tests-as-linear.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "# _Common statistical tests are linear models_: Python port\n",
    "\n",
    "Original post by Jonas Kristoffer Lindeløv ([blog](https://lindeloev.net), [profile](http://personprofil.aau.dk/117060)). Python port by George Ho ([blog](https://eigenfoo.xyz)).\n",
    "\n",
    "> This is a Python port of Jonas Kristoffer Lindeløv's post [_Common statistical tests are linear models (or: how to teach stats_)](https://lindeloev.github.io/tests-as-linear/), which originally had accompanying code in R.\n",
    ">\n",
    "> View this notebook [on GitHub](https://github.com/eigenfoo/tests-as-linear). Launch this notebook [on Binder](https://gke.mybinder.org/v2/gh/eigenfoo/tests-as-linear/master?filepath=tests-as-linear.ipynb)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/markdown": [
       "Last updated: June 28, 2019"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "# Contents\n",
       "- [_Common statistical tests are linear models_: Python port](#_Common-statistical-tests-are-linear-models_:-Python-port)\n",
       "- [1 The simplicity underlying common tests](#1-The-simplicity-underlying-common-tests)\n",
       "- [2 Python environment](#2-Python-environment)\n",
       "- [3 Pearson and Spearman correlation](#3-Pearson-and-Spearman-correlation)\n",
       "- [4 One mean](#4-One-mean)\n",
       "  - [4.1 One sample t-test and Wilcoxon signed-rank](#4.1-One-sample-t-test-and-Wilcoxon-signed-rank)\n",
       "  - [4.2 Paired samples t-test and Wilcoxon matched pairs](#4.2-Paired-samples-t-test-and-Wilcoxon-matched-pairs)\n",
       "- [5 Two means](#5-Two-means)\n",
       "  - [5.1 Independent t-test and Mann-Whitney U](#5.1-Independent-t-test-and-Mann-Whitney-U)\n",
       "  - [5.2 Welch’s t-test](#5.2-Welch’s-t-test)\n",
       "- [6 Three or more means](#6-Three-or-more-means)\n",
       "  - [6.1 One-way ANOVA and Kruskal-Wallis](#6.1-One-way-ANOVA-and-Kruskal-Wallis)\n",
       "  - [6.2 Two-way ANOVA](#6.2-Two-way-ANOVA)\n",
       "- [7 Proportions: Chi-square is a log-linear model](#7-Proportions:-Chi-square-is-a-log-linear-model)\n",
       "  - [7.1 Goodness of fit](#7.1-Goodness-of-fit)\n",
       "  - [7.2 Contingency tables](#7.2-Contingency-tables)\n",
       "- [8 Sources and further equivalences](#8-Sources-and-further-equivalences)\n",
       "- [9 Teaching materials and a course outline](#9-Teaching-materials-and-a-course-outline)\n",
       "- [10 Limitations](#10-Limitations)\n",
       "- [11 License](#11-License)"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from datetime import datetime\n",
    "from IPython.display import display, Markdown\n",
    "from tests_as_linear.utils import generate_toc\n",
    "display(Markdown(\"Last updated: {}\".format(datetime.now().strftime(\"%B %d, %Y\"))))\n",
    "display(Markdown(generate_toc()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This document is summarised in the table below. It shows the linear models underlying common parametric and \"non-parametric\" tests. Formulating all the tests in the same language highlights the many similarities between them. Get it [as an image](cheatsheets/linear_tests_cheat_sheet.png) or [as a PDF](cheatsheets/linear_tests_cheat_sheet.pdf).\n",
    "\n",
    "---\n",
    "\n",
    "[![Cheatsheet](cheatsheets/linear_tests_cheat_sheet.png)](cheatsheets/linear_tests_cheat_sheet.pdf)\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1 The simplicity underlying common tests\n",
    "\n",
    "Most of the common statistical models (t-test, correlation, ANOVA, chi-square, etc.) are special cases of linear models, or a very close approximation. This beautiful simplicity means that there is less to learn. In particular, it all comes down to $y = a \\cdot x + b$ which most students know from high school. Unfortunately, introductory statistics courses are usually taught as if each test is an independent tool, needlessly making life more complicated for students and teachers alike. \n",
    "\n",
    "This needless complexity multiplies when students try to rote learn the parametric assumptions underlying each test separately rather than deducing them from the linear model.\n",
    "\n",
    "For this reason, I think that teaching linear models first and foremost and *then* name-dropping the special cases along the way makes for an excellent teaching strategy, emphasizing *understanding* over rote learning. Since linear models are the same across frequentist, Bayesian, and permutation-based inferences, I'd argue that it's better to start with modeling than p-values, type-1 errors, Bayes factors, or other inferences.\n",
    "\n",
    "Concerning the teaching of *\"non-parametric\"* tests in intro-courses, I think that we can justify [lying-to-children](https://en.wikipedia.org/wiki/Lie-to-children) and teach \"non-parametric\"\" tests as if they are merely ranked versions of the corresponding parametric tests. It is much better for students to think \"ranks!\" than to believe that you can magically throw away assumptions. Indeed, the Bayesian equivalents of \"non-parametric\"\" tests implemented in [JASP](https://jasp-stats.org) [literally just do (latent) ranking](https://arxiv.org/abs/1712.06941) and that's it. For the frequentist \"non-parametric\" tests considered here, this approach is highly accurate for N > 15.\n",
    "\n",
    "Use the table of contents (above) to jump to your favourite section. There are links to lots of similar (though more scattered) stuff under [sources](#links) and [teaching materials](#course). I hope that you will join in suggesting improvements or submitting improvements yourself in [the Github repo for this page](https://github.com/eigenfoo/tests-as-linear) or [the repo for the original post (in R)](https://github.com/lindeloev/tests-as-linear). Let's make it awesome!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2 Python environment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "jupyter==1.0.0\r\n",
      "matplotlib==3.1.0\r\n",
      "numpy==1.16.4\r\n",
      "pandas==0.24.2\r\n",
      "patsy==0.5.1\r\n",
      "scipy==1.3.0\r\n",
      "statsmodels==0.10.0\r\n"
     ]
    }
   ],
   "source": [
    "!cat requirements.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import patsy\n",
    "import scipy\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf\n",
    "# See GitHub repo for supporting Python code.\n",
    "from tests_as_linear import plots, utils\n",
    "\n",
    "np.random.seed(1618)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3 Pearson and Spearman correlation\n",
    "\n",
    "### 3.0.1 Theory: As linear models \n",
    "\n",
    "**Model:** the recipe for $y$ is a slope ($\\beta_1$) times $x$ plus an intercept ($\\beta_0$, aka a straight line).\n",
    "\n",
    "$y = \\beta_0 + \\beta_1 x \\qquad \\mathcal{H}_0: \\beta_1 = 0$\n",
    "\n",
    "... which is a math-y way of writing the good old $y = ax + b$ (here ordered as $y = b + ax$). Using `patsy` lets us be a bit lazier and write `y ~ 1 + x` which reads like `y = 1 * number + x * othernumber`, and the task of linear models is simply to find the numbers that best predict `y`.\n",
    "\n",
    "Either way you write it, it's an intercept ($\\beta_0$) and a slope ($\\beta_1$) yielding a straight line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots.linear_regression_plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is often simply called a *regression* model which can be extended to *multiple regression* where there are several $\\beta$s and on the right-hand side multiplied with the predictors. Everything below, from [one-sample t-test](#4.1-One-sample-t-test-and-Wilcoxon-signed-rank) to [two-way ANOVA](#6.2-Two-way-ANOVA) are just special cases of this system. Nothing more, nothing less.\n",
    "\n",
    "As the name implies, the *Spearman rank correlation* is a *Pearson correlation* on rank-transformed $x$ and $y$:\n",
    "\n",
    "$\\text{rank}(y) = \\beta_0 + \\beta_1 \\cdot \\text{rank}(x) \\qquad \\mathcal{H}_0: \\beta_1 = 0$\n",
    "\n",
    "I'll introduce [ranks](#3.0.2-Theory:-rank-transformation) in a minute. For now, notice that the correlation coefficient of the linear model is identical to a \"real\" Pearson correlation, but p-values are an approximation which is is [appropriate for samples greater than N = 10 and almost perfect when N > 20](https://lindeloev.github.io/tests-as-linear/simulations/simulate_spearman.html).\n",
    "\n",
    "Such a nice and non-mysterious equivalence that many students are left unaware of! Visualizing them side by side including data labels, we see this rank-transformation in action:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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rKyvL+VeuXOHGjRsYDAaysrI4cuSI5byyyufl5REfH09ubq6ljtzcXMxmM6dPn7ZMLy5sR2E5a2vravu3vBeV9XNQl8k1kGsAd34NCgOHAOfPn2fIkCGA9nvr8OHDNGnSxDIz6sEHH6R58+bY2Njw2WefAeDv74+qqpZAYqtWrSz1mUwmrl27xueff47ZbKZVq1ZcvHiRpk2bEh0dzZ49e7Czs6Nnz54YDAbMZjMpKSlcuXKF1NTUarsGtY0ECUo4d+4cWVlZ7Nq1iyFDhhATE8Pq1av59NNPiYqKwt3dHYAGDRpw/fr1UuVbtGjB1atXi61zuVNWVlbk5eUB0LNnTz799FPOnDlD69at2blzJy+99BIffPBBsTI9evRg8eLFXL58GXd3d7777juioqL4+9//Xmb5nTu1sdSpU6c4deoU7dq14/vvvycgIMDyQVy0HaD9Zx08eHCF+iKEEHXW1aswcSL88gv87W/w3ns13SJRQFXVPEVRlgNjgUeBoaqqFkbabwIPlFWusu7u347BYKiU9zp9+jQ5OTlcunTJMhb59ddfLWORNm3a4Ovri6OjI7/++mup92zWrBnz5s3Dx8fHMhaxtbXF29sbX19fbty4gZ2dnaVc0edWVla0atUKd3d3rK2t+eGHH7C1tS01FilaXq/XM3PmTBo3bkxqairR0dGWsUhZ5Xfu3ElGRgZxcXHodDratWvH119/TUBAAN26dQMo1g7QUqINHjy42v4t70Vl/RzUZXIN5BrAnV8DLy8v4uPjAS0wkJycjKenJ7a2trz++utllimrXldXV5KTk0u95ufnV2YdnTt3LnUsNjaWgIAA2rdvf9t234na/nNw8ODBMo9LkKCEkydP0rp1a95//33++c9/4uXlxbx58+jUqRMnTpwgPT0dgJs3b/LAA6XHIg0bNqRLly5ERUXRv3//Cr330KFDmTx5Ml988QVt27blrbfe4sUXX8RsNmNtbc3ChQtLzVJQFIW5c+cya9YsAJo0acI777yDh4dHmeUdC3ZUcnNz4+OPPyYpKQlXV1fmz59fZju8vb05fPgwoaGhFeqLEELUSQYDjB4NCQnaLnbTp9d0i0QJqqo+qSjKy0A0UHR+aQO02QV1Xl0ei2RnZ9O8eXMZiwgh7lhoaKhlTwKAyMhIhg0bVuE9SBwcHOjUqdNdt8NsNnP8+PFSM8XvS2azuUr+HDhwwFzTTp48WeEy7733nnnRokXl1jd37lyz2Ww2L1y40Lxp06Yyzzt48KD5qaeeqvB736m76VdRUVFR5hEjRtzRuWvWrDG/99579/R+FXGvfautpF91i/Srbqm0fm3aZDY3aGA2e3iYzXv3Vk6d5Sj4jKyyz+D6+Kdt27ZPtG3b9pWCxw3btm17rm3bttvbtm07oODYorZt204sWa46xyOV9bNYF8Yi5bnTa1CbxyL3qr7+rq0IuQZyDczmil2DlStXmlu2bGnW6XTmli1bmleuXFmFLas+tf3noLzxiL6mgxS1jcFgKLW2r5Cvry+NGzdm8uTJxMbGMmzYsDLPCwgIoFWrVuzatasqm1rl0tPT2bx5M88//3xNN0UIIaqO2Qzvv6/NIHjwQdi/H3r1qulWidLWAp0VRdkF/Az8FZgDvKkoyj7AFlhdg+2rNDIW+R8ZiwhxfwgODiYuLg6TyURcXBzBwcE13aT7miw3KOHUqVPFNrso6eWXX76jegpz/NZGPXr0YPPmzbc9z9nZmbB7TRothBC1WWYmzJoF33yj7UMQFsYtE92LGqOqagYwoYyXKjafvg6Qscj/yFhECCGqnwQJSoiKiqrpJgghhKgOSUnwyCNw8CCEhsIrr0CRbDFC1BQZiwghhKhJEiQQQghx/4mO1gIE6emwfr221EAIIYQQQkiQQAghxH1mxQqYPRuaNdPSHJaTGkkIIYQQ4l4ZjUYiIiIYNWoUJ0+eZO/evQD4+/vTs2dPzGYzW7Zs4dKlS1hZWTF69GhcXV3LrCs/P5+NGzeSlpZGXl4e/fr1Q1EULly4wObNm7G2tsbDw4OgoCDy8vLYsmULY8aMQVfBmZKycaEQQoj7Q34+vPQSPPkk9O4Nv/8uAQIhhBBCVKkdO3bQvXt3TCYTERERPPHEE8ycOZMDBw5gNBo5deoUeXl5zJw5kyFDhrBt27Zy6zp27BgODg5Mnz6dKVOm8OOPPwKwadMmhg8fzvTp07G3t+f48ePY2NjQvHlzjh49WuE2S5BACCFE/ZeWBiNHwr//Dc8/D1u3QuPGNd0qIYQQQtRjubm5JCcn4+HhgV6vZ86cOdjb25OZmYnJZMLKyoqEhATatGkDQPPmzUlOTi63Pj8/PwYOHAigpSrUa1/nb9y4QYsWLQBo0aIFCQkJlvMPHDhQ4XZLkEAIIUT9pqrQowdERMDixfDpp2BjU9OtEkIIIUQ9FR4ejre3N+PGjWPPnj2Eh4cDoNfrMRgMLFq0CG9vb2xsbMjOzsbOzs5SVqfTYTKZ/lfZ1asQHAxr12Jra4udnR3Z2dmsWrWKQYMGAeDi4kJcXBwAMTEx5ObmAuDg4IDRaCQrK6tC7ZcggRBCiPpr61YtQHDtmhYkeOqpmm6REEIIIeqx8PBwZs+eTXx8PI6Ojly+fJnZs2dbAgW+vr68+OKL5Ofnc/ToUezs7MjJybGULzpDgIQE6NMHVq8GFxcArl+/zvLly+nYsSP+/v4AjBkzhj179rBixQqcnJxwcHCw1Ofk5ERmZmaF+iBBAiGEEPWP2awtLRgxAry9Yf9+6Nu3plslhBBCiHouJCQEo9EIQEZGBvb29hiNRt544w2WLVtGXl4eOp0OGxsbdDodLVq0IDY2FoDz58/j4eGhVXTsGAQGaimbt26FgQNJT09n5cqVDBkyhM6dO1veMzY2lnHjxjF16lSMRiOtW7e2vJaVlYWTk1OF+iDZDYQQQtQvWVnw9NNaFoPx42H5cqjgh6MQQgghxN0o3A8AtC/9Q4YMAeDMmTP4+/uzbNky9Ho9Hh4edOzYEZ1Ox9mzZ/nqq68AbVYAkZHsCQ3Fs3lz2ixZAgUzBnbv3k1mZia7du1i165dAAQHB+Pq6sqKFSuwsbHB29ubBx98ENACBPb29tja2laoDxIkEEKISlQ0zQ1oG9Z8/fXXjB49Gjc3t2Ln3rx5k3Xr1pGfn4+DgwNjx44ttiatqKysLNatW0d2djb5+fkMGzbMskFNoX379nHixAkA2rRpw4ABA7h06RIGg4EBAwZUfmdrowsXYOxYiI6GN9+EefNAL5PmhBBCCFE9vLy8iI+PByAnJ4fk5GQ8PT2xs7OjS5cudOnSpVSZkSNH/u/J99/D1Kk06dcPq08+sQQIAIKCgggKCipVXlEUFEUpdfz48eN069atwn2QkVM5EhMTmTVrFt26daNv376sWbOmppskhKgDCtPcACQnJ7N06VKuXr1a5rl79+7loYceYvr06Xh6enLo0KFy6923bx+tWrVi2rRpjBkzxpLyptC1a9c4fvw4M2bMYObMmZw9e5ZLly7h4eHBtWvXym1DvbJ/P3TtCn/8AWvXwmuvSYBA1GkyFhFCiLonNDQUR0dHy/PIyEgCAwMJDQ29feGPPoJJk6BHDzyXLKFVz5533Y7c3FwSExMt+xZUhIyeyvHCCy/Qu3dvoqKiePvtt1m4cGGFyn/44Yfs3r0bgCNHjvDEE08watQoRo4cyaxZsyzrTqKjo4tHjipRRkYGs2bNqvBulkKIu5OdnW1JcwOQl5fHxIkTS80gKPTnP/+Zjh07YjabuX79Ovb29uXWHRgYaIk8m0wmrK2LTwRr2LAhU6ZMQa/Xo9PpyM/Pt5zTvn179u/fXxldrL2++Qb69dOyFvz2mzabQIg6TsYiQghR9wQHB7N48WJatmyJTqfDzc2N8ePHExwcXH4hkwlefBH+/ndtqeS2bTzQsuU9tcPGxoZx48ah0+kqXFaCBGU4deoUaWlpTJ8+HSsrKwBcXV3vuPyRI0c4ffo0ffv2JScnh6effpp//vOfbNq0ic2bNzNq1Cieeuop8vPzq6oLgLaT5ciRI/nkk0+q9H2EuN8Vprnx8/MrlubGy8uLBx54oNxyhSluvvjiC+Li4mjVqlW559rb22NjY0N6ejrr1q1j8ODBxV63srLC0dERs9nMtm3b8PT0pHHjxgB4eHhY0uLUO/n5NPnoIy01UI8e2myCjh1rulVC3DMZiwghRN0VHBxMXFwcJ06cIC4u7tYBguxsmDwZFiyAv/xFW25wixtH1aHm9yRYsQLCwqqkai+jERwdYcYMmDr1jssdOnSIgIAATCYTJ0+e5N133+Xpp5++4/KfffYZU6ZMASAzM5ObN29adrgEGD16NM7OzmV+MH///fd8/fXX6PV63NzcePXVV2nVqhXR0dHMnz8fDw8PTp8+zQMPPMB7771H69at2bFjBwsXLiQ3Nxd7e3tefvlly26XQUFBfPjhh8ycObPcu5lCiLtXmObGaDTi7+9vSXMD3PoDoYCVlRVz5szh7NmzrF+/nmnTppV77qVLl1izZg1Dhw7F29u71Ot5eXls2LABW1tbRowYYTneoEGDCqe+qRNu3IDJk3HbsgWeeQY+/VSbSSDE3aiE8Yhl3FGeCoxHavtYJDExEXt7+1JjkZs3b9KoUSMZiwghxJ24fh0eeQR+/RXefx/mzoW7uPNf2WQmQRlOnTpFhw4dmDp1KuPHj8fBwYGhQ4dy8+ZNHn30UTp37kxMTEyZZW/cuMHBgwfp3bs3AA888ABz585l1qxZDB48mLlz57JmzRp69epVapfJffv2sWTJElasWMHGjRsZOXIkc+bMwWw2A3Dy5ElmzJjBJ598wrhx45g7dy5xcXEsWLCAxYsXs379ev71r3/x/PPPWwYCdnZ2BAQEsHPnziq8YkLcv8pLcxMSEnLbslu2bOHcuXMA2Nra3nI6WEpKCqtWrWLcuHGWHWuLMpvNfPfdd3h4eDBq1Kj/5ddF+4JQ0dQ3tV5sLPTsCT//zIXXXoOFCyVAIOqV2j4W2bRpU5ljkQULFshYRAgh7kRSkpaeec8eLVD9j3/UigAB1IaZBFOnVuguf0UkGAz4+vpWuJzBYGDMmDFMnTqV8+fP89prr/HBBx8wb948Fi9ezPz588stGx8fT5MmTYp96E6fPp3HHnuM/fv3s3//fr788ku+/PJLVq9eXazs7t27efjhhy3TCceNG0doaCjnz58HoF27dnTt2hWDwcD48eN56623+Omnn7h8+XKxu486nY6EhATatWsHaFOeC7+ICCEqV3lpbooeLyozM5ONGzcyceJEevTowebNm9m1axc6nY6HH34YgK1bt9KpUyc8PT0t5SIiIsjLy2Pr1q2Atvxg0qRJ7Nu3D1dXV0wmE3FxceTl5XH69GkABg8eTIsWLUhKSrrlUoY6Z/t2mDABrKxg2zbSPD1pWtNtEnVfJYxH7nbcUZbaPhYByhyLFKbbkrGIEKK2K5qR6vjx40RHR6PX63F3d2fEiBGYTCbWr19PWloaer2eUaNG3XI21LZt20hMTMRkMhEQEECXLl3IyMhg2bJlmM1mHBwcGD9+PDY2NmxZuZL+b72F84UL8OOPMHRoNfb89mo+SFDL5Ofnc+bMGdq3b49er8fLy4uAgABSU1OxsbG57XpAvV5fbOrewYMHOXz4MLNmzWLgwIEMHDiQF198kVGjRrF3715cXFws5xZG6Ysym83k5eUBWNYkFn3NZDIRGBjIxx9/bDl+4cIF3N3di/WporkxhRB35lZpbgoVDeI5ODgwceJEANzc3MpcXuDi4lLq/+ykSZPKfP/AwEDL43nz5pV5zokTJxg4cCAXL168oz7VWmYzfPaZtrGPry9s3AitWoHBUNMtE6JS1eWxiKEgUCJjESFEbVeYkSo3N5fIyEieffZZbGxsWLNmDTExMZbfbzNnzuTMmTPs2LGDCRMmlFnXuXPnuHbtGjNnziQvL48vvviC9u3bExMTg5+fH926dSMiIoJDhw7RIzeXHq+9RkT37ox5+WUoWJpVm8hygxLOnTtHVlYWu3btIj8/H4PBwOrVqxl7hztlt2jRgqtXr5KdnQ1omwwtXLiQAwcOWM5JSUkhMzOTtmCTeWAAACAASURBVG3bFivbp08ffvzxR0uqsjVr1tCoUSNaFuxseerUKU6dOgVo6wUDAgIYNmwYe/fu5cyZMwDs3LmT0aNHW94ftLub9eouohC1yD2luSlHu3btKrRB2a1cunQJFxeXYl8C6qTsbHjqKXjhBRg1SstgIL/XRD0lYxEhhKhaRTNSWVtbM2PGDGwKli0WZpFq3LgxJpMJs9lMdnZ2saWcJbVo0YLRo0cD2qxus9mMlZUVLi4uln2hsrOzsTp2DIYMwc3Ghit9+2JUlKrv7F2QmQQlnDx5ktatW/P+++/zz3/+Ey8vL+bNm0enTp3uqHzDhg3p0qULUVFR9O/fn1atWvGf//yHBQsWcPHiRezs7GjQoAFvvfUWPj4+pKSkWMr27t2badOm8eSTT2IymXB1deW///2v5QfSzc2Njz/+mDNnzvCnP/2J+fPn07x5c9566y1efPFFzGYz1tbWLFy40PKlJScnh8OHD9/TFxYhRPkKNycMCQkhISHhztLc3MatMiJUlIeHhyUlY5116RKMG6cFBl59Fd54A27xQS1EXVcXxiJJSUm4urqWGotkZWXh5OQkYxEhRK0UHh5OSEgI1tbW9OrVCycnJ4KDg3F2dga0lLA5OTn4+Phw48YN0tLS+PzzzzEajUyePLnceq2trbG2tiY/P5/169cTEBCAra0tDg4O7N+/nz/++IO81FQGvPeeNnNg0ybc9u4lMTERpRYGCiRIUILBYGDkyJEV2kG4pDlz5rBo0SL69+8PQM+ePenZs2eZ5xauSS4UHBxc7pcLZ2dnFi1aZJnKVygoKIigoKAyyxSmOWrYsOHddkcIcRu3+n8r7tGhQzBmDKSmwg8/wGOP1XSLhKhydWEsUlLhWKTkGAVkLCKEqB1ulZFq8uTJbN++ndTUVCZMmIBOpyMqKorWrVszZMgQrl+/zooVK3j22Wexti77K3RmZiarVq2iZcuW9O3bF4CjR48yZvRo2oSFEbNmDeuffprJb78Njo44OzsXyzpTm8itmBIMBgOtW7cu9/WnnnqKPXv28Oqrr7J27doyzwkICKBVq1bs2rWrqpp5R9LT09m8eTPPP/98jbZDCCHuyg8/QJ8+2k6/e/dKgEDcN2QsIoQQle9WGak2bdpEXl4ekyZNsiw7sLe3x97eHtD2lMrPz8dkMpVZd25uLitWrKBTp06W4CyArbU19vPnw3vv0WDoUDLbt7ekyq3N2adkJkEJp06duuWauS+//PKO6nnllVcqq0lA6Sj/nXB2dibsHnM+CyFEtTOZ4LXXIDQUeveGNWugri+ZEKICZCwihBCVr7yMVIVLolq2bMny5csB7fddYGAgGzZsYOnSpeTn5zN48GBsbW05cuQIQLElYAcOHODatWscOnSIQ4cOATBmyBAe3riRiKZNMb/xBmYvLx4ePtxS5uLFiwytZVkNCkmQoISoqKiaboIQQty/bt6EJ56ADRtg5kz4z3+gSKYIIe4HMhYRQojKV15GKltbW15//fUyyzxWxizGpk2bkpycXOxYYGBgsYxTXLwIDz9Mo2PHeHLxYpgxo9j5KSkpuLu7F8uGVZvIcgMhhBC1w9mzEBgImzfDp5/Cl19KgEAIIYQQlaKyMlI5ODjceiPZmBhtPKOqJH7+eakAAWgbJA4cOLBC71ud7momgaIoNkAY4A3YAW+rqrqxEtslhBDifhIZCY8+CmYzbN0KBVMAhRBCCCEqQ2VlpLrlJqxRUTBypJaF6ddfySjImlDSyJEjK/Se1e1uZxJMAVJVVe0LDAc+r7wmCSGEuG+YzfDFFzB0KHh6wu+/S4BACCGEEFUiODiYuLg4TCYTcXFxlZudatMmGDQIGjXS0jZ361Z5dVezu92TYBWwuuCxDsgr6ySDwXCX1VeOrKysGm9DVaiv/YL62zfpV90i/aomOTl4vvMOLj/8wM0BA0iePx9Tbi5UsI21rl9CCCGEuL8sXgzPPgsBAbBlC7i713SL7sldBQlUVU0HUBSlAVqwYF5Z55XMk1vdysrVWx/U135B/e2b9KtukX5Vg5QUGD8edu+GV16hwb/+hWJldVdV1ap+3aGDBw/WdBOEEEIIca/MZnjjDXjrLQgK0tI3l7PEoC656+wGiqK0ANYBX6iq+k3lNUkIIUS9dvQojBkDly7BN9/A44/XdIuEEEIIISomLw+eeQa++gqmT4f//hdsbGq6VZXibjcu9AC2AX9RVTWicpskhBCi3lqzBqZOBRcXbRZB16413SIhhBBC1HFGo5GIiAhGjRrF8ePHiY6ORq/X4+7uzogRIzh69ChHjhwBIC8vj4sXL/LSSy9hb29fqq78/Hw2btxIWloaeXl59OvXD0VRWL16Nenp6QCkXbtG83PnGLN8OVtee40xr7+OTl9/Egfe7UyC/wNcgFcVRXm14FiQqqqZldMsIYQQ9YrJpE3Fe/NN6NkT1q6Fpk1rulVCCCGEqAd27NhB9+7dyc3NJTIykmeffRYbGxvWrFlDTEwMnTp1sqQt3LJlC507dy4zQABw7NgxHBwcGDt2LJmZmSxatAhFUXj00UcByExMZPmCBfx5+XJsPvuM5l27cvTYsVunRaxj7nZPgheAFyq5LUIIIeqj9HR48kktMDBtGixcCOV8MAshhBBCVER2djbJycl4eHhgNpuZMWMGNgXT/k0mE9bW//vKm5ycTEpKCiNGjCi3Pj8/P9q3bw+A2WxGX3SGwJkz/DpvHt3PnqXBihUwZgx+mZmEh4fXqyBB/ZkTIYQQovaJi4PevWH9evjoIwgLkwCBEEIIIe5ZeHg43t7e+Pn5sWfPHsLDw9HpdDgXbBwYHR1NTk4OPj4+ljK7d++mf//+t6zX1tYWOzs7srOzWbVqFYMGDdJeOHCAjMGDOdekCZ0WLND2VwIcHBwwGo1kZWVVTUdrgAQJhBBCVI1du7QcwfHx8OOP8Le/gU5X060SQgghRB0XHh7O7NmziY+Px9HRkcuXLzN79mzCw8Mxm81s27aNs2fPMmHCBHQFY4+srCxSU1Np1arVbeu/fv06y5cvp2PHjvj7+8NPP8GAAZxs144OAwag79Wr2PlOTk5kZtaflfd3nd1ACCGEKNfixTBnDrRuDRs3Qtu2Nd0iIYQQQtQTISEhGI1GADIyMrC3t8doNBISEkKDBg2wtrZm0qRJlgABQHx8/B0FCNLT01m5ciVBQUHaLIRly2DWLPD35+zjj9MvMLBUmaysLJycnCqtfzVNZhIIIYSoPLm58Je/wNNPw9ChEB0tAQIhhBBCVKqEhATL4/Pnz+Ph4QFATk4Ohw8f5vLlyyxfvpxly5ZhMBgAuHLlCi4uLsXq2bNnD6dPny52bPfu3WRmZrJr1y6Wvfkmy3buJHfwYNi5k9SMjFJ1ZGVlYW9vj62tbVV0tUbITAIhhBCV48oVmDABIiNh7lx4912wsqrpVgkhhBCinvHy8iI+Ph7QAgPJycl4enpia2vL66+/XmaZ3r17lzrWpEkTrEqMVYKCgggaNgyef17bbDk4GDZtAltbnnvuuVJ1HD9+nG7dulVCr2oPmUkghBDi3v3xB3TvDr/9BitWwPz5EiAQQgghRJUIDQ3F0dHR8jwyMpLAwEBCQ0MrVI+np2fpJQiZmfDoo1qA4B//0MY15cwSyM3NJTExUdu3oB6RIIEQQoh7s2EDBAZCVpa2WeETT9R0i4QQQghRjwUHB7N48WJatmyJTqfDzc2N8ePHExwcXKF6HnjggeIHUlNhyBBtbPPJJ/D++6Av/yuzjY0N48aNK7b3QX0gyw2EEELcHbMZ3nkH5s3TshisWwfNmtV0q4QQQghxHwgODq5wUOCW4uJg+HDt7x9+0GYT3KckSCCEEKLijEaYPl37EJ0yRctm4OBQ060qxmg0EhERwahRozh58iR79+4FwN/fn549e5ZZJioqivT0dIYMGXLb+g0GAydPnmT8+PGlXouNjWXnzp0ANG3alIcffpjLly9jMBgYMGDA3XdKCCGEEJXvyBEICtJmRW7bBv361XSLapQsNxBCCFExiYnQpw+sWqXtPbBiRa0LEADs2LGD7t27YzKZiIiI4IknnmDmzJkcOHDAkjapUG5uLmvXrmX//v13VPdPP/1EREQEZrO51GvZ2dls376dyZMnM2vWLBo1aoTRaMTDw4Nr165x9erVSumfEEIIISpBRIQWFLC2hj177vsAAchMAiGEEBWxdy+MG6dF2jdvhocfrukWlSk7O5vk5GRLSqQ5c+ag1+vJyMjAZDKV2sk4Ly+Phx56CB8fH65cuXLb+lu0aEG7du04ePBgqdcSExPx8PBg27ZtXLt2jc6dO1tyJ7dv3579+/fj5uZWCb0UQghRXYrOTgMtuPz1118zevRo3NzcyMvLY8OGDVy7dg07OzsURSm3rvz8fDZu3EhaWhp5eXn069cPRVHIyMhg06ZNZGZmYjabeeSRR3BxcWHDhg2MGDECGxub6uru/SM8XJsZqSjw00/QvHlNt6hWkJkEQggh7kxYGAwcCA0bQlRUrQwQhIeH4+3tjZ+fH3v27CE8PBwAvV6PwWBg0aJFeHt7lxpoOTg40Lp16zt+nw4dOpS7SZHRaOTcuXMMGTKE4OBgoqOjSU1NBcDDw4O4uLi765wQQogaUzg7DSA5OZmlS5cWmxl26NAhbG1tmTVrFkFBQRw6dKjcuo4dO4aDgwPTp09nypQp/PjjjwBs374df39/pk+fzsCBA7ly5Qo6nY4OHTpYlsyJSmI2wwcfaEsme/WC3bslQFCEBAmEEKIWMRqNbNq0yfI8NzeXsLCwMu9u5+TksG7dOpYuXcqSJUtISkq6bf0Gg4E1a9aU+VpsbCxLlixhyZIlbNmyBbPZzKVLl/h1xw74619h5kwYMAB+/x18fe+6j1UlPDyc2bNnEx8fj6OjI5cvX2b27NmWQIGvry8vvvgi+fn5HD16tMra4ejoSLNmzXB2dsbW1hYvLy8uXrwIQIMGDcjMzKyy9xZCCFH5Ss5Oy8vLY+LEicVmhaWkpNCmTRsA3NzcuHnzZrn1+fn5MXDgQADMZjP6gt3zExMTuXHjBitWrOD48eN4e3sD4OPjw8mTJ8tc4ibugskEf/ublt7wscdg61Zo1KimW1WrSJBACCFqkdvdqSjqt99+w93dnenTpzNq1KjbTpM/fPhwxdfR29hwbc0arq5YoX2g/vgjuLjce0erQEhIiGWvgYyMDOzt7TEajbzxxhssW7aMvLw8dDodNjY2VZqqqGnTply+fBmj0YjJZCIpKYkmTZoAkJmZaVl6IIQQom44f/58sYCAl5dXqdR5np6exMTEYDabOX/+PJmZmZhMpjLrs7W1xc7OjuzsbFatWsWgQYMASEtLw97enqlTp/LAAw9YZg/o9XqcnJy4fPlyFfXwPpKVBZMmaekN//pX+O47sLev6VbVOhIkEEKIKnanswOK3qmIi4sjPDy81J2Kos6cOYOVlRWLFi3im2++sdzBKOqnn35i8eLFLFu2jIsXLzJ06FBu3rxZahpk0XX0S5cuxcnJCaf4eOjenfa//sr+efPgo4+0TX1qqYSEBMvj8+fPW+74nDlzBn9/f5YtW0ZYWBg6nY6OHTuSmZnJ999/f8s6t27dapkFcDv79u1DVVWcnJwYPHgwK1euZMmSJbRr1w53d3cAkpKSaNWq1V32UAghRHUqXMI2duxYvv32W8vMtLJ07twZOzs7li5disFgwMXFxTJDoCzXr19n+fLldOzYEX9/f0Bb+la4l0Hbtm1JTk62nO/s7Fxq011RQWlpWorDVavgww9hwQK4xb/R/az2jvaEEKKeKDk7YPPmzdy4ccPyenh4OCEhIVhbW9OrVy9sbW2xt7dHp9OVulNRlNFo5Pjx4+Tl5dGgQQO2bdvG2LFji51z4cIFpkyZgqOjIwaDATs7Oxo0aIDBYMDPzw87OztLXefOneOZZ57B1taWpR9/TIv//IfG2dl4/Pe//Hr6dBVcmcrl5eVFfHw8oC3FSE5OxtPTEzs7O7p06UKXLl2Kne/g4MDEiROLHevUqVOx5y4uLtja2pb5ft7e3papoACBgYGWxx06dKBDhw6lypw4cYKBAwdy9uzZCvVNCCFE9SpcwmY0GvHx8SE3N5fZs2cDEBwcXOr8pKQkfHx8GD58OMnJySQmJpZbd3p6OitXriQoKAgfHx/LcS8vL2JjY3nooYeIj4+3zEIDyMrKkplo9yIxUUtxGBMD33wDjz9e0y2q1SR0IoQQVeh26xhLrqNPSUlhx44dZGdn37ZuBwcH2rVrx4gRI2jQoEGxOw6grXO8evUqmzZtIiwsrNgX0zZt2nDkyBHLc8s6eicnbBcswOvXX7nYsSPs30+DAQPqxDr60NBQHB0dLc8jIyMJDAwkNDT0ruts164drq6uldE8Ll26hIuLCy61dLmGEEKI/ym6hK1wdprRaCQkJKTM8xs3bkxUVBRfffUVkZGRlqDznj17OF0i0L57924yMzPZtWsXy5YtY9myZeTm5jJs2DCOHTvGV199xZkzZ+jbty+gfZ7fuHGjWNBAVMAff0BgICQkaPsPSIDgtmQmgRBCVKGy1jEWVXIdfZs2bdi8eTO7du3iL3/5yy3r9vLywmQyodPpyMjIsExpL5STk0P37t0JDAzEZDLx3//+l6ZNmwLaLvvR0dH06NEDKFhHf+kSxqlTsf/mG5LmzqXLs89CixZkpqfXibsXhXd2QkJCSEhIwM3NjfHjx5d5x+dO3WomR0V5eHhYgkVCCCFqt6JL2IrOTit6fNq0aZbHjo6OTJ061fLcYDAA0KRJk1Jpd4OCgggKCir1no0aNeKJJ54odfz06dP4+flV6X469dbOnTBmDDg6ahkMHnqopltUJ0iQQAhR6YrmElZVlV27dqHX6+nUqVOpKd+Ftm7dipubG127dr1t/VFRUaSnpzNkyJBSr3333XcYjUb0ej02NjYEBwdz4MABXF1di03pq2qFSwgaNmyIoihkZmaW+WW16GAjLS2NRo0aMWDAAEDb5G716tXFzs/MzGTjxo1MnDiRvn37snHjRk6cOEFGRgbjxo0DtGvZqVMn3N3d6dGjhyXdn7u7u2UTxMJd9vft24erqyuKszODIyNZ6ekJr71G+8GDcW/ZEqhb6+iDg4PvKSgghBBCQPElbKDNThs0aBDHjh2rUD2enp73FHA2m80cP36ckSNH3nUd961Vq7QUhz4+2gyCgnGNuD0JEgghKl3hGvz8/Hx+/vlnnnrqKWxtbQkLC0NRFJydnS3nZmRksH79elJTU8vdoK9Qbm4umzZtIikpCd9yUvClpqby3HPPFYu2BwQE8PXXX+Pt7X3LTYQqS0XWMRYdhFy9epUjR45w4MAB7Ozs8PPz49FHHy12ftF19IWP4+LiOHDgAI0K0vcUrqNPTU1l9erVPP3005jNZq5cucKgQYNwd3fn/PnzODk5aevoo6NhwAA6pKfTITwcRo8u9p6F6+irQ9EA0/Hjx4mOjkav1+Pu7s6IESOK/bsWbipYWMbe3p5Zs2bdsv5bBZhA+xn76quvGDJkCG3atCE2NpabN28SEBBQqf0UQghRu4WGhlo+y0Ebr0RERLB48eIK1XOvM9J0Op3lJoCogE8/1bIXBAbCpk1QSUsH7xeyJ4EQolIVXYN/5coVXF1dcXBwwMrKihYtWhSLyoM2ha9///507NjxtnXn5eXx0EMPWdbolZSenk5WVhbffvstYWFhxMTEAFrqIE9PT2JjY++9g3egIusYQ0NDcXV1tXzxL28dfUV22c/IyCAlJYUmTZrQsWNHvvrqK5YtW0bLli1L77K/YgX0769Nw4uKKhUgqO519IUBptzcXCIjI3nyySeZMWMG2dnZln/PQsOHD2fatGn0798fe3t7Ro0aVW69ubm5rF27lv3799/y/X/88cdigYgHH3wQg8FwR3tECCGEqD+Cg4NZvHgxLVu2RKfT0bJlSxYvXiyz1Wo7kwn+8Q944QVtmcEvv0iA4C7ITAIhRKUouUO/k5MTffv2xb5I7tnCnMBFFX4BLbmpT1kcHBxo3bp1sQ33isrPzycwMJCePXuSmZlJWFgYzZo1w8nJyZJWsDC1UFWqyDrGouvodTpduevoK7LLfmG+ZYDevXvTu3dv4H/rIwFiY2J47OhR+Pe/YdAg+OEHaNy4VN3VuY6+aIDJbDYzY8YMy1IJk8mEdTnpF2NjY/Hx8bllOwsDTD4+PqVSTxb67bffaN68OWazudjxwk0eC/dvEEIIcX+QJWx1TE4OzJgB4eHw3HPabIIS+0GIOyMzCYQQ96zkDv2XL19m9uzZ/PLLL8WCAtnZ2cWCBpXN2dmZrl27otfrcXJywtPT0/KFsHANfnUouTlhZGQk3bp1K3W8UHBwMHFxcZhMJuLi4sockFTmLvsxhw/j+8sv2P373/D889o6vTICBNWlMA+1n58fe/bsITw8HJ1OZ1mWEh0dTU5OTpl7SuTn53P27Fl69ep1y/coDDCV5+zZs6Smppa5Z0ZhgEkIIYQQtdSNG/Dww1qA4J134PPPJUBwDyRIIIS4ZyV36Le3t8doNPKvf/2Lq1evkpmZSX5+PgkJCTRv3rzK2nH27FlWrVoFaHfwL1++bEkXlJmZWSw9XlUqmYqvcB3jvaTiq7Rd9lWVtpMm0eXbb2HxYi3KXnC3viaUF2AKDw/HbDazbds2zp49y4QJE8rc1fns2bO4ubndc/Dp8OHDpKSksGzZMk6fPs327dstyzuqM8AkhBBCiApKToZ+/bRMBsuWwSuvgGSCuCey3EAIcc+KTqM/f/68ZVO4+Ph4hg0bxsqVKzGbzXTq1ImGDRuSkpLC77//zogRI8qtc/Xq1QwfPrzYJofl2b59O+3bt+fBBx/kzJkzLFmyBJ1Ox+DBgy1f1pOSkm55J7kylUzF5+XlRWhoaI1PWXTavVtbp2drCxERUM7eDtWpvABTSEgIDRo0wNramkmTJpWb9uns2bOWtI73Yvz48ZbH69evp0OHDnh6egJagKkupIAUQggh7junTsHw4XDlirZB4fDhVfp2t9tgOT8/nw0bNnDt2jXs7Oxuucw1Pz+fjRs3kpaWRl5eHv369UNRFC5cuMC3335rmUHatWtXFEVhy5YtjBkzplpSYUqQQAhxz4ru0F90DX7hL8eSvyCbNGlSKkBQmPav0K3W4Hfq1KnY86FDh1oeDy/jw8FkMnHx4sVi51W1WrWO0WyGjz6ixT/+Af7+sGFDrUkDVF6AKScnh8OHD9OyZUuWL18OQI8ePfD29rakgAQtm0XR/Rjg7gJMzZo1K/ecupQCUgghhLhv/PYbjBoF1tbaLIJy0mxXppIbLD/77LPY2NiwZs0aYmJiuH79Ora2tsyaNYsrV66wevVqunfvXmZdx44dw8HBgbFjx5KZmcmiRYssQYKePXuWWkrZvHlzjh49WmocXBUkSCCEuGcl0wRFRkYybNiwYndnK6pr167lBgkq6uDBg/Tp06da0h/WOllZ8PTTsGIFN4cNo+HatVCL7oqXF2CytbXl9ddfL7NMYYAAYPLkycU2ZIS7DzAVeuSRR4o9j42N5bHHHrt9Z4QQQghRPdavh8cfh+bN4eefoYx9iyrbnWywnJKSQps2bQBwc3Pj5s2b5dbn5+dH+/btATCbzZZxanJyMqmpqaiqiqurK8OHD7ekxg4PD5cggRCibig5vb68HforotLW4APdunWrtLrqlAsXYOxYiI6GN98kafx4GtaiAAHU/gBTTEwMvr6+2NnZVUp94u4pimIDhAHegB3wNpAIbAYK85suVFX1+xppoBBCiOqxaBHMmQNdu8LmzVCw/1RVKSuDV3BwcJkbLKelpRETE0O7du1ISkoiMzMTk8lU5o2qwrFKdnY2q1atsmSnatasGQEBAfzpT39i165d7Ny5k2HDhuHg4IDRaCQrK6tKNwIHCRIIISpJrZpeL2D/fnjkEbh+Hdau1YIFJe641wa1PcDUtm3bSqtL3LMpQKqqqk8oiuIKHAHeAj5SVfXfNds0IYQQVc5shldfhdBQGDECvv++ymdHFm6wbDQa8ff3t2ywDNpsxu3bt5OammrZYLlz586kpKSwdOlSWrRogYuLyy1nsl6/fp3vv/+ebt264e/vD4Cvr68lCODr68tPP/1kOd/JyYnMzEwJEgghhKigb76BmTPBw0Nbr9exY0236JYkwCTu0CpgdcFjHZAHdAEURVHGoM0m+KuqquXP7RRCCFE35ebC7Nla9oJZs2DhQm0vgipW0Q2Wk5KS8PHxYfjw4SQnJ5OYmFhu3enp6axcuZKgoKBiaZ4LjzVr1qzUBs1ZWVnVspmyBAmEEKK+yM+HkBB4/33o3x9WraryKXhCVBdVVdMBFEVpgBYsmIe27GCJqqoHFUUJAV4HXipZtuS+FVUlKyur2t6rtpJrINcA5BqAXAOovGugy8ig+d/+hvOePaTMmcOV556D2NjbF6wEt9tguUmTJixcuBCABx98kCZNmrBv3z62bduGjY0NHTt2xGAwYDAYaNSoUbEv/IcPHyY9PZ2tW7dajvXt25f27duzbt069Ho99vb2dO3aFYPBQE5ODmazmTNnzlR5vyVIIIQQ9cGNGzB5MmzZAs88A59+CgWb6QhRXyiK0gJYB3yhquo3iqI0UlU1reDldcBnZZXz9fWtlvYZDIZqe6/aSq6BXAOQawByDaCSrsGlS/DEE3D4MCxeTJOnnqI6b3/czQbLRTcWLLwGer0eW1vbYtmSbnVtSmY2ANi/fz/9+vWr1J+rgwcPlnn8PtzqWwgh6pnYWOjZU9vd94svtCl4EiAQ9YyiKB7ANuBlVVXDCg7/rChKYW6pwUDZox0hhBB1T2ws9OoFJ09q6ZufeqramxAaGoqjo6PleWRkJIGBgYSGhlaoHk9Pz3tKp5ybm0tiWrPMrQAAIABJREFUYqJl34KqJjMJhBCiLtu+HSZMACsr7fGAATXdIiGqyv8BLsCriqK8WnDsRWCBoii5wEVgdk01Tggh/j979x4XdZU/fvw13BHQVFC8IIToRIQSXrG8RF5CULylFraKlltbfdva9hZ9t/1W9NtrPbbdLsuuipepLE284AUDFLHWvICXNAQREPGOF2SGGZiZ3x8jn2VgQBGQ2/v5eOxjh8/nzPmcM2rz4f055/0Wzej77y3JCc1mSE+HUaNaZRjNlWC5qUmVHR0dmTVrVpP6aAwJEgghRHtkNsPf/w6vvQaBgbBpEzQhQi1EW5eTk/MK8IqNU4/c67EIIYRoQcnJlgcgvXvD9u3QypWGOmOCZdluIIQQ7Y1eb8ns+8orMG2apYKBBAiEEEII0d4tWwbR0fDAA5b7GylF3CokSCCEEO3JhQsQHg7Ll1tqBa9fDx4erT0qIYQQQoi7ZzbD229bHoJMnAi7doG3d2uPqtOS7QZCCNFeHDpkia5fuQJffglPPtnaIxJCCCFEJ6HVaklNTWXatGkcPXqUffv2YWdnR69evYiMjESlUgFQXl5OQkKCzQz9NaWkpHDmzBlMRiOhx48z7G9/g5/8BP79bwrOnmXDv//Nq6++CkBycjLjx4/H3d29xecpZCWBEEK0D2vXwqOPgkoFe/dKgEAIIYQQ91RaWhojR46ksrKS9PR0Fi5cyOLFi9Hr9Zw8eRIAo9HIli1bcHBo+Fn06dOnuXr1KkueeorY5GT2ms3o3ngDEhO5rtXyn//8B6PRqLQfNWoUqampLTo/8V8SJBBCiLbMZII334T58yE0FPbvh4cfbu1RCSGEEKIT0ev1lJSU0Lt3bxwcHFi8eDGOt8otm0wmJSiQkpLCsGHD8LjNVkgfHx+mP/IIhIejSk7G7OmJ/VtvUWU0kpyczNSpU63ae3p6cvnyZbRabctMUFiRIIEQQrRVZWUwaxbEx8OSJZCWZsn0K4QQQghxDxUXF+Pp6QmASqVSlv3v27cPg8GAv78/2dnZuLm5ERAQcNv+HM6cwTU8HOORIyT95S+ETpiAk5MTW7duJSwsjK5du9Z5j6enJ2fOnGneiQmbJCeBEEK0Rfn5MH06/PgjfPghvPSSZauBEEIIIcQ9otFoiIuLo2vXrqjVanQ6HTExMZjNZnbu3MmVK1eYO3cuKpWKrKwsVCoV+fn5nD9/nrKyMoKCgurmETh0CKZORadS8dUf/oDv0KGMHTuWsrIyioqKKC0tZffu3eh0OtatW8ecOXMAcHd3l5UE94gECYQQoq1JT4c5cyyZfnfsgMcfb+0RCSGEEKKT0Wg0LF26FK1Wi7+/P5WVlSxduhQADw8PHBwcmD9/vpKwMDY2VnlvYmIigYGBdQMEKSkwezaVXl6seuUVwiZMYMiQIUqfL730ktL0L3/5ixIgANDpdLi5ubXUdEUNst1ACCHaCrMZPv4YJk2ylP3Zv18CBEIIIYRoFXFxccqT++LiYnr37o1Wq+X9998nKyuLixcvsnLlShITEzlx4kS9/WRnZ5OdnQ2rV0NkJPj7c+CTT7iq03Ho0CESExNJTEzk6tWrDY7n/Pnz+Pr6NuschW2ykkAIIdoCgwFefhkSEiAqCjQasLEfTwghhBDiXigqKlJeGwwGSkpK8Pb2Jisri4MHDzb43kWLFimBgz7e3pQsW2ZJxPzYY7BhA2HduhE2ZUqDfbz++uvK60uXLtGrVy+cnZ2bMCNxp2QlgRBCtLZLl2DiREuA4Le/haQkCRAIIYQQolUNGDDA6uf09HRGjBhR53iDjEZc33uPkDffhKeegm3boFu3Ro9l3759PPbYY41+n7g7EiQQQojWdPgwjBhh2Vrw2Wfw3ntgb9/aoxJCCCFEJxcfH0+XLl2Un8vLy0lNTSU+Pv6O3q+qqIC5c+n697+j+sUvYM0auMuVAFFRUbctqyiaT5OCBGq1epRard7VTGMRQojOZf16GDMGqqpgzx5LhF0IIYQQog2IiYkhISEBX19fVCoVvr6+JCQkEBMTc/s3l5Yy4Nln4euv4f334S9/ATt5Pt1e3HVOArVa/SvgGaC8+YYjhBCdgMkEb78N//d/MHq05Qu0T5/WHpUQQgghhJWYmJg7CwrUVFQETzyBS14efPEFzJvXMoMTLaYpiQtPAbOA1fU1aCjL5b1QUVHR6mNoCR11XtBx5ybzal9acl6q8nL6vvEGXXfu5NqMGZz//e8xX7sG1661yPVqkj8vIYQQQrSoI0cgIgLKyznzr3/hKwGCdumugwQ5OTnr1Wq1X0NtAgMD77b7ZnHixIlWH0NL6Kjzgo47N5lX+9Ji8yoogPnz4dgxeP997vv5z7nvVm3he0H+vNqO22WFFkIIIdqd9HSYMQM8PGDPHrQOUkivvZI/OSGEuBcyMmD2bKishK1b4TZlf4QQQghxe1qtltTUVKZNmwZAZWUlq1evZvr06Xh6epKdnU12djYAVVVVnD9/ntdffx0XF5c6fRmNRjZt2sS1a9eoqqpi3LhxqNVqLl26xObNmwHo0aMH06dPR6VSsXHjRiIjI3F0dLx3E26rvvgCFi6EgADYvh18fEBW+bVbkj1CCCFaWkICPP449OwJ338vAQIhhBCimaSlpTFy5EgASkpKWLFiBaWlpcr5kJAQFi1axKJFi+jTpw8RERE2AwQAR44cwdXVldjYWBYsWMDWrVsBSE1N5fHHH2fx4sUA5OTkoFKpeOihh9i7d28Lz7AdeP99S/LlUaMgM9MSIBDtmgQJhBCiBq1Wy4EDB5SfKysrWb58OZcvX7bZdvXq1axYsYJ169ZRWVlp3aCyEl56CX76U7QREaz+9a9ZsXevzbZGo5H169ezbNkyVqxYoVzvwIED5OfnN/9EhRBCiHZOr9dTUlJC7969ActKgXnz5uHp6VmnbUlJCZcuXWLYsGH19hcUFMRjjz0GgNlsxu5WNv65c+fi6+uL0Wjk5s2bSpDB39+f48ePYzabm3tq7YPJBK+9Br/4hWW1ZEoKdO/e2qMSzaBJQYKcnJyCnJyc0c01GCGEaG1paWkEBAQAtp9I1LR7926Cg4OJjY3F29vbKrjA5cuWFQMffQS//CW7n3+e4Icftt0WyM3NxWQysWTJEsaNG0daWhoAoaGh7NmzB5PJ1DITFkIIIdoZjUaDn58fQUFBZGZmotFoABgwYADdunWz+Z49e/Ywfvz4Bvt1cnLC2dkZvV7PV199RXh4OAB2dnZcu3aNjz/+GK1WqwQl7OzscHNz4+LFi804u3ZCr4enn4YPPrA8EFm7FupZoSHaH1lJIIQQt1Q/kbjvvvuAhp9IABQVFSkBhYCAAE6fPm05cewYjBwJ334Lq1bBn/5E0Zkzttve0rNnT0wmE2azGb1erzy9sLOzw9vbm9zc3JaYshBCCNGuaDQali5dSmFhIV26dOHixYssXbpUCRTYUlFRwZUrV7j//vtv2//169dZuXIlQ4YMITg4WDl+33338fLLLzN8+HBSUlKU4+7u7mi12qZNqr25fh2eeMISGPjjH+HDD8HevrVHJZqRBAmEEJ1e7ScSW7ZsARp+IgGWoIKzszMAzs7OVFRUwMaNEBYGFRWWZIXPPFN/2xqcnJy4du0a//jHP9i8eTOjRo1SzvXu3ZuCgoLmnLIQQgjRLsXFxSm/lJeXl+Pi4oJWqyUuLq7e9xQWFt5RgODmzZusWbOGiRMn8vDDDyvHP//8c65cuQJYvq9VNSoTVVRU4ObmdrfTaX/OnoWxYy25B1avhl/9Cu5hpSZxb0h1AyFEp1b9REKr1RIcHMzFixf53e9+R9++fYmJiWnwvc7OzhgMBhwdHdFXVOBSXAxLlsCIEbBhA/TrZ7utXl8nadJ//vMfBg4cyMSJE7l+/TqrVq3ihRdewMHBAQ8PDwkSCCGEEFhW8VUrLi5m4sSJdY7XdvnyZbrX2iufmZmJt7e3ssoPLFsSdDodGRkZZGRkABATE8Ojjz7Kxo0bsbe3x9HRUamkYDabuXHjBl5eXs02vzbt+HHLCoKrVy2VmiZNau0RiRYiQQIhRKdm64lERUUFcXFxtw0S+Pj4kJubS8jgweS98w4DjhyBBQss1QxcXW23DQkhLy+PAQMGWJ13cXHB/tZSPVdXV4xGo5KHQKfT0aVLl+aashBCCNFuDRgwgMLCQgAMBgMlJSV4e3srq/UAFi1aZPWeRx55pE4/Xl5eyvdutYiICCIiIuq09fHxUSob1JSXl0dQUJDVyoIOa88emD7dkncgIwNqrLQQHU+LBgkmTGjJ3m9Pqx1AR7yv7qjzgo47N5lX21VYmKi8Li42MnFiNvBzCgv/+9+wkBD48kvQasHBQccDD2zi2LF5ODqOY6j6C/YaltOj7CpXL03nTftf8uAv1pOX9wQGg7vSt6PjOAIDk3BwOITB0IXjx2dhMkFg4Aby88OpqgrjgQc2sn79CuzsjJw58zhJSU4ABAScpbR0IO+917S5doQ/L1va47z++tfWHoEQQrRP8fHxygpAgPT0dCZPnszs2bMb1Y+3t3eDWwpvx2w2c/ToUaKiou66j3Zj/XqIiQFfX9i+He5g64Zo32QlgRCiU3N2dkGvt+QHMBjsKSnxwNu7jKtX/7t0MDt7kfK6qsqVY8fmAaC+fJg3dsfhZKrgncDP2ddnKgAVFd2pqnKyuk5lpTtHjiyoc/0TJ2Yqr3/44ck651UqE+7u58nLkyV9QgghRPUqv7i4OIqKivD09GT27Nm3Xf1XW1MCBAAqlYpZs2Y1qY924R//gP/5Hxg1CjZvhnqSOYuOpUWDBLt2tWTvt3fiRBGBgYGtO4gW0FHnBR13bjKvtkujOVXriYQbkyZNYs6cOcTENFDhdflyeP55S1R90y7+WONzuH59ON26OdX/3kbYv/8gPXo8ysCBTc8z2xH+vGxpj/M6eLC1RyCEEO1XTExMo4MCopHMZnjjDfjDHyzbDD7/nHa3bE/cNaluIITo1GJiYkhISMDX1xeVSoWnpydjxoyp/+ajqgp+/nNLgsIJE+D776HWL6hNfTpR04gRIxg4cGCz9SeEEEII0SCDARYutAQIli61bDeQAEGnItsNhBCdXu0nEidOnLDdsLQU5s2Db76BV1+FP/0JHOQ/o0IIIYToIMrKYM4cSEmBd96BuDgpcdgJyd2tEELciePHLcvtzpyxbDWIjW3tEQkhhBBCNJ/z52HqVDhyRO51OjkJEgghxO1s2QJPP21ZapeeDmPGtPaIhBBCCCHumlarJTU1lWnTpnH06FH27dqF3YkT9PL1JfLddzE/8QSbN27kypUrAERFRdGrV696+0tJSeHMmTOYTCZCQ0MZNmwY5eXlrFq1SinpHBUVhaenJ8nJyYwfPx53d/d6+xOtS3ISCCFEfcxm+OMfLSsIBg2C/fslQCCEEEKIdi8tLY2RI0dSWVlJ+rZtLIyPZ/G6degjIjg5cCAnT54EYPHixYSHh5OWllZvX6dPn+bq1assWbKE2NhY9u7di06n49ixY4wcOZJFixbx6KOPkpqaCsCoUaOU16JtkpUEQghhi04Hzz4Ln30G8+fDsmWStEcIIYQQ7Z5er6ekpITevXtj3riRxX/6E4733Qfbt2PKysLBwYGBAwcyePBgAK5du4aLi0u9/fn4+ODt7Q1YSkOazWbs7e0JCQlh0KBBAJhMJhxu5XHy9PTk8uXLaLVausi9VZskKwmEEKIWhwsXYNw4S7mf996zBArkS0wIIYQQ7ZhGo8HPz4+goCAyMzPZt2QJqlmzcL//fvj2W/ZduYLBYMDf3x8AOzs7kpKS2LZtG8HBwfX26+DggKurK0ajkaSkJEJDQ3FycsLZ2Rl7e3suX77Mzp07GT9+vPIeT09Pzpw50+JzFndHggRCCFHTf/7D/U8+CT/+CElJ8NvfSlZfIYQQQrRrGo2GpUuXUlhYSJcuXRh48SKjli/nbHAw5rQ0UrKzyc/PZ+7cuahq3PfMmDGDl19+mc2bN2MwGOrtX6fTodFo8PT0ZOzYscrx06dPs3btWmbOnImnp6dy3N3dHa1W2zKTFU0m2w2E6CRqJqipfXz9+vVUVVXh4eFBdHQ0jo6Odd5fXl5OQkICzzzzjNV/5GvbtWsXubm52NnZ8cQTT9CvXz+r89999x1ZWVnK8rKoqCiMRiMnTpxgwoQJTZ9oU6xcCUuXYurdG3btgqCg1h2PEEIIIUQziIuLQ6vVYg8sLS/Hx8WF5cB7V6/yfno6Dg4OzJ8/XwkQHD58mBs3bjB27FgcHR1RqVRWwYOaKisrWbVqFWFhYQwZMkQ5fvHiRY4fP05MTAz33Xef1Xt0Oh1ubm4tNV3RRBIkEKKTqE5QU9vu3bsJDg4mJCSEzMxMDhw4QFhYmFUbo9HIli1blL1k9Tl37hyFhYU8++yz3Lhxgy+//JLnnnuuTpsZM2bQt29fq+PffvstpaWl9OjR4y5n2ARGI/z61/DXv0J4OAXvvstgCRAIIYQQooMoKiqiC/AlMKm4mP83cSK/B/pUVpKVlYWvry8rV64ELIkFAwMD2bhxIytWrMBkMjFlyhQcHR3Jzs4GICQkROn7wIEDXL16lUOHDnHo0CEAoqOjybqV3yApKQmAnj17Kg+rzp8/z6RJk+7V9EUjSZBAiE6gZoKa2oqKipRlYQEBAaSlpdUJEqSkpDBs2DAyMzMbvE5RUREDBw5EpVLRrVs3TCYT5eXlVpHic+fOkZmZyc2bNxk0aJBy7QcffJD9+/czZcqUpk63ca5dg6eegu3b4eWX4a9/xZiXd2/HIIQQQgjRgkL69ePT4mKGAT8zGCgpKcHb2xsnJyfeeustm+958skn6xzr06cPJSUlVsfCwsLq3DsCTJkyhcDAwDrHL126RK9evXB2dr67yYgWJzkJhOjAaieo0Wg0ddro9XrlP9LOzs5UVFRYnc/OzsbNzY2AgIDbXq9mXwBOTk7o9XqrNkFBQURFRbFw4ULOnDmjlNjp3bs3BQUFjZ1i0+TkwKhRkJoKCQnw4YdgY6uFEEIIIUS7deoUuyorCQZmAQlAeno6YWFhxMfHN6orV1dXq1UEd2Pfvn089thjTepDtCxZSSBEB1WdoEar1RIcHMzFixdZunQpOp1O2TYwZswYnJ2dMRgMODo6otfr65S4ycrKQqVSkZ+fz/nz59mwYQNPPfUU7u7uda5Z3Vc1g8Fg1Z/ZbGb06NHKsUGDBnHu3DkGDx6Mh4cHOp2u0fOsmWshJyeHjIwM7OzsCAkJYdiwYVZty8vL2bx5MzqdDnNpKTM+/JAeOp0lSFAjyU51v3eTq+HAgQP06NFDyQwshBBCCNFqDhyAqVPpajSy4623OJyYiKqoCE9PT2bPnk1MTEyjuuvatWuThxQVFdXkPkTLkiCBEB1UdYIasPwi6+Liglar5d1337V6Yp+Xl0dubi4hISHk5eUxYMAAq35iY2OV14mJiURFRdkMEIClTu4333zDmDFjuHHjBmaz2ar+rV6v55NPPuHFF1/E0dGR06dP8/DDDwN3n8CmOteC0Whkx44dPPfcczg5ObF8+XLUarXVWHfu3EnwQw8RtGMHpz/+mMsPPECPhATw9a3T793maggNDWX16tX4+flhZyeLtYQQQgjRSrZtgyefBE9P2LGDKWo1Bb//fWuPSrQDcgcrRAdVVFSkvC4uLlbyEdQ8DjBu3DiOHTvG8uXLKS4uVpIbbtiwgevXr9fbf3Z2NqdPn7Y61rdvXwYMGMCyZcv48ssvmTp1KgBHjx7l4MGDuLi4EB4ezsqVK1mxYgVeXl4MGjQIgLNnz3L//fc3ao41cy1cvnyZHj164Orqir29PT4+PhQWFlq1P1NUxI2EBFYdOcLRqCj8vvjCZoCg+nOq3mIREBBQZ67w31wNHh4eyjE7Ozu8vb3Jzc1t1FyEEEIIIZpNYiJMmwaDBsF334Fa3dojEu2IrCQQooMaMGCA8kuyoUaCmtpJYtzd3VmwYEGd98+cObPOsUWLFimv+/Tpw9mzZ+u0mTBhQp1ShsHBwcrroUOHMnTo0Drv++GHH+54f5pGoyEuLg4HBwfGjBmDm5sbY8eOtdra4OzsbJ0P4dw5rl25gsuePfxk1ix2jx3L3uzseq/ZmFwNtRM6VudXUMsXshBCCCHuJbMZ3nsP3nwTJk6E9euhGbYIiM5FggRCdFDx8fFKTgKwJKiZPHkys2fPbpb+XV1dG/3kvz4XLlyge/fudO/e/bZt68u18Pe//90qAGKVX2H/fpgxA9eYGNRvvAFPPsngc+dIS0ur9zpNydXg4eFx75MwCiGEEKJzMxotlZo++QQWLIBly8DJqVWHVDN31NGjR9m3bx92dnb06tWLyMhIVCoV//znP5V7uO7duxMdHW2zL6PRyKZNm7h27RpVVVWMGzfO6oHM9u3b8fT0ZPjw4ZjNZjZu3EhkZKTNnFKiYRIkEKKDqk5EExcXR1ETEtTUp2vXrqhUqmbpq3fv3jbLM9pSX66Fd955h9deew2dToeTkxNFRUWMGTMGNBpYsgT69GHAoEHkDh7MUKCwsBAvL696r+Pj43PXuRp0Op1VLgYhhBBCiBal08HTT0NSEvz615bVBG0gN1J17qjKykrS09N54YUXcHR0ZP369Zw8eZKBAwcC1qtV63PkyBFcXV2ZOXMmOp2OTz/9FLVaTXl5OUlJSVy5cgVPT08AVCoVDz30EHv37q2zwlXcXuv/zRFCtJiYmBgKCgowmUwUFBQ0W4CgNdWXa6GwsJDJkyezZs0ali1bRsjQoXR97z0uvfoqyT/5Cezfz+Qnn+TIkSMsW7aMU6dOMfZWRYN169Zx8+ZNq+vcba4GsORXkOoGQgghhLgnrlyxbC3YuNFSzvkPf2gTAYLKykold5SDgwOLFy9WnuqbTCYcHBw4f/48lZWVrF69mpUrV1JcXFxvf0FBQco2UbPZrCSINhgMjB8/niFDhli19/f35/jx45jN5haaYcclKwmEEO1KQ7kW1Gq1ZdnZ9esQEwPJyXg9/zyRH34Ijo7cBzzzzDN1+uzevTtOtZbj3W2uBpPJxPnz55k0aVLTJiqEEEIIcTsFBfDEE5b///JLmDOntUdkM3dUTEyMsuJy3759GAwG/P39uXjxImFhYYSGhlJaWopGo+Gll16yWSGq+l5Nr9fz1VdfER4eDqBsWc3Ly7Nqb2dnh5ubGxcvXrzjFavCovVDTEII0Qjx8fFWS/nT09MJCwsjPj7eciA3F0aPhh074OOPLfvybrMXbfjw4XWCBHfr4MGDPProo1L+UAghhBAtKzsbwsLgwgVISWkzAYKlS5dSWFhIly5dlNxRGo0Gs9lMSkoK+fn5zJ07F5VKRc+ePRkyZIjy2tXVlbKysnr7v379OitXrmTIkCFWibHr4+7urmxTFXdOVhIIIdqVBnMt7NwJc+eCvb3l9R3uQevWrVuzjW/EiBHN1pcQQgghhE2pqTBzJnTrBpmZEBTU2iMC6s8dFRcXh4eHBw4ODsyfP1/Ja5WVlcXFixeJjIykrKwMvV5vVVq6pps3b7JmzRoiIiLueFtnRUUFbm5uzTO5TkSCBEKIdicmJsY6v4LZDH/7G7z2Gjz4IGzaBM1UeUEIIYQQok3RaCA2FtRq2LYN+vdv7REpaueOmjhxImDZIpqVlYWvry8rV64EYNSoUYSGhpKUlMTy5ctRqVRER0djZ2dHZmYm3t7eBAQEKP3t2bMHnU5HRkYGGRkZgOWesL7qBWazmRs3bjSYqFrYJkECIUT7ptfDz34Gy5fDjBmwahXUE4EWQgghhGi3zGb4y1/gV7+yrJbcsAHuu6+1R2WlvtxRTk5OvPXWWzbfY6s8t5eXF/b29lbHIiIiiIiIqPfatasY5OXlERQU1GzVuDoTCRIIIdqvCxdg1iz49lv43/+F3/++1bP51qwHDCgZe6dPn66U5alWVlbGhg0bMBqNSkmf6jrBtVVWVrJhwwbKy8txcnJixowZdZbPpaSkcObMGUwmE6GhoQwbNozc3FzKysoIDQ1tmQkLIYQQouWZTJYVk3/7m2Vr5apVUM89Q2uKj49n6dKlypaD9PR0Jk+ebDMQ0BBvb+8mbQc1m80cPXqUqKiou+6jM5PMWkKI9unQIRg+HLKyLNl833671QME8N96wAAlJSWsWLGC0tJSm2337t3L0KFDiY2Nxdvbm0OHDtXb74EDB+jVqxexsbEMHTpUWWZX7fTp01y9epUlS5YQGxvL3r170el0DBo0iBMnTqDX65tvkkIIIYS4dyoqYP58S4Dg5z+Hzz9vkwECsCz/T0hIwNfXF5VKZZ07qhGami9KpVIxa9asZktM3dm0/h21EEI01tq18OijoFLB3r3w5JOtPSLAUpKnuh4wQFVVFfPmzauzgqDalClTGDJkCGazmevXr+Pi4lJv30VFRcq+vICAAE6fPm113sfHh+nTpwOWL0az2aws0wsICCA7O7vJ8xNCCCHEPXb1KkyZAl99Zdlq8MEHbeKhSENiYmIoKCjghx9+oKCgoNEBAtH62vbfMCGEqMlkgjfftETTQ0Nh/354+OHWHhUajQY/Pz+CgoLIzMxEo9EAln15DUXCVSoVJpOJjz/+mIKCAu5vINmiXq9XtiI4OztTUVFhdd7BwQFXV1eMRiNJSUmEhoYq0fPevXtTUFDQxFkKIYQQ4p46cwbGjoXvvoPPPoNf/KK1RyQ6CQkSCCHah7IyS/6B+HhYsgTS0uDWE/vW1FA94Dthb2/Piy++yLRp00hKSqq3nbOzMwaDAbAEDGytOtDpdGg0Gjw9PRk7dqxy3MPDA51O18iZCSGEEKLVHDsGYWFQVATbt8NTT7X2iEQnIkECIUTbl59v+aLcsgU+/BD+9S9oI3vMGqoHfDvJycnKtgEnJ6cGs+/6+PiQm5sLWLL1DhgwwOp8ZWUlq1atIiQkhPGozRMNAAAgAElEQVTjx1ud0+l0UiNYCCGEaC9277ZsqzSZYM8eCA9v7RGJTkaqGwgh2rb0dJgzx1L2Z8cOePzx1h6RlfrqAdc8XpNOp2PTpk3MmzePUaNGsWXLFjIyMlCpVEydOhWA7du3ExISgre3t/K+ESNGKHWE7e3tlSzBO3fu5MEHH6SoqIirV69y6NAhJQFidHQ03bt35+zZsw1uZRBCCCGa251U+/nnP/+pbKXr3r070dHRNvsyGo1s2rSJa9euUVVVxbhx41Cr1ZSWlpKUlIRKpcLLy4vIyEiqqqpITk4mOjq6fZa+++orWLAA/P0tKwh8fVt7RKITkiCBEKJtMpvhk0/gf/4H1GrYtAkGDmztUdVRXz3gmqUMFy1apLx2dXVl3rx5AHh6elqdq9a9e/c62XgdHR150kaCxkmTJgHQr18/wsLCbI4xNzeXJ598kvz8/EbNTQghhLhbtav9bNmyhRs3bijnq6qqAGx+D9Z25MgRpVSwTqfj008/Ra1Ws2PHDsLDw/Hz82PLli38+OOPBAYG0r9/fw4fPkxISEiLzK3FfPihpXrBmDGW+54ePVp7RKKTku0GQoi2x2CA55+HF1+EiAhLwp42GCAASz3gLl26KD+np6cTFhZGfHz8Xff5wAMP0KOZbgxOnjxJYGCgVdBCCCGEaEmVlZW3rfZz/vx5ZXXBypUrKS4urre/oKAgHnvsMQDMZjN2t7L7nzt3Dt9bT9oDAgKUYHhQUBAHDhxokbm1CJMJfvUreOUVmDEDdu6UAIFoVbKSQAjRtly6BLNnW/bg/fa38M47cKuUX1tUXdYnLi6OoqKiu64HXFNTawPXNHjw4GbrS4jWpFarHYHlgB/gDLwLHAcSATNwDHgxJyfH1EpDFKLT02g0xMXF4eDgwJgxY3BzcyMmJqZOHh2wrJALCwsjNDSU0tJSNBoNL730khIAqKl6dZ1er+err74i/NYefbPZrGwpcHZ2Rq/XA5ZVe1qtloqKigbLC7cJBgPExlqqF/zsZ5bVBG34vkd0DhIkEKKDqL33r+bx9evXU1VVhYeHB9HR0Tg6Olq1udM9gWazmeTkZC5cuIC9vT0PPvhgnTYHDx7k4MGD2NnZMW7cOAYPHkxubi5lZWWEhoY2PInDhyE6Gi5csHxZtpNMvjExMVIDWIiWtwC4kpOT84xare4BZN/635s5OTm71Gr1p0A0sKE1BylEZ1Vd7Uer1RIcHKxU+wFsfkf27NmTHj16oFKp6NmzJ66urpSVldUbKL9+/Tpr165lxIgRBAcHA1jlHKhd+cfNzQ2dTte2gwQ3blgqN6WmwnvvwW9+A+0xj4LocCRIIEQHUXPvX027d+8mODiYkJAQMjMzOXDggNXe9cbsCfzxxx+pqqpiyZIlFBcXs23bNqtr3rx5k++//57nnnuOqqoqVqxYgb+/P4MGDUKj0RAUFFT/svf16+EnP4Hu3S2rCIYPV07VDIDk5OSQkZGBnZ0dISEhDBs2zKqbc+fO8fnnnyvL9YcPH85DDz1k85K2Eh7VvOGorKxkw4YNlJeX4+TkxIwZM3BzcyM5OZnx48fj7u5+289MCNFsvgLW3XqtAqqAYcDuW8e2AZORIIEQraKhaj+2ggRZWVlcvHiRyMhIysrK0Ov1eHh42Oz75s2brFmzhoiICPz9/ZXjffr0oaCgAD8/P/Ly8vDz81POVVRUtO3KPiUlMHUq/PADJCbCwoWtPSIhFBIkEKID0Ov1Vnv/aioqKmLs2LGAZb9eWlqaVZCg5p5Ak8nE448/Tv/+/W1ep6ioiICAAAD69+/P1atXrc6fPXsWHx8fHBwccHBwoEePHly4cIF+/foREBBAdnY2o0aNsu7UZIK334b/+z8YPRq+/hr69LFqUh0AMRqN7Nixg+eeew4nJyeWL1+OWq22+mX93LlzjB49mjFjxtz2c6sv4VG1AwcO0KtXLyZMmMCxY8fIyMggIiKCUaNGkZqaWu+KCyFE88vJybkJoFarPbAEC94E/pKTk2O+1aQMsPkI8sSJE/dkjBUVFffsWm2VfAad9zNoqNpP9eeh1Wo5deoUly5dwtXVlYsXL/LRRx8BMHToUHJycjhx4gT33XcffWrcC2RlZXHz5k22b9+uHBs7diwDBw5k69atmEwmPDw8uP/++zlx4gQGgwGz2cypU6fuxdRtaujvgVN+Pj5Ll+Jw9SrFH31E+ciR0AH/znTWfws1tdfPQIIEQrRj9e39q0mv1ytP752dnamoqLA635g9gTX7AssyP5PJpLStfd7JyUnZH9i7d2/27dtnHSS4edMSOf/6a1i0CD79FGqtNKgZALlw4QI9evTA1dUVAB8fHwoLCwkKClLal5SUcOXKFXJycujRowdPPPFEvasXaic8OnXqlFWQoKioiEceeUQ5n5GRAViqEly+fBmtVmuVtFAI0bLUarUPlpUCH+fk5HymVqv/VOO0B3DN1vtq/rtuSSdOnLhn12qr5DPovJ9BQ9V+qj+P2p+LrZV+dnZ2ODk5WZXubejztLWKcv/+/YwbN65V/xzq/Xvw7beWlZMODrBnDwNqrYjsSDrrv4Wa2vpncPDgQZvHJUggRDtV394/nU6Hg4Pln/aYMWNwdnbGYDDg6OhYZ78eNG5PYHVf1WpmGLZ13mAwKNfz8PBAp9P9t7OCAkv+gWPH4P33LSV/aiz1txUAGTt2rNX4ayYpqtavXz9CQ0Pp27cvGRkZ7N69m8mTJ9v8DOtLeFStoQCLp6cnZ86cQa1W2+xbCNG81Gp1byAFeCknJyf11uEstVo9IScnZxcQAaS31viE6Ozi4+OV+xKwVPuZPHkys2fPblQ/3t7eTUrgW1lZyZkzZ5g5c+Zd99FikpIs+ZZ8fGD7dqixdUKItuSugwRqtdoO+BgYCuiBZ3NycvKaa2BCiIbVt/fv3XffpaCgQGmXl5dHbm4uISEh5OXl1ckw3Jg9gT4+Ppw8eZKgoCCKi4vrfIn369ePtLQ0qqqqqKqq4tKlS/Tq1QsAnU73372BGRmWCgZVVbB1K0yZYtVPfQGQv//971arAmwFPQIDA5VjgYGBbNu2rd7PsKGER2Ad9Kh93t3dXfn8hRD3xBtAd+B/1Wr1/9469grwoVqtdgJO8N+cBUKIe6y5qv00tcKPo6Mjs2bNalIfLeLTTy2lnYcPhy1bwMurtUckRL2aspJgBuCSk5MTplarRwN/xZJVWAhxDzS096+mcePGkZSUxKFDh+jSpYvyxblhwwbCw8MJDQ0lKSmJ5cuXo1KpiI6Oxs7OjszMTLy9vZUcBGD5pTs/P59ly5YBEBISAsB3331Hjx49UKvVjBw5khUrVmA2mwkPD1dWNZw9e9aydDAhwfIlOXAgbNoENkr01RcAeeedd3jttdfQ6XQ4OTlRVFRUJ/dAdWKjfv36kZ+fb7WnsbaGEh6BJSiSm5tLv3796gRYrIIeQogWl5OT8wqWoEBt4+/1WIQQtlVX+2nrS6zvKbMZ/vd/IT4eoqLgiy9A7h9EG9eUIMGjwHaAnJyc/6jV6uG3aS+EaEYN7f2ryd3dnQULFtR5f81leLaWAnp5eWFfq06vSqUiKipK+bk6EUvNRIjDhg2rU3EAIPfkSZ7ctw8++ggiIuDzz6GepwX1BUAKCwuZPHkya9aswWw2ExISQteuXbl06RLff/89kZGRREZGsm3bNuzs7HB3d1dKQiYmJtap4DB58mQ2b96M0WjE09NTKem4e/duBg8ezIgRI5QAir29vdXndP78eSZNmmRz/EIIIYQQVFbCc8/BypXw7LPwySeWXARCtHFN+VvaFbhe42ejWq12yMnJqao+0NqZHNtrNsnb6ajzgo4zN71ez9GjRxl+q4xf7XmdPHmSiooKhgwZYvP9ZWVlfPvtt0yptQy/phdffJHf/e53yj75rKwsFixYQNeuXVmzZg2hoaFWy+mrFRcXU1xczOjRowE4duwYPj4+dZb3lZeX4+bm1uCfx53+eZ0/eZKBGzfivH49VxYv5uKrr1pK/5SU2Gzv7e3NuXPnAOsASHWixEcffVRpW319f39/m0GL/Px8wJJE0dZYayZSzMnJUY6dPHkSsE6qdObMGcBSq9nJyUnpu73oKP++auuo8xJCCNF+qcrLYdo02LEDfv97+N3vrHIvCdGWNSVIcANLJuFqdjUDBHDvsgnXp6Mudeqo84KOM7ctW7YwefJkpSRh9bwqKyvZvHkzZ8+eJTAw0OZcDx8+THZ2NlVVVQ1+FoGBgfTt21fZ+zdlyhQGDx7Mc889x5YtW1CpVHXev23bNk6dOoW3t7dy7v7772f9+vWN3jNYc14NOnaMwOqgwOrV9FywgJ636ffPf/5zvcmP7vbvR9++fe94n+Pt5rVlyxZmzpxZb+6Gtqqj/PuqrT3Oq75swkIIITqACxfwXbTIUtYwIcGymqAFabVaUlNTmTZtGkePHmXfvn3Y2dnRq1cvIiMjMZlMbNq0iWvXrlFVVcW4ceNum3i5tLSUtWvX8sILLwBw9epVkpKSAEveiGnTpuHg4MDGjRuJjIzE0dGxReco7q26Nc7u3F5gKsCtnARHm2VEQrRzNUv21VZVVcXQoUMZO3Zsve93dXWtsyy+PjExMRQUFGAymQgKCuLZZ58FLOX6bD3l9vHxITIy0uqYi4sLjo6OXLhw4Y6u2SgbN0JYGFRUWJIV2tj2YEtMTAwJCQn4+vqiUqnuOvlRTU1NhFRTVFRUuwsQCCGEEOIeyM2FMWNwPnXKch/UwgECgLS0NEaOHEllZSXp6eksXLiQxYsXo9frOXnyJEeOHMHV1ZXY2FgWLFjA1q1bG+zv8OHDrFu3jvLycuXYzp07GT58OLGxsfj5+fHdd9+hUql46KGH2Lt3b0tPUdxjTQkSbAAq1Gr1t8AHwKvNMyQh2ieNRoOfnx9BQUFkZmai0WjqtHF1dWXgwIEN9jN48GCcnJwaff3blfMDy9J5W1sQevXqZVURocnMZnj3XZgxAwID4cABsFHHuCE1AyAFBQVNChAIIYQQQrS477+HMWPgxg0KV6ywJCpsYTUfTjk4OLB48WLlqb7JZMLBwYGgoCAee+wxoG75altsPbC6dOmSkszax8dHyR/l7+/P8ePHMZvNzTwz0ZruertBTk6OCXi+GcciRLtVX8k+nU6Hg4MDWq0We3t7BtvI5H+3jh8/zvfffw9YEvDdrpxfQzw8PLhx40bzDEyrhdhY+PJLy8qBhARwdW2evoUQQggh2qLkZJg7F3r3hu3bqTAaW/RyGo2GuLg4HBwcGDNmDG5ubsTExODu7g7Avn37MBgM+Pv7K/eIer2er776ivDw8Ab7tnW/6u3tTU5ODiEhIeTk5FBZWQmAnZ0dbm5uXLx40eYqWtE+SXpNIZpBfSX73n33XQoKCjhx4kSzBggAHnzwQSUbP9y+nF9Dmq2cX1GRZfVAdjb86U/w+uuSpEcIIYQQHduyZfDTn8LQobB1qyVQ0IIJdet7OAXw9NNPs3PnTq5cucLcuXOVAMH169dZu3YtI0aMIDg4uNHXnDx5Mtu2bSM7O5tBgwbRpUsX5Zy7u7tyHyw6hqZsNxBC3FK7ZF91JLXm8Ybs3LmTs2fP1ns+Ly+PzMzMBvuYPHkyu3btYtmyZRiNRiWAsHr1aoy3iWafPXsWf3//OxprvfbuhREj4NQp2LIFfvlLCRAIIYQQouMym+Htty3lDSdOhF27LAGCFlbfw6m4uDg2b95MVVUV8+fPV7Yd3Lx5kzVr1jBx4kQefvjhu7pmfn4+4eHhLFq0CJVKZXXfWFFR0TwPm0SbISsJhGgGAwYMoLCwELAu2efs7GyzfUhIiNXPkyZNqtPm9ddfV1736dNHKQlYn549e9pMePjMM89Y/ezn52e1ykCn02EymfD09Gyw/wYtXw7PPw9+frB7NzzwwN33JYQQQgjR1lVVwc9+Bv/6F/zkJ/Dvf8M9yvBf++HUxIkTAcs9aFZWFr6+vqxcuRKwlHUuKChAp9ORkZFBRkYGYMn99MMPPwB170tt6dmzJ19//TUODg54eXkxdepUwJLj4MaNG3h5eTXrHEXrkiCBEM0gPj6+3pJ9zcFsNjNmzJhm6au277777rZ70+pVVQWvvAIffgiTJsHatdC9e/MOUAghhBCiLdFqYf582LwZ3njDkqz5Hq6erO/hlJOTE2+99Vad9oGBgURERNQ53qdPH0pKSuq9Ts0HVv3791e2NNSUl5dHUFCQzcTYov2S7QZCNIOWKNlXk7u7O/b29s3SV23h4eF3l2imtBSfn/7UEiB49VXLHjwJEAghhBCiI7t8GcLDLVsrP/oI4uPv+fbK+Ph4q5wA6enphIWFER8f36h+XF1d72gVQX3MZjNHjx5l9OjRd92HaJtkJYEQzSQmJqbzlOk7fhymT6dLUZFlq0FsbGuPSAghhBCiZZ0+DVOmwJkzsH49zJzZKsOovt+Mi4ujqKjorh9Ode3atUnjUKlUzJo1q0l9iLZJggRCiMbZsgWefhq6dKEoMRG/p5+22Uyr1ZKamsq0adPIyckhIyMDOzs7QkJCGDZsmM33bN++HU9PT4YPH37Hw9m1axe5ubnY2dnxxBNP0K9fP6vzx48fZ+/evQAEBwczevRobt68SUZGhrKfTgghhBCiQYcOwdSpYDDAN9/AI4+06nA61cMpcc/JdgMhxJ0xm+GPf4Tp02HwYNi/H10DGXLT0tIYOXIkRqORHTt2sGDBAhYtWsShQ4e4efOmVdvy8nI0Gg0nT55s1JDOnTtHYWEhzz77LHPmzGHr1q1W500mE6mpqTzzzDMsWbKEAwcOoNVqcXd3x8nJiYKCgkZdTwghhBCdUEoKjB8Pzs6Wak6tHCAQoqVJkEAIcXs6HSxYAL/5DcybBxkZ4ONTb3O9Xk9JSQm9e/fm8uXL9OjRA1dXV+zt7fHx8VGS7VQzGAyMHz+eIUOGNGpYRUVFDBw4EJVKRbdu3TCZTJSXlyvn7ezsePHFF3FxcVGqOFTndggODmbfvn2Nup4QQgghOplVqyAyEvz94bvvIDCwtUckRIuTIIEQomHFxTBuHHz+Obz3Hnz2GdRIlmP7LcVKSUW9Xo+Li4tyztnZGb1eb9W+e/fu9O/fv9FD0+v1VmUmnZyc6vRtZ2fHiRMn+PTTT/Hz81NqBnt5eVmVEBJCCCGEUJjN8Ic/wMKFMHas5QFJ376tPSoh7gkJEggh6vef/8CIEfDjj5CUBL/9bYMZfDUaDX5+fsycOZPPP/8cjUZTJyhQO2jQWJ999hmJiYls3boVZ2dnDAaDcs5gMNjsOzAwkNdeew2j0cjhw4cBS/DA3t4es9l812MRQgghOgOtVsvmzZuVnysrK1m+fDmXL1+2aldeXs4HH3zAjRs3bttnaWkpn3zyifLz9evXSUxMZMWKFXzxxRdUVlYCkJycXGebYoszGuHlly33PU89Bdu2Qbdu93YMQrQiCRIIIWxbudKy/65LF0uwYPr0BptrNBqWLl1KYWEh5eXlVFZWsnTpUnbu3ElpaSk6nQ6j0UhRUdFdrRqo9vTTT7No0SKmTp2Kj48Pp06dwmw2c/36dcxms1VJIL1eT2JiIlVVVahUKhwdHZU6vmazGTs7O6nrK4QQQtxGdZ4hgJKSElasWEFpaalVG6PRyJYtW3BwuH1e9MOHD7Nu3TqrLYLfffcdQUFBxMbG4uXlxaFDhwAYNWoUqampzTib29DpYO5cS3nD11+HNWssuQiE6EQkSCCEsGY0Wr4UFy2CRx+F77+HoKDbvi0uLg6tVgtYthv07t0brVbLm2++yeTJk1mzZg3Lli0jJCSErl27cunSJZKTkxvsc926dQ0+Pejbty8DBgxg2bJlfPnll0q1gqNHj3Lw4EGcnZ0JDg4mMTGR5cuXo1KplLwHFy9ebFKwQgghhOgMauYZAqiqqmLevHnKtsJqKSkpDBs2DA8Pj9v26erqyqJFi6yOeXt7o9PplGtW5xDy9PTk8uXLyj1GiyothcmTYcMG+OAD+POfwU5+XRKdj5RAFEL817VrlmV127dbltn99a9waw//7dTc328wGCgpKcHb25uioiLUajVqtdqqvZeXF5GRkVbHJkyYYPVz9+7dcXJyavC6EyZMqPO+4OBg5fWwYcNsllw8cuSI8lRECCGEENY0Gg1xcXE4ODgwZswY3NzciImJYcCAAXXaZmdn4+bmRkBAAJmZmbfte/DgwXWOde3aldTUVI4dO0ZVVZXVd7unpydnzpypcy/RrIqK4Ikn4NQp+OILy2oCITopCRIIISxycixbCk6fhoQEeO65Rr19wIABVlUL0tPTCQ8P58iRI3c9pOHDh982SHA3bt68iV6vt3mjI4QQQnR21VsItVotwcHBXLx4kaVLlwIQExNTp31WVhYqlYr8/HzOnz9PWVkZQUFBuLu73/E1d+7cSXR0NAEBAZw8eZKkpCSefvppANzd3Vt2JcGRIxARAeXlsGMH1Hr4IERnI+tnhBCWlQOjRsHVq5Ca2ugAAUB8fLxVPoDy8nJSU1OJj4+/62F1a6EkQe7u7kRFRbVI30IIIUR7V3MLYXl5OS4uLmi1WuLi4my2j42NZdGiRSxatAhvb29GjhzZqAABWLYgVCcf9vDwULYeAOh0Otzc3O5yNreRnm6pXqBSwZ49EiAQAgkSCNG5mc2WLQWRkeDnB/v3W74o70JMTAwJCQn4+vqiUqnw9fUlISHB5hMHIYQQQrRdNbcQVucZqn38TmRnZ5OdnX1HbSMiIkhNTSUxMZHt27creYYAzp8/j6+vb6OufUe++AKmTIH+/eG776DGdkUhOjPZbiBEZ1VRAT/9KaxaBXPmQGIiNDFKHxMTI0EBIYQQop2ruYWwZp4h5xpZ/msnHqx5/MSJEwD06dOHkpKSeq/z+uuvK6+9vLxYuHBhnTaXLl2iV69eVtduFu+/D7/4heXhyMaN0L178/YvRDsmKwmE6IzOnbMsp1u1Ct5+G778sskBAiGEEEJ0DLW3EKanpxMWFtboLYSurq6EhIQ0aSz79u3jsccea1IfVkwmeO01S4BgzhxISZEAgRC1yEoCITqb/fthxgy4fh2+/hpmzmztEQkhhBCiDaleFRgXF0dRURGenp7Mnj270asFu3bt2uSxNGsOIb0eFi6EtWstVZw++ABulVoUQvyXBAmE6Ew0GliyBPr0gW+/hSFDWntEQgghhGiDOtwWwuvXLQ9Jdu2CP/0JXn/dkqxQCFGHbDcQojMwGuE3v4EFC2D0aMtqAgkQCCGEEKIzOHvWknsgMxNWr4Zf/lICBEI0QFYSCNHRXb8OMTGQnAzPPw8ffgiOjq09KiGEEEKIlnf8ODzxhKXM89atMGlSa49IiDZPggRCdGS5uTB9OuTlwccfwwsvtPaIhBBCCCHujT17LPdBLi6QkQEPP3xPL6/VaklNTWXatGkcPXqUffv2YWdnR69evYiMjAQgOTmZCxcuYG9vz/Tp0+nRo0eDfRYXF/PNN98o1SXWrVvHzZs3Abh27Rr9+/cnOjqa5ORkoqOjUcmKCXEXJEggREe1cyfMnYvWzY3Ujz5i2tKlVqe1Wi3r16+nqqoKDw8PoqOjcbSxwqC8vJyEhASeeeYZPD097+jSxcXFbN++HTs7O/z9/ZkwYYLVeYPBQHJyMteuXcNoNBIREUG/fv1ITk5m/PjxuLu73/W0hRBCCCFYv96yktLXF7Zvh/vvv+dDSEtLY+TIkVRWVpKens4LL7yAo6Mj69ev5+TJk5hMJqqqqliyZAnFxcWkpKQwf/78evvbu3cvR44csbpfmzNnDgA6nY6VK1cyZcoUHB0d6d+/P4cPH25ydQnROUlOAiE6GrMZ/vY3y9K6/v1J+/OfGRkdXafZ7t27CQ4OJjY2Fm9vbw4cOFCnjdFoZMuWLTg4NC6euGXLFmbNmkVsbCxnz57l3LlzVue//fZbevXqRWxsLNOmTePy5csAjBo1itTU1EZdSwghhBDCyj/+AU8+CaGhsHdvqwQIKisrKSkpoXfv3jg4OLB48WLll3uTyYSDgwNFRUUEBAQA0L9/f0pKShrss3v37sydO9fmuV27djFy5Eg8PDwACAoKsnlvJ8SdkCCBEB2JXg/PPgs//zlMn44+PZ2SsjJ69+5dp2nNL6aAgABOnz5dp01KSgrDhg1TvnDubAh6jEYjPXr0QKVSMXDgQPLz863anDp1Cnt7e9asWUNGRoYyDk9PTy5fvoxWq23MrIUQQgghLA9KfvtbS3nDadPgm2/gDldBNrcrV64oKzBVKpWySnLfvn0YDAb8/f3R6/U4Ozsr71GpVJhMpnr7fPDBB7G3UbKxvLyc06dPW60acHV1RavVUlFR0VxTEp2IBAmE6CguXIDwcFi+HH73O1i/nuLr1+vdIlDzi8nZ2bnOl0h2djZubm7KL/B3qvYXnrOzM3q93qqNVqtFp9OxYMECBg8eTEpKinLO09OTM2fONOqaQgghhOjkDAZYuBD+8Af46U8t2w26dLnnw9BoNPj5+fHKK6/w+eefo9FoADCbzaSkpJCfn8/cuXNRqVQ4OztjMBiU95rNZuzsGv/r2fHjx3nooYfqvNfNzQ2dTte0CYlOSXISCNERHDoE0dFw5Qp8+SUag4E4f3+6du2KWq1Gp9MxduxY0tLSABgzZozyxeTo6Iher8fFxcWqy6ysLFQqFfn5+Zw/f54NGzbw1FNP2cwX8P3333P8+HEAZsyYYRUUsNW3q6srarUagMGDB5OZmamcc3d3l5UEQgghhLhzZWUwZw6kpMA770BcXKuUONRoNCxduhStVou/vz+VlZUsvZUTysPDAwcHB+bPn68kE/Tx8eHkyZMEBQVRXFxsc+XnncjPz2fcuHF1jldUVODm5nb3ExKdlgQJhGjv1q6F2FjLcrq9e9EcP27zCyohIUHJhAuQl5dHboIBEucAACAASURBVG4uISEh5OXlMWDAAKtuY2NjldeJiYlERUXVm1Bw5MiRjBw5UvnZ3t6e0tJSunfvzqlTpxg/frxV+wEDBpCbm0vfvn0pLCykV69eyjmdTidfaEIIIYS4M+fPw9SpcOSIZTVljfuXey0uLk550FFcXMzEiRPRarW8//77TJ8+HV9fX1auXAlY8jAFBgaSn5/PsmXLAIi+lUMqMzMTb2/vO17NeeXKFbp37251rKKiAhcXF5ycnJpreqITkSCBEO2VyWTZVhAfD488Al9/Db16ETdzps0vqLi4OGJiYpS3jxs3jqSkJA4dOkSXLl2YNWsWABs2bCA8PJxu3brZvGx2djZAg9lyo6Ki+PrrrzGbzfj7+9O/f390Oh2bNm1i3rx5jB07lk2bNrFs2TLs7OyYOXOm8t7z588zSWoYCyGEEOJ2cnIsiZovXoTNmyEiolWHU1RUpLw2GAyUlJTg7e1NVlYWBw8etPmeqKioOse8vLxs5h4AuO+++3j22Wetjv3sZz+r0+7o0aOMGDGiMcMXQiFBghpq1jKtqaysjA0bNmA0GnF1dWXmzJlWe64BduzYQVFRESqVismTJ9d5Kluf0tJSkpKSUKlUeHl5ERkZaVXPtKKigvXr12MwGLC3t1d+kUtPT+ehhx7Cy8uribMW7VJZGTzzDGzcCEuW/H/27j0u6jpf/PiLqwwCpo5cTAFvTMqarikEaSqRZkKKmJrYrlpZ1um31elsZ5ft7GmLs2c7bT2qrXbNu1KZmpg3zJC8oOItdU1CUa6OCIiCMMN15vfHV2YZmMFBQG7v5+PRo5nv5fP5fCfz+533fD7vN3z6KdyKFFu7QdXfDsq0/gULFjRquv4X9jr1ZyD4+PjcNvvugAEDGt3AVCoVc+fObfS6vsLCQjw9PRv9/yWEEEIIYebIEYiIAHt7+OEH6ABfiH19fcnOzja9T05OJiwsjDNnzjSrHW9vb6s/1tiiurqa3Nxci890QthCEhfWU1fLtKGUlBRGjRplKhV38uRJs/35+fnk5uby7LPPEhUVRWJios197t69m7CwMNPU7p9//tls/6lTp0yl4gIDA0lJSQEgJCTELNmb6EYuXYKQENi+HT76CD7/3BQgABoFqJKTkxk3bpzNgavbUalUbVZzNzU1lcmTJ7dJ20IIIYToIr79VknWfM89cOhQhwgQAMTFxeFaL1lieXk5SUlJxMXFNaudlgQIAJycnJg1a5bZD49CNIcECW6prKw01TJtaOrUqdx///0YjUZKSkoaJWHz8PDAycmJ2tpaKisrm5WV9MqVK/j5+QFKGbqGpeK8vLxMSeAqKytNU49cXFxwcnLi6tWrzbpO0cklJys3Qq0Wdu9WSvw0uAG01g3KGg8Pjza76URERDSr3KIQQgghupllyyAqCgIDlQBBM6swtaWYmBiWLVuGn58fdnZ2+Pn5sWzZMrPlnkJ0BhIkuCUvL89qqbi6mqWffvopWVlZDBo0yGy/vb09dnZ2/O1vf2PdunWEhoba3K/RaDR94bJUKk6lUnHp0iU++eQTDh06xC9/+UvTPk9PT7KysmzuS3RiRiN88gk8+ih4e8OxY/DIIxYPlRuUEEIIIbocoxH++EelvOHUqcoPJ/USH3cUMTExZGVl8dNPP5GVlSXPX6JT6vY5CeLj44mNjW2yVFxAQAAODg689NJLXLp0iYSEBLM12qdPnzat766qqmLlypUMGDAADw+PRv2dO3eOo0ePAjBlyhSzX2QtlYrbt28foaGhjB07lqtXr/L1118zadIkQCmlUlpa2sqfiOhwqqqUGQPLlkFkJKxfDxb+bNUXExMjNyUhhBBCdA01NfDCC7BiBSxeDH//Ozg5tfeohOiyunWQwFot04al4nbs2MGIESMYNGgQzs7OjaZa15UXsbe3x9nZGUdHR6qqqiz2OWLECEaMGGF67+PjQ1ZWFv7+/mRkZODv79+o7brAQc+ePc1mGkipuG6gsBCio+HAAfj975Xav81YziKEEEII0amVl8OcObBzJ7z5Jrz1VqOllkKI1tWtgwTWapk2LBUXHBzM9u3b2b9/P3Z2djz++OMA7NmzhxEjRjBy5Ehyc3NZsWIFRqORkSNHolarycjIID8/n/Hjx1sdw5QpU9i2bRu1tbWo1WpTAGHdunXMnz+fsLAwvv32W44dO4bBYCAyMtIUgLh8+TKPWJlyLrqA06dhxgy4ehW++AKeeqq9RySEEEII0WYaVhqrvnyZde++yxPHjqH++9/h+ec5cOAA58+fp7a2lrFjxzJmzJgm2ywuLmbDhg0sXboUUCo/7dixgxs3blBbW8u0adO499572bFjBxMnTsTNza3Nr1OIjq5bBwlsLRWnVqvNZhbUqV/L3VKNUx8fH65cudLkGPr27Wux7aeffhpQlhQ0nDaelpaGXq/HYDBYzaMgOrnNm+FXv4LevZVZBGPHtveIhBBCCCHaVP1KY9qjR9m+fj2lPXrAxx/D3LlkZWWRl5fH4sWLqa6u5tChQ022d/r0aVJTUykvLzdtO3ToEJ6enkRFRXH16lXy8/O59957CQ4OJikpiRkzZrTpNQrRGXTrecttXSrOaDQ2K4lhcxw+fJiwsLA2aVu0I4MB/vu/YfZsuP9+OH5cAgRCCCGE6PLMKo0dP07Ns88y99tvUQ8caErWnJGRgaenJxs2bODLL78kICCgyTZVKlWjH+MuXryIg4MD69evZ//+/Qy9VR1BrVZTVFRkmmUsRHfWrYMEbV0qzs3NzVSysLWFhYVZLNcoOrGyMnjySWWt3cKF8MMPSiUDIYQQQoguKj4+Hn9/fwIDAzl48CDJv/0tTJqE782b9Nq92yxZs06nQ6vV8uSTTzJ9+nS++eYbjEaj1bYDAgJwdnY226bT6dDr9SxYsICAgAC+++470z61Wk1ubm7rX6QQnUy3DhJIqTjRYWRlwUMPQUICvP8+rFwJPXq096iEEEIIIdpMXRLx7OxsXF1dURcUMOH//o9itRoOHQKNxux4V1dXhgwZgoODA2q1GkdHx2b/8q9SqdDcajcgIACtVmva5+bmJjMJhKCbBwngX7VMDQaD1DIV7WP/fhg3DnJyYNcuePVVydorhBBCiC6vfhLxJ8rLmejiQjLwsMEAPj6Njvf19eXixYsYjUZu3rxJVVUVKpWqWX36+vpy4cIFALKzs/H09DTtk8phQii6fZBAiHb1j38o6+z69oXUVJgypb1HJIQQQghxV+Tk5GAPfAL8V14e57y8mA6cy8uzeHxAQADe3t4sX76cL7/8kscffxx7e3tOnTrFqVOnbOpzwoQJ5Ofns2LFCg4fPmyWiDw/Px8/P7+WX5gQnVy3rm4gRLuproZXXoFPP4Vp0+DLL6FXr/YelRBCCCHEXTNswAD+NzeXKOB/q6o4pNXS19ubHvWWXDZMPFj/S30dHx8fs2UDDb3++uum1yqVirlz5zY6prCwEE9PT7O+heiuJEggxN1WVKQkKPzhB/iP/4A//xnaKMGlEEIIIUSHdO0aB11c6Au8DPwN6JmczJQpU4iOjm5WUyqVitGjR7doOKmpqUyePLlFbQjRVchyAyHuprNnISgIDh+Gdevg3XclQCCEEEKI7uVWwuZ+OTkc/H//j223koir1Wqio6ObnSPMw8MDuxbmc4qIiMDd3b1FbQjRVbRoJoFGo4kCnkxPT5/fSuMRouvauhUWLAB3dyVZYVBQe4+oxSorK9m2bRuRkZFm23U6HZs3b6ampgZ3d3dmzJiBk5OTab/RaGTHjh1cvXoVBwcHnnjiCfr06WNzv9XV1axbt44nnngCtVpt8ZgjR45QVlZGeHg4ADt27GDixIm4ubndwZUKIYQQolWcOqUstayogO++4+GHHybrww/be1RCiHrueCaBRqP5EPhzS9oQolswGun797/DzJkwfDgcP94lAgQAZ8+eJcjCtezbt4+RI0eyaNEivL29OX78uNn+n3/+mZqaGp555hnCw8PNahTfjlarZdWqVRQXF1vcX11dzTfffMOxY8fMtgcHB5OUlGRzP0IIIYRoZUlJ8PDD4OgIBw8qr4UQHU5LvuAfApa21kCE6JJ0Opg3D8+PPlJmEezbB/37t/eoWkVlZSXFxcV4eXk12peTk8PQoUMBGDp0KJmZmVb3DxgwoMlkQw3V1NQwd+5cqzMIampqGDVqFBMmTDDbrlarKSoqkvrHQgghRHuIj1dmEPj5KcsuAwPbe0RCCCtuu9xAo9E8A7zaYPOi9PT0DRqNZlJT56alpbVgaC1XUVHR7mNoC131uqBrXZujVsvAl1+mx88/o/3NbyhdskRZg9dF5Ofn4+rqavG/V1lZGZmZmTg6OlJWVsb169fNjrt69SpOTk6mbbW1tfz000/Y29sWtywvL0en03Hx4kUKCwstHqPVarl586ZZv46Ojhw6dIh77723yfa70p/D+uS6hOg6dDodSUlJREZG8s9//pPU1FTs7e3x9PRk+vTpTa7PNhgMbNq0iTFjxpgCtl999RU6nQ57e3ucnJyIiYnh+PHj9OnTh8GDB9+tyxJdkdEI770Hv/0tTJoEW7bAPfe096iEEE24bZAgPT19BbDiThofPnz4nZzWatLS0tp9DG2hq14XdKFrS0mB+fOV9Xbbt1M6aFDXuC4gPj6e2NhYPDw8GDZsGCqVigkTJrB3714AQkNDcXNzY/DgwfTs2ZP8/HwuXLhgdv05OTl4eXmZtu3atYtAK78o7N27l5ycHAB+9atfmQIJqampDBkyxOqMgsrKSoqKisz61Wq19OnT57b/LbrMn8MG5Lo6jhMnTrT3EEQnt3fvXoKCgqiuriY5OZmlS5fi5OTE5s2bOX/+PBqNxuJ5xcXFJCQkUFpaypgxY0zbr127xosvvmgWXBgzZgzr1q3D39/f5iCuEGZqa+G11+Cjj2DOHFi7FqTEoBAdnpRAFKK1rVwJL7wA/v7K8oL77oMu8itnfHw8S5YsQafTMXjwYGpra1myZAnLli0zq2OckZHBhQsXGD16NBkZGfj6+pq1M3DgQM6fP09gYCB5eXkWlyzUCQsLa7Xx6/V6evbs2WrtCSFEe6isrESr1eLl5YXRaGTx4sWm5LAGgwFHR+uPd1VVVURGRpKSkmLaVlZWRkVFBV9++SUVFRWMHz+egIAA7O3t8fb25sKFC1aDDkJYVVEBTz8NmzbBK6/AX/8KEmwSolOQ/1OFaC01NfCb38AzzyjT6VJTlQBBFxIbG2ta01/35V6n0xEbG2t23MMPP8zZs2dZuXIleXl5puSGW7ZsoaSkhOHDh+Po6MiKFSvYvXs3U6dOBeDgwYNkZGQ0e1x6vZ4NGzbc9rj8/Hz8/Pya3b4QQnQkeXl5pllUdnZ2pqotqampVFVVNbk8wNvbm379+pltq62tJSQkhHnz5jF37lx2795NeXk5AF5eXmR1oaVy4u6wLymBqVOVAMF778EHH0iAQIhOpEUzCdLT038AfmiVkYhWVX+tYn0lJSVs3boVg8EAKDVhG07X3rVrF7m5uTg7OxMeHs6AAQNs7tfSOsc6FRUVbNmyhcrKSmpra5kyZQoDBw4kOTmZX/ziF40eWjqV4mKYOxe+/x5efRXefVfJ3NvF1E37B+XXKK1Wi7e3t9l2ADc3NxYsWNDo/KioKNPriIiIRvv79euHg4ODTWOpP3NBpVIxd+5cs/2jR482e19YWIinpyc9ZJqjEJ2aRqMJBv6Snp4+SaPR/BLYDly4tfuz9PT020cMO6n6y700Gg16vZ6YmBiMRiN79uzh2rVrzJkzp9n14t3c3Bg7diz29vb07NkTb29vioqK6NmzJ+7u7hIkEM2Tm4vf009DdjZ88QU89VR7j0gI0Uxd71uMAP61VrGh5ORkgoKCuO+++8jIyCApKcnsy9X58+e5du0azz33HHq9nvXr17NkyRKb+rS2zrHO4cOHGTRoEA8++CBFRUVs3ryZ559/npCQEDZv3kxMTMydX3B7OncOnngCcnOVpQaLFrX3iNqMr68v2dnZpvfJycmEhYVx5syZVmnf29ubXr16tUpbDaWmpjJ58uQ2aVsIcXdoNJrfAk8D5bc2PQC8n56e/tf2G9Xd0XC5V3V1ten+7O7ujqOjI/PmzWt2gADg0qVLHD16lJiYGKqqqigoKDAF7vV6Pa6urq16LaILO3sWHnsMp5ISSEyEVlwyKIS4e2TeTxdUf61iQ1OmTGHYsGGA5XWLhYWFDBkyBDs7O1xdXbG3t6esrMymfuvWOfr7+1vcHxISwgMPPNCobxcXF5ycnLh69aqtl9hxbN8ODz4IZWWQnNylAwQAcXFxZg+L5eXlJCUlERcX1yrtt1WAAJSZC+7u7m3WvhDirrgIzKr3/gFgukaj2a/RaFZoNJou+z+5teVe77//Pj/++CMFBQWsWbOG1atXk5aWRllZGZs2bbKp7WHDhtG3b1+WL1/OunXreOSRR0x/11++fFmqGwjb7NsH48eDwUD22rUSIBCiE5OZBF1I3TRER0dHQkND6dmzZ6Nf5+tu+kVFRezZs6fRFG1vb28OHz5MUFAQpaWlFBQUUFVVZVP/3t7eTe53cXEBlARJW7ZsMa1DB/D09CQrKwsPDw+b+mp3RqOypOB3v4MxY5RyPgMHtveo2lzdn6fY2FhycnLw9vbm//7v/zrvLBAhRKeSnp6+WaPR+NfbdBRYnp6efkKj0cQCfwReb3je3SqR2ZblOK0t9/rxxx9Zv359o+Ozs7Oprq62Oh6NRmO238/Pz5SzxWg0kpaWhsFg4OLFiwwYMMDm65KSpN3zM3BPTKT/G29QPXAgOf/4B2V9+3a7z6Ch7vjnoCH5DDrvZyBBgi6i/jTEkSNHUlBQwJIlS9Dr9aZf7ENDQwkICCAzM5OdO3cSFRXVKB/BkCFDuHz5MmvWrKFfv37079/f6jTDo0ePcu7cOQBmzZpl0xf8q1evsnnzZh599FGzGQfu7u6UlpZ2jiCBXg/PPquss5s3D1asgHqfkbV8EHWOHDlCWVkZ4eHhFvcXFxezYcMGli5d2uyhJSYmolarGTt2rNl2g8HAtm3buHbtGqD8qu7p6XlHNbBjYmJMQYHOWHpOCNGlbElPT79R9xr42NJBd+vvqbb8O7Gp5V6W+qytrcXPz8+U1PBOHDt2jKlTpzJkyBCbz5H7Qjf8DD78EP793yE0lB7ffsuwPn2632dggXwG8hlAx/8MrJVkliBBF1F/GmJ5eTkuLi7odDreeecds4RDmZmZJCYmEhMTwz333NOonWvXrtGrVy8WL15MSUkJCQkJphkADQUFBVnMe2BNYWEhGzduZPbs2Y1mHXSa0nR5eRAVBSdOwP/8D/znf0KD9Z/W8kFUV1ezbds2Ll++bPUvi9OnT5OammrKKm2r8vJyEhISuHbtWqPADyi5JgAWL15MVlYWe/fuZd68eVIDWwjR2e3WaDQvp6enHwUeASw/7XQBcXFxph8D4F/LvZYtW2bxeAcHhxYFCADGjRvXovNFF2cwwBtvKNULoqIgPh5UqvYelRCiFci3gi6i/jTE+nXnG2ad3717N7W1tSQkJLB69Wq2bdsGwJ49e7h8+TK9evUiPT2d5cuXs2XLFqZNmwbAqVOnOHXq1B2Nbd26ddTW1pKUlERNTQ2JiYmsXr2ar776ynRMp1jzeOQIjBsHP/8MW7cqSw0aBAiaygdRU1PDqFGjmDBhgtUuVCqVWdZ+W1VVVTFx4kTuv/9+i/vvu+8+08yGGzdumAI/9WtgCyFEJ7QU+ECj0fwAPAS8077DaTsxMTEsW7YMPz8/7Ozs8PPzY9myZbLcS7SPqip4+mklQPDii7BxowQIhOhCZCZBF1F/GmL9tYoNy7298MILFs9/9NFHTa/nzJnTaL+Pjw9ardamscycOdPs/dNPPw3AvHnzLB6v1+sxGAyo1WoKCwtt6uOuW7MGliyBAQOUMoeBgWa7bckHoVKpGDJkSJPBloCAgDsaXu/evenduzcZGRlWj7G3tychIYG0tDSz/8Z1NbA1Gs0d9S2EEHdTenp6FvDgrdcnUYID3UL95V5CtJvSUpg1C5KSrM6qFEJ0bhIk6CIaTkNMTk5mypQpREdHt0r7KpWqUd351nL48GHCOmoG3JoaZSrd++8rWXq//hr69jU7xJZ8EAMHDmzV9Ujnzp3j6NGjgFKxon///jadN3PmTMLDw1m+fDkvvvgizs7OUgNbCCGEELbRauHxx+Gnn5QfUH71q/YekRCiDUiQoItomHVerVYTHR3dar84tGVCwQ4bILhxQ0lMuHs3vPwy/PWv4OTU6DBb8kG0dlbTESNGMGLECJuPP336NKWlpUyYMAEnJyfs7OxMtbSlBrYQQgghbuvnn+Gxx6CoSCkBXa9KlRCia5GcBF1ITEwMWVlZGAwGsrKyZEpiS6SnQ3Aw7N0Ly5bBRx9ZDBCA7fkgrKnLB2FNRkYGBw8ebMbg/2XLli2UlJQwfPhw8vPzWbVqFevXr2fq1Kk43bqeTpEPQgghhBDt59AheOghpcLTvn2dPkCg0+lMeblASS69cuVKioqKAKU6yObNm1mxYgWrVq0ybW9KcXExn332WaPtWVlZfPDBB6b3O3bsoKysrBWuQoi2IzMJhGho1y546ilwdlbW2zWRaBBszwdRp+Gyjfr5IOq8/vq/ynz7+Phw5coVm4Y+adIks/dRUVGm108++WSj4w0GA/n5+RbH0Brql4NMT09n//792NvbM3r0aB544AGL51gr43g7tpSOPHDgAFevXmX27NlUV1ezY8cOZsyYYZpVIYQQQogGEhKU56KBAyExEbrADwv1K1FptVq2b99OaWmpaf+FCxcwGAw888wzXLx4kb1791rM2VXHWnWqkpISjhw5Qm1trWlbcHAwSUlJzJgxo5WvSojWIzMJhKhjNCpLCiIiYNAgOHbstgECUPJB1J+un5ycTEhICHFxca00LCOhoaGt0lZDJ06cYPz48W1W/rDuJlxbW8vu3btZsGABCxcu5OTJk42i6OXl5cTHx5vKNTbH6dOn2bRpU5OlIy9cuGBWxcHJyYkBAwZw+vTpZvcnhBBCdAuffQbR0XD//ZCS0iUCBA0rUdXU1DB37lyzEtJ9+/bFYDBgNBqprKy87XOSpepUtbW17Nixg8cff9xsu1qtpqioyLRUVYiOSIIEQgBUVMDChfD660rG3oMHwc/PplMblqVq7XwQbm5uODg4tEpbDY0bN44hQ4a0Sdv1b8JFRUX06dMHlUqFg4MDAwcONM2+qHO7Mo5NuV3pyOLiYk6cONFopkVgYCDHjx9vdn9CCCFEl2Y0QmysUt7w8ceV5Zf9+rX3qFokPj4ef39/AgMDOXjwIPHx8YAyI7RXr15mxzo7O3Pjxg3+9re/sW3bNoKDg5tsOyAgAGdnZ7NtJ0+eJCQkxGJeL7VaTW5ubguvSIi2I0ECIbRamDQJ1q6FP/1JqWDQs2ezmpB8EP9i6SZcWVmJi4uL6ZgePXpQWVlpdl7v3r0ZMGDAHfVp6eZcp6qqip07dxIREdHolwCVSoVOp6OiouKO+hVCCCG6nOpqWLRIKW/43HOwZUuzn4s6mrpKVNnZ2bi6upoqUdUFCho6cuQIQ4YM4eWXX+aFF14gISGBmpoam/u7efMmRUVF7Nu3j9WrV6PX69m0aZNpv5ubm8wkEB2a5CQQ3duxYzBzJpSUwDffQL01/KL5rJWD/Pjjj81yNDQMGjTXF198QVVVFZ6eno2m8TV08eJFysrK2LRpExUVFdy8eZODBw8yfvx4AHr27Iler2/ReIQQQoguoawMZs9WKju99Ra8+SZ0gbw91ipRxcbGWvxhx8XFxTSLU6VSUVtbi8FgsLk/d3d3pk2bZip//d577zF79mzTfr1eT89OHngRXZsECUT3FR8PzzwDPj5w+DCMHNneI+r0rN2E3377bV577TX0ej3Ozs7k5OS0KM/C/PnzbT52+PDhppt0VlYWx48fNwUIACoqKuRGLYQQQly9CtOnw6lT8Pnn8Oyz7T2iVtOwElV4eHij7fWFhISwdetWVq1aRW1tLY888gjOzs6cOnUKaJyEurnaMmm0EK1BggSi+6mthd//Ht59FyZOhE2boF6yGnHnrN2Es7OzmTJlCuvXr8doNDJ69Gg8PDwoLCzk6NGjTJ8+3WqbmzZt4rHHHsPNza1ZY8nMzCQnJ4eJEydaPaaiogIXFxerSxWEEEKIbuHCBXjsMbhyRalmEBHR3iNqVbZUoqqf28jZ2dliVSgfHx+0Wq3VfupXp7K2vbCwEE9PT6tVsIToCCRIILqXkhKYPx927oSlS+HDD8HJqb1H1WU0dRPWaDRoNBqz4/v169coQNAwuWDv3r1t/hJf/yY8aNAgBg0aZLbf398ff39/0/t//vOfjBs3zqa2hRBCiC7p6FFlBgFAcjLcJklfZxQXF2daDglKJaopU6YQHR3drHZUKlWLZxGkpqYyefLkFrUhRFuTxIWi+7hwAR58EL77Dj79VPlHAgStqi3KQY4dO7ZNfumvrq4mNzeXkbLMRAghRHe1YwdMngzu7kqJwy4YIIDWq0Tl4eGBXQtzNERERODu7t6iNoRoazKTQHQPe/bAnDng4KC8bvBrtWgddTfb2NhYcnJyWqUcZMOyRK3FycmJWbNmtUnbQgghRIe3fDm88AKMGqXMsPTyau8RtamYmJhuXX1KiOaQIIHo2oxG+OgjeO01CAyErVuhwRR00brkJiyEEEJ0YEYjvP02/PGPMHUqbNyozCQQQohbZLmB6LoqK5XMvK+8AjNmwKFDEiAQQgghRPdVUwPPP68ECH79a9i2TQIEQohGJEgguqb8fAgLg5Ur4b/+S6lg0Mzs+EIIIYQQXYZOB7NmKeUNf/97WLVKcjMJISyS5Qai6zl5Upk5cO0afP01WChhI4QQQoiOyhX3jgAAIABJREFUQ6fTkZSURGRkJJcvX+a7777DaDTi5ubGrFmzcHS0/shqMBjYtGkTY8aMYejQoQAkJSWRmZkJQHh4OP7+/ly4cIGbN28yZsyYu3JNHUpRkVLW8OhR+OQTePHF9h6REKIDk5kEomvZsAHGjwc7OyVL710KEOh0OrZt22Z1//nz5/n+++8t7vvuu+9YsWIFn3/+OSdOnGh234mJiRw/ftzivgMHDrBixQqWLVvGyZMnATh+/DiXLl1qdj9CCCFEW9m7dy9BQUEYjUa2bdvGjBkzWLx4MUOHDuXGjRtWzysuLmb16tVmteuvXLnC5cuXeeaZZ5g9ezaJiYkADBs2jLS0NCorK9v8ejqUzEwIDYXTp2HzZgkQCCFuS4IEomswGOAPf4B582DMGDh+HH75y7vWfd3DTUPV1dV88803ZGRkWDwvMzOT69ev88wzz7Bo0SJSUlLQ6/U29VleXk58fDznz5+3uD8rK4u8vDwWL17MwoULKS0tBWDMmDEcOHAAg8Fg49UJIYQQbaeyshKtVouXlxfXrl3D1dWVw4cPs3r1avR6PWq12uq5VVVVREZG4u/vb9rm4+PDggULsLOz48aNG7i4uJj2DR06lFOnTrXl5XQsJ09CSIgyk+D77yEqqr1HJIToBGS5gej8bt6Ep59WKhc88wx8+ik4O9+17us/3DRUU1PDqFGjzB5Q6hs4cCDe3t4A2NnZYTQacXBwsKnfqqoqJk6caDUAkZGRgaenJxs2bKCyspJHH30UAHt7e7y9vblw4QIajcamvoQQQojWFh8fT2xsLI6OjoSGhtKzZ08mTJhAbm4u06ZNo0+fPnz55Zf079+fQVYSD9fdQxuyt7cnKSmJo0ePMm3aNNN2Ly8vUlNTCQ4ObpNr6lC++w6io6FPH0hOhuHD23tEQohOQmYSiM7t0iUlQr59u1Lq8PPP71qAID4+Hn9/fwIDAzl48CDx8fGNjlGpVAwZMsRqG46OjqhUKmpra0lISGDMmDE42zj+3r17M2DAAKv7dTodWq2WJ598kunTp/PNN99gNBoB5SEpKyvLpn6EEEKI1hYfH8+SJUvIzs7G1dWVgoIClixZQlJSEn369KFfv344ODgwZMgQs6UEzfHII4/w2muvcejQIYqLiwFwd3e3ecZep7Z2LUyfDoMHw+HDEiAQQjSLzCQQnVdyMsyerdT73b0bHnnkrnVd93Cj0+kYOXKk6eFGr9ebkiuFhoYSEBBw27b0ej0bN27Ez8+PCRMmWD3u3LlzHD16FIApU6bQv3//Jtt1dXVFrVbj4OCAWq3G0dERnU5Hz549cXd3lyCBEEKIdhMbG4tOpwOU5XMuLi7odDrefvttfvOb31BcXEyfPn3Iycnhl81cPpiZmcm5c+eYPn06jo6O2NvbY2dnByj33J49e7b69XQYRiP85S/wu98pVZ6++QZ69WrvUQkhOhkJEojOx2hUlhT85jeg0cC330ITv9a3BWsPN++8806zvnxXV1ezdu1aQkJCuP/++5s8dsSIEYwYMcLmtn19fUlNTSUkJISysjKqqqpQqVSA8pDk6upqc1tCCCFEa8rJyTG9zsvLIzw8HFDy6TzxxBNs3rwZgAEDBhAQEEBZWRmJiYnMnj37tm37+fnx008/sXLlSgwGA+PGjaN3794AXL582erShU6vtlZ5NvrkE3jqKVi9+q4uvxRCdB0SJBCdS1UVvPwyLFsGkZGwfj14eNz1YVh7uKm/vSl79uxhxIgR5OTkcP36dU6ePGmqPjBjxgyuXbtGfn4+48ePb/bYtmzZQlhYGAEBAWRnZ7N8+XKMRiOPP/449vbKCqPLly83uQxCCCGEaEu+vr5kZ2cDSo4drVaLt7c3PXr0YNCgQTz33HNmx7u6uuLu7m61vZkzZ5pe29vbExERYfG4Cxcu8GRXLI2s18OCBcrMgddfV2YT2MuqYiHEnZEggeg8CguVBDwHDsDvfw9vv91uN8CmHm4sGTRoEMPrrQesSyJ47733EhIS0uh4Z2dnrly5YtNYJk2aZPY+ql7m4rp+6jMYDOTn51vcJ4QQQtwNcXFxpmV7AMnJyUyZMoXo6GiLxxuNRh566KEW9Xn+/HmGDx9u9V7daRUXw4wZSunnDz6AV15p7xEJITo5CRKIzuH0aeUGePUqfPGFMo2uHTX34aa5jEYjoaGhrdJWQydOnGD8+PGmWQVCCCHE3RYTEwMoy/dycnJQq9VER0ebtjfk4OCAm5tbi/q0JU9Qp5OTA489BhcvwldfwZw57T0iIUQXIEEC0fFt3gy/+hX07q3MIhg7tr1H1OyHm+Zq6YNQU8aNG9dmbQshhBC2iomJabX7Zrd05gxMmwbl5UoC5wYzC4UQ4k5JkEB0XAYD/OlP8NZb8OCDsGULWKmH3B7k4UYIIYQQ7WLvXoiKAnd35QeUkSPbe0RCiC5E5huLjqmsDJ58UgkQLFwIP/zQoQIEQgghhBDt4quvlCUGAwfC4cMSIBBCtDoJEoiOJysLHnoIEhLg/fdh5UroakmGhBBCCCGa6/33lbxMISHKDIKBA5vdhE6nY9u2bab31dXVrFy5kqKiIkBJcLx161ZWrlzJypUrKSgouG2bxcXFfPbZZ6b35eXlrF27ltWrV7N69WpT2zt27KCsrKzZYxZC3F0SJBAdiur4cRg3TknEs2sXvPoq2Nm197CEEEIIIdqPwQCvvQb//u8we7aSg6B37ztqau/evQQFBQGg1WpZtWoVxcXFpv3nz58HYPHixYSFhbF3794m2zt9+jSbNm2ivLzctO3s2bMEBQWxcOFCxo8fT1JSEgDBwcGm10KIjkuCBKLj+Mc/8Fu8GPr2hdRUmDKlvUckhBBCCNG+Kith/nylvOHLLyvLDVxc7rCpSrRaLV5eXgDU1NQwd+5c1Gq16Zj77ruPyMhIAG7cuIHLbfpSqVQsXLjQbNvo0aMZNmwYoMxMcHRU0qCp1WqKiopM1aGEEB2TBAlE+6uuhpdeghdeoDwkRAkQdMUyRUIIIYQQzXHjhpJ/YMMGePdd+PBDcHBodjPx8fH4+/sTGBjIwYMHiY+PB8DX15devXo1Ot7e3p6EhAR27drFyNvkPAgICMDZ2dlsW48ePXBwcKCoqIg9e/YwceJE0z61Wk1ubm6zr0EIcfdIkEC0r6IiZcbAp5/Cb39L7qefgoWblRBCCCFEt3L5Mjz8MBw8COvWwX/8xx0twYyPj2fJkiVkZ2fj6upKQUEBS5YsMQUKrJk5cyYvv/wy27Zto6qqqtn9ZmZmsmHDBqKiosxmKri5uclMAiE6OAkSiPbzz39CUJCSmXfdOvjLX+4oOi6EEEII0aX89JOSnDArC3buhAUL7rip2NhY05fy8vJyXFxc0Ol0xMbGWjz+9OnTHDhwAAAnJyfs7Oywa2ZwoqCggMTERGJiYujfv7/ZPr1eT8+ePe/gSoQQd4tjew9AdFMJCcoNz8MD9u9XggVCCCGEEN3dgQPwxBNK3oH9+2H06BY1l5OTY3qdl5dHeHh4o+31DR8+nK1bt7Jq1SoMBgNTp07FycmJU6dOAUq+gdv58ccfcXR0JCEhAYC+ffua8hzk5+fz6KOPtuiahBBtS4IE4u4yGiEuDt58U6likJAADSLMQgghhBDd0ubNEBMD/v6QmKj8u4V8fX3Jzs4GoKqqCq1Wi7e3Nz3qlZeun3jQ2dmZJ598slE7Pj4+aLVaq/28/vrrptdTp05l+PDhjY4pLCzE09PTrG8hRMcjyw3E3VNeDvPmKQGCBQtg3z4JEAghhBBCAPztb/DkkzBmDKSktEqAACAuLg5XV1fT++TkZEJCQoiLi2tWOyqVyqZZBE1JTU1l8uTJLWpDCNH2JEgg7o6cHJgwATZuVLLzrl0LKlV7j0oIIYQQon0ZjfC73ynlDSMj4fvvlXLQrSQmJoZly5bh5+eHnZ0darWa6OhoYmJimtWOh4dHs3MTNBQREYG7u3uL2hBCtD1ZbiDaXkoKzJoFFRWwfTs8/nh7j0gIIYQQov1VVcGzzyoJnJ9/XplN4Nj6j+cxMTHNDgoIIbqvO/pbSKPR9ALWAx6AM/Baenr64dYcmOgiVqyApUuVKXP79sF997X3iIQQQggh2t/NmxAdDXv2wNtvQ2zsHZU4FEKI1nanyw1eA5LS09MnAguBT1ptRKJrqKmB3/xGiY5PngypqRIgEEIIIYQAyM+HiRNh715YuRL+8AcJEAghOow7nc/0AVBZr42K1hmO6BKKi2HuXGVN3WuvwV/+0iZT54QQQgghOp30dHjsMSgshG3bYNq09h6REEKYue03N41G8wzwaoPNi9LT049pNBpvlGUHr1g6Ny0treUjbIGKiop2H0Nb6MjX5ZyRwcCXXsIxP5/8d96hZNYsuHDB5vM78rW1hFxX5yLX1bl01esSQnRBR45ARATY20NyslIOWoh6dDodSUlJREZG8s9//pPU1FTs7e3x9PRk+vTppuSReXl5fP/992blK60pLi5mw4YNLF261Gz7kSNHKCsrIzw8HIAdO3YwceJE3NzcWv26ROdy2yBBenr6CmBFw+0ajWYk8BXwenp6+j5L51qqj3o3paWltfsY2kKHva7t25Xavq6usG8f/UNCaG6Bww57bS0k19W5yHV1Lp3xuk6cONHeQxBC3G3ffquUgu7fH3bvhiFD2ntEogPau3cvQUFBVFdXk5yczNKlS3FycmLz5s2cP38ejUZDSkoKZ86cwcnJ6bbtnT59mtTUVMrLy03bqqur2bZtG5cvXza7fwYHB5OUlMSMGTPa5NpE53FHOQk0Gs0IYCMwPz09fVfrDkl0OkajsqTgiScgIACOH4eQkPYelRBCCCFEx7BsGURFQWAgHDokAQJhUWVlJVqtFi8vLxwdHVm8eLEpEGAwGHC8tXy3d+/ezJkzx6Y2VSpVo9kGNTU1jBo1igkTJphtV6vVFBUVodPpWn4xolO708SFfwZcgA81Gs0PGo1mayuOSXQmej0sWAD/+Z9KHoL9+2HAgPYelRBCCCFE+zMa4Y9/VMobTp2qLDHw9GzvUYkOJj4+Hn9/fwIDAzl48CDx8fHY2dmZpv2npqZSVVXF4MGDARgxYgQODg42tR0QEICzs7PZNpVKxRArgSq1Wk1ubm4LrkZ0BXeUTS49PV3moAjIy4OZM+HkSfif/1ECBZKZVwghhBACqqvhhReU6gWLF8Pf/w42TA8X3Ut8fDxLlixBp9MxcuRICgoKWLJkCQDz589nz549XLt2jTlz5pjyEbQlNzc3mUkg7ri6gejujhxRps2VlcHWrRAZadNp9ZOx1FdSUsLWrVspKysjNTWViIgI1Gq12THfffcdubm5GAwGxowZwwMPPGBTn/n5+ezatQs7OzscHR2ZOXOmWUKW2tpavv32W27cuEFNTQ0PP/wwGo2G48eP06dPH1PUVgghhBDCJuXlMGcO7NwJb74Jb70lP6QIi2JjY01fysvLy3FxcUGn0xEbG4u7uzuOjo7MmzfvrgQIAPR6PT179rwrfYmO606XG4jubM0apbavq6sSLLAxQAD/SsbSUHJyMkFBQUyePJnx48eTlJRktj8zM5Pr16/zzDPPsGjRIlJSUtDr9Tb1mZiYyLRp01i4cCH33XcfKSkpZvvPnDmDSqVi0aJFLFiwgJ07dwIwZswYDhw4gMFgsPn6hBBCCNG9OVy7BpMnQ2KiMnvgT3+SAIGwKicnx/Q6Ly8PLy8vAKqqqvjxxx8pKChgzZo1rF69uslKPqdOneLUqVMtHk9+fj5+fn4tbkd0bjKTQNiupgbeeAPefx/CwuDrr6FvX5tPr5+MpaEpU6bQo0cPzp8/b5aYpc7AgQPx9vYGwM7ODqPRaPNarOjoaNzd3QEsth0YGMiIESMAMBqN2NsrsTN7e3u8vb25cOECGo3G5usUQgghRDd18SL+MTFQWAhbtihJnYVogq+vL9nZ2YASGNBqtXh7e+Ps7Mwf//hHq+fdc889PPvss6b3Pj4+aLVaq8e//vrrjbaNHj3a7H1hYSGenp706NGjuZchuhiZSSBsc+OGUtf3/ffh5ZeV6LiNAQJLyVgacnV1xcHBgdLSUvbs2cPEiRPN9js6OqJSqaitrSUhIYExY8Y0SsJiTV2AIDc3l2PHjvHggw+a7Xd2dqZHjx5UVlayceNGwsLCTPu8vLzIysqyqR8hhBBCdGO3qjvZl5ZCUpIECIRN4uLicHV1Nb1PTk4mJCSEuLi4ZrWjUqkafelvrtTUVCZPntyiNkTXIDMJxO2lpys3usxMpYTPc8/ZfKq1ZCx6vd70i35oaCgBAQFkZmaSkpLCvHnzGuUjAGWN1MaNG/Hz82tUsqW+c+fOcfToUUCZodC/f3/Onj3LgQMHmD9/vsV1ViUlJWzYsIFx48YxcuRI03Z3d3cJEgghhBCiabt2wZNPQr9+ZH/yCUOkFLSwUUxMDKDkJsjJyUGtVhMdHW3abisPD48WjyUiIqLFbYiuQYIEomm7dsFTT4GzsxIVb+LLuSXWkrG88847Zl++MzMzSUxM5OGHH6Z///6N2qmurmbt2rWEhIRw//33N9nniBEjTMsHQMk5cOLECRYuXIhKpWp0fFlZGevXr2fatGmNkhTq9Xqz6K4QQgghhJnVq+HZZ2HkSNi5k6obN9p7RKKTiYmJaXZQQIi2JEECYZnRqCwt+O1v4f77ISEB7iCJScNkLOHh4Y22A+zevZva2lqOHj3K2bNn6du3L5GRkezZs4cRI0aQk5PD9evXOXnyJCdPngRgxowZXLt2jfz8fMaPH2+xf4PBwK5du+jVqxcbNmwAwM/Pj8mTJ7NlyxbCwsI4dOgQer2e/fv3s3//fkD5y9rJyYnLly9brSMrhBBCiG7MaFRKQP/hDxAeDps3g4eHskRTCCE6MQkSiMYqKuD552HtWpg9W4mQ32EpFGvJWBomRHnhhRcASEtLY/jw4abtjz76KAD33nsvIRam7jk7O3PlyhWr/dvb2/PGG29Y3BcVFQXAtGnTmDZtWqP9BoOB/Px80xiEEEIIIQCorYV/+zelesGCBbBihTLrUgghugBJXCjMabUwaZISIPjTn5QKBi2oldpayVisMRqNhIaGtkpbDZ04cYLx48ebqh0IIYQQQqDTQXS0EiB44w2lNHQ7BQh0Oh3btm0zva+urmblypUUFRUBUFtby5YtW1i1ahWff/456enpt22zuLiYzz77zKyPdevWsWrVKjZt2kR1dTVGo5GEhASqq6tb/6KEEO1OZhKIfzl2DGbOhJIS+OYbuPVLe0u0VjIWa9zc3FqlHUvGjRvXZm0LIYQQohO6dg0iI+HIEfj4Y2U2QTvau3cvQUFBAGi1WrZv305paalp/5kzZ1CpVERFRaHX6/n73//eZFnn06dPk5qaSnl5uWnbvn37GDlyJKNHj+bgwYMcP36ckJAQfvGLX5CSksKkSZPa7PqEEO1DfiIVivh4JSmhszMcPtwqAYI6MTExZGVlYTAYyMrKksQsQgghhOh8srLgoYfg5EnYuLHdAwSVlZVotVq8vLwAqKmpYe7cuWYVogIDA00l7YxG421nR6pUKhYuXGi2LScnh6FDhwIwdOhQMjMzARg8eDDnzp3DaDS21iUJIToICRJ0d7W1ylS5BQvgwQeV2QT1SgAKIYQQQnR7p05BSAhcvQp79ijLDdpZXl6eWUDA19eXXr16mR3j7OxMjx49qKysZOPGjYSFhTXZZkBAAM4Nlk5UVlaackn16NGDiooKQMn71LNnTwoKClrjcoQQHYgsN+jOSkpg/nzYuROWLoUPPwQnp/YelRBCCGGVRqMJBv6Snp4+SaPRDAVWA0bgLPBSenq6oT3HJ7qgpCRlhmWvXnDwIAQGtutw4uPjiY2NxcPDA41Gg16vb3KWZklJCRs2bGDcuHGMvIMfgnr06EFVVRVOTk5UVlbi4uJi2ufm5mYqdS2E6DpkJkF3deGCMnPgu+/g00+VfyRAIIQQogPTaDS/BZYDdd9S3gf+kJ6ePgGwA2a019hEFxUfD9OmKWWgDx/uEAGCJUuWkJ2dTXl5OdXV1SxZsoT4+HiLx5eVlbF+/XrCw8P55S9/eUd9Dhw4kAsXLgCQkZGBr6+vaV9FRQU9W5DgWgjRMUmQoDvasweCgqCwUHm9dGl7j0gIIYSwxUVgVr33DwD7br3eBYTf9RGJrslohHffVZZjPvQQHDgAAwa096iIjY01/XKfl5eHl5cXOp2O2NhYi8cfOHAAvV7P/v37Wb16NatXr6a6uppTp05x6tQpm/p8+OGHOXv2LCtXriQvL8+UKNFoNFJaWkq/fv1a5+KEEB2GLDfoToxG+OgjeO01JRK+dSsMGoROpyMpKYnIyEizw0tKSti6dSsGgzJzMyIiwmztW0ZGBgcPHjS9z8nJYenSpTbdLC5dukRycrJpPVtUVBRO9WYyGI1GPvjgA/r06QPAgAEDCA8PZ8eOHUycOLFNqxoIIYTomNLT0zdrNBr/epvs0tPT67Km3QR6NT4L0tLS2npogPKr6t3qq6PqEp9BbS1ef/kLfdavp/Sxx9D+7/9ivHIFrlyx6fS2/AxycnJMr6uqqtBqtXh7e5OTk2PqMzg4mMLCQgoLC/H398ff39+sjYyMDPR6PcXFxaZcAw1Nnz7d7BoeeOAB0+uLFy8CcOXKFTw9Pfn5558bnd8l/hy0kHwG8hlA5/0MJEjQXVRWwosvwsqVyrq6tWvh1hft+uVz6ktOTiYoKIj77ruPjIwMkpKSmDt3rmn/0KFDTdluU1JSGDhwoM3R5J07d7Jw4ULc3Nz4/vvvOXnyJMHBwab9169fx8fHh6eeesrsvODgYJKSkpgxQ2aUCiGEoH7+AXfghqWDhg8fflcGk5aWdtf66qg6/WdQUQFPPw2bNsGrr+Lx3nt43KYiQENt+Rn4+vqSnZ1tep+cnExYWBhnzpxpVp+lpaW4u7tjZ2d3R+MwGo2kpaURGRnZKNEhdIE/B61APgP5DKDjfwYnTpywuF2WG3QH+fkQFqYECP7rv5Qb360AQcPyOfVNmTKFYcOGAWAwGHB0tBxTKi0t5cyZM0ycONHmIf361782zQaw1LZWq6W0tJQ1a9YQHx9PUVERAGq1mqKiIkmSI4QQAuBHjUYz6dbracCBdhyL6OyuX4epU5XnpL/+Fd5/H5oZIGhrcXFxuLq6mt6Xl5eTlJREXFxcs9rx8PC44wABgJ2dHbNmzbIYIBBCdH4d628+0fpOnoRx45TSPV9/DW+9Bfb2xMfH4+/vT2BgIAcPHrSY8MbV1RUHBweKiorYs2eP1SDA4cOHefDBB60GESxxd3cHlOhaVlYWo0aNarR//Pjx/PrXv2bChAls2bLFtE+tVpObm2tzX0IIIbqsfwfe0mg0hwFnYFM7j0d0Vrm5MGGCkpzwyy+VpZkdUExMDMuWLcPPzw87Ozv8/PxYtmxZk9UNhBCiuWS5QVe2YQMsWgT9+kFKCoweDfwrM65Op2PkyJEUFBSwZMkS9Hq96Yt+aGgoAQEBZGZmsnPnTqKioszyEdQxGo2cP3/+tnV3jx49yrlz5wCYNWsWHh4eHD58mLS0NBYsWNAowNC/f3/sb0XvfX19uXnzJkajETs7Oym3I4QQ3Vh6enoW8OCt1+cB26exCWHJ2bPw2GNw8yYkJiqzLzuwmJgYCQoIIdqUBAm6IoNBWVYQF6dk5P3mG/D0NO2unxm3vLwcFxcXdDod77zzDllZWabjMjMzSUxMJCYmhnvuucdiVwUFBajVarOkg5YEBQWZ5T3Yv38/V65c4emnn7Z47g8//ICrqysPPfQQ+fn5ZtPi9Hq9lNsRQgghRMvt2wczZoCrK+zfDw1mNgohRHckQYKu5uZNpVzPt9/Cs8/CJ59Ag/Vi9TPj5uXlER4e3mg7wO7du6mtrSUhIQGAvn37EhkZyZ49exgxYgT33nsvRUVF9O7d2+y8upI6o2/NXGiorKyMffv24ePjY1rmEBgYyLhx49i3bx8BAQGMHz+eLVu2cOHCBezt7Zk5c6bp/Pz8fB599NE7+XSEEEIIIRRff60kKRwyBHbtAj+/9h6REEJ0CBIkaAXWSgjevHmTLVu2UFtbi0qlIioqqlGpma+++gqdToe9vT1OTk42Tx+zWEIwNxeeeAJ+/hnDRx+xe+hQrqxfT01NDZMmTSIgIIDk5GRGjhzJmTNnAPPyOQ3H9sILL1jsu/4X9MDAQAIDA832+/j4oNVqrY7dzc2NN9980+K+iRMn4uDggEqlYv78+Y32FxYW4unpabVkjxBCCCHEbX34Ibz6KoSGKj+s3Cq5bEn957zTp09z6NAhXFxcGDVqFGPGjLF6nqVjr169SlpaGpMmTWqDixJCiNYhQYJWYK2EYEpKCqNGjWLUqFH88MMPnDx5kpCQELNjrl27xosvvtjsDLONSgh+9RXBr7wCRiPs3s2Zvn0xXL7M4sWLKS0tNeUDCAkJYcGCBfz3f/+3aclBcnIyU6ZMITo6+g4/AXMqlcrqLIKWSk1NZfLkyW3SthBCCCG6OIMB3ngD3nsPZs2C9etBpWrylLrnPJ1OR3JyMs8//zwuLi6sXbuWwYMHW1ySae1YLy8vDh06RHFxMX2aCEwIIUR7kuoGLdRUCcGpU6dy//33YzQaKSkpwcXFxWx/WVkZFRUVfPnll6xcuZLz58/b3K+phKDRiOHkSRw/+gi8veHYMXjkES5evIi7uztffPEF27ZtIyAgAAAXFxf8/Pz4+OOPTZlx1Wo10dHRrZYEp6VldZoSERFhqowghBBCCGGzqiplecF778FLLynLDW4TIKj/nHf9+nW8vb1RqVTY2dnRv39/8vLyLJ7X1LEjRozg2LFjrX55QgjRWiRIcIdsKSFoZ2eHwWDg008/JSsri0GDBpntr62tJSQkhHnz5jF37lx2795yDWGaAAAgAElEQVRNeXm5Tf27u7tDVRVpr7xC1sWLjOrfXynbM2QIoESwr1+/zlNPPcVDDz3E1q1bTed6enoSGBhIVlYWBoOBrKwsyZIrhBBCiK6rtBQefxy++AL+/Gf4+GNwcLB6uKXnvD59+lBQUEBZWRnV1dVkZmZSVVVl8fymjvXy8jJLFC2EEB2NLDe4A80pIejg4MBLL73EpUuXSEhIYOHChaZ23NzcGDt2rCmvgLe3N0VFRRYz99cvIThy5EgoKODwq6+S5uLCAm9vHD/7DOz/FfNxdnampKQEOzs7/P39uXbtGgAlJSWcPXuWmpoa0tLSiIiIaFTacNeuXeTm5uLs7Ex4eDgDBgyw6XOxmCehXuWCgwcPkpGRAfwriBEbG8uOHTuYOHEibm5ulJeXs3btWgwGA4DF8QEUFxezYcMGli5datPYQEl4uGvXLuzs7HB0dGTmzJnKbIxbTp06ZUq6WFNTQ35+Pq+//jqHDx/mF7/4Bf369bO5LyGEEEJ0EFqtEiD46SdYswZ+9asmD7f2nAfKLNGvv/4aV1dXfHx8cHV1tdiGSqWyeqy7uzt6vb51r1EIIVqRzCS4A02VEFy4cCELFy4kICCAHTt2kJmZCShf2htOwb906RIbN24ElASCBQUFVr+IBgUFmdrunZ3N/mefJcdo5OmwMFzj4swCBHXjqkvul5+fT69evQAl/8C9995LaGgo48ePJykpyey88+fPc+3aNZ577jnmzJnDzp07bf5cdu7cydy5c1m0aBF9+vTh5MmTZvvHjx9vuoaqqiqmTp0KQHBwsGkcZ8+eNV2rpfGBkgho06ZNNs+6qJOYmMi0adNYuHAh9913HykpKWb7R48ebRqfj48P06ZNw8XFhZCQEL777rtm9SWEEEKIDuDnn5XkhBkZsH37bQMEYP057w9/+ANXrlxh0aJFzJ49m6KiInx9fS22YTAYrB4rpZyFEB2dBAnuQMMSgnX5CBqWEAwODmbfvn2sWbOGvXv38vjjjwOwZ88eLl++zLBhw+jbty/Lly9n3bp1PPLII7i6upr9ot3I5s2olyxh3+jR3AwOJr66mtWrV5vWtq1btw6dTkd1dTUuLi4sX76c7du3ExERAcCUKVOorKxk8ODBGAwG08yHOoWFhQwZMgQ7OztcXV2xt7enrKzMps/FlCcBLLZd58yZM1RVVTF27FgA1Go1RUVF6HQ6Ro8ezbBhw5psQ6VSmc3IsFV0dDTe3t63HZ9Wq6WwsJAHHngAUPI4ODk5cfXq1Wb3KYQQQoh2kpICDz0Eej3s2we3fpy4HWvPednZ2QAsW7aMNWvWEBwcjKurK/n5+SQmJpq1YX/rx5uGxwJcvny50RJUIYToSGS5wR3w9fU13SiaKiGoVqstfpmtX0Lwsccea7TfYglBgwH+9Cd46y0cR43izRdfVBIV1hMfH8+bb77JW2+9RWhoKFOnTuXZZ581O8bOzg6j0QgowYq5c+ea7ff29ubw4cMEBQVRWlpKQUGB1fV2DdUlFExLSyMrK4uwsLBG44uNjSUyMhKdTkd8fLwpF4JarSY3N5cePXrg4OBAUVGRxfEBpiSMzVU3vtzcXI4dO2Y10HDgwAEmTpxots3T05OsrCyLCSqFEEII0cEkJMBTT8HAgZCYCIMH23xqU895kyZNalS+sE+fPmbLK+tYOhbgp59+kkpNQogOTYIEdyAuLs60Vg3uQgnBsjL49a/hm29g4cL/396dx0dV3/sffyUhO2EzMQEhBBEOSYwiCBLAjU1RdhCXYEWEXJd6tXaxbWq3a9pfbe0u9VJErI1KRYkiuyQKERSIAirxsCYhCTsKJpN95vfHkLlZJiEhy8xk3s/Ho4/OnHPmnM85jJkzn/l+Px/yn3ySIU4SBM2pk1BQUIBhGKxYsYKZM2c2mO8/cOBACgsLeeWVV4iIiKBPnz6NzrerXSdh1qxZdOvWje3bt5OTk8O8efPq/FJfE19oaCjV1dUUFhbWie/rr78mMDCQ/v37c+TIEdauXes0vpbYt28fO3bsAOwjKPr06cMXX3zB1q1bue+++5wO9SsrK+PMmTMNMvxhYWGcP3/+kmMRERGRDvKPf8B3vwsjRtinGLTwXqKl93lWq5WxY8c2a98nTpygZ8+e9OzZs0UxiYh0JCUJLkHNr98pKSnk5+e3SwtBh9xcmD4dvvgC/vQneOIJbF991eA1TdVJqF1B19/fn/Xr15OUlOS0r++ZM2fo3r07CxYs4Ny5c6Snpzdo3Vhj5MiRjBw50vF8y5YtHDt2jPvvv79BRr0mvoSEBPLz8xvE995773HllVdy7Ngx9u3b12h8LREXF0dcXJzj+d69e8nOzmb+/PkEN9LyKC8vz+kQQM0fFBERcXM2G/zsZ/Cb38CUKbBiBTTyQ0dTWnqf19h9kjORkZEalSgibk9JgkuUlJTU/m0DP/wQ5syBqipYtw4mTWp00/rz5yZMmNBgOcCGDRuorq4mPT0dgMsuu4ypU6eyadMm4uLiiIyMZPPmzezcuZMuXbo46ijU1EioM8KhluLiYj788EN69+7taAcZHx/PiBEjePXVVx29gS+77DLy8vIYPXp0nfiOHz/OxIkTWbt2LV26dGk0viuuuMLp8Q8ePMjx48cbzeRbrVbWrVtH9+7dWbFiBQD9+/fn1ltvZdWqVYwbN47u3btz+vRpp9n9wsJCxo8f73TfIiIi4mKVlbBokb17waJFsHgxNFJ7qDk65D5PRMRNKUngrv73f+1D5QYOhHffhYvMw29unYSHH37Y6etr10mYO3dug/VO6yTU0rVrV5555hmn6+6//36eeeYZ8vLyHN0SYmJiHPGdOnWKyy+/nMDAQG677TZiY2ObjK/GD37wgzrxHTt2rNH4fH19efrpp52umzlzpuPxmDFjGqwvLS3FarW2auqDiIiItJPiYvuPKhs2wK9+Bc88A/U6SomISPOpu4G7qayExx6Dhx+2jxz45JOLJgjAPn+udu2AzMxMEhMTSU1NbZOwGtRJaKGm4vvkk09aXcDHZrM5Rie0te3btzcowigiIiJu4MQJuOUWeP99+Oc/4ec/V4JARKSVNJLAnZw+DXfdBR98AD/6kX1OnZ9fs17aoXUSLkF7x1fTerE9KEEgIiLifixffMHm3/6WW/PyWPm739mnFyxfzvHjx5kwYYKj1XJ9e/fuZfv27fj6+jJ06FBGjBhBcXExW7ZscUyzFBHxZkoSuIvPP4dp0+DYMXj1VZg3r8W7cPf5c+4en4iIiHiIHTvIeO45Rn7xBV3fe4/5N9wA2NscZ2RkMGzYsEZfumnTJh599FECAgJ44YUXuPrqq+natSsBAQHk5uYSExPTQSchIuKeNN3AHaSnQ2IilJfDli2XlCAQERER8Qpr1lB+220U9e5N5OrVcCFBYLPZWLduHXfeeSe+vo3f4kZGRlJWVkZVVRUAPhemJyQkJPDJJ5+0f/wiIm5OIwlcyWaD1FR7gZ0RI+zJgj59XB2ViIiIiHtauhQefpiCiRMJHzUKBg1yrNq/fz+XX375RQsNR0REsGTJEgICAhgyZIijhWFERESDrlAiIt5IIwlcpaQE7rnHniCYN8/e7lAJAhEREZGGbDb49a9h0SI+9PfnnsJCXk9Pd7RdBnutgaamGQCcOHGCAwcO8MQTT/DEE09gsVj48ssvAXsnJD8/P2w2W7ueioiIu1OSwBXy8+HGG+HNN+G55+Bf/4LgYFdHJSIiIuJ+qqrgv/4LfvEL/u3nx4SyMs6WlFBZWUlycrIjUVBUVES/fv2a3FVgYCD+/v74+/vj6+tLSEgIZWVlgH26gq+vr2P6gYiIt1KSoKN99JF9asGhQ/Dee/DDH6pVj4iIiIgzFgvMmgX//Cd/79aN+6urqQIKCgqIjIzEYrGQkpJCSUkJgYGBdb7gHz9+nPXr19fZXY8ePRg+fDjLli1j2bJllJeXO1o8nzx5kr59+3bk2YmIuCXVJOhIL70EjzwCMTH26QVDhrg6IhERERH3dOoUTJ0KO3bACy/w39/9rmNVRUUFRUVFREVFkZ+fT2hoKA8//HCdl/fq1Qt/f/8Gu73++uudtkfcu3cvI0eObPvzEBHxMEoSdISqKvj+9+Gvf4VJk+CNN6BnT1dH1WlYLBY2b97M1KlTna7/+OOPKS4uZsKECQ3Wbdiwgfz8fHx8fJg0aRLR0dHNOuapU6dYvXo1YL8JmTZtWp1KyjabjTVr1nDixAn8/PyIi4sDIDMzk6uvvpqIiIiWnqaIiIj3OHwYbr8djh6Ft96CmTOJfu458vLyHJtkZmYybtw49u7d63QXVquVsWPHNutwxcXFlJeXN/s+QESkM9N0g/Z29ixMnmxPEDz1FKxZowRBG8vIyHCa+a+srOTtt99m586dTl93/Phxjh49ysKFC5k5c2aDIYlN2bx5M+PHj2fBggUAmKZZZ/1XX31FVVUVDz30EBMmTGDPnj0AJCYmsnHjxmYfR0RExOt8+imMHg2nT8P778PMmQCkpqYSEhLi2KykpITNmzeTmprqdDdBQUEEBgY265Bdu3ZlypQprY9dRKQTUJKgPe3bByNHwpYtsGwZPP88dNHgjbZUXl5OUVERkZGRDdZVVVVx7bXXcuONNzp9bbdu3fD396e6upry8vImeyrXN3fuXPr37091dTXFxcWO9kk18vPzueqqqwDo27cvX3/9NWC/YfH39+fEiRPNPpaIiIjX2LgRbr4ZAgPtdZzGjHGsSkpKYsmSJfTv3x8fHx/69+/PkiVLSEpKcmHAIiKdj5IE7eW992DUKCguhg8+gAcfdHVEnUpaWhoxMTHEx8eTlZVVpwVSjeDgYAYOHNjoPmoqGP/973/n1VdfZfTo0c0+vq+vL9988w2LFy/GYrE0SFKUl5fX+fXCx8cHq9UKwOWXX05ubm6zjyUiIuIV/vUvuPNOGDgQtm+H2NgGmyQlJZGbm4vVaiU3N1cJAhGRdnBJP2sbhhEKvAb0BCqAB0zTLGzLwDyWzWZva/iTn8CwYZCeDqqU26bS0tJITk7GYrGQkJDAyZMnSU5OprS0lC4XRmqMHj2awYMHN7mfPXv20LVrV+bNm0dFRQXLli2jb9++dOvWrcG2+/btY8eOHQBMmjSJPn360KNHDx5//HE+/fRTNm7cyIwZMxzbBwYGUlFR4Xhe01YJICwsjPPnz7f6OoiIiHQKNhv87nf2e6dx4+Dtt6F7d1dHJSLitS517PsiINs0zV8bhjEf+BHwRJtF5alKS2HhQnjtNbjnHns3g1pz56RtpKSkYLFYAPt8xKCgICwWC88++2yLfqEPCgoiICAAX19fAgIC6NKlS50v9rXFxcU5ig8CvP7660yaNInLLruMgICABj2V+/Xrx/79+4mPj6egoIDutW52SktLCQ0NbcEZi4iIdFLV1fDEE/DCC3DvvbB8OQQEuDoqERGvdklJAtM0/2wYht+Fp9HAN20XkocqKIAZM+zFdn7zG/jxj6HeF8e2YLFY2LVrF7H1huB9++23rFq1iurqaoKDg5k5c6bTYj1nz55lxYoVPPLII80+5sUq+dcoKCjg/fffZ/78+QDs2rWLXr16ceWVV7bgDC8uPz+/zjFruhbUXt6UTZs2ERcXR0JCAkePHuWll17CZrORkJBAeHg4Bw8e5Pjx401WRB47dizvvPMOfn5++Pv7OzorrFq1inHjxhEbG8vhw4d56aWXABw9mAEKCwsZP358i89bRESkNWp3A9q3bx8fffQRAAkJCYwaNarR1y1fvtzx+PTp0wwdOpRRo0axZcsW7rjjjksPqLQU5s2zjxz4wQ/sowlaUB9IRETax0WTBIZhPAR8r97iB03T3GkYRgaQAEx09tqcnJzWR9gKZWVlHRJD0J499Hv8cXwsFor+/neKb70VvvqqXY6VnZ1Nv379GpzXZ599RkREBDExMXzxxResW7cOwzDqbJObm8uBAwcoLS1t0XXJysrCMAwiIiLYsWMHmzdvpm+9KRRfffUVeXl5+Pn5OfYdHBzMhg0buOmmm5pdFLA5/2ZRUVEcO3YMqNsn2cfHx+lrAwMDueKKKxzr+vbty/nz5zl//jwDBw6sU7cgJyeHsrIyTpw4cdE4EhMTHY8LCgoAGDJkCEVFRRQVFdXZd815lZeXc+7cOU6dOsWpU6eacUXcW0f9N9bRdF6epbOel0hbq+kGZLVa2bx5M4sWLSIgIIDFixdzzTXX1OkcUFtN8v/rr7/mzTff5KabbiIgIICAgAByc3OJiYlpeTBnz8L06fbihH/+s300gYiIuIWLJglM03wJeKmRdeMMwxgCrAEaVIir/2t3R8vJyWn/GF55BZKT7XUHPviAfvHx7Xao8vJytm7dSmRkZIPzGjJkiOPx/v37iY6ObrCNn58f48eP569//WuLrothGPj6+lJdXU12djZXXXUVAwYMqLONzWbjpptuYtWqVXX2XVBQQJcuXRokLBrTnH+z3//+946aBGDvkzxp0iRmz57dJv/excXFXHPNNfj5+V1842aqOa+MjAymT5/utBuDJ+qQ/8ZcQOflWTzxvLKzs10dgniZ+t2AHnvsMXx9fSkpKcFqtTbrM2/9+vVMmDCBgAvTARISEvjggw9aniTIz4fbb4dDh+CNN2Du3JaejoiItKNLGtNlGMZPDMO4/8LTYqC67ULyEFVV8P3vw/z5MHYs7NgB7ZQgqF/J/7333muwTU31/MWLF5Obm9vgSzzA4MGDHR/sLXGxSv5gn7Pv7AYjMjKyzSv512+BFB4ezuzZs9uswnHXrl3bNEFQ27hx4zpNgkBERNxfY92AfH19ycnJ4cUXXyQmJgZ/f/8m93PixAnKy8vrTCGMiIho9lQ/h717ITERiors7Q6VIBARcTuXWrhwGfDKhakIfoB39ff75ht7YcING+Dxx+H55+EiH66Xylkl/5///Of07NmzQSV/Pz8/HnvsMQ4fPkx6erpjeGBLtbSSf1PCwsLapd1fUlKS2h6JiIg0obFuQGD/HI2NjWXIkCGkp6ezZ88errvuukb3tXfvXoYNG1Znma+vL35+fthstgYFfJ3KyICZMyEsDLKy4OqrW3V+IiLSPi61cOEJ4PY2jsUzmCZMmwZHjsCSJbBoUbsezlkl/7KysgaV/NesWUNcXBwDBgxwWm2/JVpayb8ppaWljc5xFBERkfbTWDegX/7yl1RWVjJv3jy6dOmCv7//RT/bjxw5wpgxY+osq2nv26z7gjfegO98BwYPhnXroF+/Sz4vERFpXyoh2xLr1sENN8DXX9uz4e2cIICGlfxrhqrXH953ww038OGHH/LKK6+QkZHhqDa8adMmCgsLG93/wYMHycrKajKGmkr+r7zyCnv37mXcuHGAvZL/uXPnmnxtYWFhm3c3EBERkYtr7B7i0KFDJCQksHz5cpYtW4aPjw/XXHMNxcXFrFy50um+iouLGyT9T5482aCQsVN//KO9vWFiImzdqgSBiIibu9TpBt7FZrN/wP3oR3DNNfDOOxAd3SGHjo6OJi8vD6hbyb9+e8Pw8HCn0wsmTmzYeOIHP/iB43Hv3r0dnQIa069fPxYsWNBg+cyZM+s879GjBwsXLnQ8t1qtHD9+3GkMIiIi0r6auocYPnw4w4cPr7N9SEgIYWFhTvf11FNPNVi2d+9eRo4c2XgAVqu9teGf/gRz5sCrr0JQ0KWfkIiIdAiNJLiYsjJ44AH7h9ysWfY5dB2UIABITU2tk7nPzMxk1KhRpKamtsn+bTYbo0ePbpN91Zednc3YsWOb3f5QRERE2o6ze4jExMRG7yFsNluDKQWNKS4upry8nOjG7onKy+G+++wJgv/+b/t0AyUIREQ8gkYSNKWoyF5gZ8cO+PWv4Wc/g1bM9b8UNcX5UlJSyM/PJzw8nNGjR7dpJf/2MmLEiHbbt4iIiDTN2T1EU92A/Pz8mn1f0LVrV6ZMmeJ85Tff2O+fPvgAnnvO/kNLB98/iYjIpVOSoDE7d8KMGXDuHLz9tv3DzkXqV/LPyclxWSwiIiLiOTq6G1CXEyfg7rvhq6/g3/8GdSISEfE4ShI4k5YGDz0EvXvD9u2QkODqiERERETc25dfEnPvvVBSAmvXwoQJro5IREQugSaL11ZdDU8/DfPmwahR9tEEShCIiIiING3rVhg7Fp+qKtiyRQkCEREPpiRBjXPnYNo0+9y5Rx6BTZsgPNzVUYmIiIi4t7fegokTITKS3Ndfh6FDXR2RiIi0gqYbABw4YE8QHDwIixfbkwQiIiIi0rS//93evWDUKFi9msqTJ10dkVuwWCxs3ryZqVOnAlBZWcmrr77KtGnTCA8Px2azsWbNGk6cOIGfnx/Tpk2jV69eje5v69at7N+/n+rqaq6//nqGDRvGrl276NWrF1deeWVHnZaIeAmNJNi0CUaOhFOn4P33lSAQERERuRirFX78Y3j8cZg61X4Pddllro7KbWRkZDBy5EgAioqKePnllzl79qxj/VdffUVVVRUPPfQQEyZMYOPGjY3uKzc3l4KCAhYsWMD8+fM5f/48AMOGDWPr1q1Yrdb2PRkR8TremySw2eAvf4Hbb4d+/ez1B26+2dVRiYiIiLi3igp44AH43e/g4Yft0w1CQlwdlduorKykqKiIyMhIAKqqqrj77rsJrzWNNT8/n6uuugqAvn37UlRU1Oj+Dh48yOWXX86KFSt4/fXXGTx4MAC+vr5ERUVx4MCBdjwbEfFG3pkkKC+3dy948kmYPh22bYMBA1wdlYiIiIh7+/ZbmDLF3t7w2Wft0zS7aPYqQFpaGjExMcyaNYusrCzS0tIAiI6Opnv37nW2LS8vJzAw0PHcx8en0REBFouFoqIi7rrrLu68807efvttbDYbAJGRkeTm5rbPCYmI1/K+JMHx43DrrfDyy/Dzn8PKldC1q6ujEhEREXFvx4/bR11mZNjvo1JSwMfH1VG5hbS0NJKTk8nLyyMkJISTJ0+SnJzsSBTUFxgYSEVFheO5zWbD19f5bXlISAgDBw7Ez8+P8PBwunTpgsViASAsLIzS0tK2PyER8WrelST49FMYMQL27IE334Rf/Qoa+YMsIiIiIheYJiQmwv79sHo1zJ/v6ojcSkpKiuOLe0lJCUFBQVgsFlJSUpxu369fP8c0gYKCAsfUBGeio6M5dOgQNpuNb7/9loqKCoKDgwEoLS0lRFM9RKSNec/4sBUr4MEHISICPvpI7XlEREREmuPjj+1TDHx9ITPT/oOL1JGfn+94XFBQwIQJExosry02NpbDhw/z0ksvATB9+nQAsrKyiIqKctQrABg8eDB5eXksXboUm83GHXfc4Rh1UFhYyMCBA9vlnETEe3X+JIHVCs88A7/5DYwZA2+/DZdf7uqoRERERNzfu+/CPfdAnz6wYQPoC6lT0dHR5OXlAVBRUUFRURFRUVF16g7MrzX6wsfHhylTpjTYT0REBH5+fg2WT5w4scEyq9XK8ePHna4TEWmNTj3W3rekBGbOtCcIFi60z6FTgkBERETk4v73f+33UfHx9iLPShA0KjU1tc6w/8zMTBITE0lNTW3RfqKiohjQzGLa2dnZjB07ttFaBiIil6rzjiQ4fJj+994LR47A3/4Gjz2m4joiIiIiF2OzwS9+Af/zP3DHHfYpmyry3KSkpCTAXpsgPz+f8PBwZs+e7VjeXPW7IDRlhKZ9iEg76ZxJgowMuOsu/Kuq7EPjxo93dUQiIiIi7q+yEh5+GJYtgwUL7KMJ1OKwWZKSkkhKSiInJ4fY2FhXhyMicsk61/gkmw1eeAEmTYKoKI785z9KEIiIiIg0R0kJzJhhTxD8/OewdKkSBCIiXqjz/OWvqIDHH4clS2DqVPj3v6ksLHR1VCIiIiLu7+RJeweD7Gz76IHkZFdHJCIiLtI5kgQnT8KcObB1K/z0p/Y5dL6+oCSBiIiISNMOHYLbb7ffN61aBdOmtWp3FouFzZs3M3XqVLZv385nn33mKOo3ZcoUwsPDnb7O2bbV1dXk5ORwyy23tComERFpPs9PEuzeDdOn2xMFr70G997r6ohEREREPMOuXfbihFYrbN4MiYmt3mVGRgYjR44E4NixY8yYMYM+ffpc9HWNbbtt2zbOnj1Lr169Wh2biIhcnGcnCd56C77zHejZE7KyYPhwV0ckIiIi4hnWrYO77oKICFi/Hgyj1busrKykqKiIyMhIwP7FPysri+LiYgYNGsSNN97Y6Gsb2zYuLo6dO3dy2223tTo+ERG5OM8sXGi1wi9/aZ9icM019iy4EgQiIiIizbN8ub2G0+DBsH17qxMEaWlpxMTEMGvWLLKyskhLSwMgPj6eKVOm8MADD3D06FH279/f6D4a2zYyMpLc3NxWxSciIs3neSMJiovhgQfg7bdh/nx48UUIDHR1VCIiIuIChmF8Cpy/8PSIaZoPujIet2ezQWoqPPMMTJxoH5UZFtaqXaalpZGcnIzFYiEhIYGTJ0+SnJyMzWZjzpw5BAUFATBo0CCOHTvG4MGDnYRlY9SoUU63DQsLo7S0tFUxiohI83nWSILcXBgzBtLT4U9/srfoUYJARETEKxmGEQT4mKZ5y4X/KUHQlOpqePRRe4Jg3jx4771WJwgAUlJSsFgsAJSUlBAUFITFYuFXv/oV//jHP6ioqMBms3HkyJFGaxOUl5c3um1paSmhoaGtjlNERJrHc0YSbNtmL1BYVWWfQzdpkqsjEhEREde6FggxDGMj9nuan5qm+XH9jXJycjokmLKysg47Vkv5lJZyxQ9/SFhGBqcXLuTU975n72rQBvLz8x2PCwoKmDBhAgCHDh1iyJAhvPjii/j5+XH55ZdTVVXFtm3byM3N5brrrquzH2fb5uTkUFhYSLdu3dz22tbnzu+DjqJroGsAugbgudfAc5IEL7wA4eHwzjv2+XMiIiLi7SzAH4ClwNRr5gMAABytSURBVCBgnWEYhmmaVbU3io2N7ZBgcnJyOuxYLXLmjL3+wMcfw9/+Rvh3v4vzJoSXJjo6mry8PAAqKiooKioiKiqKwMBAJk+ezOTJk+tsX1FRQWlpaYNrFRsb22BbsF/XSZMm0bNnzzaMuv247fugA+ka6BqArgG4/zXIzs52utxzkgQvvwz+/uDj4+pIRERExD3sBw6apmkD9huGcQboDRx1bVhuJDcXbr/d/v9vvgmzZ7f5IVJTUx01CQAyMzOZNGkSsxs5ltVqZezYsc3a94kTJ+jZs6fHJAhERDoDz0kSBAS4OgIRERFxLwuABOBRwzD6AN2AY64NyY3s3g2TJ0NZGWzaBE20H2yNpKQkwF6bID8/n/DwcGbPnu1YXl9NccLmiIyMdLRTFBGRjuE5SQIRERGRul4ClhuGkQXYgAX1pxp4rfffh1mzoEcP++P4+HY9XFJSEklJSW4/tFZERC5OSQIRERHxSKZpVgD3uToOt5OWZm8THRtrL/Z8xRWujkhERDyIZ7VAFBERERHnbDZ47jl7e8OxY2HrViUIRESkxZQkEBEREfF01dXw5JPw9NNw992wfj107+7qqERExAMpSSAiIiLiycrK4J574K9/he99D157DQIDXR2VtJDFYmH16tWO55WVlSxbtozTp0/X2a6goIDly5c3a5+VlZW8+OKLHDx4EIADBw7w6aeftlnMItI5KUkgIiIi4qm+/hpuuw1WroTnn4c//hF8dXvniTIyMhg5ciQARUVFvPzyy5w9e7bONh999BGrV6+mqqp59TnXrl2LT6324YMGDSInJ4fy8vK2C1xEOh19ioiIiIh4oqNH7W0Nt2+H11+Hp55ydURyicrLyykqKnK0e6yqquLuu+8mPDy8znY9e/Zk7ty5zdrntm3b6Nu3b4MWkldddRW7d+9um8BFpFNSkkBERETE03z+OSQm2hMF69fbpxuIx0lLSyMmJob4+HiysrJIS0sDIDo6mu5OakrExcXh5+d30f0ePnyYM2fOMHz48AbrIiMjyc3NbXXsItJ5qQWiiIiIiCf54AOYMQNCQ+0dDK65xtURySVIS0sjOTkZi8VCQkICJ0+eJDk5GYCkpKRW7fuzzz7j3LlzLF++nNOnT3Ps2DG6du1KVFQUYWFhlJaWtsUpiEgnpSSBiIiIiKf4z3/g/vth4ED7CILoaFdHJJcoJSUFi8UCQElJCUFBQVgsFlJSUlqdJJg9e7bjcXp6OldffTVRUVEAlJaWEhoa2qr9i0jnpukGIiIiIp7gL3+xTysYMQKyspQg8HD5+fmOxwUFBY7aAbWXN8fu3btbVGOgsLCQAQMGtOgYIuJdlCQQERERcWdWK/zwh/DkkzBzJmzaBL16uToqaaXoWkmeiooKioqKiIqKqrN8/vz5DYoX9ujRg4ULFzqe9+7dG5vN1uhxZsyYwVVXXeV4fuDAARISEtriFESkk1KSQERERMRdVVTYpxf84Q/w2GP26QbBwa6OStpAamoqISEhjueZmZkkJiaSmpraov0EBwczdOjQZm27f/9+YmNjCQwMbNExRMS7qCaBiIiIiDs6fx5mzYLNm+G3v4Wnn4ZaPe/Fs9XUHUhJSSE/P5/w8HBmz57d4noE3bp1a/a2gwcPbtG+RcQ7KUkgIiIi4m6KiuCOO+DLL+GVV+A733F1RNIOkpKSWl2kUESkrSlJICIiIuJOcnLg9tvh7FlYswYmTXJ1RCIi4kValSQwDGMI8AkQaZpmWduEJCIiIuKlPvoIpk6FgAD48EMYNszVEYmIiJe55MKFhmF0A54HytsuHBEREREvlZ4OEyZAeDhs2+YWCQKLxcLq1avrLFu9ejXvv/9+k6/Ly8tj6dKlLF26lE2bNgFQWVlJenp6k5X4RUTE9S4pSWAYhg+wBPgpYGnTiERERES8zT/+AbNnw7XX2hMEV17p6ogAyMjIYOTIkY7nu3bt4uTJkxd93YYNG5g9ezYLFy6kqKiIY8eO4e/vT9++fdmzZ097hiwiIq100ekGhmE8BHyv3uI84A3TNPcYhtHoa3NycloXXSuVlZW5PIb20FnPCzrvuem8PIvOy7N01vMSL2Gzwc9+Br/5DUyZAitWQK22eK5UXl5OUVERkZGRABw9epTCwkKGDx/O6dOnm3ztwoUL8fX1paKigrKyMgICAgCIj48nLS2t2S37RESk4100SWCa5kvAS7WXGYZxEHjoQgIhCtgI3FT/tbGxsW0U5qXJyclxeQztobOeF3Tec9N5eRadl2fxxPPKzs52dQjiDiorYdEie/eCRYtg8WLo4vqa0mlpaaSkpNClSxdGjx5NaGgo06ZN48MPP+Tuu+/myy+/vOg+fH19KSgoYOXKlURERDja9AUHB2OxWCgrKyMoKKi9T0VERC7BJX0SmaZ5Vc1jwzByAZXdFREREWmu4mKYMwc2bIBf/QqeeQZ8fFwdFWlpaSQnJ2OxWEhISODkyZMkJyfzzTff4O/vT1paGsXFxVRWVhIeHt7kiIC+ffvy5JNPkpGRQVZWFrfeeisAoaGhlJaWKkkgIuKmXJ+uFhEREfEmJ07AnXfC7t2wdCk89JCrI3JISUnBYrGXmyopKSEoKAiLxcLvf/97cnNzAdi9ezenT59uNEFgs9lYvnw599xzD8HBwQQEBFBVVeVYX1ZWRmhoaLufi4iIXJpWJwlM04xpgzhEREREOr8DB+C22+yJgnfesScL3Eh+fr7jcUFBARMmTGiwvLbi4mLWr1/PnDlzHMt8fHxITEwkLS2NLl260LVrV6ZNmwbgmGZQU6NARETcj0YSiIiIiHSEHTv+LymQmQm1uga4i+joaPLy8gCoqKigqKiIqKgoAgMDHdvUHkEQEhJCWFhYg/0MGTKEIUOGNFj++eefM2LEiHaIXERE2oqSBALY+yBv3ryZqVOn1ll+7tw53nnnHaxWKwBTpkwhPDy8zja7d+9m165dWK1WDMPg5ptvbtGxP//8c3bs2MFD9YZbVldX8+677/LNN99QVVXFTTfdhGEY7Nq1i169enGlm7SHEhERuag1a2DuXIiKgvXrYdAgV0fkVGpqqqMmAUBmZiaTJk1i9uzZTre32WyMGTOmWfuurKzk6NGjzJw5s83iFRGRtufr6gDEPdTvg1wjMzOTkSNHMn/+fMaOHcvmzZvrrD979iy7du3igQceYNGiRVRXV1NdXd3s4x47dozPPvsMm83WYN3evXsJDg7mwQcfZN68eaxduxaAYcOGsXXrVkfiQkRExK0tXQrTp0NsLGzb5rYJAoCkpCSWLFlC//798fHxITw8nNmzZ5OUlOR0ez8/P7p27dqsffv7+zNr1ix83KBAo4iINE4jCaRBH+TaJk2a5BhiaLVa6VKvNdPhw4fp3bs36enpFBcXc+ONN+Ln59es41osFjIyMrjttttYvXp1g/Xx8fHExcUB9l8qfH3tOS1fX1+ioqI4cOAAhmG06FxFREQ6jM0G//M/8Itf2OsQrFwJzfxC7UpJSUmNJgVERKTz00gCL5aWlkZMTAzx8fFkZWWRlpbWYJuQkBD8/Pw4ffo0mzZtajCVwGKxkJ+fz7Rp05g7dy7r1q2jrKzsose2Wq28++67dZIQ9QUEBBAYGEh5eTlvvvkm48aNc6yLjIx0VFkWERFxO1VV8F//ZU8QPPAArF7tEQkCERERjSTwUo31QS4tLXWMFhg9ejSDBw/myJEjrF27lpkzZzaoRxASEkL//v0JDAwkMDCQiIgIzpw5wxVXXNHgmPv27WPHjh0ATJgwgbNnz7JmzRqqqqo4deoU69evp3///nVec+7cOVasWMGIESNISEhwLA8LC1OSQERE3FNJCdxzD7z3HqSk2EcTaIi9iIh4CCUJvFRjfZCfffbZOl++jxw5wvr160lKSqJHjx4N9tOvXz927txJVVUVVquVU6dO0atXL6fHjIuLc0wfAHj00UcB+Oabb1i5ciW33347OTk5jvXFxcX8+9//ZvLkyQ2KFJaWlhISEnLJ5y8iItIuTp2CqVNh505YvBgeecTVEYmIiLSIkgReqrl9kDds2EB1dTXp6ekAXHbZZUydOpVNmzYRFxfHFVdcwXXXXceyZcuw2WzcdNNNBAcHc/DgQY4fP87YsWNbHNuqVasYN24c27Zto7S0lC1btrBlyxbAPk/S39+fwsJCBg4ceKmnLyIi0ub8jx61Fyg8ehTeegtmzHB1SFJP7W5Oe/fuZfv27fj6+jJ06NAmWzMePnyYzMxMfH19CQ0NdXRoWLNmDdOnT1cxRhHpVJQk8FLN6YMM8PDDDzt9/cSJEx2PR40axahRo+qs7927N8eOHWtWLD169GDhwoWO5zUfvJMnT2by5MkNtrdarRw/frxODCIiIi716afE3HcfWK3w/vvQzLaA0rFqd3PatGkTjz76KAEBAbzwwgtcffXVBAcHO33d2rVrmT9/Pl27duX999/n008/5YYbbqBv377s2bOHoUOHduRpiIi0KxUu9FKpqal1hutnZmaSmJhIampqm+zfZrMxevToNtlXfdnZ2YwdO9bR7UBERMSlNm6Em2/GFhAAH32kBIGbqt/NKTIykrKyMqqqqgCaHA3wwAMPOFo91u72FB8fz65du9o5chGRjqVvWV6qpX2QW6pr167NboXYUiNGjNBUAxERcQ//+hfceScMHEju669DbKyrI5J6GuvmFBERwZIlS1i8eDGDBg0iKCio0X2EhYUBkJOTQ25uLtdeey0AwcHBWCyWZnV2EhHxFJpu4MXUB1lEROQS2Wzwu9/BT34C48fDW29RVVTk6qiknsa6OZWXl2OxWHjiiScICAhg1apVfPnll8THxze6r+3bt5OTk8O8efMcIwkAQkNDKS0tbTLJICLiSTSSQERERKQlqqvh8cftCYL77oO1a6F7d1dHJU401s3p+eefx9/fH39/f3x9fQkJCWlyNMCWLVvIz8/n/vvvb9BdqaysjNDQ0HY9DxGRjqSRBCIiIiLNVVoKSUmwahX88Ifw//4fqEaO22qsm1NOTg7Dhw9n2bJl+Pn50atXL4YOHUpxcTHr169nzpw5jtcVFxfz4Ycf0rt3b8dUhfj4eEaMGEFZWRlBQUEEBAR07ImJiLQjJQlEREREmispCdLT4c9/hieecHU0chFNdXO6/vrruf766+tsHxIS4qg/UKNr164888wzTvf/+eefN9k6UUTEEyn1LSIiItJcY8bYkwRKEHiElnZzstlsjGlmd4rKykqOHj1KQkJCm8QqIuIuNJJAREREpLm+/31XRyAtUFOgOSUlhfz8/It2c/Lz83O0OrwYf39/Zs2a1Waxioi4CyUJRERERKTTUjcnEZGW0XQDEREREREREQGUJBARERERERGRC5QkEBEREXEhi8XC6tWrHc8rKytZtmwZp0+fvuhrrVYr//nPfzh48KDjtenp6dhstnaLV0REOjclCURERERcKCMjg5EjRwJQVFTEyy+/zNmzZy/6urNnz7J8+XKKioocy/z9/enbty979uxpt3hFRKRz8+okQf3MfY1vv/2Wf/3rX7z88su88cYblJeXN9hm3bp1LFmyhOXLl1NQUNDiY2/dupWVK1c2WG61Wlm3bh3Lli1jyZIl7N+/H7C37Dl16lSLjyMiIiLuq7y8nKKiIiIjIwGoqqri7rvvJjw8/KKvraioYOrUqcTExNRZHh8fz65du9ojXBER8QJenSSonbmv7aOPPuLaa6/lwQcfJCoqik8//bTO+v3793PmzBkWLVrE3LlzWbt2bYuOe+DAAQ4cOOB03d69e7FarSxYsIB77rnH8UtCYmIiGzdubNFxRERExL0VFBTUSQhER0fTvXv3Zr02KiqKiIiIBsuDg4OxWCyUlZW1WZwiIuI9vLYFYv3MfW233XYbADabjXPnzhEdHV1n/alTpxg4cCA+Pj6EhITg6+tLcXFxs/rqnj17luzsbG655ZYGyQeAQ4cOERERwWuvvYbNZmPy5MkABAUF4e/vz4kTJy7ldEVERMSNpKWlkZKSQrdu3TAMg9LS0jZt0xcaGkppaSlBQUFttk8REfEOXjeSIC0tjZiYGOLj48nKyiItLa3BNj4+PlitVhYvXkxubi4DBgyosz4qKopDhw5RXV3N119/zcmTJ6moqLjosSsqKli7di1TpkzB19f5pbdYLHz99dfce++9jBkzhnfeecex7vLLLyc3N7dlJywiIiJuJS0tjeTkZPLy8igpKaGyspLk5GSn9ySXqqysjNDQ0Dbbn4iIeA+vGklQ86FssVhISEjg5MmTJCcnU1paSpcu9ksxevRoBg8ejJ+fH4899hiHDx8mPT2d+fPnO/YzcOBACgsLeeWVV4iIiKBPnz6EhIQ4PeaOHTvYt28fAMOGDaO4uJiVK1dSVlbGt99+S1ZWFmPHjnVsHxwczKBBg/Dx8SEmJoYzZ8441oWFhXH+/Hm6devWDldHREREOkJKSgoWiwWwTzeYMGECFouFlJQUp6MJiouLWb9+PXPmzGnW/svKyggKCiIgIKBN4xYREe/gVUmC2h/KJSUlBAUFYbFYePbZZ+v8Qr9mzRri4uIYMGAAAQEB+Pj41NnPmTNn6N69OwsWLODcuXOkp6c3Opxv5MiRdeoeXHPNNQDk5uaya9euOgkCsM9FPHDgAHFxcRw/frzOvMTS0lL9KiAiIuLh8vPzHY8rKiooKioiKiqqzvLaP06EhIQQFhbW6P5mzJhR5/nnn3/OiBEj2i5gERHxKl6VJKj94VuTua+/HOCGG27gvffeY8uWLfj4+HDHHXcAsGnTJuLi4oiMjGTz5s3s3LmTLl26ONbv3r0bgKFDh7Y4tldffZX77ruPYcOGsWbNGpYuXQrAlClTHNsUFhYyfvx4dTkQERFpgVtu6ZjjWCzRNDKwsI6AgG2Ul/9fUcHMzArGjTvCxo3XOo3Vx8eGv/8Yfvvbi+/b17cSwzhKTs7M5gfehpp7DTozXQNdA9A1AF0DcP9r8Pzzzpd7VZIgOjqavLw8oG7mPjAwsM524eHhdTL4NSZOnOh4PHfu3Abre/fuXadXcVNiYmLqtCy6//77HY+nT5/eYPvS0lKsVivh4eFKEoiIiHiwAQMGsH+/idVqBaCkJIA1a2IZPHiA0+1tNj8qKi5eHBnAavUnJ2dWm8UqIiLex6uSBKmpqY6aBACZmZlMmjSJ2bNnt8n+g4ODL2kUQXNs376dcePGtcu+RUREOrMPPuiY4+Tk5BMbG9uMLSNJS3uflJQU8vPziY6OJjU1laSkm9o9xvbW/GvQeeka6BqArgHoGoD7X4PsbOfLvSpJUFMMqOZDOTw8nNmzZ7dZy6H2LCioBIGIiEjnkZSU1KYtD0VERNqKVyUJQB/KIiIiIiIiIo3xdXUAIiIiIiIiIuIelCQQEREREREREUBJAhERERERERG5QEkCEREREREREQG8sHChiIiIdA6GYfgCi4FrgXJgoWmaB10blYiIiGfTSAIRERHxVDOAINM0E4EfA8+7OB4RERGPpySBiIiIeKqxwHoA0zQ/Bq53bTgiIiKeT9MNRERExFN1A87Vel5tGEYX0zSram+Uk5PTIcGUlZV12LHcla6BrgHoGoCuAegagOdeAyUJRERExFOdB8JqPfetnyAAiI2N7ZBgcnJyOuxY7krXQNcAdA1A1wB0DcD9r0F2drbT5ZpuICIiIp7qI+AOAMMwRgGfuzYcERERz6eRBCIiIuKpVgETDcPYBvgAD7o4HhEREY+nJIGIiIh4JNM0rcDDro5DRESkM9F0AxEREREREREBlCQQERERERERkQuUJBARERERERERAHxsNlu77Dg7O7t9diwiItIJDB8+3MfVMXgD3Y+IiIg0ztn9SLslCURERERERETEs2i6gYiIiIiIiIgAShKIiIiIiIiIyAVKEoiIiIiIiIgIAF1cHUBHMAxjCPAJEGmaZpmr42ktwzBCgdeAnkAF8IBpmoWujar1DMPoDvwb6AYEAE+ZprndtVG1HcMwZgJ3maZ5n6tjaQ3DMHyBxcC1QDmw0DTNg66Nqu0YhnED8DvTNG9xdSxtwTAMf2AZEAMEAs+apvmuS4NqA4Zh+AH/BAzABjxsmuYXro1KvFFn/5vYXIZhfAqcv/D0iGmaD7oyno5U+3PDMIyrgOXY/y59ATxmmqbVlfF1hHrX4DrgPeDAhdX/ME1zheuia3/OPmuBfXjRe6GRa3AUL3ovOLs3AcrwwPdBpx9JYBhGN+B57B/cncUiINs0zZuwf6n+kYvjaStPAZtN07wZmA+84Npw2o5hGH8Bfkvn+G9uBhBkmmYi8GPs/311CoZh/AhYCgS5OpY2NA84Y5rmjcDtwN9dHE9bmQpgmuYY4GdAqmvDES/Waf8mNpdhGEGAj2mat1z4nzclCOp/bvwR+NmFv7k+wHRXxdZRnFyD4cAfa70fOu2XwlqcfdZ623vB2TXwtveCs3sTj3wfdIYvLI0yDMMHWAL8FLC4OJw2Y5rmn/m/G+Jo4BsXhtOW/gT874XHXbBn3jqLbcAjrg6ijYwF1gOYpvkxcL1rw2lTh4BZrg6ijb0JPHPhsQ9Q5cJY2oxpmulA8oWn/ek8fwfF83Tmv4nNdS0QYhjGRsMwMgzDGOXqgDpQ/c+N4cCHFx6vAyZ0eEQdz9k1uNMwjC2GYbxkGEaYi+LqSM4+a73tvdDYNfCa90Ij9yYe+T7oNNMNDMN4CPhevcV5wBumae4xDMMFUbVeI+f1oGmaOw3DyAASgIkdH1nrXOS8orCPkHiy4yNrnSbOa4VhGLe4IKT20A04V+t5tWEYXUzT9Pgvn6ZpvmUYRoyr42hLpmkWA1z4YF6JPbPdKZimWWUYxivATGCOq+MRr9Vp/ya2gAX4A/ZfkwcB6wzDMLzhGjj53PAxTbOmv/i3QPeOj6pjObkGO4ClpmlmG4aRAvwC+IFLgusgjXzW/sGb3guNXINAvO+9UP/eZKInvg86TZLANM2XgJdqLzMM4yDw0IUvblHARuAmF4R3yZydV6114y7UW1gDDOzQwFqpsfMyDCMBeAP4gWmaHzZ4oZtr6t+rEzkP1M4E+3rDjaAnMwyjH7AKWGya5muujqctmab5gGEYTwOfGIYRZ5pmiatjEq+jv4mwHzh44UZ4v2EYZ4De2Ocje5vac43D8M5RTqtM06w571XA31wZTEep/1lrGMZztVZ7xXvByTXo4Y3vhdr3JkBwrVUe8z7o1NMNTNO8qmYODHAcmOTikNqEYRg/MQzj/gtPi4FqV8bTVgzDiMM+VOk+0zTXuToeadRHwB0AF4aUfu7acKQphmFEYk+QPm2a5jJXx9NWDMO43zCMn1x4asF+Y+72hYCkU9LfRFjAhVoMhmH0wT664phLI3Kdz2qNHJwMbHVhLK6ywTCMkRcejweyXRlMR2jks9ar3guNXAOvei80cm+yyxPfB51mJIGXWQa8cmGEhB/QWQoE/RZ70Zu/XJgecs40TY8o7uFlVgETDcPYhn3OWWd5/3VWP8XeCeUZwzBq5gpONk2z1IUxtYW3gZcNw9gC+ANPdoJzEs+kv4n2EXTLDcPIwl7Be4EXjqao8X3gn4ZhBAA52Idde5tHgL8ZhlGJ/Ue65Its3xk4+6x9AvirF70XnF2Dp4A/edF7ocG9CfZ/e4/7m+Bjs9kuvpWIiIiIiIiIdHqderqBiIiIiIiIiDSfkgQiIiIiIiIiAihJICIiIiIiIiIXKEkgIiIiIiIiIoCSBCIiIiIiIiJygZIEIiIiIiIiIgIoSSAiIiIiIiIiF/x/yVMC/q+0jroAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1296x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots.pearson_spearman_plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.0.2 Theory: rank-transformation\n",
