{
 "metadata": {
  "name": "Chapter1_Introduction"
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      "Probabilistic Programming\n",
      "=====\n",
      "and Bayesian Methods for Hackers \n",
      "========\n",
      "\n",
      "#####Version 0.1\n",
      "Welcome to *Bayesian Methods for Hackers*. The full Github repository, and additional chapters, is available at [github/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers). We hope you enjoy the book, and we encourage any contributions!"
     ]
    },
    {
     "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 may be no bugs in this code...\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 update our beliefs about an outcome; rarely can we be absolutely sure unless we rule out all other alternatives. \n"
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      "\n",
      "###The Bayesian state of mind\n",
      "\n",
      "\n",
      "Bayesian inference differs from more traditional statistical inference by preserving *uncertainty* about our beliefs. At first, this sounds like a bad statistical technique. Isn't statistics all about deriving *certainty* from randomness? To reconcile this, we need to start thinking like Bayesians. \n",
      "\n",
      "The Bayesian world-view interprets probability as measure of *believability in an event*, that is, how confident we are in an event occurring. 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 of events, but becomes more difficult to understand when events have no long-term frequency of occurrences. 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 occurrences defines 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. Simpley, a probability is a summary of an opinion. 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, excluding any outside information. Similarly, under this definition of probability being equal to beliefs, it is clear how we can speak about probabilities (beliefs) of presidential election outcomes: how confident are you candidate *A* will win?\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 occurring, because they possess different *information* about the world. The existence of different beliefs does not imply that anyone is wrong. Consider the following examples demonstrating the relationship between individual beliefs and probabilities:\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 is 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",
      "\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 $P(A)$. We call this quantity the *prior probability*.\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 beliefs) 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 has landed, 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",
      "\n",
      "It's clear that in each example we did not completely discard the prior belief after seeing new evidence $X$, 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 uncertainty about events, we are already admitting that any guess we make is potentially very wrong. After observing data, evidence, or other information, we update our beliefs, and our guess becomes *less wrong*. This is the alternative side of the prediction coin, where typically we try to be *more right*.\n"
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      "\n",
      "###Bayesian Inference in Practice\n",
      "\n",
      " If frequentist and Bayesian inference were 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 *probabilities*.\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 probabilities of *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 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",
      "####Incorporating evidence\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. Bayesian inference will correct this belief.\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 probabilities (instead of a scalar estimate), we *preserve the uncertainty* that reflects the instability of statistical inference of a small $N$ dataset. \n",
      "\n",
      "One may think that for large $N$, one can be indifferent between the two techniques since they offer similar inference, and might lean towards the computational-simpler, frequentist methods. An individual 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.). $N$ 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",
      "### Are frequentist methods incorrect then? \n",
      "\n",
      "**No.**\n",
      "\n",
      "Frequentist methods are still useful or state-of-the-art in many areas. Tools like Least Squares linear regression, LASSO regression, EM algorithm etc. are all very powerful and incredibly fast. Bayesian methods are a compliment to solve the problems these solutions cannot or to gain further insight into the underlying system by offering more flexibility in modeling.\n",
      "\n",
      "\n",
      "#### A note on *Big Data*\n",
      "Paradoxically, big data's predictive analytic problems are actually solved by relatively simple algorithms [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 quote 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. \n"
     ]
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     "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 $A$, beliefs formed by previous information, e.g., our prior belief about bugs being in our code before performing tests.\n",
      "\n",
      "Secondly, we observe our evidence. To continue our buggy-code 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 its discoverer 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 prior probabilities $P(A)$ with an updated posterior probabilities $P(A | X )$."
     ]
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      "##### Example: Mandatory coin-flip example\n",
      "\n",
      "Every statistics text must contain a coin-flipping example, I'll use it here to get it out of the way. Suppose, naively, that you are unsure about the probability of heads in a coin flip (spoiler alert: it's 50%). You believe there is some true underlying ratio, call it $p$, but have no prior opinion on what $p$ might be. \n",
      "\n",
      "We begin to flip a coin, and record the observations: either $H$ or $T$. This is our observed data. An interesting question to ask is how our inference changes as we observe more and more data? More specifically, what do our posterior probabilities look like when we have little data, versus when we have lots of data. \n",
      "\n",
      "Below we plot a sequence of updating posterior probabilities as we observe increasing amounts of data (coin flips)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "\"\"\"\n",
      "The book uses a custom matplotlibrc file, which provides the unique styles for matplotlib plots.\n",
      "If executing this book, and you wish to use the book's styling, provided are two options:\n",
      "    1. Overwrite your own matplotlibrc file with the rc-file provided in the book's styles/ dir.\n",
      "       See http://matplotlib.org/users/customizing.html\n",
      "    2. Also in the styles is  bmh_matplotlibrc.json file. This can be used to update the styles\n",
      "       in only this notebook. Try running the following code:\n",
      "\n",
      "        import json\n",
      "        s = json.load( open(\"../styles/bmh_matplotlibrc.json\") )\n",
      "        matplotlib.rcParams.update(s)\n",
      "\n",
      "\"\"\"\n",
      "\n",
      "#the code below can be passed over, as it is currently not important.\n",
      "%pylab inline\n",
      "figsize( 11, 9)\n",
      "\n",
      "import scipy.stats as stats\n",
      "\n",
      "dist = stats.beta\n",
      "n_trials = [0,1,2,3,4,5,8,15, 50, 500]\n",
      "data = stats.bernoulli.rvs(0.5, size = n_trials[-1] )\n",
      "x = np.linspace(0,1,100)\n",
      "\n",
      "for k, N in enumerate(n_trials):\n",
      "    sx = subplot( len(n_trials)/2, 2, k+1)\n",
      "    plt.xlabel(\"$p$, probability of heads\") if k in [0,len(n_trials)-1] else None\n",
      "    plt.setp(sx.get_yticklabels(), visible=False)\n",
      "    heads = data[:N].sum()\n",
      "    y = dist.pdf(x, 1 + heads, 1 + N - heads )\n",
      "    plt.plot( x, y, label= \"observe %d tosses,\\n %d heads\"%(N,heads) )\n",
      "    plt.fill_between( x, 0, y, color=\"#348ABD\", alpha = 0.4 )\n",
      "    plt.vlines( 0.5, 0, 4, color = \"k\", linestyles = \"--\", lw=1 )\n",
      "\n",
      "    leg = plt.legend()\n",
      "    leg.get_frame().set_alpha(0.4)\n",
      "    plt.autoscale(tight = True)\n",
      "\n",
      "\n",
      "plt.suptitle( \"Bayesian updating of posterior probabilities\", \n",
      "              y = 1.02,\n",
      "              fontsize = 14);\n",
      "\n",
      "plt.tight_layout()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Welcome to pylab, a matplotlib-based Python environment [backend: module://IPython.zmq.pylab.backend_inline].\n",
        "For more information, type 'help(pylab)'.\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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a2WxGdna2y/MvWZnY7Xb88MMPePHFF2EymRAaGopx48bJTzAMBgMyMjLk82/f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QMG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\nxMZiYmLY8OHDWVlZGau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      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The posterior probabilities are represented by the curves, and our confidence is proportional to the height of the curve. As the plot above shows, as we start to observe data our posterior probabilities start to shift and move around. Eventually, as we observe more and more data (coin-flips), our probabilities will lump closer and closer around the true value of $p=0.5$ (marked by a dashed line). \n",
      "\n",
      "Notice that the plots are not always *peaked* at 0.5. There is no reason it should be: recall we assumed we did not have a prior opinion of what $p$ is. In fact, if we observe quite extreme data, say 8 flips and only 1 observed heads, our distribution would look very biased *away* from lumping around 0.5. As more data accumulates, we would see more and more probability being assigned at $p=0.5$.\n",
      "\n",
      "The next example is a simple demonstration of the mathematics of Bayesian inference. "
     ]
    },
    {
     "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.\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 $X$ occurring 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 reduced. 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. What does it look like as a function of our prior, $p \\in [0,1]$? "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12.5,4)\n",
      "p = np.linspace( 0,1, 50)\n",
      "plt.plot( p, 2*p/(1+p), color = \"#348ABD\", lw = 3 )\n",
      "#plt.fill_between( p, 2*p/(1+p), alpha = .5, facecolor = [\"#A60628\"])\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": 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zE3PmzIHRaOT89ERERBLVtLThVFmjqaDPq9ait1+nX+mfT+oo6v3VDuyfJ6Iu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\nRERkRv4fQx4Bwq/BWx0AAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see the biggest gains if we observe the $X$ tests passed when the prior probability, $p$, is low. Let's settle on a specific value for the prior. I'm a strong programmer (I think), 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: $p$ 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, 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 look like? Below is a graph of both the prior and the posterior probabilities. \n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize( 12.5, 4 )\n",
      "colours = [\"#348ABD\", \"#A60628\"]\n",
      "\n",
      "prior = [0.20, 0.80]\n",
      "posterior =  [1./3, 2./3]\n",
      "plt.bar( [0,.7], prior ,alpha = 0.70, width = 0.25, \\\n",
      "            color = colours[0], label = \"prior distribution\",\n",
      "             lw = \"3\", edgecolor = colours[0])\n",
      "\n",
      "\n",
      "plt.bar( [0+0.25,.7+0.25], posterior ,alpha = 0.7, \\\n",
      "          width = 0.25, color =  colours[1], \n",
      "          label = \"posterior distribution\",\n",
      "          lw = \"3\", edgecolor = colours[1])\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": 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vX2RkZGDhwoUYP348Tp8+LfeJiYnBu+++i7y8PHTp0qXa2GPHjkVAQABOnz6N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\nlM2IiIiIiIh+6VQ8SLvrIiLiC1TDLu6mwC4iIiI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      }
     ],
     "prompt_number": 1
    },
    {
     "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 artificially constructed cases. We will later see that this type of mathematical analysis is actually unnecessary. First we must broaden our modeling tools. The next section deals with *probability distributions*. If you are already familiar, feel free to skip (or at least skim), but for the less familiar the next section is essential."
