07_approximate_inference.ipynb

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    "# Creative Machine Learning - Approximate inference (Sampling)\n",
    "\n",
    "### Author: Philippe Esling (esling@ircam.fr)\n",
    "\n",
    "In this course we will cover\n",
    "1. Defining [sampling](#sampling) procedure with Monte-Carlo.\n",
    "2. Motivating the use of [Markov chains](#markov) in sampling.\n",
    "2. Implementing the [Gibbs sampling](#gibbs) algorithm.\n",
    "\n",
    "We begin with the standard imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/esling/Library/Python/3.9/lib/python/site-packages/urllib3/__init__.py:34: NotOpenSSLWarning: urllib3 v2.0 only supports OpenSSL 1.1.1+, currently the 'ssl' module is compiled with 'LibreSSL 2.8.3'. See: https://github.com/urllib3/urllib3/issues/3020\n",
      "  warnings.warn(\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns; sns.set()\n",
    "import numpy as np\n",
    "from cml.plot import cml_figure_matplotlib as figure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"sampling\"></a>\n",
    "## Sampling\n",
    "\n",
    "The main idea of sampling, is that we have a very complicated distribution, for which we do not know either the closed-form or its parameters. Although it is hard to find an adequate estimation of this distribution, we can try to solve simpler problems, by estimating _expected values_ of this distribution. To do so, we will define an _estimator_, for which we know that it will provide an accurate evaluation if we have a sufficient number of samples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "#### Example with $\\pi$\n",
    "\n",
    "A simple example to understand the underlying logic is that of trying to approximate $\\pi$. We know that we have the following relations, which means that we can estimate $\\pi$ as a form of expectation, by drawing _random samples_\n",
    "\n",
    "$$\n",
    "\\begin{align}\n",
    "\\frac{\\pi}{4} &= \\mathbb{E}\\left[ x^{2} + y^{2} \\leq 1 \\right] \\\\\n",
    "&\\approx \\frac{1}{M} \\sum_{s=1}^{M} \\left[ x_{s}^{2} + y_{s}^{2} \\leq 1 \\right]\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "with $x_{s},y_{s}\\sim \\mathcal{U}(0,1)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.1410728\n"
     ]
    },
    {
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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import random as r\n",
    "import math as m\n",
    "# Number of darts that land inside.\n",
    "inside = 0\n",
    "inside_pts = []\n",
    "outside_pts = []\n",
    "# Total number of darts to throw.\n",
    "total = 10000000\n",
    "# Iterate for the number of darts.\n",
    "for i in range(0, total):\n",
    "    # Generate random x, y in [0, 1].\n",
    "    x2 = r.random() ** 2\n",
    "    y2 = r.random() ** 2\n",
    "    # Increment if inside unit circle.\n",
    "    if (x2 + y2) <= 1.0:\n",
    "        inside += 1\n",
    "        inside_pts.append([m.sqrt(x2), m.sqrt(y2)])\n",
    "    else:\n",
    "        outside_pts.append([m.sqrt(x2), m.sqrt(y2)])\n",
    "# Compute estimator\n",
    "pi = (float(inside) / total) * 4\n",
    "print(pi)\n",
    "# Plot the points\n",
    "inside_pts = np.array(inside_pts)\n",
    "outside_pts = np.array(outside_pts)\n",
    "figure(8,8)\n",
    "plt.scatter(inside_pts[:, 0], inside_pts[:, 1], s=10)\n",
    "plt.scatter(outside_pts[:, 0], outside_pts[:, 1], s=10, c='r');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Advantages of Monte-Carlo\n",
    "- Very simple to program\n",
    "- Universally applicable to lots of problems\n",
    "- Scalable to parallelization\n",
    "\n",
    "Problems \n",
    "- Usually very slow\n",
    "- Better solutions might exist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Formal introduction\n",
    "\n",
    "The goal of Monte-Carlo methods is to _estimate expected values by sampling_\n",
    "So we can define\n",
    "$$\n",
    "\\mathbb{E}_{p(x)} f(x) \\approx \\frac{1}{M} \\sum_{s=1}^{M} f(x_{s})\n",
    "$$\n",
    "with $x_{s} \\sim p(x)$. This has nice co-properties\n",
    "- This is an _unbiased_ estimator\n",
    "- Guarantees on the convergence"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Why estimate expected values ?\n",
    "\n",
    "Remember the goal of full Bayesian inference\n",
    "$$\n",
    "\\begin{align}\n",
    "p(y \\vert x, Y_{train}, X_{train}) &= \\int p(y \\vert x, w) p(w \\vert y_{train}, x_{train}) dw \\\\\n",
    "&= \\mathbb{E}_{p(w\\vert Y_{train},X_{train})} p(y \\vert x, w)\n",
    "\\end{align}\n",
    "$$\n",
    "Here we can use sample to simplify the problem by _sampling_\n",
    "\n",
    "The same situation applies for the M-step of the EM-algorithm\n",
    "$$\n",
    "\\underset{\\theta}{\\max} \\mathbb{E}_{q} \\log p(\\mathbf{x},\\mathbf{t} \\vert \\theta)\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sampling from 1d distributions\n",
    "\n",
    "We start from the simplest case, where we have a discrete 1-d distribution. Imagine we want to sample from a Gaussian, so we can use the central limit theorem\n",
    "$$\n",
    "z = \\sum_{i=1}^{12} x_{i} - 6\n",
    "$$\n",
    "If we take $x_{i} \\sim \\mathcal{U}[0,1]$, then we have $p(z)\\approx\\mathcal{N}(0,1)$.\n",
    "Of course this is a rather crude approximation, we can rather use a more refined process"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now imagine we have a more complex distribution like this"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2b5a62f70>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "import scipy.stats as stats\n",
    "x = np.linspace(-7, 8, 100)\n",
    "plt.figure(figsize=(10,8))\n",
    "plt.plot(x, stats.norm.pdf(x, -1, 1.1) + stats.norm.pdf(x, 2, 0.9), linewidth = 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can upper-bound our distribution by an approximation, for instance we have that\n",
    "$$\n",
    "\\begin{align}\n",
    "q(x) &= \\mathcal{N}(1,3) \\\\\n",
    "p(x) &\\leq 2q(x)\n",
    "\\end{align}\n",
    "$$\n",
    "We use the constant $2$ as it is impossible to upper bound a distribution without multiplying it with a constant."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "import scipy.stats as stats\n",
    "x = np.linspace(-7, 8, 100)\n",
    "plt.plot(x, 0.5 * stats.norm.pdf(x, -1, 1.1) + 0.5 * stats.norm.pdf(x, 2, 0.9), linewidth=3)\n",
    "plt.plot(x, stats.norm.pdf(x, 1, 3) * 2, c='r', linewidth=3)\n",
    "plt.savefig('sampling_approx.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2b61390d0>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-7, 8, 100)\n",
    "mean = 1;\n",
    "plt.plot(x, stats.norm.pdf(x, 0, 3) + mean, c='r', linewidth=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Now note that we can sample from this approximation $q$ such that $\\tilde{x}\\sim q(x)$\n",
    "- So how can we sample from our distribution $p$\n",
    "- We now that we have a higher probability in $q$\n",
    "- Therefore we need to *reject* some of the points\n",
    "- The rule to reject should be probabilistic\n",
    "    - Should be proportional to the height of the curves\n",
    "    - So if we sample $\\tilde{x}$ and take its coordinates $y \\sim \\mathcal{U}[0, 2q(\\tilde{x})]$.\n",
    "    - We can accept $\\tilde{x}$ with probability $\\frac{p(x)}{2q(x)}$ if $y\\leq p(x)$\n",
    "How much points do we accept ? Knowing that we have $p(x)\\leq Mq(x)$, we accept $\\frac{1}{M}$ points on average\n",
    "\n",
    "Note that we can even use this _rejection sampling_ method if we know the distribution up to a normalization factor as\n",
    "$$\n",
    "\\begin{align}\n",
    "\\frac{\\hat{p}(x)}{Z} &\\leq Mq(x) \\\\\n",
    "\\hat{p}(x) &\\leq ZMq(x) \\\\\n",
    "\\end{align}\n",
    "$$\n",
    "For instance, we can define our distributions $p$ and $q$ as follows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.stats as st\n",
    "def p(x):\n",
    "    return st.norm.pdf(x, loc=30, scale=10) + st.norm.pdf(x, loc=80, scale=20)\n",
    "def q(x):\n",
    "    return st.norm.pdf(x, loc=50, scale=30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, you can implement the algorithm for rejection sampling and test it out\n",
    "\n",
    "***\n",
    "\n",
    "<div class=\"alert alert-success\" markdown=\"1\" style=\"color:white; background-color: #192841; border-color: #779ecb\">\n",
    "\n",
    "> ### Exercice (optional)\n",
    ">   1. Implement the _rejection sampling_ loop\n",
    ">   2. Test your implementation against existing sampling methods\n",
    "\n",
    "</div>\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "(5140,)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(-50, 151)\n",
    "k = max(p(x) / q(x))\n",
    "\n",
    "def rejection_sampling(iter=1000):\n",
    "    samples = []\n",
    "    \n",
    "    ######################\n",
    "    # YOUR CODE GOES HERE\n",
    "    ######################\n",
    "\n",
    "    ######################\n",
    "    # Solution\n",
    "    for i in range(iter):\n",
    "        \n",
    "        z = np.random.normal(50, 30)\n",
    "        u = np.random.uniform(0, k*q(z))\n",
    "\n",
    "        if u <= p(z):\n",
    "            samples.append(z)\n",
    "\n",
    "    ######################\n",
    "    return np.array(samples)\n",
    "\n",
    "plt.plot(x, p(x))\n",
    "plt.plot(x, k*q(x))\n",
    "plt.show()\n",
    "s = rejection_sampling(iter=10000)\n",
    "sns.displot(s);\n",
    "s.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Summary of rejection sampling\n",
    "+ Pro : Works for most distributions\n",
    "- Con : If $q$ and $p$ too different ($M$ large), rejects most points\n",
