PythonDataBasics_ParametricDistributions.ipynb

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    "<p align=\"center\">\n",
    "    <img src=\"https://github.com/GeostatsGuy/GeostatsPy/blob/master/TCG_color_logo.png?raw=true\" width=\"220\" height=\"240\" />\n",
    "\n",
    "</p>\n",
    "\n",
    "## Data Analytics \n",
    "\n",
    "### Parametric Distributions  in Python \n",
    "\n",
    "\n",
    "#### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "\n",
    "##### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n"
   ]
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    "### Data Analytics: Parametric Distributions\n",
    "\n",
    "Here's a demonstration of making and general use of parametric distributions in Python. This demonstration is part of the resources that I include for my courses in Spatial / Subsurface Data Analytics at the Cockrell School of Engineering at the University of Texas at Austin.  \n",
    "\n",
    "#### Parametric Distributions\n",
    "\n",
    "We will cover the following distributions:\n",
    "\n",
    "* Uniform\n",
    "* Triangular\n",
    "* Gaussian\n",
    "* Log Normal\n",
    "\n",
    "We will demonstrate:\n",
    "\n",
    "* distribution parameters \n",
    "* forward and inverse operators\n",
    "* summary statistics\n",
    "\n",
    "I have a lecture on these parametric distributions available on [YouTube](https://www.youtube.com/watch?v=U7fGsqCLPHU&t=1687s).   \n",
    "\n",
    "#### Getting Started\n",
    "\n",
    "Here's the steps to get setup in Python with the GeostatsPy package:\n",
    "\n",
    "1. Install Anaconda 3 on your machine (https://www.anaconda.com/download/). \n",
    "2. From Anaconda Navigator (within Anaconda3 group), go to the environment tab, click on base (root) green arrow and open a terminal. \n",
    "3. In the terminal type: pip install geostatspy. \n",
    "4. Open Jupyter and in the top block get started by copy and pasting the code block below from this Jupyter Notebook to start using the geostatspy functionality. \n",
    "\n",
    "You will need to copy the data file to your working directory.  They are available here:\n",
    "\n",
    "* Tabular data - unconv_MV_v4.csv at https://git.io/fhHLT.\n",
    "\n",
    "#### Importing Packages\n",
    "\n",
    "We will need some standard packages. These should have been installed with Anaconda 3."
   ]
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   "source": [
    "import numpy as np                        # ndarrys for gridded data\n",
    "import pandas as pd                       # DataFrames for tabular data\n",
    "import os                                 # set working directory, run executables\n",
    "import matplotlib.pyplot as plt           # for plotting\n",
    "from scipy import stats                   # summary statistics\n",
    "import math                               # trigonometry etc.\n",
    "import scipy.signal as signal             # kernel for moving window calculation\n",
    "import random                             # for randon numbers\n",
    "import seaborn as sns                     # for matrix scatter plots\n",
    "from scipy import linalg                  # for linear regression\n",
    "from sklearn import preprocessing\n",
    "import geostatspy.GSLIB as GSLIB"
   ]
  },
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   "source": [
    "#### Set the Working Directory\n",
    "\n",
    "I always like to do this so I don't lose files and to simplify subsequent read and writes (avoid including the full address each time). "
   ]
  },
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   "source": [
    "#os.chdir(\"c:/PGE383\")                     # set the working directory"
   ]
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    "### Uniform Distribution\n",
    "\n",
    "Let's start with the most simple distribution.\n",
    "\n",
    "* by default a random number is uniform distributed\n",
    "\n",
    "* this ensures that enough random samples (Monte Carlo simulations) will reproduce the distribution\n",
    "\n",
    "\\begin{equation}\n",
    "x_{\\alpha}^{s} = F^{-1}_x(p_{\\alpha}), \\quad X^{s} \\sim F_X\n",
    "\\end{equation}\n",
    "\n",
    "#### Random Samples\n",
    "\n",
    "Let's demonstrate the use of the command:\n",
    "\n",
    "```python\n",
    "uniform.rvs(size=n, loc = low, scale = interval, random_state = seed)\n",
    "```\n",
    "\n",
    "Where:\n",
    "\n",
    "* size is the number of samples\n",
    "\n",
    "* loc is the minimum value\n",
    "\n",
    "* scale is the range, maximum value minus the minimum value\n",
    "\n",
    "* random_state is the random number seed\n",
    "\n",
    "We will observe the convergence of the samples to a uniform distribution as the number of samples becomes large.\n",
    "\n",
    "We will make a compact set of code by looping over all the cases of number of samples\n",
    "\n",
    "* we store the number of samples cases in the list called ns\n",
    "\n",
    "* we store the samples as a list of lists, called X_uniform\n"
   ]
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\n",
      "text/plain": [
       "<Figure size 432x288 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import uniform\n",
    "\n",
    "low = 0.00; interval = 0.30; ns = [1e1,1e2,1e3,1e4,1e5,1e6]; X_uniform = []\n",
    "\n",
    "index = 0\n",
    "for n in ns:\n",
    "    X_uniform.append(uniform.rvs(size=int(ns[index]), loc = low, scale = interval).tolist())\n",
    "    plt.subplot(2,3,index+1)\n",
    "    GSLIB.hist_st(X_uniform[index],low,low+interval,log=False,cumul = False,bins=20,weights = None,xlabel='Values',title='Distribution, N = ' + str(int(ns[index])))\n",
    "    index = index + 1\n",
    "    \n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=3.0, top=2.1, wspace=0.2, hspace=0.3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can observe that by drawing more Monte Carlo simulations, we more closely approximate the original uniform parametric distribution.\n",
    "\n",
    "#### Forward Distribution\n",
    "\n",
    "Let's demonstrate the forward operator. We can take any value and calculate the associated:\n",
    "\n",
    "* density (probability density function)\n",
    "* cumulative probability\n",
    "\n",
    "The transform for the probability density function is:\n",
    "\n",
    "\\begin{equation}\n",
    "p = f_x(x)\n",
    "\\end{equation}\n",
    "\n",
    "where $f_x$ is the PDF and $p$ is the density for value, $x$.\n",
    "\n",
    "and for the cumulative distribution function is:\n",
    "\n",
    "\\begin{equation}\n",
    "P = F_x(x)\n",
    "\\end{equation}\n",
    "\n",
    "where $F_x$ is the CDF and $P$ is the cumulative probability for value, $x$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_values = np.linspace(0.0,0.3,100)\n",
    "p_values = uniform.pdf(x_values, loc = low, scale = interval)\n",
    "P_values = uniform.cdf(x_values, loc = low, scale = interval)\n",
    "\n",
    "plt.subplot(1,2,1)\n",
    "plt.plot(x_values, p_values,'r-', lw=5, alpha=0.8, label='uniform PDF'); plt.title('Uniform PDF'); plt.xlabel('Values'); plt.ylabel('Density')\n",
    "plt.xlim([0.0,0.3]); plt.grid()\n",
    "\n",
    "plt.subplot(1,2,2)\n",
