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   "source": [
    "# Tutorial: Refresher for solving oridinary least squares\n",
    "\n",
    "This tutorial and the previous one explore math concepts that will be helpful for understanding the lectures and homeworks. \n",
    "\n",
    "## Goals:\n",
    "* Refresher on derivatives, logarithms and expected values\n",
    "\n",
    "This lab draws from [Paul's Math Notes](https://tutorial.math.lamar.edu/pdf/calculus_cheat_sheet_derivatives.pdf)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5zLxcLjDuMuo"
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   "source": [
    "---\n",
    "# Derivatives"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ahQqcU9qPPYd"
   },
   "source": [
    "## What is a derivative?\n",
    "\n",
    "The formal definition of a derivative is: \n",
    "\n",
    "$$\\frac{df}{dx} = \\lim_{h \\to 0} \\frac{f(x + h) - f(x)}{h}$$\n",
    "\n",
    "The plain language definition of a derivative is something along the lines of, \"How is my function $f$ changing with respect to the variable $x$?\" Put simply, you can think of a derivative as the slope of a function for given values of the variables. \n",
    "\n",
    "*See these two videos ([video 1](https://www.youtube.com/watch?v=tt2DGYOi3hc&list=PLmxWmlga0Kgoe-gvtTW4i32Lc_3JI_bEK&index=6), [video 2](https://www.youtube.com/watch?v=50Bda5VKbqA&list=PLmxWmlga0Kgoe-gvtTW4i32Lc_3JI_bEK&index=7)) for a satisfying explanation of how these definitions connect.*\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Examples\n",
    "\n",
    "Two quick examples to drive home the idea of what a derivative is: "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**1.**   The derivative of $x^2$ is $2x$. Let's plot both of these functions in R. "
   ]
  },
  {
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     "status": "ok",
     "timestamp": 1611522685078,
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    "id": "V-vZYT0SswuZ",
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   "outputs": [
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AABBBAIhQANUijKTJIIIIAAAggggAAC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\nGwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <- seq(0,5,0.1)\n",
    "head(x)\n",
    "\n",
    "f <- x^2 \n",
    "head(f)\n",
    "\n",
    "df_dx <- 2*x \n",
    "head(df_dx)\n",
    "\n",
    "library(tidyverse)\n",
    "# make a data frame so we can plot these nicely\n",
    "x_dat <- data.frame(x=x,f=f,df_dx=df_dx) \n",
    "# put data frame in long form\n",
    "x_dat <- gather(x_dat, \"func\",\"value\",f:df_dx) \n",
    "# makes it so \"f\" is the function plotted on left\n",
    "x_dat$func <- x_dat$func %>% factor() %>% relevel(\"f\")\n",
    "ggplot(x_dat,aes(x=x,y=value)) + geom_line() + facet_grid(. ~ func) # plot func"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HrR6KPlwuOtU"
   },
   "source": [
    "Notice how, in the \"f\" plot, the slope of the line increases as the value of `x` increases. This is reflected in the \"df_dx\" plot: larger values of `x` have a larger derivative, and this increase is linear. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "S4F3qppuum4P"
   },
   "source": [
    "\n",
    "**2.**   The derivative of $cos(x)$ is $-sin(x)$. Let's plot both of these. \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 437
    },
    "executionInfo": {
     "elapsed": 695,
     "status": "ok",
     "timestamp": 1611522806989,
     "user": {
      "displayName": "Patience Stevens",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gi-_9ZqhIFhAv1oMehJNvNuIKSTyrFQHzjxQKhx=s64",
      "userId": "01994571539255174942"
     },
     "user_tz": 300
    },
    "id": "-ShrJEOxvaha",
    "outputId": "aa56d06b-5c93-4f6c-a1e0-9bed288ae346"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ov1744cOVLOP/98Wbdundx1113Wx0uACCQrUHTaWdL1+JOTXZzlEEAAAQQCLJC9\ntFi6Tz5UCv7y1wC3wp7Qb7nlFikpKXEG/dJ72pliC5AgxXYJxLv/7//9P+natavceuutsm3b\ntkDETJAIIIAAAggggAAC3gusXbvWGeSrT58+cumll3ofQIBqJEEKUGe1DLWoqEiuuOIKqaio\nkPvuu6/lx/yOAAIIIIAAAggggIAj8Pvf/16qGy9Z1EvrdNAvptYFSJBatwnEJ+eee6506dJF\nHn74YSkvLw9EzASJAAIIIIAAAggg4J3AkiVL5IUXXpBx48bJGWec4V3FAa2JBCmgHWfCLiws\ndO5F2r59u/ztb38zb/MvAggggAACCCCAAAKOgLlfXa88ysjIQKUdARKkdoCC8PFFF10kubm5\ncs899zjPRwpCzMSIAAIIIIAAAggg4L7Axo0b5ZlnnpFBgwbJ8ccf736FIaiBBCkEndijRw85\n66yzZMOGDc4XIARNogkIfCXQOJx9Qxabqq9AeIUAAghESKDxbEeDnvHQH6akBO6//37nAPrF\nF1/sPCImqUIithB7HSHp8EsuucQ5ZXrHHXeEpEU0A4EvBEreeV1K5s+BAwEEEEAgggK148fJ\n1g2rpOzaayLY+tSbXFZWJo899pgz6vE3v/nN1AuMSAkkSCHp6MGDB8uJJ54oxcXF8uqrr4ak\nVTQDAQQQQAABBBBAIFkBvT99586dzv3qjFwXvyIJUvxW1s952WWXOTHefvvt1sdKgAgggAAC\nCCCAAALuCdTV1TmPgenQoYN8//vfd6+iEJZMghSiTp0wYYJMmzZN3n33XZk/f36IWkZTEEAA\nAQQQQAABBBIReP7552X9+vXOsN49e/ZMZNHIz0uCFLJVwJxFuu2220LWMpqDAAIIIIAAAggg\nEK/AnXfe6cyq96kzJSZAgpSYl/VzH3nkkTJy5EiZOXOmrFq1yvp4CRABBBBAAAEEEEAgvQLv\nvfeeLFiwQI466igZNmxYeguPQGkkSCHs5EsvvVQaGhrk1ltvDWHraBICCCCAAAIIIIBAWwLm\nwbA//OEP25qNz1oRIEFqBSbIb0+fPl369+8v//jHP2Tz5s1BbgqxIyBFJ50mXY/+OhIIIIAA\nAhEUyFq8VLodMEUKbvxLBFufXJNXrlwp//3vf2XMmDFyyCGHJFdIxJciQQrhCpCdnS0/+MEP\npKqqSswRhBA2kyZFRCBz6zbJ3LwlIq2lmQgggAACzQUyamsk6/PNkrFrV/O3ed2GwN133+18\nyr1HbSC18xEJUjtAQf343HPPlaKiInnggQeksrIyqM0gbgQQQAABBBBAAIE4BbZt2yYzZsyQ\nfv36ySmnnBLnUszWUoAEqaVISH7Xh4FpklRaWuoM2BCSZtEMBBBAAAEEEEAAgVYEHn74YefA\n+EUXXSR6RRFTcgIkSMm5BWKp73znO06cjz/+eCDiJUgEEEAAAQQQQACB5ARqa2vloYceko4d\nOzoHyZMrhaVUgAQpxOuBDvc9adIkefPNN50HhYW4qTQNAQQQQAABBBCItMCsWbNk69atcuqp\np0qnTp0ibZFq40mQUhW0fPnzzjvPiZCzSJZ3FOEhgAACCCCAAAIpCPzrX/9ylv7Wt76VQiks\nqgIkSCFfD8444wzJz8+Xf/7zn1JfXx/y1tK8MArsuP8u2fG3h8LYNNqEAAIIINCOQO3+w6T0\nuX9LxcUXtjNntD/WwRlefvllGTp0qEycODHaGGloPQlSGhBtLqJz587yjW98QzZs2OBcamdz\nrMSGQCyButGjpHbcmFgf8R4CCCCAQNgFGgedqp14gNTvs0/YW5pS+/7973+L3oN09tlnp1QO\nC38hQIIUgTXhnHPOcVqpD45lQgABBBBAAAEEEAiXgF4plJmZKWeeeWa4GuZTa0iQfIL3stqp\nU6fKvvvuKy+++KIz7LeXdVMXAggggAACCCCAgHsCixYtkqVLl8oRRxwhvXv3dq+iCJVMghSB\nzs7IyBC9Ya+6ulr0FCwTAggggAACCCCAQDgEGJwh/f1IgpR+UytLPOuss5xTr4xmZ2X3EBQC\nCCCAAAIIIJCwgB78fuqpp6SoqEiOO+64hJdngdgCJEixXUL3bt++fZ1Tr0uWLBE9FcuEAAII\nIIAAAgggEGyBV155RUpKSuS0006TDh06BLsxFkVPgmRRZ7gdCoM1uC1M+W4IdPzVNdLx5790\no2jKRAABBBCwXCBzzVrp/D+XSu7jT1geqT/hmSuDGL0uvf4kSOn1tLo0PfXarVs351RsZWWl\n1bESHAJGoMOrr0vuf2eZX/kXAQQQQCBCApnbt0vu8zMle8nSCLU6vqZu2bJFXnvtNRkxYoSM\nGzcuvoWYKy4BEqS4mMIxU05OjuiDY3fs2CEzZ84MR6NoBQIIIIAAAgggEEGBGTNmSF1dnTMQ\nVwSb72qTSZBc5bWv8G9/+9tOUOaUrH0REhECCCCAAAIIIIBAewL67KOsrCw5/fTT25uVzxMU\nIEFKECzosw8fPlwmTJggb775pqxfvz7ozSF+BBBAAAEEEEAgcgLz58+Xjz/+WI455hjp0aNH\n5NrvdoNJkNwWtrB8ziJZ2CmEhAACCCCAAAIIxClgrgTSx7gwpV+ABCn9ptaXOH36dMnLy5Mn\nn3zS+lgJEAEEEEAAAQQQQOArgaqqKnnmmWecgbf0DBJT+gVIkNJvan2JnTp1kqOOOkrWrl0r\nCxcutD5eAoy2QPkVl0vZL34abQRajwACCERUoK5/P9n926ul+uvHR1Rg72a/+OKLzoBbOvCW\nDsDFlH4BEqT0mwaixJNPPtmJ87nnngtEvAQZXYHKc86SyvPOjS4ALUcAAQQiLNDQs6dU/OBC\nqZk2NcIKezb9X//6l/MGzz7a0yWdv5EgpVMzQGUde+yxzmV2zz77bICiJlQEEEAAAQQQQCC6\nAvqoFh1oSwfdGjVqVHQhXG45CZLLwLYWX1BQIEceeaRzmd2iRYtsDZO4EEAAAQQQQAABBL4U\neOmll6S2tlZOOukkTFwUIEFyEdf2ornMzvYeIj4EEEAAAQQQQOArgeeff9755Rvf+MZXb/Iq\n7QIkSGknDU6Bepldbm6ucJldcPqMSBFAAAEEEEAgmgK7d++W2bNny5AhQ2TEiBHRRPCo1SRI\nHkHbWE1hYaEzmt2aNWtk8eLFNoZITAgggAACCCCAAAKNAv/973+lurpaOHvk/upAguS+sdU1\nmGtYGc3O6m6KdHB5//iX5D36t0gb0HgEEEAgqgIZW7ZI/j33S84770WVoKndXF7XROH6CxIk\n14ntruC4447jMju7uyjy0RX89TYpvPHmyDsAgAACCERRIGvDZ9Lxt9dJh5kvRbH5TW0uLy+X\n1157TQYOHChjx45tep8X7giQILnjGphS9TI7Hc1u9erVsmTJksDETaAIIIAAAggggEBUBGbN\nmiWVlZWMXudRh5MgeQRtczXmMjsGa7C5l4gNAQQQQAABBKIqYC6vM/tsUXXwqt0kSF5JW1yP\nucyO+5As7iRCQwABBBBAAIFICuiZo1deeUX69+8vEyZMiKSB140mQfJa3ML6OnbsKEcccYSs\nWrWKy+ws7B9CQgABBBBAAIHoCui9R3oP0oknnhhdBI9bToLkMbit1ZlTtlxmZ2sPERcCCCCA\nAAIIRFGAy+u873USJO/Nrazx+OOPlw4dOgiX2VnZPZEOqvqoI6TquKMjbUDjEUAAgagK1BcV\nSdU3vi61o0dFkkCfe/Tyyy9L79695cADD4ykgR+NzvajUuq0T8BcZqcPIVu6dKmMGhXNDZF9\nPUNEu6+/FgQEEEAAgYgK1A/aV3bee0dEWy8ye/Zs2bVrl5x55pmSkZERWQevG84ZJK/FLa7v\n5JNPdqLjMjuLO4nQEEAAAQQQQCAyAmafzNwKEZmG+9xQEiSfO8Cm6nU0Oy6zs6lHiAUBBBBA\nAAEEoipQW1srL774onTv3l2mTJkSVQZf2k2C5Au7nZV26tRJDj/8cFm5cqUUFxfbGSRRIYAA\nAggggAACERB49dVXZfv27fL1r39dMjPZZfeyy9H2UjsAdXGZXQA6iRARQAABBBBAIPQCM2bM\ncNrI5XXedzUJkvfmVteol9llZWWJDtbAhAACCCCAAAIIIOC9QF1dnTz99NPStWtXmTZtmvcB\nRLxGEqSIrwAtm9+5c2fnOlcdye6zzz5r+TG/I+C5QNbipZK9cLHn9VIhAggggIAFAo0PSM3+\naJ5krl9vQTDehfDWW2/Jli1b5IQTTpDsbAad9k7+i5pIkLwWD0B9xxxzjBPlrFmzAhAtIYZd\noMtFl0iXc78X9mbSPgQQQACBGALZH6+QriedLvl33x/j0/C+9cwzzziNO+WUU8LbSItbRoJk\ncef4FZpJkF555RW/QqBeBBBAAAEEEEAgsgI6ep0+o/LQQw+NrIGfDeecXQz9wsLCGO/G95Z5\niJfex5NKOfHV1vZcOTk5ST1UbPz48TJ48GDR07vajry8vLYraudTc2q4oKBA6uvr25nb3Y+1\nf/zuFzMSjbr4HYuuIxqHicld/dZL1/VMJ11HWk4ZjSP3eNlvXtbVsq3md+Oh/WPDOqIm5nts\nYvT6X2PihYfWlUo9+rgEnXJzc51tqNdWzevT73Z+fr40NDQ0f9uX1xpLKq7pCFrXYxu2vWYd\n0b+v+j33c9J+ibXt9SOmWN+9zLx8J5Qcj/5man/4va4uW7ZM1q1bJ6eeeqp06dKFfafGNUD/\nDumU6vc33m0hZ5Acbv7XUuD444+XiooKefPNN1t+xO8IIIAAAggggAACLgm89NJLTsknnnii\nSzVQbHsCnEGKIVRWVhbj3fje0qMO+jwhHX0klXLiq63tufSIkGbcycShz0O66667RJ/gnOro\nKZrt69Gy8sYbLdXFz0mPXibjkc6Y1UNPm+sD4PyORdcP7RNNhv2cdP3Qo3a6jrQ8upOrZx0b\nj357ZaXfG6/qas1cPXRdramp8T0WPaJbVVXl/LQWrxfv65F23b6m2jc6EE17k34nKisr25ut\n1c91HdZ41S2VclqtIIEPNA79fvu97dW/i3oFQar9l0DTY86qZ/X0x+84dNurcej6UV1dHTNW\nr97UM4yxtr1e1a/1qId+N3U9bdk32ZUVotex1Hj0N1M9dLvXMg4vPWbOnOlUpwmSfn91f8HP\nyYZ9J+0T3Y6kuu+k5cQzcQYpHqUIznPwwQc7p9y5DymCnU+TEUAAAQQQQMAXgV27dskHH3wg\nY8aMkf79+/sSA5WKkCCxFsQU0CPYehZpw4YNotfCMiHgl0B9zx5S37uXX9VTLwIIIICAjwIN\njVcX1DX+DWhoPHsQhWn27NnOWRId3pvJPwEusfPP3vqadTQ7Pc2rZ5FGjBhhfbwEGE6B7c/+\nO5wNo1UIIIAAAu0K1I0eJSXz3m93vrDMYK7c0XvBmfwT4AySf/bW13z00Uc7MZovq/UBEyAC\nCCCAAAIIIBBQAb1/8bXXXpOioiKZPHlyQFsRjrBJkMLRj660olevXjJu3DiZO3eulJaWulIH\nhSKAAAIIIIAAAgiILFy4ULZs2SJHHHGE748IiHp/kCBFfQ1op/16mZ2OPKRHNJgQQAABBBBA\nAAEE3BGYNWuWU7C5gsedWig1HgESpHiUIjzPscce67TefGkjTEHTEUAAAQQQQAAB1wT0lgYd\n8lzPIDH5K0CC5K+/9bXrJXY9e/Z0ziD5/RwN67EIEAEEEEAAAQQQSEJg27ZtsmDBApk4caJ0\n7949iRJYJJ0CJEjp1AxhWXokQ0/1bt++3bkXKYRNpEkIIIAAAggggICvAq+++qrzoHQur/O1\nG5oqJ0FqouBFawJ6H5JOjGbXmhDvuynQ7eDDpfv4g9ysgrIRQAABBCwVyJ6/QHr0308Kr7nW\n0gjTE5a5lYEEKT2eqZZCgpSqYASWP+ywwySn8UFtJEgR6Gwbm9g47KnUN/4wIYAAAghEUiBD\n/w7oT0gnvYVBHxCrowePGTMmpK0MVrNIkILVX75E27FjR5k6daosX75c1q9f70sMVIoAAggg\ngAACCIRR4IMPPpAdO3Y4tzTorQ1M/guQIPnfB4GIgMvsAtFNBIkAAggggAACARPg8jr7OowE\nyb4+sTIikyC9/PLLVsZHUAgggAACCCCAQBAFNEHKzs4WvaWByQ4BEiQ7+sH6KAYPHixDhgyR\nd955R8rLy62PlwARQAABBBBAAAHbBTZs2CDLli2TKVOmiN7SwGSHAAmSHf0QiCh0ZJWqqip5\n6623AhEvQSKAAAIIIIAAAjYL6PDeOpkrdWyONUqxkSBFqbdTbKv58r722msplsTiCMQvsP3p\nJ6T0pWfjX4A5EUAAAQRCI1A7aqRsm/OmlP/8J6FpU/OGmBGCjzrqqOZv89pngWyf66f6AAkc\ndNBBkpeXJ2+88UaAoibUoAvU9+kd9CYQPwIIIIBAsgIdOkj9Pvsku7TVy5mrcgYOHCjDhg2z\nOtaoBccZpKj1eArtzc3NdYb7Xr16NcN9p+DIoggggAACCCCAgN7XXVFR4QzvjYZdAiRIdvWH\n9dEceuihToycRbK+qwgQAQQQQAABBCwWeP31153o9B5vJrsESJDs6g/rozFDUL755pvWx0qA\nCCCAAAIIIICArQK6L5WTk+NcnWNrjFGNiwQpqj2fZLtHjRol3bp1E/1SNzQ0JFkKiyGAAAII\nIIAAAtEV2Lp1qzO896RJk6SgoCC6EJa2nATJ0o6xNayMjAznQWYlJSWyZMkSW8MkLgQQQAAB\nBBBAwFoBc6uCuTLH2kAjGhgJUkQ7PpVmcx9SKnosm6hAp4svl87nX5ToYsyPAAIIIBACgawV\nK6Vo+pmSf+8DIWjNV00wz5Q0+1RffcIrGwRIkGzohYDFYL7M3IcUsI4LaLg5CxZKzkfzAxo9\nYSOAAAIIpCKQUbZbcj74UDLXfZpKMdYtq/tQHTt2lPHjx1sXGwGJkCCxFiQssE/j8wj2228/\nef/990XH8GdCAAEEEEAAAQQQiE9g1apVsmHDBpk2bZpkZ/NI0vjUvJ2LBMlb79DUptfMVlZW\nygcffBCaNtEQBBBAAAEEEEDAbQFzBY65Isft+ig/cQESpMTNWKJRwHypzU2GoCCAAAIIIIAA\nAgi0L2ASJAZoaN/KrzlIkPySD3i9hxxyiGRmZgoJUsA7kvARQAABBBBAwDOB+vp6eeedd6RX\nr14ybNgwz+qlosQESJAS82LuLwU6d+4sEyZMkEWLFklpaSkuCCCAAAIIIIAAAu0I6H7T9u3b\nm67EaWd2PvZJgATJJ/gwVKunhvVhsW+//XYYmkMbLBXYfe01sutPf7A0OsJCAAEEEHBToG7f\nfWXn7X+Vqm+e4WY1npVtrrzh8jrPyJOqiAQpKTYWUgHz5TZfdlQQcEOg+rhjpPrE490omjIR\nQAABBCwXaOhaJFWnnSK148ZYHml84ZnnH33ta1+LbwHm8kWABMkX9nBUOmnSJMnPz+c+pHB0\nJ61AAAEEEEAAARcFdPTfOXPmyNChQ6Vv374u1kTRqQqQIKUqGOHlc3Jy5OCDD5Z169Y5PxGm\noOkIIIAAAggggECbAvpoFH1+pBkJuM2Z+dBXARIkX/mDXzmX2QW/D2kBAggggAACCLgvYIb3\nJkFy3zrVGkiQUhWM+PImQZo9e3bEJWg+AggggAACCCDQuoAmSPqIlGnTprU+E59YIUCCZEU3\nBDeIESNGOGP560h2OrY/EwIIIIAAAggggMCeAjq098KFC2X8+PGij0phsluABMnu/glEdDoS\ni37xdWx/JgTSLZB/251ScPOt6S6W8hBAAAEEAiCQ+dlGKfz9DdLhpZcDEG3rIerDYfXRKFxe\n17qRTZ+QINnUGwGN5fDDD3ciZ7jvgHag5WHnP/YPyX/gEcujJDwEEEAAATcEMjdvloI775Gc\nt95xo3jPyjT7SObWBM8qpqKkBEiQkmJjoeYC5miI+fI3/4zXCCCAAAIIIIBA1AX0+Uf6aBR9\nRAqT/QIkSPb3kfUR9unTR4YNGyY6fGVFRYX18RIgAggggAACCCDglcCGDRtk1apVMnnyZMnN\nzfWqWupJQYAEKQU8Fv1KQE8ZV1dXOw9A++pdXiGAAAIIIIAAAtEWYHjv4PU/CVLw+szKiHWg\nBp30JkQmBBBAAAEEEEAAgS8ESJCCtyaQIAWvz6yMeMqUKZKRkSHvvvuulfERFAIIIIAAAggg\n4IeAJkhdu3aVMWPG+FE9dSYhkJ3EMiyCwF4CRUVFMmrUKJk/f76Ul5dLQUHBXvPwBgLJCFR+\n83SRmppkFmUZBBBAAIGAC9T36CEVF5wvNVMnB7Ily5Ytk61bt8pJJ53kHEgOZCMiGDQJUgQ7\n3a0mH3zwwbJkyRKZO3euMIylW8rRK7f85z+JXqNpMQIIIICAI1C/T3/Zfd1vA6uho9fpxH5R\nsLqQS+yC1V9WRzt16lQnPi6zs7qbCA4BBBBAAAEEPBIw+0RmH8mjaqkmRQESpBQBWfwrAfPl\nf++99756k1cIIIAAAggggEBEBd5//33p0XiZ4NChQyMqEMxmkyAFs9+sjLpbt24yYsQImTdv\nnlRWVloZI0EhgAACCCCAAAJeCHz88cdSUlIiegsCU7AESJCC1V/WR6sbAX0e0ocffmh9rASI\nAAIIIIAAAgi4JcDldW7Jul8uCZL7xpGqwRwlMRuFSDWexiKAAAIIIIAAAl8KmH0hs28ETHAE\nSJCC01eBiNTch2Q2CoEImiCtFsiZ/aZ0ePV1q2MkOAQQQAABdwQyduyUDjP/K1nFy9ypwMVS\n9f4jfQzK8OHDXayFot0QIEFyQzXCZeqNiMOGDZOPPvpIqqqqIixB09Ml0OmXV0mnK/43XcVR\nDgIIIIBAgASyVq+WLhdeLHl//2eAohZZtWqVfP7556IHjjMyMgIVO8GKkCCxFqRdQE8la3Kk\ngzUwIYAAAggggAACURMwV9KYK2ui1v6gt5cEKeg9aGH85lpbs3GwMERCQgABBBBAAAEEXBMw\njzwx+0SuVUTBrgiQILnCGu1CzcaABCna6wGtRwABBBBAIKoCmiB16tRJRo8eHVWCQLebBCnQ\n3Wdn8L169ZIhQ4Y4Q33X1NTYGSRRIYAAAggggAACLgh8+umnsmHDBpk8ebJkZrKr7QKx60XS\na64TR7MCPYtUUVHBfUjR7H5ajQACCCCAQGQFuLwu+F1PghT8PrSyBeamRC6zs7J7AhVU7Yjh\nUjt6ZKBiJlgEEEAAgfQINBQUSM24MVLfr296CvSgFLPvY/aFPKiSKtIskJ3m8igOAUfA3Idk\njqLAgkCyAjsfujfZRVkOAQQQQCDgAnX7D5PtLz4bqFZogpSfny/jxo0LVNwE+5UAZ5C+suBV\nGgX69u0rgwYNkjlz5khtbW0aS6YoBBBAAAEEEEDAToFNmzbJ2rVrnfuPsrM5D2FnL7UfFQlS\n+0bMkaSAuQ9JHxrLhAACCCCAAAIIhF2Ay+vC0cMkSOHoRytbYS6ze/PNN62Mj6AQQAABBBBA\nAIF0CpAgpVPTv7JIkPyzD33N5ubEt956K/RtpYEIIIAAAggggIDee52bmysHHHAAGAEWIEEK\ncOfZHvo+++wjAwYMkHfeeUfq6upsD5f4EEAAAQQQQACBpAW2bt0qn3zyiUyaNEk6dOiQdDks\n6L8ACZL/fRDqCPQyu927dwv3IYW6m11tXEZJqWRsK3G1DgpHAAEEELBUoHGgp4zGxEPKyiwN\n8KuwzMi95gqarz7hVdAESJCC1mMBi9fchzR79uyARU64tgh0PXG6dDviOFvCIQ4EEEAAAQ8F\nshcvkR7jDpLCP/7Zw1qTq8rcf2T2fZIrhaVsECBBsqEXQhyD2UiQIIW4k2kaAggggAACCIie\nQcrJyZGJEyeiEXABEqSAd6Dt4Q8cOFD0XiQdya6+vt72cIkPAQQQQAABBBBIWKC0tFSKi4tl\nwoQJzkNiEy6ABawSIEGyqjvCGcyhhx4qO3bskCVLloSzgbQKAQQQQAABBCIt8P777zvtN1fO\nRBojBI0nQQpBJ9rehGnTpjkhmo2H7fESHwIIIIAAAgggkIgAAzQkomX/vCRI9vdR4CM0R1Pm\nzJkT+LbQAAQQQAABBBBAoKWAJkhZWVly0EEHtfyI3wMoQIIUwE4LWsgjRoyQrl27CglS0HqO\neBFAAAEEEECgPYFdu3bJ4sWLZezYsVJYWNje7HweAIHsAMRIiAEXyMjIkEMOOUSee+45Wb9+\nvTNoQ8CbRPgeCpS8OUukocHDGqkKAQQQQMAWgdrx42TLmuXSeHrGlpD2imPu3LnOQFRTpkzZ\n6zPeCKYAZ5CC2W+Bi1oTJJ04ixS4rvM/4MYhUxsfSe5/HESAAAIIIOC9QONBVudvgMUJ0gcf\nfOC4cHmd96uHWzWSILklS7l7CJAg7cHBLwgggAACCCAQEgGTIE2ePDkkLaIZJEisA54I6FEV\nfXia2Yh4UimVIIAAAggggAACLgrU1dXJRx99JIMGDZIePXq4WBNFeylAguSldoTrysvLk/Hj\nx8uyZctEb2ZkQgABBBBAAAEEgi6gz3isqKhg9Lqgd2SL+AMzSIPuVL/99tvOzrXeBDdw4MAW\nTfnqV5333Xff/eqNL18deeSRzlmMvT7gDU8E9CyS3sioP9oXTAgggAACCCCAQJAFzJUx3H8U\n5F7cO/ZAJEirV6+WCy+8UPbbbz/p37+/3H333XLdddfJ1KlT925R4zsLFiyQ66+/fq9Tnfo8\nHr3Mi8kfAU1s77zzTmegBhIkf/qAWhFAAAEEEEAgfQImQeL+o/SZ2lBSIBKkG264QU455RS5\n4oorRIeMfvjhh+Xmm2+Wxx9/3Pm9JeSKFStk9OjRcvvtt7f8iN99FDBHV8zGxMdQqDpAAl3O\nPEcyKipl+/NPBShqQkUAAQQQSIdA1tJi6XLhJVJ51hlS/tMfp6PItJah+zRdunSRYcOGpbVc\nCvNXwPp7kLZt2ybFxcUyffr0pmTopJNOks8++0yWLl0aU08TpOHDh8f8jDf9E9CbF/Us4Lx5\n86S2tta/QKg5UAJZ6zdI1rpPAxUzwSKAAAIIpEcgo7pastauk4yS0vQUmMZS9NmOGzdulAMP\nPLBpHzWNxVOUjwLWn0HatGmTw9OvX78mpu7duzcOid9BNm/e7JwpavrgyxeaIOXm5sqVV17p\nDAowcuRIufzyy53L81rOq2eltm7d2vS2ruSXXnpp0+/JvtBL+bp165bs4mlZLuvLZwaohZ9T\ndvYXq1lRUZEceuihzhnAdevWORsUr+PKzMz0vV/0LKhO2i+2rCP5+fled8Ue9Zl1pGvXrnu8\nr79k6nqcmeGZlX5v/O4Xs47o4CZ+XxasfaPbW7+fDm/WES/6Rs0LCgr2WhfjfcNsezt27JhS\nOfHW19Z86qbb3gYLHrZsw3dL/wboj1mf2rJz8zOzjnTq1Mn3vjH9YsM6EnPfqXNnpyvyGv9m\n5nqwX2X6Rrd77U0vv/yyM8vhhx+e9r8bZh3Vs1N+940N+06mL7RfUvk7oKMOxjNZnyBpZq47\nki138nWjUlq699EEHaBBk6o+ffrIOeecI1/72tdkxowZctlll8ljjz0m+ger+aT3K2kdZtI/\nJC3rMp8l8q9+wcyXLJHl3JjXfMncKDuRMnWlPuyww5wESU9Jm2cjJVJGOuZNR/+mIw7Wkb0V\nY/VNrSaUjT+xPtu7hPS842VdbUWs310bvr+2bMvUyou+0Z2BdNTjd3Jr1q14dvTMvG7+q4l/\nOlzTEaMt67QtfWNLHLG+ew2N+w66S5uV3bhf5eEB33i2vXPmzHFWR02Q3Fq3bekbt9qX6Pc5\n1X2n6sYzkvFM1idI+gcm1uVYmgHGOsKnCdATTzzhZJdmpRo1apScf/75MmvWLOdSveYwmv03\nz8z1y9k8YWo+bzyvdfnevXtLZWVlzAQunjLSNY/66B+ksrKydBWZVDl69ENj0TN+5hpddT/7\n7LOTKi+VhXr16uXEkUoZqS6rG92ePXtKeXm57NixI9XiUlpevy/6XdIhSv2c9MyRni3RgxvN\nv48aU7fGyzEz6upT+l4m0jbtmy1btiSySNrn1W2XninfvXu378Pid248eltVVeX8pL2hCRSo\nHvr3wFxVkMCie8zat2/fPX6P9Yu2N5Xvpm7vdLunB/H0b4Gfk7pt377d+Z77GYcetNS/5c2v\n2PAjHt3J05+dO3f6UX1Tnbrt1QO9ehtBvDtsTQun+YVe/q5xtNz2prmaNovTfRVdR/S7V1JS\nsse82Y1X+ei1BWVl5VLW7ID2HjOl8Re9okJ3wnX72970+uuvOwex9tlnn7T/jdJtr565179H\nsfaD24stnZ/bsO+kfaJx6P6KbtOSnUw57S1vfYKkX1zdgdOdyeYJkW7cYv2hM1+y5g3X+150\npydW4mPLEb7m8Yb59dChQ53kVYf6ZkIAAQQQQAABBIIooAmU3iOvz3j0+zL1IPrZHrP1gzRo\nVq5H3PVBXGbSFbK+vl6a35dkPluzZo1ztujTT7+6qVsTI83AdYhwJv8FdDQ7PZu0du1a/4Mh\nAgQQQAABBBBAIEGBDz/80NkXNSP0Jrg4s1suYH2CpJcpHHfccfLggw86pzv1coX77rtPTjjh\nBOeskPq+8cYbMnPmTId60KBBzqU6d911l3N5gyZHd9xxh+glPEcffbTl3RGN8MzGhOG+o9Hf\nqbZy5+1/lR3335VqMSyPAAIIIBBAgbqhQ2T7jH9IxQXnWxW92Yfh+UdWdUvagrE+QdKWXnLJ\nJc4oSieffLKceuqpzhmlH/3oR00Ir7zyijz55JNNv//0pz8Vfbjsaaed5gzUsGHDBrntttv2\nuESvaWZeeC5gNibm5kbPA6DCQAnUTjpAaicfGKiYCRYBBBBAID0CDY33a9VMmyr1gwelp8A0\nlWISJB39mCl8Atbfg6TkevbnlltucW6q1JurWg43e+211+7RMyNGjJC///3vzs2geo+RnoVi\nskdg3LhxTsJLgmRPnxAJAggggAACCMQnoPfGf/TRR7Lvvvs6AwfEtxRzBUkgEGeQDKgZ0cP8\n3t6/OsADyVF7St5/riN0TZgwQT7++OOURiLxPnJqRAABBBBAAIGoCyxdutQZIZizR+FdEwKV\nIIW3G6LXMnMfEqPZRa/vaTECCCCAAAJBFjCX15lbBoLcFmKPLUCCFNuFd10WMBsVs5FxuTqK\nRwABBBBAAAEE0iJgDu6ag71pKZRCrBIgQbKqO6ITjDktzX1I0elzWooAAggggEAYBPTgrt72\nMXz48DA0hzbEECBBioHCW+4L6MAb+tDY+fPn+/4UcfdbSw2pCBT+7g/S8arfpFIEyyKAAAII\nBFQgc92n0ulHP5PcJ5+yogWfffaZ6OjIkyZNkoyMDCtiIoj0C5Agpd+UEuMUmDJlilRVVcmi\nRYviXILZoiiQO/Mlyf3P81FsOm1GAAEEIi+QWVIieY3JUfb8hVZYmFsDzK0CVgRFEGkXIEFK\nOykFxitgrt01G5t4l2M+BBBAAAEEEEDADwGzz2L2YfyIgTrdFyBBct+YGloRMBsX7kNqBYi3\nEUAAAQQQQMAqAU2Q9Jmc+rgSpvAKkCCFt2+tb9ngwYNFn1VljsZYHzABIoAAAggggEBkBcrK\nymTJkiUyZswYKSgoiKxDFBpOghSFXra4jXoWadu2bbJ69WqLoyQ0BBBAAAEEEIgGFcPQAABA\nAElEQVS6wEcffST19fXC/UfhXxNIkMLfx1a3UEeB0Uk3OkwIIIAAAggggICtAuaKF3OLgK1x\nElfqAtmpF0EJCCQvYBIkfejaGWeckXxBLBlagfJL/kcyampC2z4ahgACCCDQukB9375S9sv/\nlZoJ41qfyaNPSJA8gragGhIkCzohyiGMGzfOudmRM0hRXgvabnvl985rewY+RQABBBAIrUB9\n715SfsVlvrdPL6378MMPZcCAAdK7d2/f4yEAdwW4xM5dX0pvRyA/P19Gjx4tS5culfLy8nbm\n5mMEEEAAAQQQQMB7geXLl8vu3buFy+u8t/ejRhIkP9Spcw8Bvcyurq5OFi604yFwewTHLwgg\ngAACCCAQeQE9e6TTxIkTI28RBQASpCj0suVtNBsbs/GxPFzCQwABBBBAAIGICZhbAcy90xFr\nfuSaS4IUuS63r8FmY0OCZF/fEBECCCCAAAIIiHP/UW5urowaNQqOCAiQIEWgk21v4qBBg6Rb\nt24M9W17RxEfAggggAACERTYuXOnrFixQnRgqZycnAgKRK/JJEjR63MrW6xnkTZv3izr16+3\nMj6C8k8g99/PSO6/ZvgXADUjgAACCPgmkNH4MPm8R/4m2XPm+hbDvHnznLrNLQG+BULFngmQ\nIHlGTUVtCZjL7PR5SEwINBcovPEm6fj7PzZ/i9cIIIAAAhERyPp0vXS68mrJffZ531rM/Ue+\n0ftWMQmSb/RU3FzAJEhmI9T8M14jgAACCCCAAAJ+CZh7pDmD5FcPeF8vCZL35tQYQ2DChAmS\nmZnp3AQZ42PeQgABBBBAAAEEfBHQS+z69u0r/fr186V+KvVegATJe3NqjCFQWFgoI0aMkMWL\nF0tVVVWMOXgLAQQQQAABBBDwVmDlypVSWlrK84+8Zfe9NhIk37uAAIyAnrquqamRRYsWmbf4\nFwEEEEAAAQQQ8E3AXPpvbgXwLRAq9lSABMlTbiprS8BsfMy1vm3Ny2cIIIAAAggggIDbAmaf\nhPuP3Ja2q/xsu8IhmigLkCBFufdbb3v1IQdLBpddtg7EJwgggECIBRo6d5aqo4+UuuHDfGml\nnkHKzs6WsWPH+lI/lfojQILkjzu1xhAYMmSIdOnShQfGxrCJ8lu7b/pTlJtP2xFAAIFIC9Tt\nN1h2PvqALwbl5eVSXFwso0ePlvz8fF9ioFJ/BLjEzh93ao0hkJGR4dwE+dlnn8mmTZtizMFb\nCCCAAAIIIICANwILFy6Uuro6MVe4eFMrtdggQIJkQy8QQ5OA2QiZa36bPuAFAggggAACCCDg\noYDZF+H+Iw/RLamKBMmSjiCMLwTMRshslHBBAAEEEEAAAQT8EGAEOz/U7aiTBMmOfiCKLwVI\nkFgVEEAAAQQQQMAGAT1Y261bNxk0aJAN4RCDhwIkSB5iU1X7Ap0bR6sZNmyY6HW/+kwkJgQQ\nQAABBBBAwGuB9evXy+bNm3lArNfwltRHgmRJRxDGVwJ6H1JV47DOS5Ys+epNXkVWIGvFSsn6\neEVk20/DEUAAgUgLVFRK1tJiydz0uacMXF7nKbd1lZEgWdclBMRADawDzQW6nPd9KTrjnOZv\n8RoBBBBAICIC2cuXS7djTpT82+/ytMXmXmhz6b+nlVOZ7wIkSL53AQG0FDAJkjl60/JzfkcA\nAQQQQAABBNwU0H0QffzIAQcc4GY1lG2pAAmSpR0T5bD2339/6dixo8ydOzfKDLQdAQQQQAAB