     ]
    },
    {
     "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. Graphically, a probability distribution is a curve where the probability of an outcome is proportional to the height of the curve. You can see examples in the first figure of this chapter. \n",
      "\n",
      "We can divide random variables into three classifications:\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. Discrete random variables become more clear when we contrast them 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 progressively 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. it 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. One can describe $\\lambda$ as the *intensity* of the Poisson distribution. \n",
      "\n",
      "Unlike $\\lambda$, which can be any positive number, the value $k$ in the above formula 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 probability mass distribution for different $\\lambda$ values. The first thing to notice is that by increasing $\\lambda$ we add more probability to larger values occurring. 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",
      "\n",
      "import scipy.stats as stats\n",
      "a = np.arange( 16 )\n",
      "poi = stats.poisson\n",
      "lambda_ = [1.5, 4.25 ]\n",
      "\n",
      "plt.bar( a, poi.pmf( a, lambda_[0]), color=colours[0],\n",
      "        label = \"$\\lambda = %.1f$\"%lambda_[0], alpha = 0.60,\n",
      "        edgecolor = colours[0], lw = \"3\")\n",
      "\n",
      "plt.bar( a, poi.pmf( a, lambda_[1]), color=colours[1],\n",
      "         label = \"$\\lambda = %.1f$\"%lambda_[1], alpha = 0.60,\n",
      "          edgecolor = colours[1], lw = \"3\")\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": 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a2KekpHDffff5tI8///nPXHvttd43oxuLjY31vhm9bNkyRowYwbBhw4ILbyRs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\nIiIKAhzsiYiIiIiCwP8BIuWffYpP6wcAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 48
    },
    {
     "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",
      "\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": 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BQEAACgsLceDAAYwaNUrWfezKtGnTsHTpUmzbtg0jRozAtm3bkJycDBcXF82YnvbJwcEB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\nMY7jqPXr16uPPvpIZbNZtXXrVnX48OGSff70pz+pnTt3KqWU2rdvn9q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      }
     ],
     "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 probabilities 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( 12.5, 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(\"count of text-msgs 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": 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qZnf561//iiFDhuBf//oXAgMDUaFCBXPXRURERERUbqnqpGdnZ6Ny5crmroWs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\npIuIiIiIpJhfADkIpuO9DawCAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Before we begin, with respect 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",
      "We are interested in inferring the unknown $\\lambda$s. To use Bayesian inference, we need to assign prior probabilities to the different possible values of $\\lambda$. What would be good prior probability 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, 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 prior 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 overall prior for the unknown variables 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. We next turn to PyMC, a Python library for performing Bayesian analysis, that 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 beginner to hacker. One of 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 programming variables as the model's components, that is, model components are first-class primitives in this framework. \n",
      "\n",
      "B. Cronin [5] has a very motivating description of probabilistic programming:\n",
      "\n",
      ">   Another way of thinking about this: unlike a traditional program, which only runs in the forward directions, a probabilistic program is run in both the forward and backward direction. It runs forward to compute the consequences of the assumptions it contains about the world (i.e., the model space it represents), but it also runs backward from the data to constrain the possible explanations. In practice, many probabilistic programming systems will cleverly interleave these forward and backward operations to efficiently home in on the best explanations.\n",
      "\n",
      "Due to its poorly understood title, I'll refrain from using the name *probabilistic programming*. Instead, I'll simply use *programming*, as that is what it really is. \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",
      "\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_count_data )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In the above code, we create the PyMC variables corresponding to $\\lambda_1, \\; \\lambda_2$. 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: 58 31 17\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "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_count_data )  \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": 5
    },
    {
     "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 `tau` 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": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The variable `observation` 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",
      "The below code will be explained in the Chapter 3, but this is where our results come from. One can think of it as a *learning* step. The machinery being employed is called *Markov Chain Monte Carlo* (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": [
      "### Mysterious code to be explained in Chapter 3.\n",
      "mcmc = mc.MCMC(model)\n",
      "mcmc.sample( 40000, 10000, 1 )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " \r",
        "[****************100%******************]  40000 of 40000 complete"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "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": 8
    },
    {
     "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 = 30, 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(\"$\\lambda_2$ 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 = 30, 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(\"$\\lambda_2$ 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 =2. )\n",
