lectures/L03_probability.ipynb

{
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   "source": [
    "# Probability & Statistics: II\n",
    "\n",
    "*Davide Gerosa (Milano-Bicocca)*\n",
    "\n",
    "##### Reading:\n",
    "\n",
    "- [Ivezic textbook](https://press.princeton.edu/books/hardcover/9780691198309/statistics-data-mining-and-machine-learning-in-astronomy) Chapter 3. \n",
    "\n",
    "\n",
    "This course is based on previous work by many people. See [here]((https://github.com/dgerosa/astrostatistics_bicocca_2023/blob/main/README.md) for credits.\n",
    "\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.stats\n",
    "import pylab as plt\n",
    "plt.rcParams['figure.figsize'] = [8, 8]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Monte Carlo integration\n",
    "\n",
    "You might have seen this already, but Monte Carlo integration is an absolute crucial notion in modern statistics (modern because it relies on generating a large number of data points, which has been made possible by computers). Suppose you have very a complicated integral to solve and that you can write down the integrand as a product of $f(x)$ and $p(x)$ with $\\int p(x)=1$ (this is not restrictive at all! See below). My nasty integral is\n",
    "\n",
    "$$\\int f(x) p(x) dx$$\n",
    "\n",
    "\n",
    "Provided one can **evaluate** $f(x)$ and **sample** $p(x)$, then\n",
    "\n",
    "\n",
    "$$\\int f(x) p(x) dx \\approx \\frac{1}{N}\\sum_{i=1}^N f(x_i) $$\n",
    "\n",
    "where $x_i$ are samples drawn from $p$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### An example.\n",
    "\n",
    "Ok try to integrate this crazy thing. Pen and paper? Good luck.\n",
    "    \n",
    "$$\\int_{0.3}^4 dx \\frac{\\exp(x) \\sqrt{4x+3}  \\log(x^6)}{\\tanh(x)}$$\n",
    "\n",
    "Pen and paper? Good luck. With a computer? Easy peasy!\n",
    "\n",
    "First, I divide and multiply by $4-0.3$. This is because (see below) 1/(4-0.3) is the uniform distribution $p(x)$ for x between 0.3 and 4.\n",
    "\n",
    "$$ (4-0.3) \\times \\int_{0.3}^{4} \\frac{dx}{(4-0.3)} \\frac{\\exp(x) \\sqrt{4x+3} * \\log(x^6)}{\\tanh(x)}$$\n",
    "\n",
    "Now I have $p(x)=\\frac{1}{4-0.3}$ and $f(x) = \\frac{\\exp(x) \\sqrt{4x+3} * \\log(x^6)}{\\tanh(x)}$. All I need to do is generate numbers from $p$, put them into $f$, and sum the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1395.5001407538532"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xmax= 4\n",
    "xmin=0.3\n",
    "\n",
    "xi=np.random.uniform(xmin,xmax, 100000)\n",
    "\n",
    "def fun(x):\n",
    "    return np.exp(x)*(4*x+3)**0.5 * np.log(x**6)/np.tanh(x)\n",
    "\n",
    "integral = (xmax-xmin) * np.mean(fun(xi))\n",
    "\n",
    "integral\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check the result:\n",
    "https://www.wolframalpha.com/input/?i=integrate+from+0.3+to+4+exp%28x%29+sqrt%284x%2B3%29+*+ln%28x%5E6%29+%2Ftanh%28x%29\n",
    "\n",
    "Run the cell again. And again.  We'll understand the errors in a bit.\n",
    "\n",
    "#### Always remember Monte Carlo integration, it's extremely useful!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Descriptive statistics \n",
    "\n",
    "As we've said, our goal is to estimate $h(x)$ given some measured data, allowing us to reconstruct the data-based distribution $f(x)$. An arbitrary distribution can be characterized by **location** parameters (i.e., position), **scale** parameters (i.e., width), and **shape** parameters. These parameters are called ***descriptive statistics***.\n",
    "\n",
    "The distribution we're trying to characterize could be anything, e.g. (from my field) the distribution of masses of binary black-hole systems as discovered by gravitational-wave detectors. We really don't know the answer to this well, and the problem is made more complicated by things like detector selection effects (heavier systems are more likely to be observed), and blurring effects from measurement precision."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's get back to the distribution we've seen already"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 595,
       "width": 630
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Based on Ivezic v2, Figure 6.8; edited by G. T. Richards, S. R. Taylor, and D. Gerosa\n",
    "\n",
    "# Author: Jake VanderPlas\n",
    "# License: BSD\n",
    "#   The figure produced by this code is published in the textbook\n",
    "#   \"Statistics, Data Mining, and Machine Learning in Astronomy\" (2013)\n",
    "#   For more information, see http://astroML.github.com\n",
    "#   To report a bug or issue, use the following forum:\n",
    "#    https://groups.google.com/forum/#!forum/astroml-general\n",
    "\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy import stats\n",
    "\n",
    "from sklearn.neighbors import KernelDensity\n",
    "\n",
    "from astropy.visualization import hist\n",
    "from sklearn.mixture import GaussianMixture\n",
    "\n",
    "#----------------------------------------------------------------------\n",
    "# This function adjusts matplotlib settings for a uniform feel in the textbook.\n",
    "# Note that with usetex=True, fonts are rendered with LaTeX.  This may\n",
    "# result in an error if LaTeX is not installed on your system.  In that case,\n",
    "# you can set usetex to False.\n",
    "if \"setup_text_plots\" not in globals():\n",
    "    from astroML.plotting import setup_text_plots\n",
    "setup_text_plots(fontsize=14, usetex=True)\n",
    "%config InlineBackend.figure_format='retina' # very useful command for high-res images\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# Generate our data: a mix of several Cauchy distributions\n",
    "# In reality nature generates data for you\n",
    "\n",
    "\n",
    "random_state = np.random.RandomState(seed=0)\n",
    "N = 2000 # number of data points\n",
    "mu_gamma_f = [(5, 1.0, 0.1),\n",
    "              (7, 0.5, 0.5),\n",
    "              (9, 0.1, 0.1),\n",
    "              (12, 0.5, 0.2),\n",
    "              (14, 1.0, 0.1)]\n",
    "hx = lambda x: sum([f * stats.cauchy(mu, gamma).pdf(x)\n",
    "                          for (mu, gamma, f) in mu_gamma_f])\n",
    "x = np.concatenate([stats.cauchy(mu, gamma).rvs(int(f * N), random_state=random_state)\n",
    "                    for (mu, gamma, f) in mu_gamma_f])\n",
    "random_state.shuffle(x)\n",
    "x = x[x > -10]\n",
    "x = x[x < 30]\n",
    "\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# plot the results\n",
    "fig,ax = plt.subplots(figsize=(10, 10))\n",
    "xgrid = np.linspace(-10, 30, 1000)\n",
    "\n",
    "# True distribution: you typically don't have it! Only have the samples!\n",
    "if False:\n",
    "    ax.plot(xgrid, hx(xgrid), ':', color='black', zorder=3,\n",
    "            label=\"$h(x)$, Generating Distribution\")\n",
    "\n",
    "# A simple histogram\n",
    "# But try changing the number of bins!\n",
    "if True:\n",
    "    ax.hist(x,density=True,color='C0',bins=100,histtype='step',lw=2, label='Histogram, 100 bins')\n",
    "\n",
    "# Something more sophisticated: Kernel Density Estimation\n",
    "# But try changing the bandwith! \n",
    "if False:\n",
    "    kde = KernelDensity(bandwidth=0.1, kernel='gaussian')\n",
    "    kde.fit(x[:, None])\n",
    "    dens_kde = np.exp(kde.score_samples(xgrid[:, None]))\n",
    "    ax.plot(xgrid, dens_kde, '-', color='C1', zorder=3,\n",
    "            label=\"$f(x)$, non-parametric (KDE)\")\n",
    "\n",
    "# Use Gaussian Mixtures with a pre-defined number of clusters (13)\n",
    "if False:\n",
    "    gmm = GaussianMixture(n_components=13).fit(x.reshape(-1, 1))\n",
    "    logprob = gmm.score_samples(xgrid.reshape(-1, 1))\n",
    "    fx = lambda j : np.exp(gmm.score_samples(j.reshape(-1, 1)))\n",
    "    ax.plot(xgrid, fx(np.array(xgrid)), '-', color='C2',\n",
    "            label=\"$f(x)$, parametric (13 Gaussians)\")\n",
    "\n",
    "# Plot cosmetics\n",
    "ax.text(0.02, 0.95, \"%i points\" % N, ha='left', va='top',\n",
    "            transform=ax.transAxes)\n",
    "\n",
    "ax.set_ylabel('$p(x)$',fontsize=14)\n",
    "ax.legend(loc='upper right')\n",
    "\n",
    "ax.set_xlabel('$x$',fontsize=14)\n",
    "ax.set_xlim(0, 20)\n",
    "ax.set_ylim(-0.01, 0.4001)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We all know that the **mean** of a sample is \n",
    "\n",
    "$$\\bar{x} = \\frac{1}{N}\\sum_{i=1}^N x_i$$ \n",
    "\n",
    "This is actually known as the **sample arithmetic mean**, and derives from *Monte Carlo integration* to get the first moment of the distribution, i.e. \n",
    "\n",
    "$$\\mu = E(x) = \\langle x \\rangle = \\int_{-\\infty}^{\\infty} x h(x)\\,dx \\approx \\frac{1}{N}\\sum_{i=1}^N x_i $$\n",
    "\n",
    "where $\\{x_i\\}$ are random samples from the properly normalized $h(x)$, and $E(\\cdot)$ means the **expectation value**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Computing the mean is straightforward:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.79491032639886\n"
     ]
    }
   ],
   "source": [
    "data =x.copy() #Why am I doing this?\n",
    "\n",
    "mean = np.mean(data)\n",
    "print(mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "a=[1,2,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "b=a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "b[0]=10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[10, 2, 3]"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[10, 2, 3]"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "While it's most common to compute the mean, it may surprise you to learn that some distributions do not have formally calculable means (integration gives infinity). In these and other cases, the **median** is a more *robust* estimator of the (true) mean location of the distribution.  That's because it is less affected by **outliers**.\n",
    "\n",
    "To understand the previous statement, think about multiplying all numbers above the 50th percentile (i.e. the median) by 100, or even just replacing them with larger numbers. The mean would be strongly affected by these corrupted points, but **cumulative statistics based on the ordering of samples would remain unaffected by the outlier corruption**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.752731764708434"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "median = np.median(data)\n",
    "median"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7.752731764708434 7.752731764708434\n",
      "8.79491032639886 425.52602287925964\n"
     ]
    }
   ],
   "source": [
    "# Try to unpack what is happening here\n",
    "median = np.median(data)\n",
    "\n",
    "mask = data > 15\n",
    "data2 = data.copy()\n",
    "data2[mask] = 10000\n",
    "\n",
    "newmedian = np.median(data2)\n",
    "newmean = np.mean(data2)\n",
    "\n",
    "print(median, newmedian)\n",
    "print(mean, newmean)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other descriptive statistics are related to higher order moments of the distribution. Beyond the \"average\" *location* value, we'd like to know something about **deviations** from the average (which is related to the *shape* of the distribution).  The simplest thing to compute is $$d_i = x_i - \\mu.$$  However, the average deviation is zero by definition of the mean.  The next simplest thing to do is to compute the **mean absolute deviation (MAD)**:\n",
    "\n",
    "$$\\frac{1}{N}\\sum|x_i-\\mu|,$$\n",
    "\n",
    "but the absolute values can hide the true scatter of the distribution [(example)](http://www.mathsisfun.com/data/standard-deviation.html). But this is used, see regularization schemes further on in the class. So the next simplest thing to do is to square the differences $$\\sigma^2 = \\frac{1}{N}\\sum(x_i-\\mu)^2,$$ which we call the **variance**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The *variance* $V$ is the just expectation value of $(x-\\mu)^2$ (and related to the 2nd moment)\n",
    "\n",
    "$$\\sigma^2 = V = E((x-\\mu)^2)\\int_{-\\infty}^{\\infty}  (x-\\mu)^2 h(x) dx,$$\n",
    "\n",
    "where $\\sigma$ is the **standard deviation**. Again, the integral gets replaced by a sum for discrete distributions. While most familiar for Gaussian distributions, you can compute the variance even if your distribution is not Gaussian.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "15.026052739760294 3.876345281287555\n",
      "True\n"
     ]
    }
   ],
   "source": [
    "var = np.var(data)\n",
    "std = np.std(data)\n",
    "print(var, std)\n",
    "print(np.isclose(std**2,var)) #Why am I not doing std**2==var?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is also the **Median Absolute Deviation (also MAD)** given by\n",
    "\n",
    "$${\\rm median} (|x_i-{\\rm median}(\\{x_i\\})|)$$\n",
    "\n",
    "where $\\sigma = 1.4826\\,{\\rm MAD}$ for a Gaussian distribution (but note that we aren't using a Gaussian distribution above)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.6811130664731344 2.492418232353069\n"
     ]
    }
   ],
   "source": [
    "from astropy.stats import median_absolute_deviation\n",
    "MAD = median_absolute_deviation(data)\n",
    "print(MAD,MAD*1.4826)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**$P\\%$ quantiles (or the $p^\\mathrm{th}$ percentile, $q_p$)** are computed as\n",
    "$$\\frac{p}{100} = H(q_p) = \\int_{-\\infty}^{q_p}h(x) dx$$\n",
    "\n",
    "The full integral from $-\\infty$ to $\\infty$ is 1 (100%).  So, here you are looking for the value of x that accounts for $p$ percent of the distribution.\n",
    "\n",
    "For example, the 25th, 50th, and 75th percentiles:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.674995612577169 7.752731764708434 11.637549888596837\n"
     ]
    }
   ],
   "source": [
    "# Execute this cell\n",
    "q25, q50, q75 = np.percentile(data, [25, 50, 75])\n",
    "print(q25, q50, q75)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x129e25c10>"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 465,
       "width": 484
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(data,bins=100,histtype='step');\n",
    "\n",
    "plt.axvline(np.percentile(data,50),c='red')\n",
    "plt.axvline(np.percentile(data,5),c='red',ls='dotted')\n",
    "plt.axvline(np.percentile(data,95),c='red',ls='dotted')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The region between the 5th and the 95th percentile contains 90% of the samples. In Bayesian statistics, this is the 90% credible interval."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **interquartile range** is the difference between the 25th and 75th percentiles, $q_{75} - q_{25}$.\n",
    "\n",
    "Just as with the median, the interquartile range is a more *robust* estimator of the scale of a distribution than the standard deviation.  So, one can create a standard-deviation-esque measurement (at least for a Gaussian) from the interquartile range as\n",
    "\n",
    "$$\\sigma_G = 0.7413\\times(q_{75} - q_{25})$$  \n",
    "\n",
    "The normalization makes it *unbiased* for a perfect Gaussian (more on that later)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.678746989540611 3.876345281287555\n",
      "3.678746989540611 1998.538847396505\n"
     ]
    }
   ],
   "source": [
    "# Execute this cell. Think about and discuss the results.\n",
    "from astroML import stats as astroMLstats\n",
    "\n",
    "# original data\n",
    "print(astroMLstats.sigmaG(data), np.std(data))\n",
    "\n",
    "# corrupted by outliers\n",
    "print(astroMLstats.sigmaG(data2), np.std(data2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "35.5 µs ± 322 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each)\n",
      "195 µs ± 5.78 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)\n"
     ]
    }
   ],
   "source": [
    "# Execute this cell. Cumulative statistics take longer to compute, but are more robust.\n",
    "%timeit np.mean(data), np.std(data)\n",
    "%timeit np.median(data), astroMLstats.sigmaG(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The **mode** is the most probable value, determined from the peak of the distribution, which is the value where the derivative is 0 (i.e. the turning point):\n",
    "\n",
    "$$ \\left(\\frac{dh(x)}{dx}\\right)_{x_m} = 0$$\n",
    "\n",
    "A good approximation for the mode is (the distribution needs to be somewhat close to Gaussian, for a proof: [Lupton 1993](https://press.princeton.edu/books/hardcover/9780691074290/statistics-in-theory-and-practice))\n",
    "\n",
    "$$x_m = 3q_{50} - 2\\mu$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5.668374641327581 8.79491032639886 7.752731764708434\n",
      "ModeResult(mode=array([-9.89016755]), count=array([1])) This is non sense!\n"
     ]
    }
   ],
   "source": [
    "# Execute this cell\n",
    "mode = 3*q50 - 2*mean\n",
    "print(mode, mean, median)\n",
    "\n",
    "# Note: don't rely on scipy.stats.mode()!!\n",
    "# It gives the most common value of an array, \n",
    "# but we have a random sample of unique draws\n",
    "print(scipy.stats.mode(data), \"This is non sense!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other useful ***shape*** measures include the \"higher order\" moments (the **skewness** and **kurtosis**):\n",
    "\n",
    "$$\\mathbf{Skewness}\\quad\\quad \\Sigma = \\int_{-\\infty}^{\\infty}  \\left(\\frac{x-\\mu}{\\sigma}\\right)^3 h(x) dx,$$\n",
    " \n",
    "$$\\mathbf{Kurtosis}\\quad\\quad K = \\int_{-\\infty}^{\\infty}  \\left(\\frac{x-\\mu}{\\sigma}\\right)^4 h(x) dx  - 3.$$\n",
    "\n",
    "The skewness measures the distribution's *asymmetry*. Distribution's with long tails to larger $x$ values have positive $\\Sigma$. \n",
    "\n",
    "The kurtosis measures how peaked or flat-topped a distribution is, with strongly peaked ones being positive and flat-topped ones being negative. $K$ is calibrated to a Gaussian distribution (hence the subtraction of $3$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![https://www.astroml.org/_images/fig_kurtosis_skew_1.png](https://www.astroml.org/_images/fig_kurtosis_skew_1.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.45629831452599 3.24867718616583\n"
     ]
    }
   ],
   "source": [
    "skew = scipy.stats.skew(data)\n",
    "kurt = scipy.stats.kurtosis(data)\n",
    "print(skew, kurt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Location:  8.79491032639886 7.752731764708434 5.668374641327581\n",
      "Scale:  15.026052739760294 3.876345281287555 3.678746989540611\n",
      "Shape:  0.45629831452599 3.24867718616583\n",
      "Some percentiles:  6.674995612577169 7.752731764708434 11.637549888596837\n"
     ]
    }
   ],
   "source": [
    "# Summary descriptive statistics for our distribution\n",
    "print(\"Location: \", mean, median, mode)\n",
    "print(\"Scale: \", var, std, astroMLstats.sigmaG(data))\n",
    "print(\"Shape: \", skew, kurt)\n",
    "print(\"Some percentiles: \", q25, q50, q75)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sample versus Population statistics <a class=\"anchor\" id=\"two\"></a>\n",
    "\n",
    "Statistics estimated from the *data* are called **sample statistics** as compared to **population statistics** derived from knowing the functional form of the pdf.\n",
    "\n",
    "Specifically, $\\mu$ is the **population mean**, i.e., it is the expectation value of $x$ for $h(x)$.  But we don't *know* $h(x)$.  So the **sample mean**, $\\overline{x}$, is an ***estimator*** of $\\mu$, defined as\n",
    "\n",
    "$$\\overline{x} \\equiv \\frac{1}{N}\\sum_{i=1}^N x_i,$$\n",
    "\n",
    "which we determine from the data itself."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead of the **population variance** $\\sigma^2$, we have the **sample variance**, $s^2$, where\n",
    "\n",
    "$$s^2 = \\frac{1}{N-1}\\sum_{i=1}^N(x_i-\\overline{x})^2$$\n",
    "\n",
    "The $N-1$ denominator (instead of $N$) accounts for the fact that we determine $\\overline{x}$ from the data itself instead of using a known $\\mu$. This is called [Bessel's correction](https://en.wikipedia.org/wiki/Bessel%27s_correction).\n",
    "\n",
    "Ideally one tries to work in a regime where $N$ is large enough that we can be lazy and ignore this. \n",
    "\n",
