{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Models VI: Interactions and Multicollinearity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Revisiting the Advertising dataset\n",
    "\n",
    "At the end of the last notebook we provided you with a challenge using the advertising dataset.  \n",
    "Specifically we asked you to fit a model that included an interaction between `tv` and `radio` and then explore the **correlations** between predictors with and without **centering**.  \n",
    "\n",
    "Let's take a further look here:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| Variable   | Description                     |\n",
    "|------------|---------------------------------|\n",
    "| tv     | TV ad spending in $1000 of  dollars            |\n",
    "| radio     | Radio ad spending in $1000 of  dollars            |\n",
    "| newspaper     | Newspaper ad spending in $1000 of  dollars            |\n",
    "| sales     | Sales generated in $1000 of  dollars            |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll load up the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><style>\n",
       ".dataframe > thead > tr,\n",
       ".dataframe > tbody > tr {\n",
       "  text-align: right;\n",
       "  white-space: pre-wrap;\n",
       "}\n",
       "</style>\n",
       "<small>shape: (5, 4)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>tv</th><th>radio</th><th>newspaper</th><th>sales</th></tr><tr><td>f64</td><td>f64</td><td>f64</td><td>f64</td></tr></thead><tbody><tr><td>230.1</td><td>37.8</td><td>69.2</td><td>22.1</td></tr><tr><td>44.5</td><td>39.3</td><td>45.1</td><td>10.4</td></tr><tr><td>17.2</td><td>45.9</td><td>69.3</td><td>9.3</td></tr><tr><td>151.5</td><td>41.3</td><td>58.5</td><td>18.5</td></tr><tr><td>180.8</td><td>10.8</td><td>58.4</td><td>12.9</td></tr></tbody></table></div>"
      ],
      "text/plain": [
       "shape: (5, 4)\n",
       "┌───────┬───────┬───────────┬───────┐\n",
       "│ tv    ┆ radio ┆ newspaper ┆ sales │\n",
       "│ ---   ┆ ---   ┆ ---       ┆ ---   │\n",
       "│ f64   ┆ f64   ┆ f64       ┆ f64   │\n",
       "╞═══════╪═══════╪═══════════╪═══════╡\n",
       "│ 230.1 ┆ 37.8  ┆ 69.2      ┆ 22.1  │\n",
       "│ 44.5  ┆ 39.3  ┆ 45.1      ┆ 10.4  │\n",
       "│ 17.2  ┆ 45.9  ┆ 69.3      ┆ 9.3   │\n",
       "│ 151.5 ┆ 41.3  ┆ 58.5      ┆ 18.5  │\n",
       "│ 180.8 ┆ 10.8  ┆ 58.4      ┆ 12.9  │\n",
       "└───────┴───────┴───────────┴───────┘"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import polars as pl\n",
    "from polars import col\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "from statsmodels.formula.api import ols\n",
    "from helpers import plot_predictor_correlations\n",
    "df = pl.read_csv('./data/advertising.csv')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And then fit 2 models with the same parameters:\n",
    "- One **without** centering our predictors\n",
    "- One **with** centering our predictors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Uncentered\n",
    "model = ols('sales ~ tv * radio', data=df.to_pandas())\n",
    "results = model.fit()\n",
    "\n",
    "# Centered\n",
    "model_centered = ols('sales ~ center(tv) * center(radio)', data=df.to_pandas())\n",
    "results_centered = model_centered.fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the correlations between the predictors in each model. The helper function we provided you `plot_predictor_correlations` will do this by looking at the correlations between the columns of each model's **design matrix** $X$\n",
    "\n",
    "When we look at the *uncentered* model we see that the interaction term `tv:radio` is highly correlated with both `tv` and `radio` - **this makes sense** - the product of 2 continuous variables is going to increase/decrease if *either* of the variables increase/decrease."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: title={'center': 'Correlation Matrix of Predictors'}>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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3331XsbGxMgyj3EdsbKxmzZqljRs3KigoyJkhAgAAAAAAE3JaBUYxNzc3Pfroo3r00Ud16tQp/fjjjzp37pykot1G2rVrZ98+FQAAAABgDjZmkMDFnJ7AKCkiIoJkBQAAAAAAcMipU0gAAAAAAABqwqUVGAAAAACA+sFgFxK4WK0nMF5++WX78Z///Odyn6+Jkn0BAAAAAICri8Wo5TSam5ubLBaLJKmwsLDc52uiZF91Zeuzz9T5GADqL5u1wNUhADCx499tc3UIAExq1NZNrg6hVrzxwWZXh1DG9N/d6OoQ4ER1MoWkopwIJUcAAAAAUD+xCwlcrdYTGDabrVrPAwAAAAAAOMIingAAAAAAh6ioh6uxjSoAAAAAADA9EhgAAAAAAMD0mEICAAAAAHCIZQ3harWewLjmmmtqu0tZLBYlJSXVer8AAAAAAKB+qPUERnJycpXaWSwWSWUXginv+eLnAAAAAADA1anWExgTJkyo9PyePXu0d+9eGYahwMBAderUSeHh4TIMQ2fOnNGePXuUnp4ui8WiDh06qEOHDrUdIgAAAACgmmxsQgIXq/UExsKFCys9t3TpUkVFRenNN9/UiBEj5OFROoTCwkKtXLlS06dP1/79+/XYY49p8uTJtR0mAAAAAACoR5y2C8nOnTv10EMPKTQ0VFu3btW9995bJnkhSe7u7rr33nu1ZcsWBQcH6//9v/+nnTt3OitMAAAAAABgQk5LYLz11lsqLCzUs88+q8jISIftIyIi9Oyzz6qgoEB/+9vfnBAhAAAAAKAihmGY7oGri9MSGBs3bpQk9ejRo8rX9OzZU5K0adOmOokJAAAAAADUD05LYKSmpkqS8vLyqnxNcdviawEAAAAAwNXJaQmMsLAwSdIXX3xR5Ws+//xzSVJoaGidxAQAAAAAqBqbYb4Hri5OS2AMHDhQhmHob3/7m77//nuH7Tdv3qy33npLFotFgwYNckKEAAAAAADArJyWwHjmmWfk5eWlvLw8DRo0SE899ZT27Nkjm81mb2MYhvbs2aPf//73uummm5SbmysvLy8988wzzgoTAAAAAACYUNl9TOtIbGysFi1apPvvv1/5+fl699139e6778rLy0vBwcGyWCxKS0tTfn6+pKJkhoeHhxYuXKg2bdo4K0zUI16NGqnJjb0VdF0beQUGyrBalZuWprR98Tq9batsBQW1NlbDlq0U1rGTAlpEyzOgoQybTQWZF5WdkqKMpENK3b1btl//71bEzdNTYV26KPj6dvINDZNHgway5uao4EKGLh49ovSEBF04dLDWYgauZl6BgYro3VdBbWLlHRQom7VQuWfPKi1+r1K2fF+r94dGra5VWOcuCmgRI6+GATIKbSrIzFT2qZM6f+igUnf9UOn9IeSG9grt1EX+UVHybNBAhmGo4OJFZR47qjM7d+j8gZ9rLVbgauYdFKjgtm0V3Da26BHbRt6BgZKkw2s/145XZtT6mM1uHqSY24eqUauW8goIUO65c0rds1eHPv5U5376qUp9eDVsqGtH3aOm/fvJL6KJLBaLsk6e0okN3+ng8o+Vn5FR63EDFbGx6wdczGkJDEkaM2aMYmJi9Oijj2rXrl2SihbqPHXqVJm2nTt31pw5c9S9e3dnhoh6IvC669Rq1Bh5+PpeetLLS/5+fvJv1kyNu3VT4qJFyks/d0XjuPv4quU99yi47fVlznn4+Mg3NEwh7W7QxaNHlV3O/+NiDa+5Ri3vvlfeQUGlnvfyD5CXf4AaNG2qgOgW2jeLBAZwpYLaxOraseNL3R/cvSTP5s0V0Ly5GnfvoYQF85R37grvD76+anXvGIW0a1fmnIevr3zDwhTSvoMuHjmi7FMny17v46M2EyapUctWZc+FhMgnJEShHTvp7J7dOrjsQxmFhVcUL3C1u/OL/zhtLDcvL9044xVF9uld6vkGERFqEBGh5rfeov3vL9D+hYsr7Scoto36vP6afMNKrwcXeG0rBV7bSjF3DNf3Tz+j9EQSnQCuDk5NYEhF26ju3LlTO3bs0Lp167Rv3z6lp6fLMAwFBwfrhhtu0M0336xu3bo5OzTUE35NInTt2PFy9/JSYV6eTqyPU8Yvv8jN01Mh7dsrvHsP+YY1VpsJE7VvziyHlREVcff2VuzkB+QfFSVJSk9MUFr8XuWmpUkWN3kHBcq/aTMFl/PHS0kNW7ZSm/snyM3TU9bcXJ3ZsV0ZSYeUn5kpzwYN5B0UpMDW18nT379GcQK4xC8iQq3v+53cvbxVmJer499+qwtJh+Tm6anQjh3VpEcv+TVurNhJUxT/7ts1vz/4+Oj6qQ/JP6qZJOlcwn6d3bNbuWlnZbG4yTsoSP7Nminkhg4V9tF63H325EVuWppObIhTdkqKLO5u8m/aTE0HDJSnv79CO3ZSQXa2Dq9aWaNYAZSVlXJaF5OT1aRnjzrpv9v/PmNPXpze+YMOLluhnLNnFdiypdpM+J0CmkWp3UNTlZOWpsOflZ9Y8Q0LVZ+Zf5VvSIhsVqsOfLhMJzcVrSMX2ae3Wo8dLb/GYerz5utaN/EB5aSerZPXAgBm4vQERrFu3bqRpECNRN9+u9y9vGQrLFTCgvnKPHbUfi7jlyTlpqUpeshQ+TZurIg+fXXi229qNE6L4XfKPypKtsJCJS1fprR98aXOZx49orS9e3Xk8/9IbuUvJ+PRoIGuHTNWbp6eyj5zWokL5pdb6nlm+3ZZ3N1rFCeAS2LuuEvuXt6yFRbqp3lzlXn0iP1cRtIh5Z49qxbDhssvPFyR/frr+LqvazbOnSPkH9VMtsJCHfxoqdL27il1/uKRZJ3ds1vJaz4r9/7QoGmUgtrESpJy085qz9t/k63ENuMZSUk6G79HHZ/6ozz8/NSkZy8d+/pLWbOyahQvAOmn9xfoXEKiziUkKO9cuvwimuj2Tz+u9XHCOnVU9G23SpJObNykzf/zrIxf13xLT0jUiY2bdMui+WoQ0UTtH31Ex79dr4LMzDL9tHv4QfmGhEiStv75JR3/Ns5+7uzeeJ1LSNSNM16Rb0iI2j04VTv+8mqtvxbgcswggas5bRFPoDY0aBqlRte0lCSl7txRKnlR7NSmjco+c1qSFHFjb1kqSC5UJiA6WmGdO0uSTsR9WyZ5UUaJxWhLan7rYHk2aCBbQYEO/PuDSuepUh4OXBn/qGb2ioYzO7aVSl4UO/ndBmWfTpEkRfTpV7P7Q4sYNe7SVZJ0/Jt1ZZIXZZRzfwho0eJSTBs3lkpeFMs/f15ndu6QJFnc3BTQvHm1YwVwyU/vL9Cp7zcr71x6nY5z3X3jJEk2q1W7Xn/Tnrwoln/hguJnvydJ8m7UUDF33F6mD+/gIHsS5NSWbaWSF8WOfxunU1u2SZKih9wm7+CgMm0A4LeGBAbqleC2be3HqT/8UH4jw9DZX9dY8fDzU8Nrrqn2OOG9bpQkFebl6dSmjdUPVEUl5iEdisrHz8bvVe5ZSjuBuhR8/aXpXGd27Ci/kWHY7x2efn5qWM76E45E3FhUFl6Yl6uT362v9vWS5OZ+qQAy71xahe1y0y6ds7i7rGgSQBV5+PoqvGsXSdLpHTuVk5pabrsT6zco/9eqi6gB/cqcb9q3j9w8it7zyWvXVjhe8trPJUluHh5q2rfPFcUOAPWBS38bSk5O1tmzZ5WTkyPDQT1Sv35lb+64+gS0iJFUlFjIPHmiwnYZhw9fuia6hS4cOlTlMSzu7gqOLUqUnD/w86U58m5u8mrYUDIMFWRmOqyYCGoTK3cvL0nSuX377M+7eXnJKyBA1txcysGBWhQQU+L+cOJ4he0u/JJkP27YIkYXDh6o8hgWd3cF/ZooSU9MLHV/8G7YSIaKdhBxdH/IOXvpjxrv4JAK2/mEXDqXe7b8P4QAmEdw21i5e3tLklJ37amwnc1q1bkff1KTnj0U3LatLO7upe4boR0urZ9TWT+puy+dC23fXr+sXlPj2IGqsDGFBC7m9ATGzz//rBkzZuizzz5TRhW3fbJYLLJarXUcGeoD38Zhkn79VrKCaRuSSn3j4du4cbXG8GsSITdPT0nSxaNH5envr2a3DVZIuxvsv5TYCgp04ZcknYj7VplHy05jkST/EuXeF48eVaNrWyvqppsUEN3C/nx+RobS4vfqxPo4WbOzqxUngNL8GodLKlpTovL7wxn7cXXvDw0iIuVuvz8ckad/gKKHDFVI+w72+0NhQYEykg7p+DfrdPFIcrn9nP85Ubnn0uQTHKKIPn11Zsd22QpKLyjq1aiRwroWrRWVkZys7JSUasUKwPkalpgelnGk7DS2kjKOHFWTnj3k5uGhgGbNlJGcXKKfaElS/sWLyq1kx6TctDTlZ2bKy99fAb9eAwC/ZU5NYKxatUrjx49Xbm6uw4oL4HIWDw95NijaqSM/40KlbQtzc1SYlyd3b295NWpUrXFK/kHj5uGh9k8+ZR/X/rynp4Kua6PAa1vryOdrlbL5+wr7sebkqHG3booeMrRMG6+GDRXRp6+C292gxEULlHPmTJk2AByzeHjYd/LJu+Dg/pBz6f7gHRhYrXF8w8Ptx24eHur4h2lldhBy9/RUUJtYBba+Tsn/+azcaWhGYaEOfrhUbSZOlm9oqDr8/o86ad+FxF3+UVGK7D9Qnn5+yj2XpkMrPqpWnABcwzf80u8Qjj7Tc06XSKaGNy6VwCjuJ+eM48qrnNNn5OXvL7/w6iVkAaA+cloC49ixY7rvvvuUk5Ojpk2bavr06fLz89ODDz4oi8WidevWKT09XTt37tS//vUvnTx5Un369NGLL74od3ZngGT/dlOSCquw9WFhQb7cvb3l7uXtsG1JHn5+9uOomwbJzdNT6QkJOv7NOmWfTila26JdOzW7bYg8fHwUPXSYcs+m6vyB0mXoHr5F/bh5eqr5bYNlKyjQ8W/WKXXPblmzsuQTEqLIfv0V1rmLvAMD1fq++7Vv1t9rvK0jcDUreX8ob0HMyxXmF90f3K7g/tDs5lvl5umpc/t/0rGvv1J2yil5+Pgq+IYbFD1kmDx8fdXi9juUk5qq8z8nlunr4pFk7X3nb4ro3VcRvfuo5d33lo4xL1dHv/qvUjZvljWb6WZAfeBZ4h5hzcmptK0199J5Dz/fcvtx1EdRP7lFffj6OWgJXDkbX0LDxZyWwPj73/+u7OxsBQQEaNu2bYqMjNRPP/1kPz9w4EBJ0siRI/X888/rgQce0LJlyzR//nwtWbLkisY+frziudCoP4oXs5Ikw+p4x47iNm6e1ftvXrxuRdG1njqXsF8H/v2Bfd8oa1aWTm/bpuyUFLWd+pAsbm5qPnhomQSGu5dnqbgPfvShzv14aS2MnDNnlPTxCtmsVoV37yHf0FCFd+9R40VDgauZm4en/dhWhR19jF+nJRZPF6sqd8/L7g/7f1Li4oX2+0NBVqZOb92i7JQUtXv4EVnc3BQ99PZyExiSFHJDe4Xc0L7U/c0+lrePQjt0VF56ulJ/2FmtOAG4hluJ3yFsBZVPf7blF9iPSyZhS/ZjKyiQI8VffLh7ezloCQD1n9MSGOvWrZPFYtEjjzyiyMjIStv6+vrq3//+tw4cOKCPPvpII0eO1N13313jsZs1a1aldlv+9D81HgN1z1ZiHRSLh+OqnOI2jn6BKDPOZb8sHP3i83I3vb545IjO/fSjQm5oL78mTeQbHq6c06fLjffi0SOlkhclHfvyS4V16iw3T0+FdOhAAgOoAZv10vvWrQpVe5ZfEwZV+eOg9Dil7yfJa9eUf39IPqy0H/cptH0HNYiIkF+TJqXXsLBY1HrcfQrt0FGSdHr7NqVs/l7ZZ07LYnFTg8hINR0wUMHXt9O1o8eqQUSEkv/D4nyA2ZWsonT0BYqb16UEauFllWO2/Hy5+fpWKclanOwozKOCE3WPAgy4mtO2UU3+dV7fjTfeaH/OYrHYjy9fpNPNzU1PPPGEDMPQggULnBIjzK3kh3vJKomKFH9TWpjvuJy81Dgl2ueeS6t0+9PzBw/aj/2jSifKSsZ7eXVGSdacbGWeKNpRpUGTCFnc2N0YqK6S7zc3b8fTQorvIbbq3h/ycu3HuWlpyq1gi0SpaBejYv5RzUuda9LrRnvy4uhXXyrp4+XKOnlChtUqW0G+Lh5JVuLihTrza+VFZL8BCmoTW61YAThfQYkFuT18fStpKXn4XDpvzS49VaS4H0d9FPXjU9RHDouBA/jtc1oFRtav20WWrIbwKzFP8MKFCwoJKb2V3PXXXy9J2rt37xWNfezYsSq1Oz5n1hWNg7plWK0qyMqUZwN/eTWsfGFOdx9fezlmvoMF/S6Xf/5S+/wLle+Uk3/hvP3Ys0GDy85dKPe4sn4s7u7y8PNTwa97wwOoGsNqVUFmpjz9/eXtYOFed99L94e88+erNU5eifd8yePy5Jfo+/KFPht36yGpaO76ibhvKuzj6H8/V+MuXYuu6d5D6YkJ1YoXgHOVXLjTt3FjpSf+XGHbUgt+ni694GfOmVT5hoTYd1+rTHE/2adZCBzAb5/TEhiNGjXSuXPnlJt76durkgmLpKSkMgmM4m1Wz1byDXhVREVFVakdK2WYX86ZVHnG+MsnJERyc6twq0TfsLAS11TvAz37zKVpIBY3SyUtJYvlUrWEcVks2adPK+SG4nYO+nGruB8AVZN95rQa+fvLJyTUwf2h6rsEXC4npeT9wUG1VIn7x+Xva79fdynKOX1aRiVrduRfuKD8ixnyCmhYKm4A5pRxONl+3DA6WidV8bTQhtFFlVk2q1WZl63XlnE4WcGxbeQVECCf4OAKt1L1CQmR168J0ovJlW/bCtQGG1NI4GJOq1W/7rrrJEm//PKL/bmAgABFRxftWf3VV1+VuWbdunWSpMBqbnOH366LR5IlFS125R/ZtMJ2DWNiSlxTvQ/0/PPnlZeeLknyDg6ptK13iaRbfkbpao2LyYfLbVduP8HBkop2RqjKiuMAyip+z7l7e8u/acWJ60bXtLQfZ5R4n1ZF3vl05aUX/SHh4+B97RMcaj++fOvn4oSGxd3xx7DFzb3UNQDM61xCgn2ntLDOHSts5+bhoeB2RZXG5/YnlFlf5+zeePtxZf2Edbp07mx8+WttAcBvidMSGL169ZIkbd26tdTzt99+uwzD0BtvvKFvv/3W/vzHH3+st99+WxaLRb1793ZWmDC5c/sv7VwT1qVL+Y0sFoV27iypaPuxjF+Sqj/OTz9KkrwCAuTfvHmF7YJ/neYklU5YSFLG4cP2qSDBbdtW2Id3UJAaRBQtbJt59AirIwE1VPy+laTG3bqV38hisd87rNnZykg6VO1x0vYV/ZHgFdBQAdEtKmwXcsMN9uOMw7+UOlf8bapfeBO5/zp/vTx+4U3s09OKEycAzMuanaMzO3+QJIV361qqIrSkpgP62ysnTmz4rsz5kxs32XdUajFsWIXjtRg2VFLR7ksnN266otgBoD5wWgJj6NChMgxDK1euVGGJctnp06fLz89PmZmZuuWWWxQWFqaGDRtq9OjRysnJkZubm6ZPn+6sMGFyWcePK+NwUaIgrGs3+Tcrm1yI6NNXfo3DJUkpm78v861lWOcu6jnjNfWc8ZqiBt1c7jinvt9k352gxe13lLsKeGjHjvZvctMTE8pUYMgwdHJj0S8lvmGNFdmvf5k+LG5uirnjLnsp+unt2yp87QAql3nsmC78mrBs3K2H/JtHl2kT2a+//MKbSJJOfb+x7P2hSzfd+PqbuvH1N9XsllvLHefkpu9U+Ov9IebOu+TmWXZR4dBOndWoZStJ0rmE/WXWwUlPKErGunl6qsXwO8sdx+LhoZg77ypxzf5y2wFwnhbDhmjU1k0atXWTrp8yudw2Py/5UFJRlUXn6X8oM93Mq1EjtX/0/0mS8jMu6pfP/lOmj9xz53T0y68lSRG9eihq4IAybaJuGqiIXkXr6Rz575cVTjMBapNhGKZ74OritDUwBgwYoBdeeEFWq1UnTpxQ81+/1W7evLlWrFih8ePH6/z580pLS7Nf4+3trffee089e/Z0VpioB5L/s0bXP/Sw3L28FDv5AZ1YH6eMX5KKtiFt30Hh3Ys+zHNSU+0JhOrKv3BBx9Z9reghQ+UfFaV2jzymk99tUM7p03L38VHw9dfbx7Hm5urI2rK/fEhSypbNCmnfXv5No9R88BD5hofr7J7dKsjKkk9IiCJ691XAr++F9MREnfvxx3L7AVA1yZ+tVrtHHpO7l5eun/qgjn/7jS4kHZKbp6dCO3RSk55F1YA5qWd04rsNNRoj//x5Hfvqv2oxbLj8o5qp/eNP6sSGOGWnpMjdx0ch7W6wj2PNyVHymtVl+jj53Xdq3K2HvAICFN6tu3xDQ5WydYtyzpyRxc2iBpFNFdG7r/yaFCVbsk+n6MzOHTX8VwEgSaEd2ss/6tL0U+9GgfZj/6gotRg2pFT75LVf1GicMz/s0tGv1qn5rTerab++6vf3t3Rw2XLlpJ5Vo5YtFTvxfjWIKHpvx8/5hwouXiy3n33/mKsmPXvIJzhIPV95UT8v/Uinvt8sSYrofaOuGzdGkpR7Ll0//mNejWIFgPrGaQkMi8WiF154odxzQ4YM0aFDh7RixQr99NNPslqtuvbaazVq1Cg1bVrxOge4OmWfOqmDH32oVqNGy8PHR81vG1ymTU5qqhIXLyq1H3t1ndr4nTx8fX/9xjZcre4dVaZNfuZFHfjgA+WWSLyVZFit+vlfi3Xd7ybIPypKYZ06K6xT5zLt0hMTdfCjpTWOFUCRrJMndGDJB7p2zDh5+PoqekjZ0uuc1DNKWPC+bHnV20K1pJMb1svD109NBwyUX5Mmunb02DJt8i9eVOLiheVuxWzNztL+9+eqzf0T5RMSooYx16hhzDXljpV54oR+Xryw0sU+ATgWc8ftivl1ysXlwjq0V1iH9qWeq2kCQ5J2/GWGPBr4KbL3jQrv2kXhXUtPe7UVFiph4WL9sqpsgrNYzpkz2jT9f9T7rzPkGxqq2PvvU+z995Vuc/asvv+fZ5VTyZbOAPBb4rQEhiPBwcF66KGHXB0G6onziQmK//vbirixtwKvayOvRo1kFBYqN+2s0vbt0+mtW+xTQK7Esa++VHpCgsJ79FRAixbyCgiQzWpV7tmzSk9MUMrm71Xo4I+ggosX9eM/5qhx164Kbd9Rvo0by93HR9bsbGUeP67UXT8ovcTaHgCuTHrCfu19601F9OmroNjYovuDtej+cDY+XimbN9XK/eHofz/Xuf0/qUmvG9UwJkZeAQ1ls1qVk5qq9P0/6dTmTSossfPW5bJPndSev81U465dFdS2nRpERMjDz08yDBVkZirr5Amdjd+rtL17WMATqGcK8/K16Y9Pq/mtt6jFsCEKvLaVPP39lXsuXWf37tWhFZ8o7UfHn/3nftqvL8dPUOvR9yqyX181iIiQJGWdOqmT323SgY+Wl53CCtQhdiGBq1kMJ00cmjy5aJ7gkCFDdO+99zpjyGrb+uwzrg4BgInZrFf+Ry+A367j37GOEYDyjdr621hkddqsmk2/rEszHyu7zhx+u5xWgbF48WJJ0ujRo501JAAAAAAA+I1wWgIjLCxMqampCg8Pd9aQAAAAAIBawhQSuJrTtlFt27atJOnIkSPOGhIAAAAAAPxGOC2Bcd9998kwDPtUEgAAAAAAgKpyWgJj0qRJGjRokFavXq2XXnpJTlo7FAAAAABQC2yGYboHri5OWwNj48aNmjZtmlJTU/Xyyy/ro48+0ujRo9W+fXsFBQXJ3d290uv79evnpEgBAAAAAIDZOC2BMWDAAFksFvvPBw4c0CuvvFKlay0Wi6xWa12FBgAAAAAATM5pCQxJTBsBAAAAgHqKP+fgak5LYMTFxTlrKAAAAAAA8BvjtARG//79nTUUAAAAAAD4jXHqFBIAAAAAQP1ks7k6AlztnLaNKgAAAAAAKJKdna033nhD3bt3V3BwsPz9/RUbG6tp06bp6NGjV9y/xWKp9qM8EydOrPL1ycn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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 434,
       "width": 536