      "plt.xticks( np.arange( n_count_data ) )\n",
      "\n",
      "plt.legend(loc = \"upper left\");\n",
      "plt.ylim([0,.75])\n",
      "plt.xlim([35, len(count_data)-20])\n",
      "plt.xlabel(\"$\\tau$ (in days)\")\n",
      "plt.ylabel(\"probability\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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ZEgMHDsSZM2cea+Tl6tFPtfQ3ZVExUucshaRU1nnd8ntFyInZB4WZqcb5lj6e\nuFBexMwF43EuHjMXj5mLx8zFY+byoLWRr6ys1GkDJia1X4re398faWlpyMjIgL29PbZu3YqYmBi1\nZUaOHImZM2dCqVSitLQUx48fx7x583SqgZoeqbwCWVt+1jrf+a1RwFN2AisiIiIiEktrI29mpnWW\nikKhgFKHs6lmZmaIiorC0KFDoVQqERISAi8vL6xfvx4AEBoaCk9PT7zyyivo0aMHTExMMHnyZDz9\n9NN1eCqNGz/VisfMxWPm4jFz8Zi5eMxcPGYuD1q79atXrzbojoYNG4Zhw4apPRYaGqo2PX/+fMyf\nP79B90tEREREZIy0jotxcXHR6Yd0U/3qEqR/zFw8Zi4eMxePmYvHzMVj5vKg9Yz85MmTVVeZ0XYZ\nSIVCgc2bN+unMiIiIiIi0kprI+/m5qb6d5cuXaBQKFD9SpXaLklJj+NYM/GYuXjMXDxmLh4zF4+Z\ni8fM5UFrI//++++r/r1o0SIRtRARERERkY5qv3bk/4mPj8ekSZMwfPhwTJ48GQcPHtRnXUaHY83E\nY+biMXPxmLl4zFw8Zi4eM5eH2q8xCWDVqlWIiIjAxIkT0bNnT2RmZuKNN97AO++8w6vMUKP0MPMm\niqQS3GluqXG+uV0ntHLideaJiIhIvhRS9YHvGtjb2+PAgQPo3r276rHz58/jpZdews2bN/VaYHXx\n8fHw8/MTuk/Sj5LsXPwRHFavO7s+qe6r3kP7vr7C90tERESkSUpKCgYPHlyndXQ6I69QKNClSxe1\nx9zc3HS6qys1bUUX0lFR8lDjPElZCQm1fo4kIiIiIg20NvKVlZWqfy9atAiTJk3Cxx9/DCcnJ2Rm\nZuKzzz7D4sWLhRRpDJKSkprkN8Bztu9H3v6jBtn3uQe30b11e43zFKamgqtpGprqcW5IzFw8Zi4e\nMxePmcuD1kbezOzxWTExMWrT0dHRmDRpUsNXRaRnOT/uQ0HSSY3zTFuaw2HMMDTvYCW4KiIiIiLd\naW3kr169KrIOo8dPteJpOxsPALePndY6r5mVBexHDdVHSUaPx7l4zFw8Zi4eMxePmcuD1kbexcVF\nYBlERERERFQXOn9bdc+ePZg3bx7Gjx+PsWPHYty4cRg3bpw+azMqvB6reOce3DZ0CU0Oj3PxmLl4\nzFw8Zi4eM5cHnRr5xYsXIzQ0FJWVldi2bRs6duyI/fv3w8qKY4iJiIiIiAxBp0b+66+/xq+//orV\nq1fD3Nwb/M1TAAAgAElEQVQcn3/+Ofbu3Ytr167puz6jwbFm4tU0Rp70g8e5eMxcPGYuHjMXj5nL\ng06N/L179+Dt7Q0AaN68OcrKytC7d28cOXJEr8UREREREZFmOjXybm5uOH/+PACgW7du+PLLL7F5\n82a0b88znrriWDPxOEZePB7n4jFz8Zi5eMxcPGYuDzrd2fWzzz5Dfn4+AGD58uUIDg7G/fv38cUX\nX+i1OGr8yu4VovJhmcZ5ClNTSOUVgisiIiIiahoUkiRJhi6iLuLj4+Hn52foMuj/5B9OxuXl67XO\nr3hQDFTK6hBDMysL+H0bAfNO/IsTERERiZGSkoLBgwfXaR2dzsgDwOXLl7Ft2zbcuHEDDg4OGDNm\nDLp27VrnIsm4SEolKooeGLoMIiIioiZHpzHy0dHR8PPzQ2pqKtq0aYOzZ8/Cz88PW7Zs0Xd9RoNj\nzcTjGHnxeJyLx8zFY+biMXPxmLk86HRG/oMPPkBsbCwGDhyoeuzo0aMYO3Ys3njjDb0VR0RERERE\nmul0Rv7+/fvo16+f2mN9+/bFgwccUqErXo9VPF5HXjwe5+Ixc/GYuXjMXDxmLg86NfLz5s3D+++/\nj5KSEgBAcXExFixYgLlz5+q1OCIiIiIi0kxrI+/k5KT6+eKLL7BmzRpYWlrC2toabdu2xerVq7Fu\n3TqddxQXFwdPT094eHggIiJC63InTpyAmZkZdu7cWbdn0shxrJl4HCMvHo9z8Zi5eMxcPGYuHjOX\nB61j5L///vtaV1YoFDrtRKlUYubMmTh48CAcHBzQq1cvBAQEwMvL67HlwsPD8corr0BmV8UkIiIi\nIhJKayM/aNCgBttJcnIy3N3d4eLiAgAICgrCnj17Hmvk165di9GjR+PEiRMNtu/GgmPNxOMYefF4\nnIvHzMVj5uIxc/GYuTzodNWasrIyfPbZZ/j+++9x48YN2NvbY+zYsVi4cCGaN29e6/o5OTlwcnJS\nTTs6OuL48eOPLbNnzx4kJCTgxIkTNZ7tnzFjBpydnQEAlpaW8Pb2Vh1wVX8K4rSY6ePnzyLzwW1V\n01w1nEXO06aKh6i65Zih8+U0pznNaU5zmtPGOZ2amorCwkIAQGZmJkJCQlBXOt3Zde7cuUhOTsbH\nH38MZ2dnZGZm4pNPPoG/vz9Wr15d60527NiBuLg4bNy4EQDwww8/4Pjx41i7dq1qmTFjxmD+/Pno\n06cPJkyYgBEjRmDUqFGPbUuud3ZNSkpSvXjG5K/4/8XFj9YYugyNzj3yAaMueGfX+jPW47wxY+bi\nMXPxmLl4zFw8vd3Zddu2bThz5gw6duwIAPD09ISfnx969OihUyPv4OCArKws1XRWVhYcHR3Vljl5\n8iSCgoIAAPn5+fjll1/QrFkzBAQE6PxkiIiIiIiaCp0a+Sfl7++PtLQ0ZGRkwN7eHlu3bkVMTIza\nMlevXlX9e+LEiRgxYoRRNfH8VCsex8iLx+NcPGYuHjMXj5mLx8zlQafryI8ZMwYBAQGIi4vDxYsX\n8csvv2DkyJEYM2aMTjsxMzNDVFQUhg4diqeffhr//ve/4eXlhfXr12P9+vVP9ASIiIiIiJoincbI\nV33ZNTo6WvVl19dffx0LFy6Eubm5iDpVOEZerNL8Oyg8d1nr/KLz6ciO3iuwIt3Vd4y8aasW6Lbi\nXa3zzdq0QhsPlyeozHjJ9TiXM2YuHjMXj5mLx8zF08sY+YqKCkyePBnr16/HJ598Uu/iSJ6UJQ9x\n8YPPDV2GUMrihzg7U/ux7hQ8go08ERERGVytQ2vMzMxw4MABmJqaiqjHaPFTrXgcIy8ej3PxmLl4\nzFw8Zi4eM5cHncbIz507Fx999BHKysr0XQ8REREREelAp0Y+MjISK1euhIWFBRwdHeHk5AQnJyfV\nTZmodlU3AiBxqm72ROLwOBePmYvHzMVj5uIxc3nQ6fKTP/zwg8Y7rerwPVkiIiIiItIDnc7I9+vX\nDwcPHkRISAiGDRuGkJAQ/Prrr+jbt6++6zMaHGsmHsfIi8fjXDxmLh4zF4+Zi8fM5UGnM/LTpk3D\n5cuXsXbtWjg7OyMzMxNLlixBTk4ONm3apO8aiYiIiIioGp3OyO/evRt79+7FsGHD0K1bNwwbNgw/\n//wzdu/ere/6jAbHmonHMfLi8TgXj5mLx8zFY+biMXN50KmRt7OzQ3FxsdpjJSUlsLe310tRRERE\nRERUM52G1owdOxbDhg3DzJkz4eTkhMzMTHzxxRcYN24cEhISVMu9+OKLeitU7jjWTDyOkRePx7l4\nzFw8Zi4eMxePmcuDTo38unXrAADLli1TPSZJEtatW6eaBwDXrl1r4PKIiIiIiEgTnYbWZGRkICMj\nA9euXVP9VJ9mE18zjjUTj2PkxeNxLh4zF4+Zi8fMxWPm8qBTI09ERERERI2LTkNr6Mk15rFmFQ+K\nAS0399J0IzC54Bh58RrzcW6smLl4zFw8Zi4eM5cHNvKEjC9jcOePVI3zKsuVgqtp/JSlpXh48y9I\nlZUa55u2bonmVpaCqyIiIqKmho28IElJSY32023Z7bsoyco1dBkN7tyD23o5K39j56+4ufeQ1vlP\nL5mHDs/2bPD9ykFjPs6NFTMXj5mLx8zFY+bywEaeqK4kCVJZeU0LCCuFiIiImi5+2VUQfqoVj2Pk\nxeNxLh4zF4+Zi8fMxWPm8sBGnoiIiIhIhtjIC8LrsYrH68iLx+NcPGYuHjMXj5mLx8zlgY08ERER\nEZEMsZEXhGPNxOMYefF4nIvHzMVj5uIxc/GYuTywkSciIiIikiGhjXxcXBw8PT3h4eGBiIiIx+Zv\n2bIFPj4+6NGjB/r374+zZ8+KLE+vONZMPI6RF4/HuXjMXDxmLh4zF4+Zy4Ow68grlUrMnDkTBw8e\nhIODA3r16oWAgAB4eXmplnFzc0NiYiLatm2LuLg4TJkyBceOHRNVIhERERGRbAg7I5+cnAx3d3e4\nuLigWbNmCAoKwp49e9SW6devH9q2bQsA6NOnD7Kzs0WVp3ccayYex8iLx+NcPGYuHjMXj5mLx8zl\nQVgjn5OTAycnJ9W0o6MjcnJytC7/9ddfY/jw4SJKIyIiIiKSHWFDaxQKhc7LHjp0CN988w1+++03\njfNnzJgBZ2dnAIClpSW8vb1VnxyrxnQ1tumqxxpLPY9OX79xHVUfsarGlVedzZbz9KNj5EXu/37q\nGQx/1g9A43h9RU5/+eWXsvj/aEzTqampmDZtWqOppylMVz3WWOppCtPVszd0PU1hmr/Pxfz+Liws\nBABkZmYiJCQEdaWQJEmq81r1cOzYMSxatAhxcXEAgGXLlsHExATh4eFqy509exaBgYGIi4uDu7v7\nY9uJj4+Hn5+fiJIbVFJSkurFa2wuLFiF/CMnDF1Ggzv34LZBhtd0+8+76PCs/I7RhtCYj3NjxczF\nY+biMXPxmLl4KSkpGDx4cJ3WMdNTLY/x9/dHWloaMjIyYG9vj61btyImJkZtmczMTAQGBuKHH37Q\n2MTLGf8ziGfIMfKl+Xe0zmtm2QYmzZsJrEYcHufiMXPxmLl4zFw8Zi4Pwhp5MzMzREVFYejQoVAq\nlQgJCYGXlxfWr18PAAgNDcUnn3yCO3fuqP5M3KxZMyQnJ4sq0WhVlpVDqqzUPFOhgJA/yTQhf368\nFiYtmmucZ9qqJXqs+QAtbDsJroqIiIiMjbChNQ2FQ2vqLj/xBDI2bNU6vyTnFqSycoEViWGooTU1\nMW3VEs98v8JoG3n+KVY8Zi4eMxePmYvHzMVr1ENryHAqS0tRfC3b0GUQERERUQMSemfXpoyfasVr\nbGfjmwIe5+Ixc/GYuXjMXDxmLg9s5ImIiIiIZIiNvCCPXgOXxHj0OvIkBo9z8Zi5eMxcPGYuHjOX\nBzbyREREREQyxC+7CqLPsWZld+7hYc4t7fP/uqu3fTdmHCMvHsdUisfMxWPm4jFz8Zi5PLCRNwLl\nd4twOvQjQ5dBOqisqEDx1WwUZ+RonG9m0RqW3TwEV0VERERyxEZeEF6PVbzGeB15qawc596J0Drf\nPnCIrBt5HufiMXPxmLl4zFw8Zi4PHCNPRERERCRDbOQF4ada8Rrb2fimgMe5eMxcPGYuHjMXj5nL\nAxt5IiIiIiIZYiMvCK/HKh6vIy8ej3PxmLl4zFw8Zi4eM5cHNvJERERERDLERl4QjjUTj2PkxeNx\nLh4zF4+Zi8fMxWPm8sDLT8qEsrRM6zyFmanASoiIiIioMWAjL8iTXo/16upvUXg+XeO8yjLtTX5T\n1hivI1+bigcPUZx5A5KyUuN8szatYN6p8T4nXndYPGYuHjMXj5mLx8zlgY28TDy8+RceXMk0dBmk\nZ3n7jyJv/1Gt87stC2vUjTwRERGJwzHygvBTrXhyOxtvDHici8fMxWPm4jFz8Zi5PLCRJ5IThcLQ\nFRAREVEjwaE1gnCsmXhyHCNfm1uxh3E//brGeQpTE9i8MhDm1h0EV/X/8TgXj5mLx8zFY+biMXN5\nYCNPJCP5iX8gP/EPjfMUzZuh0+BnBVdEREREhsKhNYLwU614xnY2XhcKE8P+l+ZxLh4zF4+Zi8fM\nxWPm8sAz8o1EcUYOyu8WapynaGaG8rtFgisiuZHKK5D1/W6YtDDXOL9NV1fYvPKc4KqIiIhIX9jI\nC1LbWLOii+m49NmXAisyfsY4Rr5GkoSbe+K1zrYZ/rzeG3mOqRSPmYvHzMVj5uIxc3kQ9nf4uLg4\neHp6wsPDAxERERqXmTVrFjw8PODj44NTp06JKk2IlKTfcXPPQa0/t39PMXSJRufaQ/4VQ7TU1FRD\nl9DkMHPxmLl4zFw8Zi4PQs7IK5VKzJw5EwcPHoSDgwN69eqFgIAAeHl5qZaJjY1Feno60tLScPz4\ncUybNg3Hjh0TUZ4Q9+7cQdqKrwxdRpPyoLLC0CU0OYWFmoeHkf4wc/GYuXjMXDxmLg9CGvnk5GS4\nu7vDxcUFABAUFIQ9e/aoNfI///wzxo8fDwDo06cP7t69i1u3bsHGxkZEiQ2i4v4D7TN5/W8ysHsp\nF5Dx9U9a51c+LEVJ1k0tcxVwm/EGTFu20DJbgeYdrJ68SCIiItKZkEY+JycHTk5OqmlHR0ccP368\n1mWys7MbtJGXJAmV5TWcpVUqa5wvKZUozbutcZ6JmSluHzuNiiLNzXxacgpGv/hKneqlJ3Mv/hY6\nvdjX0GU0KiUZOTXON2nWTOu87Jh9UJhqHo3X1scT7Z/zx/Wr16AseahhCQVQw2dZhYkJTJpr3zdp\nl5mZaegSmhxmLh4zF4+Zy4OQRl6h49loSZJ0Wi8lpZGOJ/dy1DprTu+lKBFYCgFhrw1k5oIUAsg6\nfw6TQqfgzMULhi6nSQkJCWm8vxONFDMXj5mLx8zlQUgj7+DggKysLNV0VlYWHB0da1wmOzsbDg4O\nj21r8ODB+iuUiIiIiEgmhFy1xt/fH2lpacjIyEBZWRm2bt2KgIAAtWUCAgKwefNmAMCxY8dgZWUl\nq/HxREREREQiCTkjb2ZmhqioKAwdOhRKpRIhISHw8vLC+vXrAQChoaEYPnw4YmNj4e7ujtatW2PT\npk0iSiMiIiIikiVh15EfNmwYLl26hPT0dLz//vsA/m7gQ0NDVctERUUhPT0dZ86cgZ+fn6jSGtxb\nb70FGxsbeHt7qz2+du1aeHl5oXv37ggPDzdQdcZJU+bJycno3bs3evbsiV69euHEiRMGrND4ZGVl\n4YUXXkC3bt3QvXt3REZGAgBu376NIUOGoGvXrnj55Zdx9+5dA1dqPLRl/s4778DLyws+Pj4IDAzE\nvXv3DFyp8dCWeZVVq1bBxMQEt29rvhAC1V1NmfN9VD+0Zc73Uf15+PAh+vTpA19fXzz99NOq3rjO\n76ESNbjExEQpJSVF6t69u+qxhIQE6aWXXpLKysokSZKkvLw8Q5VnlDRl/vzzz0txcXGSJElSbGys\nNGjQIEOVZ5Ru3rwpnTp1SpIkSSoqKpK6du0qXbhwQXrnnXekiIgISZIkafny5VJ4eLghyzQq2jI/\ncOCApFQqJUmSpPDwcGbegLRlLkmSlJmZKQ0dOlRycXGRCgoKDFmmUdGWOd9H9Udb5nwf1a8HDx5I\nkiRJ5eXlUp8+faSjR4/W+T1U2Bn5puS5555Du3bt1B778ssv8f7776PZ/13er1OnToYozWhpytzO\nzk51ZvLu3bsavzxN9WdrawtfX18AQJs2beDl5YWcnBy1e0KMHz8eu3fvNmSZRkVT5jdu3MCQIUNg\nYvL3r/M+ffogOzvbkGUaFW2ZA8C8efOwYsUKQ5ZnlLT9blm3bh3fR/VEW+Z8H9WvVq1aAQDKysqg\nVCrRrl27Or+HspEXJC0tDYmJiejbty8GDRqEP/74w9AlGb3ly5cjLCwMzs7OeOedd7Bs2TJDl2S0\nMjIycOrUKfTp00ftRm42Nja4deuWgaszTo9m/qhvvvkGw4cPN1BVxu3RzPfs2QNHR0f06NHD0GUZ\ntUczv3z5Mt9HBajKvG/fvnwf1bPKykr4+vrCxsZGNbSpru+hbOQFqaiowJ07d3Ds2DH85z//wb/+\n9S9Dl2T0QkJCEBkZiczMTHz++ed46623DF2SUbp//z5GjRqFNWvWwMLCQm2eQqHQ+T4SpLv79+9j\n9OjRWLNmDdq0aaN6fMmSJWjevDmCg4MNWJ1xejRzExMTLF26FIsXL1bNl6rdB4We3KOZW1hY8H1U\ngOq/W/g+ql8mJiY4ffo0srOzkZiYiEOHDqnN1+U9lI28II6OjggMDAQA9OrVCyYmJigoKDBwVcYt\nOTkZr732GgBg9OjRSE5ONnBFxqe8vByjRo3C2LFj8eqrrwL4+wxCbm4uAODmzZuwtrY2ZIlGpyrz\nN998U5U5AHz77beIjY3Fli1bDFidcaqe+ZUrV5CRkQEfHx+4uroiOzsbzzzzDPLy8gxdqtHQdJzz\nfVS/NGXO91Ex2rZti3/84x84efJknd9D2cgL8uqrryIhIQEAcPnyZZSVlaFDhw4Grsq4ubu748iR\nIwCAhIQEdO3a1cAVGRdJkhASEoKnn34ac+bMUT0eEBCA7777DgDw3XffqTWb9GS0ZR4XF4f//Oc/\n2LNnD1q0aGHACo2Ppsy9vb1x69YtXLt2DdeuXYOjoyNSUlL4obWBaDvO+T6qP9oy5/uo/uTn56uu\nSFNSUoJff/0VPXv2rPt7qB6/jNtkBQUFSXZ2dlLz5s0lR0dH6ZtvvpHKysqkN998U+revbvk5+cn\nHTp0yNBlGpWqzJs1a6bK/MSJE1Lv3r0lHx8fqW/fvlJKSoqhyzQqR48elRQKheTj4yP5+vpKvr6+\n0i+//CIVFBRIgwcPljw8PKQhQ4ZId+7cMXSpRkNT5rGxsZK7u7vk7OysemzatGmGLtVoaMv8Ua6u\nrrxqTQPS9ruF76P6o+045/uo/pw9e1bq2bOn5OPjI3l7e0srVqyQJEmq83uoQpI4sI+IiIiISG44\ntIaIiIiISIbYyBMRERERyRAbeSIiIiIiGWIjT0REREQkQ2zkiYiIiIhkiI08ERHVi4uLC+Lj4w1d\nBhFRk8VGnoiI6kWX24cTEZH+sJEnIpK5yMhILFiwwNBlEBGRYGzkiYhk7u2338a2bdtw69atOq0X\nERGBMWPGqD02e/ZszJ49GwCwfPlyuLu7w9LSEt26dcPu3bu1bsvExARXr15VTU+YMAEffvihavrG\njRsYNWoUrK2t4ebmhrVr19apViIiehwbeSIimVMoFAgODsb3339fp/Vef/11xMbG4v79+wAApVKJ\nn376CW+88QYAwN3dHUlJSSgsLMTHH3+MN998E7m5uTrXVDXsprKyEiNGjEDPnj1x48YNxMfHY/Xq\n1Thw4ECd6iUiInVs5ImIjMCECRPw7bff1mkdZ2dn+Pn5YdeuXQCAhIQEtGrVCr179wYAjB49Gra2\ntgCAf/3rX/Dw8EBycrLO25ckCQBw4sQJ5OfnY+HChTAzM4OrqysmTZqEH3/8sU71EhGROjbyRERG\n4K+//kJxcXGdGm0ACA4ORkxMDAAgOjpadTYeADZv3oyePXuiXbt2aNeuHc6dO4eCggKdt111Rv76\n9eu4ceOGajvt2rXDsmXLkJeXV6daiYhInZmhCyAioicTFxeHtLQ0LFy4EJs2bUL79u2RmpqKs2fP\nYsSIEfDz89O67ujRoxEWFoacnBzs3r0bx44dA/B38z1lyhQkJCSgX79+UCgU6Nmzp+ose3WtWrVC\ncXGxavrmzZtwcnICADg5OcHV1RWXL19uwGdNREQ8I09EJGPR0dFISEjA22+/jTFjxmDv3r3Ytm0b\nHBwcMG/ePKxcubLG9Tt16oRBgwZhwoQJcHNzw1NPPQUAePDgARQKBTp27IjKykps2rQJ586d07od\nX19fbNmyBUqlEnFxcUhMTFTN6927NywsLLBixQqUlJRAqVTi3Llz+OOPPxomBCKiJoqNPBGRTB07\ndgwHDx7EihUrAAAWFhZ49dVX4eDggN69eyMrKwuurq61bic4OBjx8fEIDg5WPfb0008jLCwM/fr1\ng62tLc6dO4cBAwZo3caaNWuwd+9etGvXDtHR0XjttddU80xNTfHf//4Xp0+fhpubGzp16oQpU6ag\nsLDwCZ49EREpJG1/JyUiIllbsmQJ5s6di1atWhm6FCIi0gNhZ+Tfeust2NjYwNvbW+sys2bNgoeH\nB3x8fHDq1ClRpRERGZ2ff/4Zs2bNQk5OjqFLISIiPRHWyE+cOBFxcXFa58fGxiI9PR1paWnYsGED\npk2bJqo0IiKjsmvXLnz66acIDAzEtm3bDF0OERHpidChNRkZGRgxYgRSU1Mfmzd16lS88MIL+Pe/\n/w0A8PT0xJEjR2BjYyOqPCIiIiIi2Wg0X3bNyclRXaoMABwdHZGdnW3AioiIiIiIGq9GdR356n8c\nqLqZyKPi4+NFlUNEREREJMzgwYPrtHyjaeQdHByQlZWlms7OzoaDg4PGZWu6uUljFRERgfDwcEOX\n0aQwc/GYuXjMXDxmLh4zF4+Zi5eSklLndRrN0JqAgABs3rwZwN/XRraysuL4eCIiIiIiLYSdkX/9\n9ddx5MgR5Ofnw8nJCYsXL0Z5eTkAIDQ0FMOHD0dsbCzc3d3RunVrbNq0SVRpQmRmZhq6hCaHmYvH\nzMVj5uIxc/GYuXjMXB6ENfIxMTG1LhMVFSWgEsPo3r27oUtocpi5eMxcPGYuHjMXj5mLx8zlQXZ3\ndo2Pj5flGHkiIiIiIm1SUlLk+2XXJyVJEvLy8qBUKjVe7YaMlyRJMDU1hbW1NV97IiIiajKMppHP\ny8uDhYUFWrVqZehSyACKi4uRl5en9gXppKQkDBgwwIBVNT3MXDxmLh4zF4+Zi8fM5aHRXLXmSSmV\nSjbxTVirVq2gVCoNXQYRERGRMEYzRv7mzZuws7MzQEXUWPAYICIiIrmqzxh5ozkjT0RERETUlLCR\nJ6OVlJRk6BKaHGYuHjMXj5mLx8zFY+bywEa+iXv22Wfx+++/630/aWlpGDhwIDp37oyNGzfqfX9E\nRERExo5j5GXMx8cHa9euxcCBAw1dSq1mzZoFS0tLfPbZZ3rbR1M8BoiIiMg4NOnryGty93Yxiu4+\n1Nv2LaxawKq94a6Uo1AoUN/PYRUVFTAzq9/LX591s7KyEBgYWOty69evR15eHj788MN61UZERETU\nVBj10Jqiuw9xYPc5vf3U5UOCj48PVq9ejX79+sHNzQ1vv/02SktLAQCXLl3CiBEj4OrqimeffRZx\ncXGq9dasWYPu3bujc+fO6NOnD44ePQoAmDp1KrKzsxEcHAxnZ2dERUXh5s2bGD9+PLp27YqePXti\nw4YNj9UQGRmJAQMGwNnZGUqlEj4+Pjhy5EitdVRft7Ky8rHnqG39kSNHIikpCeHh4ejcuTOuXr2q\nNacpU6Zg9+7dyMvL0zlbbTi+TzxmLh4zF4+Zi8fMxWPm8mDUjXxjs337duzYsQMpKSlIT0/HqlWr\nUFFRgeDgYAwePBhpaWmIiIhAaGgo0tPTkZaWhq+++grx8fG4fv06duzYAScnJwDAunXr4OjoiJiY\nGGRmZmLGjBkIDg6Gt7c3Lly4gN27d2PdunVISEhQq2Hnzp3Ytm0brl27BlNTUygUCigUCpSXl2us\n48qVKxrXNTFRP3RqWn/Pnj3o168fVqxYgevXr8PNzU1rRgqFAqNHj8a2bdsaMHkiIiIi48NGXhCF\nQoHJkyfD3t4eVlZWCAsLw44dO/DHH3+guLgYc+bMgZmZGZ577jm8/PLL2LFjB8zMzFBWVoY///wT\n5eXlcHR0hIuLi8btnzx5EgUFBZg/fz7MzMzQuXNnjB07Frt27VKrYcqUKbC3t4e5ubna+trq2L59\ne63r6rI+AJ2HAb3++uuIjo7Wadma8I504jFz8Zi5eMxcPGYuHjOXBzbyAjk4OKj+7ejoiNzcXOTm\n5qo9DgBOTk64efMmXF1dsXTpUkREROCpp57CpEmTkJubq3Hb2dnZyM3Nhaurq+pn9erV+Ouvv7TW\n8ChtdTy6P23r6rq+QqHQuv6j8vPzUVJSgpMnT+q0PBEREVFTxEZeoOzsbLV/29rawtbWFjk5OWpn\nq7OysmBvbw8AGDVqFGJjY3HmzBkoFAosXrxYtdyjjbGDgwM6d+6Ma9euqX6uX7+OH3/8Ua0Gbc20\nnZ2dxjoevQpMTY24tudR16vIxMfHIyUlBWFhYaqz8leuXMF///tfRERE4MyZMzpvi+P7xGPm4jFz\n8Zi5eMxcPGYuD2zkBZEkCV9//TVu3LiBO3fuYNWqVQgMDMQzzzyDli1bIjIyEuXl5UhKSsKBAwcQ\nGBiI9PR0JCYmorS0FObm5mjRogVMTU1V2+zUqRMyMjIAAH5+fmjTpg0iIyNRUlICpVKJixcv4tSp\nUzrVV1MduvD