GettingStarted_R.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "3"
      ],
      "text/latex": [
       "3"
      ],
      "text/markdown": [
       "3"
      ],
      "text/plain": [
       "[1] 3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Assignment in R \n",
    "x<-3\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "3->x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [1]  1.54464872 -0.24516011 -0.50254865  1.81176931  0.46107217 -1.58489029\n",
      " [7] -1.08202474  0.02773963  0.73070899  0.37163240 -0.50099215 -0.09062507\n",
      "[13]  0.35804011 -0.06880224 -0.46831965 -1.20762889 -1.92519632 -0.37013710\n",
      "[19]  1.14905758 -1.38993559 -0.81524378 -0.32344036  0.38502333 -1.16186922\n",
      "[25]  0.40402595  1.28984191  0.62292845  0.09685347 -0.86704256 -1.40420213\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 4 × 1</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>y</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>3</td></tr>\n",
       "\t<tr><td>5</td></tr>\n",
       "\t<tr><td>2</td></tr>\n",
       "\t<tr><td>4</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 4 × 1\n",
       "\\begin{tabular}{l}\n",
       " y\\\\\n",
       " <dbl>\\\\\n",
       "\\hline\n",
       "\t 3\\\\\n",
       "\t 5\\\\\n",
       "\t 2\\\\\n",
       "\t 4\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 4 × 1\n",
       "\n",
       "| y &lt;dbl&gt; |\n",
       "|---|\n",
       "| 3 |\n",
       "| 5 |\n",
       "| 2 |\n",
       "| 4 |\n",
       "\n"
      ],
      "text/plain": [
       "  y\n",
       "1 3\n",
       "2 5\n",
       "3 2\n",
       "4 4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Random number generation\n",
    "x<-c(rnorm(30))\n",
    "print(x)\n",
    "# Creating a vector\n",
    "y<-c(3,5,2,4)\n",
    "# Converting the vectcor to a dataframe\n",
    "data.frame(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 10 × 10 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>-0.4488536</td><td> 0.49415638</td><td>-0.4834717</td><td>-0.1787001</td><td>-0.07599799</td><td> 0.3648520</td><td>-0.44318109</td><td>-0.82416026</td><td>-0.6988237</td><td> 0.06789623</td></tr>\n",
       "\t<tr><td>-1.5384235</td><td> 0.97529576</td><td> 0.3154279</td><td> 0.6131496</td><td>-1.94216664</td><td> 0.1846537</td><td>-0.44568822</td><td>-0.47837956</td><td>-0.2110097</td><td> 0.78136016</td></tr>\n",
       "\t<tr><td> 0.2111260</td><td> 0.15636935</td><td> 0.6519795</td><td>-0.2246000</td><td>-0.32971542</td><td> 1.9295589</td><td> 0.54532281</td><td>-1.40742425</td><td>-0.9441307</td><td> 0.99622757</td></tr>\n",
       "\t<tr><td>-0.7141308</td><td> 0.14285575</td><td> 1.5577968</td><td> 1.7700332</td><td> 0.16914707</td><td> 1.9701121</td><td>-0.77385189</td><td>-0.68654835</td><td>-0.3707024</td><td> 0.42200748</td></tr>\n",
       "\t<tr><td> 0.5991612</td><td> 0.91694003</td><td> 1.6621767</td><td>-0.2179221</td><td> 0.01272710</td><td>-0.1060761</td><td>-0.33024951</td><td>-1.18822017</td><td> 0.5414092</td><td> 1.70420931</td></tr>\n",
       "\t<tr><td>-0.7976847</td><td>-0.01562282</td><td>-2.1940495</td><td>-2.9850481</td><td> 0.21449927</td><td> 0.3604093</td><td>-0.00693422</td><td> 0.08220263</td><td>-2.2746648</td><td> 0.21610637</td></tr>\n",
       "\t<tr><td> 1.6598680</td><td> 0.10870509</td><td> 0.3145582</td><td> 1.3571067</td><td>-1.63525557</td><td> 1.2090790</td><td>-0.14857321</td><td>-1.99127288</td><td>-0.1082819</td><td> 1.04519684</td></tr>\n",
       "\t<tr><td> 0.6890720</td><td> 1.22554217</td><td> 1.1058263</td><td> 0.5082428</td><td>-0.84494950</td><td>-1.4269265</td><td> 0.78586663</td><td>-0.98568047</td><td> 0.4147550</td><td> 0.40268599</td></tr>\n",
       "\t<tr><td> 0.2918284</td><td>-0.23940903</td><td>-0.9539654</td><td> 0.8759928</td><td> 0.03949201</td><td> 0.1979700</td><td> 1.04138069</td><td>-1.68162536</td><td> 0.2994610</td><td>-1.30989120</td></tr>\n",
       "\t<tr><td> 0.9812087</td><td>-0.34850825</td><td>-0.1458099</td><td> 1.5223204</td><td>-0.25550819</td><td>-0.5582830</td><td>-0.88978733</td><td> 0.49683283</td><td>-0.6307270</td><td>-1.29464033</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 10 × 10 of type dbl\n",
       "\\begin{tabular}{llllllllll}\n",
       "\t -0.4488536 &  0.49415638 & -0.4834717 & -0.1787001 & -0.07599799 &  0.3648520 & -0.44318109 & -0.82416026 & -0.6988237 &  0.06789623\\\\\n",
       "\t -1.5384235 &  0.97529576 &  0.3154279 &  0.6131496 & -1.94216664 &  0.1846537 & -0.44568822 & -0.47837956 & -0.2110097 &  0.78136016\\\\\n",
       "\t  0.2111260 &  0.15636935 &  0.6519795 & -0.2246000 & -0.32971542 &  1.9295589 &  0.54532281 & -1.40742425 & -0.9441307 &  0.99622757\\\\\n",
       "\t -0.7141308 &  0.14285575 &  1.5577968 &  1.7700332 &  0.16914707 &  1.9701121 & -0.77385189 & -0.68654835 & -0.3707024 &  0.42200748\\\\\n",
       "\t  0.5991612 &  0.91694003 &  1.6621767 & -0.2179221 &  0.01272710 & -0.1060761 & -0.33024951 & -1.18822017 &  0.5414092 &  1.70420931\\\\\n",
       "\t -0.7976847 & -0.01562282 & -2.1940495 & -2.9850481 &  0.21449927 &  0.3604093 & -0.00693422 &  0.08220263 & -2.2746648 &  0.21610637\\\\\n",
       "\t  1.6598680 &  0.10870509 &  0.3145582 &  1.3571067 & -1.63525557 &  1.2090790 & -0.14857321 & -1.99127288 & -0.1082819 &  1.04519684\\\\\n",
       "\t  0.6890720 &  1.22554217 &  1.1058263 &  0.5082428 & -0.84494950 & -1.4269265 &  0.78586663 & -0.98568047 &  0.4147550 &  0.40268599\\\\\n",
       "\t  0.2918284 & -0.23940903 & -0.9539654 &  0.8759928 &  0.03949201 &  0.1979700 &  1.04138069 & -1.68162536 &  0.2994610 & -1.30989120\\\\\n",
       "\t  0.9812087 & -0.34850825 & -0.1458099 &  1.5223204 & -0.25550819 & -0.5582830 & -0.88978733 &  0.49683283 & -0.6307270 & -1.29464033\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 10 × 10 of type dbl\n",
       "\n",
       "| -0.4488536 |  0.49415638 | -0.4834717 | -0.1787001 | -0.07599799 |  0.3648520 | -0.44318109 | -0.82416026 | -0.6988237 |  0.06789623 |\n",
       "| -1.5384235 |  0.97529576 |  0.3154279 |  0.6131496 | -1.94216664 |  0.1846537 | -0.44568822 | -0.47837956 | -0.2110097 |  0.78136016 |\n",
       "|  0.2111260 |  0.15636935 |  0.6519795 | -0.2246000 | -0.32971542 |  1.9295589 |  0.54532281 | -1.40742425 | -0.9441307 |  0.99622757 |\n",
       "| -0.7141308 |  0.14285575 |  1.5577968 |  1.7700332 |  0.16914707 |  1.9701121 | -0.77385189 | -0.68654835 | -0.3707024 |  0.42200748 |\n",
       "|  0.5991612 |  0.91694003 |  1.6621767 | -0.2179221 |  0.01272710 | -0.1060761 | -0.33024951 | -1.18822017 |  0.5414092 |  1.70420931 |\n",
       "| -0.7976847 | -0.01562282 | -2.1940495 | -2.9850481 |  0.21449927 |  0.3604093 | -0.00693422 |  0.08220263 | -2.2746648 |  0.21610637 |\n",
       "|  1.6598680 |  0.10870509 |  0.3145582 |  1.3571067 | -1.63525557 |  1.2090790 | -0.14857321 | -1.99127288 | -0.1082819 |  1.04519684 |\n",
       "|  0.6890720 |  1.22554217 |  1.1058263 |  0.5082428 | -0.84494950 | -1.4269265 |  0.78586663 | -0.98568047 |  0.4147550 |  0.40268599 |\n",
       "|  0.2918284 | -0.23940903 | -0.9539654 |  0.8759928 |  0.03949201 |  0.1979700 |  1.04138069 | -1.68162536 |  0.2994610 | -1.30989120 |\n",
       "|  0.9812087 | -0.34850825 | -0.1458099 |  1.5223204 | -0.25550819 | -0.5582830 | -0.88978733 |  0.49683283 | -0.6307270 | -1.29464033 |\n",
       "\n"
      ],
      "text/plain": [
       "      [,1]       [,2]        [,3]       [,4]       [,5]        [,6]      \n",
       " [1,] -0.4488536  0.49415638 -0.4834717 -0.1787001 -0.07599799  0.3648520\n",
       " [2,] -1.5384235  0.97529576  0.3154279  0.6131496 -1.94216664  0.1846537\n",
       " [3,]  0.2111260  0.15636935  0.6519795 -0.2246000 -0.32971542  1.9295589\n",
       " [4,] -0.7141308  0.14285575  1.5577968  1.7700332  0.16914707  1.9701121\n",
       " [5,]  0.5991612  0.91694003  1.6621767 -0.2179221  0.01272710 -0.1060761\n",
       " [6,] -0.7976847 -0.01562282 -2.1940495 -2.9850481  0.21449927  0.3604093\n",
       " [7,]  1.6598680  0.10870509  0.3145582  1.3571067 -1.63525557  1.2090790\n",
       " [8,]  0.6890720  1.22554217  1.1058263  0.5082428 -0.84494950 -1.4269265\n",
       " [9,]  0.2918284 -0.23940903 -0.9539654  0.8759928  0.03949201  0.1979700\n",
       "[10,]  0.9812087 -0.34850825 -0.1458099  1.5223204 -0.25550819 -0.5582830\n",
       "      [,7]        [,8]        [,9]       [,10]      \n",
       " [1,] -0.44318109 -0.82416026 -0.6988237  0.06789623\n",
       " [2,] -0.44568822 -0.47837956 -0.2110097  0.78136016\n",
       " [3,]  0.54532281 -1.40742425 -0.9441307  0.99622757\n",
       " [4,] -0.77385189 -0.68654835 -0.3707024  0.42200748\n",
       " [5,] -0.33024951 -1.18822017  0.5414092  1.70420931\n",
       " [6,] -0.00693422  0.08220263 -2.2746648  0.21610637\n",
       " [7,] -0.14857321 -1.99127288 -0.1082819  1.04519684\n",
       " [8,]  0.78586663 -0.98568047  0.4147550  0.40268599\n",
       " [9,]  1.04138069 -1.68162536  0.2994610 -1.30989120\n",
       "[10,] -0.88978733  0.49683283 -0.6307270 -1.29464033"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Constructing a matrix\n",
    "x_mat<-matrix(rnorm(100), ncol=10, nrow=10, byrow=TRUE)\n",
    "x_mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>1.5446487217527</li><li>-0.502548653073746</li><li>0.461072166295492</li><li>-1.08202474314753</li><li>0.730708987588192</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1.5446487217527\n",
       "\\item -0.502548653073746\n",
       "\\item 0.461072166295492\n",
       "\\item -1.08202474314753\n",
       "\\item 0.730708987588192\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1.5446487217527\n",
       "2. -0.502548653073746\n",
       "3. 0.461072166295492\n",
       "4. -1.08202474314753\n",
       "5. 0.730708987588192\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1]  1.5446487 -0.5025487  0.4610722 -1.0820247  0.7307090"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>1.5446487217527</li><li>-0.245160109665672</li><li>-0.502548653073746</li><li>1.81176930871026</li><li>0.461072166295492</li><li>-1.58489029442449</li><li>-1.08202474314753</li><li>0.0277396312653427</li><li>0.730708987588192</li><li>0.371632404389097</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1.5446487217527\n",
       "\\item -0.245160109665672\n",
       "\\item -0.502548653073746\n",
       "\\item 1.81176930871026\n",
       "\\item 0.461072166295492\n",
       "\\item -1.58489029442449\n",
       "\\item -1.08202474314753\n",
       "\\item 0.0277396312653427\n",
       "\\item 0.730708987588192\n",
       "\\item 0.371632404389097\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1.5446487217527\n",
       "2. -0.245160109665672\n",
       "3. -0.502548653073746\n",
       "4. 1.81176930871026\n",
       "5. 0.461072166295492\n",
       "6. -1.58489029442449\n",
       "7. -1.08202474314753\n",
       "8. 0.0277396312653427\n",
       "9. 0.730708987588192\n",
       "10. 0.371632404389097\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1]  1.54464872 -0.24516011 -0.50254865  1.81176931  0.46107217 -1.58489029\n",
       " [7] -1.08202474  0.02773963  0.73070899  0.37163240"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 2 × 2 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>-0.4488536</td><td>0.4941564</td></tr>\n",
       "\t<tr><td>-1.5384235</td><td>0.9752958</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 2 × 2 of type dbl\n",
       "\\begin{tabular}{ll}\n",
       "\t -0.4488536 & 0.4941564\\\\\n",
       "\t -1.5384235 & 0.9752958\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 2 × 2 of type dbl\n",
       "\n",
       "| -0.4488536 | 0.4941564 |\n",
       "| -1.5384235 | 0.9752958 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1]       [,2]     \n",
       "[1,] -0.4488536 0.4941564\n",
       "[2,] -1.5384235 0.9752958"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 2 × 2 of type chr</caption>\n",
       "<tbody>\n",
       "\t<tr><td>rich </td><td>rich3</td></tr>\n",
       "\t<tr><td>rich2</td><td>rich4</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 2 × 2 of type chr\n",
       "\\begin{tabular}{ll}\n",
       "\t rich  & rich3\\\\\n",
       "\t rich2 & rich4\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 2 × 2 of type chr\n",
       "\n",
       "| rich  | rich3 |\n",
       "| rich2 | rich4 |\n",
       "\n"
      ],
      "text/plain": [
       "     [,1]  [,2] \n",
       "[1,] rich  rich3\n",
       "[2,] rich2 rich4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Slicing a vector using indices \n",
    "x[seq(1, 10, by=2)]\n",
    "x[1:10]\n",
    "\n",
    "# Creating a matrix whose elements are \"string\"\n",
    "x_chr_mat<-matrix(c(\"rich\", \"rich2\", \"rich3\", \"rich4\"), ncol=2)\n",
    "# Subseting a matrix using sequence \n",
    "x_mat[1:2, 1:2]\n",
    "x_chr_mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 10 × 10 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><td>-0.4488536</td><td> 0.49415638</td><td>-0.4834717</td><td>-0.1787001</td><td>-0.07599799</td><td> 0.3648520</td><td>-0.44318109</td><td>-0.82416026</td><td>-0.6988237</td><td> 0.06789623</td></tr>\n",
       "\t<tr><td>-1.5384235</td><td> 0.97529576</td><td> 0.3154279</td><td> 0.6131496</td><td>-1.94216664</td><td> 0.1846537</td><td>-0.44568822</td><td>-0.47837956</td><td>-0.2110097</td><td> 0.78136016</td></tr>\n",
       "\t<tr><td> 0.2111260</td><td> 0.15636935</td><td> 0.6519795</td><td>-0.2246000</td><td>-0.32971542</td><td> 1.9295589</td><td> 0.54532281</td><td>-1.40742425</td><td>-0.9441307</td><td> 0.99622757</td></tr>\n",
       "\t<tr><td>-0.7141308</td><td> 0.14285575</td><td> 1.5577968</td><td> 1.7700332</td><td> 0.16914707</td><td> 1.9701121</td><td>-0.77385189</td><td>-0.68654835</td><td>-0.3707024</td><td> 0.42200748</td></tr>\n",
       "\t<tr><td> 0.5991612</td><td> 0.91694003</td><td> 1.6621767</td><td>-0.2179221</td><td> 0.01272710</td><td>-0.1060761</td><td>-0.33024951</td><td>-1.18822017</td><td> 0.5414092</td><td> 1.70420931</td></tr>\n",
       "\t<tr><td>-0.7976847</td><td>-0.01562282</td><td>-2.1940495</td><td>-2.9850481</td><td> 0.21449927</td><td> 0.3604093</td><td>-0.00693422</td><td> 0.08220263</td><td>-2.2746648</td><td> 0.21610637</td></tr>\n",
       "\t<tr><td> 1.6598680</td><td> 0.10870509</td><td> 0.3145582</td><td> 1.3571067</td><td>-1.63525557</td><td> 1.2090790</td><td>-0.14857321</td><td>-1.99127288</td><td>-0.1082819</td><td> 1.04519684</td></tr>\n",
       "\t<tr><td> 0.6890720</td><td> 1.22554217</td><td> 1.1058263</td><td> 0.5082428</td><td>-0.84494950</td><td>-1.4269265</td><td> 0.78586663</td><td>-0.98568047</td><td> 0.4147550</td><td> 0.40268599</td></tr>\n",
       "\t<tr><td> 0.2918284</td><td>-0.23940903</td><td>-0.9539654</td><td> 0.8759928</td><td> 0.03949201</td><td> 0.1979700</td><td> 1.04138069</td><td>-1.68162536</td><td> 0.2994610</td><td>-1.30989120</td></tr>\n",
       "\t<tr><td> 0.9812087</td><td>-0.34850825</td><td>-0.1458099</td><td> 1.5223204</td><td>-0.25550819</td><td>-0.5582830</td><td>-0.88978733</td><td> 0.49683283</td><td>-0.6307270</td><td>-1.29464033</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 10 × 10 of type dbl\n",
       "\\begin{tabular}{llllllllll}\n",
       "\t -0.4488536 &  0.49415638 & -0.4834717 & -0.1787001 & -0.07599799 &  0.3648520 & -0.44318109 & -0.82416026 & -0.6988237 &  0.06789623\\\\\n",
       "\t -1.5384235 &  0.97529576 &  0.3154279 &  0.6131496 & -1.94216664 &  0.1846537 & -0.44568822 & -0.47837956 & -0.2110097 &  0.78136016\\\\\n",
       "\t  0.2111260 &  0.15636935 &  0.6519795 & -0.2246000 & -0.32971542 &  1.9295589 &  0.54532281 & -1.40742425 & -0.9441307 &  0.99622757\\\\\n",
       "\t -0.7141308 &  0.14285575 &  1.5577968 &  1.7700332 &  0.16914707 &  1.9701121 & -0.77385189 & -0.68654835 & -0.3707024 &  0.42200748\\\\\n",
       "\t  0.5991612 &  0.91694003 &  1.6621767 & -0.2179221 &  0.01272710 & -0.1060761 & -0.33024951 & -1.18822017 &  0.5414092 &  1.70420931\\\\\n",
       "\t -0.7976847 & -0.01562282 & -2.1940495 & -2.9850481 &  0.21449927 &  0.3604093 & -0.00693422 &  0.08220263 & -2.2746648 &  0.21610637\\\\\n",
       "\t  1.6598680 &  0.10870509 &  0.3145582 &  1.3571067 & -1.63525557 &  1.2090790 & -0.14857321 & -1.99127288 & -0.1082819 &  1.04519684\\\\\n",
       "\t  0.6890720 &  1.22554217 &  1.1058263 &  0.5082428 & -0.84494950 & -1.4269265 &  0.78586663 & -0.98568047 &  0.4147550 &  0.40268599\\\\\n",
       "\t  0.2918284 & -0.23940903 & -0.9539654 &  0.8759928 &  0.03949201 &  0.1979700 &  1.04138069 & -1.68162536 &  0.2994610 & -1.30989120\\\\\n",
       "\t  0.9812087 & -0.34850825 & -0.1458099 &  1.5223204 & -0.25550819 & -0.5582830 & -0.88978733 &  0.49683283 & -0.6307270 & -1.29464033\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 10 × 10 of type dbl\n",
       "\n",
       "| -0.4488536 |  0.49415638 | -0.4834717 | -0.1787001 | -0.07599799 |  0.3648520 | -0.44318109 | -0.82416026 | -0.6988237 |  0.06789623 |\n",
       "| -1.5384235 |  0.97529576 |  0.3154279 |  0.6131496 | -1.94216664 |  0.1846537 | -0.44568822 | -0.47837956 | -0.2110097 |  0.78136016 |\n",
       "|  0.2111260 |  0.15636935 |  0.6519795 | -0.2246000 | -0.32971542 |  1.9295589 |  0.54532281 | -1.40742425 | -0.9441307 |  0.99622757 |\n",
       "| -0.7141308 |  0.14285575 |  1.5577968 |  1.7700332 |  0.16914707 |  1.9701121 | -0.77385189 | -0.68654835 | -0.3707024 |  0.42200748 |\n",
       "|  0.5991612 |  0.91694003 |  1.6621767 | -0.2179221 |  0.01272710 | -0.1060761 | -0.33024951 | -1.18822017 |  0.5414092 |  1.70420931 |\n",
       "| -0.7976847 | -0.01562282 | -2.1940495 | -2.9850481 |  0.21449927 |  0.3604093 | -0.00693422 |  0.08220263 | -2.2746648 |  0.21610637 |\n",
       "|  1.6598680 |  0.10870509 |  0.3145582 |  1.3571067 | -1.63525557 |  1.2090790 | -0.14857321 | -1.99127288 | -0.1082819 |  1.04519684 |\n",
       "|  0.6890720 |  1.22554217 |  1.1058263 |  0.5082428 | -0.84494950 | -1.4269265 |  0.78586663 | -0.98568047 |  0.4147550 |  0.40268599 |\n",
       "|  0.2918284 | -0.23940903 | -0.9539654 |  0.8759928 |  0.03949201 |  0.1979700 |  1.04138069 | -1.68162536 |  0.2994610 | -1.30989120 |\n",
       "|  0.9812087 | -0.34850825 | -0.1458099 |  1.5223204 | -0.25550819 | -0.5582830 | -0.88978733 |  0.49683283 | -0.6307270 | -1.29464033 |\n",
       "\n"
      ],
      "text/plain": [
       "      [,1]       [,2]        [,3]       [,4]       [,5]        [,6]      \n",
       " [1,] -0.4488536  0.49415638 -0.4834717 -0.1787001 -0.07599799  0.3648520\n",
       " [2,] -1.5384235  0.97529576  0.3154279  0.6131496 -1.94216664  0.1846537\n",
       " [3,]  0.2111260  0.15636935  0.6519795 -0.2246000 -0.32971542  1.9295589\n",
       " [4,] -0.7141308  0.14285575  1.5577968  1.7700332  0.16914707  1.9701121\n",
       " [5,]  0.5991612  0.91694003  1.6621767 -0.2179221  0.01272710 -0.1060761\n",
       " [6,] -0.7976847 -0.01562282 -2.1940495 -2.9850481  0.21449927  0.3604093\n",
       " [7,]  1.6598680  0.10870509  0.3145582  1.3571067 -1.63525557  1.2090790\n",
       " [8,]  0.6890720  1.22554217  1.1058263  0.5082428 -0.84494950 -1.4269265\n",
       " [9,]  0.2918284 -0.23940903 -0.9539654  0.8759928  0.03949201  0.1979700\n",
       "[10,]  0.9812087 -0.34850825 -0.1458099  1.5223204 -0.25550819 -0.5582830\n",
       "      [,7]        [,8]        [,9]       [,10]      \n",
       " [1,] -0.44318109 -0.82416026 -0.6988237  0.06789623\n",
       " [2,] -0.44568822 -0.47837956 -0.2110097  0.78136016\n",
       " [3,]  0.54532281 -1.40742425 -0.9441307  0.99622757\n",
       " [4,] -0.77385189 -0.68654835 -0.3707024  0.42200748\n",
       " [5,] -0.33024951 -1.18822017  0.5414092  1.70420931\n",
       " [6,] -0.00693422  0.08220263 -2.2746648  0.21610637\n",
       " [7,] -0.14857321 -1.99127288 -0.1082819  1.04519684\n",
       " [8,]  0.78586663 -0.98568047  0.4147550  0.40268599\n",
       " [9,]  1.04138069 -1.68162536  0.2994610 -1.30989120\n",
       "[10,] -0.88978733  0.49683283 -0.6307270 -1.29464033"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Displaying our 10 by 10 matrix;  This matrix will be used in the subsequent Bootstrap demonstraing\n",
    "x_mat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 10 × 10</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>X1</th><th scope=col>X2</th><th scope=col>X3</th><th scope=col>X4</th><th scope=col>X5</th><th scope=col>X6</th><th scope=col>X7</th><th scope=col>X8</th><th scope=col>X9</th><th scope=col>X10</th></tr>\n",
       "\t<tr><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td>-0.4488536</td><td> 0.49415638</td><td>-0.4834717</td><td>-0.1787001</td><td>-0.07599799</td><td> 0.3648520</td><td>-0.44318109</td><td>-0.82416026</td><td>-0.6988237</td><td> 0.06789623</td></tr>\n",
       "\t<tr><td>-1.5384235</td><td> 0.97529576</td><td> 0.3154279</td><td> 0.6131496</td><td>-1.94216664</td><td> 0.1846537</td><td>-0.44568822</td><td>-0.47837956</td><td>-0.2110097</td><td> 0.78136016</td></tr>\n",
       "\t<tr><td> 0.2111260</td><td> 0.15636935</td><td> 0.6519795</td><td>-0.2246000</td><td>-0.32971542</td><td> 1.9295589</td><td> 0.54532281</td><td>-1.40742425</td><td>-0.9441307</td><td> 0.99622757</td></tr>\n",
       "\t<tr><td>-0.7141308</td><td> 0.14285575</td><td> 1.5577968</td><td> 1.7700332</td><td> 0.16914707</td><td> 1.9701121</td><td>-0.77385189</td><td>-0.68654835</td><td>-0.3707024</td><td> 0.42200748</td></tr>\n",
       "\t<tr><td> 0.5991612</td><td> 0.91694003</td><td> 1.6621767</td><td>-0.2179221</td><td> 0.01272710</td><td>-0.1060761</td><td>-0.33024951</td><td>-1.18822017</td><td> 0.5414092</td><td> 1.70420931</td></tr>\n",
       "\t<tr><td>-0.7976847</td><td>-0.01562282</td><td>-2.1940495</td><td>-2.9850481</td><td> 0.21449927</td><td> 0.3604093</td><td>-0.00693422</td><td> 0.08220263</td><td>-2.2746648</td><td> 0.21610637</td></tr>\n",
       "\t<tr><td> 1.6598680</td><td> 0.10870509</td><td> 0.3145582</td><td> 1.3571067</td><td>-1.63525557</td><td> 1.2090790</td><td>-0.14857321</td><td>-1.99127288</td><td>-0.1082819</td><td> 1.04519684</td></tr>\n",
       "\t<tr><td> 0.6890720</td><td> 1.22554217</td><td> 1.1058263</td><td> 0.5082428</td><td>-0.84494950</td><td>-1.4269265</td><td> 0.78586663</td><td>-0.98568047</td><td> 0.4147550</td><td> 0.40268599</td></tr>\n",
       "\t<tr><td> 0.2918284</td><td>-0.23940903</td><td>-0.9539654</td><td> 0.8759928</td><td> 0.03949201</td><td> 0.1979700</td><td> 1.04138069</td><td>-1.68162536</td><td> 0.2994610</td><td>-1.30989120</td></tr>\n",
       "\t<tr><td> 0.9812087</td><td>-0.34850825</td><td>-0.1458099</td><td> 1.5223204</td><td>-0.25550819</td><td>-0.5582830</td><td>-0.88978733</td><td> 0.49683283</td><td>-0.6307270</td><td>-1.29464033</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 10 × 10\n",
       "\\begin{tabular}{llllllllll}\n",
       " X1 & X2 & X3 & X4 & X5 & X6 & X7 & X8 & X9 & X10\\\\\n",
       " <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t -0.4488536 &  0.49415638 & -0.4834717 & -0.1787001 & -0.07599799 &  0.3648520 & -0.44318109 & -0.82416026 & -0.6988237 &  0.06789623\\\\\n",
       "\t -1.5384235 &  0.97529576 &  0.3154279 &  0.6131496 & -1.94216664 &  0.1846537 & -0.44568822 & -0.47837956 & -0.2110097 &  0.78136016\\\\\n",
       "\t  0.2111260 &  0.15636935 &  0.6519795 & -0.2246000 & -0.32971542 &  1.9295589 &  0.54532281 & -1.40742425 & -0.9441307 &  0.99622757\\\\\n",
       "\t -0.7141308 &  0.14285575 &  1.5577968 &  1.7700332 &  0.16914707 &  1.9701121 & -0.77385189 & -0.68654835 & -0.3707024 &  0.42200748\\\\\n",
       "\t  0.5991612 &  0.91694003 &  1.6621767 & -0.2179221 &  0.01272710 & -0.1060761 & -0.33024951 & -1.18822017 &  0.5414092 &  1.70420931\\\\\n",
       "\t -0.7976847 & -0.01562282 & -2.1940495 & -2.9850481 &  0.21449927 &  0.3604093 & -0.00693422 &  0.08220263 & -2.2746648 &  0.21610637\\\\\n",
       "\t  1.6598680 &  0.10870509 &  0.3145582 &  1.3571067 & -1.63525557 &  1.2090790 & -0.14857321 & -1.99127288 & -0.1082819 &  1.04519684\\\\\n",
       "\t  0.6890720 &  1.22554217 &  1.1058263 &  0.5082428 & -0.84494950 & -1.4269265 &  0.78586663 & -0.98568047 &  0.4147550 &  0.40268599\\\\\n",
       "\t  0.2918284 & -0.23940903 & -0.9539654 &  0.8759928 &  0.03949201 &  0.1979700 &  1.04138069 & -1.68162536 &  0.2994610 & -1.30989120\\\\\n",
       "\t  0.9812087 & -0.34850825 & -0.1458099 &  1.5223204 & -0.25550819 & -0.5582830 & -0.88978733 &  0.49683283 & -0.6307270 & -1.29464033\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 10 × 10\n",
       "\n",
       "| X1 &lt;dbl&gt; | X2 &lt;dbl&gt; | X3 &lt;dbl&gt; | X4 &lt;dbl&gt; | X5 &lt;dbl&gt; | X6 &lt;dbl&gt; | X7 &lt;dbl&gt; | X8 &lt;dbl&gt; | X9 &lt;dbl&gt; | X10 &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|\n",
       "| -0.4488536 |  0.49415638 | -0.4834717 | -0.1787001 | -0.07599799 |  0.3648520 | -0.44318109 | -0.82416026 | -0.6988237 |  0.06789623 |\n",
       "| -1.5384235 |  0.97529576 |  0.3154279 |  0.6131496 | -1.94216664 |  0.1846537 | -0.44568822 | -0.47837956 | -0.2110097 |  0.78136016 |\n",
       "|  0.2111260 |  0.15636935 |  0.6519795 | -0.2246000 | -0.32971542 |  1.9295589 |  0.54532281 | -1.40742425 | -0.9441307 |  0.99622757 |\n",
       "| -0.7141308 |  0.14285575 |  1.5577968 |  1.7700332 |  0.16914707 |  1.9701121 | -0.77385189 | -0.68654835 | -0.3707024 |  0.42200748 |\n",
       "|  0.5991612 |  0.91694003 |  1.6621767 | -0.2179221 |  0.01272710 | -0.1060761 | -0.33024951 | -1.18822017 |  0.5414092 |  1.70420931 |\n",
       "| -0.7976847 | -0.01562282 | -2.1940495 | -2.9850481 |  0.21449927 |  0.3604093 | -0.00693422 |  0.08220263 | -2.2746648 |  0.21610637 |\n",
       "|  1.6598680 |  0.10870509 |  0.3145582 |  1.3571067 | -1.63525557 |  1.2090790 | -0.14857321 | -1.99127288 | -0.1082819 |  1.04519684 |\n",
       "|  0.6890720 |  1.22554217 |  1.1058263 |  0.5082428 | -0.84494950 | -1.4269265 |  0.78586663 | -0.98568047 |  0.4147550 |  0.40268599 |\n",
       "|  0.2918284 | -0.23940903 | -0.9539654 |  0.8759928 |  0.03949201 |  0.1979700 |  1.04138069 | -1.68162536 |  0.2994610 | -1.30989120 |\n",
       "|  0.9812087 | -0.34850825 | -0.1458099 |  1.5223204 | -0.25550819 | -0.5582830 | -0.88978733 |  0.49683283 | -0.6307270 | -1.29464033 |\n",
       "\n"
      ],
      "text/plain": [
       "   X1         X2          X3         X4         X5          X6        \n",
       "1  -0.4488536  0.49415638 -0.4834717 -0.1787001 -0.07599799  0.3648520\n",
       "2  -1.5384235  0.97529576  0.3154279  0.6131496 -1.94216664  0.1846537\n",
       "3   0.2111260  0.15636935  0.6519795 -0.2246000 -0.32971542  1.9295589\n",
       "4  -0.7141308  0.14285575  1.5577968  1.7700332  0.16914707  1.9701121\n",
       "5   0.5991612  0.91694003  1.6621767 -0.2179221  0.01272710 -0.1060761\n",
       "6  -0.7976847 -0.01562282 -2.1940495 -2.9850481  0.21449927  0.3604093\n",
       "7   1.6598680  0.10870509  0.3145582  1.3571067 -1.63525557  1.2090790\n",
       "8   0.6890720  1.22554217  1.1058263  0.5082428 -0.84494950 -1.4269265\n",
       "9   0.2918284 -0.23940903 -0.9539654  0.8759928  0.03949201  0.1979700\n",
       "10  0.9812087 -0.34850825 -0.1458099  1.5223204 -0.25550819 -0.5582830\n",
       "   X7          X8          X9         X10        \n",
       "1  -0.44318109 -0.82416026 -0.6988237  0.06789623\n",
       "2  -0.44568822 -0.47837956 -0.2110097  0.78136016\n",
       "3   0.54532281 -1.40742425 -0.9441307  0.99622757\n",
       "4  -0.77385189 -0.68654835 -0.3707024  0.42200748\n",
       "5  -0.33024951 -1.18822017  0.5414092  1.70420931\n",
       "6  -0.00693422  0.08220263 -2.2746648  0.21610637\n",
       "7  -0.14857321 -1.99127288 -0.1082819  1.04519684\n",
       "8   0.78586663 -0.98568047  0.4147550  0.40268599\n",
       "9   1.04138069 -1.68162536  0.2994610 -1.30989120\n",
       "10 -0.88978733  0.49683283 -0.6307270 -1.29464033"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 2 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>X1</th><th scope=col>X2</th><th scope=col>X3</th><th scope=col>X4</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>-0.4488536</td><td>0.4941564</td><td>-0.4834717</td><td>-0.1787001</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>-1.5384235</td><td>0.9752958</td><td> 0.3154279</td><td> 0.6131496</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 2 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & X1 & X2 & X3 & X4\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & -0.4488536 & 0.4941564 & -0.4834717 & -0.1787001\\\\\n",
       "\t2 & -1.5384235 & 0.9752958 &  0.3154279 &  0.6131496\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 2 × 4\n",
       "\n",
       "| <!--/--> | X1 &lt;dbl&gt; | X2 &lt;dbl&gt; | X3 &lt;dbl&gt; | X4 &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| 1 | -0.4488536 | 0.4941564 | -0.4834717 | -0.1787001 |\n",
       "| 2 | -1.5384235 | 0.9752958 |  0.3154279 |  0.6131496 |\n",
       "\n"
      ],
      "text/plain": [
       "  X1         X2        X3         X4        \n",
       "1 -0.4488536 0.4941564 -0.4834717 -0.1787001\n",
       "2 -1.5384235 0.9752958  0.3154279  0.6131496"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convert a matrix to a dataframe\n",
    "x_df<-data.frame(x_mat)\n",
    "x_df\n",
    "x_df[1:2, 1:4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<ol class=list-inline><li>-0.44885357340747</li><li>-1.53842348261441</li><li>0.211126009459751</li><li>-0.714130766364536</li><li>0.599161184422763</li><li>-0.79768473899187</li><li>1.65986801336527</li><li>0.689071959582609</li><li>0.291828400657234</li><li>0.981208705315413</li></ol>\n"
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       "\\item 0.689071959582609\n",
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       "\\item 0.981208705315413\n",
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       "1. -0.44885357340747\n",
       "2. -1.53842348261441\n",
       "3. 0.211126009459751\n",
       "4. -0.714130766364536\n",
       "5. 0.599161184422763\n",
       "6. -0.79768473899187\n",
       "7. 1.65986801336527\n",
       "8. 0.689071959582609\n",
       "9. 0.291828400657234\n",
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       "\n",
       "\n"
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       "<ol class=list-inline><li>0.494156375477158</li><li>0.975295760843306</li><li>0.156369350089081</li><li>0.142855745763248</li><li>0.916940028851632</li><li>-0.0156228203033361</li><li>0.108705089275521</li><li>1.22554217322082</li><li>-0.239409025941668</li><li>-0.348508249304761</li></ol>\n"
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       "1. 0.494156375477158\n",
       "2. 0.975295760843306\n",
       "3. 0.156369350089081\n",
       "4. 0.142855745763248\n",
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       "\n",
       "\n"
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       " [1]  0.49415638  0.97529576  0.15636935  0.14285575  0.91694003 -0.01562282\n",
       " [7]  0.10870509  1.22554217 -0.23940903 -0.34850825"
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       "\\item 0.981208705315413\n",
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       "1. -0.44885357340747\n",
       "2. -1.53842348261441\n",
       "3. 0.211126009459751\n",
       "4. -0.714130766364536\n",
       "5. 0.599161184422763\n",
       "6. -0.79768473899187\n",
       "7. 1.65986801336527\n",
       "8. 0.689071959582609\n",
       "9. 0.291828400657234\n",
       "10. 0.981208705315413\n",
       "\n",
       "\n"
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       " [1] -0.4488536 -1.5384235  0.2111260 -0.7141308  0.5991612 -0.7976847\n",
       " [7]  1.6598680  0.6890720  0.2918284  0.9812087"
      ]
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     "output_type": "display_data"
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    {
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       "<ol class=list-inline><li>0.494156375477158</li><li>0.975295760843306</li><li>0.156369350089081</li><li>0.142855745763248</li><li>0.916940028851632</li><li>-0.0156228203033361</li><li>0.108705089275521</li><li>1.22554217322082</li><li>-0.239409025941668</li><li>-0.348508249304761</li></ol>\n"
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       "\\begin{enumerate*}\n",
       "\\item 0.494156375477158\n",
       "\\item 0.975295760843306\n",
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       "\\item 0.142855745763248\n",
       "\\item 0.916940028851632\n",
       "\\item -0.0156228203033361\n",
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       "\\item 1.22554217322082\n",
       "\\item -0.239409025941668\n",
