Chapter_1.ipynb

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        "<a href=\"https://colab.research.google.com/github/rnarkk/PPBMH/blob/main/Chapter_1.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "# Probabilistic Programming and Bayesian Methods for Hackers Chapter 1\n",
        "\n",
        "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/rnarkk/PPBMH/blob/main/Chapter1.ipynb\"><img height=\"32px\" src=\"https://colab.research.google.com/img/colab_favicon.ico\" />Run in Google Colab</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/blob/master/Chapter1_Introduction/Ch1_Introduction_TFP.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View source on GitHub</a>\n",
        "  </td>\n",
        "</table>\n",
        "<br>\n",
        "<br>\n",
        "<br>\n",
        "\n",
        "Original content ([this Jupyter notebook](https://nbviewer.jupyter.org/github/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/blob/master/Chapter1_Introduction/Ch1_Introduction_PyMC2.ipynb)) created by Cam Davidson-Pilon ([`@Cmrn_DP`](https://twitter.com/Cmrn_DP))\n",
        "\n",
        "Welcome to Bayesian Methods for Hackers. The full Github repository is available at [github/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers). The other chapters can be found on the project's [homepage](https://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/). We hope you enjoy the book, and we encourage any contributions!\n",
        "\n",
        "---\n",
        "### Table of Contents\n",
        "- Dependencies & Prerequisites\n",
        "- The Philosophy of Bayesian Inference\n",
        "- The Bayesian state of mind\n",
        "- Bayesian Inference in Practice\n",
        "- Are frequentist methods incorrect then?\n",
        "- Our Bayesian framework\n",
        "- Example: Mandatory coin-flip example\n",
        "- Example: Bug, or just sweet, unintended feature?\n",
        "- Probability Distributions\n",
        "  - Discrete Case\n",
        "- Continuous Case\n",
        "- But what is $\\lambda \\;$?\n",
        "  - Example: Inferring behaviour from text-message data\n",
        "- Introducing our first hammer: Tensorflow Probability\n",
        "- specify the joint log-density\n",
        "- Specify the posterior sampler\n",
        "- Execute the TF graph to sample from the posterior\n",
        "- Plot the Results\n",
        "- Interpretation\n",
        "- Exercises\n",
        "- References"
      ]
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        ""
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        "outputId": "02103d58-0e74-4cd6-e3f3-3fb49760f94a"
      },
      "source": [
        "!pip3 install -Uq pip\n",
        "!pip3 install -Uq jax jaxlib oryx tfp-nightly[jax]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\u001b[33mWARNING: Running pip as the 'root' user can result in broken permissions and conflicting behaviour with the system package manager. It is recommended to use a virtual environment instead: https://pip.pypa.io/warnings/venv\u001b[0m\u001b[33m\n",
            "\u001b[0m\u001b[33mWARNING: Running pip as the 'root' user can result in broken permissions and conflicting behaviour with the system package manager. It is recommended to use a virtual environment instead: https://pip.pypa.io/warnings/venv\u001b[0m\u001b[33m\n",
            "\u001b[0m"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ln-qTC7S2Pm-"
      },
      "source": [
        "from jax import jit, random\n",
        "from jax.numpy import *\n",
        "from jax.numpy import int32 as i32, float32 as f32\n",
        "from jax.random import bernoulli, beta\n",
        "from oryx import bijectors as tfb\n",
        "from oryx.core.ppl import random_variable, log_prob\n",
        "from oryx.distributions import (\n",
        "    Bernoulli, Beta, Exponential, Poisson, Uniform)\n",
        "from oryx.experimental import mcmc\n",
        "from tensorflow_probability.substrates.jax import mcmc\n",
        "\n",
        "from IPython.core.pylabtools import figsize\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "\n",
        "plt.style.use('fivethirtyeight')\n",
        "\n",
        "%config InlineBackend.figure_format = 'retina'\n",
        "\n",
        "%matplotlib inline\n",
        "\n",
        "sns.set_context('notebook')\n",
        "\n",
        "TFColor = [\n",
        "    '#F15854',\n",
        "    '#5DA5DA',\n",
        "    '#FAA43A',\n",
        "    '#60BD68',\n",
        "    '#F17CB0',\n",
        "    '#B2912F',\n",
        "    '#B276B2',\n",
        "    '#DECF3F',\n",
        "    '#4D4D4D']"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dXqjzSnXRRr3"
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      "source": [
        "## The Philosophy of Bayesian Inference\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 thinking Bayesian! 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, but still not certain. 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",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
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      "source": [
        "## The Bayesian state of mind\n",
        "Bayesian inference differs from more traditional statistical inference by preserving uncertainty. 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, known as the more classical version of statistics, 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 realities, 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. Simply, 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 meaningful to 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 (whichever it is). 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, but a second doctor may have slightly different beliefs.\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 truths, but gather evidence to form beliefs. 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",
        "\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",
        "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",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
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      "source": [
        "## Bayesian Inference in Practice\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, representing an estimate (typically a summary statistic like the sample average etc.), 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: probabilities of YES and NO. The function might return:\n",
        "\n",
        ">YES, with probability 0.8; NO, with probability 0.2\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",
        "### Incorporating evidence\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",
        "Denote $N$ as the number of instances of evidence we possess. As we gather an infinite amount of evidence, say as $N→∞,$ our Bayesian results (often) 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 computationally-simpler, frequentist methods. An individual in this position should consider the following quote by Andrew Gelman (2005)[[1]](#scrollTo=nDdph0r1ABCn), 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"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rACyvZBVdqB9"
      },
      "source": [
        "## Are frequentist methods incorrect then?\n",
        "\n",
        "No.\n",
        "\n",
        "Frequentist methods are still useful or state-of-the-art in many areas. Tools such as least squares linear regression, LASSO regression, and expectation-maximisation algorithms are all powerful and fast. Bayesian methods complement these techniques by solving problems that these approaches cannot, or by illuminating the underlying system with more flexible modeling.\n",
        "\n",
        "### A note on *Big Data*\n",
        "\n",
        "Paradoxically, big data's predictive analytic problems are actually solved by relatively simple algorithms [[2]](#scrollTo=nDdph0r1ABCn)[[3]](#scrollTo=nDdph0r1ABCn). 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."
      ]
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      "source": [
        "## Our Bayesian framework\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",
        "$$ P(A|X) = \\frac{P(X | A) P(A) }{P(X) } $$\n",
        "\n",
        "$$ P(A|X) \\propto{P(X | A) P(A) } $$\n",
        "\n",
        "NOTE: ($\\propto$ is \"proportional to\")\n",
        "\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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      "source": [
        "\n",
        "## Example: Mandatory coin-flip example\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), while also demonstrating some of the best practices when it comes to evaluating tensors and plotting the data. First, the easy part: We define the values in our Tensorflow graph"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# : I\n",
        "key = random.PRNGKey(0)\n",
        "sampled_data = bernoulli(key, .5, (2000,))\n",
        "sampled_data = pad(sampled_data, array([[1, 0]]))  # 0th flip\n",
        "\n",
        "# Number of trials\n",
        "num_trials = array([0, 1, 2, 3, 4, 5, 8, 15, 50, 500, 1000, 2000])\n",
        "sampled_cumulative_data = cumsum(sampled_data)[num_trials]"
      ],
      "metadata": {
        "id": "1NwcZ46Q_07F"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "$$\n",
        "Beta(1 + \\text{number of trials} - \\text{sampled cumulative data}, 1 + \\text{sampled cumulative data})\n",
        "$$"
      ],
      "metadata": {
        "id": "mKJy-qSL_1um"
      }
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e2mxCBB41Qs8"
      },
      "source": [
        "observed_heads = Beta(\n",
        "    (1 + num_trials - sampled_cumulative_data).astype(f32),\n",
        "    1 + sampled_cumulative_data.astype(f32))\n",
        "# [0, 1]\n",
        "probs_of_heads = linspace(start = 0., stop = 1., num = 100)\n",
        "# : (R ^ 100 × 1) ^ t = R ^ 1 × 100\n",
        "observed_probs_heads = transpose(observed_heads.prob(probs_of_heads[:, newaxis]))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Visualise."
      ],
      "metadata": {
        "id": "x5Pl3ibzLBdI"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "plt.figure(figsize(16, 9))\n",
        "for i in range(len(num_trials)):\n",
        "    sx = plt.subplot(len(num_trials) / 2, 2, i + 1)\n",
        "    plt.xlabel(\"$p$, probability of heads\") if i in {0, len(num_trials) - 1} else None\n",
        "    plt.setp(sx.get_yticklabels(), visible = False)\n",
        "    plt.plot(probs_of_heads, observed_probs_heads[i], \n",
        "             label = f'{num_trials[i]} tosses,\\n {sampled_cumulative_data[i]} heads',\n",
        "             lw = 3)\n",
        "    plt.fill_between(probs_of_heads, 0, observed_probs_heads[i],\n",
        "                     color = TFColor[3], alpha = .4)\n",
        "    plt.vlines(.5, 0, 4, color = 'k', linestyles = '--', lw = 1)\n",
        "    legend = plt.legend()\n",
        "    legend.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",
        "plt.tight_layout()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 676
        },
        "id": "L3QD_QBZLBlV",
        "outputId": "676c49cc-a19a-494a-99eb-4ea4a0eda21f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1152x648 with 12 Axes>"
            ],
            "image/png": 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OtbW16OnpwcqVK9Hf348PfOADOPvsswGoQM1VV12Fa6+9FscddxwOO+wwCCGwZcsWvPbaawgEAvjWt7414Jp/9rOf4TOf+Qwef/xxLFu2DHPnzkVHRwccx8G2bduwceNGuK6Lz3zmMzBNc0zvIYQAoKoJERERERERERGNxdatW/GVr3wFtbW1OOGEE9DS0oJkMolt27Zh8+bNAIAzzzwTixYtGtXrnn322fjpT3+Kc889Fx/60IdQVVUFAPjxj38MAPjiF7+I1atX4w9/+ANOO+00nHbaaaivr8fLL7+Mbdu2oa6uDg888MCArbDuv/9+XHvttZg1axaOPfZYxGIxdHV1YdWqVbAsC5/85Cfx/ve/HwCwfft2fP7zn0c0GsUJJ5yAtrY2WJaFv//979i2bRuqq6vx9a9/Pf/auq7j17/+Nc4//3zcd999+MMf/oC5c+eira0N2WwWb731FjZv3oympiZcfPHFY3oPoLCe41caqjRcpSIiIiIiIiI6RIrvMFq3bh3WrVs35Lz58+ePKqRz+eWXI5lMYvHixXjmmWeQy+UAANdeey0aGhoAqC22Tj31VNxzzz145ZVXsGbNGjQ1NeFTn/oUFi5ciGOOOWbAa15xxRXo6OjAmjVrsG7dOsTjcUybNg3HH388LrzwQlxwwQX5xZLDDz8ct9xyC1544QVs3rwZmzdvhq7rmD59Oi655BJ86UtfGvT6NTU1eOyxx7B48WI8/PDD2LBhA9avX4+6ujq0trbi0ksvxcc+9jGEw+Exv8ff//53AOpONiIiIiIiIiKisZg/fz6uu+46rFy5Elu3bsWaNWsgpURzczPOOeccXHDBBfkbmUbjhhtugKZpePzxx/HHP/4Rtm0DKIR0NE3DPffcgzPOOAMPPPAA1q5di2w2i9bWVnzhC1/AwoUL0d7ePuA1v/GNb+CZZ57B2rVrsWbNGiSTSTQ3N2P+/Pm4+OKLcc455+Tnzps3D9/85jexYsUKvP7661i/fj0CgQDa29txxRVX4PLLL0dHR8eA129ra8Nzzz2Hhx56CI8++ig2bdqEtWvXoqGhAdOnT8cVV1wx4M9iLO9R6es5mpRy0t48kUj8FcCCSbsAogrmlzGbPXv2JF8JUWXh91Z58csjx+PxSb4SGgl+fxFNnEP5/ZVIJAAgX8mFaDKdd955WLVqFdatW4eWlpYRPWc0/w+n02lEo1EAWF5bW/svY7/S8sG1HKKJw5+HiSYGv7fKC9dyygu/v4gmDtdyaCo7+eSTkU6n8fLLLyMSiRxwfrmt5bCSDhERERERERFVnFwuh5UrV+IrX/nKiAM6REREREREREQ0ebZv344333wTd9xxx4gCOuWIIR0iIiIiIiI65Oru2zHZlzAq8UvbJvsSaJRCoRB27do12ZdBREREREREVBG4lkOHwsyZMyu+op4+2RdARERERERERERERERERERERFTpWEmHiIiIKtbtt98+2ZdAREREREREREQjxLUcIiIiqnQM6RAREVHFuuSSSyb7EoiIiIiIiIiIaIS4lkNERESVjttdERERERERERERERERERERERFNMFbSISIioop1//33A+BdWEREVD7eeOMNLFu2DOvWrcO6devw5ptvQkqJBx54AOeee+6YXrOurg4AEI/Hx/NSD6lK+BqIiIiI6MC4lkNEROXGtm28+OKLePbZZ7FixQq89dZbyGazaGxsxLx583DZZZfh9NNPH/XrVsJaSCV8DROBIR0iIiKqWNdccw0ALuwQEZWi+KVtk30JJekXv/gF7rrrrsm+DCIiIiKiScG1HCKi0sW1nKGtWLECH//4xwEALS0t+OAHP4hoNIotW7bgsccew2OPPYbrrrsOixYtmuQrpVLB7a6IiIiIiIiISsScOXNw1VVX4b777sO6deswf/78yb4kIiIiIiIiIiLaD03TcM455+DJJ5/Eli1b8Pvf/x733XcfXnzxRfzyl7+EYRj4v//7P/ztb3+b7EulEsFKOkREREREREQl4nOf+9xkXwIREREREREREY3QggULsGDBgiHPnXfeefjLX/6Chx56CA8//DA+9KEPHeKro1LESjpEREREREREU8QjjzyCj3zkI2hra0N7ezvOOeccrFy5cr/z+/v78aMf/Qgf/vCHMXPmTLS2tuLUU0/Fd7/7XaRSqUHzk8kk7r//flx44YU46aSTMH36dLS1teH000/H97//fWQymf2+18aNG3HRRRdh1qxZmDFjBj70oQ/hwQcfHPbreeONN/ClL30Jc+fORVNTE9rb23HcccfhoosuwtKlS0f+B0NERERERERENAGOP/54AMDOnTvH/Bpcz6ksrKRDRERERERENAV85zvfwQ9+8AOceuqp+Pd//3ds3LgRf/vb37Bq1So8/vjjOOWUUwbM37FjBz75yU9i8+bNaGxsxLx58xAKhbBu3TrcdtttePzxx/HEE0+grq4u/5xXX30V11xzDZqamnDUUUfhpJNOQk9PD15++WXcfPPNeOqpp/DEE08gHA4PeK8XXngB559/PjKZDGbPno3jjz8enZ2duOaaa7B58+Yhv56NGzfirLPOQjKZxNFHH42zzjoLmqZh165deO6555DNZnHuueeO/x8kEREREREREdEIvfXWWwCAlpaWMT2f6zmVhyEdIiIiIiIioing3nvvxXPPPYcTTzwRACCEwMKFC/HAAw/glltuwZIlS/JzpZS49NJLsXnzZlx22WX43//9X0QiEQBAJpPB1VdfjYcffhjXX389fvazn+Wf19HRgaVLl+L000+HrheK98bjcXzxi1/EsmXLcNddd+Gaa67Jn8tkMrj88suRyWTw1a9+FTfccAM0TQOgFnsuuOCCIb+en/70p0gmk7jxxhvx1a9+dcC5VCqFTZs2HeSfGBERERERERHR2HV1deE3v/kNAOCcc84Z02twPafycLsrIiIiIiIioing+uuvzy/oAICu61i0aBEAYOXKlbBtO39u2bJlWLNmDebNm4fbbrstv6ADAJFIBD/84Q/R1NSExYsXIx6P58+1tbVhwYIFAxZ0AKCurg633XYbAAwqW7x06VLs3LkThx9+OBYtWpRf0AGA0047DZdeeumQX8/u3bsBAGecccagc7FYbNCdZEREREREREREh4rjOLj88svR19eHBQsW4KMf/eiYXofrOZVn3CvpaJp2CYBLRjL3r3/964knnngi0uk0duzYMd6XQkRQe/oR0fjj91Z5eOmllwDwv1e54X8voolzqL6/wuEwstnsIXmvSucvtMTjcXR1dR3Ua73//e8f8jVqa2uRSCSwZcsWNDU1ASgsvHz4wx/OL57sa86cOVi+fDn+/Oc/47TTTsuPSynx8ssvY+3atejs7EQul4OUElJKAOr/w+LrWLZsGQDgzDPPxJ49ewa9z0c+8hHceeedADDgee973/vw7LPP4sorr8TVV1+NefPmIRgMjurPZCiWZSGbzaK7u/uAc9va2g76/UoB13KISgt/HiaaGPzeKg9cyylP/O9FNHG4llO+Fi1ahOXLl2P69On4zne+M+Z1Ha7nHFi5reVMxHZXswAsGMnEVCo1AW9PRERERERERPuaMWPGkOOxWAyJRAK5XC4/tn37dgDA9773PXzve98b9nV7enry/T179uCKK67AunXr9jt/37WAzs5OAEB7e/uQ8/e3ePKFL3wBa9euxcqVK/H5z38ewWAQxx57LObNm4dzzjkH73vf+4a9bhpgFriWQ0RERERERDQubr75ZvzhD39AU1MT7r///nyIZiy4nlN5JiKksw3A8pFMjMViJwKojUajmD179gRcCtHU5Sdr+b1FNL74vUU0cfj9RTRxDuX3VyKRAKDu5qGDFwgEAKjywi0tLQf1WtOnTx9y3C9l3NjYmH8P01TLBfPnz0dHR8ewrzt37tz886666iqsW7cOp556Kv7nf/4Hc+fORW1tLQKBACzLQnNzMwAM+FpCoRAAoKamZsiv0T+/7/MA4KmnnsLatWuxbNkyrF69Gi+99BI2bNiAe++9F9dffz2+9rWvDXvtQ0kkEqipqRnR/8PpdHrUr1+itoFrOUSTjj8PE00Mfm8RTRx+fxFNHK7llK9FixbhoYceQmNjI/74xz/imGOOOajX43rOgZXbWs64h3SklPcDuH8kcxOJxF8xwju1iIiIiEZrwQL1Y8by5SP6nRMRERF5/LudPv7xj+Oyyy4b0XP6+/vxpz/9CYZh4He/+x3q6uoGnN+6deuQz/MXm959990hz+9v3HfyySfj5JNPBqDKGy9evBhXX301br31Vpx33nn8hcEIcC2HiKY6KSVsAeSERM6VyLmA5UpYQsISgCOkd+z1BWALCbuo7wrAkRKOABwJuELCkWp+/tg7J6SEKwEpAQF1TgAQEnC98/45If1rBKR/vZADj2Xha9E0r/X6GrQBxwCga4DuHeuaBl0DDG/MP9b8MQ0wNQ2GBhi6BtMbN72+7rWm7s3TgYCuIeDNCfjH+r7HGoI6EDRUP2TAG1N93b9YmnK4lkNEROXsxhtvxJ133omGhgYsWbLkoAM6o8X1nPIwEZV0iIiIiErChg0bJvsSiIiIytIZZ5yBBx98EEuWLBnxok5fXx+EEKitrR20oAMAixcvHvJ58+fPx69+9Ss88sgjuP7662EYxoieN5RgMIiLLroIv/rVr7By5Ups3Lixohd1iIgqmSMk+h2JjCORdvy+UH1bjWVc1c+4al7Wlch649miseJzWS9sk3PlgFAOlRZDA4K6hqABhAwV3gkb6jhsaAgVP/TCWNjQEDZVP+L1k3tNhHSJw4w0wmZhPGJoiJoaImahDRsaA0KTjGs5RERUrm666SbccccdqKurw6OPPoq5c+ce8mvgek55YEiHiIiIiIiIiAY4++yzceKJJ2LFihVYuHAhbrzxRtTX1w+Y09XVhaeffhoXX3wxAKC5uRl1dXWIx+NYvHgxzj///PzcZcuW4c477xzyvc4991x861vfwtatW/Hd734XixYtgub9cmzlypX45S9/OeTz7r33XixYsGDQos22bdvw2muvAQBmzpw5tj8AIiIaE8uVSNoCfZZEn9cmi9qkLZHy2n6vn7JVACdpC29MIuUIBmemOFdCha9coFAzaKyCqnmjd0SzI8bA4I4f5vEfVQENVaaujgMaqkz1UOd0VJkaYgHVj3nzYwH1OhoDQERERBXp5ptvxu23347a2losWbIEJ5xwwqRcB9dzyoMm5cH+gDt2LJFMNHG4FyzRxOD3VnnxU9/xeHySr4RGgt9fRBOH+5iXj/Xr1+Paa6/NH2/ZsgXJZBJHHnnkgEWVZcuWjfg1D/Tv4XHHHYft27djw4YNOOyww/LjO3bswPnnn49Nmzahuroac+fORVtbG7LZLN566y1s3rwZTU1NeP311/PP+fGPf4wbbrgBAHDKKaego6MDb7/9Nl5++WX813/9F37wgx8MeS3Lly/Hpz71KWSzWRx99NE4/vjj0dnZiRdffBFf+tKX8NOf/nTQ80477TS8+uqrmDVrFo499ljEYjF0dXVh1apVsCwLn/zkJ/GLX/xixH9OvtH8P5xOpxGNRgFgeW1t7b+M+s3KENdyiCZOKfw87AiJuCXQmxOI5yQSlkDCEohbAglLIpEr6vvncip0k7QFsgzWEO2XBiDmBXaqTD0f3okFdNQU9au9NhbQUOO1sYCGmqA6V+3NMfTKDPxwLae8lMK/XUSVims55ePJJ5/EhRdeCAA46aST9rvF1dFHH42FCxeO+HW5njNy5baWw0o6RERERERERCUimUxi7dq1g8bfeuutQ34tbW1teO655/DQQw/h0UcfxaZNm7B27Vo0NDRg+vTpuOKKK3D22WcPeM6VV16Jjo4O/OQnP8HmzZvx2muv4dhjj8Xdd9+NCy64IL+os68FCxbgT3/6E2655Ra8+OKLeOKJJ3DkkUfi+9//Pj7/+c/nF3WKfeMb38AzzzyDtWvXYs2aNUgmk2hubsb8+fNx8cUX45xzzpmQPxcionIgpapOszcr0JMT2JMV+b4K4BT6ftubE+izJ++GTqJKJwEv0CYBiIN+vZipoTqoQjs1wUJ4pyaojmsCer5fG9RRE9BRG1Tn/TZQoUEfIiKiQ6m3t1Ctb926dVi3bt2Q8+bPnz+qkM5YcT2n9LGSDlGFYoKdaGLwe6u88O6r8sLvL6KJw7uviEau3O6+OtS4lkM0cYb791pKiZQjsTsjsDvjojsrsCcjsDvrYs++QZyswN6cy6o2RHRAUVNDrRfiqfXCO3X5vjquDal+nTevLqSjzgv/6BOwfRfXcsoL13KIJg7XcohGrtzWclhJh4iIiIiIiIiIiGgSpGyB7oxAZ9rFhj0G9lgaZF8C3RmB3VkVyPFbhm4mlqFJBHWJgC4R0IGAIWFqEqYuYerw+lDHA/qqNTQJQwcMTb2WoQF6fkxC11AY09TWR4YmoWmApgEGAM071gHoGqBBHQNqPrzn+cda/oSaK/0Dqaq2+LfnShQOJAApAQkNEoCQ6iGlBuGdEwCE1FRfAq5UxwNbwJXagNYRqu8IDY4EXL+VWtE51dpC9R2h5tsCsKXfZ3WXQyXtSKQdiV3p0Vf20TWgJqDlQzt+Wx/SvFaN1fuPYKEfMfnfmIiIiKYuhnSIiIgIUkq43sKbI6S3mOa1Xr+wCFeY6x8XFu2K+95CH+SAY39+YWHQWwSUMr9AWNxKb7x4fuG6C+NDOfWr/w8AcN/m/iHPFy927rcPQNe0/EKppvljgAZtwHH+Aa1oARbQtKJj7/WMovmGphUt5hbmGt48QwdMb46paTB1/7W5qEVEREREVGqkVNvZ7Eq73kNgV9pFZ9pFd0agK+OiK+2iKyPQ7xR/mAl5bWoyLrvkaJAIGRJhw2tN/1jkx8Nm4XxQ91pDIqSrtrjvnysEcdQjaKhQDnf9KR0yvz7hhXe84I7lt25hXPW9c64GSwA5Vx1broacq6GvPwtL6NCDEXXOO59z933osBgQGjEhgbglEbdcAKNLEYYM5EM7dSEdDV54pyGk4/+77k6EnCwe25ZBQ1iFe/w2zHAPERERVQCGdIiIiMaJK6S3GCRhCYmcK2F7x/6YJQDbVa0lJGxXIicAW0hY3nhx3xGFMcc/V9S3vTm2VMeuP3eIYyffAo5U5xwpvbvYJvtPb4LMPBMAsGplZZZI1gDvjs5CcMfUNe9OTjUW2PfYC/v44wFDQ0BTx+pu0cKx//ygriFgQLW6aoPG0P2AriFoACFvPGQU5oR0eGPqvTWGjIiIiIiozAgp0Z0R2NHv4r1+L4Tjt0WBnIHhm6lDh0Q0IBE1BapMke9HzUIbKWrDpkTUkAgXjxkSUVOFZxicmZo0DfkKRWEAA2/XGb3u7m4AQHNz8wHnCol8uCe7b+voyHrHWUdD1t33WM3JeMcZV0fGKfRZIagg5wKdGYHOzBAVfGb8CwBg5V96Bp2KmhoavDDPtLCe7zcU9fPjYR3TQjqipsb1ByIiIiopDOkQEVHFkFIFWjKORNZVD79fPJbzjnMukPGOs65E1ik670pYLpD1wjX+eF86DEsAcn2nCt8I9To5V1Zu0IVKlgTU3YOQRTetlcf/iBqgwjyGhpCugju6G0ZQB6o3dyNsqHBQ2FDBnrAX7ol4bdjQEDZVCCjsH/tzzMLcsKkh4s2JmFq+ZRUiIiIiItqXlBJ7cwLvpVzs6C96pN1CKKffRaXnb2IBMehRZQrEAlL1vUf+2PTGvEo3/FGbypmuQVVoMiVqx/m1HQFkXQ0ZR4V3Ml54J+2oMb/NOBrS+Vb188e2N8/Vx/nqyoPankv9fTxSYQOYFjIwLaznH36YZ1o+1GOgMayjMazCPQEmBImIiGgCMaRDRESHhJAS/Y4Kx6QHPQQyjjqftlVAJu3NzTgSaS9Ak3bUOf81skP0J36t1F8EGV0ZXyIaSAL5gFshWOR9f6XtCX//oA6ETQ1RL8gT9cI7EVND1CwEevx+1NDz56uK5kWL5qtxHVXeWNDgoh4RERFRKXGFRGdGYHvKwfaUi+39br7/bkr90jddQQkcU5OoDQrUhlzUBIV6BASqgwLV+2ljpoAxNX/3TzThTB2I6RKxwMGvKbkSyDoa+h0dadsP8vjHOvodDf22rh5e0Cdlq7n9jhpPOxokKv9za9aFClumR/7nXhvUvNCOgYaQng/wTPPG/GN/DrfhIiIiotFgSIeIiAaQXpim31ZtyhaDj22JlCPRbwuk7ELYJuVIpG2BtBe48UM3friGiKhUWAKwLIm+CYz2mRoQDajwTpWpSmxXecd+uKcqoEI9VQENsYCOWNGcqn2OYwEdsYAGk3f0EREREQ1JSok9WYFtSRfvpBy8k3SxLengnZSLd1MOdvS7sIfYWaVcmLpEXdBFXUgU2pBAbdBFrRfCqQ26XisQMVnVhqhSGRpQFZCoCrhAZGyvISSQcTSkbN0L7nh9WwV6UkVhn1T+oSHp9XMVXM0nYUkkLBdv9Y0s2BMzNTRG/CCPCvE0eSGepoiBJi/g0+Sd4009REREUxtDOkREFcByVXimz5ZI2RJJLzyTtARSjkSfJZC0VdAmZasxdazmpexCGCdlH4pqNERElc+RQJ8l0WdJAOP326CQAcRMFdipCmio9sI7sYAKA8UCGqq90E9xWx302qKxqKlB429uiIiIqIxkHYl3Ug629jl4O+niHS+E47flVgnH0CTqQy4aQgJRLY26gI0ZdSHUh1zUhVwvhCNQH3IRZeiGiMaRXhz0GUPFaFtgQKgn6YV4UpaeD/IkbR1Jq/i8jj5Lhysr6y+zlCORSrrYlnQBHLg6cG1QQ1PYQFNEbbnVFCmEefzxprCO5oiB2iA/txMREVUahnSIiCaRK1RYJmGpgE2fJfKBmqQt0GepNmlJJLx2wLg3L8edl2gc6JqErqlFYsNrdQ3ewz8H6FALw/65/DzvNfxzWtFrqr533usj38oBxxq8hyaL5iBfgFnTMKAYs+Zdz1DLFU/97kkAwEc//bFB5/yleymRL+8svePiOeo8IKUGOWhs4DlRNC6gqWMJCKlB+OODzhWOXX+uPy4Hj7tSg+u1NDWpbcIE9uYO/rV0DYgFNNR4oZ2afJBHR01QtdVB77x3XOsd1wTV/JqAztLeNCQpJReTqexI7wcB/r9LNLlStsDbSVcFcfocvJ0shHJ29LtlcWOJqUk0hF1M8x4NIRfTwgINYRf1IfVoCKttpvzPPN3d3QCA5ubmSbxyIqKRCehAfUigPjS6m1KkBLKulg/w+G2f1z5416NAVR1OOfvMAedSlg5RIdtzqUo9Dt7sO/DcgA6vMo8K7zR64Z1mv0pPUaCnMayz+i4RjYmmaZBSci2HylI5ruUwpENEdBCyjgrYqIdEny2QyAnvg5ZQx14/kSsO4qi5SbsclhZpNAK6zD9MXSKgo+i4qK8Vjv15pjfu9w1NnTd0CVPzz8M7Vs8vPmcUtYYmYehqYdjQCvP0ovHiQI6uoSLvyHzqk98CAFx5ywcn+Uomhh/gcaUGIQp9VwKOKIR5HKFCPo4AHC/s4wgNjtTgemN+6xQfe3Oc/DnVt8XAMbtoru1qcKSaY3vn1PyBx4Iho5Ig8tV+Di7tGTIwKLhTE9RQG9S9h+rXFPXVsepXBzTolfiX0BRlGAZc14XjOAgEApN9OUSj4jgOAEDXK3f7BqJSkXMl3k46eDPh4K0+1b7Zp/rdmdLekypqCjRFXDSGXTSGHUwLCzSG3QGhnJpgIXxDREQFmgZETImI6aI5Mviz6IOP/R8A4Kb/PXnAuJBAv7fdVp9loM8L+CQsL8jjPdSYkR9zynz9wRbArrTArvTI/m1sCOloLgruNEW8NqyjJWKotCv+HQAAIABJREFUc94xt90iIp+u63BdF7ZtIxgMTvblEI1KOa7lMKRDRFOalBIpR6I3JxDPCcQt6bWFsE3cC+Hkx4vGWMGm9BiaRNCQCOlea0gEi/oBfeCYajHgOFB0PqB7YzoQNCSS8b0I6BKtjfUqcGMgP8eo0KALlS6/mlEAEjD80fII/6kgkQrsWK4K8HTu7oEtdVTXNsDKh3pU8CfnB3y8vuVqsIqem/Nafzznqn5+7j7Po/GVc4HdrsDuLDCWMukagJqghrqgjrqQCvDUeQGeupCOOi/c45+rD6nz/jneKVhaAoEAXNdFNpsFAJimWVZ3stDUJKWE4zj5/28ZMCMaH1JKvNfv4s2EgzeKQjhvJhxs73chSvBH16Au0RRx8iGcpoiLprCLRm+sKewiGijBCyciqnC6BlQHJaqDLmZUjexzp5RAxtGQsFRwp68ozJPIt0b+OGEZSNnl8wu+ofTkBHpyAptHMLc+pKHZq9DTEhmiDetoiaqWn7uJKlswGEQmk0Emk4EQAoFAALqucz2HSlo5r+UwpENEFcEWKlzT6z8sgd6czB/7AZter4175xKWQJltV1/WQrpAyFQhmbD3UH2h2qJzoQEPke+HvQBNaJ85fjDHmODP0d12BgDQPMLFACIamqEBhgGEDAl4v+TQImr/pub6A+/ffjCEVHeiWa6GnKsjVxTgyboq4FP82Hc86z3HH8s6fl8fMFYpZbgPBQm/3LeLd1Kj//u1OqANCu/UewGe+pCOhpCeH6sP6agPaqgP6YiaGhcbJkAwGITjOHAcB+l0erIvh2jUTNPknYNEo5RzJbb2OXg94eD1uI03Eg62JFQYp7/EPnRHTYHmiIOWqKrg0BxxCm3URV1Q8OYLIqIKoWlANCARDbiYPsK1PFcAfbaORG7fAI+ORM4o9C0DiZwK+pTr53+1fu5gS2L4eRpUhZ4WrwpPi1edpyWiQ/QZmBaUsHtttETUZ25WyiUqP/4NV5ZlIZfLIZfLTfYlEY1Kua3lMKRDRCVFSImEJdGTVYn/Xi/57z96i8aKAzh93DZqXAV1iYgpEDFVgEa1cohjocI2pkTEUAGcwrxC+CbihW94wwURlQJdU9szhQyJ6jFUfRkJ6QWBsl5wxw/yZB11nHE15BwNmaLzGUcFgDLe3Iw/11HPS3vzZJku/k2kpC2RtF281z+6/55BHYXgTqgQ6PHbfD+soz6o2oaQjhBLgg9L0zREo1FYlgXbtiGEyO8NTVSqNE2DrusIBAIIBoMM8BHtR78t8HrCwWu9NrbEVRDnjYSNbUkXbon8VR/UJVqiDlqjDlqjrup7oZyWqIMYq+AQEdEwDB2oDwnUhwQA54DzhQRS3rZbcS/YowI9qq/GdMS9gE+fpZfd53oJYG9OYG9OAPF9/0xCqnm1GwBgakBzUYhHtWqbrZaoalu946pAeVctIqokmqYhEonANM38jVdClPYWtETlvJbDkA4RTRghVXWbvTmBvV7oxm97soXx3qI5cUuUZLnrUqdDBWGiXrAmagpEAyo447f5cdML1Xh9/1zEG4sYE1+NhuhQ+dGjP5nsS6ApStOgttIzBGrG8XWlBHJeyCfjqCBP2muLx4rPpYvm+McZr7Wn+NZflgC6MgJdmdEtOlSZGhrCOqZ5QZ5pYRXmmbbPWEPYwDSvP9WCPZqmIRQKIRQKTfalEBHRGKQdgdfjDjbHHWyO23gt7mBzr413U25JbK7aEHIxvcrB9KiD6VWFEE5r1EF9iJVwiIjKWbmt5egaUBMUqAkKzIwdeL4rgaQX6InnQzyq9fu9RW3OLa+FWkcCO9MCO9MH/pwdM7UB4Z3miJEP8LQWBXoawzoM3v1JdEgEAoGy2jKIqFwxpENEI5Z1JPZkXezxAjZ7sl7oJiuwJ+vmx/wATk+OgZuRUEEagSpToiqggjOqVWN+mMYfixbNi3hzQobkIiTREGbPnT3Zl0A0rjQNCHthy/oQgIOsBGQLDAjt9NuFUE/a1vP9frsQ8Om3dfQXze93dAg5tf4R6nck+lMuto9ia66YqakQjxfkUX0D08I6Gr0KPY1h/2GgNsituIiIaOI5QuKtPgcbe2xs6nWwsdfG5riqjDOZH+c1SDRFXMzwgjgzigI506MuwiYXG4iIKlWlr+UYGlAXEqgbYaWerKMh7lXi6c2pLbd6vWMV7DEQt3T05gyk7PIK9KQciVTSxdbk8J+tdQ1oDOto8arztES91qvS0xItnGN1HiIiKgcM6RBNYVlHYrcXutmTFdidKfRVAMct6gukSmwf+VJgaCowE/Mq18QCAlWmQJXXj5pCjQWkN14I2VR5gRtWrSEioskS0IHaoEBtEBhr4Mev7tOfD/Oo8E7K0ZG2daS8IE+/XQj4pOyBx9kyuzNwLFKORCrl4p0RBntMDflQT2NY3TnoB3qavHBPU1hHU0QdM9RDRETDkVKiOyOwsddWDy+UsyVhIzcxu3+OSH3IRVuVg/aYjbYqB21VhUBOwJi86yIiIioVYVOi1XTRGj3wP9i2ABJehZ7eohBPb04vHFsGerM6+uzy+YdWSKA7I9CdEfjHAeZWB7zqPEUBnuLqPP5YQ0iHzs/QREQ0SRjSIaogQkr05AR2ZwTWxXX02BqWWSnsybrYnVXje7MiH8xJ2gzdAGq/+lhAoDqoAjX+o8oUiHlhmwHjAYHqgArahFnBhqik3fGN2wEAV918zSRfCVHlKq7uMy08tr2qbQGkbR1J2wv42Lp6OF5rFcI9xY+kpaPfqcyAjyOLt+I68N2VAR35KjyNXoCn0QvwNIZ1OL066gNAOOWgKWwgbPIHGCKiSmULidfjDv7RY+cfm3pt7MmO7d/pgxUyBGbGnEFhnLYqB9EA1yWIiGggruWMXUAHGiMCjREBwB52riOAhFeRp2eIQE9v0XGyjAI9SVsiabt4q2/4UJOpIR/YUdts+RV6VEWeVq9aT3PEQHCKbV9NREQTjyEdohLnCIk9WYHujAradKVV251RYZvdGXXOr3jj5te3wl6bmKQrP7Q0SFQFJKoDQj28wI3fr/YCNsVBHH8sWD6fMYholJ7+/VMAuLBDVOoCOlAbEqgNjf6Xh64E0l6wJ+mHd7xgj99PeoEe/3yf13dE5Sy02QLYlRbYld7fn6H3s+GGLgBATUBDk7fg2BhWbZPfRnQ0h9UCZVOY5cKJiEpZwhLYWBTG+UePjdd6bViTkMepD7lor3Iws9pGe5WDjmob7TEHjWEXeuX8k0tERBOMazmHhqkD08IC08ICRx4g0KMq9KjAjh/oUUEeA7sSNvocEykRRm/OQKZMbqRxJLAj7WJH2sWBAk0NIb0oxONV6YkWgj2tXtgnxs/OREQ0QgzpEE0CISV6cwKdaRWw6coU2t0ZF91Zge60avdmxaTuAz8ZIkYhWFMdFKjx+jXFY/lzLqoDaqspBtqJiIimHkMDqoMS1UEX00exZZe/TVeyKLSTtHT0eQGfPv/YO+e3KUuHQPn/0NFnS/SN4O5CAKgyVbnw4iCPXz682VuU9I9D/IGMiGjC7Mm6WL/Hxvq9NjbstfCPHhvbkod+r6qmsIOOahXCOSxmY2a1g/YqG9XBqbZ6QURENDWoCj0uGiODAy3d3d0AgObmZgBA1tHy1Xh6iivzZAvBHn/MleXx+bEnJ9CTE9gUH77Kbcz77Fwc3GndJ9DTElFbbXG7aiKiqY0hHaJxlHUkOjMuutIuOjOq6k13RqAr4w4I43RnBJwpsnYVMQVqvVBNTdBFdVAd++Gb2qKwTY03j/vOExER0UQrbNPloiky8l9wCgn02xr6LAN9Xninz1KBnkQ+0GMgUTTeV+bBnn5H4u2ki7dH8IvguqA2ZHinJWKgtaiMeD0XJYmIhtWVdrF+r431ey1s2Gtjwx7bu9P70JkWdnBYtYOOmI3Dqu18n1tUERER0f6ETYnppovpVcP/3CIkkLT1fHinONDTky3edstAyi6PCjUpRyKVdLH1AJ+dAzry22oNDvQUPkM3R3SYLEdIRFSRGNIhGoGkrQI3u9ICnWnXC+Ko8E2nF8TpzLhIWJW9UKVDqmBNSKDWC9XU5h9eyMY7XxNwURtk4IaIiIgqi56v3OOgbYTP8YM9iaLwjmqLjnN6/nzC0pFzy2MRcl9xSyJuOdhygB1XgzpUYMdbgGz17ihUrRqfHlVbcekM8xBRhdudcfHKHhuv7LFUlZw9Fjozh26/qipTYFaNjVnVNg6v8QM5NmIM4xAREdEE0TXkf7cwC8NXqLFc5AM7PVndC/R4229lBwZ8RBlU57EF8F6/i/f6h99qSwPQGB64zVZrUYinONgTNctzDYGIaKpiSIemtLSjtpzamVZhG/VQgZt8P+0iVaFlb3RN5gM2daFC2Ka2uJ8P5QjEAoL7yBMRERGNUnGwp32Ez8m6mhfcUeGdQpBHR9wykMipts/SEc/pyJZZqMca4aKkqQHNXnin1bvDsDWq5/vTqwxMj6py4QzzEFE5SNoC671AjnrY2J46NBVyDE2iPebkwzh+2xh2wb9CiYiIqFQFDaAl6qIlOoLqPJYK8fQUVegp7vd6IZ9y+AwtAezOCuzOCrx6gLk1AQ3N+wR3WiPGgJtjWljVloioZDCkQxXJEdKreCOws9/NV7/Z2a/GOtMudqZd9FVg5ZuIKVAfdFGl51ATcNBSY6I2KFAXclHnteqYoRsiIiKiUhU2JML5Rcj9h1h8WUdTAZ5cIcSTsNTdhAlLR3fSRcIOoF8EkciVz/ZbjgR2pgV2pgWG+3MI6EBr1MD0oio8071gj+rrmF5loDpQ+guxRFQ5LFfi1R4bL3thnFd2W3g94eBQrETEAgJH1Fg4osbGkbUqjDMzZoN/DRIREVGl0jWoG45DAofXDD8342heFZ6BW2z17FOxp88qj60C+myJPtvBm33Dzyveaqt5wLbUxVttqbGgUR7rBkRE5YghHSo7SVtgV7+LXWkXO/rVFlS7vNDNrrSLXf0uujLikCx6HSqxgEB9yEV9SFW8qS8K3PjHfhAn5P3M2N3dDQBobm6exCsnIppcR/3TUZN9CUREh0TYlAib+w/1FP9s6EogZeno9QI98ZyOuFce3D/2S4fHcwbcMikXvj3lHrAaRXVAw/SogRlVKrwzoyjQ4481R1iVh4hGT0qJHf0u1u628dJuC2t3W1i/10LuEBTJaY06OKLGzodyjqi10cTqOEREVKa4lkOHQsSUaIs5aIsNP88WQCKnwjz+1lp+oMcP9/hBn3L57DySqrYAUB/S8tV4igM8LftU6KkNaqzOQ0Q0SgzpUMmQUiJuqUWtnf0qdLPDC+P4xzv7XfTZlRG/iRhe8Cas2obiAE7ID+UI1AVdBMojrE1EVHLuWHLnZF8CEVHJMYruLgScYecKCaRsPb8AWQjwqL5fLrw3ZyBh6ZAlXqEnaUskEw5eT+z/6zY1VZWnrcrADC+8M6PKQFvUwIwqPV+hJ8CSlERTWtpR21at3W3lQzm70mJC31OD2q7qqFoLR9baOKrGxhG1FmKBylgnISIiAriWQ6UloAONEReNkeFDLftutbVvRZ7iQE+uDLbaAoDenERvzsFr8eHXDYI6BlTl8SvxqDCP2q66OaKjOWwgbPJzNBERwJAOHSJ+AOc9L4Czo9/Fjn7Ha/0AjkDGLe+FJR0StSGBhpCLhrAK2dTv2/dCOBGzvL9WIiIiIqp8ugbUBAVqggKHVQ+/MOcKIGF5dxN6lXh6i0qG+3cd9mZ15ETpLko6svjOwqFpAFoiugrveGGedr/vtdOjBkwGeYgqxo5+F6u7cljVbWFNt4V/9NiYyCUMHRIzqx0cWWPhqFobs+ssHF5jI8q1BCIiIqKSM9KttqT0ttryPjMXV+fpKboppierI2mXx93b1iiq89QGtXx4p7ht2ue4MazD4OdpIqpgDOnQuEjaAjv6XbyXUqEb/x/knUUhnLRTvgtJhibR4FW9mZYP3ai2ISS8Vm05ZZTu7xuIiIiIiCaMoQMNYYGGsMCRwyzMSQmkHW3AnYQqvKP6e7NqUXJv1kDaKc0friWAzoxAZ0bglT1Df626poI8foinrcpAe8zMh3naq7i1FlGpcoTExl4bq7ssrO5Wj+GCe+OhvcrG0XUWjq5ToZwjamyEGcghIiIiqiiaBkQDEtGAg/YDbbXlolCFx7sJZt9KPb1ZA72WDlEGW20BQMKSSFgOXk8MP0/XgGkhXVXg8cI7xW1LREdTWG3D1RDi52oiKj8M6dAB2UJiZ1HwphDEcfJjfVZ5LhzpmkR9yMU0L2gzLayCN9P8QI7Xrw4KMLRLRFR+Pjb7TADAk288M8lXQkREPk0DqgISVQEH7bHhq/NkHS0f3Cm+w3BvUaBnb9ZAtgTLhQsJ7EoLb/uboYM8AR2FAE+VgfaY3zfzx7XB0vvaiCpN0hZ4qdvCqm4Lq7ssvLzbQmoCbzRqCjuYXWfh6DoVzJlda6GKW1YREREB4FoOkS9gAC1RFy3R4cPirgT6/Kq22eKbYAZW6yn1qrbFhAR2ZwV2ZwU29g6/bmBoQGNYR1M+vKOCPMXVeZrCqm0IsUIPEZUGhnSmOCklEpbE9n4X76WcfAjnvX4X21MqiLMrLVCOS0XVARW6meaHbYoCOP5xbUjA4L/HREREREQlKWxKzDBdzKja/6KkXy58r1d9xw/07M0WQjx7vUVJt8TuLrQF8E7KxTup/X99NUEN7VUGZhZV4pkZ80I93rZaXGQkGp29WRcruyys7LLwYlcOf987cVtXxQICR9dZeJ9XJWd2rYWGsJiYNyMiIiKiKcfQgPqQQH1I4IjRbLXlV+LJFSrz9GRV2CdhlcdWW4AKKXVlBLoyAq8eYK7uB3r8II8X7mneJ9zT7G25FeBnbSKaIAzpVDghJbozAttTLranHGz3wjfbU45q+10k7fKK4BiaREPYRWO4ELaZVnTc6IVxQuXzMwQREREREY1RcbnwmcNU5hESiOcGBnf27NOW4hZbfZbEJsvBpl4HQG7QeUMDZnghnpkxAzNjJjpiheP2KhNhkwuLNLXt6HfxYmcuH8rZHB/+btyx0iExq8bG++osHFOvHm1VDivzEhEREdGkG81WW45Qn5/VVlsqyONvWT2wb8AS5fPDrpBAd0agO3PgCj0AUBfU8oGdpoiO5rCBRq8yT5MX7GnyxmoCGjRuu0VEI8SQTplzhcTOtIt3Uyp8827KGdDf0e/CKqMbtIK6zAdtGiOOasMupkXcfL8uxK2niIiIiIhodHQNaAgLNIQFZu9n+ykASDuaCu5kVHhnT1HfH++zS+eOAFfCuxHDBbqGntMc0b3QjgrwdBSHeWIGYoHSCiYRHax3Uw5e2JXD850WVnTm8O4w1aoORl3QzYdxjqmzMLvOQsQsrxuhiIiIiIj2ZepAY0SgMbL/7ZuB4avz9HrVefwttxKWDony+uVe3JKIWw5eTxx4blBHPrDTFNYxLVwI8zT6YR5/PKIjavJzONFUxpBOiXOKQjjvJJ1BYZyd/S4mcJv0cRXQJZrCDhr9wE3ERZPX+sc1AQEGTYmIiIiIaLJETYlobPiqPDkX2JMxB4V4dmcKx6UU5PHvFHx5z9CLqw0hPR/Y6SgK8nTETBxWzRAPlb7tKQcvdFp4oTOH53dNTChHg8Rh1TbmNFg4tt7CnPocWqMu1zCIiIiIaMoaTXUeVwAJS88Hd3pzBuK54kCPCvPELQMpu/w+g1oC2JF2sSM9ss8iUVPzgjy6F94xivo6GsMGMkkdtQGJVlsgZrJSD1ElYUhnkgkpsSst8G7KwTvJQvjGD+TsKJMQjq5JNIZdNHmBm+aIkw/h+GM1QQZwiIiIiIio/IUMoC3moG2YIE/W1bA3Y2C3F9rx224v3NOdMZApka21enICPTmB9Xv3H+I5rLoouOOHebwx3gFIh9qOfhfP78rhhU712JYc/1BO2BB4X52FOQ0qkPO+eguxQBks0BARERERlSBDL1S3PRDLBeKWkd9yqzdroNfS0Zs1EPeDPlkdvVbpfK4erbQjkfar4u5XWDVrdyFkANNCKszjB3mmhQoBn2lhHQ2hwnhDWEeA25IQlSyGdCaYlBK9OYF3Ui7eSbrYlnTwjhfIeSflYHuqPLajqgm6aM6Hbhw0R7xKOBEXTWEH9WEBg3/XExERERERAQDChjxgkKff1rA7Y2B3xsRurxJPd8bAnqJjV07+By0/xLNuP5V4miM6DosZOKzaxCwvvHOYV4WnvcqAyYVBOkg9WRfPd1pYvjOHv+7MYusEhHLqQy7+qSGHuQ05zGmwcHi1DaM81/uJiIiIiMpa0ACaI+r3ksNttwWoG2TiOT1flSc+oFKPjrhVGE+XaaAHUBV9d6YFdqZH/kvlmqDmBXtUkKchVAjwNIS8hx/qYbCH6JBiSGccZB2Jd1MOtuVDOIX2naSDpF3ad1qZmkRjRFW/afaCN80Rx2tVGCdslPbXQERENJQrv331ZF8CERHRflUFJKoCDmbVDB3kcSXQm9WxO2uiO2MUAj1emKc7Y5ZEGXB/O62Xdg9ePDU0oL3KC/B44Z1Z1QZmeccNIZ0lu2mQfltgZZeF5btyWL4zh3/02BjvVYnWqIO5XijnnxoszKhyWP2XiIioBHAth4hGI2xItEZdtEYPHOTPuUC8KLwzINxTVLknkdNLagvrseqzJPosF28nDxx28tUENNTvE+SpCxX69fv060M6aoPciototBjSGQEpJboyAtuSQwRxks6oUouTIWIINEcLIZxmP5DjjdWHBBiMJCKiSvTRT39ssi+BiIhozAwNaIwINEYsHFs/9Jy0reUDOwPatOr35CZ3YdGVUDewpFz8bdfg89UBDYdVqy20/OCO33bETIRYsnVKsIXEK7st/NUL5by024I9zksth1XbRaGcHBojpb2WQ0RENFVxLYeIJkrIAFqiLlqiBw6tuAJIWIXwTiKnttdK7BPwiVs6EjkDlqiMz659tkSfrT7Dj5ShAXVBP7SjQj51QRXuqS9+BHXUhbT8ubqgjiA/89MUxZCOx3JVNZy3vRDO20kHb/epSjjbUi7STulWkokFBJojDloiLlqiXhAnqo6bIw5iAcm7wYiIiIiIiCpQNCAxa5hqPLYL7M6qwE5Xep82Y2BvxoDA5H1gTNoSr/bYeLVn8AKpBqCtysCsagOHV5uYVW3i8GoDh9eofn1o8qsI0di93efguZ1ZPLcjh+d35dA3zlWID6+2cNy0HI5vzGFug4WaIEM5REREREQ0MoYONIQFGsIH/hwhZWHbrYQf4LFUP1EU5umzVD9h6SWxtfV4cSWwNyewNzf6z1xRU0NdUAV3aovCPXVBLR/kqQ2qaj213jn/uMpkBR8qX1MqpJO0Bd7uU0Gct/scbE06+eOdaReiRHM4sYBAa9RRQZyoixav9YM50UCJXjgREdEke+p3TwLgXVhERDR1BQxgRpWLGVVD3wXnCGBv1kBXWlXg6fTarrQK8eyZxBCPBPBev4v3+l280GkNOl8b1HB4takeNaoCzxE16nh6VIfOxbqSkrAE/rYrh7/syOG5nVlsS478zsyRmFVt4fhpORw3LYfjpjGUQ0REVK64lkNE5UbTgIgpETFdTN/PZ+9iUgL9jpYP7CS8ajz79vemBZK2iaQbgFMhlXr2lXYk0o4c0641poZCgCekoyagoyaoocYbU8dqrDaoztd656sDGqoDOsJmZf65UumrqJCOlBI9OYGtfW4+gLM16WCbd7wnW5oLNBFToNUP4EQLFXH8QE4VQzhERERj8uMbfgSACztERET7Y+rF5b4HcwSwxwvxdKUNdGVMdHqVeDrTBnqyBuQkhXgSlsT6vTbW7x1chSdswNs2y8QRNaoSzxE1Jo6oNjEzZsDkns8TzhUSr+yx89Vy1u624I7j8kZHzMbxXqWc4xpyqA2V5poPERERjQ7Xcoio0mkaEAtIxAIO2oeZ193dDQBoampGxtWQyKlqPAlrYKAnafvjqu2zdCTtyd36+lBw8hV8AIzxJpCgDlQHdFQHVWinxm8DGqq9ME8soCMW0PJ9P+ATC2jeuBozuM5Ao1B2IR0pJXZnBbb2OeqRdIv6Dvqs0gu0mLpEc8RBa9RFa9RBi9dviaq2OiC4HRURERE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6AACg1nr++edD3QUAAAAAAABUELEcAABQ25GkAwAAaq3hw4eHugsAAAAAAACoIGI5AACgtmO5KwAAAAAAAAAAAAAAAMBhJOkAAIBaa9asWZo1a1aouwEAQIW43W6tWrVKEydO1CWXXKI2bdooKSlJ55xzjm6//XZ9/vnnVWo3MTFRiYmJQe5t9aoN7wEAAACnRiwHABCO/vrXv2r48OHq3bu3OnTooKZNm6pTp05KSUnR3//+d1lrK9Xe999/r8TERHXv3t2hHjuvNrwHp7DcFQAAqLXGjRsniamSAaAmyhzRKtRdqHHWrFmja6+9VpLUvHlz9evXT3Fxcdq1a5c++ugjffTRR/rDH/6giRMnhrinAAAAgDOI5QBAzUUs58SmTZumw4cP65xzzlHv3r1Vv3597d+/X5999plWrVqlhQsX6u2335bLxRwqIEkHAAAAAIAawRija665RmPGjFG/fv1KnZs/f75GjRqlv/zlL7rooot08cUXh6iXAAAAAAAAKOn1119Xjx49VL9+/VLHv/nmG6WkpOjjjz/Wu+++q1tvvTVEPURNQpIOAAAAAAA1wIABAzRgwIByzw0ZMkSffvqp3nrrLc2ZM4ckHQAAUONYa5XvkfI91rcV2cDrvCKrAo9VnsdXFnikQq+V22tV6JHcXiu3t/xjbq+Vx0oea+W1Crz2eH2vvbb4vGRL9cdX5ubGSJJi9x4p1V8jyWWkCOMrXcb4SkkRLsklEzgf4TKKcklRx5WRLqMo49uPdEnRLqOYiOJNJV4b1YswinbJV/r3YyON4iKNolymWv4bAQAAZ/Tt27fc4+ecc45GjhypqVOnauXKlSTpQBJJOgAAAAAAhIUePXpIkn788ccqtzF//ny9/PLL2rFjh4wx6tmzpyZMmHDCYFJOTo5mzpypBQsWaM+ePXK73Wrfvr1SUlJ03333qUGDBqXqZ2dna968eVq2bJm++eYbHTx4UC6XSx07dlRKSoruuecexcbGlnuv7du3a+rUqVqzZo0KCwvVuXNnjRw5UrfffvsJ38/u3bv1zDPPaPXq1Tp06JBiYmLUqFEj9ejRQ8OGDVNKSkqV/6wAAKjt3F6r7EKvfnFb/VLoVbbbKtvt1S+FvjLbX+YUWeUWWeW4bYnXXuUWWR0tssp1+47leeypbxoSEb4iqyC03TiJSCPFRRnF+RN3ipN3YiOM4qJcioswqh9l1CDKqEGkSw2iivddqh9p1LDEfoMoo/golxpGGUWQ/AMAQMhFRvpSMqKjo6t0vbVWr7/+umbNmqW9e/cqOjpa/fr106RJk9S1a9dyr8nIyNCMGTP08ccf6/vvv5e1Vp07d9aNN96o0aNHKyoqqlT9I0eOaO7cuVq+fLl2794diLGceeaZuvHGG3XnnXcqIiKi3Ht98cUXevrpp7Vp0yZZa3Xuuefq3nvvDcSxyrNp0yZNnz5dGzZs0OHDhxUXF6cmTZroV7/6lW677bYTPsRWW5CkAwAAAABAGNi7d68kqXnz5lW6/vHHH9czzzyjPn366PLLL9f27dv12Wefad26dVq0aJF69+5dqv6BAwd0/fXXa+fOnWratKl69eqlmJgYffnll3rqqae0aNEiLV68WImJiYFrvv76a40bN05JSUnq3Lmzzj//fGVkZGjTpk3685//rCVLlmjx4sWqV69eqXutXr1aQ4cOVV5enrp06aIePXro4MGDGjdunHbu3Fnu+9m+fbsGDRqk7OxsnXnmmRo0aJCMMUpPT9eKFSuUn59Pkg4AoNYr8Fj9J9+rjAKvMgu9yixVWmX5938OHLf6xe3VL4Ve5XtC3XsUK7LSL4VWvyi4iU4NIo3io43io12Kj3KVeO0rE6JdSog2ahTjUmKMS4nR/i3GKCHapUiSfAAAOC1paWl64403JElXXnllldq466679OGHH6pfv37q1KmTNm/erCVLlmjNmjX67LPP1L59+1L1t2/frhtuuEHp6elq1aqV+vfvL6/Xq9TUVE2cOFHLli3T3LlzSyUN/etf/9KECRPUqlUrdezYUb169dKhQ4e0ceNGpaam6tNPP9U777wjY0p/N/jggw80evRoeb1e9ejRQ2eeeaa+++473Xbbbbr77rvLfT+ffvqphg0bJrfbrR49eujXv/613G63fvzxRy1cuFANGzYkSQcAAAAAAITWoUOH9O6770qSrrnmmiq1MXPmTK1YsULJycmSJK/XqwceeECzZ8/W1KlTtWDBgkBda61GjBihnTt3atSoUZoyZUpgBpy8vDyNHTtWc+bM0YQJE/Tyyy8Hrmvbtq0WLlyoiy66SC6XK3A8MzNTI0eO1PLly/XKK69o3LhxgXN5eXkaPXq08vLy9OCDD2rSpEmBoM/q1as1bNiwct/PjBkzlJ2drYcfflgPPvhgqXNHjx7Vjh07qvTnBABAqFhrlVlodTjPo5/yvTqS59V/CjzKyPfqPwXeQFmclJOR79XRopo6ew1qgqP+2Y5+zPVW6fqGUb5knUYxLiVGGzWpF6HGMS7fVs8VeN3E/7pRjC/p5/h/wAMAoK54++23tWbNGhUVFenAgQPasGGDvF6vfv/73+u3v/1tpdvbv3+/1q5dq3Xr1qlDhw6SpIKCAt12221atmyZnn32WU2fPj1QPy8vTzfffLPS09M1efJk3XfffYGZfH7++WeNGDFCK1eu1DPPPKMJEyYErktOTtby5ct1wQUXlLr/wYMHNXToUH388cf68MMPNWTIkMC59PR0jRs3Tl6vV88++6zuvPPOwLn58+dr5MiR5b6nZ599Vm63WzNnztQNN9xQ6lxGRob27dtX6T+ncGOsDe6XeGPMcEnDK1J35cqVycnJyQm5ubk6cOBAUPsBAADQq1cvSdLGjRtD3BMAqFvq1atX5Sl8UVZRUZFGjhyptWvXqm/fvpo1a1alrj/rrLMkSZMmTSqz9vmRI0d04YUXKjo6Wps3bw5Md7xq1SqNHj1aycnJeu+990ol3EhSbm6uLrvsMmVlZemLL75QQkLCKfuRlpamK664Qt26ddO8efMCxxcsWKCHHnpIbdu21SeffFJm+uQnn3xSb775piRp165dgeOjR4/WqlWrtGDBAp1zzjmV+BM5ucLCQuXn51eobqtWrRQXFydJqxISEi4JWieqGbEcAHCOtVK2RzpSaHS40Og/hUYZhUYZ7hJbodHPbinDbVRkSW5AeIswVgmRUqMoW85W9nh8pFQyp4dYDgCEBrGc4Jg4caI++OCDwH5kZKTuu+8+jRgxQjExMRVu54cfftDAgQMlSa+88oouvfTSUue3bdumoUOHqnXr1vrXv/4VOP7uu+/q0Ucf1ZVXXqnnn3++TLuHDh3SwIED1aBBA61du7ZCibVr1qzRnXfeqSuuuKJUQtBLL72k6dOnq3fv3nrrrbfKXHffffdp2bJlatWqlVasWBE4fvXVV2vPnj3auHGj4uPjT/2HUQHhFstxYiad9pIqNP/Q0aNHHbg9AACoTkVWcnsld6A0KrJSUeCYb9/tP1ZkpSJr5LEqu0nyHHfOK8nrzyn2+vetNb5SvoCn118e7/Y5WyRJL3xXTseN5JJUPHOz77WV8R8zvipyGSnCv7nkWyc+wljfvineL96sIo0U5T8e5ZIii4+5Sh73HYv2H+MBMwDAyUyePFlr165Vy5Yt9Ze//KXK7VxyySVljjVt2lQJCQnKyspSZmamkpKSJEmfffaZJOnyyy8vk6AjSXFxcerWrZtWrVqlr776Sv379w+cs9Zq06ZNSk1N1cGDB1VQUCBrrYofEkpLSyvVVvE/wFx11VXlrm+ekpISSNIpqUePHlq1apUmT56ssWPHqlevXgQUq669iOUAQKVYK+V4pEMFRj8VGh05yVZI4g3qEI81yvAnnVVEhLFqEmXVOEpqHG01+J2tahJt9e4BqybRVo2jjpUJkcRQAAA12+OPP67HH39c+fn5+uGHHzRv3jy9+OKLWrJkiV599dVKL2EeGRmpiy66qMzxjh07SpJ++umnUseL4zmDBg0qt73mzZurXbt22rNnj9LS0gKz80i+h8TWrVunLVu26PDhwyosLJS1Vjk5OZJOHM850YzPKSkpWrZsWZnjPXr00J49e/T73/9eY8aMUXJycrnxoNrMiSSdNEmrKlKxQYMGyZIS4uLi1KVLFwe6AtRdu3fvliTGFhBk4TC2PF6rXI9Vrtsqp8i35bq9yi1+XWSV7/GXRVZ5Hqs8f1lyP99fFnqt8j1SoceqoHjzWhV4pAKPlYeZtU9bTIQUE2EU4zK+MkK+15HHjtWLNIrzl7ERRrH+sl5kidcRUlykS3GRRnFRRg0ije91pFH9KN/xaJdq7LTT4TC+gHBVneMrKytLkio0swpO7aGHHtIHH3yg5s2ba9GiRerUqVOV2zr//PPLTbiJj49XVlaWGjZsGAgWFQd5nn76aT399NMnbdfj8ZS67vbbb9f69etPWP/o0aOlglI///yzJKlr167lBqtKPmlW8vyECRO0bds2rVq1SnfeeadiYmLUvXt3XXjhhRo2bJjOPffck/b7RLKyshQfH1+hv8O5ublVukcNlCZiOUDI8X245rDW6ucCrw7kevVjjkc/5nh0INdX/lhc5nhYaqockS6rGJdVdIRVtL+MibCKcvnK4mNRLut7sMVlfQ+3BF77yxKvfQ/JHHtYxmWsvyxxXP4Hb477uWvkW3ZTkhITE0udt7b4YSAjrz32EJDXmhLnfPseKxV5jTxe34NHRV5fMkqRt8S54geVvFKh18jt3wo95ti+59i5Qo9RgdeooMjIq5r5O706eKwv0e2nQkk5J68b5ZKax0aoeaxLLeIi1CLu2OuSx5PquRThqrt/ptWJzy7AOcRywl+7du104YUXqkOHDpo0aZKefvppvf322xW6tnhWmBYtWqhVq1ZlzhfHRwoLC0vFStLT06X/z96dR1ly3XWC/96IePuW+55ZWVUqyUISkhk10MggD/iMsMeNMcbLwcc27TbTLDbCcDzYx3ih2wfTMwaMtwMjTAssNwYZLDVjIQ+mkSW0tSUsq6SSalFV1pr79vYXEffe+ePGe/myMrMqqyrflvn9nBPnxou3ZGRJkfneL7/3dwHcfffd2/o61eeeOHEC73znO9d1ML5YqVRa97UWFhYAALfccsum9ZxbbrkFAGBZ1rr7P/3pT+PEiRN49NFH8eijjyIej+O2227DT/zET+Ad73gHJicnt3Xu9TqtlrPjIR2t9b0A7t3OY1dXVx/BNmdqERER7VZam2BMztXIegpZVyPnKay6GnlPIe/pYDNrzdf260dfo+BpFH2Fsmz1d0RXqhp4Mr2BGssWQCIkkHAEEo6FREggGRJIhiykgmBPMmQFxwRSwX4qZCEVFkiHLKTDwe2QYNGLiKiBPvrRj+JP//RP0dfXhwcffPCaAjoANg3obEVK84bijjvuwMTExCUfOz4+Xtv/wAc+gKeffho/+qM/ig9/+MO4+eabkclkEAqF4LouBgYGru7kNxGPx/Hggw/imWeewbe//W08/fTT+O53v4tnnnkGf/zHf4yPfOQj+O3f/u0d+3q7GWs5RLTXeErjQkHiXEHibL46+jhXkDiXlzhbkCjugQCOBY14SCPmKMQdjYSjEHcU4iGNuKOQcMx9UUcjamvEbIVIdT8Yo/ba/RFbox0/Is7pHABgoD/W4jPZnA46D5elQEUKVKRlwjtybSv5AmXfQlEKlH2Bkm+h6AuUpdkvBcdKUqDoCxQ9CyW5/fd+ncJTMNdpQQLwtnycJYCBqIXhhI3huI2RuBmH4xZGEibcMxy3kQ6Jtp3IREREu8c73/lOfOxjH8PDDz8Mz/NqS41vx5X+nqrWc+666y709PRc8rH197/73e/G0aNH8frXvx533303brjhBqTTadi2jRMnTuD222+vdUi+VoODg3jkkUfw2GOP4ZFHHsFTTz2FZ599Fk888QQ+85nP4I/+6I/wrne9a0e+VrtqRCcdIiKiPUVrjZynseqaYM2Kq7BaUWZ0zfGViqrdXw3iZF2FnGfGPVD7ozYhNYL//zTMnMBrk3QE0mGBdNiEdtJhC5mwhUxYoKu2b6ErIsxYPRbcDrVjBZeIqA18/OMfxxe/+EX09PTggQcewKte9aqmfv3qLK2f/dmfxS/90i9t6zmFQgH/+I//CNu28bWvfQ1dXV3r7j958uSmzxseHgYAnDlzZtP7tzpedfvtt+P2228HYGaQ3X///bj77rvx+7//+/i5n/s5zuolItqDpNI4X5Q4nZM4nfdr49m8xJmcxHRJ1pZV7nQWNFJhhXRYIRla21IhhWRIrztWvyVCJljDfELrCQGEbCBka6SwM5/VAfP5v+gJFH0LBd9CobrvWSgEQZ68ZyHviWA0Wy4Yi37nhnyUBmZKCjMlhe9dIsyTcIQJ8SRsjMQtjCUcjCRsjCbMsbGEja4wgzxERHRturq64DgOfN/H8vLyjk5gutjo6CiOHz+O9773vbjrrru29Zxjx47hyJEj6O/vx3333bdh6alL1XOOHz+O06dPb3r/peo5lmXhzjvvxJ13mjlAhUIB99xzDz75yU/iQx/6EN70pjchnU5v6/w7EUM6REREAa01sp7GUllhqaKwXFkbq9uZhTCyvoB7dA7LFdP+esVVXPKJ9qy8bzo5XSheXREx6Qh0Ry10hy1EZASZkMb4/DK6I+ZYV8Qy+xELPRELvVGzz3APEe1mn/zkJ/G5z30OXV1d+MY3voGbb7656efwute9Dn/5l3+JBx54YNshnWw2C6UUMpnMhoAOANx///2bPu+OO+7Afffdh7/7u7/DRz7ykQ3FoK2et5lwOIx3vvOduO+++/Dkk0/ixRdfZEiHiGiXWqkonMr5OJX1MZWXOJ3zcToYzxUkvJ3JOTRdxFbojihkwhJdEYVM2OxXgziZYEyHFNJhiUSoPbvXUOvZAkiFNVJhCeDK2y5LBRR8E+LJuSa8k3VtZGv71ob9rGvDVZ3zP2TB1ziR9XEi62/5mJgtMJKwMJpwTJAn6WA8YWMsaUI8owkbyVDnBpqIiKjxHn/8cfi+j0wmg97e3oZ+rde97nV45JFH8MADD2w7pFNdhnxoaGhDTQa4dD3n0Ucfxf333493v/vd237eZhKJBH7jN34D99xzD86fP48TJ07gh37oh7b9/E7DkA4REe1aJV9joSyxWFZYCLbFisJScGypUr29Nl6+o031V+fWs3CIaPvyvkY+L3EWEkDwAWDh8mvCpsMCvUFop6cW4LFrQZ7eqIW+YOuP2shw5hsRdYhPfepT+OxnP4tMJoMHHngAt956a0vO441vfCNuu+02PP744/jgBz+Ij3/84+ju7l73mNnZWTz88MN4z3veAwAYGBhAV1cXVlZWcP/99+Otb31r7bHf/va38cUvfnHTr/WmN70Jv/u7v4uTJ0/i05/+ND760Y/WfmY/+eST+PM///NNn/dnf/ZnuPPOOzeEcKampvDSSy8BWL8UFxERdRatNeZKCieDIM7JnMRUzsfJrI9TOR/Llc6ZLRO2NHqiEj0RiZ6oRHdEoSsi0RUOxohCV9gcjzqd833R7mZbMIGwMIDE9kM+ZSmwWrGw6lpYde11+ysXHV9xLVTafFmuktR4JSvxSnbrf4PuiMBYwsFYEN4ZD7rwjCcdjCdtDMQsWKxJEBHtWk8+xU1bKQAAIABJREFU+SRWV1fxute9Do6zPn7x1FNP4QMf+AAA4F3vetemIZid9Iu/+Iv4kz/5E/zVX/0VJiYmcPfddyMej697zNTUFJ5++mm8/e1vBwAcPHgQlmXhpZdewuOPP4477rij9tj77rsPX//61zf9Wu9617vwuc99Do899hj+4i/+olYfAoAHH3wQf//3f7/p8z7/+c/jzW9+M8bGxtYd/973voeZmRlYllXr8LxbiZ1aO+xqcB1zosY5fvw4AHDWKO0qvtJYLCvMlRXmSxLzZYW5ksRCSWGhEgRxStKEccoKea4h1RQCGmFLI2QDjtCwLY2QVd0HQpaGLTSc2j5qty1hbldHO3iOBcC2zGxAW5ivIQQgYNYVN6P572sJ1O67uNzxX//vLwMA/v2H/sOG89Yw676r6qjNs9duAxoCWpsW0UoDUotg34xSiQ33+UqYLdiXGvAuPqbMMU8J+JpFmmZwBGrhnf6ojb7avoX+mI3+qIWBmI3+mDmW4Cw42mWa+d5wdXUVAJDJZBr+tXabhx56CL/wC78AAHj1q1+95RJX119/PT74wQ9u+3WrXW1WVlY2vf+WW27B2bNn8f3vfx/79u2rHT9//jze+ta34siRI0ilUrj55psxOjqKcrmMV155BS+//DL6+/tx7Nix2nM+//nP42Mf+xgA4Id/+IcxMTGBU6dO4dlnn8Vv/dZv4Q/+4A82PZfvfOc7ePvb345yuYzrr78eP/iDP4iZmRk88cQT+OVf/mV86Utf2vC817zmNXjhhRcwOTmJG2+8EclkErOzs3jqqafgui7e8pa34Mtf/vK2/52qruT/4WKxWC12fSeTybz2ir9YB2Ith6hx9mItR2uNpYrCiVUfr2TNdiLr48Sqj6mcRKHNP9c7QqM3KtEXk+itC+H0RNS6UE7C4bJSrTQ3NwcADV1agq5e2RdYrlhYrpgQz6c+/EUg1Yc3/Mf3YKVi1+5brrR/oGcrYQvrQjsTybX98aAbj9OhLbH24u8uomZhLadzfPWrX8Wv/dqvIZPJ4NZbb8Xg4CByuRympqbw8ssvAwDuuusu3HvvvYjFYtt6zdOnT+PWW2/F+Pg4Dh8+vOljtqr3vPjii3j729+Oc+fOobu7GzfddBOGh4eRy+Vw7NgxnDx5Erfffju+/e1v157zoQ99CPfccw8sy8Idd9yBwcFBHDlyBEeOHMFv/uZv4g//8A83PZe//uu/xq/8yq9AKYVbb70Vhw4dwtTUFJ555hn86q/+Kr70pS9teN7ExASy2SxuuOEGXH/99YhEIjh//jyefvppKKXwwQ9+EJ/4xCe29e9U1Wm1HIZ0iHYpvjmmTqG0Cd7MlhRmSxKzRYm5YN+EcEzwZi4I3rR3ea59RGyFqG3Wl486GtHqbUcjYpstbJn7w8EWsYLjdfuh4HFhWyNkBWGcIJBT3beDkEw7esMh087xoePfavGZbE1pwFOAK0UtuOMpAVcJeBJwlYArBSrBWN2vVPeDzVXVfQtlKVD2hRmlQMU3x0pS1MJIdGkJR6A/ZmEguhbcGYjbGIyZMM9gzMJgzMZAzEbM4b8ptT8WdjpDtahzOXfccQe++c1vbvt1rzakAwDlchlf+cpX8I1vfANHjhxBoVBAT08PhoeH8eM//uN44xvfiB/5kR9Z95wHH3wQX/jCF3D06FForXHjjTfife97H972trdd8lwOHz6M3/u938MTTzwB13Vx8OBBvPe978V73/veTZ/38MMP41vf+haeeeYZXLhwAblcDgMDAzh06BDe85734Gd+5mdgWVf+h5xOK+w0G2s5RI2zm2s5Rd8EcU6s+rWlZU4GYZwVtz0/6Yctjb6oj76YRF8QxOmLrt9PhxWXmuoADOl0lkvVcoq+wFLZNlvFwlLFxnLZxmJwe7li7iv4nRXmsQUwkjDhnX1Jx4ypYEzaGI7bsNv0h81u/t1F1Gqs5XSOqakpfPWrX8WTTz6JqakpLCwsQGuNgYEBvPrVr8bb3vY2vPGNb7yi17yWkA5g/pt++ctfxkMPPYRjx46hXC6jr68Po6OjeO1rX4s3velN65ZXV0rhK1/5Cr785S/jlVdegeM4uO222/CBD3wAhw4duuS5PPbYY/jMZz6DZ599FgBw44034v3vfz9uu+22TZ/3N3/zN/jnf/5nPPfcc5ienka5XMbg4CBuuukmvO9978NP/uRPXtG/VfX7BTqnlsOQDtEuxTfH1Gqu1JgpScwWFaaLMgjgKMyUJOZK0oRyiiaII9uzHtdUjtCIhxQSjkbcUUiEFOKORsypjmY/Zpv7Y44J3FT3Y3ZwLAjZtOnn9qbrhJBOM2kN+ApBeMdCyRdmkxaKvkDJrx6r3jb3lXyBom+h4Jmx6AX3d+gMtp2WDgsMxUz76sFgHIrbGIzZGI6v7XPJLWolFnaItq/TCjvNxloOUeN0ei1Ha43ZksKxVR/HVz0cW/FxfNXHsVUf5wrbXyqnWdIhif6YxEBMoj/mYyAuMRCVGIj7GIhJZMKqbSek0JVhSKez7EQtpywFlsoWFss2Fqohnrr96u1O6W4cCjrxTAQBnsmUg32pYEyabsGtqjd0+u8uonbGWg7R9nVaLce5/EOIiIjWSGWKbtNFiQtFiZliEMQpmf3p4PZiRbX6VJsqYiskHY1ESCEZUrUxGVo7lgzCN4lQEMRxqsEchXBjlyElAmA6HoVsIGRrpHDtRXKpgWI1uBMEe/KehaJnxrxvoeBZZt8Ttf2CH4yegN6wSFnnyboaWdfHsdVLPy5mCwwFoZ2hmL22Hzez4kbiFobjNpfaIiIiIqK25iuN0zmJl1c8HF31cXTFw/FVE8jJee0zCyfhKAzGfQzFpRljPgbjEkNxH/0xiZjTPudKRDsramuMJCRGElvXPpQGcq6FhSC8s1CyMV+2MV8yIZ75koOFsg1Ptb5u4SngVE7iVG7z7yfhCOwLuu/Uh3eqYZ64wzoDERFRO2FIh4iIagqewoWixIWCxIWgA850wYRxpqsBnJKC2sV1rLClkQlLpMIK6bBCKqSQqo4hBV1eQcKRGOtLrTseYsimLf3021/f6lPY1WwBpMIaqbAEriL0ozRQCAI9Oc/C2bksCtKBiHUh55pj9WPWs5B1beS9ziwulaS+ZFGtKh0WGAmCOya8Y2M4YdX2RxJmlpzFab1ERERE1ECu1DiZ83F0xTeBnGB8Jeuj0gaNcSyhMRiTGEn4GIqbrRrCGYz5SIV3cfGCaBdrVi3HEkAmopCJKBzMeJs+RmsgWxfkmSuZMM9cycF8aS3Qo1o8AangaxxZ8XFkxd/0/qGYVQvs7E85mEw52B+EeQZirevCQ0REtFcxpENEtEfkPGXCNwWJ80WJ88F+/e3VNl0H/mpZ0MhETNgmE5boiiikQ2u302ETwMlUAzlhhah96X+DubklAMBAb6QZ3wJdo1//1G+0+hToEqy6kM8wJLrcHABgYCB0yedJBeQ9C6tBgGfVtZB1TYAn55rbq66F1YqNlWC/0kFLc1U787y8RXENAMIWTGgnYWM0YWM02B8J9kcTNvpjDPIQERER0eX5SuNk1sdLKz6OLHt4ecXDy8s+Xsn68FtcJghbGsMJH8NxvzaOBGN/TILNIYh2n3aq5YhtBHmkAhYrJrBjQjwO5oL9uZKDuaLd8uXCZ0oKMyUXT81tvC/uCEwGXXj2p20cSDnYn3awP+VgPGkjZLGuQEREtNMY0iEi2gVcqXGhKHGuIHEubwI35wsS5wpm3fdzBYnsLgngJEMKXWGJTEShOyLRFVboipjbmbowTiZslpji50ii3ce21opk21X2xabhner+SsXGcsWMK64F1ebr0rsKOJ2XOJ3fegpzKAjyjCWCLWnCO2MJJxhtZMKCM+aIiIiI9gilNc7kZRDE8fHSsocjy2apKreFK1Y7wgRxRhI+RoOtut8TlfxcT0RtzbaAgZjEQEzipk3u1xrIewJzJQezJRtzRWctwFOyMVe0kfVa16K7eIkuPLYAxpOm+87+oPtONcCzP81ltIiIiK4WQzpERG1Oa40VV+NM3se5vMTZIIhztmBunytIzJUUOjmCk3BM4KY7otAdleiJmKBNV0SiOwjhdEdMAIfLStGVOP7CcQDAoZsPtfhMqNWijkbUkRiMSwCbz36rUtp06lkJQjvLQYhnpWJhuWJjqWzG5eBYq9tab8VTwJm8xJlLBHmSjjCBnaSN8YSNsaSZKTeWsDGeNMtrOfyrCBEREVHHWSxLvLBkOuMcWfbwYhDMKbawNU5/1Mdo0sd4shrC8TCa8DEQk7D5d14iCuy2Wo6odRH2tuzGU/QF5oo2ZksOZos2ZooO5koOZoomzNOqZb+lBqZyElM5iX9GZcP9w3ELQ04E4zGN20o5HEg5mEzZOJB2kA7zBzsREdFWGNIhImoxpTVmigpn8j7OBn9MPVcw++cKEmfzEoVW95e+Sl1hiZ4gdNMTVWv7EYnuaNAJJ3L5JaaIrtbdb34/AOCh499q8ZlQJ7EEkA6WwZtIbb3kFGAKVlk3CO2ULSxVbCzV7S+WTZhnsWzDU+0Xdsn7GkdXfRxd3fz7tAQwErfXBXfGEybIM5G0MZ50EHPa7/siIiIi2ivKvsbRVQ8vLnk4suzjxSCUM1tqTWuckKUxlvAwFoRxxpIexpOmK07U4Wd/Irq8vVjLiTsak2kfk+nNP5vnPYHZYhDgKTmYLZoAz0zR7LstqjdMFxWmYeN7WeC/z2bX3dcXtYKls0xo52DawYGUgwNpB10RBniIiGhvY0iHiKjBpDJLUVW7GZzN+8EocSbv43xBtrSt9NVIhhR6o7K29USCMSrRG5HojZruN+x4SkS7nS1guoBFFJDe+nHV9taLZRPiWSrbWKyOZQuLZbt2XzsttaU0assmbqU/atUCO2a0MZFcC/IkQ/xlsFdprbmcGnUcrfkHZCJqT1przJQUXljy1m0nsj5kC350JRyFiZQJ4EwkPYynfIwnPfTHJGz++ici2lHJkEYys3knHq2B5YqFmaITbPa6/cWyDd2CDsALZYWFsov/Ob/xvp6IhQNpuxbaqW4H0w66GeAhainWcqgTdWIthyEdIqJrpLTGdNAJ50xe4nTOrwVyTudMCKdTGuFYQgchG4m+mFwXxOmLSvREFHpjkp1viIiu0Fp7ax+T2Lo7j9TAasXCQhDaqd+qx+ZLNsqyfYpW82WF+bLCswubt+3ujViYSNnYF4R4JpI29qXWAj1cw373sSwLSikopWDbXKeSOotSJj1vWfzZREStU5EaR1eCIM6yhxeXfLyw5GGx0vwZPpmwNEGclIeJpIeJlAnldEcU+PcbIqLWEwJBB3MXP9DjbrjflcBcycF0wYR2poMAz3TRwUzBRkU1/33vUkVhaV7hmfmNdYTuiMCBVNB5JwjuVPfZgYeocaq1HCklHIfxAeosnVjL4VVGRHQZWmssVRRO5yRO531M5Uz45nQQwjnXIZ1wbKFrYZu+WDCu2/fRHVFcB56IqIXsWnFNAdg89KK1Wa9+oWxjoWRjvmxjoeSsC/HMl22U/Pb4gb5YUVisKHxvixDPQMx04tmXdLAvZWMy5WBfEOQZTdgIWfzrT6exbRtKKXiex5AOdRzPMz+rWJQkomZZrigcXvJweMnDE1NhHMtbOPX4haZP9kmGFPalvNo2mfIwkfSRiXRAwYOIiLYUtoGxpI+x5MYJQ9UuPNXgzoWCCfNMB2GerNv8z3PLFY1nK96mE4F6IhYO1i2fVR/gSYfbowZC1KlCoRAqlQpc1+XnYeo4nVjL6ZwzJSJqoJKvgwCOj9M5acYghHM6J5HvgFY4XWETuBmImcDNQGz97e6oYstpIqJdQAggEdJIhHzsS23dlafgiSCw45gx2BbKNuaCUI/fonXr682VFOZKm8+gswUwmrBroZ1qgGcy5WAyZaMvarEFbxsKhULwPA+VSgWWZSEUCvG/E7U9rXXt/1ugswo7RNQZtNY4k5c4vOTh+SUPhxdNMGf9sqKN/9kTtRUmUj4m6wI5+1IeetgZh4hoz6nvwnPTJl14Cp7AdLEa3HEwXbBrt+fLzX+/XO3A891N6gf9UWtD9539aRsH0w6X4SbahmpIx/M8FItFhMNh2LbNeg61tU6u5XTOmRIRXQOlNWZLClM50wnHjGuBnJlSe88McyyNgaiPgbhEf0xiIOYHo0R/VKI/5iPMiepERFSnGuSZTG8e5FEaWKlYQXjHwVzJDjYT6pkr2ch5rf3lIjVqS0g+NrOxYJhwRK37zmTKxmTSqe1PJB1EHRYSWiEUCiEcDsN1XZRKJZRKpVafEtEVCYfDCIVCrT4NIupgvtI4turj+UUPzy+5+H4QyMm6zZsAZEFjNOljX8rD/rTpjLM/7WEgJsFGhUREtB2JkMZ1GQ/XZTaGYioSmC06eOlCAbPlCHJWl+nEU3QwV7Sh0NxfNmYpbhdPzW2sHQzFrA1LZ12XcbA/5SDGugERANMVOR6Po1gswvO8WmcSok7RabUchnSIaNco+Rpn8j5OBUGcU1m/Fso5nfdRlpd/jVaJOQqDMR+DcRO8GYj5tbE/JtEVUSyiERHRjrLqlta6oXvzD94lX9QCO3PVIE/RwWxwbKlsQze58Fav4GscWfZxZHnzINJI3Kp14NmfsrG/up+20RthF55GikajsG0bnudBSgmt278rIe1tQgjYto1QKNRRRR0iar2Sr3Fk2cPzix6+v+ji+SUPR5a9ptYguiMSkykPk2kP+4NxPOkhwsk8RETUIBEbmEj5iHavAgAGBtbu8xQwFyyfdSHowHO+EMJ0wcZMyYHSzf0sPlNSmCm5eGJ2Y4BnLFFdPsuM1wVBnsmUgzDb0tMeEwqFkEwmayEdrTXrOdTWOrmWw5AOEXUMrTWWKgqn6gI4p3ISp3I+Tud8XCi2bzecZKg+hBMEcOI+BoMgTjKk2VaaqAH++BtfaPUpEHW0mKMxkfIxkfIBVDbc7ylgoWRjtmRmys0GQZ7ZIMizWGr+7Ll6F4oKF4ountykEJcKCewLwjsmxBMEedIOxhI2HKZjr4kQAuFwGOFwuNWnQkREtGOyrsLhJQ/fDwI5hxc9HF31IZv0twtbaEwkTQjnQNp0xjmQ9tAVad96CBHRlWItp/OFLGA06WM0uXFCja+AuZJtuu4UHJwPuu+cLziYLTqQTQ7wnCtInCtIPDq9/rglgPGEva77TnV/ImUjxJoB7VK2bcO2bUSj0VafCtGuxpAOEbUVqTQuFCVOBctQncqaIM7JIJST9doztRtzFIaCEM5gEL4ZjAe3Yz4SofY8b6Ld7tDNh1p9CkS7WsgChhMSw4nNp4r7Clgo25gJ2l3PlBzMFtdCPK3sxJPzNF5Y8vDC0sYuQo4AxpOm887+tFk+a38Q5JlM2UhwPXsiIqJdb7Esg+44Znt+ycUr2ea1x0mH5bogzv6gOw7fhhDRbsdazu7mWMBIQmIkIXHxZCAZBHjOF4IuPHVbszvwKA2czkuczkv8jwvrz9MRwETSXh/eyZhxPGHDZoCHiIgugyEdImo6V5plqU5mTRecagDnZE7idM6H24YTwBxLYzDmYyguMRT3MRj3MRQEcYbi7IRDRES0GcdC8Ltz8z9oeRKYK5nAzkzRBHimi2b23GzRRtZrzRoNvkbQrU8CFzZ2EBoM1rOfTDk4kDItsfenTHGuK8K/nBEREXWa2aLEc0F3nGoo51yheYGckYQJ4gzay5iIl/BDE3H0RBTrDEREtKfY6yYCrf8s7itgtm4JrWp453zBTApqZhdfXwMncxIncxI4v/48QxZMrSBYQqvafWd/ynTtZYCHiIgAhnSIqEEKnsJUTuJkzsdU1sfJ3Foo51xBQrVhY5ne6FoIx2wyCOb46Ikq8P0zUef53O98FgDw65/6jRafCRFtJmTXt8DeGIYpegIzJQczQfedmaLZnwmCPK5qzS/n2ZLCbGnzZbS6wqIW2tmfNktoHUg7OJByMBCzIPjXNiIiopbRWuNCUeG5BRffX/Lw/QUTypkpNWe2UMjSmEx5OJB2cTBjgjmTaQ9xxxRJ5ubmAAC9XF6AiPYw1nJoM84lltDyggBPfQee6v58qbkdfD0FHF/1cXx143mGLdQm+Kwtn2VqBqMJGxbrBUREewZDOkR01VYqynTAyZouONWuOKeyftMKXFciZqta+GYoEQRxYmZ/MOYj3JrJ+kTUQA//9T8AYGGHqFPFQxoHQuYPWBdTGliuWEFwZy28M1N0MFNwsFhpzS/2FVfjXxc8/OvCxnNOOAKTdaGd/bUOPDYLckRERDtMa40zedMh5/lFN+iU42Gh3Jx6RcJROJD2cDBjAjkH0y7Gkz5sNt0jIrok1nLoSoUsYCzpY2yTAI8rgemLAjzVEM9iubl/InUVcHTVx9FNAjwRuy7AU9eJZ3/awWicHXiIiHYbhnSIaEtaayxVFE5mZdAJxwRwql1xlirtF8TpjZjQzXDQDWc47mM4YbrjZMJsFU1ERLRbWALojSr0Rl3c1LOxo01Fmpl000UH0wUT4pmuBXoceC3owlPwNV5c9vHi8uYz6iaD4E51Ca1qcW48acNhQY6IiGhLWmtM5SSeC5arqi5dtVxpThvf7ojEdRk3COWYQM5QXLIGQURE1GJhG9iX8rEvtfFzeNkXZumsvIPz9Uto5R2suM2d+FORwMsrPl5e2boDz/60meRzIBUsoZU2S2ixXkBE1HkY0iHa47TWmC2poBtOEMIJlqU6mfORddtrXSpHaAzWhW/MaG4PxCWidnudLxEREbVGxAYmUj4mNinEKQ0slW1MB8EdE+Ix43TRRs5rfhceVwHHVn0c22RGnSOA8eT6DjzVwty+lIOIzYIcERHtHUprnMz6tc441aWrmlW/GIz5OJhxcV3Gw8GgU05PtP0mMREREdGlRR2NA+nNu/cWPVHrvnNxF55sk2sGl+rAE7KAiaRdVytY69g7kWS9gIioXTGkQ7QHKK1xviDXwjdZv26UKPrtFWyJO2pd+GY4vtYdpy8mwfeVREREdC0sAfTFJPpiErf0buzCk/dEENhxLhptLDS5HTYA+Bo4lZM4lZP4J1TW3ScAjAUFuWpwZ7IW5rERd7imBhERdS6pNI5nfTy3YDrjPLfo4fCih3wT6hgCGqMJ33TGqYVyXKTC7VVDISIiop0XD2kc6vJwqGtjgCfnirpls0JrAZ6ig7zX3M/gngJeyUq8kpXA+fX1AksAo4kgwJMyS2dNpqpBHhvJEOsFREStwpAO0S7hKY2z+bUQzr+eCeFcWWDu8Cym8j4qstVnuF5XWK6FcBI+Ruo646S5LBURERG1UPISxThXwnTdqQvwXAgCPLNFB1I3902MBnA2L3E2L/Gd6Y33D8ct7E856NVhjMcU/o1TrLXJzoRZkCMiovbhKY2jK35tyarvL3h4YdlrysQiCxrjKR/XZVwcTHtm6aqMh7jDQA4RERGtlwpr3BD2cEO3B6BUO641kPWsugCPs26/5Df3M7jSl64X9EdNvWAybZs6QV2Ypz9qQfCPNEREDcOQDlEHKfsaU/lgSaqcxKm6jjhn8hJyXe0oFIwbWyA2g4BGX3QtiDOSWB/KYaGLiIiIOlH4EstoSQXMl+0gtBOEeILZdDMFGxXV/FDMdFFhuuii9tHv9HLtvt6IhQNpU4DbXzeb7kDaQW+EBTkiImqcsq9xZNksV/X9RRfPL3l4cdlrygQjW2jsS3m4LmPCONdlPEymPS6fTURERNdECCATVsiEXdzYvb5rr9bAqrs+wFOd9NOKAA8AzJcV5ssu/uf8xvsSjsC+lI3JILwzWdu3Mc5ltIiIrhlDOkRtZtVVOJX1MZWTOJmrBnJ8TGUlLhQl2qlkZAmNwZjESH1HnGB/KO4j3NylWYmINrjuputafQpEtIfYFjAUlxiKS+CiZam0BpYqpiC3vgOPGYstKMgtVhQW5xW+O7+xY1AqJIKOO2tr21dn1Y0kbFgM8BAR0TblPYUXlqqBHBPKObrioxkrbzuWxv6UCeMcDEI5+1MeQqxXEBG1LdZyaDcSAuiKKHRFXPxAz+YBnvN1E30u1HXhaUW9oOBrHFn2cWR54wQlAbOM1mTKxr6Ug8lkMKZs7Es6GIhx0g8R0eUwpEPUZFprzJUUTuV8nMqZ5ammgiDOqazEYkW1+hTXcSxtAjjxIIATLE01kvDRH5NwuEoCEbWxzz3wxVafAhERAFOQ640q9EZd3NK7sSCXda1aYKe6fFY10JP1mv+XxJyn8fySh+eXNgZ4IjYwmXQwGXTeqbXFTtuY4Iw6IqI9baks8XwQyHl+0fweObHqN2XCUdjS2J9213XImUh5CLFuQUTUUVjLob2mPsBz0yYBnqxrbQjuVCf95L3mv9HRAM4VJM4VJP5lxt1wf8w2XXj2pRzsS64P8kwkbaS59DYREUM6RI3gKY1zeRkEcUz4prp/OidRaMZ0sSsQsVTQBUeuC+MMx330xST4dxYiIiKixhECyEQUMhEXr+reWODKe6I2m266sL4Dz3Kl+QGeigSOrvo4urr1jLrqsln7gy48+5JmWa0Mi3FERLuC1hrnCyaQ83zQIefwkodzhSasVwUgYiscSJslqw5mXBzKeBhPepxIRERERLtKfb3g4iW0ACDninUTfmbquva2ol4AACWp8fKKj5dXNtYMAKA7IjCRNHWCiaRjAj1JBxMpGxNJG3G+oSOiPYAhHaKrtOoqTOXMslRTwbJUU3mJU1kf5woSsr1yOIg5CqOJuo44dctT9UQU2H2QiIiIqD0lQxqHujwc6trY1abkrxXkpi/qwDNfbv7HvfoZdY9tMqOuJ2JhMui+U13TfpLLaBERtTVPaRxf9XF4ycPhIIxzeMnDUpM6AccchYPpte4412VcjCZ9TigiIiKiPS8V1kiFPVy/Sb2g6Iu10E7BxkxxbcLPQsmGQmveTC2MapYhAAAgAElEQVRXNJYrJuS9mf6ohYmkjfGkE4wmzDMe7KfYJpGIdgGGdIi24CszK2wqJ3E6768L5EzlZNOKUVciHV7rhJPWWQxEK3jVcBzDcR+ZMIM4RLT3vOHQXQCAh45/q8VnQkTUGDFH40Daw4H0xuJWRcIU4QoOjs+VMVuOYEWncKHgYK5kQ+nmvzlcqigsVRT+dWHj+YYt1NpgT6bMbLpqiGdfioU4IqJmyLoKLy6vD+O8tOKh0pwGOUiGFA7WLVl1MONhJOHDYj2DiGjPYC2HaGfEL1Ev8BQwG4R2Zgo2poP96aAbj6ta9+ZrvqwwX1Z4dpO6AbDWiWc8YWMiZWMs4WAsYbrwjCVt9EYsCP4xjIjaHEM6tGdprbFUUTgdhHBO18I4JohzNi/RZqtSAQB6IxJDQSec0YSPoYSPkaArTjK0dsJzc3MAgIFuXuZEREREe1HEBvalfOxL+ThgBe8NBwYAAL4C5kp2rQ12/TJaM0UHXgsKcq4Cjq/6OL7qA6hsuL836MIzGXThqV/ffjRhI8S/4BIRbZvSGlM5iReWPLyw7OHFJQ8vLHk4nW9SGgdAV1jWgjjVcTAmOcGIiIiIqMFCFjCW9DGW3LgkldLAcsWqTfoxHXhMJ56ZFi6jVXW5TjxRGxhLmM47YwkT3BlLrIV5RhI2Yg7fcBJRa/Gv97Sr5TwTwjlTF8KpjmdyEvk2TOFY0BiIy7XlqOJrQZyhhETUbr9zJiIiIqLO4ljASEJiJCFxcSBGaWCxXA3w2MEyWmshnpLfmo42ixWFxcrms+lsAYwk7Fpop36cSDoYiltcSouI9qxqd5xqEOfFZQ9Hln0UmlgT6Y/668I412VcLr1NRERE1IYsAfRGFXqjLm7q2biMdckXmAlCO7NFp7ZvbtuoqNZ2wS1L4ETWx4nsxgBSVW/EwmjCxmhdiGe0bhuOcyIQETUWQzrU0XKewtm8CeGcyUmcqe7nzX47LkkFABFLYShhgjhDQRhnOO5jOC4xEPfBTv5ERERE1CqWAPpjEv0xiVsvuk9rYNW1Luq+Y9dm2K24rZlRJzVwNi9xNi/xLzMbi4gRGxhPmPXsJ5I2JlJ1+0kHAzGGeIio81WkxrFVHy8teziy7OGlZQ8vLvs4V2hedxwBjdGECeQcSJtAzsGMh0y4PeszRERERHRlYo7G/rSP/emNIRgddOGZLZlltGZKa+Gd2aKD+XJrlt6+WHUS0PNLm3fjEQAGYxaGEzZG4qb7zmjcrt2uBnnYkYeIrhZDOtS2tNZYriicLchawf1cQeJsB4RwACAdkhuCONVlqbojiuupExEREVHHEQLoiih0RVzc2L0xDFP0RRDYsdetZz9ddDBXal0xrnKZmXT1IZ5qS+zxpGmPPZ40RTiHb+CJqE1IZZaqOrLiBYEcE8w5kfUhm9h81xEaEykTwrku7eJAxsOBtIeYww7ARERERHuREEBPVKEn6uLG7o33SwUslIMuPCUbc0EnntmSCfIslm1otP6ztwYwU1KYKSl8D5sHeQCgOyIwHDc1g6G4Ce4Mx20Mxa3asf6oBZv1BCK6CEM61DKe0pguSpzLS5wvyCCM4+NcXtaCOc1svXylLKExEJMmgFML4qyFchKh9j13IiIiIqJGiDsaB9Lmj7QX8xUwXzLhnWrnnVoXnhYuowVcPsRjCWAkXh/gsTGecDCWDNpjJ2ykw2yHSUQ7y1Map7I+Xl7xcXTFw9FVs3981UOlec1xAADJkMKBtFv7GX8g42E86bETMBERERFtm20Bg3GJwfjmb2Y9BSyUTGhnrmhjrrQW5pkt2Vhok048VcsVjeWKjyPLWy+tZQvTlWcoCO0MxWwMxi0MxWwMBMcHg31ODiLaOxjSoYZQWmOhrHC+YLrfVIM45woS5ws+zhckposK7R5jSYXMm4W1II7ZH4r76I9JOCxGERERERFti2PBhNoTEkBl3X1aA1nXWreW/XR1Rl3RwXzJhmrhbDqlYT7XXGLJmHRIrFvHfizp1AI8YwnTHjtis+BGRBsVfYUTqz5OrPo4uurjaBDKOZH14bWggfBAzMfBtIcDmbVQzkBMgqsCEhEREVEjhdbVDTaqduKZK5kAz1zJxnywP1+yMVe0UVHt9Yc7qYELRYULRQVcoiuPANAXtTAYtzEUszAQs+GUQ+gNadxkF9EfNeGegaiF7ogFwTfnRB2NIR26Yr7SmC0pTBdN8OZCQeJCcW08X5CYKUq47bsSVY1jaQzGTPhmMAjfDMVNN5zBuI8ku+EQEXW0D/znu1t9CkREtA1CAJmIQiaicEP35bvwzNQFeGaLNrKe3YKzXi/raRxZ8XFkZesZdH1R0/J6OFjPfiRhYyRuYTQI8QzHbSTZloJoV1Ja43xB4sSqj+PVLWuCOZcKADZS1FaYTHnYn17bJlMeOwMTEVFLsZZDRFtZ34ln4xLcWgNZz6oFduZKDubLZn++7GChZGO5YrXFkloX0wDmywrzZYUXakdDZji1vO6xIQvoj1roj9kYjFnoi5pltfpiFvqjNvpjFvqi5nhf1OKEIaI2xJAO1WitsVxRmC4qzJQkposS0wWJmSCQM1PdSgqqQ+o1FjT6giWpBuNyQyCnO6LA7nFERLvX69/xhlafAhER7YBLdeEBgKIvMFsX3JkJinHV2yXZHsGXhbLCQlnh+aWtZ8+lw6K2dv1QzMJIwrTDHqpb234wZiPMIhtR21FaY6aocDLn42TWx1TOx8msxImsj1dWfZRk64opQ3Ef+2uBHBf70x6G4pI1ESIiajus5RDR1RICyIQVMmGF6zKbf+72FLBUNh145ksmvDMfLKU1X7KxUGqPiUCX4qn67jyXlw4LE+qJ2uiJmgBPb8QK9m30Riz0Rte2pCPYqYeowRjS2QM8pTFfUpgrScyUJOZKCrNFidmSwmxwuxrC6YTuN/UsodEXlRiMmeDNQDBWb/dGuSQVEREREdFuF3d0rQvExbQGcp6F2WL9uvZmf7bNQjwAkHU1sq6Ply/RkQcwXXmG6tpgD8ZMW+zB4PZQzMZAnMU1op3mStMRZyrn41RO4mTWx8mcj1NZH1M52dIgDgB0RyT2pUxHnOo4kfIRczpkthURERERUQOF1nXj2VxFmiDPQtmEdhbKDhbLFhaCbjwL5fbtyLMZU2eQeCW7vQ6eERvoiZhltXqCbd1+1EJ32IR8qvd1hS1OJiK6AgzpdKiSrzFXklgoK8yXJeZLat3+fNmEcmaLCouVDkve1AlZGv0xE74x21oQZyAm0ReVsNunnk5ERG3mH772EADOwiIi2suEANJhhXRY4VDX5iGevCdqoZ3quvZzxbW22O04i67aleeFyzwu7ohacMe0wzYz5QaCNtimHbbZuiIWLAZ6aI+rBCGcM3kfZ/ISZ3Jm/2zB7F8oSrRD3CXuKEwkgyBO2se+lIf9KQ+ZSOfWgIiIiADWcoio9SJ2fTffzfkKWKrYWCrbWCxbZqzYWCybbSkYC37n/RGzIoHpoll55UokHIGusIVMxIxdQXinq3o7OJYJW0iHhRlDApkIJxjR3sOQThvwlVlmarGisFhWWKooLJXXbi+WZe3+hbLCQkkh77dDSejapUMS/bG1bSDmB6PZ7+JyVEREdA0+/7E/BsDCDhERbU0IIBXWSIW9Ldthl3yB+aD7znzJXhfimS+ZwpvU7fnBpehrnMpJnMpdfsacI0yHHtPieq3ldXV2XO123RhnIY06SMnXmC6aoM10wYwXgnG6KHG+IDFTVG0RwqlKhhT2pTxMJD2MJ31MBPu9UQVeekREtBuxlkNEncCxUGswcCllX2CpYtWCO9Vgz3LFwlLFxnLFxlLZQq4NJwddqYKvUfAlzhev/LmWAFKhILgTtpAJC6RDFlLVMSSQDMZUOBhDJuxTvS8REkg4gpOPqCMwpLNDKlIj6yrkPDOuuhorrsJKRWHFVViumP1lV2GloteOuQpZt53KPzsnaiv0RetDOD766273xSSi9u783omIiIiIaPeIORoTKR8Tqc2XoJIaWKlYmA9CPGZde7t227TCbv+Cm6+BmZLCTEkBuPRyW1URG+gOZsN1BzPiusLCtLuOWLX7qrPnTBHNFNI4U452gq900FlYYaEkMVdWmA86D8+VzP6FIJizXGnfGkRf1MdY0sdoohrEMWNXmGEcIiIiIqJOFXU0RhyJkUt05QEAT2JdaGfZtXF+qYRVL4SKlcRyxcJyxcZKxUK5jZbs3ilKA6uuxqorAWxvWa6tJBxRC+wkQxaSdfuJkEDcMbfjjkDMEUg4ZgLSxVsiJBC1zX7UNo9lAIh2yp4M6fhKoyQ1KlKj5GsUfY2Cp5H3NQqeQiE4lvfWblfvz7kK2SCIUwvleAqVa/t50XGSIYW+qI++qERv1ARu+qLBFuzHHc1CEhERERER7Xq2AHqjCr1RF6/q3vwxnqpb075sY7G0tl9d036pYkO1aUeerVRkfbDnylgCSIbMrLhqq+tUSCAdjHHHFNCSQXEs7lhBYU0ERTdzOxYUzKK2QMQGgz8dSGuNsgSyrqqb8KSxWjf56eLJUAvBUt9LHbTEd9RWtSDOWNLDWGItmBN12jdAREREREREjRWygcG4xGB87Q/Oc7E5AMDAwMC6x5Z8gZUgtLNcsbDqmvDO2ri2n3UtaOytz8imo0/189XO/gE/bAExRyBmC0QdgXgwrtUk1moTUVsgvMnxSHA7ZAlELCBkC0QsgbANc8wWCFnmcWFLwLHM8bAFOJa5L2QJOIL1j07WFiGdc3kff3uqBKURbBoKgNaAgjmmtYavAFeZ0VMarjKBG692fG2/Ik2BpxwEccp1oZxdslJUQ0Qshd6oRE+0Okr0RoIxKtETMcdZPCIiIiIiItq+kLWx4Haxakee2vr1lbV17JfKphX2QtlG1m3/rjzboTSQdTWyrgQKO/OaAqYQFnVQK5JVi2fVAle1sFUtgDkCCAcFsrV9wIKAECZMZAnAAmAJse72vxt3MBnfmXPvNOfyPr72SgkyqNeoYPQ1ILWGVOb/6bI0E6FK/tqkqFJQNK1OnCr6uq2WmLoWUVthJOFjKO5jJCExEvcxlPAxluASVUREREREdO1ijkbMkRi+THcewHwmy7kWVioWVlwbWdeqbavB7dXabXPMV/zQshVXAa6rsdomn2BrgR0LCAkzOkLAtsyS5k5Q57Ct6n3mmCUAWwjYArXNqt62LrrPEkE9pLqZ2+vrJeY1Rd1xAUDA7KzdrtsPPhxXn1PbD763zY7ViE13g+dd/v/f/33Ubnktpy1COlM5iU88k231aexq6bBEd0ShOyLRHTFhm+6IRHfUHO8JgjgJdr8hIiIiIiJqibWOPAqAt+Xjqm2wl4JZc8sVG8vltf3643utuKYBlKRGSVZvNdar+/ow2dXwL9OWpnISn/rXvVnL6QpLDMQkhhM+hhM+RuJmHI776I4wiENERERERO3BFkBXRKErsr1lrbUGSlIg61rIuRZyngnw5Dxze92+ZyPnWsh7Anlv73XsaQde0NjEaI/gUCe49adbX8tpi5AOXTlbaHSFFTIRia6IQiZsxuqx7mDsiZgxtPuWJyQiIiIiItqTNmuDvRmtgbwnsFSxsVKxseJaWA3CO6uuhZW6ccW1UPL5wZEIALojEgMx31xnMR8DcRPKqe5HbRY/iYiIiIho9xECiDsacUdi6DI1h3pKA0XfhHVqm2vGnLd2vOBbKHgWCp5Y2/cFKpL1CNpbhNY7W1gQQvwigF/czmOPHz/+b/v7+8OrFYXDS1vPEtwLLKFhCQVbaNhCwVo3rj9mCw1LsCBERER0OaeeewUAsP+2gy0+EyIiovanNSC1BaUFpLYgtbho34y1x0AAem/PlLulJ4RMxAKA85lMZqzV53O19lItx7YUHKFgCwXHCsaL9tkJh4iIqHVYyyEi2ptM/UFAV0eYmoTSAqpuf7PjOtjXe7xGQdvTDrWcRnTSmQRw53YeGA6HAQCZiIXXDEcacCpERES0l42+ZrjVp0BERER7gOu6Pa0+h2s0CdZyiIiIqA2wlkNERETN0MpaTiNCOlMAvrOdB549e/Y1AGzXdd3+/v4nG3AuRHvWc889d1s+n88kk8nV22677blWnw/RbsFri6hxeH0RNQ6vL6LGmJ+f/7fhcDg8Nzcn+/v7W30612IKrOUQtRx/XxM1Bq8tosbh9UXUOLy+iBqjHWo5O77c1RV9cSEegZmp9R2t9WtbdiJEuxCvL6LG4LVF1Di8vogah9cXUWPsxWtrL37PRM3C64uoMXhtETUOry+ixuH1RdQY7XBtWa34okREREREREREREREREREREREewlDOkREREREREREREREREREREREDcaQDhERERERERERERE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\n"