39691/dqG1mzfvh2JiYmYMmUKRo4cif379+Phw4fYv38/7OzsMH36dERFRelUDxER\nEY4D+LkAACAASURBVJGxYyMvSNWXOEeNGgU/Pz906dIFYWFhaNasGaKjo3Hw4EF4eHjg3XffxZdf\nfgl3d3eUlZXh008/RdeuXeHl5YWCggK1yzLOnTsXK1euhKurK9avX4+YmBikpqbCz88PHh4emDNn\nDoqKinSqr6Y6Gmr9ms7onzhxAkeOHFH9xcHCwgLDhw/Hzp07MX36dDzzzDPIyclB586ddaoH4Pg+\nQ2Dm4jFz8Zi5eMxcPGYuD0Z9Q6isq7dxYPc5vdXy8qvd4eTWXqdlfX19ERkZKYubNzVWq1atwrRp\n09CqleZr9/OGUERERCRXvCFUNRZWLfDyq931un0S45dffsGUKVNw8+ZNdOnSRad1kpKSeEZBMGYu\nHjMXj5mLx8zFY+byYNSNvFX7Vga98yo1jP/+97/4/PPPsXHjRvTv3x9hYWGGLomIiIjI4Ix6aA01\nLTwGiIiISK7qM7SGX3YlIiIiIpIhNvJktHgNXPGYuXjMXDxmLh4zF4+ZywMbeSIiIiIiGRLWyMfF\nxcHT0xMeHh6IiIh4bH5+fj5eeeUV+Pr6onv37vj2229FlUZGit+2F4+Zi8fMxWPm4jFz8Zi5PAhp\n5JVKJWbOnIm4uDhcuHABMTExuHjxotoyUVFR6NmzJ06fPo3Dhw8jLCwMFRUVOu9DZt/ZJT3gMUBE\nRERNiZBGPjk5Ge7u7nBxcUGzZs0QFBSEPXv2qC1jZ2eHwsJCAEBhYSE6dOgAMzPdr45pamqK4uLi\nBq2b5KO4uBimpqZqj3F8n3jMXDxmLh4zF4+Zi8fM5UHIdeRzcnLg5OSkmnZ0dMTx48fVlpk8eTJe\nfPFF2Nvbo6ioCNu2bavTPqytrZGXl4e7d+9CoVA0SN0N6d69e2jbtq2hyzBKkiTB1NQU1tbWhi6F\niIiISBghjbwujfXSpUvh6+uLw4cP48qVKxgyZAjOnDkDCwuLx5adMWMGnJ2dAQCWlpbw9vbGgAED\nYGNjo/oEWTW2i9NNd3rAgAGNqp6mMF31WGOpp6lMV2ks9XCa0w09zd/n/H1ujNOpqamq0SiZmZkI\nCQlBXQm5IdSxY8ewaNEixMXFAQCWLVsGExMThIeHq5YZPnw4PvjgA/Tv3x8AMHjwYERERMDf319t\nW9puCEVEREREJFeN9oZQ/v7+SEtLQ0ZGBsrKyrB161YEBASoLePp6YmDBw8CAG7duoVLly7Bzc1N\nRHlCVD9zRvrHzMVj5uIxc/GYuXjMXDxmLg9mQnZiZoaoqCgMHToUSqUSISEh8PLywvr16wEAoaGh\nWLBgASZOnAgfHx9UVlZixYoVaN++vYjyiIiIiIhkR8jQmobEoTVEREREZGwa7dAaIiIiIiJqWGzk\nBeFYM/GYuXjMXDxmLh4zF4+Zi8fM5YGNPBERERGRDHGMPBERERGRgXGMPBERERFRE8FGXhCONROP\nmYvHzMVj5uIxc/GYuXjMXB7YyBMRERERyRDHyBMRERERGRjHyBMRERERNRFs5AXhWDPxmLl4zFw8\nZi4eMxePmYvHzOWBjTwRERERkQxxjDwRERERkYFxjDwRERERURPBRl4QjjUTj5mLx8zFY+biMXPx\nmLl4zFwe2MgTEREREcmQTmPkfX19MX78eAQHB8PGxkZEXVpxjDwRERERGRu9jZH/6KOPkJiYCDc3\nNwwbNgzR0dF4+PBhvYokIiIiIqInp1MjHxgYiF27diErKwsjR47EF198AVtbW0ycOBEJCQn6rtEo\ncKyZeMxcPGYuHjMXj5mLx8zFY+byUKcx8u3bt8e4ceMwdepUODk5YefOnQgNDUXXrl3x66+/6qtG\nIiIiIiKqRqcx8pIkYf/+/fjhhx+wd+9e9O3bF+PGjUNgYCBatmyJnTt3Yvr06cjNzdV7wRwjT0RE\nRETGpj5j5M10WcjW1hYdO3bEuHHjsHz5cjg6OqrNDwwMRGRkZJ12TERERERE9afT0Jp9+/bh/Pnz\nCA8Pf6yJr3L48OGGrMvocKyZeMxcPGYuHjMXj5mLx8zFY+byoFMj//LLL2t83NraukGLISIiIiIi\n3eg0Rt7CwgJFRUVqj5WXl8PW1hYFBQV6K04TjpEnIiIiImPT4GPkn3vuOQBASUmJ6t9VsrOz0a9f\nP513FBcXhzlz5kCpVGLSpEkIDw9/bJnDhw9j7ty5KC8vR8eOHTlch4iIiIhIixob+ZCQEADAiRMn\nMGnSJFSdvFcoFLCxsdH5U4NSqcTMmTNx8OBBODg4oFevXggICICXl5dqmbt372LGjBnYv38/HB0d\nkZ+fX9/n1CglJSVhwIABhi6jSWHm4jFz8Zi5eMxcPGYuHjOXhxob+QkTJgAA+vbtC09Pz3rvJDk5\nGe7u7nBxcfl/7N17dFTV3f/x94REBbmDgLkJmCBBQkgMBCpaFCtGf8TKpY0oYBsw9QGreGlKSxUQ\ny6WyqsASqa22giC0VCKPdKQEvFAlQUEMYiEoMRduAkLARBIm5/cHi3kIScgJZM7sST6vtbIWe7Jn\nziffGWZ2Tr6zB4DU1FQyMzOrLOSXLVvGiBEjvG+m7dix40UfT0RERESksat1Ib9kyRLGjBkDwH/+\n8x8+/PDDGuf9/Oc/r/MgxcXFREREeMfh4eFkZ2dXmZOXl0dFRQW33HILJ06c4JFHHvEe/3wTJ04k\nMjISgNatWxMbG+v9rfHsu6w11njQoEFG5WkK47OXmZKnqYzPMiWPxho39FjP53o+b4zj3NxcSkpK\nACgoKPB2wtRHrW92vfPOO1m7di0AgwcPxuVy1XgDGzdurPMgq1atwu128/LLLwOwdOlSsrOzWbBg\ngXfOpEmT2Lp1K1lZWZSWljJw4EDefvttoqOjq9yW3uwqIiIiIo3NxbzZtdbtJ88u4uHMm1A3btxY\n45cdYWFhFBYWeseFhYXV9qOPiIjg9ttvp3nz5nTo0IGbb76Z7du31+uHMdn5Z87E91Rz56nmzlPN\nnaeaO081d55qHhhqXchXVlba+rIjMTGRvLw88vPzKS8vZ8WKFaSkpFSZc/fdd7Np0yY8Hg+lpaVk\nZ2fTq1evS/vpREREREQaqeBavxFc67e8XC4XHo+n7oMEB7Nw4UKGDh2Kx+MhLS2NmJgYFi9eDEB6\nejo9e/bkjjvuoE+fPgQFBTFhwoRGtZA/t+dMnKGaO081d55q7jzV3HmqufNU88BQa498fn6+rRs4\nuxONU9QjLyIiIiKNTYP2yHft2tXWl9ijXjPnqebOU82dp5o7TzV3nmruPNU8MNTaPzNhwgTvLjO1\nbQPpcrl47bXXfJNMRERERERqVetCvnv37t5/X3vttbhcLs7vwqltS0qpTr1mzlPNnaeaO081d55q\n7jzV3HmqeWCotUfeVOqRFxEREZHGpkF75M+XlZXF+PHjufPOO5kwYQLr16+vd8CmTL1mzlPNnaea\nO081d55q7jzV3HmqeWCwtZCfN28e9957Lx06dOCuu+6iffv23HfffTz33HO+ziciIiIiIjWw1VoT\nGhrKunXr6N27t/eyzz//nNtuu439+/f7NOD51FojIiIiIo2Nz1prXC4X1157bZXLunfvTlCQ7c4c\nERERERFpQLWuxCsrK71f06ZNY/z48ezevZuysjJ27drFgw8+yPTp053MGtDUa+Y81dx5qrnzVHPn\nqebOU82dp5oHhlq3nwwOrv6t5cuXVxkvW7aM8ePHN3wqERERERG5oFp75PPz823dgNOf7qoeeRER\nERFpbC6mR77WM/JOL9BFRERERMQ+2+9WzczM5LHHHmPcuHGMGTOGsWPHMnbsWF9ma1TUa+Y81dx5\nqrnzVHPnqebOU82dp5oHBlsL+enTp5Oenk5lZSUrV66kY8eOvPPOO7Rt29bX+UREREREpAa29pGP\njIzk7bffJjY2lrZt23Ls2DFycnJ45plnWLNmjRM5vdQjLyIiIiKNjc/2kT9+/DixsbEAXHbZZZSX\nl9O/f3/ee++9+qcUEREREZFLZmsh3717dz7//HMArr/+ehYtWsRrr71G+/btfRquMVGvmfNUc+ep\n5s5TzZ2nmjtPNXeeah4Yat215lwzZ87k8OHDAMyePZvRo0dz8uRJXnzxRZ+GExERERGRmtnqkTeJ\neuRFRPynrLSCivLTtuZe2epymjWzvTmaiEiT1qD7yJ9v9+7drFy5kn379hEWFsaoUaPo0aNHvUOK\niIhZTpR8z+aNX+LxVNY5t/REOcePldY5r1XrK/h/qX1p1lwLeRERX7H1DLts2TISEhLIzc2lZcuW\nfPbZZyQkJPD666/7Ol+joV4z56nmzlPNndcgNbcs9n39LcX5dX99e+Q7Kj1WnV92fikIVHqcO081\nd55qHhhsnZH/7W9/y9q1a7n55pu9l33wwQeMGTOG++67z2fhRERERESkZrZ65K+66ir27dtHSEiI\n97KKigpCQ0P55ptvfBrwfOqRFxFpWCeOl/HPv33C6dMNdxY9OCSIxBu74XK56pzbsXNLOoW2brBj\ni4gEIp/1yD/22GNMmTKFZ555hubNm1NaWsrTTz/N5MmTLyqoiIg0bqcrKtn87pe25g645Vot5EVE\nLkKtPfIRERHerxdffJEXXniB1q1b06lTJ9q0acPzzz/PSy+9ZPtAbrebnj17Eh0dzZw5c2qdt2XL\nFoKDg/nnP/9Zv5/EcOo1c55q7jzV3HmqufNUc+ep5s5TzQNDrWfklyxZUueV7fzJFMDj8TBp0iTW\nr19PWFgY/fr1IyUlhZiYmGrzMjIyuOOOOwiwXTFFRERERBxV60J+8ODBDXaQnJwcoqKi6Nq1KwCp\nqalkZmZWW8gvWLCAkSNHsmXLlgY7tikGDRrk7whNjmruPNXceQ1R86AgbRFZH3qcO081d55qHhhs\n9ciXl5czc+ZMlixZwr59+wgNDWXMmDFMnTqVyy67rM7rFxcXExER4R2Hh4eTnZ1dbU5mZiYbNmxg\ny5YtFzzbP3HiRCIjIwFo3bo1sbGx3gfc2T8Faayxxho39fHrf8vk0L7j9LouHoCdu7YBVBtfF92X\n06cr+fLrHQBce01vAMfGA7jWiHpprLHGGjs5zs3NpaSkBICCggLS0tKoL1u71kyePJmcnByefvpp\nIiMjKSgoYMaMGSQmJvL888/XeZBVq1bhdrt5+eWXAVi6dCnZ2dksWLDAO2fUqFE88cQTJCUl8cAD\nDzBs2DBGjBhR7bYCddeaTZs2ee88cYZq7jzV3HkXqvnmd7/k863FDieqvwG3XMv18WH+jmGbHufO\nU82dp5o7z2e71qxcuZLt27fTsWNHAHr27ElCQgJ9+vSxtZAPCwujsLDQOy4sLCQ8PLzKnE8++YTU\n1FQADh8+zL/+9S9CQkJISUmx/cOIiIiIiDQVthbylyoxMZG8vDzy8/MJDQ1lxYoVLF++vMqcr776\nyvvvn/3sZwwbNqxRLeL1W63zVHPnqebOU82dp5o7TzV3nmoeGGwt5EeNGkVKSgpPPfUU11xzDfn5\n+cycOZNRo0bZO0hwMAsXLmTo0KF4PB7S0tKIiYlh8eLFAKSnp1/8TyAiIgFt7+7DYHOjstBr2tKu\nw5W+DSQiEiBs9ciffbPrsmXLvG92vffee5k6dSqXX365Ezm91CMvdqnmzlPNfe/40VKOHyvzjj/+\nJJvEG5KqzXO5XOzcto+i/KNOxvO5//fTODqHtfFrBj3OnaeaO081d55PeuRPnz7NhAkTWLx4MTNm\nzLjocCIiculKjn/Pv1d/7h1/+XU+3xa29GMiERHxlzo3Dw4ODmbdunU0a9bMiTyNln6rdZ5q7jzV\n3Hlnt3IU5+hx7jzV3HmqeWCw9SkgkydP5qmnnqK8vNzXeURERERExAZbC/n58+fz3HPP0apVK8LD\nw4mIiCAiIsL7oUxSt7MfBCDOUc2dp5o77+yHKolz9Dh3nmruPNU8MNjatWbp0qU1ftKqjffJioiI\niIiID9jatebUqVPMnDmT5cuXe3etSU1NZerUqVxxxRVO5PQK1F1rREQaQuHeo6x7s+mehTdh1xoR\nEV/w2Se7PvTQQ+zevZsFCxYQGRlJQUEBzz77LMXFxbz66qsXFVZERERERC6erR751atXs2bNGpKT\nk7n++utJTk7mrbfeYvXq1b7O12io18x5qrnzVHPnNbUe+aBmtl62fEqPc+ep5s5TzQODrTPyV199\nNaWlpbRr1857WVlZGaGhoT4LJiIicr6c977iiuYhdc67stXlJA7qSnCItk4WkcbL1