    "plt.plot(x_values, P_values,'r-', lw=5, alpha=0.8, label='uniform CDF'); plt.title('Uniform CDF'); plt.xlabel('Values'); plt.ylabel('Cumulative Probability')\n",
    "plt.xlim([0.0,0.3]); plt.ylim([0,1]); plt.grid()\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.8, top=0.8, wspace=0.2, hspace=0.3); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Inverse Distribution\n",
    "\n",
    "Let's know demonstrate the reverse operator for the uniform distribution:\n",
    "\n",
    "\\begin{equation}\n",
    "X = F^{-1}_X(P)\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The P90 of our uniform distribution is 0.27.\n"
     ]
    }
   ],
   "source": [
    "p = 0.90\n",
    "x = uniform.ppf(p, loc = low, scale = interval)\n",
    "print('The P' + str(round(p*100)) + ' of our uniform distribution is ' + str(x) + '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's repeat this over a range of percentile values, plot and compare to the forward operation result above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p_values = np.linspace(0.01,0.99,100)\n",
    "x_values = uniform.ppf(p_values, loc = low, scale = interval)\n",
    "plt.plot(x_values, p_values,'r-', lw=5, alpha=0.8, label='uniform pdf');  plt.title('Uniform CDF from Sampling the Inverse of Distribution, $F^{-1}_x(x)$'); plt.xlabel('Values'); plt.ylabel('Cumulative Probability')\n",
    "plt.xlim([0.0,0.3]); plt.ylim([0,1]); plt.grid()\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.1, wspace=0.2, hspace=0.3); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That work's the plots are the same.\n",
    "\n",
    "#### Summary Statistics\n",
    "\n",
    "We also have a couple of convience member functions to return the statistics from the parametric distribution:\n",
    "\n",
    "* mean\n",
    "* median\n",
    "* mode\n",
    "* variance\n",
    "* standard deviation\n",
    "\n",
    "Let's demonstrate a few of these methods.\n",
    "\n",
    "```python\n",
    "uniform.stats(loc = low, scale = interval, moments = 'mvsk')\n",
    "```\n",
    "\n",
    "returns a tuple with the mean, variance, skew and kurtosis (centered 1st, 2nd, 3rd and 4th moments)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Stats: mean, variance, skew and kurtosis = (array(0.15), array(0.0075), array(0.), array(-1.2))\n"
     ]
    }
   ],
   "source": [
    "print('Stats: mean, variance, skew and kurtosis = ' + str(uniform.stats(loc = low, scale = interval, moments = 'mvsk')))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can confirm this by calculating the centered variance (regular variance) with this member function:\n",
    "\n",
    "```python\n",
    "uniform.var(loc = low, scale = interval)\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The variance is 0.0075.\n"
     ]
    }
   ],
   "source": [
    "print('The variance is ' + str(round(uniform.var(loc = low, scale = interval),4)) + '.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also directly calculate the:\n",
    "\n",
    "* standard deviation - std\n",
    "* mean - mean\n",
    "* median - median\n",
    "\n",
    "We can also calculate order of a non-centered moment. The moment method allows us to calculate an non-centered moment of any order. Try this out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The 4th order non-centered moment is 0.00162\n"
     ]
    }
   ],
   "source": [
    "m_order = 4\n",
    "print('The ' + str(m_order) + 'th order non-centered moment is ' + str(uniform.moment(n = m_order, loc = low, scale = interval)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Symmetric Interval\n",
    "\n",
    "We can also get the symmetric interval (e.g. prediction or confidence intervals) for any alpha level. \n",
    "\n",
    "* Note the program mislabels the value as alpha, it is actually the significance level (1 - alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The interval at alpha level 0.05 is [0.01 0.29]\n"
     ]
    }
   ],
   "source": [
    "level = 0.95\n",
    "print('The interval at alpha level ' + str(round(1-level,3)) + ' is ' + str(np.round(uniform.interval(alpha = level,loc = low,scale = interval),2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Triangular Distribution\n",
    "\n",
    "The great thing about parametric distributions is that the above member functions are the same!\n",
    "\n",
    "* we can plug and play other parametric distributions and repeat the above.\n",
    "\n",
    "This time we will make it much more compact!  \n",
    "\n",
    "* we will import the triangular distribution as my_dist and call the same functions as before\n",
    "* we need a new parameter, the distribution mode (c parameter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean is 0.17.\n",
      "The variance is 0.0042.\n",
      "The interval at an alpha level of 0.05 is [0.07 0.31]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import triang as my_dist                                    # import traingular dist as my_dist\n",
    "dist_type = 'Triangular'                                                     # give the name of the distribution for labels\n",
    "low = 0.05; mode = 0.20; c = 0.10                                            # given the distribution parameters\n",
    "\n",
    "x_values = np.linspace(0.0,0.3,100)                                          # get an array of x values\n",
    "p_values = my_dist.pdf(x_values, loc = low, c = mode, scale = interval)      # calculate density for each x value\n",
    "P_values = my_dist.cdf(x_values, loc = low, c = mode, scale = interval)      # calculate cumulative probablity for each x value\n",
    "\n",
    "plt.subplot(1,3,1)                                                           # plot the resulting PDF\n",
    "plt.plot(x_values, p_values,'r-', lw=5, alpha=0.8); plt.title('Sampling the ' + str(dist_type) + ' PDF, $f_x(x)$'); plt.xlabel('Values'); plt.ylabel('Density')\n",
    "plt.xlim([0.0,0.3])\n",
    "\n",
    "plt.subplot(1,3,2)                                                           # plot the resulting CDF\n",
    "plt.plot(x_values, P_values,'r-', lw=5, alpha=0.8); plt.title('Sampling the ' + str(dist_type) + ' CDF, $F_x(x)$'); plt.xlabel('Values'); plt.ylabel('Cumulative Probability')\n",
    "plt.xlim([0.0,0.3])\n",
    "\n",
    "p_values = np.linspace(0.00001,0.99999,100)                                 # get an array of p-values\n",
    "x_values = my_dist.ppf(p_values, loc = low, c = mode, scale = interval)      # apply inverse to get x values from p-values\n",
    "plt.subplot(1,3,3)\n",
    "plt.plot(x_values, p_values,'r-', lw=5, alpha=0.8, label='uniform pdf')\n",
    "plt.xlim([0.0,0.3])\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=3.0, top=1.1, wspace=0.2, hspace=0.3); plt.title('Sampling Inverse the ' + str(dist_type) + ' CDF, $F^{-1}_x(x)$'); plt.xlabel('Values'); plt.ylabel('Cumulative Probability')\n",
    "\n",
    "print('The mean is ' + str(round(my_dist.mean(loc = low,c = mode, scale = interval),4)) + '.') # calculate stats and symmetric interval\n",
    "print('The variance is ' + str(round(my_dist.var(loc = low, c = mode, scale = interval),4)) + '.')\n",
    "print('The interval at an alpha level of ' + str(round(1-level,3)) + ' is ' + str(np.round(my_dist.interval(alpha = level,loc = low,c = mode,scale = interval),2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The missing lower tail for the inverse is due to any value less than 0.05 having 0.0 cumulative probability.\n",