          },
          "metadata": {
            "image/png": {
              "width": 1140,
              "height": 659
            },
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jTqKXlGRmKuh"
      },
      "source": [
        "The posterior probabilities are represented by the curves, and our uncertainty is proportional to the width 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 tighten 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 (with no prior opinion, how confident would you feel betting on a fair coin after observing 8 tails and 1 head?). As more data accumulates, we would see more and more probability being assigned at $p=0.5$, though never all of it.\n",
        "\n",
        "The next example is a simple demonstration of the mathematics of Bayesian inference."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5UKnxit-mevN"
      },
      "source": [
        "## Example: Bug, or just sweet, unintended feature?\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 $∼A$, spoken not $A$), or event $X$ without bugs $(A)$. $ P(X)$ can be represented as:"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7rDu4o6DnjT7"
      },
      "source": [
        "$$ \\begin{align*}\n",
        "P(A|X) &= \\frac{P(X | A) P(A) }{P(X) } \\\\\n",
        " P(X) &= P(X \\text{ and } A) + P(X \\text{ and } \\sim A) \\\\\n",
        "  &= P(X|A)P(A) + P(X | \\sim A)P(\\sim A) \\\\\n",
        "  &= P(X|A)p + P(X | \\sim A)(1-p) \\end{align*} $$\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S48e_3wph3I_"
      },
      "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",
        "$$ \\begin{align*}\n",
        "P(A | X) &= \\frac{1\\cdot p}{ 1\\cdot p +0.5 (1-p) } \\\\\n",
        "&= \\frac{ 2 p}{1+p} \\end{align*} $$\n",
        "\n",
        "This is the posterior probability. What does it look like as a function of our prior, $p\\in[0,1]$?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MwjluXPenvAy",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 410
        },
        "outputId": "f6216442-56ec-4376-859a-aa5bfd30878e"
      },
      "source": [
        "# Define range of probabilities\n",
        "p = linspace(start = 0., stop = 1., num = 50)\n",
        "\n",
        "# Visualise\n",
        "plt.figure(figsize=(12.5, 6))\n",
        "plt.plot(p, 2 * p / (1 + p), color = TFColor[3], lw = 3)\n",
        "# plt.fill_between(p, 2 * p / (1 + p), alpha = .5, facecolor = ['#A60628'])\n",
        "plt.scatter(.2, 2 * .2 / (1 + .2), s = 140, c = TFColor[3])\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?');"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 900x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "image/png": {
              "width": 851,
              "height": 393
            },
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dvcD8UWloYxn"
      },
      "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 $1 \\text{-} p$ 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 $1 \\text{-} P(A|X)$ is the probability there is a bug given all tests passed. What does our posterior probability look like? Below is a chart of both the prior and the posterior probabilities."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Aot_QO3n1r4o",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "outputId": "40ebb123-a19f-4a05-9e45-ee0f0163b492"
      },
      "source": [
        "# Define priors and posteriors\n",
        "prior = array([.20, .80])\n",
        "posterior = array([1. / 3, 2. / 3])\n",
        "\n",
        "# Visualise\n",
        "plt.figure(figsize = (12.5, 4))\n",
        "colours = [TFColor[0], TFColor[3]]\n",
        "plt.bar([0, .7], prior, alpha = .7, width = .25,\n",
        "        color = colours[0], label = 'Prior distribution',\n",
        "        lw = 3, edgecolor = colours[0])\n",
        "plt.bar([0 + .25, .7 + .25], posterior, alpha = .7,\n",
        "        width = 0.25, color = colours[1],\n",
        "        label = 'Posterior distribution',\n",
        "        lw = 3, edgecolor = colours[1])\n",
        "\n",
        "plt.xticks([.20, .95], ['Bugs absent', 'Bugs present'])\n",
        "plt.title('Prior and Posterior probability of bugs present')\n",
        "plt.ylabel('Probability')\n",
        "plt.legend(loc = 'upper left');"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 900x288 with 1 Axes>"
            ],
            "image/png": 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          },
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            "needs_background": "light"
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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Xl6KbBeoCkiM"
      },
      "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": {
        "id": "2zNt6157C0Cr"
      },
      "source": [
        "## Probability Distributions\n",
        "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",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xG03a_sgDRlc"
      },
      "source": [
        "### Discrete Case\n",
        "\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",
        "\n",
        "$\\lambda$ is called a parameter of the distribution, and it controls the distribution's shape. For the Poisson distribution, $\\lambda$ 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",
        "\n",
        "If a random variable $Z$ has a Poisson mass distribution, we denote this by writing\n",
        " \n",
        "$$Z \\sim \\text{Poisson}(\\lambda) $$\n",
        " \n",
        "One useful property of the Poisson distribution is that its expected value is equal to its parameter, i.e.:\n",
        "\n",
        "$$E[Z| \\lambda ] = \\lambda $$\n",
        "\n",
        "\n",
        "We will use this property often, so it's 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 of larger values occurring. Second, notice that although the graph ends at 15, the distributions do not. They assign positive probability to every non-negative integer."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7x8Y_YtNqoPY",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 517
        },
        "outputId": "bc913680-29d7-40ea-dd23-3f60769c9450"
      },
      "source": [
        "x = arange(start = 0., stop = 16., dtype = f32)\n",
        "tates = array([1.5, 4.25])\n",
        "lambdas = array([.5, 1.])\n",
        "poi_pmf = Poisson(rate = tates[:, newaxis]).prob(x)\n",
        "\n",
        "# Visualise\n",
        "plt.figure(figsize=(12.5, 8))\n",
        "colours = [TFColor[0], TFColor[3]]\n",
        "for i in {0, 1}:\n",
        "    ax = plt.subplot(2, 1, i + 1)\n",
        "    ax.set_autoscaley_on(False)\n",
        "    plt.title(\"Probability mass function of a Poisson random variable\");\n",
        "\n",
        "    plt.bar(x, poi_pmf[i],\n",
        "            color = colours[i],\n",
        "            label = fr'$\\lambda = {lambdas[i]:.1f}$',\n",
        "            alpha = .6,\n",
        "            edgecolor = colours[i],\n",
        "            lw = 3)\n",
        "    plt.xticks(x)\n",
        "    plt.ylim([0, .5])\n",
        "    plt.legend()\n",
        "    plt.ylabel(r'Probability of $k$')\n",
        "    plt.xlabel(r'$k$')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 900x576 with 2 Axes>"
            ],
            "image/png": 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          },
          "metadata": {
            "image/png": {
              "width": 842,
              "height": 500
            },
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ipS19FlBEmqK"
      },
      "source": [
        "### Continuous Case\n",
        "\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 *exponential density*. The density function for an exponential random variable looks like this:\n",
        "\n",
        "$$f_Z(z | \\lambda) = \\lambda e^{-\\lambda z }, \\;\\; z\\ge 0$$\n",
        " \n",
        "Like a Poisson random variable, an exponential random variable can take on only non-negative values. But unlike a Poisson variable, the exponential can take on *any* non-negative values, including non-integral values such as 4.25 or 5.612401. This property makes it a poor choice for count data, which must be an integer, but a great choice for time data, temperature data (measured in Kelvins, of course), or any other precise *and positive* variable. The graph below shows two probability density functions with different $\\lambda$ values. \n",
        "\n",
        "When a random variable $Z$ has an exponential distribution with parameter $\\lambda$, we say *$Z$ is exponential* and write\n",
        "\n",
        "$$Z \\sim \\text{Exponential}(\\lambda)$$\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",
      "metadata": {
        "id": "o1aeMH4VE9xs",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "outputId": "87eea0af-eb3d-4e64-db96-3b9d91bd27ac"
      },
      "source": [
        "# Define data and assumptions (use linspace for continuous)\n",
        "a = arange(0., 4., .04)\n",
        "a = a[..., newaxis]\n",
        "lambdas = array([.5, 1.])\n",
        "\n",
        "# Now use TFP to compute probabilities in a vectorised manner\n",
        "exponential_pdf = Exponential(rate = lambdas).prob(a)\n",
        "\n",
        "# Visualise the results\n",
        "plt.figure(figsize = (12.5, 4))\n",
        "for i in range(lambdas.shape[0]):\n",
        "    plt.plot(transpose(a)[0],\n",
        "             transpose(exponential_pdf)[i],\n",
        "             lw = 3,\n",
        "             color = TFColor[i],\n",
        "             label = rf'$\\lambda = {lambdas[i]:.1f}$')\n",
        "    plt.fill_between(transpose(a)[0],\n",
        "                     transpose(exponential_pdf)[i],\n",
        "                     color = TFColor[i],\n",
        "                     alpha = .33)\n",
        "plt.legend()\n",
        "plt.ylabel('PDF at $z$')\n",
        "plt.xlabel('$z$')\n",
        "plt.ylim(0, 1.2)\n",
        "plt.title(r\"Probability density function of an Exponential random variable; differing $\\lambda$\");\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 900x288 with 1 Axes>"
            ],
            "image/png": 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u/1h47p80cX1JWhOFdIw378ny+p1ZMomw6Ny5asRnHpvh4/dNcGbajp2SJEmSJEmSNq5mhkh1YDKKnvfr9zNAawghfvHEKIqmgSngmiauL0lrJoTA7o4k77++wL6tySXnHx2v8LF7xvjSoRkqNauSJEmSJEmSJG08zQyRTtEIjC6+57GFNV5+8cQQQhuNc5FSTVxfktZcOhF47WCWt+3L0Zpe/C20FsHfHi7ykXvGODhSXqcdSpIkSZIkSVJzNDNEegpIANddNHYPEICffcHcX1x4fKKJ60vSuultSfCe6/K8vDvF4g3uYHi2xie/M8EfPDTJ5FxtXfYnSZIkSZIkSavVzBDp72kERu+4aOw3gArwv4cQDoQQ/jSE8Ajw0zTORPqtJq5PCOFHQwj3hBAmQwgzIYT7Qwg//YLqqJXcLx5C+JchhG+EEEZDCHMhhBMhhC+EEN7ZzL1L2ngSscCt/RnevT/PttzSbzMPnp7nv9w9xl3PFKnb4U6SJEmSJEnSFS7RxHv9ObALmD0/EEXRUyGEfwr8DnDDwhc0AqRfi6Lo95q1eAjhk8BPAXPAV2mEV28CPgG8KYTwgSiK6iu431bgb4HbgDHgPhr/btuBHwLOAl9o1v4lbVwduTjvuDbPk8NlHjg9T3WRd5q5asRfPDFDZ7rAG7pK7Fu/bUqSJEmSJEnSijQtRIqiaBT4v19k/M9CCF8B3gYMAJPAV6IoOtSstUMI76cRIA0Bd0ZRdHhhvBv4OvBe4F8BH1/m/WLAX9MIkD4O/FwURXMXPd8C7GzW/iVtfLEQuKErzWBbkntPzHFyqrro/OH5OJ85kedUmOKd1xbIp5pZGCpJkiRJkiRJq9fMSqRLiqJoBPjjNVzi3y88/rvzAdLCumdDCD8J3AX8XAjhN5ZZjfTPgTuAv4mi6N+88MkoiqaBA6vftqTNppCO8eY9WY5PVPn2yTmKlcX61gW+9ewcjwzN857rCryqP0MIS52wJEmSJEmSJEnrY8P/6nsIYQC4BSgDn33h81EU3Q2cAnqAVy/zth9eePzVZuxR0tUlhMDOLUnef32BG7tSLBULzZQj/uSRaT7+7QnOTC9ewSRJkiRJkiRJ62XDh0jAKxceH4+iqHSJOd97wdxLCiH0AjcCNeC+EMI1IYT/J4Tw2yGEj4QQ3hosFZC0DMl44FUDGd69P09XPr7k/KfHKnz0njH+6skZ5hc7WEmSJEmSJEmS1kGIosVaLV35Qgg/Q+Pcor+Koui9l5jzceBngF+Jouhnl7jfDwN/B5wDPgr8Mt/f9u9e4L1RFJ1b5h5/DPix5cy96667brrpppvaisUip06dWs4lV40zpTgni3HS8YhsfGO/bnX1iSI4VUpwcCpFJVo6hy4k6tzZWWJPoYqxtSRJkiRJkqTL1d/fTy6XA7i7ra3t9Su5dl3ORFpjhYXH2UXmzCw8tizjfh0XPf4q8L+AXwROArcCn6RxXtJngdctc487lzt3ZmZm6UmSNpwQYCBXpStT5ampFCdLyUXnz1RjfOlMnu25Cnd2zrE1bWWSJEmSJEmSpPW1GUKkZjvf4i8BfDOKoh+96LmvL1QqHQLuDCG8IYqiry/jnseAu5ezeKFQuAloy+Vy7Nu3bwXb3vzOPHoUgO6uLvKpzdCJUVerwX544vhZHp9MMV1dvM3diWKS//Vskjt3Znn7vjzZpK99XVkOHz4M4M8sbQq+nrWZ+HrWZuLrWZuFr2VtJr6etZn4el7cZgiRzpfu5BeZc75aaXoZ97t4zu++8Mkoik6GEL4IfAB4A7BkiBRF0R8Cf7iMtZmcnLyL5Vc4SdqgtqTq3LFtjolEBw+cnmexI5DqEdz1TIkHTs3xzv0Fbh/IELPHnSRJkiRJkqQ1thl+pf3YwuPgInO2v2DuYp65xD+/2JyeZdxPkl5ULMANXWnef32BXe1LZ/rT5YhPPzrNr3xrnGPjlXXYoSRJkiRJkqSr2WYIkR5aeLwhhJC9xJzbXjB3MU/x3PlKWy8xZ9vCowcYSVq1fCrGG3bneMveHK3ppd+Wn52s8iv3jvMnj0wxNe9ZSZIkSZIkSZLWxoYPkaIoOgE8CKSAD77w+RDC64ABYAi4bxn3qwB/s/Dtm17kfkngzoVv77+8XUvS9+tvTfDe6/Lc2pcmsYx35++cnOMX7xrla0eL1OrR2m9QkiRJkiRJ0lXlskOkEMLPhBB+opmbWYWPLDx+LISw9/xgCKEL+M2Fbz8aRVH9ouc+HEI4GEL4o0vcrw78ixDCWy66Jg58DNgDnAI+39x/DUlXu3gs8PKeNB+4vsCeLckl589VIz7/5Awf+cYYB4fL67BDSZIkSZIkSVeL1VQi/TrwCy/2RAjh90IIf7GKe69IFEWfA36LxhlFB0IIXwgh/CVwGLge+CvgEy+4bBtwLbDjRe73CPBvgCTwtyGEb4cQPgccAv4tMAl8MIqi0hr9K0m6yuVSMV63K8vbr8nRkV36rfrsbI1PfneC371/kpFibR12KEmSJEmSJGmzW207u3CJ8bcD71nlvVckiqKfAv4xjdZ2rwPeAhwBPgy8P4qiFX2qGkXRbwBvBL4E7AXeBSSA3wFuiqJoydZ4krRaPYUE79qf547tGdLxS73lPufRs/P80t2j/PXBGUoVz0uSJEmSJEmSdPkSL/UGmimKok8Dn17m3J8Hfn6JOXcBd61yW5K0KrEQ2N+ZYteWJA+emePgcIXFTkCq1uEfni7y7RMlfuTaAq8eyBCPLR1ASZIkSZIkSdLFVluJJElaJ+lE4DXbs7xrf56eQnzJ+dPliD87MM3Hvul5SZIkSZIkSZJWzhBJkjaYrbk4b9uX4/U7s+STS1cYnZlunJf0W9+dYGi6ug47lCRJkiRJkrQZbKp2dpJ0tQghsLsjyfa2BI+enefA2TL1xXrcAU8Mlzk4MsYP7Mjy9mvyFFL+HoEkSZIkSZKkS/MTREnawJLxwC19Gd53fYGd7Uv/XkA9gnuOl/iFr4/y1aNFKrUlkidJkiRJkiRJV63VViJ1hBC+9mLjAJd47mJRFEVvWuUeJOmq15qO8cbdOYZmqnzn5Byjxfqi80vViL96coZvHi/x7v15XtGTJoSlW+NJkiRJkiRJunqsNkRKAa9f5PnFngPwV+AlqYl6CgnedW2ep8cq3H96nmJl8bfZkWKN33twir0dSd57fYEdbcl12qkkSZIkSZKkK91qQqRPNW0XkqSmCSGwd2uKwfYkj50rc+DsPNXFC5M4Mlbh//3mOLf2pXnHtQW25uLrs1lJkiRJkiRJV6zLDpGiKPrxZm5EktRcyXjglb1prtma5MHT8xweqyx5zf2n53l4aJ7XDmZ5y948+ZRH50mSJEmSJElXKz8dlKRNLp+K8dqdWd61P09PYekKo2odvv5Mif/89VH+/sgs5ZqdRyVJkiRJkqSr0ZqESCGEeAihc+HLnkiSdAXYlovztn053rg7S0s6LDm/VI34wlOz/OJdo9z3bIl6ZJgkSZIkSZIkXU2aFiKFEH4khPCnIYRngTIwtPBVDiEcDyH8SQjhbc1aT5K0ciEEdrYned91BV7Vnya1jJh/Yq7Opw9M85FvjHHg7DyRYZIkSZIkSZJ0VbjsM5HOCyH0AZ8Dbj8/9CLTtgMfAj4UQrgX+GAURUOrXVuSdHniscCN3Wn2bk3y8JkyB0fK1JfIhoZmavzO/ZPs6Ujy7v0Fdm1Jrs9mJUmSJEmSJL0kVhUihRC2At8B+miER+eArwIHgPGFaVuAlwFvArqAO4D7Qgi3RFE0tpr1JUmrk0nEePX2DNd3pXjw9BxHx6tLXvP0WIVfvXecV/Skeee1eboLq/59BEmSJEmSJElXoNV+8vebQD8wB/ws8LtRFFVebGIIIQn8C+CXgR3AJ4AfXeX6kqQmaE3HeP2uHDd21/jeqTnOTNeWvOaRoXkOnJ3nju1Z3rYvR2vGI/AkSZIkSZKkzeSyz0QKIewEPgDUgPdEUfSblwqQAKIoqkRR9EngfUAE/KMQwo7LXV+S1HzbcnHeujfHW/bm6Mgu/SOiHsE3ny3x818f5f87OMNsub4Ou5QkSZIkSZK0Hi47RKJxxlEAPhtF0d8v96Ioiv4O+OzCtVYiSdIVJoRAf2uCd+/Pc+dghkLqxY66e75KHb7ydJGf//ooXz48y1zVMEmSJEmSJEna6FYTIr2KRkXRH17GtX9AI0S6fRXrS5LWUAiBvVtTvO/6Aq/qT5OOLx0mzVUjvnholv/89VG+drRIuRatw04lSZIkSZIkrYXVhEg3Ljx++zKuPX/NjYvOkiS95BKxwI3daT5wQ4GXdadYRpbETDni80/O8It3jfLN4yVqdcMkSZIkSZIkaaNZTYi0BZiLomhqpRcuXFNauIckaQNIJwK39Wf4wA0F9m1NsowsiYm5On/+2DT/5e5RvndyjnpkmCRJkiRJkiRtFKsJkVqBFQdIF5leuIckaQPJp2K8djDLe67LM9ieWNY1I8U6f/TIFB/9xhiPDM0TGSZJkiRJkiRJV7zlffp36WtX8ylgBMRXcb0k6SW0JRvnTbtzjMzWeODMHKemaktec2amxv98YJIdbQnecW2e/dtShLCcmiZJkiRJkiRJ6201lUiSJLEtH+cte/O8fV+O7vzyfjfg2ckqv/ndSf77tyc4PFpe4x1KkiRJkiRJuhyrqUQC6AghfO1yr13l2pKkK0hPS4K3XxPn1FSNB07PMVqqL3nNkbEK//3bE+zrSPK2a/Ls25pah51KkiRJkiRJWo7Vhkgp4PWruN5DMbQinWefpb00Qm33Xuqp9Eu9HUkvEEJgoC1Bf2ue4xNVHjwzz8Tc0mHS4bEKhw2TJEmSJEmSpCvKakKkTzVtF9IyXf/YvQycOEwUYsz272BmcB8zO/cxs3039XTmpd6epAUhBHZuSbKjPcHTYxUeOjPPTHnp3xswTJIkSZIkSZKuHJcdIkVR9OPN3Ii0pHqdrqFnAQhRncLJYxROHoNv/QNRiFHs28H0TkMl6UoSC4F9W1Ps3pLk8GiFh4fmKVZWECZtTfK2fYZJkiRJkiRJ0kthte3spHXTdvwoqcr8iz4Xojr5U8fInzr2/FBpcG8jVNqxx1BJegnFY4H9nSn2bk3y5HCZA2