    "So the mean and variance of a distribution are $\\mu$ and $\\sigma^2$.  The *estimators* of the distribution are $\\overline{x}$ (or $\\hat{x}$) and $s^2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Pill of modern astrophysics from my research.** We computed Bessel's correction in the context of Hierarchical Bayesian statistics for gravitational-wave events in a recent paper. [Moore and Gerosa (2021), \"Population-informed priors in gravitational-wave astronomy\"](https://arxiv.org/abs/2108.02462). It's a fun paper to read if you're interested in the stats+gravity interplay.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Uncertainty of sample statistics\n",
    "\n",
    "We would also like to know the uncertainty of our estimates $\\overline{x}$ and $s$. \n",
    "\n",
    "Note that $s$ is the width estimate of the underlying distribution; it is **NOT** the uncertainty of $\\overline{x}$. This is a common misconception.\n",
    "\n",
    "Rather the uncertainty of $\\overline{x}$, $\\sigma_{\\overline{x}}$ is \n",
    "\n",
    "$$ \\sigma_{\\overline{x}} = \\frac{s}{\\sqrt{N}},$$\n",
    "\n",
    "which we call the **standard error of the mean**. The uncertainty of $s$ itself is\n",
    "\n",
    "$$\\sigma_s = \\frac{s}{\\sqrt{2(N-1)}} = \\frac{1}{\\sqrt{2}}\\sqrt{\\frac{N}{N-1}}\\sigma_{\\overline{x}}.$$\n",
    "\n",
    "Note that for large $N$, $\\sigma_{\\overline{x}} \\sim \\sqrt{2}\\sigma_s$ and for small $N$, $\\sigma_s$ is not much smaller than $s$.\n",
    "\n",
    "Another useful uncertainty estimate is for computing quantiles. The **standard error of a quantile** is\n",
    "\n",
    "$$ \\sigma_{q_p} = \\frac{1}{h_p}\\sqrt{\\frac{p(1-p)}{N}}$$\n",
    "\n",
    "where $p$ is between $0$ and $1$.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Try this at home***. \n",
    "- Generate some data\n",
    "- Compute $\\bar x$ and $s$\n",
    "- Do it many times\n",
    "- Estimate the errors\n",
    "- Compare with the expressions above"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Univariate distributions  (and an intro to scipy.stats)\n",
    "\n",
    "If we are attempting to characterize our data in a way that is **parameterized**, then we need a functional form for a **distribution**.  There are many naturally occurring distributions.  The book goes through quite a few of them.  Here we'll just talk about a few basic ones to get us started."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Uniform Distribution\n",
    "\n",
    "The uniform distribution is perhaps more commonly called a \"top-hat\" or a \"box\" distribution.  It is specified by a mean, $\\mu$, and a width, $W$, where\n",
    "\n",
    "$$p(x|\\mu,W) = \\frac{1}{W}$$\n",
    "\n",
    "over the range $|x-\\mu|\\le \\frac{W}{2}$ and $0$ otherwise.  That says that \"given $\\mu$ AND $W$, the probability of $x$ is $\\frac{1}{W}$\" (as long as we are within a certain range).\n",
    "\n",
    "Since we are used to thinking of a Gaussian as the *only* type of distribution the concept of $\\sigma$ (aside from the width) may seem strange.  But $\\sigma$ as mathematically defined above applies here and\n",
    "$$\\sigma = \\frac{W}{\\sqrt{12}}.$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 360x270 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 255,
       "width": 323
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Example of a uniform distribution\n",
    "---------------------------------\n",
    "Figure 3.7.\n",
    "This shows an example of a uniform distribution with various parameters.\n",
    "We'll generate the distribution using::\n",
    "    dist = scipy.stats.uniform(...)\n",
    "Where ... should be filled in with the desired distribution parameters\n",
    "Once we have defined the distribution parameters in this way, these\n",
    "distribution objects have many useful methods; for example:\n",
    "* ``dist.pmf(x)`` computes the Probability Mass Function at values ``x``\n",
    "  in the case of discrete distributions\n",
    "* ``dist.pdf(x)`` computes the Probability Density Function at values ``x``\n",
    "  in the case of continuous distributions\n",
    "* ``dist.rvs(N)`` computes ``N`` random variables distributed according\n",
    "  to the given distribution\n",
    "Many further options exist; refer to the documentation of ``scipy.stats``\n",
    "for more details.\n",
    "\"\"\"\n",
    "# Author: Jake VanderPlas\n",
    "# License: BSD\n",
    "#   The figure produced by this code is published in the textbook\n",
    "#   \"Statistics, Data Mining, and Machine Learning in Astronomy\" (2013)\n",
    "#   For more information, see http://astroML.github.com\n",
    "#   To report a bug or issue, use the following forum:\n",
    "#    https://groups.google.com/forum/#!forum/astroml-general\n",
    "import numpy as np\n",
    "from scipy.stats import uniform\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "#----------------------------------------------------------------------\n",
    "# This function adjusts matplotlib settings for a uniform feel in the textbook.\n",
    "# Note that with usetex=True, fonts are rendered with LaTeX.  This may\n",
    "# result in an error if LaTeX is not installed on your system.  In that case,\n",
    "# you can set usetex to False.\n",
    "from astroML.plotting import setup_text_plots\n",
    "setup_text_plots(fontsize=8, usetex=False)\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# Define the distribution parameters to be plotted\n",
    "W_values = [1.0, 2.0, 3.0]\n",
    "linestyles = ['-', '--', ':']\n",
    "mu = 0\n",
    "x = np.linspace(-2, 2, 1000)\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# plot the distributions\n",
    "fig, ax = plt.subplots(figsize=(5, 3.75))\n",
    "\n",
    "for W, ls in zip(W_values, linestyles):\n",
    "    left = mu - 0.5 * W\n",
    "    dist = uniform(left, W)\n",
    "\n",
    "    plt.plot(x, dist.pdf(x), ls=ls, c='black',\n",
    "             label=r'$\\mu=%i,\\ W=%i$' % (mu, W))\n",
    "\n",
    "plt.xlim(-1.7, 1.7)\n",
    "plt.ylim(0, 1.2)\n",
    "\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel(r'$p(x|\\mu, W)$')\n",
    "plt.title('Uniform Distribution')\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can implement [uniform](http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.uniform.html#scipy.stats.uniform) in `scipy` as follows.  We'll use the methods listed at the bottom of the link to complete the cell: `dist.rvs(size=N)` which produces `N` random draws from the distribution and `dist.pdf(x)` which returns the value of the pdf at a given $x$. Lots of distributions can be accessed and used in a similar way.  \n",
    "\n",
    "Create a uniform distribution with parameters `loc=0`,  `scale=2`, and `N=10`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.62743093 -0.77497083 -0.44882156  0.6540253  -0.30968905 -0.17303483\n",
      " -0.91342038  0.15771267 -0.91380946  0.77384094  0.42251021  0.09500933\n",
      " -0.19076893  0.50015788 -0.14797962  0.44721224  0.26788934 -0.30100345\n",
      " -0.57994172  0.19215652  0.66712003 -0.40284473 -0.62607067 -0.47689907\n",
      "  0.39724261  0.38996248  0.82418674 -0.39684601  0.76114854  0.82098706\n",
      "  0.84393584 -0.41891257 -0.28607914  0.60822561  0.1020066   0.30225541\n",
      "  0.01605566  0.67025014 -0.8222708   0.55390114  0.11222505  0.0536217\n",
      "  0.52794975  0.38200307 -0.05552105 -0.67928252 -0.04464336 -0.70671563\n",
      "  0.57274769  0.4271803   0.18830468  0.20892569 -0.89594625 -0.6627208\n",
      "  0.23668288  0.37209467  0.65850132  0.32149981  0.78261567  0.64426092\n",
      "  0.51654763 -0.16592865  0.2217014   0.45248064 -0.27337276  0.50318555\n",
      "  0.37970963  0.37755955 -0.59222468 -0.20870216 -0.60311805  0.80563035\n",
      "  0.32062497  0.49279932  0.71583027 -0.50946498 -0.33121164  0.26451476\n",
      "  0.27234951  0.83321459  0.45987791 -0.80574703 -0.37892242  0.0411438\n",
      "  0.44400517  0.03017955 -0.0919799   0.13559883  0.8351495   0.38074398\n",
      " -0.60319969  0.79176197  0.0161518   0.11137191 -0.82064568  0.78158791\n",
      "  0.30882452  0.25577334  0.01519837  0.17798686]\n",
      "0.5\n"
     ]
    }
   ],
   "source": [
    "N = 100 \n",
    "distU = scipy.stats.uniform(-1,2)\n",
    "draws = distU.rvs(N) # ten random draws\n",
    "print(draws)\n",
    "\n",
    "p = distU.pdf(1) # pdf evaluated at x=1\n",
    "\n",
    "print(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<scipy.stats._distn_infrastructure.rv_frozen at 0x129e795e0>"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "distU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p = distU.cdf(1) # pdf evaluated at x=1\n",
    "p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Gaussian Distribution\n",
    "\n",
    "As many of you know, the Gaussian distribution pdf is given by\n",
    "\n",
    "$$p(x|\\mu,\\sigma) = \\frac{1}{\\sigma\\sqrt{2\\pi}} \\exp\\left(\\frac{-(x-\\mu)^2}{2\\sigma^2}\\right)$$\n",
    "\n",
    "It is also called the **normal distribution** and can be noted by $\\mathscr{N}(\\mu,\\sigma)$.\n",
    "\n",
    "\n",
    "We love using Gaussians in physics and astronomy because they can approximate many distributions and are also super easy to work with. **The convolution of two Gaussians results in a Gaussian.**  So $\\mathscr{N}(\\mu_1,\\sigma_1)$ convolved with $\\mathscr{N}(\\mu_2,\\sigma_2)$ is $\\mathscr{N}(\\mu_1+\\mu_2,\\sqrt{\\sigma_1^2+\\sigma_2^2})$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 486,
       "width": 491
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Example of a Gaussian distribution\n",
    "----------------------------------\n",
    "Figure 3.8.\n",
    "This shows an example of a gaussian distribution with various parameters.\n",
    "We'll generate the distribution using::\n",
    "    dist = scipy.stats.norm(...)\n",
    "Where ... should be filled in with the desired distribution parameters\n",
    "Once we have defined the distribution parameters in this way, these\n",
    "distribution objects have many useful methods; for example:\n",
    "* ``dist.pmf(x)`` computes the Probability Mass Function at values ``x``\n",
    "  in the case of discrete distributions\n",
    "* ``dist.pdf(x)`` computes the Probability Density Function at values ``x``\n",
    "  in the case of continuous distributions\n",
    "* ``dist.rvs(N)`` computes ``N`` random variables distributed according\n",
    "  to the given distribution\n",
    "Many further options exist; refer to the documentation of ``scipy.stats``\n",
    "for more details.\n",
    "\"\"\"\n",
    "# Author: Jake VanderPlas\n",
    "# License: BSD\n",
    "#   The figure produced by this code is published in the textbook\n",
    "#   \"Statistics, Data Mining, and Machine Learning in Astronomy\" (2013)\n",
    "#   For more information, see http://astroML.github.com\n",
    "#   To report a bug or issue, use the following forum:\n",
    "#    https://groups.google.com/forum/#!forum/astroml-general\n",
    "import numpy as np\n",
    "from scipy.stats import norm\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "#----------------------------------------------------------------------\n",
    "# This function adjusts matplotlib settings for a uniform feel in the textbook.\n",
    "# Note that with usetex=True, fonts are rendered with LaTeX.  This may\n",
    "# result in an error if LaTeX is not installed on your system.  In that case,\n",
    "# you can set usetex to False.\n",
    "if \"setup_text_plots\" not in globals():\n",
    "    from astroML.plotting import setup_text_plots\n",
    "setup_text_plots(fontsize=8, usetex=False)\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# Define the distributions to be plotted\n",
    "sigma_values = [0.5, 1.0, 2.0]\n",
    "linestyles = ['-', '--', ':']\n",
    "mu = 0\n",
    "x = np.linspace(-10, 10, 1000)\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# plot the distributions\n",
    "fig, ax = plt.subplots(figsize=(8,8))\n",
    "\n",
    "for sigma, ls in zip(sigma_values, linestyles):\n",
    "    # create a gaussian / normal distribution\n",
    "    dist = norm(mu, sigma)\n",
    "\n",
    "    plt.plot(x, dist.pdf(x), ls=ls, c='black',\n",
    "             label=r'$\\mu=%i,\\ \\sigma=%.1f$' % (mu, sigma))\n",
    "\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(0, 0.85)\n",
    "\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel(r'$p(x|\\mu,\\sigma)$')\n",
    "plt.title('Gaussian Distribution')\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 85.84795286  78.84521657  75.66203738 121.2390915  101.22244527\n",
      "  84.00959311  92.04367463  75.08450687  77.22309903  83.9421681\n",
      " 105.22775271  98.53103284 125.24686419  94.96397662 121.56608776\n",
      "  99.43895484  91.08299891 120.88188662  99.85300766  96.68952438\n",
      "  97.25360914 113.78441317  91.11588746 104.08143759  85.20383919\n",
      "  86.32213006 103.14303064 102.05685028  98.00718206  99.8683527\n",
      " 103.0275131   81.40812812  97.15698709 103.59126536  82.65735631\n",
      "  94.40832197  95.67744566  92.92839688 115.22132294 117.13520192\n",
      "  95.08599825  95.45467764  84.27459713  79.88399554  96.73499041\n",
      "  84.73156437  91.29667334  83.1968917  105.10497862  97.33043488\n",
      "  96.02545466 111.44277864 123.6866315  111.25187861 138.02017203\n",
      "  98.66084209  78.95535537 120.42094333  91.38496303 120.51921905\n",
      "  77.15323768  66.42311638  86.63834343 106.71983532 124.84339278\n",
      " 102.22714245  97.51561544  94.9104052  119.16169208  84.95572071\n",
      "  92.84520909  83.65777667  86.69551365 125.10840842  96.61112289\n",
      "  90.95078586 106.38420964  83.38747534 122.3031441   76.55133725\n",
      "  93.577622    86.64440138 116.73169333 102.22089964 110.80397243\n",
      "  95.11214501  63.22286411  89.39848725 103.86406713 110.69326948\n",
      "  99.85508541  87.47314643  92.36212428 102.9953166   83.8526576\n",
      " 109.42243653  66.39711038  99.67152337 108.19707291  94.616555\n",
      "  80.74819148 115.70798596 107.75115954 118.67708629 114.93066027\n",
      "  86.29928069  90.79177907 127.48324272 103.03789757 124.20735548\n",
      "  71.56182115  84.60711989 101.41759203 118.52661953 115.29752983\n",
      "  85.5402893   69.36788372 103.45260369  91.40083258 113.80150105\n",
      "  89.02562267  95.07535091 101.65713062 108.00560371 125.20251927\n",
      " 129.1864759  103.21835783 116.44048714  80.27961522 121.35649096\n",
      " 122.3664698   92.58922037 111.69313352 101.03471057 105.41169174\n",
      "  87.58786271  99.56958179  95.95463834  90.54758058 100.98832057\n",
      " 105.57993387 110.34207721  98.07649326  86.88111279  90.76940821\n",
      "  74.30320025 123.97645716  93.7165621   75.56421721 115.59716027\n",
      "  75.39481002 128.4349494   98.31958198  73.12816677  97.09508732\n",
      " 111.47148589 105.98776836 105.23291076  86.75134861 101.59772743\n",
      " 100.12816355  95.04378065 107.24543254 125.03667367  71.53764071\n",
      " 116.81495764 109.05191978  94.04891093  83.79132429 105.26872733\n",
      " 108.08636361  88.94586776  82.52640397  90.30236869 101.47266103\n",
      "  99.70052559  85.24738123 107.08086168 106.93137068 132.91107027\n",
      "  79.13112689  95.2545835  106.34253482  77.97547516  77.18121128\n",
      " 100.76131992  92.00725285  73.35709906  90.58632944  89.28713759\n",
      "  81.70514201 103.77317385  88.0310737   84.29866404 102.84078798\n",
      "  96.09487349  85.95973109  99.39071467 107.07991955  85.52072552\n",
      "  94.96145983 113.63533155 105.34649578 102.79960861 105.21345033\n",
      " 114.26927217 114.12902682 102.61348814 116.93327241  83.8151355\n",
      "  96.57612301  99.91804842 117.47228677  93.38140531  87.50593077\n",
      "  78.11269867  87.71824721  69.64759274  80.21386818  99.26028376\n",
      "  96.24114117 113.59594973  83.06025245  61.30417182  92.37124743\n",
      " 107.35827113  78.81057325  96.31133021 102.34229029  89.84248254\n",
      "  99.52993388  96.75043775 107.72186649 100.01091976  62.10158934\n",
      "  99.57664976  87.5988407   93.47159015  95.11675839  93.96544907\n",
      "  95.33840812  82.6352557   84.75914073  89.55633044 132.13219035\n",
      "  92.71116943 100.48853721  88.9247084  150.35846506  65.83922789\n",
      " 109.52747842 109.58580469 104.30212418 126.9320614  120.06511848\n",
      "  92.30373656  80.6454575   98.91888229 103.14677988 102.5600753\n",
      "  95.60824886  92.80464635  98.78061072  92.7223235   98.22085628\n",
      " 114.85126178 105.94173652  96.05125155 106.59056922 107.10471572\n",
      "  97.26368757  79.21067988  83.16226451 109.91979434  88.62538016\n",
      " 100.35288991  89.71402738  94.54212532  84.7858267  114.46929174\n",
      "  93.00439194 124.10055199 100.12135804  95.54431516 133.06980572\n",
      " 105.38871683  89.176184   116.26618475 104.88616005 101.85126437\n",
      " 110.54585508 102.51081357 105.14811262 105.09762569 113.06541087\n",
      " 114.59853051  94.43917022  74.68221354 114.41523118 116.20993205\n",
      "  96.95468275  95.96553336  96.21803976  86.29869801 100.27139421\n",
      " 118.98383485 117.491219   120.60453563  95.32801365  87.86430437\n",
      " 104.58289957 110.38642883  97.47014443  98.48273725 109.13237819\n",
      " 103.93851042 130.26565724 106.29098294 143.11113997 106.59681661\n",
      "  82.45738246 115.5481442  113.45645791 116.57461398 105.33258944\n",
      " 102.2682889  113.98090457 103.12043797  92.11278534  91.49648985\n",
      " 114.7887542   90.74484007  99.68587635 102.13320791 109.58176816\n",
      " 104.87658375  77.83354236 100.42704939  76.46042997 118.90533566\n",
      " 136.85713391  97.49597139 100.33852515 116.91657477  85.79071299\n",
      "  79.82490663 105.35917448 107.67350007  91.87922602 101.36588986\n",
      " 124.6431774  119.05084226  85.62516883 109.84978266  82.65819751\n",
      " 111.47022387  68.01448973 124.37273468  86.57503692  96.82187695\n",
      " 107.50368381 113.97545274  93.30435694 104.92153496  99.0835766\n",
      "  94.66950792 125.42647615 104.65841077 111.48486052 110.4321913\n",
      "  94.6406312  112.93006817  97.15124711  92.99931578 107.02401682\n",
      "  95.87050581  94.69804752  95.72088187  86.08825298  99.29785176\n",
      " 109.91908666 105.77176917  81.55357639  84.14653131 118.58773234\n",
      " 120.59519635 100.90473459 124.2394864   67.7503407   64.77110039\n",
      "  89.94211339 101.66324391 117.18332035  90.3606742   92.14132932\n",
      " 106.5685292   94.64370457  89.84125117 104.86488947  89.11418437\n",
      " 100.08042926 103.61629722  97.08651023  99.32478579 105.57878835\n",
      "  80.51613908  82.44635928 111.03228454  86.44341293  81.86110653\n",
      " 120.7217039  112.17492892 117.64418053  83.22971323 128.79243383\n",
      " 100.80076714 112.21360596  97.95829178 101.1533457  100.95371916\n",
      " 110.11192529 104.28272747 118.36980273 113.53538859  87.55657198\n",
      "  94.14565937  79.65428227 116.11984364  94.41354285 101.81091376\n",
      " 102.24686324 125.23407726 102.78245101 106.97047183  96.5154839\n",
      "  77.29024632  85.15361879 103.73849719  76.36331791  99.2941427\n",
      " 101.37807096 107.204474    85.66646671  96.25076232  70.12353757\n",
      "  91.23653501 118.76836005  82.90178272  81.53851681  90.21209818\n",
      " 115.37635724 135.47592993  78.69341982 125.42350082 101.52502647\n",
      " 102.84854091  94.21156154  63.6640953  103.87020734 113.28355619\n",
      "  94.03319792  90.99334298  63.94618056  80.45547914  92.36241248\n",
      " 119.00711589 123.9371545  111.06490035  93.36975491  61.57288051\n",
      "  94.03749116 117.6757971   87.67744896 104.064085   129.33614671\n",
      " 104.80392161 115.31145338 105.90992333  90.7201637  110.68176011\n",
      " 118.74541921 104.48868217  89.40024115 107.64295062  88.03076366\n",
      " 103.19534579  88.06267063 113.16907598  97.62951051 103.67828604\n",
      "  86.37273863  99.59680296 110.01336917  72.84699504  88.89669309\n",
      "  99.46594037 126.49737186  80.68531075  99.08505455 104.28234148\n",
      " 111.76761722 112.0162159  111.14510498  60.18642301  89.47879371\n",
