probs_n_stats_-_Statistics.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import stats\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import statsmodels.formula.api as sm\n",
    "import pandas as pd\n",
    "%matplotlib inline\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#create normally distributed data with same standard deviation\n",
    "mu_a = 3\n",
    "sigma_a=4\n",
    "data_a = np.random.normal(loc=mu_a, scale=sigma_a, size=1000)\n",
    "#create data b \n",
    "mu_b = 5\n",
    "sigma_b = 4\n",
    "data_b = np.random.normal(loc=mu_b, scale=sigma_b, size=1000)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='Density'>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Visualization\n",
    "fig, ax = plt.subplots(1, 2, figsize=[15,5])\n",
    "\n",
    "range_a = np.linspace(stats.norm.ppf(0.001, mu_a, sigma_a), stats.norm.ppf(0.999, mu_a, sigma_a))\n",
    "range_b = np.linspace(stats.norm.ppf(0.001, mu_b, sigma_b), stats.norm.ppf(0.999, mu_b, sigma_b))\n",
    "ax[1].plot(range_b, stats.norm.pdf(range_b, loc=mu_b, scale=sigma_b), color='C1')\n",
    "ax[0].plot(range_a, stats.norm.pdf(range_a, loc=mu_a, scale=sigma_a), color='C1')\n",
    "sns.histplot(data_a, ax=ax[0], color='C2' , stat='density')\n",
    "sns.histplot(data_b, ax=ax[1],stat='density')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:ylabel='Density'>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AGFEWAAAjygIAYERZAACMKAsAgBFlAQAwoiwAAEaUBQDAiLIAABhRFgAAI8oCAGBEWQAAjCgLAIARZQEAMKIsAABGlAUAwIiyAAAYURYAACPKAgBgRFkAAIwoCwCAEWUBADCiLAAARpQFAMAoItABcHu7e1B/RUXyMAJCHc9y9EhUZIQKNv3F5/3XLXjIxjQA7MJhKACAEWUBADCiLAAARraWRVlZmaZOnarJkydrz549t2w/e/asZs6cqbS0NC1atEhtbW2SpAMHDmjixInKyMhQRkaGiouL7YwJADCw7QR3dXW1iouLVVpaqsjISGVlZSk5OVkjR4707FNQUKAXX3xRY8eOVVFRkfbt26fs7GydPn1ahYWFevzxx+2Kh07wySYAXbHtlaGiokIpKSkaPHiwJCktLU1HjhzR/PnzJUmXL19WS0uLxo4dK0maOXOmNm/erOzsbJ06dUoXL17Uzp07NWrUKC1ZskSDBg2yKyr+H38/2STx6SbgTmHbYaiamho5nU7PcmxsrKqrq7vc7nQ6PdudTqd+/vOf66233tLw4cO1cuVKu2ICAHxg2zsLt9utsLAwz7JlWR2WvW3ftm2bZ/2cOXM0adIkv+576NCB3Y19C6czptduKxiY5uNw+P+Q8HdMb99HV9sCnau7Yz6/PVhy9WT/m/t2J1cwPgeDMVNP+PKaaVtZDBs2TJWVlZ7l2tpaxcbGdtheW1vrWf7oo48UGxurhoYGvfHGG/rxj38s6dMSCQ8P9+u+6+oa5XZbPZuAPn1A1NY29Ph2goVpPk5njFyuNr9v198xvXkfDkdEl9sCmau7YzqbTzDk6sn+n51Td3IF23MwFF8X6uoajYVh22GoCRMm6NixY6qvr1dzc7PKy8uVmprq2T5ixAhFRUWpqqpKkvTmm28qNTVV0dHRevnll3XixAlJ0muvveb3OwsAocHV5pbTGePzf3cP6h/oyCHLtncWcXFxys/PV05OjlwulzIzM5WYmKjc3Fzl5eUpISFB69ev1+LFi9XY2KjRo0crJydH4eHh2rhxo5YvX66Wlhbdd999Wrt2rV0xAQQxR0Q/LicTJGz9nGR6errS09M7rCspKfH8Oz4+Xr///e9vGZeUlKQDBw7YGQ0A4Ae+wQ0AMKIsAABGlAUAwIiyAAAYURYAACPKAgBgRFkAAIwoCwCAEWUBADCiLAAARpQFAMCIsgAAGFEWAAAjygIAYERZAACMbP09CwAIdncP6q+oSP9eCu8e1F+ffNxsU6LgRFkAuKNFRUb49Wt8DkeE/ufn37YxUXDiMBQAwIiyAAAYURYAACPKAgBgRFkAAIwoCwCAER+dDVFdfXbc6YwJQBqgb7ja3DzGbUJZhKjOPjvucETI5Wrrcsy6BQ/ZHQuwlSOin1/fmZB43PuKw1AAACPKAgBgRFkAAIwoCwCAEWUBADCiLAAARpQFAMCIsgAAGFEWAAAjvsENAEGoOz/32nqjzbafe6UsACAI+ftzr5K9ly6hLAKgO38xuNra5YgItykRADt15zkfbG7v9Lep7v7F4M8YLo4GBI9ge5fQHZTFZ3TW/qbLHdt5jBAAgoWtZVFWVqYdO3aora1Ns2fP1qxZszpsP3v2rBYtWqSmpiYlJSVpxYoVioiI0JUrV1RQUKC6ujrdf//9Wr9+vQYMGGBnVEm3tr/pkt5S8LU/ANjBtrKorq5WcXGxSktLFRkZqaysLCUnJ2vkyJGefQoKCvTiiy9q7NixKioq0r59+5Sdna0VK1YoOztb06ZN07Zt27R9+3YVFBTYFbVH+LEV4M5zJz7vbSuLiooKpaSkaPDgwZKktLQ0HTlyRPPnz5ckXb58WS0tLRo7dqwkaebMmdq8ebO+//3v6/jx49q2bZtn/Q9/+EO/yqJfv7Bu574nJsrz7whHhNpc3k8qOyL66X9++79+3UfRT1M63E93snVnf1/mE4hcPRnjbU6BzNXdMZ3NJxhy9WT/z84pmHJ1d0yEI8Lv531fPeel7r3++TImzLIsy+9b9sHOnTt1/fp15efnS5L279+vkydP6oUXXpAk/eMf/9DatWv1u9/9TpL03nvv6amnntLu3buVmZmpv/71r5KktrY2jR07VqdPn7YjJgDAB7Z9g9vtdiss7P+3lWVZHZa72v75/STdsgwA6Fu2lcWwYcNUW1vrWa6trVVsbGyX2z/66CPFxsZqyJAhamhoUHt7e6fjAAB9z7aymDBhgo4dO6b6+no1NzervLxcqampnu0jRoxQVFSUqqqqJElvvvmmUlNT5XA4lJSUpEOHDkmSDh482GEcAKDv2XbOQvr0o7M7d+6Uy+VSZmamcnNzlZubq7y8PCUkJOjcuXNavHixGhsbNXr0aK1evVqRkZG6fPmyCgsLVVdXp+HDh2vDhg0aNGiQXTEBAAa2lgUAIDRwiXIAgBFlAQAwoiwAAEaUBQDAiLLw4tKlS5o1a5YyMjL0ox/9SJcvXw50pB6rqanRU089penTpysrK0uXLl0KdKRecebMGY0ZMybQMXpFVVWVMjMzlZGRodmzZ9+2j7uysjJNnTpVkydP1p49ewIdp8e2bt2qadOmadq0aVq7dm2g4/SaX//61yosLDTvaKFLzz//vLVnzx7Lsizr1VdftZ577rkAJ+q52bNnW3v37rUsy7L27t1rLViwILCBesH169etrKws62tf+1qgo/SKhx9+2Dp79qxlWZa1f/9+a+7cuQFO5L8PP/zQevjhh62rV69aTU1NVnp6unXhwoVAx+q2d9991/rBD35gtba2Wjdu3LBycnKs8vLyQMfqsYqKCis5Odn65S9/adyXdxZeuN1uNTY2SpKam5t11113BThRz9TX1+vcuXPKysqSJH3ve9/Ts88+G9hQvWDNmjWaPXt2oGP0ihs3bmjBggWKj4+XJI0aNUoffPBBgFP577MXEo2OjvZcSPR25XQ6VVhYqMjISDkcDj3wwAO6cuVKoGP1yLVr11RcXKy5c+f6tD8/fuTFggULlJWVpd27d8vlcun1118PdKQeef/993XvvfdqzZo1qqyslNPp1JIlSwIdq0feeecdtbS06LHHHgt0lF4RGRmpjIwMSZ/+sbJ161Y9+uijAU7lv5qaGjmdTs9ybGysTp48GcBEPfPVr37V8++LFy/q8OHDnoug3q6WLl2q/Px8n/8YoSwkHT58WKtXr+6w7itf+YpaW1u1cuVKPfroo3r77bc1f/58vfXWW7fFhQ07m9OXv/xlnTlzRs8884x+9atfaf/+/SosLNTu3bsDlNJ3Xf0/amxs1K5duwITqoe6mtOuXbt048YNFRYWqq2tTU8//XSAEnaf6UKit6sLFy7o6aef1sKFC3XfffcFOk637d+/X8OHD9eDDz6o0tJSn8bwDe4u1NfXa8qUKfr73//uWZeSkqJDhw5pyJAhAUzWff/97381Y8YMz/W4mpublZKSohMnTgQ4Wffs379fO3fu9PyK4rlz5xQfH689e/Zo4MCBAU7XfU1NTZo3b54GDx6s9evXKzIyMtCR/HbgwAFVVlZq1apVkqRt27bJsizP79ncjqqqqpSXl6eioiJNmzYt0HF65Cc/+Ylqa2sVHh6ujz/+WNevX9f06dNVVFTU9SCbz5/cttxut/Wd73zHOn78uGVZllVZWWl997vfDXCqnps6dar15z//2bIsy/rDH/5gPfnkkwFO1HtC5QT3vHnzrMWLF1vt7e2BjtJtN09w19XVWdevX7eeeOIJ68SJE4GO1W1XrlyxkpOTrYqKikBH6XVvvPGGTye4OQzVhbCwMG3dulUvvPCCWlpaNGDAAG3ZsiXQsXpsy5YtWrZsmdatW6eBAwdqzZo1gY6Ezzhz5ozeeecdjRw5UjNmzJD06fH+kpKSACfzT1xcnPLz85WTk+O5kGhiYmKgY3XbK6+8otbW1g7Pl6ysLD355JMBTNW3OAwFADDio7MAACPKAgBgRFkAAIwoCwCAEWUBADCiLAAARpQFAMCIsgAAGP0fAzKfXuUtnYIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "l_means = []\n",
    "for _ in (range(1000)):\n",
    "    smp_a = np.random.choice(data_a, 10)\n",
    "    smp_b = np.random.choice(data_b, 10)\n",
    "    l_means.append(smp_a.mean() - smp_b.mean())\n",
    "lmeans = np.array(l_means)\n",
    "sns.histplot(lmeans, stat='density')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test of equality of two means\n",
    "\n",
    "### Pooled two-sample $t$-test\n",
    "Two *independent samples* from two *normal distributions* with *equal variances*:\n",
    "$$\\sigma_X^2 = \\sigma_Y^2 = \\sigma$$\n",
    "then:\n",
    "$$T=\\frac{(\\bar{X}-\\bar{Y})-(\\mu_X - \\mu_Y)}{S_p\\sqrt{\\frac{1}{n}+\\frac{1}{m}}}$$\n",