kJ+zJgxJCcn\nM2nSJCIiIigoKODFF19k7NixbNiwwTvv1ltv9VnQQKf9WJ2nmjtPNXdeU9tH/kDxcVvz2nVsAXT1\nSQY9zp2nmjtPNQ8MthbyL730EgCzZs3yXmZZFi+99JL3ewB79+5t4HgiIiIiIlITW82G+fn55Ofn\ns3fvXu/X+WMt4i9MvWbOU82dp5o7r6n1yJtAj3PnqebOU80Dg//fNSQiIiIiIvWmhbxD1GvmPNXc\neaq585paj7wJ9Dh3nmruPNU8MGghLyIiIiISgLSQd4h6zZynmjtPNXeeeuSdp8e581Rz56nmgcHW\nrjUiIuI7Hk8l5adO25rrcvk4jIiIBAyXZVmWv0PUR1ZWFgkJCf6OISLSYEpPnuKdN3dwqqzuxXxF\nhcf2or8pa9exBSn3xusDoUQkYGzdupUhQ4bU6zo6Iy8iYoDSk+V8X1bh7xiNRkW5h2+PlFLpqaxz\n7uXNg2nb/koHUomINCwt5B2yadMmvQPcYaq581Rz53359Q7tXFODkyWneGvZNltzb7wtul4LeT3O\nnaeaO081Dwx6s6uIiIiISADSQt4h+q3Weaq581Rz5+lsvPP0OHeeau481TwwaCEvIiIiIhKAHF3I\nu91uevbsSXR0NHPmzKn2/ddff524uDj69OnDjTfeyGeffeZkPJ/SfqzOU82dp5o7T/vIO0+Pc+ep\n5s5TzQODY2929Xg8TJo0ifXr1xMWFka/fv1ISUkhJibGO6d79+68//77tGnTBrfbzYMPPsjmzZud\niigiIiIiEjAcOyOfk5NDVFQUXbt2JSQkhNTUVDIzM6vMGThwIG3atAEgKSmJoqIip+L5nHrNnKea\nO081d5565J2nx7nzVHPnqeaBwbGFfHFxMREREd5xeHg4xcXFtc7/y1/+wp133ulENBERERGRgONY\na42rHp8rvnHjRl555RX+85//1Pj9iRMnEhkZCUDr1q2JjY31/uZ4tqfLtPHZy0zJ0xTG59fe33ma\nwnjRokUB8f/RqfG6d7KorIQBSQMB2Jz9EVDDuP8AKi3L2+9+9iy7nfG+A3u5KWmY7fkaVx/fSDSg\n53OTx3o+1/N5Yxzn5uZSUlICQEFBAWlpadSXy7Isq97XugibN29m2rRpuN1uAGbNmkVQUBAZGRlV\n5n322WcMHz4ct9tNVFRUtdvJysoiISHBicgNatMmfbCC01Rz56nmVW3b/DVbP/zap8fQB0Jduh69\nOxPRrb2tuR06tWJ77sd6nDtMzy3OU82dt3XrVoYMGVKv6zi2kD99+jTXXXcdWVlZhIaG0r9/f5Yv\nX17lza4FBQXceuutLF26lAEDBtR4O4G6kBeRpseJhbw46+774unYuZW/Y4hII3QxC/lgH2WpfqDg\nYBYuXMjQoUPxeDykpaURExPD4sWLAUhPT2fGjBl8++23PPTQQwCEhISQk5PjVEQRERERkYDh6D7y\nycnJ7Nq1iz179jBlyhTgzAI+PT0dgD//+c8cOXKEbdu2sW3btka1iD+3v0+coZo7TzV3nvaRd54e\n585TzZ2nmgcGfbKriIiIiEgA0kLeIXrDiPNUc+ep5s7TG12dp8e581Rz56nmgUELeRERERGRAKSF\nvEPUa+Y81dx5qrnz1CPvPD3OnaeaO081DwxayIuIiIiIBCAt5B2iXjPnqebOU82dpx555+lx7jzV\n3HmqeWBwbB95EZHG4PuycipOVdY90QWnK2zMk4DSrJnOf4mIObSQd4g+6th5qrnzmkLNvz1cyjtv\n2utLr/T4fiH/5dc7dFbeQRvf/oI9+bn0jO57wXntOlzJTUN7OJSq8WsKzy2mUc0DgxbyIiL1YFkW\nntM6095UfXuklGNHy/jmwIkLznPhciiRiDRl+huhQ/RbrfNUc+ep5s7T2XjnqebO03OL81TzwKCF\nvIiIiIhIANJC3iHaj9V5qrnzVHPnaR9556nmztNzi/NU88CgHnkRafI8nkq+Ly23OVu9zyIiYgaX\nZVmWv0PUR1ZWFgkJCf6OISKNyPffV+D+Ry4nSr6vc27l6UpO682uUodOXVozbPSFd7YRETnX1q1b\nGTJkSL2uozPyIiJA+anTlH9/2t8xpJGwsKisrAQ7p8pcLoKC9JceEak/LeQdov1YnaeaO081d572\nkXeenZof+eYkby371Nbt9U2KpGt0x4aI1mjpucV5qnlg0EJeRESkgVV6LI4cOmlrbkWFx8dpRKSx\n0kLeIfqt1nmqufNMq/k3B05w7GhpnfNcwKnvK3wfyAd0Nt55DV1zNdXUzbTnlqZANQ8MWsiLSKP1\nzf4SPtr4pb9jiFzQzk/3cWj/hT8p9qzrE0Jp066FjxOJSKDQPvIO0X6szlPNnaeaO097mjuvoWv+\nzYETfLF9n62vysqA2miuwei5xXmqeWDQQl5EREREJABpIe8Q9Zo5TzV3nmruPPXIO081d56eW5yn\nmgcG9ciLSEApOVbG0cN1v4EV4JsD9nYNEQkUlR6LkmNldc5zAa3aNvd9IBHxKy3kHaL9WJ2nmjvP\niZqXlVaQ9dbnPj1GINE+8s7zZ80zX98Krrr3ubnm2g4MGdbLgUTO0PO581TzwOBYa43b7aZnz55E\nR0czZ86cGuf88pe/JDo6mri4OLZt2+ZUNEfk5ub6O0KTo5o7TzV33r4De/0docnxZ80tC6xKq86v\nY0fLyM87zFe7vqnz66jN/e79Sc8tzlPNA4MjZ+Q9Hg+TJk1i/fr1hIWF0a9fP1JSUoiJifHOWbt2\nLXv27CEvL4/s7GweeughNm/e7EQ8R5SUlPg7QpOjmjvvYmvu8VSy7+tv8Xgq65z73cnyizpGY1V2\n6jt/R2hyAqHmx458R9aanbbm3nJXDO07tfRxokuj53PnqeaBwZGFfE5ODlFRUXTt2hWA1NRUMjMz\nqyzk33rrLcaNGwdAUlISx44d4+DBg3Tu3NmJiCLiR5YFWzbl8+1h8xdIIo3NvoJv8Zyu+5doXBAW\n2ZYWLS/3fSgRscWRhXxxcTERERHecXh4ONnZ2XXOKSoqajQL+YKCAn9HaHJU8/op/a78zIq6Ds2C\ngzhdUfOL/ldf7uW7E6e8Y8/pSo7beGMeQPg17bg6vI29sOLl3nSCXn1D/R2jSWmMNT980N4HUrVu\n2/zMc0UdgoOb0SwkCGxse3/Z5cFYdUzcuzefU99XEHJZM1w23iNw5qnM/p77QUHaxO98eg0NDI4s\n5O38pwOwzltE1Ha9rVu3XnImp6WlpQVk7kCmmjsv/RcPsivv4t6IGtxK776/GFOmTgb0J3AnNeWa\nFx/wz8/94IMT+HyneradpNfQwODI62ZYWBiFhYXecWFhIeHh4RecU1RURFhYWLXbGjJkiO+CioiI\niIgECEf+lpSYmEheXh75+fmUl5ezYsUKUlJSqsxJSUnhtddeA2Dz5s20bdu20bTViIiIiIg0NEfO\nyAcHB7Nw4UKGDh2Kx+MhLS2NmJgYFi9eDEB6ejp33nkna9euJSoqiiuvvJJXX33ViWgiIiIiIgHJ\nsXd3JCcns2vXLvbs2cOUKVOAMwv49PR075yFCxeyZ88etm/fTkJCglPRGtzPf/5zOnfuTGxsbJXL\nFyxYQExMDL179yYjI8NP6Rqnmmqek5ND//79iY+Pp1+/fmzZssWPCRufwsJCbrnlFq6//np69+7N\n/PnzATh69Cg/+tGP6NGjB7fffjvHjh3zc9LGo7aaP/nkk8TExBAXF8fw4cM5fvy4n5M2HrXV/Kx5\n8+YRFBTE0aNH/ZSw8blQzfU66hu11Vyvo77z/fffk5SURN++fenVq5d3bVzv11BLGtz7779vbd26\n1erdu7f3sg0bNli33XabVV5eblmWZR06dMhf8Rqlmmr+wx/+0HK73ZZlWdbatWutwYMH+yteo7R/\n/35r27ZtlmVZ1okTJ6wePXpYO3futJ588klrzpw5lmVZ1uzZs62MjAx/xmxUaqv5unXrLI/HY1mW\nZWVkZKjmDai2mluWZRUUFFhDhw61unbtah05csSfMRuV2mqu11Hfqa3meh31re+++86yLMuqqKiw\nkpKSrA8++KDer6Hab8kHbrrpJtq1a1flskWLFjFlyhRCQkIAuOqqq/wRrdGqqeZXX32198zksWPH\nanzztFy8Ll260LdvXwBatmxJTEwMxcXFVT4TYty4caxevdqfMRuVmmq+b98+fvSjH3m3z0tKSqKo\nqMifMRuV2moO8NhjjzF37lx/xmuUantueemll/Q66iO11Vyvo77VokULAMrLy/F4PLRr167er6Fa\nyDskLy+P999/nwEDBjB48GA+/vhjf0dq9GbPns3jjz9OZGQkTz75JLNmzfJ3pEYrPz+fbdu2kZSU\nVOWD3Dp37szBgwf9nK5xOrfm53rllVe48847/ZSqcTu35pmZmYSHh9OnTx9/x2rUzq357t279Trq\ngLM1HzBggF5HfayyspK+ffvSuXNnb2tTfV9DtZB3yOnTp/n222/ZvHkzf/jDH/jJT37i70iNXlpa\nGvPnz6egoIA//vGP/PznP/d3pEbp5MmTjBgxghdeeIFWrVpV+Z7L5bL9ORJi38mTJxk5ciQvvPAC\nLVu29F7+7LPPctlllzF69Gg/pmuczq15UFAQv//975k+fbr3+5aND1OT+jm35q1atdLrqAPOf27R\n66hvBQUF8emnn1JUVMT777/Pxo0bq3zfzmuoFvIOCQ8PZ/jw4QD069ePoKAgjhw54udUjVtO7tio\nfwAAIABJREFUTg733HMPACNHjiQnJ8fPiRqfiooKRowYwZgxY/jxj38MnDmDcODAAQD2799Pp06d\n/Bmx0Tlb8/vvv99bc4C//vWvrF27ltdff92P6Rqn82v+5Zdfkp+fT1xcHN26daOoqIgbbriBQ4cO\n+Ttqo1HT41yvo75VU831OuqMNm3acNddd/HJJ5/U+zVUC3mH/PjHP2bDhg0A7N69m/Lycjp06ODn\nVI1bVFQU7733HgAbNmygR48efk7UuFiWRVpaGr169eLRRx/1Xp6SksLf/vY3AP72t79VWWzKpamt\n5m63mz/84Q9kZmZyxRVX+DFh41NTzWNjYzl48CB79+5l7969hIeHs3XrVv3S2kBqe5zrddR3aqu5\nXkd95/Dhw94dacrKyvj3v/9NfHx8/V9Dffhm3CYrNTXVuvrqq63LLrvMCg8Pt1555RWrvLzcuv/+\n+63evXtbCQkJ1saNG/0ds1E5W/OQkBBvzbds2WL179/fiouLswYMGGBt3brV3zEblQ8++MByuVxW\nXFyc1bdvX6tv377Wv/71L+vIkSPWkCFDrOjoaOtHP/qR9e233/o7aqNRU83Xrl1rRUVFWZGRkd7L\nHnroIX9HbTRqq/m5unXrpl1rGlBtzy16HfWd2h7neh31nc8++8yKj4+34uLirNjYWGvu3LmWZVn1\nfg11WZYa+0REREREAo1aa0REREREApAW8iIiIiIiAUgLeRERERGRAKSFvIiIiIhIANJCXkREREQk\nAGkhLyIiF6Vr165kZWX5O4aISJOlhbyIiFwUOx8fLiIivqOFvIhIgJs/fz6/+c1v/B1DREQcpoW8\niEiAe/jhh1m5ciUHDx6s1/XmzJnDqFGjqlz2yCOP8MgjjwAwe/ZsoqKiaN26Nddffz2rV6+u9baC\ngoL46quvvOMHHniA3/3ud97xvn37GDFiBJ06daJ79+4sWLCgXllFRKQ6LeRFRAKcy+Vi9OjRLFmy\npF7Xu/fee1m7di0nT54EwOPx8Pe//5377rsPgKioKDZt2kRJSQlPP/00999/PwcOHLCd6WzbTWVl\nJcOGDSM+Pp59+/aRlZXF888/z7p16+qVV0REqtJCXkSkEXjggQf461//Wq/rREZGkpCQwJtvvgnA\nhg0baNGiBf379wdg5MiRdOnSBYCf/OQnREdHk5OTY/v2LcsCYMuWLRw+fJipU6cSHBxMt27dGD9+\nPG+88Ua98oqISFVayIuINALffPMNpaWl9VpoA4wePZrly5cDsGzZMu/ZeIDXXnuN+Ph42rVrR7t2\n7dixYwdHjhyxfdtnz8h//fXX7Nu3z3s77dq1Y9asWRw6dKheWUVEpKpgfwcQEZFL43a7ycvLY+rU\nqbz66qu0b9+e3NxcPvvsM4YNG0ZCQkKt1x05ciSPP/44xcXFrF69ms2bNwNnFt8PPvggGzZsYODA\ngbhcLuLj471n2c/XokULSktLveP9+/cTEREBQEREBN26dWP37t0N+FOLiIjOyIuIBLBly5axYcMG\nHn74YUaNGsWaNWtYuXIlYWFhPPbYYzz33HMXvP5VV13