvNgn2mtnZdSVn2OCE1vN+pzRNIZY35K7FkMN1trH9xOOfU3InFNaTfqb0S2\nMcacC/wR2AI8CnwNdABuBHoA11hrn4iXVX8jQtPbTaH2N0oCSYsxxpwK/C/Qn9iD6n4A/gbcY639\nJqVcETAJuBToDmwC3gJui496ENlrZNFujgFuB04GyoCNwHxgeiLBKrK3iI9kuBq4htgfbwHgXeBO\na+2/65VVnyNC1u1GfY5InDFmHPAQcLW19sntlFN/IxKXRbtRfyMSZ4wZAEwk9pyTfYAq4GPgodQb\n1OpvRLbJot0UXH+jJJCIiIiIiIiIiIiIiEgB0jOBRERERERERERERERECpCSQCIiIiIiIiIiIiIi\nIgVISSAREREREREREREREZECpCSQiIiIiIiIiIiIiIhIAVISSEREREREREREREREpAApCSQiIiIi\nIiIiIiIiIlKAlAQSEREREREREREREREpQEoCiYiIiIiIiIiIiIiIFCAlgURERERERERERERERAqQ\nkkAiIiIiIiIiIiIiIiIFSEkgERERERERERERERGRAqQkkIiIiIiIiIiIiIiISAHytnQAIiIiIiIi\njTHGXAQErLV/aulY8o0xpiNwLfCItXZzS8cjIiIiIiJ7nkYCiYiIiIhILpsK/Lilg8hTpwJTgPYt\nHYiIiIiIiLQMJYFERERERCQnGWP2AQ5u6Tjy2ICWDkBERERERFqWy3Gclo5BREREREQkjTHmOeCK\neqvnW2t/FN8+Erga6Af4gO+BPwP3WGs3phznR8A/gd8DE4BHgMHxfT4ErrfWfmWMOR+4FegL1MaP\ndaO1tirlWCuAbkAn4FJgTPx9FfAWMMlau6re52gF3AwMB/oAYeBr4HngUWttOKXsncRG7lwbX3Ub\nUGutNfHtXmAscBlwCFACrIt/vjuttcvi5boDyzNU66nW2nnGGAfAWuuqXyCl3q+11j5eb91ZwAnA\nNcB/rLVnpOzXpOshIiIiIiJ7lkYCiYiIiIhILnoJeDz++mPg58CvAIwxjwIvAF2Bp4AHgJXAOODf\nxphOGY5XDMyNv34E+AgYArwRT2D8GvgAeBjYDIyKl8tkWvxcb8VfLwFGAu8YY5JTr8UTQPOBu4gl\nlh4EngBK4+d5zRiT6f9kxwJ3Ar8BZqasfxb4JdA6vpwGfBU/9wfGmC7xcpXx+vom/v7e+PuKRj5P\nU51HLAE1E/hdYuVOXg8REREREdkDvC0dgIiIiIiISH3W2jnGGD+xUSdfWGsfADDGnAFcB3wKDLLW\nVif2McbcQ2w0z300HEV0DnC/tfbW+Pu7jTEfAMcTS2ocZ639On6cR4DvgOHGmCuttfWnT/hvoJ+1\ndl3KeV+Prx9LLOkCMBk4jliC6erEcYwxtwJzgLPjcT5b7/gjgYHW2k9SPlsPYqOPfgD61/vcrwDn\nA9cDt1hrtwIPGGPOAXoCv7bWrmhYy1m7EDjSWvt9yrl39nqIiIiIiMgeoJFAIiIiIiKST66KLyen\nJhzi7gZqiCVvSuptixJLRqR6L758JZEAArDWrge+BNoC+2eIYWYiARQv7wCPxt8OBTDGuIArgRAw\nMTWRZK0NAnfE316e4fhfpSaA4iqJTWM3PMPn/nN8eWSGY+1O81MTQHE7ez1ERERERGQP0EggERER\nERHJJwPiy43xZ9/U9zVwNHAosChl/bfW2i31yiae97M4w3ES2zIlLz7IsO6r+PKQ+LInsB+xadHK\njDFl9cpvIJaYOibDsRbVXxGP/Z+QTDDtQyxJlfpcn+ZOtDSIi52/HiIiIiIisgcoCSQiIiIiIvkk\nMTLnve2Wgo713ldmKOM0YZsrw7Z1GdZtii8TzwRKxNkVWN5IjADtjDEl1lr/DmLFGHMyMAUYCBRt\n55jNJVNcO3s9RERERERkD1ASSERERERE8kkiOXMZUH/6sVSfNmMM0QzrElNtJ5I5iTi/BW7awfHC\n9d5H6hcwxpwKzAU8wIvA28QSTxFiI23uqL9PM2gQF7lxPUREREREpBFKAomIiIiISD75AegGLLTW\nLmmhGDpkWJcYAbQ2vvwhvmxlrf3TbjjnLcQSQJOttdNSNxhjinfD8ROyHbGTC9dDREREREQa4d5x\nERERERERkZzxYXw5JNNGY0zP+DNzmlP/DOsOiy+/BbDWriA2bdz+xpgj6hc2xriMMT2zOGeP+PL1\nDNuGZnEciI9WMsa0T11pjPECR2Z5rFy4HiIiIiIi0gglgUREREREJFclplZLHXnzdHw5wRiTNiLH\nGDMAWALMa+a4rjPGlKec1wX8T/ztX1LKJWKdZozx1DvGOKDCGDO1ief8Pr48LHWlMWYkcHr87T71\n9slUfwDfxJdn1Vt/E9ue8dNUuXA9RERERESkEZoOTkREREREctVSIAicaYx5DohYa0cbY34FXAt8\nboz5HbFn4/QFLiD2fJ1bmzmut4FPjTF/JjYd2hnAIOBr4Ncp5aYRS9D8P+ATY8xrxJ6hcxJwWvzz\nPdbEcz4HDAZ+ZYz5L2KfeSDQD/hv4APgCGPMw8AfrLXvAV8AZwLPGmP+Ccy31r4CPAM8ADxljDkJ\nWE9sdNPR8fivbWpFWGv/lgPXQ0REREREGqGRQCIiIiIikpOstRuBG4CNwE+IJU+w1o4FLiOWRBkN\nTAFOAV4GBlhr323m0O4DfgH8CLgdOBR4ATjFWludEn9tvMxkwAXcDEwCugIPAidaa9c15YTW2ueJ\nJVpWAdfEf9YR+7wfA/9LLPkyCugV3+1+4J9AH+BSIDF66eF43GuBq4mNYqoBTowfMys5cD1ERERE\nRKQRLsdxWjoGERERERGRnGeMWQF0Aw611n7VstGIiIiIiIjsmEYCiYiIiIiIiIiIiIiIFCAlgURE\nRERERERERERERAqQkkAiIiIiIiIiIiIiIiIFSEkgERERERERERERERGRAuRyHKelYxARERERERER\nEREREZHdTCOBRERERERERERERERECpCSQCIiIiIiIiIiIiIiIgVISSAREREREREREREREZECpCSQ\niIiIiIiIiIiIiIhIAVISSEREREREREREREREpAApCSQiIiIiIiIiIiIiIlKAlAQSERERERERERER\nEREpQEoCiYiIiIiIiIiIiIiIFCAlgURERERERERERERERAqQkkAiIiIiIiIiIiIiIiIFSEkgERER\nERERERERERGRAqQkkIiIiIiIiIiIiIiISAFSEkhERERERERERERERKQA/f9PJ48pM0r7hAAAAABJ\nRU5ErkJggg==\n", + "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [], + "image/png": { + "width": 832, + "height": 277 + } + } + } ] - }, - "metadata": { - "image/png": { - "height": 222, - "width": 834 - }, - "tags": [] - }, - "output_type": "display_data" - } - ], - "source": [ - "rand_x_vals = tf.linspace(start=-8., stop=7., num=150)\n", - "\n", - "density_func_1 = tfd.Normal(loc=float(-2.), scale=float(1./.7)).prob(rand_x_vals)\n", - "density_func_2 = tfd.Normal(loc=float(0.), scale=float(1./1)).prob(rand_x_vals)\n", - "density_func_3 = tfd.Normal(loc=float(3.), scale=float(1./2.8)).prob(rand_x_vals)\n", - "\n", - "[\n", - " rand_x_vals_,\n", - " density_func_1_,\n", - " density_func_2_,\n", - " density_func_3_,\n", - "] = evaluate([\n", - " rand_x_vals,\n", - " density_func_1,\n", - " density_func_2,\n", - " density_func_3,\n", - "])\n", - "\n", - "colors = [TFColor[3], TFColor[0], TFColor[6]]\n", - "\n", - "plt.figure(figsize(12.5, 3))\n", - "plt.plot(rand_x_vals_, density_func_1_,\n", - " label=r\"$\\mu = %d, \\tau = %.1f$\" % (-2., .7), color=TFColor[3])\n", - "plt.fill_between(rand_x_vals_, density_func_1_, color=TFColor[3], alpha=.33)\n", - "plt.plot(rand_x_vals_, density_func_2_, \n", - " label=r\"$\\mu = %d, \\tau = %.1f$\" % (0., 1), color=TFColor[0])\n", - "plt.fill_between(rand_x_vals_, density_func_2_, color=TFColor[0], alpha=.33)\n", - "plt.plot(rand_x_vals_, density_func_3_,\n", - " label=r\"$\\mu = %d, \\tau = %.1f$\" % (3., 2.8), color=TFColor[6])\n", - "plt.fill_between(rand_x_vals_, density_func_3_, color=TFColor[6], alpha=.33)\n", - "\n", - "plt.legend(loc=r\"upper right\")\n", - "plt.xlabel(r\"$x$\")\n", - "plt.ylabel(r\"density function at $x$\")\n", - "plt.title(r\"Probability distribution of three different Normal random variables\");" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "HAxWLKGcIA0A" - }, - "source": [ - "A Normal random variable can be take on any real number, but the variable is very likely to be relatively close to $\\mu$. In fact, the expected value of a Normal is equal to its $\\mu$ parameter:\n", - "\n", - "$$ E[ X | \\mu, \\tau] = \\mu$$\n", - "\n", - "and its variance is equal to the inverse of $\\tau$:\n", - "\n", - "$$Var( X | \\mu, \\tau ) = \\frac{1}{\\tau}$$\n", - "\n", - "\n", - "\n", - "Below we continue our modeling of the Challenger space craft:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "F3DBYxvAIA0B" - }, - "outputs": [], - "source": [ - "reset_sess()\n", - "\n", - "temperature_ = challenger_data_[:, 0]\n", - "temperature = tf.convert_to_tensor(temperature_, dtype=tf.float32)\n", - "D_ = challenger_data_[:, 1] # defect or not?\n", - "D = tf.convert_to_tensor(D_, dtype=tf.float32)\n", - "\n", - "beta = tfd.Normal(name=\"beta\", loc=0.3, scale=1000.).sample()\n", - "alpha = tfd.Normal(name=\"alpha\", loc=-15., scale=1000.).sample()\n", - "p_deterministic = tfd.Deterministic(name=\"p\", loc=1.0/(1. + tf.exp(beta * temperature_ + alpha))).sample()\n", - "\n", - "[\n", - " prior_alpha_,\n", - " prior_beta_,\n", - " p_deterministic_,\n", - " D_,\n", - "] = evaluate([\n", - " alpha,\n", - " beta,\n", - " p_deterministic,\n", - " D,\n", - "])\n" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "PxOWy25CIA0D" - }, - "source": [ - "We have our probabilities, but how do we connect them to our observed data? A *Bernoulli* random variable with parameter $p$, denoted $\\text{Ber}(p)$, is a random variable that takes value 1 with probability $p$, and 0 else. Thus, our model can look like:\n", - "\n", - "$$ \\text{Defect Incident}, D_i \\sim \\text{Ber}( \\;p(t_i)\\; ), \\;\\; i=1...N$$\n", - "\n", - "where $p(t)$ is our logistic function and $t_i$ are the temperatures we have observations about. Notice in the code below we set the values of `beta` and `alpha` to 0 in `initial_chain_state`. The reason for this is that if `beta` and `alpha` are very large, they make `p` equal to 1 or 0. Unfortunately, `tfd.Bernoulli` does not like probabilities of exactly 0 or 1, though they are mathematically well-defined probabilities. So by setting the coefficient values to `0`, we set the variable `p` to be a reasonable starting value. This has no effect on our results, nor does it mean we are including any additional information in our prior. It is simply a computational caveat in TFP. " - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "vRqoyxqnofbT" - }, - "outputs": [], - "source": [ - "def challenger_joint_log_prob(D, temperature_, alpha, beta):\n", - " \"\"\"\n", - " Joint log probability optimization function.