PythonDataBasics_BootstrapConfidence.ipynb

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   "source": [
    "<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",
    "### Bootstrap Confidence Intervals in Python \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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    "### Bootstrap Confidence Intervals in Python \n",
    "\n",
    "Here's a simple workflow, demonstration of bootstrap for modeling workflows. This should help you get started with this important data analytics method to evaluate and integrate uncertainty in any sample statistics or model.  \n",
    "\n",
    "#### Bootstrap\n",
    "\n",
    "The uncertainty in an estimated population parameter from a sample, represented as a range, lower and upper bound, based on a specified probability interval known as the **confidence level**.\n",
    "\n",
    "* one source of uncertainty is the paucity of data.\n",
    "* do 200 or even less sample data provide a precise (and accurate estimate) of the mean? standard deviation? skew? 13th percentile / P13? 3rd central moment? experimental variogram? mutual information? Shannon entropy? etc.\n",
    "\n",
    "Would it be useful to know the uncertainty due to limited sampling?\n",
    "* what is the impact of uncertainty in the mean porosity e.g. 20%+/-2%?\n",
    "\n",
    "**Bootstrap** is a method to assess the uncertainty in a sample statistic by repeated random sampling with replacement.\n",
    "\n",
    "Assumptions\n",
    "* sufficient, representative sampling, identical, idependent samples\n",
    "\n",
    "Limitations\n",
    "1. assumes the samples are representative \n",
    "2. assumes stationarity\n",
    "3. only accounts for uncertainty due to too few samples, e.g. no uncertainty due to changes away from data\n",
    "4. does not account for boundary of area of interest \n",
    "5. assumes the samples are independent\n",
    "6. does not account for other local information sources\n",
    "\n",
    "The Bootstrap Approach (Efron, 1982)\n",
    "\n",
    "Statistical resampling procedure to calculate uncertainty in a calculated statistic from the data itself.\n",
    "* Does this work?  Prove it to yourself, for uncertainty in the mean solution is standard error: \n",
    "\n",
    "\\begin{equation}\n",
    "\\sigma^2_\\overline{x} = \\frac{\\sigma^2_s}{n}\n",
    "\\end{equation}\n",
    "\n",
    "Extremely powerful - could calculate uncertainty in any statistic!  e.g. P13, skew etc.\n",
    "* Would not be possible access general uncertainty in any statistic without bootstrap.\n",
    "* Advanced forms account for spatial information and sampling strategy (game theory and Journel’s spatial bootstrap (1993).\n",
    "\n",
    "Steps: \n",
    "\n",
    "1. assemble a sample set, must be representative, reasonable to assume independence between samples\n",
    "\n",
    "2. optional: build a cumulative distribution function (CDF)\n",
    "    * may account for declustering weights, tail extrapolation\n",
    "    * could use analogous data to support\n",
    "\n",
    "3. For $\\ell = 1, \\ldots, L$ realizations, do the following:\n",
    "\n",
    "    * For $i = \\alpha, \\ldots, n$ data, do the following:\n",
    "\n",
    "        * Draw a random sample with replacement from the sample set or Monte Carlo simulate from the CDF (if available). \n",
    "\n",
    "6. Calculate a realization of the sammary statistic of interest from the $n$ samples, e.g. $m^\\ell$, $\\sigma^2_{\\ell}$. Return to 3 for another realization.\n",
    "\n",
    "7. Compile and summarize the $L$ realizations of the statistic of interest.\n",
    "\n",
    "* calculate and display the histogram or CDF to see the full distribution\n",
    "\n",
    "* report the percentiles representing the lower and upper confidence intervals, e.g. for a confidence level of 95%, the 2.5 and 97.5 percentiles.\n",
    "\n",
    "This is a very powerful method. Let's demonstrate a bunch of measures.\n",
    "\n",
    "* when available, I compare to the distributions from the analytic expressions.\n",
    "\n",
    "Let's demonstrate for a variety of parameters / statistics:\n",
    "\n",
    "* mean / arithmetic average\n",
    "\n",
    "* proportion\n",
    "\n",
    "* interquartile range\n",
    "\n",
    "* coefficient of variation\n",
    "\n",
    "* correlation coefficient\n",
    "\n",
    "#### Objective \n",
    "\n",
    "The objective is to remove the hurdles of subsurface modeling workflow construction by providing building blocks and sufficient examples. This is not a coding class per se, but we need the ability to 'script' workflows working with numerical methods.    \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 - sample_data_biased.csv at https://git.io/fh0CW"
   ]
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need some standard packages. These should have been installed with Anaconda 3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "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           # plotting\n",
    "import matplotlib                         # plotting\n",
    "import seaborn as sns                     # plotting\n",
    "from scipy import stats                   # summary statistics\n",
    "import math                               # trig etc.\n",
    "import scipy.signal as signal             # kernel for moving window calculation\n",
    "import random                             # random sampling\n",
    "from scipy.stats import gaussian_kde      # for PDF calculation\n",
    "from scipy.stats import t                 # Student's t distribution for analytical solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "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). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "os.chdir(\"c:/PGE383\")                     # set the working directory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Set the Random Number Seed\n",
    "\n",
    "For repeatability, set the random number seed.\n",
    "\n",
    "* this ensures that the same random samples are drawn each run and everyone in the class will have the same results.\n",
    "\n",
    "* change this seed number for a new set of random realizations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "seed = 73073\n",
    "np.random.seed(seed = seed)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Loading Tabular Data\n",
    "\n",
    "Here's the command to load our comma delimited data file in to a Pandas' DataFrame object.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('sample_data_biased.csv') # load our data table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's drop some samples so that we increase the variations in bootstrap samples for our demonstration below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using 6 number of samples\n"
     ]
    }
   ],
   "source": [
    "df = df.sample(frac = 0.02)                 # extract 50 random samples to reduce the size of the dataset   \n",
    "print('Using ' + str(len(df)) + ' number of samples')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualizing the DataFrame would be useful and we already learned about these methods in this demo (https://git.io/fNgRW). \n",
    "\n",
    "We can preview the DataFrame by printing a slice or by utilizing the 'head' DataFrame member function (with a nice and clean format, see below). With the slice we could look at any subset of the data table and with the head command, add parameter 'n=13' to see the first 13 rows of the dataset.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>Facies</th>\n",
       "      <th>Porosity</th>\n",
       "      <th>Perm</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <th>131</th>\n",
       "      <td>320</td>\n",
       "      <td>99</td>\n",
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       "      <td>13.154686</td>\n",
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       "      <th>180</th>\n",
       "      <td>750</td>\n",
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       "      <td>0.074619</td>\n",
       "      <td>0.089169</td>\n",
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       "      <th>276</th>\n",
       "      <td>730</td>\n",
       "      <td>79</td>\n",
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       "      <td>0.134691</td>\n",
       "      <td>15.160833</td>\n",
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       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>300</td>\n",
       "      <td>400</td>\n",
       "      <td>1</td>\n",
       "      <td>0.118448</td>\n",
       "      <td>8.495566</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      "text/plain": [
       "       X    Y  Facies  Porosity       Perm\n",
       "131  320   99       1  0.141749  13.154686\n",
       "180  750  679       0  0.074619   0.089169\n",
       "120  900  559       1  0.133474  13.104697\n",
       "276  730   79       1  0.134691  15.160833\n",
       "13   300  400       1  0.118448   8.495566"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "df.head()                                  # display first 4 samples in the table as a preview"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Summary Statistics for Tabular Data\n",
    "\n",
    "The table includes X and Y coordinates (meters), Facies 1 and 0 (1 is sandstone and 0 interbedded sand and mudstone), Porosity (fraction), and permeability as Perm (mDarcy). \n",
    "\n",
    "There are a lot of efficient methods to calculate summary statistics from tabular data in DataFrames. The describe command provides count, mean, minimum, maximum, and quartiles all in a nice data table. We use transpose just to flip the table so that features are on the rows and the statistics are on the columns."
   ]
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  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>X</th>\n",
       "      <td>6.0</td>\n",
       "      <td>628.333333</td>\n",
       "      <td>253.725574</td>\n",
       "      <td>300.000000</td>\n",
       "      <td>422.500000</td>\n",
       "      <td>740.000000</td>\n",
       "      <td>765.000000</td>\n",
       "      <td>900.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Y</th>\n",
       "      <td>6.0</td>\n",
       "      <td>467.500000</td>\n",
       "      <td>351.097565</td>\n",
       "      <td>79.000000</td>\n",
       "      <td>174.250000</td>\n",
       "      <td>479.500000</td>\n",
       "      <td>649.000000</td>\n",
       "      <td>989.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Facies</th>\n",
       "      <td>6.0</td>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.516398</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.250000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Porosity</th>\n",
       "      <td>6.0</td>\n",
       "      <td>0.112892</td>\n",
       "      <td>0.030695</td>\n",
       "      <td>0.074373</td>\n",
       "      <td>0.085576</td>\n",
       "      <td>0.125961</td>\n",
       "      <td>0.134387</td>\n",
       "      <td>0.141749</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Perm</th>\n",
       "      <td>6.0</td>\n",
       "      <td>8.457717</td>\n",
       "      <td>6.605513</td>\n",
       "      <td>0.089169</td>\n",
       "      <td>2.679906</td>\n",
       "      <td>10.800132</td>\n",
       "      <td>13.142189</td>\n",
       "      <td>15.160833</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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       "          count        mean         std         min         25%         50%  \\\n",
       "X           6.0  628.333333  253.725574  300.000000  422.500000  740.000000   \n",
       "Y           6.0  467.500000  351.097565   79.000000  174.250000  479.500000   \n",
       "Facies      6.0    0.666667    0.516398    0.000000    0.250000    1.000000   \n",
       "Porosity    6.0    0.112892    0.030695    0.074373    0.085576    0.125961   \n",
       "Perm        6.0    8.457717    6.605513    0.089169    2.679906   10.800132   \n",
       "\n",
       "                 75%         max  \n",
       "X         765.000000  900.000000  \n",
       "Y         649.000000  989.000000  \n",
       "Facies      1.000000    1.000000  \n",
       "Porosity    0.134387    0.141749  \n",
       "Perm       13.142189   15.160833  "
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe().transpose()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Visualizing Tabular Data with Location Maps \n",
    "\n",
    "It is natural to set the x and y coordinate and feature ranges manually. e.g. do you want your color bar to go from 0.05887 to 0.24230 exactly? Also, let's pick a color map for display. I heard that plasma is known to be friendly to the color blind as the color and intensity vary together (hope I got that right, it was an interesting Twitter conversation started by Matt Hall from Agile if I recall correctly). We will assume a study area of 0 to 1,000m in x and y and omit any data outside this area."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "xmin = 0.0; xmax = 1000.0               # range of x values\n",
    "ymin = 0.0; ymax = 1000.0               # range of y values\n",
    "pormin = 0.05; pormax = 0.25;           # range of porosity values\n",
    "permmin = 0.01; permmax = 10000\n",
    "nx = 100; ny = 100; csize = 10.0\n",
    "cmap = plt.cm.plasma                    # color map\n",
    "cumul_prob = np.linspace(0.0,1.0,100)   # list of cumulative probabilities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try out location maps, histograms and scatter plots. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 7 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(231)\n",
    "plt.scatter(df['X'],df['Y'],s = 20,c = df['Porosity'],cmap = plt.cm.inferno,linewidths = 0.3,edgecolor = 'black',alpha = 0.8,vmin = pormin,vmax = pormax)\n",
    "plt.colorbar(); plt.xlabel('X (m)'); plt.ylabel('Y (m)'); plt.title('Porosity Location Map')\n",
    "\n",
    "plt.subplot(234)\n",
    "plt.hist(df['Porosity'],color = 'red',alpha = 0.3,edgecolor='black',bins = np.linspace(pormin,pormax,int(len(df)/3)))\n",
    "plt.xlabel('Porosity (fraction)'); plt.ylabel('Frequency'); plt.title('Porosity Histogram')\n",
    "\n",
    "plt.subplot(232)\n",
    "plt.scatter(df['X'],df['Y'],s = 20,c = df['Perm'],cmap = plt.cm.inferno,linewidths = 0.3,edgecolor = 'black',alpha = 0.8,vmin = permmin,vmax = permmax,norm=matplotlib.colors.LogNorm())\n",
    "plt.colorbar(); plt.xlabel('X (m)'); plt.ylabel('Y (m)'); plt.title('Permeability Location Map')\n",
    "\n",
    "plt.subplot(235)\n",
    "plt.hist(df['Perm'],color = 'red',alpha = 0.3,edgecolor='black',bins=np.logspace(np.log10(permmin),np.log10(permmax),int(len(df)/3)))\n",
    "#sns.kdeplot(x=df['Perm'],color = 'black',alpha = 0.2,levels = 1,log_scale = True,bw_adjust = 1)\n",
    "plt.xlabel('Permeability (mD)'); plt.ylabel('Frequency'); plt.title('Permeability Histogram'); plt.xscale('log')\n",
    "\n",
    "plt.subplot(233)\n",
    "plt.scatter(df['Porosity'],df['Perm'],s = 20,color = 'red',alpha = 0.3,edgecolor='black')\n",
    "#plt.contour(df['Porosity'],df['Perm'] Z, colors='black');\n",
    "plt.ylabel('Permeability (mD)'); plt.xlabel('Porosity (fraction)'); plt.title('Permeability-Porosity Scatter Plot')\n",
    "plt.yscale('log')\n",
    "sns.kdeplot(x=df['Porosity'],y=df['Perm'],color = 'black',alpha = 0.2,levels = 4)\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=3.0, top=2.2, wspace=0.2, hspace=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bootstrap Method in Python                       \n",
    "\n",
    "If you are new to bootstrap and Python, here's the most simple code possible for bootstrap.\n",
    "\n",
    "* specify the number of bootstrap realizations, $L$\n",
    "* declare a list to store the bootstrap realizations of the statistic of interest\n",
    "* loop over L bootstrap realizations\n",
    "    * n MCS, random samples with replacement for a new realization of the data\n",
    "    * calculate the realization of the statistic from the realization of the data\n",
    "* summarize the resulting uncertainty model, histogram, summary statistics etc.\n",
    "\n",
    "#### Bootstrap of the Sample Mean, Arithmetic Average\n",
    "\n",
    "Let's demonstrate bootstrap for uncertainty in the arithmetic average with a simple workflow.\n",
    "\n",
    "```python\n",
    "por_avg_real = []                      # declare an empty list to store the bootstrap realizations of the statistic \n",
    "for k in range(0,L):                   # loop over the L bootstrap realizations\n",
    "    samples = random.choices(df['Porosity'].values, k=len(df)) # n Monte Carlo simulations\n",
    "    por_avg_real.append(np.average(samples)) # calculate the statistic of interest from the new bootstrap dataset\n",
    "```\n",
    "\n",
    "We will compare the bootstrap uncertainty in the sample arithmetic average distribution with the analytical expression:\n",
    "\n",
    "\\begin{equation}\n",
    "\\overline{x} \\pm t_{\\frac{\\alpha}{2},n-1}\\sqrt{\\frac{s^2}{n}}\n",
    "\\end{equation}\n",
    "\n",
    "The remaining code in this block is just a super cool set of plots with the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "# Bootstrap method for uncertainty in the sample mean\n",
    "L = 1000                               # set the number of bootstrap realizations   \n",
    "por_avg_real = []                      # declare an empty list to store the bootstrap realizations of the statistic \n",
    "for k in range(0,L):                   # loop over the L bootstrap realizations\n",
    "    samples = random.choices(df['Porosity'].values, k=len(df)) # n Monte Carlo simulations\n",
    "    por_avg_real.append(np.average(samples)) # calculate the statistic of interest from the new bootstrap dataset\n",
    "\n",
    "# Analytical solution for the uncertainty in the sample mean, Student's t distribution with the correct mean and standard deviation\n",
    "analytical = t.pdf(np.linspace(pormin,pormax,100), len(df)-1,loc=np.average(df['Porosity']),scale=math.sqrt(np.var(df['Porosity'].values)/len(df)))\n",
    "\n",
    "# Plot of the original data and bootstap and analytical results   \n",
    "fig = plt.subplot(131) \n",
    "plt.hist(df['Porosity'],color = 'red',alpha = 0.3,edgecolor='black',bins = np.linspace(pormin,pormax,int(len(df)/3)))\n",
    "#plt.plot([np.average(df['Porosity']),np.average(df['Porosity'])],[0,100])\n",
    "plt.axvline(x=np.average(df['Porosity']),linestyle=\"--\",c='black')\n",
    "plt.text(np.average(df['Porosity'])+0.005, 8.8, r'Average = ' + str(round(np.average(df['Porosity']),3)), fontsize=12)\n",
    "plt.text(np.average(df['Porosity'])+0.005, 8.3, r'St.Dev. = ' + str(round(np.std(df['Porosity']),3)), fontsize=12)\n",
    "plt.text(np.average(df['Porosity'])+0.005, 7.8, r'P10 = ' + str(round(np.percentile(df['Porosity'],10),3)), fontsize=12)\n",
    "plt.text(np.average(df['Porosity'])+0.005, 7.3, r'P90 = ' + str(round(np.percentile(df['Porosity'],90),3)), fontsize=12)\n",
    "plt.xlabel('Porosity (fraction)'); plt.ylabel('Frequency'); plt.title('Original Porosity Histogram')\n",
    "\n",
    "plt.subplot(132)\n",
    "plt.hist(por_avg_real,color = 'red',alpha = 0.2,edgecolor = 'black',bins=np.linspace(pormin,pormax,100),label = 'bootstrap',density = True) # plot the distribution, could also calculate any summary statistics\n",
    "plt.plot(np.linspace(pormin,pormax,100),analytical,color = 'black',label = 'analytical',alpha=0.4)\n",
    "plt.axvline(x=np.average(por_avg_real),linestyle=\"--\",c='black')\n",
    "plt.fill_between(np.linspace(pormin,pormax,100), 0, analytical, where = np.linspace(pormin,pormax,100) <= np.percentile(por_avg_real,10), facecolor='red', interpolate=True, alpha = 0.5)\n",
    "plt.fill_between(np.linspace(pormin,pormax,100), 0, analytical, where = np.linspace(pormin,pormax,100) >= np.percentile(por_avg_real,90), facecolor='red', interpolate=True, alpha = 0.5)\n",
    "plt.text(np.average(por_avg_real)+0.009, L*0.07, r'Average = ' + str(round(np.average(por_avg_real),3)), fontsize=12)\n",
    "plt.text(np.average(por_avg_real)+0.009, L*0.066, r'St.Dev. = ' + str(round(np.std(por_avg_real),3)), fontsize=12)\n",
    "plt.text(np.average(por_avg_real)+0.009, L*0.062, r'P90 = ' + str(round(np.percentile(por_avg_real,90),3)), fontsize=12)\n",
    "plt.text(np.average(por_avg_real)+0.009, L*0.058, r'P10 = ' + str(round(np.percentile(por_avg_real,10),3)), fontsize=12)\n",
    "plt.xlabel('Bootstrap Realizations and Analytical Uncertainty Distribution for Mean'); plt.ylabel('Frequency'); plt.title('Distribution of Average')\n",
    "plt.legend()\n",
    "\n",
    "fig = plt.subplot(133) \n",
    "plt.hist(df['Porosity'],color = 'red',alpha = 0.2,edgecolor='grey',bins = np.linspace(pormin,pormax,int(len(df)/3)))\n",
    "#plt.plot([np.average(df['Porosity']),np.average(df['Porosity'])],[0,100])\n",
    "plt.axvline(x=np.average(df['Porosity']),c='black')\n",
    "plt.axvline(x=np.percentile(por_avg_real,90),linestyle=\"--\",c='black')\n",
    "plt.axvline(x=np.percentile(por_avg_real,10),linestyle=\"--\",c='black')\n",
    "plt.text(np.percentile(por_avg_real,90)+0.009,8.8, r'Average = ' + str(round(np.average(por_avg_real),3)), fontsize=12)\n",
    "plt.text(np.percentile(por_avg_real,90)+0.009,8.3, r'Average P90 = ' + str(round(np.percentile(por_avg_real,90),3)), fontsize=12)\n",
    "plt.text(np.percentile(por_avg_real,90)+0.009,7.8, r'Average P10 = ' + str(round(np.percentile(por_avg_real,10),3)), fontsize=12)\n",
    "plt.xlabel('Porosity (fraction)'); plt.ylabel('Frequency'); plt.title('Porosity Histogram with Uncertainty in Average')\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.2, wspace=0.2, hspace=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Bootstrap of the Proportion\n",
    "\n",
    "Let's demonstrate another case for which we have the analytical solution. \n",
    "\n",
    "We will compare the bootstrap results with the analytical expression:\n",
    "\n",
    "\\begin{equation}\n",
    "\\hat{p} \\pm t_{\\frac{\\alpha}{2},n-1}\\sqrt{\\frac{\\hat{p}(1-\\hat{p})}{n}}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "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": [
    "# \n",
    "L = 100000                               # set the number of bootstrap realizations   \n",
    "sand_prop_real = []                      # declare an empty list to store the bootstrap realizations of the statistic \n",
    "shale_prop_real = []\n",
    "for k in range(0,L):                   # loop over the L bootstrap realizations\n",
    "    samples = random.choices(df['Facies'].values, k=len(df)) # n Monte Carlo simulations\n",
    "    sand_prop_real.append(samples.count(1)/len(df)) # calculate the statistic of interest from the new bootstrap dataset\n",
    "    shale_prop_real.append(samples.count(0)/len(df)) # calculate the statistic of interest from the new bootstrap dataset       \n",
    "sand_prop = np.sum(df['Facies'] == 1)/len(df); shale_prop = np.sum(df['Facies'] == 0)/len(df)\n",
    "\n",
    "analytical_shale = t.pdf(np.linspace(0.0,1.0,100), len(df)-1,loc=shale_prop,scale=math.sqrt(shale_prop*(1.0-shale_prop)/len(df)))\n",
    "\n",
    "\n",
    "fig = plt.subplot(121) \n",
    "barlist = plt.bar(x=['shale','sand'],height = [1-sand_prop,sand_prop],color = 'red',alpha = 0.3,edgecolor='black')\n",
    "barlist[0].set_color('blue')\n",
    "plt.text(-.3, shale_prop+0.02, r'Prop. Shale = ' + str(round(shale_prop,2)), fontsize=12)\n",
    "plt.text(0.7, sand_prop+0.02, r'Prop. Sand = ' + str(round(sand_prop,2)), fontsize=12)\n",
    "plt.xlabel('Rock Type / Facies'); plt.ylabel('Proportion'); plt.title('Facies Histogram')\n",
    "plt.ylim([0,1]); plt.yticks(np.arange(0, 1.1, 0.1))\n",
    "\n",
    "plt.subplot(122)     \n",
    "plt.hist(sand_prop_real,color = 'red',alpha = 0.2,edgecolor = 'black',bins=np.linspace(0.0,1.0,40),label = 'sand',density = True) # plot the distribution, could also calculate any summary statistics\n",
    "analytical = t.pdf(np.linspace(0.0,1.0,100), len(df)-1,loc=sand_prop,scale=math.sqrt(sand_prop*(1.0-sand_prop)/len(df)))\n",
    "plt.plot(np.linspace(0.0,1.0,100),analytical,color = 'black',label = 'analytical',alpha=0.4)\n",
    "plt.axvline(x=sand_prop,linestyle=\"--\",c='black')\n",
    "plt.fill_between(np.linspace(0.0,1.0,100), 0, analytical, where = np.linspace(0.0,1.0,100) <= np.percentile(sand_prop_real,10), facecolor='red', interpolate=True, alpha = 0.5)\n",
    "plt.fill_between(np.linspace(0.0,1.0,100), 0, analytical, where = np.linspace(0.0,1.0,100) >= np.percentile(sand_prop_real,90), facecolor='red', interpolate=True, alpha = 0.5)\n",
    "plt.text(np.average(sand_prop_real)+0.009, 7.0, r'Prop. = ' + str(round(sand_prop,2)), fontsize=12)\n",
    "plt.text(np.average(sand_prop_real)+0.009, 6.4, r'Prop. P90 = ' + str(round(np.percentile(sand_prop_real,90),2)), fontsize=12)\n",
    "plt.text(np.average(sand_prop_real)+0.009, 5.8, r'Prop. P10 = ' + str(round(np.percentile(sand_prop_real,10),2)), fontsize=12)\n",
    "\n",
    "plt.hist(shale_prop_real,color = 'blue',alpha = 0.2,edgecolor = 'black',bins=np.linspace(0.0,1.0,40),label = 'shale',density = True) # plot the distribution, could also calculate any summary statistics\n",
    "plt.plot(np.linspace(0.0,1.0,100),analytical_shale,color = 'black',alpha=0.4)\n",
    "plt.axvline(x=shale_prop,linestyle=\"--\",c='black')\n",
    "plt.fill_between(np.linspace(0.0,1.0,100), 0, analytical_shale, where = np.linspace(0.0,1.0,100) <= np.percentile(shale_prop_real,10), facecolor='blue', interpolate=True, alpha = 0.5)\n",
    "plt.fill_between(np.linspace(0.0,1.0,100), 0, analytical_shale, where = np.linspace(0.0,1.0,100) >= np.percentile(shale_prop_real,90), facecolor='blue', interpolate=True, alpha = 0.5)\n",
    "plt.text(np.average(shale_prop_real)+0.009, 7.0, r'Prop. = ' + str(round(shale_prop,2)), fontsize=12)\n",
    "plt.text(np.average(shale_prop_real)+0.009, 6.4, r'Prop. P90 = ' + str(round(np.percentile(shale_prop_real,90),2)), fontsize=12)\n",
    "plt.text(np.average(shale_prop_real)+0.009, 5.8, r'Prop. P10 = ' + str(round(np.percentile(shale_prop_real,10),2)), fontsize=12)\n",
    "\n",
    "\n",
    "plt.xlabel('Bootstrap Realizations and Analytical Uncertainty Distributions for Proportion'); plt.ylabel('Frequency'); plt.title('Distribution of Bootstrap Proportions')\n",
    "plt.legend(loc = 'upper left')\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.2, wspace=0.2, hspace=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Bootstrap of the Interquartile Range\n",
    "\n",
    "To prove that we can bootstrap any statistic let's select a more complicated measure of dispersion, the interquartile range."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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uu+66pGNIUiWOTZKkJLmEVcpg2bJlSUeQpCocmyRJSXIGUpIkSZKUFQtISZIkSVJWLCAlSZIkSVnxHEgpg+OPPz7pCJJUhWOTJClJFpBSBr/5zW+SjiBJVTg2SZKS5BJWSZIkSVJWLCClDIYMGcKQIUOSjiFJlTg2SZKS5BJWKYOVK1cmHUGSqnBskiQlyRlISZIkSVJWLCAlSVLievfuzSGHHMKWLVuSjpKotWvXctFFF9GkSRM6duzIpEmTMraNMTJy5EgKCgooKCjglltuIcYIwCeffMJpp51GQUEB+fn5nHLKKcyZM6d833HjxpGTk0Nubm75Y9asWbX99iQdACwgJUlSopYvX87s2bMJIfDnP/+5Vo6xbdu2Wum3pt10003Ur1+fNWvWMHHiRG644QYWLVpUbduxY8cydepUCgsLWbBgAdOnT+ehhx4CIDc3l0cffZSioiLWrVvHyJEj6d+/f6XP4ZRTTqG0tLT80bt3733xFiXt5ywgpQxOOeUUTjnllKRjSFIlB+LY9Nhjj9GrVy+GDh3K+PHjy1+fO3curVu3Zvv27eWv/elPf6J79+4A7Nixg1/96lcceeSRFBQUMGDAANauXQukitIQAr/73e/o0KEDffr0AeA73/kOrVu3Ji8vjzPOOKNScfbpp5/Sv39/mjVrxsknn8ztt9/O6aefXr59yZIlfOtb36J58+YcffTRTJ48uUY/h40bNzJlyhRGjRpFbm4up59+Oueffz4TJkyotv348eMZMWIE7dq1o23btowYMYJx48YB0LBhQ44++mjq1atHjJGcnBzWrVtX/vlI0hdlASllcNddd3HXXXclHUOSKjkQx6bHHnuMwYMHM3jwYGbOnMmaNWsA6NWrF02aNOGvf/1redtJkyYxaNAgAO6//36mTp3KSy+9xOrVqznkkEO46aabKvX90ksvsXjxYmbOnAlA3759eeedd/j444858cQTGTx4cHnbm266iSZNmvDRRx8xfvz4SsXsxo0b+da3vsWgQYP4+OOPeeKJJ7jxxhszzg7eeOON5OfnV/vYWQDvatmyZeTk5NC5c+fy13r06JHxGIsWLaJHjx6f27Z79+40bNiQ888/n+9973u0atWqfNs//vEPWrRoQefOnRk1atR+M0srKVkWkJIkKTEvv/wyH3zwAQMGDKBnz54ceeSRlc77GzhwIE888QQAJSUlPPPMMwwcOBCAhx56iF/84he0a9eOBg0acOedd/LUU09VKoTuvPNOmjRpQqNGjQD47ne/S9OmTcvbFxYWsn79erZv386UKVP4z//8Txo3bsyxxx7LVVddVd7P9OnT6dSpE1dffTUHHXQQJ554IpdccglPPfVUte9r9OjRFBcXV/tYsGBBtfuUlpaSl5dX6bW8vDxKSkqyap+Xl0dpaWn5eZAACxYsYMOGDUyaNKnSbOoZZ5zBwoUL+fjjj5kyZQpPPPEE//3f/13tcSSpIgtIKYNLLrmESy65JOkYklTJgTY2jR8/nrPPPpsWLVoAMGjQoEozf4MGDeKPf/wjW7Zs4Y9//CMnnngiHTt2BOCDDz7goosuKp/Z69KlCzk5OeUzmADt27cv/3n79u38+Mc/5sgjj6RZs2Z06tQJSF1wpqioiG3btlVqX/HnDz74gFdffbXSTOLEiRP56KOPauyzyM3NZcOGDZVe27BhA02bNs2q/YYNG8jNzSWEUKldw4YNGThwIL/61a8oLCwE4IgjjuDwww+nXr16dOvWjTvuuCNjMSxJFXkfSCmDTz/9NOkIklTFgTQ2bd68mcmTJ7N9+3Zat24NwJYtWyguLqawsJAePXpw7LHH0rFjR2bMmFFp+SqkCrxHH32U0047rUrfy5cvB6hUTE2aNImnn36aF154gU6dOrF+/XoOOeQQYoy0bNmSgw46iJUrV5YvIV2xYkWlY33jG9/g+eefz+q9XX/99Tz++OPVbuvYsWO1y1I7d+7Mtm3beOeddzjqqKMAKCwspGvXrtX207VrVwoLC/nqV7+627YAW7du5b333qu07HWnEEKlmUtJysQZSEmSlIipU6eSk5PD22+/zfz585k/fz6LFy/m61//Oo899lh5u0GDBnH//ffzt7/9je985zvlr19//fX85Cc/4YMPPgCgqKiIp59+OuPxSkpKaNCgAQUFBWzatInbbrutfFtOTg4XX3wxd955J5s2bWLJkiWVMvTr149ly5YxYcIEtm7dytatW3n99ddZvHhxtccaM2ZMpSucVnxkOqexSZMmXHzxxdxxxx1s3LiROXPm8PTTT3PFFVdU2/7KK6/kvvvuY9WqVaxevZp7772XoUOHAqkLEL388suUlZWxefNm7r77btasWcPXvvY1AGbMmFE+U7tkyRJGjRrFBRdckPGzk6SdLCAlSVIixo8fz9VXX02HDh1o3bp1+eP//J//w8SJE8vPZRw4cCCzZs2iT58+5UtdAf7jP/6D888/n7PPPpumTZvSq1cvXn311YzHu/LKK+nYsSNt27bl2GOPpVevXpW2P/DAA6xfv57WrVtzxRVXMHDgQBo0aABA06ZNee655/jDH/