      "  95.18451149  82.45093391 108.36696158  98.29702964 110.89737892\n",
      "  87.8932321  100.18514412  78.78307128  83.21876077  92.41336013\n",
      "  85.4052052  115.40143869  92.02007381 102.29727018  94.55156396\n",
      " 121.99915087 102.76622552  86.83954667  81.70066595 112.79221226\n",
      "  73.86742307 100.34695488  89.1522762  115.3426371  102.95647926\n",
      " 103.37207553  80.82984035  85.43677136  97.61276416  91.3612469\n",
      " 111.57653802  99.4003891  102.97311197  87.23677926  95.14991341\n",
      " 106.05538588  92.6884677  105.41794822  94.55438023 109.42723659\n",
      " 100.99933938  97.27676666  91.80954628  63.20189275 127.65128529\n",
      " 114.16759151  71.76536286 117.28642213  76.16515485  89.68920884\n",
      " 112.98503891 105.03120681  71.62187419 122.44634247  86.75025975\n",
      " 104.08077366 100.91643831 100.93337988  85.20563575 118.19736386\n",
      " 102.46069568  93.2066606   94.80041874  84.80115328  97.13602592\n",
      " 106.20740621  95.25823162  98.89390215  91.60544573 101.59158298\n",
      " 101.7732756  109.12012648  91.3272384  121.85640913 103.35723876\n",
      "  95.60222141 114.2823675   97.90933174 127.49932508  81.71633511\n",
      "  91.04028351  89.64106045  83.47861298  82.40132958 111.80032337\n",
      "  92.21933752 123.93268697 114.48038769  77.72492969  93.88265608\n",
      " 101.47738539 110.03666393  73.26703573 126.32752368 112.23125746\n",
      "  94.57972757 134.29904901 104.79190719 108.34453866  91.77975122\n",
      "  82.78469785  74.68902128 122.30192491 115.39559971  84.6900309\n",
      "  85.66112127 111.54905385 131.75031362 110.41098296 103.21280375\n",
      " 102.88088228  92.005692   115.02269118 116.19135597  92.2866899\n",
      "  96.29149471  94.98021757 109.07212689  84.88177699  82.5878401\n",
      "  65.24781092  98.05216335 102.52713725  87.77659107 121.28369783\n",
      "  96.56441688 101.42465698 108.46331631 105.07800529 130.07576142\n",
      "  71.13379453  73.08184039 100.19827226 117.71838337  91.86143715\n",
      "  91.26212304  74.75053535  93.82405274 134.29104694 112.22917025\n",
      " 100.87117367 101.62230533  73.89839985 126.32787003  93.32463805\n",
      " 130.96896992 114.25016906 108.99255384 112.92120941 114.22529114\n",
      " 117.60485413  87.0201896  127.63061956 108.47263624 103.41619179\n",
      " 118.83120065 115.11476074  92.72754612  93.10069747  92.93870221\n",
      " 108.22723907  86.9719855   78.38523371 124.45937114 121.70004157\n",
      " 111.99723903 104.19172171  81.68294702  92.4774457  130.2334967\n",
      "  98.02564549  85.53807404  90.90402851  98.49304232 110.88288779\n",
      " 108.24741706  88.75629384 106.02306696  72.32480654  68.45791919\n",
      " 105.55149272  89.65013696  98.72431804  91.69616908 108.93084437\n",
      "  69.82166257 121.60575216  97.23675848 102.4568236   96.68117008\n",
      " 101.03881434  66.77797491 126.42167251  90.27777604  99.90062054\n",
      " 110.66696693  83.52182648  80.4101952  103.157615    94.92287246\n",
      "  78.2492533   97.63281522  96.88715391  86.98870566 124.09042747\n",
      "  85.29316252  93.69017656 131.95638913 104.78908124 116.42483553\n",
      "  98.87152305  75.70262493  70.59939584 109.1762988   85.96655649\n",
      "  70.62042405  59.59140591 110.31738826  88.04454443  94.71794664\n",
      "  94.50193722  82.63986009 129.38265616 109.06373247 119.33106049\n",
      " 105.89162312 107.58919601 103.38975554 101.63672148 108.32627656\n",
      "  91.96004377 123.00088835 107.8898966   61.8793622   88.29307454\n",
      "  95.0699138   88.5005671   99.19383408  95.34337685  91.39626701\n",
      "  83.02867215 117.52001386 119.83356254 107.95774353  97.21464946\n",
      " 101.67766241 113.72222231 100.14207765 106.85547933  88.6101782\n",
      "  97.87860504 103.84133918  99.11492571 106.55884276  99.56171143\n",
      " 131.21952295 101.49488545 105.31139303 110.72288056  85.56087737\n",
      " 114.31699012  81.37095615  82.94888479 119.51110696 105.34920545\n",
      "  84.60136849 132.14404375 117.26589195 102.29731981 120.72499707\n",
      "  89.01609661 121.26856516 117.25457185  97.80535379  85.35669171\n",
      " 105.29627185 105.93353768  95.36544124 101.74630658  79.45843485\n",
      " 117.44101233 108.69671065 111.03167083 106.20847726  94.40086237\n",
      " 119.72389906 114.26164345 115.06421798  92.39069078 100.27710792\n",
      " 102.75020976  85.40449969 137.57481269  97.8733926   89.5715783\n",
      "  91.82066811 103.70069106 108.30356042  95.00163743 147.13800232\n",
      "  96.31715638 109.15211349  87.84471475 100.13039353  76.09950659\n",
      "  86.61081415 105.27771052 111.03160416  85.3449294  115.66309446\n",
      "  80.68720837 120.62087572 118.34872606  81.70176773  97.35351444\n",
      "  77.50287114 134.08794793 103.43343742  70.12662935 120.21256272\n",
      " 130.7149704   90.2720764   99.69269576 100.14804908 106.15092562\n",
      "  91.54812684  91.10498854 112.70777605 106.51249077  79.37211335\n",
      "  91.30556639 102.45947517 106.43991692  94.93882989 116.25696073\n",
      "  97.02270252 117.79679894 128.89862271  94.73764007 126.59377104\n",
      " 118.20555593  93.48269824 100.87449184 101.86569323 105.31896785\n",
      " 105.59564146 113.29667261  96.37403125  86.91874228 116.70146788\n",
      "  88.81056381 113.46233405 102.92758434 111.75647917  74.80729438\n",
      " 105.71598841 114.49632827 100.91789755 107.29010238 109.09326249\n",
      "  72.02364133 122.98451946  86.18464202  86.24671566  93.97314932\n",
      "  93.47964418 102.2215998  117.11068055 108.80416706  78.69838152\n",
      "  78.99555386  98.94639209  93.95347377 118.36856009  91.50671568\n",
      "  92.67689802 100.03818911 129.69734618 107.1480059  119.65958162\n",
      "  98.51823291  92.9726269   91.2479857  116.62217039  93.4263258\n",
      " 114.3573213  123.44934273  82.08160008  84.44016654  89.78743732\n",
      "  92.93184827  76.46981737  97.21384041 111.48948095  97.47676379\n",
      "  91.96131804  98.80597509 100.28236528 120.24811166 107.22389618\n",
      " 106.17770807 117.77384253 116.13606814 116.08945005 122.81285756\n",
      " 110.97992194 139.87829656 109.6833915  108.79034884  84.64765296\n",
      "  81.7936981  100.54932535 138.25620266 102.43111889 141.43386446\n",
      " 108.31409326 100.2230075   84.54930395  88.17712427 102.75661139\n",
      "  82.22094182 117.86566688  92.44218335 110.71629692 110.57653761\n",
      " 107.37871505 116.41544895 110.95144792  96.73256673  88.46157047\n",
      "  88.68038335 128.87271772  89.60546929  99.09596088 122.62012278\n",
      " 112.9766506   85.8338392  112.63303129  98.24790972  87.89129484\n",
      "  89.35634484 107.72091053  91.84610544 102.33938987  98.43712397\n",
      " 133.14664574  99.31572716 103.5553087   96.49264028  96.16033755\n",
      "  91.11186262  99.28134431 118.54102223  83.17798201  90.23710969\n",
      "  92.32054874  97.70959043 107.19567962 110.04793699 105.46819148\n",
      "  88.61142463  89.05570142  84.09995941 123.54752302 108.85194004\n",
      "  94.64761962  72.62025935 102.66399409  98.26347193  91.3563414\n",
      "  89.79264662  88.72834293 108.90505025  72.36147754  71.3456217\n",
      " 113.9753392   86.91781845 109.62293184  85.285537   100.39930683\n",
      " 108.79435512  98.41647107 100.14277324 120.77556555  96.48417248\n",
      " 113.36501915  82.48463707  60.93620891  90.38112555 111.17495111\n",
      " 112.13525611  93.52417468 102.23098936  92.96132229 105.88802255]\n",
      "5.940600124901435e-12\n"
     ]
    }
   ],
   "source": [
    "distG = scipy.stats.norm(loc =100 , scale=15) # Normal distribution with mean = 100, stdev = 15\n",
    "draws = distG.rvs(1000) # 10 random draws\n",
    "p = distG.pdf(0) # pdf evaluated at x=0\n",
    "\n",
    "print(draws)\n",
    "print(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 20.,  46., 126., 208., 239., 180., 116.,  49.,  12.,   4.]),\n",
       " array([ 59.59140591,  68.66811183,  77.74481774,  86.82152366,\n",
       "         95.89822957, 104.97493549, 114.0516414 , 123.12834732,\n",
       "        132.20505323, 141.28175915, 150.35846506]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 461,
       "width": 479
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(draws)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cumulative distribution function, cdf is the integral of pdf from $x'=-\\infty$ to $x'=x$:\n",
    "\n",
    "$$\\mathrm{cdf}(x|\\mu,\\sigma) = \\int_{-\\infty}^{x'} p(x'|\\mu,\\sigma) dx',$$\n",
    "\n",
    "where $\\mathrm{cdf}(\\infty) = 1$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 486,
       "width": 508
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## Let's play with Gaussians! Or Normal distributions, N(mu,sigma)\n",
    "\n",
    "xgrid = np.linspace(-100,200,1000) # generate distribution for a uniform grid of x values\n",
    "gaussPDF = distG.pdf(xgrid)  # this is a function of xgrid\n",
    "\n",
    "# actual plotting\n",
    "fig, ax = plt.subplots(figsize=(8,8))\n",
    "\n",
    "# Python3 f strings are awesome!\n",
    "plt.plot(xgrid, gaussPDF, ls='-', c='black', \n",
    "         label=f'$\\mu={mu},\\ \\sigma={sigma}$')\n",
    "plt.xlim(0, 200)\n",
    "plt.ylim(0, 0.03)\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel(r'$p(x|\\mu,\\sigma)$')\n",
    "plt.title('Gaussian Distribution')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1295ef670>"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 486,
       "width": 498
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# The same as above but now with the cdf method\n",
    "gaussCDF = distG.cdf(xgrid)\n",
    "fig, ax = plt.subplots(figsize=(8,8))\n",
    "plt.plot(xgrid, gaussCDF, ls='-', c='black', \n",
    "         label=r'$\\mu=%i,\\ \\sigma=%i$' % (mu, sigma))\n",
    "plt.xlim(0, 200)\n",
    "plt.ylim(-0.01, 1.01)\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel(r'$CDF(x|\\mu,\\sigma)$')\n",
    "plt.title('Gaussian Distribution')\n",
    "plt.legend(loc=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Gaussian confidence levels\n",
    "\n",
    "The probability of a measurement drawn from a Gaussian distribution that is between $\\mu-a$ and $\\mu+b$ is\n",
    "\n",
    "$$\\int_{\\mu-a}^{\\mu+b} p(x|\\mu,\\sigma) dx.$$\n",
    "\n",
    "- For $a=b=1\\sigma$, we get the familar result of 68.3%.  \n",
    "- For $a=b=2\\sigma$ it is 95.4%.  \n",
    "- For $a=b=3\\sigma$ it is 99.7%. \n",
    "\n",
    "So we refer to the range $\\mu \\pm 1\\sigma$, $\\mu \\pm 2\\sigma$, and $\\mu \\pm 3\\sigma$ as the 68%, 95%, and 99.7% **confidence limits**, respectively. Note that if your distribution is not Gaussian, then these confidence intervals will be different!\n",
    "\n",
    "***We often still refer to uncertainty regions of distributions as $1\\sigma$ or $2\\sigma$ regions, which for non-Gaussian distributions usually means (for $1\\sigma$) the region enclosing the $16\\%$ and $84\\%$ quantiles.***"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6826894921370859\n"
     ]
    }
   ],
   "source": [
    "upper = distG.cdf(100+15)\n",
    "lower = distG.cdf(100-15)\n",
    "p = upper-lower\n",
    "print(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is the probability enclosed between $-2\\sigma$ and $+4\\sigma$? (*Verify first that you get the correct answer for the bullet points above!*)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9772181968099877\n"
     ]
    }
   ],
   "source": [
    "upper = distG.cdf(100+4*15)\n",
    "lower = distG.cdf(100-2*15)\n",
    "p = upper-lower\n",
    "print(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Log Normal\n",
    "\n",
    "Note that if $x$ is Gaussian distributed with $\\mathscr{N}(\\mu,\\sigma)$, then $y=\\exp(x)$ will have a **log-normal** distribution, where the mean of y is $\\exp(\\mu + \\sigma^2/2)$, the median is $\\exp(\\mu)$, and the mode is $\\exp(\\mu-\\sigma^2)$.  Try it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.7003363919203258\n",
      "<scipy.stats._distn_infrastructure.rv_frozen object at 0x1293d4b50>\n"
     ]
    }
   ],
   "source": [
    "# Execute this cell\n",
    "x = scipy.stats.norm(0,1) # mean = 0, stdev = 1\n",
    "y = np.exp(x.rvs(100))\n",
    "\n",
    "print(y.mean())\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The catch here is that stats.norm(0,1) returns an *object* and not something that we can just do math on in the expected manner.  What *can* you do with it?  Try ```dir(x)``` to get a list of all the methods and properties."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['__class__',\n",
       " '__delattr__',\n",
       " '__dict__',\n",
       " '__dir__',\n",
       " '__doc__',\n",
       " '__eq__',\n",
       " '__format__',\n",
       " '__ge__',\n",
       " '__getattribute__',\n",
       " '__gt__',\n",
       " '__hash__',\n",
       " '__init__',\n",
       " '__init_subclass__',\n",
       " '__le__',\n",
       " '__lt__',\n",
       " '__module__',\n",
       " '__ne__',\n",
       " '__new__',\n",
       " '__reduce__',\n",
       " '__reduce_ex__',\n",
       " '__repr__',\n",
       " '__setattr__',\n",
       " '__sizeof__',\n",
       " '__str__',\n",
       " '__subclasshook__',\n",
       " '__weakref__',\n",
       " 'a',\n",
       " 'args',\n",
       " 'b',\n",
       " 'cdf',\n",
       " 'dist',\n",
       " 'entropy',\n",
       " 'expect',\n",
       " 'interval',\n",
       " 'isf',\n",
       " 'kwds',\n",
       " 'logcdf',\n",
       " 'logpdf',\n",
       " 'logpmf',\n",
       " 'logsf',\n",
       " 'mean',\n",
       " 'median',\n",
       " 'moment',\n",
       " 'pdf',\n",
       " 'pmf',\n",
       " 'ppf',\n",
       " 'random_state',\n",
       " 'rvs',\n",
       " 'sf',\n",
       " 'stats',\n",
       " 'std',\n",
       " 'support',\n",
       " 'var']"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "? scipy.stats.norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.6487212707001282 1.6064085166771476\n"
     ]
    }
   ],
   "source": [
    "distLN = scipy.stats.norm(0,1) # mean = 0, stdev = 1\n",
    "x = distLN.rvs(10000)\n",
    "y = np.exp(x)\n",
    "\n",
    "print(np.exp(0 + 0.5*1), y.mean())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### $\\chi^2$ Distribution\n",
    "\n",
    "We'll run into the $\\chi^2$ distribution when we talk about Maximum Likelihood in the next lecture.\n",
    "\n",
    "If we have a Gaussian distribution with values ${x_i}$ and we scale and normalize them according to\n",
    "$$z_i = \\frac{x_i-\\mu}{\\sigma},$$\n",
    "then the sum of squares, $Q$ \n",
    "$$Q = \\sum_{i=1}^N z_i^2,$$\n",
    "will follow the $\\chi^2$ distribution.  The *number of degrees of freedom*, $k$ is given by the number of data points, $N$ (minus any constraints).  The pdf of $Q$ given $k$ defines $\\chi^2$ and is given by\n",
    "$$p(Q|k)\\equiv \\chi^2(Q|k) = \\frac{1}{2^{k/2}\\Gamma(k/2)}Q^{k/2-1}\\exp(-Q/2),$$\n",
    "where $Q>0$ and the $\\Gamma$ function would just be the usual factorial function if we were dealing with integers, but here we have half integers.\n",
    "\n",
    "This is ugly, but it is really just a formula like anything else.  Note that the shape of the distribution *only* depends on the sample size $N=k$ and not on $\\mu$ or $\\sigma$.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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Uq1atynwnMTGx1CPLqmLKlCmS5DwS+tNPP1XDhg3VsGHDMruuhxoKeDXl5eVpxYoV6t69uyfFnBlwAAAAAF44UoCPFPDo6GhNnjxZffv21dChQzVv3jzVq1fP7+OOHDmy1PnNN98sKTyWrVPAq+BI0R48eLDmzJmj/Px8rVu3TieccELQszADDgAAAMALl19+uS6//PJSryUkJGjp0qUBHTecl/3zHHAXkpOTNXfuXLVs2VJSyX/4/Px8Sd49D5wZcAAAAAAIDxRwF+Li4nTmmWeqTp06klRqYwGvngfODDgAAAAAhAcKeDX4FnBmwAEAAAAAx0MBr4YzzjjDOc7IyFBRUVHQMzADDgAAAADhgQJeDS1atFCzZs0kSdnZ2frhhx+CnsG3gDMDDgAAAAChiwLuwvbt2xUfH6/Vq1c7r/Xs2dM5XrhwYdAz+S5BZwYcAAAAAEIXBdylI7ueH+F1AWcGHAAAAADCAwW8Co48B1zyvoDXqVNHMTElj3PPzc1Vbm5u0DMAAAAAACpGAa+mHj16KCqq5F/j999/r+zs7KCOb4xhIzYAAAAACAMU8CrwnQFPSEhQly5dlJKSonPPPVe7d+8Oeh7uAwcAAACA0BfjdYBIMHPmTDVo0KBUMQ8m7gMHAAAAgNBHAa+Co4t2amqqR0lKMAMOAAAAAKGPJegRgBlwAAAAAF5ZuXKljDH6/PPPAz7WlClTdMkll+iEE05Q7dq11bFjR9133306cOBAwMf2Bwp4FXi11PxYmAEHAAAA4JWMjAxJJRtUB9pf//pXRUdH6y9/+YtmzJihm266Sf/61780ePBgFRcXB3z86mIJup+sWbNG6enpWrhwoS677DKdc845QRubGXAAAAAAXsnIyFCbNm2UkpIS8LGmT5+uhg0bOudnnXWWUlJSdM0112j27NlB7WFVwQx4FZQ3Az5x4kRdd911mjhxombMmBHUPMyAAwAAAPBKZmZmqdnvrKwsXXrppWrSpInS09P9OpZv+T7i9NNPlyRt3rzZr2MFAgXchdTUVK1Zs0bNmjUr817Pnj2d44ULFwYzFjPgAAAAADxhrdWSJUucAr58+XL16NFDmzdvVkZGhs4666wyny8sLKzwp6ioqNIZjpT8k046yX+/WIBQwF2Ijo5WmzZtFBNTduW+bwFfvHixCgsLg5aLAg4AAADACz///LMOHDigHj16aNKkSerVq5cGDRqk9PR0NW/evMzn09PTFRsbW+HPwIEDKzX+5s2b9dBDD2nQoEFBuQe9uijgftK8eXPnD9ihQ4f0/fffB21s33st9uzZE7RxAQAAAEjjxo2TMaZSPzfccEOZ799www2V/v64cePKfH/48OGV/v6LL75Y5vvTp0+v8u+emZkpqeSW3BtvvFH/+te/NGHCBMXFxZX7+bS0NC1atKjCn4kTJ1Y4dnZ2ti644ALFxMTolVdeqfLvEExswuZHPXv21LRp0ySVLEPv2rVrUMb1LeDMgAMAAAAIloyMDCUlJWnq1Km69dZbNXr06ON+PiEhQd26davwuhU9eSonJ0fDhw93NsNu0aKFm9ieYQbcheLiYu3Zs+eY29t7dR+47xJ0ZsABAAAABEtGRoaGDBmi8ePHa/z48c6E5LH4Ywl6QUGBLr30Ui1evFiffPKJTjnlFH//WgFjrLVeZwgLxpgMSd0ladOmTce8n2HAgAGSpC5dumjFihVByZaVlaX69etLkurWravs7OygjAsAAADUBCtXrpQUHpt8BZO1VsnJybr33nt177336vbbb9fLL7+s2bNnOzuTH+3AgQP66aefKrx2YmKiOnbsWOb14uJiXXHFFZo+fbo++uijSt8rLlX83zEtLU2ZmZmZ1tq0Sl/UJZag+1FaWpqioqJUXFysH374QVlZWapXr17Ax01MTFR0dLSKiop08OBB5efnH/OeCwAAAADwh9WrV2v//v3OkvJnnnlGq1ev1ogRI7Rw4UK1atWqzHcSExOrtVnaLbfcovfee08PPPCA6tatq2+++cZ5r0WLFiG/FJ0l6FVwrPsREhISnOUP1lotXrw4aHnYCR0AAABAMGVkZEiSU8Cjo6M1efJkNW7cWEOHDlVWVpbfx/z0008lSY899ph69+5d6ufll1/2+3j+RgH3M6/uA2cndAAAAADBdPnll8taqyZNmjivJSQkaOnSpVq+fHlAVgOvW7dO1tpyf8rbIT7UsAS9Co63I98FF1ygxMRE9ezZU3379g1aJmbAAQAAACC0UcCr4HgF/Pzzz9f5558fxDQlmAEHAAAAgNDGEvQIQQEHAAAAgNBGAa+Cih4K7wWWoAMAAABAaKOAV0FlC3hBQYG2bNkS4DQlmAEHAAAAgNBGAQ+AlStXqn///qpfv75GjhwZlDGZAQcAAACA0MYmbFVQ0Qx4gwYN9PXXX0sqeTZefn6+4uLiApqJGXAAAAAACG3MgLvQqFEj5ebmKjU1tcLPtWvXTpKUl5enpUuXBjwbBRwAAAAAQhsF3AVjjOLj4yt1D3jv3r2d4wULFgQyliSWoAMAAABAqKOAB0ivXr2c42AUcGbAAQAAACC0UcADJNgz4BRwAAAAAAhtFHAXCgsLtWLFChUWFlb42VNPPVW1a9eWJG3YsCHgjyM7egm6tTag4wEAAAAA3KGAu7B7926dcsopysrKqvCzMTExOv30053zb775JpDRFBcXp7p160qSioqKdODAgYCOBwAAAABSyWOYjTH6/PPPAz7W7NmzZYwp85OUlBTwsf2Bx5AFUO/evTVnzhxJJcvQL7744oCOl5ycrIMHD0oqWYZer169gI4HAAAAABkZGZKkHj16BG3M8ePHl5rwjIkJj2obHilDTGV2QZe8uQ9806ZNkkqWobdu3TrgYwIAAACo2TIyMtSmTZtS+1IF2kknnVRq4+twwRL0ADryB6JevXpq0KBBwO/LZiM2AAAAAMGWmZlZavY7KytLl156qZo0aaL09HQPk4UeCngVVHYGvHHjxvrhhx+0Z88effDBB5X+XlXxLHAAAAAAwWSt1ZIlS5wCvnz5cvXo0UObN29WRkaGzjrrrDKfLywsrPCnqKjouONeddVVio6OVoMGDXTllVdqw4YNAfsd/YkCHmAnnXSSoqOjgzIWM+AAAAAAgunnn3/WgQMH1KNHD02aNEm9evXSoEGDlJ6erubNm5f5fHp6umJjYyv8GThwYLnj1a9fX3fffbdefvllzZw5U3/84x/15Zdfqnfv3tqxY0egf91qo4BXQaBnsquKAg4AAAAE37hx45zduMeNG1fm/bvvvtt5/29/+1uZ92+44Qbn/RdffLHM+1deeaXz/ltvvVXm/eHDhzvvT58+vcz7AwYMcN6fPXt2mffL+05lZWZmSpImTpyoG2+8Uf/61780YcIExcXFlfv5tLQ0LVq0qMKfiRMnlvv90047TX/96181fPhwnXXWWbrjjjs0Y8YMbd++XePHj6/y7xEsbMIWQXwL+O7duz1MAgAAAKAmyMjIUFJSkqZOnapbb71Vo0ePPu7nExIS1K1btwqv62bSs3v37urQoYMWLVpU6e94hRnwKnA7A75mzRq98cYbuuWWW7R9+/YApZIaNGjgHFPAAQAAAARaRkaGhgwZovHjx2v8+PGaNm3acT9f3SXoxxOqK5V9mUDvzB0pjDEZkrpL0v79+109Y7t///76+uuvJUnTpk3TRRddFJCM77//vvOs8REjRuiDDz4IyDgAAABATbJy5UpJJfs74X+stUpOTta9996re++9V7fffrtefvllzZ49u9Qzun0dOHBAP/30U4XXTkxMVMeOHSuVY/HixerZs6ceeOABPfroo8f8XEX/HdPS0pSZmZlprU2r1MBVwBJ0F4wxSkpKcv03K71793YK+IIFCwJWwH1nwHft2hWQMQAAAABAklavXq39+/c7S8qfeeYZrV69WiNGjNDChQvVqlWrMt9JTEws9cgyt6666iq1adNG3bt3V1JSkpYsWaLHH39czZs312233Vbl6wYLS9BdaNSokfbs2aPExERX3+vdu7dzvGDBAn/HcrAEHQAAAECwZGRkSJJTwKOjozV58mQ1btxYQ4cOVVZWlt/HPPnkk/Xhhx9qzJgxGjJkiJ599lldfPHFWrhwoVJTU/0+nr+xBL2SjDEZjRs37r5t2zbX3922bZuaNm0qSapVq5aysrIUGxvr74javn27mjRpIqmkjDMLDgAAAFQfS9AjQygsQWcGPAiaNGmi1q1bS5Jyc3P13XffBWQc313Q9+7dq+Li4oCMAwAAAABwjwIeJMFYhh4bG+tsDldcXKx9+/YFZBwAAAAAgHsUcBfy8/P1+eefq6ioyPV3g3UfuO99DyxBBwAAAIDQQQF3Ye/evRoyZIjy8/Ndf7dXr17OMRuxAQAAAEDNQwEPkq5du6pWrVqSpHXr1mnr1q0BGcd3BpwCDgAAAAChgwJeBW6fAy5JcXFxpR5GH6hZcJ4FDgAAAAChKcbrADXJFVdcoa5du+rMM89Uv379AjIGS9ABAAAAIDRRwKugKjPgknTzzTf7OUlZbMIGAAAAAKGJJegRhhlwAAAAAAhNFPAqqOoMeDBQwAEAAAAgNFHAPVJYWBiQJeIsQQcAAACA0EQBr4LqzIBnZmZq0KBBSk5O1m9+8xs/pirBDDgAAAAAhCYKeBVUp4DXrl1bX331lbKzszV//nxZa/2YjAIOAAAAILhWrlwpY4w+//zzgI81YMAAGWPK/fnVr34V8PGri13QXYiOjlanTp2qdY2OHTsqJSVFe/bs0a5du7Rq1Sp16NDBTwnLPgfcWhvS96wDAAAACG8ZGRmSpB49egR8rAkTJigrK6vUawsWLNBdd92lESNGBHz86qKAu5CamqoVK1ZU6xpRUVHq06ePPvroI0nSvHnz/FrAa9eurTp16ujQoUMqLCzUgQMHVK9ePb9dHwAAAAB8ZWRkqE2bNkpJSQn4WJ07dy7z2ksvvaS4uDhdccUVAR+/uliC7oK/ZpL79OnjHM+fP98v1/TFRmwAAAAAgiUzM7PU7HdWVpYuvfRSNWnSROnp6QEd+9ChQ3rvvfc0fPjwoPwFQHVRwD1w5plnOsfz5s3z+/W5DxwAAABAMFhrtWTJEqeAL1++XD169NDmzZuVkZGhs846q8znCwsLK/wpKiqq1Pjvv/++Dhw4oGuuucbvv1sgUMA90KNHD8XElKz+X7lypfbs2ePX61PAAQAAAATDzz//rAMHDqhHjx6aNGmSevXqpUGDBik9PV3Nmzcv8/n09HTFxsZW+DNw4MBKjT9p0iQ1atRI5513nr9/tYCggLtw6NAhvfbaa9XeubxOnTrq3r27c75gwYLqRiuFJegAAABA8IwbN+6YO3O7/Rk+fPhxrz9u3Lgy7w8fPrxaY5Z3zcrKzMyUJE2cOFE33nij/vWvf2nChAmKi4sr9/NpaWlatGhRhT8TJ06scOwtW7boyy+/1FVXXeVMcIa68EgZIrKysnTttdf6ZXnDmWeeqW+//VZSyX3gQ4cOrfY1j2AGHAAAAEAwZGRkKCkpSVOnTtWtt96q0aNHH/fzCQkJ6tatW4XXrcz+W2+88YaKi4vDZvm5xAy4Z3w3YvP3feAUcAAAAADBkJGRoSFDhmj8+PEaP368pk2bdtzP+3MJ+muvvaauXbuqa9eu/vp1Ao4ZcI8cKeB169ZVYmKiX5/XzRJ0AAAAIHjGjRtXrWXc1b3+9OnTAzb28RzZgO3ee+/VzTffrJ9++klXX321WrZsqdNPP73c7xxZgl6RxMTE476/ePFi/fDDD3rmmWeqlN0rFHCPNGvWTEuXLlWXLl38fr8CM+AAAAAAAm316tXav3+/s6T8mWee0erVqzVixAgtXLhQrVq1KvOdxMTEUo8sq6pJkyYpJiZGV111VbWvFUwsQXfJX7PUktS1a9eAbBbgW8CZAQcAAAAQCBkZGZLkFPDo6GhNnjxZjRs31tChQ5WVlRWQcQsKCvT222/rV7/6lRo1ahSQMQKFGfAI5LsEnRlwAAAAAIFw+eWX6/LLLy/1WkJCgpYuXRrQcWNjY7Vz586AjhEozIC75M8Z8EBhCToAAAAAhB4KuMc2b96sd999V7fffrs2btzol2uyBB0AAAAAQg9L0F3y9wz4mDFj9MUXX0iSzjjjDL9sIpCQkKC4uDjl5+crNzdXhw4dUp06dap9XQAAAABA1TED7pK/C/iZZ57pHPvreeDGGJahAwAAAECIoYC7EBcXV6kHwrsRiAIu8SxwAAAAAAg1FHAXUlJSNGPGDL9es2fPnoqOjpYkLV++XPv27fPLdZkBBwAAAIDQQgH3WGJiovPcPGutFixY4JfrUsABAAAAoIS11usIkijgIaFfv37O8ddff+2Xa7IEHQAAAPCPI/tAFRQUeJwEVVVYWCjJ+8dKU8BDQN++fZ3juXPn+uWazIADAAAA/pGQkCBJ2rRpkw4dOqSioqKQmVHFsVlrVVRUpEOHDmnTpk2S/vff0is8hsyF7OxsPf300/rDH/7g1+v6FvBvv/1WeXl5io+Pr9Y1eRY4AAAA4B+pqanKyclRbm6u1q9f73UcVFFMTEyplcJeYAbchezsbD300EN+v27jxo114oknSpLy8vK0ePHial/T9w8WM+AAAABA1dWqVUvt2rVTgwYNFBcXp6goalS4iIqKUlxcnBo0aKB27dqpVq1anuZhBjxE9O3bV6tWrZJUsgzd9/FkVcESdAAAAMB/oqKi1KhRIzVq1MjrKAhjFHCXAnXT/gUXXKDY2Fj17dtX55xzTrWvxxJ0AAAAAAgtFPAQccEFF+iCCy7w2/VYgg4AAAAAoYWbF1zyetv6ymIJOgAAAACEFgp4hKpfv76io6MlSQcOHFB+fr7HiQAAAACgZqOAuxSMGfCioiLnOXVVFRUVpZSUFOecWXAAAAAA8BYF3KVAFvAdO3Zo6NChatCggfr06VPt67ERGwAAAACEDgp4CElJSdGcOXO0f/9+bdy4URs2bKjW9Xw3YqOAAwAAAIC3KOAuBXIGPCYmRr1793bOv/7662pdr2HDhs7xzp07q3UtAAAAAED1UMBdqFWrln79618HdIy+ffs6x3Pnzq3WtRo1auQcU8ABAAAAwFsUcBeSkpI0ceLEgI4RqAK+Y8eOal0LAAAAAFA9FPAQ07NnT8XExEiSVqxYoT179lT5WhRwAAAAAAgdFPAQU7duXXXv3t05nz9/fpWv5XsPOAUcAAAAALxFAQ9B/fr1c46rsxEb94ADAAAAQOiggLuQlZWle+65J+Dj+Os+cJagAwAAAEDooIC7cOjQIb344osBH+fMM890jhctWqScnJwqXYcCDgAAAAChgwIegho2bKhOnTopPj5evXr1qnJ5TklJcZ5bvnfvXhUUFPgzJgAAAADAhRivA4SbI4U20D7++GM1b95c8fHxVb5GdHS0UlNTnfu/d+3apaZNm/orIgAAAADABWbAQ1Tbtm2rVb6PYBk6AAAAAIQGCrhLwZoB9xcKOAAAAACEBgq4SxRwAAAAAEBVcA94CNu7d6/mzJmj9PR0de/eXaNGjXJ9jYYNGzrHPAscAAAAALxDAXcpmDPg06ZN0/XXXy9JGjp0aJUKODPgAAAAABAaWIIews466yzneO7cuSoqKnJ9DQo4AAAAAIQGCrhLwZwBb9eunfPYsP3792vZsmWur0EBBwAAAIDQQAF3oW7durrtttuCNp4xRv3793fO58yZ4/oa3AMOAAAAAKGBAu5CYmKiHnzwwaCO6bsMPT093fX3mQEHAAAAgNBAAQ9xR8+AW2tdfZ8CDgAAAAChgQIe4jp37qzU1FRJ0u7du7Vy5UpX369fv75iY2MlSdnZ2crJyfF7RgAAAABAxSjgIc4Yo379+jnnbpehG2O4DxwAAAAAQgAF3IW9e/dq7NixQR/X9z7wqmzExjJ0AAAAAPAeBdyFvLw8ffzxx0Ef1/c+8PT0dO4DBwAAAIAwFON1AFTs1FNP1dixY9WrV69SZbyyfAs4S9ABAAAAwBsUcJeMMUEfMzo6Wi+++GKVv88MOAAAAAB4jyXoNYDvJmwUcAAAAADwBgXcJS9mwKuLGXAAAAAA8B4F3CWvC7i1Vj/88IP27dtX6e9wDzgAAAAAeI8CHkb+9Kc/qVGjRurSpYs++uijSn+PGXAAAAAA8B4F3CUvZ8CNMdq1a5ckd88D5x5wAAAAAPAeBTyMHP088Mo6egbc7XPEAQAAAADVRwF3ycsZ8DPOOEPx8fGSpJ9//llbt26t1Pfq1q2rOnXqSJLy8vKUnZ0dsIwAAAAAgPJRwF2oV6+eHn74Yc/Gr1Wrlnr37u2cV2cWHAAAAAAQXBRwF+rUqaPrrrvO0wwDBgxwjmfNmlXp73EfOAAAAAB4iwIeZnwL+OzZsyv9PWbAAQAAAMBbFPAw07NnT9WqVUtSyX3gW7ZsqdT3eBY4AAAAAHiLAh5mjr4PvLKz4MyAAwAAAIC3KOAu7N69WyNHjvQ6RpWWoVPAAQAAAMBbMV4HCCcFBQXKzMz0OoYGDBigmJgYnX766Tr55JMr9R3fTdhYgg4AAAAAwUcBD0N9+vTR3r17lZCQUOnvMAMOAAAAAN5iCbpLxhivIygmJsZV+ZYo4AAAAADgNQq4S6FQwKuCAg4AAAAA3qKA1xBH3wNeXFzsYRoAAAAAqHko4C6F0gz4zJkzdd9996lXr17auHHjcT8bFxen5ORkSVJRUZF2794djIgAAAAAgMMo4GHs8ccf1xNPPKGFCxdW6nFkTZo0cY63bdsWwGQAAAAAgKNRwF0KpRlw3+eBz5o1q8LPU8ABAAAAwDs1uoAbY/5sjLHGmGu9zlIVZ599tnNcmRnwpk2bOscUcAAAAAAIrrAs4MaYRsaYN40xPx3+mWKMaeHyGi0k3VWFsd1+JWB69OihOnXqSJLWrl2r9evXH/fzzIADAAAAgHfCroAbY+IkfSEpTlIXSZ0lHZQ0yxjj5uHYf5E0083YSUlJevbZZ918JaDi4uJ05plnOucVzYL7FvCtW7cGKhYAAAAAoBxhV8AlXSPpVEn3WGsLrbVFku6R1FbSTZW5gDEmTdKZkv7pZuDatWvrV7/6lcu4geVmGToz4AAAAADgnXAs4JdI2mCtXXPkBWvtNkk/HH6vMv4m6QFJef6PF1y+G7FRwAEAAAAgdMV4HaAKTpX0czmvr5U0sKIvG2MulFRb0juSznIz8M6dO5WWllbuexkZGW4u5Tc9evRQ3bp1dfDgQa1bt07r1q1T69aty/0sm7ABAAAAqOmO1elWrlwZ8LHDcQY8VdKBcl7PklTHGFP7WF80xsRKelLS3dZaG6B8QRUbG6u+ffs658ebBececAAAAADwTjjOgFfHTZK+t9bOrcqXrbVKTU3VZ5995udY1TNgwAAn06JFi3TttdeW+7mUlBTFxMSosLBQ+/btU25urmrVqhXEpAAAAADgrWOtXk5LS1NmZmZAxw7HAr5LUmI5r9eTdMham1Pel4wxSZLuk9S/qgMXFRVp8+bNVf16wFx00UVKTEzUOeeco06dOh3zc1FRUWrcuLHzO2zfvl0nnHBCsGICAAAAQI0WjgV8maTyWmYbScuP871ekgolvefzLO8jjy171Bhzh6Rp1tpHjzd4KD0H/IiOHTuqY8eOlfpskyZNnAK+bds2CjgAAAAABEk4FvBpkiYaY1pba9dJkjGmsaSTVDLD7Tj8+k5rbbG1doaklke9P0DSLEkPWWtfDXjyEOC7ERv3gQMAAABA8ITjJmyvqmSm+0ljTIwxJkrSEyrZBf1fRz5kjDlT0hZJz/tz8FCcAXeDR5EBAAAAgDfCroBba/MlDZZUpJJnf69Uyf3f51hrs30+mi1pv6Qy07zGmEbGmKWSXj780qPGmKXGmB6BzB5o1lr98ssvevnll1VcXFzuZyjgAAAAAOCNcFyCLmvtdklXVvCZ7ySlHOO9HZK6VWXsUJ4BP+OMM7R48WJJJc8H79atW5nPUMABAAAAwBthNwOOY2vXrp1zPHPmzHI/wz3gAAAAAOANCrhLoTwDfs455zjHX331VbmfYQYcAAAAALxBAY8gAwcOdI7nzJmjgoKCMp+hgAMAAACANyjgLoXyDHjbtm3VqlUrSVJ2drYWLVpU5jONGzd2jrdt2yZrbdDyAQAAAEBNRgF3oUGDBnrllVe8jnFMxphSy9DLuw+8bt26SkxMlCTl5+dr7969QcsHAAAAADUZBdyFuLi4cncWDyW+y9CPdR+470ZsLEMHAAAAgOCggEcY3xnw+fPnKycnp8xnuA8cAAAAAIKPAh5hmjVrpk6dOkkqWWI+f/78Mp+hgAMAAABA8FHAI1BFjyOjgAMAAABA8FHAXdi6dat69+7tdYwKDR48WN26ddPdd9+tYcOGlXnf9x7wrVu3BjMaAAAAANRYMV4HCDflPVs71Fx44YW68MILj/k+M+AAAAAAEHzMgLsUys8BrywKOAAAAAAEHwW8BqKAAwAAAEDwUcBdCscZ8Nzc3FLnvgWce8ABAAAAIDgo4BHsiSee0FlnnaWkpCTt2LHDeb1hw4aKiir5T797927l5+d7FREAAAAAagwKuEvhNAP+8ccfa86cOcrLy9OsWbOc16Ojo9WoUSPn3LecAwAAAAACgwIewQYNGuQcf/HFF6Xe4z5wAAAAAAguCrhL4TQDfnQBt9Y659wHDgAAAADBRQGPYGeccYYSExMlSRs2bNAvv/zivNe0aVPnmBlwAAAAAAg8CrhL4TQDHhsbq7PPPts5912GzhJ0AAAAAAguCrgLjRo10pQpU7yO4YrvMvQvv/zSOaaAAwAAAEBwUcBdiI6OVvPmzb2O4crgwYOd45kzZ6qwsFAS94ADAAAAQLBRwCNcx44dnb802L9/vzIyMiSVvgecAg4AAAAAgUcBj3DGmFKz4EfuA2/WrJnz2ubNm4OeCwAAAABqGgq4C8XFxcrKyvI6hmtH7gNPTk5WUVGRpNIFfOvWrSouLvYkGwAAAADUFBRwF7Zv366hQ4d6HcO1oUOHatGiRdq5c6cefvhhSVLt2rWVnJwsSSosLNTOnTu9jAgAAAAAEY8CXgMkJSWpR48eio6OLvW674ZyLEMHAAAAgMCigLsUTs8BrwgFHAAAAACChwJeg1HAAQAAACB4KOAuhfMM+JYtW/T6669r9OjR2rZtW6kCvmXLFg+TAQAAAEDki/E6AILnqquu0uzZsyVJ5557Lo8iAwAAAIAgYgbcpXCeAT/yODJJ+vLLL1mCDgAAAABBRAGvQQYPHuwcf/HFF8yAAwAAAEAQUcBdCucZ8LS0NCUlJUkquef74MGDznsUcAAAAAAILAp4DRIdHa1zzjnHOV+yZIliYkq2Adi7d69ycnK8igYAAAAAEY8C7lI4z4BLpZehf/nll2ratKlzzk7oAAAAABA4FHAXmjRpohkzZngdo1p8N2KbPXt2qQLOMnQAAAAACBwKuAvGGMXFxXkdo1ratWunNm3aSJKys7NVq1Yt5z0KOAAAAAAEDgW8hjHGaMiQIc45G7EBAAAAQHBQwGsg3wK+fft255h7wAEAAAAgcCjgLhQWFmrdunVex6i2c845R9dff73ee+89Pfjgg87rzIADAAAAQOBQwF3YuXOnbrjhBq9jVFu9evX00ksv6dJLL1WHDh2c1yngAAAAABA4FPAarnnz5s4xBRwAAAAAAocC7lK4Pwf8aM2aNXOOt2zZImuth2kAAAAAIHJRwGu4uLg41alTR5KUn5+v3bt3e5wIAAAAACITBdylSJoBf/rpp5WSkqJDhw45r7EMHQAAAAACgwJeg6WmppZ6DrhEAQcAAACAQKGAuxRJM+Dnnntumdco4AAAAAAQGBTwGqx58+bq0qVLqdco4AAAAAAQGBRwlyJpBlyShgwZUup8y5YtHiUBAAAAgMhGAa/hji7gzIADAAAAQGBQwF0wxigxMdHrGH7Vr18/xcfHO+dr1671MA0AAAAARC4KuAtNmjTRO++843UMv6pdu7Z69erlnG/cuNHDNAAAAAAQuSjg0NChQ53j7Oxs5eXleZgGAAAAACITBRw6//zzS50zCw4AAAAA/kcBhzp37lzqPvANGzZ4mAYAAAAAIhMF3IW8vDwtXbrU6xh+Z4wptRv6rl27PEwDAAAAAJGJAu7Cnj179PDDD3sdIyBatGjhHPMoMgAAAADwPwo4JEnNmzd3jjdt2uRhEgAAAACITBRwl4wxXkcIiFatWjnHGzZsUE5OjodpAAAAACDyUMAhSWrZsqVzPH36dI0dO9bDNAAAAAAQeSjgLtWEGfC8vDx99tlnKi4u9jARAAAAAEQWCjgklb4HXCrZCX3x4sUepQEAAACAyEMBdylSZ8Dj4uLUpEmTUq99+umnHqUBAAAAgMhDAYfDdxm6JH3yySceJQEAAACAyEMBdylSZ8Cl0huxSdKiRYu0c+dOj9IAAAAAQGShgLsUyQX86Blwa60+//xzj9IAAAAAQGShgLsQExNTZpY4kpT3u3EfOAAAAAD4BwXchUaNGunvf/+71zECprwCzuPIAAAAAMA/KOBw+C5Bj4mJkcTjyAAAAADAXyjgcPjOgEdFlfzR6NKli/bv3+9VJAAAAACIGDFeB0DoaNy4sWJjY1VQUKD8/Hz9+OOP6tixo9exAAAAACAiMAPuwqFDh5Senu51jICJiopSixYtnHNrrYdpAAAAACCyUMBd2LdvnyZMmOB1jIDyvQ98w4YNHiYBAAAAgMhCAUcpvveBb9y40cMkAAAAABBZKOAuGWO8jhBQvgV8/fr1Wrp0qR5//HGNGDGCx5EBAAAAQDWwCZtLkV7AfZegb9y4UUOGDNGOHTskSYsXL9YZZ5zhVTQAAAAACGvMgKMU3xnwTZs26bzzznPOP/74Yy8iAQAAAEBEoIC7VJNmwDds2KChQ4c65x999JEXkQAAAAAgIlDAXYr0An70JmyDBw9WTEzJnQqZmZnasmWLV9EAAAAAIKxRwFFK/fr1lZCQIEnKyclRYWGh+vXr57z/ySefeBUNAAAAAMIaBdylSJ8BN8aU2YjNdxk694EDAAAAQNVQwFHG0cvQhw0b5px/8cUXysvL8yIWAAAAAIQ1CrgLcXFxOvnkk72OEXBHb8TWoUMHtWvXTpJ08OBBpaenexUNAAAAAMIWBdyF1NRU3XvvvV7HCLijZ8CNMaVmwVmGDgAAAADuUcBRhm8B37BhgySVug/8m2++CXomAAAAAAh3FHCUcfQmbJLUv39/PfTQQ1qwYIHmz5/vVTQAAAAACFsxXgdA6Dl6CbokxcfH65FHHvEqEgAAAACEPWbAXThw4IA++ugjr2MEXIsWLZzjzZs3q6ioyMM0AAAAABAZKOAuHDhwQFOmTPE6RsDVrl1bDRs2lCQVFRVp69atHicCAAAAgPBHAUe5jn4Uma+dO3dq0qRJ3AsOAAAAAC5QwF0yxngdISh8C/j69eud44kTJ6px48a65pprNHHiRC+iAQAAAEBYooCjXG3atHGO161b5xx3795d1lpJ0qeffqri4uJgRwMAAACAsEQBd6mmzIC3bt3aOfYt4GlpaWrcuLGkkqXoixYtCnIyAAAAAAhPFHCU61gFPCoqSueff75z/vHHHwcxFQAAAACELwq4SzVxBnzt2rWl3hs6dKhzPH369GBFAgAAAICwRgF3qaYU8BNOOME5Xr9+fal7vc8991zFxcVJkpYuXaqNGzcGPR8AAAAAhBsKOMpVr149paSkSJLy8/O1bds2573ExEQNGDDAOWcWHAAAAAAqRgF3qabMgEvH3gldkkaMGOEcf/jhh8GKBAAAAABhiwLuQu3atdW7d2+vYwTNsTZik6Thw4c7x7NmzdKBAweClAoAAAAAwhMF3IXk5GRdd911XscImuMV8FatWqlr166SSpaof/7550FMBgAAAADhJ8brAAhdxyvgkjR69GgtX75cI0aM0ODBg4MXDAAAAADCEAUcx3S8R5FJ0l133RXENAAAAAAQ3liCjmOqaAYcAAAAAFB5FHAX9u/fr3feecfrGEHjW8CPfhY4AAAAAMAdCrgLBw8e1OzZs72OETQJCQlKTU2VJBUUFGjr1q3H/GxeXp7S09ODFQ0AAAAAwg4FHMdVmWXoY8aMUcOGDTVgwAD9/PPPwQkGAAAAAGGGAu6SMcbrCEFVmQK+b98+5zng06dPD0IqAAAAAAg/FHAcV2UK+IgRI5zjDz/8MMCJAAAAACA8UcBdqskz4OU9ikyShg4d6vx7mTt3rnbv3h2MaAAAAAAQVijgLtW0At6mTRvn+Fgz4I0aNVLv3r0lScXFxfrkk0+CEQ0AAAAAwgoFHMdV2WeBDx8+3DlmGToAAAAAlEUBd6mmzYCfcMIJzvGGDRtUVFRU7ud87wOfMWOG8vLyAp4NAAAAAMIJBRzHVbduXTVs2FDS8Z8FftJJJ6ldu3aSpOzs7Br1vHQAAAAAqAwKuEs1bQZcqtwydGNMqVnwDz74IMCpAAAAACC8UMBdSEhI0KBBg7yOEXSVvQ/8wgsvdI7/+9//qri4OHChAAAAACDMxHgdIJzUq1ev1CxvTeG7E/qxHkUmSX369FGzZs10yimn6MILL1RhYaHi4uKCEREAAAAAQh4FHBWq7Ax4TEyM1q5dS+kGAAAAgHKwBB0VqmwBl0T5BgAAAIBjoICjQm4KOAAAAACgfBRwF/bs2aNXX33V6xhBV9lngR/NWqvdu3cHKhYAAAAAhBUKuAu5ublatmyZ1zGCrk6dOmrSpIkkqbCwUBs3bjzu57dt26Y77rhDbdq00dChQ4MREQAAAABCHgUcldKuXTvnePXq1cf9bFxcnJ577jmtX79eCxcu1ObNmwMdDwAAAABCHgXcJWOM1xE80bZtW+e4ogKekpKiAQMGOOcffvhhoGIBAAAAQNiggKNS3MyAS9KFF17oHP/3v/8NQCIAAAAACC8UcJdq6gy42wJ+wQUXOMczZ87Uvn37AhELAAAAAMIGBdwlCnjlCnjLli2VlpYmqWTjtk8++SRg2QAAAAAgHFDAUSlHF3BrbYXfueiii5xjlqEDAAAAqOko4C7V1Bnwhg0bKiEhQZJ04MAB7dq1q8Lv+N4H/umnnyo3NzdQ8QAAAAAg5FHAUSnGGNfL0Dt37qz27dtLkrKzs/XVV18FLB8AAAAAhDoKuEs1dQZccn8fuDGG3dABAAAA4DAKuAv169fX8OHDvY7hGbcFXPrffeCnnnqqunTpEpBcAAAAABAOYrwOEE7q1q2rvn37eh3DM1Up4L169dLq1avVtm3bQMUCAAAAgLDADDgqrSoFPCoqivINAAAAAKKAw4WqFHAAAAAAQAkKOCqtZcuWiokpuWth27ZtOnjwYJWuU1xc7M9YAAAAABAWKOAu7Nq1Sy+88ILXMTwTExOj1q1bO+dr1qyp9Hc3bdqkJ598UmeccYbuu+++AKQDAAAAgNBGAXchPz9fGzZs8DqGp6q6DH3p0qW69957tWjRIk2dOlXW2kDEAwAAAICQRQF3qSY/B1yqegEfPHiwEhMTne8tW7bM79kAAAAAIJRRwOFKVQt4fHy8hg0b5pxPnTrVr7kAAAAAINRRwF1iBrzqO6FffPHFzjEFHAAAAEBNQwF3iQJe9QJ+3nnnqXbt2pKkH374QT/++KNfswEAAABAKKOAw5W2bds6x+vXr1dhYWGlv1u3bl396le/cs6ZBQcAAABQk1DAXarpM+B16tRR06ZNJUmFhYWud4W/5JJLnONp06b5NRsAAAAAhDIKOFzznQV3uwx92LBhio2NlSRlZmZq7dq1fs0GAAAAAKGKAu5STZ8Bl6p3H3j9+vU1ePBg55xZcAAAAAA1BQXcJQp49Qq49L9l6E2aNFFUFH8EAQAAANQMMV4HCCcpKSkaOXKk1zE8V90CfvHFF6tDhw7q3bu3oqOj/RkNAAAAAEIWBdyF2rVrq0uXLl7H8Fz79u2d41WrVrn+flJSkvr27evPSAAAAAAQ8lj/C9dOPPFE5/iXX35RcXGxh2kAAAAAIDxQwOFaSkqKUlNTJUm5ubnatGmTx4kAAAAAIPRRwFElvrPgVVmGLkn79u3TpEmTNGzYML344ov+igYAAAAAIYkC7sK2bds0fvx4r2OEhA4dOjjHP//8c5Wu8fbbb+uaa67Rxx9/rDfffNNf0QAAAAAgJFHAXSgqKtL+/fu9jhES/FHAL774YucxZF9//bW2bNnil2wAAAAAEIoo4C7xHPAS/ijgjRs31oABAyRJ1lpNnTrVH9EAAAAAICRRwFEl/ijgknTZZZc5x++++261MgEAAABAKKOAu8QMeAnfZ4GvXbtW+fn5VbqO7zL0uXPnavPmzX7JBwAAAAChhgKOKqlTp45atmwpqeTe+LVr11bpOg0bNtQ555zjnE+ZMsUv+QAAAAAg1FDAXWIG/H98l6FX9VFkEsvQAQAAANQMFHBUme+zwKtzH/hFF12k6OhoSdL8+fO1cePGamcDAAAAgFBDAXeJGfD/8ddGbKmpqRo4cKBzzjJ0AAAAAJGIAo4q81cBl/63DL127drau3dvta4FAAAAAKEoxusAbhljGkn6u6Qeh19aLukOa+2mCr6XIOl3koZJqn34p1jSfyT93VprKzl+FZNHHn8W8IsuukiJiYkaOnSo6tatW91oAAAAABBywmoG3BgTJ+kLSXGSukjqLOmgpFmHC/bxtJb0Z0lPWGvTrLWdJd0v6a+SHqjM+KmpqRo1alQV00ee1q1bKyam5O9wNm/erIMHD1b5WikpKbrsssso3wAAAAAiVlgVcEnXSDpV0j3W2kJrbZGkeyS1lXRTBd89KOkFa+1HR16w1n4oaZmkiyszeHx8vFq0aFGl4JEoNjZWbdu2dc5/+eUXD9MAAAAAQGgLtwJ+iaQN1to1R16w1m6T9MPh947JWrvWWvu7ct6qJ2mnX1PWIP5chg4AAAAAkSzc7gE/VVJ5LW+tpIHlvH5Mxpi6ku6TdOSfFdqxY4fS0tLKfS8jI8PN8BHD3wW8oKBAs2bN0rvvvqvTTz9dv/3tb6t9TQAAAAA44lidbuXKlQEfO9wKeKqk8ppulqQ6xpja1tqcii5ijJkr6QxJqyVdbK3N9G/MmsNfzwI/4u2339Y111wjSVq2bBkFHAAAAEDECLcC7hfW2r7GmFhJv5b0lTHmD9baf1b0vYKCAl111VW66667Ah8yTPh7Bnz48OGKjY1VQUGBFi1apDVr1pS6zxwAAAAAquNYq5fT0tKUmRnYudlwuwd8l6TEcl6vJ+lQZWa/j7DWFlhrJ0l6TdJfjTFNKvO94uLiyg5RI/i7gCcnJ+vcc891zt97771qXxMAAAAAQkG4FfBlKnmc2NHaqOR54MdkjIkzxpQ34/+dSh5rdkplAvAc8NKaNWumOnXqSJL27Nmj3bt3V/ual112mXP87rvvVvt6AAAAABAKwq2AT5N0gjGm9ZEXjDGNJZ0kaarvB40xjY0xvr/f/ZL+UM41j1yr+s2xBoqKiip1H/iqVauqfc0RI0YoLi5OkpSZmemXawIAAACA18KtgL+qkpnuJ40xMYcL9hMq2QX9X0c+ZIw5U9IWSc8f9f1bjDGdfT7XVyXPD58jaUllAjADXpa/l6EnJSVpyJAhzvnkyZOrfU0AAAAA8FpYFXBrbb6kwZKKVPLs75Uquf/7HGttts9HsyXtl7TV57XXJL0p6S1jzHfGmO8lTZD0uKSh1lobhF8hIvkW8J9++skv17zyyiud47feekv85wEAAAAQ7sJuF3Rr7XZJV1bwme8kpRz12lpJ9xz+qTJmwMvq2LGjc+yvZ+cNHz5cdevW1cGDB/Xjjz/qu+++U7du3fxybQAAAADwQljNgCM0nXTSSc7xjz/+6Jdr1q1bVxdccIFz/vbbb/vlugAAAADgFQq4S8yAl9WpUyfneNWqVSooKPDLdY8sQzfGaMuWLX65JgAAAAB4hQKOaktISFDLli0lSYWFhVq9erVfrnvuuefq2Wef1caNG/X666/75ZoAAAAA4BUKuEvMgJfPdxbcX/eBx8bG6vbbb1fz5s39cj0AAAAA8BIF3IXGjRvr2muv9TpGSPK9D9xfBRwAAAAAIgkF3IWYmBjVr1/f6xghiQIOAAAAAMcXdo8hQ2gKxE7ovlasWKG3335bRUVFeuKJJ/x+fQAAAAAINAo4/OLoAm6t9dv98itWrNApp5wiqeTxZA899JDq1Knjl2sDAAAAQLCwBN2F4uJi5ebmeh0jJDVs2FApKSmSpOzsbG3atMlv1+7SpYs6duwoSTp48KA++ugjv10bAAAAAIKFAu7C1q1b9e9//9vrGCHJGBOQndCPXPvIM8El6a233vLbtQEAAAAgWCjg8JtAbsT261//2jn+9NNPtXfvXr9eHwAAAAACjQLuEs8BP7ZAFvATTzxRPXr0kCTl5+dr2rRpfr0+AAAAAAQaBRx+E+id0FmGDgAAACCcUcBdYgb82AL9LPDLL7/c+fc/a9Ysbd261e9jAAAAAECgUMDhN61atVKtWrUkSTt27NCePXv8ev1mzZppwIABkiRrrd555x2/Xh8AAAAAAokC7hIz4McWHR3tPC5MCswsOMvQAQAAAIQrCjj8KtDL0C+55BLFxsZKkg4cOKADBw74fQwAAAAACIQYrwOEG2bAjy/QBTw5OVkTJ07Uaaedpq5du/LfAwAAAEDYoIDDrwK9E7okjRkzJiDXBQAAAIBAYgm6S8y4Hl+gZ8ABAAAAIFxRwF1o1qyZfvOb33gdI6SdeOKJiooq+WO1bt065eTkeJwIAAAAAEIDBdwFY4yio6O9jhHS4uPj1bZtW0kljwr76aefAjbWzp079c9//lODBw9Wfn5+wMYBAAAAAH+ggMPvOnfu7Bz/8MMPARnDWqs+ffrotttu05dffqlPPvkkIOMAAAAAgL9QwOF3J598snO8YsWKgIxhjNFll13mnL/++usBGQcAAAAA/IUC7kJBQYH27t3rdYyQF4wCLklXX321czx9+nTt2bMnYGMBAAAAQHVRwF3YsWOH3n//fa9jhLxgFfBOnTrp9NNPl1TylyPvvvtuwMYCAAAAgOqigMPvOnTo4GxWt3btWmVnZwdsrNGjRzvHkyZNCtg4AAAAAFBdFHCXeA54xeLj49WhQwfnPFAbsUnSFVdcoZiYGEnSggUL9MsvvwRsLAAAAACoDgo4AiJYy9BTU1N13nnnOedsxgYAAAAgVFHAXWIGvHKCVcCl0svQX3/9dVlrAzoeAAAAAFQFBRwBEcwCPmzYMNWvX19SyT3n8+bNC+h4AAAAAFAVFHCXmAGvnGAW8Fq1aunyyy+XJDVs2FCbN28O6HgAAAAAUBUxXgdAZGrXrp3i4+OVl5enrVu3as+ePUpJSQnYeLfddptGjBihc889V7GxsQEbBwAAAACqihlwl5gBr5zo6Gh17tzZOf/+++8DOl6XLl00dOhQyjcAAACAkEUBR8AEcxk6AAAAAIQ6CrgLxhjFx8d7HSNsUMABAAAA4H8o4C40a9bM2ewLFfOigOfm5mrKlCkaMWKEXnjhhaCMCQAAAACVwSZsCJijC7i1NuD30E+aNEm//e1vJUnbtm3TjTfeGNDxAAAAAKCymAFHwLRs2VKJiYmSpD179mjbtm0BH/PSSy9VXFycJGnRokVauXJlwMcEAAAAgMqggCNgjDFBX4aekpKiYcOGOeevvPJKwMcEAAAAgMqggLtw5JnWqLwuXbo4x8G6D/y6665zjidNmqSCgoKgjAsAAAAAx0MBd2HXrl2aNWuW1zHCihcbsQ0ZMkRNmzaVJG3fvl0zZswIyrgAAAAAcDwUcASUFwU8JiZGo0ePds5Zhg4AAAAgFFDAXQr0Lt6RxreAf//99youLg7KuGPGjHGOp0+frh07dgRlXAAAAAA4Fgo4AqpRo0Zq2LChJOngwYNau3ZtUMbt2LGj+vTpI0kqLCzUm2++GZRxAQAAAOBYKOAuMQPujjFGXbt2dc6/++67oI3tOwv+n//8R9baoI0NAAAAAEejgCPgvCrgl112merUqaP4+Hh16dJFhw4dCtrYAAAAAHC0GK8DhBtmwN3zqoDXq1dPH3zwgdLS0pScnBy0cQEAAACgPBRwBJxXBVySBg0aFNTxAAAAAOBYWILuEjPg7nXq1EmxsbGSpHXr1mnfvn3eBgIAAAAAD1DAXaKAuxcXF6fOnTs758uWLfMsS0FBgWdjAwAAAKjZKOAuxMTEqF69el7HCEteLkOXpG+//VY33nijGjdurA0bNgR9fAAAAACggLvQpEkTDRkyxOsYYcnrAv7HP/5REydO1N69e/Xaa68FfXwAAAAAoIAjKLwu4L7PBH/llVdUXFwc9AwAAAAAajYKOILCt4CvWLFChYWFQR3/wgsvVFJSkiRp7dq1mjNnTlDHBwAAAAAKOIIiNTVVzZs3lyTl5uZq1apVQR2/Vq1auvLKK53z//znP0EdHwAAAAAo4C4cPHhQ69ev9zpG2PJ6Gfp1113nHE+ZMkVZWVlBzwAAAACg5vJbATfG9DLGjDPGzDDGLDPGrDLGLDDGvGqMGWOMSfbXWF7Zu3evMjMzvY4Rtrwu4N27d9epp54qScrJydE777wT9AwAAAAAaq5qF3BjzDXGmOWS5ku6U1IdSaskLZS0V1JPSS9L2ny4jLep7pgIT14XcGNMqc3YXn755aBnAAAAAFBzVauAG2OWSXpC0ieS0iQlWWv7W2svsdaOstaeb609SVKKpLGSGkn6wRhzeXWDe8UY43WEsOV1AZekUaNGKS4uTlLJs8GXLVvmSQ4AAAAANU91Z8D/LamNtfYea+0Sa60t70PW2v3W2jettedL6iVpXzXHRRg68cQTVbt2bUnSli1btHPnzqBnSE1N1cUXX+ycv/TSS0HPAAAAAKBmqlYBt9b+w1qbK0nGmH6V/M531trPqjOul5gBr7ro6GidfPLJzrlXs+Bjx46VJPXt21f9+/f3JAMAAACAmsefu6C/Y4xpcqw3jTEJfhwLYSoUlqEPGDBAK1eu1Ndff62RI0d6kgEAAABAzePPAj5f0hRjTMzRbxhjWkqa58exPMMMePWEQgGPiopSp06dPBkbAAAAQM3lzwI+RlJDSX/3fdEYk6aSHdGL/DgWwlS3bt2c46VLl3qWAwAAAACCzW8F3Fp7QNKlksYYY66SJGPMhZLSJWVIqtQ94qGOGfDq6dq1q/Pv8IcfflBOTo7HiaTi4mKtWrXK6xgAAAAAIlx1H0M2yBiTdOTcWrtc0s2SJhpj/iZpikqeAX6BtfZgdcYKFRTw6klMTFSHDh0kSUVFRVq+fLlnWXJzc/X444/rxBNPVM+ePZWbm+tZFgAAAACRr7oz4J9L2m2M+cUYM9kYc7ekDZI+knSrpN9Za++w1hZXN2goiI+PV2pqqtcxwl737t2d44yMDM9yxMXF6aWXXtKaNWu0d+9eTZ061bMsAAAAACJfdQt4Z0mjJX0oqYmkhyTNlHSZpGxJ/Y0x/2eMOdcY06iaY3muYcOG6tWrl9cxwp5vAc/MzPQsR1RUlK6//nrn/MUXX/QsCwAAAIDIV93ngP9orX3TWnuXtXaAtba+pE6SrpT0b5WU8vskzZC0tdppERHS0tKcYy8LuCSNGTNG0dHRkqQ5c+boxx9/9DQPAAAAgMjlz13QJUnW2p+ttZOttX+w1p5jrU2W1EHSr/09FsLTaaed5hwvX75ceXl5nmVp2rSpRowY4Zy//PLLnmUBAAAAENn8XsDLY639xVr7bjDGQuhLSkpS27ZtJUkFBQX6/vvvPc0zduxY5/jVV1/19C8EAAAAAESumOp82Rgzujrft9ZOqs73gy0rK0urV69Wu3btvI4S9tLS0rRmzRpJJcvQfe8LD7Zzzz1XrVq10oYNG7R79269//77uuKKKzzLAwAAACAyVauAS3q1Gt+1ksKugK9atYoC7gfdu3fXe++9J6lkJ3TfzdCCLTo6Wtdff70eeughSdJLL71EAQcAAADgd9XdhC2qGj/R/volEH5CZSf0I8aMGaOoqJL/cZg5c6ZWrVrlcSIAAAAAkSYo94BHEmOM1xEigm8B/+6771RQUOBhGqlFixYaOnSoc85mbAAAAAD8jQIOT6SmpqpVq1aSpLy8PK1cudLjRNINN9ygVq1a6dFHH9Wtt97qdRwAAAAAEaa694DLGJMo6R5JwyU1l3RQ0gpJUyW9Ya3Nr+4YoYQZcP/p3r27NmzYIKlkGfqpp57qaZ7zzz9fa9ascZ4LDgAAAAD+VK0ZcGNMkqRvJN0vqZ6k5ZK2SRog6WVJPxpj+lYvIiJVWlqacxwK94FHRUVRvgEAAAAETHWXoP9R0gmShlpr21hrz7bW9pSUKukGSQWSvjLGDKvmOCGDGXD/8b0PPCMjw8MkAAAAABB41S3gF0l6zFr7qe+L1toca+3LkrpJ+kDSG8aYZsaYWGPMk9Uc01MUcP/xnQFfunSpioqKPExT1k8//aQpU6Z4HQMAAABAhKhuAW8uaeGx3rTW5kgaJWmjpAmSFku6q5pjIkI0btxYzZo1kyQdOnRIP//8s8eJSuzZs0eDBg1Sp06dNGbMGB04cMDrSAAAAAAiQHUL+B6V3Pt9TIc3YZsgaYSkeEn9qjmmp5gB969QXIaenJysLVu2SJKys7P1xhtveJwIAAAAQCSobgFfqJJiXZEfJVlJXa2131RzTM/UqVNHTZo08TpGRPFdhr548WIPk/yPMUY333yzcz5hwgRZaz1MBAAAACASVLeAvyBplDFmSAWfayppr7U2r5rjeSolJUVdunTxOkZE6dGjh3O8aNEiD5OUdvXVV6tu3bqSpBUrVmju3LkeJwIAAAAQ7qpVwK21MyS9LukDY8z/GWNqHf0ZY0y0pNslLajOWIhMp59+unO8ZMkSFRQUeJjmf+rXr69Ro0Y55xMmTPAwDQAAAIBIUN0ZcEkaK+k1SU9I2mKM+Zcx5jZjzJXGmHslfa+S3dAf88NYiDCNGzfWCSecIEnKycnR999/73Gi/7npppuc46lTp2rbtm0epgEAAAAQ7qpdwK21xdba30o6T9IKlTz/+1lJb0j6i6QESSPD+d5vBJbvLPi3337rYZLSunbtqjPPPFOSVFBQoH//+98eJwIAAAAQzvwxAy5JstZ+Zq3tr5L7vc+VdImk3pJaW2s/9Nc4Xtq3b59WrVrldYyIc8YZZzjHoXQfuKRSm7FNnDhRhYWFHqYBAAAAEM78VsCPsNbusNZ+aa1931q70FobMY0lOzvbeTwV/Me3gIfSDLgkXXLJJWrYsKEkaePGjfr44489TgQAAAAgXFWrgBtjPjTGnObi87WMMXcZY26szriILN27d3eer75ixQodPHjQ40T/Ex8fr+uvv945//LLLz1MAwAAACCcVXcGfJ2kb4wxCw9vvNbdGBPj+wFjTDNjzIXGmH9L2irpN5IyqzmuZ44URfhPYmKiOnfuLEkqLi7WkiVLPE5U2m9/+1tdc801+vbbb/XPf/7T6zgAAAAAwlR1H0N2m6TOkr6VNE7SIkm5xpg9xpitxpgcSRslTZPURdIdkk611obWOmN4LpSXoZ9wwgl69dVXS20WBwAAAABuxVT8keOz1q6WdKsx5m6VbLrWU1IzSbUk7Zb0o6Q51tr11R0rFDADHhinn366XnnlFUmhV8ABAAAAwB+qXcCPsNbmS0o//BOxKOCBEcoz4AAAAADgD37dBd0Yk2yMucAYc50xZrAxprY/r4/Idcoppyg+Pl6StHbtWu3atcvjROXLysrS+PHjdemll8pa63UcAAAAAGHEbzPgxphzJE2VVN/n5YPGmH9KGnd4hjzsMQMeGHFxcerWrZsWLlwoqeR54Oedd57HqUrLz89Xhw4dtH37dknS3Llz1a9fP49TAQAAAAgX/pwB/7ukLZIGSGoiqbuk5yXdIindGFPXj2MhAoX6MvS4uDiNGDHCOf/HP/7hYRoAAAAA4cafBbyDpPuttXOstTustUuttfdKOklSQ0mP+XEszzADHji+BXzRokUeJjm22267zTl+//33tWHDBg/TAAAAAAgn/izgmyUVHv2itXaLpD9JutyPY3kiMTFRzZs39zpGxDp6BjwU77E++eSTNXDgQEklzyx//vnnPU4EAAAAIFz4s4C/KelOU/4U8UZJiX4cyxP169fXCSec4HWMiNW+fXvVr1+yhcDOnTu1fn1oPrnOdxb8pZde0qFDhzxMAwAAACBc+LOAd1LJM8C/Msb0OvKiMSZK0hhJs/w4FiJQVFSUTj/9dOf8yIZsoWbo0KFq27atJGnv3r164403PE4EAAAAIBz4s4C3lhStkk3Y5hljNhpjvlHJ0vR+ku7x41iIUL16OX93owULFniY5Niio6N16623Oufjx48PyeXyAAAAAEKL3wq4tbanSpaZd5V0naT3VXJPeIKkVpKWG2PWG2OmGWPu99e4iCy9e/d2jkO1gEvSmDFjlJCQIEn6/vvvNXPmTI8TAQAAAAh1/pwBl7W2yFq73Fr7mrX2NmttX0n1JHWRNFrSFEkpkv7gz3GDZffu3fr555+9jhHRfGfAlyxZopycHA/THFv9+vV17bXXOuc8kgwAAABARfxawMtjS6y01r5prb3bWjvAWpsc6HEDIScnR3v37vU6RkRLSUlRx44dJUkFBQXKyMjwONGx/e53v5MkNWrUSGlpaSxDBwAAAHBcAS/ggFvhsgy9Y8eO+vzzz7VhwwY9/PDDPCMeAAAAwHFRwF2iZAVenz59nONQLuCSNHjwYMXHx3sdAwAAAEAYoIAj5Bw9A87SbgAAAACRgALuEjPggde5c2fVq1dPkrRt2zatX7/e40SVt2bNGhUXF3sdAwAAAEAIooC7RAEPvKioKPXs2dM5D/Vl6JI0e/ZsDRs2TO3bt9dnn33mdRwAAAAAIYgCjpAULhuxHTF9+nR9/PHHstZq/PjxXscBAAAAEIIo4C4xAx4cvgV8/vz5HiapnFtuucX5szFjxgytXLnS40QAAAAAQg0FHCHJdwn6d999p0OHDnmYpmJt27bVBRdc4Jz//e9/9zANAAAAgFBEAXeJGfDgSE5O1kknnSRJKiws1OLFiz1OVLG77rrLOZ40aZJ27NjhYRoAAAAAoYYC7kJSUpJatGjhdYwaI5yeBy5Jffv21emnny5JysvL0/PPP+9xIgAAAAChhALuQkJCgho1auR1jBoj3DZiM8bo97//vXM+YcIE5eTkeJgIAAAAQCihgCNkHV3ArbUepqmciy++WCeccIIkadeuXZo0aZLHiQAAAACECgo4QlanTp2UlJQkSdqxY4dWr17tbaBKiImJ0R133OGcP/PMMyouLvYuEAAAAICQQQFHyIqKiip1H/jXX3/tYZrK+81vfqP69etLkn7++Welp6d7nAgAAABAKKCAu7Bjxw798ssvXseoUfr16+cch0sBT0xM1M0336xLLrlE8+fP19lnn+11JAAAAAAhIMbrAOEkPz8/5J9HHWl8C/jcuXM9TOLOY489xiPrAAAAAJTCDDhCWo8ePRQfHy9JWrVqlbZt2+ZxosqhfAMAAAA4GgXcJYpVcMXHx+uMM85wzsNpFhwAAAAAfFHAXaKAB1+4LkM/4uDBg3r++ef19NNPex0FAAAAgIe4Bxwhr2/fvs5xuGzEdsTq1at1xhlnaM+ePUpISNDYsWOdR6sBAAAAqFmYAXeJGfDg69Onj/PvfenSpcrKyvI4UeW1bdtWTZs2lSRlZ2frxRdf9DgRAAAAAK9QwBHy6tevr65du0qSiouLtWDBAo8TVZ4xRnfffbdz/o9//EP5+fkeJgIAAADgFQq4S8yAe8N3GXq43Qd+5ZVXqkmTJpKkLVu2aPLkyR4nAgAAAOAFCjjCgu9GbOF2H3h8fLx+97vfOedPP/20rLUeJgIAAADgBQq4S8yAe8N3BnzhwoXKy8vzMI17N910k+rWrStJWrFihT755BOPEwEAAAAINgq4Cw0aNFDz5s29jlEjNWvWTG3btpUk5ebmKjMz0+NE7qSkpOi3v/2tc/744497mAYAAACAFyjgLtSuXVv16tXzOkaNFc7L0CXpzjvvVGxsrCRp3rx5YXcvOwAAAIDqoYAjbIR7AW/RooWuvvpq5/yJJ57wMA0AAACAYKOAu8D93946uoAXFRV5mKZq/u///k/GGDVo0EA9e/ZkMzYAAACgBonxOgBQWSeeeKKaNm2qrVu3av/+/fruu+/UvXt3r2O50rFjR3344Yc6++yznU3ZAAAAANQMzIC7sGXLFq1du9brGDWWMUYDBgxwzmfPnu1ZluoYNmwY5RsAAACogSjgLhQVFamwsNDrGDXa2Wef7RzPmjXLwyQAAAAA4A4F3CXuA/eW7wz4nDlzwvI+8KP9+OOP2rVrl9cxAAAAAAQYBRxhpX379mrWrJkkKSsrS0uXLvU2UDUsW7ZMl1xyiTp37qxnnnnG6zgAAAAAAowC7hIz4N4yxpRahh6u94FL0qpVqzRt2jRZa/X8889r//79XkcCAAAAEEAUcIQd32Xo4Xwf+IUXXqgOHTpIKpnNnzhxoseJAAAAAAQSBdwlZsC951vAv/7667DdGC86Olr33HOPc/73v/9dubm5HiYCAAAAEEgUcISddu3aqUWLFpLC/z7wUaNGqXnz5pKkbdu26bXXXvM4EQAAAIBAoYC7xAy4945+Hng4L0OPi4vT3Xff7Zw/9dRTYTujDwAAAOD4KOAIS74FPJw3YpOksWPHKiUlRZK0Zs0avfPOOx4nAgAAABAIFHCXmAEPDZFyH7gkJSQk6LbbbnPOH3vssYh4vjkAAACA0ijgLjRq1EhNmjTxOgYktW3bVi1btpQkHThwQEuWLPE4UfXcdtttSkxMlCStXLlSU6dO9TgRAAAAAH+jgLsQHx+vWrVqeR0Diqz7wCUpOTlZt956q3P+1VdfeZgGAAAAQCBQwBG2zj77bOc4EgrrnXfeqeHDhys9PZ1nggMAAAARKMbrAEBVDRw40Dn++uuvlZubG9YrFFJTU/Xhhx96HQMAAABAgDADjrDVqlUrdejQQZKUk5OjBQsWeJwIAAAAAI6NAu7Cxo0btWnTJq9jwMegQYOc4y+//NLDJIFRUFAga63XMQAAAAD4AQUcYS1SC3h+fr5efPFFdejQQV988YXXcQAAAAD4AQXcJZ4DHloGDBigqKiSP8aLFy/W3r17PU7kH+PGjdNvf/tbrVu3To8++iiz4AAAAEAEoIAjrCUnJ6tHjx6SpOLiYs2ePdvbQH5y0003KTY2VpI0b968iPm9AAAAgJqMAu4SM+Chx3cZeqQs127ZsqXGjBnjnD/66KMepgEAAADgDxRwhL1IvQ/8vvvuU0xMyZMCZ8+era+//trjRAAAAACqgwLuEjPgoad3796qXbu2JGnVqlVav369x4n8o3Xr1rr66qud8z/96U8epgEAAABQXRRwhL1atWqpX79+zvlXX33lYRr/uv/++51N5r744gt98803HicCAAAAUFUUcJeYAQ9NkboMvX379rryyiud80ceecTDNAAAAACqgwKOiHB0AS8uLvYwjX898MADziz4jBkzNH/+fI8TAQAAAKiKsCzgxphGxpg3jTE/Hf6ZYoxpUYnvNTXGPGKMWWaMWWGM+dEYM80Yc4qLsasXHgHRtWtXNWjQQJK0c+dOLV++3ONE/tOpU6dSs+BPPfWUh2kAAAAAVFXYFXBjTJykLyTFSeoiqbOkg5JmGWMSKvj6w5J+LWmotfZkSd0kFUlaWJkS3rRpU6fkIbRERUVp4MCBzvnnn3/uYRr/e/jhh5WUlKQHHnhAr7zyitdxAAAAAFRB2BVwSddIOlXSPdbaQmttkaR7JLWVdFMlvv+UtXajJFlrcyXdK6m2pBsq+mJMTIzzWCiEnl/96lfO8YwZMzxM4n/t27fX5s2b9ec//1nJyclexwEAAABQBeFYwC+RtMFau+bIC9babZJ+OPze8fxO0n+Oem3L4X/SasLckCFDnOOvv/5a2dnZHqbxvzp16ngdAQAAAEA1hON07qmSfi7n9bWSBpbzusNaW1jOyx0O/3N2RQNv27ZNaWlp5b6XkZFR0dcRYM2aNdOpp56qZcuWqaCgQLNmzdLw4cO9jgUAAAAghByr061cuTLgY4fjDHiqpAPlvJ4lqY4xprbL690g6XtJr1fmw9Zal5dHMPkuQ//ss888TBJYq1ev1rXXXqtPPvnE6ygAAAAAKikcZ8D9xhgzUNLlkvpba/Mq+nxBQYE+//xzpaamBj4cqmTIkCHOLuGRdh/4EZMnT9aoUaNUVFSk5cuX67zzzmN3fgAAAKCSjrV6OS0tTZmZmQEdOxxnwHdJSizn9XqSDllrcypzEWNMV0mvSRphrf3Bj/ngoTPPPFN169aVVDJL/Msvv3icyP/OOussxcbGSpIyMzP1wQcfeJwIAAAAQGWEYwFfJql1Oa+3kVSphz8bY06V9F9JV1hr57sZnJnG0BYfH69zzjnHOY/EWfCmTZvqlltucc4feughFRcXe5gIAAAAQGWEYwGfJukEY0zrIy8YYxpLOknSVN8PGmMaG2OijnrtVEkfSLraWjv38GtNjTETAx0cwRHJjyM74p577nFm+pcvX64pU6Z4nAgAAABARcKxgL+qkpnuJ40xMYcL9hMq2QX9X0c+ZIw5UyWPGHve57VTJH0l6TNJrY0xo4wxo1RyH3jHygzODHjo8y3gs2bNUm5urodpAqNhw4a67bbbnPNx48apqKjIw0QAAAAAKhJ2Bdxamy9psKQilTz7e6VK7v8+x1rr++DnbEn7JW31ee0Rleyi/luV7Hp+5OfvlR2fAh762rZtqxNPPFGSdOjQIc2dO9fjRIHx+9//XomJJdshrFy5Um+//bbHiQAAAAAcT9gVcEmy1m631l5pre1gre1orb3EWrvxqM98Z61NsdY+6vPaxdZac4yfAUH/RRAwNeFxZCkpKbrzzjud80ceeUSFheU96h4AAABAKAjLAu4lZsDDw5AhQ5zjSL0PXJLuvPNOJSUlSZJ++eUXvfLKK94GAgAAAHBMFHCXKODhYcCAAYqLi5MkrVixQhs2bPA4UWAkJSXp//7v/5zzcePGReQ97wAAAEAkoIAjItWtW1cDBgxwzj/++GPvwgTYbbfdpiZNmigtLU2vvfaaatWq5XUkAAAAAOWggLvEDHj4GDZsmHP80UcfeZgksOrWrav58+fr22+/1aBBg7yOAwAAAOAYKOAutGjRwtl1GqFv6NChzvHMmTN16NAhD9MEVps2bRQVxf84AwAAAKGM/4/dBWMMM+BhpG3bturcubMkKTc3VzNnzvQ4EQAAAICajAKOiFZTlqH7Kioq0htvvKFHH3204g8DAAAACBoKOCLa0QXcWuthmsDbs2ePTjvtNF199dV69NFHtWrVKq8jAQAAADiMAu5CQUGBiouLvY4BF3r37q3k5GRJ0ubNm/Xdd995nCiwkpOT1aBBA0klM+F//OMfPU4EAAAA4AgKuAvbtm1TTk6O1zHgQkxMjM477zznPNKXoRtj9MQTTzjn77zzjjIyMjxMBAAAAOAICjgiXk27D7xnz5666KKLnPP777/fwzQAAAAAjqCAu8Qu6OFnyJAhio6OliR9++232r59u8eJAu+xxx5zHkv2+eefswM8AAAAEAIo4Ih4KSkp6tOnjyTJWqtPP/3U40SBd9JJJ2nMmDHO+b333hvxG9ABAAAAoY4C7hIz4OGppi1Dl6SHH35Y8fHxkqRFixZp2rRpHicCAAAAajYKOGoE3wL+2WefKTc318M0wdGyZUvdeuutzvl9992n/Px8DxMBAAAANRsF3CVmwMPTSSedpBNPPFGSlJ2dXWPuib733nuVlJQkSVq1apVeeuklbwMBAAAANRgFHDWCMUYXXHCBc/7f//7XuzBB1KBBAz344IOKjY3VXXfdpV//+tdeRwIAAABqLMPGTJVjjMmQ1D03N9e5rxbhZd68eerbt68kqVGjRtqyZYuzO3oky8vL06ZNm9SuXTuvowAAAAAhKy0tTZmZmZnW2rRAjcEMOGqMXr16qVGjRpKkHTt2aOHChR4nCo74+HjKNwAAABACKOAuGGO4BzyMRUdHa8SIEc55TVmGDgAAACA0UMBdaNGiheLi4ryOgWq48MILneP333+/Rj4be9OmTbr22mtrzAoAAAAAIFRQwFGjDBw4UHXr1pUk/fLLL1q5cqXHiYLrnXfeUYcOHfTaa6/p97//fY38CwgAAADAKxRw1Ci1atXSeeed55zXtGXoaWlpKiwslCTNnTtX77//vseJAAAAgJqDAo4ax/dxZB988IGHSYKvffv2uuWWW5zze+65R/n5+R4mAgAAAGoOCrgLubm5LNmNAEOHDnUeP/btt99q8+bNHicKrgcffFBJSUmSSpbhv/DCC94GAgAAAGoICrgLO3fupIBHgOTkZA0YMMA5r2mz4A0aNNCDDz7onD/yyCPau3evh4kAAACAmoECjhrJdzf0adOmeRfEI7/73e/Upk0bSdKePXv0l7/8xeNEAAAAQOSjgLvEc8Ajw0UXXeQcz549Wzt37vQwTfDFx8friSeecM7Hjx+vNWvWeJgIAAAAiHwUcNRIzZs315lnnilJKioqqnHL0CVp5MiR6tWrlyQpPz9fv//97z1OBAAAAEQ2CrhLzIBHjksvvdQ5njJliodJvGGM0bPPPuucv//++8rMzPQuEAAAABDhKOCosS6++GLn+KuvvtKePXs8TOONnj17avTo0erQoYM++eQTde/e3etIAAAAQMSigKPGatWqlXr27ClJKiwsrJHL0CXpH//4h5YvX67zzjvP6ygAAABARKOAo0ar6cvQJSkpKUlxcXFexwAAAAAiHgUcNdoll1ziHH/xxRfat2+fd2FCSFFRkdcRAAAAgIhDAUeN1qZNG6WlpUmSCgoKNH36dI8TectaqylTpqhjx45avny513EAAACAiEIBdyE2NtbrCAgAlqH/z3333aeRI0dq9erVuv3222Wt9ToSAAAAEDEo4C40bdrU6wgIAN8C/tlnnykrK8vDNN4aNWqUoqOjJUmzZs3S+++/73EiAAAAIHJQwFHjtW/fXt26dZMk5eXl1ehl6CeffLJuuukm5/zuu+9Wbm6uh4kAAACAyEEBBySNHDnSOZ48ebKHSbz3yCOPKCUlRZK0bt06/e1vf/M4EQAAABAZKOCApCuuuMI5/uyzz7Rnzx4P03grJSVFf/rTn5zzv/zlL9q8ebOHiQAAAIDIQAF34eDBg15HQIC0bdtWZ5xxhqSS3dCnTZvmcSJv3XDDDTrllFMkSYcOHdIf/vAHjxMBAAAA4Y8C7sLu3bu9joAA8p0Fr+nL0GNiYvSPf/zDOX/77bc1e/Zs7wIBAAAAEYACDhx22WWXyRgjqWQH8G3btnmcyFtnn322LrvsMuf8lltuUUFBgYeJAAAAgPBGAQcOa968ufr37y9JKi4u1nvvvedxIu8988wzSkhIkCRt2bJFK1as8DgRAAAAEL4o4IAPlqGX1rx5cz3yyCO69tpr9dNPP+m0007zOhIAAAAQtoy11usMYcEYkyGpO/++ItuuXbvUpEkTFRUVSSp5DNcJJ5zgcSpvWWudpfkAAABApEpLS1NmZmamtTYtUGMwAw74SE1N1eDBg53zd955x8M0oYHyDQAAAPgHBRw4yq9//WvnmGXo5VuyZIny8vK8jgEAAACEFQo4cJQLLrhA8fHxkkqK5g8//OBxotCxd+9e3XzzzUpLS9Nf//pXr+MAAAAAYYUC7gJLcWuG+vXra9iwYc75G2+84WGa0DJ58mT961//krVWjz32mNatW+d1JAAAACBsUMCBclx99dXO8Ztvvqni4mIP04SOsWPHqlu3bpKknJwc3X777d4GAgAAAMIIBdyFI8uSEfnOO+88NWjQQJK0YcMGzZkzx+NEoSEmJkYTJkxwzj/88EN99NFHHiYCAAAAwgcF3IVGjRp5HQFBEhcXp8svv9w5Zxn6//Tu3Vu/+c1vnPPbbrtNOTk5HiYCAAAAwgMFHDgG32Xo7733HiXTxxNPPKGUlBRJ0tq1a/WnP/3J40QAAABA6KOAA8fQs2dPtW/fXpKUlZWl6dOne5wodKSmpurJJ590zp9++mktX77cw0QAAABA6KOAA8dgjNGoUaOc89dff93DNKHnuuuuU79+/SRJhYWFGjt2rIqKijxOBQAAAIQuCrgLWVlZXkdAkPkW8BkzZmjnzp0epgktUVFRmjhxouLi4iRJCxcu1AsvvOBxKgAAACB0UcBd2L9/v9cREGTt2rVTnz59JJXM8r7zzjseJwotJ510ku677z5JUv/+/TVw4ECPEwEAAAChiwIOVMB3FnzSpEkeJglN9913n958803NmjVLnTp18joOAAAAELIo4EAFLr/8cmeZ9aJFi/T99997nCi0xMfH68orr1RUFP/rBAAAADge/j9moAIpKSm64IILnPNXXnnFwzQAAAAAwhUFHKiEMWPGOMevv/66CgoKPEwT2goKCvTUU0/pnnvu8ToKAAAAEFIo4EAlnHvuuWrevLkkaceOHfrkk088ThSa9uzZo9NPP1333HOPnn76aS1cuNDrSAAAAEDIoIC7YIzxOgI8Eh0drdGjRzvnLEMvX3Jyspo2bSpJstbqhhtuYLUAAAAAcBgFHKika6+91jn+6KOPtH37du/ChChjjCZMmKDatWtLkpYtW6a//e1vHqcCAAAAQgMFHKikDh06qG/fvpKkoqIivfHGGx4nCk1t2rTRI4884pyPGzdOP/30k4eJAAAAgNBAAQdc8N2M7T//+Y+stR6mCV133nmnunfvLknKy8vTddddp6KiIo9TAQAAAN6igLtQp04dryPAYyNHjnT+HPzwww9atGiRx4lCU0xMjP7zn/8oJiZGkjR//nw999xzHqcCAAAAvEUBdyElJcXrCPBYYmKiRo4c6Zz/+9//9jBNaOvataseeOAB5/y+++7T6tWrPUwEAAAAeIsCDrj0m9/8xjl+6623lJ2d7WGa0Hb//ffrlFNOkSTl5OTo+uuvV3FxscepAAAAAG9QwAGX+vbtq06dOkmSsrOzNXnyZI8Tha64uDi98sorio6OliRt27aN3eMBAABQY8V4HQAIN8YY3XDDDbrrrrskSS+++KKuv/56j1OFrrS0NN13330qKirSQw89pFq1ankdyZX33ntP27Zt0759+3TnnXcqISGh1Pu/+tWvtH37duXl5WnevHlKTk4u9X6PHj2Uk5OjWrVq6bPPPlNqamqp9//0pz8pNjZWycnJuuaaa8Lu3w8AAAAqz7CLc+UYYzLq1avXff/+/V5HQQjYvXu3mjVrpvz8fElSZmamTjvtNI9ToSoee+wxLVu2TGvXrtWUKVPUqlWrUu+3adNG69atkyStXr1abdu2LfV+s2bNtHXrVknS5s2b1axZs1Lv16tXTwcOHJAk7dmzp1RBt9aqdu3aysvLkyQdPHiw1GaP1lq1adNGKSkpat68uaZOnaq4uLhS1y8uLlZUFIuZAAAAqistLU2ZmZmZ1tq0QI3B/9fmAvf64ogGDRro0ksvdc5feuklD9PgeGbPnq2nnnpKo0eP1po1a8q8P23aNL377rtatGiRNm7cWOb9pKQk53jv3r1l3vedsc7NzT1ultq1a5c6z8nJccp3XFxcmff37t2r9evXa8mSJZo9e3aZ8p2dna26deuqS5cuGjlyJI/FAwAACHEsQQeq6IYbbtBbb70lSXrjjTf09NNPq27duh6nCg/WWr311lsaMGCAmjdv7pdr7ty5U3Fxcapfv36p15988knNmDFDkjR8+PAyM9ht27ZVZmamJDkz2b4uvfRS9enTR8nJyWWWj0vS1KlTZa1VfHy8WrRoUeb9jIwM5eXlKTc3V/Hx8WXe/8tf/qI9e/aosLBQxphS723evNk5Lu/f0+rVq5Wbm6sffvih3O9v3LhRV199tU4++WT16tVLo0aNKnMNAAAABA8FHKii/v37q0OHDvr555914MABvfvuuxozZozXsULepk2bdOONN+rjjz/WsGHD9OGHH5Ypjm48++yzGj9+vNauXasJEybopptuKvX+ySef7BTwFStWlHqMnFTyFynDhw9XmzZtnB3bffk+Sq08Fd16cOKJJx7zvTp16ui+++475vudO3fWxo0btXnzZud2B19HlsZLUvv27cu8v2zZMqWnpys9PV3Lly8vU8C3b9+ulStXqnv37qpXr95xfw8AAABUHwUcqKIjm7H9/ve/l1SyGRsFvGKrV6/Wxx9/LEn66KOP9Prrr2v06NEVfm/37t3KyspSmzZtSr2en5+vtWvXSpK+/fbbMgV80KBBOnTokE4++WT179+/zHUHDx5c1V8l4KKjo9WiRYtyZ9Yl6YILLtC+ffu0evXqcv8SY8WKFc5xeX+58Mknn+i6666TJN188816/vnn/ZQcAAAA5eEecKAarrnmGue+3G+++UbLli3zOFHoO+uss3TzzTc757feeqs2bNhwzM8vWLBAffv2VaNGjXTvvfeWef/ss8+WVHIPdXmzxEOGDNHzzz+vm266SV26dPHDbxBa6tevr+7du5c7E3/NNddo+vTpevzxx3XRRReVeX/RokXOcXlL3N9//309/PDD+uKLL5yN5AAAAFB1FHAXqrNMFpEpNTVVF198sXM+YcIED9OEj6eeekrt2rWTJGVlZem6665TcXFxuZ9NTEzUvHnzVFxcrBkzZqigoKDU+6eddprmz5+vAwcO6M033wx49nDSpEkTDRs2TPfee68GDhxY5v2WLVuqa9euio6OVo8ePcq8/+abb+rRRx/VueeeqzfeeCMYkQEAACIajyGrJGNMRnR0dPfCwkKvoyDEzJkzR2eddZYkqW7dutq8eXOZjcBQ1rx589S/f3+neA8YMEAHDhzQN998o5iY/90dY61V69attXHjRvXq1UvvvPOOWrZs6VXsiJSTk6Po6OhSu6xba9WsWTNt27ZNkvTdd9/p1FNPLfW93//+94qPj9fAgQN15plnlrvJHAAAQLgIxmPIKOCVRAHHsVhrdeqppzr3244fP1633nqrx6nCw3333acnnnii1GtffvllmdnahQsXqm3btmrYsGEw49VoRUVFeu+99zR37lwtXbpU6enpio6Odt7Pz89XSkqKDh48KKn8Z6QDAACEE54DDoQBY0ype5onTJjA85iPIScnR/v27XPOx40bV2ZWddq0aWW+17NnT8p3kEVHR+uKK67Qc889p7lz55Yq31LJ/eNHynfr1q3LlO/c3Fz97ne/0/Tp053PAQAA1HQUcMAPRo0apcTEREnSjz/+qJkzZ3qcKLSsWrVKt9xyi5o2baqnn37aeT0+Pl6TJk0qVe4aNWrkRUS4dMopp2jq1Km6+eaby93Ffs6cOXr++ec1YsQI9erVy4OEAAAAoYcC7sKRggUcLTExUddcc41zzuOcSsvIyNCECRO0f/9+vfrqqyoqKnLe69q1q/785z8756+88opycnK8iAkX6tWrp4svvljPP/+8HnnkkTLvf/rpp85xeRvA/fLLL/rmm2+OufkeAABAJKKAu1CvXj2vIyCE+T5/+oMPPtDGjRs9TOOd3NzcMq9dcsklatasmSSpdu3aZR479oc//EF9+vTRlVdeqSVLlqh27dpByYrAufLKK3XPPffolFNO0fnnn1/m/eeee069e/dWy5YtNXnyZA8SAgAABB8FHPCTzp07O8+kLi4u1osvvuhxouDauXOnHnzwQTVr1kyrV68u9V5sbKzGjx+vmTNnatWqVWrTpk2p96Ojo/X555/rzTffVHJycjBjI0BOP/10PfHEE1q2bJkGDx5c6j1rrd5//31J0pYtW5SSklLm+8yMAwCASEQBB/zolltucY5ffPFF5eXleZgmuEaNGqXHHntMe/fu1XPPPVfm/UsuuURnn322jDHlfr9u3bqBjgiPHP3f/ODBgxo0aJBSU1NVv359DRgwoNT71lp1795dl19+uaZNm6b8/PwgpgUAAAgcCjjgRyNGjFDz5s0lSTt27NC7777rcaLgueuuu5zjefPm+WUn+E8++aTUrumIDAkJCfr3v/+trVu36ptvvin1/HFJ+v777/Xdd9/p3Xff1dVXX62CggKPkgIAAPgXBdyFPXv2eB0BIS42NrbUI8meffbZiHsk2fbt2/XKK6+Uef3cc8/V6NGj9e6772rBggXHnOmujEOHDummm27S0KFDddNNN0Xcv0OUiImJUadOncq8Pnv2bOd4+PDhZVZHbN26VV988YUKCwsDHREAAMCvKOAusDMzKuOGG25QrVq1JEmZmZmaN2+ex4n8o7i4WA8++KDatm2r6667TpmZmaXeN8botdde08iRI8s8M9qtmTNn6oUXXpAkTZ48Wa+//nq1rofw8rvf/U4rVqzQH//4R40dO7bM+2+88YbOPfdcNWvWjCcOAACAsEIBB/wsNTVVo0aNcs6fffZZ78L4UVRUlL7//nsdOnRIkvTAAw8EbKxhw4bpuuuuc85vueWWMhu7IbJ16dJFjz76aLmPMDuya/rOnTvZMR8AAIQVCjgQALfffrtz/P7772vdunXehfGjP//5zzLG6NRTTy214Vwg/OMf/9CJJ54oScrOztZVV13FvcBQYWGh+vfvr2bNmqlWrVq69NJLy3zm/vvv1yuvvKKsrCwPEgIAABwbBRwIgJNPPtmZuSsuLg67ZbIrVqzQ/fffX+be6y5dumju3LlasmSJhg0bFtAMCQkJeuuttxQTEyNJWrhwoR599NGAjonQFxMTo7///e/asGGDFi1apHr16pV6f9u2bXryySd13XXXqWnTpuzdAQAAQgoF3IXqbCqFmueOO+5wjl966SVlZ2d7F6aSrLW644471K1bNz3++OP68MMPy3ymT58+iooKzv/q6NGjh/785z8753/5y1/09ddfB2VshLbo6GidfPLJZV5/6623nGeI9+jRo9xnjAMAAHiFAg4EyPnnn6/27dtLkvbv36/XXnvN40QVM8aooKBARUVFkqR77rnHKTNe+cMf/qCzzz5bUslqglGjRvFoMhzTr3/9a/31r39V165dNXr06DLvT5s2TYMHD9bkyZOVm5vrQUIAAFCTGR7vUznGmIyYmJju3IMKN/75z3/qtttukyS1b99eP/74Y7V3CA+03bt368QTT9Rpp52mZ599VqeccorXkbRp0yZ17drVWU582WWXafLkyaxKwXEVFxeXWa1x3nnnacaMGZKkRx55RA899JAX0QAAQAhKS0tTZmZmprU2LVBjMAMOBNC1116r+vXrS5J++eUXffDBBx4n+p+CggK9/PLLzmz3EQ0aNFBmZqa+/PLLkCjfktSiRQu9/PLLzvlnn32m9evXe5gI4eDo8r179259+eWXzvnVV19d5jv8JSsAAAgkCjgQQImJibr55pud8yeffLLMxmZeWLx4sdLS0jR27Fg999xzZd5v3bp1yM0uX3TRRRo7dqz69u2r7777Tq1bt/Y6EsJMgwYNtGbNGj366KMaM2aM2rRpU+r9nJwctWnTRtdff70yMjI8SgkAACIZS9AriSXoqKpt27bphBNOUH5+viQpPT1d/fv39zTT/fffr8cff1ySVLduXf34449q0aKFp5kqIzc3V7GxsSG/jB/h6a233tJVV10lSWrVqpXWrFnDnzUAAGoQlqCHmCNLiQE3mjRpomuuucY5f+qppzxMU+Lhhx/Wqaeeqjp16uiRRx5RkyZNvI5UKbVq1aIQIWBmz57tHN9www1l/qwdfbsGAACAWxRwF+rWret1BISpu+++21nS/fHHH2vFihVBG7uoqMiZfT8iPj5eb7/9tpYtW6a7777bedZ2OJo/f365j0sD3Jo4caLmzZunq6++Wr/5zW/KvH/bbbdpwIABeuedd8r8zxSA/2fvvuOp7P8/gL+OGRkNIpRVQorQpEJDEqGlvffe3e1Ud3vdpbrbe4sKpT2UFkmKQiSkkOzt+v3h2/XrdNSt4lyH834+Hh45n891znn1/d5x3tdnEUIIqQgqwAkRgmbNmsHFxYV9vHHjRqG87/v372Fra1vuTs/GxsbQ19cXSo6qUFpainXr1qFTp04YMmQIYmJiuI5Eqjkej4cOHTrgyJEjArNCsrKycOTIEdy5cwfu7u548OABRykJIYQQUp1RAU6IkMybN4/9/vjx40hISKjS94uIiICpqSnu3buHDRs21LiCIScnB//++y9KSkqQlZWF/v37o6CggOtYpIa6f/8+8vLyAACGhobo3LmzwDW0pwohhBBC/gsV4IQISbt27dCxY0cAQHFxMbZu3Vql72dgYABTU1MAZSN7oaGhVfp+wqaoqIgzZ85AWloaABASEoK5c+dynIrUVD169MC7d++wfPlyLFiwQOCUgCdPnqBVq1Y4cOAAW6gTQgghhHyPdkGvIB6PFywvL2+ek5PDdRRSjfn6+sLJyQkAoKCggPfv36NOnTpV9n5JSUlwcnLCP//8Aysrqyp7Hy5t27YNM2bMYB97eXnBzc2Nu0BELA0bNgxHjx4FULaB27///stxIkIIIYT8KtoFXcTQpjvkT/Xs2RPGxsYAgOzsbOzevbvSXru8jd00NDTw9OnTGlt8A2UbY327vn7UqFGIjY3lLhARO7m5ubh06RL7eMyYMRymIYQQQogoowKcECGSkJDgmya9bds25Ofn/9FrFhUVYebMmWjZsmW5u4F/P1W2puHxeDhw4AC0tbUBABkZGRgwYADdMCNCIy8vj5iYGKxfvx4DBgxA69at+foZhkH//v1x8ODBP/73TgghhJDqjaagVxCPxwuWlpY2pw/15E8VFhZCV1cXSUlJAMqOPho3btxvv95ff/2FtWvXAgCUlJTw5MkTGBgYVErW6uTRo0ewtrZGcXExAGD69OlVvs6ekIq4du0aunfvDgDQ0dFBVFRUtT76jxBCCKmpaAo6ITWQjIwMZs6cyT5es2YNioqKfvv1Zs+ezY7+2traChyfJC7atm2LdevWsY+3bduGM2fOcJiIkDLfLjVxcnKi4psQQggRY1SAE8KBCRMmoH79+gCAuLg4HD9+/LdfS0VFBefPn8fq1atx/vx5KCkpVVbMamfmzJno3bs3gLIbHbm5uRwnIgTYu3cv1q9fD11dXUyfPl2g//z587h69SodY0YIIYSIAZqCXkE0BZ1Utr///huLFi0CADRp0gQRERH/OTJWXFyMN2/esBu5EUEZGRno27cv1qxZA0tLS67jEMJiGEZgT4aioiLo6ekhISEBJiYmOH/+PJo2bcpRQkIIIUS80RR0QmqwKVOmsEeQRUdH49SpUz+9PisrC71790b79u3x6tUrISSsnpSVlXHt2jUqvonIKW9DxLNnzyIhIQEA8OnTJzRq1EjYsQghhBAiRFSAE8IRJSUlvrXgq1atQklJyQ+vd3d3h7+/PzIzM9GrVy+kp6cLI2aNUVpaynUEQgS0b98eU6dORe3atTF58mTUqlWLr//jx494/fo1R+kIIYQQUtmoACeEQ9OmTWPXbL9+/Rpnz5794bWrV69G7dq1AQADBw6EsrKyUDLWBG/evIGFhQXu3r3LdRRC+Ojq6uKff/7B+/fvy10fvnnzZhgZGcHZ2RnBwcEcJCSEEEJIZaICnBAO1alTB9OmTWMfr1q16ocjtWZmZjh58iQOHTqE1atXQ0KC/vlWxK1bt9C6dWuEhoaif//+7PFvhIiSunXrCtxUy8rKwr///guGYXDp0iV2qjohhBBCqi/6BP8L6taty3UEUgPNmDEDCgoKAICXL1/C29sbAJCTkyNwrZOTE4YPHy7UfNVd06ZNISsrC6BsOm///v3/6Ng3QoQlPT0dHTt2BFD237GTk5PANV/PvSeEEEJI9UAF+C+Qk5PjOgKpgerXr48pU6awj1esWIEFCxagTZs2+Pz5M4fJagYtLS2cOnWKnTFw//59zJ07l+NUhPy3xo0b49KlS4iIiMDevXsFZr28fPkSjRs3xtq1a5GRkcFRSkIIIYT8CjqGrIJ4PF6wtra2eVxcHNdRSA2UkpICHR0dgXOrrayscPXqVcjLy3OUrOZYv3495s+fzz4+evQohgwZwmEiQv7MyJEjcejQIQDAgAED/vMkBUIIIYT8HB1DRoiYUFVVxcSJEwXaadlD5Zk7dy5cXV3Zx2PGjMHTp085TETI7ysoKMCdO3fYx9/uJUEIIYQQ0UUFOCEiYs6cOXxHENnZ2cHb25tGvysJj8fDoUOHYGxsDKCsgHFxcUFycjLHyQj5dbKysoiMjMTBgwcxcuRIdOjQga+fYRjMnz8fQUFBHCUkhBBCSHmoAP8Fnz594joCqcHU1dUxadIk9nFycjJ4PB6HiWoeJSUlXLhwAXXq1AEAJCYmok+fPigoKOA2GCG/QUZGBiNGjMCBAwcE+u7cuYP169ejQ4cO6N69+w9PVyCEEEKIcFEB/gtKSkq4jkBqmMTERCxYsID9b2vBggXsjuivXr3CyZMnuYxXIzVp0gSnT59mN7R68OAB/v33X45TEVK51q9fz36vq6tLxxYSQgghIoJ+IxPCkbi4OHTq1Anr1q3D2LFjUVpaClVVVcyaNYu9ZtmyZSgsLOQwZc3UvXt3tkCZP38+Jk+ezHEiQirX+vXrMXz4cMjKymLOnDkC/a9evUJeXh4HyQghhBDxRrugVxCPxwuWkZExp6mqpLIsW7YMHh4eAAApKSk8fPgQFhYWyMjIgJ6eHnsE2a5duzBhwgQuo9ZIDMPgwYMHsLKy4joKIVXm8+fPqFevHl9bcXExDA0NkZ2djVmzZmHKlCm01wQhhBAC2gWdkBpt2bJlGDVqFGRkZODt7Q0Li7J/58rKyliwYAF7nYeHB41UVQEej0fFN6nxvi++AeDs2bOIiYnBx48fsXbtWlpeRQghhAgRFeCEcERCQgJ79uzBo0eP0KtXL76+yZMno2HDhgCADx8+wNPTk4uIYqekpARbtmxBTk4O11EIqTI8Hg+ampoAyo4vU1RU5DgRIYQQIj6oACdESLKzswXaJCUlYWZmJtAuLy+PJUuWsI/XrFmDzMzMqown9tLT09GrVy/MmjULI0aMoF2jSY3l7u6OmJgY7N27F1OnThXoX7duHcaPH4+3b99ykI4QQgip2WgNeAXRGnDyJ968eQM7OzusWLECo0ePrtBzCgsLYWhoiNjYWABlU9aXL19ehSnF24kTJzB48GD28aJFi7Bq1SoOExHy+969e4fPnz8jKysLFhYWqF27NtvHMAy2bt2KwsJCFBQU8P1ZWFiIgwcPskfz9enTBxoaGnyvLSEhARkZGcjKykJGRgbDhg2DtrY23zXe3t6QlZWFgoIC2rdvD2lp6ar/SxNCCCF/SBhrwKkAryAqwMnvevv2LTp16oTExEQAwJ49ezB27NgKPffo0aMYNmwYAEBBQQGxsbFQUVGpsqzibtq0adi+fTv7+PDhw+z//oQIU0lJCVJSUtiv1NTUH/65ePFi9OvXj+/5pqamCAsLAwCEhISgVatWbB/DMJCUlERl/f6/e/cuOnbsyNcmJyeH/Px8AMCXL1+grKzM9sXExMDU1BQKCgqoU6cO6tWrx/dVv359gcdqampQU1ODjIxMpWQmhBBCyiOMAlyqql6YEFJGWVkZampqSExMhLy8PAwNDSv83EGDBmHt2rV49eoVsrOzsWbNGmzatKkK04q3zZs3Izo6GpcvXwYAjBkzBrq6ugLFBSF/KiEhAe/evUNCQgISExORkJDAfiUmJiIpKQnFxcUVeq2kpCSBNiUlJfb775ev8Hg8yMrKsgXyn5KVlRVo+/b4RAUFBb6+rKws5OTkICcnBx8/fvyl96pXrx7U1NSgrq4OdXV1qKmpYfXq1bSLOyGEkGqDCnBCqlj9+vVx/fp1uLq6YtmyZb9UzElKSmLVqlVwc3MDAOzYsQOTJ0+Gnp5eVcUVa1JSUjh16hSsrKwQHh6OoqIiuLq64tGjR9DX1+c6HqlGsrKyEBMTg5iYGBgaGqJ58+Z8/f3790dQUFClvdf3DAwMkJmZCUVFRdSqVUugf/r06WAYhm8quYyMDCQk/n9rGIZhwOPx+J53+vRpPHjwAI0bN4a9vT3U1NTYDd2+Ki0thZubG7Kzs1FUVARJSUm+/vL2w6ioz58/4/Pnz4iIiABQNh1+48aNfNdERkbC2toajRs3Rtu2bbFr1y6+/vz8fEhJSUFKij4CEUIIET6agl5BPB4vuGHDhubljTQQUhHlfZit6POsra3x4MEDAGUf3E+fPl3Z8cg34uLi0LZtW3z69AkAYGhoiKCgINSpU4fbYESkMAyD5ORkZGVlwcDAgK9v5syZ2Lp1KwBgxYoVWLp0KV9/v379cO7cuZ++/tfRXhUVFaiqqv7wT21tbdSvX79S/27lSUpKgq6uLju6ffPmTdja2v7y65SWliInJwdZWVn48uULPn/+jLS0NLa4/vYrLS0Nqamp+PjxIz59+iSwOaKamhqSk5P52q5evQp7e3sAgI2NDW7dusXXv2PHDsycORPa2trQ19eHvr4+mjRpwn6vp6dHI+qEECKmaAq6iKG1Z6Qivnz5gg8fPsDIyIiv/XeK76/P27RpE9q3bw8AOHPmDGbMmME+JpVPR0cHPj4+sLW1RUFBASIjI9G3b19cvnyZNpMSUzk5OXjx4gWeP3/Ofr18+RIZGRmwtbXFzZs3+a7/9t9/TEyMwOu1aNEC7969g5aWFvulqanJfq+hoQE5Obkq/3v9Ch6Ph5EjR+LgwYMwNzeHjY2NwDUlJSUCI97fk5CQgKKiIhQVFQU2ePuZkpISthhPTk5GcnJyuWeYx8fHs983atSo3P7i4mJ2hkJ5GjZsyBbkTZs2haGhIQwNDdG0aVP6LEAIIeSP0Ah4BfF4vGBtbW3zuLg4rqMQEZabmwt7e3u8evUK/v7+aNu2baW99oABA3DmzBkAQPv27XH//v3fLupJxZw6dQoDBw5kH8+ePVtguiupeT5//oynT5/i6dOnCA0NxfPnzxEVFfXDTcvU1dXx4cMHvrYHDx5g9OjR0NfXR7du3TB9+nRhRBeKpKQkpKWloUWLFnztjx8/xsCBA7FgwQIMHz6cs0K1pKQEHz9+xPv371G7dm2YmJjw9Y8fPx579uz5rdeWlJSEvr4+DA0NYWRkBDs7O3Tv3r0yYhNCCBEBtAu6CKECnFTEwIEDcerUKQBlGw9FRUVBXV29Ul47NjYWhoaG7PTPs2fPom/fvpXy2uTHPDw8sGzZMhgaGsLPz4/W39cweXl5ePbsGR4/fownT57g8ePHiI6OrvDzlZSUYGRkhDt37pS7GZk4cXZ2xqVLlwAAkyZNgqenJ8eJfiw3Nxdv375FTEwMoqOj2dHwmJgYxMXFlTuyXp7Jkydjx44dfG2XLl1CSkoKWrZsiebNm4vcTAZCCCE/RlPQCalm5syZg+vXryM1NRUrVqyotOIbAHR1dTF16lR2F/T58+fDyclJ7D/0V7UlS5ZAXl4eY8aMoTXgNUh4eDhGjBiB0NDQChVbEhISaNasGUxNTWFqagozMzO0aNECGhoaNBMFZbMGvu5TAZQV4KJMXl4eJiYmAqPjAFBcXIz4+Hi2MH/z5g0iIyMRERGBd+/e8V37/VIjANi1axd7ksLp06fRv39/vv6EhARoaGjwbXhHCCFEfNAIeAXxeLxgWVlZ88o6toXUXJGRkfD19cWcOXMq/bXT09PRpEkTfP78GUDZsVkzZ86s9PchpCZgGAZRUVG4d+8ehgwZwnezKiUlBQ0aNCj3edLS0jA1NUXr1q1hYWEBU1NTGsmsgOzsbOzatQuxsbHYuXMnX19paSn+/fdfDB48mO+ItOomJycHb968QUREBCIiItCvXz+0bNmS7xotLS0kJiYCACIiIviOniwpKYGioiIkJCRgYmICMzMzWFhYwNzcHCYmJnRDlRBCOEZT0EUIFeBEVGzbtg0zZswAANStWxfR0dGoV68et6HE0O3bt6GhoSGw+zURHe3atcOjR48AAPfv30eHDh34+o2MjBAZGQlDQ0O0bt0abdq0QZs2bWBqakqFUCXz8fGBq6sr6tSpg7/++gvz5s3jOlKVKC0txerVq/HixQtERkYiJCSE77izN2/eoFmzZuU+V1paGiYmJmxBbmFhgRYtWtCNH0IIESKagk6IiAsICEC7du2grKwstPecOHEiduzYgejoaKSnp2PlypXYsmWL0N6fACdPnsTw4cOhpaWFoKAgqKmpcR1JbH3+/Bm3bt2CiooKOnfuzNdnaGjIFuCBgYECBfjZs2ehpaVFSwuqGMMwWLlyJYCyUyJSU1M5TlR1JCQksGTJkh/2JycnQ1VVFSkpKQJ9RUVFePbsGZ49e8a2SUpKwtjYGBYWFrCwsEDbtm1hampKO7ETQkg1RiPgFUQj4OR7169fh4ODA4yNjeHn5wctLS2hvff58+fRp08fAGWjJi9fvkTTpk2F9v7i7NOnT9DT00NOTg4AwNLSErdv30bt2rU5TiYeGIZBaGgo/P39cfnyZQQFBaG0tBSurq44f/4837VHjx7F1KlT0bFjR4wcORJubm4cpRZvpaWlOHz4MP7++28kJiYiNjZW4KZVYWGhWBWVHz9+xPPnzxESEoKQkBAEBwfj7du3FXqurKwsWrVqhfbt22PTpk20BwEhhFQimoIuQqgAJ99KTU2Fvr4+MjMzAQAODg7w9/cX2vszDINOnTohMDAQAODo6AhfX1+hvb+48/X1Re/evVFaWgqg7H9/Hx8fvqmmpPJkZGTg2rVruHz5Mi5fvixw5BcA1KlTB6mpqXxnUBcWFkJSUvI/z6UmwlFcXIznz5/DwoL/M01eXh6aN2+Onj17Yt68eWjcuDFHCbmVnp6O0NBQBAcHs0X5mzdvfni9kZERXr16xdcWGxuLqKgotGnThmZ2EELIbxBGAU5bcBLyG1RUVPDPP/9ASkoKmpqav32m7O/i8XjYunUrO/Lh5+dHBbgQ9erVi2+TKT8/P0yaNOmH50STX5eYmAhPT09069YNKioq6NevHw4cOCBQfPN4PLRt2xaTJ0/G9zdIZWRkqPgWIVJSUgLFNwAcOHAAsbGx8PT0hI2NDXtjS9zUrVsXtra2mDNnDk6cOIHXr18jIyMDd+/exZYtWzBw4EC+YxDbtm0r8BqnT5+Gvb096tati8WLFwszPiGEkAqi4RpCftPw4cOhqamJBg0aCHX6+VcWFhYYM2YM9u7dCwCYMWMGunbtilq1agk9izgaP3483r9/j9WrVwMA9u7di8aNG9OH3j8QGRkJb29veHt748mTJz+8rn79+ujRowccHBxgb28PFRUVIaYkle3mzZvs9zNmzKDjub6hpKSEjh07omPHjmxbSkoKHj9+XO4u/g8fPmS/19XVFej/+++/ISkpCSsrK1haWtLvC0II4QBNQa8gmoJORFFKSgoMDAzw5csXAMDq1auxcOFCbkOJEYZhMGLECBw5coRtO3jwIEaMGMFdqGqEYRi8ePECp0+fhpeXF16/fv3Day0sLNCzZ0/07NkTrVu3ppHtGoRhGFy7dg07d+7EiRMnIC8vz9d//PhxtGzZEi1atOAoYfWxdOlS+Pv74/nz53j27BnfOecMw0BNTY3dAE5GRgatW7eGlZUVrK2t