\n", - " \n", - " Args:\n", - " D: The Data from the challenger disaster representing presence or \n", - " absence of defect\n", - " temperature_: The Data from the challenger disaster, specifically the temperature on \n", - " the days of the observation of the presence or absence of a defect\n", - " alpha: one of the inputs of the HMC\n", - " beta: one of the inputs of the HMC\n", - " Returns: \n", - " Joint log probability optimization function.\n", - " \"\"\"\n", - " rv_alpha = tfd.Normal(loc=0., scale=1000.)\n", - " rv_beta = tfd.Normal(loc=0., scale=1000.)\n", - " logistic_p = 1.0/(1. + tf.exp(beta * tf.to_float(temperature_) + alpha))\n", - " rv_observed = tfd.Bernoulli(probs=logistic_p)\n", - " \n", - " return (\n", - " rv_alpha.log_prob(alpha)\n", - " + rv_beta.log_prob(beta)\n", - " + tf.reduce_sum(rv_observed.log_prob(D))\n", - " )" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "oHU-MbPxs8iL" - }, - "outputs": [], - "source": [ - "number_of_steps = 60000\n", - "burnin = 50000\n", - "\n", - "# Set the chain's start state.\n", - "initial_chain_state = [\n", - " 0. * tf.ones([], dtype=tf.float32, name=\"init_alpha\"),\n", - " 0. * tf.ones([], dtype=tf.float32, name=\"init_beta\")\n", - "]\n", - "\n", - "# Since HMC operates over unconstrained space, we need to transform the\n", - "# samples so they live in real-space.\n", - "unconstraining_bijectors = [\n", - " tfp.bijectors.Identity(),\n", - " tfp.bijectors.Identity()\n", - "]\n", - "\n", - "# Define a closure over our joint_log_prob.\n", - "unnormalized_posterior_log_prob = lambda *args: challenger_joint_log_prob(D, temperature_, *args)\n", - "\n", - "# Initialize the step_size. (It will be automatically adapted.)\n", - "with tf.variable_scope(tf.get_variable_scope(), reuse=tf.AUTO_REUSE):\n", - " step_size = tf.get_variable(\n", - " name='step_size',\n", - " initializer=tf.constant(0.5, dtype=tf.float32),\n", - " trainable=False,\n", - " use_resource=True\n", - " )\n", - "\n", - "# Defining the HMC\n", - "hmc=tfp.mcmc.TransformedTransitionKernel(\n", - " inner_kernel=tfp.mcmc.HamiltonianMonteCarlo(\n", - " target_log_prob_fn=unnormalized_posterior_log_prob,\n", - " num_leapfrog_steps=2,\n", - " step_size=step_size,\n", - " step_size_update_fn=tfp.mcmc.make_simple_step_size_update_policy(),\n", - " state_gradients_are_stopped=True),\n", - " bijector=unconstraining_bijectors)\n", - "\n", - "# Sampling from the chain.\n", - "[\n", - " posterior_alpha,\n", - " posterior_beta\n", - "], kernel_results = tfp.mcmc.sample_chain(\n", - " num_results = number_of_steps,\n", - " num_burnin_steps = burnin,\n", - " current_state=initial_chain_state,\n", - " kernel=hmc)\n", - "\n", - "# Initialize any created variables for preconditions\n", - "init_g = tf.global_variables_initializer()" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "eNkhSXDkthRs" - }, - "source": [ - "#### Execute the TF graph to sample from the posterior" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 51 - }, - "colab_type": "code", - "id": "XJyZIwoyth2j", - "outputId": "dde1e7af-ef4a-4814-e3ad-bcbcbc3b137e" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "acceptance rate: 0.6273333333333333\n", - "final step size: 0.01369297131896019\n" - ] - } - ], - "source": [ - "# In Graph Mode, this cell can take up to 36 Minutes\n", - "evaluate(init_g)\n", - "[\n", - " posterior_alpha_,\n", - " posterior_beta_,\n", - " kernel_results_\n", - "] = evaluate([\n", - " posterior_alpha,\n", - " posterior_beta,\n", - " kernel_results\n", - "])\n", - " \n", - "print(\"acceptance rate: {}\".format(\n", - " kernel_results_.inner_results.is_accepted.mean()))\n", - "print(\"final step size: {}\".format(\n", - " kernel_results_.inner_results.extra.step_size_assign[-100:].mean()))\n", - "\n", - "alpha_samples_ = posterior_alpha_[burnin::8]\n", - "beta_samples_ = posterior_beta_[burnin::8]" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "xIGyBkilIA0G" - }, - "source": [ - "We have trained our model on the observed data, now we can sample values from the posterior. Let's look at the posterior distributions for $\\alpha$ and $\\beta$:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 390 - }, - "colab_type": "code", - "id": "Pdgjgw9RiluO", - "outputId": "e57131fd-5b59-41d7-e812-b39d2384b085" - }, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "" + }, + { + "metadata": { + "id": "iI7Fosv1IA0T", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "Above we also plotted two possible realizations of what the actual underlying system might be. Both are equally likely as any other draw. The blue line is what occurs when we average all the 20000 possible dotted lines together.\n" ] - }, - "metadata": { - "image/png": { - "height": 373, - "width": 818 - }, - "tags": [] - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize(12.5, 6))\n", - "\n", - "#histogram of the samples:\n", - "plt.subplot(211)\n", - "plt.title(r\"Posterior distributions of the variables $\\alpha, \\beta$\")\n", - "plt.hist(beta_samples_, histtype='stepfilled', bins=35, alpha=0.85,\n", - " label=r\"posterior of $\\beta$\", color=TFColor[6], normed=True)\n", - "plt.legend()\n", - "\n", - "plt.subplot(212)\n", - "plt.hist(alpha_samples_, histtype='stepfilled', bins=35, alpha=0.85,\n", - " label=r\"posterior of $\\alpha$\", color=TFColor[0], normed=True)\n", - "plt.legend();" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "gp0QmuZvIA0L" - }, - "source": [ - "All samples of $\\beta$ are greater than 0. If instead the posterior was centered around 0, we may suspect that $\\beta = 0$, implying that temperature has no effect on the probability of defect. \n", - "\n", - "Similarly, all $\\alpha$ posterior values are negative and far away from 0, implying that it is correct to believe that $\\alpha$ is significantly less than 0. \n", - "\n", - "Regarding the spread of the data, we are very uncertain about what the true parameters might be (though considering the low sample size and the large overlap of defects-to-nondefects this behaviour is perhaps expected). \n", - "\n", - "Next, let's look at the *expected probability* for a specific value of the temperature. That is, we average over all samples from the posterior to get a likely value for $p(t_i)$." - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 51 - }, - "colab_type": "code", - "id": "EIzyJL_3IA0P", - "outputId": "f82a2e44-05e7-463d-b47e-47354a31946c" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "beta mean: 0.14313675\n", - "alpha mean: -8.920171\n" - ] - } - ], - "source": [ - "alpha_samples_1d_ = alpha_samples_[:, None] # best to make them 1d\n", - "beta_samples_1d_ = beta_samples_[:, None]\n", - "\n", - "\n", - "beta_mean = tf.reduce_mean(beta_samples_1d_.T[0])\n", - "alpha_mean = tf.reduce_mean(alpha_samples_1d_.T[0])\n", - "[ beta_mean_, alpha_mean_ ] = evaluate([ beta_mean, alpha_mean ])\n", - "\n", - "\n", - "print(\"beta mean:\", beta_mean_)\n", - "print(\"alpha mean:\", alpha_mean_)\n", - "def logistic(x, beta, alpha=0):\n", - " \"\"\"\n", - " Logistic function with alpha and beta.