\nBHwQqK6ulkWLFonZH/EhBKr0WYAEyecOoPq9BTIzM50jNp9++qls3bp17xl4BwEEEEAAAQQQ\ncElAB4rSJMlc0eJSNRRrsQAJksWdE+XQzDW/5hrgKFvQdgQQQAABBBDwTmDOnDlOZSRI3pnb\nVhMJkm09QjyOwIEHHuj8S4LECoEAAggggAACXgp88MEHTnUkSF6q21VXtl3hEA0CXwiYmyJJ\nkFgj6jt3koxsNlWsCQgggEAkBbKypb5LZ5H8PM+arwlSp06dZOjQoZ7VSUV2CbDXYVd/EM2X\nAvrk6sGDB8uCBQukvr5e9L4kpmgKbP/v89FsOK1GAAEEEJDasaNlW/ECzyT04bDr1q2Tww47\njH0Pz9Ttq4i9Tvv6hIi+FNCzSOXl5fLxxx9jggACCCCAAAIIuC5gLq8z90K7XiEVWClAgmRl\ntxCUCkyYMMGB4HlIrA8IIIAAAggg4IWAecQI9x95oW1vHSRI9vZN5CMzR2/mz58feQsAEEAA\nAQQQQMB9AXMGydwL7X6N1GCjAAmSjb1CTI7A6NGjJbvx5vx58+YhggACCCCAAAIIuCqg9zzr\nQdkhQ4aI3gvNFF0BEqTo9r31Lc/NzZVRo0bJsmXLnHuRrA+YABFAAAEEEEAgsALLly+XsrIy\nHhAb2B5MX+AkSOmzpCQXBPQUd11dnSxatMiF0ikSAQQQQAABBBD4QsBcscL9R6wRJEisA1YL\ncB+S1d3jSXBdjzxeuk051JO6qAQBBBBAwC6B7IWLpMeQUVJ47fWuB2bueSZBcp3a+gpIkKzv\nomgHaEayM0d1oq0RzdZnVFRIRnlFNBtPqxFAAIGoCzTeF6R/B6SmxnUJ3dfQe5/HjRvnel1U\nYLcACZLd/RP56PQp1vo0axKkyK8KACCAAAIIIOCaQEVjEqb3POsAUXl5ea7VQ8HBECBBCkY/\nRTbKjIwMGT9+vHz66aeybdu2yDrQcAQQQAABBBBwT0DvddZ7nrm8zj3jIJVMghSk3oporOY+\nJM4iRXQFoNkIIIAAAgi4LMD9Ry4DB6x4EqSAdVgUw+U+pCj2Om1GAAEEEEDAOwFzENYclPWu\nZmqyUYAEycZeIaY9BMzTrM3Ga48P+QUBBBBAAAEEEEhRQPcxCgsLZf/990+xJBYPg0B2GBpB\nG8It0Lt3b+nbt6/zdOtwt5TWxRLY/vijktE4ihETAggggED0BGpHjJCS2a9IfVFn1xpfUlIi\n69atk2nTpklmJucOXIMOUMGsBQHqrCiHqmeRtm/fLqtXr44yQyTbXj9oX6nbb3Ak206jEUAA\ngcgL5OVK3bAh0tCzp2sU5v4jc8WKaxVRcGAESJAC01XRDtRstLjMLtrrAa1HAAEEEEAg3QJm\n38Lsa6S7fMoLngAJUvD6LJIRm42WOcoTSQQajQACCCCAAAJpFzAJkhkUKu0VUGDgBEiQAtdl\n0QxYn4Wkz0T66KOPoglAqxFAAAEEEEDAFQE9+NqrVy/p16+fK+VTaPAESJCC12eRjNiMLLNk\nyRKpqamJpAGNRgABBBBAAIH0CujgDDpIg7lSJb2lU1pQBUiQgtpzEYxbN15VVVVSXFwcwdbT\nZAQQQAABBBBItwCX16VbNBzlkSCFox8j0QpzdMdszCLRaBopnX78c+n8g8uQQAABBBCIoEDW\nylXS5VvnSd5Dj7rSerNPYfYxXKmEQgMnQIIUuC6LbsDm5knuQ4rWOpAz5wPJeff9aDWa1iKA\nAAIIOAIZu3ZJhzfeEk2U3JjM4E9mH8ONOigzeAIkSMHrs8hGPHLkSMnLyxNztCeyEDQcAQQQ\nQAABBFIWqKurk0WLFsmQIUOkc2f3HkSbcqAU4LkACZLn5FSYrEB2draMHTtWPvnkE9nVeESJ\nCQEEEEAAAQQQSFZg2bJlUlFRIZw9SlYwvMuRIIW3b0PZMrMRW7BgQSjbR6MQQAABBBBAwBsB\nc0UK9x954x2kWkiQgtRbxNo0DCf3IbEyIBAtgTfffFM2bNgQrUbTWgQQcFXA3H9EguQqcyAL\nJ0EKZLdFN+iJEyc6jTcbtehK0HIEoiNQX18vp556qhx55JHRaTQtRQAB1wX0DFJOTo6MHj3a\n9bqoIFgC2cEKl2ijLjBw4EDp1q0bAzVEaEUou+qXIrV1EWoxTW0poPcd7t69Ww466KCWH/E7\nAgiEXKBuwADZddOfpHb/YWltaXl5uSxfvty5t7lDhw5pLZvCgi9AghT8PoxcC/Q+pFdffVU2\nbtwoffv2jVz7o9bgqpO/EbUm094WAuaM8YEHHtjiE35FAIGwCzR07yaV55yV9mYuXLhQ9Ow0\nl9elnTYUBXKJXSi6MVqNMBszc3NltFpPaxGInoBJkDiDFL2+p8UIuCVgtitmn8Kteig3mAIk\nSMHst0hHbe5DIkGK9GpA4yMkoDsymZmZHOmNUJ/TVATcFjD7EGZ0XLfro/xgCZAgBau/iLZR\nYPz48Y6D2biBggAC4RWoqamRpUuXij4ourCwMLwNpWUIIOCpgO5DdOrUSYYOHeppvVQWDAES\npGD0E1E2E9BBGnSwBr1+uKGhodknvEQAgbAJFBcXS3V1tXD/Udh6lvYg4J/Atm3bZP369c4B\n14yMDP8CoWZrBUiQrO0aAmtLQE+J66hWOroVEwIIhFfA3CdAghTePqZlCHgtYK5A4f4jr+WD\nUx8JUnD6ikibCZhrhvUsElO4BfLvfUDy77g73I2kda0KkCC1SsMHCERCIHPT51Lw51ukw6uv\np629JkEy+xJpK5iCQiNAghSaroxWQ8x9SGbnKVqtj1Zr8+9/SAruvDdajaa1TQL6HddnlIwZ\nM6bpPV4ggEB0BDI3bZLCv/xVcl6bnbZGmwTJDPqUtoIpKDQCPAcpRldmZyfPYq5l1X9TKSdG\nWAm/paM+2RKHBq8exifhxrRYQE+La1kLFixI2NnvfsnKynJaY1vftCD29FezXmjf7HVfmV4f\n3vifl/3mZV2xoM06ot9hv2PRGDQeP+LQBzl+/PHHzn0Cubm5DpUXcaT63TT955dby3VK4zDf\nsZafef27F/3XVpvUwpbvlcZpwzqi64bG4edk1s9Y3z0TW2Ya96v06hN9jmL//v33arauH7at\nI3sF6cMbfn93tU90irWOJMJh1rX2lkk+E2iv5AB/rqOapDrpipSOclKJw2xU/F6pc3JynGbo\nCFR77fwm2UC1HT58uCxevFjy8/Pj3nnTL5jf/WK+nOridyxmHTF9lGR3pLyYWUc7duy4V1mZ\nGY0bxcY/jF5Z2bCOmD8EeubEvN4LxqM3tG90PTEJikfVOtWYBzlOnjy5aQfOi/VA25yXl5d0\nU833SsvQPvRz0rbo9ypd295U2qIuXvRfWzHq98mG77jZ5hUUFDgPK20rZrc/s8HDtDHmOlLw\nxeiV+l3KTsP+2Zo1a6SkpEROOeWUmOujxqB/p8332MTm9b9mHUnnvlOybbBhHUnXvlNdXV1c\nDCRIMZhKS0tjvBvfW7oS6R9FHZo2lXLiq63tuXTDqytUWVlZ2zO6/GmXLl1EY9mxY4fEu2LG\nE9LYsWNl2bJl8t5778no0aPjWUR69erle7/oRq9nz57OyFxq4uekO07aJxUVFX6GIV27dnX+\nGG3fvn2vHblu9XWSUd/gWb9p3/j93dUdge7du0tlZaXs2rXL177p3LmzVFVVOT9eB/LWW285\nVeoQ37W1taKJfKp9o0eN25t0+52Ku27vdLun217tQz8nXY/Sve1Npj19+vRxtjWp9l8ydTdf\nRhN9/dm5c2fztz1/rdteTRZ1PdNRGv2cevToIbG2vV7GpPsquo7o97zlOpK9a6d0bQymsnE7\nVJbC/plpz+zZX1yqp9uVlnXpPHrQVZMjHQjKz0m3vbq/oOuquvg52bDvpH2icej3RdfXZCct\nJ55HRnAPUrLCLOe7APch+d4FBICAqwLmHkNupHaVmcIRiJSAXpqvE9uVSHV7wo0lQUqYjAVs\nETAbN7OxsyUu4kAAgfQIaIKkZ2N4kGN6PCkFAQREzIGXcePGwYFAqwJcYtcqDR/YLjBq1Cjn\n9LPZ2NkeL/ElJ1B1yjdEqvy9BCW5yFkqFQG9LEzvFZg6darv92Gl0g6WRQCB1ATqGy8TrTjn\nLKmdeEBqBTUurffiLVq0SPbdd1/n0u6UC6SA0AqQIIW2a8PfML3XS68hLi4udq7zT+Wm6vBr\nBbeFZb/6ZXCDJ/KkBcyZYXOmOOmCWBABBAItUD9gH9l905/S0gZ9uLzeW3TUUUelpTwKCa8A\nl9iFt28j0TK9D0lvXly6dGkk2ksjEYiKgDkzTIIUlR6nnQi4L8CBF/eNw1IDCVJYejKi7WCg\nhoh2PM0OvYDZkTHf8dA3mAYigIDrAma7woEX16kDXwEJUuC7MNoNMBs5c7Q52hq0HoHwCOh3\nWod/13sFmBBAAIF0COh2RYcUHzNmTDqKo4wQC5Aghbhzo9A0fVis3ntkjgpFoc20EYGwC2ze\nvFk2btwonD0Ke0/TPgS8E9Bn/i1ZssQZFTPWQ8m9i4SagiBAghSEXiLGVgX0IWr6kFi98dLv\nB+K2GiQfIIBAQgLmjDAJUkJszIwAAm0I6IPl9cHNbFfaQOKjJgESpCYKXgRVQC+z06E7Fy5c\nGNQmEHcbAjnvzZGcd95rYw4+CpuASZDMJbRhax/tQQCB+AUydu2SnNffkKwVK+NfKMacbFdi\noPBWqwIkSK3S8EFQBMxOlNn4BSVu4oxPoNNP/lc6X3x5fDMzVygEzHfZfLdD0SgagQACSQlk\nrVwlRd8+X/IeeSyp5c1C5lJ8ziAZEf5tS4AEqS0dPguEgNnYmY1fIIImSAQQaFVAzwb36dNH\nevfu3eo8fIAAAggkIqD7CFlZWc5l+Yksx7zRFCBBima/h6rVQ4YMEb3h0hx1DlXjaAwCERNY\nt26dlJSUCGePItbxNBcBFwWqqqpE70EaMWKEM7CTi1VRdEgESJBC0pFRboYO2Tlu3DjRHavS\n0tIoU9B2BAIvYA50mDPDgW8QDUAAAd8F9GHyNTU1HHjxvSeCEwAJUnD6ikjbEDBHm83OVRuz\n8hECCFgsYL7D5jttcaiEhgACAREwl+Bz4CUgHWZBmCRIFnQCIaQuYHamGMkudUtKQMBPAZMg\nsSPjZy9QNwLhEmC7Eq7+9KI12V5UQh0IuC1gdqbMRtDt+ijfO4G6wYMko6LCuwqpyTeB+vp6\nWbRokQwaNEiKiop8i4OKEUDAHoGGxofB1w4dIg09eiQdlJ5Bys3Nde5BSroQFoyUAAlSpLo7\nvI0dMGCAdOvWjYEaQtjFO/7xSAhbRZNiCZgHPh977LGxPuY9BBCIoEDdiOFS+sYrSbe8vLxc\nVqxY4TwgNicnJ+lyWDBaAlxiF63+DnVr9SzS559/Lps2bQp1O2kcAmEVMGeAzSWzYW0n7UIA\nAe8E9NJ7PTvNdsU78zDURIIUhl6kDY6AuczO3IwJCwIIBEvAJEjmuxys6IkWAQRsFDD3JrNd\nsbF37I2JBMneviGyBAXM0SGzk5Xg4syOAAI+C+h3NzMzU8aOHetzJFSPAAJhETD7BGYfISzt\noh3uCpAguetL6R4KmI0fZ5A8RKcqBNIkUFtbK8XFxTJs2DApKChIU6kUgwACURfQfQLdpgwd\nOjTqFLQ/AQESpASwmNVugV69eknfvn2FBMnufiI6BGIJaHKkT7vnMphYOryHAALJCOzYsUNW\nr17tnJXWs9NMCMQrwNoSrxTzBUJAzyKVlpbKunXrAhEvQcYhUN44xHfjKERM4RYwBzZIkMLd\nz7QOgYQFGgdYkLIyaTyCkvCi5v4jc4VJwgWwQGQFSJAi2/XhbPi4ceOchplrjsPZymi1qttR\nx0v3KYdFq9ERbK3ZkSFBimDn02QE2hDIXrhIeg4bI4XX/bGNuWJ/ZPYF2K7E9uHd1gVIkFq3\n4ZMACpijRPPmzQtg9ISMQHQF9AxSVlaWjBo1KroItBwBBNIqYBIks2+Q1sIpLNQCJEih7t7o\nNc4cJTKX60RPgBYjEDyB6upqWbZsmfOU+7y8vOA1gIgRQMBKAT0z3aVLFxk0aJCV8RGUvQIk\nSPb2DZElIVBUVORsCBcvXiwNDQ1JlMAiCCDgtYAO0FBTU8MADV7DUx8CIRbYunWrbNiwge1K\niPvYzaaRILmpS9m+COh9SLt375ZPPvnEl/qpFAEEEhMwZ3zNGeDElmZuBBBAYG8Btit7m/BO\n/AIkSPFbMWdABMxOlrnpOyBhEyYCkRVgRyayXU/DEXBNwNx/ZPYJXKuIgkMpQIIUym6NdqPM\nxpAEKdrrAa0PjoAmSDk5Oc49SMGJmkgRQMBmAZMgMUCDzb1kb2zZ9oZGZAgkJzB27FhnQXNU\nOrlSWMoWgdKXn7clFOJwQaCyslKWL18uo0ePlg4dOrhQA0UigECQBWrHjpGtxQukIcHtgx4k\n7dGjh/Tr1y/IzSd2nwQ4g+QTPNW6J9CpUycZMmSILFq0SOr1AXNMgRZoaOxP/WEKp8CSJUuk\nrq6OG6nD2b20CoHUBRqH/2/o0lkkP/4RLjdu3Chbtmxhu5K6fmRLIEGKbNeHu+E6UENFRYWs\nWLEi3A2ldQgEXMCc6TWXxga8OYSPAAIWCLBdsaATAh4CCVLAO5DwYwuYnS2zkYw9F+8igIDf\nAuY7ar6zfsdD/QggEHwBs13Rg6VMCCQjQIKUjBrLWC9gNopmI2l9wASIQEQF9Duam5srw4cP\nj6gAzUYAgXQLmL/9HHhJt2x0yiNBik5fR6qlOlBDRkaGMJJdpLqdxgZMoLy83Hle2ahRoyQ7\nmzGDAtZ9hIuAtQL6t793797Oj7VBEpjVAiRIVncPwSUrUFhYKEOHDhVzA3iy5bAcAgi4J2AG\nUuEor3vGlIxA1ATWr18vJSUlDNAQtY5Pc3tJkNIMSnH2COhOlxlC2J6oiCRRgc7nfk+6nP6t\nRBdj/gAIcBlMADqJEBHwWSBr2XLpetQJkn/bnXFFYq4cMZfax7UQMyHQQoAEqQUIv4ZHwGwc\nzU5YeFoWrZZkr1wl2Ss+iVajI9JasyPDGaSIdDjNRCAJgYzGZ6VlNyZJmZ9vjmtp8zef7Upc\nXMzUigAJUiswvB18AbNxNBvL4LeIFiAQLgH9bubn58uwYcPC1TBagwACvgmYAy/mIKlvgVBx\noAVIkALdfQTflsDo0aMlMzOTgRraQuIzBHwS2L17t6xcuVLGjBkjWY0PgmRCAAEE0iGgCVK/\nfv2kZ8+e6SiOMiIqQIIU0Y6PQrMLCgpk//33l6VLl0pNTU0UmkwbEQiMgDnKa870BiZwAkUA\nAWsF1q1bJ6WlpcLZI2u7KDCBkSAFpqsINBkB3fmqrq6WZcuWJbM4yyCAgEsCJEguwVIsAhEW\nMJfUc+AlwitBmppOgpQmSIqxU8AcRTIbTTujJCoEoidgvpPmOxo9AVqMAALpFjAHXtiupFs2\neuXxZL7o9XmkWmyOIpmNZqQaH5LG7vrLjSJ1dSFpDc0wApog6fPKhgwZYt7iXwQQQGAvgbr9\nBsuORx+QugH77PVZyzc48NJShN+TFSBBSlaO5QIhMGrUKOcGcBKkQHRXzCBrpk2N+T5vBldg\nx44dsmbNGpk6daozkEpwW0LkCCDgtkBD585SffSRcVWjf+v79+8v3bt3j2t+ZkKgNQEusWtN\nhvdDIZCXlycjRoyQ4uJi516kUDSKRiAQcAFzwMKc4Q14cwgfAQQsEFi9erXs3LlT2K5Y0Bkh\nCIEEKQSdSBPaFtCNpY5ip0kSEwII+C9gLoNhR8b/viACBMIiwIGXsPSkHe0gQbKjH4jCRQFz\ns6bZKXOxKopGAIE4BMx3kQQpDixmQQCBuATYrsTFxExxCpAgxQnFbMEVMDthZuMZ3JYQOQLh\nENDvYufG+woGDRoUjgbRCgQQ8F3A/I0fO3as77EQQPAFSJCC34e0oB2BkSNHSk5OjpiNZzuz\n8zECCLgoUFJSIuvXrxfdicnIyHCxJopGAIGoCDQ0NMiiRYtk4MCB0rVr16g0m3a6KECC5CIu\nRdsh0KFDB9Ekafny5VJZWWlHUEQRt0DBH/8shddeH/f8zGi3gDlQYc7s2h0t0SGAgN8CmY0H\nVDr+4irJ/c9zrYayatUq2b17NwM0tCrEB4kKkCAlKsb8gRTQ+5DqGp+lY3bOAtmIiAad9/R/\nJO+Jf0e09eFrNjdSh69PaRECbgpkbt0m+Y/9XbI/+LDVaszfdg68tErEBwkKkCAlCMbswRQw\nG80PP2x9AxvMlhE1AsESMDsyEyZMCFbgRIsAAtYKmO2KGZTJ2kAJLDACJEiB6SoCTUXAbDTn\nzp2bSjEsiwACKQrojkxRUZEMGDAgxZJYHAEEEPhCwJyZNn/rcUEgVQESpFQFWT4QAvqwWL0X\niTNIgeguggypwNatW2Xjxo3cJxDS/qVZCPghUF9f7wzQMHjwYGd0TD9ioM7wCZAgha9PaVEM\nAR3FbtSoUc7DYsvLy2PMwVsIIOC2AJfBuC1M+QhET2DlypWif9fNpfTRE6DFbgiQILmhSplW\nCujGU480LVmyxMr4CAqBsAuYy2DYkQl7T9M+BLwT4MCLd9ZRqik7So2lrdEWMDtl8+bNk4MO\nOijaGAFqfcX3vytSXROgiAm1NQF2ZFqT4X0EEGhNoL53byn78WVSe+DEmLOY7Yr5Gx9zJt5E\nIEEBEqQEwZg9uAJm1CxzFDu4LYlW5BUXXxStBoe4tfrd69atm+yzzz4hbiVNQwCBdArU9+0j\n5Vf+b6tFmr/p+vBpJgTSJcAldumSpBzrBYYNGyZ5eXliNqbWB0yACIRIYMuWLbJp0yZhlKkQ\ndSpNQcBnAX2+4eLFi2Xo0KHSsWNHn6Oh+jAJpJQg6Y7mjBkz5KWXXnJM1q5dGyYb2hIygays\nLDnggANEb+gsKysLWetoDgJ2C5jLYEiQ7O4nokMgSAIrVqyQiooKDrwEqdMCEmtSCdLSpUv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DNUS1FVBvtwgggpoGaNDobm6VzXJIIB6B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\nGSG2YdeW+gAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <- seq(0,5,0.1)\n",
    "f <- cos(x)\n",
    "x_min <- x[which.min(f)] # find the x value where f is at minimum\n",
    "df_dx <- -sin(x)\n",
    "\n",
    "#plotting\n",
    "# make a data frame so we can plot these nicely:\n",
    "x_dat <- data.frame(x=x,f=f,df_dx=df_dx) \n",
    "# put data frame in long form:\n",
    "x_dat <- gather(x_dat, \"func\",\"value\",f:df_dx) \n",
    "# makes it so \"f\" is the function plotted on left\n",