fLzFWXESaNVjg82giT3r4vz17DJEmSJEmSJGndrDpECiGkgfcAtwCtwATwHeALURRVV3t/6bz208eXPfd5odK9X2mESr3bmRncu/C1h1omt3ablfSiErHAy7rT7N+W4uDIysKkjxsmSZIkSZIkSetqVSFSCOEO4LNAz4s8fSyE8J4oig6sZg3pvNbhM5d9bYjq5E8fJ3/6ON33fZWIQKmnn5kde5nZuZfpwb3UcoUm7lbSYpLx58KkJ4fLPHZu5WHSW/fm2bc1SQhhHXYsSZIkSZIkXX0uO0QKIfQDfwO0AQGoAyNA58L3u4AvhRBujKJosgl71VVubGAXxWqMrsmzpOZLq7pXICI3dJLc0Em6vnsXAKXOHmYG9zEz2AiVqi1tTdi1pMUk44GX96S5rnPlYdLh0Ql2tSf44b15buhKGSZJkiRJkiRJTbaaSqR/DbQD4wv//JkoisohhAzwz4CPAX3ATwC/utqNSiM7r+F0YSedWwp0VGZoOXuCwtBJWs6eJDlXXPX9s8NDZIeH6Lz/HgDmOjoXWt/tY2ZwD+W2DvBDamlNXG6Y9MxEld++f5KB1gQ/vDfHK3rSxPxzKkmSJEmSJDXFakKkNwMR8DNRFP3p+cEoiuaATyyESb8M/DCGSGqmEJhv62C+rYORa14BUUR6arzpoVJmbJjM2DDbHroPgHLrFmYG9zCzYw8zg3uZ29ZjqCQ12QvDpANny8zXlg6TTk5V+f0Hp+jOx3nz3hy39mWIx/zzKUmSJEmSJK3GakKk3TRCpL+4xPOfpREi7V7FGtLSLhkqnaRw9iQtZ0+QLK0+VEpNjdNx4H46DtwPQDWbfy5U2rGXYu8AxOKrXkfS5YdJZ2dr/Mkj03zp0Cxv3pPn9oEMybhhkiRJkiRJknQ5VhMitQBnFyqPvk8URccXzqfIr2INaeWeFyq9vBEqTU9QuBAqnSJVnF71MonSLO0HH6X94KMA1FJpZgd2XahUmu0fJEqmVr2OdDW7OEx6YrjMY8sMk8ZKdf78sWn+9vAsb9qd4wd2ZEknDJMkSZIkSZKklVhNiASNSqSl+KmdXlohMN+6hfnWLYzuexlEEanZqYVQ6RSFcyfJTE+uepl4eZ7WowdpPXoQgHo8QbFvBzPbdzO7Yw8z23dRyxVWvY50NUrGA6/oSXN9Z4qnRhqVSaVlnJk0NV/n80/O8PdHZnn9rhx37sySS8bWYceSJEmSJEnSxrfaEEnaeEKgXGhjrNDG2J4bAEgWZy5UKhXOnSI7ObbqZWK1KoUTRymcOAr3fgWAUmcPM9v3MLvQBq/c1uG5StIKJOOBG7vT7O9McXi0woGz88yUlw6TZisRXzw0y1ePFnntYJbX78zSmrH9pCRJkiRJkrSY1YZIHSGEr61iThRF0ZtWuQdp1Sq5AuO79jO+az8AiVKRwrlGoFQ4e4rs+HBTSuqyw0Nkh4fofPBbAJRb2pnZsVCptGMPpa4+iFklIS0lEQtc15ni2m1Jnh6r8OhQmcn5+pLXzVUj/uHpIl9/psjtAxneuCtHV8Hfp5AkSZIkSZJezGo/OUsBr1/FnOW0w5PWXTWbY2LwGiYGrwEgXp4jP3xmof3dKXKjQ8TqS39gvZTU9AQdjz9Ix+MPAlBLZ5gZ2LXQ/m43xf5B6qn0qteRNqtYCOzbmmJPR5LjE1UeGZpnrLT0n81qHb717Bz3PjvHy3vS/NCeHDvbk+uwY0mSJEmSJGnjWE2I9Kmm7UK6wtVSGab6dzHVvwuAUK2SHx26cKZSfvgM8Wpl1evE5+doe/pJ2p5+EoAoxCj2DjC7fXfjbKXtu6m0tq96HWmziYXAri1JdrYnODlV5eGhMsOztSWvi4BHhuZ5ZGievR1JfmhPjus7UwTbTEqSJEmSJEmXHyJFUfTjzdyItJFEiQQz3QPMdA8At0O9Tm783IVKpcK5UyTm51a9Tojq5E8/S/70s3R95y4A5ts6mN3xXKhkCzzpOSEEtrclGWhNcGamxiND85yZXjpMAjgyVuHI2CR9LXHetDvHLX0Z4jHDJEmSJEmSJF29PAhCaoZYjOLWHopbezh3/S0QRaSnxhcCpdMUzp0iPTPZlKXSk2OkD4zRceB+oNECb3ZgJzPb9zC7fTez/YPU05mmrCVtVCEE+loS9LUkODdb5ZEzZU5MVZd17enpGn/8yDR/89Qsb9id447tGdIJg1pJkiRJkiRdfQyRpLUQAvNtHcy3dTC672UAJIsz5IdPXwiWsuPDhGj1x4LF5+doffogrU8fBCAKgVJ3P7MDu5jdvouZ7bspt28F23PpKtWVT/DmvQnGSzUOnC3z9FhlWQfyjc/V+csnZvjy4VleO5jldTtztKQNkyRJkiRJknT1MESS1kklV2Bi8BomBq8BIFYpkx8+cyFUyo+cIVZbXqXEYkIUkRs6SW7oJJ3339NYO9+ycK7SLmYHdlHs20GUSK56LWkj2ZKNc+fOLDf3pXn8XJmnRspU60tfV6xE/N2RIl89WuRV/RlevytHb4s/PiVJkiRJkrT5+SmY9BKpJ1NM9w0y3Te4MFAjN3qOwvDphYql0yTnik1ZKzk7TfvBR2g/+EhjqVicYt92Zgd2M7u9UbFUaWlvylrSla6QinH7QIabetIcHCnz+Lkyc9Wla5Oqdbj3xBz3npjjus4Ub9yV49ptSYJVfpIkSZIkSdqkDJGkK0UsTrGzl2JnL9A4Vyk1M9moUloIlbKTo81Zql6jcPIYhZPH4NuNsfm2LRQHdjEz0KhWKvX0W62kTS2dCLyiJ80NXSmOjFZ47FyZqflllCYBTw6XeXK4TG9LnDfsynFrX4Zk3DBJkiRJkiRJm4shknSlCoFySztjLe2M7bkeaJyXpmpOAAAgAElEQVR/lB85cyFYyo8MNaUFHkB6cpz05DhbHn8QgHo8QbF3e+NspYGdjWql1i1NWUu6kiRigf2dKa7ZluTZiSqPnp1npLi8MOnMdI1PPzrNFw7O8IODOV47mPXcJEmSJEmSJG0ahkjSBlJLZ5jq38VU/67GQL1Gbmz4uVBp+DSp0mxT1orVqhROPkPh5DMXxsqt7c+FSgO7KPZut1pJm0YsBHZuSTLYnmBopsaBs2VOTi0vpJ0uR/zt4Vn+4elZbuvP8AbPTZIkSZIkSdIm4Cdc0kYWi1Pc1kNxWw9wM0QRyeI0hXNnLoRKufFhQrT0eS/LkZqaIPXEQ2x54iGgUa1U6ulntv98sLSTcvtW8IwYbWAhBHpbEvS2JBgr1jhwrswz4xXqy/hjVK3DfSfmuG/h3KQ37Mqyf1vKc5MkSZIkSZK0IRkiSZtJCFTyrYzvamV817UAxCoVcmNnyZ873WiFN3yaxPxcU5aL1arkTx0nf+o4fLcxVskVKA7sZLa/ESrN9g1Sz2Sbsp603jpycV63M8ttfWmeGC7z1EiF+dryQtkL5yYV4rxuV47b+jOkPDdJkiRJkiRJG4ghkrTJ1ZNJZroHmOkeaAxEEenpiYVKpUaolJkYpVkfbSeLM7Qdeoy2Q481liMw19lzIVQqDuyk1NkLMc+N0caRS8W4tT/DTb1pjoxWeOxcman5ZZ6bNFPjzw5M89cHZ3jN9iw/OJhlWy6+xjuWJEmSJEmSVs8QSbrahMB86xbmW7cwtucGAGLlefIjQ+RHzpAfPkN+5AyJ8nxzliMiO3yG7PAZtj18HwC1VJpi3w5m+3dS7B9ktn+QSuuWpqwnraVELLC/M8W125KcmKry+LkyZ6Zry7q2WIn46tEiXzta5MbuFK/bmeOarUlb3UmSJEmSJOmKZYgkiXoqzXTfINN9g42BKCI9NX4hVCoMnyEzMdK0aqV4eZ6WY4dpOXb4wli5pW0hUNrJbP8gxb4d1NO2wdOVKYTAjrYkO9qSjBZrPH6uzNFlnpsUAQfOljlwtkxPIc6dO7O8qj9DOmF1niRJkiRJkq4shkiSvl8IzLd1MN/W8Vy1UqXcqFZaqFTKD58hUW7O2UoAqelJUgcfpf3go8D5NnjdF1Ur7aTU1Qdx24DpyrI11wiCbu1P8+RwmYPDyz83aWimxmcem+ELB2e5fXuGOwezdOb90SxJkiRJkqQrg59USVqWejLFdO8Opnt3NAbOn600MkRu5EzjcWyYEC3vnJilNNrgDZEdHoKHv93YQyJJsXc7s32DFPt3UOzfyfyWbWA7MF0BcskYt/RleEVP49ykx8+VmVzmuUmlasRdz5S4+5kS13eleN3OLNduSxHztS1JkiRJkqSXkCGSpMtz8dlKu69rDFWr5MbONSqVFsKl9Ox005aMVSsUThylcOLohbFqJrdwvtIgxb7G+UrVlramrSmt1MXnJp2arvHkuTInpqrLujYCHj9X5vFzZbryce4czPKqgQzZpK3uJEmSJEmStP42VYgUQvhR4CeBlwNx4CDwB8BvRdHqyiNCCP8C+O2Fbz8ZRdGHV3M/aTOKEglmu/qY7eq7MJYozjTa4J0PlkbPEq9WmrZmYq5I69GDtB49eGGs3NJOsX/HQsVS43ylWibXtDWl5QghMNCaYKA1wdR8nSeHyxweLVOuLe/6c7M1PvfEDH/91Ay39GV47WCW7W3Jtd20JEmSJEmSdJFNEyKFED4J/BQwB3wVqABvAj4BvCmE8IHLDZJCCIPAf6PxS+L2FpJWoJorMLljL5M79jYG6nWyk6PkRoYWQqUhshOjhGh5Z8gsR2p6gtTBiQvnKwHMbe1qVCr17aDYt4NSzwD1VLppa0qLaU3HuH0gw829aZ4eq/DEcJmJueX9SCrX4L4Tc9x3Yo4dbQleO5jl5r4Mqbg/jiRJkiRJkrS2NkWIFEJ4P40AaQi4M4qiwwvj3cDXgfcC/wr4+GXcOwC/B8SAPwL+aZO2LV2dYjFKWzopbelkdN/LGkOVCrmxs88LlprZBg8gM3qOzOg5Og58D4AoBOY6exqt8Poa1Uql7n6ihJUeWjvJ+HOt7s5M13hiuMyzk8trdQfw7GSVP310mr98Yobbt2f4wR1Zugub4ke5JEmSJEmSrkCb5ZOnf7/w+O/OB0gAURSdDSH8JHAX8HMhhN+4jGqkf0mjoulngK3N2Kyk56snk8x0DzDTPXBhLFGaXThXaehCG7xEZb5pa4YoInvuDNlzZ9j68HcAiGIxSl19F0KlYt8OSl19EI83bV0JGq3u+loT9LUmmF5odXdoBa3uStWIu54pcdczJa7ZmuQHB7O8vDtNPGZ1kiRJkiRJkppnw4dIIYQB4BagDHz2hc9HUXR3COEU0A+8Grh3BffeBfwy8E0abfH+UzP2LGlp1Wyeye17mNy+pzEQRaSnxsmPDpEbOUt+dIjs2DCx+jI/dV+GUK+TGzpJbugkPPgtAOrxBKWeAYq92xvBUu92Sp29BktqmpZ0jFcNZLi5b6HV3bky48tsdQdwaLTCodEKrekYd2zPcMeOLFuyvj4lSZIkSZK0ehs+RAJeufD4eBRFpUvM+R6NEOmVLDNEWmhj9/s0/hv9RBRFUWNI0ksiBObbOphv62Bs9/WNoVqNzMTI84KlzORYU89XitWq5E8dI3/q2IWxeiJJqbufYu92Zvt2UOrbQamzB2J+cK/Ll4gFrt2W4pqtSc7O1jg4XObYRJX6Ml/OU/N1vnykyN8dKXJjd4o7tme5vitFzJ9dkiRJkiRJukybIUTatfB4fJE5z75g7nJ8GHg98HNRFB26jH1JWmNRPE5pazelrd1wTWMsVimTHTtHfnThjKXRs6RnJpu6bqxauRAsdS6M1RNJij39FHsXqpUMlnSZQgj0FBL0FBKUKnUOjVZ4aqTMTHl5aVIEHDhb5sDZMu2ZGK/enuE1A1k6cr4WJUmSJEmStDKbIUQqLDzOLjJnZuGxZTk3DCHsAT4K3A/8t8vf2oX7/RjwY8uZe9ddd9100003USwWOXXq1GqX3pSmpqYpz8de6m3oSpYuQF8B+hqt8JLzc7RMjtA6MULrxCgtkyNk5opNXTJWrVA4eYzCyWMXxmrxBFNbu5nc1sPUth4mt/UwvaWT6KJWeGfOnGnqPrT5dAGdHTA8H+fZYoLh+TiwvOqiibk6Xz5c5MuHZ9mRq3JjW5ldhSrxNShOOnz48NKTpA3C17M2E1/P2kx8PWuz8LWszcTXszaTzfx67u/vJ5fLXda1myFEaqqL2tglabSxa8aBKzuB1y1n4szMzNKTJK1IJZ1hrGuAsa6BC2OpueJCqDRyIWBKleebum68VmXLuVNsOfdcIFyLxZnu6FwIlXobwVJHF/WEb8e6tBCgK1OjK1OjVA2cKCY4UUpSri83DQo8W0zybDFJNl7n+tYKN7SVaU8t/+wlSZIkSZIkXX02w6eW51OX/CJzzlcrTS/jfj8D3An8QhRFj65mYxc5Bty9nImFQuEmoC2Xy7Fv374mLb85fOfEdwBobW0hn02+xLvRxtdOraePcWAcIIpIzU6TGz373NfYWRLNDpbqNdpHhmgfGQIeBiAKMUpdvZR6B55rh9fdTz2Vbura2jx2A7V6xPGJKgdHygzNLP/3HUq1GA+Mp3lgPM3ejiR37MhyU0+a5GWWJ53/LR1/Zmkz8PWszcTXszYTX8/aLHwtazPx9azNxNfz4jZDiHRs4XFwkTnbXzB3Me9deHxzCOGF1UM7z88JIdwIzERR9I6lbhhF0R8Cf7iMtZmcnLyLZVYtSWqiECgXWikXWpkYXPiBEUWkpyfJjZ0Pls6RHTtHotLcYClEdXJnT5E7e4qtDzfC0ojA/LYuij0DFHu2U+rdTrF3gFp2sbxcV5N4LLC7I8nujiTjpRpPjVQ4MlamvIL62SNjFY6MVfhcMnBbf4Y7tmfpa90MfzWQJEmSJElSM2yGT4oeWni8IYSQjaKo9CJzbnvB3OV4zSLP9S18Ta7gfpI2mhCYb21nvrWd8Z3XNsbOB0sLlUprFiwRkRk5S2bkLB2PPXBhfL5tC6We7RR7Bi4ES5WW9ka/M121tmTjvHp7nFv70zwzXuGpkQrnZpefJhUrEXcfK3H3sRI72hK8enuGW/oy5JKePydJkiRJknQ12/AhUhRFJ0IIDwI3Ax8E/uji5xeqiQaAIeC+Zdzv9Zd6LoTw88B/Aj4ZRdGHL3/Xkjasi4OlXesbLAGkJ8dJT47T/tRz3TYruQKlnoGFYKlRuTS/tROCAcDVJhEL7NuaYt/WFOOlGodGKxwZrTBfi5Z9j2cnqzw7OcNfPjHDy3vSvHogw7XbUsQMKiVJkiRJkq46Gz5EWvAR4LPAx0II90ZRdAQghNAF/ObCnI9GUXThBPEQwoeBDwPfjaLon6z3hiVtIpcIllIz54Olc42v0XMkynNNXz5ZnCF59CCtRw9eGKslU5S6+58Ll3oGKHX1EiVTTV9fV6Yt2Ti3D8S5tS/N8YkqT42WOTO9/Oqkah0ePD3Pg6fnac/EuH0gw+0DGTrzm+WvDpIkSZIkSVrKpvgkKIqiz4UQfgv4SeBACOErQAV4E9AK/BXwiRdctg24lkaFkiQ1VwiUW9opt7QzcVErvNTsNNmxc8ROH6dlcpS2qXGSc8WmLx+vlCmcfIbCyWcujEUhMLete6Ed3nMBUy1XaPr6unJcfHbS1HydQyNlDo9VKFWWX500MVfn744U+bsjRfZ0JLl9IMMre9NkEla7SZIkSZIkbWabIkQCiKLop0II3wR+GngdEAcOAr8P/NbFVUiS9JIIgXKhlXKhlfHWbQBsaWsjWZolN3qW7PmKpbFzpIozzV8+isgOD5EdHqLjwPcujJdb2xuBUvcApZ5+St39zHdssx3eJtSajnFrf4ab+9KcmKxyaKTCyakqy4+T4OmxCk+PVfjc4zPc1JtmgDj92eVXOEmSJEmSJGnj2DQhEkAURZ8GPr3MuT8P/PwK77/iayRpUSFQyRWYzBWY3L7nwnBirkh2bJjc2LkL4VJmemJNtpCamiA1NUHboccujNVSaUpdfY02eN39FHv6mevqo55Kr8ketL5iITDYnmSwPclsuc6h0QqHR8vMlJcfJ5VrEd89Ocd3KdCarPGDYZbb+jNsy8XXcOeSJEmSJElaT5sqRJKkzaKayTHdN8h03+CFsVilTHb8fLC08DgxSliDQst4ef772+ERmN/auRAqDSycudRPpaUdQmj6HrQ+8qkYr+xNc1NPiqGZGodHKxybqFBdwctqqhLnS4dm+dKhWXZvSfKqhXZ3uaTVbJIkSZIkSRuZIZIkbRD1ZIrZrn5mu/ovjIValczEKLmxYbLjjYql7PgI8Wql6esHIjKj58iMnmPLEw9dGK9m841AqbuPYnejHd5cVy9RItn0PWjthBDobUnQ25Lg1bUMx8YrHBqtcG52Za3qjo5XODpe4XOPT3NjV5rb+jNc35UiETNolCRJkiRJ2mgMkSRpA4viCUpbuylt7b5oMCI9PfG8qqXs+DCp0uya7CFRmqXl2CFajh16bgshxtzWLkrdfQsBk1VLG0kqHrhmW4prtqWYnGtUJx0Zq1CsLL/dXbUODw/N8/DQPPlk4Oa+DLf1Z9jZniD4GpAkSZIkSdoQDJEkabMJgfnWLcy3bmFi8JoLw4nS7EKwNNw4Z2l8mPTUOGvxcX6I6mRHhsiODMHjD14Yr2ZzjUCpq/+5gKmrlyiZWoNdqBnaMnFu7Y9zc1+a01M1Do+WOT5Zpb78PInZSsQ9x0vcc7xEZz7Obf0Zz0+SJEmSJEnaAAyRJOkqUc3mmc7mme7beWEsVqmQnWhUKjUqlkbIjg8Tr1XXZA+JUpGWY4dpOXb4wlhEYL5jWyNU6upnbiFcmt+yFYJn6lwpYiEw0JZgoC3BfDXi6HiFw6NlRoorO5NreLb2vPOTbutvnJ+UT/n/WpIkSZIk6UpjiCRJV7F6MslsZx+znX0XDdZJz0xeCJZy4wvt8Ioza7KHQERmbJjM2DBbnnzkwngtmWKuq5dSV1/ja+HcpVqusCb70PKlE4HrOlNc15ni0LNDnC4lOFtOM7uCdnfw/POTrutMcUtfhpd1p0gnDJQkSZIkSZKuBIZIkqTni8VetB1efL60ECo1qpWy48NkJkeJ1VdWibJc8UqZ/Knj5E8df954udDaqFbq7KPU3dcImjptifdSaUlGXJuscGfPVoamaxwZq3BsokJ1BS+LWgSPnSvz2LkyqTjc2J3m1r4M13WmSMQ8P0mSJEmSJOmlYogkSVqWWjrLTO8OZnp3XBgLtRrpqfHGWUvjw2QmRsiND5MsFddsH6mZKVIzU7Q+ffDC2PmWeHPnq5a6eil19zHf0Qkxz91ZD7EQ6GtN0Nea4I56huMTVY6MlTk9VWMl9UnlGjx4ep4HT8+TSwZu6klzS1+GvVuTxIKBkiRJkiRJ0noyRJIkXbYoHmduyzbmtmxjnOsujCdKxYWzlkYunLOUmRwjVq+tyT4ubonXfvC5lnj1eIK5zh5KXb3PC5gqrVvAQGLNJGKBPR1J9nQkKVbqHB2r8PRYhdHSyqrWipWIe0/Mce+JOVrTMW7pawRKO9oSBP//SZIkSZIkrTlDJElS01WzOaazg0z3Dj43WK+RmRwnO3G+Hd4I2YmRNTtrCSBWq5IbOklu6OTzxmvpDKXOXuY6ey8KmHqp5lsMl5osl4xxY3eaG7vTjJca7e6OjlVWfH7S1Hydrz9T4uvPlOjMxbmlL83NfRl6W/yrjCRJkiRJ0lrxkxdJ0vqIXVS1tGv/heH4/NxCsLRQsTQxSnZihHi1smZbic/PUTj5DIWTzzxvvJrNN1rhdfVdFDD1Usvm12wvV5Mt2Ti39TcCoKGZGkcXzk8qr7BAbbhY48tHinz5SJHeQpxX9mV4ZW+anoJ/rZEkSZIkSWomP22RJL2kaukMM90DzHQPPDcYRaRmJslOjDaqlhZCpvT0BCFaWQXLSiRKs7QcP0LL8SPPGy8XWpnrWqhc6uxd+Oceapncmu1lM4uFQF9Lgr6WBK/ZnuHkVJWj4xWenahSW+H/3jMzNc4cmuVLh2bpa4nzyt5GoNRtoCRJkiRJkrRqfsIiSbryhEC5pZ1ySzuT2/c8N1ytkplsVCplJ0bJLDyuZUs8gNTMFKmZKVqPPvW88XJL2/cFS6XOXuqZ7JruZzOJxwKD7UkG25NUahHPTlZ5eqzCqakqK40LT0/XOD09yxcPzdLXkuDm3jSv7EvTlfevO5IkSZIkSZfDT1UkSRtGlEhQ2tpNaWv388bj83MXAqVGwDRCZnyURGV+TfeTmp4kNT1J69GDzxsvt7Qz19Vz4dyluc4eK5eWIRkP7OlIsqcjyVy1zrHxRoXS0MwK+90Bp6ernJ6u8jeHZhloTfDK3jSv7E3TaaAkSZIkSZK0bH6SIkna8GrpDLPdA8y+oCVesjjTCJQmLqpemhwlVlt5KLESqekJUtMTtD79wnCprREobTtftbQQLuUKa7qfjSiTiLG/M8X+zhSz5TpHxyscHaswWqqv+F4np6qcnKryhadm2d6a4KbeNDf1WqEkSZIkSZK0FD89kSRtTiFQybdQybcw1b/rufF6nfTM5EKw9FxLvMzUOCFaeUCxEs9VLj2/LV4lV1ioVro4XOqlmm+BENZ0TxtBPhXjZd1pXtadZnKuxtHxKs+MV5iYW/n/rxNTVU4sBEp9LXFe0ZPmpp4MvS1xgv+tJUmSJEmSnscQSZJ0dYnFmG/dwv/P3p3HyJbe531/fufU1tX7eteZO3fm3hmSI1FDLbTkIKSiiWHLEGQroqNEEWI5QICQEu3IESQKhgMmtmMytgzIlkTEcKSxYTOwNsgwBG2UNJQoaiNF2qRGw5nh3H2/t/eu7Sxv/jinqk4tvVdv1d8PcHBOveett071nNvTXU//3rc+Ma2Vp6+0mi2KVFxbSoOldsBUXFvWQUcL+cq68jfe0viNtzraw9KIanNn0+ql5v6MGlMzknkHfFXH02TJ13vO+XrPuaKWqpGuLQW6thRqpb77QClZQ6miX32zovlyEih93bmiLk3mCJQAAAAAAABEiAQAgCTJ+b5qU3OqTc11tFsYqrS62AqXSivJVlxbOfBwKVerauz2NY3dvtbRHufyqs2daYdL6XF9Zl7OPz3/a58e8TU94us955yWa/G+AqVHlUiferuiT71d0VTJSyuUinp2Ji+PQAkAAAAAAJxSp+eTJgAA9sDlcqrOLKg6s9DRbmGg0sqiRlaa4VISNBXWDz5c8sJA5fu3Vb5/u/NaPU/1mfl2sDR3Jj1eUFwcOeCrOjpm1hEoLVVjXVtOAqXVPQRKy7VYn75e1aevVzVeML37bFFfd7aoq7MF5TwCJQAAAAAAcHoQIgEAsAcul1d19oyqs2c62r0gULFZubSShEuHVblkcazS4wcqPX7Qc64xPtkKleqZgCkYnxyqdZfMTDNlXzNlX19/zmmxmlYoLQdaq7tdj7fWcPr9mzX9/s2aRnKmFxcKevfZot45X1ApdzqnFAQAAAAAAKcHIRIAAAMU5/uHS81p8Uori8maS61waVnmdh9u7FZhbUWFtRVNXHujoz0qFDuqluqzC8l+Zk4ulz/w6zpIZqbZsq/Zsq9vOF/Uk2qsG8uBru9xyrtq6PS5u3V97m5dOU96fragrz1T1NeeKWiy5B/AOwAAAAAAADhahEgAAByCTafFi0IVV5dVWmkHS6XlRRXXluTFuw86dstv1DV696ZG797svF4z1admk6ql2TOqzS2oPndWtdkFhaPjJ656ycw0V/Y1V/b1Deel5Wqk68uhbiwHelLd/dc5jKXXHjX02qOG/v2XpWemcmmgVNTZMV92wr4+AAAAAAAA/RAiAQBwhJyfU216TrXpOS1nT8SxiusrrfWWWlVMK4vyw+DAr8ucU2npsUpLjzX55p91nAtLI6rPJtVL5cKI1qdmVcpJ9emTU700NeLrpRFfL50rarWeVCjdWA71cCPa03jXl0NdXw71H7+yoflRX+9OK5QuT+flESgBAAAAAIATihAJAIDjyPNUn5hWfWJaK9l255SvrLfWWmoGS6WVReXr1UO5tFytqtyd6xq9c12zzcbfTKqXGlOzqs0uqDZ7RvW5BdVmF1SfPXOs116aKHqtKqJKI9b1laRC6f5apL1MNPhoI9JvvV3Rb71d0VjB9DULydgvzBVUzB3PrwEAAAAAAEA/hEgAAJwkZgpGxxWMjmvt/KWOU36tmgRLq0vtcGl1UYX1VR1GdGHOqbj0WMWlx5p867WOc1GhmKy3NLuQ7pNKpvrsguJC8RCubmfKBU/vmi/oXfMF1cJYN9MKo7troeI9JErrDac/vF3TH96utdZRenGhoK9ZKGqmzDpKAAAAAADgeCNEAgBgSESlEW2ULmrjzMWOdgvDJFhaXVRxZbEdMq0uyov2Nn3bbvmNusr3bql871bPucb4pOoz810h04Ia03Ny/tH9qFLKeXp+rqDn5woKIqfbq6FuLoe6tRqosYcvW3YdpZ//s3WdH/f1YlqldGkqx7R3AAAAAADg2CFEAgBgyLlcTtWZeVVn5rtOOBU2VltVS8XVpVbAlK9VDu36CmsrKqytaPzGW52XZ57qUzOqZ4Kl5j6YmJLMO7RrzPumy9N5XZ7OK3Yl3V+LdHMl1I2VQBuNvUx6J91di3R3raLf/Goy7d275ov6mjMFvWOuoJH84b03AAAAAACAzRAiAQBwWpmpMTapxtikVi9c7jjlN2oqriy1K5jScKm4tiwvjg/n8lys0tJjlZYeS13T48W5vOozc6rPpOFSs5JpZl7h2MSBrr/kmen8RE7nJ3L6CxeLWqzGurEc6OZKqMXq3r426w2nP75T0x/fqckz6cpMXl9zpqgXFwpaGOXHNQAAAAAAcDT4VAIAAPSICiVV5s+pMn+u80Qcq7i+quJqMi2ePbqv8vqKxiprh1q95IWBRh7e08jDez3nokKxI1TKTpUXjYwONGAyM82Wfc2WfX39eWmtHuvmShIo3V+LtJcapdhJbzwJ9MaTQL/0mjRf9vWuhYLeOV/Q1dmCCj7T3gEAAAAAgMNBiAQAAHbO81SfmFJ9YkqrkpaWlyVJ01NTSfXS6nJaubTcrmBaXZYXhYd2iX6jrvL92yrfv91zLiyV01BpXvXpJGCqzSb7QQRM40VPLy4U9eJCUfXQ6dZKoFuroe6shntaR0mSHlUiffp6VZ++XlXek67MFvSu+YJeXChoniolAAAAAABwgPjkAQAADERUKKkyd1aVubOdJ5xTvrKmUjo9XnPtpeLqkgobqzrMuppcraLc3RsavXuj51xYGkkCpta2oPrM3J4rmIo505XZgq7MFhQ7pwfrkW6thLq1Emqlvrdp74JY+vNHDf35o4Z+kSolAAAAAABwwAiRAADAwTJTMDqhYHRCa+cvdZ6KQhXXltPKpTRgWltScXX5UKfHk6Rcrarc3ZsavXuz51xYHEnXYMqETNPJ452sweSZ6dx4TufGc3rvRWmlFun2arivae8kqpQAAAAAAMDB4tMFAABwZJyfU21qTrWpOa10nWtOj5cNlppBkx8Gh3qduXpVuXu3NHrvVs+5KF9Ig6U5NabnVcuETcHElGRez3MmS74mS75eXCiqETndWU0qlG6vhqqFe4uUuquU5sqe3jFX1DvmC3p+Nq+RfO91AAAAAAAAbIUQCQAAHEtbTY+Xq1Va6y0V15ZUXFtuHXvRHhcf2iM/aKj84I7KD+70nIv9nBrTs0nV0nQSNCUVTHNqTM3K5fIq+KbL03ldns4rdk6PNyLdTAOlxerepr2TpMeVWJ+5WdVnblblmfTMVF7vnC/oHXMFPT2Vk7fP9Z8AAAAAAMDwI0QCAAAni5nCkVGFI6PaOHOx85xzylfW0+qlpJueSJAAACAASURBVIqpGTAV1pflxXsPZfbCi0KVHj9Q6fGDnnNOpmBiKg2W2gHT6My8zs7O6RsvjKnSiHV7NQmU7qyGCvZ4+bGT3l4K9PZSoF95Y0PlvOmFuYLeOVfQO+YLmh7x9/lOAQAAAADAMCJEAgAAw8NMwei4gtFxrZ97uvNcHKuwsari2kq6DlMaNK0tq7C+cugBk8mpsLqkwuqSxq+/2XM+HBlVfWZO75pOwqXq1JxujJ/VV/1p3azn9lWlVAmcvnCvri/cq0uSzoz6SZXSfEFXZgoq5qhSAgAAAAAAhEgAAOC08Dw1xqfUGJ/Smi51notjFTbWknAp3UqrSyquraQB0+FOkSdJueqGcnc2NHrnRqvtWUn/lZJp8h4tPKUvn/8avT5zWW8X51S3vf9Y92Aj0oONql69XpVv0uXpvF6YK+iFuYKenszJ9wiVAAAAAAA4jQiRAAAAPE+N8Uk1xic3D5jWl9tVTK1tRV4UHv7lRqHO3LumM/eu6WVJkXl6e+aSXpt/Xq8tXNWdyfN7Hjty0luLgd5aTKa+K+VMV2baodLZMV/GekoAAAAAAJwKhEgAAABbyQZM57rOOad8daMrWGqHTX7QOJRL9F2sq0+u6eqTa/prr/+6Votjen3+iv58/qpen7+qteLYnseuhU5fftjQlx8m72Wi6On52XaoxHpKAAAAAAAML0IkAACAvTJTUB5TUB7T+pmLneecU65WbVUwFdaWVVxfaYVM+VrlwC5ror6u997+ot57+4uKZbo7cVZ/Pn9Fr89f1VdnnlHo7/1HwNV6rM/dretzd5P1lBZGfT0/W9ALc3ldnS1otOAN6m0AAAAAAIAjRogEAABwEMwUjpQVjpS1Md87vZwXNFRcX1GhOUVeJmAqbKzKnBvIZXhyurh6TxdX7+kvffX3VPfzemv2cqtK6f74wr7Gf7gR6eFGVZ+5WZUknR/P6fnZJFC6MptXOU+oBAAAAADASUWIBAAAcATifEHV6XlVp+f7nIySdZjWVpKgqRkwra/ue5q8YhToxYdv6MWHb0iSlkqTranvvjL/nDYKo3seW5LuroW6uxbq1etVmXO6mKvr6rh09UxZzz01qZFifl/jAwAAAACAw0OIBAAAcNx4vhrjU2qMT2mt+5xz8hu1dN2lNGBKQ6bC+ooKG2uyXbzUdG1F33Lr8/qWW59XLNOdibP6ytxz+sr8FX115hk1coU9vw1npltRSbeWpd9ejmWvP9FTGw/1fOOxruYqem7CVJydkWZnk21qWvKoXAIAAAAA4LggRAIAADhJzBQVR1Qpjqgyd7b3dBSqsLGWCZeaQdOqCmsrygX1TYf25PTU6j09tXpP//Xbn1Hg+bo+/XQSKs09pxtTFxV7/p4v3Zmnm2NndVNn9SlJXhzp0pu3deUPv6irT67pmZU7GpkoS7Nz0sxMsp+dTR/PStPTkr/31wcAAAAAALtDiAQAADBEnJ9TfWJa9Ynp3iomSX691g6YmmsyNafMW1+TubjVNx9Huvrkmq4+uabv+MqnVM0V9dbsZX1l7open39O98fP7OtaY8/XtZlLujZzSb959VtlLtbFlbu6+uSarrx9Xc997gsaDart9+Z5SbVSs3Jppms/PSPlmS4PAAAAAIBBIUQCAAA4RaJiSdViSdXZPgFQHCtfXU+qlpoh0/pqa1+qrOtrH7yur33wuiRpuTiuN+ae0xtzz+rNuWf1pDyzr2tz5unW1EXdmrqo337uv5QknV+9pytPruvKk2u68uS6JhafSItPpDc3GWNysjNc6g6aSqV9XSMAAAAAAKcJIRIAAAASnqdgdELB6IR05mLP6e6p8grrq7q6vqIXb/++Cq//qla9YhIozT6rN+ae1fLI1L4v6e7EOd2dOKffvfwtkqQz64/0XFoddeXJdU3XVjqvcWVFWlmRrr3ddzw3OpqGSzM9e39jQ1G5vO9rBgAAAABgWBAiAQAAYEe2myrPCxqaXF/VX9xY1beu/Ik2Hoa67Y3rRmlOb49f0GppfN/X8GBsXg/G5vXZS++VJE1XlvTs4k09t3hdzy3e0Lm1B/LkNn2+bWxIGxvSrZs9556TFPt+pnqpN2hiyjwAAAAAwGlCiAQAAICBiPMF1abnVJuea7XNptt7XE1r9Q09qjrdCwu67Y2p4hf3/ZpL5Wl9vjytz1/8OknSSFDV5Uyo9PTybRXicMfjeVEkPXqYbJtwExNJmNQKmGbaQdP0jDQ+Lpnt+70BAAAAAHDUCJEAAABw4MykiZKviZL0nGI5t6rl2Nf9MN/aqs7f9+tU8yN67cwLeu3MC5IkPw719PIdPbd4Q88uXtezSzc11qjs772srkqrq9KN633Pu1wuU7k03VnFND2d7FmbCQAAAABwAhAiAQAA4NCZSdN+pGk/0juLNTknrcWe7oeFJFSK8lqP9x8qRV5O12Yu6drMJUnvkySdWXuoZ5du6vLiDV1euqUz64+2nAJvtywMpYcPkm0TrlxOq5kywVIraErbcvyoDgAAAAA4WvxmCgAAgCNnJk34sSb8mp4v1iRJ67HXUam0Gg/mR9cH4wt6ML6gP3j6GyVJI42qLi/f1OXFm3p26aYuLd1SKWoM5LU2Y5WKVKlId25v2sdNTKYB03Q7XJqZlqamk8Bpckry9x+0AQAAAACwGUIkAAAAHEtjXqwrhbquFOqSpEpsehDmdT8s6EGY12LsS9r/2kPVwoheW3hBry0kU+CZi3V+9b4uL93Ss0s3dHnxpuYqiwN4pd2x1RVpdWXzafPMkiCpI2jq2k9OSp53uBcOAAAAABgahEgAAAA4Ecqe0+VCQ5cLSZVQw5kehjk9CPN6EOb1KMorGkDU48zTncnzujN5Xp955i9IksaCii4v3dLlJ9f0zNJtPb18+8CrlbZjzknLS8l2rX8f53lJkDSVBk3Nfet4RpqalHx+LQAAAAAA9OK3RQAAAJxIBXO6mA90MR9IkiInPYnaodLDKK+aG0wVznq+rC8tvKAvtaqVnM7F67pUe6LLa3d1afGmzj65LW99NVkT6ZiwOJaWlpJts6DJTJqY6A2YWsHTVHJcKBzuxQMAAAAAjhwhEgAAAIaCb9JCLtRCLtTXqirnpNXYT0KlKK8HYW5g6yo5M931x3V3dFx/MPqMdPYvqmSxns7XdckqeiZc1jOVh5pYX5LW16SNDWl9XdpYlzY2kiqiY8Kck1ZWkm2TqfMkyY2O9lY0TaUhU/N4ZCRZ4AoAAAAAMBSGKkQys++V9EFJ75bkS3pd0s9K+oRzLt7hGJ6kb5b0VyV9m6R3ShqTtCjp85L+pXPulwd/9QAAABgkM2nSjzTpR3peNUlSNTY9TKuUHoZ5PY5yA5kCT5JqztMbjRG9oRFJs1LxOc2MhLp0oa5n8g09nW/oqVxDRUVylUoSKDWDpfXm8Ya0sS6rVgdyTYNkGxvJ9d25vWkfVyi0g6VmBVP3fnKC6fMAAAAA4IQYmt/ezOynJH1IUk3Sb0kKJL0s6SclvWxmH9hhkPSspN9Pjxcl/bGkpbT92yV9u5m9Iul/cu4Y/QkpAAAAtjXiOV0qNHRJyXpGzSnwHoV53a45PVFJNeUH9nqLcU6LtZy+UBuVJJmczuYCXco39PR4Q5dm6jqfC5TryrFcGLYCpWy41BE01esDu85BsUZDevgg2TbhzKTxia5wKRM6TabH5TJVTQAAAABwxIYiRDKz71YSIN2X9D7n3Jtp+xlJvyPpuyR9WNJP7GA4J+m3Jf0TSb/pnIsyr/N+Sb8i6fsl/a6SKicAAACcUNkp8M7XliVJ+YmZpFopzOlhlNeTKCc3oGolJ9O9sKB7YUF/mBYb5eR0Ia1UupRv6Ol8XWd8yZuclCYnNx8rCNrh0sa6tN51XNk4nkGTc9LqSrLdvLFpP5cvSFOTaag0nRxnQ6apqeSYtZoAAAAA4MAMRYgk6cfS/Y82AyRJcs49MLMPSnpV0kfM7F9sV43knPuqkgqmfuc+bWYfk/QPJH2fCJEAAACGzpgXa6xQ17OFJIAJnfQ4yutRmNOjKAmXKs4f2OuFMt0IiroRFPV7aVvJYj2VmQLv6XxDc37YWZiTz7fDlE10Bk3ZffvYarWBvZdBsqAhPXqUbFtw5XI7UJrMhEutAGpKmpiUcsPyqw8AAAAAHJ4T/5uUmV2U9A2SGpJ+vvt8GvzckXRByVpHn93nS34h3V/c5zgAAAA4AXImnc0FOpsLJCXlQxux1wqVHoU5PY7yCgdUrSQl6yu92SjpzUap1TaSBktPbRUsddtJ0BSGUiUNltYzIVMlEzpVKgN8d4NllYpUqUh3727Zz42PJ2HS1FRnuDQ1lVR8TU6xXhMAAAAAdBmG35Dek+7/zDm32QrEf6IkRHqP9h8iXU339/Y5DgAAAE6oUS/WaKGhZ9K1lWInLUV+Eiqlaywtx4P9UbvqPL3RKOmNrmDpYr6hp3ONVuXStsFSt1wuCVMmNp86T3EkV6m2K5iaoVN3VVO8kyVIj4atrUlra9Kd21v2a4VNk5ObBE1T0sREEtABAAAAwJAbhhDpcrrffEJ16WZX3z0xs7Kkv50+/MVdPO/7layjtK1XX331pZdeekmVSkV37tzZ9TWeBqura2rUvaO+DGAglpaXj/oSgIHgXsYw2ev97Ek6k26SFMjTkopaUqm11Qb843e1T8VSUaHOakNnVdEZbeiMKppVVQP76alcTra5+c525+Q1GvJqNfm1mvxaVX6tJq9WlV9tt3lBMKgrORA7DZuiUknh6JjC0VFFY2Ot43B0LH2cHLsjXrPpzTff3L4TcEJwP2NYcC9jmHA/Y5gM8/184cIFlcvlPT13GEKksXS/sUWf9XQ/vs/X+mklQdRrkv7lLp73jKT376Tj+vr69p0AAABw7OUVa0FVLahdLF+VryWVtKxSK2AKNLj1lSSprpxuaFI31K4syinSgqo6ow2dTYOlBVWUkxvcC5spLhYVF4sKJ7eoaoqirpCpGTClgVN6fJyrmiS1rrP45PGW/eJ8vh02ZYOm0VGFY6MKy2OKxkYVjZS1uxIyAAAAADh4wxAiHQoz+/uS/qakFUn/rXOuvounX5f06Z10HBsbe0nSZLlc1tWrV7ftf5r80a0/kiRNTIxrdITpQ3CyNf/KfXqLNSqAk4B7GcPkMO7naUnnJUmRpIqcq2gt9vQoyutxlNPjMK8nUW6g6ytJUihfdzWmu62/v5I8OZ3JBbqYC3QxXWfpQr6hsjfAYGmvnJOr19Np8yrt6fMqyfpMrWn0alWZOwbXuwUvCFRYXlJheWnLfs7zpPHxZNq85nR6E9njiXZbsbjt6zb/ipLfKTAMuJ8xLLiXMUy4nzFMuJ+3NgwhUrN0Z3SLPs3fltf28gJm9ncl/Z/pa327c+7PdvN859wrkl7ZSd+VlZVXtcOqJQAAAJxsZtKEH2vCr+s5JX+jFDtpOfb1OEyCpSdRTotRTtGAg6VYpnthQffCgv6k1v5RetYPdSHX0IVcoAv5hi7kGpr1o8MtkjGTSqVkm5ndvF8cy1WrneFSJQ2dMgGU1WqHd+17ZHEsrawk2zZcsdgZLk10hUwTE8qtrSnc43QVAAAAANA0DCHS9XR/aYs+T3X13TEz+7CkH5dUlfQdzrk/2O0YAAAAwE55Js34kWb8SM+nbYcVLEnSk3T8/5ypuy9ZrPO5hi7kg1bAdD4fqGBHXAXkedLoaLJtwUWRVK20q5oq2X37+CSETZJk9br06GGybeLZdO9Gx9KgaaIzcOo+HhuX/MFOrQgAAADg5BuGEOkL6f5FMxtxzlX79Pmmrr47YmY/IOmfS6pJ+k7n3I6mpAMAAAAGaetgKacn6XR4BxUs1Zynt4OS3g5KrTaT04IfptVKSdXS+VygKe+Qq5Z2wveTkGRs6yVSO8OmilTdaB83Q6dqRapWD+CrfDBsY13aWJfu3d2ynzOTxtLAaTwTOo1nAqfm8TiBEwAAAHBanPgQyTl3y8z+VNLXS/obkv5N9ryZvV/SRUn3Je24isjM/hdJPympLumvO+c+NbCLBgAAAPYpGyypayq8J1FOT8IkVHoS5RTIG/jrO5keRHk9iPL600x72SKdzwU6lw90PpdULp3LBSodh7WWtrPDsElxlE6jV+ndqtkqp6rMxYdz7ftkzklra8mmO9v2d6Nj0mQmZOreN8Om8Qkpz3qmAAAAwEl14kOk1D+W9POSPm5mn3XOvSVJZrYg6afTPh9zrv0bnJn9oKQflPTHzrn/MTuYmf3P6fPqkr7LOffrh/AeAAAAgH3JBktXC0mw5Jy0FnvpNHX51lR4VTf4YEmSKs7XW4GvtzJVS5I0k661dD4X6FxauTTvh/JPSklPludLo2PJthXn5Gq1TLhU6TxutVVlQeNwrn1AWhVO2rrCSZJcaaQdKmXDpX6B08iIjl8pGwAAAHB6DUWI5Jz7BTP7hKQPSvqSmX1KUiDpZUkTkn5ZSVVR1pykF5RUKLWY2UuS/h9JJumapO8xs+/p87KPnXM/PNA3AgAAAAyYmTThx5rwG7qsdlBRaQVL7YqltfjgpihbTF/nS5m1lnJyOpuGSudzDZ1N11qaPo5T4u2FWRKKjIxImt2yqwsCqVpNqpi6q5zSKfSS0OnkVDc1Wa0q1arSwwfb9nW5XBooNYOmbOCUbUuPc0PxKy0AAABwbA3NT9zOuQ+Z2Wck/YCk90vyJb0u6WckfSJbhbSNKak1xfk70q2fG5IIkQAAAHAilb1YZa+hp/LtYKnhLA17/Fbos3RA6yxJUijT7bCg22FB0mirvWixzuWCVsCUhEyBJoYlXOonn0+2iYmt+zknV69JlWpnRVMzeEqDpnh9Xf4Jq26SJAtDaWkp2XbAlcvJ9IPj473h01j2cVo5xlpOAAAAwK4MTYgkSc65T0r65A77flTSR/u0vyqdmHVyAQAAgIEpWFIZdDYXtNpiJ63G7VBpMUrWXKq6g/swvu48XQ+Kuh4UO9pHLNa5dI2l5nY2F2jci4c3XOpmJpVGkk0zm3Z7cP+eFMc6NznVFTJV+z62en3TsY4za1Zr7aTKyUwqj3YGTmNbHI+NSd7BTPsIAAAAnBRDFSIBAAAAGCzPpCk/0pQf6Vm1g4ZqbJlgKalYWo59xQf491hV5+ntoKS3u9ZbKluUhl9hKwQ7mws0NcyVSzvhedLoaLJtw0VRx5R5HVPoVauZ7QQHTs4l6zhtrEv3723b35klX7uxzQKnsXbYNJ7ufX7FBgAAwHDhJ1wAAAAAuzbiOV3wAl3Id1YtrcS+ltKKpaUop6U4p/UDXGtJkirO19uBr7eDzvaSxTqTCZXO+sl+xo/kneZwqR/fT0KQsbFtu7ooStY46qhm6gqcmudrtSS8OYHMOWl9Pdl2EDpJmen1ssFSdwg1lgmfCgWd7qQTAAAAxx0hEgAAAICB8Eya9iNN+5GezbQ3nGmpGSo1A6Y4p4Y72KnCas7TjaCoG13T4uUV60wu1EIu0JlcoDN+UsE0nwtVsJMZeBwq30/WFxrdPnBSHMvV630qmvqHThZFB3/9B2g30+tJksvn24HSWJ/KptFsGMW6TgAAADh8hEgAAAAADlTBnM7kQp3Jha0256SK87QY5bScBkzLaRVTdMBLlAbydDss6HZY6Gg3Oc34kc74abiUC9LrDjRmp2jdpUHyPGlkJNm245xcELSrmLJbrc9xrXbiF7O1IJCWFpNth1y5nIRJY2O94VNHIJVuI2XWdgIAAMCeESIBAAAAOHRm0qjFGvUaeirfbndOWos9Lce5VvXS8iGstyRJTqYnUU5Popxea3SGHmWLWoHSgh9oIa1kmvND5U96knFcmCXTuxUK0sTk9v3jWK5Wk2q1rnCpKlVrPcGTNRoH/x4OQava6dHDHfVvre2UDZ6ax801n7qPywRPAAAASBAiAQAAADg2zKQJP9aE39DTmXApdtJq7CdVS2nAtBzltHoI4ZKUrLt0LfB1rWtqPJPTrB9qwU9CpYVc2AqZpryI6qWD5HlJ2FEu76h7ay2nntCp1rVPq5yGJXTKru20s1n2kuCpXG4HTj0hVObx6Jg0lj7O8REDAADAsOEnPAAAAADHnmfSlB9pyo/0jNof7sdOWov9JFSKk6nxlmNfK4cwLZ6UVC89jvJ6HOV7qpcKFrfDJT/UfGsfatSLD/za0GU3azlps9Cp1tWWVkLVqrJ6/YDfwOEx56SNjWTbafIkyZVK7dBpbEwqj7aPO4Kn0fbjkRGRtgIAABxfhEgAAAAATizPpEk/0qQfSV3h0no6Ld5yWrW0nFYyhTqcaboarv/aS1IyPd5CLtR8Gi7N+2H6ONCI5w7l+rCN3YZOcdwRKqlaleq1zuApe75Wk8XDFSZa8/09ebzj5zjP6wyVWsftx2Ora4pKJalUbLcXCoRPAAAAh4AQCQAAAMDQ8TaZFs85qeI8LUe+VtKKpaRyyVfF+Yd2fRXn63rg63rX9HiSNO5FmvcDzTdDpjRomvNDAqbjbJfT68k5uSDIVDbVpHrmuFZLQ6hq63iYqp2aLI6ltbVk28T5Pm0ul+sMm8qjnQFUeZPjYpHwCQAAYBcIkQAAAACcGmbSqMUa9WJdUNBxruFMK2m4lIRMOa1E/qGtu9S0Fvtai329HfSeG7NIc2m4NJcJl+ZyocYs5rPxk8QsqaYpFKSJyR09xcWxVK/3qWzqV+2UTrMXhgf8Ro6GhaG0spJsu+B8vzNYKpe7HmfDp3JnP+9wqhgBAACOE0IkAAAAAJBUMJdU/6jzQ/fmuksracVSc78a51R1h/uh8rrztb5JBVPJ4iRcygUaka8p1bVWL2ouF2rKi+QRMJ18npesITQysn3fVLK2U6ayKRsybfLYgj4J5pCwKJJWV5Ntl9zISDto6gmfyn2Cp/Qx1U8AAOAEI0QCAAAAgC10rLuU7zxXj02rcTZYSqbIW4l9RYdYvSRJNefpVljQrbAgaTRpXEp2vpxm0uqluVyo2fS4uS8xTd7walbejI7u+CkuitJAqd4ZNDXbatW0IioTRNXrh3zHHz6rpmtdaedrPkmS83xptNwOlbIBVPNxuTuISttY+wkAABwxQiQAAAAA2KOi5zTv9VYvOSdtOK9VubSaBkyr6VR17pA/bo9kehTl9SjKS43e82Ne1BEqzfqhZtL9tB/J5zPs08X301Bj58GT4liu0egMm+q13jAqGz7V60M73V6WxdG26z5txvl+Z8jUHTqNlNOAKj1uhVFlqVhiCj4AALBvhEgAAAAAMGBm0pjFGuuz9lLspPXY00qcS4KlZgVT7Gsj9g49YJKk9djXetx/mjxPTlN+pNk0VOrcIo0zVR6kJKwolZJtF1wYdoVO9a7gqa7a6rK8RqCCi1vtFscH9EaOF4v2EUCZJVMflkel8kgmZErbRkbagVRzqr5W/7KUz2//IgAAYOgRIgEAAADAIfJMmvBjTfi9JUFRuv7Sap/qpfUjCphimRajnBajnN7scz6XTpU3m6lcalYyzfihxr2YkAmby+Wk3Jg0OrZpl6X79yRJ586eSxqc6wqfugKoer0rlGofWxQdxrs6Fsw5qVJJtj1wuVy78mkkux/Z2WNCKAAAhgIhEgAAAAAcE75JU36kqT7rL0UuqRhai71WyLSWCZniI1qRJpTpYZTXw6j/B8bNkCnZotZxM3CapJIJu2WWBBT5vDQ2vqundoRPjX5hU7/wqSEL+swDOeQsDKXV1WTbA5fPd4ZKzcqnjuOutuw51oMCAOBYIEQCAAAAgBPAN2nSjzTpR1KfKfIqzmsFSw+rgTaUV90vaS3y1dDRrYuyXcjky2k6DZSmvXbQNJ3up/xIBXOHfNUYWjuofOrHxZFUb3SGTM0QqlHvCqHq7fOnrPopy4JAClak1ZU9Pd95XiZcSoOl0khnKJUNo5ptpZH2OaqhAADYN0IkAAAAADjhvMwaTFKgheqyJGl6fErOSQ1nmaolT2tp9dLaEa7D1BTJ9DjK6/EmIZMkjXtJwDTdFTBN+6GmvUhjXkzBAg6W57eDiV1qVT81Q6hGZ5VTZ1vn8WlZ+6kfi2NpYz3Z9qg1JV9HuJQJoHq2crKuV/YxQRQA4JQjRAIAAACAIWYmFc2p6IWaU9hzPnLSRhosrcZ+OmVeEjatx77q7uiqmJqagdfN3suXlEyZN51WLTXDpik/aoVM036oEY9qJhyRVvXTLp/XWvupGSw12gFTR+jU6DxuVkCFm/yDOUX2OyWflAZR3cFSaUQaKfUGT82gqlRKw6q0vViSvKP/XgoAwF4QIgEAAADAKeabNOHHmvBjXeiaJk9KqpjW05BpPWpXMjXXZwqPcKq8plCmR1Fej7aoZipZrKk0VGoGTFPp8VR6TNCEYyW79pN2N/2eJLkoagdMPSFUVwVUo/ecOf49SGkQtb6ebPvgSiVdzuUVFwvSxGQmdCp1hU9dYVR2er5CgTAKAHDoCJEAAAAAAJsqmEvXKYqkrozGOameTpXXnBovu1+PfYVHOFVeVs15uh8WdH+LPiWL02ApqWrqPY5UNqbOwwnh730Kvs4qqEZnCNUKoDZ5nB4TQnWyWk151aR1SU+e7GkMZ5ZUNTWDp1botMnjbL+OtpLk85EgAGBn+D8GAAAAAGBPzKSSOZW8UPN9psprhkzrsa/1dHq85n4tPQ6OQSVTU815uh95ur9FRVNesab8SJNepMk0XJpMq5km06BpwouUI2jCSdZRBbUH/UKojjBqi0Aq3SyKBvuehoA5J9WqyaalfY3l8vnOcKmUmXqvJ3zq9zjTRnUUAAw1QiQAAAAAwIHIhkxzm/Spx6YN1w6YNrr2FedJx6SaSZICeXoUecnUeb2z/7WMe1ErVJr0wlbwNJEJoEYtlnd83howOPsNoaQkhGo0+gZMnSFUQwr6PaYaaisWBFIQSGtr+x7LFQpJmNQMoIqbBE/FYv9Qqpjpk8uJck8A8QJdsgAAIABJREFUOF4IkQAAAAAAR6boORWVTpfXR+SkSrOKyfWGTBvHaMq8rOYUf7d7C7RafDlNpIFSM1ia8NrHzT1T6OFUyuWSrVze2/Ob1VB9A6hNgqmgtx9B1Pa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          },
          "metadata": {
            "image/png": {
              "width": 840,
              "height": 283
            },
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_1fhqQhAFLkk"
      },
      "source": [
        " \n",
        "## But what is $\\lambda$?\n",
        "\n",
        "**This question is what motivates statistics**. In the real world, $\\lambda$ is hidden from us. We see only $Z$, and must go backwards to try and determine $\\lambda$. The problem is difficult because there is no 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 best! \n",
        "\n",
        "Bayesian inference is concerned with *beliefs* about what $\\lambda$ might be. 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 values of a non-random variable? Ah, we have fallen for our old, frequentist way of thinking. Recall that under 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": {
        "id": "JrRddMMfHHKJ"
      },
      "source": [
        " \n",
        "#### Example: Inferring behaviour from text-message data\n",
        " \n",
        "Let's try to model a more interesting example, one that concerns the rate at which a user sends and receives text messages:\n",
        "\n",
        ">  You are given a series of daily text-message counts from a user of your system. The data, plotted over time, appears in the chart below. You are curious to know if the user's text-messaging habits have 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",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cOBOnwa2IIaB",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 299
        },
        "outputId": "c510c6ff-06c5-4483-c72f-12b9aeb1b618"
      },
      "source": [
        "# Define data and assumptions\n",
        "count_data = array([\n",
        "    13, 24, 8, 24, 7, 35, 14, 11, 15, 11, 22, 22, 11, 57,  \n",
        "    11, 19, 29, 6, 19, 12, 22, 12, 18, 72, 32, 9, 7, 13,  \n",
        "    19, 23, 27, 20, 6, 17, 13, 10, 14, 6, 16, 15, 7, 2,  \n",
        "    15, 15, 19, 70, 49, 7, 53, 22, 21, 31, 19, 11, 18, 20,  \n",
        "    12, 35, 17, 23, 17, 4, 2, 31, 30, 13, 27, 0, 39, 37,   \n",
        "    5, 14, 13, 22,\n",
        "], dtype = f32)\n",
        "days = arange(count_data.shape[0], dtype = i32)\n",
        "\n",
        "# Visualise the results\n",
        "plt.figure(figsize=(12.5, 4))\n",
        "plt.bar(days, count_data, color = '#5DA5DA')\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, count_data.shape[0]);"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 900x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "image/png": {
              "width": 836,
              "height": 282
            },
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "i-PRmpvsIZKq"
      },
      "source": [
        "\n",
        "Before we start modeling, see what you can figure out just by looking at the chart above. Would you say there was a change in behaviour during this time period? \n",
        " \n",
        "How can we start to model this? Well, as we have conveniently already seen, a Poisson random variable is a very appropriate model for this type of *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 what the value of the $\\lambda$ parameter really is, however. Looking at the chart above, it appears that the rate might become higher late in the observation period, which is equivalent to saying that $\\lambda$ increases at some point during the observations. (Recall that a higher value of $\\lambda$ assigns more probability to larger outcomes. That is, there is a higher probability of many text messages having been sent on a given day.)\n",
        " \n",
        "How can we represent this observation mathematically? Let's assume that on some day during the observation period (call it $\\tau$), the parameter $\\lambda$ suddenly jumps to a higher value. So we really have two $\\lambda$ parameters: one for the period before $\\tau$, and one for the rest of the observation period. In the literature, a sudden transition like this would be called a *switchpoint*:\n",
        " \n",
        "$$\\lambda = \n",
        "\\begin{cases} \\lambda_1  & \\text{if } t \\lt \\tau \\cr\n",
        "\\lambda_2 & \\text{if } t \\ge \\tau\n",
        "\\end{cases}\n",
        "$$\n",
        "\n",
        "If, in reality, no sudden change occurred and indeed $\\lambda_1 = \\lambda_2$, then 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 $\\lambda$ can be any positive number. As we saw earlier, the *exponential* distribution provides a continuous density function for positive numbers, so it might be a good choice for modeling $\\lambda_i$. But recall that the exponential distribution takes a parameter of its own, so we'll need to include that parameter in our model. Let's call that parameter $\\alpha$.\n",
        "$$\n",
        "\\begin{align}\n",
        "&\\lambda_1 \\sim \\text{Exponential}( \\alpha ) \\\\\n",
        "&\\lambda_2 \\sim \\text{Exponential}( \\alpha )\n",
        "\\end{align}\n",
        "$$\n",
        "$\\alpha$ is called a *hyper-parameter* or *parent variable*. In literal terms, it is a parameter that influences other parameters. Our initial guess at $\\alpha$ does not influence the model too strongly, so we have some flexibility in our choice.  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",
        "An alternative, and something I encourage the reader to try, would be to have two priors: one for each $\\lambda_i$. Creating two exponential distributions with different $\\alpha$ values reflects our prior belief that the rate changed at some point during the observations.\n",
        " \n",
        "What about $\\tau$? Because of the noisiness of the data, it's difficult to pick out a priori when $\\tau$ might have occurred. Instead, we can assign a *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 distribution for the unknown variables look like? Frankly, *it doesn't matter*. What we should understand is that it's an ugly, complicated mess involving symbols only a mathematician could love. And things will only get uglier the more complicated our models become. Regardless, all we really care about is the posterior distribution.\n",
        "\n",
        "We next turn to [TensorFlow Probability](https://tensorflow.org/probability), a Python library for performing Bayesian analysis that is undaunted by the mathematical monster we have created."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mCz2BozPcYNy"
      },
      "source": [
        "## Introducing our first hammer: TensorFlow Probability\n",
        "\n",
        "TensorFlow Probability (TFP) is a Python library for programming Bayesian analysis. It is intended for data scientists, statisticians, machine learning practitioners, and scientists. Since it is built on the TensorFlow (TF) stack, it brings the runtime benefits of TF to Bayesian analysis. These include write-once run-many (ability to run your development model in production) and speedups via state-of-the-art hardware (GPUs and TPUs). \n",
        "\n",
        "Since TFP is relatively new, the TFP community is actively developing documentation, \n",
        "especially docs and examples that bridge the gap between beginner and hacker. One of this book's main goals is to solve that problem, and also to demonstrate why TFP is so cool.\n",
        "\n",
        "We will model the problem above using TFP. 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; it is probabilistic in the sense that we create probability models using programming variables as the model's components. \n",
        "\n",
        "B. Cronin [[4]](#scrollTo=nDdph0r1ABCn) 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",
        "Because of the confusion engendered by the term *probabilistic programming*, I'll refrain from using it. Instead, I'll simply say *programming*, since that's what it really is. \n",
        " \n",
        "TFP code is easy to read. The only novel thing should be the syntax. Simply remember that we are representing the model's components ($\\tau, \\lambda_1, \\lambda_2$ ) as variables."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gYVjgZQ3hOw-"
      },
      "source": [
        "## Specify the joint log-density\n",
        "\n",
        "We'll assume the data is a consequence of the following generative model:\n",
        "\n",
        "$$\\begin{align*}\n",
        "\\lambda_{0}^{(0)} &\\sim \\text{Exponential}(\\text{rate}=\\alpha) \\\\\n",
        "\\lambda_{1}^{(0)} &\\sim \\text{Exponential}(\\text{rate}=\\alpha) \\\\\n",
        "\\tau &\\sim \\text{Uniform}(\\text{low}=0,\\text{high}=1) \\\\\n",
        "\\text{for }  i &= 1\\ldots N: \\\\\n",
        "\\lambda_i &= \\begin{cases} \\lambda_{0}^{(0)}, & \\tau > i/N \\\\ \\lambda_{1}^{(0)}, & \\text{otherwise}\\end{cases}\\\\\n",
        " X_i &\\sim \\text{Poisson}(\\text{rate}=\\lambda_i)\n",
        "\\end{align*}$$\n",
        "\n",
        "Happily, this model can be easily implemented using TF and TFP's distributions:\n",
        "\n",
        "\n",
        "This code creates a new function `λ_`, but really we can think of it as a random variable: the random variable $\\lambda$ from above. The [gather](https://https://www.tensorflow.org/api_docs/python/tf/gather) function assigns `λ_0` or `λ_1` as the value of `λ_`, depending on what side of `τ` we are on. The values of `λ_` up until `τ` are `λ_0` and the values afterwards are `λ_1`.\n",
        "\n",
        "Note that because `λ_0`, `λ_1` and `τ` are random, `λ_` will be random. We are **not** fixing any variables yet.\n",
        "\n",
        "TFP performs probabilistic inference by evaluating the model parameters using a joint_log_prob function, which we'll describe more in Chapter 2.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YBCXrK9gj8Gx"
      },
      "source": [
        "def joint_log_prob(key, count_data, λ_0, λ_1, τ):\n",
        "    _ = random.split(key)\n",
        "    rate = (1. / mean(count_data))\n",
        "    rv_λ_0 = random_variable(Exponential(rate = rate))\n",
        "    rv_λ_1 = random_variable(Exponential(rate = rate))\n",
        " \n",
        "    rv_τ = random_variable(Uniform())\n",
        " \n",
        "    λ_ = array([λ_0, λ_1])[(\n",
        "            τ * size(count_data).astype(f32)\n",
        "                <= arange(size(count_data)).astype(f32),\n",
        "            ).astype(i32)]\n",
        "    rv_observation = random_variable(Poisson(rate = λ_))\n",
        " \n",
        "    return (\n",
        "          rv_λ_0.log_prob(λ_0)\n",
        "        + rv_λ_1.log_prob(λ_1)\n",
        "        + rv_τ.log_prob(τ)\n",
        "        + sum(rv_observation.log_prob(count_data)))\n",
        "\n",
        "\n",
        "# Define a closure over joint_log_prob\n",
        "def unnormalised_log_posterior(λ_0, λ_1, τ):\n",
        "    return joint_log_prob(count_data, λ_0, λ_1, τ)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "t7Vvrj68jsr7"
      },
      "source": [
