{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<div align='left' style=\"width:400px;height:120px;overflow:hidden;\">\n",
    "<a href='http://www.uff.br'>\n",
    "<img align='left' style='display: block;height: 92%' src='imgs/UFF.png' alt='UFF logo' title='UFF logo'/>\n",
    "</a>\n",
    "<a href='http://www.ic.uff.br'>\n",
    "<img align='left' style='display: block;height: 100%' src='imgs/logo-ic.png' alt='IC logo' title='IC logo'/>\n",
    "</a>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Machine Learning\n",
    "# 3. Linear Classification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### [Luis Martí](http://lmarti.com)\n",
    "#### [Instituto de Computação](http://www.ic.uff)\n",
    "#### [Universidade Federal Fluminense](http://www.uff.br)\n",
    "$\\renewcommand{\\vec}[1]{\\boldsymbol{#1}}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "### About the notebook/slides\n",
    "\n",
    "* The slides are _programmed_ as a [Jupyter](http://jupyter.org)/[IPython](https://ipython.org/) notebook.\n",
    "* **Feel free to try them and experiment on your own by launching the notebooks.**\n",
    "\n",
    "* You can run the notebook online: [![Binder](http://mybinder.org/badge.svg)](http://mybinder.org/repo/lmarti/machine-learning)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "If you are using [nbviewer](http://nbviewer.jupyter.org) you can change to slides mode by clicking on the icon:\n",
    "\n",
    "<div class=\"container-fluid\">\n",
    "  <div class=\"row\">\n",
    "      <div class=\"col-md-3\"><span/></div>\n",
    "      <div class=\"col-md-6\">\n",
    "      <div class='well well-sm'>\n",
    "              <img src='imgs/view-as-slides.png'/>\n",
    "      </div>\n",
    "      </div>\n",
    "      <div class=\"col-md-3\" align='center'><span/></div>\n",
    "  </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "import random, math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.cm as cm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "plt.rc('text', usetex=True); plt.rc('font', family='serif')\n",
    "# plt.rcParams['text.latex.preamble'] ='\\\\usepackage{libertine}\\n\\\\usepackage[utf8]{inputenc}'\n",
    "\n",
    "# numpy - pretty matrix \n",
    "np.set_printoptions(precision=3, threshold=1000, edgeitems=5, linewidth=80, suppress=True)\n",
    "\n",
    "import seaborn\n",
    "seaborn.set(style='whitegrid'); seaborn.set_context('talk')\n",
    "\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "# Fixed seed to make the results replicable - remove in real life!\n",
    "random.seed(42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Classification\n",
    "\n",
    "* Given an input vector $\\vec{x}$ determine $p\\left(\\left. C_k\\right|\\vec{x}\\right)$ where $k\\in \\{1\\ldots K\\}$ and $C_k$ is a discrete class label.\n",
    "* We will discuss **linear models** for classification.\n",
    "\n",
    "**Note:** the algorithms described here can also be applied to transformed input, $\\phi(\\vec{x})$, to determine $p\\left(C_k\\right|\\left.\\phi(\\vec{x})\\right)$, where $\\phi(\\cdot)$ may be a nonlinear transformation of the input space."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Our **first model assumption** is that our target output can be modeled as\n",
    "\n",
    "$$y(\\phi(\\vec{x})) = f(\\vec{w}^\\intercal\\phi(\\vec{x}))$$\n",
    "\n",
    "where $y$ will be a vector of probabilities with $K$ elements. \n",
    "\n",
    "* Elements of $\\vec{y}$ are $y_k = p\\left(C_k\\right|\\left.\\phi\\left(\\vec{x}\\right)\\right)$ i.e. the probability that the correct class label is $C_k$ given the input vector $\\vec{x}$. \n",
    "* Often we will have simply that $\\vec{w}^\\intercal\\phi(\\vec{x}) = \\vec{w}^\\intercal\\vec{x}+w_0$ in which case we will simply omit $\\phi()$ from the notation.\n",
    "* The function $f()$ is known as the **activation function** and its inverse is known as the **link function**. \n",
    "* Note that $f()$ will often be nonlinear."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "It should be noted that nearly all of the material presented fails to be a fully Bayesian treatment of the classification problem. Primarily this is because a Bayesian approach to the classification problem is mathematically intractable. However, Bayes' Theorem will appear often in the discussion, which can lead to confusion. Where appropriate, I will try to clarify the difference."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The target variable, $y$, does **not provide a decision** for a class assignment for a given input $\\vec{x}$. \n",
    "\n",
    "* In real world cases where it is necessary to make a decision as to which class $\\vec{x}$ should be assigned;\n",
    "* one must apply an additional modeling step based on [*decision theory*](https://en.wikipedia.org/wiki/Decision_theory)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "There are a variety of decision models, all of which leverage the class posterior probability models, $p\\left(C_k\\right|\\left.\\vec{x}\\right)$, such as\n",
    "\n",
    "* Minimizing the misclassification rate - this effectively corresponds to choosing the class with the highest probability for a given $\\vec{x}$.\n",
    "* Minimizing the expected loss - minimizes the expected value of a given loss function, $\\ell(\\cdot)$, under the class posterior probability distribution.\n",
    "* Reject option."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Linear classification models\n",
    "\n",
    "The models discussed today are called *linear* because, \n",
    "* when the decision criteria is that of minimizing the misclassification rate, \n",
    "* they divide the input space into $K$ regions, \n",
    "* where the boundaries between regions are linear functions of the input vector $\\vec{x}$. \n",
    "* The decision boundaries will correspond to where $\\vec{w}^\\intercal\\vec{x}=\\text{constant}$, and thus represent a linear function of $\\vec{x}$. \n",
    "* In the case of transformed input, $\\phi(\\vec{x})$, the decision boundaries will correspond to where \n",
    "$\\vec{w}^\\intercal\\phi(\\vec{x})=\\text{constant}$, and thus represent a linear function of $\\phi(\\vec{x})$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<div class=\"container-fluid\">\n",
    "  <div class=\"row\">\n",
    "      <div class=\"col-md-4\"><span/></div>\n",
    "      <div class=\"col-md-4\">\n",
    "          <div class='well'>\n",
    "              <img class='img-thumbnail' src='https://upload.wikimedia.org/wikipedia/commons/2/20/Svm_separating_hyperplanes.png'/>\n",
    "          </div>\n",
    "      </div>\n",
    "      <div class=\"col-md-4\" align='center'><span/></div>\n",
    "  </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Probabilistic generative models\n",
    "\n",
    "Our first step is to form a model of the class posterior probabilities for the *inference stage:*\n",
    "\n",
    "This can be done by modeling: \n",
    "* the *class-conditional densities*, $p\\left(\\vec{x}\\right|\\left.C_k\\right)$,\n",
    "* the class priors, $p(C_k)$, and\n",
    "* applying [Bayes' theorem](https://en.wikipedia.org/wiki/Bayes%27_theorem) to obtain the posterior model, or\n",
    "\n",
    "*Note:* It can also be done directly, as in *probabilistic discriminative modeling* (forward pointer)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Remembering Bayes' theorem\n",
    "\n",
    "Bayes' theorem describes the probability of an event, based on conditions that might be related to the event.\n",
    "\n",
    "$$ P\\left(A\\right|\\left.B\\right) = \\frac{P\\left(B\\right|\\left.A\\right) \\, P(A)}{P(B)}\\,,$$\n",
    "where $A$ and $B$ are events.\n",
    "\n",
    "* $P(A)$ and $P(B)$ are the probabilities of $A$ and $B$ without regard to each other.\n",
    "* $P\\left( A \\right|\\left.B\\right)$, a *conditional probability*, is the probability of observing event $A$ given that $B$ is true.\n",
    "* $P\\left(B\\right|\\left.A\\right)$ is the probability of observing event $B$ given that $A$ is true."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "* We will see that our class posterior probability model will depend only on the input $\\vec{x}$...\n",
    "* ...or a fixed transformation using basis functions $\\phi()$, and\n",
    "* class labels, $C_k$. \n",
    "\n",
    "In this case, for $K$ classes, our activation function will take the form of the *softmax function*,\n",
    "\n",
    "$$\n",
    "f_k = p\\left(C_k\\right|\\left.\\vec{x}\\right) = \n",
    "\\frac{p\\left(\\vec{x}\\right|\\left.C_k\\right)p\\left(C_k\\right)}{p(\\vec{x})} =\n",
    "\\frac{\\exp(a_k)}{\\sum_j \\exp(a_j)}\\,,\n",
    "$$\n",
    "\n",
    "where \n",
    "\n",
    "$$a_j = \\ln\\left(p\\left(\\vec{x}\\right|\\left.C_k\\right)p(C_k)\\right).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "In the **case of $K=2$**, the activation function will reduce to the *logistic sigmoid* function\n",
    "\n",
    "$$f(\\vec{x}) = p\\left(C_1\\right|\\left.\\vec{x}\\right) = \\frac{1}{1+\\exp(-a)} = \\sigma(a)\\,,$$\n",
    "\n",
    "where \n",
    "\n",
    "$$a = \\ln \\frac {p\\left(\\vec{x}\\right|\\left. C_1\\right)p(C_1)} {p\\left(\\vec{x}\\right|\\left. C_2\\right)p\\left(C_2\\right)}\\,.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "* Note this is not the only possible form for the class posterior models. For example, one might also add a noise term to account for misclassification. \n",
    "* This particular form for the activation function is a consequence of the model we choose for $p(\\vec{x}|C_k)$ in sections below. \n",
    "* Showing the outcome may be a bit of \"putting the cart before the horse\" but it will simplify the notation as we proceed.\n",
    "* Although we have applied Bayes' Theorem, this is **not** a Bayesian model. \n",
    "    * Nowhere have we modeled the parameter posterior probability $p(\\vec{w}|\\vec{y})$. \n",
    "* Indeed, we will see shortly that we will use a *maximum likelihood* approach to determine $\\vec{w}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "These models are **known as generative models** because they can be used to generate synthetic input\n",
    "data by applying [inverse transform sampling](http://en.wikipedia.org/wiki/Inverse_transform_sampling) to the marginal distribution for $\\vec{x}$:\n",
    "\n",
    "$$p(\\vec{x}) = \\sum_k p(\\vec{x}|C_k)p(C_k)\\,.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Model assumptions\n",
    "\n",
    "To move forward, it is necessary to start making **model assumptions**. \n",
    "Here we will *assume* that:\n",
    "* we have continuous inputs, i.e. $x\\in \\mathbb{R}^n$ (see Bishop p.202 or Andrew Ng's Lecture 5 pdf for discrete input using Naïve Bayes & Laplace), and\n",
    "* that the *class-conditional densities*, $p(\\vec{x}|C_k)$, are modeled by a Gaussian distribution. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Transformation under the Gaussian assumption\n",
    "\n",
    "Under the Gaussian assumption, the class-conditional density  for class $C_k$ is\n",
    "\n",
    "$$p(\\vec{x}|C_k) = \\frac{1}{\\left(2 \\pi \\right)^{n/2}} \\frac{1}{\\left|\\vec{\\Sigma}\\right|^{1/2}} \\exp \\left( -\\frac{1}{2} \\left(\\vec{x} - \\vec{\\mu}_k\\right)^\\intercal \\vec{\\Sigma}^{-1} \\left(\\vec{x} - \\vec{\\mu}_k\\right) \\right)\\,,$$\n",
    "\n",
    "where:\n",
    "* $n$ is the dimension of the input vector $\\vec{x}$, \n",
    "* $\\vec{\\Sigma}$ is the *covariance matrix*, and\n",
    "* $\\vec{\\mu}$ is the mean vector.\n",
    "\n",
    "*Note:* here we have *assumed* that all classes share the same covariance matrix."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "A [logistic function](https://en.wikipedia.org/wiki/Logistic_function) or logistic curve is a common \"S\" shape (sigmoid curve), defined as\n",
    "\n",
    "$$\\sigma(x)={\\frac {L}{1+\\exp(-k(x-x_{0}))}}\\,,$$\n",
    "\n",
    "where:\n",
    "\n",
    "* $x_0$: the x-value of the sigmoid's midpoint,\n",
    "* $L$: the curve's maximum value, and\n",
    "* *k*: the steepness of the curve."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "In the case of **two classes**, this result is substituted into the logistic sigmoid function and reduces to\n",
    "\n",
    "$$p(C_1|\\vec{x}) = \\sigma \\left( \\vec{w}^\\intercal \\vec{x} + w_0 \\right)$$\n",
    "\n",
    "were we have defined: \n",
    "\n",
    "$$\\vec{w} = \\mathbf{\\Sigma}^{-1} \\left( \\mathbf{\\mu}_1 - \\mathbf{\\mu}_2 \\right),$$\n",
    "\n",
    "$$w_0 = -\\frac{1}{2} \\vec{\\mu}_1^\\intercal \\vec{\\Sigma}^{-1} \\vec{\\mu}_1 + \\frac{1}{2} \\vec{\\mu}_2^\\intercal \\vec{\\Sigma}^{-1} \\vec{\\mu}_2 + \\ln \\frac{p(C_1)} {p(C_2)}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### What about  $p(C_k)$?\n",
    "\n",
    "* The class prior probabilities, $p(C_k)$, effectively act as a bias term. \n",
    "* Note that we have yet to specify a model for these distributions. \n",
    "\n",
    "If we are to use the result above, we will need to make **another model assumption**. \n",
    "* We will *assume* that the *class priors* are modeled by a [Bernoulli distribution](https://en.wikipedia.org/wiki/Bernoulli_distribution) with $p(C_1)=\\gamma$ and $p(C_2)=1-\\gamma$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "These results can be extended to the case of $K>2$ classes for which we obtain\n",
    "\n",
