simple_linear_regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams['figure.figsize'] = (20.0, 10.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Gender</th>\n",
       "      <th>Age Range</th>\n",
       "      <th>Head Size(cm^3)</th>\n",
       "      <th>Brain Weight(grams)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4512</td>\n",
       "      <td>1530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3738</td>\n",
       "      <td>1297</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4261</td>\n",
       "      <td>1335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3777</td>\n",
       "      <td>1282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4177</td>\n",
       "      <td>1590</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Gender  Age Range  Head Size(cm^3)  Brain Weight(grams)\n",
       "0       1          1             4512                 1530\n",
       "1       1          1             3738                 1297\n",
       "2       1          1             4261                 1335\n",
       "3       1          1             3777                 1282\n",
       "4       1          1             4177                 1590"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Reading Data\n",
    "data = pd.read_csv('headbrain.csv')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Collecting X and Y\n",
    "X = data['Head Size(cm^3)'].values\n",
    "Y = data['Brain Weight(grams)'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.263429339489 325.573421049\n"
     ]
    }
   ],
   "source": [
    "# Calculating coefficient\n",
    "\n",
    "# Mean X and Y\n",
    "mean_x = np.mean(X)\n",
    "mean_y = np.mean(Y)\n",
    "\n",
    "# Total number of values\n",
    "n = len(X)\n",
    "\n",
    "# Using the formula to calculate b1 and b2\n",
    "numer = 0\n",
    "denom = 0\n",
    "for i in range(n):\n",
    "    numer += (X[i] - mean_x) * (Y[i] - mean_y)\n",
    "    denom += (X[i] - mean_x) ** 2\n",
    "b1 = numer / denom\n",
    "b0 = mean_y - (b1 * mean_x)\n",
    "\n",
    "# Printing coefficients\n",
    "print(b1, b0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABJwAAAJQCAYAAADL1H4pAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xl4lOd9//vPrXUEAgESCAkNizH7JkACgxBgG4GdBS/x\nShYnjuPESZNfmtI2yy9NTtP0ShOyNIl/8XFPnaU9JO6p24ambiPhDUmsEovN5uAFM1oASSAhIc1I\no7nPHxLEwhJomZlnlvfrunqVufXomS8zzyjo4+/9fYy1VgAAAAAAAECwJDhdAAAAAAAAAGILgRMA\nAAAAAACCisAJAAAAAAAAQUXgBAAAAAAAgKAicAIAAAAAAEBQETgBAAAAAAAgqAicAAAAAAAAEFQE\nTgAAAAAAAAgqAicAAAAAAAAEVZLTBYRCVlaWnT59utNlAAAAAAAAxIzq6upGa+3EwRwbk4HT9OnT\nVVVV5XQZAAAAAAAAMcMY885gj2VLHQAAAAAAAIKKwAkAAAAAAABBReAEAAAAAACAoIrJGU796erq\nUk1Njbxer9OlYIRcLpfy8vKUnJzsdCkAAAAAAKAfcRM41dTUaMyYMZo+fbqMMU6Xg2Gy1qqpqUk1\nNTWaMWOG0+UAAAAAAIB+xM2WOq/Xq8zMTMKmKGeMUWZmJp1qAAAAAABEsLgJnCQRNsUI3kcAAAAA\nACJbXAVOAAAAAAAACD0CpzBKTExUfn6+Fi5cqA9+8INqbm52uqQ+3ve+9wWlpm9+85vatm3be9ZX\nr1494nMDAAAAAIDIR+AURmlpaTp8+LCOHj2qCRMm6MknnwzKef1+f1DO8/zzz2vcuHFBOVd/du/e\nHbJzAwAAAACAyEHg5JBVq1aptrb26uPvfe97Kiws1OLFi/WNb3zj6vq3vvUtzZkzR2vWrNHDDz98\ntXNo/fr1+uIXv6iCggL9/d//vRoaGvShD31IhYWFKiwsVGVlpSTplVdeUX5+vvLz87V06VK1traq\nvr5ea9euvdptVV5eLkmaPn26GhsbJUk/+MEPtHDhQi1cuFA/+tGPJEmnT5/WvHnz9KlPfUoLFizQ\nxo0b1dHRMei/c3p6uiTp5Zdf1vr163Xfffdp7ty5+vCHPyxrrSSpurpa69at0/Lly7Vp0ybV19cP\n9yUGAAAAAAAOSXK6ACf88uS/653W2hsfOATTxkzRI3PvGdSx3d3deuGFF/TJT35SklRaWqpTp05p\n//79stZq8+bN2rVrl9LS0vTcc8/pyJEj6urq0rJly7R8+fKr5+ns7FRVVZUkacuWLfrTP/1TrVmz\nRmfOnNGmTZt04sQJbdu2TU8++aSKiorU1tYml8ulp59+Wps2bdLXvvY1dXd3q729vU991dXV+vnP\nf659+/bJWquVK1dq3bp1Gj9+vE6dOqVf//rX+od/+Ac98MADeu655/SRj3xkyK/XoUOHdOzYMeXm\n5qqoqEiVlZVauXKlPv/5z+u3v/2tJk6cqGeffVZf+9rX9Mwzzwz5/AAAAAAAwDlxGTg5paOjQ/n5\n+aqtrdW8efNUUlIiqSdwKi0t1dKlSyVJbW1tOnXqlFpbW3XXXXfJ5XLJ5XLpgx/8YJ/zPfjgg1f/\nvHPnTh0/fvzq40uXLqmtrU1FRUX60pe+pA9/+MO69957lZeXp8LCQj366KPq6urS3Xffrfz8/D7n\nraio0D333KPRo0dLku69916Vl5dr8+bNmjFjxtXjly9frtOnTw/rtVixYoXy8vIkSfn5+Tp9+rTG\njRuno0ePXn1duru7lZOTM6zzAwAAAAAA58Rl4DTYTqRguzLDqb29XZs2bdKTTz6pL3zhC7LW6itf\n+Yo+/elP9zn+yla2gVwJhCQpEAho7969crlcfY758pe/rPe///16/vnnVVRUpN///vdau3atdu3a\npf/6r//Sxz/+cX3pS1/Sxz72sUH9HVJTU6/+OTExcUhb6q53Hr/fL2utFixYoD179gzrnAAAAAAA\nIDIww8kBo0aN0o9//GN9//vfl9/v16ZNm/TMM8+ora1NklRbW6vz58+rqKhI//mf/ymv16u2tjb9\n7ne/G/CcGzdu1E9+8pOrjw8fPixJevPNN7Vo0SL95V/+pQoLC3Xy5Em98847ys7O1qc+9Sk99thj\nOnjwYJ9zFRcX6z/+4z/U3t6uy5cv69///d9VXFwcgleirzlz5qihoeFq4NTV1aVjx46F/HkBAAAA\nAEBwxWWHUyRYunSpFi9erF//+tf66Ec/qhMnTmjVqlWSeoZr//M//7MKCwu1efNmLV68WNnZ2Vq0\naJEyMjL6Pd+Pf/xjfe5zn9PixYvl9/u1du1aPfXUU/rRj36kl156SQkJCVqwYIHuvPNO/eY3v9H3\nvvc9JScnKz09Xb/61a/6nGvZsmX6+Mc/rhUrVkiSHnvsMS1dunRI2+f+5m/+pk+HVk1NzQ2/JyUl\nRf/6r/+qL3zhC2ppaZHf79cXv/hFLViwYNDPCwAAAAAAnGeu3B0slhQUFNgrw7SvOHHihObNm+dQ\nRcPX1tam9PR0tbe3a+3atXr66ae1bNkyp8tyXLS+nwAAAAAARCtjTLW1tmAwx9LhFOEef/xxHT9+\nXF6vV4888ghhEwAAAAAAiHgEThFu+/btTpcAAAAAAAAwJAwNBwAAAAAAQFAROAEAAAAAACCoCJwA\nAAAAAAAQVAROAAAAAAAgovnKd6jlibVqfmCWWp5YK1/5DqdLwg0QOIXRt7/9bS1YsECLFy9Wfn6+\n9u3bN+RznD59us8g8cOHD+v5558fcW2JiYnKz8/XwoULdf/996u9vV2SlJ6ePqR6AAAAAAAIJl/5\nDnU89VXZxjrJWtnGOnU89VVCpwhH4BQme/bs0e9+9zsdPHhQr776qnbu3Cm32z3k8wQjcPL7/e9Z\nS0tL0+HDh3X06FGlpKToqaeeGlY9AAAAAAAEk3f7NqnT23ex09uzjohF4DSAYLfr1dfXKysrS6mp\nqZKkrKws5ebmSpIOHDig1atXa8mSJVqxYoVaW1t1+vRpFRcXa9myZVq2bJl2794tSfryl7+s8vJy\n5efn6+/+7u/0V3/1V3r22WeVn5+vZ599VpcvX9ajjz6qFStWaOnSpfrtb38rSfrFL36hzZs367bb\nbtPtt99+3VqLi4v1xhtv9Fmz1urP//zPtXDhQi1atEjPPvvse+r54Q9/OKLXCAAAAACAa9mm+iGt\nIzIkOV1AJLrSrnclQb3SridJqcWbh3XOjRs36q//+q81e/ZsbdiwQQ8++KDWrVunzs5OPfjgg3r2\n2WdVWFioS5cuKS0tTZMmTVJZWZlcLpdOnTqlhx9+WFVVVfrOd76jbdu26Xe/+50kKTs7W1VVVfrp\nT38qSfrqV7+q2267Tc8884yam5u1YsUKbdiwQZKudldNmDBhwDr9fr/++7//W3fccUef9X/7t3/T\n4cOHdeTIETU2NqqwsFBr1659Tz0AAAAAAASTyczp2U7XzzoiFx1O/QhFu156erqqq6v19NNPa+LE\niXrwwQf1i1/8Qq+//rpycnJUWFgoSRo7dqySkpLU1dWlT33qU1q0aJHuv/9+HT9+fFDPU1paqu98\n5zvKz8/X+vXr5fV6debMGUlSSUnJgGFTR0eH8vPzVVBQoKlTp+qTn/xkn69XVFTo4YcfVmJiorKz\ns7Vu3TodOHBg2K8HAAAAAACD4dqyVUpx9V1McfWsI2LR4dSPULXrJSYmav369Vq/fr0WLVqkX/7y\nl1q+fHm/x/7whz9Udna2jhw5okAgIJfL1e9x76nRWj333HOaM2dOn/V9+/Zp9OjRA37flRlOAAAA\nAABEkis7jbzbt8k21ctk5si1ZeuwdyAhPOhw6sdAbXkjadd7/fXXderUqauPDx8+rGnTpmnOnDmq\nr6+/2i3U2toqv9+vlpYW5eTkKCEhQf/0T/+k7u5uSdKYMWPU2tp69TzXPt60aZN+8pOfyForSTp0\n6NCwa3634uJiPfvss+ru7lZDQ4N27dqlFStWvOf5AQAAAAAIttTizcr42S6N+5dTyvjZLsKmKEDg\n1I9QtOu1tbXpkUce0fz587V48WIdP35c3/zmN5WSkqJnn31Wn//857VkyRKVlJTI6/Xqs5/9rH75\ny19qyZIlOnny5NXupMWLFysxMVFLlizRD3/4Q9166606fvz41aHhX//619XV1aXFixdrwYIF+vrX\nvz6Sl+Kqe+65R4sXL9aSJUt022236bvf/a4mT578nnoAAAAAAADMlU6YWFJQUGCrqqr6rJ04cULz\n5s0b9Dl85Tto14tgQ30/AQAAAADAyBhjqq21BYM5lhlOA0gt3kzABAAAAAAAMAxsqQMAAAAAhJyv\nfIdanlir5gdmqeWJtfKV73C6JAAhFFcdTtZaGWOcLgMjFIvbQAEAAIBY5ivfoY6nvip1eiVJtrGu\n57HEzhIgRsVNh5PL5VJTUxNhRZSz1qqpqUkul+vGBwMAAACICN7t266GTVd1envWAcSkuOlwysvL\nU01NjRoaGpwuBSPkcrmUl5fndBkAAAAABsk21Q9pHUD0i5vAKTk5WTNmzHC6DAAAAACIOyYzR7ax\nrt91ALEpbrbUAQAAAACc4dqyVUq5ZixGiqtnHUBMipsOJwAAAACAM64MBvdu3ybbVC+TmSPXlq0M\nDAdiGIETAAAAACDkUos3EzABcYQtdQAAAAAAAAgqAicAAAAAAAAEFYETAAAAAAAAgorACQAAAAAA\nAEFF4AQAAAAAAICgInACAAAAAABAUIUscDLGPGOMOW+MOXrN+ueNMSeNMceMMd991/pXjDFvGGNe\nN8Zsetf6Hb1rbxhjvhyqegEAAAAAAILNWquADThdRtglhfDcv5D0U0m/urJgjLlV0l2SllhrfcaY\nSb3r8yU9JGmBpFxJO40xs3u/7UlJJZJqJB0wxuyw1h4PYd0AAAAAAAAj4vX7VFFfrTJPpd4/fb3W\n5hY6XVJYhSxwstbuMsZMv2b5CUnfsdb6eo8537t+l6Tf9K6/bYx5Q9KK3q+9Ya19S5KMMb/pPZbA\nCQAAAAAARJzay+dU5qnUrroD6vB7NW3MFI1OSnO6rLALZYdTf2ZLKjbGfFuSV9JWa+0BSVMk7X3X\ncTW9a5LkuWZ9ZTgKBQAAAAAAGIzuQLeqG46p1FOhYxdOKckk6pbJ+Spxr9GsjGkyxjhdYtiFO3BK\nkjRB0i2SCiX9izHmpmCc2BjzuKTHJWnq1KnBOCUAAAAAAMCALvpa9FLNPr1Qs1sXfC3Kco3XQ7Pe\nr/W5K5WROsbp8hwV7sCpRtK/WWutpP3GmICkLEm1ktzvOi6vd03XWe/DWvu0pKclqaCgwAa5bgAA\nAAAAAFlrdfLiWyqrqdT+c0fUbQNanDlXj867T0snzleCCdn92aJKuAOn/5B0q6SXeoeCp0hqlLRD\n0nZjzA/UMzR8lqT9koykWcaYGeoJmh6StCXMNQMAAAAAgDjX4fdeHQLuaavX6KQ0bZq6ViXu1Zo8\naqLT5UWckAVOxphfS1ovKcsYUyPpG5KekfSMMeaopE5Jj/R2Ox0zxvyLeoaB+yV9zlrb3XueP5H0\ne0mJkp6x1h4LVc0AAAAAAADvVtN2VmWeSpXXHVBHt08zxuTp8QUPafXkpUpNTHG6vIhlevKe2FJQ\nUGCrqqqcLgMAAADACPjKd8i7fZtsU71MZo5cW7YqtXiz02UBiAP+QLeqzr+mMk+ljl98Q8kJSbol\nO18b3Ws0M2NqXA4BlyRjTLW1tmAwx4Z7Sx0AAAAgiTAB1+cr36GOp74qdXolSbaxruexxHUCIGQu\neFv0Ys0evVC7R82+S5romqCHZ31A66es1NiUdKfLiyoETgAAAAg7wgTciHf7tqvXx1WdXnm3b+Ma\nARBU1lqduPimSj0VOnD+NVlrtSRrrkrmP6D8rHkMAR8mAicAAACEHWECbsQ21Q9pHQCGqt3vVUVd\nlUo9Faq9fE7pyaP0vmnrtCFvtbJHZTldXtQjcAIAAEDYESbgRkxmjmxjXb/rADASntZ6lXoqVVFf\nJW+3TzPHTtVnFjysVZPzlcIQ8KAhcAIAAEDYESbgRlxbtvbZdilJSnHJtWWrc0UBiFr+gF8Hzr+m\n0jMVOtn8lpITkrV68lKVuIs0M2Oq0+XFJAInAAAAhB1hAm7kytZKBssDGIkmb7NerNmjF2v2qLmz\nVZPSMvXh2Zu1LneFxqSMdrq8mEbgBAAAgLAjTMBgpBZv5poAMGTWWh27cEplnkpVNRyVtVZLs+ap\nxL1Gi7PmMAQ8TAicAAAA4AjCBABAMLV3dWhX3QGVeSpV135e6cmj9YFp63V73mpNGpXpdHlxh8AJ\nAAAAAABErXdaa1XmqVRFXbV8gU7Nypimzy7copXZ+UpJTHa6vLhF4AQAAAAAAKKKP+DXvnOvqsxT\nodeb31ZKQrKKcpapxF2kGWPdTpcHETgBAAAAAIAo0dhxUS/U7NGLtXt0qbNNk0dl6aNz7tLa3BVK\nTx7ldHl4FwInAAAAAAAQsQI2oKMXTqnsTIWqG45JkpZNXKCN7iItzJzNEPAIReAEAAAAAAAiTltX\n+9Uh4GfbGzQ2OV2bZ9yu2/NWaWLaBKfLww0QOAEAAMQpX/kOebdvk22ql8nMkWvLVu4aBwBw3NuX\nalTmqVRlfbU6A12aPW66PjRzk1ZmL1FyAjFGtOCdAgAAiEO+8h3qeOqrUqdXkmQb63oeS4ROAICw\n6wr4tffsYZV5KnSq5R2lJqRoTc5ylbjXaPrYKU6Xh2EgcAIAAIhD3u3broZNV3V65d2+jcAJABA2\nDR0XtLNmt16q2avWrsvKGTVRH5tzt9bmrtDo5DSny8MIEDgBAADEIdtUP6R1AACCJWADerXpdZV5\nKnWo4bgkqWDSQpW4i7RwwmwZYxyuEMFA4AQAABCHTGaObGNdv+sAAIRCW9dlvVy7Xzs9u3Wuo1EZ\nKWN0900bdHveKmW6xjtdHoKMwAkAACAOubZs7TPDSZKU4pJry1bnigIAxKS3LnlUeqZCu88eUleg\nS3PGzdADN9+pFdmLlcQQ8JjFOwsAABCHrsxp4i51AIBQ6Ozu0t5zh1V6pkJvXjqj1MQUrcst1AZ3\nkaaNyXW6PIQBgRMAAECcSi3eTMCEiOEr30EACsSA8+1NPUPAa/epreuyckdP0sfn3qvinAKNYgh4\nXCFwAgAAAOAoX/mOPls8bWNdz2OJ0AmIAgEb0JHGkyr1VOhI40kZY1QwcaE2Tl2j+eNvZgh4nCJw\nAgAAAOAo7/ZtfeeJSVKnV97t2wicgAjW2nlZL9fu086aSp3vuKBxKWN0z00luj1vlSa4xjldHhxG\n4AQAAADAUbapfkjrAJz1Rss7KvNUas/ZQ+oK+DVv/Ew9NOsDKpy0WEkJiU6XhwhB4AQAAADAUSYz\nR7axrt91AJGhs7tTu88eUpmnUm9d8siVmKr1U1aqJK9I7jF8VvFeBE4AAAAAHOXasrXPDCdJUopL\nri1bnSsKgCTpbHuDdnp26+Xa/brsb9eU0dn6xNwPqTi3QGlJLqfLQwQjcAIAAADgqCtzmrhLHRAZ\nAjagQw3HVeap1JGmk0o0CSqctFgl7iLNGz+TIeAYFAInAAAAAI5LLd5MwAQ47FJnm16q3audnt1q\n9F7U+NQM3TfzDt065RZNcGU4XR6iDIETAAAAAABxylqrN1reUamnQnvPHpbfdmv++Jv1kTl3afnE\nhQwBx7AROAEAAAAAEGd83Z3aXX9QpZ4KnW6tVVpiqm7LW6WN7jWakp7tdHmIAQROAAAAAADEifrL\nDdpZU6lXavfrsr9D7vQcPTrvPhXnFMiVlOp0eYghBE4AAAAAAMSwgA3oYMMxlXkq9WrT60o0iVqR\nvVgb3Ws0Z9wMhoAjJAicAAAAAACIQc2+Vr1cu1cv1OxRo/eiJqSO0/0336nbptyicaljnS4PMY7A\nCQAAAACAGGGt1R+a31aZp1J7zx1Rt+3Wwgmz9bE5d2vZxAVKZAg4woTACQAAAACAKOf1+1R5tlpl\nnkq901qnUUkulbiLVOIuUu7oSU6XhzhE4AQAAAAAQJSqu3xeZZ4KvVJ3QB1+r6aNydVj8x9Q0eRl\nDAGHowicAAAAAACIIt2Bbh1sOKZST4WOXjilRJOoW7KXaOPUNZqVMZ0h4IgIBE4AAAAAAESBZt8l\nvVi7Vy949uiCr1lZrvF68Ob369YpK5WROsbp8oA+CJwAAAAAAIhQ1lq93vyWSj2V2n/uVXXbbi3O\nnKNPzPuQlk2crwST4HSJQL8InAAAAAAAiDAdfq8q6nuGgHva6jU6KU2bpq7Rhrwi5Yye6HR5wA0R\nOAEAAAAAECFq2s6qzFOp8roD6uj2afqYKXp8/oNanbNMqYkpTpcHDBqBEwAAAAAADvIHulV9/jWV\neip1/OIbSjKJWjV5qUrcRbo5YxpDwBGVCJwAAAAAAHHJV75D3u3bZJvqZTJz5NqyVanFm8P2/Bd9\nLXqhZo9erNmri74WZbnG6+FZH9D6KSs1NiU9bHUAoUDgBAAAAACIO77yHep46qtSp1eSZBvreh5L\nIQ2drLU6cfFNlXoqVHX+NXXbgJZkztVj8+9XftY8hoAjZhA4AQAAAADijnf7tqth01WdXnm3bwtJ\n4NTu96qirkqlngrVXj6n9ORRunPqOm1wr1b2qKygPx/gNAInAAAAAEDcsU31Q1ofLk9rvcpqKlVe\nVyVvt083jXXrMwse1qrJ+UphCDhiGIETAAAAAEQYp2cLxQOTmSPbWNfv+kj5A34d6B0CfvLim0pO\nSNKqyUu10b1GMzOmjvj8QDQgcAIAAACACOLUbKF449qytc/rLElKccm1Zeuwz3nB29w7BHyPmjtb\nNSktUx+evVnrcldoTMroIFQNRA8CJwAAAAAxJ5o7hMI9WyheXXktR3qdWGt17MIbKvNUqKrhqKy1\nys+ap43uNVqcNYch4IhbBE4AAAAxIpp/wQaCKdo7hMI1Wwg918Nwr4n2rg7tqj+gMk+l6i6fV3ry\naL1/2nptyFutSaMyg1wpEH0InAAAAGJAtP+CDQRTtHcIhXK2EEbundY6lXkqVFFfLV93p27OmKYn\nFm7RLdn5SklMdro8IGIQOAEAAMSAaP8FGwimaO8QCsVsIYyMP+DXvnOvqsxTodeb31ZyQrKKcpap\nxF2km8a6nS4PiEgETgAAADEg2n/BBoIp2juEgjVbCCPX5L2onZ49erF2jy51tik7LUsfmX2X1k0p\nVHoyQ8CB6yFwAgAAiAHR/gs2EEyx0CE0ktlCGJmADejYhVMq9VSq+vxRSdLSifO10b1GizJnMwQc\nGCQCJwAAgBgQC79gA8FChxCG43JXh16p26+dnkrVtzdoTPJofXDGbdqQt1oT0yY4XR4QdQicAAAA\nYgC/YAN90SGEwTp9qVZlngpV1h+UL9CpWRnT9dmFG3XL5HwlJ/ArMzBcfHoAAABiBL9gA4hkvvId\nEROKdwX82nfuiErPVOhUy2mlJCSrKGe5StxFmjE2z5GagFhD4AQAAAAACClf+Y4+235tY13PYyms\noVNDxwW9ULNHL9Xs1aWuNk0eNVEfnXO31uWu0OjktLDVAcQDAicAAAAAQEh5t2/rO2NOkjq98m7f\nFvLAKWADeq3pDyrzVOpgwzFJ0vJJC1XiLtLCCbMYAg6ECIETAAAAAESASNpyFmy2qX5I68HQ1tWu\nV2r3a2dNpc62N2psSrrumrFBt+etUlba+JA9L4AeBE4AAAAA4LBI2XIWbFdCNFnb79dNZk7Qn/Ot\nSx6VeSq1u/6gOgNdmjNuhu6beadWZC9mCDgQRnzaAAAAAMBhTm45C5VrQ7T3SHHJtWVrUJ6rs7tL\ne88dVpmnUm+0vKPUhBQV5xaoxF2kaWOmBOU5AAwNgRMAAAAAOMyJLWeh1m+I1stk5QZly+D59ibt\nrNmtl2r3qa3rsnJHT9Ijc+/R2pxCjWIIOOCokAVOxphnJH1A0nlr7cLetW9K+pSkht7Dvmqtfb73\na1+R9ElJ3ZK+YK39fe/6HZL+XlKipP/HWvudUNUMAAAAAE4wmTmyjXX9rkerAcMyY5Txs13DPm/A\nBvRq4+sq9VTocOMJGWNUMHGhStxrtGDCzTLGDPvcAIInlB1Ov5D0U0m/umb9h9babe9eMMbMl/SQ\npAWSciXtNMbM7v3yk5JKJNVIOmCM2WGtPR7CugEAAAAgrFxbtr53+1kQt5w5IdghWmvnZb1St19l\nnkqd72hSRsoY3XNTiW7LW6VM17iRlgsgyEIWOFlrdxljpg/y8Lsk/cZa65P0tjHmDUkrer/2hrX2\nLUkyxvym91gCJwAAAAAx48rWsli6S12wQrQ3W870DAE/e0hdgS7NHT9TD816vwonLVISQ8CBiOXE\np/NPjDEfk1Ql6c+stRclTZG0913H1PSuSZLnmvWVYakSAAAAAMIotXhzVAdM1xpJiNbZ3ak9Z3uG\ngL956Yxcialal7tCG91Fco+J3m2GQDwJd+D0M0nfkmR7///3JT0ajBMbYx6X9LgkTZ06NRinBAAA\nAACMwFBDtHPtjdrp2a2X6/apratdU0Zn6xNzP6Q1uQUaleQKYaUAgi2sgZO19tyVPxtj/kHS73of\n1kpyv+vQvN41XWf92nM/LelpSSooKLBBKhkAAAAAEEIBG9DhxhMq81TqSONJGWNUOGmRNrrXaN74\nmQwBB6JUWAMnY0yOtfbKrQrukXS09887JG03xvxAPUPDZ0naL8lImmWMmaGeoOkhSVvCWTMAAAAA\nIPgudbbp5dp92unZrQbvBY1LHat7Z27UbVNWaYIrw+nyAIxQyAInY8yvJa2XlGWMqZH0DUnrjTH5\n6tlSd1rSpyXJWnvMGPMv6hkG7pf0OWttd+95/kTS7yUlSnrGWnssVDUDAAAAAELHWqs3W86o1FOh\nvecOqyvg1/zxN+vDsz+o5ZMWKSkh0ekSAQSJsTb2dp8VFBTYqqoqp8sAAAAARsRXviOm7lqG+OXr\n7tTus4dUdqZCb7fWKC0xVcW5hSpxFykvfbLT5QEYJGNMtbW2YDDHcg9JAAAAIAL5ynf0uaW8bazr\neSwROiEpdw9QAAAgAElEQVRq1F9u0M6a3Xqldr8u+9vlTs/Ro/Pu05qc5UpjCDgQ0wicAAAAgAjk\n3b7tath0VadX3u3bCJwQ0QI2oIMNx1XmqdSrTSeVaBK0InuJNrqLNGfcTQwBB+IEgRMAAADgsP62\nztmm+n6PHWgdocX2xhtr8bXqpdp9eqFmtxq9FzUhNUP3z7xTt+XdonGpY50uD0CYETgBAAAADhpw\n69zoDKmt+T3Hm8yccJcY99jeODBrrU61nFapp1L7zh6W33Zr4YRZ+uicu7V84gIlMgQciFsETgAA\nAICDBto6Z1LTZFNcfb+W4pJry9bwFgi2N/bD6/ep8uxBlXkq9U5rrdKSXNrgXq0N7iJNGZ3tdHkA\nIgCBEwAAAOCgAbfOtTUr7fPfZxtXBGB74x/VXz6vUk+ldtXtV7vfq6npuXps/v0qmrxcrqRUp8sD\nEEEInAAAAAAHmcwc2ca6ftdTizcTMEWA671H8aA70K2DjcdVeqZCRy/8QYkmUSt7h4DPHjeDIeAA\n+kXgBAAAADjItWVrn/lAktg6F2Hi9T1q9rXqxdo9esGzRxd8zcp0jdODN79P66fconGpY5wuD0CE\nI3ACAAAAHHSlg4mtc5Ernt4ja61eb35bpZ4K7T/3qrpttxZlztYn5t2rpVnzGQIOYNCMtdbpGoKu\noKDAVlVVOV0GAAAAAEQFr9+nivpqlXkqdaatTqOSXFqXu0Il7iLljJ7kdHkAIoQxptpaWzCYY+lw\nAgAAAIA4Vdt2TmU1ldpVd0Adfq+mjZmiT81/UKsnL2UIOIARIXACAAAAgDjiD3SruuGoyjyVOnbh\nlJJMom6ZnK8S9xrNypjGEHAAQUHgBAAAAABx4KKvRS/W7NULNXt00deiLNd4PTTr/Vqfu1IZDAEH\nEGQETgAAAGHiK98RF0OHAUQOa61OXHxTZZ5KHTj/qrptQEsy5+qT8+7T0onzlWASnC4RQIwicAIA\nAAgDX/mOPrdVt411PY8lQicAQdfh96q8rkplnkrVXD6r0UmjdMfUtdrgXq3JoyY6XR6AOEDgBAAA\nEAbe7duuhk1XdXrl3b6NwCmO0OWGUPO01avMU6nyuip5u32aMTZPn17wkFZNXqrUxBSnywMQRwic\nAAAAwsA21Q9pHbGHLjeEij/Qrarzr6nUU6ETF99UckKSbsnO18apazRz7FSGgANwBIETAABAGJjM\nHNnGun7XER/ockOwXfA264WaPXqxdq+afZc00TVBD8/6gNZPWamxKelOlwcgzhE4AQAAhIFry9Y+\n3S2SpBSXXFu2OlcUwoouNwSDtVbHL77ROwT8NVlrtSRrrkrmP6D8rHkMAQcQMQicAAAAwuBKBwvz\ne+IXXW4YiXa/V+V1B1TmqVTt5XNKTx6l901bpw15q5U9Ksvp8gDgPQicAADAoDDseORSizfzmsUx\nutwwHGda63qGgNdXydfdqZljp+ozCx7Wqsn5SmEIOIAIRuAEAABuiGHHwMjR5YbB8gf82n/uVZV5\nKnWy+S0lJyRr9eSlKnEXaWbGVKfLA4BBMdZap2sIuoKCAltVVeV0GQAAxIyWJ9b2vxUoK1cZP9vl\nQEUAEHuavM16oWa3XqzZq5bOVmWnZWmDe7XW5a7QmJTRTpcHADLGVFtrCwZzLB1OAADghhh2DACh\nYa3V0Qt/UJmnUtUNx2St1dKJ81XiLtLizDkMAQcQtQicAADADTHsGACC63JXh3bV7ddOz27VtZ/X\nmOTR+sD0W7Uhb7Umpk1wujwAGDECJwAAcEMMOwaA4HintValZypUWX9QvkCnZmVM02cXflgrs5co\nJTHZ6fIAIGgInAAAwA0x7BgAhq8r4Nf+c0dU6qnQH5pPKyUhWUU5y1TiLtKMsW6nywOAkCBwAgAA\ng5JavJmACQCGoLHjYs8Q8Nq9utTZpsmjsvTROXdpbe4KpSePcro8AAgpAicAAAAgivjKd9BtGMEC\nNqCjTX8cAi5JyycuUIm7SAszZzMEHEDcIHACAAAAooSvfEefeWq2sa7nsUTo5LC2rnbtqtuvMs9u\nnW1v0NjkdN0143bdlreKIeAA4hKBEwAAABAlvNu39R3eL0mdXnm3byNwcsjblzwq81Sqsv6gOgNd\nmjNuhu6buUkrspcoOYFftwDEL34CAgAAAFHCNtUPaR2h0dndpX3nDqvMU6lTLe8oNSFFxbkF2pBX\npOljpzhdHgBEBAInAAAAIEqYzBzZxrp+1xF6DR0XtNNTqZdq96m167JyR03SI3PuUXFuoUYnpzld\nHgBEFAInAAAAIEq4tmztM8NJkpTikmvLVueKinEBG9CrTa+r7EyFDjWekCQVTFqoje41WjBhlowx\nDlcIAJGJwAkAAACIElfmNHGXutBr67qsl2v3a6dnt851NCojZYzuvmmDbs9bpUzXeKfLA4CIR+AE\nAACAqOIr3xHXgUtq8ea4+vuG25stZ1TmqdTus4fUFejS3HE36YGb79SK7MVKYgh4VIj3nxFApOAn\nJgAAAKKGr3xHny1ltrGu57HEL5QYts7uTu052zME/M1LZ5SamKJ1uYXa4C7StDG5TpeHIeBnBBA5\nCJwAAAAQNbzbt/WdXyRJnV55t2/jl0kM2bn2Ru2s2a2Xa/epratdU0Zn6+Nz71VxbqFGJbmcLg/D\nwM8IIHIQOAEAACBq2Kb6Ia0D1wrYgA43nlCZp1JHGk/KGKPCSYtU4i7S/PE3MwQ8yvEzAogcBE4A\nAACIGiYzR7axrt914Houdbbp5dp9eqFmt853XNC41LG696aNui3vFk1wjXO6PAQJPyOAyEHgBAAA\nECdiYZCua8vWPvNZJEkpLrm2bHWuqAgQre9tqOu21urNS2dUeqZCe88dVlfAr3njZ+rhWR9UwaRF\nSkpIDNpzITLwMwKIHAROAAAAcSBWBuleqTUaw5VQidb3NpR1+7o7tfvsIZV5KvT2pRq5ElN165Rb\ntMG9Wu50Ol1iGT8jgMhhrLVO1xB0BQUFtqqqyukyAAAAIkbLE2v732aSlauMn+0a9HkG25ESrR03\n0ShY7224haLus+0NKvPs1iu1+3XZ36680ZNV4i5ScW6B0hgCDgAjZoypttYWDOZYOpwAAADiQDAG\n6Q62IyVaO26iVbQOSQ5W3QEb0KGG4yr1VOrVppNKNAkqnLRYG91rNHf8TQwBBwCHEDgBAADEgWAM\n0h3s7ca5LXl4ReuQ5JHWfamzTS/V7tVOz241ei9qfGqG7pt5h27Lu0XjUzOCXS4AYIgInAAAAOJA\nMAbpDrYjJVo7bqJVtA5JHk7d1lqdanlHpZ4K7Tt7WH7brQUTZukjc+7S8okLGQIOABGEwAkAACAO\nBGOQ7mA7UqK14yaSDGUGVrQOSR5K3V6/7+oQ8NOttUpLcul292qV5BVpSnp2uEsHAAwCQ8MBAAAw\nKNfOZpIkpbiU9pm/ve4Mp4GOQ/94/f6o/vJ5lXkq9UrdfrX7vXKn52ije43W5CyXKynV6fIAIO4w\nNBwAAABBN9iOlGjtuIkUA87A+vm34uI17A5062DjcZV5KvRa0x+UaBK1MnuJStxFmjNuBkPAASBK\n0OEEAAAARJDmB2ZJA/wbPe0LP4jZ0KnZ16qXavfqhZrdavI2a0LqOK3vHq+VO/5DY+s8BJcAEAHo\ncAIAAACi1EAzsCTF3J3+rLX6Q/PbKvVUat+5I+q23Vo4YbYemXuvFpx8U53/+L+vdnvZxrqerYZS\nTL0GABCrCJwAAACACOLaslUdP/5Sv1+LlTv9ef0+VdRXq8xTqTNtdRqV5FKJu0gl7iLljp4kSWr5\nxuf631oYY6EbAMQqAicAAAAggqQWb1bHM38ttTW/52vRfqe/2svnVOap1K66A+rwezVtTK4em/+A\niiYve88Q8IHCtVgJ3QAg1hE4AQAAICx85TsYJD5IaY/+Vb93qnNt2epcUcPUHehWdcMxlXoqdOzC\nKSWZRK2cnK+N7iLNypg+4BDwgbYWRnvoFun4nAIIFgInAAAAhJyvfEefAIV5PNcXC3f6u+hr0Us1\n+/RCzW5d8LUoyzVeD978ft06ZaUyUsfc8PtdW7bGTOgWLficAggm7lIHAACAoBmoO6LlibX9d6tk\n5SrjZ7scqBShYK3VyYtvqaymUvvPHVG3DWhx5lyVuIu0bOJ8JZiEIZ2Pbpvw4nMK4Ea4Sx0AAADC\n7nrdEczjiW0dfu/VIeCetnqNTkrTpqlrtSFvtXJGTxz2eVOLNxMwhRGfUwDBROAEAACAoPBu3zbg\nXcWYxxObatrOqsxTqfK6A+ro9mnGmDw9vuAhrZ68VKmJKU6XhyHicwogmAicAABAzGI7Tnhdrzsi\n7fPfZx5PjPAHulV1/jWVeSp1/OIbSjKJWjV5qTa612hmxtQBh4Aj8jE3C0AwETgBAICYxPDb8Lte\nd0QsDMGOdxe8LXqxZo9eqN2jZt8lTXRN0MOzPqD1U1ZqbEq60+UhCPicAggmhoYDAICYxPDb8POV\n71DHk38hdfv/uJiYpLTPfbffX1jpQIt81lqduPimSj0VOnD+NVlrtSSrZwh4fta8IQ8B7w/XAQBE\nD4aGAwCAuMfwW4dcu51qgO1VdKBFtna/VxV1VSr1VKj28jmlJ4/S+6au0wb3amWPygra83AdAEDs\nInACAAAxieG34efdvk3yd/Vd9HfJu33be8KD6w0YJ2hwjqe1XqWeSlXUV8nb7dPMsVP1mQUPa9Xk\nfKWEYAg41wEAxK6QBU7GmGckfUDSeWvtwmu+9meStkmaaK1tND2TBf9e0vsktUv6uLX2YO+xj0j6\n373f+jfW2l+GqmYAABA74n34rRPblIbSVRbPHWiRtoXMH/DrwPnXVHqmQieb31JyQpJWT16mEneR\nZmZMDelzx/N1EC8i7XoHED6h7HD6haSfSvrVuxeNMW5JGyWdedfynZJm9f7fSkk/k7TSGDNB0jck\nFUiykqqNMTustRdDWDcAAIgB8Tz81qltSkPpKovXDrRI2kLW5G3WizV79GLNHjV3tmpSWqY+PHuz\n1uWu0JiU0WGpIV6vg3gRSdc7gPALWeBkrd1ljJnez5d+KOkvJP32XWt3SfqV7ZlgvtcYM84YkyNp\nvaQya+0FSTLGlEm6Q9KvQ1U3AACIHanFm+PylxqntikNpassXjvQnN5CZq3VsQunVOapVFXDUVlr\nlZ81Txvda7Q4a05QhoAPRbxeB/HC6esdgLPCOsPJGHOXpFpr7RHTd4DkFEmedz2u6V0baL2/cz8u\n6XFJmjo1tK2/AAAAkcypbUpD6SqL1w40p96b9q4O7ao7oDJPperazys9ebQ+MG29bs9brUmjMkP6\n3NcTr9dBvGDLJBDfwhY4GWNGSfqqerbTBZ219mlJT0tSQUGBDcVzAAAARAMntykNpassHjvQwv3e\nvNNaqzJPpSrqquULdOrmjGn67MItWpmdr5TE5JA851DF43UQL9gyCcS3cHY4zZQ0Q9KV7qY8SQeN\nMSsk1Upyv+vYvN61WvVsq3v3+sthqBUAACBqsU0pcoXjvfEH/Np37lWVeSr0evPbSk5IVlFOzxDw\nm8a6b3wCIEj4WQTEt7AFTtba1yRNuvLYGHNaUkHvXep2SPoTY8xv1DM0vMVaW2+M+b2kvzXGjO/9\nto2SvhKumgEAAKIR25QiVyjfm8aOi3qhZo9erN2jS51tmjwqSx+ZfZfWTSlUenJ4hoAD78bPIiC+\nmZ453SE4sTG/Vk93Upakc5K+Ya39x3d9/bT+GDgZ9dzR7g5J7ZI+Ya2t6j3uUfVsxZOkb1trf36j\n5y4oKLBVVVVB/NsAAAAAkSdgAzp64ZTKzlSouuGYJGnZxAUqcRdpUebssA8BBwDENmNMtbW2YFDH\nhipwchKBEwAAgPN85TvobAiRtq527ao7oJ2eStW3N2hscrpuzbtFt+et0tiqCl53AEBIDCVwCutd\n6gAAABAffOU7+sxusY11PY8lwo8RePtSjco8laqsr1ZnoEuzMqbrc4s2aWX2EiUnJPG6AwAiBoET\nAAAAgs67fVvfQcGS1OmVd/s2go8h6gr4tffsYZV5KnSq5R2lJqRoTc5ybXAXacbYvD7H8roDACIF\ngRMAAACCzjbVD2kd79XQcUE7a3brpZq9au26rJxRE/WxOXdrbe4KjU5O6/d7eN0BAJGCwAkAAABB\nZzJzZBvr+l3HwAI2oFebXleZp1KHGo5LkpZPWqiN7iItmDDrhkPAed0BAJGCwAkAAABB59qytc8s\nIUlSikuuLVudKyqCtXVd1su1+7XTs1vnOho1NiVdd83YoA3uVcp0jR/0eXjdAQCRgsAJAAAAQXdl\nXhB3S7u+ty55VHqmQrvPHlJXoEtzxs3Q/TffqZXZi5WUMPR/qvO6AwAihbHWOl1D0BUUFNiqqiqn\nywAAAECQ+Mp3RE2IcqNaO7u7tPfcYZWeqdCbl84oNbFnCHiJe42mjcl1sPKhidT3JFLrAoBYYIyp\nttYWDOZYOpwAAAAQ0XzlO/psE7ONdT2PpYgLEq5Xa8vyop4h4LX71NZ1WbmjJ+mRufdobU6hRg0w\nBDxSRep7Eql1AUA8osMJAAAAEa3libX9D8LOylXGz3Y5UNHArq01IOm4e5JeyZ+rY5PHyRijgokL\nVeJeowUTbpYxxrliRyBS35NIrQsAYgUdTgAAYNDYfoJIZ5vqh7QeTtd+fq6EHW2pydo9Z6p2zZum\nprGjNbbdq3tuKtFteauU6RrncNUjF6nvSaTWBQDxiMAJAIA4xvaT+BVNQeO7g5xr153U3+fn9MRx\nemX+dFXdlCt/UqJm1TfpngMnlN+aoMy7f+ZovcEUqe9JpNYFAPEowekCAACAc7zbt/W9fbokdXp7\n1hGzrgQltrFOsvZq0Ogr3xG087c8sVbND8xSyxNrR3xe15atUoqr72KKq2fdQVc+P52JCdo9263v\n3F2sv7u7WIem52j1Hzz63//6sr70u91aXnNR6Q//maO1BlukvieRWhcAxCM6nAAAiGNsP4lP1wsa\nR9rlFIquuSvfF2kdWee6WlS+cr52z3ar3ZWinIuterDyNa08VaNRGZNkm9tksnIjotZgi9T3JFLr\nAoB4xNBwAADiGAN241PzA7Ok/v4NaIzG/cupEZ071q+pgA3oUMNxlXkqdaTppBICAeWfPqt1x05r\n1tkmGcXO3zVcoml7JwDEO4aGAwCAQXFt2dqnG0US20/iQCjn3MRq19ylzja9VLtXOz271ei9qPGp\nGbo7abpWbv+VxrW0/PFAPj9Dwhw5AIhdNwycjDEzJdVYa33GmPWSFkv6lbW2OdTFAQCA0GL7SXwK\nZdAYS0ObrbV6o+UdlXoqtPfsYfltt+aPv1kfmb1ZyyctUlJConzJM/j8jEAot3cCAJw1mA6n5yQV\nGGNulvS0pN9K2i7pfaEsDAAAhEdq8WZ+sYszoQwaY6Frztfdqd31B1XqqdDp1lqlJabqtrxVKnEX\nKS99cp9j+fyMTKx2xAEABhc4Bay1fmPMPZJ+Yq39iTHmUKgLAwAAQOiEKiiJ5q65+ssN2llTqVdq\n9+uyv0Pu9Bw9Ou8+rclZrrQk141PEGPCMVspljriAAB9DSZw6jLGPCzpEUkf7F1LDl1JAAAAiGbR\n1PUTsAEdbDimMk+lXm16XYkmQSuyl2iju0hzxt0kY4zTJToiXLOVYqEjDgDQv8EETp+Q9BlJ37bW\nvm2MmSHpn0JbFgAAABA6zb5WvVy7Vy/U7FGj96ImpI7T/Tffqdum3KJxqWOdLs9xA81W6njmr4Pa\n9RTNHXEAgOsztr9b4ka5goICW1VV5XQZAAAACJPBbP+y1uoPzW+rzFOpveeOqNt2a+GEWdroXqNl\nExcoMSHRoeojT/MDs6TB/J6Q4lLaZ/6WgAgA4oQxptpaWzCYYwdzl7oPSPqWpGm9xxtJ1lrLf/oB\nAACA4260/cvr96nybLXKPJV6p7VOaUkulbhXa4O7SFNGZztZesQaaLbSe3BHOQDAAAazpe5Hku6V\n9JqNxXYoAABiSDiG/ALBFIxrdqDtX6d3/ER7J/r1St0Bdfi9mpqeq8fm36+iycvlSkoN4t8i9vQ7\nW2kA3FEOANCfwQROHklHCZsAAIhs4RryCwRLsK7Zdwce3cbotWnZenn+dL0+ZaISPbt1S/YSbZy6\nRrMypsftEPCh6m+2knwdsq0X33Msd5QDAPRnMIHTX0h63hjziiTflUVr7Q9CVhUAABiygbo8on27\ny1A7YELR5UXnWGgE65o1mTlqvtykyrlTVTF3mi6mp2l8W4fuOlarOz77jxqXOibIlceHa+82eG1A\nKIk7ygEABjSYwOnbktokuSSlhLYcAAAwXANta4nm7S5D7YAJRZcXnWOhM9Jr1lqr15vf0v/cd6eq\nOs+qOzFB82rO68Hdr2nh2UtK//S3lUrYFDTcUQ4AMBSDCZxyrbULQ14JAAAYkYGG/EbzdpehdsCE\nossrVjvHIsFwr9kOv1cV9T1DwD1t9RqdlKYNKVO1+n/+R5PeOd0ThHz627w/IXBt1xMAAAMZTOD0\nvDFmo7W2NOTVAACAYet3yG+Ub3cZagdMKLq8BrpT17vPOdwtdwN930i38PX3/VLkdaYM9ZqtaTur\nMk+lyusOqKPbp+ljpujx+Q9qdc4ypSamSLf/WVDrYyslAADDN5jA6QlJW40xPkldkowka60dG9LK\nAADAkMTkdpfRGVJbc//r/Qh2l5evfId6/+kz4DmHu+VuoO/zv16trpeeG/YWvn7P+3/+UrJW6vYP\n65yhMphr1h/oVvX511TqqdTxi28oySTqlsn52uheo5szpoVsCDhbKQEAGBkTizefKygosFVVVU6X\nAQAARqjl0cL+74o1ZrwynjnwnvWBhhqnfeZvhxUStDyxdsAOp7Qv/ECpxZsHPMZk5SrjZ7uGfu6E\nRCnQPeTzDabm4Z7TCRd9LXqhZo9erNmri74WZbnGq8RdpPVTVmpsSnrIn3+47ysAALHMGFNtrS0Y\nzLGD6XCSMWa8pFnqGRwuSbLW8r+0AAAgpGx/3U3XWQ92l9f1tuJdOedwt/EN+PV+wqbBnG+oxw31\n2HCw1urExTdV6qlQ1fnX1G0DWpI5V4/Nv1/zTryhzu/+Xwo01aslDN17sTiEHwCAcLph4GSMeUzS\n/5KUJ+mwpFsk7ZF0W2hLAwAA8W44W+SCOdR4wOfPyh1Rjdf7vgE7nAa5LXDA8w5wbCRo93tVUVel\nUk+Fai+f0+ikUbpj6lptcK/W5FETezrX/u+vhXV7WywO4QcAIJwSBnHM/5JUKOkda+2tkpZK6v8/\nKwIAAASRa8tWKcXVdzGMg9AH8/zDrXGg70sueWhEf+d+z5uULCVe898ZI2CgvKe1Xs+c+Fd97pVv\n6ucnn1NKYrI+veAh/Z9139BH5tylyaMmSrr+nQJDxelrDwCAaDeYLXVea63XGCNjTKq19qQxZk7I\nKwMAAHHP6UHog3n+4dZ4ve/zzVk+7L/zQOcdTo2h4A/4daB3CPjJi28qOSFJqyYvVYm7SDdnTOv3\ne5zY3ub0tQcAQLS74dBwY8y/S/qEpC+qZxvdRUnJ1tr3hb684WFoOAAAQGS54G3uHQK+R82drZqU\nNkEb8oq0bsqKGw4BZ4A3AACRIahDw6219/T+8ZvGmJckZUj6nxHUBwCO85Xv4L9aI+yuve6Slt8q\nf/VLXIeIWdZaHbvwhn5/6P/TQf95WSMtPNeiT0xdq4I1jyjBDGa6Q8/2tv7uPsj2NgAAItd1Aydj\nTKKkY9bauZJkrX0lLFUBQAhde9v0cAyfBfq77rp+//9e/TrXIWJJe1eHdtUfUJmnUnWXz2u09/9n\n787D4zivO9//XuwAF4AkuIFoUhT3RVxEiBtIaiNoWdbiRZYleomdeDySnXHudXQnj51J4tiO7Lmj\n+E6czDjxJLaTXNMe3ZtJwucmM0ZTG4nmClIUJYqUKIoiGwsXkACIhVj7vX8AoECwAXQD1V1V3d/P\n8+gRUF2oOl1VDbIOzznVpQffuaCtp85reku7lHNE3ZnTxt0myGcFAADviqWl7p8l/Ttr7YXkhDR+\ntNQBGAmtGXDDcNfdUFyH8LPzLXUKhqtUVX9Unb1dWjB5rra+/JrWnnhbOb2RW9blWgcAwH8cbamT\nNEXSSWPMYUltAwuttfyTEgBfcmP4LBDr9eX2dUi7KeLVE+nRoUsnFAxX6Z2mc8rOyNbm/iHgCwrn\nqumH/1WK8g+cbl/rwHjRJg0AI4sl4fQHCY8CAJLITJsdvcJp2mwXokG6GO66i7aeW2g3RTyudjRq\nT/iAXq49oOtdrZqZX6zPLn5M981Zr4nZE26u5/TvXJKi8ALapAFgdLEMDWduE4CUwvBZuCHqdTeU\ny9dhx64Xbo+vq0Mdu17ghgmSpIiN6OS1M6oMh3T08luSpLXTl6siUK5V05ZEHQLu5O9ckqLwiqi/\nL4fi9yeANDdqwskY0yJpaB10s6RqSb9rrX0/EYEBQKIwfBZuiHbdea39gnZTDKet+4ZeqzusPeGQ\n6tuvaFL2BD06/wFtL92s6flTR/xZJ3/nkhSFV/ilTRoA3BRLS91/llQjaZckI+kpSQskHZP0U0n3\nJSo4AEiU3K2PcXOCpIt63X35j90JJgraTTHUB9drFQxXKVR/TJ2RLi0qvENfXblDG2auVk5mdszb\ncep37niSorTiwUl+aJP2Cz6bQOqKJeH0mLV29aDvf2KMOW6t/T1jzLcSFRgAAEgu2k0hSd2RHh26\n9IYqL1TpTPMHysnIVvnsdaoIbNb8yQFXYxtrUpRWPDjND23SfsBnE0htsSSc2o0xT0r6f/u/f0LS\nwG/W2x85AgAAfIl20/R25cY1vVRzQK/UHNT17lbNKpiuzy/5uLaV3KOJ2QVuhydp7ElRWvHgND+0\nSfsBn00gtRkb5TG1t6xgzJ2S/kzSJvUlmA5K+t8l1UpaZ62tSnSQ8SorK7PV1dVuhwEAAOBpERvR\nm6xNdhoAACAASURBVFffVTAc0rErJyVJ62asVEWgXCunLoo6BNxtY2m/aXpykRTt77zGqOjFMwmK\nFMBo+GwC/mOMOWqtLYtl3VieUve+pEeHedlzySYAAACMrLW7Xa/VHtaempAutjdocvZEPT7/QT1Y\nulnF+VPcDm9EY5kHlYj5ZMydAcaP2YFAaoulpQ4AAAAp4P3rYQXDIe2vP6auSLeWFM3XEws+qvUz\nVyk7I3X/Wuj0fDLmzgDOYHYgkNpS928WAAAkCJUN6SFVznNXb7cOXjquYDik95rPKzcjR1tLylQR\nKNe8SXPcDi8pnJ5PxtwZwBnMDgRS26gznPyIGU4AgEQZWtkgScrJU/4zz3vuL8heSph4KZZY4vHT\neR7O5far2lOzX6/UHlJrd5tKCmaoIlCubSX3qCA73+3wfI25MwCAdOXoDCdjTK6kT0m6Y/D61trv\njDVAAAD8yi+VDV5q+fFSLLHG45fzPFTERnSi4R1Vhqt0vOGUjKTVtde07Y3TWtqZo/ydK5Q7j2TT\neDF3BgCA0cXSUvfPkpolHZXUmdhwAADwNnu1Pq7lbvFSwsRLscQaj1/O84CWrja9VndYwXBIl29c\nVWHOJD2aNVcbf/n3mtLUfHM95gw5g7kzAACMLpaEU6m19qGERwIAgA/4pbLBzYTJ0Ha1aMcrWbHE\ns9/By/1yns82X+gbAn7xdXVHurV0ygI9tehjumfGXWr72gOyg5JNknxRpeUHzJ0BAGB0sSSc9htj\n7rLWvpnwaAAA8Di/VDa4lTCJ1q42HLeSN7EcGy+f567eLh242DcE/Oz1C8rNzNG9JetVEdisuZNK\nbq6XyKSj12ZyuSF362Np954BAIhHLAmnLZK+aIw5p76WOiPJWmtXJTQyAAA8yC+VDW4lTKK2q0nq\n/+tDUmMZTizHxovn+VJ7g/aE9+vVukNq7W7XnAkz9aWln9KWkjIVZOXdtn6iko5em8kFAAC8adSn\n1Blj5kVbbq09n5CIHMBT6gAAcKcKZdind0kyxSVJiSWW9+2XCp2Ijeh4wykFwyG90XBaxhjdM+Mu\n7Qhs0bIpC2SMGfZnE/WkveZnt0VPZBWXqPDHe8e8XYyNX65lAEBqiOcpdcMmnIwxk621140xU6O9\nbq29No4YE4qEEwAg0Zy6yUu1m0W3kxFjSbKM5Rwk+rxd72rVq7WHtCe8X1c6rqkod7IenLNJD5Ru\n1NS8opi3k4g4h00qGqOiF8+Ma9uDpdpnIxESlVQEAGA48SScRmqp2yXpEfU9nc6qrxZ+gJV055gj\nBADAx5xqKUrF1iS3Zx/F+0S8sZyDRJ03a63ONl9QZbhKBy8dV3ekR8unLNTOxY+qbMZdysrIjHub\niZgzlIz5YE4f41RNXnntCZAAAAw2bMLJWvtI///nJy8cAAC8z6mbvFS8WXR79lG8g7LHcg6cPm+d\nvV3af/F1BS9U6VxLjfIzc3X/nI3aHtiswERvPRVPSk5S0cljnIqJ3QFuPo0SAIDRxDI0HAAADOLU\nTV6q3SwOrSLJ/3d/mvQb+nirb8ZyDpw6b/VtV7SnZr9eqz2stp52lU6Ypd9c9oS2zF6n/ChDwL0i\nGUlFJz8bqZjYHWAmFsm2NN6+3KUnQAIAMBgJJwAA4uRUS1EyWpOSxStVJPFW34zpHEwolFqb4vuZ\nfhEb0bErbysYDunE1dPKNBlaP3O1KkrLtXTKnSMOAfeSRLTqDebkZyPVErsDOvftlm1vuf2FrGzX\nngAJAMBgGW4HAACA3+TtfE7KGVKBMoaWIqe24wUjVZEkU+7Wx5T/zPMyxSWSMTLFJSMOUI73HHTu\n2y11tN3+QmbWiOetubNF//T+Hv3Ovu/pT4//jWpa6/XpBR/Vn2/7Q3191Re0bOrIT5xLN05+NoZL\nUvkxsTtYx64XpN6e21/Im+D7yi0AQGoYtcLJGPP31trPj7YMAIB04VRLkdvzjpzkpSqSeKpv4j0H\nHbtekHq6b1tuCibd9jPWWp1p/kCV4ZAOXTyuHturFVMX6fNLPq5101cocwxDwNOFk58NtwfZD+bk\n8PJhP1ttzeOIEAAA58TSUrdi8DfGmExJ60b7IWPMT9X3lLvL1tqV/cu+K+lxSRFJlyV90VpbZ/r+\nSe/PJD0sqb1/+bH+n/kNSf+hf7Pfs9b+bSxvDACARHKqpSjRrUnJMloL1M0b7YY6KSNTivTKFJck\nNMEW6819POdg2MTaoBa7jp5OhS4eU+Wpf9UF26q8rm5tDTeqYvkjml/29NjeTBpy8jMm6dbrb1D1\nXbI+f063naZSSy4AIDUN21JnjPmmMaZF0ipjzPX+/1rUlyj65xi2/XNJDw1Z9p+staustWsk/X+S\n/rB/+UclLer/7yuSftwfw1RJfyRpg6T1kv7IGDMl1jcHAACSY6QWqIEb7Zs3x5FeSR/ecHfu2+14\nPLfs01rH9jVSe1Z922X97el/1Nf2flt//faL6r1ar537Tuj7vwjqyZcPacpP/iQh7xWjy9362IfX\naBKuv2icbjtNpZZcAEBqGjbhZK39vrV2kvqSRJP7/5tkrZ1mrf3maBu21u6VdG3IsuuDvp0gyfZ/\n/bikv7N9DkoqMsbMlvQRSUFr7TVrbaOkoG5PYgEAAJeNNDsp6o32gATNeUrUTKmhN/m9xuj4goD+\n/FPb9Y3Q9xUMh7SmeLme23tav/8Pr2rr6fPK6+l1bP8YO7fnjDnddhrvvDIAAJJt1JY6a+03jTFz\nJM0bvH5/Qiluxpg/kfQFSc2S7u9fPEdSeNBqNf3LhlsebbtfUV91lObOnTuW0AAAwDgM1wI12g11\nIuY8JWqm1MD7u/wP/1n7ZuSqavmdaizI0dRsqycDD+v+ORtVlDtJTd/7Tlz7d3K2D6JL9pyxoed0\nPE83HE6qtOQCAFJTLEPDfyDpKUlvS+r/JzpZSWNKOFlrf1/S7xtjvinpt9XXMjdu1tqfSPqJJJWV\nldlRVgcAAAky9EbbTCySbWkcdv1EzJxJxHwba63eaTqnysImHf7Y3eq1vbpr2mJ9KbBFdxcvv2UI\neDz7d3q2D6JL5syjaOdUWdlSZtatT5ajBQ4AkMJiGRr+CUlLrLWdDu/7F5L+VX0Jp1pJgUGvlfYv\nq5V035DlrzocBwAAcEjUG+3MrL6b7ShPd0vUDbeTTybr6OlUVf1RBcMhXWitU0FWnnYEyrU9UK6S\nCTPGvf+RWr1IODknmU+ri3pOe7plJk2RcvOpZAMApIVYEk7vS8qWNO6EkzFmkbX2TP+3j0s63f/1\nbkm/bYz5lfoGhDdba+uNMb+W9PygQeE7JI06PwoAAL/za4tV1Bvt3h5pYpFMXkHSnlJ3y5PJxngM\na1svKVgT0t66I7rR06F5k+bo3yz/jDbPWqu8rFzH9p/sVq905cQ1EauRnmZY9NMjju8PAAAvGjbh\nZIz5c/W1zrVLOm6MeUmDkk7W2q+PtGFjzC/VV51UbIypUV8l08PGmCWSIpLOS3qmf/V/lfSwpPf6\n9/el/n1cM8Z8V9LAn8zfsdbeMogcAIBU4+cWq2GTJG3NKvxZdVJjGct8m55Ir45eeUvBcEgnr51R\nlsnUxllrVBHYokWF82SMcXz/PN4+eZI184hzCgDAyBVOA38rPKq+CqS4WGufjrL4b4ZZ10r62jCv\n/VTST+PdPwAAsUhGJVG8+/Bzi1W8N9rxHJtEnqvGzma9XHNQL9UcUGNns4rzpuipRR/TfSUbVJg7\nadj9S+OvmElmqxeSg3MKAMAICSdr7d8mMxAAAJItGZVEY9mHn1us4rnRjufYJOJcWWt1qvGsguGQ\njlw+oV4b0appS/Vby57Q2unLlWEyRt7/f/09ydqbQ6DHGlMyW72QHJxTAAAk01dcNMIKxrypvta6\nwZrVVwH1PWvt1QTFNmZlZWW2ujq5ZfsAAP9pfnZb9Gqc4hIV/nhMD2N1ZB/JiCuRYq1Eiud9OnlM\nbvR0aF9dtYLhkGraLmpCVr7unbNBFYHNmlUwPerPDLf/aPxynuBffp3xBgDwP2PMUWttWSzrxjI0\n/H9K6pW0q//7pyQVSLoo6eeSHh1DjAAAuC4ZlURj2Yff23FinZMTz7Fx4lyFW+sVDIe0r65aHb2d\nmj+pVF9Z8ZQ2z1qr3MycMcU63nWBePl5xhsAIL3EknDabq29e9D3bxpjjllr7zbGfC5RgQEAkGjJ\nGOw7ln2kSztOPMdmrOeqJ9Kr6stvqjJcpVONZ5WdkaWNM9doR2CLFhTOjXkI+HD7H25dIFH8POMN\nAJBeYkk4ZRpj1ltrD0uSMeYeSZn9r/UkLDIAABIsGZVEY91Hsp6m5aZ4jk28x/FaR5Neqjmgl2sP\nqqnzuqbnTdXTix7RfXM2aHLORGdizcq+ZYbTaDElGm1W6cHPM94AAOklloTTlyX91BgzUZKRdF3S\nl40xEyR9P5HBAQCQSMmoJEqXaqWxiOfYxLKutVZvN77XPwT8TVlrtbp4qSqWP6k1xctuGQLuVKyx\nxp9otFmlj2RUZgIA4IRRh4bfXNGYQkmy1jYnNCIHMDQcAJCuhla5ZK27Xz1HX3E9IZJI7T0d2ld3\nRMFwSLVtlzQxu0D3zdmg7aWbNbOg2O3wbhqpAmm81Ul+HzSfDpyqQBuaXJQk5eQp/5nnU+6zDQDw\nHkeGhhtjPmet/b+NMd8YslySZK394biiBAB4Di05/hatyqX717+4+XqqVb1caKnrGwJeX63O3i4t\nmDxXz6x4WptmrVHOKEPAk22kCiRJ465Oos3K25ysQKNqEgDgFyO11E3o//+kZAQCAHAXLTn+F3WY\n8FA+Hy7cE+nR4UsnFAyHdLrpfWVnZGvzrLWqCJRrQeFct8Mb1kiDnge+jvZarOeJNitvc3rQdzrM\neAMA+N+wCSdr7V/1//+PkxcOAMAtPPnI/2KtZvFj1cvVjia9VLNfL9ccVHNXi2bkT9NnFz+me0vW\na1LOhNE34LKxVCDFc57GOpyeqsbkoAINAJCORh0aboxZLOnHkmZaa1caY1ZJesxa+72ERwcASBpu\niPxvuCqXaOv5gbVWb117V8FwSEevnJS1VmuLl6kisEWripeMawh4so1WgTTe6qSxtFlR1Zg8VKAB\nANJRLE+p+2+S/g9JAxVPJ4wxuySRcAKAFMINkf/l7XxON370u5JGeCBIDFUvbmvrvqG9dYe1J7xf\nde2XNTF7gh6Zd58eLN2sGQXT3A5vTEarQBpLddJQ8bZZUdWYPGOtQAMAwM9iSTgVWGsPDwwL79eT\noHgAAC7hhsj/crc+phs/+sawr5viEk+3TJ1vqVXlhSqF6o+pM9KlRYXz9NWVO7Vh5hrlZGa7Hd64\nxFKBlOzWNqoak4dB3wCAdBRLwqnBGLNA/f9caox5QhJ/EwGAFMMNkffFMm/HFJdEr1QrLlHhj/cm\nK9SYZwN1R3p0+NIbqgxX6d2mD5STka3y2XerIlCu+ZMDnop1vNsbqQLJjSHQfqtq9Pu8KQZ9AwDS\nTSwJp69J+omkpcaYWknnJH02oVEBAFzBDZF3xTpvxwuVarHE2nCjsW8IeO1BXe9q1ayCYn1+yePa\nVrJeE7MLPBWrm9tLJC9cK7Hy03EFAAB9jLUjzHkYvKIxEyRlWGtbEhvS+JWVldnq6mq3wwAAwDHN\nz26LuXLJ7UqQ4WK1xSUKf/cnN4eAS9Ld01doR6BcK6ctdmUIeDzH1Y3tJZrb10qs/HZcAQBIVcaY\no9basljWHbbCyRhzVdIhSSFJ+yUd8kOyCQCAVBTPvB23K9WGxtSWk62DiwPau3yeLh/7K03OnqjH\n5j+oB0s3aXr+VJei7OP0HCO/zUVy+1qJld+OKwAAGLmlbr6kjZI2S/qmpHXGmHPqS0CFrLUvJiE+\nAIDH+aVCwu/8NG9nINYL0wr12vJ5OrKwVN1Zmbrzaqs+fdfntGHmamVnxNLVn3hOH1c/nSc/4bgC\nAOA/w9auW2uvW2srrbXfttbukDRX0s8lfUzSL5MUHwDAwwbmqtiGOsnam3NVOvftdju0lJO38zkp\nJ+/WhR6ct9PV262jT35O/+fjW/X9T25T9YI52nCmRt/afUB/WPqotsxe55lkk+T8cfXLefIbjisA\nAP4zUktdifqqmzZLuqd/8VFJ/0HSgcSHBgDwuo5dL9w6cFiSujrUsesFqpwc5vWnCF65cU17wiG9\nUntILd1tmjVztj79xrvaePykJkyarryd3/JMrIM5fVy9fp78iuMKAID/DDs03BgTkXRM0v8l6f+x\n1nYlM7DxYGg4ACRH05OLpGh/jhijohfPJD8gJFXERnTi6jsKXqjS6w2nJEllM1aqIlCulVMXyxjj\ncoS0fA7gOAAAACc4MjRcUrmkTZI+IekbxpgP1FfZdEBStbW2c7yBAgD8jbkq6am1u02v1h7WnvB+\nXbrRoMKcSfr4ndv1YOkmTcub4nZ4Nw20fA5U4Q20fEpKq2QLxwEAALhh2Aqn21Y05g5Jj0r6HUml\n1tq8EX/ARVQ4AUByDL2RlSTl5Cn/mee5kU1BZ5svKBgOaf/F19Ud6daSovnaEdii9TNXKctDc5kG\nND+7LXpCtLhEhT/e60JE7uA4AAAApzhV4SRjzFJ9OMepXFKRpIOS/nK8QQIA/I+5Kqmvq7dLBy4e\nVzAc0tnrF5SbmaN7S+7R9kC55k0qcTu8Edmr9XEtT1UcB6QLWkcBwFtGGhreIKlOfS10eyX9wFr7\nXrICAwD4Q+7Wx/gLfQq61N6gPTX79WrtIbV2t6tkwgx9cekntXV2mQqy82+u5+UbPFo++3AckA5o\nHQUA7xmpwmmBtbY5aZEAAABXRWxExxtOKRgO6Y2G0zLGqGz6Su2Yu0XLpyy8bQi412/w8nY+F7Xl\nM2/nc+4F5QKOA9IBT00FAO8ZNuFEsgkAgPRwvatVr9Ye0p739uiK7dDk9g49fP6atq99QrPWfHrY\nn/P6DR4tn33S/Th4uQoPzqF1FAC8x3sTPgEAruCmzL/Gcu6stTp7/YL+V/WvdKirTj2ZGVpUd1WP\nnzqnNecuKtNa6fBJdZrcYbcVrU1LGvkG72asDXVSRqYU6ZUpLknY9UbLZ590PQ5er8KDc2gdBQDv\nIeEEAPDUTRmJr/jEe+46e7u0/+LrCoardO56jXK7e7T53bC2nTqvOY0tt648QrVS577dkoyk2592\nO9wN3m1PNYz0xhQzMFZer8KDc2gdBQDvGTXhZIzJlfQpSXcMXt9a+53EhQUASCav3JR5KfHlF7Ge\nu4vtVxQM79drtYfV1tOuORNm6qnjF7Th+FvK6+4ddvvDVSt17HpB0ZJNkoa9wYsa6wgxA+NFm1X6\nSPfWUQDwolgqnP5ZUrOko5I6ExsOAMANTt2Ujbc6ySuJLz8Z6dxFbESvX3lbleGQTlw9rUyToXtm\nrFJFoFzLpixQ858tlmz0pNGA4aqVRro2hm3BG+V6IgkAp9FmlV7StXUUALwqloRTqbX2oYRHAgBw\njRM3ZU5UJ1GNEL9o564lL0f7716hqn3fU0NHo6bkFuqJBQ/p/jkbNTWvcMSfvcUI7SjDXjPFJbd8\nPzgJKZMh2eGrqUgCeJsf211pswIAwD0ZMayz3xhzV8IjAQC4Jm/nc1JO3q0Lo9yUde7breZnt6np\nyUVqfnZb/xyfPiNVJ8VquIRDshMRI71Prxk4d1bS+zOm6Gf3rdW3dlbon1aUakb+NP1vq7+oH239\nA31qwUduSTYN/tloTHGJ8p95ftiEQizXzEAS0jbU9VVSRYZPNpEE8Lah53Igoezlz4bUl+zOf+b5\nvkSoMaNe1wAAwDmxVDhtkfRFY8w59bXUGUnWWrsqoZEBAJImltkXo1UwOVGd5IVqBL/NkbKbPqLD\nPXXac+V1hYsKlNfdq3tzAvrohs9rzsSZI/7seGaexPKzw85s6n86XTKeUjeYHyt0vMLP7a60WQEA\n4A5jR5vdYMy8aMuttecTEpEDysrKbHV1tdthAEBKaX52W/T2q4lFKvpZ9bCvm+ISFf54b8z7cTsp\n4NT7SLT6tssKhkN6re6w2ns6FJg4WxWBcm2dXaa8rFy3w5MkNT25KPqMKGNU9OKZpMZy2xPyJCkn\nj2qXGHnpXAIAAPcYY45aa8tiWXfYCidjzGRr7XVJLcOtAwBIH8NWKrU2qXPfbseqk9yuRvDiHKmB\nJFzPtYt6a8US7dt8j05GGpVpMrR+5mrtCJTrjjffUufz31TH1Xp1TputrHX3q+foK65W83hpYLOf\nK3Tc1rlv97Dzt5i7BQAAhjNSS90uSY+o7+l0Vn2tdAOspDsTGBcAwGNGGjDdseuFm9U/fm9Z8lKS\nROq72b/0828rdOdM7at4QI0T8zWlpV6fLFymivIvqih3cl/1zl/9/i1tgN2//sXNbbjVFuiFFskB\nXkwk+sHNyrBo87eYuwUAAEYwbMLJWvtI///nJy8cAEh9breMjVXezud040ffiPrawE17oqqTknnM\nvJIksdbq3aZz+pd3/0HHntiq3swMLa25oicPvKW7zl9S1rSTKnzg65JGmJU0mAvVPOOZEeU0ryUS\n/WKkOVy0IwIAgJHEMjRcxpgpkhZJuvk4GmutdwZZAIBPuDWQ2omETe7Wx9Txs+/KtjTe9loib9qT\nfcycTpLEe+w7ejpVVX9UwXBIF1rrlD9jkra9/YG2nfpAs5rbbq43uDIn1iodN6p53G6RHJCMRKJf\nk8kjGfaasRHfvzcAAJBYoyacjDFflvQ7kkolHZe0UdIBSQ8kNjQASD1uzJFxMmGT96U/SHr1jxvH\nzKkkSTzHvrbtkoLhkPbWHdGNng7Nm1SiLy9/Unf94JvKuVRz27YHJ/lGancc7mfSTaKrrfz2dMNY\nURkGAADGKpYKp9+RdI+kg9ba+40xSyU9n9iwACA1uTFHxsmEjRstUn6evTPase+N9OrolZOqDFfp\n5LUzyjSZ2jhztXbM3aJFhXfIGKPOz3xj1CRf1OqdoZi3k9Bqq1QdSu6VFlMAAOA/sSScOqy1HcYY\nGWNyrbWnjTFLEh4ZAKQgN6oFnE7YJLtFys8VFsMd46b2a3rpbKVeqtmva53