Chapter1_Introduction[1].ipynb

{
 "metadata": {
  "name": "Chapter1_Introduction[1]"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "**Note:** This is modified version of the notebook published by [CamDavidsonPilon@github](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers.git).\n",
      "       \n",
      "Severel of the visualizations were converted into interactive views, using [Exhibitionist](https://github.com:Exhibitionist/Exhibitionist). Where available, you can hit the \"freeze\"\n",
      "to convert the view into a static image for saving with the notebook. Double-clicking\n",
      "the static image will convert it back into a dynamic view.\n",
      "\n",
      "You can install the Exhibitionist library, using:\n",
      "\n",
      "> pip install git+https://github.com/Exhibitionist/Exhibitionist.git\n",
      "        \n",
      "If you experience issues please update your installation to the latest\n",
      "git master.\n",
      "If they persist, please report them on the [GH issues page](https://github.com/Exhibitionist/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/issues).\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import exhibitionist as xb # make sure xb is available\n",
      "import  xbviews.app as app\n",
      "views = app.get_views()\n",
      "views\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12.5,4)\n",
      "import scipy.stats as stats"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Chapter 1\n",
      "======\n",
      "***"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Philosophy of Bayesian Inference\n",
      "------\n",
      "  \n",
      "> You are a skilled programmer, but bugs still slip into your code. After a particularly difficult implementation of an algorithm, you decide to test your code on a trivial example. It passes. You test the code on a harder problem. It passes once again. And it passes the next, *even more difficult*, test too! You are starting to believe that there are may be no bugs present...\n",
      "\n",
      "If you think this way, then congratulations, you already are a Bayesian practitioner! Bayesian inference is simply updating your beliefs after considering new evidence. A Bayesian can rarely be certain about a result, but he or she can be very confident. Just like in the example above, we can never be 100% sure that our code is bug-free unless we test it on every possible problem; something rarely possible in practice. Instead, we can test it on a large number of problems, and if it succeeds we can feel more *confident* about our code.  Bayesian inference works identically: we can only update our beliefs about an outcome, rarely can we be absolutely sure unless we rule out all other alternatives. We will see that being uncertain can have its advantages. \n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "###The Bayesian state of mind\n",
      "\n",
      "\n",
      "Bayesian inference differs from more traditional statistical analysis by preserving *uncertainty* about our beliefs. At first, this sounds like a bad statistical technique. Isn't statistics all about deriving *certainty* from randomness? The Bayesian method interprets probability as measure of *believability in an event*, that is, how confident one is in an event occuring. In fact, we will see in a moment that this is the natural interpretation of probability. \n",
      "\n",
      "For this to be clearer, we consider an alternative interpretation of probability: *Frequentist* methods assume that probability is the long-run frequency of events (hence the bestowed title). For example, the *probability of plane accidents* under a frequentist philosophy is interpreted as the *long-term frequency of plane accidents*. This makes logical sense for many probabilities and events, but becomes more difficult to understand when events have no long-term frequency of occurences. Consider: we often assign probabilities to outcomes of presidential elections, but the election itself only happens once! Frequentists get around this by invoking alternative realities and saying across all these universes, the frequency of occurences is the probability. \n",
      "\n",
      "Bayesians, on the other hand, have a more intuitive approach. Bayesians interpret a probability as measure of *belief*, or confidence, of an event occurring. An individual who assigns a belief of 0 to an event has no confidence that the event will occur; conversely, assigning a belief of 1 implies that the individual is absolutely certain of an event occurring. Beliefs between 0 and 1 allow for weightings of other outcomes. This definition agrees with the probability of a plane accident example, for having observed the frequency of plane accidents, an individual's belief should be equal to that frequency. Similarly, under this definition of probability being equal to beliefs, it is clear how we can speak about probabilities (beliefs) of presidential election outcomes. \n",
      "\n",
      "Notice in the paragraph above, I assigned the belief (probability) measure to an *individual*, not to Nature. This is very interesting, as this definition leaves room for conflicting beliefs between individuals. Again, this is appropriate for what naturally occurs: different individuals have different beliefs of events occuring, because they possess different *information* about the world.\n",
      "\n",
      "- I flip a coin, and we both guess the result. We would both agree, assuming the coin is fair, that the probability of heads if 1/2. Assume, then, that I peek at the coin. Now I know for certain what the result is: I assign probability 1.0 to either heads or tails. Now what is *your* belief that the coin is heads? My knowledge of the outcome has not changed the coin's results. Thus we assign different probabilities to the result. \n",
      "\n",
      "-  Your code either has a bug in it or not, but we do not know for certain which is true. Though we have a belief about the presence or absence of a bug.  \n",
      "\n",
      "-  A medical patient is exhibiting symptoms $x$, $y$ and $z$. There are a number of diseases that could be causing all of them, but only a single disease is present. A doctor has beliefs about which disease.\n",
      "\n",
      "- You believe that the beautiful girl in your English class doesn't have a crush you. You assign a low probability that she does. She, on the other hand, knows for certain that she *does indeed* like you. She (implicitly) assigns a probability 1. \n",
      "\n",
      "This philosophy of treating beliefs as probability is natural to humans. We employ it constantly as we interact with the world and only see partial evidence. Alternatively, you have to be *trained* to think like a frequentist. \n",
      "\n",
      "To align ourselves with traditional probability notation, we denote our belief about event $A$ as $P(A)$.\n",
      "\n",
      "John Maynard Keynes, a great economist and thinker, said \"When the facts change, I change my mind. What do you do, sir?\" This quote reflects the way a Bayesian updates his or her beliefs after seeing evidence. Even --especially-- if the evidence is counter to what was initially believed, the evidence cannot be ignored. We denote our updated belief as $P(A |X )$, interpreted as the probability of $A$ given the evidence $X$. We call the updated belief the *posterior probability* so as to contrast it with the *prior probability*. For example, consider the posterior probabilities (read: posterior belief) of the above examples, after observing some evidence $X$.:\n",
      "\n",
      "1\\. $P(A): \\;\\;$ the coin has a 50 percent chance of being heads. $P(A | X):\\;\\;$ You look at the coin, observe a heads, denote this information $X$, and trivially assign probability 1.0 to heads and 0.0 to tails.\n",
      "\n",
      "2\\.   $P(A): \\;\\;$  This big, complex code likely has a bug in it. $P(A | X): \\;\\;$ The code passed all $X$ tests; there still might be a bug, but its presence is less likely now.\n",
      "\n",
      "3\\.  $P(A):\\;\\;$ The patient could have any number of diseases. $P(A | X):\\;\\;$ Performing a blood test generated evidence $X$, ruling out some of the possible diseases from consideration.\n",
      "\n",
      "4\\.  $P(A):\\;\\;$ You believe that the probability that the lovely girl in your class likes you is low.  $P(A | X): \\;\\;$ She sent you an SMS message about this Friday night. Interesting... \n",
      "\n",
      "It's clear that in each example we did not completely discard the prior belief after seeing new evidence, but we *re-weighted the prior* to incorporate the new evidence (i.e. we put more weight, or confidence, on some beliefs versus others). \n",
      "\n",
      "By introducing prior uncertainity about events, we are already admitting that any guess we make is potentially very wrong. After observing data, evidence, or other information, and we update our beliefs, our guess becomes *less wrong*. This is the alternative side of the prediction coin, where typically we try to be *more right*.\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "###Bayesian Inference in Practice\n",
      "\n",
      " If frequentist and Bayesian inference were computer programming functions, with inputs being statistical problems, then the two would be different in what they return to the user. The frequentist inference function would return a number, whereas the Bayesian function would return a *distribution*.\n",
      "\n",
      "For example, in our debugging problem above, calling the frequentist function with the argument \"My code passed all $X$ tests; is my code bug-free?\" would return a *YES*. On the other hand, asking our Bayesian function \"Often my code has bugs. My code passed all $X$ tests; is my code bug-free?\" would return something very different: a distribution over *YES* and *NO*. The function might return \n",
      "\n",
      "\n",
      ">    *YES*, with probability 0.8; *NO*, with probability 0.2\n",
      "\n",
      "\n",
      "\n",
      "This is very different from the answer the frequentist function returned. Notice that the Bayesian function accepted an additional argument:  *\"Often my code has bugs\"*. This parameter is the *prior*. By including the prior parameter, we are telling the Bayesian function to include our personal belief about the situation. Technically this parameter in the Bayesian function is optional, but we will see excluding it has its own consequences. \n",
      "\n",
      "\n",
      "As we acquire more and more instances of evidence, our prior belief is *washed out* by the new evidence. This is to be expected. For example, if your prior belief is something ridiculous, like \"I expect the sun to explode today\", and each day you are proved wrong, you would hope that any inference would correct you, or at least align your beliefs better. \n",
      "\n",
      "\n",
      "Denote $N$ as the number of instances of evidence we possess. As we gather an *infinite* amount of evidence, say as $N \\rightarrow \\infty$, our Bayesian results align with frequentist results. Hence for large $N$, statistical inference is more or less objective. On the other hand, for small $N$, inference is much more *unstable*: frequentist estimates have more variance and larger confidence intervals. This is where Bayesian analysis excels. By introducing a prior, and returning a distribution (instead of a scalar estimate), we *preserve the uncertainity* to reflect the instability of stasticial inference of a small $N$ dataset. \n",
      "\n",
      "One may think that for large $N$, one can be indifferent between the two techniques, and might lean towards the computational-simpler, frequentist methods. An analyst in this position should consider the following quote by Andrew Gelman (2005)[1], before making such a decision:\n",
      "\n",
      "> Sample sizes are never large. If $N$ is too small to get a sufficiently-precise estimate, you need to get more data (or make more assumptions). But once $N$ is \"large enough,\" you can start subdividing the data to learn more (for example, in a public opinion poll, once you have a good estimate for the entire country, you can estimate among men and women, northerners and southerners, different age groups, etc etc). $N$ is never enough because if it were \"enough\" you'd already be on to the next problem for which you need more data.\n",
      "\n",
      "\n",
