{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [],
   "source": [
    "from datascience import *\n",
    "path_data = '../../../assets/data/'\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plots\n",
    "plots.style.use('fivethirtyeight')\n",
    "\n",
    "np.set_printoptions(suppress=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multiple Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [],
   "source": [
    "def standard_units(any_numbers):\n",
    "    \"Convert any array of numbers to standard units.\"\n",
    "    return (any_numbers - np.mean(any_numbers))/np.std(any_numbers)  \n",
    "\n",
    "def correlation(t, x, y):\n",
    "    return np.mean(standard_units(t.column(x))*standard_units(t.column(y)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we have explored ways to use multiple attributes to predict a categorical variable, let us return to predicting a quantitative variable. Predicting a numerical quantity is called regression, and a commonly used method to use multiple attributes for regression is called *multiple linear regression*.\n",
    "\n",
    "## Home Prices\n",
    "\n",
    "The following dataset of house prices and attributes was collected over several years for the city of Ames, Iowa. A [description of the dataset appears online](http://ww2.amstat.org/publications/jse/v19n3/decock.pdf). We will focus only a subset of the columns. We will try to predict the sale price column from the other columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>SalePrice</th> <th>1st Flr SF</th> <th>2nd Flr SF</th> <th>Total Bsmt SF</th> <th>Garage Area</th> <th>Wood Deck SF</th> <th>Open Porch SF</th> <th>Lot Area</th> <th>Year Built</th> <th>Yr Sold</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>35000    </td> <td>498       </td> <td>0         </td> <td>498          </td> <td>216        </td> <td>0           </td> <td>0            </td> <td>8088    </td> <td>1922      </td> <td>2006   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>39300    </td> <td>334       </td> <td>0         </td> <td>0            </td> <td>0          </td> <td>0           </td> <td>0            </td> <td>5000    </td> <td>1946      </td> <td>2007   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>40000    </td> <td>649       </td> <td>668       </td> <td>649          </td> <td>250        </td> <td>0           </td> <td>54           </td> <td>8500    </td> <td>1920      </td> <td>2008   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>45000    </td> <td>612       </td> <td>0         </td> <td>0            </td> <td>308        </td> <td>0           </td> <td>0            </td> <td>5925    </td> <td>1940      </td> <td>2009   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>52000    </td> <td>729       </td> <td>0         </td> <td>270          </td> <td>0          </td> <td>0           </td> <td>0            </td> <td>4130    </td> <td>1935      </td> <td>2008   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>52500    </td> <td>693       </td> <td>0         </td> <td>693          </td> <td>0          </td> <td>0           </td> <td>20           </td> <td>4118    </td> <td>1941      </td> <td>2006   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>55000    </td> <td>723       </td> <td>363       </td> <td>723          </td> <td>400        </td> <td>0           </td> <td>24           </td> <td>11340   </td> <td>1920      </td> <td>2008   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>55000    </td> <td>796       </td> <td>0         </td> <td>796          </td> <td>0          </td> <td>0           </td> <td>0            </td> <td>3636    </td> <td>1922      </td> <td>2008   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>57625    </td> <td>810       </td> <td>0         </td> <td>0            </td> <td>280        </td> <td>119         </td> <td>24           </td> <td>21780   </td> <td>1910      </td> <td>2009   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>58500    </td> <td>864       </td> <td>0         </td> <td>864          </td> <td>200        </td> <td>0           </td> <td>0            </td> <td>8212    </td> <td>1914      </td> <td>2010   </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (1992 rows omitted)</p>"
      ],
      "text/plain": [
       "SalePrice | 1st Flr SF | 2nd Flr SF | Total Bsmt SF | Garage Area | Wood Deck SF | Open Porch SF | Lot Area | Year Built | Yr Sold\n",
       "35000     | 498        | 0          | 498           | 216         | 0            | 0             | 8088     | 1922       | 2006\n",
       "39300     | 334        | 0          | 0             | 0           | 0            | 0             | 5000     | 1946       | 2007\n",
       "40000     | 649        | 668        | 649           | 250         | 0            | 54            | 8500     | 1920       | 2008\n",
       "45000     | 612        | 0          | 0             | 308         | 0            | 0             | 5925     | 1940       | 2009\n",
       "52000     | 729        | 0          | 270           | 0           | 0            | 0             | 4130     | 1935       | 2008\n",
       "52500     | 693        | 0          | 693           | 0           | 0            | 20            | 4118     | 1941       | 2006\n",
       "55000     | 723        | 363        | 723           | 400         | 0            | 24            | 11340    | 1920       | 2008\n",
       "55000     | 796        | 0          | 796           | 0           | 0            | 0             | 3636     | 1922       | 2008\n",
       "57625     | 810        | 0          | 0             | 280         | 119          | 24            | 21780    | 1910       | 2009\n",
       "58500     | 864        | 0          | 864           | 200         | 0            | 0             | 8212     | 1914       | 2010\n",
       "... (1992 rows omitted)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "all_sales = Table.read_table(path_data + 'house.csv')\n",
    "sales = all_sales.where('Bldg Type', '1Fam').where('Sale Condition', 'Normal').select(\n",
    "    'SalePrice', '1st Flr SF', '2nd Flr SF', \n",
    "    'Total Bsmt SF', 'Garage Area', \n",
    "    'Wood Deck SF', 'Open Porch SF', 'Lot Area', \n",
    "    'Year Built', 'Yr Sold')\n",
    "sales.sort('SalePrice')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A histogram of sale prices shows a large amount of variability and a distribution that is clearly not normal. A long tail to the right contains a few houses that had very high prices. The short left tail does not contain any houses that sold for less than $35,000."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sales.hist('SalePrice', bins=32, unit='$')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Correlation\n",
    "\n",
    "No single attribute is sufficient to predict the sale price. For example, the area of first floor, measured in square feet, correlates with sale price but only explains some of its variability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZMAAAFWCAYAAACsOXBmAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAgAElEQVR4nOzdeXRUVb7A+2/NqcxkhBBJBEJABqMoILcdABVweDY2iqxeeOU2goItogHUKIIiCojKawNt09jt5S7FC61voaJ9VSLtAAYbwxgggAQCISFDZazx1Hl/hDqkkhAqZAR+n7VcLXV2Ve3ajed39t6/vbfOZrOpCCGEEK2g7+wKCCGEuPRJMBFCCNFqEkyEEEK0mgQTIYQQrSbBRAghRKtJMBFCCNFqEkyEEEK0mgQTIYQQrSbBRLSrvLy8zq7CJU/asG1IO7YvCSZCCCFaTYKJEEKIVpNgIoQQotUkmAghhGg1CSZCCCFaTYKJEEKIVpNgIoQQotUkmAghhGg1Y2dXQAhx6SgqKWdJ5nrKKqqIiggjY9Zk4mIiO7taoguQnokQImBLMtdzqrgMl8vDqeIylqz6sLOrJLoICSZCiICVVVSh1+kA0Ot0lNqqOrlGoquQYCKECFhURBheVQXAq6pERYR1co1EVyHBRAgRsIxZk+kZH4XZbCQhLoqMWZM7u0qii5AJeCFEwOJiInl7weOdXQ3RBUnPRAghRKtJMBFCCNFqEkyEEEK0mgQTIYQQrSbBRAghRKtJMBFCCNFqEkyEEEK0mgQTIYQQrSbBRAghRKtJMBFCCNFqEkyEEEK0mgQTIYQQrdahwWTw4MFERkY2+ufBBx8EQFVVXnvtNfr370/37t25++67yc3N9fsMp9PJ3Llz6d27NwkJCTz00EOcPHnSr4zNZmP69On06tWLXr16MX36dGw2m1+ZEydOMGnSJBISEujduzfz5s3D5XL5ldm3bx933XUX3bt3Z8CAASxduhT17PbbQgghzunQYJKVlcXBgwe1f7Zu3YpOp+O3v/0tACtXriQzM5OlS5eyZcsWYmNjmTBhAlVV5w7gee655/j0009Zu3YtmzdvpqqqikmTJqEoilZm2rRp7N69mw0bNrBx40Z2797NjBkztOuKojBp0iSqq6vZvHkza9euZdOmTWRkZGhlKisrmTBhAnFxcWzZsoXXX3+dP/3pT7zzzjsd0FJCCHFp6dAt6GNiYvz+vG7dOsLCwvjtb3+LqqqsXr2ap556ivvuuw+A1atXk5KSwsaNG5k6dSoVFRWsW7eOzMxMRo0aBcC7777L4MGD+fbbbxkzZgwHDx7k66+/5ssvv2T48OEAvPXWW4wfP568vDxSUlLYsmULubm57Nmzh8TERAAWLVrEk08+yYsvvkh4eDgbNmzAbrezevVqrFYr11xzDYcOHWLVqlU88cQT6M6eNieEEKIT50xUVWXdunVMmjSJ4OBg8vPzKSoqYvTo0VoZq9XKyJEj+emnnwDIycnB7Xb7lUlMTCQ1NVUrk52dTWhoqBZIAEaMGEFISIhfmdTUVC2QAIwZMwan00lOTo5W5qabbsJqtfqVKSwsJD8/vx1aRAghLl2ddjhWVlYW+fn5TJkyBYCioiIAYmNj/crFxsZSWFgIQHFxMQaDgejo6EZliouLtTLR0dF+PQedTkdMTIxfmYbfEx0djcFg8CuTkJDQ6Ht815KTk8/72/Ly8i7cAFcQaY/WkzZsG9KOFy8lJaXZ650WTN5//32