    "x_dat$func <- x_dat$func %>% factor() %>% relevel(\"f\")\n",
    "\n",
    "ggplot(x_dat,aes(x=x,y=value)) + geom_line() + facet_grid(. ~ func) +\n",
    "      geom_vline(xintercept = x_min,linetype=\"dashed\",color=\"red\")# add line where f is min"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "JJQxNP4Yw8t5"
   },
   "source": [
    "At `x = 0`, the slope of the function is 0. Then it becomes negative, with increasing steepness from `x = 0` to around `x = 1.5`, and decreasing steepness from there to around `x=3`. This description of the slope matches how the derivative looks. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bimNQey1sxV9"
   },
   "source": [
    "The main reason for us to work with derivatives in this class is as a tool for finding what value of $x$ minimizes $f(x)$. When $f(x)$ reaches a local minimum or maximum, the derivative is 0 (like at the red dotted line in the second example above). So if we're trying to find the value of $\\beta_0$ that minimizes the Mean Squared Error (MSE - see lecture on Least Squares Solution), we can take the derivative of MSE with respect to $\\beta_0$ ($\\frac{dMSE}{d\\beta_0}$), set it to 0, and then solve for $\\beta_0$. We'll work through a couple examples of finding the value that minimizes a function. But first, a few tips on *how* to calculate the derivative of a function. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "T4Masuo8PVEK"
   },
   "source": [
    "## Tips on calculating the derivative"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "49ssxVafV-Ab"
   },
   "source": [
    "### 1. A constant function\n",
    "\n",
    "If your function is a constant, e.g. $f(x) = 3$, then the derivative is 0. This makes sense if you picture the plot of $f(x)=3$. No matter what the value of $x$, the value of $f(x)$ is 3, so the plot of $f(x) = 3$ is a flat line with slope 0. As a general expression of this rule: \n",
    "$$\\frac{d}{dx}(c) = 0$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "k1u5C0fCPbUk"
   },
   "source": [
    "### 2. The Power Rule\n",
    "\n",
    "If the function you're working with fits the format $f(x) = x^n$, then you can calculate the derivative as $\\frac{df}{dx} = nx^{n-1}$. For example, $\\frac{d}{dx}(x^3) = 3x^{2}$, and $\\frac{d}{dx}(x^{p+q+1}) = (p+q+1)x^{p+q}$. The general expression of this rule is: \n",
    "$$\\frac{d}{dx}(x^n) = nx^{n-1}$$\n",
    "\n",
    "Note that a lot of functions can be rewritten to match the $x^n$ format:\n",
    "\n",
    "* $\\frac{d}{dx}(\\frac{1}{x}) = \\frac{d}{dx}(x ^ {-1}) = -x^{-2} = -\\frac{1}{x^2}$\n",
    "\n",
    "* $\\frac{d}{dx}(\\sqrt{x}) = \\frac{d}{dx}(x^{\\frac{1}{2}}) = \\frac{1}{2}x^{-\\frac{1}{2}} = \\frac{1}{2\\sqrt{x}}$\n",
    "\n",
    "* $\\frac{d}{dx}(x) = \\frac{d}{dx}(x^1) = 1x^0 = 1$. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "VRngGu2fYQpG"
   },
   "source": [
    "### 3. Taking out a constant \n",
    "\n",
    "If your function is multiplied by a constant, your derivative will also by multiplied by that constant. For example, $\\frac{d}{dx}(4x^2) = 4(2x) = 8x$. As a general expression of this rule: \n",
    "$$\\frac{d}{dx}(cf(x)) = c\\frac{df}{dx}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "X1ETBv6oZMl5"
   },
   "source": [
    "### 4. Added functions\n",
    "If your function is actually two functions added together, like $3x - x^2$, then you can just take the derivative of each term separately ($3x$, then $-x^2$) and add them together: $\\frac{d}{dx}(3x-x^2) = 3 - 2x$. As a general expression of this rule: \n",
    "$$\\frac{d}{dx}(f(x) + g(x)) = \\frac{df}{dx} + \\frac{dg}{dx}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yKlLq4ZCuAIv"
   },
   "source": [
    "### 5. Functions with two variables\n",
    "\n",
    "The reason we talk about taking the derivative *with respect to $x$* is that in cases where the function has multiple variables, you need to specify which variable you are focusing on: my function $f(x_1,x_2)$ could change with respect to $x_1$ differently from how it changes with respect to $x_2$, and thus $\\frac{df}{dx_1} \\neq \\frac{df}{dx_2}$. If you're calculating the derivative with respect to one variable, you can treat the other variable as if it is a constant. For example, the derivative of $2x_1 + 4x_1x_2 - {x_2}^2$ with respect to $x_1$ is $2 + 4x_2$. We ignore the last term because it doesn't contain $x_1$, so we view it as a constant and its derivative (according to rule 1 above) is 0. The derivative of this function with respect to $x_2$ is $4x_1 - 2x_2$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "F71i433ByKkn"
   },
   "source": [
    "## Using the derivative to find minimizing values: 2 worked examples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "t_EZvjP7yQ4Z"
   },
   "source": [
    "Now we'll practice finding the value of $x$ for which $f(x)$ is minimal.\n",
    "\n",
    "**Example 1** $f(x) = (x-2)^2 + 6$\n",
    "\n",
    "Let's see what a plot of this function looks like: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 437
    },
    "executionInfo": {
     "elapsed": 474,
     "status": "ok",
     "timestamp": 1611447050260,
     "user": {
      "displayName": "Patience Stevens",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gi-_9ZqhIFhAv1oMehJNvNuIKSTyrFQHzjxQKhx=s64",
      "userId": "01994571539255174942"
     },
     "user_tz": 300
    },
    "id": "wPAikNwQuXKf",
    "outputId": "206d4709-0127-4fd9-a2a6-7d465391e7a6"
   },
   "outputs": [
    {
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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <- seq(0,5,0.1)\n",
    "f <- (x-2)^2 + 6\n",
    "x_dat <- data.frame(x,f)\n",
    "require(ggplot2) #in case you need to load the library again\n",
    "ggplot(x_dat,aes(x=x,y=f)) + geom_line()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TTZw9NTTuscG"
   },
   "source": [
    "Just looking at the plot above, we can tell the minimum of $f(x)$ is where $x=2$. But let's make sure, using the derivative method! \n",
    "\n",
    "$$\n",
    " \\frac{d}{dx}((x-2)^2 + 6) = \\frac{d}{dx}(x-2)^2 + \\frac{d}{dx}6 \\\\\n",
    "   = \\frac{d}{dx}(x^2-4x+4) + 0\\\\\n",
    "  = \\frac{d}{dx}(x^2)-4\\frac{d}{dx}x+\\frac{d}{dx}4 \\\\\n",
    "  = 2x - 4\n",
    "$$\n",
    "\n",
    "In the first line, I split up the function using rule **4**. Then I expanded the $(x-2)^2$ term using the [Foil method](https://www.mathsisfun.com/definitions/foil-method.html), set $\\frac{d}{dx}6$ to 0 as in rule **1**, and finally took the derivative of $x^2 - 4x + 4$ by applying rule **2** to the first term, rules **2** and **3** to the second term, and rule **1** to the last term. \n",
    "\n",
    "Now let's set it to 0 and solve for x. \n",
    "\n",
    "\n",
    "$$\n",
    " 2x - 4 = 0  \\\\\n",
    " 2x  = 4  \\\\\n",
    " x  = 2\n",
    "$$\n",
    "\n",
    "So $f(x)$ is at a minimal value when $x=2$, which matches what we see in the plot above. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qIYnrqwCxz0n"
   },
   "source": [
    "**Example 2** $f(x_1,x_2) = 4x_1x_2 + \\frac{1}{x_2} + {x_1}^2$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "rHW_ZfDizPPi"
   },
   "source": [
    "This one's a little trickier to visualize since there's two input variables, so let's just jump right into finding the minimizing solutions for $x_1$.\n",
    "\n",
    "$$\n",
    " \\frac{d}{dx_1}(4x_1x_2 + \\frac{1}{x_2} + {x_1}^2) = \\frac{d}{dx_1}(4x_1x_2) + \\frac{d}{dx_1}(\\frac{1}{x_2}) +  \\frac{d}{dx_1}{x_1}^2 \\\\\n",
    "   = 4x_2  + 2x_1\\\\\n",
    "$$\n",
    "\n",
    "We split up the three terms. The second term becomes 0 because when we're taking the derivative with respect to $x_1$, we can think of terms that only contain $x_2$ as constant (rule **5**) and then apply rule **1**. The first term, $4x_1x_2$, can be expressed as $(4x_2)x_1$, and the $4x_2$ term can be moved outside the derivative as a constant (rules **3**,**5**). Then use rule **2** to find $\\frac{d}{dx_1} x_1$ and $\\frac{d}{dx_1} {x_1}^2$. \n",
    "\n",
    "Setting $\\frac{df}{dx_1}$ to 0 and solving for $x_1$, we find that the minimizing value of $x_1$ is $-2x_2$.\n",
    "\n",
    "Repeat for $x_2$:\n",
    "\n",
    "$$\n",
    " \\frac{d}{dx_2}(4x_1x_2 + \\frac{1}{x_2} + {x_1}^2) = \\frac{d}{dx_2}(4x_1x_2) + \\frac{d}{dx_2}(\\frac{1}{x_2}) + \\frac{d}{dx_2}({x_1}^2)  \\\\\n",
    "   = 4x_1 - \\frac{1}{{x_2}^2}  \\\\\n",
    "$$\n",
    "\n",
    "The derivative of the third term is 0 because of rules **1** and **5**. We find the derivative of the second term using rule **2** and of the first term using rules **3** and **5**. \n",
    "\n",
    "Setting the derivative to 0 and solving for $x_2$: \n",
    "\n",
    "$$\n",
    "  4x_1 - \\frac{1}{{x_2}^2} = 0  \\\\\n",
    "   {x_2}^2 = \\frac{1}{4x_1}  \\\\\n",
    "$$\n",
    "\n",
    "Since we know the minimizing value for $x_1$ is $-2x_2$ from our work above, we can try plugging that in here to find the values of $x_1$ and $x_2$ that will minimize the whole function: \n",
    "\n",
    "$$\n",
    "  {x_2}^2 = \\frac{1}{4(-2x_2)}  \\\\\n",
    "   -8 {x_2}^3 = 1  \\\\\n",
    "   {x_2}^3 = -\\frac{1}{8} \\\\\n",
    "   {x_2} = -\\frac{1}{2}\n",
    "$$\n",
    "\n",
    "Plugging this into our equation for $x_1$, we get $x_1 = -2x_2 = 1$. So $f(x_1,x_2)$ is minimized at $x_1 = 1$, $x_2 = -\\frac{1}{2}$\n",
    "\n",
    "That's all for derivatives! Let's move on to logarithms. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wrTQ74JuSr9t"
   },
   "source": [
    "---\n",
    "# Logarithms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jcg9BsdCj6E1"
   },
   "source": [
    "## What is a logarithm?\n",
    "\n",