\n", - " \n", - " Args:\n", - " x: independent variable\n", - " beta: beta term \n", - " alpha: alpha term\n", - " Returns: \n", - " Logistic function\n", - " \"\"\"\n", - " return 1.0 / (1.0 + tf.exp((beta * x) + alpha))\n", - "\n", - "t_ = np.linspace(temperature_.min() - 5, temperature_.max() + 5, 2500)[:, None]\n", - "p_t = logistic(t_.T, beta_samples_1d_, alpha_samples_1d_)\n", - "mean_prob_t = logistic(t_.T, beta_mean_, alpha_mean_)\n", - "[ \n", - " p_t_, mean_prob_t_\n", - "] = evaluate([ \n", - " p_t, mean_prob_t\n", - "])" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 294 - }, - "colab_type": "code", - "id": "Ri4BriJHPJNg", - "outputId": "b1fc59fb-4ff3-4a0b-f5f2-dd2b78c3d1a4" - }, - "outputs": [ - { - "data": { - "image/png": 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q3PkGaUyMmr8hVah8OH/T81ek/uMPJVXmLiR1fVL/n/tfkf7Tf2EI4c+BDTHG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CzFp5+GDTUhWhtitNZHWVFuY6iO0GVlsmXegmQPGDYEeWpVZYfxerbi9WzN9VFUj1W9AXvujVjl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\nRMKfMYYxXve6o6MDIFJKboyiKJSWlkZ9v7Hze+qpp3jqqac+1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0e+Nl1JGDlFGLmFmDkF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HI03Hfq8Ziq62Cq26Eq2mEr3G3Ec3wiGwJd62aYujKK6/MsDltmxzvfQ0+r7dcXXK6W7mJmpy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\nknTaaafx2muv8eqrr1ZJsuy55541Zhb17t2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- "text/plain": [ - "" + }, + { + "metadata": { + "id": "XpRl_4Beof6G", + "colab_type": "code", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 297 + }, + "outputId": "58b09484-4510-4a8a-e16d-75d4393eace2" + }, + "cell_type": "code", + "source": [ + "alpha_samples_means_ = np.array(alpha_samples_1d_.mean(axis=1))\n", + "beta_samples_means_ = np.array(beta_samples_1d_.mean(axis=1))\n", + "sorted_alpha_means_ = np.sort(alpha_samples_means_)\n", + "sorted_beta_means_ = np.sort(beta_samples_means_)\n", + "alpha_index_ = sorted_alpha_means_.shape[0]\n", + "beta_index_ = sorted_beta_means_.shape[0]\n", + "upper_alpha_quantile_ix_ = int(alpha_index_ * float(0.975))\n", + "lower_alpha_quantile_ix_ = int(alpha_index_ * float(0.025))\n", + "\n", + "upper_beta_quantile_ix_ = int(beta_index_ * float(0.975))\n", + "lower_beta_quantile_ix_ = int(beta_index_ * float(0.025))\n", + "\n", + "def find_nearest(array, value):\n", + " array = np.asarray(array)\n", + " idx = (np.abs(array - value)).argmin()\n", + " return idx\n", + "\n", + "alpha_upper_quantile_ix_ = find_nearest(alpha_samples_means_, sorted_alpha_means_[upper_alpha_quantile_ix_])\n", + "alpha_lower_quantile_ix_ = find_nearest(alpha_samples_means_, sorted_alpha_means_[lower_alpha_quantile_ix_])\n", + "beta_upper_quantile_ix_ = find_nearest(beta_samples_means_, sorted_beta_means_[upper_beta_quantile_ix_])\n", + "beta_lower_quantile_ix_ = find_nearest(beta_samples_means_, sorted_beta_means_[lower_beta_quantile_ix_])\n", + "\n", + "p_t_low = logistic(t_.T, beta_samples_1d_[beta_lower_quantile_ix_], alpha_samples_1d_[alpha_lower_quantile_ix_])\n", + "p_t_high = logistic(t_.T, beta_samples_1d_[beta_upper_quantile_ix_], alpha_samples_1d_[alpha_upper_quantile_ix_])\n", + "\n", + "[ \n", + " p_t_low_, p_t_high_\n", + "] = evaluate([ \n", + " p_t_low, p_t_high\n", + "])\n", + "qs = np.stack([p_t_low_[0][::50], p_t_high_[0][::50]], axis=0)\n", + "\n", + "fig, (ax1) = plt.subplots(1, 1, sharex=True)\n", + "\n", + "ax1.fill_between(t_[::50].T[0], qs[0], qs[1], alpha=0.7, color=TFColor[6])\n", + "plt.plot(t_[::50].T[0], qs[0], label=\"95% CI\", color=TFColor[6], alpha=0.7)\n", + "\n", + "plt.plot(t_.T[0][::50], mean_prob_t_[0][::50], lw=1, ls=\"--\", color=\"k\",\n", + " label=\"average posterior \\nprobability of defect\")\n", + "\n", + "\n", + "\n", + "plt.xlim(t_.min(), t_.max())\n", + "plt.ylim(-0.02, 1.02)\n", + "plt.legend(loc=\"lower left\")\n", + "plt.scatter(temperature_, D_, color=\"k\", s=50, alpha=0.5)\n", + "plt.xlabel(\"temp, $t$\")\n", + "\n", + "plt.ylabel(\"probability estimate\")\n", + "plt.title(\"Posterior probability estimates given temp. $t$\");" + ], + "execution_count": 16, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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ruI3btNVs1cKWhdPVdAAYl7GOK5RKp5TqS4VdyHnR/LhC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iiSeOqa8333wzn332GS+++CL5+fl06NCB7du3s2bNGnr27Mlvv/2mt+3evTs333wzH3zwAXff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\nQqDjr7V9uCB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+ "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [], + "image/png": { + "width": 832, + "height": 280 + } + } + } ] - }, - "metadata": { - "image/png": { - "height": 277, - "width": 832 - }, - "tags": [] - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize(12.5, 4))\n", - "\n", - "plt.plot(t_, mean_prob_t_.T, lw=3, label=\"average posterior \\nprobability \\\n", - "#of defect\")\n", - "plt.plot(t_, p_t_.T[:, 0], ls=\"--\", label=\"realization from posterior\")\n", - "plt.plot(t_, p_t_.T[:, -8], ls=\"--\", label=\"realization from posterior\")\n", - "plt.scatter(temperature_, D_, color=\"k\", s=50, alpha=0.5)\n", - "plt.title(\"Posterior expected value of probability of defect; \\\n", - "plus realizations\")\n", - "plt.legend(loc=\"lower left\")\n", - "plt.ylim(-0.1, 1.1)\n", - "plt.xlim(t_.min(), t_.max())\n", - "plt.ylabel(\"probability\")\n", - "plt.xlabel(\"temperature\");" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "iI7Fosv1IA0T" - }, - "source": [ - "Above we also plotted two possible realizations of what the actual underlying system might be. Both are equally likely as any other draw. The blue line is what occurs when we average all the 20000 possible dotted lines together.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 297 - }, - "colab_type": "code", - "id": "XpRl_4Beof6G", - "outputId": "8cd6c435-55fd-4290-e748-fb7086189ab4" - }, - "outputs": [ - { - "data": { - "image/png": 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te3KfTp45qe37tmv7vu3R8ntuvScKge760V3K5XNa+qylWnreUs2f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\nZ9za0MkbRNnsNkJMIdw58k5CjCG+wVS1NaI0ARb4neKv+uvRodNO++dtp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- "text/plain": [ - "" + }, + { + "metadata": { + "id": "rtcc9pBFIA0X", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "The 95% credible interval, or 95% CI, painted in purple, represents the interval, for each temperature, that contains 95% of the distribution. For example, at 65 degrees, we can be 95% sure that the probability of defect lies between 0.25 and 0.75.\n", + "\n", + "More generally, we can see that as the temperature nears 60 degrees, the CI's spread out over $[0,1]$ quickly. As we pass 70 degrees, the CI's tighten again. This can give us insight about how to proceed next: we should probably test more O-rings around 60-65 temperature to get a better estimate of probabilities in that range. Similarly, when reporting to scientists your estimates, you should be very cautious about simply telling them the expected probability, as we can see this does not reflect how *wide* the posterior distribution is." ] - }, - "metadata": { - "image/png": { - "height": 280, - "width": 832 - }, - "tags": [] - }, - "output_type": "display_data" - } - ], - "source": [ - "alpha_samples_means_ = np.array(alpha_samples_1d_.mean(axis=1))\n", - "beta_samples_means_ = np.array(beta_samples_1d_.mean(axis=1))\n", - "sorted_alpha_means_ = np.sort(alpha_samples_means_)\n", - "sorted_beta_means_ = np.sort(beta_samples_means_)\n", - "alpha_index_ = sorted_alpha_means_.shape[0]\n", - "beta_index_ = sorted_beta_means_.shape[0]\n", - "upper_alpha_quantile_ix_ = int(alpha_index_ * float(0.975))\n", - "lower_alpha_quantile_ix_ = int(alpha_index_ * float(0.025))\n", - "\n", - "upper_beta_quantile_ix_ = int(beta_index_ * float(0.975))\n", - "lower_beta_quantile_ix_ = int(beta_index_ * float(0.025))\n", - "\n", - "def find_nearest(array, value):\n", - " array = np.asarray(array)\n", - " idx = (np.abs(array - value)).argmin()\n", - " return idx\n", - "\n", - "alpha_upper_quantile_ix_ = find_nearest(alpha_samples_means_, sorted_alpha_means_[upper_alpha_quantile_ix_])\n", - "alpha_lower_quantile_ix_ = find_nearest(alpha_samples_means_, sorted_alpha_means_[lower_alpha_quantile_ix_])\n", - "beta_upper_quantile_ix_ = find_nearest(beta_samples_means_, sorted_beta_means_[upper_beta_quantile_ix_])\n", - "beta_lower_quantile_ix_ = find_nearest(beta_samples_means_, sorted_beta_means_[lower_beta_quantile_ix_])\n", - "\n", - "p_t_low = logistic(t_.T, beta_samples_1d_[beta_lower_quantile_ix_], alpha_samples_1d_[alpha_lower_quantile_ix_])\n", - "p_t_high = logistic(t_.T, beta_samples_1d_[beta_upper_quantile_ix_], alpha_samples_1d_[alpha_upper_quantile_ix_])\n", - "\n", - "[ \n", - " p_t_low_, p_t_high_\n", - "] = evaluate([ \n", - " p_t_low, p_t_high\n", - "])\n", - "qs = np.stack([p_t_low_[0][::50], p_t_high_[0][::50]], axis=0)\n", - "\n", - "fig, (ax1) = plt.subplots(1, 