    "- Con : $M$ is large for d-dimensional distributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"markov\"></a>\n",
    "## Markov chains\n",
    "\n",
    "**Here explain the principle of Markov chains**\n",
    "\n",
    "Using Markov chain for sampling\n",
    "- We want to sample from p(x)\n",
    "- Build a Markov chain that converges to $p(x)$\n",
    "- Start from any $x^{0}$\n",
    "- For $k=0,1,\\cdots$\n",
    "$$\n",
    "x^{k+1}\\sim T(x^{k}\\rightarrow x^{k+1})\n",
    "$$\n",
    "- Eventually $x^{k}$ will look like samples from p(x)\n",
    "\n",
    "### Do chains always converge ?\n",
    "\n",
    "- Imagine a binary distribution\n",
    "- Will never converge\n",
    "- We need chains that do converge\n",
    "\n",
    "**Definition** : A distribution $\\pi$ is called _stationary_ if\n",
    "$$\n",
    "\\pi(x')=\\sum_{x} T(x\\rightarrow x') \\pi(x)\n",
    "$$\n",
    "\n",
    "**Theorem** : If $T(x\\rightarrow x') > 0$ for all $x, x'$, then there exists a unique $\\pi$ such that\n",
    "$$\n",
    "\\pi(x')=\\sum_{x} T(x\\rightarrow x') \\pi(x)\n",
    "$$\n",
    "And the Markov chain converges to $\\pi$ from any starting point."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gibbs sampling\n",
    "\n",
    "One of the easiest method to construct Markov chains to sample from a distribution. Say we have a 3-d distribution that we know up to norrmalization.\n",
    "$$\n",
    "p(x_{1}, x_{2}, x_{3}) = \\frac{\\hat{p}(x_{1}, x_{2}, x_{3})}{Z}\n",
    "$$\n",
    "The method of Gibbs sampling starts with $(x^{0}_{1}, x^{0}_{2}, x^{0}_{3})$ that we can set to $(0,0,0)$ for instance.\n",
    "\n",
    "Then we are going to sample each dimension at a time by sampling from the conditional\n",
    "$$\n",
    "\\begin{align}\n",
    "x^{1}_{1} \\sim &p(x_{1} \\vert x_{2} = x^{0}_{2}, x_{3} = x^{0}_{3}) \\\\\n",
    "&= \\frac{\\hat{p}(x_{1}, x^{0}_{2}, x^{0}_{3})}{Z}\n",
    "\\end{align}\n",
    "$$\n",
    "Then we reapply the same idea for the next dimensions.\n",
    "$$\n",
    "\\begin{align}\n",
    "x^{1}_{2} &\\sim p(x_{2} \\vert x_{1} = x^{1}_{1}, x_{3} = x^{0}_{3}) \\\\\n",
    "x^{1}_{3} &\\sim p(x_{3} \\vert x_{1} = x^{1}_{1}, x_{2} = x^{1}_{2}) \\\\\n",
    "\\end{align}\n",
    "$$\n",
    "Note that in this case, we cannot parallelize these sampling steps.\n",
    "\n",
    "We can prove that Gibbs sampling indeed converges to the desired distribution $p$. So we want to prove\n",
    "$$\n",
    "p(x',y',z') = \\sum_{x,y,z} q(x,y,z\\rightarrow x',y',z') p(x,y,z)\n",
    "$$\n",
    "\n",
    "Pros :\n",
    "- Reduce multidimensional sampling to sequence of 1d sampling\n",
    "- A few lines of code\n",
    "Cons :\n",
    "- Highly correlated samples\n",
    "- Slow convergence (mixing)\n",
    "- Cannot be parallelized"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Metropolis-Hastings\n",
    "\n",
    "- Sometimes Gibbs samples are too correlated\n",
    "- Idea of MH is to apply rejection sampling to Markov chains\n",
    "Let's start with any Markov chain $Q$ \n",
    "- Sample $x'$ from a _wrong_ $Q(x^{k}\\rightarrow x')$ for $k=1,2,\\cdots$\n",
    "- Use a critic to accept proposal $x'$ with probabiility $A(x^{k}\\rightarrow x')$\n",
    "- Otherwise stay at $x^{k}$, such that $x^{k+1}=x^{k}$\n",
    "So overall, the scheme works as\n",
    "$$\n",
    "\\begin{align}\n",
    "T(x\\leftarrow x') &= Q(x\\leftarrow x')A(x\\leftarrow x'), \\forall x\\neq x'\n",
    "T(x\\leftarrow x) &= Q(x\\leftarrow x)A(x\\leftarrow x)\\\\\n",
    "&+ \\sum_{x\\neq x'} Q(x\\leftarrow x')(1 - A(x\\leftarrow x'))\n",
    "\\end{align}\n",
    "$$\n",
    "\n",
    "How to choose A : $\\pi(x')=\\sum_{x} T(x\\rightarrow x') \\pi(x)$, we need to introduce the _detailed balance_ condition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"gibbs\"></a>\n",
    "## [Bonus] Gibbs Sampling implementation\n",
    "\n",
    "The Gibbs sampler is the simplest and most prevalent MCMC algorithm. If a posterior has $k$ parameters to be estimated, we may condition each parameter on current values of the other $k-1$ parameters, and sample from the resultant distributional form (usually easier), and repeat this operation on the other parameters in turn. This procedure generates samples from the posterior distribution. Note that we have now combined Markov chains (conditional independence) and Monte Carlo techniques (estimation by simulation) to yield Markov chain Monte Carlo.\n",
    "\n",
    "Here is a stereotypical Gibbs sampling algorithm:\n",
    "\n",
    "1.  Choose starting values for states (parameters):\n",
    "    ${\\bf \\theta} = [\\theta_1^{(0)},\\theta_2^{(0)},\\ldots,\\theta_k^{(0)}]$.\n",
    "\n",
    "2.  Initialize counter $j=1$.\n",
    "\n",
    "3.  Draw the following values from each of the $k$ conditional\n",
    "    distributions:\n",
    "\n",
    "    $$\\begin{aligned}\n",
    "    \\theta_1^{(j)} &\\sim \\pi(\\theta_1 | \\theta_2^{(j-1)},\\theta_3^{(j-1)},\\ldots,\\theta_{k-1}^{(j-1)},\\theta_k^{(j-1)}) \\\\\n",
    "    \\theta_2^{(j)} &\\sim \\pi(\\theta_2 | \\theta_1^{(j)},\\theta_3^{(j-1)},\\ldots,\\theta_{k-1}^{(j-1)},\\theta_k^{(j-1)}) \\\\\n",
    "    \\theta_3^{(j)} &\\sim \\pi(\\theta_3 | \\theta_1^{(j)},\\theta_2^{(j)},\\ldots,\\theta_{k-1}^{(j-1)},\\theta_k^{(j-1)}) \\\\\n",
    "    \\vdots \\\\\n",
    "    \\theta_{k-1}^{(j)} &\\sim \\pi(\\theta_{k-1} | \\theta_1^{(j)},\\theta_2^{(j)},\\ldots,\\theta_{k-2}^{(j)},\\theta_k^{(j-1)}) \\\\\n",
    "    \\theta_k^{(j)} &\\sim \\pi(\\theta_k | \\theta_1^{(j)},\\theta_2^{(j)},\\theta_4^{(j)},\\ldots,\\theta_{k-2}^{(j)},\\theta_{k-1}^{(j)})\\end{aligned}$$\n",
    "\n",
    "4.  Increment $j$ and repeat until convergence occurs.\n",
    "\n",
    "As we can see from the algorithm, each distribution is conditioned on the last iteration of its chain values, constituting a Markov chain as advertised. The Gibbs sampler has all of the important properties outlined in the previous section: it is aperiodic, homogeneous and ergodic. Once the sampler converges, all subsequent samples are from the target distribution. This convergence occurs at a geometric rate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Example: Inferring patterns in UK coal mining disasters\n",
    "\n",
    "Let's try to model a more interesting example, a time series of recorded coal mining \n",
    "disasters in the UK from 1851 to 1962.\n",
    "\n",
    "Occurrences of disasters in the time series is thought to be derived from a \n",
    "Poisson process with a large rate parameter in the early part of the time \n",
    "series, and from one with a smaller rate in the later part. We are interested \n",
    "in locating the change point in the series, which perhaps is related to changes \n",
    "in mining safety regulations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "disasters_array = np.array([4, 5, 4, 0, 1, 4, 3, 4, 0, 6, 3, 3, 4, 0, 2, 6,\n",
    "                            3, 3, 5, 4, 5, 3, 1, 4, 4, 1, 5, 5, 3, 4, 2, 5,\n",
    "                            2, 2, 3, 4, 2, 1, 3, 2, 2, 1, 1, 1, 1, 3, 0, 0,\n",
    "                            1, 0, 1, 1, 0, 0, 3, 1, 0, 3, 2, 2, 0, 1, 1, 1,\n",
    "                            0, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 2,\n",
    "                            3, 3, 1, 1, 2, 1, 1, 1, 1, 2, 4, 2, 0, 0, 1, 4,\n",
    "                            0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1])\n",
    "\n",
    "n_count_data = len(disasters_array)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are going to use Poisson random variables for this type of count data. Denoting year $i$'s accident count by $y_i$, \n",
    "\n",
    "$$y_i \\sim \\text{Poisson}(\\lambda).$$\n",
    "\n",
    "For those unfamiliar, Poisson random variables look like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 8))\n",
    "for l in [1, 5, 12, 25]:\n",
    "    plt.hist(np.random.poisson(l, 1000), alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The modeling problem is about estimating the values of the $\\lambda$ parameters. Looking at the time series above, it appears that the rate declines over time.\n",
    "\n",
    "A **changepoint model** identifies a point (here, a year) after which the parameter $\\lambda$ drops to a lower value. Let us call this point in time $\\tau$. So we are estimating two $\\lambda$ parameters:\n",
    "$\\lambda = \\lambda_1$ if $t \\lt \\tau$ and $\\lambda = \\lambda_2$ if $t \\geq \\tau$.\n",
    "\n",