    "\n",
    "#### Gaussian Distribution\n",
    "\n",
    "Let's now use the Gaussian parametric distribution.\n",
    "\n",
    "* we will need the parameters mean and the variance\n",
    "\n",
    "We will apply the forward and reverse operations and calculate the summary statistics.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean is 0.15.\n",
      "The variance is 0.0025.\n",
      "The interval at an alpha level of 0.05 is [0.05 0.25]\n"
     ]
    },
    {
     "data": {
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NbKqZfVFDuZnZ7Wb2nZl9ZmZbxp2jiIiIiIhIbRpn68RmtiZwOtDd3ReY2ePA4cCgbF1TJFaLF8O4cfD55zB+PCxZsrysaVNYbz3YdFNYf31onLX/aiJSs0HAHcDgGsr3BtZPPLYF7k58FRGRTFmyBBYsgIULqz8WLQqfpRYtCsdUfl28OHxdujR8rfy+8rFsWXgUCTN7EOgFTHX3TVKUG3AbsA8wH+jv7h/Fm6WIiORStlsTGgMrm9kSoBkwJcvXE8muBQvgxRfhuedg7NjwAbIu5eWhAa93b9hjj/BcRLLO3d8ysy61HNIbGOzuDrxvZq3NbA13/zmWBEVECsHSpTBrVnjMnr38MWcOzJ27/Ou8edUfCxbA/PnpfVYqbYNQJ5OISH5zD51GVTuRUn2f3NGUIVlruHP3yWZ2IzARWAC87O4vJx9nZicCJwJ07tw5W+mIrJiff4bHH4cRI8KH0/pYvBg+/DA8br0VDjoIDj4Y2rbNTq4ikq41gZ+qPJ+UiKnhTkSKX0VFaIz75Rf49dfwddq08Jg+PXydNSs0zEnWqJNJRCRN7vDbbzBlCkyeHL7OmxdtLKupEa2mY9JphKuoyOmPns2psqsSKpp1gN+AJ8zsSHd/pOpx7j4QGAjQs2dPz1Y+Ig2yeDHcfz88/HBmWsxnzoT77oPBg+Gkk+CII6BRoxU/r4g0hKWIReohdTCJSMGqqAgNchMnwo8/hkflzc7kyeFzjuS7tDqZVFeJSFFYuLB6w9zkycsfU6aEkdwlKJtTZfcAfnD3aQBm9jSwA/BIra8SyRcffQRXXx0+7GbaokVw++3w0ktwySWw4YaZv4aI1GUSsFaV551IsaSDOphEpCDMmhXW3v3mG/j++7D+7vjx4TOHFLK0OplUV4lIwVi2LNRT48bBpEnVG+hmzMh1dnkpmw13E4HtzKwZYars7sCYLF5PJDOWLIGbb4Ynnqj72Hbtwvp1m2xSferr1Klh04ovvggfpGsybhz06wf9+8PJJ0NZVjd6FpHqngVOM7PhhPWCZmvqkYgUhN9/D2vtfvFFeHz9dfjskY/KyqBZM1hppeWPpk3DY6WVwtq/VR9NmoRHeXnY3CvVo1Ej2H//XP9kcUmrk0lEJC9VVMBPP8GXX8JXX4Wv48apU6mesrnG3Qdm9iTwEbAU+JhEL5BI3vrtNzj3XPj445qPKS+HP/0JDjsMNtgALFVHaIJ7aMAbPhxeey31dNuKCnjwQfjuuzDCr1mzFf85RAQzGwb8EWhnZpOAy4AmAO5+D/ACYZe+7wg79R2Tm0xFROowY0b4bPLRR+Hx/ffhM0YczKBVK1h1VWjdOnxf+WjRYvmjefPwWGWV8FlmlVVg5ZVDI1xtn5WkLupkEpHCMWMGfPJJ6FwaOzY01v3+e66zyoyysto7lFJ9/+GHGbl0VneVdffLCDdKIvnvhx/gzDPDEN1UGjcOo+P69g0fXNNhBj16hMe0aTBoUNjkItWH7bfeguOOg1tugdVXb/CPISKBu/epo9yBU2NKR0QkfQsWhIa6998Pj/Hjs3OdZs3CZ47KR4cO0L59eLRrF2YTtG6t9XizSJ1MIlLQFi0KDXWV9dW332b3ek2bwpprQseO4WvbtjU3oNXWoJZ8XF2vadSoYZ1QDzyQkR87qw13IgVj1Cg477yaewN69IABA6Br14Zfo337MJpvn33gqqvCCLtk334bGgdvvRW6d2/4tURERKSwTJ0Kb78dOvJGj87cxhHNm0OXLtC5M6y9Nqy1FnTqFG56WrXSaLgcUyeTiBQU9zDqu7Kh7qOPMrvRkRmstlqooyrrqjXXXP5o06Yk6y013ImMHh1G2qV6w2nUKJQddljm1p/beGN45JEwPXZgitnjM2fCKafAPfdo0woREZFi9ssv8Oqr8MorYd2fFVFWFjoYu3ULS3msu2543r59Sd7kiIhIhriHjY9eeSU8apqhVh8tW4b74vXXr95At/rqYYkFqUYNd1LaPvkE/va31I12LVvC9ddDz56Zv27jxnDiieGN6pJLwrbXVf3+O5x6Ktx7L6y3XuavLyIiIrkxZ07YVf6FF8I6uA211lrLN8iqvPkpL89cniIiUrrcwwyxysa6n35q+LmaNQsDUjbeOMwq6949NNSpUyltariT0vXll3D66dFGMwjTSW69NXzNpl13DfPe//a36G5ws2eHkXcDB4YpLiIiIlKYKirg3Xfh2WfDdNglS+p/jvXWg622gi23hC22CNOFREREMmn2bHj+eRgxouHrq663XqirNt4YNtoo3MtmavZaiVLDnZSm776D006D+fOjZd27wx13hBF3cejWDR5+GP7yF5gwoXrZzJkh/sADoVdCRERECseMGfDMM/D002FabH20aQPbbw/bbQfbbquGOhERyQ73sPvpv/4Fr79e/86lVVcNddV228E224QlGiSj1HAnpWfWrDDCbe7caNkGG8TbaFepfXu4664wfXbSpOpl06bB2WeHxrtmzeLNS0REROpv3Liwnu3LL8OyZem/rmtX+OMfYeedQ0eiRiiIiEi2zJ8PI0fCY4/BxInpv66sLIz83nHH0Fi33nqqr7JMDXdSWpYsgfPPh59/jpZ17Roaz+JutKvUoQPcfTeccEK0V/7bb+Gyy+Af/9CbooiISD5yh//+F4YMCSMX0tW1K+y5J+yxh5bGEBGR7Js+PTTWPfVUWHc1HWahse7//g92312jwGOmhjspHe5www1hy+pknTuHRrPWrePPq6o11gi7yZ5wQhhpV9V//gP33QcnnZSb3ERERCSqogLeeAPuvz/supeONm1g772hV6+wqYSIiEi2/fQTPPRQ2Bxp6dL0XtOjB+y1V2isa9cuu/lJjdRwJ6XjiSfCGjPJWraE22+Htm3jzymVTp3CxhjHHguLFlUvu+8+WHfd0CsvIiIiueMe1gIaOBC+/77u481gp53ggAPC9KJGjbKfo4iIyOTJoXPp+edDZ1NdWrcOHUv776+R4HlCDXdSGr74Am66KRovKwvTTzt1ij+n2nTrBldcARdcEC27/PLQO7/22rGnJSIiIsCoUWFN3LFj6z521VVDY90BB4SR9SIiInH49Ve491547rn0Guy22SbUVbvsAuXl2c9P0qaGOyl+8+bBRRelXhz63HNh663jzykde+wRpszed1/1+MKF4ed56CG9oYqIiMTp22/DqPgPPqj72C5d4IgjYJ99oGnTrKcmIiIChPvfQYNg6FBYvLj2Y5s0CUs3HHlkWHNV8pIa7qT4XXcdTJkSjR90EBxySPz51McJJ4TpN6+/Xj0+bhzceWfYHVdERESya/bssBbu00/XPWphk03guOPCdFhtKCUiInFZtizUUwMHwqxZtR/bsiUcfDAcdlj+LBklNVLDnRS3F16AF1+Mxrt3h3POiT+f+iorC1Njv/suukX30KGw7bawww45SU1ERKToVVTAk0+GjaPq2nlvs83gxBPDVCOzePITEREB+OSTsATUt9/WflzLlnDUUaHBrlmzeHKTFaaGOyleP/0URtsla9YMrr02DAsuBM2awTXXwDHHRHf/ufxyGD5c23GLiIhk2rhxof6tax27bt3gtNNgu+3UYCciIvGaOTNstPjcc7Uf17JlmA572GGwyirx5CYZo4Y7KU4VFXDZZTB/frTsggvybzOKumy0EZx6Ktx2W/X4zJlw9dVh4w3dLIiIiKy4BQvCYt6PPlr7tNhOneCUU8KatJoSKyIicXIPjXW33FL7iPDycujTB/r3hxYtYktPMksNd1KcHn8cPvssGv/Tn8Lim4XoiCPCYtjvv189/tZb8MorsOeeuclLRESkWHz8cRjNPnlyzcc0axbWoD388MIZvS8iIsVjypQwIryujZL22Qf+8hftaF4E1HAnxWfKFLjjjmi8Y8cw2q5QR6aVlcEVV4QbheTFRm+4Iayp07p1bnITEREpZIsWwV13hVF27jUft99+YQS8FvIWEZG4ucO//hVG2S1YUPNxG20U7ns33ji+3CSrNK5fiot7mDq6cGG07PLLoXnz2FPKqLZt4cILo/FZs8J0WREREamfr78Oo9qHDq250a5rV3jwQbj0UjXaiYhI/KZPhzPOCGu119Ro17JluFd8+GE12hWZrDXcmVk3M/ukymOOmZ2ZreuJADByJIwaFY0ffDBsuWX8+WTDbruFR7IXX4R33ok/HxERkUJUURFG2PXvDxMmpD6mvDysYzd0KPToEWd2IiIiwVtvwaGHwrvv1nzM3nvDU0/BQQdp3dUilLWpsu4+DtgcwMwaAZOBf2XreiJMnx6GDSfr0AH++tf488mm88+H0aNh7tzq8WuvhSee0E5BIiIitZk5M4zEr+0mqEePcEznznFlJSIistzixWFzwsceq/mY1VaDiy6CHXeMLy+JXVxNsbsD37v7jzFdT0rRbbdFG7IALr64+Bqy2raFs86KxqdOhYED489HRESkUHzyCfTtW3OjXZMmcPrpcP/9arQTEZHc+OmnMCK8tka7/fcPmzKq0a7oxdVwdzgwLFWBmZ1oZmPMbMy0adNiSkeKzkcfhamiyfbZp3jfyHr1gm23jcaHDYPx4+PPR0REJJ+5hzrypJPCKP1UNtggTIvt109TjUREJDfefBOOPBK++SZ1eZs2cPPNMGBA8Q1QkZSy/onEzMqB/YAnUpW7+0B37+nuPdu3b5/tdKQYLVsWdlVN1qpV6lFpxcIsjCZs2rR6vKICrr++9l3xRERESsn8+aHOvOmm8Lkhlb59YdCgsBGFiIhI3Coq4J//hLPPhnnzUh/zhz+EUXg77xxvbpJTcXQl7g185O6/xnAtKUVPPgnffhuNn3YatG4dfz5x6tgRjj02Gh8zBl59Nf58RERE8s3PP4e68uWXU5e3bg233ho6+8rL481NREQEYM4cOPPMsCNsKk2ahAa9m2+GVVeNNzfJuTga7vpQwzRZkRU2cybcfXc03r079O4dfz65cNRR0KlTNH7LLWGEgYiISKn69NMw7fW771KX9+gRdpbdaad48xIREak0YUJYz66mtVfXXBMeegj69AmzrqTkZLXhzsyaAf8HPJ3N60gJu+MO+P33aPz880tnbZrycjjnnGh86lR44IH48xEREckHI0eG9exmzUpdfthhcO+9Yfd5ERGRXBg1KjTaTZyYunznneGRR2DDDWNNS/JLVls23H2+u7d199nZvI6UqK+/hmefjcZ794aNN44/n1zaaaew3kGyRx+FKVPiz0dERCRX3MNo/CuugKVLo+VNm8LVV8O554apRyIiIrnw9NNheadUA1HM4JRT4MYboUWL+HOTvFIiQ5Kk6LiHqaDJWrQIb36l6Oyzo2vzLFkSRiWKiIiUgiVL4PLLax5x3qEDPPgg/OlPsaYlIiLyPxUV4R7t2mvD98lWWSXc6x57bOnMIpNa6a9ACtM778CHH0bjJ59cuot1duoU1rtL9vLL8MUX8ecjIiISp3nzwsLezz+funyTTWDIEOjWLd68REREKi1ZApddFnYxT6Vz57BBhdZelSrUcCeFZ9kyuO22aLxzZzjooPjzySdHHw1t2kTjt94aRimKiIgUo5kz4cQT4YMPUpfvvTcMHAht28abl4iISKX58+GMM+DFF1OXb7VVaNDr0iXOrKQAqOFOCs+IEWHnnWSnnw6NG8eeTl5p1iyMOkz2ySfwxhuxpyMiIpJ1v/wCxx8P48alLj/+eLjyyuhyEiIiInGZNSvcp40albp8v/3C9NmWLePNSwqCGu6ksMybF3aAS7bFFrDLLvHnk49694Z11onGb789DM0WEREpFj/+CMcdl3o3vrIyuPjicKNkFn9uIiIiAFOnwgknwNixqctPOgkuuUQbJkmN1HAnhWXw4DAdJtmZZ+pDeaVGjcIQ7GQ//RR2LhIRESkG33wTRtP9+mu0bKWV4Oab4YAD4s9LRESk0uTJoa5KNWOsrAwuvTQ06uleVmqhhjspHDNnwqOPRuN77QUbbxx/Pvlsxx1h662j8QcegAUL4s9HJAfM7E9mNs7MvjOzC1KUdzaz/5jZx2b2mZntk4s8RaQBvvoqjKSbNSta1qIF3HWXFvYWEZHc+vHH0Gg3ZUq0rLwcbrwxTK3UMwEAACAASURBVJEVqYMa7qRwPPhgtNGpSRM49dTc5JPPzFKPQpw5E4YNy01OIjEys0bAncDeQHegj5l1TzpsAPC4u28BHA7cFW+WItIgX34Jf/kLzJkTLWvTJmxC0aNH/HmJNIA6mUSK1PjxYSTdtGnRsubN4c47Yeed489LCpIa7qQw/PwzPPVUNH7IIdCxY/z5FIJu3WDPPaPxwYNT3+yIFJdtgO/cfby7LwaGA72TjnGgcgXgVkCK7lARySuffw6nnAK//x4tW2ONMLJ8/fXjz0ukAdTJJFKkvv8+rFuXaomn1q3hnnvCGu0iaVLDnRSG++6Lbqyw8srQv39O0ikYJ50U1k6o6vffYciQ3OQjEp81gZ+qPJ+UiFV1OXCkmU0CXgD+Gk9qItIgX3wRRtnPmxct69w5NNqttVb8eYk0nDqZRIrN+PE1L+XQvn0YFb7hhvHnJQVNDXeS/378EZ57Lhrv2zdMiZGade4cdplNNmwYzJgRfz4i8Um1wq8nPe8DDHL3