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_predictor_correlations(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But when we look at the *uncentered* model we see that the correlations have now been reduced!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: title={'center': 'Correlation Matrix of Predictors'}>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 434,
       "width": 686
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_predictor_correlations(model_centered)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's try to understand **why** this matters by revisiting one of the assumptions of the GLM we haven't discussed yet: **multicollinearity**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multicollinearity - the other assumption\n",
    "\n",
    "<div align=\"center\">\n",
    "<img src=\"./figs/mc.png\" width=\"40%\" alt=\"Figure 1\">\n",
    "</div>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Previously we discussed the fundamental assumptions of GLMs that can be summarized as **i**ndependent & **i**identically **d**istributed errors (**iid**):\n",
    "- errors should be independent of each other\n",
    "- errors should be independent of predictors\n",
    "- errors should be approximately normal\n",
    "\n",
    "Now let's explore **multicollinearity** - a situation in which the predictors of a GLM are **correlated** with each other. How correlated? There isn't actually a principled answer for this because it depends on the goals of your analysis!  \n",
    "\n",
    "Instead in this notebook we'll explore the key points you should understand about this assumption:\n",
    "\n",
    "- Why it matters\n",
    "- How it affects parameter estimates\n",
    "- How it affects estimate uncertainty (standard-errors & confidence intervals)\n",
    "- How to check for it\n",
    "- How to deal with it\n",
    "\n",
    "We'll also ask you to skim the following paper which provides a more detailed discussion of what (and what not to) worry about when it comes to multicollinearity:\n",
    "\n",
    "[Vanhove, J. (2021). Collinearity isn’t a disease that needs curing. Meta-Psychology, 5.](https://paperpile.com/shared/sM2u33xdnTMGoFTl59avK1Q)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Why it matters\n",
    "\n",
    "<div align=\"center\">\n",
    "<img src=\"./figs/x1.png\" width=\"30%\" alt=\"Figure 1\">\n",
    "<img src=\"./figs/x12.png\" width=\"30%\" alt=\"Figure 1\">\n",
    "<img src=\"./figs/x12c.png\" width=\"30%\" alt=\"Figure 1\">\n",
    "</div>\n",
    "\n",
    "Intuitively, collinearity matters because in the *worst case*, when 2 or more predictors are *perfectly correlated*, we **can't tell the difference** between how much 2 or more variables uniquely predict $y$!\n",
    "\n",
    "In the figures above, the overlap in circles shows how much $X1$ and $X2$ predict $y$ and how much overlap (corelation) exists between $X1$ and $X2$. In the right most figure, we see that $X1$ and $X2$ are so overlapping that it doesn't even make sense to use both of them in the same model!\n",
    "\n",
    "In linear algebra terms:\n",
    "- If any of the predictors in $X$ is a perfect linear combination of the other predictors, we say that $X$ is **rank-deficient** - it doesn't need as many columns as it has to reflect the overall variance that it does\n",
    "- In this case, there is no unique solution for $\\hat{\\beta}$, because the matrix $ (X^TX)^{-1} $ is not invertible."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see this with some 3d plots of a multiple regression with 2 predictors X1 and X2\n",
    "\n",
    "Remember that graphically, fitting a *multiple regression* with 2 predictors is extending the idea of a **line** of best fit to a **plane** or **sheet** of best fit.\n",
    "\n",
    "In this first movie X1 and X2 are uncorrelated and we can see that the regression plane is stable across repeated samples\n",
    "\n",
    "![Regression with 2 predictors](figs/movie_regression_2preds.gif)\n",
    "\n",
    "In the second, the two predictors are correlated.  The regression plane tips on a ridge defined by the correlated predictors, and is unstable across repeated samples:\n",
    "\n",
    "![Regression with 2 predictors](figs/movie_regression_colinear.gif)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Key Takeaways\n",
    "In general we want to avoid multi-collinearity because it makes it harder to identify the unique contribution of each predictor in our GLM. Concretely we'll see this reflected in our calculations in the following ways:\n",
    "- Our parameter estimates can become very large and even flip sign from negative to positive\n",
    "- Our *uncertainty* in those estimates becomes larger so our standard errors *always* increase\n",
    "- As a result our confidence intervals become *wider* \n",
    "- So our statistical *power* decreases - we're less certain of our estimates so our ability to make reliable conclusions given the same sample size *decreases*\n",
    "- Our overall model fit *does not change* - in other words our error in predicting our dependent variable does not increase as a result of collinearity - but our model does get *less interpretable* - we can't pinpoint the unique contribution of each predictor!\n",
    "\n",
    "You can see this reflected in the following figure just plotting the estimates and 95% confidence intervals for two predictors with varying levels of collinearity:\n",
    "\n",
    "<div align=\"center\">\n",
    "<img src=\"./figs/collinear.png\" width=\"70%\" alt=\"Figure 1\">\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inspecting collinearity: VIF\n",
    "\n",
    "We already saw one way of checking for collinearity: **visual inspection of predictor correlations**\n",
    "\n",
    "We can also generalize this idea to calculate what's called a **variance inflation factor (VIF)** for each predictor in our model:\n",
    "\n",
    "$$\n",
    "\\text{VIF}_k = \\frac{1}{1-{R^2_{(-k)}}}\n",
    "$$\n",
    "\n",
    "where $R^2_{(-k)}$ refers to $R$-squared value you would get if you ran a regression using $X_k$ as the outcome variable, and all the other $X$ variables as the predictors. The idea here is that $R^2_{(-k)}$ is a very good measure of the extent to which $X_k$ is correlated with all the other variables in the model. Better yet, the square root of the VIF is pretty interpretable: it tells you how much wider the confidence interval for the corresponding coefficient $b_k$ is, relative to what you would have expected if the predictors are all nice and uncorrelated with one another. If you've only got two predictors, the VIF values are always going to be the same.\n",
    "\n",
    "\n",
    "To calculate VIF we can use the `variance_inflation_factor()` function from `statsmodels`. However, this function only calculated VIF for a single predictor, so we'll write our own function (we've also provided it in `helpers.py` which you can import using: `from helpers import vif`) to calculate the VIFs for all of our predictors at once. We'll also return the square-root of the VIF to get a sense of how much wider our CIs would be:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import statsmodels function\n",
    "from statsmodels.stats.outliers_influence import variance_inflation_factor\n",
    "\n",
    "# Just showing you the code here\n",
    "\n",
    "# For future just do: \n",
    "# from helpers import vif\n",
    "\n",
    "def vif(model):\n",
    "    \"\"\"Calculate VIFs for all predictors in a model\"\"\"\n",
    "    vifs = []\n",
    "    for i in range(model.exog.shape[1]):\n",
    "        this_vif = variance_inflation_factor(model.exog,i)\n",
    "        vifs.append(this_vif)\n",
    "\n",
    "    return pl.DataFrame({\n",
    "        'variable': model.exog_names, \n",
    "        'VIF': vifs, \n",
    "        'CI_increase': np.sqrt(vifs)\n",
    "        })"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use this to calculate the VIFs for our uncentered and centered models:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "}\n",
       "</style>\n",
       "<small>shape: (4, 3)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>variable</th><th>VIF</th><th>CI_increase</th></tr><tr><td>str</td><td>f64</td><td>f64</td></tr></thead><tbody><tr><td>&quot;Intercept&quot;</td><td>13.803357</td><td>3.715287</td></tr><tr><td>&quot;tv&quot;</td><td>3.727848</td><td>1.930764</td></tr><tr><td>&quot;radio&quot;</td><td>3.907651</td><td>1.976778</td></tr><tr><td>&quot;tv:radio&quot;</td><td>6.93786</td><td>2.633982</td></tr></tbody></table></div>"
      ],
      "text/plain": [
       "shape: (4, 3)\n",
       "┌───────────┬───────────┬─────────────┐\n",
       "│ variable  ┆ VIF       ┆ CI_increase │\n",
       "│ ---       ┆ ---       ┆ ---         │\n",
       "│ str       ┆ f64       ┆ f64         │\n",
       "╞═══════════╪═══════════╪═════════════╡\n",
       "│ Intercept ┆ 13.803357 ┆ 3.715287    │\n",
       "│ tv        ┆ 3.727848  ┆ 1.930764    │\n",
       "│ radio     ┆ 3.907651  ┆ 1.976778    │\n",
       "│ tv:radio  ┆ 6.93786   ┆ 2.633982    │\n",
       "└───────────┴───────────┴─────────────┘"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Uncentered\n",
    "vif(model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div><style>\n",
       ".dataframe > thead > tr,\n",
       ".dataframe > tbody > tr {\n",
       "  text-align: right;\n",
       "  white-space: pre-wrap;\n",
       "}\n",
       "</style>\n",
       "<small>shape: (4, 3)</small><table border=\"1\" class=\"dataframe\"><thead><tr><th>variable</th><th>VIF</th><th>CI_increase</th></tr><tr><td>str</td><td>f64</td><td>f64</td></tr></thead><tbody><tr><td>&quot;Intercept&quot;</td><td>1.002983</td><td>1.00149</td></tr><tr><td>&quot;center(tv)&quot;</td><td>1.010291</td><td>1.005132</td></tr><tr><td>&quot;center(radio)&quot;</td><td>1.003058</td><td>1.001528</td></tr><tr><td>&quot;center(tv):center(radio)&quot;</td><td>1.007261</td><td>1.003624</td></tr></tbody></table></div>"
      ],
      "text/plain": [
       "shape: (4, 3)\n",
       "┌──────────────────────────┬──────────┬─────────────┐\n",
       "│ variable                 ┆ VIF      ┆ CI_increase │\n",
       "│ ---                      ┆ ---      ┆ ---         │\n",
       "│ str                      ┆ f64      ┆ f64         │\n",
       "╞══════════════════════════╪══════════╪═════════════╡\n",
       "│ Intercept                ┆ 1.002983 ┆ 1.00149     │\n",
       "│ center(tv)               ┆ 1.010291 ┆ 1.005132    │\n",
       "│ center(radio)            ┆ 1.003058 ┆ 1.001528    │\n",
       "│ center(tv):center(radio) ┆ 1.007261 ┆ 1.003624    │\n",
       "└──────────────────────────┴──────────┴─────────────┘"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vif(model_centered)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### VIF rule-of-thumb"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So how should we interpret these? A decent **rule-of-thumb** is to be concerned about VIFs that are 5 or greater - **but this is not a hard-and-fast rule**.\n",
    "\n",
    "Why 5? Because it means our estimates are going to be 2.5x as uncertain as they would have been with no collinearity. Is 2.5x the right number? It depends on how much *certainty* you need in your specific estimates and what kind of statistical inference you want to make. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that when we *don't center* our predictors - the *widths* of our confidence intervals are larger by a factor of about `np.sqrt(VIF)` for each predictor relative to our *centered* predictors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>6.261383</td>\n",
       "      <td>7.239058</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tv</th>\n",
       "      <td>0.016135</td>\n",
       "      <td>0.022067</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>radio</th>\n",
       "      <td>0.011298</td>\n",
       "      <td>0.046423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>tv:radio</th>\n",
       "      <td>0.000983</td>\n",
       "      <td>0.001190</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  0         1\n",
       "Intercept  6.261383  7.239058\n",
       "tv         0.016135  0.022067\n",
       "radio      0.011298  0.046423\n",
       "tv:radio   0.000983  0.001190"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Uncentered CIs\n",
    "results.conf_int()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept    0.977675\n",
       "tv           0.005933\n",
       "radio        0.035125\n",
       "tv:radio     0.000207\n",
       "dtype: float64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Uncentered widths\n",
    "widths = results.conf_int()[1] - results.conf_int()[0]\n",
    "widths"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Intercept</th>\n",
       "      <td>13.815204</td>\n",
       "      <td>14.078745</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>center(tv)</th>\n",
       "      <td>0.042833</td>\n",
       "      <td>0.045922</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>center(radio)</th>\n",
       "      <td>0.179723</td>\n",
       "      <td>0.197519</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>center(tv):center(radio)</th>\n",
       "      <td>0.000983</td>\n",
       "      <td>0.001190</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                  0          1\n",
       "Intercept                 13.815204  14.078745\n",
       "center(tv)                 0.042833   0.045922\n",
       "center(radio)              0.179723   0.197519\n",
       "center(tv):center(radio)   0.000983   0.001190"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Centered CIs\n",
    "results_centered.conf_int()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept                   0.263541\n",
       "center(tv)                  0.003089\n",
       "center(radio)               0.017796\n",
       "center(tv):center(radio)    0.000207\n",
       "dtype: float64"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Centered Widths\n",