uv/56hgwZ4vd6w+EjVVUvOKTUsExT5QMp0/D1purS3Ht9LtToVxLf0KK4eNKGbUPasX11yjDXmTNn2Lx5M//5n/+pvRYfHw+g9Qx8SkpKtB5BXFwciqJQWlrabJmSkhK/rCtVVSktLfUr0/B7SktLURSl2TIlJSVA496TEEJc6TolmHzwwQdYLBbuv/9+7bWkpCTi4+PJysrSXnM4HGzbtk2b/0hLS8NkMvmVOXnyJAcPHtTKDBs2jOrqarKzs7Uy2dnZ1NTU+JU5ePCgX0pxVlYWFouFtLQ0rcy2bdtwOBx+ZXr06EFSUlJbNocQQlzyOjyYqKrKf//3f3P//fcTFhamva7T6Xj88cd5++232bRpE/v372fmzJmEhIQwceJEACIiIpgyZQoLFizg22+/ZdeuXcyYMYOBAwdy2223AZCamsrtt9/OnDlz2LFjB9nZ2cyZM4exY8dqXdzRo0czYMAAHnvsMXbt2sW3337LggULePjhhwkPDwdg4sSJWK1WZs6cyf79+9m0aRNvv/02M2fOlEwuIYRooMPnTL777juOHDnCX/7yl0bXZs+ejd1uZ+7cudhsNoYOHcrHH3/sF3SWLFmCwWBg6tSpOBwObrnlFv785z9jMBi0MmvWrGH+/Plaz2f8+PEsW7ZMu24wGPjoo49IT09n3LhxBAUFMXHiRBYvXqyViYiI4JNPPiE9PZ1Ro0YRGRnJrFmzeOKJJ9qjWYQQ4pKms9lssqRbtBuZ9Gw9acO2Ie3YvmRvLiGEEK0mwUQIIUSrSTARQgjRahJMhBBCtJoEEyGEEK0mwUQIIUSrSTARQgjRahJMhBBCtJoEEyGEEK0mwUQIIUSrSTARQgjRahJMhBBCtJoEEyGEEK0mwUQIIUSrSTARQgjRahJMhBBCtJoEEyGEEK0mwUQIIUSrSTARQgjRasbOroAQl7uiknKWZK6nrKKKqIgwMmZNJi4msrOrJUSbkp6JEO1sSeZ6ThWX4XJ5OFVcxpJVH3Z2lYRocxJMhGhnZRVV6HU6APQ6HaW2qk6ukRBtT4KJEO0sKiIMr6oC4FVVoiLCOrlGQrQ9mTMRop1lzJrMklUfUmo7N2dyqZN5INGQBBMh2llcTCRvL3i8s6vRpnzzQHqdTpsHaslvlGB0+ZFhLiFEi7V2HkiSEi4/HR5MTp8+zWOPPUafPn2Ij49n+PDhfP/999p1VVV57bXX6N+/P927d+fuu+8mNzfX7zOcTidz586ld+/eJCQk8NBDD3Hy5Em/MjabjenTp9OrVy969erF9OnTsdlsfmVOnDjBpEmTSEhIoHfv3sybNw+Xy+VXZt++fdx11110796dAQMGsHTpUtSz499CXKlaOw8kSQmXnw4NJjabjbFjx6KqKv/7v//LTz/9xLJly4iNjdXKrFy5kszMTJYuXcqWLVuIjY1lwoQJVFWd+8v23HPP8emnn7J27Vo2b95MVVUVkyZNQlEUrcy0adPYvXs3GzZsYOPGjezevZsZM2Zo1xVFYdKkSVRXV7N582bWrl3Lpk2byMjI0MpUVlYyYcIE4uLi2LJlC6+//jp/+tOfeOedd9q5pYTo2jJmTaZnfBRms5GEuKgWzwNJUsLlR2ez2TrsMfvll1/mhx9+4J///GeT11VVpX///jz66KOkp6cDYLfbSUlJ4ZVXXmHq1KlUVFTQt29fMjMzefDBBwEoKChg8ODBbNy4kTFjxnDw4EGGDx/Ol19+yYgRIwDYtm0b48ePZ8eOHaSkpPDVV1/x4IMPsmfPHhITEwH46KOPePLJJ8nLyyM8PJy1a9eycOFCDh06hNVqBWD58uW899577N+/H93ZJytxfnl5eaSkpHR2NS5pl2MbFpfYGiUltPecyeXYjl1Jh/ZMPv/8c4YOHcrUqVPp27cvv/nNb/jLX/6iDRvl5+dTVFTE6NGjtfdYrVZGjhzJTz/9BEBOTg5ut9uvTGJiIqmpqVqZ7OxsQkNDGT58uFZmxIgRhISE+JVJTU3VAgnAmDFjcDqd5OTkaGVuuukmLZD4yhQWFpKfn9/WzSPEFcOXlLDuzXmsfOlxmXy/DHRoNtexY8dYu3YtM2fO5KmnnmLPnj3Mnz8fgOnTp1NUVATgN+zl+3NhYSEAxcXFGAwGoqOjG5UpLi7WykRHR/v1HHQ6HTExMX5lGn5PdHQ0BoPBr0xCQkKj7/FdS05ObvJ35uXlBdYgVwhpj9aTNmwb0o4X70K9ug4NJl6vl+uuu46XXnoJgGuvvZajR4/y17/+lenTp2vlGg4fqap6wSGlhmWaKh9ImYavN1WX5t4LF270K4kMLbSetGHbkHZsXx06zBUfH09qaqrfa/369aOgoEC7Dmg9A5+SkhKtRxAXF4eiKJSWljZbpqSkxC/rSlVVSktL/co0/J7S0lIURWm2TElJCdC49ySEEFeyDg0mI0aM4PDhw36vHT58mKuuugqApKQk4uPjycrK0q47HA62bdumzX+kpaVhMpn8ypw8eVKbdAcYNmwY1dXVZGdna2Wys7OpqanxK3Pw4EG/lOKsrCwsFgtpaWlamW3btuFwOPzK9OjRg6SkpDZpEyGEuBwYnn322YUd9WWJiYksXboUvV5P9+7d2bp1K4sXL2bOnDkMHToUnU6Hoii89dZb9O3bF0VRyMjIoKioiLfffhuLxUJQUBCnT59mzZo1DBo0iIqKCubMmUN4eDiLFi1Cr9cTExPDzz//zMaNGxkyZAgnT55kzpw5XH/99Vp6cHJyMp9++ilbtmxh4MCBHDhwgPT0dB544AHuvfdeAPr06cPf/vY39uzZQ0pKCtu2bWPBggU89dRTfpP74vzKysoazW+JxopKyslY/nc+2JTF1u27GToohZDgIEDasK1IO7avDk0NBvjnP//Jyy+/zOHDh0lMTOTRRx9lxowZ2hyEqqq8/vrr/P3vf8dmszF06FDeeOMNrrnmGu0zHA4HL774Ihs3bsThcHDLLbewYsUKv8ys8vJy5s+fzxdffAHA+PHjWbZsGZGR57JGTpw4QXp6Ov/6178ICgpi4sSJLF68GIvFopXZt28f6enp7Ny5k8jISKZOncr8+fMlLThAMk4dmNmLVmvbk3hVlZ7xUdr2JNKGbUPasX11eDARVxb5DzgwU55ehsvl0f5sNhtZ9+Y8QNqwrUg7ti/Zm0uILkBWhItLnQQTIbqA1m5PIkRnky3ohegCLsdt6sWVRXomQgghWk2CiRBCiFaTYCKEEKLVJJgIIYRoNQkmQgghWk2yuYQQ51VUUs6SzPWUVXTcIVbi0iQ9EyHEeS3JXM+p4jJcLg+nistYsurDzq6S6KIkmAghzqusogr92X3o9DodpbaqTq6R6KokmAghzku2eRGBkmAihDgv2eZFBEom4IUQ5yXbvIhASTAR4iJIlpMQ/mSYS4iLIFlOQviTYCLERZAsJyH8STAR4iJIlpMQ/iSYCHERJMtJCH8yAS/ERZAsJyH8Sc9ECCFEq0kwEUII0WoSTIQQQrSaBBMhhBCtJsFECCFEq0kwEUII0WodGkxee+01IiMj/f7p16+fdl1VVV577TX69+9P9+7dufvuu8nNzfX7DKfTydy5c+nduzcJCQk89NBDnDx50q+MzWZj+vTp9OrVi169ejF9+nRsNptfmRMnTjBp0iQSEhLo3bs38+bNw+Vy+ZXZt28fd911F927d2fAgAEsXboU9exCNSGEEOd0eM8kJSWFgwcPav/8+OOP2rWVK1eSmZnJ0qVL2bJlC7GxsUyYMIGqqnNbVTz33HN8+umnrF27ls2bN1NVVcWkSZNQFEUrM23aNHbv3s2GDRvYuHEju3fvZsaMGdp1RVGYNGkS1dXVbN68mbVr17Jp0yYyMjK0MpWVlUyYMIG4uDi2bNnC66+/zp/+9Cfeeeeddm4hIYS49HT4okWj0Uh8fHyj11VVZfXq1Tz11FPcd999AKxevZqUlBQ2btzI1KlTqaioYN26dWRmZjJq1CgA3n33XQYPHsy3337LmDFjOHjwIF9//TVffvklw4cPB+Ctt95i/Pjx5OXlkZKSwpYtW8jNzWXPnj0kJiYCsGjRIp588klefPFFwsPD2bBhA3a7ndWrV2O1Wrnmmms4dOgQq1at4oknnkB3dl8mIcTFk92XLx8d3jM5duwYAwYMYMiQIfzXf/0Xx44dAyA/P5+ioiJGjx6tlbVarYwcOZKffvoJgJycHNxut1+ZxMREUlNTtTLZ2dmEhoZqgQRgxIgRhISE+JVJTU3VAgnAmDFjcDqd5OTkaGVuuukmrFarX5nCwkLy8/PbuFWEuDLJ7suXjw7tmdxwww2sWrWKlJQUSkpKWL58OXfeeSfbt2+nqKgIgNjYWL/3xMbGUlhYCEBxcTEGg4Ho6OhGZYqLi7Uy0dHRfj0HnU5HTEyMX5mG3xMdHY3BYPArk5CQ0Oh7fNeSk5PP+zvz8vICao8rhbRH612ubXi8oBC359wQdf4JZ7v+1su1HTtCSkpKs9c7NJjccccdfn++4YYbSEtL44MPPuDGG28EaDR8pKrqBYeUGpZpqnwgZRq+3lRdmnuvz4Ua/UriG1oUF+9ybsNeiT04VVyGXqfDq6okxEW122+9nNuxK+jU1ODQ0FD69+/P0aNHtXkUX8/Ap6SkROsRxMXFoSgKpaWlzZYpKSnxy7pSVZXS0lK/Mg2/p7S0FEVRmi1TUlICNO49CSEujuy+fPno1GDicDjIy8sjPj6epKQk4uPjycrK8ru+bds2bf4jLS0Nk8nkV+bkyZMcPHhQKzNs2DCqq6vJzs7WymRnZ1NTU+NX5uDBg34pxVlZWVgsFtLS0rQy27Ztw+Fw+JXp0aMHSUlJ7dAaQlx5fLsvr3tzHitfelwm3y9hhmeffXZhR33ZCy+8gNlsxuv1cvjwYebOncvRo0d56623iIyMRFEU3nrrLfr27YuiKGRkZFBUVMTbb7+NxWIhKCiI06dPs2bNGgYNGkRFRQVz5swhPDycRYsWodfriYmJ4eeff2bjxo0MGTKEkydPMmfOHK6//notPTg5OZlPP/2ULVu2MHDgQA4cOEB6ejoPPPAA9957LwB9+vThb3/7G3v27CElJYVt27axYMECnnrqKb/JfdG8srKyRnNcomWkDduGtGP7atGcya5du1i+fDk//vgjFRUVfPPNN6SlpfHyyy8zcuRIbr/99mbff+rUKaZNm0ZpaSkxMTHccMMNfPXVV/Tq1QuA2bNnY7fbmTt3LjabjaFDh/Lxxx8TFnbuFLslS5ZgMBiYOnUqDoeDW265hT//+c8YDAatzJo1a5g/fz73338/AOPHj2fZsmXadYPBwEcffUR6ejrjxo0jKCiIiRMnsnjxYq1MREQEn3zyCenp6YwaNYrIyEhmzZrFE0880ZImE0KIK4LOZrMFtKR727Zt/Pa3vyU5OZlbb72VNWvWkJWVRVpaGosXL2b//v188MEH7V1fcYmRSc/WkzZsG9KO7SvgnsmiRYsYPXo0H3zwAYqisGbNGu3akCFDWL9+fbtUUIj2JIvmhGgbAU/A79q1iz/84Q/odLpGqbHR0dFappMQlxJZNCdE2wi4Z2KxWKitrW3yWlFREeHh4W1WKSE6SllFFfqzD0d6nY5SW9UF3tFxfL2m4wWF9ErsIb0m0aUF3DMZMWIEq1ev9ttQ0ddDWbduHbfcckvb106IdhYVEYb37Jokr6oSFRF2gXd0HF+vye1RumSvqaiknNmLVjPl6WXMXrSa4hJbm5YXl5aAg0lGRga7d+/mN7/5DcuWLUOn0/Hhhx9yzz338PPPPzN//vz2rKcQ7aIrL5rryr0maPkQoQwpXt4CHuYaPHgwn3/+OQsWLGDFihWoqsqaNWu46aab+OyzzyRLQlySfIvm2lpbTOxHRYRxqrgM6Hq9Jmh5sOvqwVG0TovWmaSlpbFp0yYcDgfl5eVEREQQHBzcXnUToku4mMDgewrX63TaU3hLg1bGrMksWfUh+SecXa7XBOeCnW9frQsFu5aWF5eWgIe53G43NTU1AAQFBdGjRw8tkNTU1OB2u9unhkJ0sosZnmmLp3Bfr2nZvCldcquRlg4RduUhRdF6AfdM/vjHP+LxePjrX//a6NqcOXMwmUxkZma2aeWE6AouJjBcCU/hLR0ibK8hRdE1BNwz+f7777nrrruavDZ+/Hi2bt3aZpUSoiu5UMZXU1lK7fEULtlQoisLOJicOXOGmJiYJq9FR0dz5syZNquUEF3JhQJDU8Ng7bEbrmRDia4s4GGu2NhY9u/f3+R6kv379xMVFdWmFROiq7jQ8ExHZSl1hWwo2X5GnE/APZOxY8eyfPly9u7d6/f6vn37WLFiBePGjWvzyglxKeiohY+t+Z62GiKT3pE4n4CDyfPPP09ERAS33XYbd955J4888ghjx47l1ltvJTw8nBdeeKE96ylEl9VRWUqt+Z62CgJdoXckuqaAh7mio6PZsmULmZmZfPvtt+zZs4fo6GieeeYZZs6cSURERHvWU4guq6OylFrzPW0VBK6ELDVxcVq0aDEyMpKMjAwyMjLaqz5CiHbQVkHAt5Cy1HZuzkQIaGEwEUJcmtoqCMhaEXE+zQaTe++9lxUrVtCvXz/tbPTz0el0bNq0qU0rJ4RoGxIE2oZks51fs8FEVc+d6Ov1ehsdinW+skKIi9fwhjX5ruHINqpdQ1vsuXa5ajaYfPbZZ9q/f/755+1eGSFE4xvWux/+HyNuvL6zqyWQbLbmBJQa7HK5+P3vf88PP/zQ3vURokN1xS1KGt6wbFVNn3AqOl5XPkytswUUTMxmM1u3bsXr9bZ3fYToUG2x/qKtA1LDG1ZEWNc65qErBuCOIjsfn1/A2VzDhw/n559/5uabb27P+gjRodpi2CKQcXTfPEhhcSm/FhSRnBhPQlx0kxO4DTOvJt81/OJ/YDu4kucNJJHh/AIOJosXL+b3v/89ISEh3H333XTv3r3RhLxeH/CCeiG6hIbrL4IsZmYvWt2ibJ1AApLvBpybdxy704Xd7gR0Td6IG96w8vLyWv9D25DMG4imBBxMRo4cCcCzzz7Ls88+2+i6TqejtLS07WomRAdo2AuotTubfepuKjU0kAWBvhuw2+NBr9PhcntadCNuSc+mvckqeNGUgIPJvHnzmk0NFuJS1LAXMOXpZc0+dTc1xBPIgkDfDdhkNGJ3urCaTS26EbekZ9PeZBW8aErAweS5555r8y9fsWIFr7zyCo8++ijLly8H6tarvP7667z//vvYbDaGDh3KG2+8wYABA7T3OZ1OXnjhBf7xj3/gcDi45ZZbWLFiBT179tTK2Gw25s2bx5dffgnAuHHjWLZsGZGR557iTpw4QXp6Ot999x1BQUFMnDiRxYsXYzabtTL79u1j7ty57Ny5k27duvHII49IYL0M+Z78d+UeQVG89E3qidlsanSzb2qIJ5BxdN8NWAf8WnD6bM8isAnckvJKsrbn4HS6qaiuJTjI0uKeTVuSeQPRlAsGE6fTyVdffcWvv/5KREQEY8eOJT4+vtVfvGPHDt5//30GDhzo9/rKlSvJzMwkMzOTlJQUli1bxoQJE9ixYwdhYXX/YT/33HNs3ryZtWvX0q1bNzIyMpg0aRJbt27FYDAAMG3aNAoKCtiwYQM6nY4nn3ySGTNm8NFHHwGgKAqTJk2iW7dubN68mfLych5//HFUVdUCW2VlJRMmTGDkyJFs2bKFvLw8Zs2aRXBwMH/84x9b3Qai8zQcrrI7nJRX1tDnqgQOHSvg14LTjBpxbaObva+H4XF7OPRrAQajgdmLVl9wuKk1N+B313+FonhRFC94VWpq7cRGRcoQk+hSdDab7bxL10+dOsVvf/tbDh8+rK1wDwkJYcOGDdx0000X/aUVFRXceuutrFy5kmXLlnHNNdewfPlyVFWlf//+PProo6SnpwNgt9tJSUnhlVdeYerUqVRUVNC3b18yMzN58MEHASgoKGDw4MFs3LiRMWPGcPDgQYYPH86XX37JiBEjANi2bRvjx49nx44dpKSk8NVXX/Hggw+yZ88eEhMTAfjoo4948sknycvLIzw8nLVr17Jw4UIOHTqE1WoFYPny5bz33nvs379feicByMvLIyWl663fnr1otd+4/8GjxxnQJ0m7bjYbWffmvEbvKy6xsWTVh2zZluPXg+kZH9VuT+sTHl2AFz1H8k/hcLmwO5yMHDqw0+ZMLlVd9e/i5aLZ9KtXX32VkpISMjMz2b59O+vXrychIYF58xr/R9YSTz31FPfddx+33nqr3+v5+fkUFRUxevRo7TWr1crIkSP56aefAMjJycHtdvuVSUxMJDU1VSuTnZ1NaGgow4efS6kcMWIEISEhfmVSU1O1QAIwZswYnE4nOTk5WpmbbrpJCyS+MoWFheTn57eqDUTnajhcBbqAFqP5ehjXDujDoH5XE2Qxt/twU0RYMGaziYH9krluYAoTx9/ChswX2uw4YCHaQrPDXN9//z3PP/88kyfXdfVTU1OJiopi7Nix2Gw2v/mHQL3//vscPXqUd999t9G1oqIioO6I4PpiY2MpLCwEoLi4GIPBQHR0dKMyxcXFWpno6Gi/noNOpyMmJsavTMPviY6OxmAw+JVJSEho9D2+a8nJyU3+xq6WytnZumJ7GPBSXV2NTqdDVVWu6Z2A1WLAVlVLRFgwk+8a3my9G74/Niq83X7nY5Pv5N0P/y/guonzk3a7eBfq1TUbTE6ePMngwYP9XhsyZAiqqlJQUNDiYJKXl8fLL7/MF1984TfJ3VDD4SNVVS84pNSwTFPlAynT8PWm6tLce+HCjX4l6apDC8uef6xRRlJLnvJb+/4Wycvjb282TscXLdNV/y5eLpoNJoqiYDT6F/H92ePxtPjLsrOzKS0t9ZtvURSFH3/8kffee4/t27cDdU/99YefSkpKtB5BXFwciqJQWlpKTEyMXxnfWpi4uDhKSkr8goeqqpSWlvp9jm/Iy6e0tBRFUfzK+Hop9b8HGveexKWltRlJrX2/bGUuLjcXzOb6+9//rqXXwrmn+/fee88vq0un0/H88883+1l333031113nd9rs2bNok+fPjz99NP07duX+Ph4srKyuP76ul1SHQ4H27Zt4+WXXwYgLS0Nk8lEVlYWDzzwAFDXg/JNugMMGzaM6upqsrOztdeys7OpqanxK/PGG29w8uRJLaU4KysLi8VCWlqaVmbhwoU4HA6CgoK0Mj169CAp6dxkrRD1NRUoVFS/12rtTmxVNV16SxIJeKIlms3m6tatW+AfpNNRVlbW4grcfffdWjYXwNtvv82KFSvIzMykb9++vPHGG/z4449+qcFPP/00X3zxBatXr9ZSg9eaQuAAACAASURBVG02m19q8MSJEzl16hQrV65EVVWeeuoprrrqKr/U4Jtvvpno6GgWL16spQbfc889Wl0qKiq48cYb+c1vfkN6ejqHDx9m1qxZzJs3T1KDA3QlDi00zBTrGR+FqtIge+wEA/r00t5jNht54/lHm7x5t6YNWxMQmvodXS3gtcSV+HexIzXbMykvL++oemhmz56N3W5n7ty52qLFjz/+WAskAEuWLMFgMDB16lRt0eKf//xnLZAArFmzhvnz53P//fcDMH78eJYtW6ZdNxgMfPTRR6SnpzNu3Di/RYs+ERERfPLJJ6SnpzNq1CgiIyOZNWsWTzzxRAe0hGitznqyPt/eVf7ZYypeVfXbkuTcDsZudu7NI2t7DqNGpDU6HKslv6s1mzLKHlyiJZrtmQjRWp35NNjRT9a+m/xX3+/EVllNsNWCxWxi5PUDCbZa/OrSLTyEYKuFUlsVQWYzOh18l70Xg0GPR1HweBQMBj1DBvTBqFOIi41ttMAykN815elluFzn5jfPt36mKQ3bLyEuipUvSc9ENC3g7VR89u7dy48//khZWRlTp04lPj6eo0ePEhsb69d7EKKzdfSTta8X4PWquN1uyl0uTEYj/957iP95cz5/Wb+5yewv303bYNBjd7qoqXUQGmLFZDSi1+nIyc0nxaFw9HghTreHWruDYUNSMZtNF/xdrdmUUfbgEi0RcDBxOp1Mnz6dTz/9VJuEHzduHPHx8SxYsIC+ffuycOHCdqyqEC3T0bvb+oKX1+tFrzegnj1M7sSpM4x7JIPh1/VvctW6730pyT3Jyz9Jrd2JxWQkJbmntpDy6PFCHE4XOp0ORVE4dKyAQf2uvuDvak1ACCRjTSbphU/AB5C88sorfPvtt7z77rvk5eVp6y0A7rjjDr755pt2qaAQF6ujT8XznZBoNhnxqiper4rL5cHtUaiqsbP34LEmT3PU3mc20adXAj1iu2Ew6jlyopDIsBCu7Z+E0+2pWyAJRIaHYjAYAvpdvoCw7s157bJivi1OqhSXh4B7Jv/4xz944YUXeOCBB1AUxe9aUlISx48fb/PKCdEaHb27ra8XACpV1bVU1tSi49ziVltFdZPDUvV7D0dPFJLYIxZrkAWvqhISbOEPv7uHPy7+GxWV1VhMJvokJZCcGN8l5i9kkl74BBxMysrK6NevX5PXvF4vLperzSolREOXwnBK/eBVXGLjuntm4nZ7UBQFXz++qWGp+u+rP2HuuzlHR4bx+dpXuuT8hRyUJXwCDiZJSUns2LGj0eaMAP/+97/p27dvm1ZMiPq6+rnjTQW7u24bxo879+FwurE7nESGhzQ7LFVUUs6BIyewVdZgMRnp3asH3WPr1np11TNEZJJe+AQcTB566CHefPNNevXqxb333gvULVT817/+xapVq5o8yleIttLVh1OaCnavpj/Sov27lmSuJyEuGrvDicvl5vSZMv76+hwqys904C9pma4a5ETHCziYzJ49m7179zJjxgyefPJJoG4hoMPh4He/+x0zZsxot0qKK0NzQ1mdPZxyoWG2iz2Bsb6yiiqCLGYGpiQDdWtC4mIiu3QwEcIn4Gwug8HAe++9x+eff84TTzzBww8/zIwZM9i0aRNr1qxpzzqKy1xRSTmzF63mjinP8vUPO6msqm2UGdTRmVkNXShryZeRBc2fh9KctvgMITpLixctjhw5UtudV4i24LtR19qdVFXXUlpeRUy3cJxOJ7MXrQ540v1CvYfWTOJfaJitLeYOmvqMopJyXl39DxT0bf6bhGhLsp2KaFeBbGHhy2D6fsdeXB4POiAsNBiP28Ow6wYEvB1Kw+0/ukWEYLVYmtypt6Xbq3TW1iKzF63m8K8nCA0NbbLOl9tmjO1JtlNpX832TLp16xbwOec6nY7S0tI2qZS4svjmQ6xWC55qD3qdHqvFjEuvb9Gke8Pew/Zfcknt3UubFK+/U29LJ/E7I2upqKScrO051NQ4sAZZSEnu2ajOXT0xQVw5mg0m8+bNCziYCHGxfDfqg0fNWMxG+ib1xGw2cazgdKOddRuqP8xz4MgJEuKiCbKYz8496C64U2+gzjeZ3p7DTEsy16MoXhSvF4fLzaFjBdz+H9f7lensxAQhfGSYS7SrlgwtFJfY/J7+Z0y+67ybI0LdjfyePyygorIas8lEYo9YymyVpPa5qslhrfo79TZ3429JgGjPYaYpTy+jsqqWA4ePowJBQWa+Xve6X10atpnMmZyfDHO1rxZPwAvRXpp6+q//56KSch599m1+2nUAUDHqDVRU16LX6XC43BScPsN1A/tqW6xf7I22JQskC4tLyc07jtvjwWQ00pb9+KiIMBxONynJPbAGB5MQF9Wo/rLOQ3QVLQomLpeLr776isOHD+NwOPyu6XQ65s0L7JwEIXwC6QX4ymRtz6GkrBKLyYjBaKSqphaDXk9wkAWdTofL5fYb5omLieS5mQ9pn/9q5ocBZUO1ZB7i14Ii7E4Xqqpiq6zmh39XMXvR6oAC14V+u2/4L/+Es1PSoYVoiYCHuQoLCxk3bhzHjx+v2730bD58/TmVizm2V1zeLjS0EMgwka/M7twjlNmq0Ov1hIcGU1VrJzjIgtlkpLyyBqNBz92jhrH4mUcanRVyvs8P5Ijd5jK3/p9pC/h5Tx4OR93edBFhVm64dkBAw12BDpHJ8EzbkHZsXwEvWlywYAExMTHs3bsXVVX55ptvyMnJ4ZlnnqF3797k5OS0Zz3FZSqQXoCvjMloxGDQo6oqKhAWYkXxKFRU1mDQ6Ugb0Jvyyhq/BYUX+vymrrdkgWThmXKsQRaMRgN6gx6nWwk4q0oyscTlJOBhrm3btvHKK6/Qo0cPAPR6PUlJSWRkZOD1epk/fz4ffihnGYiWiYoI49cTp7VTBCPDQygusfkN9/gyllKSe+JR6s4GCbaaMegNXNWnFweOnMCrquSfKmZgSrLfTblhtlOQ2czsRaspLC7l14Kiuq3iq2oJDg7CYjLyHzcMbFHm1tWJ3bE7nNTYHei9KsFWS0CZZ1ERYQSZzTicbsnEEpeFgHsmZWVldO/eHb1eT0hICDabTbt2yy238MMPP7RLBcXlLWPWZArPlOFyu7GYjCTERTfaqsTXUwgNtTL2lhv45bNV7P7iXQalJmM9O8yFquJ2e/xuykUl5dgdTg4ePU7ukeNEhoWg09UNYe3PO06ZrQpbZTWK10tNjZ0LzZ43taVKj7goBvRN4qa0AURHhRNsDfLrzfi2ipny9DLu+cMCjhUUae/X6+nULWKEaEsB90wSEhK0RYnJycls2bKF2267Dajbgt5isbRLBcXlLS4mkv59rtLO8AAaDfc01VOov127Qa/HYNRjMZv8bspLMtdTXlnDgD5J2kFTpba6oSW3x4Nep0P1QnhYMHq9jkH9rsbuPP+5PPWHpTxuD198u4OqGjtOlwuL2cyYkWmsyJjh16uqnxlmq6zB7nAyMCUZvU5HrcPFy0//Z7MJAkJcKgIOJjfffDM//PAD99xzD1OnTiU9PZ09e/ZgMpn45ptvmDp1anvWU1zGgsxmdu7Nw+1WMJkMjLx+4AXf03C79sjwUD5b+8oFd/L1DXvpdDoqq2vwKB4qq2uIigxvdqip4VkjDqeTkvIq7bPdHg8HjxY0CgT162AxGXG53MC5jRybSkOun4EWFRHG5LuGI9PGoqsLOJi88MILlJeXA/CHP/wBj8fDJ598QmlpKbNnz5a0YHHRfAmBXtVLuc3Ojzv3XTC99nzbtcO5uYlduUdQFK+2oj4qIozpD43nkXkrsFVW41EUQoKD8CheVNXLsYLTuJwubrzvj1yd2J0ecVFMnzyev3z4BVnbd+FyuTEa9LjcbmyVtXWjYjodKiqK4qWq2t6onr7g5XK5cSseauwOco/kMyJtABmzJvPMkr80CnhLMtf7zSN9uz2Hr9YtJS4mskM2duyszSNl08pLW8BzJtHR0X6nKc6YMYMvv/ySf/3rXyxYsICgoKB2qaC4/Nkqq9Gho7rWgVf14nC6taf0+nMOsxetprikbq6uue3afU/7fa5KAODXgtPa8Nfbf///qK11oKpgNOgJtlq5+cbBmM1mkhO7c+R4IWW2KvYfzudUcRlT567gVHEZDocLj+LFYNBz3cAUTCYDer0vRb7uf0NDrX6/q/6czc97DoEKw4b0J7V3L4KtFuJiIpv8HWUVVRw9XojD6QJVparars0jXWgr/LbQEd/Rlb5XtI2Ag0lDFRUV/PLLL5w8ebIt6yMuMyXllU0GA5+iknK2/3KAolIbTqcbl9uD3eH0e0pv6gbTXPqub2jJbDYxqN/VXDugNytfepy4mEh+ysnF6fag04FXhYrK6rM387o9u1zuurkU99n/raq2131Wg0n+HrFRREWGYTDU9SpCg628vzzd77fVn7MJsVowGY2YzSa/NOCmfkdURNjZOupQAZPJqJXviHTizkpZllTpS1uzweSbb75h4cKFjV5fsWIFKSkpjBkzhsGDBzNt2jQ8Hk/jD2hgzZo1jBw5kquuuoqrrrqKO+64g3/+85/adVVVee211+jfvz/du3fn7rvvJjc31+8znE4nc+fOpXfv3iQkJPDQQw81Cmg2m43p06fTq1cvevXqxfTp0/2yzwBOnDjBpEmTSEhIoHfv3sybNw+Xy3/ydd++fdx11110796dAQMGsHTpUm2xpgjMu+u/avZpc0nmekwmAwZ93UaMqGA9u1Gj7ynd4/aw79AxduceYcu2HC11+O0Fj7PuzXlaoPBp/pApHagqIVYr+rPDawlxUYxIG4BXVTGbjHhVFZOx7n9DQ614VZU+SQlYLCYslrpJ/pULHiMsNBizyUSw1cKtw4cQExXh99vq3xzNJhNOt6dRnZr6HRmzJhMZHoJX9WK3O3E6XRw4coLiEluHHKDVWYd0yeFgl7Zmg8l7773H4cOH/V7Lyspi8eLFpKSk8NprrzF16lQ+/vhjVq9efcEvS0hIYNGiRWzdupWsrCxuueUWfv/737N3714AVq5cSWZmJkuXLmXLli3ExsYyYcIEqqrOPaE899xzfPrpp6xdu5bNmzdTVVXFpEmTUBRFKzNt2jR2797Nhg0b2LhxI7t37/Y7VlhRFCZNmkR1dTWbN29m7dq1bNq0iYyMDK1MZWUlEyZMIC4uji1btvD666/zpz/9iXfeeeeCv1OcU1FVe8FFg1aLhdCQYKIiwjGbjYSEWP2e0g/9WoDD5a7bQVfxXnD4o7ley/Br+2Mw6qmxO9DpdHQ/e33xM4/QMz6KASm9iI4M45qUJBLionh/eTo946MIDwvm9v+4nq/XLWXlS4+z8csfcDrdhARbsVrM/LL/cLOnL/ZJSiAyPCSgNOC4mEg+X/sK0ZHhdetfzGZ6xEaxZNWHHXLiZGedatnZp2mK1ml2O5XBgwczd+5cHn74Ye21adOm8fnnn5OTk0N8fDwAzzzzDD///DNbt25tcQWSk5N56aWXeOSRR+jfvz+PPvoo6el1wwV2u52UlBReeeUVpk6dSkVFBX379iUzM5MHH3wQgIKCAgYPHszGjRsZM2YMBw8eZPjw4Xz55ZeMGDECqFtwOX78eHbs2EFKSgpfffUVDz74IHv27CExMRGAjz76iCeffJK8vDzCw8NZu3YtCxcu5NChQ1itdWPhy5cv57333mP//v2yNX+AHnn6dWqcdavC7Q4nhWfK6H92V9+MWZN5NfNDjhUUceT4KVwuNxHhoXy+9hVUVJZkrqewuIwf/r2PILMJa5CFxB6xnCou5doBvVs8SVtUUs6LK97n86xsFEUhMjyU1N5XER8bidVi4VRxKccKirTJ9+Y+e8rTy8jOOYDXe25boeHX9dc2mSwqKeeFN97np10HUDwKFrOJPskJJMRFB7xv1x1TnsXprMv+6puUwInTZ7h2QB+ZnL5Isp1K+2q2Z1JSUsLVV1/t91pWVhYjRozQAgnAnXfeyZEjR1r0xYqi8I9//IOamhqGDRtGfn4+RUVFjB49WitjtVoZOXIkP/30EwA5OTm43W6/MomJiaSmpmplsrOzCQ0NZfjw4VqZESNGEBIS4lcmNTVVCyQAY8aMwel0atvCZGdnc9NNN2mBxFemsLCQ/Pz8Fv3WK9ljk+/UnjYLz5SREBftN+SVMWsyV18Vz3UD+zL+tmH8ffkzvJr5IXdMeY6vv9+J2+0hMiyEoCAzA/slc6KwGMWjXNQkrW8OIzQ4iNBgK0aDgSCLme2/5HKquIzcswsZfZPvzX12VEQYRoMBFfAoCtW1dnblHtHmhZZkrsdWVVN3GJcOnG43ep0+4DprZ5koXlwuN7/sO3L232VyWnRNzaYGh4aGUltbq/35yJEjlJWVccMNN/iVCwsL8xtmas6+ffu48847cTgchISE8D//8z8MHDhQu9HHxsb6lY+NjaWwsBCA4uJiDAYD0dHRjcoUFxdrZaKjo/16DjqdjpiYGL8yDb8nOjoag8HgVyYhIaHR9/iuJScnn/c35uXlBdQWV4LoyDBmTb4dgHnL1uH2uKnx1D1t559wUlF+RrsO8Orq9Zwpq6SmphavVyX3cD5JPWM5caoEl9OBV/HSKyGGmpoa7TMCbe/jBYW4PXV/TxVFwe5wUF1djdvlwV5bi93hwKuC3e7EXlurfXZJeSXvrv+KiqpaIsKCeXD8SIqKz+DxeKipqcXp8qDX67DbneTm/crshf8vObn5uNwejEYDLpcbvV7fojofLygkIbYbx0+VoKp1B2QlxHa7qN8tzpE2u3gX6tU1G0xSUlLYvHkzY8eOBWDz5s3odDq/ngFAfn5+o5tzc5/53XffUVFRwaZNm3j88cf57LPPtOsNh49UVb3gkFLDMk2VD6RMw9ebqktz7/WRrvQ59YcWeiX2aLQbb8O2UtATGhqKNSgIh9OFCoSHh3NH32RWvvR4k2exN9fe9dcuFBSXkxAXzTV9kzh0rACDwUBC9zhOFJby897DdRlcBj0x3SKwBgcTGR7COx98Tdb2HG29So1T4aV3NpCc2J20gSnsPfgrpbZKwkKCUYFTZ2ycLq1Ab9Cj8+hQvCpOt4du4aGEhIQEVOf6bRXVLZLq6mqKy6uIjIwI+HeLxmSYq301G0xmzpzJlClTKC8vJy4ujg8++IBrrrlGm4vw+eyzzxg0aFBAX2g2m+nduzcA1113HTt37mTVqlXaPElxcbHf8FNJSYkWqOLi4lAUhdLSUmJiYvzKjBw5UitTUlLiFzxUVaW0tNTvc3w9IZ/S0lIURfEr4+ul1P8eaNx7EoGpf456kMVMrd3JlKeXaXMAKioHjpygorIaVVWpqXWADo4VnObJ/7z3bCApJb+giOTE7iScXVQ4e9FqbREjKjhcLu0z668w7xEbRWFxKal9ruL2/7hem7NxuFy43Aper4riVUCty/CqtTs5VVyG01k3+X8k/xS9EuI4evwUx08WYzQYsFhM+NaZ+M5UCQqy0DepJ0fyT+Fye4gMD+U3Nw6k1nGuXi1pq9iocJY/P6PRqZNCdCXNBpN77rmH1157jXfeeQebzcYNN9zAW2+95fdkfvLkSb777jtefvnli6qA1+vF5XKRlJREfHw8WVlZXH993TnXDoeDbdu2aZ+dlpaGyWQiKyuLBx54QPt+36Q7wLBhw6iuriY7O1t7LTs7m5qaGr8yb7zxBidPnqRnz55A3VyQxWIhLS1NK7Nw4UIcDoe2IDMrK4sePXqQlJR0Ub/1StZwdXNpeSW/7D+sbaFidzixBlnoERuF3e7kTHklBp2O4Wn9MZqMPPPqGpISu6PX6UlK7E7C2bM/6vdUdu7JAx0M6ne1Nq9QPz3XGmQhtc9V2iQ51GWTVdbYMRj0GA11U4gms4GVLz3OlKeXaVvfK966NTA5uUdQveDVeXGpKnanE7PJSE2tAxWVhLhohg7uh62qhpTknhz6tQCD0UCQxcIrTz8S8KR5/f3I6p6ok+RERdGlXXA7lccee4zHHnvsvNd79uzJ8ePHA/qyhQsXcuedd9KzZ0+qq6vZuHEj33//Pf/7v/+LTqfj8ccf19aw9O3blzfeeIOQkBAmTpwIQEREBFOmTGHBggXExsbSrVs3MjIyGDhwoLbpZGpqKrfffjtz5sxh5cqVqKrKnDlzGDt2rNbFHT16NAMGDOCxxx5j8eLFlJeXs2DBAh5++GHCw8MBmDhxIkuXLmXmzJmkp6dz+PBh3n77bebNmyeZXAHwBY/jBYX0SuyB3eGkvLIGl8vNzr15nD5TjtFgIMRqwev1sj3nANcO6H2ubb0qXkPdv3rcHk4UlmCrrMFsMtInKaHJRXweRcG3DMjj9rBlWw6gQ/Eo9Ls6EaPJ2GjtQlREmDZ8qaoqer0eRfEye9FqbTuWHrFR7M87jqqqOFwujAYDHsXL2TcRER6C6gWTycANQ/qx+JlHWLLqQ776biflldVYLWa+/mEndoeTv7z2VLu2t2xFIprTnn9PLnoF/MUoKipi+vTp3Hjjjdx3333s3LmTjRs3cscddwAwe/ZsZs6cydy5cxk1ahSnT5/m448/Jiys3lYZS5Zom02OGzeOkJAQ1q9fj8Fg0MqsWbOGQYMGcf/99/O73/2OQYMG8e6772rXDQYDH330EcHBwYwbN46pU6dyzz33sHjxYq1MREQEn3zyCYWFhYwaNYq5c+cya9YsnnjiiQ5oqUufb3jJ7VE4VVzG9pxc9DodR/JP4XS6UVUVxeulutZBVY2dM6U2Dhw5wYGjx+u2EdGBqnjJyz/JoV8Lzq5YV3E4XRzOP6kFhfprOYwGAyZT3d+DQ78WoCherk7sDjo4cuIUkWEh2B1Ov9X4GbMmkxAXjUGvw2AwEBkRgslk9NuOJffIcbpFhjIsrT96vR6PR8FkNGAw6DEYDKQN6Mt1A/tquw77ehUGo4HgIAt6vR6n0832nANNttX5toy5mPaWbC/RnPb8exLwsb1CtMSUp5fhcnmoqakhJCSE3CPHuTqxO9k5B3B7PHgUr3b8s8mgJ6pbODqdjjNlNsxGE6EhQRiNRlDBZDaSGB/D8cJi3G4PFouJr89ufFhcYtPmFqwWMwB2p4tduUfrAglwJP8UiuIlNNRKj9gorEEWv2Ny9x08xiPzVlBdbT9bphvWenvN7c49ypABdfN8O3YdoKKqFqPRgNFgICzUyuD+vXG53BzOP4nBoGfUiDQyZk3m9inzqbW78CoK1bUOFK9Cz+6xDL+2P6+mB360cCATx7729jGbjX7DeUIm4KF9/54EvGuwEC3h2y0XwO5wYtDr+feeQzjdblSVs8fvAqiYzCb0ej1uj4LRaMSreqmqcRDdLYyR1w8k2GrhVHEZA1OStUwm3434fKci+m7QuXn52J0uzCYjx08Vc+LUGWK6hfsNlf1l/RckJ3bXbub5BafPzs/o/LZU0et0WK0WrEEWBqVejcPp4sSpYg4ePU5peRVhIVb6JSdqT3wj0gbww7/3UVJag+vsXltFZ8r5147dflvN/9+//o3BoKdPUgJBFvNF7UnV8ETJjt6KRIbZLg3t+fekQ4e5xJXDtzWGyWig8EwZ8THdUBRv3YFUWoq1itlsQvGquN1uOHvD9vVYUEGvD3ybjfrDRXaHk27hISiKV+ux6NS6hI+GQ2WFxaXk5uWTs/8wuXn5JMRF+33f+8vT6RZe17tSVRWL2YTD6eTfe/M4caqYk4Wl1NQ6OFNWwZ5Dv5Kbl8/R43VrowwGPZ6za7CMBgNer5eKylq/TSwNBj12p4sj+aca/QdeVFLOq6v/ccEhsM7eikSG2S4N7fn3RIa5RLvKy8vj5dWf8Mvew5wps+FVwePxoEOHyWQgJNiKw+FCp4fI8FCcThegqzurpF8yquqlR1x0QE+8TQ0XqWrdMb27c4/gdivYnU7qNo3Xcc/o4bya/gh3/+FFSsoqsDucKIqX4CALOza9o23pUlZRxYEjJ0iIiybo7CaUh48VcPxkMYrX/z+fIIuJkGArHreHYdcNQK/T8e1Pu3C7PGf3mKwLmPePu7kuJdnlweVyk5d/EsXj5c5bhvr9xtmLVnP41xOEhoY2OQTWnI7sLVwKw2wyzNW+ZJhLXJQL3ajqZ3MVFJdjd7oIDQ6mxm5H1evwKCput0JFVQ3dwkPR6fWYTUbKK6rxer0YjUZtLy8Vnd9JhOe7mTa1hfmK56fzwpt/r5uzUBR06LCYjbg9Ct/+tJu7//AiCbFRnDxdgtdbl81lMBpYsupDLRC5XG6OnzpDwakzRHcLJ7FHbJOBBMDrVXE4XLg9Crl5+aQk9yQqIoyiM+VaGbPJhF5/bsjBbDYxoG/dxpIrX/L/bWUVVVqGW/2NMgMJFOd6C3UZdFnbc7T5nLYOKp09zCY6n+HZZ59d2NmVEJeejOV/51RxGV6vSmVN3b5U4269sdF1p9NFeGgIhUWlmEwGwkKCcbo8eL11B015vSq1DhdhIcGU2arweBT0egN2u4PTJeVUVddQWl5Jua2KiLPZWN//vI8PNmWxdftuevWI5dXMD/lgUxYHjpzAGmTBaDTgVVXioiOZeNfNfP39L1iDLDhdbmpq7dQ6nOjQ4XS6qKquRVG96ACL2YzZZMQaZCEiPBS704XXq3Lw6Alq7Xa8qorBoKfgdAkej3LuiMizTEYDZpOJoCAzXq8XdDoqa2pJSe7JmbIKIsNC6RYeyuD+V6M36Fn8zCPsyj2Cy+0hLrpu6/mQYP9D5rZu301ZeQVms1n7TeNvu/GC7Q/wwaYsrf5OpxuvVyU42Npk2dYaOijlgr+ls5WVlTXaikm0HemZiItyqriU3LzjuNyeuoOj8H9Kb7hYcNh1/ekZH02prYqvv/+F0GArNWdv0FC3V5bn7L5ZqteLTq9D8Xhxut3U2l11q8vdnro1HfV6Ko/MW6FNntdf4V5/lXhZRRXWIAsD+yWz79AxThaV1s3JnJ2bplmRvQAAIABJREFUcThcOJxuHE732cOuVHblHsViNmnnzKuAonipOXsaZGx0BLbKGtweD16vSpDFSEJcDNW1DswmIynJPSkoPIPi8ZKcGE9cdCS2qhq/J/fzJQ/UlzFrMvOX/BkP+ka/qamt/ev3WA4cOUGP2Chcbg+cXXzZXodOBfJbxOVNgom4KMcKirA7XXVbyztd5BcU+V2vn81Vl4EVrd1shoybwfFTZ7SyurNP8IpHwUvdtiS+9Rxnj8wCVMpsVVx7TW/0Oh0VVTXsPnAUu8NFQeEZQoOD0Ov1GA0GrBYzZRVVvJpZtytxkNnMzr15uN0Ker0evV539jt0BFksnCmrQA+4FS+4weVy0zc5EbPJSGFxKQ6XG51aN6eDDtxuD/379OLI8VPYHU7cboW0a3pTeKYck8mASt0k/YCUc0NX9VOYW7IdSlxMJM8//rtGY/3nG1Z6YcX7/PjzPjyKgk5Xt2AzKMiM4lFISe4pQ1Ci3Ug2l2gRX8aUrbIGh6NuI0arpe789PrqZ3M1zBrx9UZ8VFXF4/GgN+gwmYyo6rlNNVWtDKh4QVX5bscetv+SS63diaqq2B0uzpRVUl5RzemScrZm7/bLKvKNRul0YNDrSOweQ2x0BBFhIbhcblSviqfe/IdXVSkoPKNtv/IfQwcSGxOJTg8OhwvT2SBzTd8koiLDSbumD0ePn6bMVqWdb1L/3PmiknIy3vg7W7btYlfuEewOZ6v/fzhfVo7vWGKvV8WjePF4Fb5e9zp33Hw9oaFWvzq1dqGkEPVJNpdokYbrN6xBZr/J46KScl5Y8T4/5eQCOq7pncCLTz7MX9Z/oR0+dfTYKZR6AUWvg9iYSKqq7SgeL3qDjrBQK1XVduwOlxYMLGYTJqMRl9uN82zmkJZGTF0mVd3qdCO3DB8C1GUVAX6ZRl7Vqw257co9SlFxGS6PB9+GjXV10tXNvXjr5kl8dXA63aiA2WQgsXssiT1iOHr8NGdKK9DpITTEytBB/fyymWYvWs3XP+ysO+hKV5cAcMdvrg94WKglWUhDxj9Gba1Da5fg4CB2f/Hn8/7/2NRCyaYm9+tntl2q60gkm6t9Sc9EtIhvrL5PUgJWixnF4/V7Ml6SuZ4ff95Hrd1Fba2DX/b/yiPzVmiHT5WUVfgFEgCvCpVVtVjMJsLDggm2BhEZFso3/7OUkOAgzMa6UxbTrumLy+0hPDQEvV7fqMcRFhKM0Vg3zFT3uXVDOg3PFvcNua17cx6jRlxLZEQounqBBEBFxeX28P+39+bxUdX3Hvf7LLNlJslkDyGEAIEAkUWQRVArordF2+eq14rUx1ZeVRC5T722UUSs1YsVEde21LYWa2u9aqW2F6u1ywWtC1utgLKvkQRIyDKTzGTWc87zx5kZMtkIJCEx/N6vl62c+c2cM7+R8z3f7fONahqhcCSRU4mvCEc0jlRV89HHuzlZ78XA9AQCgXCbUFK9t4lIxAw7SUA0qvVK3gLMscQ2mwVJkrDZLEybMLrddR3lXKD9nhHRRyI4HSJnIjgj4rF6u82ayAncv/gmfrjaVOjdvvsQoXAYSZLRdJ3GpgA19Y0cPHKsTXgrjoT5xB8OR7FYVTLSXBQX5jN21FBumHNp0hO0zWpBNwycDjtN/mbAQFUV0px2ZFnCneYixWFDN3SOVFYjAe40JxlpTgKhZAn4z/Ye5v0tn+Jp9CddmyxJpLlS8Pr8dHDJgFkGrFrMrI4EWC0qzhR7m7BeZnoqFouS8ExURem1vMUPy2/tUm6ms1LejgxNR8ZHIADhmQjOkPZi9S2fWsPhCHWeJmobGqn3+ghHNQzD6NCQgJkXMQBZlnClOJBliUG5me2e73+eWUKWO5VoNEqK3cbMyWOZOn4UUc1AlmRSXSn89qklFORmUVyYjyRJNDT6SXHYeOL+2wH43qO/4K6Hn+Ob312F19eMJJkGTZYkbFYLgNnc2IUAsK7rOFMcpKe5mHnRBcy5fArP/mBRUgho2eJ5zJxcRkqKnRSHlZkXlfVah3q8quqlp+5tcx0t6awTurUn1553J5L4gtYIz0RwRrRXAtrySdYM5UiJUFNXkDB7NFRVQZZM9d740Kt4niUu2pjhTuXiSWNp8pl6VlaLhf1HqrDZrIwfMxzdMPjFq29T720iGomy/0gVwXCYjz4O89f3/4UEjBpWSDAU4fjJelLsdsKRqGnQDANLbMxuJKIlntpPd/HeRh/5uZkdylPkZrvPmfT8gpvm8ItX/9ylfEdHOZuWg7laejdnU40mOH8QCXhBt2mZzP1k536afAFcTgd1DY1tbsbxbm6zN8WcQYJhYFFVJo8bSUqKWXEEtJvoj4swtjweDkewWiyMLB7M/iNVCYXgJl8zUU2nyecHzHJgl9OB3WahbGQxH/zzM6KRKJGolrhOWTJlXnIy3RiGwbHqujZm0WpVMXQdTTNDbJIs82+XXEimO61LCeq4ATheU8fhymqKC/MoyM3q8D2tE8ft9ZLElZCPVJ5IEq1sKSnTkSrx+YJIwPcuwjMRdJn4TexYTR0HjhwjHI6gqAoTRg9L5CRSUuw0+QJ4m/ztPtWbwwylWPmvzujhQzhZ76W23suHH+9CUSRyMt0oikzJ0MEEgiF8zUF8/gAYFYTCEYYNMQsA9h6qpK6hKdE3sufQUQLBEOFIlEAohLfRj8WioukaKXYHzYEAHm8U3YCTtR6QIKrrKKqMpOlouhmOkyQ5oW4sKxK6bhDrcUSK5Tx0SSLVacMAQuEIf/9wG5luFyVDBxMMRZJUgVsbmHhYcPf+zwmEwgQCIUDqVCqmJS1HEXsbfTT5AqiKTDgSpckfoDAvG6vVIvIdgnOKMCaCLtPyJniyzoMkS6TY7fz1Hx+j6TqqqhAOR9sYEVkCWVFQZFNBV4+tjWqw5+Dn6C36SjTNwNPoQ5ZkDlBFIBSOTVA0qKquBQO27T7A6OFFKIpEZrqLIQW57NhziGDI7JR3OuyJAVuSBBZFxdccMENYEbNEOKTrSBKxvIiMalFRYwbD0HUam5pJdTrIzkzH7w/iTLFjUc3OdotF5UjlCRoa/fibA1gtKsFwhFAowsGKY5SNKqaquo6vfvtBPI1+bBaV4UWDEsYiHhYMhsP4mwP4fAGggtYqAu1RXdvAhk3bCIUiWFQVRVFo8DbhSnGAJCFJsO9IJReMGpaU2xC6WYLeRiTgBV0mfhOM5xhMXa0goYg57CoYirTrjegGKLFSXrOpT0LTDQzdiIkltioV1g1SUmwoiowzxYGEuUTCzKfU1jeyZdsePI1+igvzqDx+khS7LfE0HgqbOlQWVUGSZFwuB3Isyd6S+KXquk4kEsUwzExPRNOIRKJYLCqjhxeRmZHG+DEjKBtVjGpRGZSbyZ/WLOeaWVNwOmI5F8OgyR8gEAzFwk3VeBt9EJsOeejz4wmPIJ7MDgTC5vhfiXZVBNrj0dWvomk6mqYTDJuy/ebERxm71cLEMSNQFCUpsd7X8vSC8wPhmQja8Nnew8y/96nE5MFfrypn7Kihp1RuLSoSIMnSqVnopyHVZQcDwmEfhmGW0sb7RFrbn6imoyoKs6ZPBODP727B0+g3q8L02IRGzH6NTdv2oMgSsiSTnubE5w8SjUZRFCWmEgw2i4UUhx1FkQlForRGlmRz3K8Bmq4nhnY1NjUTCkeQZYm9h46iRTUUVWHnvsNs2LSdaRNGk+o0B2dhgK+5mWA4QkFuJhKwY88hGrzm921qDmK3mnNV4gluZ4odo9kgxW7F3o6KQHvUe5soGTqYgxXHCEeiWKwWrp4yLUn3a9b0CW3Uh8/HHIng3CI8E0Eb5t/7FLX1Xhoamzhy9ARzbl1GTa2HBfPmUFF5glA4gsVqISPN1ZXIDAChUBSr1YKqyhgQawhs3xDpus7Jei91DY0snHc17jQXsmzqdYFpbELhCKFwBE3TCUc0NENHlmUmjBmGzWbFMHQ0XcdmVUGClBSbOe2wnfPFcyGGBFpUB8wciT8QZNMnu6muaWBIfjZIUFvnJRzRaPI18+b/baSiqhqP14evOUBGeiozJ5fx7A8WxUqbTymLKZJE7PITlVRzLp/CzIsuYPK4UsaMHJooh+6MzPRUrFYLZaOKmTB2BLOmT+CH5bcKz0PQ5wjPRNAGn88M12i6KbrYHApxzbe/Tyg2zElRZBx2Gy5XCiOHDeYfWz477Wf6m4Nounnj76zk1qIqxJMZ//x0H9+65wmGFeYT1TSCoTDeJn+iy7wlqmx6FicbGpk4doTpSWjmXBQJicbGZgwM3GkumoMhQuFI4r1mgt3sjK86cRIDiUgLDyYYDvPhx7uS/mwYRsKjkmNDrxRFTuqP2bBpG+40VyLX0hwMJ13zssXzeOCpF9n0iSk94051UlPr6VSmpL2yXaHYK+gPCGMiaIPL5aC2wYsUu+kbhoG30YduGNTWNybW1dZ7qDpRi81qSeQNwNTQanmzBrPRLX6D7qx3IxLVkGVTLt3b6E+EtYYMyuV4TR1lo4rZ8NF29Ngo3DiaYU4prPc2mZ30qoqmR/A2+khJsZOe5qTR10xzKISqKBgWwwyDyTKKLJPlTmPqhFH8qa4hSccL2obh9FZDsQzMEmdFkRNeQW62m1nTJyYlvu1WK3c9/FxSdZfDZqN0eBGyJOFp8p+2oksYDkF/RRgTQRt+vaqcObcuIxCKYLWYVVhN/gDBVk/WhgHNgRAOuxVVkdANc8BUR0SiWoevJX+wGeqK6jqNfti570jMq4nSHAglzVWPo2kadQ2NbNi0HU3TSHc5Y7NJTFXjuPz64coTRGLDuarrPKBrRNEIR6M0eP1cfOFYNmzafkb7JQEWi8qs6RPJzXYnlVBXVFYzKDeTYzX1NAeCYJxqmnz0p690qpElEHyREDkTQRvGjhrK2y8+QnFhLukuJ8FQmHAk0mF6xJniQFEUVEVB03WaA6bEutn/0fXzShLYLGpMf0vHYlFx2KwEwxHqvU0EgiGCoTBOh63NezXNYP3GbaiKAoDH5yfd5eSrs6czvGgQ+49UsevA59isFi6dekGb0q76hkY2fbKbj/61q43n0RXiTYfQsg9EZmhhPsdr6hmUk0l9QxMn671s2b6XaCSaCFUJmRLBQEB4JgKgrSxHXUMjjb5mvI3+03oUkYipqNua092UbRY10X0uyzKKIpHhTmPc6GHsPXSUYYX5HKw4RiAURovqaOjouk6Kw27agoSlMvMX0ajZw5LqTMHAIBg2cyzbdh1EliES0dF1jXc3baemzpt0LZpu0OhrBjB7YDr4zi3zPYosoaoqg/OyeOfXjyZyHa29jSZfgObA8UTIMBKNsu9IJVfOnNShdIlA8EVDGBMBkNxVfaymno8+3kkkEu3wptoSb1PzWZ0zLc0JSNhiY273HDqKp9HP3kOfo8iK2XgI+GMNhwYGmqYTCIaxWi1Eo1EMAywWC7Jsdqprmo4BNDeHsFlNKXa7zYKvOZgwQq0NSZz4Z0SjWtKclDbrWhgUd7qTi8aPSkqat1bkdbkceBr9OB02/IFQQn9MJM8FAwlhTATAqafpYCjMwYpjiSmGPUXLm7Msm3M96hsasdttKHJK4qkdw6Cmzouh6xw9fpL01BSQJBw2sylRVWTqPI1kpLsAaGj0o0gSF5aN4MDnx/D5g6Q4rNisKiVDBxMOR2jyBxMhsngYrD1kSUKSiVWxmdfc2ruKG5H4aGGLohIIta3SaultPHzX/8u37nkCb6OPnMx0RgwtMOfCn+VwqfaGV33RBlUJBh7nNGfy1FNPMWvWLIYMGcKIESOYO3cuu3btSlpjGAYrVqxg9OjR5Ofnc80117B79+6kNaFQiHvuuYfhw4dTUFDATTfdRFVVVdIaj8fDggULKCoqoqioiAULFuDxJI8mPXr0KHPnzqWgoIDhw4dz7733Eg4n3xh27tzJ1VdfTX5+PmPGjGHlypU9epPtL8Rj93sPHTWHPfXwd7RYzJyK1aJiUVV0w7xpR6Ma3kYfByqqaPI3o+kaWlQjEtWIRjU8jX7C4QieJh8NjU2MGFpApjvV1MfSDTLSnGS4XWRmpPGVy6bwyZ9+yt9eeowUh51dBz5n8/Y9hCPmb2oYRkJOpT103UA3zPLka2ZNJSsjrZNvZDZQ1tR52XPwaNLY29Yy8GNHDeWtNcu5etZULryghOLCvG6Fs8SgKkF/5Jwakw8++IBvf/vb/OUvf2HdunWoqsq1115LQ0NDYs2zzz7L6tWrWblyJevXrycnJ4frrruOpqZTVS5Lly7lzTffZM2aNbz99ts0NTUxd+5ctBYVPrfddhs7duzg9ddfZ+3atezYsYOFCxcmXtc0jblz5+Lz+Xj77bdZs2YN69atY9myZYk1jY2NXHfddeTm5rJ+/Xoee+wxfvzjH/OTn/ykl3fq3BOX3PA2+gFTiqQn0TWD9NQUJAkiUbOMOFF6jNmjkZWRjhHrQo97BJqmmz0dukE0EuVYTR0Wi+kNGDGpElPbyqwsK3/0F0z66p1UVFbj8wfMcmQD0lwpp22wlGWJFLuNKeNHkeKwEWhVvQZm3t5mVVFkUy3YnHGfddobelfnjHQFUQEm6I/0qQS9z+ejqKiIl19+mTlz5mAYBqNHj+b222+nvLwcgEAgwMiRI1m+fDnz58/H6/VSUlLC6tWrufHGGwGorKxk3LhxrF27ltmzZ7N3716mTZvGO++8w/Tp0wHYuHEjc+bMYevWrYwcOZK//e1v3HjjjXz66acUFhYC8Nprr/Gd73yH/fv3k5aWxpo1a3jooYfYt28fDocDgFWrVvHCCy+wa9euhJx6f+RsQyHj5yykORCmydfcplfkbFFkmfTUlFiYSuFkvbfNZ+fnZHDplHG8tWEzgaCpomu0CClZLSquFDszLiqjsdHP1k/3oWk6US2KLMlkulNN+ZOY2q9hGGbYSjK70OWY9EtnDpcsyzhsVqKahqoq2G1WfP5AUg+NIpvqkbpuYLUouFNdGIDdbuXvLz3WK+Gm1tLpree3F+RmtpFPEbRFSND3Ln1aGuzz+dB1Hbfb/AtYUVFBdXU1V1xxRWKNw+FgxowZbN68GYBt27YRiUSS1hQWFlJaWppYs2XLFlwuF9OmTUusmT59Ok6nM2lNaWlpwpAAzJ49m1AoxLZt2xJrLr744oQhia85fvw4FRUVPb0dXaK6toG7Hn6OW777OHc9/FxSeKUlZxsKmT5xjClB0gOYIS0FWZZo9DVT7/EBkOZytFl7ss6Dt8lPfnYGdpuZ83DYrSix/IphGPgDQT7be4R/frYfTdNxOmzouhku03UjIfAYJ56HUS0qun7KuHT0CKDrOuGo2YMSjWo0NplNk6ZgpLnGlKI3O/RD4SjVdR5qG7xUn2zgylvu6/Q36Yiu/qZxhHCjoD/Spwn4++67j3HjxjF16lQAqqtN1dScnJykdTk5ORw/fhyAmpoaFEUhKyurzZqamprEmqysrCTPQZIksrOzk9a0Pk9WVhaKoiStKSgoaHOe+GvFxcXtfq/9+/d3bQPOgh8+93tO1jciSRL19R6WPPoz7l/0H23WfV55PKmkt+JoqEvXde0Vk9i8bXdSyPBsicRG9saxKQrNgWC74SPdMPA2NjIox03psEHYrRZq6r18svsIwWCIaFTDwOBYdS12m5VIOII/EEwIRsZl6oHkfI8EaU4HqqIwZFAW2/dUoOs6umEOt2qNqWSsI+u6OSjLqhKJaMR1tnTDQG9V4abrBpFIBL+/mQOHj3b4m3REV37T1r/d4nlXJv7d23ASb8PJLp/vfKY3/24OdE7n1fWZMbn//vvZtGkT77zzDkqrCpvW4aN4fL0zWq9pb31X1rQ+3t61dPZeOP2mdwcNGZfLlfhzFLnd8xUVDmoTCmlvXetwWCAYYtTwImrqvES1tjf9M+HUXpmx/Yx0FxPGjOC9zW07zA0DPv7sEKkuO+GIxozJYykZVkSK08mnew7T4PURjkRj2l5R0tJcMU8DmvyBhAhka2RJora+EQM4ftLMzVlUhSx3OpFIBE+THwkJh8NGaoqd6jovptEAq8XCV6+YTorDxutvv08gEOpQCsYwwGG343K5OvxNOgo9nu43FeGZnkHsY+/SJ2GupUuX8vvf/55169YlPd3n5eUBJDyDOLW1tQmPIDc315TOqKvrdE1tbW3SE6phGNTV1SWtaX2euro6NE3rdE1tbS3Q1ns6V3S1Y7oroZDq2ga++u0H+fO7W/jkswMcqazmw493snt/BaF2mhDPhNQUe+JmHw8v1dR5eHfTtnYbHMH0Lhq8fvzNQdZ/tI09B49SUVlNQ1yjC8Aw0Ayd5uYgTb5mnA47s2dMxJlix2azxnpLzM+TpNjclFbniUQ1vE0+mvxBCvKy+I85l/LJn37KlAmlMdFG8x9d19m0bQ/33zmPGZPHkpudgc1maffaZUVmxNCCTn+TB578NX/5xz/52wf/4tV1G5j8tcV8ffEj7Dl4NJYnEl3wgi8u59yYLFmyhLVr17Ju3TpGjRqV9NrQoUPJy8tjw4YNiWPBYJCNGzcm8h8TJ07EYrEkramqqkok3QGmTp2Kz+djy5YtiTVbtmzB7/cnrdm7d29SSfGGDRuw2WxMnDgxsWbjxo0Eg8GkNYMGDWLo0KE9tSVnRFfj5R1VD8Xj8zcufoQp/8//x5HKE6YAYjDEnoOfc+xEHZUnajsVY+wKTc3BWM4iVgKs6bFwUNfCZ5qms3XHXiqqagiFwolOeUWR0TSdDLeLCWNHEIpE2L7nEGDgsFtjDxCmNYnPTWmPUDiKpusEAmE++tdOM6ckSeRkuROVUqFIlBM19Xz129/Hnepi3OhhXD5tgpmEb8XVl08hLTWl099k87bdeBp9aJpORNPwNQfZvf9zCnKzOHGyXuRABF9ozmmYq7y8nNdee43f/va3uN3uRI7E6XTicrmQJIlFixbx5JNPMnLkSEpKSnjiiSdwOp3ccMMNAKSnp3PLLbfw4IMPkpOTQ0ZGBsuWLaOsrIzLL78cgNLSUq688kruvvtunn32WQzD4O677+bLX/5yws294oorGDNmDHfccQePPPIIDQ0NPPjgg3zzm98kLc3sL7jhhhtYuXIld955J+Xl5Rw4cIBnnnmGe++9t88qubrTMR33RLyNPvzNIYIhU2Y+gtaht9BTxLdLVZU2uZSOiCfVWx+z260Eg2E2b9vdaXVWvPS4IwzDwNPkIxC0cKy6PiEf3/IdUU2jorKaaFSjbNRQtu85jKoqENWQFRldN8jKSCPTndaFijkJTdMTzZBSbGql3WaldMQQXnrq3tPuiUDQXzmnxuSXv/wlAP/+7/+edHzJkiUsXboUgLvuuotAIMA999yDx+Nh8uTJvPHGG6SmnnL9H330URRFYf78+QSDQS677DJ+9rOfJeVenn/+eZYsWcL1118PwJw5c3j88ccTryuKwmuvvUZ5eTlf+cpXsNvt3HDDDTzyyCOJNenp6fzhD3+gvLycWbNm4Xa7Wbx4Mf/5n//Z85tzDnh09at4Gv3mxMNoNDYyt/eId73LkoSqyoQjWqwo4OzPqxsGzYFQQkyyI6wWNZaUP83n6UZsXslOrrh4QkKfq+XrqBJNzUH2HqqkdPgQRgwZxL4jlXgafbjTXJQMHZyomHvmwUUd5kamTRjNWxs2E41qsemQZsmzCG0JBgJ92mciOLfc8t3H2bp9H/Wexk47wXuDuHhirKq217HGRCS72slvURWyMtJpbPITjUYJt6jYsqgyedmZaJrO+DHDE8d37D7EqOGFiRG68V6TH65+hSOV1bHjEdxpLv60ZjkADzz5Ipu27UGLathsFkYMLUgoDnfk1XQncSykV04hEvC9izAm5wHxG8qGTduoqfUQCkfOyQ29NRZVQdMNZMkcvXtqqG3fo8gSVosFp9OOrzlo5jUiUVRFxqKqTJlQyvGT9RQX5ic0zD7ZeYBQJIqh6xDT8hpakEtxYT679lcQDEcS6sbXzJpy1uHJ7twEWzc4Ds7LPG+FJYUx6V3EPJPzgHgD44ghBUnjZruDVVXOOG8U70zXdB1JAqu1/cqonuBMU1qyImNgYLOYs+1lyZRNsVotZLpTGTYkn1+vKmdwXibBUIiPPt6JPxAgFAqbJcthU7alztPE4coThCORRLOlzaL2meSJkF4RnCuEavAApWV4Y/vug4wYUhCTM1EJ0f0Ql6IqiWotw+h8FG+c1tMRezPU1lWDGVNbQZYV8nMzmDahlA/+uRNFUUixW7FZrVwypSwhV/LMg4uYeM0i87u0OoemaQSCIYoLS6ioNBWN7VYLw4sG9VlOpLUcvsjNCHoL4ZkMUFrKqWiazr4jlQDY7T3jDQRDEaKabkqZnKWr0x/Ul+OVxOmpDmQkGrx+FEVh/Ojh2G02IlGNjZ/sYee+IwnJk6PHToLRNkSn6wZ2m5WC3Cz+tGY5s6aPR1ZkjlSdIBAMnbHMSk8gpFcE5wrhmQxQWoY3SoYO5nDlCQxD73Kfx+k4nSFQZHMAVGvvQ5YlMt2pNPkCPSYk2RGny8kosdJeu9WCVbXg9TXz6d7DeBv9VB4/iUVVcKY40KIa8+95kqGF+YTDETRNb/fzDMwy4XiS22G3UTp8CLIk0dDoT1R7dZczSaqL4VuCc4XwTAYoLTvlrVYL0yaM5nBlNarauz+5osg4U+xkulPbDWPpukFtfWOvGxLoXPLGoprzVSyqORclrgxcU+shomnmbBPdIBSKMGpYIU2+AOFwhK079rbbCClJpjryW2uWdzi+t6fyFWKeiaA/IozJAKV1eEOSwNvow+cPnv7N3cCdmkIwFOJkfWOvnieOqnT8n/Dpwm+6oZtDuLQovuYAPn8AAwM95nlEohrBcIhAKIzL5eBARRWRSBRZkdsYKouqkpud0WZ8b1ekb84UkVQX9EeEMRmgtJZT8cS63ruT9O7sxh2nzuNrV423t5DakTbpCpGoRiSA9ITBAAAgAElEQVRi9qGkuVJw2CzouoGqKGj6qTCWphns2l/Br1eVoygyiqpgiU2MlCQJRZZML0dVmDm5LOkcvZWv6C0jJRB0B2FMBhCdzcXYd6SKSLR71VPRDnIFfUl3c/impInGReNHk5vtRmmlPixJEjarhbGjhjJr+kSmTRhNdlY6hmFgt1nIyXKT6U4lOzONH5bfmnxt9EwZdmtEUl3QHxEJ+AFEPJYuS1KSvAdAJBI9496LLwLRaDcLCgyDQCjEJzv30xwMtwmNGYapD1Zd20AgGOJw5XFkWaYgP4uiQbk47LaExH/rJHhnv0d3EEl1QX9EGJMBQnVtAxs2bScYDGO1qIwYWkCdp+lU5Y+nKWkKYUsUWUr0jHyRkSUJq1U9I9FKA3MgVqOv2TQMuo5FUYjEemIURcbpsHHVLUvRohqjhhWiWlQy05047DbqPKcqqlojchuC8wlhTAYIj65+FS0m0x4MhTlQUcWVMyclno7daS6O19S3eZ8ECQVbMzDTPeLijn2BbhhmJ3o7WGJqxe2hyBKGAaFwBEd8XknEHI6V6nIgKzLBmNeyv6KKspHFNAfD/PzR/+r0ekTDoOB8QuRMBgj13iZGDSvEbrOYiWJFZtnieYmn41HDCtt9X0F+FpnuVNOI9EAYrK8bETuq4MpIT6UwP5usjDTyst3kZbuxWlRkSUKWZSIxSZRQRCPV5cBqteBOc6IoMiVDB2O1qGAYRCJRdMNsTjzd3HaR2xCcTwjPZICQmZ5KMBShbGRxUgw//nRst1nbfZ+mGXgafX1uBHqb+LezqAqKLKMbRsJTif+/3ariSnGgKBKXXHQBumFQUXkCq9VU9z1QUYWiyBTkZtIcCJ02HyJyG4LzCeGZDBCWLZ5HRrqT3Qcr2HvoKM2BEDv3HaE5EGLvoaN8tvdwu++rrm3oMJcyULCoCjarSjgSwWE3tbZkSYp1vpuClXabhSnjS9F1PZHUlyWJ4sJ8MtKcHK48gaLITJ84hmWL5xEMhxP5kGgkyvqN2zr1Unqbzir5BIJzgTAmA4TcbDcOm43S4UWMGVGEp8nPvO+s4K0Nm6k+2cCJ2oZ232cY3c+T9HdkWSIcjmK1WCgpHsx/f/dbKKpCqiuFnCwz5JXqcmK3WbFYzM54MENmg3IzE7IoY0YMTciitOz12He4Ek3T+7QjXXTFC/oaYUwGEK2rh6qqaxMyIbre/3pEuovShSZKAF3XMQyDQChMRWV1m2IFkHCnObFaVWZMKuOSKWVJeY72qrJa5kMUVaFk6OCk1881onJM0NeInMkAonX1EIZ5I9U41dwny9IACmsZOOwWykqKOVHbwImT9UmNlRbV9DA03aCpOUBGmoviwvxEscL+mDyK1aokaWq1xm61smX7HryNzYDBoNwsgEQ+JD6ACnqvI/104o6ickzQ1wjPZADR8mnZneoEKd4/YhoPSTLH2dpiuYIvMhlpTrIz0sl0p3G8tp6yUcWoqoLdasFus2CxqOi6jizLWFQZV4oDWZYYlJtJZnoqqkVl5NDBsZCWxA9Xv9JhnkGSoMkXQIvNMAkGQzzw1IuJHEUgGCIj5tn0VtXW6cJYonJM0NcIz2QA0Pqp9cn7F7DsyReRZYn4PCpFlpgyvpSiwbnmDHJNo7beS6iDvoz+jDs1BUVVsahmc+bhyhPoRixxLkkoshybcggZ6S4kSULTdBRFSdxkH/3pK6zfuA0kGFaY32mHeiAUxpXiSBhl3TDY9MluSocXxUb4Rhicl8kvVnTed9IdThfGEpVjgr5GGJMBQHuyHZu37UaWZGRZT4zqrayu5djJesBg5uQyDAM2bPqE2vovRnzdoiqk2G2kpbnQohojiwejGwY2q4W9hypRFQUdMz9k5ogMGhp9ZKanMqakiOLCvERo6JkHF3HLdx9PanLsKM+QmZ6KxaIQCkVAkhLezLnMUYgwlqC/I8JcA4D2n1pPdaLHx+pWHa/l6LEajh6r5fd/fp9/bN1Bg9fXh1fedWxWC1kZaUy7cAx/f+kxrrp0Ei6Xg2M1dWSmp1JT60EzdDTN9FC0WFe/oRs0eJs4VlPXJvTTVfXdZYvnMXNyGSkpdlIcVmZeVMa0CaPPqXKvCGMJ+jvCMxkAxJ9aw+FIorFOls2ZG6qiIKkSoXDELAGO/Y9mQG2dF60fJ+MlyfxudpuVC0qHJUp1W4Z0bvnu43zy2QEMQwckdF0DCSSkxB6kuZyMHjGkTYJ92eJ5PPrTVzrV1wIzhNQ6hFVT6+nSe3sKEcYS9HeEMRkALFs8jweefJG3NmxB0zQy0lPJz06j6ngtkiR3WELbXw2JBNhtVlJSbKS5nEydMIrmYDjpph3PE23ffYjaBi8pdjuBUAhNkpAwpx4aMZ0wi0VJeA5nMvK2Mzq7uffUOQSCLxIizDUAiM8bdzpspDpTiESi7D1cSVpqCrnZ6bhS7F3uyegrWsrjG0A4EsHT6MfnD6Dr4LBZqfc2Jaqu4nmiYYX5yLJMcyhEdkY6uVlusjLSURTF1NuKRGnw+qiorOauh5/jgSd+3evNfaKBUHA+0r/vMIIuU+9twmqxYGAq90ajOg6bjbKRxVxYNpL8nIye0HHsNVpLg2m6gabp1HsbeWvDZt7f8mnSzTmeJ7LbrEwZX0pedgYXXlDC1AmlNAeCptyJLGNRVTRN48DnxzhWU8/m7Xt6PXEuGggF5yPn3Jh8+OGH3HTTTYwZMwa3283LL7+c9LphGKxYsYLRo0eTn5/PNddcw+7du5PWhEIh7rnnHoYPH05BQQE33XQTVVVVSWs8Hg8LFiygqKiIoqIiFixYgMeT3Edw9OhR5s6dS0FBAcOHD+fee+8lHA4nrdm5cydXX301+fn5jBkzhpUrV/a5KGJ7OkyZ6amMGFqA3WZBksBuM8UJAYKhMBaL2i9lU2RZRpYkJOlUdVTr16NRjYYmv/lnSeJYdR17Dh7lXzsPsHPfEQzDYNb0Cbz01L1kpKficNixqCqKIqNpGoZhDgeTYzL7vZ04F2N1Becj59yY+P1+xo4dy2OPPYbD4Wjz+rPPPsvq1atZuXIl69evJycnh+uuu46mplNPd0uXLuXNN99kzZo1vP322zQ1NTF37lyzqSzGbbfdxo4dO3j99ddZu3YtO3bsYOHChYnXNU1j7ty5+Hw+3n77bdasWcO6detYtmxZYk1jYyPXXXcdubm5rF+/nscee4wf//jH/OQnP+ml3eka7YVRli2ex7AheVxYVsKcy6fyzos/ZNiQPKxWlWM1dRQNysUWn9VxGs6lB6PrulkwIJ2Sr4+fX5FlohGNcCRKMBjm3U3b2bbrAPuPHCMnI43m5iA1dR627TrIwnlXA6ZXYLOoibCZgYEkgUVV0Q2D6RPHdFgV1VNiiaLySnA+Ink8nj57YB08eDCPP/44N998M2DeTEaPHs3tt99OeXk5AIFAgJEjR7J8+XLmz5+P1+ulpKSE1atXc+ONNwJQWVnJuHHjWLt2LbNnz2bv3r1MmzaNd955h+nTpwOwceNG5syZw9atWxk5ciR/+9vfuPHGG/n0008pLDRnfbz22mt85zvfYf/+/aSlpbFmzRoeeugh9u3blzB8q1at4oUXXmDXrl2xgVLnntb9EVaryktP3dth4je+fvvuQ9Q1eDscEtUbSIDVaiEU7nj6ocNmxeW00+gLAKbmlq7rRKIauqYnPCpJAofdhjvNha7rNHhN6XxJlvn3K6fzixX/xV0PP8fhoyfYf6SKBm8TkiSRn5PJyOLBDIrd2DtKhsdlUeK9HIPzMs+4gqo3ku/79+9n5MiR3foMgdjH3qZf5UwqKiqorq7miiuuSBxzOBzMmDGDzZs3A7Bt2zYikUjSmsLCQkpLSxNrtmzZgsvlYtq0aYk106dPx+l0Jq0pLS1NGBKA2bNnEwqF2LZtW2LNxRdfnORBzZ49m+PHj1NRUdELO9A1OgqjtPZYHnjSlPzYvvsgn+07nGja6ywZ39Pm0aDj+Y0Wi4rDbiMzIxVVUcnJTGfGpLFcOmUcl00dz+D8LKxWC7IsYYl1vLtSHKiqjKfRZwo4Ahg6m7btAUyvYHhRPheNH8Xcr17O9rd/xidv/ZTfrV7Gsz9Y1OmNvSdyHSL5Ljhf6VelwdXV1QDk5OQkHc/JyeH48eMA1NTUoCgKWVlZbdbU1NQk1mRlZSV5DpIkkZ2dnbSm9XmysrJQFCVpTUFBQZvzxF8rLi5u93vs37+/y9/5bJh39TR+/spf8TQ1k56awryrp7F//34+rzxOJKoRjkQ4XFlDXUMTqqqQ6nQgSVBReYIJo4eiaxrHT7YN4aiqjK4ZPZoTsqgyegvxRTNrcerfraqMqshceMEwTtY3EomECYdD5GSmMWnMMDYG91Lv9SX6SCQMykYUmj0ynCojjoQjiX1fPO/KxPm8DSfxNpzs0rUq6Ph8vsTo4ZzMtDP+LeO/QZyKo6Ee+e+ht/+bOl8Q+3j2nM6r61fGJE7r8JFhGKcNKbVe0976rqxpfby9a+nsvXD6Te8uI4HpUya1OV5UOIhjNfUc2V9Bo6855hWAPxAkOzOdC8tKyExPZVRYp6bOi24YyJJMepqTQDCELMn4o8EevdaoZootArEk+6n+FlmWsVotRDWd5pBGTUMTxYV5FORmJfIMDzz5Ih9+vBNvo5/0NCczJpXxw/JbE8ejUQ1VUZh5UVm39/3x++9o04h4piGq+G8QD5UV5GZ2+7pEeKZnEPvYu/QrY5KXlweYT/0tw0+1tbUJjyA3NxdN06irqyM7OztpzYwZMxJramtrk4yHYRjU1dUlfU485BWnrq4OTdOS1sS9lJbngbbeU38g3tH92Z7DiVLbSCSKJksEgiEy01Op9zYRiZj5FsMAzdBRFZlBOZl4fX78gbbGJG4E9JjGV2tkSYqFm9oGtAwDtJhnYg7ikhJ5FFeKHX8ghNViQYpNNWydp+hIPPGR793a4x3oPdFl3tWueoFgoNGvciZDhw4lLy+PDRs2JI4Fg0E2btyYyH9MnDgRi8WStKaqqiqRdAeYOnUqPp+PLVu2JNZs2bIFv9+ftGbv3r1JJcUbNmzAZrMxceLExJqNGzcSDAaT1gwaNIihQ4f2wg60pbq2gduXPsP4OQsZP+cObr/vmQ6rjOI3w0umXIAWGwgF5k08GtFYMG8Oew4eZdO23THtKtNQhEIRnv3BHUQi7Sfm495Ee4bEbrMwKC8Tu9WCoiqmhEnstdYensNmxWazmnkbWabJHyAUjlBcmBc7T9fzFPHv+tJT9542F3Iu6a/XJRD0NufcmPh8Pnbs2MGOHTvQdZ3Kykp27NjB0aNHkSSJRYsW8cwzz7Bu3Tp27drFnXfeidPp5IYbbgAgPT2dW265hQcffJB3332X7du3s3DhQsrKyrj88ssBKC0t5corr+Tuu+9m69atbNmyhbvvvpsvf/nLCTf3iiuuYMyYMdxxxx1s376dd999lwcffJBvfvObpKWlAXDDDTfgcDi488472bVrF+vWreOZZ57hzjvvPGeVXI+ufpWP/rmT5kCY5uYgH/1r52mTupIEqqIgy3GvDAKhCHNufYDUFAcY5s1dkmQy0l2kOOz8/H/+nPBYWtOR7IokQUYs+a/rOlaLijs1BVmWzNLcFtZHlsDptJOTlY6qKKSk2El1OrBZLRypMnNloidDIPjics7DXJ988glf+9rXEn9esWIFK1asYN68eTz33HPcddddBAIB7rnnHjweD5MnT+aNN94gNfXUTebRRx9FURTmz59PMBjksssu42c/+xmKcmrg0/PPP8+SJUu4/vrrAZgzZw6PP/544nVFUXjttdcoLy/nK1/5Cna7nRtuuIFHHnkksSY9PZ0//OEPlJeXM2vWLNxuN4sXL+Y///M/e3OLkqj3NhHVNPNpX5KIRLSkp/f2SlEDoTA5mekEQ2EavE1ouoEsg785wL92Hki81zAMmnzNhG1W/vzeFjTN9Fa6mn83DIhqGkPzcqk+6cGI6gSJkOk2f6va+sakczUHQsyaPtHsQo9qWK3mTPZjNXVYrWq/CwsJjS2BoOv0aZ+J4PTc9fBz/P2DfxGKRMEwsNksXDlzEs/+IHlkrCxJeBp97D7wOeFIhEg4iqzIRKIasizhTnNRHzNCqqIQjTV4KoqMoeu053y0rLzqDAmzzNccxqWboazMdI6eOEk0anagK7JEXk4m776yih+ufqVNkjr+ffoTPdF30hOIxHHPIPaxd+lXCXhBW5YtnkcwFGLjJ7sBiWkTRic9vbfsjdix+xDBcJj4LBNDi3WXy+b0wTiyLCEbkjmJMM0V83Tamo2uPmUYgMvpSJxDVRTKSosJR6L4mwOoqgqSxFWXTCI3291jSere9hyExpZA0HWEMenn5Ga7+fmjHY+DbTmBLxSOxDoxTiW/p00YzfY9B1EVJTYhMGYijFiYyx84bV+J1aIS7iCfIsXiYvHz6YaBy+VIaIXtPfg5umGQnuZMGI2ems3R3oTJnvQcxHRDgaDr9KtqLsGZ01IHSpalRPLbLIsGp9PBDXMuY/f//ZKrZ01JlOHarBYURULX9XYFFuPIskxWRhrZGWkoiozNaj5/xCvBVEWiIC+LLHcqqqKQ6U7l16vKE1phY0YUMufyqby1ZnmP5xt623MQGlsCQdcRnskXlNYhnifvX4ChG6zfuM0cWyvpZGWk4U41GxJv+e7jbN99kGkTR2O1WgiHI2z8ZFdsIqFEOBxFVRV0XTcT9jGDk57mZPzo4QRDYY7V1DF6xBAwDHbuqyAQDONyOfj1qnLGjmpbKr30zptY8ujPE3NIejoM1dueg5huKBB0HZGA78dU1zbwwBO/ZvP2PYCpePvI924lN9vdbnL4/jvb5iLiyW5/c4DNn5j9JYoso6oKsiThdDrAMGgOhshIczFqWCH7jlSiKArTJoxGlqHe62PzJ3tMLS2bleFFgxhelN/mRtvawNU1NLJ1+x4MJCwWhZmTyzpsQjwb2hudOxCrrUTiuGcQ+9i7CGPSj7nr4ef4+4f/IhSKgCRhs6rMnFyGw27jr//4GEWRYzNMrAnl4NbEFYM/2PpZm+52m9VCljsVTddRFYVLppQljceN35jvevg5/rR+E/7mIJqmY7GoTBk/iuLC/KTkd+sqrY8+3olFVbCoKoZhkJJiZ8eff3ZO9m4gIW6CPYPYx95FhLn6MfXeJkLhCL7mALpuICsyH368k7Eji1EUmUAozMGKY4wZOTQpxNPSQ9hz8CgFuVmJUmAgIWSo6zqyIlNWOiypPLe6toEfrn6F4zV1HK6sxtPox9PoR9dNscWoFuZfnx3AarUmJb9b5zB0XUdCiZ+UrteHCQSCLxoiAd+PyUxPpTkQIhqb6WHoOp5GP7IkMbJ4MA67FU3T2ySHW8qgD8rJ5HhNXSKsBafEKi0WFS3a/vsPHz3BB//cyZHKauo9jWiajhGrAJMwZ7S3Tn63lsYflJOJNdZ/YrOoTJ845txsnEAgOOcIY9KPWbZ4Hu40l1nWK8tkpKfhTnOiGwZWq4UxJUP5t8smt9GAaukhOOw2SkcM4W+/WUFxYR6KIqHIEjmZ6YwrHYbL5UgkyOOaX8dq6vjnp/sIBENEYwOqgEQVWHpqCmpsciGckkFpXf3026eXMOPCUqZOHM2Vl0zike/dem43UCAQnDNEmKsfk5vt5qpLJiXlIdypTpwptk4b/tqrcho7aij/euun1NR6eODJF9m0bQ+f7j2MoRs0eBqxWa0EQyF+/uh/caSymkgkiiRJ6LqBIkuosZnqrhSHmUwfW0J2Zlqb5HfrpPz9i/5DxKkFgvMAYUz6Oe11i5+uYqmzDvPcbLfprQwfQk2dh6im0eQPgiTHuuxhWGE+x07UEY5GkdCRFYnBeVlcNH4UgVDbBL1AIBAIY9LPOZteh9xsN0vvvCmRhG/d49EyDBZPxpvqjuaxQbmZXDR+FAc/P0Y4HCE9zdUrTYcCgWDgIHImA5TOZpHHE+UZaS5kyexyt9ksTJswGiDRvX5hWUmvda8LBIKBhfBM+pDeFCps6X2EwxHWb9zOLd99nMz0VBbOu5pfvPo2EnC48kSbUbmi81sgEJwpwpj0Ib0pVNgyCX+gogoMEl7KL159WxgLgUDQowhj0oecrVBhVzyalkl4RZEZMaTgjM8jEAgEXUXkTPqQ1k1+XRUq7CwfEqflLPJZ0yeiWtQzPo9AIBB0FWFM+pCzlTg/U49GSKkLBILeRoS5+pCzTXSfqfS6SKgLBILeRngmX0CEpyEQCPobwjP5AiI8DYFA0N8QnolAIBAIuo0wJgKBQCDoNsKYCAQCgaDbCGMiEAgEgm4jjIlAIBAIuo0wJl3gl7/8JePHjycvL48vfelLfPTRR319SQKBQNCvEMbkNLzxxhvcd999fO973+Mf//gHU6dO5etf/zpHjx7t60sTCASCfoMwJqdh9erVfOMb3+Bb3/oWpaWlrFq1iry8PF544YW+vjSBQCDoNwhj0gnhcJht27ZxxRVXJB2/4oor2Lx5cx9d1RcLMf+9+4g97BnEPvYuwph0Ql1dHZqmkZOTk3Q8JyeHmpqaProqgUAg6H8IY9IFpJhCbxzDMNocEwgEgvMZYUw6ISsrC0VR2nghtbW1bbwVgUAgOJ8RxqQTrFYrEydOZMOGDUnHN2zYwLRp0/roqgQCgaD/IVSDT8PixYtZuHAhkydPZtq0abzwwgucOHGC+fPn9/WlCQQCQb9BeCan4frrr2fFihWsWrWKSy+9lE2bNvG73/2OoqKivr60XufDDz/kpptuYsyYMbjdbl5++eWk1w3DYMWKFYwePZr8/HyuueYadu/enbQmFApxzz33MHz4cAoKCrjpppuoqqpKWuPxeFiwYAFFRUUUFRWxYMECPB5Pr3+/c8VTTz3FrFmzGDJkCCNGjGDu3Lns2rUraY3Yy855/vnnmTFjBkOGDGHIkCFcddVV/OUvf0m8Lvav7xHGpAvcdtttfPrpp9TU1PDee+8xc+bMvr6kc4Lf72fs2LE89thjOByONq8/++yzrF69mpUrV7J+/XpycnK47rrraGo6NUZ46dKlvPnmm6xZs4a3336bpqYm5s6di6ZpiTW33XYbO3bs4PXXX2ft2rXs2LGDhQsXnpPveC744IMP+Pa3v81f/vIX1q1bh6qqXHvttTQ0NCTWiL3snIKCAh5++GHee+89NmzYwGWXXcbNN9/MZ599Boj96w9IHo/H6OuLEPR/Bg8ezOOPP87NN98MmE+Co0eP5vbbb6e8vByAQCDAyJEjWb58OfPnz8fr9VJSUsLq1au58cYbAaisrGTcuHGsXbuW2bNns3fvXqZNm8Y777zD9OnTAdi4cSNz5sxh69atA7I3wOfzUVRUxMsvv8ycOXPEXp4lxcXF/OAHP+DWW28V+9cPEJ6J4KyoqKiguro6qaHT4XAwY8aMREPntm3biEQiSWsKCwspLS1NrNmyZQsulyupoGH69Ok4nc4B2xjq8/nQdR232w2IvTxTNE3j97//PX6/n6lTp4r96yeIBLzgrKiurgZot6Hz+PHjANTU1KAoCllZWW3WxMuta2pqyMrKSurbkSSJ7OzsAdsYet999zFu3DimTp0KiL3sKjt37uTf/u3fCAaDOJ1Ofvvb31JWVpa40Yv961uEMRF0i7Np6Gy9pr31A7Ux9P7772fTpk288847KIqS9JrYy84ZOXIk77//Pl6vl3Xr1rFo0SL+9Kc/JV4X+9e3iDCX4KzIy8sD6LShMzc3F03TqKur63RNbW0thnEqdWcYBnV1dQOuMXTp0qX8/ve/Z926dRQXFyeOi73sGlarleHDh3PhhRfygx/8gHHjxvHTn/5U7F8/QRgTwVkxdOhQ8vLykho6g8EgGzduTMScJ06ciMViSVpTVVWVSHQCTJ06FZ/Px5YtWxJrtmzZgt/vH1CNoUuWLGHt2rWsW7eOUaNGJb0m9vLs0HWdcDgs9q+foNx3330P9fVFCPonPp+PPXv2UF1dzUsvvcTYsWNJS0sjHA6Tnp6Opmk8/fTTlJSUoGkay5Yto7q6mmeeeQabzYbdbufEiRM8//zzXHDBBXi9Xu6++27S0tJ4+OGHkWWZ7Oxs/vnPf7J27VrGjx9PVVUVd999N5MmTRowJZnl5eW8+uqrvPjiixQWFuL3+/H7/YD5tC1JktjL0/DQQw9htVrRdZ2qqiqee+45fve73/HQQw8xYsQIsX/9AFEaLOiQ999/n6997Wttjs+bN4/nnnsOwzB47LHHePHFF/F4PEyePJknnniCsWPHJtYGg0G+//3vs3btWoLBIJdddhlPPvkkhYWFiTUNDQ0sWbKEP//5zwDMmTOHxx9/PFHt9EWno++xZMkSli5dCiD28jQsWrSI999/n5qaGtLS0igrK+M73/kOs2fPBsT+9QeEMREIBAJBtxE5E4FAIBB0G2FMBAKBQNBthDERCAQCQbcRxkQgEAgE3UYYE4FAIBB0G2FMBAKBQNBthDERCLpIVVUV99xzD1dddRWDBg3C7XZTUVFxxp9TUVHBihUrOHLkSJfWL1q0CLfb3e4/0WgUgBUrVnS7F+LIkSMsWrSICRMmkJubS0lJCVdddRWPPPJI0rpx48a1ey1f+cpXunV+wRcbIfQoEHSRQ4cO8cc//pGJEydy8cUXs379+rP6nM8//5yVK1dy8cUXJ2l0dUZ2djavvPJKm+Oq2jN/hT///HO+9KUvMWTIEO69916Kioo4efIkH3/8MevWreOBBx5IWj979mzuu+++pGOpqak9ci2CLybCmAgEXWTmzJns378fgN/85jdnbUzOBqvVypQpU7r1GZqmYRhGuwbopZdewu/3s27dOjIzMxPHr7/+epYvX95mfVZWVrevRzCwEGEugaCLyHLX/rpUV1dzxx13MHr0aHJzcyktLWXu3LmcPHkySaLm2muvTYSI3n///R6/XolfR3cAAAONSURBVLfbzfLly3n66acZP348OTk57Ny5s921Ho8Hu91Oenp6m9e6+r0F5zfCMxEIepiFCxdy9OhR/vu//5vBgwdz8uRJ3nvvPZqbm5kwYQJPPPEE5eXlrFy5kkmTJgFQWlp62s+N50fiyLJ82hv9//zP/1BcXMzy5ctxOp0MGjSo3XWTJk3i+eefZ/78+SxcuJCLLroIm83W4ecahtHmehRFEXM/zmOEMREIepitW7fy/e9/PzFrHEwvJE7ccJSWlnY5VHTs2DGys7OTjpWXl7fJZbTGMAzeeOMNHA5Hp+tuuukmtmzZwosvvsi6deuwWq1MnjyZq6++mttvvx273Z60/vXXX+f1119POvbHP/6Ryy+/vEvfRzDwEMZEIOhhLrzwQn784x9jGAaXXXYZY8eO7fYTe05ODr/73e+SjuXn55/2fbNnzz6tIQFzwuDTTz/NXXfdxV//+le2bNnC+++/z/e//31eeeUV/u///i/pc6666iruv//+pM8oKSnp4rcRDEREMFQg6GF+9atfMWfOHH70ox8xc+ZMxowZw8qVK9F1/aw/02KxcOGFFyb901HIqiVdMTgtKS4uZsGCBfzyl79k165d3HXXXezatYuXXnopaV1GRkab6xHVXOc3wpgIBD1MTk4OTzzxBLt372br1q184xvfYMWKFfzqV78659fSHY9IURS+973vAbB3796euiTBAEUYE4GgFxk5ciQPPvggbreb3bt3AyQS24FAoC8vLYljx44lzT6PEy+Fjs9ZFwg6QuRMBIIz4H//938B2LZtGwB///vfyc7OJisri0suuQSv18u1117L17/+dUaNGoXFYuGtt97C4/Ewa9YswMwtqKrKb3/7WzIyMrDZbJSUlPRpmOjpp5/mvffe4xvf+Abjx49HVVV27tzJj370IzIzM7n55pv77NoEXwyEMREIzoBvfetbSX+Oh4FmzpzJW2+9hd1uZ8KECfzmN7/h6NGjyLJMSUkJzz//PNdccw0AmZmZrFq1imeeeYZrrrkGTdN48803ufTSS8/594kzd+5cotEor732Gk899RTNzc3k5+dz+eWXc++99zJ48OA+uzbBFwMxtlcgEAgE3UbkTAQCgUDQbYQxEQgEAkG3EcZEIBAIBN1GGBOBQCAQdBthTAQCgUDQbYQxEQgEAkG3EcZEIBAIBN1GGBOBQCAQdBthTAQCgUDQbf5/VboA7NrFXNEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sales.scatter('1st Flr SF', 'SalePrice')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6424662541030225"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(sales, 'SalePrice', '1st Flr SF')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In fact, none of the individual attributes have a correlation with sale price that is above 0.7 (except for the sale price itself)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation of SalePrice and SalePrice:\t 1.0\n",