    "\n",
    "`scipy.stats.rankdata` simply takes an array of numbers and \"replaces\" them with the integers of their rank (1st smallest, 2nd smallest, 3rd smallest, etc.). `pd.DataFrame.rank` performs a similar function, but with support for `pandas.DataFrames`. So the result of the rank-transformation `scipy.stats.rankdata([3.6, 3.4, -5.0, 8.2])` is `[3, 2, 1, 4]`. See that in the figure above?\n",
    "\n",
    "A _signed_ rank is the same, just where we rank according to absolute size first and then add in the sign second. So the signed rank here would be `[2, 1, -3, 4]`. Or in code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def signed_rank(df):\n",
    "    return np.sign(df) * df.abs().rank()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I hope I don't offend anyone when I say that ranks are easy; yet it's all you need to do to convert most parametric tests into their \"non-parametric\" counterparts! One interesting implication is that *many \"non-parametric tests\" are about as parametric as their parametric counterparts with means, standard deviations, homogeneity of variance, etc. - just on rank-transformed data*. That's why I put \"non-parametric\" in quotation marks."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.0.3 Python code: Pearson correlation\n",
    "\n",
    "It couldn't be much simpler to run these models with `statsmodels` ([`smf.ols`](https://www.statsmodels.org/stable/example_formulas.html#ols-regression-using-formulas)) or `scipy` ([`scipy.stats.pearson`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.pearsonr.html)). They yield identical slopes, `p` and `t` values, but there's a catch: `smf.ols` gives you the *slope* and even though that is usually much more interpretable and informative than the _correlation coefficient_ $r$, you may still want $r$. Luckily, the slope becomes $r$ if `x` and `y` have a standard deviation of exactly 1. You can do this by scaling the data: `data /= data.std()`.\n",
    "\n",
    "Notice how `scipy.stats.pearsonr` and `smf.ols (scaled)` have the same slopes, $p$ and $t$ values. Also note that statistical functions from `scipy.stats` do not provide confidence intervals, while performing the linear regression with `smf.ols` does."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "correlated = pd.DataFrame()\n",
    "correlated[\"x\"] = np.linspace(0, 1)\n",
    "correlated[\"y\"] = 1.5 * correlated.x + 2 * np.random.randn(len(correlated.x))\n",
    "\n",
    "scaled = correlated / correlated.std()\n",
    "\n",
    "r, p = scipy.stats.pearsonr(correlated[\"x\"], correlated[\"y\"])\n",
    "res1 = smf.ols(formula=\"y ~ 1 + x\", data=correlated).fit()\n",
    "res2 = smf.ols(formula=\"y ~ 1 + x\", data=scaled).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value</th>\n",
       "      <th>p-values</th>\n",
       "      <th>t-values</th>\n",
       "      <th>0.025 CI</th>\n",
       "      <th>0.975 CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>scipy.stats.pearsonr</th>\n",
       "      <td>0.249694</td>\n",
       "      <td>0.080332</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>smf.ols</th>\n",
       "      <td>1.512744</td>\n",
       "      <td>0.080332</td>\n",
       "      <td>1.78652</td>\n",
       "      <td>-0.189770</td>\n",
       "      <td>3.215258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>smf.ols (scaled)</th>\n",
       "      <td>0.249694</td>\n",
       "      <td>0.080332</td>\n",
       "      <td>1.78652</td>\n",
       "      <td>-0.031324</td>\n",
       "      <td>0.530712</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         value  p-values  t-values  0.025 CI  0.975 CI\n",
       "scipy.stats.pearsonr  0.249694  0.080332       NaN       NaN       NaN\n",
       "smf.ols               1.512744  0.080332   1.78652 -0.189770  3.215258\n",
       "smf.ols (scaled)      0.249694  0.080332   1.78652 -0.031324  0.530712"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "utils.tabulate_results([r, p, None, None, None],\n",
    "                       [res1, res2],\n",
    "                       [\"scipy.stats.pearsonr\", \"smf.ols\", \"smf.ols (scaled)\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.0.4 Python code: Spearman correlation\n",
    "\n",
    "Note that we can interpret the slope which is the number of ranks $y$ change for each rank on $x$. I think that this is a pretty interesting number. However, the intercept is less interpretable since it lies at $\\text{rank}(x) = 0$ which is impossible since x starts at 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "ranked = np.argsort(correlated, axis=0)\n",
    "\n",
    "r, p = scipy.stats.spearmanr(ranked[\"x\"], ranked[\"y\"])\n",
    "res = smf.ols(formula=\"y ~ 1 + x\", data=ranked).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value</th>\n",
       "      <th>p-values</th>\n",
       "      <th>t-values</th>\n",
       "      <th>0.025 CI</th>\n",
       "      <th>0.975 CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>scipy.stats.spearmanr</th>\n",
       "      <td>0.233421</td>\n",
       "      <td>0.102803</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>smf.ols (ranked)</th>\n",
       "      <td>0.233421</td>\n",
       "      <td>0.102803</td>\n",
       "      <td>1.663134</td>\n",
       "      <td>-0.048772</td>\n",
       "      <td>0.515615</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                          value  p-values  t-values  0.025 CI  0.975 CI\n",
       "scipy.stats.spearmanr  0.233421  0.102803       NaN       NaN       NaN\n",
       "smf.ols (ranked)       0.233421  0.102803  1.663134 -0.048772  0.515615"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "utils.tabulate_results([r, p, None, None, None],\n",
    "                       res,\n",
    "                       [\"scipy.stats.spearmanr\", \"smf.ols (ranked)\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4 One mean\n",
    "\n",
    "## 4.1 One sample t-test and Wilcoxon signed-rank\n",
    "\n",
    "### 4.1.1 Theory: As linear models\n",
    "\n",
    "**t-test** model: A single number predicts $y$.\n",
    "\n",
    "$y = \\beta_0 \\qquad \\mathcal{H}_0: \\beta_0 = 0$\n",
    "\n",
    "In other words, it's our good old $y = \\beta_0 + \\beta_1*x$ where the last term is gone since there is no $x$ (essentially $x=0$, see left figure below).\n",
    "\n",
    "The same is to a very close approximately true for **Wilcoxon signed-rank test**, just with the [signed ranks](#3.0.2-Theory:-rank-transformation) of $y$ instead of $y$ itself (see right panel below).\n",
    "\n",
    "$\\text{signed_rank}(y) = \\beta_0$\n",
    "\n",
    "[This approximation is good enough when the sample size is larger than 14 and almost perfect if the sample size is larger than 50](https://lindeloev.github.io/tests-as-linear/simulations/simulate_wilcoxon.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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xHeORPn36UFZWRnl5OevXr6dv374d13V+XlhYyPDhwxk8eDBFRUX83//7f+nTp88245HO19fW1vLYY49x+OGHM3jwYGbPnt0xHunu+t/+9rds2LCB2tpaYrEYxx9/PPfffz9jxozh4x//OECXHADZbJbzzjtvl3/GCxcu3O4xCwlSHtuZN+52//7v/77f8+nA8tprr3Hsscfyne98h3/5l3+htLSUr3/965xyyiksWbKEDz/8EIAPPviAQw/d9u+5Qw45hLFjx7JgwYKOgtbOuuCCC7jqqqu46667OO644/jmN7/Jl770JXK5HEVFRUyfPn2b2Q5lZWV89atf5YYbbgDgiCOO4L/+678YMmRIt9e3z2YYNGgQd9xxB2+//TYDBw7ku9/9brc5ysrKeOWVV0ilUrvUF+2+IAiOpnXGwV1hGP4kCILvdjo8AGiIJpmkj5JKpbrcagkQj8f991O7xfHIfhqP5HK5SL5eeumlXE/12muvRR0hMvnc91wu//r/wAMP5OLxeA7o+IrH47kHHngg6mj7Vb793jvbm33/9re/nfvxj3+83df56le/msvlcrnp06fnqquruz1v4cKFuc997nN7LdNH2Z2+L1iwIHfxxRfv1Lk///nPc9/+9rd3+TVyuVyu7T0ysvfoA/HruOOOG3LcccfVHHfcced1aqs+7rjjzml7/OPjjjvu77e+zvFIz2Tf888DDzyQSyQSuVgslkskEnk3Fsnl8vd3n8s5HtlVPWE84urFUh5LJpNUVVWRSCSIxWIkEgmqqqpIJpNRR9MBqKamZpv7DNuVl5dz+OGHc9VVV/H6669z4YUXdnvemDFjGD58OL/73e/2ZdR97sMPP2TOnDncdNNNUUfJJ/8KlAD/FgTBs0EQPEvr7Q3/GQTBi0Af/rqGgqQeJplMUltby5IlS6itrWXcuHHMnj0baF2nZsaMGcyaNYvHHnus2/VxpHaOR/5qX45HvLVBynPJZJJkMpnX9+Vp71i6dCnDhw/f7vGvfe1rO/V92vc/7onOOOMM5syZs8PzDj74YGbu6aba2iVhGN4M3NzNoV2blyopcvPnz2fRokUUFxcDrQs+X3TRRRx99NE888wzLF68mJNOOinilOqpHI/81b4cjzgjQZK0VyxYsGC7nwBIkrSzSkpKmDRpUsfz9evXc/TRRwOtC/N2Xixa2prjkf3DQoIkSZKkHuOEE07osq1uSUkJtbW1ACxbtoxNmzZFlExSOwsJkiRJkiKVTqcpKytj1KhRlJWV8eijj3Ycu+yyy3j++ee57777OOigg+jfv3+ESSWBhQRJkiRJEUqn01RUVJDJZMjlcmQyGaZNm8aaNWsAeP3117n88su59tpryWazTluXegAXW5QkSZIUmcrKSrLZbJe2xsZG6uvrARg4cCD33XcfxcXFlJWVMXLkyChiSurEQoIkSZKkyHS3eGJDQwPTp0/nRz/6EUEQEARBBMkkbY+3NkiSJEmKTGlp6S61S4qehQRJkiRJkUmlUsTj8S5t8XicVCoVUSJJO2IhQZIkSVJkkskkVVVVJBIJYrEYiUSCqqoqkslk1NEkbYdrJEiSJEmKVDKZJJlMUlNTQ3l5edRxJO2AMxIkSZIkSdJOs5AgSZIkSZJ2moUESZIkSZK003ZrjYQgCIqBmUAZ0Be4JQzDX3U6/ingG8BmYGYYhjP2PKokSZIkSYra7s5IuBpYG4bhJ4C/A37YfqCtyPB94EJgHFARBMGQPQ0qSZIkSZKit7uFhJ8B/9b2OEbrzIN25cDyMAz/EoZhM/A88MndjyhJkiRJknqK3bq1IQzDDwGCIBgAPAx8vdPhQ4D3Oz3/ADi0u+9TU1OzOy+/zzU2NvbYbPtaPvcd8rv/9t2+55t87rskSdKe2K1CAkAQBEcDjwB3hWH4k06H1gMDOj0fADR09z166h6x+bx/bT73HfK7//bdvuebntz3hQsXRh1BkiRpu3Z3scUhwJPAF8IwfHqrwzXAyCAIBgIf0npbw217lFKSJEmSJPUIuzsj4V+BEuDfgiBoXythBnBQGIZVQRB8CXiC1jUYZoZh+PaeR5UkSZKUD1asWMFTTz3F5MmTefjhh/nwww8BaGho4KijjuKzn/1sxAml/La7ayTcDNz8EcergerdDSVJkiQpP82fP59FixZRXFwM0FE02LhxI/feey8TJkyIMp4kdn/XBkmSJEna60pKSpg0adI27c8++yynn346AwYM6OYqSfuThQRJkiRJkUqn05SVlTFq1CgmTpxIdXXXyc0bNmzgrbfe4pRTTokooaTOLCRIkiRJikw6naaiooJMJkMulyOTyTBt2jTWrFnTcc5rr73GiSeeSEGBf75IPYH/J0qSJEmKTGVlJdlstktbY2Mj9fX1Hc/ffPNNRo4cub+jSdoOCwmSJEmSIlNXV9dte3Nzc8fjtWvXUlJSsr8iSdoBCwmSJEmSIlNaWrpNW0NDA/Pmzet4/k//9E/069dvf8aS9BEsJEiSJEmKTCqVIh6Pd2mLx+OkUqmIEknaEQsJkiRJkiKTTCapqqoikUgQi8VIJBJUVVWRTCajjiZpO4qiDiBJkiQpvyWTSZLJJDU1NZSXl0cdR9IOWEiQJEmS1KOsWLGCp556ismTJ7Nhwwaqq6vZuHEjuVyOT3/60wwcODDqiFJes5AgSZIkqceYP38+ixYtori4GIB58+YxevRoRo0axVtvvcWaNWssJEgRc40ESZIkST1GSUkJkyZN6nheX1/P+vXrue+++1i8eDFlZWXRhZMEWEiQJEmSFLF0Ok1ZWRmjRo1i4sSJVFdXdxxraGigX79+XHvttRx66KHMnz8/wqSSwEKCJEmSpAil02kqKirIZDLkcjkymQzTpk1jzZo1APTv358gCAA47rjjWLlyZZRxJWEhQZIkSVKEKisryWazXdoaGxupr68HoLS0lNdffx2ATCbDEUccsd8zSurKxRYlSZIkRaaurq7b9ubmZgAuvPBCqqureemll+jXrx+XX375/ownqRsWEiRJkiRFprS0lEwm06WtoaGBefPmAXDYYYdxzTXXRBFN0nZ4a4MkSZKkyKRSKeLxeJe2eDxOKpWKKJGkHbGQIEmSJCkyyWSSqqoqEokEsViMRCJBVVUVyWQy6miStsNbGyRJkiRFKplMkkwmqampoby8nBUrVjB79mwmT57MqlWr+OlPf8rAgQMBOO200zjxxBMjTizlNwsJkiRJknqM+fPns2jRIoqLiwFYtWoVZ555Jn/7t38bcTJJ7by1QZIkSVKPUVJSwqRJkzqer1y5ktdff51Zs2bxy1/+kqampgjTSQILCZIkSZIilk6nKSsrY9SoUUycOJHq6uqOY8OGDeOCCy5gypQplJSU8Nvf/jbCpJLAQoIkSepFgiA4IwiCZ9senxoEwdtBEDzb9vX3EceT1I10Ok1FRQWZTIZcLkcmk2HatGmsWbMGgPLyco488siOx++8806UcSXhGgmSJKmXCILgn4FrgA1tTWOB74VheHt0qSTtSGVlJdlstktbY2Mj9fX1ADzwwANcdNFFDBs2jDfffJOhQ4dGEVNSJxYSJElSb/EGcDlwf9vzsUAQBMFlwOvAF8Mw/GDri2pqavZfwl3Q2NjYY7Pta/Y9v/peV1fXbXtzczM1NTWccMIJPPLIIxQUFNCvXz9OO+20XvkzysfffTv7fuD13UKCJEnqFcIw/HkQBGWdmv4A3B2G4cIgCCqBfwe+svV15eXl+ynhrmnfBi8f2ff86ntpaSmZTKZLW0NDA/PmzWPGjBkAebFjQz7+7tvZ957Z94ULF273mGskSJKk3uqRMAzbR0GPAKdGGUZS91KpFPF4vEtbPB4nlUpFlEjSjlhIkCRJvdUTQRCc3vb4PGD7H61IikwymaSqqopEIkEsFiORSFBVVUUymYw6mqTtsJAgSZJ6q38Evt+2i8NZwC3RxpG0PclkktraWpYsWUJtbS3jxo1j9uzZXc5ZvHgx99xzTzQBJXXhGgmSJKnXCMOwFjiz7fHLtBYQJB1A5s+fz6JFiyguLu5oW7VqFa+88gq5XC7CZJLaOSNBkiRJUo9RUlLCpEmTOp5ns1meeeYZJkyYEGEqSZ1ZSJAkSZLUY5xwwgkUFhYC0NLSwq9+9SsuvPBC+vbtG3EySe0sJEiSJEmKVDqdpqysjFGjRlFWVsajjz4KtN7SsG7dOn7961/z8MMPs3r1ah5//PGI00pyjQRJkiRJkUmn01RUVJDNZgHIZDJMmzaNm2++mWHDhvFP//RPADQ0NPDwww/zd3/3d1HGlYQzEiRJkiRFqLKysqOI0K6xsZH6+vqIEknaEQsJkiRJkiJTV1e3TVtDQwPTp0/v0nbYYYdxww037K9Ykj6ChQRJkiRJkSktLd2ldknRs5AgSZIkKTKpVIp4PN6lLR6Pk0qlIkokaUcsJEiSJEmKTDKZpKqqikQiQSwWI5FIUFVVRTKZjDqapO1w1wZJXaxYsYKnnnqKyZMnd2l/8cUXeeWVVzo+MbjkkksYNGhQBAklSVJvk0wmSSaT1NTUUF5ezooVK5g9ezaTJ09m9erVVFdXAzBw4EAuvfRSCgr8PFSKkoUESR3mz5/PokWLKC4u3ubYqlWr+PSnP82RRx4ZQTJJkpQvth6PPP3005x33nkkEgkeffRRwjCkvLw84pRSfrOUJ6lDSUkJkyZN6vbYqlWreP7555k5cybPPffcfk4mSZLyxdbjkUmTJpFIJNiyZQsffvgh/fr1izCdJLCQIOW9dDpNWVkZo0aNYuLEiR1TB7c2atQoLrnkEq677jrq6+tZtmzZfk4qSZJ6q48ajxQUFNDQ0MBdd91FNptlyJAhESaVBBYSpLyWTqepqKggk8mQy+XIZDJMmzaNNWvWdDkvl8tx5plnEo/HKSwsZOTIkaxatSqi1JIkqTfZmfHIYYcdxk033cRpp53Gk08+GWFaSWAhQcprlZWVZLPZLm2NjY3U19d3aWtqamL69Ok0NzeTy+V46623XCtBkiTtFTsaj/z0pz9l7dq1APTp04dYLLbfM0rqysUWpTxWV1fXbXtzczMAixcvprm5mbFjxzJ+/HjuvfdeCgsLGT58OCNHjtyfUSVJUi+1o/HI2WefzS9/+UsKCwspLi7mU5/61P6MJ6kbe1RICILgDOA7YRies1X7/wfcAKxua7oxDMNwT15L0t5XWlpKJpPp0tbQ0MC8efMAGD16dEf7ySefzMknn7xf80mSpN5vR+ORo48+mqlTp0YRTdJ27PatDUEQ/DNwN9DdsqljgWvDMDyn7csigtQDpVIp4vF4l7Z4PE4qlYookSRJyjeOR6QDz56skfAGcPl2jo0FpgVB8HwQBNP24DUk7UPJZJKqqioSiQSxWIxEIkFVVRXJZDLqaJIkKU84HpEOPLt9a0MYhj8PgqBsO4cfBH4ErAceCYLgkjAM52x9Uk1Nze6+/D7V2NjYY7Pta/ncd8jP/o8ZM4a5c+fS2NjYsS9zvv0M8vH33s6+52ffJamnSSaTJJNJampqKC8vZ8WKFcyePZvJkyfzzjvvMHfuXGKxGEVFRXz605/m4IMPjjqylNf2+mKLQRDEgDvCMHy/7fmvgVOBbQoJ5eXle/vl94r2f8DyUT73HfK7//bdvuebntz3hQsXRh1BkiIzf/58Fi1aRHFxMQCPP/44F110ER/72Md46aWXmD9/PhMmTIg4pZTf9sX2j4cArwZBcHBbUWE84IhIkiRJ0g6VlJQwadKkjudXXHEFH/vYxwBoaWmhqMiN56So7bVCQhAEVwVBUNE2E+Ffgd8AzwFLwjB8bG+9jiRJkqTeJZ1OU1ZWxqhRo5g4cSLV1dUdxwYMGABAfX09f/zjHznzzDOjiimpzR6V88IwrAXObHv8k07t9wP371EySZIkSb1eOp2moqKCbDYLQCaTYdq0adx8880d57z66qs899xzXHXVVRx00EFRRZXUxnlBkiRJkiJTWVnZUURo19jYSH19PQCLFi1i4cKFTJ48mf79+0cRUdJWLCRIkiRJikxdXV237c3NzbS0tDB37lwOPfRQHnroIQASiQTnnnvu/owoaSsWEiRJkiRFprS0lEwm06WtoZosGBsAACAASURBVKGBefPmUVBQwNe+9rWIkknann2xa4MkSZIk7ZRUKkU8Hu/SFo/HSaVSESWStCMWEiRJkiRFJplMUlVVRSKRIBaLkUgkqKqqIplMRh1N0nZ4a4MkSZKkSCWTSZLJJDU1NZSXl0cdR9IOOCNBUhcrVqxg9uzZ27S/9tprzJgxgxkzZrBgwYL9H0ySJOWN7sYjjz/+OC+99FI0gSR14YwESR3mz5/PokWLKC4u7tLe0tLC008/zec+9zn69OnDXXfdxUknnbTN/YySJEl7auvxyIYNG3j00UdZu3YtgwYNijidJHBGgqROSkpKmDRp0jbtBQUFfP7zn6dfv35s3LiRlpYWCgsLI0goSZJ6u63HI83NzYwbN46TTjopwlSSOrOQIOW5dDpNWVkZo0aNYuLEiVRXV3d7XkFBATU1Nfz4xz+mrKxsm1kLkiRJu+ujxiMlJSUcddRREaaTtDULCVIeS6fTVFRUkMlkyOVyZDIZpk2bxpo1a7o9v7y8nC996Uts2bKFP//5z/s5rSRJ6o12dTwiKXqukSDlscrKSrLZbJe2ww47jA8++KBLW1NTE3fffTfFxcXEYjEKCgoYPnz4/owqSZJ6qe7GI42NjdTX10eUSNKOWEiQ8lhdXV2X52eddRannnoquVwOgMWLF9Pc3Mypp55KNpvl0EMPpaCggNWrVzNixIgoIkuSpF5m6/FIu+bm5v2cRNLO8tYGKY+VlpZ2eb5u3TqefvppYrEYAKNHj2bs2LEUFBRw0UUXEYvF2LRpEwUFBa6RIEmS9oqtxyMADQ0NzJs3r0vbOeecw2mnnba/Ykn6CBYSpDyWSqW6bOE4cOBAzj//fPr27dvlvJaWFn7zm99w+umns2HDBlpaWti0adP+jitJknqhrccjAPF4nFQqFVEiSTtiIUHKY8lkkuuuu65jK8eGhgaKira946mgoIBzzz2XP/zhD8TjcTZv3kxNTc3+jitJknqhZDJJVVUViUSCWCxGIpGgqqqKZDIZdTRJ22EhQcpj6XSae++9ly1btgCtCy22tLR0rJHQbuPGjfzyl79k7NixZLNZcrkcLS0tUUSWJEm9UDKZpLa2liVLllBbW8u4ceOYPXs20Hrr5cyZM5k1axZz5szZZpwiaf+zkCDlsa1XSV63bh1PPfVUR5Fg8eLFLFy4kP79+zNhwgRefvllDjnkEICOdRQkSZL2pvnz51NdXc3mzZsBeOKJJxg/fjxTpkwBYOnSpVHGk4SFBCmvZTKZLs9ramr44IMPOtY/aF9ssampiVdffZUzzzyT9evXM3DgQBdblCRJ+0RJSQmTJk3qeL5q1SoSiQQAI0aM4M0334wqmqQ2FhKkPFZQ8NH/BLTPSOjbty+jR49mwYIFlJSUkMvlnFYoSZL2mnQ6TVlZGaNGjWLixIlUV1d3HMvlch0zIfv27UtTU1NUMSW12XZVNUl5o7t1DtavX8/q1auB1hkJAE1NTSxevJjJkydTVFTEnDlzdliEkKQoBEFwBvCdMAzPCYJgBDAbyAGvAp8Pw9AFXqQeJp1OU1FR0XG7ZSaTYdq0adx8881A19spm5qa6NevXyQ5Jf2VfwlI2q6tZyTMnj2bmTNnEovFOOmkk6KOJ0ldBEHwz8DdQPtfGd8Dvh6G4SeAGHBZVNkkbd/WazYBNDY2Ul9fD8DQoUOpra0FYPny5ZSWlu7viJK24owEKY8dfvjhrF27tktbQ0MDjzzyCDNmzOiYkQAwduxYxo4du78jStKueAO4HLi/7flY4Ldtj+cCFwKPbH1RT93OtrGxscdm29fse371va6urtv25uZmampqOPbYY3nsscdoaWlhwIABDB8+vFf+jPLxd9/Ovh94fbeQIOWxO++8kylTpnQsrghQXFzMnXfeGWEqSdo9YRj+PAiCsk5NsTAM2xd0+QA4tLvrysvL93W03VJTU9Njs+1r9j2/+l5aWrrNAtANDQ3MmzePGTNmAHD66adHEW2/ysfffTv73jP7vnDhwu0e89YGKY8lk0lmzZpFIpEgFouRSCSYNWsWyWQy6miStDd0Xg9hANAQVRBJ25dKpYjH413a4vE4qVQqokSSdsRCgpTnkskktbW1LFmyhNraWosIknqTV4IgOKft8UXAcxFmkbQdyWSSqqqqLh9sVFVVOSaRejALCZIkqbf6MvCfQRC8CPQBHo44j6TtaP9gY9GiRdx+++1s3LiR+++/f5u1nCT1DK6RIEmSeo0wDGuBM9seLwPGRRpI0i5588036dOnDzfccANr1qxh7ty5XH311VHHkrQVZyRIkiRJ6hHWr1/PiBEjABg0aBCrV6+OOJGk7lhIkCRJktQjHHbYYSxbtoxcLseKFSv44IMPaGlp2fGFkvYrb22QJEmSFKl0Ok1lZSX19fVcccUVLF26lDFjxjB06FAKCvzsU+pp/L9SUhcrVqxg9uzZ3R7btGkTM2fOZM2aNfs3lCRJ6rXS6TQVFRVkMhmOPPJI/vznP/PNb36Turo6SkpKoo4nqRvOSJDUYf78+SxatIji4uJtjq1cuZI5c+awfv36CJJJkqTeqrKykmw2C8C6desYP348xcXFLFiwgO9973sRp5PUHWckSOpQUlLCpEmTuj22efNm/v7v/55Bgwbt51SSJKk3q6ur63iczWa57777uOeee7jnnnsYMGBAhMkkbY+FBCnPpdNpysrKGDVqFBMnTqS6urrb80pLSzn00EP3czpJktTblZaW7lK7pOhZSJDyWOd7EnO5HJlMhmnTprkGgiRJ2m9SqRTxeLxLWzweJ5VKRZRI0o5YSJDyWOd7Ets1NjZSX18fUSJJkpRvkskkVVVVJBIJYrEYiUSCqqoqkslk1NEkbYeFBCmPdb4nsbPm5mYAFi9ezMKFC/dnJEmSlIeSySS1tbUsXryY22+/ncbGRmbNmuUsSamHspAg5bHu7j1saGhg3rx5AIwePZqxY8d2OT558mQXXJQkSfvEqlWraGlp4frrr+eTn/wkzzzzTNSRJHXDQoKUx7wnUZIk9SQDBgygpaWFXC5HU1MTBQX+uSL1REVRB5AUnfZ7DysrK6mrq6O0tJRUKuU9iZIkab9Kp9NUVlbS0NDAtddeyxtvvEFhYSFXXXVV1NEkdcNCgpTnkskkyWSSmpoaysvLo44jSfvdOedEnaB72WwpW00ayxv2PeoU+9e7777LsmVH09IymwkTlvPaawX86EcjOOWUYaxb9yh//OM/0tLS+/9sycfffTv7HnWK7t1++/aPOVdIkiRJUmTeeustWlpaANi4sZimpiJaWlpYtmwVsdgWoCXagJK20ftLe5J2yYoVK3jqqaeYPHlyl/YwDPnd735HQUEBp5xyyjaLMErSgerZZ6NO0L2amrq8nSlm3/Or7wUFfwvkAFiwoA+XXXYZU6YcTGFhIcnk/8u3v90n2oD7ST7+7tvZ957Z94/avM1CgqQO8+fPZ9GiRRQXF3dp37JlC0888QSf+9zn6NOnDzNnziQIAg4++OCIkkqSpN6itLSUTCYDtG5B/bOf/QyARCLBjBkzoowmaTu8tUFSh5KSEiZNmrRN+5o1axg4cCD9+/ensLCQo48+uuMNX5IkaU+4i5R04LGQIOW5dDpNWVkZo0aNYuLEiTz88MOsXr26yzlNTU00NzczY8YM7rnnHtatW0dTU1NEiSVJUm+STCapqqoikUgQi8VIJBJUVVW5i5TUg+1RISEIgjOCIHi2m/ZPBUHwxyAIXgyC4HN78hqS9p10Ok1FRQWZTIZcLsdRRx3FkiVL2LRpU5fzioqKWLVqFVdffTWTJ09m5cqVESWWJEm9UTKZpLa2ljlz5vAf//EfbNq0ibvvvptbbrmFxsbGqONJ2spuFxKCIPhn4G6g31btxcD3gQuBcUBFEARD9iSkpH2jsrKSbDbb8XzdunX86le/orm5eZtzY7FYx+NcLtexurIkSdLeMnz4cCZPnszkyZMZOnQoF110Ef369dvxhZL2qz1ZbPEN4HLg/q3ay4HlYRj+BSAIgueBTwI/24PXkrQP1NXVdXleU1NDaWlpR5Fg8eLFNDc3c8QRRzB06FAeeOABcrkcRx55JAUF3hklSZL2jZUrV7J69WouvvjiqKNI6sZuFxLCMPx5EARl3Rw6BHi/0/MPgEO7+x41NTW7+/L7VGNjY4/Ntq/lc98h//p/6KGH0tDQALTOOLj44osZNmwYAH/4wx8YMGAARUVFvP3226xbt46ioiKKiorYsGEDa9as6TU/q3z7vXdm3/Oz75LU06TTaSorK6mrq6O0tJQvfOELXHHFFVHHkrQd+2L7x/XAgE7PBwAN3Z3YU/fLrKmp6bHZ9rV87jvkX/8LCws7Hh9//PEUFRXx0EMPcc011/Dmm29y5ZVXArBq1Sqefvppbr75Zvr06cNtt93GFVdcweGHHx5V9L0q337vndn3ntn3hR+1cbMk9TLtaza132757rvvkslkeOGFFxg+fHjE6SR1Z18UEmqAkUEQDAQ+pPW2htv2wetI2kPr1q3reFxaWsry5csB2LhxIytXruy4taFfv34ce+yxPPjgg+RyOQYNGsTGjRujii1JknqRrddsSiQSvPHGG1RXV7tzg9RD7bWbnIMguCoIgoowDDcBXwKeAF4EZoZh+Pbeeh1Je09paWnH4759+9LY2EhDQwPz5s0jFosxatQoxo4dy+DBg1m/fj3XXnstV199NdlsttsFGSVJknbV1ms2HX744fzlL3/Zpl1Sz7FHMxLCMKwFzmx7/JNO7dVA9R4lk7TPTZw4kenTpwPQ1NRE3759O9pzuVzHgopHHHEEH//4x0mn0xx66KEMGzaMeDweWW5JktR7lJaWkslkOp6/8MILQOvMBEk9k8uuS3nsscce63hcV1fHyJEjAfjjH//IkCF/3bV1w4YNNDc3M3XqVC6++GLWr1/P4MGD93teSZLU+6RSqW0+oIjH46RSqYgSSdqRfbFGgqQDROcpg0uXLuXYY4/l+uuvB2DChAm8+OKLDBw4kOOOO47Vq1czY8YMCgsLueCCC9z+UZIk7RXt6yB03rUhlUq5PoLUg1lIkPJY56mEuVyOOXPmAK1TCQcNGsSgQYM6zv3Upz4VSUZJktT7JZNJkslkj95RR9JfWUiQ8lgqleqy3RI4lVCSJEXrueeeY9myZWzZsoXTTjuNMWPGRB1J0lYsJEh5zKmEkiSpJ3nvvfdYuXIlU6dOZdOmTR0LL0rqWSwkSHnOqYSSJKmneOeddxg8eDAPPfQQTU1NXHDBBVFHktQNV0uTJEmSFKl0Ok1ZWRk/+clPeOihh9i8eTMXX3wxv/jFL8jlclHHk7QVCwmSJEmSIpNOp6moqCCTyZDNZnn11Ve58cYbeeKJJygqKuqylpOknsFCgiRJkqTIVFZWdhQL6urqGDFiBNlslltuuYXm5mb69+8fcUJJW3ONBEmSJEmRqaur63i8bNkyEokEn/vc54jFYkycOJGCAj/7lHoaCwmSJEmSIlNaWkomk+l4Pm/ePAASiQT/+7//G1UsSR/BQoIkAHK5HHPmzOHdd9+lsLCQSy+9lIEDB3Ycf+GFF3j11VeJxWKcffbZ7vAgSZL2ilQqRUVFRZe1EOLxOKlUKsJUkj6K84QkAfD222+zefNmrr/+es4//3yefPLJjmONjY38/ve/5/rrr+fqq6/miSeeiDCpJEnqTZLJJFVVVSQSCWKxGIlEgqqqKpLJZNTRJG2HMxIkAbBmzRpGjx4NwFFHHcXKlSs7jhUXF3PYYYfR3NzMpk2biMViUcWUJEm9UDKZJJlMUlNT46xH6QDgjAQpz7Xv2/zggw9y4403kk6nAYjFYrS0tHScd8ghh3DXXXfxv//7v5x++ulRxZUkSZIUMWckSHmsfd/mbDbL8ccfz/vvv09FRQXQumZC+yrJy5cv58MPP+Tmm28G4IEHHqC0tJRhw4ZFll2SJElSNJyRIOWxrfdtHjlyJNlsljvuuIMhQ4Z0nNevXz+KioooLCykqKiIfv360djYGFVsSZIkSRFyRoKUxzrv27x06VKOPfZYrr/+egAmTJjAiy++yMCBAwmCgDfffJN77rmHWCzG0UcfzTHHHBNVbEnaJUEQvAysb3v6VhiGU6LMI0nSgc5CgpTHOu/b3L79I7Tu2zxo0CAGDRrUce65557LueeeG0lOSdpdQRD0A2JhGJ4TdRZJknoLCwlSHnPfZkl54GQgHgTBk7SOe/41DMMFnU+oqamJJNiONDY29ths+5p9z8++Q373377b9wOJhQQpj7Xvz1xZWUldXR2lpaWkUin3bZbUm2SB24C7gZHA3CAIgjAMN7ef0FO3msvnbfDse372HfK7//bdvvc0Cxcu3O4xCwlSnnPfZkm93DJgeRiGOWBZEARrgaFAfbSxJEk6cLlrgyRJ6s2mArcDBEFwJHAIsCrSRJIkHeAsJEiSpN7sHuCwIAieBx4Cpna+rUFSz7Rhwwa+//3vs2bNmqijSOpGpLc2nHNOlK++fdlsKfF41Cmikc99h/zuv32POkU07HvUKbp3++1RJ+g9wjBsBq6KOoeknbdlyxbmzJlDUZF3YUs9lTMSJEmSJPUYTz75JGPHjmXAgAFRR5G0HZGW+Z59NspX376amrq8XXQun/sO+d3/117L8Oabb/Luu+9SWFjIpZdeysCBAwF45513ePzxxzvOXbFiBVdeeSUjRoyIKu5elc+/d/veM/v+EYskS1Kv9tZbb3HwwQczYsQInn/++ajjSNoO5wtJAuDtt99m8+bNXH/99axYsYInn3ySK6+8EoCPfexjTJ48GYAlS5ZwyCGH9JoigiRJil46naayspLx48fTt29fXnzxRXK5HI888gj/8A//wMEHHxx1REmdWEiQBMCaNWsYPXo0AEcddRQrV67c5pzm5maeffZZpkyZsr/jSZKkXiqdTlNRUUE2m2XWrFkAxONxvvGNb/CZz3zGIoLUA7lGgpTn0uk0ZWVlPPjgg9x4442k02kAYrEYLS0tXc595ZVXOOGEE4j31BXqJEnSAaeyspJsNtulLZvN8tZbb0WUSNKOWEiQ8lj7JwCZTIampibef/99KioqSKfT5HI5Cgq6/hOxePFixowZE1FaSZLUG9XV1XXbXlVVxaBBg/ZzGkk7w0KClMc6fwJQV1fHyJEjyWaz3HHHHQwZMqTLuY2NjWzevJlDDz00iqiSJKmXKi0t3aV2SdGzkCDlsc6fACxdupQjjzySadOmcf7553PGGWfw4osvEoYhAH/60594//33ufvuu/n1r39NLpeLKrYkSepFUqnUNrdNxuNxUqlURIkk7YiLLUp5rLS0lEwmA8Dxxx/PypUrueuuuzjttNM4+eSTO3ZtaGpq4uWXX+amm24iHo8zf/58stksBx10UJTxJUlSL5BMJoHWmZJ1dXWUlpaSSqU62iX1PM5IkPJY508ASktLWb58OfF4nC9+8Ytddm2or69nyJAhPPnkk8yaNYuDDjrIIoIkSdprkskktbW1LF68mDvvvJOmpiZmzpzJe++9F3U0Sd2wkCDlsWQyyXXXXUdhYSF9+/alubmZ6667jmQy2WXXhvaVk88//3ySySS///3vWbt2bcTpJUlSb7Nq1SoApk6dyvjx43nmmWciTiSpO97aIOWxdDrNvffey5YtW2hqaqK4uJh7772Xs846q8uuDfF4nGHDhnXs41xaWso777zD4YcfHmV8SZLUywwbNowgCABoaGigX79+ESeS1B1nJEh5bGd3bRg6dCjvvfce2WyWlpYW3n77bY444oioYkuSpF4mnU5TVlbGqFGjOOaYY/je977H3LlzGT16dNTRJHXDQoKUx7betWHz5s1cf/31nHzyyUyYMKFj14aDDjqI8847jwceeIC7776b448/nsGDB0eYXJIk9RbpdJqKigoymQy5XI5MJsO//du/ceSRR1JdXU1zc3PUESVtxVsbpDzWedeGXC7HnDlzAEgkEgwaNIhBgwZ1nHviiSdy4oknRpJTkiT1Xp1nSJ500kkccsghPP/889xyyy184QtfIBaLRZxQ0tackSDlMfdtliRJUes8Q7KmpoahQ4cyZcoUxo0bx4QJEyguLo4wnaTuOCNBymPu2yxJkqLWeYbkpk2b+NnPfga0zpC8++67o4wmaTuckSDlufZ9m5csWUJtba1FBEmStF85Q1I68DgjQRLw1zUS3n33XQoLC7n00ksZOHBgx/G5c+dSX19Pnz59ALjyyivdkkmSJO0xZ0hKBx4LCZIAePvttzt2bVixYgVPPvkkV155ZcfxVatWcfXVV2/ziYEkSdKeSiaTJJNJlixZwrJly2hoaGDGjBl88pOfJAiCqONJ2oqFBEkArFmzpmOv5qOOOoqVK1d2HMvlcqxbt47q6mo2bNjAqaeeyqmnnhpVVEmS1EtlMhn69+/PZz7zGTZu3MiPf/xjCwlSD+QaCVKeS6fTlJWV8eCDD3LjjTeSTqcBiMVitLS0ANDc3Mzpp5/O5ZdfTjKZ5I9//CPvvvtulLElSVIvdNRRR3HuuecCrR9kFBT454rUE+32jIQgCAqAu4CTgSbghjAMl3c6fidwNvBBW9NlYRi+vwdZJe1l6XSaiooKstksxx9/PO+//z4VFRVA1zfv4uJizjjjjI7tl4YPH84777zDkCFDIssuSZJ6j3Q63WWNhG9961u0tLQwfvz4qKNJ6saelPg+DfQLw/BvgH8Bbt/q+FhgQhiG57R9WUSQepjKykqy2SzQuofzyJEjyWaz3HHHHV2KBGvXrmXmzJm0tLSwZcsW6urqGDp0aFSxJUlSL9L+wUYmkyGXy/GXv/yFF154gWw223HbpaSeZU8KCWcDjwOEYbgAOK39QNtshZFAVRAE84MgmLpHKSXtE3V1dR2Ply5d2rHY4sknn8yECRN48cUXCcOQI444gpNOOol77rmH2bNnc/LJJzN48OAIk0uSpN6i8wcbBx10ENdccw1PPPEE3/nOdyJOJml79mSxxUOAzrMMtgRBUBSG4WbgIOB/gO8BhcBvgiB4KQzDRZ2/QU1NzR68/L7T2NjYY7Pta/ncd8i//n/sYx9j1apVwF+3fwQYOnQoX/7ylznssMNoaWmhpqaGgQMHcvbZZ3dc25t+Tvn2e+/Mvudn3yWpJ+n8wcYnPvEJ+vfvz7hx4wCYPXs2yWSy4/ZKST3DnhQS1gMDOj0vaCsiAGSBO8MwzAIEQfAMrWspdCkklJeX78HL7zs1NTU9Ntu+ls99h/zr/6233tqxRkK7eDzOrbfemlc/h3z7vXdm33tm3xcuXBh1BEnab0pLS8lkMgA8/vjjPP744wAkEglmzZoVZTRJ27EntzbMByYCBEFwJrC407HjgPlBEBQGQVBM620QL+/Ba0naB5LJJFVVVSQSCWKxGIlEgqqqKpLJZNTRJElSnkilUsTj8S5t8XicVCoVUSJJO7InMxIeAS4IguAFIAZMCYLgS8DyMAx/FQTB/cACYBNwXxiGS/Y8rqS9LZlMkkwme/Sns5Ikqfdq/wCj864NqVTKDzakHmy3CwlhGLYA/2er5qWdjt8K3Lq731+SJElSfvCDDenAsie3NkiSJEmSpDyzJ7c2SOpF2ndtePfddyksLOTSSy/9/9u7/+i66zrP48+kNW0DadlQxJGSRKF8iPVH2TL8qMBUflj5ObjKwenl7JQNFFDWBccVnc4Zz+4x6/gbXA/jhm1R1njsDA4jP2zBQwRKaacSQWG8fLSz0BQpSMAW2DSh+bF/JA03aQLf/Lrfm3yfj3M43O/n+733vt83TfrpK5/v90t1dfVBx/zwhz8khMCJJ544yitJkiRJmslckSAJgGeffZZnnnkGgK6ursFbQRa6//772bVr1+CVlSVJkiRlj0GCJACeeeYZDjnkEBoaGjj//PPZtWvXkP2/+c1vaGtro6KiIqUKJUmSJJUCgwQp45qbm6mrq+Pxxx/n7rvvprm5mUWLFtHT00Nvby8Af/jDH3jkkUeora096HQHSZIkSdniNRKkDGtubmbNmjV0dHQAsGfPHtasWXPQcVu3buWll15i9uzZPP/887S3t7Njxw6OPfbYYpcsSZIkKWWuSJAybO3atUNChJqaGjo6OrjxxhspLy+nvLz/R0RlZSWHH3744PP6+vpSqVeSJElS+lyRIGVY4UUTH3/8cc466ywaGhqoqKjgqKOOYuvWrVRXV3POOecMHve9732PqqoqVyNIkiRJGeWKBCnDZs2aNfj4qaeeGrxrw/79+7nwwgtHfE5dXR21tbXFKE+SJElSCXJFgpRhPT09g4/7+vqG3PLxlltuYeHChQc9Z8WKFcUoTZIkSVKJckWClGGjrSxwxYEkSZKk0RgkSBnW2NhIZWXlkLHKykoaGxtTqkiSJElSqTNIkDIsl8vR1NREbW0tZWVl1NbW0tTURC6XS7s0SZIkSSXKayRIGZfL5cjlcuTzeerr69MuR5IkSVKJM0iQJEkzVgihHLgZ+ADQBVwRY9yRblWSJE1vBgmSgDfu2vDCCy8wa9YsLrroIqqrqwf3b9++nV/96lcALF++nCVLlqRVqiSNxcXA3BjjqSGEU4BvAH+eck2SJE1rBgmSAPj9739Pd3c3DQ0NPPvss9x333184hOfAKCjo4NHH32Uq666iu7ubm6++Wbe8573UFZWlnLVkvSWTgM2AcQYt4UQThx+QD6fL3pRSXR2dpZsbVPN3rPZO2S7f3u39+nEIEESAO3t7bzvfe8DYNGiRTz33HOD+yorK7n66qspLy9nz549zJ492xBB0nQxH9hbsN0TQpgdY+w+MFCq14fJ8rVr7D2bvUO2+7d3ey81ra2to+7zrg1SxjU3N1NXV8ePfvQjrrrqKpqbmwEoKyujt7d38Ljy8nK2b9/OunXrBgMHSZoGXgGqCrbLC0MEyNDIzAAAG6BJREFUSZI0dq5IkDKsubmZNWvW0NHRwfHHH8/evXtZs2YN0H/NhPLyoVnjSSedxLJly2hububpp5/mXe96VxplS9JYbAEuBP5h4BoJT6RcjyRJ054rEqQMW7t2LR0dHQC0tbWxePFiOjo6uPHGGznyyCMHj2tvb2fDhg2D4cKsWbM8tUHSdHEH0BlCeAT4FnB9yvVIGoP9+/ezfv162tvb0y5FUgFXJEgZ1tbWNvj4qaee4phjjqGhoQGAlStXsnXrVqqrqwkhcOSRR7Ju3TrKyso49thjqaurS6lqSUouxtgLXJ12HZLG7rnnnuPuu+/mlVdeSbsUScMYJEgZVlNTw86dO4E3bv8IUFtby8KFC1m4cOHgsStWrGDFihVplClJkjKou7ubSy+9lDvuuCPtUiQN46kNUoY1NjZSWVk5ZKyyspLGxsaUKpIkSepXU1PDggUL0i5D0ggMEqQMy+VyNDU1UVtbS1lZGbW1tTQ1NZHL5dIuTZIkZciBu0hde+21XH311XzlK18ZcvcoSaXFUxukjMvlcuRyuZK+h60kSZq5Cu8itXPnTlpaWqisrGTRokX+ckMqUa5IkCRJkpSawrtIHdDR0cHatWtTqkjSW3FFgiRJkqTUFN5FaqTx1atXF7EaSUm4IkGSJElSampqasY0Lil9BgmSJEmSUuNdpKTpxyBBkiRJUmq8i5Q0/XiNBEmSJEmp8i5S0vTiigRJkiRJkpSYQYIkSZIkSUrMIEGSJEmSJCVmkCBJkiRJkhIzSJAkSZIkSYkZJEiSJEmSpMQMEiRJkiRJUmIGCZIkSZIkKTGDBEmSJEmSlJhBgiRJkiRJSswgQZIkSZIkJWaQIEmSJEmSEjNIkCRJkiRJiRkkSJIkSZKkxAwSJEmSJElSYrPH+8QQQjlwM/ABoAu4Isa4o2D/lcBVQDfwpRjj3ROsVZIkSZIkpWwiKxIuBubGGE8FPg9848COEMI7gE8DHwRWAl8OIcyZSKGSJEmSJCl9EwkSTgM2AcQYtwEnFuw7CdgSY+yKMe4FdgDvn8B7SZIkSZKkEjDuUxuA+cDegu2eEMLsGGP3CPteBRYMf4F8Pj+Bt586nZ2dJVvbVMty75Dt/u3d3rMmy71LkiRNxESChFeAqoLt8oEQYaR9VcCe4S9QX18/gbefOvl8vmRrm2pZ7h2y3b+923vWlHLvra2taZcgSZI0qomc2rAFOA8ghHAK8ETBvu3A6SGEuSGEBUA98OQE3kuSJEmSJJWAiaxIuAM4J4TwCFAGXB5C+AywI8Z4Zwjh28Bm+sOKtTHGzomXK0mSJEmS0jTuICHG2AtcPWz4qYL9twC3jPf1JUmSJElS6ZnIqQ2SJEmSJCljDBIkSZIkSVJiBgmSJEmSJCkxgwRJkiRJkpSYQYIkSZIkSUrMIEGSJEmSJCVmkCBJkiRJkhKbnXYBkiRJkjTc1q1beeyxx6isrATgggsuYOHChSlXJQkMEiRJkiSVoN27d3PxxRfzzne+M+1SJA1jkCBJkiSp5OzevZuHH36Y1157jcWLF3P66aenXZKkAQYJkg4SY+Shhx6ivLycpUuXsmzZsiH7n3/+eTZu3EhZWRmzZ8/m4osv5tBDD02pWkmSNN01Nzezdu1a2traqKmpobGxkSVLlnDSSScxZ84cNmzYwG9/+1uOO+64tEuVhEGCpGF6enq49957ufLKK6moqGD9+vWEEIYEBZs2beLcc8/lHe94B48++ihbtmxh5cqVKVYtSQcLIZQBzwK/GxjaGmP8QoolSRpBc3Mza9asoaOjgzPPPJOamhp+/vOfc8YZZ7BixQoAFi9ezO7duw0SpBJhkCBpiPb2dqqrq5k3bx4ARx99NDt37mTJkiWDx3zsYx+jqqoKgN7eXmbP9keJpJJ0DPDLGOOFaRciaXRr166lo6MDgJaWFgDmzJlDdXU1r7/+Om9729t4+umnOeGEE9IsU1IBZ/+Shujq6mLu3LmD23PmzKGrq2vIMQdChF27dvGLX/yC1atXF7NESUpqGXBUCOHnwD7g+hhjHH5QPp8vemFJdHZ2lmxtU83es9V7W1vbQWNdXV3cd999LFq0iFmzZvH2t7+d7u7uGf3ZZPFrf4C9T7/eDRKkjDtwTuIxxxzD4sWLOeqoo3j3u989uH94sHDAk08+yebNm1m1ahWHHHJIMUuWpIOEEBqA64cNfwr4cozxH0MIpwE/AP50+HPr6+uLUOHY5fP5kq1tqtl7tnqvqalh586dB43v2bOHT3/60ylUlI4sfu0PsPfS7L21tXXUfQYJUoYVnpO4c+dOWlpaOPTQQ/nCF77Avn37qKiooK2tjeXLlw953q9//WtaW1tZvXr14CkQkpSmGOM6YF3hWAihEuge2P9wCOGdIYSyGGNfGjVKGlljY+PgfOSAyspKGhsbU6xK0psxSJAyrPCcxANee+01Nm7cyBFHHEFfXx9Lly5l/vz5vPjii2zfvp1zzz2XjRs3smDBAjZs2ABAbW0tH/rQh9JoQZLezBeBl4CvhhA+AOwyRJBKTy6XAzjorg0HxiWVHoMEKcNGOicRYMuWLWzevHnI2BFHHMH5558PwA033DDltUnSJPg74AchhPPpX5mwOt1yJI0ml8uRy+VKepm3pDcYJEgZNto5iTU1NSlUI0mTK8b4R+D8tOuQJGmmKU+7AEnpaWxspLKycsiY5yRKkiRJejMGCVKG5XI5mpqaqK2tpaysjNraWpqamjwnUZIkSdKoPLVByjjPSZQkSZI0Fq5IkCRJkiRJiRkkSJIkSZKkxAwSJEmSJElSYgYJkiRJkiQpMYMESZIkSZKUmEGCJEmSJElKzCBBkiRJkiQlZpAgSZIkSZISM0iQJEmSJEmJGSRIkiRJkqTEDBIkSZIkSVJiBgmSJEmSJCkxgwRJkiRJkpTY7LQLkFR6Yow89NBDlJeXs3TpUpYtWzbicU888QTbt2+noaGhyBVKkiRJSosrEiQN0dPTw7333stll13G6tWr+eUvf8lrr7120HG7d+/mscceo6+vL4UqJUmSJKXFIEHSEO3t7VRXVzNv3jxmzZrF0Ucfzc6dO4cc09HRQUtLCytXrkypSkmSJElpMUiQMq65uZm6ujqWLFlCXV0dd911F3Pnzh3cP2fOHLq6uga3e3t7ufPOO/nwhz/MnDlz0ihZkiRJUoq8RoKUYc3NzaxZs4aOjg7OPPNMampq2LFjB4cffvjgMV1dXUOChd27d/Pyyy9zzz330N3dzYsvvsimTZv4yEc+kkYLkiRJkorMIEHKsLVr19LR0QFAS0sLAOXl5Vx33XXs27ePiooK2traWL58+eBzjjrqKD75yU8CsGfPHm6//XZDBEmSJClDDBKkDGtraztorLe3l3vuuYfjjz+evr4+li5dyvz583nxxRfZvn07559/fgqVSpIkSSoVBglShtXU1Bx0IUWAzs5OrrzyyiFjRxxxxEEhwmGHHcYVV1wxpTVKkiRJKi1ebFHKsMbGRiorK4eMVVZW0tjYmFJFkiRJkkqdQYKUYblcjqamJmpraykrK6O2tpampiZyuVzapUmSJEkqUZ7aIGVcLpcjl8uRz+epr69PuxxJkiRJJc4VCZIkSZIkKbFxrUgIIcwDfgC8HXgV+MsY44vDjvkJsBDYD+yLMZ47wVolSZIkSVLKxrsi4RrgiRjj6cBtwN+McMxi4LQY4wpDBEmSJEmSZobxBgmnAZsGHm8Ezi7cGUI4EjgMuCuE8HAI4YLxlyhJkiRJkkrFW57aEEJoAK4fNvwCsHfg8avAgmH7K4BvADcB1cCWEML2GOMfCg/K5/PjqXnKdXZ2lmxtUy3LvUO2+7d3e8+aLPcuSZI0EW8ZJMQY1wHrCsdCCP8EVA1sVgF7hj3teeC7McZu4A8hhMeAAAwJEkr1CvFZvnp9lnuHbPdv7/aeNaXce2tra9olSJIkjWq8pzZsAc4beHwusHnY/rOBfwQIIRwKvBfw1z6SJEmSJE1z47prA/D3wPdDCA8DrwOrAEIIXwVujzFuDCGsDCFsA3qBv44xtk9KxZIkSZIkKTXjChJijB3AJSOMf67g8XUTqEuSJEmSJJWg8Z7aIEmSJEmSMsggQZIkSZIkJWaQIEmSJEmSEjNIkCRJkiRJiRkkSJIkSZKkxAwSJEmSJElSYgYJkiRJkiQpMYMESZIkSZKU2Oy0C5AkSZoMIYSPApfEGFcNbJ8C3AR0A/fFGP9bmvVJkjRTuCJBkiRNeyGEm4AvM3Ru811gFXAacHII4YQ0apMkaaZxRYIkSZoJHgH+GbgKIIQwH5gTY/y3ge17gbOBx4Y/MZ/PF7HM5Do7O0u2tqlm79nsHbLdv73b+3RikCBJkqaNEEIDcP2w4ctjjBtCCCsKxuYDrxRsvwq8e6TXrK+vn9QaJ0s+ny/Z2qaavWezd8h2//Zu76WmtbV11H0GCZIkadqIMa4D1iU49BWgqmC7CtgzJUVJkpQxXiNBkiTNODHGV4DXQwjHhBDKgJXA5pTLkiRpRnBFgiRJmqmuBpqBWfTfteFfUq5HkqQZwSBBkiTNCDHGB4AHCra3AaekVY8kSTOVpzZIkiRJkqTEDBIkSZIkSVJiBgmSJEmSJCkxgwRJkiRJkpSYQYIkSZIkSUrMIEGSJEmSJCVmkCBJkiRJkhIzSJAkSZIkSYkZJEiSJEmSpMQMEiRJkiRJUmIGCZIkSZIkKTGDBEmSJEmSlJhBgiRJkiRJSswgQZIkSZIkJWaQIEmSJEmSEjNIkCRJkiRJiRkkSJIkSZKkxAwSJEmSJElSYgYJkiRJkiQpMYMESZIkSZKUmEGCJEmSJElKzCBBkiRJkiQlZpAgSZIkSZISM0iQJEmSJEmJGSRIkiRJkqTEDBIkSZIkSVJiBgmSJEmSJCkxgwRJkiRJkpSYQYIkSZIkSUrMIEGSJEmSJCVmkCBJkiRJkhKbPZEnhxA+ClwSY1w1wr4rgauAbuBLMca7J/JekiRJkiQpfeNekRBCuAn48kivEUJ4B/Bp4IPASuDLIYQ5430vSZIkSZJUGiZyasMjwDWj7DsJ2BJj7Iox7gV2AO+fwHtJkiRJkqQS8JanNoQQGoDrhw1fHmPcEEJYMcrT5gN7C7ZfBRYMPyifzycss7g6OztLtrapluXeIdv927u9Z02We5ckSZqItwwSYozrgHVjfN1XgKqC7Spgz/CD6uvrx/iyxZHP50u2tqmW5d4h2/3bu71nTSn33tramnYJkiRJo5rQxRbfxHagMYQwF5gD1ANPTtF7SZIkSZKkIpnUICGE8BlgR4zxzhDCt4HN9F+HYW2MsXMy30uSJEmSJBXfhIKEGOMDwAMF298seHwLcMtEXl+SJEmSJJWWidy1QZIkSZIkZYxBgiRJkiRJSswgQZIkSZIkJWaQIEmSJEmSEjNIkCRJkiRJiU3q7R8lSZLSEkL4KHBJjHFVwfbXgV0Dh3wxxvhgWvVJkjRTGCRIkqRpL4RwE7ASeLxgeBnwuRjjj9OpSpKkmckgQZIkzQSPAP8MXFUwtgw4IYRwHbAduCHG2D38ifl8vjgVjlFnZ2fJ1jbV7D2bvUO2+7d3e59ODBIkSdK0EUJoAK4fNnx5jHFDCGHFsPGf0R8uPA18F7ga+M7w16yvr5+CSicun8+XbG1Tzd6z2Ttku397t/dS09raOuo+gwRJkjRtxBjXAesSHr4+xrgHIITwE+BjU1aYJEkZ4l0bJEnSjBNCKAN+HUJYNDB0FjD6r1YkSVJiBgmSJGnGiTH2AVcA/xRCeBCoBG5JtypJkmYGT22QJEkzQozxAeCBgu37gPvSqkeSpJnKFQmSJEmSJCkxgwRJkiRJkpSYQYIkSZIkSUrMIEGSJEmSJCVmkCBJkiRJkhIzSJAkSZIkSYkZJEiSJEmSpMQMEiRJkiRJUmIGCZIkSZIkKTGDBEmSJEmSlJhBgiRJkiRJSswgQZIkSZIkJWaQIEmSJEmSEjNIkCRJkiRJiRkkSJIkSZKkxAwSJEmSJElSYgYJkiRJkiQpMYMESZIkSZKUmEGCJEmSJElKzCBB0oj279/P+vXraW9vH/WYZ555hm9961tFrEqSJGXJ8PlIT08PP/7xj1m3bh233nrrm85TJE0dgwRJB3nuuee49dZbefnll0c9Zu/evWzbto2enp4iViZJkrJipPnI7373O3p7e2loaOCMM86gpaUlxQql7DJIkHSQ7u5uLr30UhYuXDjq/nvuuYfzzjuvyJVJkqSsGGk+cvjhh9Pb20tfXx9dXV2Ul/vPGSkNfudJGdfc3ExdXR1Lliyhrq6O5uZmampqWLBgwajP+elPf8qpp57K/Pnzi1ipJEmaqZLORyoqKtizZw/f+c53uOuuuzj55JNTqljKttlpFyApPc3NzaxZs4aOjg7OPPNMampqaGlpoa+vj8suu2zE57z66qu0tbXx8ssv8+CDD7Jv3z5uv/12Pv7xjxe5ekmSNBOMZT6ybds2jjnmGM4++2z27t3LbbfdxjXXXMPs2f6zRiomv+OkDFu7di0dHR0AQ84xvP/++0cNEqqqqrj22msHt7/+9a8bIkiSpHEby3xk7ty5zJo1C4B58+bR09NDb29v8YqVBHhqg5RpbW1ticf37dvHhg0bprokSZKUMWOZj5x66qns3r2bW2+9ldtuu42zzjqLioqKqS5R0jCuSJAyrKamhp07d444DrB69erBsXnz5nHppZcedOxnP/vZKatPkiTNfGOZj1RUVHDJJZcUqzRJo3BFgpRhjY2NVFZWDhmrrKyksbExpYokSVLWOB+Rph+DBCnDcrkcTU1N1NbWUlZWRm1tLU1NTeRyubRLkyRJGeF8RJp+PLVByrhcLkculyOfz1NfX592OZIkKYOcj0jTiysSJEmSJElSYgYJkiRJkiQpMYMESZIkSZKUmEGCJEmSJElKbEIXWwwhfBS4JMa4aoR9NwGnAa8ODP15jHHvRN5PkiRJkiSla9xBwkBQsBJ4fJRDlgErY4zt430PSZIkSZJUWiZyasMjwDUj7QghlAOLgaYQwpYQwn+awPtIkiRJkqQS8ZYrEkIIDcD1w4YvjzFuCCGsGOVphwD/E/gmMAv4eQjh0RjjrwsPyufzY6+4CDo7O0u2tqmW5d4h2/3bu71nTZZ7lyRJmoi3DBJijOuAdWN83Q7gphhjB0AIoQX4ADAkSKivrx/jyxZHPp8v2dqmWpZ7h2z3b+/2njWl3Htra2vaJUiSJI1qQhdbfBPHARtCCCfQf/rEacD3p+i9JEmSJElSkUxqkBBC+AywI8Z4Zwjh/wDbgP3AbTHGf53M95IkSZIkScU3oSAhxvgA8EDB9jcLHn8N+NpEXl+SJEmSJJWWidy1QZIkSZIkZYxBgiRJkiRJSswgQZIkSZIkJVbW19eXyhu3tram88aSJE0Dy5YtK0u7hixwPiJJ0uhGm4+kFiRIkiRJkqTpx1MbJEmSJElSYgYJkiRJkiQpMYMESZIkSZKU2Oy0CyiGEEI5cDPwAaALuCLGuKNg/w3AXwCvAF+NMd4dQngX8H2gDNgJrIkxdhS83j3AT2KM3y1qM2M0mb2HEM4Fvjgw3gp8KsZYshfZmOTe/wpYBfQC/yPGeEdxuxmfEMLJwFdijCuGjV8I/C3QDayPMd4SQpgH/AB4O/Aq8JcxxhdHOraYPUzEJPX/F8B1A8c+AXwyxthbxDbGZTJ6L3hOE/ByjPHzxap/Iibp6/6nwDfp/1nwPHBZjLGziG1oBnI+4nwE5yMrho3P+PlIluci4HyEGTwfycqKhIuBuTHGU4HPA984sCOE8D76fyCfAnwY+O8hhErga8B3Y4ynAw8Anyl4vS8B/644pU/YpPQeQqgaGL8gxngy8AywsIh9jMdk9X4Y8F+AUweOvbGYTYxXCOFzwP8G5g4bfxvwLfp7+TNgTQjhSOAa4ImB3m8D/uZNji15k9T/PPq/3z8UY/wgsAC4oHhdjM9k9F7wnKuA9xWp9AmbpK97GXALcHmM8TRgE1BbvC40gzkfcT7ifOSN8Rk/H8nyXAScjzDD5yNZCRIOfPDEGLcBJxbsqwceiDF2DqQ7vwPeD7wH2DhwzJaB1yCE8HH6U+BNxSl9wiar9+X0J6DfCCFsBl4oTAhL1GT1/v/o/23AIQP/TYsEGPg34D+MMF4P7Igx/jHG+DrwMHAGBZ8X/Z/B2W9y7HQwGf13AcsP/PaP/lVcJZECv4XJ6J0QwnLgZOB/TXnFk2cyej8OeAm4PoTwIFAdY4xTXrmywPkIzkdwPnJAFuYjWZ6LgPORGT0fyUqQMB/YW7DdE0I4cFrHE8AZIYSqEMLh9P8FdQjwOHDRwDEXAYeEEN5Lf2r8t8Upe1JMSu/0p/0fAm4AzgWuCyEcV4T6J2KyegfYBfwG+CXw7akufDLEGH8M7B9h1/DP5VX60+3C8ZHGCsdL3mT0H2PsjTG+ABBC+M/AocDPpqzoSTIZvYcQ/oT+pcPXTmGpk26S/twvpP9nwnfo/4v8rBDCmVNVszLF+cgbnI/0cz7yhhk3H8nyXAScjzDD5yNZCRJeAaoKtstjjN0AMcY8/V+cTQP//xegHfgr4KIQwgNA38DYfwSOAlqA1fQvM/tIcVoYt8nq/SXgFzHG52OMrwEPAUuL1cQ4TVbv5wJ/ArwLqAEuDiGcVKQepsLwz6UK2DNsfKSxwvHpbCz9E0IoDyF8HTgH+Fgpn4ebwFh6v4T+v8B+Sv9S3FUhhNVFq3TyjaX3l+j/bUE+xrif/p8Thb9BlMbL+cgbnI/gfITszkeyPBcB5yMzYj6SlSBhC3AeQAjhFPrTXwa2jwCqBs45uho4GniS/m/Uvx64OEYP8LMY4+dijCcPjH0P+GaMsdSXFE5K7/Qn3+8NISwcSNFPoT8RL2WT1fsfgX1A18Cywz3AYcVrY9LlgcUhhOoQQgX9y6m2UvB50T9Z2fwmx05nY+kf+pfRzQUuLlhWOF0l7j3G+O0Y47KB74W/A34YY/xeCjVPlrF83f8vcGgI4diB8dOBfy1yvZqZnI/gfATnIwdkeT6S5bkIOB+ZEfORTNy1AbgDOCeE8Aj9V7y8PITwGWAHcBdQH0L4BfA68F9jjD0hhAg0hxC66P+CfSql2idqUnqPMe4PIXwBuHfgdf8hxvhk0bsZm8ns/WxgWwihl/5zmabFkrJCIYRVwKExxqaBz+Fe+sPE9THG34cQ/h74fgjhYfo/k1UDvR90bFo9TMR4+g8h/Huggf4f5i0hBICb4jS5SvYB4+k9xXIn1Tj/3L8eQmgAfhj6L3T0SIzxntSa0EzifMT5iPORDM9HsjwXAecjzLD5SFlf33RfGSNJkiRJkoolK6c2SJIkSZKkSWCQIEmSJEmSEjNIkCRJkiRJiRkkSJIkSZKkxAwSJEmSJElSYgYJkiRJkiQpMYMESZIkSZKU2P8HkHud0TUBL64AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1296x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots.ttest_wilcoxon_plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1.2 Example data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>y2</th>\n",
       "      <th>y_sub_y2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.767785</td>\n",
       "      <td>1.064062</td>\n",
       "      <td>-0.577012</td>\n",
       "      <td>1.641074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.057987</td>\n",
       "      <td>0.097191</td>\n",
       "      <td>-3.181132</td>\n",
       "      <td>3.278323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.217646</td>\n",
       "      <td>0.631879</td>\n",
       "      <td>0.168813</td>\n",
       "      <td>0.463066</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.562267</td>\n",
       "      <td>0.285328</td>\n",
       "      <td>-0.667796</td>\n",
       "      <td>0.953124</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.125368</td>\n",
       "      <td>1.973527</td>\n",
       "      <td>2.138589</td>\n",
       "      <td>-0.165062</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          x         y        y2  y_sub_y2\n",
       "0  0.767785  1.064062 -0.577012  1.641074\n",
       "1  2.057987  0.097191 -3.181132  3.278323\n",
       "2 -0.217646  0.631879  0.168813  0.463066\n",
       "3  0.562267  0.285328 -0.667796  0.953124\n",
       "4  0.125368  1.973527  2.138589 -0.165062"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.DataFrame()\n",
    "data[\"x\"] = np.random.normal(loc=0.0, scale=1.0, size=50)  # Used in correlation where this is on x-axis\n",
    "data[\"y\"] = np.random.normal(loc=0.5, scale=1.0, size=50)  # Almost zero mean\n",
    "data[\"y2\"] = np.random.normal(loc=0.8, scale=1.0, size=50)  # Used in two means\n",
    "data[\"y_sub_y2\"] = data[\"y\"] - data[\"y2\"]\n",
    "\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1.3 Python code: One-sample t-test\n",
    "\n",
    "Try running the Python code below and see that the linear model (`smf.ols`) produces the same $t$, $p$, and $r$ as `scipy.stats.ttest_1samp`. The confidence interval is not computed by `scipy` but would theoretically also be identical:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "t, p = scipy.stats.ttest_1samp(data.y, 0)\n",
    "res = smf.ols(formula=\"y ~ 1\", data=data).fit()  # Equivalent linear model: intercept-only"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value</th>\n",
       "      <th>p-values</th>\n",
       "      <th>t-values</th>\n",
       "      <th>0.025 CI</th>\n",
       "      <th>0.975 CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>scipy.stats.ttest_1samp</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.034067</td>\n",
       "      <td>2.180309</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>smf.ols (y ~ 1)</th>\n",
       "      <td>0.309537</td>\n",
       "      <td>0.034067</td>\n",
       "      <td>2.180309</td>\n",
       "      <td>0.024239</td>\n",
       "      <td>0.594834</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                            value  p-values  t-values  0.025 CI  0.975 CI\n",
       "scipy.stats.ttest_1samp       NaN  0.034067  2.180309       NaN       NaN\n",
       "smf.ols (y ~ 1)          0.309537  0.034067  2.180309  0.024239  0.594834"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "utils.tabulate_results([None, p, t, None, None],\n",
    "                       res,\n",
    "                       [\"scipy.stats.ttest_1samp\", \"smf.ols (y ~ 1)\"],\n",
    "                       coeff=\"Intercept\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1.4 Python code: Wilcoxon signed-rank test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "signed_rank_data = signed_rank(data)\n",
    "\n",
    "_, p = scipy.stats.wilcoxon(data.y)\n",
    "res = smf.ols(\"y ~ 1\", data=signed_rank_data).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value</th>\n",
       "      <th>p-values</th>\n",
       "      <th>t-values</th>\n",
       "      <th>0.025 CI</th>\n",
       "      <th>0.975 CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>scipy.stats.wilcoxon</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.034099</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>smf.ols (y ~ 1, signed rank)</th>\n",
       "      <td>8.78</td>\n",
       "      <td>0.032656</td>\n",
       "      <td>2.198632</td>\n",
       "      <td>0.754979</td>\n",
       "      <td>16.805021</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                              value  p-values  t-values  0.025 CI   0.975 CI\n",
       "scipy.stats.wilcoxon            NaN  0.034099       NaN       NaN        NaN\n",
       "smf.ols (y ~ 1, signed rank)   8.78  0.032656  2.198632  0.754979  16.805021"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "utils.tabulate_results([None, p, None, None, None],\n",
    "                       res,\n",
    "                       [\"scipy.stats.wilcoxon\", \"smf.ols (y ~ 1, signed rank)\"],\n",
    "                       coeff=\"Intercept\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.2 Paired samples t-test and Wilcoxon matched pairs\n",
    "\n",
    "### 4.2.1 Theory: As linear models\n",
    "\n",
    "**t-test** model: a single number (intercept) predicts the pairwise differences.\n",
    "\n",
    "$y_2-y_1 = \\beta_0 \\qquad \\mathcal{H}_0: \\beta_0 = 0$\n",
    "\n",
    "This means that there is just one $y = y_2 - y_1$ to predict and it becomes a [one-sample t-test](#4.1-One-sample-t-test-and-Wilcoxon-signed-rank) on the pairwise differences. The visualization is therefore also the same as for the one-sample t-test. At the risk of overcomplicating a simple substraction, you can think of these pairwise differences as slopes (see left panel of the figure), which we can represent as y-offsets (see right panel of the figure):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots.pairs_wilcoxon_plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly, the **Wilcoxon matched pairs** only differ from **Wilcoxon signed-rank** in that it's testing the signed ranks of the pairwise $y_2-y_1$ differences.\n",
    "\n",
    "$\\text{signed_rank}(y_2-y_1) = \\beta_0 \\qquad \\mathcal{H}_0: \\beta_0 = 0$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2.2 Python code: Paired sample t-test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "t, p = scipy.stats.ttest_rel(data.y, data.y2)\n",
    "res = smf.ols(formula=\"y_sub_y2 ~ 1\", data=data).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value</th>\n",
       "      <th>p-values</th>\n",
       "      <th>t-values</th>\n",
       "      <th>0.025 CI</th>\n",
       "      <th>0.975 CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>scipy.stats.ttest_rel</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.174559</td>\n",
       "      <td>-1.377691</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>smf.ols (y_sub_y2 ~ 1)</th>\n",
       "      <td>-0.371131</td>\n",
       "      <td>0.174559</td>\n",
       "      <td>-1.377691</td>\n",
       "      <td>-0.912482</td>\n",
       "      <td>0.170221</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                           value  p-values  t-values  0.025 CI  0.975 CI\n",
       "scipy.stats.ttest_rel        NaN  0.174559 -1.377691       NaN       NaN\n",
       "smf.ols (y_sub_y2 ~ 1) -0.371131  0.174559 -1.377691 -0.912482  0.170221"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "utils.tabulate_results([None, p, t, None, None],\n",
    "                       res,\n",
    "                       [\"scipy.stats.ttest_rel\", \"smf.ols (y_sub_y2 ~ 1)\"],\n",
    "                       coeff=\"Intercept\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2.3 Python code: Wilcoxon matched pairs\n",
    "\n",
    "Again, we do the signed-ranks trick. This is still an approximation, but a close one:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "_, p = scipy.stats.wilcoxon(data.y, data.y2)\n",
    "res = smf.ols(formula=\"y_sub_y2 ~ 1\", data=signed_rank_data).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value</th>\n",
       "      <th>p-values</th>\n",
       "      <th>t-values</th>\n",
       "      <th>0.025 CI</th>\n",