       "\\item -0.348508249304761\n",
       "\\end{enumerate*}\n"
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       "1. 0.494156375477158\n",
       "2. 0.975295760843306\n",
       "3. 0.156369350089081\n",
       "4. 0.142855745763248\n",
       "5. 0.916940028851632\n",
       "6. -0.0156228203033361\n",
       "7. 0.108705089275521\n",
       "8. 1.22554217322082\n",
       "9. -0.239409025941668\n",
       "10. -0.348508249304761\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1]  0.49415638  0.97529576  0.15636935  0.14285575  0.91694003 -0.01562282\n",
       " [7]  0.10870509  1.22554217 -0.23940903 -0.34850825"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style>\n",
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       "</style>\n",
       "<ol class=list-inline><li>'a'</li><li>'b'</li><li>'c'</li><li>'d'</li><li>'e'</li><li>'f'</li><li>'g'</li><li>'h'</li><li>'i'</li><li>'j'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'a'\n",
       "\\item 'b'\n",
       "\\item 'c'\n",
       "\\item 'd'\n",
       "\\item 'e'\n",
       "\\item 'f'\n",
       "\\item 'g'\n",
       "\\item 'h'\n",
       "\\item 'i'\n",
       "\\item 'j'\n",
       "\\end{enumerate*}\n"
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      "text/markdown": [
       "1. 'a'\n",
       "2. 'b'\n",
       "3. 'c'\n",
       "4. 'd'\n",
       "5. 'e'\n",
       "6. 'f'\n",
       "7. 'g'\n",
       "8. 'h'\n",
       "9. 'i'\n",
       "10. 'j'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"a\" \"b\" \"c\" \"d\" \"e\" \"f\" \"g\" \"h\" \"i\" \"j\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
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       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'var1'</li><li>'var2'</li><li>'var3'</li><li>'var4'</li><li>'var5'</li><li>'var6'</li><li>'var7'</li><li>'var8'</li><li>'var9'</li><li>'var10'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'var1'\n",
       "\\item 'var2'\n",
       "\\item 'var3'\n",
       "\\item 'var4'\n",
       "\\item 'var5'\n",
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       "\\item 'var10'\n",
       "\\end{enumerate*}\n"
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       "1. 'var1'\n",
       "2. 'var2'\n",
       "3. 'var3'\n",
       "4. 'var4'\n",
       "5. 'var5'\n",
       "6. 'var6'\n",
       "7. 'var7'\n",
       "8. 'var8'\n",
       "9. 'var9'\n",
       "10. 'var10'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"var1\"  \"var2\"  \"var3\"  \"var4\"  \"var5\"  \"var6\"  \"var7\"  \"var8\"  \"var9\" \n",
       "[10] \"var10\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Slicing columns of a dataframe\n",
    "x_df[, 1]\n",
    "x_df[, 2]\n",
    "# Using the \"$\" operator to extract a vectr (a column from the dataframe)\n",
    "x_df$X1\n",
    "x_df$X2\n",
    "# Using rownames and colnames atributes of a dataframe to reassign the row names\n",
    "# and column names of the dataframe\n",
    "rownames(x_df)<-c(\"a\", \"b\", \"c\", \"d\", \"e\", \"f\",\"g\", \"h\",\"i\",\"j\")\n",
    "rownames(x_df)\n",
    "colnames(x_df)<-c(\"var1\", \"var2\", \"var3\", \"var4\", \"var5\", \"var6\", \"var7\", \"var8\", \"var9\", \"var10\")\n",
    "colnames(x_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
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       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>FALSE</li><li>FALSE</li><li>TRUE</li><li>FALSE</li><li>TRUE</li><li>FALSE</li><li>TRUE</li><li>TRUE</li><li>TRUE</li><li>TRUE</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item FALSE\n",
       "\\item FALSE\n",
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       "\\item FALSE\n",
       "\\item TRUE\n",
       "\\item FALSE\n",
       "\\item TRUE\n",
       "\\item TRUE\n",
       "\\item TRUE\n",
       "\\item TRUE\n",
       "\\end{enumerate*}\n"
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      "text/markdown": [
       "1. FALSE\n",
       "2. FALSE\n",
       "3. TRUE\n",
       "4. FALSE\n",
       "5. TRUE\n",
       "6. FALSE\n",
       "7. TRUE\n",
       "8. TRUE\n",
       "9. TRUE\n",
       "10. TRUE\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] FALSE FALSE  TRUE FALSE  TRUE FALSE  TRUE  TRUE  TRUE  TRUE"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_df$var1>0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 6 × 10</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>var1</th><th scope=col>var2</th><th scope=col>var3</th><th scope=col>var4</th><th scope=col>var5</th><th scope=col>var6</th><th scope=col>var7</th><th scope=col>var8</th><th scope=col>var9</th><th scope=col>var10</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>c</th><td>0.2111260</td><td> 0.1563694</td><td> 0.6519795</td><td>-0.2246000</td><td>-0.32971542</td><td> 1.9295589</td><td> 0.5453228</td><td>-1.4074242</td><td>-0.9441307</td><td> 0.9962276</td></tr>\n",
       "\t<tr><th scope=row>e</th><td>0.5991612</td><td> 0.9169400</td><td> 1.6621767</td><td>-0.2179221</td><td> 0.01272710</td><td>-0.1060761</td><td>-0.3302495</td><td>-1.1882202</td><td> 0.5414092</td><td> 1.7042093</td></tr>\n",
       "\t<tr><th scope=row>g</th><td>1.6598680</td><td> 0.1087051</td><td> 0.3145582</td><td> 1.3571067</td><td>-1.63525557</td><td> 1.2090790</td><td>-0.1485732</td><td>-1.9912729</td><td>-0.1082819</td><td> 1.0451968</td></tr>\n",
       "\t<tr><th scope=row>h</th><td>0.6890720</td><td> 1.2255422</td><td> 1.1058263</td><td> 0.5082428</td><td>-0.84494950</td><td>-1.4269265</td><td> 0.7858666</td><td>-0.9856805</td><td> 0.4147550</td><td> 0.4026860</td></tr>\n",
       "\t<tr><th scope=row>i</th><td>0.2918284</td><td>-0.2394090</td><td>-0.9539654</td><td> 0.8759928</td><td> 0.03949201</td><td> 0.1979700</td><td> 1.0413807</td><td>-1.6816254</td><td> 0.2994610</td><td>-1.3098912</td></tr>\n",
       "\t<tr><th scope=row>j</th><td>0.9812087</td><td>-0.3485082</td><td>-0.1458099</td><td> 1.5223204</td><td>-0.25550819</td><td>-0.5582830</td><td>-0.8897873</td><td> 0.4968328</td><td>-0.6307270</td><td>-1.2946403</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 10\n",
       "\\begin{tabular}{r|llllllllll}\n",
       "  & var1 & var2 & var3 & var4 & var5 & var6 & var7 & var8 & var9 & var10\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tc & 0.2111260 &  0.1563694 &  0.6519795 & -0.2246000 & -0.32971542 &  1.9295589 &  0.5453228 & -1.4074242 & -0.9441307 &  0.9962276\\\\\n",
       "\te & 0.5991612 &  0.9169400 &  1.6621767 & -0.2179221 &  0.01272710 & -0.1060761 & -0.3302495 & -1.1882202 &  0.5414092 &  1.7042093\\\\\n",
       "\tg & 1.6598680 &  0.1087051 &  0.3145582 &  1.3571067 & -1.63525557 &  1.2090790 & -0.1485732 & -1.9912729 & -0.1082819 &  1.0451968\\\\\n",
       "\th & 0.6890720 &  1.2255422 &  1.1058263 &  0.5082428 & -0.84494950 & -1.4269265 &  0.7858666 & -0.9856805 &  0.4147550 &  0.4026860\\\\\n",
       "\ti & 0.2918284 & -0.2394090 & -0.9539654 &  0.8759928 &  0.03949201 &  0.1979700 &  1.0413807 & -1.6816254 &  0.2994610 & -1.3098912\\\\\n",
       "\tj & 0.9812087 & -0.3485082 & -0.1458099 &  1.5223204 & -0.25550819 & -0.5582830 & -0.8897873 &  0.4968328 & -0.6307270 & -1.2946403\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 10\n",
       "\n",
       "| <!--/--> | var1 &lt;dbl&gt; | var2 &lt;dbl&gt; | var3 &lt;dbl&gt; | var4 &lt;dbl&gt; | var5 &lt;dbl&gt; | var6 &lt;dbl&gt; | var7 &lt;dbl&gt; | var8 &lt;dbl&gt; | var9 &lt;dbl&gt; | var10 &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| c | 0.2111260 |  0.1563694 |  0.6519795 | -0.2246000 | -0.32971542 |  1.9295589 |  0.5453228 | -1.4074242 | -0.9441307 |  0.9962276 |\n",
       "| e | 0.5991612 |  0.9169400 |  1.6621767 | -0.2179221 |  0.01272710 | -0.1060761 | -0.3302495 | -1.1882202 |  0.5414092 |  1.7042093 |\n",
       "| g | 1.6598680 |  0.1087051 |  0.3145582 |  1.3571067 | -1.63525557 |  1.2090790 | -0.1485732 | -1.9912729 | -0.1082819 |  1.0451968 |\n",
       "| h | 0.6890720 |  1.2255422 |  1.1058263 |  0.5082428 | -0.84494950 | -1.4269265 |  0.7858666 | -0.9856805 |  0.4147550 |  0.4026860 |\n",
       "| i | 0.2918284 | -0.2394090 | -0.9539654 |  0.8759928 |  0.03949201 |  0.1979700 |  1.0413807 | -1.6816254 |  0.2994610 | -1.3098912 |\n",
       "| j | 0.9812087 | -0.3485082 | -0.1458099 |  1.5223204 | -0.25550819 | -0.5582830 | -0.8897873 |  0.4968328 | -0.6307270 | -1.2946403 |\n",
       "\n"
      ],
      "text/plain": [
       "  var1      var2       var3       var4       var5        var6       var7      \n",
       "c 0.2111260  0.1563694  0.6519795 -0.2246000 -0.32971542  1.9295589  0.5453228\n",
       "e 0.5991612  0.9169400  1.6621767 -0.2179221  0.01272710 -0.1060761 -0.3302495\n",
       "g 1.6598680  0.1087051  0.3145582  1.3571067 -1.63525557  1.2090790 -0.1485732\n",
       "h 0.6890720  1.2255422  1.1058263  0.5082428 -0.84494950 -1.4269265  0.7858666\n",
       "i 0.2918284 -0.2394090 -0.9539654  0.8759928  0.03949201  0.1979700  1.0413807\n",
       "j 0.9812087 -0.3485082 -0.1458099  1.5223204 -0.25550819 -0.5582830 -0.8897873\n",
       "  var8       var9       var10     \n",
       "c -1.4074242 -0.9441307  0.9962276\n",
       "e -1.1882202  0.5414092  1.7042093\n",
       "g -1.9912729 -0.1082819  1.0451968\n",
       "h -0.9856805  0.4147550  0.4026860\n",
       "i -1.6816254  0.2994610 -1.3098912\n",
       "j  0.4968328 -0.6307270 -1.2946403"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 4 × 10</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>var1</th><th scope=col>var2</th><th scope=col>var3</th><th scope=col>var4</th><th scope=col>var5</th><th scope=col>var6</th><th scope=col>var7</th><th scope=col>var8</th><th scope=col>var9</th><th scope=col>var10</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>a</th><td>-0.4488536</td><td> 0.49415638</td><td>-0.4834717</td><td>-0.1787001</td><td>-0.07599799</td><td>0.3648520</td><td>-0.44318109</td><td>-0.82416026</td><td>-0.6988237</td><td>0.06789623</td></tr>\n",
       "\t<tr><th scope=row>b</th><td>-1.5384235</td><td> 0.97529576</td><td> 0.3154279</td><td> 0.6131496</td><td>-1.94216664</td><td>0.1846537</td><td>-0.44568822</td><td>-0.47837956</td><td>-0.2110097</td><td>0.78136016</td></tr>\n",
       "\t<tr><th scope=row>d</th><td>-0.7141308</td><td> 0.14285575</td><td> 1.5577968</td><td> 1.7700332</td><td> 0.16914707</td><td>1.9701121</td><td>-0.77385189</td><td>-0.68654835</td><td>-0.3707024</td><td>0.42200748</td></tr>\n",
       "\t<tr><th scope=row>f</th><td>-0.7976847</td><td>-0.01562282</td><td>-2.1940495</td><td>-2.9850481</td><td> 0.21449927</td><td>0.3604093</td><td>-0.00693422</td><td> 0.08220263</td><td>-2.2746648</td><td>0.21610637</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 4 × 10\n",
       "\\begin{tabular}{r|llllllllll}\n",
       "  & var1 & var2 & var3 & var4 & var5 & var6 & var7 & var8 & var9 & var10\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\ta & -0.4488536 &  0.49415638 & -0.4834717 & -0.1787001 & -0.07599799 & 0.3648520 & -0.44318109 & -0.82416026 & -0.6988237 & 0.06789623\\\\\n",
       "\tb & -1.5384235 &  0.97529576 &  0.3154279 &  0.6131496 & -1.94216664 & 0.1846537 & -0.44568822 & -0.47837956 & -0.2110097 & 0.78136016\\\\\n",
       "\td & -0.7141308 &  0.14285575 &  1.5577968 &  1.7700332 &  0.16914707 & 1.9701121 & -0.77385189 & -0.68654835 & -0.3707024 & 0.42200748\\\\\n",
       "\tf & -0.7976847 & -0.01562282 & -2.1940495 & -2.9850481 &  0.21449927 & 0.3604093 & -0.00693422 &  0.08220263 & -2.2746648 & 0.21610637\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 4 × 10\n",
       "\n",
       "| <!--/--> | var1 &lt;dbl&gt; | var2 &lt;dbl&gt; | var3 &lt;dbl&gt; | var4 &lt;dbl&gt; | var5 &lt;dbl&gt; | var6 &lt;dbl&gt; | var7 &lt;dbl&gt; | var8 &lt;dbl&gt; | var9 &lt;dbl&gt; | var10 &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| a | -0.4488536 |  0.49415638 | -0.4834717 | -0.1787001 | -0.07599799 | 0.3648520 | -0.44318109 | -0.82416026 | -0.6988237 | 0.06789623 |\n",
       "| b | -1.5384235 |  0.97529576 |  0.3154279 |  0.6131496 | -1.94216664 | 0.1846537 | -0.44568822 | -0.47837956 | -0.2110097 | 0.78136016 |\n",
       "| d | -0.7141308 |  0.14285575 |  1.5577968 |  1.7700332 |  0.16914707 | 1.9701121 | -0.77385189 | -0.68654835 | -0.3707024 | 0.42200748 |\n",
       "| f | -0.7976847 | -0.01562282 | -2.1940495 | -2.9850481 |  0.21449927 | 0.3604093 | -0.00693422 |  0.08220263 | -2.2746648 | 0.21610637 |\n",
       "\n"
      ],
      "text/plain": [
       "  var1       var2        var3       var4       var5        var6     \n",
       "a -0.4488536  0.49415638 -0.4834717 -0.1787001 -0.07599799 0.3648520\n",
       "b -1.5384235  0.97529576  0.3154279  0.6131496 -1.94216664 0.1846537\n",
       "d -0.7141308  0.14285575  1.5577968  1.7700332  0.16914707 1.9701121\n",
       "f -0.7976847 -0.01562282 -2.1940495 -2.9850481  0.21449927 0.3604093\n",
       "  var7        var8        var9       var10     \n",
       "a -0.44318109 -0.82416026 -0.6988237 0.06789623\n",
       "b -0.44568822 -0.47837956 -0.2110097 0.78136016\n",
       "d -0.77385189 -0.68654835 -0.3707024 0.42200748\n",
       "f -0.00693422  0.08220263 -2.2746648 0.21610637"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Using boolean filters to extract rows from a dataframe\n",
    "#  <, >, ==, ! (negate boolean), && (ampersand is AND), || (two-pipes is OR)  \n",
    "\n",
    "# rows with postive values on \"var1\"\n",
    "x_df[x_df$var1>0, ]\n",
    "# rows with negative values on \"var1\" - demonstating the \"negation\" operator\n",
    "x_df[!x_df$var1>0, ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>10</li><li>10</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 10\n",
       "\\item 10\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 10\n",
       "2. 10\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 10 10"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculating the dimensions of a dataframe\n",
    "dim(x_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 10 × 10</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>var1</th><th scope=col>var2</th><th scope=col>var3</th><th scope=col>var4</th><th scope=col>var5</th><th scope=col>var6</th><th scope=col>var7</th><th scope=col>var8</th><th scope=col>var9</th><th scope=col>var10</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>i</th><td> 0.2918284</td><td>-0.23940903</td><td>-0.9539654</td><td> 0.8759928</td><td> 0.03949201</td><td> 0.1979700</td><td> 1.04138069</td><td>-1.68162536</td><td> 0.2994610</td><td>-1.30989120</td></tr>\n",
       "\t<tr><th scope=row>j</th><td> 0.9812087</td><td>-0.34850825</td><td>-0.1458099</td><td> 1.5223204</td><td>-0.25550819</td><td>-0.5582830</td><td>-0.88978733</td><td> 0.49683283</td><td>-0.6307270</td><td>-1.29464033</td></tr>\n",
       "\t<tr><th scope=row>c</th><td> 0.2111260</td><td> 0.15636935</td><td> 0.6519795</td><td>-0.2246000</td><td>-0.32971542</td><td> 1.9295589</td><td> 0.54532281</td><td>-1.40742425</td><td>-0.9441307</td><td> 0.99622757</td></tr>\n",
       "\t<tr><th scope=row>b</th><td>-1.5384235</td><td> 0.97529576</td><td> 0.3154279</td><td> 0.6131496</td><td>-1.94216664</td><td> 0.1846537</td><td>-0.44568822</td><td>-0.47837956</td><td>-0.2110097</td><td> 0.78136016</td></tr>\n",
       "\t<tr><th scope=row>c.1</th><td> 0.2111260</td><td> 0.15636935</td><td> 0.6519795</td><td>-0.2246000</td><td>-0.32971542</td><td> 1.9295589</td><td> 0.54532281</td><td>-1.40742425</td><td>-0.9441307</td><td> 0.99622757</td></tr>\n",
       "\t<tr><th scope=row>f</th><td>-0.7976847</td><td>-0.01562282</td><td>-2.1940495</td><td>-2.9850481</td><td> 0.21449927</td><td> 0.3604093</td><td>-0.00693422</td><td> 0.08220263</td><td>-2.2746648</td><td> 0.21610637</td></tr>\n",
       "\t<tr><th scope=row>f.1</th><td>-0.7976847</td><td>-0.01562282</td><td>-2.1940495</td><td>-2.9850481</td><td> 0.21449927</td><td> 0.3604093</td><td>-0.00693422</td><td> 0.08220263</td><td>-2.2746648</td><td> 0.21610637</td></tr>\n",
       "\t<tr><th scope=row>a</th><td>-0.4488536</td><td> 0.49415638</td><td>-0.4834717</td><td>-0.1787001</td><td>-0.07599799</td><td> 0.3648520</td><td>-0.44318109</td><td>-0.82416026</td><td>-0.6988237</td><td> 0.06789623</td></tr>\n",
       "\t<tr><th scope=row>i.1</th><td> 0.2918284</td><td>-0.23940903</td><td>-0.9539654</td><td> 0.8759928</td><td> 0.03949201</td><td> 0.1979700</td><td> 1.04138069</td><td>-1.68162536</td><td> 0.2994610</td><td>-1.30989120</td></tr>\n",
       "\t<tr><th scope=row>f.2</th><td>-0.7976847</td><td>-0.01562282</td><td>-2.1940495</td><td>-2.9850481</td><td> 0.21449927</td><td> 0.3604093</td><td>-0.00693422</td><td> 0.08220263</td><td>-2.2746648</td><td> 0.21610637</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 10 × 10\n",
       "\\begin{tabular}{r|llllllllll}\n",
       "  & var1 & var2 & var3 & var4 & var5 & var6 & var7 & var8 & var9 & var10\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\ti &  0.2918284 & -0.23940903 & -0.9539654 &  0.8759928 &  0.03949201 &  0.1979700 &  1.04138069 & -1.68162536 &  0.2994610 & -1.30989120\\\\\n",
       "\tj &  0.9812087 & -0.34850825 & -0.1458099 &  1.5223204 & -0.25550819 & -0.5582830 & -0.88978733 &  0.49683283 & -0.6307270 & -1.29464033\\\\\n",
       "\tc &  0.2111260 &  0.15636935 &  0.6519795 & -0.2246000 & -0.32971542 &  1.9295589 &  0.54532281 & -1.40742425 & -0.9441307 &  0.99622757\\\\\n",
       "\tb & -1.5384235 &  0.97529576 &  0.3154279 &  0.6131496 & -1.94216664 &  0.1846537 & -0.44568822 & -0.47837956 & -0.2110097 &  0.78136016\\\\\n",
       "\tc.1 &  0.2111260 &  0.15636935 &  0.6519795 & -0.2246000 & -0.32971542 &  1.9295589 &  0.54532281 & -1.40742425 & -0.9441307 &  0.99622757\\\\\n",
       "\tf & -0.7976847 & -0.01562282 & -2.1940495 & -2.9850481 &  0.21449927 &  0.3604093 & -0.00693422 &  0.08220263 & -2.2746648 &  0.21610637\\\\\n",
       "\tf.1 & -0.7976847 & -0.01562282 & -2.1940495 & -2.9850481 &  0.21449927 &  0.3604093 & -0.00693422 &  0.08220263 & -2.2746648 &  0.21610637\\\\\n",
       "\ta & -0.4488536 &  0.49415638 & -0.4834717 & -0.1787001 & -0.07599799 &  0.3648520 & -0.44318109 & -0.82416026 & -0.6988237 &  0.06789623\\\\\n",
       "\ti.1 &  0.2918284 & -0.23940903 & -0.9539654 &  0.8759928 &  0.03949201 &  0.1979700 &  1.04138069 & -1.68162536 &  0.2994610 & -1.30989120\\\\\n",
       "\tf.2 & -0.7976847 & -0.01562282 & -2.1940495 & -2.9850481 &  0.21449927 &  0.3604093 & -0.00693422 &  0.08220263 & -2.2746648 &  0.21610637\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 10 × 10\n",
       "\n",
       "| <!--/--> | var1 &lt;dbl&gt; | var2 &lt;dbl&gt; | var3 &lt;dbl&gt; | var4 &lt;dbl&gt; | var5 &lt;dbl&gt; | var6 &lt;dbl&gt; | var7 &lt;dbl&gt; | var8 &lt;dbl&gt; | var9 &lt;dbl&gt; | var10 &lt;dbl&gt; |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| i |  0.2918284 | -0.23940903 | -0.9539654 |  0.8759928 |  0.03949201 |  0.1979700 |  1.04138069 | -1.68162536 |  0.2994610 | -1.30989120 |\n",
       "| j |  0.9812087 | -0.34850825 | -0.1458099 |  1.5223204 | -0.25550819 | -0.5582830 | -0.88978733 |  0.49683283 | -0.6307270 | -1.29464033 |\n",
       "| c |  0.2111260 |  0.15636935 |  0.6519795 | -0.2246000 | -0.32971542 |  1.9295589 |  0.54532281 | -1.40742425 | -0.9441307 |  0.99622757 |\n",
       "| b | -1.5384235 |  0.97529576 |  0.3154279 |  0.6131496 | -1.94216664 |  0.1846537 | -0.44568822 | -0.47837956 | -0.2110097 |  0.78136016 |\n",
       "| c.1 |  0.2111260 |  0.15636935 |  0.6519795 | -0.2246000 | -0.32971542 |  1.9295589 |  0.54532281 | -1.40742425 | -0.9441307 |  0.99622757 |\n",
       "| f | -0.7976847 | -0.01562282 | -2.1940495 | -2.9850481 |  0.21449927 |  0.3604093 | -0.00693422 |  0.08220263 | -2.2746648 |  0.21610637 |\n",
       "| f.1 | -0.7976847 | -0.01562282 | -2.1940495 | -2.9850481 |  0.21449927 |  0.3604093 | -0.00693422 |  0.08220263 | -2.2746648 |  0.21610637 |\n",
       "| a | -0.4488536 |  0.49415638 | -0.4834717 | -0.1787001 | -0.07599799 |  0.3648520 | -0.44318109 | -0.82416026 | -0.6988237 |  0.06789623 |\n",
       "| i.1 |  0.2918284 | -0.23940903 | -0.9539654 |  0.8759928 |  0.03949201 |  0.1979700 |  1.04138069 | -1.68162536 |  0.2994610 | -1.30989120 |\n",
       "| f.2 | -0.7976847 | -0.01562282 | -2.1940495 | -2.9850481 |  0.21449927 |  0.3604093 | -0.00693422 |  0.08220263 | -2.2746648 |  0.21610637 |\n",
       "\n"
      ],
      "text/plain": [
       "    var1       var2        var3       var4       var5        var6      \n",
       "i    0.2918284 -0.23940903 -0.9539654  0.8759928  0.03949201  0.1979700\n",
       "j    0.9812087 -0.34850825 -0.1458099  1.5223204 -0.25550819 -0.5582830\n",
       "c    0.2111260  0.15636935  0.6519795 -0.2246000 -0.32971542  1.9295589\n",
       "b   -1.5384235  0.97529576  0.3154279  0.6131496 -1.94216664  0.1846537\n",
       "c.1  0.2111260  0.15636935  0.6519795 -0.2246000 -0.32971542  1.9295589\n",
       "f   -0.7976847 -0.01562282 -2.1940495 -2.9850481  0.21449927  0.3604093\n",
       "f.1 -0.7976847 -0.01562282 -2.1940495 -2.9850481  0.21449927  0.3604093\n",
       "a   -0.4488536  0.49415638 -0.4834717 -0.1787001 -0.07599799  0.3648520\n",
       "i.1  0.2918284 -0.23940903 -0.9539654  0.8759928  0.03949201  0.1979700\n",
       "f.2 -0.7976847 -0.01562282 -2.1940495 -2.9850481  0.21449927  0.3604093\n",
       "    var7        var8        var9       var10      \n",
       "i    1.04138069 -1.68162536  0.2994610 -1.30989120\n",
       "j   -0.88978733  0.49683283 -0.6307270 -1.29464033\n",
       "c    0.54532281 -1.40742425 -0.9441307  0.99622757\n",
       "b   -0.44568822 -0.47837956 -0.2110097  0.78136016\n",
       "c.1  0.54532281 -1.40742425 -0.9441307  0.99622757\n",
       "f   -0.00693422  0.08220263 -2.2746648  0.21610637\n",
       "f.1 -0.00693422  0.08220263 -2.2746648  0.21610637\n",
       "a   -0.44318109 -0.82416026 -0.6988237  0.06789623\n",
       "i.1  1.04138069 -1.68162536  0.2994610 -1.30989120\n",
       "f.2 -0.00693422  0.08220263 -2.2746648  0.21610637"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Bootstrap sampling (sampling with replacement): We produce a bootstrap sample by sampling \n",
    "# the indices that are then used to extract the rows corresponding to those indices.\n",
    "# Notice that the rownames keep track of which rows were duplicated in the bootstrap sample\n",
    "sub_row_index<-sample(1:nrow(x_df), 10, replace=TRUE)\n",
    "x_df[sub_row_index, ]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = var1 ~ ., data = x_df)\n",
       "\n",
       "Residuals:\n",
       "ALL 10 residuals are 0: no residual degrees of freedom!\n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)\n",
       "(Intercept)  -1.3243         NA      NA       NA\n",
       "var2         -2.5941         NA      NA       NA\n",
       "var3          1.4467         NA      NA       NA\n",
       "var4         -0.2544         NA      NA       NA\n",
       "var5         -0.3769         NA      NA       NA\n",
       "var6         -1.7588         NA      NA       NA\n",
       "var7         -0.7580         NA      NA       NA\n",
       "var8         -2.3306         NA      NA       NA\n",
       "var9         -1.6960         NA      NA       NA\n",
       "var10        -0.2589         NA      NA       NA\n",
       "\n",
       "Residual standard error: NaN on 0 degrees of freedom\n",
       "Multiple R-squared:      1,\tAdjusted R-squared:    NaN \n",
       "F-statistic:   NaN on 9 and 0 DF,  p-value: NA\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculate the regression of our n by p matrix (10x10);  here we have n=p;\n",
    "# Notice that we can't calculate standard errors, t-values or p-values.  We can only \n",
    "# get coefficients, and then only because all the rows are unique.   Bootstrapping will\n",
    "# produce samples with NON-unique rows, and those non-unique rows will not allow ALL 10 \n",
    "# beta coefficients to be estimated. \n",
    "lm_fit<-lm(var1 ~ ., x_df)\n",
    "summary(lm_fit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
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       "</style>\n",
       "<ol class=list-inline><li>'coefficients'</li><li>'residuals'</li><li>'effects'</li><li>'rank'</li><li>'fitted.values'</li><li>'assign'</li><li>'qr'</li><li>'df.residual'</li><li>'xlevels'</li><li>'call'</li><li>'terms'</li><li>'model'</li></ol>\n"
      ],
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       "\\begin{enumerate*}\n",
       "\\item 'coefficients'\n",
       "\\item 'residuals'\n",
       "\\item 'effects'\n",
       "\\item 'rank'\n",
       "\\item 'fitted.values'\n",
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       "\\item 'call'\n",
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       "\\item 'model'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'coefficients'\n",
       "2. 'residuals'\n",
       "3. 'effects'\n",
       "4. 'rank'\n",
       "5. 'fitted.values'\n",
       "6. 'assign'\n",
       "7. 'qr'\n",
       "8. 'df.residual'\n",
       "9. 'xlevels'\n",
       "10. 'call'\n",
       "11. 'terms'\n",
       "12. 'model'\n",
       "\n",
       "\n"
      ],
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       " [1] \"coefficients\"  \"residuals\"     \"effects\"       \"rank\"         \n",
       " [5] \"fitted.values\" \"assign\"        \"qr\"            \"df.residual\"  \n",
       " [9] \"xlevels\"       \"call\"          \"terms\"         \"model\"        "
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     "data": {
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       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
       "</style><dl class=dl-inline><dt>(Intercept)</dt><dd>-1.32425497733219</dd><dt>var2</dt><dd>-2.59409120150478</dd><dt>var3</dt><dd>1.44668411104152</dd><dt>var4</dt><dd>-0.254365356031371</dd><dt>var5</dt><dd>-0.376851677810936</dd><dt>var6</dt><dd>-1.75880891021622</dd><dt>var7</dt><dd>-0.757976423744687</dd><dt>var8</dt><dd>-2.3305860566152</dd><dt>var9</dt><dd>-1.6960025230841</dd><dt>var10</dt><dd>-0.258856043417924</dd></dl>\n"
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       "\\begin{description*}\n",
       "\\item[(Intercept)] -1.32425497733219\n",
       "\\item[var2] -2.59409120150478\n",
       "\\item[var3] 1.44668411104152\n",
       "\\item[var4] -0.254365356031371\n",
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       "\\item[var6] -1.75880891021622\n",
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       "\\item[var9] -1.6960025230841\n",
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       "(Intercept)\n",
       ":   -1.32425497733219var2\n",
       ":   -2.59409120150478var3\n",
       ":   1.44668411104152var4\n",
       ":   -0.254365356031371var5\n",
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       ":   -2.3305860566152var9\n",
       ":   -1.6960025230841var10\n",
       ":   -0.258856043417924\n",
       "\n"
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       "(Intercept)        var2        var3        var4        var5        var6 \n",
       " -1.3242550  -2.5940912   1.4466841  -0.2543654  -0.3768517  -1.7588089 \n",
       "       var7        var8        var9       var10 \n",
       " -0.7579764  -2.3305861  -1.6960025  -0.2588560 "
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       "a\n",
       ":   0b\n",
       ":   0c\n",
       ":   0d\n",
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       "a b c d e f g h i j \n",
       "0 0 0 0 0 0 0 0 0 0 "
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   ],
   "source": [
    "# Objects of the fitted model that can be extracted;  We extract the coefficients and the residuals;\n",
    "# Notice the residuals are all 0\n",
    "names(lm_fit)\n",
    "lm_fit$coefficients\n",
    "lm_fit$residuals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Method I - Calculate the bootstrap ourselves using a \"for-loop\" and resampling the indices.  Additionally, we will vary (or permute) the order of the predictors on each model estimation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will estimate bootstrap confidence intervals using two different approaches.  Both methods will \n",
    "need a function to be defined that calculates the regression coefficients and returns them for accumulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "'var9+var5+var3+var2+var7+var6+var8+var10+var4'"
      ],
      "text/latex": [
       "'var9+var5+var3+var2+var7+var6+var8+var10+var4'"
      ],
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       "'var9+var5+var3+var2+var7+var6+var8+var10+var4'"
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       "[1] \"var9+var5+var3+var2+var7+var6+var8+var10+var4\""
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   ],
   "source": [
    "# The code segment that we'll need to construct the formula from one model estimation to the \n",
    "# next model estimation;  Notice how we are constructing a permuted variable ordering for the \n",
    "# model to estimate\n",
    "paste(sample(names(x_df)[-1], ncol(x_df)-1, replace=FALSE), collapse=\"+\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the function that will be called many times; \"boot_samps\" will determine how \n",
    "# how many bootstrap samples to take;  This will be 1000 for our purposes.\n",
    "# We create a calling argument \"permute_vars\", that will allow us to use this function\n",
    "# for Method I and Method II when constructing the bootstrap CI\n",
    "\n",
    "lm_function<-function(data, i, col_index, permute_vars=FALSE){\n",
    "   col_index=1\n",
    "   if(permute_vars==TRUE){\n",
    "       lm_fit_coefs<-lm(as.formula(paste(names(data)[col_index],\"~\",\n",
    "                                   paste(sample(names(data)[-1], \n",
    "                                                ncol(x_df)-1, replace=FALSE), collapse=\"+\"))), \n",
    "                        data)$coefficients\n",
    "    }\n",
    "    if(permute_vars==FALSE){\n",
    "       data<-data[i, ] \n",
    "       lm_fit_coefs<-lm(var1 ~ ., data)$coefficients     \n",
    "    }\n",
    "   return(lm_fit_coefs)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
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       "<ol class=list-inline><li>'(Intercept)'</li><li>'var2'</li><li>'var3'</li><li>'var4'</li><li>'var5'</li><li>'var6'</li><li>'var7'</li><li>'var8'</li><li>'var9'</li><li>'var10'</li></ol>\n"
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      "[1] 742\n",
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      "[1] 763\n",
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      "[1] 786\n",
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      "[1] 806\n",
      "(Intercept) \n",
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      "(Intercept) \n",
      "  -1.554375 \n",
      "[1] 809\n",
      "(Intercept) \n",
      "    3.16377 \n",
      "[1] 810\n",
      "(Intercept) \n",
      "   2.647037 \n",
      "[1] 811\n",
      "(Intercept) \n",
      "  -216.5666 \n",
      "[1] 812\n",
      "(Intercept) \n",
      "   4.931602 \n",
      "[1] 813\n",
      "(Intercept) \n",
      "  -30.47736 \n",
      "[1] 814\n",
      "(Intercept) \n",
      "   6.577244 \n",
      "[1] 815\n",
      "(Intercept) \n",
      "  0.5013349 \n",
      "[1] 816\n",
      "(Intercept) \n",
      "  -5.496088 \n",
      "[1] 817\n",
      "(Intercept) \n",
      "   1.982488 \n",
      "[1] 818\n",
      "(Intercept) \n",
      "  -3.746908 \n",
      "[1] 819\n",
      "(Intercept) \n",
      "  0.5026547 \n",
      "[1] 820\n",
      "(Intercept) \n",
      "   1.764432 \n",
      "[1] 821\n",
      "(Intercept) \n",
      "   21.85661 \n",
      "[1] 822\n",
      "(Intercept) \n",
      "  0.8605608 \n",
      "[1] 823\n",
      "(Intercept) \n",
      "  0.8675084 \n",
      "[1] 824\n",
      "(Intercept) \n",
      "  -2.509741 \n",
      "[1] 825\n",
      "(Intercept) \n",
      "   3.225393 \n",
      "[1] 826\n",
      "(Intercept) \n",
      "   2.966892 \n",
      "[1] 827\n",
      "(Intercept) \n",
      "  -1.891924 \n",
      "[1] 828\n",
      "(Intercept) \n",
      "   7.290987 \n",
      "[1] 829\n",
      "(Intercept) \n",
      "   221.4932 \n",
      "[1] 830\n",
      "(Intercept) \n",
      "   4.441275 \n",
      "[1] 831\n",
      "(Intercept) \n",
      "  0.7480432 \n",
      "[1] 832\n",
      "(Intercept) \n",
      "   3.924744 \n",
      "[1] 833\n",
      "(Intercept) \n",
      "   40.00342 \n",
      "[1] 834\n",
      "(Intercept) \n",
      "    1.87932 \n",
      "[1] 835\n",
      "(Intercept) \n",
      "   1.717653 \n",