      "#### A note on *Big Data*\n",
      "Paradoxically, big data's predictive analytic problems are actually solved by relatively simple models [2][4]. Thus we can argue that big data's prediction difficulty does not lie in the algorithm used, but instead on the computational difficulties of storage and execution on big data. (One should also consider Gelman's qoute from above and ask \"Do I really have big data?\" )\n",
      "\n",
      "The much more difficult analytic problems involve *medium data* and, especially troublesome, *really small data*. Using a similar argument as  Gelman's above, if big data problems are *big enough* to be readily solved, then we should be more interested in the *not-quite-big enough* datasets. "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Our Bayesian framework\n",
      "\n",
      "We are interested in beliefs, which can be interpreted as probabilities by thinking Bayesian. We have a *prior* belief in event $A$: it is what you believe before looking at any evidence, e.g., our prior belief about bugs being in our code before performing tests.\n",
      "\n",
      "Secondly, we observe our evidence. To continue our example, if our code passes $X$ tests, we want to update our belief to incorporate this. We call this new belief the *posterior* probability. Updating our belief is done via the following equation, known as Bayes' Theorem, after Thomas Bayes:\n",
      "\n",
      "\\begin{align}\n",
      " P( A | X ) = & \\frac{ P(X | A) P(A) } {P(X) } \\\\\\\\[5pt]\n",
      "& \\propto P(X | A) P(A)\\;\\; (\\propto \\text{is proportional to } )\n",
      "\\end{align}\n",
      "\n",
      "The above formula is not unique to Bayesian inference: it is a mathematical fact with uses outside Bayesian inference. Bayesian inference merely uses it to connect $P(A)$ with an updated $P(A | X )$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "#####Example: Bug, or just sweet, unintended feature?\n",
      "\n",
      "\n",
      "Let $A$ denote the event that our code has **no bugs** in it. Let $X$ denote the event that the code passes all debugging tests. For now, we will leave the prior probability of no bugs as a variable, i.e. $P(A) = p$. \n",
      "\n",
      "We are interested in $P(A|X)$, i.e. the probability of no bugs, given our debugging tests $X$. To use the formula above, we need to compute some quantities from the formula above.\n",
      "\n",
      "What is $P(X | A)$, i.e., the probability that the code passes $X$ tests *given* there are no bugs? Well, it is equal to 1, for a code with no bugs will pass all tests. \n",
      "\n",
      "$P(X)$ is a little bit trickier: The event $X$ can be divided into two possibilities, event $X$ ocurring even though our code *indeed has* bugs (denoted $\\sim A\\;$, spoken *not $A$*), or event $X$ without bugs ($A$). $P(X)$ can be represented as:"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{align}\n",
      "P(X ) & = P(X \\text{ and } A) + P(X \\text{ and } \\sim A) \\\\\\\\[5pt]\n",
      " & = P(X|A)P(A) + P(X | \\sim A)P(\\sim A)\\\\\\\\[5pt]\n",
      "& = P(X|A)p + P(X | \\sim A)(1-p)\n",
      "\\end{align}"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We have already computed $P(X|A)$ above. On the other hand, $P(X | \\sim A)$ is subjective: our code can pass tests but still have a bug in it, though the probability there is a bug present is less. Note this is dependent on the number of tests performed, the degree of complication in the tests, etc. Let's be conservative and assign $P(X|\\sim A) = 0.5$. Then\n",
      "\n",
      "\\begin{align}\n",
      "P(A | X) & = \\frac{1\\cdot p}{ 1\\cdot p +0.5 (1-p) } \\\\\\\\\n",
      "& = \\frac{ 2 p}{1+p}\n",
      "\\end{align}\n",
      "This is the posterior probability distribution. What does it look like as a function of our prior, $p \\in [0,1]$? "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize( 9, 4 )\n",
      "p = np.linspace( 0,1, 50)\n",
      "plt.plot( p, 2*p/(1+p), color = \"#348ABD\" )\n",
      "plt.fill_between( p, 2*p/(1+p), alpha = .4, facecolor = [\"#348ABD\"])\n",
      "plt.scatter( 0.2, 2*(0.2)/1.2, s = 140, c =\"#348ABD\"  )\n",
      "plt.xlim( 0, 1)\n",
      "plt.ylim( 0, 1)\n",
      "plt.xlabel( \"Prior, $P(A) = p$\")\n",
      "plt.ylabel(\"Posterior, $P(A|X)$, with $P(A) = p$\")\n",
      "plt.title( \"Are there bugs in my code?\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAjUAAAEgCAYAAABM5oItAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n"
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see the biggest gains if we observe the $X$ tests passed are when the prior probability, $p$, is low. Let's settle on a specific value for the prior. I'm a (I think) strong programmer, so I'm going to give myself a realistic prior of 0.20, that is, there is a 20% chance that I write code bug-free. To be more realistic, this prior should be a function of how complicated and large the code is, but let's pin it at 0.20. Then my updated belief that my code is bug-free is 0.33. \n",
      "\n",
      "Recall that the prior is a probability distribution: $p$ is the prior probability that there *are no bugs*, so $1-p$ is the prior probability that there *are bugs*.\n",
      "\n",
      "Similarly, our posterior is also a probability distribution, with $P(A | X)$ the probability there is no bug *given we saw all tests pass*, hence $1-P(A|X)$ is the probability there is a bug *given all tests passed*. What does our posterior probability distribution look like? Below is a graph of both the prior and the posterior distributions. \n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize( 9, 4 )\n",
      "prior = [0.20, 0.80]\n",
      "posterior =  [1./3, 2./3]\n",
      "plt.bar( [0,.7], prior ,alpha = 0.80, width = 0.25, \\\n",
      "            color = \"#348ABD\", label = \"prior distribution\" )\n",
      "plt.bar( [0+0.25,.7+0.25], posterior ,alpha = 0.7, \\\n",
      "          width = 0.25, color =  \"#A60628\", label = \"posterior distribution\" )\n",
      "\n",
      "plt.xticks( [0.20,.95], [\"Bugs Absent\", \"Bugs Present\"] )\n",
      "plt.title(\"Prior and Posterior probability of bugs present, prior = 0.2\")\n",
      "plt.ylabel(\"Probability\")\n",
      "plt.legend(loc=\"upper left\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAikAAAELCAYAAAAcHxa+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkGENvZsAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Notice that after we observed $X$ occur, the probability of bugs being absent increased. By increasing the number of tests, we can approach confidence (probability 1) that there are no bugs present.\n",
      "\n",
      "This was a very simple example of Bayesian inference and Bayes rule. Unfortunately, the mathematics necessary to perform more complicated Bayesian inference only becomes more difficult, except for artifically constructed cases. We will later see that this type of mathematical anaylsis is actually unnecessary. First we must broaden our modeling tools."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "_______\n",
      "\n",
      "##Probability Distributions\n",
      "\n",
      "\n",
      "**Let's quickly recall what a probability distribution is:** Let $Z$ be some random variable. Then associated with $Z$ is a *probability distribution function* that assigns probabilities to the different outcomes $Z$ can take. There are three cases:\n",
      "\n",
      "-   **$Z$ is discrete**: Discrete random variables may only assume values on a specified list. Things like populations, movie ratings, and number of votes are all discrete random variables. It's more clear when we contrast it with...\n",
      "\n",
      "-   **$Z$ is continuous**: Continuous random variable can take on arbitrarily exact values. For example, temperature, speed, time, color are all modeled as continuous variables because you can constantly make the values more and more precise.\n",
      "\n",
      "- **$Z$ is mixed**: Mixed random variables assign probabilities to both discrete and continuous random variables, i.e. is is a combination of the above two categories. \n",
      "\n",
      "###Discrete Case\n",
      "If $Z$ is discrete, then its distribution is called a *probability mass function*, which measures the probability $Z$ takes on the value $k$, denoted $P(Z=k)$. Note that the probability mass function completely describes the random variable $Z$, that is, if we know the mass function, we know how $Z$ should behave. There are popular probability mass functions that consistently appear: we will introduce them as needed, but let's introduce the first very useful probability mass function. We say $Z$ is *Poisson*-distributed if:\n",
      "\n",
      "$$P(Z = k) =\\frac{ \\lambda^k e^{-\\lambda} }{k!}, \\; \\; k=0,1,2, \\dots $$\n",
      "\n",
      "What is $\\lambda$? It is called the parameter, and it describes the shape of the distribution. For the Poisson random variable, $\\lambda$ can be any positive number. By increasing $\\lambda$, we add more probability to larger values, and conversely by decreasing $\\lambda$ we add more probability to smaller values. Unlike $\\lambda$, which can be any positive number, $k$ must be a non-negative integer, i.e., $k$ must take on values 0,1,2, and so on. This is very important, because if you wanted to model a population you could not make sense of populations with 4.25 or 5.612 members. \n",
      "\n",
      "If a random variable $Z$ has a Poisson mass distribution, we denote this by writing\n",
      "\n",
      "$$Z \\sim \\text{Poi}(\\lambda) $$\n",
      "\n",
      "One very useful property of the Poisson random variable, given we know $\\lambda$, is that its expected value is equal to the parameter, ie.:\n",
      "\n",
      "$$E\\large[ \\;Z\\; | \\; \\lambda \\;\\large] = \\lambda $$\n",
      "\n",
      "We will use this property often, so it's something useful to remember. Below we plot the probablity mass distribution for different $\\lambda$ values. The first thing to notice is that by increasing $\\lambda$ we add more probability to larger values occuring. Secondly, notice that although the graph ends at 15, the distributions do not. They assign positive probability to every non-negative integer.."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize( 12.5, 4)\n",
      "import scipy.stats as stats\n",
      "a = np.arange( 16 )\n",
      "poi = stats.poisson\n",
      "lambda_ = [1.5, 4.25 ]\n",
      "colours = [\"#348ABD\", \"#A60628\"]\n",
      "\n",
      "plt.bar( a, poi.pmf( a, lambda_[0]), color=colours[0],\n",
      "        label = \"$\\lambda = %.1f$\"%lambda_[0], alpha = 0.95)\n",
      "plt.bar( a, poi.pmf( a, lambda_[1]), color=colours[1],\n",
      "         label = \"$\\lambda = %.1f$\"%lambda_[1], alpha = 0.60)\n",
      "\n",
      "plt.xticks( a + 0.4, a )\n",
      "plt.legend()\n",
      "plt.ylabel(\"probability of $k$\")\n",
      "plt.xlabel(\"$k$\")\n",
      "plt.title(\"Probability mass function of a Poisson random variable; differing \\\n",
      "$\\lambda$ values\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAvYAAAEcCAYAAACs1vBZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nPQAAAOADDPYAAACAD/wLUXlySRWtVYQAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "views['PoissonDistribution'] # show interactive view"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Continuous Case\n",
      "Instead of a probability mass function, a continuous random variable has a *probability density function*. This might seem like unnecessary nomenclature, but the density function and the mass function are very different creatures. An example of continuous random variable is a random variable with a *exponential density*. The density function for an exponential random variable looks like:\n",
      "\n",
      "$$f_Z(z | \\lambda) = \\lambda e^{-\\lambda z }, \\;\\; z\\ge 0$$\n",
      "\n",
      "Like the Poisson random variable, an exponential random variable can only take on non-negative values. But unlike a Poisson random variable, the exponential can take on *any* non-negative values, like 4.25 or 5.612401. This makes it a poor choice for count data, which must be integers, but a great choice for time data, or temperature data (measured in Kelvins, of course), or any other precise *and positive* variable. Below are two probability density functions with different $\\lambda$ value. \n",
      "\n",