1, sharex=True)\n", - "\n", - "ax1.fill_between(t_[::50].T[0], qs[0], qs[1], alpha=0.7, color=TFColor[6])\n", - "plt.plot(t_[::50].T[0], qs[0], label=\"95% CI\", color=TFColor[6], alpha=0.7)\n", - "\n", - "plt.plot(t_.T[0][::50], mean_prob_t_[0][::50], lw=1, ls=\"--\", color=\"k\",\n", - " label=\"average posterior \\nprobability of defect\")\n", - "\n", - "\n", - "\n", - "plt.xlim(t_.min(), t_.max())\n", - "plt.ylim(-0.02, 1.02)\n", - "plt.legend(loc=\"lower left\")\n", - "plt.scatter(temperature_, D_, color=\"k\", s=50, alpha=0.5)\n", - "plt.xlabel(\"temp, $t$\")\n", - "\n", - "plt.ylabel(\"probability estimate\")\n", - "plt.title(\"Posterior probability estimates given temp. $t$\");" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "rtcc9pBFIA0X" - }, - "source": [ - "More generally, we can see that as the temperature nears 60 degrees, the CI's spread out over $[0,1]$ quickly. As we pass 70 degrees, the CI's tighten again. This can give us insight about how to proceed next: we should probably test more O-rings around 60-65 temperature to get a better estimate of probabilities in that range. Similarly, when reporting to scientists your estimates, you should be very cautious about simply telling them the expected probability, as we can see this does not reflect how *wide* the posterior distribution is." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "lesq_3oIIA0Y" - }, - "source": [ - "### What about the day of the Challenger disaster?\n", - "\n", - "On the day of the Challenger disaster, the outside temperature was 31 degrees Fahrenheit. What is the posterior distribution of a defect occurring, given this temperature? The distribution is plotted below. It looks almost guaranteed that the Challenger was going to be subject to defective O-rings." - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 258 - }, - "colab_type": "code", - "id": "AYbamYmdUdBZ", - "outputId": "1bdab35d-4dc5-41a0-a3c1-842416444ef7" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[0.94 0.957 0.964 ... 0.99 0.987 0.988]\n" - ] - }, - { - "data": { - "image/png": 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- "text/plain": [ - "" + }, + { + "metadata": { + "id": "lesq_3oIIA0Y", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "### What about the day of the Challenger disaster?\n", + "\n", + "On the day of the Challenger disaster, the outside temperature was 31 degrees Fahrenheit. What is the posterior distribution of a defect occurring, given this temperature? The distribution is plotted below. It looks almost guaranteed that the Challenger was going to be subject to defective O-rings." ] - }, - "metadata": { - "image/png": { - "height": 224, - "width": 825 - }, - "tags": [] - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize(12.5, 3))\n", - "\n", - "prob_31 = logistic(31, beta_samples_, alpha_samples_)\n", - "\n", - "[ prob_31_ ] = evaluate([ prob_31 ])\n", - "print(prob_31_)\n", - "\n", - "plt.xlim(0.900, 1) # This should be changed to plt.xlim(0.995, 1), but illustrates the error\n", - "plt.hist(prob_31_, bins=10, normed=True, histtype='stepfilled')\n", - "plt.title(\"Posterior distribution of probability of defect, given $t = 31$\")\n", - "plt.xlabel(\"probability of defect occurring in O-ring\");" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "WjAFZ8W9IA0c" - }, - "source": [ - "### Is our model appropriate?\n", - "\n", - "The skeptical reader will say \"You deliberately chose the logistic function for $p(t)$ and the specific priors. Perhaps other functions or priors will give different results. How do I know I have chosen a good model?\" This is absolutely true. To consider an extreme situation, what if I had chosen the function $p(t) = 1,\\; \\forall t$, which guarantees a defect always occurring: I would have again predicted disaster on January 28th. Yet this is clearly a poorly chosen model. On the other hand, if I did choose the logistic function for $p(t)$, but specified all my priors to be very tight around 0, likely we would have very different posterior distributions. How do we know our model is an expression of the data? This encourages us to measure the model's **goodness of fit**.\n", - "\n", - "We can think: *how can we test whether our model is a bad fit?* An idea is to compare observed data with artificial dataset which we can simulate. The rationale is that if the simulated dataset does not appear similar, statistically, to the observed dataset, then likely our model is not accurately represented the observed data. \n", - "\n", - "Previously in this Chapter, we simulated an artificial dataset for the SMS example. To do this, we sampled values from the priors. We saw how varied the resulting datasets looked like, and rarely did they mimic our observed dataset. In the current example, we should sample from the *posterior* distributions to create *very plausible datasets*. Luckily, our Bayesian framework makes this very easy. We only need to gather samples from the distribution of choice, and specify the number of samples, the shape of the samples (we had 21 observations in our original dataset, so we'll make the shape of each sample 21), and the probability we want to use to determine the ratio of 1 observations to 0 observations.\n", - "\n", - "\n", - "Hence we create the following:\n", - "\n", - "```python\n", - "simulated_data = tfd.Bernoulli(name=\"simulation_data\", probs=p).sample(sample_shape=N)\n", - "```\n", - "Let's simulate 10 000:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "MvFwyz9hwROg" - }, - "outputs": [], - "source": [ - "alpha = alpha_mean_ # We're basing these values on the outputs of our model above\n", - "beta = beta_mean_\n", - "p_deterministic = tfd.Deterministic(name=\"p\", loc=1.0/(1. + tf.exp(beta * temperature_ + alpha))).sample()#seed=6.45)\n", - "simulated_data = tfd.Bernoulli(name=\"bernoulli_sim\", \n", - " probs=p_deterministic_).sample(sample_shape=10000)\n", - "[ \n", - " bernoulli_sim_samples_,\n", - " p_deterministic_\n", - "] =evaluate([\n", - " simulated_data,\n", - " p_deterministic\n", - "])" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 734 - }, - "colab_type": "code", - "id": "gDyVY1wmgjx4", - "outputId": "d48ffb1b-57bf-41e5-eda5-4289bef1ad4a" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Number of simulations: 10000\n", - "Number data points per simulation: 23\n" - ] - }, - { - "data": { - "image/png": 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- "text/plain": [ - "" + }, + { + "metadata": { + "id": "AYbamYmdUdBZ", + "colab_type": "code", + "outputId": "36119446-ebdd-47c8-95d3-3fb29e86c041", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 241 + } + }, + "cell_type": "code", + "source": [ + "plt.figure(figsize(12.5, 3))\n", + "\n", + "prob_31 = logistic(31, beta_samples_, alpha_samples_)\n", + "\n", + "[ prob_31_ ] = evaluate([ prob_31 ])\n", + "#print(prob_31_)\n", + "\n", + "plt.xlim(0.995, 1) # This should be changed to plt.xlim(0.995, 1), but illustrates the error\n", + "plt.hist(prob_31_, bins=10, normed=True, histtype='stepfilled')\n", + "plt.title(\"Posterior distribution of probability of defect, given $t = 31$\")\n", + "plt.xlabel(\"probability of defect occurring in O-ring\");" + ], + "execution_count": 21, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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VJEnSLMZikCRJksbj913W/6EuF2xb3+lFZKuX\nQLdjPVKXi/R4/tY5FmqtiIgXA3tQhtJ6TZfzdNItpxecY6Jl5v0R8WPgbZTh6r5dN21FKZh0m+eo\naTz3thcvr8s/dNn+WNufW3PbvBpoH/Kvaf6ImDsz/zJMTOtY3QowLYu3xXfLdTxGe59Hk8tk5t3U\n6Wezl22ddCoEQekxBKWYCTOen27Hv4+JKQZ1yqc9l+G0iivtxcuOag+4VgHpibq8nDLfWNMhwMFt\n6ybiXo/lPkuSJGnAWQySJEnSeDzXZX1rOOL2l/mdeheM9FK2daxO5+q0rnWcoca6kyjDhD0MfBa4\njTKMGJQi0Xpdzt3t+jqdYzKcSikG7QB8u/aAeSNwSXNoqGGM5972YqT70D4sdSvuXmC3EY79txG2\nt461LcP32Gj1qGld41zdAsdhtPd5NLlMZt5Nw/X8GevweSMZ6fmZ7J+vXt0OrEHp2XVVD/ErUIZ8\nu68xJOFHKXP2tB+33WTc61nlPkuSJGkSWQySJEnSeHTrUdLqEfRwD8do9aZYrMv2Vq+LRzpsW4Q6\n/FvDwnX5OEBELEEppkwH1s3Mu5rBEbHTMLl1u77nnWMSnUfplfD2iHg58P66/vQe9/89ZRi4sdzb\nXrR6PbT3AGtpP29r3qJ5MvO77cGj9DtKT4sbOswH08nDlJf0i44UOAajfYYfbls/nNHEjmTxkUNm\nqlaPm27Pz1IzK5ER/AD4AKVX3pd6iH9vXV7cWpGZP+gSOzPMKvdZkiRJk6j9m3qSJEnSaLyxfUVE\nvIgZ8/Xc28MxrqvLdbtsf1Nb3LDnZ8a8LLfV5dKUb8b/qkMhaEFgrWFyW6MOMTfSOSZFZv4ZOJsy\n18jmwDaUXjDn9XiI8dzbXrR6NqzSvqFOWr9Gc11m/oZSOFksIl7XYZ9pEbFcj+e+pi7f1mljRCxX\nh+tqub4uN+wQ+68R8d2I+ECP52432vvcymX9+vPSzOVlEXFeRHx1DLFQe+PVZ7sZOwfwzz1dzcxz\nR112en5WAV41c9Pp6izgIeAtEbH5cIER8QpgT0qPri/OhNx6cTelx9HSETFvh+3/MpPzkSRJ0hSw\nGCRJkqTxWCkitmhbtxWlh8QtmflAD8e4GHiQ8rL7eS/qIyKArYFngDM77PupiFigET8N+GT94wV1\n+WBdLh0RL2vEvgw4hRlD2XWa/2cRYOe2nNajTLb+CPCzkS6uB63zd+uFdGpd7gusBJybmU93ie20\n73PAzhHxvF4hEbENsBxwfWb+YnQp/8NVwFPAWhGxZtu23eg8x0qrcHF4h0Lbp4G7IuKQHs7dOs4e\nEfG8excRawO/Ai5rrD6dMhzW9hGxaCN2TuBAYFPg/kb8dGChLsXAdqN6hjPzFsrwdUtQepw07Qhs\nRh3aazSx1d11uUlb7G5077k0VS6hfCbviYhXt1bWz+QYymcw5TJzOqV34XPAGd2KhhHxWuBHlDl6\nDuyxx9qkq0PVXUUpKn+suS0idqBDMU6SJEmDx2HiJEmSNB7fBk6OiH8HbgWWBLanvDTdp5cDZOZf\nI+KDwPeAiyLibOAu4NWU3jBzAx/KzE5Dmf0Q+HlEXEgZCumtlF4YSZkniMy8PyJ+VLddERHnUyZ3\n34LS6+Ioyjf4P1ULRM1v858P7BcRbwVuBl5JebEPsG9mjjSvTS/uAJ4FNo6I04C/Z+aHWxsz8+qI\nSMpwb9D7EHFk5q0RcTBwKOU+fQd4jPLydzPgD8CHux9hxOP/pR7/C8AlNf8ngTUpPa7OohQHmw4H\n3g68B7ixfh5DlF41b6Xcj+N7OPcPIuLLlGLdLyLim/V6VqY8N38D9m/E3xQRn63rboyIbwB/pdyH\nVYATMvOKxiluA1YHvh8RdwFfysyOPcHG+AzvCFwKnBoRbwN+TelxtjmlKLX3GGNPAY6m/FyuSyla\nvpFSwDyJtuLmVMrMuyPidEqbcXV9Ph+nXNe9lGLr+lOY4j/U521Tys/f1yNif0r78ztgfkovuA0p\nz/LemflfU5ZsZ4dShrv7XES8gdJer0LpWfcFYL8pzE2SJEkzgT2DJEmSNB53AxtRiiu7U4YxuxF4\nV2ZePNyOTZl5CaWIcyGwMTN6alwBrJ+ZX+uy676UHgRvBfaizAnzdWDDOsRay9aUXjKL133eBZxQ\n159G6aHwCuBDlG/Pt9wDvIVS3PoEsF1dt11mntLr9Q0nMx8DPkUp0ryPzkONta7/AUpRYDTHP4zy\ncj2BbSnFkDdQigar154nY5aZxwA71dx2plzL34H1gPs6xD8DbED5jKdRhtTal1I4+TywTmb+vn2/\nLuf+eL2mOyhFrYMoxYNzgLUz86q2+M9Q7vG9Nde9aq67AB9vO/wnKcPgbUQpGM3JMEb7DGfmDZQC\nwpnAO2ru6wInA2tl5qNjiaX8PBxAmWtoJ8pz+zSwDjPmNuonOwGfo3wOO1HakHMpz2zL0BTk9QKZ\neSGlN92+wKOU9uMQSt4vp9z7FfqwEERm/ojyPN5IKcR+kvLl0HUpxUXok/ssSZKkyTFtaMjf9yRJ\nkjQ6tTfIQcBRmbnvFKcz8CLiPZReSkdk5gFTnY80M0TEdZReZm/OzCunOp9BFRG7AMcBX83MHac6\nH0mSJE0Oh4mTJEmS+t8ulJ4TJ051ItJEiYgXAasCy2TmuW3b5qT09IPSG0/jEBFLUe71TZl5f9vm\n1pxB3mdJkqQB5jBxkiRJUh+rk9W/Azirw0tcaVZ3PvCdiNiwbf0ulLl4bsrMB2d+WgNnZ+ACypxd\n/xARyzBjHrQLZ3JOkiRJmonsGSRJkiT1mYhYkDIPySrA+ynzv+w5pUlJEywzn4uIPShzIX0/Ir4B\n3A+sTpnfZjqw6xSmOEi+CGwFbFd7CV0OLEppXxYETsjMm6cwP0mSJE0yewZJkiRJ/Wc+4DBgC+CH\nlDlTHpralKSJl5lnAxsBlwLvBA4A1gbOAdbJzCumML2BkZm/B9ajFIVeBewDbA/8mlJ4/vjUZSdJ\nkqSZYdrQ0NBU5yBJkiRJkiRJkqRJYs8gSZIkSZIkSZKkAWYxSJIkSZIkSZIkaYBZDJIkSZIkSZIk\nSRpgFoMkSZIkSZIkSZIGmMUgSZIkSZIkSZKkAWYxSJIkSZIkSZIkaYBZDJIkSZIkSZIkSRpgFoMk\nSZIkSZIkSZIGmMUgSZIkSZIkSZKkAWYxSJIkSZIkSZIkaYBZDJIkSZIkSZIkSRpgFoMkSZIkSZIk\nSZIG2P8DXepLAhqrvdcAAAAASUVORK5CYII=\n", + "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [], + "image/png": { + "width": 833, + "height": 224 + } + } + } ] - }, - "metadata": { - "image/png": { - "height": 683, - "width": 818 - }, - "tags": [] - }, - "output_type": "display_data" - } - ], - "source": [ - "simulations_ = bernoulli_sim_samples_\n", - "print(\"Number of simulations: \", simulations_.shape[0])\n", - "print(\"Number data points per simulation: \", simulations_.shape[1])\n", - "\n", - "plt.figure(figsize(12.5, 12))\n", - "plt.title(\"Simulated dataset using posterior parameters\")\n", - "for i in range(4):\n", - " ax = plt.subplot(4, 1, i+1)\n", - " plt.scatter(temperature_, simulations_[1000*i, :], color=\"k\",\n", - " s=50, alpha=0.6)\n", - " " - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "RFSaMzNQIA0l" - }, - "source": [ - "Note that the above plots are different (if you can think of a cleaner way to present this, please send a pull request and answer [here](http://stats.stackexchange.com/questions/53078/how-to-visualize-bayesian-goodness-of-fit-for-logistic-regression)!).\n", - "\n", - "We wish to assess how good our model is. \"Good\" is a subjective term of course, so results must be relative to other models. \n", - "\n", - "We will be doing this graphically as well, which may seem like an even less objective method. The alternative is to use *Bayesian p-values*. These are still subjective, as the proper cutoff between good and bad is arbitrary. Gelman emphasises that the graphical tests are more illuminating [3] than p-value tests. We agree.\n", - "\n", - "The following graphical test is a novel data-viz approach to logistic regression. The plots are called *separation plots*[4]. For a suite of models we wish to compare, each model is plotted on an individual separation plot. I leave most of the technical details about separation plots to the very accessible [original paper](http://mdwardlab.com/sites/default/files/GreenhillWardSacks.pdf), but I'll summarize their use here.\n", - "\n", - "For each model, we calculate the proportion of times the posterior simulation proposed a value of 1 for a particular temperature, i.e. compute $P( \\;\\text{Defect} = 1 | t, \\alpha, \\beta )$ by averaging. This gives us the posterior probability of a defect at each data point in our dataset. For example, for the model we used above:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 425 - }, - "colab_type": "code", - "id": "3ho1cPLAIA0l", - "outputId": "753be416-5530-43c0-e44c-bb5d62dfc358" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "posterior prob of defect | realized defect \n", - "0.36 | 0\n", - "0.25 | 1\n", - "0.28 | 0\n", - "0.31 | 0\n", - "0.33 | 0\n", - "0.20 | 0\n", - "0.18 | 0\n", - "0.24 | 0\n", - "0.69 | 1\n", - "0.48 | 1\n", - "0.26 | 1\n", - "0.10 | 0\n", - "0.34 | 0\n", - "0.78 | 1\n", - "0.34 | 0\n", - "0.13 | 0\n", - "0.25 | 0\n", - "0.07 | 0\n", - "0.12 | 0\n", - "0.08 | 0\n", - "0.14 | 1\n", - "0.13 | 0\n", - "0.66 | 1\n" - ] - } - ], - "source": [ - "posterior_probability_ = simulations_.mean(axis=0)\n", - "print(\"posterior prob of defect | realized defect \")\n", - "for i in range(len(D_)):\n", - " print(\"%.2f | %d\" % (posterior_probability_[i], D_[i]))" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "-q4yysOiIA0n" - }, - "source": [ - "Next we sort each column by the posterior probabilities:" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 425 - }, - "colab_type": "code", - "id": "i3TkXUhSIA0n", - "outputId": "3de583e0-0204-4fa1-f67b-caee128c5569" - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "probb | defect \n", - "0.07 | 0\n", - "0.08 | 0\n", - "0.10 | 0\n", - "0.12 | 0\n", - "0.13 | 0\n", - "0.13 | 0\n", - "0.14 | 1\n", - "0.18 | 0\n", - "0.20 | 0\n", - "0.24 | 0\n", - "0.25 | 1\n", - "0.25 | 0\n", - "0.26 | 1\n", - "0.28 | 0\n", - "0.31 | 0\n", - "0.33 | 0\n", - "0.34 | 0\n", - "0.34 | 0\n", - "0.36 | 0\n", - "0.48 | 1\n", - "0.66 | 1\n", - "0.69 | 1\n", - "0.78 | 1\n" - ] - } - ], - "source": [ - "ix_ = np.argsort(posterior_probability_)\n", - "print(\"probb | defect \")\n", - "for i in range(len(D_)):\n", - " print(\"%.2f | %d\" % (posterior_probability_[ix_[i]], D_[ix_[i]]))" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "ajvopQADIA0p" - }, - "source": [ - "We can present the above data better in a figure: we've creates a `separation_plot` function." - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 237 - }, - "colab_type": "code", - "id": "tFR1_yu8IA0p", - "outputId": "e5508fb9-0448-483c-d42e-157d82b60500" - }, - "outputs": [ - { - "data": { - "text/plain": [ - "" + }, + { + "metadata": { + "id": "WjAFZ8W9IA0c", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "### Is our model appropriate?\n", + "\n", + "The skeptical reader will say \"You deliberately chose the logistic function for $p(t)$ and the specific priors. Perhaps other functions or priors will give different results. How do I know I have chosen a good model?