    "$$a_k(\\vec{x}) = \\left[\\vec{\\Sigma}^{-1} \\vec{\\mu}_k \\right]^\\intercal \\vec{x} - \\frac{1}{2} \\vec{\\mu}_k^\\intercal \\vec{\\Sigma}^{-1} \\vec{\\mu}_k + \\ln p(C_k)$$\n",
    "\n",
    "which is used in the first activation function provided at the begin of this section. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### What about the posterior class densities?\n",
    "\n",
    "We have not formulated a complete model for the posterior class densities, in that we have not yet solved for the model parameters, $\\vec{\\mu}$ and $\\vec{\\Sigma}$. \n",
    "\n",
    "We do that now using a **maximum likelihood** approach."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Likelihood function\n",
    "\n",
    "* A **function of the parameters** of a statistical model **given** some data.\n",
    "\n",
    "The likelihood of a set of parameter values, $\\theta$, given outcomes $x$, is the probability of those observed outcomes given those parameter values,\n",
    "\n",
    "$$\\mathcal{L}(\\theta |x)=P(x|\\theta)$$\n",
    "* Frequently, the natural logarithm of the likelihood function, called the **log-likelihood**, is more convenient to work with."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Maximum Likelihood Solution\n",
    "\n",
    "Considering the case of two classes, $C_1$ and $C_2$, with \n",
    "* Bernoulli prior distributions, $p(C_1)=\\gamma$ and $p(C_2)=1-\\gamma$, and\n",
    "* Gaussian *class-conditional density* distributions $p(\\vec{x}|C_k)$, \n",
    "* assume we have a training data set, $\\Psi$, with $m$ elements of the form\n",
    "\n",
    "$$\\Psi = \\left\\{\\left\\langle\\vec{x}_i, t_i\\right\\rangle\\right\\}$$\n",
    "\n",
    "where $t_i=0$ indicates that $\\vec{x_i}$ is in class $C_1$ and $t_i=1$ indicates that $\\vec{x}_i$ is in class $C_2$.\n",
    "\n",
    "The likelihood function is then given by\n",
    "\n",
    "$$p\\left(\\vec{t}, \\vec{X} \\mid \\gamma, \\vec{\\mu}_1, \\vec{\\mu}_2, \\vec{\\Sigma}\\right) = \\prod_{i=1}^m \\left[\\gamma \\mathcal{N} \\left(\\vec{x}_i \\mid \\mu_1, \\vec{\\Sigma}\\right)\\right]^{t_i} \\left[\\left(1-\\gamma\\right) \\mathcal{N}\\left(\\vec{x}_i \\mid \\mu_2, \\vec{\\Sigma}\\right)\\right]^{1-t_i}\\,.$$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Taking the derivate of this expression with respect to the various model parameters, $\\gamma$, $\\mu_1$, $\\mu_2$, and $\\vec{\\Sigma}$, and setting it equal to zero, we obtain\n",
    "\n",
    "$$\\gamma = \\frac{N_1}{N_1+N_2}$$\n",
    "\n",
    "where $N_1$ is the number of training inputs in class $C_1$ and $N_2$ is the number in class $C_2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "#### similarly...\n",
    "\n",
    "$$\\mu_2 = \\frac{1}{N_2} \\sum_{i=1}^m t_i \\vec{x}_i\\,,$$\n",
    "$$\\mu_1 = \\frac{1}{N_1} \\sum_{i=1}^m (1-t_i) \\vec{x}_i\\,,\\ \\text{and}$$\n",
    "\n",
    "$$\\vec{\\Sigma} = \\frac{1}{m}\\left[ \\sum_{i\\in C_1} (\\vec{x}_i-\\mu_1)(\\vec{x}_i-\\mu_1)^T + \\sum_{i\\in C_2} (\\vec{x}_i-\\mu_2)(\\vec{x}_i-\\mu_2)^T \\right]\\,.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Example\n",
    "\n",
    "* We will choose some *truth* values for our parameters and use our generative model to generate synthetic data. \n",
    "* We can then use that data as input to the maximum likelihood solution to see the estimates of the truth parameters. \n",
    "* Let's use 1-D input for simplicity. \n",
    "* We will be using a basic form of inverse transform sampling.\n",
    "* Specifically, we wish for our training input data,  $\\vec{x}$, to be derived from a distribution modeled by the marginal distribution $p(\\vec{x})$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "* To obtain this, we first formulate the cumulative distribution function, \n",
    "$CDF(\\vec{X}) = \\int_{-\\infty}^{\\vec{X}} p(\\vec{x})d\\vec{x}$ (note that the range of the CDF is $[0,1]$).\n",
    "* To obtain appropriately distributed $\\vec{x}$ values, we choose some value from a uniform distribution on $[0,1]$, say $y$, and find the value $\\vec{X}$ such that $CDF(\\vec{X})=y$. \n",
    "* This value of $\\vec{X}$ is our input $\\vec{x}$.\n",
    "* This approach requires us to find the inverse of the CDF, which we will do numerically.\n",
    "* Once we have obtained a value for $\\vec{x}$ we need to assign it to a particular class. \n",
    "\n",
    "We will *assume* that the correct class is that for which the posterior probability $p(\\left.C_k\\right|\\vec{x})$ is greatest, **unless** the difference between the two posterior probabilities is less than some minimum value in which case we will chose randomly - this will add some \"noise\" to our input training data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Select truth data values, these will *NOT* be known to the training algorithm, they are only used in generating the sample data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "true_mu1 =-2.0\n",
    "true_mu2 = 2.0\n",
    "true_sigma = 2.0\n",
    "true_gamma = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "import scipy.integrate as sci_intgr\n",
    "import scipy.optimize as sci_opt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Defining probability functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def p_xCk(x, mu, sigma):\n",
    "    'Class conditional probability p(x|Ck)'\n",
    "    denom = math.sqrt(2.0 * math.pi * sigma)\n",
    "    arg = -0.5 * (x - mu) * (x - mu) / sigma\n",
    "    return math.exp(arg) / denom"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def p_x(x, mu1, mu2, sigma, gamma):\n",
    "    'Marginal probability p(x)'\n",
    "    return gamma * p_xCk(x, mu1, sigma) + (1.0 - gamma) * p_xCk(x, mu2, sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def p_Ckx(x, mu1, mu2, sigma, gamma):\n",
    "    'Posterior class probability vector (p(C_1|x), p(C_2|x))'\n",
    "    a = math.log(p_xCk(x, mu1, sigma)*gamma/(p_xCk(x,mu2,sigma)*(1-gamma)))\n",
    "    pc1 = 1.0/(1.0 + math.exp(-a))\n",
    "    return (pc1, 1.0 - pc1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def cdf(x, mu1, mu2, sigma, gamma):\n",
    "    'Cumulative distribution function P(x<X)'\n",
    "    return sci_intgr.quad(func=p_x, a=-np.inf, b=x, args=(mu1, mu2, sigma, gamma))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def inv_cdf(y, mu1, mu2, sigma, gamma):\n",
    "    'Inverse of the CDF'\n",
    "    f = lambda x: cdf(x,mu1,mu2,sigma,gamma)[0] - y\n",
    "    return sci_opt.newton(f, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Class conditional probabilities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "-"
    }
   },
   "outputs": [],
   "source": [
    "domain = np.linspace(-5, 5, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "px_class1 = [p_xCk(x, true_mu1, true_sigma) for x in domain]\n",
    "px_class2 = [p_xCk(x, true_mu2, true_sigma) for x in domain]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA3AAAAI/CAYAAAA2kzvaAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAAWJQAAFiUBSVIk8AAAIABJREFUeJzs3Xl0FFl+J/pvpnYhQBIgQGKVgACxS0BR1EJVIXX1Ur24\nG6huu93TXgraHrs9Hr8Bl5dz/N6b5x7weGx3e+yB8thuu8ftKuiluqq7qwvVXlSxSGJHXEDJLhBC\nG9q3zPdH3JAyIiOlzFRm3sjM7+ccjtBVRORPkZnK+MW993ddPp8PRERERERE5Hxu1QEQERERERFR\naJjAERERERERJQgmcERERERERAmCCRwREREREVGCYAJHRERERESUIJjAERERERERJQgmcERERERE\nRAmCCRwREREREVGCYAJHRERERESUIJjAERERERERJQgmcERERJQwNE2rUh2DSpqm5WuaVqE6DiJS\nx+Xz+VTHQERERDQhTdP2AJghhNgbo+NXANgnhKie5HHyAWwAUAogH4AHQI0QosPm8TzW9hCOfwjA\nASFEzWTiJKLExB44IiIicjxN03YBeD5WyZtUCj3xioimabs0TasD0A5gL4BK+aONAOo0Tdvnt20p\ngLfCTd6kFwAcYE8cUWpKVx0ApR5N07YDeB5ABfQPS0C/O9kBoAbAEetdRU3TDgDYBf0O5qTujFJ8\nyIuTRvltmRDCY/l5HfTXQIcQomASjxOV4zhFsr/WVf5+k33s8V5r4x072V6jKhg9YwAWq47FjhzW\neQD6Z9peANtsErO9mqbt0zTtgBBiN4Aj0D/7wiaE6NA0bQeAtzRNWxxhEkhECYo9cBQ3mqZVaZrW\nCOAQgO0YS94g/18BYA+AI3KYDBEREaB/brzgxERF9qoZyViBEGJ/sDhl72Gh/CwshX7TMiJCiHoA\nrwB4KdJjEFFiYg8cxYVMyIyhIx75/1eMDznZW2PcuawCUK8iToqrlwHUQu95dcJxiCYS6WuNr9FJ\nkJ8fhUKIw6pjsZJz0bYDOCyE2BHibt8CUCf/f2SSIewD0KhpWoVM6IgoBTCBo5izJG+2H3JyeJ0H\nQA0/iFKDEGL/eD+X813KoE/UDzrMaKLjEEVLpK+1aL3WU9iL0JMeR/FL3mrCSN4ghKjXNM0D/aZl\n7WRiEEJ4NE07DL0XrnKi7YkoOXAIJcWU37wFIMQPOSZvJO2FPqSWk/Qp2fG1HoScM50P4KDqWPzJ\nG5Pbofeqhpy8+fEAqI/SkNADACrkSBYiSgFM4CjW/MfmR/IhR0REqetF2JTfV0kmSsaNyb0RxubB\nJHvfDH5Fv3ZH43hE5HxM4ChmZO+bcUc56KRuIiKiICrgvDnRB+RXjxAi0p7BQkx+/pu/eug9gkSU\nAjgHjmLpeb//Hwi6VRTIZHE3xhZOBfS7mwfGm/guF1vdB71wirHf6HIG8Cu0Esn2Efwe/oVcSuWx\n2+Tx9wWbHxNkvxoA3wo2JNWv7PlBIcRuOVTpRYwl3fVy/3ELB8ihRLvl43rkfhOu02RXdt0yX9Jw\nSNM0/+8PyhLcQY9j81hKzk+kr8vJsp4Tm6U7PNBfTweD7Gf8zvnQf+cqAPlCiDLL9mGfV5tYt2Ps\n9RM0Nss+UTmv4T52pMsQTOa1Dv3vyiH5fUGwvy/yuWqX31Y6YSi6X09VKfRkZ4elHdCHR9bbre0m\nnx8gjERHvjZelN+WQj/ne+XPdgHwf95Cfp1ajl8lv53M51q0F+GuAbBH07R83iwlSn7sgaNYMj7k\nECzxiAZZwrkO+gVSBfSEp00+/iE50dxuv1IA1+R+xsWbB/oFxXboH85VkW4fwe+xC/q6acbxO+Sx\nS2Vbo98Fjf9+e4Lstx36wrETLskgz9EhmJd2qIB+/oLe1ZX7GRdogH5XebuMJ5KLGyMBrA/SVo+x\nteVCour8RPq6jLJSuQaZdemOUuiLAAf93eW6VtcwNjer0PLzyZ5X/9g2+B1/3NiidF4jeuwoC+m1\nLhNS44L8RQS3yziGE5I36YBM2rYB2K5p2gH5utoHfUmAHTKhrZDPh9VG+TWkoYby2LvlcY3H3aNp\n2h759xWyfS/k+zeC38l/mGLEN2GinLwBY0luxIuQE1HiYAJHsZQvv8ajqtph6HedXUKIMtlTYFTk\n2m58eFsckDEe9t9PCOGS+x6G+eIq3O1D5rcIrPG7FAghCuSxy6BfNHTAci7l7+U/F8Plt98Ouc8+\n2QMQzC7oF93VfvtWY4KLRnlMI3mxxrwDESSzQojDQohKIUSl3+PvNdrkv5ArAao8P1Ikr8toKoX+\nmq2WMfj/3oD+u9s9TxugXxDmQ/8dquG3gHKUzquRTJbJfQugnxvjPRQsNmDy53Uyjx0VYb7WjR7B\n8X4vI7GI6WiHUMkbG4cAfdFp2bwLwA6ZYPn3EhlFOKw3Q0ot+4/3eKXQk7fRBEvuVwP9PVrt17O6\nF2M34cK1U36td1jF0Db5lYVMiFIAEziKJeOudkw/5IQQe+UFQb2l3X8on92QPuNOZcAFjxCiXh7T\nM4ntw2Ec86D14kYI4RFCHJQXmqO/o99wTkC/KDIlNvLO/Tb57a4JLkh3+98Rlv83zllAZTz52MbF\npF3Mh6G4aI3K8yO3ifR1GU0d0BMd/9gPw1xu3C4G43cyLrZHi0hE8bx2ANjm/56R7yNTQmPdKUrn\nNaLHVsgooZ8fpBfeGBoLOKda4/PQF5k2kitAP7d259Xjt4+/CoS+dt6+IMc2bmK8bLNtWH+j5O9h\n3JiMdg8aNE2r0zStUdM0XwQVJY1zWDbuVkSUFJjAUSwZdwQLx90qtoyLPLsPQ+MDL9S5LOFuHxLZ\nW2DEF85F4z6MzR+xHcojL2oP+m1vS9jP+RkdtmRzMWH0OnX43/G2UH13WuX5mch4r8to8tj1XsjE\nxXitVcmkzGp/kPMWrfNqG5v0wgSxBRPqeY3FY8eMjNU413bvN6PtcCi9VXHS5heLcUMg2BzhUstX\n03FCfcAgN9CMXrzD/tsJISIprOUf38kw952QvIFQI/8f1t9Pv9/FEa9ZIootJnAUS8YHipIhHfLi\nK9/ve2scxh3ZPfLO5z55JzuYcLcPlZEQhnvxZfRsTHQn2JgbESzWSBIt41xG/S50FKk8P0GF8LqM\nF//kK2DejLApKiFF67yOx793LaQ5PVE8r2E/dpwYvfRVNr/bLss2yllu7Bh/44IVIwn2XBUixB44\nYbPGqN/f52jNCfSPM1Y3qEoxub+rKm+YElGcsAolxVIN9Iu3fE3TSmM9X8CvwlgVQrgLKYTYr2na\nRujzm4wlD/bIKnAHrT1L4W4fBuMiI9zzY1xMTHQn2H/YZYV16BlCH6Lkz4g56neho0jl+RkV7usy\nXoQQHr+Kh9YL6PFei9E6r5HGZhwzJuc1lMdWQQhRo2maB3pMuyF7UP2GVHaICApjyKIw4w0fnrAS\nbQgmSvqNYiV2r7uQe+AieNzJiOjzzG+u3ng3SCYzfNcxf2OIKHaYwFEsvQy9gh3gd8ERbXKOzSGY\n5yYY1Qr95+sEEELssJQkNxKTXZqm7QSw2DK3K6zt42SiO66x/ECfEcNjR4uS8zOZ16UDhHJxyvMa\nf/ug97LtwtjfU2PeWKRz30oxfi/ppHp0ZM+osYxAsL+NRqJl7aFrm+TjGz1/L4+7Vej8k8mQewct\ndiNIPH49hk4e2UBEDsAEjmJGCFGvaVo9xnqqvhXt5EbezTQ+9A9Cr+Lmv27bhMO3ZM/Abrl9PvQq\nY0bFyX2wzDkJd/sQRDrU1CjbPtGkdf9hYNHqBTV6AhzTQ2FD2fmJxusy1izD8EIq0y7F/LwGiy0e\n53US5yXmhBAHZWXPfL9eTaMHLqLhk3ZDD6Ns3F4wmZAbyfgrlh93YHI3AqqA0b/Z0eD/O4Qdl/y8\nqJhoeHIk8frN13TKHEgiiiHOgaNYe8Hv/7FY98pIlmqEELsnmyAKITpkwQrjuOOWEg93+yCMu7Hh\nFk0wLiaCrtMmGXehx7sDHi7jAiOmpdYnSeX5ierrMkb8y62Hc8EYj/Pqv4akf2zxOK/BHtspjJ62\nKr/hkzUOK2nvb6L5b0YCedDm+TRuFIXNL5m3PS+RrMMo45vM375glTIN1TAPPS6Vc633yaGu44lL\n1WcicgYmcBRTltLeVaF8aMoPrVAX0p0o4QlahGCCIgcB8y7C3T5Usgy7cac56Ie0pmn5lh4G47wG\nPV/y7rZxkRfpHD07xt3+/HEuLCb7eJNd10jl+Yn4dRllweaPVWBseHO4Q++idV6DxZYPv2U1LD+O\n1nmN5LFjKZzXuvF+ex5jc8ccU7zEhpHoBCTDfiMYgi0vENLfVeMzw3IDzBhaGtDzJxPfSOfvGnGO\nt/5jADlns3GCmwIbIOOV79HtsreuCuOvAQiMvTcaw4mLiBITEziKOZmgGB962+U6N7usvU2aplXI\n4UGNCP1i2rirW2VdvFd+P96FTaOsJrndPxb5wWlcJNVMYvtwGHehd2madsg/WZTnZR+AdvitkyTv\nuBvnaZ+maQeM/WSytwd+w80iKXAQjHxs4wJ3jzWJk99PdpFq42786O8sz31Id85Vnh9M7nUZTfma\nph2xvF53Aajz2yasualRPK92sW0HcG2c2KJ1XiN57FgK+bUuz79RIKoKevGSyRYZiQm/+W+A/Ty7\nl6AnHtuC9KbWyeNMlNjWQf8bvNOvzUgc7Y6727p+Yajk6/kw9NdQSK83+Z4oG+8xtbE15k7Kz5Qq\nv+1rMfHr0bh54ahhv0QUG5wDR3EhKzjWQ7/AKpVfD2iaFmztmpA+GIUQh/0qsx2QH6j+8yZs51DI\nC4sO6BcVh2SbdbPRtbLC3T5cssLcbui/93boia51sw5Y7hrLOTHAWGGDXTb77R9nzkXEhBC75UVH\nFfQkbg/M5/sgJpfEvQxZ7VPTNF+EMSo5P5G+LmPAA31oVbt8r/k/Zgf0hbjDHoYYpfPaAf38BIst\n4KI+iuc17MeOsXBf6wegv+8qAESUiMSJkUQdBvC8pmn+C8Ib1S8rx+mVMpL/KozfI5oPvYfPWDj8\nAPSbYvug/z31/zv+EibZ2y6LWR2C/ro3qkoGDF2UPdH7oFfynOh5Ms5VoXyM0e1DrHBcLbd14rBf\nIooy9sBR3AghaoQQZdA/WGtgvtjyQP8A3iuEcIV5d7QS+gVCh/znkd/vkD+zi6VDCFEgtzmMsXkD\nxhyH/UKIMuNiI9ztIyHn0pVBv1DxP34N9PNSYHen3W8/4xwY+x2GfnEUs54EIUQ19AtI43E98vsC\nTLKXSb4GjN/J6HXYK48dznFUnZ+wX5cx0CEXB96LseFoxu++eDK9jlE4rx7592AvzK93I7ZgF6LR\nOK+RPnZMhPtal38HjHPu5OGT/vPf9gI4JEcYGD2p455rmRR1+B1nvMdpA/CSTKwOCX2x7h0AamRv\n6yHIOWjRmC8oj70D+o2ARvkY++RQzkOaptXJn28LsYe0GvrvuhvAxhB6Ha0qYF7bkYiSmMvni+jG\nNhEROZTsgdgFoF4mcJREZE9SOxz+/Gqa1gg9wSmLNGmSr+Wd8gZazMmhtC+F83hyyOMG6DckO6Df\nIAjr5oimae0AXpEjG7ZDH+mxI5Tkz+/1ENL2RJT4OISSiIgosRhDkx3b++Y3/61jkj1e+6APVQxr\nMfh4knFFHJvf/Lcj8niH5ZSD3ZC9apqmVY2TFO6Cg+dCElH0cQglERFRYtkNjA5jdapx138LlV/R\nlmReoN3uXOVDDu+VPXzjDal8EfGtmkpEijGBIyIicjBLtcw90C/m41klMxITrf8Wjt3QK49GuqSI\n01UjcL1EY/4fADwfLFmXwy0Ry7nOROQ8TOCIiIic7ZpcfqURek9UR6Rl8ONBG1vfDYjCwtKyF24/\nkrsXzjocdi/0qqT7MH4SvA/ACzGLiogciXPgiIiInK0G+jA7o1z+jvE3V0dWX/Rf8+2IXGKiepJV\nT/fKdTh3OXzoaNhkRUtrWz0mqL4pC7zUcO4bUephFUoiIiJyPNmzVwc9GZx0z16Qxwi7CqUKMs7d\ncikXIkoxHEJJREREjifniFUitkMpPQBqY3j8SZOJ7PNM3ohSF3vgiIiIiIiIEgR74IiIiIiIiBIE\nEzgiIiIiIqIEwQSOiIiIiIgoQTCBIyIiIiIiShBM4IiIiIiIiBIEEzgiIiIiIqIEka46AJq8uro6\nrgVBRERECaWystKlOgaiRMQeOCIiIiIiogTBHrgkUllZqTqEhNDQ0IDe3l7k5uZixYoVqsMhic+L\n8/A5cSY+L87D5yQ8dXV1qkMgSmjsgSMiIiIiIkoQTOCIiIiIiIgSBBM4IiIiIiKiBMEEjoiIiIiI\nKEEwgSMiIiIiIkoQTOCIiIiIiIgSBBM4IiIiIiKiBMEEjoiIiIiIKEEwgSMiIiIiIkoQTOCIiIiI\niIgSBBM4IiIiIiKiBMEEjoiIiIiIKEEwgSMiIiIiIkoQTOCIiIiIiIgSBBM4IiIiIiKiBJGuOgAi\nSl0+nw99A8N42DOIm/f70NbZh+xsH4rnD2B6Xpbq8IgcY9g7gqut19E12I3Wnha4hoAZmYDX64Xb\nzXuxRESphAkcEcXV4NAI3