      "When a random variable $Z$ has an exponential distribution with parameter $\\lambda$, we say *$Z$ is exponential* and write\n",
      "\n",
      "$$Z \\sim \\text{Exp}(\\lambda)$$\n",
      "\n",
      "Given a specific $\\lambda$, the expected value of an exponential random variable is equal to the inverse of $\\lambda$, that is:\n",
      "\n",
      "$$E[\\; Z \\;|\\; \\lambda \\;] = \\frac{1}{\\lambda}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = np.linspace(0,4, 100)\n",
      "expo = stats.expon\n",
      "lambda_ = [0.5, 1]\n",
      "colours = [ \"#A60628\", \"#348ABD\"]\n",
      "for l,c in zip(lambda_,colours):\n",
      "    plt.plot( a, expo.pdf( a, scale=1./l), lw=3, \n",
      "                color=c, label = \"$\\lambda = %.1f$\"%l)\n",
      "    plt.fill_between( a, expo.pdf( a, scale=1./l), color=c, alpha = .33)\n",
      "    \n",
      "plt.legend()\n",
      "plt.ylabel(\"PDF at $z$\")\n",
      "plt.xlabel(\"$z$\")\n",
      "plt.title(\"Probability density function of an Exponential random variable;\\\n",
      " differing $\\lambda$\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAvQAAAEZCAYAAAD47rHXAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngg==\n"
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "You can experiment with different values of the $\\lambda$ parameter by executing\n",
      "the cell below. Hit \"Freeze\" to store a static version in the notebook."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "views['ExponentialDistribution'] # show interactive view\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "###But what is $\\lambda \\;\\;$?\n",
      "\n",
      "\n",
      "**This question is what motivates statistics**. In the real world, $\\lambda$ is hidden from us. We only see $Z$, and must go backwards to try and determine $\\lambda$. The problem is so difficult because there is not a one-to-one mapping from $Z$ to $\\lambda$. Many different methods have been created to solve the problem of estimating $\\lambda$, but since $\\lambda$ is never actually observed, no one can say for certain which method is better! \n",
      "\n",
      "Bayesian inference is concerned with *beliefs* about what $\\lambda$ is. Rather than try to guess $\\lambda$ exactly, we can only talk about what $\\lambda$ is likely to be by assigning a probability distribution to $\\lambda$.\n",
      "\n",
      "This might seem odd at first: after all, $\\lambda$ is fixed, it is not (necessarily) random! How can we assign probabilities to a non-random event. Ah, we have fallen for the frequentist interpretation. Recall, under our Bayesian philosophy, we *can* assign probabilties if we interpret them as beliefs. And it is entirely acceptable to have *beliefs* about the parameter $\\lambda$. \n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "##### Example: Inferring behaviour from text-message data\n",
      "\n",
      "Let's try to model a more interesting example, concerning text-message rates:\n",
      "\n",
      ">  You are given a series of text-message counts from a user of your system. The data, plotted over time, appears in the graph below. You are curious if the user's text-messaging habits changed over time, either gradually or suddenly. How can you model this? (This is in fact my own text-message data. Judge my popularity as you wish.)\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize( 12, 3.5 )\n",
      "count_data = np.loadtxt(\"data/txtdata.csv\")\n",
      "n_count_data = len(count_data)\n",
      "plt.bar( np.arange( n_count_data ), count_data, color =\"#348ABD\"  )\n",
      "plt.xlabel( \"Time (days)\")\n",
      "plt.ylabel(\"# Text-msg received\")\n",
      "plt.title(\"Did the user's texting habits change over time?\")\n",
      "plt.xlim( 0, n_count_data );"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAs0AAAD/CAYAAAAKYusOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n"
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Before we begin, with resepect to the plot above, would you say there was a change in behaviour\n",
      "during the time period? \n",
      "\n",
      "How can we start to model this? Well, as I conveniently already introduced, a Poisson random variable would be a very appropriate model for this *count* data. Denoting day $i$'s text-message count by $C_i$, \n",
      "\n",
      "$$ C_i \\sim \\text{Poisson}(\\lambda)  $$\n",
      "\n",
      "We are not sure about what the $\\lambda$ parameter is though. Looking at the chart above, it appears that the rate might become higher at some later date, which is equivalently saying the parameter $\\lambda$ increases at some later date (recall a higher $\\lambda$ means more probability on larger outcomes, that is, higher probability of many texts.).\n",
      "\n",
      "How can we mathematically represent this? We can think, that at some later date (call it $\\tau$), the parameter $\\lambda$ suddenly jumps to a higher value. So we create two $\\lambda$ parameters, one for behaviour before the $\\tau$, and one for behaviour after. In literature, a sudden transition like this would be called a *switchpoint*:\n",
      "\n",
      "$$\n",
      "\\lambda = \n",
      "\\begin{cases}\n",
      "\\lambda_1  & \\text{if } t \\lt \\tau \\cr\n",
      "\\lambda_2 & \\text{if } t \\ge \\tau\n",
      "\\end{cases}\n",
      "$$\n",
      "\n",
      "\n",
      " If, in reality, no sudden change occurred and indeed $\\lambda_1 = \\lambda_2$, the $\\lambda$'s posterior distributions should look about equal.\n",
      "\n",
      "What would be good prior distributions for $\\lambda_1$ and $\\lambda_2$? Recall that $\\lambda_i, \\; i=1,2,$ can be any positive number. The *exponential* random variable has a density function for any positive number. This would be a good choice to model $\\lambda_i$. But again, we need a parameter for this exponential distribution: call it $\\alpha$.\n",
      "\n",
      "\\begin{align}\n",
      "&\\lambda_1 \\sim \\text{Exp}( \\alpha ) \\\\\\\n",
      "&\\lambda_2 \\sim \\text{Exp}( \\alpha )\n",
      "\\end{align}\n",
      "\n",
      "$\\alpha$ is called a *hyper-parameter*, or a *parent-variable*, literally a parameter that influences other parameters. The influence is not too strong, so we can choose $\\alpha$ liberally.  A good rule of thumb is to set the exponential parameter equal to the inverse of the average of the count data, since we're modeling $\\\\lambda$ using an Exponential distribution we can use the expected value identity shown earlier to get:\n",
      "\n",
      "$$\\frac{1}{N}\\sum_{i=0}^N \\;C_i \\approx E[\\; \\lambda \\; |\\; \\alpha ] = \\frac{1}{\\alpha}$$ \n",
      "\n",
      "Alternatively, and something I encourage the reader to try, is to have two priors: one for each $\\lambda_i$; creating two exponential distributions with different $\\alpha$ values reflects a prioer belief that the rate changed after some period.\n",
      "\n",
      "What about $\\tau$? Well, due to the randomness, it is too difficult to pick out when $\\tau$ might have occurred. Instead, we can assign an *uniform prior belief* to every possible day. This is equivalent to saying\n",
      "\n",
      "\\begin{align}\n",
      "& \\tau \\sim \\text{DiscreteUniform(1,70) }\\\\\\\\\n",
      "& \\Rightarrow P( \\tau = k ) = \\frac{1}{70}\n",
      "\\end{align}\n",
      "\n",
      "So after all this, what does our prior distribution look like? Frankly, *it doesn't matter*. What we should understand is that it would be an ugly, complicated, mess involving symbols only a mathematician would love. And things would only get uglier the more complicated our models become. Regardless, all we really care about is the posterior distribution anyways. We next turn to PyMC, a Python library for performing Bayesian analysis, and is agnostic to the mathematical monster we have created. \n",
      "\n",
      "\n",
      "Introducing our first hammer: PyMC\n",
      "-----\n",
      "\n",
      "PyMC is a Python library for programming Bayesian analysis  [3]. It is a fast, well-maintained library. The only unfortunate part is that documentation can be lacking in areas, especially the bridge between problem to solution. One this book's main goals is to solve that problem, and also to demonstrate why PyMC is so cool.\n",
      "\n",
      "We will model the above problem using the PyMC library. This type of programming is called *probabilistic programming*, an unfortunate misnomer that invokes ideas of randomly-generated code and has likely confused and frightened users away from this field. The code is not random. The title is given because we create probability models using pogramming variables as the model's components. This will be the last time I use the term *probablistic programming*. Instead, I'll simply use *programming*, as that is what it really is. \n",
      "\n",
      "\n",
      "The PyMC code is easy to follow along: the only novel thing should be the syntax, and I will interrupt the code to explain sections. Simply remember we are representing the model's components ($\\tau, \\lambda_1, \\lambda_2$ ) as variables:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc as mc\n",
      "\n",
      "n = count_data.shape[0]\n",
      "\n",
      "alpha = 1.0/count_data.mean() #recall count_data is \n",
      "                              #the variable that holds our txt counts\n",
      "\n",
      "lambda_1 = mc.Exponential( \"lambda_1\",  alpha )\n",
      "lambda_2 = mc.Exponential( \"lambda_2\", alpha )\n",
      "\n",
      "tau = mc.DiscreteUniform( \"tau\", lower = 0, upper = n )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the above code, we create the PyMC variables corresponding to $\\lambda_1, \\; \\lambda_2$ in lines `8,9`. We assign them to PyMC's *stochastic variables*, called stochastic variables because they are treated by the backend as random number generators. We can test this by calling their built-in `random()` method."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"Random output:\", tau.random(),tau.random(), tau.random()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Random output: 64 59 36\n"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "@mc.deterministic\n",
      "def lambda_( tau = tau, lambda_1 = lambda_1, lambda_2 = lambda_2 ):\n",
      "    out = np.zeros( n )  \n",
      "    out[:tau] = lambda_1 #lambda before tau is lambda1\n",
      "    out[tau:] = lambda_2 #lambda after tau is lambda2\n",
      "    return out"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This code is creating a new function `lambda_`, but really we think of it as a random variable: the random variable $\\lambda$ from above. Note that because `lambda_1`, `lambda_2` and `alpha` are random, `lambda_` will be random. We are **not** fixing any variables yet. The `@mc.deterministic` is a decorator to tell PyMC that this is a deterministic function, i.e., if the arguments were deterministic (which they are not), the output would be deterministic as well. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "observation = mc.Poisson( \"obs\", lambda_, value = count_data, observed = True)\n",
      "\n",
      "model = mc.Model( [observation, lambda_1, lambda_2, tau] )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The variable `observations` combines our data, `count_data`, with our proposed data-generation scheme, given by the variable `lambda_`, through the `value` keyword. We also set `observed = True` to tell PyMC that this should stay fixed in our analysis. Finally, PyMC wants us to collect all the variables of interest and create a `Model` instance out of them. This makes our life easier when we try to retrieve the results.\n",
      "\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "### Myserious code to be explained later.\n",
      "mcmc = mc.MCMC(model)\n",
      "mcmc.sample( 100000, 50000, 1 )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " \r",
        "[****************100%******************]  100000 of 100000 complete"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The above code will be explained in the Chapter 3, but this is where our results come from. The machinery being employed is called *Monte Carlo Markov Chains* (which I delay explaining until Chapter 3). It returns thousands of random variables from the posterior distributions of $\\lambda_1, \\lambda_2$ and $\\tau$. We can plot a histogram of the random variables to see what the posterior distribution looks like. Below, we collect the samples (called *traces* in MCMC literature) in histograms."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lambda_1_samples = mcmc.trace( 'lambda_1' )[:]\n",