0aFDB9SvX5+r6IQQIhJoDbgIoQJcvDEMg4sXL8LJyUnkRmc8PT0xZcoUAIC8vDwiIyPRqFEjjlOJj8LCQjg6OuL69esAynYt9vb2hpOTE8fJRF9JSQk0NDTw6dMngT4pKSnY2NjA1dUVvXv3hqamJgcJCddSUlKgo6OD3NxcuLi44NChQ0I9daK6ysvLg6ysLN/vq58dgfaVkZERrK2tYWNjg86dO9O/O0KI2KE14ISIiB07dsDFxQX9+vVjd78WFePHj0fLli0BALm5uZgzZw7HicSLjIwMvLy8YGpqCqCsqOzfvz8SEhI4TiZaYmNj8fLlS742SUlJ9OvXj30sLy8PNzc3HD16FJ8+fcK1a9cwadIkKgLE2ObNm5Gbmwug7L8hJSUljhNVD3JycgI3i1VUVLBv3z6MHDnyh6dmREREYO/evRg8eDC0tLRgYGCAsWPH4vjx40hMTBRGdEIIqfFoBLyCaARcfD169AgdOnRgNwZavHgxe6atqLh79y7fGcg3b96Era0th4nET3JyMqytrREbG4vdu3dj7NixXEcSCU+ePMHMmTNx//59ODs748KFC3z9QUFB+OeffzBgwADY29tDTk6Oo6REFIWEhGDlypXw8fHB2bNn0bdvX77+vLw81KpVi47i+g0fP37EgwcPcP/+fQQGBiI4OBjFxcU/fU6TJk1gY2MDGxsbDBw4UORmhBFCyJ+iKegihMfjBWtpaZm/f/+e6yhEyIqLizFnzhxs27YNbdq0we3bt0WySBg8eDBOnDgBAGjevDmePXsGaWlpjlOJl7dv3yIsLAwuLi5cRxEZr1+/hqGhIYCyM+s/ffpExyORX/by5UsYGRkJFHzu7u5ITEzE4sWL0b17dyrE/0Bubi6ePHmCu3fv4vbt23jw4IHAyQJfaWtrIy4ujq+ttLSUCnJCSLVHU9BFDG36I56kpKSwdetWHDp0CD4+PiJZfAPA+vXrUbt2bQBlH1a/PSaLCIeenp7YFt/h4eGYM2cOvr9J2axZM7Rt2xaSkpLo1q0b0tLSOEpIqrPmzZsLFHeRkZE4c+YMAgMD0aNHD4ElDuTXyMvLo3PnzliyZAlu3LiBL1++4O7du/Dw8ICdnR3fjuk2NjYCz/f09ESTJk0wfvx43L9/X4jJCSGkeqECnJAKGj58OBo2bMh1jB/S1NTEkiVL2MdLly5FUlISh4kIAGRmZmLixIlIT0/nOkqly8nJwcGDB9G+fXu0aNECmzZtwrFjxwSu27NnD5KSkuDn5wd9fX0OkpKaKCgoCFJSZaep9uzZk2/Hb/LnZGVl0bFjx3IL8oEDBwpcf/v2bcTExGDPnj0ICQkR6BfX890JIeR7NAW9gng8XrC2trb591OuSM0UFhbGbmxWnRQUFKBly5Z48+YNAKBv3744e/Ysx6nEV0pKChwcHBAcHIwOHTrg6tWr7CyF6iw0NBR79uzB8ePHkZmZyddnaGiIV69e0VRgIhTx8fFYv349Bg8ejPbt2/P1BQYGIi4uDu7u7myhTqoGwzDQ1tZmZ8C8evUKRkZGfP3GxsbQ1NRE165d0bVrV7Rq1YpmFhJCRA6tARchPB4vuFGjRubx8fFcRyFVbP/+/RgzZgyWLVuGpUuXVrs1bbdu3YKdnR37+NKlS+jVqxeHicSXt7c33Nzc2Mc9evTAhQsXICMjw2Gq35OdnY2TJ09i7969ePLkiUC/tLQ0XF1dMXLkSNjb21MBTjjFMAw6deqEwMBA6Ovr48iRI+jQoQPXsWq0goICPHr0CIGBgfjrr7/4fgbExMSgSZMmfNfXrVsXdnZ2bEGur69PPzcIIZyjAlyE8Hi84Fq1apnn5eVxHYVUoSdPnsDa2hqFhYUAgE2bNmHWrFkcp/p1I0eOxKFDhwAAjRs3xsuXL6GgoMBtKDH1zz//YPr06ezjPn364NSpU9VmRC46Ohqenp44ePAgMjIyBPoNDAwwbtw4DBs2DKqqqhwkJETQ7du32ZMgpKWlERMTg0aNGnGcSnwdP34cQ4YM+ek12trasLe3h729Pbp06ULnvRNCOEEFuAihAlw8pKamwt3dHTdu3EDLli3x4MGDajllODU1FYaGhuyGV7NmzcKmTZs4TiW+li1bBg8PD/bxkCFDcPjwYZGdXVFaWoqrV69i+/btuHz5Mr7/PSErK4u+ffti7Nix6NSpE41aEZHz5csXbN++HVu2bEHfvn2xZ88evv6ioiIUFhZWy5/v1VViYiJu3LiB69ev4/r16/jw4cMPr5WUlESHDh1gb2+PHj16oFWrViL785IQUrNQAS5CqAAXH8XFxVixYgVGjhwJPT09ruP8tiNHjmD48OEAAAkJCTx9+hStWrXiOJV4YhgGs2fPxpYtW9i2sWPH4t9//xWp4jUjIwOHDh2Cp6cnoqKiBPqbNm2KiRMnYtiwYahfvz4HCQn5NVlZWcjPzxeYnXHw4EHMmzcPs2bNwuTJk6GkpMRRQvHEMAwiIiLYYvzWrVvIzs7+4fWqqqro3r07evToge7du6NBgwZCTEsIESdUgIsQKsBJdcMwDLp27YqbN28CACwtLfHw4UPa9IYjDMNg0qRJ2L17N9s2bdo0bN26VSSK8PXr12PlypUCH4J5PB569uyJKVOmoHv37jQKRaq9kpISGBoaIjo6GgCwbt06zJs3j+NU4q2oqAgPHz5EQEAArly5guDg4B9e6+rqivPnzwsxHSFEnNA54IQIQW5uLtcRqgSPx8Pu3bshKysLAHj69Cl27NjBcSrxxePx4OnpiWHDhrFt//zzDxYtWsRhqv8nKyvLV3wrKytj5syZePPmDXx9fdGjRw8qvkmNEBcXh6KiIgBAnTp1MGHCBI4TEWlpaXTs2BGrVq3C06dP8fHjRxw7dgxDhgwRmL3Qo0cPged7enpiz549ePfunbAiE0LIb6MR8AqiEfCa6dmzZ7C3t8fu3bv5dquuSVatWsWeD66goIBXr17RZkQcKi4uxqBBg9jj4czNzXHv3j3Iy8sL5f1LS0sRFBQEKysrvvasrCw0btwYDRs2xLRp0zBkyBDauI/UWEVFRTh27BgKCgoECvAvX77g77//xowZM6ChocFRQvJVaWkpQkNDceXKFQQEBODIkSPQ1tZm+xmGgaamJrum/PHjx2jdujVXcQkh1RxNQRchVIDXPBkZGTA3N8fbt28BANu3b8eUKVM4TlX5CgsLYWZmhoiICABAz5494evrKxLTnsVVYWEh+vbti9TUVPj7+6NOnTpCed+jR49izZo1iIiIKPdDalRUFPT19Wmkm4i1rzctZWRksHz5cvz1119cRyI/ERYWBlNTUwBlR5t9+vSJ75SJ9PR0+Pr6wsHBASoqKlzFJIRUEzQFnZAqlJSUhNLSUgCAoqIiunXrxnGiqiEjI8O3A7C/vz+OHDnCYSIiIyODM2fO4OrVq0IrvgHA19eXvRFT3q74TZs2peKbiLXs7Gx2s8TCwkJoampynIj8F3V1dWzduhX29vZwdXUVOOLx8uXLGDZsGBo0aIAOHTpg9erVCA0NFTjdgRBChIVGwCuIRsBrpvT0dIwcORKDBg1C//79uY5TpaZNm4bt27cDKFvf+/LlS/pwKYJev36NZs2a/fHrlJaWChTTz58/h5mZGRQVFTFhwgSsW7eOZkIQ8g2GYeDv74+VK1fi06dPeP36NaSlpfmu+fjxI9TU1DhKSH6GYRiBn2mDBg3CyZMnBa7V1NREz5494ejoiK5du9KRdIQQADQCXiV4PJ4sj8fbyOPxSnk8ng3XeQi36tatC29v7xpffAPAmjVr2GPVMjIyMH78eBoBEDEHDx6EsbExdu7c+duvkZ6eDg8PDzRr1gxZWVl8faampjh58iTi4+Oxfv16Kr4J+Q6Px4OjoyOCgoLw4MEDgeI7Li4OjRs3Rr9+/RAaGspNSPJD5f1M69ChAzp06CBwQzIxMRF79+6Fi4sL6tWrhx49emD79u3ssjRCCKkq1W4EnMfjNQCwBYDl/5peAJjBMExCBZ5rAuDY/x6aArBlGOZ2Bd+XRsBJtXfnzh3Y2Niwjw8fPsy3KzfhzoULF+Dq6sreFNmxYwcmT55c4ed/+fIFW7ZswdatW5GZmQmAjlcipLJNnDiRPUrQxsYGt27d4jgRqai0tDRcuXIFfn5+uHLlCtLT0394raGhIXr16gVnZ2e0b99eYFo7IaTmohHw7/B4PBkA1wDIAGgOwBhADoBbPB6vItv1LgQwH8DW33n/Bg0a/M7TiIgoLS3FtGnTEB4eznUUznTu3Jlvo7np06cjKSmJw0TkKxsbG7Rp04Z9PGXKFHh6ev7n8zIzM7Fy5Uro6OjAw8ODLb4BwMfHh2Y5EFJJGIZBWloa+3jx4sUcpiG/qn79+hg8eDBOnDiBT58+4d69e5g/fz5MTEwEro2MjMTGjRvRqVMnqKurY/jw4fDy8kJOTg4HyQkhNU21KsABDAfQEsB8hmGKGYYpQVlBrQdgYgWeP4xhmIDffXOarlm9rV+/Htu3b0ebNm3EehOyNWvWQFdXF0DZqClNRRcNysrKCAgIQLt27di2nxXhWVlZ+Pvvv6Gjo4OlS5ciIyOD7TM0NMTRo0dx9+5d+rlFSCXh8Xg4c+YMnj17hkWLFsHOzk7gmgULFuDatWv0M1XESUlJwdraGmvXrsWLFy8QFxeHnTt3wtHREbVq1eK7Ni0tDUeOHEHfvn0RGRnJUWJCSE1S3QrwPgDiGYZhF+gwDJMM4NX/+n6KYZjiKsxGRFhqaipWrVoFAMjLyxPrUXAFBQUcOHCAfezr64vjx49zmIh8paysjCtXrggU4Tt27GAf5+TkYP369dDV1cWiRYv4plEaGBjg+PHjCA8Px5AhQ2jaJCFVwMzMDKtWrRK4ufX48WOsW7cO3bt3h5WVFYqKijhKSH6VtrY2Jk6cCF9fX3z+/Bm+vr4YP348GjZsyF6joaEBc3NzvuclJyfDw8ODdlUnhPySarUGnMfjJQF4wzCMzXftFwF0YRimQltY8ni8EQAO4hfXgMvIyJiXN1UJAIKDgyvyMoRDL168wMCBA1GnTh3cunVLYHMdcfPt6GrdunXx4sUL2hVdRGRmZsLe3h4PHz5k27Zs2QI5OTksX74cycnJfNfr6+tj2bJlGDhwIBXdhHDE1dUVPj4+AMp23qYbm9VfaWkpQkJCcPHiRcjLy2PBggV8/Xv37sW4ceMAAP3798fp06e5iEkI+Q0WFuUv8Y6IiEBeXl6VrgGvbp/UVACUV+lmApDn8XhyDMNU2S5p1elmBRHUokULPHnyBJmZmWJffAPA2rVr4efnh7i4OPY4titXrtA50CJASUkJAQEBfEX4zJkzBa77Ov186NChVHgTwrGtW7dCQ0MDBw4cwKJFiwT64+LioKWlRf9WqxEJCQlYWlrC0tKy3P6LFy+y3387c+mrZ8+eQVtbG/Xq1auyjISQ6qe6jYAXAghgGMbpu/ZjAAYDkK9IAf67I+BycnLmubm5v5ybEFF1584d2NrasjeXtm7diunTp3Ocinzl6+sLd3d3gY1/NDU1sXTpUowYMQIyMjIcpSOElOfLly+oU6cOX1tpaSlatmyJnJwczJ07F6NGjRJYa0yqn/Pnz8PLywv+/v54+vQp9PX1+fqbNWuGmJgYdOzYEc7OznBxcWH3YCGEiCZh7IJe3QpwTqegUwFevcTGxqJevXpQVlbmOopIW7BgAdatWwcAkJWVxZMnT9CiRQuOU4m3uLg4TJw4EVeuXOFrr127NpYsWYKpU6dCXl6eo3SEkF914cIFuLi4ACjbhyM+Ph5169blNhSpNMXFxQIzG16/fg1DQ0OBa1u2bAlXV1e4uLjA1NSUNsokRMTQMWSCwgDolNOui7LzwAkBAOTn58PFxQVmZmZ862iJIA8PD5iZmQEACgoKMHjwYOTn53MbSswpKCjg/v377GNZWVn06dMH8fHxmD9/PhXfhFQzGRkZqF+/PoCys8Sp+K5ZyltWkJ6ejrZt2wq0h4WFYcWKFWjVqhX09PQwc+ZM3L17FyUlJcKISggRAdWtAD8PQJvH4+l8beDxeGoAjAB4fXshj8dT4/F41e3vRyrJ3LlzERYWhri4OHTr1o1vp2jCT0ZGBidOnGCnQ7548YLOt+WYiooK5s2bBwkJCYwaNQpRUVE4d+6cwDrCz58/04c2QqqBYcOG4d27d9iyZUu5+zns2LEDM2bMQEJCAgfpSFVo164dHj58iKSkJOzduxe9evWCrKws3zVxcXHYunUrOnfuDHV1dYwePRq+vr50E5yQGq66TUGXAfAUQATK1nyXAtgPwBpAK4Zhsv93nRWAuwD2MAwjcD44TUGv+c6ePYuxY8ciIyMDu3btwoQJE7iOJPI8PT0xZcoU9vH169fRpUsXDhPVfCUlJTh06BDev3+P5cuX8/Xl5OQgLi4OzZs3L/e5aWlpsLGxgYmJCY4cOUIbCxJSTeXn50NXVxfJycmQlpbG9evX0alTJ65jkSqQlZWFK1euwMfHB76+vsjMzCz3utq1a8PBwQEuLi5wdHQU2FOAEFJ1aA14Of434r0FgCUABkA4gBkMw7z/5hpTALcAbGUYxuOb9gEA/gJQD0AjADEAsgFMYhjmwX+8LxXg1UxcXBwOHDiAFStW0BqrCmAYBj179mTXHWtqauLFixc0VbKKfP78GV26dEFoaCgkJSURFhYGY2PjCj03OzsbNjY27PGHvXv3xunTpwVGVwghou/EiRMYPHgwgLKzpt++fUv/lsVAYWEhbt++DW9vb1y4cAEfPnwo9zopKSksWLAAK1euFHJCQsQTrQEvB8MwHxmGGcQwjAHDMM0YhunzbfH9v2ueMwxT79vi+3/tpxmGMWMYpjHDMDyGYZr87/FPi29SPeno6MDDw4OK7wri8Xg4ePAgVFRUAACJiYkYN24cHb9XRerWrctOKS8pKcHatWsr/Fx5eXm+I28uXLgAJycnZGdnV3pOQkjVGjhwIPz8/GBtbY05c+YIFN8fPnxAYGAgR+lIVZGRkUH37t2xa9cuJCQkICgoCPPmzUPTpk35risuLkajRo0Env/582dhRSWEVLJqNwLOFRoBJ+LCx8cHrq6u7GOawl85GIYRuBkUFhYGKysrzJkzB3Pnzv2lzdUYhsH8+fOxYcMGtq1Nmzbw8/Njb6IQQqqXkpISSEpK8rXNmjULW7ZsQceOHbFu3Tq0b9+eo3REGBiGQUREBLy9veHj44OQkBAkJiZCXV2d75rGjRtDUVERrq6umD9/PpSUlDhMTUjNQVPQRQgV4KLtzZs3WLhwIXbs2MH3S4r8nokTJ2L37t0AynbgfvjwIbtTOvk1paWlOHr0KPbt24cbN24InNudmZn52x+cGIbBqlWrsHTpUrbN0NAQV69eLXfEhBBSvaSmpkJbWxtfP3v4+vrC0dGR41REmD5+/Ag1NTW+tuDgYFhaWgIom0318eNH2geEkEpCU9AJqYCioiIMHToUXl5eaNGiBa5du8Z1pGpv8+bNaNmyJYCyo8n69++PrKwsjlNVP2FhYejUqRNGjBiBwMBA7NixQ+CaPxm14PF4WLJkCXbu3MmOrkdGRsLKygqRkZG//bqEENFQVFQEd3d3SEtLo2XLlujZs6fANXQSQs32ffENlP2cl5OTAwD06tVLoPj28/PD2LFjcfnyZRQWFgolJyGk4qgA/wUSEvQ/lyi6efMmHj9+DKDsrFVVVVWOE1V/cnJyOHPmDGrXrg0AiIqKwoQJE2g9eAVlZGRgxowZMDc35zvP++DBgygtLa3095s4cSJOnTrFfgh7//49rK2t2X8XhJDqqWHDhti/fz9iYmJw4MABgWUsoaGh0NXVxebNm+kmqRgZPHgwUlNTcf78eUydOlWg/9ixY9i3bx969uyJBg0aYMiQIfD29gbN4iRENNAU9Ari8XjB2tra5nFxcVxHIeW4ceMGhg8fjqlTp2L+/Plcx6kxjh8/jiFDhrCP9+3bh9GjR3OYSLQxDIMTJ05gzpw5SE5OZtulpKQwe/ZsLFmyhL2pURWuXbsGV1dX5OTkAAD69euHM2fOVNn7EUK45e7ujtOnTwMARowYgYMHD3KciHAtPz8fqqqq5W7KKS8vDwcHB7i5uaFXr160bpyQctAacBFCBbjo+/LlCxQVFQU2sCF/ZvTo0Thw4ACAspHxx48fw8TEhONUoufly5eYPHky7ty5w9duZ2eHHTt2wMjISCg5Hj9+jJ49e8LAwADXrl2r0oKfEMKd7OxsNGvWDElJSQDK1gWbm5tznIpwrbS0FA8fPsT58+fh5eWFH31ulZGRQdeuXdGnTx84OzvT5p2E/A8V4CKECnAirnJzc9GmTRu8fPkSAGBkZIQnT55QYfc/WVlZWLFiBbZt24bi4mK2XUNDA5s3b0b//v2FfhTe69evoaqqyh5zRgipmfLz83HkyBE8ffoUe/bs4etjGAZz586Fu7s7u2EXES8MwyA0NBReXl44f/48IiIiyr1OUlISnTt3hpubG1xdXaGhoSHkpISIDirARQgV4KIlNjYWjRo1gpSUFNdRxMKrV69gaWmJvLw8AMCgQYNw7NgxsT9j/eLFi5g8eTISEhLYNklJScyYMQPLli2DoqIih+kEXbx4Eb169aL9LAgRA1euXIGDgwMAwMnJCRcuXBD7n9niLiIigh0Zf/bs2Q+v69ChA9zc3ODm5gZdXV0hJiSEe7QLuogpKiriOgJB2YijnZ0drK2taadnITE2NsbOnTvZxydOnMD27ds5TMStDx8+oF+/fujduzdf8d25c2eEhoZi48aNIld8b9u2Db1794a7uzvy8/O5jkMIqWLr169nv9fV1aXim8DIyAiLFi1CSEgI3r59i40bN6JDhw4C1z148ABz5sxBhw4dqmTjUELEHRXgv+DLly9cRyAA5s6di7i4ODx69AhdunRBQUEB15HEwogRIzB27Fj28ezZs3Hv3j0OEwlfaWkp9uzZAyMjI5w7d45tV1VVxdGjR3Hr1i2RXB9///59zJw5EwBw9uxZdOvWDZ8/f+Y4FSGkKm3ZsgWDBg2CrKwsZs2aJdAfGhpKu2KLMV1dXcyePRv3799HYmIiPD09YWdnx7ePjouLi8CMqZCQEISEhNCpKIT8ASrASbXCMAwaN27MHre0YcMGyMrKcpxKfGzfvh2tW7cGABQXF6Nfv37sBkA1XWRkJGxsbDB+/HhkZGSw7SNHjkRkZCSGDBkisiNM7dq14zuqJjAwEFZWVj/cnIcQUv2Zmpri+PHjSEpKgra2Nl9fYWEhevXqBW1tbXh4eJS7YzYRHxoaGpg0aRJu3LiB5ORk7N+/H46Ojujfv7/AtStWrICFhQX09PRw8+ZNDtISUv3RGvAK4vF4wfLy8uZfj/ch3AoLC8OpU6ewevVqkS16aqr379/D3NwcqampAID27dvj9u3bkJGR4ThZ1Zo5cya2bt3KPm7SpAn+/fdf2NnZcRfqFzAMgy1btmD27Nlsm5qaGvz8/GBhUWXLnAghIujw4cMYMWIEgLKfA3FxcahVqxa3oYjIy8rKgqqqKjvzMCoqCk2aNOG7pqSkhE6jIdUarQEn5AdatmyJv//+m4pvDjRq1AinT59mp6UFBQWVO72xpvHw8GA3/lu4cCHCwsKqTfENADweD7NmzcLp06fZmyUfP35E586d4efnx3E6Qogw1apVix0Vnz59ukDxXVJSwkUsIuIyMzPRr18/KCsro2XLlgLFd1RUFNTU1DBq1Cj4+fnREkFCfoBGwCuIRsAJ4bdhwwbMmzePfXz48GEMGzaMw0SVJycnB0VFRahTpw5f+927d1GnTh20bNmSm2CV5O7du+jduze7r4WEhAS2bNmCqVOn0k0tQsREUVERzpw5g549e6Ju3bp8fXPmzMHz588xe/Zs2Nvb088FwqewsBAJCQnQ09Pja1+3bh0WLFjAPlZUVESvXr3Qp08f9OjRg44vJdUCHUMmQqgA505GRgbWr1+PhQsX0g9vEcIwDPr3789uRlarVi3cuXMHbdq04TjZn7lz5w5GjRqFdu3a4fjx41zHqTIRERFwcHDAu3fv2LaFCxdi9erVHKYihHAtIyMDjRo1QlZWFgDg2rVr6Nq1K8epSHXg5OQEX1/fcvvk5OTQo0cP9OnTB7169YKysrKQ0xFSMTQFXcTQHWBuzJ8/H3///TdatmyJwMBAruOQ/+HxeDhw4ACMjIwAAPn5+XBxcUFiYiLHyX7fy5cvYWNjg7dv3+LEiRPw8fHhOlKVMTIywqNHj9CuXTsAgKysLJycnDhORQjh2t27d/F1sMHQ0LBaLbUh3Lpw4QIePnyIuXPnCoyO5+XlwdvbG0OGDIGqqip69uyJ/fv3IyUlhaO0hHCHCnAi0p49e4Z///0XAPD27Vt8+PCB40TkW4qKirhw4QI7ffHDhw/o3bt3tT3apnnz5hg6dCgAoE6dOigqKuI4UdVSU1PDzZs3MXDgQBw6dIgtxgkh4svJyQnR0dGYPn06Fi5cKHAMVVhYGKZOnYqYmBiOEhJRJSEhgbZt22L9+vWIjo5GaGgolixZAmNjY77rioqKcPnyZYwZMwbq6uqws7ODp6dntb6BT8ivoCnoFcTj8YJr165tTkd1CBfDMDh06BBmzZqFzp07w9vbm2YiiKCbN2+ie/fu7MY9/fv3x6lTp6rl/1fp6emYNWsWVq9eDQ0NDa7jCAXDMOX+f5Wbmwt5eXkOEhFCRNXw4cNx5MgR8Hg8bNy4USw24SR/LjIyEufPn8f58+cRHBz8w+vat28PNzc3jBo1CvXq1RNiQkLK0BpwEUIFOLeSk5MBAOrq6hwnIT+ya9cuTJo0iX28YsUKLF26lMNEP3fz5k2sWLECFy9epLVo5YiKikKnTp2wdu1aDB8+nOs4hBARkJycjMaNG7Ozgx4+fIi2bdtynIpUN3FxcWwx/uDBA5RXiyQkJEBTU5ODdETc0RpwEUPnGnJHXV2dim8RN3HiRL4CfNmyZTh79iyHicqXk5ODyZMno0uXLrh79y7mzp3LdSSRk56ejl69eiE5ORkjRozAnDlzUFxczHUsQgjH1NTU4O/vD3t7e1hbWwsU3wzD4NixY6ANa8nP6OjoYNasWQgMDERiYiI8PT3RpUsX9nN2u3btBIrviIgILFmyBKGhoeUW7IRUJzQCXkE8Hi9YR0fHPDY2lusoNd6PpsMS0VdUVAQHBwfcuHEDQNmup/fu3YOFRZXdRPwljx49wtChQxEVFcW21atXD5GRkVBVVeUwmWhJSEhAz5498eLFC7atW7duOHXqFE0JJIQAKNtUS05Ojq/txo0b6Nq1K+rWrYvZs2dj0aJFHKUj1VFqaiouXryIunXrwtXVla9v6dKlWLlyJQBgypQp2L59OxcRiRigEXAiltavX49+/fqx085J9SEtLY2zZ8+iadOmAMo+oDk5OSE+Pp7TXEVFRVi2bBmsrKz4im9nZ2eEh4dT8f0dLS0t3L9/H87OzmzbtWvX0KZNG4SHh3OYjBAiKr4vvgFg06ZNAMpm0SQlJQk7EqnmVFRUMGrUKIHiGwDOnz/Pft+5c2eB/sjISJqpRaoNKsCJSImKisLy5ctx7tw5GBsbIywsjOtI5BfVrVsXly5dQp06dQCU7Yzu4OCAL1++cJInMjISHTp0gIeHB7tJnKKiIg4cOAAfHx80bNiQk1yiTlFREd7e3nzr+GNiYtCuXTt4e3tzmIwQIooYhoGjoyN0dXXB4/Ewc+ZMgWuio6PZn8OEVBTDMPDw8MCgQYOgrq4OBwcHvv7CwkK0b98eDRs2xJgxY3D58mUUFhZylJaQ/0YFOBEpvr6+yM/PBwDo6uoKHF1BqodmzZrB29sb0tLSAIBXr17B1dUVBQUFQstQWlqK7du3o1WrVnj69Cnb3rFjRzx//hwjR46kpQ7/QUJCAitWrICXlxdq164NoGwNvZubG5YvX47S0lKOExJCRAWPx8PkyZMRFRWFwMBANGnShK+/qKgItra2aNq0KbZs2YK8vDyOkpLqhsfjwc3NDcePH0dCQgL7++irW7du4cuXL0hNTcX+/fvRs2dPqKqqYsiQIfD29q62R6OSmosK8F/wtTAkVWfmzJm4fv06DAwMsH//fkhJSXEdifwmGxsbHDp0iH18+/ZtjBo1SiibpyQkJMDe3h7Tpk1j/93KyMhg/fr1uHXrFnR1das8Q03i5uaGoKAg6OnpsW0rVqxAnz59aDSLEMJHUlISHTp0EGg/f/48EhISEBsbi7Vr19INUPJbytsQOT09XWA2W2ZmJo4fPw43Nzeoqqqib9++OHnyJDIzM4UVlZAfogL8F2RlZXEdQSx06dIFr169gpmZGddRyB8aNGgQ1qxZwz4+ceJElW/Kc+rUKbRo0QLXr19n21q0aIEnT55g7ty5dJrBb/r6v2HXrl3ZtmbNmtH/noSQCsnKymI3cZw4cSJq1arF119QUEC7W5Pf4u7ujoSEBDx48ACzZ8+Gjo4OX39ubi68vLwwaNAgqKqqwsnJCQcPHkRaWho3gYnYo13QK4jOASfk9zAMg4kTJ+Lff/9l23bv3o3x48dX6vtkZWVhypQpOHLkCNvG4/Ewd+5ceHh4QFZWtlLfT1wVFxdj/vz5iIiIwKVLl6gAJ4RUWG5uLo4fPw4nJyeBo0Xnz5+PK1euYMaMGRg4cKBAgU5IRTEMg9DQUHh5ecHLywuRkZHlXicpKQlbW1u4ubnB1dWVjrslAISzCzoV4BVEBXjVeffuHRo1agQJCZqQUVMVFxfDxcUFfn5+AMrWFp8/fx69e/eulNd//PgxBg0ahJiYGLZNR0cHhw8fRqdOnSrlPQi/oqIido3/V1++fIG8vDxkZGQ4SkUIqY5ycnKgpaXFbtZ54cIFvlMYCPkTERER8PLywvnz5/Hs2bNyr+HxeLCyssLSpUvRrVs3ISckooSOISM1Xm5uLjp37gxra2va8bwGk5KSwqlTp9jzwEtLSzFgwADcvn37j163pKQEa9asgZWVFV/xPXToUDx//pyK7yr0ffFdUlKCfv36wdbWFomJiRylIoRUR8HBweyu1fr6+nB0dOQ4EalJjIyMsHjxYoSEhCAmJgYbNmxA+/bt+a5hGAaBgYEoKiriKCURJ1SAE055eHjg3bt3CAoKQvfu3YW6SzYRLgUFBfj6+kJfXx9A2Xo/Z2dnBAcH//ZrFhcX4/Tp0+zZn0pKSjh+/DiOHDkCJSWlSslNKmbZsmW4fv06Hjx4AHNz8z++uUIIER+dOnVCQkIC1q9fj2XLlgksbQkPD0fHjh1x+vRpKpDIH9HT08OcOXPw4MEDJCQkYPv27bCxsYGEhASUlJTQpUsXvutzc3PRpk0bLFu2DGFhYbRPAakUVIATTsnLy7MjaWvWrKF1ujWcuro6rl27xu5WmpWVhR49euD169e/9XqysrI4ceIE5OTk0L59e4SGhmLQoEGVGZlUkLKyMruM5NOnT+jatSs2bNhAH1YIIRVSt25dzJ07F0OHDhXo27ZtGwIDA+Hu7o6pU6dykI7URJqampgyZQpu3bqF5ORk+Pj4CHwOvXLlCp48eQIPDw+4u7vT7v2kUlAB/gvoH13lW7p0KcLCwjBr1iwMHz6c6zhECHR1dXH16lXUqVMHAJCamoru3bvj/fv3//nc/Px8gYLO2NgYd+7cwd27d+l4MQ7NnTsXN27cQIMGDQCUTUmfN28enJ2daadZQshvy83NxenTp9nH5RXohPwpVVVV2NraCrRfuHCB/d7NzU2g//bt27h79y4dyUl+CRXghHOGhobYtGkTbcImRkxMTODv7w95eXkAQHx8PLp3747U1NQfPicsLAytWrXi2039q9atW9OZ8SLAxsYGISEhfGcA+/r6wszMDIGBgRwmI4RUV/Ly8nj9+jWWLVsGBwcHgTPGGYbB4MGDcfDgQeTl5XGUktRUO3fuxNmzZ+Hu7o5+/foJ9C9evBidO3eGhoYGxo8fj6tXr9IyCfKfaBf0CuLxeMEKCgrmdBY4IZUnICAATk5O7C8rS0tLXL9+HcrKynzX3blzBz169EB+fj5q1aqF4OBgGBsbcxGZVEBRUREWLlyIjRs3sm2SkpJYuXIl5s+fTzfbCCGV5u7du+jcuTMAoHHjxoiJiaEbskQoPnz4AE1NTYGZeXXq1IGzszP69OmDbt26QU5OjqOE5HfQLuikRjp79ixyc3O5jkFEgL29PY4ePcou73j69CkcHBzw/Y2u1q1bo0mTJgDKjjB78+aN0LOSipOWlsaGDRtw6dIl1KtXD0DZlPSFCxdi69at3IYjhNQou3btYr93cHCg4psITXFxMcaPHw81NTW+9i9fvuDIkSPo3bs3VFVV0a9fP5w4cYI9Zo8QGgGvIB6PF1y3bl3zz58/cx2lWrt9+zZsbW2hq6sLT09PODg4cB2JiIA9e/Zg/Pjx7ONOnTrB398ftWvXZtsiIiIwatQoHDx4EIaGhlzEJL8hISEBAwcORGBgIIyMjPDkyRO+/18JIeRPpKWlYf/+/di5cycuXbqEFi1a8PUfOXIEWVlZGDZsGBQVFTlKSWqykpISBAUFsWeNx8fHl3udtLQ0bG1t4eLigt69e0NDQ0PISUlFCGMEnArwCuLxeME6OjrmsbGxXEeptgoLC2FqaorIyEgAQN++fXH27FmOUxFRsX37dkybNo19bGtrCz8/P76pWwzD0GaI1VBxcTE8PDzQv39/mJiYcB2HEFIDlZaWCixvKSkpQZMmTRAXFwdFRUXcuHEDrVu35ighEQcMwyA4OBheXl7w8vJCVFTUD69t27YtXF1d4eLigmbNmgkxJfkZKsBFCBXgf660tBQHDx7EvHnzUFRUhIiICGhqanIdi4iQVatWYcmSJezjHj16lHssCKkZGIaBh4cHhgwZwp4PTwghleXSpUtwdnYGANSvXx8JCQmoVasWx6mIuGAYBq9evYKPjw+8vb0RHBz8w2sHDBiAU6dOCTEd+RFaA05qFAkJCYwePRqRkZHw8vKi4pvwefLkCQ4cOMDXduXKFfTr1w+FhYUcpSJV6ciRI1i+fDnMzMxw5MgROjOcEFKpOnfujB07dsDQ0BAjR44UKL7fvXuHv/76CzS4QqoCj8dD8+bNsWjRIjx9+hTv3r3DP//8Azs7O0hKSvJda2pqKvD8uLg42lG9hqIR8AqiEXBCqgbDMNi2bRs7M6I8vXv3xunTp2kkvAbJzs6GtrY2vt1XY8CAAdi9ezd7RjwhhFQGhmGQl5fHHn351aJFi/D333+Dx+Nh8eLF8PDw4CghETdpaWnw8/ODt7c3AgICEBwcDCMjI75rzMzM8O7dO/Tq1Qtr1qyBlpYWR2nFC42Aixg6X5KQyvX582e4urpi5syZbPGtpKSEM2fOYP78+ex1Fy5cgJubG/Lz87mKSiqZgoICAgIC0LRpU7bt9OnTMDU1xb179zhMRgipaXg8nkDxXVhYiH379gEoK9DNzc25iEbEVP369TFs2DB4e3sjLS1NoPiOjY3F8+fP8eXLF5w5cwZKSkocJSVVgQrwX5CTk8N1hGqnoKAAc+fORXJyMtdRiIh5+vQpLCwscOHCBbbN0tISz549Q79+/bBmzRrMmzeP7fP394ezszMdYVeDWFpaIiQkBGPGjGHb4uPjYWNjg8WLF9PUO0JIlZGUlMSePXvQo0cPNGrUCL169RK4Zvny5bh58yYtjyFVqrxzwt+9e4fGjRsDALp27SpQgN+6dQudO3fG1q1bERcXJ4yYpBLRFPQK4vF4wQoKCubfn09Mfm716tVYvHgxlJSUsHHjRowdO5brSIRjDMNgz549mDZtGt/a7hkzZmDdunWQkZHhu3bp0qVYtWoV22Zra4tLly7RUVY1jJeXF8aOHYv09HS2rVWrVjhy5AjtnE4IqVLZ2dlQUFDga4uIiICxsTEAoHnz5ggJCeH7/URIVWMYBs+ePUNpaSksLS35+qZMmQJPT0/2sZmZGVxcXODq6ooWLVrQiTF/gKagixj6j/nXpKSkYPXq1QCAzMxMFBQUcJyIcC03NxfDhw/HhAkT2OJbWVkZ3t7e2LJli8CHGx6Ph5UrV/Kty7t16xYcHBxAN8Nqlj59+iAsLAy2trZs27Nnz2BhYQFfX18OkxFCarrvi28A2L17N/u9gYEBFd9E6Hg8HszNzQWKb4ZhcOnSJb620NBQLF++HKamptDX18esWbNw584dFBcXCzMyqSAqwEmVUVVVhY+PDwwMDGBqaooJEyZwHYlw6M2bN2jbti2OHj3KtpmamiI4OBguLi4/fe6SJUuwdu1a9vG9e/fQvXt3vtFSUv1paWnh+vXr2LRpE7vhXr169dChQweOkxFCxM24ceMwefJkKCoqYuLEiQL9586dw+bNm5GamspBOiLOeDweHj16hD179sDBwUHg5lBsbCy2bNkCGxsbqKmpYdiwYTh37hwNXIgQmoJeQTweL1hRUdE8MzOT6yjVTmFhIT58+ABtbW2uoxCOeHl5YeTIkXw//EeOHAlPT89y1z79yJYtWzBr1iz2cYsWLRAQEICGDRtWal7CvYiICAwfPhzLli2Do6Mj13EIIWIqOzsb8vLykJDgH7OytLREcHAwZGRk4O3tjZ49e3KUkIi7zMxMXL58GT4+PvDz8/thoS0jIwNbW1s4OzvD2dmZdlX/AWFMQacCvIKoACfk1xUVFWH+/PnYsmUL2yYrKwtPT0+MHj36t17T09MTU6ZMYR/r6enh2rVr0NPT++O8RLSUlpYKfOgFyv4b6NWrF93UI4Rw4tmzZ+yu6bKyskhKSkK9evU4TkVI2ebHN2/exMWLF3Hx4kUkJSX98Fpzc3M4Oztj5syZtMv6N2gNOCGk2kpMTIStrS1f8a2np4egoKDfLr4BYPLkyThy5AgkJSUBAG/fvoW1tTXCw8P/ODMRLeUV31evXsWUKVPQokULHDhwgHYnJoQIXdOmTbF37160bdsWffv2FSi+P3/+jH79+sHf3x8lJSUcpSTiSFZWFg4ODti1axcSEhLw9OlTLFmyBKampgLXhoSE8C35IsJDBTipVAkJCXBwcEBYWBjXUQjHbt68ifv377OPnZyc8PTpU7Rq1eqPX3vo0KHw9vZmf2l8+PABnTp1QlBQ0B+/NhFdRUVFGDduHAAgKysLo0ePRs+ePfHu3TuOkxFCxImCggLGjBmDhw8fYv/+/QL9R48exblz5+Do6AhXV1cOEhJStlbcwsICHh4eCA0NRVxcHLZv345u3bpBSkoKANCjRw+BAtzf3x/9+/fHsWPH8PnzZy6i13hUgJNKNXfuXFy5cgXm5ubYvHkz13EIh4YOHYrRo0dDQkICa9asgY+PD+rWrVtpr+/k5ISAgAAoKioCANLT09G1a1cEBARU2nsQ0SItLY2TJ0+iadOmbNuVK1fQvHlzbN++HaWlpRymI4SIo++LF4ZhsHfvXvZxeeeLE8IFbW1tTJkyBVevXkVqaipOnTqFadOmCVx39uxZnD17FkOHDqXP8lWE1oBXEK0B/2+xsbEwMDBgjzy4ffs2OnfuzHEqwqW8vDw8e/asSnexDgkJQY8ePZCSkgIAkJKSwr59+zB8+PAqe0/CrdzcXCxcuBD//PMP3xT09u3bY9++fezZvYQQwoXXr19j37598PLywvPnz9kbxV+NGTMGSkpKGDlyJFq0aMFRSkIElZSUQF1dnd3d//Hjx2jdujXfNTt37kSrVq3Qtm3bcpeKVXe0CZsI4fF4wSoqKuZfP+ST8r169QpTp06FmpoaTpw4wXUcIiSvX7/GkiVLcPDgQdSuXZuT9+/evTvi4+PZNg8PDyxevBg8Hk/oeYhwBAUFYcyYMXj16hXbJiMjg8WLF2P+/Pl0bi8hhFMMwwj8Dvr48SM0NTXZteFxcXG0oSQRGQzD4NWrV7h48SLu37+Pixcv8hXZHz9+RMOGDcEwDBo0aAAnJyc4OTmha9eunHz+qwpUgIsQHo8XrKOjYx4bG8t1FJHHMAzy8vIgLy/PdRQiBBcvXsSQIUOQlZUFd3d3nDhxgpOiNzExET179uTbf2DMmDHYtWsXu9aJ1DwFBQVYs2YN/v77bxQVFbHtkydPxo4dOzhMRgghgnbs2IGpU6cCAKytrXHv3j2+/uLiYvB4PHajUUJEyYEDB8rdSFdWVhY2Njbo1asXHB0doaury0G6ykG7oJNqicfjUfEtRlJSUtgzJ318fBAREcFJDk1NTdy7dw9du3Zl2/bt24fevXsjOzubk0yk6snKymL58uUICQlBmzZtAAC1a9fG3LlzOU5GCCGCJk6ciCtXrmDAgAEYP368QL+Pjw90dHSwaNEixMTEcJCQkB8zNjbGqFGjoKqqytdeUFCAgIAATJ06FXp6emjevDnmz5+Pe/fusUtTyf+jEfAKohHwHytvihURLxMmTEBAQADOnz9fKbuc/4nCwkKMGTMGR48eZdssLCxw6dIlNGzYkMNkpKqVlJRg+/btkJOTE/hgW1JSQiNKhBCR5+joCH9/fwDA0qVLsWLFCo4TESKopKQEjx8/xsWLF+Hn54cXL1788Nq6devCwcEBjo6O6NGjh8CxfaKGpqCLECrAy/fq1Sv0798f69evR8+ePbmOQ4SgtLRUYNONgoICZGdno379+hyl4scwDJYsWYLVq1ezbVpaWrh06RLMzMy4C0Y4s2DBArx+/Rrbtm1D48aNuY5DCCECcnNzoa+vj+TkZADA27dvBabyfm2jgQ8iSt69ewc/Pz/4+fnhxo0bKCgoKPc6CQkJWFlZwdHREX369EGTJk2EnPS/0RR0EZOTk8N1BJHCMAxmzpyJly9fwtHREYsXL+Y6Eqlip06dQocOHQSmdMvKyopM8Q2ULYNYtWoV/v33X/ZmQUJCAqytrXHhwgWO0xFhe/nyJTZt2gQfHx8YGRlhw4YNfOvFCSFEFMjLy+Pdu3fw9vbGokWLBIrv/Px8WFhYoGnTpvDw8PhhkUOIsGlra2PSpEnw8/NDWloaLl68iPHjx0NTU5PvutLSUty7dw8LFizA+fPnOUrLPSrAfwH9oOMXHx+Phw8fAii7o9WvXz+OE5GqUlxcjDlz5mDgwIF49OgRRo8ejeowe2bcuHHw9/eHkpISgLKbaK6urli/fn21yE8qR0BAALsGLTc3F/PmzUOrVq0ENj8ihBCuycjIwMXFBatWrRLo8/HxwZcvXxATE4OjR4/SSQ9EJNWuXRtOTk7YvXs33r9/j2fPnmHlypVo164d38wNR0dHgedOmTIFe/fuRVJSkjAjCx0V4OS3aWtrIyoqCuPGjcOECRNgamrKdSRSBVJSUtC9e3ds2rSJbQsNDWXPiBR19vb2CAoKgp6eHoCymRvz58/HqFGj6KaamJg1axbu3bsHExMTtu3ly5fo1KkTRo4cCTpekhBSHaSlpUFZWRkAMGTIEIFp6OHh4bh48SIKCwu5iEeIAB6PBzMzMyxevBhBQUFITk7GoUOHMGHCBBgbG/NdGxcXB09PT4wbNw76+vrIz8/nKHXVozXgFcTj8YKVlJTMMzIyuI4ikmgjtprp6dOncHNzw/v379k2Z2dnHDlyhP0QUF2kpqbCzc2Nb9TT2toa586dg5qaGofJiLAUFRVh27ZtWL58Od+Sorp162LdunUYPXq0wP4GhBAiSvLy8nDx4kW0b99eYD+LsWPHYt++fahfvz48PT0xYMAAjlIS8us8PT0xZcoUAICDgwO7GeFXwcHBiIyMhL29PVRUVKosB60BJ9UGFd81z9GjR2Ftbc0W3zweDx4eHvD29q52xTcAqKio4Pr16xg5ciTbFhgYCAsLCzx+/JjDZERYpKWlMWfOHERERMDNzY1tT09Px7hx49CmTRt8/PiRw4SEEPJzcnJyGDBggEDxnZeXh7NnzwIoGylv1KgRF/EI+W29evXC5s2bYWdnBxcXF4H+/fv3Y8iQIWjQoAHatm2LFStW4PHjxygtLRV+2D9EI+AVRCPg/y8vLw9ycnJcxyBVpLi4GAsWLOCbcq6srIwTJ07UiJ3uGYbBxo0bMX/+fHYduIyMDHbt2oVRo0ZxnI4Ik7+/P6ZMmYKvp1tYWlri0aNHNApOCKl2vnz5gvXr1+PYsWOQkZFBVFQU3+AIwzAYOHAgunTpgn79+qFOnTrchSXkFzEMA11dXbx7906gT0VFBfb29nBwcKiU0XE6hkyEUAFe5tmzZ+jevTuWLVuGCRMmQEpKiutIpBKlp6fD3d0dV69eZduMjY1x4cIFkTwq4k8EBARg4MCBSE9PZ9smTZqELVu20MY2YiQ3Nxdr167Fxo0bcePGDbRv357rSIQQ8ttKS0uRkJAgMEIeGBiIjh07AgAaNmyI9+/fQ1JSkouIhPyywsJCrF+/HpcvX8bDhw9/OOrN4/HQpk0bODg4wMHBAZaWlr98U50KcBFCBXjZ3afOnTuza2gnTZoET09PjlORyhIREQFnZ2dER0ezbc7Ozjh69Ci7i3hNExMTA1dXV7x48YJts7a2xtmzZ6Gurs5hMiJsaWlpAkfplZSUoF+/fhgyZAhcXV1pqQ0hpNoaP3489uzZw36/e/duvv7s7GzIyclRUU5E3ufPn3Ht2jX4+/vjypUr+PTp0w+vVVFRQY8ePeDg4IDu3btXaHSc1oATkZKcnIzExEQAgJSUFKZNm8ZxIlJZfH190bZtW77ie8mSJfD29q6xxTcA6OvrIygoCP3792fbAgMDYWZmhlu3bnGYjAhbeefY79+/H97e3ujTpw+6du2K8PBwDpIRQsifW7FiBTZv3oxWrVph6NChAv1r166FpqYmpk+fjoiICA4SElIx9erVw4ABA3D48GF8+PABT58+xcqVK9GhQweB0e7U1FQcO3YMgwcPRoMGDdCuXTusWLEC2dnZHKUvQyPgFUQj4GXy8/Oxbds25OTkwMPDg+s45A8xDIM1a9Zg8eLF7HpoeXl5HDp0SKzOdWcYBhs2bMBff/3FTmuSkJDA8uXLsWjRIloTLIZKS0vRvHlzREZGsm0SEhIYP348li1bRjvnE0Kqre9PrmEYBk2aNMHbt28BAOfPn4erqytX8Qj5bRUZHVdSUkJqaiqkpaXZtm//TdAUdBFCBTipaXJzczFq1CicPn2abdPW1oaPjw/MzMy4C8ahGzduYNCgQXw/sLt3745jx45BVVWVw2SEC58/f8ayZcuwa9culJSUsO0KCgqYP38+Zs2aBXl5eQ4TEkLIn0tISIClpSU+fvwIZWVlJCcno1atWnzX7N+/H3Z2dtDV1eUoJSG/prS0FM+ePcPly5f51o737duXPTHgq5MnT2Lt2rXo3r07fH19ERkZSQW4KODxeMFqamrmycnJXEch5I/Fx8fDxcUFz549Y9s6d+6Ms2fPin2hmZSUhEGDBuHOnTtsm4aGBk6dOsVuYEPES3h4OGbMmIEbN27wtWtoaGDVqlUYNmwYrZskhFRrJSUluH37NuLj4/mO6wSAqKgoGBgYACj7rHDz5k2aGUaqna+j4w0bNkSnTp34+kaMGIHDhw8DKNuk8MOHD7QGXFSI69FbaWlpXEcglezLly94/fo1+3jixIm4du2a2BffQFlRdf36dSxcuJBtS0pKgq2tLdatW1ctz5skf8bExATXrl2Dr68vjI2N2fakpCSMGjUKVlZWfCPkhBBS3UhKSqJLly4CxTdQNjr4lbKyMhXfpFr6unb8++KbYRjcvn2bfSyMvY/oXxD5qWfPnkFLSwuzZ8/mO66JVG8tW7bEkSNHIC0tjd27d2Pnzp18a2HEnZSUFFavXo3Lly+zm3OVlJRgwYIFcHJy+umOm6Rm4vF4cHR0xPPnz7Fnzx6+XfJtbW1pBJwQUmNZWFigZ8+ekJKSwsCBAwX6PT090b17d+zbt48GbUi1w+PxEB4ejkuXLmHWrFmoXbt21b8nTUGvGB6PF6yjo2MeGxvLdRShYRgGXbp0YXeDdnd357sLSqq/9+/fo1GjRlzHEGnv37+Hu7s7Hjx4wLY1aNAABw8eRM+ePTlMRriUnZ2NTZs24eDBg3j+/DmUlZX5+jMyMgTaCCGkOktNTYWCgoLA+nArKyv2d+S///6LcePGcRGPkEpBx5ARTmVmZqKgoABA2dSkpUuXcpyI/I6UlBQ4OTmVe4QSFd//rVGjRrh9+zbmzp3Ltn369AmOjo6YMmUK8vLyOExHuKKgoIBly5YhKipKoNCOiYmBhoYGpk6dCto3hBBSU6ioqAgU358+fcLDhw8BlH1WLG/39MuXL9PIOCHfoAL8F+Tk5HAdQaiUlZURGBiIM2fOYMWKFTAyMuI6EvlFL168QOvWreHr64vevXvTL8DfJC0tjfXr1yMgIIBv6rGnpycsLCwQGhrKXTjCqfKWbixfvhy5ubnYsWMH9PT08Ndff+Hz588cpCOEkKrVoEEDxMXFYfPmzZg2bZrAXjJpaWlwcnKCuro6HBwcUFhYyFFSQkQHFeC/QBx/aPB4PPTr1w+LFi3iOgr5TampqQCA2NhYXL16leM01Vv37t3x4sULuLi4sG0RERFo06YNNm7cSBu0ERQVFSE+Pp59nJeXh7Vr10JPTw+rV69GdnY2h+kIIaTyNWrUCDNnzsTmzZsF+nx8fFBSUoLi4mJ8+fIFMjIyHCQkRLRQAU5IDdaiRQscPXoUysrKuHDhQrmbp5Bfo6KigvPnz2Pv3r3sGdBFRUWYO3cuunXrhvfv33OckHBJWloat2/fhr+/P8zMzNj2jIwMLF68GHp6eti2bRvy8/O5C0kIIUJSr149tGvXDgDQv39/gf7Tp0+ja9eu2LlzJz58+CDseIRwgjZhqyAejxesrKxs/uXLF66jVLn4+Hg0btyY6xjkNzAMAx6PJ9D++fNn1KtXj4NENdubN28wePBgPH36lG1TUlLC5s2bMWrUqHL/vyDio7S0FF5eXliyZAnfsX9A2YjRwoULMXbsWNpBnRBS48XHx0NBQUHgs0jfvn3h5eUFAFi9ejXfEaCEcIE2YSNCFxsbCwMDA/Tp0wfR0dFcxyG/ICYmBu3atcPz588F+qj4rhoGBgZ48OABFi1axJ6LmpmZiTFjxqBHjx58U5GJ+JGQkEC/fv0QHh6OAwcO8N3YfP/+PQ4dOkTn6RJCxELjxo0FPosUFBTgypUr7GM3NzeB5507dw5hYWGgAUNSk9BvfsJnwYIFKCgowPnz5zF69Giu45AKun79Olq3bo3Hjx+jd+/e7LpvUvWkpaWxatUq3L17F02bNmXbr169ChMTE+zdu5c+OIg5KSkpjBw5Em/evME///yDBg0aAACWLVtGsyQIIWJLVlYWr1+/xo4dOzBy5EgYGhry9RcUFGD06NEwNTVFkyZN8PHjR46SElK5qAAnrOLiYr4dfdesWcNhGlIRDMNg27Zt6NGjB9LT0wEAycnJfFOiiXBYWVkhNDQUs2bNYouqrKwsjBs3Dvb29nj37h3HCQnXZGVlMXXqVLx9+xaHDh1Cjx49+PpLSkrQpUsX/PPPP3S8HSFELGhqamLy5Mk4cOCAQN/NmzeRmZkJoOzzztebl1+VlJSgqKhIKDkJqUxUgBOWlJQUjh07hkePHsHDwwMdOnTgOhL5ia93hmfMmIGSkhIAQMOGDXH37l2BD/ZEOOTl5bFp0yYEBgbCwMCAbb927RpMTEywe/du2imdoHbt2hg+fLjA6Pfp06dx8+ZNTJ8+HXp6eti6dStyc3M5SkkIIdxSVVXFwIEDoaioCDc3N4Gfmbdv30aDBg0wdOhQBAQEcJSSkF9Hm7BVkDhtwkZE34cPH+Dm5oaHDx+ybW3btsX58+ehoaHBYTLyVV5eHpYuXYrNmzfzFd1WVlb4999/0bx5cw7TEVFkZ2eHW7du8bWpqqpixowZmDRpEurUqcNNMEII4VBBQQFyc3NRt25dvvYpU6bA09MTADBjxgxs2bKFi3ikhqFN2AghAp48eQJLS0u+4nv48OG4ffs2Fd8iRE5ODhs2bEBgYCCaNWvGtt+/fx9mZmZYuHAhTTMmfPz8/PDPP//w/TtOSUnBokWL0LhxY8yfPx/JyckcJiSEEOGTlZUVKL4BICQkhP3e2dlZoH/Tpk1YunQpnj59SrPPiEihEfAK4vF4wXXq1DH/us62JomIiECzZs1oN95q4NixYxgzZgwKCgoAlO2yvGnTJkyfPp02cxJheXl5WLVqFTZs2MC3Xk1PTw87d+6Evb09h+mIqMnPz8e+ffuwfv16gXPlZWVlMXLkSCxfvhxqamocJSSEEO4xDIOQkBD4+fnhr7/+4tvHiGEY6Orqsvuv3Lx5E7a2tlxFJdUIjYCLGDk5Oa4jVLqUlBS0a9cObdq0wZ07d7iOQ36gpKQEc+fOxdChQ9niu27durhy5QpmzJhBxbeIk5OTw+rVq/Hs2TNYWVmx7W/fvkWPHj0waNAgGtkkrFq1amHKlCmIjo7GwYMH+XYGLigowOHDh+nscEKI2OPxeLCwsMDSpUv5im8ACA8PZ4tvZWVlWFtb8/UzDIOTJ0/i06dPQstLyFdUgP8CWVlZriNUuhUrViAzMxPBwcEYP348u5kXER3p6elwdHTExo0b2TYjIyM8fvwY3bp14zAZ+VXNmzfH3bt3sXfvXr71vCdPnoSRkRF27tyJ4uJi7gISkSIjI4MRI0bg5cuXOH/+PFq3bg0AGDt2LFRUVPiuzcnJoePuCCHkf/T09HD27FkMGzYMgwcPFijQX758iUGDBkFdXR0ODg4cpSTiigpwMaeqqopatWoBANavX0+jKiImIiICbdu25dvd08nJCQ8fPkSTJk04TEZ+l4SEBMaMGYPIyEgMHjyYbf/y5QsmT54MS0tL3L17l8OERNRISEjA1dUVjx49wo0bNzB37lyBa6ZOnYpWrVrhyJEjKCws5CAlIYSIjtq1a6Nv3744fPgwu1Hbty5evAigbCRcSUlJoD89PR1ZWVlVnpOIJyrAxdyyZcvw5s0b/P3333BycuI6DvmGr68v2rZti6ioKLZt8eLF8PHxKfeXBale1NTUcOzYMVy9ehX6+vps+/Pnz9G5c2cMHDhQYP0vEW88Hg92dnbQ0tLia09OTsbx48fx/PlzDB8+HDo6OlizZg0+f/7MUVJCCBFtenp66NixIyQkJMrdwM3T0xP169dH165dcfnyZQ4SkpqMCnCCRo0a4a+//qJ1xCKCYRisXbsWzs7O7N1XeXl5nDlzBitXrqTN8mqYbt26ITw8HKtWrYK8vDzbfurUKRgaGmL16tXIz8/nMCERdU+ePOGbvfThwwcsXLgQjRo1wuTJk/lu4hFCCAHc3d1x9+5dfPz4ES4uLgL9/v7+KCoqwo0bN1DeBsy05If8Cfok/wuys7O5jkDEQH5+Pk6dOsX+cG/cuDHu37+Pfv36cZyMVJVatWph0aJFiIyMhLu7O9uem5uLxYsXw9jYGD4+PvQLn5TLyckJ79+/x+rVq6Gurs625+bmYufOnWjWrBlcXFxw+/Zt+m+IEEK+oaKigtq1a/O1FRUVsUt5JCQkyj2pxNbWFj179sSOHTuQmZkplKyk5qBjyCqoJh1DFhoaiqZNmwr8wCGiIy4uDpaWljA2Nsa5c+fQoEEDriMRIbp79y6mTp2KsLAwvvZOnTph48aN7GZchHyvoKAAp06dwubNmwX++wGAcePG4d9//+UgGSGEVC+JiYl48uSJwAj5p0+foK6uDoZhICkpiZSUlHLPKSfVEx1DRipdTk4OHB0dYWBggMOHD6O0tJTrSKQcOjo6uHv3Lq5fv07Ftxjq1KkTgoOD4enpyfdL/e7du2jTpg0GDRqEuLg47gISkSUrK4vhw4cjNDQU165dE9jd19HRkaNkhBBSvWhqapY7PT0wMJCdTdShQweB4jshIQFdu3bF+vXry70RSgiNgFdQTRkB9/DwwLJlywAA6urqiIqKgoKCAsepxBfDMNi9ezekpaUxZswYruMQEZSWlobly5dj9+7dfEeUycjIYOrUqVi0aBHdeSc/9erVK+zYsQP37t1DaGgo33rxoqIijBo1CoMGDYK9vT3tMUEIIRUQGxuLy5cvo0GDBujbty9f38GDBzFq1CgAQJcuXXD9+nUuIpLfRCPgpNLp6emxawRXrVpFxTeHCgsLMWHCBEyaNAmTJk1CYGAg15GICKpfvz62b9+Oly9fws3NjW0vLCzEpk2boK+vjy1btqCgoIDDlESUGRsbY+fOnXj+/LnAUZM+Pj44duwYevbsCUNDQ2zZsoV2TyeEkP+gq6uLSZMmCRTfAPiOju3evbtAv5eXF+bPn4+bN2/S724xRQW4mBkyZAiioqKwdetWjBgxgus4Yq24uBhPnjwBUDYKtWbNGo4TEVFmYGAALy8vBAYGol27dmx7eno6Zs2aBQMDA+zfv59vlJyQb5U3uv3t+bhRUVGYNWsWNDQ0MHToUNy7d482bSOEkF+0adMmHDhwAO7u7ujZs6dA/7Fjx7B+/Xp06dKF9uQQUzQFvYJqyhR0Ilri4+NhaWmJ7t27Y+/evZCTk+M6EqkGGIbBuXPnsGDBArx9+5avr2nTplixYgUGDBhA04nJf4qOjsauXbuwf/9+ZGRkCPQbGRlh3LhxGDZsGOrVq8dBQkIIqTmKioqgoqLC7pweGRmJZs2a8V2zbt06qKuro0uXLtDS0uIiplgTxhR0KsAriMfjBdetW9ecpuaRyvb+/XtoaWnROezklxUWFmLXrl1YvXo1UlJS+PpatGiBlStXwtnZmf7bIv8pJycHJ06cwJ49e/D06VOBfllZWVy4cKHc43gIIYRUTFFREa5cuYKAgAC8evUKN27c4PsdnZ+fj7p16yI/Px8AkJSUhIYNG3IVVyzRGnBSKUJCQpCYmMh1DLFWUlKCuXPnYufOnQJ9jRo1ogKJ/BYZGRlMnz4db9++xapVq6CsrMz2vXjxAi4uLmjXrh2uXr1KU4nJT9WuXRtjx47FkydPEBwcjPHjx/PtESIhIYG2bdtymJAQQqo/aWlpODk5YceOHbh586bA57+goCC2+DYwMBAovjMzMzF37lxcuXIFOTk5QstNKhcV4DVcUVERBg8eDAMDAyxfvpz+sXIgPT0djo6O2LhxI6ZPn447d+5wHYnUMAoKCli0aBFiY2OxcOFC1K5dm+17/Pgx7O3t0aFDB/j7+1MhTv6Tubk5du/ejQ8fPmDPnj2wtLTEgAEDUKdOHb7rHjx4gAEDBuDy5cu09wAhhFQCPT09/P333+jSpUu5x0beuXMHGzduhIODA2xtbTlISCoDTUGvoOo6BX3nzp2YPHkyAEBRURHR0dF0rrQQvXr1Cr1790Z0dDTbNnLkSBw4cIDDVKSm+/TpE9asWYNdu3YJ7LBqYWGBxYsXw9nZmdaIkwrLz89HrVq1+NrGjBmD/fv3AwC7cdvw4cNhZGTERURCCKnxZsyYgW3btgEA5syZgw0bNvD137lzB48ePULnzp1hbm4OaWlpLmJWazQFXcTIy8tzHeGXNW/eHKampgCAhQsXUvEtRJcuXUK7du34iu/Fixdj3759HKYi4qBBgwbYsmULoqOjMXHiRMjIyLB9wcHBcHV1RatWrXD27FmUlpZymJRUF98X33l5eThz5gz7OCkpCevWrYOxsTHatWuH3bt3gzYtJYSQyuXm5oYZM2agRYsW6Nq1q0D/sWPHMH/+fLRr106gOCeig0bAK4jH4wXr6uqaf7/jcHVQUlKCkydPok+fPrTLthAwDIPVq1dj6dKl7HRfeXl5HD58uNzzIgmpaomJiVi/fj327NnDri37ysjICAsWLIC7uztfoU7IfwkPD8fhw4dx9OhRfPz4UaBfVlYWLi4uGDlyJLp27SpwBjkhhJDKpaenh9jYWADA3bt30bFjR77+1atXg2EY2NjYoE2bNvR7vxy0C7oIqc4FOBGerKwsjBw5El5eXmybjo4OfHx82JkIhHAlOTkZmzZtws6dO5Gbm8vXp6WlhZkzZ2Ls2LFQVFTkKCGpjoqLi3HlyhUcOnQIFy9eRFFRkcA1b9++ha6uLgfpCCFEPJSWluLQoUPsNPTnz59DVlaW7WcYBurq6vj06RMA4Pnz52jZsiVXcUUWFeAihApw8l9ev34NV1dXREREsG22trY4c+YMVFRUOExGCL/U1FRs2bIF27dvR1ZWFl+fsrIyJk2ahGnTpkFdXZ2jhKS6SktLw8mTJ3Ho0CEEBwcDAGxsbHDr1i2+6z58+IDc3Fzo6+tzEZMQQsROREQEjI2NAQD16tVDSkoK314wRUVFcHJyQtu2bdGxY0d06dJFLE/poQJchFSnAvz58+coLi6GhUWV/XdDvnPx4kUMHToUmZmZbNvUqVOxadMm2gCDiKz09HTs2rUL27ZtY++IfyUjI4Phw4dj9uzZaNasGUcJSXUWFhaGw4cPo0OHDujTpw9f3+LFi7F69Wq0bdsWgwcPRv/+/aGmpsZRUkIIqfm+fPmCS5cu4c6dO5CTk8P27dv5+h8+fIj27dsDKJvKHhMTw9fPMIxYFORUgIsQHo8XXL9+ffPU1FSuo/wUwzCwsrJCUFAQhg4dirVr10JDQ4PrWDVWaWkpli9fjpUrV7JttWrVwp49ezB06FAOkxFScfn5+Thy5Ag2btyIqKgogX4HBwdMnz4d3bp1o53TyR9jGAb6+vrsOkWg7Jzxrl27YvDgwXBxcYGSkhKHCQkhRPysW7cOCxYsAAAMGzYMhw8f5uv39/fH9OnTYW1tDTc3Nzg5OXERs8rRLugipjrsFnzu3DkEBQUBAE6dOoW8vDyOE9Vc6enpcHJy4iu+tbW1cf/+fSq+SbVSq1YtjBs3DhEREfDy8kKbNm34+i9fvowePXqgefPm2LlzJ7KzszlKSmqCL1++wMTEBFJSUmxbaWkprl69iuHDh0NNTQ19+vTBqVOnBJZIEEIIqRojRozAyZMnMXHiRLi4uAj0BwYGIjo6GocOHcLNmzcF+j9//ozCwkIhJK3+qACvYUxNTdG7d28AZVOgaX1d1Xjx4gVat24Nf39/tq1bt24IDg6Gubk5h8kI+X2SkpJwc3PDw4cPcefOHfTq1YtvullkZCQmT54MLS0tzJ49G9VhSQ4RPXXr1sXFixeRnJyM3bt3o1OnTnz9+fn5OH/+PAYOHIgGDRrg/fv3HCUlhBDxoaamBnd3d+zcuROurq4C/Q8fPmS/t7a2FuhftGgR6tSpA1tbW4F9Pwg/moJeQTweL7hevXrmaWlpXEepkFu3bsHMzAx169blOkqNc+rUKYwePZpvF+kFCxZg1apVdMwOqXGio6OxY8cOHDhwQGA0ksfjwdnZGdOmTYOtra1YrA0jVSM+Ph6nTp3CiRMn8Pz5c7bd0NAQr1694vtv6+teGzRNnRBChKegoADBwcG4f/8+RowYAVVVVb5+ExMTvHz5EgBw48YN2NnZ8fUHBASgYcOGaN68uUh/XqY14CKkuhXgpOpMnz4d//zzDwCgdu3aOHz4sMAGQ4TUNFlZWTh06BC2b99e7jrxZs2aYdy4cRg+fDjq16/PQUJSU0RGRuLcuXM4e/YsevfuDQ8PD77+rVu3Yv78+bC3t0e/fv3g5OSEOnXqcBOWEEII8vPz0bx5c7x9+xZSUlL48uULateuzfYzDAMNDQ0kJydDQUEBL168gI6ODneBf4IKcBFCBTj5qqioCF27dkVycjK8vb3ZIx0IEQelpaUICAjAtm3bEBAQINAvIyODvn37Yvz48ejYsSONipM/UlxczLdWHACsrKzw4MED9rGUlBRsbGzg4uICZ2dnNGrUSNgxCSGEAEhMTER4eDjs7e352uPi4qCrqwugbPZSenq6wBFo48ePR5s2bdC+fXuYmpoKNfe3qAAXIaJcgL958wbh4eFwdXWlD7tVoLxjF1JSUiAjIwNlZWWOUhHCvcjISGzfvh1Hjx4td7MsQ0NDjBs3DsOGDaNRcVIp8vPzYWVlhZCQkB9eY2FhARcXF/Tu3RsmJib0e5EQQjgWGRmJRYsWISgoCCYmJrh69Spf/9OnT9G6dWsAgI6ODt8pGUDZzX8ejyeUn+e0CzqpkLlz56JPnz7o3LkzXrx4wXWcGoNhGGzfvh19+/YV2AFfVVWVim8i9gwNDeHp6YmkpCTs27eP/eX5VWRkJGbNmgVNTU0MGTIEd+7cqRanSRDRVatWLQQHByMqKgpr1qyBhYXg56Pg4GAsWbIELVu2ZE8FIYQQwh1DQ0N4eXkhMTER58+fF+j/9mf117PIv3X58mVoaGjA2dkZR44cqdKswkAFeDV369YtXLx4EUDZ8QBFRUUcJ6oZSktLMWjQIEybNg3nz5/HunXruI5EiMhSUFDA6NGj8fjxY4SEhGDChAlQVFRk+wsKCnD8+HHY2NhAX18fy5cvpx3UyR9p0qQJFixYgKdPnyI+Ph47duxAt27d+Karq6ioCByp9/nzZ5w7dw4ZGRnCjkwIIWKPx+NBQUFBoL1bt27YuHEj+vTpgx49egj0P378GMnJybh06VK5M6BevnyJ+/fv822QLMqoAK/mWrZsienTp0NKSgpDhw6lI7AqiYSEBDQ1NdnHPj4+dHODkApo1aoVdu3ahaSkJOzduxeWlpZ8/XFxcVixYgX09fXRuXPncndXJ+RXNGrUCJMnT8bVq1eRkpKC48ePo3///hg4cKDA+nE/Pz/069cPKioqsLW1xcaNGxEREQFajkcIIdwxNDTE7Nmzce7cOQwbNkygPywsjP3++9l2ALBjxw5YW1tDSUkJe/bsqdKslYHWgFeQKK8BB4CoqCgoKCigYcOGXEepMYqKimBnZ4fmzZtj69atqFWrFteRCKmWQkJCsH//fpw8eRLp6ekC/fLy8nBzc8Pw4cNhZ2fHtzELIZXJ3d0dp0+fFmjX1dVFz5494ejoCBsbG8jJyXGQjhBCSHlKSkrw+vVrPHnyBN26dYOGhgZf///WbQMArl27hq5du/L1//XXX8jOzoaFhQWcnJx+ui8NbcImQng8XnCjRo3M4+PjuY5CqkBBQQHy8/MF1nXn5eXRBzFCKklBQQEuXbqEQ4cO4cqVKygpKRG4RktLC+7u7hg4cCBatWpFG2iRSrVx40acPHnyp5u4ycnJwc7ODrNnz4atra0Q0xFCCPlVDMNg7NixuH//Pt68eYO0tDSBoym1tLSQmJgIAHjx4gVMTEz4+l+9egU9PT3UqlWLCnBRwuPxgnV1dc1p3WLN8+7dO/Tv3x8qKiq4dOkSjb4RIgTJyck4fvw4Dh06hPDw8HKvMTAwwMCBA+Hu7g5DQ0MhJyQ12YcPH3D58mX4+fnh6tWryM7OFrjm3Llz6NOnD19bfn4+zYYihBARlZ2dLbDG/OPHj1BXVwdQdoM1MzOTb3lSUVERFBUVUVJSwhbmoaGhVICLAlEqwBMTE3H69GlMnjwZsrKyXMep1vz8/DBs2DB8/vwZALBq1SosWrSI41SEiA+GYfDs2TMcPnwYx48fx4+W+ZiZmbHFeOPGjYWcktRkhYWFuHfvHvz8/ODv74/Xr19DSkoKaWlpUFJSYq8rKChAgwYNYGJigu7du6N79+5o3bq1wDpzQgghoiMvLw+3b99GcHAwsrKyBDZWDgsLY88db9y4MVRUVGgEXFSIUgE+bNgwHD16FHp6eti9eze6devGdaRqp7CwEAsXLsSmTZvYNikpKWzcuBHTp0/nMBkh4quoqAjXrl3DyZMn4ePjU+6oJABYWVmhX79+cHNzQ6NGjYScktR00dHRCA0NRd++ffnab968iS5duvC1KSsrw87Oji3I9fT0hBmVEELIH7p9+zbGjh2L6OhouLi4ID4+ngpwUSEqBfi3B9UDwI0bN2BnZ8dhouonNjYW7u7uePz4MdumoaGBM2fOwMrKisNkhJCvcnNz4efnh1OnTsHPzw8FBQXlXtemTRv06dMHbm5uaNKkiZBTEnGybds2zJw586c7puvr68POzg6Ojo7o3bu3ENMRQgj5E1++fEFmZiZcXV2pABcVPB4vuH79+uapqamc5igqKsLu3buxdOlS2NnZwcvLi9M81c25c+cwZswYvjNgHR0dcejQIaioqHCYjBDyIxkZGfDx8cHJkydx/fr1cjdvA8qOZezTpw/69OkDY2Nj2sCNVLrU1FTcuHEDV69exdWrV5GQkFDudc7Ozrhw4QJfW0lJCSQlJYURkxBCyG+iTdhEiKgU4F+lpaWhoKBAYBt+Ur78/HzMmjULu3btYtukpKSwdu1azJw5kzZeI6SaSElJgbe3N7y8vHDz5k0UFxeXe12zZs3g6uoKJycntG3blgofUukYhkFkZCRbjN++fRu5ubkAgC1btmDGjBl8148ZMwYPHz6Era0tbG1t0blz558ehUMIIUT4qAAXIaJWgJOKe/36NQYMGIDnz5+zbTo6Ojh16hTatm3LYTJCyJ9IT0/HpUuX4OXlhYCAgB9OU1dVVUXPnj3h5OSE7t27Q1FRUchJiTgoKCjAo0ePcOvWLQwcOBAGBgZ8/Xp6eoiNjWUf83g8tGzZEra2tujUqROsra2hqqoq7NiEEEK+QQW4CKECvHo6evQoJk6ciJycHLatT58+2Ldvn8AZgYSQ6isrKwv+/v7w8vKCv78/37/5b8nIyMDW1hZOTk7o1asXtLW1hZyUiKOPHz9CS0vrhzM2vmrWrBmsra2xfPlyaGlpCSkdIYSQr6gAFyFcFuBv377Fxo0bsWLFCro7XkGZmZmYNm0aDh8+zLbJyspi8+bNmDhxIq0NJaQGy8vLw9WrV3Hp0iX4+vri48ePP7y2RYsWcHBwgL29PaysrOhoR1JlcnJycP/+fdy6dQu3b9/GkydPfrifQWpqKt/09IKCAoSHh8PU1JSOPSOEkCpEBbgI4bIAd3Nzg7e3N5SVlbF3717069dP6Bmqk6CgIAwZMgTf7lhvYGCA06dPw8zMjLtghBChKy0txdOnT3Hp0iVcunSJbynK92rXrg1bW1v06NED9vb2tKs6qVJZWVkIDAzE7du3cf/+fTx58gSFhYUwNjbGy5cv+a4NDAxEx44doaCggPbt28Pa2hpWVlZo3bo131nlhBBC/gwV4CKEqwI8ODgYlpaW7OOHDx/SuuUfKC4uxurVq7Fy5Uq+UYWhQ4fC09OT1n0SQvDu3Tv4+vri0qVLuHXrFgoLC394rb6+Puzt7dGjRw/Y2tpCQUFBiEmJuMnPz8fTp0+RlZUFBwcHvr61a9fir7/+EngOj8dD8+bN0a5dO/bLyMiINhYlhJDfRAW4COGqAGcYBn5+fpg5cyY6dOjAN6Wa8EtJSYGJiQk+ffoEAFBWVsauXbswcOBAjpMRQkRRVlYWbt26hYCAAFy5coVv1sz3pKWlYW1tja5du8LW1haWlpaQlpYWYloizjZs2IB//vnnh8eefcvd3R0nT54UQipCCKl5qAAXIVxvwlZYWIjc3FzaOOw/+Pv7w9HREZ06dcKRI0dogyVCSIVFR0fjypUrCAgIwK1bt364kRsAKCgooFOnTrCzs4OtrS1MTU3pqDNSpRiGQXx8PAIDAxEYGIiHDx8iLCwMpaWlfNetW7cO8+bN42v766+/8P79e7Rt2xaWlpYwNTWFvLy8MOMTQki1QAW4COG6ACeC8vLyICcnJ9AeEBCArl270odhQshvKygowP3799mCPCws7KfX161bFzY2NrC1tYWdnR2MjY1ps0dS5bKzsxEcHIyHDx+yX6dPn0anTp34rmvWrBnevHnDPpaUlISxsTEsLS1haWkJCwsLmJqaolatWsL+KxBCiEihAlyEUAEuWvz8/DBu3DgcOnQI3bp14zoOIaSGS0pKwvXr13Hr1i3cvHkT8fHxP72+QYMG6Ny5Mzp27Ahra2u0bNmSbgqSKvf1M923N3/S0tKgoqLyn8+VkpKCiYkJjh8/DmNj4yrLSAghoowKcBHC4/GCtbW1zePi4qr8vYKDgzFv3jxs376dfgmWY9euXZg0aRIAQEtLC+Hh4VBWVuY4FSFEXDAMg7dv37LF+M2bN3961BkAKCoqokOHDmxB3qZNm3Jn8BBS2YqLixESEoKHDx/i6dOnePr0KSIjI/Gjz3/fH4GWk5ODWbNmwdzcHGZmZjAxMUHt2rWFFZ8QQoSKCnARwuPxgnV1dc1/tklPZSgtLUX79u3x+PFjSElJYd++fRg+fHiVvmd18/HjRzRv3hxpaWlQU1ODr68v307xhBAiTAzDIDIyki3Gb926hfT09J8+R1paGpaWlmxBbmVlhXr16gkpMRF3WVlZePbsGYKDg9mi/M2bN9DR0UFsbCzftV+PQPuKx+PBwMAApqamMDMzg5mZGUxNTdGwYUNadkEIqfaoABchwirAHz58CGtra5SUlEBWVhbh4eF0Fm05zp07h7Nnz2Lnzp18d+oJIYRrpaWlePHiBe7du8d+ffjw4T+fZ2BgwB4l1bZtW7Ro0YJ2WidCk5GRgffv38PExISvfevWrZg5c+Z/Pl9VVRWOjo44ePBgVUUkhJAqRwW4CBFWAQ4AL168wKRJk2BnZ4cVK1ZU+fuJsnv37uHhw4eYO3cu11EIIeS3MAyD2NhYBAYG4t69ewgMDERkZOR/Pk9OTg6WlpZ8RbmmpqYQEhPy/168eAF/f388f/4coaGheP36tcDO61+5uLjA29ubr+3UqVMICAiAiYkJTExM0Lx5c2hqatJoOSFEJFEBLkJ4PF6wjo6O+fdTs6oKwzAoLi4W29GPjIwMLFiwALt37waPx8OdO3f4psARQkh1lpKSgvv377NF+bNnz1BUVPSfz9PS0mKPkrKwsICFhQVNXSdClZubi5cvXyI0NBShoaF4/vw5nj9/juzsbCxfvhzLli3ju37EiBE4fPgwX5uysjJbkH8tyk1MTKCqqirMvwohhAigAlyE8Hi8YBUVFfOUlBSuo9R4Fy5cwKRJk5CUlMS2mZub4+nTp3THnBBSI+Xn5+PZs2d8x0n9107rX+no6LDF+NcvWppDhKm0tBSxsbGQk5ODhoYGX1+rVq0QGhpaodfZsmULZsyYwdf2oyNHCSGkKlABLkKqsgAvLi5m13yLs+TkZEydOhXnzp3ja3dycsLOnTuhpaXFUTJCCBG+Dx8+4NGjR2xB/uTJE+Tm5lbouVSUE1Fx9+5dPH/+HOHh4QgPD8fLly+RkZFR7rWXLl1Cr169+NoMDAyQmZkJQ0NDga/GjRtDQkJCGH8NQoiYoAJchFRlAb5t2zZ4enrC09NTLM+0ZhgGBw4cwJw5c/Dlyxe2XU1NDdu3b0ffvn1p5JsQIvaKi4sRHh6OJ0+eIDg4GMHBwQgLC0NhYWGFnq+pqQlTU1O0bNmS/dPAwABSUlJVnJyQ/8cwDBITE9li/Gth/urVK7x8+RI6OjrstQUFBahduzZKSkrKfa1atWqhWbNmbEE+depUutFECPkjVICLkKoqwJOSkmBkZITMzEwAgJeXF9zc3Cr1PURZZGQkJk2ahFu3bvG1jxo1Chs2bKC1jYQQ8hOFhYV4+fIlW5AHBwfj+fPnFS7KZWVl0bx5c4HCnIoYImylpaXg8Xh8N9xjYmLQvHlzFBQUVOg1vj/DPD09HStWrICBgQGaNm2KJk2aoHHjxpCUlKz0/ISQmoEKcBFSVQX4jRs30LdvX3z58gXNmjVDWFgYZGRkKvU9RFF2djZWrlyJLVu28G08pKenhz179qBLly4cpiOEkOqrqKio3KK8okUMUDZa3rJlS5iYmMDY2BjNmzeHkZERFBQUqjA5IYJKSkoQHx+PyMhIga9Pnz6x16moqOD7z2gPHjyAlZUVX5u0tDR0dXXZgrxJkyZo2rQpmjZtCj09PaH8nQghoosKcBFSlVPQk5OTMX36dEyYMAG2traV/vqihGEYnD17FrNmzUJiYiLbLiEhgdmzZ2P58uWQl5fnMCEhhNQ8xcXFiIqKwvPnzxEWFsb+mZCQ8Euv07hxYzRv3hzGxsZ8hbmSklIVJSfkxz5//ozXr18jMjISubm5mDx5Ml//gQMHMHr06Aq9lqGhISIiIvjaYmJi8ObNGzRt2hTa2tpiezINIeKECnARQrug/7nIyEhMmTIFN27c4Gu3trbGjh07YGpqylEyQggRT2lpaQgLC+MrysPDw39ptBwoOx7ta2FuaGgIAwMDGBgYoGHDhrSHB+HMixcv4Ovri6ioKERHRyMqKgrJycnlXuvk5ISLFy/ytW3YsAHz5s0DUDZQ0KhRI+jq6pb7pa6uThvCEVIDCKMAp51XSJX70XTzBg0aYOPGjRgyZAh9QCOEEA7Ur18ftra2fLOvvo6Wh4WF4dWrV+zmWFFRUSguLi73dRISEpCQkICAgAC+dgUFBRgYGKBZs2Z8fxoYGEBRUbFK/26EtGjRAi1atOBry87ORnR0NPv1tThv3bq1wPOjo6PZ70tLS/Hu3Tu8e/cOt2/fFrh2/Pjx2L17N19bWFgYiouLoauri7p161bOX4oQUu1RAf4LKqtIDAsLQ4MGDaCurl4pryfqJkyYgOPHj7OPJSQkMGXKFKxYsQJ16tThLhghhBABUlJSMDIygpGREV97YWEhoqOj8fLlS77C/M2bN3w3V7+VnZ2NkJAQhISECPQ1bNhQoChv0qQJdHV1UatWrSr5uxGioKAAMzMzmJmZ/ee1BgYG6Ny5M6KiopCUlPTTa7W1tQXalixZwo6qKysrQ1tbG40bNy73q2HDhnQiASFigqagVxCPxwtWVVU1/3bDj9+Rm5uLVq1a4dOnT9i0aRNGjhxZ40d/w8PDYWpqitLSUlhZWcHT05OmmxNCSA1RVFSEmJgYtjB/8+YN3rx5g9evX//wvOef4fF4elH64QAAGyVJREFU0NTUhJ6eHvT19QX+rF+/fo3/vUlET35+Pt69e4fY2Nhyv3bu3IkBAwbwPadly5Z48eJFhV7/yJEjGDp0KF/bmTNnULt2bbZIV1ZWrrS/DyGkfLQGXIRUVgE+c+ZMbN26FQCgpKSEN2/eQE1NrRISioaIiIhyRy+WLFmCpk2bYujQofTBiRBCxADDMEhJScHr16/5ivI3b94gOjr6h6Pm/0VJSQl6enpsQf61ONfR0UHjxo0hKytbyX8TQv4bwzACn28GDhyIFy9e4O3bt8jLy/vp82/fvo3OnTvztamoqCAtLY19rKSkhEaNGqFx48bQ1NTk++rcuTNq165deX8hQsQUFeAihMfjBevq6pq/ffv2j14nMDAQw4cPx9u3b7F3716MGTOmkhJyKz4+Hh4eHjh06BBWr16N+fPncx2JEEKIiCouLsa7d+8ECvOYmBjEx8ejtLT0t19bXV0d2traP/yiHduJsDEMg0+fPuH9+/eIj48v9ysoKAi6urrsc3Jycn7p2L+3b9/yPT87OxujR48WKNQ1NTWhoaFByzwI+QEqwEVIZRXgQNkPxcOHD2PSpEk1ZjR4//797M0EJSUlREdHQ1VVleNUhBBCqpuioiK8e/cOb9++RUxMDGJiYvi+z8nJ+aPXr1OnDho3blxucd6oUSM0aNAAkpKSlfS3IeT3fP78GfPmzeMr0n82ip6fn883++P169cwNDT84fUqKipsMa6lpYU9e/bw9RcUFKCwsBAKCgo15rMqIRVBBbgIqcwCvCYqLi5G8+bN8ebNG3Tp0gV79uyBnp4e17EIIYTUIF+ntZdXnL979w6JiYl/NHoOAJKSktDQ0ICmpia0tLTK/ZNGEImwMQyDtLQ0xMfH4/3790hMTGS/srKy4OXlxXf9zZs30aVLlwq9dsOGDQU2mQsICECPHj0gLy8PdXV19qthw4Z8j9XV1aGpqYmGDRtW2t+VEC7RMWRE5KSlpWHbtm3o1KkTunbtyrZLSUlh586d4PF4sLOz4zAhIYSQmorH46FBgwZo0KAB2rVrJ9BfVFSExMREvHv3DvHx8eyxUV+/4uPjkZ+f/9P3KCkpwfv37/H+/fufXqeioiJQmH8tRL4WKaqqqjSaTioFj8eDiooKVFRUYG5u/p/XGxkZ4ciRI3yF+tev5ORklJSUsNeWdyrPhw8fAJRtHvz27Vv8bACqXbt2CAoK4mu7evUqfH19oaqqClVVVTRo0IDvzzp16tC56URsUQH+C37nrnpycjL69++Pf/75p0JHXoiq5ORkbN68GTt37kROTg46dOiALl268E1LquidVkIIIaQqSEtLQ0dHBzo6OuX2f12L+31h/rU4T0hI4Nv06mdSU1ORmpqK0NDQH14jISHBHjv67cjh1++/bfuV9b6E/JeGDRsK7Kr+VUlJCT5+/IjExER8+PAB0tLSAtfk5uaiVq1a/3nDCii/gL9//z62b9/+w+dISUlBRUUFqqqqGDRoEBYsWMDXHx4ejoyMDLZoV1ZWpqnwpMagAvwX5Obm/tL1paWlGDp0KO7du4d27dph9+7dGDFiRNWEqyJxcXHYvHkz9u7dy/dD+MGDBwgMDETHjh05TEcIIYRUHI/Hg5qaGtTU1NCmTZtyr8nLy0NSUhISExORkJDA9+fX7z98+MA3gvgjpaWlSE5ORnJy8k8LdaDsfOrvC/TvRw+/fk+jh+RPfF1moaGh8cNrJk2ahIkTJyIzM5P9bzg5ORkfPnzge5ycnIxmzZoJPP+/Tg0qLi5mn1/etRs2bMCRI0fYx9LS0lBRUUH9+vX5vurVqwdnZ2d06NCB7/kZGRmQl5cv9+YCIVyjArwKvXz5kp2SU1hYCC0tLY4TVVxQUBC2bNkCLy8vgZF/ExMTLF68WOCHHSGEEFLdycnJsceb/ci3I4jfF+nfFikVHU0HyjZojY6ORnR09H9eKykpCRUVFYHCnAp2Upl4PB6UlZWhrKxcbpH9MwMHDkTTpk2RkpKClJQUfPr0ie/PrKws9toGDRoIPP/7oryoqAgfPnxgp8Z/S0tLS+Azac+ePfHgwQMoKSmVW7R/+9jGxuanNyMIqWxUgFehFi1aICQkBAMGDICDgwPfmmlRVFxcDG9vb2zevBkPHz4U6LewsMDixYvh7OxMv8gJIYSIrW9HEFu3bv3D6woLC/Hx40eB0cNvRxG/fl9QUFDh9/96A+Djx48Vzvt1/fC3Bcj3f37fRhvNkd/VqVMndOrU6Yf9+fn5bHFeXgFuZGSE9PR0tmjPzs7+4WvVr19foO3rza/MzExkZmYiNjb2h8/38/MTKMD19fVRWFiIunXrok6dOnx/fv+9jY0NFBUVf/j6hHyPCvAqZmBggKCgIJHehCUpKQn/1969B8lVlnkc/z7Tk7nPEEICRImEpbImSBJDcFOoKVCQ2yKEBJYUkRJZAQNuLUqAFZfsRdRQlrEWiErAwJaueEVTIZgNLKACa8RokEsS2BICASYyk8lkLj3TMz3P/nG62+me7unbpDs98/tUnTr37megZ9K/877nPRs2bODee+/l9ddfH7H/zDPPZNWqVZxzzjm6/0ZERCRHNTU1zJgxgxkzZox6nLvT2dmZFND37duX1GI4fPngwYN51ZFvYI9raGjIGM7j83gYGT61tLToQr2Mqq6ubtTfjbVr1yatxwN7e3s77e3t7N+/P7G8YMGCtK9hZuTytKfUAO/u7N27l0gkwt69e7Oev2vXrqQeAr29vcycOTMpuE+ePJkjjjiClpYWWlpakpYvuugiqqv/EsniNes79/ilAF4Ch+MV5KGhIbZu3co999zDpk2bRtzLVlNTw+WXX84NN9zA/Pnzy1SliIjI+GdmiS/pc+bMyXp8f39/IpRnCunFBPa43t5eent7cwohqT9PS0tL2nA+2hQ/vqmpSQFekmQL7Kl27drF0NAQBw4cSAT1dOG9vb2dd7/73UnnhsNhIpFIzrVNnjw5aT3ecv/OO+/kdP7AwEDS+vPPP88pp5ySNqynLh999NFcffXVSef39vbS0dFBU1MTTU1Nh3Uj4ESlAJ6HXK5Eff3rX2f58uUjfpkPF+3t7dx999088MADvPbaayP2T506lZUrV3LdddelHdVSREREyqu2tpbjjjsu57Fl4oE9NYCkzlO3DQ4OFlRfvEW/s7OzoPOrqqoSIaO5uTmxnGnbaMdoEK6Jq6qqiilTpjBlyhRmzZqV83n19fUcOHCAjo6OnOZHHnlk0vkdHR05v1dDQ0NS6zcE3eaj0SgdHR1ZX2vGjBkjAviWLVtYtmxZ0s/T1NREc3Nz0rypqYl58+axevXqpPN3797Nc889l/b45uZmGhoa1DpfJAXwMbRu3TpWrVrF2rVr2bhxI6eeemq5SxrB3bn99ttH/KN6+umnc80117B06dLDssVeRERECpNvYIfg+0JXV1fWoN7Z2cmBAwcSU0dHx6j36+Yi3nJ54MCBol4HgpbTTKE9HioaGxuT5pmWGxsbaWxsVIviODd88LlCzJkzh9bW1hFBPX4/emdnZ2KerqfH8AHqsklXY+rvXzgcJhwOp22Rb29vHxHAN2/ezI033pjxPc2MxsZGmpubueSSS7jzzjuT9j/44IM8/vjjNDY20tDQQENDQ2I5dT5z5sycezWMJwrgY+Ttt99OfFjfeust1q1bx/3331+2elpbW9m0aRMLFy7klFNOSWyfOnUq5557Lg8//DBTpkzhyiuv5Oqrr2b27Nllq1VEREQOL/Fu5C0tLZxwwgl5nTs4ODgimOc6dXR00NPTM2Y/R19fH319fVkfi5WP+vr6vEN7fX19IoxkWo6vq/t9ZQuFQonHHRbivPPOo7+/PxHYh4f21ACfbgC6UCjE9OnT6erqynoxrKmpacS2bBcA3J3u7u7ElOqpp57ivvvuy/JTBm655RbWrFmTtG358uVs3rw5Y2iPz+vr61m+fPmIwf42b97MwYMHqa+vp76+nrq6usRy6npdXV1Zft8UwMfI9OnTefjhh7n00kuZNWsW3/zmN