jp5E28cu4Gb97owPOIN2Oaf37yD8tIZeHTVXDyyai5mF+YqiJRIrf7h\nAZy5dxEnbp9GfdM59Az1BWzjuuhCQc50bCpZh+eWV6FoygwFkRIRUTwxgSOiuOjtH8LPPrqOV99v\nREfXwLjben3A+cZWnG9sxUuvnkdpyXR8cvNCPLt5EdxuV5wiJlLjaut1/KjhDZy+dxFDI0PjbuuD\nD219HXjj6rt4s/F9PLZgAz6//BNYkF8Sp2iJiCjemMARUUx19w3hh+9cwc+OXkNP/3BEx/Dc6cTf\n/eAsPjjdhP/0lfUoKmCPHCWfYe8Ifnjx5/jhxZ/D6wvsmZ6I1+fFBzdO4IMbJ1BZvBo7Vn4GpYUL\nYxApERGpxASOiGLmVnMX/u9/OIbmtt6oHO9c4wN887+/g9/60lpsrZgXlWMSOcHdrvv422P/hCtt\n16NyvLqmczh19wJ+vWInPrFka1SOSUREzsAEjohi4szlFnzruyfG7XXbWD4bpcXTMW1KJro6HyAd\nw+gbduNGqwunL7fYzo/r6R/Gf/8/dThx8R5+60trkZeTEctfgyimfD4f3vIcxXdPHcLAyGDQ7RZM\nL8HGkrXQZpah8UYj2ns7MeweQVpeBj66WWs7P87r8+If6v4d97pa8NW1X2SxEyKiJMEEjoii7s3j\nN/B3h89gxOsL+Fma24WnKufhS08vxfzZU0fbGxoG0dvbi9zcXHx9xQr09g+h7tJ9vHn8Bk5fbgk4\nzvun7qDhehv+7Dc3Y8GcaTH9fYhiYXhkGN85/s/4+Fad7c8Lc/LxmWXbsLFkDeZMLRptz+pwoTdD\nf6+sWLECX137RRxp/AA/FW+hvb8z4DivX34L93oe4Jubfw3Z6azuSkSU6JjAEVHUeL0+/MvPLuIH\n71y1/flnHluMLz69JKQ5bLnZGXhiXQkeX1uMN47dwD+8eh6DQyOmbVra+/CnBz7G/t99gpUqKaF4\nfV78zxPfDZq8PTq/Ei9UfgV5WVMmPFZORjY+t7wan1r6FN6/fhz/fv41dPY/NG1Te+cM/uzt/4E9\nT/wWCnPyo/I7EFFq0zStFMBeAFUASmWzR/47AuCwEMLjt70PAIQQCV2NTNO0PQDKhBC7VcXA8RRE\nFBUjXh/+8v/U2SZvmelu7P3aBnzji2vCLkDicrnwqUcX4W/+81YsmR944dn2sB9/euAjtHf1Rxw7\nUTz5fD78Y/3LOHqzNuBnORnZ+J1Hvo7/9OhvhJS8+ctIy8C2ssfxraq9WDA9sAqlp/0m/vjIftzr\nuh9x7EREAKBp2gEAjQB2yaYa+Q/QE7p9AJQlONGmaVq+pmlVmqYdgf67KcUEjoii4l9/dhHvn74T\n0J6fl4X/77cfw+NrJ1fWfF7RVPzF7z6B56uXwWW5d3f3QQ/+7OAx9PSNX3KdyAleOf863rz6fkD7\n8pll+Itn/wRPLnoELuuLPAwzpxTi/9n2B1g3pzzgZ6197dj3wd+jdzBwzhwRUShkErMLek9btRCi\nTAhRLf+VASgDcBDASZVxRov8fduh9ypWKQ4HABM4IoqCd+tv2/a8zZ+dh7/45hNYvrAwKo+TnubG\nVz+5At/44pqAn3maOvH//uNx9A9GtlQBUTz87PLb+MHFnwW0ryxahj956veithB3bkYO9j7x2/hE\n2ZMBP7vTdQ/fPvaP8HrDX6qAiFKb7Hmrgp68VQohaqzbCCE8QojdQojDcQ8wNg5B702shkN6FZnA\nEdGkXLnVju+8fCqgfXXZTOz/3ScxZ0Z4w8BC8ekti/HVTy4PaL/gacW+f6m1rV5JpNp7147hn08d\nCmgvLViA//L4N5CZFt2KqmnuNPxG5ZfxtXXbA35Wf/c8/v38T6L6eESU3DRNq8DYkMkdQogOlfHE\nixDioPwXkKyqwgSOiCLW/rAff/5PJzA4bE6Y5hXl4Y9/bVNMS/zvrFqGzz1ZGtBe29CMl358LmaP\nSxSJSy1X8fcn/zWgvXjqbPzRk7+D3IycmDyuy+XCc9o2fH75JwJ+9uOGX+DozaQY4URE8fGi/Foj\nhKhXGkmKYxVKIorI0PAIvvXdk3jQaS4eMiU7HX/y649gSozXZ3O5XPiNz65Cd+8Q3q69ZfrZzz66\njo3lc7BhxeyYxkAUit6hPnzn+D/D6zPf6JiRW4A/eeqbmJY9Ncie0fOV1Z/Hzc4mnLp73tT+9yf+\nFXPzZqO0cEHMYyCihGd050e1iIdNNcsO6AVRXrDr5dM0bRf0oYwVsskjtz/gn1iGul0iYgJHRGHz\n+Xz4Xz88h4brbaZ2twvY86sbUTIrLy5xuN0ufHPnOvT0DeH4hXumn3375VP4zv/1NKbncd0rUuu7\npw6jpafV1DY1Kw9/uvWbmJkbnfmhE3G73fi9zb+OP6rZh6au5tH2wZEh/MWH/wvf+sQfIj+b6ylS\n6vnsH7zqBvBNAM8BSKb1aHoBvA7g26/95ecnPa9AJlkGT9ANI9MovxqVLAuhJ4vbNU0rsyxFsA/A\nHhnDQdlcirGhnbvD2S5RMYEjorB9cPoO3jx+I6D968+tRMXyIps9YictzY3/8qsb8Pt/9S5uNXeP\ntrd3DeDvfnAGf/i1jZOq6Ec0GSfvnME71z4ytbngwh9seQHF0+bENZbczBzsefwb+KOa/egdGqtC\n2drXjr8/8a/4wyd+m+8VSkXfBPBXqoOIkW0AfAD+JgrHGk3g/BOqKNkthDjo36BpWhX0qo8HoBcP\nMewB4JHVLv23z4ee+IW7XULiHDgiCktX7yBe+vH5gPanK+fhC1vLbPaIvayMNPznr1QizW2++Pzo\n7F28U3dbSUxEHf0PceDk9wLaP7u8CuVFyxREBBRPm4Pfe/TX4YL5vXLq7vmgi4oTJbktqgOIscdU\nBzARa/Im22qgD6UcLdsvky/Iduv2HUZiGep2iYwJHBGF5Z9eu4CO7gFT25L5+fidHeuU3r1fMj8f\nX3lWC2g/8KOzuN/eqyAiSmU+nw8HTn4PDwe6Te0Lppfg+VWfVRSVbv3cVfjlNV8IaP+n+lfQPdij\nICIipT6aeJOEdjRKx/EfxhhYQSw22uTj5QN68iXjqNA07ZDspQsQ6naJjEMoiShkZ6+24MiJm6a2\n9DQXfv/L65GZkaYoqjHbn16K2ovNuHSjfbStt38Yf/39U/iv39gCt5vDwyg+3vYcRV2TuRpqujsd\nv7v568iI8nIBkfjs8irU3jkD0Tp2I7pzoAvfO/MjfGPjVxVGRhR335Zfk3UO3HeicTAhhEfTRm+S\nViDK8+BkkrUDY4VM/BVirDdtB4C3MDZHDgDqAey1lPkPdbuExASOiEIyODSC/3noTED79meWYcEc\nZxQ/SEtz4/d/uQK/95fvon9wZLT9XOMD/OSDRnxh6xKF0VGqaO5uwXdPB65f++XVn8XC/HkKIgrk\ndrmxa+OvYM+bf44R79h75W3PUTy5cJOyIZ5E8SYLfPy1/EfjOww9Idot/x8VmqYdgZ64dQB4Bfrc\ntw7oC2jn+28rq0cWyAqT1XK/CgBHNE0bnUsX6naJikMoiSgkr9RcRtMD8/Cqkll52LFtqaKI7BXP\nzMNvfG5VQPv33riE1s4+mz2Iouu7pw6jf9g8zHjFrKV4bpmzRvHMn15suz7cwdp/w+DIkIKIiMjh\nviW/VslFvSdN07QD0JOr/UKIAiHEbiHEYdlL1hZsP7mw9g4hRAH03jZAX4ogou0SDRM4IprQjbsP\ncfjtKwHt/3HHWkcMnbR6dvPCgDXgBgZH8L2fX1IUEaWK880CtU1nTW056dn4j4/8B7jdzvvI/WL5\npzA3z1w5tqmrGT9ueENRRETkVLJXy+i5OuRXLGQyquSx7ZKqkKpFCiEOQx8eWTpeTKFulwic92lC\nRI7i9frwt4dOY8TrM7V/4pGFWF02U1FU43O5XPjdneuQk2VOLt+qvQnPnU5FUVGy83q9+BeboZO/\nsvYLKJoyQ0FEE8tMy8Cujb8S0P6jhl/gduddBRERkZMJIXZDX6utFEBdsAIhmqbt0zQtlNK2RuXI\n7f6NcuhjvqUtXxYlKbW2y3gghOgIdbsQYnMszoEjonEdOXHTVBQEAPLzsvBrz5Uriig0hdOy8aVn\nlpp63Xw+4H//5Dz+6ze2cL0rirr3bxzH9Q7zshXzps3FttLHFUUUmpVFy/DU4kfx7rWPR9tGvCN4\nqe77+LOnf5/vFSIyEUJUy6GPu6DPKfNA79kyEiQjcQqlWIgxhPKQpmk10BO6DdDnq1mVYqwoiQdj\nhVSMJHJvmNuFRCapxlp0RlxVcrFwAGiM95w69sARUVADQyP4/puBww5f+MIq5OVmKogoPF/YugQz\n83NMbWevPsDJi82KIqJk1T88gO+ffTWg/WvrvoQ0t/OGGVv96tovYlpWnqmtoeUKzty7qCgiInIy\n2RNXibEhlduhJ16AnrhVCyGq7fa1HOcw9ITKAz3B2gCgFkAZ9KTQf9t6y2Ma29cD2CGE2B/OdmHY\nAX1h8D3zAt2PAAAgAElEQVQYSwJL/dp2h3m8SWMPHBEF9fOPrqG1s9/UVqEV4Yl1JYoiCk9WRhq+\n9ukV+B//ZvoMwD++dgEVy4uQnsZ7WBQdr106gvZ+8/DctXPKsW7uSkURhWdqVh6+tm47/vb4P5va\nv3/2VayZswJuF98rRGQmE6WQkxchhG13vkyo7JKqykgfM9zYJjjW7mgdK1r4F5mIbPX2D+GVGnPh\nEpcL+Ppz5Qk1pGrr+nlYMt88V/lOSzfe+Pi6kngo+bT1duAnl46Y2lwuF3517RcVRRSZxxduxOL8\n+aa2ax23cOL2aUURERGRHSZwRGTr1fc96OodNLU9uW4eFhdPVxRRZNxuF37TZlmBf/uFQLfl9yOK\nxL+f+wkGRsyvpW2LH8OC/MToqTa4XW58ec3nAtpfPveaaa04IiJSiwkcEQV42DOIH7171dTmdrvw\ny5/UFEU0OStLZ+DR1XNNbV29g3i55rKiiChZXGu/hfeuHzO1ZadnYefqzyqKaHLWzVmJ5TPLTG13\nuu7hgxsnFEVERERWTOCIKMAP3r6CvoFhU1v1pgUonpkXZA/n+/pz5UhPMw/9fP3Da1zcmybl+2d/\nDB/MS2z80opPIj97mqKIJsflcuEraz4f0H7o/OsY4uLeRESOwASOiExaO/vw+oceU1tGuhtfrk7M\n3jdD8cw8PPe4aUkYDI948aN3GxVFRInO03YTpy1VGmfmFuIzy55RFFF0rJi1FOvmmJcJaeltQ03j\nh4oiIiIif0zgiMjk5ZrLGBz2mto+89jigHL8iWhn1bKAxb3fOHYdnd0DiiKiRPbjhl8EtO1c9Rwy\n052/xMZEvrw6cC7cDy/+HP3DfK8QEanGBI6IRt1r7cGbx26Y2nKy0rD9maWKIoquqbmZ+PSWxaa2\ngcERvGbpcSSayJ2H93D89ilT28zcQjy+cJOiiKKrtHAhNs8zr6PbOdCFn19+R1FERERkYAJHRKNe\nPnIZI17zfJ7PP7kE0/OyFEUUfZ9/sgwZ6eY/fa9/eA29/ZzfQ6H7ccMvAua+fW55NdITYNHuUO1c\n/VzAkiE/ufQm+ob6g+xBRETxwASOiAAAbQ/78W79LVPb1NwMfGFrWZA9ElPBtGx84pGFpraeviH8\n7KPragKihHO/pzWgKuP07Gl4ZvEWRRHFxrxpc7F14WZTW89QH9659pGiiIiICGACR0TS6x96MDxi\n7lH4wtYlmJKToSii2PniU0uQ5jb3LLz6XiMGhrjWFU3stUtH4PWZ54k+t2xbUsx9s9q+8tMBvXA/\nFW9xXTgiIoWYwBER+gaG8XNLD1R2Zho+tWWRknhiragwF1sr5pnaOroHUHP8RpA9iHQdfZ1423PU\n1DYlIwfVS55QFFFsFeXNDJgL19LbhuO3TyuKiIiImMAREWpO3ER3n3kOWPUjCzE1N/l6FAzbn1kK\nS8cCfvDuVQyPeO13IALw08tvY8hrXiPxk0ufRm5G4ldpDeazWlVA22viCHw+n83WREQUa+mqA4gF\nTdPyAbwIoBRAG4BCAEeEEAcjPF4pgH0A8uUxPQAOBTuepmnbAewGcEBua5S4q5Lte4UQ9ZHEQhRt\nIyNevPq+eS00twv43BOlQfZIDvNnT8WW1cU4erZptK2lvQ/v1t1G1aYFCiMjp+oe7MGbV983tWWl\nZeJTy55WFFF8LJmxCCtmLUVDy5XRtsa2G2houYryouSoUEtElEiSrgdOJm91ABqFEDuEELuFEDsA\n7NA07UAEx6uCnry9IISoFkKUATgE4ICmaXVBdiuEnqwdkrG0y3+HoCd+TN7IMT4+fxfNbb2mtkfX\nFGPOjCmKIoqf7dsCLz4Pv30loBInEQC8ceU99A2bKzBWlT2BaVl5iiKKn89q2wLaXhc1CiIhIqKk\nS+AAvATAY9M7tgPALtk7Fo69MhHsMBrksfcCqBgnKawHYOzjAXAYQFmkvYBEseDz+fCjd68GtP9S\nklWeDGbJvHxULC8ytd1p6UZdQ7OiiMiphkaG8MYV8xpoae402+GFyaiieDXmTjW/V2qbzqLp4T1F\nERERpa6kSuBk79t26D1dJjIBq4E+hDHU4+2CPgwygBBiv/zvLvm4Vt8SQhQIIVxCiDKZBHK1YHKU\ni9facPlmh6ltZekMaAsLFUUUfzu3LQto++nRawoiISc7dusUHg50m9q2LtqMwly7P//Jx+1y2yar\nr4u3FERDRJTakiqBA7BTfg2WKHmgD20MVTWAQ+P02hmPsyGMYxI5Rir3vhnKFxdiybzpprZ6cR93\nWrqD7EGp6I2r7wa0PbcscFhhMnty4SMBw0Xfu3Ecnf0PFUVERJSaki2Bq5ZfgyVwjcDovLZIjmtl\ndF2kxi1YSip3Wrpx4qJ5+FPJrCnYWD5HUURquFwufOaxwIItP2MvHEmethu40mp+Pawq0jBv+lxF\nEamRmZ6JZ5dsNbUNjQzhF5bCLkSUGjRNK9U07YCmaY2apvnkv0ZN045omrZHFgH0396naVpCTjLX\nNK1K/l7t8t+RCKZlRU2yJXDGC6UtyM+NhKsiyM+tXoA+123vBI9nmzBqmrZL07R98t8BOSSTyBFe\nfa8R1irgn9+6BG7LAtep4In1JZiaa16w/K2TN9E3MBxkD0olb1x9L6Dtk0ufin8gDvDskq3ISDO/\nV35x9T0MDg8qioiIVJA1IBoBGNe2NfIfoI9224cwpi05mbx+PwJ9xF0Nxkb0HYqkQGI0JFsClw+M\nzncbz4xQDiaE6BBC7Lc7nqZpFfLxPEGqSr4of7ZX/tsNvRJmwPw8onjr7R/CO3W3TG3TpmTimQ3z\nFUWkVlZGGj7xyEJTW0//MN6tv60oInKKroFuHL1x0tQ2I7cAlcWrFUWk1rTsqXhq0WZTW9dANz6+\nxeLKRKlC07Qj0BM3D4BqWeuh2q9aexmAgwBOjnecRCB7EQ8AOChrW+wQQlQCqITeMbRLRQdNsiVw\nE1VeMHrmojHk8UX51e7uQi30ZQesNZb3AtiussuVCADerb+N/sERU9untyxGVkaaoojU+9SWxQEL\ne//0Qw8XK05xb3s+Cli4u7rsCaS5U/e98hmbJQVqGj9QEAkRxZvscaqCnrxV2lzrQgjhkct4HY57\ngNG3F0CH7IgZJTtvdshv98U7qKRcyDvW5By67QD2B3nh2t6KFELUa5rWAf2JjvqLuqGhIdqHTEp9\nfX2jX1PxnPl8Pvz4nZumNpcLKJ05qPR8OOF5WT5/Chpu9ox+f+NeF372Tj1K5+YqiUc1JzwnKnl9\nXvz0krnKYprLjfkjRSn/XinNmw9P91gvvmj14N1TH2J2dkgDXJKOE54ToliTo8+M3qYdIYx4SwYb\noPcmBhBC1Mjr+nxN0yriuc5zsiVwbRi/d83ooYv4BSeXDDgEvSs12Ny48Xigrx9XGu1lBXp7eyfe\niEb5fL6UPGe3HwzgbtuAqW1ZcTYyXUPo7R1SFNUYlc9LZVmOKYEDgPfPtWLO9CA7pIhUfa9c7bmB\njiFzhcXleaVwDwK9g+rPh8rnZXXeUlMCBwDHmk+hetYWJfE4Raq+VyhlGKPPauKZrCi2Y4Kf10Lv\nkSyFvgZ0XCRbAgdAT7JieFfgEIBXrF2pYTCGcZYieLXMiOTmpmYvQbj6+vrg8/ngcrmQk5OjOpy4\nO309sOT3llWFyl8/TnheVpXmYGZdJx48HEtkL93qw5AvA9OnZIyzZ3JywnOi0ul7IqBty+wKvlcA\nrMlegZoHH6NnuG+07ULXVXxq/lZkuvleofExyU1YxhSgqA4ZlPPM9mIsETLWbn4hSB2KXdCnMBlF\nCT1y+wP+iWWo240nhM6WSXcORSLZEjjj5BXC/kQavXONkRxcjvv1jJe8yRfLPuhdywHDK21iiZoV\nK1ZE+5BJqaGhAb29vcjJyUm5c9bdN4Sz3zW//GcV5ODzVRuQprj6pFOel196OgsvvXp+9HuvD2h8\nkIlf2bBcWUyqOOU5UaGpqxmNZ81DjcsKFqKq4im4rJMl48wpz0v1yJP4ccMvRr8f8A6iNacbz5Sm\nXi+cU56TRFFXV6c6hFE7X/4tN4BvAngOQDLdCe8F8DqAb7/y/N97J3swy5IAUe2AwNh1uVHJshB6\nsrhd07Qy/yRK07R9APbIGIyhjaUYG9q5O5ztosBIDmujdLyQJFsCVwP9RAZLjozB+WGfZE3T9gCA\nNXmTQyoL/V5cO+TjV2CsnKo/I1NPla5ncpB3am9hcMhcvOTZRxYqT96c5JmNC/CvP28wFXl549h1\n7Kxahoz0ZKv7RMG8eSVw6YBnl25Vnrw5ybbSx0wJHKAXM0nFBI4S2jcB/JXqIGJkGwAfgL+JwrFG\nE7hoTwECsFsIYZpnJutNHIFeAdJ/PeY90DtTyizb58NczDDU7SImk0RAr4kR1x64ZLsaeVl+DVyV\n16893HG78kVUFqTnbafl8eqhvxD3BzlchYwh2i9+onH5fD68cey6qc3tdqFq0wI1ATlUXk4Gnqo0\nL6fQ0TWAY+fuKoqI4m1geBDvXj9mapuaOQVbFmxQFJEzzc6bhbVzyk1tV9uu43r7rSB7EDlSst9x\neEx1ABOxJm+yrQb6aLoqo00mX4DNKDu59JcnnO0mQxZ02QOgPsKaGJOSVAmcTMw6YM7U/W2HTSUZ\nuZL8PuuK8fJnFdCHQwbraq2GuUfvZQTpAZSJIBB8YXCimGm43oab97pMbY+snIMZ0zlfw+ozjy0O\naKs5edNmS0pGJ26fRu9Qn6nt6dLHkJmWenO7JlJd9kRA2xEuKUCJ5SPVAcTY0Sgdx38YY7COkmhr\nk4/nv86zUQzwkN91tUmo20VK/v5vyccIXFclDpJtCCUAvADgJU3T9vp3Z8q5aR2wT572QU/uSuFX\nbUa+YN6S/99ps5/xghrdRy4V8GKQcqL7oHfnBuudI4qZNz6+HtD2yc2L4h1GQlg0dxqWLyzApRvt\no22nLt9HS3sfZhUw4U12714PvJ6rKnX8TWwlKopXoyB7Otr7O0fbPrhxAl9d+0XkZGQrjIwoZN+W\nX5N1Dtx3onEwIYRH0zTj2wpEeR6cTLJ2YKyQiT//2hY7oF+bG3PkAH30215L7YlQtws3zlIAdZDJ\nm6qlFJIugRNCHDYyY03TXoB+gndCT9yCneiXob9gXra0v4SJi40EDMcUQuyQGb8H+vjdUuiTJT3+\nyR5RvHT1DuLDM02mttmFuVi3bJaiiJyvatMCUwLn8wFv193E81XaOHtRorvf04pzzebqkytmLcWc\nqUWKInK2dHcani7dgh9e/PloW//wAI7ePIkqm945IqeRBT7+Wv6j8R2GnhDtRhTXM9Y07Qj06/AO\nAK9Av3bugF753XQdLjtHCmTHTLXcrwLAEU3TRufShbpdmHHmQyZvQojKiH7ZKEm6BA4AhBD7NU07\nCD1xq4LNJEbL9odh80KcTLIlk7hS+fht0Idhct4bKfF27S0MDZuLUD27eSHcLF4S1BPrSnDwx+dN\nRV/eOnELO7ctYyGLJPbetY8D2p5e/KiCSBLHttLH8KOLb8AH32jbkcYPmMARJZ9vQU/gqqK1cLWs\n8F4FvRDIXsvPgq7vLBOwg3K77dCTvb2wTJUKdbsQ4nRM8gYk2Rw4f3KS4kEhxH6ZoKmIwSNjOMzk\njVTx+Xz4haV4SRqLl0woNzsDj62Za2q729qDC55WRRFRrHl9XrxrSeCy07OweX5FkD0IAGZNmYF1\nc1ea2q6134Kn7YaiiIgoFmTCZiQ+h/yKhUxGlTy23RSnkKpFyuv8egCl48UU6nZWfslbhxOSNyCJ\nEzgi0l251YFbzd2mts2r56JgKuenTKR608KANhYzSV4X719GS2+bqe3R+ZXITs9SFFHisCtmYq3k\nSUSJTxb1q4E+PaguWIEQWRwwlAX/jMqR2/0b5dDHfEtbvpyiVGptx1il+Y5QtwshNkcmb0CSDqEk\nojHv1AaW9P6ETWJCgVaWzsDswlw0t/WOth0904RdX1iN3GxWJEw279gOn0z2CuPRsX7uyoBiJkdv\n1uJra7+E9DReahAlEyFEtRz6uAv6nDIP9J4tI0EyEqdQioUYQygPaZpWAz2h24CxBbL9lWKsKIkH\nY4VUrFXeQ90uFC/J43kmSEi/Fc8Rf+yBI0piQ8NevHfqjqmtcFoW1rJ4SUjs1snrHxzBUUtBGEp8\nvYN9OHb7lKlt7tQiaDPjVS07saW50/D4wo2mtq6Bbpy6d0FRREQUS7InrhJjQyq3Q0+8AD1xqxZC\nBFvWy/84h6EnVB7oCdYG6MtzlcFSKFAO4fR/TGP7eui1JvaHs12IjF7AUuhJZbB/UVkcPFS8LUaU\nxGobmtHVO2hqe6piPtJYvCRkz2yYj3/7xSX4xuozoObkTVQ/wl7MZPLRrVoMjQyZ2p5a9CgL1oRh\n66LNeM1Snfu968ewsWStooiIKJZkohRsnWS77W3/oMqEyi6pChiyGOpjhhvbOMeZMAlVgT1wREns\nnbrA4ZPPbJivIJLEVVSQi7VLzD2WF6+14U5Ld5A9KBG94zGv/eZyubB10WZF0SSmBfklWJxv/vtS\n13QO3QM9iiIiIkpOTOCIktTDnkGcvHjP1FY2bzoWzp2mKKLEZVex8y0WM0katzvv4krbdVPbujnl\nKMyNRoG11PLkokdM3494R/DRrVpF0RARJScmcERJ6oPTdzA84jO1PVPJ3rdIbF49F1OyzSPO3zp5\nCyNeX5A9KJG8c+2jgDYWL4nMYws3wu0yX1q8d/24omiIiJITEziiJGWtPpnmduHJ9fMURZPYsjLS\n8GSF+dy1PezHKXFfUUQULSPeEbx/44SpLS9zCiqLVyuKKLHlZ0/DujnlprYrrdfQ1NWsKCIiouTD\nBI4oCd2+3wVxs93UVrl8NvKncj2rSFVtDBxG+W7dbQWRUDSda76Ezv6HprbHF25ERhqXiYjUkzZz\nB9/nmnBERFHDBI4oCb1ts/Ybi5dMztL5+Zg/e6qp7diFu+gfGFYUEUXDhzdOBrQ9tehRBZEkjw3F\nq5GbkWNqe//6CXh9XkURERElFyZwREnG6/XhHUvP0JScDGwsn60oouTgcrnwlGUY5cDgCI5fuBdk\nD3K6geFBnLhz2tRWMnUOFhfwZsdkZKZn4tH55urfD3rb0NByVVFERETJhQkcUZI573mABx19prYn\n1pUgMyNNUUTJ48n1JQFt753iMMpEVdd0Dv3DA6a2xxZu5NpvUWC3BMN7HEZJRBQVTOCIkozd8Mlt\nHD4ZFXNmTMHyhQWmtvpL9/GwZzDIHuRkH94MHD75+IINCiJJPtrMUsyeMtPUduxWPQaG+V4hIpos\nJnBESaR/cBgfnW0ytc2dOQWaJemgyG21DKMc8fpw1HLOyfm6B3tw6u55U9uSwkWYM7VIUUTJxeVy\nBawJ1z88gJOWIatERBQ+JnBESaS2oRl9AyOmtmc2zOeQsCh6bG0x3G7z+XyvnsMoE83xW6cw4jW/\nVx5fuFFRNMnJmsABwNGbXNSbiGiymMARJZH3T90JaNvKtd+iqmBqNtYtnWVqu+BpRUt7X5A9yIms\nwyddLhe2WApv0OTMzpuFZTNKTW2n711E92CPooiIiJIDEziiJNHbP4TaBvNiuUvn52PuzCmKIkpe\nWysCi5m8z2ImCaOttwMX718xta0uWo78nOmKIkpeWxaYk+IR7whO3D6jKBoiouTABI4oSRw7fw9D\nw+Z1luyqJtLkbV41F5np5j+frEaZOI7erIUPPlMbh0/GxqPzK+GCecjxRxxGSUQ0KUzgiJLEB6cD\nh08+toYJXCzkZmdg48o5prZrTQ9x495DRRFROD68ecL0fYY7HZtK1imKJrkV5ExHedFSU9v5+wKd\n/XyvEBFFigkcURLo6h3EKXHf1Fa+uBCzCnIURZT87OYW2s1BJGe58/AerrWbl9qoKF6N3Ey+V2Jl\ny3zz0gxenxfHb59SFA0RUeJjAkeUBD46excjXvOQsCfXsfctljasKMKU7HRT23v1t+Hz+YLsQU5w\n1G7tNw6fjKlH5q+H22W+3Dh6s05RNEREiY8JHFES+OC0ef6V2wVsWVusKJrUkJGehi1rzOe4ua0X\n4ma7oohoIj6fDx/eMCdwORnZWD93laKIUsO0rDysmb3c1Hap5SraejsURURElNiYwBEluPaH/Th3\n9YGpbfWSmSiYmq0ootRhXdQb4JpwTuZpv4l73S2mtkfmrUdmWoaiiFLHlgXmYZQ++PDxLfbCERFF\nggkcUYI7erYJltGTeGId136Lh1VlM1E4LcvU9tHZu/BanxByBLuE4fEFHD4ZD5tK1iHdbR5yzGqU\nRESRYQJHlOCs1SfT3C5sWTNXUTSpJc3twmNrzXMN2x7249KNNkURUTA+nw8f36o3tU3LysPKomWK\nIkotuZk5WD93pantStt13O9+EGQPIiIKhgkcUQJrae/DxWvmZGG9VoSpuZmKIko9j60JnGt49EyT\ngkhoPNfab6Klp9XUtmneeqS50xRFlHqsi3oDwEccRklEFDYmcEQJ7MMzgWXrn2D1ybhasagwYBjl\n0bNNHEbpMNbeNwDYPG+9gkhSV2XxGmSlmW8ucRglEVH4mMARJbD3LcMnM9Ld2LxqTpCtKRbcbhe2\nrDb3wrV29kPcYDVKp/D5fDhmSeCmcvhk3GWnZ6GyeLWp7XrHbdx5eE9RREREiYkJHFGCuvugB1dv\nmctwb1gxG7nZrKgXb4/ZLNlw9CyHUTrFtfZbaO4xz7XaVLKOwycVsFajBNgLR0QULiZwRAnqI5sE\ngcMn1VixeAYKpnIYpVMdux04fPLR+RUKIqF1c1ciJ8O8xMnx26cVRUNElJiYwBElqI/OmRO4zIw0\nbFwxW1E0qU2v/GnuhXvQ0YfLtziMUjW76pNTM6egnMMnlchMy8CG4jWmtpudd9DU1awoIiKixMME\njigB3W/vxeWb5uGTlcuLkJ2VHmQPijVWo3SmGx230WxZvHtjyVqkc/ikMo/YFI85fuuUgkiIiBIT\nEziiBPTxubsBbdYeIIqv8tIZyLcZRunzcRilSrbVJ+cHlrOn+Fk3pxxZ6eb3yvHbTOCIiELFBI4o\nAVnnv6WnubGpnMMnVUpzu/DoavMC6i3tfbhiKTRD8WNXfTIvcwpWzdYURUQAkJmeGbCot6f9Ju5b\n1ukjIiJ7TOCIEkz7w340XDcv3r1u2SxWn3SAx22qUX7IYZTK3Oi4g7vd901tHD7pDHZr8J1gLxwR\nUUiYwBElmI/P34V1VN5ja+bab0xxtbJ0JvLzLMMoz9zhMEpFjt2uC2hj9UlnWD93FTLc5jm7nAdH\nRBQaJnBECcY6fNLtdmHTSiZwTmA3jPI+h1EqYVd9ckpmLlbNXq4oIvKXk5GNtXPKTW2i1YO2Xr5X\niIgmwgSOKIF0dg/gXKN5nsiaJTMxbUqmoojIitUoneFWZxPudlmGTxZz+KSTbLbpDT1xh2vCERFN\nhAkcUQI5fuFewOLQrD7pLKvKZgQk1B+fu8thlHF2zGY+lV3CQOpUFq9GmiWhZjVKIqKJMYEjSiDW\n4ZMuF7B51RxF0ZCdtDR3wDDKu609uHGvS1FEqenkbXNPTm5GDtZw+KSjTMnMxeoic0XQiy1X0Nn/\nUFFERESJgQkcUYLo7hvCmSvmBYnLF89AwdRsRRFRMJtXBc5JtFu7j2KjubsFNzrvmNoq5q5CehoX\nunca66LePp8PJ++cURQNEVFiYAJHlCBOXryH4RHr8EkWL3GitUtnIifLnCwcYwIXNyduByYAm+at\nUxAJTWRjyVq4XC5TG4dREhGNjwkcUYKwDp8EgC2rOf/NiTLS07DRsrC6p6kT91p7FEWUWqyFMDLc\n6VhnqXhIzjAteyrKZy01tZ1vFuge5HuFiCgYJnBECaBvYBj1l8wV9bSFBZiZn6MoIpqIdR4cABw7\nz164WOvof4jLDzymtjVzViA7g0ONnWrzPHNxmRGfF7V3ziqKhojI+ZjAESWA+kv3MTjsNbWx983Z\nKpfPRka6+U8s58HFXu2dM/DBPNR4UwmHTzrZpnnr4AKHURIRhYoJHFECsOu54fw3Z8vJSse6ZbNM\nbQ3X29De1a8ootRwwlJ90u1yo7JkjaJoKBQFOdOxbGapqe1s8yX0Dw8oioiIyNmYwBE53PCIFycv\n3jO1LS6ehjkzpiiKiEL1qKUapc8HnLhwL8jWNFm9g304d1+Y2lbMWoJpWXmKIqJQWXtJh0aGcPZe\ng6JoiIicjQkckcOdb3yAnv5hU5tdmXpynk0r58BtHhnGYZQxVH/3HEa8I6Y2Dp9MDBttekmtxWiI\niEjHBI7I4Y6dD+yxYQKXGKbnZaG8dIap7cyVB+jtH1IUUXKzWz5g47y1CiKhcM2ZWoT5083zeuua\nAhNyIiJiAkfkaD6fL2D+W1FBDhYXT1MUEYXLOoxyeMSL2oZmRdEkr8HhQZy6d8HUVlawEDNzCxVF\nROHaWGJOtnsGe9HQclVRNEREzpU+8SaJR9O0fAAvAigF0AagEMARIcTBCI9XCmAfgHx5TA+AQ+Md\nL9oxUGq6ersDrZ3mohebV80NWPiWnGvz6rl46dXzpraPz93Fk+vnKYooOZ1tvoQBS9EL9r4llk0l\na/HDiz83tZ28cwarZmuKIiIicqak64GTiVMdgEYhxA4hxG4hxA4AOzRNOxDB8aqgJ28vCCGqhRBl\nAA4BOKBpWl08YqDUxeGTia+oIBdL5k03tdVdasbgEIeGRZPdfKlN8zj/LZEsLliAGTkFpraTd87A\n5/MF2YOIKDUlXQIH4CUAHpuerh0Admmatj3M4+2VSViH0SCPvRdARZCELNoxUIqyDp+cmpuB8sUc\nEpZoNlsW9e4bGMHpKy2Kokk+I94R1FkWfi6eOhvzpvFmRyJxuVwBwygf9LbhesdtRRERETlTUiVw\nsudrO/QeMhOZgNUA2B3G8XYBsO0xE0Lsl//dJR83JjFQ6mpq6cbNe12mto3lc5CWllRv25RgnQcH\nANvIp7sAACAASURBVMdYjTJqLj1oRNdgj6mNvW+JyW7Y60lWoyQiMkm2K8Gd8qsnyM89AKrCOF41\ngEPj9JgZj7MhhjFQiuLwyeQxf/ZUlMwyr9t3/MI9jHg5NCwaTt62GT7J5QMS0opZSzElI8fUdtKm\nuigRUSpLtgSuWn4Nljw1AqPz2iI5rpUxrDLfry1WMVCKsQ6fzMxIw3ptlqJoaDJcLldA8v2wZxDi\nRpuiiJKHz+dDbZN5+GRhTj5KCxcoiogmI92dhori1aa2G5130NzNIcdERIZkS+BK5ddgV0VGwlUR\n4vFegD7Xbe8Ej+exaYtWDJSC2rv6cclycb9+2SxkZyZl4diUYNd7etyml5XCc6uzCfd7Wk1tG4rX\nwO1Kto+31GGdBwcAJy1zHImIUlmyfcLlA6NzzcYzY4KfwziOEGK/3fE0TauQj+cRQtTHKgZKTScu\nNMNaeI3DJxPbsgUFyM/LMrUdv8B5cJN18k7g8LoNNgkAJY51c8qR4TbfrLJ7nomIUlWyJXATlecz\nujTyx90qNC/Kr9aCJPGMgZKUdfik2wVsLJ+tKBqKBrfbFfAc3mnpwe37XUH2oFBYh0/mpGdjZdFS\nRdFQNGRnZGP1nBWmtksPruJhP98rRERAki7kHWty/tp2APuFEDWq4zE0NDSoDiEh9PX1jX514jnr\nH/Ti9OX7prZFs3PQdMuDJkUxxYPTn5doKJk+HND22ttn8dRaZy4N4fTn5OFQNxrbbpjaSqfMw9XL\nVxVFFB9Of16iYZ67CP5DW3w+H16vexPrC8uVxTSeVHhOiMg5ki2Ba8P4PVvGVdJEwxuDkssEHAJw\nUAhhNzcu5jEE09vbG+1DJjWfz+fIc3bhZi+GR8zjJ5cWZzoy1lhw6vMSDSUFLqSnuUzP77lrD7Fp\nabbCqCbm1OfkXKcIaFucPc+RscaCU5+XaFiQPieg7Xz7ZWjZi+IfTBiS+TkhIudItgQOgJ5khTAH\nLVKHALwihBh3LbcYx2ArNzc3ng+XsPr6+uDz+eByuZCTkzPxDnHWeK8zoG390kLk5mYoiCZ+nP68\nRIs2LxcXboytWXb7wSC8rkzk5Tjvz7HTn5NrzeYFnt1wYeWMZchNd3ZCPFlOf16iIRe5WJBbjJu9\nY+MObvQ2IT07A5lu5/0tTIXnJJqY5BJNjvOuGCbHSJgKYd/DZfSMNUZycE3TDkAvWjJe8hbTGMaz\nYsWKiTciNDQ0oLe3Fzk5OY47ZyMjXlz5t2umtkVzp+GxTWsURRQ/Tn5eoqmqKxcXboytW+YD0DE0\nDRsrFqoLKggnPyd9Q/24dv6OqW1F0VJUrl6vKKL4cfLzEk1Pujbje2d+OPr9kG8YQ/nA2hLn/c6p\n8pxES11dneoQiBJashUxMeajBRvCaFR+rA33wJqm7QEAa/KmaVq+pmmlfk0xi4GSX8P1NnT1Dpna\nHlkZOJSIEtfG8jlwucxtxy9wOYFwnbl3EcNe85xCu/LzlLg2lATeuLIWrSEiSkXJlsC9LL+WBvl5\nKQBYyv5PSBYtKQvS87bT8ngxiYFSg92F/CYmcEllel4Wli80Fy05dbkF/YOBBU4ouFqbdcE2FCd/\nT3UqKZ46G8VTzZVb65rOwevzKoqIiMgZkiqBk0lRB4DqIJtsB3DQ2qhpWqmmafssPWnGzyoA7Bhn\n2GQ1/HrTIo2ByOfzBSRwBVOzsGQeV5xINptXmZPywaERnLncoiiaxDPiHUH93fOmtgXTS1CUN1NR\nRBQrlcWrTd939j8MqDxKRJRqkiqBk14AsFNWixyladou6ImVXeXIfQD2yK/+++QDeEser93mnw/A\ndptiJZHEQCnu9v1u3H3QY2rbtHIO3G5XkD0oUT1isyg7h1GG7tKDRnQPmt8rdsPtKPHZDqO06X0l\nIkolyVbEBEKIw7In7S1N014A4IE+zHEvgG1BKkO+DKAKY8MfDS9h4gW3A4ZCRhgDpbgTHD6ZMkpm\n5aFkVh7utHSPtp24eA8jXh/SmLBPiMMnU8eyGaWYmjkFXX4Je23TWXxlzecVRkVEpFbSJXAAIITY\nr2naQehJUxX0ypFl42x/GMBhm/Yd8YqByNoDk5mRhrVLZymKhmJt86o5+ME7YwtOd3YP4vKNdqxY\n7MxFvZ3C5/Oh9s4ZU1tBznSUFi5QFBHFUpo7DeuLV+H968dH2251NqG5uwWz8/j3kYhSU1ImcAAg\ne7mUzjVzQgyUGDq7B3DpRpupbf2yWcjKSFMUEcXaIyvnmhI4ADh+4S4TuAncfngXzT0PTG0bitfA\n7UrGGQEE6M+vfwIH6MVMPr3sGUURERGpxU88Igc4ebEZPp+5jcsHJLdlCwswPS/T1MZ5cBM7ael9\nAzj/LdmtnVOOdLf5fjPnwRFRKmMCR+QAJy6aL9xdLmBD+ewgW1MySHO7sKncnKTfvt+NJr95cRSo\nznLhnp2ehVVFmqJoKB5yMrKxqmiZqe1iy5WAQjZERKmCCRyRYoNDI6gX901t2oICFEzNVhQRxYtd\nkRprMk9jOvof4qqlhPzaOeXISMtQFBHFi7WX1evz4vTdi4qiISJSiwkckWJnrz7AwOCIqY3VJ1PD\nuqWzkJFu/jN84kKzomicr77pPHwwjzW2rhNGyanSpspobROHURJRamICR6SY3bwnzn9LDdlZ6QGV\nRi9ca0V376CiiJytznLB7oILFXNXKYqG4mlGbgEWF8w3tZ2+ewHDI8OKIiIiUocJHJFCXq8vYP23\nuTOmYP7sqYoioniz9rZ6vT7UXbofZOvUNTgyhLP3Gkxty2aWYlo23yupwrrWX+9QHxoeXA2yNRFR\n8mICR6RQ450OtD3sN7VtWjkHLhcXc04Vm2yK1dgt6p7qzjcLDIyYeyY5fDK1bChZG9DGapRElIqY\nwBEpxOGTNGN6DsrmTTe11V1qxvCIV1FEzmQdPgkE9shQcluUPw8zcgpMbbVNZ+GzrsFCRJTkmMAR\nKXTSUrBiSk4GF3JOQdblBHr6h3HxWquiaJzH5/OhrumcqW32lJkomcabHanE5XKhssTc69rS04pb\nnU2KIiIiUoMJHJEiLe198DR1mto2LJ+N9DS+LVONNYEDWI3S37X2W2jr6zC1VRav5lDjFGTX62pN\n7omIkh2vFIkUOdkQOHxy00ou3p2KyuZNR+E087p/Jy7c49AwyW74ZGUJh0+movKiZchKzzK1MYEj\nolTDBI5IEWuhCrfbhQqtSFE0pJLL5QqoRnm3tQe373crishZrBfouRk5WDFrqaJoSKXMtAysmb3c\n1Hal9Ro6+x8qioiIKP6YwBEp0D8wjLNXH5jaVi6egbzcTEURkWqsRmmvrbcDnvabprZ1c8qR7k5T\nFBGpZl3U2wcfTt29oCgaIqL4YwJHpMDpKy0YGjZXGeTwydS2ZuksZGaYk5ITF5nA2Q2Ps17AU2qp\nKF4FF8zzHzmMkohSCRM4IgXselbsCllQ6sjKSMP6ZbNMbZeut+Fhz2CQPVKDdf6b2+XG+rkrFUVD\nTpCfPQ1LChea2s7cu4ihkSFFERERxRcTOKI483p9ONlgrjBYMisPxbPyFEVETrHRksR7fUBtQ+pW\noxwYHsS5+8LUps0sQ17WFEURkVNYi9j0Dw/gYssVRdEQEcUXEziiOLt6uwMdXQOmNmsBC0pNtvPg\nUngY5bnmhoBeFS7eTYC+jIRV3R0OoySi1MAEjijO7IZPbrS5cKfUUzAtG8sW5Jva6i/dD5gvmSpq\n79gtHxB44U6pZ8H0EszILTC11TWd5dIbRJQSmMARxZm1RyUvJwPliwoVRUNOY50L2TcwjAueB0G2\nTl5enxf1d8+b2uZOLULxVN7sIH3pDWsvXEtvG251NimKiIgofpjAEcVRS3sfrjWZ1yuqXD4baWl8\nK5LObjjtiYupNw/O03YTHZa1vVh9kvzZDadlNUoiSgW8aiSKo5MNNtUnuXwA+Vk0dxpm5ueY2k5c\nuJdyQ8PsLsQ32Mx7otRVXrQMWelZpjYmcESUCpjAEcWRdf5bmtuFiuVM4GiMy+UKmBPZ3NaLW81d\niiJSo95yIT4lIwfLZpYpioacKDMtA2tnrzC1XWm9hk5Lzy0RUbJhAkcUJ/0Dwzh71TyXaWXpDOTl\nZCiKiJzKbk3AVBpG2drbjmsdt0xt6+auRLo7LcgelKqs8+B88OHU3QuKoiEiig8mcERxcupyS0A1\nQVafJDtrlsxEVqY5WTmZQssJ1DedD2jj/Deys754FVxwmdpqmwKrlxIRJRMmcERxYncBbtfTQpSZ\nkYZ1S2eZ2i5db8PDnkFFEcVXneUC3O1yY93cckXRkJPlZ0/DksKFpraz9wLXDyQiSiZM4IjiwOv1\n4WSDeQhcyaw8FM/KUxQROd1GS3Lv9QG1Dck/jHJgeBDn7gtT2/KZZcjLnKIoInK6yhJz72z/8AAu\ntlxRFA0RUewxgSOKg6u3O9DRNWBqsysXT2SwG16bCsMozzVfCug9qWD1SRqHdR4cANTdYTVKIkpe\nTOCI4sBafRIANnH+G42jcFo2ls7PN7XVi/sB8yiTDZcPoHAtmF6CmbmFpra6u+dSbukNIkodTOCI\n4uCkpYJgXk4GViwqDLI1kc46jLK3fxgXPa2Kook9r88bsHzA3LwiFE9jbzUF53K5UFG8ytTW0tOK\nW51NiiIiIootJnBEMdbS3gdPU6eprXL5bKSl8e1H47PrpT1hsxh8srjefgvt/eb3CodPUig22FQp\nrb8bWM2UiCgZpEfzYJqmrQNQBWAjgFIA+QAK5VcA6ADgkf9OAqgRQpyOZgxETlNrc8G9aSWHT9LE\nSkumY8b0bLR29o+2nbzQjN/83Cq4XK5x9kxMtTbDJ+3mNxFZlRctQ1Z6FgaGx+Ya1905iy+seFZh\nVEREsTHpBE7TtEUAdgPYBT1Rc2EsSbsGoA164uafzJUB2AHAp2laB4CXAewTQtyYbDxETmNdgNnt\ndqFCK1IUDSUSl8uFjeVz8MbH10fb7rb24Pb9bsyfPVVZXLFiHT6Zm5GD5bOWKIqGEklmWgbWzF6O\nk3fOjLZdbr2Gh/1dmJadfO8VIkptESdwmqZNA7AfeuJWA+C/Qe9ROxXGMSoAbANQDcCjadohAC8I\nIboijYvISfoHhnHmSoupbeXiGcjLzVQUESWajeWzTQkcoFejTLYErq2vA572m6a2dXPKke5OC7IH\nkVll8RpTAueDD6fuXsDWxZsVRkVEFH0RTcLRNO1LAK4D8AEoE0J8QgjxF+EkbwAghKiX+30CwFIA\nnQCua5r2S5HEReQ0Z660BFQNtCsPTxTM2qWzkJlhTmKsvbrJwNr7BugX5EShqpi7MqDNrqopEVGi\nCzuB0zTtv0HvdVsshPgtIcS1aAQihPAIIXZDH175x5qm/Xk0jkukkt2FNtd/o3BkZaRh3dJZpraG\na6142DOoKKLYsF5ou1wurJtbrigaSkT5OdOxpHCRqe3MvYsYHhlWExARUYyElcBpmvYCgFYhxLNC\niM4Jd4iAEKJDCLEBgFvTtN+MxWMQxYPX6wtYeLlk1hSUzMpTFBElKmuvrdcH1F9Knl64weFBnGu+\nZGpbPrMMU7P4XqHwWIve9A3342LLFUXREBH9/+zdeXhU15ku+reqNM/zDAgJsRCTmCcbYwzYjhMn\njm2Ik7iTTscxTvftpzvnpk18+/Y5t8/pjoN9+3Snh6Rtp7szdTrY2EmcOB4ADxgzSgIEQlqAJJDQ\ngNA8D1W1zx8qgVbtKtBQpb2r6v09jx5ZX9Xe+zPFFvXVWutb/jHVEbhSKeWLfsnEjZTyOwDKZuNa\nRP5Q09iFzt5hJea+rxfRZHiadhtM0yjPtUqMOEaVGLtP0nR4+nvjaXouEVEgm1IBN9U1bjM129cj\n8qWTlR6mT7KAo2lITYzGgrxEJVZefR12h9PLEYGlrLFCF+P6N5qOeUl5SI1JVmJlTeegaZpBGRER\n+R53Eibyk1Nu+7/FRoejeH6KQdlQoHMfve0fsqOytt2gbHxH0zSUNasjJJlx6ciJZ7MfmjqLxYLV\n2eoo3PX+NjT26PfjJCIKVIYUcEKIfxVCOIQQ902IJQoh/sK1GThRQGvvHkTNNXWZ6GqRgTAbPzOh\n6fE0envyQuC/Ka3rbEDnoNu9krMsKDcqp9mxysM0SnajJKJgYtS7yRoAr2Bsk28AgJSy27W+rpDN\nSyjQeVqftJbdJ2kGCvMSkZIQpcROVV4P+KlhZU366ZNruP6NZmBppkCkTd1r09PfMyKiQGVUAdcl\npXxGSnnG/QEp5esAkgzIichn3LtPWq0WrF6UYVA2FAwsFouumUlzez+utfYZlJFvuI+MxIRHY1F6\nkUHZUDCIsIVjWeYiJSbba9E7HNj3ChHROEMKOCnlK0KIb4//LITYJoRwuqZVtgNYa0ReRL4wNGLH\n2Ys3lFhxfgriYyK8HEE0OZ72EHT/sCCQdAx2obazXomtyFqMMKvNyxFEk+PejVLTNJxurjQoGyIi\n3/J7ASeE+KEQ4utCiHy3hyYWcXsA7AZwP4BdUsov+DsvIn85e/EGRuxqd0B2nyRfKClKR0S4WtwE\n8nYCntq7s/sk+YKn7QRKOY2SiIJE2Cxc4wsYK840IUQXgIMADri+XhFCPA+gTEr5yizkQuR3nt5Q\nr1vCjno0c5HhNqwoSleal1TVtaOnfwQJsYE3wlvqVsBZLBaszF5iUDYUTJKiE1GYMg81HVdvxs42\nX4DdYUeYbTbe+hAR+c9sTKEslVJaARQBeA6ABcALAGpdX48DSBJCzJuFXIj8yunUdFPactJikZcR\nb1BGFGzc18E5NaCsOvBG4YbtIzh3vVqJLUorRFxkrEEZUbBxH80dtA/hwo1LBmVDROQ7s1HA7QYA\nKWWtlPJlKeUuKWUKxta57QVQh7FRulohRLsQYt/E7QWIAsnla13o7B1WYp7WLRFNl3sBBwAnKwNv\nHdz5VolRx6gS8zTtjWi6PHUz5XYCRBQMplzACSESpvJ8KWWdl3i5lPIFKeX9bgVdsus7UcDxtC8X\nCzjypdTEaCzIS1Ri5bIVo27rLs2urFG/Honr38iX5iXlITUmWYmVNVUE/NYbRETTmQieKoS4grG9\n3MbXs5VKKXtmkoiUshxAOcamVxIFpFOV6lS2uOhwLM5PMSgbClbrFmfh8oSN4geG7LhQ246ShekG\nZjV5mqahrFkdCcmKS0dOPNeKku9YLBaszlmG9y4fvhlr7W9HQ3cT5iblGpgZEdHMTHkEzjWiVuA6\n9lmMFXCdQohLro6TK3ycI1FAuNE5iNqmbiW2elEmbDajtlukYOVpU3hPo79mVddZj85Bt3slZzks\nFotBGVGwWuNhVJfTKIko0E2rFZOUsksI8TjUUbha18OGDzcIIZIw1jClAEAHxnI6IKV82Qfn3gug\n5nbncv3Z7AbwEm41awGA7a74HteIIwURz9MnOaJAvleYm4jUxCi0dw/djJ280IKnPrc0IIogT2+g\nuf6N/GFxxkJEhkVi2H5rbXJZ0zl8fvGDBmZFRDQz0yrghBDzAbwKYLWU8vQkn78XwHtSyh9N55pT\nyC0JQBmAvVLKPRPiB4QQq6WUu6d53lUY+3/YjrF9624nxfW87R4e283iLTi5F3A2qwWrFrGAI9+z\nWCxYuzgL7xy7cjPW0j6Aa619mJNp/o6n7gVcTHg0FqUvMCgbCmYRtnCUZBbjZOOZm7FL7XXoHupB\nYtSUlvQTEZnGdOd2vYqxDbfvWLwBY9MupZS7ANTNQpfJVwDUehgh2wngadfo2KQJIfYKIcow1ilz\nKoVXOYAu13/XAtgPoNAXo4BkPoPDdlRcalNiSwpSERcdblBGFOwCtRtlx0AXajvrldiKrMUIs9q8\nHEE0M+6juxo0nG6uNCgbIqKZm/IInBBiG4A6b90lb0dKeQjAISHEvwohkqSUb0z1HHfILQlj+8rp\nRtlc0z4Puh7bP9lzuo3iTaX4e15KOenrUGA7c7EVdofaBZDdJ8mfSorSERFuw8io42bsRGULHruv\nyMCs7szz9El2nyT/WZWzFBZYoOFW98nSxgrcO3+jgVkREU3fdEbgCgCcnMlFpZTPALjfDyNxu1zf\na708XgvP0xqJZuRkpX4j5XWLWcCR/0SG27DSretk9dUOdPcNeznCHEqb1O0DrBYrVuYsMSgbCgWJ\nUQlYkJqvxM5er8KI2z6ERESBYjoFXJIvLuwq4p7xxbkm2OH67q2AqwEAIQSLOPIZp1NDaZVawM3J\njEN2WqxBGVGoWO82yqtpwKkL+g8TzGJodAjnr1crseL0BYiL4L1C/uXejXLYPowLrRcNyoaIaGam\nU8DVAij00fWfF0I876NzAWOjg8BY50lPxtekrfLhNb0SQjztWkO3VwjxkhDi6dm4Ls2uiw2d6HIb\n9eDoG82GNYsz4d500szbCVRcr8ao067EOH2SZoOnLqfuo8FERIFiOgVcOW5NVZwRVxOU1b44l0uS\n67xdd3heqg+v6c1zGGumssf1tRvATiHEa7NwbZpFnhpHcP0bzYbk+CgsnJusxE7LVmVdnJl4esO8\nJpcFHPnfnMQcpMeq//SXNZ2DpmlejiAiMq/pbuRdJ4T4vI9yKPfhWrg77UE3PjLnk2mgt1EK4BtS\nyoNu8T0AHp9qJ0wyN/cCLiE2AmKe4dshUohwn0Y5NOJAxeU2L882jtPpRLlbA5O8hGxkxaV7OYLI\ndywWi24Urn2gE1e7rhmUERHR9E1rHzgALwN4AcCvfJBDDcamNL7vg3OZgrd93qSU5UKILoztJ+fz\nDpVVVVW+PmVQGhwcvPl9pn9mHb2juNrSq8SKcqJwUVZ7OYK88eXrEkrSovVNS949UoVYrzPJJ8+X\nr0l9fzN6hvuUWH5kDl/raeC9Mj0Zdv1nt2+ffR/3Zq6b8bn5mhDRbJpWASelfFkI8awQ4pdSyidm\nmEMhAF99XNyB24+ujQ+L3GmKpT/VAlglhCiQUnprtjItAwMDvjxd0NM0bcZ/Zmcu9epiBZlhfC1m\nwBevSyiJj9CQHGdDZ9+taZOVV/vwwMo4WNwXyE2TL16T8+1SF5sXkcPXegZ4r0xNhjUZEZZwjGi3\nuk9WdV3GuvilPrsGXxMimg3THYEDxjpIvieE6JBS/vEMzrMSwEszOF7HtceckUXa7Yx/LF4A790y\npyUmJsaXpwtag4OD0DQNFosF0dHRMzrX5ZZ25Web1YJlBSmIipjO8tLQ5svXJdQsyY/HkfO3fuX1\nDjrQOWhDXlrUjM7ry9ekdrBB+TnWFo0FKfNgtfBemSreK9NXlJCPyu5LN39uGW7DaJgDiRHxMzov\nX5OpYZFLNDPTLuCklAeFEN8B8D0hxBqMrfk6O5VzCCFWYmxftp3TzcPN+DuYFHgeZRsfnavx0fV0\nXJ0m9wLY6WENnKdcfKa4uNjXpwxKVVVVGBgYQHR09Iz+zPoGRlDbckmJrViYjpUl3NNqOnz1uoSi\nkbA0HDl/VIndGIjGjuJFMzqvr16Tlt5W3KjoVGJr567AksW8V6aD98r0bYvpReVx9fd2T+wgNiyY\n2TRKviZTU1ZWZnQKRAFtRh99SilfAPAKgDUYa0byXSFEwmSOdT3vZQAHpZQ9M8ljgvGCyVtxNN6C\nqtRH1/Nkp+v63rYqGJ/G6XGdHAWO0upWOJ1qBzP3hhJEs2FJQSpio9TP40546I5qlFK35iWAfl8u\notmwInuJbtS3tJHbCRBRYJnx3BVXe/xnAFgw1mWxUwjxrhDiKSFEvvvzhRAJQohHAdRhrMjZPdMc\nJtjn+l7g5fECV87+LJ7KAex2FbeerHLl4NPpkzT7Tpxv1sW4fQAZIcxmxeriTCVW29iNG52DBmWk\nKnPbPiDcGoblWRyloNkXFxGLxelFSux860UMjg4ZlBER0dT5ZPGBlPJljI3CncFYIbcdY+vaaoQQ\nDiHEJSHEKSFEO4BOAK8BSAZwv5Tyii9ycOVRjrGpkzu8POVxjI36KYQQBa7Ntr0VflOxD15GAIUQ\n213/uccH1yEDjdqdKKtuVWIL5iQhNZFrH8gYnkZ/T1UZPwrXN9yPqhuXldjSzEWICos0KCMKde57\nD9qddpxtuWBQNkREU+ez1eNSynIp5WqMbfI9XsiNfxVibMPuZNfPhwAUSikP+er6E3wDwC4hhFJE\nudamdcFz8bQXwLOu77czPv2x0NsTXEXkWiGEpymUezG2ube30TkKEOdq2jA4bFdinD5JRlq1KBM2\nq9p10gzTKE83V8KpOZUYp0+SkTz9/eM0SiIKJDPpQumRlHI/gP1CiESMjcQV4NbasxoAr0opu319\n3YnXd42kHRJCfANjnR53Yaxw2+alO+U+V6773B9wbbr9HMb+P8aLwqeFELtc597nXpBJKXcKIV4T\nQtQCOOA6djfGijdfNWwhA7lv3g2wgCNjxUWHY2lhKs5eurUrS8WlNgwMjSImKtywvEqb9G+M3TdU\nJppNGXFpmJuYi/ruxpux8ubzcDgdsFltBmZGRDQ5Pi/gxrmKtNf9df47XPsFIcTLGCvctmOscLrd\nqNl+eNlY+3aP3SGHna5CcjvGtg7YyXVvwUHTNN3IRkZyNPKzJ9W/h8hv1i3OUgo4u8OJ0/IG7irJ\nMSQfu8OOMy2VSqwweR5SYnzehJdoStbkLlcKuL6Rfsi2GizOWGhgVkREk+O3As5orpE23Xq3Wc6h\n1ugcyPdqG7vR1qU2h1i3JMtnmyYTTde6JVl45TfnldiJymbDCrjKG/rmEKtzOfpGxluTsxxvXHhb\niZU2VrCAI6KAwB1UiabI07qiDUuyDciESJWVGqsbCT514TocDqeXI/zrVKN+a1CufyMzKEiZi+So\nRCV2qqkCmqZ5OYKIyDxYwBFNkXsBFxsVhiWFqV6eTTS73Ndi9g2OorKufdbz0DRN1xgiPSYF85Ly\nZj0XIndWixWr3bpRXu+7gcYe4xv/EBHdyZSmUAoh5gN42k+5eFIjpfzRLF6P6LZudA6itlHttT8A\nzgAAIABJREFUwbO6OBNhNn4WQuawYWk29h28qMSOn2/B8gXps5pHbWc9OgbVnlFrc0s41ZhMY03O\nchys+ViJnWo8i7xEzqggInOb6rvOJIxtBTBbX1zpTqZyslK/eTe7T5KZFOYlIi0xSomdON8861PD\nTjWe0cXW5JbMag5Et7M0UyDSbT9CT11TiYjMZkojcFLK0wCe