TsA+wBAzi9SLZnaimY0xszHTUk13EJHsGzcO/vpXmD8/WtalS7gR6tAh9rREVlDGOplUV4nkgQkTam60W221UFd17Rp7WlL41HAn+e+ee6CionqsZUs46qjc5FNoTjghLH5a1cKFYc1AkeI1Cag69KYT0VEKxwGPA7j7e8BKQLvkE7n7QHfv6e4927dvn6V0RaRG48eH6bFz50bLunaFe++FdpH/uiKFIGOdTKqrRHJs0qSw/mqq6bFrrBFmkGlUuDSQGu4kv33zDbzySjTev39Y1FPq1qFDWAsw2VNPhbUDRYrTaGB9M1vHzMoJ6wI9m3TMRGB3ADPbiNBwp2EKIvlk4sQwemH27GhZ166hc69t2/jzEsmMjHUyiUgO/fJLaLRLNdp1jTVCB5PWZZcVoIY7yW8DB0Zj7drBoYfGn0sh698fmjWrHlu6FB56KCfpiGSbuy8FTgNeAr4iLOz9pZldaWb7JQ47GzjBzD4FhgH93T15pIOI5ErljVCq0Qtrrx0a7bRkhhQ2dTKJFLqZM8Oo8FQDIlZfXY12khFquJP8NW4cvPFGNH7ccbDSSrGnU9BWXRWOOCIaf/ZZjbqTouXuL7j7Bu6+rrtfk4hd6u7PJr4f6+47uvtm7r65u7+c24xF5H9mzQobUfz6a7RszTXh7rvVaCcFT51MIgVu7lw47bQwOjxZ+/ahg0mNdpIBariT/JVqtN1qq6XebEHq1rdvdHqxRt2JiEi+mT8fzjgjbE6VbLXVwo2QNqKQIqFOJpECtXAhnHlmWNopWZs2oYOpU6f485KipIY7yU/jxsGbb0bjxx4b3WhB0tOiRWi8S/bMMxp1JyIi+WHxYjj7bBg7NlrWpk1otFtjjfjzEhERqbR0KVx4IXz6abSsRQu4886w47lIhmS14c7MWpvZk2b2tZl9ZWbbZ/N6UkRqGm23777x51JM+vSJjrpbtkw7zIqISO5VVMDll8Po0dGy5s3hjju0I5+IiOSWO1xzDbz9drRs5ZXh9tth/fXjz0uKWrZH3N0G/NvdNwQ2I6zdIFI7jbbLnppG3T37LExJ3sRMJD+Y2RgzO9XMVs11LiKSRf/8J7ycYhZgeTnccgtssEH8OYmkSXWVSIm4+24YOTIab9IEbroJNt00/pyk6GWt4c7MWgI7Aw8AuPtid/8tW9eTIlLTaLv99ovGpf769AkNeFVp1J3kt8OBjsBoMxtuZnuZmeU6KRHJoOHDYciQaLysDP7xD9hii/hzEqkf1VUixe7pp1PfM5nB1VfDNtvEn5OUhGyOuOtK2Kr8ITP72MzuN7NVkg8ysxMTPVRjpk3TzuYl75tvUo+2O+640IshK66mUXfPPQe//BJ/PiJ1cPfv3P1iYAPgUeBBYKKZXWFm2lZSpNC9/noYpZDKpZfCH/4Qbz4iDaC6SqTIvf02XHdd6rLzz4fdd483Hykp2Wy4awxsCdzt7lsA84ALkg9y94Hu3tPde7Zv3z6L6UhBSLXDqda2y7xUo+6WLoXBg3OTj0gdzKwHcBNwA/AUcDAwB3g9l3mJyAr6/HMYMCCsGZTslFOgV6/4cxJpINVVIkXqq6/CZhQVFdGy446Dgw+OPycpKdlsuJsETHL3DxLPnyQ05ImkNmECvPpqNN6/v0bbZVrz5nD44dH4iBEwY0b8+YjUwsw+BG4BRgM93P10d//A3W8Cxuc2OxFpsClTwg6yixdHyw48EI45Jv6cRBpIdZVIkfrlFzjzTFi4MFq2775w8snx5yQlJ2sNd+7+C/CTmXVLhHYHxmbrelIEHnoo2uPerh307p2bfIpdnz7QrFn12OLF8MgjuclHpGaHuPvu7v6ouy8CMLN1ANz9wNymJiIN8vvv4UZo5sxo2c47h2lHWh5MCovqKpFiM29eqKtSDWzYbju4+GLVVRKLbO8q+1dgqJl9BmwOXJvl60mhmjwZXnwxGu/XTzvJZkvLlnDIIdH4k0/Cb9pHRvLKk2nGRKQQLFsGF1wA41MMQtpoI7jmGmjUKP68RFaM6iqRYlJRARddBN99Fy1bf/2wcVLjxvHnJSUpq39p7v4J0DOb15AiMWhQdM2A1q3hgANykk7JOOKIsJPfokXLYwsWwLBh8Je/5C4vEcDMNgQ2BlqZWdXRCi2BlXKTlYissJtugvffj8Y7dIBbboGVV44/J5EGUl0lUqRuvRX++99ovH17uO02WCWy76ZI1qiJWHLv119h5Mho/Igj9OE929q0CesIDRtWPT58OBx5ZHQDC5F4dQN6Aa2BqjvUzAVOyElGIrJinn4aHn88Gm/WLNwktWsXf04iK0Z1lUixGTECHn00Gl955VBXdegQf05S0tRwJ7k3ZEjY0bSqFi3g0ENzk0+pOeqoMD12yZLlsXnz4Ikn4Nhjc5eXlDx3fwZ4xsy2d/f3cp2PiKygjz4KU4uSlZXBtdfCBhvEn5PIClJdJVJkPvoIrrsuGjeDq6+Gbt2iZSJZpoY7ya1Zs+Bf/4rGDz9cw4/j0qFD2BHp6aerx4cNg759YSXN8pDcMLPz3P16oK+Z9Ukud/fTc5CWiDTElClw3nlhfbtkZ54JO+0Uf04iGaC6SqSIVNZVyYNKAP76V9hll/hzEkENd5JryeurQRiCfPjhucmnVPXvH4aEV11ncNYsePZZjXyUXPoq8XVMTrMQkRUzfz6cdVbqjY969w67nIsULtVVIsVgwQI455zUddV++4VZSiI5ooY7yZ1581Kvc3PggdCqVfz5lLKOHWGvvaI7+w4eHP49tGOS5IC7j0x8fTjXuYhIA7nDlVem3pVvs83g/PPD9CORAqW6SqQIVNZV33wTLdtss7ATuuoqySHdjUvuPPUUzJ1bPda4cdiUQuLXv3+04e6XX+Cll+DPf85JSlLazGwk4DWVu/t+MaYjIg0xZAi8+mo0vtpqcMMNUF4ef04iGaS6SqQIDB4Mr7wSjauukjyhhjvJjcWLYejQaLxXL+3Skyvrrgs77wxvvVU9PmgQ7L13WDxcJF435joBEVkBH3wAd9wRjTdtCrfcEnY2Fyl8qqtECtl779VcV918s+oqyQtquJPceO45mDGjeqysDPr1y00+EvTvH224++GHEPvjH3ORkZQwd38z1zmISANNmQIXXlh97dRKl12mHWSlaKiuEilgkyfDxReHqbLJLr1UO8hK3tAQGonfsmXwcIplQHbfHTp3jj8fWa5HD9hyy2j8oYdSV2giWWRmjye+fm5mn1V5fG5mn+U6PxGpwaJFYYHvOXOiZUcdBXvuGX9OIlmiukqkQC1cCOeem7qu6tcvrP8tkic04k7i99proXcjWf/+saciKRxzDHz0UfXYl1+G2FZb5SYnKVVnJL72ymkWIpI+d7juutQLfG+zDZx2Wvw5iWSX6iqRQuMO115bc1116qnx5yRSC424k3i5px5tt8MOGoqcL7bbDjbcMBpP9e8mkkXu/nPi64/AImAzoAewKBETkXzzzDMwcmQ0vsYa4SapUaP4cxLJItVVIgXoqafghRei8TXWgL//XXWV5B013Em8Ro2CceOicY22yx9mcPTR0fi776bulRLJMjM7HhgFHAgcDLxvZsfmNisRifjqK7j++mi8vDzEW7eOPyeRmKiuEikQX34JN6bYU6a8POwg26pV/DmJ1EFTZSVegwZFY5tsAltsEXsqUovdd4dOnWDSpOrxhx+Ga67JTU5Sys4FtnD3GQBm1hZ4F3gwp1mJyHJz5sB554Vd45Odfz5stFH8OYnES3WVSL777bdQVy1dGi278MLUs45E8oBG3El8xo6F0aOj8aOPDqO8JH+UlYUFxJO98krYKVAkXpOAuVWezwV+ylEuIpKsoiLsvvfzz9Gy/faD3r3jz0kkfqqrRPJZRQVccgn8+mu07MADYd99489JJE0acSfxSbVG2tprwy67xJ+L1K1XL7j3Xpg5c3msogIeeST0VIlkmZmdlfh2MvCBmT0DONCbMB1JRPLBI4/AO+9E4926hdF2IkVMdZVIgXjwQXjvvWi8e/ewE7pIHtOIO4nHxInw+uvReL9+YXSX5J+mTeHww6PxZ56BWbPiz0dKUYvE43tgBOFGCOAZIMXQHhGJ3SefwB13ROMtWoR17Zo2jT8nkXiprhLJd6NHhwEJyVq2hH/8I6xvJ5LHNOJO4vHII2FH2arat4e9985NPpKeQw4J6xLOn788tmgRPPYYnHxyztKS0uDuV+Q6BxGpxaxZYU2giopo2RVXwJprxp+TSMxUV4nkuenT4eKLo/eiAFdfHXaSFclzGuok2TdjBjz3XDTet696N/JdixZw0EHR+OOPw4IF8ecjJcnM2pvZDWb2gpm9XvnIdV4iJa1yXbtp06JlRx0FO+8cf04iOaS6SiQPVVSERruqS/9UOvZY2GGH+HMSaYCsNtyZ2QQz+9zMPjGzMdm8luSxxx6L7jLXvHlYBFTyX58+0DhpcO6cOWHKrEg8hgJfA+sAVwATgBQ73YhIbB5+OPVaQT16wKmnxp+PSO6prhLJN/fdBx9+GI1vtZVmD0lBiWPE3a7uvrm794zhWpJv5s+HJ56Ixg8+GFZZJf58pP46dIB99onGH3kk9VbqIpnX1t0fAJa4+5vufiywXa6TEilZn34Kd98djbdqBdddF+3sESkNqqtE8smoUXD//dF4mzZwzTVaZ10Kiv5aJbtGjIC5c6vHmjQJo7ikcBx1VDT2yy/w6qvx5yKlaEni689m9mcz2wLolMuERErW7Nlw0UWp17W76qrQ2SNSmlRXieSLmTNhwIDounZmYV27du1yk5dIA2W74c6Bl83sQzM7MdUBZnaimY0xszHTUq2TIoVryZIwKitZr17Qtm38+UjDrbNO6vWKBg9OvdCrSGZdbWatgLOBc4D7gb/lNiWREuQeNp349ddo2dFHa60gKXWqq0TyQUUFXHJJ6nXtjj8ettkm/pxEVlC2G+52dPctgb2BU80scufv7gPdvae792zfvn2W05FYvfwyTJ1aPWYGRx6Zm3xkxRx9dDT2zTfw/vvx5yIlxd2fc/fZ7v6Fu+/q7lu5+7N1vc7M/mRm48zsOzO7oIZjDjWzsWb2pZk9mvnsRYrIsGHw1lvReI8e8Je/xJ+PSB5paF0lIhn28MPwwQfReM+ecMIJ8ecjkgFZbbhz9ymJr1OBfwFq3i4V7uFNM9kf/whrrx17OpIBm20Wbs6SDR4cfy5SUsysq5mNNLPpZjbVzJ4xs651vKYRcCeh46g70MfMuicdsz5wIaGTaWPgzCz9CCKF7+uv4fbbo/EWLcJaQVrXTkpcQ+qqxOvUySSSKZ99lnoN1lVXDVNkta6dFKis/eWa2Spm1qLye2BP4ItsXU/yzLvvwvjx0Xi/fvHnIpmTatTd6NEwdmz8uUgpeRR4HFgd6Ag8AQyr4zXbAN+5+3h3XwwMB3onHXMCcKe7z4L/dTKJSLL588O6dqk2JLrsMlhjjfhzEsk/9a6r1MkkkkFz5tS8BuuVV2pdOylo2WxyXg14x8w+BUYBz7v7v7N4PcknqUbbbbEFbLpp/LlI5vzhD6lHTGrUnWSXufsQd1+aeDxCWEO1NmsCP1V5PikRq2oDYAMz+6+ZvW9mf8pgziLF44YbYOLEaPzQQ8NIehGBhtVV6mQSyQT3MKLul1+iZf36wfbbx5+TSAZlreEuUQFtlnhs7O7XZOtakmc+/xw++iga12i7wldWlvrf8fXX4aefonGRFWBmbcysDfAfM7vAzLqY2dpmdh7wfF0vTxFLvoFqDKwP/BHoA9xvZq1T5KFNlKR0/fvfMHJkNL7BBnCmBv6IrGBdlbFOJtVVUtL+9a9wP5Jsk03glFPiz0ckw7QgiWTekCHRWNeusOOO8ecimbf33mHtiOnTl8cqKmDoULgg5dIsIg31IaGxrbIR7qQqZQ5cVctrJwFrVXneCZiS4pj33X0J8IOZjSM05I2uepC7DwQGAvTs2VPbKEvpmDwZrr02Gl9ppRAvL48/J5H8syJ1VX07mToBb5vZJu7+W7UXqa6SUjV+PNx0UzTevHmoq7QGqxQBrc4omTVxIvznP9F4v35aDLRYlJdD377R+LPPpt52XaSB3H0dd++a+Jr8qGvB79HA+ma2jpmVA4cDybv7jQB2BTCzdoRRDSkW5xQpQUuXwsUXh/Xtkp13HnTpEntKIvloBeuqdDuZnnH3Je7+A1DZySQiixeHde0WLYqWDRgAHTvGn5NIFqglRTJryJCwxkBVHTrAXnvlJh/JjgMPhFVWqR5bvBgeeyw3+UhRM7MmZna6mT2ZeJxmZk1qe427LwVOA14CvgIed/cvzexKM9svcdhLwAwzGwv8BzjX3Wdk82cRKRgDB8IXKfYU23NP2Hff+PMRyXMNqatQJ5PIirn1Vvjuu2j8gANgjz3iz0ckS9RwJ5kzYwY891w0fsQR0KSuzy1SUJo3h4MOisafeCL16AyRFXM3sBVwV+KxVSJWK3d/wd03cPd1K9dZdfdL3f3ZxPfu7me5e3d339Tdh2fxZxApHB9+CA89FI137BhGNliq2X0iJa/edZU6mURWwFtvweOPR+PrrANnnx1/PiJZlNaEbzN7CngQeNHdU+yvLAIMHw5LllSPtWgRejyk+PTpA8OGVf83nzMHRoxIPZVWpOG2dvfNqjx/PbFjuYhk2pw5cMkl0dHzZWVhx77mzXOTl0j+a1Bd5e4vAC8kxS6t8r0DZyUeIgIwbRpceWU03qQJXHNNWItVpIikO+LubqAv8K2ZXWdmG2YxJylE8+aF0VbJDjkEmjWLPx/JvvbtYZ99ovGhQ8PaSCKZs8zM1q18YmZdgWU5zEekOLmHxrmpU6NlJ50EPXrEn5NI4VBdJRKHigq47DL47bdo2RlnhF3PRYpMWg137v6qux8BbAlMAF4xs3fN7Jg01m6QUvDUU/D779Vj5eVw2GG5yUficdRR0SlTv/4KL72Um3ykWJ0L/MfM3jCzN4HXAc2BEMm0Z56B11+PxrfcEo45Jv58RAqL6iqROAwdCqNGReM77aR7Tylaae+NbGZtgSOBo4CPgaHATsDRhO3JpVQtXgyPPhqN9+oFbdvGn4/Ep0sX2HlnePPN6vGHH4a999ZOwrLCzKwMWEDYQa8bYMDX7p5i+zARabAff4Qbb4zGW7SAq67S+7lILVRXicTk66/hzjuj8TZt4NJLtQarFK20PoWZ2dPA20AzYF9338/dH3P3vwJa7KTUvfgiTJ9ePVZWFkZjSfHr3z8aGz8e/vvf2FOR4pNYV/Umd1/k7p+5+6e6ERLJsCVLYMAAWLgwWjZgAKy2Wvw5iRQQ1VUiMViwAC6+OPWSPFdeGRrvRIpUut2n9yd23fu