       "      <th>0.975 CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>scipy.stats.wilcoxon</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.214810</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>smf.ols (y_sub_y2 ~ 1, signed rank)</th>\n",
       "      <td>-5.14</td>\n",
       "      <td>0.218208</td>\n",
       "      <td>-1.247322</td>\n",
       "      <td>-13.421116</td>\n",
       "      <td>3.141116</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                     value  p-values  t-values   0.025 CI  \\\n",
       "scipy.stats.wilcoxon                   NaN  0.214810       NaN        NaN   \n",
       "smf.ols (y_sub_y2 ~ 1, signed rank)  -5.14  0.218208 -1.247322 -13.421116   \n",
       "\n",
       "                                     0.975 CI  \n",
       "scipy.stats.wilcoxon                      NaN  \n",
       "smf.ols (y_sub_y2 ~ 1, signed rank)  3.141116  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "utils.tabulate_results([None, p, None, None, None],\n",
    "                       res,\n",
    "                       [\"scipy.stats.wilcoxon\", \"smf.ols (y_sub_y2 ~ 1, signed rank)\"],\n",
    "                       coeff=\"Intercept\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For large sample sizes (N >> 100), this approaches the **sign test** to a reasonable degree, but this approximation is too inaccurate to flesh out here."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5 Two means\n",
    "\n",
    "## 5.1 Independent t-test and Mann-Whitney U\n",
    "\n",
    "### 5.1.1 Theory: As linear models\n",
    "\n",
    "**Independent t-test model:** two means predict $y$.\n",
    "\n",
    "$y_i = \\beta_0 + \\beta_1 x_i \\qquad \\mathcal{H}_0: \\beta_1 = 0$\n",
    "\n",
    "where $x_i$ is an indicator (0 or 1) saying whether data point $i$ was sampled from one or the other group. [Indicator variables (also called \"dummy coding\")](https://en.wikipedia.org/wiki/Dummy_variable_(statistics)) underly a lot of linear models and we'll take an aside to see how it works in a minute.\n",
    "\n",
    "**Mann-Whitney U** (also known as **Wilcoxon rank-sum test** for two independent groups; no *signed* rank this time) is the same model to a very close approximation, just on the ranks of $x$ and $y$ instead of the actual values:\n",
    "\n",
    "$\\text{rank}(y_i) = \\beta_0 + \\beta_1 x_i \\qquad \\mathcal{H}_0: \\beta_1 = 0$\n",
    "\n",
    "To me, equivalences like this make \"non-parametric\" statistics much easier to understand. The approximation is appropriate [when the sample size is larger than 11 in each group and virtually perfect when N > 30 in each group](https://lindeloev.github.io/tests-as-linear/simulations/simulate_mannwhitney.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.1.2 Theory: Dummy coding\n",
    "\n",
    "Dummy coding can be understood visually. The indicator is on the x-axis so data points from the first group are located at $x = 0$ and data points from the second group is located at $x = 1$. Then $\\beta_0$ is the intercept (blue line) and $\\beta_1$ is the slope between the two means (red line). Why? Because when $\\Delta x = 1$ the slope equals the difference because:\n",
    "\n",
    "$\\text{slope} = \\Delta y / \\Delta x = \\Delta y / 1 = \\Delta y = \\text{difference}$\n",
    "\n",
    "Magic! Even categorical differences can be modelled using linear models! It's a true Swiss army knife."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots.dummy_coding_plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.1.3 Theory: Dummy coding (continued)\n",
    "\n",
    "If you feel like you get dummy coding now, just skip ahead to the next section. Here is a more elaborate explanation of dummy coding:\n",
    "\n",
    "If a data point was sampled from the first group, i.e., when $x_i = 0$, the model simply becomes $y = \\beta_0 + \\beta_1 \\cdot 0 = \\beta_0$. In other words, the model predicts that that data point is $beta_0$. It turns out that the $\\beta$ which best predicts a set of data points is the *mean* of those data points, so $\\beta_0$ is the mean of group 1.\n",
    "\n",
    "On the other hand, data points sampled from the second group would have $x_i = 1$ so the model becomes $y_i = \\beta_0 + \\beta_1\\cdot 1 = \\beta_0 + \\beta_1$. In other words, we add $\\beta_1$ to \"shift\" from the mean of the first group to the mean of the second group. Thus $\\beta_1$ becomes the *mean difference* between the groups.\n",
    "\n",
    "As an example, say group 1 is 25 years old ($\\beta_0 = 25$) and group 2 is 28 years old ($\\beta_1 = 3$), then the model for a person in group 1 is $y = 25 + 3 \\cdot 0 = 25$ and the model for a person in group 2 is $y = 25 + 3 \\cdot 1 = 28$. \n",
    "\n",
    "Hooray, it works! For first-timers it takes a few moments to understand dummy coding, but you only need to know addition and multiplication to get there!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.1.4 Python code: independent t-test\n",
    "\n",
    "As a reminder, when we write `y ~ 1 + x` with `patsy`, it is shorthand for $y = \\beta_0 \\cdot 1 + \\beta_1 \\cdot x$ and Python goes on computing the $\\beta$s for you. Thus `y ~ 1 + x` is the `patsy` (and/or R) way of writing $y = a \\cdot x + b$.\n",
    "\n",
    "Notice the identical `p` estimates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>0</th>\n",
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       "          y  group\n",
       "0  0.091536    0.0\n",
       "1 -0.668538    0.0\n",
       "2 -0.308284    1.0\n",
       "3  0.168813    1.0\n",
       "4 -1.428736    1.0"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "groups = pd.DataFrame(data=np.concatenate([data.y, data.y2]),\n",
    "                      columns=[\"y\"])\n",
    "groups[\"group\"] = np.concatenate([np.zeros_like(data.y), np.ones_like(data.y2)])\n",
    "groups = groups.sample(frac=1).reset_index(drop=True)  # Shuffle\n",
    "groups.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "_, p = scipy.stats.ttest_ind(data.y, data.y2)\n",
    "res = smf.ols(\"y ~ 1 + group\", groups).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value</th>\n",
       "      <th>p-values</th>\n",
       "      <th>t-values</th>\n",
       "      <th>0.025 CI</th>\n",
       "      <th>0.975 CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>scipy.stats.ttest_ind</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.123488</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>smf.ols (y ~ 1 + group)</th>\n",
       "      <td>0.371131</td>\n",
       "      <td>0.123488</td>\n",
       "      <td>1.553663</td>\n",
       "      <td>-0.102908</td>\n",
       "      <td>0.845169</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                            value  p-values  t-values  0.025 CI  0.975 CI\n",
       "scipy.stats.ttest_ind         NaN  0.123488       NaN       NaN       NaN\n",
       "smf.ols (y ~ 1 + group)  0.371131  0.123488  1.553663 -0.102908  0.845169"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "utils.tabulate_results([None, p, None, None, None],\n",
    "                       res,\n",
    "                       [\"scipy.stats.ttest_ind\", \"smf.ols (y ~ 1 + group)\"],\n",
    "                       coeff=\"group\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.1.5 Python code: Mann-Whitney U"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "groups.y = signed_rank(groups.y)  # Only rank `y`, not `group`\n",
    "\n",
    "_, p = scipy.stats.mannwhitneyu(data.y, data.y2)\n",
    "res = smf.ols(\"y ~ 1 + group\", groups).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>value</th>\n",
       "      <th>p-values</th>\n",
       "      <th>t-values</th>\n",
       "      <th>0.025 CI</th>\n",
       "      <th>0.975 CI</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>scipy.stats.mannwhitneyu</th>\n",
       "      <td>NaN</td>\n",
       "      <td>0.05151</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>smf.ols (y ~ 1 + group, signed rank)</th>\n",
       "      <td>13.92</td>\n",
       "      <td>0.19835</td>\n",
       "      <td>1.295038</td>\n",
       "      <td>-7.410484</td>\n",
       "      <td>35.250484</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                      value  p-values  t-values  0.025 CI  \\\n",
       "scipy.stats.mannwhitneyu                NaN   0.05151       NaN       NaN   \n",
       "smf.ols (y ~ 1 + group, signed rank)  13.92   0.19835  1.295038 -7.410484   \n",
       "\n",
       "                                       0.975 CI  \n",
       "scipy.stats.mannwhitneyu                    NaN  \n",
       "smf.ols (y ~ 1 + group, signed rank)  35.250484  "
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "utils.tabulate_results([None, p, None, None, None],\n",
    "                       res,\n",
    "                       [\"scipy.stats.mannwhitneyu\", \"smf.ols (y ~ 1 + group, signed rank)\"],\n",
    "                       coeff=\"group\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.2 Welch’s t-test\n",
    "\n",
    "This is identical to the (Student's) [independent t-test](#5.1.4-Python-code:-independent-t-test) above except that Student's assumes identical variances and **Welch's t-test** does not. So the linear model is the same and the trick is in the variances, which I won't go further into here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "t, p = scipy.stats.ttest_ind(data.y, data.y2, equal_var=False)\n",
    "\n",
    "# TODO: linear model with per-group variances\n",
    "# See https://stats.stackexchange.com/q/142685 and https://github.com/eigenfoo/tests-as-linear/issues/12"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 6 Three or more means\n",
    "\n",
    "ANOVAs are linear models with (only) categorical predictors so they simply extend everything we did above, relying heavily on dummy coding. Do make sure to read [the section on dummy coding](#5.1.2-Theory:-Dummy-coding) if you haven't already."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.1 One-way ANOVA and Kruskal-Wallis\n",
    "\n",
    "### 6.1.1 Theory: As linear models\n",
    "\n",
    "Model: One mean for each group predicts $y$.\n",
    "\n",
    "$y = \\beta_0 + \\beta_1 x_1 + \\beta_2 x_2 + \\beta_3 x_3 +... \\qquad \\mathcal{H}_0: y = \\beta_0$\n",
    "\n",
    "where $x_i$ are indicators ($x=0$ or $x=1$) where at most one $x_i=1$ while all others are $x_i=0$. \n",
    "\n",
    "Notice how this is just \"more of the same\" of what we already did in other models above. When there are only two groups, this model is $y = \\beta_0 + \\beta_1*x$, i.e. the [independent t-test](#5.1-Independent-t-test-and-Mann-Whitney-U). If there is only one group, it is $y = \\beta_0$, i.e. the [one-sample t-test](#4.1-One-sample-t-test-and-Wilcoxon-signed-rank). This is easy to see in the visualization below - just cover up a few groups and see that it matches the other visualizations above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots.one_way_anova_plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A one-way ANOVA has a log-linear counterpart called [goodness-of-fit](#7.1-Goodness-of-fit) test which we'll return to. By the way, since we now regress on more than one $x$, the one-way ANOVA is a **multiple regression** model.\n",
    "\n",
    "The **Kruskal-Wallis** test is simply a **one-way ANOVA** on the rank-transformed $y$ (`value`):\n",
    "\n",
    "$\\text{rank}(y) = \\beta_0 + \\beta_1 x_1 + \\beta_2 x_2 + \\beta_3 x_3 +...$\n",
    "\n",
    "This approximation is [good enough for 12 or more data points](https://lindeloev.github.io/tests-as-linear/simulations/simulate_kruskall.html). Again, if you do this for just one or two groups, we're already acquainted with those equations, i.e. the [Wilcoxon signed-rank test](#4.1-One-sample-t-test-and-Wilcoxon-signed-rank) or the [Mann-Whitney U test](#5.1-Independent-t-test-and-Mann-Whitney-U) respectively. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.1.2 Example data\n",
    "\n",
    "We make a three-level factor with the levels `a`, `b`, and `c` so that the **one-way ANOVA** basically becomes a \"three-sample t-test\". Then we manually do the [dummy coding](#5.1.2-Theory:-Dummy-coding) of the groups."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>group</th>\n",
       "      <th>group_b</th>\n",
       "      <th>group_c</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.080830</td>\n",
       "      <td>a</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-2.316629</td>\n",
       "      <td>a</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.138365</td>\n",
       "      <td>a</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.003775</td>\n",
       "      <td>a</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.051200</td>\n",
       "      <td>a</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          y group  group_b  group_c\n",
       "0  1.080830     a      0.0      0.0\n",
       "1 -2.316629     a      0.0      0.0\n",
       "2 -0.138365     a      0.0      0.0\n",
       "3  2.003775     a      0.0      0.0\n",
       "4  2.051200     a      0.0      0.0"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_points = 20\n",
    "\n",
    "a = np.random.normal(0.0, 1, num_points)\n",
    "b = np.random.normal(3.0, 1, num_points)\n",
    "c = np.random.normal(-1.5, 1, num_points)\n",
    "\n",
    "df = pd.DataFrame()\n",
    "df[\"y\"] = np.concatenate([a, b, c])\n",
    "df[\"group\"] = list(\"\".join([num_points * char for char in \"abc\"]))\n",
    "df = df.join(pd.get_dummies(df.group, prefix=\"group\", drop_first=True).astype(np.float64))\n",
    "\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With group a's intercept omni-present, see how exactly one other parameter is added to predict `value` for group b and c in a given row. Thus data points in group b never affect the estimates in group c."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.1.3 Python code: one-way ANOVA\n",
    "\n",
    "OK, let's see the identity between `scipy`'s dedicated **ANOVA** function (`scipy.stats.f_oneway`) and the dummy-coded in-your-face linear model with `smf.ols`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "F, p = scipy.stats.f_oneway(a, b, c)\n",
    "res = smf.ols(\"y ~ 1 + group_b + group_c\", df).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>F statistic</th>\n",
       "      <th>p value</th>\n",
       "      <th>df</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>scipy.stats.f_oneway</th>\n",
       "      <td>121.816955</td>\n",
       "      <td>2.620302e-21</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ols (y ~ 1 + group_b + group_c)</th>\n",
       "      <td>121.816955</td>\n",
       "      <td>2.620302e-21</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                 F statistic       p value   df\n",
       "scipy.stats.f_oneway              121.816955  2.620302e-21  NaN\n",
       "ols (y ~ 1 + group_b + group_c)   121.816955  2.620302e-21  2.0"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table = pd.DataFrame(index=[\"F statistic\", \"p value\", \"df\"])\n",
    "table[\"scipy.stats.f_oneway\"] = [F, p, None]\n",
    "table[\"ols (y ~ 1 + group_b + group_c)\"] = [res.fvalue, res.f_pvalue, res.df_model]\n",
    "\n",
    "table.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that [`sm.stats.anova_lm`](https://www.statsmodels.org/stable/generated/statsmodels.stats.anova.anova_lm.html) gives you a pretty ANOVA table with relevant statistics, if you give it the fitted `res` object. By default it computes type-I sum of squares, which is widely discouraged. There is a BIG polarized debate about whether to use type-II (by passing `typ=2`) or type-III sum of squares (`typ=3`), but let's skip that for now."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.1.4 Python code: Kruskal-Wallis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "signed_rank_df = df.copy()\n",
    "signed_rank_df[\"y\"] = signed_rank(signed_rank_df[\"y\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "_, p = scipy.stats.kruskal(a, b, c)\n",
    "res = smf.ols(\"y ~ 1 + group_b + group_c\", signed_rank_df).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>p value</th>\n",
       "      <th>df</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>scipy.stats.kruskal</th>\n",
       "      <td>5.028679e-11</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ols (y ~ 1 + group_b + group_c, signed rank)</th>\n",
       "      <td>6.551841e-22</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                   p value   df\n",
       "scipy.stats.kruskal                           5.028679e-11  NaN\n",
       "ols (y ~ 1 + group_b + group_c, signed rank)  6.551841e-22  2.0"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table = pd.DataFrame(index=[\"p value\", \"df\"])\n",
    "table[\"scipy.stats.kruskal\"] = [p, None]\n",
    "table[\"ols (y ~ 1 + group_b + group_c, signed rank)\"] = [res.f_pvalue, res.df_model]\n",
    "\n",
    "table.T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.2 Two-way ANOVA\n",
    "\n",
    "### 6.2.1 Theory: As linear models\n",
    "\n",
    "Model: one mean per group (main effects) plus these means multiplied across factors (interaction effects). The main effects are the [one-way ANOVAs](#6.1-One-way-ANOVA-and-Kruskal-Wallis) above, though in the context of a larger model. The interaction effect is harder to explain in the abstract even though it's just a few numbers multiplied with each other. I will leave that to the teachers to keep focus on equivalences here :-)\n",
    "\n",
    "Switching to matrix notation:\n",
    "\n",
    "$y = \\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + \\beta_3 X_1 X_2 \\qquad \\mathcal{H}_0: \\beta_3 = 0$\n",
    "\n",
    "Here $\\beta_i$ are vectors of betas of which only one is selected by the indicator vector $X_i$. The $\\mathcal{H}_0$ shown here is the interaction effect. Note that the intercept $\\beta_0$, to which all other $\\beta$s are relative, is now the mean for the first level of all factors.\n",
    "\n",
    "Continuing with the dataset from the one-way ANOVA above, let's add a crossing factor `mood` so that we can test the `group:mood` interaction (a 3x2 ANOVA). We also do the [dummy coding](#5.1.2-Theory:-Dummy-coding) of this factor needed for the linear model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>group</th>\n",
       "      <th>group_b</th>\n",
       "      <th>group_c</th>\n",
       "      <th>mood</th>\n",
       "      <th>mood_happy</th>\n",
       "      <th>mood_sad</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.080830</td>\n",
       "      <td>a</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>happy</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-2.316629</td>\n",
       "      <td>a</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>sad</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.138365</td>\n",
       "      <td>a</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>happy</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.003775</td>\n",
       "      <td>a</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>sad</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.051200</td>\n",
       "      <td>a</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>happy</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          y group  group_b  group_c   mood  mood_happy  mood_sad\n",
       "0  1.080830     a      0.0      0.0  happy         1.0       0.0\n",
       "1 -2.316629     a      0.0      0.0    sad         0.0       1.0\n",
       "2 -0.138365     a      0.0      0.0  happy         1.0       0.0\n",
       "3  2.003775     a      0.0      0.0    sad         0.0       1.0\n",
       "4  2.051200     a      0.0      0.0  happy         1.0       0.0"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[\"mood\"] = (df.shape[0] // 2) * [\"happy\", \"sad\"]\n",
    "df = df.join(pd.get_dummies(df.mood, prefix=\"mood\").astype(np.float64))\n",
    "\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\beta_0$ is now the happy guys from group a!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots.two_way_anova_plot(df)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.2.2 Python code: Two-way ANOVA\n",
    "\n",
    "<div class=\"alert alert-warning\">\n",
    "    <b>Note on Python port:</b>\n",
    "    Unfortunately, <code>scipy.stats</code> does not have a dedicated function to perform two-way ANOVA, so we cannot demonstrate directly that it is fundamentally a linear model. Nevertheless, we will write the code to perform the linear regression.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# scipy.stats does not support two-way ANOVA\n",
    "res = smf.ols(\"y ~ 1 + group * mood\", df).fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.3 ANCOVA\n",
    "\n",
    "This is simply ANOVA with a continuous regressor added so that it now contains continuous and (dummy-coded) categorical predictors. For example, if we continue with the [one-way ANOVA](#6.1-One-way-ANOVA-and-Kruskal-Wallis) example, we can add `age` and it is now called a **one-way ANCOVA**:\n",
    "\n",
    "$y = \\beta_0 + \\beta_1 x_1 + \\beta_2 x_2 + ... + \\beta_3 \\text{age}$\n",
    "\n",
    "... where $x_i$ are our usual dummy-coded indicator variables. $\\beta_0$ is now the mean for the first group at $\\text{age}=0$. You can turn all ANOVAs into ANCOVAs this way, e.g. by adding $\\beta_N \\cdot \\text{age}$ to our **two-way ANOVA** in the previous section. But let us go ahead with our one-way ANCOVA, starting by adding $\\text{age}$ to our dataset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Update data with a continuous covariate\n",