8VMuRKbnPn3SZrVg1aJMg7Ih0rNY\nLFi/NBtvfVJ3M9baOYi6ph4U5Cbe5kjfOuU2fTI2IgbF6Qtm7fpEdxJhC0dJVjFOXrv1YcPl9ivo\nGuxGUvTs3StERFPFeV9Ek9Q/OIpzNW1KbFlhGuKijdtji8gTT6PCJ87rR4/9paXvBhq6m5TY6uxl\n3GOLTGdtjjoqrEFDadM5g7IhIpocFnBEk1RWfR12hzoNbR2nT5IJLS1MQ2yUOsHi+PnZa85Q6qH7\n5No8Tp8k81mZs1S3LtPT318iIjNhAUc0ScfOeVj/tpQFHJlPeJgVq4vVqb21Td1o7RiYleu7bx8Q\nbg1DSWbxrFybaCoSIuNQnKZO7a24Xq3bv5CIyEx8XsAJIRKFEM8LIbb6+txERhm1O1BWfV2JFeYl\nIiM5xqCMiG5vw1J9J73jHprw+FrPUC+q22qU2LKsYkSFR3k5gshYa92a69iddpxpqTQoGyKiO/PH\nCNxeAHsAHBRC5Ls/KIR4TAjxqB+uS+Q3Zy+1YXDYocQ2eniDTGQWqxdlIMymTg07MQvTKMuazuk6\nXq7l5t1kYmvzVuhiExubEBGZjT8KuC4AOwEcAtDh/qCU8nUAqUKIfZ4KPCIzOu6hAYSnEQ4is4iJ\nCsfyInXvt/O17egdGPHrdU+5tWG3wKLbMJnITDJiU5HvtsF8efN52B12gzIiIro9fxRwiVLK16WU\n90spezw9QUr5ipTyCwC+wyKOzM7h1HQjF9lpsZibFW9QRkST4/4hg9Op4dSF616ePXPD9hFUtFxQ\nYgvTCpAUleC3axL5wjq3UbjB0SGcb71oUDZERLfnjwKufApTJPe4vohMS17tQFffsBLbsDRb17mM\nyGzWLdbvUXjCj+vgKq5XYcQxqsTWcvSNAoD7OjjA82b0RERm4PMCTkr5Cm5Nkfy8EMLrR69Sym5f\nX5/I1zy1X+f6NwoEqYnREHOTlVh5dStGRh1ejpiZU9c8bB+Qq19fRGQ2cxNzkRGbqsRKGyvg1JwG\nZURE5J0/ulAmYGwN3E4A+wF0CiEuCSF+KIR4dGJB5/rvAl/nQOQrmqbhuNv2AUnxkRDzkr0cQWQu\n7ltdDI04cPbSDZ9fx+F0oMxt/VtuQhay4zN8fi0iX7NYLFjn9mFD51A3LrdfMSYhIqLb8McUyh9h\nrJHJHgCvADgDoBDAbgCvYaygaxdCXALQ6YoRmVJ9Sy+a2/uV2PolWbBaOX2SAoOnZjue9jScKdlW\ni94R9V7xNC2NyKw8bTZ/kpt6E5EJhfnjpFLKXe4xIcRKANsB3A9gG4AkADullG/4IwciX2D3SQp0\neRlxyEmLRVPbreLqRGULHE4NNh9+EHHy2mldjAUcBRKRWoiEyDj0DPfdjJ26dgZfXv4I1zwTkan4\nYwROt3UAAEgpT0spX5RS7gCQDOA5ADtut0aOyGjH3Aq46MgwlBSlGZQN0dRZLBZsXKZ+6NDTP4IL\nde0+u4amaTjh1vAhJToJhSnzfHYNIn+zWq1Y47ZnYXNfKxp7/b9/IhHRVPijgKsRQtx21bqUsltK\n+QLGiri9fsiBaMZaOwdQc03ts7OmOBPhYTaDMiKank3Lc3QxX06jrO2sR/tApxJbl7sCVos//okh\n8h9u6k1EgcAfXShfBPCMEOK+2z1PCJEgpewCwHkJZErue78B7D5JgWlBXhLSEqOU2LGKJmia5pPz\nn/AwfdJ9Xy2iQLAscxEiwyKV2CmugyMik/HLx6NSymcArBZCvOtpNE4IMR9jzUzeBeCbdxBEPua+\n/i3MZsXqYnbUo8BjtVqwwW0aZVv3EC41dM343Jqm6Qq4+IhYFKcvmPG5iWZbhC0cK7OWKLGajqu6\nEWYiIiP5bX6La73bAwDqPDxWB6AHwA4AZf7KgWi6evpHcL5WXSNUUpSGmKhwgzIimplNy/wzjbKx\npwXNva1KbE1uCWxWTjWmwLTOQzdKjsIRkZn4fYGCt826pZTJAJKllD/ydw5EU3WyshlOpzo4zO6T\nFMgWz09BQmyEEjvqg2mUnqZPruf0SQpgK7OXwua2ftPT33MiIqMYusLcW3FHZLRPKtSRCYtlbP83\nokBls1l1f4eb2vpRf713Rud1b/AQHRaFpZmLZnROIiPFRsRgaaZQYhduXELP0MzuFSIiX5lSATfb\nLf+5xQAZoX9wFGcu3lBii+enIjkhyssRRIHB190oW/vaUNfVoMRW5ixFhI1TjSmwrc9bpfysaRqn\nURKRaUx1BO7/uVN3SV9xXee52bgW0USnLrTA7nAqsU3LOX2SAl9JURqiI8OU2LGK6RdwJxv17dU5\nfZKCwbrcEt3m3ZxGSURmMaUCTkr5HQDfEUJ810/5AACEEN8DsEdKyQKOZt1RDyMSnhpAEAWa8DAb\n1i7OVGK1Td1oae+f1vlOuE2fDLeG6Tr4EQWihKh4LE4vUmLnrlejb2R69woRkS9NeQ2clPJ+AKlC\niEtCiK/7MhkhxKNCiEsAEl0dLIlm1dCwHWXVakc9MTcZaUnRBmVE5Fu+6kbZOdiNi221SqwkazGi\nwjnVmILD+ryVys8OzYmyxnMGZUNEdMu0mphIKXcD+CaA54QQ7UKI7woh9H13J0EIsUII8bwQoh3A\nXgDPSCm/OZ1zEc1UWXUrRkYdSozTJymYrFqUgYgw9Vf/dAq4U41noblt48nNuymYrMvV/33mNEoi\nMoOwOz/FMynlQQALhBCPAxifWqkBKAdQCqALQLvreweAFABJAFJd39cAGF8lfBrAd6SUr0w3HyJf\nOFrRpIt5avxAFKiiI8OwUmTgRGXLzVjVlQ509AwhZQqNety7T1otVqzJWe6zPImMlhKTBJFaANl+\na6T5bMsFDI4OIZojzURkoGkXcOOklPsB7BdCzMfYxtyPA/gCxoo0b2pdX98BsN+1sTeRoUZGHThV\n1aLECnISkZUaa1BGRP6xaXm2UsABwPHzzXho0/xJHd833I/KVqnElmQsRFwk7xUKLuvnrFQKuFGn\nHaebz2PT3DUGZkVEoW7GBdw4VxH2susLAOAq6oCxYq6LhRqZ2WnZisFhTp+k4Ld2cRZsVgscEzar\n/+Rs06QLuNKmCjg0tVMru09SMFqXtxI/PfO6Ejt+7TQLOCIylM8KOE9YsFEg8dh9ktMnKQjFx0Rg\n2YI0Zb/D8zVt6O4bRmJc5B2PP95QrvxsgQVrPawXIgp0GbGpKEiei9rO+pux082VGLaPIDIswsDM\niCiUTauJCVGwGbU7dVPK5mTGY05mvEEZEfnX3SXqhxNOzfOHGO76RwZw9nqVEluUXojk6ESf5kdk\nFu7dKIftwzjbcsGgbIiI/FjAubpLPuXqMPnt2doAnGg6Ki7fQP/gqBLj9EkKZhuWZsNqVTcq/uRs\n4x2PO9V4Fg6nOtV4Q94qL88mCnzr56zUxY6zGyURGcgvUyiFEK8CeAzA+LsDzRXXMLZB99/547pE\n03W0Qj/ycBenT1IQS4yLxPLCNJy5dGsa5bnLd55G6Wn6pKc3uETBIic+E3MTc1HffesDjrKmCow6\nRhFuCzcwMyIKVT4fgRNCfA9jTUueAbATwB4ArwOoc13vRSFEmxBiq6+vTTQdDocTx8+rBVx2aizy\nsxMMyohodtzlYRrl7faE8zR9UqQVICX6dk2HiQKfe5OewdEhnLsuvTybiMi//DGFskBKeb+U8hUp\n5etSyhellLuklAsAFGJs64BuAAeFEJ/3w/WJpqSyrh09/SNKbNPybFgsFi9HEAWHjcs8TaPU74U4\nzuP0yTmcPknBz30dHAAcv1bu4ZlERP7njwKuw9sDUso6KeULUspCAM9hbP+4eX7IgWjSPj7Dzbsp\nNI1Po5yo4vINdPcNe3y+p+mTXP9GoWBOYg6y4zOU2KlrZ2B32A3KiIhCmT8KuC4hxB3nnkkpXwDw\nAIAX/JAD0aQ4HE4crVALuIzkaBTN4ZQwCg2TnUbpdfpkDO8VCn4WiwUb56xWYv2jg6hwuyeIiGaD\nPwq45wHsncwTpZQHcavRCdGsq7jcpps+eXdJLqdPUsiY7DRKTp+kULfJrYADgKP1ZQZkQkShzucF\nnJSyG8DLQohTk2xUovk6B6LJ+viMvm365hW5BmRCZIzEuEgsK0xVYhWuTb0ncp8+CXD7AAotcxJz\nkJuQpcRONZ3FiGPUyxFERP7hjy6U2wCUAViNsUYl7UKId117wa1we+5jGOtOSTTr7A5NN1UsOzUW\nhXnckJhCy10l6ocWTqemdGYddAx7mD5ZyOmTFFIsFotuFG5wdIibehPRrPPHFMq9GNs6YA+AVwB0\nAtiBsbVuZUIIh6uguwRgu5TyO55OIoR41w+5Ed10qakffW6bd9+9IofTJynkbFqWDbdZlDgyobmP\n7KnVTZ/cyOmTFII2zvU0jbLUgEyIKJT5YyPvUinlixMDQohEAGsA3A9gO8YKOgAoFEI8DaAcQCmA\nAwDKpJRXXc8j8puK2j5djNMnKRQlxkVi2YI0nL3UdjNWUdOGz61PgAVAZdcl3TGcPkmhKC8hW7ep\nd2nTOdybsNbArIgo1PijgDsghHgewEtSyivAzXVxh1xfAAAhxEqMFWn3A9iGsSmXT7se80NaRLfY\nHRoqr6oFXG56HDfvppB1V0muUsA5nRrOX+lFUa6Gmr565bmcPkmhbNPc1ag/d6uAG7YP41LPFcyP\n4AeARDQ7/NHE5HUALwN4RgjxQyHEo16ed9q1yfcOKaUVYwXcMwDeADtTkp9dbh7C0IhTiW1ewe6T\nFLo2LtVPo6yo7cPl/no4NPVe4fRJCmXu2wkAQGW3fpSaiMhf/DECByllHQCPa9tuc8xpAKcBvCKE\nSMJtNgQnmqnK+kFdbPMKbt5NoSspXj+N8nLzAKzdl3XP5fRJCmXZ8RmYnzQHdV0NN2MXe65gJHUU\nMQbmRUShwx9NTGZMStkFYL/ReVBwGrU7Ia+pBdy8rHjMzeL0SQptd7t1o9RsI6gfUveEW8Tpk0S6\nZiajmh2X++u9PJuIyLdMWcABgJRyl9E5UHCqbujHiF3dfvBuNi8hwqblOQiz3ZpHaUtpASxu98o8\nNmsg8rSpd3VfrQGZEFEo8ssUSqO5pmA+B6AAY1MxUwAckFK+7INz7wVQc6dz+TMHmpmztb26GLtP\nEgEJsRFYKTJw6sJ1AIAtVd0n0WqxcvokEYCMuDQsSMnH5Y4rN2O1A9cw5Bg2LikiChmmHYGbLlfh\nVIaxImunlHK3lHIngJ1CiJdmcN5VQogDAJ4FcNv5Q/7KgWZuaNiOqoZ+JVaQk4jc9DiDMiIyl3tW\n5gEALBGDsMV3Ko8tz1yEhKh4I9IiMh33ZiYOzQHZU2dQNkQUSoKugMPY5uG1Hka6dgJ4Wgjx+FRO\nJoTYK4QoA/AFjO1XN+s5kO+cqrqOUd30STYvIRq3fkkWIsJtY9Mn3dw9b50BGRGZ08a5+tHo810X\nDciEiEJNUBVwrpGvxwG85v6YqzHKQQC7p3JOKeUeKeVqKeUeAKeMyIF856Pya7oYp08S3RIdGYYN\nS7J00yfDrGFYm1tiUFZE5pMWkwKRWqDELvfWo2e4z8sRRES+EVQFHIDxxifeVhLXYmzz8GDPgTzo\nHRhBWfV1JbZwbhKyUmMNyojInJYsjoQ1tkeJpVvzER0eZVBGROa0ae4a5WcnnDjeUGZQNkQUKoKt\ngNvh+u6teKoBACGEPwsoM+RAHhw52wS7Q50+uWVVnkHZEJlXd7h+HU/3tVRomubh2USha9Pc1bBa\n1LdSH1+942QdIqIZCbYCbnwug7dNwLtc3/3ZRs0MOZAH7tMnrRZOnyRyp2mabgRBs4ehvSEBF+s7\nvRxFFJoSoxKwPHOREpNtNWjtbzcoIyIKBcFWwCUBN9ea3U5qkOdAblo7BlBZq/6DWpQbg+R4Tgkj\nmqiusx7Nfa1KzNGZCWg2HD7daFBWROa1ed56XezI1ZMGZEJEoSLYCriUOzw+Pip2220AgiAHcvPR\naX3zkpWFCQZkQmRuRzxM/3K0ZwMAPj7TCIeT0yiJJlqbuxzhFnVb3Y+vnuSUYyLym6DcyDtUVVVV\nGZ2CKWmahnePXVVi4TYLCjJt/DMzkcHBwZvf+boYw6lpOFx3XIlpoxFw9ox9LtXZO4y33i9HUW6M\nEemRC+8V8ymKm4cLvTU3f27sacEHpw8jOzrDwKyIKFgFWwHXgduPbI2Pjt1pemNA5jAwMODrUwaF\nls4RXO8cUWIiLwoRYRb+mZmQpml8XQxSP9iMnlF1o3tHRxYmTtYovdiB3ORZTow84r1iHovjFigF\nHACU3ajEfWlxBmVERMEs2Ao4AGN7sU1iDVrQ5RATw0/FPak616+LLc+PgcViQXR0tAEZkSeDg4PQ\nNI2vi4EudlzVxWIG8tA94eeqhiE8vjkK4WHBNgM/cPBeMZ/5yEO0NQqDzqGbseq+Wjw0Z4uuSyXx\nA2eimQq2Am68YEqB5xGu8ZGxGg+PBXwOxcXFvj5lwHM6NbzwWr0Si42yoTA7CtHR0fwzM5GqqioM\nDAzwdTHIiGMUVVWvKLGk8AQUZuTgyI1bGxMPjTjR60zGXcU5s50iufBeMZ+qqioUxxegvPvCzViv\nvR9aqg3Fbl0qCSgr4155RDMRbB8LHXR99zaFcbzzY2mQ50AulbXtaOseUmIlBXGwWS0GZURkTqWN\nFRgYHVRiy5MFSvL1G90fKq3XxYhC3eL4BboY94QjIn8ItgJun+t7gZfHCwBASlke5DmQy4fl7D5J\nNBmHrxzXxUqSFyE9MRxz0tXtNsqqW9HVOzxbqREFhJzIdKREJCqx49fKMeIYNSgjIgpWQVXAuYqi\nLgA7vDzlcQAvuweFEAVCiL1CCG9Fl99zIN8bGXXgk7PqvlVZqTGYm8G934gm6hrqwZmWC0qsKHU+\n0iLHupWsLlI/9HA6NRz2sDUHUSizWCxYliSU2ODoEMqbzhmUEREFq6Aq4Fy+AWCXEEKZwiiEeBpj\nhdUeD8fsBfCs6/vtjHeQLPRDDuRjpVXX0T9kV2JbVubBYuH0SaKJjlw9BafmVGJb8m9tTlxSEI8w\nm3rfHCptmJXciALJcrcCDhjbE46IyJeCroCTUu4H8DyAQ0KIVUKIJFfhtAfANi+dIfdhrLDa5/6A\nEOJxIUSZEKITwEuu8NNCiE5X/Fkf5UA+9r6HN5hbVuUZkAmRublPnwyzhmHTnDU3f46NsmHt4izl\nObWN3bjS3DMr+REFirSoZBQkz1Vi5c3n0TPc5+UIIqKpC7YulAAAKeULQoiXAewCsB1ArZTS66iZ\nq+DaP9XHfJkD+VZX7zBKq64rsQV5iZiTGY+qDoOSIjKhq13XcKVLnQ65OmcZ4iLV5iVbV8/BsXPN\nSuyD0gZ87eElfs+RKJBsnrcOtZ23Gv04nA58cvUUPrVwq4FZEVEwCcoCDgBco1yGrjUzQw6h6sPy\na3A4NSW2be1cL88mCl2Hr5zQxSZOnxy3pjgT8TER6B0YuRn7sLwBX/n0YnZ1JZpg87x1+PnZN+CY\nMC35w7pjLOCIyGeCbgolkaZpOHRKbXMeZrPinpWcPkk0kcPp0K3PiY+Mw4os/ahaeJgVW1bmKrGO\nnmGcvXjDrzkSBZqEqHisylmmxOq6GnClk41/iMg3WMBR0KnxsDZn/ZIsJMRGGJQRkTmdu16NriH1\nXrlr7hqE2TxPzti6Zo4u5mmtKVGou3f+Rl3swyvHDMiEiIIRCzgKOu6jbwCwfR2nTxK5+8jD3m/3\n5m/w+vyiOUnIy4hTYsfON2NgiPtcEU20MnspEiLVe+Xjqydhd9i9HEFENHks4CiojNod+Mht8+6U\nhEisXJhuUEZE5jQwOoiTjWeVWF5CNuYne/+ww2Kx4D63UbiRUQeOVjT5JUeiQBVmtWHzPHUtae9w\nH8qbzxuUEREFExZwFFROVl5H74A6GrB19RzYbPyrTjTR8YZyjDrUe+We/PV33Cfx3lVz4P4U7glH\npHfvfP1o9od1nEZJRDPHd7UUVA56mD7J7pNEeu5vJC2wYPO8dXc8Lj05GssXpCmx8zXtaGnv92l+\nRIFuXlIe5ierI9blzed1606JiKaKBRwFjY6eIZRXq3u/ibnJmJMZb1BGRObU2NOC6rYaJbY0UyA1\nJnlSx7tPowSAAyf1H54Qhbqt8zcpPzs1J464dX4lIpoqFnAUND4sa4Db1m/Ytlb/RpMo1L1f+4ku\ndl/BJg/P9GzTshzERKmdKg+erIfD4fRyBFFoumvuGoRZ1Xvlg7pj0DTNyxFERHfGAo6CgqZpuumT\n4WFWbObeb0QKu8Ou6z4ZFxGLtbkrJn2OqMgwbHG7tzp6hlBW3eqTHImCRXxkHNbkLFdiDd1NqOvk\niDURTR8LOAoKlxq60HC9T4ltXJqNuOhwgzIiMqfSpgr0DKv3yj356xFhm9q9cv+GebrYeyeuzig3\nomDkuZmJfgsPIqLJYgFHQcHT+ptt3PuNSOeQp+mT8yc/fXLcgrwkFOQmKrFTVdfR3j047dyIglFJ\n1mIkRSUosY/rT2LEwf0TiWh6WMBRwBsctuv2fktLjEJJEfd+I5roRn87KlqqlFhR6nzMTcqd1vnu\nX6+OwjmdGt7nlgJECpvVhnvy1T3h+kcGcKLhtEEZEVGgYwFHAe/w6WsYHLYrsW1r58Jmvf1+VkSh\n5oO6o9CgNk/YVnD3tM+3ZVUeIsLUf0beO3EVTvduQkQhztMo98Hajw3IhIiCAQs4CnjvHLui/Gyx\n6EcGiEKd0+nEB7Xq3m9RYZHYNGfVtM8ZFx2Ou0pylFhL+wDO1bRN+5xEwSgnIQuL04uUWNWNy7jW\n3WxQRkQUyFjAUUC73NCFy9e6ldjqRZnISIkxKCMiczp7/QLaBzuV2F1z1yIqPGpG531gQ74uxmYm\nRHrbCzfrYgdrOApHRFPHAo4C2jvHr+hiD3rojkcU6jw1L9lWcNeMz7t4fgpy02OV2NGKZvT0j8z4\n3ETBZH3eCsRHximxj64cx4id9woRTQ0LOApYA0OjuuYlqYlRWFOcaVBGRObUNdSDssYKJTYvMReF\nKTP/sMNiseimLNsdTnxYxmYmRBOF28Jxb766pUD/6CCONZQblBERBSoWcBSwPiq/hqERhxK7f/08\n2Gz8a0000Ud1x+HQnErsvoK7YLH4ptHP1jVzdE2D3jtxFZrGZiZEE3EaJRH5At/pUkDSNA3vHFPX\n2VgtwI51nD5JNJFTc+JQ7RElFm4Nw+Z563x2jeT4KKxfmqXErrb0ovpKp5cjiEJTdnwGlmYIJSbb\na1Hf1WhQRkQUiFjAUUC61NCF2ia35iXFmUhPjjYoIyJzqmipQkvfDSW2Pm8l4iJjvRwxPZ46v771\nSZ1Pr0EUDDyPwh3x8EwiIs9YwFFAct86AAAe3Jg/22kQmd47lz/Sxe5fcI/Pr7NiYQYy3bq/flLR\niM7eIZ9fiyiQrcstQWJkvBI7fPUEhtnMhIgmiQUcBZz+wVEcPqNON0lLisbqRWxeQjRRa18bTjed\nV2LzEnMh0gp9fi2b1YKHNs1XYnaHhveOc0sBoonCbGG4d/5GJTYwOohjDWUGZUREgYYFHAWcD8sa\nMOypeYnVNw0ZiILFezWHoUFtJPJA0b0+a17ibsf6uYgIU/9ZeefYFTgcTs8HEIWobYV362IH2MyE\niCaJBRwFFE3T8PtjV5SY1WrB/evnGpIPkVmN2Efwfu1RJRYTHo2756312zXjYyJwz8o8JdbWPYQT\nlS1+uyZRIMqKS8fyzGIldqm9DrUd9QZlRESBhAUcBZSKS22ob+lVYmuLM5GayOYlRBN9Ul+KvpF+\nJXbv/I2ICov063U/ffd8XYzNTIj0tnsYhXvn0oeznwgRBRwWcBRQ3vy4Vhf79F36N4xEoUzTNLxz\n+UNd/IEFW/x+7QV5SRDzkpVYxeU21Lf0+P3aRIFkTW4JUqKTlNiR+lPoHuK9QkS3xwKOAkZzWz9O\nValTseZkxmPFwnSDMiIyp0vtdajrbFBiJVmLkR2fMSvX/4yHD1U4CkekCrPadB+q2J12HOCWAkR0\nByzgKGD87pNaaGo/Bjy8ucBvDRmIAtW7HrYOmI3Rt3F3leQgMS5CiX1Q1oCBodFZy4EoEGwrvBvh\ntnAlduDyYdgddoMyIqJAwAKOAsLA0CgOnlQXd8dGh2PrqjwvRxCFpu6hHhxrKFdi6bGpWJW9dNZy\nCA+z4YEN+UpscNiB90sbPB9AFKISIuOwea7aWKhzqBvHr5V7OYKIiAUcBYj3SxswMKR+IvnA+nmI\nigwzKCMiczpU+wnsTvVeub/wHlits/vr/sEN+XDf2eP3R+uguQ+jE4W4Ty3cqov9/uIHBmRCRIGC\nBRyZntOp4bduzUusFjYvIXJndzpw4LK6l1S4NQxbCzbNei7pydFYvzRbiTVc78PZSzdmPRciM5uX\nlIclGQuV2OWOK7jUznWjROQZCzgyvXLZiqY2tR36+qXZyEiJMSgjInM63lCG9sFOJXbX3LVIiIwz\nJB9PH7L86qMaAzIhMrdPFXkahXvfgEyIKBCwgCPTcx99A4DPbi4wIBMi89I0Db+tPqiLP1h07+wn\n47J8QRrmZcUrsfLqVlxtZpt0oonW5CxHemyqEjveUI6OgS6DMiIiM2MBR6bWcL0X5bJVic3PScCS\nglQvRxCFpspWiboutUnI0gyBgpS5BmUEWCwWPLJlgS7+q48uG5ANkXlZrVY8uOBeJebQnHiv5rAx\nCRGRqbGAI1P73RHPo2/cOoBI9VupH317eNF2AzJRbVmVi5SESCX2Ufk1tHcPGpQRkTliff/vAAAg\nAElEQVTdV7AJkWHqvXKg5mOMOLj9BhGpWMCRaXX3DeOQW9vxhNgI3LOSWwcQTVTf1YjTzZVKLC8h\nGyuylhiU0S3hYTZ85m51yrPdoeF3R9iggWii2IgYbMlfr8R6h/tw+MoJgzIiIrNiAUem9dYndRge\ncSixBzfmIyLcZlBGROb0u4uHdLGHxXbTjFR/amM+oiLU+/btY1cwOMzNiokm8tTM5M3q9+B0Og3I\nhojMigUcmdLQsF03fTI8zIrPcOsAIkXnYDc+vnpSiSVFJeDueWu9HDH74mIisGP9PCXWPziKAyev\nGpQRkTnlJmRhdc4yJdbSdwMnGk8blBERmRELODKl905cRe+AOu9/+9q5SE6IMigjInN6+9IHcDjd\nRqqL7kW4LdygjDz77OYC3cbevzlcC4eDIwtEEz1S/IAu9puq96BpmgHZEJEZsYAj0xm1O3V7RVkt\nwOfv1XezIwplQ6NDOHBZ7VIXaYvA/YX3GJSRd1mpsdi0PEeJtXYM4Oi5ZoMyIjInkVaIRWmFSqy2\nsx7nrlcblBERmQ0LODKdw6evoa1L7VB3V0kustNiDcqIyJzerzuK/lH1XtlasAlxkea8Vzx9CPOr\nDy9zZIHIjcdRuOr3DMiEiMyIBRyZitOp4fUP9HtEPbaVo29EEzmcDrx18X0lZrFY8OmF9xmU0Z0t\nnJus28PxUkMXzte2G5QRkTmtzF6KOYnqiPW569Wo6eC6USJiAUcmc+pCCxqu9yqxVSIDhXlJBmVE\nZE5Hrp7CjX618FmftxKZcekGZTQ5j3oYhXv14EUDMiEyL4vFgkcWeV4LR0TEAo5MQ9M0vPb+JV38\nsfs4+kY0kdPpxBsX3tbFPyt2GJDN1KwpzkReRpwSO3PxBqqvdBiUEZE5bZq7GukxKUrsxLXTaO5t\nNSgjIjILFnBkGpW17ZBXO5XYwrlJWFaYZlBGROZ0tKEUzX3qm7iSrGIsSM03JqEpsFot2LV9oS7+\nywPSgGyIzMtmteHhReqHMho0vFl9wKCMiMgsWMCRaXha+/b4fUWm2YyYyAycTide9zD69tjiTxuQ\nzfTcs0LflKisuhUX6zu9HEEUmrbO34T4SHXE+qMrx9Ex2GVQRkRkBizgyBQu1neitOq6EstNj8P6\nJdkGZURkTsevnUZjT4sSW5ohsCi90MsR5mOzWbFrm34Ubt8BroUjmigyLAIPFW1VYnanHW9yLRxR\nSGMBR6bwi3f1+9s8tnUBrO47/xKFMKfmxOsXfq+LP77kIQOymZl7V+chIyVGiZ280IKaaxxZIJro\ngaItiAqLVGIHaj5GxwDvFaJQxQKODFd9pQNl1ep6nsyUGGxdM8egjIjMqbSxAg3dTUqsOL0IizP0\no1lmF2azYte2Il18HztSEiniImLxYNG9SmzUaccbVfqp1EQUGljAkeH+8x396NsTOxYizMa/nkTj\nNE3D/sq3dPFAHH0bd9+auUhLilZix84140pzj0EZEZnTw2I7osOilNih2k/Q1s/urUShKMzoBPxB\nCJEE4DkABQA6AKQAOCClfHk2zieEeBzAbgAvAah1fQHAdld8j5SyfDq5BJvzNW04c+mGEstOi8XW\n1Rx9I5qorOkcrnRdU2IitQBLM4RBGc1ceJgVO7cV4YevVyjxfQck9nxlrUFZEZlPfGQcHlp4nzKF\n2uF04I0Lb+PptV82MDMiMkLQDXG4iq0yADVSyp1Syt1Syp0AdgohXpql86VgrFh7zXVsp+vrNQCv\nsXi75Rfv6luHf/F+ARtH34hu0jQNr1fq1749tuTTAd+ldce6uUhNVEcWPqloQn0LR+GIJvqM2IaY\ncHXE+oO6o7jed8PLEUQUrILxXfIrAGo9jI7tBPC0a3RsNs5XDmB8hXEtgP0ACqc7ChiMKi7fwLma\nNiWWmx6He1bmGZQRkTmVNlWgpvOqEluQko+SrGKDMvKd8DAbHtuqroXTNM8f7hCFstiIGHxGbFdi\nDs3ztiJEFNyCqoBzjZY9jrGRLoWUsgvAQYxNYZyN8z0vpUyWUlqklIWu0btaL88NOZqm4edv69e+\nfekBARs7TxLd5HA68IuKX+vijy95KOBH38bdv2EekuPVLnufVDRBXuX6HqKJHlq4FXER6h6Kh6+c\nQHNvq5cjiCgYBVUBB2CX67u3QqkWY1MbjTofuZy+eANVV9Q3Z3Oz4nF3Sa5BGRGZ00dXjuv2fStK\nycfK7KUGZeR7keE27Nqu76T5k7eqoGmaARkRmVNMeDQ+u2iHEnNqTo8NjogoeAVbATf+W81bwVUD\nAEKIyRZdvj4fYWz07RceOk9+6YFF3PeNaIIR+whePf87XfzLJZ8PmtG3cQ9syEdWqrov3LmaNpRL\njiwQTfTggi2Ij4xTYkeunsK1nmaDMiKi2RZsBVyB67u3eTfja9JWzcb5hBBPCyH2ur5eEkI8Pcnr\nBrWj55oh6zuV2PycBGxcmm1QRkTm9PalD9ExqG7WuzJ7aUDu+3Yn4WFWPPmgfk3fT966AKeTo3BE\n46LCo/C5RfcrMQ0aflHxG4MyIqLZFmwFXBJwc33a7aTOwvmew1jzkz2ur90Y61ypW08XSkbtTvzk\ndxd08S9z9I1I0TfSj19XvaPELLDgS8s/Z1BG/rd5RS4KchOVWF1TDw6fvublCKLQ9MCCLUiMSlBi\npY1ncaH1okEZEdFsCrYCLuUOj4+PpCX5+XylAL4hpTzoFt8D4PFpdMIMGm99Uofm9n4ltmheMtYt\nyTIoIyJz+nXVe+gfHVRim+etw7yk4O3SarVa8NVPL9bFf/ZONUbtDgMyIjKnyLAI7FzykC7+kzP7\n4dScBmRERLMpKDfyNpq3fd6klOVCiC4AezG2rYBPVVVV+fqUPjUw5MAv3q3TxbeVxKG6Wr8mzl8G\nBwdvfjf7n1ko4etyS/dIL34vDykxm8WKVdHFs/pnY8RrEqVpWJATg8tNAzdjrR0D+PGvTuDupcmz\nkoPZ8V4xHyNekxwtDemRybgxfGtJQl1nA1499muUJAf+FiNE5F2wFXAduP3o2viI2p2mRPrrfMBY\nQ5RVQogCX28rMDAwcOcnGeidsi4MDqufDC6ZG430OM2Q3DXNmOvS7fF1AQ62fgK7po44rUxYjEh7\nGAbswX+vbF0WpxRwAHDwdDsWzwlHVHiwTRyZPt4r5jPbr8mWlLXY3/yeEjvQfBT54bkItwbbWzwi\nGheUd7cQImkS69aMOt/4tMsCeO9uOS0xMTF3fpJB2rpHcOpSnxKzWS14eGMWYmLCZzWXwcFBaJoG\ni8WC6OjoWb02ecfXZcz1oXac67mkxCKt4bgvdyNiwmb3z8Wo16QoJgbL5w+gou7W74yBYSdOXhzC\ng2vTZi0Ps+K9Yj5GvSZLowXKe6tQ29dwM9Zr78eZfoktmWtnLY+p4gcPRDMTbAXceJGVAs+jYuOj\naTX+Op+r0+ReADs9rIHzdKzPFBebd8rEd398Eg63afmfu6cQd61bMuu5VFVVYWBgANHR0ab+Mws1\nfF3GPr1/9cN/gAa16+Ijix/EmiWTbZ7rO0a+Jn+SNgd//ML7cEzoQHn4fBeeeGgVstNib3Nk8OO9\nYj5GvibPZMdjz3vPK783jraX44n1n0NSdOJtjjROWVmZ0SkQBbRgm4syXjB5K47Gu0WW+vF8O13P\n9/Zua3zapcd1csGosrYdx86p+9PEx0Rgp4eNe4lC2bGGclS6dZFLikrAp8U2gzIyTk56HB7YME+J\n2R1O/Og35w3KiMic8pPnYEv+BiU2ZB/2uIckEQWHYCvg9rm+F3h5vADw3mTER+crB7BbSvmCl2NW\nuY7x6fRJs3I6Nfzbm/o3XF96QCAuenanThKZ2ZB9GD8787ou/mTJo4gKizQgI+N9+cFixLtNsT55\noQWlVdcNyojInJ5Y9llE2iKU2KG6T1Df1WhQRkTkT0FVwLkKqS4AO7w85XEAL7sHhRAFrs22lUJt\nmufbBy8jdkKI7a7/3OPlfEHn/dJ6XGpQZ5/mpsfhwY35xiREZFK/uvAO2gfVDe5FWiE2z1tnUEbG\nS4iNwJOf0k9He/nX57itANEEKTFJeHjRdiWmaRr+4/Sr0DTNy1FEFKiCqoBz+QaAXUIIpYhyrU3r\ngufiaS+AZ13fZ3Q+V9G3VgjhaQrlXoxt7u1tdC6odPcN499/q9+0+2ufWYwwWzD+1SOanpbeVvzW\nbcmsBRb80aovwGIJ7Q3uH9iQj4IcdR1Pc1s/fv3RZJcyE4WGz4odSHLb3Luy9SI+vnrSoIyIyF+C\n7l20lHI/gOcBHBJCrBJCJLmKrT0AtnnpJrkPY8XYPvcHpnM+KeVOAM+5RvW2CyGeFkKUYax4K/TZ\n/6zJ/eStC+gdGFFiK4rSuWk3kZsfn34Ndqddie0o3Iz5yXMMysg8bFYLdj+6TBffd/Ai2roGPRxB\nFJqiwqPwpeWP6OI/PbMffSP9BmRERP4SdAUcALhGuLYBWAPgaQAdUsrC22ywvV9Kmewq1mZ8Ptcx\nOwG8hLF1ch0Y60q5cyb/X4GksrYdB07WK7HwMCu++djykB9RIJqorOkcypvVdaLxEbF4YtlnDcrI\nfBbPT8XW1XlKbHjEgX//baVBGRGZ05b8DVicXqTEeob78IuK3xiUERH5Q7BtI3CTa2RMt95tNs/n\nalTisxwChd3hxA9eP6uLP35fEXLS4wzIiMicRhyj+HH5q7r4E8s+h7jI0G6V7+4PP7MEx8+3YHD4\n1kjlx2ca8eDGeVi+IN3AzIjMw2Kx4Kk1X8RfvPu3cDhvrRM9VHME9+ZvwMI0bz3ZiCiQBOUIHBnr\nNx/VoL6lV4llp8Xi8fuKvBxBFJreuPA2rve3KbH5yXOwreAugzIyr5SEKHzxfqGL/2B/BUZG2dCE\naFxeQjYeFm4NTaDhlbL/Uoo6IgpcLODIp653DOAX70ld/JuPLkdEuM2AjIjMqa6zAb+uelcX//qq\nJ2C18lezJw9vLsCcTHUUv/FGH/7Lw+8colD22OKHkB6bqsSudl3D25c+NCYhIvIpvksgn9E0DS/9\nSv9p+D0rcrFSZBiUFZH52J0O/PDkT+HUnEr83vkbOcXpNsJsVuz+/HJd/I0PL+NSQ6eHI4hCU2RY\nBL6+6gldfN/536JtoMOAjIjIl1jAkc8cOduEUxfUDXZjosLw9c8tNSgjInN6s/o9XOm6psSSoxLx\nlRWPGZRR4CgpSscDG+YpMadTwz/uO4NRu9PLUUShZ1XOUqzPW6nEhu3D+FHZL7k3HFGAYwFHPtHR\nM4Qfemhc8pVPFSMlIcqAjIjMqaG7Cfsrf6+LP7Xmi4iLYOOSyfjaZ5YgNVH9vXKluQf7D100KCMi\nc/rDlTsRFRapxMqbzuGDumMGZUREvsACjmZM0zT806tn0DswqsQXzEnCg5vmG5QVkfk4nU788OTP\ndHu+bZq7BmtzSwzKKvDERofjTx7X/3ntO3gRdU3dBmREZE6pMcn4wtKHdfGfnH4Nrf3tBmRERL7A\nAo5m7MDJepRWqVMnw8Os+NYTK2Gzcs83onFvXXwflzuuKLH4yDj80cpdxiQUwNYuztLtDedwavjH\nfafhcHAqJdG4TxVtRXH6AiU2aB/yuA6XiAIDCziakesdA/jRb87p4l95qBhzsxIMyIjInJp7W/HL\n82/q4l9f9QUkRMUbkFHg+8Yjy5AUr04Pu3ytG298eNmgjIjMx2q14o/XfQWRblMpK1sv4h12pSQK\nSCzgaNqcTg3/8MtyDA6rXSeXFqbis5sLDcqKyHzsDju+f+zfMOpQpxmvzS3BxjmrDcoq8MXHROCb\nj+q7Uv7i3Wp2pSSaIDMuHV/10CTpPyt+jcaeFgMyIqKZYAFH0/bmx7U4X6POoY+OtOHPvrASVk6d\nJLrpFxW/Rm1nvRKLDY/GU6u/CIuF98pMbFqeg7tKcpSY3aHhxZ+VYWBo1MtRRKFnW8HdWJm9RImN\nOkbxzyd+zA2+iQIMCzialqstPfjp7y/o4l//7DJkpbKTHtG4083n8buLh3TxP1r1BJKjEw3IKPg8\n8/nluqmUze39+MH+CrZLJ3KxWCzYvfZJxEbEKPGajqt448LbBmVFRNPBAo6mbHDYju/95JRuz6U1\nxZm4f/1cg7IiMp/OwW78y4mf6OL35K/H5vx1BmQUnJLiI/GtL67SxT86fQ2HTjUYkBGROaVEJ+Gp\n1foNvvdf+D3OXa82ICMimg4WcDQlmqbhn189g2utfUo8PiYcf7prBaeDEbk4NSf++cR/oGdYvVey\n4zLw1Cr9GyiamVUiA49tXaCL/+uvKnCttdeAjIjM6a65a3VrbzVNwz8e+3d0DHQZlBURTQULOJqS\n3x+9gsNnGnXxP921ght2E03wm6r3cO66VGI2qw1/tvHriArnveIPT36qGAvnJimx4REHXvxZGUbt\nXONDNO6p1U8gLSZFiXUP9+Ifjv0Idq6HIzI9FnA0aRfrOz1uGfDIlkJsXJbj4Qii0FR9owb7zv9W\nF/+DkkdRkMJpxv4SZrPiL55cg5ioMCVe29SNf3+z0qCsiMwnPjIO39r0FGxWmxKvbqvBL8/9xqCs\niGiyWMDRpPT0j+B7Pz0Fu0NtCFCcn4KvfnqxQVkRmU/7QCf+7ujLug1yV+Usw6eKthqUVejISo3F\n//X4Cl38d5/U4eDJqwZkRGRORanz8dUVj+vib1YfwMlrZwzIiIgmiwUc3ZHTqeHv/6scNzoHlXhi\nXAT2fGUNwmz8a0QEAMP2Ebx45F/RPdSjxJOjE/HH677CNaKzZPPKXOxYpx/p/Jf9Faiq6zAgIyJz\nemDBFo97Uf7g5E/R0nfDgIyIaDL4zpvu6PCZRpRWXVdiFgvw7S+vRmpitEFZEZmLpmn44amf6fZ7\ns1ms+LMNf4SEyDiDMgtNTz+yDPnZCUrM7nDiuz85qfswiihUWSwWPLP2SeTEZyrxgdFB/HvZLw3K\niojuhAUc3VHpheu62JceWIQVCzMMyIbInH5V9Q6O1pfq4l9btQuLMxYakFFoi4oMw19+bR3iYyKU\neFfvMP7mP05gaMRuUGZE5hIdHoX/tukbiLCFK/GK69UYdYwalBUR3Q4LOLqjBXPUrm6rRAZ2beMb\nUqJxpxrP4pfn3tTFdxRuxv0LthiQEQFj6+Ge++pa2Kzq1NXaxm58/5enuck3kcvcpFw8vebLSmxe\nYi7C3Yo6IjKHsDs/hULdw3fPR9/ACCout6FoThL+4KFiWK1cy0MEAPVdjfin4/+hiy9OL8LXVu4y\nICOaaNmCNOz+/DL84PUKJX7kbBPysy/iCzuEQZkRmcs9+esRYQvHWxffR0JkHH9/EZkYCzi6I5vN\niic/VWx0GkSm09rfjr89/E8Ysg8r8fTYVPy3Td9AmI2/Ys3gU5vmo665B28fvaLEf/5ONVISorBj\n/TxjEiMymQ1zVmHDnFVGp0FEd8AplERE09A11IO/+fD76BzsVuKRYZF49u5nkBAVb1Bm5MnTjyzD\nssI0XfyfXzuDoxVNBmREREQ0PSzgiIimqH9kAH/70T/p2mxbYMGfrv9DzEvKMygz8ibMZsWer6xB\nZkqMEndqwIs/L8PZi2yZTkREgYEFHBHRFAzbR7D34x/gatc13WNfX/0FrMvTbyJN5pAYF4n/uXsj\nkuIjlbjd4cTf/McJXKzvNCgzIiKiyWMBR0Q0SXanA//76CuobqvRPfbEss+y42QAyEmLw/98eiNi\no9T1iUMjDvx/rxxDfUuPlyOJiIjMgQUcEdEk2B12fP/Yv+F083ndY59euA2fL37QgKxoOubnJOKv\nvr4BEeE2Jd47MIq/eukoGq73GpQZERHRnbGAIyK6gxH7CF785F9x4tpp3WNb8jfgD1Y8CouFW2sE\nkiUFqR73iOvoGcZ3/uUIaq51GZQZERHR7bGAIyK6jcHRIXz38D/jdHOl7rE1uSV4Zu2TsFr4qzQQ\nrSnOxLe+uArutXdP/wj+8oefoKquw5jEiIiIboPvOoiIvOgb7sf/+vD7uHDjku6xkqxi/PnGr8Nm\ntXk4kgLFllV5+OPHSnRFXP+QHf/95aPsTklERKbDAo6IyIOuoR789Qd/j8sdV3SPrctdgWfv/iYi\nbOGznxj53IMb8/GtL66C1W065dCIA3/9b8dxsrLFoMyIiIj0WMAREbmp72rEXx58AVe7G3WPbZ63\nDt/a9BTCWbwFla2r5+A7X1mDMJtaxI3anfjbH5/E747UQtM0g7IjIiK6hQUcEdEEZU3n8P8eehE3\n+tt1j+0o3Iw/Wf9VTpsMUhuX5eCv/kjfndLp1PDSr87hh69XwO5wGpQdERHRGBZwREQANE3Dm9Xv\n4YWPf4gh+7Du8YfFdjy1+otsWBLkVi3KwF9/YwOiI8N0j7197Ar+x8vH0NM/MvuJERERufCdCBGF\nvFHHKH5w8qf4+dlfQYN+mtyXlj+CJ0u4VUCoWFqYhr/95iYkx0fqHqu43IZvf/8w94ojIiLDsIAj\nopDW0tuK//7+3+GjK8d1j0WGReLbd+3GI8UPsHgLMUVzkvG//3wLCvMSdY81t/fj//7+YXxUfs2A\nzIiIKNSxgCOikHX4ygk8+953UdNxVfdYakwy/td938a6vBUGZEZmkJYUje/9yd24qyRH99jgsB3/\n/3+W4e//qxwDQ6MGZEdERKFKP8mfiCjIDYwO4kdlv8SRqyc9Pr4wtQDfvns3kqISZjkzMpuoiDA8\n++Qa/DJT4r/ek7rH3y9tQNWVDvzFk6tRNCfZgAyJiCjUcASOiELKxbZa7Hn3u16Lt3vzN+J/bP1z\nFm90k9VqwZceWIRn/2ANoiL0HUib2/rxF//4Mfa/fwkOJ7caICIi/+IIHBGFhIGRQfzi3K9x4PLH\nHhuVRIVF4qnVX8Q9+esNyI4CweYVuSjITcSLPy9FzbX/096dxsZx3ncc/81ePESRFHVTl0VaenT4\niCVfipM4isW0Sdw4NSQFLRCgRSu5QNGiQFCrbt/0TVvILVC0RQtYRosWRdC4EtLUzWnJSWzHshNF\nsi0f8iNLlGSd1kHxErncY6YvZpaipF2Kovaa5fcDEM9wZnb0t4dc7m+eeZ7pu2Zb1vX0H9//QK+/\nc1p/uPFTunNRa4WqBADUOnrgANQ0z/P0xsn9+pMf/qVeOvJq3vDW2bZEz37xzwlvuKkFs5v0t3/0\nWX3t0c6824+c6tM3/+EVPf/ddxkbBwAoCXrgANSs84MX9a8HXtBbZ9/Lu92Ro6+u6NLX7/oNxaK8\nHWJi4rGofu+rd+m+5XP0998+oN6Ba58b6HrSi691a+/BM9r6m3fr4bvmM4spAKBo+MQCoOb0jwzq\nOx/8UC8deVUZN5N3n9mNbfqDB7+hu+euKHN1qBVrVszRP31zvf5519t6871zN2y/2JfUX//7Pq3u\nmKnfeXyVVixpq0CVAIBaQ4ADUDOS6aS+d/gn+r8Pd2s4k8y7T8SJ6HGzQRtXf1n1sRsf1Azcitbp\ndfqL331Ib7x7Vjv+56Au9t34c/d+9yX96T++pnV3z9c3vrRSi+ZOr0ClAIBaQYADEHrJzIh+2r1X\n3zn0I/Ul+wvut2zmUm29/7e1pHVhGavDVLDu7vm6d9ksfevHH+p7r3Ur32SUb7x7Vr9476wee2Cx\nNj62TO2zmspfKAAg9AhwAEKrL9mvH330in585BUNpq4U3G9avEG/dc/XtKHzM4o4zN2E0misj2vL\nE3dr/dpF+pdd7+ijk7037ON60u5ffqw9+z7Wurvn68nP3ynDrZUAgFtAgAMQOmcGPtH37cv62fE3\nlc4WnukvHo3ry8vW64mVX1RTYloZK8RUdufCVv3dH39Or79zRv/5w0M6e+nGiwueJ+09eFZ7D57V\n6o6ZenL9nVq7Yq6iESY7AQCMjwAHIBRSmZTePPWWftL9uj648NG4+zqOo/VLP61Nq7+imY0zylQh\ncFUk4uiz9y3Qunvm68dvntC3d9sbZqvMeb/7kt7vvqRZrQ3qenCxNjywWHPaGstcMQAgLAhwAKqW\n53k62nNCPzv+hn5+Yp+G0sPj7u84jh5aeJ823/W4FjbPL1OVQGGxaERfeWSpvnD/Ir346lH976vd\nGhhK5d33Yu+w/uslq2/vtrp32Wx98cElemD1XNUn+FMNALiKvwoAqornefro0jG9efKA3jz1li5c\nuXTT18Sjca2/Y50eN49p3vQ5ZagSuDUNdTF9vcvoic91as++j/XdV47qk56hvPt6nvT24Qt6+/AF\n1SWiun/lXD1yT7seWDlX9XX82QaAqY6/BAAqLpkZ0eH+4/rw8lEdGTqhvncHJ/S66Ylp+rVlj+rX\n7/y8muuZmh3Vr74upsc/06EvrbtDe989q+/89CMdOdVXcP+RVFavv3NGr79zRol4VGtXzNGCVleL\n2hw1cpclAExJNRngjDGtkp6R1CGpR1KbpN3W2h3lOl6xawBqieu6OtF3WgfPHdI75z7QhxePFnzg\ndj6r5yzX+qWf1sML71MilihhpUBpRKMRffZTC/SZe9t1+OPLeukXH+u1t09peCRb8DWpdFZvvHt2\n9Ps5rT16+J6M7ls+R6uWtqmxPl6O0gEAFVZzAS4ITvslbbfWbhuzfrcxZq219qlSH6/YNQBhN5xO\n6qNLx2QvHpW92K2PLh0r+KDtQmbUt+jRpQ/rC0s/zW2SqBmO48gsaZNZ0qbff+Iu/fzt09r9y491\n6HjPTV97vjelF1/t1ouvdiviSHfMb9GKO2Zo5dKZWnVHm2bPaJDjMKslANSamgtwkp6X1J2np2uT\npMvGmN3W2l0lPl6xawBCoy/Zr+O9p3Ts8kkdv3xSx3pP6tzABXnK82Tjm2ipm64HF35KDy9ao1Wz\nlykaiZagYqA6NNTF1PXQEnU9tERnLgzq9YNn9PrBMzo6zi2WOa4ndZ/pU/eZPv1g73FJUktTQh3t\nLepYcPVr/qwmHlUAACFXUwEu6PnaKOmGHi5rba8xZk+wbULhaTLHK3YNQDUayai6WV8AAA/0SURB\nVKR04colfXLlos70f6LT/Wd1euATnek/p4FxHqg9Ec3xJq1bslYPL1qjlbPuVCTCg7cx9bTPbtKm\nx5Zr02PLde7SFe09eEZ7D57V4ZOX5U3wWkjfYEpvHb6gtw5fGF0Xj0XUPmuaFs6droVzmrRwznS1\nz5qmuW2Nap6WoMcOAEKgpgKcpM1B211ge7ekrSU+XrFrAMoqnU2rb2RAPUO96hnOffWpZ+iyzl+5\npPNXLqo32V+0fy8RjWv1nOWaqzYtiM/RopZ2rVq1qmjHB8Ju3sxpenL9Mj25fpn6r6T0g5+9rQ+O\n96n7XEp9QxMfOypJ6YyrE+cGdOLcwA3bGuqimtvmh7nZrQ1qa6nXzJYGzWyp18yWerU116uhLkbI\nA4AKq7UA1xW0hcLTUUkyxmyw1u4p0fGKXQNwy1zPVSqT0lAmqeG0/zWUHtZQeliDqSsaTA0FX1c0\nOHJFfSMD6k8OqG9k4KbPWrtdjfEGLZ+5VMtndWrFrA4tn9WpRDSuQ4cOaWhoiA+HwDiapyV0b8d0\nLZsXVUNDg5raFur9Yz06dOySDh3v0blL+R9NMBHDI1kdP9uv42cLX6CJxyJqaapTa1NCLU11ammq\nU1NDXE2NCU1vjI8uN9TF1Fgf07T6uBrrY2qoiykapTcdAIqh1gJcR9AWGv3dG7RrJE0kPE3meMWu\noaZ5ee4FyjtWKu8q78ZNnje6zbthnS/lppVy04pmUxpOJ/09vdxrxi77r/XkyfM8ucE2V27QevI8\nd3Sbm1v2XLmev831PGW97Oi6rJuV63lyvayynqusm1XWyyrrusq4WWXdrDJuxl/2skpn00q7GaWz\nGaXdtDLZjFJuRqlsSulsWqlsWqlMSiPZtJKZpEYyKSWzKY1kRiZxNoovHo1rcUu7lrYu0tIZi2Vm\ndWhh83xuiwSKwHEcLZ7XrMXzmvWldXdIknr6kzp0vEdHTvaq+3Sfuk/3qXeweO8H6Yyri73Duth7\n6xd64rGI6hNR1SViaqjz27p4VIlYRIl41F+ORxWPRUa/YrnlaESxqP99NBJRPOYoGokoGnUUjVxd\njjjOaBuJ+NsiEUeOEyw7jhxHiowuB9+PWfa/gmU5130vyXHk+M2okbSrVMZVLO0qmcqMXojK7XJ1\nX+ea111dnf/CVb61+XblwhcwtdRagGuV/LFmN9lvZgmPV+waKi6VTWvHvm9p3+l3bnnmwKr3fqUL\nqA1RJ6J5TXPU3jxXC5rnaWHzfN3RulALmucx8QhQRm3N9XrknnY9ck+7JP8iWU9/Ut2n+3T8bL9O\nnR/UqfMDOnV+UEPJW7v98nalM67SGVcDQ+my/rvld6TSBdwWx5HM4hna8rW7tXzxjEqXAyCPWgtw\nbTfZnusVay3h8Ypdw4QdOnSo2IeUJP303Jt69fwvS3JshEd9JKGWRLNmJJrVGrQzEs1qS7Sqra5F\nUWdMUBuWrgz36/A4t2Jdb3h4eLQt1c8ybg3npDpN5rw0OdJd7dJd7Q2SGuR5szUwnNX53pQuD6TV\nM/ZrMK3Boewk5o1FLfA86cMTl/VX//aG/uzrSytdDoA8ai3ATWlDQ5Mf+zCeS8M360xEWMWdmOqj\ndWqM1qsx2jDaTovWqynWqKboNE2PTVNTrFGJSIGHBLvSyHDxbtHyPK9kP8uYHM5Jdbrd8xKT1N4q\ntbfGJV37+511PQ0msxoYyqp/2NXAUFaDyayuJF0NjfjtYDKr4ZSrZIqoV4suD6b5vQeqVK0FuB6N\n37OV6x2baCKZzPGKXcOENTY2FvuQkqS1s1frvYHDXI2tsKgTUcyJKubEFIvEFI/EFHOifhuJKRGJ\nKxFJKBGJKR6JKxGJqz5ap7pIQnXRhOoiCdVHE6qP1qkhWq+GaJ1ikep5CxgeHpbneXIcRw0NDZUu\nB+KcVKtynZfpTdL8Ceznup6SaVfDI1kNjbhKprJKplwl065GgjaZ8m+fTGW80fFiqbSndNZVJuMp\nnfX8WyyznjJZT9nsZJ4ciWK6f1lzyT5XEAyB21M9n96KyBjTOoExaCU9XrFrmIiVK1eW5rhaKdNp\n9KvTB5Wc4OQYtzScOs/g6/wDt/OuvWH/sfs5ue1jBpBfvHhRmXRG8Xhcs2fPDgajO6N7Xx187owu\nRxxHjiLBcfz9Ik5EjuMo4kQUCV6fW861juMo6kTHrPeXo5GIok50TBtVLBK0TlSxSMwfqB+JKxaN\nKRbxX1fLcrNQNjQ0lOxnGbeGc1KdpsJ58TxPWdcPdal0VlnXUybjKuO6ymY9ZbJBG3yfdV1lsp5c\n1/MnjMr6rZtrvWAyKteT6/mh0590SkHryXUlyZPnKfjyQ2Rusi3Xy01yFcyNNbpdunDxgtLptOKx\nuGbOmjX633Dtf1OBibsKJNV8q/O9fqIm+lLHkcySGXpw1Twl4qUZw7x///6SHBeYKmotwOUCU5vy\n93DlesaOlvB4xa6hKnS2LVFn25JKl1EUuQ8/jY2NNfvhBwDCzHEcxaKOYtGIGuqq/6PKoUMef1cA\nlE2tXdLPTctf6BbG3MyPvyrh8YpdAwAAAABIqr0A90LQdhTY3iFJ1toDJTxesWsAAAAAAEk1FuCC\nUNQrqavALhsl7bh+pTGmwxiz3RhzTeiazPEmWwMAAAAA3ExNBbjAFkmbjTHX3MJojNkqP1hty/Oa\n7ZKeDtpiHG8yrwEAAACAcVX/yOBbZK3dFfSkvWyM2SKpW9Jm+aHpsQIzQ74gaYOu3v54W8ebZA0A\nAAAAMK6aC3CSZK191hizQ35o2iCp21rbOc7+uyTtKtbxJvsaAAAAABhPTQY4SQp6uYo21mwyxyt2\nDQAAAACmtlocAwcAAAAANYkABwAAAAAhQYADAAAAgJAgwAEAAABASBDgAAAAACAkCHAAAAAAEBIE\nOAAAAAAICQIcAAAAAISE43lepWvAbdq/fz8nEQAAhMratWudStcAhBE9cAAAAAAQEvTAAQAAAEBI\n0AMHAAAAACFBgAMAAACAkCDAAQAAAEBIEOAAAAAAICQIcAAAAAAQEgQ4AAAAAAgJAhwAAAAAhAQB\nDgAAAABCggAHAAAAACFBgAMAAACAkCDAAQAAAEBIEOAAAAAAICQIcAAAAAAQEgQ4AAAAAAgJAhwA\nAAAAhAQBDgAAAABCIlbpAgAA1cMY0yrpGUkdknoktUnaba3dUdHCgJAwxjwn/3dmV6VrAVCbCHAA\nAEmj4W2/pO3W2m1j1u82xqy11j5VueqmLmNMh6TtklrlB+tuSTsJ1dXHGLNG0lZJuytdC4DaxS2U\nwDiMMc8ZYzZWug6gTJ6X1J0nGGyStJXfhfIzxmyQH962WGu7rLWdknZKes4Ys7+y1SGP5ytdAIDa\nR4ADChhzJRUVYozpMMbsDHqAjgYt56QEgt63jfLDwTWstb2S9kiiB678tllrNwXnQJIUBOxtktYE\nt+uhCgTvTb+qdB0Aah8BDiiMK6kVRM9D2W0O2u4C27slbShTLdBoIMgb0Ky1zwaLW4PwjQoKzkGn\nuHUSQBkQ4IA8uJJaFeh5KK+uoC0U4I5Ko8Ea5dElaec4t67mztX9ZaoHhW2X9DeVLgLA1ECAA67D\nldTKo+ehIjqCtqfA9lyQXlOGWnCtrgLrc+eE34MKCi5q7B97sQkASokAB9yIK6mVR89D+bVKo+Pd\nxjOzDLXAt0V+j/O2AttzobtQrynKYxMzggIoJx4jAIwx9kqqMabS5cAPcvmepUTPQ/G13WR7rmeO\n/+dlEoTpZ/NtCyZZapU/a+iBshaGUcaYp+Vf9AOAsiHAAdfaxLOuqsIWSfskFbqqTc8Dprpngpb3\nqwoJns8301rL+xCAsiLAAQGupFYPeh4qokfj967leugY51NhwZ0CGyU9a63dU+l6prBtXPADUAmM\ngQPEldSQoeehhJgYproF52enpB3W2kJj41BiwfhcJroCUBEEOMC3jQ9D1Y+eh5LK9awVGguXC3ZH\ny1ALCtsp6b/p+am4LmttvvG5AFBy3EKJUDLG7JT/QX4yDlhr1445FldSQ4Ceh5LbI/8RAYV64HKz\nT/J8xAoJnn3YTXirrOBC0gZjzP48m3Pjc7cbY56RpLF/bwCgGAhwCCVr7abJ3uqVZ5r0Lj4Q3b5i\nhuoC6HkorRckPS3/A2i+sYUdksS4w8oIxujq+p//4H2wjdu/yyfo/e/Mt23MWOpt9NABKBUCHEKr\nGA9N5Upq8RQ5VF+DnofSs9YeMMb0qvCjGzaq8KygKKHgfaqzwM//ZvmzsRLgAGCKIMBhSuNKanEV\nI1Rfj56Hstoi6XljzLax59IYs1X+GDluXS2zYNbV8R5v0iX/vKE65G41vtlzFQFg0ghwAKoWPQ/l\nZa3dFczI+rIxZov8/7eb5Qe3x0oR0FFYcJHi5WB5c55dWiW/97ucdeFGxpjd8u/ayN258ZwxZpuk\nPdw5AKDYCHBAYVxJrSB6HirDWvusMWaH/OC2Qf6tq3l7qVFyz2v8Z/NJ+ccrosystV2VrgHA1OF4\nnlfpGoCqkudKquT3RHAltUyCnodj4+yS63lwylMRAABAdaAHDrgOV1KrAj0PAAAAedADBwAAAAAh\nEal0AQAAAACAiSHAAQAAAEBIEOAAAAAAICQIcAAAAAAQEgQ4AAAAAAgJAhwAAAAAhAQBDgAAAABC\nggAHAAAAACFBgAMAAACAkCDAAQAAAEBIEOAAAAAAICQIcAAAAAAQEgQ4AAAAAAgJAhwAAAAAhAQB\nDgAAAABCggAHAAAAACERq3QBAIDqYYx5WlKnpLZg1RZrba8xZquktZJ6JbVK2mat7a1QmQAATFn0\nwAEAJEnGmOck7bHWPmWt3RSs3hmEtx5r7VOS9knaKumZStUJAMBURg8cACDX87bTWntgzOp9krZL\n6h0T6J4K2t3lrA8AAPgIcAAASeqy1j573brOoH1hzLpNktqstd3lKQsAAIxFgAOAKc4Y0yppW55N\n9wftntyKYNwbY98AAKgQx/O8StcAAKhCxhhPUre1tvOmOwMAgLJgEhMAwA2MMWuCxT3j7ggAAMqK\nAAcAyGdD0DJZCQAAVYQABwDIpytob+iBM8ZsLHMtAAAgQIADAMgY0zFmuVV+D1zv9Q/rDp4JBwAA\nKoQABwBTnDHmsqSjQXCT/Ad1S1JPnt27rLW7ylMZAAC4HgEOAKawILS1Stpjre0Nvu+U/7y3jlyo\nM8a0GmOeU/7HDQAAgDLhMQIAMMUFt0WuHbNqWxDmtsoPcrmHdm/nAd4AAFQWAQ4AAAAAQoJbKAEA\nAAAgJAhwAAAAABASBDgAAAAACAkCHAAAAACEBAEOAAAAAEKCAAcAAAAAIUGAAwAAAICQIMABAAAA\nQEgQ4AAAAAAgJAhwAAAAABASBDgAAAAACAkCHAAAAACEBAEOAAAAAEKCAAcAAAAAIUGAAwAAAICQ\nIMABAAAAQEgQ4AAAAAAgJAhwAAAAABASBDgAAAAACIn/B04XCuKWGYABAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111d4d2e8>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 287,