5AmzZtaN26NSNHjqzx+1aOHj2azZs306pVKwYOHMiDDz5YPqs4e/ZscnNzy9sOGzaM/v37061bN4477jjOO+88hg0bBqRmcm+66SYKCgpo27YtzzzzDH/5y19o06YNAC+++CLdu3enSZMmnHvuuVx88cWVCmpJyiTsD8sVTjrppPjGG28kHUNfMjvvh+WNlaU9M+/ZZ+nZsmW12/4wYwaX9+1b/X5FRfQ855y9Pv6B/m/3QH9/dcnIkSPLr8gqSV8mIYR5McaTqtvmOZBSBmeeeWbSESSpCsem2rNkyRLKysro1q0br7/+Or/73e945JFHko4lSXWKBaSUwU9/+tOkI0hSFY5NtaekpISBAweyevVqWrVqxYgRIzwvUJJ2YQEpSZIEnHzyybz77rtJx5CkOs2L6EgZ9O3bl74ZztWSpKQ4NkmSkuQMpJTB5s2bk44gSVU4NkmSkuQMpCRJSszLL7/MqaeeSl5eHs2bN+e0007j9ddfB2DcuHGcfvrpn7t/p06daNSoEU2bNiU/P59TTz2VMWPGsGPHjn0R/wuJMTJy5EgKCgooKCjglltu4fOuij9p0iQ6duxIkyZNuPDCC1m7di2QulXHNddcQ8eOHWnatCknnHACM2bM2FdvQ9KXlAWkJElKxIYNG+jXrx/f//73Wbt2LatWreJnP/tZ+b0XszVt2jRKSkr44IMP+PGPf8zdd9/NNddcU0up997YsWOZOnUqhYWFLFiwgOnTp/PQQw9V23bRokUMGzaMCRMmsGbNGho3bsyNN94IwLZt22jfvj0vvfQS69evZ9SoUQwYMIDly5fvw3cj6cvGAlKSJCVi2bJlAAwcOJCcnBwaNWrE2WefTffu3Vm8eDHXX389r7zyCrm5ueTn5++2v7y8PM4//3yefPJJxo8fz8KFC4HUTN3NN99Mhw4dOPTQQ7n++uvLlwJ36dKF6dOnl/exbds2WrRowZtvvlkL7zhl/PjxjBgxgnbt2tG2bVtGjBjBuHHjqm07ceJE+vfvzxlnnEFubi6jRo3ij3/8IyUlJTRp0oQ777yTTp06Ua9ePfr168fhhx/OvHnzai27JFlAShn069ePfv36JR1Dkio5kMamzp07k5OTw1VXXcWMGTNYt25d+bYuXbowZswYTjnlFEpLSykuLs66369+9au0a9eO2bNnAzBy5EiWLVvG/Pnzeffdd1m1ahX/9V//BaSK1yeeeKJ835kzZ9KiRQtOPPHE3R5n0qRJ5OfnZ3z861//qna/RYsW0aNHj/LnPXr0YNGiRVm1PfLII6lfv3558V3RmjVrWLZsGV27dt1tdkn6oryIjpTBzTffnHQESariQBqbmjVrxssvv8zdd9/Ntddey0cffcS5557Lww8/zKGHHrpXfbdp04a1a9cSY+Thhx9mwYIFNG/eHIDbbruNQYMGcddddzFo0CBOOOEENm3aROPGjZk0aRKDBg3K6hiDBg3Kum1FpaWl5OXllT/Py8ujtLSUGCMhhM9tu7N9SUlJpde2bt3K4MGDueqqqzjmmGP2OJMkZcsZSEmSlJguXbowbtw4Vq5cycKFC1m9ejXDhw/f635XrVpF8+bNKSoqYtOmTfTs2bN8ZvCcc86hqKgIgK985St06dKFadOmsWnTJv785z9/oaJwT+Tm5rJhw4by5xs2bCA3N7dK8Vhd253tmzZtWv58x44dXHHFFdSvX58HHnig9oJLEhaQUka9e/emd+/eSceQpEoO5LHpmGOOYejQoeXnLlZXUGXj9ddfZ9WqVZx++um0aNGCRo0asWjRIoqLiykuLmb9+vWUlpaWt9+5jPXpp5/m2GOP5Stf+UpWx5k4cSK5ubkZH5mWsHbt2pXCwsLy54WFhRmXne7a9r333mPLli107twZSF3R9ZprrmHNmjVMmTKFgw8+OKvskvRFWUBKkqRELFmyhHvvvZeVK1cCsGLFCp544gl69eoFwKGHHsrKlSspKyvLqr8NGzYwffp0Lr/8coYMGUK3bt2oV68e1157LT/84Q/5+OOPgdTs5MyZM8v3u/zyy3nuued48MEH92j2cfDgwZSWlmZ8dOjQodr9rrzySu677z5WrVrF6tWruffeexk6dGjGY0ybNo3Zs2ezceNG7rjjDi6++OLyGcgbbriBxYsXM23aNBo1apR1dkn6oiwgJUlSIpo2bcqrr77K1772NZo0aUKvXr047rjjuPfeewHo06cPXbt2pXXr1rRo0QKAX/7yl/Tt27dSP/3796dp06a0b9+eX/ziF/zoRz/i97//ffn2u+++m6985Sv06tWLZs2acdZZZ7F06dLy7YcddhinnHIKf//737nssssq9Z2bm1t+MZ6aMmzYMPr370+3bt047rjjOO+88xg2bFi1x+zatStjxoxh8ODBtGrVipKSEkaPHg3ABx98wEMPPcT8+fNp3bp1+cznxIkTazSvJFUUPu/GtXXFSSedFN94442kY+hLZucSsVmzZiWaQ9rfzHv2WXq2bFnttj/MmMHlu/zyX75fURE9zzlnr49/oP/bPdDfnyQpeSGEeTHGk6rb5gykJEmSJCkr3sZDymDAgAFJR5CkKhybJElJsoCUMrjxxhuTjiBJVTg2SZKS5BJWKYNNmzaxadOmpGNIUiWOTZKkJDkDKWVw7rnnAl6oQlLd4tgkSUqSBaRUx7w1dy5lxcXVbqufn0+39P3RJEmSpH3NJaxSHVNWXEzPli2rfWQqLCVpf9WpUycaNWpEbm4uhx56KFdffTWlpaUArFq1igsuuIDmzZvTrl07xowZU2nf+fPn07NnTxo3bkzPnj2ZP39+jedbu3YtF110EU2aNKFjx45MmjQpY9sYIyNHjqSgoICCggJuueUWKt4uLYRAkyZNyu/X+L3vfa98W3FxMVdddRWtWrWiVatW3HnnnTX+XiSpJlhASpKkRE2bNo3S0lLefPNNXn/9dX7+858DMGTIEA4//HDWrFnDX/7yF2677Tb+93//F4CysjIuuOAChgwZwrp167jqqqu44IILKCsrq9FsN910E/Xr12fNmjVMnDiRG264gUWLFlXbduzYsUydOpXCwkIWLFjA9OnTeeihhyq1KSwspLS0lNLSUh555JHy13/4wx+yadMmli9fzmuvvcaECRP4/e9/X6PvRZJqggWkJEmqE9q2bUvfvn1ZuHAhpaWlzJo1i5/85CccfPDB9OjRg0svvZRHH30USJ0Dum3bNoYPH06DBg34wQ9+QIyRv/71rzWWZ+PGjUyZMoVRo0aRm5vL6aefzvnnn8+ECROqbT9+/HhGjBhBu3btaNu2LSNGjGDcuHFZHWvatGnccsstNG7cmE6dOnHNNdeUv1dJqkssIKUMhg4dytChQ5OOIUmVHMhj04oVK3jmmWc44YQTypd+VlwCGmNk4cKFACxatIju3bsTQijf3r1794yzgzfeeCP5+fnVPrp3717tPsuWLSMnJ4fOnTuXv9ajR4+Mx1i0aBE9evT43LZnnHEGrVu35uKLL2b58uWVtmV6r5JUl1hAShkcyLZuNBwAACAASURBVL+kSdp/HYhj04UXXkh+fj6nn3463/jGN7jtttto2rQpp512GqNGjeKzzz7jzTffZMqUKeW3MCktLSUvL69SP3l5eZSUlFR7jNGjR1NcXFztY8GCBdXus6fH2LV9Xl4epaWl5YXhSy+9xPLly1myZAlt2rShX79+bNu2DYBzzjmHX/3qV5SUlPDuu+/y6KOPersWSXWSV2FVnVNXrkL6ySefANCiRYt9cjxJysaBODZNnTqVs846q8rrEydO5KabbqJ9+/YcccQRDB48mLfffhuA3NxcNmzYUKn9hg0baNq0aY3l2tNj7Np+w4YN5Obmls+SnnHGGQDUr1+f3/72tzRr1ozFixfTrVs37r//fr7//e9z1FFHUVBQwMCBA3niiSdq7L1IUk1xBlJ1Tl25Cumll17KpZdeus+OJ0nZ+DKNTR07dmT69OkUFRXx6quv8umnn/LVr34VgK5du7JgwYJKyz4XLFhA165dq+3r+uuvL7/66a6PTPt07tyZbdu28c4775S/VlhYmLF9165dKSwszKotpK7KujN/8+bNmThxIh999BGLFi1ix44d5e9VkuoSC0hJklQnLV68mJKSEsrKynj88cd57rnn+NGPfgRA7969ycnJ4f7772fLli088MADAPTp06favsaMGVN+9dNdH5nOaWzSpAkXX3wxd9xxBxs3bmTOnDk8/fTTXHHFFdW2v/LKK7nvvvtYtWoVq1ev5t577y1fbrxo0SLmz5/P9u3bKS0tZcSIEbRt25YuXboA8M9//pNPP/2U7du3M2PGDMaOHcvtt9++Nx+fJNUKC0hJklQnzZw5kyOOOIJDDjmEMWPG8Oyzz9KyZUsgtQx06tSpPPbYY+Tn5/Poo48ydepU6tevX6MZRo8ezebNm2nVqhUDBw7kwQcfLJ9VnD17Nrm5ueVthw0bRv/+/enWrRvHHXcc5513HsOGDQNgzZo1XHbZZTRr1owjjjiC5cuXM336dA4++GAA5s2bR7du3WjatCm33norEydO/NzZS0lKiudASpKkxOx6JdKKhg8fzvDhwzNuP+GEE5g3b14tpPq35s2bM3Xq1Gq3ff3rX6e0tLT8eQiBX//61/z617+u0rZPnz4sXbo043EGDBjAgAED9j6wJNUyZyAlSZIkSVlxBlLK4IYbbkg6giRV4dgkSUpSrRaQIYR84BHgOCAC3wWWAk8CnYDlwIAY47razCF9EZdddlnSESSpCscmSVKSansJ62+BZ2OMxwA9gMXAj4EXY4xHAS+mn0t1zooVK1ixYkXSMSSpEscmSVKSam0GMoTQDDgDGAoQYywDykIIFwC9083GA7OAkbWVQ/qidl6mfdasWckGkaQKHJskSUmqzRnII4Ai4PchhH+EEB4JITQBDo0xfgiQ/rNVdTuHEK4LIbwRQnijqKioFmNKkqSkdOrUiUaNGpGbm8uhhx7K1VdfXX5l08mTJ3PqqafSuHFjevfuXWXf+fPn07NnTxo3bkzPnj2ZP39+jedbu3YtF110EU2aNKFjx45MmjQpY9sYIyNHjqSgoICCggJuueUWYoxZ533zzTc544wzyj+L3/72tzX+fiRpb9VmAXkQcCLwYIzxBGAje7BcNcY4NsZ4UozxpJ33fJIkSQeeadOmUVpayptvvsnrr7/Oz3/+cyB1C43hw4fz4x9X/fWhrKyMCy64gCFDhrBu3TquuuoqLrjgAsrKymo020033UT9+vVZs2YNEydO5IYbbmDRokXVth07dixTp06lsLCQBQsWMH36dB566KGs8n7yySecc845DBs2jE8//ZR3332Xs88+u0bfiyTVhNosIFcCK2OMr6afP0WqoFwTQjgMIP3nx7WYQZIk7Sfatm1L3759WbhwIQBnnXUWAwYMoE2bNlXazpo1i23btjF8+HAaNGjAD37wA2KM/PWvf62xPBs3bmTKlCmMGjWK3NxcTj/9dM4//3wmTJhQbfvx48czYsQI2rVrR9u2bRkxYgTjxo3LKu99993Ht7/9bQYPHkyDBg1o2rQpXbp0qbH3Ikk1pdYKyBjjR8CKEMLR6ZfOBN4G/gxclX7tKuDp2sogSZL2HytWrOCZZ57hhBNO2G3bRYsW0b17d0II5a9179494+zgjTfeSH5+frWP7t27V7vPsmXLyMnJoXPnzuWv9ejRI+MxFi1aRI8ePaptu7u8c+fOpXnz5px66qm0atWK/v37869//Wu3n4Mk7Wu1fR/I7wMTQwj1gfeAq0kVrZNDCNcA/wK+U8sZpC9kxIgRSUeQpCoOxLHpwgsv5KCDDiIvL4/zzjuP2267bbf7lJaWkpeXV+m1vLw8SkpKqm0/evRoRo8evUe59vQYu7bPy8ujtLSUGONu+1q5ciVvvvkmzz//PN26deOWW25h4MCBzJkzZ48yS1Jtq9UCMsY4Hzipmk1n1uZxpZrQv3//pCNIUhUH4tg0depUzjrrrD3aJzc3lw0bNlR6bcOGDTRt2rTGcu3pMXZtv2HDBnJzcwkh7LavRo0acdFFF3HyyScD8LOf/YwWLVqwfv36KoWnJCWptu8DKe23li5dytKlS5OOIUmVODaldO3alQULFlS6yumCBQvo2rVrte2vv/56cnNzq31k2qdz585s27aNd955p/y1wsLCjO27du1KYWFhtW13l3fX5a07f67YXpLqAgtIKYNhw4YxbNiwpGNIUiVfprFp+/btfPbZZ2zbto0dO3bw2WefsXXrVgB69+5NTk4O999/P1u2bOGBBx4AoE+fPtX2NWbMGEpLS6t9ZDqnsUmTJlx88cXccccdbNy4kTlz5vD000+X34tzV1deeSX33Xcfq1atYvXq1dx7770MHTo0q7xXX301f/rTn5g/fz5bt25l1KhRnH766eTn53/hz0+SaoMFpCRJqpMmTJhAo0aNuOGGG5g9ezaNGjXi2muvBaB+/fpMnTqVxx57jPz8fB599FGmTp1K/fr1azTD6NGj2bx5M61atWLgwIE8+OCD5bOGs2fPJjc3t7ztsGHD6N+/P926deO4447jvPPOKy/2d5e3T58+/PKXv+S8886jVatWvPvuu597z0lJSkptX0RHkiQpo+XLl2fcNnTo0PIZvOqccMIJzJs3r+ZDVdC8eXOmTp1a7bavf/3rlJaWlj8PIfDrX/+aX//619W2313eG264gRtuuGHvAktSLXMGUpIkSZKUFQtISZIkSVJWXMIqZXD77bcnHUGSqnBskiQlyQJSymBP70kmSfuCY5MkKUkuYZUymD9/PvPnz086hiRV4tgkSUqSM5BSBsOHDwdg1qxZyQaRpAocmyRJSXIGUpIkSZKUFQtISZIkSVJWLCAlSZIkSVmxgJQkSZIkZcWL6EgZ/PKXv0w6giRV4dgkSUqSBaSUwamnnpp0BEmqwrFJkpQkl7BKGfz973/n73//e9IxJKkSxyZJUpKcgZQyuO222wDvtSapbnFskiQlyRlISZIkSVJWLCAlSZIkSVmxgJQkSZIkZcUCUpIkSZKUFS+iI2Xwm9/8JukIklSFY5MkKUkWkFIGxx9/fNIRJKkKxyZJUpKyWsIaQjiutoNIdc0LL7zACy+8kHQMSarEsUmSlKRsZyDHhBDqA+OASTHG4tqLJNUNP//5zwE466yzEk4iSf/m2CRJSlJWM5AxxtOBwUB74I0QwqQQwrdqNZkkSZIkqU7J+iqsMcZ3gNuBkcA3gPtDCEtCCBfXVjhJkiRJUt2R7TmQ3UMI/wMsBvoA/WOMXdI//08t5pMkSZIk1RHZngP5APAwcFuMcfPOF2OMq0MIt9dKMkmSJElSnZJtAXkusDnGuB0ghFAPaBhj3BRjnFBr6aQEPfTQQ0lHkKQqHJskSUnKtoB8ATgLKE0/bww8B5xaG6GkuuDoo49OOoIkVeHYJElKUrYX0WkYY9xZPJL+uXHtRJLqhmnTpjFt2rSkY0hSJY5NkqQkZTsDuTGEcGKM8U2AEEJPYPNu9pH2a/feey8A/fv3TziJJP2bY5MkKUnZFpDDgf8XQlidfn4YcFntRJIkSZIk1UVZFZAxxtdDCMcARwMBWBJj3FqrySRJkiRJdUq2M5AAJwOd0vucEEIgxvhYraSSJEmSJNU5WRWQIYQJwJHAfGB7+uUIWEBKkiRJ0pdEtjOQJwHHxhhjbYaR6pIJE7zFqaQ989bcuZQVF2fcXj8/n269eu3VMRybJElJyraAXAi0Bj6sxSxSndK+ffukI0jaz5QVF9OzZcuM2+cVFe31MRybJElJyraAbAG8HUJ4Ddiy88UY4/m1kkqqA5588kkALrvMCw5LqjscmyRJScq2gLyzNkNIddGDDz4I+EuapLrFsUmSlKRsb+PxUgihI3BUjPGFEEJjIKd2o0mSJEmS6pJ62TQKIVwLPAU8lH6pLTC1tkJJkiRJkuqerApI4CbgNGADQIzxHaBVbYWSJEmSJNU92RaQW2KMZTufhBAOInUfSEmSJEnSl0S2F9F5KYRwG9AohPAt4EZgWu3FkpL31FNPJR1BkqpwbJIkJSnbAvLHwDXAW8Aw4BngkdoKJdUFLVq0SDqCJFXh2CRJSlK2V2HdATycfkhfCuPGjQNg6NChieaQpIocmyRJScqqgAwhvE815zzGGI+o8URSHeEvaZLqIscmSVKSsl3CelKFnxsC3wGa13wcSZL2zFtz51JWXFz+vGTtWgDmPfss9fPz6darV1LRJEk64GS7hPXTXV76TQjhZeCOmo8kSVL2yoqL6dmyZfnzpgcfDEDPli2ZV1SUVCxJkg5I2S5hPbHC03qkZiSb1koiSZIkSVKdlO0S1nsr/LwNWA4MqPE0kiRJkqQ6K9slrN+s7SBSXfPMM88kHUGSqnBskiQlKdslrD/6vO0xxvtqJo5UdzRu3DjpCJJUhWOTJClJe3IV1pOBP6ef9wf+BqyojVBSXTB69GgAbrzxxoSTSNK/OTZJkpKUbQHZAjgxxlgCEEK4E/h/Mcbv1VYwKWmTJ08G/CVNUt3i2CRJSlK9LNt1AMoqPC8DOtV4GkmSJElSnZXtDOQE4LUQwp+ACFwEPFZrqSRJkiRJdU62V2H9RQhhBvD19EtXxxj/UXuxJEmSJEl1TbZLWAEaAxtijL8FVoYQDq+lTJIkSZKkOijb23j8jNSVWI8Gfg8cDDwOnFZ70aRkzZo1K+kIklSFY5MkKUnZzkBeBJwPbASIMa4GmtZWKEmSJElS3ZNtAVkWY4ykLqBDCKFJ7UWS6oZ77rmHe+65J+kYklSJY5MkKUnZXoV1cgjhISA/hHAt8F3g4dqLJSVv+vTpANx8880JJ9l7b82dS1lxcbXb6ufn061Xr32cSNIXdSCNTZKk/U+2V2G9J4TwLWADqfMg74gxPl+rySTVmLLiYnq2bFnttnlFRfs4jSRJkvZXuy0gQwg5wMwY41nAHheN6f3fAFbFGPulr976B6A58CZwRYyxbE/7lSRJkiTtW7s9BzLGuB3YFELI+4LH+A9gcYXndwP/E2M8ClgHXPMF+5UkSZIk7UPZngP5GfBWCOF50ldiBYgx/uDzdgohtAPOA34B/CiEEIA+wKB0k/HAncCDexZbqn2NGjVKOoIkVeHYJElKUrYF5F/Sjz31G+AW/n3LjwKgOMa4Lf18JdC2uh1DCNcB1wF06NDhCxxa2jszZsxIOoIkVeHYJElK0ucWkCGEDjHGf8UYx+9pxyGEfsDHMcZ5IYTeO1+upmmsbv8Y41hgLMBJJ51UbRtJkiRJ0r6zu3Mgp+78IYQwZQ/7Pg04P4SwnNRFc/qQmpHMDyHsLFzbAav3sF9pnxg1ahSjRo1KOoYkVeLYJElK0u4KyIozhkfsSccxxltjjO1ijJ2Ay4G/xhgHA/8LXJpudhXw9J70K+0rL774Ii+++GLSMSSpEscmSVKSdldAxgw/742RpC6o8y6pcyJ/V0P9SpIkSZJq0e4uotMjhLCB1Exko/TPpJ/HGGOzbA4SY5wFzEr//B7w1S+UVpIkSZKUmM8tIGOMOfsqiCRJkiSpbsv2Nh7Sl05BQUHSESSpil3HprfmzqWsuLjatvXz8+nWq9e+iCVJ+pKwgJQymDJlTy88LEm1b9exqay4mJ4tW1bbdl5R0b6IJEn6EtndRXQkSZIkSQKcgZQyuvXWWwG46667Ek6iA4nLDbW3HJskSUmygJQyeOWVV5KOoAOQyw21txybJElJcgmrJEmSJCkrFpCSJEmSpKxYQEqSJEmSsuI5kFIG7dq1SzqCJFXh2CRJSpIFpJTB448/nnQESarCsUmSlCSXsEqSJEmSsmIBKWUwfPhwhg8fnnQMSarEsUmSlCSXsEoZzJ8/P+kIklSFY5MkKUnOQEqSJEmSsmIBKUmSJEnKigWkJEmSJCkrngMpZdC5c+ekI0hSFY5NkqQkWUBKGYwdOzbpCJJUhWOTJClJLmGVJEmSJGXFAlLK4LrrruO6665LOoYkVeLYJElKkktYpQyWLVuWdARJqsKxSZKUJGcgJUmSJElZsYCUJEmSJGXFAlKSJEmSlBXPgZQyOP7445OOIElVODZJkpJkASll8Jvf/CbpCJJUhWOTJClJLmGVJEmSJGXFAlLKYMiQIQwZMiTpGJJUiWOTJClJLmGVMli5cmXSESSpCscmSVKSnIGUJEmSJGXFAlKSJEmSlBULSEmSJElSVjwHUsrglFNOSTqCJFXh2CRJSpIFpJTBXXfdlXQESarCsUmSlCSXsEqSJEmSsmIBKWVwySWXcMkllyQdQ5IqcWySJCXJJaxSBp9++mnSESSpCscmSVKSLCAlSfuNzz77jJKSEkpLS9myZQsNGzZkw8aNbM7Lo1H9+knHkyTpgGcBKUmqs3bs2ME///lP3n33Xd5//32Kioqqbfe3hQs5pHFj2ubn07p9ez756KN9nFSSpC8HC0hJUp2zZcsW/vGPf/Daa6+xbt06Dj74YDp06EC3bt045JBDaNKkCQ0aNGDLli0seuUV8nNyWF1czAdr19LlhBPYsWMHk157jfz8fGKMhBCSfkuSJB0QLCClDM4888ykI0hfOjFG3nrrLZ577jk2btxI+/btOfPMMznmmGPIycmpdp+1S5fSs2XL8v3Pv+UWWrVtS17jxrzz8ce893//L6eccgrHH398xj72J45NkqQkWUBKGfz0pz9NOoL0pbLps8+YMGEC77//Pm3atOHyyy+nXbt2e9RHCIGS9espWb+esT/4AX9ZupSPNm1i+vTpzJkzhz59+tC1a9f9ekbSsUmSlCQLSElS4t79+GNmL1xIvYMO4txzz6Vnz57Uq7d3d5rKqVePti1a0P/b3+bdd9/lhRdeYMqUKbzyyiv069ePww47rIbSS5L05WEBKWXQt29fAGbMmJFwEunAFWNkzj//yYtLltC0USOGfu97NG/evEaPEULgqKOO4sgjj+Stt97i+eef5+GHH+bkk0+mT58+NGjQoEaPV9scmyRJSbKAlDLYvHlz0hGkA1qMkWcWLuSNDz7guDZtaNemTY0XjxXVq1ePHj16cPTRR/Piiy/y2muvsXTpUi666CI6duxYa8etaY5NkqQkWUBKkva5HTEyfcEC/rFiBacecQRndenCm598sk+O3bBhQ8477zya5OTw+vz5jBs3jiMPO4yj27UrXzZbPz+fbr167ZM8kiTtT/buBBNJkvZQjJGn58/nHytWcMZRR3FWly6JXNSmKfAf3/wmJ7Rvzz8//JA3ly6lfcOG9GzZkrLi4n2eR5Kk/YEFpCRpn3pu8WIWrFrFN48+mm8efXSiV0Stf9BBnN+jB5eddBIbPvuMsbNn8+r77xNjTCyTJEl1mUtYpQz69euXdATpgLN2xw6WvvceX+3Uia9/5StJxyl3TOvWtDvkEP5cWMizixbR+pBDOO6b36Rhw4ZJR6vCsUmSlCQLSCmDm2++OekI0gHl7Q8/pChGurRuzbfr4L0Ycxs0YODJJ/PKe+/xwuLFPPzwwwwYMIBDDz006WiVODZJkpLkElZJUq37uKSEqfPn0xC46IQTqFfHisedQgiceuSR9OrShbKyMh555BEKCwuTjiVJUp1hASll0Lt3b3r37p10DGm/99nWrUx+4w0aHHQQbevV4+CcnKQj7VZBs2YMGzaMtm3bMnXqVKZPn862bduSjgU4NkmSkmUBKUmqNTuvuLp20yYuPfFEDqqjM4/Vyc3N5corr+TUU09l3rx5jBs3jpKSkqRjSZKUKAtISVKteeW991iyZg1nd+lCx4KCpOPssXr16vGtb32LAQMG8PHHHzN27FhWrlyZdCxJkhJjASlJqhUfrV/Pi0uWcEzr1nzt8MOTjrNXunTpwjXXXMNBBx3EuHHjPC9SkvSlZQEpSapxW7dvZ8o//kHj+vXp3717nbvi6hdx6KGHcu2119K+fXumTp3KzJkz2bFjR9KxJEnap7yNh5TBgAEDko4g7beef/ttPiktZcjXvkbj+vWTjlNjGjduzJAhQ5g5cyZz586lqKiISy65hEaNGu2zDI5NkqQkWUBKGdx4441JR5D2S0XFxbz+wQd87fDDObJlyxrp8625cykrLq522/uLF9Ozho6TjZycHM4991xat27NX/7yFx555BEuv/xyWmaR4Z+LF2fcVj8/n269eu22D8cmSVKSLCClDDZt2gSkZhwkZWfLli0seP99Cpo04axjjqmxfsuKizMWie+88UaNHWdPnHjiibRo0YLJkyfzyCOPcMkll+x2nx0bN2Z8H/OKirI6rmOTJClJngMpZXDuuedy7rnnJh1D2q+88MILbC4r44IePThoP7jf497q0KED1157LQUFBTzxxBO89+GHxBhr9ZiOTZKkJDkDKSWgLi3Hk2rK8uXLeeONNzi8dWvaN2+edJx9Ji8vj6uvvpqpU6fy9ttvMy1GzuvWjZx6/h+tJOnAYwEpJaAuLseT9sa2bduYNm0ahxxyCMe0a5d0nH3u4IMP5tJLL2XSI4/wjxUrWLdpEwN69qTRAXQBIUmSwCWskqQaMGfOHNauXUu/fv3I+RIsXa1OCIFj2rfnwuOPZ8W6dTwyZw6flpYmHUuSpBplASlJ2ivr1q3j5ZdfpmvXrhxxxBFJx0lcj3btuLJXLz7bupVH5szh/U8+STqSJEk1xiWsUgZDhw5NOoK0X5g5cyYhBM4+++yko9QZHZo353unncYTr7/O46++ynndunFihw410rdjkyQpSbVWQIYQ2gOPAa2BHcDYGONvQwjNgSeBTsByYECMcV1t5ZC+KH9Jk3Zv2bJlLF26lLPOOotmzZolHadOOaRJE7572mk89eabTFuwgE9KS2vkCq2OTZKkJNXmEtZtwIgYYxegF3BTCOFY4MfAizHGo4AX08+lOueTTz7hE5eeSRlt27aNZ599lhYtWtCrV6+k49RJDQ8+mEEnn8zJnTrxynvvsXrHDrZu375XfTo2SZKSVGsFZIzxwxjjm+mfS4DFQFvgAmB8utl44MLayiDtjUsvvZRLL7006RhSnTVnzhzWrVvHueee+6W9cE426tWrx7nHHce3jz2WUmDC3LlsKiv7wv05NkmSkrRPLqITQugEnAC8ChwaY/wQUkUm0CrDPteFEN4IIbxRVFS0L2JKkrJU8cI5hx9+eNJx9gu9jjiCNvXq8eH69fxuzhzWbtyYdCRJkvZYrReQIYRcYAowPMa4Idv9YoxjY4wnxRhPaulN1SWpTnn22We9cM4X0DQEruzVi81lZfxuzhxWrfMSAJKk/UutFpAhhINJFY8TY4x/TL+8JoRwWHr7YcDHtZlBklSzlv3/7d15XFVnmuDx38O+qSAIoii4IBGN4oIScY1iTOKWUmPimtJUdTrp6amZ6p6prqrpmerpT0119dR0VXWluspU4prFxCTlFnGpRHHFYFwQUDQR3AUxiCKyvvPHPRA0gKz3cOH5fj7nc+8959z3POe83MN57vve92Rnk52dzaRJk3TgnGbo0707KxMT8fbwYM3hw5y9ft3ukJRSSqlGa7MEUkQEeBPIMsb8v1qLtgDLrefLgc1tFYNSSqnWVV5ezo4dO3TgnBYKDghgZWIioV26sDEtjaM5OXaHpJRSSjVKW94HMhFYCqSLyAlr3o+BXwDvi8hK4CKwoA1jUKrZ/vqv/9ruEJRqdw4ePEhhYSHLli3TgXNayN/bm+VPPMFHx4+z4/Rp+oeHM9IYHN+/1s/uc1P6kSOUFRbWucwrMJDH9YsFpZTq0NosgTTGHADq+y84ta22q1RrWbhwod0hKNWu6MA5rc/Lw4PnR48m+fRpPs/N5eOPP2bOnDkNJud2n5vKCgsZVc/YBMd00DullOrw2rIFUimXdunSJQD69OljcyQOxhjul5Vx48YNysvLqaiowMvLCz8/P/z9/fH09LQ7RNXBJScn4+bmpgPntDI3EZ4eOpQ7lZWkp6dz//59FixYUO9nur2dm5RSSnUumkAqVY+lS5cCsHfvXqdv2xhDQXExuQUFXLx1i+tFRdwqLqaiqoo9x4/X+Z6goCDCw8Pp3bs3gwYNIiQkxMlRq47s7NmzZGdnk5SUpAPntAERYWDv3gyMi2Pbtm1s2LCBF198ER8fn2+ta+e5SSmllNIEUql2whjD9aIi8quq+N1nn3Hr3j0A/Ly8iAgMpH+PHtytqmJwfDyenp54eHhQWlpKSUkJRUVF3Lhxg2vXrpGZmcnu3bsJDg5m6NChjBo1yuY9U66uvLyc5ORkQkJCGDt2rN3hdGijRo3Cx8eHjz76iDVr1rBkyRICAgLsDksppZSqoQmkUjYrragg/coVjuXmcr3IcavU/n5+JPTvT7+QEIL9/WsG1TiWn09sbGyD5d2+fZuzZ89y5swZ9u3bx/79++kZFESEtzdh2nKkmkEHznGuIUOG4OPjw8aNG3nrrbdYunQpQUFBdoellFJKAZpAKgXUPargTz4w7gAAIABJREFUnVu3apa1xaiCd+7fJ/XCBdJycymtqCCsa1eeGTqU7MxMFrdge926dWPMmDGMGTOGW7ducfToUY6lpfGHlBSG9e7NlJgYAv38WnFPVEdWPXDO0KFDdeAcJxowYADLli3j7bff5q233mLJkiWEhYXZHZZSSimlCaRSUPeogl2sASzqG66+ue7evcvpnBx25OdTVVVFbHg4Cf370zswEBHhy6ysVttW9+7dmTFjBt0qKrhbWMjRCxfIuHaNCQMHMn7gQNzd2uxWsKqDSE5Oxt3dnaSkJLtD6XQiIiL47ne/y4YNG1izZg2LFi3SgXOUUkrZThNIperxwyVLWrW80tJSDh06xOHDh6koL2dE