    "widths_centered = results_centered.conf_int()[1] - results_centered.conf_int()[0]\n",
    "widths_centered"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept                   0.979132\n",
       "center(tv)                  0.005963\n",
       "center(radio)               0.035179\n",
       "center(tv):center(radio)    0.000545\n",
       "dtype: float64"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# These look as wide as our uncentered predictors' CIs!\n",
    "\n",
    "# Centered widths * sqrt(VIF)\n",
    "widths_centered * vif(model).select('CI_increase').to_numpy().flatten()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Handling multi-collinearity\n",
    "\n",
    "Aside from visual inspection or VIF calculations the most direct way you can handle multi-collinearity is to simply removing one or more variables from your model that are redundant with other variables!\n",
    "\n",
    "A few other approaches we won't cover in details in this course:\n",
    "- Creating new un-correlated predictors using [Principal Components Analysis (PCA)](https://scikit-learn.org/stable/modules/decomposition.html#pca)\n",
    "- Adding *regularization* to OLS via [Ridge Regression](https://scikit-learn.org/stable/modules/linear_model.html#ridge-regression-and-classification) which will force the model to keep $\\beta$ values small\n",
    "- Adding *regularization* to OLS via [Lasso Regression](https://scikit-learn.org/stable/modules/linear_model.html#lasso) which will force the model to set some of the $\\beta$ values to zero\n",
    "\n",
    "If the collinearity is because of **interactions** between variables that you've created - you can **center** or **z-score** each variable **before** calculating the interaction like we've seen before.\n",
    "\n",
    "Let's explore this with a challenge:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Challenge\n",
    "\n",
    "Fit and explore a new model like the ones above (including an interaction) but this time z-score each predictor in the model:\n",
    "\n",
    "1. Create new z-scored columns for `tv` and `radio` in your DataFrame and fit a new model using those columns those with `ols`\n",
    "2. Fit a second model using the `standardize()` transformation in the model formula itself with the *original* columns; see how we used `center()` above - is there any difference?\n",
    "3. Then use `plot_predictor_correlations` to visualize the correlations between predictors from either model. How does this compare to the uncentered and centered models?\n",
    "4. In notebook `04_models` in the \"Gram Matrix\" section we created a histogram of 3 predictors. Recreate the histogram for the original and z-scored columns. How are they different?\n",
    "5. Inspect the parameter estimate from the z-scored model. How would you interpret these compared to the *centered* model?\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1) Create new z-scored columns and use them to fit a new model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your code here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "zscore = lambda name: (col(name) - col(name).mean()) / col(name).std()\n",
    "df = df.with_columns(\n",
    "    tv_z = zscore('tv'),\n",
    "    radio_z = zscore('radio'),\n",
    "\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "model_z = ols('sales ~ tv_z * radio_z', data=df.to_pandas())\n",
    "results_z = model_z.fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2) Fit another model using the original columns and `standardize()` in the formula\n",
    "Is there any difference?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your code here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "model_z_formula = ols('sales ~ standardize(tv) * standardize(radio)', data=df.to_pandas())\n",
    "results_z_formula = model_z_formula.fit()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept       13.946974\n",
       "tv_z             3.809978\n",
       "radio_z          2.800424\n",
       "tv_z:radio_z     1.384913\n",
       "dtype: float64"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results_z.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept                             13.946974\n",
       "standardize(tv)                        3.800441\n",
       "standardize(radio)                     2.793414\n",
       "standardize(tv):standardize(radio)     1.377988\n",
       "dtype: float64"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results_z_formula.params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3) Use `plot_predictor_correlations` to compare correlations between either z-scored model and the centered and uncentered models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your code here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: title={'center': 'Correlation Matrix of Predictors'}>"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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CrrjT8/zzzydrd9q0aak+v3///bepUaNG5nIFChQwnT592madmfks2SMjPTFiY2NNRYoUsXnetuyJkfR6jhkzJtU5IjY21vz3uHLliqlEiRLm4wYMGGC6ePFiqrZDQkJS9Zix1bumffv25nKFCxc2rV69OlWZH3/80eTh4WFyc3Oz6/Niz99/3759yXoqNGjQwLRz506rZa9cuWL66KOPTFOnTk21LzOfpZs3bybrSVepUiVTUFBQqnLz5883eXh4mMv16NHDrufs4uJicnNzM02fPj1Vr7+kz+a9e/eSvT/ef/99m/9LQkNDTbNmzbL6/AEAOYskBpAFlt1N33zzzWytOz4+3lShQgVz/U888YTN4RYJCQmmXr16Jbv4s5YwsLywlGTy8/NLdzhByqEVnp6epuPHj6d7TFLCw8fHJ9UX6ZTWr19vrr9GjRpWn6e9X/rs9cEHH5jr++abb2yWy4kkRm68tlWqVEkzOfPkk0+ayz733HN2Pa+02EpiLFiwwPz7d999N9VxHTt2NEkyGY1G04ULF0wmk/1JDHvFxsaa6tata5ISh+bcvHkz3eeQmSRG0hfTyMjIdI/LyPt59OjR5rIVKlQwJ7tiYmJMDRo0MO/r2rWrXTGn5+TJkyaj0WhXYuTmzZsmf39/c9nhw4fbLJsXkhhfffVVstfru+++S7bfMokhyTRq1Kh02x8xYoTd5ePi4pIlKBYtWpSqzOrVq837DQaD1YRxkkWLFiWLN6tJjJYtW5rLNG7cOM1zSFoy81maNGmS+ZiCBQtaTXom+eWXX5I9Z1uJWMvnLMk0f/78NGM4fPiwuWzLli3tihsAkPuY2BPIpPDw8GQTtBUsWDBb61+zZo15Mj83Nzd9+eWXNod4GAwGff311+YJEU+dOmXXxGeTJk1KNlO/PcaOHauqVaumWebzzz83d7MdP368qlevnmb5Dh06qHPnzpKk4OBg7d+/P0MxZYbl0IbcXqEgN17bDz74QN7e3jb3jxgxwrwdFBSUkfAzpE+fPuZhAz/88EOyfZcuXdL69eslJb4HypQpkyMxuLq6atCgQZKk6Ohobd26NUfakaSpU6fKw8MjW+ucNm2aedjBmTNn9MILL0iSJkyYYP6sFC9eXLNnz86W9r7//nvzRKh169bV2LFjbZYtVKiQpk6dav554cKFun37drbEkZ0SEhI0Y8YMvfLKK+bfFStWzPy+sMbd3V0ffvhhmvVev37dvLKOr69vusO98uXLpylTpph/trbE64wZM8zb/fv3V+vWrW3Wl97+jNi1a5e2bdsm6cFwprTOIdnJZDIlG0o4ceJElStXzmb5Pn36qEuXLuafv/3223TbaNq0aZqvt6Rkk3TaM0QFAOAYzIkBZFLK1Ray+2LPcr6NLl26qGTJkmmWL126tB577DH9/vvvkqQNGzaYEwPWGAyGVHNB2OOpp55Kt4zlHAv2lJcSv8SuXr1aUuLKJw0bNsxwbJYSEhK0d+9eHThwQBcvXlR4eLjN1TgOHDiQpbYyKqdfW3d3d3Xv3j3NOhs0aGDetmelgszy8PDQk08+qdmzZ+v48ePatWuXAgICJEnz5883f1keMmRIltq5deuWdu7cqSNHjig0NFR3795NtiKJ5TwbBw4cUI8ePbLUnjWFChVK83XJLE9PTy1cuFABAQGKjY3VggULVKBAAfPcNJI0e/ZsFS9ePFvas3x/Dh8+PN2VQ/r06aPChQvr5s2biomJ0Y4dO/TYY49lSywZNX/+/GRLXptMJvOcIpar/BiNRs2cOTPN83anTp1UqFChNNtbt26deV6W7t272/V/ICAgQJ6enoqMjLSaULNc7ejpp59Ot74hQ4Zoy5Yt6ZZLz6pVq8zbjzzyiGrWrJnlOu0VHByskJAQSYmvjeUSzbaMGjVKf/zxhySlWiHKGnv+F1kmTv78808FBwfbnLcEAOA4JDGATEo5Kd3du3eztX7L3gj2ThjasmVL8xfd9CYS9Pf3V+HChTMUk6urq3nZTFtCQ0OTLZn66aef2rV84tGjR83b9iwpaktcXJy+/PJLTZs2TRcvXrTrmLSWW80JOf3aVqtWTW5ubmmWsZxUL6fvnA8ZMsTcS2DevHnmJEZSzwxvb289/vjjmar74sWLeu211/TTTz+Zv0ymJ6de7/r16yeb3Da7637//ffNPQks7zyPHTtWXbt2zZZ2TPcnQU1iz/vT1dVVTZs2NX8J3rdvn8OSGOvXrzf37rGlRIkSmjlzprp165ZmuUaNGqXb3o4dO8zbf//9d5q9ViwlnRPDwsIUEREhLy8vSYm9k65fv24ul/RZSUuzZs3sajM9O3fuNG9bLpGaGyzPidWrV7drslLL92ZISIguX76sUqVK2Sxvz+tZpkwZtWjRQtu3b1d4eLgaN26sQYMGqU+fPmrVqpXDJqMFACRHEgPIpAIFCsjFxcU8pOTWrVvZWr/lhWz58uXtOsbf39+8nd4Xtcx0lS1UqJBcXNI+bVy5ciXZz998802G27FcPSAjklaHWLNmTYaOS9mrJqfl9Gub1ooLSZKGp0hKNiwqJ7Rt21bly5fXuXPnFBgYqE8//VSHDx/WkSNHJEmPP/64+UtcRuzfv1+PPPJIht8vOfV653T385dfflmrVq1KNpyoVq1a+uijj7Ktjdu3byfrsZQT78/cZDAY5OPjo2LFiqlBgwbq0qWLBgwYYNeQH3tez8uXL5u3g4KCMjU0KywszPz+tzw3eHp62vVlvmzZshlu0xrLlVAqVqyYLXXaKzPnxBIlSsjd3d28OsqNGzfSTGLY+/mcNWuW2rdvrytXrigyMlLff/+9vv/+e+XLl0916tRRmzZt1KVLFz366KPp/j8EAOQM5sQAssDyYsuyJ0F2sOzZYe8XPMty6X1Ry8y4fXuOyY67+pn9Uv3WW2+ZExhGo1EDBw7UkiVLFBwcrNu3bys2NlamxAmNZTKZzMdZbueGnH5t7en5kpsMBoO5W3xoaKhWrFihefPmmffb03U8pZiYGD3xxBPmBEaJEiU0efJkbdy4URcuXFBERIQSEhLMr7XlfBGWw0yyU3bPhZGSwWBINWTksccek7u7e7a1kbJHWU68P3PS7Nmzk33GExISdPv2bZ08eVJLlizRiBEj7H6dHHG+s/z7e3p62nV8ZhKA1li+brk1F0aSzJwTU5bNrv951apV08GDB/Xyyy8n660YHx+vAwcO6IsvvlCXLl1Uvnx5ff/993bHCgDIPqSQgSxo1aqVec36Xbt2ZWvdlheRERERdh1jWc5R3V4tLyoLFiyY6V4VGRUTE6Mvv/zS/PO8efPSnMTNkV+0nPW1zYohQ4bo3XfflZR4pzPp81K2bFm1a9cuw/X9/PPP5slRy5Qpoz179qhEiRI2yzvy9c4uCxcuTDUR5GeffabHH39cLVq0yJY2Un55tRzqkBZnf39mluXf5rPPPtNLL72Upfos//6RkZF2HWPvOSQ9lq9bdg+PTE9mzokpy2bn+65YsWKaNm2apk6dql27dmnz5s3aunWrtm3bZp788/Lly3r22Wd1+PBhffHFF9nWNgAgffTEALKgQ4cO5u1z585p+/bt2Va3ZdfX8+fP23XMuXPnzNsZXXUku1h+kbx161aybsI5affu3eYL7zp16qQ7C73l3yq3OetrmxVVqlQxj91fvny5+X0xePDgTM0jYTnvwcsvv5xmAkNy7OudHc6dO2delUSSecWf+Ph4DR48ONmqClnh6+ubbKjRw/L+zCzL992JEyeyXJ/luSEyMlKhoaHpHpOVOYQsWT6XpARhbsnMOfHatWvmoSRSzrzvXF1d1apVK02YMEErV67UjRs3tGrVKrVt29Zc5ssvv8zRFZ4AAKmRxACyoG/fvskunKZNm5ZtdVuuHmFvciRpeTxJWV7dI7NKliyZbIb3jM5PkVmWY9Nr1aqVbvnNmzfbVW9ODM1w1tc2q6ytQJLZVUly4vXOa8NwkiQlKpKGLnTs2FFBQUHmpY7PnDmjMWPGZEtbBoNB9evXN/9sz/szLi5Ou3fvNv/srO/PzLCceDNpdaWsKF26dLIv9JaTbdpiTxl7WE4QarlCTWZk9LNkeU48duyYbt68me4xludEPz+/NOfDyC6urq7q3Lmz1qxZk2yS66RJlwEAuYMkBpAFHh4eevHFF80///zzz/r5558zXE9ERESqLwuWvTxWrlypa9eupVlHSEhIsiXyLI/PbZaz/n/22We5MueE5d389LphJyQkaPr06XbVaznfgK0lWjPKmV/brHjqqaeUP39+889NmjQx9yjIqIy83nv37rXrTmlOvNbZYcqUKealOIsUKaI5c+bI29tbCxcuNPeamD9/vn788cdsac/y/TV37tx0P7/Lli0z9xhwd3dX8+bNsyUOZ9C5c2fz5I4nT57U8uXLs1yn5fCq+fPnp1t+7ty5WW5TSlzuOcn69esVHByc6boy+lmqUaOG/Pz8JCUm7ex53pbz3OT2aipubm7q2LGj+WfLSVEBADmPJAaQRePHj0925/Hpp5/O0F2Zw4cPKyAgIFWPhU6dOqlChQqSEud7GDdunM06TCaTXnzxRcXGxkqSKlWqpEcffTQDzyJ7vfLKK8qXL58kac+ePXrrrbfsPjYkJCRTbVrOpr9p06Y0J9z76KOPdPDgQbvqtVwd4NKlS5mKLSVnfm2zolChQtq3b595FYfMJPySWL7ev/32m81ykZGRevbZZ+2qMyde66zatWuX3n77bfPP33//vfmOc6NGjZLte/7557Nl2MwzzzxjThLt27cvzYTf7du3NX78ePPPAwYMsGt1nH+K0qVLa/Dgweafn3vuObvfOwkJCVaH240cOdK8HRgYqC1bttisIzAw0JzgyqqmTZualy01mUwaMmRIpufGyOhnyWAwJPucvv3222ket2LFimT/Z5977rlMxZlSWFiY3RP/Wg57yemViQAAyZHEALIof/78WrJkiXnVgKioKPXu3VtDhgyxeSfLZDIpKChIQ4cOVf369c1LTVoyGo364IMPzD//+OOPeuaZZ1JdVN65c0cjR47UkiVLzL+bOnVqpuYZyC6VKlXSf//7X/PPb731loYNG6aLFy9aLR8fH69169ZpyJAhme6K3qBBA5UuXVpS4hervn37JhtyICUmDCZNmqTXXnvN7hnwLbsML168OFOxpeTMr21W1axZU40bN1bjxo2ztDRk9+7dzdvz5s3TJ598ovj4+GRlTp48qU6dOmnfvn12vd4VK1Y0lzt37lyyIRKOcPfuXQ0aNMi8esWoUaPUp0+fZGXGjx9vvnN/+/ZtDR48ONXfIaMqVaqk0aNHm38eO3asvv7661Rf7k6dOqVOnTqZJzcuUKCAJk6cmKW2ndGUKVNUsmRJSYlf2Js0aaKffvrJ5pfhS5cu6fPPP1f16tUVGBiYan+nTp3Mcy6YTCb17t3b6rC8RYsWafjw4XJzc8u25/LFF1+Ye0vt2bNHbdq0sfk5CAkJ0ccff2x1id/MfJbGjRtnPoeHhobqkUce0YEDB1KVCwwMVP/+/c0/9+jRQ23atEm3fnv89ttvqlKlij766COb84JER0frs88+S5aE7dq1a7a0DwCwD6uTANmgYsWK2rVrl3r06KG//vpLCQkJ+uGHH/TDDz/I399fdevWVdGiRRUfH6+QkBAdOHAgVfdTazOr9+vXT5s3b9bXX38tSZoxY4YCAwPVvn17lShRQteuXdOff/6ZbOWFcePG6YknnsjZJ2yHyZMn6+zZs+auznPnztX8+fPVoEEDVa9eXd7e3goPD9e5c+d08OBB8xd4yzt4GWE0GvXOO+9oxIgRkqS1a9eqatWqatGihcqXL6/Q0FBt3LjRvFrK9OnT0538U5KeeOIJfffdd5Kkb7/9Vvv27VPDhg2TLX/4/PPPq1KlShmK15lf27ygc+fOatu2rTZt2iSTyaRXX31VX3/9tRo2bChfX1+dOHFC27dvV3x8vEqXLq2XXnopWY8Ba4xGo3r37m1eAaR9+/Z67LHHVK5cOXPPosKFC2vChAk5/vykxORBUoKgSpUq+uyzz6zG/MMPP6hu3boKCwvT1q1b9f777ydLImbGxx9/rD179igoKEhxcXEaO3asPvjgA7Vq1Ure3t46deqUNm/ebE6YuLi4aObMmeYeRg+TkiVL6rffflPXrl1148YNXblyRX379lXx4sUVEBCgEiVKKCEhQaGhofrrr790+vTpNIfoGAwGzZw5U82bN9f169d18+ZNde7cWfXr11f9+vUVHx+v3bt36/jx45ISh+yl1ZsrIxo2bKiZM2dq2LBhiouL0/79+xUQEKBq1aqpQYMG8vX11e3bt3X06FHz/zprK7Jk5rNUqFAhLVy4UF26dFFkZKSOHz+uhg0bKiAgQDVr1lRsbKx27dqVbALVKlWqaObMmdny3JOcPn1a48eP1/jx41WuXDnVrVtXxYsXl8lkUkhIiHbu3Jls1a1BgwZl2+pAAAA7mQBkmzt37pjefvttU8GCBU2S7HrUq1fP9Msvv6RZ7zvvvGPKnz9/mvW4u7ubpkyZkmY9GzZsMJdv27atXc/pzJkz5mPKly9v51/igS+//NJUqFAhu/4WBoPB1LNnT6v1TJ482Vxu8uTJNtubMGFCun+nb7/91mQymZL9Pi2DBw9Os84NGzYkK1++fHnzvjNnzqRZtyNfW3ufvz0s2y9RokSW6goODrYrtpCQEFPDhg3T/NvVrFnTdOTIEdPs2bPNvxs6dKjNOs+fP28qVaqUzfpSfgbsrTel9N7PgYGB5v0uLi6m3bt3p1nf4sWLk5XftWuX3bHYcufOHVO/fv3S/dyWLFnStHLlynTry8jnIiMs6509e3aW6ho6dGim6zp79qzpkUcesfvcX6JECdOqVats1nfw4EFTxYoV0zxfTpgwwWQy2fdZzsjff/369aYKFSrY9TzeeOMNq3Vk9LOUZMeOHWk+76THo48+arp27VqazyOj77klS5aYDAaDXc/baDSaXnjhBVNsbGy69QIAshc9MYBs5O3trYkTJ+rFF1/UihUrtHbtWu3du9d8N83NzU2FCxdW9erVFRAQoN69e9s1fOK///2vnn76ac2YMUOrV6/WmTNndOvWLRUsWFAVK1ZU586dNWrUqGSrguQVY8eO1dChQ/XDDz9o7dq1OnjwoK5fv67o6Gj5+PioTJkyqlWrltq1a6euXbtmaYiBJL333nvq0qWLvvrqK23dulXXr183t/PYY49p5MiRqlKlSobqnDdvnrp166YFCxbowIEDunHjRrKl/bLCmV9bRytRooS2b9+uGTNmaNGiRfrrr78UGRmp4sWLq1q1aurfv78GDRokT09Pu4eGlC1bVgcPHtSXX36pNWvW6Pjx47pz5455SEduuHDhQrLhHG+99ZaaNGmS5jF9+/bVsGHDNGfOHMXFxWnQoEHav3+/vL29Mx2Ht7e3AgMDNW7cOP3www/auHGjLl++rKioKBUtWlS1a9dW9+7dNWLECLuHZ/2TlS9fXuvWrdOOHTu0ZMkSbd68WRcuXFBYWJhcXFxUpEgRValSRY0bN1anTp3Url0786Sg1tStW1eHDx/Wt99+q8WLF+vvv/9WTEyMSpUqpZYtW2r06NE51gOgQ4cOOn78uBYtWqTly5drz549unbtmmJiYuTr66vKlSurefPm6tOnj1q3bm21jsx+lpo1a6bg4GDNnz9fS5cu1YEDB3Tt2jW5urrKz89PrVq10oABA9SpU6dsf95PPvmkrly5ojVr1mjbtm06ePCgTp8+rVu3bklKXIK4atWqatWqlYYMGaKaNWtmewwAgPQZTKZcWDYAAAAAAAAgi5x3djgAAAAAAPBQIYkBAAAAAACcAkkMAAAAAADgFEhiAAAAAAAAp0ASAwAAAAAAOAWSGAAAAAAAwCmQxAAAAAAAIIVr165p+fLlmjRpkrp06aKiRYvKYDDIYDBo2LBhOdLmokWL1LlzZ5UsWVLu7u7y9/fX008/rZ07d9pdR2hoqCZPnqx69erJ19dXBQoUUL169TR58mSFhobmSNy5yWAymUyODgIAAAAAgLzEYDDY3Dd06FDNmTMn29qKjo5W3759tXz5cqv7jUaj3nzzTU2cODHNeoKCgtSrVy9duXLF6v5SpUrpt99+U+PGjbMcs6PQEwMAAAAAgDSULVtWnTp1yrH6R44caU5gtG/fXkuXLtXu3bs1c+ZMVapUSQkJCZo0aZJmzJhhs45Lly6pR48eunLlilxcXDR+/Hht3rxZmzdv1vjx4+Xi4qLLly+re/fuunTpUo49l5xGTwwAAAAAAFKYPHmymjRpoiZNmqhEiRI6e/asKlSoICl7e2Js2rRJ7dq1kyT16NFDv/76q/Lly2fef+PGDTVq1Ejnz59XoUKFdPr0aRUsWDBVPcOGDdPcuXMlSYsXL1bfvn2T7V+yZIn69esnSRo+fLhmzZqVLfHnNnpiAAAAAACQwltvvaXu3burRIkSOdrOhx9+KEnKly+fvvnmm2QJDEkqWrSopk6dKkkKCwvTzJkzU9Vx9epVzZ8/X5LUuXPnVAkMSerbt686d+4sSZo3b56uXr2arc8jt5DEAAAAAADAAe7evav169dLkjp27KgyZcpYLff444+rQIECkqRffvkl1f5ly5YpPj5eUmIvC1uSJiSNj4/XsmXLshK6w5DEAAAAAADAAXbv3q2YmBhJUtu2bW2Wc3NzU7NmzczH3Lt3L9n+LVu2mLfTqsdy39atWzMVs6O5ODoAAAAAAAAy6+LFi3aVs9XLwZGCg4PN29WrV0+zbPXq1bVmzRrFxcXpxIkTqlmzZqp6fH195efnZ7OOkiVLqkCBAgoPD0/WtjMhiQEAAAAAcFply5a1q1xeXNPiwoUL5u30kiyWz/PChQvJkhhJ9diTqClbtqyOHDmSrG1nQhIjhcXNWjk6BAB5WO9Vvzs6BAB5WEJcnKNDAJBHuRct5ugQsgXfl7LXnTt3zNve3t5plvXy8jJv371712o96dVhWU/KOpwFSQwAAAAAgNNy1h4FkhQdHW3ednNzS7Ns/vz5zdtRUVFW60mvDst6UtbhLEhiAAAAAACcVl6c68Je7u7u5u3Y2Ng0yyZNACpJHh4eqeqJjIxMtw7LelLW4SxIYgAAAAAA7GM0ODqCfxQfHx/zdnrDOyIiIszbKYeN+Pj4KDIy0q4hIkn12DP0JC9iiVUAAAAAABzAshdJequsWA6bSTmZaVI99qzUklSPvROi5jUkMQAAAAAAcADLFUaOHTuWZtmk/S4uLqpcubLVem7fvq2QkBCbdVy5ckXh4eGSpBo1amQqZkcjiQEAAAAAsIvBYMxzD2fWpEkT82ScmzZtslkuNjZWO3fuTHVMklatHqwak1Y9lvtatmyZqZgdzblfcQAAAAAAnJSPj48eeeQRSdK6detsDgf55ZdfzD0o+vTpk2p/z549ZTQmfr2fPXu2zfbmzJkjSTIajerZs2dWQncYkhgAAAAAAOSAOXPmyGAwyGAw6M0337Ra5tVXX5UkxcXFacyYMYqPj0+2/8aNG/rPf/4jSSpYsKBGjRqVqg4/Pz8NGjRIkrR69Wr99NNPqcosWbJEq1evliQ9/fTT8vPzy/TzciRWJwEAAAAA2MXwEK1OsnXrVp08edL8840bN8zbJ0+eNPdqSDJs2LBMtdOhQwc99dRTWrRokZYtW6aOHTtq3LhxKlWqlA4fPqz33ntP58+flyR98MEHKlSokNV63nvvPa1atUrXr1/XgAEDtGfPHnXv3l2StHz5cn3yySeSpGLFiundd9/NVKx5AUkMAAAAAABSmDFjhubOnWt137Zt27Rt27Zkv8tsEkOSZs2apfDwcK1cuVIbNmzQhg0bku03Go2aOHGiRo8ebbOOsmXL6vfff1fv3r0VEhKiqVOnaurUqcnK+Pn5aenSpclWRXE2DCcBAAAAAMCBPDw8tGLFCi1YsEAdO3ZU8eLF5ebmprJly2rgwIHaunWrzeEolgICAnT48GH997//Ve3ateXt7S1vb2/VqVNH//3vf/XXX38pICAg559QDjKYTCaTo4PISxY3a5V+IQAPrd6rfnd0CADysIS4OEeHACCPci9azNEhZIuf27Z3dAipPLFpQ/qF8I9BTwwAAAAAAOAUSGIAAAAAAACnwMSeAAAAAAD7GLgPDsfiHQgAAAAAAJwCSQwAAAAAAOAUGE4CAAAAALCLwWhwdAh4yNETAwAAAAAAOAWSGAAAAAAAwCkwnAQAAAAAYBeDgeEkcCx6YgAAAAAAAKdATwwAAAAAgF0MRu6Dw7F4BwIAAAAAAKdAEgMAAAAAADgFhpMAAAAAAOxjZGJPOBY9MQAAAAAAgFMgiQEAAAAAAJwCw0kAAAAAAHYxGBhOAseiJwYAAAAAAHAKJDEAAAAAAIBTYDgJAAAAAMAuBiP3weFYvAMBAAAAAIBTIIkBAAAAAACcAsNJAAAAAAB2YXUSOBo9MQAAAAAAgFMgiQEAAAAAAJwCw0kAAAAAAPYxMpwEjkVPDAAAAAAA4BRIYgAAAAAAAKfAcBIAAAAAgF0MBu6Dw7F4BwIAAAAAAKdAEgMAAAAAADgFhpMAAAAAAOxiYHUSOBg9MQAAAAAAgFMgiQEAAAAAAJwCw0kAAAAAAHYxGLkPDsfiHQgAAAAAAJwCPTEAAAAAAPYxMLEnHIueGAAAAAAAwCmQxAAAAAAAAE6B4SQAAAAAALsYjAwngWPREwMAAAAAADgFkhgAAAAAAMApMJwEAAAAAGAXg4H74HAs3oEAAAAAAMApkMQAAAAAAABOgeEkAAAAAAD7sDoJHIyeGAAAAAAAwCmQxAAAAAAAAE6B4SQAAAAAALsYDAwngWPREwMAAAAAADgFkhgAAAAAAMApMJwEAAAAAGAXg5H74HAs3oEAAAAAAMApkMQAAAAAAABOgeEkAAAAAAD7sDoJHIyeGAAAAAAAwCmQxAAAAAAAAE6B4SQAAAAAALuwOgkcjXcgAAAAAABwCiQxAAAAAACAU2A4CQAAAADALgZWJ4GD0RMDAAAAAAA4BXpiAAAAAADsYjDSEwOORU8MAAAAAADgFEhiAAAAAAAAp8BwEgAAAACAfQzcB4dj8Q4EAAAAAABOgSQGAAAAAABwCgwnAQAAAADYhdVJ4Gj0xAAAAAAAAE6BJAYAAAAAAGk4f/68Xn31VdWoUUNeXl4qXLiwmjZtqo8//liRkZGZrnfjxo0yGAwZerRr185qXf7+/nYd7+/vn+l48wKGkwAAAAAA7GJ4CFcnWbFihQYNGqTbt2+bfxcZGamgoCAFBQVpxowZWrlypSpWrJgr8VSrVi1X2smrSGIAAAAAAGDFwYMH1a9fP0VGRsrb21uvv/662rdvr6ioKC1atEjff/+9jh8/rm7duikoKEje3t4Zqr9JkyY6fPhwuuXGjh2rTZs2SZKGDh2aZtlevXrp3Xfftbnfzc0tQzHmNSQxAAAAAACwYty4cYqMjJSLi4vWrFmj5s2bm/d16NBBVapU0fjx43Xs2DFNmzZNkyZNylD9Xl5eql27dpplbt26pZ07d0qSKleurBYtWqRZvmDBgunW6cwevr5AAAAAAIDMMRry3iOHBAUFaePGjZKkkSNHJktgJHnllVdUo0YNSdJnn32me/fuZXscgYGBiomJkSQ9/fTT2V6/syGJAQAAAABACkuXLjVvDx8+3GoZo9GoIUOGSJLCwsLMSY/sNG/ePEmSwWAgiSGSGAAAAAAApLJlyxZJiUM+GjVqZLNc27Ztzdtbt27N1hhOnTql7du3S5Jat26tChUqZGv9zogkBgAAAADALhldDjQ3HjklODhYUuI8FC4utqeTrF69eqpjsktSLwwp/Qk9k2zevFl169aVl5eXPD09VaFCBfXv319Lly6VyWTK1vgcgYk9AQAAAABO6+LFi3aVK1OmjN11RkdH68aNG3YdV6hQIXl5eSkiIkIXLlywuw17zJ8/X5Lk4eGhJ5980q5jzpw5k+zns2fP6uzZs1q8eLFatmypwMBAlS5dOlvjzE0kMQAAAAAATqts2bJ2lctIL4Q7d+6Yt+1ZNjUpiXH37l2720jPli1bdPr0aUlSnz59VKBAgTTLu7m5qWfPnurUqZNq164tX19f3bp1Szt27NC3336rCxcuaNu2berYsaN27NghX1/fbIs1N5HEAAAAAADYxWB8OGYkiI6ONm+7ubmlWz5//vySpKioqGyL4YcffjBvJ00empbdu3erYMGCqX7frl07jR07Vk8++aTWrFmj4OBgvfXWW5o2bVq2xZqbSGIAAAAAAJxWdg/hkCR3d3fzdmxsbLrlk5ZA9fDwyJb2Y2JitGTJEklSqVKl9Oijj6Z7jLUERhIfHx8tXrxYlSpVUmhoqKZPn64PPvjArgRNXkMSAwAAAADgtDIy14W9fHx8zNv2DBGJiIiQZN/QE3v89ttvunXrliRp0KBBypcvX5br9PX11VNPPaWvv/5aERER2rNnj1q0aJHlenMbSQwAAAAAgH1ycDWQvMTd3V1FixbVjRs30p04NCwszJzEsHd+jvRYrkpiz1ASe9WsWdO8fenSpWyrNzc9HAOaAAAAAADIgBo1akiSTp48qbi4OJvljh07luqYrLh27ZpWr14tSWrYsKFq166d5TqT/BOWWCWJAQAAAABACq1atZKUOFRk7969Nstt2rTJvN2yZcsst7tw4UJz0iQ7e2FI0tGjR83bpUqVyta6c0uuJTE6dOigDh06aMSIEXYvO3P27Fl16NBBjzzySA5HBwAAAABIj8FozHOPnNK7d2/z9uzZs62WSUhIMA/9KFiwoNq3b5/ldpPqc3Fx0cCBA7NcX5Lbt28rMDBQkuTp6anGjRtnW925KdeSGBs3btSmTZs0d+5cNW/eXGfOnEn3mIiICG3cuFEbN27M+QABAAAAALivadOmat26tSRp5syZ2rFjR6oyn3zyiYKDgyVJL730klxdXZPtnzNnjgwGgwwGg95888102zxy5Ij2798vSerSpYuKFStmV6yrVq1Kc3nXO3fuqF+/fgoNDZUkjRw50rwsrLPJ9Yk9TSaTjhw5oqZNm+qnn35S27ZtczsEAAAAAEBmPCQTeyb5/PPP1bJlS0VFRalTp06aMGGC2rdvr6ioKC1atEjTp0+XJFWtWlWvvPJKltubO3eueXvo0KF2H/fBBx9o0KBBevzxx9WqVStVqlRJ3t7eunXrlnbs2KFvv/3WvBRttWrV7Eqo5FW5nsSYOHGiPv74Y4WGhqpTp0768ssv9eyzz+Z2GAAAAAAApKlBgwYKDAzU4MGDFR4ergkTJqQqU7VqVa1YsSLZsqyZkZCQoIULF0qSChUqpO7du2fo+Js3b2rGjBmaMWOGzTJt2rTRwoULVbhw4SzF6ki5PrFn//79tWnTJpUuXVr37t3T888/rxdffFEJCQm5HQoAAAAAAGnq0aOHDh06pJdffllVq1aVp6enChYsqMaNG2vq1Knav3+/KleunOV21q9fb172tH///hka7vHxxx/rgw8+UK9evVS9enUVLVpULi4uKlCggKpXr66hQ4dq1apV2rhxo0qXLp3lWB3JYMqlNVaMRqMMBoMOHz6smjVr6vLly+rdu7f27Nkjg8GgRx99VIGBgSpYsKD5mCNHjqhOnToyGAyKj4/PjTC1uFmrXGkHgHPqvep3R4cAIA9LSGMJPgAPN/ei9s1tkNdtGfeio0NIpfVnXzg6BOQihy2xWqpUKW3evFn9+/eXyWTSunXr1KxZM504ccJRIQEAAAAAgDzMYUkMSXJ3d9ePP/6ot956S5J04sQJBQQEaO3atY4MCwAAAAAA5EEOTWIkmThxohYvXiwPDw/dunVL3bp10xdf0CUIAAAAAPKSpOVC89IDD5c8kcSQpCeeeEJbtmxR2bJlFRcXp5dfflnjxo1zdFgAAAAAACCPyDNJDClx+Zpdu3apadOmMplM+vPPPx0dEgAAAAAAyCPyVBJDkvz8/LRp0yYNHDhQubRwCgAAAADAHkZD3nvgoeKSWw2dOXNGkuxakzZ//vyaP3++HnnkEZ0/fz6nQ4OTyV+ooArXrKnCNWskPmpUV/77S/OeWbFSQe9MyfY2yz76iCp07yrfypXk5uOj6Js3df3AQZ386VfdPHLErjrcChRQlX5PqnTbNvIs6SeDwaCIy1d0adNmnVj8k2LDw7M9buBhdiUkRAsCF2vz9m0KCbkqVzc3lStTRp0feUT9n3xCHu7u2dLOH2vWauny5fr75EmF37mjokUKq2G9+nrqySdVr07tNI/t3Lu3Ll8JSbeNUiX9tHrp0myJF0CiKyEhWvjTT9qyfYeuXL0qN1dXlS1TRp07tFe/xx/PvnPEunX6bcVKnTh1KvEcUbiwGtSrp6ce76O6tdM+R0iSyWTS2g0btHLNWh09flxht27JaDCoSJHCql2jpnp166qWAQHZEisAOAODyUm7O1y/fl3ffvutJGnSpEnZVu/iZq2yrS7kjH47t9rcl91JDKObm1pMeUelWrW0uj8hPl5HZ8zS0dlz06ynUI3qavXhB/IoVtTq/shr17Vt/GsKO3Y8yzEjZ/Ve9bujQ4AdNm/dptcmT9adu3et7vcvX17ffDpNZe1IrNsSExOjVyZM0Kat26zuNxqNen7UKD03coTNOkhi/PMkxMU5OgTYYfP27Zrw1tu2zxHlyunrjz9SmSyeI16dOFGbt223ut9oNOq5ESM0evgwm3XcuXtX4157XXv270+zrc6PPKL3Jv5Xrq6umY4XOc+9aDFHh5Attr4yztEhpNLqk88cHQJyUa71xMhu165d05tvvimDwZCtSQw4l4iQq7pz9qz8muXMHYgmb7xmTmBc3bNXJwKXKOrGDRWsVEnVhz4tn7JlVHv0M4oKDdWZZcut1uFRrKhafTxVHkWKKCEuTn//GKjL97/0lGrVUlUH9Jdn8WJq9cmHWjdspKKu38iR5wI8LI7/fUKvvvGGoqKj5enpqVFDh6hJo0aKiYnRH2vW6uffftPZc+c05t//1qLZs+Xp6Zmpdia99545gdG0USMN6t9fxYsV1YmTp/T93Lm6cPGivp4+XcWKFtETvXqlWVf7Nm30r+dG29zPFxMg+xw/cUL/N3GSoqOj5enhoZFPP60mjRoqOiZGq9et08/LftfZ8+c19v/Ga+GM7zN9jnjz/Q/MCYwmDRtqUL++Kla0qE6cOqWZ837QhUuX9M2MGSpWpIge79nDah2vTX7TnMAoXaqkhg0cqMoVKyouLl7Bx49p9oKFCrt1S6vXr1dB3wKa8MormfujABlgMOS5GQnwkHHaJAYeXkdmzNLN4GO6GRysmJth8izpp+6//pTt7RRrUF/lO3eSJF3aslXb/zNBpoQESVJY8DFd2rJVHefMlFdJP9Ud84Iu/rlR96zc0an93LPyKFJEkrRz0lu6+OcG874bBw/pZvAxtZjyjjyKFFHtZ59R0HvvZ/tzAR4mUz/9VFHR0XLJl0//++Jz1a9Tx7wvoHFjlS9bVtO++kpnzp7T3IU/6vlRIzPcRtC+fVq5eo0kqV3rVvps6lTly5dPklS7Zk21a9Na/YcO05WQEE376mt17NBBBXx8bNbn4+OtKpUqZTgOABn34edfKPr+OeK7zz5VPYshHQGNGqlcmbL69JtvdObcOc1bFKjnRgzPcBt79u/XyrVrJUltW7bUp+9PeXCOqFFD7Vq10oARI3Xl6lV9+s03erR9u1TniKPHjmnrzp2SpDKlSmnxnDny8nqQUGnaqKE6deigvsOG6c6du1qy9Dc9N2KEChcqlOF4AcCZkEaD0zkyY5aubNuumJthOdpOtcEDJSV2Dd734SfmBEaS2Nu3dejrxCFN+X0LqELP7qnqyF+4kDkRcmXHrmQJjCQX/9ygKzt2SZLKd+ms/IW5+AAy66+jRxW0b58kqU/PnskSGEmGDhqoiv7+kqT5gYG6l4nu/7N/mC9Jypcvn974v/HmLydJChUsqJfHjJEkhYeH69dlyzLcBoDs91dwsLlnQ+/u3ZMlMJIMGfCU+RyxYPHiTJ0j5ixYKOn+OeLVV6yeI1564XlJUvidO/p1eerenPsPHzZvD+rXL1kCI0lJPz/16tpNkpSQkKDDR49mOFYAcDYkMQArXDw8VKJxI0nS1aA9irp+3Wq5Sxs3KfZ+74sy7dqk2l+6dSsZXRI7PJ1dscJme2dXrJQkGV1cVLo187IAmfXnpk3m7d7du1ktYzQa1aNrV0mJCYagvXsz1EZkZKR27dkjSWrWtIn8ShS3Wu7R9u3k7eUlSVq3cWOG2gCQMzZs3mze7tWtq9UyRqNR3R/rLCkxwbBnX9rzUaQUGRmpXffPK82aNFaJ4jbOEW3bms8Rf27anGp/3L175u0ypUvZbK+sxb57sfdslgOyi8FoyHMPPFxIYgBWFK5ZQ/ny55ckXd93wGa5hLg43fzryP1jasqQ4k5L0Xr1zNtp1XN9/4N9RevWzXjAACRJew8clCR5eHioZvXqNss1btjAvL3/4KEMtXH46FHFxsYm1tOgoc1yrq6u5pUH/jpyNFN3cwFkr333P+8eHh6qWa2azXKNG1icIw5l8BwRHGw+RzSqX99mOVdXV9WpVUtSYi+ylOeI8mXLmbcvXrpss54LFvvKlyuboVgBwBmRxACsKHC/G6kkhZ87l2bZ8HOJywAbXVzkUzb5xUMB//KSpNg7dxR986bNOqJDQ809OnzuHwMg486cPStJKlemjFxcbE/7VKH8g8/Z6fvH2Ov0mQflK6TzeU1qJy4+XufPX7BZbu/+A3p80CA1bdtOTdq01WO9++jVN97Q+k2b5KSLiAF50pn7/9PLlS6d9jmi3IMEwplzZzPWhsU5xfJcY7Wd8ontxMXH6/yF5OeIFgFNVapkSUnSwiVLFBkVler4q9euadnKxN6c9WrXZm4dAA8FkhiAFR4W3cOjrl1Ls2zU1Qf7PVJ0K0/6Oeqa9eEo1urxtNE1HUDaYmJiFHbrliTZ7L6dxLdAAXl4eEiSQq5ezVA7IdcelPdLpx2/EiWsHpfSpcuXdeLkKUVFRys6JkaXrlzR6nXrNW78fzT02dG6ms55CED6LM8RxdP57BZIdo7I2OcvxOLzWqJYOucIizhCUnzO3dzc9P7kSfItUEAXLl1Sv6HDtGTpUu0/dEhB+/Zp7o8/6qkRIxV+545KlSyptydMyFCcQKYZjHnvgYcKq5MAVrhaLKcWZ+XOh6W46Af7XTw9rNaTXh2J9UQn1uGRuaXcgIddRGSkedvTwyONkok83N0VFRVl9e5mmu1EPGjHI512PDzczduRFvElcXVxVbvWrdUiIECVK1WUj7e37ty5o4OH/1LgL78o5OpV7T90SM/+60XNnzlDPt7eGYoVwAO5dY6w/Kx7eqZ3jniwPyoydTv169RR4OxZWvjTT1q45Ce9+9HHyfZ7enjo+ZEj1f/xPipUsGCG4gQAZ0USA7DC6OZm3k64l/Y49gSLSbSS5tFIWU/CvfQn2kq4P342X363dEoCsCZpDLqUONY8PW73P58xMTE51o6b64PPc7SVdhbOnmV16dUmjRppQN8n9e/XJ2j7rl06ffasvp0xQ+PHjctQrAAeSP7ZTf8S2M0t8fOd0XNEjGU7aQxZSYzjwTkkOjZ1OyaTSWs3btS6DRsVZ2VencioKK1ev16l/PzUs2uXDMUJAM7qoUliXLx40dEhwIkkWFyAGNO50DG6PbgAiU9xoZMQGyujh4eMdnyhSkp4xMfEplMSgDVuFsnHe3YkDpO+0ORPkXzMznZi7z34PLtbacdaAiOJl5eXPp7ynro+/oRu3b6tn5b+ppfHjLErQQMgteSf3fQn2o29f5Mio+eI/JbtpDOhr+U5xN0teTsJCQn6z+TJWnN/efY+3bur/xOPq2L58opPSNDxEyc0Z8FCbdy6VRPfe09/nzqpV//1rwzFCmQGq4HA0R6aJEbZsvbN1hwY0DKHI4EzuGfRFdQlnS6nLu4P9sel6Ap6LzJSLh4e6daRWE9it/O4qNRdzgGkz8tiGJg93b+j7g/hsqdbebJ2vB60E5VOO1FR0eZtT8+MDxXz8fbWYx07atFPPykqKkpHgoNVnxWMgEzJrXOE5Wc90soQkWRtWMThkWLoSeAvv5oTGM+PHKHnRoxItr9B3bpqULeu3njnHS1ftVo/LApU00aN1KZFiwzFCwDOhllQACssJ/P0SGfyr2STgKaY/CtpQk+P4sXSbTOpnsgMTiAGIFH+/PnNY8LTmwjzdni4+cuD5eSb9iiRxkR8KVlOGupXPGPtJKlUwd+8ffV6+pMEA7DO8hxxLZ3Pbniyc0TGJty2nMzz6vV0zhEWcaScKPjX5cslJSZfRgwebLOOF0ePNm//8vvvGYoVAJzRQ9MT48IF20vbWdr+5FM5HAmcQbjFEooFypfXZW2xWbbA/eXREuLidDfFsKXwM2dVuEZ1ufn4yL1wYZvLrLoXKSK3+xP23Tmb9pKuAGyr4O+vsAMHdP7iRcXFxdlcQvGMxdLJFS2WVLZHpQoVHtRz9pzU1nbZpHZc8uVTubJlMtROElZYBbJPhfLlFXbrls5fupT2OeL8eYtj/DPURkWLxOOZdJZpP3N/mXaXfPlUrkyZFPsSj63o759sKExKJYoXV5HChRV686bOnjtvsxyQXQysBgIHc9p3oJubm8qVK6fy6ay/naRMmTJ2PQBJuhkcrPj74+WLNaxvs5zRxUWFa9dKPOZosBJSjH29cfCQeTuteoo1eLDvxqHDGQ8YgCSpYb16khK7aB89dsxmuT379pu3G2RweEbtGjXM81Ls2b/PZrl79+7p0F9/SZJq1ayZ6bksTp05Y94uXrRopuoAkCjp8x4VFaWjx4/bLLdn/4NzRP06dTLURu3qD84Rew8csFnu3r17OnzkiCSplsV5JUm+fPkkSfHx8em2mTTpZ9IxAPBPlmtJjBUrVth1ErZXlSpVdPbsWZ0+fTrb6gSSxEVG6dqevZKkEk0ay6OY9eEgpdu1NfeguLRpc6r9l7dsVcL9971/t2422/Pv1lWSlBAfr8tbtmYpduBh1qFtG/P20uUrrJZJSEjQ7ytXSpJ8fHzUpHGjDLXh5eWlgMaNJUm7dgcpxMYQsHUbNupuRIQk6ZG2aXTXSMOdu3e1et06SYnLPdaqUSNT9QBI1L5Na/P2bytWWi2TkJCg5atWS5J8fLzVpFHDDLXh5eWpgEaJ55VdQXtsDm9bt2mT+RzRoU2bVPtLlywpSTp55ozC79yx2d6J06d1Ozw82TFAjjIa8t4DD5VcS2L06NFDfn5+Gjt2rLZv355bzQJW+Xfron47t6rfzq2qNWqE1TLHF/woKbG3RcP/+7cMxuQfFzdfX9Ud87wkKTb8jk4vW56qjuibN3V+9VpJUsnmASrTvl2qMmU6tFfJ5gGSpHOrVtsccgIgfXVq1VLD+vUlSb8uW6YDh1P3bJq7YKFOnz0rSRrcv1+qJRCXLl+uOgHNVCegmb75/nur7QwbPEiSFBcfr/c++ihVkj7s1i19+vXXkhITJY/36pmqjq07dig6OjrV75NERETo1Qlv6Nbt25KkPj17pNmlHED66tSsae6xtXT5ch2831vK0rwfF5nPEYP69k11jvhtxUrVa9lK9Vq20rczZ1ptZ8jAAZISzxFTPplm9Rzx+TffSkpMlDzeo3uqOtq2TJxsPjY2Vh9/+aVMVsaWxcTEaOqnn5l/btOSST0B/PPl6pwYoaGh+vbbb/Xtt9+qfPnyGjRokAYMGKCaNWvmZhhwckXr1ZV3mdLmn/P7FjRve5cpI/9uyddJP7vij0y1c23vPp1fs07lOj2q0m1aq80Xn+pE4GJFXb8h30qVVGPYEHmV9JMkHfrmO92zcZfk8HfT5dcsQO6FC6nZO2/q+MJFurItMZFXsmULVRuYOA9L9M0w/fWd9S9MAOz32r9f1pBnnlV0TIxGv/iSnhk6VE0aNVJMTIz+WLtWPy1dKknyL1dOQwcOzFQbAY0bq0vHjvpj7Vpt3LJFz/7rRQ1+qr+KFyumv0+e0vdz5uhKSIgkadwLL8i3QIFUdcycN0+vTZqsR9u3U4N69VS2dGl5enrqzp07Onj4LwX+8ot5YlD/8uX1wqhRmYoVQHLjx72kYc89r+iYGD037mWNGjJETRo2UHRMrFatX6eff1smSSpftqyGPDUgU20ENGqkxx59RKvWrdfGrVs1etzLGtyvn4oVLaoTp09pxtx5unL/8/3Sc8+pgJVzxNNP9devy5frZliYfluxUucvXFTf3r1VoXw5xSck6Njff2vhkp/MCZeK/v7q1bVr5v4oAOBEci2JERgYqIULF+qPP/5QbGyszp49qylTpmjKlCmqV6+eBg8erKeeekqlSpXKrZDgpCr07K4K3az/ky5Wr66K1Us+vj2zSQxJCnpvily8PFWqZQuVaNxIJVJ0O0+Ij1fw7Lk6vfQ3m3VEXbumrf/3H7WcOkUeRYuqxpDBqjEk+SzjUTduaNt/JiiKlQeALKtRrZo+eu9dvT75Td2NiNDn336bqox/uXL6eton8vLyynQ7b//3Dd2NiNCW7du1e+9e7d67N9l+o9Go0SOGq9/jfWzWcTs8XD//tsz8pcmaRg0aaOrbb8nX1zfTsQJ4oEbVqpr69lt64+13dDciQl/873+pypQvW1ZfffxRsiWVM+qtCRMUERGpLTt2KGjfPgXtSz6HjtFo1LPDhqpv795Wjy9UsKC+nTZN/35jgi5dvqL9hw5p/6FDVstWq1JFn33wfqbn3gEygok94Wi5lsTo27ev+vbtq1u3bumnn37SggULtGXLFiUkJOjAgQM6ePCgxo8fr7Zt22rw4MF64oknrGalgdwUHxOrra+MV7lOHeXfrYsKVqksV29vRd8M042DB3Vyyc8K/etIuvXcPHJUqwcNVdX+fVWqTWt53R+zGnHlsi5v3qq/Fy1W7P3xrACyrl3r1vp5wXzNDwzUlm3bdfXaNbm4uqpcmTLq9EgHDejbVx7u7llqw93dXd98Ok0rVq/Wb8tX6PiJE7pz966KFC6shvXraUDfvmlOCPjqiy9qZ1CQDh7+S2fPn9OtW7d1584dubu7q1ixoqpTq5a6duqkFgEBMhgY7wtkp3atWmnJvLlasHiJtmzfrqvXr8vV1UXlSpdRxw7t9dQTT2T9HJE/v776+COtXLNGv638Q3+fPHn/HFFIDevW01NPPqF6tWunWUf1qlX007x5+v2PP7Rhy1adOHVKt8PDZTAYVLhQQVWvUlUdO7RX50ceSTXsBQD+qQwmawPscsmlS5f0448/asGCBTp48GBiQPcv1Nzc3NStWzcNGjRI3bp1y7VxwIubtcqVdgA4p96rfnd0CADysJSrVAFAEvei1ieKdza7Jr7h6BBSCXjnPUeHgFzk0L5ApUuX1quvvqr9+/fryJEjmjBhgvz9/WUymRQTE6Nff/1VTz75pPz8/BwZJgAAAABAcvxKJKxO8tDLMwOaatSooXfffVenTp3Stm3b9MILL8jHx0cmk0m378/MDgAAAAAAHl55JomR5ObNmzp06JAOHTqku3fvOjocAAAAAACQR+SJGYCio6P122+/acGCBVqzZo3u3bsnSeb1sJs3b+7I8AAAAAAAYnUSOJ7DkhgJCQlau3atFixYoKVLlyoiIkLSg8RF9erVNWjQIA0cOFAVKlRwVJgAAAAAACCPyPUkxs6dO7Vw4UItXrxY169fl/QgcVGyZEk99dRTGjRokBo2bJjboQEAAAAAgDws15IYkyZN0sKFC3XmzBlJDxIXPj4+evzxxzVo0CA98sgj5iVWAQAAAAB5i4HVQOBguZbEePfdd83brq6ueuyxxzR48GD16NFD7u7uuRUGAAAAAABwUrk6nKRVq1YaNGiQ+vXrp0KFCuVm0wAAAAAAwMnlWhJj9uzZqlChgpo0aSIPDw+7jomOjtbu3bslSW3atMnJ8AAAAAAA6WH4Pxws15IYw4cPl9Fo1KFDh1SzZk27jrl06ZLatWsno9GouLi4HI4QAAAAAADkZbm6yG/SZJ65dRwAAAAAAPjnyPUlVjMiISFBkpQvXz4HRwIAAAAAMBhz9T44kEqefgeePXtWkuTr6+vYQAAAAAAAgMPlWE+M8+fPW/39lStX5O3tneaxMTExOnXqlCZOnCiDwaBatWrlRIgAAAAAAMCJ5FgSo0KFCql+ZzKZ1KlTpwzXNWTIkOwICQAAAACQBQZWJ4GD5VgSw9ZknBmZpNPd3V0vvviiRowYkV1hAQAAAAAAJ5VjSYzZs2cn+3n48OEyGAx65513VLp0aZvHGQwGubu7q2TJkmrQoEG6Q08AAAAAAMDDIceSGEOHDk328/DhwyVJvXv3Vs2aNXOqWQAAAABATmF1EjhYri2xumHDBknW58oAAAAAAABIT64lMdq2bZtbTQEAAAAAcgATe8LR6AsEAAAAAACcAkkMAAAAAADgFHJtOAkAAAAAwMkZuA8Ox+IdCAAAAAAAnAJJDAAAAAAA4BQYTgIAAAAAsIvByOokcCx6YgAAAAAAAKdAEgMAAAAAADgFhpMAAAAAAOxiYHUSOBjvQAAAAAAA4BRIYgAAAAAAAKfAcBIAAAAAgH1YnQQORk8MAAAAAADgFEhiAAAAAAAAp8BwEgAAAACAXVidBI7GOxAAAAAAADgFkhgAAAAAAMApMJwEAAAAAGAXA6uTwMHoiQEAAAAAAJwCSQwAAAAAAOAUGE4CAAAAALAPq5PAwXgHAgAAAACQhvPnz+vVV19VjRo15OXlpcKFC6tp06b6+OOPFRkZmaW633zzTRkMBrseGzduTLe+0NBQTZ48WfXq1ZOvr68KFCigevXqafLkyQoNDc1SrHkBPTEAAAAAAHZ5GCf2XLFihQYNGqTbt2+bfxcZGamgoCAFBQVpxowZWrlypSpWrOjAKBMFBQWpV69eunLlSrLfHzp0SIcOHdKMGTP022+/qXHjxg6KMOtIYgAAAAAAYMXBgwfVr18/RUZGytvbW6+//rrat2+vqKgoLVq0SN9//72OHz+ubt26KSgoSN7e3llq7/Dhw2nur1Chgs19ly5dUo8ePXT16lW5uLjo3//+t7p37y5JWr58uaZNm6bLly+re/fu2rt3r0qXLp2lWB2FJAYAAAAAAFaMGzdOkZGRcnFx0Zo1a9S8eXPzvg4dOqhKlSoaP368jh07pmnTpmnSpElZaq927dqZPvaNN97Q1atXJUkLFy5U3759zftat26txo0bq1+/frp69aomTpyoWbNmZSlWR2FODAAAAACAfQzGvPfIIUFBQeY5KEaOHJksgZHklVdeUY0aNSRJn332me7du5dj8aTl6tWrmj9/viSpc+fOyRIYSfr27avOnTtLkubNm2dOeDgbkhgAAAAAAKSwdOlS8/bw4cOtljEajRoyZIgkKSwszK6JN3PCsmXLFB8fL8l2rJI0bNgwSVJ8fLyWLVuWG6FlO5IYAAAAAACksGXLFkmSl5eXGjVqZLNc27Ztzdtbt27N8bisSYpVSh5PSnkh1qwiiQEAAAAAsIvBaMhzj5wSHBwsSapcubJcXGxPJ1m9evVUx2RWx44dVaRIEbm5ual48eJq166dPvjgA4WFhdkVq6+vr/z8/GyWK1mypAoUKJAtsToKE3sCAAAAAJzWxYsX7SpXpkwZu+uMjo7WjRs37DquUKFC8vLyUkREhC5cuGB3G9asW7fOvH39+nVt2rRJmzZt0tSpUzVnzhz16tXL6nFJ7drzHMuWLasjR45kOVZHIYkBAAAAAHBaZcuWtaucyWSyu847d+6Yt+1ZNjUpiXH37l2727BUp04d9e7dW02bNlWpUqV07949HT9+XAsWLNCaNWt069YtPfHEE/r999/VpUsXm/HaG6ukTMfqaCQxAAAAAAB2MeTgaiB5SXR0tHnbzc0t3fL58+eXJEVFRWW4rXHjxunNN99M9fuAgAANGTJE//vf//Tcc88pPj5eo0aN0smTJ+Xh4WE13pyONS8giQEAAAAAcFo5MSzC3d3dvB0bG5tu+ZiYGElKlVywR8GCBdPcP3r0aO3Zs0czZszQ5cuX9csvv2jQoEGp4o2MjMzxWPMCkhgAAAAAAKeVkbku7OXj42PetmfYRUREhCT7hnNkxujRozVjxgxJ0qZNm1IlMXx8fBQZGZknYs1pD0dfIAAAAABA1hkNee+RA9zd3VW0aFFJ6U8cGhYWZk4M2Ds/R0bVrFnTvH3p0qVU+5MSOfZMcprUcyWnYs1pJDEAAAAAAEihRo0akqSTJ08qLi7OZrljx46lOia7pTcpaVKS4/bt2woJCbFZ7sqVKwoPD5eUc7HmNJIYAAAAAACk0KpVK0mJwy/27t1rs9ymTZvM2y1btsyRWI4ePWreLlWqVKr9SbGmjCel3Ig1p5HEAAAAAADYxWA05rlHTundu7d5e/bs2VbLJCQkaN68eZISJ+hs3759jsTyv//9z7zdtm3bVPt79uwp4/2/ha1YJWnOnDmSJKPRqJ49e2ZvkLmEJAYAAAAAACk0bdpUrVu3liTNnDlTO3bsSFXmk08+UXBwsCTppZdekqura7L9c+bMkcFgkMFgsLqM6uHDh3Xy5Mk04/jf//6nmTNnSpL8/PzUp0+fVGX8/PzMk32uXr1aP/30U6oyS5Ys0erVqyVJTz/9tPz8/NJsN69idRIAAAAAAKz4/PPP1bJlS0VFRalTp06aMGGC2rdvr6ioKC1atEjTp0+XJFWtWlWvvPJKhuvfu3evRo0apfbt26tLly6qU6eOihQpori4OB07dkzz58/X2rVrJUn58uXT//73P3l5eVmt67333tOqVat0/fp1DRgwQHv27FH37t0lScuXL9cnn3wiSSpWrJjefffdzPw58gSSGAAAAAAA+xhyZjWQvKpBgwYKDAzU4MGDFR4ergkTJqQqU7VqVa1YsSLZsqwZER8fr3Xr1mndunU2yxQpUkQzZ85McwhI2bJl9fvvv6t3794KCQnR1KlTNXXq1GRl/Pz8tHTp0hxZlja3kMQAAAAAAMCGHj166NChQ/r888+1YsUKXbx4UW5ubqpcubL69u2rsWPHytPTM1N1d+3a1TxUZf/+/bp69apCQ0NlMplUuHBh1atXT4899piGDRumAgUKpFtfQECADh8+rM8//1xLly7V2bNnJUkVKlRQr169NG7cOBUpUiRTseYVBlN6a7U8ZBY3a5V+IQAPrd6rfnd0CADysIQ0luAD8HBzL1rM0SFki6Ozvnd0CKnUHPGMo0NALqInBgAAAADALjm5GghgD96BAAAAAADAKZDEAAAAAAAAToHhJAAAAAAAuxgestVJkPfQEwMAAAAAADgFemIAAAAAAOzDxJ5wMN6BAAAAAADAKZDEAAAAAAAAToHhJAAAAAAAuzCxJxyNnhgAAAAAAMApkMQAAAAAAABOgeEkAAAAAAC7GFidBA7GOxAAAAAAADgFkhgAAAAAAMApMJwEAAAAAGAfA/fB4Vi8AwEAAAAAgFMgiQEAAAAAAJwCw0kAAAAAAHYxGA2ODgEPOXpiAAAAAAAAp0ASAwAAAAAAOAWGkwAAAAAA7MPqJHAw3oEAAAAAAMApkMQAAAAAAABOgeEkAAAAAAC7sDoJHI2eGAAAAAAAwCmQxAAAAAAAAE6B4SQAAAAAALsYWJ0EDsY7EAAAAAAAOAWSGAAAAAAAwCkwnAQAAAAAYB9WJ4GD0RMDAAAAAAA4BXpiAAAAAADswsSecDTegQAAAAAAwCmQxAAAAAAAAE6B4SQAAAAAALsYmNgTDkZPDAAAAAAA4BRIYgAAAAAAAKfAcBIAAAAAgH1YnQQOxjsQAAAAAAA4BZIYAAAAAADAKTCcBAAAAABgF4OR++BwLN6BAAAAAADAKZDEAAAAAAAAToHhJAAAAAAA+xgMjo4ADzl6YgAAAAAAAKdAEgMAAAAAADgFhpMAAAAAAOzC6iRwNN6BAAAAAADAKZDEAAAAAAAAToHhJAAAAAAAuxiMrE4CxyKJkULvVb87OgQAedjSx3o4OgQAeVifP9c4OgQAAP7RGE4CAAAAAACcAj0xAAAAAAD2MXAfHI7FOxAAAAAAADgFkhgAAAAAAMApMJwEAAAAAGAXVieBo9ETAwAAAAAAOAV6YgAAAAAA7GJgYk84GO9AAAAAAADgFEhiAAAAAAAAp8BwEgAAAACAfYzcB4dj8Q4EAAAAAABOgSQGAAAAAABwCgwnAQAAAADYxWAwODoEPOToiQEAAAAAAJwCSQwAAAAAAOAUGE4CAAAAALCLgdVJ4GC8AwEAAAAAgFMgiQEAAAAAAJwCw0kAAAAAAPZhdRI4GD0xAAAAAACAUyCJAQAAAABAGs6fP69XX31VNWrUkJeXlwoXLqymTZvq448/VmRkZJbqDg8P16JFi/TMM8+oYcOGKliwoNzc3FSsWDG1a9dOH3/8sW7dupVuPf7+/jIYDOk+/P39sxSvoxlMJpPJ0UHkJbG3whwdAoA8bOljPRwdAoA8rM+faxwdAoA8ytXT09EhZIsr27c6OoRUSrZolaP1r1ixQoMGDdLt27et7q9WrZpWrlypihUrZrjuP/74Q3369FFMTEya5UqUKKEff/xR7du3t1nG399f586dS7fN8uXL6+zZsxkNNc9gTgwAAAAAAKw4ePCg+vXrp8jISHl7e+v1119X+/btFRUVpUWLFun777/X8ePH1a1bNwUFBcnb2ztD9YeGhiomJkZGo1EdO3bUY489pnr16qlgwYK6ePGiFixYoMDAQF29elXdu3fXtm3bVL9+/TTr7NWrl959912b+93c3DIUY15DEgMAAAAAACvGjRunyMhIubi4aM2aNWrevLl5X4cOHVSlShWNHz9ex44d07Rp0zRp0qQM1e/q6qrRo0drwoQJKleuXLJ9DRo0UI8ePdSyZUu9+OKLioyM1CuvvKL169enWWfBggVVu3btDMXhTJgTAwAAAABgF4PRmOceOSUoKEgbN26UJI0cOTJZAiPJK6+8oho1akiSPvvsM927dy9DbfTv31/fffddqgSGpX/9619q3LixJGnjxo0KDQ3NUBv/NCQxAAAAAABIYenSpebt4cOHWy1jNBo1ZMgQSVJYWJg56ZHd2rVrJ0lKSEjQmTNncqQNZ0ESAwAAAACAFLZs2SJJ8vLyUqNGjWyWa9u2rXl769acmfjUcuJPYw72PnEGD/ezBwAAAADYz2DIe48cEhwcLEmqXLmyXFxsTydZvXr1VMdkt02bNkmSXFxcVLly5TTLbt68WXXr1pWXl5c8PT1VoUIF9e/fX0uXLtU/YXFSJvYEAAAAADitixcv2lWuTJkydtcZHR2tGzdu2HVcoUKF5OXlpYiICF24cMHuNuy1YsUKHTp0SJLUuXNnFShQIM3yKYebnD17VmfPntXixYvVsmVLBQYGqnTp0tkeZ24hiQEAAAAAcFply5a1q1xGeiHcuXPHvG3PsqlJSYy7d+/a3YY9bt68qTFjxkiS8uXLp3feecdmWTc3N/Xs2VOdOnVS7dq15evrq1u3bmnHjh369ttvdeHCBW3btk0dO3bUjh075Ovrm62x5haSGAAAAAAAu+TkaiB5SXR0tHnbzc0t3fL58+eXJEVFRWVbDPHx8Ro0aJDOnTsnSfrvf/+rBg0a2Cy/e/duFSxYMNXv27Vrp7Fjx+rJJ5/UmjVrFBwcrLfeekvTpk3LtlhzE0kMAAAAAIDTyokhHO7u7ubt2NjYdMsnTbzp4eGRbTG88MILWrVqlSSpW7dumjhxYprlrSUwkvj4+Gjx4sWqVKmSQkNDNX36dH3wwQd2JWjyGpIYAAAAAAC7GHJwIs3MyshcF/by8fExb9szRCQiIkKSfUNP7PH6669r+vTpkqRWrVppyZIlypcvX5bq9PX11VNPPaWvv/5aERER2rNnj1q0aJEd4eaqh6MvEAAAAAAAdnJ3d1fRokUlpT9xaFhYmDmJYe/8HGmZOnWqPvjgA0lSw4YNtXz58mzr4VGzZk3z9qVLl7KlztxGEgMAAAAAgBRq1KghSTp58qTi4uJsljt27FiqYzLrm2++0WuvvWaua/Xq1dk6Aec/YYlVkhgAAAAAALsYjMY898gprVq1kpQ4VGTv3r02y23atMm83bJly0y398MPP2js2LGSpIoVK2rdunXm3iDZ5ejRo+btUqVKZWvduYUkBgAAAAAAKfTu3du8PXv2bKtlEhISNG/ePEmJE2u2b98+U2398ssvGj58uEwmk8qUKaP169dne5Lh9u3bCgwMlCR5enqqcePG2Vp/biGJAQAAAABACk2bNlXr1q0lSTNnztSOHTtSlfnkk08UHBwsSXrppZfk6uqabP+cOXNkMBhkMBj05ptvWm1nzZo1GjBggOLj41W8eHGtW7dO/v7+GYp11apVaS7veufOHfXr10+hoaGSpJEjR5qXhXU2rE4CAAAAALBPDg7fyIs+//xztWzZUlFRUerUqZMmTJig9u3bKyoqSosWLTKvIFK1alW98sorGa5/586d6tOnj2JjY+Xq6qpPP/1U9+7d019//WXzmDJlyqRaTvWDDz7QoEGD9Pjjj6tVq1aqVKmSvL29devWLe3YsUPffvuteSnaatWq2UyoOAOSGAAAAAAAWNGgQQMFBgZq8ODBCg8P14QJE1KVqVq1qlasWJFsWVZ7rVq1SpGRkZKke/fuadCgQekeM3v2bA0bNizV72/evKkZM2ZoxowZNo9t06aNFi5cqMKFC2c41ryCJAYAAAAAADb06NFDhw4d0ueff64VK1bo4sWLcnNzU+XKldW3b1+NHTtWnp6eDo3x448/1vr167Vjxw4dP35cN27c0K1bt+Tp6alSpUopICBAAwYMUKdOnWQwGBwaa1YZTP+ENVayUeytMEeHACAPW/pYD0eHACAP6/PnGkeHACCPcnXwl9zscuPgfkeHkErReg0cHQJy0cM1oAkAAAAAADgtkhgAAAAAAMApMCcGAAAAAMAuhodsdRLkPbwDAQAAAACAUyCJAQAAAAAAnALDSQAAAAAA9jFwHxyOxTsQAAAAAAA4BZIYAAAAAADAKTCcBAAAAABgF4PR4OgQ8JCjJwYAAAAAAHAKJDEAAAAAAIBTYDgJAAAAAMAuBiP3weFYvAMBAAAAAIBTIIkBAAAAAACcAsNJAAAAAAB2MRhYnQSORU8MAAAAAADgFOiJAQAAAACwDxN7wsF4BwIAAAAAAKdAEgMAAAAAADgFhpMAAAAAAOxiMHAfHI7FOxAAAAAAADgFkhgAAAAAAMApMJwEAAAAAGAXg9Hg6BDwkKMnBgAAAAAAcAokMQAAAAAAgFNgOAkAAAAAwC4GI/fB4Vi8AwEAAAAAgFMgiQEAAAAAAJwCw0kAAAAAAPYxcB8cjsU7EAAAAAAAOAWSGAAAAAAAwCkwnAQAAAAAYBeD0eDoEPCQoycGAAAAAABwCiQxAAAAAACAU2A4CQAAAADALgZWJ4GD5XoS4/z585IkX19f+fr62nVMfHy8Ll26JEkqV65cjsUGAAAAAADyrlxPo/n7+6tChQqqUKGC1q5da9cxx44dk7+/vypWrJjD0QEAAAAAgLzKIX2BTCaTbt26pW7duumLL77I0HEAAAAAAMcwGI157oGHi0NecYPBIF9fX8XFxenll1/Ws88+q7i4OEeEAgAAAAAAnITD0la//vqrWrRoIZPJpJkzZ+rRRx9VaGioo8IBAAAAAAB5nMOSGMWLF9eGDRs0bNgwmUwmbdmyRU2bNtXRo0cdFRIAAAAAIC1GQ9574KHi0AFErq6umjVrlj788EMZDAadPXtWzZs31/Llyx0ZFgAAAAAAyIPyxCwor776qn777Td5e3vrzp076t27tz788ENHhwUAAAAAsGAwGPPcAw+XPPOKd+vWTdu3b5e/v78SEhL0+uuva+jQoYqNjXV0aAAAAAAAIA/IM0kMSapVq5aCgoLUpk0bmUwmzZ8/X+3atVNISIijQwMAAAAAAA6Wp5IYklSkSBGtW7dOo0aNkslk0q5du/T44487OiwAAAAAeOgZjIY898DDJc8lMSTJxcVF06dP17Rp02Q0GnX37l1HhwQAAAAAABzMJbcbbNOmjQwGg7y8vNItO27cOFWvXl0DBgzQ7du3cyE6AAAAAACQV+V6EmPjxo0ZKv/YY4/pzJkzJDEAAAAAwNFYDQQOlutJjMwoWLCgChYsaHXfiRMn1LlzZxkMBp06dSp3AwMAAAAAALnGKZIYaYmNjdXZs2dlMDChCwAAAAAA/2ROn8QAAAAAAOQOVgOBozGgCQAAAAAAOAWSGAAAAAAAwCkwnAQAAAAAYBcDq5PAwXgHAgAAAAAAp0ASAwAAAAAAOAWGkwAAAAAA7GNgdRI4Fj0xAAAAAACAUyCJAQAAAAAAnALDSQAAAAAAdjEwnAQORk8MAAAAAADgFEhiAAAAAAAAp+D0w0mKFy+uyZMnOzoMAAAAAPjnM3IfHI6VJ5IYJpNJp0+f1s2bNyVJhQsXVoUKFWS04wNSrFgxkhgAAAAAADwEHJrEWL16tb766itt3LhRkZGRyfZ5enqqffv2Gjt2rDp16uSgCAEAAAAAQF7hkL5AsbGxGjBggLp27aqVK1cqIiJCJpMp2SMiIkIrVqxQly5dNHDgQMXGxjoiVAAAAABAEoMh7z3wUHFIT4yBAwfq119/lclkkouLizp27KiAgAD5+fnJZDLp6tWr2r17t9auXat79+4pMDBQcXFxWrx4sSPCRR52JSRECwIXa/P2bQoJuSpXNzeVK1NGnR95RP2ffEIe7u7Z0s4fa9Zq6fLl+vvkSYXfuaOiRQqrYb36eurJJ1WvTu00j+3cu7cuXwlJt41SJf20eunSbIkXeFjlL1RQhWvWVOGaNRIfNaorf8GCkqQzK1Yq6J0p2d5m2UcfUYXuXeVbuZLcfHwUffOmrh84qJM//aqbR47YVYdbgQKq0u9JlW7bRp4l/WQwGBRx+YoubdqsE4t/Umx4eLbHDeCBK1euaP6PP2rz1q0KuXIl8XqibFl17tRJT/XtKw8Pj2xra+WqVVq6bJn+PnFC4eHhKlqkiBo2bKgB/fqpXt26dtVx69Ytzf/xR/25YYMuX7kik8mk0qVKqUP79ho8YIAK3j/vAcA/kcFkMplys8EVK1aoR48eMhgMateunWbNmqXy5ctbLXv+/HmNGDFCf/75pwwGg37//Xd17do1R+OLvRWWo/Uj+2zeuk2vTZ6sO3fvWt3vX768vvl0msqWLp3pNmJiYvTKhAnatHWb1f1Go1HPjxql50aOsFkHSYx/lqWP9XB0CEhDv51bbe7L7iSG0c1NLaa8o1KtWlrdnxAfr6MzZuno7Llp1lOoRnW1+vADeRQranV/5LXr2jb+NYUdO57lmJHz+vy5xtEhIIM2bdmi1yZMsHk9UcHfX998+aXKlimTpXZiYmL07/HjtWnzZqv7jUajXhg9Ws89+2ya9Rw+ckQvjhun6zduWN1fvFgxffHpp6pdq1aW4kX2c/X0dHQI2eKejc+KI7l6ezs6BOSiXO+JMWfOHElSvXr1tGrVKrm6utosW65cOf3xxx8KCAjQwYMHNXv27BxPYsA5HP/7hF594w1FRUfL09NTo4YOUZNGjRQTE6M/1qzVz7/9prPnzmnMv/+tRbNnyzOT/zQmvfeeOYHRtFEjDerfX8WLFdWJk6f0/dy5unDxor6ePl3FihbRE716pVlX+zZt9K/nRtvcn9ZnAUDGRYRc1Z2zZ+XXLCBH6m/yxmvmBMbVPXt1InCJom7cUMFKlVR96NPyKVtGtUc/o6jQUJ1ZttxqHR7FiqrVx1PlUaSIEuLi9PePgbp8/5xTqlVLVR3QX57Fi6nVJx9q3bCRirpu/UsLgMw5dvy4Xh0//sH1xIgRatq4ceL1xOrV+umXX3Tm7Fm98OKLCpw/P9PXE5I06a23zAmMpk2aaPCAASpWvLhOnDih72fN0oULF/TVt9+qaNGievLxx63WcfXaNY196SWFhobKxcVFQwYPVtvWrSUlJmPmzZ+va9eva8xLL2nxwoUqUbx4puMFgLwq15MYO3fulMFg0CuvvGLXlzZXV1e9+uqrGjx4sHbu3JkLEcIZTP30U0VFR8slXz7974vPVb9OHfO+gMaNVb5sWU376iudOXtOcxf+qOdHjcxwG0H79mnl6sQ7au1at9JnU6cqX758kqTaNWuqXZvW6j90mK6EhGjaV1+rY4cOKuDjY7M+Hx9vValUKcNxALDfkRmzdDP4mG4GByvmZpg8S/qp+68/ZXs7xRrUV/nOiZNOX9qyVdv/M0GmhARJUljwMV3aslUd58yUV0k/1R3zgi7+udHqnavazz0rjyJFJEk7J72li39uMO+7cfCQbgYfU4sp78ijSBHVfvYZBb33frY/F+BhNvXjjxOvJ1xcNP2bb1S/Xj3zvoCmTVWuXDlN++wznTlzRnN/+EHPj7Z9MyItQXv2aMUff0iS2rVpo8+nTTNfU9SpVUvt27ZVv4EDE68pPv9cnTp2tHpN8cVXXyk0NDQx9ilT1LljR/O+Rg0bqlbNmnpl/HiFhobqy2++0btvvpmpeAGkdv78eX3xxRdasWKFzp8/r/z586ty5crq16+fXnjhhSwlOS0tWrRIs2fP1qFDhxQWFiY/Pz+1bt1aY8aMUbNmzeyqIzQ0VF988YWWLl2qs2fPymQyqUKFCurdu7defPFFFbl/7eGscn1iz+vXr0uSatasafcx1atXlyTdsNFtDg+Xv44eVdC+fZKkPj17JktgJBk6aKAq+vtLkuYHBupeXFyG25n9w3xJUr58+fTG/403X2wkKVSwoF4eM0aSFB4erl+XLctwGwCy15EZs3Rl23bF3MzZoYHVBg+UJCXExWnfh5+YExhJYm/f1qGvv5Uk5fctoAo9u6eqI3/hQuZEyJUdu5IlMJJc/HODruzYJUkq36Wz8hculK3PA3iYHT5yREF79kiS+vTqlSyBkWTY00+rYoUKkqQfFi7UvXv3MtXWrLmJw8ry5cun/06YkPqaolAhvfzSS5ISryl++fXXVHXcCA3V8pUrJUktW7RIlsBI0rljR7Vs0UKS9Pvy5bpxP+EBZCtDHnzksBUrVqhu3br65JNPdOzYMUVGRiosLExBQUH6v//7PzVs2FCnT5/OUhvR0dHq0aOHBgwYoDVr1igkJEQxMTE6d+6c5s+fr5YtW+qdd95Jt56goCDVqVNHb7/9tg4dOqTw8HDduXNHhw4d0ttvv626detqz/1zn7PK9SSGl5eXJJmzyPa4efOmJGVbdgvO7c9Nm8zbvbt3s1rGaDSqx/2hR+Hh4QrauzdDbURGRmrX/Q93s6ZN5FfCenfMR9u3k/f99/S6jRsz1AYA5+Ti4aESjRtJkq4G7VHU/eR8Spc2blLs/d4XZdq1SbW/dOtWMrokdog8u2KFzfbOrkj80mJ0cVHp1q2yFDuAB/7c8CBx2MfGkFCj0aie3ROTkJm5npDuX1Ps3i1Jah4QIL8SJayW6/jII/K+P65/3Z9/ptq/cdMmxcfHS5J69+xps71ePRLnboqPj9dGi2smAJlz8OBB9evXT7dv35a3t7fee+89bd++XevXr9czzzwjSTp+/Li6deumu1mYL2TkyJFavjxx+Gn79u21dOlS7d69WzNnzlSlSpWUkJCgSZMmacaMGTbruHTpknr06KErV67IxcVF48eP1+bNm7V582aNHz9eLi4uunz5srp3765Lly5lOlZHy/UkRrVq1SRJgYGBdh+zaNGiZMfi4bb3wEFJkoeHh2re76VjTeOGDczb+w8eylAbh48eNS/r27hBQ5vlXF1dVbd24uokfx05mqkeHwCcS+GaNZQvf35J0vV9B2yWS4iL082/jtw/pqYMKe68FrW465tWPdf3P9hX1M6VCwCkb9/9Xp0eHh6qWaOGzXKNGzV6cMz+/Rlu5/Bffz24prCoKyVXV1fVvd+79K8jR1L1+th7P15JapJGPU2yGC+A5MaNG6fIyEi5uLhozZo1mjBhgpo3b64OHTpo+vTp+vDDDyVJx44d07Rp0zLVxqZNm7Rw4UJJUo8ePbR27Vr16tVLTZo00YgRI7Rz506VK1dOkjR+/HjdunXLaj1vvPGGrl69KklauHChpk6dqtatW6t169aaOnWquY2rV69q4sSJmYo1L8j1JEbPnj1lMpk0e/Zs8ySfaZkzZ45mz54tg8Gg3r1753h8yPvOnD0rSSpXpoxcXGxP61LBYtWb0/ePsdfpMw/KV/C3vnpOynbi4uN1/vwFm+X27j+gxwcNUtO27dSkTVs91ruPXn3jDa3ftEm5vEgQgCwocH+omiSFnzuXZtnwc+clJfai8ClbNkU9ieeO2Dt3FH2/x6E10aGh5h4dPumcjwDY7/SZM5KkcmXLpn09cX84iSSduX9MZtpJWZfVtu6fX+Li4nT+/Hmr9fh4e6toUeurGUlSsWLFzD06TmciXiBdBkPee+SQoKAgbbzf23rkyJFq3rx5qjKvvPKKatxPhH722WeZGnaWlAjJly+fvvnmm1RDzooWLaqpU6dKksLCwjRz5sxUdVy9elXz5ycOh+/cubP69u2bqkzfvn3VuXNnSdK8efPMCQ9nk+tJjH/9618qWbKkTCaTRo4cqW7duunnn3/WxYsXde/ePd27d08XL17Uzz//rK5du2rkyJEymUwqVaqUxo4dm9vhIo+JiYlR2P3MY3ozbvsWKGBe1z0kgx/QkGsPyvul045lt1DL41K6dPmyTpw8pajoaEXHxOjSlStavW69xo3/j4Y+O1pXr13LUIwAHMPDYnhZVDqf26irD/Z7pBiWlvRz1DXrw1Gs1eNpY2gbgIxJdj1hY3hHkmTXEyHpL5mekuUx6V27+Pn5PTguxbVL0s/pxSs9uDbJ6PUPgOSWLl1q3h4+fLjVMkajUUOGDJGUmGDYmMEh5nfv3tX69eslSR07dlQZG8s5P/744ypQoIAk6Zdffkm1f9myZeYhZ7ZilaRhw4ZJShxytsxJ5/TL9dVJvLy8tHz5cj366KMKCwvTqlWrtGrVKpvlTSaTChUqpOXLlzMnBhQRGWne9rx/QZEWD3d3RUVFKTIqKmPtRDxoxyOddjw83M3bkRbxJXF1cVW71q3VIiBAlStVlI+3t+7cuaODh/9S4C+/KOTqVe0/dEjP/utFzZ85Qz6scw3kaa4W/4vi0jm3xEU/2O/imfxcklRPenUk1hOdWIcH/weB7BAREWHetut6wsMjU9cTUoprl3SuZT3cbV9TRN6P2Z7r4aRrF2vXJQDst2XLFkmJ32EbpTGMq23btubtrVu3qqOViXdt2b17t2JiYlLVk5Kbm5uaNWumNWvWaPfu3bp3716y1T6TYk2vnpSxJs3r4UxyvSeGJDVo0ECHDx/WE088IaPRKJPJZPVhNBr15JNP6tChQ6pnZcZoPHySxpRKsmuJXjc3N0kynxhyoh03VzfzdrSVdhbOnqUvP/5IA/o+qSYNG6p61apq0qiRRg0bqqU/LlSLgABJiUNevk1joh4AeYPR7cFnPuFe2vPgJMQ+6FKaNI9GynoS7Oh2mnD/nJQvv1s6JQHYIyaT1xPW/s+n25bFMeleU7jZvqZIitk1jaEv5nrut5PR6x8AyQUHB0uSKleunOaws+oW8/QlHZPRNlLWk1Y7cXFxOnHihNV6fH19k/XqSqlkyZLmHh0ZjTWvyPWeGElKlSqlJUuWKCQkRBs2bNBff/1lXoWkcOHCql27ttq1a6eSJUtmS3sXL160q1xxb69saQ85w/Kfuz3jzZKSEflTfHnIznZi7z24EHK30o61dd6TeHl56eMp76nr40/o1u3b+mnpb3p5zBi7LqgAOEaCxZcfo2va/0aNbg8+y/EpvkwkxMbK6OEhox2f96SER3xMbDolAVy9dk3h4eFW9xUoUEAlihdX/kxeT1j7P58ey2uQdK8pYm1fU+R3c1NUdLRdk4jH3m8no9c/gLOy97ueraEa1kRHR+vGjRt2HVeoUCF5eXkpIiJCFy7YniPPGsvy6bVT1mJ+rQsXLqhmzZqp6rHnOZYtW1ZHjhzJcKx5hcOSGEn8/Pw0YMCAHG+nbIoJ1WyJCbM9uRocz8uiC6U9XTqj7nfBtqeraLJ2vB60E5VOO1FR0ebtzAx58vH21mMdO2rRTz8pKipKR4KDVZ8VCIA8655F92yXdM4tLu4P9sdFJj+X3IuMlIuHR7p1JNaT2MU8Loqu4UB6vvjqK/32++9W9/Xq0UPvvf22vLwe3LSy63rifpmMXk9IKa5d0hnekXTdIqW+pvD08lJUdLRdQ0TM8TIUGw8Je7/rZWQy/Tt37pi3ve0Y7p2UxMjoMqsZacfy3JWynaR67I3VWh3OwiHDSYDMyp8/vwoVLChJ6U6EeTs83PxP3Naa7LZYTrwVkk47lpNm+RXPWDtJKlXwN29fvZ7+JH8AHMdyMk+PdCbpSzYJ6NXk55KkCT09ihdLt82keiKvMgEwkB2SXU+kM/llsuuJNLpo22I5EWd61y6Wk4CmvHZJujaxZzWBpGuTjF7/APYx5MFH9ou2SCpa9tK2JannU3o3QLPSjmXvqpTtJNWTk7HmFQ7viZFbnLWrDFKr4O+vsAMHdP7iRcXFxdkcn3bGYunDihZLItqjkuVyamfPSbbnxjG345Ivn8qVtb+LmiVWWAWcR7jFEswFypfXZW2xWbZA+cQ13RPi4nQ3RVfX8DNnVbhGdbn5+Mi9cGGby6y6Fykit/t3Ve6cTXtJVwDSe2+/rffefjvdchUrVNDe/ft1/sKFtK8nMrBEqjWVKlZMXlf79jbLJi0j7+LionLlyqWq52hwsO7cvasbN27YXGb1+vXr5rurFTMRL+CMcuK7nrvFRLuWQ71sSZqDJr1FAbLSjuU8NynbcXd3V2RkZI7GmlfkWBJj8+bN5u02bdpY/X1mWNaVEfaOf4q9FZap+pF7Gtarp30HDigqKkpHjx1T3dq1rZbbs2+/ebtBBodn1K5RQ66urrp375727N+nUUOHWC137949HfrrL0lSrZo1Mz2XxSmLC6Tiaaz9DsDxbgYHKz42Vvnc3FSsYX0d+2G+1XJGFxcVrl0r8ZijwUpIMY79xsFD8u/6mCSpWMP6urDuT6v1FGtQ/8Exhw5nwzMAICVONL93//7E64ngYNWtU8dquT179z44pn79DLdTu1atB9cUe/dq1IgRVsvdu3dPhw4nfsatXVM0bNBAv69YIUkK2rtXXTp3tlpPUBbjBZxRRua6sJePxbx29gy7SFr1yJ7hHJltx3JlpZTt+Pj4KDIyMkdjzStyLInRrl07GQwGGQwGxVlcuCX9PjNS1oWHU4e2bTRj7lxJ0tLlK6wmMRISEvT7ypWSEj/QTRrbXhLJGi8vLwU0bqytO3Zo1+4ghVy9Jr8SqbuNr9uwUXfvnwQeSWMpo7TcuXtXq9etk5S4tFqtGjUyVQ+A3BEXGaVre/aqZIvmKtGksTyKFVOUlWFgpdu1NfeguLQpdQL/8patShj/ioz58sm/WzebSQz/bl0lSQnx8bq8ZWs2PhPg4fZI+/aaMWuWJOnX336zmsRISEjQsuXLJSVO1N20ceMMt+Pl5aVmTZtqy7Zt2rl7t0KuXrU6zGPt+vXmLx+PdOiQan/7tm31zpQpSkhI0NJly2