    "Using a logarithm is the opposite of using an exponent: You can re-write the function $4^x = 16$ as $x = \\log_{4}16$. The small number at the base of $\\log$ (the *base*) is the number that will be raised to a certain power, and the big number is what we get once it's been raised to that power. $\\log_{5}25 = 2$ because $5^2 = 25$, and $\\log_{2}16 = 4$ because $2^4=16$. \n",
    "\n",
    "When we use logarithms in this class, we'll use the *natural log*: this is a logarithm where the base is always [$e$](https://www.youtube.com/watch?v=_-x90wGBD8U). We write natural logs as $\\ln$.\n",
    "\n",
    "$$\\ln{x} = \\log_{e}x$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_I2Gz5SlA_JU"
   },
   "source": [
    "## Working with logarithms\n",
    "\n",
    "Here's a couple basic rules for working with natural logarithms. You can read more about these rules [here](https://mathinsight.org/logarithm_basics). \n",
    "\n",
    "### 1. e\n",
    "\n",
    "Taking the natural log of $e$ is 1. Similarly, $\\ln e^x = x$ and $e^{\\ln{x}} = x$. Try proving this to yourself using our definition of natural logs above. \n",
    "\n",
    "### 2. Product\n",
    "\n",
    "The natural log of a product is the sum of the natural logs of its factors:\n",
    "\n",
    "$$\\ln{xy} = \\ln{x} + \\ln{y}$$\n",
    "\n",
    "### 3. Quotient\n",
    "\n",
    "The natural log of two terms divided is the natural log of the numerator minus the natural log of the denominator. \n",
    "\n",
    "$$\\ln{\\frac{x}{y}} = \\ln{x} - \\ln{y}$$\n",
    "\n",
    "### 4. Exponents\n",
    "\n",
    "You can move the exponent inside a log term to the outside as a coefficient. \n",
    "\n",
    "$$\\ln{x^y} = y\\ln{x}$$\n",
    "\n",
    "### 5. Derivative\n",
    "\n",
    "The derivative of $ln(x)$ is $\\frac{1}{x}$ (relatedly, the derivative of $e^x$ is $e^x$).\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yj7qrZadBBUp"
   },
   "source": [
    "## Why are we using logarithms in this class?\n",
    "The logarithm function is monotonically increasing. For our purposes, that means that when we take the log (natural log or otherwise) of a function, the values of the input variables where that function reaches a local minimum or maximum are the same before and after the transformation. Here's a quick demonstration of that idea: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 437
    },
    "executionInfo": {
     "elapsed": 1061,
     "status": "ok",
     "timestamp": 1611504916553,
     "user": {
      "displayName": "Patience Stevens",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AOh14Gi-_9ZqhIFhAv1oMehJNvNuIKSTyrFQHzjxQKhx=s64",
      "userId": "01994571539255174942"
     },
     "user_tz": 300
    },
    "id": "0-9HpVuSKkUt",
    "outputId": "6675b346-4c6c-490d-c569-9eed593a88f8"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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KFIM0EigAACCCCAAAIIIIBAJAIUSJEo\nsQ4CCCCAAAIIIIAAAgiEQoACKRRpJkgEEEAAAQQQQAABBBCIRIACKRIl1kEAAQQQQAABBBBA\nAIFQCFAghSLNBIkAAggggAACCCCAAAKRCFAgRaLEOggggAACCRdYsWKFbNq0KeH90AECCCCA\nAAJlCVAglaXDfQgggAACrgnccccdkpmZKVu3bnWtTzpCAAEEEEDgSAEKpCNF+BsBBBBAwHWB\ngoICWbhwoTRr1kzq1avnev90iAACCCCAgC1AgWRL8BMBBBBAwDOB5cuXy969e6V79+6ejYGO\nEUAAAQQQUAEKJB4HCCCAAAKeC+jeI126devm+VgYAAIIIIBAuAUokMKdf6JHAAEEjBBYsGCB\nNQ72IBmRDgaBAAIIhFqAAinU6Sd4BBBAwAwBLZCqVasmbdq0MWNAjAIBBBBAILQCFEihTT2B\nI4AAAmYIbNmyRTZs2CAdO3aU5GTelszICqNAAAEEwivAO1F4c0/kCCCAgBEC9uF1Xbp0MWI8\nDAIBBBBAINwCFEjhzj/RI4AAAp4LUCB5ngIGgAACCCBQRIACqQgGvyKAAAIIuC+gBZIeWteh\nQwf3O6dHBBBAAAEEjhCgQDoChD8RQAABBNwTyMnJkSVLlsgJJ5xgTdLgXs/0hAACCCCAwNEF\nKJCO7sKtCCCAAAIuCHz99deSl5dnTdDgQnd0gQACCCCAQLkCFEjlErECAggggECiBOzzjzi8\nLlHCtIsAAgggEK0ABVK0YqyPAAIIIOCYgF0gderUybE2aQgBBBBAAIF4BCiQ4tFjWwQQQACB\nmAUKCwvliy++kPr160ujRo1ibocNEUAAAQQQcFKAAslJTdpCAAEEEIhYYNWqVbJz507OP4pY\njBURQAABBNwQoEByQ5k+EEAAAQRKCNiH13Xs2LHEfdyAAAIIIICAVwIUSF7J0y8CCCAQcoGF\nCxdaAhRIIX8gED4CCCBgmAAFkmEJYTgIIIBAWAR0D1LlypXlpJNOCkvIxIkAAggg4AMBCiQf\nJIkhIoAAAkETyMrKktWrV0u7du0kNTU1aOERDwIIIICAjwUokHycPIaOAAII+FXAPryO6b39\nmkHGjQACCARXgAIpuLklMgQQQMBYAbtA4gKxxqaIgSGAAAKhFaBACm3qCRwBBBDwTsCewa59\n+/beDYKeEUAAAQQQOIoABdJRULgJAQQQQCBxAocOHZJFixZJq1atpFatWonriJYRQAABBBCI\nQYACKQY0NkEAAQQQiF1g8eLFcvDgQS4QGzshWyKAAAIIJFCAAimBuDSNAAIIIFBSwD68jusf\nlbThFgQQQAAB7wUokLzPASNAAAEEQiVgF0hM0BCqtBMsAggg4BsBCiTfpIqBIoAAAsEQ0AIp\nIyNDWrRoEYyAiAIBBBBAIFACFEiBSifBIIAAAmYLrF+/XrZt2ybsPTI7T4wOAQQQCLMABVKY\ns0/sCCCAgMsC9uF1nH/kMjzdIYAAAghELECBFDEVKyKAAAIIxCswb948qwkKpHgl2R4BBBBA\nIFECFEiJkqVdBBBAAIESAlogVaxYUX71q1+VuI8bEEAAAQQQMEGAAsmELDAGBBBAIAQCWVlZ\n8t1331nFUVpaWggiJkQEEEAAAT8KUCD5MWuMGQEEEPChgH3+UefOnX04eoaMAAIIIBAWAQqk\nsGSaOBFAAAGPBezzjyiQPE4E3SOAAAIIlClAgVQmD3cigAACCDgloAVSUlISU3w7BUo7CCCA\nAAIJEaBASggrjSKAAAIIFBXIycmRxYsXy4knnijVqlUrehe/I4AAAgggYJQABZJR6WAwCCCA\nQDAFvvzyS8nLyxMOrwtmfokKAQQQCJIABVKQskksCCCAgKECnH9kaGIYFgIIIIBACQEKpBIk\n3IAAAggg4LTA/PnzrSY7derkdNO0hwACCCCAgKMCFEiOctIYAggggMCRAvn5+bJw4UJp2rSp\n1K9f/8i7+RsBBBBAAAGjBCiQjEoHg0EAAQSCJ7B06VLJzs7m/KPgpZaIEEAAgUAKUCAFMq0E\nhQACCJgjMHfuXGswHF5nTk4YCQIIIIBA6QIUSKXbcA8CCCCAgAMCTNDgACJNIIAAAgi4JkCB\n5Bo1HSGAAALhFFiwYIHUrl1bWrRoEU4AokYAAQQQ8JUABZKv0sVgEUAAAX8JrF69WrZv3y4c\nXuevvDFaBBBAIMwCFEhhzj6xI4AAAgkW4PC6BAPTPAIIIICA4wIUSI6T0iACCCCAgC1gX/+o\nc+fO9k38RAABBBBAwGgBCiSj08PgEEAAAX8L6B6k9PR0Oemkk/wdCKNHAAEEEAiNAAVSaFJN\noAgggIC7Alu3bpV169ZJhw4dJCUlxd3O6Q0BBBBAAIEYBSiQYoRjMwQQQACBsgXs84+YoKFs\nJ+5FAAEEEDBLIKnwp8WsITk7mry8vLgaTE5OFv0XbztxDeKXjZOSkqzfTEiZfhtcUFBg/XMi\ntnjaqFChguTn58fThCPban7ssZiQI33cao68XtREFxNypCaaGxPyE4bn0E033STPPvusfPrp\np9K7d2/rcVDWf0693ubm5lqH9ZXVl94X7+u6U+Mtb5yR3K+vP/qP53xxLVNeB017f7Dfq4pr\nuf+Xac8hFeD9ofjjwJTHilPPIX3dr1SpUvEgj/JX4I952LZt21HCjvymjIwMqVixojVNrddP\nmipVqlhP3Ozs7MgDSMCa+oJWv3590Q8hO3fuTEAP0TVZp04d2bFjh+cvapqf6tWry549e+TA\ngQPRBeHw2vrhu1q1asbkR19g430uOkGk+dHHrQn5qVu3ruTk5FiPFydii6eNevXqJSQ/06dP\ntw6ta9asWUTt62O2atWqsmvXLjl06FDMIaWlpUVUIMX7mKxRo4bVj74OxltsxRzsLxvqG35q\naqrs3bs33qbi3r5BgwaWh07v7vVSq1Yty8SE/OhY9u/fb/3z0kU/aOp1yUzJjz52dSxef8bS\ncyXVRnPk5aJj0OeQSZ+xsrKyPP/yRfOjr7nxfsbSzyORFEgcYufls4C+EUAAgYAK6Af1pUuX\nysknnxxRsRJQBsJCAAEEEPChAAWSD5PGkBFAAAHTBRYuXGh9I8z03qZnivEhgAACCBwpQIF0\npAh/I4AAAgjELcAEDXET0gACCCCAgEcCFEgewdMtAgggEGQBCqQgZ5fYEEAAgWALUCAFO79E\nhwACCLguoCcXL1q0SFq1aiU60Q0LAggggAACfhKgQPJTthgrAggg4AOBr7/+Wg4ePCicf+SD\nZDFEBBBAAIESAhRIJUi4AQEEEEAgHoG5c+dam1MgxaPItggggAACXglQIHklT78IIIBAQAXm\nzJljRdalS5eARkhYCCCAAAJBFqBACnJ2iQ0BBBBwWSA/P18WLFggjRs3lmOOOcbl3ukOAQQQ\nQACB+AUokOI3pAUEEEAAgV8EFi9ebF2JvmvXrpgggAACCCDgSwEKJF+mjUEjgAACZgrYh9dR\nIJmZH0aFAAIIIFC+AAVS+UasgQACCCAQoYA9QQMFUoRgrIYAAgggYJwABZJxKWFACCCAgD8F\nCgoKZP78+dKwYUNp0qSJP4Ng1AgggAACoRegQAr9QwAABBBAwBmBZcuWye7du4W9R8540goC\nCCCAgDcCFEjeuNMrAgggEDgB+/wjpvcOXGoJCAEEEAiVAAVSqNJNsAgggEDiBDj/KHG2tIwA\nAggg4J4ABZJ71vSEAAIIBFagsLBQ5s2bJ3Xr1pUWLVoENk4CQwABBBAIvgAFUvBzTIQIIIBA\nwgVWrlwpWVlZnH+UcGk6QAABBBBItAAFUqKFaR8BBBAIgQDnH4UgyYSIAAIIhESAAikkiSZM\nBBBAIJECdoHEDHaJVKZtBBBAAAE3BCiQ3FCmDwQQQCDgAjpBQ0ZGhhx33HEBj5TwEEAAAQSC\nLkCBFPQMEx8CCCCQYIFVq1bJtm3bpHPnzpKUlJTg3mgeAQQQQACBxApQICXWl9YRQACBwAsw\nvXfgU0yACCCAQKgEKJBClW6CRQABBJwXsAskLhDrvC0tIoAAAgi4L0CB5L45PSKAAAKBEtAJ\nGqpXry4nnnhioOIiGAQQQACBcApQIIUz70SNAAIIOCKwbt062bRpk3X+UXIybymOoNIIAggg\ngICnArybecpP5wgggIC/BZje29/5Y/QIIIAAAiUFKJBKmnALAggggECEAvb5R1z/KEIwVkMA\nAQQQMF6AAsn4FDFABBBAwFwB3YNUpUoVadOmjbmDZGQIIIAAAghEIUCBFAUWqyKAAAII/Ffg\nhx9+kA0bNkjHjh2lQoUK/72D3xBAAAEEEPCxAAWSj5PH0BFAAAEvBTi8zkt9+kYAAQQQSJQA\nBVKiZGkXAQQQCLgAEzQEPMGEhwACCIRUgAIppIknbAQQQCBeAd2DVLlyZWnXrl28TbE9Aggg\ngAACxghQIBmTCgaCAAII+Edgy5YtsmbNGunQoYOkpqb6Z+CMFAEEEEAAgXIEKJDKAeJuBBBA\nAIGSAvb5R126dCl5J7cggAACCCDgYwEKJB8nj6EjgAACXgn85z//sbru1q2bV0OgXwQQQAAB\nBBIiQIGUEFYaRQABBIItoAWSnn/061//OtiBEh0CCCCAQOgEKJBCl3ICRgABBOIT2LRpk6xd\nu1Y6deokaWlp8TXG1ggggAACCBgmQIFkWEIYDgIIIGC6AIfXmZ4hxocAAgggEI8ABVI8emyL\nAAIIhFDALpC6d+8ewugJGQEEEEAg6AIUSEHPMPEhgAACDgvMnj1bqlSpIm3btnW4ZZpDAAEE\nEEDAewEKJO9zwAgQQAAB3whs2LBB9F/nzp0lJSXFN+NmoAgggAACCEQqQIEUqRTrIYAAAgiI\nfXhdjx490EAAAQQQQCCQAhRIgUwrQSGAAAKJEZg1a5bVMNc/SowvrSKAAAIIeC9AgeR9DhgB\nAggg4BuBOXPmSPXq1aVNmza+GTMDRQABBBBAIBoBCqRotFgXAQQQCLHAmjVrRK+B1LVrV0lO\n5u0jxA8FQkcAAQQCLcA7XKDTS3AIIICAcwI6e50uHF7nnCktIYAAAgiYJ0CBZF5OGBECCCBg\npAATNBiZFgaFAAIIIOCwAAWSw6A0hwACCARVQPcgZWRkyPHHHx/UEIkLAQQQQAABoUDiQYAA\nAgggUK7AypUrZdu2bdb5R0lJSeWuzwoIIIAAAgj4VYACya+ZY9wIIICAiwL24XXdu3d3sVe6\nQgABBBBAwH0BCiT3zekRAQQQ8J0ABZLvUsaAEUAAAQRiFKBAihGOzRBAAIGwCBQWFsrcuXOl\nbt260qpVq7CETZwIIIAAAiEVoEAKaeIJGwEEEIhUYPny5ZKVlSUcXhepGOshgAACCPhZgALJ\nz9lj7AgggIALArNmzbJ64fpHLmDTBQIIIICA5wIUSJ6ngAEggAACZgvYF4hlD5LZeWJ0CCCA\nAALOCFAgOeNIKwgggEAgBQoKCqzzjxo2bCjNmjULZIwEhQACCCCAQFEBCqSiGvyOAAIIIFBM\nYMmSJbJnzx7h8LpiLPyBAAIIIBBgAQqkACeX0BBAAIF4BezpvXv06BFvU2yPAAIIIICALwQo\nkHyRJgaJAAIIeCNgT9DA+Ufe+NMrAggggID7AhRI7pvTIwIIIOALgby8PJk/f740btxYGjVq\n5IsxM0gEEEAAAQTiFaBAileQ7RFAAIGACnz99deyf/9+rn8U0PwSFgIIIIDA0QUokI7uwq0I\nIIBA6AU4vC70DwEAEEAAgVAKUCCFMu0EjQACCJQvMGPGDGulnj17lr8yayCAAAIIIBAQAQqk\ngCSSMBBAAAEnBXJycuSLL76Q1q1bS7169ZxsmrYQQAABBBAwWoACyej0MDgEEEDAG4G5c+dK\nbm6u9OrVy5sB0CsCCCCAAAIeCVAgeQRPtwgggIDJAvb5R1z/yOQsMTYEEEAAgUQIUCAlQpU2\nEUAAAZ8LzJw5UypUqCBdu3b1eSQMHwEEEEAAgegEKJCi82JtBBBAIPACWVlZsmTJEjnllFOk\natWqgY+XABFAAAEEECgqQIFUVIPfEUAAAQTEPryO2et4MCCAAAIIhFGAAimMWSdmBBBAoAwB\nu0Di/KMykLgLAQQQQCCwAhRIgU0tgSGAAAKxCej1jypXrizt27ePrQG2QgABBBBAwMcCFEg+\nTh5DRwABBJwW2LBhg6xfv96anCE1NdXp5mkPAQQQQAAB4wUokIxPEQNEAAEE3BOYPn261RnX\nP3LPnJ4QQAABBMwSoEAyKx+MBgEEEPBUgPOPPOWncwQQQAABAwQokAxIAkNAAAEETBAoLCy0\nZrCrXbu2nHDCCSYMiTEggAACCCDgugAFkuvkdIgAAgiYKbB06VLRayDp9N5JSUlmDpJRIYAA\nAgggkGABCqQEA9M8Aggg4BeBmTNnWkPl+kd+yRjjRAABBBBIhAAFUiJUaRMBBBDwoQAFkg+T\nxpARQAABBBwXoEBynJQGEUAAAf8J5Obmyrx58+TYY4+VRo0a+S8ARowAAggggIBDAhRIDkHS\nDAIIIOBngS+++EJycnKs84/8HAdjRwABBBBAIF4BCqR4BdkeAQQQCIDAjBkzrCi4/lEAkkkI\nCCCAAAJxCVAgxcXHxggggEAwBPT6RzpzXbdu3YIREFEggAACCCAQowAFUoxwbIYAAggERWDP\nnj2yaNEiOfnkk6VWrVpBCYs4EEAAAQQQiEmAAikmNjZCAAEEgiPw+eefS35+PucfBSelRIIA\nAgggEIcABVIceGyKAAIIBEFg6tSpVhhc/ygI2SQGBBBAAIF4BSiQ4hVkewQQQMDnAp999pmk\npaVJx44dfR4Jw0cAAQQQQCB+AQqk+A1pAQEEEPCtwObNm2X58uVWcVS5cmXfxsHAEUAAAQQQ\ncEqAAskpSdpBAAEEfCgwc+ZMa9QcXufD5DFkBBBAAIGECFAgJYSVRhFAAAF/CEyfPt0aaO/e\nvf0xYEaJAAIIIIBAggUokBIMTPMIIICAqQKFhYWiBVLt2rWtKb5NHSfjQgABBBBAwE0BCiQ3\ntekLAQQQMEhgyZIlsmPHDunbt691kViDhsZQEEAAAQQQ8EyAAskzejpGAAEEvBXQ6x/p0q9f\nP+sn/yGAAAIIIICACAUSjwIEEEAgpAL2+UdnnHFGSAUIGwEEEEAAgZICFEglTbgFAQQQCLxA\ndna2LFiwQFq3bi2ZmZmBj5cAEUAAAQQQiFSAAilSKdZDAAEEAiQwe/ZsOXTokDB7XYCSSigI\nIIAAAo4IpDjSikONzJgxQ6pVqya//vWvi7VYUFAgixcvlkWLFkn9+vWlT58+UrFixWLr8AcC\nCCCAQOQC9vlHFEiRm7EmAggggEA4BIzZg6TFz3333SfLli0rJr99+3YZMmSIPPzww/LDDz/I\ns88+K1deeaXs2bOn2Hr8gQACCCAQuYCef1SpUiXp3Llz5BuxJgIIIIAAAiEQ8HwPUl5enrz+\n+uvWv6SkpBLkY8eOtY6Pf+6556z7cnJyrILp7bfflmuuuabE+tyAAAIIIFC2wMaNG2X16tXW\n4XVaJLEggAACCCCAwH8FPN+DNHHiRPnoo4+sPUSNGzf+78h++S09PV0uv/zyw7dXrlxZjj/+\nePnxxx8P38YvCCCAAAKRC9iH15166qmRb8SaCCCAAAIIhETA8z1I3bt3l7POOktSUlLE3ktU\n1L5ocaS3Z2VlyVdffSUjRowoupr1u77p79q16/DtderUkTZt2hz+O5ZfkpN/riFN+JY1NTVV\n9Mr3WiR6udh7+tTG67Gog47HlPzoeNLS0jy/6KbmxpT86Dg0RyY8VvR1Rhf7MWz94cF/aqKL\njscLl5kzZ1r99+/f3+rftPzoOaZ2rqyBJui/eO0rVKhgjUzHq6/PXi7av44n3picisGUx5Q+\n10zJj9pqnkzIkSn5sZ9DaqKfb7xcNDcmuOgYdDHl+azj0c9YJuRHXdz6jJX0U8DePiI12l8W\nLYb0Dfu3v/2tfVOxn7m5uXLbbbfJ7t27ZdSoUSXekAYNGiQrVqw4vE2HDh1k9OjRh//mFwQQ\nQCDsAvn5+aJfHlWpUkX0ULsgLnootgkfQoNoS0wIIICAnwW0ltAiq7zF8z1I5Q3Qvl8nZbj7\n7rutyRmefPLJEsWRrvf73/9edu7caW8i9erVs4qpwzfE8Ise4qffKmhR5vViJ1ST6+Wi3yZU\nr17dmiJYr6Xi9VK1alXZt2+f18OwnnD6oWz//v2i59Z5uei3pvqNjyn50fGYMLGKmmiBoNNb\ne7moh87YefDgQTlw4ICrQ5k/f761p33gwIGHX9d0LHv37nV1HEfrTPOj3/br81nzFM8SSYEU\n7+u69qGvy2qns616uej7lD6u9DHl9aLvD+phwuuyvofrc8yE/OhYtHj3+j1cHx+mvG/an7H0\n/cHr7+tN+Yyl+alRo4ZRn7H0c40J+dHXXP1cE897uMZh51qtS1t8USDpTHY33XST9Y3nM888\nYz1wjhaQHqp35LJp06Yjb4rqb33D1kVf1Lx+cGhhomPw+kOvvgnrG6B+gPF6LJob+03HhPzo\nk1ff/Nz+0KsORRc9PEk/MJmSH33smjAWdTElP1qUaCHttsukSZOsh0qPHj0O960fltweR9HH\nq/27HlKiBZI+f+J5A4zkzU/7jDdmfY5pXzper78U0fcqU57zdoEUr6/9uIjnp/14MiE/+l6l\nj2uvXfT1WMfi9Tg0r/bhjzoWr9/DdTwmvFfpGLRAMu0zltdfMmh+9DNWvF8s2od1antlLZ5P\n0lDW4PS+LVu2yPDhw0UncHj66adLLY7Ka4f7EUAAAQREdHpvfQPu2bMnHAgggAACCCBwFAHj\n9yA9/vjjVhV9wQUXFDu/SL+hatas2VFC4iYEEEAAgaMJ6CFlOslN27ZtJSMj42ircBsCCCCA\nAAKhFzC6QNKpvOfMmWMl6cYbbyyWLL244WOPPVbsNv5AAAEEEChdYNasWda5GEzvXboR9yCA\nAAIIIGBUgfTaa68Vy0hmZqbY09EWu4M/EEAAAQSiFvj8p0sh6NK7d2/rJ/8hgAACCCCAQEkB\n489BKjlkbkEAAQQQiEVACySd3lsvgcCCAAIIIIAAAkcXoEA6ugu3IoAAAoESWLVqlfzwww+i\ns9e5cRHWQOERDAIIIIBAqAQokEKVboJFAIGwCtiH13H+UVgfAcSNAAIIIBCpAAVSpFKshwAC\nCPhYQKf31oXzj3ycRIaOAAIIIOCKAAWSK8x0ggACCHgnoBfHnT17tjRt2lSOPfZY7wZCzwgg\ngAACCPhAgALJB0liiAgggEA8AvPnz5ecnBzh8Lp4FNkWAQQQQCAsAhRIYck0cSKAQGgFPvvs\nMyv2Pn36hNaAwBFAAAEEEIhUgAIpUinWQwABBHwqoAVSamqq9OzZ06cRMGwEEEAAAQTcE6BA\ncs+anhBAAAHXBTZu3CgrV66ULl26SHp6uuv90yECCCCAAAJ+E6BA8lvGGC8CCCAQhcC0adOs\ntU8//fQotmJVBBBAAAEEwitAgRTe3BM5AgiEQGDq1KlWlJx/FIJkEyICCCCAgCMCFEiOMNII\nAgggYJ6ATu89c+ZMady4sbRq1cq8ATIiBBBAAAEEDBSgQDIwKQwJAQQQcEJg7ty51vTep512\nmhPN0QYCCCCAAAKhEKBACkWaCRIBBMIoYB9ex/lHYcw+MSOAAAIIxCpAgRSrHNshgAAChgvo\nBA0VK1aUbt26GT5ShocAAggggIA5AhRI5uSCkSCAAAKOCaxfv15WrVolXbt2ZXpvx1RpCAEE\nEEAgDAIUSGHIMjEigEDoBPTisLpw/lHoUk/ACCCAAAJxClAgxQnI5ggggICJAvb5RxRIJmaH\nMSGAAAIImCxAgWRydhgbAgggEIPAgQMHZPbs2XLsscdK8+bNY2iBTRBAAAEEEAivAAVSeHNP\n5AggEFCBOXPmML13QHNLWAgggAACiRegQEq8MT0ggAACrgro7HW6ML23q+x0hgACCCAQEAEK\npIAkkjAQQAABW0DPP6pUqZI1g519Gz8RQAABBBBAIDIBCqTInFgLAQQQ8IXA2rVrRf/ptY+0\nSGJBAAEEEEAAgegEKJCi82JtBBBAwGgBpvc2Oj0MDgEEEEDABwIUSD5IEkNEAAEEIhWwp/fm\n/KNIxVgPAQQQQACB4gIUSMU9+AsBBBDwrUBOTo7oDHYtWrSQpk2b+jYOBo4AAggggICXAhRI\nXurTNwIIIOCggF776ODBg8LFYR1EpSkEEEAAgdAJUCCFLuUEjAACQRXg/KOgZpa4EEAAAQTc\nFKBAclObvhBAAIEECuj5R5UrV5YuXboksBeaRgABBBBAINgCFEjBzi/RIYBASARWrVol69ev\nlx49ekjFihVDEjVhIoAAAggg4LwABZLzprSIAAIIuC4wZcoUq09mr3Odng4RQAABBAImQIEU\nsIQSDgIIhFNg8uTJVuB9+/YNJwBRI4AAAggg4JAABZJDkDSDAAIIeCWwe/duWbBggbRp00Yy\nMzO9Ggb9IoAAAgggEAgBCqRApJEgEEAgzAI6e11+fr6cccYZYWYgdgQQQAABBBwRoEByhJFG\nEEAAAe8EPv30U6vzfv36eTcIekYAAQQQQCAgAhRIAUkkYSCAQDgF8vLyZNq0aVKvXj1p27Zt\nOBGIGgEEEEAAAQcFKJAcxKQpBBBAwG2B+fPni56DpJMzJCUlud09/SGAAAIIIBA4AQqkwKWU\ngBBAIEwC9uF1nH8UpqwTKwIIIIBAIgUokBKpS9sIIIBAggW0QNILw/bs2TPBPdE8AggggAAC\n4RCgQApHnokSAQQCKLB69WpZs2aN9OjRQ9LT0wMYISEhgAACCCDgvgAFkvvm9IgAAgg4ImAf\nXsfsdY5w0ggCCCCAAAKWAAUSDwQEEEDApwKTJ0+2Rn766af7NAKGjQACCCCAgHkCFEjm5YQR\nIYAAAuUK7Nq1SxYsWCBt2rSRzMzMctdnBQQQQAABBBCITIACKTIn1kIAAQSMEtBrH+Xn5wuz\n1xmVFgaDAAIIIBAAAQqkACSREBBAIHwCnH8UvpwTMQIIIICAOwIUSO440wsCCCDgmEBeXp7o\nHqR69epJ27ZtHWuXhhBAAAEEEEBAhAKJRwECCCDgM4H58+fL7t27pW/fvpKUlOSz0TNcBBBA\nAAEEzBagQDI7P4wOAQQQKCFgz17H+UclaLgBAQQQQACBuAUokOImpAEEEEDAXYEpU6ZIxYoV\npWfPnu52TG8IIIAAAgiEQIACKQRJJkQEEAiOwOrVq2XNmjXSo0cPSU9PD05gRIIAAggggIAh\nAhRIhiSCYSCAAAKRCDB7XSRKrIMAAggggEDsAhRIsduxJQIIIOC6gH3+kU7QwIIAAggggAAC\nzgtQIDlvSosIIIBAQgR27dolCxYskDZt2kjDhg0T0geNIoAAAgggEHYBCqSwPwKIHwEEfCMw\ndepUyc/Pl379+vlmzAwUAQQQQAABvwlQIPktY4wXAQRCK/Dxxx9bsQ8YMCC0BgSOAAIIIIBA\nogUokBItTPsIIICAAwIHDhyQadOmyTHHHGMdYudAkzSBAAIIIIAAAkcRoEA6Cgo3IYAAAqYJ\nzJgxQ3JycuSss84ybWiMBwEEEEAAgUAJUCAFKp0EgwACQRWYNGmSFRqH1wU1w8SFAAIIIGCK\nAAWSKZlgHAgggEApAjoxg07vnZGRIZ06dSplLW5GAAEEEEAAAScEKJCcUKQNBBBAIIECOrV3\nVlaWnHHGGVKhQoUE9kTTCCCAAAIIIECBxGMAAQQQMFyA2esMTxDDQwABBBAIlAAFUqDSSTAI\nIBBEAT3/qHLlytKrV68ghkdMCCCAAAIIGCVAgWRUOhgMAgggUFxg6dKlsmHDBundu7dVJBW/\nl78QQAABBBBAwGkBCiSnRWkPAQQQcFDAPrzuzDPPdLBVmkIAAQQQQACB0gQokEqT4XYEEEDA\nAAE9vE4nZujbt68Bo2EICCCAAAIIBF+AAin4OSZCBBDwqYAeWrds2TLp2rWr1KxZ06dRMGwE\nEEAAAQT8JUCB5K98MVoEEAiRAIfXhSjZhIoAAgggYIwABZIxqWAgCCCAQHEBu0Dq379/8Tv4\nCwEEEEAAAQQSJkCBlDBaGkYAAQRiF9ixY4foBWLbtm0rmZmZsTfElggggAACCCAQlQAFUlRc\nrIwAAgi4IzB58mQpKCgQZq9zx5teEEAAAQQQsAUokGwJfiKAAAIGCejsdbpQIBmUFIaCAAII\nIBAKAQqkUKSZIBFAwE8C2dnZMmPGDGnWrJkcd9xxfho6Y0UAAQQQQMD3AhRIvk8hASCAQNAE\npk2bJgcPHmTvUdASSzwIIIAAAr4QoEDyRZoYJAIIhEnAnr1uwIABYQqbWBFAAAEEEDBCgALJ\niDQwCAQQQOBngby8PJkyZYrUrVtX2rdvDwsCCCCAAAIIuCxAgeQyON0hgAACZQnMmjVL9uzZ\nI3rto6SkpLJW5T4EEEAAAQQQSIAABVICUGkSAQQQiFXgo48+sjY9++yzY22C7RBAAAEEEEAg\nDgEKpDjw2BQBBBBwUiA/P1/0/KNatWpJt27dnGyathBAAAEEEEAgQgEKpAihWA0BBBBItMDs\n2bMlKytLdHKGlJSURHdH+wgggAACCCBwFAEKpKOgcBMCCCDghcCHH35odcvhdV7o0ycCCCCA\nAAI/C1Ag8UhAAAEEDBAoKCiwDq+rUaOG9OjRw4ARMQQEEEAAAQTCKUCBFM68EzUCCBgmMG/e\nPNm+fbs1e11qaqpho2M4CCCAAAIIhEeAAik8uSZSBBAwWGDChAnW6M455xyDR8nQEEAAAQQQ\nCL4ABVLwc0yECCBguIAeXjdx4kSpVq2a9OzZ0/DRMjwEEEAAAQSCLUCBFOz8Eh0CCPhAYMGC\nBbJ161bp16+fpKWl+WDEDBEBBBBAAIHgClAgBTe3RIYAAj4RYPY6nySKYSKAAAIIhEKAAikU\naSZIBBAwVaCwsNA6vK5KlSrSu3dvU4fJuBBAAAEEEAiNAAVSaFJNoAggYKLAF198IZs2bbIO\nr6tYsaKJQ2RMCCCAAAIIhEqAAilU6SZYBBAwTcCevW7gwIGmDY3xIIAAAgggEEoBCqRQpp2g\nEUDAFAGdvS49PV369OljypAYBwIIIIAAAqEWoEAKdfoJHgEEvBRYuHCh/PDDD9K3b1+pXLmy\nl0OhbwQQQAABBBD4RYACiYcCAggg4JHA+PHjrZ7PPvtsj0ZAtwgggAACCCBwpAAF0pEi/I0A\nAgi4JPD+++9be45OO+00l3qkGwQQQAABBBAoT4ACqTwh7kcAAQQSIKCz161bt060ONJzkFgQ\nQAABBBBAwAwBCiQz8sAoEEAgZALvvPOOFTGH14Us8YSLAAIIIGC8AAWS8SligAggEESBsWPH\nSqVKlawJGoIYHzEhgAACCCDgV4Gkn67iXujXwUcy7kOHDkWyWqnrbNiwQd566y0ZNmyY1KlT\np9T13LgjOfnneragoMCN7srsIzU1VXQc+fn5Za7nxp0pKSmSl5fnRldl9qH5qVChgjUWE55W\nOhZT8qNwpuRIc+N1fr788kvp0qWLDB48WMaMGVPm48qNO4P2HMrNzZUqVaqUSxfv+4M+x/R5\nH2875Q40ghWSkpJE/5nw/qCPJ11MeM6b8jqouVEXfU02JUem5MeU5xCfsY7+QhO09wd93Ecy\na+zPr2JHNwnErTt27IgrjtGjR8t9990nWhBcfvnlcbUV78b6hq8f7LKzs+NtKq7t9UWkXr16\noh9Cdu3aFVdbTmxcu3ZtycrK8vxDr55HUr16ddm7d68cPHjQidBibkNf0KpWrWpMfvRDSrzP\nxZgximxYrVo163HrdX5ef/11a1TnnXeeES5169Y1YhyaH32d2717d1xFh75eR1IgxfuY1Oe7\nPu91vF5/2NS9kRq3vv54vdSvX9/yiNfXiThq1qwp+/btMyI/Opb9+/d7/h6uxVpGRoYRz3k1\n0ceuKe/h+pjz+jOW5kefQ/rFy86dO514GsTVhn7G0nF4Xdjbn7H0+XzgwIGYY9LPIxRIP/HF\n+03x+eefbxVI7733nlx22WUxJ8SJDe1vvuONKd6xFO2/6O/xthvP9rZNPG04ua3XLnb/9k8n\nY4u1Lcbys5w66OuJfoA/88wzPf/gZufThPzYY9Cf9u/2+BLx06k+3BpvWQb2GJyKqay+Ir3P\nlLHYNpGOOxHrFbUo+nsi+oq0TVPGoeM1JUdanJjiYoKJ/VgyYSx2XuIdi92OHVtpPzkHqTSZ\nX25v3ry5dO7cWebOnSubNm0qZ23uRgABBMoWWLBggXVx2EGDBjF7XdlU3IsAAggggIAnAhRI\nEbBffPHF1jcKEyZMiGBtVkEAAQRKF9C9R7pcdNFFpa/EPQgggAACCCDgmQAFUgT0F154oXXy\n67vvvhvB2qyCAAIIHF1AT9DWL1pq1Kgh/fv3P/pK3IoAAggggAACngpQIEXA37BhQ+natat8\n/fXX8v3330ewBasggAACJQVmzZplnRit1z5KS0sruQK3IIAAAggggIDnAhRIEaZAp+PV5f33\n349wC1ZDAAEEigvYh9fp7HUsCCCAAAIIIGCmAAVShHnRb3x16mQOs4sQjNUQQKCYgE6L//HH\nH4tOqd29e/di9/EHAggggAACCJgjQIEUYS5q1aolp556qqxcuVKWL18e4VashgACCPws8Nln\nn8mePXvknHPOsS4ojAsCCCCAAAIImClAgRRFXjjMLgosVkUAgWIC9uF19utIsTv5AwEEEEAA\nAQSMEaBAiiIVOuuUXvHZ/qATxaasigACIRbQK7N/+umncswxx0j79u1DLEHoCCCAAAIImC9A\ngRRFjqpWrSp9+/aV9evXy1dffRXFlqyKAAJhFvjkk08kJydHdO+RXqmdBQEEEEAAAQTMFaBA\nijI39uEx7EWKEo7VEQixgP16Yb9+hJiC0BFAAAEEEDBegAIpyhSddtpponuSPvjgAykoKIhy\na1ZHAIGwCezatUs+//xzadmypZx00klhC594EUAAAQQQ8J0ABVKUKdNzkAYMGCBbtmyRuXPn\nRrk1qyOAQNgEJk6cKIcOHbIOrwtb7MSLAAIIIICAHwUokGLImn2RR/uwmRiaYBMEEAiJgP06\nMWjQoJBETJgIIIAAAgj4W4ACKYb89ezZUzIyMuSjjz6yvhmOoQk2QQCBEAhs27ZNZs+eLSef\nfLK0aNEiBBETIgIIIIAAAv4XoECKIYcpKSkycOBA2blzp8yYMSOGFtgEAQTCIGCfq8jkDGHI\nNjEigAACCARFgAIpxkzah9m9++67MbbAZgggEHSB999/3wrx3HPPDXqoxIcAAggggEBgBCiQ\nYkxl586dpUGDBmJf3yTGZtgMAQQCKrBhwwZZuHChdOrUybpAbEDDJCwEEEAAAQQCJ0CBFGNK\n9WKPuhdp//79MmnSpBhbYTMEEAiqwLhx46zQhgwZEtQQiQsBBBBAAIFAClAgxZHW888/39r6\nnXfeiaMVNkUAgSAKjB07VlJTU4XD64KYXWJCAAEEEAiyAAVSHNk94YQTrAs/6kQNW7dujaMl\nNkUAgSAJfPnll7JmzRrp27ev1KxZM0ihEQsCCCCAAAKBF6BAijPFuhepoKBAmKwhTkg2RyBA\nArr3SJcLLrggQFERCgIIIIAAAuEQoECKM896HlJycrLYH4jibI7NEUDA5wKHDh0Snb2uVq1a\ncvrpp/s8GoaPAAIIIIBA+AQokOLMeb169aRXr16ydOlSWbFiRZytsTkCCPhdYOrUqdY10gYN\nGmSdg+T3eBg/AggggAACYROgQHIg40zW4AAiTSAQEAF70hb7dSEgYREGAggggAACoRGgQHIg\n1QMGDJAqVarI+PHjrfORHGiSJhBAwIcCu3btEt2D1Lx5cznllFN8GAFDRgABBBBAAAEKJAce\nA+np6TJw4EDZsmWLzJw504EWaQIBBPwo8MEHH0hubq6w98iP2WPMCCCAAAII/CxAgeTQI8Ge\nrYrJGhwCpRkEfChgP/+HDh3qw9EzZAQQQAABBBBQAQokhx4H3bp1k8zMTJk4caJkZ2c71CrN\nIICAXwS+//57WbhwoXTu3FkaN27sl2EzTgQQQAABBBA4QoAC6QiQWP9MSkoS/dY4JyfHKpJi\nbYftEEDAnwL23iMOr/Nn/hg1AggggAACtgAFki3hwE/7g5E9i5UDTdIEAgj4RGDcuHFSsWJF\nOeecc3wyYoaJAAIIIIAAAkcToEA6mkqMt7Vq1Uratm0rs2bNkk2bNsXYCpshgIDfBObPny/r\n1q2Tfv36SfXq1f02fMaLAAIIIIAAAkUEKJCKYDjxq+5FKiwslHfffdeJ5mgDAQR8IGAfXmdP\n1uKDITNEBBBAAAEEEChFgAKpFJhYbz7vvPOkQoUKwmF2sQqyHQL+Ejh48KBMmDBBateuLb17\n9/bX4BktAggggAACCJQQoEAqQRLfDfohqU+fPvLtt9/KkiVL4muMrRFAwHiBKVOmyO7du2Xw\n4MGSkpJi/HgZIAIIIIAAAgiULUCBVLZPTPcyWUNMbGyEgC8FOLzOl2lj0AgggAACCJQqQIFU\nKk3sd+iJ2tWqVbPOQ8rLy4u9IbZEAAGjBXbs2CFTp06Vli1bWhO0GD1YBocAAggggAACEQlQ\nIEXEFN1KlSpVkkGDBsn27dtFD79hQQCBYAro3iP9EuQ3v/lNMAMkKgQQQAABBEIoQIGUoKRf\ncsklVstvvfVWgnqgWQQQ8FpAn986KQuz13mdCfpHAAEEEEDAOQEKJOcsi7X0q1/9Slq3bi2f\nffaZbN26tdh9/IEAAv4X+PLLL2XlypXSt29fqVevnv8DIgIEEEAAAQQQsAQokBL4QLj44osl\nPz9fxowZk8BeaBoBBLwQsPcO6/OcBQEEEEAAAQSCI0CBlMBcDh06VFJTU+Xf//53AnuhaQQQ\ncFsgOztb3n//falbt66cdtppbndPfwgggAACCCCQQAEKpATi6jWR+vfvL2vWrJG5c+cmsCea\nRgABNwU+/PBD2bdvn1x44YVc+8hNePpCAAEEEEDABQEKpAQj24ffsBcpwdA0j4CLAvbhdRdd\ndJGLvdIVAggggAACCLghQIGUYOVTTz1VMjMzZcKECdY3zgnujuYRQCDBArpHeN68edK5c2dp\n0aJFgnujeQQQQAABBBBwW4ACKcHiycnJ1mE4OTk58t577yW4N5pHAIFEC9h7g+29w4nuj/YR\nQAABBBBAwF0BCiQXvO3DcOzDclzoki4QQCABAvaslFWqVJGzzz47AT3QJAIIIIAAAgh4LUCB\n5EIGmjRpIt27d5evvvrKum6KC13SBQIIJEBg6tSp1nXNBg8eLOnp6QnogSYRQAABBBBAwGsB\nCiSXMmAfjvPmm2+61CPdIICA0wL2XmD7+ex0+7SHAAIIIIAAAt4LUCC5lIOzzjpLqlevLmPH\njpVDhw651CvdIICAUwLbtm2TKVOmyHHHHSennHKKU83SDgIIIIAAAggYJkCB5FJCKlWqJEOG\nDJGsrCyZPHmyS73SDQIIOCXwzjvviJ6DxN4jp0RpBwEEEEAAATMFKJBczAuTNbiITVcIOCyg\ns9elpKTI+eef73DLNIcAAggggAACJglQILmYjbZt28pJJ50kn3/+uWzatMnFnukKAQTiEZg/\nf76sWrVK+vXrJ7Vr146nKbZFAAEEEEAAAcMFKJBcTpAenlNQUCBjxoxxuWe6QwCBWAXsax9d\ncsklsTbBdggggAACCCDgEwEKJJcTpechpaWlic6GVVhY6HLvdIcAAtEK7Nu3T95//31p0KCB\nnHrqqdFuzvoIIIAAAggg4DMBCiSXE1azZk3rApPr16+3DrVzuXu6QwCBKAXGjRsnOTk5oucQ\nVqhQIcqtWR0BBBBAAAEE/CZAgeRBxi677DKr19dff92D3ukSAQSiEXj11VclOTlZfvvb30az\nGesigAACCCCAgE8FKJA8SFznzp2ldevW1nTfP/74owcjoEsEEIhEQCdnWLFihZxxxhlyzDHH\nRLIJ6yCAAAIIIICAzwUokDxK4BVXXGFN1jB69GiPRkC3CCBQnsBrr71mrXL55ZeXtyr3I4AA\nAggggEBABOIqkL755hsZO3asfPLJJxbHunXrAsKS+DCGDh0q6enp8uabb0peXl7iO6QHBBCI\nSmDHjh3y4YcfSpMmTaR3795RbcvKCCCAAAIIIOBfgZgKpGXLlkmvXr2kXbt2csEFF8j//d//\nWQL693333ScHDx70r4hLI69WrZrojHZbtmyxDrVzqVu6QQCBCAXefvttyc3NFT1nMCkpKcKt\nWA0BBBBAAAEE/C4QdYG0Z88eOeuss2T16tVy6623SteuXS2D/Px8GTBggDzwwAMyfPhwv7u4\nMn77sB09CZwFAQTMEdAp+HUSFZ2SX2evY0EAAQQQQACB8AhEXSD961//kt27d8ucOXPkscce\nk0aNGllaOv2tXkzxlltuET1uf//+/eFRjDHSNm3ayCmnnCIzZ86UNWvWxNgKmyGAgNMCn3/+\nueghw2effbbUrl3b6eZpDwEEEEAAAQQMFoi6QPrqq6+s4/H1uPyjLfptq55T8/2X24QnAABA\nAElEQVT33x/tbm47QkAna9DFPhn8iLv5EwEEPBCwp+C3p+T3YAh0iQACCCCAAAIeCURdIOnE\nAnoOUmlLdna2dRffupYmVPz2c845R/TisWPGjJEDBw4Uv5O/EEDAdQGden/y5MnWVPw6JT8L\nAggggAACCIRLIOoCqVOnTrJy5Up59913S0jp+Ul//vOfJTMzUxo0aFDifm4oKVCpUiW58MIL\nZdeuXTJhwoSSK3ALAgi4KqBT7xcUFIi9d9fVzukMAQQQQAABBDwXiLpA+t3vficdOnSwZmDr\n1q2btTdJJ2zQq8xrUTRt2jR58sknPQ/MTwNgsgY/ZYuxBllADw/Wqfd1T7lOxc+CAAIIIIAA\nAuETiLpASklJkYkTJ8qwYcNk3rx5snTpUlm4cKH1oUIPFdNj93WPCEvkAs2bN5eePXvKl19+\nKUuWLIl8Q9ZEAAFHBfTQOp16X6fg16n4WRBAAAEEEEAgfAJRF0hKVLduXXnppZdEL6Q4f/58\nq2BasWKFNevTpZdeGj5FByK29yIxWYMDmDSBQIwC9pT79vMxxmbYDAEEEEAAAQR8LBBTgWTH\nq3uMOnbsKGeeeaZ1QnNqaqp9Fz+jFOjfv7/Ur19fxo8fL/v27Ytya1ZHAIF4BXSqfZ1yX6fe\n1yn4WRBAAAEEEEAgnAJRF0hPPPGENG3atNx/4eSMPWo9dPGSSy4RnQVw7NixsTfElgggEJOA\nvfeWyRli4mMjBBBAAAEEAiMQdYFUp04dOe6444r9a9GihejeI50eNycnxzp+PzBCLgaiE10k\nJyeLfZiPi13TFQKhFtDXLZ1qX/eK69T7LAgggAACCCAQXoGUaEPXY/NLOz5fD1HRQ8UaNmwY\nbbOs/5OATo+ufh9//LHMmjVLevTogQsCCLggMG7cOGuq/T/84Q+iU++zIIAAAggggEB4BaLe\ng1QWlc7GNnLkSHnwwQclPz+/rFW5rxSBa665xrrnxRdfLGUNbkYAAacFRo0aZe291csYsCCA\nAAIIIIBAuAUcLZCUsnHjxrJ371757rvvwi0bY/RdunSxThCfMmWKfP/99zG2wmYIIBCpwIwZ\nM6yLX+tkM40aNYp0M9ZDAAEEEEAAgYAKOFog6QQDzz33nFSoUEGaNGkSULLEh3X11VdLYWGh\nNZV64nujBwTCLWDvrdXnHQsCCCCAAAIIIBD1OUj6YUKvgXTkcujQIes6SHptpCuvvNK6Ev2R\n6/B3ZAKDBw+2DlP897//LXfccQcXrIyMjbUQiFpAz5ucOnWqtG3bVjp37hz19myAAAIIIIAA\nAsETiHoPUm5uruzfv7/EPz3nSK8d8vDDD8uzzz4bPCkXI0pLS7MmwlDnt956y8We6QqBcAnY\nX/aw9yhceSdaBBBAAAEEyhKIeg/SiBEjRP+xJFZAr8Xyz3/+U15++WXRD286/TcLAgg4J7Bn\nzx55++23pW7dunLuuec61zAtIYAAAggggICvBfjUbWj69EPboEGDZP369TJ58mRDR8mwEPCv\ngO6d1fMm9csI3WvLggACCCCAAAIIqEC5e5A2b94sek5MtMvcuXOj3YT1jxDQKb/Hjh0ret7X\ngAEDjriXPxFAIFaBgoICa++sfThrrO2wHQIIIIAAAggET6DcAkk/SOi5MCzuC5x88snWieNz\n5syRZcuWSceOHd0fBD0iEECBSZMmyYYNG+TCCy+UOnXqBDBCQkIAAQQQQACBWAXKLZAyMzNl\n8eLFsbbPdnEK6F6kefPmWXuRKJDixGRzBH4R0AvD6sLkDL+A8AMBBBBAAAEEDgtwDtJhCjN/\n6d+/v3Xxyvfee0+2b99u5iAZFQI+EtAvfPQQYPuizD4aOkNFAAEEEEAAARcEHC+Q9AKnM2fO\ndGHo4ehCL7o7bNgwOXjw4FGvPxUOBaJEwDmBF154wWpM986yIIAAAggggAACRwrEVCDp1NPt\n27eXxo0bS4MGDax/9evXl9q1a0vFihWlV69eR/bD33EIXHzxxVK5cmWrQNIL8rIggEBsAlu3\nbpVx48ZZr126d5YFAQQQQAABBBA4UiDqAkn3Dulx+9988400bdpUtmzZYh0CptNS79u3z7pe\nz/PPP39kP/wdh0CNGjXkN7/5jWU9fvz4OFpiUwTCLaAXhtWLXV911VVcWyzcDwWiRwABBBBA\noFSBqAukDz/80PpgsXbtWpk1a5aceOKJ1kxQS5YskaVLl4ruSdLDwlicFdAPdLpQfDrrSmvh\nEdDDVHXK/CpVqshFF10UnsCJFAEEEEAAAQSiEoi6QFq9erV07drV2mukPf3617+2TnjW31u2\nbCmPPPKI3Hvvvfoni4MCLVq0sK6FtGjRIs7xctCVpsIj8M4774geYnfZZZdJ9erVwxM4kSKA\nAAIIIIBAVAJRF0i1atWyzoexe2ndurV89dVX9p/SrVs360PIxo0bD9/GL84I3HzzzVZDzz77\nrDMN0goCIRHQ67np3teUlBQZPnx4SKImTAQQQAABBBCIRSDqAun4448XvXCpnnukix5i9/33\n38v69eutv/Uwu+TkZElNTbX+5j/nBHRa4s6dO8uMGTO4NpVzrLQUAoGJEyeKHhZ8wQUXHN77\nHYKwCREBBBBAAAEEYhCIukC6/PLLrT1IrVq1kunTp8tpp51mHdM/dOhQefjhh+X666+3DsHT\nc5FYnBe46aabrEbZi+S8LS0GV+CZZ56xgrP3wgY3UiJDAAEEEEAAgXgFoi6QdLa6d9991zr3\n6MCBA6KH3OmhK3puzMiRI2XDhg1y4403xjsuti9FYMCAAXLccceJTpahe+5YEECgbAGdTEZn\n3ezbt6+1x7vstbkXAQQQQAABBMIuEHWBpGDdu3e39h7169fP8tOTnvWco48//lh0Egc9jIUl\nMQJJSUkyYsQIsc+pSEwvtIpAcATsvUe6d5sFAQQQQAABBBAoTyDqAunpp5+WG264wZqYQT+s\n24seUqd7N/TisSyJFRg8eLBkZmbKmDFjZPv27YntjNYR8LHA4sWLrXP2OnbsKJ06dfJxJAwd\nAQQQQAABBNwSiLpAqlixonVI3SmnnCK/+tWv5B//+EfCP6QXFhZah8i8/fbb8uOPP7plY2w/\nOgHGtddeK3pdl1GjRhk7TgaGgNcC9rl6uteVBQEEEEAAAQQQiEQg6gLp97//vfzwww/y1FNP\nWVPm6qQBujdDJ2nQ82Ly8vIi6TfidXbs2CEXX3yx/PWvf7UO37v66qutc530ELMwL5deeqnU\nrFlTXnnlFdm3b1+YKYgdgaMKrFu3znpN0gllzjjjjKOuw40IIIAAAggggMCRAlEXSNpAvXr1\nrIkYFi5cKMuWLZPbbrtN9PdzzjnHOsTujjvuOLKfmP8eP368ZGdny2uvvSb33HOPVZjpNNdf\nfPFFzG0GYcP09HT53e9+J3v27JHXX389CCERAwKOCujkMfpFiu49Kno4sKOd0BgCCCCAAAII\nBE4gpgKpqMIJJ5xgTe+9YMEC0b07mzdvlr///e9FV4nr99zcXGumPPu6Sg0aNJAKFSpITk5O\nXO0GYeNhw4ZJpUqV5MUXXxR1YkEAgZ8F9Nw8PSRX926fd955sCCAAAIIIIAAAhELpES85lFW\n1EO7dA/PG2+8IZ999pnouUL9+/e39mwcZfWYbtL2Jk2aJDoTVYcOHeS9996Tpk2bWr8f2aCe\nn1S0UNDiQYspJxZtR+PzctEL8OoY7Jh0T94ll1wiL7/8sjX1uv7uxmJ/G68/7bG40W9ZfZiS\nHx2j5slrF+3flPzoONwey0svvWSdo3fddddZXyLYjx0dhyn5MeWxYtt4/Zi1Peyf8YxH8xzJ\nEk8f2r7djwmPKR2D28+z8ozj9S2v/Ujut01MeP/W8drjiWTsiVrHftyakh+NU8diQo5Myo8J\nY7Efg5of+3Fj3+b2T32N0yXe11u7nfLGn/TTAzKqT/16jtEnn3xiFUUffPCBdfhby5Yt5cor\nr5QrrrjC8avU6yEyWgC8+uqr1gcdLYD0fKRu3bqViG3QoEGyYsWKw7drQTV69OjDfwfxF70W\nkp5joTnQwx29fgAH0ZiY/CWwd+9eadKkifUiun79eutC1v6KgNHGK6BHGFSuXDneZtgeAQQQ\nQCBgAlpHpKWllRtV1HuQHnzwQfnzn/9sfei48MILrb1FvXr1KrejWFd44oknrPOb/vWvf1mF\nwH/+8x9rkoY//vGPctpppxVrtk+fPtK6devDtzVv3twq4A7fEMMvOmufVs56HpTXS0rKz+kq\nOhGG7kUaMmSINeW3Tvut54G5seg5UDqOonvs3Oj3aH3onkKd0S/KWv9oTcV1m+ZHn3Q6lvz8\n/Ljaindj/YZED0vVsXi9aH60cHfrsFjd27xr1y656667rH6LPnfVRL908To/6qEf4A8dOmT9\nMyFHeuFvrxfNj/7TscQzEU+k+S362Igldn2+6/NeH9tev/7o+5Q+7/Ux5fWij231MOExpe/h\nahLP48kJT82PjkXfM4u+hzvRdrRt6OuPjsWU/Jj8GStaW6fW189Y+jpmynt4kD5j6WtBJAVS\n1HuQ9EO4HlqnxVHVqlWdeiwctR0N4txzz5XLL7/c6s9eaeTIkdYD529/+5t9U6k/N23aVOp9\nkdyRkZFhvZDouVVevwFWqVLFGsORb+q656hv377WtOsTJ06MJKy41tE3Yb3ulb647ty5M662\nnNi4Tp06orMdmpCf6tWrWyZev/Hoh7Zq1aoZkx99A9yyZYsT6S6zDX0R79q1q1Ug6XmRtWvX\nLra+5kc/oJiQn7p168r+/futiVaKDdKDP/SLlq1bt3rQc/Eu9TGr7yt6Dlk8H/T1ze/I3Bfv\n6ee/4n1/qFGjhugHmW3btnn+oVe/iNDiUveger3oucJaBJhwnb5atWpZJl4XJZofHYtOrKTP\ney8XLZD0+WFKftTGhM9Y+lxWGxPyo88hkz5jZWVlef4lg+ZHX3P1c2c87+H6eUTf88pbot6D\npIWRm4siaGFQdNHg9EWG5WeBE0880SqQpkyZYp0LduSeNZwQCIvAm2++ab3RXnXVVRF9QA6L\nC3EigAACCCCAQOQCcc9iF3lX0a+peyp69+5tTfG9ceNG6xspneJb/1EEFPe89dZbrRsef/zx\n4nfwFwIhEdC9R//85z+tPb7XX399SKImTAQQQAABBBBwWiDqPUhOD6C89vRCtPqhXy8Wq7th\n9bA7PeRu8ODB5W0aqvvbtWvHXqRQZZxgjxQouvdIDwFlQQABBBBAAAEEYhEwvkDS49H/9Kc/\nyZ133il6DKQeN2hPVhBLwEHeRvci6WF2jz32GHvYgpxoYishwN6jEiTcgAACCCCAAAIxChh9\niF3RmHTvkV70keKoqErx3+29SIsWLbLORSp+L38hEFwBe+/RpZdeak0gEtxIiQwBBBBAAAEE\nEi3gmwIp0RBBad8+F0n3IrEgEAYB9h6FIcvEiAACCCCAgHsCFEjuWbvSE3uRXGGmE4ME9GLQ\nOkXsZZddxt4jg/LCUBBAAAEEEPCrAAWSXzNXxrhvu+026172IpWBxF2BENC9R3phWL3o4YgR\nIwIRE0EggAACCCCAgLcCFEje+iek97Zt21oz2nEuUkJ4adQgAfYeGZQMhoIAAggggEBABCiQ\nApLII8NgL9KRIvwdNAH2HgUto8SDAAIIIICAGQIUSGbkwfFRsBfJcVIaNEyAvUeGJYThIIAA\nAgggEBABCqSAJPJoYbAX6Wgq3BYEAfYeBSGLxIAAAggggICZAhRIZubFkVGxF8kRRhoxUIC9\nRwYmhSEhgAACCCAQEAEKpIAksrQw7L1Ijz76qBQWFpa2Grcj4BuBnJwc+ec//8nMdb7JGANF\nAAEEEEDAXwIUSP7KV9Sj1b1IZ555pnzzzTcyYcKEqLdnAwRMExg1apRs2bJFrrzySq57ZFpy\nGA8CCCCAAAIBEKBACkASywvhrrvukuTkZPnb3/4mhw4dKm917kfAWIGdO3da1z2qXr263HDD\nDcaOk4EhgAACCCCAgH8FKJD8m7uIR96qVSu5+OKL5fvvv5c33ngj4u1YEQHTBP7xj3/I3r17\nrYvC1qpVy7ThMR4EEEAAAQQQCIAABVIAkhhJCLfeeqtUrlxZnnzySdm/f38km7AOAkYJbNy4\nUV555RVp0KCBXH311UaNjcEggAACCCCAQHAEKJCCk8syI9EPlddcc41s375dXnjhhTLX5U4E\nTBTQiUZyc3NFJx7RYp8FAQQQQAABBBBIhAAFUiJUDW1z+PDhooclPf/881ahZOgwGRYCJQSW\nLVsm48aNEz1c9De/+U2J+7kBAQQQQAABBBBwSoACySlJH7SjJ7bfeOONkp2dLU888YQPRswQ\nEfhZ4KGHHrKmqb/nnnukQoUKsCCAAAIIIIAAAgkToEBKGK2ZDV9xxRVyzDHHWJM16KQNLAiY\nLjB79myZNm2adOzYUfr372/6cBkfAggggAACCPhcgALJ5wmMdvgVK1YUnfY7Ly/PmvY72u1Z\nHwG3BR544AGry3vvvdftrukPAQQQQAABBEIoQIEUwqSfd955cuKJJ8oHH3xgXUA2hASE7BMB\nvbjx119/LQMGDLD2IPlk2AwTAQQQQAABBHwsQIHk4+TFOnS9aOzIkSOtzR988MFYm2E7BBIq\nYO/l1Mfr3XffndC+aBwBBBBAAAEEELAFKJBsiZD97NOnj3Tv3l1mzZplnd8RsvAJ1wcCelHj\ntWvXykUXXWTNXueDITNEBBBAAAEEEAiAAAVSAJIYawj2OR16jkd+fn6szbAdAo4L7NmzRx5/\n/HGpVKmSdd0jxzugQQQQQAABBBBAoBQBCqRSYMJwc7t27WTIkCGyYsUKee2118IQMjH6RECL\nox07doheu0svcsyCAAIIIIAAAgi4JUCB5Ja0of3oXqT09HR59NFHJSsry9BRMqwwCXz33Xfy\n8ssvW9PRjxgxIkyhEysCCCCAAAIIGCBAgWRAErwcgn47f9NNN8nu3buZ9tvLRND3YQEt2vWQ\nzz/96U9SuXLlw7fzCwIIIIAAAggg4IYABZIbyob3ce2110qzZs1k9OjRsnjxYsNHy/CCLDBx\n4kSZOXOmNYHI2WefHeRQiQ0BBBBAAAEEDBWgQDI0MW4OKy0tTf7yl79IYWGh2BM3uNk/fSGg\nAgcOHJD7779fKlSoIEw/z2MCAQQQQAABBLwSoEDySt6wfk8//XTRfwsWLJBx48YZNjqGEwaB\n5557TjZu3ChXXnmltG7dOgwhEyMCCCCAAAIIGChAgWRgUrwaku5FSk1Ntb69379/v1fDoN8Q\nCmhh9Mwzz0hGRgbTeocw/4SMAAIIIICASQIUSCZlw+Ox6HlIv//972XLli3y1FNPeTwaug+T\nwJ///GfrELu7775batSoEabQiRUBBBBAAAEEDBOgQDIsIV4P58Ybb5T69evLv/71L1mzZo3X\nw6H/EAj85z//kY8++kjatm0rF198cQgiJkQEEEAAAQQQMFmAAsnk7HgwtipVqsgf//hHOXTo\