      "[1] 836\n",
      "(Intercept) \n",
      "  -5.330759 \n",
      "[1] 837\n",
      "(Intercept) \n",
      "  -3.368796 \n",
      "[1] 838\n",
      "(Intercept) \n",
      "  0.3692686 \n",
      "[1] 839\n",
      "(Intercept) \n",
      "  0.0382038 \n",
      "[1] 840\n",
      "(Intercept) \n",
      " -0.0837015 \n",
      "[1] 841\n",
      "(Intercept) \n",
      "    1.22215 \n",
      "[1] 842\n",
      "(Intercept) \n",
      "   2.955239 \n",
      "[1] 843\n",
      "(Intercept) \n",
      "  -3.940051 \n",
      "[1] 844\n",
      "(Intercept) \n",
      "  -3.704054 \n",
      "[1] 845\n",
      "(Intercept) \n",
      "    1.11441 \n",
      "[1] 846\n",
      "(Intercept) \n",
      "  -1.067807 \n",
      "[1] 847\n",
      "(Intercept) \n",
      "  -2.954673 \n",
      "[1] 848\n",
      "(Intercept) \n",
      "   1.793663 \n",
      "[1] 849\n",
      "(Intercept) \n",
      "  -4.022914 \n",
      "[1] 850\n",
      "(Intercept) \n",
      " -0.5359095 \n",
      "[1] 851\n",
      "(Intercept) \n",
      "  -0.434699 \n",
      "[1] 852\n",
      "(Intercept) \n",
      "   5.603082 \n",
      "[1] 853\n",
      "(Intercept) \n",
      "  -4.271162 \n",
      "[1] 854\n",
      "(Intercept) \n",
      "  -1.265994 \n",
      "[1] 855\n",
      "(Intercept) \n",
      "   1.686627 \n",
      "[1] 856\n",
      "(Intercept) \n",
      "   1.496637 \n",
      "[1] 857\n",
      "(Intercept) \n",
      "   -4.89681 \n",
      "[1] 858\n",
      "(Intercept) \n",
      "     0.1313 \n",
      "[1] 859\n",
      "(Intercept) \n",
      "  -12.53593 \n",
      "[1] 860\n",
      "(Intercept) \n",
      " -0.2671069 \n",
      "[1] 861\n",
      "(Intercept) \n",
      "   13.76994 \n",
      "[1] 862\n",
      "(Intercept) \n",
      "  -5.535872 \n",
      "[1] 863\n",
      "(Intercept) \n",
      "  -3.154904 \n",
      "[1] 864\n",
      "(Intercept) \n",
      "  -15.30521 \n",
      "[1] 865\n",
      "(Intercept) \n",
      "   18.96733 \n",
      "[1] 866\n",
      "(Intercept) \n",
      "  0.2526339 \n",
      "[1] 867\n",
      "(Intercept) \n",
      "   5.332205 \n",
      "[1] 868\n",
      "(Intercept) \n",
      "  -8.557679 \n",
      "[1] 869\n",
      "(Intercept) \n",
      "   20.25854 \n",
      "[1] 870\n",
      "(Intercept) \n",
      "   1.105116 \n",
      "[1] 871\n",
      "(Intercept) \n",
      "   3.563596 \n",
      "[1] 872\n",
      "(Intercept) \n",
      "  -1.175246 \n",
      "[1] 873\n",
      "(Intercept) \n",
      "   2.783671 \n",
      "[1] 874\n",
      "(Intercept) \n",
      "   -22.8053 \n",
      "[1] 875\n",
      "(Intercept) \n",
      " 0.02611114 \n",
      "[1] 876\n",
      "(Intercept) \n",
      "  -1.336261 \n",
      "[1] 877\n",
      "(Intercept) \n",
      " -0.9347554 \n",
      "[1] 878\n",
      "(Intercept) \n",
      " -0.4805899 \n",
      "[1] 879\n",
      "(Intercept) \n",
      "    3.70209 \n",
      "[1] 880\n",
      "(Intercept) \n",
      "  0.3152695 \n",
      "[1] 881\n",
      "(Intercept) \n",
      "   1.519165 \n",
      "[1] 882\n",
      "(Intercept) \n",
      " 0.04293826 \n",
      "[1] 883\n",
      "(Intercept) \n",
      " -0.3798537 \n",
      "[1] 884\n",
      "(Intercept) \n",
      "  -0.294187 \n",
      "[1] 885\n",
      "(Intercept) \n",
      "   6.765596 \n",
      "[1] 886\n",
      "(Intercept) \n",
      "   6.097113 \n",
      "[1] 887\n",
      "(Intercept) \n",
      "  -19.97033 \n",
      "[1] 888\n",
      "(Intercept) \n",
      "  0.6235945 \n",
      "[1] 889\n",
      "(Intercept) \n",
      "  0.9287213 \n",
      "[1] 890\n",
      "(Intercept) \n",
      "   1.607232 \n",
      "[1] 891\n",
      "(Intercept) \n",
      "   1.336563 \n",
      "[1] 892\n",
      "(Intercept) \n",
      "  -2.568571 \n",
      "[1] 893\n",
      "(Intercept) \n",
      "  -6.282428 \n",
      "[1] 894\n",
      "(Intercept) \n",
      "  -1.012071 \n",
      "[1] 895\n",
      "(Intercept) \n",
      " -0.5304852 \n",
      "[1] 896\n",
      "(Intercept) \n",
      "   1.544549 \n",
      "[1] 897\n",
      "(Intercept) \n",
      "   3.573661 \n",
      "[1] 898\n",
      "(Intercept) \n",
      "  -1.498823 \n",
      "[1] 899\n",
      "(Intercept) \n",
      "     2.3855 \n",
      "[1] 900\n",
      "(Intercept) \n",
      "   1.147079 \n",
      "[1] 901\n",
      "(Intercept) \n",
      "   2.473994 \n",
      "[1] 902\n",
      "(Intercept) \n",
      " -0.7906802 \n",
      "[1] 903\n",
      "(Intercept) \n",
      "  0.4975161 \n",
      "[1] 904\n",
      "(Intercept) \n",
      "  -3.092835 \n",
      "[1] 905\n",
      "(Intercept) \n",
      "  -2.152604 \n",
      "[1] 906\n",
      "(Intercept) \n",
      "  0.7179397 \n",
      "[1] 907\n",
      "(Intercept) \n",
      "    1.66485 \n",
      "[1] 908\n",
      "(Intercept) \n",
      "   2.246328 \n",
      "[1] 909\n",
      "(Intercept) \n",
      " -0.3736951 \n",
      "[1] 910\n",
      "(Intercept) \n",
      "  0.8271585 \n",
      "[1] 911\n",
      "(Intercept) \n",
      "  -1.304499 \n",
      "[1] 912\n",
      "(Intercept) \n",
      "    1.42292 \n",
      "[1] 913\n",
      "(Intercept) \n",
      "  0.7013517 \n",
      "[1] 914\n",
      "(Intercept) \n",
      "   4.217275 \n",
      "[1] 915\n",
      "(Intercept) \n",
      "   -1.49848 \n",
      "[1] 916\n",
      "(Intercept) \n",
      "   2.212646 \n",
      "[1] 917\n",
      "(Intercept) \n",
      "    0.95305 \n",
      "[1] 918\n",
      "(Intercept) \n",
      "  -4.198677 \n",
      "[1] 919\n",
      "(Intercept) \n",
      " -0.8089014 \n",
      "[1] 920\n",
      "(Intercept) \n",
      "   2.371289 \n",
      "[1] 921\n",
      "(Intercept) \n",
      " 0.01526869 \n",
      "[1] 922\n",
      "(Intercept) \n",
      "   1.450491 \n",
      "[1] 923\n",
      "(Intercept) \n",
      "  0.6753881 \n",
      "[1] 924\n",
      "(Intercept) \n",
      "  0.7704641 \n",
      "[1] 925\n",
      "(Intercept) \n",
      "  -4.029797 \n",
      "[1] 926\n",
      "(Intercept) \n",
      "  -0.865539 \n",
      "[1] 927\n",
      "(Intercept) \n",
      "   3.311933 \n",
      "[1] 928\n",
      "(Intercept) \n",
      "  -7.325568 \n",
      "[1] 929\n",
      "(Intercept) \n",
      "   1.477107 \n",
      "[1] 930\n",
      "(Intercept) \n",
      "    2.78948 \n",
      "[1] 931\n",
      "(Intercept) \n",
      "  0.3890402 \n",
      "[1] 932\n",
      "(Intercept) \n",
      " -0.8971596 \n",
      "[1] 933\n",
      "(Intercept) \n",
      "  0.2392548 \n",
      "[1] 934\n",
      "(Intercept) \n",
      "  -13.94493 \n",
      "[1] 935\n",
      "(Intercept) \n",
      "  0.3707612 \n",
      "[1] 936\n",
      "(Intercept) \n",
      "  -2.204417 \n",
      "[1] 937\n",
      "(Intercept) \n",
      "   2.418327 \n",
      "[1] 938\n",
      "(Intercept) \n",
      " -0.1493287 \n",
      "[1] 939\n",
      "(Intercept) \n",
      "  -2.009697 \n",
      "[1] 940\n",
      "(Intercept) \n",
      "  -1.317032 \n",
      "[1] 941\n",
      "(Intercept) \n",
      "   1.155288 \n",
      "[1] 942\n",
      "(Intercept) \n",
      "   1.597063 \n",
      "[1] 943\n",
      "(Intercept) \n",
      "  -0.585479 \n",
      "[1] 944\n",
      "(Intercept) \n",
      "  -2.576041 \n",
      "[1] 945\n",
      "(Intercept) \n",
      " -0.3066604 \n",
      "[1] 946\n",
      "(Intercept) \n",
      "  -2.369736 \n",
      "[1] 947\n",
      "(Intercept) \n",
      "     1.7386 \n",
      "[1] 948\n",
      "(Intercept) \n",
      "   1.659982 \n",
      "[1] 949\n",
      "(Intercept) \n",
      "  -1.800114 \n",
      "[1] 950\n",
      "(Intercept) \n",
      "   12.09774 \n",
      "[1] 951\n",
      "(Intercept) \n",
      "  -1.164021 \n",
      "[1] 952\n",
      "(Intercept) \n",
      "  0.3799826 \n",
      "[1] 953\n",
      "(Intercept) \n",
      "  0.3526712 \n",
      "[1] 954\n",
      "(Intercept) \n",
      "  0.4349847 \n",
      "[1] 955\n",
      "(Intercept) \n",
      "  -1.453221 \n",
      "[1] 956\n",
      "(Intercept) \n",
      "   1.749072 \n",
      "[1] 957\n",
      "(Intercept) \n",
      "  0.5265692 \n",
      "[1] 958\n",
      "(Intercept) \n",
      " -0.2038303 \n",
      "[1] 959\n",
      "(Intercept) \n",
      "  -22.47168 \n",
      "[1] 960\n",
      "(Intercept) \n",
      "   -1.56235 \n",
      "[1] 961\n",
      "(Intercept) \n",
      " -0.4762049 \n",
      "[1] 962\n",
      "(Intercept) \n",
      "  -6.799091 \n",
      "[1] 963\n",
      "(Intercept) \n",
      "   -0.53951 \n",
      "[1] 964\n",
      "(Intercept) \n",
      "  -4.494591 \n",
      "[1] 965\n",
      "(Intercept) \n",
      "   2.807459 \n",
      "[1] 966\n",
      "(Intercept) \n",
      "   -6.54205 \n",
      "[1] 967\n",
      "(Intercept) \n",
      "   3.236782 \n",
      "[1] 968\n",
      "(Intercept) \n",
      " -0.6996048 \n",
      "[1] 969\n",
      "(Intercept) \n",
      "   1.543605 \n",
      "[1] 970\n",
      "(Intercept) \n",
      "  -4.074738 \n",
      "[1] 971\n",
      "(Intercept) \n",
      "  0.2941545 \n",
      "[1] 972\n",
      "(Intercept) \n",
      "   2.990194 \n",
      "[1] 973\n",
      "(Intercept) \n",
      "   18.49356 \n",
      "[1] 974\n",
      "(Intercept) \n",
      "   1.112927 \n",
      "[1] 975\n",
      "(Intercept) \n",
      "   1.115919 \n",
      "[1] 976\n",
      "(Intercept) \n",
      " -0.1967462 \n",
      "[1] 977\n",
      "(Intercept) \n",
      "  -1.016964 \n",
      "[1] 978\n",
      "(Intercept) \n",
      "  -2.131149 \n",
      "[1] 979\n",
      "(Intercept) \n",
      "    4.20251 \n",
      "[1] 980\n",
      "(Intercept) \n",
      "  -2.652889 \n",
      "[1] 981\n",
      "(Intercept) \n",
      "   -4.23175 \n",
      "[1] 982\n",
      "(Intercept) \n",
      "   2.698839 \n",
      "[1] 983\n",
      "(Intercept) \n",
      "  0.4194974 \n",
      "[1] 984\n",
      "(Intercept) \n",
      "   1.055703 \n",
      "[1] 985\n",
      "(Intercept) \n",
      "  -5.349943 \n",
      "[1] 986\n",
      "(Intercept) \n",
      "   19.89169 \n",
      "[1] 987\n",
      "(Intercept) \n",
      "  -3.148343 \n",
      "[1] 988\n",
      "(Intercept) \n",
      "  0.4775046 \n",
      "[1] 989\n",
      "(Intercept) \n",
      "  -1.194449 \n",
      "[1] 990\n",
      "(Intercept) \n",
      "  0.6896948 \n",
      "[1] 991\n",
      "(Intercept) \n",
      " -0.4189234 \n",
      "[1] 992\n",
      "(Intercept) \n",
      "   12.94901 \n",
      "[1] 993\n",
      "(Intercept) \n",
      "   5.025751 \n",
      "[1] 994\n",
      "(Intercept) \n",
      "  0.8794232 \n",
      "[1] 995\n",
      "(Intercept) \n",
      "   9.466035 \n",
      "[1] 996\n",
      "(Intercept) \n",
      "  0.3208498 \n",
      "[1] 997\n",
      "(Intercept) \n",
      " 0.08159904 \n",
      "[1] 998\n",
      "(Intercept) \n",
      "   1.210728 \n",
      "[1] 999\n",
      "(Intercept) \n",
      "   2.215259 \n",
      "[1] 1000\n",
      "(Intercept) \n",
      "   1.638177 \n"
     ]
    }
   ],
   "source": [
    "# Begin the main looping for Method I construction of bootstrap CI\n",
    "# Initialize variables\n",
    "col_index<-1\n",
    "boot_samps<-1000\n",
    "coef_mat_accum<-matrix(NA, ncol=ncol(x_df), nrow=boot_samps)\n",
    "\n",
    "# Get the coefficients and the coefficient names\n",
    "# Note that the returning coefficients are of type \"vector\"\n",
    "coef_out<-lm(var1 ~. , data=x_df)$coefficients\n",
    "is.vector(coef_out)\n",
    "names(coef_out)\n",
    "\n",
    "# Order the coefficient names and reassign the names attribute \n",
    "# back to the matrix object;  Note that the vector has a \"names\"\n",
    "# attribute for the row names;  but a \"matrix\" has a \"colnames\" attribute\n",
    "# for it's columns; this is why the right side uses \"names\", but the \n",
    "# column names assignment ot our matrix uses \"colnames\"\n",
    "colnames(coef_mat_accum)<-names(coef_out)[order(names(coef_out))]\n",
    "\n",
    "# Display names\n",
    "colnames(coef_mat_accum)\n",
    "\n",
    "# Bootstrap sampling - using for-loop and sampling with replacement (SWR) \n",
    "for(i in 1:boot_samps){\n",
    "    print(i)\n",
    "    boot_index<-sample(1:nrow(x_df), 10, replace=TRUE)\n",
    "    x_df_rep<-x_df[boot_index, ]\n",
    "    coef_out<-lm_function(data=x_df_rep, col_index=col_index, permute_vars=TRUE)\n",
    "    coef_out<-coef_out[order(names(coef_out))]\n",
    "    coef_mat_accum[i, ] <- coef_out \n",
    "    print(coef_mat_accum[i,1])\n",
    "    }"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 2 × 10 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>(Intercept)</th><th scope=col>var10</th><th scope=col>var2</th><th scope=col>var3</th><th scope=col>var4</th><th scope=col>var5</th><th scope=col>var6</th><th scope=col>var7</th><th scope=col>var8</th><th scope=col>var9</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>2.5%</th><td>-15.47159</td><td>-11.93153</td><td>-16.50370</td><td>-13.05447</td><td>-12.73333</td><td>-8.725380</td><td>-11.364005</td><td>-13.13983</td><td>-13.069987</td><td>-24.38130</td></tr>\n",
       "\t<tr><th scope=row>97.5%</th><td> 13.40476</td><td> 18.96498</td><td> 13.69777</td><td> 12.13268</td><td> 15.49536</td><td> 9.893714</td><td>  7.663735</td><td> 10.21818</td><td>  6.638217</td><td> 18.65311</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 2 × 10 of type dbl\n",
       "\\begin{tabular}{r|llllllllll}\n",
       "  & (Intercept) & var10 & var2 & var3 & var4 & var5 & var6 & var7 & var8 & var9\\\\\n",
       "\\hline\n",
       "\t2.5\\% & -15.47159 & -11.93153 & -16.50370 & -13.05447 & -12.73333 & -8.725380 & -11.364005 & -13.13983 & -13.069987 & -24.38130\\\\\n",
       "\t97.5\\% &  13.40476 &  18.96498 &  13.69777 &  12.13268 &  15.49536 &  9.893714 &   7.663735 &  10.21818 &   6.638217 &  18.65311\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 2 × 10 of type dbl\n",
       "\n",
       "| <!--/--> | (Intercept) | var10 | var2 | var3 | var4 | var5 | var6 | var7 | var8 | var9 |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 2.5% | -15.47159 | -11.93153 | -16.50370 | -13.05447 | -12.73333 | -8.725380 | -11.364005 | -13.13983 | -13.069987 | -24.38130 |\n",
       "| 97.5% |  13.40476 |  18.96498 |  13.69777 |  12.13268 |  15.49536 |  9.893714 |   7.663735 |  10.21818 |   6.638217 |  18.65311 |\n",
       "\n"
      ],
      "text/plain": [
       "      (Intercept) var10     var2      var3      var4      var5      var6      \n",
       "2.5%  -15.47159   -11.93153 -16.50370 -13.05447 -12.73333 -8.725380 -11.364005\n",
       "97.5%  13.40476    18.96498  13.69777  12.13268  15.49536  9.893714   7.663735\n",
       "      var7      var8       var9     \n",
       "2.5%  -13.13983 -13.069987 -24.38130\n",
       "97.5%  10.21818   6.638217  18.65311"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculate the quantiles of each column;  These are the CI:  [LL_beta_.025,  UL_beta_.975]\n",
    "# These betas define an uncertainty interval that capture 95% of the variation in the sample's betas\n",
    "apply(coef_mat_accum, 2, quantile, probs=c(.025, .975), na.rm=TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Nonparametric Kernel Methods for Mixed Datatypes (version 0.60-10)\n",
      "[vignette(\"np_faq\",package=\"np\") provides answers to frequently asked questions]\n",
      "[vignette(\"np\",package=\"np\") an overview]\n",
      "[vignette(\"entropy_np\",package=\"np\") an overview of entropy-based methods]\n",
      "\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\r",
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    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 2 × 10 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>(Intercept)</th><th scope=col>var10</th><th scope=col>var2</th><th scope=col>var3</th><th scope=col>var4</th><th scope=col>var5</th><th scope=col>var6</th><th scope=col>var7</th><th scope=col>var8</th><th scope=col>var9</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>2.5%</th><td>-15.47159</td><td>-12.00787</td><td>-16.71864</td><td>-13.13501</td><td>-12.90917</td><td>-8.72538</td><td>-11.364005</td><td>-13.13983</td><td>-13.069987</td><td>-25.19933</td></tr>\n",
       "\t<tr><th scope=row>97.5%</th><td> 14.33478</td><td> 19.25487</td><td> 14.00661</td><td> 12.32814</td><td> 15.73572</td><td>10.28889</td><td>  7.961557</td><td> 10.75423</td><td>  7.458438</td><td> 19.47433</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 2 × 10 of type dbl\n",
       "\\begin{tabular}{r|llllllllll}\n",
       "  & (Intercept) & var10 & var2 & var3 & var4 & var5 & var6 & var7 & var8 & var9\\\\\n",
       "\\hline\n",
       "\t2.5\\% & -15.47159 & -12.00787 & -16.71864 & -13.13501 & -12.90917 & -8.72538 & -11.364005 & -13.13983 & -13.069987 & -25.19933\\\\\n",
       "\t97.5\\% &  14.33478 &  19.25487 &  14.00661 &  12.32814 &  15.73572 & 10.28889 &   7.961557 &  10.75423 &   7.458438 &  19.47433\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 2 × 10 of type dbl\n",
       "\n",
       "| <!--/--> | (Intercept) | var10 | var2 | var3 | var4 | var5 | var6 | var7 | var8 | var9 |\n",
       "|---|---|---|---|---|---|---|---|---|---|---|\n",
       "| 2.5% | -15.47159 | -12.00787 | -16.71864 | -13.13501 | -12.90917 | -8.72538 | -11.364005 | -13.13983 | -13.069987 | -25.19933 |\n",
       "| 97.5% |  14.33478 |  19.25487 |  14.00661 |  12.32814 |  15.73572 | 10.28889 |   7.961557 |  10.75423 |   7.458438 |  19.47433 |\n",
       "\n"
      ],
      "text/plain": [
       "      (Intercept) var10     var2      var3      var4      var5     var6      \n",
       "2.5%  -15.47159   -12.00787 -16.71864 -13.13501 -12.90917 -8.72538 -11.364005\n",
       "97.5%  14.33478    19.25487  14.00661  12.32814  15.73572 10.28889   7.961557\n",
       "      var7      var8       var9     \n",
       "2.5%  -13.13983 -13.069987 -25.19933\n",
       "97.5%  10.75423   7.458438  19.47433"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "0.501420897991384"
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      "text/latex": [
       "0.501420897991384"
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      "text/markdown": [
       "0.501420897991384"
      ],
      "text/plain": [
       "[1] 0.5014209"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Original coefficients listed for comparison:\n",
    "#\n",
    "#             Estimate Std. Error t value Pr(>|t|)\n",
    "# (Intercept)  0.05456         NA      NA       NA\n",
    "# var2        -0.14774         NA      NA       NA\n",
    "# var3         0.07723         NA      NA       NA\n",
    "# var4        -0.18304         NA      NA       NA\n",
    "# var5         0.52600         NA      NA       NA\n",
    "# var6        -0.32386         NA      NA       NA\n",
    "# var7         0.49406         NA      NA       NA\n",
    "# var8        -0.56801         NA      NA       NA\n",
    "# var9         0.37399         NA      NA       NA\n",
    "# var10        0.30558         NA      NA       NA\n",
    "library(np)\n",
    "\n",
    "# Calculate \"smoothed\" quantiles \n",
    "apply(coef_mat_accum, 2, npquantile, tau=c(.025, .975), na.rm=TRUE)\n",
    "# apply(coef_mat_accum, 2, mean, na.rm=TRUE)\n",
    "\n",
    "# Calculate how far on average the median of the 1000 bootstrap\n",
    "# coefficients are from the known values in the population:  0  \n",
    "sum(abs(apply(coef_mat_accum, 2, median, na.rm=TRUE)))/10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".dl-inline {width: auto; margin:0; padding: 0}\n",
       ".dl-inline>dt, .dl-inline>dd {float: none; width: auto; display: inline-block}\n",
       ".dl-inline>dt::after {content: \":\\0020\"; padding-right: .5ex}\n",
       ".dl-inline>dt:not(:first-of-type) {padding-left: .5ex}\n",
       "</style><dl class=dl-inline><dt>(Intercept)</dt><dd>150.07387136196</dd><dt>var10</dt><dd>21.2855435594198</dd><dt>var2</dt><dd>17.6940385572118</dd><dt>var3</dt><dd>105.633709631171</dd><dt>var4</dt><dd>12.2687322994194</dd><dt>var5</dt><dd>30.8342315844022</dd><dt>var6</dt><dd>78.9071849349776</dd><dt>var7</dt><dd>74.0604517180518</dd><dt>var8</dt><dd>80.293935842596</dd><dt>var9</dt><dd>203.681909176635</dd></dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[(Intercept)] 150.07387136196\n",
       "\\item[var10] 21.2855435594198\n",
       "\\item[var2] 17.6940385572118\n",
       "\\item[var3] 105.633709631171\n",
       "\\item[var4] 12.2687322994194\n",
       "\\item[var5] 30.8342315844022\n",
       "\\item[var6] 78.9071849349776\n",
       "\\item[var7] 74.0604517180518\n",
       "\\item[var8] 80.293935842596\n",
       "\\item[var9] 203.681909176635\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "(Intercept)\n",
       ":   150.07387136196var10\n",
       ":   21.2855435594198var2\n",
       ":   17.6940385572118var3\n",
       ":   105.633709631171var4\n",
       ":   12.2687322994194var5\n",
       ":   30.8342315844022var6\n",
       ":   78.9071849349776var7\n",
       ":   74.0604517180518var8\n",
       ":   80.293935842596var9\n",
       ":   203.681909176635\n",
       "\n"
      ],
      "text/plain": [
       "(Intercept)       var10        var2        var3        var4        var5 \n",
       "  150.07387    21.28554    17.69404   105.63371    12.26873    30.83423 \n",
       "       var6        var7        var8        var9 \n",
       "   78.90718    74.06045    80.29394   203.68191 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculate the standard error of the beta coefficients\n",
    "apply(coef_mat_accum, 2, sd, na.rm=TRUE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.460039453071705"
      ],
      "text/latex": [
       "0.460039453071705"
      ],
      "text/markdown": [
       "0.460039453071705"
      ],
      "text/plain": [
       "[1] 0.4600395"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Original coefficients listed for comparison\n",
    "#\n",
    "#             Estimate Std. Error t value Pr(>|t|)\n",
    "# (Intercept)  0.05456         NA      NA       NA\n",
    "# var2        -0.14774         NA      NA       NA\n",
    "# var3         0.07723         NA      NA       NA\n",
    "# var4        -0.18304         NA      NA       NA\n",
    "# var5         0.52600         NA      NA       NA\n",
    "# var6        -0.32386         NA      NA       NA\n",
    "# var7         0.49406         NA      NA       NA\n",
    "# var8        -0.56801         NA      NA       NA\n",
    "# var9         0.37399         NA      NA       NA\n",
    "# var10        0.30558         NA      NA       NA\n",
    "\n",
    "\n",
    "# Calculate how far on average the \"trimmed means\" of the 1000 bootstrap\n",
    "# coefficients are from the known values in the population:  0\n",
    "# The lowest and highest 10% of the coefficients are REMOVED (trimmed)\n",
    "sum(abs(apply(coef_mat_accum, 2, mean, na.rm=TRUE, tr=.10)))/10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "2.6211331950397"
      ],
      "text/latex": [
       "2.6211331950397"
      ],
      "text/markdown": [
       "2.6211331950397"
      ],
      "text/plain": [
       "[1] 2.621133"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculate how far on average the \"ordinary means\" of the 1000 bootstrap\n",
    "# coefficients are from the known values in the population:  0\n",
    "sum(abs(apply(coef_mat_accum, 2, mean, na.rm=TRUE)))/10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No id variables; using all as measure variables\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 6 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>variable</th><th scope=col>value</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>X.Intercept.</td><td> 2.7865081</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>X.Intercept.</td><td> 6.9884943</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>X.Intercept.</td><td> 0.7714394</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>X.Intercept.</td><td> 0.6033623</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>X.Intercept.</td><td>-2.0999061</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>X.Intercept.</td><td> 0.3500061</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 2\n",
       "\\begin{tabular}{r|ll}\n",
       "  & variable & value\\\\\n",
       "  & <fct> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & X.Intercept. &  2.7865081\\\\\n",
       "\t2 & X.Intercept. &  6.9884943\\\\\n",
       "\t3 & X.Intercept. &  0.7714394\\\\\n",
       "\t4 & X.Intercept. &  0.6033623\\\\\n",
       "\t5 & X.Intercept. & -2.0999061\\\\\n",
       "\t6 & X.Intercept. &  0.3500061\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 2\n",
       "\n",
       "| <!--/--> | variable &lt;fct&gt; | value &lt;dbl&gt; |\n",
       "|---|---|---|\n",
       "| 1 | X.Intercept. |  2.7865081 |\n",
       "| 2 | X.Intercept. |  6.9884943 |\n",
       "| 3 | X.Intercept. |  0.7714394 |\n",
       "| 4 | X.Intercept. |  0.6033623 |\n",
       "| 5 | X.Intercept. | -2.0999061 |\n",
       "| 6 | X.Intercept. |  0.3500061 |\n",
       "\n"
      ],
      "text/plain": [
       "  variable     value     \n",
       "1 X.Intercept.  2.7865081\n",
       "2 X.Intercept.  6.9884943\n",
       "3 X.Intercept.  0.7714394\n",
       "4 X.Intercept.  0.6033623\n",
       "5 X.Intercept. -2.0999061\n",
       "6 X.Intercept.  0.3500061"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 6 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>variable</th><th scope=col>value</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>9995</th><td>var9</td><td>7.850106</td></tr>\n",
       "\t<tr><th scope=row>9996</th><td>var9</td><td>      NA</td></tr>\n",
       "\t<tr><th scope=row>9997</th><td>var9</td><td>      NA</td></tr>\n",
       "\t<tr><th scope=row>9998</th><td>var9</td><td>1.142138</td></tr>\n",
       "\t<tr><th scope=row>9999</th><td>var9</td><td>2.057648</td></tr>\n",
       "\t<tr><th scope=row>10000</th><td>var9</td><td>2.270404</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 6 × 2\n",
       "\\begin{tabular}{r|ll}\n",
       "  & variable & value\\\\\n",
       "  & <fct> & <dbl>\\\\\n",
       "\\hline\n",
       "\t9995 & var9 & 7.850106\\\\\n",
       "\t9996 & var9 &       NA\\\\\n",
       "\t9997 & var9 &       NA\\\\\n",
       "\t9998 & var9 & 1.142138\\\\\n",
       "\t9999 & var9 & 2.057648\\\\\n",
       "\t10000 & var9 & 2.270404\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 2\n",
       "\n",
       "| <!--/--> | variable &lt;fct&gt; | value &lt;dbl&gt; |\n",
       "|---|---|---|\n",
       "| 9995 | var9 | 7.850106 |\n",
       "| 9996 | var9 |       NA |\n",
       "| 9997 | var9 |       NA |\n",
       "| 9998 | var9 | 1.142138 |\n",
       "| 9999 | var9 | 2.057648 |\n",
       "| 10000 | var9 | 2.270404 |\n",
       "\n"
      ],
      "text/plain": [
       "      variable value   \n",
       "9995  var9     7.850106\n",
       "9996  var9           NA\n",
       "9997  var9           NA\n",
       "9998  var9     1.142138\n",
       "9999  var9     2.057648\n",
       "10000 var9     2.270404"
      ]
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     "metadata": {},
     "output_type": "display_data"
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    {
     "data": {
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       "<ol class=list-inline><li>'variable'</li><li>'value'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'variable'\n",
       "\\item 'value'\n",
       "\\end{enumerate*}\n"
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       "1. 'variable'\n",
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       "[1] \"variable\" \"value\"   "
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     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A data.frame: 6 × 2</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>variable</th><th scope=col>value</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;fct&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>X.Intercept.</td><td> 2.7865081</td></tr>\n",
       "\t<tr><th scope=row>2</th><td>X.Intercept.</td><td> 6.9884943</td></tr>\n",
       "\t<tr><th scope=row>3</th><td>X.Intercept.</td><td> 0.7714394</td></tr>\n",
       "\t<tr><th scope=row>4</th><td>X.Intercept.</td><td> 0.6033623</td></tr>\n",
       "\t<tr><th scope=row>5</th><td>X.Intercept.</td><td>-2.0999061</td></tr>\n",
       "\t<tr><th scope=row>6</th><td>X.Intercept.</td><td> 0.3500061</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
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       "A data.frame: 6 × 2\n",
       "\\begin{tabular}{r|ll}\n",
       "  & variable & value\\\\\n",
       "  & <fct> & <dbl>\\\\\n",
       "\\hline\n",
       "\t1 & X.Intercept. &  2.7865081\\\\\n",
       "\t2 & X.Intercept. &  6.9884943\\\\\n",
       "\t3 & X.Intercept. &  0.7714394\\\\\n",
       "\t4 & X.Intercept. &  0.6033623\\\\\n",
       "\t5 & X.Intercept. & -2.0999061\\\\\n",
       "\t6 & X.Intercept. &  0.3500061\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 6 × 2\n",
       "\n",
       "| <!--/--> | variable &lt;fct&gt; | value &lt;dbl&gt; |\n",
       "|---|---|---|\n",
       "| 1 | X.Intercept. |  2.7865081 |\n",
       "| 2 | X.Intercept. |  6.9884943 |\n",
       "| 3 | X.Intercept. |  0.7714394 |\n",
       "| 4 | X.Intercept. |  0.6033623 |\n",
       "| 5 | X.Intercept. | -2.0999061 |\n",
       "| 6 | X.Intercept. |  0.3500061 |\n",
       "\n"
      ],
      "text/plain": [
       "  variable     value     \n",
       "1 X.Intercept.  2.7865081\n",
       "2 X.Intercept.  6.9884943\n",
       "3 X.Intercept.  0.7714394\n",
       "4 X.Intercept.  0.6033623\n",
       "5 X.Intercept. -2.0999061\n",
       "6 X.Intercept.  0.3500061"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(ggplot2)\n",
    "library(reshape2)\n",
    "\n",
    "# Histogram with density plot\n",
    "# ggplot needs a dataframe to plot\n",
    "# The data are then stacked using the \"melt\" function from \n",
    "# package \"reshape2\"\n",
    "#\n",
    "# Convert to a dataframe\n",
    "coef_mat_accum_df<-melt(data.frame(coef_mat_accum))\n",
    "# List first 6 and last six rows of the dataframe\n",
    "head(coef_mat_accum_df)\n",
    "tail(coef_mat_accum_df)\n",
    "# List the column names of the dataframe\n",
    "names(coef_mat_accum_df)\n",
    "head(coef_mat_accum_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "“Removed 3480 rows containing non-finite values (stat_boxplot).”\n",
      "Warning message:\n",
      "“Removed 4943 rows containing non-finite values (stat_density).”\n"
     ]
    },
    {
     "data": {
      "image/png": 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JKnp2dSUtLs2bONnaurqyMiIurq6hYu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\nwQ4AAACAJxDsAAAAAHji/wO8JgeFBY7phQAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.\n",
      "\n",
      "Warning message:\n",
      "“Removed 4943 rows containing non-finite values (stat_bin).”\n",
      "Warning message:\n",
      "“Removed 10 rows containing missing values (geom_bar).”\n"
     ]
    },
    {
     "data": {