374kDhhAd3//Vt1OXbw8PEgaPJixUVHsyspib3Y2mdeuMXvYsDbftnJdOnCO/UJDQ1mxYgXr169n3bp1LFy4kB/+8Id2h6WUUqoT0wRSqXrMmjgRaPl9zSoqKkhLS2P//v3cu3ePIUOG0MPDg0k2tCR09fVl/siRPN67N9vT03nz0CFievdu1M3LVedSPXBOjx49dOCch9TV5b3ahayseu+R2FyBgYEkDBvGgaNHefeddxgVHU1YUBDHkpPbbJtKKaVUfTSBVKoeZ3NyHE+a2UJojOHMmTPs3LmT27dv079/f6ZOnUqvXr1qLvzsEhMWRmT37mw7dYqMy5d5++23ee655/B3Qmuocg06cE796uryXu1cWlqbbNOtpIRXxo9nQ2oqadnZjOvTh2nDh7fpNpVSSqm66A+glKrHX/385/zVz3/erPfevHmTDRs28P777+Pt7c2SJUtYunQpvXr1auUom8/H05N5I0fyeL9+5ObmsmrVKq5du2Z3WKod0IFz2idfLy+WJiRQeOsW+3NzSb9yxe6QlFJKdULaAqlUKyotLWXfvn2kpqbi6enJjBkziI+Px80Jg9U0p1udiBAZGsoTSUm89957rF69mrlz5z7yViGq4zLGsGPHDh04p53y8fTk5OHDPD52LB8dP05lVZXdISmllOpkNIFUqhUYY0hPT2f37t3cvXuXuLg4pk2b5tQuoS3pVhceHs73vvc9Nm7cyAcffMC0adMYN26c/i6yE8rMzOTcuXNMnz5dB85ppyorKzmVmsp3ly9n88mThOnnVCmllBNpF1alWuj69eusWbOGjz/+mK5du7Jy5UrmzJnjcr8nDAgIYPny5QwZMoQ9e/awa9cujDF2h6Wc6P79+yQnJxMeHq4D57RzVZWVvBgfT3RoKDeMIfXCBbtDUkop1UloC6RSj1DffRnLKio4n5fHhcuX8fHxYdasWYwYMcKlW+08PDyYN28e/v7+HDlyhOLiYubMmaODqHQSe/bsobi4mEWLFjml27UzNHRfVVcfvdTD3Z2Fo0fz608+ITkjg8qqKsYNGGB3WEoppTo4TSCVqsdPV64E4OatWw9cZFYZwxcXL7L/zBlKysuJj49nypQp+Pr62hVqqxIRZsyYQUBAAJ9++ikVFRXMmzdPk8gO7tKlSxw7doyEhATCw8PtDqfVVBUXO33E1LZWfW4CcHdzo5ebG549e7I7K4uKqiomRkfbGJ1SSqmOThNIpeoxzerC996OHTXzcgsK2JGRwY2iIqKCg+nbqxdTnnnGrhDbjIgwYcIEPD092blzJ5s2bWL+/PmaRHZQlZWVbN26lW7dujFlyhS7w1GPMO2h7sUiwnfi4nAX4bOzZ6kyhsmDBtkUnVJKqY5OE0il6nHi7Nma50UlJezOyuL01at09fFh/siRxIaH88XNmzZG2Pb8gSGRkWScOcMbr7/OqIEDa7o2egUG8nhCgr0BqlZx8OBB8vPzefHFF/Hy8rI7HPUI1eemuJiYmnlubm7MiYvDTYR92dkYTSKVUkq1EU0glarHD371K9zc3Jg3axa/27uXKmOYGB3N+IED8ewkLXFlhYXMf/xx+gYEsCMjgy8vXmTBqFG4u7lxLD/f7vBUKygoKCAlJYXY2FgGacLhEn7wq18BsHfVqgfmu4kwe/hwECHl3DmqjKFb9+52hKiUUqoD0wRSqToYYwjr3Zt+gwdz0xgG9+hBUmwsQX5+dodmizH9+oEIO06f5v1jx1gwcqTdIalWYIxh+/bteHh4MGPGDLvDUa1ARJg9bBhuIhw4f54B4eGMMsalB/dSSinVvmgCqdRDvrp5k92ZmcSOGsWdwkIiAgJ4fvRou8NqM40dpXJMVBQCfHL6NJu++IIBffs6KULVVo4fP86FCxd49tln6dKli93hqFYiIsx8/HFEhGO5uezevZukpCRNIpVSSrUKTSCVstwoKmJPVhbn8/Pp5utLxrFj5F25wujnnrM7tDbVlFEq46OiMMCO06e5U1HBqKqqDnO7h86msLCQnTt3EhUVxahRo+wOR7UyEeHZoUO5WVLC4cOHMcYwffp0TSKVUkq1mF75qU4vLy+PY+fO8YeUFC4XFjI9Npa/mTyZvCtX7A6tXRoTFcXUxx7jakEB27Ztwxhjd0iqiYwxbN68GYA5c+ZoUtFBiQhDo6IYM2YMR44cYefOnfp5VUop1WLaAqk6rfz8fPbt20dGRgbubm5MGDiQJ/r3x9cahfLnr70GwMWrV+0Ms10aP3AguUVFHD9+HC8vL5566ilNQlzI0aNHycnJYdasWQQGBtodjmqi6nNTY4gIM6zPZ2pqKlVVVTz99NP6eVVKKdVsmkCqTic/P5+UlBROnz6Nl5cX48ePx+/ePZ7o1euB9cYNHw5oAlmfmIgIukdEkJqaire3t94/0EXk5eWxZ88eoqOjGTFihN3hqGaoPjc1lojw1FNP4ebmVtOd9ZlnntEkUimlVLNoAqk6jZs3b5KSkkJ6ejqenp4kJiYybtw4/Pz8OJac/K31D508aUOUrqO6ZaO8vJyUlBS8vLxITEy0OyzVgPLycjZt2oS3tzezZ8/WBMJFVZ+bmpJIikjNQDqHDh2iqqqKmTNn6t+AUkqpJtMEUnV41Ynj6dOn8fDweCBxbMiPX38dgFcaGESnoRFMvQIDeTwhoXlBuwgRYebMmZSXl7Nnzx68vLyIj4+3OyxVj507d5Kfn8+SJUsICAiwOxzVTNXnpofvA/koIsK0adNwc3PjwIEDGGOYNWuWJpFKKaWaRBNI1WFV3yA9PT0dDw8PnnjiCcaNG4e/v3+rbaOhEUyP5ee32nbaMzc3N+bOnUtZWRmffPIJXl5eDG9iFzvV9jIzMzl27Bjjxo1jwIABdoejbCIiPPnkk4gI+/fvr0kidTRlpZRSjaUJpOpwnJE4qge5u7uzYMEC3nnnHTZv3oynpyexsbF2h6UsN2/eZPPmzfTq1Ysnn3zS7nCUzUSEKVOm4Obmxr59+zDGMHv2bE0ilVJKNYomkKrDKCwsZN++fZw8eRJ3d3cSEhJITEzUxNFJPDw8eOGFF9iwYQMffvghnp6eREdH2x1Wp1daWsrGjRvx8PDg+eefx93d3e6QVDsgIkyePBkRYe/evRhjmDNnjiaRSimlHkkTSOXyioqKSElJ4fjx44gIY8aMYfz48fobLxt4eXmxaNEi1q5dy/vvv8/ixYuJioqyO6xOq/p+jwUFBSxdupRu3brZHZJqZyZNmoSI8Nlnn1FVVcVzzz2nSaRSSqkGaQKpXNbdu3c5cOAAaWlpGGMYOXIkEyZMoGvXrq1S/q9/+EMAznz1VauU11n4+PiwZMkS1qxZw7vvvsuyZcvo3bu33WF1SikpKWRlZTF9+nT69etndziqlVSfm1rLxIkTERE+/fRTjDF85zvf0SRSKaVUvTSBVC7n3r17HDx4kKNHj1JZWUlcXBwTJ05s9Ruix8XEAJpANoe/vz/Lli1j9erVbNiwgZdeeomwsDC7w+pUTp48yd69exk+fDgJHXw04M6m+tzUmiZMmICbmxt79uyhsrKSefPm4eGhlwhKKaW+Tb9iVC6jvLKS81eu8Jvf/IZDhw4RGxvLa6+9xuzZs1s9eQTYk5rKntTUVi+3s+jSpQvLli3D09OT9evXU1BQYHdIncaFCxfYsmUL/fr109s0dEBtdW5KTExkxowZnDlzhnfeeYeysrJW34ZSSinXpwmkaveMMaRfucLre/dy5vJl+vXrx6uvvspzzz1HcHBwm233n998k39+8802K78zCAwMZNmyZRhjWLduHYWFhXaH1OFdv36djRs3EhwcrIPmdFBteW4aO3Ysc+bMIScnh/Xr11NSUtIm21FKKeW6NIFU7drFW7f404EDfHT8OL6eniQMHswLL7xAj3ruvajan5CQEJYuXUpZWRnr1q3jzp07dofUYeXl5bF+/Xq8vb1ZvHgxPj4+doekXFBcXBwLFizg6tWrrF27lrt379odklJKqXZEE0jVLhWVlLDp2DFWHzrEndJS5sbF8f0JEwhppQFylHP17NmTxYsXc/fuXdavX8+9e/fsDqnDKSgoYN26dbi5ubF8+XIdcVW1yODBg1m0aBG3bt1i9erV3L592+6QlFJKtROaQKp2pbKykq+uXXN0V71xg0nR0fynKVMYHhGhv+NycRERESxatIivv/6aDRs2aNe4VpSXl8fatWsBWL58Od27d7c5ItURDBgwgCVLllBcXMxbb71FXl6e3SEppZRqBzSBVO3GxYsXWbVqFZkXLxIZHMyrkyYxOSYGT/0NV4cRFRXF888/T15eHuvWraO4uNjukFze5cuXWb16NcYYli1bRkhIiN0hqQ6kb9++vPTSS1RVVfHWW2+Rk5Njd0hKKaVspgmksl1JSQmbN29m9erV3L9/n1HR0bwYH093f39b4/rjj3/MH3/8Y1tj6Iiio6N54YUXuHnzJmvWrNHfRLbAuXPnWLduHb6+vqxYsYLQ0FC7Q1JO4OxzU8+ePVm5ciVdunRhw4YNXNURlZVSqlPTBFLZKisri9dff51Tp04xbtw4XnvtNcK7d28X3VVjoqKIiYqyO4wOaeDAgSxevJiioiJWr17NrVu37A7JpRhjOHToEO+++y7BwcGsWLGCoKAgu8NSTmLHuSkwMJAVK1bQu3dvvjh/nsN6f1yllOq09C7ByhbFxcXs2LGDjIwMevbsyZIlS+jZs6fdYT1ga0qK3SF0aFFRUSxdupR33nmHN998k8WLF9OrVy+7w2r3ysvL2bZtG6dOnWLw4MHMnTsXLy8vu8PqcL7Myqp32YWsLEbZOBJ09blp1sSJTt2ur68vS5cu5c3f/55dmZncLinhqdjYdvGFn1JKKefRBFI5lTGGjIwMduzYQWlpKVOmTCExMbFd3qvuVxs2APDKc8/ZHEnHFRERwYoVK9iwYQNr1qzh+eefZ+DAgXaH1W7duHGDjz76iLy8PKZMmcKECRP04r2NVBUX15sknktLc3I0D6o+Nzk7gQTw8PBgVHQ0+Xl5pF64QOG9ezw3YgTeHno5oZRSnYV2YVVOc+fOHTZu3MiHH35IUFAQ3//+95k4cWK7TB6V84SEhLBy5Uq6d+/OO++8Q2pqKsYYu8NqV4wxHDlyhDfeeIPi4mIWL17MxIkTNXlUthARZgwZwowhQ8jOy+PNgwf5WgfEUkqpTkO/MlRtzhjDyZMn2blzJxUVFSQlJZGQkICbm35/4coa6uIH4BUYyOMJCY0qq0uXLqxYsYKPPvqI5ORk8vLyeOaZZ/TLBRytjtu3b+fSpUsMGjSI2bNn42/zAFNKiQhj+/WjR0AAH3zxBW8cOMCCUaPsDksppZQTaAKp2tSdO3fYunUr586do0+fPsyZM4fg4GC7w1KtoKEufgDH8vObVJ6XlxcLFy7k008/5cCBA+Tl5TF//ny6devW0lBd0v3799m/fz9HjhzB29ubOXPmMHz4cG11VO1K/x49+N748bz7+eesT01lSGQkI43Rv1OllOrANIFUbcIYw+nTp/nkk0+oqKjgqaeeYuzYsXpRoRokIkydOpWePXuyZcsW/vjHPzJ37lwGDRpkd2hOU1FRQVpaGikpKZSUlBAXF0dSUhJ+fn52h6ZUnbr7+/NyYiIfHj/O6ZwcPLdu5emnn8bT09Pu0JRSSrUBTSBVqysuLmb79u1kZWURERHB3LlzXbLVcf0//RMAB48ftzmSzmfIkCH07NmTTZs28e677zJ69GiSkpI69Gij5ZWVXLh+nZR//3eKioro378/06ZNIzw83O7QVDtTfW5qjIa6mjelm/mjeHt68kJ8PO8eP87x48e5evUq8+fPJyQkpFXKV0op1X5oAqlaVWZmJtu3b6e0tJRp06bxxBNPuOxvHfu0s9uKdDbBwcGsXLmSPXv2kJqaypdffsmcOXOIjIy0O7RWVVRSwrGLF0nLzeVeWRl9+/Zl9uzZDBgwwO7QVDvVlHNTQ13Nm9rN/FHcRHisTx/iJ03iz3/+M6tWrWLmzJkMGzasVbejlFLKXppAqlZRUlLCjh07SE9PJzw8nLlz5xIaGmp3WC2ycdcuu0Po9Dw8PJgxYwaDBw9m8+bNrFmzhuHDhzNt2jQCAgLsDq/Zqqqq+DI/n+OXLnHmxg2MMQwKDSUkJISkBQvsDk+1c9XnpoXTp9scSd0GDRrEK6+8wocffsjHH39MTk6OdmlVSqkORBNI1WLZ2dls3bqVe/fuMXnyZMaPH98hRs/8j02bAL0PZHsQGRnJK6+8wv79+zl8+DBZWVlMmDCBMWPGuEy31qqqKi5dukRGbi6fnThBcWkpvp6ePNGvH6MjIwny92/1FiHVMVWfm9prAgnQtWtXli9fzt69e9m/fz+XL19m3rx5hIWF2R2aUkqpFtIEUjXb/fv32blzJydOnCA0NJRFixbp77VUm/Hy8mLq1KnExcWxa9cu/vKXv3D48GESExMZPXp0u0wky8vL+fLLLzl79izZ2dncu3cPNxEGhYUxPCKC6NBQ3F20i7dSj+Lm5saTTz5JZGQkH3/8MatWrWLixIkd5ktGpZTqrDSBVM1y/vx5tm7dyp07dxg/fjyTJk3Cw0P/nFTbCw4O5sUXX+TSpUvs3buX3bt3k5KSwvDhw4mPj7d10I6qqiquXr1KTk4Oubm55OTkUFFRgbe3N4MGDSImJoa7OTmM1d/Xqk5kwIABvPrqqyQnJ7N3717OnDnDnDlz6KmfA6WUckl6xa+apLi4mOTkZE6fPk1ISAgrVqwgIiLC7rBUO9TQ6I8XL12ib58+dS5r7MiQffr0YenSpVy+fJmjR4+SlpbG0aNH6dWrF0OGDGHw4MEEBQU1O/7GKC4u5vr161y9epWLFy9y8eJFysrKAOjRowcjRozgscceIzIysqbF5dilS20akytr6G/mQlZWg/cdVe2bn58f3/nOd4iNjWXbtm288cYbTJgwgQkTJmhrpFJKuRhNIFWjGGM4ceIEu3btory8nEmTJjF+/HhtdVT1amj0x3NpaYwaObLOZU39HWBERAQRERFMnz6dkydPkpGRwe7du9m9ezdBQUFERUXRp08fwsLCCA0NbfLfrDGGu3fvUlhYSGFhIQUFBVy7do3r169TVFRUs15ISAjDhg0jKiqKyMhIlx7kxy6P+ptRru+xxx6jb9++JCcns2/fPrKysnj66aeJioqyOzSllFKNpFf/6pEKCgrYtm0bOTk59O3bl5kzZ9KjE7QEbPrlLwHYc/iwzZGoxggICCAxMZHExERu3bpFdnY2OTk5ZGZmcty6l6eI0KVLF7p27UqXLl3w9vbGy8sLd3d3jDFUVVVRUVHB/fv3KSkpoaioiMLCQiorKx/YVkhICJGRkfTs2ZPw8HB69uyJr6+vHbutOqHqc5Orqm6NHDJkCDt27GDt2rXExsaSlJREYGCg3eEppZR6BE0gVb1KS0tJSUkhNTUVDw8Pnn32WUaNGoWI2B2aU4TohYzL6t69OwkJCSQkJFBVVcXXX3/NjRs3uHHjBrdv36aoqIj8/HzKysooKyujoqICNzc3RAQPDw98fX3x8fEhLCyMQYMGERgYSGBgIEFBQQQGBurtCJStOsq5KSYmhv79+3Po0CEOHDhAdnY248aNY/z48foZU0qpdkwTSPUtVVVVnDhxgk8//ZTi4mKGDx/O1KlT6dKli92hOdWarVsB8NFuui7Nzc2N4OBggoODiY2NtTscpVqs+tz00qxZNkfScp6enkyaNIm4uDj27NlDSkoKJ06cYPLkyQwbNkx/H6mUUu2QXhmrB+Tm5pKcnMz169fp06cPixYtolevXnaHZYvqizS9D6RSqj3pSAlktW7dujFv3jxGjx7Nrl272LJlC/v372fChAmaSCqlVDujCaQC4MqVK+zbt49z587RtWtX5s2bx5AhQzpNd1XVfjQ0EmdjR2hVSrU/6UeOUFZYWOey6s92ZGQkL7/8MufOnWPv3r2aSCqlVDukCWQnd/nyZfbt28f58+fx9fXlySefJCEhQX9/omzT0EicTR2hVSnVfpQVFjbqsy0iDBo0iOjo6AcSyX379hEfH8+IESPw8/NzVthKKaUeoglkJ2SM4dKlS+zfv/+BxHHMmDF4e3vbHZ5SSin1QCKZnZ3NkSNH2LNnD3v37mXo0KGMGTOG8PBwu8NUSqlORxPITqSsrIz09HTS0tK4fv06fn5+TJ06lfj4eE0clVJKtUsiQkxMDDExMeTl5XH06FFOnTrFiRMniIiIIC4ujtjYWL2VjlJKOYkmkJ1Afn4+aWlpnDx5ktLSUsLCwnj22WcZNmwYXl5edofXbn3y298CsOWzz2yORCmlvlF9buqMQkNDmTlzJtOmTePEiROkpaWxbds2PvnkEwYOHMjQoUOJiYnR/21KKdWGNIHsoAoKCsjKyiIzM5Nr167h7u5ObGws8fHxRERE6OA4jeDn42N3CEop9S16bgIfHx8SEhIYO3Ys169fJz09nYyMDLKzs/H09CQ6OpqBAwcyYMAAunbtane4SinVoWgC2UEYY8jLy+Ps2bNkZmZy48YNAHr37k1SUhLDhw/H39/f5ihdy+8/+ACA7gEBNkeilFLfqD43vbpggc2R2E9ECA8PJzw8nKSkJC5evEh6ejrZ2dlkZmYCjlbLAQMGMHDgQCIiIrR1UimlWkgTSBdljCE/P5+cnBxycnLIzc3l3r17APTp04ennnqKwYMH061bN5sjdV3v794N6H0glVLtS/W5SRPIB4kIkZGRREZG1nypev78eb788ktSU1M5fPgwIkJYWBgRERE1U/fu3bVXjlJKNYEmkC6gsrKSmzdvcuPGjZrp6tWrlJSUAI4bMEdHRxMVFUX//v21u45SSqlOrTpRDAsLIzExkbKyMnJzc7l06RKXL1/m1KlTpKWlAY7usD169KiZQkND6dGjBwEBAZpYKqVUHWxJIEVkBvAbwB34kzHmF3bE0V5UVVVx79497t69S2FhIV9//TWFhYU1U0FBAZWVlQC4u7vTo0cPYmJiiIyMJCoqisDAQJv3QCmllGq/vLy8iI6OJjo6GnD837158yaXLl3i2rVr5Ofnk5WVxRdffFHzHg8PDwIDA2umbt260a1bN/z9/QkICMDf3x8/Pz9NMpVSnY7TE0gRcQdeB5KAy8DnIrLFGJPp7Fhaqri4mPv371NRUfGtqbKykoqKCsrLyyktLf3WdO/ePYqLiykuLq5pSazNy8uLoKAggoKCiI6OrvkmNTg4GHd3dxv2VimllOoY3NzcCA0NJTQ0tGaeMYbi4mLy8vLIz8+nsLCQ27dvU1hYyJUrV+r8Xy0i+Pn54evri7e397cmHx8fvL298fT0xN3dHQ8Pj0c+urm5ISI1j7WnuuZVT0op5Sx2tECOAc4bY74CEJH3gDmAyyWQO3bsICMjo9Hr1/6n4uvrS48ePYiKisLf379mCgwMJCgoCB8fH/2HoJRSSjmJiBAQEEBAQAD9+/f/1vLS0lKKiopqvvy9e/duzfP79+/XfEF8586dmtdlZWVOi/+ZZ54hPj7eadtTSnVeYoxx7gZF5gMzjDEvW6+XAmONMX/z0HrfB75vvYwBzjZhMyHAzVYIV9lD68+1af25Nq0/16b159q0/lyf1qFr0/r7RqQxpkddC+xogayrWe1bWawxZhWwqlkbEEkzxoxuznuV/bT+XJvWn2vT+nNtWn+uTevP9Wkdujatv8Zxs2Gbl4E+tV5HAFdtiEMppZRSSimlVBPYkUB+DkSLSD8R8QJeALbYEIdSSimllFJKqSZwehdWY0yFiPwNsBPHbTzeMsY0fiSaxmlW11fVbmj9uTatP9em9efatP5cm9af69M6dG1af43g9EF0lFJKKaWUUkq5Jju6sCqllFJKKaWUckGaQCqllFJKKaWUahSXTSBFpLuI7BaRc9ZjUD3rLbfWOSciy615fiKyXUTOiEiGiPzCudF3XiIyQ0TOish5EflRHcu9RWSjtTxVRKJqLfsHa/5ZEXnKmXErh+bWn4gkicgxEUm3Hp90duyqZZ8/a3lfEbkrIn/nrJjVN1p4/hwmIoet/3npIuLjzNhVi86fniKy1qq3LBH5B2fHrhpVfxNF5AsRqbDueV572beuRZVzNbf+RCSu1rnzlIgsdG7k7ZQxxiUn4JfAj6znPwL+pY51ugNfWY9B1vMgwA+YYq3jBewHnrZ7nzr6hGPQpC+B/tZxPwnEPrTOq8AfrOcvABut57HW+t5AP6scd7v3qTNNLay/EUAv6/lQ4Ird+9PZppbUX63lHwIfAH9n9/50tqmFnz8P4BQw3HodrOdPl6q/RcB71nM/IAeIsnufOtPUyPqLAoYB64D5tebXeS1q9z51pqmF9TcIiLae9wKuAYF275Pdk8u2QAJzgLXW87XA3DrWeQrYbYy5ZYz5GtgNzDDG3DPGfAZgjCkDvsBxP0rVtsYA540xX1nH/T0c9Vhb7XrdBEwVEbHmv2eMKTXGXADOW+Up52l2/Rljjhtjqu/3mgH4iIi3U6JW1Vry+UNE5uK48GntUbNV47Sk/qYDp4wxJwEBqSiVAAALVUlEQVSMMQXGmEonxa0cWlJ/BvAXEQ/AFygDipwTtrI8sv6MMTnGmFNA1UPvrfNa1BlBqxrNrj9jTLYx5pz1/CqQB/RwTtjtlysnkGHGmGsA1mNoHev0Bi7Ven3ZmldDRAKBWcBf2ihO9Y1H1kftdYwxFcBtHN+WN+a9qm21pP5qmwccN8aUtlGcqm7Nrj8R8Qf+O/AzJ8Sp6taSz98gwIjITquL1n9zQrzqQS2pv01AMY6Wj4vA/zXG3GrrgNUDWnINotcv9muVOhCRMThaML9spbhcltPvA9kUIrIH6FnHop80tog65tXct8T6Nu9d4LfGmK+aHqFqogbr4xHrNOa9qm21pP4cC0WGAP+Co0VEOVdL6u9nwL8ZY+5aDZLK+VpSfx7AeCAeuAf8RUSOGWP0i1PnaUn9jQEqcXSfCwL2i8gevW5xqpZcg+j1i/1aXAciEg6sB5YbYx5uZe502nUCaYyZVt8yEbkhIuHGmGtWpebVsdplYHKt1xHA3lqvVwHnjDG/boVw1aNdBvrUeh0BXK1nnctWgt8NuNXI96q21ZL6Q0QigI+BZcaYTv/tnQ1aUn9jgfki8ksgEKgSkfvGmN+1fdjK0tLz5z5jzE0AEfkEGIn2vHGmltTfIiDZGFMO5InIQWA0ji7lyjlacg3yqGtR1fZadA0pIl2B7cBPjTFHWjk2l+TKXVi3ANUjWS0HNtexzk5guogEiWOU1unWPETkn3GcnH/ghFiVw+dAtIj0ExEvHIMEbHlondr1Oh/41Dh+ubwFeMEapa4fEA0cdVLcyqHZ9Wd1Fd8O/IMx5qDTIla1Nbv+jDETjDFRxpgo4NfAzzV5dLqWnD93AsPEMQK5BzAJyHRS3MqhJfV3EXhSHPyBBOCMk+JWDo2pv/rUey2qnKbZ9Wet/zGwzhjzQRvG6FrsHsWnuROO3wX8BThnPXa35o8G/lRrvRU4Blw5D3zXmheBo+k6CzhhTS/bvU+dYQKeAbJx9B//iTXvn4DZ1nMfHKM8nseRIPav9d6fWO87i46a61L1B/wUx294TtSaQu3en842teTzV6uM/4WOwupy9QcswTEA0mngl3bvS2ecWnD+DLDmZ+BI/P/e7n3pjFMj6i8eR0tXMVAAZNR677euRXVyjfqzzp3lD12/xNm9P3ZPYh0cpZRSSimllFKqQa7chVUppZRSSimllBNpAqmUUkoppZRSqlE0gVRKKaWUUkop1SiaQCqllFJKKaWUahRNIJVSSimllFJKNYomkEop5QJEpFJETojISRH5QkTGtXL5P27N8h4q+yURybfiPyMi/6UFZU0WkW3W89ki8qNmlBEnIs/Uet2sclpKRCaISIZ1XHwfWna3Ee//gYj4tV2ETWfVda9ar/8kIrHW8xwRCWlCWXtF5Kz1N/+5iMS1RcxKKaWaRhNIpZRyDSXGmDhjzHDgH4D/08rl15lAWjcvb43/FRuNMXFAIvATEenT0gKNMVuMMb9oxlvjcNwTrKXltNRi4P9a9VrSjPf/AGhSAiki7s3YTlPKfgmoSSCNMS8bYzJbUOxi62/+98C/tixCpZRSrUETSKWUcj1dga+hJsH7VxE5LSLpIrLwEfPDRSTFavU6bbWC/QLwtea9LSJRIpIlIr8HvgD6iMh/iEia1WL2s+pArFalfxGRo9Y0sKHAjTEFOG6mHW69v4eIfGi1MH0uIonW/DEickhEjluPMQ+XZbV2/c56fqLWVCIik+oqQ0S8cNw8eqG17sKHyokUkb+IyCnrsa81f42I/NYq5ysRmV/f8awjzqlWDOki8paIeIvIy8DzwD+KyNv1HS+rxXWviGyyWm/ftur2b3Ekap+JyGfWutNF5LA4Wqg/EJGAWnX0jyJyAFggIqOsVr3D1X8jDx9P6/U2EZlsPW+o/qvLfhEYDbxtHQ9fK/bRdezXEuvv5YSI/FEendgeBnrXen9D8fzMOgbpIvKYNb+HiOy25v9RRHLFag1tRixKKdWpaQKplFKuoTrBOwP8Cfjf1vzv4GhRGw5MA/5VRMIbmL8I2Gm1Bg4HThhjfsQ3LZyLrXJjgHXGmBHGmFzgJ8aY0cAwYJKIDKsVW5ExZgzwO+DXDe2ElZD5AKesWb8B/s0YEw/Ms/YN4Aww0RgzAvhH4OcNlWvFHgf8DyANOFRXGcaYMuv5Rus9Gx8q6nfWfg8D3gZ+W2tZODAemAlUt1h+63g+tL8+wBpgoTHmccAD+GtjzJ+ALcDf1zrm9RmBo7UxFugPJBpjfgtcBaYYY6ZYydBPgWnGmJHWMfivtcq4b4wZb4x5D1gN/K0x5olHbLe2huq/uuwN1nYXN9SqKiKDgYXWfsQBlThaYxsyA/hzI+O5aR2D/wD+zpr3P4FPrfkfA9VfDDQnFqWU6tQ87A5AKaVUo5RYF7iIyBPAOhEZiiOhedcYUwncEJF9QHwD8z8H3hIRT+DPxpgTdW0MyDXGHKn1+nkR+T6O/xvhOJKZ6iTw3VqP/1ZPeQtFZAqOxPR7xpj71vxpQKyIVK/XVUS6AN2AtSISDRjA81EHyFr3X4EnjTHlItKzqWUAT+BIvgHWA7+stezPxpgqIFNEwqx5jzqeMcAFY0y29Xot8BqPSLQfctQYc9naxxNAFHDgoXUScNTJQetYeuFotau20Xp/NyDQGLOv1j4+3YgYGqr/h5PwR5kKjAI+t2L1BfLqWfdtEfEH3IGRjYznI+vxGN/U5XjgOQBjTLKIfN2MWJRSSqEtkEop5XKMMYeBEKAHIPWsVud8Y0wKMBG4AqwXkWX1vL+4piCRfjhacqZaLXPbcbQi1hRbz/PaNhpjhgATgF9ZyR04/g89Ud2CaIzpbYy5g6OF9TNjzFBg1kPb+xYryXgfR3J61ZrdpDLqUXt/SmtvEhp1POurn6aovd1K6v7yV4DdtY5jrDFmZa3lxbXWq6+OKnjwusAHGlX/xTSNAGtrxRpjjPlf9ay7GOgHvAO83sh4qo9X7WPV0OeksbEopZRCE0illHI51u+63IECIAVH6567iPTAkcwcrW++iEQCecaYN4A3+aZVp9xqRatLVxxJwm2r5e3hFquFtR4P0wAr+V0P/Gdr1i7gb2rtW/VIm91wJGXgGJjlUVYDq40x+2vNq6+MO0CXeso5BLxgPV/Mt1v6HtDA8ax2BoiSb34buhTYR+uovR9HgMTq7YiIn4gMevgNxphCHPU43ppVu7tmDhAnIm7iGORojDX/UfVfX0z1+QswX0RCrVi7W8exTsaYchzdcxOsLqdNiafaARy/OUVEpgNBzYlFKaWUdmFVSilX4Wt1XwRHq8lyY0yliHyMo9vlSRwtS//NGHO9gfnLgb8XkXLgLlDdYrYKOCUiXwA/qb1hY8xJETkOZABfAQcfis1bRFJxfCn5YiP25V+AL0Tk58DfAq+LyCkc/5NSgFdwdB1dKyL/Ffi0ocKsC/75wCARWWHNfrmBMj4DfmQdz4dHs/1bHF1S/x7IB777iH2ZTN3HEwBjzH0R+S7wgYh44Ojy+odHlNlYq4AdInLN+h3kS8C7IuJtLf8pkF3H+76LYx/vATtrzT8IXADSgdM4BlBqTP3Xtgb4g4iU4Pj7+xZjTKaI/BTYJY4RfstxdOvNra9QY0yJiPwK+DtjzMomxFPtZziOzUIcCfw14I4x5mZTY1FKqc5OjKmvJ4tSSinVMBHJAUYbY27aHYtqOhGJArZZ3Xw7LCuprjTGVFi/If6P6t8UK6WUahptgVRKKaVUR9cXeN9qZSwDvmdzPEop5bK0BVIppZRSSimlVKPoIDpKKaWUUkoppRpFE0illFJKKaWUUo2iCaRSSimllFJKqUbRBFIppZRSSimlVKNoAqmUUkoppZRSqlH+PwKrJ+h7OoXYAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "L = 1000                               # set the number of bootstrap realizations   \n",
    "iqr_real = []                      # declare an empty list to store the bootstrap realizations of the statistic \n",
    "for k in range(0,L):                   # loop over the L bootstrap realizations\n",