    "where $S^2_p$ is the pooled sample variance, an unbiased estimator of the common variance $\\sigma^2$:\n",
    "$$\n",
    "S^2_p = \\frac{(n-1)S^2_X + (m-1)S^2_Y}{n+m-2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### calculation from scratch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.14502315473434588, 0.8847072175967754)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#calculation from scratch\n",
    "#create normally distributed data with same standard deviation\n",
    "n = 1000\n",
    "m = 1000\n",
    "\n",
    "#create data a\n",
    "mu_a = 5\n",
    "sigma_a=4\n",
    "data_a = np.random.normal(loc=mu_a, scale=sigma_a, size=n)\n",
    "#create data b \n",
    "mu_b = 5\n",
    "sigma_b = 4\n",
    "data_b = np.random.normal(loc=mu_b, scale=sigma_b, size=m)\n",
    "\n",
    "sp = np.sqrt(((n-1)*np.var(data_a, ddof=1) + (m-1)*np.var(data_b, ddof=1))/(n+ m -2))\n",
    "\n",
    "T = (np.mean(data_a) - np.mean(data_b))/(sp * np.sqrt(1/n + 1/m))\n",
    "T, 2*(1-stats.t.cdf(T, df=(n+m-2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### calculaton with scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ttest_indResult(statistic=0.14502315473434588, pvalue=0.8847072175967756)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.ttest_ind(data_a, data_b, equal_var = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ANOVA\n",
    "\n",
    "### One way ANOVA\n",
    "Comparing 2 means of independent unrelated groups "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# defining 3 groups with different means:\n",
    "\n",
    "# group size\n",
    "size = 100\n",
    "\n",
    "mu_a = 5\n",
    "sigma_a=4\n",
    "group_a = np.random.normal(loc=mu_a, scale=sigma_a, size=size)\n",
    "\n",
    "mu_b = 4\n",
    "sigma_b=4\n",
    "group_b = np.random.normal(loc=mu_b, scale=sigma_b, size=size)\n",
    "mu_c = 4.5\n",
    "sigma_c=4\n",
    "\n",
    "group_c = np.random.normal(loc=mu_c, scale=sigma_c, size=size)\n",
    "\n",
    "groups = [group_a, group_b, group_c]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
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7D7feeiteeOEFJBKJyd8nEgnE4/FpbTOZzMFxRLVDbUixWACJRLbeYVCT4vFFQOU4yOfLVd+uz+eqyXYbwVz93ZiWg6N9KeztGcP+nnH0DufgTIyGdbX6cMXqGFZ2hbCiK4j2Fu85F/6RoBuFgjGjfQe8Ov7sK48DqHwQm0iVkMoZaAm68PLBIew8dP5ZN51RDzIFFeOZMjJn7Nu0HBzsGcPxvhQ0TZl1awNFlmFPs89dZ6sfA6O5We33TDdfsxSGaVVte2f+vQQ9Km7c2okX9g8jUzCx68goBkfzuHxVa9WSY77/XxjPj1RLsz2+ZFm66GBXzZK7wcFBfOQjH8GXv/xlXHvttQCAzZs348SJEzh58iQWLVqEn/70p3j7299eqxCIiIjmDSEEhsYK2Ht8DPt6xnDw1DgM04EiS1jRFcKt1y7BykUhLO8MwufW5iyusUwZqZyBiF9HNOg67+iREALFcmX6ZbFsQ5ElvO/W9XjkiSNwBGCYleIthbINlG0oigTXRJGWmbRPWAi8LhWv3dSBnUdH0T9awMh4EY/vHMCVa+OIcJomEV1AzZK7f/qnf0K5XMYXvvCFydve+c534gtf+AI+9rGPoVwu48Ybb8Sb3vSmWoVARETU0EzLwcFT43j5yCh2HxvFWKYyetPW4sVrN3Viw7IWrOkOw+OqT1vaVLaMZKaMoFdDa9h9TmInhEChbGEsXUbRqCR1sbAbIZ+Ot//eKvz4qWOQgcmiILbtwLAcGKaDQslCAZUiLS6tsv6vGfvazYaiyLh8dQwtwSz2HB9D2bDxzJ5BbFnVikWxhbVMhYimpmZni09/+tP49Kc/fd7f/fjHP67VbomIiBpavmRi99EkXj6SwJ4TlQt2l6bgsmUtuP26FmxY2hjNrDN5AyOpEnxuFW0tnrMSLyEEckULY5kyyqYNVXklqbvYSJyiyPAoMty6gO2IyUItpuVAlgDXRMEXjua9QpIkLOsIIujV8cLBYZiWwEuHR5HJm1i3ZHptKIio+dXno0AiIqIFZDxbxo5DI3jpcAKHe9NwhEDIr+Pa9W3YsqoV65ZEoKmN07x7x8FhDI0V4XEp6Ii+sp5PCIFMwcR4pgzDcqCpMtoiHgR8GuRpJBmSJEFVKn30PC4FpuWgZNgolitfuibDrStsA3CGaMiN123pwvP7h5EtmDjan0a2YODy1bEF2SOQiM6PyR0REVENpHNlbD+UwIsHR3CkNwUBoLPVh1uuWYytq2JY2hGYVkI0V8YyJXz+X16ES6s02JZlCY4jkM4bGM+WYdkCLk1GR9QDv0eb9ciRJEnQNQW6psB2BEqGjbJRab+gKRLcLhWqInGECoBnYh3ejkMJDI8XMTxexNO7B3HVujh8nrlbh0lEjYvJHRERUZWk8wZ2HBrB9oMjOHSqktB1xXx4y2uX4cq1cXREffUO8aJyRRO/OzCC1rAHHr0yGjSWKWE8a8B2BDy6graIC163WpNkS5El+NwqPC4FZcNGybCRLZhQZAluV6UAy0JP8lRFxlXr4jhwMoWj/WnkSiae3DWIK9fF0Rpy1zs8IqozJndERESzkMkb2HE4gRcPDONQbwpCAB1RL978mmXYtjaOrtbGTuhOK5s2nt8/DEkC/uSOTfjSv+5AOm9AiEofvZagC945KuwiSxI8LhVuXUHZrEzZzBctFCXA7VLhdS3sBE+SJKxfGoHfq2HnkVFYjoPn9g3hitUxdM6T442IaoPJHRER0TQVyxZ2HErg+f1DOHByHEIA7S1e3H7dUly5No6ueVbJ0LYd/G7/MIplC2G/C5/51nOQAAS8GsIBF9x6fdYDSpIEt67ApckwLQdFw0ahZKFk2PDoCnRtYY/kLY774XOreGH/MCxbYPuhBDaaNpZ1BOsdGhHVCZM7IqImEgp7p93k2OerTc+sWm13thxHzKgao+0I/G7vIB5/qQ8v7BuCYTloj3rxjt9fjddu6cKS9kDDJRofvGPzJe+Tzhv4zN8/g1Su0nRcAHjXTWvw/N6BhilocnpdnqbKk8VX8iULRUOCZ4FP14wG3bhhSyd+t28YuZI12TJhzeILV9K0bQexWGCOI21chmkjnSrUOwyiqmByR0TURHRNwbcf2jXl+3/wjs3YcWCoBnGoMEyr6tuthivWtU/5OQtRKfCRyZvIFk04joCuVgqNLIr5EAm4UCoa+OVzJ2oc9fT5fK4LPk8hBIqGjUzOQKZgAgBURUJryA2/V8PdN6/F9hocF7N1Oslz6ypKhoVieWK6pizB61IWbK88n1vDazd3YvuhESRSJRzuS6Nk2ti0Inreoj2KIk/rfaLZTeVDEKL5gskdERHRq5RNG9m8iUzBgGULSBLg92i49+7L8dL+oXnbh82yHWTyJtJ5A6bl4PSz8HvUs1oeNLpXj+QVyjZyRQuKLMHrVhdkawBNlXH1+jbsPjqKUyN5nBrOoWzY2LYmBqVBRmCJqPaY3BEREaEyVS1TMJHJGyibDoBKIZHWkAa/R4MsS7hyfTt2Hhyuc6TTY9sOskULuYKBQtkGALh1BT6/jlTOgG+eJXZnOjPJM0wHxbKFbMGEpkjwuNWGmVY6V2RJwuaVrfC6NRw8lcLweBHP7RvGNRvaFtxrQbRQMbkjIqIFSwiBfMlCJm8gV6xMI3VpMmJhNwJebd5eEJuWjeP9afQl8iiUKs9LU2W0BF0IeCv90HqHc5V+dS3zM7E7kyRJcE0UWCkZNkrlylRaXZPhcalQ5ulI60xIkoTV3WG4XSp2HhnFWLaMZ/YM4brL2hfkiCbRQsPkjoiIFpyyYSOTr6w3sx0BRZYQ9usI+XS46lQZcjaEEMgUTIyMFzEyXsBYpgyByjq6SKCS0LkmKkvatoNTw3lIkjTZpLxZSBMtFFy6glK50ifPMA24dQW27dQ7vDm1OO6HW1fwwoFhpPMGnt4ziOsva592wSUiml+Y3BER0YJwetrlz5/vwVimDKCy1izo0+GrUVPuWioZNsYyJSRSRQyPF1EyKlMugz4dKxeFsLQzhJ6B1FnPSwiBgWQBlu1gUdzXtCM5slRZe+fSFRTLldYJh3tTcE20VZhv/69nKh724LUbO/DM3mFkCyae2j2I12zqqHdYRFRDTO6IiKhpCSFQKFtI516ZdhkJuBALuxH0avOm0IQQAoWShWSmhLFMGclMCfmJ6ZaqIiEW9qAt4kE87IF7otG4z+fCycH0WdsYGS+iWLbR3uKBZ44akteTIkvwezRYugPbrkzBLRkLq7JmyO/CjVs68PTuQeRLFp7cNYB337K+3mERUY00/zs7EREtOJWqkAbSOROm7UA+Y9rldZu7atL+oVrOXAeYzhtI5wyk8mUYE0VeNFVGS8CFxW0BRIMuhP2uKU2tTOUMpPMmWgIuBH16rZ9GQ1EVGd1xH04OZSYra6pKZXRvvq6rnA6fW8ONWzrx9O5BFMo2PvHlx3HF6tiCSPCJFhr+VRMRUVM43yidx6UgGvLA79XO2++rnk7HmyuYyBUrX9lipVqnZQsAgCQBAY+GtogHYb8L0WCl0Mt0R5zyJROJVAk+j4poqDGby9famZU1y4aN4kTRFddE0ZVmWnt4Pm5drSR4e4YwlinjiV0DeN3mzsmRXiJqDvyLJiKiee18o3SRQGWUrt7FIyzbQaFkVb7KFvIl85V/F0044pX76poMv0fDopgfIZ+OkF9HwKtBkWc3smSYNgZHC9CbpDLmbEmSBLdLha4rKJZtlA0bZdOAx6XArStN/fpoqoLXburA8cEsDp4cx+M7B/C6rZ1w67wcJGoW/GsmIqJ5RwiBYtlGKleu6yjd6TgKJXMieZtI5Eom8mVrcirlaaebbPvcKuIRDwKeSg89v0erSSJqOwL9owVIkoSuJquMOVuyJMHnVuHWZBTK9mSi53Gr0Od4PZ5tO/jgHZvnbH+W7eB//OPz2Hk4gef3j+Drf/56RILuOdv/bGRyZXz/FwfrHQZRw2JyR0RE84bjCGQKBlJZA4Y1N6N0QghYtkDZtPHQb49i17FkJZmbGIETZ4y+SQA8LhVet4qOFi+8bhVel1b5PsdJg+MIDI4WYFoOupu4MuZsKYqMgFeGaVVGWfNFC6WJJHyuXjNFkfFnX3l8TvYFAFesa0e+UIbXrSCTN/D+z/4CS9p8UNXGb5PwpU+8rt4hEDU0JndERNTwDMtBOltGOm/AEYBLU9DeUv1ROtsRKBs2SoaFsunAMG0YljOZwP3vn+6DrsrwulWE/Do6W33wTiRzXrdaWbvVINP6Xj48gkLZQltkYVTGnC1NlRH0aTBMB4WyhWzBhK7K8Libswn66dHcgdEC8iULJ4fzWNLuXxAFZoiaGd/tiYioIVUKjthIZcuTZf8DXg1hv16VtVFCCJRNB6WJPmglo5LInaYqlQIcIZcKl6ZA12R88WM34P88dmBW+50LPUNZHD6VQsRfWbtHUyNJElx65f918XQT9FylCbrbpTRM4l4tlUb23lcSvKEcEzyieY7JHRERNRQhBLIFE+PZMsqmA0WW0BJ0IezXZ33RadkOjvenMZisXMw6ExVNFFmCW1cQ8GpwuxS4NeW8PfD83sZPlEbTRew5nkRH1Ae/p/Gn2TUiaaIJultXUJhI/sumDY9Lbbom6JMJXrKAfLGS4C1t98+bHpBEdDYmd0RE1BAcRyCdNzCeLcOyBXRVRlvEg4Bv5lMvK6NzNrKFSpGTsung+EC20tz6jKmUqiI1xQV7vmTixYMJ+NwartvUgT1HE/UOaV6Tz2iCfrrqadmQ4HE31+WTJEnojHoxmCwgV7TQMzyR4M2yUisRzb3menciIqJ5x7IdjGcNpHNlOKJS9TIeccHnVmeccBlmpYdZtlBpjwBUttsacmHbunYc6xtvimTuTKbl4IX9IwCAq9bF694GopmoioyAV5ssupIrmHh8Rx90TYKrSV7nygieD/2J/OQUzaXtfshM8IjmFSZ3RERUF6blYCxTQjpvAgD8Hg0tAX3GTZUdR0w2AS+WbQCA162iJeiC36tNFsWIBN1Nl9gJIfDS4QRyRRPXbGiD36PVO6Smc2YT9JJhYzRdhGk5CPl0REOuplmn1tnqRV8ij2LZxqnhPBa3+ZjgEc0jTO6IiGhOGaaNsUwZmYIJCUDIpyMS1KHPsAy7ZTtI5QykcwZsR0BTZbSG3Aj6tKa54L6U/SfHMTxexMblLYiFPfUOp6lJkgSPS8XrLl+E32zvRSpnIFsw0BJ0IxzQ533RFUmSsCjmw6nhHMqmg96RPLrjTPCI5gsmd0RENCfKE0ldtmBCkoCwX0ck4JpxLzFjYuQvMzHy5/OoiPhd8LhmX0lzPjk1ksOx/gyWtgewrCNY73AWDJdeaUQf9utIpEoYTZeQzpXRGvbA75n5lOJGIEkSuuM+nBrJo2w66B8toDvur3dYRDQFTO6IiKimyoaNZKaMXLGS1EUClaRupqNqpuUgmS69MvLn1xEJzHzkbz4by5Sw++goWkNuXLaspd7hLEi6pqAr5kO+ZCGRKmIwWYBbVxALu+d1f0FZlrE47sPJ4RyKZRt9iTwWxXz1DouILmH+vusQEVFDMy0Ho+nS5EhdS8CFcGDm7Qxs20EyU0Y6ZwATI38tweZZ6zRdhbKFFw6OwO1SsW1NDHITNtqeT3xuFd42PzJ5E6PpEnpH8gh4NbSG3DMena43WZaxpM2PnqEcCiULg8kCOqLeeodFRBfB5I6IiKrKsh2MpvMYy5QmR+paAq4Z980SQiCVM5BMl+AIIOjTEA3O3wvmarAsBy/sH4bjCFx9GStjNgpJkhDy6wh4NYxlyxjPVkasIwEXWgKueZmAy7KMJe1+nBjMIVswoSpFruskamBM7oiIqCpsR2B84oJWiEqhlJbgzNfUAUCxbGFkvIiy6cDrVhELu5um9PxMCSGw43AC2YKJq9e3ITAPGqsvNLIsoTXkRsinYzRdwtjEiPPpQj/zbT2eIstY2ubHiaEsxrMGZFlGNOiqd1hEdB5M7oiIaFYcIZDKGhjLluE4AgGvhvaoDxLEzLfpCCRSJaTzBlRFQkfUO++LVFTL/p5XKmPGIxxBaWSaKqMj6kXYbyGRKmF4vIjxXBnxsAfeedYIXVVlLGkP4ORgFsl0CZoMBP1M8Igazfx6ZyEiooYhhECuaGE0VYRpC3jdKlpDbrh1BbqmwDCtGW23ULIwNFaAZQuE/TpaQ+55OZ2tFk4OZXFsIINlHayMOZ94XCq64z7kiiYSqRL6Enn4Jkai59OUWl2V0d3mw6nhPIbGS1AUGT72VCRqKEzuiIho2sqGjZFUEcWyDV2V0RXzwjfLkQhHCIymSkjlDGiqjO64d15XG6y2RKqI3ceTiIXd2MDKmPOOJEkIeHX4PFplpDtTQs9QDmG/jkzeqHd4U+bWVXS1etE/WkD/aAGL23xw6/w7JWoU/GskIqIps+xKG4J03oQsS4hHKuuKZjtdsmzaGEwWYJgOR+vOI1c0sf1gAn63hm1r4vO+UfZCJksSWoIuBH0akukyUjkDH/r8r+B1KQj7Z/+3NBd8Hg1tLR4MjxXRO5zHso4A1AVc4IiokTC5IyKiSxJCYHxitMERlTYE0ZAbShUSsEzewPB4EbIkobPVCz+neZ3FMG38bv8wJAm4an18QVcJbSaqIqOtxYNwQEc05MVLh0aQmii6Mh/Wl4Z8OkzLwVimjJ7hHJZ1+KHIPDaJ6o1/hUREdFGFkoWTQzmMpkvwuFQsbfcjHvHMOrETQmB4vIihsSLcuoIl7X4mdq/iOALbDyVQLFu4cl0cPjdfn2bj0hT8jw9di65WLyQAg8kC+hJ5lAy73qFdUmvIjaBXg+MInBrOQ4iZF1EiourgyB0REZ2XbTtIpEvI5E2oSnVH1SzbwcBoASXDRsSvozXsbviRirkmhMDuY0mMpkvYuqoV0aC73iFRDfk8GrxuFem8gWS6jFPDOYR8OlpDM+8RORfao14YVg4lw0bvSB7dcR//lonqiMkdERGdRQiBTKFS1c9xBCIBF6LB6jVgLhs2+kfzsB2B9qgHQfZpO69jAxmcGslh1aIQuuP+eodDc0CSJIT9LgS8OsbSJYznDGSLJlpDrqqsba2V7rgPPUNZlAwbQ2NFdES99Q6JaMFickdERJMM08bweKUKpltX0BbxwKVXr1R7rmhiMFmALEvojvvhruK2m0l/Io/9PePojHqxdnG43uHQHFNkCbGIB0G/jpHxIkbGS0jnDMQjnoasICtJEhbH/TgxmEO2YEJTSmgNc6SZqB4ad5yfiIjmjBACo+lKafayYSMe8aA77qtqYpfKlTEwWoCuyljMxO6CkukSXj6SQEvQha2rWxt2tIZqz6UpWBTzoSPqge0I9I7kJ3pAOvUO7RyKImNJuw8SgLFsGelcud4hES1IjffxDxERzamyYWNorICy6SDg1RALu6FWcY2PEAJjmTKSmTJ8bhUdUS/bHFxAtmDghQMj8Lo1XLU2zuqD9Ep/PLeGZKaM8WwZuYKJ1nB12pBUk6Yq6Ir50JfIY3i8BE2V4WURIKI5xbMGEdEC5QiBH/zqME4O52DZAp1RLzqi3qondiOpEpKZMoJeDZ2tTOwupFS28Pz+YciyhGvWx6FrHNmkV8iyhFjYjaXtlVHvkfES+hJ5GGZjVdX0ulXEJ6Zk9iUKKM+Dqp9EzYQjd0REC1C2YODlI6NI5Qz4PRraIu6qV+QTQmBorIhswUQkUGlM3kijDI3EtBw8f2AYhungNRvbOdpBF6RrldGx00WPTg7l0BJyoSXgapi/r3DAhZJpI5M30TuSw5L2APszEs0R/qURES0gQggc7U/jiZ0DyJcsfPKPtqGz1VuTxG4wWUnsWkMuxMKehrnwbDSVXnYjyOZNXLk2jpDfVe+QqMFJkoSQT8fSid6QyXQZJ4dzKJateoc2qS3igVtT4AigdyQHuwHXCRI1IyZ3REQLRKFk4Zm9Q9jfM454xIPXb+3Ea7d2VX0/Qgj0DueQK5qIhd1oYX+2CxJC4KXDCSRSJWxeGUU84ql3SDSPqIqMjlYvOlu9cCYKroyMF+E49W8mLkkSumJeKLIEyxboS+QbIi6iZlfT5C6Xy+G2225DX18fAOAv//IvcdNNN+Etb3kL3vKWt+CXv/xlLXdPREQTBpJ5PLFzAJm8ga2rWnHl2jjcevVn5gshMJAsIFMwEAu7EQlwFOpCTjcpH0gWsH5pBIvbAvUOieYpv0fDkvYAQj4dqZzRMKN4iiJjUcwHACibDgaSBQjBBI+olmq25m7Xrl349Kc/jZ6ensnb9u7diwcffBDxeLxWuyUiojPYjoN9J8bRM5RF2K/jitUx+Dy1Wc91eipmvmihI+pDwMtl3RcihMD+k+M4OVxpUr6yK1TvkGieU2QJbS0eBLwahsYK6B3JIxp0oSVY37V4Ll1BR9SLwWQBhZKF4bEi2lo4TZuoVmo2cveDH/wA999//2QiVywWMTAwgPvuuw+33347vvrVr8JxOP+aiKhWsgUDT+0aRM9QFis6g3jNxo6aJnZDY8XJqZjREKdiXszR/jSO9WewtD3AJuVUVV63iiXtAQS8ldYJvSN5GFZ9K1YGvBrCfh0AkCmYGE2zBx5RrdQsufvc5z6Hbdu2Tf48OjqKa665Bg888AB+8IMfYPv27fjRj35Uq90TES1YQgicGs7iyV2DKBk2rl4Xx4ZlLTVrQSCEwMh4CdmCiWjIxamYl3BiMIMDJ1PoavVh4/IWjmBQ1SmyhI6oF+1RDwzTxsmhHNJ5o65TImNhN1xa5bJzPFvp10dE1Tdnc2a6u7vxjW98Y/Lne+65B4888gjuuuuuaW0nGvVXO7SGFotxDQbVDo+v5lMomdhzYhw9gxnEIx5cu7HjkmX1dW12p4KR8QLSeQOtITfao76qbbeWZhObzzfz5PXEQBp7jo+hK+bDazZ31bzn32yeZzX+/9WyCftMtl3NeBxH4Ip17VXbXjW3daZ80cTzewcxPFaErim4cn17Tfd3prJp4/DJ8cmfl7QHcbQvBQBIpEpw6+qMqsPO5m/wQl59PuT5kWqplsfXnJ15Dx06hJ6eHtx8880AKp/0qur0d59M5hZMtaVYLIBEIlvvMKhJ8fhqPsNjBXzzP/ahdziLNYvDWL0oBGE7yOcv/gm5Yc688EI6Z2BkvIiAV0MkoE9uS9fUWW231mYT26VezwvpHcnh5SOjaA25sWVFFMWiMeMYpsLnc83qeVbj/59do+UXiizPaNvVjEeWJfz8+Z6qbOtdN6+t2rbORwgBj0tB73AOfSNHsbQjiHSu9iNnN1+z9JzjqD3qxcBoAYosoXckB0cI+NzTux6c6d/gxZx5PuT5kWpptseXLEsXHeyas1YIQgg88MADSKfTME0T3//+9/HGN75xrnZPRNTUdh8bxV//y3aksmVcu6ENa7rDNZ/ulyuaGB4vwutW0c4CCRd1ZmJ31bp41fsKEl2MJEnwuFQEfRokScKJgQyKZasu0zT9nsoHQbYjoCoSBkbzKBn1XRNI1Ezm7Oyydu1afOhDH8Ldd9+NW2+9FevWrcNtt902V7snImpKQgj85Nke/O0PdyMWcuPL996IWLj2vdKKZQuDyQJcmoLOqJeJ3UW8OrFTmdhRnaiKjKBPQ9Cro1i2kStacOqQ4LWG3PDoCixbQJYk9CfqX/SFqFnUfFrmb37zm8l/v/vd78a73/3uWu+SiGhBKJYt/PPPDmDH4QSuWd+G996yFm0t3prv1zBt9I8WoCoyumLemq8bm89OjeSwk4kdNRBZktDV5sPxgTSKZRuZvImAR53T0WRJktAe9eLUcA6yDNgO0J8ooDvu498I0Sw17mp3IiK6oOGxAr720B4MJvP4w99biZuu7J6T0TPLdtCXyEMC0NXq5YXYRZwazmLn0SRaQ25czamY1EBOT9NUFRm5ool03oTfo0LXlDmLQVNltLV4MDBaQMCrIle00J/Iozvu5wdGRLPA5I6IaJ7ZfSyJf/jxPiiyhD//wy1Yt7RlTvbrOAL9owXYjkB3zDenF4LzzfGBDPaeGEMs7MZVa5nYUWPSVBlBn45cwUSuaMHjCLh1Zc6mWfs9GkI+Hem8gWjQhWSmjIHRArpinOpNNFNM7oiI5pHfvtSHB395GN0xPz56x0a0zsH6OqCytm94vIiyYaMz6oXbxdPH+QghcOBkCkf70+iIenH56taatgMgmi1FlhD0aciXLBTLNmxbwOdR5yy5ioXdKJYtpHIGYmE3EqkShsaKLNJENEM8OxMRzQOOEPjRb4/hsRdOYfOKKD78lg1w63P3Fj6eNSpNyoMu+L0X75u3UDlCYPfRJE6N5LCkzY9NK6K8OKV5QZIk