F4MGDeeCBB+jevTvXXXcdAN999x0ul4uO\nHTtSWVnJq6++yo4dO2q9nb59+/L666/j8Xhwu928//773u/179+fVq1aMXfuXMrKyvB4POzYsYOP\nP/64YYogItJEaSEvIhKgNm/ezPr165k7dy4ArVq14sc//jFhYWH079+fwsJCunXrVuftjB49mqys\nLEaPHu29rFevXjz++OMMHDiQLl26sGPHDgYNGlTrbbzwwgusWbOGdu3asWzZMu655x7v95o1a8b/\n/u//8umnn9K9e3euuuoqHnzwQUpKSi7hpxcREZdV299JRUQkoD377LNMnjyZFi1a+DuKiIj4gBby\nIiKN0FtvvcUtt9zCgQMHiI6O9nccERHxAbXWiIg0Mm+++SbPPPMMw4cPZ+XKlf6OIyIiPqIz8iIi\nIiIiAUhn5EVEREREAlDA7SOflZXl7wgiIiIiIg1uyJAh9ZofcAt54IIfbuIPc+bMISMjw98xvEzL\nA8pkl2mZTMsDymSHaXlAmewwLQ8ok12mZTItDyiTHVu3bq33ddRaIyIiIiISgLSQbwAFBQX+jlCF\naXlAmewyLZNpeUCZ7DAtDyiTHablAWWyy7RMpuUBZfIVLeQbQO/evf0doQrT8oAy2WVaJtPygDLZ\nYVoeUCY7TMsDymSXaZlMywPK5CsBt/1kVlaWcT3yIiIiIiKXYuvWrU3jza41sSyLQ4cO4fF4cLlc\n/o4jPmJZFs2aNaNTp066n0VERKRJc2wh73a7efTRR/F4PIwfP77au4Sfe+45Xn/9dQBOnz7NF198\nweHDh2nbtq2t2z906BCtWrWiRYsWDZ5dzFJaWsqhQ4fo3LnzJd3Opk2bGDRoUAOlahimZTItDyiT\nHablAWWyw7Q8oEx2mZbJtDygTL7iSI+8x+Nh0qRJuN1udu7cyfLly/niiy+qzHniiSfYtm0b27Zt\nY9asWQwePNj2Iv7sMbSIbxpatGiBx+PxdwwRERERv3KkR/6jjz5i+vTpuN1uAGbPng3Ar3/96xrn\njx49miFDhpCWllbte7X1yO/fv5+rr766AVOLyXR/i4iISGNyMT3yjpyRLy4uJiIiwjsODw+nuLi4\nxrmlpaW88847jBgxwoloIiIiIiIByZEe+fq8KXHNmjUMGjTogm01EydOJDIyEoDWrVsTGxvLtdde\ne8k5JfBs2rQJwNvjVp/x2X9f7PV9MV60aBGxsbHKc4Fxbm4uDz30kDF5zjr3MaU8+v/WGPLo/1vg\nPr5NywN6fNd2/JKSEuDMnvY1daLUxZHWms2bNzNt2jRva82sWbMICgqq8WNx77nnHn7605+Smppa\n422ptUagYe7vTZvMe5OLaZlMywPKZIdpeUCZ7DAtDyiTXaZlMi0PKJMdF9Na48hC/vTp01x33XVk\nZWURGhpK//79Wb58OTExMVXmHT9+nO7du1NUVETz5s1rvC0t5BvWD37wA5577jl+8IMf+PQ4eXl5\npKWl8fXXXzN16lQmTJhwSben+1tEREQaE2P3kQ8ODmbhwoUMHToUj8dDWloaMTExLF68GID09HQA\nVq9ezdChQ2tdxNfXwWNFHCk50CC3VZMOrbvQuW24z26/LnFxcSxYsICbb775om/jww8/bMBEtTub\nc+bMmY4cT0RERKSxc2QhD5CcnExycnKVy84u4M8aN24c48aNa7BjHik5wIw30uueeJGeSl3s14W8\ny+XiYv+gcvr0aYKDL+7uv5jrFhYWMnz48Is6nq+Y9ic1MC+TaXlAmewwLQ8okx2m5QFlssu0TKbl\nAWXyFUd2rZEzZ8+ff/55Bg4cSPfu3Xn44Yc5deoUALt27WLYsGF069aNH/zgB973EgC88MIL9O7d\nm2uuuYakpCQ++OADAH7xi19QVFTE6NGjiYyMZOHChezfv59x48bRo0cP4uPj+dOf/lQtw/z58xk0\naBCRkZF4PB7i4uJ477336sxx/nUrKyur/Yy1Xf/uu+9m06ZNZGRkcM011/DVV181bHFFREREmiBH\neuQbUn165HcWfOzzM/K9IhNtzY2Li6NVq1asXLmSFi1acO+993LTTTfxq1/9iqSkJMaMGcOkSZP4\n6KOPuP/++8nKysKyLIYPH8769evp3LkzRUVFnD59mq5duwLQt29f5s+fz80334xlWdx6663cdddd\nPProoxQXF3PPPffw3HPPceutt3oztGvXjmXLltGhQwcuv/xy720MHDiQAQMGVMuxYcMGrr322hqv\ne66KiooLXj8lJYWf/OQn3H///Q1Se/XIi4iISGNi7D7ycqYNZsKECYSGhtK2bVsef/xxVq1axccf\nf0xpaSmPPvoowcHB3HTTTdx+++2sWrWK4OBgysvL+e9//0tFRQXh4eHeRfz5PvnkE44cOcITTzxB\ncHAw11xzDWPGjOHNN9+skuHBBx8kNDS02kK8thz/+Mc/6ryunesDF2wDKikpYdKkSYwePZobb7yR\ne++9l3HjxlFWVlafMouIiIg0GVrIOygsLMz77/DwcA4cOMCBAweqXA4QERHB/v376datG7///e+Z\nM2cO1113HePHj+fAgZrfvFtUVMSBAwfo1q2b9+v555/nm2++qTXDuWrLce7xaruu3etf6PMEtm/f\nzgsvvMDcuXN5+OGHWb58OX/7298a7I3PNTl3n11TmJbJtDygTHaYlgeUyQ7T8oAy2WVaJtPygDL5\nihbyDioqKqry7y5dutClSxeKi4urnK0uLCwkNDQUgBEjRrB27Vq2b9+Oy+Vi+vTp3nnnLozDwsK4\n5ppr2Lt3r/fr66+/5o033qiSobbF9NVXX11jjnPbVy60EK/t57Db/nLTTTfRrFkz3nrrLeLj421d\nR0RERKQp00LeIZZl8Ze//IV9+/bx7bffMm/ePIYPH84NN9xA8+bNmT9/PhUVFWzatIl169YxfPhw\n9uzZw/vvv8+pU6e4/PLLueKKK2jWrJn3Nq+66iry8/MBSEhIoGXLlsyfP5+ysjI8Hg9ffPEF27Zt\ns5XvQjnsSExMrPP6dt6OsXHjRq677jpbx7xUJr5T3bRMpuUBZbLDtDygTHaYlgeUyS7TMpmWB5TJ\nVxzbftIfOrTuwlOpi316+3a5XC5GjhzJiBEjOHDgAHfddRePP/44ISEhLFu2jCeffJI//vGPhIaG\nsmjRIqKioti5cyfPPPMMu3fvJjg4mKSkJP74xz96b3Py5MlkZGTw9NNP8+STT7J8+XJ+97vfkZCQ\nwKlTp4iOjua3v/2trXwXytFQ17/QGX2AEydO0KJFC1vHExEREWnqGvWuNSY5d4cZuXQNcX+buH+s\naZlMywPKZIdpeUCZ7DAtDyiTXaZlMi0PKJMd2rVGRERERKSJ0Bl5h+iMfMMy/f4WERERqY+LOSPf\nqHvkTfLpp5/6O4KIiIiINCJqrZEmy8T9Y03LZFoeUCY7TMsDymSHaXlAmewyLZNpeUCZfEULeRER\nERGRAORYj7zb7ebRRx/F4/Ewfvx4MjIyqs159913mTx5MhUVFXTs2JF333232pxA7ZGXhqX7W0RE\nRBoTY3vkPR4PkyZNYv369YSFhdGvXz9SUlKIiYnxzjl27BgTJ07knXfeITw8nMOHD9frGAH2nl25\nRLq/RUREpKlzpLUmJyeHqKgounbtSkhICKmpqWRmZlaZs2zZMkaMGEF4eDgAHTt2rNcxmjVrRmlp\naYNlFnOVlpZW+YTbi2Vib5xpmUzLA8pkh2l5QJnsMC0PKJNdpmUyLQ8ok684cka+uLiYiIgI7zg8\nPJzs7Owqc/Ly8qioqOCWW27hxIkTPPLII4wZM8b2MTp16sShQ4c4duxYnZ8g2tCOHz9OmzZtHD3m\nhZiWBxouk2VZNGvWjE6dOjVAKhEREZHA5chC3s7CuqKigq1bt5KVlUVpaSkDBw5kwIABREdHV5s7\nceJEIiMjAWjdujWxsbEMGjSIzp07e3+7OvtJXU6Ne/bs6ejxAi1PQ487d+58ybc3aNAgY36ecz9Z\n7txPmlOemsfnZjMhj8b6/9YY8+j/W+A+vk3Lc5Ye31XHubm5lJSUAFBQUEBaWhr15cibXTdv3sy0\nadNwu90AzJo1i6CgoCpveJ0zZw5lZWVMmzYNgPHjx3PHHXcwcuTIKrdV25tdRUREREQC1cW82dWR\nHvnExETy8vLIz8+nvLycFStWkJKSUmXO3XffzaZNm/B4PJSWlpKdnU2vXr2ciHfJzv+tzt9MywPK\nZJdpmUzLA8pkh2l5QJnsMC0PKJNdpmUyLQ8ok68EO3KQ4GAWLlzI0KFD8Xg8pKWlERMTw+LFiwFI\nT0+nZ8+e3HHHHfTp04egoCAmTJgQMAt5ERERERGnObaPfENRa42IiIiINDbGttaIiIiIiEjD0kK+\nAZjWY2VaHlAmu0zLZFoeUCY7TMsDymSHaXlAmewyLZNpeUCZfEULeRERERGRAKQeeRERERERP1OP\nvIiIiIhIE6GFfAMwrcfKtDygTHaZlsm0PKBMdpiWB5TJDtPygDLZZVom0/KAMvmKFvIiIiIiIgFI\nPfIiIiIiIn6mHnkRERERkSZCC/kGYFqPlWl5QJnsMi2TaXlAmewwLQ8okx2m5QFlssu0TKblAWXy\nFS3kRUREREQCkHrkRURERET8TD3yIiIiIiJNhGMLebfbTc+ePYmOjmbOnDnVvv/uu+/Spk0b4uPj\niY+PZ+bMmU5Fu2Sm9ViZlgeUyS7TMpmWB5TJDtPygDLZYVoeUCa7TMtkWh5QJl8JduIgHo+HSZMm\nsX79esLCwujXrx8pKSnExMRUmffDH/6Qt956y4lIIiIiIiIBzVaPfN++fRk3bhyjR4+mc+fO9T7I\nRx99xPTp03G73QDMnj0bgF//+tfeOe+++y7z5s1jzZo1F7wt9ciLiIiISGNzMT3yts7IP/XUUyxZ\nsoSpU6dy8803M2bMGIYPH84VV1xh6yDFxcVERER4x+Hh4WRnZ1eZ43K5+PDDD4mLiyMsLIznnnuO\nXr161Xh7EydOJDIyEoDWrVsTGxvLoEGDgP/7M4nGGmusscYaa6yxxhqbOs7NzaWkpASAgoIC0tLS\nqK967Vpz9OhRVq5cydKlS9mxYwf33HMPY8aM4dZbb73g9VatWoXb7ebll18GYOnSpWRnZ7NgwQLv\nnBMnTtCsWTNatGjBv/71Lx555BF2795d7bZMPCO/adMm7x1jAtPygDLZZVom0/KAMtlhWh5QJjtM\nywPKZJdpmUzLA8pkh893rWnfvj1jx47lF7/4BREREfzzn/8kPT2dHj168O9//7vW64WFhVFYWOgd\nFxYWEh4eXmVOq1ataNGiBQDJyclUVFRw9OjR+sQTEREREWkybJ2RtyyLd955h6VLl7JmzRoGDBjA\n2LFjGT58OM2bN+ef//wn//M//8OBAwdqvP7p06e57rrryMrKIjQ0lP79+7N8+fIqb3Y9ePAgnTp1\nwuVykZOTw09+8hPy8/Or3ZaJZ+RFRERERC6Fz3rku3TpQseOHRk7diyzZ8+udjZ9+PDhzJ8/v/aD\nBAezcOFChg4disfjIS0tjZiYGBYvXgxAeno6//jHP1i0aBHBwcG0aNGCN954o14/iIiImOXgsSKO\nlJw5wdOhdRc6tw2v4xoiIlIftlpr3n77bT7//HMyMjKqLeLPevfddy94G8nJyezatYs9e/YwZcoU\n4MwCPj09HTjzBtYdO3bw6aef8uGHHzJgwIB6/Bj+dfYNDKYwLQ8ok12mZTItDyiTHabkOVJygBlv\npDPjjXTWb3jH33GqMaVOZ5mWB5TJLtMymZYHlMlXbC3kb7/99hov79SpU4OGERERERERe2z1yLdq\n1YoTJ05UuayiooIuXbpw5MgRn4WriXrkRUQCw86Cj5nxxpm/uj6VuphekYl+TiQiYq4G75G/6aab\nACgrK/P++6yioiIGDhxYz4giIiIiItIQLthak5aWRlpaGsHBwYwfP947Hj9+PIsWLeLNN990KqfR\nTOuxMi0PKJNdpmUyLQ8okx2m5QHY9vF2f0eoxrQ6mZYHlMku0zKZlgeUyVcueEb+gQceAGDAgAH0\n7NnTiTwiIiIiImJDrT3yS5YsYcyYMQD85S9/weVy1XgDP//5z32XrgbqkRcRCQzqkRcRsa9Be+SX\nL1/uXcgvWbLEmIW8iIiIiIhcoEd+7dq13n+/++67bNy4scYvMa/HyrQ8oEx2mZbJtDygTHaYlgfU\nI2+HaXlAmewyLZNpeUCZfKXWM/KVlZW2biAoyNZW9CIiIiIi0oBq7ZG3s0B3uVx4PJ4GD3Uh6pEX\nEQkM6pEXEbGvQXvkv/