      "lambda_2_samples = mcmc.trace( 'lambda_2' )[:]\n",
      "tau_samples = mcmc.trace( 'tau' )[:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12.5, 10)\n",
      "#histogram of the samples:\n",
      "\n",
      "ax = plt.subplot(311)\n",
      "ax.set_autoscaley_on(False)\n",
      "\n",
      "plt.hist( lambda_1_samples, histtype='stepfilled', bins = 60, alpha = 0.85, \n",
      "        label = \"posterior of $\\lambda_1$\", color = \"#A60628\",normed = True )\n",
      "plt.legend(loc = \"upper left\")\n",
      "plt.title(r\"Posterior distributions of the variables $\\lambda_1,\\;\\lambda_2,\\;\\tau$\")\n",
      "plt.xlim([15,30])\n",
      "plt.xlabel(\"$\\lambda$ value\")\n",
      "plt.ylabel(\"probability\")\n",
      "\n",
      "ax = plt.subplot(312)\n",
      "ax.set_autoscaley_on(False)\n",
      "\n",
      "plt.hist( lambda_2_samples,histtype='stepfilled', bins = 60, alpha = 0.85, \n",
      "          label = \"posterior of $\\lambda_2$\",color=\"#7A68A6\", normed = True )\n",
      "plt.legend(loc = \"upper left\")\n",
      "plt.xlim([15,30])\n",
      "plt.xlabel(\"$\\lambda$ value\")\n",
      "plt.ylabel(\"probability\")\n",
      "\n",
      "plt.subplot(313)\n",
      "\n",
      "\n",
      "w = 1.0/ tau_samples.shape[0] * np.ones_like( tau_samples )\n",
      "plt.hist( tau_samples, bins = n_count_data, alpha = 1, \n",
      "         label = r\"posterior of $\\tau$\",\n",
      "         color=\"#467821\", weights=w, rwidth =1. )\n",
      "\n",
      "plt.legend(loc = \"upper left\");\n",
      "plt.ylim([0,.75])\n",
      "plt.xlim([35, len(count_data)-20])\n",
      "plt.xlabel(\"days\")\n",
      "plt.ylabel(\"probability\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAvIAAAJsCAYAAACf90d/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3XlYVHX/P/7nAIqiILiA7ItgoiCIu5lZaKZ3Yjfq/SFK\n0VxQsVywuG23VbzzlyJ3hVaWKaa3u4Voght1CSqpmKbgxiKI4IIKAg7n+4c/JgYYGJB5D2d4Pq5r\nrstz5iyv8+TEvDi95xyFJEkSiIiIiIhIVoz0XQARERERETUcG3kiIiIiIhliI09EREREJENs5ImI\niIiIZIiNPBERERGRDLGRJyIiIiKSITbyREREREQyxEaeiOo0ZcoUjBw5Utj+PvjgA3h4eAjZf/Vt\nDx8+HDNmzNDJvmrbX3O3ePFi2NjYwMjICOvWrdN6PV3nqCuN+floc6xy+7kTkXyY6LsAopZkypQp\nqobI2NgY9vb2GD16ND755BN07Njxsbc/YsQIODo6Yu3atY+9rUqrVq1CRUVFk21P1/tvSAbVt61Q\nKKBQKBpVpzY16DvLhkhOTkZkZCR27dqFAQMGwMLCotblajvWpspRtMb8fLQ5VrnmQUTNH6/IEwk2\nbNgw5OXl4erVq4iKisK2bdswefJkfZdVQ1lZGQDA3NwcHTp0aJJtNUZT7L+6pjy2hhC9v8eRnp4O\nIyMjvPDCC7C2tkabNm30XZLO6Pp8kCQJIh6ifvr0aQwdOhR79uzR+b6aw36JiI08kXCtWrWCtbU1\n7OzsEBAQgHnz5iE+Ph6lpaUoLy/Hv//9bzg4OMDU1BS9evXCxo0b1dZPSkrCk08+CQsLC1hYWMDX\n1xf79u3DlClTkJiYiB9++AFGRkYwMjLC4cOHVeutWrUKPXr0QNu2bdG9e3d8+umnUCqVqveHDx+O\n6dOn491334WtrS1cXFwA1BwWoE2NmrZV3YMHDzB79mxYWlqiY8eOmDNnDkpLS9WWqb5/TcdfuWzV\nDIyNjXHo0CGtjw0AlEol/v3vf6NLly7o0KEDQkND1WqqbSjFxx9/DFdX11prqPpzaGyWM2bMwEcf\nfQRbW1t06tQJISEhuH//vlaZ1Ka+/U6ZMgWTJ09GRUWFKsfaaMobeNS81lUzUP85Wd2aNWtgaWlZ\n4xyJjIyEs7MzJEnCr7/+iuHDh6NTp06wtLTE8OHDcezYsRqZanM+aLMtoP5zpjb1HXtDf6YA0Lt3\nb7z22mt466236lyuqelrv0QEQCIiYUJCQqSRI0eqzVu+fLmkUCiku3fvSosWLZI6deokbdmyRUpP\nT5c+/fRTycjISEpISJAkSZLKy8slKysrKTw8XMrIyJAyMjKkHTt2SElJSdKdO3ekYcOGSUFBQdL1\n69el69evS2VlZZIkSdL7778vOTs7Szt27JCuXLkixcXFSU5OTtK7776rquPpp5+WzM3NpdmzZ0vn\nzp2Tzpw5U2vN9dVY17aqmz9/vmRtbS3t2rVLOn/+vLRo0SLJwsJC8vDwUC0zZcoU1f41Hf+RI0ck\nSZI0ZqDtsT399NOShYWFNHPmTOmvv/6Sdu/eLVlbW0sLFixQLTN8+HBpxowZasfx0UcfSS4uLnXW\n8DhZWlpaSgsXLpTOnz8v7du3T+rYsaPqZ1dfJrWpb7937tyRVq5cKZmYmKiOoTZ15V1XzZKk3TlZ\n2/7atm0rbdq0SW1+z549pbfffluSJEnavn279L///U+6cOGCdPbsWWn69OlSx44dpcLCQrVMtTkf\ntN1WfedMSEiINGLECK2PvTE/00qlpaWStbW1lJycXO+yTUlf+yVq6djIEwlU/QP9zz//lNzc3KTB\ngwdLxcXFUuvWraWvvvpKbZ1//vOf0rPPPitJkiTdvHlTUigU0sGDB2vd/ogRI6SpU6eqzbt//75k\nZmYm7d27V23+Dz/8IFlaWqqmn376aemJJ56os+b79+9LpqamddZY17aqunfvntSmTRvpm2++UZvf\nr18/tUa+6v7rO35Jqj0DbY6tcjlXV1epoqJCNW/16tVSmzZtpOLiYkmS6m/kNdVQfX8NydLX11dt\nmdmzZ0uDBw+WJEm7TKrSdr9r166VTExM6t2eprzrqlnbc7I2QUFB0j/+8Q/V9LFjxySFQiFduHCh\n1uWVSqVkZWUlbdiwQa0+bc4HbbdV3zlT/ede37E39Gda3RtvvFHr+adrIvf79ttvS97e3pKzs7Pk\n7Ows9ejRQ/L09JROnDghZP9EzQWH1hAJdvDgQZibm8PMzAze3t5wd3fHhg0bkJ6ejvLycgwbNkxt\n+WHDhuHPP/8EAFhZWWH69OkYNWoUxowZg8jISJw/f77O/f35558oKSlBYGAgzM3NVa9Zs2ahqKgI\nhYWFqmX79u1b57YyMjJQVlZWZ43abuvixYsoLS3FkCFD1OY/+eSTGscT13b8Fy5cqHM/2tZTacCA\nAWpfTBwyZAhKS0tx8eJFrdbXlrZZKhQK+Pj4qC1ja2uL69evA2h4Jg35GTZWfTU35JysLiQkBPv2\n7UNBQQEAYN26dRg4cKDqTkeXL1/GpEmT4OHhgQ4dOqBDhw64c+cOMjMz1bajzfmg7bYacs5oc+yP\nc54DwCuvvIJNmzbhzp07avPnzZun9TYao7b9fvPNN/jvf/+LGTNm4OHDh02yn61bt2Ls2LE4ffo0\nFi5ciN9//x3nzp3D2bNn4efn1yT7IJILNvJEgg0aNAinTp3CX3/9hdLSUuzdu1c1vlobq1evxokT\nJzBy5EgcOnQI3t7eWL16NQDU2gBX3oVjy5YtOHXqlOp15swZpKenw8rKCsCj5qtdu3ZNcIRNu63q\nqh+/l5eX6viboh5Nf0RUMjIyqrFMeXm5VtturNatW6tNKxQKtburNCYTXaurZm3PydqMHDkSnTt3\nxoYNG1BeXo6ffvoJISEhqvdfeOEFZGdn48svv0RycjJOnjwJa2trtS9ca3s+aLMtoP5zpiptj72x\nP9P8/Hx899136Nu3L3788UcAj87PlStX4pdfftG6zoaqbb+HDh1C//79ERYWhg4dOmDlypVNsq/x\n48dj4MCBAIDffvsNdnZ2TbJdIjliI08kWJs2beDm5gYnJyeYmPx9B1h3d3eYmpqqvixYqbJZr6pX\nr15YsGAB4uLiMG3aNNUHfOvWrWtc9erVqxfatGmDixcvws3NrcbLyEj7XwMNqbE+3bp1Q+vWrfHb\nb7+pzf/tt99q3Kqv+rSm4wdqz6Ahjh07ptYk//777zA1NUW3bt0AANbW1sjJyVFbJzU1Va1GbWpo\nyiyBujPR5X4bk/fjnJPGxsZ4+eWX8eOPP2LPnj0oKipCUFAQAKCwsBDnzp3Dv//9b4wcORI9evSA\nqakp8vPzG3xcDdlWfedMY49d259ppb/++gtz5szBhx9+iHnz5iEmJgbAoy/Yz5s3D46Ojg3OQRua\n9nvlyhXVl6jd3Nxw9erVJt1vXl6ezv+IJmrueB95ombCzMwMr7/+Ot5991106dIFvXv3xpYtW7Br\n1y7s378fwKPhKKtXr0ZAQAAcHBxw7do1HD58GP369QPw6MPywIEDuHTpEiwsLGBpaYn27dvjrbfe\nwltvvQWFQgF/f388fPgQaWlpOHnyJJYuXQpAu1vkaVOjtttq164dZs2ahXfeeQc2Njbo3r07vv32\nW1y4cAHW1tZqy1ZuKyMjA2vWrFE7/iNHjqgNk3B1dVXLoEOHDg26/V9hYSHCwsIwb948XLx4Ee+9\n9x5mzZqFtm3bAnh03/TZs2djy5Yt8PX1xZYtW5CUlARLS0uNNVhaWqr90daUWWqTSWP2q63G5K3t\nOanJ5MmTsXz5cnzwwQcYO3asKnsrKyt06dIFq1evhpubGwoKCvDmm2+qfnaVtDkftN0WUP8509Bj\nb+jPFAAOHDiA999/Hzt27ICFhQUCAgIwd+5c/Pbbb3jyySfrPNbjx4+jqKgIzz77bJ3LNXS/kyZN\nUt2pKCUlBS+++GKT7RcAtm3bpvrdR9RSsZEnEqi+B8N88sknMDIywvz583Hjxg14eHhgw4YNeOaZ\nZwA8an4zMjIQFBSEGzduoFOnTnjhhRfw+eefAwDCw8ORlpYGHx8fFBcX48CBAxg2bBjeeecd2Nra\nIjo6GuHh4Wjbti2eeOIJTJkypd7aqs+vr0ZtjrPS0qVL8eDBA0yaNAkAEBQUhLCwMGzZsqXWbbVv\n377O468tg8TERK2PTaFQYOLEiTA3N8fQoUNRVlaGoKAgtcYyJCQEZ86cQVhYGMrKyvDKK6/g9ddf\nVw0nqOvn0FRZNjST6rTZb+V+6qNt3tXnaXNOauLt7Q1fX1+cOnUKS5YsUc03MjLC//73P7z++uvo\n3bs3XFxc8MknnyAiIqLOWmqb35Bt1XfONPTYG/ozzczMREREBH755RfVg+VatWqFhQsXYsWKFfU2\n8rGxsUhMTMTJkyfrXK4x+zU3N8eFCxdQVlZWo5Fv7H4rHT16FHPmzGnUukSGQiE1ZHAfERERydIz\nzzyDAwcO1Pret99+i2nTpjX5PktLS/H222/jk08+gampqbD9ErUUHCNPRETUwlW/w01T+e677/D+\n++/D1NQU27dvF7ZfopZCSCP/6quvwsbGps4vUr3++uvw8PCAj48P/vjjDxFlERERtQjR0dFIT0/H\nZ599htzcXLX3fvnlF4wYMaLJ9xkXF4eIiAi4ubmhS5cuuHnzppD9ErUkQobWHDlyBO3bt8fkyZOR\nlpZW4/24uDhER0cjLi4OycnJmDdvHo4eParrsoiIiIiIZEvIFfmnnnqqzvsC79q1S3Uf4IEDB+L2\n7duqB4cQEREREVFNzeKuNTk5OWr3t3VwcEB2djZsbGzUlktISBBdGhERERGRzvn7+zd4nWbRyAM1\nn4yn6bZncnz8cmRkZI1blpFuMXPxmLl4zFw8Zi4eMxePmYuXmpraqPWaxV1r7O3tkZWVpZrOzs6G\nvb29HisiIiIiImremkUjHxAQgHXr1gF49IAHS0vLGsNq5CwzM1PfJbQ4zFw8Zi4eMxePmYvHzMVj\n5vIhZGjNSy+9hEOHDqGgoACOjo5YsmQJysvLAQChoaEYM2YM4uLi4O7ujnbt2mHt2rUiyhLGy8tL\n3yW0OMxcPGYuHjMXj5mLx8zFY+byIasnuyYkJMhyjDwRERERkSapqany/rLr45AkCfn5+VAqlRq/\nJEuGp/JvUAsLC7Rv317P1RARERGJZRCNfH5+PszNzWFmZqbvUkgwSZJw8+ZNlJaWolOnTqr5SUlJ\nGDp0qB4ra3mYuXjMXDxmLh4zF4+Zy0ez+LLr41IqlWziWyiFQoFOnTqhtLRU36UQERERCWUQY+Rz\nc3Nha2urh4qoueA5QERERHLV2DHyBnFFnoiIiIiopWEjTwYpKSlJ3yW0OMxcPGYuHjMXj5mLx8zl\ng408EREREZEMsZFv4YYMGYLff/9d5/tJT0/HsGHD4OzsjDVr1uh8f/y2vXjMXDxmLh4zF4+Zi8fM\n5cMgbj9Zm+Kr1/Dg2nWdbb+NnQ3MnO10tn1t+Pj4YNWqVRg2bFijtyGiiQegqvPjjz8Wsj8iIiIi\nQ2ewjfyDa9dxZlGkzrbv9XmE3ht5hUKBxt506OHDhzAxadyPvzHrZmVlITAwsN7lYmJikJ+fj3ff\nfbdRtVXiPXDFY+biMXPxmLl4zFw8Zi4fHFojiI+PD1asWIHBgwfDzc0Nr732mure5+fPn8fYsWPh\n6uqKIUOGID4+XrXeypUr4eXlBWdnZwwcOBBHjhwBAMyaNQvZ2dkIDg6Gk5MToqOjkZubi5CQEHTv\n3h19+vTB6tWra9QQFRWFoUOHwsnJCUqlEj4+Pjh06FC9dVRft6KiosYxalp/3LhxSEpKQkREBJyd\nnXHp0iWNOc2cORM7duxAfn5+I5MmIiIiahnYyAu0ZcsWbN26FampqcjIyMDy5cvx8OFDBAcHw9/f\nH+np6YiMjERoaCgyMjKQnp6Ob775BgkJCbh69Sq2bt0KR0dHAMDXX38NBwcHbNy4EZmZmQgLC0Nw\ncDC8vb1x9uxZ7NixA19//TUSExPVati2bRs2b96My5cvw9jYGAqFAgqFAuXl5bXWcfHixVrXNTJS\nP3XqWn/nzp0YPHgwli1bhqtXr8LNzU1jRgqFAhMmTMDmzZsfK2teSRCPmYvHzMVj5uIxc/GYuXyw\nkRdEoVBgxowZsLOzg6WlJcLDw7F161YcP34cxcXFmD9/PkxMTPDUU0/hueeew9atW2FiYoKysjL8\n9ddfKC8vh4ODA1xcXGrd/okTJ1BYWIhFixbBxMQEzs7OmDRpErZv365Ww8yZM2FnZwdTU1O19TXV\nsWXLlnrX1WZ9AFoPA3rppZcQGxur1bJERERELRUbeYHs7e1V/3ZwcEBeXh7y8vLU5gOAo6MjcnNz\n4erqik8//RSRkZF44oknMH36dOTl5dW67ezsbOTl5cHV1VX1WrFiBW7cuKGxhqo01VF1f5rW1XZ9\nhUKhcf2qCgoKUFJSghMnTmi1fG14D1zxmLl4zFw8Zi4eMxePmcsHG3mBsrOz1f7dtWtXdO3aFTk5\nOWpXq7OysmBn9+iLtOPHj0dcXBxOnToFhUKBJUuWqJar2hjb29vD2dkZly9fVr2uXr2Kn376Sa0G\nTc20ra1trXXY2trWuy4AjcdRdX1tJCQkIDU1FeHh4aqr8kVFRdi9eze++OKLBm2LiIiIyJCxkRdE\nkiR8++23uHbtGm7duoXly5cjMDAQffv2Rdu2bREVFYXy8nIkJSVh3759CAwMREZGBg4fPozS0lKY\nmpqiTZs2MDY2Vm2zS5cuuHLlCgDAz88P7du3R1RUFEpKSqBUKnHu3Dn88ccfWtVXVx3a6NevX73r\n1ze0ZsuWLTh8+DBmzpyJcePGYe/evXjw4AEsLCzg6+uLsrIyrWoBOL5PH5i5eMxcPGYuHjMXj5nL\nBxt5QSq/xDl+/Hj4+fmhW7duCA8PR6tWrRAbG4v9+/fDw8MDb775Jr766iu4u7ujrKwMH330Ebp3\n7w5PT08UFhaq3ZZxwYIF+Pzzz+Hq6oqYmBhs3LgRaWlp8PPzg4eHB+bPn4+7d+9qVV9ddTTV+nVd\n0T927BgOHTqk+j8O5ubmGDNmDLZt26bV/omIiIhaGoXU2BuR60FCQgL8/PxqzM/Nza0xhKO5PRDK\n19cXUVFRj/XwppYsKysLsbGxiIiIqPX96ucA74ErHjMXj5mLx8zFY+biMXPxUlNT4e/v3+D1DPaB\nUGbOdnp/YBM1HRn9vUlEREQkBIfWULN379497N69G6dOncK5c+e0WodXEsRj5uIxc/GYuXjMXDxm\nLh8Ge0W+uTl58qS+S5Ct9u3bIywsDGFhYfouhYiIiKjZ4BV5Mki8B654zFw8Zi4eMxePmYvHzOWD\njTwRERERkQwZ7F1rqGXhOUBERERy1di71gi7Ih8fH48ePXrAw8MDkZGRNd4vKCjA888/D19fX3h5\neeH777/Xetsy+luEdITnABEREbU0Qhp5pVKJuXPnIj4+HmfPnsXGjRtr3H0kOjoaffr0wcmTJ3Hw\n4EGEh4fj4cOHWm3f2NgYxcXFuiidmjlJklBYWAhTU1O1+RzfJx4zF4+Zi8fMxWPm4jFz+RBy15qU\nlBS4u7vDxcUFABAUFISdO3fC09NTtYytrS1Onz4NACgqKkKnTp1gYqJdedbW1sjPz8ft27frfHqo\nvty5cwcdOnTQdxkGp/IqvIWFBdq3b6/naoiIiIjEEtLI5+TkwNHRUTXt4OCA5ORktWVmzJiBZ599\nFnZ2drh79y42b95c67bCwsLg5OQE4FED5+3tjaFDh8LGxkb1F2Tl/U853XKnhw4d2qzqaQnTlfOa\nSz0tZbpSc6mH05xu6mn+Pufvc0OcTktLQ1FREQAgMzMT06ZNQ2MI+bLr1q1bER8fjzVr1gAA1q9f\nj+TkZKxatUq1zMcff4yCggKsWLECFy9exMiRI3Hq1CmYm5urltH0ZVciIiIiIrlq1l92tbe3R1ZW\nlmo6KysLDg4Oasv8/vvvmDhxIgCgW7ducHV1xfnz50WUp3PVr5yR7jFz8Zi5eMxcPGYuHjMXj5nL\nh5BGvl+/fkhPT8eVK1dQVlaGTZs2ISAgQG2ZHj16YP/+/QCA69ev4/z583BzcxNRHhERERGR7Ai7\nj/yePXswf/58KJVKTJs2DYsXL0ZMTAwAIDQ0FAUFBZg6dSoyMzNRUVGBxYsXIzg4WG0bHFpDRERE\nRIamsUNrDOKBUEREREREctWsx8i3dBxrJh4zF4+Zi8fMxWPm4jFz8Zi5fLCRJyIiIiKSIQ6tISIi\nIiLSIw6tISIiIiJqQdjIC8CxZuIxc/GYuXjMXDxmLh4zF4+ZywcbeSIiIiIiGeIYeSIiIiIiPeIY\neSIiIiKiFoSNvAAcayYeMxePmYvHzMVj5uIxc/GYuXywkSciIiIikiGOkSciIiIi0iOOkSciIiIi\nakHYyAvAsWbiMXPxmLl4zFw8Zi4eMxePmcsHG3kiIiIiIhnSaoy8r68vQkJCEBwcDBsbGxF11Ypj\n5ImIiIjI0Oh0jPx7772Hw4cPw83NDaNHj0ZsbCwePHjQ4J0REREREVHT0KqRDwwMxPbt25GVlYVx\n48bhyy+/RNeuXTF16lQkJibqukbZ41gz8Zi5eMxcPGYuHjMXj5mLx8zlo0Fj5Dt27IjJkydj1qxZ\ncHR0xLZt2xAaGoru3bvj119/1VWNRERERERUjVZj5CVJwt69e7F+/Xrs3r0bgwYNwuTJkxEYGIi2\nbdti27ZtmDNnDvLy8nRaLMfIExEREZGhaewYeRNtFuratSs6d+6MyZMnY+nSpXBwcFB7PzAwEFFR\nUQ3eOVFj3buYCVT5G7R1Zyu0trTQY0VEREREYmk1tOaXX37Bn3/+iYiIiBpNfKWDBw82ZV0GhWPN\nGuZexlUUHjmuet27cKXGMhmRq5EaEqF6leXfVHufmYvHzMVj5uIxc/GYuXjMXD60uiL/3HPP4ebN\nmzXmW1tbIz8/v8mLopbtfkYmzn/0X9W0x5vT0b67i/4KIiIiImqGtLoiX15eXus8pVLZ5AUZoqFD\nh+q7hBaHmYvHzMVj5uIxc/GYuXjMXD7qvCL/1FNPAQBKSkpU/66UnZ2NwYMHa72j+Ph4zJ8/H0ql\nEtOnT0dERESNZQ4ePIgFCxagvLwcnTt35nAdIiIiIiIN6mzkp02bBgA4duwYpk+fjsob3CgUCtjY\n2Gj97VqlUom5c+di//79sLe3R//+/REQEABPT0/VMrdv30ZYWBj27t0LBwcHFBQUNPaYmp2kpCT+\ndSsYMxePmYvHzMVj5uIxc/GYuXzU2chPmTIFADBo0CD06NGj0TtJSUmBu7s7XFxcAABBQUHYuXOn\nWiMfGxuL8ePHq75M27lz50bvj4iIiIjI0Gls5H/88UdMmjQJAPDbb7/h999/r3W5V199td6d5OTk\nwNHRUTXt4OCA5ORktWXS09NRXl6OZ555Bnfv3sW8efNU+68qLCwMTk5OAAALCwt4e3ur/mqs/JY1\np5vvdPmdu/Bq1xEAkHzmNIxMTDBq6sswNm2tWt4Dj5y5f1Ntuvr2Kt+v3F7V94cOHdosjrclTVfO\nay71tJTpSs2lHk5zuqmn+fucv88NcTotLQ1FRUUAgMzMTNUomIbS+ECoMWPGIC4uDgAwfPhwKBSK\nWjdw4MCBeneydetWxMfHY82aNQCA9evXIzk5GatWrVItM3fuXKSmpiIhIQHFxcUYPHgwfvnlF3h4\neKiW4QOh5K848xqOv7RQNW3c3gwur44HjP7+3vXtE3+i8Mhx1bT7wqno/PQA1bTCxBhn3liGu2cz\nVPM8P1kAk3ZmqunWnS3RzvXvPx6JiIiImqsmfyBUZRMPPP494u3t7ZGVlaWazsrKqnE/ekdHR3Tu\n3Blt27ZF27ZtMWzYMJw6dUqtkZerqn/VkjrlvWJcjPqxzmUuRa/H1bXb1OaV3y5Smz739hdq03cC\nn8LY8LCmKZK0wvNcPGYuHjMXj5mLx8zlQ+PtJysqKrR6aaNfv35IT0/HlStXUFZWhk2bNiEgIEBt\nmXHjxiEpKQlKpRLFxcVITk5Gz549H+/oyCBUlJWj/NYdtRdq/x9JRERERC2GxivyJiYa31JRKBRa\n3UvexMQE0dHRGDVqFJRKJaZNmwZPT0/ExMQAAEJDQ9GjRw88//zz6N27N4yMjDBjxgyDaeT5V614\nA3p66buEFofnuXjMXDxmLh4zF4+Zy4fGbv3SpUtNuqPRo0dj9OjRavNCQ0PVphctWoRFixY16X6J\niIiIiAyRxqE1Li4uWr2oftXvLkG6l3L2jL5LaHF4novHzMVj5uIxc/GYuXxovCI/Y8YM1V1marsN\nJPBoaM26det