        "Notice that the implementation is arguably very close to being a 1:1 translation of the mathematical model. The main difference is merely that once we've specified the probabilistic model, we return the sum of the `log_prob`."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KnyDyY8Tjyiy"
      },
      "source": [
        "## Specify the posterior sampler"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zy6DFZgPEXyU",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 353
        },
        "outputId": "0416d211-c9cb-4095-e253-9cb261788c7c"
      },
      "source": [
        "# Wrap the mcmc sampling call in a @jit to speed it up\n",
        "@jit\n",
        "def run_chain(*args, **kwargs):\n",
        "    return mcmc.sample_chain(*args, **kwargs)\n",
        "\n",
        "num_results = 5000\n",
        "num_burnin_steps = 1000\n",
        "\n",
        "# Set the chain's start state\n",
        "initial_chain_state = [\n",
        "    mean(count_data).astype(f32) * ones((), dtype = f32),\n",
        "    mean(count_data).astype(f32) * ones((), dtype = f32),\n",
        "    .5 * ones((), dtype = f32)]\n",
        "\n",
        "\n",
        "# Since HMC operates over unconstrained space, we need to transform the\n",
        "# samples so they live in real-space\n",
        "unconstraining_bijectors = [\n",
        "    tfb.Exp(),  # R+ → R\n",
        "    tfb.Exp(),  # R+ → R\n",
        "    tfb.Sigmoid()]  # [0, 1] → R\n",
        "\n",
        "step_size = .2\n",
        "\n",
        "kernel = mcmc.TransformedTransitionKernel(\n",
        "    inner_kernel = mcmc.HamiltonianMonteCarlo(\n",
        "        target_log_prob_fn          = unnormalised_log_posterior,\n",
        "        num_leapfrog_steps          = 2,\n",
        "        step_size                   = step_size,\n",
        "        state_gradients_are_stopped = True),\n",
        "    bijector     = unconstraining_bijectors)\n",
        "\n",
        "kernel = mcmc.SimpleStepSizeAdaptation(\n",
        "    inner_kernel         = kernel,\n",
        "    num_adaptation_steps = int(num_burnin_steps * .8))\n",
        "\n",
        "\n",
        "# Sample from the chain\n",
        "(λ_0_samples, λ_1_samples, posterior_τ), kernel_results = run_chain(\n",
        "    num_results      = num_results,\n",
        "    current_state    = initial_chain_state,\n",
        "    kernel           = kernel,\n",
        "    num_burnin_steps = num_burnin_steps,\n",
        "    seed = random.PRNGKey(0))\n",
        "    \n",
        "τ_samples = floor(posterior_τ * size(count_data).astype(f32))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "error",
          "ename": "TypeError",
          "evalue": "ignored",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-45-ecaa344815da>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     42\u001b[0m     \u001b[0mkernel\u001b[0m           \u001b[0;34m=\u001b[0m \u001b[0mkernel\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     43\u001b[0m     \u001b[0mnum_burnin_steps\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnum_burnin_steps\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 44\u001b[0;31m     seed = random.PRNGKey(0))\n\u001b[0m\u001b[1;32m     45\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     46\u001b[0m \u001b[0mτ_samples\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfloor\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mposterior_τ\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0msize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcount_data\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf32\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-45-ecaa344815da>\u001b[0m in \u001b[0;36mrun_chain\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0;31m# @jit\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mrun_chain\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mmcmc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msample_chain\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      6\u001b[0m \u001b[0mnum_results\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m5000\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/tensorflow_probability/substrates/jax/mcmc/sample.py\u001b[0m in \u001b[0;36msample_chain\u001b[0;34m(num_results, current_state, previous_kernel_results, kernel, num_burnin_steps, num_steps_between_results, trace_fn, return_final_kernel_results, parallel_iterations, seed, name)\u001b[0m\n\u001b[1;32m    328\u001b[0m         current_state)\n\u001b[1;32m    329\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mprevious_kernel_results\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 330\u001b[0;31m       \u001b[0mprevious_kernel_results\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mkernel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbootstrap_results\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcurrent_state\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    331\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    332\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mtrace_fn\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/tensorflow_probability/substrates/jax/mcmc/simple_step_size_adaptation.py\u001b[0m in \u001b[0;36mbootstrap_results\u001b[0;34m(self, init_state)\u001b[0m\n\u001b[1;32m    441\u001b[0m     with tf.name_scope(mcmc_util.make_name(\n\u001b[1;32m    442\u001b[0m         self.name, 'simple_step_size_adaptation', 'bootstrap_results')):\n\u001b[0;32m--> 443\u001b[0;31m       \u001b[0minner_results\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minner_kernel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbootstrap_results\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minit_state\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    444\u001b[0m       \u001b[0mstep_size\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstep_size_getter_fn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minner_results\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    445\u001b[0m       return SimpleStepSizeAdaptationResults(\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/tensorflow_probability/substrates/jax/mcmc/transformed_kernel.py\u001b[0m in \u001b[0;36mbootstrap_results\u001b[0;34m(self, init_state, transformed_init_state)\u001b[0m\n\u001b[1;32m    491\u001b[0m           \u001b[0mtransformed_state\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mtransformed_init_state\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    492\u001b[0m           inner_results=self._inner_kernel.bootstrap_results(\n\u001b[0;32m--> 493\u001b[0;31m               transformed_init_state))\n\u001b[0m\u001b[1;32m    494\u001b[0m       \u001b[0;32mreturn\u001b[0m \u001b[0mkernel_results\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    495\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/tensorflow_probability/substrates/jax/mcmc/hmc.py\u001b[0m in \u001b[0;36mbootstrap_results\u001b[0;34m(self, init_state)\u001b[0m\n\u001b[1;32m    559\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0mbootstrap_results\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minit_state\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    560\u001b[0m     \u001b[0;34m\"\"\"Creates initial `previous_kernel_results` using a supplied `state`.\"\"\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 561\u001b[0;31m     \u001b[0mkernel_results\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_impl\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbootstrap_results\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minit_state\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    562\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstep_size_update_fn\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    563\u001b[0m       \u001b[0mstep_size_assign\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstep_size_update_fn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstep_size\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m  \u001b[0;31m# pylint: disable=not-callable\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/tensorflow_probability/substrates/jax/mcmc/metropolis_hastings.py\u001b[0m in \u001b[0;36mbootstrap_results\u001b[0;34m(self, init_state)\u001b[0m\n\u001b[1;32m    271\u001b[0m     with tf.name_scope(mcmc_util.make_name(\n\u001b[1;32m    272\u001b[0m         self.name, 'mh', 'bootstrap_results')):\n\u001b[0;32m--> 273\u001b[0;31m       \u001b[0mpkr\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minner_kernel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbootstrap_results\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minit_state\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    274\u001b[0m       \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mhas_target_log_prob\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpkr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    275\u001b[0m         raise ValueError(\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/tensorflow_probability/substrates/jax/mcmc/hmc.py\u001b[0m in \u001b[0;36mbootstrap_results\u001b[0;34m(self, init_state)\u001b[0m\n\u001b[1;32m    773\u001b[0m           \u001b[0minit_target_log_prob\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    774\u001b[0m           \u001b[0minit_grads_target_log_prob\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 775\u001b[0;31m       ] = mcmc_util.maybe_call_fn_and_grads(self.target_log_prob_fn, init_state)\n\u001b[0m\u001b[1;32m    776\u001b[0m       result = UncalibratedHamiltonianMonteCarloKernelResults(\n\u001b[1;32m    777\u001b[0m           \u001b[0mlog_acceptance_correction\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mtf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros_like\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0minit_target_log_prob\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/tensorflow_probability/substrates/jax/mcmc/internal/util.py\u001b[0m in \u001b[0;36mmaybe_call_fn_and_grads\u001b[0;34m(fn, fn_arg_list, result, grads, check_non_none_grads, name)\u001b[0m\n\u001b[1;32m    295\u001b[0m     fn_arg_list = (list(fn_arg_list) if is_list_like(fn_arg_list)\n\u001b[1;32m    296\u001b[0m                    else [fn_arg_list])\n\u001b[0;32m--> 297\u001b[0;31m     \u001b[0mresult\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgrads\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_value_and_gradients\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfn_arg_list\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mresult\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mgrads\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    298\u001b[0m     if not all(dtype_util.is_floating(r.dtype)\n\u001b[1;32m    299\u001b[0m                for r in (result if is_list_like(result) else [result])):  # pylint: disable=superfluous-parens\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/tensorflow_probability/substrates/jax/mcmc/internal/util.py\u001b[0m in \u001b[0;36m_value_and_gradients\u001b[0;34m(fn, fn_arg_list, result, grads, name)\u001b[0m\n\u001b[1;32m    263\u001b[0m       \u001b[0;31m# tensorflow eager mode (see below), so we will handle that case\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    264\u001b[0m       \u001b[0;31m# separately.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 265\u001b[0;31m       \u001b[0;32mreturn\u001b[0m \u001b[0mtfp_math_value_and_gradients\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfn_arg_list\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    266\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    267\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mresult\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/tensorflow_probability/substrates/jax/math/gradient.py\u001b[0m in \u001b[0;36mvalue_and_gradient\u001b[0;34m(f, output_gradients, use_gradient_tape, auto_unpack_single_arg, has_aux, name, *args, **kwargs)\u001b[0m\n\u001b[1;32m    450\u001b[0m       \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf_vjp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maux\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mjax\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvjp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhas_aux\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    451\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 452\u001b[0;31m       \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf_vjp\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mjax\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvjp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    453\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0moutput_gradients\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    454\u001b[0m       \u001b[0moutput_gradients\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnest\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmap_structure\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mones_like\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/api.py\u001b[0m in \u001b[0;36mvjp\u001b[0;34m(fun, has_aux, reduce_axes, *primals)\u001b[0m\n\u001b[1;32m   2568\u001b[0m   \u001b[0mreduce_axes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_ensure_str_tuple\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mreduce_axes\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2569\u001b[0m   return _vjp(\n\u001b[0;32m-> 2570\u001b[0;31m       lu.wrap_init(fun), *primals, has_aux=has_aux, reduce_axes=reduce_axes)\n\u001b[0m\u001b[1;32m   2571\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2572\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_vjp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mlu\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mWrappedFun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mprimals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhas_aux\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mreduce_axes\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/api.py\u001b[0m in \u001b[0;36m_vjp\u001b[0;34m(fun, has_aux, reduce_axes, *primals)\u001b[0m\n\u001b[1;32m   2577\u001b[0m     \u001b[0mflat_fun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout_tree\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mflatten_fun_nokwargs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0min_tree\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2578\u001b[0m     out_primal, out_vjp = ad.vjp(\n\u001b[0;32m-> 2579\u001b[0;31m         flat_fun, primals_flat, reduce_axes=reduce_axes)\n\u001b[0m\u001b[1;32m   2580\u001b[0m     \u001b[0mout_tree\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mout_tree\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2581\u001b[0m   \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/interpreters/ad.py\u001b[0m in \u001b[0;36mvjp\u001b[0;34m(traceable, primals, has_aux, reduce_axes)\u001b[0m\n\u001b[1;32m    132\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mvjp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtraceable\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprimals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhas_aux\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mreduce_axes\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    133\u001b[0m   \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mhas_aux\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 134\u001b[0;31m     \u001b[0mout_primals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpvals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mjaxpr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mconsts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlinearize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtraceable\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mprimals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    135\u001b[0m   \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    136\u001b[0m     \u001b[0mout_primals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mpvals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mjaxpr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mconsts\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0maux\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlinearize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtraceable\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mprimals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhas_aux\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/interpreters/ad.py\u001b[0m in \u001b[0;36mlinearize\u001b[0;34m(traceable, *primals, **kwargs)\u001b[0m\n\u001b[1;32m    121\u001b[0m   \u001b[0m_\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0min_tree\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtree_flatten\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprimals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mprimals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    122\u001b[0m   \u001b[0mjvpfun_flat\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout_tree\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mflatten_fun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mjvpfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0min_tree\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 123\u001b[0;31m   \u001b[0mjaxpr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout_pvals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mconsts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpe\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtrace_to_jaxpr_nounits\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mjvpfun_flat\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0min_pvals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    124\u001b[0m   \u001b[0mout_primals_pvals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout_tangents_pvals\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtree_unflatten\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mout_tree\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout_pvals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    125\u001b[0m   \u001b[0;32massert\u001b[0m \u001b[0mall\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mout_primal_pval\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mis_known\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mout_primal_pval\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mout_primals_pvals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/_src/profiler.py\u001b[0m in \u001b[0;36mwrapper\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m    292\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0mwrapper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    293\u001b[0m     \u001b[0;32mwith\u001b[0m \u001b[0mTraceAnnotation\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mdecorator_kwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 294\u001b[0;31m       \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    295\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mwrapper\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    296\u001b[0m   \u001b[0;32mreturn\u001b[0m \u001b[0mwrapper\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/interpreters/partial_eval.py\u001b[0m in \u001b[0;36mtrace_to_jaxpr_nounits\u001b[0;34m(fun, pvals, instantiate)\u001b[0m\n\u001b[1;32m    798\u001b[0m   \u001b[0;32mwith\u001b[0m \u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnew_main\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mJaxprTrace\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname_stack\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcurrent_name_stack\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mmain\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    799\u001b[0m     \u001b[0mfun\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtrace_to_subjaxpr_nounits\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmain\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minstantiate\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 800\u001b[0;31m     \u001b[0mjaxpr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mout_pvals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mconsts\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0menv\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcall_wrapped\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpvals\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    801\u001b[0m     \u001b[0;32massert\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0menv\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    802\u001b[0m     \u001b[0;32mdel\u001b[0m \u001b[0mmain\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0menv\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/jax/linear_util.py\u001b[0m in \u001b[0;36mcall_wrapped\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m    166\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    167\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 168\u001b[0;31m       \u001b[0mans\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mdict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    169\u001b[0m     \u001b[0;32mexcept\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    170\u001b[0m       \u001b[0;31m# Some transformations yield from inside context managers, so we have to\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/tensorflow_probability/substrates/jax/mcmc/transformed_kernel.py\u001b[0m in \u001b[0;36mtransformed_log_prob_fn\u001b[0;34m(*state_parts)\u001b[0m\n\u001b[1;32m    121\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0menable_bijector_caching\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    122\u001b[0m       \u001b[0mstate_parts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mtf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0midentity\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msp\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0msp\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mstate_parts\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 123\u001b[0;31m     \u001b[0mtlp\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlog_prob_fn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstate_parts\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    124\u001b[0m     \u001b[0mtlp_rank\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mprefer_static\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrank\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtlp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    125\u001b[0m     \u001b[0mevent_ndims\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprefer_static\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrank\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msp\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mtlp_rank\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0msp\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mstate_parts\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m<ipython-input-38-700e40229859>\u001b[0m in \u001b[0;36munnormalised_log_posterior\u001b[0;34m(λ_0, λ_1, τ)\u001b[0m\n\u001b[1;32m     22\u001b[0m \u001b[0;31m# Define a closure over joint_log_prob\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     23\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0munnormalised_log_posterior\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mλ_0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mλ_1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mτ\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 24\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mjoint_log_prob\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcount_data\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mλ_0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mλ_1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mτ\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;31mTypeError\u001b[0m: joint_log_prob() missing 1 required positional argument: 'τ'"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NpNv545ZkLjb"
      },
      "source": [
        "acceptance_rate = mean(\n",
        "    kernel_results.inner_results.inner_results.is_accepted.astype(f32))\n",
        "print(f\"Acceptance rate: {acceptance_rate}\")\n",
        "\n",
        "final_step_size = mean(\n",
        "    kernel_results.inner_results.inner_results.accepted_results.step_size[-100:])\n",
        "print(f\"Final step size: {final_step_size}\")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vIxEqx9qkhWr"
      },
      "source": [
        "## Plot the Results"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "viLRm6DEkRPM"
      },
      "source": [
        "plt.figure(figsize=(12.5, 15))\n",
        "\n",
        "ax = plt.subplot(311)\n",
        "ax.set_autoscaley_on(False)\n",
        "\n",
        "plt.hist(λ_0_samples, histtype='stepfilled', bins = 30, alpha = .85,\n",
        "         label = r\"Posterior of $\\lambda_0$\", color=TFColor[0], density=True)\n",
        "plt.legend(loc = 'upper left')\n",
        "plt.title(r\"Posterior distributions of the variables $\\lambda_0,\\;\\lambda_1,\\;\\tau$\")\n",
        "plt.xlim([15, 30])\n",
        "plt.xlabel(r\"$\\lambda_0$ value\")\n",
        "\n",
        "ax = plt.subplot(312)\n",
        "ax.set_autoscaley_on(False)\n",
        "plt.hist(λ_1_samples, histtype = 'stepfilled', bins = 30, alpha = .85,\n",
        "         label = r\"Posterior of $\\lambda_1$\", color=TFColor[6], density = True)\n",
        "plt.legend(loc='upper left')\n",
        "plt.xlim([15, 30])\n",
        "plt.xlabel(r\"$\\lambda_1$ value\")\n",
        "\n",
        "plt.subplot(313)\n",
        "w = 1.0 / τ_samples.shape[0] * ones_like(τ_samples)\n",
        "plt.hist(τ_samples, bins = shape_count_data[0], alpha=1,\n",
        "         label = r\"Posterior of $\\tau$\",\n",
        "         color = TFColor[2], weights = w, rwidth = 2.)\n",
        "plt.xticks(arange(shape_count_data[0]))\n",
        "\n",
        "plt.legend(loc='upper left')\n",
        "plt.ylim([0, .75])\n",
        "plt.xlim([35, len(count_data) - 20])\n",
        "plt.xlabel(r\"$\\tau$ (in days)\")\n",
        "plt.ylabel(\"Probability\");"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7uYCt_SEEX2Z"
      },
      "source": [
        "plt.figure(figsize=(12.5, 15))\n",
        "\n",
        "ax = plt.subplot(311)\n",
        "ax.set_autoscaley_on(False)\n",
        "\n",
        "plt.hist(λ_0_samples, histtype = 'stepfilled', bins = 30, alpha = .85,\n",
        "         label=r\"Posterior of $\\lambda_0$\", color = TFColor[0], density = True)\n",
        "plt.legend(loc = 'upper left')\n",
        "plt.title(r\"Posterior distributions of the variables $\\lambda_0,\\;\\lambda_1,\\;\\tau$\")\n",
        "plt.xlim([15, 30])\n",
        "plt.xlabel(r\"$\\lambda_0$ value\")\n",
        "\n",
        "ax = plt.subplot(312)\n",
        "ax.set_autoscaley_on(False)\n",
        "plt.hist(λ_1_samples, histtype = 'stepfilled', bins = 30, alpha = .85,\n",
        "         label=r\"Posterior of $\\lambda_1$\", color = TFColor[6], density = True)\n",
        "plt.legend(loc = 'upper left')\n",
        "plt.xlim([15, 30])\n",
        "plt.xlabel(r\"$\\lambda_1$ value\")\n",
        "\n",
        "plt.subplot(313)\n",
        "w = 1.0 / τ_samples.shape[0] * ones_like(τ_samples)\n",
        "plt.hist(τ_samples, bins = shape_count_data[0], alpha = 1.,\n",
        "         label=r\"Posterior of $\\tau$\",\n",
        "         color=TFColor[2], weights = w, rwidth = 2.)\n",
        "plt.xticks(arange(shape_count_data[0]))\n",
        "\n",
        "plt.legend(loc = 'upper left')\n",
        "plt.ylim([0, .75])\n",
        "plt.xlim([35, len(count_data) - 20])\n",
        "plt.xlabel(r\"$\\tau$ (in days)\")\n",
        "plt.ylabel(r\"Probability\");"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FfiTXgF80sDA"
      },
      "source": [
        "## Interpretation\n",
        "\n",
        "Recall that 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 wider the distribution, the less certain our posterior belief should be. We can also see what the plausible values for the parameters are: $\\lambda_1$ is around 18 and $\\lambda_2$ is around 23. The posterior distributions of the two $\\lambda$s are clearly distinct, indicating that it is indeed likely that there was a change in the user's text-message behaviour.\n",
        "\n",
        "What other observations can you make? If you look at the original data again, do these results seem reasonable? \n",
        "\n",
        "Notice also that the posterior distributions for the $\\lambda$s do not look like exponential distributions, even though our priors for these variables were exponential. In fact, the posterior distributions are not really of any form that we recognize from the original model. But that's OK! This is one of the benefits of taking a computational point of view. If we had instead done this analysis using mathematical approaches, we would have been stuck with an analytically intractable (and messy) distribution. Our use of a computational approach makes us indifferent to mathematical tractability.\n",
        " \n",
        "Our analysis also returned a distribution for $\\tau$. Its posterior distribution looks a little different from the other two because it is a discrete random variable, so it doesn't assign probabilities to intervals. We can see that near day 45, there was a 50% chance that the user's behaviour changed. Had no change occurred, or had the change been gradual over time, the posterior distribution of $\\tau$ would have been more spread out, reflecting that many days were plausible candidates for $\\tau$. By contrast, in the actual results we see that only three or four days make any sense as potential transition points. \n",
        "\n",
        "### Why would I want samples from the posterior, anyways?\n",
        "\n",
        "We will deal with this question for the remainder of the book, and it is an understatement to say that it will lead us to some amazing results. For now, let's end this chapter with one more example.\n",
        "\n",
        "We'll use the posterior samples to answer the following question: what is the expected number of texts at day $t, \\; 0 \\le t \\le 70$ ? Recall that the expected value of a Poisson variable is equal to its parameter $\\lambda$. Therefore, the question is equivalent to *what is the expected value of $\\lambda$ at time $t$*?\n",
        " \n",
        "In the code below, 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 has not yet occurred), else we use $\\lambda_i = \\lambda_{2,i}$. \n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DgNkjkmO1h4I"
      },
      "source": [
        "# τ_samples, λ_0_samples, λ_1_samples contain\n",
        "# N samples from the corresponding posterior distribution\n",
        "\n",
        "N = τ_samples.shape[0]\n",
        "expected_texts_per_day = zeros(N, shape_count_data.shape[0])  # (10000, 74)\n",
        "\n",
        "plt.figure(figsize=(12.5, 9))\n",
        "\n",
        "day_range = arange(0, shape_count_data[0], step = 1, dtype = i32)\n",
        "\n",
        "# Expand from shape of 74 to (10000, 74)\n",
        "day_range = expand_dims(day_range, 0)\n",
        "day_range = tile(day_range, array([N, 1]))\n",
        "\n",
        "# Expand from shape of 10000 to 10000,74\n",
        "τ_samples_per_day = expand_dims(τ_samples, 0)\n",
        "τ_samples_per_day = transpose(tile(τ_samples_per_day, array([day_range.shape[1], 1])))\n",
        "\n",
        "τ_samples_per_day = τ_samples_per_day.astype(i32)\n",
        "# ix_day is (10000, 74) tensor where axis=0 is number of samples, axis=1 is day. each value is true iff sampleXday value is < tau_sample value\n",
        "ix_day = day_range < τ_samples_per_day\n",
        "\n",
        "λ_0_samples_per_day = expand_dims(λ_0_samples, 0)\n",
        "λ_0_samples_per_day = transpose(tile(λ_0_samples_per_day, array([day_range.shape[1], 1])))\n",
        "λ_1_samples_per_day = expand_dims(λ_1_samples, 0)\n",
        "λ_1_samples_per_day = transpose(tile(λ_1_samples_per_day, array([day_range.shape[1], 1])))\n",
        "\n",
        "expected_texts_per_day = (\n",
        "    (sum(λ_0_samples_per_day * ix_day.astype(f32), axis = 0)\n",
        "     + sum(λ_1_samples_per_day * ~ix_day.astype(f32), axis = 0))\n",
        "    / N)\n",
        "\n",
        "plt.plot(range(shape_count_data[0]), expected_texts_per_day, lw=4, color='#E24A33',\n",
        "         label = \"Expected number of text-messages received\")\n",
        "plt.xlim(0, shape_count_data.numpy()[0])\n",
        "plt.xlabel('Day')\n",
        "plt.ylabel('Expected # text-messages')\n",
        "plt.title(\"Expected number of text-messages received\")\n",
        "plt.ylim(0, 60)\n",
        "plt.bar(arange(len(count_data)), count_data, color = '#5DA5DA', alpha = .65,\n",
        "        label='Observed texts per day')\n",
        "\n",
        "plt.legend(loc='upper left');"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cgCrDy8M3IZT"
      },
      "source": [
        "The analysis shows strong support for believing the user's behaviour did change ($\\lambda_0$ would have been close in value to $\\lambda_1$ had this not been true), and that the change was sudden rather than gradual (as demonstrated by $\\tau$'s strongly peaked posterior distribution). We can speculate what might have caused this: a cheaper text-message rate, a recent weather-to-text subscription, or perhaps a new relationship. (In fact, the 45th day corresponds to Christmas, and I moved away to Toronto the next month, leaving a girlfriend behind.)\n",
        "\n",
        "\n",
        "## Exercises\n",
        " \n",
        "1.   Using `λ_0_samples` and `λ_1_samples`, what is the mean of the posterior distributions of $\\lambda_0$ and $\\lambda_1$?\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ddpQzca9ACJF"
      },
      "source": [
        "# Type your code here"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p4krLq5J_356"
      },
      "source": [
        "2.   What is the expected percentage increase in text-message rates? `hint:` compute the mean of `λ_0_samples / λ_1_samples`. Note that this quantity is very different from `λ_0_samples.mean() / λ_1_samples.mean()`"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qWoCGbmEAEvb"
      },
      "source": [
        "# Type your code here"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vGHVkSlp_9zf"
      },
      "source": [
        "3. What is the mean of $\\lambda_1$ **given** that we know $\\tau$ is less than 45? That is, suppose we have been given new information that the change in behaviour occurred prior to day 45. What is the expected value of $\\lambda_1$ now? (You do not need to redo the TFP part. Just consider all instances where `tau_samples < 45`.)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lKYX1MKHgsm0"
      },
      "source": [
        "# Type your code here"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nDdph0r1ABCn"
      },
      "source": [
        "## References\n",
        "\n",
        "[1] Gelman, Andrew. N.p.. Web. 22 Jan 2013. [N is never large enough](http://andrewgelman.com/2005/07/31/n_is_never_larg)\n",
        " \n",
        "[2] Norvig, Peter. 2009. [The Unreasonable Effectiveness of Data](http://static.googleusercontent.com/media/research.google.com/en//pubs/archive/35179.pdf).\n",
        "\n",
        "[3] 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",
        "\n",
        "[4] 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>."
      ]
    }
  ]
}