wmMZLmAzEajWqfyWsTAIk9G4oWLaobN26kO3FoWFiYOTFg7/wcSSwTMBcvXlTjNM4zlj1OUrZTpkwZXb161a5JTpPqyWiseUWOzomRtFSqrd9n5gHUqVVLDe/fWfh12TIdOJz6zuTcBQt1+n6XzMH9+6Vajmzp8uWqE9BMdQKa6Zvvv7fazrDBgyRJcfHxeu+jjxQfH59sf9itW/r0668lJSZKHu/VM1UdW3fsSDbOLaWIiAi9OuEN3bp9W5LUp2cPu8axAcg5/t26qN/Oreq3c6tqjbJ+x/T4gh8lJfa2aPh//5bBmPzfqZuvr+qOeV6SFBt+R6eXLU9VR/TNmzq/eq0kqWTzAJVp3y5VmTId2qtk88RlmM+tWm1zyAmAjKtTu7YaNWggKTGJceDgwVRl5vzwg07f7y05aOBAqz0uly5bptoNGqh2gwb6+rvvrLY1bEhij864uDi99/77qa8pwsL06eefS0pMljzRp0+qOooWLapuXbpIkrZt3641a9emKrN67Vpt275dktSjWzebQ04A2KfG/ZuLJ0+eTPNm+rFjx1IdYy/LFUYs60mrHRcXF1WuXNlqPbdv3042v05KV65cMa/glNFY84oc64mxYcOGDP0eyIjX/v2yhjzzrKJjYjT6xZf0zNChatKokWJiYvTH2rX6aelSSZJ/uXIaOnBgptoIaNxYXTp21B9r12rjli169l8vavBT/VW8WDH9ffKUvp8zR1funyDGvfCCfO+vt2xp5rx5em3SZD3avp0a1KunsqVLy9PTU3fu3NHBw38p8JdfzJNv+ZcvrxdGjcpUrAASFa1XV95lSpt/zu9b0LztXaaM/Lt1SVb+7Io/MtXOtb37dH7NOpXr9KhKt2mtNl98qhOBixV1/YZ8K1VSjWFD5FUycQLAQ998p3sWM49bOvzddPk1C5B74UJq9s6bOr5wka5sS/wCUrJlC1Ub+JQkKfpmmP76znrCFUDmvTZ+vJ4ePlzR0dF69oUX9MyIEWrapEni9cTq1Vry88+SEv9HD3v66Uy3E9C0qbp07qw/Vq/Whk2b9Mzzz+vpgQNVrFgxnTh5UtNnznxwTfHii1avKSTpxbFjtW37dt0MC9P4CRN05OhRtb0/1HrT5s2aOz9xeFvhQoX0rzFjMh0vgEStWrXSli1bFBERob179yogIMBquU2bNpm3W7ZsmaE2mjRpIjc3N8XGxmrTpk167bXXrJaLjY3Vzp07kx2TMtYffvjBHE///v2zPda8wmCie0MyzInhPDZu2aLXJ79pHs6Rkn+5cvp62icqZ6Wb1NLlyzXxnXclSc+PGqkXnnnGah3R0dH69+sTtOX+XY2UjEajRo8YbvP44c8/n2xuDlsaNWigqW+/lWxVFORNSx/r4egQkIYmEyeowv3hF/ZY3KxVqt/5d+uiphPfkCQdmTFLR2bMsnpsvvxuaj7lXZVq2cLq/oT4eAXPnmvz+CSFa9VUy6lT5GHjjmnUjRva9p8JunnkaJr1IG/o8+caR4eADNq4aZNe++9/bY4j9y9fXt988UWqiTaTLF22TP+dPFmS9Pzo0Rrz3HNWy0VHR+vl//s/bdlqfViY0WjU6GeesXl8kkOHD+vFf/9bN27csLq/aNGi+mLaNJtzfMBxXP8hS97G2rHMb25zy6G/7e7du82Ji9GjR+s7K72tEhISVLt2bQUHB6tgwYK6du1ahufJ69q1q/744w+5uLjozJkzVuf4WLRokQYMGCBJ+vDDD/V///d/yfaHhISodOnSSkhIUOfOnbVq1SqrbT322GNavXq1jEajLl26lKlVlxyNJVbhtNq1bq2fF8zX0wOekn+5cvJwd5ePj49q1aihl8eO0eIf5llNYGSEu7u7vvl0mj54+y01b9pUhQsVkqurq/xKlFDXzp00d/r/bCYwJOnVF1/UuDEvqH2bNqrgX16FChaUS7588vbyUgX/8urZrau++/wzzf72GxIYgJOJj4nV1lfGa+ektxSya7eib95UfGysIkKu6tzqNdow+oV0ExiSdPPIUa0eNFRHZ83RrZOndC8iUvciInXr5EkdnTVHqwcOIYEB5KB2bdvql8BADRk0SP7ly8vD3V0FfHxUq2ZN/full7Tkxx9tJjAywt3dXd9++aWmTpmi5s2aqXDhwonXFH5+6tali+bNmpVuAkOS6tapo18XL9boUaNUpXJleXp6ytPTU1WqVNHoUaO0dMkSEhhANmnatKlat24tSZo5c6Z27NiRqswnn3yi4OBgSdJLL72UKoExZ84c81yRb775ptV2Xn31VUmJQ87GjBmTasjZjRs39J///EeSVLBgQY2y0nvbz89PgwYlDodfvXq1fvrpp1RllixZotWrV0uSnn76aadMYEj0xEiFnhgA0kJPDABpoScGAFvoiZFzcqonhiTt379fLVu2VFRUlLy9vTVhwgS1b99eUVFRWrRokaZPny5Jqlq1qvbs2ZNstREpMYkxfPhwSdLkyZNtJjIGDBigRYsWSZLat2+vcePGqVSpUjp8+LDee+89nTp1SpL03XffafTo0VbruHDhgho1aqTr16/LxcVFr7zyirp37y5JWr58uT755BPFxcWpWLFi2rdvX46s6pIbcmxODAAAAAAAnFmDBg0UGBiowYMHKzw8XBMmTEhVpmrVqlqxYkWqBEZGzJo1S+Hh4Vq5cqU2bNiQai5Jo9GoiRMn2kxgSImrjfz+++/q3bu3QkJCNHXqVE2dOjVZGT8/Py1dutRpExhSDiYxRthYAzsrDAaDZs6cme31AgAAAABgTY8ePXTo0CF9/vnnWrFihS5evCg3NzdVrlxZffv21dixY+WZxd4gHh4eWrFihRYuXKg5c+bo4MGDunXrlkqUKKHWrVtr7Nixat68ebr1BAQE6PDhw/r888+1dOlSnb2/YmOFChXUq1cvjRs3TkWKFMlSrI6WY8NJjEajDAZDttVnMplkMBhSjQ/KbgwnAZAWhpMASAvDSQDYwnCSnJOTw0mQ9+RYT4xy5cqlmcSIjIzU9evXzT+7ubmpcOHCMplMCgsLU2xsrKTE3hdFixbNcmYLAAAAAJA1zKgIR8uxJEZStxVr9u3bpyeffFJhYWF65plnNGLECNWvX1/58uWTJMXH/397dx4XVfX/cfw9bIKICrnigpqamvtuLqDmkmipqamVW2q7+W37Vr9My+/XrGyzrG+aS4uWlntqruCSe2mYK5K44I64AIIs9/cHMoEwMMAww+jr+XjM43Gde+45H0quM597Puek6M8//9TMmTM1Y8YMeXt76+eff1bTpk0LK1wAAAAAAFDE2X13kjNnzqhJkya6cuWKVq5cqY4dO+bYfuPGjerevbtKlSqlPXv2qGLFioUaH+UkAHJCOQmAnFBOAsCS26WcJCEuztEhZOHp7e3oEGBHLvYecMqUKTp//rzGjh2bawJDkgIDAzV27FidP39eH3zwgR0iBAAAAAAARZHdkxi//PKLTCaTgoODrb4mve2KFSsKKywAAAAAAFDEFdqaGJacOnVKkuTp6Wn1Nelt068FAAAAANgfC3vC0ew+E8P7Zr3Srl27rL5m586dksQOJQAAAAAA3MHsnsRo3ry5DMPQpEmTMm2xasn58+f17rvvymQyqUWLFnaIEAAAAAAAFEV2T2I899xzkqTTp0+rVatWWrJkiVJTU7O0S01N1dKlS9WmTRtFRUVJksaMGWPXWAEAAAAA/zCMovfCncXua2L06NFDY8aM0dSpU3X8+HE9/PDD8vX1VZMmTVSuXDmZTCadO3dOe/fu1aVLl5S+A+yYMWPUvXt3e4cLAAAAAACKCLsnMSTpk08+UZUqVTR+/HjFx8fr0qVL2rBhQ6Y26ckLLy8vTZw4US+++KIjQgUAAAAAAEWEQ5IYkvTSSy/p8ccf1zfffKN169Zp3759iomJkST5+vqqQYMGuv/++zV06FCVK1fOUWECAAAAAG5KpX4DDmYyDP4WZnTjcoyjQwBQhC3p3svRIQAowvpsWOPoEAAUUe63yU6LsVdjHR1CFiVKlnB0CLAjuy/sCQAAAAAAkB8OKycBAAAAADgXJvLD0ZiJAQAAAAAAnILDkhg3btzQ7Nmz9dBDD6latWoqUaKEXF1dc3y5uTFxBAAAAACAO5VDsgJHjhxR7969dfjwYaYjAQAAAICT4OsbHM3uSYy4uDg98MADOnbsmFxcXPTQQw+pbNmymjFjhkwmk958803FxMRo9+7d2r59u0wmk9q0aaMuXbrYO1QAAAAAAFCE2D2J8b///U/Hjh2Tq6urVq9erU6dOmn//v2aMWOGJOntt982t927d68ee+wxbd++XQMHDtRzzz1n73ABAAAAAEARYfc1MZYvXy6TyaQBAwaoU6dOObZt3LixQkJCVK5cOb344ov6/fff7RQlAAAAAOBWqYZR5F64s9g9iXHgwAFJUp8+fbI9f+saGWXLltWLL76o5ORkff7554UeHwAAAAAAKJrsnsS4fPmyJCkgIMD8XrFixczHsbGxWa5p27atJGnjxo2FGxwAAAAAACiy7J7EKF68uCTJZDKZ3ytdurT5+MSJE1muSW979uzZwg0OAAAAAGCRYRhF7oU7i92TGNWrV5cknT592vxemTJl5OfnJ0n67bffslyTvhaGh4eHHSIEAAAAAABFkd2TGM2bN5ck7d69O9P7nTt3lmEY+uCDDxQdHW1+PzIyUu+9955MJpMaN25sz1ABAAAAABmkphpF7oU7i92TGF26dJFhGFq2bFmm98eMGSNJ+vvvv1W7dm31799fwcHBatSokU6dOiVJGj16tL3DBQAAAAAARYTdkxg9e/ZUhw4d5OPjo4iICPP7bdu21VtvvSXDMBQTE6NFixbp119/1bVr1yRJw4cP1+DBg+0dLgAAAAAAKCLc7D1g8eLFFRoamu25CRMmqH379vr666+1f/9+JScnq1atWhoyZIgefvhh+wYKAAAAAMiEhTThaHZPYnz77beSpHvuuUetWrXKcr5z587q3LmzvcMCAAAAAABFnN3LSYYNG6bhw4fr+PHj9h4aAAAAAAA4MbvPxChVqpSuXr2qWrVq2XtoAAAAAEABpFJOAgez+0yM6tWrS5JiYmLsPTQAAAAAAHBidk9i9OnTR4ZhaPny5fYeGgAAAAAAODG7JzFeeOEFBQQE6Msvv9SGDRvsPTwAAAAAIJ9SU40i98Kdxe5JjJIlS2rt2rWqU6eOunXrptGjRys0NFSXLl1iux4AAAAAAGCR3Rf2dHV1NR8bhqGZM2dq5syZVl1rMpmUnJxcWKEBAAAAAIAizO5JjFtnWzD7AgAAAACcA1/f4Gh2T2KMHz/e3kMCAAAAAIDbAEkMAAAAAADgFOyexAAAAAAAOKdU6kngYHbfnQQAAAAAACA/SGIAAAAAAACnQDkJAAAAAMAqqamUk8CxmIkBAAAAAACcAkkMAAAAAADgFCgnAQAAAABYxWB3EjgYMzEAAAAAAIBTIIkBAAAAAACcAuUkAAAAAACrpFJOAgdjJgYAAAAAAHAKzMQAAAAAAFiFmRhwNGZiAAAAAAAAp0ASAwAAAAAAOAXKSQAAAAAAVjFSKSeBYzETAwAAAAAAOAWSGAAAAAAAwClQTgIAAAAAsAq7k8DRmIkBAAAAAACcAkkMAAAAAADgFCgnAQAAAABYhWoSOBozMQAAAAAAgFMgiQEAAAAAAJwC5SQAAAAAAKukplJPAsdiJgYAAAAAAHAKJDEAAAAAAIBToJwEAAAAAGCVVLYngYMxEwMAAAAAADgFkhgAAAAAAMApUE4CAAAAALCKQTkJHIyZGAAAAAAAwCmQxAAAAAAAwAHi4+P1wQcfqGXLlvLz81OJEiVUt25dvfzyyzpx4kSB+09OTtbatWv1yiuvqH379ipbtqzc3d1VunRpNW3aVC+//LIiIiJy7WfYsGEymUxWvSIjIwscd04oJwEAAAAAWIXdSWwnIiJCwcHBOnz4cKb3Dx06pEOHDunrr7/WvHnz1KNHj3z1f+HCBdWtW1fR0dFZzl25ckV79uzRnj179Nlnn+n999/XCy+8kK9x7I0kBgAAAAAAdhQbG6uePXuaExijRo3SwIED5eXlpZCQEL377ru6cuWK+vfvr23btqlhw4Z5HiMxMdGcwGjcuLEeeughtWrVSuXLl9eVK1e0atUqffbZZ0pISNDYsWPl5eWl0aNH59inv7+/Vq9enWObSpUq5TnWvCCJAQAAAACAHU2ZMkWHDh2SJL3//vt65ZVXzOfatGmjjh07qkOHDoqPj9fYsWO1YcOGPI9hMpnUpUsXvfPOO2rdunWW8x07dtTDDz+sjh076vr163r11Vc1aNAg+fj4WOzT3d1d9evXz3MstsSaGAAAAAAAq6SmGkXu5WySkpL06aefSpLq1q2rl156KUubNm3a6IknnpAkhYSE6Pfff8/zOJUqVdKaNWuyTWCka9WqlZ555hlJaSUm69aty/M49kYSAwAAAAAAOwkNDdXly5clSUOHDpWLS/Zfy4cNG2Y+XrRoUaHF07FjR/OxNYt8OhrlJAAAAAAAq7CuZ8Ft3rzZfBwYGGixXfPmzeXt7a24uDht2bKl0OJJTEw0H1tKqBQlJDEAAAAAAE7r1KlTVrWrXLlyIUdinYMHD5qP69SpY7Gdm5ub7r77boWFhWW6xtY2btxoVTySFB0drfbt22vfvn26fv26/Pz81LBhQ/Xq1UsjRoxQ8eLFCy3OdCQxAAAAAABOq0qVKla1M4rINJKTJ09Kkry9vVW6dOkc21apUkVhYWG6cOGCEhMTVaxYMZvGcubMGc2ePVuSVKZMmUylJdmJjY3NNCvk7NmzOnv2rNasWaPJkydrwYIFuu+++2wa461IYgAAAAAArJJaRBIBzuzatWuSpBIlSuTa1tvb23wcGxtr0ySGYRh66qmnzPGMGzdOXl5e2bY1mUxq3bq1evXqpaZNm6p8+fJKSEjQvn37NHPmTO3cuVNRUVHq2rWrNm/erCZNmtgszluRxAAAAAAAOK30mQ3OIiEhQZLk4eGRa9uMSYvr16/bNI5JkyZp2bJlktIW93zuuecstv3444+znTXSpk0bjRo1Sm+++aYmTZqkuLg4jRw5Urt375bJZLJpvOlIYgAAAAAAnFZhrXWRnJwsd3f3Avcze/bsTDuNeHp6SpJu3LiR67UZF920NEsiP+bOnatx48ZJkqpVq6Z58+bluKhnTmUvJpNJ//3vf7Vz506tW7dOf/zxh7Zu3aq2bdvaLN6Miv7SowAAAACAIiE11ShyL2fj4+MjKa08JDdxcXHmY2vKT6yxYsUKDR8+XIZhqHz58lq7dq0qVKhQ4H6ffPJJ83HGxUJtjZkYAAAAAADcws3NzSa7glSsWDHTnytXrqwdO3YoLi5Oly9fznGWQ3qpTNmyZW2yHkZoaKj69eunpKQk+fr6as2aNapZs2aB+5WkevXqmY+joqJs0md2SGIAAAAAAJCN3LYczY969epp4cKFkqRDhw6pdevW2bZLTk5WRESEJKlu3boFHnfnzp3q1auXEhISVKJECa1atUoNGzYscL/p7LX7C+UkAAAAAACrGIZR5F7Opl27dubjnMoudu/ebS4nKej6EmFhYerevbtiY2Pl6emp5cuXq1WrVgXq81YHDhwwH/v7+9u074xIYgAAAAAAYCdBQUEqVaqUJOmbb76xmIiZM2eO+bhPnz75Hu/IkSPq2rWrYmJi5O7uroULFyooKCjf/Vny1VdfmY8DAwNt3n86khgAAAAAANiJh4eHxowZI0k6ePCgpkyZkqXNtm3bNHPmTElpCYEWLVpkaRMZGSmTySSTyWQxKXHixAndf//9OnfunFxdXTVv3jz16NEjT/Fu375dZ86csXjeMAy9+eabWr9+vSSpUaNGhbYzicSaGAAAAAAAKznhZiBF0iuvvKL58+fryJEjevXVV3X06FENHDhQXl5eCgkJ0aRJk5ScnCwvLy998skn+RojOjpa999/v3lx0Jdeekl16tTRX3/9ZfEaX19fVapUKdN7v/76qyZPnqzu3burS5cuqlevnkqXLq3ExESFhYVp5syZ2rlzpySpePHimjFjhkwmU75itgZJDAAAAAAA7MjHx0crVqxQjx49FB4erunTp2v69OmZ2pQsWVJz585V48aN8zXGvn37FB4ebv7z+++/r/fffz/Ha4YOHZqpjCVdYmKili5dqqVLl1q8tmrVqpo3b162s0ZsiSQGAAAAAAB2VrNmTe3Zs0fTpk3TTz/9pKNHj+rGjRuqUqWKevTooRdeeEEBAQGODlPDhw9X+fLltW3bNoWFhen8+fOKjo6Wm5ubypQpo6ZNm6pXr14aPHiwPD09Cz0ek+GMy7kWohuXYxwdAoAibEn3Xo4OAUAR1mfDGkeHAKCIci9e3NEh2MT2PRGODiGL1k3udnQIsCMW9gQAAAAAAE6BJAYAAAAAAHAKrIkBAAAAALBKKqsRwMGYiQEAAAAAAJwCSQwAAAAAAOAUKCcBAAAAAFglNZVyEjgWMzEAAAAAAIBTIIkBAAAAAACcAuUkAAAAAACrsDkJHI2ZGAAAAAAAwCkwEwMAAAAAYJVUpmLAwZiJAQAAAAAAnAJJDAAAAAAA4BQoJwEAAAAAWMWgnAQOxkwMAAAAAADgFEhiAAAAAAAAp0A5CQAAAADAKqmplJPAsZiJAQAAAAAAnAIzMW6Rmpzs6BAAFGF9NqxxdAgAirDFnbo6OgQARdSA7VscHQJwWyCJAQAAAACwCtUkcDTKSQAAAAAAgFMgiQEAAAAAAJwC5SQAAAAAAKsYBvUkcCxmYgAAAAAAAKdAEgMAAAAAADgFykkAAAAAAFZJpZwEDsZMDAAAAAAA4BRIYgAAAAAAAKdAOQkAAAAAwCpUk8DRmIkBAAAAAACcAkkMAAAAAADgFCgnAQAAAABYJTWVehI4FjMxAAAAAACAUyCJAQAAAAAAnALlJAAAAAAAq6SyPQkcjJkYAAAAAADAKTATAwAAAABgFSZiwNGYiQEAAAAAAJwCSQwAAAAAAOAUKCcBAAAAAFiFhT3haMzEAAAAAAAAToEkBgAAAAAAcAqUkwAAAAAArGJQTgIHYyYGAAAAAABwCiQxAAAAAACAU6CcBAAAAABglVSqSeBgzMQAAAAAAABOgSQGAAAAAABwCpSTAAAAAACskko9CRyMmRgAAAAAAMApkMQAAAAAAABOgXISAAAAAIBVDKpJ4GDMxAAAAAAAAE6BJAYAAAAAAHAKlJMAAAAAAKySSj0JHIyZGAAAAAAAwCmQxAAAAAAAAE6BchIAAAAAgFUMykngYMzEAAAAAAAAToEkBgAAAAAAcAqUkwAAAAAArJJKNQkcjJkYAAAAAADAKdhtJsY777wjSQoICNDQoUOtuubChQv68ssvJUlvvfVWocUGAAAAAMhdKgt7wsHslsSYMGGCTCaTJGnDhg2aMWOGPDw8crzm/Pnz5utIYgAAAAAAcGezezmJYRj6/vvvFRQUpHPnztl7eAAAAAAA4KTsnsTo3r27DMPQjh071LJlS+3du9feIQAAAAAA8sFILXov3FnsnsSYMmWKPvvsM7m6uurkyZNq166dFi5caO8wAAAAAACAk3HI7iTPPvusVq1aJV9fX8XHx2vAgAHmhT8BAAAAAACy47AtVjt37qzt27erdu3aMgxDb7/9th555BElJCQ4KiQAAAAAQA5SDaPIvXBncVgSQ5Jq1aqlHTt2qEuXLjIMQz///LPat2+v06dPOzIsAAAAAABQBDk0iSFJpUqV0qpVq/Tcc8/JMAz98ccfatGihXbt2uXo0AAAAAAAKDTx8fH64IMP1LJlS/n5+alEiRKqW7euXn75ZZ04caLA/YeGhspkMln1mjBhQq79JScn66uvvlKHDh1UtmxZeXl5qWbNmnrqqad04MCBAsdrDTe7jJILFxcXTZ06VfXr19fzzz+vM2fOKDAwUGPHjnV0aAAAAACAm6jesJ2IiAgFBwfr8OHDmd4/dOiQDh06pK+//lrz5s1Tjx49HBRhZtHR0QoODtaOHTsyvR8REaGIiAjNmTNHX3zxhUaMGFGocRSJJEa60aNHq3bt2urfv7+io6P13nvvOTokAAAAAABsKjY2Vj179jQnMEaNGqWBAwfKy8tLISEhevfdd3XlyhX1799f27ZtU8OGDQs85qxZs9SiRQuL58uVK2fxXEpKivr27WtOYPTt21ejRo2Sn5+fduzYof/85z86f/68Ro8erUqVKqlbt24FjteSIpXEkKSgoCBt375dvXr10qFDhxwdDgAAAAAANjVlyhTz9933339fr7zyivlcmzZt1LFjR3Xo0EHx8fEaO3asNmzYUOAxq1evrvr16+fr2u+++06bNm2SJD3zzDOaNm2a+VzLli31wAMPqFmzZrp69aqef/55HThwQG5uhZNusNuaGLNnz9asWbNUuXLlXNvefffd2rFjhx577DEFBgaqQ4cOdogQAAAAAJATR+9EcjvsTpKUlKRPP/1UklS3bl299NJLWdq0adNGTzzxhCQpJCREv//+u11jvNUHH3wgSfL19TUfZ1SzZk29/vrrkqTw8HAtXbq00GKxWxJj6NChGjp0qEqWLGlVex8fH3377bcKCQlRSEhIlvPx8fHatGmTORsEAAAAAEBRFxoaqsuXL0tK+57s4pL91/Jhw4aZjxctWmSHyLIXHh5uXrTzkUceUfHixbNtZ694i1w5ibWOHTumoKAgubi4KDk52dHhAAAAAACQq82bN5uPAwMDLbZr3ry5vL29FRcXpy1bttgjtGxZG2+FChVUu3ZtHTlypFDjdfgWqwVlOOH0IQAAAABwRqlG0Xs5m4MHD5qP69SpY7Gdm5ub7r777izX5Ncbb7yhypUry8PDQ76+vmrSpIn+9a9/6ciRIzaJN+P5kydPKi4ursAxZ8dpZ2IAAAAAAHDq1Cmr2lmzPqM9nDx5UpLk7e2t0qVL59i2SpUqCgsL04ULF5SYmKhixYrle9xt27aZjy9fvqy9e/dq7969mjp1qsaNG6fx48fLZDJZjFfK/b9hlSpVJKVNNjh16pTuueeefMdrCUkMAAAAAIDTSv/inJuiMov/2rVrkqQSJUrk2tbb29t8HBsbm68kRsWKFdW3b1+1a9dONWrUkJubm06cOKHly5fru+++U1JSkt5++23duHFDkyZNshivNTHfGm9hIIkBAAAAALBKUUkEOLOEhARJkoeHR65tMyYtrl+/nuexWrRooePHj8vd3T3T+02bNlXv3r315JNPqmvXrrpy5YomT56sAQMGqHHjxtnGa03MBY3XGk6/JgYAAAAA4M518uRJq155lZycLJPJVODXnDlzMvXr6ekpSbpx40auMSQmJpqPvby88vwzeHt7Z0lgZNSyZUtNmzZNUlqCKv04o/R4pdxjLmi81mAmBgAAAADAaRWVtS6s5ePjI8m6couMi2NaU36SH4888oieffZZXblyRRs3bsxyPj1eKS3mjEmNW9kjXpIYAAAAAACrpN5B5SRubm422RWkYsWKmf5cuXJl7dixQ3Fxcbp8+XKOi3umzyApW7ZsgRb1zImbm5tq166tXbt2KSoqKsv5jEmiU6dOqUyZMhb7So/XZDIVWnKJJAYAAAAAANnIbUvR/KhXr54WLlwoSTp06JBat26dbbvk5GRFRERIkurWrWvzODLKaa2TevXqmY8PHTqUZc2MjA4dOiQpbbHVjIt82hJrYgAAAAAAYCft2rUzH2dXvpFu9+7d5vKMtm3bFlo8ycnJOnLkiCTJ398/y3lr4z179qy5n8KMlyQGAAAAAMAqhlH0Xs4mKChIpUqVkiR98803FmdBZFwQtE+fPoUWz48//qirV69KkgIDA7Ocr127tnkmyIIFCxQfH59tP/aKlyQGAAAAAAB24uHhoTFjxkiSDh48qClTpmRps23bNs2cOVNSWmKhRYsWWdpERkaad0AJCgrKcj4mJkahoaE5xrJz5049//zzktLWsXjqqaeybffyyy9Lki5duqRXX301y/mIiAi9++67kqS77767UJMYrIkBAAAAALBKaqoTTn0ogl555RXNnz9fR44c0auvvqqjR49q4MCB8vLyUkhIiCZNmqTk5GR5eXnpk08+ydcYV65cUceOHdWwYUP17t1bzZo1U8WKFeXq6qoTJ05o+fLl+u6775SUlCQpLVHRvHnzbPsaOnSoZs2apd9++03Tpk3T2bNnNWrUKPn6+mrnzp2aOHGirl69KhcXF3322Wdycyu8VANJDAAAAAAA7MjHx0crVqxQjx49FB4erunTp2v69OmZ2pQsWVJz587NcSFNa4SFhSksLMzieVdXV40bN05vvfVWjm2WLFmiHj16aNeuXVq4cKF5cdJ0Hh4e+vzzz/XAAw8UKN7cOG0S45577tGxY8ccHQYAAAAAAHlWs2ZN7dmzR9OmTdNPP/2ko0eP6saNG6pSpYp69OihF154QQEBAfnu39/fXz/99JO2bdumnTt3KioqShcvXlRCQoJKlSqle+65R0FBQRo5cqSqVauWa39lypTR1q1bNWPGDM2bN08HDx5UXFyc/P391blzZ73wwgu699578x2vtUxGTnupFKJz584pNDRUf/31ly5duiRJ8vPzU/369RUUFKTy5cs7IiwlXLzgkHEBOAfX4oWzVRSA28PiTl0dHQKAImrA9i2ODsEmPp+/w9EhZPHcI60cHQLsyO4zMc6cOaMXX3xRixYtUnJycrZtXF1d1a9fP3344YeqWLGinSMEAAAAAABFkV13J/nzzz/VsGFDLViwQElJSTIMI9tXcnKy5s+fr0aNGmnfvn32DBEAAAAAABRRdktixMXFKTg4WNHR0TIMQ/fff7/mz5+vyMhIJSQkKCEhQZGRkVqwYIG6du0qwzB08eJFBQcHW9yHFgAAAABgP4ZR9F64s9gtifH555/r9OnTcnFx0YwZM7RmzRr1799fVatWlYeHhzw8PFS1alX169dPv/76q77++muZTCZFRUVp2rRp9goTAAAAAAAUUXZLYixdulQmk0nDhg3TE088kWv7ESNGaPjw4TIMQ4sXL7ZDhAAAAAAAoCizWxLjyJEjkqSBAwdafc2gQYMyXQsAAAAAcJxUwyhyL9xZ7JbEiI2NlZS2jaq1fH19JaWtpwEAAAAAAO5sdktilC1bVpJ08OBBq69Jb1umTJlCiQkAAAAAADgPuyUxWrduLcMw9NFHHyk5OTnX9klJSfrwww9lMpnUunVrO0QIAAAAAMiJo3ciYXcS2C2JMWTIEEnS3r17FRwcrNOnT1tsGxUVpZ49e2rv3r2SpGHDhtkhQgAAAAAAUJS52WugXr16qXfv3lqyZInWrVunGjVqqEuXLmrVqpXKly8vk8mks2fPaseOHVq7dq2SkpIkSX369FFwcLC9wgQAAAAAAEWU3ZIYkvTDDz9oyJAh+umnn3Tjxg2tXLlSK1euzNLOuDknqH///vr222/tGSIAAAAAwAJ2A4Gj2a2cRJKKFSum+fPna/ny5XrggQfk5eUlwzAyvby8vPTAAw/ol19+0fz581WsWDF7hggAAAAAAIoou87ESBccHKzg4GClpKTo77//1qVLlySlbb9ao0YNubq6OiIsAAAAAABQhDkkiZHO1dVVtWrVcmQIAAAAAAArpVJNAgezazkJAAAAAABAfpHEAAAAAAAATsHm5SQjRoyQJJlMJs2cOTPL+/lxa18AAAAAAPsz2J0EDmYybPy30MXFRSaTSZKUkpKS7ft5YRiGTCZTpr4KU8LFC3YZB4Bzci3u7egQABRhizt1dXQIAIqoAdu3ODoEm/jgu62ODiGLVx6/z9EhwI5sPhOjatWq2SYrLL0PAAAAAABgDZsnMSIjI/P0PgAAAADAObA7CRyNhT0BAAAAAIBTsPlMDAAAAADA7YmFPeFozMQAAAAAAABOgSQGAAAAAABwCjYvJ3F1dbV1lzKZTEpOTrZ5vwAAAAAA66WmOjoC3OlsnsSgRgoAAAAAABQGmycxxo8fn+P5FStWaPfu3ZKke++9Vy1btlT58uVlGIbOnz+vXbt26a+//pLJZFLz5s3Vo0cPW4cIAAAAAACckF2TGBMnTtTu3bvVqFEjTZ8+XS1atMi23e7duzV69Gjt3r1bPXv21Lhx42wdJgAAAAAgj1KZeA8Hs9vCnuvXr9f48eNVu3ZtbdmyxWICQ5KaN2+uzZs3q2bNmpowYYLWrVtnrzABAAAAAEARZbckxtSpU2UymfTaa6/J29s71/be3t567bXXZBiGPvvsMztECAAAAAAAijKbl5NYkr4ORsOGDa2+plGjRpKkXbt2FUpMAAAAAADrsZEDHM1uMzEuXbokSbpy5YrV11y9elWSFBMTUygxAQAAAAAA52G3JIa/v78kaeHChVZf8/PPP0uSKlasWCgxAQAAAAAA52G3JEb37t1lGIa++uorLViwINf2P//8s7766iuZTCa2WQUAAACAIiDVKHov3FnslsR44403VLJkSaWmpmrQoEHq3bu3lixZoqioKCUlJSk5OVlRUVFasmSJ+vTpo0ceeUQpKSny8fHR66+/bq8wAQAAAABAEWW3hT0rVaqkpUuX6sEHH9S1a9e0fPlyLV++3GJ7wzDk4+OjpUuXqlKlSvYKEwAAAAAAFFF2S2JIUmBgoMLCwvTiiy9q2bJlSklJybadq6urHnroIX344YcKCAiwZ4hwMmfOntW8n3/W5q3bdObcOXm4u6tK5crq1qmjBvTtKy9PT5uMs2rdOi1dsVLhERG6eu2ayvj5qUmjRhrYt48a1q+f6/WGYWhtSIhWrlmrA4cPK+byZbmYTLrrLj/Vr1tPDwX3UNtWrWwSK4DsnTlzRt//8IM2bdmis2fOyN3DQ1WrVFG3rl01sH9/eXl52Wyslb/+qiXLlulIeLiuXr2qMnfdpaZNm2rQgAFqZOUuXZcvX9b3P/ygDSEhOn3mjAzDUCV/f3Xq2FGPDRqk0qVL2yxe4E5RzLe0/OrVk1+9ummvunVU7Obv0rEVK7Vr4iSbj1nl/s6q3rOHStW8Wx4+Pkq4dEkX9v6poz8v1qX9+63qw6NkSdUa0E+VAjuoeMUKMplMijt9RlEbNyl8wc+6cXMxfMAeUtmdBA5mMhy0R87Zs2cVEhKiffv2KSYmRoZhyM/PTw0aNFDHjh1VoUIFR4SlhIsXHDIu8m7T1q164+13dC02Ntvz1apW1bQpH6hyAWbyJCYm6uVx47Tpt63ZnndxcdFTI0boyeHDLPZxLTZWY197Xbv37MlxrG6dO+u/496Uu7t7vuNF4XMt7u3oEJAPGzdv1mtvvGHxflG9WjV98dlnqlK5coHGSUxM1IuvvqqNmzZle97FxUXPPPmknho9Osd+9u3frzFjx+rCxYvZni9Xtqymfvyx6t97b4Hihe0t7tTV0SEgBwO2b7F4ztZJDBcPD903aaL827XN9nxqSooOfD1LB2Z/k2M/vnXrqN37k+VVtky25+PPX9Bvr76mmEOHCxwzCldOf/+cyfgZmx0dQhZvj2rv6BBgRw5LYhRVJDGcw+HwcA156mklJCSouJeXnnj8cbVo1lQJiYlavW6dFi5LK1WqHhCgeV/PUPHixfM1zusT3tbKtWslSS2aNtWjA/qrbJkyCo+I0Mxvv9PJqChJ0vh//1t9H+yVbR/PvvSytmzfLkmq5F9RwwYPVs0aNZScnKKDhw9p9tx5irl8WZL0SN8+euOll/IVK+yDJIbzOXT4sB4fNkzXExJUvHhxjRwxQi2bN1diYqJWrV6tnxctkiRVr15d87//Pt/3C0n69xtvaMWqVZKkli1a6LFBg1S2XDmFh4drxqxZOnnypCRpwrhx6te3b7Z9nDt/XgMGD1Z0dLTc3Nw05LHHFNg+7cPZxs2b9e333ys5OVl33XWXFsybp/LlyuU7XtgeSYyiLeOXyLiz53QtMlIVWqfNhLR1EqPV228poFva34dzu39X+PyfdP3iRZW++27VGfq4fKqkJU13TZqsY8t+ybYPr7JldP+cmfK66y6lJifryA/zdXrLb5Ik/3ZtVXvQI3Jxc9P16GitG/aErl/IPvGJooEkRuEhiXFnsWs5CWAr7386VQkJCXJzddX/PvlYjTKUdLRq1kxVK1fRx198oWPHj+vbH+frqRHD8zzG7j17zAmMwLZt9fG7k+Tq6ipJql+3roLatdOgEU/ozLlz+viLL3R/xyCV9PHJ1MeBQ4fMCYzK/v5aMGeOvL3/+YLUsllTde3USf2HDdO1a7H6aclSPTVihPx8ffMcL4DsvTdliq4nJMjNzU3Tv/hCjRs1Mp9r1bKlqlatqo8++UTHjh3TN999p6effDJf4+zavducwAjq0EGffvSR+Z7R4N571TEwUAMGD9aZs2f10aefqmuXLlnuGZI09fPPFR0dnRb7pEnq1qWL+Vyzpk11b716eunVVxUdHa3PvvhC/5kwIV/xAnei/V/P0qWDh3Tp4EElXopR8YoV1HPxzzYfp2yTxuYERtTmLdr67zdkpKZKkmIOHlLU5i3qMmemvCtWUMNnn9GpDaFKymamWP2nRsvrrrskSdvfelunNoSYz138M0yXDh7SfZMmyuuuu1R/9Cjt+u+7Nv9ZgFvxCByOZrfdSQBb+evgQXNpRu+ePTMlMNINGTRQNapVkyTNXbBAScnJeR5nztx5ktLWaPm/l18yfxlJ51u6tF545mlJ0tVr17T4l6xPUfbs22c+fnTAgEwJjHQVK1TQQz2CJUmpqanad+BAnmMFkL19+/dr1+7dkqQ+Dz2UKYGRbtjjj6tG9eqSpO/mzVNSUlK+xpr1TdqUcFdXV735xhtZ7xm+vvrXCy9Ikq5evapFixdn6eNidLR+WblSktT2vvsyJTDSdevSRW3vu0+StPyXX3TxZsIDQO72fz1LZ37bqsRLMYU6zj2PDZYkpSYn64/3PzQnMNLduHJFYdO+lCQVK1VS1R/smaWPYn6+5kTImW07MiUw0p3aEKIz23ZIkgIe6KZifjwEAXD7c1gSIyYmRqGhofr555/13Xff6dtvv83xBaQLyVBr/lBwj2zbuLi4qGf3bpLSEgy7/8h5PYpbxcfHa8fvv0uSWrdobnG69v2BgSrhnVZesGFj1hr45AxfhipX8rc4XpUM55Ju5O8LFICsNoT886G/z0MPZdvGxcVFD/ZM+wJx9epV7br5u58X8fHx2rFzpySpTatWqlC+fLbtunTurBIlSkiS1m3YkOV86MaN5kWvez/4oMXxHuqVVr6WkpKi0I0b8xwvgMLj5uWl8s2bSZLO7dqt6xeyL1WOCt2oGzdnX1QO6pDlfKX27eTiljZpOnLFCovjRa5IS3y6uLmpUvt2BYodAJyB3ctJQkNDNX78eG3ZYn1NmMlk0pAhQwoxKjiTP/4MkyR5eXmp3j33WGzXvEkT8/GesDC1adnC6jH2HTyoGzduSJKaNW5ssZ27u7sa3Huvtu3cqb8OHFBScrLc3f75tQqoUtV8fCrqtMV+TmY4F1C1itVxAsjZH3/8Ienm/aJuXYvtmjdr9s81e/bovtat8zTOvr/+Mt8zMvZ1K3d3dzVs0EBbt23TX/v3KykpKdNivr/fjFeSWuTQT4tb4rW0vgYA+/OrV1euxYpJki78sddiu9TkZF36a78qtG4lv3r1ZHJ1lZFh574yGWaO5dTPhT3/nCvTsKH+Xro837ED1kilnAQOZteZGF9++aXuv/9+bdmyRYZh5OkFpDt2/LgkqWqlSnJzs5yHq171nwTCseOReRsj8p/21XPZ5rd6QNo4ySkpOnFz0b5097VqKf+KFSVJ8376SfHXr2e5/tz581p2c/p4o/r1Vevuu/MUKwDL/j52TJJUtUqVnO8XN8tJJOnYzWvyM86tfWU71s1St+TkZJ04cSLbfnxKlFCZMtnvRCBJZcuWNc/o+Dsf8QIoPCVv/o5L0tWbn1ksuXo87R7g4uYmnyqZH2KUrJb2+ePGtWtKuHTJYh8J0dHmGR0+1XL+zAIAtwO7JTEOHjyoMWPGyDAMNWjQQEuWLNGKm1PjTCaTIiIitHv3bv3vf/9T06ZNJUnt2rXT/v379ffff9srTBRxiYmJ5p08yuWyIn/JkiXl5eUlSTp77nyexjl7/p/25cvmPE6FDHFkvE6SPDw89O74t1SqZEmdjIrSgKHD9NOSJdoTFqZdf/yhb374QQNHPKGr167Jv2JFvfPGG3mKE4BlGe8X5S2Ud6QrlfF+cfZsnsfKeE1uu4Vk3EL87Llzmfu5+efc4pVkLlm5tQ8AjuVV/p97wPXzOX/+uJ7h80nG6zL++fr53HfOS++neHl2KwJw+7NbOclnn32mlJQUlS1bVps3b5aPj4/2799vPl+9enVVr15dTZs21ahRo/Taa6/pgw8+0PPPP69169bZK0wUcXHx8ebj4je/cOTEy9NT169fz3YGRE7iM45TPOdxvDLEcT0+6ziNGzTQ/NmzNO/nnzXvp5/1nw+mZDpf3MtLTz/xhB7p20e+pUvnKU4AlsXFxZmPrbpfeHnl634h3XJvymWLVi9PT/NxxnuNJMXfjNmabV7T7z239gHAsdwz/P4m53I/SU7457zbLZ830vvJrY+0fhLS+vDK/xbRgLVSmSUPB7NbEmPjxo0ymUwaM2aMfLLZUi4jk8mk9957T7///rtCQkI0a9YsjRgxokDjnzp1yqp2ZTyLFWgcFK70mnNJcnfP/a+vh0darXliYmKexknMOE4OU9DT4vinnj3hRtZxDMPQ2tBQrQsJVXI2u6TEX7+u1evXy79CBT3Y44E8xQnAsky/xxl+Ty3x8PCQJCXk8X4hZb7H5DZW+jjZjZUec273HUnycM/f/Q1A4XLJ8DuempTz7mipGRbzTl9H49Z+Uq3YMSn15r3DtZhHLi0BwPnZLYmRnkRILxWR0pIV6W5d3EySRo8erQ0bNuj7778vcBKjShXrFku8fiFvZQewr4wf/pNy+WAgSTdufjgoVixvyaliGcfJZXvWjNsxenpkHic1NVX/Hj9ea25ui9anZ0898nBf1QgIUEpqqg6Hh2vO3HkK3bJF4/77Xx2JOKqXn38+T7ECd6Jz58/r6tWr2Z4rWbKkypcrl/n32IovAelJUs883i+kzPeY3MbKmIy9daxiHh66npBg1bbQN5Lyd38DULhSM/yOu+TywMXF45/Pvim3JCRTb9yQi5eXXKxIwqYnPFISb+TSEig4JmLA0eyWxEi4Oc3N3/+frSS9b25NKaVtuXrrGgc1a9aUJB04cMAOEcIZeGeYomnNlO/rN//eWTOVPKOMU7njsykRyTRGhji8bpkKOn/RYnMC4+knRuipW5JxTRo2VJOGDfV/Eyfql19X67sf56tls2bqcN99eYoXuNNM/fxzLV2e/Qr8D/Xqpf++806mf2Osul/cbJPX+4V0y70pl/KO9PuSlLVspLi3t64nJFhVImKO14rSEwD2k5Th99ctl/uJm+c/55Nv+byRFB8vNy+vXPtI6yetTC35OuVlAG5/dlvY08/PT1LmGuWyZcuaZ2McOXIkyzUXL16UJF2+uTBbQZw8edKqF4q2YsWKmdeNOJ/LYllXr141f8ivkMeFrjIu5nkul9k5GRfzrHBLIm7xL79ISvuCM+Kxxyz2MebJJ83Hiyx8MQOQNxnvF+dyWfzySsb7RYaFN62VcSHOc7ncmzIuAlrhlgU80xcFzS1e6Z8FPW/tA4BjZVzM0yuXhX4zLQJ6yyLk6Qt6epUrm+uY6f3E53EhcwBwRnabiVGnTh2dP39e4eHhuu/mU+bixYurVq1aCg8P17Jly9SuXbtM1yxbtkxSWrKjoCpXrmxVu4SLua8ADceqHhCgmMuXdSIqSsnJyRa3TTyWYevC6gHV8jRGjer/tD+Wy/Zox25uj+bm6qqqt/w9S7+2RrVqmUphblW+XDnd5een6EuXFHn8hMV2ANL895139N933sm1XY3q1fX7nj06cfJkzveLPGyRmp27a9TI3FfHjhbbpm/h7ObmpqoZtoJO7+fAwYO6FhurixcvWtxm9cKFC4q9uaVijXzEC6DwXD0WaT4uGRCg09pssW3Jm9u0pyYnK/aW9duuHouUX9068vDxkaefn8VtVj3vukseN7dcvhaZ82cWwBZSKSeBg9ltJka7du1kGIY2bdqU6f2+ffvKMAxNnTpVs2bNUlxcnC5cuKApU6Zo+vTpMplM6tSpk73ChBNo0rChpLSp1AcOH7bYbveePebjxg0a5GmM+nXqmtdo+X3vXovtkpKStO/mLjv31q2bZV0XV1dXSVJKSkquY6Yv+pl+DYCCa9KkiaSb94uDBy222/377/9c07hxnsepf++95t//jH3dKikpSWH79kmS7q1XL8s9o+nNeCVpVw797CpgvAAKz6WDB5Vyc12Msk0bW2zn4uYmv/r3pl1z4KBSb1kL5+KfYebjnPop2+SfcxfD9uU9YABwMnZLYvTs2VOStHTpUvP6GJL00ksvyc/PT0lJSRo1apRKliypChUq6N///reSk5Pl6emp1157zV5hwgl07NDefLx0xcps26SmpuqXX1dLknx8SqhFs6bZtrPE27u4WjVrJknasWu3xenh6zZuVOzNEqlOHTpkOV+pYkVJ0tFjx3T12jWL44X//beu3FykMP0aAAXXOcOMiMVLl2bbJjU1Vctuln6V9PFRy+bN8zyOt7e3WrdsKUnavnOnudTjVmvXrzfPoOicTYK+Y2CgXFzS/mlecnM2YnbS1wNxcXFRx8DAPMcLoPAkx1/X+d1picbyLZrLy8KM4kpBgeYZFFEbN2U5f3rzFqXefAhSLTjY4njVgntIklJTUnR685YCxQ4AzsBuSYxWrVpp9uzZeu+99xQTE2N+/6677tLq1atVrVo1GYaR6VWuXDktXrxYdevWtVeYcAIN6tVT00aNJElLfvlFf/71V5Y23/7wo/6+OWX70f79s2xXuHTFSjVq206N2rbTlzNnZjvOkMGDJEnJKSma9OFHWWZTxFy+rE+/+FJSWqKkb6+eWfoIbNtWUtpuBFM++0xGNss5JyYm6r2PPzH/uUNbFvUEbKVB/fpqdnN2w+KlS7X3zz+ztJnz3Xf6+2Y5yaODB2e7ReqSZctUv0kT1W/SRNP+979sxxo2ZIiktFlV/3333az3jJgYffzpp5LSkiUP9+mTpY8yZcoo+IG0rZZ/27pVa9auzdJm9dq1+m3rVklSr+BgiyUnAApHteAHNGD7Fg3YvkX3jsx+97zDc3+QlDbboukrL8rkkvkjt0epUmr47NOSpBtXr+nvZb9k6SPh0iWdWJ12D6jYppUqdwzK0qZyp46q2KaVJOn4r6stlpwAtnTrd7ai8MKdxW5rYkjS0KFDs32/WbNmOnTokDZs2KD9+/crOTlZtWrVUrdu3Vh1Hdl6dewLGvbU00pITNRTY/+lkUOGqEXTJkpIvKFf16/TwqVpTzADqlTRkIGD8jVGq2bN1P3+zvp13XqFbtmiJ8f+S48NGKCyZcoo/O8Iff3Ntzpz82nrC089pZIlS2bp4/GBj2jxL7/oUkyMlq5YqRMnT6l/796qHlBVKampOnTkiOb99LM54VKjWjU91KNH/v6jAMjWa6++qseHD1dCQoJGP/OMRo0YoZYtWigxMVGrVq/WTwsXSpKqBQRo2OOP53ucVi1b6oFu3bRq9WqFbNyoUU8/rccHD1bZsmUVfvSops+cqTM3F/UcO2aMSmVzz5CkMc89p9+2btWlmBi9+sYb2n/ggAJvzvTauGmTvvn+e0mSn6+vnn/22XzHC9yJyjRqqBKVK5n/XKxUafNxicqVVS34gUztI1esytc453//QyfWrFPVrverUof26jD1Y4XPX6DrFy6q1N13q+6wIfKumLaIcNgX/1OShdma+/43XRVat5Knn69aT5ygw/N+1Jnf0pKYFdvep3sGD5QkJVyK0V//m5GvWAHA2dg1iZETd3d3devWTd26dXN0KHACdWvX1nvvvK3/e2eiYuPiNPWrr7K0CahSRZ9P+UDe3vlPhL39xhuKi4vX5m3btOuPP7Trjz8ynXdxcdHoYUPVv3fvbK/3LV1aX370kV78vzcUdfqM9oSFaU9YWLZt76lVS59Mfjfbp8AA8q9unTqaMnmyXnvzTcXGxurTzz/P0qZaQIC+mDo107as+TFxwgTFxsVp85Yt2rlrl3bu2pXpvIuLi54cNUoD+vWz2EfFChX0+aefasyLL+rixYuaOWeOZs6Zk6lNmTJlNPWjj9iZBMij6g/2VPXg7B8WlG3UUGUbNcz0Xn6TGJK067+T5OZdXP5t71P55s1UvnmzTOdTU1J0cPY3+ntJ9qVuUtpOJ1te+bfavjdJXmXKqO6Qx1R3SObdzq5fvKjf/v2Grl9gcXoAdwa7JTHSF+d8/PHHNXz4cHsNi9tYULt2+unbbzR3wU/avHWrzl24IHd3N1WtVFldOnXUwIcfltfNfdPzy7NYMX0+5QOtXLNGS1eu0pGjR3UtNlZ3+fmqacNGGtjvYTWqXz/HPurUrqWfv/1Wy1etUsjmLQqPiNCVq1dlMpnk51tadWrVVpdOHdWtc+csZS8AbCMoMFCL5s/X9/PmadOWLTp37pzc3d1VpUoVdevSRYMeeUReXl4FHsfT01NffvaZVqxapSXLlunwkSO6du2a7rrrLjVr0kSDHnlEjW+Ww+WkYYMGWrxggb6fN08bQkMVdfq0JKlSpUrqFBioxx99VKVvbh8LoGhKSbyhLS+9qqpdu6ha8AMqXaum3EuUUMKlGF38808d/Wmhov/an2s/l/Yf0OpHh6r2I/3l36G9vG+unRV35rROb9qiIz8u0I2b62oB9sDuJHA0k2GnIiJ3d3elpqZq3bp16pjD1nOOxharAHLiWrxgT+oB3N4Wd+rq6BAAFFEDtt8eC6++/PlGR4eQxZTnWOT6TmK3hT3LlSsnSTw5AgAAAAAA+WK3JEajm9Nnjxw5Yq8hAQAAAAA2lGoUvRfuLHZLYowcOVKGYeh/FramAwAAAAAAyIndkhh9+/bVY489po0bN2rEiBGKi4uz19AAAAAAAOA2YLetEL799lt17txZYWFh+uabb7R06VL16tVLDRs2lK+vr1xdXXO8fsiQIXaKFAAAAACQnVT77AsBWGS3JMawYcNkMpnMf46JidF3331n1bUmk4kkBgAAAAAAdzi7JTEk6dbdXO20uysAAAAAALgN2C2JcezYMXsNBQAAAAAoBDyHhqPZLYkREBBgr6EAAAAAAMBtyG67kwAAAAAAABSEXdfEAAAAAAA4r9RUR0eAOx0zMQAAAAAAcID4+Hh98MEHatmypfz8/FSiRAnVrVtXL7/8sk6cOFHg/k0mU55f2UnfbdSaV2RkZIHjzoldZ2Lc+j+hatWqNmkLAAAAACh8qSzsaTMREREKDg7W4cOHM71/6NAhHTp0SF9//bXmzZunHj162C2m2rVr222s/LJrEqNatWrmzI7JZFJycrJN2gIAAAAA4CxiY2PVs2dPcwJj1KhRGjhwoLy8vBQSEqJ3331XV65cUf/+/bVt2zY1bNgwX+Ps27cv1zbffPONpkyZIkkaOnRojm39/f21evXqHNtUqlTJ+gDzwe5rYhh52JMnL20BAAAAAHAGU6ZM0aFDhyRJ77//vl555RXzuTZt2qhjx47q0KGD4uPjNXbsWG3YsCFf49SvXz/XNps2bZKUNnngsccey7Gtu7u7VX0WJrsmMTp06GCxxqYgbQEAAAAAhY8HzQWXlJSkTz/9VJJUt25dvfTSS1natGnTRk888YS++uorhYSE6Pfff1ezZs1sHsvhw4e1c+dOSVJQUJBTLONg1yRGaGhoobQFAAAAAMAZhIaG6vLly5LSyjdcXLLfb2PYsGH66quvJEmLFi0qlCTGt99+az7OrZSkqGB3EgAAAAAA7GTz5s3m48DAQIvtmjdvLm9vb0nSli1bbB6HYRiaO3euJMnb21sPP/ywzccoDCQxAAAAAABWSTWK3svZHDx40Hxcp04di+3c3Nx09913Z7nGVkJDQ3X8+HFJUt++fVWiRIlcr4mOjlb79u1VunRpFStWTBUrVlS3bt30+eefKz4+3uYxZsfuC3sCAAAAAGArp06dsqpd5cqVCzkS65w8eVJS2uyH0qVL59i2SpUqCgsL04ULF5SYmKhixYrZLI6MpSRDhgyx6prY2NhMs0LOnj2rs2fPas2aNZo8ebIWLFig++67z2YxZsduSYxOnTpJSts6derUqVZleSIjIzVixAiZTCatX7++sEMEAAAAADiZKlWqWNWuqCxKeu3aNUmy6jtxejmJlJZAsFUSIz4+XgsXLpSUltxJ/75uiclkUuvWrdWrVy81bdpU5cuXV0JCgvbt26eZM2dq586dioqKUteuXbV582Y1adLEJnFmx25JjNDQUJlMJm3cuFG7du3SsmXLVL169RyviYuLM18HAAAAAHAsZyzfKGoSEhIkSR4eHrm2zZi0uH79us1iWLJkiTmZ8thjj1lcXDTdxx9/nO2skTZt2mjUqFF68803NWnSJMXFxWnkyJHavXt3oX2Pt/uaGIZhaP/+/WrZsqU2btxo7+EBAAAAALeRkydPWvXKq+TkZJlMpgK/5syZk6lfT09PSdKNGzdyjSExMdF87OXlleefwZK8lpLkVPZiMpn03//+V/fff78k6Y8//tDWrVsLHKMldk9ijBs3Tl5eXoqOjlbXrl01ffp0e4cAAAAAALhNVK5c2apXUeHj4yMprTwkN3FxceZja8pPrHHmzBmtW7dOktSiRQvVrVvXJv0++eST5uPCnLBg94U9H3nkEfXq1Ut9+vRRVFSUnn76af3111/65JNPcp3CAgAAAABwnCKyrIRduLm52WRXkIoVK2b6c+XKlbVjxw7FxcXp8uXLOc5ySJ9BUrZsWZuthzF37lylpKRIsn5BT2vUq1fPfBwVFWWzfm/lkN1Jmjdvrh07dqh3797avXu3pk2bpsOHD2v+/Pm5rs4KAAAAAIA95LQFan7Vq1fPvKjmoUOH1Lp162zbJScnKyIiQpJsNltCkr777jtJkru7uwYNGmSzfu21cKrDpj74+/tr06ZNeuSRR2QYhtatW6fWrVsrPDzcUSEBAAAAAFCo2rVrZz7Oqexi9+7d5nKStm3b2mTsvXv3KiwsTJIUHBysu+66yyb9StKBAwfMx/7+/jbr91YOrd/w9PTUDz/8oLfffluSFB4erlatWmnt2rWODAsAAAAAkI1UwyhyL2cTFBSkUqVKSZK++eYbizMYMi4I2qdPH5uMnXFBz6FDh9qkz3RfffWV+TgwMNCmfWdUJBahGDdunBYsWCAvLy9dvnxZwcHBmjp1qqPDAgAAAADApjw8PDRmzBhJ0sGDBzVlypQsbbZt26aZM2dKSksItGjRIkubyMhI8w4oQUFBuY6bkpKiH374QZJ01113KTg42Kp4t2/frjNnzlg8bxiG3nzzTa1fv16S1KhRI5vNHMmOQ9bEyM7DDz+sGjVqqHfv3jp58qT+9a9/qVOnTo4OCwAAAAAAm3rllVc0f/58HTlyRK+++qqOHj2qgQMHysvLSyEhIZo0aZKSk5Pl5eWlTz75xCZjrl69WmfPnpUkDRo0SO7u7lZd9+uvv2ry5Mnq3r27unTponr16ql06dJKTExUWFiYZs6cqZ07d0qSihcvrhkzZshkMtkk5uwUmSSGJDVp0sS84OfOnTu1YcMGR4cEAAAAALgp1fmqN4okHx8frVixQj169FB4eLimT5+u6dOnZ2pTsmRJzZ07V40bN7bJmBlLSfK6K0liYqKWLl2qpUuXWmxTtWpVzZs3L9tZI7ZUpJIYklShQgVt3LhRTzzxhObNm+focAAAAAAAsLmaNWtqz549mjZtmn766ScdPXpUN27cUJUqVdSjRw+98MILCggIsMlYV69e1bJlyySl7biSl0TD8OHDVb58eW3btk1hYWE6f/68oqOj5ebmpjJlyqhp06bq1auXBg8eLE9PT5vEmxOTYad9UI4fPy5JqlSpktzcrMudzJ49WydOnJAkjR8/vtBiyyjh4gW7jAPAObkW93Z0CACKsMWdujo6BABF1IDtWxwdgk0Mn1z0ZsvPfo1lCO4kdpuJkZ8M0vDhwy2eu3Dhgr788ktJ0ltvvZXvuAAAAAAA1qGcBI5WJHYnyY/z589rwoQJ5u1ZAQAAAADA7c1pkxgAAAAAAODOUuQW9gQAAAAAFE2Uk8DRmIkBAAAAAACcAjMxAAAAAABWsc/eloBlzMQAAAAAAABOgSQGAAAAAABwCpSTAAAAAACswsKecDRmYgAAAAAAAKdAEgMAAAAAADgFykkAAAAAAFZJZXsSOBgzMQAAAAAAgFMgiQEAAAAAAJyC05aTeHh4qGrVqnJxIQ8DAAAAAPbA7iRwNLtlAFasWKGUlBSb9VerVi1FRkbq77//tlmfAAAAAACg6LJbEqNXr16qUKGCnnvuOW3dutVewwIAAAAAgNuEXWsxoqOj9eWXX6p9+/aqUaOGxo0bpwMHDtgzBAAAAABAPqUaRe+FO4vdkhjz58/XQw89JHd3dxmGocjISE2aNEkNGjRQ06ZN9dFHH+n06dP2CgcAAAAAADgZuyUx+vfvr8WLF+vs2bOaPn26AgMDZTKZZBiG9u7dq1deeUVVq1ZV586dNXv2bF29etVeoQEAAAAAACdg9609SpcurZEjRyokJETHjx/X+++/r0aNGskwDKWmpio0NFQjR45U+fLl1a9fPy1evFg3btywd5gAAAAAgFs4unSEchI4dH/SSpUq6eWXX9aePXu0f/9+vfHGG6pWrZoMw1BiYqIWL16sfv36qUKFCo4MEwAAAAAAFAEOTWJkVLduXf3nP/9RRESEfvvtNz3zzDPy8fGRYRi6cuWKo8MDAAAAAAAO5uboAG516dIlhYWFKSwsTLGxsY4OBwAAAABwk0H5BhysSCQxEhIStHTpUs2dO1dr1qxRUlKSJMm4+RvSpk0bR4YHAAAAAACKAIclMVJTU7V27VrNnTtXS5YsUVxcnKR/Ehd16tTRo48+qsGDB6t69eqOChMAAAAAABQRdk9ibN++XfPmzdOCBQt04cIFSf8kLipWrKiBAwfq0UcfVdOmTe0dGgAAAAAgB+wGAkezWxLjrbfe0rx583Ts2DFJ/yQufHx81LdvXz366KPq3LmzTCaTvUICAAAAAABOxG5JjP/85z/mY3d3d3Xv3l2PPfaYevXqJU9PT3uFAQAAAAAAnJRdy0natWunRx99VAMGDJCvr689hwYAAAAAFBDlJHA0uyUxZs+ererVq6tFixby8vKy6pqEhATt3LlTktShQ4fCDA8AAAAAABRxdktiDB8+XC4uLgoLC1O9evWsuiYqKkpBQUFycXFRcnJyIUcIAAAAAMgJMzHgaC72HCx9MU97XQcAAAAAAG4fdk1i5FVqaqokydXV1cGRAAAAAAAAR7Prwp55FRkZKUkqVaqUYwMBAAAAAOjmc2bAYQotiXHixIls3z9z5oxKlCiR47WJiYmKiIjQuHHjZDKZdO+99xZGiAAAAAAAwIkUWhKjevXqWd4zDENdu3bNc19DhgyxRUgAAAAAAMCJFVoSw9JinHlZpNPT01NjxozRiBEjbBUWAAAAACCf2J0EjlZoSYzZs2dn+vPw4cNlMpk0ceJEVapUyeJ1JpNJnp6eqlixopo0aZJr6QkAAAAAALgzFFoSY+jQoZn+PHz4cElS7969Va9evcIaFgAAAAAA3KbstjtJSEiIpOzXygAAAAAAFH2Uk8DR7JbECAwMtNdQAAAAAADgNuTi6AAAAAAAAACsYbeZGAAAAAAA50Y5CRyNmRgAAAAAAMApkMQAAAAAAABOgXISAAAAAIBVUigngYMxEwMAAAAAADgFkhgAAAAAAMApUE4CAAAAALAKu5PA0ZiJAQAAAAAAnAJJDAAAAAAA4BQoJwEAAAAAWIVyEjgaMzEAAAAAAIBTIIkBAAAAAACcAuUkAAAAAACrUE4CR2MmBgAAAAAAcArMxAAAAAAAWCWFmRhwMGZiAAAAAAAAp0ASAwAAAAAAOAXKSQAAAAAAVmFhTzgaMzEAAAAAAIBTIIkBAAAAAACcAuUkAAAAAACrsDsJHI2ZGAAAAAAAwCmQxAAAAAAAAE6BchIAAAAAgFXYnQSOxkwMAAAAAADgFEhiAAAAAAAAp0A5CQAAAADAKuxOAkdjJgYAAAAAAHAKJDEAAAAAALCj2NhYbdq0SVOmTNGAAQNUvXp1mUwmmUwmVatWrVDG3LZtmx5//HFVq1ZNnp6eqlixorp3764ff/zR6j6Sk5P11VdfqUOHDipbtqy8vLxUs2ZNPfXUUzpw4EChxH0rykkAAAAAAFahnMQ2evXqpdDQULuN98477+jtt99Wamqq+b2zZ8/q7NmzWr16tebNm6cFCxbI09PTYh/R0dEKDg7Wjh07Mr0fERGhiIgIzZkzR1988YVGjBhRaD+HxEwMAAAAAADsyjD+yQb5+vqqS5cuKlGiRKGM9fXXX2v8+PFKTU3V3XffrZkzZ2rnzp1asmSJOnbsKElavny5Ro4cabGPlJQU9e3b15zA6Nu3r1atWqUdO3Zo6tSpKleunBITEzV69GitXr26UH6OdCYj4389KOHiBUeHAKAIcy3u7egQABRhizt1dXQIAIqoAdu3ODoEm6j3/HpHh5DFgc86OzqEPJs+fbpKlCihli1bqmbNmpKkatWq6fjx4woICFBkZKRNxrl8+bKqV6+uy5cvq2rVqvr9999VpkwZ8/mUlBT16dNHy5cvlyRt3LhRHTp0yNLPnDlzNHz4cEnSM888o2nTpmU6f/ToUTVr1kxXr15VrVq1dODAAbm5FU7hBzMxAAAAAABWSUk1FbmXMxo9erQGDx5sTmAUlhkzZujy5cuSpPfeey9TAkOSXF1d9cUXX8jV1VWS9MEHH2TbT/r7vr6+2bapWbOmXn/9dUlSeHi4li5daqsfIQuSGAAAAAAA3IaWLFkiSSpZsqT69u2bbZvKlSvr/vvvlyStXbtWsbGxmc6Hh4ebF+185JFHVLx48Wz7GTZsmPl40aJFBYzcMpIYAAAAAADcZm7cuKGdO3dKktq0aSMPDw+LbQMDAyVJiYmJ2rVrV6ZzmzdvztIuOxUqVFDt2rUlSVu2FF75FEkMAAAAAIBVUoyi90L2wsPDlZycLEmqU6dOjm0znj948GCmcxn/bG0/J0+eVFxcXJ7itRZbrAIAAAAAnNapU6esale5cuVCjqRoOXnypPk4t5+9SpUq2V6X334Mw9CpU6d0zz33WB2vtUhiAAAAAACcVsYv4Dm50zbmvHbtmvk4t+1bvb3/2YHv1jUxbNWPrZDEuIVnmbKODgFFxKlTp8w3xJMnT95xmVsAlnF/gCW3yxaKKBjuEbidHf2ik6NDyML0paMjKJoSEhLMxzmthyFJxYoVMx9fv369UPqxFZIYAAAAAACndWv5g60kJyfL3d29wP3Mnj07084d9uLp6Wk+vnHjRo5tExMTzcdeXl459pPxz3npx1ZIYgAAAAAAnBaznbLn4+NjPs6ttCPjIpy3lozc2k9OSYyc+rEVkhgAAAAAANzCzc0ty04d+VGxYkUbRJN3GZM7uS1+mnE2y61rjNzaT5kyZXLtx2QyFVpyiSQGAAAAAADZyG1L0aKsdu3acnV1VUpKig4dOpRj24zn69atm+lcvXr1MrVr3Lhxrv1UqVIl0yKftuRSKL0CAAAAAACH8fDwUMuWLSVJ27Zty3FdjI0bN0pKW5izefPmmc61a9cuS7vsnD17VkeOHJEktW3bNt9x54YkBgAAAAAAt6HevXtLkq5evapFixZl2+bUqVNat26dJKlz586Z1sCQ0mZ0pM/OWLBggeLj47PtZ86cOebjPn36FDByy0hiAAAAAADgZCIjI2UymWQymRQUFJRtm5EjR6pUqVKSpNdee03R0dGZzqekpOiZZ55RSkqKJOnll1/Otp/09y9duqRXX301y/mIiAi9++67kqS77767UJMYrIkBAAAAAIAdHT16VFu2bMn0XvoOIrGxsZlmNUhS9+7dVaFChTyP4+fnp/fee09PPfWUjh8/rlatWun//u//1KBBA50+fVqffPKJQkJCJEmDBg1Sx44ds+1n6NChmjVrln777TdNmzZNZ8+e1ahRo+Tr66udO3dq4sSJunr1qlxcXPTZZ5/Jza3wUg0kMQAAAAAAsKMtW7Zo+PDh2Z6Ljo7Oci4kJCRfSQxJevLJJ3X69GlNnDhRERERGjFiRJY2PXr00KxZsyz24erqqiVLlqhHjx7atWuXFi5cqIULF2Zq4+Hhoc8//1wPPPBAvuK0FkkMwILKlSvLMAxHhwGgCOL+ACAn3CMAFDVvv/22unXrpmnTpmnz5s06d+6cSpcurUaNGmn48OEaNGhQrn2UKVNGW7du1YwZMzRv3jwdPHhQcXFx8vf3V+fOnfXCCy/o3nvvLfSfxWRwhwUAAAAAAE6AhT0BAAAAAIBTIIkBAAAAAACcAkkMAAAAAADgFEhiAAAAAAAAp0ASAwAAAAAAOAWSGAAAAAAAwCmQxAAAAAAAAE6BJAYAANmoVq2aTCaThg0bluVcaGioTCaTTCaTQkND7R4bAEyYMMF8H8pOTvcwAHBmJDHgtObMmWP+xzsyMtLR4QAAAAAAChlJDAAAAGSLBwYAgKLGzdEBAADgbIKCgmQYhqPDAACLSDoBuF0xEwMAAAAAADgFkhhwOukL6g0fPtz8XvXq1c3TXdNfc+bMkYuLi0wmk958881c+12wYIH52uXLlxcoxsjIyCzx5PQKCgoq0HgAAAAAcCcgiYHbVrVq1dS2bVtJ0rx583Jtn97Gz89P3bt3L9TYAPzj1hX2r1y5ookTJ6pJkyYqXbq0OSkpSXFxcZo/f75Gjhypxo0bq1SpUnJ3d1fZsmUVGBioKVOmKDY21qpxV65cqQceeEBly5ZV8eLFVbt2bb344os6ffp0rtdauztJbGysJk+erDZt2sjPz0/FihVT5cqV1a9fP/3yyy9WxZkXQUFBeUqgMt0clvDAIOsY6fehRYsWqUePHvL395ebm1uWfrdv364333xTQUFBqlChgjw8PFSyZEnVq1dPTz/9tA4cOGDV2KdOndKzzz6rGjVqyNPTU/7+/nrwwQe1bt06q663dneS5cuXq1+/fqpcubKKFSumu+66S23atNHkyZOtvp9aK+MaK9a8JkyYYNPxAdweWBMDTqdFixbat2+fli5dav7AtHr1avn7+2dqV716dT366KPasmWLjh07pq1bt+q+++7Lts+YmBitWrVKkjRgwAC5u7sXKMZKlSpp3759ObZZsGCBJk6cKEkKCAgo0HjA7SI8PFxdu3a1+OU6ODhYGzduzPL+xYsXtWnTJm3atElffPGFVq5cqTp16lgcZ+zYsfr000+zjP3xxx9r7ty5WrlyZYF+Dknas2ePevbsmSUpEhUVpYULF2rhwoXq27ev5s6dK09PzwKPBzhC+gODLVu2aN68efrPf/6TY/ui9sAgKCjIfE85duyYqlWrZrGtYRgaMmSIvvvuO4tt5syZkynxky4pKUkHDx7UwYMHNWPGDE2dOlXPPPOMxX42btyoBx98UFevXjW/d+bMGS1fvlzLly/X22+/bcVPl7OEhAQNHjxYixcvzvT+pUuXtH37dm3fvl2fffaZVqxYocaNGxd4PACwFZIYcDre3t6qX7++du/ebX6vdu3a2X7wGDBggMaMGaOkpCTNmzfPYhLj559/1o0bNyRJjz76aIFjdHd3V/369S2e3717t6ZMmSJJqlu3rj777LMCjwncDvr166eoqCg9//zzevDBB+Xr66vw8HBzoi85OVkNGjTQgw8+qObNm8vf31+GYej48eNavHixFixYoGPHjql3797au3dvtsmBDz/80JzA8Pf31+uvv66WLVsqISFBK1as0CeffKJ+/fopPj4+3z9HVFSUOnfurJiYGPOT0IEDB+quu+7SgQMH9OGHH+rPP//UokWLNHToUM2fPz/fY2U0e/ZsxcXFWTx/4cIF9enTR1euXFGpUqVUqlQpm4yL2w8PDLL65JNPFBYWpvbt2+vpp59W7dq1dfny5UxJ1+TkZPn6+urBBx9UYGCgatWqJW9vb50+fVp//PGHpk6dqosXL+q5555TnTp11KlTpyzjREZGqlevXrp27ZpcXFw0evRo9evXT6VKlVJYWJgmT56s8ePHq3nz5gX6eYYOHWpOYDRq1EgvvfSS6tatq0uXLunHH3/UnDlzdPr0aXXu3FlhYWGqVKlSgcaTpN69e+ca9yuvvKJff/1VEg95AFhgAE5q9uzZhiRDknHs2DGL7Xr16mVIMsqWLWskJSVl2yYwMNCQZAQEBBipqamFFHGaqKgoo1KlSoYkw8/PzwgPDy/U8YCibvz48ebfZRcXF2PNmjUW2x45ciTHvtauXWu4uLgYkoyvv/46y/mzZ88axYsXN/++nzlzJkub9evXG25ubuaYhg4dmqVNSEiI+XxISEiW8/369TOfzy6OhIQEo2PHjuY2K1euzPHnsoXExESjbdu2hiTD1dXVWLVqVaGPCednzb+10dHRhru7uyHJePbZZy32NX36dHNfmzdvLqSI/7Fr1y7Dy8vLkGTUrVvXuHLlSpY26f/+W/r5jh07Zj4vyRgyZEiOnxNOnTplxMXFWTx/+fJlo2HDhoYko127dtm26du3r3m8efPmZTl/9epVo1GjRpniyk5AQIDFe9gvv/xivrZz585GYmJiljYZ/38NGDDA4s9kS59//rl5zEcffdQuYwJwPqyJgdveY489JintCeTatWuznD916pQ2b94sSRo8eLC5Lr8wXL9+Xb1791ZUVJTc3Nz0008/qWbNmoU2HuBshg0bpi5dulg8X6tWrRyvv//++/Xggw9KkpYsWZLl/DfffGOeYfHhhx+qQoUKWdp06tRJo0aNykPUmZ05c8b8dLNbt2564oknsrQpVqyYZs2aJTe3tAmRn3/+eb7Hs9ZTTz2l3377TZL0wQcfFImp/Lg9ZCwNWbBggZKTk7NtN3fuXElpT9fT16wqLKdPn1bv3r11/fp1+fn5admyZSpZsmSB+ixdurQ+//zzHD8nVKpUScWLF7d4vlSpUnrnnXckSVu2bFF0dHSm82fOnNHSpUslST179tSgQYOy9OHj46Pp06fn50cwmzZtmqS0maOzZ8+Wh4dHljajRo3S/fffLyltHZAzZ84UaMzcrF+/XmPHjpUktWzZUl9//XWhjgfAeZHEwG2vV69e8vHxkfTPB6iMfvjhB6WmpkpKS2IUphEjRmjXrl2SpKlTp2Y7jRS4k+W1nOvChQsKDw/XX3/9ZX6VLVtWkvTnn39maZ++IJ6vr68eeughi/2OGDEiT3FkFBISopSUFEnKNoGRrlq1auaETWhoqPmawjBlyhTNnj1bUtrP9q9//avQxsKdyVkfGISGhsowDBmGkeN6GFLmzxPWiouLU2RkpPbv32++R2Uso7n1PpXx/pHd2hrpWrZsqXvvvTdPsaRLTk42rwPSpUsXValSxWLb9IRucnJyjosYF1R4eLj69++v5ORkVapUSUuWLGGtIAAWsSYGbnteXl7q27evvvnmGy1ZskTx8fGZnpKkJzYaNWqU4zoWBTVx4kT9+OOPkqRnnnlGTz/9dKGNBTirhg0b5trmt99+09SpU7Vu3TpdunTJYruLFy9meS+9fr5JkybmWRDZady4sTw8PMxr5eTFX3/9ZT5u1apVjm1btWqlVatWKT4+Xn///XeuM03yY8WKFfr3v/8tSWrXrp2+/PJLm48BpH/Bv3btmubOnasHHngg0/nb4YGBNfcnKe3e89FHH2nhwoUKDw+XYRg5ts0o4xofLVq0yHGcli1bav/+/VbFlNHff/9tnpFmzT0qXcZ7my1dvnxZvXr1UkxMjLy8vLR06VJVrFixUMYCcHtgJgbuCOlPd+Pi4szTNCXpwIED5qcgtljQ05KFCxdq/PjxkqTOnTtn2RUBQBpfX98cz0+YMEHt2rXTggULckxgSGlPY28VExMjSSpXrlyO17q5ucnPzy+XaLOXMa7y5cvn2DZjOUtuP09+7N+/X4MGDVJqaqoCAgK0aNGibKeNAwWV/sBAkvmBQUa3wwOD3O5PkvT777+rTp06evfdd3XkyJEcExhS1vtU+j1Kyv0+ldv9xZKidI9KSUnRI488osOHD0tK292lWbNmNh8HwO2FJAbuCJ07dzZn9TOWlKQfm0ymbOtObWHPnj0aMmSIDMNQzZo1tWDBghyfAAN3MldXV4vn1q9fb95WsEaNGvriiy8UFhamy5cvKzk52TwlfNy4cbmOY81U9ty+fNhCYY5x8eJF8w4HJUqU0PLly82lNkBhuN0fGOR0f5KkGzduaMCAAYqOjpa7u7tefPFFbdy4UWfOnFFCQoL5HhUREWG+5tZ7QMY/53afssX9ozDLeqzxr3/9S2vWrJEkvfXWWxowYIBD4wHgHEhiwGnl5R9eFxcXDRw4UJK0Zs0a8/TNH374QZIUGBioypUr2zzGs2fP6qGHHlJ8fLxKlSql5cuX5/vpLnCnmzFjhqS0xfW2bdump59+Wg0aNFCpUqUyfbnI+CTzVulPUs+dO5fjWMnJyTn2k5OMv+O5jZPxvC3vDUlJSerXr5+OHTsmk8mk77//Xg0aNLBZ/0B27vQHBhs2bNDff/8tKW3hzA8//FAdOnRQhQoVVKxYMXO7nO4tebl/nD9/Pl9xZhzj7NmzObbNeN7Wn1+mT59u3mL+4Ycf1oQJE2zaP4DbF0kMOK2MCz4lJibm2j796U9SUpJ++uknbd26VceOHct0zpYSEhLUu3dvnTx5Uq6urvrxxx9Vp04dm48D3CnSa787deqU4zTr3bt3WzyX/kV+7969FndQkNIW28vPehiSMk2V37FjR45td+7cKUkqXry4qlevnq/xsvPss8+aF+7773//m+MipkBOeGBgvYzrU6T/d8iONfcoSeZ1PSzJ7bwlNWrUMK8NZu09SpJNy4BCQ0P13HPPSUpbo+jbb791+KwQAM6DJAacVsZFnzJOzbSkWbNm5iTC3LlzzU+GPDw81K9fP5vHN3LkSPOHA7YzBAouPelwa619Rnv37tX27dstnk/fLvDSpUtavny5xXazZs3KZ5RSUFCQeWbIzJkzLbY7ceKEeReHoKAgmz01/uSTT8yzVh599FG9/vrrNukXdyYeGFgvY2LU0n0qNTU1x+1RO3bsaL5/fPPNNxbb7d69O98Lbbq5uSkwMFCStHbtWp08edJi2/RtTl1dXRUUFJSv8W4VERGhfv36KSkpSeXLl9fSpUtz3JYWAG5FEgNOq0mTJuYPV+PGjdOaNWt05MgRHT16VEePHs12Ub/0D1Bbt27V999/L0kKDg5W6dKlbRrbrFmzzEmSTp06qUuXLpm2gLz1lf4BD4Bl6Tt3bNmyxTxlO6MLFy6Yt3m0ZOjQofLy8pIkvfjii9lO1964cWOOXzJy4+/vrz59+kiSVq9enW1C5MaNGxoxYoSSkpIkyfxEsqB+/fVXvfzyy5LSdi5I/wIC5Nft/sAgKChIJpNJJpNJkZGRBYol4+5ClhIQr7/+uv744w+LfVSsWNE8c2rZsmVasGBBljaxsbEaPXp0gWJ99tlnJaUlm0aMGJHtzLNZs2aZ16t4+OGHbbJjyNWrV9WrVy9FR0erWLFiWrJkSY5bvAJAdlhdEE7Lx8dHY8aM0fvvv68//vhD3bp1y3Q+JCQky1ODwYMHa9y4cTIMQ1evXpVUOE+GTpw4YT7esGFDrrXogYGBhbr/OnA7GDJkiJYvX67Y2FgFBgbq3//+t5o1aybDMLR161Z99NFHOnv2rNq0aaNt27Zl20f58uU1ceJEvfzyy4qMjFSzZs30+uuvq2XLlkpISNDKlSv18ccfq1KlSoqPj9eFCxfyFevHH3+s9evXKyYmRiNHjtRvv/2mgQMHys/PT4cOHdKUKVO0d+9eSdKAAQOybEeZHzExMRo4cKBSUlJUokQJ/ec//9HRo0dzvOaee+6Ru7t7gcfG7Sv9gUFCQoLGjRsnNzc3VatWTS4uac/BKlWqZE4Mpnv00Uc1btw4bd261bxlqD0fGFji7e1t07KtW3Xr1k3lypXT+fPn9X//9386fvy4HnzwQZUpU0ZHjx7VjBkztH79erVt21a//fabxX4+/PBDrV27VteuXdPgwYO1ceNG9evXTyVLllRYWJgmT56sI0eOqHnz5jmWpuQkODhY/fv3108//aR169apVatWeumll1S3bl3FxMToxx9/NCdg/fz89NFHH+VrnFs999xzOnjwoCRp7NixKlGiRI7/z8qVK5frLi0A7kAG4MRSU1ONGTNmGO3btzf8/PwMV1dXQ5IhyQgJCcn2mjZt2pjblCxZ0rh+/brN4xo/frx5DGtegYGBNo8BcBYZf19yM3z4cIu/R66ursYnn3xiVX9jxoyx2E+ZMmWMXbt2GQEBAYYkY+jQoVmuDwkJyfVe88cffxj+/v45/u737dvXZvegY8eO5em+I8k4duyYTcbG7e3VV1+1+Hcou7//ERERWdr9/PPPNo/LFv/WBgYG5vj7kPH3avbs2bnG9Ouvvxqenp4WYwgKCjL++uuvXPsMCQkxfHx8LPYzfvz4XO91Od3DDMMwrl+/bvTp0yfH/2b+/v7Gnj17cv25rZXxv7c1r/Hjx9tsbAC3D8pJ4NRMJpNGjhypTZs2KTo6OtM2i5ZqN7du3Wpuc+XKlUz1vrYyYcIE8xjWvJiFAVhn1qxZ+u6779S+fXv5+PioWLFiCggI0OOPP66tW7fqhRdesKqfTz/9VCtWrFC3bt3k5+cnT09P1axZU2PGjNGePXvUvHnzAsfapEkTHT58WO+++65atWql0qVLy8PDQ/7+/urbt6+WLVumhQsXFso9CLClyZMna8aMGWrfvr38/Pxy3Wq0Ro0aatOmjfnPJUuWVHBwcGGHWSR069ZNu3fv1mOPPSZ/f3+5u7urbNmyCgwM1PTp07V+/Xp5e3vn2k9QUJD279+vp59+WgEBAfLw8FD58uUVHBysX3/91SY7eXh6emrRokVatmyZ+vbtK39/f3l4eMjX11etWrXSu+++q8OHD6tx48YFHgsAbMlkGIW4ST0AAAAAAICNMBMDAAAAAAA4BZIYAAAAAADAKbA7CWDBkSNHst1yLDespA0AAAAAhYM1MQALqlWrpuPHj+f5uvHjx9tkwS0Ad57z58/r/Pnzeb7Ow8NDtWvXLoSIgMLFAwPnkpSUpMOHD+fr2urVq1u1qCkA5IaZGAAAFBFffPGF3n777TxfFxAQoMjISNsHBBSyrl278sDAiURFRalBgwb5ujYkJMTiznEAkBckMQAL+EIAAAAAAEUL5SQAAAAAAMApsDsJAAAAAABwCiQxAAAAAACAUyCJAQAAAAAAnAJJDAAAAAAA4BRIYgAAAAAAAKdAEgMAAAAAADgFkhgAAAAAAMApkMQAAAAAAABOgSQGAAAAAABwCiQxAAAAAACAUyCJAQAAAAAAnAJJDAAAAAAA4BRIYgAAAAAAAKdAEgMAAAAAADgFkhgAAAAAAMApkMQAAAAAAABOgSQGAAAAAABwCiQxAAAAAACAUyCJAQAAAAAAnML/A7ZcaFXXztRcAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 435,
       "width": 536
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "plot_predictor_correlations(model_z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: title={'center': 'Correlation Matrix of Predictors'}>"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 434,
       "width": 686
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "plot_predictor_correlations(model_centered)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: title={'center': 'Correlation Matrix of Predictors'}>"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 434,
       "width": 536
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "plot_predictor_correlations(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How are they different?  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Your response here*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4) Create a histogram of the z-scored predictors and compare it to a histogram of the original predictors\n",
    "\n",
    "We've given you starter code below..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot from 04_models using raw data\n",
    "ax=sns.histplot(data=df, x='tv', kde=False, label='TV')\n",
    "ax=sns.histplot(data=df, x='radio', kde=False, label='Radio')\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your code here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "ax=sns.histplot(data=df, x='tv_z', kde=False, label='TV')\n",
    "ax=sns.histplot(data=df, x='radio_z', kde=False, label='Radio')\n",
    "ax.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How are they different?  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Your response here*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5) Compare parameter estimates from z-scored and centered models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Your code here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  sales   R-squared:                       0.968\n",
      "Model:                            OLS   Adj. R-squared:                  0.967\n",
      "No. Observations:                 200   F-statistic:                     1963.\n",
      "Covariance Type:            nonrobust   Prob (F-statistic):          6.68e-146\n",
      "============================================================================================\n",
      "                               coef    std err          t      P>|t|      [0.025      0.975]\n",
      "--------------------------------------------------------------------------------------------\n",
      "Intercept                   13.9470      0.067    208.737      0.000      13.815      14.079\n",
      "center(tv)                   0.0444      0.001     56.673      0.000       0.043       0.046\n",
      "center(radio)                0.1886      0.005     41.806      0.000       0.180       0.198\n",
      "center(tv):center(radio)     0.0011   5.24e-05     20.727      0.000       0.001       0.001\n",
      "============================================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.28e+03. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "# Solution\n",
    "print(results_centered.summary(slim=True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                  sales   R-squared:                       0.968\n",
      "Model:                            OLS   Adj. R-squared:                  0.967\n",
      "No. Observations:                 200   F-statistic:                     1963.\n",
      "Covariance Type:            nonrobust   Prob (F-statistic):          6.68e-146\n",
      "======================================================================================================\n",
      "                                         coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------------------------------\n",
      "Intercept                             13.9470      0.067    208.737      0.000      13.815      14.079\n",
      "standardize(tv)                        3.8004      0.067     56.673      0.000       3.668       3.933\n",
      "standardize(radio)                     2.7934      0.067     41.806      0.000       2.662       2.925\n",
      "standardize(tv):standardize(radio)     1.3780      0.066     20.727      0.000       1.247       1.509\n",
      "======================================================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "# Solution\n",
    "print(model_scaled.fit().summary(slim=True)) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How would you interpret them in natural language?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Your response here*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
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  "language_info": {
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    "name": "ipython",
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