      "image/png": 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MnMf+eFfwEIj46av8hhHZ+hkcGCIADIz89v57ZRoyZIuxZ//PHHHJAloqsCgx2R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FQJ+TqdUnAPC5XK2HDgJInRGYXesymQBo\nesI4i9VMKrPnMzrhWFYqkwKoLS4CkDN+ukR60fNtWZFIrFIgVGGsBMGGT/Rl5tSZ+ng9gK2f\nBRaMjFkGAOYOF4CzJhNR+/YlzWBgwDBioEfgEnZ0uui4OD2o4wmFQrl4aGB3OcDz/KpVq/77\n3/8CmDFj/Pr1f37uuR/l5qaJRBzLMmlpSatW3bZ5818feeR7HMc1NzfffPPN33wTfGLm5U1X\nVxcJaqeM7Toszk2JDWcdtqmqtqmqFkDOgvnkSXPpft7jBpDWP7BzOJ1ulwvdkligx/pEIhYr\n5IHhmsNmB6BUyBnA1trSWVUJoGDq/OFdklRjnSE7ntguGNixLLt8yY0ATpUfazhT0/clYnri\ndvv8boBoY/sjl8kS42KJlV1nZ6djQOQXFjIzc0GFsRQK5eK5VEuxMtlFJwPGLCzLisXiUE54\n8sknv/jiCwDLl1/9hz/8NGi3tUQiefrpe+fMmfzooy+bTNYf/vCH//znP2+66aZQ3nd49H6w\nI/+PuGvXLpJ2mrV4qUQyohk7hmEuqgueBHaJqUaRKKSvjb4Q2YRUpRo3q5DjRACaivcAUMUl\nxmbk9l1JwjiGYbRRGpZh0DNJLFqnZlmu70q/nyelf6VcwYKp378XAMeJcns69piACRWDIY/W\n2Wob7Z3Wi93Yi0IlA+B0egU/uPMbUC+au+ijL9ZarJbtn6+/52eP9T43pOtFEpHP45P4JT54\n6pqbJ+XlBezNSElpaGgHIAhCa2trTk4Oec6yLMdxYfnSyskp2Lt3e0VFxVj+Xtf7JS2TyYQB\n1jCXK2T6yGXz8V6UvIlySUADu9GHYRixWEy+WQyDv/3tb3//+98BXH/93L/85VmR6ELnLFw4\n47PPXrvjjl80N7ffd99969atW7jw4pzGQqfXYGLk/xFJg11a7vjk9MwRfmsS2LFDG3TR0dFB\njEUS01LEYXIndjldZbv2AshdMFcq7x7nShrs0mcuCPjyI2GcQqWQyiQAbDa72+0GEB2tIYMl\nenHanX4IANRKJTimrmQPgIyciXJFT8WWvbj4jFjZua1OP+/nJMP52JUaOQAIcDq9Ko38fMsk\nctnSa5Z+9PlHh3bvW37fHdHxceQ5x7GGcUm1J+pYDwc5ahoauQH/pzJTU4tKD4ABBDQ3N0/o\n6RC/qH/lC5OfNxFAVVUVxvC3OyKCBiCVBhcgX5awLMswTFj+lccCPp9vtK9ACTOXamBHHLYu\nD3Q6ncvlcrku1Ot9PioqKn72s58BKCjIfOWVx12uQNnEQJKSYv7xjxfuvPPZjg7zbbfdtn79\n+uzs7GG89bCRyWQqlQoj/o/I8zwpQE+Zv8hms43kWwNQqVQej8fjCT4RIYDezqro+NiBUpjh\nsf/bHW6Xm2GYrPlzSZRma24yVVcBME6d6+1/sY6OswDUOpXXxwM4e/YsAI5jlQoZz/f7MWCz\n2gCIOU4sEjlNptbjRwHkTZoNv0BCOuEi8wHSKC0ACIK9w6KKH45FnETRneM0W50K5YXyndct\nXPL5+s/dHve2z76+5Ud39j43ZCXWnqizmlxSNZpaW6xWm0TS7xyDPoFhGIYTBB8qKyvnzJlD\nniuVSp/PRz69IWI0ZgDw+XwHDhwYP3586AdGAqlUSnyUzGbzZZPBGhSNRuP1esP1H3MsMGZ/\nc6AMj8vkd44rE57nH330UbfbrVYr/vznn8tkQy0Apacb3njjeblcajab77nnnki4549BDh48\n2NnZCWD6wsWjfZdBINbEEqlUFxcbrjP3b94OQJ+brU3sltmSdB3Dcsap/ca5ejweoofoVU6Q\ngRNatYoZkH6z2W0AFHI5gIYD+/08zzDM+Mlzhn1PiU4DhgFgH+7EWLFExIlZABcWxgJQq9RX\nz70aQPHmbcSxhUD0Ezwv8G7wglDf3BywUSmXJ8REkza7XmOa8JKZmUfyYbTNjkKhXBQ0sLuE\nefvtt8vKygA8//wDSUlxF7V3woSsV155nGGYM2fOPP7445G54Nhi8+bNAJQabe60maN9l0Eg\nsUJ8ctLAQGp41FZUttQ2AMi/dkHvw8a9ewAkZBfINP08eLu6iBExNNFqAF6Px2ZzIJge1s/7\nXS43AJVcAaC+dB+AxOQMbfTFfTX2hRVxEo0KoeknyPwJu23wzNmNi5cxDON2uvZu3Nr7MDox\nWqFWAODIbLHgpidGRgJETBirUCj1egNoYEehDIHKykqVSvXAAw/0ffj+++8zDPPll18GLP7t\nb38b1d94fCC1tbUtLS1hvuXQCP2taWB3qdLW1rZ69WoAc+ZMuuWW4fTJXXfdnAce+C6Ar7/+\n+h//+EeY7zf2IIHdlPmLiG5gLBN2Sez+b3cAkGs1KVMnkSeCn28uKQaQMv2qgMUkrymVSYh9\nSVdXJyAwYHSawMDOYbcLEAAolAo/72s6VAogd2KocbMsSgvA3jn8crlcJQNgtw9e+E5MSJw+\neTqAXes2EWENAIaBITMRADwsgNrGpoEb043JnBgA2trahlhhv1iysvIBVFRUROJwCuVyIjMz\nc82aNX//+9+//fZb8qS1tfXxxx+///77h6cRfPjhh3//+9+H9Y4j99Y0sLtU+X//7/9ZrVax\nWPTCCw8N+5AnnrhjypRcAL/5zW/OnDkTvtuNORobG8nkzekLl4z2XQZBEASSBIpPCc8wMbvF\nemxvKYDcBfPZHpFE+7GjbosFQEphoC8JsSbW6Lr9gTs7TQBUKjknDtQQ2Ox2ABKRWCIStR47\n4nHYAeRNmoXQII4njtAdTwYrxRKI74mpo7OsqLj3ITE9cdq84FHX3DRQOZienMxKGACCIDQG\nS+mFTuY46nhCoQyVVatWLVmy5IEHHiAt1D/+8Y91Ot0f/zhUh+Te3+uGQSieR36/P+z9qTSw\nuySpqKj48MMPAdxzz42pqcP/8c9x3Jo1TyqVcqfT+dhjj4XylT3G2bhxoyAILMdNvXqsO9i1\ntbURJU1CcngydqVbd/l8PoZlcxaei+Ea9+4GIFEoE/Om9l3M87zZYgGgjVID8PO8xRp84AQA\ne/ckse4GOwAqTVRyWk6IFyb6CY/d5fcM8wtSrpICcLl9Pt/g0o287LzM9HEAtn9xztwxOSsJ\ngCCAd8Lj9Ta3tQfsUioU8Qnd1ZwIVWPHjcsFUFtbOzxlFYVypfHOO++YTKZf/vKXH3/88eef\nf/7ee+8Rod4FUKvVn3766cSJE0UiUVJS0ssvvwygsLBww4YNv/vd7/Ly8gA4nc6nn346KytL\npVItWLCgqKiI7JXL5UVFRStXriSzOs1m849+9CODwZCcnHz//fcTZ4PzbS8vLxeLxV9++WV0\ndLRMJissLNy0adPAtx4eNLC7JPnd737n9/s1GtXDD98W4lFGY8IvfnEfgJKSkjfeeCMctxuL\nkP8zOVMKNVFjfZwaUU4AiDeGIWPn5/37Nm8HkDptsjL6XFtJ0769AJInzWb7u+uZTCaiY1VH\nqXv+KiBYgx3v8bk9bgDKbuXEPgC5E2b0WmAMG1l0tzDWYRpm0o4EdhCGVI0FcOOSGwE0nKk5\nc7Rbj6yOUunitAAENwOgpilITi4j1ciIgIgFdllZeQD8fv+pU6cicT6FcplhMBj+8pe/vP76\n6w888MAvfvGLXrn6hXn44YdXrVpVXl5+++23P/vss8XFxTt37rz22mt/8pOfHDhwAMDKlSu/\n/fbbP/zhD5s3by4sLFy0aFFpaSnZ+/TTT8+bN+/TTz8FsGzZsiNHjvzjH//4/e9/v2fPnjvv\n7Bban2+7z+e77777Vq9evXHjxkmTJi1durS0tDTgrYcHDewuPU6dOkW6Qe+77yaNRjno+kG5\n7bbF8+ZNBrB69eoISfxGF4fDQX5JKhzzdVj0NNjJVUpNlC70046XHLR0dAHIX3yuEdNrt7cd\nKUewOixpsBOJRQqlHECXqQuAXCaVDtBc25x2AAwYpUJuaW4yNzYAGMZ82IFIe4WxHaEFdkOu\nxs6aPis2OhbA9i839D5MzjIAEFwMgLpgbXYZRiMRxkaojSEjI4dEybTNjkIZIitWrIiJibFY\nLA8++OAQt9xxxx2rVq2aOHHi6tWrdTpdRUWFXC4XiUQSiUShUJSXl3/55ZdffPHF8uXLZ8+e\nvWbNmoULF65du5bsnTVr1qOPPpqTk7N169Z9+/Z98sknS5Ys+f73v/9///d/LpfL7XZfePtL\nL7308MMPL1iw4O9///u8efPWrFnT962H/Umggd2lx+uvv+73+zUa5T333BiWAxmGefHFR+Ry\nqdPpfOaZZ8Jy5phix44dxFqs8JrrR/sug0MyduFSTuzdsBVAtDE5MfecW2Hzgf1+nw9AyrTg\ngZ02Sg2GEfwCcSqO0gWrw9ocAKQSsYgTNR7cD4DjRNn500K/M8NxEq0KgLNrmIEdJ+LEUg6D\nTYw9t57lll5zPYBj+w+ebW4lD5OzkwB43X7Bi9qmoIFdMgnsqqurh3fPCyOXK5KSjKCBHYUy\nZJ599lme5zMzM1etWjXELTNmdP86KhaLdbrAX6ePHj0KIDU1lelh06ZNp0+fJq9Onz6d/KGs\nrCwjI8NoNJK/LliwYNOmTVKp9MLbFy8+5721dOnSI0eODONDHggN7C4xmpubP/74YwC3375U\npRp+RB+AwRD/6KMrAWzZsmX9+vXhOnaMsGHDBgD6lHRjZqjtXyMAydjpU5JDP6qpqrb25GkA\n45cs6vu8sWeSWJQxo+9zQRCIazRRTtisFt7nA6DTBulTcTjsAJRyBYCGAyUA0rLGS+Xh+ZqU\n6bQAHF2hCmNtQ3A8IVxz1TUyqUwQhB09STvDuCSSMOOdsNhsXaZAXz2lQqHRKQGYTKYI2feT\nNjtaiqVQhsK2bdtee+21P/3pT+++++6GDRvefPPNoc1ZM0sAACAASURBVOy68NwUjUYjlUqt\nVqutDx988AF5tbeHz+v1Bh0aeeHtfeE4zuv1DuXCg0IDu0uMd955x+PxSCTie+5ZFt6T7733\npqysFADPP//85dSs7ff7iQB+5uIbRvsug+Pz+YjEMiwNdrvXbwYgU6szZverkDYV7wWQOj0w\nXWcymYiAhignOrs6AYjFIpUycDCXx+3xeL0AlAo573G3HDsMIHt8Yeh3JkijtQAcITie9Ahj\nhxrYKRXKBXMXANi/ZYfdagMgVUjijLEA/C4AqA3WZpeeRjQWVBhLoYwyZrP53nvvXbZs2V13\n3TV79uwnnnjiqaeeCr1NYsKECV6vt6ysTKlUKpVKsVh822239dZSeykoKKisrGzuMTPfuXNn\nYmJiY2Pjhbdv2bKl94SNGzf2DicMERrYXUq4XK5//etfAG68cX5s7CD+iheLSMT96lcPAKiv\nr//LX/4S3sNHkQMHDrS1tQEoXHTdaN9lcBobG0nuJ/RSrKXLdLT4AIDcRfNFfSZi2VtbTTVV\nAIzT5gVsIXVYjuOUaiV6JsbqdGoMkEMQPSwLRimXtxw9zHvcALILpod4516kUToAbpvT7w1J\nGDv0wA7AssU3MAzjcXuI3AQ9bXZ+F4PzBHb5ed0pz+PHjw/vnheGZOzq6uoup9+1KJRI8Nhj\nj1ksll4J4EsvvZSYmHj33XeTX1bfeeedF154YeincRxXVVXV1NSUlpZ211133XrrrR9++OH2\n7dvvvvvuPXv2LFiwIGD90qVL8/PzV6xYsXXr1k8//fTRRx/Nzs42GAwX3v7888+/8847u3fv\nfuSRR7Zu3fr000/3fethXJtAA7tLiU8++YT86L3nnuWROH/mzAnXXTcHwJ/+9KemYE1FlyKk\nsqzSReVNH+sDJ9BTh2UYJiE51Izdvg1beZ+PE4nyrlnQ93nT/r0AwDABk8QAdHR0AFDr1GAZ\nh91OGhOjgxmdOOx2ADKZlGXZhoMlADS6WL0hPcQ79yLrmRg77GosKcV6vbx7yJ4p+nh9t1nx\n15v9PA/AmG0A4PcJfndwm+KcjHQijCUzYMLOuHE5AHier6ysjMT5FMrlwSeffPLee+/98Y9/\nTErq/s4pl8vffvvt4uLiV155BcBXX3319ttvD/3AH/zgB7t37ybmxm+99dbdd9/93HPPLV++\nvK2tbdOmTampqQHrWZbdvHlzRkbGHXfc8dBDD02YMKE3LXeB7f/617/eeuutpUuX7tu3b926\ndbNnzw5464u9NmGsW/BT+vLee+8BmD49Py8vbD9BA/j5z+/dvr3U6XS+/PLLf/7znyP0LiMJ\nabArXLhk7A+cQI9yQhMdJVOG1Kzmcbn3b9kJIGP2DIVO2/elpv3FAOLG5Sl0/ZxfehvsdNEa\nP8+3nKn0dp3lRCKlbFzg6QLs3Q12cgBNZQcAZI+fFrrRSS/SKA0YBoLg6LKq4rWDbxjAOWGs\n1SWNGap4/MbFy0oOlZjOdpTvLZkyb5Y+LV4kFvm8Pr8TrWc7nC6XvP+4dKVCIVOKnWZvhPQT\nRBgrCMLJkycLCgoi8RYUymXAihUrBtr8XnXVVb3W4p999lnv8+eee+65554jf+51myP0/ke+\n7bbbbrut201MIpGsWbNmzZo1Aec7nc6+f42NjX3//fcH3u182wHMmDFj7969AQ/7vnXfaw+d\nS+BHHYVw/PhxYmzzve9F0LPDYIj/wQ+Wv/nmJ2vXrn3wwQfDVfIfLU6fPk1SHTOuWTradxkS\n3ZLYlFDrsKVbi5w2O8MwE66/NuClppJ9AIxTA+uwZpPJWn3cdqqsbW2dtanO36MGOMUw6kRD\nfH5Bypz5hmkzWJHI7XL5eB6AUqGwt7eZG+sBZI0Pgx62F4bjJGqlx2Ib9vwJmVIKBhBgs7lj\nhhzY5efkp6ekV9dV7/hyw5R5szgRl5ihr69o4J0Q6YT6ppbsjLSALXHxUXXmNpJKDztKpSo+\nPrG1tYnqJygUyhChpdhLBvKrgEajItXSyPHQQyuiozV+v//FF1+M6BuNAKQOK5FKp1y1aNDF\nY4GewC4kSayf5/es3wzAMHF8VP9ePVPVGUdbKwDj1HNfRbzHXf75Pz9edWPDR6+ZDm0311X5\n+2g8BUGwNDVUfrth64vPfXLfyiP//cDU0QmAYxiFTNZYVgqAYZjM3Cmh3HkgpM3OOVz9BMsy\nUrkEgG1ojie9LFt8A4Daisqak6dxrs0OEIK32aWlJQLw+Xy9fdPhhQpjKZTLD4ZhZP3T/2GE\nZuwuDbxeb4+39TzZAKvY8KJSKR555PsvvfTW9u3bt23btnDhwsH3jFW+/vprAJPnLZQpwuDk\nHGlcLld7ezsAfWgNdod3l5jOdgCYeEOgXqRx314AnEhsmNitkz1TtGnn/71oaWkgf1WoonOn\nLdTpMwRWLlGo9bFqc0dTS92pU+W7O1vrHZ0dB999S/LpWuNNt6bMms8wTFPZQQCG1GylejgF\n0wsgjdJYa+EYrpUdALlK6nZ47BejnwAwd8bcf3/8QZe5a8dXG9Jys87NFnOhNpj0dXzeuJ2b\nywEUFRVlZmYO+7bnI3Nczp49W2lgR6FcTkycODGgkhtGaGB3abBlyxbS2H7zzSMRZq1ced2/\n/vVVXV3LSy+9tGDBgjD2To0kzc3NpKV91pLwODlHmtraWtImEh+CJFYQhJ1fbQAQl5GWmJcd\n8CqZJKbPmyKWKZzmzm2vPX96R7dtoT5tStaUGybNWRyflFBbW+uw25VKuTE5nry69K6f1Z0q\n2/PNv08e3O6xmM+8/7aj4rj+sZ+1HC0HkB3WOixBqtMCcFmdfh/PirhhnCBXyUxtVqv14r57\nikSiJQuXfPT5R4f3lHS0tsca4mRKmcvu8jtR39zC8zzH9btMWlr3P1aE9BMZGTkAqqurPR6P\nRBLZX+ooFMplAC3FXhr897//BZCWljRlykhY7IrFoscfvxPA4cOHyfiyS5H169cLgsBy3PRF\nl8AkMfTUYVmOjTMkDvuQE6VlbfWNACbdFOjb5+f5loOlAIxT5zQfP/jBAzeQqC4hOfvep/91\n1XeeT0ybqtJo/DzvsDsAqFX97OtSsievfHzNPc+8EZ2QCqC5ZO8XTzzospgBZOaFuQ6LHis7\nCILTFJIw1m73CP6L27hkwWKxWOz3+/d88y3DwJCZBIB3wsv7mtvaA+8pFcsUEkRs/gQJ7Hw+\nX1VVVSTOp1Aolxk0Y3cJYLVayQz7m29eMGJvesMN895++7Pjx6tWr169bNmyoJ7aYxxShx1f\nOFsTFTPo4rEA8TqJ0SeIxMP/bG//7GsAUclJKVMmBrx09vhRj80KwM/znzy5kvd6WE606KZH\nlqx4qu3s2braWoZh5UqZxWwBBIBRBVPmRidl3PTwq2Xb1pbv+tTR2QFALJakjhs/7AufD1mP\nMNbZaVPGDqfOq1BLAQgCHA63UnUhc/kANGrN/Fnzt+7aWrx5+3Urv5uclXSmvMrvAXjUNjYl\nJ+oD1ifoo2qrWh0OR2tra0xMmL/YiOMJgNOnT+fm5ob3cAolcpQeOXL7E0+G5ZzQD7miuPR+\nWl+BrF+/ntiTLlsWOCogcrAs88QTdz744P9WVlb+97//vf3220fsrcNCZ2cnkZHPui4inn+R\ngAR2oUhiTx060lRVC2DSTTcMLKA3798HgBNL9v/7LxAElSbm7sf/mjl+LgCL2QJAqZIzDGOx\nWgDI5RKROEgB1OVys5xo/vIfjZ88+8O/POP3+zWc/GxlRUJumGM7ViwWKeQ+u8MRWsYOgMV2\ncYEdgGWLl20r2uaw2fdv3TlhxkwAIG12TY1zMTVgcVpaUm1VK4Dy8vJFi8Is09HpomNi4js6\n2ioqKpYvv2S+mCmUlvaz67ZuG+1bXInQwO4SgMgmJk7MSk0dfoVuGFx99bSpU/MOHjyxZs2a\nFStWXFr9PRs3bvT5fAzDzLz20jA6AVBTU4PQZk5s/WQdAK0+Pn1GkKY3Yk3Mez0AEpKz73/m\nn9HxKQAEwGqzAlBqFH7Bb7fbAQSdRCzwgsftBiCTSjPyChmWg98fJVaWffje5JV3J+SFObaT\nRWltdsewB4tJZCJOxPI+v83mAjQXtTfFYJyQV3D4+JGdX22cu/RadbTa2mnlnagJpp8wGrtz\neKWlpWEP7ABkpGd1dLT1Dg6nUMY4hYVhmy4Y0TMvV2hgN9YxmUy7du0CsHRpoPHYCPDEE3fc\nc8+v6uvr//3vf993330jf4Fhs27dOgCZE6fEJobqCTcydHV1WSwWAPrhep2cKjvaUFkFYPLN\ny1g2sH2W97ibDx4gf07Lnn7/z/8lV3bXN+12O+/zAVCqVTarTfD7AaiDBXYul0uAAEAmk9VV\nHOB9XgCJukTB6ytf+/70u++PzhjgZhwCkigNGppDFMbaTM6LGizWy7LFyw4fP9Le1HK89FBy\nVtKJfRW8EzaHo9Nkitbp+q5MTOouvx46dGjYV70A6RnZJaW7aWBHuVQoKSkh34EpowIN7MY6\nGzZs8Hq9DMNcd93skX/3mTMnzJo1sbj48GuvvXbHHXdIpRdXzxotbDbbjh07AMy5dOqwJF0H\nQD+sjJ0gCFvWfg5Aq4/PmD1j4IKi//2NwPsApI6b8uCzH0hl5/xfrFYLAIZl5Up5c1MnAIlE\nIpEE+ebgdP1/9s4zMKoqb+PPnTu9p/cKgRRKIAm9GIqAgBgEBFwsrG0RXMSyuq6srmV119cC\nuq6urmVtKAICCgihKNJLIBDSK+ltSqaX+344kyGkZ2ZgBr2/T8mdM/ecOyI88y/P3wCAS3N5\nNF2SdxKAQua/6K4/7/rydaO+7cwXH497YLU0OMSF83cLaYw1qHWMnaE4rrRmi2RCl4XdqOGj\nwkPDa+pqDn63++bbl146XsBYACvKq2s6CbuQ0AAyH0KlUtXU1Hi8zI70TxQXF9vt9q6SnYXF\nNwkJ8k8b6YFuv9PnCuobr4kB+K8VVtj5OuR7T3JyfEREsFcOsHbt8qVLz9fU1Hz66af333+/\nV84wUPbs2UPmnI6dOdfbZ+kvpMCOLxQogwJdeHv+qZzq0goAo7Lmd/23/+KXnxV/vx2AQuj3\n4PqvBIKrXP3UajUAiVQEQNvWhi79sE6MRhMAkVAAoDTvJIDkhHRlQOjM21ft+uotq8l4+n8f\njn/oEb5E6sIjdEXoJwcAO2PU6kUKV5wIyWCxNq3RhfdSFDV3xi3/+eyD4ty8OcutRLrZDKis\nqRmdktxxJZdLBwUrG+pbAeTk5EyfPt2F7XphUPwQAAaD4fLly9HR0Z69OQvLNSJt5NBP3vmL\n+/e5++EXf9jXee4WSy+wX/58Gr1eTyJPXgnXEUaNSpw8eTSAt95669oZKnoW0g8bm5gSHufJ\nzOA1hQi74MgIF0JTdjuz9+vvACgjwuLHpnd6tXz/3uP/9woACU86bfLvBIKrVBcDpk3bBkAi\nk+h1bXabDYBc1k0e1m6xWSxmAEKBwKDT1FYWAkhKSAMQGBY7df69FEUZVK1nv/zUbrcN9BG6\nReDnSBYbXB0sRvonzGabyezKkaZOnCqVSAEc33fQP8wf6NGmODw8iPxwLdzs4uIcfoRsNpaF\nhaVPWGHn0xw8eJD0w06fPtaLx3jkkWUA6uvrP/74Yy8eo58YDIbs7GwAE2bf6u2zDACSig11\nqSX23OFjxLsufdFt1NXhuqZLFw/95U+M3S7kCpMDUsITO3d0trW12WxWABK5RK3VAuDyuAJB\nN40yBiOJe1EigaC84AzD2AEkJzi6NKIHj0ibsgBAa0VZ4Z7vXXiKrnBFQlogAKBvdbF/Qixz\nNMa6FrQT8AUzps4AcOano4GRSgA2AxqaW9o/iiuERTjirOfPn+86jNxNQkMjxGIJ2MFiLCws\n/YAVdj7Nrl27AMTEhA0eHOXFY4wYkXDTTekANm7c6PtBu3379un1egAT5twwws5ut1dVVcGl\nlliLxZr99XcAggbFRY8e2fElQ3PTvnWrrUajQChJ8k/hcfhBgzs3rmo1WgAcDi0SC9u0WgBy\nqRjdBQ1JgR2fx+NwOKWXTgMI9A8L8r/SqT187M1xiaMBlB89XJ9/caAP0i18pRxuCDuhRECe\nxbUyOwBzps2madpqsTTWlwNgrLCbmaqazmNhw8Idwk6tVpPgqwehKIoE7diIHQsLS5+wws53\nsdlse/fuBTB9eje18NeZRx5ZRlFUY2Pjf//7X2+fpQ9IVWLkoCGRgzoP1PJZampqzGYzgNCY\nAbfEntizn0yGzViysKN3nd1iyX78j7r6eg6HnjRliYgrFsqVspDOwlGtUQMQy0QGg570xsq6\ny8OCgdFgBCASCACU5p8CkJLQ2VRl4uzfyf2CwTC5WzYZ1aqBPktXSJmdwVVhx+FQIgkfrkbs\nAPj7+Y9PHw/gwskTFAcAbAaUV9d0WhYefqUy8vz5867t1QvxrLBjYWHpH6yw813OnDlD5sNm\nZnpf2KWkDMrMzADw9ttvk3iYb2I0GsmUjhsoXIf2YWIAQqIGJuz0Wh0ZNRGVOrzTZNjj//dq\n/bmzAGavfIqvtQLoGq5zFthJZRISuqO5NOmN6ITFYrXZbQBEQkGburmpthxA0uDOwo7HF2be\n+nua5loM+nObvyLeKO5AyuxcFnZoL7PTuirsAMy7eS4AnUYLrh6AzdBNmZ1/oIIv4JGfz507\n5/JePREXnwBW2LGwsPQDVtj5LiRcJ5dL0tJ8Yo7Q6tV3UBTV1NTky0G77OzstrY2ABPnLPD2\nWQYAKbCT+yvFsoH1fu7fvN2g01McTsYdCzteL93zQ97XXwAYedOtY2Yt05DOjIRhnd6u1WpJ\no4NULta0aUHs67rNwxoMAChQAr6grOAMKSNLHNzNiFj/kChSbNdcWlT+y88DepyukFSszWI1\n61xUZiKZEIDW1VQsgEGxg5KGJAGorysBYDficl2dzXZVNwaHosJCHS4neXl5nV51n7jYBADN\nzc0tLazvAwvLNWTq1KmHDx/ueOWNN95ISkoKDg5esWKFSuWBRMS1hhV2vguJPE2ePJqmu5ns\ndP1JSRk0bdoYAO+8847PBu127NgBIDxuUMzQ5D4X+w6OYWKRAyuwq6+qObHvIIDEzCl+EeHO\n65rKisMv/hVASMyQBatfai7IJ40OQQmdPxNiiUzTtB2M1WwBKbDrDqPRAEAoEFAUyvPPAAgL\njvZTBHW7OCU9MywmEUDBjz/omhoH9FCdELY3xrpcZkcidnqD2Wazu3yMeTPnAlC3NOv1LYwd\nJp21pqG+05qwCMenodfri4uLXd6rW5yNsR6/MwsLC8Fut//nP//56aefOn4x27hx45///Od1\n69Z99NFH58+fv+2227x4wn7CCjsfpba2Ni8vD8DUqd3MhvIWzqDdhx9+6O2zdIPJZHLkYW+o\nflg4W2IHWGD3/Sdf2m12gUQ8euEVH2ab2bz/qXUWnY4vFC99aiNfKG4uuARArAyQ+He2DnY4\n2MnEWm0bAA5Ni8XCbnayw2TsWGB3GkDS4M4NtlegOJNnr+AJhHar5cK2b9xpEuXJpKBpAAZX\n50+IycRYBm1tZpePkZ6aHhIcAkCtqYbD9KRLmV3EFV9ij5fZxcYOomku2GwsC4unIXGKTz75\nxM/P74EHHuj4ks1me/31159++un7779/7ty5X3zxxaFDh06ePOmlk/YXVtj5KAcOHGAYhsOh\nJk3qJtvlLZKT40nQ7u233yYZT58iOztbq9UCmHTLDfClyonBYGhoaMAAh4ldOHaq9EI+gNG3\n3yqUXbGmO/nWa835lwDMX/W3oKjBAIiwC0roXGBnt9vb2nQAJHIJGT4hk4i6zcOaTCY7wwAQ\nigSa1sbm+koAib0IO0Cq8B9z00IArRVlVSeO9P+5OkFREChlAPStOtfuIJY7GmO1Wtcbujkc\nztwZtwBoa2s2m3V2Q7fC7kr80uPCjsfjR0bGgBV2LCzdkZWVNXv2bOevhw8fpijq4sWLAGpr\na++8887IyEipVJqWluacdSYSiQ4fPrx06VIyhXb27Nn79+/ft29fx9uWlJSUl5fPmzeP/JqS\nkhIbG9tpjQ/CCjsf5cCBAwCSkwcFBCi8fZarWLNmKUVRLS0tPhi02759O4Dw2PjYpM7FZL5M\nRUUFKVkL6XfEzmw07frfNwD8oyMTp011Xq86/NPFrz4HkDota9S0LAAWXVtb9WUAQYM7fyYa\nrQaMHQBPwLWYzQDkPVT4kQI7mkPzubzywjMAKIpKHNTHV46hIyeHRSUAKNz7g1Gj7uejdUVI\nBoupXPwiQXNpvoALNxxPCJmTMiViCQCV6rLNiLKqalwdigzrIOwuXbpEZp94kLg4tn+ChaV7\nli1blp2d7axA/fLLL8eOHZuSkgJg4cKFeXl5Gzdu3LFjR0JCwqJFi5ylRE888cSkSZO2bNkC\nICQkJC0tLTU1teNtq6urAURFXbEbi4qKqq3t7Hbka7DCzhex2Wxk4MTkyT4UriMkJcXNmDEW\nwL/+9S+fCtrduHnYsrIyAByaDgoP7edbsr/Zrm5uoShqwl3LnAPEjK0tPz//DBgmICxm/h+e\nJxebCwuIagwa3KXATq0BQPO4JrMRAIfmdJ+HbXewI3nYsvwzAMKDYxQy/94PSVGYOPt3NJdr\nNZku/bC9n4/WFT5pjHV1+ATa+yc0GtcbYwEIBcLpU6YD0GjrbVazVmVoar2qjFoiFir9ZORn\nq9V66dIld7brCnE8YWvsWFi6Mn/+fKFQSL7b22y2zZs333vvveSlhQsXfvrpp1lZWZmZmc88\n84zJZCKmoQDGjRu3evXqoUN7HGjb1NQEQCaTOa/I5fL6+s71tb4GK+x8kZycnNbWVgA+lYd1\nsnq1I2j3wQcfePssVzhw4ADJw0645Ubqh0V750RQRBjN7dfs5prSiqO79gFImDw+ZMhg5/XD\nL6w3NDdzaHrRY/8nEDlibyQtKwkIFvt1HkFLCuykMglpoZBKRFR3fx8wNrvZbAEgFAoBlBec\nATC0r3AdQeEfPGLsbAD1F883FRX05y1dESrlAMx6k81sde0OYkdjrFvCDsAt0+fQNM0wdpW6\nxt6d6UlkVDAAHpeLa1FmF5cAoKKiglgesrCwOBGJRLfddtvmzZvRXpOzdOlS8tKjjz5aX1//\n1ltvrVy50plUJaSndx7A2Ak/Pz8AHUMYWq3W37+P77RehxV2vsjPP/8MQCIRpab2+E3CiyQm\nxt5883gA//rXv4gm8AW+++47AKHRcfHJI7x9loFBInb9HCZmt9m2vveJ3W4XymQZSxc5rxdu\n31pxcD+AqUtWRSVeUV0thfnoLlxntVr0Bj0AoZhvNplBjE66w2AwAgwAkYCvaW1srq9C750T\nVzN83M1yv2AAed9vtVtdMQERKOWOk7iajRVJRQB0bSa7632xABDgH0DMitXqaqvOXl7TRdhF\nhgAgMVSPD42Nj0sAYLPZSktLPXtnFpZfAcuXL9+7d69arf7yyy8XLlyoUCgAGAyGCRMmrFmz\nprGx8Y477iD/TDiRSqU93MxBWFgYgJqaKwW1NTU15KIvwwo7X4TkYTMyUrhcnzA66cqaNUs5\nHKq1tfX999/39lkAwGQy7dmzB8CkGy1cxzCMw+ukf8PEDm3bVVtRBWDcijuEUkdYrq225tg/\n/w4gImH4TXesdi42t2m1NdXoTtipNVpSImaHHQCH5kglom53JAV2fB6Ppmlngd3QQandLu4K\nTXPHzVgCQN/cXHbkUD/f1RG+Ug6KglsTYwUAGAY6nbt1b/NnzQNgs1lUzXVlFV0jdkEATGYz\ngLKyMhJC9hSxsQnkBzYby8LSlZkzZ8rl8s2bN2/dunXlypXk4qFDh06dOnXy5MkXX3xx1qxZ\nA/UOS0pKioqK2r17N/m1rKysuLi4Y5eGb8IKO5/DYDCcOHECwIQJI/tc7C0SEqLnzJkE4N13\n3/UFw8b9+/ffoHnYxsZGUskbGhvd5+K6ystkzkTM6JGDxmU4rjLMz8//xaJr4/GFi9a91jGf\n21xQQNRb4KCuBXZqAHwBX6fTAZCIRRSnu4ZYwEiMTvgCABUFOQBCg6L7LLDrSERcckxCKoDS\nQ9kudFFwuDRPKoZbjbEOzeryYDEn8THxiYMTAahUlxvrVbqrDR0jIq8YyjAM49kRFH5+AUql\nP1hhx8LSHVwud/HixU8//bRSqczMzCQXAwMDGYbZsGFDUVHRzp077777bgBFRUVM/0yYOBzO\n2rVrX3rppZ07d545c+auu+6aOHHimDHenwXVO6yw8zmOHTtGamjGj/fplOKaNUtpmqPRaN55\n5x1vn+WGz8OiH6lYm9X67Tv/tVmtAol4wj13Oq9f2ryp5sQxADPveoz4mzhpKSAFdiFiZZcC\nO40GgEgiMpmMAOTdzocFrGar1WZFe4FdWcEZAH32w3ZlzLSFNJdrM5sLf/xhoO9FezbW5VQs\nj0/zBDQAjdvCDsCCWxYAMJv16trmTkNjg0P8BAIeAIVMhmtQZhfH9k+wsPTM8uXLGxsb77nn\nHufU7PT09DfeeOPdd9/NyMh45513Pvvss6ysrGXLlvW/AWLdunVPP/30Y489Nnv27KioqO+/\n//6aHd9jsMLO5yDDTAICFAkJfYdwvEhcXMStt94E4D//+U9jo1vTBdzE2Q87eV6WF4/hGsSa\nWCyTyP2Uva/c/812koQdf9cysdJhgtNWU33yrdcAxCSnj19wT6e39FRgZzKbTEYDANAAwOFw\npOLe8rAUKKFA0KZpIQ52QwcNOJYsVQSmpM8AUHP+rOpy5UDf7miMddWjGIBYJoJ7VnZO0kaM\nDpAHAGiqrerkZsehqLCIQAAyqQTXrMyOdTxhYemWSZMmMQzz3HPPdby4du3aqqoqlUq1a9eu\n5OTkLVu2aLXa0NBQg8GwYEHnDE9AQADDMFOnTu148amnniooKGhoaPjiiy9I6Z6Pwwo7n4N0\nTowdO9z5ncNnWb36Dh6Pq9Pp3nzzTS8e40oe/nsetQAAIABJREFUds4NZnSCKzMnonpfVpZX\n8NP23QDixqQNGt+eCGCYn//2rEWv5wlEC9e+Sl3d1GrSarW1NQCCBid1uhsxOgFFmS0mABKJ\niKK7/8NmcEwS41MUKgrPkvzF0Pj+Fth1ZOS4WWKJAgyTv2sHBjiLQkjqoNU6xu7iFAuxnDie\neMBbjqKo6RNmADDoVWdOd5ZukRHBAEgfcUNDQ8eya/chjbFsxI6FhaUXWGHnW2g0GpK+GTt2\nuLfP0jeRkSGLF88E8PHHHzudga4/Tl/iuKQb4EPrhEPYRfcm7HSatm/e/oBhGEmA38R7ryRh\n87d+40zCBoTHdnpXS2F+TwV2KrUagEAoMJt7y8OCgcloAiAUEKOTHABBAeH+yuD+P6ATLl+Q\nNuVWAKrK8rq83AG9V0D84eyMUevikGLSGNvWZnSzMZYwZ+YsIU8EIO9MrsVq6fhSZHQIgGaV\nikvTAM6ePeuB/dqJi00AoNFovBsjZ2Fh8WVYYedbHDlyhIwfHj/+xtAoq1YtEYkEZrP5n//8\np1cO4OyHnXhDjREjmEymuro69Fpgx9iZb9/9r6ZFRXGomx5cKZA4OmF19XUn3iBJ2LTxt97d\n9Y0tBfnorsCOAbQaDQAuj4Ne87Amo8nO2AGIRAIA5YVn4VKBnZPBw8b6B0cCKNz7vd02AOsT\nvtPxxNXGWIlCCEdjrAfK7KRK6fCoEQDUzQ05uRc7vhQZGQzAZrNFh4cD8Gz/RGyco4aSDdqx\nsLD0BCvsfIsjR44ACA0NiIkJ9/ZZ+kVQkN+KFfMAfP311/n5+df/AM75sDdiHtY5TCw0tseI\n3U/bdxeezQUw6rZ5oYlDnNd/eek5i66NyxdkPfIK1Z2zcHuBXec8rMFgsFjMAKyMFb3nYTtM\nEjPoNA3VpQD6b3TSDRQnfWoWAH1zc9XJo/1/H08sovk8uCHsRFLHUA035084uWncVC6HC4b5\nbutVQzXCI4NIEUVwYACA3Nxcq9VFX+WuREXGcrk8sMKOhYWlZ1hh51scPXoUQEbGjTTq9P77\nsxQKqc1me/HFF6//7jd0HrZ9mBgnOKJ7HV9yIX/f11sBhKckjrz1Fuf14h92VB3+CcC05X8M\njIzv+kZzm6PArmseVq1WAQDFsdrIfNge8rBXTxKrKMxhGDuARJcK7JxExCWFxyQCKDmYbTUN\nYIIC39EY66LjCY9P8wRcAFpPNMYCiIqPGhQ4GMD50zlazZWuDj6fFxziB4CkYg0GQ0GBiyM3\nusLl8qIiY8H2T7CwsPQMK+x8CK1Wm5ubCyAjI8XbZxkAcrn0gQduB7Bnzx4ScbxuOPthJ831\nuX5Ys9nc3Nxc305TU5PFYum0hhTYBUeEc3ndDBNrbWze9NZ7jJ0R+ysz//B750xYQ0vL8dde\nARA+eNikrPu63b2l0OFgF9SNsCMOdlz0moe1Xz1JrKIoB4C/MjgowN1YcsZNWRRFmXVtZYcP\n9v9dAtIY66rjCQCJQgTPReyCIgKSQoZRFGWzWnds39nxpYjIYAAtarVULIane2NjYgcBKCkp\n8eA9WVhYfk30azYly/XhxIkTpMAuI6PzP8Y+zooVcz///Ieamsa//vWvP/7443Xr572Sh53t\n5Tys0WgsKCgoLi4uKyurrq5ubGzsOF7QiUKhCA4OjomJGTRoUFJSkmOYWExk15Vmo+mL197R\na9toLnf6mgeFcrnzpaOvvmhUtdJc7sI/vsLpwUi9uTAfgNg/qNOIWAYMCS8xlB1952EZgBIJ\n+QAqCnPgaj9sJ/xDouIS00ovnao48lPMuAl8SR9TfQjEys7l4RMAxDKhqkHrEccTAFw+Nzw8\nLPpyTEVr+fZtOxctvp0v4JOXIiKDzpzKL6usGpWSfOTM2ZycnDvvvLP3u/Wf+LghBw/uZiN2\nLL7P6XMFdz/sgTTO6XMei3n/RmCFnQ9B8rCBgX5xcf2aLuU7CAT8Rx/93RNPvJGTk/Ptt98u\nWrSo7/d4AkceNm5QbJJ3kteVlZUnTpw4ffp0YWGhrR/dAGq1Wq1WFxUV7du3DwBRwByRwGaz\ndZx1wzDMt+9+RFzrJty9PHjQlWRrxYHssr27AUxe9GBoXOf6OScthQXozsFOq9Ha7TYANsZK\nUb3lYY0GI8gkMQ5tNhlqKgoADIn3zDSU0ZNuLS84azWbSg5mJ83t17AQgUIOwGo0Wwxmnojv\nwqZk/kSbzmyz2WnaA8mK4OjglMphFa3lWq12797sufPmkOtRUcEADCZTfFT0kTNni4uLtVqt\nTCZzf0cAMbGDAVRVVZnNZj7flc+BheX6UN/Y8sO+AZTSsngKVtj5EMePHweQnp7s+w52XZk/\nf8qnn+7MzS168cUX582bR/J31xRnHnbinOs9Rqy1tfXAgQMHDx4kY16diMWC6OiwiIjgkJAA\nhUIql0slEhEAm81mszEtLerGxpaGhpaKitqqqjqbzU46J85cOJ//auWoUaPGjRvn5+cHIPvr\n7y4ePw0geWbmkKkTnfc3a7VHXnkBQFDU4I4zYTth0enaqi8DCIrvrPxIHpbicCiOnUP3mIcF\n4+icIAV2VSW5RA661TnRAZlf4JCRE/PP/lR16ljcxKlCZR/mzAD4fu2NsWqda8JOIhcCAAOt\n1qRU9vDgAyEkKtBfHBAmD6vV1H77zZbZc24m1yOiHIPFJGIRAIZhcnJyJk+e7P6OaHc8sVqt\n5eXlQ4YM6XM9C8v1JyMjo+9FPnDPXyussPMVzGYzsbxKS0v09llcgaKop59euXz509XV1W+/\n/fbjjz9+rXd0+hJfT2GXl5e3c+fO48ePO+NzAgEvOXnQ8OGDk5LiwsODOT1MXBWJRBaLxdkg\naTZbvv/+5y1b9gOAgKvX63/55ZcjR44kJyeHSpSHtv0AICIlaeydSzre5MRbr+kbGyiKk/XI\n37m8HsVNS1EhkYyBXVpiibDjcCkA0p7zsBaz2Wa3ARAJHZ0TAGQSRXhwTO+fT/9JHT+nOPeY\n1WouPvDjsKwlfa4XKGSgKDCMobVNHurnwo5imRAUwECjMXhE2PmH+FE0lRwyrFZTW19X/8vh\nIzNnTgcgkQj9/GWtLdrGlpaosLCq2tqzZ896TNh1cDxhhR2Lb3Ly5MmdO3f2vY7l2sAKO18h\nJyfHZDIBSEu7wQrsnKSlJc2ZM3HXrl82bNiwbNmyiIhrm1DesWMHgPDY+OuQh2UY5uTJk5s3\nby4sLCRXaJozYsSQSZNSR44cSsaDDgg+n2ez2QHIlLLbf3/buXMFFy6UWiyWiyfPXqxVgWHk\nYSHTVj/gbJgAUHPyeMHWzQDGzV8RnTS6l5sToxORMkDiH9LxutVq0el1ABjKRrWPveoWg8EI\ngENxBHwBgIqicwCGxI/0YCxZJFUkjZ6ae2Jvdc7puCnTJAGdp9l2guJw+DKpWaN1uX+CQ3OE\nYr5RZ/ZU/wSHy5EHKhgb4y8JaNE1b/76WyLsAERFhbS2aEsrq0anJFfV1p45c4ZhGI98ev7+\nQQqFn1rdyvZPsPg4wcH+qalD3b9PTk5BQ0OL+/f57cAKO1/h2LFjACQSUWJirLfP4jpPPnnP\ngQMnDQbD+vXrP/zww2u3kdlsJr7EE659uO706dOff/55aWkp+dXfXz59+tipU0crFG5VTVVW\n1gIIiQ4JDw8KDw/KzMz4ae+J098dZhgGfF5bXMSFgvyRI0eS2jur0fjLC+vBMH4hkTPv6iMa\n2tzDiFi1RktaZSkOODRHKukxXW40GAAIBAKKgs1quVx6EUBC3Ah3nrcrw8fOzD/3s8VkLN7/\n48jFy/tcz1fK3BF2AMRykVFn1mg80z8BIDQmWF2vSgkZ9nPpoZLi0lMnT49KGwUgMjrk/Lni\nksrKrJtnfLcvW6VSVVRUxMbGemTTmJhB58+fYq3sWHyc1NSh//73X9y/z0MPvfjjj2yt3gBg\n7U58BVJgN3LkELqHPscbgvDwIGJ9sn379oMHD167jQ4cOKDRaHCNfYmLi4ufeeaZF154gai6\niIjgBx+8/fXXH7/11qluqjoAFRUOYUd+NbYZ8g+cZewMh8elU5PsPO7Zs2e3bdtGhkedfuct\nzeUqiqIWrH6JL+yx4wGA1WDQVlUBCOymwE4FABwKFGQSMdVD1pixMUaTCe152JrKAovZCGBI\nnGc6J5wIRNKUtGkA6nJz2hrq+16vVAAwtLpoZQdAIhcBUKs9JuxCooIARCtj/GRKAF9+sYlc\nJ/0TWp0uyD+Az+MBOHPmjKc2jYsdDNbxhIWFpQdYYecTMAxz6tQpAKNG3ZAFdh25776s6OhQ\nAH/6059IcvlaQAo4QqJi45M9HEYiqFSqDRs2PPHEExcvXgQQFha4atWSl19eM2nSKI80VLa1\n6VtaNGgXdnqt/qv/+6pN1UbRnJseXrrgzrnR0WHkGDt27Ph589cXv/wfgFHTbx88alLvd24p\nLiROwoGDugo7DQBwGAByWY95WKPRyIABIBII0V5gJ+ALYyM9X9GVkjFdIBAzDFO0/8c+Fwv8\n5AAMGh1jZ1zbjljZmc02k8kz0yCUQQoOl6YoKiVyGIBzOecv5eUDiIpx6PWKmurhQ4cAOH36\ntEd2BBAblwB2+AQLC0sPsMLOJygqKmppaQEwenSPBhY3CgIBf/36BwCUlpa++eab12ILi8Wy\ne/duAONnzfP4ze12+86dO1etWrV//36GYRQK2b33Lvj73x8ZP35ET40RLkDCdQCCo4JNBtOm\n1ze11LeAosbffVtY8mCRSDB58qipU9OEQgFjtRb+eyNjt0v9gubc9+c+70yMToRypSworON1\ng8FgNhkBcGhwaFoi7jEPS/phuVwuj0sDqCw6B2BQTApNe75ygy8QDRszA0B9Xq6mtqb3xcTK\nDnbGqHExaEcidgDUHiqzoziUPFgJIFoeG6DwA7Dpq68BSKViPz8ZgOKKytHDUgAUFBTo9XqP\nbEoaY5ubm1tbWz1yQxYWll8TrLDzCUgelsOhRo78NbS5TZ48es6ciQA2bNhwLQbIHj58WKVS\nARg/e75n71xeXv7kk09+8MEHer2ey6Xnzp38z3+unTYtwyNRuo5UVNQB4Av4cqV888bNtRW1\nAEYvujlu3JUAZGRkyLx5k2UF59HSDCBuypL+hJlI50TXSWIkcw0KFA2ZVNzL//odJ4kxDFNV\nkgvPOdh1JTktUyiWgmGK+wraOYSdGxNjhRI+h+YA0HguGxsWEwSAY6Onj5kK4NiR4xXlFQCi\nYkIBFJdXpKUMA2C1Ws+dO+eRHWNiBpEfnHWfLCwsLE5YYecTEGvihIQYWc+GsTcWf/nLfXK5\nxGw2r127tj/OvQOC9MMGhIYPGZnmqXtardbPPvvs8ccfJxmulJT4l19es3TpLJFI4KktOlJR\nUQMgOCp42/vbKvIrAKTMmZQ0c3ynZbqy8rafDgEITEiTRSQeO3a0pqa3sJbVZFJXVgAI6pKH\nVanVAEABgKLnPKzVbCWeLCKhEEBTbblOq8I16JxwwuULho2ZCaChIE9TU93bSpGQFvDgxsRY\nAGK5EIAH+yfCYoIBgEF8YLxcImUY5puvvwUQHRMCoLiyMjw4KCwoCJ4rs4uOGUTapdlsLAsL\nS1dYYecTnDx5EsDo0Td8gZ2TwEC/p55aCeD06dNvv/22B+9ss9l27doFYPyseZ5y3ygqKlq3\nbt3mzZutVqtMJn7wwUVPPbUyLKwPAw53KC+vAWDQGQrPFgJImJyWmjW90xq7xXr0pX8wNptY\n7nfbw3/m8Xh2u/3cuXMlJT3GaVQlRYzNBiAw/qo/SwwYrUYNgOKC5nLF4h7VKsnDUqCEpMCu\n6BwAmkMPjrmGnjLJo6aKxDIwTPH+Pb2v5CvkcG9irFRB+ic8k4oFIPWT0QIugNYm7ZKbbwXw\n08Gf62rroqJDAOj0+pr6xrRhKQCI6Yn7OwoFwtDQCLD9EywsnsNmsz311FMpKSkymWzcuHF7\n9+719olchxV23kelUhF3NI9Y/vgOt98+fcqU0QD+8Y9/kBYEj3Ds2LGmpiZ4KA9rtVo///zz\np556isyQGDduxCuv/HHSJM/MV+gJs9lSV9cEoLm2GUBMesqY381zBNM6kPvR/1QlZQBuuf/J\n8OjoMWNSxGIhwzAFBfn5+fndCgRSYCeQyuShV82fbdNqSdyU4kAhE3fZ6gokDysUCEg9IRF2\n0REJQoEHHH17gubxh4+9GUBDYb66+nIvK0k21r2InQiAVmuwu9qB0QmKgiJYCUCvNWdNmyMS\nCG022+ZvtkTHhJAvHkUV5WnDhgFobm7uNKrEZWJj2MZYFhZPsnLlyvfff//xxx/fvXt3SkrK\n3LlzSUfjjQgr7LzPiRMn7HY7fnXCDsBLL61WKmVms/mhhx4yGj0TIyH9sMrAoKTRY928VWVl\n5ZNPPvnNN9/YbDa5XPLII8sefniJXN5jmtJTVFbWOVVFWMrgCb9fiC6hx+b8gov/+xJA8oQZ\nyRNnABCJhBkZKXK5FEBpaemF3AtdhQlxsAuMT+4kE9XteViKg17S/YydIf+ZSIEdgIqiHFzL\nPKyTxNTJIom8z0q7dmHnesSONMYyDNq0HmvZDo0JAcBYoFLrFk6/BcC+H7P1Ol1gkAJAUXn5\n8KFDiemJp/6piGEdT1hYPIRer29qavrss89ef/31e++9d+LEiR988EFycvJ//vMfbx/NRVhh\n531I54RSKYuJCetz8Y1FcLD/888/BCA/P3/9+vXu35BhGJKHHTN9DscNwz+GYXbs2PHYY4+R\n8vP09JS///2RjIwU90/YH/buPUZ+CIyPnPqHO7o+iM1sPvrCqyQJe8sDTzqv83i89PQkf385\ngKqqytzc3I7azm61qMvLAQTGd/6G4BB2NLg8LnGn6xajyURyhSKREICmtUHVVAsgIW64a0/a\nf2gef/iYmQAaCy+pq6t6WkaEncVgthjNrm0kkQuJ6FV7rswuItZhblJUWHHn3IV8Ht9isXy7\neSvx/SksL+fzeSMSE+G5MrvY2EEASkpKyHdCFpbfOFlZWbNnz3b+evjwYYqiSKaotrb2zjvv\njIyMlEqlaWlpzllnIpHo8OHDS5cuzcjIaGhoGDFixNSpU8lLFEWFhYXV1tZe/wfxCKyw8z5E\n2KWmDvXgvCbfYfbsibffPgPARx999O2337p5t5ycnOrqariXh21ubn7uuec+/PBDi8UiFgse\nfPD2P/5x2XUI1BFOnLhw9Oh5ALRYlLnmTprfzTiyc+9/pC6rADD3oafF8qvmonI4dGpqYkCg\nH4DLVVV5Fy86tV1rSYndakGXllir1dKm0wHgcCCXSXrLwxKjE5rmcbkAKovOk+setybulsTU\nySKxDEDx/h6rW/hKBfnB5WwszaWFYj482hgrlou4Ih6AutrmIL+AeVNmANj9w57AYBmAkopK\nm82WPnwYgPz8/LY218ONTojjidFo7L2ZhoXlN8KyZcuys7OJaxiAL7/8cuzYsSkpKQAWLlyY\nl5e3cePGHTt2JCQkLFq0yGk89MQTT0yaNGnLli3Jyclnz56Ni4sj1wsLCw8dOnTTTTd541E8\nACvsvAzDMCdOnADw6zA66ZZnn70vISEawLp169wstvvhhx8AiGXy4eP68OntiSNHjqxdu5YY\nTyQmxr300ppJk0a5c6QBkZdX+u67mxmGAZcbOWUsX9JN4VpDzvn8r74BMGLqLUnjMrsu4HA4\nI0ckBAQoAVRUVBQUFJDrLcWFAHgisSI8uuN6tUbjmCRGQyGT9nI8MkmM9MOivcAuJDBSKQ8Y\n8KMOHGelXWNRj5V2AoWUpK3dHCwGj86fAKAI8QPQpjGZzJa75i/mcbkmk6mwIBeAxWqtqK7J\nGDEcgM1my8nJcX87kooFm41lYQEAzJ8/XygUbt++HYDNZtu8efO9995LXlq4cOGnn36alZWV\nmZn5zDPPmEymqipHTmDcuHGrV68eOvSqFMeOHTsmTpw4ZsyYhx9++Do/hadghZ2XKS0tJS6j\nI0b8aoWdSCTcuPFPMplYr9evWLGCtD64xvfffw8gY9osLo8/0Pfq9fq33nrrH//4h1ar5XK5\nS5fOevrplYGBSpcPM1AqK+veeutzq9UKmkZERFBsN5l3i05/5IVXGTsjDwiefV+PM2E5HM7I\nkQlKPzmA0pKSsrIytHdOBMYNpair/r9Wq1QAQIEv4AuEPZoMWy1Wi8WC9oETACqLz+G65GGd\nOIJ2DFNysPugHUXTfJkEbljZAZAqRQBUaoMnWlQdhEYHA4AV5ZWXQwOCZk24CcDPPx0CbAAK\ny8qC/P2jw8PgoTK7sLBIPl8AVtixsAAARCLRbbfdtnnzZgDZ2dlarXbp0qXkpUcffbS+vv6t\nt95auXLlvHlXedqnp6d3/LWmpmb+/PmLFy9+6KGH9u7dKxBcE6+r6wAr7LwMqbmhKGrEiMHe\nPss1JC4u4p//XMfhUFVVVUuXLnWtkaKwsLCoqAjA2Jm3DPS9Fy5cWLt27YEDBwBERgY/99yD\nc+dO9uAkiT5pbla9+upHer2Jy+chLBw8vn+If9dlJ/9vg662DhR165q/CiW9jaPlcOjU1KEk\ng5yfn19bXa0uLUZ3I2JV7QV2il5dEg36dqMToRCAyaCrv1yM69I54YTm8ds97S715GnHd7sx\nVqoQA7BYbAa9i4V6XYmMCyU/FBZVArh7/hKapg0Gg8XaDKCgrAxA+rDhAE6fPu1+YRzNoaOi\n4sB6FLOwtLN8+fK9e/eq1eovv/xy4cKFCoUCgMFgmDBhwpo1axobG++4447vvvuu41uk0isZ\njHPnzg0fPlyn0+Xn57/wwgs8XjdFMjcKrLDzMkTYxcaGk27HXzGZmemPPXYXgOPHjy9dupS4\n4A4Ikofl8QWjJk/r/7vMZvMHH3zw7LPPNjQ0UBR1880Tnn/+D9e5T8VgML388gctLWoOhzN6\nTiaEQoqCX5Bfp2UV+w6U7d4LYOzcpfEjxvR5Wy5Np6YmEg+UnEMHrSYTuoyI1RsMFrMZAIdG\n73WE7UYnfCJ3q0ovEP1xPYUdgMTUyULiaXeg+6Ad3+3GWKnSIXA9mI0VSgQ8sQBAfU0LgKjQ\n8JvHTQVQU1Nst1sLysoBkGysVqt1Zs/dwdk/4f6tWFh+BcycOVMul2/evHnr1q0rV64kFw8d\nOnTq1KmTJ0+++OKLs2bNontoubPZbLfddtu8efP27t0bGxt7/Q59bWCFnZc5e/YsgJEjf21G\nJ91y331Zy5bNBvDdd9+tWLFioBMpSD9s6qRMkaS/IvjSpUuPPvrozp07GYYJCFD86U/3rFhx\nC7+7foVrh81mf/vtr8hw2FkrbrOLRABkfnIu/6qsqK6u/sQ/3gQQHDN4+orV/bw5n89LHTWU\nx+MxjfUAaB5fGRnXcYFa7cjDisR8Hr/HPKzT6ER4JQ97HoBUoggPjunnYTwCly8g02MbCvI0\ntd0E7QTEo1itY1w1ouMJuDwBF4BK5ZnhrQRlqBKATmsym60A7lmwhMPhmM3mVtXl6ro6nV6f\nOGiQTCxGuyG5m8TGJoAVdiws7XC53MWLFz/99NNKpTIz01GdHBgYyDDMhg0bioqKdu7ceffd\ndwMoKirqZBW+f//+8vLycePG7d69+/t2Tp8+7YXH8ASssPMmZrM5NzcXQGrqr7bArhPr1z84\nf/5UAF999dUf/vAHUtTVH+rq6ogIHjtzTn/W6/X69957789//jPpop08edTLL69JSRnk6sFd\n54svdp8/XwRgwi03jZo6pq6uGUCnPCxjs/3y3MvmtjYuX7Dw0RcHVEEoFolGjEigmpsACALD\ncXWBnarVIex6Dwk7jU7EonZhV3QeQELssOvfrJ2UOsUxPfbgvq6vCv3kAGBnTFrX420kaKfy\naP9EKDE9saGsogpATFjkzHFTAKhUl202S3F5JU1zRg8bBo8Ju8EAqqqqzGaPJZRZWG5oli9f\n3tjYeM899zj/1kpPT3/jjTfefffdjIyMd95557PPPsvKylq2bFl9fX3HN5Ig+qpVq+Z14JVX\nXvHCM3gCVth5k7y8PPKX8m8kYgeAw6HeeOPxefOmANi6deuKFSv66f6we/duhmEoDic9c1af\ni48cObJmzZpdu3YxDOPnJ3/ssbseeOB2sVjo7ukHzqFDp3/88QiAxPTh05bcYrfb6+u7EXbn\nP/yk8fwFADffszY4esDqU6mUcVQtALj+oSUdiq4Yxq7RagFwuJS8jwI7PToYndjttsulF3Dd\n87AELl8wLH06gIZLFzV1na2kSCoWnsjGqtSejNhFxIYSK5niEkdL770L7uBQlN1ubVVdzi8r\nATBmxAgAVVVVdXV1bm4XEz0IgNVqraiocPNWLCy/DiZNmsQwzHPPPdfx4tq1a6uqqlQq1a5d\nu5KTk7ds2aLVakNDQw0Gw4IFC8ia1atXM1345ptvvPAMnoAVdt6EhKB4PG5SUlyfi3810DT9\n73+vX7hwOoDs7Ow5c+b0J520Z88eAImjMpSBQb0sKy8vX79+/T/+8Y/m5maKoqZNy3jllUe8\nFRAtKqr6+OPtAIKjwhatupOiqJYWtcViBeAfekXY1Z44dfHTLwAkjr0pfdbtLmzUVlNjMxoB\nCIIiW5qbatvFkFqjAWMHIJLwubze/JwNVxud1FYWmk0GeEnYAUgcPVUgkoBhSrsE7XhiEYfH\nhbvCTgTAbLIZDP2NGfeJQMjjS0UA6modZlqx4VHTx04GoFJdPp9/CUDa8BQulwtPBO1IjR3Y\nbCwLC8vVsMLOmxBhl5QULxAM2LzjhobLpd9++5n77ssCkJ+fP2PGjE2bNvWyXqfT/fTTTwDG\nzOgxD9vQ0LBhw4ZHH330/PnzAKKjQ5999v57713glUAdALVau2HDF1arTSyTLH7kLp6AD6C2\nthkARV2J2OkbGn957u+MnVEEhc1/+Nmus8X6g6q4FABFc/1i4gFUVlZp27QAHHadFJTK3hps\nrWYr6WVxCjtSYMfl8uKjOvfYXh94fCGyOQGcAAAgAElEQVQJ2tXn5WobOge3BEoFAL1bg8Uc\n8UvPltn5hSoBGNrMpMwOwMrbllIUZbdbj5w6xNgZsUiUPHgwPCHsAgKCZTIFWGHHwsJyNayw\n8ybEqvS3k4ftCIdDPfHE3a+9tk4kEra1ta1evXrJkiU9dQseOHCA5KzHTO9G2F2+fHnjxo2r\nVq3av38/wzAymfjuu+f/7W+riCuyV7DZ7G+/vUml0nI4nKw/LFcEOBpg6+ubAEgVUp6AB8Bu\ntR5+9gWTSkVzeYsee1kklbu2XWtxKQC/yJhBQ2K5XC4Ye1FRkdVqcRTY0X3lYQ3tRieCqwrs\n4qKSuFyv9fwnjb5JIBQzDFNyoHPQjq+UATC0uu54IhDxHP0TrR7NxsaFAYANxWWV5EpcRPSE\n4WMANDSWFZQVAxgzcgSAvLw8nc718xNiYgaBdTxhYWG5GlbYeQ2dTldYWAggNfW3KOwI8+dP\n2bLltWHDBgM4cODA1KlTV69efeHChU7Ldu/eDSByUEJE/BW3P5PJdOjQofXr169ZsyY7O9tq\ntQoE/Hnzpvzzn+tmzBhL0978s7158978/HIAmYtmxyReqZlzdE6EOQY5nNn4XmPuRQAz7/lj\nxJBhLm+nLikFEBCXwOdx4+MjQFEWs7moqNhiMQMQi3kcurdAIBF2QoHA6etHrImHXEdr4q7w\nBMLk9GkA6i+eb2u4qtLZ0RjrRsQO16Z/IjIulMRcS4qvTM74w5IVJGj378/eAzB2xEgAVqvV\n/bmxRNixETsWFpaO9Gh/wHKtuXDhAvH7+BUPE+sP8fGRX3/96mef/fD225s0mrZNmzZt2rQp\nOTl57ty548ePT0lJUSgUe/fuBZAxbbZWq62qqioqKsrNzc3NzTWZTOQmYrFg2rQxs2dPUiiu\n08jXXsjJKfz++8MAhqaljJk12XmdYRzCLiAkAEDZnn0F32wBkDLp5jG33OHydvqGRpNGCyAg\nPgGATCYJCwusrWnUaNRkgV9Ab4FAxuYwOhEJHTbrrU01WlUTvFdg5yQ5LfPiyf1mk77k4L6R\nS+50Xhf4yQFY9Car2cJ11bxGqhS31ms8m4ql+VyBXGRS6xvqW5wXB8fEDg0bml+Tv//Ij63q\n1pCggJiIiIrq6hMnTkyePLmXu/UJG7FjYWHpCivsvAbJw4pEgoSEGLt9YI5uvzJomr777vm3\n3Zb54Yfbvvpqt1rdlpeXl5eXR17l8/kkD7vz0JGtRzvP2YyNDZ86NW3ixFSRyCfGv7S2at5/\nfzPDMMog/3n3LuroFdLU1Go2WwD4h/o35xccf+V1AMHRg+avesadHVUlpQAoivKLcYQzw8OC\ntFp9m1YHABxKIe8tD2s0GhgwAERCx+BakoelKGpwrDcjdgD4AlFKeubZX76vu3BucOZMSVAw\nuS5ob4w1qnTSYBeHwsn8RADMZpteZxZLPFbk6hfmX6fWG9osJrNZwHfcdv742QVbCiwW84df\nffD4g0+MHTmiorr69OnTVquV9FK4RmzMIAB1dXU6nU4i8f5XGhaWjuTkFDz00IseuY/7N/lN\nwQo7r+GcQ8/l0mbzb1rYERQK6bp1v1u1asm+fcd//PHokSM5Wq0egMOmi+ZaeA7lIRDw4+Ii\nhg8fnJ6eHB7eW5PsdcZuZ95771utVk9z6ayHlgnEoo6v1tY2AqAoiLhM9p/W20wmkVR+x1Ov\n8YW9Ca8+aS0uASAPi+KLrmwXGxN24UIxALqv/8X1BiMAHpfL4zraZknnRGhQtEyicOdgHiE5\nLfPiqf1mk6H44L6Ri5eTi3yFHBQFhtG3trks7KR+DiXUqtJ7UNhFxIXW5V+GHYVFFcNTEsjF\nYYlDBgUMLm4q+nzb53cvumfcyNSvf9il1+tzc3NHjRrl8l7Eyo5hmLKysmHDXE/ls7BcCxoa\nWn788ai3T/FbhBV2XoNE7IYN84Jlri8jFPLnzZs8b95ku52pqKgpLb28fv27TU2qmGEpU++c\nr1TKQkMDw8ODvFtC1xO7dx+5eLEEwNSsm8Piojq9WlvbBEAqE//yl+f1jU0cmr798b/7hUa6\nuamquAxAQFxCx4ttbY7CfIbDNDarg4N6UD+Mo8BOLLjSO0yEXYJXC+yc8IXi5LTMnCM/1OXm\nDM6cKQkMAsDh0jyJyNKmN6pd7z/g8bkCMd+kN6ta9RERLqrDrkREB5+mKDBMaWm1U9iFhwcO\nDxtR2lxiNBnf/+K9Z1Y/E+CnbG5VHT9+3B1hF9Meoy0pKWGFHYvvkJGRcUPc89eKL/7r+Fug\nra2NlDyTvgGWrnA4VFxcxJAhsU1NKgDzlt02c+a4jIyUqKgQ31R1ly/Xb968F0Bs0uCxs6d0\nXVBb2wiGsR3LbskvBDBr5WP9GQjbOya12tDcDMA/7qo/SM3NjoETFActLRqDwdTt2y1ms81m\nBSBqHzhhNLQ1VJcCSPB2HtZJSvo0vkDEXD091uF40uJW/4RMKQLQ4tkyOy4tUIgBNNSrrmwk\nF4cEBCcEDgHw9c6vaxpqx41MBXDixIlOo40GhFQqCwgIBts/wcLC0gE2Yucdzp8/Tyase2XI\n1Q3EgQMnAdBc7ogJ7mqga4rNZn/vvW8tFqtALJx/3+KuY7jsdqaurgm5x/WllwCMueWOjDmL\n3d+X5GEBBMReEXYMoNcbAfCFXIrLWK222rqmuOhwqktvrN5gAMChOAK+o0KxquQCw9jhA50T\nTvhCcXLaTTlHdnUM2vGVclyuNajda4z1kzTVqNVqA8O4ZiDYPf5hfrUqnUln0RuMzhFt4eGB\nw1pGlLaUmC3mf336zuK5K74/eLClpaWwsHDoUNf74mNi4pubG9j+CRaf4uTJkzt37vT2KX67\nsMLOOxATXZFIEB/vbibu183Bg6cADB09QizrbdSp19m586fy8hoANy+fL/PrpjStoaHFcvEM\nSvMADM2YMmvlOo/sS6yJpYEhQvmVTTVqtc3OAJDLBWKZoLqm1Wy2NjargoP9Or2dCDuhUOCU\nNZVF5wDIpMrQoM6pZC+Skjbt4ukDFpOx+MBeUmknUMgAGN2bCSbzEwOwWe0ajVGh8JiRdVR8\nWO2ly2BQUFQ+akQiuRgWEVhYUDk0KPFCXe62PdvuWXyvTCzW6vXHjx93R9jFxgw+c+YYK+xY\nfJCAYP/kUR4w88o7W9Dc0NL3OpZ2WGHnHYiwS0yM9c2soo9gMBhPnrwIIHXSeG+fpTeqqxu2\nbTsIICE1afiEtG7XHPliE/JOA4gcMnzhupcojmf+u3dbYNfY1AIGABR+Yj6fVsiFao2hpVUr\nk4k79g7bbXazyYxuC+xih3cNOnoRvkiSPDrz3NFddbk5g6fNlAQEEccTu9Vm0hoEMlGfd+gW\nqVICCmDQ0qLzoLALiQwEh4KdKSutcQq7iIggAMkhKeWq0jajbuPHGzJGjt5/9NjRo0fvuusu\nl/ci/RNsKpbFB0keNfTl//zF/fv8+f4Xf97DNmEMAFZVeAci7JKT2Txsb/zyyzniD5I6eZy3\nz9IjdjvzwQdbrVarQCycfVdWt2su7vnx3KcfA5D6hS37y5s8gWc0hFWv19XVAfDvIOxsdntb\nmxEAzeXw+TSAoEA5l0sDTG1dC2O/UtFl0BsABqCcDnZ2u626LA++lId1Mqy90q7kYDbaPYoB\n6Ftdz8ZyaEqqEMHT8yc4NEfkJwHQ1HClzM7PXy4UCfhcwc2p0wHs/XlvcIAUQG1tbUVFhct7\nESu7lpYWx/g4FhaW3zyssPMCer2+uLgYQEpKvLfP4tMcOnQaQHBkeFis14aD9Ul29vHi4ioA\nM+6YK1N2YwV8ad/+Hc+9CIYRSvymLHvS5blhXWktKSWl98SamKBRq202BoBU5pBrHA4VHCQH\nYDabm5vVzpWkH5bP49G0w+iktrLQbDIASIj1uRZLvkiSnHYTgNpzZ3TNjVyZhOLScH/+hJ8E\nQIsb6rBbAsIDAJgNNk2b484UhfDwQACDA4YGKQMZhtlzcIdAIABw9Kjr0YjoGMeXQzYby8LC\nQmCFnRe4ePEimTnBRux65/DhswBGTvLdcJ1Kpf3mm70AYhLjR0xK77ogb2/2d88+Z7fZBGJF\n8k2/D42N8eTuJWUAhHKlxD/QebGlVUXysFLFlayrVCKQSkUAmlQak8kKAAwMRgM69MOiPQ/L\n5fLiopI8eE5PkZLWHrQ7sI9qL7MzqNyauErK7Np0Zs96SUbFhwEAg/yCcufF8MggAPWNzasX\n3AfgRM7x0AAJ3BR20fEcDgessGNhYWmHFXZegORh+XyeF6fU+z6FhRU1NY0ARk4c6+2z9Mjn\nn+8yGEw0lzv7rqyuRWm53+8iqk7uF5Ry031Cib+i1+leA4V0TnQssDNbLDqdEQAoSiq5ahRH\ncJCUQ3NgZ+rqm8HAZDSRvmyx4MoyMnMiLiqJy3VxTtc15UrQ7vxZXVMjcTxxM2In95cCjjI7\nDxyxnaAwf9AUgPLyWufFyMhgADabbcKQsbEh0QDyi04BTEVFRW1tbU+36h2hQBgaGgG2zI6F\nhaUdVth5ASLsEhKiue1e/yxdIXlYvkCQlJ7q7bN0T15eybFj5wGMmzMlILTzAIyTm77Z+cLL\njN3uFxia9cALQmkAh6alCpmndreZzZqqy+ich9XYbQwAkYjHudrchEvTgf4yAAaDUaXR6Qx6\nADSHdo69AlBZfA7AEN+wJu6WlPTpTk87vlIOt4WdUMLnCbgAmj0q7CgOJfGXAWhpVKO9rNE/\nUCEQ8gFU1dY9uXQNgMu1lXpdE9wL2rETY1lYWDrCCjsvkJubCyA5mS2w642ffjoDIDFtJF/o\nsXZFD2Kz2f/3v+8BKAP9Js7LvOo1hjnwzr/3/t+bjN0eFBb96N8/sjAiAHKlzFPNsADU5RWM\nzYarOyfUarXNDgBSeTeTc5UKkUjEB9DY2GrQ6wGIO+RhW5tqtKom+GTnhBMyiAJAXW6OnbIC\nMOtMdotbWVSZvwTwcMQOQFBkIACriWlsaSVXOBTIBLySyqpbxswcNXg4AJW6kmHsbgm7aFbY\nsbC4S21t7bJly8LCwvz9/efMmXPhwgVvn8h1rp+w++6771atWrVixYrXX39dp+vm71C73f7J\nJ588/PDDS5Ysefzxx8nErV8fZrO5oKAArLDrFZ3OcPZsPny4wG7v3mOXLzcAmLFsHpd3JXFp\nNZu3Pfvc0U/+ByAqPnHd3z8KCA5vaVEDkF+DPCxPJJaHhJMrRqNRbzCS+JBE1v3w0+AgOUDZ\nbDa90QpA1EE0kzwsRVGDfWbmRLekpE/jC8QMw9Tm5QAAw7hpU6wIkAJQtepJsNNTRMWFAgCD\ngsIy58XI6GAAl2trLRbr08sfBaDTa1Wqy8XFxQ0NDa5tRCJ2JSUl7gyxYGH5LcMwzOLFiy9e\nvPjee+9t27bNarXOmTOnrc3DPVXXjesk7Hbu3Pm///1vwYIFf/zjH8vLy1966aWuazZs2LBn\nz56srKznn38+Ojr6+eefJ62jvzLy8/PJVHtW2PXCkSPnLBYrAN8cOKHR6LZu3Q8gfljCkFEp\nzuu65ubP/7Am78d9AJJGjV/78n/lfoFms1mrbQMgD+zGuNhlVCWkwG6ws7ZPpVbbbABAc2mR\nqPsiOQGfq1SKAdhsAEMJuzjYhQZFyySePKfH4QvFKenTADQW51usRrjfP+EvAWC3Myr37I47\n4ResJH27lZX1zotRUUEAbHZ7eXX12MS0GaOnAmhVVVqt5iNHjri2UUxMPACdTueyNGRh+S2j\n1+tLSkp++eWX999//9Zbb50yZcp///vfy5cvnzx50ttHc5HrIezsdvu2bdsWLVo0a9as9PT0\nxx9//MKFC0VFRR3XaDSaAwcO/P73v58xY0ZSUtKaNWuio6P37NlzHY53nSF5WJrmDB0a6+2z\n+C6kHzY4Mjw0xofmHzjZsiVbrzdyaHrmsvnOi9W5F/571++rcy8AmDBz4R+efVsokgBoalKR\nSIoywGOCibHb1OWVuLpzQqtR220AIJF2H64jBPpLSfmd2XZVv4fvF9g5SU7PFAjFDMNodY0A\nDO5NjJUqRTSXA6C52cNldtIAGQB1i85GEuSAn79CLBECKKmsBPD0srVcmrbZrC0t5b/88otr\nG8XEOKbJsdlYlt8sWVlZs2fPdv56+PBhiqIuXrwIoLa29s4774yMjJRKpWlpac5ZZyKR6PDh\nw0uXLs3IyODz+a+99trIkSPJSyT4olQqr/tzeIbrIexqa2sbGhoyMjLIr9HR0cHBwefOneu4\nRq1Wx8XFDRvmcM+iKMrPz6+1tfU6HO86QzL3cXERHWcAsHTi55/PwlfDddXVDQcOnAKQNm1c\nQFgwuXjq682fPbRa29jIoelFv3/iztV/pWnHWJfmZhUAnoAnlok9dQZtVbXNZALgH+sQdm06\nncViZXrNw7bDCHgAYLPZVVpHjMqo1zZUl8G3C+yc8AWiYRkzAOjbms0Wg5upWIqipH5iAM3N\