    "We need to assign prior probabilities to both $\\{\\lambda_1, \\lambda_2\\}$. The gamma distribution not only provides a continuous density function for positive numbers, but it is also *conjugate* with the Poisson sampling distribution. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "lambda1_lambda2 = [(0.1, 100), (1, 100), (1, 10), (10, 10)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2bYrzzz9/0McPlfe+973xpVtuihUrVsQLL24esvM2lOtj9sQp8Xd3/60rQQzIrFmzYtmyZbF48eJYt27dSA+HxJmPjDbmJKOJ+Tg0Xn/uwL4MKIJeeeWViIhYu3Ztv/Vr1qyJD3/4w7F58+aYMWNGv23Tp0+PiIiNGzdGqVSKxsbGGDduXDQ3N/fbZ+PGjQMZSj+VSiWefvrpQR8/VF5/wt2OHTtiy5YtQ3be9rFjY0q+Jp555pnYunXrkJ2XdKxbt25U/DcCEeYjo485yWhiPh6Y/bkVLmKAD0Z48skno7OzM+bPn99v/QknnBBr166NFStW7PGAg3POOSfWr18fzz33XDzwwAPR2dnZb59yuRynnXZarFy5ciBDAQAAGJQBXQnatWtXfO1rX4vbbrstKpVKPPvss3H++efHmWeeGSeddFJs27YtLrvssvj6178e3/jGN+Lkk0+OG264oe/DVFtbW2Pp0qVx2223RUtLS7S0tMQNN9wQO3bsiO9973sH5QUCAAC80YA/J+jqq6+OlpaW+Iu/+IuYNGlS/Mu//Eucf/75fQ8mWLhwYdx+++3x+OOPx5YtW+Kqq66KpUuX9h1/xRVXRHd3d3z729+OcrkcDz30UCxYsCC6urqG7lUBAAC8hQFHUJZlccstt8Qtt9yy1+3/9E//FCeddNJbHt/T0xNXXnllXHnllQP90gAAAAdsQO8JAgAAONSJIAAAICkiCAAASIoIAgAAkiKCAACApIggAAAgKSIIAABIiggCAACSMuAPS2UfsizGlMrxjrFjh+yUjWPGRLlUiokTJw7ZOUdCR0dHtLa2jvQwAABInAgaQuVyOfJZTyx4z/Gx69++c8jOW1OsifHl+mj8wqXR0dE5ZOcdbtu2tcTtt98phAAAGFEiaAjV1dVFLqqRL+yInt6tQ3beXNRG5MdGZ+eG6OhoH7LzDqdSaWxMnHhElMtlEQQAwIgSQQdBpbc7uitDd8Uml++NarU2Ojp2R3t725Cdd7iVy0eM9BAAAMCDEQAAgLSIIAAAICkiCAAASIoIAgAAkiKCAACApIggAAAgKSIIAABIiggCAACSIoIAAICkiCAAACApIggAAEiKCAIAAJIiggAAgKSIIAAAICkiCAAASIoIAgAAkiKCAACApIggAAAgKcWRHsDhJssiivnaqC2W+q2v9laj2tszQqMCAABeJ4KGUKlUimpPLiaM+TdRX5jab1s164oXtq4VQgAAMMJE0BCqra2N3t6I1l3dsWt3W9/6YrEYjY11UcgXRBAAAIwwEXQQVKuV6Km8OXbqRmQsAABAfx6MAAAAJEUEAQAASRFBAABAUkQQAACQFBEEAAAkRQQBAABJEUEAAEBSRBAAAJAUEQQAACRFBAEAAEkRQQAAQFJEEAAAkBQRBAAAJEUEAQAASRFBAABAUkQQAACQFBEEAAAkRQQBAABJEUEAAEBSRBAAAJAUEQQAACRFBAEAAEkRQQAAQFJEEAAAkBQRBAAAJEUEAQAASRFBAABAUkQQAACQFBEEAAAkRQQBAABJEUEAAEBSRBAAAJAUEQQAACRFBAEAAEkRQQAAQFJEEAAAkBQRBAAAJEUEAQAASRFBAABAUkQQAACQFBEEAAAkRQQBAABJEUEAAEBSRBAAAJAUEQQAACRFBAEAAEkRQQAAQFJEEAAAkBQRBAAAJEUEAQAASRFBAABAUkQQAACQFBEEAAAkRQQBAABJEUEAAEBSRBAAAJAUEQQAACRFBAEAAEkRQQAAQFJEEAAAkBQRBAAAJEUEAQAASRFBAABAUkQQAACQFBEEAAAkRQQBAABJEUEAAEBSRBAAAJAUEQQAACRFBAEAAEkRQQAAQFJEEAAAkBQRBAAAJEUEAQAASRFBAABAUkQQAACQFBEEAAAkRQQBAABJEUEAAEBSRBAAAJAUEQQAACRFBAEAAEkRQQAAQFIGHUGTJk2KLVu2xI033ti3bubMmbFixYrYtWtXbNmyJb761a9GXV1dv+Muv/zy2LBhQ7S1tcWjjz4aH/jABwY/egAAgAEadAR961vfiilTpvT9/1KpFPfdd19Uq9U444wz4hOf+EScd955ceedd/bt85nPfCZuuumm+NKXvhQnnnhiPPTQQ/HjH/84jj322AN7FQAAAPtpUBH0uc99Lt75znfGSy+91LduyZIlMWHChFi8eHE8+eSTcf/998c111wTn/zkJ6OpqSkiIq677rq49dZb4+677461a9fG1VdfHRs2bIhLL710aF4NAADAPgw4gmbPnh033XRT/Mf/+B+ju7u7b/2CBQvi4YcfjtbW1r519913X9TW1sYHP/jB+J3f+Z04+uijY/ny5f3Ot2rVqli4cOEBvAQAAID9VxzIznV1dXHPPffETTfdFKtXr+63bebMmfHTn/6037rm5ubYvXt3TJ06Nbq6uiIi4vnnn++3z6ZNm2Lq1KmDGXufYrEY8+bNO6BzDIVp06ZFRES+WIza2tq+9cViMWpqijFmzJiorQ7oWx4REXU1NVEul2Py5MnR0dk5ZOMdTnV1Y6Kudnwcf/zxsXPnzpEeTjJmzZrV708YSeYjo405yWhiPg6N2trafhdq3sqAfiP/8z//89i2bVvcdttte2xrbGyMtra2Pda3trZGQ0NDNDY2RkTssc/r2w/EtGnT4qmnnjqgcwyFzs7O2PrqqzGusTEaGsf2rc/n8tHYWBuT3jknIt874PPmI6IxX4z5c+ZGLp8bwhEPn2o1F+3t74iPfexTUSgURno4yVm2bNlIDwH6mI+MNuYko4n5eODWr1+/z332O4LOPvvsWLJkScydOzeyLNtje3Nzc9TX1++xvlwux/bt26O5uTkiIurr66OlpWWP7Qdi06ZNcf755x/QOYbCueeeG3988cXRvGtX7G777W2BxWIxenrqY8v6ddFT7RrweetqamJS/dj4l1+sPsSvBE2PpUvvcSVoGM2aNSuWLVsWixcvjnXr1o30cEic+choY04ympiPQ+Pee+/dr/32O4IWLlwYjY2N8dxzz/WtK5VKcfXVV8eVV14ZK1eujBkzZvQ7prGxMcaNGxcbN26Ml19+OSIiZsyYEb/4xS/69pk+fXps3Lhxf4exV5VKJZ5++ukDOsdQmDt3bkRE9FYq/S7DZb1Z9PRUoq2tLborA4+YntraGJsrxNatW/d6te1QUF/fEOXy2HjmmWdi69atIz2c5Kxbt25U/DcCEeYjo485yWhiPh6Y/bkVLmIAD0a45ZZbYvbs2XHCCSf0LS+++GL8zd/8TZxwwgnx4x//OE499dQol8t9xyxatCja2trioYceitWrV8emTZti0aJF/c67cOHCWLly5f4OAwAA4IDs95WgV199NV599dV+63p6emL79u3xy1/+Ml566aX40pe+FH/7t38bN954Y7zrXe+Ku+66K26//fa+hyLccccdccMNN8SGDRvi+eefjz/5kz+JI444Ir7xjW8M7asCAAB4CwN/VNlbaG1tjQULFsRdd90VP/vZz6K5uTn++3//7/Ff/st/6dvnq1/9atTV1cWtt94a48ePjyeeeCLOPPPMPeIKAADgYDmgCDrmmGP6/f9169bFmWee+bbHfPnLX44vf/nLB/JlAQAABm3AH5YKAABwKBNBAABAUkQQAACQFBEEAAAkRQQBAABJEUEAAEBSRBAAAJAUEQQAACRFBAEAAEkRQQAAQFJEEAAAkBQRBAAAJEUEAQAASRFBAABAUkQQAACQFBEEAAAkRQQBAABJEUEAAEBSRBAAAJAUEQQAACRFBAEAAEkRQQAAQFJEEAAAkBQRBAAAJEUEAQAASRFBAABAUkQQAACQFBEEAAAkRQQBAABJEUEAAEBSRBAAAJAUEQQAACRFBAEAAEkRQQAAQFJEEAAAkBQRBAAAJEUEAQAASRFBAABAUkQQAACQFBEEAAAkRQQBAABJEUEAAEBSRBAAAJAUEQQAACRFBAEAAEkRQQAAQFJEEAAAkBQRBAAAJEUEAQAASRFBAABAUkQQAACQFBEEAAAkRQQBAABJEUEAAEBSRBAAAJAUEQQAACRFBAEAAEkRQQAAQFJEEAAAkBQRBAAAJEUEAQAASRFBAABAUkQQAACQFBEEAAAkRQQBAABJEUEAAEBSRBAAAJAUEQQAACRFBAEAAEkRQQAAQFJEEAAAkBQRBAAAJEUEAQAASRFBAABAUkQQAACQFBEEAAAkRQQBAABJEUEAAEBSRBAAAJAUEQQAACRFBAEAAEkRQQAAQFJEEAAAkBQRBAAAJEUEAQAASRFBAABAUkQQAACQFBEEAAAkRQQBAABJKY70AFKRy+Wjtlja67ZqbzWqvT3DPCIAAEiTCBoG+Xw+xpbHxVET3h29vdU9tlezrnhh61ohBAAAw0AEDYN8Ph+5yEfrrq7o6u7qt61YLEZjY10U8gURBAAAw0AEDaOeSiV6KnsLnbphHwsAAKTKgxEAAICkiCAAACApbodjv9TWlqJYrBn08eXy2AM6HgAAhooIYp9qa0sxf/YHopwf/HQpFmuikm+IsWPHxtatW4dwdAAAMDAiiH0qFmuinC9GfuOvotrRNqhz5MeOi9Kxvxel0t4/KwkAAIaLCGK/VTvaotKxe1DHFou13oAGAMCoIIIYNrl8PsaPHx+TJ08e1PEdHR3R2to6xKMCACA1IohhkaupjXHvaIpLLrwgmluaB3WObbt3x+1f/4YQAgDggIgghkW+UIxCbzWy538ZbS9sHPDxpYZ3xMR3zYpyuSyCAAA4ICKIYdW1uzXam5sHdeyYoR0KAACJ8l51AAAgKa4EMWxyuVyUSqUYM2bg13TK9fVRKpVi4sSJB2FkI8sDHwAAhpcIYlgUCoWora2NOXPeHcdOnzrw48v1Ef92dlx++Weis7PjIIxw5Gzb1hK3336nEAIAGCYiiGGRyxcil8tFlnVET8/OAR/fW+yOXLU1Ojs3RscgP6toNCqVxsbEiUd44AMAwDASQQyrarUneipdAz4uq9RErtITHR27o7398IqFcvmIkR4CAEBSPBgBAABIiggCAACSIoIAAICkiCAAACApIggAAEiKCAIAAJIiggAAgKSIIAAAICkiCAAASMqAI2js2LFx1113xUsvvRSdnZ3x7LPPxkUXXdS3ff78+fHII49EW1tbvPDCC3HddddFLpf77RfM5+Pmm2+Ol156KVpbW2PVqlUxe/bsIXkxAAAA+zLgCPrWt74V5557blxyySVx4oknxg9+8IP41re+FWeffXZMmTIl7rvvvnjuuefilFNOicsuuywuv/zyuOaaa/qOv+WWW+LTn/50fOYzn4nf//3fj82bN8eqVauiqalpSF8YAADA3hQHsvPkyZPjD/7gD2Lx4sXxwx/+MCIiVq9eHaeffnpcfvnl8dRTT8WOHTvi4osvjt7e3li9enW8613vii9+8Yvxla98JcaMGROXXXZZfPazn4177703IiIuvvjieOWVV2Lx4sVx1113Df0rBAAAeIMBXQk66qijYsuWLfHkk0/2W79169Y46qijYsGCBbFy5cro7e3t23bffffFlClTYt68efH+978/yuVyLF++vG97T09PPPzww7Fw4cIDfCkAAAD7NqAIevrpp2PatGnx/PPP962bNWtWnHXWWfHzn/88Zs6c2W9bRMSmTZsiImLq1Kkxc+bMaGlpie3bt++xz9SpUwf7GgAAAPbbgG6He7MlS5bEHXfcES0tLXH99dfHkiVLoq2trd8+ra2tERHR0NAQjY2Ne2x/fZ+GhoZBj6NYLMa8efMGffxQmTZtWkRE5IvFqK2t7VtfU1MT+Xw+aos1kUVvv2OKxWLU1BRjzJgxUVvd+19HXU1NlMvlmDx5cnR0dh68F/AW6urGRLm+PmLM2Ogt5PZ9wF6U6kqRy+WiVCrF2LED/7vOl8ZE1NfHpMlHRFfX2EGNYTSqqxsTdbXj4/jjj4+dO3cO+flnzZrV708YSeYjo405yWhiPg6N2tra6O7u3ud+g4qgY489NpYuXRqnnnpq/OhHP4pLLrkktmzZEs3NzVFfX99v33K5HBER27dvj6ampj22v77Pm68ODcS0adPiqaeeGvTxQ6WzszO2vvpqjGtsjIbG3/6iXswXoq6uLiZOmhi9b4qgfC4fjY21MemdcyLyvW8+5Wv7RERjvhjz58yNXH5wEXIgqtVctL3UFaXaLArVfU+qvekujo3dxWLMnDkzitnRAx9DoTY6Z7wr5p3+u1EoZIMaw2hUreaivf0d8bGPfSoKhcJB+zrLli07aOeGgTIfGW3MSUYT8/HArV+/fp/7DDiCTj/99PiHf/iH2L59e5x33nn93t+zefPmmDFjRr/9p0+fHhERGzdujFKpFI2NjTFu3Lhobm7ut8/GjRsHOpQ+mzZtivPPP3/Qxw+Vc889N/744oujedeu2N3W2re+VFeK4qRibHt1W3RVuvodUywWo6enPrasXxc91a43nzIiXrsSNKl+bPzLL1aP2JWg46fNjVi3Jno797yStz/GTJoWExqPjueffz5279w64OPzpTER3bl45v5fRFfX4MYwGr12JWh6LF16z0G7ErRs2bJYvHhxrFu3bsjPDwNhPjLamJOMJubj0Hj94Wv7MqAIKpfLcc8998SaNWti0aJFfbe6vW7FihXxkY98JL7whS/0rTvnnHNi/fr18dxzz8WWLVuis7MzFi5cGN/97nf7znnaaaf1O2agKpVKPP3004M+fqjMnTs3IiJ6K5V+l+EK+UL09vZGd6Vnj8tzWW8WPT2VaGtri+7K3gOnp7Y2xuYKsXXr1r3eTniw1dc3RMeE9sjadkelY/egzlFo7Iwsy6KzszN2727d9wFvUqxmkWtvj1e3vhLt7QM/frSqr2+IcnlsPPPMM7F168DjcH+tW7duVPw3AhHmI6OPOcloYj4emP25FS5igBF01llnxZQpU+Kiiy6KyZMnx+TJk/u2dXR0xDe/+c247LLL4utf/3p84xvfiJNPPjluuOGG+PznPx8Rr733Z+nSpXHbbbdFS0tLtLS0xA033BA7duyI733vewMZCgAAwKAMKIKOO+64iIj48Y9/vMe2Bx98MM4444xYuHBh3H777fH444/Hli1b4qqrroqlS5f27XfFFVdEd3d3fPvb345yuRwPPfRQLFiwILq69n4rGAAAwFAaUATddtttcdttt73tPv/0T/8UJ5100ltu7+npiSuvvDKuvPLKgXxpAACAIXFAj8iG4ZQvFKJcPrDHY1cqPdHdPfwPlwAAYPQQQRwS8jW1MWH8kTE/l49KpWfQ5+norcSTax8RQgAACRNBHBJyxZoo9maR3/CryHY3D+ochfKYKM84LorFGhEEAJAwEcQhpdrZPujHdEdEDP9HzQIAMNrkR3oAAAAAw0kEAQAASRFBAABAUkQQAACQFBEEAAAkRQQBAABJEUEAAEBSRBAAAJAUEQQAACRFBAEAAEkRQQAAQFJEEAAAkBQRBAAAJEUEAQAASRFBAABAUkQQAACQFBEEAAAkRQQBAABJEUEAAEBSRBAAAJAUEQQAACRFBAEAAEkRQQAAQFJEEAAAkBQRBAAAJEUEAQAASRFBAABAUkQQAACQFBEEAAAkRQQBAABJEUEAAEBSRBAAAJAUEQQAACRFBAEAAEkRQQAAQFJEEAAAkBQRBAAAJEUEAQAASRFBAABAUoojPQAYTvlCIcrlsYM+vlLpie7uziEcEQAAw00EkYx8TW1MGH9kzM/lo1LpGdQ5Onor8eTaR4QQAMAhTASRjFyxJoq9WeQ3/Cqy3c0DPr5QHhPlGcdFsVgjggAADmEiiORUO9uj0rF7UMfmhngsAAAMPw9GAAAAkuJKEIywYrEmJk6ceFDO3dTUFNVqNZqammLy5MkH5WscTB0dHdHa2jrSwwAADjMiCEZQTU1dzJ797vjCFy6Njo6hf5/RhAnjo619W3z60/8htm/fMeTnP9i2bWuJ22+/UwgBAENKBMEIKhZrolQqRpZtjY6OV4f8/F3du6O+viW6uv81OjpeGfLzH0yl0tiYOPGIKJfLIggAGFIiaBTI5fJRWyztsb7aW41q7+Ae5cyhpaurLdrbh/4X/a6usVEoZAft/AdbuXzESA8BADgMiaARls/nY2x5XBw14d3R21vtt62adcULW9eO0MgAAODwJIJGWD6fj1zko3VXV3R1d/WtLxaL0dhYF4V8ISJ6R26AAABwmBFBo0RPpRI9lTff+lY3ImMBAIDDmc8JAgAAkiKCAACApLgdLhG1taUoFmsGdWy5PDYK+UJUhnhMAAAwEkRQAmprSzF/9geinB/cX3ehpjYmNE6MVwd5PAAAjCZ+q01AsVgT5Xwx8ht/FdWOtgEfn2+aFIXZkyOfd/ckAACHPhGUkGpHW1Q6dg/4uEJ5zEEYDQAAjAz/tA8AACRFBAEAAEkRQQAAQFJEEAAAkBQRBAAAJEUEAQAASRFBAABAUkQQAACQFBEEAAAkRQQBAABJEUEAAEBSRBAAAJAUEQQAACRFBAEAAEkRQQAAQFJEEAAAkBQRBAAAJEUEAQAASRFBAABAUkQQAACQFBEEAAAkRQQBAABJEUEAAEBSRBAAAJCU4kgPAA4l+UIhyuWxB3SOSqUnurs7h2hEAAAMlAiC/ZSvqY0J44+M+bl8VCo9gz5PR28lnlz7iBACABghIgj2U65YE8XeLPIbfhXZ7uZBnaNQHhPlGcdFsVgjggAARogIGsVyuXzUFksR+d4oFGqjXB4bWfba27jcUjVyqp3tUenYPejjc0M4FgAABk4EjVL5fD7GlsfFURPeHblcFuViTcye3RiVSiUiIrq72+MXv1glhAAAYIBE0CiVz+cjF/lo3dUVlWpP1NfUxbatu6Kn0hO1tbXxjnH1bqkCAIBBEEGjXE+lEtVqJar5QnR3d0VPz+tvyC+P6LhgOBSLNTFx4sSRHsao09HREa2trSM9DAA4ZIkgYFSqqamL2bPfHV/4wqXR0eGK5xtt29YSt99+pxACgEESQcCoVCzWRKlUjCzbGh0dr470cEaNUmlsTJx4RJTLZREEAIMkgoBRraurLdrb/bL/RuXyESM9BAA4pOVHegAAAADDSQQBAABJEUEAAEBSRBAAAJAUEQQAACRFBAEAAEkRQQAAQFJ8TtAhIpfLRU1NTURE1BRrolgsRn19feRyvfs8tlyuj5piTWQ1NZGv1PbbVu3tjWq1clDGDAAAo5EIOgTkc7kYU18fU446Knp7e6NQKEZTUznmjXlvVKvd+zy+UKiNicXJUWg9KqK7o9+2ak8lXnzxRSEEAEAyRNAhoFAoRKFYjEoW0dNbjWIuF91ZFq09uahUc/327c0qUe2t9ltXU8hFY6kSuZ6u6O3u6ltfzOejVFMThXw+qv0PAQCAw5YIGuXy+XxMaRgbDZGLUqkUvb21kc/nY0yUYtzY4yLLsn77Z1GNts7myLLf3iaXLxRjTM3Y2N2bRVXtAACQOBE0yuXz+aip9kbNi+ujZ/euiGpvFAvFqBkzNnra26Lyhqs++Vw+ausKUeh4td/VoPzYcZGfcXzkc/mQQAAApE4EHSp6eiLr6oqsWo2sWBO52tqodHb0ey9Pli9E5Gqit6sjent/uz5fWx6JEQMAwKgkghL3xqfOvZWaYvG1K1I1NdFbU/u2+77OU+cAABitRFDCfvvUuSOjt/dtHrU9pinqSqWYPOWI6G0au1/n9tQ5AABGKxGUsHwuF7l8Pjorleiu9LzlfoW6rihkvdHe0xOVNzxd7q146hwAAKOZCCKqvdW3fWpcrppFlmXRu4/9AADgUCCCYJjlC4Uol1+7rbBUGhP5fDFKpTFRX9+wX8dXKj3R3d15MIfIKFcs1sTEiRNHehgD1tTUFNVqNZqammLy5MlDfv6Ojo5obW0d8vMCcPgRQYeZXC4XhXz/v9Z8Ph+5yL3FEYeWQqEQtfv5cIY3e7sHPAzXgxzyNbUxYfyRMT+Xj0qlJ0p19TG+UBdz3nlCdB7RsV/n6OitxJNrHxFCiaqpqYvZs98dX/jCpdHRcWjNgQkTxkdb+7b49Kf/Q2zfvmPIz79tW0vcfvudQgiAfRJBh5FcLhe1xVI0lCf1+7DUKDVEsVAbkcuP3OCGQC6Xi0mTJ0eu2ji4E7zNAx6G60EOuWJNFHuzyG/4VWS7myPKY6PYsivi5Q2RdbTt8/hCeUyUZxwXxWKNCEpUsVgTpVIxsmxrdHS8OtLDGZCu7t1RX98SXd3/Gh0drwzpuUulsTFx4hFRLpdFEAD7JIIOI7lcLiJy0d1Vicob3rtTrOmNYuQiP4wR9OZHbxfyr33tYrE4qCs5r1/FKdQUo62rJypv9zS7t/BWD3gYiQc5VDvbo9KxO6qRi+juimpHW1Q6du/XsYU33E63L3V1Y6JazUVdXf/b7dxSd+jr6mqL9vZD65f9rq6xUShkB23sDQ1HH5K3CQ4HtwoC9CeCDkPV3t7o7f3tb/O92cCD4UDs7dHbhYaJkc8XYvzECdFQP4hpN6Yp6kp1USyVorU1G9QDGg6HBzy8+Xa6fSnX10fbS11x/LS50TGhvW+9W+o43BzKtwkOB7cKAvQnghhye3v0dl2lErWRRWdPT3Tsx2O236xQ1xU1WRa5fP43V7zStMftdPsyZmyUarOIdWsia3vtSpNb6jgcHcq3CR5sbhUE2NOIRFA+n48bb7wxPvWpT0VDQ0M8/vjj8Sd/8iexdu3akRgOB8kbH739+tWoau+BXcXhNa/fTrcvvYVcFKrd0dvZ/3a7dDOSw92heJvgcCiXjxjpIQCMKiMSQbfccktcdNFFcckll8TGjRvji1/8YqxatSre/e53x86dO0diSCTuze9h2pu3e7rc25w44g3x9uZzFPv+fzFqK/s+Z02xmPSVMGBwDtXHqh9s9fX1Iz0EYIQMewQ1NDTEZZddFp/97Gfj3nvvjYiIiy++OF555ZVYvHhx3HXXXcM9JBK3t/cw7dXbPF1ub3K5XJRL5ejo7PjtVaw3naOQr41SqRSTp0yJSnXf7/GJMU1RWy5FXV1d9HbuTzQVIrLX/nz9gRSFmprI15Zi/PhJ/X4B6KlUo2c/b1X0YAU4dHi/1FsrFOre/uc+cNga9gh6//vfH+VyOZYvX963rqenJx5++OFYuHChCDpIcrmIfK7Q7zOE8vliROSjkC9GIb+3W81yEZG99jlDuVzk88XfHP/a+r0Z7ocwDIW9vYdpb97q6XJvpa6mJsYWC9FVrfad983nqClE1JV6o72nO7or3fs+Z301yoViTJ5yRFTese9/wawpFqO70hOTjjgixlV+8/jvckMUjzomJk7u/yj1rLc3du7YEb3Vff8ddmSVWP3cY9HTs+/vQy6fj2wQv2SUy+UoFAtRLpdjzJgxe2zvqVSiu2vg7y+D1Hi/1N6VSmNjwoTfjUqlctA+wPdQVigUDtmHCB1MB/P7crA/UPpgO9SeQvnWv80eJJ/73OfipptuinHjxvVbf+edd8Ypp5wS73nPewZ0vvb29qipqYmXX355CEc5OPX19dHY2BiVarXfL5e5yEW+UIjeajWyN32732rbG9cXcrnIVSr9z5nL9/8soLdbn89HrliMqFT63Zr12v4Rke1jEuRyEYViRHXP4/eURRZZ5HO56M2y3+6fL0SuWBNZT3fEYEIpn49coSZy1cproTWY9wf95hxZpaf/GHK5Pcc7kOPfyt7O++Zz5HKRi3xksZ+v6Tffx+jpfu2YfQ8i8vn8b/6l8zfnz/1mDG/8+8xF5CO3x/x8q3NmhUL05nr3/dMjF2/4HuzHqfsdm4t8rhhZVtnr+8GyLIuenp4Y5h9hIy6XL0RNsS4qlc5D7l+w8/lC1NeXo729o98TLIfCofx9Odh8b/Yul8tHTU0pamqK0dnpe9Nf7g2/7Kf1M/btHdzvSz6fj1KpdMjOx2o1i7a2thEf+5QpU6Knp2eft7sO+5WgxsbGaGvb80MhW1tbo6GhYS9HvL2u3/xLcHf3vv8V/WDr7u6O5ubmkR4GAAAkqaenp68P3s6wR1Bzc/Ney6xcLsf27dsHfL6mpqahGBYAAJCI/HB/wc2bN0djY+Met8NNnz49Nm7cONzDAQAAEjPsEfTAAw9EZ2dnLFy4sG9duVyO0047LVauXDncwwEAABIz7LfDtba2xtKlS+O2226LlpaWaGlpiRtuuCF27NgR3/ve94Z7OAAAQGJG5MNSr7jiiuju7o5vf/vbUS6X46GHHooFCxbs15uYAAAADsSwPyIbAABgJA37e4IAAABGkggCAACSIoIAAICkiCAAACApIggAAEiKCAIAAJIigoZAPp+Pm2++OV566aVobW2NVatWxezZs0d6WBymxo4dG3fddVe89NJL0dnZGc8++2xcdNFFfdvnz58fjzzySLS1tcULL7wQ1113XeRyub7t5isH06RJk2LLli1x44039q2bOXNmrFixInbt2hVbtmyJr371q1FXV9fvuMsvvzw2bNgQbW1t8eijj8YHPvCB4R46h5kLLrgg1qxZEx0dHbFhw4b4/Oc/37fNz0mGU6lUiltvvTU2btwYzc3N8Y//+I8xb968vu1nnXVWPPXUU9He3h6//OUv45JLLul3fLlcjr/+67+OV199NVpaWuIHP/hBHH300cP9Mg5LmeXAlq985SvZyy+/nJ133nnZnDlzsv/1v/5XtmXLlqypqWnEx2Y5/Ja/+7u/y1544YXs3HPPzebMmZPdfPPNWZZl2dlnn51NmTIl27FjR7Z06dJszpw52Yc//OHs1Vdfza699tq+481Xy8FcfvjDH2ZZlmU33nhjFhFZqVTK1q9fny1fvjybP39+duaZZ2a//vWvs29+85t9x3zmM5/Jdu/enS1ZsiSbPXt29pWvfCVra2vLjj322BF/PZZDc1m0aFHW2dmZff7zn8/mzJmTXX/99VmWZdmpp57q56Rl2JdvfvOb2fPPP5+dddZZ2fz587Pvfe972fbt27MpU6Zkc+bMyTo7O7Obb745mz17dvaHf/iHWXt7e7Z48eK+47/73e9mv/zlL7MPfvCD2fz587MVK1Zka9euzYrF4oi/tkN8GfEBHNJLQ0ND1t7enl100UV962pqarIdO3Zk//k//+cRH5/l8FomT56cVSqV7MILL+y3/mc/+1m2cuXK7Oabb85+/etfZ/l8vm/bVVddlW3ZsiXL5/Pmq+WgLp/73OeyNWvWZC+++GJfBF188cVZS0tL1tDQ0LffBRdckHV1dfX9Qrlp06bsz/7sz/qd65lnnsn+4i/+YsRfk+XQXJ544ons9ttv77fuRz/6UXbLLbf4OWkZ1qVYLGZdXV395lO5XM46OjqySy65JPvOd76TPfjgg/2Oueuuu7Kf//znWURkxx13XJZlWXb66af3bZ88eXJWrVazD33oQyP++g7xZcQHcEgvixYtyrIsyyZMmNBv/f/9v/83W758+YiPz3J4LfPmzcs2bdqUzZw5s9/6v//7v89Wr16dPf7449mdd97Zb9sJJ5yQZVmWzZ8/33y1HLRl9uzZWXNzczZnzpxsw4YNfRH0v//3/95jbo0bNy7Lsiz7yEc+kv3O7/xO3/x84z533HFHtmbNmhF/XZZDb5k8eXKWZVn2e7/3e3vd7uekZTiX8ePHZ1mWZRdccEHfukKhkO3evTu77LLLsldeeSW74oor+h1z/vnn983B//Sf/lPW0tKS5XK5fvv8v//3//aYx5aBLd4TdIBmzpwZLS0tsX379n7rN23aFFOnTh2hUXG4evrpp2PatGnx/PPP962bNWtWnHXWWfHzn/88Zs6c2W9bxGtzMSJi6tSp5isHRV1dXdxzzz1x0003xerVq/tt29ucbG5ujt27d/fNyYjY67w1JxmMOXPmRETEMcccE48//njs2LEjnnjiifj4xz8eEXufk35OcrDs2LEjHn300bjmmmvimGOOiVKpFF/+8pejWCzGgw8+GJMnT97nfNywYUNkWbbHPubjgSmO9AAOdY2NjdHW1rbH+tbW1mhoaBiBEZGSJUuWxB133BEtLS1x/fXXx5IlS/aYj62trRER0dDQYL5yUPz5n/95bNu2LW677bY9tu1rzjU2NkZE7HXempMMxvjx4yMi4tZbb41rr702fvWrX8WHPvSh+M53vhPVanWvc9LPSQ6mT33qU/HYY4/F+vXro7e3N/L5fNx0002xbdu2iNj7z7+Ifc/HCRMmHPzBH8ZE0AFqbm6O+vr6PdaXy+U9/hUJhsqxxx4bS5cujVNPPTV+9KMfxSWXXBJbtmzZ63wsl8sREbF9+/ZoamoyXxlSZ599dixZsiTmzp27x79URuz7Z2Rzc3NERNTX10dLS8se22Gg8vnXbnK56qqr4vvf/35ERDzxxBNx4oknxqWXXurnJMNq0qRJcf/998fatWvjhhtuiJaWlvjoRz8a119/fTz77LMREW87H/2eefC4He4Abd68ORobG2PcuHH91k+fPj02btw4ImPi8Hb66afHk08+GdOmTYvzzjsvzj333HjppZci4rX5OGPGjH77T58+PSIiNm7caL4y5BYuXBiNjY3x3HPPRUdHR3R0dMSMGTPi6quvjo6Ojr3Oydfn4OtzMiL2Om/NSQbjlVdeiYiItWvX9lu/Zs2aOOqoo/ycZFhdeOGFcdRRR8XHP/7xuP/+++OJJ56Iq6++Oh544IG48MILY+fOnXudj93d3fHiiy/G5s2b++bnm/cxHw+MCDpADzzwQHR2dsbChQv71pXL5TjttNNi5cqVIzgyDkflcjnuueeeWLNmTcydOzeWL1/eb/uKFSv6zcWIiHPOOSfWr18fzz33nPnKkLvlllti9uzZccIJJ/QtL774YvzN3/xNnHDCCfHjH/84Tj311L5/2YyIWLRoUbS1tcVDDz0Uq1evjk2bNsWiRYv6nXfhwoXmJIPy5JNPRmdnZ8yfP7/f+hNOOCHWrl3r5yTDqljc+01XXV1d0dbWFitWrNjj598555wTP/3pT/u2jx8/Pk4++eS+7UceeWTMmTPHfBwCI/50hkN9+drXvpa9+OKL2aJFi7L3ve992U9+8pPsueeey+rq6kZ8bJbDaznvvPP6PhNo5syZ/ZYjjzwymz59erZr167s61//ejZnzpzskksuydrb27NPf/rTfecwXy0He3nj0+EaGhqyzZs3Z//n//yf7IQTTsguvPDCbNu2bX3bIyL74he/mLW0tGQf+9jHsve85z3Z3XffnW3bti2bNGnSiL8Wy6G5/Lf/9t+yV155Jfv4xz+ezZ07N7vhhhuynp6e7Pd+7/f8nLQM6/L6fHv44Yez008/Pfvd3/3d7Nprr816enqyM844IzvxxBOznp6e7E//9E+zuXPnZldffXXW09OTLViwoO8c9957b/bMM89kp556anbGGWdkTz75ZPbwww+P+Gs7DJYRH8Ahv9TU1GS33nprtnXr1qy1tTX74Q9/mE2fPn3Ex2U5/JYrrrgieysPPPBAFhHZ+973vuzxxx/POjo6svXr1+/xuRbmq+VgL2+MoIjIZs2ald1///1ZW1tb9uKLL2Z/9md/tsfjXq+55pps06ZNWVtbW/bQQw9lc+fOHfHXYTl0l1wul1177bXZpk2bss7Ozuypp57q95kqfk5ahnM5/vjjs+9///vZyy+/nO3atSt77LHH+s3H8847L1uzZk3W0dGRrV27tt/jtCMia2xszP7n//yf2c6dO7OdO3dm3/nOd3xw7xAsud/8DwAAgCR4TxAAAJAUEQQAACRFBAEAAEkRQQAAQFJEEAAAkBQRBAAAJEUEAQAASRFBAABAUkQQAACQFBEEAAAkRQQBAABJEUEAAEBS/j/WtZcclSe3CAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 8))\n",
    "for p in lambda1_lambda2:\n",
    "    plt.hist(np.random.gamma(*p, size=1000), alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will specify suitably vague hyperparameters $\\alpha$ and $\\beta$ for both priors:\n",
    "\n",
    "\\begin{align}\n",
    "\\lambda_1 &\\sim \\text{Gamma}(1, 10), \\\\\n",
    "\\lambda_2 &\\sim \\text{Gamma}(1, 10).\n",
    "\\end{align}\n",
    "\n",
    "Since we do not have any intuition about the location of the changepoint (unless we visualize the data), we will assign a discrete uniform prior over the entire observation period [1851, 1962]:\n",
    "\n",
    "\\begin{align}\n",
    "&\\tau \\sim \\text{DiscreteUniform(1851, 1962)}\\\\\n",
    "&\\Rightarrow P(\\tau = k) = \\frac{1}{111}.\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementing Gibbs sampling\n",
    "\n",
    "We are interested in estimating the joint posterior of $\\lambda_1, \\lambda_2$ and $\\tau$ given the array of annnual disaster counts $\\mathbf{y}$. This gives:\n",
    "\n",
    "$$\n",
    " P( \\lambda_1, \\lambda_2, \\tau | \\mathbf{y} ) \\propto P(\\mathbf{y} | \\lambda_1, \\lambda_2, \\tau ) P(\\lambda_1, \\lambda_2, \\tau) \n",
    "$$\n",
    "\n",
    "To employ Gibbs sampling, we need to factor the joint posterior into the product of conditional expressions:\n",
    "\n",
    "$$\n",
    " P(\\lambda_1, \\lambda_2, \\tau | \\mathbf{y}) \\propto P(y_{t \\lt \\tau} | \\lambda_1, \\tau) P(y_{t \\geq \\tau} | \\lambda_2, \\tau) P(\\lambda_1) P(\\lambda_2) P(\\tau)\n",
    "$$\n",
    "\n",
    "which we have specified as:\n",
    "\n",
    "$$\\begin{aligned}\n",
    "P( \\lambda_1, \\lambda_2, \\tau | \\mathbf{y} ) &\\propto \\left[\\prod_{t=1851}^{\\tau} \\text{Poi}(y_t|\\lambda_1) \\prod_{t=\\tau+1}^{1962} \\text{Poi}(y_t|\\lambda_2) \\right] \\text{Gamma}(\\lambda_1|\\alpha,\\beta) \\text{Gamma}(\\lambda_2|\\alpha, \\beta) \\frac{1}{111} \\\\\n",
    "&\\propto \\left[\\prod_{t=1851}^{\\tau} e^{-\\lambda_1}\\lambda_1^{y_t} \\prod_{t=\\tau+1}^{1962} e^{-\\lambda_2} \\lambda_2^{y_t} \\right] \\lambda_1^{\\alpha-1} e^{-\\beta\\lambda_1} \\lambda_2^{\\alpha-1} e^{-\\beta\\lambda_2} \\\\\n",
    "&\\propto \\lambda_1^{\\sum_{t=1851}^{\\tau} y_t +\\alpha-1} e^{-(\\beta+\\tau)\\lambda_1} \\lambda_2^{\\sum_{t=\\tau+1}^{1962} y_i + \\alpha-1} e^{-\\beta\\lambda_2}\n",
    "\\end{aligned}$$\n",
    "\n",
    "So, the full conditionals are known, and critically for Gibbs, can easily be sampled from.\n",
    "\n",
    "$$\\lambda_1 \\sim \\text{Gamma}(\\sum_{t=1851}^{\\tau} y_t +\\alpha, \\tau+\\beta)$$\n",
    "$$\\lambda_2 \\sim \\text{Gamma}(\\sum_{t=\\tau+1}^{1962} y_i + \\alpha, 1962-\\tau+\\beta)$$\n",
    "$$\\tau \\sim \\text{Categorical}\\left( \\frac{\\lambda_1^{\\sum_{t=1851}^{\\tau} y_t +\\alpha-1} e^{-(\\beta+\\tau)\\lambda_1} \\lambda_2^{\\sum_{t=\\tau+1}^{1962} y_i + \\alpha-1} e^{-\\beta\\lambda_2}}{\\sum_{k=1851}^{1962} \\lambda_1^{\\sum_{t=1851}^{\\tau} y_t +\\alpha-1} e^{-(\\beta+\\tau)\\lambda_1} \\lambda_2^{\\sum_{t=\\tau+1}^{1962} y_i + \\alpha-1} e^{-\\beta\\lambda_2}} \\right)$$\n",
    "\n",
    "Implementing this in Python requires random number generators for both the gamma and discrete uniform distributions. We can leverage NumPy for this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Function to draw random gamma variate\n",
    "rgamma = np.random.gamma\n",
    "\n",
    "def rcategorical(probs, n=None):\n",
    "    # Function to draw random categorical variate\n",
    "    return np.array(probs).cumsum().searchsorted(np.random.sample(n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, in order to generate probabilities for the conditional posterior of $\\tau$, we need the kernel of the gamma density:\n",
    "\n",
    "\\\\[\\lambda^{\\alpha-1} e^{-\\beta \\lambda}\\\\]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "dgamma = lambda lam, a, b: lam**(a - 1) * np.exp(-b * lam)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Diffuse hyperpriors for the gamma priors on $\\{\\lambda_1, \\lambda_2\\}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha, beta = 1., 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For computational efficiency, it is best to pre-allocate memory to store the sampled values. We need 3 arrays, each with length equal to the number of iterations we plan to run:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Specify number of iterations\n",
    "n_iterations = 1000\n",
    "# Initialize trace of samples\n",