      "Correlation of 1st Flr SF and SalePrice:\t 0.6424662541030225\n",
      "Correlation of 2nd Flr SF and SalePrice:\t 0.3575218942800824\n",
      "Correlation of Total Bsmt SF and SalePrice:\t 0.652978626757169\n",
      "Correlation of Garage Area and SalePrice:\t 0.6385944852520443\n",
      "Correlation of Wood Deck SF and SalePrice:\t 0.3526986661950492\n",
      "Correlation of Open Porch SF and SalePrice:\t 0.3369094170263733\n",
      "Correlation of Lot Area and SalePrice:\t 0.2908234551157694\n",
      "Correlation of Year Built and SalePrice:\t 0.5651647537135916\n",
      "Correlation of Yr Sold and SalePrice:\t 0.02594857908072111\n"
     ]
    }
   ],
   "source": [
    "for label in sales.labels:\n",
    "    print('Correlation of', label, 'and SalePrice:\\t', correlation(sales, label, 'SalePrice'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "However, combining attributes can provide higher correlation. In particular, if we sum the first floor and second floor areas, the result has a higher correlation than any single attribute alone."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7821920556134877"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "both_floors = sales.column(1) + sales.column(2)\n",
    "correlation(sales.with_column('Both Floors', both_floors), 'SalePrice', 'Both Floors')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This high correlation indicates that we should try to use more than one attribute to predict the sale price. In a dataset with multiple observed attributes and a single numerical value to be predicted (the sale price in this case), multiple linear regression can be an effective technique.\n",
    "\n",
    "## Multiple Linear Regression \n",
    "\n",
    "In multiple linear regression, a numerical output is predicted from numerical input attributes by multiplying each attribute value by a different slope, then summing the results. In this example, the slope for the `1st Flr SF` would represent the dollars per square foot of area on the first floor of the house that should be used in our prediction. \n",
    "\n",
    "Before we begin prediction, we split our data randomly into a training and test set of equal size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1001 training and 1001 test instances.\n"
     ]
    }
   ],
   "source": [
    "train, test = sales.split(1001)\n",
    "print(train.num_rows, 'training and', test.num_rows, 'test instances.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The slopes in multiple regression is an array that has one slope value for each attribute in an example. Predicting the sale price involves multiplying each attribute by the slope and summing the result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicting sale price for: Row(1st Flr SF=1207, 2nd Flr SF=0, Total Bsmt SF=1135.0, Garage Area=264.0, Wood Deck SF=0, Open Porch SF=240, Lot Area=9510, Year Built=1962, Yr Sold=2006)\n",
      "Using slopes: [ 9.52065867  8.58939769 11.48702417  9.50389131  9.09151019  9.86944284\n",
      " 10.71929443 10.88966608  8.33339346]\n",
      "Result: 169429.7032316262\n"
     ]
    }
   ],
   "source": [
    "def predict(slopes, row):\n",
    "    return sum(slopes * np.array(row))\n",
    "\n",
    "example_row = test.drop('SalePrice').row(0)\n",
    "print('Predicting sale price for:', example_row)\n",
    "example_slopes = np.random.normal(10, 1, len(example_row))\n",
    "print('Using slopes:', example_slopes)\n",
    "print('Result:', predict(example_slopes, example_row))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is an estimated sale price, which can be compared to the actual sale price to assess whether the slopes provide accurate predictions. Since the `example_slopes` above were chosen at random, we should not expect them to provide accurate predictions at all."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual sale price: 147000\n",
      "Predicted sale price using random slopes: 169429.7032316262\n"
     ]
    }
   ],
   "source": [
    "print('Actual sale price:', test.column('SalePrice').item(0))\n",
    "print('Predicted sale price using random slopes:', predict(example_slopes, example_row))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Least Squares Regression\n",
    "\n",
    "The next step in performing multiple regression is to define the least squares objective. We perform the prediction for each row in the training set, and then compute the root mean squared error (RMSE) of the predictions from the actual prices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE of all training examples using random slopes: 68153.56796456952\n"
     ]
    }
   ],
   "source": [
    "train_prices = train.column(0)\n",
    "train_attributes = train.drop(0)\n",
    "\n",
    "def rmse(slopes, attributes, prices):\n",
    "    errors = []\n",
    "    for i in np.arange(len(prices)):\n",
    "        predicted = predict(slopes, attributes.row(i))\n",
    "        actual = prices.item(i)\n",
    "        errors.append((predicted - actual) ** 2)\n",
    "    return np.mean(errors) ** 0.5\n",
    "\n",
    "def rmse_train(slopes):\n",
    "    return rmse(slopes, train_attributes, train_prices)\n",
    "\n",
    "print('RMSE of all training examples using random slopes:', rmse_train(example_slopes))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we use the `minimize` function to find the slopes with the lowest RMSE. Since the function we want to minimize, `rmse_train`, takes an array instead of a number, we must pass the `array=True` argument to `minimize`. When this argument is used, `minimize` also requires an initial guess of the slopes so that it knows the dimension of the input array. Finally, to speed up optimization, we indicate that `rmse_train` is a smooth function using the `smooth=True` attribute. Computation of the best slopes may take several minutes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The best slopes for the training set:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>1st Flr SF</th> <th>2nd Flr SF</th> <th>Total Bsmt SF</th> <th>Garage Area</th> <th>Wood Deck SF</th> <th>Open Porch SF</th> <th>Lot Area</th> <th>Year Built</th> <th>Yr Sold</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>68.7068   </td> <td>74.3857   </td> <td>56.0494      </td> <td>36.1706    </td> <td>26.4397     </td> <td>21.4779      </td> <td>0.558904</td> <td>534.101   </td> <td>-528.216</td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE of all training examples using the best slopes: 29311.117940347867\n"
     ]
    }
   ],
   "source": [
    "best_slopes = minimize(rmse_train, start=example_slopes, smooth=True, array=True)\n",
    "print('The best slopes for the training set:')\n",
    "Table(train_attributes.labels).with_row(list(best_slopes)).show()\n",
    "print('RMSE of all training examples using the best slopes:', rmse_train(best_slopes))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpreting Multiple Regression \n",
    "\n",
    "Let's interpret these results. The best slopes give us a method for estimating the price of a house from its attributes. A square foot of area on the first floor is worth about \\$75 (the first slope), while one on the second floor is worth about \\$70 (the second slope). The final negative value describes the market: prices in later years were lower on average.\n",
    "\n",
    "The RMSE of around \\$30,000 means that our best linear prediction of the sale price based on all of the attributes is off by around \\$30,000 on the training set, on average.  We find a similar error when predicting prices on the test set, which indicates that our prediction method will generalize to other samples from the same population."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test set RMSE for multiple linear regression: 33025.064938240575\n"
     ]
    }
   ],
   "source": [
    "test_prices = test.column(0)\n",
    "test_attributes = test.drop(0)\n",
    "\n",
    "def rmse_test(slopes):\n",
    "    return rmse(slopes, test_attributes, test_prices)\n",
    "\n",
    "rmse_linear = rmse_test(best_slopes)\n",
    "print('Test set RMSE for multiple linear regression:', rmse_linear)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the predictions were perfect, then a scatter plot of the predicted and actual values would be a straight line with slope 1. We see that most dots fall near that line, but there is some error in the predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def fit(row):\n",