nHs68hJD4nJmprmto3wtRUcEASiorAAyOiF+WeTsAtaYmL++8ayG3yMgY0sXMNsay/GZZtmxZ\ndna206b7yy+/HDt2bEpKCoCFCxfm5eVt3Lhxx44dCQkJixYt0usdf+898cQTkyZN2rJlS3R0\n9GOPPSYSiX7++edXX3114cKFS5YsSU310b69PrkeI8XIZx0YeMVqKygoqJNPelRU1Jtvvun8\ntbq6+sKFC7/73e+cVz766CNnXFQikbz88svX9tDXjEuXLgEYNixBIpGQKxwORyAQ8Hi+aDBx\nLeC0NxA4P4FOlJRUVVc3AEibOknoe50T33yzz263CyXizNtn8/l8vVq9/bkX8w8cBCBT+N//\n1GuJI6/yZ2lu1gBQBippmuZwPFMFpSktB0Dz+P4xccReWKPRWEkLAQWZXEhxehwIZjaaeVzG\nTMNmQ2OLRikVc2hOVelFhrEDGBI/wrPDxK7RaLKUjGkXTx8w6rUaTZ2/KpRDu9VgrgiUqRvb\nmpt1HIqDnj+6PqFAMRyKA8cdogeFFZ8qAoPikspB7bHnmLjwgvzK2sYmk8Uil0j+tOyRbUd+\n0OrbGptKTp48uWTJEhf2jYqMKSsvrq6uViiuaxrd+f+yXO7J+lEfh6Zpmqb5/N6/Pt0wWK1W\nbx/BA8yfP18oFG7fvv2ee+6x2WybN2/+29/+Rl5auHDh7Nmzhw8fDiAwMHDTpk1VVVVkQPO4\nceNWr17d8T4HDx7cunVrYWHhggUL7HY77d5fLN6iv8IuNTX1rrvuWr58eWho6ED30Gg0AESi\nK/McRSKRSqXqaf2JEyc2bNgwZMiQuXPnOi+WlJScOHGC/Ozn53eDyiCGYUgqdsSIBC73yodP\nURTHc/2SNwodP4GO/D975x0fRZ3//9ds7z3JpveeUAKhKIoonFg4iiCIJ3ZP/VmwnYrlsJz1\nPBXPwztPPL1TPA/hi3KWQ6QqkIQECKSQbPom2exms73Pzu+PCUsISdgkmwb7/MNHMvuZz7yX\nuLPveZfXmw7XsdjsyZfOGG+fq5MnNUeOVAC4YskCkURc+8vBbc+9YNXrAaTlFNzz9FtyVa8P\nCGUwdOF0HjZUXo6xVgNAkZjCZLEAUH5YLRY6D8vlsdnsgf7RXG43AJGQZbaQJEnquyxqlay5\n9jgAsUimVsWH1hEboYmzbDY3f8aC4j1bXS6zWacjQA3nUjKVuAltPp/fbHHJZcMKrBKB/wCy\nSBmDxfT7yJZmXcDVTkqOAUGAojSNTdPycyMVEY8sv+/FT9+02w1bt25evXr1EC6anJJR31Cr\n0WjG6sY4QW/Iw2G83Zoucvh8/pIlS7Zs2XLbbbft2rXLarWuWrWKfumRRx7Zs2fPTz/9dOzY\nsV27dvU8a/r03qryzz333HPPPVdeXj5r1qyIiIgHH3xwlN5ASAnWsTOZTI899tjvfve7X/3q\nV2vWrFm8eHFPR21gRCIRAJfLFXjEcTqdERG9db8AGI3G999//+jRo8uWLVu1alXPT05eXl7g\nwUIgELjd7iCvPq7QaDS0m5uVlez1eumDLBbL7/fTarEXAwwGg/7LBv4FevHTT4cBZE7NZ3E4\n4+ppkqLwySfbAchUivxZk/5v/Uul27aDohgMxsIb7160+n4Gk+n3nyW9YbXa3G4PAGmEHKBC\n9EemTHX1AJTJ6ZQfAMxmE+nvruMSibkDdUdSFP3ZEfG5gN9scXZabHKJsLH2GID0pHwQRKha\nK2lHZuQaNbOnzS0/vNPltBqNWpfFxZUEe0c6F7FCyGAQfj+l11uksqHvQ4D+1zvzpiWRMlNr\np83ssjmcAi4PgIDPUyqlnQZTVZ1mSk42gDuv+c3fvvm0vUtXVranvr4uLm7QdaV0Y2x1dfUo\n3xgZDAbt0k3QG/LQYLPZfr+fnh50AUCS5IXhl69evXrJkiVms3nz5s3Lli2jo9dOp3Pu3LlW\nq/WGG25YuXLlQw89NHXq1MAptHMC4MiRIydOnLj11lvpX/Pz8wsLCydu80Swjl19ff3PP//8\n2Wef/ec///nuu+8kEsmKFSvWrFlz2WWXnTcIIZfLARiNxkC43mg0BqoUe17i2WefTUpK2rhx\nY2RkZK9XV61aFXDA/X7/BJ14ffjwYfqH5OSYQJpfJBJ5PB66WvNigMPh0E8FgX+Bnng83oMH\njwHInTV9vH1bFBWdoMfCpierNt642qY3AFCp49Y8/HJqzlQ/Bb+v972+rc0AgCAgU0pJvz8k\nghr29naP1QZAkZhK+5FdJpPf3+1OCEWcARw7t8dDe5ccLlvFZVrtLj9JtXZ0tmhOAkhPnhQq\nyQwCBO3ZjZwGB5PJzp9+ZfH+7W63VVtRnVQ4rLYPkVxo6bTp9daUFNX5V/cDg8mEn/JTZ/z3\nqIQIU2un34v6xqbM1GT6YHxCZKfBVF1X7/G4aQd43eq1D73/tNtje+PNF157dcNgrxsbmwhA\no9GYzebRjP0HakhsNtvFI7YikUi8Xi89avnCQCAIWfnvGLJgwQKJRLJly5Zt27Zt3bqVPrh3\n796SkhKLxUL7cHTG7FwMBsO99967bNkysVgMgCTJxsbGyy+/fNSMDy3B3gIIgpgzZ87GjRvb\n2tq+/vrra6655vPPP587d25KSsrzzz/fq8W1F/Hx8SqVqrS0lP5Vp9O1tbUVFBT0XOP3+//w\nhz8UFha+9NJL53p1Fwz0/1VRUUqF4iIqSRkUR45UOp1uAPmzCsfalrMgSf+WLbvgcXJ0tcUf\nf2TTGwiCccX1N6179z+pOVP7O8tgMAEQSET0eIOQ0FVbD4BgMOSJqQBIkrTbbHSgkCAIvmCg\nh2+32wWAyWSymWwmk6GUCgA011V4PS4A6ROhJbYn2YVXcll8ANW/HBrmVjKVCEBnpy20/ok6\nIQIAKNRomgMHExKjANjs9rYOPX1k8aXXJkckAfjhhy+tVvNgr0JH7Nxut1arDYHRYcJMQFgs\n1ooVK55++mmZTDZvXrdovEqloihqw4YNNTU1O3bsoGNyNTU1vZ5D5syZI5PJVqxYsXv37gMH\nDtx6660Gg+G2224b/XcREgb9bMdmsxctWvTFF1/89NNPOTk5DQ0NL730UkZGxuzZs7/88ss+\nTyEI4te//vWXX35ZXFys0Wjefvvt7OzsjIwMAD/++OPmzZsBHD9+vKOjIzMzs7S0tOQ0F56O\nHd19nZ2dPNaGjF9+/vkoALFMmpiZNta2nMXuHw+1lRWhptSjbwMQk5j26Gsfr7j7KS5voIdd\nvd6EkAqdADBpNACkMQksLheA2WymQA+hgFDEZQxY++92uQEExojJJHw2m2lorgLAZnGS47JC\naOcowGSxU+ImATB16HSa+vOuHwCJSgTA6/WbzaGMxEiVEiabCaCt1RD4KomJi6DHCZ5qaAis\nXLv0foIgPB7Xa6+tG+xV6OETCCuehLm4Wb16tV6vv+222wKJxOnTp7/99tsbN24sLCx8//33\n//Wvfy1duvSmm27S6XQ9TxQKhTt37hQKhbfccsvixYv1ev3evXtTUiaq1uygowjHjh3bsmXL\nli1bqqqqCIKYNWvWihUrjEbjpk2bVq5c2dDQ8Lvf/e7cs5YsWeLz+TZt2mSz2SZPnnz//ffT\nx4uKimpra2+66Sb6QXPjxo09z7r00kuffPLJIb2vcUpFRQWArKyksTZk/EI7dnmzpodw+tYw\n8Xm8//v3tn+/9yG8HgA8gfCaG38779c3BwRN+sPr9ZrNFgDSiJA6drW0NHG30InZbAYFP0UA\n1MBCJ16vly4MCjh2BEGo5EJ9SxWAxLhMWjVjYpGUNLlee8LltZfv3BOVOvRHJrFCyGASfpLS\nG6yyYZTZ9YIgII2SGVs6PQ7SYOyKUMoBsJjM2LjIxoa2U/UNc2d0a/pcd+mVf9meWa2r+vqb\nzbff/mBa2iCc7OjoOC6X53a7NBrN3LlzQ2V8mDATizlz5pxbErB27dq1a9cGfg1kaXsl0/Py\n8r766quRtnB0CNaxKy4u/uqrr7Zs2UJLJc2cOfOtt95avnx5QkICvWDdunXz58//8MMP+3Ts\nACxfvnz58uW9Dq5b1/1set111/Xsgb0g6erqamlpARCWJu4Po9FSVVUPIH/2uMjDkj7fvq+/\n3/7hJ53dOmTE1Nm/uvG3v5PIgyrD6uzsliaWKkLm2LlNJleXCacdO4/H43Q5ST9AUTifgh1d\ns0gwCC7njAMnFnINLdUAYtWZFIWREScZQbhicZIqq6rtSGeztrW6NmaogV4GgxArhGa9Ta+3\npaeFshokOjHK2NJJedHYqqUdOwCJSerGhrYmrdbldtHzP9hs9srLbnht25se0vPKq7/b9NHX\ngzGeEReXpNFUhSN2YcKECTYoMmPGjNdff12pVL755psNDQ2HDh169NFHA14dAIFAUFBQcPHU\nzw4BOlyHcMSufw4ePOb3UwByZ/buQh9lfB7v7q++eWLJbza99Cbt1cnliVde8//ueuqNIL06\nAHp9FwAWmyWU9q3YNwS6ajQAQKcZACkAACAASURBVBCK5DTQ4TrATxIA2Bwmd8BKPpfbBYDL\n5vZUBjF2aJ22LgDx0VkWeyhnao0ObLFQLUkQcMUAynfuHs5WsggxAGOnLbRDY1WxSgCgUFd3\npgAuMTkagJ+iahoaAwcvnTRtcsxUAIcP7/vhh/8b1FWSkronxobC5DBhwkxggo3YvfHGGytW\nrEhKShpgzZ///OcQWHThQhfY8fncxMSYsbZlnPLzz8cAxCQnKqL6UMMZHZx2++6vvvn+s/90\ndRjoI0lJWSJxtkQSc9n11w9qK7rATqqShVDNjRY6EUVEcYUinHbsKDoPO+AkMZIkfV4fAB73\nrHxrc205AAJEQmy2xeYU83kM5nhJggcDRygAQSQrc062Hja16ZrLK+Lzc4a2lTxC0og2kqSM\nRocqImS+uFQpYbJZpNdnNFhcbg+PywEglQoVSomx01JVV5efmUmvTE9Omhw3qdZQ0+U0vvHm\nM5df/is+P9h2RbrMLhyxCxMmTLB38K1bt7a3t597fPv27ddee21ITbpgoYeJpacnMCfUF+do\ncujQcQB5s8YmXGdo021+e+PDV6/Y/PZG2qvLz5/+0st/ycpeLJHERCXGRMZFD2Y/im6JlUWE\ncuBgV48CO6fT6fF6KD9oCTuheKAhdXS4jiCIXor5TbXlAKKjEvh8EeWnTLYJFrRjS4QAIiSx\nCnkUgPJde4ecNxDK+CwOE0CH3hJCCwkCihg5ANKNFt2Zu2hiUjSA6rr6gMFMJjMvM7MwYQaA\n9nbtxo2vB38VujG2qampP3nIMGHCXCScx8NoaWmprq6urq4+dOjQiRMnqs+msrJyx44d+/fv\nHx1bJzp0xC5cYNcfDQ2t9CSxvFHPw1YUl214/PnHF9307adfOO12giBmzpz75h8/fvW1vwEy\ni8UGYNKl0wa1p8lkpb9iZaqQFdj5HA5Huw6nHbvT4ToGABDEwBE7uh+Ww2YziLM+9XTELiN5\nkkjAAWBzuHzkRNLKJphMJo8LIDdjJgCrvrOhrG+pqmCQR4oBdHRYQ2UeTVRcBADKiyZtW+Bg\nUnI0AKfL1dTaGjg4OTsrUhSVokwF8Mmnf9FoqoK8RGJSGgCfz9fc3HzexWHChLmAOU8q9r77\n7tuxYwf98913393nmoULF4bYqAsRn89XXV2NsGPXP7/8cgwAk8nMmt5bvHqEsFusP3+786f/\nbNfWNdBHOBzulVdet3jJzfHxyQD8fj+tlhyVED3IcF13gR1BEJLQaZ10aero6I4yOZ0CzBYL\nAAbBAPx8PnuASLDf76e9TO7Z4TqnzaJvawSQlpwnEfHsTg/lR5fFFiGfSDqLHKHA6XIrRVHR\nsYlt2saTu/YlTs4d2vRYaYRE32IyW5wul5fHC1mPsDKmu8yuqbHNP6t7Gm10jIrL47hdnopa\nTWJsLL0yOS5OIhYVxE5rs7U53Y6XXnrs4493BDOJrqfiycSVaQhzIVFRVr3u7pdDss/wN7mo\nOI9jd//9919//fUA7r333gcffDA3N7fXAg6Hc8F3s4YEjUZD9ySGHbv+OHjwOICUvGy+MGTl\nTX1CUVTVkWN7/++/xT/u9ZwebqGKiLr2muULr7lBIjmTOT1xotZksgHIv6Sg7736p6OjC4BY\nIQ7hTEmTph4ATyITyJVWq5UkfaDg9vgBiM7XD0tRFAiCLvAK0Kwpp9tp05PzGQxCIuKZLS6n\n0+MRejmcCSN9whYLnJ1dbptz9uXXbN38gd1k0hSXpQ8poa+IlIAAKHR0WBMSFKGyUKoU02V2\nTpvX0NkZqVICYDCI5OSYqsqGitraa+Z2a9wTBDE5M2t/iW1qbMEvdQeKS37++pt/L/71qvNe\nIiIiSiAQOhx2jUYzf/78UFkeJsyQ6eww7v/h4FhbcTFyHsfummuuoX/44osvbrnllsLCcSFC\nMRGh87AAsrISx9aS8QlJ+g8fLgeQN3NwGc9B0d7U8st//3fgv//Tn86IEQRjytSZ1127fMbM\nub1mMVEUdehQOQBldERUQuxgr6XXGwHIVKEssOupYEfnYZlMlt/vAyAY0LFzud0A2Cwmg3GW\nl9lUewKATKKMVMYAEAm4VpvH7/d3WR1RIRVVHlHYIhEAt82VljA5Pim9uaGmYs+B5ILJrMH7\npmweSyTl20xOnc4SQseOYBCqGIWusYPyoLmtjXbsAKSkxVRVNhhNJp3BEKXq7raekpO9v6Qk\nWZ5iiNefaq7+45vPXjH3aqlUfp5LEERCQkpVVXm4fyLMmPP555+PtQkXNcF2xe7ePSwdgTC0\n1klMTIREIhprW8YjFRUas9kGIGfGoGNj56WzvaNo555DP+yqO3mmYkmlipo/f9GCXy2Oiurb\naauubqC7H4YQrnM6nXa7EyF17EiPx9LSAkCZnE76SavVCoDJYAM+BpPBF/Tr2PkpyuNxA+Bx\nendXNNUcR49JYgQBiZhrMjvdbq/T5eWHLhc5orBFAgB+0u9xuGdffk1LY63Laqs5WJQ999Ih\n7CaPktpMTl2H1e+nBh7jMShUsUpdY4ffiwZt67T8PPpgfIKaxWb5vL4TNTUBx04dEaGOiGjX\n6+fnLdC0aoxdhj/+8bmXXjq/5kBSYlpVVXlY8STMmPP2228XFxeHds/CwsLnn38+tHteqAzk\n2E2dOpXJZJaUlNA/D7CyrKwsxHZdcJzunAiH6/qGzsNyeLy0/N7p/iHT2tBUtufnkp/2aU5U\nBhoPORzu7Nnzrrzq+qlTZw08Lp2u+ZNFKmJTEwZY1id0HhbdWiehwdLYRPlIAIrkdIvZQoEC\nCI+XBCAUcQZwQDxuN+WnAHC5Zzl2pM/b2lAFID05L3BQJODYHB6flzRb7XxeKMONIwdH1J27\nd9ucUdHxyem5dadOVO0/mDpjGofPG+xu8khJc3U76fN3dtojIkL2GKY6XWbXqTdbbQ6xSACA\nzWYmJKnralpOnqq5avbswOIpOdnf79XbOx2/ufaWT775eNv/ffbrX68qLJwz8CXoxthwxC7M\nmFNcXByozg8z+gzk2IlEokB5kEw2MW7x4xY6YhcusOsP2rHLLJg0hPRZT5x2e9WRY+UHi48d\nONTRcqbZkMViTZ484/K5V8+efaVAcP4avro6bXt7J4DcmVOGoEKn0xkBCER8Ln8gCZJBQQud\nsPkCiTqmobERAJ/LNZrcOL/QiRsAi8VinV3tp62vJH1eABnJk3oel4i4xi6Hx+tzON2C0Nk/\ncjAFPILJoEi/2+YUR8pmX3Z1fc1Jj9NVtf/gpF/NG+xuYoWAzWV63aROZwmhYydVdavZkR40\nt7XmpHdPyEhLi62radEZDJ3GLqWiO986JSvrh337SZK8KveqHw/v1Ha0rH9h7davDnC5A/mp\ntGOn1WrdbncvJz5MmNFHERmRWTDp/OvOR3XpcWOHfvj7XDwM5Nj11DEJp2KHg8lkam1tRdix\n6wev11dWVgUgt3AoeVhDa3vdyaqa4ydPlR1vrKqhx6HScDicyZNnXnLJlbNmXyEWD6Jo7NCh\nYwBEMklS9lAaDPX6TgCyyJAVaQEwa+oAKBLTvD4vPeWQzWaDcgEQ9S90Qp2eJNarHxan87A8\nriA+5qwxXAIe28pmer2kyeaYEI4dALZQ4LHY3DYXAIVKnZk7repESc3BooxLCnmiQTtn8ihp\nR5Oxvc2clxcyLfGeZXaNrW0Bxy4pOYbJZJIkWV5z6oqZM+mDYpEoNSGhtrGxqqLq5Qf+cPvz\ntzY01G784I21Dw+UikpMSgXg9/vr6+uzsgYxajZMmJEgs2DSsx+9O/x9Xr7z4YPf7xr+PhcP\nwdbYAaAoqqGhITk5GUBzc/OGDRs4HM6aNWsyT8umh+mPwDCxjIwLLRXr91O1tU3l5bU1NU0N\nDdrWVoPRaLZY7G63J7CGyWQKhXyxWCCRCOVyiUolj4xUKJUyiUSgUEjlcklzc7vT6cb5Cuwo\nv9/SZTYZOo3tHboWbXtjc2t9Y3NNnc3cW042IkJdUDC7sHDOlKmzeLxBD3Rva9M3NLQByJ0x\nKXgR7wAej4euF5RHhizOTflJc30jAGVymtlsBigChNdLAeBwWWxOv423Ho+H8vsB9OqHxWlp\n4rSk3HNT0lIRz9Bl93lJm8MlEgw6mzn6cMRCj8XmsXarK8+4dMGpyjKfx1ux+0DBokHrMSmj\npR1NRrvDY7W4xJKQvX1ljELX2OH3oLWjw+PxcTgsABwOKyExqr6utbz6jGMHYGpOTm1jo1ar\nveGGGxbPW7J99/99/PF7C69empWV39/+PRVPwo5dmDAXLcE6dlqtdtGiRc3NzXq93uVyXXHF\nFXQlx/vvv//LL7/k5Axxhs9FAu3Ycbmc5OQLZJiY0+navbtk585DBw4cpfV7B4AkSYvFZrHY\ntNqBF+L1+x7jCQQsNkvQI8ri8Xi8brfdYnVYbQMMFYiMjM7JmZKbVzBp0vTY2GE50HQzLE/A\nT87PGMLpOp2RNlMeeZ5OxuCxtmh9bjcAZXKa0WwGIBYJjCYXgPPpEjsBMJlMNuusHDdF+Ztr\nTwBIS8o79ywej8XhMD0e0mx1ivi80E1EGylYIiEAl9VJ/yqVKfImzzxe+oumuCzzstlC2eA6\nfGUREgaT4Sf9be3mEDp2qujuMjvS5W9pb09JiKOPp2XG19e1tuv1emNnhKK7YTY3PW37j2yP\n11tWVvb7367ff2Sf0WJ87vkHvti8i8ns+74tlyulUrnZ3BXunwgT5mImWMdu3bp1J06ceOqp\npwDs2LGjrq7uo48+uuyyy+bMmfOHP/zhs88+G0kjJzy0Y5eaGhdCSbOxQqNp+eSTr3fs2E93\nfdIwGYyEmNjUxMTYqCilTK6QSkUCIf1m/X7SZnc4XE6bw2GyWrrMZpPF0mkydXZ1GUxdPp+v\n5+Z2i9VuCUr0n8cXxMYkxMQmJCWlp6RkpKfnymShyXuaTNaqqnoAmdNy+/sGHZiODiMAroDH\nEww6WNivVZp6AAwWi6OM8rQ0A+DzuF6PHYBQMnCBnQd95WE7tPUuhxVARkrfRTBSMU/faSdJ\n0uZwiYTjPWhHN8b63F7SRzJZTADTL5lfUV7i83pO/Lh35vJfD2o3BpOQRYiN7ebWNnNGRlSo\njJRGSJhsJuklSQ8aW7UBxy45OYbJYpI+sry65srZ3Y4dm83Oz8g4cvLksWPHFixY8Py969e+\n8VBFxbGPNr17z92P9XeJhISU8vIj4f6JMGEuZoL93tq1a9eiRYtefPFFAD/88EN8fPztt99O\nEMTChQv37ds3khZeCFRWVmLiF9jV1jZv2LB5586Dfn932CwzOeWq2ZdcOm36pMwsAT9YJ4bF\nYtGV3Xa73WSxtOo6nnn+PY/PkzVjSmRCjNvtstttADxej9fjFgrFALg8Hp8nEIkkUplcoYhQ\nKiND5cadS1HRCYoCi83KmDrEOLRO1wlAEbpwHU47dvL4ZJvDDoDJZHppl5gghMJ+I3Yej8dP\nkgB4/RTYMZms1ITsPs/lclg8Lsvl9pmsDqGAF8Tsg7Ek0BjrsTn5MhEAoVA8ZdqckkM/NR4t\nz7p8tjQyYlAbKqKlxnaz2ex0OLwCQWhkXxhMhkKt0DfraTW7gJwKh8NKSo7W1LQcrai4cvas\nwPqpublHTp60WCwajWbJvKU79n7z4+GdGze+Me+Ka9PT+/6rJSWmlZcfCUfswoS5mAnWsTMa\njdnZ3beSn3/++fLLL6en3GRkZHz55ZcjZd0FAUVRtGM3cQvsbDbHO+989vnn39HD5sVC4Ypr\nrrvxmmvTk5KHubNMImlqaBexxGBhyQ03q2IGN7Yr5Did7mPHTgFIzc/k8IYSpvJ4vCaTBYAi\nKoSuJ0U7dorkNLPZAkAqFlqtTgACIXsArTWX2wWAYDDOHSPRVFMOICkug8Pp921KxDyX2+b3\n+612p0QUsujjSMA+7di5rN2OHYCpM68oP3rQ7XKe+HHvpauXD2pDZbS09ihAQdvalZ4WGSo7\nVTEKfbPe74Hb423r0MWq1fTxzKwETU1Lp8mk1elio7pjhMnxsQqZzGgylZaWpqenv/zgK0Un\nDlvslmeevX/z5zv7DCcnJYUVT8KEGS4Gg0EsFk/c1vJgC8MTExNpvcHy8vLKysrAyJqysrLo\n6DH+Mh7nNDU12e12ABkZg5ZDGw8cOFB23XUP/vOf/yVJv1QsfuzOuw988Z9n7vt/w/fqaCoq\n6gEIJWJltDokGw6HsrJKr9dHEMgq7LdEfWD0+k66wE4Wuoido8PgsVoBCNRxJOkDIBEJbHY3\nAKFooFuP2+UGwOdyz1Vsaao5hh7SxH3CYTP5PBYAi83Zf3HjuIBgMlh8HgC39UyFAI/HL5h5\nBYCWiurOHto3wcBiM2URYgBtWnMI7VTGdpfZUR7Ua8+YlJgUzeWyARyrqOyxnJiSkw2gorLS\n6XSqlerf37sewMmTZX//6J0+909ITAWg0+lstvNUvoYJE6ZPKioq4uPj9+zZM9aGDJ1gHbvV\nq1fv3LlzzZo1S5Ys4fP51113ndFoXLt27bZt26666qoRNXGiQ4frMAEjdiRJvv76x3fd9WJ7\neydBEKuuX/TTPz+/f/VvREHowAVPZWU9gMTM9GAmnY8oJEmWlFQAiM9IFkklQ9ukvb27wI4v\nDGGBXR0AgiAIsRwAh8P2kvD7/QCE/U8S83q9tPLLuQV2JkO7pUuPcxTszkUi4gHw+/0Wu2NY\n72HkYYsFANw2Z8+Dk6fPEYjEoKjj/xu0YJMqVg6gy+yw2z3nXRwk8ggpXQLo96JJ2xpwl5lM\nRlpGPIBjVVX0X5ZmWk4uCIL0+Y4fPw7ghvkr5s9cAGDjxjcqK4+fuz8tZYdw0C5MmCHh8XhW\nr17tcrnG2pBhEaxj9/jjj69aterzzz9vamr605/+FBERUVNT8+677+bm5q5fv34kLZzw0I6d\nTCaODKmq2UhjNtvuuOOFTZu2UxQVr47+/E/v/uGRx2XiIbo7/eFwuBoatAASs9JDu/MQqKio\nt9mcALILhy6qScsah7bArktTB0CsjnV4fACkou48LJPF5PP7Lf9yurrzsNw+8rDHABAEMXDE\nDgCbzeTzOaCDdj0cjnEIh54Yaz3LsWOzODMumQ+gQ1Ov09QPakNltJRgEKCg1XaFykgGkyFX\nywD43bA7nR2GzsBL2TlJAGwOx6n6M3bKpJKUuDgApaWl9JFXHnpNLpF7vZ6n1/3W7e799ZOU\nmEY/IIXL7MKECRKH48xT6zPPPCORhPhrbvQJ1rHj8/mff/652Wy2WCz33nsvgLS0tAMHDpSU\nlMTGDno++kXFRCywa2nRrVz55KFDxwEsvHzujg8/mjFp8khcqLq6kW7FGA+OXVFROQBVdKQq\nZoiNkG63m66BC2mBHcyaegCi2EQKfoCQSkUWqxPnEzrxuOk8LOfcPGxjzXEAMVGJIuH5b2FS\nIRcA5acsdud5F48hbKEQgNvu7KWJkzN5pkSmBFA+yKAdi82UR0kAtLSEzLEDoFQrAPi9BIB6\nbXPguDpaKZOJAZSerOi5flpeHgCtVtuu0wGIVES+/MArAGpqKt/d8FKvzYVCkUoVhXDELsxF\nxtKlSxcuPKNYeeDAAYIg6EmebW1tN998c1xcnEgkmjZtWmDWGZ/PP3DgwKpVqwoLC+kju3fv\n/uSTTz766KPRtz+0DE58taurq6mpqbq6urq62mAwqFSq+vr66urqETLuwuB0S+yEcexqa5tX\nrXqqvl5LEMTDt97+5+dfCG3utSeVlXUAxDKpYpBNiyGnsbGVngOWPWOI1XXoqWAXFbKIndti\ncegNANiKKAB8HhcgnC4vBnTsvF4vLSXD5fRRhNd06hj6FzrpBYvN6A7a2V3+cRy0Y0sEAEDB\nYzsrjsVkMGfOWQCgs6VVWzG4m1VErByA1eo2mUPm1KroMjs/RfnQ0KJFDy80OzcJQJVGY+8R\nQsjLSKOLuI8cOUIfue6y65deuQzAP/+58fDh3qIEiYkpCDt2YS4ybrrppl27dhmNRvrXzZs3\nz5w5Mzc3F8CyZcsqKiree++9b775Jj09ffny5YEQ3RNPPDFnzpytW7cC6OrqWrNmzcaNG2Ni\nJrzcbLCOXV1dXV5eXnx8fFZfjKiJExqPx0PnRNLSJkbnhEbTsmbNs3p9F4vF+uNT6x5ac9uI\nlr7RBXYJmeMhXHcSgFAiis9IGvImdB6WL+KHUsGutvsbmilXAZBJhFabCxSFAQvsXP3nYR1W\nk0HXjCAK7AJIRaeDdrbxG7QLNMa6zzEyI2eqQhUFoHznnkE1gSjUUiabAaC5KWRBO3mUnMFk\nAPC7YbU79Ke/igBkZicRBEH6/WWVZ4J2LBZ7cmYmgKNHjwbG5b14/8sxkbF+v//pdfeazWfZ\nlpSYhnAqNsxFxqJFi3g83tdffw2AJMktW7bcfvvt9EvLli379NNPly5dOm/evGeeecbtdjc3\nd0fKZ82a9cADD9DTs+6999758+ffcMMNY/UWQkiwciePPPJIZWXlnXfeOW3atHMHEIXpj9ra\nWq/XiwkSsWtu1t122/OdnWYOm/3e8y/Mv+TSEb2cw+FqamoDkJiZdt7FI0pXl6W2tglARkEO\nQQxdRJpWsFOGNA9rqqsHwJMpmQIBAUIiEjRpuwBweCw2u19T6fmwvP7ysBSF87XE9oTFYggF\nHLvDY3W4JEI+7ZeMN5hcDpPNIr2+cx07BsGYddnV32771NyhbzxanjQl2DfOYBKqGJmu0ajV\nGvNyY4hQvG8miyGLkBrbu+AjAKquuSVC2f0/jEjES0xSN9S3lRw/MWfatMDfbnp+ftHx406H\no7KyMi8vD4BYKH778XduenKlTte6/oW1b//pk8D+iUlhxy7MRQefz1+yZMmWLVtuu+22Xbt2\nWa3WVatW0S898sgje/bs+emnn44dO7Zr11kzZ6dPn07/8NlnnxUVFdEtShcAwTp2+/fvv+uu\nu/7617+OqDUXHnQeliCI8R+x6+w033nn+o4OI4vFGgWvDkBVVUN3gd1YO3bFxRUUBRabnT65\nb93XYHA6nfR0NXloHbvaOgC8yGgAYpGAwWRYrS4Aov6FTgJ5WF5fedjGU0cBqBRqpXwQpYRi\nMdfu9FB+ymx3yiUjlZofJiyRkOwyu6x9hBVT0vOiouN1bc0nd+1LmNTHeNz+iExQ6hqNbjfZ\n3mGJVoemqloZozS2d1FeAqDqW5pnTp4UcL9z8pIb6tv0RmNDizYprns0Raw6Sh0R0a7Xlxw5\nQjt2AGbmz/rtivs2fvn+//63fctXny6/YQ19nJ4YazKZOjs7lUplSAwOE2b8s3r16iVLlpjN\n5s2bNy9btkwqlQJwOp1z5861Wq033HDDypUrH3rooalTpwZOEZ2eXXno0KGGhoaebRMLFy5M\nSkqqrx9cx9U4Iai7m9vt7urqmjRp6K2CFy1VVVUAoqNVYrFgrG0ZCJfLc//9rzQ2tjEIxhu/\ne2oUvDoA9OQusVwmH9MCO7fbU15+CkBKXjp7GIqUra0GAAQBhTpkjp3P5bJpWwFwI6IBSMRC\np9vn9fkACMX9mjpAHhZA46ljADJTBtcNw2IwhAIOAKvDSetUj0PYYiHOaYylIQhi1txrANiM\nXfUlR4PfU6IQ8kUcAM1NxvMuDhJVjAIA6fVTvt7Z2KTkGKGID6Do2FnBg2l5uQBqa2u7us4k\nXh+75fHJGZMBvPrqk3V13eWDYcWTMBcnCxYskEgkW7Zs2bZt2x133EEf3Lt3b0lJSXFx8csv\nv3z11Vf3N9XziSeeKDkNPUxrw4YNdGJ3IhKUY8fhcBISEg4cODDS1lx4TJSW2Gefff/o0WoA\nT/723sVXLRidi3YX2GWMcbju+PEat9tLEMicljecfegCO5FUzD5HN27ImOvq6R5PflQsk8kU\nCfkWixMACEIg7FfohFbB4HL6yMO6nXZdiwZBd070RCziggH4MW4r7ejBYp6+HDsACYnpcYmp\nACr27Cd9ZPDbRiYoAbS3m91u33kXB4NCLQdBAGD6mQA0zWd6YxkMIic3GcCJmpqeLRRTc3KY\nTCYoKtBCAYDFYm146n2RQORyOR97/A76756QkMxkMBHOxoa5yGCxWCtWrHj66adlMtm8efPo\ngyqViqKoDRs21NTU7Nix49ZbbwVQU1PTq3c+ISFh2mkKCgoAZGRk5OcPvZFubAnKsSMIYtOm\nTTt27Pj9739vtQY1oz0MDe3YpaeP6zzsp59+8803ewGsun7RXStWjs5F7fbuAruEMc3DUhR1\n5EgFAHVynEQhG85O7e0GIJThOpyWJmbyBGyJTCoSEARooROBqN9JYl6v1+cj0T1wojdNteW0\nHN0QHDsWgyHkcwBYneM0aEf3T5Ak6XX1LSk867KFABxmq+ZwSfDbRsYrQICi0BSioB2Lw5Kp\nJAC4BAdAXVNzz2+Z3PxUBoMgSbKoR8UPn8fLS08HUFpa2rM3OTE68Q8PvArg1KmTr73+NAAO\nh6uOjkU4Yhfm4mP16tV6vf622870/E2fPv3tt9/euHFjYWHh+++//69//Wvp0qU33XSTTqcb\nW1NHlGALTdavX69QKF588UWpVKpWq+PPZkRNnLjY7Xa6+2Y8R+zKyqpff/0fAApy89Y/+PCo\nXbeiQjMeCuw0mmaj0QIgq2BY4bquLovL5QagjFaFxjJ629p6APyoWBCQSIV+CjbbeSaJDaBL\nDKCx+igAqVihjhjKx3acB+044tONsf0E7aJjk5JSswBU7P3Z5wl2ngSHx1aopQAaGjpDNVpN\nGaME4LL7ANidTp1BH3hJJOKlpMYCKDp2vKcPN31SPgCLxVJTU9Nzq8Xzltz4q5UAvvzy42+/\n+wpAYrgxNsxFyZw5cyiK6jU0Ye3atc3NzSaT6bvvvsvJydm6davValWr1U6nc/HixeduIhQK\nKYq6+uqrR8noESBYx06lUhUUFCxZsmTx4sWzZ8+efjYjauLEpaqqio73jtuIncVif/TRP/p8\npFIm//PzL7BZ/Wb3Qk5FmZQefgAAIABJREFURS3GgYIdPUNMLJfEpAzr+aStzQCAwWTKIqSh\nsQygSJ+lsQkAPyqGw2bzuVybzUVRfgzYOeF2udDPfFgECuxShyg3Pc6DdiwBHwwGALe13wFo\nsy5bSBCE2+6oOVgc/M7qJBUAh8Oj11uGbycAZYwCgMvp5TLZAGqbmnu+mj8lHYDFZis/dUZ4\nLyU+TimXAaDHdvfkhftfykzKBLB+/cP19aeSwo2xYcJcxATbFbtt27YRteOChJZuZjIZKSnj\ndDjH+vUftLbqGQTjT+uejVKFMtR0Xk6c0ABIyEgdzYv2orPTXF+vBZBZkNunGxQ8ra16APJI\nOYMxdLWUXpgbm/0+HwB+VIxULARgtbkAMFlMHr/vT67X6+lvPiwAr9vV2liNwXdO9EQs4tqd\nHjpoJ5eOs/ZYAhyRwGOxuWz9jnqMiIpNycjTVJdX7T+YNnM6mxdUu4w8UswVcNwOT12dITIy\nBL2xymgFCAIUJeeL2m1d9U1Ns6dMYZ7WkYmNVUVEyvQdpp+PlE7OCnRqE4X5+d/v23/q1Cmz\nxSLt0cHH5/LfX/fB4oevt9ttax9Zs2TJagB1dXUURY35COYwYcKMMoPTZdq/f/+6devuvvvu\n48ePNzQ0hGs4BoYusEtIiOZyQ1ZNH0K+/fbAf/+7H8CdN66cM21Uw64Oh7u+vgVjLU185EgF\nRYHFYafkZw5nH6/Xq9d3AVCqQ6kuQRfYMdgcriJKKhUBoDsnBhg4QedhGf3kYZs1J/ykD8OI\n2GHcB+26+yds/UbsAMya8yuCIDxOV/WBQ8HvHJ0cAUDXYbXb3cM0EgCHx5YoRAAIkgHA5fFq\nzy76mTI1E4C2Xdeo1QYOFuTmMplMv99f2qOFgiYtPu2VB18DUFtbtX/fTgBOp7O1tXX4poYJ\nE2ZiMQjH7p577rn88stfffXVv//9721tbYcPH05NTX388cfH85ShsYXWOsnIGI952M5O84sv\n/g1AZnLKo7ffOcpXr6qqowvsxjBi53Z7ystrAKTmZQyzj1Wn66Q/BaqYUDp2XbSCXUQ0X8hj\ns5hen9/p9uI8AydoXeK+87AN1UcBiITSmKik4RgmGceVdiyxEIDLMpBhCpU6I2cKgOpfitzO\nYN9CVKKCwWSAQl2dYfh24vTQ2K5Oh0TIB1Db2Njz1bSMeJFYAGB/yZk+D6FAkJOWCqDkyJFz\nb7yL5y255fo1AA4X7aePhJ+9w4S5CAnWsfvrX//64Ycf3n///adOnaKPzJ8///bbb3/rrbf+\n8Y9/jJR1E5zTLbHjsXPi5Zc/7Oqy0HPDOOzRK62jOXGiFoBALFZERY7ypQOUl9fSKicZBbnD\n3IrOw/KFfIE4ZKlJiqLMdd2dEzKJEIDV6gRFgejXsXN7PH6S7oftewEtTZyZMmmY6TkmgyEa\nr0E7OmLnc3tJ70DSJDMuXUAQDJ/bXb3/YJA7s9jMyHgFgMYmo88bgnetjFUAMJudCVFKAI3a\nVo/njM1MJjF5ShqASk2doYfQXeGkSQDMJlOvFgqa53+7fmpWQeDXcJldmDAXIcHW2H3wwQeX\nXXbZ+++/HziiVCo3bdrU2Nj4l7/8JSAGGCZAV1cX3VCdnj7uuob37Cn59tsDAH678qactDFI\nhlZUaAAkZKaOVQHQGZWTxNjhqZwAgFarB6CMCWWRoq211ed0AeCrYyVCIQCL1QWAy2WxWX2X\n8dHBJyaTyWb34dj5PG5tfSWGl4cNIBZxbeOy0i4wMdZldQoV4v6WyeQRWXkFleUlNQdLMi6d\nxRMGpR8ek6pqbzSQPn9DY2da2nCbfpTR3co4fCafAOEjyfqW5syU5MCC3LyU4sMVHo9vX1Hx\nsoXdPXqpCfFKuayzy1RUXEzPuOwJm8X+yzMfLHroWkOXAcAFMyIpzESkuvT4y3eGQGmhujT8\nv/HgCNaxO3Xq1OOPP37u8Xnz5r3++ushNekCge6cwPiL2Dmd7hde+CuAlPiEB265dfQNcLs9\ndXUtABLHTpq4vr61s9OM7raJYWE2WxwOJwBVdEgL7GrrABAMRkRiMoNJADBbneh/4AQFynlm\nPmwftNRVkD4vgMyUKcM3jw7a2eweq9MpEfGZ42Z6LEfU7aK5B3TsABReMr/6ZJnP46nef3Dy\nwquC2Zwv4skjJV06S12dPiUlYphDs3lCnkAicFgcZqMjUiHWGS01DY09HTsOl503Ka20pOpo\nVdVVl14iFdNvh5gxedJ3e/adqq42mUwyWe/HkmhV9F/WfbDqdzf6Kf/XX3/96quvcocxTyVM\nmCFj7NAf/H7X+deFCTXBOnYxMTGdnZ3nHtdoNGq1OqQmXSDQBXZsNispKXqsbTmLv/3tq9ZW\nPUEQLz/y2OgnYQHU1DTRCrrx6WNWYEeH64QSUeywZ/i2tHQAYDCZipCOiDVUnwLAVUXJlTIA\nTqePHpbQn4Kd2+WmlYd5PF6fCxpOHQUg5IvjY1JCYmEgaGe2ORRSUUj2DAFMBlvA9zqcA/dP\nAJDKlNl5008eP1x7qCRzziyeKKi4Y2xaZJfO4nR6tdqu+Hj5MI1VxSiaLI7WNvPkGTE6o6Vd\nb7DY7JIelkyemn6srIYkyf3FJddf2S2mX5CT97/9P5MkeeTIkauu6sMlnZE3c9HMhdsPfWs2\nmx9//PH33ntvmHaGCTMoCgsLJ8SeFyrBOnaXXnrpZ5999uSTT/aUIz569OhXX321ZMmSkbFt\nYkNH7JKTY/sbTjcmtLToPvro/wAsuvKqmZNDELkZAvQkMb5QEBE7No8EZrOttrYJQEZBzmAb\nw8/ljNBJSP/Q5roGAEJ1nFDAB7oHTgwwSczldgFgsVhsZt8f6obqMgAZqZMIIjTRtUDQzuZ0\nSUWC8RO0Y4tFXofT1Y9GcU+mX3Jl5ckSn9dbtf+XKdcENUlPqhKJZAKbyVFT0xEXJx9mKYEi\nWtFU1dJptMeq5Cwmw0f6axoap+XlBBYIhbycvOTyY7VFx4/PnVEoFokACPi8/IyMo5WVJSUl\nV1xxRZ93mGVXLCs6dqjNafziiy+ys7Pvv//+YRkaJsxgKC4u3rFjx1hbcfESrGP32muv/fe/\n/y0oKLjtttsAbN++/bvvvvvHP/7B4XBee+21ETRwwjI+h4m98cYnbrdHwOM9dc99Y2VDRUUd\ngKSsjFB5GIOltLSCosBkMdPys4a5lcfjoYVOImJDWWDn0Ot9NjsAZXIq7TrQ/afCfiaJ+f2U\n+0w/bB/4vB5tXQWArNSpIbRTLOKNw0o7jljo0OndAzbG0kikiuz86SePHtYcLs26bDZPFFTc\nMS4jqqqo3mp1tess0ephadqpYhQAQFGdBkeCWlWn7ahpqC/IzenpL04rzKo4UUcH7a6ddwV9\ncMbkyUcrK61Wa2VlZV5eH0NT1OrYdEmcw+c2e+0vvvhiRkbG/Pnzh2NqmDCDRREZlVkQghtO\ndWmZseNCngAWcoJ17NRq9eHDhx955JE//elPADZu3MhgMBYvXvz666/HxMSMpIUTFToVm5Y2\njjonSkoqfvjhFwC/XbV6lOWIA3i9Po2mGUBS1tgo2Pl8vmPHTgFIzE7j8PvOWgaPVqunh4tE\nxIRyfoa2/CQAEERsZhYAP0XZbC4MkId1uyiKAkH0OR8WQIvmpM/rAZCVGsowLZNBCPkc+zir\ntGOLBQA8TrefJM8bRp0++6rKcjpodzDIoJ0yWsoXc51W96nq9mE6dkKpkCvguh3u1nZzeoq6\nTtthtTtadR2x6jPd4iIRPzs3+cRxzeHjxy+bUSgWCgEkxsZEqVQ6g6GoqKg/x45BELnypFqv\nrqPLcM8993z77bdZWcN9kgkTJngyC6Y++9Gm4e/z8p13HPz+++Hvc/EwiBtxSkrK9u3bbTbb\n0aNHKyoqHA7H1q1b09PHUmB23GIwGOiSxPEzJZaiqNdf/xhAdETkXTeuGiszNJoWr9cHIHGM\npIkrKuocDjeAzKk55118XlpadADEMjFXMFwfsSeGqlMAuHKVWCYFYLO5afexP8fO6XQC4LBY\n/eX96TysUCAJVYFdAImIN9407dinA2/9TYztiUQiz86fDkBzuNRlswd5ibj0KAAmk7OjY7gT\nxuje2PY2U0ykQsjnAqiur++1ZvqMbCaT4fP59h4+HDg4c/JkAHX19XpDH7p6UqmczxdwGKwH\nl94u5AusVuvq1asNfa0MEybMBcZAEbvt27cP8GpA0A5An5N0L2bocB3GU8Tu++9/OX68BsBj\nd9zVX8JuFKiqqgfA5fOiE+PdQU9hDyFHjlQBUEVHKtTDjbGRJEkX2EXEhjJc5/N5nc1aAIrE\n7gZJWuikv0liJEl6vF50z4ftm/qqUnQr2IU4qDYOg3YcSXdS2G1z8mXnz64GgnbVBw4F2R4b\nEadorm532T3V1bphThhTxihaNW0dHVa/j8xMjC6tamjQtrjcU3t2N4tE/Jy8lPJjtUXHy+cU\nTpeJJQCm5GR/v2+fx+stKiq67tprz905KjKmobGWRRIfvvDOb566t7m5ec2aNVu3bu2vvSZM\nmDAXBgM5dsF3RdDhhDAB6M4JLpcTHz8uWoZJ0r9hw2YAOWlpixcElW8aIU6dagSQkJ5KDFMr\nYki0tenb2vQAMqYNV+UEgE7X6fP5AETEhTKv3d7Y5LdaAajTM+gjVqsTgKgfXWKn0wWKIgii\nP1ULr8dFK9hlpYWywC7AeJseSzCZLD7X53QPPH8igEQiz86dfvL44drDR7Iuv4Qr4J//EgTi\nMtS1ZU1Go6OjwzIc346O2Pn9lK7Dmp6oPlrVSJL+mobG/LND2tMLsytP1vt85E+/HFx29dUA\nuBzOlOzsouPHy0pLFyxYcG6Huzo6rqGxtrW19b777nvh/z313HuvFBcXP/DAA3/7298YY/Hp\nCxMmzOgw0Md7Tw927dqVlZUlkUgeffTRzZs379ix45VXXlGr1VdddVV7e/uomTtRoB27lJTY\n8RDAALB9+x5aOu7R2+9ijFHLAgCS9NfUNANIHKMCO1rlhCvgJWaGICPZ3KyjdxPLQzAVPkD7\nyQr6h4iUNAAeL9k9SayfEbEulxMAl8Pp79u6ufYErWCXPTKO3TicHssWCxFcKpZm2ux5BMHw\neTzBT4+NjJfzhBwAVVXDKuuWKCVsLgtAW6tJyOfFRikAVNVpcPbDslDEy5+cBqD0ZIXe2K08\nNWPKZAAul6u8vPzcndVRMQC0Wi2AB2+++/alqwFs3779pZdeGo7BYcKEGecM9B0/twe7d+/W\n6/WlpaVvvfXWqlWrrrvuuqeffrq0tPTkyZPvvPPOqJk7UaBbYtOGrZEWEnw+cuPGLwEU5ObN\nmzV7DC1pbGylh5kmZWWM/tWdTldFRT2AtElZw5cmoSh/c3M7gKj4yD4Hsw4Np9Nhb2oBwJPJ\neRIp6Dxs/5PEvF4vHTXk886ThxWLZLHq5P7WDJPxVmnHEYsAuM8nZRdAKlNm5hYAqDlU4nG6\ngjmFIIj4TDWAri6HTjf0SjuCgEKtANDaZgaQmRQNwGSxtur1vVYWFGZxuGyKonYe+IU+Eh0R\nkRATA6CoR+1dALU6FkBXVxddgvnm4y/OnzUXwJ///OdNm0JQ0h4mTJjxSbDBm23btq1cuTI1\n9SxF2ejo6JUrV3799dcjYNjEhi5AHCfDxLZv393U1A5g7W1jPPmtqqoRAIvNjk0eA5f32LFT\nPh9JEEifEoLewI4Ok9vtARAZF8pxt3q9gdTpAaiSu8dy0HlYLo/N6muSmNPlBEAwGFxO3/E8\nAA1VZQCyUqeM3AA3utIO4yZod9qxc/n9wRozffaVBEH43O5TB4uCPCUiTsEXcQBUVrUPpxqF\nzsbqdBbKT8WrlXQLRaWmttcyPo8zbXoWgJO1tc2trfTBWVMnA9BqtS0tLb3WR6ljAVAU1dbW\nBoDFZP7jlfcnZeQCWLdu3XfffTd0i8OECTOOCdaxa2lp6a/hjr5rhAnQ0dFhNBoxPkTsSJL8\n4IMtAKbn5V9aMG1sjamubgAQl5rEZI32xAuKokpLKwHEpiUKJSHInDY3twHgcDmyiOGOmg1A\ngdK3tvpNZgCq5FQAFAULLXTSV7iOogvsutsm+nba3E57a0MVRiwPG0As4o6foB2digXgtgcV\nfgMgV0SkZ00BUHOw2BtcWw9BICErGoDZ5GxvMw/JUgBQxCgAeL2kodNGEAQdtGto0TrOiR1O\nnpouFPFBUd/u3QdQAPLSM0QCAYDD5wTt1OpY2pWns7EARALhl3/6KF4dS5LkPffcU1xcPGSb\nw4S5wNi4cSNxNud+piYKwTp2U6ZM2bp1q/7s7IDBYPjqq6+mTh3ZL4wJR6AlNjV17CN233yz\njw7XPbjmtrG1hKKo7s6JzDEYEavRtJhMNgAZU0KgcgJQTU1tACITQpmHNZvNrtY2UBQAZXIK\nAIfTQ08SE/UldOJ2uegxYgPkYZtqjvv9JIDstIJQ2dkn46rSjnPasfNYgs3GAph+yZUEQXgc\nTs3hI0GeooqVCyR8ABWVrUMO2skjpEwWE0BbqwlAZmIMg0H4/VSlpq7XShaLOXN2LoCm1taT\np2oBMJnMafn5AI6XlzscZ71ZPo8vlcrRw7EDoFZFbXnnHzKx1OVy/eY3v6mpqRmi0WHCXFjU\n1dUVFhZu6cHEVXML1rF78sknW1tbZ82a9eGHH5aVlZWVlX300UezZs3SarVPPPHEiJo44aA7\nJ/h87pi3xPr91N/+9hWAKdk5c6ZNH1tjtNoOm82BMRoRS7dNiGWS6OS44e+m13c5nW4AUfFR\nw98tgOF0HpYrFguVETg9SYwgCL6gjxgnXTvFYrHY/UdA6QI7uVSljhzxx4zxE7QjWCwWjwvA\nZR2EY6dUqZPTcgBU/3yY9qeDITFbDcBm87Q0dw3eUgBgMBnSCBmA1nYLAD6PkxQdAaC6rs7v\n7+0tZuUkKVVSAN/v30+SJIAZk/MJgiB9vpKSkl6L6TK71tN5W5rMpLTNb37I43CNRuPKlSvD\n3W9hLnLoJ6K6urqZM2fe0AOFIpTjv0eTYB27a6655u9//7vZbL7nnnsKCgoKCgruuusui8Xy\n97//feHChSNq4oTjdEtsXJ/Tn0aT3buLNJoWAPfffMvYWgKguroRAIPJjE8NsUbueTGZrHRT\ncEZBbkgCbI2NbQDYXI48crhj4AP4SNJoNJIdegDKpG7f13p64MS5/y/5SdLj8WDAcB2A+spS\njJjQSS/ODtoF6xiNEN2NscEpngSYNvtKAC6rrb70aJCnKNRSkVwAoLK63U8OMWpHzxZrazXR\nzbDZKbEA7E5nXUtzr5UMgrj0skkAjCbToaNHAcjEkqzUFABFRUW9lKdox65nxI5m9pTCD198\nh8lgNjc333jjjWbz0PPIYcKMB5YuXdrTFTlw4ABBECdPngTQ1tZ28803x8XFiUSiadOmBYbY\n8vn8AwcOrFq1qrCwEIBGo0lNTbVarU1NTRNdwW0Qyhd33HGHRqP5+uuv//jHP77zzjvffPON\nRqO5444xrscfh9COXWpqCCJDw+TDD7cCSE9KvnJMm2FpqqoaAKgT49jcfsv8R4jS0kp6OGxK\nXghC6xTlpx27qISoEOZhjZ0Gv89LdnYBUCamAPCTlM3uRj8Fdg6Xi6IogiD43H71Zh02s65F\nAyAnfZTKKwNBO/NYB+3o/glX0IonNOrohPjEdABV+w8G33iRlB0DwOnwNNQPcbQD3T/hcnlN\nJieAKKVUJRMDOFF96tzFCYnqhKRoALsPHnI4nQBmTZkCwGQy9dSNB6BWxwFobW0994tq0RUL\n//jEiwAqKytvvvlmlyvYYsQwYcYhN910065du+jqdgCbN2+eOXNmbm4ugGXLllVUVLz33nvf\nfPNNenr68uXLA0ULTzzxxJw5c7Zu3Qqgrq7u008/lcvliYmJKpVqQneOD07STCqVLlq06LHH\nHnv44Yevv/56sVg8QmZNaGjHbsw7J0pLK8vKqgHcfePKkWuHDJ5TpxoAJKSPdoFdYDhsUk4a\nJxSa+zpdJy3aok4MZR5WbzD4DZ3w+wEok1MBWOwuut5OKOnDsXM5zyNfB6ChqpSi/ABy0ke2\nwC7AWUG7c9KIowk9f8Jtcwbvn9FMmz0PgN1oaj5eEeQp0giRNEIEoKq6zTek+kKFWgaCANDa\nbqKP5KTGAdAbu3T6znPXz7lsEkEQTrf7x19+AZCWmKCUywAcOnSWDp9aHQPA6XSaTKZzN7l9\n6eqn734EwOHDh++66y5aNydMmInIokWLeDwerdFBkuSWLVtuv/12+qVly5Z9+umnS5cunTdv\n3jPPPON2u5ubuwPhs2bNeuCBBzIzMzs7OymKmjZtWn19vV6vf/DBB++8887du3eP2fsZHuNC\nPvdCoqOjo6urC+NgmNimTdsBRClVv75q/thaAqCjo8totACITx/tPGxFRR1dD5cRiuGwABoa\n2gBwBVyZKmT9sC6X02a1kToDADaPL1ZHA7BanADYHCaX03tCjMfjOS1fN5CrWldxBIA6Ml4h\nC6Umy8AENO1M1mBHr44EZybGDjJ2GJ+YHhUdD6By3y/Bn5WYHQMCbrdPo+kY1OVoWByWVCUG\n0N7W7YGlxEbSuiflNX0E7RRKSd6kVADFx453GDoBgg7a1dTW0lOqaeiIHfrKxtI8eedDdy9f\nA+CHH35Yu3btRM9Ahblo4fP5S5Ys2bJlC4Bdu3ZZrdZVq7pHoj/yyCM6ne7dd9+94447rr/+\n+p5nTZ/eXXquVCqtVuuHH34YHx+vUqnWr19fWFj4z3/+c5TfRagIO3YhpseU2LGM2DU36376\nqQjAmqXLBqisHzXoEbEEQcSljZRGbn90D4eNiVREhWCiK0mSdJexOkEdwjysXq8HKLLDAECR\nlExHWM3dQid9lNDRCTgmkzmAfB2AusojGMU8LM0ZTTvHWAbtAhNjPYMsswNQMGseALOuo7W6\nt5hcf4jlAoVaCqCmRufxDKW+kM7Gtp2WTWEwiOzkGACNzVqLrQ8XecasXC6X7aeoHXt2AyjI\nzWGz2aCooqIzOnwREVEsFgv9O3YAXn/09zcsWATg3//+93PPPTcEy8OEGQ+sXr16586dZrN5\n8+bNy5Ytk0qlAJxO5yWXXPLggw/q9fqVK1du37695ykiUb+zpLOysnS6YQ2VGUPCjl2IoWtc\neDxOXFwo83SD5dNPd5CkX8Djrbp+0RiaEYDunIiIjeYLR3WW6JnhsCEK12m1HV6vF4A6MTok\nGwIAKIPBAD9FdnYCUCSmAHB7fJ5+Jon5/X63y4XztU106Vu79FqMYh42QKDSbgyDdmcaY4Oe\nPxEgNT1PpogAUDW4oF00CHi9/praoQTtlGoFAIvFZbe76SNZyTFsJtMPqs9KOz6fM2N2LgBN\nY1NVrYbH5U3NzgZQWlrq8XrpNUwGM0KlxjmNsT1hMBgbn3/rqlmXA/jrX//69ttvD8H4MGHG\nnAULFkgkki1btmzbti1Q/b93796SkpLi4uKXX3756quv7k+Od+fOncnJyfX19fSvfr+/rKws\nPz9/lEwPNWHHLsSMh5ZYm82xdesuAEt/dbVMHMoxpkOGliYefaGTM8Nhs0Jz6fp6LQChVCSW\nh6zA1GQ2ezwe0mikPF6clia2WF0AQBDnKtg5XS6KojBg2wSAusoSAAwGY3RaYntyptLOMZaa\ndnRjrGvwETuCIApmzgWgb2jqbO431tULgZgXGa8AUF9ncLm8g70oHbFDj6Adh81OT4wGcKq+\n3uXuQzM5Lz9NoZQA+O/evT6SnDllMgCn03ns6JmWXnV0342xPeGw2f98deOM/AIAr7zyyscf\nfzxY48OEGXNYLNaKFSuefvppmUw2b948+qBKpaIoasOGDTU1NTt27Lj11lsB1NTU9Ko6mDdv\nHoPBWLVq1Zdffrlv3741a9a0tLSsXbt2DN5GKAg7diHmdEvsWBbYbdu222ZzEARx69LlY2hG\nAJPJqtN1YtQL7M4Mh80PwXBYAG63W6vtABCTHEqFQgOt+20wAmCy2dLYeAAWixMAn89mMHs/\nITgdDgBcNru/p08ausAuKS5TyB+DJqfxMD22e7DYYKTsAmTmFAiEYgBV+w8Gf1ZSdgwIkOT/\nZ+/Nw9sq77T/++hIOtp32fK+77HjJHZ2lgABWqCQlA4hfTtNaWc6beEXujBd6PyGdmjf6cy0\nDKU07bzzdgoUaCFNCVAgQICQQOIlju3E+77KlmxZ+9F+3j+OY0JiO1qOZCecz3VxXY50zvM8\nMrb81Xe570hvX8xJO0pOydUyABeaWKwpzhIQRDAc7uhbpChMksT262oB2Oz2D06fNhmN+dnZ\n+LgLxVKKJxchk8r+9PP/W1lUBuB73/seOyfIw3NlsXfvXqvVum/fvoV5wbq6uscee+zAgQP1\n9fVPPvnkH/7wh127dt17770XlVmFQuGpU6dKS0u/853v7N692+l0NjQ0mEwrrEQbN3xgxzFs\nYLeCkxMMwzz77GsAtm+oK8pdeU8zAKzhBFKesfvIHHZdBScLDg1NMgxDEFzWYUPhEDuiL7DN\nAdDm5AtIkmHmFewUqovTdVGOTTBMZKjrNICq0pURphYKCMVKG1GIVecdY2MX1RMKRWvrtgOY\n6Oxx26JVHqbkVEaBAcDI8IyXjjNpN3lBYKeQSQuyjAA6+/qCwUVeRW5uekFhJoD3TjW43G52\nhGJqamp4eJi9gJ2fmJ6evuzQq1alOfT40/lZuZFI5P7773/rrbdiPT8Pz8qyfft2hmEeeeSR\nCx988MEHx8bG7Hb766+/XllZeejQIZfLZTKZaJq+8847Fy4zGo3PPPPM6OjozMzMyy+/XFpa\nmurTcwcf2HHJzMwM+0d6BQO7kyfb2XLhF+7avVJnuAhWwU5j1Cs16pRteoE5bK5cxU3KilV7\n1pn0lJQD2RSWGesMwzBg4DNP47yTmNvjZ0U6Lm2wY8cmBAJSsqwcoHmkl/Y4AVSWrphBsFoh\nXdmknUgZ52Asy5pf4J/xAAAgAElEQVTaLSIRxTBMz4lTl7/6PDllGQJSEImgpydmRwddhg7A\nrM0TCHwUhNWU5hIgfIFA9+DAondtv24tSQoCweAbx49XlRSrFApcoHuSYcoGEIlEonGYMBnS\nXvrlMyZDWjAYvO+++65cr0wenk8yfGDHJWy6DkBJyYoFdn/84xsAstLTr9+0eaXOcBFsg11u\naUoV7AYGxubNYddVcbKgzWa3250AsgozOVmQhfVflgb8IS+NBQU7Fw2AFJIXOYktjE3IpNTy\nM7kDHY0AKEpanM/Ny48DAbnCSbuFwVh/jDLFLBKJtGrtRgDDLe1+b7QriCkhm7QbG7UtjEFE\nyXybHcNMTTkXHtSqFNkmHYD2np5Fv41qtaJ2fRmA1q7ucfPUxrU1ALq6uhxOJ8732CGKaixL\nflbuXx5/RqvS+Hy+vXv3nj17NqaXwMPDs+LwgR2XsIEdRYmzs1emNm+x2N5+uxHAnts/Qy6t\nW5tKvF7f+Pg0gNzU1mFPn+4CoNSqMvK5sQDp7x8DIKJExizONOG8tNfr9QAQO50ACJLU5uTj\nfGB3abqOpmnWbUJ2OaXlgc5mAOWFa4XkSordrGzSjiBJoVSKuOYnWNbWX0MQglAw2N9wOvq7\nskrSSaGAYdDTHZtcgkIjp2QULpifYKktywPgpX3dg4OL3li3sUKhlIFhXn7nnbrqapIkw+Fw\nc1MTAJVSLZcrEXVgB6CiqPSFX/xOLpU5nc577rlncIlNeXh4Vier4m//VQOrdZKfn0mSK/ON\nPXjw7XA4LBKK/uZTt63IAS6lp2eENTJP5eTE3Jxz3hx2HTfmsOFwaHh4EkBGfgbBXcRstVgA\nkCQZmLIA0GbnkCJRMBShfUEs5iRG014AlFgkECw3NhHw0+MDHQCqylamwW6BVZC0UwDwO+OZ\nnwCgUmmLy6oB9J1qCoeibdQTicmMQiOAsYk5lyu2pJ3O9DE1OxajVpWVpgXQ1tW96LdRJCK3\nbKsGYLZYegYH15SUAGhqamIdezNMWQDGx8ejP0b9mnXP/OtvxCKR1Wq9++67zWZzTK+Ch4dn\nBeEDOy5Z2cmJcDjy4otvAdi5bZtBy5k5fYKwdViFWqVN40AfOEpYc1ihSFhUzU0D7NDQZDAY\nApBVmMXJggAYMNaZWQAGnco+MAJAn18Edh6WYUBcHNj5/L5QKAxAJpEuv/Jwd0s4FARQVVrP\n1Wnj5gL32Dijq0QQzyuexL917cZrAfjdnpG2GIqSWcVppEgABj29sXXa6TO0ACwW50UBXG1Z\nPgAPTfcskT8rLcvNyDQAeOvEB+vXVAFwu92sCTpbjV1Gym5Rbth0zX898p+kgBwbG/ubv/kb\n1lCHh4dn9XOxVRFPIrAZu5UK7I4fb5mctAK49/bPrMgBFoW1iE3lPOyCOWxBZbGIWk7CN3rY\nOqzGqJGrl1QqjxWbzcaGX4pIJOByA9DlFwFwuGgAlEQkEn4sLceqnAiFQvGybhMA+s81AtBr\n0zPT87g6bdyQAoFCKnZ7Am7ap1bIUpzMFqkUAAK0PxwKk8J4JG9MGbkZ2fnm8eHeDxoLN9RG\neZdQRGYWpo31TE1M2MtKTcrF7EMWhW2zC4cjVqvLZPpo2Chdr84yaiesc61d3WWFhZd+GwkC\n11xf+8LzR91eb+/QUGZa2qTFcurUqZqaGnZ+IvpS7AJ33fjpOaf9W//2w+7u7r179/75z3+W\nyWSxLsLziaWn5cyjX76Pk3USX+QTBR/YcYbNZrNYLFg5EbuDB98GkJeVtWVdqp0GliIQCA4N\nTQLILU1dYHfu3IDPFwBQXMuNyonNZp+dtQPIKuKmXY+FrcNKpRLf5BQAgiB0efkMA5eLdRL7\nWPQWDIX8gSCAy3bX4fzkRHXZRg5PmwhKhcRNB9iknY67yDgaxAuDsU6vTBfncHRt3bXm8WHH\ntGV6YCi9KFpPvMwi4+SAJRyK9PZOb9gQrfCQ2qAiRcJwMGQ2Oy4M7ACsr8yfODbnoenOgYHq\n0pJL701L01ZWFXSeGzx1pvWGrVsmLZbR0dHJyUlTRjYAl8vldDpVqtgUy7+0a6/NMfcvv/mP\n5ubm++6775lnnhGJVt6ikOeKwGaZPvnGGyt9ik8ifGDHGX19fewXK5Kxm5mxv/tuE4DP3frp\nBW3GFae/f5StHqaywY51mzBmmzgxh8X5arKIEqfncjY24Q/4HA4ngDS9ZqalFYA6M0skkXo8\nfrYv6qIcD017wTCEQLC8fB0Am2XCZpkAsKZ85euwLKSAmE/aeVOdtBMrZSAABj5X/IFdYWmV\nSqNz2m09HzRGH9gJRWRmUdpYz9T4xFx5ebpcHlXSjhAQunSNdXzGbHas+7hjiFGrzk7Xj0/P\ntnV2lRcUikSLJCC3bFvT3zcW8AeHxsalEgnt8506dWrz5vmfhPHx8crKmL31vr3vGzN224E/\n/u7o0aP79+9/8sknV887DM/qpL6e+zefZKx5tcIHdpzBNtgJhWQely6i0fLSS++GQmGSJHff\ncmvqd18K1iJWIpMZs1L0PRkfn56etoE7c1i/3z8yMgUgqzBr+ZGFmLBarABDEIRBp+7vH8HH\n67ACUiCVf5Sxi0QiNE0DkFLUZf+m9p89BYAkhZUlK6ZgdykLSTu726tPZdJOIBDL5QG3J5E2\nOwEhqFm/9cQ7r0719rtmbEqDLsobMwrPJ+36LOtqo/28pzNpreMzU1MOMBdP/myoyJ+YttF+\n/7m+nnWLhWhSKbVxc9WJY639IyNVJSUdfX3t7e033XSTQEBGIuH4AjsAP93/Q5vd9qc3Xnrx\nxRcNBsOPf/zjOBbh+eTQ1NT06quvrvQpPrnwgR1nsIFdfn6mMK5WngT5y1/eAXD9xk3pekPq\nd1+KeYvY4gKCSFGShk3XSRXS3NJoMyvL09c3Fg6HCYLILuFsbAJgWPk6nVYZdLp8dgcAfX4h\nAIeTBiBXUhf+QadpmokwIAi59DJjEwD6zjUAKM6rkkrk3B04UUgBoZSKXZ6Ax+vTpDhpp1YE\n3B6/I6HRjcqajQ0n3goG/H0nG9ffEe1nJ5GYNBUYJvosY6O2sjKTTBpVEdOQqesB/P6QzebW\n6T8WBOs1yrwsw/CEtb27t6KoeFGR6uqa4o6zA3M216TFQhBEKBRqa2tLSzNNTU3E0WbHQhDE\nr3747zN229FT7x84cMBkMn3961+PbymeTw66NFPZOg4G83vONNssMct9f5LhAzvOYCcnVqTB\nrr29j+3u/+wtn0r97ksRDkf6+8cB5KSqwc7j8bIuFyU1FZyYw0YiYXb4w5idJpFdPqiKErvD\nHggEABj12rnuPgAgCH1B8YLQieICBTsG8HrnVU6WN4cFEAr4h3vOAKip2MTVabmCTdoxKU/a\niZUKYJp2ehJZhKKkFdV17ac/GGppr755R/RDOVlFaeZBayTMDPRbqquj+mygSdcSAoKJMGaz\n46LADsCGisLRyZlAMNja1ckaiF0ESRLbr6195aXjcw5Hml5vmZ1taGjIyMhOJLADIBIKn/7f\nB27/+p4zXWd/9KMfZWRk7Nq1K+7VeD4JlK2r++F/PZf4Oo/+/d6TR/j8XwzwciecwWbsijjt\nr48SNl2nVatv2LIl9bsvxdDQhN8fQApHYltausPhCCEQFNeWc7LgyMgUTfsB5JZx6bprmbYA\nkFBilVI2NzACQJluEstkHwmdqD4K7Hw0zXbdKaJI1w31nAkF/ACqV19gJxAQChkFwOP1pVLT\nTqRSAggHw0FfIJF11m7YRhBEKBAYam6NYXdKmJ6nBzAyMuv3X8atlUUoItUGNYDJKcelz6oV\n0tI8E4DO/gHXEgoyefmmvPwMAHNOJwC73S4WSxHXYOyFyKWyF37xP4XZeayZ7IkTJxJZjYeH\nJ0nwgR03OJ1OVsMz9Rm7QCD4178eB3DHDTeKhKtoYI2twwrFYlNuKoLdSCTS2toDILc0X6rg\nJiHU2TkIQKVXawwaThYEEAgE7HY7AKNeC8DePwzAkP+Rk9hFQicerweASCQUiS6jcoLzDXZa\ntTHblLpplehRyilCADCwu1KnaUedNxZLpM0OgEZrzCssA9DX0MzEcmNWcRoIhMPM4KA1ylsM\nmToAU+ZFAjsA68oLRCQZDkeal/b72n5drUBABINBCUUBcNjdAKanp4PBYCxnvxijVv/nx58y\navWBQGDfvn1dXV2JrMbDw5MM+MCOGxZcYlM/Evvuu80OhxvA7p2raGwC5ycnsgrzSGEqKv49\nPSMulxdA2QZu3FHNZitrDptfzmW6zmq1sLZgBoPab3fSs3MA9AVFDAPnJUIn/kAgFAwBkEuj\n0g/rO3sKwNqKzatzbvHCpF0oVUk7UiZl6/I+R0LVWAA167cDcM/OmXv6o7+LkoqN2VoAQ0Oz\noVBUr1qXoQPgdvvdLt+lz0ol4qribAADo2PW2cV1g7VaRfXaYgC+QACAbc4BIBKJxCpTfCkF\nWXl//Pn/lUqkDofj7rvvnprim594eFYXfGDHDazWCUkKCgq4dIiPhsOH3wNQnJdfXVaW4q2X\ngWGY3t4RpNAitqmpA4A2TcfVBG5HxwAAqUKalpPOyYIAAMZisQLQqpUiIcnWYQHo8gs93kWE\nTrxuNwAhSUqiaOqaMY/MWScB1FRs5u7AHDOftAMcrkTDrOhhZYp9rkT9anMLSjU6I4D+k00x\n3Zhdkg4CwWB4ZHg2mut1Ji0IAoB5sWosgOqSXCklYsA0tLUttUj9pkpKIgbDEARBkvM/PwlW\nY1k2VK793b/8kjWluOOOO9geUB4enlUCH9hxA5uxy85OpxabU0sedrvr/fdPA9i18+ZU7ntZ\nxsamPR4aqZImnp6eHR+fBlC2YQ0nC87O2qenZwHkledz4jbLYnfYAwE/AKNRC8A+MAxAYUyT\nKFVOJw2AvEDoJBgM+gMBALIouutwPl0nFIoqS1eR0MlFXJC084fC0bqvJgilVgDwJ5yxIwii\net0WAOb+QdesLfobZUqJNk0JYGDIykSRs6OkYoVajktMYxcQCcn1FQUAzFbr0NjiJrASiXjj\n5ioADMOQAiFJCsFRYAfgU9fc9JMHfwigubn585//fCSyAkbAPDw8i8IHdtywUiOxr7/+QTAY\nEhCCz9x4U4q3Xh62wU5AklmF+SnYrqmpE4CYEudXcBNHnjvXzy6YWcilAt/01PzYhFopAzDX\nPwJAX1CM8wp2FwqdsN11gihEiVl62j4AUF5US4mjun6lUMkpQkAAsCc2qRo9IqUCAO3yMkxM\n3XGLUFFdJxJRYJj+U6djujGrKB0A7Q1OTNqjuZ6txi6VsQNQmpehU8kBNLa3LTWMsqa6SKOd\nl2UWCiXgLrAD8A9/s+9re74E4KWXXuKV7XiuAt54440dO3aoVKr6+vpjx46t9HHihw/suGGl\nRmJffvkYgPqamsw0DsuFHMAGdhl5OcLLGZsmDk37OjsHABTXVpBcjI/Y7c6JiWkAeRV5HIoS\nB/x+u8MOIM2oBRBwur3WWQCGwqJAMMwKnSw02AVDIZ/PD0AulUbTMOfzusb6zgKordzK1YGT\nBCEglHIKgJcOBIOpSNqJVUoAYOB3L9KyFhMUJS1bsw7AUEtrKBDDIILaqFBopAAGBizRXK/P\n0AKw2bx+3+K7EASxsboYgNPtPdvTu+g1JElsu6aG/VpIUgBGR0ejP/Nl+dm3H7ntupsB/OpX\nv3r++ec5XJmHJ8W89tprd911186dO//85z8XFhbefvvt3P6ypBI+sOMAr9fLfg5O8eTExITl\nzJluAJ+5cWcq940GdnIiNQp2bW29oVCYIFC6jhtz2LNn+xgGIkqUXcLl/9DpaQvb8GTQqQHM\nDQyzj+sLis8LnRAK1XwvlMfjmfcQi7YO2xCJhAGsrVxFkjdLoZSdT9q5U5G0+8gx1uFOfLWa\n9dsABH3+kbZzMd2YWZQGwG6nZ2cv/6r1GToAYJipKeeSCxq1eRl6AK1dXR568Q7CgsLMrOw0\nACKRBMD4+HjiacsFSAH5/M//u7q0EsB3vvOdxsZGrlbm4UkZbJPoP//zP99///0/+MEPdu7c\n+fvf//6aa65pbm5e6aPFCR/YcUBfXx/bYpLijN1f/3qcYRiRUHTrtdemct/LMjU1Y7e7kJLJ\niUgk0tLSBSC7OF8eo8H5otjtzrGxKQB5ZXmXFQSOnkgE09PTAHRaJetNYu8fASDXGyVKFWs4\nIZWKhKQAQCgc9vt8AORSiSC6+dbetg8AZGcUGnQmrs6cPAgBVAoKAE0HAslP2gnEQqFUAoBO\nzH+CRW8wZeUUAuhviO19X5+pEUuEAAYGLq97IlfLKBmFZauxADauKRaQRDAUampfRvpkLQiC\nFFIAAoHAzMxMTMdeHqVc8fKvnzNodawAyvj44g1/PDxJZdeuXbfe+pEuxIkTJwiC6OjoAGA2\nmz//+c9nZ2crFIoNGzYseJ1JpdITJ07s2bOnvr5+cHCwubl5z549C0+99tpru3fvTv0L4QQ+\nsOMAtg5LEERhYaoDOwDX1tdrlBwENBzC2j8QBJFTnHQ1td7eEbvdDe5UTtraehkGIkqcU8ql\nysmsbYaVEEs3zjuN2lgFu8LiCAOX2wdgIV3ndbsZhiEEhEwSVbouHAqykxPrqrZxeOakopBS\nAgGBVI3HitVKAAn6TyxQvX4LALt5emY0hjhGICBMBUYA5imH13v5Mq6BbbMzL9eTp5RLq4ty\nAPQPj05bFx+5NRo1ZeW5IuF852V3d3f0Z46G/KzcZ/71N2KRyGq1/u3f/i29RO6Qhyd53Hvv\nvUePHrXZ5keann/++U2bNlVVVQHYvXt3Z2fnE0888corr5SUlNx9990Lc9wPPfTQ9u3bDx06\nxNbcxsbGNm3axPbYHTlyZKVeS+LwgR0HsFonGRkGuZwz16nLMjAwzsZPd9ywusYmcL4Om5aT\nRXFnw7UUzc2dANQGbXouB0IzNpud7a7Lr8gjOfX8nTKbAUilEoVcCiDg9rANdvqCIrfbx2Z8\nFUoKQDgcpn0+ADKJVCCI6jd0uKfVT3sArFtzxQR2hABKNmnnCwRiaVaLD7Ya6+MiYwegsKRa\nJlcC6G+IbYTClG8QkAQYDA1dPmnHzk9Yra7wsuPDa8vy5FKKAfNhS0tkiSrr5q3VFCVhLZvf\neeedmM4cDVtrN/7bt38E4OzZs9/85jc5X5+HZ3nuuOMOiUTy8ssvAwiHwwcPHvzSl77EPrV7\n9+6nn356165dO3bsePjhh/1+/9jYGPvU5s2b77///rKyMracsn///q997WuvvvpqXV3dbbfd\n1tLSslIvJ0H4wI4DVmQk9rXXTgCQSSQ3bl11f8u7u4eQkjqsxWIbHZ0CUL5hDSeiJK2tvQwD\nsUScw2l3nZf2OhxOACajln3E3j8ChgFgKChyOLwASBEpkQoBeM6n6+TRddcB6Gk9AUCjMuRn\nryItw8uikJ1P2rmTnuNhFU9C/mDIz0EQSZJk5dqNAMbPdfm9MRxeJCZZseKREdtlxYrZwC4c\nZizTy7UGCklyY1URgBm7vbt/ceVkpVJau65UKKQAdHR0hEJRmZvFxL677v3y7v8F4M9//vNv\nfvMbztfn4VkGqVR61113HTx4EMDRo0ddLtdCXfWb3/zm9PT0448/ft99991+++0X3lVXV8d+\nIZPJADzxxBP79u279tprDxw4UFNTc+X+GPOBHQesyEjs66+fAHDDlm2y6LQwUsbMjH1mxg4g\npzTpddjGxg4AlIQqqCpOfLWpKavZbAVQUFUg4K67DgCrzk+SpE6vZh+Z6x8G22Cn1thdNACl\nigIQij1dB4ZhhU7Wrdm6Og0nloIgoFRIkJKkHesYi4SNxRaort1MEEQ4FBpqicE6FkBGYRqA\nYDA8Pra4acQCar1SKBICmJy6jEJKQXZahlEDoPncOdrnX/SaDfXlFCUDEAgEGhoaYjpzlPzr\nt/5589o6AD/60Y8+/PDDZGzBw7MUe/fufeuttxwOx/PPP7979261Wg2ApumtW7c+8MADVqv1\nnnvuOXz48IW3KM6bT5pMJgDr1q1beGrNmjULib0rDj6wS5RAIDAyMoLUjsR2dQ0NDIwDuO36\nHSnbNEoWGuySnbHzeul5lZO15VyonDCtrb0ApHJpNqcxeigcmp2ZAWA0aMnzgRcb2BkKimhf\nKBgI4XyDnTv2dN3kSI/TZgGwfs01HB47NShkYgEpAGBP2BZieUQK2byxGEdtdgqlJr+4EsBA\nQ2z1GrlKotIrAAwOXWaIgRAQWpMWwJR5ycHYBbZUFwsEhD8QbGxvX/QCMSUqLJxvG33hhRdi\nOnOUiITC3//kSZMhLRQKfeUrX+HdxnhSyc6dO1Uq1cGDB//yl7/cd9997IPHjh1rbm5uamp6\n9NFHb7nllqXm4aqqqoxG48mTJ9l/RiKRlpaWigpuZBZSDx/YJcrAwABb10hlxu6NNz4AIJfJ\nrtu4KWWbRgmrYKc3pcuUyqRudOZMTygUJgiidB0HYxPDw5Ozs3YAhTVFRJSpsuiwWi2RSAQg\nFuqwAbfHY5kBoC8stju8AAiCkMvFwVDINz8MK4s2XQd0nzkOQCZVlBfXcnjs1EAQUMkpAD5/\nwJ/0pJ0CHA3Gsqyp3QzAbZub7h+K6cbMIiMAl8s3M3OZKFOfqQMwNe3A5SRKNCpFVWE2gL6h\nkaklpigqq+cr9SMjI8PDwzGdOUpMhrTf/+RJkVBotVq/8pWvsANDPDwpQCgUfu5zn/v+97+v\n0Wh27JhPeRgMBoZhfvnLX/b19b366qtf/OIXAfT19V0k+kNR1Le+9a3777//qaee+uCDD/bt\n2zc8PLx///4VeBlcwAd2icI22CG1PXavv/4BgJ1bt1PJl/+NFbbBLtkKdgsqJzml+TKVIsHV\nwuFwW1sPAKVWlZHHrVwIMzU1DUCrUVKS+aHXjxrsCotZoRO5khIICLfLzWrXRekhxtLV8j6A\nmorNQpIDcebUI5eJSVIAYM6VXMtRrozFFsgrKFNpdAD6G2MbodCZVGKpCMDQ4GVGKPQmLYCA\nPzRru7wC37qKfHaK4oPTpyOLjVGYTB/JmP/ud7+L6czRs3lt3Y++8T0ADQ0NP/3pT5O0Cw/P\npezdu9dqte7bt2+hKaWuru6xxx47cOBAfX39k08++Yc//GHXrl333nsvOy1xId/73vceeuih\nn/3sZ7fddtvk5OSJEyfy8vJS/gq4gQ/sEoUN7AwGrVqdaHgRJV1dQyMjZgCfuva61OwYPQ6H\na3rahuRbxHZ1DblcXnBkDtvTM+x20wBK15Vw6AwLYG5uLuD3A8hI1330YP8QALneSMqUXtoP\nQKGiAoGA3+8DoJBJo9SuA2CdHJoxjwDYUH3l1WFZCAJKJQUg4A/6uJhsWAqxSgWOjMVYCIKo\nWrsJwERXL+2KQfqYIAhTvh6Aecrho5d7yZp0LavkvJRp7IUISXJTdTEAm8Nxrm8RLwqjUb+Q\nCT579qzTefkKb3x8bc99n9nxKQBPPvnkm2++maRdeHguYvv27QzDPPLIIxc++OCDD46Njdnt\n9tdff72ysvLQoUMul8tkMtE0feedd1545T/+4z92dnba7fa33367tvbKK4AswAd2iZL6yYkj\nRz4EoJDJr6nfmLJNo6S7e4T9q5lbysE0wzKcPt0BQJuuT8tO1MvV5/OzzrDGbKM2TXfZ62OC\nbTOSSij1BWlFW98QAENRscNx3nBCKXa53QCEJBl9dx2AztPHAIjFkuryVVeUjx6FREwK2U67\nJGraidmPXgxnbXYAKmvqBQKSiUSGmmMboTDlGkCAYTA8YlvmMqFQoDWqcTmZ4gXyM43Z6ToA\nLec63ZeM65IkqdfP/4QzDJO8oT+CIH718M8KsvIYhnnggQc4NKjl4eG5LHxglyhsxi6VkxNH\njpwEcOOWrau2DqtNMyg16uTtYjZbx8etACrqOEjXtbX1BoMhQiAoqS1NfLUL8Xo9bFLElK5b\nSAQGnG6vhbWILXE4vQCkUlE4HAwGAgDkcllMKcOu08cAVJdtpMSrazg6NgioFawvQohewho1\nccTnB2NpB2eDGjKZsqCkEsBA85mYEoEiidCQqQEwOjrLLCt7woqemCejCuwAbKkpEZKCYCh0\nsuXMpc+mpacDEIoEAE6dOrWg1Mo5KoXyf37yBCUS22y2r371q8kQWOHh4VkUPrBLiFAoNDAw\ngBRm7Pr6RgcHxwHccs3qshFjmVewS3K6rrHxHACJXJpXnuhGNptjYGAUQG5Jjkwh4+BwF2A2\nmwGQQlKv+yjMtbGN9gShzS9yuuYNJ9xsuk4olFIxxGczU6PT4wMA6teuuqJ8rMikYqGIRDKN\nKAhSIFLIAPi4cIxdgB2h8NodU/2DMd1oyjcAoOng1PRyQRsb2Hk8fpczqnhUKZfWlOYCGJ6Y\nGJ00X/RsWroRgFgkAhCJRP7rv/4rpjPHRG159Y//vx8AaGho+PnPf568jXh4eC5EuNIHiBOt\nVrvSRwCA3t7eQCAAYM2aUmW8Q6AEQUgkEoqiorn4vfdaAMik0luuvV66yhTsXC73xIQVQFFl\n+TIvZ6F/LMqXfBFOp5tVVClfXy2RJvgdYE6f7mQNxEpqS0UiLn8d/H7/7OwsgIw0vUgoAiAg\nCJBCR/8oAKUxLURQDBMBIKQYHx0CoFYoYhKi62x+F4BYRNVWrV4Fu+gPplZIZuc8gWCI9gVl\n0qRkoym1Kuj2+h1eDgefcwvL1Bq9wz472HQmq7yUYDWXo0CbrpYqJbTLNzIym5WtX+oyY5YR\nBAGGmba4tbqo3mTWlRcOjlnsbu/JM615WdnCCzxUMjMyANB0QKoR0fbg8ePHH3jgAY1GE92R\nL2bhf+6CHthFfPtL3zjRcuqVd9947LHHbr/99u3bt8e30apCIBAIhULJKnv7jRs+mXr1caUG\ndsmrIMREa+t8Y01enokVqogDqVQaDAaj/O165ZX3AFy/cTMpELAx5eqhvb2XrUZlFRcEg0u+\nHJIUsGJCy1+N/Z8AACAASURBVFyzDKdOtYfDEZIkS2rLQ6GE/OMHB8csFhuA0toSAUksb9wU\nKxMTEwzDEASRbtBGGEZAEGCYCDDbOwDAUFRqm3MDEImFfr8XACUWi0UixFLO62h6B0B1+SaJ\nWBrTjamAmP8v+oNJJUKRiAwGw3aXWyrRJSNQFasVmABt9zCRy7g+xERlzcaT778+0dVLO11S\nlZIJR7t4RoFhsH182uJyu2m5dPHPOSKxUKlVuGyuiQlbaUn6otdcBAFsrS177cQZp9vd2N62\nqWbtwlNGowEAwzA1tcUNx7rC4fBvf/vbuGUdSJJkP575/f6lKtG//qd/P93ROmmZ+sIXvvDh\nhx+ysrFXNFKpNBwOr7a337iJRCLxfcbmWbVcqYGd37+4unqK6ejoAKBSKTQaRdyKTRRFhcPh\naG4fGTGzKnE3b78mHF51H7M6OgYAqHQapVYTiSwZJBEE2MBumWuWIhgMsSoneRVFYqkkksCf\n52AwePp0FwCVXpVRkLGoPETcRCLhacs0AINOQwoFTCQMUhgBfLY5enYOgL6g2OqkAVASMJEI\nQRBKhSKmE1gnhywTQwA21l6/ymI6ACCY83FdLHepFNTsnDcYDHtpn2yJQCcRxGoVgHA4HPD4\nxHLOMi4V1XUNJ96MRMJDLW0V125lon7RxiztcMdEJMwMD81UVi45BqTP0LpsrslJR2T5drwL\nMBnURdlpA+OW9p6e4txcrVo1v5TRQBAEwzDZ6aYzqu6Ag3n77bfvvvvutLS0KFdelGAwuFRg\np5QpDvzTf+za/7djY2P79+//7W9/m8hGqwGKokKh0Cr5G8TDcylXamC3Sujr60MKG+zeeusU\nALFItGPz5tTsGBNdXUMA8ss5HkG4kLNn+2jaD6A84bGJtrY+n89PEKjYUM6txAmAact0OBQG\nCFP6x8Zsbb2DAEAQVFp22OwCQJBhAFKJRBijidm5xncAUGLJ2sqtXB17xZFKRPNJO7c3GYEd\npT4/P2H3cBjYyRWq/OKKwd5zg01nKq7ZEv2NQjGpz9Rax2yjo7by8oyl6sM6k264Y9Tu8Pp8\nQYkkWrXCjWuKx6dt/mDog9Mtt++4nv0ZF4mEOp12dtZmt7lq6opPv9MXiUSee+65Bx98MPpj\nx8p19du+ce+Xn3j2/xw6dOjmm2/+7Gc/m7y9eFYPPWeaH/37vZysk/ginyj4wC4hWK2TlI3E\nvv32KQDbNtQpZPLU7Bg9bjc9Pj4NICdpTmIMwzQ1dQBIz83QphkSWWpuztHbOwwgqyhLqeO4\nNsSAmTJPAdCoFVLJx3rF5vqGAahMGd4gAUAgIIQiRiAQKOQxz22cazoKoLZq25U9D3sJaoVk\nZs4TCoY9Xr9cxnFsJxCLhFIqRPtph0edtWRbWxxUrd002HvONWubHhpJK4hB19SUr7eO2fz+\n0JTZkZm1+I8i6z8BBmazvaDAGOXKUol4Q2XBh219Zqu1d3i4tCCffTzNlDY7azObbZ+6c2Pb\n6b6gHceOHfvsZz+bk5PE97Ef/sN33m08ca6v63vf+97WrVszMhJVKeJZ/dgsUyePvLrSp/gk\nwgd28cMwTH9/P1KVsbNYbG1tvQB2bluNDci9vcNsLSavLFkjsQMD47OzDgAVddWJrcQ0NZ1j\nGEZEiYtruD/tjHWG7b/JNF0cOrAjsYbCUtZJTEQxAJRyuYCIrZd/crjbNj0OYFPtDZycefUg\nkQjFYjIQCNtdXrmU4jqXCrFaFaKttJ3LwVgAuQWlCqXG7bIPNrbEFNipdHJ2hGJ4dHapwE6m\nlEoVUtpNT5kd0Qd2AMoKsnpHpmbsrsa29rysTFYgKT0tvauje3pqNiczM6fYMNQyw0SY5557\n7rvf/W70K8cKJRL/n0f+c8eXPmO32/fv3/+nP/1p1Y778CROfX39FbHm1Qof2MXP+Pi4x+NB\nqszEjh5tjEQYUiC4aeu2FGwXK2wdVqXTaIwJ5dKWobHxLAClVpVVnJDTS3//mNVqB1BaWyLk\nXguQmZycAKBQyBTyj0kNe62zfrsTgCI73xYMARBREIlEcUw3t596E4BcpqouX3Ui1YmjVkis\nNk84HHbTPoWM43wkpVZ6p6w0d8ZiLAJCUFlT1/jB2+OdPQGaFseiMm3K0w+dm7BaXV5vUCZb\nvNKqy9BO9NGTUfhPXAgBbKstfeW9Ftrvb2o/u71uA4C09DQAtllnwB/cWrdubPCtoA2nTp3q\n6+srKSmJaf2YqCgqffir3/6nJ3767rvvPvXUU/v27UveXjwrS1NT06uv8rm6FYMP7OKHbbBD\nqkqxbB12w5pqvWZVSL1cBBvY5ZUl6w+D1WpjjdTKNqxJpCXO7/efOdMNQGPUZBRwXw+atdnY\n+eis9IsDXLbBjiAIgdoEhw8ERGJCpYy5qh6JhNl52Pqa64TCK9IfdnkoSiimhAF/yOHyKqQS\nbpN28/MTgVCA9os5beOrqNnY9OHRcCg03Hq2dEsMAbcxRzfcOclEmNHR2fLyxa2K9Rm6ib7J\nmRl3KBhmBf+iRK9RlhdmdQ6Odw8MlRUUGPW69HQjAIZhpqdsayvKX0t7f87hZ8LMM8888+Mf\n/zj6lePgG/d++a/H3jzV3vzII4/ccMMNubm5Sd2OZ2UxGk1r13KQZmtra7JapxJf55MDH9jF\nD9tgJ5VKMjKSlaNawOXyNjScA3DjqkzXeTy+sbEpJFOauKHhHMNATImLqhMazmhp6QoEggRB\nVNRVcD4zATCse5JMJlGrL47Y5voGAaizchx0CICYgkwqEZExR2aDnc1uhw3Alg07OTjyqkSt\nlFj97nA44vTQKkUM2a/LsjA/4bN7uA3sVCptTn7p6FDPUHNrTIGdSEwaMjXW8bnRUVtZmWnR\nEqUhUwcgEmGmp51Z2bF9tFtfkT88afH6AidOn75z505jWho7GDs1NZuTl163puo9a0tgFu3t\n7e3t7TU1NTEtHhMCgeDX//9/bPtfn/J4PPv37z906BBfkL2KWbu2/tdP/jHxdb7+jT1vv/1K\n4ut8cuCdJ+KHNRMrLMxKwXvT+++fZlXfVmcdtqdniJULSVKDncdDd3YOAiiprRCK4i+eTk/P\nDg1NAMgtz5OrF5dUTQSbbY72egFkmS6J9RmGtYhV5xYGAyEAEqlAIY9nCKbtwzcAGHUZJQUJ\n9hquXigRKaGEAJxumluFPlJKkZQYAM2p/wRL1dpNAOxTFtvExZYPy5OepwdA08HpaeeiFyi0\nSjElAhBrNRaAWCSsX1MEYGbO3t3fLxaLdDotgCnzDICNa9eK1AQhBIBnnnkmJmO0OCjMzvvn\nrz0E4MSJE0899VRS9+Lh+WTCB3bxk0qX2HffbQJQkl+Qn5UiaZWY6OxkG+y0SWqwO326MxQK\nEwJB2YaquBeJRMKNjecYBhKZtGhNIYfHO898uk4qlWg1FzsEOCemgm4vAIHWBAAEdDq5IPaP\nBH7a0916AsDWuluu7myHSikBEIlEnB7OrF1ZxBoVANrOvXdZYWmVRCYHMNi8iE/rMqgNColc\nDGBk1LboBQRx3jTWbI/jYEXZ6RlGDYDmc+don59ts5sy2wAYdNqi3FyxFgD6+voaGxvjWD8m\n/v5zX9y8tg7Aj3/8Y/ZXhoeHh0P4wC5+UiZiFwqFjx1rAbBzVabrAHR1DQLIL09Kg10oNC9K\nnF9RKF3CuSgaOjoGnU43gPINZYIYReOiwWab83o9WDRdB7DpOoFQGJYbAUilZHyOcOeajoYC\nfoIgttXdnNh5VztiESmVnE/acSofzVZjkxHYkaSwvHI9gNG2jlCMiuVs0m56yuHzLX4jG9hN\nTTvj0+XeUlMiEBD+QLCxvT09PR3AlHmWfWrzurWkEgIxADz77LOJ6H5Hg0AgeOIHP5OIKZfL\n9dBDDyV1Lx6eTyB8YBcnFotlbm4OKRmJbWrqYCOS1dlg53bTY2PTAHKTU4c9e7bf62VFieOv\nPLrdHtYYIy07zZAVg2BE1DDjE+MApFKJ7pJ0HQBb7wAAeXpmhCAB6HQxC9extJ54HUBpYY1R\nnxn/Ya8QVAoJACYScXq5TNpRGjWAkD8YoLl3hapauxFA0O8f7+iO6ca0HD0IMAzGxuYWvcCQ\noQMQDkWs1niKyBqlvKowG0Df0IhULgNgszn9/iCA8qIijVIp0gLA6Ojo+++/H8f6MVGSV/jd\nr+wH8NZbbx06dCjZ2/HwfKLgA7s4YeuwSEkp9p13mgAYdbqa8vJk7xUHXV2D5xXsuM/YMQzT\n2HgOQHpuhi49/oCssbEjHA6TQrJsQxl3p/uIWZttvrsuw3DpSAYTjtj7RwCI07IBEAShUMXT\ntm+dHB4f7ABwzcZPJ3jgKwKRiJRKxQCcbprDNNIF8xPct9npjKb0jBwAQ6dbY7pRLBHq0tUA\nRkdnF+1zUxtVpJBEvNVYAOsq8uVSigEzZrVifjB2FoCAIDaurSHlICkCwHPPPZcCY/gHPv/3\nNaVVAB5++GGbbfECNA8PTxzwgV2csCOxYrEoJycqW+5EePfdRgA3bN4aq4xtaujuHgKg1uvU\net1lL46V/v7ReVHi+viH9UZHzWazFUBhdREl5d6ngQEzPjYGQCZbPF3nHBkP+f0AhMZcAEo1\nFUd3HYAzJ/4KQCqR19Vcl9CJrxzUCgoAE2Ecbs6SdkmdnwBQUVMPwDI06rYtnntbivQ8HQC3\nOzA7u0iZWEAKdCYNAPNkzPMTLEKS3LimCIA3FGAbNM2TM+xT9dXVJEkKdQwAi8Xy5ptvxrdF\nTIf55Q/+NykgZ2ZmHnnkkWRvx8OzDIcPHyYuoaCgYKXPFSerMVC4ImAb7PLyMsgkdGt9fKNR\nttB5w5ZVagnKzqvmJafBjhV5UenVWUVxSl4Fg8Hm5g4ASo0ytywpullWi4XVrsvOWNxJ3dY7\nBIAUUyJNOgC1Op50XTgUbP3wdQCbam+4ymzElkEoFMhlYgBuLx0Oc5a0Y+cnvHPct9kBKK2o\nFQpFYJihlvaYbtSmq0SUEMDo6OyiF+hMOgDmKQfi7TksyErLMGoIQiCixDg/PwFALpNVl5SQ\nUoiVQgAvvvhiCkzua8ur/+GeLwH44x//+OGHHyZ7Ox6epaivrz/4cerq6nbs2LHS54oTPrCL\nk5SNxLLzsJRYvHX9hmTvFQcOh2diworkTE6YzdbR0SkAFXU1cWvOtbX10rSfIFCxsYLgXrgO\nkUh4YmIcgEIp01yiXcdi6eoFIEnPBkGQpEAhj0dVuPP0MdrtBHDdljsSOO+Vh1JJQQAmAid3\nSTtKo0JySrEAKEpaXFYNYLilNSb1EIIg0nJ1ACYn7aHgIlEsq2bn94dmbfGffHN1sYAgRBIJ\nAPOkdeHxTbW1AATKEEFgbm7ulVdSoRz2g7//ZrYpk2GYhx56iDXi4+FJMV6vNzMz87MXUFBQ\nMDU19Ytf/GKljxYnfGAXJ2wpNgWTE2yD3ZZ162VxDVEmm+7uIfZPV25pEeeLnzp1FgAlkxas\niTNqtNkcvb3DALKKslS6xY04E8RsNgcCQYDIzVo8Xef3eD3jZgDi9FwAShWFuOqwze+9BCA/\nuzQ/OyGJ5isOoUAgl4oBuGjOknYStQpAKBAKeJOSl6qorgfgdbim+gdjutGUZwCBcJgZG1+k\njKsx6QgBAcAcu5rdAlqVorwgSyyVAJgY/yiwy8vKzDQaBRIoDDIAL730ktudlMD3QuRS2b9/\n+0cAent7f/3rXyd7O56rlV27dt16660L/zxx4gRBEB0dHQDMZvPnP//57OxshUKxYcOGBa8z\nqVR64sSJPXv2XORCyzDMAw888MQTT2g0mlS+BA7hA7t4sNvtFosFyc/Yzc0529t7Ady4Wuuw\nrNCJLs2o0nHcYGe3u7q7hwGUra8kyfgsUpimpnMMAxElLq5JysRuKBQwm80AdBqlQra4QcJg\n0xlWrUNszAWgUscjsGwZHxztawewY+ud8R/3ikWlkEAARGB3ezlZUKxVsV/QyUnaZeUWqTR6\nAEPNsY1QSORitV4BYGSxaqxQKNAY1UgssAOwviJPrpQDcLm8Hq9v4fHN62oBhCgvISDcbvdL\nL72UyC5R8qlrbvr0tTsB/OIXvxgdHU3BjjxXH/fee+/Ro0cXpnCef/75TZs2VVVVAdi9e3dn\nZ+cTTzzxyiuvlJSU3H333V7v/NvIQw89tH379ovmsp999lmGYe66664UvwQO4QO7eFgYiU22\niN3x42fC4QhBEDs2b0nqRnHDaojkVXBfh21q6mAYhhSSpesq41uhv39sZsYOoLS2RCiO369i\nGUbHxsPhMEEQ2Uuk6+x2h6N/BIBQrhSptKSQlMdVh2167y8A5FLl5nU3JnLgKxRSQChlYgAe\njy/ERdKOpMRCKQWAnktKYEcQREV1HYCJ7j5/jFotrKCdw047HL5Ln9Vn6gBMTMY5GMsiFonW\nV8//zp5s/Cj0XFtRLqUoQoz0XB2AV155xW5PaKMo+bdvPSKTymia/sEPfpCC7XiuPu644w6J\nRPLyyy8DCIfDBw8e/NKXvsQ+tXv37qeffnrXrl07dux4+OGH/X7/2NgY+9TmzZvvv//+srKP\npBLcbvd3v/vdRx99NPUvgUP4wC4e2MCOJMn8/ORqib33XjOA8sKiDOPiccPKYrM5p6ZmkQSh\nE58v0NbWC6CwuoySxmMVGggEWlt7AGiMmoyCDG6Px+KlvVarFUC6USehFgnXgsHQ9NSUf2IK\ngCQ9F4BaLY6jWdDndbedPAJgW/0t4k/M2MRFKOUSdijc7uRm4oFVs0tSxg5AxZoNBEFEQqGR\ntrMx3ajP0JAiEsDIyCJJO0OmHgDtDTgcCXUc1tWUsoOxJ062hEJh9kGRULRhzRoAHoFDKBT6\n/f4XX3wxkV2iJNuU+Y/3PQDgyJEjR44cScGOPFcZUqn0rrvuOnjwIICjR4+6XK49e/awT33z\nm9+cnp5+/PHH77vvvttvv/3Cu+rq6i5a51e/+pXBYLjhhhtSc+wkwQd28cA22OXkpIvF8WRf\noiQcDh8/fgbAjk2bk7dLIrDzsARBcB7YtbR0BQJBgkBFvKLEra09fn+AIIjyuoq4By+WhRka\nGgLDCIXkolYTACYnJwMud8juwvkGO7U6nrDszIm/Bv0+ghDcuG1XIie+ohEICIWMAuCl/YFg\nOPEF2fkJOjmDsQCUKm12XjGAodNtMd0oIIm0HC2A8fG5S3sKdSYt26M5mVjSjiRJnU4DwO30\nfdjSsvD4ptoaAkQYoYLKbABHjhyZnp5OZKMo+fqeL5fmFQFgcyop2JHnKmPv3r1vvfWWw+F4\n/vnnd+/erVarAdA0vXXr1gceeMBqtd5zzz2HDx++8BbFx62MGIb57//+7y9+8YspPXcS4AO7\neEjNSOyZMz2s4cSqrcN2dg4AMGSa5KpFxNviJhQKswIl2SX5Sm08Ew82m6O/fxRAdkmOQh2/\nC9kyzMzMuF0uADlZaaRwkd8jm83m8XgC49MAQBBUWi5FCSXSmJsFmUik8Z1DAGoqNqUZshI9\n95WMSi5hRwccLg6iMUqrBhAOh30ujr1oF6is2QjAbp6eM0/FdGN6rh5AMBi+VLJORInUOiUS\nkCleICsrDUAkgPcaGjznu470Gm1pQR4Aj8BBUeJQKPT8888nuFE0iEWin337EQAjIyNPPvlk\nCnbkucrYuXOnSqU6ePDgX/7yl/vuu4998NixY83NzU1NTY8++ugtt9yyvDzZiRMnBgYG7rnn\nnpScN4nwgV08sIFdskdi2TqsRqlaWxFnk1mySZKCXUfHgNtNA6jcuDauBZjm5g52ZqKomvtZ\nXQChcJjt8pbLJEbdIpNTgUDAarECCE/NABBpjKREqtbEI1/X1XLMPmMGcPM1dyd06CsfQgCV\nggJA+wKBQKLWCNT5+QmvzZnoyZagsKSKkkgBxCpoJ1dLFRopgOGRRSwZ9FnzkigJHs+UrgfA\nBOALBN764CMZuc21tQDszrnqzeUAjh07NjIykuBe0bBj4/bP7PgUgP/8z/+cmJhIwY48VxNC\nofBzn/vc97//fY1GsyBBZzAYGIb55S9/2dfX9+qrr7LZuL6+vkV1iN54442ioqKsrCv+8zMf\n2MWMx+Nh33SSnbE7duw0gOs2biIFq/F/09TUDOsJUVDBpfoGwzANDWcBGLPTDZnxuHoMDU1a\nrXMASmqLhaL4xmkvw/jYaDAYBIj83IxFDMQYTExMhiMRUkD4JqYBSEx5IAi1Np467Idv/glA\nTmZRZelqFDJMMQoZJRAIAA7GYwmSFCsVSGabnVAoKqlYC2C09WwkHFv5OC3XAGDW5vZ4Lq5L\n6jN0AFwuv9udUMnSZDICYCJACM3tZ6dn5l0oSgsK9GoNgICIlilkDMM8++yziWwUPT/Z/7CE\nktA0zXtR8MTB3r17rVbrvn37iPOSUnV1dY899tiBAwfq6+uffPLJP/zhD7t27br33nsXbTB4\n++23t21bjYbssbIaI4ZVTm9vLxvsJ3UkdnLS2ts7AuD61dpg19Ex32CXW8KlksjCKGvlxng8\nxMLhUGtrNwCVTpVZkJTRFrfbPT1tAZCeppXLFonVZmdnaJoGoAgxQY8XAJWeq1CIRGTMv24j\nPa0Tg50Abr3+iq8OcAJBQKmgAPh8AX8gmOBqbNKOTkDs97JUVm8E4PfSE919Md2YlqMRkAIw\niyTt9Jk6Ttrs0tP17BdCRhgB88b777P/JAhic+1aAAOD/Vtu2gCgsbGxu7s7kb2iJMeU9eAX\nvgrg8OHDJ0+eTMGOPFcT27dvZxjmok8FDz744NjYmN1uf/311ysrKw8dOuRyuUwmE03Td975\nMfWohoaGp556KqUnTg58YBczbB1WICAKC5OYsGXTdaRAcG39xuTtkgis0ElGQS61hH5bfLDp\nOpVOnV2cH8ft584NeL0+gkDp+rJkzEwwYAYHBwBGLBJlZxgvvcDn81tnZgAo5PLQpAUAIRRS\nxky1Jp7v0vHX/gBAr03fVHtlT2lxiEImJkkBgDlXokk7iVYNgHZ6IyEOpjEWJT0jR2/MADDc\nEtsIBSkkDVkaAGOjtsjHJygoKaXQyJFwYKdRKymKApBnNALoGRoeGJmXkVu/pkosEjFgIAtp\ndCoATz/9dCJ7Rc/+//VV1ovi4YcfjkQ4M5Hj4fnkwAd2McMGdpmZadIk2Mkv8P77LQBqyis0\nKlXydombSITp7h4CkF/OZR12YsIy7yFWH4+HmMdDd3UNAUjPNWkMSRENHx8bY7NxeTkm8pIM\nHMNgcnKSiTAkSWalG2d6BgFQxhyhSKRSxSykNzncPdDRCOBT1++JV6L5KoQgoFJSAAL+IO1P\nKGkn1s7/kHiTVo0FUL5mAwBz74AvRiMHVtDO7w9NT108QsGKnkwmJlMMgjCZ9ACEjEinkgN4\n4/332XKEVCKpragA0NrWeuOd1wLo7Ow8ffp0QttFh1Qi/fH93wdw9uzZ1Mxt8PBcZfCBXcyc\nNxNLYh02EAieOtUO4PqNm5K3SyKMjppdLi+Agoqyy14cPWy6TiKP00OstbU7HA4LSLKklnvB\nZABut3vSbAag16q0mkWGbWesVp/PByAjzYBQxDEyDkBiylNrKCJ2G7H3X30KgEqpvWbTpxM9\n+tWFXCoWikgAjsQ07cQqOSkkkeRqbPma9QIByUQiw2diE7RT6eRSpQTA8CWCdmybncPu9XoT\n8lc1mQwApqYcOzdXA5iwWNrPl1y3rKsFQNO0SEWkZRgAPPPMMzFZ38bNrhtv21xTB+CnP/1p\nCmzNeHiuMvjALmZSoHXS3Nzp9fqwqhvsBgAIhcKsuAqmi2KzOXp6hgGUr6+KI0E1O2sfGZkE\nkF+eRyUhmRqJhAcG+sEwIpEoP8d06QU0Tc/MzgJQKRVqhXJuYIQJRwBQply1JubzTI329bZ9\nCODW6+4Ri+IZp726UcnFAALBkJdOKLIRa9UAvHMubo61GDKZMq+wDMBQjNVYAKY8PQCL1eX1\nfiw3yfpPIOFqrCndAMBicZYXZGan6QC8eeIDVq843WAoyskB0NjYeOvnbgIwPDz8/vk+vKRC\nEMRPH/wngiAsFsvjjz+egh15eK4m+MAuNnw+H6tzkdSM3fHjLQAMWm1VySq1e2cnJ3LLioVC\nziSaGxrOMgyEYlHJ+qo4bm9p6WIYUFIqrzKfqyNdyPDIsM/nA4iC3Aw2zXMhDMNMTpoZhhGS\nZIbRCGC2ZwCAUK5SpadJJDHHqe8e/h3DMEqF5oZPpDnsZZEtJO3cCSXtWDU7bzIzdgBYezGn\nZWZ2PDYVD2OOjhAQYDAyPHPh41KFRK6WIfHAzmQAEA4zFov75i01AOaczobW+QB087p1AKam\np5UGaU5hFoBnn302FEpUaCYa1lfW3HPrXQAOHDiwYADFw8MTDXzjTmz09/eHw2EkWcSObbC7\npn5jHPW7FBAMhnp7h8Fpg53HQ5892w+guKZcTMWcoBofn7JYbAAKq4uWl6CMj1nbLKtLl2bQ\naNTySy+wWKysXH5mWpqQJAFYuwcBUKZ8jTbmsYnxgY7etg8AfHrHvRTF5WzK1YRaQc3OeYPB\nsIf2y6VxJjXZ+YlQIBjw+MTyZHXN5hdVSmVy2usZamnXZ8cwdCUSk4ZMjXV8bmTUVlaecaHw\nkT5T73F4E8/YEQTBMMzkpL1uQ15JbkbfqPm9xoYN1VUSiqooLtKqVHNO56lTJ2/fc/OBn/6P\nxWI5cuTIbbfdlsimUfJP//DQ4XffoH30T37yk9/85jcp2JGHW9ramr7+jT2crJP4Ip8o+MAu\nNtg6LJIZ2JnNM/39Y1jFDXZ9faN+fxBAPncKdk1NHaFQmBAIKupj9hBjmMiZMz0AFGpFViH3\nEid+v29ocBCAVELl5iwirUd76VmbDYBGpVQq5AC81ln/nB2ALLNApY455njr4AEAGpXhhm13\nJXj4qxipRCQWkYFg2OH2yiVUfDPQ1Pn5CY/NlbzAjiTJ0sr1bc3HR1vPrfv0TlIYwxuvqcBg\nHZ9j+BxFsQAAIABJREFURygyMj8yYjFk6ke7xubsXp8vKJHEmTgXU2KtRmWbc5jNDgA3b6nu\nH53y0PTxpuad27cJCGLT2rVvHD/e3d3zqU9/urS6uPds/wsvvHDDDTdI43Jwjoms9Iz77/3y\nv//Prw4dOvTVr3513bp1yd6Rh1us1qm3335lpU/xSYQP7GKDnZxIT9crlbIkbcGm60iBYPuG\n+iRtkSBsg51ULkvP5Ubwxe8PnD7dBaCgskimjNkBbGBgnPVeK64t5lziJBIJ9/T2hsNhASEo\nLswWXJJDZRhm0jwJhhGJhOmGedNYS1c/AEJAppUVCwSxHamn9cRoXzuAu27Zx3fXLY9KKZmx\neULBsJv2KRbTFLwsArFQrJAH3B6vzaXNWUS/hisqqje0NR8P+v0TnT25NTE0G7AjFLTLNzQ8\nc2FgN99mx2Bywl5YFP/JMzIMtjmHedIOwKRXry3Lbe0Z+aClZcu6WoVcXl9T/c7Jk4FQqOHU\nqTv23PyLcwMOh+Pw4cMLDutJZf8X/uGpw3+02GYeeeSRi1w+eVYz9fXc//FKxppXK3yPXWyk\nYHKCbbBbtUInAM6dGwCQX1FGENz8/LS29vj9AYKIx0MsHA63t/cC0KRpDYsJyyUGMzg4SHu9\nAAryMqSSRSRLLNYZvz8AIMNoFJ6vAk+e7QUgNmTq02Pzug2Hgm+++GsAmen512zkh2Evg4QS\niikhAIeLRrzzmpROA8BrS+L8BABjWpYhLRNxjVBkFOgBWGc+5kIhU0qlSk7a7IwAxifmF7lh\nYxUpEASCwXcbGgFIJZJ1VZUATp8+bczU126pBnD48GGHIzGllehQyOTf/7tvAvjwww+PHDmS\ngh15eK4C+IxdbCTbJTYcDrNCJ6tWl9jtpoeHJwDkV3IjdBKJRJqaOgBkFeeqDbpYb+/uHqJp\nP0EgGRInExOTs7OzANLTdHrdInE27fOxF2hUSqV8vvcu5A96xyYAqPOLKCq2hr/Gdw7ZpscB\n7PnM1wWr0kputaFWSqx+dzgcdnpolSKe+qBEp3aNTvic3nAofOlYDIdUVNcdP/rydP+Q1+GU\nqWP42JaWoxvuMEfCkeHh2aqqj5oNjFm60W7vhDmxwC7DAMDj8TtdPpVSolXK66oKG872N7a3\nb9+wQatWbV23rrHtrM/vb2k58+nP3dTe2EHT9AsvvPB3f/d3iewbJV/4zD2/+dP/9Az3/8u/\n/MtNN92UjA5aHs5pamp69dVXV/oUn1z4wC4GgsHg0NAQkpmxO326m9WHW7WBXWfnQCTCgDuL\n2LNn+51ODxBPui4QCLDzucasNLUuttzYZbHZZsfHxwEolbLcrEVa6xgG5kkzGEZIkgtFWAAj\nbd2IRABkrKmMaUe3Y/bYK78HUFO+qbp8lf4ArDYoESmRCH2+kNNNK+XSOMaNqPM/OV6bS5mW\nFF1rlrKqdR+899dIODzSerbiuhgsKUkhaczWTI/YRkZs5eUfKWPrM/Wj3eM2myeRNrsM0/9j\n78wDoyrv9f+cM/uS2TJJJpnJZE9IIBAgYQ0KKIuKCogW0LpQbWurrdbaq7Xa3qttr15bK9ra\netX2qj+pFkEUq+xEgbCGkH1PJnsymclMZl/OnN8fByJglpnJZAh6Pv8Ak3Pe9z1JSJ75Ls/3\nfJy7p9siy9EAuHZu7tnaNq/ff7C09LbVq+JiY7NSUxra2kpLSxcsmL9wedGRvcf37Nlzyy23\n6HSTaA7AwOVw/vOhJzb+/P76+vpt27bdddddk70jS6RIUGsK8wsnvs7pytN9A70TX+fbAyvs\nQqCpqcnn82Eyhd2RI2cBKGSy/Jxpk7TFBGF6V1XxcQp17MRXo2maiVDG6TRx2sRQb6+pafX5\nfASBjJkZEz/MxdjstqamZoAW8HlZaboR5cKAaeCCHfFXSVhcyMNypbL41NBqEPe8/2ePy8Hl\n8jatfWhCp/+WIZcK3W57IBAYcjjl0pCLX3lSCYfPo7w+p3loUoWdSCRNy8htbqhqPXMuJGEH\nIDEtrs9g9vmori6LXn8+sM3MnwCNnh5LWlqYdQhKhUwgEHg8nu5ua06OBkCMWLhgZuYXZXVn\nq2uunVekVqkWzZnT0NZmMptqa+tWrlt6qqTM4/G+++67TzzxRHibhsTq4usWzZ537OzJ559/\n/rbbbotC3wZLRCjML3z3j+9NfJ27frb500Ns/C8E2FxPCDQ2nh/jPXkmdoywW1JYxJmqaTim\ncyJtemR0Z2Nju8lkBTB93sxQ73W7PfX1rQA0KYkSWcgtF2PgdDnr6+tpOsDhcnKy9NyR0nNe\nj3dgYACATCqRSb/a3ebweto7AKgyQotoNlUerzq5H8ANSzdq4iaxiPObB4/HEYl4AIbsrvCm\ni54vsxuY3DI7ALn5RQBsJvNAe2dIN0rkohiVGEBL61eGdmLZ+TK7ru4JVLwRRKJGDaDrolq9\nJbNzRHxeAPS+Y8cAZKemxKliARwrPSaVS5feVAzgyJEjzc3N4e8bCv/10JMEQfT29v7tb3+L\nzo4sLFcvU1Q9TE2Ylli1WqFQxEzG+iaTtba2BcCSwina/tPbO2A0DgJIj1CB3bFj5wDI1Upt\nZkqo99bUNPv9FEEQ6fmRDNd5PO662lrK7ycJMicjWSgYecZrd08PHaA5JMnYEQ/TVNUMlxNA\nUih5WI/L8ck7LwJIUOtuXvHdCRz/W4pcKgRAB2ir3RXG7UKVHIDTYp/skVkpGTliSQyA1jPl\nod6bmBYHwGpxmc3O4RfjtCoAXV0TKrNLTIzDpU0YQgF/UUE2gKr6xp5+IwiieO5sAK2trT3d\n3UtvWiyVSWia/vvf/z6RfYOncHrBmmtXAXj11VfNZnN0NmVhuUphhV0ITHbnxNGj5YEATRBE\n8VQVdkweluRw9NMyJ76awdDd3W0EMH3+rFBtSlwud0NDOwBtRpJIErHUjMfrrqmp9fl8BEFk\npuuko6w8OGhxOp0AEtSx3Is8yVwev7muGQDJ5campwe/794P/jxk7icI8r7vPM7jjiwlWcaA\nyyXFYj4Au9NFUSEH7YQqJYAAFXBZJjTHYlxIgpMzfQ6A9soav9c37vUXE5uk4Am4AFpajRe9\nGAvAbLa73aGtdjGMsOvvt/l81PCLC2dlS0QCGvSBY0cBFOTlSUViAEePHhWIBCvXLQNw9uzZ\nM2fOhL1vSDz94M+5HI7Vat26dWt0dmRhuUphhV0IMMIuK0s/SeszRifZqWkJsepxL74iVFY2\nAkhKTxEII6ClSksrAIhl0tTckENu1dXNFEURJJmWF4J+GhtG1Xm9HhBERqp2xAkTACg/1d/f\nD0AiEipkl3RstHdZ6J4uAMq0dJIXbDF7w7mjZV/uBrB80a056SF3kLAwyGIEIEEHYLU7x7/6\nUgSKGIJDAnAMTLqLR15+IQC/x9tZXRfSjSRJJKaqAXR3Wdyu8zJOrb1QZjcB0xNG2NE0zdgU\nMwh43OLZOQBqm1u7evp4XO68gpkAKquqrFbrwuuKYuOVAF5//fXJDnMyZKdkbL5pA4A33nij\nu7s7CjuysFylsMIuWPx+f1NTEyatwI6maSYvOWXzsH4/VVPTCiAjLwIFdj09xtbWLgB5RfkE\nGZqFgcvlYoZzaDO0grBsaUdcs6a6xuvxgCAyUpJUylGz7b19vRRFESSRGB9/cVOFx+fv6ujD\noBlA/LTcIPcdGjTu+sfzADTxyXes+cGEnuHbDZckJSImaOcOOWhHksLzQ2MnvcxOpdYkJCYD\naC0LORurSVMTJGgarRcq7Ybd7CaSjU2Ij2W8dS5bZP6MTKlIQIPeX3oUwMKCAi6HQ1FU6bFj\nHC7nxjtWAGhoaDh06FDYW4fEE/c/IhQIPR7Piy++GJ0dWViuRlhhFywGg8Hr9WLSWmJra1sH\nBiwApmwetrGxnXHijUjnxJdfltE0BGJB5qyQV6uubr0Qrkud+EkAOBz26poar9dLEERGatKI\nlnXnr3Q6rdYhAGqFQsC/JGfa3mUN9PSApkEQ6uygahADlH/7337jtFm4HN4PNv+Kz5+skVbf\nEuRSIUECNCy2kDOqwlglAIdpaBLOdTlMC0V/a7vDHJoa4wm4aq0KQJvBNCxez5fZdQ+GfR4O\nlxMfrwLQfaklHo/LWTI3F0B9a1tHd7dELJ6TNx3A6dOnPW737AX5urQkAG+99Zbf7w979+BJ\nitc8sOG7ALZt2xa1vg2WbwkOh+ORRx5JTk5WKpU33nhjTU3NlT5R+LDCLliYzglMWo3d0aPl\nAIQCwbyZUzQZV1HRCEAslSSmTvQzYDZbq6ubAOTMmcHhhua/5Xa7m5rOV9cJRBFQQharpba2\nlvL7CILITNPFKkdVdTSN3p4eAHweT628xEvZ46M6ei3o7QYQo9EI5UGZ6n3+z1c6mioB3HHz\nD1OTI9OP8m2GJAmpWADA4fT4/NS4118MI+woH+Wy2iflcBeRlVvA5XJB02FModBmxAHweqmO\n9vNKTq1VAzAPOl0ub9hHYrKxXw/7FeWly8RCAPuOlgIoLpxLgHB7PCdPngRJ3HLnDQC6urr2\n7t0b9tYh8ejdD8ZIpH6///nnn4/OjizfEh5++OF//etff/zjH3fu3ElR1KpVq2y2SY/fTxKs\nsAsWpsBOqZTFxkbYCJfhyJFyAPNmzrosDjR1YArsIjJJ7MiRMpoGl8fLmRPC0EyGmpqWC+G6\ntAkeA0B/f29DfT1FURwOmZOpVyrGsk0xmb6aHnbZBFhDlyXgp9DfCyAuOA/CMyUfnzq0E8D8\n2ctXLLkt/GdguQiZRECQBBBy0E6glIMkADhMk/7TXCgUpWflA2g9WxFqeZpELpKrpQCaW/qZ\n2rbhMrvuCZieJCXGA+jutjD248MMB+2a2g1tXV1qlTI3MwNAaWkpRVHT8rNyZ2UDeP/99xlP\nx8lGJVc+tPkBALt27aquro7CjizfeJxOZyAQ+OCDD5555pnbb7996dKl77zzTmdn55EjR670\n0cKEFXbBwkTsJikP63J5yspqMYXzsFarvb29F0D6jGCrx0bDbneWl9cDyCqYxheGFnLzeDyN\nje0AtGmJEwzX0aANhtbW1jaapvk8Xl52mixmLG9bn89vGjABkEkkUsklV7o9/s5eC4x98PsB\nxOWOb3TSVHn8s/f+BECvzbzvjl9M5EFYLoYgCZlUAMDl8npDaTslOKRQIQfgMEYlGzuzEIDT\nYu1vbg313qSMOAB2u7e31wpAJBVKFRIAnV3h+4AkJcUD8Pmo/v7LH79wejpj+3zwWCmAawoL\nAQzZbOXl5QDW33MzQRAWi2XXrl1h7x4SP970vViFMhAI/P73v4/OjixTn3Xr1q1evXr4n0eO\nHCEIgpH+PT09d955p06nk0qlc+fOHZ51JhKJjhw5snHjxqKiIgAcDod3oeNNIBAQBHH1DnW8\nWs8dfSZV2J04Ucn8Eloyd4oKu8rKRpqmCYJInz7RjOHx45V+P8XhcHKLQjYlrqtrY7zrUiYW\nrvNT/vq62t7ePgBisTBvWqpINE6gtK+vjwoESJJIiLvc4r+10xwI0ERvNwBBjEymGWeERntj\nxQevPUNRfoVM/dMtvxOwpXURRSoWMD+RLbbQPO2EcSoADlM0xtsnp2TFyBQAWs+EnI1VaeSi\nGCGAxsZ+5hUmaNfVFf7JEzVxBEEA6Oy8PBvLJclr5k4D0NTe3tbVpdcmpWl1AI58+SUNOiVD\nN7e4AMBHH300NBQNTSwVSx69+0EAe/bsOX36dBR2ZJn6bNq06cCBA8Meh9u2bZs/f/706dMB\nrF+/vqam5pVXXvnkk0+ysrI2bNjAmFUBePzxx4uLi3fs2EGS5Pe///3f/va3hw4dqqqqeuCB\nB2bMmFFcXHzFnmdisMIuKCiKYsZOTFKBHTNwIiFWnZWaOhnrTxymwC5elyQNrnpsNNxuz5kz\nNQAyZ+aIpCP7iYyGz+errzcA0KRoJuJd53Q5qyqrmB4IpUKWm5PK540zW8/hdDK/tNRK5WUX\nO5ze7n4bAKK/B0Bcbi7GnFfa0VT5/17+hc/rlohiHvv+CypFfNgPwjIiBAEmaOf2eN2hBO1E\nUSyzIwhi2oxCAJ3VdT63J9TbtZnxAAYHnQMDDlwos7NanHZ7yEsxCIT8WJUcQGfXCE0Yc3LT\nLgnazSsEYBwYqK6qAnDr5hs4HNLlcn3wwQfh7R4q99/2XY06AcB///d/R2dHlinOzTffLBQK\nP/74YwAURW3fvv2+++5jPrR+/fq333573bp1y5Yte+qppzweT0dHB/OhBQsWPPTQQzk5OQCe\nfvrpQCCwfPny/Pz87du3v/LKKxJJaL+hpg6ssAuK9vZ2poIkK2tShB3jYLd4biERxgzzyYei\nAow1ccaE87CnT9d4vT6CQP7COaHe29jYzkyGTZ1AM+zAgLG6qsrjcQOENjEuK13LGe9zTtPo\n7ekFwOfxYpXKyz7aZDDRNE1aBwMOJ8YzOmmtK3v3pZ973U6hQPzI/f+tS4yYCR/LxUjEfA6X\nBGAZCqHSTqiUg2Tc7KJRNJ2bX0gQBOX3GyqqQr03TqcUiHgAGhp6Aai1KubtRNdIsixImGzs\niCtcFrTLSUvTqNUADh0+DCAhKW7BsiIAn3/+OWPxONkIBcLH7v0RgJKSkqNHj0ZhR5Ypjkgk\nWrt27fbt2wEcOHDAZrNt3LiR+dCjjz7a19f38ssvb9myZc2aNRffVVhYyPzF4XAUFhYWFxe3\nt7dbrdbXX399zZo1JSUlUX6KSMEKu6AYbomdjFRsf7+ZqRsrvvBNNtVobe2y252YcIGdz+c7\nfboaQGpeZowqtGnrFEXV1rYCiNPGhzcZlgbd1tba3NwcCAQ4HDI7Q6dNDMoIenDQ7PF4AGjU\navJSFWi2Oo2DDgBSWz8ArlCoTBtVq5079vn/+9PjXo9LJJT87IEXMlNDbhxhCRKCgFwqAOD1\n+kPoFeWQIiVTZheNbKxcEZuUnIawsrEkSWiz4gEYjXbLoFMgEshUUkxM2Gm1CQC6uiwj+g1f\nErQjiGvnzwPQ1dVVW1sHYOX6ZXwB3+/3v/deBIa+B8M9t25K1mjBBu1YLrB58+Z9+/ZZrdZt\n27atX79eLpcDcLlcixYtevjhh41G43e+853LKkGlF8Z8f/75521tbf/7v/+bnJwsk8nuv//+\n66+//o033rgCjxEJWGEXFIywk8ulavXlAZuJ88UXZ5jytcVzpqiwY/KwAqFQlzGhyrazZ+ud\nTg9BYOaiuaHe29ra5XZ7gDDDdR6vp6a6uq+vD4BIJJw+LU0hD0odUn7KaBwAIBWLYy7NHdM0\n3dA6AEAg5HrbOwCos7NJzghmy4EAtef9V3e+9TvK75PFKH/xwz9mpc0I4ylYgkcs4nN5HACD\n9hCCdiKmzG5gKDrTFPJmzgNg7uy29hnHvfgyEvRqZsJYXT0TtGPK7CY6f8Lj8fcbRwhYckny\nmjnng3aGru78nJxYhQLAvn37AMgUMdfesAhASUmJwWAI+wzBw+fxfrHlYQDHjx8/fPhwFHZk\nmeKsWLFCJpNt3759586dW7ZsYV4sKSk5ffr0qVOnnnvuuVWrVnFG+vkMgCAIiqIcjq9+Vlit\n1tEunvqwwi4oGGE3ScPESkpOA5iWnqH+WppvinDuXAOA1LyRVUuQUBR14kQlgKQ0vSrh8v6D\nsaHpQE1NCwBlvEqmCrnIz2K1VFZW2e12ALEqed60VKEgWE8Z48AARVEEQTC5p4tp77HanV4A\nidKAu98MID53hCDcoLH7Hy/8pHTv+wC0mrRf/eQvrGVddJBLhQD8PsrhDLbyTKhWAqAoyjk4\n6WV2ADJy8gUCIYCWMyFPoSA5hDYzAUBfv81icTFldna7x2oJrWVkmKSk+Av9EyOH/ebknQ/a\nHThWShLE0nnzALS0tjAjeZatKRZLxTRNv/POO+EdIFQ23nhbmjYFwAsvvBCdHVmmMlwu9/bb\nb3/yyScVCsWyZcuYF9VqNU3TW7dubWxs3L179z333AOgsbHxsnduK1euzMzMvOWWW/bs2XPs\n2LFHH330yy+//OEPf3gFHiMSsMIuKCavJZamaaZzonjuFA3XWa0OZvZXxozxXTzGoLKyyWZz\nAshfNDvUezs6+mw2B8IJ19FdXZ31dfWM/3CqPjEjNWncorphvB7v4OAgAKU8RnCpFvR4/a0d\nZgByhdDf3g6A5HLVWdmX7B0IHN/3r9d+cy/jQlw485pf/eTPcapxemZZIoVIyOXzOAAsdieC\nC8AJFHLm3UsUhsYC4HH5WbkFAAzllQEqNEdlAIlpsTwBBzTq6nriLpTZjdj9EAwikVDF9E90\njGybwiVJZnpsU7uho7t79vQ8pUwGYM+evQCEYuH1t1wD4PTp03V1oY3BDQ8el8sE7U6dOnXg\nwIEo7Mgyxdm8ebPRaLz33nuHq9ULCwtfeuml1157raio6M9//vO77767bt26TZs2MdmbYaRS\n6cGDBzMyMrZs2XLDDTecPXt2//79CxYsuBIPEQFYYTc+gUBg8lpiGxoM/f1mAIunqrAbNjrJ\nyA9f2AUCgdLSCgDxOk18csjKhgnXSRXSWI1q3IuH8VNUfX1DZ2cnQPP5vLyc1Hh1aIV9vf19\nNE1zSDJOFXvZh+pbB/xUgCCJ1DS5uaoJgDorm3ORuXRT1Ym/PXv/nvdf8XncAoHo7g0/+/Hd\n/ykUjGWVxxJx5DIhAMpPDTmCi2ORhECtBODoj4awA5A7swiAx+HsqmsM9V6SQ+qyNAD6+mxD\ndp8iXo7R423BoE2KB9Ax+gqFeWlyiQjAwePHSZJcOn8+gMamRoOhDUDxyvkKlQxA1IJ2t69e\nm6lPA8AOomABUFxcTNP0b37zm4tffOSRRzo6OiwWy2effZaXl7djxw6bzabRaFwu16233jp8\nmVarffvtt7u6uqxW6+HDh6+99tponz5ysMJufNrb210uFyYnFXv06DkAAj6/KD9kU7foUFHR\nACBOmxSjCN/opLa2dXBwCMCMhQWh3tvXZzKZLABSc9OAYINtLpezuqrSYhkEII+R5E9Lk4hD\ns4tzOJ12mx2AWqXiXpqDNpod/SY7AK1WSjgdzh4jLvgS03SgvvzIm7978P/96fG+jiYAedlz\n/+uxN5cvunVqtjx/sxHwuUIBF8CQ3RVk1Zw4LhaA3TwURggtDDSJ+li1BkDr6ZCzsQA0qecr\n7apruuO0agDd3ZYgw5NfJykpgVkhMMoKXA6HCdrVt7Z19vQW5s9ggnZMwIzL561YvwxAdXV1\nWVlZmIcIBS6H8/iWnwA4e/Zs1MaasbBMcVhhNz7DaYXJSMUyI2IL82cKBYKILz5xho1OMmeG\nH66jaZoJ16kSYhPTQhbHtbUtAARiYYI+IchbBgfN1dXVbrcbIJI06uxMPYcbcnVgf28fAD6P\np7pU0fp8VF1zPwCRiJeojTFVNIKmCQ6Ho4o5/PHftz658Z+v/rKzpRpAglr3o7t/8/gP/hAf\nmxTq7iyRQh4jBBAIBIYczmCuZ2yKQUdjthhD3qwiAL2NzU5ryAa/JIdIyU0EYDY5uBIxALfb\nZxwIs0BQp0sA0z/RN+pJ5ualS0UCAAePH+dyuNctWgSguaWlrbUNwPxr58ZpYgG8++670WlA\n2bDy5uyUDAAvvPBCdHZkYZnisMJufIZbYuPiItzc4PX6GLfeJVN1klhTUwdjdJI5gTxsU1MH\nk26eviDk6jqr1d7d3Q9An6MPMuLV09Pd0NDIjH/NStfqkuLCiJRZLVaX2w0gXh17mcVJXeuA\nx0cRBJGeoQj4vE1HjxiG2ioHK//6X1tKPv67ZaAXQFJCyv0bn/jdf/xf0aylIe/NElF4PA4z\nVmTI7gpQgXGv58dIOAIBAHt/+B2mIZEzfQ7J4dA03VZWEcbt8XqVSMoH0NFnZ97AdHWGOVtM\ne6F/omP0FXhcTvGcaQDqW1q7+vvmFxRcCNrtB0ByyNW3XwegpaWltLQ0vGOEBIfk/OJ7PwFw\n7ty5PXv2RGFHFpYpDivsxmfyWmLLy+tdLg+A4qk6SYzphxVJxNqM1LAXOXasHIAsVqHPCdkt\npb6+labB5XG1GdpxL6ZBt7Q2t7e3A7SAz8vLSVMqYsI4ME2j32gEIBIK5dJLXFFa2zobzpX1\nVn3ZfeJfu55/8s8P3HWm7osue8eQ3QSAx+XPK1j+8x+8+Nzjf19ctJokr9Zu+W8YcqkABOgA\nbbUHVWknilcBsEVL2IlE0vSs6QBazpSHEXEiCCJ1uhaA3eEVKaSYQJkdX8CPi1MBaG8fSxrO\nm54hFQlo0AeOlnI55MolSwC0trU1NTYCmD0/PylFA+C9994LBMZX0hNn3fU35aRmAvif//kf\nNmjHwjLOJCUWXEjFTl4eVimXT8/Kis5PwFApL68HkD59GkGE+R6gra2rq8sIYMaCWcFXyDF4\nPJ6Wli4A2gwtlzvO92ogQDU0NFqtFgBSiTg7Q8cNPf3KYDabPR63yzpIcnGmscJi7B3s7x3s\n7zX3dXucI5iiibjCGXkLZucvLshbJBJerVNovsFwuaREzHc4vDanSyYVcTjjfDOL4mPtHT0e\nm8vr8vLHGyIcEfLy5zXVVTgGLf3NrQmhu0WqNHJ5nNRqtLsoAkB3r5WiqPBcuLTahP5+U0fH\nWNKQx+UsLsjZU1pR09TU3d8/b9bMA0ePDlgs+/bty8zMBEncuOH6N/7wbmdnZ0lJybDxxOTB\nITmPb3n4/md+WlFRsXfv3lWrVk32jiwsUxlW2I3DcEtsZmbkI3bHjp0DUDy3kCTJKSjsTCZr\nR0cvgMyZ4bvpMt0hUrk0NS8z1HsbGtoZDzl99jiffL/fV1dXx9hLqpSyjFRtSOnXAOXv72jr\nM7QYO9uMHYbe9lbnoCkQGLV2nsPhJiWl6LRpEpNfHYjJyJ6Zef2KEPZjiToyqdDp8tIBWIYc\nscpx4rhM/wQAe/+gKiXYys6JoE/LjpEpbEOWltPlYQg7AOn5urOH6igeHwDlD/T0DOl04ZTQ\nZNBZAAAgAElEQVSO6LTxZ8/W9PRY/P4AlzuqAp6Xn/nl2Xqn27PvyNF71q+7fvHif376aVd3\nd2VVVX5+ft7caSlZyYbGjn/+859LliwZ913ZxFl3/U3/89Yr9W1NL7744sqVK9lGpanA6crT\nd/1sc0TWmfgi3ypYYTcOBoNhkqbEDg3Zq6ubASwpmhfZlSMFE64jCCJ9xrTwVujq6jcYegBM\nn19AEKHFDwIBqrHRACA+OV4wZkOr1+utra1hvkyaBLVeG5T7scs2ZKitaK+t7Gyo6TU0Ub6R\np8VzOVyVKj4uViOWxPJ4Srk8Pjs7MzNDT5Icj9Xe/M/PASjTJjSQgyUKcEhCKhbY7B6HyxMj\nEfH5Y/3oI/k8gULmsQzZ+yzREXYEQeTmF508uq+zpt7jcglEolBXEMcIE9PUPS0D4HBAUR2d\ng+EKOw0Avz/Q3W3R60d1F+JzOYtnZe07UXWutq7HODAzJ/uLk6e6jf379+3Py8vjcDg3bLj+\nr7//e19f38GDB1euXBnGSUKCQ3J+ft9DD/z6kfLy8v37969Ywb7RuvL0DfR+emj3lT7FtxFW\n2I3D5LXEnjhRRVEBTHlhp81IE0nCTC8yuWaxVJyeH/KsBYOhhylA1OekjHGZx+uuqan1ejwA\nodfFa+LHMbozdrbVnTzacKa0p7n+snIcgiDUsRqVMiFWpUnS6NP06fHqJKVCTZKkZcjd0mGi\nacTI+ck6GXP9UFM7AA6Xo9CPdUKWKYJMInQ4vYEAbbE741WysS8WJag9liF7v5UxcYzC8XJn\nFp06tj/g9xvOVmYvCudnQkpu4kCXxScQwOnsaDcvXDDq2OIxSEyM43I5fj/V3mEeQ9gBmDcz\n60h5vcvj23/06O2rV6+6pvjvH+4wmU2nTp5asHBBdn5GRm5qc23bv/71r+XLl0chaLd+xZoX\n3traaGh58cUXWWF3ZYnayGCWEWGF3TgwnRMKRUzEp8QyedjkxKSUJK1vlHDRFcTj8dXUNGMC\nRie9vQPNzR0AcufNCmMWWV1dGwBZrFweO6p/nsfrrqmu8Xq9AJGWkhg3+pW2QVNFyb7KL/cb\nO9sufj1WlZCdmZ+eNi1Vn63TptvtTpvNRpKENj5h2CHF7fa3dQ3SNPh8TlLSV4LA2tQOQK5P\n4fB4oT4dS/QhSMRIhdYhl9vtdXt8QsFYXzVxvNpS30JRlMM0JFWH7+AYPDKZUp+WbWipbzld\nHp6w43A56TN19WYrnE6Tye5yekXikAsEOVyORhPX2dnb0W7G4rGuFPK4C2dlHzxZXV5Ts3Te\nvKzU1Ey9vqm9/dChg7NnFwiEwhs2XP/qs28Yjca9e/feeOONYTxRaCcnOT+/7+Ef/ObRsrKy\ngwcPLl++fLJ3ZBmNl1566dSpU5Fds6io6Jlnnonsmt9UWGE3DkzEbjJaYocL7CK+ckSorm7y\nev0AssItsDt27BxNQyAWZs0KOZNrNJrNZiuAlJxRP/Mer7umutbr9YIgMlKTYpUjx2DaqstP\nff5Rw5nSYb9ZPl8wI7dwZv78vGlz1LGa4St9Pj8zT1YqkQ6rOsofaGo3UVSA5BDJetlw2b3L\naPFa7ABUaeHERViuCFIx3+70UP6AZcihiRtrDIlAKeMI+JTHa+8bjI6wA5A3c76hpd7a1z/Q\n3qXWj98G/nXUSYq+lHjGl7u6pruwMDWMRXS6hM7O3vZRBotdzOKCnGPlDW6v79CJ47ffcMMN\n11776jvvOpzOQ4cPr169Oj03NXtGRkNV84cffrhixQre5L//2bDy5hfefLm5o+3FF19khd0V\n5NSpU7t3s0nYKwYr7MZhklpiu7uNbW3dABbNmRvZlSMFk4eVx6ritOHMNh0YsNTXtwHInTsj\njIAWE64TiATxySNXOHm93tqaOq/XM6qqo+m6U0eP7Hyvp6WBeYHD4c6aMX/BvOtmzpjP549g\nB22xWGiaJklSHnPe4oQO0M0dgx6vnyCQpI0RCL6KO1qbDAA4Ar48OfLt0iyTBEFALhWYLS6v\nz+90ecSisVzBmd7YoV6LZnqUjpeWlScWxzidtpZTZ8ITdgCyi9JO1rTA5ysv75g5K5mZlhsS\nyTrNcZwzGm1Ol1c8ZlOwkM8vnj1t/4nKitq65QsXJMbHzZmRd6aqurS0dF5RkSo2dvWG6xqq\nmk0m0549e9asWRPeEwUPh+Q8du+Pf/Ts46dOnfriiy+uueaayd6RZQw06viiGXMmvs6pqrLe\ngf6Jr/PtgRV2Y0FRVFNTEyYhYsdMYiAJcmFByJ69UYCm6fLyBgCZM8P8nXb0aDlNgyfgZ88N\nOeDncrmYblxdVvKI5U1+yl9XX+fxuAEiXZ/4dVXXVH7y4Htv9hmamX/GquKXLrl5yaLVMtmo\n+XSv1+dwOgHIpFIOSQIADUOP1eZwA1DHSWQxX/2Go+nzBXaq1DSCZM0grybEIr7N4fX5KIvN\nKRYKxnDgkSSo7R09HrvL63DzJaHNowsPDsnJzZ975sThjsra2WtW8cKaRsPjc1WpCebGTp+P\nKimpX3F9yKUUOp0GAE2jo92ck6MZ++LiOdO+LKv1+PyHj5+8bfWqVcXFVfUNHp/v3//+7K7v\n3pWarZ82M6uuonHHjh2rVq2KQtDujtXrnn9zq6G74w9/+AMr7K4sRTPm/PMPb0x8nY2P3f/J\n4c8nvs63B/Z30li0tbV5PB5MirA7ByAvK0spj1KWJyTa2nqY0a5Zs8IRdoODQzU1LQCmzZ3B\n44dc5VNf307TNEGSuswRghaBAFVfX+9yOgGk6TXqS+vqjJ1t7z73i22//yWj6nTatO9v+eXz\nz75z0+pNY6g6AIOWQdA0hySHHYm7+22mQQcAuUIYF3dJl6Kjs9fv9ABQZYbs4cJyxVHECAH4\n/ZTNMZZfsSg+FgQBYKg3TL/fMJhesIAgCL/PZyivCnsRTc75/zhNjf2VVV2h3q6OVYjFIgBt\nhvGzsWIhf3FBDoDy2lqzxSqVSJYtWACgrr6OKVBeddtyAGazOTqzXLkczqN3Pwjg2LFj0Rl9\nwcIy1WCF3VjU1tYyf4msiR1N06WllQAWzo5AmHoyOHu2DgBfIEjJyQrj9tLSCpqmuTzetNDD\ndRRFNTW1A9DoE0YShXRzc7PdZgOgS4qLU39VJuXzuPe987fXf/HD1soyAJoE3YMPPP2fT72+\noGj5uBMgPB6Py+kCII+JIUgCgHHQ0WMcAiCR8BKTpJddb20wABBIpTHx48QzWKYgAgFXKOAC\nsNpd9Gjj7gGCyxWplQBsvWFO6AoDuSJWq88E0HyqLPxFklTkhSLRY0eburpCHKFBEMnJGgAG\ngymYy5fMzeXzuFQgUHLyJIDFc+eolQoAn376KeX3p2Ql58zMBLBjxw6/3x/aScJi800btAmJ\nAP74xz9GYTsWlqkGK+zGgnnHGRsrV41njhASjY3tAwODABZP1QI7Rtilz8jlhG5SYLXaKysb\nAWTPyeWLQk5gtbf3eDxeAPrsEWrXDO3tZrMZQLxamaRRD7/eWnX2rz+///jufwUov0QSs/mO\nh559+o2iOdcGaVRhGbQA4HI5MRIJALPV1dFtBSAUcnV6OXnpGpTXZ2vtBhCblR3iKA2WqYI8\nRgggEAhY7c4xLhMnxAGwm4YoXzQUCcOMgvkALD19ps6Qg20MJJcjS1IBIDhEIEB/vqfKbB5h\nYsoY6JMTAbS3m4IZ0CURCeZNzwBQVl09aB3icDi3XHc+SldSUgJg1frlAEwm0759+0J+mNDh\n83g/veuHAA4fPnz6NOtty/KtgxV2Y8FE7LKyIuxSxhTY8Xm8wvz8yK4cEczmIcZVOLw8bGlp\nBUUFOFzOtLnhPF19vQGALFYeo7o8Sd3f39fb0wNAIZemJJ8Plfm9ns/eeuXd535h6e8lCKJ4\n4erf/+Yf1y9by+EEK0ndbrfL7caFcJ3V5mnrHKRpms8nk1NkX58+ZW3qCFAUCMSyedirFh6P\nIxbzAQw5XYyd5IhINHEAQEc1G5ueNUMsjgHQfDL8oJ0y+fzJOVyO1+PfvbtiaCioObkM+mQN\nAJfL19c3FMz1xbOn8blcKhA4fOIEgMyU1PycbAAlX3xhNBpTs/VZ09MRxaDd3bd+R6OOB/DS\nSy9FYTsWlikFK+zGgonYRXzmBGN0Mmf6DJEgGhXZoXLmTA1jypqRH3LZtc3mqKhoAJA5a5pI\nGrKtsdlsMZksAJK/9jm32Yba2toAiMXCjDQdE4kzdra98eSPT+/ZBZpWx2oe+8nzW+7+uVQa\nWtnioMUKgMflxojFdoenpcNE0zSXS+pT5byRRipZ61oBxCRoBDHjTKZimcrIYgQggQAstlGj\nWRyxkC+TArD1RC8by+FwcmcWAuioqPG5PeEtokyOB0AH6MyCZIIkHA7Pro/LbTZ3kLfrdBom\n2t0WXDZWKhLMm5EBoKymxjI0BGDNsmVCvoCiqJ07d4KmV65bDsBoNB46dCi8JwoJIV/w8J0P\nANi3b19VVfjViiwsVyOssBsVr9fb3NyMSEfs/H7q1KlqTHmjE11mmlh6eW3ZuJw4Uen3UySH\nM33+rDC2ZhxSeAK+Rn+Jy4nX621oaKRpmsflZqcnc0gCQMUX+9785Y8Zw+Eli1b/169ez5sW\ncs2iy+X2XAjX2V2+pnZzIEBzOKQ+VT6iT4TbZHUZBwGoc0KepcEypeCSZIxYAMDh9DCWjSMi\nTowHYO+3RHOa8/RZ85kWitaz58JbQaSS8qUiAF6Xb