    "df[\"age\"] = df[\"y\"] + np.random.randn(df.shape[0])  # Correlated with y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is best visualized using colors for groups instead of x-position. The $\\beta$s are still the average $y$-offset of the data points, only now we model each group using a slope instead of an intercept. In other words, the one-way ANOVA is sort of [one-sample t-tests](#4.1-One-sample-t-test-and-Wilcoxon-signed-rank) model for each group ($y = \\beta_0$) while the **one-way ANCOVA** is sort of [Pearson correlation](#3-Pearson-and-Spearman-correlation) model for each group ($y_i = \\beta_0 + \\beta_i + \\beta_1 \\text{age}$):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots.ancova_plot(df)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-warning\">\n",
    "    <b>Note on Python port:</b>\n",
    "    Unfortunately, <code>scipy.stats</code> does not have a dedicated function to perform ANCOVA, so again, we cannot demonstrate directly that it is fundamentally a linear model. Nevertheless, we will write the code to perform the linear regression.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "res = smf.ols(\"y ~ 1 + group + age\", df).fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 7 Proportions: Chi-square is a log-linear model\n",
    "\n",
    "Recall that when you take the logarithm, you can easily make statements about *proportions*, i.e., that for every increase in $x$, $y$ increases a certain percentage. This turns out to be one of the simplest (and therefore best!) ways to make count data and contingency tables intelligible. See [this nice introduction](https://www.uni-tuebingen.de/fileadmin/Uni_Tuebingen/SFB/SFB_833/A_Bereich/A1/Christoph_Scheepers_-_Statistikworkshop.pdf) to Chi-Square tests as linear models.\n",
    "\n",
    "\n",
    "## 7.1 Goodness of fit\n",
    "\n",
    "### 7.1.1 Theory: As log-linear model\n",
    "Model: a single intercept predicts $\\log(y)$.\n",
    "\n",
    "I'll refer you to take a look at [the section on contingency tables](#contingency) which is basically a \"two-way goodness of fit\".\n",
    "\n",
    "\n",
    "### 7.1.2 Example data\n",
    "\n",
    "For this, we need some wide count data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>counts</th>\n",
       "      <th>mood_meh</th>\n",
       "      <th>mood_sad</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>happy</th>\n",
       "      <td>70</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sad</th>\n",
       "      <td>60</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>meh</th>\n",
       "      <td>90</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       counts  mood_meh  mood_sad\n",
       "happy      70         0         0\n",
       "sad        60         0         1\n",
       "meh        90         1         0"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(index=[\"happy\", \"sad\", \"meh\"])\n",
    "df[\"counts\"] = [70, 60, 90]\n",
    "df = df.join(pd.get_dummies(df.index, prefix='mood', drop_first=True).set_index(df.index))\n",
    "\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.1.3 Python code: Goodness of fit\n",
    "\n",
    "Now let's see that the Goodness of fit is just a log-linear equivalent to a one-way ANOVA. We set `family=sm.families.Poisson()` which defaults to setting a logarithmic [link function](https://en.wikipedia.org/wiki/Generalized_linear_model#Link_function) (you can verify that `res.model.family.link` is a logarithm).\n",
    "\n",
    "Note that `smf.ols` does not support GLMs: we need to use `sm.GLM`. While `sm.GLM` does not have a `patsy`-formula interface, we can still use `patsy.dmatrices` to get the [`endog` and `exog` design matrices,](https://www.statsmodels.org/stable/endog_exog.html) and then feed that into `sm.GLM`.\n",
    "\n",
    "<div class=\"alert alert-warning\">\n",
    "    <b>Note on Python port:</b>\n",
    "    Unfortunately, <code>statsmodels</code> <a href=\"https://stackoverflow.com/q/27328623\">does not currently support performing a one-way ANOVA test on GLMs</a> (the <code>anova_lm</code> function only works for linear models), so while we can perform the GLM, there is no support for computing the F-statistic or its p-value. Nevertheless, we will write the code to perform the generalized linear regression.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "chi2, p = scipy.stats.chisquare(df.counts)\n",
    "\n",
    "# The `-1` is to remove the intercept term from the model\n",
    "# See https://patsy.readthedocs.io/en/latest/formulas.html#intercept-handling\n",
    "endog, exog = patsy.dmatrices(\"counts ~ 1 + mood_meh + mood_sad - 1\", df)\n",
    "res = sm.GLM(endog, exog, family=sm.families.Poisson()).fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.2 Contingency tables\n",
    "\n",
    "### 7.2.1 Theory: As log-linear model\n",
    "\n",
    "The theory here will be a bit more convoluted, and I mainly write it up so that you can get the *feeling* that it really is just a log-linear [two-way ANOVA model](#6.2-Two-way-ANOVA). Let's get started...\n",
    "\n",
    "For a two-way contingency table, the model of the count variable $y$ is a modeled using the marginal proportions of a contingency table. Why this makes sense, is too involved to go into here, but [see the relevant slides by Christoph Scheepers here](https://www.uni-tuebingen.de/fileadmin/Uni_Tuebingen/SFB/SFB_833/A_Bereich/A1/Christoph_Scheepers_-_Statistikworkshop.pdf) for an excellent exposition. The model is composed of a lot of counts and the regression coefficients $A_i$ and $B_j$:\n",
    "\n",
    "$$n_{ij} = N \\cdot A_i \\frac{n_i}{N} \\cdot B_j \\frac{n_j}{N} \\cdot \\frac{n_{ij} N}{n_i n_j}$$\n",
    "\n",
    "What a mess!!! Here, $i$ is the row index, $j$ is the column index, $n_{\\text{something}}$ is the sum of that row and/or column, $N = \\sum_{i, j}{n_{ij}}$. Remember that $n$ is a count variable, so $N$ is just the total count.\n",
    "\n",
    "We can simplify the notation by defining the *proportions*: $\\alpha_i = A_i \\frac{n_i}{N}$, $\\beta_i = B_j \\frac{n_j}{N}$ and $\\alpha\\beta_{ij} = \\frac{n_{ij} N}{n_i n_j}$. Let's write the model again:\n",
    "\n",
    "$$n_{ij} = N \\cdot \\alpha_i \\cdot \\beta_j \\cdot \\alpha\\beta_{ij}$$\n",
    "\n",
    "Ah, much prettier. However, there is still lot's of multiplication which makes it hard to get an intuition about how the actual numbers interact. We can make it much more intelligible when we remember that $\\log(A \\cdot B) = \\log(A) + \\log(B)$. Doing logarithms on both sides, we get:\n",
    "\n",
    "$$\\log(n_{ij}) = \\log(N) + \\log(\\alpha_i) + \\log(\\beta_j) + \\log(\\alpha\\beta_{ij})$$\n",
    "\n",
    "Snuggly! Now we can get a better grasp on how the regression coefficients (which are proportions) independently contribute to $y$. This is why logarithms are so nice for proportions. Note that this is just [the two-way ANOVA model](#anova2) with some logarithms added, so we are back to our good old linear models - only the interpretation of the regression coefficients have changed! And we cannot use `smf.ols` anymore in `statsmodels`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.2.2 Example data\n",
    "\n",
    "Here we need some long data and we need it in table format for `chisq.test`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mood</th>\n",
       "      <th>sex</th>\n",
       "      <th>value</th>\n",
       "      <th>mood_meh</th>\n",
       "      <th>mood_sad</th>\n",
       "      <th>sex_male</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>happy</td>\n",
       "      <td>male</td>\n",
       "      <td>100</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>sad</td>\n",
       "      <td>male</td>\n",
       "      <td>30</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>meh</td>\n",
       "      <td>male</td>\n",
       "      <td>110</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>happy</td>\n",
       "      <td>female</td>\n",
       "      <td>70</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>sad</td>\n",
       "      <td>female</td>\n",
       "      <td>32</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>meh</td>\n",
       "      <td>female</td>\n",
       "      <td>120</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mood     sex  value  mood_meh  mood_sad  sex_male\n",
       "0  happy    male    100         0         0         1\n",
       "1    sad    male     30         0         1         1\n",
       "2    meh    male    110         1         0         1\n",
       "3  happy  female     70         0         0         0\n",
       "4    sad  female     32         0         1         0\n",
       "5    meh  female    120         1         0         0"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(data=[[100, 70], [30, 32], [110, 120]],\n",
    "                  columns=[\"male\", \"female\"],\n",
    "                  index=[\"happy\", \"sad\", \"meh\"])\n",
    "df.index.name = \"mood\"\n",
    "df.columns.name = \"sex\"\n",
    "df = df.reset_index().melt(id_vars=[\"mood\"])\n",
    "df = df.join(pd.get_dummies(df.mood, prefix=\"mood\", drop_first=True))\n",
    "df = df.join(pd.get_dummies(df.sex, prefix=\"sex\", drop_first=True))\n",
    "\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.2.3 Python code: Chi-square test\n",
    "\n",
    "Now let's show the equivalence between a chi-square model and a log-linear model. This is very similar to our [two-way ANOVA](#6.2-Two-way-ANOVA) above:\n",
    "\n",
    "<div class=\"alert alert-warning\">\n",
    "    <b>Note on Python port:</b>\n",
    "    Unfortunately, <code>statsmodels</code> <a href=\"https://stackoverflow.com/q/27328623\">does not currently support performing a two-way ANOVA test on GLMs</a> (the <code>anova_lm</code> function only works for linear models), so while we can perform the GLM, there is no support for computing the F-statistic or its p-value. Nevertheless, we'll go through the motions of performing the generalized linear regression.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "chi2, p, dof, _ = scipy.stats.chi2_contingency(df.value)\n",
    "\n",
    "endog, exog = patsy.dmatrices(\"value ~ 1 + mood_meh*sex_male + mood_sad*sex_male - 1\", df)\n",
    "res = sm.GLM(endog, exog, family=sm.families.Poisson()).fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 8 Sources and further equivalences\n",
    "\n",
    "Here are links to other sources who have exposed bits and pieces of this puzzle, including many further equivalences not covered here:\n",
    "\n",
    " * [My original exposition of the idea](https://stats.stackexchange.com/questions/303269/common-statistical-tests-as-linear-models) at Cross Validated\n",
    " * [An earlier question by me](https://stats.stackexchange.com/questions/210529/are-parametric-tests-on-rank-transformed-data-equivalent-to-non-parametric-test?noredirect=1#comment399981_210529) about non-parametric tests and a helpful answer.\n",
    " * [This question and replies](https://stats.stackexchange.com/questions/59047/how-are-regression-the-t-test-and-the-anova-all-versions-of-the-general-linear) on t-tests and ANOVA at StackOverflow\n",
    " * [These slides by Christoph Scheepers](https://www.uni-tuebingen.de/fileadmin/Uni_Tuebingen/SFB/SFB_833/A_Bereich/A1/Christoph_Scheepers_-_Statistikworkshop.pdf) on Chi-Square as log-linear models.\n",
    " * [This notebook by Philip M. Alday](https://rpubs.com/palday/glm-test) on Chi-square, binomial, multinomial, and poisson tests as log-linear and logistic models. These \"equivalences\" are less exact than what I presented above, and were therefore not included here. They are still great for a conceptual understanding of these tests, though!\n",
    " * [This article by Kristoffer Magnusson](https://rpsychologist.com/r-guide-longitudinal-lme-lmer) on RM-ANOVA and growth models using `lme4::lmer` mixed models.\n",
    " * [This post by Thom Baguley](https://seriousstats.wordpress.com/2012/02/14/friedman/) on the Friedman test. That post was actually the one that inititated my exploration of linear equivalences to \"non-parametric\"\" tests which ultimately pushed me over the edge to write up the present article."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 9 Teaching materials and a course outline\n",
    "\n",
    "Most advanced stats books (and some intro-books) take the \"everything is GLMM\" approach as well. However, the \"linear model\" part often stays at the conceptual level, rather than being made explicit. I wanted to make linear models the *tool* in a concise way. Luckily, more beginner-friendly materials have emerged lately:\n",
    "\n",
    "* Russ Poldrack's open-source book \"Statistical Thinking for the 21st century\" (start at [chapter 5 on modeling](http://statsthinking21.org/fitting-models-to-data.html))\n",
    "\n",
    "* [Jeff Rouder's course notes](https://jeffrouder.blogspot.com/2019/03/teaching-undergrad-stats-without-p-f-or.html), introducing model comparison using just $R^2$ and BIC. It avoids all the jargon on p-values, F-values, etc. The full materials and slides [are available here](https://drive.google.com/drive/folders/1CiJK--bAuO0F-ug3B5I3FvmsCdpPGZ03).\n",
    "\n",
    "Here are my own thoughts on what I'd do. I've taught parts of this with great success already, but not the whole program since I'm not assigned to teach a full course yet.\n",
    "\n",
    "I would spend 50% of the time on linear modeling of data since this contains 70% of what students need to know (bullet 1 below). The rest of the course is fleshing out what happens when you have one group, two groups, etc.\n",
    "\n",
    "Note that whereas the understanding of sampling and hypothesis testing is usually the first focus of mainstream stats courses, it is saved for later here to build upon students' prior knowledge, rather than throwing a lot of conceptually novel material at them.\n",
    "\n",
    "1. **Fundamentals of regression:**\n",
    "    1. Recall from high-school: $y = a \\cdot x + b$, and getting a really good intuition about slopes and intercepts. Understanding that this can be written using all variable names, e.g., `money = profit * time + starting_money` or $y = \\beta_1x + \\beta_2*1$ or, suppressing the coefficients, as `y ~ x + 1`. If the audience is receptive, convey the idea of these models [as a solution to differential equations](https://magesblog.com/post/modelling-change), specifying how $y$ *changes* with $x$.\n",
    "   \n",
    "    2. Extend to a few multiple regression as models. Make sure to include plenty of real-life examples and exercises at this point to make all of this really intuitive. Marvel at how briefly these models allow us to represent large datasets.\n",
    "   \n",
    "    3. Introduce the idea of rank-transforming non-metric data and try it out.\n",
    "   \n",
    "    4. Teach the three assumptions: independence of data points, normality of residuals, and homoscedasticity.\n",
    "    \n",
    "    5. Confidence/credible intervals on the parameters. Stress that the Maximum-Likelihood estimate is extremely unlikely, so intervals are more important.\n",
    "    \n",
    "    6. Briefly introduce $R^2$ for the simple regression models above. Mention in passing that this is called [the Pearson and Spearman correlation coefficients](#3-Pearson-and-Spearman-correlation). \n",
    "\n",
    "2. **Special case #1: One or two means (t-tests, Wilcoxon, Mann-Whitney):**\n",
    "\n",
    "    1. **One mean:** When there is only one x-value, the regression model simplifies to $y = b$. If $y$ is non-metric, you can rank-transform it. Apply the assumptions (homoscedasticity doesn't apply since there is only one $x$). Mention in passing that these intercept-only models are called [one-sample t-test and Wilcoxon Signed Rank test respectively](#4.1-One-sample-t-test-and-Wilcoxon-signed-rank).\n",
    "    \n",
    "    2. **Two means:** If we put two variables 1 apart on the x-axis, the difference between the means is the slope. Great! It is accessible to our Swiss army knife called linear modeling. Apply the assumption checks to see that homoscedasticity reduces to equal variance between groups. This is called an [independent t-test](#5.1-Independent-t-test-and-Mann-Whitney-U). Do a few worked examples and exercises, maybe adding Welch's test, and do the rank-transformed version, called Mann-Whitney U.\n",
    "    \n",
    "    3. *Paired samples:* Violates the independence assumption. After computing pairwise differences, this is equivalent to 2.1 (one intercept), though it is called the [paired t-test and Wilcoxon's matched pairs](#4.2-Paired-samples-t-test-and-Wilcoxon-matched-pairs).\n",
    "    \n",
    "3. **Special case #2: Three or more means (ANOVAs)**\n",
    "\n",
    "    1. *[Dummy coding](#5.1.2-Theory:-Dummy-coding) of categories:* How one regression coefficient for each level of a factor models an intercept for each level when multiplied by a binary indicator. This is just extending what we did in 2.1. to make this data accessible to linear modeling.\n",
    "    \n",
    "    2. *Means of one variable:* [One-way ANOVA](#6.1-One-way-ANOVA-and-Kruskal-Wallis).\n",
    "    \n",
    "    3. *Means of two variables:* [Two-way ANOVA](#6.2-Two-way-ANOVA).\n",
    "\n",
    "4. **Special case #3: Three or more proportions (Chi-Square)**\n",
    "\n",
    "    1. *Logarithmic transformation:* Making multiplicative models linear using logarithms, thus modeling proportions. See [this excellent introduction](https://www.uni-tuebingen.de/fileadmin/Uni_Tuebingen/SFB/SFB_833/A_Bereich/A1/Christoph_Scheepers_-_Statistikworkshop.pdf) to the equivalence of log-linear models and Chi-Square tests as models of proportions. Also needs to introduce (log-)odds ratios. When the multiplicative model is made summative using logarithms, we just add the dummy-coding trick from 3.1, and see that the models are identical to the ANOVA models in 3.2 and 3.3, only the interpretation of the coefficients have changed.\n",
    "    \n",
    "    2. *Proportions of one variable:* [Goodness of fit](#7.1-Goodness-of-fit).\n",
    "    \n",
    "    3. *Proportions of two variables:* [Contingency tables](#7.2-Contingency-tables).\n",
    "\n",
    "5. **Hypothesis testing:** \n",
    "\n",
    "    1. *Hypothesis testing as model comparisons:* Hypothesis testing is the act of choosing between a full model and one where a parameter is fixed to a particular value (often zero, i.e., effectively excluded from the model) instead of being estimated. For example, when fixing one of the two means to zero in the [t-test](#5.1-Independent-t-test-and-Mann-Whitney-U), we study how well a single mean (a [one-sample t-test](#4.1-One-sample-t-test-and-Wilcoxon-signed-rank)) explains all the data from both groups. If it does a good job, we prefer this model over the two-mean model because it is simpler. So hypothesis testing is just comparing linear models to make more qualitative statements than the truly quantitative statements which were covered in bullets 1-4 above. As tests of single parameters, hypothesis testing is therefore less informative However, when testing multiple parameters at the same time (e.g., a factor in ANOVA), model comparison becomes invaluable.\n",
    "    \n",
    "    2. *Likelihood ratios:* Likelihood ratios are the Swiss army knife which will do model comparison all the way from the one-sample t-test to GLMMs. BIC penalizes model complexity. Moreover, add priors and you've got Bayes Factors. One tool, and you're done. I've used LRTs in the ANOVAs above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 10 Limitations\n",
    "\n",
    "I have made a few simplifications for clarity:\n",
    "\n",
    "1. I have not covered assumptions in the examples. This will be another post! But all assumptions of all tests come down to the usual three: a) independence of data points, b) normally distributed residuals, and c) homoscedasticity.\n",
    "\n",
    "2. I assume that all null hypotheses are the absence of an effect, but everything works the same for non-zero null hypotheses.\n",
    "\n",
    "3. I have not discussed inference. I am only including p-values in the comparisons as a crude way to show the equivalences between the underlying models since people care about p-values. Parameter estimates will show the same equivalence. How to do *inference* is another matter. Personally, I'm a Bayesian, but going Bayesian here would render it less accessible to the wider audience. Also, doing [robust models](https://en.wikipedia.org/wiki/Robust_statistics) would be preferable, but fail to show the equivalences.\n",
    "\n",
    "4. Several named tests are still missing from the list and may be added at a later time. This includes the Sign test (require large N to be reasonably approximated by a linear model), Friedman as RM-ANOVA on `rank(y)`, McNemar, and Binomial/Multinomial. See stuff on these in [the section on links to further equivalences](#8-Sources-and-further-equivalences). If you think that they should be included here, feel free to submit \"solutions\" to [the GitHub repo](https://github.com/eigenfoo/tests-as-linear/) of this doc!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 11 License\n",
    "\n",
    "<a rel=\"license\" href=\"http://creativecommons.org/licenses/by/4.0/\"><img alt=\"Creative Commons License\" style=\"border-width:0\" src=\"https://i.creativecommons.org/l/by/4.0/88x31.png\" /></a>\n",
    "\n",
    "_Common statistical tests are linear models_: Python port by [George Ho and Jonas Kristoffer Lindeløv](https://eigenfoo.xyz/tests-as-linear/) is licensed under a [Creative Commons Attribution 4.0 International License](https://creativecommons.org/licenses/by/4.0/).\n",
    "\n",
    "Based on a work at https://lindeloev.github.io/tests-as-linear/.\n",
    "\n",
    "Permissions beyond the scope of this license may be available at https://github.com/eigenfoo/tests-as-linear."
   ]
  }
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