rqq0sOJCIiIiIivlHrafeuXbva+hLzeqxMywPKZJdpmUzLA8pkh2l5QD3y\ndpiWB5TJLtMymZYHlMlXaj0jP2HCBF5++WUA7+4153O5XLz22mu+SSYiIiIiIrWqtUd+1qxZTJky\nBYBp06bhcrk4f6rL5eLpp5+2dSC3282jjz6Kx+Nh/PjxZGRk1Dhvy5YtDBw4kJUrVzJ8+PBq31eP\nvIhIYFCPvIiIfQ3aI392EQ9nFvKXwuPxMGnSJNavX09YWBj9+vUjJSWFmJiYavMyMjK44447qv3S\nICIiIiIi/8f23pFZWVmMHz+eO++8kwkTJrB+/XrbB8nJySEqKoquXbsSEhJCamoqmZmZ1eYtWLCA\nkSNHctVVV9m+bROY1mNlWh5QJrtMy2RaHlAmO0zLA+qRt8O0PKBMdpmWybQ8oEy+UusZ+XPNmzeP\nOXPm8LOf/Yz4+HgKCgq47777ePLJJ3niiSfqvH5xcTERERHecXh4ONnZ2dXmZGZmsmHDBrZs2VLr\nJ8kCTJw4kcjISABat25NbGwsgwYNAv7vTnFynJub69fjm57nXKbkMXWcm5urPHWM9fgOnDzbPt7O\n0YIy2kc2NyKP6Y9v0/Lo/5vGDTnW47vm45eUlABQUFBAWloa9VVrj/y5QkNDWbduHb179/Ze9vnn\nn3Pbbbexf//+Og+yatUq3G63982zS5cuJTs7mwULFnjnjBo1iieeeIKkpCQeeOABhg0bxogRI6rd\nlnrkRUQCg3rkRUTsa9Ae+XO5XC6uvfbaKpd1797d9qe6hoWFUVhY6B0XFhYSHh5eZc4nn3xCamoq\nAIcPH+Zf//oXISEhpKSk2DqGiIiIiEhTUutKvLKy0vs1bdo0xo8fz+7duykrK2PXrl08+OCDTJ8+\n3dZBEhMTycvLIz8/n/LyclasWFFtgf7VV1+xd+9e9u7dy8iRI1m0aFHALOLP/3Ofv5mWB5TJLtMy\nmZYHlMkO0/KAeuTtMC0PKJNdpmUyLQ8ok6/UekY+OLj6t5YvX15lvGzZMsaPH1/3QYKDWbhwIUOH\nDsXj8ZCWlkZMTAyLFy8GID09vb65RURERESatFp75PPz823dgNOf7qoeeRGRwKAeeRER+xq0R97p\nBbqIiIiIiNhnex/5zMxMHnvsMcaNG8eYMWMYO3YsY8eO9WW2gGFaj5VpeUCZ7DItk2l5QJnsMC0P\nqEfeDtPygDLZZVom0/KAMvmKrYX89OnTSU9Pp7KykpUrV9KxY0feeecd2rZt6+t8IiIiIiJSA1v7\nyEdGRvL2228TGxtL27ZtOXbsGDk5OTzzzDOsWbPGiZxe6pEXEandwWNFHCk5AECH1l3o3Da8jmv4\njnrkRUTsu5geeVtn5I8fP05sbCwAl112GeXl5fTv35/33nuv/ilFRMRnjpQcYMYb6cx4I927oBcR\nkcbJ1kK+e/fufP755wBcf/31LFq0iNdee4327dv7NFygMK3HyrQ8oEx2mZbJtDygTHYcLSjzd4Rq\n1CNfN9PygDLZZVom0/KAMvmKrU92nTlzJocPHwZg9uzZjB49mpMnT/Liiy/6NJyIiIiIiNTMVo+8\nSdQjLyJSO5P60k3KIiJiugbdR/58u3fvZuXKlezbt4+wsDBGjRpFjx496h1SREREREQuna0e+WXL\nlpGQkEBubi4tW7bks88+IyEhgddff93X+QKCaT1WpuUBZbLLtEym5QFlskM98vaYdr+ZlgeUyS7T\nMpmWB5TJV2ydkf/tb3/L2rVrufnmm72XffDBB4wZM4b77rvPZ+FERERERKRmtnrkr7rqKvbt20dI\nSIj3soqKCkJDQ/nmm298GvB86pEXEamdSX3pJmURETGdz/aRf+yxx5gyZQplZWf+XFtaWspvfvMb\nJk+eXP+UIiIiIiJyyWpdyEdERHi/XnzxRV544QVat25Np06daNOmDc8//zwvvfSS7QO53W569uxJ\ndHQ0c+bMqfb9zMxM4uLiiI+P54YbbmDDhg0X9xP5gWk9VqblAWWyy7RMpuUBZbJDPfL2mHa/mZYH\nlMku0zKZlgeUyVdq7ZFfsmRJnVd2uVy2DuLxeJg0aRLr168nLCyMfv36kZKSQkxMjHfObbfdxt13\n3w1Abm4u99xzD3v27LF1+yIiIiIiTU2tC/nBgwc32EFycnKIioqia9euAKSmppKZmVllIX/llVd6\n/33y5Ek6duzYYMf3tUGDBvk7QhWm5QFlssu0TKblAWWyo31kc39HqCY+Mc7fEaox7X4zLQ8ok12m\nZTItDyiTr9jataa8vJyZM2eyZMkS9u3bR2hoKGPGjGHq1KlcdtlldV6/uLiYiIgI7zg8PJzs7Oxq\n81avXs2UKVPYv38/69atq/X2Jk6cSGRkJACtW7cmNjbWe2ec/TOJxhprrHFTHH99aBdnbft4O0cL\nvvdbnjPHL/P+YmFCfTTWWGONTRnn5uZSUlICQEFBAWlpadSXrV1rJk+eTE5ODk8//TSRkZEUFBQw\nY8YMEhMTef755+s8yKpVq3C73bz88ssALF26lOzsbBYsWFDj/A8++IDx48eza9euat8zcdeaTZs2\nee8YE5iWB5TJLtMymZYHlKkuOws+5tG5Y2kf2dzvO8Wcu2vNsKj/4b7h9X+R8iWT7jcwLw8ok12m\nZTItDyiTHT77ZNeVK1eyfft2b7tLz549SUhIoE+fPrYW8mFhYRQWFnrHhYWFhIeH1zr/pptu4vTp\n0xw5coQOHTrYiSgiIiIi0qTY2n7yUiUmJpKXl0d+fj7l5eWsWLGClJSUKnO+/PJLzv5xYOvWrQAB\ns4g36bc5MC8PKJNdpmUyLQ8okx3qkbfHtPvNtDygTHaZlsm0PKBMvmLrjPyoUaNISUnhqaee4ppr\nriE/P5+ZM2cyatQoewcJDmbhwoUMHToUj8dDWloaMTExLF68GID09HRWrVrFa6+9RkhICC1btuSN\nN964+J9KRERERKSRs3VGfu7cudx2221MmjSJG264gYcffphbb72VuXPn2j5QcnIyu3btYs+ePUyZ\nMgU4s4BPTz/TP/mrX/2KHTt2sG3bNj744AP69et3ET+Of5x9A4MpTMsDymSXaZlMywOGvt0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      }
     ],
     "prompt_number": 9
    },
    {
     "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 the posterior distributions for the $\\lambda$'s do not look like any exponential distributions, though we originally started modeling with exponential 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. Its posterior distribution looks a little different from the other two because it is a discrete random variable, hence it doesn't assign probabilities to intervals. We can see that near day 45, there was a 50% chance the users behaviour changed. 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. "
     ]
    },
    {
     "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 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 occurred yet), else we use $\\lambda_i = \\lambda_{2,i}$. \n",
      "\n",
      "\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize( 12.5, 5)\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 occurring 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\" \n",
      "    # (in the lambda1 \"regime\") or\n",
      "    #  \"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",
      "         label = \"expected number of text-messages recieved\")\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, 50 )\n",
      "plt.bar( np.arange( len(count_data) ), count_data, color =\"#348ABD\", alpha = 0.65,\n",
      "            label=\"observed texts per day\")\n",
      "\n",
      "plt.legend(loc=\"upper left\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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171tgYCB2794trP/WrVtIT0+Hv7//G4/RL774Anp6erh16xbWrFmDbdu21flu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\n"
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Our analysis shows strong support for believing the user's behavior did change ($\\lambda_1$ would have been close in value to $\\lambda_2$ had this not been true), and 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 percentage increase in text-message rates? `hint:` compute the mean of `lambda_1_samples/lambda_2_samples`. Note that this quantity 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\\. 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 occurred 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_samples<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 Effectiveness 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.\n",
      "- [5] Cronin, Beau. \"Why Probabilistic Programming Matters.\" 24 Mar 2013. Google, Online Posting to Google . Web. 24 Mar. 2013. <https://plus.google.com/u/0/107971134877020469960/posts/KpeRdJKR6Z1>."
     ]
    },
    {
     "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:16% !important;\n",
        "        margin-right:auto;\n",
        "    }\n",
        "    h1 {\n",
        "        font-family: Helvetica, serif;\n",
        "    }\n",
        "    h4{\n",
        "        margin-top:12px;\n",
        "        margin-bottom: 3px;\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: 130%;\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": 3,
       "text": [
        "<IPython.core.display.HTML at 0x50cf0f0>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}