\" This is absolutely true. To consider an extreme situation, what if I had chosen the function $p(t) = 1,\\; \\forall t$, which guarantees a defect always occurring: I would have again predicted disaster on January 28th. Yet this is clearly a poorly chosen model. On the other hand, if I did choose the logistic function for $p(t)$, but specified all my priors to be very tight around 0, likely we would have very different posterior distributions. How do we know our model is an expression of the data? This encourages us to measure the model's **goodness of fit**.\n", + "\n", + "We can think: *how can we test whether our model is a bad fit?* An idea is to compare observed data with artificial dataset which we can simulate. The rationale is that if the simulated dataset does not appear similar, statistically, to the observed dataset, then likely our model is not accurately represented the observed data. \n", + "\n", + "Previously in this Chapter, we simulated an artificial dataset for the SMS example. To do this, we sampled values from the priors. We saw how varied the resulting datasets looked like, and rarely did they mimic our observed dataset. In the current example, we should sample from the *posterior* distributions to create *very plausible datasets*. Luckily, our Bayesian framework makes this very easy. We only need to gather samples from the distribution of choice, and specify the number of samples, the shape of the samples (we had 21 observations in our original dataset, so we'll make the shape of each sample 21), and the probability we want to use to determine the ratio of 1 observations to 0 observations.\n", + "\n", + "\n", + "Hence we create the following:\n", + "\n", + "```python\n", + "simulated_data = tfd.Bernoulli(name=\"simulation_data\", probs=p).sample(sample_shape=N)\n", + "```\n", + "Let's simulate 10 000:" ] - }, - "metadata": { - "tags": [] - }, - "output_type": "display_data" }, { - "data": { - "image/png": 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- "text/plain": [ - "" + "metadata": { + "id": "MvFwyz9hwROg", + "colab_type": "code", + "colab": {} + }, + "cell_type": "code", + "source": [ + "alpha = alpha_mean_ # We're basing these values on the outputs of our model above\n", + "beta = beta_mean_\n", + "p_deterministic = tfd.Deterministic(name=\"p\", loc=1.0/(1. + tf.exp(beta * temperature_ + alpha))).sample()#seed=6.45)\n", + "simulated_data = tfd.Bernoulli(name=\"bernoulli_sim\", \n", + " probs=p_deterministic_).sample(sample_shape=10000)\n", + "[ \n", + " bernoulli_sim_samples_,\n", + " p_deterministic_\n", + "] =evaluate([\n", + " simulated_data,\n", + " p_deterministic\n", + "])" + ], + "execution_count": 0, + "outputs": [] + }, + { + "metadata": { + "id": "gDyVY1wmgjx4", + "colab_type": "code", + "outputId": "d48ffb1b-57bf-41e5-eda5-4289bef1ad4a", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 734 + } + }, + "cell_type": "code", + "source": [ + "simulations_ = bernoulli_sim_samples_\n", + "print(\"Number of simulations: \", simulations_.shape[0])\n", + "print(\"Number data points per simulation: \", simulations_.shape[1])\n", + "\n", + "plt.figure(figsize(12.5, 12))\n", + "plt.title(\"Simulated dataset using posterior parameters\")\n", + "for i in range(4):\n", + " ax = plt.subplot(4, 1, i+1)\n", + " plt.scatter(temperature_, simulations_[1000*i, :], color=\"k\",\n", + " s=50, alpha=0.6)\n", + " " + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "Number of simulations: 10000\n", + "Number data points per simulation: 23\n" + ], + "name": "stdout" + }, + { + "output_type": "display_data", + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [], + "image/png": { + "width": 818, + "height": 683 + } + } + } ] - }, - "metadata": { - "image/png": { - "height": 203, - "width": 780 - }, - "tags": [] - }, - "output_type": "display_data" - } - ], - "source": [ - "import matplotlib.pyplot as plt\n", - "\n", - "def separation_plot( p, y, **kwargs ):\n", - " \"\"\"\n", - " This function creates a separation plot for logistic and probit classification. \n", - " See http://mdwardlab.com/sites/default/files/GreenhillWardSacks.pdf\n", - " \n", - " p: The proportions/probabilities, can be a nxM matrix which represents M models.\n", - " y: the 0-1 response variables.\n", - " \n", - " \"\"\" \n", - " assert p.shape[0] == y.shape[0], \"p.shape[0] != y.shape[0]\"\n", - " n = p.shape[0]\n", - "\n", - " try:\n", - " M = p.shape[1]\n", - " except:\n", - " p = p.reshape( n, 1 )\n", - " M = p.shape[1]\n", - "\n", - " colors_bmh = np.array( [\"#eeeeee\", \"#348ABD\"] )\n", - "\n", - "\n", - " fig = plt.figure( )\n", - " \n", - " for i in range(M):\n", - " ax = fig.add_subplot(M, 1, i+1)\n", - " ix = np.argsort( p[:,i] )\n", - " #plot the different bars\n", - " bars = ax.bar( np.arange(n), np.ones(n), width=1.,\n", - " color = colors_bmh[ y[ix].astype(int) ], \n", - " edgecolor = 'none')\n", - " ax.plot( np.arange(n+1), np.append(p[ix,i], p[ix,i][-1]), \"k\",\n", - " linewidth = 1.,drawstyle=\"steps-post\" )\n", - " #create expected value bar.\n", - " ax.vlines( [(1-p[ix,i]).sum()], [0], [1] )\n", - " plt.xlim( 0, n)\n", - " \n", - " plt.tight_layout()\n", - " \n", - " return\n", - "\n", - "plt.figure(figsize(11., 3))\n", - "separation_plot(posterior_probability_, D_)" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "tBuY2lSaIA0s" - }, - "source": [ - "The snaking-line is the sorted probabilities, blue bars denote defects, and empty space (or grey bars for the optimistic readers) denote non-defects. As the probability rises, we see more and more defects occur. On the right hand side, the plot suggests that as the posterior probability is large (line close to 1), then more defects are realized. This is good behaviour. Ideally, all the blue bars *should* be close to the right-hand side, and deviations from this reflect missed predictions. \n", - "\n", - "The black vertical line is the expected number of defects we should observe, given this model. This allows the user to see how the total number of events predicted by the model compares to the actual number of events in the data.\n", - "\n", - "It is much more informative to compare this to separation plots for other models. Below we compare our model (top) versus three others:\n", - "\n", - "1. the perfect model, which predicts the posterior probability to be equal 1 if a defect did occur.\n", - "2. a completely random model, which predicts random probabilities regardless of temperature.\n", - "3. a constant model: where $P(D = 1 \\; | \\; t) = c, \\;\\; \\forall t$. The best choice for $c$ is the observed frequency of defects, in this case 7/23. \n" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 618 - }, - "colab_type": "code", - "id": "RbX1nHrBIA0s", - "outputId": "d705df41-b68e-4f98-983a-df76934e9ffc" - }, - "outputs": [ - { - "data": { - "text/plain": [ - "" + }, + { + "metadata": { + "id": "RFSaMzNQIA0l", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "Note that the above plots are different (if you can think of a cleaner way to present this, please send a pull request and answer [here](http://stats.stackexchange.com/questions/53078/how-to-visualize-bayesian-goodness-of-fit-for-logistic-regression)!).\n", + "\n", + "We wish to assess how good our model is. \"Good\" is a subjective term of course, so results must be relative to other models. \n", + "\n", + "We will be doing this graphically as well, which may seem like an even less objective method. The alternative is to use *Bayesian p-values*. These are still subjective, as the proper cutoff between good and bad is arbitrary. Gelman emphasises that the graphical tests are more illuminating [3] than p-value tests. We agree.\n", + "\n", + "The following graphical test is a novel data-viz approach to logistic regression. The plots are called *separation plots*[4]. For a suite of models we wish to compare, each model is plotted on an individual separation plot. I leave most of the technical details about separation plots to the very accessible [original paper](http://mdwardlab.com/sites/default/files/GreenhillWardSacks.pdf), but I'll summarize their use here.