       "width": 440
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,4))\n",
    "plt.plot(domain, px_class1, label='Class 1')\n",
    "plt.plot(domain, px_class2, label='Class 2')\n",
    "plt.xlabel('$x$'); plt.ylabel('$p(x|C_k)$');plt.legend(bbox_to_anchor=(1.37,1), fancybox=True);\n",
    "plt.title('Class conditional probability - $p(x|C_k)$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Marginal distribution of $x$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "px = [p_x(x, true_mu1, true_mu2, true_sigma, true_gamma) for x in domain]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAq4AAAI9CAYAAAD7DfrrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111d3cfd0>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 286,
       "width": 343
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,4))\n",
    "plt.plot(domain,px)\n",
    "plt.xlabel('$x$');plt.ylabel('$p(x)$');plt.title('Marginal distribution - $p(x)$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Posterior distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pc1x, pc2x = [], []\n",
    "for x in domain:\n",
    "    pck = p_Ckx(x, true_mu1, true_mu2, true_sigma, true_gamma)\n",
    "    pc1x.append(pck[0]); pc2x.append(pck[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAqgAAAI/CAYAAAC72yunAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEFABAADgKf8/LsTLWnN0SVcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1143fa978>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 287,
       "width": 340
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,4))\n",
    "plt.plot(domain, pc1x, label='Class 1')\n",
    "plt.plot(domain, pc2x, label='Class 2')\n",
    "plt.xlabel('$x$');plt.ylabel('$p(C_k|x)$');\n",
    "plt.title('Posterior distributions - $p(C_1|x)$ and $p(C_2|x)$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Or model is ready, let's generate some data and test it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(123456789) # do not do this in real life\n",
    "num_samples = 1000\n",
    "x = np.zeros(num_samples)\n",
    "t = np.zeros(num_samples)\n",
    "pcx = np.zeros(num_samples)\n",
    "n1 = 0\n",
    "nae = 0\n",
    "assignment_epsilon = 0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Assigning `x` to `1` for **class 1** and `0` for **class 2**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "for i in range(num_samples):\n",
    "    rv = np.random.uniform()\n",
    "    x[i] = inv_cdf(rv, true_mu1, true_mu2, true_sigma, true_gamma)\n",
    "    pcx1 = p_Ckx(x[i], true_mu1, true_mu2, true_sigma, true_gamma)\n",
    "    pcx2 = pcx1[1]\n",
    "    pcx1 = pcx1[0]\n",
    "    #we don't want a perfect dividing line for our domain, otherwise why would we need a learning algorithim?\n",
    "    if math.fabs(pcx2-pcx1) <= assignment_epsilon:\n",
    "        nae = nae + 1\n",
    "        if np.random.uniform() <= 0.5:\n",
    "            t[i] = 1\n",
    "            n1 = n1 + 1\n",
    "        else:\n",
    "            t[i] = 0\n",
    "    elif pcx1 > pcx2:\n",
    "        t[i] = 1\n",
    "        n1 = n1 + 1\n",
    "    else: t[i]=0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Plot the simulated data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAqEAAAI7CAYAAADcX0J7AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nIVREREREBvf/ASZFOYM03/8JAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114659e48>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 285,
       "width": 336
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,4))\n",
    "plt.scatter(x, t, marker='.', alpha=0.1)\n",
    "plt.axvline(0, linestyle='--')\n",
    "plt.xlabel('$x$');plt.ylabel('Class ($t$)'); plt.title('Simulated training data');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Estimating the parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n2 = num_samples - n1\n",
    "e_gamma = n1/num_samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "e_mu1 = 0\n",
    "for x_i, t_i in zip(x,t): \n",
    "    if t_i == 1:\n",
    "        e_mu1 += x_i\n",
    "    # e_mu1 += x_i*t_i\n",
    "e_mu1 /= n1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "e_mu2 = 0\n",
    "for x_i, t_i in zip(x,t):\n",
    "    if t_i == 0:\n",
    "        e_mu2 += x_i\n",
    "    # e_mu2 += x_i*(1-t_i)\n",
    "e_mu2 /= n2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def Sn(Z, ck, mu=(e_mu1,e_mu2)):\n",
    "    idx = 1-int(ck)\n",
    "    return (Z[0]-mu[idx]) * (Z[0]-mu[idx])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "e_sigma = 0\n",
    "for x_i, t_i in zip(x,t): \n",
    "    e_sigma += Sn((x_i, t_i), t_i)\n",
    "e_sigma /= float(num_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The number of inputs in C1 is 505\n",
      "The number of inputs that were assigned based on the assignment factor is 121\n",
      "True model parameters: gamma=0.5, µ1=-2.0, µ2=2.0, ∑=2.0\n",
      "Estimated model parameters: gamma=0.505, µ1=-2.069287615754436, µ2=2.095874429059065, ∑=1.7242111261175646\n"
     ]
    }
   ],
   "source": [
    "print('The number of inputs in C1 is {0}'.format(n1))\n",
    "print('The number of inputs that were assigned based on the assignment factor is {0}'.format(nae))\n",
    "print('True model parameters: gamma={0}, µ1={1}, µ2={2}, ∑={3}'.format(true_gamma, \n",
    "                                                                       true_mu1, true_mu2, \n",
    "                                                                       true_sigma))\n",
    "print('Estimated model parameters: gamma={0}, µ1={1}, µ2={2}, ∑={3}'.format(e_gamma, e_mu1, \n",
    "                                                                            e_mu2, e_sigma))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Probabilistic discriminative models\n",
    "\n",
    "Probablistic discriminative models assume the same generalized linear model\n",
    "\n",
    "$$y(\\phi(\\vec{x})) = f(\\vec{w}^\\intercal\\phi(\\vec{x}))$$\n",
    "\n",
    "as in the probabilistic generative models. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "* Instead of formulating models for the *class-conditional* densities, $p\\left(\\phi(\\vec{x})\\right|\\left.C_k\\right)$, and the *class priors*, $p(C_k)$, \n",
    "* the discriminative approach explicitly models the *class posterior* probabilities, $p\\left(C_k\\right|\\left.\\phi(\\vec{x})\\right)$ with model parameters $\\vec{w}$. \n",
    "* As in the probabilistic generative approach, maximum likelihood is used to estimate the model parameters given some training data set, $\\Psi$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The **key difference** is the form of the likelihood function. \n",
    "* In the **probabilistic generative case**, the likelihood function is a function of the joint probability,\n",
    "$p\\left(\\phi(\\vec{x}),C_k\\right)=p\\left(\\phi(\\vec{x})\\right|\\left.C_k\\right)p(C_k)$. \n",
    "* In the **probabilistic discriminative approach**, the likelihood function is a function of the conditional class posteriors, $p\\left(C_k\\right|\\left.\\phi(\\vec{x})\\right)$ only."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "*Note*: The section on probablistic generative models focused on models that used the input, $\\vec{x}$, directly. However, as noted previously, those models, and the results, hold equally well for input that undergoes a **fixed** transformation using a set of basis functions, $\\phi()$. In this section, we will focus on the inclusion of an input transformation via the basis functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Logistic Regression\n",
    "\n",
    "* Logistic regression is one specific example of discriminative modeling, for the case of **two classes**. \n",
    "* It assumes a model for the class posterior probabilities, $p(C_k|\\phi(\\vec{x}))$, in the form of the logistic sigmoid\n",
    "\n",
    "$$p\\left(C_1\\right|\\left.\\phi(\\vec{x})\\right) = f(a) = \\sigma\\left(\\vec{w}^\\intercal\\phi(\\vec{x})\\right)$$\n",
    "\n",
    "with \n",
    "\n",
    "$$p\\left(C_2\\right|\\left.\\phi(\\vec{x})\\right) = 1 - p\\left(C_1\\right|\\left.\\phi(\\vec{x})\\right).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* We apply maximum likelihood to obtain the model parameters. \n",
    "* Assume that our training set is of the form $\\Psi=\\left\\{\\phi(\\vec{x}_i),t_i\\right\\}$ where $t_i \\in \\{0,1\\}$,\n",
    "and $i=1,\\ldots, m$. \n",
    "* The likelihood function of the training data is then\n",
    "$$p(\\Psi|\\vec{w}) = \\prod_{i=1}^m \\sigma(\\vec{w}^\\intercal \\phi(\\vec{x}_i))^{t_i} (1 - \\sigma(\\vec{w}^\\intercal \\phi(\\vec{x}_i)))^{(1-t_i)}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Defining the error function, $E(\\vec{w})$, as the negative of the log-likelihood function, and taking the gradient with respect to $\\vec{w}$, we obtain\n",
    "$$\\bigtriangledown E(\\vec{w}) = \\sum_{i=1}^m \\left[\\sigma(\\vec{w}^\\intercal \\phi(\\vec{x}_i)) - t_i\\right] \\phi(\\vec{x}_i).$$\n",
    "\n",
    "* this error function looks the same as that obtained for **linear** regression under the assumption of a Gaussian noise model which had a closed form solution.\n",
    "* the nonlinearity of the *sigmoid* function, $\\sigma\\left(\\vec{w}^\\intercal \\phi(\\vec{x}_i)\\right)$ prevents a closed form solution in the **logistic** regression problem. \n",
    "* We must apply an iterative method to obtain a numerical solution for the parameters, $\\vec{w}$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Here we will consider the *Newton-Raphson* method for which minimizing the error function takes the form\n",
    "\n",
    "$$\\vec{w}^{(\\tau+1)} = \\vec{w}^{(\\tau)} - \\vec{H}^{-1}\\bigtriangledown E(\\vec{w}),$$\n",
    "\n",
    "where $\\vec{H}$ is the *Hessian* matrix composed of the second derivatives of the error function\n",
    "\n",
    "$$\\vec{H} = \\bigtriangledown \\bigtriangledown E(\\vec{w}) = \\Phi^\\intercal \\vec{R} \\Phi,$$\n",
    "\n",
    "where $\\Phi$ is the $n \\times m$ design matrix whose $n$-th row is given by $\\phi(\\vec{x_n})^\\intercal$ and $\\vec{R}$ is an $n \\times n$ diagonal matrix with elements.\n",
    "\n",
    "$$R_{i,i} = \\sigma(\\vec{w}^\\intercal \\phi(\\vec{x}_i)) \\left[1-\\sigma(\\vec{w}^\\intercal \\phi(\\vec{x}_i))\\right].$$ \n",
    "\n",
    "This can be reduced to a form equivalent to that of locally weighted linear *regression* as follows\n",
    "\n",
    "$$\\vec{w}^{(\\tau+1)} = \\left( \\Phi^T \\vec{R} \\Phi \\right)^{-1} \\Phi^T \\vec{R} \\vec{z}$$\n",
    "\n",
    "where $\\vec{z}$ is an $n$-dimensional vector defined by\n",
    "\n",
    "$$\\vec{z} = \\Phi \\vec{w}^{(\\tau)} - \\vec{R}^{-1}(\\vec{y} - \\vec{t})$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<h2>Example 2</h2>\n",
    "Let's consider an example with two classes and 2D input, $\\vec{x}_n = (x_n^{(1)},x_n^{(2)})$. \n",
    "*  As an experiment, you can try increasing the number of training points, `N`. \n",
    "* Eventually, the training points will overlap so that it will not be possible to completely seperate them with the transformation provided."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# preparing training dataset\n",
    "np.random.seed(123456789) # fixing for reproducubility\n",
    "N = 100 #number of data points\n",
    "D = 2   #dimension of input vector\n",
    "t = np.zeros(N) #training set classifications\n",
    "X = np.zeros((N,D)) #training data in input space\n",
    "sigma = .25\n",
    "mu0 = 0.0\n",
    "mu1 = 1.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def create_scatter(X, t, ax):\n",
    "    'Generates a two-class scatter plot'\n",
    "    C1x, C1y, C2x, C2y = [], [], [], []\n",
    "    for i in range(len(t)):\n",
    "        if t[i] > 0: \n",
    "            C1x.append(X[i,0])\n",
    "            C1y.append(X[i,1])\n",
    "        else: \n",
    "            C2x.append(X[i,0])\n",
    "            C2y.append(X[i,1])\n",
    "    ax.scatter(C1x, C1y, c='b', alpha=0.5)\n",
    "    ax.scatter(C2x, C2y, c='g', alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Generating test data\n",
    "\n",
    "* Pick a value from a uniform distribution on $[0,1]$. \n",
    "* If it is less than 0.5, assign class 1 and pick $x_1, x_2$ from a $\\mathcal{N}(\\mu_0,\\sigma)$ \n",
    "* otherwise assign class 2 and pick $x_1,x_2$ from $\\mathcal{N}(\\mu_1,\\sigma)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "for i in range(N):\n",
    "    #choose class to sample for\n",
    "    fac = 1\n",
    "    if np.random.rand() <= 0.5:\n",
    "        thismu = mu0\n",
    "        t[i] = 1\n",
    "    else: \n",
    "        thismu = mu1\n",
    "        t[i] = 0\n",
    "        if np.random.rand() < 0.5: fac = -1\n",
    "    X[i,0] = fac * np.random.normal(thismu, sigma)\n",