7u/8MYGZNAdy9Z9ayk/xXUQGDB0fju+0Ga60Vfz4Sv003DdOokj38cPy5SLF62cwOMlM3qkhW3HMPfPVVNL7ffrD77vHnI1KYVFeJZNMtt4TR4cmOOAK22y7+fERilG7D3dUpYu9lMhEpUG++mfoN9Oij489FcifVv/cnn8Bnn8WfixSjs4AngEVmNsfM5prZnFwnJVIUxoxJ3QG31lpwzjnx5yNSuFRXiWTLG2/A009H4xtsAKeeGns6InGrdY07M1sdWBNY2cy2IKzXANCSMG1WSpl76lFV22wDG20Ufz6SOzvsAOutB999Vz0+aBDcfHNOUpLi4e4tcp2DSFGaMyesCeRePd6oEVxzjXaFF6kH1VUiWTJtWlhrNVnTpqGuKi+PPyeRmNW1OcVeQH+gE1D17nsucFGWcpJC8fHH8MUX0bhG25UeM+jXL9wAVvXWW2G9u65dc5OXFDQz60Coa9YDPgOuc3eNXhDJBHe49lqYOjVadvLJ0L17/DmJFCDVVSJZVFEBl18Os2dHy846C9ZZJ/aURHKh1qmy7v6wu+8K9Hf3Xas89nP3FGNVpaQ89FA01q1bGHEnpWfPPWH11aNxrXUnDTcYmAf8E2gB3J7bdESKyPPPw6uvRuNbbqkOOJH6UV0lki3Dh8MHH0TjO+8MBx4Yfz4iOVLXVNkj3f0RoIuZnZVc7u6aA1eqxo2D91Isc3j00dqGu1Q1bgxHHgk33lg9/u9/h9Eba6yRm7ykkK3u7hcnvn/JzD7KaTYixWLSJLj++mi8efOwM19Zuksgiwiqq0Sy45tv4J//jMbbtoVLLtE9p5SUuj6ZrZL42pzQg5T8kFI1aFA01qmTdp8rdb17Q6tW1WPLlsEjj+QmHyl0ZmarmlkbM2sDNEp6LiL1tWxZWNZg/vxo2UUXpR45LSK1UV0lkmmLFsGAAbBkSbTs8sth1VVjT0kkl2odcefu9ya+XhFPOlIQJk6E116Lxvv1CwtaS+laeWXo0wfuuad6fMQIOP54VbJSX62AD1m+MRJA5UgGB7R4okh9PfBA6h2/99knLHkgIvWlukok0267LayTnaxvX9h++/jzEcmxtOZCmNn1ZtbSzJqY2WtmNt3MjkzztY3M7GMze27FUpW8MXhwWCi0qnbtoFev3OQj+eXQQ6M7ES5aBMOG5SYfKVju3sXdu7r7OikeuhESqa/PP4f774/GO3aE88+PPx+RIqC6SiTD/vtfePzxaHy99eC00+LPRyQPpLuIyZ6J3ZF6AZOADYBz03ztGcBXDchN8tHUqfBcijbYvn21FbcELVumXiz2iSdg3rz48xERkTA1dsCAaMdbWRlcdRWsskrq14mIiMRl5ky4IsVkv/JyuOYa3W9KyUq34a5J4us+wDB3n5nOi8ysE/BnIEX3rhSkRx+FpUurx1q0gIMPzk0+kp+OOAKaNKkemzsXnnoqN/mIiJS6G2+EyZOj8WOPhc02iz8fERGRqtzDBkkzUzQ1nH46rLtu/DmJ5Il0G+5GmtnXQE/gNTNrDyxM43W3AucBFTUdYGYnmtkYMxszbdq0NNORnJg9G55+OhpPNTVSSlv79qmnTg8dCosXx5+PiEgpe+01ePbZaHzjjcP6oyIiIrn25JPwzjvR+A47wGGHxZ+PSB5Jq+HO3S8Atgd6uvsSYB7Qu7bXmFkvYKq7f1jHuQe6e09379m+ffs005acGD48ugtd06Zw+OG5yUfy21FHhSlYVc2YAc88k5t8pKCZ2U5mdkzi+/Zmtk6ucxIpCFOnhulFyVZeGa6+GhrXuk+ZiNSD6iqRBho/Hm65JRpv3RouuwzMomUiJSTdEXcAGwGHmVk/4GCgrq3HdgT2M7MJwHBgNzN7pEFZSu7Nmxca7pLtv792CpXUOneGPfaIxgcPjk63FqmFmV0GnA9cmAg1AVSfiNSloiLc8MyZEy0791xYa634cxIpUqqrRBpo8eKwBmuqWTmXXgpt28afk0ieSXdX2SHAjcBOwNaJR8/aXuPuF7p7J3fvAhwOvO7uae1EK3noySfDGmVVNW4M/frlJh8pDMccE439/DO8+GL8uUghOwDYjzDaG3efArTIaUYihWDoUBg9OhrfbTfYd9/48xEpbqqrRBri7rvhm2+i8YMOgp13jj8fkTyU7vyInkB3d/dsJiN5atGi8OE/Wa9esNpq8ecjhWP99UOF+9Zb1eMPPQR//nN0Kq1Iaovd3c3MAcxM21+K1GXcOLjzzmi8fXu4+GJNOxLJPNVVIvU1ahQMGRKNr702/O1v8ecjkqfSvWv+Ali9oRdx9zfcPcVK9VIQRoyI7u5TVgZHH52bfKSwHHtsNDZxYlgsXSQ9j5vZvUBrMzsBeBW4L8c5ieSvhQtD41yqZQmuuAJatYo/J5Hip7pKpD5mzw7LOSRr3DiszbrSSvHnJJKn0h1x1w4Ya2ajgEWVQXffLytZSf5YsgQefjga33NPrY0j6dlkE9hmm9CjVtWDD4Y18DTqQ+rg7jea2f8Bc4BuwKXu/kqO0xLJX7feChMmRONHHBHej0Uk41RXidSDe9ggadq0aNkpp8CGG8afk0geS7fh7vJsJiF57Pnnw450yVKNohKpyXHHRRvuvv0W3n5ba1dInczsb8ATugESScNbb4V1aZOtvz6cemr8+YiUCNVVIvUwYgT85z/R+NZbw5FaFl8kWVpTZd39TWAC0CTx/WjgoyzmJflg6dIwKirZrrtC167x5yOFa8stoUePaPz++0OPm0jtWgIvmdnbZnaqmWlxTZFUpk+HK6+MxsvLw7Sj8vL4cxIpHaqrRNLx449w003ReMuWYTkHrYEtEpHurrInAE8C9yZCawIjspWU5IkXX4QpU6LxVDuFitTGLIy6SzZ2LLz3Xvz5SEFx9yvcfWPgVKAj8KaZvZrjtETyS0UFXH45/PZbtOzMM9XhJpJlqqtE0rBkSViDdeHCaNmAAdChQ/w5iRSAdJuzTwV2JKzZgLt/C+h/VTFbtgweeCAa33FH6N49/nyk8O2wA2y0UTQ+cKBG3Um6pgK/ADNQHSRS3fDh8P770fhOO8Ehh8Sfb37InAAAIABJREFUj0jpUl0lUpO77oKvv47Ge/eG3XaLPx+RApFuw90id19c+cTMGgO60y5mL70EkyZF4yecEH8uUhzMUv/9fPEFfPBB/PlIwTCzv5jZG8BrhM2STnD3FHOvRUrUN9/AP/8ZjbdpA5deqk2ARGKgukqkDh98AEOGROOdO8M558Sfj0gBSXdzijfN7CJg5cRuSacAI7OXluRURUVYeyzZ9tuHHUJFGuoPf4ANNgg3mVUNHAjbbqubS6nJ2sCZ7v5JrhMRyTsLF8JFF4XpR8kuvzw03olIHFRXidRk1qzQkZSsceOwBuvKK8efk0gBSXfE3QXANOBz4CTgBWBAtpKSHHvpJZg4MRrXaDtZUTWNuvvsMxg9Ov58JK+ZWcvEt9cDE82sTdVHLnMTyRs33wwTJkTjhx8eligQkaxSXSVSB/ew6cSMGdGyU05JvZSOiFST1og7d68wsxHACHefluWcJJcqKlKvbbfNNql3BRWpr112gfXXh2+/rR4fODBsAa9Rd7Lco0Av4EPC8gxV/zgc0Gr7Utr+8x94+ulofL314PTT489HpDSprhKpzeOPwzvvRONbbw1HHhl/PiIFqNYRdxZcbmbTga+BcWY2zcxSjHOVovDSS6l77jXaTjKlrAyOPz4a/+QTjbqTaty9V+LrOu7eNfG18qEbISltU6fCVVdF4+XlcO214auIZJ3qKpFafPMN3HZbNN6qVRiFV5buBECR0lbX/5QzCbvJbu3ubd29DbAtsKOZ/S3r2Um8li2D++6Lxnv2hC22iD8fKV677gpdU3yWvece7TArEWb2WjoxkZJRUQEDBsCcOdGys89O/f4qIlmlukokyYIFcPHFsHhxtOzSS6GDNl0WSVddDXf9gD7u/kNlwN3HA0cmyqSYvPBC6rXtTjwx/lykuJWVpf67+uwzeO+9+PORvGRmKyXWB2pnZqtWWTOoC9Axt9mJ5NCDD8JHH0Xju+wCBx4Yfz4iJWxF6yoz+5OZjTOz78zsglqOO9jM3Mx6Zi57kSy66Sb44Ydo/NBDQ30lImmrq+GuibtPTw4m1rlrkp2UJCeWLk092m6bbWDLLePPR4rfbruFte6SadSdLHcSYc2gDRNfKx/PAHfW9WLdDElR+uSTsCZosvbt4ZJLtE6oSPwaXFeZWaPEMXsD3YE+ZtY9xXEtgNOBDzKauUi2vPIKjBgRja+7LpxxRvz5iBS4uhruUoxrTatMCs3IkTBlSjR+8snx5yKloawMTjopGh87Ft5+O/58JO+4+23uvg5wTtK6QZu5+x21vVY3Q1KU5swJ044qKqrHzcJ6d61b5yYvkRK2InUVsA3wnbuPd/fFwHCgd4rjriLsWrsws9mLZMGUKXD11dF406bw97+HryJSL3XtKruZmaVYQAUDVspCPpILixfD/fdH4zvsoJ1kJbt22QU23BC+/rp6/J57YKedtGCtAODu/zSzTQgNcCtViQ+u5WX/uxkCMLPKm6Gx/9/encdJUZx/HP88u9xnWLlcFGERiIDEAxX1F4zGeIshGoNGJV544X2f8Yy3osQoaFQ03hgNGtTEgEc0iICCCooIiIgcERXlWmDr90fNZnene++Znpme7/v1mtfOVvXsPsWwXdPVVU8lHVd+MXRBSoMWSTXn/IXQ8uXBuhNO8PloRSRjGthXdQO+qPT9Enw+8f8xsx2BrZ1zL5qZ+irJbhs3wqWXwpo1wTrlYBVpsBqvip1zhc65diGPts45LZWNi+efD78Q0Gw7STez8P9n8+bBlCnRxyNZycx+D4xJPPbGD7QNreVlYRdD3ZJ+7v8uhmr5/SPNbLqZTV+5cmV9wxdJjQkTYPLkYPnAgcpFK5IFGthXha1t/1++EDMrAO4Ezq/D71dfJZl3773w0UfB8n32gWHDoo9HJCY0nSXfrV8Pf/5zsHzIEOgXWFUmknp77gkDBgTL77vP73QsAkcAPweWOeeOB34C1LbOImUXQ865cc65Qc65QZ06dap71CKpMm8e3HFHsLxNGz8Lr7Aw+phEJFlD+qolwNaVvt8KqJy7pi0wAHjNzBYBg4GJYTlZ1VdJxr39NjwSMsF0yy2Vg1WkkTRwl++efBK+/jpYrtl2EhUzOO20YPnChfD3v0cfj2Sjdc65MmCTmbUDVgC1rbVI2cWQSEatXQuXXOKXHyW74goo1gbLIlmiIX3Vu0BvM+tpZs2A4cDE8krn3HfOuY7OuR7OuR7AVGCoc256epog0kArVsBVVwXLCwrghhugbdvoYxKJkbQN3CW2Rp9mZrPM7CMzuyZdv0saaPVqGD8+WL7vvtCnT/TxSP6qbvfisWN9DkbJd9PN7EfA/fid+mYC02p5jS6GJPc5BzfdBIsXB+sOP9z31yKSLerdVznnNgGjgFeAucDTzrmPzOxaM6ttma1Idti82d9I+vbbYN0ZZyhnukgK1LY5RWNsAPZxzv1gZk2Bf5vZS865qWn8nVIf48fD999XLSsoCJ/9JJJOZjBqlE+wXtny5T6v09FHZyYuyQrOudMTT+8zs5eBds652bW8ZpOZlV8MFQIPll8MAdOdcxNrer1IVnjhBZg0KVjeuzecd1708YhItRrSVyVeNwmYlFQWMnUJnHM/a2ycIik3dizMnBks3313OPbY6OMRiaG0Ddw55xzwQ+LbpomHq/4VEqmVK/0y2WSHHQbbbBN9PCIDB/rcim+8UbX8wQf9/8vWrTMTl2SMmYVMw6yoc86FfEqsoIshyWmffQY33xwsb9ECbrwRmteWOktEotDYvkokp/3nP/DQQ8Hyjh3hmmv8pBARabR0zrjDzArxU8W3Be5xzr0TcsxIYCRA9+7d0xmOVPbAA7BhQ9WyZs3g5JMzE48I+On0b77pl4eV+/ZbeOwx7ZqYn26voc4B+0QViEik1q6Fiy4K9tMAl14KPXpEHpKIVEt9leSnFSv8phMuaW5OeV67oqLMxCUSQ2kduHPObQZ2SOR7eM7MBjjnPkw6ZhwwDmDQoEGakReFxYvh+eeD5b/5DXTuHH08IuV69YIDDwwuDfvLX+CII/QBIM845/bOdAwikXMO/vAH+PzzYN0hh8DBB0cfk4hUS32V5KVNm/yNpLC8dqecAjvvHH1MIjGW1oG7cs65b83sNeAA4MNaDpd0++MffRLRylq3ht/9LiPhiFRx6qnwj3/4DwTl1q6F+++Hiy/OXFySMWZ2XFi5c+6RqGMRSbvnnoOXXw6Wl5ToHCiSxdRXSV655x6YNStYvttucPzx0ccjEnPp3FW2U2KmHWbWEtgX+Dhdv0/qaNYsmDw5WD5iBLRvH308IsmKi/1uicmefRYWLYo8HMkKu1R6/BS4GtBuexI/H38Mt90WLG/Rwue7a9ky+phEpK7UV0l+mDIFHn00WN6pE1x3nfLaiaRBOmfcbQmMT+S5K8Bvb/5iGn+f1MY5GD06WN6xIxx1VPTxiFTnxBP9bopr11aUlZXB3XfDHXdkLi7JCOfcmZW/N7P2QMgnRpEctnq1z2tXWhqsu+wy6Nkz+phEpM7UV0leWLwYrr46WF5Q4NM8KK2NSFqkbTjcOTfbObejc26gc26Ac+7adP0uqaN//Qs++CBYftppuosv2aWoKHya/RtvwIwZ0ccj2WYt0DvTQYikTFmZT/C9dGmwbtgwOOig6GMSkcZSXyXxsn69v8G0Zk2wbtQo2HHH6GMSyROR5LiTLFBaCmPGBMt79YJDD40+HpHaHH00PPOM37GqstGjYfx4TcPPI2b2An5nPvA3nPoBT2cuIpEUe/BBeOutYHmfPnDBBdHHIyL1pr5KYq1846T584N1e+0Fxx4bfUwieUQDd/liwgT48stg+TnnaABEslPz5v7u3VVXVS2fOxdeecXvPiv5onLSr03A5865JZkKRiSlpk6FsWOD5W3bwq23+nOhiOQC9VUSX888A5MmBcu32sovnTWLPCSRfKIRm3zw7bfwwAPB8sGDYffdo49HpK4OOAD69g2Wjxnjp+tLXnDOve6cex14D5gLrDUzJVGR3Ld0qc9f51yw7pproFu36GMSkQZRXyWxNWtWeI7pZs3gllv8jSYRSSsN3OWDe+/1Sa8rM4Ozz85MPCJ1VVDgZ4UmW7HCL5eVvGBmI81sOTAbmA7MSHwVyV3r1/tlsMn9M8AJJ8CQIdHHJCINpr5KYmnlSp/XbtOmYN1ll/mUDiKSdhq4i7t58+C554Llhx4KvZUvV3LALrvAT38aLB8/Hr76Kvp4JBMuBPo753o450qccz2dcyWZDkqkwZyDG27wfXSyXXeFU0+NPiYRaSz1VRIvpaVw8cXw9dfBuiOOgEMOiT4mkTylgbs4cw5uu83vVldZq1ZwxhmZiUmkIc49F5okpeQsLYW77spMPBK1z/C784nEw5NPwksvBcu7dvUDeso9K5KL1FdJfDjnl8HOnh2sGzgQzjsv+phE8pg2p4izV1+FmTOD5SefDFtsEX08Ig3VvbvfZfaRR6qWv/oqzJgBO++cmbgkKpcCb5vZO8CG8kLn3FmZC0mkgaZPhzvvDJY3a+ZvtnXoEH1MIpIK6qskPp59Fp5/PlheVAQ33+z7LBGJjG7pxtX69TB6dLC8e3cYPjz6eEQa68QT/YeFZLfdBps3Rx+PRGksMBmYis8ZVP4QyS1LlvhcQckz4QGuuAJ+/OPoYxKRVFFfJfEwc6bf1TxZkyZ+Fl6nTtHHJJLnNOMurh56CJYvD5ZfcAE0bRp9PCKN1bo1nHmm32mxsk8/9XcFjzwyM3FJFDY557QmQ3LbmjV+aVHYZhTDh8NBB0Ufk4ikkvoqyX1Ll/obTGE3xS+6CHbYIfqYREQz7mLp88/Dd9z8v/+DPfaIPh6RVDn4YOjfP1h+zz3w3/9GH49EZUpit74tzayo/JHpoETqrKwMrrwSFiwI1u20U/ju2SKSa9RXSW5bu9bnlf7222Ddr37lHyKSERq4ixvn4Kabglt2N2miJKKS+woK4MILg+Vr1oTnjJK4OJpE7iAqlh5Nz2hEIvVx773wxhvB8uJinysoefMdEclF6qskd5WV+ZQNn30WrNthh/DP3yISGX1SjJuXX4Z33w2WH3ecz28nkusGDIBf/jKYMPeVV2DoUNhtt8zEJWnjnOuZ6RhEGuzFF336imQtW8Ltt2szCpGYUF8lOe3uu8NvMHXp4vPaKdWSSEZp4C5OVq8On3VUXOwT+4vExZlnwmuvBafy33wzPPmkdrqKGTM7LqzcOfdIWLlI1pg5E66/Przu2muhd+9o4xGRtFFfJTnruefgL38Jlrdo4a8twzaHE5FIaalsnPzpT7BqVbD84ouhefPo4xFJl/bt4ayzguWLF8PDD0cejqTdLpUePwWuBoZmMiCRWi1e7DeESk5dAXDKKbD33tHHJCLppL5Kcs8778CNN4bXXXcd9OkTbTwiEkoz7uJi1iy/s2ayffaBPfeMPh6RdDvkEHjhBXjvvarlDz0Ev/gF9NSKlbhwzp1Z+Xszaw88mqFwRGq3erXfcCJsB9n994eTToo+JhFJK/VVknM++8zvFFtWFqw780zdYBLJIppxFwelpX7JjXNVy1u18nf7ReKooAAuvRQKC6uWb9zo7xCGfQiRuFgLaI2hZKfSUjj/fD/jLtnAgfD734NZ9HGJSNTUV0n2WrnSr15ZsyZYd+ihPj+6iGQNzbiLg/vvh88/D5afcgp07hx9PCJRKSmBY46B8eOrls+eDU89BUcdlZm4JKXM7AWg/M5EAdAPeDpzEYlUo6wMrrwyOBMYfL7Z229XDk6RmFJfJTljzRo4+2xYvjxYN2gQXHaZbjCJZJm0DdyZ2dbAI0BXoAwY55y7K12/L299/HFw0AKgXz8YPjz6eESidvLJMHkyfPFF1fJ77oEhQ6Bbt8zEJal0W6Xnm4DPnXNLMhWMSLVGj4Z//StY3qaNr9MOsiJxpr5Kst/GjXDhhTBvXrCuRw/tICuSpdK5VHYTcL5zbjtgMHCGmfVL4+/LP5s2+SWyyUsCmzTxS3GSlxCKxFGLFn6GS7L16+GGG4JLyCVnmNm2Zranc+71So+3gJ5m1ivT8YlU8fjj/pGsSRN/IVRSEn1MIpJ26qskZ5SVwTXXwLRpwbqiIrj7bmjXLvq4RKRWaRu4c8595ZybmXj+PTAX0NSXVBo/PvxuyYknQi99TpA8stNO8OtfB8unTfNb3EuuGg18H1K+LlEnkh1eegnuuCO87ve/h113jTYeEYmS+irJfs75md8vvxysa9HC1xUXRx+XiNRJJJtTmFkPYEfgnSh+X16YOxfGjQuWb7st/O53kYcjknFnnglduwbL77wTlmilSo7q4ZybnVzonJsO9Ig+HJEQb70FV18dXjdqFBx4YKThiEjk1FdJ9nv44fBZ4QUFcNNNPs2SiGSttA/cmVkb4FngHOfc6pD6kWY23cymr1y5Mt3hxMP69X5p4ObNVcsLCuCqq5SXQPJTq1Zw+eXB8nXr/N9F8t+L5IIWNdS1jCwKkerMmgUXXRR+fjniCBgxIvqYRCRq6qsku/31rz73c5grroD/+79o4xGRekvrwJ2ZNcUP2j3mnPtr2DHOuXHOuUHOuUGdOnVKZzjxMWYMLFoULB8xQndLJL/tvjsMHRosnz07fBMXyXbvmtnJyYVmdiIwIwPxiFT49FM45xzYsCFYt/fefkBPu/KJ5AP1VZK9XnkFbrwxvO7008M/N4tI1knnrrIG/BmY65yrJvGL1NvUqfDUU8HyPn1g5Mjo4xHJNhdcANOnw9KlVcvHjvUDe9ttl5m4pCHOAZ4zs99ScfEzCGgGDMtYVCKLFvkLnu9D0loNGuQ3ximIJBuJiGSe+irJTq+/7ledhG3UdtRRcPzx0cckIg2Szk+VewLHAvuY2fuJx0Fp/H3x9913fiegZM2awfXXa4msCPgls9deG7xo3rzZLzFfty4zcUm9OeeWO+f2AK4BFiUe1zjndnfOLctkbJLHliyB006Db74J1m23Hdx+u++XRSQvqK+SrPT223DJJeGpHA46CM49V7PCRXJI2mbcOef+DehskCplZX5nurA8gKNGQUlJ9DGJZKsddvBLxx96qGr5okVw663+7qPkDOfcFGBKpuMQ4auv4NRTw/vibbaBu++G1q2jj0tEMk59lWSNadP8CpSNG4N1e+3lryk1K1wkp+gvNlc89hj8+9/B8l12geHDo49HJNuNHOmXkCebOBEmTYo+HhHJbStW+Jl2y0Im0Gy5pU/83aFD9HGJSE4zswPM7BMzm29ml4TUn2dmc8xstpn9y8y2yUSckiOmT/ez6UpLg3W77urz3RUWRh+XiDSKBu5ywQcfwB//GCxv1w6uvlp3TETCNG3ql5A3bx6su/HG8A1eJFZ0MSQps2wZnHyyXyabrFMnuPde6No1+rhEJKeZWSFwD3Ag0A84ysySd5p7DxjknBsITABuiTZKyRnvvlv9pkk77KBUDiI5TCM+2W71arj00vD8BFdfDV26RB6SSM4oKfE7OyZbt87n/Qj7YCOxoIshSZmlS/0M3i+/DNYVFflBu622ij4uEYmDXYH5zrkFzrlS4EngsMoHOOemOOfWJr6dCuiEI0FTp8LZZ8P69cG6/v3hrrugZcvo4xKRlNDAXTYrz2sXtizn6KNhyJDoYxLJNUOHwoEHBsvnz4ebbw7faUviQBdD0nhffukH7ZJ3qQY/6/1Pf4IePSIPS0RioxvwRaXvlyTKqnMi8FJYhZmNNLPpZjZ9ZVgeTomvN9+E884LXx7br59fuaX8qyI5TQN32ez++/2JOFn//nDmmdHHI5KLzPys1e7dg3UTJ8KECdHHJFHQxZA0zoIFcNJJ4TfP2reH++6DbbeNPi4RiZOwjfxC7yia2THAIODWsHrn3Djn3CDn3KBOnTqlMETJav/4h9+IImzQ7sc/9oN2bdtGH5eIpJQG7rLVlCl+4C5Z27Y+P1fTptHHJJKrWrWCm24Kz+tx220wc2b0MUm66WJIGm7OHJ/TLmygtkMHGDs2fPMbEZH6WQJsXen7rYDAFF8z2xe4HBjqnFOeD/H+9je44orwlEr9+vlZ4e3aRR+XiKScBu6y0YIFfolsmKuvhuLiSMMRiYU+fcLz3W3e7PPdLV8efUySTroYkoaZMQNOPRW++y5YV1TkB+00005EUuNdoLeZ9TSzZsBwYGLlA8xsR2Asvp9akYEYJds4B+PHw3XX+dRKybbfXoN2IjGjgbtss3o1nH8+rF0brBs5EvbaK/qYROLil7+Eww8Plq9a5ZcZhCX0lVyliyGpv9de86kowvrgjh398tiSksjDEpF4cs5tAkYBrwBzgaedcx+Z2bVmNjRx2K1AG+AZM3vfzCZW8+MkH5SVwZ13wpgx4fU77wz33ANt2kQbl4ikVZNMByCVlJb6wYMvvgjWDRnic+2ISONccIHfmGLWrKrlc+fCVVf5JbUFuqeR65xzm8ys/GKoEHiw/GIImO6cm0jViyGAxc65odX+UIm3p5+GW28N37CmuNjvHtutpjSJIiL155ybBExKKruq0vN9Iw9KslNpqV+V9c9/htfvuSfccgs0bx5tXCKSdhq4yxbO+enOYbm2evTwdRpMEGm8pk39h5pjj4UVSZOsJk+G0aP9zlyS83QxJHVSVuaTdz/ySHh9SYmfvaD8hiIikimrV/ubz9XlZT7gAD+opzzoIrGkkaBscd998FLIhoatW8Ptt2sLb5FU2mILP7MmbLOKxx+Hp56KPiYRid6GDT6xd3WDdv37+42iNGgnIiKZsngx/O531Q/aDR8O116rQTuRGNPAXTb429/gz38OlhcW+sGFbbaJPiaRuOvf32/2Eub22+H11yMNR0QitnKl3zn2H/8Ir99zT788tn37aOMSEREpN326H7RbvDi8/owzfH50rcwSiTX9hWfa5Mlwww3hdZdfDrvuGm08Ivlkv/18IvpkZWVw6aX+w5KIxM/cuTBiBMyZE14/bBjccQe0ahVtXCIiIuDTKD39NJx+ul8mm6xJEz/L7vjjwefpFZEY08BdJr39Nlx2Wfg23iedBEOVI10k7Y47Dn71q2B5aSmcey588EH0MYlI+rz8su9jk3NcljvtNN83FxZGG5eIiAj4z6DXXedzModdJ7ZpA3ffDQcdFH1sIpIRGrjLlJkz4cILYdOmYN1BB8Epp0Qfk0g+MoOLL4Y99gjWrVsHZ50Fn34afVwiklobN/r0E1dc4XPbJWvWzM9eOPFEzV4QEZHMWLrU90MTJ4bXd+sGDz+sVVkieUYDd5nw4YdwzjnhFw577AFXXqmLBpEoFRbCTTfB9tsH677/3ucPWbAg+rhEJDVWrvQ3xKrbeKaoCMaO1ewFERHJnLfegmOO8ekcwuy0E4wfDz16RBqWiGSeBu6i9t57PlfB2rXBuh139FOitSOQSPRatYK77oLevYN1q1b5i/5586KPS0Qa5z//gd/+FmbPDq/v08fvKhs2cC8iIpJuGzf6z6Bnnx2ezw7g17+GP/0JfvSjaGMTkayggbsoTZvmE+GHDdr16wejR0OLFtHHJSJeu3Zwzz3QvXuw7ptv4NRTq09mLyLZpfxC6Mwz/eB7mP3287u6d+0abWwiIiIAX37pl8Y++mh4fdOmPu/qxRf7DSlEJC+lbeDOzB40sxVm9mG6fkdOeestvzx2/fpgXUkJjBkDrVtHH5eIVFVUBPfeC1tuGaxbvdonrq9u5o6IZIfFi+GEE6q/ECoshAsu8Lu6t2wZbWwiIiLOwd/+BkcdVf1N4a5d/c2lsE3URCSvpHPG3cPAAWn8+bnjxRfhvPP8DkHJevWC++6D9u2jj0tEwnXp4vNdFRcH69as8YN3b7wRfVwiUrOyMnjiCX8hVF2OoC228H/fw4crn6yIiERv1So4/3y/c2zYSizwec8fe8yvyhKRvJe2gTvn3BtANWtT8oRz8MADcPXVsHlzsL5vX3/xUFQUeWgiUoviYrj//vBlsxs2+Nk6EyZEH5eIhFu61A+q3357+OZPAIMHw+OPww47RBubiIiIczBpEhxxRPU3gAsL4ayzfAolTewQkYSML5Q3s5HASIDuYRfIuWrzZrjxRnj++fD6AQP88ti2baONS0TqrksXGDfODwYsXFi1rqzM70S7bJnfcKZAKUNFMmLzZr9b7L33wrp14ccUFsKoUX6TCv2tiohI1L76Cv7wB79hUnWKi/0xAwZEF5eI5ISMf3p1zo1zzg1yzg3q1KlTpsNJjW++gTPOqH7Qbqed/K5AGrQTyX4dO/qZsX37htc//LBPGFzdUgcRSZ+PP4YRI+COO6oftNtqK3joITj2WA3aiYhItDZu9DuXH3lkzYN2hx7qUz1o0E5EQmR8xl3sfPyxX0K3bFl4/X77+aWzzZpFGpaINEJRkV82e/HF4R+6pkyBRYv8Er04zRwWyVarV/sB9Wee8bNfq3PkkX5XWW1AISIiUXv3Xbj5Zv8ZsTodOsDll8PPfhZVVCKSg3TrOZUmTfK72FU3aHfccXD99Rq0E8lFrVrBnXfC0KHh9QsX+r/xN9+MNi6RfFJWBs8+C8OG+eWx1Q3ade3qZ7ZfdJEG7UREJFpffOH7n9NOq3nQbr/9fF+mQTsRqUXaZtyZ2RPAz4COZrYE+L1z7s/p+n0ZtXYt3HKL3z02TEGBn4V35JHRxiUiqdWkCVx5pR8UGDcuWP/DD3DuuXD00T6flgbpRVLDOT/bdcwY+PTT6o8z80m/R42C1q2ji09EROTbb/3GhM88E74xYbnOneGSS2DIkOhiE5GclraBO+fcUen62Vllzhw/vfmLL8Lr27Xzm1Tstlu0cYlIepjByJHQq5df9h6WV+vxx2H6dLjhBujZM/IQRWLlww/9gN2MGTUft+22cNllMHBgNHGJiIiAv3H7xBPw2GP+eXUKCvzNpdNPhzZtootPRHKectw11KZy1d3eAAAVM0lEQVRNMH68n3VT3R2V3r19zqvi4mhjE5H0+/nPoUcPOP98WLIkWD9vHhxzDJx1Fvz610qKL1Jfc+f6mQuvv17zcS1bwkkn+R1jm+hjjYiIRGTNGnjyST9gt3p1zccOHOhn2fXpE01sIhIr+oTbEHPmwHXX1bxcZ//94YorlFtHJM569fI7hV1xBbz9drB+wwa49VZ45RW/xFaz70Rq98EHfsDurbdqP/agg/zmE3HZlV5ERLLfqlV+OexTT9U+YNexI5xxBhx8sG7iikiDaeCuPtau9TtLPvZY9QmxW7aECy/0W3qbRRufiESvXTsYPdovkRgzxs/GTTZ7ts97d8IJMGKEct+JJCsrgzfegL/8Bd5/v/bj+/f3s121LFZERKKycKG/Dpw0CUpLaz62ZUv/me+3v9VEDhFpNA3c1UVZmT9BjxkDX39d/XE//jH84Q/QvXt0sYlI5hUU+A9mgwb5HFuffx48ZuNGGDsWXngBzjkH9t5bg/siP/wAf/+7X2pUXa7YyrbZxs9c0N+PiIhEYfNmPwN8woTw1RXJCgvhsMPglFNgiy3SH5+I5AUN3NXmvff8bJqPPqr+mIICOO44f4Ju2jS62EQku/Tt62cM3XWX/4AXZulSuOgi2GUXOPtsP+Avkm8+/tj/jbz8MqxfX/vxXbr4PHZDh/qLIhERkXRauhSef97fcF25svbjCwv9iqsTTlB+cxFJOQ3cVWfOHLj3XvjPf2o+rk8fuOoqXXyLiNeypU8+vN9+cP31sHhx+HHvvus3r9hnHzj1VCgpiTZOkah9/TW89JKfYVdTjtjKiov9RdDBB+vGmIiIpNf33/u0DZMmwbRp4Fztr2nSxOdbPekkDdiJSNpo4C7Z7Nl+t9jadrFr1syfoI87TrvYiUjQTjv5vHdjx/pZeNXlxZw8GaZM8QN9I0ZotzGJl9Wr4bXX4NVXYerU6v8OkvXqBcceCwccoD5WRETSZ80af9336qt+wsbGjXV7Xdu2cPjhcOSR0LlzemMUkbynT8PgLyT+/W+/O2RdkmLvs4/PUaW7KiJSk+bN4ayz4JBD4I47/MBFGOf8zrOvvAKDB/sbArvsohxekptWroQ33/QDdtOmhW/YUp3Bg32+yMGD9f9fRETSY/lyeOcdP7vu7bdr32iisuJiv+HY0KHQqlX6YhQRqSS/B+6++cbnLXj2Wfjyy9qP33ZbuOACn4BeRKSuSkr85jZvvukH8JYsqf7YqVP9o6QEjjjCL79o0ya6WEXqa/Nmnwd26lT/f3zu3Pq9vnVrP7h9+OFaMi4iIqm3bh3MnFnxGWvhwvq9vqAA9toLhg3zN5YKCtITp4hINfJv4G7TJn+H5e9/98vT6jIduls3v/HEAQfoRC0iDWMGQ4bA7rvDxInwwAM1JztesABuuQXuvtsvoz3wQNh5Z52DJPPKynyOupkzYcYMn69xzZr6/5yBA/3Oe/vt53NDioiIpMIPP/ibSB9+6Gd+v/9+3ZfAVtatmx+sO/RQ7RArIhmVHwN3ZWUwaxb885/+8c03dXtd+S52hx6qHDsikhpNm/qZRYcc4mf7PvRQzeek9ev9QN/EiT6Hyv77w777wnbbaRBPorF6tb/4KX/MmtWwgTrw/erBB/vHNtukNk4REck/69fDvHl+5vecOf5rdRuD1cUWW8DPfw6/+AX85Cf6rCUiWSG+o1Fr18L06T7Hzptv1n2wDnxS7BEj/Albu9iJSDo0b+5zpBx+OLz4Ijz6aM1LaAFWrPDHPfoodOrkl20MGeJn4jVvHk3cEl/OwbJlfrbnJ5/Axx/7r3VJJVGTzp0rLoIGDNBFkIiI1N+mTT433Zdfwhdf+EG6OXPgs8/qvvFRdYqKKvqpHXZQPyUiWSc+A3elpf4i4913/VLYWbN83p362G03nxR7992VFFtEotG8uR+8GzbM32h44gl4773aX7dyJUyY4B/NmvkPmoMH+xycfftCYWHaQ5cctXZtxYXP55/7mQkLF/oBu7VrU/M7Skr8oPKQIRqsExGR2jnnJ1osXer7qPJH+ffLljV+gK6yvn3956Y99oAdd1Q/JSJZLXcH7las8LkLPvrI5y348MP67QhUrkMHvyvQsGGw1Vapj1NEpC4KCvyO1fvs4wdQ/vpXPxPvhx9qf21pqc/hMm2a/75lS9h+ez+Y17+/X1ZbVJTe+CU7bNoEX38N//2v7yeXL/ePZcv8xc/SpfWbgV5XrVv7nZB3281fBHXrlvrfISIi2cE5P4i2ebPvd8IeleuSj9uwAb76KjhAt25d+mLu2NEP1A0eDLvuqs9FIpJTsn/grrTUzwaYP98/Pv3UL935738b/jObNfOzAA480F9gaDmsiGSTkhK/g/WoUfDGG/Dyy/DWW3WfRbxuXdWBPICuXaFPH787dvlj6611/stWzvn3cc0a+P57P4C7erV//t13/vHtt/6xapUfjFu1yn8fhVat/MDwjjv6pdr9+2uWp4hItli+3G9wVdsAWk11tR2X7bp3h379fP+0667+s5VWVIlIjsqugbvvv4fHHqu6hOerr/wFTGM1a+aXwP7sZ7D33tCmTeN/pohIOrVo4Xfc3G8/PyAzebJfTjttWv0/NC9b5h9vvFFRVlAAxcV+k4Ctt/bPNfO4Zhs2+JtHlS9eNm6suKDZuLHqo7TUPzZsqPha/li/3g/OrV/vH2vWVAzWrV2bmr4vFcz8/5Htt/fLXgcM8AO/GqgTEWk0MzsAuAsoBB5wzt2UVN8ceATYGfga+I1zblGNP3TVKnj66bTEm5W6dvWDdOWP7baDtm0zHZWISMpk18DdkiVw552p+3mdO/vp0D/9qf/asmXqfraISJR+9CP41a/844cf4O23/cY777zjP6A3RFmZP+/WtilGjkrLxdCCBT4Xaly1auVnJfTq5fP/9O0LvXv7chERSSkzKwTuAX4BLAHeNbOJzrk5lQ47EfjGObetmQ0HbgZ+E320WaBDB5+KobgYevSoGKjTslcRibnsGrhrrA4d/NKdnXf2A3XbbKMp0SISP23aVMzEc86nEZg6FWbO9BvzrF6d6QgzThdDNSgo8LMTttrK95Pdu/uvPXv6cvWbIiJR2RWY75xbAGBmTwKHAZX7qsOAqxPPJwB/NDNzLlumZadQ8+Z+YK78Ub4SoLjYP3QTSUTyVFoH7mqb7dAoTZr4WQDld1p22MFffOiCQ0TyiZk/F/buDcce62fRLVzoN+2ZM8dv4jN/fmp3YssN+Xsx1KEDdOrkE3F37gxduvgBuS5d/IVQly6+DxURkUzrBnxR6fslwG7VHeOc22Rm3wFbAFUSfpvZSGAkwE+aNUtXvBUKCnxfUljovyY/r62uY8fgAF2HDrqWExEJkbZP7nWc7VA3nTv7mQCVk6r36uXz1omISIWCAn9+7NULDj/cl61fX7HBT/lj0aLGbfKT/XL3Yqhc8+Z+dmXr1j5XT7t2/mvbtn7pdPv2/mtRkX906OC/14YjIiK5ImyUKvnmUV2OwTk3DhgHMKikxHHBBXUbQKvLQFvYgFxBQeNbLyIidZLOW+51me1QVevWMGyYv+vSrVvFEh7lphMRabgWLSo2FahszRq/CdDixbB0qd8YaOlSmDEjM3GmVnouhoqKHH36BC9mmjatKGvWzH/ftKl/Xv598+b+vWjWrOJ5y5YVX1u29MuAWrb0/aFmxYmIxN0SYOtK328FLK3mmCVm1gRoD9Sc3LaoCIYPT2GYIiKSSem8KqjLbIcqMxm6d+8Ol1+expBEROR/WreuSDdQ2X33ZSae1ErPxVBJCTz+eArDFBGRPPYu0NvMegJfAsOBo5OOmQiMAP4DHAFMzvmUDiIiUi/pnONc55kMzrlBzrlBnTp1SmM4IiKSR/53MWRmzfAXQxOTjim/GAJdDImISMScc5uAUcArwFzgaefcR2Z2rZkNTRz2Z2ALM5sPnAdckploRUQkU9I5464usx1ERERSLpGzrvxiqBB4sPxiCJjunJuIvxh6NHExtAo/uCciIhIZ59wkYFJS2VWVnq8Hfh11XCIikj3SOXBXl6nfIiIiaaGLIRERERERyXVpG7irbrZDun6fiIiIiIiIiIhInKR1y7qw2Q4iIiIiIiIiIiJSu3RuTiEiIiIiIiIiIiINpIE7ERERERERERGRLGTOuUzH8D9m9j3wSabjiEhH4L+ZDiIiamt85VN786mtfZ1zbTMdRDbKs34K8uv/vdoaX/nU3nxqq/qqaqivijW1Nb7yqb351NaU9FVpzXHXAJ845wZlOogomNl0tTV+8qmtkF/tzbe2ZjqGLJY3/RTk3/97tTWe8qm9+dbWTMeQxdRXxZTaGl/51N58a2sqfo6WyoqIiIiIiIiIiGQhDdyJiIiIiIiIiIhkoWwbuBuX6QAipLbGUz61FfKrvWqrQP792+RTe9XW+Mqn9qqtAvn3b5NP7VVb4yuf2qu21lNWbU4hIiIiIiIiIiIiXrbNuBMRERERERERERE0cCciIiIiIiIiIpKVIhm4M7MDzOwTM5tvZpeE1Dc3s6cS9e+YWY9KdZcmyj8xs/2jiLcxGtpWM+thZuvM7P3E476oY2+IOrR3iJnNNLNNZnZEUt0IM/s08RgRXdQN08i2bq703k6MLuqGqUNbzzOzOWY228z+ZWbbVKrLqfcVGt3euL23p5rZB4n2/NvM+lWqy6nzcX2pr6pSr76qoi6nzmnqq6rUx6avyqd+CtRX1UR9VZV69VUVdXE7p6mvIpbvq/qqirr6nY+dc2l9AIXAZ0AJ0AyYBfRLOuZ04L7E8+HAU4nn/RLHNwd6Jn5OYbpjzlBbewAfZroNaWhvD2Ag8AhwRKXyImBB4muHxPMOmW5TOtqaqPsh021IcVv3Blolnp9W6f9xTr2vjW1vTN/bdpWeDwVeTjzPqfNxmv5t1Fepr8rqc5r6qnj2VfnUT9Wjveqr1Fepr6ooj+M5TX1VPN9X9VWuYefjKGbc7QrMd84tcM6VAk8ChyUdcxgwPvF8AvBzM7NE+ZPOuQ3OuYXA/MTPy1aNaWsuqrW9zrlFzrnZQFnSa/cH/umcW+Wc+wb4J3BAFEE3UGPammvq0tYpzrm1iW+nAlslnufa+wqNa2+uqUtbV1f6tjVQvoNRrp2P60t9VVXqq7xcO6epr6okRn1VPvVToL6qJuqrqlJf5cXxnKa+Kp7vq/oqr97n4ygG7roBX1T6fkmiLPQY59wm4Dtgizq+Nps0pq0APc3sPTN73cx+mu5gU6Ax708c39uatDCz6WY21cx+mdrQUq6+bT0ReKmBr80GjWkvxPC9NbMzzOwz4BbgrPq8Noepr6rmGPVVsXtvaxK781kludxX5VM/BeqraqK+qppj1FfF7r2tSS6d09RXVU99VS2vraxJo0Ktm7C7Hq6Ox9TltdmkMW39CujunPvazHYGnjez/kmjtNmmMe9PHN/bmnR3zi01sxJgspl94Jz7LEWxpVqd22pmxwCDgL3q+9os0pj2QgzfW+fcPcA9ZnY0cAUwoq6vzWHqq+p2jPqq3H9vaxK78xnEoq/Kp34K1FfVRH1V3Y5RX5X7721Ncumcpr4q7ED1VfV+b6OYcbcE2LrS91sBS6s7xsyaAO2BVXV8bTZpcFsT0yS/BnDOzcCvc+6T9ogbpzHvTxzf22o555Ymvi4AXgN2TGVwKVantprZvsDlwFDn3Ib6vDbLNKa9sXxvK3kSKL/jlYvvbX2or6rmGPVVsXtvqxXH81lM+qp86qdAfVVN1FdVc4z6qti9t9XKsXOa+qok6qsa9NpINqdogk+k2JOKpH39k445g6qJRZ9OPO9P1aR9C8juJKqNaWun8rbhExx+CRRluk2NbW+lYx8mmER1IT7RZofE86xtbyPb2gFonnjeEfiUpMSV2fSo4//jHfEfgnonlefU+5qC9sbxve1d6fmhwPTE85w6H6fp30Z9lfqqrD6nNbKtcTyfxaKvamRbc+p9rUd71Vepr6qpreqrsri9jWxrTp3TGnn+jt37WkNbc+p9rUd7U9ZXRdWog4B5iTfp8kTZtfhRVoAWwDP4pHzTgJJKr7088bpPgAMz/Qalq63A4cBHiTdwJnBoptuSovbugh9RXgN8DXxU6bUnJP4d5gPHZ7ot6WorsAfwQeK9/QA4MdNtSUFbXwWWA+8nHhNz9X1tTHtj+t7elTgXvQ9MoVIHlGvn4zT826ivUl+V9ee0hrY1puez2PRVDW1rLr6vdWyv+ir1VdW2FfVVcTinqa+K5/uqvqritfU6H1viRSIiIiIiIiIiIpJFoshxJyIiIiIiIiIiIvWkgTsREREREREREZEspIE7ERERERERERGRLKSBOxERERERERERkSykgTsREREREREREZEspIE7kUrM7DUz2z+p7Bwz+1MNr/kh/ZGJiIh46qtERCTbqa8SSR0N3IlU9QQwPKlseKJcREQkG6ivEhGRbKe+SiRFNHAnUtUE4BAzaw5gZj2AYuB9M/uXmc00sw/M7LDkF5rZz8zsxUrf/9HMfpd4vrOZvW5mM8zsFTPbMlF+lpnNMbPZZvZk+psnIiIxoL5KRESynfoqkRRpkukARLKJc+5rM5sGHAD8DX9X6ClgHTDMObfazDoCU81sonPO1fYzzawpMAY4zDm30sx+A9wAnABcAvR0zm0wsx+lqVkiIhIj6qtERCTbqa8SSR0N3IkElU/rLu9gTgAM+IOZDQHKgG5AF2BZHX5eX2AA8E8zAygEvkrUzQYeM7PngedT2AYREYk39VUiIpLt1FeJpIAG7kSCngfuMLOdgJbOuZmJqdmdgJ2dcxvNbBHQIul1m6i6/Ly83oCPnHO7h/yug4EhwFDgSjPr75zblLqmiIhITKmvEhGRbKe+SiQFlONOJIlz7gfgNeBBKpKntgdWJDqXvYFtQl76OdDPzJqbWXvg54nyT4BOZrY7+CneZtbfzAqArZ1zU4CLgB8BbdLVLhERiQ/1VSIiku3UV4mkhmbciYR7AvgrFTshPQa8YGbTgfeBj5Nf4Jz7wsyexk/T/hR4L1FeamZHAHcnOp4mwGhgHvCXRJkBdzrnvk1vs0REJEbUV4mISLZTXyXSSFaHHJAiIiIiIiIiIiISMS2VFRERERERERERyUIauBMREREREREREclCGrgTERERERERERHJQhq4ExERERERERERyUIauBMREREREREREclCGrgTERERERERERHJQhq4ExERERERERERyUL/DwsOcibRiDw2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm as my_dist                                      # import traingular dist as my_dist\n",
    "dist_type = 'Gaussian'                                                       # give the name of the distribution for labels\n",
    "mean = 0.15; stdev = 0.05                                                    # given the distribution parameters\n",
    "\n",
    "x_values = np.linspace(0.0,0.3,100)                                          # get an array of x values\n",
    "p_values = my_dist.pdf(x_values, loc = mean, scale = stdev)                  # calculate density for each x value\n",
    "P_values = my_dist.cdf(x_values, loc = mean, scale = stdev)                  # calculate cumulative probablity for each x value\n",