0UxkREREREWmksZF3c3NT/btbt25QKBSofqdKTbekJHUcayYex8iLx/NcPGYuHjMX\nj5mLx8zlQ2Mjv3jxYtW/P/jgAxG1EOmMpFSiJOe62rxWVh3QyrydnioiIiIiejwax8hXl5CQgOnT\np2PMmDGYMWMG9u/fr8u6DArHmlUh6P/iVB8jX1GuxNm3v8DxlxaqXuWFt4XU0lLwPBePmYvHzMVj\n5uIxc/nQqpFfvnw5XnrpJXTq1An/+Mc/0LFjR7z88sv4/PPPdV0fyVzRuQxkbdileuXHHdZ3SURE\nREQGof6bxeNRI5+YmAgvr7/HHU+ePBkjRozg7SK10JLHmpXmFuDyl7HC98sx8uK15PNcX5i5eMxc\nPGYuHjOXD62uyCsUCnTr1k1tnpubG4yMtB6ZQyQWv4hNREREBk5jJ15RUaF6ffDBB5g+fTouXLiA\nkpISnD9/HjNnzsSSJUtE1ipbHGsm3t61G3D1uy2qV/b6nSi9XqDvsgwaz3PxmLl4zFw8Zi4eM5cP\njUNrTExqvrVx40a16djYWEyfPr3pqyJ6TPfOX8bV7C36LoOIiIhIZzQ28pcuXRJZh0HjWDPxvNp1\n1HcJLQ7Pc/GYuXjMXDxmLh4zlw+NjbyLi4vAMoiIiIiIqCG0/rbqzp07sXDhQoSEhGDSpEmYPHky\nJk+erMuB4OWAAAAgAElEQVTaDAbHmol35v5NfZfQ4vA8F4+Zi8fMxWPm4jFz+dCqkV+yZAlCQ0NR\nUVGBzZs3o3Pnzti7dy8sLS11XR8REREREdVCq0b+22+/xa+//ooVK1bA1NQUX3zxBXbv3o3Lly/r\nuj6DwLFm4nGMvHg8z8Vj5uIxc/GYuXjMXD60auTv3LkDb29vAEDr1q1RVlaGAQMG4NChQzotjoiI\niIiIaqdVI+/m5oY///wTANCrVy989dVXWLduHTp25FVPbXCsmXgcIy8ez3PxmLl4zFw8Zi4eM5cP\njXetqerjjz9GQcGjh+ksXboUwcHBuHfvHr788kudFkekS4pWWp3+RERERM2SQpIkSd9FaCshIQF+\nfn76LoMa4EbiUZx7d4W+y6iVRS8PGJm2Vk07BI9Fx8G+eqyIiIiIWqLU1FT4+/s3eD2tL0leuHAB\nmzdvxrVr12Bvb4+JEyeie/fuDd4hUXNR9Ge62rTtiyP0VAkRERFRw2k1Rj42NhZ+fn5IS0tD+/bt\ncfr0afj5+WHDhg26rs8gcKyZeBwjLx7Pc/GYuXjMXDxmLh4zlw+trsi//fbbiIuLw7Bhw1Tzjhw5\ngkmTJuHll1/WWXFEIimMtH4+GhEREZHeaTVGvkuXLrh27RpatWqlmldeXg47OzvcuHFDpwVWxTHy\n8tOcx8hX18G7O8y6Oamm2/dwg+3YZ/VYEREREbUEOh0jv3DhQixevBgfffQR2rZti+LiYrz//vtY\nsGBBg3dIhkNZUory23f+nqFQoKzgNpQPHqhmPcjJ00NljXMn7QLupF1QTVuPeoqNPBERETVbGht5\nR0dHtem8vDysXLkSVlZWuHXrFgDA1tYWb731llY7io+Px/z586FUKjF9+nRERETUutyxY8cwePBg\nbN68GYGBgdoeR7OWlJRkkE9JK799B6nT3kbFg1LVvIqycqAZ3AjpzP2bfLqrYIZ6njdnzFw8Zi4e\nMxePmcuHxkb+xx9/rHdlhUKh1U6USiXmzp2L/fv3w97eHv3790dAQAA8PT1rLBcREYHnn38eMror\nZotWUVqGitIyfZdBRERE1OJobOSHDx/eZDtJSUmBu7s7XFxcAABBQUHYuXNnjUZ+1apVmDBhAo4d\nO9Zk+24O+FeteLwaLx7Pc/GYuXjMXDxmLh4zlw+txsiXlZXh448/xo8//ohr167Bzs4OkyZNwjvv\nvIPWrVvXu35OTo7aUB0HBwckJyfXWGbnzp1ITEzEsWPHNF7tDwsLg5PToy8kWlhYwNvbW3XCVd4u\nidNipn9PScH5uwXo1cocwN+3fKxsouU+nZp9GQVV/veivvPmNKc5zWlOc5rThjGdlpaGoqIiAEBm\nZiamTZuGxtDqrjULFixASkoK3n//fTg5OSEzMxMffvgh+vXrhxUr6r8jydatWxEfH481a9YAANav\nX4/k5GSsWrVKtczEiROxaNEiDBw4EFOmTMHYsWMxfvx4te3I9a41SUmGMdZMqqhQmy4rvI1jQQvU\nxsg3F00xRt561FPo8V5YE1Vk+AzlPJcTZi4eMxePmYvHzMXT6V1rNm/ejFOnTqFz584AgB49esDP\nzw+9e/fWqpG3t7dHVlaWajorKwsODg5qy5w4cQJBQUEAgIKCAuzZswetWrVCQECA1gdDunX7+Blc\njvlJNS0pK5plE09ERETUEmjVyD+ufv36IT09HVeuXIGdnR02bdqEjRs3qi1z6dIl1b+nTp2KsWPH\nGkwTbyh/1VaUlePeX5fqX7AZ4Bh58QzlPJcTZi4eMxePmYvHzOVDq0dZTpw4EQEBAYiPj8e5c+ew\nZ88ejBs3DhMnTtRqJyYmJoiOjsaoUaPQs2dP/N///R88PT0RExODmJiYxzoAIiIiIqKWSKtGftmy\nZRgxYgTmzp2Lvn374rXXXsOzzz6LZcuWab2j0aNH4/z588jIyMDixYsBAKGhoQgNDa2x7Nq1aw3m\nHvLA319yIHEqv7hK4vA8F4+Zi8fMxWPm4jFz+ah3aM3Dhw8xY8YMxMTE4MMPPxRRExERERER1aPe\nK/ImJibYt28fjI2NRdRjkDjWTDyOkReP57l4zFw8Zi4eMxePmcuHVkNrFixYgPfeew9lZXyCJxER\nERFRc6BVIx8VFYXPP/8c5ubmcHBwgKOjIxwdHVUPZqK6cayZeLoaI3/n9Hlc27pX9bp3/rJO9iNH\nPM/FY+biMXPxmLl4zFw+tLr95Pr162t90qoWz5IiMihFJ8+p3Uu/19JFaP+Eqx4rIiIiopZKq0Z+\n8ODB+Pjjj7Fx40Zcu3YNdnZ2CAoKwjvvvKPr+gyCXMea3T2bgfI7d1XTxZez9VhNwzTJGPmKCpTf\nvQ9UeaJthVL5+Ns1UHI9z+WMmYvHzMVj5uIxc/nQqpGfPXs2Lly4gFWrVsHJyQmZmZn45JNPkJOT\ng7Vr1+q6RtKTGweOIjv2Z32XoTc3DhzFnbQLavPKb93RUzVERERE6rQaI79jxw7s3r0bo0ePRq9e\nvTB69Gjs2rULO3bs0HV9BoFjzcRrijHy0kMlSvNuqL0qSvmFb014novHzMVj5uIxc/GYuXxo1cjb\n2tqiuLhYbV5JSQns7Ox0UhQREREREdVNq6E1kyZNwujRozF37lw4OjoiMzMTX375JSZPnozExETV\ncs8++6zOCpUzjjUTj/eRF4/nuXjMXDxmLh4zF4+Zy4dWjfzXX38NAPjss89U8yRJwtdff616DwAu\nX+at+IiIiIiIRNCqkb9y5YqOyzBsSUlJzf6v27KCW7j03/V4eO/vIVT3zl3UY0WP58z9m7wqL5gc\nznNDw8zFY+biMXPxmLl8aNXIk+GTIOFWShrKbxfpuxQiIiIi0oJWX3alx8O/asXj1XjxeJ6Lx8zF\nY+biMXPxmLl8sJEnIiIiIpIhNvIC8H6s4jXFfeSpYXiei8fMxWPm4jFz8Zi5fLCRJyIiIiKSIYUk\nSZK+i9BWQkIC/Pz89F2GQSotuInUkH/zy64NZDvOH+2fcFNNt3WwgWVfLz1WRERERHKTmpoKf3//\nBq/Hu9YQPYbcnQkAElTT9v96no08ERERCcGhNQJwrJl4HCMvHs9z8Zi5eMxcPGYuHjOXDzbyRERE\nREQyxEZeAN6PVTzeR148nufiMXPxmLl4zFw8Zi4fbOSJiIiIiGSIjbwAHGsmHsfIi8fzXDxmLh4z\nF4+Zi8fM5UNYIx8fH48ePXrAw8MDkZGRNd7fsGEDfHx80Lt3bzz55JM4ffq0qNKIiIiIiGRHyO0n\nlUol5s6di/3798Pe3h79+/dHQEAAPD09Vcu4ubnh8OHD6NChA+Lj4zFz5kwcPXpURHk6x7Fm4nGM\nvHg8z8Vj5uIxc/GYuXjMXD6ENPIpKSlwd3eHi4sLACAoKAg7d+5Ua+QHDx6s+vfAgQORnZ0tojT6\n/ylM+EiBpnB9zxHc/euyatqkXVu4vzkDbaw76bEqIiIiMkRCurecnBw4Ojqqph0cHJCcnKxx+W+/\n/RZjxoyp9b2wsDA4OTkBACwsLODt7a36y7FyTFdzm66c11zqGTp0KG7/cRbbl/wHAODbxR6QJPxx\n7SogSaqr2ZXjzOU4XXWMvND9378Jr7v3VdPGZm3gjhkAms/5qKvpr776Shb/PRrSdFpaGmbPnt1s\n6mkJ05Xzmks9LWG6evb6rqclTPP3uZjf30VFRQCAzMxMTJs2DY2hkCRJatSaDbB161bEx8djzZo1\nAID169cjOTkZq1atqrHsgQMHEBYWht9++w1WVlZq7yUkJMDPz0/X5Ta5pKQk1Q+vubiVchppCz7V\ndxk6c+b+zWYxvMbEvB381i1rEVfkm+N5buiYuXjMXDxmLh4zFy81NRX+/v4NXs9EB7XUYG9vj6ys\nLNV0VlYWHBwcaix3+vRpzJgxA/Hx8TWaeDnjfwziNYcmHgAqHj5EWX4hyvILVfNad7JCG9sueqxK\nN3iei8fMxWPm4jFz8Zi5fAhp5Pv164f09HRcuXIFdnZ22LRpEzZu3Ki2TGZmJgIDA7F+/Xq4u7uL\nKItI5ypKSnEy9D21eV7L/22QjTwRERGJJeT2kyYmJoiOjsaoUaPQs2dP/N///R88PT0RExODmJgY\nAMCHH36IW7duYfbs2ejTpw8GDBggojQhqo7vIzF4H3nxeJ6Lx8zFY+biMXPxmLl8CLkiDwCjR4/G\n6NGj1eaFhoaq/v3NN9/gm2++EVUOEREREZGs8cmuAjTHsWZGrVvpuwSdai5j5FuS5nieGzpmLh4z\nF4+Zi8fM5UPYFXnSr7yfDyJv137VdHnRPT1WQ0RERESPi1fkBWgOY83Kbt5C0Z8ZqldJVp6+S9Ip\njpEXrzmc5y0NMxePmYvHzMVj5vLBRp6IiIiISIbYyAvAsWbicYy8eDzPxWPm4jFz8Zi5eMxcPtjI\nExERERHJEBt5ATjWTDyOkReP57l4zFw8Zi4eMxePmcsHG3kiIiIiIhliIy8Ax5qJxzHy4vE8F4+Z\ni8fMxWPm4jFz+eB95A1Q+d37yI8/DOX9EtW8goMpeqyIqlI+KMX9S1mqaaPWrdDWoaseKyIiIiI5\nYiMvQFJSkk7/un1YUoKKkjLVtPTwIbI3/oLS6wU622dzd+b+zWZ7Vf7c21+oTTtPmwDnVyfoqZqm\no+vznGpi5uIxc/GYuXjMXD7YyBuA+xeu4tx7K9XmlRXc0lM1RERERCQCG3kBdP5XrSSxca+muV6N\nN2S8eiMeMxePmYvHzMVj5vLBRp5IzwoOpkBh9Pf3zo3N2sB61DC06tBej1URERFRc8dGXoCmHmtW\n9GcG7mdcUU2X5Fxvsm0biuY8Rr66+xczcf9ipmraqI0pIElQGBur5nXw64l2bk76KE9rHFMpHjMX\nj5mLx8zFY+bywUZehu6dy0DGF9/ruwzSkYoHpbgY9aPavN6r3tNTNURERNRcsZEXgH/ViieXq/Ha\nkpRKtf/zYtTKBKbWnfRYUU08z8Vj5uIxc/GYuXjMXD7YyBPJwJnwpYDi7+lur02C3YTn9VcQERER\n6R2f7CpAUlJSo9etKCvH7eNncPPoSdXrXsbVJqzOMJ25f1PfJTQpSamE9LDKS5L0XVINj3OeU+Mw\nc/GYuXjMXDxmLh+8It/MSRUVyFjxPYovZ+u7FCIiIiJqRnhFXgCONRPP0MbIywHPc/GYuXjMXDxm\nLh4zlw828kREREREMsRGXoCGjDV7ePc+HlzLV73KbxdBUip1WJ1hMrQx8tVd27oPF5bGqF6X/7sB\nJTnXUZyVq3qV374rtCaOqRSPmYvHzMVj5uIxc/ngGHkB0tLSNP5vquKsXCjv3VdNl9++i7Nv/X9q\ny1SUleu0PkN0+cFdgx5eU5KVi5KsXLV5WbG71aY9P3wdrawsVdOtrMzRztVRZzXVdZ6TbjBz8Zi5\neMxcPGYuH8Ia+fj4eMyfPx9KpRLTp09HREREjWVef/117NmzB2ZmZvj+++/Rp08fUeXpVFFRkcb3\n7qSeRfqyNQKraRnuVzzUdwl6d+69KLVpj4gZOm3k6zrPSTeYuXjMXDxmLh4zlw8hjbxSqcTcuXOx\nf/9+2Nvbo3///ggICICnp6dqmbi4OGRkZCA9PR3JycmYPXs2jh49KqI8oZTFJdXmNL/bCJJhytuV\ngJKr11TTrTtbwfbFEUCVW1kqWreCkQn/Rx0REZEcCPnETklJgbu7O1xcXAAAQUFB2Llzp1ojv2vX\nLoSEhAAABg4ciNu3b+P69euwsbERUWKTuHfhMoqrNEqVLhw9jvxff4PCxBg5m/eg/M7fY5fLb94R\nWWKLkV9e/Q8munvuEu6eu/T3DGMj5O5OVFvGtLMVFFUaebvxo9DpST+ttp+ZmdkkdZL2mLl4zFw8\nZi4eM5cPhSTgyTJbtmzB3r17sWbNoyEk69evR3JyMlatWqVaZuzYsVi8eDGGDBkCABgxYgQiIyPR\nt29f1TIJCQm6LpWIiIiISDh/f/8GryPkirxCoah/IaDG0yqrr9eYAyQiIiIiMkRCbj9pb2+PrKws\n1XRWVhYcHBzqXCY7Oxv29vYiyiMiIiIikh0hjXy/fv2Qnp6OK1euoKysDJs2bUJAQIDaMgEBAVi3\nbh0A4OjRo7C0tJTV+HgiIiIiIpGEDK0xMTFBdHQ0Ro0aBaVSiWnTpsHT0xMxMTEAgNDQUIwZMwZx\ncXFwd3dHu3btsHbtWhGlERERERHJkrAnu44ePRrnz59HRkYGFi9eDOBRAx8aGqpaJjo6GhkZGTh1\n6hT8/LS7U0Zz8+qrr8LGxgbe3t5q81etWgVPT094eXnVeg99ejy15Z6SkoIBAwagT58+6N+/P44d\nO6bHCg1LVlYWnnnmGfTq1QteXl6Iinp0z/qbN29i5MiR6N69O5577jncvn1bz5UaDk2Zv/HGG/D0\n9ISPjw8CAwNx5w7vhNVUNGVeafny5TAyMsLNm4b9JGmR6sqcn6O6oSlzfobqzoMHDzBw4ED4+vqi\nZ8+eqr64UZ+hEjWpw4cPS6mpqZKXl5dqXmJiojRixAiprKxMkiRJys/P11d5Bqu23J9++mkpPj5e\nkiRJiouLk4YPH66v8gxObm6u9Mcff0iSJEl3796VunfvLp09e1Z64403pMjISEmSJGnp0qVSRESE\nPss0KJoy37dvn6RUKiVJkqSIiAhm3oQ0ZS5JkpSZmSmNGjVKcnFxkQoLC/VZpkHRlDk/R3VHU+b8\nDNWt+/fvS5IkSeXl5dLAgQOlI0eONOozVNgV+ZbiqaeegpWVldq8r776CosXL0arVq0AAF26dNFH\naQatttxtbW1VVydv377NL083oa5du8LX1xcA0L59e3h6eiInJ0fteRAhISHYsWOHPss0KLVlfu3a\nNYwcORJGRo9+lQ8cOBDZ2dn6LNOgaMocABYuXIhly5bpszyDpOl3y9dff83PUR3RlDk/Q3XLzMwM\nAFBWVgalUgkrK6tGfYaykRcgPT0dhw8fxqBBgzB8+HAcP35c3yW1CEuXLkV4eDicnJzwxhtv4LPP\nPtN3SQbpypUr+OOPPzBw4EC1h7jZ2Njg+vXreq7OMFXNvKrvvvsOY8aM0VNVhq1q5jt37oSDgwN6\n9+6t77IMWtXML1y4wM9RASozHzRoED9DdayiogK+vr6wsbFRDW1qzGcoG3kBHj58iFu3buHo0aP4\nz3/+g3/961/6LqlFmDZtGqKiopCZmYkvvvgCr776qr5LMjj37t3D+PHjsXLlSpibm6u9p1AotH6G\nBGnv3r17mDBhAlauXIn27dur5n/yySdo3bo1goOD9VidYaqauZGRET799FMsWbJE9b6k++cqtjhV\nMzc3N+fnqADVf7fwM1S3jIyMcPLkSWRnZ+Pw4cM4cOCA2vvafoaykRfAwcEBgYGBAID+/fvDyMgI\nhYWFeq7K8KWkpOCf//wnAGDChAlISUnRc0WGpby8HOPHj8ekSZPw4osvAnh0BSEvLw8AkJubC2tr\na32WaHAqM3/llVdUmQPA999/j7i4OGzYsEGP1Rmm6plfvHgRV65cgY+PD1xdXZGdnY2+ffsiPz9f\n36UajNrOc36O6lZtmfMzVIwOHTrgH//4B06cONGoz1A28gK8+OKLSExMBABcuHABZWVl6NSpk56r\nMnzu7u44dOgQACAxMRHdu3fXc0WGQ5IkTJs2DT179sT8+fNV8wMCAvDDDz8AAH744Qe1ZpMej6bM\n4+Pj8Z///Ac7d+5EmzZt9Fih4aktc29vb1y/fh2XL1/G5cuX4eDggNTUVP7R2kQ0nef8HNUdTZnz\nM1R3CgoKVHekKSkpwa+//oo+ffo07jNUR1/GbbGCgoIkW1tbqXXr1pKDg4P03XffSWVlZdIrr7wi\neXl5SX5+ftKBAwf0XabBqcy9VatWqtyPHTsmDRgwQPLx8ZEGDRokpaam6rtMg3HkyBFJoVBIPj4+\nkq+vr+Tr6yvt2bNHKiwslPz9/SUPDw9p5MiR0q1bt/RdqsGoLfO4uDjJ3d1dcnJyUs2bPXu2vks1\nGJoyr8rV1ZV3rWlCmn638HNUdzSd5/wM1Z3Tp09Lffr0kXx8fCRvb29p2bJlkiRJjfoMVUgSB/cR\nEREREckNh9YQEREREckQG3kiIiIiIhliI09EREREJENs5ImIiIiIZIiNPBERERGRDLGRJyIiIiKS\nITbyRESkNRcXFyQkJOi7DCIiAht5IiJqAIVCAYVCoe8yiIgIbOSJiAxKVFQU3nrrLX2XQUREArCR\nJyIyIK+99ho2b96M69ev1/p+ZGQkJk6cqDZv3rx5mDdvHgBg6dKlcHd3h4WFBXr16oUdO3Zo3JeR\nkREuXbqkmp4yZQreffdd1fS1a9cwfvx4WFtbw83NDatWrXqcQyMiomrYyBMRGRCFQoHg4GD8+OOP\ntb7/0ksvIS4uDvfu3QMAKJVK/O9//8PLL78MAHB3d0dSUhKKiorw/vvv45VXXkFeXp7W+64cdlNR\nUYGxY8eiT58+uHbtGhISErBixQrs27evCY6SiIgANvJERAZnypQp+P7772t9z8nJCX5+fti+fTsA\nIDExEWZmZhgwYAAAYMKECejatSsA4F//+hc8PDyQkpKi9b4lSQIAHDt2DAUFBXjnnXdgYmICV1dX\nTJ8+HT/99NNjHBkREVXFRp6IyMDcuHEDxcXFGhvw4OBgbNy4EQAQGxuruhoPAOvWrUOfPn1gZWUF\nKysrnDlzBoWFhVrvu/KK/NWrV3Ht2jXVdqysrPDZZ58hPz//MY6MiIiqMtF3AURE1HTi4+ORnp6O\nd955B2vXrlVdaa9qwoQJCA8PR05ODnbs2IGjR48CeNR8z5w5E4mJiRg8eDAUCgX69OmjuspenZmZ\nGYqLi1XTubm5cHR0BAA4OjrC1dUVFy5c0MFREhERwCvyREQGIzY2FomJiXjttdcwceJE7N69Gw8e\nPKixXJcuXTB8+HBMmTIFbm5ueOKJJwAA9+/fh0KhQOfOnVFRUYG1a9fizJkzGvfn6+uLDRs2QKlU\nIj4+HocPH1a9N2DAAJibm2PZsmUoKSmBUqnEmTNncPz48aY/cCKiFoqNPBGRATh69Cj279+PZcuW\nAQDMzc3x4osvahyTHhwcjISEBAQHB6vm9ezZE+Hh4Rg8eDC6du2KM2fOYOjQoRr3uXLlSuzevRtW\nVlaIjY3FP//5T9V7xsbG+Pnnn3Hy5Em4ubmhS5cumDlzJoqKiproiImISCFp+n+mTejVV1/FL7/8\nAmtra6SlpdW6zOuvv449e/bAzMwM33//Pfr06aPrsoiIiIiIZEvIFfmpU6ciPj5e4/txcXHIyMhA\neno6Vq9ejdmzZ4soi4iIiIhItoQ08k899RSsrKw0vr9r1y6EhIQAAAYOHIjbt29rfJgJERERERE1\nk7vW5OTkqO50AAAODg7Izs6GjY2N2nIJCQmiSyMiIiIi0jl/f/8Gr9MsGnkANW5vVnkv4ur8/PxE\nlNOkIiMjERERoe8yWhRmLh4zF4+Zi8fMxWPm4jFz8VJTUxu1XrO4a429vT2ysrJU09nZ2bC3t9dj\nRUREREREzVuzaOQDAgKwbt06AI9uoWZpaVljWI2cZWZm6ruEFoeZi8fMxWPm4jFz8Zi5eMxcPoQM\nrXnppZdw6NAhFBQUwNHREUuWLEF5eTkAIDQ0FGPGjEFcXBzc3d3Rrl07rF27VkRZwnh5eem7hBaH\nmYvHzMVj5uIxc/GYuXjMXD6E3Ee+qSQkJMhyjDwRERERkSapqany/rLr45AkCfn5+VAqlRq/JEuG\nSZIkGBsbw9ramj97IiIialEMopHPz8+Hubk5zMzM9F0K6UFxcTHy8/PVvleRlJRU56Plqekxc/GY\nuXjMXDxmLh4zl49m8WXXx6VUKtnEt2BmZmZQKpX6LoOIiIhIKIMYI5+bmwtbW1s9VETNBc8BIiIi\nkqvGjpE3iCvyREREREQtDRt5MkhJSUn6LqHFYebiMXPxmLl4zFw8Zi4fbOSJiIiIiGSIjXwLN2TI\nEPz+++863096ejqGDRsGZ2dnrFmzRuf747ftxWPm4jFz8Zi5eMxcPGYuHwZx+8na3L5ZjLu3H+hs\n++aWbWDZUb93yvHx8cGqVaswbNiwRm9DRBMPQFXnxx9/LGR/RERERIbOYBv5u7cfYN+OMzrb/nMv\neum9kVcoFGjsTYcePnwIE5PG/fgbs25WVhYCAwPrXS4mJgb5+fl49913G1VbJd4DVzxmLh4zF4+Z\ni8fMxWPm8sGhNYL4+PhgxYoVGDx4MNzc3PDaa6+htLQUAHD+/HmMHTsWrq6uGDJkCOLj41XrrVy5\nEl5eXnB2dsbAgQNx5MgRAMCsWbOQnZ2N4OBgODk5ITo6Grm5uQgJCUH37t3Rp08frF69ukYNUVFR\nGDp0KJycnKBUKuHj44NDhw7VW0f1dSsqKmoco6b1x40bh6SkJERERMDZ2RmXLl3SmNPMmTOxY8cO\n5OfnNzJpIiIiopaBjbxAW7ZswdatW5GamoqMjAwsX74cDx8+RHBwMPz9/ZGeno7IyEiEhoYiIyMD\n6enp+Oabb5CQkICrV69i69atcHR0BAB8/fXXcHBwwMaNG5GZmYmwsDAEBwfD29sbZ8+exY4dO/D1\n118jMTFRrYZt27Zh8+bNuHz5MoyNjaFQKKBQKFBeXl5rHRcvXqx1XSMj9VOnrvV37tyJwYMHY9my\nZbh69Src3Nw0ZqRQKDBhwgRs3rz5sbLmlQTxmLl4zFw8Zi4eMxePmcsHG3lBFAoFZsyYATs7O1ha\nWiI8PBxbt27F8ePHUVxcjPnz58PExARPPfUUnnvuOWzduhUmJiYoKyvDX3/9hfLycjg4OMDFxaXW\n7Z84cQKFhYVYtGgRTExM4OzsjEmTJmH79u1qNcycORN2dnYwNTVVW19THVu2bKl3XW3WB6D1MKCX\nXnoJsbGxWi1LRERE1FKxkRfI3t5e9W8HBwfk5eUhLy9PbT4AODo6Ijc3F66urvj0008RGRmJJ554\nAtTaN5gAACAASURBVNOnT0deXl6t287OzkZeXh5cXV1VrxUrVuDGjRsaa6hKUx1V96dpXW3XVygU\nGtevqqCgACUlJThx4oRWy9eG98AVj5mLx8zFY+biMXPxmLl8sJEXKDs7W+3fXbt2RdeuXZGTk6N2\ntTorKwt2dnYAgPHjxyMuLg6nTp2CQqHAkiVLVMtVbYzt7e3h7OyMy5cvq15Xr17FTz/9pFaDpmba\n1ta21jpsbW3rXReAxuOour42EhISkJqaivDwcNVV+YsXL+Lnn39GZGQkTp061aDtERERERkqNvKC\nSJKEb7/9FteuXcOtW7ewfPlyBAYGom/fvmjbti2ioqJQXl6OpKQk7Nu3D4GBgcjIyMDhw4dRWloK\nU1NTtGnTBsbGxqptdunSBVeuXAEA+Pn5oX379oiKikJJSQmUSiXOnTuHP/74Q6v66qpDG/369at3\n/fqG1mzZsgWHDx/GzJkzMW7cOOzduxcPHjzA3r17YWtrizlz5iA6Olqreji+TzxmLh4zF4+Zi8fM\nxWPm8sFGXpDKL3GOHz8efn5+6NatG8LDw9GqVSvExsZi//798PDwwJtvvomvvvoK7u7uKCsrw0cf\nfYTu3bvD09MThYWFardlXLBgAT7//HO4uroiJiYGGzduRFpaGvz8/ODh4YH58+fj7t27WtVXVx1N\ntX5dV/SPHTuGQ4cOqf6Pg7m5OcaMGYNt27Zhzpw56Nu3L3JycuDs7KxVPURERESGTiE19kbkepCQ\nkAA/P78a83Nzc2sM4WhuD4Ty9fVFVFTUYz28qaVbvnw5Zs+eDTOzmrlXPwd4D1zxmLl4zFw8Zi4e\nMxePmYuXmpoKf3//Bq9nsA+EsuxopvcHNlHT2bNnD2bOnInc3Fx069ZN3+UQERER6R2H1lCz9/PP\nP+Pzzz9HSEgIduzYodU6vJIgHjMXj5mLx8zFY+biMXP5MNgr8s3NyZMn9V2CbL3wwgt44YUX9F0G\nERERUbPCK/JkkHgPXPGYuXjMXDxmLh4zF4+ZywcbeSIiIiIiGRLWyMfHx6NHjx7w8PBAZGRkjfcL\nCgrw/PPPw9fXF15eXvj+++9FlUYGiOP7xGPm4jFz8Zi5eMxcPGYuH0IaeaVSiblz5yI+Ph5nz57F\nxo0bce7cObVloqOj0adPH5w8eRIHDx5EeHg4Hj58qNX2ZXQHTdIRngNERETU0ghp5FNSUuDu7g4X\nFxe0atUKQUFB2Llzp9oytra2KCoqAgAUFRWhU6dOMDHR7ru4xsbGKC4ubvK6SR6Ki4vVnngLcHyf\nPjBz8Zi5eMxcPGYuHjOXDyF3rcnJyYGjo6Nq2sHBAcnJyWrLzJgxA88++yzs7Oxw9+5dbN68Wevt\nW1tbIz8/H7dv367z6aH6cufOHXTo0EHfZRgkSZJgbGwMa2trfZdCREREJJSQRl6b5vrTTz+Fr68v\nDh48iIsXL2LkyJE4deoUzM3N1ZYLCwuDk5MTAMDCwgLe3t4YOnQobGxsVH9BVo7t4nTLnR46dGiz\nqqclTFfOay71tJTpSs2lHk5zuqmn+fucv88NcTotLU01EiUzMxPTpk1DYygkAYOLjx49ig8++ADx\n8fEAgM8++wxGRkaIiIhQLTNmzBi8/fbbePLJJwEA/v7+iIyMRL9+/VTLJCQkwM/PT9flEhEREREJ\nk5qaCn9//wavJ2SMfL9+/ZCeno4rV66grKwMmzZtQkBAgNoyPXr0wP79+wEA169fx/nz5+Hm5iai\nPJ2rfuWMdI+Zi8fMxWPm4jFz8Zi5eMxcPkyE7MTEBNHR0Rg1ahSUSiWmTZsGT09PxMTEAABCQ0Px\n1ltvYerUqfDx8UFFRQWWLVuGjh07iiiPiIiIiEh2hAytaSocWkNEREREhqZZD60hIiIiIqKmxUZe\nAI41E4+Zi8fMxWPm4jFz8Zi5eMxcPtjIExERERHJEMfIExERERHpEcfIExERERG1IGzkBeBYM/GY\nuXjMXDxmLh4zF4+Zi8fM5YONPBERERGRDHGMPBERERGRHnGMPBERERFRC8JGXgCONROPmYvHzMVj\n5uIxc/GYuXjMXD7YyBMRERERyRDHyBMRERER6RHHyBMRERERtSBs5AXgWDPxmLl4zFw8Zi4eMxeP\nmYvHzOWDjTwRERERkQxpNUbe19cXISEhCA4Oho2NjYi6asUx8kRERERkaHQ6Rv69997D4cOH4ebm\nhtGjRyM2NhYPHjxo8M6IiIiIiKhpaNXIBwYGYvv27cjKysK4cePw5ZdfomvXrpg6dSoSExN1XaPs\ncayZeMxcPGYuHjMXj5mLx8zFY+by0aAx8h07dsTkyZMxa9YsODo6Ytu2bQgNDUX37t3x66+/6qpG\nIiIiIiKqRqsx8pIkYe/evVi/fj12796NQYMGYfLkyQgMDETbtm2xbds2zJkzB3l5eTotlmPkiYiI\niMjQNHaMvIk2C3Xt2hWdO3fG5MmTsXTpUjg4OKi9HxgYiKioqAbvnP4fe/cfF2Wd7///OQhlpvj7\nJwOiQYlKCmHqrrWVlVGfqPyxS5bZWTRON91T1rYed9u2XHeTtm6leEqOddpV8tfJkmptMtAy6gga\nppSVaCI/RF1/ICooOMz3j75MIUyOyFzXzMXjfrvN7cb7mvfM9ZqXl9e8ePOaawAAAICW8aq15p//\n/Ke++uorzZ49u0kR3+Cjjz5qzbgshV4z45Fz45Fz45Fz45Fz45Fz45HzwOFVIX/rrbc2u71Xr16t\nGgwAAAAA73jVI9+pUyedOHGi0ba6ujr16dNHR44c8Vlw56JHHgAAAFbjkx756667TpJUU1Pj/rlB\nWVmZRo8e7fWOHA6HHn30UTmdTk2bNk2zZ89uMuejjz7SrFmzVFdXpx49etCuAwAAAHjwk4V8SkqK\nJGnLli2aNm2aGhbvbTabevfu7fVvDk6nUzNnzlR2drbCwsI0YsQIJSUlKSYmxj2nsrJSM2bM0Acf\nfCC73a7Dhw+39DX5ndzcXI0ZM8bsMNoUcm48cm48cm48cm48cm48ch44frKQf/DBByVJo0aN0qBB\ng1q8k/z8fEVFRSkyMlKSlJycrKysrEaF/PLlyzVhwgT3h2l79OjR4v0BAAAAVuexkF+2bJmmTJki\nSfr000/12WefNTvv17/+9Xl3Ul5ervDwcPfYbrcrLy+v0ZyioiLV1dXpxhtv1IkTJ/TII4+49/9j\nM2bMUEREhCQpNDRUsbGx7t8aGz5lzZjxmDFj/CqetjBu2OYv8bSVcQN/iYcx49Yecz7nfG7FcWFh\noaqqqiRJJSUl7i6YC+Xxw66333671q1bJ0m64YYbZLPZmn2CjRs3nncna9askcPh0JIlSyRJmZmZ\nysvLU3p6unvOzJkzVVBQoJycHFVXV2v06NH65z//qejoaPccPuwKAAAAq2nph109Xn6yoYiXvv8Q\n6saNG5u9eSMsLEylpaXucWlpaZPr0YeHh+vWW2/VZZddpu7du+v666/X9u3bL/T1+KVzV87ge+Tc\neOTceOTceOTceOTceOQ8cHgs5Ovr6726eSMhIUFFRUUqLi5WbW2tVq1apaSkpEZz7rrrLuXm5srp\ndKq6ulp5eXkaPHjwxb06AAAAwKKCPd4R7PEuN5vNJqfTef6dBAdr0aJFGjdunJxOp1JSUhQTE6OM\njAxJUmpqqgYNGqTbbrtNV199tYKCgjR9+nTLFPI/7jmDMci58ci58ci58ci58ci58ch54PDYI19c\nXOzVEzRcicYI9MgDAADAalq9Rz4yMtKrG86PXjPjkXPjkXPjkXPjkXPjkXPjkfPA4bF/Zvr06e6r\nzDR3GUjp+9aapUuX+iYyAAAAAB55LOQHDhzo/vmKK66QzWbTuV04ni5JicboNTMeOTceOTceOTce\nOTceOTceOQ8cHnvk/RE98gAAALCaVu+RP1dOTo6mTZum22+/XdOnT1d2dvYF76ytotfMeOTceOTc\neOTceOTceOTceOQ8cHhVyL/wwgu699571b17d91xxx3q1q2b7rvvPj3//PO+jg8AAABAM7xqrenX\nr5/Wr1+voUOHurd99dVXuvnmm1VRUeHTAH+M1hoAAABYjU9ba2w2m6644opG2wYOHKigIK87cwAA\nAAC0Io+VeH19vfv29NNPa9q0adq1a5dqamr07bff6qGHHtIzzzxjZKwBi14z45Fz45Fz45Fz45Fz\n45Fz45HzwOHx8pPBwU3vWrFiRaPx8uXLNW3atNaPCgAAAMBP8tgjX1xc7NUTGPntrvTIAwAAwGpa\n2iPvcUXeyAIdAAAAwIXx+tOqWVlZeuyxxzR16lRNmTJFDzzwgB544AFfxmYZ9JoZj5wbj5wbj5wb\nj5wbj5wbj5wHDq8K+WeeeUapqamqr6/X6tWr1aNHD33wwQfq0qWLr+MDAAAA0AyvriMfERGhf/7z\nn4qNjVWXLl1UWVmp/Px8/fnPf9a7775rRJyS6JEHAF85XVOn2jNnm2y/5NJgtb8sxISIAKDtaPUe\n+R87fvy4YmNjJUmXXHKJamtrde211+rjjz++4B0CAPzP8aPV+uf/7miy/Y5JV6t9WGcTIgIAnI9X\nrTUDBw7UV199JUkaMmSIXnnlFS1dulTdunXzaXBWQa+Z8ci58ci58Vo75656V5MbGuM4Nx45Nx45\nDxxercjPmzdPhw8fliTNnz9fkydP1smTJ/Xyyy/7NDgAAAAAzfOqR95f0CMPAL5xsPy43lu1vcn2\n//erYertZWtNvbNeJd8dVV2ts9H2zl0vU69+oa0SJwBYkU975CVp165dWr16tfbv36+wsDBNmjRJ\nV1555QXvEABgTS5JX+SV6Mihk422X3v9QAp5APABr3rkly9frvj4eBUWFqpjx47asWOH4uPj9cYb\nb/g6Pkug18x45Nx45Nx4gZLzbworlLt+V5PbgbLjZod2wQIl51ZCzo1HzgOHVyvyf/jDH7Ru3Tpd\nf/317m2ffPKJpkyZovvuu89nwQEA/FPl0Wo5zzZuoQkKCtLZOmeTuVXHalR1rKbJ9rABXX0WHwC0\nBV4V8idPntTo0aMbbRs1apROnTrlk6CsZsyYMWaH0OaQc+ORc+OZmfM9Xx/SF3klpu3fLBznxiPn\nxiPngcOr1prHHntMc+bMUU3N9ysq1dXV+v3vf69Zs2b5NDgAAAAAzfNYyIeHh7tvL7/8shYsWKDQ\n0FD16tVLnTt31ksvvaTFixd7vSOHw6FBgwYpOjpaaWlpHudt2bJFwcHBeuutty7slfgxes2MR86N\nR86NZ0TOjx+rUVnx0Ua38n3HVHm02uf79kcc58Yj58Yj54HDY2vNsmXLzvtgm83m1U6cTqdmzpyp\n7OxshYWFacSIEUpKSlJMTEyTebNnz9Ztt92mALoqJgBY1ifrd5kdAgDAA4+F/A033NBqO8nPz1dU\nVJQiIyMlScnJycrKympSyKenp2vixInasmVLq+3bH9BrZjxybjxybjxybjxybjxybjxyHji8+rBr\nbW2t5s2bp2XLlmn//v3q16+fpkyZoieffFKXXHLJeR9fXl6u8PBw99hutysvL6/JnKysLG3YsEFb\ntmzxuNo/Y8YMRURESJJCQ0MVGxvrPuAa/hTEmDFjxowvbJy/ZbP27NujK/oPlSTt2felJPl0HPp5\nlQZE/z+/eP2MGTNmbOS4sLBQVVVVkqSSkhKlpKSoJbz6ZtdZs2YpPz9ff/rTnxQREaGSkhLNnTtX\nCQkJeumll867kzVr1sjhcGjJkiWSpMzMTOXl5Sk9Pd09Z9KkSfrtb3+rkSNH6sEHH9Sdd96pCRMm\nNHqeQP1m19zcXPc/HoxBzo1Hzo3Xmjn39M2uvjTqxivUo1fHJts7hrbX5Z0uNTQWb3GcG4+cG4+c\nG8+n3+y6evVqbd++XT169JAkDRo0SPHx8br66qu9KuTDwsJUWlrqHpeWlsputzea8/nnnys5OVmS\ndPjwYb3//vsKCQlRUlKS1y8GAPCDirJK1Z9tvFZz6WXB6tG7U5O5tiDvPvPUmjZv3NPs9qTJcX5b\nyAOAP/GqkL9YCQkJKioqUnFxsfr166dVq1ZpxYoVjeZ899137p//7d/+TXfeeadlinh+qzUeOTce\nOTfe+XJe8Ok+HShv/O2pnbpcprD+XZrMrTlZ26qxWRXHufHIufHIeeDwqpCfNGmSkpKS9NRTT6l/\n//4qLi7WvHnzNGnSJO92EhysRYsWady4cXI6nUpJSVFMTIwyMjIkSampqS1/BQAAr52orNE3lU2/\nZdWfnKw6rbras4222Ww2de/VUZdcasj6EwAEBK965Bs+7Lp8+XL3h13vvfdePfnkk7r0UuP+/EmP\nPLxFzo1Hzo13vpz/c9X2Jivygap9hxDdc/816tDx/BdY8CWOc+ORc+ORc+P5rEf+7Nmzmj59ujIy\nMjR37twWBQcAAACgdXm1It+3b1+VlJQoJCTEiJg8CtQVeQDwpROVNTrrrG+0rV27IG3859c6fPCk\nSVG1Ln9ZkQcAX/DpVWtmzZqlp556Ss8884xX140HABinePcR5W/67vwTAQCWEuTNpIULF+r5559X\np06dZLfbFR4ervDwcPcXM+GnNXwRAIxDzo1Hzo1Hzo1Hzo1Hzo1HzgOHVyvymZmZzX7TqhddOQAA\nAAB8wKse+TNnzmjevHlasWKF+6o1ycnJevLJJ9W+fXsj4pREjzyAtu34sWrVVNc12b7n60P6ZkeF\nCREZhx55AFbm0x75hx9+WLt27VJ6eroiIiJUUlKiv/zlLyovL9frr79+wTsFAFy4o4dPacO7X5sd\nBgDAT3jVI7927Vq9++67SkxM1JAhQ5SYmKh33nlHa9eu9XV8lkCvmfHIufHIufH27PvS7BBM56p3\n6fTpuia32nO+UKq1cJwbj5wbj5wHDq9W5Pv27avq6mp17drVva2mpkb9+vXzWWAAADRik86edTba\nVO90aeN7X+vE8dONtseN6q/oIb2NjA4ADOdVj/z8+fO1fPlyzZw5U+Hh4SopKdHLL7+syZMna8SI\nEe55N910k0+DpUceQFu2t+hfbbq1pmuPDrKp6YUXjh05pXPfyUbfFKXBw1lsAhAYfNojv3jxYknS\ns88+697mcrm0ePFi932StHfv3gsOAAAAbxw7XG12CADgV7zqkS8uLlZxcbH27t3rvp07poj3jF4z\n45Fz45Fz49EjbzyOc+ORc+OR88DhVSEPAAAAwL9QyBtgzJgxZofQ5pBz45Fz413Rf6jZIbQ5HOfG\nI+fGI+eBw6seeQCAcU5VndHxyqb94CcqTzczGwDQVrEibwB6zYxHzo1HzltPdXWt3n+zsMltyyeN\nP4tEj7zxOM6NR86NR84DB4U8AAAAEIC8uo68v+A68gDagn8dOKF3lm8zO4yAFta/q/pHdW+yvVff\nUHXv1dGEiADAM59eRx4AgEBSvu+Yyvcda7L9lruHUMgDsAxaawxAr5nxyLnxyPmFO11Tp+++PaTd\nOw82uh0oO+7V4+mRNx7HufHIufHIeeBgRR4ATFLvdOn/Nu7R6eo6s0NpM9q1Y/0KgHXQIw8AJqk+\nWau3Mz+nkDdQpy7tdVmHS5ps//nYaHXrebkJEQEAPfIAAJzXicrTXI8fgGXwN0YD0GtmPHJuPHJu\nPHrkjcdxbjxybjxyHjgMK+QdDocGDRqk6OhopaWlNbn/jTfe0LBhw3T11Vfr5z//uXbs2GFUaAAA\nAEDAMaRH3ul06qqrrlJ2drbCwsI0YsQIrVixQjExMe45//d//6fBgwerc+fOcjgcevrpp7V58+ZG\nz0OPPAArqT5Vq7eX0SPvD+6Zcg098gBM49c98vn5+YqKilJkZKQkKTk5WVlZWY0K+dGjR7t/Hjly\npMrKyowIDQAMseurAzp+rKbRtnpnvWpPnzUpIgBAoDOkkC8vL1d4eLh7bLfblZeX53H+a6+9pttv\nv73Z+2bMmKGIiAhJUmhoqGJjYzVmzBhJP/R0+du4YZu/xNMWxufm3ux42sL4lVdeCYj/j2aN172X\nrUP7q3RF/6GSfuhvv5jx/gN7dd3IO1vt+dryOC/v/9SpS3vO53445nzO+dyK48LCQlVVVUmSSkpK\nlJKSopYwpLVmzZo1cjgcWrJkiSQpMzNTeXl5Sk9PbzJ348aNmjFjhj799FN17dq10X2B2lqTm5vr\n/seDMci58cj5T/sw6yuV7DnSqs+5Z9+X7kIUF8fb1hqOc+ORc+ORc+P5dWtNWFiYSktL3ePS0lLZ\n7fYm83bs2KHp06fL4XA0KeIDGf8ZjEfOjUfOjUcRbzyOc+ORc+OR88BhyFVrEhISVFRUpOLiYtXW\n1mrVqlVKSkpqNKekpETjx49XZmamoqKijAgLAAAACFiGFPLBwcFatGiRxo0bp8GDB+tXv/qVYmJi\nlJGRoYyMDEnS3LlzdezYMT388MOKi4vTtddea0Rohvhxfx+MQc6NR86Nx3XkW0/p3qP6prCi0W33\n14dUe+Zso3kc58Yj58Yj54HDkNYaSUpMTFRiYmKjbampqe6fX331Vb366qtGhQMAgNvW3L1NtnUM\nvVT2SOu0eQKwHr7Z1QD0mhmPnBuPnBuPHnnjcZwbj5wbj5wHDsNW5AGgLThUUaUjh0422maz2XTs\nX6dMiggAYFWsyBuAXjPjkXPjkfPvHT54Up/l7G50+zS7SCeqTrf6vuiR9636epdO19Tp2JFT7tv7\n67J1/Fi12aG1KZxbjEfOAwcr8gDQAscOn1Ll0aYF3aH9VSZEA1+oPlmrNX/f2mjbnn27dHm7cF0/\n7iqTogKAHxjyhVCtJVC/EAqA9ZTsOaIPs74yOwyYIHpIbwp5AK2qpV8IRWsNAAAAEIAo5A1Ar5nx\nyLnxyLnx6JE33p59X+rwwZPa9eUBfVtY0ej2rwO0VfkC5xbjkfPAQY88AAAX4NjhU/pk/a4m239+\nS7R69gk1ISIAbRWFvAG4HqvxyLnxyLnxuI688X4q56dP1enIoRNNtre/7BJd3ulSX4ZlaZxbjEfO\nAweFPAD8hLo6p87WOZveYTM+Fvi3zz8r1uefFTfZftv4WAp5AD5Bj7wB6DUzHjk3nlVzfqLytLIy\ntzW5ffz+N2aHRo+8Cci58ax6bvFn5DxwsCIPAOdx6uQZs0MAAKAJVuQNQK+Z8ci58ci58eiRNx45\nNx7nFuOR88DBijwASHI661VzqrbJ9gD6zjwAQBvDirwB6DUzHjk3XqDn/GytU+vf/lJvLf280e29\nlV+YHZpH9GsbryU5D2pnk/NsfZObq55fEr0R6OeWQETOAwcr8gDw/6urc6qutpkr1AAXYdMH3+qS\nS5u+3d54R4y6dOtgQkQArIJC3gD0mhmPnBsv4HMegJeTpF/beC3J+cmqM5L4wHRLBfy5JQCR88BB\nIQ+gzflmR4UO7a9qtM3lcqn6ZNMeecBXXPUunTh+usn2yztdqqCgAPzNEoDhKOQNkJuby2+3BiPn\nxguknB+qqFLRzoNmh3HR9uz7klV5g7VmzrPeKJBsjQv2kJB2GhIX1uQvRN17dVT4gG6tst9AE0jn\nFqsg54GDQh4AABM4nS5JjT/w6jxb3+y3ww6JD2uzhTwAzyjkDcBvtcYj58bzx5wfOXRSp0407k22\nBdlUVdm0nSEQsRpvPHJuPH88t1gdOQ8cFPIAAt6Z03Wqq2t6tZmD+6v0fxt2mxAR0LqO/euUSvYc\nUf05l6zs1Lm9uvfqaFJUAMxGIW8Aes2MR86NZ2bODx88qQ3v7Wyy/WxdvQnRGIceeeOZlfP9pZXa\nX1rZZPv1t11l+UKe87nxyHng4AuhDFBYWGh2CG0OOTeeETmvPlWr8n3HmtyOH6tR7Rlnk9u5q5dW\ns//AXrNDaHP8LeeuepeqT55pejtVq5pmbs6zgffLLedz45HzwGHYirzD4dCjjz4qp9OpadOmafbs\n2U3m/Md//Ifef/99dejQQX//+98VFxdnVHg+VVVVdf5JaFXk3HhG5Lz2zFk51vAG06DmzCmzQ2hz\n/C3nn23YrZCQdk22B7VrevnKdu2CdNuEWIV2ucyI0FoN53PjkfPAYUgh73Q6NXPmTGVnZyssLEwj\nRoxQUlKSYmJi3HPWrVun3bt3q6ioSHl5eXr44Ye1efNmI8ID4Gfq6106daLpB1L5SnugMefZeq9X\n2W1BNjmd9aqqrGlyX6fO7WWzce16INAYUsjn5+crKipKkZGRkqTk5GRlZWU1KuTfeecdTZ06VZI0\ncuRIVVZW6uDBg+rdu7cRIfpUSUmJ2SG0OeTceC3Necl3R3Tk4MlG21wu6evt+3X2rLPJdvzgWOUh\ns0NocwI55656l95eVtDkS4xDLmmnKwb1ajK/a/fL1aVHhybb23cIUZeuTbf7Cudz45HzwGFzuXz/\n1vjmm2/qgw8+0JIlSyRJmZmZysvLU3p6unvOnXfeqTlz5uhnP/uZJOnmm29WWlqarrnmGvecnJwc\nX4cKAAAAGG7s2LEX/BhDVuS9/XPdub9TnPu4lrxAAAAAwIoMuWpNWFiYSktL3ePS0lLZ7fafnFNW\nVqawsDAjwgMAAAACjiGFfEJCgoqKilRcXKza2lqtWrVKSUlJjeYkJSVp6dKlkqTNmzerS5culuiP\nBwAAAHzBkNaa4OBgLVq0SOPGjZPT6VRKSopiYmKUkZEhSUpNTdXtt9+udevWKSoqSpdffrlef/11\nI0IDAAAAApJhXwiVmJiob7/9Vrt379acOXMkfV/Ap6amuucsWrRIu3fv1vbt2xUfH29UaK3q17/+\ntXr37q3Y2NhG29PT0xUTE6OhQ4c2ew19XJzm8p6fn69rr71WcXFxGjFihLZs2WJihNZSWlqqG2+8\nUUOGDNHQoUO1cOFCSdLRo0d1yy236Morr9Stt96qysqm30SJlvGU8yeeeEIxMTEaNmyYxo8fr+PH\nj5scqXV4ynmDF154QUFBQTp69KhJEVrPT+Wc91Hf8JRz3kN95/Tp0xo5cqSGDx+uwYMHu+vi8s8G\nBAAAIABJREFUFr2HutCqNm3a5CooKHANHTrUvW3Dhg2um2++2VVbW+tyuVyuQ4cOmRWeZTWX91/8\n4hcuh8PhcrlcrnXr1rluuOEGs8KznIqKCte2bdtcLpfLdeLECdeVV17p2rlzp+uJJ55wpaWluVwu\nl2v+/Pmu2bNnmxmmpXjK+fr1611Op9Plcrlcs2fPJuetyFPOXS6Xq6SkxDVu3DhXZGSk68iRI2aG\naSmecs77qO94yjnvob516tQpl8vlctXV1blGjhzp+uSTT1r0HmrYinxbcd1116lr166Ntr3yyiua\nM2eOQkJCJEk9e/Y0IzRLay7vffv2da9OVlZW8uHpVtSnTx8NHz5cktSxY0fFxMSovLy80fdBTJ06\nVWvXrjUzTEtpLuf79+/XLbfcoqCg70/lI0eOVFlZmZlhWoqnnEvSY489pueee87M8CzJ07ll8eLF\nvI/6iKec8x7qWx06fP9dDLW1tXI6neratWuL3kMp5A1QVFSkTZs2adSoUbrhhhu0detWs0NqE+bP\nn6/HH39cEREReuKJJ/Tss8+aHZIlFRcXa9u2bRo5cmSjL3Hr3bu3Dh48aHJ01vTjnP/Y//zP/+j2\n2283KSpr+3HOs7KyZLfbdfXVV5sdlqX9OOe7du3ifdQADTkfNWoU76E+Vl9fr+HDh6t3797u1qaW\nvIdSyBvg7NmzOnbsmDZv3qy//e1v+uUvf2l2SG1CSkqKFi5cqJKSEr344ov69a9/bXZIlnPy5ElN\nmDBBCxYsUKdOnRrdZ7PZ+Mp3Hzh58qQmTpyoBQsWqGPHju7tf/nLX3TJJZdo8uTJJkZnTT/OeVBQ\nkP7617/qmWeecd/v4iuHW92Pc96pUyfeRw1w7rmF91DfCgoK0hdffKGysjJt2rRJGzdubHS/t++h\nFPIGsNvtGj9+vCRpxIgRCgoK0pEjR0yOyvry8/N1zz33SJImTpyo/Px8kyOylrq6Ok2YMEFTpkzR\n3XffLen7FYQDBw5IkioqKtSrV9OvfUfLNeT8/vvvd+dckv7+979r3bp1euONN0yMzprOzfmePXtU\nXFysYcOGacCAASorK9M111yjQ4cOmR2qZTR3nPM+6lvN5Zz3UGN07txZd9xxhz7//PMWvYdSyBvg\n7rvv1oYNGyRJu3btUm1trbp3725yVNYXFRWljz/+WJK0YcMGXXnllSZHZB0ul0spKSkaPHiwHn30\nUff2pKQk/eMf/5Ak/eMf/2hUbOLieMq5w+HQ3/72N2VlZal9+/YmRmg9zeU8NjZWBw8e1N69e7V3\n717Z7XYVFBTwS2sr8XSc8z7qO55yznuo7xw+fNh9RZqamhp9+OGHiouLa9l7qI8+jNtmJScnu/r2\n7eu65JJLXHa73fU///M/rtraWtf999/vGjp0qCs+Pt61ceNGs8O0nIa8h4SEuPO+ZcsW17XXXusa\nNmyYa9SoUa6CggKzw7SMTz75xGWz2VzDhg1zDR8+3DV8+HDX+++/7zpy5Ihr7NixrujoaNctt9zi\nOnbsmNmhWkZzOV+3bp0rKirKFRER4d728MMPmx2qZXjK+Y8NGDCAq9a0Ik/nFt5HfcfTcc57qO/s\n2LHDFRcX5xo2bJgrNjbW9dxzz7lcLleL3kNtLhfNfQAAAECgobUGAAAACEAU8gAAAEAAopAHAAAA\nAhCFPAAAABCAKOQBAACAAEQhDwAAAAQgCnkAgNciIyOVk5NjdhgAAFHIAwAugM1mk81mMzsMAIAo\n5AHAUhYuXKjf//73ZocBADAAhTwAWMhvfvMbrV69WgcPHmz2/rS0NE2aNKnRtkceeUSPPPKIJGn+\n/PmKiopSaGiohgwZorVr13rcV1BQkL