    "lambda1, lambda2, tau = np.empty((3, n_iterations + 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The penultimate step initializes the model paramters to arbitrary values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "lambda1[0] = 6\n",
    "lambda2[0] = 2\n",
    "tau[0] = 50"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can run the Gibbs sampler.\n",
    "\n",
    "***\n",
    "\n",
    "<div class=\"alert alert-success\" markdown=\"1\" style=\"color:white; background-color: #192841; border-color: #779ecb\">\n",
    "\n",
    "> ### Exercice (optional)\n",
    ">   1. Implement the _Gibbs sampling_ procedure\n",
    ">   2. Compare your implementation to existing sampling methods\n",
    "\n",
    "</div>\n",
    "\n",
    "***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Sample from conditionals\n",
    "for i in range(n_iterations):\n",
    "\n",
    "    ######################\n",
    "    # YOUR CODE GOES HERE\n",
    "    ######################\n",
    "\n",
    "    ######################\n",
    "    # Solution\n",
    "    # Sample early mean\n",
    "    lambda1[i + 1] = rgamma(disasters_array[:int(tau[i])].sum() + alpha, 1./(tau[i] + beta))\n",
    "    # Sample late mean\n",
    "    lambda2[i + 1] = rgamma(disasters_array[int(tau[i]):].sum() + alpha,\n",
    "                            1./(n_count_data - tau[i] + beta))\n",
    "    # Sample changepoint: first calculate probabilities (conditional)\n",
    "    p = np.array([dgamma(lambda1[i + 1], disasters_array[:t].sum() + alpha, t + beta) *\n",
    "                  dgamma(lambda2[i + 1], disasters_array[t:].sum() + alpha, n_count_data - t + beta)\n",
    "                  for t in range(n_count_data)])\n",
    "    # ... then draw sample\n",
    "    tau[i + 1] = rcategorical(p/p.sum())\n",
    "    \n",
    "    ######################"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the trace and histogram of the samples reveals the marginal posteriors of each parameter in the model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  1.,  62., 441., 276., 205.,  13.,   1.,   0.,   1.,   1.]),\n",
       " array([33., 36., 39., 42., 45., 48., 51., 54., 57., 60., 63.]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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REalC/0EGERERqUJ3QYbdOBksySAiIlKF7oIMIiIi0gb9BRmcII2IiEgT9Bdk2GJ1CRERkSr0H2QQERGRKnQXZNg2/CQiIiJ16C7IsMVZWImIiNSh+yCDiIiI1KHDIMOmuoQFGURERKrQYZBBREREWqC7IIPtPomIiLRBd0GGLQ4rTkREpA7dBxlERESkDv0FGawvISIi0gT9BRm2WF1CRESkCv0HGURERKQK3QUZHFaciIhIG3QXZNhi7xIiIiJ16C7IYEkGERGRNuguyLDDggwiIiJV6D/IICIiIlXoL8hgbQkREZEm6C/IsGFgfQkREZEqdB9kEBERkTp0F2QIrC8hIiLSBN0FGbY4TgYREZE69BdkcJwMIiIiTdBfkGGLJRlERESq0H+QQURERKrQXZDBYcWJiIi0QXdBhi02/CQiIlKH7oMMIiIiUodJ7QTIjtUlRLIwGI24b9hg1Gh8Bw5s3IrDW3+XZb9lKlVEl+eegp+fCZvmLcS1Cxdl2e/tpGrDesi6fgOpFy+pnRQip/QXZNhibQmRR9oOegi9xo0BAER3fxCzBg3HuaMnvN7v8NkfoE6zOwEAdZrfiWm9B3u9z9vJo9MmIrr7gyjIy8eydyZj79oNaieJyCFWlxCRqIcmvGL1vu/rL3m9z1LlypoDDAAIj6iNKg3qeb3f20W1OxoguvuDAAA/fxOGfvCuyimSrnK9CFSqVUO140dER6Fm08aqHf92pbuSDNaWEClDjmDAPzDQbllgSLDX+71dNL7vHrWT4JG+419Cu0cGorCwEGtnfoLrscd9evxB/3sTrfr1BAD8tmARNsxd4NPj3850X5LBWViJZCJDBG8w2l9yhMJCr/d72yiBveVCwyqh3SMDAQBGoxG9X33Bp73+QsMqmQMMAOg86gn4mXT3fK1Z+gsyWJRBpFkGo/3NRSjkb1bPajZtZLfMYPLz2fHDI2rbLQsqXcpnx7/d6S/IsFUCI38iLZJjhmODQaQkgw8GkpXEcX/EvnNfKiwosFtm9PNdkHO703+QQUTaIXKTFARWl0hV8kIMwOhnf5vxZbBUmG8fZLC6xHd0F2TI8bRFRCJk+GmJ3XBYXaJvYu1wfFm6UZCfb7fM6MPqmtud7oIMWyWxeJFIr4xiDT9ZXSJdCbyeiX3nPi3JEKsuYUmGz+g+yCAiecgRDPAJ0jsl8aFJrLEvxJYppLCQ1SVq0l9O86nIJ9o9MhAxvboiJ/kacgrsiyNJh+QIMkQa3Ik96ZIDJTHIEKka8W2wZH8sk7+/D49/e9NfkGGr5P0mNa9WVBP0HX9r9Me9yUkqpoZKEqOf/SVH9EnXC9UjG8Lo54fEI8dk3a9WGf38RKsEtELthp9iQayfv7q3vmZdOmHgxDdgNPphxaTp2LtmvarpUZLbjxDVq1fHzz//jLS0NCQnJ2P9+vWIiopSIm0eYUGG8vq+9qLV+7+vnFclHQaDAY3vuxdNOrYrkcXIJY0s1SViNxyjfFUoXceMwsvLv8GLS79Cvzdelm2/Wqb1c1+0kacP0ywWxPqpWJJhMBjQ9/UXEVSqFAKCg9D39Rd1XX3jdpCxZs0aVK9eHT179kT37t3h7++PjRs3omzZskqkz2ta/wGWJJVq1UB4RG2UrRymdlIAAAMnTsCITz7Ek3Oml6g5HG5nYtUlcpVkmAID0XnUE+b39w4dgJCyobLsWyvErmdivTe0ROz79W2atVVdUq5KZYSGVTK/DykbimqRDVVLj9Lc+qZjYmIQHR2Np59+Gjt37sQ///yDxx9/HFWqVME995TMMfVJmo5PPoo3fl2O11cvRbkqlZ2uazT5ofF996JOc+9LuAJDQhDTqxsatG5ptTyoTGmroYJb9OiCUuXLeX08ckwQBER364y3Nv2MV39ejFp3uj/ZlGibDJm6M5apUN5umaMJufz8/XFX3x5o0eNBzdykwyNq45FpEzHwvTdQpmIF8ZVE4jG5q5vkZhALLH1akqG96pLbiVs5XbZsWfz99984cuSIeVleXh4AIDhYG5McsTuc/PxMJvR86TnJ64+e/zHqt4oBAKyd9Sm2ffW9R8c1+vlh7A8LUbluHQDA6g/n4PdvfwAAlBYJKMqGhyHjWqpHxyqJqjasX1TU6u+PtR99ijMHDil6vIDgYAycOAEBwUEAgIfeHIfZg590ax9+Ir1L5LpJigUwjtoqjJg7HXfc0wYA0PDuVlj61vuypMFTBoMBoxd8bA7gK9SohnlPjZG0rVHG6iYliJa+qFxdYgoIUORYd7RtjZheXZF08jS2f/OD6Lw8YvcoPRe4uxVkbN26FXfffbf5fUhICCZOnIjk5GRs3brVswSYTIiOjvZoWzG1a1uPUx8SUkrW/d+OgiUUOUdGRgIAKtWvaw4wAKDnS88hdf8RR5s5VatVC3OAAQC9X33BPHtj6XD7KpvIyEjcGR2NmKEPobCgEHu+/xEp8Wc9OrZSIrt0RN17WuPauQvY8/1y5GVmSdvuZv4W/wsAPae8hXI1qgEARsyZhpUvvqlooyTb2VJrNmnk9m+rWkP7YuGGd9yBcvD+RhlaJdxuWYP6DRAWGGK1rEzlMHOAAQB39emBU6s3ojAvXzSffaFyo4ZWJYQNWrdEixYt7G5IVapUtdu2WfNmyMvKVjyNnqpV237ukPoN6gNwnc9lKoehQp1auHI6Hpkp1zw6fqX6de2W1WvQAP7X0j3anyOhVSuj97Rb1bZVq1bDsfWb7dYLqWhf4taw4R2oaLKfodhbSp7PAQEByM3NdbmeAR6O47dy5Ur069cPAPDGG29g6tSpbu8jLi4OERERska1R69dwYbzceb34UGl8Gj9O2Xbf0mTkZeLi1kZCAsKQWiAZydxRl4u5p/Y53Sdl5sWXbT3JF/Ajov/iX7mrq0XzuDA1Yui+7qWk41Fpw5YffZIvTux6uxxZOQXla6VDwjC8AbNNNMuJykzHT/E3wq4WodVxz2Va3q0r6z8PHx+fK/VssF1m6BaSBmv0mjpo8N/u1zH3e827vo1/PLfCatlA+o0Qs3S3rfpSsnOxDenrUtzHqsfhUpB1kHGmfRUrDxrPdX4c41aIlCk54uvnExLwdrEU1bLxjZpBT+bqqQ/Lv6Hf5IvWC17tlFLBKmYdlf2pSRhe5J1sD+iYXOUDQhyut3FzBv4MeEo8oVCBBr9MKReU1QIdL/E/HzGdSxLOGq1rGuNemhcTt62Zb+cPYG4dOtASOz3kZ6bgy9O7rdaNqRuE1SV8bfrK/Hx8ahXr57TdTw+M8eMGYNp06ahZ8+emDx5MpKTk/Hll1+6vZ/ExET07dvX02TYiWjbCvc8Pdz8/tixY2gx8HHZ9l+SlKpUEd3eew1BoWWQm5WFzVNm4+rZRLf3E1Q2FP3nOg8ihw4diuPHj6NRtwcQM+Qhq89atGjh9jEBoOUjAxDZpaPovkqHh6HvjIlWn415czzaPPmI+f213Gzce39HZKVd9+j4cuvyzjiEWTxV7b5yHmO69ZG0bWRkJJYsWWLO58AypTHg0+lW64wYORKXjp2ULb2PfvuZy3Xc/W5rxjTDfWNHWy0b/fTTuHj0hIMtpCtXoxp6TnnLatmA/v2RdsE6UK0W1Rj3j3vealn7du2Rl51tl8++UqtVC7R//imrZa1bt0GhzZDYzQf0QdNeXayWdezYETk3MhRPo6ciu3REy0cGWC0b++KL+PqzeU7z+cE3X0b4HUUlHjmFBZj4/VfY+elCt48f1rAeurz1itWyd997D3E7drm9L2f6zpyE0mEVrZaJ/T5KVayAfrOsq+cef/xxJMedkTU9gP11Q06rV6+WtJ5bQUZUVBQqVKiA7du34/z58zh//jx2796Nu+66Cw899JBHQUZ+fj7279/vekWJjNUrw7IJalZWlqz7L0kefutVBIUWRccBwcFo2OtBfD7ieRdb2StdoTz6u1jn+PHj2L9/P8pGNUKMzWee5n+tB++DbSFf8b4q1qiOvjafXbh4EbYOHzmC61eSPTq+3LoF2ZckuZs3xflcqlxZDLD5LC4uDqdE9le5bh34+fvjwgnrJ2WDwYAajSORkZaGq+cu2G33qIT0uJv+grDyuM9mWVx8HE7K8ButnmV/oz169CguJ1g/RWeVDsL9NusdPHgQOZmZ5vfF+ewrQuWKdssOxR5CXnaO1bKq7dugqc16h48cwY2rnlUl+ELonfZF9fHxCQCc5/OjNwOMYrVbx2DOU+5fv+r6AV1slp2/kCT799vjZgmqJbFjVKheFf1slp04eRL/HfKsWlkKJc5nKVUlgJtBRu/evTFu3DiEhYWZG3wCQFBQEBISEtxLoUI4QdotbQdZlyhYtpVwh1qNaZ0dNyyilt0ysVoRbTUEtk9gcGgouo99GqXLl8PWhd9JHkBK9O8SyYD7RwxDjxefBQD8ufQnrJw8w/zZEx9PQ5OO7VCQl49l70zG3rUbzJ+VqWR/0xNjMBpFG7c54ifa00Ce3h3i3WNv7Ts8ojbysnMcjNsgSxI8Jt44UmwQK2nbaonoBGk+7BEjlj9K9C6R2gBXznFhSgK3ft3ff/89AgICsHjxYtxzzz1o0aIFPvroI7Rt2xbz5s1TKo1eUfoHWKPxHajasL7rFW8XbuR3h8eHYuLv6/DSsq+tGniaibbCNmDEJzMw8rOPxA4uPZ0qEDsX+7/zGtoO7Ieozh3x9Jdz4S9S2iF1X7aLjH5+5gADAO4Z/LC5f36dZneiScd2AIouuLbjjNgGqA7T4ebNQslxMsQGNCq+wfV/53W8vnop3li3HHcP6Gu/nso3arE8EBu4TOz3pZUuuI5occRPJcbJkHoeq50fvubW2XnmzBn06dMHtWvXxubNm7Fx40Y0a9YMnTt3xu7du5VKo2b1Hf8SXlr2Ncb99B26PDdS7eQoRokfQIUa1dBr3BiUrlAeNRrfgW4vPC1pu/qtW6LxfeJjsmj+hyqSvOZdOpn/H1S6FFr27i5tV6I3FusD+AfaByzVbhZBN+5wr9P9P/i0tK6pBjcDO7EJ0uQqyRB7OjUYDChfrYo5sPAzmdBE5G+3zc/wO+rjzgc6+G5kSC+CB63P/aL23CWiI34GKBFkSPseNH+dkpnbZUa//fYbfvvtNyXSIg8fFY+XKlcW7R4ZaH7/4NNPYssX3yBfYj2VLxTk53s9XK3Rzw/DZ30gU4puuW/YYKv3d3ayrakXrxJo83Bvh/sU+5GLPg3KpEGbu9C0YzucOXgY+9dtcrm+lItLucr23TCl7kvSRe7mdnJVI7n7FO2qSsMbYkGG0WhE/bukNE69lZ//XrmAB98sGpL87MHDmPOo8g8QYjdi0SnSRYI6rZdkGCSUyFSuF4HG7dvi3NETOLV7j9wpsFsidh56fRSJwYPob0CmQFuLtNvvSSbhEbURWCoEORmZrld2Q1gd+77fIeXK4vrlK7IexxsFed4HGXfc0wYRLZp5tQ+xevvWDzkOFooJhdLaHdz6zH6RUgMV1Wgciae/mAOgaPhqCAL2r3cefEu5CJkCpQ0SJFrPbbt7HzwwuV1dIvJ9yFddYv90ajAaUZDvepZgy7zbeelWF+zazZqi4d2tcHLXP7Kk0RGj1KG3RYNL+2XNunRC1+dGIiM1DcsnTsWlOOs2cxVqVEPX50aisKAQGz5ZgNSLlzxPvAvOqrGAolFZX1q6yFxVuGjs6zi8dYdsxxd/+JD/uiB1CHtfPwypTb9/2U3+QYF4ffVSVG3ovC+vuwTBvrGbUWPFYAV59q2d3dVVhmog2yeyFj27OGx7YDAaUbtZ06InepGnbWdFw+JPecp8J5az0ALA0Knvud5IwvkhVsUhuiuxv8tm/06fcOUqyXDznBerLpGruF+sasNgNCI/T0KQ4SQNdVs2h9Hkh96vjcWE9T/h0WkTEVS6lFdptTu+WJWCaCDpuoFoYKkQDJn8NsIjaiMiOgoPTXjFbpuRn32EmJ5dcVef7hg+W56SSoPRiCr169oN7y/+5H7r7+j2wtNW14OhH7wrueGxtHSJlGTIXPpzz5D+kgMX0RIqjZdGeUN3JRli186y4WHo9vxobPz8S5SrHI4Tf/3jdbWGaIt6DQQZVRrUQ5dnn0J+bi6CQ70f3MXdm7Ro63ebH9CDT48Q3dbo54fnvvkcdZo5HjzNWR25eCt2ZUoyIqKt52WRctGS0n6huEGaf1AgwuvUxtULSci6bj8yoehNyWb/zorbxXph+ZlMkp76XaXDGV9XlxiMBruxJsQ4C5ZMJn80bn+PuYqvYo1qOH/8JLYtWux5YkXSab9MYh2/zVNwix5drIJV215lletFIDziVklszSaNUKZiBaSnXHUnyVaMfn4YNX82GrRuiewbGVg09nWc/qdosDjxHkW3/l7bNjKBISF4b9taj9NifyzXJQeBpULQ8clH4R8QiO1fL3YrLx56cxzuGfyw9PT4qGRFK3QXZDjSpGM7NLrvHhiNRpw/fhKzBz9pntegRc8uaNyuLeL2HsCuH382b2MwGnHvkP4Ij6iNf1b9isTDt0aNEyvKF3tK8yWDwYCRn810OYGZu/v0lu0POqy2+CiXLXt3dxpgAM7zWKzIsaQVQ/oF+KN0hfJ4dtFnqFy3Dq5fSca8kS/YrSflpuTuzfuDf7Zh9Yw5+GPJcsnbFKfDPygQnUc/ibKVw7Dz+2U452BwLdEbjpJtMgxGFEgoyXAW//n5+2PIlHeslvV8+XlZgwyx6FxqyahtMOmqh1JgqRC7ZZZzeZSpVBGhYRWRdDLO4dwvtpp0bGeexDCodCn0Hf8SZjxUNNKKUay7qAIljMGhZZCTmYnCfOs0i1VFGW1GSH10+v/QuH1Rg/JG7dtiep8hko5ZplJFpwHGC4u/xN61G/DnDyssji2t/Y1e6O8vc1IMXPxFVo9siKb3twcANLz7LjzywXuI7v4g+r/9GqK7dTavf/+Tw9B3/EtoO+ghjPl2PkIt5suo3ayJ3f69bf/grTrRUbIGGADcKp0JLBWCkHL2w0NbPkkUT64lpudLzzr8rJizPJZavKwaCUkxBQTgniH9zV16Q8Mqoevzo+x3JaFNhtMLl8jPxM/fhJ4vPyd6E3Lo5kF7vzoWnZ56DC17dcPz38x3uA/x3iUyTfUu2ibDgAKRQZLs0+A4r/z8TQgqJW/1iN3xxb5P0QaTIots889FTZjYrLfFDYEbtG6J8WuX4eUfv8Gziz6T/OB0zyDrG23VBreqp12VZMjx/fd8+Xn8b8d6TPpjIxre3cr2YPbHt8hbP5PJHGAARYPX1WzSSNJxLf9OMbWjmuChCa9YzVgs+bvWCf3+ZS40atcWADDgvTeslj86/X/m/3cfe6tbpZ+/CQ+MvDU8eb837Os5fdbdzYGg0qVl36fUC0D15nfi7d9+wf1PDrPfh8WTREhZx3NUSJmq3VmQIfaZloohJTX8DPC36z4a9UAHkX25bhTorITAUe8S/8BANGh9l8t02qaj7cBbYxj6BwXi3qED0GZAX/R8+Xmronmx8QnkKskQe2