    "    X[i,1] = fac * np.random.normal(thismu, sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAArIAAAKoCAYAAACLNBx9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114634438>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 340,
       "width": 345
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5, 5))\n",
    "ax = fig.gca()\n",
    "ax.set_xlabel('$x_1$')\n",
    "ax.set_ylabel('$x_2$')\n",
    "ax.set_title('Training data set')\n",
    "create_scatter(X, t, ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "The training data does not have a linear boundary in the original input space.\n",
    "* So lets apply a transformation, $\\phi()$ (function `phi(...)`) to try to make it linearly separable\n",
    "* *Note*: This transformation is not the only one that works. \n",
    "    * For example try switching the values of $\\mu_1$ and $\\mu_2$. \n",
    "    * The result will be a different mapping that is still linearly separable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def phi(x, mu, sigma):\n",
    "    detSigma = np.linalg.det(sigma)\n",
    "    fac = math.pow(2 * math.pi, len(mu) / 2.0) * math.sqrt(detSigma)\n",
    "    arg = -0.5 * np.dot((x - mu).T, np.dot(np.linalg.inv(sigma), x - mu))\n",
    "    return math.exp(arg) / fac"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "phiX = np.zeros((N,D))\n",
    "MU1 = np.ones(D)*mu0\n",
    "MU2 = np.ones(D)*mu1\n",
    "SIGMA = np.diag(np.ones(D))*sigma\n",
    "for i in range(N):\n",
    "    phiX[i,0] = phi(x=X[i,:], mu=MU2, sigma=SIGMA)\n",
    "    phiX[i,1] = phi(x=X[i,:], mu=MU1, sigma=SIGMA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAp4AAAKGCAYAAADj85tlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111da6160>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 323,
       "width": 335
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,5)); ax =fig.gca()\n",
    "ax.set_xlabel('$x_1$'); ax.set_ylabel('$x_2$')\n",
    "create_scatter(phiX,t,ax)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Now, lets apply machine learning to determine the boundary!\n",
    "\n",
    "* We will assume M = 3, i.e. that there are 3 free parameters,\n",
    "* that is $\\vec{w} = [w_0, w_1, w_2]^\\intercal$ and,\n",
    "* `phi_n = [1, phiX[0], phiX[1]]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "M = 3\n",
    "Phi = np.ones((N,M))\n",
    "Phi[:,1] = phiX[:,0]\n",
    "Phi[:,2] = phiX[:,1]\n",
    "w = np.zeros(M)\n",
    "R = np.zeros((N,N))\n",
    "y = np.zeros(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def sigmoid(a):\n",
    "    return 1.0 / (1.0 + math.exp(-a))\n",
    "\n",
    "def totalErr(y,t):\n",
    "    e = 0.0\n",
    "    for i in range(len(y)):\n",
    "        if t[i] > 0:\n",
    "            e += math.log(y[i])\n",
    "        else:\n",
    "            e += math.log(1.0 - y[i])\n",
    "    return -e"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Starting Newton-Raphson. \n",
    "\n",
    "* As a stopping criteria we will use a tolerance on the change in the error function and a maximum number of iterations\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "max_its = 100\n",
    "tol = 1e-2\n",
    "w0 = [w[0]] \n",
    "w1 = [w[1]]\n",
    "w2 = [w[2]]\n",
    "err = []\n",
    "error_delta = 1 + tol\n",
    "current_error = 0\n",
    "idx = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "from functools import reduce"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "while math.fabs(error_delta) > tol and idx < max_its:\n",
    "    #update y & R\n",
    "    for i in range(N): \n",
    "        y[i] = sigmoid(reduce(lambda accum, Z: accum + Z[0]*Z[1], zip(w, Phi[i,:]), 0))\n",
    "        R[i,i] = y[i] - y[i]*y[i]\n",
    "    #update w\n",
    "    z = np.dot(Phi,w) - np.dot(np.linalg.pinv(R),y-t)\n",
    "    term_1 = np.linalg.pinv(np.dot(np.dot(Phi.T,R),Phi))\n",
    "    term_2 = np.dot(np.dot(term_1, Phi.T),R)\n",
    "    w = np.dot(term_2, z)\n",
    "    w0.append(w[0])\n",
    "    w1.append(w[1])\n",
    "    w2.append(w[2])\n",
    "    idx += 1\n",
    "    temp = totalErr(y,t)\n",
    "    error_delta = current_error - temp\n",
    "    current_error = temp\n",
    "    err.append(error_delta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The total number of iterations was 13\n",
      "The total error was 0.003482221426895694\n",
      "The final change in error was 0.00577180168397616\n",
      "The final parameters were [ -17.844  -14.062  163.065]\n"
     ]
    }
   ],
   "source": [
    "print('The total number of iterations was {0}'.format(idx))\n",
    "print('The total error was {0}'.format(current_error))\n",
    "print('The final change in error was {0}'.format(error_delta))\n",
    "print('The final parameters were {0}'.format(w))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Our decision boundary is now formed by the line where $\\sigma(a) = 0.5$, i.e. where $a = 0$, which for this example is where $\\phi_2 = -\\frac{w_1}{w_2}\\phi_1$, i.e. where $\\vec{w} \\cdot\\vec{\\phi} = 0.5$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAp4AAAKGCAYAAADj85tlAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114642e48>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 323,
       "width": 335
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,5)); ax =fig.gca()\n",
    "ax.set_xlabel('$x_1$'); ax.set_ylabel('$x_2$')\n",
    "create_scatter(phiX,t,ax)\n",
    "\n",
    "bdryx = (-0.2,1.1)\n",
    "bdryy = (-(w[0]+w[1]*bdryx[0])/w[2], -(w[0]+w[1]*bdryx[1])/w[2])\n",
    "ax.plot(bdryx, bdryy, linestyle='--');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAooAAAKGCAYAAADNtrr3AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nKSiKiIiIiCcFRRERERHx9P8D2thuYK9wBWAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114d4ccf8>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 323,
       "width": 325
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,5))\n",
    "plt.plot(w0, 'bo-', label='$w_0$')\n",
    "plt.plot(w1, 'rx-', label='$w_1$')\n",
    "plt.plot(w2, 'gs-', label='$w_2$')\n",
    "plt.plot(err, 'm*-', label='error delta')\n",
    "plt.legend(loc='upper left', frameon=True)\n",
    "plt.xlabel('Newton-Raphson iterations');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<h1>Readings</h1>\n",
    "<ul>\n",
    "    <li>Bishop: 4.2.0-4.2.4, 4.3.0-4.3.4, 4.4, 4,5</li>\n",
    "    <li>Ng: Lecture 2 pdf</li>\n",
    "    <li>Ng: Lecture 5 pdf</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<hr/>\n",
    "<div class=\"container-fluid\">\n",
    "  <div class='well'>\n",
    "      <div class=\"row\">\n",
    "          <div class=\"col-md-3\" align='center'>\n",
    "              <img align='center'alt=\"Creative Commons License\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png\"/>\n",
    "          </div>\n",
    "          <div class=\"col-md-9\">\n",
    "              This work is licensed under a [Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License](http://creativecommons.org/licenses/by-nc-sa/4.0/).\n",
    "          </div>\n",
    "      </div>\n",
    "  </div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "application/json": {
       "Software versions": [
        {
         "module": "Python",
         "version": "3.6.2 64bit [GCC 4.2.1 Compatible Apple LLVM 6.1.0 (clang-602.0.53)]"
        },
        {
         "module": "IPython",
         "version": "6.1.0"
        },
        {
         "module": "OS",
         "version": "Darwin 17.0.0 x86_64 i386 64bit"
        },
        {
         "module": "scipy",
         "version": "0.19.1"
        },
        {
         "module": "numpy",
         "version": "1.13.1"
        },
        {
         "module": "matplotlib",
         "version": "2.0.2"
        }
       ]
      },
      "text/html": [
       "<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>3.6.2 64bit [GCC 4.2.1 Compatible Apple LLVM 6.1.0 (clang-602.0.53)]</td></tr><tr><td>IPython</td><td>6.1.0</td></tr><tr><td>OS</td><td>Darwin 17.0.0 x86_64 i386 64bit</td></tr><tr><td>scipy</td><td>0.19.1</td></tr><tr><td>numpy</td><td>1.13.1</td></tr><tr><td>matplotlib</td><td>2.0.2</td></tr><tr><td colspan='2'>Tue Aug 29 10:55:29 2017 -03</td></tr></table>"
      ],
      "text/latex": [
       "\\begin{tabular}{|l|l|}\\hline\n",
       "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
       "Python & 3.6.2 64bit [GCC 4.2.1 Compatible Apple LLVM 6.1.0 (clang-602.0.53)] \\\\ \\hline\n",
       "IPython & 6.1.0 \\\\ \\hline\n",
       "OS & Darwin 17.0.0 x86\\_64 i386 64bit \\\\ \\hline\n",
       "scipy & 0.19.1 \\\\ \\hline\n",
       "numpy & 1.13.1 \\\\ \\hline\n",
       "matplotlib & 2.0.2 \\\\ \\hline\n",
       "\\hline \\multicolumn{2}{|l|}{Tue Aug 29 10:55:29 2017 -03} \\\\ \\hline\n",
       "\\end{tabular}\n"
      ],
      "text/plain": [
       "Software versions\n",
       "Python 3.6.2 64bit [GCC 4.2.1 Compatible Apple LLVM 6.1.0 (clang-602.0.53)]\n",
       "IPython 6.1.0\n",
       "OS Darwin 17.0.0 x86_64 i386 64bit\n",
       "scipy 0.19.1\n",
       "numpy 1.13.1\n",
       "matplotlib 2.0.2\n",
       "Tue Aug 29 10:55:29 2017 -03"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%load_ext version_information\n",
    "%version_information scipy, numpy, matplotlib"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<link href=\"https://fonts.googleapis.com/css?family=Fira+Sans:300,300i,600,600i\" rel=\"stylesheet\">\n",
       "<link href=\"https://fonts.googleapis.com/css?family=Inconsolata\" rel=\"stylesheet\">\n",
       "<link href=\"https://fonts.googleapis.com/css?family=Titillium+Web:400,400i,700,700i\" rel=\"stylesheet\">\n",
       "<style>\n",
       ".text_cell_render {\n",
       "font-style: regular;\n",
       "font-family: 'Fira Sans', sans-serif;\n",
       "display: block;\n",
       "}\n",
       "/*font-weight: 200;*/\n",
       "/*text-align: left;\n",
       "line-height: 100%;\n",
       "display: block;\n",
       "}*/\n",
       ".text_cell_render h1 {\n",
       "/*font-size: 24pt;*/\n",
       "font-family: 'Titillium Web', sans-serif;\n",
       "font-weight: bold;\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.5em;\n",
       "color:#4a4a4a;\n",
       "}\n",
       "\n",
       ".reveal h1 {\n",
       "font-family: 'Titillium Web', sans-serif;\n",
       "/*font-size: 24pt;*/\n",
       "font-weight: bold;\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.5em;\n",
       "color:#4a4a4a;\n",
       "}\n",
       ".text_cell_render h2 {\n",
       "/*font-size: 21pt;*/\n",
       "    font-family: 'Titillium Web', sans-serif;\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.3em;\n",
       "color:#595959;\n",
       "}\n",
       ".text_cell_render h3 {\n",
       "    font-family: 'Titillium Web', sans-serif;\n",
       "/*font-size: 19pt;*/\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.3em;\n",
       "color:#595959;\n",
       "}\n",
       ".text_cell_render h4 {\n",
       "    font-family: 'Titillium Web', sans-serif;\n",
       "/*font-size: 17pt;*/\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.3em;\n",
       "color:#595959;\n",
       "}\n",
       ".text_cell_render h5 {\n",
       "    font-family: 'Titillium Web', sans-serif;\n",
       "/*font-size: 15pt;*/\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.3em;\n",
       "color:#595959;\n",
       "}\n",
       "div.text_cell_render{\n",
       "line-height: 120%;\n",
       "font-size: 100%;\n",
       "font-weight: 400;\n",
       "text-align: justify;\n",
       "margin-left:0em;\n",
       "margin-right:0em;\n",
       "}\n",
       ".reveal div.text_cell_render{\n",
       "line-height: 120%;\n",
       "font-size: 74%;\n",
       "font-weight: 400;\n",
       "text-align: justify;\n",
       "margin-left:0em;\n",
       "margin-right:0em;\n",
       "}\n",
       "\n",
       ".reveal h2 {\n",
       "font-family: 'Titillium Web', sans-serif;\n",
       "/*font-size: 24pt;*/\n",
       "font-weight: bold;\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.5em;\n",
       "color:#595959;\n",
       "}\n",
       ".reveal h3 {\n",
       "font-family: 'Titillium Web', sans-serif;\n",
       "/*font-size: 24pt;*/\n",
       "font-weight: bold;\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.5em;\n",
       "color:#595959;\n",
       "}\n",
       ".reveal h4 {\n",
       "font-family: 'Titillium Web', sans-serif;\n",
       "font-weight: bold;\n",
       "margin-bottom: 0.1em;\n",
       "margin-top: 0.5em;\n",
       "color:#595959;\n",
       "}\n",
       ".reveal .code_cell {\n",
       "    font-size: 92%;\n",
       "}\n",
       ".reveal code {\n",
       "font-family: 'Inconsolata', monospace;\n",
       "}\n",
       ".reveal pre {\n",
       "font-family: 'Inconsolata', monospace;\n",
       "}\n",
       "code {\n",
       "font-family: 'Inconsolata', monospace;\n",
       "}\n",
       "pre {\n",
       "font-family: 'Inconsolata', monospace;\n",
       "}\n",
       ".CodeMirror{\n",
       "font-family: \"Inconsolata\", monospace;\n",
       "}\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# this code is here for cosmetic reasons\n",
    "from IPython.core.display import HTML\n",
    "from urllib.request import urlopen\n",
    "HTML(urlopen('https://raw.githubusercontent.com/lmarti/jupyter_custom/master/custom.include').read().decode('utf-8'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "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": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}