777jv3+MEHH9Qf//hH93j//v2aMGGCevXqpYEDByo9Pf1i\nXhoA4BwU8gBgITabTZMnT9ayZcuavf/ee+/VunXrdPLkSUmS0+nU//7v/+q+++6TJEVFRSk3N1dV\nVVX605/+pPvvv18HDhzwet8NbTf19fW68847FRcXp/379ysnJ0cvvfSS1q9f3wqvEgAgUcgDgOU8\n+OCD+vvf/97sfREREYqPj9fbb78tSdqwYYM6dOiga6+9VpI0ceJE9enTR5L0y1/+UtHR0crPz/d6\n3y6XS5K0ZcsWHT58WE8++aSCg4M1YMAATZs2TStXrryIVwYA+DEKeQCwmH/961+qrq72WIBPnjxZ\nK1askCQtX77cvRovSUuXLlVcXJy6du2qrl276ssvv9SRI0e83nfDivy+ffu0f/9+9/N07dpVzz77\nrA4dOnQRrwwA8GPBZgcAAGg9DodDRUVFevLJJ/X666+7V9p/bOLEiXr88cdVXl6utWvXavPmzZK+\nL74feughbdiwQaNHj5bNZlNcXJx7lf1cHTp0UHV1tXtcUVGh8PBwSVJ4eLgGDBigXbt2+eBVAgAk\nVuQBwDKWL1+uDRs26De/+Y0mTZqkd999V6dPn24yr2fPnrrhhhv04IMPauDAgbrqqqskSadOnZLN\nZlOPHj1UX1+v119/XV9++aXH/Q0fPlxvvPGGnE6nHA6HNm3a5L7v2muvVadOnfTcc8+ppqZGTqdT\nX375pbZu3dr6LxwA2igKeQCwgM2bNys7O1vPPfecJKlTp066++67PfakT548WTk5OZo8ebJ72+DB\ng/X4449r9OjR6tOnj7788kuNGTPG4z4XLFigd999V127dtXy5ct1zz33uO9r166d3nvvPX3xxRca\nOHCgevbsqYceekhVVVWt9IoBADaXp7+ZAgAAAPBbrMgDAAAAAYhCHgAAAAhAAXXVmpycHLNDAAAA\nAFrd2LFjL/gxAVXIS1J8fLzZIQA+kZaWptmzZ5sdBtDqOLZhZRzfaA0FBQUtehytNQAAAEAAopAH\n/ERJSYnZIQA+wbENK+P4hpko5AE/MXToULNDAHyCYxtWxvENMwXUdeRzcnLokQcAAIClFBQUtI0P\nuzbH5XLp0KFDcjqdstlsZocDH3G5XGrXrp169erFvzMAAGjzLFHIHzp0SJ06dVKHDh3MDgU+Vl1d\nrUOHDql3795mh9LqcnNzNWbMGLPDAFodxzasjOMbZjKsR97hcGjQoEGKjo5WWlpak/uff/55xcXF\nKS4uTrGxsQoODlZlZaVXz+10Oini24gOHTrI6XSaHQYAAIDpDOmRdzqduuqqq5Sdna2wsDCNGDFC\nK1asUExMTLPz33vvPb300kvKzs5utN1Tj3xFRYX69u3rk9jhf/j3BgAAVtLSHnlDVuTz8/MVFRWl\nyMhIhYSEKDk5WVlZWR7nL1++XPfee68RoQEAAAAByZAe+fLycoWHh7vHdrtdeXl5zc6trq7WBx98\noJdffrnZ+2fMmKGIiAhJUmhoqGJjY3XFFVe0ftDwe7m5uZLk7k0M9PErr7yi2NhYv4mHMePWGjf8\n7C/xMGbM8c3Y7HFhYaGqqqokff9dBCkpKWoJQ1pr1qxZI4fDoSVLlkiSMjMzlZeXp/T09CZzV61a\npeXLlze7Yk9rDSTr/nvn5vKBKVgTxzasjOMbrcGvW2vCwsJUWlrqHpeWlsputzc7d+XKlbTVGOhn\nP/uZPvvsM5/vp6ioSNdff7369+/v/oUOjfFGAKvi2IaVcXzDTMFG7CQhIUFFRUUqLi5Wv379tGrV\nKq1YsaLJvOPHj2vTpk1avnz5Re/zYGWZjlQduOjn8aR7aB/17tL8LyNGGTZsmNLT03X99de3+DmM\nKOIlueOcN2+eIfsDAACwOkMK+eDgYC1atEjjxo2T0+lUSkqKYmJilJGRIUlKTU2VJK1du1bjxo3T\nZZdddtH7PFJ1QHNXpl7083jyVHKG6YW8zWZTSzujzp49q+Dglv3zt+SxpaWlGj9+fIv211bw51lY\nFcc2rIzjG2Yy7DryiYmJ+vbbb7V7927NmTNH0vcFfEMRL0lTp05tldV4fzRs2DC99NJLGj16tAYO\nHKjf/OY3OnPmjCTp22+/1Z133qkBAwboZz/7mRwOh/txCxYs0NChQ9W/f3+NHDlSn3zyiSTp3//9\n31VWVqbJkycrIiJCixYtUkVFhaZOnaorr7xScXFx+u///u8mMSxcuFBjxoxRRESEnE6nhg0bpo8/\n/vi8cZz72Pr6+iav0dPj77rrLuXm5mr27Nnq37+/vvvuu9ZNLgAAQBtkWCEP6c0339SaNWtUUFCg\n3bt364UXXtDZs2c1efJkjR07VkVFRUpLS1Nqaqp2796toqIivfrqq8rJydG+ffu0Zs0a99V/Fi9e\nLLvdrhUrVqikpEQzZszQ5MmTFRsbq507d2rt2rVavHixNmzY0CiGt956S6tXr9bevXvVrl072Ww2\n2Ww21dXVNRvHnj17mn1sUFDjQ+enHp+VlaXRo0frueee0759+zRw4EDfJzsAsaIDq+LYhpVxfMNM\nFPIGsdlsmj59uvr166cuXbro8ccf15o1a7R161ZVV1fr0UcfVXBwsK677jrdeuutWrNmjYKDg1Vb\nW6tvvvlGdXV1stvtioyMbPb5P//8cx05ckS//e1vFRwcrP79+2vKlCl6++23G8Xw0EMPqV+/frr0\n0ksbPd5THG+++eZ5H+vN4yX9ZBtQVVWVZs6cqcmTJ+vnP/+57r33Xk2dOlU1NTUXkmYAAIA2w5Ae\neXwvLCzM/bPdbteBAwd04MCBRtslKTw8XBUVFRowYID++te/Ki0tTd98841uuukmzZs3T3369Gny\n3GVlZTpw4IAGDBjg3lZfX6/Ro0d7jOHHPMVx4MAPHxj29FhvH2+z2Tw+fvv27VqwYIEqKiqUm5ur\n5ORkj3Otij5LWBXHNqyM4xtmYkXeQGVlZY1+7tOnj/r06aPy8vJGq9WlpaXq16+fJGnChAlat26d\ntm/fLpvNpmeeecY978eFcVhYmPr376+9e/e6b/v27dPKlSsbxeCpmO7bt2+zcfz4eu0/VYh7eh3e\nXu/9uuuuU7t27fTOO+8oLi7Oq8cAAAC0ZRTyBnG5XHrttde0f/9+HTt2TC+88ILGjx+va665Rpdd\ndpkWLlyouro65ebmav369Ro/frx2796tTZs26cyZM7r00kvVvn17tWvXzv2cPXv2VHFxsSQpPj5e\nHTt21MKFC1VTUyOn06mvv/5a27Zt8yq+n4rDGwkJCed9vDdX2Nm4caOuuuoqr/ZpNazowKo4tmFl\nHN8wk2Vba7qH9tFTyRk+ff4LYbPZNHHiRE2YMEEHDhzQHXfcoccff1whISFavny5nnjiCb344ovq\n16+fXnnlFUVFRWnnzp3685//rF27dik4OFgjR47Uiy++6H7OWbNmafbs2frTn/6kJ554QitWrNAf\n//hHxcfH68yZM4qOjtYf/vAHr+L7qTha6/E/taIvSSdOnFCHDh282h8AAEBbZ3O19ELkJsjJyVF8\nfHyT7RUVFV63cJhl+PDhWrhw4UV9eRO+Fwj/3i1BnyWsimMbVsbxjdZQUFCgsWPHXvDjaK0BAAAA\nAhCFPOAnWNGBVXFsw8o4vmEmy/bI+5svvvjC7BAAAABgIazIA34iNzfX7BAAn+DYhpVxfMNMFPIA\nAABAADKskHc4HBo0aJCio6OVlpbW7JyPPvpIcXFxGjp0qG644QajQgP8An2WsCqObVgZxzfMZEiP\nvNPp1MyZM5Wdna2wsDCNGDFCSUlJiomJcc+prKzUjBkz9MEHH8hut+vw4cNeP38AXUETrYB/bwAA\nAINW5PPz8xUVFaXIyEiFhIQoOTlZWVlZjeYsX75cEyZMkN1ulyT16NHD6+dv166dqqurWzVm+Kfq\n6upG325rJfRZwqo4tmFlHN8wkyEr8uXl5QoPD3eP7Xa78vLyGs0pKipSXV2dbrzxRp04cUKPPPKI\npkyZ4tXz9+rVS4cOHVJlZeV5vz0Ugcvlcqldu3bq1auX2aEAAACYzpBC3pviuq6uTgUFBcrJyVF1\ndbVGjx6tUaNGKTo6utG8GTNmKCIiQpIUGhqq2NhYjRkzRr1793b/VtzQr8bYmuPevXv7VTytNW7Y\n5i/xMGbcWuMxY8b4VTyMGXN8MzZ7XFhYqKqqKklSSUmJUlJS1BI2lwENx5s3b9bTTz8th8MhSXr2\n2WcVFBSk2bNnu+ekpaWppqZGTz/9tCRp2rRpuu222zRx4kT3nJycHMXHx/s6XAAAAMAwBQUFGjt2\n7AU/zpAe+YSEBBUVFam4uFi1tbVatWqVkpKSGs256667lJubK6fTqerqauXl5Wnw4MFGhAf4hYbf\n2AGr4diGlXF8w0zBhuwkOFiLFi3SuHHj5HQ6lZKSopiYGGVkZEiSUlNTNWjQIN122226+uqrFRQU\npOnTp1PIAwAAAB4Y0lrTWmitAQAAgNX4dWsNAAAAgNZFIQ/4CfosYVUc27Ayjm+YiUIeAAAACEAU\n8oCfaLi+LGA1HNuwMo5vmIlCHgAAAAhAFPKAn6DPElbFsQ0r4/iGmSjkAQAAgABEIQ/4CfosYVUc\n27Ayjm+YiUIeAAAACEAU8oCfoM8SVsWxDSvj+IaZKOQBAACAAEQhD/gJ+ixhVRzbsDKOb5iJQh4A\nAAAIQIYV8g6HQ4MGDVJ0dLTS0tKa3P/RRx+pc+fOiouLU1xcnObNm2dUaIBfoM8SVsWxDSvj+IaZ\ngo3YidPp1MyZM5Wdna2wsDCNGDFCSUlJiomJaTTvF7/4hd555x0jQgIAAAACmlcr8sOHD9eLL76o\ngwcPtmgn+fn5ioqKUmRkpEJCQpScnKysrKwm81wuV4ueH7AC+ixhVRzbsDKOb5jJqxX5p556SsuW\nLdOTTz6p66+/XlOmTNH48ePVvn17r3ZSXl6u8PBw99hutysvL6/RHJvNps8++0zDhg1TWFiYnn/+\neQ0ePLjJc82YMUMRERGSpNDQUMXGxrr/EzX8eYsxY8aMGTNmzJgxY38dFxYWqqqqSpJUUlKilJQU\ntYTNdQHL4EePHtXq1auVmZmpL7/8Uvfcc4+mTJmim2666Scft2bNGjkcDi1ZskSSlJmZqby8PKWn\np7vnnDhxQu3atVOHDh30/vvv65FHHtGuXbsaPU9OTo7i4+Mv5PUBASM3N9f9nxywEo5tWBnHN1pD\nQUGBxo4de8GPu6APu3br1k0PPPCA/v3f/13h4eF66623lJqaqiuvvFIffvihx8eFhYWptLTUPS4t\nLZXdbm80p1OnTurQoYMkKTExUXV1dTp69OiFhAcAAAC0GV4V8i6XSw6HQ/fff7/69u2rZcuW6T//\n8z914MABFRUVaf78+ZoyZYrHxyckJKioqEjFxcWqra3VqlWrlJSU1GjOwYMH3T3y+fn5crlc6tat\n20W8NCCwsKIDq+LYhpVxfMNMwd5M6tOnj3r06KEHHnhA8+fPb7KaPn78eC1cuNDzToKDtWjRIo0b\nN05Op1MpKSmKiYlRRkaGJCk1NVVvvvmmXnnlFQUHB6tDhw5auXLlRbwsAIA/OFhZpiNVByRJ3UP7\nqHcX+3keAQDwllc98lu3blVCQoIR8fwkeuRhZfRZwop2lmzVo889oG4Rl+mp5AwNjjD/vQRoTZy7\n0Rp82iN/6623Nru9V69eF7xDAAAAABfPq0K+rq6u2W1Op7PVAwLaKlZ0YFXdIi4zOwTAZzh3w0w/\n2SN/3XXXSZJqamrcPzcoKyvT6NGjfRcZAAAAAI9+spBvuDj9li1bNG3aNPdVZWw2m3r37t2iXh4A\nzaPPElZ1tKSGVXlYFudumOknC/kHH3xQkjRq1CgNGjTIiHgAAAAAeMFjIb9s2TL3teE//fRTffbZ\nZ83O+/Wvf+2byIA2hhUdWBWr8bAyzt0wk8dCfsWKFe5CftmyZbLZbM3Oo5AHAAAAjOexkF+3bp37\n548++siIWIA2jT5LWBU98rAyzt0wk8dCvr6+3qsnCAry6gqWAAAAAFqRx0I+OPgnPwcr6fur13At\neaB1sKIDq2I1HlbGuRtm8litf/fdd0bGAQAAAOACeCzkIyMjDQwDAH2WsCp65GFlnLthJo+F/PTp\n07VkyRJJcl+95lw2m01Lly71TWQAAAAAPPL4SdWBAwe6f77iiisUFRWlK664osnNWw6HQ4MGDVJ0\ndLTS0tI8ztuyZYuCg4P11ltvef3cgBWwogOrYjUeVsa5G2byuCI/Z84c989PP/30Re3E6XRq5syZ\nys7OVlhYmEaMGKGkpCTFxMQ0mTd79mzddtttcrlcF7VPAAAAwMq8vnZkTk6Opk2bpttvv13Tp09X\ndna21zvJz89XVFSUIiMjFRISouTkZGVlZTWZl56erokTJ6pnz55ePzdgFbm5uWaHAPjE0ZIas0MA\nfIZzN8x0/mtMSnrhhReUlpamf/u3f1NcXJxKSkp033336YknntBvf/vb8z6+vLxc4eHh7rHdblde\nXl6TOVlZWdqwYYO2bNni8ZtkZ8yYoYiICElSaGioYmNj3X/WavjPxJhxII4LCwv9Kh7GjFtj3C2i\nvaTvi/ltW7drcESCX8XHmDFjxmaMCwsLVVVVJUkqKSlRSkqKWsLm8qKHpV+/flq/fr2GDh3q3vbV\nV1/p5ptvVkVFxXl3smbNGjkcDveHZzMzM5WXl6f09HT3nEmTJum3v/2tRo4cqQcffFB33nmnJkyY\n0Oh5cnJyFB8f7/WLAwCYa2fJVs1dmSpJeio5w13IAwB+UFBQoLFjx17w44K9mWSz2Zp8sHXgwIFe\nf6trWFiYSktL3ePS0lLZ7fZGcz7//HMlJydLkg4fPqz3339fISEhSkpK8mofAAAAQFvisRKvr693\n355++mlNmzZNu3btUk1Njb799ls99NBDeuaZZ7zaSUJCgoqKilRcXKza2lqtWrWqSYH+3Xffae/e\nvdq7d68mTpyoV155hSIebUrDn94Aq6FHHlbGuRtm8rgiHxzc9K4VK1Y0Gi9fvlzTpk07/06Cg7Vo\n0SKNGzdOTqdTKSkpiomJUUZGhiQpNTX1QuMGAAAA2jSPhfx3333XqjtKTExUYmJio22eCvjXX3+9\nVfcNBIKGD8EAVsN15GFlnLthJo+FfGRkpIFhAABa6mBlmY5UHXCPu4f2Ue8u9p94BADACrz6sKsk\nZWVl6eOPP9aRI0dUX1/vvjzk0qVLfRYc0Jbk5uaysoMWOVJ1wH1lGOn7q8P4UyF/tKSGVXlYFudu\nmMmry84888wzSk1NVX19vVavXq0ePXrogw8+UJcuXXwdHwAAAIBmeFXIv/baa/rwww/10ksv6dJL\nL9WLL76od999V3v37vV1fECbwYoOrIrVeFgZ526YyatC/vjx44qNjZUkXXLJJaqtrdW1116rjz/+\n2KfBAQAAAGieV4X8wIED9dVXX0mShgwZoldeeUVLly5Vt27dfBoc0JZwLWJYFdeRh5Vx7oaZvPqw\n67x583T48GFJ0vz58zV58mSdPHlSL7/8sk+DAwAAANA8rwr5O+64w/3zyJEjtWfPHp8FBLRV9FnC\nquiRh5Vx7oaZvL785K5du7R69Wrt379fYWFhmjRpkq688kpfxgYAAADAA6965JcvX674+HgVFhaq\nY8eO2rFjh+Lj4/XGG2/4Oj6gzaDPElZFjzysjHM3zOTVivwf/vAHrVu3Ttdff7172yeffKIpU6bo\nvvvu81lwAAAAAJrn1Yr8yZMnNXr06EbbRo0apVOnTvkkKKAtos8SVkWPPKyMczfM5FUh/9hjj2nO\nnDmqqfn+z6PV1dX6/e9/r1mzZvk0OAAAAADN81jIh4eHu28vv/yyFixYoNDQUPXq1UudO3fWSy+9\npMWLF3u9I4fDoUGDBik6OlppaWlN7s/KytKwYcMUFxena665Rhs2bGjZKwICFH2WsCp65GFlnLth\nJo898suWLTvvg202m1c7cTqdmjlzprKzsxUWFqYRI0YoKSlJMTEx7jk333yz7rrrLklSYWGh7rnn\nHu3evdur5wcAAADaGo+F/A033NBqO8nPz1dUVJQiIyMlScnJycrKympUyF9++eXun0+ePKkePXq0\n2v6BQECfJayKHnlYGedumMmrq9bU1tZq3rx5WrZsmfbv369+/fppypQpevLJJ3XJJZec9/Hl5eUK\nDw93j+12u/Ly8prMW7t2rebMmaOKigqtX7++2eeaMWOGIiIiJEmhoaGKjY11/ydq+PMWY8aMGbe1\ncUP7SkPRbHY8DeNuEe3d8W3bul2DIxL8Kj7GjBkzNmNcWFioqqoqSVJJSYlSUlLUEjaXy+U636RZ\ns2YpPz9ff/rTnxQREaGSkhLNnTtXCQkJeumll867kzVr1sjhcGjJkiWSpMzMTOXl5Sk9Pb3Z+Z98\n8ommTZumb7/9ttH2nJwcxcfHe/O6gICTm5vr/k8OXIidJVs1d2Wqe/xUcoa7YDbbzpKtevS5B9Qt\n4jK/igtoLZy70RoKCgo0duzYC35csDeTVq9ere3bt7vbXQYNGqT4+HhdffXVXhXyYWFhKi0tdY9L\nS0tlt9s9zr/uuut09uxZHTlyRN27d/cmRAAAAKBN8erykxcrISFBRUVFKi4uVm1trVatWqWkpKRG\nc/bs2aOGPw4UFBRIEkU82hRWdGBV9MjDyjh3w0xerchPmjRJSUlJeuqpp9S/f38VFxdr3rx5mjRp\nknc7CQ7WokWLNG7cODmdTqWkpCgmJkYZGRmSpNTUVK1Zs0ZLly5VSEiIOnbsqJUrV7b8VQEAAAAW\n51Uh/9xzz2nevHmaOXOm+8Ou9957r5588kmvd5SYmKjExMRG21JTf+jp/N3vfqff/e53Xj8fYDX0\nWcKqjpbUsCoPy+LcDTOdt5A/e/aspk+froyMDM2dO9eImAAAAACcx3l75IODg7V+/Xq1a9fOiHiA\nNosVHVgVq/GwMs7dMJNXH3adNWuWnnrqKdXW1vo6HgAAAABe8KqQX7hwoZ5//nl16tRJdrtd4eHh\nCg8Pd38xE4CL1/CFEYDVNHxZFWBFnLthJq8+7JqZmSmbzdZkuxffJQUAAADAB7xakR/jc3rRAAAP\nZUlEQVQ9erSys7OVkpKixMREpaSk6MMPP9SoUaN8HR/QZtBnCauiRx5WxrkbZvJqRf7hhx/Wrl27\nlJ6eroiICJWUlOgvf/mLysvL9frrr/s6RgAAAADn8KqQX7t2rfbs2aOuXbtKkoYMGaKRI0fqiiuu\noJAHWgnXIoZVcR15WBnnbpjJq9aavn37qrq6utG2mpoa9evXzydBAQAAAPhpXq3IT5kyRYmJiZo5\nc6bCw8NVUlKil19+WQ888IA2bNjgnnfTTTf5LFDA6ljRgVWxGg8r49wNM3lVyC9evFiS9Oyzz7q3\nuVwuLV682H2fJO3du7eVwwMAAADQHK8K+eLiYh+HAYA+S1gVPfKwMs7dMJNXPfIAAAAA/IthhbzD\n4dCgQYMUHR2ttLS0Jve/8cYbGjZsmK6++mr9/Oc/144dO4wKDfALrOjAqliNh5Vx7oaZvGqtuVhO\np1MzZ85Udna2wsLCNGLECCUlJSkmJsY9Z+DAgdq0aZM6d+4sh8Ohhx56SJs3bzYiPAAAACDgGLIi\nn5+fr6ioKEVGRiokJETJycnKyspqNGf06NHq3LmzJGnkyJEqKyszIjTAb+Tm5podAuATR0tqzA4B\n8BnO3TCTISvy5eXlCg8Pd4/tdrvy8vI8zn/ttdd0++23N3vfjBkzFBERIUkKDQ1VbGys+89aDf+Z\nGDMOxHFhYaFfxcM4sMYNxXJDG4vZ8TSMu0W0d8e3bet2DY5I8Kv4GDNmzNiMcWFhoaqqqiRJJSUl\nSklJUUvYXC6Xq0WPvABr1qyRw+HQkiVLJEmZmZnKy8tTenp6k7kbN27UjBkz9Omnn7q/SbZBTk6O\n4uPjfR0uAASUnSVbNXdlqnv8VHKGu2A2249j86e4AMCfFBQUaOzYsRf8uGAfxNJEWFiYSktL3ePS\n0lLZ7fYm83bs2KHp06fL4XA0KeIBAAAA/MCQHvmEhAQVFRWpuLhYtbW1WrVqlZKSkhrNKSkp0fjx\n45WZmamoqCgjwgL8SsOf3gCroUceVsa5G2YyZEU+ODhYixYt0rhx4+R0OpWSkqKYmBhlZGRIklJT\nUzV37lwdO3ZMDz/8sCQpJCRE+fn5RoQHAAAABBxDCnlJSkxMVGJiYqNtqak/9HS++uqrevXVV40K\nB/A7DR+CAayG68jDyjh3w0x8sysAAAAQgCjkAT9BnyWsih55WBnnbpiJQh4AAAAIQBTygJ+gzxJW\nRY88rIxzN8xEIQ8AAAAEIAp5wE/QZwmrokceVsa5G2aikAcAAAACEIU84Cfos4RV0SMPK+PcDTNR\nyAMAAAABiEIe8BP0WcKq6JGHlXHuhpko5AEAAIAARCEP+An6LGFV9MjDyjh3w0wU8gAAAEAAMqyQ\ndzgcGjRokKKjo5WWltbk/m+++UajR49W+/bt9cILLxgVFuA36LOEVdEjDyvj3A0zBRuxE6fTqZkz\nZyo7O1thYWEaMWKEkpKSFBMT457TvXt3paena+3atUaEBAAX7WBlmY5UHZAkdQ/to95d7CZHBABo\nSwxZkc/Pz1dUVJQiIyMVEhKi5ORkZWVlNZrTs2dPJSQkKCQkxIiQAL9Dn2XgOVJ1QHNXpmruylR3\nQY+m6JGHlXHuhpkMWZEvLy9XeHi4e2y325WXl9ei55oxY4YiIiIkSaGhoYqNjXX/J2r48xZjxowZ\nGzHed+hbNdi2dbuOlpw2LZ6G9pWGotkf8vN9PO3d8W3bul2DIxL8Kj7GjBkzNmNcWFioqqoqSVJJ\nSYlSUlLUEjaXy+Vq0SMvwJo1a+RwOLRkyRJJUmZmpvLy8pSent5k7jPPPKOOHTvq8ccfb3JfTk6O\n4uPjfR0uYIrc3Fz3f3IEhp0lWzV3Zaok6ankDHeRamYcZsdyrp0lW/Xocw+oW8RlfhUX0Fo4d6M1\nFBQUaOzYsRf8OENaa8LCwlRaWuoel5aWym63G7FrAAAAwJIMKeQTEhJUVFSk4uJi1dbWatWqVUpK\nSmp2rgF/IAD8Eis6sCp65GFlnLthpmBDdhIcrEWLFmncuHFyOp1KSUlRTEyMMjIyJEmpqak6cOCA\nRowYoaqqKgUFBWnBggXauXOnOnbsaESIAAAAQEAxpJCXpMTERCUmJjbalpr6Q09nnz59GrXfAG0N\nfZawqqMlNazKw7I4d8NMfLMrAAAAEIAo5AE/wYoOrIrVeFgZ526YiUIeAAAACEAU8oCfaPjCCMBq\nGr6sCrAizt0wE4U8AAAAEIAo5AE/QZ8lrIoeeVgZ526YiUIeAAAACEAU8oCfoM8SVkWPPKyMczfM\nZNgXQgFASxysLNORqgPucffQPurdxW5iRAAA+AcKecBP0GfZvCNVBzR35Q/fAv1UcgaFfIChRx5W\nxrkbZqK1BgAAAAhAFPKAn6DPElZFjzysjHM3zEQhD/iJwsJCs0MAfOLEwVqzQwB8hnM3zGRYIe9w\nODRo0CBFR0crLS2t2Tn/8R//oejoaA0bNkzbtm0zKjTAL1RVVZkdAuATZ8/Umx0C4DOcu2EmQwp5\np9OpmTNnyuFwaOfOnVqxYoW+/vrrRnPWrVun3bt3q6ioSP/93/+thx9+2IjQAAAAgIBkSCGfn5+v\nqKgoRUZGKiQkRMnJycrKymo055133tHUqVMlSSNHjlRlZaUOHjxoRHiAXygpKTE7BMAnao6fNTsE\nwGc4d8NMNpfL5fL1Tt5880198MEHWrJkiSQpMzNTeXl5Sk9Pd8+58847NWfOHP3sZz+TJN18881K\nS0vTNddc456Tk5Pj61ABAAAAw40dO/aCH2PIdeRtNptX8879neLcx7XkBQIAAABWZEhrTVhYmEpL\nS93j0tJS2e32n5xTVlamsLAwI8IDAAAAAo4hhXxCQoKKiopUXFys2tparVq1SklJSY3mJCUlaenS\npZKkzZs3q0uXLurdu7cR4QEAAAABx5DWmuDgYC1atEjjxo2T0+lUSkqKYmJilJGRIUlKTU3V7bff\nrnXr1ikqKkqXX365Xn/9dSNCAwAAAAKSIR92bYnTp0/rF7/4hc6cOaPa2lrdddddevbZZ/X000/r\n1VdfVc+ePSVJzz77rG677TaTowUunNPpVEJCgux2u959910dPXpUv/rVr7Rv3z5FRkZq9erV6tKl\ni