+NwqFNlGsWzDKZjwe7Q5mR4pTzRcPzWcQ6FkTY7gKbKEWNjNvyGiaWJyR0TU4AzTxj/+dD+2H0rg9y7vwrvesHpO16TkiiZG0yUEPBpagtVvHtwMbNvBjsMJDI0Vsbo7NCetKIiq6fQ6PEWWkCtayOQNBLzanEwpdukKWidG7bxuBWG/jlTOgKrIfM8hmiYmd0REDSxbMPC1f9+Do/1p3PX6lbj5qrMLp4TC3nPWvvl807sY0rULnwpKhoWhZBFuXUF3W2BaSeXFtlsrjhCwalhS3bYdfPCOzWfdlisY+H/+9wsYHi/iv75tI259zfKa7X+63nXz2hk/9kufeF31AqF5Q9cUBCUJ2aKJTN6E36tBU2uf4IX9OvIlC6PpMrrjPtiOwGi6BEWREPLpNd8/UbNgckdE1KCGxwr48g93YTxbxp+89TJsWxs/5z66puDbD+2a/PmDd2zGjgNDU97Hu25ei4HR3Hl/5wiBTM6AQOWT9aGx/JS3q8gybMeZ8v2rpbPVX9PtK4qMP/vK45M/l00bA6MFmJaDjqgHv9l+Cr/ZfqqmMUyVrqkX/H97KTdfsxQ/f75nVvv/l/vfNKvHU/2oE4VWsgUT2cLcVNKUJAntLR6cHMpheKyIRXEfbFtgeKwIRZbg93A6ONFUTOmjmPvuu++c2z7+8Y9XPRgiIqo40pfC5767A4WShb+4e+t5E7taEkIgVzDhiEpFO4Wlyc+RK5roHc7BcQS64z4EvBxdoOahyBKCXg2KUpmmWTJq32RcVSrtEcqmg/Gsgc5WL1yajMFkAcWyVfP9EzWDi47c3X///RgeHsaOHTswNjY2ebtlWejt7a15cEREC9HOI6P45iN7EQ268Im7NqMtUvvG5K9WKNuwbAGfW52TKVnziRAC41kDo+kSXJqMzlYfXyNqSvJEgpcrWiiULAhR+1YJfo+GoFfDWKYMv1tFV8yH3pE8+kcLWBz31Wy/RM3iosndnXfeiSNHjuDQoUO4+eabJ29XFAVbtmypdWxERAvO8/uG8I8/PYDFbX7ce9fmuowGGaaNsmHDpStw6exld6ayaWNorDgxVU1De4uHDZepqUmSBL9HnWyVIATgcdU2wYtFPCiULQyNFbG4zY+umBe9w3n0JfJIpos12y9RM7hocrdx40Zs3LgR1113Hdrb2+cqJiKiBenxl/vx3Z8fwuruMD5+5yZ46tBLzrYd5IoWFEWC18XE7kyGaeOTX3uq0hIi5EJLwMWKmLQgnG6VIKEyPVMIAa+7dr3wFFlCW4sH/YkCkpkSYmHPxAheDvd/6zmsXxKGpvL9ieh8pnTlMDg4iL/4i79AOp2GEGLy9p/85Cc1C4yIaCF59PmT+OHjx7BpRRR/8tbLal684HyEEMgVLUhSZWoUE5cKIQQyeRMjqSL8Hg2drV4Wd6AFR5KkiYTOriR4sCoJX43eJ3xuDSGfjvGsAZ9Hg9elorPVh/5EDrmCgWs2tEGROR2a6NWmlNz99//+33HHHXdg/fr1PNkTEVWREAIPPXkcP3vuJK5aF8cHblsPdQ76Sp0vjnzJgu2ISm8rTjUEANiOwMhYEdmiCY9LwVf/7PX4/Hd+V++wiOrilQQPKJZtQFjweWqX4MXCbhRKFoaTRSxp98PnVnHv3Zfjfz64AzsOjWLb2hhkXpcSnWVKyZ2qqnj/+99f61iIiBYURwj86y8P4zcv9eOGzZ14z81r6rZ+q2w6MEwHHpfC4iATimULg8kCLFtMTsNsDXvqHRZR3Z2eMl4s20CxdgmeLEtoi3rQN5JHIlVCW4sHN2xdhEefOYG9J8aw+2gSm1dGOfBAdIYpJXerVq3CoUOHsGbNmlrHQ0S0INiOg3/+2UE8t28Ib7pqMd7x+hV1u0CxbAeFkgVNkeBmARU4jkAyU8J41oCqSOiO++qy/pGokc1Vgud1qYgEKtMz/d7KdOjlnUEYlo3DvWmoqowNSyNM8IgmTOls1dvbi7e//e3o7OyEy+WavJ1r7oiIps92HHzrx/vx4sERvO2G5bjt2iV1uzDJFgzkCiZkCfBxnR3yRRPD40VYtkDQpyEW9nCKKtEFzFWCFw26kStaGB57pd/dmu4wTMvB8YEMdFXG6u5w1fdLNB9NKbm79957ax0HEdElhcLeuhQaqSbbdvC//vUlvHhwBH98+wa87XUrZ73ND96xeUaPE0Lgb//tZTgCCHq1BV3S37IdJFIlZAsmNFXGopgXXjdH64gu5awEr1SbIivyRPXMvpE8vvvoAUiorP+7bFkLTMvBwVMpaKqMZR3Bqu6XaD6a0plr9erVtY6DiOiSdE3Btx/aVe8wZkwIgZcOj6J/NI91SyIYHcvP+vn4fC7sODA0+fOXPvG6KT82lTNwpC8Dr0uBukDX2QkhkM5VGpILAUSDLkSCLhZpIJqGMxM8CVZN2iR4XSpCfh0/ffo4rrusHdGgG5IkYcvKVpiWgz3HxyY+mPFXdb9E882UkrtrrrkGkiRBCDH5xxqLxfDkk0/WNDgiomYhhMDLR04ndmGsWhSqazwlw8ZoqoRt69pwrG+8rrHUw+m2D6PpEkyrUkimLeKZ9yPDRPXicakQovLeAsmuSZ/MWMgNXVOw6+gobtzSCUWWIcsStq2J4fn9w3j5yCg0RUZbi7fq+yaaL6b0Ue3Bgwdx4MABHDx4ELt27cLnPvc5vOUtb6l1bERETUEIgZ1Hk+hL5LF2cRirFoXrGo/jCAwmC5AVCZ9459YFt85uKJnHqZE8BpMFSBLQ2erFopiPiR3RLHlcCly6grJhV6ZpVpksS/joO7YgV7RwuDc9ebuiyLhqXRuCXh0vHkogmS5Vfd9E88W05+Houo477rgDzzzzTC3iISJqKkII7DqaRO9IDmu6ww2x6H9kvAjTctDR4kXI77r0A5qAEAKFkoW+RB6/3dEH23bQ1uLBkjY/G7YTVYkkSfC6FLg0GSXDxuFT1Z8VcPmaOLrjfhztSyOVK0/erqkyrtnQBq9Lxe8ODCN9xu+IFpIpJXepVGrya3x8HE899RQymUytYyMimteEENh1LIlTIzms7g5hzeJwvUNCJm8gUzDREnQtiIIhQghkCwZOjeTRl8ijbNjYsjqGpR0BhHw6kzqiKjvd6FxTZew4OIJswaz6PjYsi0DXFOw8moTjiMnbXZqCaze0QVNlPLd/GLli9fdN1OimveYOAKLRKP7bf/tvNQ2MiGg+E0Jgz/ExnBrOYdWiENY0wIidYdoYHi/CrSuIBpt7xM5xBNJ5A6lsGaYtoKky4hE3gl4d65a2nFWEhoiqS5Ik+D0qFEXGULIARfZV9cMkXVWwaUULXjyYwNH+9FkzIjwuFdduaMfTewbx3L4hvGZjB/tU0oIypaP94MGDtY6DiKipHDyVQs9QFiu7gli7OFz3ESIhBAaTRUiShI6ot+7x1IIQAvmSiWS6iGzBhBCAW1fQGnbBX6P+W0R0fpIk4Yati/DTp45jYDSP7rgfLr1661o7oj50RvM43JtCZ6sPfo82+Tu/R8O169vwzN4hPLdvCNdv7ICLa2ppgZjStEzHcfDtb38b99xzD+6++258/etfh2VZtY6NiGheOtqfxpG+NJa0+bFuSaQhkorRdAll00ZbxAOtydoeOI5AsWwhnTdxYiCDbMFEwKuhO+7D4jY/Al6uqSOqB5emoCvmgyxL6EvkYVpOVbd/2fIWyLKE3ceSk7PLTgv5Xbh6XRsKZRvP7xuu+r6JGtWUzvBf+tKX8Pzzz+O9730v3v/+9+Pll1/GF7/4xVrHRkQ075wazmJ/zzg6o15sWhFtiKSiULIwnjUQ8ukIeLVLP2AecByBkmEjkzeQyhkolm3IEtDV6sOKziDaW7ycikXUADRVRlfMByEE+hJ52Hb1kiy3rmL9kghG0yX0JfLn/D4acuPKNTFkCgZeODAMq4r7JmpUU0runnrqKfz93/893vCGN+Cmm27C3/3d37HHHRHRqwwk89h5NIlY2I3LV8caIrGzHYGhsQI0VUYs7K53ODMmhIBtOyiVrcmErlCyJqdehnwagj4dkaAbslz/152IXnF6BM+yHfSPFs4qgjJbS9oDiARc2HdiDGXz3PYLbS1ebF3VimSmjO0HE7CruG+iRjSl5E4IAU175dNeXdfP+pmIaKFLpIp46VACkYALV66NN0SCIYTA8FgRli3QEfU0REzT4QgBw7SRL5pI5wyk8yYKZRtCVPpphXwaQn4dXnelcAMRNS6PS0VHixclw8ZAsnDONMqZkiQJm1dEYdoO9veMnfc+i2J+bF4ZxUiqiB2HEnCqtG+iRjSls+HatWvxwAMP4NSpU+jt7cUDDzyA1atX1zo2IqJ5YTxbxgsHRuDzaLh6XRxqgyQa2YKJXNFENOSCW2/8KYpCCJiWg0LJQjpnIJU1kCtaMEwHiiLD61YR8usI+XV4XEzoiOYbv1dDPOJGoWRhJFW9RuNBn46VXSH0juSRSBXPe58lbQFctqwFQ2MFvHx4tGrJJVGjmdKZ8f7770cmk8E73/lOvOMd78D4+Dg+85nP1Do2IqKGly0YeH7/MFx6pb+S3iAV2UzLwchE24OWQGO2PThzqmW2YGI8ayBbMFEybEhSZXQu4NUQDlTWCrp1Bco8G30korOF/S5EAjrSOQPj2eo1Gl+9KASfW8XuY0nYzvnX1i3vDGLdkjD6R/PYdfTcIixEzeCiH+UahoHPfOYzeMMb3oAvfOELAIAPfehDUBQFfr9/TgIkImpUxbKF5/YNQ5YkXLuhrWFGx4SorLMD0HBtDxxHwLQdmFbl6/S1lSxLcGkyNFWGqsqQGyhmIqqu1pAbhukgkSpBV2X4PLNf6qMoMjatiOK5fcM40pvG2iWR895v1aIwbFvgcF8aiiLhsmUts943USO56MjdV7/6VeRyOVx++eWTt332s59FJpPB1772tZoHR0TUqEzLxvP7K9XXrtnQBp+7cdYhj2fLKJZtxBug7cE5Uy1zBvJFC6blQDtjqmXYr8Pn0aBrChM7oiZ3ut+mS5MxmCygbJxbCGUmYmEPFsV8ONKfRrZgXPB+axaHsbwziBODWRw4meIIHjWVi571H3/8cXzpS19CNBqdvK2trQ1f/OIX8atf/armwRERNSLbEXjxYAK5ookr18YR8un1DmnS0b4URtNl+D1a3doe2BN95y401TLo0xD26/BzqiXRgiXLEjpbfZAkCf2j+aq1KdiwrAWaIl902qUkSdiwNIIlbX4c7U/jB786XJV9EzWCiyZ3mqbB7T63dLbf74euN87FDBHRXBFCYOfRUYymS9iyshWxsKfeIU1yHIEvfW8HVEVCW8Q9Z9MxhRCw7FdG59I5A7miCdt24NJk+D0qIgEdQV+lEIqqyA01VZSI6kNTZXS1emE7AgOjhapUsXRpCtYvjWAsW8bJ4dwF7ydJEjatiGJRzIcHHzuIX7xwatb7JmoEF10gIssycrncOevrcrkcLMuqaWBERI3o4KkU+hN5rF0cRne8sdYeJ9IlpHMGFsV8Na8kKYSA7QgYpgPDcib7VqmKBI9LmVh/KJjEEdFFuV0q2lu8GEwWMDxWRHuLZ9bvG91xP/oSeezvGUN7i+eC66ElScKWVa1Y0hHCv/3mKDRNweu3ds1q30T1dtGz/2233YZPf/rTKBQKk7cVCgV8+tOfxk033VTz4IiIGknPUBZH+tJY0ubHqkWheodzltxEL7i33rgCXnftCrucnnKZzhnI5CvTLWUJ8LpVhP0cnSOi6Qt4NURDLmQLJsYys6+geXpUznEE9p44f++702RJwp+9+wpsWhHFgz8/hKd2D8x6/0T1dNHk7r3vfS8CgQCuv/563HXXXbjzzjtx/fXXIxgM4iMf+chcxUhEVHdDYwXsPpZEW8SDjSuiDZW4WLaD4bEidE3GPbesq/r2hRAomzYy+cqUy2LZhixL8J2R0Ll1Zd41SSeixtEScCHg1ZDMlJEtmLPent+jYVV3GAOjBYyMFy56X02V8ZG3XYb1y1rwnf88iN9s7531/onq5ZLTMj/72c/iv/7X/4p9+/ZBlmVs2rQJ8Xh8ruIjIqq78WwZOw4lEPbruGJNrKGqOQohMDxehOMILIr5qtpnz3YEyoaNsmlDCECWALeuwMUiKERUZZIkoa3FA9NyMDRWgK764dJn9362siuE/kQOu4+N4XVb3VAvMl1dUxV87I6N+Nsf7cbf/ttL+MBt63HNhvZZ7Z+oHqY0d6