\n", + "\n", + "For each model, we calculate the proportion of times the posterior simulation proposed a value of 1 for a particular temperature, i.e. compute $P( \\;\\text{Defect} = 1 | t, \\alpha, \\beta )$ by averaging. This gives us the posterior probability of a defect at each data point in our dataset. For example, for the model we used above:" ] - }, - "metadata": { - "tags": [] - }, - "output_type": "display_data" }, { - "data": { - "image/png": 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- "text/plain": [ - "" + "metadata": { + "id": "3ho1cPLAIA0l", + "colab_type": "code", + "outputId": "753be416-5530-43c0-e44c-bb5d62dfc358", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 425 + } + }, + "cell_type": "code", + "source": [ + "posterior_probability_ = simulations_.mean(axis=0)\n", + "print(\"posterior prob of defect | realized defect \")\n", + "for i in range(len(D_)):\n", + " print(\"%.2f | %d\" % (posterior_probability_[i], D_[i]))" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "posterior prob of defect | realized defect \n", + "0.36 | 0\n", + "0.25 | 1\n", + "0.28 | 0\n", + "0.31 | 0\n", + "0.33 | 0\n", + "0.20 | 0\n", + "0.18 | 0\n", + "0.24 | 0\n", + "0.69 | 1\n", + "0.48 | 1\n", + "0.26 | 1\n", + "0.10 | 0\n", + "0.34 | 0\n", + "0.78 | 1\n", + "0.34 | 0\n", + "0.13 | 0\n", + "0.25 | 0\n", + "0.07 | 0\n", + "0.12 | 0\n", + "0.08 | 0\n", + "0.14 | 1\n", + "0.13 | 0\n", + "0.66 | 1\n" + ], + "name": "stdout" + } ] - }, - "metadata": { - "image/png": { - "height": 146, - "width": 780 + }, + { + "metadata": { + "id": "-q4yysOiIA0n", + "colab_type": "text" }, - "tags": [] - }, - "output_type": "display_data" + "cell_type": "markdown", + "source": [ + "Next we sort each column by the posterior probabilities:" + ] }, { - "data": { - "image/png": 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- "text/plain": [ - "" + "metadata": { + "id": "i3TkXUhSIA0n", + "colab_type": "code", + "outputId": "3de583e0-0204-4fa1-f67b-caee128c5569", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 425 + } + }, + "cell_type": "code", + "source": [ + "ix_ = np.argsort(posterior_probability_)\n", + "print(\"probb | defect \")\n", + "for i in range(len(D_)):\n", + " print(\"%.2f | %d\" % (posterior_probability_[ix_[i]], D_[ix_[i]]))" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "stream", + "text": [ + "probb | defect \n", + "0.07 | 0\n", + "0.08 | 0\n", + "0.10 | 0\n", + "0.12 | 0\n", + "0.13 | 0\n", + "0.13 | 0\n", + "0.14 | 1\n", + "0.18 | 0\n", + "0.20 | 0\n", + "0.24 | 0\n", + "0.25 | 1\n", + "0.25 | 0\n", + "0.26 | 1\n", + "0.28 | 0\n", + "0.31 | 0\n", + "0.33 | 0\n", + "0.34 | 0\n", + "0.34 | 0\n", + "0.36 | 0\n", + "0.48 | 1\n", + "0.66 | 1\n", + "0.69 | 1\n", + "0.78 | 1\n" + ], + "name": "stdout" + } ] - }, - "metadata": { - "image/png": { - "height": 146, - "width": 780 + }, + { + "metadata": { + "id": "ajvopQADIA0p", + "colab_type": "text" }, - "tags": [] - }, - "output_type": "display_data" + "cell_type": "markdown", + "source": [ + "We can present the above data better in a figure: we've creates a `separation_plot` function." + ] }, { - "data": { - "image/png": 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- "text/plain": [ - "" + "metadata": { + "id": "tFR1_yu8IA0p", + "colab_type": "code", + "outputId": "e5508fb9-0448-483c-d42e-157d82b60500", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 237 + } + }, + "cell_type": "code", + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "def separation_plot( p, y, **kwargs ):\n", + " \"\"\"\n", + " This function creates a separation plot for logistic and probit classification. \n", + " See http://mdwardlab.com/sites/default/files/GreenhillWardSacks.pdf\n", + " \n", + " p: The proportions/probabilities, can be a nxM matrix which represents M models.\n", + " y: the 0-1 response variables.\n", + " \n", + " \"\"\" \n", + " assert p.shape[0] == y.shape[0], \"p.shape[0] != y.shape[0]\"\n", + " n = p.shape[0]\n", + "\n", + " try:\n", + " M = p.shape[1]\n", + " except:\n", + " p = p.reshape( n, 1 )\n", + " M = p.shape[1]\n", + "\n", + " colors_bmh = np.array( [\"#eeeeee\", \"#348ABD\"] )\n", + "\n", + "\n", + " fig = plt.figure( )\n", + " \n", + " for i in range(M):\n", + " ax = fig.add_subplot(M, 1, i+1)\n", + " ix = np.argsort( p[:,i] )\n", + " #plot the different bars\n", + " bars = ax.bar( np.arange(n), np.ones(n), width=1.,\n", + " color = colors_bmh[ y[ix].astype(int) ], \n", + " edgecolor = 'none')\n", + " ax.plot( np.arange(n+1), np.append(p[ix,i], p[ix,i][-1]), \"k\",\n", + " linewidth = 1.,drawstyle=\"steps-post\" )\n", + " #create expected value bar.\n", + " ax.vlines( [(1-p[ix,i]).sum()], [0], [1] )\n", + " plt.xlim( 0, n)\n", + " \n", + " plt.tight_layout()\n", + " \n", + " return\n", + "\n", + "plt.figure(figsize(11., 3))\n", + "separation_plot(posterior_probability_, D_)" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [] + } + }, + { + "output_type": "display_data", + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [], + "image/png": { + "width": 780, + "height": 203 + } + } + } ] - }, - "metadata": { - "image/png": { - "height": 146, - "width": 780 + }, + { + "metadata": { + "id": "tBuY2lSaIA0s", + "colab_type": "text" }, - "tags": [] - }, - "output_type": "display_data" + "cell_type": "markdown", + "source": [ + "The snaking-line is the sorted probabilities, blue bars denote defects, and empty space (or grey bars for the optimistic readers) denote non-defects. As the probability rises, we see more and more defects occur. On the right hand side, the plot suggests that as the posterior probability is large (line close to 1), then more defects are realized. This is good behaviour. Ideally, all the blue bars *should* be close to the right-hand side, and deviations from this reflect missed predictions. \n", + "\n", + "The black vertical line is the expected number of defects we should observe, given this model. This allows the user to see how the total number of events predicted by the model compares to the actual number of events in the data.\n", + "\n", + "It is much more informative to compare this to separation plots for other models. Below we compare our model (top) versus three others:\n", + "\n", + "1. the perfect model, which predicts the posterior probability to be equal 1 if a defect did occur.\n", + "2. a completely random model, which predicts random probabilities regardless of temperature.\n", + "3. a constant model: where $P(D = 1 \\; | \\; t) = c, \\;\\; \\forall t$. The best choice for $c$ is the observed frequency of defects, in this case 7/23. \n" + ] }, { - "data": { - "image/png": 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- "text/plain": [ - "" + "metadata": { + "id": "RbX1nHrBIA0s", + "colab_type": "code", + "outputId": "d705df41-b68e-4f98-983a-df76934e9ffc", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 618 + } + }, + "cell_type": "code", + "source": [ + "plt.figure(figsize(11., 2))\n", + "\n", + "# Our temperature-dependent model\n", + "separation_plot(posterior_probability_, D_)\n", + "plt.title(\"Temperature-dependent model\")\n", + "\n", + "# Perfect model\n", + "# i.e. the probability of defect is equal to if a defect occurred or not.\n", + "p_ = D_\n", + "separation_plot(p_, D_)\n", + "plt.title(\"Perfect model\")\n", + "\n", + "# random predictions\n", + "p_ = np.random.rand(23)\n", + "separation_plot(p_, D_)\n", + "plt.title(\"Random model\")\n", + "\n", + "# constant model\n", + "constant_prob_ = 7./23 * np.ones(23)\n", + "separation_plot(constant_prob_, D_)\n", + "plt.title(\"Constant-prediction model\");" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "display_data", + "data": { + "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [] + } + }, + { + "output_type": "display_data", + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [], + "image/png": { + "width": 780, + "height": 146 + } + } + } ] - }, - "metadata": { - "image/png": { - "height": 146, - "width": 780 - }, - "tags": [] - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize(11., 2))\n", - "\n", - "# Our temperature-dependent model\n", - "separation_plot(posterior_probability_, D_)\n", - "plt.title(\"Temperature-dependent model\")\n", - "\n", - "# Perfect model\n", - "# i.e. the probability of defect is equal to if a defect occurred or not.