NKs6bos8s/Jjun7NB\nhbmTblk3liRftHW88JS6dOLnxOhIvDSHCwAA+EssCacaY0yRpH+SFDTGNEo6n9iwACA1uVEt4OeE\njeTvCovBx95Kem/WVL22/A69Pr9EkbP/U6umLdGXlj2hu6cvV4bJGHY7sST5oq7z5T8e71tIaU7O\nXPL752wkXpnDBQAA/GXUhJO19hP9X37bGPOKpEJJ/yuhUQFAinKjWsDPCRvJ3xUWeTufU+Nf/4EO\nzSvW3uV3qG7qZOV3dqsiO6CPbPyCZk+Y7naIacvpmUt+/5wBAAA4zVhrh3/RmExJJ621S5MX0viV\nlZXZ6upqt8MAAM9IxadneV1N68W+IeDhA+pQrwINzbrvQqO2bP6CJm/7xOgbQEI1P7stekVScYkK\nfzy2B/HyOQMAAKnOGHPUWlsWy7ojVjhZa3uNMe8YY+Zaay84Ex4ApBcv3ITSEjM28Z67nkivqi+/\nqWA4pLcb31OWydSm2WtVESjXwsJ5MsY4ti8v8GPMAxIxc4nPGQAAwIdimeE0RdJJY8xhSW0DC621\n/I0KAEaRqo9KTwfxnLtrHc16ueaAXqo9oKbO6yrOm6KnFz2i++Zs0OSciY7uyyv8GPNgqTxzKVX4\nOaEJAABGaamTJGPMvdGWW2tfS0hEDqClDoBXJKJtB8kx2rmz1upU41lVhqt05PKbitiIVk9bqh1z\nt2hN8bIRh4DHuy8v8mPMgw1NmEmScvKU/8zzJDU8gPMDAIA3OdZSJ92aWDLGFEu6akfLUgEAJKXu\no9LTwXDnqP36FR26UKXKcJVq2y5pYnaBHp57r7YHNmtmQbGj+/LydeLHmAe7bRj9xCJZa3Xjz39X\nHbteoJrGZR27Xrg12SRJXR3q2PUC5wUAAJ8YNuFkjNko6QeSrkn6rqS/l1QsKcMY8wVrLU+qA4BR\n0LbTJxGtMYlutxl67mqnTNLe5Xfo0MJSdZ7+B803k/TMiqe1adYa5WTmOLqvwcu9yo8xDzUwc8mJ\n9kDav5zl94QmAACQRqr3/wtJz0v6paSXJX3ZWjtL0jZJ309CbADge3k7n5Ny8m5dmGaPSh+4mbcN\ndZK1N2/mO/ft9tQ2h8rb+Zx6srNVfWeJ/vSRzfreE/dp/+KA1n5Qr9/7x7369z//H9r4/sVxJ5sG\n9uXEddK5b7ean92mpicXqfnZbY4ej6FS6doeqZomFsm4HtPNcIlLPyU0AQBIdyO11GVZayslyRjz\nHWvtQUmy1p4e6Sk7AIAP3da2k4aVD4lojUl0u83Vjia9PDtbez7zgK7n56j4eps+efCkNr0b1sTO\n7lvicGJ/TlwnyR7inUrX9niraWj/cl7ezueiznDyY0ITAIB0NVLCKTLo6xtDXmOGEwDEKN0flZ6I\n1piEbNNanbx2RsFwSNVX3pK1ViuuNOrekx9oec3lqCXBTrb3jPc6cSPpkSrX9njbA2n/cl4qJTQB\nAEhXIyWcVhtjrksykvL7v1b/93nD/xgAYCTpNuslEbN+nNxme/cN7a07omA4pLr2y5qYPUEPZZZq\n87/8i6Zd+GDUOLyCpMfYjbeaJhXmWXlRqiQ0AQBIV8POcLLWZlprJ1trJ1lrs/q/Hvg+O5lBAkCq\nSMdZL4mY9ePENs+31Oqv335RX33t2/rbd/5RBdn5enblTv0wc50e/Zu/GTXZ5LX2HmbejF3u1seU\n/8zzMsUlkjEyxSXKf+b5mJMdqTTPCgAAwCkjVTgBAByWjrNeEtEaM9Zt9kR6dOjSCQXDVXqn6Zyy\nM7JVPvtuVQTKdefkgCSp+bu/e/s5GpCRKUV6ZYpLPFeZxsyb8RlPNQ3tXwAAALcz1qbeOKaysjJb\nXV3tdhgAcJumJxdJ0X7vGqOiF88kP6A00XCjUS/VHNDLtQd0vatVM/OLVREo171z7tHE7Am3rfXv\nLAAAIABJREFUrOvnc+REu6aXWj69FAsAAAAkY8xRa21ZLOtS4QQAScSsl+SJ2IjeunZGwQtVOnrl\npCRp7fTl2hHYorumLVaGid5V7udzNN6ZN8l+0p1fYgEAAED8SDgBQBLR9pR4rd3t2lt3RHvCIdW3\nX9Gk7Al6dP4D2l66WdPzp4768+l8jrzU8umlWNLJaFVlVJ0BAIBYkXACgCRi1kvinLteo2A4pFD9\nUXVFurWo8A59deUObZy1RtkZsf9xl87nyEtPuvNSLOlitKoyqs4AAEA8SDgBQJLxqG/ndEd6dPDi\ncQXDVTrTfF45ytA9H1zSva+f0lwdVd7O+couianF/Bbpeo681E443lioxInfaFVlVJ0BAIB4kHAC\nAPjOlRvXtKdmv16pOaiW7jbNKpiup7MXquxv/5sK2lolSVbNVF/EyUvthOOJhUqcsRmtqoyqMwAA\nEA8STgDgIKoqEidiIzpx9R0FwyG9fuVtSdK6GStVESjXyqmL1PLV+2T7k003UX0RFy+1E44nFipx\nxma0qjIvVcABAADvS1jCyRjzU0mPSLpsrV3Zv+w/SXpUUpeks5K+ZK1t6n/tm5J+S1KvpK9ba3/d\nv/whSX8mKVPSX1trf5ComAFgPMZTVUGianit3W16tfaw9oT369KNBk3OmajH52/Xg6WbVJw/5eZ6\nVF84w0vthGONhWthbEarKvNSBRwAAPC+RFY4/VzSX0j6u0HLgpK+aa3tMcb8R0nflPR7xpjlkp6S\ntEJSiaQ9xpjF/T/zXyRVSKqRdMQYs9ta+3YC4waAMRlrVQXtP9G9fz2sygtV2n/xdXVHurWkaL4+\nvfCjWj9zVdQh4FRfYADXwtiMVlXmpQo4AADgfQlLOFlr9xpj7hiyrHLQtwclPdH/9eOSfmWt7ZR0\nzhjznqT1/a+9Z619X5KMMb/qX5eEEwDPGWtVBe0/H+rq7dbBS8dVeaFKZ69fUG5GjraVlKkiUK55\nk+aM+LNUX2AA18LYjVZV5qUKOAAA4G1uznD6TUn/vf/rOepLQA2o6V8mSeEhyzdE25gx5iuSviJJ\nc+fOdTRQAIjFWKsqaP+RLrdf7RsCXntIrd1tKpkwQ7+x9BPaNvseFWTnx7QNqi8wgGsBAADAfa4k\nnIwxvy+pR9IvnNqmtfYnkn4iSWVlZdap7QJArMZaVZGu7T8RG9EbDadVGa7SGw2nZYxR2fSVqghs\n0YqpC2WMiXubTlVfMFPL/6jEAQAAcFfSE07GmC+qb5j4g9bagcRQraTAoNVK+5dphOUA4CljrapI\nt/aflq42vVp7SHtqQrp845oKcybpE3dW6IHSTZqWV+R2eMzUAgAAAByQ1IRT/xPn/r2ke6217YNe\n2i1plzHmh+obGr5I0mFJRtIiY8x89SWanpK0M5kxA0A8xlJVkS7tP+81n1cwHNKBi6+rO9KjpVMW\n6KlFj+ieGXcpKyNLnft2q9kDxyARM7WomAIAAEC6SVjCyRjzS0n3SSo2xtRI+iP1PZUuV1Kwv1Xi\noLX2GWvtSWPMi+obBt4j6WvW2t7+7fy2pF9LypT0U2vtyUTFDABuSdX2n67eLu2/+LqC4ZDevx5W\nXmau7i3ZoB2BcgUmfdgy6KWqIqdnannpvQEAAADJYj7saksdZWVltrq62u0wACBtXWpvUDAc0qu1\nh9XW0645E2ZqR2CLtpSUqSAr77b1m5/dFn2OVXGJCn+8N659j7eayMlYErE9AAAAwC3GmKPW2rJY\n1nXzKXUAgBQSsREdbzilygtVeuPqaWWYDN0z4y7tCGzRsikLRhwC7lRVUdRqoh99Qzd++h3l/+Yf\nxpR4cnqmFk8hBAAAQDoi4QQAGJfrXa16pfag9oT3q6GjUUW5k/WpBR/RA3M2aWpeYUzbcOpJfVHn\nL0lSa1PMbWxOz9RK16cQAgAAIL2RcAIAxM1aq/eaz6syXKWDF4+rx/Zq+ZSF+tzix7Ruxl3KysiM\na3tOVRWNWDUUZfD3cO13Ts7USrenEAIAAAASCScAQBw6e7u0v/6YKsNV+qClVvmZuXqgdJMqAuUq\nnThrzNt1qqpouGqiAYMTUska5p0uTyEEAAAABmNoOABgVPVtV7SnJqTXag+rreeGAhNnqyJQri2z\n1yk/yhBwtwxNIg01eFA3w7wBAACA+DA0HAAwbhEb0bErJxUMh3Ti6jvKNBlaP3O1dgTKtaTozhGH\ngLvlZjXRz74r29J464tD2tgY5g0AAAAkDgknACltuBk9qcDJ9zZ4Wy2zAzr0+Mf1WlaTGjoaNTW3\nUJ9e8FE9ULpRRbmTHX4XzhuYvzTa8WGYt3+k8ucYAAAgVZFwApCykjWjZzzGeiPt5Hvr3Ldb7X/5\nLb1flK/X7lujY/NL1NtzTssjU/T51V/SuukrlBnnEHAvGG3wN8O8/cEPn2MAAADcjhlOAFKW12f0\nRJ03lJOn/GeeH/VG2qn31tHTqT1/+rRem1ukmmmFyuvq1qZ3w9r29nnNzp7sieOUSFTOeJ/XP8cA\nAADphBlOACDvz+jp2PXC7cOtuzrU8bPvjpoEGe97q2u7rGC4Sq/VHdGNtfM052qzdu57Q/e8V6u8\nnt6+bZm2+N/UOLiR/IlWBUUSylu8/jkGAABAdCScAKQsr8/oGfZGuqVR6h94PVz70FjeW2+kV8eu\nnFRluEpvXTujTJOpDTNXa/N/36U73z2joSPAk3mcvNI25ZU48CGvf44BAAAQXYbbAQBAouTtfE7K\nybt1oYdm9MR8w9zV0VcNNUg8762p87r+x/uV+vq+7+mHb/xM9e1X9JmFD+svtv2R/t2qz2vlQ8/K\nuHychq32GvK+3Yrjxo++oeZnt6lz3+6kxgPvf44BAAAQHRVOAFLWQEWKV9ujog6tHsbQaqjR3pu1\nVu80va/KcEiHL51Qr+3VXdMW60vLPqm1xctvGQLuhePklbapkfZHtZM7vHB9AgAAIH4MDQeABBtp\nJtDQ12xHu9TadNs2Yh2Q3NHTqX311QqGQwq31qsgK0/3lqxXRaBcsyfMcPy9OcWJwdBOzF4aLo6x\nxgQAAACkEoaGA0AUbgyDHm0m0NCh1cM9uW609qGa1osKhkPaV3dEN3o7NW/SHP2b5Z/R5llrlZeV\n6/wbc1jUaq842qacmr0US9UZw6oBAACA0ZFwApAW3BoGPdJsomj7jad9qCfSq6OX31RlOKS3G99T\nlsnUxllrVBHYokWF82TM0DHg3jXetql4j3NMcQxT6cSwagAAAGB0tNQBSAtutWw1PblIivZ71hgV\nvXgmpv0O1djZrJdqDujlmoNq7GxWcd4UbQ9s1n0lG1SYO2lM20yWRFWZJeI4D1dtlv/M88wPgme5\nUckJAADSBy11ADDEeIdSj7VCyqlHultrdarxrCrDVaq+/KZ6bUSrpy3Vby17QmunL1eG8f5DRxNZ\nZebUcR6MYdXwG7cqOQEAAKIh4QQgLYw3ITHWlq3xziZq7+lQVV21KsNVqm27pAlZBXpo7jZtD2zW\nrILpMW3DK5xqe4tmvMd5OENnbMGbqOrpk8jPGAAAQLxIOAFIC+NNSIy1QmqsVTLhlnoFa0LaV1et\njt5OzZ9cqn+74iltmrVWuZk5McXsNeOtMhsJ1Ujpi6qeDyXyMwYAABAvEk4A0sJ4ExLjqZCKtUqm\nJ9KrI5dPqDIc0unGs8rOyNLGmWu0Y+4WLZg811dDwKNJRNvbYOlSjUQ1z62o6vlQoj9jAAAA8SDh\nBCBtjCchkaiWLUm61tHUPwT8gJq6WjQ9b6qeXvSI7puzQZNzJo57+16RyGOYLqjmuR1VPR/iMwYA\nALyEhBMAxMDpli1rrU5ee0/BcJWqr7wla61WFy9VRaBca4qX+WIIeLxoexs/qnluR1XPh/iMAQAA\nLzE22mOkfa6srMxWV1e7HQYA3Ka9+4b21h9RMBxSXdtlTcwu0H1zNmh76WbNLCh2Ozx4XNOTi6Ro\nf24bo6IXzyQ/IA8YWvUlScrJU/4zz5NoAQAAcJgx5qi1tiyWdalwAoAkON9Sp2C4SlX1R9XZ26UF\nk+fqmRVPa9OsNcrx6RBwP/L7/COqeW5HVQ8AAIA3kXACgATpifTo0KUTCoar9E7TOWVnZGvzrLWq\nCJRrQeFct8NLO6kw/4gZPdGly8B4AAAAPyHhBAAOu9rRqD3hA3q59oCud7VqZn6xPrv4Md1bsl6T\ncia4HV7aSoX5R1TzAAAAwC9IOAHwPS+0SVlr9da1d1UZDuno5bckSWunL1dFoFyrpi1JySHgfpMq\nTzOjmgcAAAB+QMIJgK+53SbV1n1De+sOKxgOqb79iiZlT9Cj8x/Q9tLNmp4/NeH7R+yYfwQAAAAk\nDwknAL7mVpvUB9drFQxXKVR/TJ2RLi0qnKevrvysNsxcrZzM7ITtF2PH/CMAAAAgeUg4AfC1ZLZJ\ndUd6dOjSG6q8UKUzzR8oJyNb5bPvVkWgXPMnBxzfH5zF/CMAAAAgeUg4AfC1ZLRJXblxTS/VHNAr\nNQd1vbtVswqK9fklj2tbyXpNzC5wbD9IPOYfAQAAAMlBwgmAryWqTSpiI3rz6rsKhkM6duWkJGnd\n9BWqCJRr5bTFDAEHAAAAgBGQcALga063SbV2t+u12sPaUxPSxfYGTc6eqMfnP6gHSjcxBFzeeCIg\nAAAAAO8j4QTA95xokzp3PazKcEj764+pK9KtJUXz9cSCh7R+5mplZ/CrUnL/iYBuIckGAAAAxI+7\nKABpq6u3W4cuHVdlOKT3ms8rNyNHW0vKtL20XHdMnuN2eJ7j1hMB3ZSuSTYAAABgvEg4AUg7l9uv\nak/Nfr1Se0it3W0qKZih31jyCW0tuUcTsvPdDs+zkvlEQK9IxyQbAAAA4AQSTgDSQsRGdKLhHVWG\nq3S84ZQkqWzGSu0IbNGKqYtkjHE5Qu9LxhMBvSYdk2wAAACAE0g4AUhpLV1teq3usILhkC7fuKrC\nnEn6+J3b9WDpJk3Lm+J2eL6SqCcCjsTt+UnpmGQDAAAAnEDCCUBKOtt8QcFwSPsvvq7uSLeWFt2p\nzyx8WOtnrlIWQ8DHxOknAo7GC/OT3EiyAQAAAKnAWGvdjsFxZWVltrq62u0wACRZV2+XDlw8rmA4\npLPXLyg3M0dbZ5dpe6Bc8yaVuB0e4tT87Lbo1UXFJSr88d6kxeF2lVUs/BAjAAAA/M8Yc9RaWxbL\nuvwzPwDfu9TeoD3h/Xq17pBau9s1Z8JMfXHpJ7W15B4VZOW5HR7GyCvzk3K3Pubp5I0XKsEAAACA\noUg4AYibF6opIjai4w2nFAyH9EbDaRljdM+Mu1QRKNfyKQsZAp4C3Jif5IVrO148SQ8AAABeRMIJ\nQFzcrqa43tWqV2sPaU94v650XFNR7mR98s4deqB0o6bmFSV8/0ieZM9PcvvaHiuvVIIBAAAAg5Fw\nAhAXN6oprLU623xBleEqHbx0XN2RHi2bskA7Fz+qshl3KSsjMyH7TQY/VtQkS7KHlPu1UsgLT9Lj\nOgYAAMBQJJwAxCWZ1RSdvV3af/F1BS9U6VxLjfIyc3X/nI3aHtiswET/P5berxU1yZTM+Ul+rRRy\n+0l6XMcAAACIhoQTgLgko5qivu2K9tTs12u1h9XW067SCbP0paWf0taSMuWn0BBwv1bUpCozsUi2\npTHqci9LdiXYUFzHAAAAiIaEE4C4JKqaImIjOnblbQXDIZ24elqZJkP3zFilHYEtWjrlzpQcAu7X\nippUZa2Na7mXuPkkPa5jAAAAREPCCUBcnK6maO5s0Su1h/RSzX41dDRqSm6hnljwkB4o3agpuYVO\nhu45Xpi9g0HamuNbDklcxwAAAIiOhBOAuI23msJaqzPNH6gyHNKhi8fVY3u1YuoifW7J41o3feWo\nQ8BTZUCx27N33Oa180jiZGzS/ToGAABAdCScACRNR0+nQhePKRgO6XxLrfKz8vRgYLMqSss1Z+LM\nmLaRSgOK3Z694yYvnsesdfer+9e/iLocw0vn6xgAAADDM36YTRGvsrIyW11d7XYYAPrVt11WZTik\nvXWH1d7TocDE2doR2KIts9cpLys3rm01P7stehVKcYkKf7zXqZCRYF48j16MCQAAAPASY8xRa21Z\nLOtS4QQgIXojvTrW8LYqL1TprWvvKtNkasPM1aoIlGtJ0fwxDwFnQHFq8OJ59GJMAAAAgF+RcALg\nqKbOFr1ce0AvhQ/oWmeTpuYW6cmFD+v+ORtUlDt53Ntnzk5q8OJ59GJMAAAAgF+RcAIwbtZavdN0\nTpXhKh2+dEK9tlcrpy7WF5d9UncXL1fmKEPA48GA4tTgxfPoxZgAAAAAvyLhBGDMOno6VVV/VMFw\nSBda61SQlaeKQLkqAuUqmTAjIftkQHFq8OJ59GJMAAAAgF8xNBxA3GpbLylYE9LeuiO60dOheZNK\nVBHYovJZd8c9BBzO6ty3m4QJAAAAgIRgaDgAx/VEenX0ylsKhkM6ee2MskymNsxaox2Bci0qvGPM\nQ8DhnM59u29pCbMNdX3fSySdAAAAACQVCScAI2rsbNbLNQf1Us0BNXY2qzhvij6z8GO6f84GFeZO\ncjs8DNKx64Vb5w9JUleHOna9QMIJAAAAQFKRcAJwG2utTjWeVTAc0pHLJ9RrI1o1bal+c9kTunv6\ncmWYDLdDRBT2an1cywEAAAAgUUg4AbjpRk+H9tVVKxgOqabtoiZk5esjc7dpe+lmzZ4w3e3wMAoz\nbbZsQ13U5QOcnvHEzCgAAAAA0ZBwAqBwa72C4ZD21VWro7dT8yeV6isrntLmWWuVm5njdniIUd7O\n526Z4SRJyslT3s7nJDk/44mZUe4gyQcAAAA/IOEEpKmeSK+qL7+pynCVTjWeVZbJ1KZZa7UjsEUL\nCucyBNyHBpIOwyUjnJ7xxMyo5CPJBwAAAL9IWMLJGPNTSY9IumytXdm/7NOSvi1pmaT11trqQet/\nU9JvSeqV9HVr7a/7lz8k6c8kZUr6a2vtDxIVM5AOrnU09Q0Brz2gps7rmp43VU8vekT3zdmgyTkT\n3Q4vZSWrKiV362PDbtfpGU/MjEo+knwAAADwi0RWOP1c0l9I+rtBy96S9ElJfzV4RWPMcklPSVoh\nqUTSHmPM4v6X/4ukCkk1ko4YY3Zba99OYNxAyrHW6u3G9/qHgL8pa61WFy9VxfIntaZ4GUPAE8wr\nVSmxzHhyc3sYHUk+AAAA+EXCEk7W2r3GmDuGLDslKVqrzuOSfmWt7ZR0zhjznqT1/a+9Z619v//n\nftW/LgknIAbtPR3aV3dEwXBItW2XNDG7QA/PvVfbA5s1s6DY7fDShleqUkab8eT29jA6knwAAADw\nC6/McJoj6eCg72v6l0lSeMjyDdE2YIz5iqSvSNLcuXMTECLgHxda6vqGgNdXq7O3Swsmz9UzK57W\npllrlMMQ8KTzSlXKaDOe3N4eRkeSDwAAAH7hlYTTuFlrfyLpJ5JUVlZmXQ4HSLqeSI8OXzqhYDik\n003vKzsjS5tn3a2KQLkWFJKEdZOXqlJGmvHkhe05JVWf5EaSDwAAAH7hlYRTraTAoO9L+5dphOUA\nJF3taNJLNfv1cs1BNXe1aEb+NH128WO6t2S9JuVMcDs8iKqUZPPKzKxE8WqSDwAAABjMKwmn3ZJ2\nGWN+qL6h4YskHZZkJC0yxsxXX6LpKUk7XYsS8AhrrU5eO6PKcJWOXjkpa63WFC/TjsAWrSpewhBw\nj6EqJbm8MjMLAAAASGcJSzgZY34p6T5JxcaYGkl/JOmapD+XNF3SvxhjjltrP2KtPWmMeVF9w8B7\nJH3NWtvbv53flvRrSZmSfmqtPZmomAGva+u+cXMIeF37ZU3MnqBH5t2nB0s3a0bBNFdjS9UWJqdQ\nlZI8XpmZBQAAAKSzRD6l7ulhXvrHYdb/E0l/EmX5v0r6VwdDA3znfEutKi9UKVR/TJ2RLi0snKev\nrtypDTPXKCcz2+3wUr6FCf7ipZlZAAAAQLrySksdgCG6Iz06fOkNVYar9G7TB8rOyFb57L4h4HdO\nDoy+gSSihQlewswsAAAAwH0knACPabjR2DcEvPagrne1alZBsT63+HHdO+ceTcz25hBwWpjgJczM\nAgAAANxHwgnwgIiN6K2r7yoYDunolb4xZXdPX6GKQLnumrbY80PAaWGC1zAzCwAAAHAXCSfARa3d\n7dpbd1jB8H5dbL+iydkT9dj8B/Vg6SZNz5/qdngxo4UJAAAAADAYCSfABeeu1ygY7hsC3hXp1qLC\nO/Spuz6iDTNXKzvDfx9LWpgAAAAAAIP5784W8Kmu3m4dunRcwXBIZ5rPKzcjR1tmr9P2QLnmTy51\nO7xxo4UJAAAAADCAhBOQYFduXNOecEiv1B5SS3ebZhdM1xeWfFzbStZrQna+2+GhX+e+3VRoAQAA\nAIBDSDgBCRCxEZ24+o6CF6r0esMpSdK6GSu1I1CuFVMXeX4IuF+NNWnUuW/3LTOobENd3/cSSScA\nAAAAGAMSToCDWrvb9GrtYe0J79elGw2anDNRj8/fru2BTZqWN8Xt8FLaeJJGHbteuHXguSR1dahj\n1wsknAAAAABgDEg4wVe82vZ0tvmCguGQ9l98Xd2Rbi0pmq9PL/yoNsxcpSwfDgH3o/EkjezV+riW\nIzZe/bwCAAAASDzuhOEbXmt76urt0oGLfUPAz16/oNzMHG0rKVNFYIvmTSpJejzpbjxJIzNttmxD\nXdTlGBuvfV4BAAAAJBcJJ/iGV9qeLrU3aE/Nfr1ae0it3e0qmTBDv7H0E9o2+x4VMATcNeNJGuXt\nfO6W5IgkKSdPeTufczLEtOKVzysAAAAAd5Bwgm+42fYUsREdbzilYDikNxpOyxijsukrVRHYohVT\nF8oYk/AYMLLxJI0GEiC0fzmHNkUAAAAgvZFwgm+40fZ0vatVr9Ye0ks1+3X5xjUV5UzSJ+6s0AOl\nmzQtryhh+3VCus3PGW/SKHfrYyl9fJKNNkUAAAAgvZFwgm8kq+3JWquz1y+o8kKVDl46ru5Ij5ZO\nWaCnFj2ie2bc5Ysh4Ok6P4ekkXfQpggAAACkN+/fOQP9Et321Nnbpf0XX1cwXKVz12uUl5mre0s2\naEegXIFJ/qrKYH4O3EabIgAAAJDejLXW7RgcV1ZWZqurq90OAz5xsf2KguH9eq32sNp62jVnwkzt\nCGzRlpIyFWTluR3emDQ9uUiK9tk2RkUvnkl+QAAAAAAA3zPGHLXWlsWyLhVOSEsRG9HrV95WZTik\nE1dPK9NkqGzGXdoR2KJlUxb4fgg483MAAAAAAG4i4YS0cr2rVa/UHtSe8H41dDRqSm6hPrXgI3pg\nziZNzSt0OzzHMD8HAAAAAOAmEk5IedZanWk+r2C4SgcvHleP7dXyKQv1ucWPad2Mu5SVkel2iI5j\nfg4AAAAAwE0knJCyOno6bw4B/6ClVvmZuXqgdJMqAuUqnTjL7fASbmjSqWPXC7csR2rr3LebhCMA\nAAAA15BwQsqpb7usYDik1+oOq72nQ4GJs/Wby57QltnrlO/TIeBj0blv9y1tdbahru97kXRKdZx7\nAAAAAG4j4YSU0Bvp1bGGtxUMV+nNq+8q02Ro/czV2hEo15KiO30/BHwsOna9cOsMJ0nq6lDHrhdI\nOqQ4zj0AAAAAt5Fwgq81dbboldqDeqlmv652NGlqbpE+vfCjemDORhXlTnY7PFfZq/VxLUfq4NwD\nAAAAcBsJJ/iOtVbvNp1TZTikQ5feUK/t1cqpi/QbSz6hu6evUGYKDgEfCzNttmxDXdTlSG2cewAA\nAABuI+EE3+jo6VTo4lFVXgjpQmud8rPyVBHYrO2Bcs2ZMNPt8Dwnb+dzt8zxkSTl5Clv53PuBYWk\n4NwDAAAAcBsJJ3hebdsl7QmH9FrdEd3o6dDciSX68vJPq3zWOuVl5bodnmcNfUodTypLH5x7AAAA\nAG4z1lq3Y3BcWVmZra6udjsMjENvpFdHr5xUZbhKJ6+dUabJ1MaZq7Vj7hYtKrwjLYeAAwAAAADg\nJmPMUWttWSzrUuEET2nsbNYrNYf0Us1+Xets1rS8In1m4cO6b85GFeVOcjs8AAAAAAAQAxJOcJ21\nVqcb31ewJqTDl95Qr41o1bQl+tKyT2lt8XKGgAMAAAAA4DMknOCaGz0dqqo/qmA4pHBrvSZk5esj\nc7dqe+lmzZ4ww+3wAAAAAADAGJFwQtLVtF5UMBzSvrojutHbqTsmzdFXln9Gm2ffrdzMHLfDAwAA\nAAAA40TCCUnRE+nV0ctvqjIc0tuN7ynLZGrjrDXaEdiihYXzGAIOAAAAAEAKIeGEhLrW0ayXaw/o\n5ZqDauxsVnHeFD296BHdN2eDJudMdDs8AAAAAACQACSc4DhrrU41nlVluEpHLr+piI1o9bSl+vLy\nT2tN8TJlmAy3QwQAAAAAAAlEwgmOae/pUFVdtSrDVaptu6QJWQX66Nxt2h7YrFkF090ODwAAAAAA\nJAkJJ4xbuKVeleGQquqr1dHbqfmTS/VvVzylzbPWKoch4AAAAAAApB0SThiTnkiPjlx+U5UXqnS6\n6X1lZ2Rp06y1qgiUa2HhPLfDAwAAAAAALiLhhLhc7WjSyzUH9HLNATV1tWhG/lTtXPSo7p2zniHg\nAAAAAABAEgknxMBaq5PXzigYDqn6yluy1mpN8TJVBMq1ungpQ8ABAAAAAMAtSDhhWO3dN7S37oiC\nNSHVtV3WxOwCPTzvXm0v3ayZBcVuhwcAAAAAADyKhBNuc76lVsFwSFV1R9UZ6dKCyXP17Mqd2jhz\nNUPAAQAAAADAqEg4QVLfEPBDl04oGK7SO03nlJ2Rrc39Q8AXFM51OzwAAAAAAOAjJJzSXMONRr1U\nc0Av1x7Q9a5Wzcwv1mcXP6b75qzXxOwJbocHAAAAAAB8iIRTGorYiN66dkbBC1U6euWkJGnt9OWq\nCJRr1bQlDAEfg859u9Wx6wXZq/Uy02Yrb+dzyt36mNthAQAAAADgChJOaaS1u1176478GCQWAAAO\nuUlEQVRoTzik+vYrmpQ9QY/Of0DbSzdrev5Ut8Pzrc59u3XjL78ldXVIkmxDXd/3EkknAAAAAEBa\nIuGUBs5dr1EwHFKo/qi6It1aVHiHvrpyhzbMXK2czOz/v717D7arqu8A/v0BecCgQmKggVChJYMP\ntBkNiFJSq4L4mIC1tQ5tDY4t1bG10ynF2n+o2od1mFJppzi2qGiLaO3DSK0aFUcUUaPEoCiCIhKI\nEhLEIiQEsvrH2TceLnlds3PPzb2fz8yZ7P3ba++zNsyaDd/stc6ou7ff23zFRdvDpu0e3JzNV1wk\ncAIAAGBGEjhNU1u3PZTrfrAmq27/fG6+93uZfcCsnLrwGTn9mGfnuMceM+ruTStt4/oJ1dk3TGsE\nAACYOgRO08yGBzblk+uuzdXrrsv/bf1Jfu6QBfmdE87OsqNOyqGzDhl196almr8w7e47d1hncpjW\nCAAAMLUInKaBbW1b1m68Katu/3yu33BjkuQZR5yY0485NSfOW2wR8H1s7jnnPyLsSJLMnpu555w/\nuk7NMKY1AgAATC0Cp/3YfVt/ks/c8aV88vZr88MH7s5jZx2as457Xp636Nl5/MGHj7p7M8ZYoGE6\n1+iY1ggAADC1CJz2Q9/98e35xPc/l2t/cH22btuaEw47Lr9x/Atz8pFPy6wD/CsdhTmnLRcwjZBp\njQAAAFOLdGI/8eDDW3PdD9fkE9//XL7z4+9nzgGzs+yopTn9mFPzhMccPeruwUiZ1ggAADC1CJym\nuLvu3zhYBPyOL+a+rT/JUYcckRUnvDTLjjoph8w6eNTdgynBtEYAAICpReA0hb3/2x/JR753daoq\nSxcMFgF/yrzFqapRdw2mHNMaAQAApg6B0xR2/GHH5qW/cHqeu+hZmT/3sFF3hz205ZqV3rQBAABg\nRhM4TWEnHfHUnHTEU0fdDSZgyzUrH7GWULv7zsF+InQCAABgxjhg1B2A6WTzFRc9cuHqJHlw86AO\nAAAAM4TACXrUNq6fUB0AAACmI4ET9KjmL5xQHQAAAKYjgRP0aO455yez5z6yOHvuoA4AAAAzhEXD\noUdjC4P7lToAAABmMoET9GzOacsFTAAAAMxo+2xKXVW9q6ruqqqvD9XmVdWqqrq5+/Pwrl5VdUlV\n3VJVa6vq6UPnrOja31xVK/ZVfwEAAADox75cw+k9Sc4cV/uzJJ9qrS1O8qluP0lemGRx9zkvyaXJ\nIKBKcmGSZyY5OcmFYyEVAAAAAFPTPgucWmufTbJpXPmsJJd325cnOXuo/t42cF2Sw6pqYZIXJFnV\nWtvUWrsnyao8OsQCAAAAYAqZ7F+pO7K1tr7b/kGSI7vto5PcPtRuXVfbWf1Rquq8qlpdVas3bNjQ\nb68BAAAA2GOTHTht11prSVqP13tna21pa23pggUL+rosAAAAABM02YHTD7upcun+vKur35HkmKF2\ni7razuoAAAAATFGTHTitTDL2S3Mrknx4qP7K7tfqTklybzf17uNJzqiqw7vFws/oagAAAABMUQft\nqwtX1fuTPCfJ46tqXQa/NvfWJB+sqlcnuS3Jy7vmH03yoiS3JLk/yauSpLW2qarekuTLXbs3t9bG\nL0QOAAAAwBRSg6WUppelS5e21atXj7obAAAAANNGVX2ltbZ0T9qObNFwAAAAAKYngRMAAAAAvRI4\nAQAAANArgRMAAAAAvRI4AQAAANArgRMAAAAAvRI4AQAAANArgRMAAAAAvRI4AQAAANArgRMAAAAA\nvRI4AQAAANArgRMAAAAAvRI4AQAAANArgRMAAAAAvRI4AQAAANArgRMAAAAAvRI4AQAAANArgRMA\nAAAAvRI4AQAAANArgRMAAAAAvRI4AQAAANArgRMAAAAAvRI4AQAAANArgRMAAAAAvRI40ast16zM\nva9dlh+9fHHufe2ybLlm5ai7BAAAAEyyg0bdAaaPLdeszAPv+PPkwc1Jknb3nYP9JHNOWz7KrgEA\nAACTyBtO9GbzFRdtD5u2e3DzoA4AAADMGAInetM2rp9QHQAAAJieBE70puYvnFAdAAAAmJ4ETvRm\n7jnnJ7PnPrI4e+6gDgAAAMwYFg2nN2MLg2++4qK0jetT8xdm7jnnWzAcAAAAZhiBE72ac9pyARMA\nAADMcKbUAQAAANArgRMAAAAAvRI4AQAAANArgRMAAAAAvRI4AQAAANArgRMAAAAAvRI4AQAAANAr\ngRMAAAAAvRI4AQAAANArgRMAAAAAvRI4AQAAANArgRMAAAAAvRI4AQAAANArgRMAAAAAvRI4AQAA\nANArgRMAAAAAvRI4AQAAANArgRMAAAAAvRI4AQAAANArgRMAAAAAvRI4AQAAANArgRMAAAAAvarW\n2qj70Luq2pDktlH3A2aoxye5e9SdAJIYjzCVGI8wdRiP8LN7QmttwZ40nJaBEzA6VbW6tbZ01P0A\njEeYSoxHmDqMR5gcptQBAAAA0CuBEwAAAAC9EjgBfXvnqDsAbGc8wtRhPMLUYTzCJLCGEwAAAAC9\n8oYTAAAAAL0SOAG7VVVzq+pLVfW1qvpGVb2pqx9XVV+sqluq6gNVNburz+n2b+mOHzt0rTd29Zuq\n6gWjuSPYP+1iLL6nqm6tqjXdZ0lXr6q6pBtza6vq6UPXWlFVN3efFaO6J9jfVdWBVXV9VV3V7Xs2\nwojsYDx6PsIICZyAPbElyXNba7+UZEmSM6vqlCR/m+Ti1trxSe5J8uqu/auT3NPVL+7apaqenOQV\nSZ6S5Mwk/1RVB07qncD+bWdjMUn+tLW2pPus6WovTLK4+5yX5NIkqap5SS5M8swkJye5sKoOn8T7\ngOnkj5J8c2jfsxFGZ/x4TDwfYWQETsButYH7ut1Z3acleW6SD3X1y5Oc3W2f1e2nO/68qqqufmVr\nbUtr7dYkt2TwMAf2wC7G4s6cleS93XnXJTmsqhYmeUGSVa21Ta21e5KsyuB/dIEJqKpFSV6c5F+6\n/YpnI4zE+PG4G56PMAkETsAe6V5RXpPkrgwevt9J8qPW2kNdk3VJju62j05ye5J0x+9NMn+4voNz\ngD0wfiy21r7YHfqrblrAxVU1p6vtbMwZi9CPv09yQZJt3f78eDbCqIwfj2M8H2FEBE7AHmmtPdxa\nW5JkUQZ/8/rEEXcJZqTxY7GqTkzyxgzG5ElJ5iV5wwi7CDNCVb0kyV2tta+Mui8w0+1iPHo+wggJ\nnIAJaa39KMnVSZ6VwevHB3WHFiW5o9u+I8kxSdIdf1ySjcP1HZwDTMDQWDyztba+mxawJcm789Pp\nODsbc8Yi7L1Tkyyvqu8luTKDqXRvj2cjjMKjxmNV/avnI4yWwAnYrapaUFWHddsHJzk9gwUZr07y\n612zFUk+3G2v7PbTHf90a6119Vd0v9RzXAYLNX5pcu4C9n87GYvf6tadGFs/5uwkX+9OWZnkld2v\n8ZyS5N7W2vokH09yRlUd3i2GekZXA/ZQa+2NrbVFrbVjM1j0+9Ottd+KZyNMup2Mx9/2fITROmj3\nTQCyMMnl3a/mHJDkg621q6rqxiRXVtVfJrk+yWVd+8uSvK+qbkmyKYMHf1pr36iqDya5MclDSV7X\nWnt4ku8F9mc7G4ufrqoFSSrJmiSv6dp/NMmLMliE+P4kr0qS1tqmqnpLki937d7cWts0ifcB09kb\n4tkIU8W/eT7C6NTgL1YAAAAAoB+m1AEAAADQK4ETAAAAAL0SOAEAAADQK4ETAAAAAL0SOAEAAADQ\nK4ETADAtVdV94/bPrap/7Onan6mqpTuov6Sqrq+qr1XVjVX1+139NVX1yr38zqVVdcneXGOC33dZ\ndx9rq+pDVXXoZH03ALD/O2jUHQAAmA6qalaSdyY5ubW2rqrmJDk2SVpr79jb67fWVidZvbfXmYA/\nbq39OEmq6u+S/EGSt07i9wMA+zFvOAEAM05VLaiq/6iqL3efU7v6yVX1he4tpWur6oSufnBVXVlV\n36yq/0py8A4u+5gM/jJvY5K01ra01m7qzv+Lqjq/qo6qqjVDn4er6gk768+4Pj+nqq4aut67ujet\nvltVr9/JfZ5ZVV/t3lT61NC5l1fVNVV1W1X9WlW9rapuqKqPdcFZhsKm6u637c0/cwBgZvGGEwAw\nXR1cVWuG9uclWdltvz3Jxa21z1XVzyf5eJInJflWktNaaw9V1fOT/HWSlyV5bZL7W2tPqqqnJfnq\n+C9rrW2qqpVJbuvCnauSvL+1tm2ozZ1JliRJVb0uya+01m6rqit20p9deWKSX80g6Lqpqi5trW0d\nO1hVC5L8c5JlrbVbq2re0Lm/2J375CRfSPKy1toFXZj24iT/3V3j3UlelOTGJH+ym/4AAGwncAIA\npqsHWmtLxnaq6twkY+suPT/Jkwcv7yRJHtutUfS4JJdX1eIM3uiZ1R1fluSSJGmtra2qtTv6wtba\n71bVU7vrn5/k9CTnjm/XvcH0e0l+eVf9aa3dN/7cIf/TWtuSZEtV3ZXkyCTrho6fkuSzrbVbu75t\nGjr2v621rVV1Q5IDk3ysq9+Qbhpgd86rqurAJP+Q5DeTvHsX/QEA2E7gBADMRAckOaW1tnm42C0q\nfnVr7aVVdWySz0z0wq21G5LcUFXvS3JrxgVOVbUwyWVJlg8FSjvsz25sGdp+OBP777otXV+3VdXW\n1trYdLlt46/TWnu4qq5MckEETgDAHrKGEwAwE30iyR+O7VTV2JtQj0tyR7d97lD7zyY5p2t7YpKn\njb9gVR1aVc8ZKi1Jctu4NrOS/HuSN7TWvr0H/dkb1yVZVlXHddect5v2w/2sqjp+bDvJ8gymGwIA\n7BGBEwAwE70+ydKqWltVNyZ5TVd/W5K/qarr88g3fS5NcmhVfTPJm5N8ZQfXrCQXVNVN3dpRb8qj\np9M9O4NpfW8aWjj8qF3052fWWtuQ5Lwk/1lVX0vygQmcXhlMLbwhg2l2CzO4bwCAPVI/fYMaAAAA\nAPaeN5wAAAAA6JXACQAAAIBeCZwAAAAA6JXACQAAAIBeCZwAAAAA6JXACQAAAIBeCZwAAAAA6JXA\nCQAAAIBe/T8k+ZZ6MjiLKAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7facbeea8320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting Values and Regression Line\n",
    "\n",
    "max_x = np.max(X) + 100\n",
    "min_x = np.min(X) - 100\n",
    "\n",
    "# Calculating line values x and y\n",
    "x = np.linspace(min_x, max_x, 1000)\n",
    "y = b0 + b1 * x\n",
    "\n",
    "# Ploting Line\n",
    "plt.plot(x, y, color='#58b970', label='Regression Line')\n",
    "# Ploting Scatter Points\n",
    "plt.scatter(X, Y, c='#ef5423', label='Scatter Plot')\n",
    "\n",
    "plt.xlabel('Head Size in cm3')\n",
    "plt.ylabel('Brain Weight in grams')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "72.1206213784\n"
     ]
    }
   ],
   "source": [
    "# Calculating Root Mean Squares Error\n",
    "rmse = 0\n",
    "for i in range(n):\n",
    "    y_pred = b0 + b1 * X[i]\n",
    "    rmse += (Y[i] - y_pred) ** 2\n",
    "rmse = np.sqrt(rmse/n)\n",
    "print(rmse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.639311719957\n"
     ]
    }
   ],
   "source": [
    "# Calculating R2 Score\n",
    "ss_tot = 0\n",
    "ss_res = 0\n",
    "for i in range(n):\n",
    "    y_pred = b0 + b1 * X[i]\n",
    "    ss_tot += (Y[i] - mean_y) ** 2\n",
    "    ss_res += (Y[i] - y_pred) ** 2\n",
    "r2 = 1 - (ss_res/ss_tot)\n",
    "print(r2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Validation using Scikit Learn\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_squared_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X = X.reshape((n, 1))\n",
    "reg = LinearRegression()\n",
    "reg = reg.fit(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Y_pred = b0 + b1 * X\n",
    "mse = mean_squared_error(Y, Y_pred)\n",
    "r2_score = reg.score(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "72.1206213784\n",
      "0.639311719957\n"
     ]
    }
   ],
   "source": [
    "print(np.sqrt(mse))\n",
    "print(r2_score)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}