    "\n",
    "plt.subplot(1,3,1)                                                           # plot the resulting PDF\n",
    "plt.plot(x_values, p_values,'r-', lw=5, alpha=0.8); plt.title('Sampling the ' + str(dist_type) + ' PDF, $f_x(x)$'); plt.xlabel('Values'); plt.ylabel('Density')\n",
    "plt.xlim([0.0,0.3])\n",
    "\n",
    "plt.subplot(1,3,2)                                                           # plot the resulting CDF\n",
    "plt.plot(x_values, P_values,'r-', lw=5, alpha=0.8); plt.title('Sampling the ' + str(dist_type) + ' CDF, $F_x(x)$'); plt.xlabel('Values'); plt.ylabel('Cumulative Probability')\n",
    "plt.xlim([0.0,0.3])\n",
    "\n",
    "p_values = np.linspace(0.00001,0.99999,100)                                  # get an array of p-values\n",
    "x_values = my_dist.ppf(p_values, loc = mean, scale = stdev)                  # apply inverse to get x values from p-values\n",
    "plt.subplot(1,3,3)\n",
    "plt.plot(x_values, p_values,'r-', lw=5, alpha=0.8, label='uniform pdf')\n",
    "plt.xlim([0.0,0.3])\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.8, top=0.8, wspace=0.2, hspace=0.3); plt.title('Sampling Inverse the ' + str(dist_type) + ' CDF, $F^{-1}_x(x)$'); plt.xlabel('Values'); plt.ylabel('Cumulative Probability')\n",
    "\n",
    "print('The mean is ' + str(round(my_dist.mean(loc = mean, scale = stdev),4)) + '.') # calculate stats and symmetric interval\n",
    "print('The variance is ' + str(round(my_dist.var(loc = mean, scale = stdev),4)) + '.')\n",
    "print('The interval at an alpha level of ' + str(round(1-level,3)) + ' is ' + str(np.round(my_dist.interval(alpha = level,loc = mean,scale = stdev),2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Log Normal Distribution\n",
    "\n",
    "Now let's check out the log normal distribution.  \n",
    "\n",
    "* We need the parameters $\\mu$ and $\\sigma$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean is 0.102.\n",
      "The variance is 0.0004.\n",
      "The interval at alpha level 0.05 is [0.07 0.15]\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import lognorm as my_dist                                   # import traingular dist as my_dist\n",
    "dist_type = 'Log Normal'                                                     # give the name of the distribution for labels\n",
    "mu = np.log(0.10); sigma = 0.2                                               # given the distribution parameters\n",
    "\n",
    "x_values = np.linspace(0.0,0.3,100)                                          # get an array of x values\n",
    "p_values = my_dist.pdf(x_values, s = sigma, scale = np.exp(mu))              # calculate density for each x value\n",
    "P_values = my_dist.cdf(x_values, s = sigma, scale = np.exp(mu))              # calculate cumulative probablity for each x value\n",
    "\n",
    "plt.subplot(1,3,1)                                                           # plot the resulting PDF\n",
    "plt.plot(x_values, p_values,'r-', lw=5, alpha=0.8); plt.title('Sampling the ' + str(dist_type) + ' PDF, $f_x(x)$'); plt.xlabel('Values'); plt.ylabel('Density')\n",
    "plt.xlim([0.0,0.3])\n",
    "\n",
    "plt.subplot(1,3,2)                                                           # plot the resulting CDF\n",
    "plt.plot(x_values, P_values,'r-', lw=5, alpha=0.8); plt.title('Sampling the ' + str(dist_type) + ' CDF, $F_x(x)$'); plt.xlabel('Values'); plt.ylabel('Cumulative Probability')\n",
    "plt.xlim([0.0,0.3])\n",
    "\n",
    "p_values = np.linspace(0.00001,0.99999,100)                                        # get an array of p-values\n",
    "x_values = my_dist.ppf(p_values,  s = sigma, scale = np.exp(mu))             # apply inverse to get x values from p-values\n",
    "plt.subplot(1,3,3)\n",
    "plt.plot(x_values, p_values,'r-', lw=5, alpha=0.8, label='uniform pdf')\n",
    "plt.xlim([0.0,0.3])\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.8, top=0.8, wspace=0.2, hspace=0.3); plt.title('Sampling the Inverse the ' + str(dist_type) + ' CDF, $F^{-1}_x(x)$'); plt.xlabel('Values'); plt.ylabel('Cumulative Probability')\n",
    "\n",
    "print('The mean is ' + str(round(my_dist.mean(s = sigma, scale = np.exp(mu)),4)) + '.') # calculate stats and symmetric interval\n",
    "print('The variance is ' + str(round(my_dist.var(s = sigma, scale = np.exp(mu)),4)) + '.')\n",
    "print('The interval at alpha level ' + str(round(1-level,3)) + ' is ' + str(np.round(my_dist.interval(alpha = level,s = sigma, scale = np.exp(mu)),2)))"
   ]
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    "There are many other parametric distributions that we could have included.  Also we could have demonstrated the distribution fitting. \n",
    "\n",
    "#### Comments\n",
    "\n",
    "This was a basic demonstration of working with parametric distributions. \n",
    "\n",
    "I have other demonstrations on the basics of working with DataFrames, ndarrays, univariate statistics, plotting data, declustering, data transformations, trend modeling and many other workflows available at [Python Demos](https://github.com/GeostatsGuy/PythonNumericalDemos) and a Python package for data analytics and geostatistics at [GeostatsPy](https://github.com/GeostatsGuy/GeostatsPy). \n",
    "  \n",
    "I hope this was helpful,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "#### The Author:\n",
    "\n",
    "### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "*Novel Data Analytics, Geostatistics and Machine Learning Subsurface Solutions*\n",
    "\n",
    "With over 17 years of experience in subsurface consulting, research and development, Michael has returned to academia driven by his passion for teaching and enthusiasm for enhancing engineers' and geoscientists' impact in subsurface resource development. \n",
    "\n",
    "For more about Michael check out these links:\n",
    "\n",
    "#### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n",
    "\n",
    "#### Want to Work Together?\n",
    "\n",
    "I hope this content is helpful to those that want to learn more about subsurface modeling, data analytics and machine learning. Students and working professionals are welcome to participate.\n",
    "\n",
    "* Want to invite me to visit your company for training, mentoring, project review, workflow design and / or consulting? I'd be happy to drop by and work with you! \n",
    "\n",
    "* Interested in partnering, supporting my graduate student research or my Subsurface Data Analytics and Machine Learning consortium (co-PIs including Profs. Foster, Torres-Verdin and van Oort)? My research combines data analytics, stochastic modeling and machine learning theory with practice to develop novel methods and workflows to add value. We are solving challenging subsurface problems!\n",
    "\n",
    "* I can be reached at mpyrcz@austin.utexas.edu.\n",
    "\n",
    "I'm always happy to discuss,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "Michael Pyrcz, Ph.D., P.Eng. Associate Professor The Hildebrand Department of Petroleum and Geosystems Engineering, Bureau of Economic Geology, The Jackson School of Geosciences, The University of Texas at Austin\n",
    "\n",
    "#### More Resources Available at: [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n"
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