\n", - "p_ = D_\n", - "separation_plot(p_, D_)\n", - "plt.title(\"Perfect model\")\n", - "\n", - "# random predictions\n", - "p_ = np.random.rand(23)\n", - "separation_plot(p_, D_)\n", - "plt.title(\"Random model\")\n", - "\n", - "# constant model\n", - "constant_prob_ = 7./23 * np.ones(23)\n", - "separation_plot(constant_prob_, D_)\n", - "plt.title(\"Constant-prediction model\");" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "etHuMg8OIA0u" - }, - "source": [ - "In the random model, we can see that as the probability increases there is no clustering of defects to the right-hand side. Similarly for the constant model.\n", - "\n", - "In the perfect model, the probability line is not well shown, as it is stuck to the bottom and top of the figure. Of course the perfect model is only for demonstration, and we cannot infer any scientific inference from it." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "_I_3h7lsIA0v" - }, - "source": [ - "## Exercises\n", - "\n", - "1\\. Try putting in extreme values for our observations in the cheating example. What happens if we observe 25 affirmative responses? 10? 50? " - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "_B-K0Neyx7pZ" - }, - "outputs": [], - "source": [ - "#type your code here." - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "ulECHYwMIA0v" - }, - "source": [ - "2\\. Try plotting $\\alpha$ samples versus $\\beta$ samples. Why might the resulting plot look like this?" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/", - "height": 294 - }, - "colab_type": "code", - "id": "21v-EuHZIA0v", - "outputId": "ac7f87d4-4b14-45c4-ace4-dd2e7aa2eb28" - }, - "outputs": [ - { - "data": { - "image/png": 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HT5GD2hvIrTi/nhzevowcdL1owurfSq62/BmDI0mSpMPDOY8kSZKk8fqVQ1/UzO3y6UAc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2r/De3YilPa0SDwKs6sRJMvGxjtL1uilBHE9Xkc/EuqsmmS04gNT9zvUxPa8joiY+fTZ2Xaec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ylTW1K2DoIz5sac7KIl8FbNZoRDuO17akRERETEb4uYeRQRERERERER8YnCGHic6Q/5RRWw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\nKPrQeq6VTlAt9btmAlX2cwf7NIueC7VE1zuFGmlcPB1WrmuQ96F31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- "text/plain": [ - "" + }, + { + "metadata": { + "id": "etHuMg8OIA0u", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "In the random model, we can see that as the probability increases there is no clustering of defects to the right-hand side. Similarly for the constant model.\n", + "\n", + "In the perfect model, the probability line is not well shown, as it is stuck to the bottom and top of the figure. Of course the perfect model is only for demonstration, and we cannot infer any scientific inference from it." + ] + }, + { + "metadata": { + "id": "_I_3h7lsIA0v", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "## Exercises\n", + "\n", + "1\\. Try putting in extreme values for our observations in the cheating example. What happens if we observe 25 affirmative responses? 10? 50? " + ] + }, + { + "metadata": { + "id": "_B-K0Neyx7pZ", + "colab_type": "code", + "colab": {} + }, + "cell_type": "code", + "source": [ + "#type your code here." + ], + "execution_count": 0, + "outputs": [] + }, + { + "metadata": { + "id": "ulECHYwMIA0v", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "2\\. Try plotting $\\alpha$ samples versus $\\beta$ samples. Why might the resulting plot look like this?" + ] + }, + { + "metadata": { + "id": "21v-EuHZIA0v", + "colab_type": "code", + "outputId": "ac7f87d4-4b14-45c4-ace4-dd2e7aa2eb28", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 294 + } + }, + "cell_type": "code", + "source": [ + "#type your code here.\n", + "plt.figure(figsize(12.5, 4))\n", + "\n", + "plt.scatter(alpha_samples_, beta_samples_, alpha=0.1)\n", + "plt.title(\"Why does the plot look like this?\")\n", + "plt.xlabel(r\"$\\alpha$\")\n", + "plt.ylabel(r\"$\\beta$\");" + ], + "execution_count": 0, + "outputs": [ + { + "output_type": "display_data", + "data": { + "image/png": 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HT5GD2hvIrTi/nhzevowcdL1owurfSq62/BmDI0mSpMPDOY8kSZKk8fqVQ1/UzO3y6UAc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2r/De3YilPa0SDwKs6sRJMvGxjtL1uilBHE9Xkc/EuqsmmS04gNT9zvUxPa8joiY+fTZ2Xaec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ylTW1K2DoIz5sac7KIl8FbNZoRDuO17akRERETEb4uYeRQRERERERER8YnCGHic6Q/5RRWw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\nKPrQeq6VTlAt9btmAlX2cwf7NIueC7VE1zuFGmlcPB1WrmuQ96F31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+ "text/plain": [ + "" + ] + }, + "metadata": { + "tags": [], + "image/png": { + "width": 839, + "height": 277 + } + } + } + ] + }, + { + "metadata": { + "id": "e6RYS1_jIA0y", + "colab_type": "text" + }, + "cell_type": "markdown", + "source": [ + "## References\n", + "\n", + "[1] Dalal, Fowlkes and Hoadley (1989),JASA, 84, 945-957.\n", + "\n", + "[2] Cronin, Beau. \"Why Probabilistic Programming Matters.\" 24 Mar 2013. Google, Online Posting to Google . Web. 24 Mar. 2013. .\n", + "\n", + "[3] Gelman, Andrew. \"Philosophy and the practice of Bayesian statistics.\" British Journal of Mathematical and Statistical Psychology. (2012): n. page. Web. 2 Apr. 2013.\n", + "\n", + "[4] Greenhill, Brian, Michael D. Ward, and Audrey Sacks. \"The Separation Plot: A New Visual Method for Evaluating the Fit of Binary Models.\" American Journal of Political Science. 55.No.4 (2011): n. page. Web. 2 Apr. 2013.\n" ] - }, - "metadata": { - "image/png": { - "height": 277, - "width": 839 - }, - "tags": [] - }, - "output_type": "display_data" + }, + { + "metadata": { + "id": "TxfPXLi0IA0z", + "colab_type": "code", + "colab": {} + }, + "cell_type": "code", + "source": [ + "from IPython.core.display import HTML\n", + "def css_styling():\n", + " styles = open(\"../styles/custom.css\", \"r\").read()\n", + " return HTML(styles)\n", + "css_styling()\n" + ], + "execution_count": 0, + "outputs": [] } - ], - "source": [ - "#type your code here.\n", - "plt.figure(figsize(12.5, 4))\n", - "\n", - "plt.scatter(alpha_samples_, beta_samples_, alpha=0.1)\n", - "plt.title(\"Why does the plot look like this?\")\n", - "plt.xlabel(r\"$\\alpha$\")\n", - "plt.ylabel(r\"$\\beta$\");" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "colab_type": "text", - "id": "e6RYS1_jIA0y" - }, - "source": [ - "## References\n", - "\n", - "[1] Dalal, Fowlkes and Hoadley (1989),JASA, 84, 945-957.\n", - "\n", - "[2] Cronin, Beau. \"Why Probabilistic Programming Matters.\" 24 Mar 2013. Google, Online Posting to Google . Web. 24 Mar. 2013. .\n", - "\n", - "[3] Gelman, Andrew. \"Philosophy and the practice of Bayesian statistics.\" British Journal of Mathematical and Statistical Psychology. (2012): n. page. Web. 2 Apr. 2013.\n", - "\n", - "[4] Greenhill, Brian, Michael D. Ward, and Audrey Sacks. \"The Separation Plot: A New Visual Method for Evaluating the Fit of Binary Models.\" American Journal of Political Science. 55.No.4 (2011): n. page. Web. 2 Apr. 2013.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 0, - "metadata": { - "colab": {}, - "colab_type": "code", - "id": "TxfPXLi0IA0z" - }, - "outputs": [], - "source": [ - "from IPython.core.display import HTML\n", - "def css_styling():\n", - " styles = open(\"../styles/custom.css\", \"r\").read()\n", - " return HTML(styles)\n", - "css_styling()\n" - ] - } - ], - "metadata": { - "accelerator": "GPU", - "colab": { - "collapsed_sections": [], - "name": "Ch2_MorePyMC_TFP.ipynb", - "provenance": [], - "version": "0.3.2" - }, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.6.6" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} + ] +} \ No newline at end of file