9lhAi1y7vHNuRtWERkZqdDQULVr104hISHKz8/n/A3T+O03u7Zv314bN27UF198oR07dmjjxo3K\nzc2VzWbTY489pm3btmnbtm28ESBgLViwQIMHD3Z/qHv+/Pm65ZZbtGvXLo0dO1bz5883OUKg5c49\nvjl3wypsNps++ugjbdu2Tfn5+ZI4f8M8flvIS1KHDh0kSbW1tXI6nerataukple3AQJNWVmZ1q1b\np2nTprmP5x9/l8LUqVO1du1aM0MEWqy549vlcnHuhmWceyxz/oZZ/LqQr6+v1/Dhw9W7d2/deOON\nGjJkiCQpPT1dw4YNU0pKiiorK02OErhws2bN0t/+9jcFBf3wX/DgwYPuD3j37t2bL0RDwGru+LbZ\nbJy7YQk2m00333yzEhIS3N+Pw/kbZvHrQj4oKEhffPGFysrKtGnTJn300Ud6+OGHtXfvXn3xxRfq\n27evHn/8cbPDBC7Ie++9p169eikuLs7jCqXNZvP6+xcAf+Lp+ObcDav49NNPtW3bNr3//vv6r//6\nL33yySeN7uf8DSP5dSHfoHPnzrrjjju0detW9erVy/2fZNq0ae7+NCBQfPbZZ3rnnXc0YMAA3Xvv\nvdqwYYOmTJmi3r1768CBA5KkiooK9erVy+RIgQvX3PH9wAMPcO6GZfTt21eS1LNnT91zzz3Kz8/n\n/A3T+G0hf/jwYfefXmtqavThhx8qLi7O/R9Fkt5++23FxsaaFSLQIn/9619VWlqqvXv3auXKlbrp\nppu0bNkyJSUl6R//+Ick6R//+IfuvvtukyMFLlxzx/fSpUtVUVHhnsO5G4GqurpaJ06ckCSdOnVK\n69evV2xsLOdvmMaQ68i3REVFhaZOnar6+nrV19drypQpGjt2rB544AF98cUXstlsGjBggPta9ECg\navgT7H/+53/ql7/8pV577TX35cuAQOZyudzH9+9+9ztt376dczcC2sGDB3XPPfdIks6ePav77rtP\nt956qxISEjh/wxR+ex15AAAAAJ75bWsNAAAAAM8o5AEAAIAARCEPAAAABCAKeQAAACAAUcgDQBv1\n4IMP6o9//KPZYQAAWohCHgDaKL6BEgACG4U8ALRhXIEYAAIXhTwAtBHbtm1T/P/X3h2DpPbGYRz/\nHkxLKA9YFFGQ0djUxSJcirbAwpCsIXFwaBFqbmuvhpbAKUgLCsXJ3SapoelAtIRCLUGlBEZG/oc/\nV27c4d5Jr5znM75wXt5ne3j58Z4fP/B4PKyvr/P+/g7A6+srwWCQwcFBvF4vS0tLPDw8AHBxcYHf\n7/+2z8HBQfPPlfl8nsnJSTweD6Ojo+zv77c2lIiIjanIi4jYwMfHB6FQiFgsxsvLC6urq2QyGQzD\n4Ovri3g8Trlcplwu43a7SSQSACwvL3N/f8/t7W1zr5OTE2KxGADxeJxkMkm1WsWyLBYWFtqST0TE\njlTkRURsoFgs8vn5ydbWFg6Hg3A4zPT0NABer5eVlRV6enro7e1lZ2eHQqEAQHd3N5FIhFQqBYBl\nWZRKJYLBIAAulwvLsqhWq5imydTUVHsCiojYkIq8iIgNPD4+MjIy8m1tbGwMgFqtxubmJj6fD9M0\nmZubo1KpNOfnY7EYp6enwP+38WtrazidTgAymQz5fB6fz8f8/DzFYrGFqURE7E1FXkTEBoaHh5tz\n7z+VSiUajQZ7e3vc3d1xdXVFpVKhUCjQaDSaRX52dhaXy8Xl5SVnZ2dEo9HmHn6/n1wux9PTE6FQ\niEgk0tJcIiJ2piIvImIDgUCArq4uDg8PqdfrZLNZrq+vAXh7e8PtdmOaJs/Pz+zu7v72fTQaJZFI\n4HK5CAQCANTrddLpNJVKBYfDQV9fHw6Ho6W5RETsTEVeRMQGnE4n2WyW4+Nj+vv7OT8/JxwOYxgG\n29vb1Go1BgYGCAQCLC4u/va+fDQaxbIsNjY2vq2nUinGx8cxTZNkMkk6nW5lLBERWzMaekRYRET+\noFarMTQ0xM3NDRMTE+0+joiIoBt5ERH5C0dHR8zMzKjEi4j8Q7rafQAREfm3+Xw+DMMgl8u1+ygi\nIvILjdaIiIiIiHQgjdaIiIiIiHQgFXkRERERkQ6kIi8iIiIi0oFU5EVEREREOpCKvIiIiIhIB1KR\nFxERERHpQP8Blxd9q/XGUnQAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 58
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "views['MCMCView'] # show interactive view\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Interpretation\n",
      "\n",
      "Recall that the Bayesian methodology returns a *distribution*, hence we now have distributions to describe the unknown $\\lambda$'s and $\\tau$. What have we gained? Immediately we can see the uncertainty in our estimates: the more variance in the distribution, the less certain our posterior belief should be. We can also say what a plausible value for the parameters might be: $\\lambda_1$ is around 18 and $\\lambda_2$ is around 23. What other observations can you make? Look at the data again, do these seem reasonable? The distributions of the two $\\\\lambda$s are positioned very differently, indicating that it's likely there was a change in the user's text-message behaviour.\n",
      "\n",
      "Also notice that posteriors' distributions do not look like any Poisson distributions, though we originally started modelling with Poisson random variables. They are really not anything we recognize. But this is OK. This is one of the benefits of taking a computational point-of-view. If we had instead done this mathematically, we would have been stuck with a very analytically intractable (and messy) distribution. Via computations, we are agnostic to the tractability.\n",
      "\n",
      "Our analysis also returned a distribution for what $\\tau$ might be. Had no change occurred, or the change been gradual over time, the posterior distribution of $\\tau$ would have been more spread out, reflecting that many values are likely candidates for $\\tau$. On the contrary, it is very peaked. It appears that near day 45, the individual's text-message behavior suddenly changed."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "###Why would I want samples from the posterior, anyways?\n",
      "\n",
      "\n",
      "We will deal with this question for the remainder of the book, and it is an understatement to say we can perform amazingly useful things. For now, let's , let's end this chapter with one more example. We'll use the posterior samples to answer the following question: what is the expected number of texts at day $t, \\; 0 \\le t \\le70$? Recall that the expected value of a Poisson is equal to its parameter $\\lambda$, then the question is equivalent to *what is the expected value of $\\lambda$ at time $t$*?\n",
      "\n",
      "In the code below, we are calculating the following: Let $i$ index samples from the posterior distributions. Given a day $t$, we average over all possible $\\lambda_i$ for that day $t$, using $\\lambda_i = \\lambda_{1,i}$ if $t \\lt \\tau_i$ (that is, if the behaviour change hadn't occured yet), else we use $\\lambda_i = \\lambda_{2,i}$. \n",
      "\n",
      "\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "___________________"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize( 12.5, 4)\n",
      "# tau_samples, lambda_1_samples, lambda_2_samples contain\n",
      "# N samples from the corresponding posterior distribution\n",
      "N = tau_samples.shape[0]\n",
      "expected_texts_per_day = np.zeros(n_count_data)\n",
      "for  day in range(0, n_count_data):\n",
      "    # ix is a bool index of all tau samples corresponding to\n",
      "    # the switchpoint occuring prior to value of 'day'\n",
      "    ix = day < tau_samples\n",
      "    # Each posterior sample corresponds to a value for tau.\n",
      "    # for each day, that value of tau indicates whether we're \"before\" (in the lambda1 \"regime\")\n",
      "    # or \"after\" (in the lambda2 \"regime\") the switchpoint.\n",
      "    # by taking the posterior sample of lambda1/2 accordingly, we can average\n",
      "    # over all samples to get an expected value for lambda on that day.\n",
      "    # As explained, the \"message count\" random variable is Poisson distributed, \n",
      "    # and therefore lambda (the poisson parameter) is the expected value of \"message count\"\n",
      "    expected_texts_per_day[day] = (lambda_1_samples[ix].sum() \n",
      "                                    + lambda_2_samples[~ix].sum() ) /N\n",
      "\n",
      "    \n",
      "plt.plot( range( n_count_data), expected_texts_per_day, lw =4, color = \"#E24A33\" )\n",
      "plt.xlim( 0, n_count_data )\n",
      "plt.xlabel( \"Day\" )\n",
      "plt.ylabel( \"Expected # text-messages\" )\n",
      "plt.title( \"Expected number of text-messages received\")\n",
      "#plt.ylim( 0, 35 )\n",
      "plt.bar( np.arange( len(count_data) ), count_data, color =\"#348ABD\", alpha = 0.5,\n",
      "            label=\"observed texts per day\")\n",
      "\n",
      "plt.legend(loc=\"upper left\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAukAAAEaCAYAAACsKskhAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n"
      }
     ],
     "prompt_number": 59
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Our analysis shows strong support for believing the user's behavior did change ($\\lambda_1$ would have been been close in value to $\\lambda_2$ had this been true), and the the change was sudden rather then gradual (demonstrated by $\\tau$ 's strongly peaked posterior distribution). We can speculate what might have caused this: a cheaper text-message rate, a recent weather-2-text subscription, or a new relationship. (The 45th day corresponds to Christmas, and I moved away to Toronto the next month leaving a girlfriend behind)\n"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##### Exercises\n",
      "\n",
      "1\\.  Using `lambda_1_samples` and `lambda_2_samples`, what is the mean of the posterior distributions of $\\lambda_1$ and $\\lambda_2$?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#type your code here."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "2\\.  What is the expected percent increase text-message rates? `hint:` compute the mean of `lambda_1_samples/lambda_2_samples`. Note that quanitity is very different from `lambda_1_samples.mean()/lambda_2_samples.mean()`."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#type your code here."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "3\\. Looking at the posterior distribution graph of $\\tau$, why do you think there is a small number of posterior $\\tau$ samples near 0? `hint:` Look at the data again."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "4\\. What is the mean of $\\lambda_1$ **given** we know $\\tau$ is less than 45.  That is, suppose we have new information as we know for certain that the change in behaviour occured before day 45. What is the expected value of $\\lambda_1$ now? (You do not need to redo the PyMC part, just consider all instances where `tau_trace<45`. )"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#type your code here."
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### References\n",
      "\n",
      "\n",
      "-  [1] Gelman, Andrew. N.p.. Web. 22 Jan 2013. <http://andrewgelman.com/2005/07/n_is_never_larg/>.\n",
      "-  [2] Norvig, Peter. 2009. [*The Unreasonable Effectivness of Data*](http://www.csee.wvu.edu/~gidoretto/courses/2011-fall-cp/reading/TheUnreasonable EffectivenessofData_IEEE_IS2009.pdf).\n",
      "- [3] Patil, A., D. Huard and C.J. Fonnesbeck. 2010. \n",
      "PyMC: Bayesian Stochastic Modelling in Python. Journal of Statistical \n",
      "Software, 35(4), pp. 1-81. \n",
      "- [4] Jimmy Lin and Alek Kolcz. Large-Scale Machine Learning at Twitter. Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data (SIGMOD 2012), pages 793-804, May 2012, Scottsdale, Arizona."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.core.display import HTML\n",
      "def css_styling():\n",
      "    styles = open(\"../styles/custom.css\", \"r\").read()\n",
      "    return HTML(styles)\n",
      "css_styling()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<style>\n",
        "    @font-face {\n",
        "        font-family: \"Computer Modern\";\n",
        "        src: url('http://mirrors.ctan.org/fonts/cm-unicode/fonts/otf/cmunss.otf');\n",
        "    }\n",
        "    div.cell{\n",
        "        width:800px;\n",
        "        margin-left:auto;\n",
        "        margin-right:auto;\n",
        "    }\n",
        "    h1 {\n",
        "        font-family: \"Charis SIL\", Palatino, serif;\n",
        "    }\n",
        "    div.text_cell_render{\n",
        "        font-family: Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
        "        line-height: 145%;\n",
        "        font-size: 120%;\n",
        "        width:800px;\n",
        "        margin-left:auto;\n",
        "        margin-right:auto;\n",
        "    }\n",
        "    .CodeMirror{\n",
        "            font-family: \"Source Code Pro\", source-code-pro,Consolas, monospace;\n",
        "    }\n",
        "    .prompt{\n",
        "        display: None;\n",
        "    }\n",
        "    .text_cell_render h5 {\n",
        "        font-weight: 300;\n",
        "        font-size: 16pt;\n",
        "        color: #4057A1;\n",
        "        font-style: italic;\n",
        "        margin-bottom: .5em;\n",
        "        margin-top: 0.5em;\n",
        "        display: block;\n",
        "    }\n",
        "    \n",
        "    .warning{\n",
        "        color: rgb( 240, 20, 20 )\n",
        "        }\n",
        "</style>\n",
        "<script>\n",
        "    MathJax.Hub.Config({\n",
        "                        TeX: {\n",
        "                           extensions: [\"AMSmath.js\"]\n",
        "                           },\n",
        "                tex2jax: {\n",
        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
        "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
        "                },\n",
        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
        "                \"HTML-CSS\": {\n",
        "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
        "                }\n",
        "        });\n",
        "</script>"
       ],
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "<IPython.core.display.HTML at 0x8225dd8>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}