I2GI2Smp84rS7x4nddo/Ed6Pny84jp2dX58SX2GhGfttwfjdrfg7oxzYt35pzI31rcxqz3a2PNAVVEdBSiHuhot674Ph1/ZBRr+Clj8F89siE6PvEIjH5+CCpVCt1eGI2Ynl3xzpbVeO2XHxDRPMpuG8sAXKwErFSFcpKOLbWXVp/XXhQ99q1lnl2nDEYjWvR4EK369VJsZllv3TbVJXZunuMVqtnPauhItZuDbjn6Mk0SRpGL6twRIeXKYv+vm6yGMZaDWLGgLVNAgFvtUaTeAFoNH4zgMuJBjmW7CG8DMadBhoI3MF9p2rG9pPVEq0sMttUlrhuHipPeKNTROdfdYtyTtoMewqTOfZF1/TpqNm1st65lOitUr4pB/3sTFapXw47vlmLn4h8lp0Xs92cwGKQVRTvJF0/P2QrVq2LM91+Yg5SA4GDsWv6z6LpSGyeKLRvxyYfmEsxN875CVrp9G55W/Xqh96svIDcrC7t/sp9zojjIqWYzsGDbQQ/hwAb7mUTt0+84j0V7XcjYZdN2jKJaTRtjwLvj4R8UiLLhYaID/Vk/fIgOFSzp2MUl4q6Ur1bl1tFEHnw8rdYdOPENtOrbEwDQovuDmDdyjEf7UVLJugJLoOQw0oIg4P4RwzBt7++in4tF7JZ6vPQsHv9oCga88zqe/1aeEVLLVKyALs+NxH2PDZHUM8E/yPnMh7akPnGUqmA/fXExyxuRlEDMGWfFt2JPnJqq65Tx6U20UadddYmTpyMnvxO3fkMS/qbAkGC0HzYIZSpWEB1IzTI46jZmNOq3ikGF6lXRd/xLqFijuuSkiD4xG42SiqJfWrYI49f+iFp3Rdt95udvQqGTodMDS4Wg/zuv4/lv56NN/1sT3nV++kmrc7L/O6853IfY7yymVzdM/nsz3v/rN0R1LipRECuZs6widTSIWt/xLyG4TGmUDQ/Dg8/YN7x2mEcST1ln1wmxBzmroMrL30XNJvZzo7hql2KZj2I3eKmlX/cOcTWr0811LX6vHo9xY8PPZDIHGADQoE1Lq1JDrbhtSzI8Ka4rV6Wy1TDNtlwVq1pWJVS7o4HX/e9b9u6OIZPfNr/PznA9E6Orm3xAcBAatLkLV89fQNLJOFmKNR/9cBIqR9TBsZ1/4Z9V3rUad1aS0VpkoC65SzLuHdof3ce6bjsiRs4iYtF92VWXOD6e00DCjSBDau+j6pEN0fNl8cmtLC/yLXpYT2X1wOjhWPb2ZEnHEA0y/YySesCEVqoIVKqIciPtq/v8/P2d5knHJx81jygaER2FxCPHcP7YSdFGzH7+/rjvsSEoXaEcdi7+EdduzhArlo+WAUO/N15G7JbfJZ3PYscNDHE+RbqjgFSs/YYYZ+e25VO8lPXdFRDs/vTvlkGGaA+0m9/33QP7of5dLXDiz9121y6p42IA1g8FYoGiJ9W6ASH27Z4q1appNyGg2m7bIOOuPj1Qo7F9BOxMherOq1bcbfhZrWF9XDn7H5p0aIekU3GI+3ef5G39TCarAAOApMZpzop+TQEBeGnZ1wiPqI2C/HwsHv+eLBeDhm2K6vjb9O+DvJwcF2s75yyPxapr5AwyQsqGove4sR5PriRrkCGhvt7T7rvuFGTUbNwIx3b+JWndlr27iS53FgS4cwMRrS4zGN0qihYr6TMF+DsNyjqPesLqfdfnRmHh8+NEe2Y8/OY4czDcokcX/O+B3ijML3D5XYWGVUL5qpUllcw1e/B+l+vYqtKgLlLOnbdbLrkbrYP1TAEBKFOxgv36lg0/vRw1zpPfuNGq4ad93guCgGZdOqH/20WlT827PoDrKSk4vvPW9PCFYoMFOjyeRVAj1pPIkyAj2L60Rou96bSXIm+5cYV01TLYXQEhwXhg9BN4ZuEn6PjEIy5vKqHhlfDKiu/Q742X8exXn6J51wcAAEFlSmPk57Pw4cE/MXrBxwgOtY+Yqzdq6FEanQUZLXt3Mxe3+ZlMGPL+27KXBFgOxe4JdwM5d3509VvFoNNTj6N6pHjeNu/6gCKzN3pCdD4GmwuV01IGZzfN0U84/MzWU5/NROV6Ea5XdHI8Z+l0JzATOzdGzZ+NJ+dMl7wPMSZ/8SCjy7NPia5ftnJRLzSxMUcsS9vKVKxg/s2L9cCwJQiCYg2Zn5wzHS162k6ILj3/HX2HDqst5Kw69ODGalV9IXqNE/DotIlWSwZPestuHU+O504X1oo1a2DI5HfQ/93X7YI1sYBYi23QtHHF1In+77xeVOyKohtWyrkLOPTbNofr3/eYdV/sYR9OwoENmxHTowsi720DAGh4dyvc1bc7dny71GpdT1sjO6suKa73LeYfFCi5TtZX3B2LRGqbjKb334cnPp4KoKhXUcK+g/h0+DOytvGRt7rEcTe4ijVroNOIYQitHGa3TjFnf5VldzspXlu1xOU6YoN/FZPrwqjUBdZoMokGSQ8+MwK/zV9ktzw/t6jLrJQxJirdbHMi6bwWlL2JPPLBe3bLJJdkiM0PYvJDp6ceF1lbejWbLbGxMDxqzyChTYZtQGd7k3fn92x5DLFSK0czs45eMNvcLik8ojY+G36rqjZQpJRv+KwPMK33YKRevITyVasoMhGcu3QXZPhmejRxoTZD4daNae40yHDkoTfHWb3v8+pYuyDD037Vbo+YqaVxJgAEl3FvFFOpF6DiAKNYRItmqBMdhYR9B83LROdSsTyWwYA7O3dEQFAQDmzYbN+LR9bqErHeCH4wGI14dtGnDidaqx3VBD1fehZV6teVLS3ecnWO+ZlMqNP8TqRdSUby2USH60npXeUJk7+/w+9ebHjx4u/ddlAoUTf/diklFEJhoe+Lwx1kaUR0FMLr1sHhrTuQcS1V9HfWY+yz6DB8qPhuLYNkN7629//chMsJZ7Hw+XFI/u/czX25/71b9vAQfWCT8HDhTnBj+feKz1Njn4baUU2tGj7Xi4mGKTAQ+TernB014n/qs5kADKhYoxrSLlzEjTx1J+3UXZChJWUlzqjpCU97TTgNMkR/7doKMtxpbAVIuxA4Gjiqx9hn8Mnjt7piis1XY6nfhFfMo//d1bcHPn/yOfj5+yOsTi10GjEMpUQGKvOUo1k7G7a5y+lMru5UhchKwiB5op/5+eG5rz9H7WZNUZCXj+/Hv4tDm7aKrqvUEPJ+/iaHJVpiQa85yJBQklF8fnoz74WSxH4/LXo8iEemFlUldBszGlN7DhQNeh0FGEU79vy6Eh5RG+2HDcbKyTMAeDYIoquGmM56ExVzpzTGk5KM0hXte+yZAvzNQYajgQ0tA5Oy1arg8LXLktOpBAYZCrKMsOWuS3XVXdYRp71LROcd0VaQ4S4p+e5olFTbGVFF56uxYDm8cP27WqDjE4847FHhiUJBQOPundF8+CBcv5Ji97nR5IfSTroSq8nZg6Gzc6xJx3bmG4KfvwmPfOA4yFDqKd8UEOAwyBC7ERQPY14gJcgoLsmQUF1i8DOKjrGgJLHeJZY97MpUrIB7hvR3O2jwdsTPewY/jJWTZ3g8yrJlfouWCkspyXBjrA9XbTKkzmdisqj+cDZ6sqW/Lp+TtJ5SdBdkKDlOhrssfzty16UqUpIh1upZgw2J3CHlAuaoCqZmk0bo8PhQbP+mqM2Bq+oSW3IGGABw5NoVtBjcz+HnRaNbun4CU4PT2XOdlEDYbudsVEOl2iv4mUwO81UsQHW3JKPXK2OcP/VbrOv7kgz734/t39yyVzfkZbvXa6x4vwGlS3n8ABYcGorRX3zs0baWVSSe5qk7Qa1lMCQ1oBALoEz+t85/d8c8UovuggxNsSrJkH5C5ufmuhwi1tMfZnGQ4WcyIah0KWSmXTcHZqIXaY21yXCXlHx3NFIpAHQf+wz2rFmPG1evSSpCVYp/UBB+uxDvdB2jn59cM7jLznlbIHnOMaVuwAaDwWGAWd5ZkCGhTYblVAWuGI1G3/cekPD7DwgJdrtrusFgwJ+XEjHwsw89TRla9+uJmm4OQ2A+vp/z6hKH2xkMt66XHo5a6mgk1wrVq+LBZ56CIBRi4ydfiJZWe1KSobaS/ZiqIDl+zNaNfaSfyLnZ2S7XMXnYatjkb0KF6lUxbuX3+N/ODXj6y7kILB7URay6RGNtMtwlpZ4+ONRxkOHnb0Lzrp0AuK4uUdI9z7huS6GleVpsOev6K3XAp2Lthw2+NU+H5X4UmqDQWQlRuaoiQUae9N4l7jD6+fm+JEPSiK4hbl8vg8uXw+4r9uNyuKPXOM+H0LbuXSJ9ZuDRX8wxr+9pcCxWPWPwM2LEpzNxV5/uaNW3J4bPmSZekhEQgDvatkbX50eZZ711xSTjEO6e0F9JhkyPcnJcsK3qHSWWZDz4zAjkZeUALto3ejoZTvGIg8XjYdRvFYMWPbpg1/KfHUzSVLKDDCk9Dlz1WClVrhyCypQWHVTIV2pE24/iaMtoNMp2/svN+ey57p1jfV4bCwD4bcEibJi7wLx/y0na5GQwGhx2WwsNq2S//s2LemGBhCnm3UmHweDz2TqlBA/BZUoj7ZJ76arevKmnSZKFJ20kgKJZahu1uxtHtv/h+aRmIjf9KnUjUMVivJmajSMRVruG3XpNO92HbiKzMjtjUrnKmyUZIlo/1Eueadstrp1SBtsBigb4kdIIzLZRolR+/v64d+gAq2XFcypIGaq6pJFWkuE8yLirbw+8s/kXr56cfMHoZ9RUmyRL7nadlsJypM0oD0a5lKqoJEM8X8WKrIsbV8v9VcT06uZ2F25v2ZacOLouutsl2tOqBrm4GlbcWQlO8fXT0wcwsaAmSKTKtlR5+0bF7gYYAODPIENeclxkuz4/SpaRHT0pyQDsB32x3Rdg3QDIHV1tZiy0OYjL45Y0T3w8FWVsxi+x5erCXb5qlVtVShpmMPpptiTD2bw+3txwigNyRxODycFoNDqsKhNrfOfn7w+D0Yg7O90nazo6PfUYIqLtpy1Xku3v31F3b3epPfy1ZZAh9gAoJX2eBsdSq7zExmDxhL9CXbul0l2QIYfQsEryFI1bNvz08ou2HUbc05KMSrXsi+CKiUXmalYRyKXny885/bykNKByxWjyU3UwOmecDYPvTRVAo3ZtAXj+e5DCYHBSkiEWZJhMiLz3bsXS41MKBRlqD39teaMXbSPhJPBteHcrhIaHod5dLSQfz7LRuNS/PUimvPZXu9RI1aNrWFjtml7vwwAD/Pz90euVMXh5+Tde7eulZV+jeZdO5veeNvx0Rmz2Rj1o2Ut8Yq5ivq7nVorRaCyRzXSNXpSWPTlnOlr164Xg0o4b73qrbOUwh8G2WIDq5++Pu/p0Vyw9vlT84OEfFIhqdzRA+ar2M6p6okrjO2TZj6csq6TFShZcBQLvblmNAe+8Lvl4QoHzIEOsxFhsllVPqN0mgw0/HQirXcvrfUTe2wbT9+2QITVFhs14H7WimqB6ZENZ0mdJbBK224W7vRu0yujnB6NGJnBzR5fnRiLpdDxiN2/3aPtB/5sgb4LcINYWQSuT6MnBPyAQES2a4bGZk+2mTSjJrMbJEO1doly4LtqpQCTI8A90MLmcm85npqN8rRrA/v2y7M9d+ri6KqB5985qJ0HUfY8NQf1WMeaZHuXSsldXWfenNQ1at8TTX8zFI9Mm2rXREGt0VRIZ/fwkNzDWmuGzPkCFGtXUToYsZGk0rhFlK4fh+W/m6SrAAIqq757+ci7qtYwWDzJkfvCwLC0VK7UQLcmQsRr3gfFjRXtC+YJ+fg0y83SQl5KqzYC+aidBUU/O/dD8ozUFBOCHCRNRvmoVCIKAZgr2TPAlo9Go2FgRvvDg0yPUToIsAkuFIPtGhtrJIBcatG6Janc0MM+BYknukgyj0WgeyEssqBEbb0XOdkaBpUshrE4tXL+SLNs+pSq5VyQHNNq4XvMs+2jrkeVTQdQDHRD1QAf1EqMQg59R0wNyuVK+mjz1/WqrHtkQ1SMdN3Ql7ShVrixa9etpt1yJ31G/Ca+geqOGVhOYFRN7qK1Qraqsx79w4pSs+5NKd0EG0e3KaPQr0UX19d1orU8klwZt7rJbpkTXfcsJFH0tI+Uasq6nq3LskntFcohFGXR7aj9sEOL2qtO4i6ik8qR3SUmTfumKasfWV04S3ebqxUSrnQSiEq+kT6dgKy8rS7VjM8ggIiKyoPaw53LLZZAhH63O3UBERCWDlIkVS5K8DAYZREREmtBWxUaaSmBJBhERkUbUatpY7STIKj87W7Vj6y/IYHUJERGRWUF+gWrH1l+QQURERGZCAYMMIiIiUkAhgwz5SK0tObV7D9bNmadsYoiIiFRWyOoS37pyNhHznhqDswcPq50UIiLdO/3vPrWTcFtjSYaMJI2TcXMdNTOeiOh2kXEtVe0k3NYYZKhEzSIkIqLbQeKRYyjMz1fl2CunzFTluFrDhp8+VlzaUcCSDEVcTjirdhKISCNWTZ2t2rX2zx9WqHJcrWFJhpzcGCejsECd6FrvVk6ZiQKVnlyISFvOHDjEqmmVMchQiZZO/P9ijyL14iVVjr1o7Ouy7u/U3//ig+4DZN0n6cP54yfxzStvqp0M8pHiBp9qVk3v+3Wjz4+Zl5Pj82M6w94lKtFSm4z0lKvYuXi5KsdWYjS4a0kXZd8nlXwFefnIuZGhdjJ0KzdLveGjxRTk5QFQ94Fu42df4npyik+POa3XYJ8ezxWWZMhIgOvqEnfaZOxc/CPyc3O9TpcrQmEB/lyqTv2hIBSqcly6/RQWFiD/5o2H5GfQ2OyhxdWmat7kkv87hxn9HsGnTzzrs2rca0kXNfWgxZIMHxPc6MKaevEyZg1+EpsXfI3vxr2FnExlZrMrLChEXnYOdq9co8j+nREKvZvvJcjPZP7/pnlfeZuc20LCvoM+OU5m2nWfHEcqoaAQBXlsr6MUo9FP7SRYKe5VonYj+4zUNMTv2Y8bKdd8dkyjn3a+C/YukZM7DT8lRncXT8Vh/dz5OLBxi6epcqk48FHjpiAUFuLKmf883n5YvTux94eV+P61d7Dx0y9kTJn+7Fz8I95s2xmfPP60T44Xv++AT44jVUFBgSolZynnLvj8mGrwdUnGsT92Of28uCpWK1XThYW+S8cfS7TTs4XVJSrxJOONRu+y7N9ffnX6uTq9MgT89P6HHjdWCjH549j6zdi//jeZ06VNGalpOPHn3x5tu2rqLGSn3/D42LkZmW6tn+Pm+koTCgrhHxjo8+N6E0SXJL5+es6+nu70cy1Ul1jyZTp2fLfUZ8dyhUGGnAwSInkvRvw0+HmXZZcTnF/slBq05tzRE9i7dgMunDhl95lQKODU7j2Y8fAwj/ZtkJLnPnblbKIi+z3+x9/44umXsODpl3Bw01a3tl329mSvj5/rZnVdtsYaWRYWFkAo9H1JhgZPUV3IcnF+FT+UaSXI2PjZQo+2WzVtttvbyN2W71L8GRzb+RfOHIwV/dxZKTiDDBn5SYjkzQ0/PSjC87YkIz9P/MQrvlErVZKxbdH3WPLGRBzd8ZfdZ4U3L/rJZxM9aqykxev3gQ2b8VqL9rKWrqSnXMUXz7yExCPHAAApiefc2v6fVWu9TkOem70HcjJ8H2Rs+nwhlk+cKvpZYWEhzhyIVaVasFCF4EbvcrOcB73FvTrUGvHT1sGNWxC3Z79b23z25HPY+f0yvHLn3VgzYy5O/7tPlWrh6X2G4MtnX8G1C+LX6HNHjzvclkGGjPwCAiSv68lgXN4WRzpq9Ga4Gbzk57gX/Uq9cBYHVmJPkZLme5FZ2uUruHDytKLHKMjLw4m/dsu2P9t8ynHjhi9XX/28bPeCjGwVqkt+m78If6/4RfSz/JxcFOTn4/vX3lH8+7elladpPXF2vcrPy8PBjUWlfWo3/CyWn5uLz0c8j+1fL5G8jWXp4fZvluDzJ59TtYG7o/PYWQmhwN4l8jH5m1yvdJOvLzoHNm5xWYSW4+LJwFPFJ6DYE4XlyelJ1Ye721yKP4NpvQfjcvwZt48lVXFAcFXOBn82QYarpzhL//zsfSkGoP2SjF9nf27+XYldyNNvPtme+Gs3Zj48DGmXr/gsbUKBtksyHBWDu+sPiUNpiz3wuNvzx1F35E3zvsLHQ0bgzIFDALQV4AmFhVj/yQKc+nuPpPXdLV3eu3aDJ8mSrNDBeezsgZMlGTLy8/eXvK6vWzz/Nu8rxyUZN+/TednKjBRXfGKKPVFYdmE1GJQ/JS6ejkdORiaMJukBoafi9x5A8n/uVWs4YluSIbV9xJHtf+DUbmkXNFfcLcm4nnxVluNKtWv5KvP/N3y6wO5zu0GRFChEO7z1d/uFBoNPexZ4wiBTxeP2rxe7XCcr/QY+e+JZZF4vqrZKOhWHeU+Nwf8e6I2rF5IkHyvfQWPxnd8vs2r/pbUALz8nB8v/N03SugVujOuy+YtvsMJiv0rc3B2VWDgKPpRKh1S3ZZBhHifDh3W0x3b+hYun4x2WZBTf3HPdvIlIbSNS3G1Q7GSz6lLogwYWxT9aPx8EGYIgYN7IMfjrx59l2Jn1WyklGZ89+Ry+GvOq98e+qcDNxmTuVr9547tX30bW9VttLcSeAK9fSVY0DYWFhVg0drz4ZxrpRumQTK1THdXZWxEEnDkYi6k9B2HGw4/io4GP49TuPbhx9Rp+ev9DycdyNG6Q3bVVgy1vpQYP+W6U7qyfM89q1NVzx064nS5XChxU8yc5qX5kkCEjSdUlTtonKCXtUlGxsMMT++aP0J0ieHcUl1aIPVF4W13iruIiVqPJdfuWHd8v8+wgFqUO1y5cxE+Tpnu2H8td2kQZCfsOudzmwgn32x38+8s6h59lX3ev+6svu0TbDmldmF+AG1etBz86uesfn6XHltYbfsr527Oc4lxsqPHicznjWiqSTsZZBWDHdzof+8LSMZGG5ID2Si7ESA0yvGm0+rNMU81blro4ytvYLdsdbs8gQ0Z+JuklGUBR1yRfXHyKj+koKi4eREeszn3Dp19g21ffi24ntfdEcSDhsrrEy94zUuTnSivJSDx63OO+5ko0Zt1nU9d6Lemi0xKSk3//a/VkL8V3497Csnccd3U9sWmb5PP1l+kf+7RVv1h1xOYFX5vTu3Pxj9Kesr3gqGTPYDBoql2AKA9ijNRLl63eH9tZdNP/84cV+O7Vt7Fp3leYNWi4/YYufh4rJAblOZmZ4kGMzYBrGizIkFxC4c0w+P/FHsX3r7/r8fYAsGbGXOz+abX5vdjv//MRz5uvq2LUDPr0F2S40SYDKKo7nNZ7MGb2f0yhFBUpvsAVOOjCWkzsB3t46w7cuJYquv6Jv3ab6/ud/RgkV5f4gJTqkqVvTcLsQU8oflNyx+/f2gc8P02ajo8GPC66/tcOiu2L2Y6zMbP/YziwcYvDEraWlaoi81oqfnx3Ci4nnMXJXf+IBpmX4s/g7xW/4O8Vq3xaklFcWmdp5+If8UGPAZjeZwhWTZ3l9TF+m78I7z/Yz+3t/jt8TPNBhsFgwJqZnzj8/L/DR3E54az5/cld/2DJGxPNf1dedg7WzvrM/PmBDZux8dMvrLYp5ioI3yWxelEQxBs62rUP0GCUITUAd6dNhpj96zZh3sgXPNr2csJZbP9midU1Qew8Tk+56vD8bh1W3aNjy0V3QYaU6pKr560bNiWfTRQdpEpOxSeJw5KM4uoSB20yHDVay8nIxPxRYzHn0ZGY3nuIw+Nnpxf1MhANMixKMs4fO+lwH3IpbvzqLMhwFpVLce6ofV3ops89G4gHAOaPGmtX9F/s/HHxPMvJdN59dNPnC3E54SwK8vKx/eslLs/BdpVrAQD+XfUrpvUejPmjxiLuX/s+/9P7DMHyiVORm5XtsyAj8ehxh3XCV89dwCU3ehKdPXjY6edSxnKxvFnnZGbhd5sLtVY5arR54cQprHx/Bj5/agx2Lv4R2xYtxrfj3kLcv/swd9gorJo6C7OHPImLp+KkHUiGkr5L8WeQdf26aL7aXq+0OGCf1BIKR431XZ2nlk79/S8uno6XvH4x0WBQbFGh+JxAxzZuxT2Va7p9XDnpLsiQMk7Guo8/90FKrBVH9q4afor1HjAFBDhstJZ66TKEwkKcPXgYKefOOzx++s0bpFiQYVn8tnaW4ycpuRTngbMxR9wZLS/7RoZVAHExLgHHdvxpt97Gz77EnjXrrZb9Ovszu/XEOAowitkOF3/20BGX+7x4Oh7Teg/Gay3aYc3MuS7XF7tQ71mzDlkWw5Tblo744sa64dMvMN/DJzWxWZOdVReZJI6Ds/3rxfjhzUnYvOBrzBo0HJlp1z0afM+Xkk4WBQhijWNn9n8MiUeO4frlK1g1dRbWfvQJsm4O6f1f7FHsXPyjWzcxb6qIL56Ox/ljJ83fk9iN0L54XntBhuSSDAfrrZwyw+r9snemON3P3MdGS0uYBwoLCkSv7VdOuR/YyE355v0+dui3rXhgpHjxNQCs+N900eJDANizZj1a9urm1fFTL11GaKWKdjfQ4sjeUdGbsy6s/oEBDovCUi9eFl1u68bVoq6M4tUlty4SSSfj8OWzr6B5twe8zgtHivPg/PGTqHVnY9F1XNWXXr+SjNCwSigsKMCSCRNxZNtOnDt2AmUqVsD+db85LA5e+uYknD9+Eo3atUX83gPYs3o9erz4rHd/EIrGh4jq3BGBISEoLCzEtq++83qfUuRl52D+qLG4f8QwZKSmYt1smwBaxifIfes2oUX3B62WXU9OwW8yD0zkrCjfP1D6YHt7Vls3oNVySUZBfv6tQNkHT/0J+103WhZz9XwSPuz3iMv1bL9DT0oyrp5Pwk/vT8fIzz2rZtvy5bdOP5fabstRkHHu6Al88ezLaNb5fpyNPYJ/fnY+g3Z2+g18+dw4PPXpDKfrWZKab4UFBaLp1EIJku6CDFfF/Ye37XD42fqP53l9Y824morN879G/3des1peXCXhsBrg5smQJ/IE72cyOQwy0m3GHdi68FvcP8K+fUnxRFliJSK2F99jO//CsZ1/KRZkFBdTbl7wNVr17Qk/kSouy7YrBXn5duvM7P8YGrZthUtxCebv/Mi2nS6PLQgCdny7FDtutq8oVa6sx3+HpfTkFEzvPQRNO7XH+eOnfDaVOwAkHj6Kb156Q/Qzuab+/uLZl3F85y5UqV8X1RrWNy93NLKnN5y1nfBmcjWttsm4eiEJi19716Mh/aX68d0pGDhxAoCim6bUEjxboqUWUm7WHtzrzh8/ieN/2E9E+PeKX/DHD8sx7ifxxvBA0eywv3/7g/sHFeEsOD2+c5dbvXGO7/wL+9dtQrRNsO6twoJC0fPb17PyitFddQkAXBSpjy+WmZrm8LPUS5ftpoQ+uMm96d3XzZ2HXcvtG01duznAjeOSjKKTITv9htXgUdkZGUjYf0g0Ss3Nyrb7Abga7U+skaejH9FvCxY53ZenioOM1IuX8Mnjo/Hf4aP261gEY7YXxP3rf8ONq9ewb+1Gr9uQSH2akbJe6qXL+GPJCp8GGK4YRSb02/jZl1bvf5vv+nsuHjl17cxPzFVZqRcvyXYht2TZRsiWyY2SDFtKBBlyDC/906Tpso326cjulWuw+I33sP2bJfjk8aeR7OEEgpa9HIpJKSHy5Ina0XcdEBxkrlqytGneV5g9ZARejb4XXz7zMjIcNJZXkyAI+P71dzH+rg6S15eisLDQQYkLgwxFHNtgPztmYWEh1sz8xGVDuJ8/+Mg8c+XWr76z690gNh16cWBycNNW8zgAlsNIZ9/IME+OletoRE+LH+HKyTOQdvkKMtOuY+X7M5CfmytaAvHju/Z1gGmXrmDWoCeslh39/Vb7BLELuKMTedvC7/Hn0p/E0+sFywZK/8UexU+T7Af/sWyTsfvnNeZgIu3yFWz+4hvZ0iL3TIlyse2pcdXDqcrFLrR//bgSfy79CRdPx2P710tES4AsG0db9mo48dduzOz/GL564TV82O8Rr6atB4DEw8fsljkbmVNqmwwxcndVP/r7n/hr2Ur8F1sUJHt6Lvlqsrh9azdizYy5+E9CeyFH/lxmfz1wFhSaeRJkOOopeHNf6SnWo9n+tWwlEg8f1f6ga5B/ZOfCgnzRv5vVJQq5cOgIapcui7M30pCRmobVH85B3J59krpDHtvxJybe3xN+/v7mhlWWMlOvo2zlMKtl03oNgn9QoNW02j9/MBPpKVdRplIF/P7tUvNJ5WiwLcuT4cRfu/G/Tr2tPhe7QB7avF10X+eOHseu5atw94C+uJZ00erJVXSCNAcX35zMTKycPAP3DH5Y9HNP2V+M7S9SliUZ2ek38PHQEahUqwbSLl+Rdfry3KxsHN62A007tnexpm8nkVv69vsYveBjAEXf/T/f/gj0HOj2fi7Fn8H5YydRvVFDAEXdHm+kXMPKybfqhWs0vsNuu69eeA1NOtwLP5PJbkC0ywlnHbZrcte6jz9Hk47tzONb/PzBTKd9+v2DiqpLCgsL3Z4RWe6xAn6d/RnSk1Mw55GnYPAzQigoxH2PDUGvcWOcbnfq7z1o0KYlAODK2URzkFISiAWVYo13bXlysyuuGjuwcQuad+lkXr59UVEPnJ8mTceQKe8gMCQEWxd+a1d1fDsRCsRLMrRQXaLLIEMoLMRDtSNxX7cu+PevXW4/beVmZQMOJqLKSEuzCzIK8vNRcMP6C87NyhbtxSIlyBAj3vXU8UVzxf+mYdXUWSgsLLCKcAvF6lSlPInIyL6rlf3fbhuIFOTnu9UN0h3fvfoO7h38MIwmE+57bDBKVyivyHHccXLXP1gw+kXUjWmOk7v+QagXD2fzR72ADsOHoiC/QLSL5BWRovMrZxOxecHXnh9UossJZzFvxPOI7v4gLpw4hV0//owyYZUcru8fcLNNhgddMB0Nx+yJX2d/Zu7NIQiCeZbL7d8swY1rqRgy+W2H23477k10Hv0kTIEB2CJjqZxqJHwXntzqikutNn32JarUr4tKNavjjyUrzF3GY7f8jpP394KfyeSz0iCtKiwUb5OhhfFJdBlkAEU37RuXk70uzrV1YMNmq4Zv7p7cDovyXJwMiUdEipVd1DGLFt+KNtzybat723SJNfz0ZpQ9d+Xn5GD7N0UzhrZ+qJdokJHnwzlAip34a7d5qvro6GiP95ORmoZfbXudWMjJyMRv8xeh8+iiarZfZ3/ucOIrJcTt2Y+4PbfG+xCcnNfJ5zyf7C5h30HUairem8ldtm23LLlqo5CZdh2/TJ8tSzqUdGjzdkQ90MH8ftsi8TE8pDykXHAyr4YjpoCi6pJL8WfwYd+housUN2jXK8ltMvLFu7D6YsJLV9RPQQmz8/sfrWaSXDPD9fgGUrgqybh67gL2rL41xsP6ufM9Oo54dYmvSzKsAwixQbm8HWVPTpcTznrcUK6k2PDJAnzQYwCmdOuPrQudd/1TmrML69ab3RI9GTZ+60Lp3YqPbXDe4NvZ71Xrc6RItWHufHO7h5RzFxzOIyTluziy/Q+rErMjv7qeDsGbRr6eUroBrrskd2F10I6J1SUlUG5WFmb0ewR3PtABV878Z/UE5hUJ58IPb/4Pu5avQl5Otse9KkS7oPn4omg7BoZYkOHtiJ8eE/keFo193ffpUIFlryY1OSqhi9uz/1aDVA/iYlcDqlnKdfGELNZrp5iWx+NwR3EJQqXaNXHxdLzjUgMJQYZQWIiPh47AXX164MbVqxCSktGkR2en25irxhS09O33MXjSWwCKAqkFo17Eyyu+QaWaNQAUtREqCSwHe7RsHH1BA+193A4ySpcujWnTpqFfv36oUKECEhISMG3aNHz99dcKJE+bMlLTZB8f4HK8tIZ0Zw54NohOMbEgQ6ydhpJs528xipVk+HDODVfkauRI0jh6MrYc40ZKY0MxGalpksZGcRXkOiuG9rYkQws9AoplpBY1nncm2clIw5ayrqebJzyUUv1XXF2ipH9X/YrLCWdRsUY1HNn+B3IyMzFr4HDc+UAHpCZdMs8LpXXFgfnStydj0P8mwD8wEL9/+wMyU6QH1kpxO8hYtGgRWrVqhVGjRuG///7DoEGDsGjRIiQlJWHjxo1KpPG28Nt8eUdNdES0C6vKJRlijWFVK8nwbbxFIhyVZORled9OROoN/MqpOGRdT0dwaBnx/Tjp2aKXkgyp9vyyDj1efAYhoaEAgF0rVsmyX19Vl5w9eNhqHpLsGxn4d9WvTrbwHcnj+Nw85/av24STf+2GKTAAaZeueNWWSy5uBRnh4eHo168fhg4dirVri8Z9OHToEDp06IAXX3yRQYYXxGawVIJomwyVZmEtdmb/IaRdumLutXPmQKxPGx6StjgKBKzGqHFw8XXUbsDVvi35GQy4ejYRP3/wER56axyEgkK7YMNZ91lnbZxcDZZXEuXn5uLjoU+h/aODcD05xdzF1FuuhgUnca5KnnzNrSCjevXqSEpKwt69e62WX758GfXq1ZM1YbcTJYcTtiU+4qdvH99te5cIgoAFz7yErs+NRH5OjtOeEKR/jkqxLIMMsSe81EuXHfaAMHMSZOTl5MBoMKJznTvwTV4+9q/dYJ7GfGas9dDRzhrUOTrE5YSzDmdZLemSzyZajb3iqczr1xESGoorZxNFRxelksetIGP//v2oWdN62tjIyEh07twZy5Y5f4JwmACTSfYincjISKt/tSb2l/W4s8+teUEOLv3ZZ8VaVevaB4NNmzZFrpcDXLmT1w3q1Ud4UCm75Qe/KTqH6lSpijpVqnqVHk8FihTRaqHIUevntNwyUq6hVEXrrsQ1q1WD8eZ3YRRpE7Fp4oeoV70GUL2Gw/36mcTncinML8DyZ1/FHXfcgVe//c5lPteqXRu5Ds6L2g0a2C3b+P5MpCScRZ3KVVGnsvNz2yTSRkkL56CcxPL3RnIKNkz8EGXCK+Fa4nk0qF0HqF3H52nTkqCgILvvPiw8zG49R+eHkteNgIAA5EoY5dYAL2qhhw0bhtmzZyM7OxstW7ZEUlKS640sxMXFISIiQlMNnXwhIz8XGxLjcDH7BhqGVsT9VevAz83RCz11Jj0VK88et1r2TGRLBItc2Ip9dNh+kiJLLzdt49Z2TzRohvKBwS5Sqo6FJ/cjLde6qsbR30fKOZdxHT8mWLeM71+nEWqVLmq0+fGR3SiwKc2Q8j3NPfoP8kSqDI0w4MWmrR1uZ3su96sdiYgy5UTXPZp6BRvOWc+tMeqOFijtL62Nwb7kJGy/eKuxcc1SoRgQIc/4Hlpim6dl/QMx4g59BVPOuLquAkCFwGAMb9DMatm2pDPYn2Jd+q3WNSo+Pt5lLYZHXVjr16+PhQsXon379vj1118xatQotwOMYomJiejbt69H2zoSGRmJJUuWYOjQoTh+/LjrDW4jVZrcgQdeH2u1rGPHDk677D36resZG8Xy2tF2vXv2QobNvANa0efD91CmcrjVshYtWqiUmltut3O6YkRtdJto3XX4qSdHIPnmKJuDv5ht1zBQyvc0+ItZMInM5JqXn4cWLVo4zOe7Rz2GevcWXcjTLyfj4cc7OWwXUrddG7QdaT0T8gMdOyI3U3y0X1v+QUHo/OZLqFC7JrKvp2P+Ox/ggzP6GqclMjIS97/7Kq7n3QrodyxdgU9/GaFiqnxLynU1Pj4eLWzmoop5pD8adbnfapmjc1/J68bq1dKqs9wOMjp06IBffvkFKSkp6N27N9asWeN24izl5+dj/36Zxpqwcfz4ccX2XVLV9zfiAZtlsbGxTkcujVyz3uG07ye27ACathHN63YHD6N2s6Z22xw8cECz8wx0zcmFbX8CLZ1Dt8s5XT0rA7Zn3JFDh3DhxCkAwICCAruLl5R8Geig/ZFQWGi1vW0+H3rhMNoNHYCg0NL4c8kKu8m5LAXWr223bO+evW41Zt7bbw/CI2oh7dIV3Q6ZPaVaBJafjoWfvz9Szl3A8o/mis4XpVePSlgnOzvb7ryu2bk9Gtms5+rcV+K6IaWqBHAzyAgODsYPP/yA2NhYdOvWDenpt88JoRdivUucdccDgA1zF6DJffciOLQM8vPy8NfSlajSoC5Szp3Hf5t3AmNfE93u5w8+wotL7bvmqtY9VQJPRpIkBYjUoIrNgOz2bj2smi3IyzMPPe+K6Ai2bs7QWpCXJzqduZ7UKVMOv745GVcyMxC/d7+sEx+SdrgVZHTu3BlVqlTB8OHDER4ejvDwW8XKWVlZuHDB8Xj+pA1nY49ajQqXnnIVmS66PF1LuogZDz2K+q1b4vzxE1YXP2cN0hKPHMPv3y3FfcMGWy3X0pDhtm639kFa5Scyzbd1ryQPg0EHX+9hkenuPSU2Fw+DV3HXL17G0dugZO525lZrwwY3W01v2LABp0+ftnotXqzPrll6k5+Tg5+nzkJ+bi5yMrOwauosSRfA1EuXsWf1OrefrhL2HrBPQ57vJxujksUkEmRYzt7r6U173Zx5dsuKZky2X+6pAg2X1FEJI3Ke7/91k9V7X42x5Cm3goyZM2fCYDCIvjp27KhUGklmfy9fhQmtO+GtezrjwIbNih7rYlyC3TKHM9ES3ZQlMnuy1ciwHhYM/PPzWiQevdUAbvfKNZg1aDhSEuWbt2XvrxutZhEunkmXSA6JR45h37qiQCMnMwsrJk1XOUXOcYK025Sv5ga5cuY/HP39TzS+7x4AUH2GT1dYrK0NSSdP43LCWYRHFDWiPP3vPlnq7LPTb2DuIyNRvnpVpF9JQU6m/FOFZ6ffwJI3JuLBp59ERmoaVk2dJfsx6Pa2+PV3sWHuAmRnZCDjWqrayXGKQQYpbtHY1xF5793IzcrC6X/2ut6ACMD8kS+g06jhyM/Nxeb5i2Tbb0F+PpLPKtsl9ODGLTi40fl08USWMq6l4vC2nWj9UC/zstUfznG4forEienUxiCDFFdYUICjv/+hdjIkObbjL4QNG6R2MghF7YB+clAUzBInKuni9x5A3Zjm5vfbvl6M2C2/o07zO1G5bh3sXbsBp/4pGbPAOsMgg8jC1oXfomWfbuYZJb8b95bKKSIxt9tMp6Q/q2fMxaj5sxASGoqkU3HYtXwVstNv4MO+Q2HwM+qm7RqDDCIL6SlXMfPhx9CkYztcPBWHuD3sXqdFS99+H0/OuVXKsf1raWNYEGlF4uGjmNZ7MMpXrYqkU3HmwdoEQYCgkwADYJBBZCf14iX8qcMpufXk+B9/Y+/aDYju1hnnjp3AzsU/qp0kIrfdSLmGGynX1E6GohhkEFGJU5CXhyVvTMSSNyaqnRQicsI3U38SERHRbYdBBhERESmCQQYREREpgkEGERERKYJBBhERESmCQQYREREpgkEGERERKYJBBhERESmCQQYREREpgkEGERERKYJBBhERESmCQQYREREpgkEGERERKcIAQFDr4JmZmTCZTEhMTJR1vwEBAahRowbOnTuH3NxcWfdN1pjXvsF89g3ms28wn31DyXyuWbMm8vPzERIS4nQ9VYOMa9euITAwEElJSWolgYiIiNxUtWpV5OTkoHz58k7XUzXIICIiIv1imwwiIiJSBIMMIiIiUgSDDCIiIlIEgwwiIiJSBIMMIiIiUgSDDCIiIlIEgwwiIiJSBIMMIiIiUgSDDCIiIlIEgwwiIiJSBIMMIiIiUgSDDCIiIlKE7oIMo9GIyZMn48KFC0hPT8fmzZvRpEkTtZNVopQuXRqffvopLly4gOzsbBw7dgzDhw83fx4TE4OdO3ciIyMDZ8+exZtvvgmDwWD+nN+B+8LCwpCUlIRJkyaZl9WrVw/r1q3D9evXkZSUhI8++giBgYFW27344otISEhARkYGdu3ahXbt2vk66SXGgAEDEBsbi6ysLCQkJGDMmDHmz3hOyyMoKAgzZszAmTNnkJqaiq1btyI6Otr8eefOnbFv3z5kZmbixIkTGDVqlNX2wcHBmD9/Pq5cuYK0tDSsXLkSNWrU8PWfoWn79u3DiBEjrJbJcf662oc3BD29pk6dKly8eFHo3bu3EBUVJXz99ddCUlKSUL58edXTVlJey5cvF86ePSv07NlTiIqKEiZPniwIgiB06dJFqFKlinD16lVh4cKFQlRUlNCnTx/hypUrwoQJE/gdePFau3atIAiCMGnSJAGAEBQUJMTHxwtr1qwRYmJihE6dOgmnT58WFixYYN7m6aefFm7cuCEMGzZMaNKkiTB16lQhIyNDqF+/vup/j9Ze3bp1E7Kzs4UxY8YIUVFRwltvvSUIgiC0b9+e57SMrwULFghxcXFC586dhZiYGOHHH38UUlJShCpVqghRUVFCdna2MHnyZKFJkybCY489JmRmZgpDhw41b7906VLhxIkTwv333y/ExMQI69atE44cOSKYTCbV/za1X6VKlRLGjRsnCIIgjBgxwrxcjvNXyj68eKmfeXK9ypQpI2RmZgrDhw83L/P39xeuXr0qPPfcc6qnryS8wsPDhfz8fGHgwIFWy//8809h/fr1wuTJk4XTp08LRqPR/Nmrr74qJCUlCUajkd+BB6/nn39eiI2NFc6fP28OMkaOHCmkpaUJZcqUMa83YMAAIScnx3xhSExMFN577z2rfR0+fFj48MMPVf+btPbas2ePMGvWLKtlv/76qzBlyhSe0zK9TCaTkJOTY5VPwcHBQlZWljBq1Chh8eLFwvbt2622+fTTT4V///1XACA0aNBAEARB6NChg/nz8PBwoaCgQOjRo4fqf5+ar9dff10oKCgQilkGGXKcv6724WX61c9AuV7dunUTBEEQKlasaLV81apVwpo1a1RPX0l4RUdHC4mJiUK9evWslv/888/CoUOHhN27dwtz5861+qx58+aCIAhCTEwMvwM3X02aNBFSU1OFqKgoISEhwRxkLFu2zC6/ypUrJwiCIDz88MNCo0aNzHluuc7s2bOF2NhY1f8uLb3Cw8MFQRCEFi1aiH7Oc1qeV4UKFQRBEIQBAwaYl/n5+Qk3btwQXnjhBeHSpUvCK6+8YrVN3759zXn7zDPPCGlpaYLBYLBa58CBA3bfz+32qly5stCsWTOhWbNmdkGGHOevq314k3ZdtcmoV68e0tLSkJKSYrU8MTERVatWVSlVJcv+/ftRs2ZNxMXFmZdFRkaic+fO+Pfff1GvXj2rz4Ci/AWAqlWr8jtwQ2BgIH744Qe8//77OHTokNVnYvmcmpqKGzdumPMZgOh3wXy2FhUVBQCIiIjA7t27cfXqVezZsweDBw8GIJ7XPKfdd/XqVezatQtvvPEGIiIiEBQUhA8++AAmkwnbt29HeHi4y3xOSEiAIAh269zu+Xzp0iUcPHgQBw8etPtMjvPX1T68YfJqa40JDQ1FRkaG3fL09HSUKVNGhRSVfMOGDcPs2bORlpaGt956C8OGDbPL4/T0dABAmTJl+B24Yfr06UhOTsbMmTPtPnOVj6GhoQAg+l0wn61VqFABADBjxgxMmDABp06dQo8ePbB48WIUFBSI5jXPac888cQT+PvvvxEfH4/CwkIYjUa8//77SE5OBiB+vgKu87lixYrKJ76EkuP8dbUPb+gqyEhNTUVISIjd8uDgYLsojpyrX78+Fi5ciPbt2+PXX3/FqFGjkJSUJJrHwcHBAICUlBSUL1+e34EEXbp0wbBhw9CsWTO7JzfA9bmcmpoKAAgJCUFaWprd53SL0VhUYPvqq69ixYoVAIA9e/agVatWGD16NM9pmYSFhWHLli04cuQI3n33XaSlpaF///546623cOzYMQBwms+8fntGjvPX1T68oavqknPnziE0NBTlypWzWl6rVi2cOXNGlTSVRB06dMDevXtRs2ZN9O7dGz179sSFCxcAFOVxnTp1rNavVasWAODMmTP8DiTq2rUrQkNDcfLkSWRlZSErKwt16tTB+PHjkZWVJZrPxflanM8ARL8L5rO1S5cuAQCOHDlitTw2NhbVq1fnOS2TgQMHonr16hg8eDC2bNmCPXv2YPz48di2bRsGDhyIa9euieZzbm4uzp8/j3Pnzpnz3XYd5rNjcpy/rvbhDV0FGdu2bUN2dja6du1qXhYcHIz77rsP69evVzFlJUdwcDB++OEHxMbGolmzZlizZo3V5+vWrbPKXwDo3r074uPjcfLkSX4HEk2ZMgVNmjRB8+bNza/z58/jiy++QPPmzbFhwwa0b9/e/DQBAN26dUNGRgZ+//13HDp0CImJiejWrZvVfrt27cp8trF3715kZ2cjJibGannz5s1x5MgRntMyMZnEC8ZzcnKQkZGBdevW2Z2v3bt3xx9//GH+vEKFCmjTpo3582rVqiEqKor57IQc56+rfXhL9Zazcr7mzJkjnD9/XujWrZvQtm1bYePGjcLJkyeFwMBA1dNWEl69e/c2j4lRr149q1e1atWEWrVqCdevXxc+++wzISoqShg1apSQmZlp1dqZ34FnL8veJWXKlBHOnTsn/PTTT0Lz5s2FgQMHCsnJyebPAQgvv/yykJaWJgwaNEho2bKl8N133wnJyclCWFiY6n+L1l7Tpk0TLl26JAwePFho1qyZ8O677wp5eXlCixYteE7L9CrOxx07dggdOnQQ7rzzTmHChAlCXl6e0LFjR6FVq1ZCXl6e8PbbbwvNmjUTxo8fL+Tl5QkPPPCAeR+rV68WDh8+LLRv317o2LGjsHfvXmHHjh2q/21aetn2LpHj/JWyDy9e6meanC9/f39hxowZwuXLl4X09HRh7dq1Qq1atVRPV0l5vfLKK4Ij27ZtEwAIbdu2FXbv3i1kZWUJ8fHxdmMF8Dvw7GUZZAAQIiMjhS1btggZGRnC+fPnhffee8+ue98bb7whJCYmChkZGcLvv/8uNGvWTPW/Q4svg8EgTJgwQUhMTBSys7OFffv2WY29wHNanlfTpk2FFStWCBcvXhSuX78u/P3331b53Lt3byE2NlbIysoSjhw5YtXdFYAQGhoqfPXVV8K1a9eEa9euCYsXL+aAZzYv2yADkOf8dbUPT1+Gm/8hIiIikpWu2mQQERGRdjDIICIiIkUwyCAiIiJFMMggIiIiRTDIICIiIkUwyCAiIiJFMMggIiIiRTDIICIiIkUwyCAiIiJFMMggIiIiRTDIICIiIkX8H0nKtLOoIo6iAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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AAMYiVAAAgLEIFQAAYCxCBQAAGItQAQAAxiJUAACAsQgVAABgLEIFAAAYy+tQOe+881RQUKAjR46ora1NH374oWbPnu0+P2bMGO3YsUOtra06fPiwli1bpoiIiP99wMhIrVixQkeOHJHT6VRpaalGjhzpk2EAAEBo8TpU1qxZo6lTp2revHm6+uqrtX79eq1Zs0a33HKLhgwZopKSEh08eFBjx47VggULtHDhQi1dutR9/5UrV2rOnDm65557dN1116m2tlalpaVKTk726WAAACD4RXmzePDgwbr99tuVl5en1157TZK0b98+3XDDDVq4cKH27NmjpqYmzZ07V59++qn27dunyy+/XA888IAeffRRDRw4UAsWLNC9996rjRs3SpLmzp2rY8eOKS8vTwUFBb6fEAAABC2vXlFJS0tTfX29du/e7XH8+PHjSktLU05OjoqLi/Xpp5+6z5WUlGjIkCHKzs7W9ddfL5vNpqKiIvd5l8ul7du3Kzc3t4+jAACAUOPVKyp79+7V0KFDPY5lZmZq0qRJ+tvf/qZbb71V69at8zhfU1MjSUpNTVVGRoaam5vV2NjYbc3YsWN7s39JUlRUlLKzs3t9/0DLzMz0+LO37Ha7L7YDL4wYMUJRUef+MvLVcxxMwm3mcJtXYuZw4M95Y2Ji1NHRcc51XoXKF82cOVNPPvmkmpub9fOf/1wzZ85Ua2urxxqn0ylJSkhIUGJiYrfzp9ckJCT0eh9Dhw7Vnj17en1/UxQWFvbp/i6XSw0NDT7aDXqisLBQ0dHRXq0PN+E2c7jNKzFzOPDXvFVVVedc06tQGTZsmFavXq0JEybo9ddf17x581RfXy+Hw6H4+HiPtTabTZLU2Nio5OTkbudPr/niqyzeqKmp0W233dbr+wdaZmamCgsLlZeXp4qKil4/jt1uV35+vg93hnPJy8tTZWXlOdf56jkOJuE2c7jNKzFzOMzsz3lPv1f1XLwOlRtuuEEbNmxQY2Ojpk2b5vF+k9raWmVkZHisT09PlyRVV1crLi5OiYmJSkpKksPh8FhTXV3t7VbcOjs7tXfv3l7f3xQVFRV9mqOzs9OHu0FPHDhwQOXl5T1e39fnOBiF28zhNq/EzOHAH/P25Ns+kpdvprXZbFq3bp3Ky8s1atQoj0iRpE2bNnV7U+yUKVNUVVWlgwcPauvWrWpra/NYY7PZNHHiRBUXF3uzFQAAEAa8ekVl0qRJGjJkiGbPnq3Bgwdr8ODB7nOnTp3Ss88+qwULFujpp5/WM888o2uvvVbLly/XfffdJ+mz96KsXr1aq1atUnNzs5qbm7V8+XI1NTXp5Zdf9u1kAAAg6HkVKsOHD5ckbd68udu5bdu26cYbb1Rubq6eeOIJvfvuu6qvr9fPfvYzrV692r1u0aJF6ujo0PPPPy+bzaaysjLl5OSovb29j6MAAIBQ41WorFq1SqtWrfrSNbt27dI111xz1vMul0uLFy/W4sWLvfnQAAAgDPGPEgIAAGMRKgAAwFiECgAAMBahAgAAjEWoAAAAYxEqAADAWIQKAAAwFqECAACMRagAAABjESoAAMBYhAoAADAWoQIAAIxFqAAAAGMRKgAAwFiECgAAMBahAgAAjEWoAAAAYxEqAADAWIQKAAAwFqECAACMRagAAABjESoAAMBYhAoAADAWoQIAAIxFqAAAAGMRKgAAwFiECgAAMBahAgAAjEWoAAAAYxEqAADAWIQKAAAwFqECAACMRagAAABjESoAAMBYhAoAADAWoQIAAIxFqAAAAGMRKgAAwFiECgAAMBahAgAAjEWoAAAAYxEqAADAWIQKAAAwFqECAACMRagAAABjESoAAMBYhAoAADAWoQIAAIxFqAAAAGMRKgAAwFiECgAAMBahAgAAjEWoAAAAYxEqAADAWIQKAAAwFqECAACMRagAAABjESoAAMBYhAoAADAWoQIAAIxFqAAAAGMRKgAAwFiECgAAMBahAgAAjEWoAAAAYxEqAADAWIQKAAAwFqECAACM1adQ2bNnj+bMmeNxbMyYMdqxY4daW1t1+PBhLVu2TBEREf/7gJGRWrFihY4cOSKn06nS0lKNHDmyL9sAAAAhqlehMnDgQC1evFjZ2dkex4cMGaKSkhIdPHhQY8eO1YIFC7Rw4UItXbrUvWblypWaM2eO7rnnHl133XWqra1VaWmpkpOT+zYJAAAIOV6HyoMPPqiWlhb99re/7XbuvvvuU1NTk+bOnat9+/Zpw4YNeuyxx3TfffcpMjJSCQkJWrBggZYsWaKNGzdq3759mjt3rmJjY5WXl+eTgQAAQOiI8vYOa9eu1ebNmyVJ//73vz3O5eTkqLi4WJ9++qn7WElJiR577DFlZ2dr8ODBstlsKioqcp93uVzavn27cnNzVVBQ0LshoqK6vboTTDIzMz3+7C273e6L7cALI0aMUFTUub+MfPUcB5Nwmznc5pWYORz4c96YmBh1dHScc53XoXLs2DEdO3bsjOfsdrvWrVvncaympkaSlJqaqoyMDDU3N6uxsbHbmrFjx3q7FbehQ4dqz549vb6/KQoLC/t0f5fLpYaGBh/tBj1RWFio6Ohor9aHm3CbOdzmlZg5HPhr3qqqqnOu8TpUvkxiYqJaW1s9jjmdTklSQkLCGc+fXpOQkNDrj1tTU6Pbbrut1/cPtMzMTBUWFiovL08VFRW9fhy73a78/Hwf7gznkpeXp8rKynOu89VzHEzCbeZwm1di5nCY2Z/zbty4sUfrfBoqDodD8fHxHsdsNpskqbGxUcnJyd3On17zxVdZvNHZ2am9e/f2+v6mqKio6NMcnZ2dPtwNeuLAgQMqLy/v8fq+PsfBKNxmDrd5JWYOB/6Ytyff9pF8HCq1tbXKyMjwOJaeni5Jqq6uVlxcnBITE5WUlCSHw+Gxprq62pdbAQAAIcCnv/Bt06ZNys3N9Tg2ZcoUVVVV6eDBg9q6dava2to81thsNk2cOFHFxcW+3AoAAAgBPg2VZ599VmlpaXr66aeVlZWlefPmafny5Vq5cqWkz96Lsnr1aq1atUqTJ0/WuHHj9Oqrr6qpqUkvv/yyL7cCAABCgE+/9fPRRx8pNzdXTzzxhN59913V19frZz/7mVavXu1es2jRInV0dOj555+XzWZTWVmZcnJy1N7e7sutAACAENCnUPn8r8Y/bdeuXbrmmmvOeh+Xy6XFixdr8eLFffnQAAAgDPCPEgIAAGMRKgAAwFiECgAAMBahAgAAjEWoAAAAYxEqAADAWIQKAAAwFqECAACMRagAAABjESoAAMBYPv23foBwM2zYsB6ts9vtcrlcstvt6uzs9POuzq6pqUl1dXUB+/gA4C1CBeiFuIhIWZalgoKCHt+noaFB+fn5ftzVuZ1qa9OE8eOJFQBBg1ABeiEmMlIRERHa5WxQS5cr0NvpkcQB0RqXcIFSUlIIFQBBg1AB+qCly6UTXR2B3gYAhCzeTAsAAIxFqAAAAGMRKgAAwFiECgAAMBZvpv0SaWlpSklJ8fvH8dXv2Ojp7/QAACBYECpnkZaWpu07dsgWF9cvH8+E37EBAIBpCJWzSElJkS0uLqh+T0ZqdJxGDUwO9DYAAPAZQuUcgun3ZCQO4OkEAIQW3kwLAACMRagAAABjESoAAMBYhAoAADAWoQIAAIxFqAAAAGMRKgAAwFiECgAAMBahAgAAjEWoAAAAYxEqAADAWIQKAAAwFqECAACMRagAAABjESoAAMBYhAoAADAWoQIAAIxFqAAAAGMRKgAAwFiECgAAMBahAgAAjEWoAAAAYxEqAADAWIQKAAAwFqECAACMRagAAABjESoAAMBYhAoAADAWoQIAAIxFqAAAAGMRKgAAwFiECgAAMBahAgAAjEWoAAAAYxEqAADAWIQKAAAwFqECAACMRagAAABjESoAAMBYhAoAADAWoQIAAIxFqAAAAGMRKgAAwFiECgAAMBahAgAAjBWQUImMjNSKFSt05MgROZ1OlZaWauTIkYHYCgAAMFhUID7oypUrNXv2bM2bN0/V1dV64IEHVFpaqiuuuEInTpwIxJaAsDFs2LB++Th2u10ul0t2u12dnZ29fpympibV1dX5cGcAgkm/h0pCQoIWLFige++9Vxs3bpQkzZ07V8eOHVNeXp4KCgr6e0tAWIiLiJRlWf36NdbQ0KD8/Pw+PcaptjZNGD+eWAHCVL+HyvXXXy+bzaaioiL3MZfLpe3btys3N5dQAfwkJjJSERER2uVsUEuXK9Db6ZHEAdEal3CBUlJSCBWEhLS0NKWkpAR6Gz1mt9vV1dUV0D1ESLL68wPOnz9fjzzyiJKSkjyOP/XUUxo7dqyuvPJKrx7v5MmTio6O1tGjR324Syk6OlqDBg1S+6ef6tP+/RT12oCICMVERAbVnqXg3Dd77h+RilBsZKSam5v79O2j/hAVFaWUlBQ1NTUZv1dfYWbvZo6MjFRSUpIiIiL8tDv/cTgcamtr8+ljDhkyRC6XS/Hx8V+6rt9fUUlMTFRra2u3406nUwkJCV4/Xnt7uySpo6Ojz3v7vI6OjjPuEwDOprm5OdBb6HfM7B2n0+nDnQQ3l8vl/jv8y/R7qDgcjjPWk81mU2Njo9ePl5yc7IttAQAAA/X7jyfX1tYqMTGx27d+0tPTVV1d3d/bAQAABuv3UNm6dava2tqUm5vrPmaz2TRx4kQVFxf393YAAIDB+v1bP06nU6tXr9aqVavU3Nys5uZmLV++XE1NTXr55Zf7ezsAAMBgAfmFb4sWLVJHR4eef/552Ww2lZWVKScnp0dvqgEAAOGj3388GQAAoKf4RwkBAICxCBUAAGAsQgUAABiLUAEAAMYiVAAAgLEIFQAAYCxCBQAAGItQ6QeRkZFasWKFjhw5IqfTqdLSUo0cOfKs6+Pi4vTUU0+pvr5eJ0+e1FtvvaVRo0b14477ztuZr7jiCr3xxhs6ceKEPvroI+Xn52vgwIH9uGPf2bNnj+bMmfOla+x2uzZt2qSWlhbV19frd7/7nWJjY/tph77Xk5mvvPJKbd26VU6nU06nU8XFxRoxYkQ/7dC3ejLv5/3gBz+QZVmy2+1+3JV/9WTmULh2fV5PZg72a9d5552ngoICHTlyRG1tbfrwww81e/bss64P1LXL4ubf26OPPmodPXrUmjZtmpWVlWWtXbvWqq+vt5KTk8+4/q9//au1f/9+66abbrKuvfZaa9u2bdaBAwesAQMGBHwWf8yclJRkHT161Fq7dq2VnZ1tTZ061froo4+sdevWBXwOb24DBw60Fi9ebFmWZc2ZM+es6+Li4qyqqiqrqKjIGjNmjHXzzTdb//3vf61nn3024DP4a+aLLrrIcjgc1t/+9jdrzJgx1vjx461du3ZZVVVVVmxsbMDn8PW8n79ddtllVnNzs2VZlmW32wM+gz9nDoVrlzczh8K16+9//7t1+PBha+rUqVZWVpa1YsUKy7Is65Zbbum2NoDXrsB/okL5lpCQYJ08edKaPXu2+1h0dLTV1NRk/eQnP+m2/mtf+5plWZY1atQo97HLLrvM+vjjj62srKyAz+OPmWfNmmWdOnXK4y+sH/7wh1ZnZ6dls9kCPk9Pbg8++KDV1dVlnfZlF7e5c+dazc3NVkJCgvvY9773Pau9vf2s8WrizZuZFy9ebJ04ccKKiYlxHxs+fLhlWZY1ffr0gM/i63lP3wYMGGC9/fbb1htvvBGUoeLNzKFw7fJ25mC/dg0ePNjq7Oy07rzzTo/jO3futIqLi7utD9S1i2/9+Nn1118vm82moqIi9zGXy6Xt27d7/AvSp02ZMkXl5eX64IMP3Meqqqp04YUXat++ff2y577yduZBgwaps7NTHR0d7mNtbW0aMGCAoqOj+2XPfbV27Vp94xvf0OjRo8+5NicnR9u3b5fT6XQfKykpUUxMjG666SY/7tK3vJl50KBB2r59u8dzfPz4cUlSWlqav7boU97Me9qvfvUrdXV16dFHH/XfxvzIm5lD4dolef+/62C+dqWlpam+vl67d+/2OH78+PEzfl0G6tpFqPiZ3W5Xc3OzGhsbPY7X1NQoNTW12/qsrCwdPnxYDz30kKqrq3X06FG98sorGj58eH9tuc+8nXnz5s2KjY3VypUrFRcXp4yMDC1ZskSlpaVqaWnpr233ybFjx/TBBx94XKTPxm63q7Ky0uOYw+HQJ598csbPj6m8mXnp0qW69dZbPY799Kc/lST961//8sv+fM2beSVp/Pjxmj9/vmbOnKmuri4/784/vJk5FK5dknczB/u1a+/evRo6dKjH9SgzM1OTJk0649dloK5dhIqfJSYmqrW1tdtxp9OphISEbsdTUlI0adIkXXnllZoxY4a+//3va9CgQfrnP/+p5OTk/thyn3k783/+8x/94he/0JIlS9Ta2qpDhw5p2LBhuv/++/tju/3O289PqElKStJzzz2nhx56SGvXrtWOHTsCvSWfO//88/XCCy/ogQce0KFDhwK9nX4RCtcub4XatWvmzJnauXOnmpub9fOf/7zb+UBduwgVP3M4HIqPj+923GazdXvFQfrsp2WcTqe++93vaufOndq2bZumT5+u1NRUfetb3+qPLfeZtzPPmDFDK1eu1MqVK3X11Vfrm9/8pj744ANt2rQpJP/i9vbzE0ruuusuHTx4UDNmzNCSJUt09913B3pLfvHHP/5Ru3fv1po1awK9lX4TCtcub4XKtWvYsGEqKyvTX/7yF7399tu66qqrVF9f321doK5dUX57ZEiSamtrlZiYqKSkJDkcDvfx9PR0VVdXd1t/7NgxVVVVqa2tzeNYQ0ND0Hwv39uZFy5cqK1bt2rZsmXuYwcOHNDhw4d1880369VXX/X/pvtRbW2tMjIyPI6d/nyd6fMTKp566inNnz9fr7zyihYtWqTDhw8Hekt+M3nyZMXHx+vUqVOSPvtLXJL279+vDRs2aPr06YHcnl+EwrXLW6Fw7brhhhu0YcMGNTY2atq0aR7vLfyiQF27eEXFz7Zu3aq2tjaPN5HabDZNnDhRxcXF3dbv3LlTw4cP13nnnec+dtFFF+nCCy/U/v37+2XPfeXtzFFR3Xu5vb1dks74MmOw27RpkyZMmCCbzeY+NnnyZLW2tqqsrCyAO/Of73znO5o/f74WLVqkO+64I6QjRZKuuuoqZWVlafTo0Ro9erR+9KMfSZK+/e1vB+23Bc4lFK5d3gr2a5fNZtO6detUXl6uUaNGfWmkSIG9dgX8R6RC/Zafn2/V1dVZkydPtsaNG2dt2bLFOnjwoBUbG2vFxcVZdrvdiouLs6TPfn6/srLS2rx5szVu3Djruuuus8rKyqzdu3dbERERAZ/FHzPff//9lmVZ1kMPPWSNHj3auv76662SkhLrww8/dK8JptsXf6Txi/MmJCRYtbW11iuvvGKNHj3auvPOO62Ghgbr4YcfDvje/TXz+vXrrX//+9+W3W7vdjvvvPMCvn9fz/vF28SJE4Pyx5O9mTlUrl3ezBzs165p06a5f2fKF78uL7roIpOuXYH/ZIX6LTo62nr88cet48ePW06n03rttdes9PR0S/rfBWzixInu9RdffLH1yiuvWJ988onlcDisl19+2UpNTQ34HP6cedasWdb7779vOZ1Oq66uznrppZesiy++OOBz9Ob2xYvbmebNzMy03nzzTau1tdWqq6uzfvWrXwXtxbwnM5eXl1tnM2vWrIDv3x/P8edvoRgqoXrt8nbmYL52LVq06Kxfl1u3bjXm2hXx//8DAACAcXiPCgAAMBahAgAAjEWoAAAAYxEqAADAWIQKAAAwFqECAACMRagAAABjESoAAMBYhAoAADAWoQIAAIxFqAAAAGP9P42uW4Xt+EW0AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(lambda1)\n",
    "plt.figure()\n",
    "plt.hist(lambda1)\n",
    "plt.figure()\n",
    "plt.plot(lambda2)\n",
    "plt.figure()\n",
    "plt.hist(lambda2)\n",
    "plt.figure()\n",
    "plt.plot(tau)\n",
    "plt.figure()\n",
    "plt.hist(tau)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}