8tWy9q1a1m1ahXuzvXXX58UwAFuvvlmrrjiCi688EK1douIiMiYqq6uTgzcVoiBgQG6urqSAkjqerpt6dZzeV57vuItim1tbWP+2hD0WBgtqKcL7emW6+rq0k61tbVJ66ldoKX8ampqEk8uyNeKFStYsWIFEPQmCYfDiTDe3d2dtDxt2rQR58+ePZtly5alPb6rq4twOJw4Nl2A7+3tzbnWxsbGEduGv1828+fPHxHAV69eze9///uc3v/nP/85F110UdK2V155Jadzi6HfuNzN3r9//6gHnHXWWfzmN7+hpaWF+vr6Q15Qe3s727dv5+yzz07avmDBgsQIihs3buSuu+5Kuldj8eLFh7w2OTwtXLgQgO3bt5e5EpHi6LMs44U+yyNNmjQpce9uMdydcDicMaD39PTQ3d2dmOeyPJat85n09/fT39+f173ExQiFQqMG9GwBvq6ujnvuuYeqqipuu+22Eftramqora2lpqYmMWVaV+v/2Kqqqkr0wsjVZZddxmWXXZZxfzQapaenh66uLmpra0fsv+qqqzjttNPo7e2lp6eHnp6exHLqfObMmSPOzyfAp8tbfX19OZ+friEy1gPgkHYNrsgAbmZHA98A4jdZPw/c4O5Zh+k0s0nAauBSYBA4CNzs7k/lW4e7jxiEYPhjCMZaa2sr27Zt4+mnn+axxx5jx44dALS1tSX9I7V48WKmTZvGSSedxJIlSxgYGKCmpuaQ1SUiIiJyuDGzRGvwWA0sG29RzDW4d3d3Ew6H6e3tTczj0/D14ceUWjxQjcXFhWuvvbao80OhUM5hvZD1+PKkSZPSTtXV1Xnvm2gXDUKhUOL2lHQWL15cVGPfo48+mvi9GC28h8NhFi1aNOL8Cy64gLlz5yZ6qvT19SWWh099fX0laTBNp+ICuJnVAI8CLwPvAxzYADxhZgvcPVt/hbuAjwIfcvd3zOzTwFYz+6C77xjtxOG/YM888wy33XYbDz30UMGDNIxm//79vPDCCzz77LNs27aNbdu2pX1GN8CTTz7J0qVLE+vV1dXs2bOnbB8qERERkfGokBbFfLg7fX19o4b0bPviy/H734dP/f39SevhcDinZ2WXSjQaTfwclaKqqqrg8J5tf3V1NaFQiOrq6sNuuaqq6pCMhl5dXT1qwM/mjjvuKOr96+rq8mpFL0TFBXDgk8A84GJ3HwQws1uAN4GVwNcynWhm7wWuAT7t7u8AuPt9ZvY54MvA3+ZSwIYNG1i5ciWRSIQLL7yQLVu2FBR2BwYGeOONN9izZw+vvPIKL774YmJqbW3Nen4oFOIDH/hA2kdsKHyLiIiIVBYzSwwQVeg99PlwdwYHBzMG9GwBPj6tX78ed2fJkiUj9kUiESKRCP39/YnlTOuVaGhoKHHbwESTLaSHQiFCoRBVVVUjltNty7a/FOccinEjUlViAF8GvO7uf4pvcPdWM3spti9jAAcuBgx4ImX748BnzKwphxZ0jj32WCKRCAA7d+5kz549I0YR37dvH7t376atrY0TTzyR+fPnJ+1fsmQJmzZtYmhoKNvbJdTV1bFw4UIWLVrEGWecwemnn17w1SERERERmdjMLNHa2tzcXPDrPPLIIwCsX7++4NeIXwzINawXsx6JRBgYGEg7DQ4O5rVvIotGo0Sj0Ql58aEYlRjA5xF0P0/1KnBmDucOAal9uV8l+G9xEvDbTCdHIhEaGhqAoHtENBqlq6uLz372szz22GNJx37/+9/n85//PAA33XTTiABeV1c3aviura1lzpw5zJ8/n0WLFrFo0SLmzp2btrVbRERERKSSDb8YcKi6+I81dycajeYU3gsJ99FolMHBwcT8cFrOpxFRktnhdN9HLswsAvy3u388Zfv3gBVAg7unHcHCzLYCp7l7c8r2TwP3Aue7+y8ynDsIhDLsY8GCBUnb2traEvdsH3XUURx//PFJ+99880327dvHpEmTEgNDDH82XbpRBUWKtXPnTgDmzJlT5kpEiqPPsowX+izLeKDP8cQUz5HunpgyrRc7H8vXAtI+RjB+QQWIuvsha6hWACfnAP4qMAPI1MdiV14/iIiIiIiIiJRDpkeN1QJvuPsJh+qNK7ELehuQ7iaVFqA3U/gedm6DmYXcffgd9vEbqdsznXgo/yeIiIiIiIjI+FeJD677IzAzzfYTCJ4Hnu3cKoKW7NRzB4GXii1OREREREREJJ1KDOAPAceb2cz4BjM7BpgD/HT4gWZ2jJkN/xl/RvDc8DNSXvMjwNZcRkAXERERERERKUQlBvAHCFq67zCz6ljAXkMwkvm34geZ2YeAt4B18W3uvhtYD3zBzKbGjvsUcCLwxVL9ACIiIiIiIjLxVFwAd/cI8DEgStBlfCfBPdwfTWnB7gY6gbdTXuIfgB8DT5vZC8A1wNnuvuMQly4iIiIiIiITWMWNgi4iIiIiIiJSiSquBVxERATAzH5tZj58TBARERGRbMxsupltMbOSt0YrgGdhZkeb2X+Z2e7Y9BMzO67cdYnkyszeb2b3mtlOM3vezF4yszvNbFq5axMplJktAz5c7jpEimFmy8zsV2a23cz+ZGa/M7Mryl2XSK7M7FQz+8Ww7xi/NbNLy12XyGjMbCnwvwTjgI123CQz+5KZ7TKzF8zsGTMr+ruHAvgozKwGeBSoAd4HnAT0AE+YWVM5axPJww+AKcCp7j6XYAyFswnGQagva2UiBYj9bV4DPFLuWkQKZWafIxgA9nJ3Xwi8F3gZOLOshYnkKNb76H+ANmBu7DvGBuBHZvbxctYmksUtBN+Hn85y3F3AZcBidz+Z4PO91czeX8ybK4CP7pPAPOAWdx909yjB/7C/AlaWtTKR/Nzi7j0A7v4m8DVgFnB+WasSKcz1wLOxSaTixILLGuBad98L4O4DwCrg7jKWJpKP8wkGQl7r7oMA7v5t4CBweTkLE8niQ+7+ymgHmNl7CQbrXuPu7wC4+30ET976cjFvrgA+umXA6+7+p/gGd28lGH19WdmqEsnPPHf/v5Rtb8XmR5a6GJFimNkU4CbgC+WuRaQIVwAH3D3pIpK7v+XuvytTTSL5GozNq+MbzMwI8kWoLBWJ5CB+wSiLiwEDnkjZ/jhwdjG9oRXARzeP4CpHqleBuSWuRaQgsUf3pfprwIFflbgckWKtBr7n7nvKXYhIET4IvBa7B/zXsfsLnzGzq8pdmEgefgDsAv7ZzJrMrAq4FagFvl3WykSKNw8YAl5P2f4qwUWnkwp94ersh0xoU4HtabYfBBrMrN7dwyWuSaQoZhYC/h74jru/XO56RHJlZrOAvwPmlLsWkSLNAGYSdDm/GPgzQc+6B81sursX1b1RpBTc/aCZnQncT3AfeDfQCXzM3X9Z1uJEijcV6I3dgjzcwdj8qEJfWC3gIhPPbcAAcEOZ6xDJ1x0E92J1lrsQkSLVAY3ATe7e6u5D7v5jYCNwq5k1lLc8kexi98j+FthDMNjr0QQDCz5kZueVszaRw5kC+OjagOY021sIroio9Vsqipl9iqAF8bz4oGwilcDMFgMnA98qdy0iY6ArNt+Rsv0PQANFdG0UKaEvAZOBf3T33tiFpB8Q3N72n2amnrZSydoIejynjmfQEpu3F/rCCuCj+yNBF7FUJwDPl7YUkeLEni17I/BRd/9zuesRydPHCAb1edbMdpjZDuAzsX2PxLZpVH+pFLti89TvYdEM20UOR3OBvWkapF4GphF8XxapVH8k+Fs8I2X7CQQDEL5U6AvrD/zoHgKOjz0uBAAzO4bg/sOflqsokXyZ2ScIHqF3Vmwkf8zsAjO7pryVieTG3Ve7+4nu/v74xF8G+Tk/tk3PBZdKsSk2n5ey/WQgDLxY2nJECvJnYHqalu7jCQZ67Sh9SSJj5mcEn+MzUrZ/BNjq7t2FvrAC+OgeIGjpvsPMqmOjO64hGP1O3SClIpjZCuBegs/zWWb2iVgg/zjwrnLWJiIyQf2Q4Dn2t8cfZRO7zeIS4Mu6RUgqxF0E3XH/Pfb4MczsI8BS4Ifu3lbO4kSK4e67gfXAF8xsKiRu5TyRYKyDgpm7F1/hOBZr8f4GcCrBVZAXgBvc/Y2yFiaSIzPbT+bnff+bu/9rCcsRKVqsq/lXgGOBY4CdQCTWKi5SEWLPtL8DOBvoA/qBu9z93rIWJpIHMzsH+CeCv8dRgsc2fRe40937y1mbSCZm9jWCW9veQ/Ad+bnYrr8Z/vheM5sE/AtwKcEAxl3Aze7+66LeXwFcRERERERE5NBTF3QRERERERGRElAAFxERERERESkBBXARERERERGRElAAFxERERERESkBBXARERERERGRElAAFxERERERESkBBXARERERERGRElAAFxERERERESkBBXARERERERGRElAAFxERERERESkBBXARERERERGRElAAFxERERERESkBBXARERERERGRElAAFxERkSRmdq6ZbTSzVjOLmNmrZrbWzI4sd20iIiKVTAFcREREADCzkJl9B3gY6ACuA84H7gOuBZ4xsyPKWKKIiEhFM3cvdw0iIiJyGDCze4BPAUvc/ZGUfecDm4Gvuvut5ahPRESk0imAi4iICGZ2DrAFuNXdv5rhmNeALnefW8raRERExgsFcBEREcHMfgXMA97l7r0ZjnkSmOfuU0pZm4iIyHihe8BFREQmODM7Bvgw8KNM4TumAegpTVUiIiLjjwK4iIiIzAMMeCnTAWbWAJwMvFCqokRERMYbBXARERFpjs3bRjnmcqAeeOjQlyMiIjI+KYCLiIjIW7H5e9LtjLV+3wS8Dny3VEWJiIiMNxqETUREZIIzs0nAawT3d7/P3QeG7aslCN0XA2e5+y/LUqSIiMg4oAAuIiIimNlFwE+APwD/AbwNzAauI2gZv8LdN5avQhERkcqnAC4iIiIAmNkHgS8CpwFHxjZvAq539zfKVpiIiMg4oQAuIiIiI5hZPbADiACnunt/eSsSERGpfBqETUREREZw9zBwJXAScHt5qxERERkf1AIuIiIiIiIiUgJqARcREREREREpAQVwERERERERkRJQABcREREREREpAQVwERERERERkRJQABcREREREREpAQVwERERERERkRJQABcREREREREpAQVwERERERERkRJQABcREREREREpAQVwERERERERkRJQABcREREREREpAQVwERERERERkRJQABcREREREREpAQVwERERERERkRJQABcREREREREpgf8HnO+IQc1ilpwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 491,
       "width": 496
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "r\"\"\"\n",
    "Example of a chi-squared distribution\n",
    "---------------------------------------\n",
    "Figure 3.14.\n",
    "This shows an example of a :math:`\\chi^2` distribution with various parameters.\n",
    "We'll generate the distribution using::\n",
    "    dist = scipy.stats.chi2(...)\n",
    "Where ... should be filled in with the desired distribution parameters\n",
    "Once we have defined the distribution parameters in this way, these\n",
    "distribution objects have many useful methods; for example:\n",
    "* ``dist.pmf(x)`` computes the Probability Mass Function at values ``x``\n",
    "  in the case of discrete distributions\n",
    "* ``dist.pdf(x)`` computes the Probability Density Function at values ``x``\n",
    "  in the case of continuous distributions\n",
    "* ``dist.rvs(N)`` computes ``N`` random variables distributed according\n",
    "  to the given distribution\n",
    "Many further options exist; refer to the documentation of ``scipy.stats``\n",
    "for more details.\n",
    "\"\"\"\n",
    "# Author: Jake VanderPlas\n",
    "# License: BSD\n",
    "#   The figure produced by this code is published in the textbook\n",
    "#   \"Statistics, Data Mining, and Machine Learning in Astronomy\" (2013)\n",
    "#   For more information, see http://astroML.github.com\n",
    "#   To report a bug or issue, use the following forum:\n",
    "#    https://groups.google.com/forum/#!forum/astroml-general\n",
    "import numpy as np\n",
    "from scipy.stats import chi2\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "#----------------------------------------------------------------------\n",
    "# This function adjusts matplotlib settings for a uniform feel in the textbook.\n",
    "# Note that with usetex=True, fonts are rendered with LaTeX.  This may\n",
    "# result in an error if LaTeX is not installed on your system.  In that case,\n",
    "# you can set usetex to False.\n",
    "if \"setup_text_plots\" not in globals():\n",
    "    from astroML.plotting import setup_text_plots\n",
    "setup_text_plots(fontsize=8, usetex=False)\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# Define the distribution parameters to be plotted\n",
    "k_values = [1, 2, 5, 7]\n",
    "linestyles = ['-', '--', ':', '-.']\n",
    "mu = 0\n",
    "x = np.linspace(-1, 20, 1000)\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# plot the distributions\n",
    "fig, ax = plt.subplots(figsize=(8,8))\n",
    "fig.subplots_adjust(bottom=0.12)\n",
    "\n",
    "for k, ls in zip(k_values, linestyles):\n",
    "    dist = chi2(k, mu)\n",
    "\n",
    "    plt.plot(x, dist.pdf(x), ls=ls, c='black',\n",
    "             label=r'$k=%i$' % k)\n",
    "\n",
    "plt.xlim(0, 10)\n",
    "plt.ylim(0, 0.5)\n",
    "\n",
    "plt.xlabel('$Q$')\n",
    "plt.ylabel(r'$p(Q|k)$')\n",
    "plt.title(r'$\\chi^2\\ \\mathrm{Distribution}$')\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Chi-squared per degree of freedom\n",
    "\n",
    "In practice we frequently divide $\\chi^2$ by the number of degrees of freedom, and work with:\n",
    "\n",
    "$$\\chi^2_\\mathrm{dof} = \\frac{1}{N-1} \\sum_{i=1}^N \\left(\\frac{x_i-\\overline{x}}{\\sigma}\\right)^2$$\n",
    "\n",
    "which (for large $k$) is distributed as\n",
    "\n",
    "$$ p(\\chi^2_\\mathrm{dof}) \\sim \\mathscr{N}\\left(1, \\sqrt{\\frac{2}{N-1}}\\right) $$\n",
    "\n",
    "(where $k = N-1$, and $N$ is the number of samples). Therefore, we expect $\\chi^2_\\mathrm{dof}$ to be 1, to within a few $\\sqrt{\\frac{2}{N-1}}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Poisson distribution\n",
    "\n",
    "This is a distribution for a discrete variable, telling you the probability of $k$ events occuring within a certain time when the mean is $\\mu$. \n",
    "\n",
    "$$ p(k|\\mu) = \\frac{\\mu^k \\exp(-\\mu)}{k!} $$\n",
    "\n",
    "where the mean $\\mu$ completely characterizes the distribution. The mode is $(\\mu-1)$, the standard deviation is $\\sqrt{\\mu}$, the skewness is $1/\\sqrt{\\mu}$, and the kurtosis is $1/\\mu$.\n",
    "\n",
    "As $\\mu$ increases the Poisson distribution becomes more and more similar to a Gaussian with $\\mathcal{N}(\\mu,\\sqrt{\\mu})$. The Poisson distribution is sometimes called the ***law of small numbers*** or ***law of rare events***."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 482,
       "width": 495
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Author: Jake VanderPlas\n",
    "# License: BSD\n",
    "#   The figure produced by this code is published in the textbook\n",
    "#   \"Statistics, Data Mining, and Machine Learning in Astronomy\" (2013)\n",
    "#   For more information, see http://astroML.github.com\n",
    "#   To report a bug or issue, use the following forum:\n",
    "#    https://groups.google.com/forum/#!forum/astroml-general\n",
    "import numpy as np\n",
    "from scipy.stats import poisson\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "#----------------------------------------------------------------------\n",
    "# This function adjusts matplotlib settings for a uniform feel in the textbook.\n",
    "# Note that with usetex=True, fonts are rendered with LaTeX.  This may\n",
    "# result in an error if LaTeX is not installed on your system.  In that case,\n",
    "# you can set usetex to False.\n",
    "if \"setup_text_plots\" not in globals():\n",
    "    from astroML.plotting import setup_text_plots\n",
    "setup_text_plots(fontsize=8, usetex=True)\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# Define the distribution parameters to be plotted\n",
    "mu_values = [1, 5, 15]\n",
    "linestyles = ['-', '--', ':']\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# plot the distributions\n",
    "#   we generate it using scipy.stats.poisson().  Once the distribution\n",
    "#   object is created, we have many options: for example\n",
    "#   - dist.pmf(x) evaluates the probability mass function in the case of\n",
    "#     discrete distributions.\n",
    "#   - dist.pdf(x) evaluates the probability density function for\n",
    "#   evaluates\n",
    "fig, ax = plt.subplots(figsize=(8,8))\n",
    "\n",
    "for mu, ls in zip(mu_values, linestyles):\n",
    "    # create a poisson distribution\n",
    "    # we could generate a random sample from this distribution using, e.g.\n",
    "    #   rand = dist.rvs(1000)\n",
    "    dist = poisson(mu)\n",
    "    x = np.arange(-1, 200)\n",
    "\n",
    "    plt.plot(x, dist.pmf(x), color='black',\n",
    "             linestyle=ls,\n",
    "             label=r'$\\mu=%i$' % mu)\n",
    "\n",
    "    plt.scatter(x, dist.pmf(x), edgecolor='black',facecolor='white')\n",
    "    \n",
    "plt.xlim(-0.5, 30)\n",
    "plt.ylim(0, 0.4)\n",
    "\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel(r'$p(x|\\mu)$')\n",
    "plt.title('Poisson Distribution')\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Student's $t$ Distribution\n",
    "\n",
    "Another distribution that we'll see later is the Student's $t$ Distribution.\n",
    "\n",
    "If you have a sample of $N$ measurements, $\\{x_i\\}$, drawn from a Gaussian distribution, $\\mathscr{N}(\\mu,\\sigma)$, and you apply the transform\n",
    "\n",
    "$$t = \\frac{\\overline{x}-\\mu}{s/\\sqrt{N}},$$\n",
    "\n",
    "then $t$ will be distributed according to Student's $t$ with the following pdf (for $k$ degrees of freedom):\n",
    "\n",
    "$$p(x|k) = \\frac{\\Gamma(\\frac{k+1}{2})}{\\sqrt{\\pi k} \\Gamma(\\frac{k}{2})} \\left(1+\\frac{x^2}{k}\\right)^{-\\frac{k+1}{2}}$$\n",
    "\n",
    "As with a Gaussian, Student's $t$ is bell shaped, but has \"heavier\" tails.\n",
    "\n",
    "Note the similarity between $t$ and $z$ for a Gaussian (as defined in the $\\chi^2$ section above), which reflects the difference between data-derived estimates of the mean and standard deviation and their true values.\n",
    "\n",
    "In fact, although often approximated as a Gaussian distribution, the mean of a sample actually follows a Student's $t$ distribution (**Try this at home: check this property with scipy**). This matters when sample sizes are small, but mostly irrelevant for \"Big Data\" examples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 486,
       "width": 496
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Example of Student's t distribution\n",
    "-----------------------------------\n",
    "Figure 3.15.\n",
    "This shows an example of Student's t distribution with various parameters.\n",
    "We'll generate the distribution using::\n",
    "    dist = scipy.stats.student_t(...)\n",
    "Where ... should be filled in with the desired distribution parameters\n",
    "Once we have defined the distribution parameters in this way, these\n",
    "distribution objects have many useful methods; for example:\n",
    "* ``dist.pmf(x)`` computes the Probability Mass Function at values ``x``\n",
    "  in the case of discrete distributions\n",
    "* ``dist.pdf(x)`` computes the Probability Density Function at values ``x``\n",
    "  in the case of continuous distributions\n",
    "* ``dist.rvs(N)`` computes ``N`` random variables distributed according\n",
    "  to the given distribution\n",
    "Many further options exist; refer to the documentation of ``scipy.stats``\n",
    "for more details.\n",
    "\"\"\"\n",
    "# Author: Jake VanderPlas\n",
    "# License: BSD\n",
    "#   The figure produced by this code is published in the textbook\n",
    "#   \"Statistics, Data Mining, and Machine Learning in Astronomy\" (2013)\n",
    "#   For more information, see http://astroML.github.com\n",
    "#   To report a bug or issue, use the following forum:\n",
    "#    https://groups.google.com/forum/#!forum/astroml-general\n",
    "import numpy as np\n",
    "from scipy.stats import t as student_t\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "#----------------------------------------------------------------------\n",
    "# This function adjusts matplotlib settings for a uniform feel in the textbook.\n",
    "# Note that with usetex=True, fonts are rendered with LaTeX.  This may\n",
    "# result in an error if LaTeX is not installed on your system.  In that case,\n",
    "# you can set usetex to False.\n",
    "if \"setup_text_plots\" not in globals():\n",
    "    from astroML.plotting import setup_text_plots\n",
    "setup_text_plots(fontsize=8, usetex=False)\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# Define the distribution parameters to be plotted\n",
    "mu = 0\n",
    "k_values = [1E10, 2, 1, 0.5]\n",
    "linestyles = ['-', '--', ':', '-.']\n",
    "x = np.linspace(-10, 10, 1000)\n",
    "\n",
    "#------------------------------------------------------------\n",
    "# plot the distributions\n",
    "fig, ax = plt.subplots(figsize=(8,8))\n",
    "\n",
    "for k, ls in zip(k_values, linestyles):\n",
    "    dist = student_t(k, 0)\n",
    "\n",
    "    if k >= 1E10:\n",
    "        label = r'$\\mathrm{t}(k=\\infty)$'\n",
    "    else:\n",
    "        label = r'$\\mathrm{t}(k=%.1f)$' % k\n",
    "\n",
    "    plt.plot(x, dist.pdf(x), ls=ls, c='black', label=label)\n",
    "\n",
    "plt.xlim(-5, 5)\n",
    "plt.ylim(0.0, 0.45)\n",
    "\n",
    "plt.xlabel('$x$')\n",
    "plt.ylabel(r'$p(x|k)$')\n",
    "plt.title(\"Student's $t$ Distribution\")\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### What's the point of all these distributions?\n",
    "\n",
    "* There are many other distributions that we haven't covered here (see the textbook).\n",
    "* The point is that we are going to make some measurement. \n",
    "* To understand the significance of our measurement, we want to know how likely it is that we would get that measurement in our experiment by random chance. \n",
    "* To determine that we need to know the shape of the distribution. Let's say that we find that $x=6$. If our data is $\\chi^2$ distributed with 2 degrees of freedom, then we would integrate the $k=2$ curve above from 6 to $\\infty$ to determine how likely it is that we would have gotten 6 or larger by chance.  If our distribution was instead $t$ distributed, we would get a *very* different answer.  \n",
    "\n",
    "Note that it is important that you decide *ahead of time* what the metric will be for deciding whether this result is significant or not.  More on this later, but see [this article](http://fivethirtyeight.com/features/science-isnt-broken/)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**FUN FACT:** \"Student\" was the pen name of W. S. Gosset, who worked for the Guinness brewery in Dublin, Ireland. He was interested in the statistical analysis of small samples, e.g., the chemical properties of barley when the sample size might be as small as $3$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![https://thatsmaths.files.wordpress.com/2014/04/gosset-plaque.jpg](https://thatsmaths.files.wordpress.com/2014/04/gosset-plaque.jpg)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Time to get your hands dirty!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. A gaussian integral\n",
    "\n",
    "Using Monte Carlo integration, check that\n",
    "\n",
    "$$ \\int_0^\\infty x^3 \\exp\\left(-\\frac{x^2}{2\\sigma^2}\\right) \\,dx = 2\\sigma^4 .$$\n",
    "\n",
    "- Does the result converge with the number of samples? And how does the error go down?\n",
    "- Do it many times. For a given $N$, how are the result distributed? We'll talk about model fitting at lenght later on, but for now try to fit it by hand with a parametrized model. (If N is large enough you should get something that looks *very* accurate! And if $N$ is small?)\n",
    "- How does the distribution change if $N$ increases?\n",
    "\n",
    "(Hint: think about sample mean and sample variance)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[My solution](https://github.com/dgerosa/astrostatistics_bicocca_2023/blob/main/solutions/S03_cubegaussianintegral.ipynb) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Kicking horses\n",
    "\n",
    "A famous early  application of low-number statistics was an analysis of Prussian cavalryman horse-kick deaths by [Bortkiewicz](https://www.wikiwand.com/en/Ladislaus_Bortkiewicz) in 1898.\n",
    "\n",
    "He studied the distribution of 122 men kicked to death by horses among 10 Prussian army corps within 20 years (so a total number of corpes of 200). He recorded the number of corps with a given number of deaths:\n",
    "\n",
    "| Number of deaths | Number of groups |\n",
    "| --- | --- |\n",
    "| 0 | 109 |\n",
    "| 1 | 65 |\n",
    "| 2 | 22 |\n",
    "| 3 | 3 |\n",
    "| 4 | 1 |\n",
    "\n",
    "- Plot the resulting probability distribution. Careful with the normalization\n",
    "- How does it look like? Again try to fit it by hand.\n",
    "\n",
    "(Hint: think about sample mean and sample variance)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
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