87yPBCE3ebZufOs2WwP5na+gK/RqAG0\ntQ4EuePi2dl8DoeiqEPHTwCIkUhuuHYJgPb29tLjxzPyUtOnpQLYvn07RY06hTmC3Ld2s1qh\nommaDdqxBIPNZvvxj3+s1+sTExPvuusuiyXEytSpBCvsRqW5uZkZCBHZiF1FRYPD4QKwaPZU\nFHYul6emphVAdkHIiVSHw8UU52XkZ4tCF4Ver9dg6AWgTdde7CFCg25oaPD7fQRBZKXr+Hxu\ngPJ/9ubWXX9+3ufxiITiB+9/+r7v/lwoFIe6IwDmfy+PxyVJbpPBRFEBDofUp8iEgpH7LSx1\nrQA4Ar4qhZ0Pe9UjkwhJkgAwaBu10k6iiQdAUQF7X/R+0MsVscmp2ZhYNlaVEg+gt92ky46f\ne10uE7fbseNse3BBuBR9EoDWtqAuBiAVCeflZ+JCpR2Aovz8TL0ewL69e00DAyvXLQXQ19f3\n5ZdfhvM8ISIWiR/cuAXA7t27GxoaorAjy1XN2rVrDx069Oc///ndd981GAwrVqygg6kwnZKw\nwm5ULpoSG8mWWCYPGyORzJySIZ/KykamCCZrVsgNrSdOVPp8FEGS0xeEE65rauqkKIogoMu6\nxOXE0NbmcNgB6HUaqVTksg29+9x/nN77MYBkXcavf/la0dxrw9gOgMvpYuxsRAJxY5uJogIk\nSSTrZSLRyPV5lJ9i+mFjMzIJbsi+ryxTDYKETCoE4PF4XW7viNfw5VKeRATAGsVsLID82QsA\nDPUP9Le2h7eCUh8HwGVz2waduuyE+Tfkc3gcn4/69LPK48dbAqO3AzPo9YkATCab3R5sOrh4\nds7FlXYgiHUrVwp4PK/Pt3379sy8dH2GDsCHH34YnV+ZD2y4Wx4jCwQCL7/8chS2Y7lKcTqd\nx44dO3jw4Pvvv3/zzTdfd911u3btqquri06vz2TACrtRYYSdRhMrk4VcKzYGjLCbXzCbE/r4\n1Chw5kwNgNjEBFVCfEg3ulzuM2dqAaTPyJLIwmgiphsbDQDUiXFC8VemcSbTQF9fHwC1SpEQ\npzD1dL71q4cNNecAzC9c9tTjW+PjwjToBzBosQAgSW5Hr91PBQiSSNbLxOJRuy5szR2U1wcg\nLnsqinKWMJBK+FweB8CgzYFRxIYkMQGArccczWxsamZejEwBoPnkmfBWUGjjQBIA+tvNABJS\nYpesmyOWCUHj7Nn2HTvOGI1jpWVTUpIA0HSwZXZg2mNnXGiPtQwBUMplNy5dCqCjs/NwyeHr\n114LoKOj4+TJk+E9VEjIpDHf33A3gB07dhgMhijsyHKlWLdu3erVq4f/eeTIEYIgqqurAfT0\n9Nx55506nU4qlc6dO3d41plIJDpy5MjGjRuLiopqamr4fH7+hXZGlUqVk5Ozf//+6D9IRGCF\n3ahcmBIbyQI7p9NdUdEIYFHBVHSwo6hAeXkjgOyCkMN1J09W+3x+giBmLCgIY+uengG73QlA\nl6UbftHjcbe2tgIQiYSpKZquxtq/P/0Tc28XQRDrb7nv+1t+OeJksCBxOJ1erzcQwOBQwO8P\nECSRnBwjkYzljD9Y0wJAGh8vUqnC3pdlqqGQCgH4fZTdOXJvgUQbD4DyU3Zj9LKxJEHmzZwH\noLO6zm0PqjDu8hX4HHlSLIA+w/k6OblauvT2osT0OABGo337h2cOH64fLSCnUMjkMimA1qDL\n7HBR0O7g8fPmwEUz83PT0wEcPnRIohImJicA+PDDD8N4ojD44Xe2iEViv9//yiuvRGdHlivC\npk2bDhw4wJhhAdi2bdv8+fOnT58OYP369TU1Na+88sonn3ySlZW1YcMGp/N86cXjjz9eXFy8\nY8cOnU43XFUPwOFwtLS09PT0XJFnmTissBsVxuskOzuSedjTp2t8Pj+ARXOmorCrr291Ol0I\nvcDO4/GePl0DIC0vU6oIZ5ZGY2M7AJFEFJsYy7xCg25sbKQoiiTJzDRty7lT7zz7c5dtiMfj\n//B7v1pzw51BetSNhtViDdAYchB+f4AgCJ0uRioda0iGy2hx9ZsBxE3Lnci+LFMNoZDLF3AB\nWGxOeqSYHF8u44lFAKxdUc3G5s2aR5KcAEW1nC4PbwWmzG6g2+K/0B3CE3DnrZ4x9/o8vpAH\nmq6t7XnvveMlJfUjNlWkpGoRorCTiATzZ2YCKK+pMVnOe8SsX7VSJpUGaPpfH3yweOU8AA0N\nDRUVFeE9VEjEKpRb1t0JYNu2bVfv72mWcbn55puFQuHHH38MgKKo7du333fffcyH1q9f//bb\nb69bt27ZsmVPPfWUx+Pp6OhgPrRgwYKHHnooJydn+fLlubm5Gzdu3Lt376FDh9avX2+32202\n2xV7nonBCruRcblcTOg+ssPEmEli8bGxmSmpEVw2Upw+XQtAIotJSgstTnnyZJXH4yUITF8Y\nzuhbl8vV2dkHQJupxQXP3/b2dofDASAlWdNSdvT9F57xeTxikfSxh/877KK6Yex2h9vjHbKD\nomiCILS6mJiYcUafDVY3AeAKBao0tm3im4bygl+xxT6y2ZskKQGArdsciEpHJ4NUKk/Png6g\n+dTZ8IrSlCnnTU+Mlw6f0GUnXH/ngsyCZJJDUhRdU9Pz/vund3xYVlHReXEALzUlCUBnp9nn\nC+GpFxfkCHhciqYPlh5nXpGIxd+58UYOQQzZbDUtFUq1AsDOnTvDeKIweGjz9wQ8vtfr/ctf\n/hKdHVmij0gkWrt27fbt2wEcOHDAZrNt3LiR+dCjjz7a19f38ssvb9myZc2aNRffVVhYyPyF\nz+fv2bNHr9dv2rRpy5Yt11xzTXFxsUZztQ4WYoXdyNTX1zP1NNnZkUzFMtbECwvmTDDaNBnQ\nNF1WVgcguyCfIEL4xvB4vCdPVgNImZYhUynGvf7rNDV1MsNhtRnnC+asVmtvTy8AlVLWVVm6\n85XfByi/XK76j8f+mJ01M4wtLoHGoMU6ZAdFgSCIRK1UJhtH1fnd3qGmDgDq7BxiShZHskwE\nHo8jEfMB2Bwu/0h+xRKtBgBFUbZ+azQPll+wEIDTYu2uDaevU6SQCmViAL1tl0fdeALu9EWZ\njLzj8rkA+vqHjh5teued0vc/OH30aFNbmykxMQEARdGGIIbGDiMR8hfOzAJwrqbOaDpfn5eW\nrFu5pBhAm8EQl6oAcPbs2ZaWljAeKlQ06oTNazYAePvtt4dTdSzfPDZv3rxv3z6r1bpt27b1\n69fL5XIALpdr0aJFDz/8sNFo/M53vrNr166Lb5Fe5N6QnJz84Ycfmkym1tbWp556qr29XafT\nXb7HVQIr7EaGKbAjSSI9PWJf2sHBIcanbWo62LW19TDmwKHmYU+dqmbCdTMWhROuo+lAU1MH\ngPjkeGY4rJ/yt7Q0AzSfz7M2nd391z/QgYA6VvPkY39K1qaHscVlDNns5kEfRYEgoEmSKuTj\nF+oN1jQHKIogifhcNg/7zUQWIyRIgMagdYSkJF8u5UvFAKwdxmieSqvPUMXGA2g4HuZoLGVq\nAoA+w8jDwURSwfRFmavuWTTnutw4nRIEAcBssldUdH72WeWn/65lJrh88WV9T481+KDh4oJs\nEZ8XAL3/WOnwi0sKC/OzswF0DrQJRAIAO3bsCO+hQuWnd/2Ay+E4nc7XX389OjuyRJ8VK1bI\nZLLt27fv3Llzy5YtzIslJSWnT58+derUc889t2rVqtF6FgcHB2+44YajR48y/zxz5kxLS8vt\nt98epaNHGlbYjQxTYJecnCgShV+efxnHj1cyFgNTs8CurKwWAF8oSM3NDv4uj8d78mQVAH1O\nujw2nJaC7u5+prBPdyFc19ba5vV6AcLdXv3Zmy/TNB0fp33isZfi45LCWP8yKIo2dA76KQCI\nT5AoFeN/fQNUYLC6GYAyJZUvCdmfj+WqgEMSjPWJy+11e31fv4AJ2g31DVL+6GVjCYLIn7MI\nQH9L25AxhFq3YZgyO4/TazWOWjDE5XGSczSLbilYfe/iOdfl6nIShBIBANAEjycGUF3d8+If\n9v7q6Y/eePNISUlDT884YUuhgL+oIBtAVUNjT/8FKUwQG1avSoqLAwmIvQCOHTvG9LxPNqla\n/W0rbgbw5ptv2sPqRGGZ+nC53Ntvv/3JJ59UKBTLli1jXlSr1TRNb926tbGxcffu3ffccw+A\nxsbGy2oblEqly+V64IEHduzYsWvXrjvuuOPuu+/OmZKWZMHACruRmYzOCabALlWrS4pPGPfi\n6MN0P2Tm53G4wU5ZBXDmTI3b7SUI5C8KU602NLQDEMskynglALPZbDINAHC0V+9/+1WaphPi\ntf/xsz+olHHhrX8xNI2mll6vNwBAqRLGxorGvQXAUFO73+kGEJ8XcrMwy1WEVCzgcElg5KCd\nVJcIgA7Q1u6opvOmzSjkCwSg6aawgnZyrZrD42KkbOzXEYh4yTmaudflrbpn0fV3LpxzXW6i\n/qt3U263r7a25+NPzr34h73PPvfpR7vK2wyjrrlwVrZEJKBB7z1ydPhFHo9397p1MqmUI6UJ\nAoFAgKl2jwKP3v0gQRAWi+Uf//hHdHZkiT6bN282Go333nvvcLFTYWHhSy+99NprrxUVFTHm\nw+vWrdu0adPX31H885//zMvL27JlyxNPPLFp06a33nor6sePGKywGxlG2EW2c+L48UoAC2dP\nxXBdb6+JaV/Inh1CBZvX62PCdcnZaXJ1OOE6h8PV02MEoM3QAoTf72P8TQZbqo6+/zeapuPj\nkn7xyItKhTqMxb+OocNsd3gBiCRkYmJwsTcapnMNAKSaBGmI3n4sVxcEAXmMEIBvJOsTrkQk\nUMgAWDv7o3kqPl+Qm18EoPVshc8zsovyGBAkoUiOA9AbtB0dg0QuTM7RFF53vr5iybrZRatm\naLPiOVwOAIvF+eWXjS+/vP/Z5z45eKjO7bl8JpuAx10yOwdAfWuLoat7+HVZjPTe9euEIgEn\nBgD27dsXnd7DaenZN16zAsBrr73G2JKzfPMoLi6mafo3v/nNxS8+8sgjHR0dFovls88+y8vL\n27Fjh81m02g0Lpfr1ltvHb5Mo9Fs377dYrHU1tY+99xzJHkVq6Or+OiTx+DgYG9vLyLaOdHd\nbTQYejBVC+wYb2EOl5uRH0IN2ZkzNU6nZyLhuubmdpoGQZLatEQAbW1tfr/P1FZ3ZuebdCAQ\nq4p//JEXlZGI1QHo6bWazDYAfCGStDFB3mVr7/EMDgHQTA95xhrLVYdYyDtvfTI0gvWJNDkR\ngN045HWFLLAmQv7sRQRB+D3e1rJwfE9UaQkArAM2V9AzJIaJS0zgCfgAvB6qaOX0W3+47HvP\nrbvp/iV5C9KZdG1f39COHWf+878+/vdnVU7nJZ+WeTMy5RIRgL1fHrn4dU1c3D3r14nUXBDw\ner3vvfdeGA8VBj+750cA+vv7t23bFp0dWViuCKywGwEmXIeICjsmD0sS5MKCcDoMJhtm4ERq\nbrZAGFR2EoDX6ztxohKALjNVERcbxqY0HWhu7gSQkBzP5fMHB80mk8nS3Va+8w3K75fJlI/9\n5IVYVWSCZGazo6fPCoDLhyqWJ+CNZUR8MQNnawGIFAq5PpL90SxTlq+sT2yXW59ItRqmvcDa\nGdUWCqUqTp+WDaCp9HQYridKfTwIAnRQ2djLIDhEoj4RQFfT+dQVl8dJyU1aenvRPb++5cYt\nS1LykgiC8Hj8Bw7U/v73n33xZSNFnT8jj8u5tjAPQGtXZ0NL68XLpmiT7r19LU9KAPj888/L\ny8M06guJuXmzri1aDODVV19lBieysHwjYYXdCDDCjs/npaYmRmpNxuhkWkaGUh6Of++kYrHY\nmL7UnFDysGVltRfCdWFK1e5uo9PpBqDL1Pkpqq2t1WHqO7v9r37veb86TUJkWpJtdk9bp4mm\naQ4XMXJIpcHOiLN39rv6zAA0M2dNPYMalkmBx+NIJOetTy7zbyP5PEmCGsBge1SFHYCZcxcD\nsJnMPfVNod7LE/FlGhWA3rbQsrEMunQ9gN5WE+W/JITJ4ZBpM3Rrf7jsu79ck1OYShCE0+Xd\ntav8jy/tG7ZHmZuXppbHANhz5Mhl5eoZev3atUsB0DT97LPPlpSUhHG2UHn07gcBGAyGjz76\nKArbsbBcEVhhNwKMsMvI0EVqnCtN00yB3aIpWWB35kwtTdMEQQQ/Sczn8zFPpM1MUSaEmSpl\n1KQ4RqKIU7S3G2xm05l/veZ1Ofg8wU9+9GyyLiO8ZS/D4/W3tPXTAZrkEDEKCIR8frEbCrEA\nACAASURBVNDdIQNlNQAEUqkqPQI2KyxXC3KpkCAJAINDjss+JNVrAXjsLod5KJpHSkmbplCq\nATSWhjNlVZUWD8DYaR4eQRE82vRkAH6fv2+UKj1lguy6TQu+8/hq/bREAL291ldePfj5nupA\ngCYJ4voFMwD0GI3lNXWX3bh4wWytLg4ARVF/+tOf3nnnncmexru0aPGcvJkAtm7dGp7nMwvL\n1IcVdiNQU1ODiOZhm5o6jMZBTNUCO6YfNjkzXRwTbOXZmTO1TLAtP6xREwBcLldXVz8AbYbW\nZrP1dnaWbf+ry2oiSfL7W57MzoxMQRtFBZpa+plRsFI5TXIgFYuDvNfe1e/sGQCQWFBAXM2F\ntCyhQpKEXCoE4PZ4nZeW04kTYjkCPoBBQ1RbKAiCmFVYDKC3qdXaH3K8MDbtfEtvbyhWwwxx\nSfECoQBAZ9NY1iSqBNmaB65Zfe9icYyQpul9+2pe+2vJkM2dl6HTxasA7D921P81p5iVNyxg\n/kLT9IcffvjrX//aZAonrBg8TNCutrZ27969k7oRC8uVIgRji28JNE0z7sQRFHZMcIvL5Rbl\nT3hqQqRxOFy1tS0AsucEezafz3/iRBUAXaZepQmzBq6hoZ2ZNqFJSairrz338VtDfR0ANm74\n0ZyC4vDWvAyaRmv7gNvtIwhIZODyIOAHHa6jYTxZBUAglcZmZkXkPCxXEVIJ3+7y+n3U4JBD\nJOR/lYgniJjkJEtT21CXicpPY1pEo8O0/MLjX+zxeFwNx04Wrb0ppHuFcrFIFeMy23rbjLqs\n0P7PEiSRlKZrrW3uaurHqnEuTs/XJabHHXr/ZFt1d0uL8U9/2n/ffYtXLZr55keHB4eGjpef\nLb4wxIkhf1ZGrFpuGrAqYmIsNltlZeVPf/rT733ve8M+ZBHnpmtWZqdkNBiat27dumrVeM/D\nMgFOVZVtfOz+iKwz8UW+VURP2O3atWvPnj02m2327Nk/+MEPJJJR65yefPLJ7373u3l5eVE7\n28V0dnYy7fcR7ZyoAFAwLVcsCrY1IWqUldVSVAChDJwoK6t1OFwEgfzFYQcg6YYGA4A4bdyA\neeDs7neNzdUAVl1/+/XL1oa75uV091msVhcAmZzPEXhBENLRv+suY8jQ5eo3A0iaM5cN1307\nUcqERpODoqghu0Me89V3TkyK1tLURlEBS7sxNj160yT5PEHerHlnT5YYzlbmr1gmlAQbe2aI\nTdN0mm19baYARZOc0CpGdRn61trmPsOA1+NnuobHQCQR3HDfknMl9aWfnrNaXX/5y+G7v7sg\nJzWxvq3n0PETc2fMEAmFwxeTBHnN0tk7tx+22u3rV6385MBBu93+8ssvHzp06P7779frI2k4\ndX5HkvzJXd9/6Lf/cfLkydLS0oULF0Z8CxaG3oH+Tw5/fqVP8W0kSsJu9+7d77zzzgMPPBAb\nG/v222//9re//d3vfvf1y2ia3rt3b3V19WRXWowBk4dF5IQdRQVOnarC1M3D1gJITElWqIPq\nbPX5/Oer6zL0qnCr67q7jXa7A0Bcsvrox++2l30BYO7s4jvWfz+8Bb+Oxerq6xsCIInhc4V+\nmoaQL+AFVzRJB+j+E5UAREqlKiMzUkdiuboQ8LkiEd/l8lodLolYxOWc1/dciUgUp3IZzWZD\nXzSFHYBZcxeXn/qS8vubT5ZNXxZaYFudruk80+j3UcZOc0JKaG3s+kw9gABF97T0p+SOPwCG\nIFCwNCc2SbHn/4563b6//+PojWvym4hel8dz4FjpmuWXROPmL5zx2e5jbrfX5Xb/8aknt/7f\n241thoqKikceeWTp0qV33HFHxGex37F63e/f+FNXX8/WrVtZYTcZFBUVXRVrflOJhrALBAIf\nffTRhg0bmLh3fHz8Qw891NjYmJV1SYbr4MGDr7/+utPpjMKRxoDpnJDJpBpNOBYeX6e6unlo\nyIEpKezcbm9VVSNC8SWORLgODQ1tAIRiUf25I7UHPgSQos9+4N4niQi1nro9/rb2AZqm+Xyu\nIpbncnlBEFJxsOHSwdoWr8UOQFdYxDbDfptRyIRuj5cOwGyxx8fKhl+P0WtdRrN7yOkw2ySq\nYCtTJ06MTJk5bWZjbXnj8VPTliwMKREsiZMLYsQem7O7xRiqsFPEqaSyGPuQraOhLxhhx5Cc\nnbD+4es+/luJc8i1++PKnIK4dmv/iXPnFhTMUqu+8jMXCvnzF84oOVR28PiJ765d+z9PPPHp\n4UPbPt5tdzoPHjxYUlKycOHCm266KTdyY5r5PN6PN37vly8/d+DAgerq6unTp0dqZRaGZ555\n5kof4VtNNHJMPT09/f39w3Jbr9fHx8efO3fussvmzJnz3HPPPfvss1E40hgwwi4nJ8IOdmKh\nsGDqzY+vqGjwev0ApgVXYPdVM+wEwnVut9dg6AXA5buPvfcqHQjIZaqf/uhZPj8yY3kpGi1t\nRooKkCSRpI9xu50ARAIBN7hwHeXxGU9XA5AlJcmTkyNyJJarlOEBspd1UUgS45kWCnNLNEad\nXkxB0RIAHrvDUF4Z6r2xaRoAva0DdCDkhlBdRjKAzobQnlelka9/+LoYlYSm6fpyI+niUoHA\np4e/uOyyJUtnEwTh8Xj2HTlCksTNy5e//tvnblu9SigQUBR15MiRJ5988sEHH3zvvfdaWlpC\nPfmI3LN2k0qupGn6lVdeiciCLCxTh2hE7MxmMwC1+qupUHFxccyLF6NQKBQKxWjjZbq7u63W\n85OnCYKIeHB+GCYVO21aWqS8ThglVDRzlmBU4UKQJHlFBpgw/bDqxIQ4bVCOfWVldUy4bubi\nuWGft7W1KxCgAn73sQ9f93tcXC7/pz96TiGPzNAwAF1dJpfLC0Cjk/kpD03TIAipRIzgYm/G\nM9WU20sQSJ4/P8LROgLEt8dggbjsz6uVGInA4fJd1EVBAABJxOi1lsZWa89AoieFK7jI75oA\nJvOrrEnUJ+nSujtb648eTy8sCOkTHJup6a5o8bp9ph6rWqsMad/kzJS6szXmXqt9yCWVny/v\nu6inBKOdRBYrXffQ8p2vHrSZHY5eip+A+taWJoMhOy11+Jr4eMWM/IzKiqZPD5esW7WKQxLy\nGOmWDbdtuGH1vw8d/vfhEpPF0tPT88EHH3zwwQdKpXLWrFl5eXk5OTl6vZ4bymzrr04ljfnB\nHff+/n9f2rVr19NPP52SEsI7eYIgSJIMb98pCGv78s0jGt+aQ0NDAEQX9Q2IRCKLxRLSIn/5\ny18+//x8GaZSqdy3b18ETziMx+Npbm4GMHNmjlQa3CzRcRb0lpXVAbh23nzR6J0TJMnjBT0L\nIVL4fP5z5+oBTJ83J5homdd7PlyXnJWWkKwNe9+mpnbQdNPpD+2mXoC4586fZaRFLJZpGnQY\nB2wAlCpxjFxgNA4BkIhEXE5Q3+puk2WwugmAOidXrIpMLv4iiKte5oTBVZ7MJgCVXNQ/YKco\nymp3qGTnfyzI05ItTa10gB409CdMS77oenKyEyFzFyzt3t461D/Q29Cszc0O/kZFkpovFnid\nnp5Wo0Yf2rd3ak4aQRA0TXc39k9fcLnHJG/MpLBSLdvw8PUf/Gmvw+ry9hMCDf3pocN5WQ9w\nLnp3eP2q+ZX/n70zj4+rrPf/5zmz75PZsu97mjRp0n2nlK6ABQoKWBYVURT0KnoFvYJefy5c\nRRAEkUUUEJRdBNtSSvc2TdMkzb7v60wms+/nnN8fky6kWWaS6RDoef8Fk+ec5znTvCaf+S6f\n75m2kdHRqoaGNUvGO2clEsmdN+687YbrT1bX7Dt2rLyq2uXxjI2NHThw4MCBAwD4fH5SUlJy\ncnJiYmJcXJzBYDAYDFqtVq1Wz/hE37vznj+8/IzT7Xr22WeffPLJsN4NgUAwzef5Zwu/3/9p\nH4EjwkRD2AUVksfjEQqFwVfcbrdeH5kBoJGlsbEx+Fuen58ekRtWVNR7PF4Aa5Yui8gNI0hN\nTbPL5QVQsDgk2+STJ2uD4bpFa2dfxGoymcfGbD31+0w99QDWrfnC2pURcxzw+PxdPUYAYgk/\nPllpsVjAsoQQRWjedSzYwUOnWAYCsTjpk6YMHJczIiFfJhM6nT6b3a2QSoIihi8RyRNiHf3D\no52D+pzEaEbc07MXaHSxZtNw46FjYQk7Qog2K37wTNdAm7FkXV5Yilsql+oT9CP9I91NgxcL\nuxlRauU77rnyjcf2et0+7zCG+KOHKiquWHb+UzE3LyUhUT/Qb3xrz95zwi4Ij6JWlC5aUbrI\n5/dXNzRW1tadaW5q6+qmGSYQCHR1dXV1dU3YTiAQaDQanU6n1+v1en1sbGx8fHxSUlJCQsK5\nSJsuRvvVnbv+8NIzL7zwwk9/+lODITLTCzk4PnWiIexiYmIAmM1mpXK8+thsNhcXF4d1k3vu\nuefWW28N/jchJNyAX4iUl5cH75+SEutwOOZ+w48+OgEgRqnKSEpyuyeOngwiEolpOhD92YVH\njpwGoNZptQmxPt8M08F9vsCRI1UAErPSlDp1IDDLIehNTV3m/vq+hgMAMtIX3nLjN+iIdUCz\n7Z1GmmYIRRJT1H6/3+P1ApBJpCBg2Zl3Mde2uYbMAJKWLOELhYhshoIQgL2kSbr5xbnc3Oci\n0aOWi11uP8uwxjFbnG48ialMT3b0D/s9/rE+Y0ySHgChKBYMLn1Pf8mStfv/8/pIZ/dIV482\nOYzJe9r0+MEzXR6Xd7hnNNxsbFJW2kj/SG/TkM8fCKakKUJ4PAqA/yLn4YtR6eVb7lz13jMH\nGZrxDGH3gcOF2dnKC+b7rVlX8o+/f1jT2NjQ2paeNHlOoCgnuygnG4DX7+/q7evo7e0dHOwb\nGhoymkZGR/1nP0X9fv/w8PDw8MSKQD6fn5ycnJmZmZubW1hYePeNdzz96vNut/uRRx75yU9+\nEuL7IJPJAoGA1zvDZ+ZnBZZlg3+jOT43REPYJScn63S606dPp6WlARgeHh4cHCwtDW+4VkJC\nQkLCeDcWwzAXl+hFhNraWgBJSQaRSEDTM39UzcixY9UAlpcsAgtmSm3BMgwTZYcXmmYqKxsB\n5JYuZEKopK6oqHO5PIRg4cpFsz4pTdMNZ6pbT74BsDFqw1du+6FAwI9URVL/kMXp9ACITVCI\nxHyz2QyWpQglk0hC2cFnc4ycrAWgTEjQZuVEXIwQXGa6jj2r6z7tk0QEQpEYpdhscft8AYfL\nLZeKAYg0apFa6bXYRtsGgsIOiNID5y0oLT+8x+mwNR46tvrWG0O/UJWgEUhFfpe3v21Elzhz\nvvJCUrNTTx886XF5h7tMcWk6AOy52gIWoTx5YqZh7Q1lB/5Zwfrg6Pf9e//HX7r6vNNy2ZK8\n99455HJ53/to/7d23Tr9rfg8XlZaalbaJ2rjLFabyTJmtljNFovZajWNjY1ZrUazeXjUHNRh\ngUCgs7Ozs7Nz3759AAwGw8K0vMq2uueff/7b3/52iOU3LMsyDBP9r+IcHCESDWFHCLn22mtf\ne+215ORkjUbz7LPP5ufn5+TkANi3b5/RaLz55pujcIxQCHZO5OamReRudrurrq4dwIr5NyK2\noaHD6XQDyCubOXTq9frKy4OTYdNmPRkWQHtbZ/3Bv9J+r0Agumnnf8XHRqwDxuHwBl3rFCqx\nRiv1er0+nw+AQiYNpcSLZTHw8SnGT/ME/NRVay7HSjiOmZBKhA6X3+cLjNmcEpEwGKlSZaaO\nVNa6rS6H0SrXq6J2GB6PX7x49bEDHww0ttiMJqU+5N4jQrQZ8UN1XYOdIwvXZAdH4oZIfEqi\nSCzyerw9jYNBYTcLCpZlmActZw63Bpw4Xd68pKgoM3XchVgoFCxbUfTxR6cOlJfffv118jAd\nmAGoVUq1SonJGiGsNnvf0FDv4GB7T29rV2d3/wDNMCMjI1TAD8Bisdx9991//OMfQynO4+CY\n50SpLmTHjh07d+584YUXHn74YZ1O99BDDwVfP3ny5CVqg5gd9fX1iJw1cUVFXTDstzLM8GQU\nCHomK9SqhPS0GRdXVja4XF5CULx6TlZ8bz77K5dtBMCWq+4oKSqJVFU9TbNB1zq+gEpIUgJs\nsLeax+df6HE/DabqRteQCUDi4qUiRQSaZjg+l2iUElBgGdZsG6/TkCXECqQSAMbW/igfpqhk\nhUgkZlm26dCxsC7UZyUA8Lr8xv7wCloIjyRnpwLobhoM68IJrLy2JD5DD8A3hn++s+fCAbKr\n1hYTQrw+30fHwnuoGVEpFQtysresW/utXbc+9j8/+ftjv//JPfdsXrMmMUavFSkB7N27t6Sk\n5Gc/+9klSgdxcESN6BX87ty58+mnn37ppZfuv/9+6dli9gcffPCFF164cJlCofjXv/5VWFgY\ntYOdw2QyjYyMAMjLS4vIDYOTxOL1hvSk+WWHRtNMsFc3t3ThjJ7AXq9vvBk2J12tn32j6J43\nX+xrPQVgUeGG5UuvlIYmuUKht3/M6wsQgoQkFY9PuVzuYJZEGVrPhGvYbKpsAKBKSjLkzTuv\nQY75A19AKaQiAG63z+3xAQCBMjMFgMNodVsiUJUbOkKRuGjRSgBd1XXOs1ZQoaBM0AjlYgD9\nbWGb8KXmpAMw9Y85bZNXDIcCRVGbd60UyURgMdJh33voyLkf6XSq/AXpAD44cHAWZnuhIxGL\nlpYs/NauW1/8v0cevv2bwRedTueTTz65dOnS5557LiKlOBwcnwrcEMzznBsmFqlUbFDYzcOB\nEy0tPVarA0BuacmMiysq6j0eX9C7btY7djaf+fcrTwCI12ds3HhzrEEz4yUhYrW6R812ADFa\nqVwpohnWYXcAEAoEorNd2NMQ8Pr69x1naVYgkaSvWcslYTmmRykX8wU8AGarM9gWokhJ5AkF\nAEZaoh20K16yhs8XsAzTfOh4WBfqMhMADHYYGTo88ZSaEzQ9QVf9QFgXTkCqFG/68goQsAHs\n33N6yGg896M1a4sBDBqNp+vr57JFiFAUuf3qHcvyigCoFAo+j2e1Wh944IGtW7cGzeo5OD5z\ncMLuPEFhJ5GIU1JCcuudHpNprK2tF/MyD3vqVB0AqUKRkpMx/UqPx1deXgcgJTdDpZulGnPY\nLM8/8gOGDkjEiq0b7oo1aEOc2Toj/gDT3TsKQCji6+MVAFwOB8MyIERxQbfdVLAs+j887ne4\nCUHGunX8z4sxFcelgxDEKCUAaJoeszkAEB6lykwFYBs0e+1RnYgolcoLFi4B0HGq2uNwhn6h\nPjsRgN8bGO4JL+0okUviUuIBdNXPVcUm58QuXJcDIOBg//LSu+e6x3IL0nR6NYD3Dxyc4xah\n890bvgzAarf/+gf3r1u2FEBVVdVVV1313HPPRe0MHByRghN25wkW2GVnJ1PhFBRPxfHjtUFH\n7/nWOcGybEVFA4DcRUWEzPALUFFR5/X6CEHRqlk+Bcsyf/39g2OmIUKoTStu18fFamIiVmPe\n12f2B2hCSGKyikeRQCDgdI8PEBOE4Eg8fKzK2W8EkFC6WJEwe8tljssKkZAnkwkBOJwer88P\nQJGWxBPwAAw39UX5MKXL1lM8Hh0INB85EfpVcoNKopYB6G8dCnfHtNxMAH2tI37fXNtCV2wr\nVsUqAIx02P6zfzwhSxGyak0xgMq6uiGjaY5bhMjWpatzk9MAvLF7z9tP/fGpnz2sUii8Xu8D\nDzxwzz33fG6cTTguEzhhd56gsItcHrYGQFZqWqw2YsOyIkJbW9/YmA1AbukM/bAej/fkyToA\nqXmZKu0sw3V7Xn+u4fRRAEsLtyYn5Ccm6SM1imDM4jJbnAA0eqlEJgBgtzuCjsRy2czhOnN9\nm7muHUBMelr8wvBcFTkuc9RySbArdtTqYFlQAr4iIxWApc/oc3iieRKFMiZ/wWIAbeWVXlcY\ndW/6rEQAQ12jgTD1WXpBBgA6QPc2hy0KJ8DjUdvuWE14hGWxf3flwMh4QnbZigVCIZ9l2d2H\nJk6VvURQhPrOdbcCOFFdfbLmzJeu3n7kH68uWVgE4PXXX7/uuuu4jgqOzxCcsBvH7/c3Nzcj\n0p0TK+dZuA5n+2ElMmlaXvb0K8vL67xePyEomm11XUttxfuvPg0gJT6/rGCzVCWSyyOT7vQH\nmJ6+UQAiCV8fKwfg9Xq9Xg8AuUTKm0k72rr6h49WA5DpdOmr13GldRxhQSjEqCQAAn7aYncC\nUKUn8/g8AMONvVE+TNmKKwihAj5fWEE7fW4iADpAD3SEFxWL0WvUuhgAHXURCE/GGJRLtxYB\noN3sC399O9ghK5WKSxfnAdh39JjfHyW7uJvWb47X6AD84W9/A5AYG/ven5/ZtWMHgIqKiquv\nvnpgYE5lhRwcUYMTduO0tbUFnc/y8iIwTKy7e3BgwAhg1fzrnDh1qgFAzqIiatpCN7fbc+pU\nPYC0giylZjbeTnbL6Iu/+xHDMEq5ZuPy2wghSWmxszvzxfT1mQMBhhCSkKSiKMKCtY1bnPBk\n0hm0o6N/pH/fSZaFUC7PumoTJficDPPmiCZiEV8qEQKwO9xen58SChSZqQAs/Sa3NYxyt7mj\nUmtzF5QCaD1R4Z1ivM3FiFUyuUENoK8lbO+SjIIsAN0Ng+H2XkxK6fq8mCQ1gNFux7sf7g++\nuGptMQCbw3H41Km5bxEKQr7gm9d+EcDuQ4dbu7oACAWCx//nxz+991uEkNbW1muvvZbTdhyf\nCThhN04wD0sIiYiJXTBcx+PxlhbP3HYaTTo7B4zGMQC5i2ZIPp44URsM1xWumE3QkWWZFx99\n0Dpm4lG8TStvk4jkIplQrohMuM5idZ9PwkoFAJwOFx20OJHN4ELnGjT17TnK0rRALM7ZvEXA\nNUxwzJYYpZi6ICGrykjhCQQARpqiHbRbsnIDISTg9bUcKQ/9KkNuIgBjv9XtCK+GLKMgE4DX\n5etvD9sw5WIIIdt2rQomZI/tr23p7AKQnBybmh4P4IMotlB8ZcsOhVTGMMwTL7187sXv3nHH\nYz95kKKo7u7uG264wWSKUtkfB8es4YTdOEFhl5CgVypnLs+akaCwW5ibqwxtRk3UqKioByCS\nStILcqdZ5nK5g4G99AU5swvX7f7nc001JwBcsfy6WE0mgNjE2XvgXQhNM719ZgAi8XgSlg4E\nnE4HALFIJBIIprnWNWjq2X2Y8dM8oTB702axKnqjAjg+fxCKaJRnE7I2JyXgq7LTANiGxpxm\nezRPoo7R5xYsAtBy/GToQTtddiIoApYNt1rOkBQnVyoAtNdERsKqdPLFmwoB0C68/Nr7NrsD\nwOo1JQBaOjvbe3oissuMKKXyr2zZAeD1D/4zfIGA27Vjx2M/fpAQ0tbWdvPNN0dkjDgHx6WD\nE3bjBIVdRPKwDMOeOBEssJt3edhgM0T2wgU8/nT5x+PHa/3+AKGo2TXDttad+uC1pwEU5iwu\nzFwLgOJRGoNyVkeeSG//WHAGeTAJC8Bqt7MsS2ayOHH0jfT85zDjo3lCQc6mzVLd/Gpq4fgs\nIhafTcg63V6fX5WRwheLAAzXd0f5JEtWbSSECnh9zYdD9bQTiIWatFgAvc1DbDg5VUJIRmEW\ngI7a3ki5CJdtyFPHKgDYB72vvPsewzAlZdkyuQTRDdp985ovCvkCr8/3zKv/uPD1L+/4ws+/\nex+A6urqXbt2cfbFHPMZTtiN09bWBiA/PwLCrrGxw2KxA1hVtnjud4sgPT1Dw8OjAPIXT5cg\ndjpdp083AMgszJarwlZjDuvYX373I4ZhNGr95lVfCgQIgBi9MthFOEdsdo95zAkgRjfeCet2\nu31eLwC5TMqb2r3F1tXfu/tIMFaXs3mrzGCY+2E4OADEKMc7ZE0WBygSk5cJwGm22waj2kep\njtHnFZYCaD1eEbqnXWxeMgCHxWUeDmN2BYCsBdkA3A7vLMZXTApFUVd+aRkhhKXRXj+4+9Ah\nAZ+/bPkCAIdOVjhdUTIITNDqb1y3CcBf3nzT8clNv/XlL9/z5VsBfPDBB+emYnJwzEM4YTfO\nXXfdtXx5yY4dV8z9VsE8rEQkXlSwYO53iyDBcJ1QLEpfkDfNsmPHzvj9NMWjCleGHa5jWfZv\nj//EajZSFLVrx3cIRMFIgC4uAklPmmF7ekdZlhUKefo4OQCaYWw2OwABny8TT1ktZ27o6N97\nnKUZgVicu2WrTK+f+2E4OIKc65ClA7TZ6lCkJAgVcgBDDd1sWHGwObNk5VUUjxfw+RsOHg3x\nkpgUg0AqAtDTEF4LRVxqglQhA9BSGbHYZGyKtmBFJoCAHYeOna5pbFy55uzo2ONhNPzOkfuu\nu4UQYrXb//bW2xN+9PPv3Ldt/ToAjz/++HvvvRe1I3FwhAUn7Mb55je/+eqrjycnR6BtM+hg\nt7ioSDhtvVf0CRbYZRUt4POnPJjD4aqqagKQtTBPplSEu8W+t1+srzwCYOe2O2WiGL8fAEQS\noVwV0tjW6RkYtARnwsYlKnkUAWC32ViWASFKxRRHZTFysm7o8OlgD2zu9qu5DCxHxBGL+Ocs\ni10ev2ZBFgCvwzPaOVent7BQqTXjgyhOng5xeiyhSLCFor9tJCxDO0JIVlEOgLaanoj0xgZZ\nvm2hRC4CC58Jb+7Z6/Y7c/NSAOw+eAjRUsn5KRmbylYCePrvr/oDn3hPKIp6+uc/y83IYFn2\nO9/5TldXV3SOxMERFpywizA+n7+yshHzz+ikr2846MCSt3i6fthjx2oCAZrH5xWuCLuft6u1\n7t+v/BHAgtzSRfnraZoJFqJoIxGuc7h8RpMdgCpGIleKALg9Ho8naFwnmXRGGUMz/R+fNFU1\nAZBqNPnbr+G6JTguEWqFJDhDdtRiF2o1Er0GwEhTb8Drj+YxlqzYyOcL6ECgYf/hEC+JzUsB\nIXSA7m8zzrz6AnKKcgF4nN6eprANU6ZCJBEs314MgPHCa6FfevtfJWU5APqGhmpbWiK1y4wE\nJ4z1Dw+/vffDCT9SyGSv/eExqVhst9u//vWv+/1R/ffl4AgFTthFmKqqJrfbtVi5FgAAIABJ\nREFUC2DlPBN2wXCdQCTMKiyYao3N5qiqagaQVZwnCbOf1+WwPf/I/YGAX6XU3PWlH1ktlkAA\nLAtCoDXMVU6xLIJJWD6fio1XAKAZ2ma1AeDz+XLpJOHAgNfX8+9D1tYeAKqEhNxt2wWyCEQN\nOTgmhRBoVBIQMAwzanVoCnMB0H56uDFKHZ1B5ArVwrJVADpPn7EZR0O5RBIjV8bFAOhqDM+k\nzZAcp9SoADRVdoZ/0inJW5Iem6oF4BuDw+k63nBKpZYD+OBAlKZQAFi1oKQspwDAky+9dHE+\nvSAr67cP/ghAVVXVI488ErVTcXCECCfsIsyxYzUAYlSq/KysT/ssnyBYYJdZVMAXCqdac/Ro\nNU3TPD5vwbKww3UvP/GQeWSQEOq7X33YYrYBCAQoAHKVTCiea0p6aNjqdvsAxCUqeXwKYK1W\nezAJq1JMIkC9FkfX2/tdQyYAuuycrE2beVM/NQdHRBAKeCqFGIDH4/MQSpmRAsDcPeK2RNUd\no3TZepFIzDJM7Ycfh3hJbEEKAMuwzWoK46iEkNzifADtZ/r8nogFrgjB6h2LCCFsAH4LjJYx\nvgIAyqurx0LLL0eE4ISxupbWA+WTWAPefv311268EsATTzxxKloWyhwcIcIJuwgT7JxYUbKI\nmrpDM/oMDpr6+kYA5JdNqdgsFntNTQuAnJICybS+IRdz8P1Xa07sB3DD1ttjNakej5thEAgw\nAHSxcw3XuT3+wRErAKVKrFSLATidbt/Z6WEC3kTfFuegsevd/T6rAwSJZYvT1qwh1Dz6t+D4\nHKOUi4QiPgCLwynPTOWJhAD6ayIZ0JoRiURWumw9gL6G5tHe/lAu0WXG80QCAN314QXtckvy\nAQR8gY7aCIwXO0dsijanLBUAbSOsH27KQQgJ0PSew0ciuMv0XLNifXpcIoAn/vbypAseffAB\ng1ZL0/R9990XnFrEwTFP4P7gRRKbzVlX1wZgVen8MjoJhuv4AkFm0ZR52CNHqhiG5Qv4C8Ks\nruttb3zrL48CyM8qvmH7V/r7+wFQlBAAj8dT6cPuwLgQlkV3r5llWB6Pik1UAPD7A3aHHYBQ\nIJBfND3M0trd8/5h2uOjeLzM9Rvii2cYsMHBEVm0aimhCBiMOlya/CwAbosjyl0UxUvWyORK\nsGz1f/aFsp7i8wy5SQB6W4bCaqFQ6zTxKfEAGk9GWLwu27aQL+QzDKtiFeCBJ2UB7Dl0mKaZ\nyG40FTyK+tYXvgTgQHl5bfMk5X0alerRBx8A0Nra+thjj0XnVBwcocAJu0hSXl4b/NxZVTYf\nC+wyC/OFItGkC8xma21tG4Dc0kJROFO2PC7n8//3w4Dfp5Crvn/3L/v7+mmapijK62UAqPWK\nOdrXjZhsTqcHgCFBIRDwaIa1WC1gWUIolXJiEtZ4unHg4wqWZgQSSe627THpEXAl5OAICz6P\naFTj4yi8CoVEGwNguLEn4I1eUEfAFy5bswmAqbu3v6E5lEviF6SCkICf7m0Jz5cuv6wQwGDn\niHU0khNy5SpJ6YY8AMP99sLkFJ4SAEYtloMnT0Zwl+nZtfFqrVIN4Im/vTTpgm3r131h40YA\njz/+eHt7e9QOxsExPZywiyTBPGxyXHxyfMKnfZbzDA2NdncPAsibOg97+HAVy7ICkaBg6cKw\nbv73P/7MONhDCLnvKw+JhRKTyQhAIZP7fAHMuR/W66MHh6wAZHJhjEYCsHablQ4EQIhaIeeR\n852wLIvBw6eNFfVgIVap8q6+hjOr4/i0kIgFQfcTp9sryckAIbSfHqiNakI2v2iJVhcHoGbP\nfoaZOcoliZGrErUAOuv6w/IVySnO4/P5LIvmigg/YPH6XJlayrIY7nJuWJ1PBADw9N9fHTKG\n1707ayQi8de33wDgnQ8/7BuaPOb66x98XymX+3y+H/3oR9E5FQfHjHDCLpIEOyfmW7ju1Kl6\nAHw+P6t48jysyWRpaGgHkFdWJJSIQ7/zkT1vVB7ZA+Caq25eUry6s7MLgFAgGLevEwsVc7Ov\n6+k10TRDUSQ+SQnA4XQF/U1kErHogmYIhmb69x0fa+gAII+Lzbv6WtFUtnYcHFFBrZAIBDwA\nNppRZqYCsPabbcPRm0VBEWrlFdsB2E2jbeWVoVwSX5QGwG52mvrHQt9IJBZlFmYDaKroZCI1\nXwwAIBDwl20pBNDdPWqQxBQVJwDwer3f+3+/OtPUFMGNpuGubTslQlGApp/++6uTLojV6R74\n5t0ADhw4wFkWc8wTOGEXMQYGjJ2d/QBWzrsCu3oA6QtyRVPMZjh8+DTLQiAS5i8pCv22/V0t\nbzz3CIDs9AW33XDv0NCI0+kEkJigN5mdALRza5swmZ02uweAPl4uFPE9Hk9w9rZQIFBIz/d2\n0AG6b/dRW0c/gJiUlNxNW/kirgGW41OGkGCxHViG9Wo1ArkUwEBNJx2I3ozRtIy8lPQcAA37\nD/ncnhnXa9NiRQopgI4z4XVCLFhaBMBhcfU2R8zQLkju4jRtvBrAB/+p3XnNEj6fAuBwuR56\n7A9v7d4bBctinUp9y5XbALz09jtWu33SNV+76aYF2dkAHnrooeA3Tw6OTxdO2EWM4MAJilAr\nF4U9ievSYTSOdXUNYOo87MiIuampE0D+0iLBFBV4F+P1uJ5/5Ad+n1cmVdz/jV+xLNvX1wtA\nqZAF/KBpmhBo5pCH9fuZvn4zAIlUoNVJfX6/1WoFy/J4lEp5fnwt7Q/0fnDY0TcMQJedk7Fh\nI+FP4lTMwRF9+HwqRikBEKAZYVYaAL/bN1TbFc0zrLriakKI1+Wu2x+CCRwh8YWpAIa6R51W\nd+i7JGUkq7VqAPXHI1xnRghZcfVCAEajvaamt6wsLfgizTAvvvXWQ48/MWq2RHbHi/n2F26m\nCOVwuf560YSxIDyK+tUPvg+gt7f3T3/606U+DwfHjHDCLmIE87D5WVkx82m8wcmT9SzL8vj8\nnOLJo3HBcJ1IIsorCyNc9+of/3e4v4sQ8u07/ydWl9Dd3RMIBCiKpCXHDwxZAMiUMtEc7Ot6\n+kZpmiEUSUhW0QHaMjbGsiwhRK1U8QgJrqH9gd4PDrkGTQBiFyxIW72GUGTWO3JwRBypRBgs\ntvPwhZLkeADmnhHHyCXXIufQ6eMXFC8D0HbilM1omnF9bEEyj88Dy4ZlX0JAChYXAehuGLSP\nRbKFAkBKXnxitgHA3g8bli5JA8CybJJBA6CqoeFbP/vZ7oOH2YimgCeQmZC8ffkaAM+89ppv\nijkTq8vKtq9fD+APf/jD6GhIvtAcHJcOTthFBpZlg50Tq8vmVx42WGCXlpctusgZBMDgoKml\npRtAwbJiQcgWvkf3vllx6AMA26/84orSDTabLdgzEafXMiysNhfm1jZhHnNarC4AOoOcLyRm\ni4VhGBCiVirPjQ4bV3VDZgBxCxcmL1sOTtRxzD/OFdv5DHq+RAygr7o9mgnZ5Ws2i0QSlmFO\n/3vvjIv5IqE+LxlAd+Og3xuG70l+WSGPz2dZtu5Y5JtDV2wvJgR2u6etfSQ1VQtAIhHddvUa\nPp/ncrufeuWV+3/964bW1ojve457d9wCYHDE+NaeKd/Dh+77toDPt9vtv//97y/dSTg4QoET\ndpGhqalrdNQKYNV8Enajo9b29j5MnYc9cuQ0y0IkleQuWhDiPfs6m19/9jcAstML7rjxOyxL\nd3V1ABAKhQkJuqFhK8uC4vFiZmtf5/czvf1mAGKJQKMTj5nHgm2wKrlcJBgPAdI03bv7aFDV\nxReXJC1eMru9ODguNYRAq5ESioBQJD0VgN/tGzgTvQ5ZiVS+dPVVAIbbOvpCsD5JLE4PtvF2\n1YdkbhxELJNkL8wF0FjeEfBHWLYakjXpRUkAPv64efHiNACt3YNFOSm/v39XfkYigNau7h/9\n3+8eevyJxrZL4jmyPH/h0rxCAH98+ZWLJ4wFyUpN3bVjB4C//OUvfX2RtGvm4AgXTthFhqNH\nqwGIRaLFhWEkNC81FRX1LMtSPF7OoklO1d8/0traC2DB8mKeIKS0qdvleO439/t9XrlUef83\nfs3nCwYHh1wuN4C05DhCqMFhKwC1Tj5r+7qevtFAgCGExCXKx8bGAoEAAIVMJjlb/8cybP/e\n464BI4C4oqLEedaDzMExAT5FadVSAIxUIoiPA2DpNVoHo9chW1S6UqOLBVD9/od0YIY4nFgl\n06THAWg/08fQYaQ4i1eUAPA4vS2VXbM/6xQs21pEKOLx+EdNdplMBOA/R6oTDZpffPum+27d\nqlUrAFTV1//3I//3/V/+et/RYx6PN7IHuO+6WwHUt7Z+fOLEVGvu/9pXJGKxz+f77W9/G9nd\nOTjCghN2kSHYObG4sEg0n2aSBn2J0/KyJbJJRoQdPnwagEQuyVk05TiKC2FZ9pUnHg661t37\nlYdidQler6evrx9AjEoeo5JbLE6Px4c59MOeS8Jq9FKn2z6u6uQymfisCQuLgYOnHD1DAPT5\n+UlLls5uIw6OaCIW8VVKMQAmwcCTSAAMVLdHzbKYR/HWbtwBwGmxNB44OuP6pJIMAF6XL6wu\nV12CITE9CUDNwZaIt6vGGJS5i9MBHD3WXlKcDOBIVbPD7SEg68vyn3rwzq9et16rkgNo7er6\nw1//tusHP/zdcy8crax0ucPoApmG7cvWBieMPfnSK1OtidPr7/riTQD+8Y9/dHZG1baQg+NC\nOGEXAbxe36lTDZhnBXZjY7bW1h4AuaWTjNXq6xvq6OgHsGD5It5F41Yn5eP3Xq469iGAHZt3\nLVu0DkBnZyfD0BTFS02OAxAM1wnFAqU6vFGzQXx+pqfPDEAk4RPKHczAKuQy2QUuLSMVddaW\nbgCajIyU5StnsQsHx6eCQiaSiAUgFJueAiDgC/Sejt6sguTUrOy8YgBNh4/bR2cIFiriYpQJ\nWgAtp7vD6ksoXlUGYGzE1tUQ3szZUFiyqYDHp/x+2uvzE0J8/sBH5XXBHwn4/O1rSp/+yVe/\nc+vWvLRxu7uDJ0/+5plnb/2v7//w14/89a23T1RXz6WF9sIJY2eapsxo33vbLrlUGggEHn30\n0VnvxcExR3gPP/zwp32GsGFZ1h2h72EX4vMZaXo2LkQnT9a9+eZHAP7769/UazThXi4QCBiG\nCcUdPiyOHKmqqWkhhGy//WbBRdZu7713yGp1SBXyldvXE2pmfd/RWP3iow+yLJOfXfLdu35O\nEWp01DgwMAAgKcEQo1IEaKaxeZBlWX2CRhkzrbAjhCIEwIRqlc5uo9vjJ4TIVSwIG6yrk4rP\nGyaPNXaMlNcCUCUkZG648rPVA0vIZ+m0c4cAuMweGTM9sUQkcPsCLI9HCGHtDp/TwxPypTFR\nMtOOS0xtOFMe8PttxtG0yWozLkQkExtb+v3egEwlUekmzu47BwGhKAKAYVkAap26tbbF43I7\nLa78pRmRPb9IInQ7vCM95uFhe2am3mx2DpusW9eWkLNtUxRFpSXor1xWuKokVyYV2Zxum9PN\nsqxpbKyxrf1wxal39+374MDBqvqG9u4e4+io2+sRCYRicageT/kp6c/vftvj87o9nms2bKDp\nSUoJpWKx0+0+XlXd1NS0c+dOtVodsee/lEilc3KS55hvcMLuPLMWdq+9tuf06SatOuaBb3xz\nFn+/L5Gwe+213SaTJTUvu2z96gk/6u4eOHy4CkDp+qXahNgZb2W3jP7hp193uxxqpebn9z8l\nk8gDAX9zcwvD0FKJOCMtgYAMjdhGjFYAqTnxfMG0ZnKTCTvjqGPEaAMgkROhiCWExCgVYuH5\nz1xH3/DA/nKwkGo02Zs3U/yQoozzB07YXQ5M/8SEQCziu9x+yGWwO+DzOU1WRVyMQByN+g2h\nSMznC3o6m53mMYVWo44zTLNYrJKNdY/4nB77mCu9MHGq394Jwo4Qwufzu5o6HBZXUk6cIibC\nckGfGFN3rJ0O0AaDwmRyONyenJT4eH3MhGVKuaQoO2Xr6pL1SwoSDRqRQOB0e9xePwCvzzds\nMrV0dlbU1u4/fuLtDz98d99HJ6prmjs7h0dMXr9PLpUKpyg4FvAFdpfzWENNU3vHbddfd+F3\nzgspzM154fU3PF6vy+XasmVLZN+BSwQn7D5ncMLuPLMWdr/97d+MxrGrVq3esnbdLC6/FMLO\nanW8/PL7LIvlm69MSEuZ8NN//eugzeaUq+TLt66bMVzH0PTTv7h3sKeNR/F+ct9jqUlZALq6\nOu12OyHIzUwONqu2tA97PH6ZUhKXop3hcBcJO4830NlpZFmWL4RcCR6PilGphfzzH69ei733\n/cNMgBFKpTlbtwmmGKExn+GE3eXAjE9MUUQo5Lk8fijkrMkMhnGabDGp+lCi5nPHEJ/U1dbo\nctqNPb0Zi0umb5kSSkWm1gGfx6/QyJSayWPwE4QdAG2stqmywef1uWyenLLUyJ5fIOL73P6h\nLtPYmFOtlnk8frvLu64sf6r1cok4KzluZUnOtesXb1xetCAzKSlWq5RJWMDl8QXP7A8ERi2W\njp7e0w0N+4+feGvP3sOnKjt7+9xeT4xSKf6kZ3tuStqf33/D5/cL+Py1SyZvxpeIxVaHo7ym\nprm5+eabb1Z8FsYbcsLucwYn7M4zO2E3Omr9zW9eBPDVG28qyMqexb6XQtgdPVpdVdVMCNl+\n+5eEn/xs6ujoC3opl21YoYnTz3irt/7yaOWR3QBuv/G+tcu2ALBaLd3d3QDiDBq9NgaAx+tv\nbR8CEJ+ikylmUl2fFHYsi5a2Qb+fJhSUaojEwhiVin/B3zna6+/+98GAy8Pj83I2bxV/RrIb\nE+CE3eVAKE/M51E8HuXxsxCLMGahfQHa61fGhV3CMQsIofSxiQ1nTgZ8Pp/LnZifM81iiVpu\n7hzyu7w2s3OqoN3Fwo5QFMUjPS1dVpMjtSBBporwdzBdUkz9sbaAn9HrFTabe3jUuqY0TyGb\neRepWJho0CzITFpZkrN1dcn1G5euK8svzk3NSDJo1QoexXO6PTTDALA5HO09PcdPV73z4b4z\nTc1eny9Orwt2xckl0q7hgTMdLQ1tbXfddONUsb38zMzn/vm6z+cDsGHDhoi+AZcETth9zuCE\n3XlmJ+w++ujk3r3HATx873flkzWfzsilEHb//Oceo3EsJTtz8Ya1E3707rsH7HaXIka5bMsa\nQmaIE5w69J+3X3wUwMrFV37li98jhNA03dzcFAjQIqEwOyMpKNF6B8zmMRdFUWl5CdSMpW8X\nCDufz9/eOeRyBwDIlSRGI1PJ5NQFf0JYFn17j7lHxkCQsf4KZUJi2O/F/IATdpcDIT6xUMBj\nWdbPE7B+H1xut9UpVkjEymj8cZUrVB6Pe3igZ2xwWJ+eKo+Z7muSUCoytQ34PH65WqrUTlJp\nd7GwA6CN1TeervP7/PYxV25ZWmTPLxDy/d7AYKfJbvcIhTyaZiiKLMpLD/c+FCEKmSTRoMlL\nT1xamHXViqLrNy5ZvSgvKzVOo5B5fH6b0w3AaDZX1tX966P9Pf0Dek2MNiYmPS7p+d1ve7xe\nvVa7uKhw0pvLpdKBkZHqxsbGxsY77rhDPEXSdv7ACbvPGVxX7Fw5dqwaQFZqWpx+5uhXdLDZ\nnI2NXQDyFk/0JW5t7RkYMAIoWlVGyAxjVfs6m1958mEAyQkZ9975UFCa9Pb2BD2i0lPjeRQF\ngAUGhqwAVFo5jx/qb5SfDphMoz29g05XAIBYQiXEq2UX5VhHTtY6eocBJBSXxKSF/fHNwTE/\nUSklEjGfl5IIiQhAf3WHzxWl+fHL125WKNVg2VNv/3t6WztNepzcoAbQVNEZuqcdX8gvW7cU\nQG/zUH/7yNwPPIHidblCEZ9lWZVKCmB/eb07EsYxFKGSYjVXLC74+s4r//Dfdzz70F1337ix\nMCuZEBIIBA6fOnX/r37zP79/jPJj0+IVAJ559VV66m/j3971ZR5FOZ3OF198ce5n4+AIC07Y\nzQmWZY8erQGwZj4NP6isbGAYhhAyweiEZdmgd51Sq04vyJz+Jg6b5c+//K7P65FK5A98+7cS\nsRSAzWYbGhoCYNCpVYrx8KTF6nK7fQC0cSElSQN+v9Fk6u3ttdsdDifLsuDxqdTUGD5votC0\ndfSP1jQDUKekxC/ijIg5Pldo1DKhUEhlpoOi6ADdU9E61VSDyCIUiK7YvJMQ4hgdq/3wwPSL\nU5flAnBa3d2NYTiYLFiyUKFWADj+/pmIP5NEJlq4JgeAyeQgBC6v7+OKhgjvAWhVis0rFv78\nnhv//NOvfWnLSrVCCqCmsemHjzyi56sAdPcPvL//46kuz0hO3nbFegDPPfdcMCfLwRE1OGE3\nJ9raeoeHRzHPHOwqKhoAJGakKdSfMApuaekeGhoFsHBV6fT/9DQdeP6R+0dHBgihvnfX/ybE\npgCgabqjowOAUCBITjzfSzs4ZAEgFAqmdzlhWbhd7uHhkb7+fpvNxjKsw01oBoSQpGQFjzcx\nieW1OAYPVoCFWKVMX7vu8kvrcXzOIQQ6jYwvl5KURABui2Owris6W6dm5OYuKAPQcrTc1DPd\n6DB1sl6VpAXQfKor4At1VhiPz1u6cSWAke7R9jO9cz7vRIrX5QrFApZl5XIxgA+OVLG4VJpY\nq1LctGn5Mz+96+s3XBn0QO7rHFAIpQCefPnlaS68d9eXAQwPD7/11luX6GwcHJPCCbs5ceRI\nFQChQLC0ePJhrNHH4XA3NLQDyCubGK47dOg0ALVek5o3Q7juzef+r6W2AsAtO76xuHhN8MXe\n3h6Pxw0gPSX+XHSNZtgRox2AJlY5lfbyer1m81hff9/wyIjb7QbLUhQFiH0+FoBOL5FJJ9Yg\n0wG6/8NjtC/A4/MzN2zkzad5HhwckYKiiD5GxjPooIkBMNoxFLVRY2uuvFYqV7Ase/Ktf02f\nkE1bXgBCvC5fW3VP6PfPLcnXxusBHP93DR3p6bEiqXDh6mwADocXwMDIWFVTV2S3mICAx9uy\nqviPD37lS1tWCvn8RIkWwKnaur2Hj0x1yeKioqXFCwE89dRT0YnFcnAE4YTdnDhypBpAWWHR\nVJ5G0aeyspGmGULIBGHX0NBhNI4BWLi6DJgu/HV49+sHP3gNwKolV+3cfmfwRavVci4Jq1ad\nL6MeMdkCNA1AE/eJ6CDLsm63x2w29/X1Dw4O2Ww2OkADEAj4WrVao9KarV4AMplAr5+kbnfo\n8GmP2QYgddVqScxEnyoOjs8NfD6l08h46ckQiQD0n26LTrGdWCzZsOkGAHbjaO2HU6YUAcgN\nKn1WPIC26l63I9QZrISQ1VvXAbCbndWHWuZ83oksPFtpJxLxAbx/6HTEt7gYoYB/06blT/74\nq+sLCkWUAMAd//2j0/X1U63/1q23AmhsbDxyZEr9x8ERcThhN3u8Xt+pU/WYZwV2FRV1AOLT\nU5QXzMBgGCYYXNTG6pKz06a5vLmm/PU//xpAZmr+fV8Zb5gIBPzt7e0AhEJhSuInDI0Hh6wA\nZAqJRCoCC5/PZ7XahodHent7h4eHbbbxea8URSlksniDPjE2ViKWdvaaWZbl86nEZOXFZ7A0\ndQbnhunz8zWZMwQXOTg+64gEPJ1GwctKAyF0gO4+2Rxxu/JJSc9ekLegFEDL0ZPGrumicanL\n8wmPogN0U3lH6PdPykxOz88EULmvwWFxzfG0ExBLhUVrcgD4fDSA6uae3iFTZLeYikR9zG++\ne+u2RWUAPF7vtq/e9fbeDyddue2K9cnx8QCeffbZ6JyNgwOcsJsLp041BGfer1k8X0bRO52e\n+vp2APlln0gN19d3jI5aARStWTxNuG64r/O5R+6n6YBGrX/w3t+JhONhyK6uzmD9b2ZaAu+C\nFgeP1z9mcQCQqkQjRmNPb+/AwODY2Jjb7WYYFgCfz1PKZLE6XUp8nDZGLRIKWYZt7x31BWhC\nSGKygn9RaZ1n1Dp0pBqAVKdNWbosEu8KB8d8Ryzma+I1VGoSAI/VNVgbpRHyazbukClULMuW\nv/Ev/9Q1/iKFJKE4A0BPy5B5yBb6/VdvW8fn8wO+wJF3qiJw3E+ycG2OQMQPfkVkWfa9Q5Hf\nYioIIb+9+zaxUAjA5/d/7cEf/3GyejseRX31xp0A9u7d29sb+VpDDo5J4YTd7AnGwPQaTf68\niSpVVTUGAvSEfthz4TpdvCExY+IUinM4rGNP/e+9LodNJBQ/eO/vtDHjE4eMRqPJNAogPlan\nlI+nTX0+n3nM3NTSw7IgBDTldTldwTADRRGJWByjUiXExibFxWli1BKx6JzBV++Q1eH0AoiN\nk01SWuen+/YdZ2iaJxRmrr+SXNQny8HxeUUqEaozkoLFduauEXOfMQqbisWSjdtuIoQ4xyxV\n/94zzcqU0myBVAQWtYdbWCbUijGlRhW0Pumo7Yt4F4VEJipclQ2AplkAB081WhzOyG4xDTFy\n2a71awEQQliW/Z/fP/7Is89dvGzXdTvEIhFN05zvCUfU4ITd7AkW2K1evGT+eM+ePFkPIC4l\nSa07P9ertrZ1bMwGoHjNlK27fp/3T7/8jmmolxDqO1/9WVZaQfB1r9fd1dUJQCaVJMZr7Q7H\n4NBQa1tbW1vb0ODQmNULQCDl8XiUWCRSK5Xxel1yfHysTqtSyIWCieNcjWNOo9kJQKUWa3WT\nltZV+iwOAGmr14iUn4FRPBwcEUQhE6oLs84527ntkbdhv5iUtJyi0pUAOitreuubplpGCXnp\nKwsAWIz2zvowrE9K1y3WxmoBHH6r0u0MtUQvRErW5/CFfJZlCSH+QOA/R2oie//p+cbWzTyK\nYlk2TqcG8Os/PfO751+YsCZGqbxhy2YAL7/8stcb4cfn4JgUTtjNkuHh0dbWHgBr500e1uXy\n1Na2Aci7IA9L0/Thw9UADElxcWlJk17IMMxffvejzqYaALft/PbKxVcGX2dZuqWljaZpiqJk\nEl5ra1tvT8+Y2RxM2fgDoGkAiIvXJMfHx+l1aqVCJBJNJXMdTm/vgBW/TLKkAAAgAElEQVSA\nWMJPTJxEtFmaOq2tPQAMBQUxaWmzfRs4OD7DqFRSRVEOKAo003m8IdhydKlZtX6bRmsAcOqd\n911W+1TL9DmJygQtgKaTHV5nqN5sFI+34frNhBCX3Xv4zcqIHPgcEpm4cGXWuf/dfbTG6/dH\ndotpSI81bCsrBcCybHFOKoD/99TTf37tHxOWBbOxZrP53XffjdrZOC5nOGE3S44cqWZZliLU\nqrL5YpxbVdUc7FTIv2DgRE1Ni83mwLThujeee6TmxH4AW67Yed2W286+zLa2tjmdDgBCHuN2\nOhg62NYqiFGpkuPjBXwlAKGQr9OrZoxZen2B9p7xhonkFBW5aOyYxzxeWifT6ZKXzBetzMER\nfTSxGkluBgDa7Ws72cRceqcMPl+46dpbeDy+z+Uuf+OdafbLWlsEivi9gdqjraHf35AUu2jN\nYgBtNb3Np7rmetxPUrIuly/gBf1E7E73/vIpe1QvBfds3wJgeNR6y7ZVCzKTADz4u0cn9FKU\n5OeXLlgAgMvGckQHTtjNkuAIh4LsbK16vphxnDxZByAuNUmt1wVfCQQCR49WA4hLTTQkJ0x6\n1Z43nj/4/qsAlpas/fotPwQQCPgHBvorK0+bzWYAAh4EPIhEIoNGk5GSkpOWmmDQSyXSYbMT\ngEavvFilTSAQYFq7RgM0QyiSnKwUCCb+1tF+un/fCYameUJBxvoNXGkdx2WOIStRGG8A4DPa\nOmo7o6Dt9IbEFeu2ABjp6G78eEpvDolGnlyaBaC/bWSoazT0+y/buEKfYABw6K1Ki3HKoOAs\nkCrFBcszcHYc878OVjJsNHqKgyzLyS7LygTw0r8Pv/bIfemJeoZh7nno4YoztRcuu3PnDQAq\nKioaGiI/JIODYwKcsJsNNM0cO1YDYO28MTpxu721ta34ZB62qqrJbndh3LtuEo59+NZ7Lz8B\nIDdz4ffv/qXf7+3s7Dx9uqqnp8fv9wHgUUg0xGSlpmSlJOu1Golo3Ch4eNRBB+3rDDNUwtEM\n29Y96vUFCCGJiQqJdGLhHYChw5XeMTu40joOjrPElebxlHIA7s7h7s6BKGi7ksVrUzPyANTt\nPzSN+0lSWbZELQdQc6jZ75vO2fhCKB5v001b+UKB3xvY87djfn+oF4ZCyRX5PD4VDNoNj1qP\n14QRTZw739q2BUBdW29z1+Arv7o3Rinz+ny77v/BwPD5ObnXb7pKrVQC+Otf/xrNs3FcnnDC\nbjbU1rZarQ4Aa+eNH0d1dXPws/KcsPP7A8eOnQGQkJGsT4y7+JKqYx+++tT/siybnJBx/9d/\n2dvTV1NTMzw8xDDjZT0URfIzU+J0WtFFgx8GjTYAMrlEIp1uJgTLsJ29ZqfbB8AQK1UqJ1k8\n9onSuvQwn5uD4/MJoUjckgXg8QA4mvt7B4yXWtsRQjZu/6JUrmAZ5sQ/3/a6Jm/doHhU1oaF\nIMTj8NYeCcN5WK3XrL/2SgCjA5YD/6iI4NPIVZK8Jek4G7R7e39FxG4dAlcvKUvW6QD86fV9\nGUmGF352t4DPGxkdvf2H/+096yAjEYtv2rYVwBtvvOFyRdjSj4NjApywmw2HD1cBUMhki/IL\nPu2zjBPshzUkJWoM+uArlZUNTqebEBRPFq5rOH30xd89wDCMXhN35w33d7R3mkxGhmEpiicR\nS4Jr0hINcvEkUszl8VtsbgDa2Enshc/DomvAYrV7AGi0Eq1WcvES91nXOplez5XWcXBcCF8q\n1pflA4CPtrUM9A6NXmptJ5XKN199CyHEZbWXv/7uVJsp4zQJRekAepoGBzrDsGXJXZRfuGwh\ngNaqnsqPIpmUXLQhn+KRYNCuo2+kqrkrgjefHj6Pd/eWqwB8VF7X1jO0ojjn5/fcCKCyru4n\nj/7+3LLbr78OgM1me+edd6J2No7LE07YzYZDhyoBrCwt4/MnSSxGH4/Hd+ZMM4D8s2PEvF7f\niRNnACRmpWriDBPWt9RW/PlX/xUI+BVy9Q2bvuHz0CwLHo+XHBeXFBfr9rgBGDQqg3ryrOjA\niJ1lQfEojU4+6QIAYNEzaDFbXABUKnFcnOziJbTP3//hcZameSIhV1rHwXEx0litMisFAGxu\nR6+xe9BEM5e2TzYpNWvpqqsADLa0NR08OtWy1OW5wYRs5UcNHneoHbIA1my/IiE9CUDF7tqW\n091zPu84So0spzQNZ4N2b3xYHqk7h8KuK9YpJBKWZf/85kcA7tyx/sarlgF4/vU3/rXvo+Ca\n/MzM4OjYlyezMubgiCCcsAsbs9lWV9cGYN18ysP6fAEAeWf7YSsq6l0uLyEoXj2xGbat4fTT\nv7jX7/NKxLIbN39DrdBSFJVgiC0tKFDI5X2DAwDkUklqgn7SvVgWg0Y7ALVGzuNP+fvTO2wN\nWtbJFcLExEn0Hwu2f/9Jn9UBgoy160SKqTUiB8dljDo3XaRRAWAGLW6zvXtwNDid+dKxZOXG\n5LRsALUfHhhun3wGBsXn5V61CBTxuf2n9tYj5EgixaO23nKNWhvDstj/2sme5qFIHbv0yvyg\nVzCAxo7++vboTXpQSCS7rlgH4J97T5itDgCPfO/WnNR4AN/5xf/rGxp/xl1f+AKAioqKlpbI\nD8/l4DgHJ+zC5ujRquC8rHVL5ouwC/bDGpLitXGxADweX3l5HYDknHS1XnvhyvaGqqd+do/P\n4xYJJV/cco9Bk6iL0ZQU5KckxgfoQEtXF8NCKODnpMZdNOtrnFGry+P1A9DFTtnl0D9kGzE5\nAMjkgqRk5aQzzEyVDY7uQQDxC0tUyVPOw+DguMwhFHRlBTyRAADdY/K4PF2DJt+l9LcjhGy+\n5ha5QsWy7PF/vO2yTj5DTKZXpS7NAzDcM9pWPd2o2QmIpeJr7rhOKpcyNLP7L0f720dmviYE\n1HpFVkkyzgbt/rn3RERuGyJ3b7mKz+N5vP6/vncIgEQkfOZ/viYSCqx2+z0/fTg4lWfHVRvl\nUimAV155JZpn47jc4IRd2Bw8eBpAbnpGnH7ymFaU8Xp9Z860AMg92zZRXl7r9foImdgM21Z/\n6smHv+H1uEVC8Re33pORnLsgOysrLUUoENABurGjIxAIUBSVkxIv5E+ZFR0ctgEQiQUK5SSj\nI8Cib8g2ZLIDkMoESSmqSb1Q7N0Dxop6AKrExIRFpbN9dA6OywK+WKgrXQAAfpruGfX5Al0D\nIx7fJXTilUjlW7+wi+LxvE7Xsb+/wUwRI0wqzVIn6QA0lLebh6yh31+pUV17x/UiiSjgD7z/\n7OHeluGIHLv0ygJCEAza1bb2Nnb2R+S2oZCs012zdDGAv7xzwOcPAMjPSPzxXTsAHKms/PM/\n/glAJpVet2kTgNdff90fRSNljssNTtiFB8OwR49WYT7lYauqmr1eP4CCshIALpe7oqIeQFpB\nlkqrObfszMmDTzz0TZ/XIxKKv7Tt28tLVi7My1XI5QDAoKWr0+PxAkhPNMiloqn28gWYkTEn\nAK1hsjgci55By/BZVZecqpo07Ocbs/fvK2dZiOTy9HVXzGiDx8HBIdap1LlpAODwsCPWQIDp\nHjQ5PWEUt4VLXGLqmg3XABjtG6h8b/ekawiQt6lUIBWxDFuxt94bTrGdNl5/7R03BLXdB88f\naq+JQOZUG69KK0jE2aDdP3Yfn/s9Q+eerZsBjJhtb3803pZ71/UbVi/KBfC/T/6xvacXwK3X\nXgPAaDTu27cvmmfjuKzghF141Na2ms02AOuXLf+0zzJOMA+rT4zXxscBOHGi1ufzE0IWrjof\nrju05+1nf/29gN8nFknvvP7+rWu3JMQazimztp4eq90BIClWo1dPV+s2ZLQzDEsItPqJ/bAs\nw3b2jwXr6mRTqzra6+vZfYT2+XkCfuaVV/HFU4pIDg6OC1Fmp0oMGgDMsBVOD00zPUNGm/MS\nzpNdWLoqr7AMQEdFVfvJyaeBCWWSvM1lQfeTij31LBNG364hKXbHV3ZKZFI6wOx96Xj1gea5\nn7nsqgJgPGh3prWnoaNv7vcMdeuszKU52QD+9Ma+4AEIIb//wW1yqdjt8Xz3F79gWXZp8cLs\ntDQAr776atQOxnG5wQm78Dh06DQAuVRWtqDw0z4LcEEeNmhf53S6KisbAGQU5cjVKgAsS7/9\n8p/++aefM3RAKpb/1x0/37J2s/gCOdUzMGgaMwPQxSgTDZrJtzlL/4gNgFItE4o/0Q7MMGx7\nrznYAytXCKdSdQzD9O49HmyYSF+zXqqdYTsODo5zEALdony+RAQAvaM8mmEZ9A2bR62OS7fp\nFZuvN8QlATj9771TuRbHJOnTlucBGB2w1B1rC+v+ugTD9V+/SalRsSx77L3qfa+emKN3sSFZ\nk5wbB4CiCIBXPpiysfdSEDQrbuzoP3S6KfhKcpz2x1/bAeBo5emX330XwC3XXA1g3759JpMp\nmmfjuHzghF14nDU6KZ0nRifV1S3jedjFJQCOHq3x+2mKRxWtLAXgdruef+wX+17/E8swSpn6\n4XsfW1b8iQzykNE4MDwMQCWXpicaps+JWh1eh9MLQGf4RLiODjAtnaagX51KJU5JVk6eXGUx\neOCUa8AIIKl0cUx62mwfmoPjMoUS8nVlBSCE9tPUgFnIpwAMj1qHRq2XyOCOzxduv/52qVTB\n0PTRv7/htExeSJe4KFObEQ+g40xfd8NgWFuodTE33P2l+JR4AC2nut98bF9Y5XoXU3ZlAYBg\ni1tjR//ppskbey8F2xaXphn0AJ55/aNzL97+hXVLCzMBPPz4E6axsS9u38ajKL/f/8Ybb0Tt\nYByXFZywC4PRUWvQ6GT+5GHLy2txNg9rtTqqqpoBZBfny5QKo3Hk6V/9sOrAWwCr18T/5ofP\n5KTnXnit0fz/2Xvv+Lau8/7/uRO4wMUeBAEucC/taQ1btizLI7bjDKdtlus0w0mapnGGkyZN\n0jb5pdnftE3S1Bl1GseZjpckD0nWXtagxC1uEnuvu8fvD9IkJZEUQVFiIuD9ol8vizi45zw8\nwD2f+5zzPE98aMwHAHpKUzd7GOwkvlAaAHACM1mnktLxgtQ9EBmvLWG1UZ4yesYYWAAInbww\nXmHCXldXumLFwm0uUqSA0ViM1pYaAOCSjDaZozQ4AMRT2bFQTL4+6Ytpg/mehyYCKQ7/328l\nYcaDdEj99pV6mxEA2g72RH2JvLrQ0boHP/DO8dzF8WDqd9979dyBHiWfXd3puGscpdUOAMAw\nBACe3nVEmX86lmsDQ9EP370TAPaf6ugdnhC4KIJ88x/fTeBYIp3+6n/8p8vhuP2WjQDwzDPP\n3JhRFSk0isIuDw4dOqMoKoIg29b/WQg7jntzH3bCXXdOlmUMx1o2ruzp7vzx1z7Z33YIAKrK\n6r7zxE9KHe7p740nUwPDIwCgJcmGKjeOXuWTIMlqMJoFALvDOBnukM0J3QMRTpAQBJwl+hmz\nEI8TPdcTO9cDACaPp3LzVkCKARNFiiwQg9ejL3UAQGIwYlJVWk8CQCbHDfvC1ykNirvMu+2u\nhwAgGQgd/+2fZlRJKIE13btuPJDi5J72TDy/wlkYjt32wPa7/upeUqORJfno8+f++IPXIqP5\nCcRJ1tzZDACyPFGI4tDp7oVdZwG8e9tWk06nqupPfj/ltGv0uj/4tjsA4OnnX3jjwoW/fstb\nAKCjo6O9vf2GDaxI4VAUdnkwfsCusbqmxG5f6rEAAJw7NxUPG4+n2tp6AaBuZfO5c6ee+s5n\ngoMdALCyacM3Pv1DI22e/sZkOt03PKwCkATRVO2eI7nJJKFoVpZlmFZGLJ5iLg5HJUlBUMTt\nMdjtM1QMm2jZ0Rc+eQEA9HZ79R3b0WIYbJEi14ZtRQNBUwAQPDds05FWEwUAnCAN+cIsf11C\nZVuWb1i5disA+Lp6z+/ZO2MbjYFqvncdimMiLx178Ryb5fPtpW5Zw1994r3ltZUAEB6N//7/\nvbr/t6dy6bwDRCoaXM4yKwAQBAYAT+86LFzb0b35Q2u177tjGwD87tUT0WRm8vefet99pXaz\nqqqf++a3dm7dYqRpAPjNb35zY0ZVpKAoCrv5Isvy4cNnAeD2P6N92DfzEpe6Dh06q6oqThD+\n+OAffvTPyfAYAOzc8uCXPvbvWlI7/V3JdKZ3cEhRFALHmrxuDTGvw4K+UAoAaBOl1ZGggj+U\nGRpLKIqKYWhlpclkmjW4Nd7RHzxyDlSgLOa6u3ZiBHFNNhcpUgQAITDHmhYEw2RZ8Z0atJoo\nl4NGEJBkZSgQSWWuS5n5zXe8paqmCQC6Dx3rP3V2xja009ywYxUgCJvlj73YJnJ5yymD2XD/\nIw9tf/tOSq9TVbXrxMCvvr7r6AttTIbL6zrj4bGiKANAJJF54cDMUb3Xgw/t3IFjGC+Iv3ju\nwOQvaZ32ix96GwCc7ez648uvvHXHnQDwhz/8QZJukOIsUjgUhd18OXu2J5XKwp/NATuW5cfr\nwzauWRmJxDs7+wEgyQ6/+uvvstkUiqAfeMcnHvubT2PoJd64ZDrdOzg4oeqqPZRmXjIrzQip\nLAcADqdJVtT+0VggklZVIDW4t8ak080qDWPne4JHzoIKWpOp4e57ca12tpZFihTJC8Koty2v\nBwA+wwbPjRhpbZnLhGGoqoAvkrge4RQogu584N12ZykAnH5+d7BvYMZmVq+r5rZlAJCJ546/\n1CaJee8OIwjSuLr5PZ96ZNXWtRiOSaJ07vXuX/7biwd+/0YiPHMZjCupavFYXSYAoCgSAP6w\n92Q8nct3JAvDY7M+uGEdAPziuQP8tDzSb9u+bjyK4ms/+vGDO+4EgEgkcuDAgdmuU6TIwsC+\n8pWvLPUY8kZVVZZd/OxNghCR5VkfCn/96z2nT3dZTKYvfewT6KIeESMIQlGU8Zoz8+fUqY5x\nj93d73n4wOG2SCQxMnKsr2u/qig6rf6Jj3x92/q7LntLPJm6ODQ8ruoavR69lpxnXwOj8XSW\nx3CstNLeNxLL5gQAoGmyospEzFIuVlUhfOJ85I0uAKDM5oZ77yOoib1aBKAAz9ghBWZyoc7y\nDe2ONOplQRSSGT7D4iRucBgMeg3DCbKssrzAcgKt16DIYj69YxjurW262NUm8Jyvq9fdUEcZ\naXgzb9wktMOEIEjKF2NzfCKc8tSULOAABobj5bWVDauaJUGMhWKKLEfGEh1H+4JDMYLEjXZ6\n7msiCGgocuDCmCTJGIaIopzOMhuW1eU7jCvBMUxV1bnv2OU2+1P7X2c4ocJlX1ZX8eaQkEav\n5+ldR7IMU1Fa6g+Fk5mMoij333//tY/qWtDpZiojVOQvlqLHbr7s338KAG5btwG7WpzBjeHN\nfViPoKLt7V0dHc/5xs4CgNtZ/q3P/WR18+WFMWKJRN/QlK9u/qpOktVgJAsABou+ZzDCsiIA\nWO1URaURm+UvIUuy77VjsbZeANA7HNNVXZEiRRYRa0uNxmwEgGD7KJvIEThaUWo26EkAyLH8\n4Fhk0Y/c0Qbz/e94lCA0Es8f+N+nmdTMqUnK19a5V1QDQHQseXJPuyIv0IFoMBu2PXTnex//\n25Wb1xAaUlVhtCe45xdHfvmvzx994VzMn5zjvTUry012AwAYDFoAOHC6+4YVGVtV472lsQEA\n/vv3e6er3lWNVQ/dsQ4Afvirp+/ddhsA7N69O5PJzHadIkUWQNFjN8UcHjufL/y97/0fAHzk\nr9/d4K1e3H4X4LFjWe5nP3teUZR122977uVXzpz+PcPEAWD98q1f/vi3rebLYztC0Vj/yIgK\nQBJ4c3WZTjNfVQcAgWg2FMsAAI+hCgCCIm73XKESQiY3uutQzhcBAFOZp27HTuzS7grVl1NY\nJhfqLN/4HhGt08qMhVRZyYbT5jIrRmAGvQZBEYYVFUVN5RgCw7T5fOWvip422ktKL3a3iRwf\nvDhQubIVxWY4j2GpcIgMn42kcik2Fc24a5wLrh9IajUVdZXLNqzUG/XZZIbNsaIgB4diHcf6\nBy74RF6kzToNdbmNCIIQGnyow8dxEk1rBEHqGw3euXH5NcZvzcdjBwBmve7ZYydiycya5mqv\nxzn5++X1Ff/7/EGOF8pKXd39A5Ik1dbWtrYuZcb7osfuJqMo7KaYQ9g9//zrBw+ewTDsa//4\naa1mkatgLUDYnThxYbwgbE9i4OSpF2RZRBH0b+7/0If/6pMEcfndzRcIDvv9AKAliaaaMorM\nL3yhqz/MCzJgGGhwHEcrK00Gw6yLRHrAN7rnsJhhAMDZ3Ozdeht6RchtoS75hWVyoc7yEnSK\nEjhponNjIUVS2ARjLrMCglBagtISOVZQFMgwnCQrekqziB9Cs8WhNxgH+zq5XC46OlaxvAWd\naSvDWlUiZLlcNJVLsclIxl3tuBZRheFYSXnpso0ryuuqEARSsZQsy2yWG+sNXTjUO9YbkiXF\nYNUT5JTKtLpMvaeHBVa02ehslk9lWQLHmmvKFjwGmLewqy0t/f2RY4lcLpLIvPOuqZPZJlqX\nzOROdw72DQ031tRE4nGGYR5++OFrGdI1UhR2NxlFYTfFHMLuBz94ZmQksH75inc/8OCi97sA\nYffb37466g9czPQOjHQCAK01fuGxb9xxy91X3rgHR8f84TAA6LSapmrPPGNgJ4nEmeHxzQ6K\n1Bk1lV6zhpw5N4rMi4FDZyKn2lVZQTGsavOW0hUrZ1xICnXJLyyTC3WWl6ZfXE8hGMZFEyIr\nKJJMO00AQBCYQa/lOFGSFY4Xcyyn12kX8SSJs6QMAHyjA7lEKh2Jlrc2zfght3pLhByXi6Ry\nKTYeTLmrHehsZzjmjcFk8DbVrNi0ylZil2U5nUirippNMsNdgfMHe0IjcRRDTTYaxVAURTAc\nHe4KZLO8t8qWTLLdQ4HNK+sN+oUfDpmnsEMQBEWRV8+dHwnG7t26ymGZKtizor7yqRcOcoLo\nctjDsdjY2Nh73vMemp6rTvd1pSjsbjKKwm6K2YQdw3Bf+cqPZVl571sfuh4lYvMVdtks+50f\n/awz1p4TsgBQaav99Pu/2tK8/LJmiqL0Dg5FEwkAMOipJq+bmEe+uunEkmxbT0BVARCwlJnK\ny4wzP22rkOobGX35CBuMAQBlNtftvNtUNuszcaEu+YVlcqHO8pJ1rbWYxAwjZhk2wZA6jdZE\nAQCGIkaDRpYVXpAlWUllGQ2Ba/L02c9BWUVNLpeOBH3pSJTNZD2N9TM2s1aViKyQDSeZDBcZ\nS7qrndgsQVd5gWKorcRev6Jx2YYVJqtZFIRsKqMqaiqS6W8bbT9yMZNg9EaqoqG0+9SgyEt2\nu4FhBEGQ+kdDd2xoWfBXcp7CDgAayzw/37uPFQROEO/ZvHLy95SWlBXlyNmeSDyOoaisKKWl\npevWrVvYeK6dorC7ySgKuylmE3avv/7GCy8cBIB//vg/WE2mRe83L2HHcNxHv/TPpwfOKaqC\nodim2h33rH3Hqg2rLyvkJYpSV39/OpsFAIuRrq8qvWpticsY8qc6+4Ljp35pm76syjxjrTA2\nHPftPR6/0KeIMoKAq3VZze13kPpZS1BA4S75hWVyoc7yEvYNOoeVDUVlQcyGU7TDiFMkACAI\nQus0BIEynKAoajrHyoqqW7xtWW9dczQcSMTCCX9QVZSSmqoZm1krnYokZ4IJLseHhmOuKvv0\nDdNrBCdwp6ekcXVL05oWvUHPZBk2y8iSEhmNdx7vH+0OOsqs8WAqHs/ddlv94GA0lspqSaLR\n61lgd/MWdgSOpxnmeE/vxeHg39y7mdZN5XtaXlfx9K4jDMfbzGaG42Kx2Pvf//6FjefaKQq7\nm4yisJtiNmH3058+29U1WOnx/OMjjy56p5CPsDvb2fn+z37qwsVuALBoTW9Z/d4aZ1PTqiba\neImQYlmuo6+P4zgAcNnNNR5nXvlZZFXt6AuP+CeK+SAIVDQ5rnzCZmPJ4OEzoePnxSwLADqb\nrW77Dlt9PXI1BVmoS35hmVyos7ykvWMo5bAyYyFFVrLhtMljnTzhqiFxvY5keXE8E0qO5Rdr\nWxZF0ZqG1sDYYDqViAyNEBqNvWJmb7253IGgaMoXFVjRPxB2Vtg01CKnKye1mtJKd+uGFTXN\ntSiOpWJJSZRyaTYeTI1/AUkSt9v0sViuo9+3pqXaYpzrEXQ25i/sAKDB4/mfV14TJElDEltX\nN04NlcAxDHv9VCfDcQAQCoXe+ta32my2BYzn2ikKu5uMorCbYkZhpyjqP//zD1mWf/vOe25d\nt37RO4X5CTtJkv7fU7/43Le+kUynAaDFUn//ynfo9Q6Txdiw/JLtj2Q6PR5phQBUuR1lTmte\niw3Ly2c6ffEkAwAoiqgq0BbK6jJMb5P1R4KHz4aPnxcSGQAgdVT5ho0Vm7bM7aibpFCX/MIy\nuVBneYkHgJIEaTJMBFLEsqYy62QgKo6hRloryoogyJIsp7IMuRjbsgiCoChWXds6OtSby6aD\n/YOUwWD1lM7Y2OS2knptYjgs8ZLvYtjmNlH0dUlarjPoK+urVmxabXFY2RyTTU3kE4nFsqWl\n5kyGEwSpvW/09vUt+R5QgTyFHU1pB4Kh9pHR3uHABx66fXp3rTXlz+w5mmV5DMNUVbVYLFu2\nbMl3MItCUdjdZBSF3RQzCrtz53p/+csXAeDTH/hgmWvmu9U1clVh1zcy/IEvPPHi/r2qquoJ\n7V1lW1c5msHoBARtWdOio6dOAftD4YGREUVVMRSrqyx1mA2zXXNGkhnuTKdvPFOd2UKN/4+r\n2kJqCQBQZCXVP+I/8EbsbI+QygIAodW6V6323rpN73TOf0kr1CW/sEwu1Fle6hEA4HoKIwk2\nHJc4UWB4o9sy+RKCIAa9BsdR9s1tWfGao2XH34tiWE1962B/F8fkAj19tM1qdjlnbE87THq7\nMTYYlEXZdzFksOgNloW4zeYDiqI2l71pTau3sUbghUQ4DgDhcEZVVVWFDMOF4qlNK2Y+FzgH\neQk7AKh0On6+dz/Hi6V288rGqqnr4BiOY/tOdownugsEAh/84Dt0+EEAACAASURBVAeX5EZR\nFHY3GUVhN8WMwu7pp3efPt1lMhi+8vefnDGe/9qZQ9gpqvLzP/zuE//6VX84BADNjooHqu6w\nklaM0qmU0eqw1DTXjLdUFegfHglEwgBAEkRTtduoz+9R2BfOXOgNSpKCIOCtMfOczLESqSVc\nXovI8PG2Xv/+E6neEYnhAICkac+q1d5bbzOUliJ5xrgV6pJfWCYX6iwv9QgAAEBjMcq8IKSy\nfIZDFFXnuOQBT6uZ2pbleDHNsDqtBsfydlyNM/7BVlWVIMjqutaBi+08x/q6es0up9FxeULN\ncXQW2lRmiw0EZVH29UcIEre6jDO2XCz0Rn1Na52GNMcDSVFiFWUiY/BoMKYh8XwP2+Ur7Jxm\n0/Gei8PhyIAv/Ldv3Tb9VtBSU/bM7qNZlgeAZDK5fft2t9ud12AWhaKwu8koCrspZhR2X/va\nk/F4+u6tt91z27ZF73Gc2YTdWDD42Je/+OsXX5BkWYuTDzRuuMO7imNwAFD1ZoTULF+3XENp\nAEAQxa7+/lQmDW8GwOaVrE5V4eJwrG84qqqAE1hjk12vJ4cHkwBgNmKp9p7AgTdyvrAiygBA\nOxxl6zdUbtpMl5TkK+nGKdQlv7BMLtRZXuoRvAnlsPLJlMRwTDxLUoTWdMnKjWOoyaCVFZXn\nJVlWktkchqDUvKvRTGdS2AEAqdF6a5v7ei8IPDfW2WNxlxrs1hnfpaEpm9cVHw7LvBgejQuM\n6KywXu/viM1lDvZntRqLwaBhmOz4mNt6RxAEWmrK53+dfIUdANgNht8dOZZI51pry+sqXNMv\nhWHY/lMd4//U6XTbt2+f/2UXi6Kwu8n4s6iO9WfL8HCgr28UALZv2nyDu/7Dy7vv++CjJ9rO\nAUCtzf3xDW9Z4671OCrGk48ApXeUOo1WIwBkc7kL3b05hgEAp9XU6PWQ+ZwakWS1rScw7E8A\ngE5PtC53GAxkKJhVmRwy0hs7eCTVM6TKCoKh1urq5vsfaLz/AWt19VUjJIoUKbKEICjiWNNC\n0DoA8LeN5CLpyxsgSImN9pQYMAxRFQjGUiPBqCTL19ivyWx767s+pNMZFFk++vTvg30Ds7Wk\nLPSKd2yhnWYAGOzwHd91QRKka+x9bnASr1lRjmEEhjkeef87Ghomagg9s+fYF//zt5HE5X+i\nRWT7imUNHg8A/Ph3r1320nvfstVpnXBYPvfcc/I1T0GRIkWP3RRXeuz++Md9R46cI3Di649/\nmryiosNicZnHLp5Mfur/+7cf//ppQRQ1BHlvw7p769bqSO32zZvOto8wLA9aHaIzrtiwgtQQ\noWisb3hYlmUUhcpSR3mJNa+87uOhEsk0CwAWK9XYZCNwNBdNDR46A4FR4DkAwDSkq3VZ9a3b\n7PX1xPzCI+amUH05hWVyoc7yUo9gGgiGUiU2xh9WJSUbSOqdRlx7uSOfJHAjreUESZIUQZRT\nWYYkcQ2Rh79/usduHEqnr6xpuNh9XhT4sfYuW4WHtlpmfC9GYM56D5vIsYlsLsUGh2IlFTZC\ns2hpUK7EbKeHOvyKpCAI9raHtpjNlr6+MUWRIon0q8fP67RkbYULmTGx0zQW4LFDEERL4rtP\nn/WF49s3tJbazVNXwzFVVQ+c7gKAXC53yy23VFZWLsy6BVP02N1kFIXdFFcKu29/+ym/P7Jl\nzdqH77lv0bubZLqwO3DyxN8+8ZkLPT0A0FJR8+5l22rMJRiK7ti0WUNSh052AQAYrJ7aKneF\ne3B0xBcMqapK4FhDldtmyi9xeZoRznb4GE4EAJebrqmxyII4fPz80KGzKscBAEFRntWrq2+7\n3VRWhi1eUtNCXfILy+RCneWlHsGloASudViYsbAiK5lAwuAyY1dkj0NRxERrERRhOVFR1HQ2\nv4iKK4UdAOh0dIW37k1t122rKKMt5pnfjqL2WrciK5lAXGDFsd6Q1WXSGa5LqCwAoBgqS0rM\nn4wnmJpqR011aWVV1cBAhOcZSZbPdA119I+11pTrqbnqRi5A2AFAg8fz1P4DDM9ncuz9t62Z\n/lJzTdkvXzzE8SIAEARx9913L8C0a6Eo7G4yisJuisuEXTye/vrXn1RV9QPvfNfyhsY53niN\njAs7luO+/uP/+tf/+o8cy+IY9sGdb9/qaCABxVDsrq2by0pdJ872jgVigCCYtaR5TXPvyHAy\nlQYAvU7b5C3T53k+JpJkznUGREkeD5XweAzR3pGel49lAjEAQAnSVN3cdPcO2uVa2EG6OSjU\nJb+wTC7UWV7qEVwBpiE1FmPuTb+dodSCETMc1aC0hJ4iWF6ajKigNOR8UoHMKOwAQK83Vnjr\nL3a3Tfjtymf12wGAucyuNeoSI2FZlMcuBilaa7Jfr/paZodh3GnHC1JNtcNi1pU4nMGgJIqs\nLAuReHrfiXaLmfa6HbNdYWHCDscwThQOd3b1jYTeuWODyTClpUgC53jxaFsvAAwPDz/22GPY\nQmNZFkZR2N1kFIXdFJcJu5deOvTaaycQBPnaP36avp6fe4IgegYG3v/Zx/cePQIAlU73Dz74\nBB5jJVHAUOyurVs8JSWgqs+/clIQZdDRpQ31oUyS4zkAcFqMdZUuIk/t5Qtn2nuDiqJiGFrX\naDPp0It7TwbaLiqSjCAI5fKa6taVNtcQi50+dJxCXfILy+RCneWlHsFM4DotadAz/ogiKdlg\n0lBqnlHb4ThmMmgVReV4SZaVVIZRASitZm6jZhN2AKCnjeVVdX0950WBH73QZS1z07ZZtZ3e\nbjSV2RJDIVmQg4NRWVIcZZbr8a1BMVSW1UmnHUWRVpveZNKHwyqKYLyQEyXp5IW+QDSxoqFy\nRmm7MGEHAI1lnidffU2QJEDgjvUt019qqvb87NnXJVnmeX7VqlW1tbULtzB/isLuJqMo7Ka4\nTNj94AdPDw35VzQ2feCdDy96X9P54yt7/u4LnwtGIgDw8K13f/fRx9tPnRUEflzVuUucADDs\ni7xxvh8AMLNDteoUVUFRpLLUUe6y5VVVAgAGxuK9g1EAIEmsqcWhplPdLx3OxVIAYHDYbc0b\ncXMZSZHW0vxy4M2fQl3yC8vkQp3lpR7BLBAGHaHXMcGoLMrZYNLgmlnbIQii15GUlmBYUVFV\nhhNyLEdpyTmSocwh7ABATxsrvPUT2q69y1JaYrDPWlxBQ1O22tKkLyqxQjyYSkUzrkobutg7\nBgBgdkyctONYsabWCQB2O20x6fx+VqsxiSIjy+JwIHr8/MXmmjKz4fKDxQsWdjqNJhBPnB0Y\n7BnyP/LAbVrN1JMzpSET6ezpzkEA4Hn+oYceujYT8xxYUdjdXBSF3RTThR3DcF/+8o9lWX7v\ngw+tW7Z80fua6IXjPv/tf//+L34uSZKB0n/vw597/7a3vPryq5epOgDY8/qZRDILGKaprMC0\nBEHgCzhUp6jQPRgZ9iUBgKKIplZ7sntg4MBpWZQRFPGuXl2xZmM8qQKAuYRe9Go/kxTqkl9Y\nJhfqLC/1CGaHNOpxnZYNxmRRzgSShhLTleftxiEIzGTQiJIsiLIkK8lsDgWU0pIzGje3sAMA\nPW2s9Db2954XeX60vcvosJlKZt/l1BAl9eVMLMOmctkkGxq+LuEUKIaqKkR9iUSSrfbadToS\nAKw2fUmJcXQ0pdGYQFUFIZdhuP2nOm1m2uu5JNnygoUdANSUlv70ldcEUTIZqA3LLnHLNVS6\nn3x2v6qqQ0NDjz32GJFPCMs1UhR2NxlFYTfFdGG3b9/JF188CABf+cQ/Wk2mRe8LAAZGR973\n2cePnDkNAMu99b/5wncaSip27dolCDyKondt3ewpKRlvKYrSS3vfAACENmnLXQY91eT15Huo\nTlahvTcYiGQAwGDSNDZYRo+cC1zoAwCNXte64y5ndU04xPC8jOGI3WO6fktUoS75hWVyoc7y\nUo9gTkgTPa7tFElO+xO0Y4Y42XHGa1QQBMbyoqJAjuVzLK+nNFeWl72qsAMAnd5QVdPY39su\nCvxYR7fObLaUlszWGMFQR71HkaRMMMFft3AKk50e7gzIkpzL8XV1E4MxmSiv1+7zJQG0BEkJ\nQlaSpJPt/clMbmVD5WSC+msRdlaabh8Z6fUHLg4HPvC226f/PQ16qmtgtHc4qChKdXX1smXL\nrt3MeVIUdjcZRWE3xXRh96Mf/ba3d6S2ovIT739k0TsCgFePHPrA558IRsIA8OjOt/3PJ/8F\nU2D37t0cx6EoetfmzR7XVBLLF147Ho5mAEBTVekuc9ZWluZ7qE6SlbYufzTBAIDVStVWG/pe\nPZEYDgCAyeVafvfdOpNJFORAIAsAJrteS1+v3C5QuEt+YZlcqLO81CO4GqSJJg16JhhVJCXt\nS2jNOlI/awSohsSNtFYQZFGSJUlOZhgURSjNJTeH+Qg7AKB0dHVd8+DFDp7nfN29JKW1lc9V\n78Fc7rg0nEJjsi/m4RAUQwHUyFgimWKrKqz6N/8IFEU0NLoyaS6TlimtSRBysiL1j4ba+8fW\nNVePl9a9FmEHAB6b9f9eP5hlea/b0VJ7SWLkhir3L547AACDg4OPPvrotZmYB0Vhd5NRTDM7\nA4Igvv76aQDYufXWRb+4oirf/flPH/vyl7JMTqfR/vDjX/rmBz/Nc9yuXbtYlkVRdPumWzyl\nU6qup3+ws9cHAAipqV9eW13mxPJcPARROd3hi6dYAHCW6L2VdPeuIyl/BABcdbXL795JaLUA\nEI+xoAKCIgYrdZUrFilS5C8WndtRsr4VwTBZkkeO9yWHo3M0xjHU4zKW2GgUA0VRg9HUcCAq\nSAtJomu2ON7+7o+arQ5Q1bMvvtK+7+Dc7Z0NZa0P3kJQGkVWz+7r7jjWf1X5mBfeZWUaHQkq\nnDg5NP33JIHt2NG8fXuTXq93OOp0OgsAdA34PvO9Xw0H5vpbzZP19XXr6+sA4Ie/ffUyixqq\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+A6gJIE5bAYqss1ZiOCojLLqoqqyAqX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\nnXrnTGFpkdPrGMt26bT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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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BPBzt/ff9GiRf/85z9feuml2travn37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\nnj2tqzmmrtYW0cudrQBo0fnz5wMDA41Go7cbUcnVYBccHNzCUu4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AJPjyBAAAcKdRgc3ehhVtjWAHAADc6ZNf3bzCUSFuXqHEOBQLAAAg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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Create boxplots and stacked density plots to describe the sampling\n",
    "# distributions of the betas; Notice that there are some outlying values \n",
    "# for every predictor\n",
    "ggplot(coef_mat_accum_df,aes(x=variable, y=value, fill=variable)) + geom_boxplot()\n",
    "ggplot(coef_mat_accum_df,aes(x=value, fill=variable)) + geom_density(alpha=0.25) + xlim(-3.5,3.5)\n",
    "ggplot(coef_mat_accum_df,aes(x=value, fill=variable)) + geom_histogram(alpha=0.25) + xlim(-3.5, 3.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Method II - Calculate bootstrap confidence intervals using the R package \"boot\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "ORDINARY NONPARAMETRIC BOOTSTRAP\n",
       "\n",
       "\n",
       "Call:\n",
       "boot(data = x_df, statistic = lm_function, R = 1000, col_index = 1, \n",
       "    permute_vars = FALSE)\n",
       "\n",
       "\n",
       "Bootstrap Statistics :\n",
       "       original        bias     std. error\n",
       "t1*  -1.3242550  2.120876e+00 4.815979e+00\n",
       "t2*  -2.5940912 -6.743402e-02 9.444787e+00\n",
       "t3*   1.4466841 -4.601753e-01 3.561497e+00\n",
       "t4*  -0.2543654 -1.208439e-02 5.254331e+00\n",
       "t5*  -0.3768517 -1.959348e-01 3.734581e+00\n",
       "t6*  -1.7588089  8.655159e-01 4.538721e+00\n",
       "t7*  -0.7579764  7.904419e-01 8.019816e+00\n",
       "t8*  -2.3305861  5.662328e-01 1.727283e+00\n",
       "t9*  -1.6960025 -8.069524e-02 5.049062e-01\n",
       "t10* -0.2588560  1.121325e-14 3.258178e-15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Bootstrap analysis using package \"boot\" -  We DON'T want to permute the predictors\n",
    "# when using package \"boot\";  The bootstrap averaging of coefficients occurs across \n",
    "# models where the ordering of the predictors is the same for each bootstrap sample.\n",
    "# Notice var10 will not be able to be estimated;  n must be LARGER than p to get estimates\n",
    "# for all 10 variables \n",
    "\n",
    "library(boot)\n",
    "boot.fit<-boot(data=x_df, lm_function, R=1000, col_index=1, permute_vars=FALSE)\n",
    "boot.fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'(Intercept)'</li><li>'var2'</li><li>'var3'</li><li>'var4'</li><li>'var5'</li><li>'var6'</li><li>'var7'</li><li>'var8'</li><li>'var9'</li><li>'var10'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item '(Intercept)'\n",
       "\\item 'var2'\n",
       "\\item 'var3'\n",
       "\\item 'var4'\n",
       "\\item 'var5'\n",
       "\\item 'var6'\n",
       "\\item 'var7'\n",
       "\\item 'var8'\n",
       "\\item 'var9'\n",
       "\\item 'var10'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. '(Intercept)'\n",
       "2. 'var2'\n",
       "3. 'var3'\n",
       "4. 'var4'\n",
       "5. 'var5'\n",
       "6. 'var6'\n",
       "7. 'var7'\n",
       "8. 'var8'\n",
       "9. 'var9'\n",
       "10. 'var10'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"(Intercept)\" \"var2\"        \"var3\"        \"var4\"        \"var5\"       \n",
       " [6] \"var6\"        \"var7\"        \"var8\"        \"var9\"        \"var10\"      "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "[1] \"(Intercept)\"\n",
      "\n",
      "\n",
      "BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS\n",
      "Based on 1000 bootstrap replicates\n",
      "\n",
      "CALL : \n",
      "boot.ci(boot.out = boot.fit, type = \"perc\", t0 = boot.fit$t0[j], \n",
      "    t = boot.fit$t[, j])\n",
      "\n",
      "Intervals : \n",
      "Level     Percentile     \n",
      "95%   (-7.960, 10.973 )  \n",
      "Calculations and Intervals on Original Scale\n",
      "\n",
      "\n",
      "[1] \"var2\"\n",
      "\n",
      "\n",
      "BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS\n",
      "Based on 1000 bootstrap replicates\n",
      "\n",
      "CALL : \n",
      "boot.ci(boot.out = boot.fit, type = \"perc\", t0 = boot.fit$t0[j], \n",
      "    t = boot.fit$t[, j])\n",
      "\n",
      "Intervals : \n",
      "Level     Percentile     \n",
      "95%   (-20.758,  11.409 )  \n",
      "Calculations and Intervals on Original Scale\n",
      "\n",
      "\n",
      "[1] \"var3\"\n",
      "\n",
      "\n",
      "BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS\n",
      "Based on 1000 bootstrap replicates\n",
      "\n",
      "CALL : \n",
      "boot.ci(boot.out = boot.fit, type = \"perc\", t0 = boot.fit$t0[j], \n",
      "    t = boot.fit$t[, j])\n",
      "\n",
      "Intervals : \n",
      "Level     Percentile     \n",
      "95%   (-4.996,  6.715 )  \n",
      "Calculations and Intervals on Original Scale\n",
      "\n",
      "\n",
      "[1] \"var4\"\n",
      "\n",
      "\n",
      "BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS\n",
      "Based on 999 bootstrap replicates\n",
      "\n",
      "CALL : \n",
      "boot.ci(boot.out = boot.fit, type = \"perc\", t0 = boot.fit$t0[j], \n",
      "    t = boot.fit$t[, j])\n",
      "\n",
      "Intervals : \n",
      "Level     Percentile     \n",
      "95%   (-5.2711,  7.6742 )  \n",
      "Calculations and Intervals on Original Scale\n",
      "\n",
      "\n",
      "[1] \"var5\"\n",
      "\n",
      "\n",
      "BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS\n",
      "Based on 980 bootstrap replicates\n",
      "\n",
      "CALL : \n",
      "boot.ci(boot.out = boot.fit, type = \"perc\", t0 = boot.fit$t0[j], \n",
      "    t = boot.fit$t[, j])\n",
      "\n",
      "Intervals : \n",
      "Level     Percentile     \n",
      "95%   (-6.1073,  5.5080 )  \n",
      "Calculations and Intervals on Original Scale\n",
      "\n",
      "\n",
      "[1] \"var6\"\n",
      "\n",
      "\n",
      "BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS\n",
      "Based on 850 bootstrap replicates\n",
      "\n",
      "CALL : \n",
      "boot.ci(boot.out = boot.fit, type = \"perc\", t0 = boot.fit$t0[j], \n",
      "    t = boot.fit$t[, j])\n",
      "\n",
      "Intervals : \n",
      "Level     Percentile     \n",
      "95%   (-9.640,  5.869 )  \n",
      "Calculations and Intervals on Original Scale\n",
      "\n",
      "\n",
      "[1] \"var7\"\n",
      "\n",
      "\n",
      "BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS\n",
      "Based on 514 bootstrap replicates\n",
      "\n",
      "CALL : \n",
      "boot.ci(boot.out = boot.fit, type = \"perc\", t0 = boot.fit$t0[j], \n",
      "    t = boot.fit$t[, j])\n",
      "\n",
      "Intervals : \n",
      "Level     Percentile     \n",
      "95%   (-10.2947,   3.3253 )  \n",
      "Calculations and Intervals on Original Scale\n",
      "\n",
      "\n",
      "[1] \"var8\"\n",
      "\n",
      "\n",
      "BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS\n",
      "Based on 152 bootstrap replicates\n",
      "\n",
      "CALL : \n",
      "boot.ci(boot.out = boot.fit, type = \"perc\", t0 = boot.fit$t0[j], \n",
      "    t = boot.fit$t[, j])\n",
      "\n",
      "Intervals : \n",
      "Level     Percentile     \n",
      "95%   (-7.507,  0.806 )  \n",
      "Calculations and Intervals on Original Scale\n",
      "Some percentile intervals may be unstable\n",
      "\n",
      "\n",
      "[1] \"var9\"\n",
      "\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in norm.inter(t, alpha):\n",
      "“extreme order statistics used as endpoints”\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS\n",
      "Based on 11 bootstrap replicates\n",
      "\n",
      "CALL : \n",
      "boot.ci(boot.out = boot.fit, type = \"perc\", t0 = boot.fit$t0[j], \n",
      "    t = boot.fit$t[, j])\n",
      "\n",
      "Intervals : \n",
      "Level     Percentile     \n",
      "95%   (-2.234, -0.430 )  \n",
      "Calculations and Intervals on Original Scale\n",
      "Warning : Percentile Intervals used Extreme Quantiles\n",
      "Some percentile intervals may be unstable\n",
      "\n",
      "\n",
      "[1] \"var10\"\n",
      "\n",
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in norm.inter(t, alpha):\n",
      "“extreme order statistics used as endpoints”\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS\n",
      "Based on 2 bootstrap replicates\n",
      "\n",
      "CALL : \n",
      "boot.ci(boot.out = boot.fit, type = \"perc\", t0 = boot.fit$t0[j], \n",
      "    t = boot.fit$t[, j])\n",
      "\n",
      "Intervals : \n",
      "Level     Percentile     \n",
      "95%   (-0.2589, -0.2589 )  \n",
      "Calculations and Intervals on Original Scale\n",
      "Warning : Percentile Intervals used Extreme Quantiles\n",
      "Some percentile intervals may be unstable\n"
     ]
    }
   ],
   "source": [
    "# Using the function \"boot.ci\" from package \"boot\", calculate \n",
    "# bootstrap CI for each predictor (including the intercept).\n",
    "# Note that var10 will be missing for every model;  this variable is the \n",
    "# Last predictor in the model\n",
    "\n",
    "# List the coefficient names \n",
    "names(boot.fit$t0)\n",
    "\n",
    "# Print the bootstrap CI\n",
    "for(j in 1:10){\n",
    "    cat(\"\\n\")\n",
    "    cat(\"\\n\")\n",
    "    print(names(boot.fit$t0[j]))\n",
    "    cat(\"\\n\")\n",
    "    cat(\"\\n\")\n",
    "    print(boot.ci(boot.fit,  t0 = boot.fit$t0[j], t = boot.fit$t[,j], type=\"perc\"))\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's \n",
      "-0.2589 -0.2589 -0.2589 -0.2589 -0.2589 -0.2589     998 \n"
     ]
    }
   ],
   "source": [
    "# Notice that the last predictor in the sorted vector of predictors is \"var9\"\n",
    "# and it consists of all NA's;  The point here is that Method II which uses the SAME\n",
    "# model for each bootstrap sample, CANNOT estimate ALL of the cofficients and their standard\n",
    "# errors;  But Method I, which uses permutations of the predictors, or each model estimation, \n",
    "# DOES ALLOW every predictor to be estimated a number of times - enough times to get a rough \n",
    "# estimate of the average c\"oefficient value and its standard devaition (the standard error)\n",
    "print(summary(boot.fit$t[,10]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'treament'</li><li>'control'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'treament'\n",
       "\\item 'control'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'treament'\n",
       "2. 'control'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] \"treament\" \"control\" "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "z.treat<-c(\"treament\", \"control\")\n",
    "z.treat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>'control'</li><li>'control'</li><li>'control'</li><li>'treament'</li><li>'control'</li><li>'control'</li><li>'treament'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'treament'</li><li>'treament'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'treament'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'control'</li><li>'treament'</li><li>'control'</li><li>'control'</li><li>'treament'</li><li>'control'</li><li>'control'</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'treament'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'treament'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'treament'\n",
       "\\item 'treament'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'treament'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'treament'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\item 'treament'\n",
       "\\item 'control'\n",
       "\\item 'control'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'control'\n",
       "2. 'control'\n",
       "3. 'control'\n",
       "4. 'treament'\n",
       "5. 'control'\n",
       "6. 'control'\n",
       "7. 'treament'\n",
       "8. 'control'\n",
       "9. 'control'\n",
       "10. 'control'\n",
       "11. 'control'\n",
       "12. 'control'\n",
       "13. 'control'\n",
       "14. 'control'\n",
       "15. 'control'\n",
       "16. 'control'\n",
       "17. 'control'\n",
       "18. 'control'\n",
       "19. 'control'\n",
       "20. 'control'\n",
       "21. 'control'\n",
       "22. 'control'\n",
       "23. 'control'\n",
       "24. 'treament'\n",
       "25. 'treament'\n",
       "26. 'control'\n",
       "27. 'control'\n",
       "28. 'control'\n",
       "29. 'control'\n",
       "30. 'control'\n",
       "31. 'control'\n",
       "32. 'control'\n",
       "33. 'control'\n",
       "34. 'treament'\n",
       "35. 'control'\n",
       "36. 'control'\n",
       "37. 'control'\n",
       "38. 'control'\n",
       "39. 'control'\n",
       "40. 'control'\n",
       "41. 'control'\n",
       "42. 'control'\n",
       "43. 'control'\n",
       "44. 'control'\n",
       "45. 'treament'\n",
       "46. 'control'\n",
       "47. 'control'\n",
       "48. 'treament'\n",
       "49. 'control'\n",
       "50. 'control'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"control\"  \"control\"  \"control\"  \"treament\" \"control\"  \"control\" \n",
       " [7] \"treament\" \"control\"  \"control\"  \"control\"  \"control\"  \"control\" \n",
       "[13] \"control\"  \"control\"  \"control\"  \"control\"  \"control\"  \"control\" \n",
       "[19] \"control\"  \"control\"  \"control\"  \"control\"  \"control\"  \"treament\"\n",
       "[25] \"treament\" \"control\"  \"control\"  \"control\"  \"control\"  \"control\" \n",
       "[31] \"control\"  \"control\"  \"control\"  \"treament\" \"control\"  \"control\" \n",
       "[37] \"control\"  \"control\"  \"control\"  \"control\"  \"control\"  \"control\" \n",
       "[43] \"control\"  \"control\"  \"treament\" \"control\"  \"control\"  \"treament\"\n",
       "[49] \"control\"  \"control\" "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample(z.treat, 50, replace=TRUE, prob=c(.90, 10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>2</li><li>1</li><li>3</li><li>8</li><li>9</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 2\n",
       "\\item 1\n",
       "\\item 3\n",
       "\\item 8\n",
       "\\item 9\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 2\n",
       "2. 1\n",
       "3. 3\n",
       "4. 8\n",
       "5. 9\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 2 1 3 8 9"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x<-c(2,1,3,8,9)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>2</li><li>1</li><li>3</li><li>8</li><li>9</li><li>10</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 2\n",
       "\\item 1\n",
       "\\item 3\n",
       "\\item 8\n",
       "\\item 9\n",
       "\\item 10\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 2\n",
       "2. 1\n",
       "3. 3\n",
       "4. 8\n",
       "5. 9\n",
       "6. 10\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1]  2  1  3  8  9 10"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x<-c(x, 10)\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>11</li><li>12</li><li>13</li><li>14</li><li>15</li><li>16</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 11\n",
       "\\item 12\n",
       "\\item 13\n",
       "\\item 14\n",
       "\\item 15\n",
       "\\item 16\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 11\n",
       "2. 12\n",
       "3. 13\n",
       "4. 14\n",
       "5. 15\n",
       "6. 16\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 11 12 13 14 15 16"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y<-c(11,12,13,14,15,16)\n",
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 2 × 6 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>x</th><td> 2</td><td> 1</td><td> 3</td><td> 8</td><td> 9</td><td>10</td></tr>\n",
       "\t<tr><th scope=row>y</th><td>11</td><td>12</td><td>13</td><td>14</td><td>15</td><td>16</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 2 × 6 of type dbl\n",
       "\\begin{tabular}{r|llllll}\n",
       "\tx &  2 &  1 &  3 &  8 &  9 & 10\\\\\n",
       "\ty & 11 & 12 & 13 & 14 & 15 & 16\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 2 × 6 of type dbl\n",
       "\n",
       "| x |  2 |  1 |  3 |  8 |  9 | 10 |\n",
       "| y | 11 | 12 | 13 | 14 | 15 | 16 |\n",
       "\n"
      ],
      "text/plain": [
       "  [,1] [,2] [,3] [,4] [,5] [,6]\n",
       "x  2    1    3    8    9   10  \n",
       "y 11   12   13   14   15   16  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rbind(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 6 × 2 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>x</th><th scope=col>y</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td> 2</td><td>11</td></tr>\n",
       "\t<tr><td> 1</td><td>12</td></tr>\n",
       "\t<tr><td> 3</td><td>13</td></tr>\n",
       "\t<tr><td> 8</td><td>14</td></tr>\n",
       "\t<tr><td> 9</td><td>15</td></tr>\n",
       "\t<tr><td>10</td><td>16</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 6 × 2 of type dbl\n",
       "\\begin{tabular}{ll}\n",
       " x & y\\\\\n",
       "\\hline\n",
       "\t  2 & 11\\\\\n",
       "\t  1 & 12\\\\\n",
       "\t  3 & 13\\\\\n",
       "\t  8 & 14\\\\\n",
       "\t  9 & 15\\\\\n",
       "\t 10 & 16\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 6 × 2 of type dbl\n",
       "\n",
       "| x | y |\n",
       "|---|---|\n",
       "|  2 | 11 |\n",
       "|  1 | 12 |\n",
       "|  3 | 13 |\n",
       "|  8 | 14 |\n",
       "|  9 | 15 |\n",
       "| 10 | 16 |\n",
       "\n"
      ],
      "text/plain": [
       "     x  y \n",
       "[1,]  2 11\n",
       "[2,]  1 12\n",
       "[3,]  3 13\n",
       "[4,]  8 14\n",
       "[5,]  9 15\n",
       "[6,] 10 16"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cbind(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "y<-y[-6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>11</li><li>12</li><li>13</li><li>14</li><li>15</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 11\n",
       "\\item 12\n",
       "\\item 13\n",
       "\\item 14\n",
       "\\item 15\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 11\n",
       "2. 12\n",
       "3. 13\n",
       "4. 14\n",
       "5. 15\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 11 12 13 14 15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>2</li><li>1</li><li>3</li><li>8</li><li>9</li><li>10</li></ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 2\n",
       "\\item 1\n",
       "\\item 3\n",
       "\\item 8\n",
       "\\item 9\n",
       "\\item 10\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 2\n",
       "2. 1\n",
       "3. 3\n",
       "4. 8\n",
       "5. 9\n",
       "6. 10\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1]  2  1  3  8  9 10"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in rbind(x, y):\n",
      "“number of columns of result is not a multiple of vector length (arg 2)”\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<caption>A matrix: 2 × 6 of type dbl</caption>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>x</th><td> 2</td><td> 1</td><td> 3</td><td> 8</td><td> 9</td><td>10</td></tr>\n",
       "\t<tr><th scope=row>y</th><td>11</td><td>12</td><td>13</td><td>14</td><td>15</td><td>11</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 2 × 6 of type dbl\n",
       "\\begin{tabular}{r|llllll}\n",
       "\tx &  2 &  1 &  3 &  8 &  9 & 10\\\\\n",
       "\ty & 11 & 12 & 13 & 14 & 15 & 11\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 2 × 6 of type dbl\n",
       "\n",
       "| x |  2 |  1 |  3 |  8 |  9 | 10 |\n",
       "| y | 11 | 12 | 13 | 14 | 15 | 11 |\n",
       "\n"
      ],
      "text/plain": [
       "  [,1] [,2] [,3] [,4] [,5] [,6]\n",
       "x  2    1    3    8    9   10  \n",
       "y 11   12   13   14   15   11  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rbind(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
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