    "    return sum(best_slopes * np.array(row))\n",
    "\n",
    "test.with_column('Fitted', test.drop(0).apply(fit)).scatter('Fitted', 0)\n",
    "plots.plot([0, 5e5], [0, 5e5]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A residual plot for multiple regression typically compares the errors (residuals) to the actual values of the predicted variable. We see in the residual plot below that we have systematically underestimated the value of expensive houses, shown by the many positive residual values on the right side of the graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test.with_column('Residual', test_prices-test.drop(0).apply(fit)).scatter(0, 'Residual')\n",
    "plots.plot([0, 7e5], [0, 0]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As with simple linear regression, interpreting the result of a predictor is at least as important as making predictions. There are many lessons about interpreting multiple regression that are not included in this textbook. A natural next step after completing this text would be to study linear modeling and regression in further depth."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nearest Neighbors for Regression\n",
    "\n",
    "Another approach to predicting the sale price of a house is to use the price of similar houses. This *nearest neighbor* approach is very similar to our classifier. To speed up computation, we will only use the attributes that had the highest correlation with the sale price in our original analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>SalePrice</th> <th>1st Flr SF</th> <th>2nd Flr SF</th> <th>Total Bsmt SF</th> <th>Garage Area</th> <th>Year Built</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>270000   </td> <td>1673      </td> <td>0         </td> <td>1673         </td> <td>583        </td> <td>2000      </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>158000   </td> <td>986       </td> <td>537       </td> <td>1067         </td> <td>295        </td> <td>1949      </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>249000   </td> <td>1506      </td> <td>0         </td> <td>1494         </td> <td>672        </td> <td>2005      </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (998 rows omitted)</p>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_nn = train.select(0, 1, 2, 3, 4, 8)\n",
    "test_nn = test.select(0, 1, 2, 3, 4, 8)\n",
    "train_nn.show(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The computation of closest neighbors is identical to a nearest-neighbor classifier. In this case, we will exclude the `'SalePrice'` rather than the `'Class'` column from the distance computation. The five nearest neighbors of the first test row are shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>SalePrice</th> <th>1st Flr SF</th> <th>2nd Flr SF</th> <th>Total Bsmt SF</th> <th>Garage Area</th> <th>Year Built</th> <th>Distance</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>137000   </td> <td>1176      </td> <td>0         </td> <td>1158         </td> <td>303        </td> <td>1958      </td> <td>55.0182 </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>146000   </td> <td>1150      </td> <td>0         </td> <td>1150         </td> <td>288        </td> <td>1961      </td> <td>63.6475 </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>126175   </td> <td>1163      </td> <td>0         </td> <td>1162         </td> <td>220        </td> <td>1955      </td> <td>68.1909 </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>157900   </td> <td>1188      </td> <td>0         </td> <td>1188         </td> <td>312        </td> <td>1962      </td> <td>73.9865 </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>150000   </td> <td>1144      </td> <td>0         </td> <td>1169         </td> <td>286        </td> <td>1956      </td> <td>75.1332 </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>"
      ],
      "text/plain": [
       "SalePrice | 1st Flr SF | 2nd Flr SF | Total Bsmt SF | Garage Area | Year Built | Distance\n",
       "137000    | 1176       | 0          | 1158          | 303         | 1958       | 55.0182\n",
       "146000    | 1150       | 0          | 1150          | 288         | 1961       | 63.6475\n",
       "126175    | 1163       | 0          | 1162          | 220         | 1955       | 68.1909\n",
       "157900    | 1188       | 0          | 1188          | 312         | 1962       | 73.9865\n",
       "150000    | 1144       | 0          | 1169          | 286         | 1956       | 75.1332"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def distance(pt1, pt2):\n",
    "    \"\"\"The distance between two points, represented as arrays.\"\"\"\n",
    "    return np.sqrt(sum((pt1 - pt2) ** 2))\n",
    "\n",
    "def row_distance(row1, row2):\n",
    "    \"\"\"The distance between two rows of a table.\"\"\"\n",
    "    return distance(np.array(row1), np.array(row2))\n",
    "\n",
    "def distances(training, example, output):\n",
    "    \"\"\"Compute the distance from example for each row in training.\"\"\"\n",
    "    dists = []\n",
    "    attributes = training.drop(output)\n",
    "    for row in attributes.rows:\n",
    "        dists.append(row_distance(row, example))\n",
    "    return training.with_column('Distance', dists)\n",
    "\n",
    "def closest(training, example, k, output):\n",
    "    \"\"\"Return a table of the k closest neighbors to example.\"\"\"\n",
    "    return distances(training, example, output).sort('Distance').take(np.arange(k))\n",
    "\n",
    "example_nn_row = test_nn.drop(0).row(0)\n",
    "closest(train_nn, example_nn_row, 5, 'SalePrice')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One simple method for predicting the price is to average the prices of the nearest neighbors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "143415.0"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def predict_nn(example):\n",
    "    \"\"\"Return the majority class among the k nearest neighbors.\"\"\"\n",
    "    return np.average(closest(train_nn, example, 5, 'SalePrice').column('SalePrice'))\n",
    "\n",
    "predict_nn(example_nn_row)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can inspect whether our prediction is close to the true sale price for our one test example. Looks reasonable!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual sale price: 147000\n",
      "Predicted sale price using nearest neighbors: 143415.0\n"
     ]
    }
   ],
   "source": [
    "print('Actual sale price:', test_nn.column('SalePrice').item(0))\n",
    "print('Predicted sale price using nearest neighbors:', predict_nn(example_nn_row))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Evaluation\n",
    "\n",
    "To evaluate the performance of this approach for the whole test set, we apply `predict_nn` to each test example, then compute the root mean squared error of the predictions. Computation of the predictions may take several minutes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test set RMSE for multiple linear regression:  33025.064938240575\n",
      "Test set RMSE for nearest neighbor regression: 36067.116043510105\n"
     ]
    }
   ],
   "source": [
    "nn_test_predictions = test_nn.drop('SalePrice').apply(predict_nn)\n",
    "rmse_nn = np.mean((test_prices - nn_test_predictions) ** 2) ** 0.5\n",
    "\n",
    "print('Test set RMSE for multiple linear regression: ', rmse_linear)\n",
    "print('Test set RMSE for nearest neighbor regression:', rmse_nn)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For these data, the errors of the two techniques are quite similar! For different data sets, one technique might outperform another. By computing the RMSE of both techniques on the same data, we can compare methods fairly. One note of caution: the difference in performance might not be due to the technique at all; it might be due to the random variation due to sampling the training and test sets in the first place.\n",
    "\n",
    "Finally, we can draw a residual plot for these predictions. We still underestimate the prices of the most expensive houses, but the bias does not appear to be as systematic. However, fewer residuals are very close to zero, indicating that fewer prices were predicted with very high accuracy. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "test.with_column('Residual', test_prices-nn_test_predictions).scatter(0, 'Residual')\n",
    "plots.plot([0, 7e5], [0, 0]);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}