    "    samples = random.choices(df['Porosity'].values, k=len(df)) # n Monte Carlo simulations\n",
    "    iqr_real.append(np.percentile(samples,75) - np.percentile(samples,25)) # calculate the statistic of interest from the new bootstrap dataset\n",
    "\n",
    "iqr = np.percentile(df['Porosity'],75) - np.percentile(df['Porosity'],25)\n",
    "\n",
    "plt.subplot(111)\n",
    "plt.hist(iqr_real,color = 'red',alpha = 0.2,edgecolor = 'black',bins=np.linspace(0.0,0.125,100),label = 'bootstrap',density = True) # plot the distribution, could also calculate any summary statistics\n",
    "plt.axvline(x=iqr,c='black')\n",
    "plt.axvline(x=np.percentile(iqr_real,10),linestyle=\"--\",c='black')\n",
    "plt.axvline(x=np.percentile(iqr_real,90),linestyle=\"--\",c='black')\n",
    "sns.kdeplot(x=iqr_real,color = 'grey',alpha = 0.1,levels = 1,bw_adjust = 1)\n",
    "plt.text(np.percentile(iqr_real,90)+0.009, L*0.07, r'Average = ' + str(round(np.average(iqr_real),3)), fontsize=12)\n",
    "plt.text(np.percentile(iqr_real,90)+0.009, L*0.066, r'St.Dev. = ' + str(round(np.std(iqr_real),3)), fontsize=12)\n",
    "plt.text(np.percentile(iqr_real,90)+0.009, L*0.062, r'P90 = ' + str(round(np.percentile(iqr_real,90),3)), fontsize=12)\n",
    "plt.text(np.percentile(iqr_real,90)+0.009, L*0.058, r'P10 = ' + str(round(np.percentile(iqr_real,10),3)), fontsize=12)\n",
    "plt.xlabel('Boostrap Realizations of Interquartile Range'); plt.ylabel('Frequency'); plt.title('Distribution of Interquartile Range')\n",
    "# plt.legend()\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.2, wspace=0.2, hspace=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Bootstrap of the Coefficient of Variation\n",
    "\n",
    "Here's another statistic that requires multiple measures from the each bootstrap realization of the data.\n",
    "\n",
    "* this reinforces that we bootstrap dataset realizations and then calculate the statistic on this dataset realization\n",
    "\n",
    "For the coefficient of variation we will:\n",
    "    \n",
    "* calculate a bootstrap realization of the dataset with $n$ samples with replacement\n",
    "* calculate the mean and standard deviation from this bootstrapped realization of the dataset\n",
    "* calculate a boostrap realization of the coefficient of variation as the standard deviation divided by the mean\n",
    "\n",
    "Repeat this $L$ times and then evaluate the resulting distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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LSkpyOgSpp9Q2RKS2lECKiIgEuNdee83pEKSeUtsQkdrSEFYRERERERHxihJIERGRADdx4kQmTpzodBhSD6ltiEhtaQiriIhIgFu3bp3TIUg9pbYhIrWlHkgRERERERHxihJIERERERER8YoSSBEREREREfGK5kCKiIgEuPbt2zsdgtRTahsiUltKIEVERALcP//5T6dDkHpKbUNEaktDWEVERERERMQrSiBFREQC3L333su9997rdBhSD6ltiEhtaQiriIhIgMvIyHA6BKmn1DZEpLbUAykiIiIiIiJeUQIpIiIiIiIiXlECKSIiIiIiIl7RHEgREZEA17NnT6dDkHpKbUNEaksJpIiISID7xz/+4XQIUk+pbYhIbWkIq4iIiIiIiHhFCaSIiEiAGz16NKNHj3Y6jAapvLyccJeLxJYt2bJlC3l5eVhrnQ7LZ9Q2RKS2NIRVREQkwO3bt8/pEBqckrIy1uzZw1e7dnH54MEA/Pvf/wbA5XJx5ZVX0rt3b4KDg50M84KpbYhIbSmBFBEREankYEEBb6xaRf7x4yTHxvLd119z+MgR5i5YwIEDB9i4cSPvv/8+3377LSNGjCAxMdHpkEVE6ozfhrAaY9oYY/5jjEk3xmw2xvy353isMeZjY8x2z3+b+ysGERERkdrYtH8/r65cSZm1jO3Xj3EDBnBw717yjxyhVatW9O7dm7FjxzJq1ChKSkqYOXMmO3fudDpsEZE64885kKXAw9baTkA/4AFjTGfgMeBTa+0lwKeezyIiIiKO2rJ/P4vWrqVVTAz3XnklKfHx1V5njOGSSy7h17/+Nc2bN2f+/PlkHzlSx9GKiDjDb0NYrbUHgAOe94XGmHSgNTAcGOS5bDawHHjUX3GIiIg0dv3793c6hHovp6CAVdu20aZ5c0ZffjlNvZjbGBUVxV133cXs2bNZu2MHvVu0IDEqqg6i9R21DRGprTqZA2mMSQEuBb4FEj3JJdbaA8aYi2q4517gXoC2bdvWRZgiIiIB6S9/+YvTIdRrR44cYXVGBrHh4Yzs08er5PG00NBQbr/9dqZNncqCVau4Z+BAIkJD/Ritb6ltiEht+X0bD2OMC1gETLTWFnh7n7X2n9bay6y1lyUkJPgvQBEREWm0ysrKWLRoEQCj+vYlLCSk1mVERUXRp0MHik+eZMmGDQG1zYeIyJn8mkAaY5riTh7nWWvf8hzONsa09JxvCRzyZwwiIiKN3S9+8Qt+8YtfOB1GvfT555+TlZVF99RUYsLDz7ucmIgIftKhA9uys9m0f78PI/QvtQ0RqS1/rsJqgFeBdGvt3yqdehcY63k/FnjHXzGIiIgI5Obmkpub63QY9c6+fftYsWIFPXv2pFVc3AWX169dO5JiYnh/0yaKTpzwQYT+p7YhIrXlzx7IK4AxwGBjzDrP63rgGeBaY8x24FrPZxEREZE6U15eznvvvUdkZCQ///nPfVJmkDEM79mTU2VlfJSe7pMyRUTqG3+uwroSMDWc/qm/6hURERE5l9WrV3Pw4EFuvfVWQn246E28y0X/du1YuWMH/VJTaRUT47OyRUTqA78voiMiIiJSnxQVFfHZZ5+RlpZG586dfV7+wLQ0wkNC+Dg9XQvqiEjAqZNtPERERMQ5P/2pBv5Utnz5ckpKShgyZAjuJRt8K7RpUwa1b8+yTZvIyM6mQ4sW57xn4zffcCo/v8bzITExdOvXz5dhAmobIlJ7SiBFREQC3B//+EenQ6g3cnNzWbt2LZdddhlxPlg4pya92rbl28xM/rNtG+0TE895/an8fHqfZduyNYcP+zK8CmobIlJbGsIqIiIijcZnn31GkyZNuOqqq/xaT3BQEFdecgnZhYVsP6Qdy0QkcCiBFBERCXBDhgxhyJAhTofhuKysLLZs2cKAAQNwuVx+r69rq1bEhIWxYvv2ejsXUm1DRGpLCaSIiEiAO378OMePH3c6DMctX76csLAw+vfvXyf1BQcFMSAtjX35+eQWFtZJnbWltiEitaUEUkRERALe/v372bFjB/379/fpth3ncmmbNkSEhrJz//46q1NExJ+UQIqIiEjA++KLL2jWrBl9+/at03qbBAfTNyWFw0ePkpOTU6d1i4j4gxJIERERCWgHDx5k27Zt9OvXr057H0/r3bYtQcawatWqOq9bRMTXtI2HiIhIgLvxxhudDsFRK1euJDQ0lMsvv9yR+iNCQ2kZF8e6desYPHiwI0lsTRp72xCR2lMCKSIiEuB+97vfOR3CBdv4zTecys+v8XxITAzd+vX70fEjR46wZcsW+vfvT7NmzfwZ4lmlJCaSlZPDhg0b6NOnj2NxnCkQ2oaI1C0lkCIiIlLvncrPp3dCQo3n1xw+XO3xr7/+GmMM/apJLutSc5eLVq1a8d1333HZZZdhjHE0HhGR86U5kCIiIgFu0KBBDBo0yOkw6tyxY8f4/vvv6d69O5GRkU6HQ+/evcnJySErK8vpUCo01rYhIudPCaSIiIgEpFWrVlFaWsqAAQOcDgWALl260LRpU77//nunQxEROW9KIEVERCTglJWVsWrVKi6++GISzjL0tS6FhobSuXNnNm3aRElJidPhiIicF82BFBERkYCzZcsWiouLK1ZePdciPJnp6WedY+krPXv2ZP369aSnp9O9e3e/1yci4mtKIEVERCTgrFq1itjYWNLS0oBzL8KzffXqOokrOTmZmJgY1q1bpwRSRBokJZAiIiIBbsSIEU6HUKcOHDjA3r17+dnPflbvVjs1xtCzZ0+WL1/O0aNHiY6OdjSextY2ROTCKYEUEREJcBMmTHA6hDr13Xff0bRpU3r27Ol0KNXq1q0by5cvZ/PmzY4v8NPY2oaIXDgtoiMiIhLgjh07xrFjx5wOo04cO3aMjRs30r17d5o1a+Z0ONWKjY2lVatWbNq0yelQGlXbEBHfUAIpIiIS4K6//nquv/56p8OoE99//z1lZWX06dPH6VDOqmvXrhw4cIDc3FxH42hMbUNEfEMJpIiIiASE8vJyVq1aRXJyMomJiU6Hc1ZdunQBqBe9kCIitaEEUkRERALC9u3bOXr0KH379nU6lHOKiooiOTmZTZs2Ya11OhwREa8pgRQREZGA8N133xEVFUXHjh2dDsUrXbt2JScnh0OHDjkdioiI17QKq4iIiDR4RcePs2vXLn7yk58QFOT7v4+fOHaMNR98UOP5zPT0s+4zWZ2OHTvy3nvvsXXrVlwXGqCISB1RAikiIhLgxo0b53QIfrc7O5vg4GB69+7tl/JtWdlZE8Ttq1fXukyXy0Xbtm1JT0+nT0rKBUR3/hpD2xAR31ICKSIiEuACPUk4WVrKvsOH6dK1KxEREU6HUysdO3bko48+orhFC0fqD/S2ISK+pzmQIiIiAS4nJ4ecnBynw/Cb9fv2UVpeXu+37qhOp06dADh45Igj9Qd62xAR31MPpIiISIC79dZbAVi+fLmzgfiBtZZVu3cTHRFBUlKS0+HUWkxMDC1btuRgXp4j9Qdy2xAR/1APpIiIiDRYmbm55BQVkVrP9308m44dO3KkqIjCEyecDkVE5JyUQIqIiEiDtSozk/CQEFrGxTkdynk7ve3ItuxshyMRETk3JZAiIiLSIOUfO8a27Gx6tW1LsB+27qgrCQkJhIeGsl0JpIg0AA33X1sRERFp1Fbv2QPAZcnJDkdyYYwxXBQTw66cHErKypwOR0TkrLSIjoiISIC7//77nQ7B50rLylj7ww90aNGC6LAwdq5addbrM9PTz7qPo9MSY2LYnZ1NZk4O7etwPmcgtg0R8S8lkCIiIgHutttuczoEn9u0fz/HS0rom5ICQHlx8VkTxO2rV9dRZOcnNiqKkOBgMrKz6zSBDMS2ISL+pSGsIiIiAW7v3r3s3bvX6TB8xlrLd7t3k+BykdKAF8+pLDgoiLSEBDIOHcJaW2f1BlrbEBH/Uw+kiIhIgBszZgwQOHv9ZeXnc+DoUa7v2hVjjNPh+MwliYmkHzzIwYICWkZH10mdgdY2RMT/1AMpIiIiDcp3u3cT2qQJPZKSnA7Fpy656CIAth865HAkIiI1UwIpIiIiDUbRyZNs3r+fHklJhDQJrIFUrtBQWkRFsfPwYadDERGpkRJIERERaTDW7NlDubX08SyeE2jSEhLYd+QIJ0tKnA5FRKRaSiBFRESkQSgtK2PVnj1cnJBAvMvldDh+kZaQQLm1ZObmOh2Kzw0aNIjmzZtz8uRJp0NxVF5eHjfffDMREREkJyczf/78Gq997rnn6Nq1K5GRkaSmpvLcc89VOf/VV1/Rt29fIiMj6d69OytXrvR3+CJaREdERCTQPfzww06H4BObDxyg+ORJ+rVr53QotbYzPf2s50/vU9k2NpamwcHsPHyYji1a+D2uumobu3fvZsWKFURHR/Puu+/yy1/+0ud1lJaW0qQBDGt+4IEHCAkJITs7m3Xr1nHDDTfQo0cPunTp8qNrrbXMmTOH7t27s3PnTq677jratGnD7bffTl5eHsOGDWP69OnccsstLFiwgKFDh7Jr1y6aN2/uwJNJY6EeSBERkQA3dOhQhg4d6nQYF8Ray7eZmcS7XLSLj3c6nFo7vU9lTa/S4mLAvZ1Halxcnc2DrKu2MWfOHPr168e4ceOYPXt2xfFvvvmGFi1aUFZWVnHs7bffpnv37gCUl5fzzDPPkJaWRlxcHCNGjCAvLw9wJ6XGGF599VXatm3L4MGDAfjlL39JixYtiI6O5qqrrmLz5s0VZefm5jJ06FCioqLo06cPjz/+OAMHDqw4v3XrVq699lpiY2Pp0KEDCxcu9On3UFxczKJFi5gyZQoul4uBAwcybNgw5s6dW+31jzzyCL169aJJkyZ06NCB4cOH8+WXXwLu3sfExER++ctfEhwczOjRo0lISOCtt97yacwiZ1ICKSIiEuC2bdvGtm3bnA7jghwpKuLA0aNcnpoaUFt3VKddQgJHjh0jz5NU+lNdtY05c+Zwxx13cMcdd/Dhhx+SnZ0NQL9+/YiIiOCzzz6ruHb+/PmMGjUKgBdffJHFixfz+eefs3//fpo3b84DDzxQpezPP/+c9PR0PvzwQwCGDBnC9u3bOXToEL169eKOO+6ouPaBBx4gIiKCgwcPMnv27CrJbHFxMddeey2jRo3i0KFDLFiwgAkTJlRJQCubMGECMTEx1b5OJ8BnysjIIDg4mPbt21cc69GjR411VGatZcWKFRU9ldbaH+0Zaq1l06ZN5yxL5EIogRQREQlw9913H/fdd5/TYVyQXQcO0Kxp04DbuqM6FyckANRJL2RdtI2VK1eyZ88eRowYQe/evUlLS6sy72/kyJEsWLAAgMLCQpYtW8bIkSMBeOmll3jqqadISkoiNDSUyZMn8+abb1JaWlpx/+TJk4mIiCAsLAyAX/3qV0RGRlZcv379eo4ePUpZWRmLFi3iz3/+M+Hh4XTu3JmxY8dWlLN06VJSUlK46667aNKkCb169eIXv/gFb775ZrXPNW3aNPLz86t9bdiwodp7ioqKiD5jj8/o6GgKCwvP+T1OnjyZ8vJy7rrrLgAGDBjA/v37WbBgASUlJcyePZudO3dy7Nixc5YlciGUQIqIiEi9lp+fz8EjR+jdti1Ng4OdDsfvYiMiiAkLC5jtPGbPns11111HvGfo8ahRo6r0/I0aNYq33nqLkydP8tZbb9GrVy+Sk5MB2LNnDzfffHNFz16nTp0IDg6u6MEEaNOmTcX7srIyHnvsMdLS0oiKiiLFs1pvTk4Ohw8fprS0tMr1ld/v2bOHb7/9tkpP4rx58zh48KDPvguXy0VBQUGVYwUFBURGRp71vqlTpzJnzhzee+89QkNDAYiLi+Odd97hb3/7G4mJiXzwwQdcc801JDWCP7KIs+r/TGMRERFp1L777jsMBOzWHWcyxtAuIYFN+/dTVl5OcFDD/Xv/8ePHWbhwIWVlZbTwLAp08uRJ8vPzWb9+PT169KBz584kJyfz/vvvVxm+Cu4Eb+bMmVxxxRU/Knv37t0AVYY0z58/n3feeYdPPvmElJQUjh49SvPmzbHWkpCQQJMmTdi3b1/FENK9e/dWqevqq6/m448/9urZxo8fz2uvvVbtueTk5GqHpe5/EzYAACAASURBVLZv357S0lK2b9/OJZdcAsD69eurXUDntJkzZ/LMM8/wxRdf/Cg5vPrqq1m1ahXgXkQoLS0tYBbNkvqr4f6LJCIiIgHv1KlTfP/997SIjSXaM0SxMbg4IYFTpaXsO3LE6VAuyOLFiwkODmbLli2sW7eOdevWkZ6ezpVXXsmcOXMqrhs1ahQvvvgiX3zxRZUVWsePH88f/vAH9uzZA8Dhw4d55513aqyvsLCQ0NBQ4uLiOHbsGJMmTao4FxwczC233MLkyZM5duwYW7durRLDjTfeSEZGBnPnzqWkpISSkhJWrVpFeg0r6M6YMYOioqJqXzXNaYyIiOCWW27hiSeeoLi4mC+//JJ33nmHMWPGVHv9vHnzmDRpEh9//DHtqll9+Pvvv6ekpISCggJ+97vfkZSUxM9+9rMavx8RX1ACKSIiIvXW+vXrOXHiBKl1sKVFfZIaH48xpsEPY509ezZ33XUXbdu2pUWLFhWv//qv/2LevHkVcxlHjhzJ8uXLGTx4cMVQV4D//u//ZtiwYVx33XVERkbSr18/vv322xrru/POO0lOTqZ169Z07tyZfv36VTk/depUjh49SosWLRgzZgwjR46sGBIaGRnJRx99xOuvv06rVq1o0aIFjz76qM/3rZw2bRrHjx/noosuYuTIkUyfPr2iB3LFihW4Ku1x+vjjj5Obm0ufPn1wuVy4XC7Gjx9fcf7ZZ58lPj6eNm3acODAAd5++22fxipSHQ1hFRERCXCPP/640yGcl/Lycr766itat25N80q/VDcGzZo2JSkmhp2HDzO4Y0e/1ePvtvHBBx9Ue3zEiBGMGDGi4nPbtm0pLy//0XVBQUE89NBDPPTQQz86l5KS8qNVSF0u1496KO+8886K9wkJCbz33nsVnx999NEqw0I7dOhQ5bw/xMbGsnjx4mrPXXnllRQVFVV8zszMPGtZpxcfEqlLSiBFREQC3DXXXON0COdl8+bN5Ofn87Of/Yxiz3y3xiQtIYHlGRkcO3XKb3U01LZxvrZu3cqpU6fo1q0bq1at4tVXX+WVV15xOiyRBkVDWEVERALc6blnDYm1lpUrV5KQkECHDh2cDscRaZ7tPHb5cRhrQ2wbF6KwsJBbbrmFiIgIRowYwcMPP8zw4cOdDkukQVEPpIiISICbOHEiAMuXL3c2kFo4vRH8TTfdVGWVzcakVUwMzZo2ZWdODkmtWvmljobYNi5Enz592LFjh9NhiDRo6oEUERGRemflypVER0fTtWtXp0NxTJAxpMbFkZmT86O5fiIiTlECKSIiIvXKnj172Lt3L/379yc4ONjpcByVEh/P0ePHOebjlUDr0sqVKxkwYADR0dHExsZyxRVXVOxdOGvWLAYOHHjW+1NSUggLCyMyMpKYmBgGDBjAjBkzql10p76w1vLoo48SFxdHXFwcjzzyyFn/CDB//nySk5OJiIjgpptuIi8vD3DvmXn33XeTnJxMZGQkl156Ke+//35dPYZItZRAioiISL2ycuVKwsPD6dWrl9OhOC41Lg6A3IIChyM5PwUFBdx44408+OCD5OXlkZWVxZ/+9KeKrTO8tWTJEgoLC9mzZw+PPfYYf/3rX7n77rv9FPWF++c//8nixYtZv349GzZsYOnSpbz00kvVXrt582buu+8+5s6dS3Z2NuHh4UyYMAGA0tJS2rRpw+eff87Ro0eZMmUKI0aMYHcjXFRK6g8lkCIiIlJvHDx4kB07dnD55ZfTtGlTp8NxXLzLhSs0lJwGmkBmZGQA7n0eg4ODCQsL47rrrqN79+6kp6czfvx4vv76a1wuFzExMecsLzo6mmHDhvHGG28we/ZsNm3aBLh76n73u9/Rtm1bEhMTGT9+PMePHwegU6dOLF26tKKM0tJS4uPjWbt2rR+e2G327Nk8/PDDJCUl0bp1ax5++GFmzZpV7bXz5s1j6NChXHXVVbhcLqZMmcJbb71FYWEhERERTJ48mZSUFIKCgrjxxhtJTU1lzZo1fotd5FyUQIqIiAS4p59+mqefftrpMLyycuVKQkJC6Nu3r9Oh1AvGGFLi4sgtKPDLPEh/t4327dsTHBzM2LFjef/99zly5EjFuU6dOjFjxgz69+9PUVER+fn5Xpfbt29fkpKSWLFiBeDezzEjI4N169axY8cOsrKy+J//+R/AnbxW3i/xww8/JD4+3qse7vnz5xMTE1Pj64cffqj2vs2bN9OjR4+Kzz169GDz5s1eXZuWlkZISEhF8l1ZdnY2GRkZdOnS5Zyxi/iLEkgREZEAN2DAAAYMGOB0GOeUnZ3N5s2b6du3L82aNXM6nHojNT6ekyUl5OTk+Lxsf7eNqKgoVq5ciTGGe+65h4SEBIYNG0Z2dvYFl92qVSvy8vKw1vLyyy/z97//ndjYWCIjI5k0aRKvv/46AKNGjeLdd9/l2LFjgDspHDVqlFd1jBo1ivz8/Bpfbdu2rfa+oqIioqOjKz5HR0dTVFRU7R8Bzrz29PWFhYVVjpWUlHDHHXcwduxYOnbs6FX8Iv7gt208jDEzgRuBQ9barp5jk4F7gNMbGk2y1i7zVwwiIiICX331FYCjSeTGb77h1Fl6mEJiYtiUmUloaGiDSHbr0ul5kJmZmSR49ob0lbpoG506daoYvrl161ZGjx7NxIkTq/QKno+srCxiY2M5fPgwx44do3fv3hXnrLWUlZUBcPHFF9OpUyeWLFnC0KFDeffdd/n+++8vqO5zcblcFFQadlxQUIDL5ap2S5ozrz19fWRkZMXn8vJyxowZQ0hICFOnTvVf4CJe8Oc+kLOAqcCcM47/3Vr7vB/rFRERkUomTZoEOLvX36n8fHqfJfn5ZNcuMjIyGDx4MGFhYXUYWf0XEx5OWEgIu3fv9vnQ3rpuGx07dmTcuHEVC8qc7x6fq1atIisri4EDBxIfH09YWBibN2+mdevW1V5/ehhreXk5nTt35uKLL/aqnnnz5nHffffVeH7Lli3V9kJ26dKF9evXV/y81q9fX+Ow09PXnrZr1y5OnjxJ+/btAXcyfPfdd5Odnc2yZcs0N1gc57chrNbaL4A8f5UvIiIigcFay9a9e4mIiODyyy93Opx6xxhDfHQ0mZmZDW4/yK1bt/LCCy+wb98+APbu3cuCBQvo168fAImJiezbt49Tp055VV5BQQFLly7l9ttvZ/To0XTr1o2goCDuuecefvvb33Lo0CHA3Tv54YcfVtx3++2389FHHzF9+nSvh68C3HHHHRQVFdX4qmkI65133snf/vY3srKy2L9/Py+88ALjxo2rsY4lS5awYsUKiouLeeKJJ7jlllsqeiDvv/9+0tPTWbJkif64IvWCE3Mg/8sYs8EYM9MY07ymi4wx9xpjVhtjVh8+fLimy0RERKSB25WTQ25hIVdeeSUhISFOh1MvxUVGcuLECQ4ePOh0KLUSGRnJt99+y+WXX05ERAT9+vWja9euvPDCCwAMHjyYLl260KJFC+Lj4wH3wj5DhgypUs7QoUOJjIykTZs2PPXUUzz00EP861//qjj/17/+lYsvvph+/foRFRXFNddcw7Zt2yrOt2zZkv79+/PVV19x2223VSnb5XJVLMbjK/fddx9Dhw6lW7dudO3alRtuuKFKT2blOrt06cKMGTO44447uOiiiygsLGTatGmAe0/Ul156iXXr1tGiRQtcLhcul4t58+b5NF6R2vDnENbqTAemANbz3xeAX1V3obX2n8A/AS677LKG9ec2ERER8Yq1ls+2biUsJKTKHDapKi4qCoDdu3fTsmVLh6PxXuvWrVm4cGGN50NCQnjvvfeqHDs9rPY0b/Y8bNas2TlXlP3000+rPV5UVHTO8mvLGMOzzz7Ls88+61Wdo0aNqrZnNDk5ucH1Okvgq9MeSGtttrW2zFpbDrwMaI1uERGRRmzrwYPsP3qU9klJNGlS13/XbjjCQkOJi4sjMzPT6VBEpJGr03+pjTEtrbUHPB9vBjbVZf0iIiKN0T/+8Q+nQ6hWeXk5n23bRrzLRWvP8EWpWUpKChs3bqSsrIzg4GCflFlf24aI1F/+3MZjATAIiDfG7AP+BAwyxvTEPYR1N1DzslYiIiLiEz179nQ6hGqt3rOHnKIiRvTuzbHzXI2zMUlNTWXNmjUcOHCApKQkn5RZX9uGiNRfXg1hNcZ0rW3B1tqR1tqW1tqm1toka+2r1tox1tpu1tru1tphlXojRURExE8++eQTPvnkE6fDqKL45En+k5FBanw8HVu0cDqcBiElJQXAp8NY66JtpKSkEBYWhsvlIjExkbvuuqtiDmBWVhbDhw8nNjaWpKQkZsyYUeXedevW0bt3b8LDw+nduzfr1q3zeXx5eXncfPPNREREkJyczPz582u89h//+Aft2rUjKiqKVq1a8dvf/pbS0tKK83/84x/p1q0bTZo0YfLkyVXuXb58OUFBQRUL4bhcLmbPnu3z5xHxN2/nQM4wxnxnjJlgjInxa0QiIiLiU08++SRPPvmk02FU8dm2bZwqLWVIly7nvRdgYxMREUFiYqJXi8p4q67axpIlSygqKmLt2rWsWrWqos7Ro0eTmppKdnY27733HpMmTeI///kPAKdOnWL48OGMHj2aI0eOMHbsWIYPH+71lh/eeuCBBwgJCSE7O5t58+Zx//33s3nz5mqvHTp0KGvXrqWgoIBNmzaxfv16XnzxxYrzF198Mc8++yw33HBDtfe3atWqyjYgY8eO9emziNQFrxJIa+1A4A6gDbDaGDPfGHOtXyMTERGRgLQ/P5+1P/xA39RUEjx73Yl3UlJS+OGHH6r0ejUkrVu3ZsiQIWzatImioiKWL1/OH/7wB5o2bUqPHj249dZbmTlzJuDusSstLWXixImEhobym9/8xr1q72ef+Sye4uJiFi1axJQpU3C5XAwcOJBhw4Yxd+7caq9PS0sjJsbdl2KtJSgoiB07dlScHzt2LEOGDKnYw1EkEHm9Cqu1djvwOPAocDXwojFmqzHmFn8FJyIiIoHFWsuyTZuICA1l0CWXOB1Og5OamkppaSn79u1zOpTzsnfvXpYtW8all15asT1F5W0qrLVs2uReY3Hz5s107969Sg919+7da+wdnDBhAjExMdW+unfvXu09GRkZBAcH0759+4pjPXr0qLEOgPnz5xMVFUV8fDzr16+vsr/juRw6dIjExERSU1P57W9/S3Fxsdf3itQX3s6B7G6M+TuQDgwGhlprO3ne/92P8YmIiEgAWb9vH1n5+VzTsSOhTZs6HU6Dk5ycjDGmwW3ncdNNNxETE8PAgQO5+uqrmTRpEpGRkVxxxRVMmTKFEydOsHbtWhYtWsSxY8cA916J0dHRVcqJjo6msLCw2jqmTZtGfn5+ta8NGzZUe09t6wD3no0FBQVkZGQwfvx4EhMTvfoOOnbsyLp16zhw4ACfffYZa9as4aGHHvLqXpH6xNseyKnAWqCHtfYBa+1aAGvtfty9kiIiIiJndaKkhE/S00lq3pwePlpFtLFp1qwZLVu29Ok8yLqwePFi8vPz2bNnD9OmTSMsLAyAefPmkZmZSZs2bbj//vu54447KlaYdblcFBQUVCmnoKDAp8NDL6SOSy65hC5dujBhwgSv6mrRogWdO3cmKCiI1NRUnn32Wd58883zilvESd4mkNcD8621xwGMMUHGmHAAa231g8RFRESkXnjppZd46aWXnA6D5RkZFJ86xfVdu2rhnAuQmprKvn37fLKYjNNtIzk5maVLl3L48GG+/fZbcnNz6du3LwBdunRhw4YNVYa4btiwgS5dulRb1vjx46uscFr5VdM97du3p7S0lO3bt1ccW79+fY3Xn6m0tJSdO3d6+7hVGGOqPJtIQ+FtAvkJEFbpc7jnmIiIiNRzHTp0oEOHDo7GUHjsGN/t3k2vtm1pecaQQamd1NRUysvL2bt37wWX5XTbSE9Pp7CwkFOnTvHaa6/x0UcfVQzrHDRoEMHBwbz44oucPHmSqVOnAjB48OBqy5oxY0aVFU4rv2qa0xgREcEtt9zCE088QXFxMV9++SXvvPMOY8aMqfb6V155hUOHDgGwZcsW/vKXv/DTn/604nxJSQknTpygvLyc0tJSTpw4QVlZGeBeFOiHH37AWsvevXt57LHHGD58+Pl9cSIO8jaBbGatLTr9wfM+3D8hiYiIiC8tWbKEJUuWOFa/tZZNe/YQ2qQJP+3Y0bE4AkWbNm0ICgryyTxIp9vGhx9+SLt27WjevDkzZszggw8+ICEhAYCQkBAWL17MnDlziImJYebMmSxevJiQkBCfxjBt2jSOHz/ORRddxMiRI5k+fXpFD+SKFStwuVwV13755Zd069aNiIgIrr/+eq6//nqefvrpivP33HMPYWFhLFiwgKeeeoqwsLCKFV3Xrl1L//79iYiIYMCAAXTt2rXKFiAiDUUTL68rNsb0Oj330RjTGzjuv7BERETEV1544QXAvYedE7Zs2UJuQQHXd+1KuI9/+W+MQkJCSEpK8kkCWRdt42zzNSdOnMjEiRNrPH/ppZeyZs0aP0T1/8TGxrJ48eJqz1155ZUUFVX0ofCvf/3rrGXNmjWLWbNmVXvuoYce0qI5EhC8TSAnAv82xuz3fG4J3OafkERERCRQnDp1io8++oio8HB6Jyc7HU6DtTM9vcrn0LIyfti/n2+WLqVpkyaExMTQrV8/h6ITkcbEqwTSWrvKGNMR6AAYYKu1tsSvkYmIiEiDt3LlSgoKChjQuTNBWjjnvJUXF9PbM7QTIC4oiO1ZWTQ3hg4JCaw5fNjB6ESkMfG2BxKgD5DiuedSz8pRc/wSlYiIiDR4eXl5fPXVV3Tr1o3YcC2d4EtJMTE0CQoiMzeXDi1aOB2OiDQiXi2iY4yZCzwPDMSdSPYBLvNjXCIiItLAffjhhwQHB3Pttdc6HUrAaRIcTNvYWHbn5Dgdiog0Mt6uwnoZcIW1doK19kHP6zf+DExERER8Y+7cuRUrQdaV7du3k5GRwVVXXeXVpuw709NZ88EHNb4yz5gDKJASF0d2YSHFJ0+edxl10TZSUlIICwvD5XKRmJjIXXfdVbEwzcKFCxkwYADh4eEMGjToR/euW7eO3r17Ex4eTu/evVm3bp3P48vLy+Pmm28mIiKC5ORk5s+fX+O1zz33HF27diUyMpLU1FSee+65H13zv//7v6SmphIREUGnTp3IyMgA4D//+Q/dunUjJiaGuLg4br75ZrKysnz+PCL+5m0CuQnQ+AgREZEGqE2bNrRp06bO6istLeWDDz4gLi6Ofl4u7HJ6jl9Nr9LiYj9H3fCkxscDsDs397zLqKu2sWTJEoqKili7di2rVq3iySefBNwroE6cOJHHHnvsR/ecOnWK4cOHM3r0aI4cOcLYsWMZPnw4p06d8mlsDzzwACEhIWRnZzNv3jzuv//+GveNtNYyZ84cjhw5wgcffMDUqVN5/fXXK86/8sorvPrqq7z33nsUFRWxdOlS4j0/p86dO/Phhx+Sn5/P/v37ueSSS7j//vt9+iwidcHbBDIe2GKM+dAY8+7plz8DExEREd944403eOONN+qsvm+++Ya8vDyGDBlCcHBwndXb2LSKjiakSZMLSiDrum20bt2aIUOGsGnTJgCuueYaRowYQatWrX507fLlyyktLWXixImEhobym9/8Bmstn332mc/iKS4uZtGiRUyZMgWXy8XAgQMZNmxYjb2yjzzyCL169aJJkyZ06NCB4cOH8+WXXwJQXl7On//8Z/7+97/TuXNnjDGkpaURGxsLQGJiYpXnDA4OZseOHT57FpG64m0CORm4CXgaeKHSS0REROq56dOnM3369Dqpq7i4mBUrVtChQwfS0tLqpM7GKigoiOTYWDIvYB5kXbYNgL1797Js2TIuvfTSc167efNmunfvjqm0em/37t1r7B2cMGECMTEx1b66d+9e7T0ZGRkEBwfTvn37imM9evSosY7KrLWsWLGCLl26ALBv3z727dvHpk2baNOmDampqfzpT3+ivLy84p4ffviBmJgYwsLCeP7553nkkUfOWY9IfePtNh6fG2OSgUustZ8YY8IB/UlRREREqvjiiy8oKSnhmmuucTqURiE1Pp7thw5x3MfDOn3tpptuokmTJkRHR3PDDTcwadKkc95TVFREdHR0lWPR0dEUFhZWe/20adOYNm1areKqbR2VTZ48mfLycu666y7AnUACfPTRR2zcuJH8/Hyuu+46kpKSuOeeewBo27Yt+fn55OXl8fLLL9OxY8daxStSH3iVQBpj7gHuBWKBNKA1MAP4qf9CExERkbq08ZtvOJWfX+P5c21Wn5uby+rVq+nVq1fFvC/xr5S4OAByCwocjuTsFi9eXOs/KrhcLgrOeK6CggKvFmXydx1Tp05lzpw5rFixgtDQUADCwsIA9zDX0z2f9913H8uWLatIIE+LjY1l7Nix9OjRg6ysLJo0qc3OeiLO8nYI6wPAFUABgLV2O3CRv4ISERGRuncqP/+sC9mcLbkE+PTTTwkODq52NU3xjxZRUTRr2rTeJ5Dno0uXLmzYsAFrbcWxDRs2VAwZPdP48eNxuVzVvmq6p3379pSWlrJ9+/aKY+vXr6/xeoCZM2fyzDPP8Omnn5KUlFRxvEOHDoSEhFQZcns2paWlHDp06EcJrEh9520CedJaWzE2whjTBLBnuV5EREQakb1795Kens4VV1yBy+VyOpxGwxhDalwcOQ00CSkrK+PEiROUlpZSXl7OiRMnKCkpAWDQoEEEBwfz4osvcvLkSaZOnQrA4MGDqy1rxowZFBUVVfuqaU5jREQEt9xyC0888QTFxcV8+eWXvPPOO4wZM6ba6+fNm8ekSZP4+OOPadeuXZVz4eHh3HbbbTz77LMUFhayb98+Xn75ZW688UYA3nrrLbZt20Z5eTmHDx/moYce4tJLL61YZEekofA2gfzcGDMJCDPGXAv8G1jiv7BERETEV958803efPNNv5VvreXjjz/G5XLRv39/v9Uj1UuJj+f4yZMcOXKk1vf6u22cy9y5cwkLC+P+++9nxYoVhIWFVQz3DAkJYfHixcyZM4eYmBhmzpzJ4sWLCQkJ8WkM06ZN4/jx41x00UWMHDmS6dOnV/RArlixosofRB5//HFyc3Pp06dPRe/m+PHjK85PnToVl8tFq1at6N+/P6NGjeJXv/oVAFlZWfz85z8nMjKSbt26ERQUxNtvv+3TZxGpC94OuH4MuBvYCNwHLANe8VdQIiIi4ju+mo+4Mz292uMH8vLYu3cvN954o89/uZdzS/XMg8zMzKR58+a1urcu5qru3r27xnPjxo1j3LhxNZ6/9NJLWbNmje+DqiQ2NpbFixdXe+7KK6+kqKio4nNmZuZZy4qKiqqyL2RlDz74IA8++OD5BypST3i7Cms58LLnJSIiIg3IrFmzAM76i7o3youL6Z2QUPVYeTlfb9qEq1kzr7ZmEN+Ld7kIbdqU3bt306tXr1rd66u2ISKNh7ersGZSzZxHa227ai4XERGResSfScKm/fvJLS6m9yWXEBTk7cwY8SVjDHFRUWRmZmKt9XoRF1ACKSK15+0Q1ssqvW8G/BL3lh4iIiLSSJWXl/PF9u0kRkbSopZDJ8W34qOi2J+ZSU5ODgln9BKLiPiSV38qtNbmVnplWWv/AVS/BJaIiIg0Cqd7H69u375WvV7ie/FRUQDs2rXL4UhEJNB5lUAaY3pVel1mjBkP+G4XVxEREWlQyq2t6H3s2KKF0+E0euHNmtG8eXMlkCLid94OYX2h0vtSYDcwwufRiIiISIOw9cABcouLubVXL/U+1hPt2rVj48aNlJWVERwc7HQ4IhKgvF2F9Sf+DkRERET8Y9myZT4tz1rLyp07iY2IoFPLlj4tW85fWloaa9asYd++fSQnJ3t1j6/bhogEPm9XYX3obOettX/zTTgiIiLia+Hh4T4tLzM3lwNHj3Jjt24Eqfex3khNTcUYw65du7xOIH3dNkQk8Hm73vZlwP1Aa89rPNAZ9zxIzYUUERGpx6ZNm8a0adN8Vt6XO3bgCg2lR1KSz8qUC9esWTNat25dq3mQvm4bIhL4vE0g44Fe1tqHrbUPA72BJGvtn621f/ZfeCIiInKhFi5cyMKFC31S1sGjR9mVk8Plqak00Ty7eqddu3ZkZWVx4sQJr673ZdsQkcbB2wSyLXCq0udTQIrPoxEREZF67dvdu2kaHEzvtm2dDkWq0a5dO6y1ZGZmOh2KiAQob1dhnQt8Z4x5G7DAzcAcv0UlIiIi9U6ptWzMyqJnUhJhISFOhyPVSEpKIiQkhJ07d9KpUyenwxGRAOTtKqxPGWPeB670HLrLWvu9/8ISERGR+uaotZRZS9/UVKdDkRoEBweTkpKi/SBFxG+87YEECAcKrLX/MsYkGGNSrbUaHyEiItIIlJeXk28tqXFxXBT54/Xzdqann/X+zPR0eick+Cs8qaRdu3ZkZGRw5MgRmjdv7nQ4IhJgvN3G40+4V2LtAPwLaAq8Blzhv9BERETEF5YvX37BZWzNzqYUaux9LC8uPmuCuH316guOQbyTlpYGwM6dO7nsssvOeq0v2oaINC7eLqJzMzAMKAaw1u5H23eIiIg0Gt9lZtIUaJ+Y6HQocg5xcXFERUVpGKuI+IW3CeQpa63FvYAOxpgI/4UkIiIivvT888/z/PPPn/f92QUF7MnLI8YYgozxYWTiD8YY2rVrR2ZmJuXl5We99kLbhog0Pt4mkAuNMS8BMcaYe4BPgJf9F5aIiIj4ytKlS1m6dOl53/9tZiZNgoKIVvLYYKSlpXHixAkOHDhw1usutG2ISOPjVQJprX0eeBNYhHse5BPW2v/rz8BERETEecdPnWJjVhbdk5IIVgLZYKR65qru2LHD4UhEJNCcM4E0xgQbYz6x1n5srf0/1trfWWs/rovgRERExFnf791LZ9iAxQAAIABJREFUaXk5fVNSnA5FaiEiIoJWrVopgRQRnztnAmmtLfv/27vz6LjOMs/j30ertVqLZVuWZEuWHXmXbSl7YpI4CQmMIYZAaIYM6emQoYGTSQ8N0zBDL2SGpuFwuodpeiANNJDQCSEkkAWHLE5wQqIksiXbsiVL3i0vkhfJsrUv7/xRV0a2JVmWVHWrSr/POffo3lt3earqUUlPve99L9BhZtNDEI+IiIiECeccVYcOUZCZyaz0dL/Dkcu0cOFCGhsb6ejo8DsUEYkiY70GsgvYbmY/MrPvDk7BDExEREQmR1JSEklJSZe936GWFk6cPcuquXODEJUE28KFC4HRu7GONzdEZOoa030ggRe8SURERCLMhg0bxrXfloMHSYiLY2lu7iRHJKEwZ84cUlJSaGhoYMWKFcNuM97cEJGpa9QC0szmOucOOud+GqqARERExH9dvb3sOHKE0vx8EuLG+n2zhBMzY8GCBezatYuBgQFiYsba8UxEZGSX+iT59eCMmf0qyLGIiIhIEDz88MM8/PDDl7VPzZEj9A0MsFrdVyPawoUL6erqorGxcdjHx5MbIjK1XaqAHDpe9/xgBiIiIiLB8eqrr/Lqq69e1j5bDh5kVno6udM1hl4kKy4uJiYmhoaGhmEfH09uiMjUdqk+KW6EeREREYlSR0+f5ujp09y5dCmmez9GhD21tSM+lpmSwvbqatauXRvCiEQkWl2qgCw1szYCLZFJ3jzesnPOaUxvERGRKLPl4EHiYmJYnpfndygyRgPt7ZTl5Az7WFd+Pq/U1nL69Gmmq0VZRCZo1C6szrlY51y6cy7NORfnzQ8uq3gUERGJMr39/Ww/fJglubkkJST4HY5MgitmzgRGv52HiMhYaTguERGRKJednU12dvaYtt159CjdfX2692MUmZGaSlJi4rDXQV5OboiIwNjvAykiIiIR6le/GvtA6lsOHiQrJYV5WVlBjEhCycyYOX06e/fupa+vj7ght2W5nNwQEQG1QIqIiIjnbGcnB0+dYnVBgQbPiTIzMzPp7e3lwIEDfociIhFOBaSIiEiU+8pXvsJXvvKVS2538PhxYswozc8PQVQSSjPS04mLi6O+vv689WPNDRGRQerCKiIiEuXefvvtS27T399P4/HjXDFrFqnTpoUgKgml2JgY5s+fT319PXfccce5Fuax5IaIyFBqgRQRERF27dpFT18fqwsK/A5FgqSkpITW1laampr8DkVEIljQCkgz+7GZNZtZzZB1WWb2spk1eD8zg3V+ERERGbuqqiqmJSRQ7N3yQaJPSUkJZkZtba3foYhIBAtmC+RPgDsuWPdXwKvOuYXAq96yiIiI+Oj06dPs3r2bgpwcYjR4TtRKSUlh7ty51NXV+R2KiESwoBWQzrlNwKkLVn8Y+Kk3/1PgrmCdX0RERALy8/PJH2VgnKqqKgAKcnJCFZL4ZNGiRTQ3N3PqVOBftEvlhojIhUI9iM4s59xRAOfcUTMbsZ+MmT0APAAwVzczFhERGbfHHntsxMcGBgaorq5m/vz5JCcmhjAq8cOiRYv43e9+R11dHdddd92ouSEiMpywHYXVOfcI8AhAeXm58zkcERGRqLRv3z5Onz7NrbfeSndjo9/hSJDsGXLdY3pyMpVvv01iW9u5dQkZGSy/5ho/QhORCBPqUVibzCwXwPvZHOLzi4iITDkPPfQQDz300LCPVVVVkZSUxKJFi0IclYTSQHs7ZTk5lOXksDo/n5azZ7kiLY1Hf/YzHv3Zz+hpbfU7RBGJEKEuIJ8FPu3Nfxr4TYjPLyIiMuVUV1dTXV190fqOjg7q6upYsWIFcXFh2ylJJtni2bMB2NXURPWuXVTv2uVzRCISSYJ5G4/HgbeBEjNrNLM/A74J3GZmDcBt3rKIiIj4YNu2bfT397Nq1Sq/Q5EQyklLIys5mbpjx/wORUQiUNC+bnTO/ckID60N1jlFRERkbJxzVFVVkZeXx6xZs/wOR0LIzFg0ezYV+/YRFxdHX1+f3yGJSAQJdRdWERERCQOHDx+mublZrY9T1OLcXAacI1tfHojIZdIFDyIiIlHuiiuuuGhdVVUV8fHxLFu2zIeIxG95GRmkJiZSVFzMdF3/KiKXQZ8YIiIiUe6RRx45b7mnp4eamhqWLl1Kou79OCUNdmPt7uvj4T/5E7adOuV3SCISIdSFVUREZIrZsWMHPT096r46xS3JzaW3v5+Gpia/QxGRCKICUkREJMo98MADPPDAA+eWq6qqmDFjBgUFBT5GJX6bl51Nf28vP9u40e9QRCSCqAuriIhIlKuvrz83f/z4cQ4dOsRtt92GmfkYlfgtxoyjjY3kFhTQ19/vdzgiEiHUAikiIjKFVFVVERMTQ2lpqd+hSBhoPnyY2Lg4mlpb/Q5FRCKECkgREZEpor+/n61bt1JSUkJKSorf4UgYOH3qFN1dXRw9edLvUEQkQqgLq4iIyBRRV1dHR0eHBs+R8zQfOUJSUhLd3d0alVdELkkFpIiISJTYXlFBzzBdEedkZADw+40bycjIoLi4ONShSZhaWVJCbFwcA86xa9cuVqxY4XdIIhLmVECKiIhEiZ7WVspyci5a/+9f+xonzp7le6+/ztq1a4mJ0RUsEvBPX/wizjm+9fLL7NixQwWkiFyS/oKIiIhMAZUHDmBm6r4qFzEz5mRlsWfPHrq6uvwOR0TCnApIERGRKHfv3/wNbzU0kJuVpcFz5Dyf+trX+NTXvkZudjb9/f3U1dX5HZKIhDkVkCIiIlGuNy6O2Lg45s2c6XcoEmYam5pobGoiIyWF6dOns3PnTr9DEpEwpwJSREQkyuUVFtLe1kZWWprfoUiYMjOWLl3Knj176Ozs9DscEQljKiBFRESi2NHTp0nPzOSwdw2kyEiWLl3KwMCAWiFFZFQqIEVERKJY5YED9Pf10XTokN+hSJjLzc0lOzubmpoav0MRkTCm23iIiIhEqa7eXrYfPozr7OTKJUv8DkfC0LVDbtthZixfvpzXX3+dtrY20tPTfYxMRMKVCkgREZEote3wYXr7+/nzO+9kTkYGm48f9zskCTN//4UvAJzLjcECcvv27Vx//fV+hiYiYUpdWEVERKKQc47KAweYM306czIy/A5HIkRWVhZ5eXls377d71BEJEypgBQREYlCh1paOH7mDGXz5vHRL32Jj37pS36HJGFouNxYvnw5TU1NNDc3+xSViIQzFZAiIiJRqHL/fhLj4lg2Zw4nT5/m5OnTfockYWi43Fi6dClmplZIERmWroEUERGJMu3d3ew8doyyuXNJiNOferm0PbW15y3PSE9n83vvMb2nh8TMTJZfc41PkYlIuNFfFRERkShTfegQ/QMDlM+b53coEiEG2tspy8k5txzX3c2vq6uZFRdHc2urj5GJSLhRF1YREZEo4pxj88GDzMvKIictze9wJEItmj2buJgYth0+7HcoIhJm1AIpIiISRfYcP05LRwe3lJScW7f2qqt8jEjC2Ui5kRgXR8ns2ew8epSZM2eGOCoRCWcqIEVERKJI5YEDJCcksDg399y6r91/P4DuAykXGcyNJzZsuOix5Xl57DhyhOMagElEhlAXVhERkSjR2d1NfVMTqwoKiI3Rn3iZmAU5OSTFx3P45Em/QxGRMKK/LiIiIlHi4PHjOKDsgsFz7nzwQe588EF/gpKwNlpuxMbEsCQ3l6aWFnp6ekIcmYiEKxWQIiIiUaC/v5+Dzc0syMkhMzn5vMc6u7ro7OryKTIJZ5fKjeV5efQPDFBXVxfCqEQknKmAFBERiQL19fV09/ZSXljodygSReZmZZGUkEBNTY3foYhImNAgOiIiIlGgsrKSaQkJLNSImTKJzIxkYHdDA2899xyJ8fEXbZOQkcHya64JfXAi4gsVkCIiIhHu5MmT7N27l5L8fGLM/A5HokxaXx8ngbieHsrmzLnocY3uKzK1qIAUERGJcJs3byYmJoaCnJxhH/8PN94Y4ogkUowlNxLNmJWWxrbGRq5SF2mRKU8FpIiISATr6+ujurqaRYsWMS0hYdht/vLeewG1FMnFBnNjuPtADrUiP5+Xa2s5cfYsM1JTQxGaiIQpFZAiIiIRbMeOHXR2dlJWVkZLff2o2+6prR318X21tZSN0IopU9vyvDxeqa1la2Mjaxct8jscEfGRCkgREZEItnnzZrKzsykqKhqxgLzpgQcA+Oz69aMWiA2VlUGJUcLX0NwYTdq0aRTn5LCtsZFbSkowXWsrMmXpNh4iIiIRqqmpiUOHDlFWVqZ/6CXoSgsKaOvqYt/Jk36HIiI+UgEpIiISoSorK4mLi2PlypV+hyJTQMmsWSTGxbGtsdHvUETERyogRUREIlB3dzfbtm1j6dKlJCUl+R2OTAHxsbEsnTOHnUeP0tPX53c4IuITFZAiIiIRaPv27fT09FBeXu53KDKFlObn09vfz86jR/0ORUR8okF0REREIoxzjsrKSmbPnk1eXt4lt//4bbeFICqJRJebGwWZmWQlJ7OtsZGVBQVBikpEwplaIEVERCJMY2MjTU1NYx4853Mf+xif+9jHQhCZRJrLzQ0zY0V+PvtOnuR0Z2cQIxORcKUCUkREJMJs3ryZhIQEli9fPqbtO7q66OjqCnJUEonGkxul+fkAbNVgOiJTkgpIERGRCNLR0UFNTQ0rVqwgMTFxTPt84MEH+cCDDwY5MolE48mNjORk5mVlsa2xEedckCITkXClAlJERCSCbN26lf7+fg2eI74qLSjgZHs7h1tb/Q5FREJMBaSIiEiEGBw8p6CggFmzZvkdjkxhS2bPJi4mhmp1YxWZclRAioiIRIh9+/Zx6tQptT6K7xLj41mcm8uOI0foHxjwOxwRCSEVkCIiIhGisrKSpKQklixZ4ncoIpTm59PV20tTS4vfoYhICOk+kCIiIhHgzJkz1NXVUTR7NltfeWXYbfbV1lKWk3PR+vvWrQt2eBKhJpIbRTNmkDZtGo0nTkxiRCIS7lRAioiIRIAtW7bgnOMDJSVkp6YOu01DZeWw6weLhCc2bAhafBKZJpIbMWasyMvjrT17OHPmDGlpaZMdnoiEIXVhFRERCXMDAwNs2bKFGenpIxaPoznR2soJjZYpw5hobqwqKMAB1dXVkxeUiIQ1FZAiIiJhrqGhgba2NuaNc+TVu7/8Ze7+8pcnOSqJBhPNjezUVLLT08+1kItI9FMBKSIiEuYqKytJS0tjVmam36GIXGTuzJm0trayd+9ev0MRkRBQASkiIhLGWlpa2L17N6tXrybGzO9wRC4yOzOTpKQktmzZ4ncoIhICKiBFRETCWGVlJWbG6tWr/Q5FZFixMTGUlpZSV1fH2bNn/Q5HRIJMBaSIiEiY6u3tpaqqisWLF5Oenu53OCIjKisrY2BggK1bt/odiogEmW7jISIiEqZqamro7OzkyiuvnNBx/vzuuwFw/f2TEZZEkcnKjRkzZjBv3jy2bNnCddddh6m7tUjU8qWANLP9wBmgH+hzzpX7EYeIiEg42V5RQY93SwXnHG/W1JCWlMSJ2lpO1tWxr7aWspycyz7uPbffDug+kHKxycyN1atX88wzz7B//36KioomfDwRCU9+dmG92Tm3UsWjiIhIQE9rK2U5OZTl5DA7Pp7THR3cWFxM+cyZlOXk0NfePq7jHjp2jEPHjk1ytBINJjM3Fi9ezLRp0zSYjkiUUxdWERGRMPTu/v0kxsVRmp8/4WPd+9d/DcBn16+f8LEkukxmbsTHx1NaWkplZSXt7e2kpKRM+JgiEn78aoF0wEtmttnMHhhuAzN7wMwqzazy+PHjIQ5PRETEP2e7u9lx5Ail+fkkxOm7XokcZWVl9Pf3U1VV5XcoIhIkfhWQ1zvnVgN3Ap83szUXbuCce8Q5V+6cK88Zx/UeIiIikWrLwYMMOMeVhYV+hyJyWXJycigqKuK9995jYGDA73BEJAh8KSCdc0e8n83AM8BVfsQhIiISbgYGBth84ADzZ8xgRmqq3+GIXLarrrqKtrY2du3a5XcoIhIEIS8gzSzFzNIG54HbgZpQxyEiIhKOdjU10dbVpdZHiVhXXHEF06dP59133/U7FBEJAj8urJgFPOPdHygO+Hfn3Is+xCEiIhJ2KvbtIyMpiStmzZq0Y37xU58CoH2co7hK9ApGbsTExHDllVfyyiuv0NTUxKxJzGUR8V/IWyCdc3udc6XetNQ5979DHYOIiEg4ajl7loOnTnF1URExk3gj9nVr1rBuzUXDDYgELTdWr15NfHw8FRUVk35sEfGXhnYTEREJE3uPHiUxLo5Vc+dO6nF37d8/qceT6DEZubGntnbY9XlZWWzdupXc6dO56qabJnweEQkPKiBFRETCQEtLC0dPneK64mISJ/nWHf/lG98AdB9Iudhk5MZAeztlw4yYPz85mf/b1ER9fb0KSJEo4tdtPERERGSId955BzPjag2eI1EiMyWFxbm5HGhupru72+9wRGSSqIAUERHxWVdXF1VVVczJyiI9KcnvcEQmzXXFxfT197N582a/QxGRSaICUkRExGebN2+mp6eH+bm5fociMqnyMjLITk/n7bffpre31+9wRGQSqIAUERHxUX9/P++88w5FRUVMT0nxOxyRSbcwL4+zZ89SVVXldygiMgk0iI6IiIiPampqOHPmDOvWraNtz56gnON//tmfAXDi1KmgHF8iVyhyIzstjblz5/Lmm2+yevVq4iZ5kCgRCS21QIqIiPjEOcdbb71FTk4OCxYsCNp5br36am69+uqgHV8iVyhyw8xYs2YNZ86cobq6OqjnEpHg01dAIiIiPtm1axfNzc3cddddmFnQzlO9a1fQji2RLVS5MX/+fAoKCti0aROlpaXEx8eH5LwiMvnUAikiIuID5xybNm0iMzOT5cuXB/VcD33nOzz0ne8E9RwSmUKVG2bG2rVrOXPmDO+++27QzyciwaMCUkRExAe7d+/m6NGj3HDDDcTE6M+xRL958+axYMEC3nzzTbq6uvwOR0TGSX+xREREQmyw9XH69OmUlpb6HY5IyKxdu5auri7efPNNv0MRkXFSASkiIhJiDQ0NNDY2csMNNxAbG+t3OCIhM3v2bJYvX05FRQUtLS1+hyMi46BBdERERELIOcdrr71GZmYmq1at8jsckZC79dZbqaur46WXXuKee+5he0UFPa2tI26fkJHB8muuCWGEIjIaFZAiIiIhtHPnTo4dO8b69etD1vr4jc9/HoCDR46E5HwSOfzIjfT0dG688UY2btzI3r176WltpSwnZ8TtNx8/HrLYROTS1IVVREQkRAYGBnjttdfIyclh2bJlITvvdaWlXKdrLWUYfuXGtddeS2ZmJhs2bKB/YCDk5xeR8VMBKSIiEiKbN2/m5MmT3HLLLSEdefWtrVt5a+vWkJ1PIodfuREXF8edd97JiRMn2KOWcZGIoi6sIiIiIdDV1cXrr79OYWEhJSUlIT33V7/3PQA+u359SM8r4c/P3Fi4cCHLly+npqaG4wsWkJOWFvIYROTyqQVSREQkBN544w06Ojq4/fbbMTO/wxEJC+9///uJi43l2a1bGXDO73BEZAxUQIqIiATZqVOneOeddygtLSU3N9fvcETCRkpKCkvnzaOxtZU3d+/2OxwRGQMVkCIiIkHknOO3v/0tsbGxrF271u9wRMJOXnY2S+fM4ff19Rwe5XYeIhIeVECKiIgEUW1tLXv27OHmm28mTdd4iVzEzPjgsmWkJibydFUV3X19fockIqPQIDoiIiJB0tPTw+9+9ztmzZrFVVdd5Vsc//TFLwJQt3evbzFIeAqX3EhKSGD9ypX8rKKC57Zt46OrVulaYZEwpRZIERGRIHnllVdoa2vjgx/8YEhv23GhlSUlrAzxyK8SGcIpNwpnzOCWRYvYceQI7+zb53c4IjICtUCKiIgEwf79+3nvvfe4+uqrKSgo8DWWV955x9fzS/gKt9y4vriYxpYWXq6tZfb06RRmZ/sdkohcQC2QIiIik6ynp4dnn32WzMzMsBg453/96Ef8rx/9yO8wJAyFW26YGXetXElWSgpPVlZyqr3d75BE5AJqgRQREZkk2ysq6GltZdvevbS0tHDt4sVse/XVc48fPHSIuaO0Ru6rraUsJycUoYqErWnx8fzJlVfywzff5N/ffZeyRYv8DklEhlABKSIiMkl6WltJ6u3l4PHjXF9czK3Fxec93lBZSdnq1SPu31BZGewQRSJCVkoK95SX8+g77/Derl2U3X47CQkJfoclIqgLq4iIyKTp7O7mue3bycvI4OYwGZhEJFLNy87mo6tW0Xr2LE888QR9ur2HSFhQASkiIjIJ+vr62NzQwIBzfGTVKmJ9HHVVJFoszs2ldP589u3bx1NPPUV/f7/fIYlMeerCKiIiMgk2bNhAa3s7Hy8rIyslxe9wzvODr34VgKraWp8jkXATCbmRn5NDbkkJGzZs4De/+Q3r16/XPSJFfKQCUkREZIK2bNnCli1bKM7NZXFurt/hXKSksBAI7yJB/BEpuXHVVVfR3d3Nxo0biY2NZd26db7eW1VkKlMBKSIiMgH79u3jhRdeoLi4mEVhes+65zZt8jsECVORlBs33HADfX19bNq0iZ6eHj7ykY8QGxvrd1giU46+uhERERmnEydO8OSTT5Kdnc3dd98dtt3qvvPYY3znscf8DkPCUCTlhplx8803c/vtt7Nz504ef/xxenp6/A5LZMpRASkiIjIObW1t/PznPyc2NpZPfvKTTJs2ze+QRKaEa6+9lnXr1rF3714ee+wxurq6/A5JZEpRF1YREZEx2l5RQU9rKz29vbxVW0tXdzfXLFnCnooKAPbV1lKWk+NzlCLRZc8I12euKi6mas8evv+97/Gn99/P9OnTQxyZyNSkAlJERGSMelpbWZqRwaMVFXR2d/Opq66icMaMc483VFb6GJ1IdBpobx/2i5mynByWZGfzRGUl//qv/8onPvEJ8vPzfYhQZGpRF1YREZEx6u3r49GKCo61tfGxsrLzikcRCb3inByuX7KEhIQEfvKTn7B9+3a/QxKJemqBFBERGYOOjg4q6uo409HBx8vLKZk1y++QxuzRr38dgD9UVfkciYSbaMiNtORk7r//fp588kmefvppTpw4wU033RS2g1qJRDoVkCIiIpdw+vRpHn30Uc50dHBPeTlXRFDxCFAwe7bfIUiYipbcSE5O5t577+X5559n06ZNNDY2sn79elJTU/0OTSTqqIAUEREZxbFjx3j88cfp7u7m6kWLIq54BPjFSy/5HYKEqVDkxkiD4AyarMGnYmNj+dCHPkR+fj4vvvgiP/jBD/jIRz5CUVHRhI8tIn+kAlJERGQEdXV1PP300yQlJXHfffdxuLra75DG5f899RQAn12/3udIJNyEIjdGGgRn0GQOPmVmlJWVkZ+fz1NPPcWjjz7KmjVrWLNmDTExGvpDZDLoN0lEROQCAwMDbNy4kV/84hfMnDmT+++/n9lR0tVPZCqYNWsWn/nMZ1ixYgW///3v+fGPf0xzc7PfYYlEBbVAioiIDNHW1sYzzzzD/v37WblyJR/4wAeIj4/3OywRuUwJCQncddddLFiwgA0bNvCDH/yANWvWcMMNNxAbG+t3eCIRSwWkiIiEje0VFfS0to74eEJGBsuvuSYo53bO8cLTT7O1thbnHKXz55OfmMi2V189t81kXaslIpPnUtdYJmRk8LnPfY4XX3yR119/ndraWtatW0deXl6IIhSJLiogRUQkbPS0to5aoG0+fjwo521ububFF19k3759zM3K4sOlpWSlpFy03WReqyUik+NS11huPn6clJQUPvrRj7J06VJeeOEFfvjDH7JixQrWrl1Lenp6CKMViXwqIEVEZMpqbW3ljTfeoKqqisTERJbNm8dHli2LuvvHPfWtbwHwyttv+xyJhJuplhuLFi2iqKiIN954g4qKCmpra7nhhhu49tpr1VVdZIxUQIqIyJTinOPQoUNs3ryZmpoazIzy8nJuuukmajdtirriEWBGRobfIUiYmoq5kZiYyK233srq1at5+eWXee2119i8eTNr1qxh5cqVuj5S5BJUQIqISMhc6hrHYF1j2N/fz+HDh6mvr6euro6TJ0+SmJhIeXk5119/fdR3YfvJc88BMC1Of/blfFMhN0a7RnLB9On0ZGdzqrub559/no0vv8zCvDzyZswgxvsy6eChQ8wtKBjxGMG8NlskHEXvp4WIiISdS13jeDnXGDrn6Onpobu7+9w0dLmzs5OTJ0/S3NzM0aNH6evrIyYmhsLCQq677jqWLVtGQkLCZDytsDdYJOg+kHKhqZAbY7kP5YN33EFDczOv7drF1r17aWxq4rriYlbk5dFQWUnZ6tUj7h+sa7NFwpUKSBERCRsDznHs9GlOnD3Lme5uznZ1cba7m/aeHjp7emjr7ub3O3eeKxYvZdq0aeTk5FBeXs7cuXMpLCwkKSkpBM9ERCKJmXHFrFksnDmTumPH2NTQwHPbtvHarl1MGxigq7eXabpGUgRQASkiIj7pHxjgyOnTHDh5ksOtrRw/c4aTAwM0vPHGuW1iY2JITUwkNTGR5IQEXGwss+fNIzExkYSEBBITE8+bLlyXlJQUldc0ikhwmBmLc3NZNHs2+06c4A979rD3xAn+8dVXKZ87l6uLikjXl1AyxamAFBGRkHDO0dbRwaaGBvadOEFjSwt9AwMAZKWkMCstDTo6uHnVKnJSU0lPSiIxLu68AnDz8eOU3XGHX09BRKYIM2N+Tg7zc3L4yW9/S9rMmby9dy8V+/axdM4criwsJD8jQ19QyZSkAlJERIKmr6+PAwcOsGvXLurr6zl9+jQAs9PTKZs3j3lZWczNyiIlMRGAJzZsYOmcOSMe71I3DNdgFyIy2aaZ8dHVq7ll0SIq9u6lurGR7YcPMzs9nSujNGf1AAARw0lEQVQLC+mfItdSiwxSASkiIpOqo6OD+vp66uvr2bNnDz09PcTFxVFcXMy8rCxuKy4mddq0cR17LINhaLCLi/32u98F4NnXXvM5Egk3yo2xy0xO5s5ly7hl0SK2NTby3oEDPLdtG3ExMRzr76e0tJS5c+eqVVKingpIERGZEOcczc3N1NfX09DQwKFDhwBIS0tj+fLlXHHFFRQVFREfH8/mF18cd/Eo45es11xGoNy4fIlxcVxZWEj5vHkcPHWKVxoaqKmpoaqqiszMTJYvX87ixYuZNWuWikmJSiogRUTksvX29rJ///5zReNg19Q5c+bwvve9j5KSEmbPnq1/nsLEv/zylwBkpab6HImEG+XG+JkZ87KzWTkwwPJbbqG2tpatW7eyadMmNm3aREZGBosWLaKkpISCggJiY2P9DllkUqiAFBGR82yvqKCntfW8df0DA7SePcvJtjZOdXTQ0tZGf38/8fHxFBcXs2bNGhYuXEhaWhrbKyo4snUrR7ZuvejY+2prR+2CGmyXuobS7/iC5cmXXwai+15/Mj7KjcmRkJBAaWkppaWlnD17lvr6eurq6njvvfeoqKggPj6egoICCgsLKSwsJDc3l7i4wL/hw33mnndsXbstYUYFpIiInKe7pYXC5GSOtLZy2JuOtbXR742YOj0lhauvvpqioiIKCwvP/RM0qKe1dcQirKGyMujxj2Ys11CKiExEamoqq1evZvXq1XR3d7N3717279/P/v372bhxIwAxMTHk5OSQm5tLb0sL5bm5ZKemkpqYeFHPjal67baEL18KSDO7A/g/QCzwQ+fcN/2IQ0RkqnLO0dnZSUtLC62trbS0tHD8+HGam5tpbmpiwDkA4mNjmTN9OlcXFlKQlcW8rCx2nj5N2W23+fwMRETCX2JiIosXL2bx4sUAtLe3c/DgQY4cOcKxY8doaGigvb2dHQcOAJAQG0t2aiqZycmkT5tGelISJ3p6mHnoEOnp6aSlpRETE+PnUxIJfQFpZrHA94DbgEbgPTN71jm3M9SxiIiEM+fcuWlgYGDEnwMDA/T29p6benp6zv3s7Oyko6OD9vZ2Ojo6zs2fPXuWnp6e886Xnp7OzJkzSQaWzZrFnOnTyUlN1T8rIiKTJCUl5byC0jnHH557jjkJCZxsb+fE2bOcam/nWFsb9U1N5+6Vu2X37nPHSEpKIikpieTkZJKTk8/NJyYmkpCQQHx8/Hk/B+fj4+OJjY0lJiYGMyMmJmbYSdeuy6X40QJ5FbDbObcXwMyeAD4MqIAUkSnNOcc3vvGNc8Wh81oBJyomJubcPxopKSnk5uaSmppKRkYGGRkZZGZmkpGRQaJ3L8bNL77Iqii8DlBEJNyYGUkJCczPyWH+BZ+7zjm6enupOHqU/OXLaWtro62tjY6ODjo7O+ns7KStrY1jx47R2dlJb2/vpMU1+MXhYDFpZnz1q19VcSkA2GT9gzLmE5rdDdzhnLvfW74XuNo594ULtnsAeMBbLAF2hTTQsZsBnPA7CAkLygUZpFyQQcoFGaRckEHKBRkUzrkwzzk37LfJfrRADvfVxUVVrHPuEeCR4IczMWZW6Zwr9zsO8Z9yQQYpF2SQckEGKRdkkHJBBkVqLvhxYUsjUDBkOR844kMcIiIiIiIichn8KCDfAxaaWZGZJQCfAJ71IQ4RERERERG5DCHvwuqc6zOzLwC/I3Abjx8753aEOo5JFPbdbCVklAsySLkgg5QLMki5IIOUCzIoInMh5IPoiIiIiIiISGTSzb1ERERERERkTFRAioiIiIiIyJiogByFmd1hZrvMbLeZ/dUwj68xsy1m1ufd33LoY582swZv+nToopZgmGAu9JtZtTdpwKgIN4Zc+G9mttPMtpnZq2Y2b8hj+lyIEhPMA30mRJEx5MJnzWy7936/aWZLhjz2FW+/XWb2/tBGLpNtvLlgZoVm1jnkc+H7oY9eJtOlcmHIdnebmTOz8iHrwv9zwTmnaZiJwAA/e4D5QAKwFVhywTaFwArgZ8DdQ9ZnAXu9n5nefKbfz0lT6HPBe+ys389BU0hz4WYg2Zv/c+AX3rw+F6JkmkgeeMv6TIiSaYy5kD5k/kPAi978Em/7RKDIO06s389Jky+5UAjU+P0cNIUuF7zt0oBNQAVQ7q2LiM8FtUCO7Cpgt3Nur3OuB3gC+PDQDZxz+51z24CBC/Z9P/Cyc+6Uc64FeBm4IxRBS1BMJBckuowlF15zznV4ixUE7nUL+lyIJhPJA4kuY8mFtiGLKcDg6IUfBp5wznU75/YBu73jSWSaSC5IdLlkLngeBr4FdA1ZFxGfCyogR5YHHBqy3OitC/a+En4m+n5OM7NKM6sws7smNzQJscvNhT8DNoxzXwlfE8kD0GdCNBlTLpjZ581sD4F/Fh+8nH0lYkwkFwCKzKzKzH5vZjcGN1QJskvmgpmtAgqcc89f7r7hIOT3gYwgNsy6sX5TNJF9JfxM9P2c65w7YmbzgY1mtt05t2eSYpPQGnMumNmngHLgfZe7r4S9ieQB6DMhmowpF5xz3wO+Z2afBP4n8Omx7isRYyK5cJTA58JJMysDfm1mSy9osZTIMWoumFkM8I/AfZe7b7hQC+TIGoGCIcv5wJEQ7CvhZ0Lvp3PuiPdzL/A6sGoyg5OQGlMumNmtwP8APuSc676cfSUiTCQP9JkQXS739/oJYLDVWZ8J0WXcueB1VzzpzW8mcN3bFUGKU4LvUrmQBiwDXjez/cA1wLPeQDoR8bmgAnJk7wELzazIzBKATwBjHS3vd8DtZpZpZpnA7d46iUzjzgUvBxK9+RnA9cDOoEUqwXbJXPC6pfyAQNHQPOQhfS5Ej3HngT4Tos5YcmHhkMUPAg3e/LPAJ8ws0cyKgIXAuyGIWYJj3LlgZjlmFuvNzyeQC3tDErUEw6i54Jw77Zyb4ZwrdM4VErhO/kPOuUoi5HNBXVhH4JzrM7MvEPgHLxb4sXNuh5l9Hah0zj1rZlcCzxAYUXGdmf2dc26pc+6UmT1MIIEAvu6cO+XLE5EJm0guAIuBH5jZAIEvbL7pnNM/ixFqLLkAfBtIBX5pZgAHnXMf0udC9JhIHqDPhKgyxlz4gtca3Qu0EOiyiLfdkwS+QOgDPu+c6/fliciETSQXgDXA182sD+gHPqu/D5FrjLkw0r4R8blgzoVdt1oREREREREJQ+rCKiIiIiIiImOiAlJERERERETGRAWkiIiIiIiIjIkKSBERERERERkTFZAiIiIiIiIyJiogRUR8Zmb9ZlZtZlvNbIuZXTfJx//qZB7vgmPfZ2bHvfjrzOwvJnCsm8zseW/+Q2b2V+M4xkoz+8CQ5XEdZ6LM7EYz2+G9LkkXPDbbzJ4wsz1mttPMfmtm47ppuJk9aGa1ZvZz775hr3jnvMfMfmhmS0bZd9yvjZllmNnnJhLvkHUpZnbSzKZfsO2vzezjl3HsOWb21CW2KTSzTw5ZLjez717OcxARmep0Gw8REZ+Z2VnnXKo3/37gq8659wXj+BesNwJ/BwYmcOz7gHLn3BfMLBvYBaxyzh0ax7FuAv7SOfcfJiOe8R5jMpjZ94F3nHP/dsF6A94Cfuqc+763biWQ5px7YxznqQPudM7tM7NrgH+YzNwZ5byFwPPOuWWXud+5eC9Y/zjwonPup97ydGAPMNc51zGG48Y55/rGsN1NTDDHRESmOrVAioiEl3QCN5jGAr5tZjVmtt3M7rnE+lwz2+S1QNV4rWDfBJK8dT/3WmBqzexfgC1AgZn9PzOr9FrM/m4wEDPbb2b/YGbvetOC0QJ3zp0EdgO53v45ZvYrM3vPm6731l9lZm+ZWZX3s+TCY3ktm//szVcPmTrN7H3DHcPMEoCvA/cMaYUbepx5ZvaqmW3zfs711v/EzL7rHWevmd090us5TJxrvRi2m9mPvVbA+4GPA389tKXNczPQO1g8eq9btXPujZHeV+88X/Jew22D75FXpM4HnjWz/w48Bqz04i02s9fNrNzb9g4LtG5vNbNXh3mNR3qv/tZ7Xq97r82DXkjfBIq9c317mNflv3nPo8bMHhom3gtbqh8HPjFkeT2BgrJjpHzx4v+lmT0HvOTldo33WKGZveE956Gt+t8EbvTi/gs7v9U7ywKtntvMrMLMVlziNRARmZqcc5o0adKkyccJ6AeqgTrgNFDmrf8o8DIQC8wCDhIozkZa/0Xgf3j7xhJo1QI4O+RchcAAcM2QdVlD9nkdWOEt7x9yvP9EoMXpwtjvA/7Zm5/rPY9p3vK/AzcMeazWm08H4rz5W4FfefM3DZ5j6HGHnGsd8AYQP8oxztvvgvieAz7tzf9n4Nfe/E+AXxL4UnUJsNtbP+zrOeTY04BDwBXe8s+Ah4Yc8+5hXq8HgX8cIQ9Gel9vBx4BzIvxeWDNkPdoxoWvn7f8OlAO5HhxFl3wfg99bUZ6r/6WQItpIjADOOm9/oVAzQjPowzYDqQAqcAOAq3S58V7wT4JQDOQ7S2/CHzwEvlyH9A45PmciwlI5o95uBCoHOE1OrcM/F/gb7z5W4Dq0V4Dvz83NGnSpMmvKQ4REfFbp3NuJYCZXQv8zMyWATcAjzvn+oEmM/s9cOUo698Dfmxm8QSKo+oRznfAOVcxZPnjZvYAEEegYFkCbPMee3zIz38c4Xj3mNnNQAnwGedcl7f+VmCJmQ1ul25macB04KdmthBwBAqSUXnbfhu4xTnXa2azL/cYwLXAR7z5R4FvDXns1y7QlXenmc3y1l3q9SwB9jnn6r3lnwKfB/5pDLEMZ6T3dQ2BIrLK2y6VQFG0aYzHvQbY5Lxuo865U8NsM9J7BfCCc64b6DazZgLF7aWexzPOuXYAM3sauHFI/BdxzvWY2bPA3Wb2K2Al8JL38Gj58vIIzyce+GcLdA/uB8ZyjekNBIp4nHMbzSzb/nhd5nCvQeMYjikiEnXUhVVEJIw4594m0MqRQ6DFaTjDrnfObSJQbBwGHjWz/zTC/u3nDmRWBPwlsNY5twJ4gUDL2rnDjjA/1C+cc0sJFAnf8Yo7CPyNudY5t9Kb8pxzZ4CHgddc4Pq5dRec7yJmlgI8SaA4PeKtvqxjjGDo8+keekoY0+s50vszmh0EWuiGM9r7/fdDXscFzrkfXcY5jZHfu0EjvVdw/mvTD5f88nk8rwv8sRvr3cBvnHO93vrR3ut2hvcXQBNQSqAVNmEM5x8u7sHX7XJfAxGRqKUCUkQkjJjZIgJdGE8SaGG6x8xizSyHQDHz7kjrzWwe0Oyc+1fgR8Bq77C9XivacNIJ/BN+2mt5u/OCx+8Z8vPt0WL3it9Hgf/qrXoJODeYjdcaBIEWpcPe/H2jHdPzb8C/ufMHmRnpGGeANIb3Fn+8zu4/Am+OdtJRXs9BdUCh/fHa0HuB3492TGAjkGhmnxlynivN7H2M/H7/DvjPZjY40FKemc28xHmGeht4n/dlAWaWNcw2I71XIxntdd4E3GVmyV7xv55A1+NLeY1Ay+rn+WPLN1x+vgzuc9RrVb6XwO/UWOL+j3BusJ0Tzrm2MZ5PRGTKUAEpIuK/wUFuqoFfELhOrx94hkBX0q0ECo8vO+eOjbL+JqDazKoIdMX7P97xHwG22cUDuuCc20qga+EO4MfAHy7YJNHM3iFQFI7lFh3/APyp1/3xQaDcG5RkJ/BZb5tvAX9vZn/gj//YD8sr4u4mUEANDqRTPsoxXiPQFbPahgxC43nQi20bgaLivzK6mxj+9QTA66r7p8AvzWw7gWtLv3/hQS7YxxEoqG6zwG08dhC4xu4II7yvzrmXCFyj+LZ3nqcYuQga7pzHgQeAp81sK4Ecu9BI79VIxzwJ/MEbJOfbFzy2hcA1oO8C7wA/dM6N2H11yH4DwK+AbM7vnjvmfBniX4BPm1kFge6rgy2V24A+CwwmdGE+/y3ea0BgsJ1Pj/FcIiJTim7jISIiwzKz/QRuiXHC71hEREQkPKgFUkRERERERMZELZAiIiIiIiIyJmqBFBERERERkTFRASkiIiIiIiJjogJSRERERERExkQFpIiIiIiIiIyJCkgREREREREZk/8PNBxZpVDyHWwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "L = 1000                               # set the number of bootstrap realizations   \n",
    "cv_real = []                      # declare an empty list to store the bootstrap realizations of the statistic \n",
    "\n",
    "for k in range(0,L):                   # loop over the L bootstrap realizations\n",
    "    samples = random.choices(df['Porosity'].values, k=len(df)) # n Monte Carlo simulations\n",
    "    cv_real.append(np.std(samples)/np.average(samples)) # calculate the statistic of interest from the new bootstrap dataset\n",
    "\n",
    "cv = np.std(df['Porosity'])/np.average(df['Porosity'])\n",
    "\n",
    "plt.subplot(111)\n",
    "plt.hist(cv_real,color = 'red',alpha = 0.2,edgecolor = 'black',bins=np.linspace(0.1,0.4,100),label = 'bootstrap',density = True) # plot the distribution, could also calculate any summary statistics\n",
    "plt.axvline(x=cv,c='black')\n",
    "plt.axvline(x=np.percentile(cv_real,10),linestyle=\"--\",c='black')\n",
    "plt.axvline(x=np.percentile(cv_real,90),linestyle=\"--\",c='black')\n",
    "sns.kdeplot(x=cv_real,color = 'grey',alpha = 0.1,levels = 1,bw_adjust = 1)\n",
    "plt.text(np.percentile(cv_real,90)+0.009, 16, r'Average = ' + str(round(np.average(cv_real),3)), fontsize=12)\n",
    "plt.text(np.percentile(cv_real,90)+0.009, 15, r'St.Dev. = ' + str(round(np.std(cv_real),3)), fontsize=12)\n",
    "plt.text(np.percentile(cv_real,90)+0.009, 14, r'P90 = ' + str(round(np.percentile(cv_real,90),3)), fontsize=12)\n",
    "plt.text(np.percentile(cv_real,90)+0.009, 13, r'P10 = ' + str(round(np.percentile(cv_real,10),3)), fontsize=12)\n",
    "plt.xlabel('Boostrap Realizations of Coefficient of Variation'); plt.ylabel('Frequency'); plt.title('Distribution of Coefficient of Variation')\n",
    "# plt.legend()\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.2, wspace=0.2, hspace=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Bootstrap of the Correlation Coefficient\n",
    "\n",
    "Here's a statistic that requires us to work with multiple, paired features at once. \n",
    "* this reinforces that we boostrap for a new realization of the dataset, a set of samples with all their features.\n",
    "\n",
    "For the correlation coefficient we will:\n",
    "    \n",
    "* calculate a bootstrap realization of the dataset with $n$ samples with replacement as a new DataFrame with all features\n",
    "* calculate the the correlation coefficient between 2 paired features\n",
    "\n",
    "Repeat this $L$ times and then evaluate the resulting distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Yu/322yVJ999/f6j6X//hD+rYtKlGjhoVZVtpiQAJAAAAINbeeuutpOqXFBVpbVYWATICnMIKAAAAAAiFAAkAAAAACIUACQAAAAAIhWsgAQAAAMRaly5dkqrvkJOjttnZEXWT3giQAAAAAGLtySefTKr+nttuYx7IiHAKKwAAAAAgFEYgAQAAAMTa2LFjJUkPPfRQqPpxv/2t2jdtqmuuvTbKttISARIAAABArC1atCip+hVr1mhjVpauiaifdMYprAAAAACAUAiQAAAAAIBQCJAAAAAAgFC4BhIAAABArJ144olJ1Xc//njlNGkSUTfpjQAJAAAAINbGjx+fVP2P/uM/mAcyIpzCCgAAAAAIhRFIAAAAALE2ZswYSeFHIu/7n/9RTpMmuiFYD3WHAAkAAAAg1lauXJlU/QcffqjtWVkRdZPeOIUVAAAAABAKARIAAAAAEAoBEgAAAAAQCtdAAgAAAIi1goKCpOrzTjhB7Zs2jaib9EaABAAAABBrDz30UFL1t3z728wDGRFOYQUAAAAAhEKABAAAABBrV199ta6++urQ9Xf9/Oe6+q67IuwofXEKKwAAAIBY27BhQ1L1m4uLtZt5ICPBCCQAAAAAIBQCJAAAAAAgFAIkAAAAACAUroEEAAAAEGtnnnlmUvUn9+mjjswDGQkCJAAAAIBYu//++5Oq/+43vsE8kBHhFFYAAAAAQCgESAAAAACxNmLECI0YMSJ0/ffvvVcjvv/9CDtKX5zCCgAAACDWtm3bllT9jp07VcE8kJFgBBIAAAAAEAoBEgAAAAAQCgESAAAAABAK10ACAAAAiLXzzz8/qfpBBQXq3KxZRN2kNwIkAAAAgFi76667kqr/5r/9G/NARoRTWAEAAAAAoRAgAQAAAMTasGHDNGzYsND1N991l4bdfHOEHaWvyAOkmWWa2TtmNj14/jkzm2tmq8xsspk1iroHAAAAAA3Xnj17tGfPntD1ZXv3ak9ZWYQdpa/6GIH8D0lFlZ7/TNKv3L23pI8lXV8PPQAAAAAAjlKkAdLMukj6sqTHg+cm6YuSpgQlT0i6PMoeAAAAAAB1I+oRyIck3SapInjeTlKJu+8Pnm+QdHx1K5rZGDObb2bzt3L3JAAAAABIucim8TCziyVtcfcFZjbk4OJqSr269d19vKTxkjRw4MBqawAAAAAc+y6++OKk6j8/aJC6NG8eUTfpLcp5IM+WdKmZDZeULamlEiOSrc3suGAUsoukjRH2AAAAAKCBu/XWW5Oqv2bkSOaBjEhkp7C6++3u3sXde0i6StK/3P3rkl6RNDIou07Sc1H1AAAAAACoO6mYB/IHkr5nZquVuCZyQgp6AAAAANBADBkyREOGDAldP+a22zRkzJjoGkpjUZ7C+il3nyVpVvB4jaRB9bFfAAAAAEDdScUIJAAAAACgASJAAgAAAABCIUACAAAAAEKpl2sgAQAAAOBIXXnllUnVX3DuuerGPJCRIEACAAAAiLWbbropqforLr6YeSAjwimsAAAAAGJt9+7d2r17d+j6srIy7S4ri7Cj9EWABAAAABBrw4cP1/Dhw0PX3/zjH2v4zTdH2FH6IkACAAAAAEIhQAIAAAAAQiFAAgAAAABCIUACAAAAAEJhGg8AAAAAsTZ69Oik6i+54AL1aNEimmbSHAESAAAAQKwdSYBkHshoECABAAAAxFpxcbEkKScnJ1R9yY4dKs7KirKltMU1kAAAAABibeTIkRo5cmTo+tvuu08jb7stwo7SFwESAAAAABAKARIAAAAAEAoBEgAAAAAQCgESAAAAABAKd2EFAAAAEGs33nhjUvUjv/xlndCyZUTdpDcCJAAAAIBYGzVqVFL1F553HvNARoQACQAAACDW1q9fL0nq2rVrqPqPtm7V+gMHpMzMKNtKSwRIAAAAALF2zTXXSJJmzZoVqv7Hv/iFWmRladx990XYVXriJjoAAAAAgFAIkAAAAACAUAiQAAAAAIBQCJAAAAAAgFC4iQ4AAACAWLvllluSqr/6q19Vr1atIuomvREgAQAAAMTaJZdcklT9uYMHMw9kRAiQAAAAAGJtxYoVkqS8vLxQ9e9v2KDmpaVSs2ZRtpWWCJAAAAAAYu2GG26QFH4eyJ8+/DDzQEaEm+gAAAAAAEIhQAIAAAAAQiFAAgAAAABCIUACAAAAAELhJjoAAAAAYu3OO+9Mqv76r31NJzIPZCQIkAAAAABibejQoUnVn3HqqcwDGRECJAAAAIBYW7RokSSpoKAgVP2K995T5vbtUtu2UbaVlgiQAAAAAGJt7NixkmqeB7JwzhyVl5SoUevWyh88WOMee4x5ICPCTXQAAAAANGjlJSU6LTdX5SUlqW7lmEeABAAAAACEQoAEAAAAAIRCgAQAAAAAhMJNdAAAAADE2k9/+tOk6r8zerROat06om7SGwESAAAAQKydddZZSdWf0rcv80BGhAAJAAAAINbefPNNSeGD5OLly7W3dWs17tw5yrbSEgESAAAAQKzdcccdkmqeB7Kq30ycyDyQEeEmOgAAAACAUAiQAAAAAIBQCJAAAAAAgFAIkAAAAACAULiJDgAAAIBYe+ihh5Kqv+WGG9S3TRsdiKifdEaABAAAABBrBQUFSdXn9eypAuaBjESoU1jNrH/UjQAAAABAdV5++WW9/PLLoevnvvOOXp47N8KO0lfYEcjfmlkjSRMl/dndS6JrCQAAAAD+z7333itJGjp0aKj6CU89xTyQEQk1Aunu50j6uqSukuab2Z/N7ILDrWNm2WY2z8wWm9kyM/vvYPnnzGyuma0ys8lBMAUAAAAAxFzou7C6+ypJd0r6gaTzJD1sZu+a2VdrWGWvpC+6+ymSCiRdZGaDJf1M0q/cvbekjyVdfzRvAAAAAABQP8JeA3mymf1KUpGkL0q6xN37BI9/Vd06nvBJ8DQr+PJgnSnB8ickXX7k7QMAAAAA6kvYEchfS1oo6RR3/467L5Qkd9+oxKhktcws08wWSdoiaYak9ySVuPv+oGSDpONrWHeMmc03s/lbuXsSAAAAAKRc2JvoDJe0x90PSJKZZUjKdvfd7j6pppWC+gIzay3pr5L6VFdWw7rjJY2XpIEDB1ZbAwAAAODY99hjjyVVf8fNN6t/mzb6pPZSJCnsCOTLkppUet40WBZKcNfWWZIGS2ptZgeDaxdJG8NuBwAAAED6ycvLU15eXuj6Hl26KK9Hj+gaSmNhA2R2pesZFTxuergVzCw3GHmUmTWRNFSJayhfkTQyKLtO0nPJNg0AAAAgfUybNk3Tpk0LXT97zhxNmz07wo7SV9gAWWpmAw4+MbPTJO2pZZ1Okl4xsyWS3pY0w92nK3EX1++Z2WpJ7SRNSL5tAAAAAOli3LhxGjdu3CHLS3fu1K7t27W2qOgzy5989lmNe/LJ+movrYS9BnKspGfM7ODppp0kjTrcCu6+RNKp1SxfI2lQMk0CAAAAQFUV+/erRVaW9peWprqVtBEqQLr722Z2kqQ8SSbpXXffF2lnAAAAAIBYCTsCKUmnS+oRrHOqmcnd/xhJVwAAAACA2AkVIM1skqSekhZJOhAsdkkESAAAAABIE2FHIAdK6uvuzMcIAAAAoF5NmlTj1PPVuvv739fJbdtqS0T9pLOwAXKppI6SNkXYCwAAAAAcomvXrknVd8zNVdfcXG3ZujWijtJX2ACZI2m5mc2TtPfgQne/NJKuAAAAACAwefJkSdKoUYedCOJTL736qla3bKlepx4yKQSOUtgA+ZMomwAAAACAmjz66KOSwgfIKX//u1pkZWkcAbLOhZ3G41Uz6y6pt7u/bGZNJWVG2xoAAAAAIE4ywhSZ2bckTZH0WLDoeEl/i6opAAAAAED8hAqQkr4j6WxJOyXJ3VdJah9VUwAAAACA+AkbIPe6e/nBJ2Z2nBLzQAIAAAAA0kTYm+i8amZ3SGpiZhdIuknStOjaAgAAAICEKVOmJFX/8x/9SKfk5OiDffsi6ih9hR2B/KGkrZIKJd0g6QVJd0bVFAAAAAAclJOTo5ycnND1rVu1Uk7r1hF2lL7C3oW1QtLvgi8AAAAAqDcTJ06UJI0ePTpU/bQZM1TYooXyBw+Orqk0FSpAmtlaVXPNo7ufUOcdAQAAAEAlRxIgW2RlaRwBss6FvQZyYKXH2ZKukNS27tsBAAAAAMRVqGsg3X1bpa8P3f0hSV+MuDcAAAAAQIyEPYV1QKWnGUqMSLaIpCMAAAAAQCyFPYV1XKXH+yW9L+nKOu8GAAAAABBbYe/C+oWoGwEAAACA6rzwwgtJ1T989906NTdXRbt2RdRR+gp7Cuv3Dve6u/+ybtoBAAAAgM9q2rRpUvXZ2dlqmp0tESDrXDJ3YT1d0vPB80skzZa0PoqmAAAAAOCgRx55RJJ00003hap/Zvp0zW3eXGcMGRJhV+kpbIDMkTTA3XdJkpn9RNIz7v7NqBoDAAAAAEl6+umnJYUPkDNmz1aLrCwCZARCTeMhqZuk8krPyyX1qPNuAAAAAACxFXYEcpKkeWb2V0ku6SuS/hhZVwAAAACA2Al7F9b7zOwfkj4fLPqGu78TXVsAAAAAgLgJOwIpSU0l7XT3P5hZrpl9zt3XRtUYAAAAACTjvaIiSVLZ7t1q0apVirs5NoWdxuO/lLgTa56kP0jKkvSkpLOjaw0AAAAApFmzZoWqqygt1Wm5ubpr9GhdNWyYFmzdGm1jaSjsTXS+IulSSaWS5O4bJbWIqikAAAAAQPyEPYW13N3dzFySzKxZhD0BAAAAwKcefPBBSdKtt94aqn76669rQ3GxvnDRRVG2lZbCjkA+bWaPSWptZt+S9LKk30XXFgAAAAAkTJ8+XdOnTw9dv3DFCk1/7bUIO0pfYe/C+qCZXSBppxLXQf7Y3WdE2hkAAAAAIFZqDZBmlinpn+4+VBKhEQAAAADSVK2nsLr7AUm7zYz74AIAAABAGgt7E50ySYVmNkPBnVglyd1vjqQrAAAAAAg0adIkqfpGWVlqkp0dUTfpLWyA/HvwBQAAAAD16h//+EdS9T+89lrmgYzIYQOkmXVz93Xu/kR9NQQAAAAAiKfaroH828EHZjY14l4AAAAA4BD33HOP7rnnntD1z77yiu55/PEIO0pftQVIq/T4hCgbAQAAAIDqzJw5UzNnzgxdv3TNGs2cNy/CjtJXbQHSa3gMAAAAAEgztd1E5xQz26nESGST4LGC5+7uLSPtDgAAAAAQG4cNkO6eWV+NAAAAAADiLew0HgAAAACQEu3atUuqvkXTpmrXqlVE3aQ3AiQAAACAWJs6NbkJIf7za19jHsiI1HYTHQAAAAAAJBEgAQAAAMTc7bffrttvvz10/VMvvaTbf/3rCDtKX5zCCgAAACDW3nrrraTqV61frx2lpRo5alREHaUvRiABAAAAAKEQIAEAAAAAoRAgAQAAAAChcA0kAAAAgFjr0qVLUvVtW7ZUlw4dIuomvREgAQAAAMTak08+mVT9d6+4gnkgI8IprAAAAACAUAiQAAAAAGJt7NixGjt2bOj6J154QWPHjYuwo/TFKawAAAAAYm3RokVJ1X+waZP27N2rayLqJ51FNgJpZl3N7BUzKzKzZWb2H8HytmY2w8xWBd/bRNUDAAAAAKDuRHkK635Jt7h7H0mDJX3HzPpK+qGkme7eW9LM4DkAAAAAIOYiC5DuvsndFwaPd0kqknS8pMskPRGUPSHp8qh6AAAAAADUnXq5BtLMekg6VdJcSR3cfZOUCJlm1r6GdcZIGiNJ3bp1q482AQAAAMTQiSeemFR9p5wc9ezaNaJu0lvkAdLMmkuaKmmsu+80s1Druft4SeMlaeDAgR5dhwAAAADibPz48UnVf+uyy5gHMiKRTuNhZllKhMc/ufuzweLNZtYpeL2TpC1R9gAAAAAAqBtR3oXVJE2QVOTuv6z00vOSrgseXyfpuah6AAAAANDwjRkzRmPGjAld/7vnntOY++6LsKP0FeUprGdLukZSoZkdnLjlDkkPSHrazK6XtE7SFRH2AAAAAKCBW7lyZVL1m4qLdaCiIqJu0ltkAdLdX5dU0wWP50e1XwAAAABANCK9BhIAAAAAcOwgQAIAAAAAQqmXeSABAAAA4EgVFBQkVd+9U4uWJz4AACAASURBVCfl9egRTTNpjgAJAAAAINYeeuihpOqvGz6ceSAjwimsAAAAAIBQCJAAAAAAYu3qq6/W1VdfHbr+1888o6vvuivCjtIXp7ACAAAAiLUNGzYkVb99504ddxxRJwqMQAIAAAAAQiFAAgAAAGhwCufMUdnu3aluI+0QIAEAAAA0OOUlJfIDB1LdRtrhxGAAAAAAsXbmmWcmVd+7a1f17dkzom7SGwESAAAAQKzdf//9SdV/7cILmQcyIpzCCgAAAAAIhQAJAAAAINZGjBihESNGhK7/1VNPacT3vx9hR+mLU1gBAAAAxNq2bduSqt+1e7e27dgRUTfpjRFIAAAAAEAoBEgAAAAAQCgESAAAAABAKFwDCQAAACDWzj///KTq+59wgvJPPDGibtIbARIAAABArN11111J1X/1C19gHsiIcAorAAAAACAUAiQAAACAWBs2bJiGDRsWuv6BP/5Rw26+OcKO0hensAIAAACItT179iRVX75vn/aUlUXUTXpjBBIAAAAAEAoBEgAAAAAQCgESAAAAABAK10ACAAAAiLWLL744qfoBeXkqOOmkiLpJbwRIAAAAALF26623JlV/8TnnMA9kRDiFFQAAAAAQCgESAAAAQKwNGTJEQ4YMCV1/94QJGjJmTHQNpTECJAAAAAAgFAIkAAAAACAUAiQAAAAAIBQCJAAAAAAgFKbxAAAAABBrV155ZVL1g/v318B+/SLqJr0RIAEAAADE2k033ZRU/YVnnME8kBHhFFYAAAAAsbZ7927t3r07dP3e8nLtLiuLsKP0RYAEAAAAEGvDhw/X8OHDQ9f/bNIkDb/55gg7Sl8ESAAAAABAKARIAAAAAEAoBEgAAAAAQCgESAAAAABAKEzjAQAAACDWRo8enVT9eaeeqjNOPjmaZtIcARIAAABArFUOkIVz5qi8pERri4pqrD9vwADmgYwIp7ACAAAAiLXi4mIVFxdLkspLSnRabq72l5bWWL+ztFTFJSX11V5aIUACAAAAiLWRI0dq5MiRoesf+stfNPK22yLsKH0RIAEAAAAAoRAgAQAAAAChECABAAAAAKEQIAEAAAAAoTCNBwAAAIBYu/HGG5Oqv2DQIJ1VUBBRN+mNAAkAAAAg1kaNGpVU/Zn5+Rp14YXMAxkBAiQAAACAWFu/fr3eXbhQbRs31tqiIp2Wm3vY+m07dmj9Rx9JmZn11GH64BpIAAAAALF2zTXX6Id33aXTcnO1v7S01vrfTJmia37843roLP0QIAEAAAAAoUQWIM3s92a2xcyWVlrW1sxmmNmq4HubqPYPAAAAAKhbUY5ATpR0UZVlP5Q00917S5oZPAcAAAAANACRBUh3ny1pe5XFl0l6Inj8hKTLo9o/AAAAgPRwwF079uxJdRtpob7vwtrB3TdJkrtvMrP2NRWa2RhJYySpW7du9dQeAAAAgLi55ZZbtHrBgkOWZzdpop59++q9igr9+pVXlOsuSfry2Wfr3NNOq+8200Jsb6Lj7uPdfaC7D8yt5Ta9AAAAAI5dl1xyic4dPPjT56V792pzRYW+PGKEuvbsqeZm6tSqlTa5a9bKlRqQl6dLzj03hR0fu+o7QG42s06SFHzfUs/7BwAAANDArFixQu9v2CBJcndNXbhQJe5at2aN5v7rX+qckaFrBw9WSzO9unKl1uzZo2Vr1qS462NTfQfI5yVdFzy+TtJz9bx/AAAAAA3MDTfcoJ8+/LAkaZe71m7bpvZmevvNN7UnmBfyuMxMdTTT0JNO0r5GjTR+1ix5cEor6k6U03g8JektSXlmtsHMrpf0gKQLzGyVpAuC5wAAAABQq/L9+7XVXR1btlRrs0NeNzOd3auXFr39ttq2b6/iHTtS0OWxLcq7sH7N3Tu5e5a7d3H3Ce6+zd3Pd/fewfeqd2kFAAAAgGq9umqV9ksanp8vqyZAHrT63XdVtnu3VmzYwChkHYvtTXQAAAAA4KDmLVpozpo1ammmrm3aHLa2oqJC769cqZLSUq1evbqeOkwPBEgAAAAAsZd/yinKysxU7mFGHiv7aP16NW3cWK+88gqjkHWIAAkAAAAg1m688UblduigL+Tl6bgQAfIrQ4boR//+7+p9/PHatGmTVqxYUQ9dpgcCJAAAAIBYKy0tVdPGjXV69+6h6vN79tTQM87Q8Tk5atu2rWZxR9Y6Q4AEAAAAEFubN2/W+vXr1TQzUxkZ4eLL+5s2adGKFcow03nnnafNmzerqKgo4k7TAwESAAAAQGwtWLBABw4c0JOTJ4de548vvKCx48ZJkvr376927drp9ddfj6rFtEKABAAAABBL5eXlWrx4sbZu3ary8vIj2kZGRoZOP/10bdq0SZs3b67jDtMPARIAAABALC1dulTl5eXauHHjUW0nPz9fGRkZWrRoUR11lr4IkAAAAABiaf78+Wrfvr127NhxVNtp2rSp8vLytGTJEh04cKCOuktPBEgAAAAAsbNx40Zt2rRJp512Wp1sr6CgQLt379bq1avrZHvp6rhUNwAAAAAAVc2fP19ZWVk6+eST9dOf/lTvzpkTet2rLrhAQwcP/syynj17qlmzZlq0aJHy8vLqut20wQgkAAAAgFgpKyvT0qVL1b9/f2VnZ+uss87SKX37hl7/xG7ddNYpp3xmWWZmpk4++WStXLlSpaWldd1y2iBAAgAAAIiVwsJC7du3TwMHDpQkvfnmm1q8fHno9VeuW6c3Fy8+ZHlBQYEqKipUWFhYZ72mGwIkAAAAgFhZvHixOnTooM6dO0uS7rjjDv1m4sTQ6/9lxgzd8ZvfHLK8ffv26ty5sxZXEy4RDgESAAAAQGwUFxfrww8/1MknnxzJ9k855RR99NFH+uijjyLZ/rGOAAkAAAAgNpYsWSIzU35+fiTbz8/PV2ZmJnNCHiECJAAAAIBYcHctWbJEJ5xwglq0aBHJPpo0aaITTzxRS5cuVUVFRST7OJYRIAEAAADEwgcffKAdO3bolCp3UK1r+fn5Ki0t1Zo1ayLdz7GIeSABAAAAxMKSJUvUqFEjnXTSSZ9Z/tBDD2n5G2+E3s61w4frorPP1oEaXu/du7eys7O1dOlS9erV6yg6Tj+MQAIAAABIuX379mn58uXq27evsrKyPvNaQUGB8nr2DL2tHp06qSAvr8bXjzvuOPXp00dFRUXat2/fEfecjgiQAAAAAFJuxYoV2rt3b7V3X3355Zc19513Qm+r8L339PLcuYetyc/PV3l5uVasWJF0r+mMAAkAAAAg5ZYsWaKWLVuqR48eh7x27733asJTT4Xe1l9nzdK9EyYctqZ79+5q0aKFli5dmmyraY0ACQAAACClPvnkE61evVr5+fkys3rZZ0ZGhvr3769Vq1Zpz5499bLPYwEBEgAAAEBKFRYWyt0jv/tqVfn5+aqoqNCyZcvqdb8NGQESAAAAQMq4u9555x116dJFubm59brvjh07Kicnh9NYk0CABAAAAJAyGzZs0NatW3Xqqace8lrhnDkqnDMnsn2bmfLz8z+dfxK1I0ACAAAASJmFCxeqUaNG6t+//yGvlZeUqLykRI899pjuuPnm0Nv85qWX6rE77ghVm5+fLylxGi1qR4AEAAAAkBJ79+7VsmXL1K9fPzVq1KjGury8PPXo0iX0djvn5iqvmru5VqdNmzbq2rWrFi9eLHcPvY90RYAEAAAAkBJLly7Vvn37dNpppx22btq0aZqdxKmsC959V9Nmzw5df+qpp6q4uFjr168PvU66IkACAAAASImFCxeqffv26ty582Hrxo0bpyeffTb0dv/+xhsa9+SToesPjoAuXLgw9DrpigAJAAAAoN599NFH2rhxowYMGFBvcz/WpFGjRsrPz9eyZctUVlaW0l7ijgAJAAAAoN4tXLhQmZmZOvnkk1PdiiRpwIAB2r9/PzfTqQUBEgAAAEC92rdvnwoLC9WnTx81adIk1e1Ikjp16qSOHTtq4cKF3EznMAiQAAAAAOrV0qVLVVZWpgEDBqS6lU+ZmQYMGKCPPvpImzZtSnU7sXVcqhsAAAAAkD4qKir0xhtvqEOHDuoRcqqNSZMmacmsWaH38Z2RI3XpkCHakmRv+fn5eumll7Rw4cJab+yTrhiBBAAAAFBvioqKtG3bNn3+858PffOcrl27qmNubuh9tGvVSl07dky6t+zsbPXr10+FhYUqLy9Pev10QIAEAAAAUC/cXa+99pratWunPn36hF5v8uTJeunVV0PXv1VYqMkvvXQkLWrAgAEqLy/XsmXLjmj9Yx0BEgAAAEC9WLlypTZv3qxzzjlHGRnho8ijjz6qKX//e+j6GfPm6dEpU46kRXXt2lW5ubl66623uJlONQiQAAAAACJ3cPSxdevWys/PT3U7NTIznXvuudq6dauWL1+e6nZihwAJAAAAIHJr167Vhx9+qLPPPluZmZmpbuew+vbtq5ycHL366quMQlZBgAQAAAAQuddee03NmzdXQUFBqlupVUZGhs477zxGIatBgAQAAAAQqbVr1+r999/XWWedpeOOaxgzCTIKWT0CJAAAAIDIlJeXa9q0aWrTpo0GDhyY9PrvFRXprhtv1HeuuCL0OmOvukpTfv7zpPdVWUZGBtdCVoMACQAAACAyM2fO1Mcff6xLL71UWVlZSa9fUVqq83v1UtOQc0ZKUstmzZTTunXS+6qqX79+jEJWQYAEAAAAEIkPPvhA8+bN0+mnn64ePXoc8XYmTpumVxcuDF3/6sKFmjht2hHv76DKo5DMC5lAgAQAAABQ58rLy/Xcc8+pTZs2Gjp0aFLrFs6ZowUvvqi1RUWSggD5zjuh13/1nXfqJEBKiVHIDh066MUXX1RpaWmdbLMhI0ACAAAAqHOVT11t1KhRUuuWl5TotNxc7Y9BYMvIyNBXv/pVlZWV6bnnnkv7U1kJkAAAAADq1LJly+rk1NW4aN++vS644AKtWrVK8+bNS3U7KUWABAAAAFBnCgsLNXXqVHXr1i3pU1fjbNCgQerdu7dmzJihzZs3p7qdlCFAAgAAAKgTixcv1l//+ld1795dX//615M+dTXOzEyXXXaZsrOz9eyzz2rfvn2pbiklGsYsngAAAABip3DOHJWXlKhR69ba37ixnn/+eZ1wwgm66qqrjmjKjpq88PDDeuaf/wxd/4NrrtEVX/qSinbtqrMeJKlZs2a6/PLL9ac//UlTp07ViBEj6vR9NgSMQAIAAAA4IuUlJTqxRQvNnT9fzz//vHr16lXn4VGSmmZnq3ESo5mNGzVS0+zsOu3hoF69emnYsGFasWKFnnjiibS7MysBEgAAAEDS9u/fr9UbN+p/X3lFm7Zv1znnnKNRo0ZFMiL3yDPP6KW5c0PXvzR3rh555pk67+OgQYMG6corr9TmzZs1YcIEbdu2LbJ9xQ2nsAIAAAB1qPJpnfmDB8due8nud9369erWteun+9+yZYuWL1+uJUuW6OOPP1Zehw7q3LGjzj3//M+sK6nO+n16xgxt2b49dP2cpUu1ZuNGnTFkSJ3svzp9+vTRddddp6eeekoTJkzQ8OHD1bdvX2VkHNtjdARIAAAAoA4dnMNwwdatR7R+1cB4tNs7UuUlJRqQk6Nlb7+tpp06aWFhoWYvWKDi4mJJUk6bNuretKmuOv30Q3orLymp115TpUuXLrr++us1efJkTZ06Va+++qrOPfdc9evX75gNkikJkGZ2kaT/kZQp6XF3fyAVfQAAAAC1qe8RwDCB8Wh6OnDggMrLy1VWVqa9e/d+5mvXrl3atWuXdu7cqY3r1umlsjKVV1Ro7YIFkqQePXpo0KBBOumkk7TyjTe0av78o3qvx4K2bdvqhhtuUFFRkWbPnq1nn31Ws2bNUv/+/dWjRw916dLlmLrRTr0HSDPLlPQbSRdI2iDpbTN73t2X13cvqeDun/le3bKw32tiZke9rPJrYZelk9p+BlG+fiTrVl1W2/OwNVLNx0Cclh/tNg733+DRLAuz7/p8XlstgPpX2+8M9hVuX+6uioqKQ74OHDhQ7fKqX+vXrtUJLVtq1XvvSc2a1Vq/4cMPtXP7dm0sLdX2GTNC7aPy187iYi1dvVo7y8u1ZNMm7dq+XYuOO06f7NunhevXq6KiQrt37lR2Zqb27N+v2QsWfPo+q/uqqKj49PG+ffu0f//+w35mWVlZatmypTIzMnTK8cdr3bp1uuTss/VhWZkGffnL9fSTa1gyMjLUr18/9e3bV++++67efPNNvfbaa5o9e7YyMzN1/PHHq127dmrVqpVatWqlli1bqlOnTmrSpEmqW09aKkYgB0la7e5rJMnM/iLpMkkNLkD+7W9/0/Lly4868B1LjjR4pjKQhXkdQPVqC5lhQmh9bKM+Hct/hLMvpLO3g+8LV68OVb9Sid9N72/ZooyMjFBfmZmZMjMdqKhQhbtMUmZmpjIzMtQ4K0t73dWsWTOZmXzvXrVp3Fgle/eqbfv2MrNPvzIyMj7zN9fHW7fKy8v1ySefqFVurho3a6ZuPXsqOztbjRs3/sxX8+bN1bhxY5mZFrz4ok7LzdVfNmzQ8a1b66MkT6F9r6hIkkKNkla93nJtUZFOy81Nan9xYGbq06eP+vTpo7KyMq1fv17vv/++1q1bp5UrV37mjq2jRo3SSSedlMJuj4zV9y9OMxsp6SJ3/2bw/BpJZ7j7d6vUjZE0JniaJ2lFvTZ6bMiRVJzqJoCjwDGMho5jGA0dxzAaOo7hI9Pd3atN8KkYgazun4kPSbHuPl7S+OjbOXaZ2Xx3H5jqPoAjxTGMho5jGA0dxzAaOo7hupeKWwNtkNS10vMukjamoA8AAAAAQBJSESDfltTbzD5nZo0kXSXp+RT0AQAAAABIQr2fwuru+83su5L+qcQ0Hr9392X13Uea4BRgNHQcw2joOIbR0HEMo6HjGK5j9X4THQAAAABAw5SKU1gBAAAAAA0QARIAAAAAEAoB8hhiZleY2TIzqzCzGm9XbGYXmdkKM1ttZj+szx6BwzGztmY2w8xWBd/b1FB3wMwWBV/chAspV9vvVTNrbGaTg9fnmlmP+u8SqF6I43e0mW2t9Hv3m6noE6iJmf3ezLaY2dIaXjczezg4xpeY2YD67vFYQoA8tiyV9FVJs2sqMLNMSb+RNExSX0lfM7O+9dMeUKsfSprp7r0lzQyeV2ePuxcEX5fWX3vAoUL+Xr1e0sfu3kvSryT9rH67BKqXxN8Fkyv93n28XpsEajdR0kWHeX2YpN7B1xhJj9ZDT8csAuQxxN2L3H1FLWWDJK129zXuXi7pL5Iui747IJTLJD0RPH5C0uUp7AUIK8zv1crH9hRJ55uZ1WOPQE34uwANnrvPlrT9MCWXSfqjJ8yR1NrMOtVPd8ceAmT6OV7S+krPNwTLgDjo4O6bJCn43r6Gumwzm29mc8yMkIlUC/N79dMad98vaYekdvXSHXB4Yf8uGBGc+jfFzLrWT2tAneHv3zpU7/NA4uiY2cuSOlbz0o/c/bkwm6hmGXO5oN4c7hhOYjPd3H2jmZ0g6V9mVuju79VNh0DSwvxe5Xcv4irMsTlN0lPuvtfMvq3EaPoXI+8MqDv8Dq5DBMgGxt2HHuUmNkiq/C+HXSRtPMptAqEd7hg2s81m1sndNwWnlmypYRsbg+9rzGyWpFMlESCRKmF+rx6s2WBmx0lqpcOfbgXUl1qPX3ffVunp78Q1vGh4+Pu3DnEKa/p5W1JvM/ucmTWSdJUk7mKJuHhe0nXB4+skHTKqbmZtzKxx8DhH0tmSltdbh8ChwvxerXxsj5T0L3fnX78RB7Uev1WuFbtUUlE99gfUheclXRvcjXWwpB0HL5lB8hiBPIaY2Vck/a+kXEl/N7NF7v4lM+ss6XF3H+7u+83su5L+KSlT0u/dfVkK2wYqe0DS02Z2vaR1kq6QpGBamm+7+zcl9ZH0mJlVKPGPYA+4OwESKVPT71Uzu1vSfHd/XtIESZPMbLUSI49Xpa5j4P+EPH5vNrNLJe1X4vgdnbKGgWqY2VOShkjKMbMNkv5LUpYkuftvJb0gabik1ZJ2S/pGajo9Nhj/AAoAAAAACINTWAEAAAAAoRAgAQAAAAChECABAAAAAKEQIAEAAAAAoRAgAQAAAAChECABICbM7ICZLTKzxWa20MzOquPt31GX26uy7dFmtjXo/10z+8+j2NYQM5sePL7UzH54BNsoMLPhlZ4f0XaOlpl93syWBZ9LkyqvdTSzv5jZe2a23MxeMLMTI+pjVjAdzuFqxppZ00rPXzCz1nW0/2vNbGnwWSw3s1uPcDu5ZjbXzN4JPtsrzKzIzF4xs4Fm9nAt6x/xezKzy82s75GsCwDHEgIkAMTHHncvcPdTJN0u6f463n61ATKYWLku/n8w2d0LJJ0t6Udm1vVoN+juz7v7A0ewaoESc34d7XaO1tclPRj8XPccXGhmJumvkma5e09376vEz6dDmI2aWWaV53XxMxwr6dMAGcwdXHKU25SZDQu2faG795M0QNKOI9zc+ZLedfdT3f01SddLusndv+Du89395sOtfJTv6XJJBEgAaY8ACQDx1FLSx9Kn4eAXwQhOoZmNqmV5JzObHYx6LQ1Gah6Q1CRY9icz6xGM3DwiaaGkrmb2qJnND0aJ/vtgI2b2vpn9zMzmBV+9Dte4u29TYrLmTsH6uWY21czeDr7ODpYPMrM3g9GkN80sr+q2gpHNXwePF1X62mNm51W3DTNrJOluSaOC2lFVttPdzGaa2ZLge7dg+UQzezjYzhozG1nT51lNn+cHPRSa2e/NrLGZfVPS/2/v/kP9qus4jj9fbWur/WoyKwpKEdscYjec5ErzmjMosF8uF6gzlUVQXKWsiMTECnESGlSYlnOOXCallP1gS+e21q6Ttbu7tiSCrSIp+2H+GFlrvvvj8z67x+/OOfd7//LSfT3gsM/5nHM+Pw/sfu7ncz73IuA6Sd/peeRc4HD+geuq3UYiYltHvw7mTNs9wN6WPnyXpB0qM9j3SZrTUNZj+lnSEPA6YLOkzbV+X5jhT2Z5fi3p6oyr8r8j09qonlnW9Dngmoh4Iuv5fETckWkMSBrOvrhf0oKMP0nSzyTtkrRN0mJJA8Aa4D3ZF18AzgJuy/aqz1zPkbQ2229U0oUNdbok3+cRSd9UDsolPSfpyyorAYYlvUZlNcB7gZvz/pMa6mlmNjVEhA8fPnz4mAQHcAQYAR6nzNCcnvEXApuAaZQZqj9QBmdt8Z8CPp/PTgPmZvi5Wl4nAC8AZ9bijqs98whwWp4frKW3CniwoewfAb6W4TdkPWbl+T3AWbVrv8nwPGB6hpcD38/wYJVHPd1aXhcA24AZHWm86Lme8v0IuCzDVwAPZPgu4D7KL1eXAL/L+Mb2rKU9C/gj8KY8vxu4upbmiob2GgJuaXkP2vp1EDgEnNjUh8BCYCswO88/C1yX4UeApX3088JaOQ5mmqcDe4HZwBxgH/CWzP+/wEDe/z3gkob6/AOY31LXUeCcDN8A3Jrhh4CTM/xW4OGWfq3Xa5Cx9+amKq08X9BTp1PyPZiR8d8AVmU4gAsyvAa4tqsvffjw4WOqHdMxM7PJ4l9RloAiaRlwt6RTKbMsGyLiCPAXSVuAMzriHwPulDSDMjgaacnv9xExXDu/SNJHgemUAcsSyg/4ABtq/97Skt5KSecCi4DVEfF8xi8Hlkiq7psnaS4wH1gn6WTKD+0zxmugvPdm4J0RcVjSayeaBrAM+GCG11MGCZUHIuIFYL+kajnpeO25CDgQEb/N83XAx4Fb+yhLk7Z+fQbYGREHavfW+/BMSp9tz7Z+ObCjIf2ufm4rz/0RcQhA0g+As4EfUupdtccuyqCyL5LmA6+KiC0ZtQ6oZk3fluHq9pn9ppuWAx+uTiLiqZ7r51EGxo9lHq8Ansxr/wEezPAu4PwJ5m1m9n/NS1jNzCahiNhBmSk5HlDLbY3xEbEVeAfwJ2C9pFUtzx86mpB0InANcF5EnAb8mDKzdjTZlnDdvVG+cTsb+EoO7qD8X7MsyneAAxHx+oh4FvgisDkiTqXMKs5qTvZoGWdTZrlWRy6HnGgaLer1+Xc9S+irPdv6p8s+ygCmSVd6hzrOBWyqtfOSiLjyRQmP388TLU+9vY5A4y+mu+ra5GXAP2v1GIiIUybwPJQyt72n1fV1tfQXRcT1ee1wRFTPttXJzGzK8gDSzGwSkrSYssTw75RliSslTZN0PGUws7MtXtIbgSejfGf2bcqmJQCHcxatyTzKYOTpnHl7d8/1lbV/m2a1jsrB73rgqozaCHyiVreBDM6nDMqgLE0cz1pgbZTNUyptaTwLzG1J55eMzU5dDPyiK9OO9qw8DpygsW9DLwW20O1hYKak1bV8zpB0Du39PZ5h4O1VOSS9Usfu6trVz21tthV4f6Y3G/gAZQlxv24E1lS/UFD5PnQoIp4GntLYN6WXAlsi4hnggKQP5f2S9OYJ5AfHvnMLeq4/BKyQ9Oq8flz2c5eud8rMbMrwANLMbPKoNrkZAe6lfKd3hLJb5yiwhzLw+ExE/LkjfhAYkbSb8j3dVzP924FRHbuhCxGxB9hNmS26E9jec8tMSY9SBoX9/ImOm4DLc6nqELA0NzPZD3ws71kD3ChpO2Ww3Cp/uF8BXKGxjXSWdqSxmbJsdkS5CU3NUJZtlDJouYpugzS3J1A2hQEupyy53Ev5LvG23kR6ngnKQOx8lT/jsQ+4HniC9n7tFBF/pQyiN2TdhoHFPfd09fPtwE+Vm+jUnvkV5fu/ncCjwLciYvd45ak9/xPg68DPs567GJvVu4yyMc0oZefcGzL+YuBKSXuyrO/rN7/0JWCByqY/eyibFtXLtB+4FtiYeW8iN33q8F3g0yqbJXkTHTObsjS2SsPMzOxYkg5SNir520tdFjMzM3tpeQbSzMzMzMzM+uIZSDMzMzMzM+uLZyDNzMzMTAZy3gAAADJJREFUzMysLx5AmpmZmZmZWV88gDQzMzMzM7O+eABpZmZmZmZmffEA0szMzMzMzPryPzrwkKNWQU7XAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "L = 1000                               # set the number of bootstrap realizations   \n",
    "corr_real = []                      # declare an empty list to store the bootstrap realizations of the statistic \n",
    "\n",
    "for k in range(0,L):                   # loop over the L bootstrap realizations\n",
    "    samples = df.sample(n=len(df),replace=True,random_state = seed + k) # n random samples with replacement as a new DataFrame   \n",
    "    corr_real.append(samples[['Porosity','Perm']].corr()['Porosity'][1]) # calculate the statistic of interest from the new bootstrap dataset\n",
    "\n",
    "corr = df[['Porosity','Perm']].corr()['Porosity'][1]\n",
    "\n",
    "plt.subplot(111)\n",
    "plt.hist(corr_real,color = 'red',alpha = 0.2,edgecolor = 'black',bins=np.linspace(0.5,1.0,100),label = 'bootstrap',density = True) # plot the distribution, could also calculate any summary statistics\n",
    "plt.axvline(x=corr,c='black')\n",
    "plt.axvline(x=np.percentile(corr_real,10),linestyle=\"--\",c='black')\n",
    "plt.axvline(x=np.percentile(corr_real,90),linestyle=\"--\",c='black')\n",
    "sns.kdeplot(x=corr_real,color = 'grey',alpha = 0.1,levels = 1,bw_adjust = 1)\n",
    "# plt.text(np.percentile(corr_real,90)+0.009, 16, r'Average = ' + str(round(np.average(corr_real),3)), fontsize=12)\n",
    "# plt.text(np.percentile(corr_real,90)+0.009, 15, r'St.Dev. = ' + str(round(np.std(corr_real),3)), fontsize=12)\n",
    "# plt.text(np.percentile(corr_real,90)+0.009, 14, r'P90 = ' + str(round(np.percentile(corr_real,90),3)), fontsize=12)\n",
    "# plt.text(np.percentile(corr_real,90)+0.009, 13, r'P10 = ' + str(round(np.percentile(corr_real,10),3)), fontsize=12)\n",
    "plt.xlabel('Boostrap Realizations of Correlation Coefficient'); plt.ylabel('Frequency'); plt.title('Distribution of Correlation Coefficient')\n",
    "# plt.legend()\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.2, wspace=0.2, hspace=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Comments\n",
    "\n",
    "This was a basic demonstration of bootstrap. \n",
    "\n",
    "* you can use bootstrap to calculate uncertainty in any statistic!\n",
    "\n",
    "* you are calculating a set of realizations of the statistic, representing uncertainty due to small sample size\n",
    "\n",
    "* note the assumptions of bootstrap, including stationarity and representativity\n",
    "\n",
    "* remember, get a dataset realization by bootstrap and then calculate the realization of the statistic from the dataset realization\n",
    "\n",
    "* if your statistic has multiple inputs (e.g. P25 and P75), calculate each from the same bootstrap realization of the dataset.\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 https://github.com/GeostatsGuy/PythonNumericalDemos and 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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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