erqwtdXZyDTEQLT75k4ncHhuHSFFy1ru2iFwf1cLw/jXzRQizsnvWF0GmW7aBUtmFYlep1uirDpStQFamhRizPRwgBXbv0qW0q96nFY4nowmRJQmerFyeHc+gfzWNJm39W64cVuTI989m9wzjSl8a6C/S+O03XFHz8zk345iP78O2f7ocsS7hqXduM909UDzxDERFdgGk5eOHACIQArlnfBneVkqdqyRVN7Dg4Aq9LQdg/uwrGp/vRlQwbll0pjjIfR+kkScLA6IUr5AHAxpWtl7zPxczmsXOps7WxCv4QTYWqyOiMetE3ksdAsoBFMd+sPlRqDXnQHa+0POhq9SF4idY1Lk3BZ/7L1fj0N5/Gt368H7IkYdtazlij+aOxPoImImoQQgi8dDiBXMHEtjUx+OvUM+5CHKcSnyJLaGvxzurix7QcZAomckULjiPgcSkIB3R43eq8SuyIqDl4XCriLR4UyzYSqdKst7d+aQSaImP3sQv3vnv1/v/0HZuxvDOIf/jxPrx0ODHrGIjmCpM7IqLzOHAyheHxIi5b3tJQvexOO9yXQipn4Mr17dDUmb2VF8sWPvP3zyJbMCEcAa9bRchfqXbZSOsKiWjhCfl0hP06UjkDmbwxq22d2fvu1EV6353J41Jx712bsaQ9gL97ZC92Hh2dVQxEc4XJHRHRq/SN5HC0v9LyYGl7oN7hnGMsU8KR3jQWxXxYPIP4DNNG/2gevSN5nBhMw+tSEPJXKl42+po6Ilo4YmE3PC4Fw2NFFMuz66/cHfcjGnRh/8lxlA17So/xuFT833dtQXfcj28+vAe7jyVnFQPRXGByR0R0hvFsGTuPjiIadGHj8sZqeQAAluXgpSOj8LhUbFwendZjHUcgkSqiZyiHYslCNOjCt/7yDXC71IZ7nkREkiShM+qFokgYTBZg2c6strVpRRSW7WBfz8V7353J61bxZ+/cgs5WH77+0B7sPcEEjxobkzsiognFsoUXDozAravYtjbekH3b9p4YQ6FkYeuq1ilPxxRCIFsw0DOUxXjWQNCnYWlHANGQG153Y60lJCI6k6LI6Gr1wXYEBkYLMK2pjbqdT8CrY1VXCH2JPBKp4pQf53Nr+PN3bkVH1Iuv/TsTPGpsNU3ucrkcbrvtNvT19QEAnn32Wdx+++246aab8OUvf7mWuyYimhbbdvDiwRFYtoOr1sXhqmK/uGoZTOZxaiSHVYtCiIbcU3qMYdroT+QxmCxCkSV0x31ob/E2XEsHIqILcekK2ls8KBk2/uHhPbPa1qruEHxuFbuPJWE7Ux8J9Hs0/Pk7t6C9xYuv/mgP9hxngkeNqWZn9127duHuu+9GT08PAKBUKuG+++7DN7/5Tfznf/4n9u7diyeeeKJWuycimjIhBHYeTSKVM3DF6tglS2XXQ6lsYdfRJEI+HWu6w5e8vxACY5kSTg7lUDJsxMNuLG7zw+NiBxwimn8CXh2RgAs/f/4kTg5lZ7wdRZaxaUUU+ZKFI33pacfwF3dvRWerF1/7993YxSIr1IBqltz94Ac/wP333494vNIbZPfu3ViyZAm6u7uhqipuv/12PPbYY7XaPRHRlB3tT6N/NI91S8Joj3rrHc45hBB4+egobEfgitWxS04XNUwbvSN5jKbL8HlULO0IIBxwcV0dEc1rrSEXtq6OYc/xJMaz5RlvJxb2oCvmw5G+NLKF6VXirIzgbUVXzI+vP7QHO48wwaPGUrOPcD/3uc+d9fPIyAhisdjkz/F4HMPDw9PebjS6sJqyxmKNV6mPmsd8PL58PldVt9c3ksOBkyksaQ9g8+p4QyZAB3vGkEiVcOX6NrTFzn0P1LXKW7kQAo88cQwnh3OQJQmL4n6EfPoln5Mi1+Zzvlpttxr7nU1s9XpeM1Hv51nL12om2652PNXc3lwfV3O1v9PvT9XyF/dswwcf+BW2H0rg5muWzHg2wpXr2/GzZ05gX884hBDnnA8vdn6MAfjCR1+L//4Pz+Kbj+zBJ++5Etdu7JhRHLQw1fL6a87m5ziOc9YFhhBiRhdRyWQOjnPpBpTNIBYLIJGY+dQDoouZj8dXLBZAPj/zT2tfLZM38OzuQYT9Oi5bGkFhmp/gzoV0roxdRxJob/GiPew+5/n7fC4YpgXTcjA0VsC+E2PwuVW0tXigKvKUig9MZ93JVCmyXJPtTsVU9jub2Or1vGai3s+zVq/VTI+vasdTze3N9XE1V/szzNm1MHi1gFfHtjUxPL17EE++3IfrNrTPuPjV+iUR7DqWxK9f7MXmZZHJ26d6fvzTt2/C//rBTvy//9+L+PCbN2Db2viM4qCFZbbXX7IsXXSwa84+Jmpvb0cikZj8OZFITE7ZJCKaa2XTxgsHRqAqMq5cG4fSgAVGLNvBjsOj0FQFm1deuC1Drmji5FAWZcPGn/5hZT0IC6YQUbMK+XRsXhnFWKY8rbYGr7a4zY+WgAv//JN9056eCUy0SfjDLVjWEcTf/8c+vHBg+jPSiKptzs7+mzdvxokTJ3Dy5EnYto2f/vSnuOGGG+Zq90REkxxHYPvBEZQMC1etizdskZH9PePIFU1sXd163uqdjiPw0sERDIwWoKkKFrf78YarFjfk1FIiompaFPNjeUcQJwaz6B3JzWgbp3vfFUomfvjbYzPahsel4t67NmNFVxDf+vF+PL9/aEbbIaqWOUvuXC4XvvCFL+BjH/sY/uAP/gDLly/Hm970prnaPRERgMqU8D3Hk0hmytiyqhWRQHXX8FXL0FgBPUNZLO8MIh72nPP7QsnE03sGcejUOMJ+Hd1tPuhq47VvICKqlfVLI4gG3dh1LIlUbmZT9oM+HW973crJ99OZOJ3grVwUwrd/sh/P7WWCR/VT8+TuN7/5DRYtWgQAuPbaa/HjH/8YP//5z3Hffffx02UimnM9Q1mcHM5hZVcIi85TnKQRlAwbO4+OIujVsG5J5JzfDyYLeGLnIHJFE6/Z3Il4xAOZ76dEtMDIsoRta2LQVRkvHhxB2ZxZg/M/fONqtIbc+P9+fgimNbO1iG5dxb3v2Iw13WH840/346ldAzPaDtFscVEGES0YiVQRe4+PoS3iwbol4XqHc16VnnujsGyBy9fEoMhnF6I6dCqFFw+OwOtWceOWTnS3zb+Kp0RE1eLSFVy5No6yYWPHoQQcMf2ie25dxR/dtAaDyQIe+93JWcXyp+/YjPXLWvC/Hz2IX+/om/G2iGaKyR0RLQi5oonthxLwezVcsTrWsDMHTgxmMTJexIalEQS9rzRTt2wH2w8lcKg3he64D6/Z1A6fW6tjpEREjSEScGHTiihG0yUcODmzqZWbVkRx5do4fvLsSQwkZraGDwBcmoKPv30Ttq5qxfd+eRiPPj/zZJFoJpjcEVHTMy0HLxwYgQTgqnVxqGpjvvVl8gb294whHvFgafsrI3L5komndg9iMFnAhmURbFnZOq96rRER1dritgCWtgdwrD+D/tH8jLZx9xtWQVMl/N2/74aYwQjgaZoq4/9662W4al0cP3z8GB556vistkc0Hbw6IKKmJoTAjsMJ5Esmtq2NNexol+042HE4AVWVsWVl6+TIYiJVxJO7BlEybFyzoQ0rOkMNO+pIRFRPly1rQSTgws4jo8jkp9/aIOx34e03rsDOIwk8v392bQ1URcaHbt+A12zswI+f6cEPfnuUCR7NCSZ3RNTU9veMY2S8iI3LWtAaOrfqZKM40DOObMHE1pWtcOuVqpcnh7J4ft8wXJqC127qOG/VTCIiqpBlCVeuiUFVZLxwcASGNf0CK6/b0oXVi8P4/q+PIF8yZx3P+/5gLX7/8kX4+Qu9+O4vDs9oTSDRdDRmcycioio4NZLDsYEMlrYHsLQjWO9wLmhorIDjg1ks6wigrcULIQQOnkrhSF8a8bAHV6yJQWvQqaRERBfiOAJXrGuv6jZt28EH79h80fv8/jVJ3PfNZzCaMfCZP74asnzp2Q6x2CtT4T9y5xbc+5Un8NPnT+Gj79gy25Dxp++6HOGQG//+26OQFRkfv2sLFKX27+mGaSOdKtR8P9RYmNwRUVMay5Sw++goWkNuXLaspd7hXFCxbOHlI6MI+XSsXxqB7QjsPDKK/tE8lrT5sXFFlG0OiGhekmUJP3++p6rbfNfNa/He//HYJe/n0hVsPzCMP/xvP4PXffHL3c5WPwzTmvxZ11SEfBp+/vxJ7D8+Co9r9pfLQghEgy78ZnsvXtg3hI6oB5Ik4Yp17cjnZ9aj71IulQRTc+JHwUTUdIplCy8eHIHbpWLbmtiUPrWtB0eISuluR+CKNTHYtsDz+4bQP5rHuiVhbGJiR0Q0Iy5Nhq7JKBk2jBn0v4sG3VAVCcNjxaqslZMkCdGQG7GwG7miiYHRAqdoUk0wuSOipmLZlcqYtiNw9bo4dE2pd0gXdOhUCmPZMjavjEKSgKf3DGE8W8blq1uxalGYhVOIiGZIkiT43CoUWUKuaMG2p9ecXJYlxCMeGJaDsUz1RtYiARfiETfyJQv9iTzMGawLJLoYJndE1DSEqExpTOcNXLE6hsAZfeIazUiqiCN9aSyO+xH06nh69xDKho1rN7RjUcxf7/CIiOY9SZLg92qQJCBbtKY9Auf3aAh4NSQzZZRnMPp3IWG/C+0tHhTLNn79Yi/KBhM8qh4md0TUNA73pTGQLGD9kgjaWrz1DueCSoaFlw4nEPBo6Ir58MyeIUgScP2mdkRD7nqHR0TUNBRZgt+jwXEEcjNI8GJhNxS5etMzTwv6dHS2epHJG3h6zyAKZevSDyKaAiZ3RNQUBpJ5HDqVwqKYDyu6GrcyphACLx0ehW0LLOsI4oUDI9A1Ga/Z2I5gA480EhHNV5oqw+tSYFoOStMcJVMVGbGwGyXDRio3/d55F+P3aHj9FYtQNm08vXsQ2UJ1t08LE5M7Ipr30nkDLx8eRSTgmli/1rhr1Y70pTGaLmFRzIc9J5LweVRcv7ED3gZtrk5E1AxcugJdlVEsT7/ASsCrwedWMZouzag4y8XEIl5cv7EDQgg8s2cIqWxtKmfSwsHkjojmtbJh44UDw9BUGVeujUGRG/dtLZEq4uCpFMJ+HSeHc4j4Xbj+svbJpuVERFQbkiTB56kUWMkXLdjO1KdYSlKluIoEYHi8utMzASDk03H9xg6oioxn9g4hkSpWdfu0sDTuVRAR0SU4jsCLh0ZgmA6uWheHW2/c1p3FsoUdhxLQNRmpnIF4xINrNrRBU5nYERHNhdMFVgAgVzCnlaRpqozWcKUISjpf/emTfo+G12xsh9et4nf7hzGYzFd9H7QwMLkjonlJCIHdx5IYy5SxZWUrwn5XvUO6INsRePHgCEzbgWE66Gr14aq1cagK34KJiOaSIkvweTXYjkB+mgVWQj4NHpeC0VQJpjW91gpT4XapuP6ydoT8Lrx4MIFTw9mq74OaH68siGheOjGYxamRHFYvCqEr5qt3OBe193gSqZwBIYCl7QFcvrq1YRurExE1O12V4XEpMKZZYEWSJLS1eCFQm+mZAKBrCq7d0IZY2I2dR5M40peqyX6oeTG5I6J5Z2S8iL0nxtDe4sWaxeF6h3NRJ4ezODmcAwCsWhTCxuUtDV3whYhoIXDrCrSJAiu5ojnlx+mqjFjIjULJqsn0TKBSofOqdW3oavXhwMkU9p4YY4JHU8bkjojmlVzRxI5DCQS9Gi5f3drQidJ4toxdR5MAgDXdIaxbEmnoeImIFgpJkuD3qJBlCb3D2WlNswz5dXhdKhKpEgyrNg3IFVnC5atbsbwziBODWWw/lIDtVH8qKDUfJndENG/kiiZ+t38YkgRcta6x16yVDAvP7h0CAKxeFMKaxZE6R0RERGeSJAkBjwohgIHRPJwpVtCsTM+sVM8cStZmeubp/Vy2rAUblkYwmCzg+X3DNUsmqXk07pUREdEZbMfB//zudhTKFq5cG2/ovnCW7eDxnQOwHYHlHQGsXcLEjoioESmKjO42P8qmg6GxwpQTNU2VEY94UDJsjGdr23x8RVcIV6xuxVi2jGf2DKFYtmq6P5rfmNwR0bzw/V8fxUuHRrBpeRTRkLve4VyQbTt4/OUBGKaDzlYvLlserXdIRER0EQGvjljYjVzRQjI99SbiAa8Gv0dFMl1CeRqFWWaiK+bHNevbUCxbeGr3IDI1Wu9H8x+TOyJqeL99uR+/2tGHt964AkvaA/UO54Is28ETuwZQKFuIhlzYtiZe75CIiGgKwn4dIZ+GsWwZqezUErzTzc1lWZrWqN9MxcIeXL+xA0IAz+wZQjJdqun+aH5ickdEDW1/zxi+94vD2LQiivfdtqHe4VyQZTl4evcgckULfo+Ga9e31zskIiKaotOJmseloD+Rm/LUR1WR0dbiQdl0kMxMfdRvpkI+Ha/d1AGXruC5fUMYGGWzczobkzsialhDYwV88+G96Gj14sNv3gClQXvDmZaDp/cOIVMw4dJkvGZTO/vYERHNM5IkoTPqhabKGBgtTLmCpt+jIejVMJYpozAH6+G8bhWv2Vhpdr79UALHBtJslUCTmNwRUUPKl0z87Q93QVEk/OnbN8HjUusd0nkZlo1n91bWPyiyhOsv64CuKvUOi4iIZkBRZCxpD0IIgf5pVNCMRzzQVBlDyQJsu/YtC3RNwXUb2tAR9WLfiXHsOT4GhwkegckdETUgy3bwzYf3Ipkp4SNv24jWsKfeIZ1X2bTx7J4hpPOVBrhXrovD723cKp5ERHRpLl1BR6sXhulgMDm1tXSyLKEj6oVlCwyN1a49wpkURca2NTGs6AyiZyiLFw6MwJpGvz5qTkzuiKihCCHwr786ggMnx/HeN63F6u5wvUM6r7Jh49mJqZgAsHF5C+INmoQSEdH0+Nwa4mE38iULo1MsXOLWFcQmHpPKzU01S0mSsGFZCzYtb0FivIin9w6yVcICx+SOiBrKr3f04fGX+3HLNYtx/caOeodzXqWJxC5XrCR2S9sDWNrAVTyJiGj6wgEXwn4d41ljyhU0w34dPreK0VQJpRq3RzjT0o4grl7fhkKp0iohnat9cRdqTEzuiKhh7D42iv/z6yPYuqoVb79xRb3DOa+SYeHZvUPIl0wIAbS3eHDZ8hZIEguoEBE1m1jYDZ9bxUiqhOzETI2LkSQJ7S0eyIqEwWRhymv2qiEe8eA1GzsgAXh6zxBe2D80Z/umxsHkjogawsmhLP7ukX1YHA/gg7evh9yAyVKxbOGZPUMolEwIAC0BF65YHWvIWImIaPYkqbKWzq0rGEoWpjTlUVFkdLR4YVoORsaLcxDlK4I+Ha/d3AG/R8Pn/vl3+PWOvjndP9UfkzsiqrtkuoSv/HAX/B4Vf/qOTXDrjVcZs1i28MzeIZQMC5Ikwe/WcNW6OBSFb6NERM1MliV0tXqhqjL6Rwsom5eebul1q2gJupApmEjn52b93WluXcX1G9tx5fp2fO+Xh/Gvvzo8pyOIVF+8KiGiuiqULHzlh7tgWA4+8Y7NCPtd9Q7pHIWSiWf2DKFsWJBlGZoq45oNbdA1tjwgIloIFEXGopgPEoD+RB7WFNodRIMueFwKRsaKKBlzW+REVWT85fuuwk1XduNX2/vwtz/ajUKJhVYWAiZ3RFQ3lu3gGw/vwdBYAR9922XoivnrHdI58iUTz+wdgmHak/3rrt3Q1rB994iIqDY0VUZXzAfbEehL5GFfYjTs9JRORZEwMFqYUkJYTYos4Z2/vwr33LwG+3vG8LnvbsfwWGFOY6C5x+SOiOpCCIF/eewgDpwcx/tuWYt1S1vqHdI5csXKiJ1pOXC7VJQtB1eviyPg1esdGhER1YFbV9A50QNvYDR/ycbhqiKjs7WSEE61Z161vX5rF/7sD7cgWzDx2X/Zjn0nxuY8Bpo7TO6IqC5+8kwPntkzhLe8ZllDtjzIFU08u3cItu3A41KRL5nYtiaGlqC73qEREVEd+dwa2ls8KJZtDE+hYblbV9AWqdw/kZpaz7xqW7skgs+8dxsiQRe+/INd+OX23rokmlR7TO6IaM49s2cQjzx9Atdf1o43X7+03uGcI1sw8MyeIdhOJbHLFSuJXXuLt96hERFRAwj6dLSGXMgWTCRSpUsmSkGfjrBfRypnIDPHBVZOi4U9uO+PrsDmlVH8n18dwXcePQjTmtupolR7TO6IaE7t7xnDdx49iHVLInjvLWsbrj9cpmDgmb1DEMKB16UhO5HYdUR99Q6NiIgaSGSiyXkqZyCZuXTT8FjYDY9LwfB4cU4bnJ/J41LxkTs24rbrluCp3YP4n//2ct2STaoNVgQgojlzYjCDrz20B+1RLz7ytsugzrCNgNut1aQFwXi2hOf2DkOWAI9HRypbxvWbOtHdFqj6voiIaH6TJAmxsBuOEBjLlCFLElqCF674fLrAyqnhHAZG8+iO16eImCxJuOOGFVgU8+OffnYAn/2XF/Gxt2/CYp7rmgKTOyKaE4PJPL78g10IeDT833dtgdetzXhbiiJjx4GhKkYHlAwbfYk8JAioiozxTBkdUS9GxvIYGctXdV/VdMW69nqHQES0YEmShLaIB8IBRtMlyDIu2tLndIGV3pFKglfPaZFXrWtDPOLB1/59Dx54cAf++A/W4ap1bXWLh6qD0zKJqObGMiV86fs7IUvAn71zCyKBxuplVzKsVxI7VUbZdNAR9SDgnXkCSkREC4MkSWiPeuBzqxgZLyGdu/g0R7euoCPqRdl08OzugboWNlnaHsRn3rsN3XE//v4/9uHffn1kzls2UHUxuSOimsoWDHzp+ztRLFu4964taIs0VlGSQtlC30geMgQURUbZcNAe9bDdARERTZkkSeho9cLrVjE8XkT6EuvY/B4N8YgbA6N57D4+VtcEL+x34f/3rsvx+5cvwi9e7MXf/NtOpHOXXkNIjYnJHRHVTMmw8JUf7kYiVcLH374JS9obaz5/vmSiP5GHLEuQZBmm5aCz1YsgEzsiIpomWZLQGfXC61IxPFa8ZKGSsN+FdUtbcHIoi0O9qbkJ8gJURca7b1qND962Hj2DGfzVd17Ekb76xkQzw+SOiGrCtBx846E9ODmUxf/11g1YszhS75DOkiuYGEgUoCqVap227aCr1Qe/h1MxiYhoZmRZQmerFx6XgqEpJHibV7VicdyPw71pnBjMzFGUF3btZe34b+/ZBpeq4Iv/+jJ+xX548w6TOyKqOscR+PZP92Nfzzjed8tabF0Vq3dIZ8nkDQwkC9BUGbYtIASwKO6H180aU0RENDuyLKGr1TeZ4F1sDZ4kSdi0Mor2Fg/2HB9D70huDiM9v+64H//9fduwcXkU//qrI/j2T/ajXKfWDTR9dbmSueeeezA2NgZVrez+r//6r7F58+Z6hEJEVSaEwHd/cQjbD47grtevxGs2ddQ7pLOkcgZGxovQVAmG5UBTZSyK+aCp/KyLiIiq43SCN5AsYHi8CCEEwhcoJiZLEq5YHcPvDozg5SOjkCUJXbH69lb1ujV89O0b8bPnTuKRJ4+jN5HDR9+2EW0tjbVuns4158mdEAI9PT347W9/O5ncEVFzEELgwV8exhM7B3DrtUvwpqsX1zuks4xny0ikStDUyvo6j66gs9Vbk555RES0sJ2eojmYLGAkVYIjcME+eIoi46p1cTy/fxgvHU5AloGOaH0TPFmScPt1S7GsI4B/+I99+Ot/eRF//AfrccWaxpqNQ2eb8yua48ePAwD++I//GG9+85vx4IMPznUIRFQDQgj866+O4Lcv9eNNVy3GHTcsr3dIk4QQSKZLSKRKUBUJpuUg4NXQFfcxsSMiopo5XWQl4NEwmi5hNF264Bo2VZFxzbo2hAMubD+UwMBoY/RYvWxZFPe//0q0Rbz4xsN78L1fHIZpcZpmo5rzobNMJoNrr70Wn/nMZ2CaJt7znvdg2bJluP7666f0+GjUX+MIG0ss1ljVBam5VOv4EkLgH3+8F7/e0Ye33LAC/+XNGyBJUlW2/Wo+X+VTT1278NvXX9yzDS1BN4DK+r9//sk+/MeTxxDwasgVTbz31vV4++tX1izGufaum9ee9fOXPvG6aT1ekWuT4NZqu9XY72xiq9fzmol6P89avlYz2Xa146nm9ub6uJqr/dViP7XY5qvPKRc7x8zE4nYVA6N5jGXKEALobPVNnoNOn9dO+/0ru/HES/3YcSgBVVOwrDM04/1O9zxv2855P/SMxQL4X/e+Dv/ys/34jyeP4cRQFp98zzZ0xZr7uvxCr8ds1fL6fs6Tu61bt2Lr1q2TP99555144oknppzcJZM5OM7CqNoTiwWQSGTrHQY1qWodX0II/OC3R/HzF3rxhm2L8OZrF2N0tDYLwmOxAPL5Mnw+FwzTuuD9WoJuvPd/PAYhBPJFC4ZVaciaLZjwe1T85Klj+MlTx2oS41zrbPVj4IzX++ZrluLnz/dM+fH/cv+bYDvVb1iryHJNtjsVU9nvbGKr1/OaiXo/z1q9VjM9vqodTzW3N9fH1Vztrxb7qcU2zzyn6Jp60XPMTLWGXJAkYCxThmHZ6JhYv5bPn9tT7sq1MbxwYATP7x1CvmBgWUdwRvuc7nk+Fgvg2w/tuuh9rloXx84jo/jIF3+DTSui6I43b4L3wTs2V/1afLbXX7IsXXSwa84/fty+fTuee+65yZ+FEFx7RzRPCSHwo8eP4ecv9OL3L1+Eu39/VcOMhgkhkMkbk4mdLEsI+TTomlLnyIiIaCGSJAmtITdiYTfyRQv9o3mUzfNPb1QVGVevj6MtUqmiefDkeMO0JGhv8eLGLZ0I+3W8fGQULx9JwLLnz4dezW7Ok7tsNosvfvGLKJfLyOVyePjhh/HGN75xrsMgolkSQuChJ4/j0d+dwuu3duFdb2ycxC6dKyOdM3D6XKNrMkI+jevriIio7iIBFzqiHpTKNn75u5PIFc3z3k+RZVy5Ll7pg9eXxs6jyYaZveZxqbj2snas7g6hdySPJ3cNIH2Jnn40N+Z8yOz1r389du3ahbe+9a1wHAfvete7zpqmSUSNTwiBh586gZ89dxI3bunEu29a3TCJnWk5+PiXfovT5z+fW4WuyQ0THxERUcCrQ1VkDI+X8PTuQVy5Lo7oxFrxM8mShM0ro3C7FBzuTaNYtrBtTawhZqHIkoS1iyNoDbqx4/Aonto1gA3LWrC0PcBzbh3VZT7kJz7xCXziE5+ox66JaJaEEPjh48fw2O9O4bWbOnDPzWsgN8ibeLFkoS+RhwAgS0DAy9E6IiJqTB6XipuuXozfbu/Fc3uHsHll63nXr0kTSZTPrWHX0VE8uXsQV62LI+jV6xD1uVrDHrxuaydePjKKPcfHkEgVsXllK1wNkIAuRLzqIaIpc4TAd39xGI9NTMV87y1rGyaxG8+W0TuR2P3etm6E/DoTOyIiamgBr47XbupAJODGy0dGse/EGJwLrK3rjvtx3cZ22LaDp3YNoj/RGK0SAMClKbh6XRwblkYwMl7Eb1/ux/BYod5hLUi88iGiKbEdB//00wN4/OV+3HL1YvzRTasbIrGzHYG+kTwSqRIAoL3Fg3vvvpxTQoiIaF7QNQXXbmjDso4Ajg1k8Py+YRgXKLTSEnDjhs2dCPp07DicwO5jSdgNsg5PkiSs6Arhhs2dcGkKfndgBLuOjrLYyhxjckdEl2RaNv7ukX14bt8Q3nbDctz5uhUNkTxlCwZODGRQKFtQZAnL2v0I+hpjmgoREdFUybKEjcuj2LIyirFMCU/uGkQ6d26LBKAynfP6y9qxojOInqEsnto9iEyhcYqZBH06btjciRWdQZwczuGJnQMYz57/uVD1MbkjoosqlEx86fu78NLhBO5+wyrcft3Suid26VwZfSM5DCaLcATgcSlY1hGAxvn9REQ0jy1uC+D6jR1whMBTuwdxYjBz3hYIsixhw7IWXLU2jpJh4cmdAzjan26YdgnKRHzXXdYGRwg8vXsQB0+ON0y1z2bG5I6ILmg8W8YXvvcSjvWn8aE3r8cbt3XXNZ5swcCe40k8+lwPCuXKlJWIX8eimA+yXP+RRCIiotmKBFy4cUsnWkOVHnc7DidgWuef2tge9eL1W7oQj3iwv2ccT+8ZQqaBWhK0hjx43ZYudMV8ONyXxhO7BpC6wIgkVQe7hxPNE6Gwt+qlj2OxwAV/1zeSxf/7f15GNl/G/R+4BlvXxKu67+mwbAePPdeDf/35QeSKJnxuDYWSiY++YwveePWSusVFRERUCy5NwdXr4zjan8bBkymkcwO4fHUMkYDr3PvqCq5cG0dfIo99J8bwxK4BrOgMIlcwLnqev5AP3rG5Gk/hHC/sH8I3frgLT+8ZwttfvxJ337QGmtoYM24yuTK+/4uD9Q6jKpjcEc0Tuqbg2w/tqtr2fD4X8vnzf3o2mi7hxYMjkCTgmnVt2L5vENv3DVZt31MlhMBgsoCDp1LIFU20tXhRMiwUyhZ8Hg0PPnYADz524JzH/cv9b5rzWImIiKpJkiSsWhRGS8CNl44k8PTuQazqDmF1d/icgmaSJKE77p8cwTvan8FH/udvsDjuR3fcP+XlFD6fCzsODNXi6QAAIgEdlmXjh78+gv944hjaox649fqnI1/6xOvqHULV1P/VJKKG0juSw86jo/C5NVy9Pg6fW5vzGIQQGBgt4HBfCtmCCb9Hw1Vr41jeHcZTO/vgdetIpotzHhcREdFci4bceN2WLuw5nsTh3jRGxou4fHUMfs+552eXpmDrqlYsafMjkS5j59Ekjg9ksGZxBO0tnrqvmVdkCe1RL/xeEyPjRZwaziMS0BENurm8okqY3BERgEpCdbg3jUO9KbSG3Ni2NgZ9jqdLVJK6PA71ppErVpK6K1a3orPVB0mSIEkSfG6t6tNTiYiIGpmmyrh8dQxtLV7sPpbE4zsHsLY7jOVdwfO2JWoJuvHJ916F//GtZ3HwVAovHhxByKdjdXcI7S3euid5fo8Gj0tFIlXEeNZArmAi3uKpywfKzYbJHRHBsh3sPDKKgWQBi2I+bFnZOqefoFm2g/5EHscGMsgVTQQ8Gq5YHUNna/1PQERERI2iq9WHaMCF3ceT2H9yHP2jeWxZ1YrQedoASZKErpgfHa0+9I3kcLgvjRcPJuBzq1jeGUR3zA9VrV9tRUWW0N7iRdBrYXi8iP5EAQGvhljYDVVhzceZYnJHtMAVyhZeODCCTN7A+iURrOgKzllCVSxbODGYwcnhHEzLQdCnYduaGDqiTOqIiIjOx+1SceXaOAaTBew+nsSTuwawvDOINd3h8yZFsiRhcVsAi+J+DCULONafxp7jY9jfM46umA9L2gII+/W6nXe9bhVL2v0Yy5QxnikjX7IQC7kR9Gm8FpgBJndEC1gyXcKLh0bgOAJXr4+jLeKt+T6FEBjLlnFiIIPBZAECQEfUi2UdQUSDLr6RExERXYIkSehs9aE15Ma+nnEc68+gP5HHhmUt6LzAB6TyxGM6ol6M58o4OZRDfyKPU8M5+Nwqulp9WNEdgRBizs/FsiShNeRG0KtheLyI4fEiMnkD8YgHLp1LMaaDyR3RAiSEwMGeMew8nIDXreLqy9rg99Z2nnvJsNGXyKF3OIds0YSmyFjeGcSyjgC8nGNPREQ0bfoZBVR2Hx/DjkMJnAy5sWFZywUfI0kSWgJutATcuGxZCwaSefQn8jjcl8bhvjRURYLXrcLn1uB1q1DmcJmGrilYFPMhkzeRSJdwcjiHsF9HNOSe0zjmMyZ3RAuMaTnYeXQUg8kC2lu82LqqFVqN5tw7jqhUwxrJYni8CCEqzVk3r4iiK+bjnHoiIqIqaAm6cePmDvQMZXHwVApP7ByApr0MSTjwuC58ua+pMpa0BbCkLYCSYSGVN7H/RBK5golM3gQAeHQFbpcCt67CrStQFammI3uSJCHk1+H3qBjNlJHKGcgWzMrIHqdqXhKTO6IFJJ03sP3gCAolC1tWx9Bdg4Ilp6ddDozmMTCaR9l04NIqo3SL434EvOcu+iYiIqLZkSQJyzqC6Ir5cKQ3jcdf6oMQAss7g1jRGbxkpWm3rmJFxIdUtgQhBIqGjULRQr5sYTxrADAAVAqhuF0KXJoCXZPhUhVoqlz1QmyKIqMt4kHYp2NkYqpmKm8gHnZfNGFd6PjKEC0AQgicGMxif88YNFXBdZe1Y3Fn6IJNzGey/VTOQP9EQlcybMiyhLaIp9JUNexh/xoiIqI5oKsKNixrwafedxX+6lvP4UhfGicGMxNJXmhKs3UkSYLXpcLrUtEKwBECZcNG6YyvfNE66zGaIkHTFGiKDFWVJr7Lle+zGO1z6QoWxX3IFkwkUiX0juQR8GpoDblrNvNoPmNyR9TkyqaNnUdGMTxeRFvEgy2rWuGqQp84RwiMZcoYGitgKFlAoWxBkoB42IP1S3xob/HWtcQyERHRQtYe9eGKNTGsWhTCod4UDvemcWIwi2UdASzvuPRI3plkSYLHpZ41YuY4AqblwLBsGKZT+bIqiZ/jiHO2oSoS1IlEr/JdPue2C30QLEkSgj4dfo+GsWwZ49kycgUT4YCOliDX452JyR1RExseL2DnkSRMy8Zly1qwrCMwq2mYluVgJFXE0FgBw+NFmJYDWQJaQ55KY9Sod84bnxMREdGFBX06rlwbRzpXnkzyjvVnsKQtgBVdwRlPcZRlCS5dOW81S8cRsGwHpu3AssTE98rPZdNBvmRBnJv/QZZQSfbUcxO/0/+OBl0I+XQk0yWMZw1k8iZagq66tnNoJEzuiJqQZTnY1zOGk8M5BLwarlkfR8jvmtG2imWrMjo3VkAyXYIjKguw2yIetLd4EQ97OEJHRETU4EJ+F65a14ZMwcDRiamaJ4Yy6Iz6sKwzgJaAu2r7kmUJuqxcdHTQnkgALVvAtp2JZPCV2wzThmWfmwFKUuU6RFdlBLwqSoaDRKqE8WwZrSE3At6FXXSFyR1RkxlNF7HzSBKFsoWVXUGsWRyGIk89+bJtB8lMGYlUESOpIrKFSrUsn1vFso4g2lu8iARdkBfwGycREdF8FfTquHx1DGsXR3B8MINTw1n0j+YR9utYu7QFjiPmZJ28IktQZAWui3RDEkJUkkCrkvBZtjMxFbQyDdS0HJxO/yxbYGisiOGxIty6Aq9bnSz8osi1rfDZSJjcETUJw7Kxv2ccp4Zz8LpVXL+xHdHgpT+FE0IgUzCRGC8ikS5Ojs7JUqW0cvcSP9pbvDXvg0dERERzx+tWcdmyFqxdHEbvSA4nBjN4fu8QZAkIeHUEfRrculLXpEiSpMlpmecjhIBlV9b+lU0LhaKFgmGjOPF1miJLcOvKWV9Kk7ZjYnJHNM8JITCYLGDP8SQM08GKriDWdIcv2kOuZFgYSZfQN5xFIlVE2XQAAAGvhqUdQcTDHrQEXexDR0RE1ORURcayjiCWtgdQMBy8uH8ImYKBdN6ArsoI+iqJXiNeE0iSBE2VoKkyvG4VkcDEh9Z5E8lMCZYtKlU8VRmGaSNfeqXCp6bIcLsUeFwqeoezEEI0xegekzuieSxXNLH3xBhGxosI+XRcsz563rV1tu0gmS1XRudSRWQmplrqmoxYyINYxIN4yA03+8YQEREtSJIkId7iRXvUi5gjkC2YyOQNjKZLGE2X4POoCHg0+DxaQ1enPN0EPeDTkM4ZGMuUUSjbcOsKWsM6ZElC2XRQMiwUShayBRN/8sXfQNdktATcaA25J9fuzUe8kiOahyzbwZG+NI71pyHLEjYsjWBZZ3ByHdzkVMtUJZlLZsqVOfQTUy3XLfFjcUcQuoym+JSKiIiIqkeRJYT9OsJ+HWXTRiZfqUqZL1qQUITXrSLgbexET5YkRAIuhPw6MvlKkjeYLMKlyWgJuhEJeAEApuXgzTesxMOPH0EyXWnxBAAuTcaGlXGs7gzU82lMG5M7onlECIG+RB4HTo6jZNhYFPNh/dII3LqKkmFPJnOJVAllszLXPODVsLQ9gHjYjZage3Jahc/nqloTcyIiImpOLk1BLOxBa8iNkmEjWzCRK5rIj1kAivC5Vfi9GnxutSGnbsqShLC/0j4hUzAnkrwCdFVGJOBCwKfhjVcvQU9/CgBQKFsYnfhgfKZtIupp/kVMtEDtOpLAk7sGkc4bCPt1bF3VCgA4NpCpTLXMT0y1VGXEwh7Ewm7Ewp55+cZEREREjUU6o5F5LFxJ9HJFE9nC6UQPk1UqfW617sVYXk2SJIR8OoJeDdmiifFMGcPjRYymS/jN9lOT9/O6VCxuC2BxWwCXr40jkcjWMerp41UfUYPrGcrg4SdPYM/xJFyajK6YD4Zp43cHRuA4ApIERINurFviQyzsQcjHJp5ERERUO2cmeq0hd6UxedFEvmRhLFPGWKYMRZYmEz2fW22Y6pSSJCHo1RHwaCiUbYxny9h+YAQR3/xcY/dqTO6IGkQo7D2r2WfPYAbfe+wAnt87BLdeqeZULFvoT+QR9OlYuSiMjqgXsYgX2gybiPt8M2tsTkRERLPnOKKm5+KZbPuKde2z2mfZsDCYLGBgNIfB0QKyhSIAIBxwoS3iRVuLF7GI56INzl+9vb3HRmcV0/lIkjSZeH7ynm349kO7qr6PemByR9QgdE3Btx/ahVSujCN9aQwmC1AVCWu6wwh4NQT8Luw/noTXrVaSOeFgcDSHwdHcDPenwjCtS9+xgcz2hENERNRIZFnCjgNDNdn2u25eO+1t65qKgRleV5yPz63ArckwbQe5goFUtoxDp8YBVIq2aKoMTZWhKhduMn7zNUurFs9CwOSOqAEIIbDn6Cie2zeERKoEVZGwalEIKzqDk59sffCOzfizrzxe30CJiIiIpkiSJKiqBFWV4XGd3XTcsh2UDBuliWbjily5nzbRtFxu0CqcjY7JHVEdWbaDFw4M45cv9uHkcBa6JmPdkjCWtgdnPNWSiIiIqBGd2XQcODfZKxs2TtfxlmUJmiLBmKj+TVPD5I6oDsazZTy1ewC/fbkf6ZyBjqgXf/L2TTjZn2qYBcdEREREtXShZM+ynUrSZwvkS2ado5xfmNwRzRFHCOzvGcMTLw/g5SOjcITAZcta8F/+oBvrl7WgLR5smsW8RERERNP16mQPACIBdx0jmn+Y3BHVkBACvSM5PL9vGL87MIzxbBl+j4abr+rGDVs60Rbx1jtEIiIiImoSTO6IamA0XcTv9g/j+X3D6B/NQ5ElXLasBX/4eyuxdVWM6+mIiIiIqOqY3BFVyWiqiF3HknjhwDCO9KUBACsXhXDPTauxbW0cAa9e5wiJiIiIqJkxuSOaIdtxcKw/g13HRrH7WBL9iTwAoLPVhztuWI5r1rehNeypc5REREREtFAwuSOahvFsGYd6x7H7WBJ7jiWRL1lQZAmru8N47e91YNPKVrS3cB0dEREREc09JndVEAp7JxtNV1ssFqjJdueaYdpIpwr1DmNahBAYTZdwuDeFQ70pHO5NYWS8CADwezRsXtmKzStbsWFpC7xu/ikRERERUX3xirQKdE2pSQl7n8+FfL586TvOAx+8Y3O9Q7ikYtlC70gOJ4eyODGYwaHeFMazldff51axujuM12/twuruMJa0BSDLUp0jJiIiIiJ6BZM7WnCEEMgUTPQlcjg1lMXJ4SxODmUxPDEqBwBhv47V3eHJr85WH2SJyRwRERERNS4md7P00uEEXn70IHr604AESKg0YKx8r/zn9L8lSJBkQJEkKIoEWZIgyxIU+VXfJ243HAHTsKDKMlSlcpvEBGPKyoaN4fEChsZe+RoeK2BorIhi2Zq8X2vIjSVtAVx3WTuWtAewuC2AsN9Vx8iJiIiIiKaPyd0sjWVKODmYQSpXhgAAURkZEgCEAATExG2VfzsCcBwxo31JABRFgqrIE1/S5HdFPvNn+Yz7TXyXpXNuVxR5Xo5GmZaDXNFEvmgiUzAwni1jLFOqfM+WMZYpYzxbQr5knfW4aNCFthYvrt3QhrYWL7pafVjcFoDfo9XpmRARERERVQ+Tu1l6w7Zu3H3L+mmtuRPilSTPdgSciS9bCNiOM3m7pqnIFQzYtgPLdmDZApbtwJ74bjmV74WyA8s2J+5XeexUybJ0/sRPPv39jFHFiRHFV/98+t+SXBmdPD2CCbwyYrn32CjGxvKwhZh8frYt4IjK97JlwzBslE0bJdOGYTiT/y6WTOSKFnJFE7mSibJhn/e5BLwaIgEXWkNurOoOoSXgQjziRXuLF/GIB64aFb0hIiIiImoETO7qQJIkKBKgyBIuNmY004IqQohKkndGQng6EXz1bWf9bFeSS8sWKBlm5f5nJJ8zHHAEADyzd2jK91VkCW5dga4pcGkKPC4VIb+OzlYfAl4NPo8Gv0dDwKNNJnSRgAuayuSNiIiIiBauuiR3P/nJT/B3f/d3sCwL733ve/Hud7+7HmE0LUmSoKkSNFWu6nbPHHF0zhiBm0z+Tk9BBV75DgEhgFtfswLZbBGKLJ+1vvD0v3VVnkzoVKW6cRMRERERLQRzntwNDw/jy1/+Mh566CHouo53vvOduPrqq7Fy5cq5DoWm6cwRx+navDqGRCJbg6iIiIiIiAioQ3L37LPP4pprrkE4HAYA3HzzzXjsscfw0Y9+dEqPb9TeYn5v9YtyeN0aJOFUfbv10qj/7xrJpY6jSNBdtX1pqgLTml8zs31uDZGgG5qqwDDPv/bytNaQZ46iqq9wwHXWa+Fza9N+7rV4rWRZmnHxqNl49etxPjN5jc40X46tqbwWFzLb1+i0Wr1WMzm+ZvN6nE+1XqPT5vK4qvZrcSHVfo1Oq/Y2wwHXWefDuTw/nj6v1cp0tz2V8+tcq/VrdNqFrsFqcf06m21e6rGSEGJOz77/8A//gEKhgHvvvRcA8MMf/hC7d+/GZz/72bkMg4iIiIiIqKnM+eImx3HO6tUmhGDvNiIiIiIiolma8+Suvb0diURi8udEIoF4PD7XYRARERERETWVOU/urrvuOjz33HMYGxtDsVjEL37xC9xwww1zHQYREREREVFTmfNqCm1tbbj33nvxnve8B6Zp4s4778SmTZvmOgwiIiIiIqKmMucFVYiIiIiIiKj62C2aiIiIiIioCTC5IyIiIiIiagJM7oiIiIiIiJoAkzsiIiIiIqImwOSuQX3lK1/B1772tcmfM5kMPvShD+GWW27Bu9/97rN6BRLNxMMPP4zXvOY1eMtb3oK3vOUt+PKXv1zvkKgJ/OQnP8Ef/MEf4KabbsL3vve9eodDTeaee+7BrbfeOvm+tWvXrnqHRE0gl8vhtttuQ19fHwDg2Wefxe23346bbrqJ50aatVcfX3/5l3+Jm266afJ97Je//GVV9zfnrRDo4rLZLD7/+c/jZz/7GT7wgQ9M3v6Vr3wF27Ztw7e+9S088sgj+NznPoevfOUr9QuU5r29e/fiU5/6FG677bZ6h0JNYnh4GF/+8pfx0EMPQdd1vPOd78TVV1+NlStX1js0agJCCPT09OC3v/0tVJWXL1Qdu3btwqc//Wn09PQAAEqlEu677z5897vfRUdHBz784Q/jiSeewI033ljfQGleevXxBVSuvx588EHE4/Ga7JMjdw3m17/+NZYuXYr3v//9Z93++OOP4/bbbwcA3HbbbXjyySdhmmY9QqQmsWfPHjz88MO4/fbb8ed//udIp9P1DonmuWeffRbXXHMNwuEwvF4vbr75Zjz22GP1DouaxPHjxwEAf/zHf4w3v/nNePDBB+scETWDH/zgB7j//vsnL7R3796NJUuWoLu7G6qq4vbbb+f7GM3Yq4+vYrGIgYEB3Hfffbj99tvx1a9+FY7jVHWfTO4azFvf+lZ86EMfgqIoZ90+MjKCWCwGAFBVFX6/H2NjY/UIkZpELBbDn/zJn+DHP/4xOjo68Nd//df1DonmuTPfpwAgHo9jeHi4jhFRM8lkMrj22mvxjW98A9/5znfwb//2b3jmmWfqHRbNc5/73Oewbdu2yZ/5PkbV9Orja3R0FNdccw0eeOAB/OAHP8D27dvxox/9qKr75LyGOnn00Ufx+c9//qzbli9fju985ztTerwQArLM3JwubSrH2gc+8AG88Y1vnOPIqNk4jgNJkiZ/FkKc9TPRbGzduhVbt26d/PnOO+/EE088geuvv76OUVGz4fsY1VJ3dze+8Y1vTP58zz334JFHHsFdd91VtX0wuauTW265BbfccsuU7x+PxzE6Oor29nZYloV8Po9wOFy7AKlpnO9Yy2az+M53voP3ve99AConr1ePFhNNV3t7O7Zv3z75cyKRqNmaAlp4tm/fDtM0ce211wKovG9x7R1VW3t7+1lF6/g+RtV06NAh9PT04OabbwZQm/cxDv3MEzfeeCMeeeQRAMB//ud/Ytu2bdA0rb5B0bzl9Xrxj//4j5OV5h588EGO3NGsXXfddXjuuecwNjaGYrGIX/ziF7jhhhvqHRY1iWw2iy9+8Ysol8vI5XJ4+OGH+b5FVbd582acOHECJ0+ehG3b+OlPf8r3MaoaIQQeeOABpNNpmKaJ73//+1V/H+NHXvPEn/7pn+JTn/oUbr31VgQCAfzN3/xNvUOieUxRFHzlK1/BX/3VX6FUKmHp0qX44he/WO+waJ5ra2vDvffei/e85z0wTRN33nknNm3aVO+wqEm8/vWvx65du/DWt74VjuPgXe9611nTNImqweVy4Qtf+AI+9rGPoVwu48Ybb8Sb3vSmeodFTWLt2rX40Ic+hLvvvhuWZeGmm26qetVySQghqrpFIiIiIiIimnOclklERERERNQEmNwRERERERE1ASZ3RERERERETYDJHRERERERURNgckdERERERNQEmNwRERERERE1ASZ3RERERERETYDJHRERERERURP4/wMhfSPBcqfcuAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1080x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Visualization\n",
    "fig, ax = plt.subplots(1, 1, figsize=[15,5])\n",
    "for i, group in enumerate(groups, 1):\n",
    "    sns.histplot(group, kde=True)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "F_onewayResult(statistic=5.63470489555496, pvalue=0.003964274608520181)"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# scipy.stats:\n",
    "stats.f_oneway(group_a, group_b, group_c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear regression with statsmodels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x26500fbddc8>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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   ],
   "source": [
    "x = np.arange(100)\n",
    "y= 0.5*x -20 + np.random.randn(len(x))\n",
    "df = pd.DataFrame({'x':x, 'y':y})\n",
    "sns.lineplot(x=df.x, y=df.y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.995</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.995</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>1.793e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 08 Nov 2020</td> <th>  Prob (F-statistic):</th> <td>8.50e-113</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>18:21:36</td>     <th>  Log-Likelihood:    </th> <td> -148.91</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   100</td>      <th>  AIC:               </th> <td>   301.8</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    98</td>      <th>  BIC:               </th> <td>   307.0</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>  -20.1782</td> <td>    0.215</td> <td>  -93.804</td> <td> 0.000</td> <td>  -20.605</td> <td>  -19.751</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x</th>         <td>    0.5027</td> <td>    0.004</td> <td>  133.921</td> <td> 0.000</td> <td>    0.495</td> <td>    0.510</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 1.467</td> <th>  Durbin-Watson:     </th> <td>   2.412</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.480</td> <th>  Jarque-Bera (JB):  </th> <td>   1.263</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.100</td> <th>  Prob(JB):          </th> <td>   0.532</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.487</td> <th>  Cond. No.          </th> <td>    114.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.995\n",
       "Model:                            OLS   Adj. R-squared:                  0.995\n",
       "Method:                 Least Squares   F-statistic:                 1.793e+04\n",
       "Date:                Sun, 08 Nov 2020   Prob (F-statistic):          8.50e-113\n",
       "Time:                        18:21:36   Log-Likelihood:                -148.91\n",
       "No. Observations:                 100   AIC:                             301.8\n",
       "Df Residuals:                      98   BIC:                             307.0\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept    -20.1782      0.215    -93.804      0.000     -20.605     -19.751\n",
       "x              0.5027      0.004    133.921      0.000       0.495       0.510\n",
       "==============================================================================\n",
       "Omnibus:                        1.467   Durbin-Watson:                   2.412\n",
       "Prob(Omnibus):                  0.480   Jarque-Bera (JB):                1.263\n",
       "Skew:                          -0.100   Prob(JB):                        0.532\n",
       "Kurtosis:                       2.487   Cond. No.                         114.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = sm.ols('y~x', data=df).fit()\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What do the parameters mean?\n",
    "\n",
    "- **R-squared**\n",
    "- **Adj. R-squared**: also adjusts for the number of terms in a model.\n",
    "$$\n",
    "R^2_{adj} = 1- \\left[\\frac{(1-R^2)(n-1)}{n-k-1} \\right]\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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