nkDXNsgdDoMsQCeTl5R2eGEQnZkhO5iUpROknVAQQQAABBIwU4NOIkWnxdlBDhgyRTp06ydSp\nU2XKlCneDobeAy3wyiuvyLfffivnn3++dOjQIdCxEhwCCCCAAAII+EOAAskfeXJ9lA888IAk\nJSXJyJEjJTs72/X+6TD4Aps3b5a///3vonstmV4++PkmQgQQQAABBPwiQIHkl0y5PM6TTz5Z\nrr76atmwYYM8+uijLvdOd2EQ0AkZ9u7dK/qzXr16YQiZGBFAAAEEEEDABwIUSD5IkldDvPPO\nO6VRo0YyatQoWbRokVfDoN8ACkyYMEE++eQTad++vXXdowCGSEgIIIAAAggg4FMBCiSfJs6N\nYaenp1t7jwoKCuTWW2+1Jm5wo1/6CLbArl27rEPq9Jpbjz/+OBMzBDvdRIcAAggggIDvBCiQ\nfJcydwfcu3dv6wT65cuXy3PPPedu5/QWSAG95tG2bdtEp5Q/7rjjAhkjQSGAAAIIIICAfwUo\nkPybO9dGfv/990vt2rXlySeflFWrVrnWLx0FT2DmzJny9ttvW4XR9ddfH7wAiQgBBBBAAAEE\nfC9AgeT7FCY+gIyMDNFZ7XJzc+X222+XwsLCxHdKD4ET0NkQ9fGjsyPqoXVpaWmBi5GAEEAA\nAQQQQMD/AhRI/s+hKxEMHjxY+vbtK/PmzZNXX33VlT7pJFgCOqX3+vXr5aqrrrImZwhWdESD\nAAIIIIAAAkERoEAKSiZdiONvf/ubdc2aBx98UDZu3OhCj3QRFIGFCxfKiy++KMccc4zcdddd\nQQmLOBBAAAEEEEAggAIUSAFMaqJCyszMtC4cu2/fPhk+fHiiuqHdgAnk5eXJNddcIzobol5T\nS2dHZEEAAQQQQAABBEwVoEAyNTOGjuuKK66Qjh07il7H5p133jF0lAzLJIHHHntMvvnmGxk6\ndKj06dPHpKExFgQQQAABBBBAoIQABVIJEm4oS0BPsH/iiSekYsWK1jTNmzdvLmt17gu5wOLF\ni60JPurUqSM6vTcLAggggAACCCBgugAFkukZMnB8rVq1Ej0faefOnXLDDTcwq52BOTJhSDk5\nOTJixAjrAsN6/pHOhsiCAAIIIIAAAgiYLkCBZHqGDB2fXuTz9NNPl1mzZskLL7xg6CgZlpcC\nusdIr5ul5x+de+65Xg6FvhFAAAEEEEAAgYgFKJAipmLFogJ6qN2oUaOsvQK6N2nJkiVF7+b3\nkAtMnjxZXnvtNWnZsqXo9N4sCCCAAAIIIICAXwQokPySKQPH2aBBA+uCn4cOHbJmtdNDqlgQ\n2Lp1q9xyyy2Smpoqzz77LLPW8ZBAAAEEEEAAAV8JUCD5Kl3mDbZ///5y6aWXWodS/eUvfzFv\ngIzIVYHCwkK56aabJCsrS+688045+eSTXe2fzhBAAAEEEEAAgXgFKJDiFWR7uf/++6VFixby\n6quvyqeffopIiAVeeukl+fzzz6V79+7yhz/8IcQShI4AAggggAACfhWgQPJr5gwat174Uw+l\nSklJkZtvvlm2bdtm0OgYilsCK1askIceekhq1qwpTz/9tOh5aiwIIIAAAggggIDfBCiQ/JYx\nQ8fbtm1b65AqPbRKD7FiCZfAwYMHrfPQ9KdOytCwYcNwARAtAggggAACCARGgAIpMKn0PhA9\npKpbt24ybdo00evesIRH4IEHHhDdg3TRRRfJwIEDwxM4kSKAAAIIIIBA4AQokAKXUu8CSk5O\ntg6tqlWrlugH5rlz53o3GHp2TWD8+PHy8ssvS/Pmza28u9YxHSGAAAIIIIAAAgkQoEBKAGqY\nm8zMzJTnn39eCgoK5Nprr5VNmzaFmSPwsS9dulRuv/12aypvnaChSpUqgY+ZABFAAAEEEEAg\n2AIUSMHOryfR9erVS+655x7Zvn27XHPNNZKbm+vJOOg0sQI7d+6UYcOGiV7/6qmnnpLWrVsn\ntkNaRwABBBBAAAEEXBCgQHIBOYxdDB8+XM4++2z58ssvZeTIkWEkCHTMuodQc7xhwwYZMWKE\nletAB0xwCCCAAAIIIBAaAQqk0KTa/UDtvQqjR4+WN954w/0B0GPCBP7617/K9OnT5dRTT5W7\n7747Yf3QMAIIIIAAAggg4LYABZLb4iHqT6+PpCfvV69e3dqLpHuTWPwv8OGHH1rXvWrcuLE8\n99xzopNzsCCAAAIIIIAAAkER4JNNUDJpaBzNmjWzPkzn5eXJ1VdfzUVkDc1TpMP69ttvretc\nVapUySp+dcZCFgQQQAABBBBAIEgCFEhByqahsZx++uly2223yebNm62Z7bRYYvGfwJ49e6xJ\nGbKzs+Wxxx6Tk046yX9BMGIEEEAAAQQQQKAcAQqkcoC42xmBm266Sfr37y/z5s2zZrhzplVa\ncUtAi9rrrrtO1q5da81MOGTIELe6ph8EEEAAAQQQQMBVAQokV7nD21lSUpJ1EVmdClonbHj8\n8cfDi+HDyG+55Rb5/PPPpWfPnvLHP/7RhxEwZAQQQAABBBBAIDIBCqTInFjLAYFq1arJm2++\nKXoxWS2QmNnOAVQXmnjooYdk7Nix0qZNG9GLwaakpLjQK10ggAACCCCAAALeCFAgeeMe2l4b\nNmwob731ltSsWVPuuusumTRpUmgt/BD4iy++aE2y0aRJE9Hp2qtWreqHYTNGBBBAAAEEEEAg\nZgEKpJjp2DBWgVatWsmrr74qaWlp1sVG58+fH2tTbJdAgffff1/+9Kc/Se3ata2itm7dugns\njaYRQAABBBBAAAEzBCiQzMhD6EbRsWNHef755yU3N1euuOIKWblyZegMTA541qxZcsMNN4he\ny0oPhdTp2lkQQAABBBBAAIEwCFAghSHLhsaos9o98sgjsnv3brnkkkvkxx9/NHSk4RrWkiVL\nrOm8CwsLZdSoUdKuXbtwARAtAggggAACCIRagAIp1On3Pvjf/va3cvvtt1vFkRZJu3bt8n5Q\nIR7B+vXrRXOyb98+efLJJ6V3794h1iB0BBBAAAEEEAijAAVSGLNuWMw333yzXHbZZdZhdhdd\ndJFkZWUZNsJwDGfdunVy/vnny7Zt2+S+++6ToUOHhiNwokQAAQQQQAABBIoIUCAVweBX7wT+\n+te/Wh/Iv/nmG+tD+vbt270bTAh7XrVqlZx33nmyceNG0Yv66kVhWRBAAAEEEEAAgTAKUCCF\nMesGxpycnCz/+Mc/5NJLL5UVK1ZYH9Y3bdpk4EiDN6Tly5fLkCFDZPPmzXLnnXfKHXfcEbwg\niQgBBBBAAAEEEIhQgAIpQihWS7yAFkmPPvqoXHXVVbJ69erDezQS33N4eyi6x+7++++XG2+8\nMbwYRI4AAggggAACCPwkQIHEw8A4gQceeECuv/560QkDBg8eLGvXrjVujEEY0MKFC+WCCy6Q\nnTt3WrMJXnvttUEIixgQQAABBBBAAIG4BCiQ4uJj40QJ3HPPPXLbbbdZs9vpuTFcJ8lZ6dmz\nZ4tOiLF//37r0EadJIMFAQQQQAABBBBAgD1IPAYMFrjlllvk3nvvla1bt1rnyOjhYCzxC0yd\nOtU610sv0vvcc89Ze5Hib5UWEEAAAQQQQACBYAiwBykYeQxsFMOHD5eHHnrImvpbD7d79913\nAxurG4E9//zzcvnll0tBQYG8+OKLcu6557rRLX0ggAACCCCAAAK+EaBA8k2qwjvQ3/3udzJq\n1CjRSRxGjBghDz/8sPUBP7wi0Ud+4MAB67wuPb+rdu3aMmbMGOnfv3/0DbEFAggggAACCCAQ\ncAEKpIAnOCjhnXXWWTJhwgRp3LixPPPMM3LFFVfI3r17gxJeQuPQ6dJ179v48eOlbdu2MmnS\nJOnUqVNC+6RxBBBAAAEEEEDArwIUSH7NXAjHfcIJJ8jHH38s3bt3Fz2PZuDAgdZ04CGkiDhk\nnaluwIABoudv6WQXeohiZmZmxNuzIgIIIIAAAgggEDYBCqSwZdzn8WZkZMhbb70lw4YNk1Wr\nVllF0ieffOLzqBIz/FdffVWGDh0q27dvl5EjR8qzzz4rlStXTkxntIoAAggggAACCAREgAIp\nIIkMUxgpKSny4IMPymOPPSY5OTnWRAOPPPKI6KxsLCL79u2Tm2++Wa677jqpVKmSvP7669a5\nW9gggAACCCCAAAIIlC9AgVS+EWsYKnDJJZfI2LFjpWHDhvLUU08dPpTM0OG6Mqzp06dLnz59\nZPTo0aKHJE78//buBOqOqj4A+M1KCNlDTNjDDpEtoGwWkL1QQMGqtUU51tpFFA60KqWtldKi\npa0Ua6FaQDzlnCJqK4pUBBSBGEBA9k0QEcoWCBDISkia/63z+CDL9yUz33vz5v3uOZPv5S13\n7v3dmTfzf/fOnSuvTAcddFBb1m0lBAgQIECAAIEmCAiQmtCKPVyHt7/97enOO+9M73//+9MD\nDzyQh9ydffbZPdebFL1Gn/zkJ9MHPvCBFJMyfOITn0izZ89OW2+9dQ9vHapOgAABAgQIEFh7\nAQHS2pv5RM0Exo8fn3uQLrnkkjRlypSe60267rrrWr1G2267bZ7t76/+6q/SeuutV7OWUhwC\nBAgQIECAQP0FBEj1byMlHKBADCWLYOHNvUmLFy8eYA7d9bZ58+blXqMYahi9Rh//+MfTD37w\ngzRz5szuqojSEiBAgAABAgRqJCBAqlFjKEp5gXHjxqVzzjknT0xQ9Cbtu+++KXqXli5dWn4F\nNchhwYIF+V5Qe++9d77WaLvttktXXHFFOv300/Ua1aB9FIEAAQIECBDobgEBUne3n9KvRuDg\ngw/OvUkf/ehH09y5c9OnPvWptN9+++VJHZYtW7aaT9X76egJu+CCC1IERmeddVYO+OK6o5jm\nfLfddqt34ZWOAAECBAgQINAlAgKkLmkoxVx7gehNOuOMM9KsWbPS8ccfn5544ol00kkn5et1\nvve976Xly5evfaYd+ET0fEUPWNwg9zOf+UyaP39+nrb75ptvztN5u9aoA41ilQQIECBAgEBj\nBQRIjW1aFSsENt544xQz291www3puOOOyzeYjZ6lww8/PF166aX5vkHFe+v09/nnn889RtHz\nFT1gccPXj3zkI+mmm27KN36dOHFinYqrLAQIECBAgACBRggIkBrRjCoxEIHp06fna3d+9KMf\npSOPPDLdc8896dRTT0277rprnuDg+uuvT50efhc3u417F334wx/Oky1Ej1H0fMVEDNETduaZ\nZ+aZ+gZSX+8hQIAAAQIECBBYe4Hha/8RnyDQ3QIxqUFcy/OLX/wiXXbZZelb3/pW+q//+q+8\nxE1n3/Oe96T3vve9KabMble64447clkuv/zy9MILL+TVbrPNNul973tfLk+USyJAgAABAgQI\nEBh8AQHS4BtbQ00Fttpqq3TaaaelT3/60+knP/lJDlDi2qQvfelLeZk6dWraY489Wssuu+yS\nRo0aVbo2cVPXCIhuu+22dOutt6bbb7+9FRTFsLnoPYoAzcQLpallQIAAAQIECBBYawEB0lqT\n+UDTBIYMGZInQIhJED73uc+lCJJi2uwIYGK4WyyRhg8fnnbaaac89C2Cpwhm+i6bbLJJfl8M\niXv66adz0BO9QcXy5JNP5jwfeOCBN0wQMW3atHTMMcfk5ZBDDkkjR47M+fiHAAECBAgQIECg\n/QJDVszk1R1Tea2jTcz4VSbFDGFxYlw2nzJlKD47YsSIfGJdh/v5bLDBBnma6TrchHX99ddP\nCxcuLJgq/fvwww+nW265JcWMcfH33nvvLXWdUrRhXPO01157pT333DP/3XTTTSstc2Q2dOjQ\nFOuqS/tEEBr3b+p0iuDztddey0snyxLtE9vtq6++muK6s06nwdyH1qZu0T6x3cb+XOZ6wPjs\n2LFj+1112e/1oryxbXf6UDps2LAUSx22p9GjR+f2W7RoUb9tMNhviGN4mNShfWIEQnwn1+EY\nXpd9vk7nWHGuF6kO7VOnc6zYbuuwL0f7xPYSZYnj+LqmgR4fGt+DVPYEsfg1v2w+69qQfT8X\nJ5nxJd/pskQ5YueNjazTZQmfwTwAbrbZZimWuC4pUgyPu//++/OMcnF/pegdir+xvPTSS3nH\njZODCRMmpEmTJuUepvgbS9y4dsaMGSvdzHUwDIuTpcHIO0OsxT/RPlGeOpQlyhFBSSydTFGO\nOEGJL/k6uERZ6lCOIrCP9ilzkhL5DCSVrXO0YwR0Ud4yB+yBlLW/98Sxqg7HhyhnfAfWpSx1\nap+wie267HYX+ZRJcQyP7+VOlyPqEO0TqQ5BbJQjbDrt0kvnWGG+Nim229iH2vFDkACpn5aJ\nQCBSHXbeiJ7rcNApTj7qEiAVJvF3sFN8mce1SKtKsa3EvZciaFrTry3t+PItfmlpx7pWZdH3\nuWiXoo36Pt+Jx8WXa6ddil8q6xIg1aV9ih+k4vu2TBBb5NPfNlZ2OyiuSYzylgno+ivnQF6P\nk6pIZes0kHUN5D112aYiWKtT+9Rhn49tZcyYMbXYVqJ9IsV2G9tMJ1P84FGXACkc6nSOFftQ\nlKeTKdonUhwbynzPFfn0V5eB/czWXy5eJ0CAAAECBAgQIECAQAMEBEgNaERVIECAAAECBAgQ\nIECgGgEBUjWOciFAgAABAgQIECBAoAECAqQGNKIqECBAgAABAgQIECBQjYAAqRpHuRAgQIAA\nAQIECBAg0AABAVIDGlEVCBAgQIAAAQIECBCoRkCAVI2jXAgQIECAAAECBAgQaICAAKkBjagK\nBAgQIECAAAECBAhUIyBAqsZRLgQIECBAgAABAgQINEBAgNSARlQFAgQIECBAgAABAgSqERAg\nVeMoFwIECBAgQIAAAQIEGiAgQGpAI6oCAQIECBAgQIAAAQLVCAiQqnGUCwECBAgQIECAAAEC\nDRAQIDWgEVWBAAECBAgQIECAAIFqBARI1TjKhQABAgQIECBAgACBBggIkBrQiKpAgAABAgQI\nECBAgEA1AgKkahzlQoAAAQIECBAgQIBAAwQESA1oRFUgQIAAAQIECBAgQKAaAQFSNY5yIUCA\nAAECBAgQIECgAQICpAY0oioQIECAAAECBAgQIFCNgACpGke5ECBAgAABAgQIECDQAAEBUgMa\nURUIECBAgAABAgQIEKhGQIBUjaNcCBAgQIAAAQIECBBogIAAqQGNqAoECBAgQIAAAQIECFQj\nIECqxlEuBAgQIECAAAECBAg0QECA1IBGVAUCBAgQIECAAAECBKoRECBV4ygXAgQIECBAgAAB\nAgQaICBAakAjqgIBAgQIECBAgAABAtUICJCqcZQLAQIECBAgQIAAAQINEBAgNaARVYEAAQIE\nCBAgQIAAgWoEBEjVOMqFAAECBAgQIECAAIEGCAiQGtCIqkCAAAECBAgQIECAQDUCAqRqHOVC\ngAABAgQIECBAgEADBARIDWhEVSBAgAABAgQIECBAoBoBAVI1jnIhQIAAAQIECBAgQKABAgKk\nBjSiKhAgQIAAAQIECBAgUI2AAKkaR7kQIECAAAECBAgQINAAAQFSAxpRFQgQIECAAAECBAgQ\nqEZAgFSNo1wIECBAgAABAgQIEGiAgACpAY2oCgQIECBAgAABAgQIVCMgQKrGUS4ECBAgQIAA\nAQIECDRAQIDUgEZUBQIECBAgQIAAAQIEqhEQIFXjKBcCBAgQIECAAAECBBogIEBqQCOqAgEC\nBAgQIECAAAEC1QgIkKpxlAsBAgQIECBAgAABAg0QECA1oBFVgQABAgQIECBAgACBagQESNU4\nyoUAAQIECBAgQIAAgQYICJAa0IiqQIAAAQIECBAgQIBANQICpGoc5UKAAAECBAgQIECAQAME\nBEgNaERVIECAAAECBAgQIECgGgEBUjWOciFAgAABAgQIECBAoAECAqQGNKIqECBAgAABAgQI\nECBQjYAAqRpHuRAgQIAAAQIECBAg0AABAVIDGlEVCBAgQIAAAQIECBCoRkCAVI2jXAgQIECA\nAAECBAgQaICAAKkBjagKBAgQIECAAAECBAhUIyBAqsZRLgQIECBAgAABAgQINEBAgNSARlQF\nAgQIECBAgAABAgSqERAgVeMoFwIECBAgQIAAAQIEGiAgQGpAI6oCAQIECBAgQIAAAQLVCAiQ\nqnGUCwECBAgQIECAAAECDRAQIDWgEVWBAAECBAgQIECAAIFqBARI1TjKhQABAgQIECBAgACB\nBggIkBrQiKpAgAABAgQIECBAgEA1AgKkahzlQoAAAQIECBAgQIBAAwQESA1oRFUgQIAAAQIE\nCBAgQKAaAQFSNY5yIUCAAAECBAgQIECgAQICpAY0oioQIECAAAECBAgQIFCNgACpGke5ECBA\ngAABAgQIECDQAAEBUgMaURUIECBAgAABAgQIEKhGQIBUjaNcCBAgQIAAAQIECBBogIAAqQGN\nqAoECBAgQIAAAQIECFQjIECqxlEuBAgQIECAAAECBAg0QECA1IBGVAUCBAgQIECAAAECBKoR\nECBV4ygXAgQIECBAgAABAgQaICBAakAjqgIBAgQIECBAgAABAtUICJCqcZQLAQIECBAgQIAA\nAQINEBAgNaARVYEAAQIECBAgQIAAgWoEBEjVOMqFAAECBAgQIECAAIEGCAiQGtCIqkCAAAEC\nBAgQIECAQDUCAqRqHOVCgAABAgQIECBAgEADBARIDWhEVSBAgAABAgQIECBAoBoBAVI1jnIh\nQIAAAQIECBAgQKABAgKkBjSiKhAgQIAAAQIECBAgUI2AAKkaR7kQIECAAAECBAgQINAAAQFS\nAxpRFQgQIECAAAECBAgQqEZAgFSNo1wIECBAgAABAgQIEGiAgACpAY2oCgQIECBAgAABAgQI\nVCMgQKrGUS4ECBAgQIAAAQIECDRAQIDUgEZUBQIECBAgQIAAAQIEqhEQIFXjKBcCBAgQIECA\nAAECBBogIEBqQCOqAgECBAgQIECAAAEC1QgIkKpxlAsBAgQIECBAgAABAg0QECA1oBFVgQAB\nAgQIECBAgACBagQESNU4yoUAAQIECBAgQIAAgQYICJAa0IiqQIAAAQIECBAgQIBANQJdFyB9\n4xvfSA8//HA1tZcLAQIECBAgQIAAAQIE+gh0VYD03e9+N33xi18UIPVpQA8JECBAgAABAgQI\nEKhOoGsCpCeeeCJ95StfSSNGjKiu9nIiQIAAAQIECBAgQIBAH4GuCJCWLl2azjzzzHTCCSek\n9ddfPw0ZMqRPFTwkQIAAAQIECBAgQIBANQJDlq9I1WQ1eLlceOGF6Z577klf+MIX0lFHHZVO\nOumkdPjhh6+0wuOPPz499NBDrednzpyZzj///Nb/1+VBBGOxLFu2bF0+Xulnohx1aa6hQ4fm\nstShPHVzqcO2EhteXVyiHJFsK5mh9Y99qEXRehDbSixl96FFixal0aNHt/Jd3YOy66mqvKsr\n39o+H+Wpy34WZa9LWepQjvCIfb7sNhf5VJHqtK1Usc9XYRJ51MXF8WHVLVrFPvTqq6+m9dZb\nb9Ur6PPs8D6Pa/kwAqNvf/vb6aKLLsob7poKOW7cuDRhwoTWW8aOHVv6yygaoy47b5QjUh2+\n7Iudtw5f9sOGDSvdzq2NpsSDvu1TlzaqS/sEax3KUmy3dWmfKEcdXOqyD1X1fTvQ9i1rX1V5\nS3zttD5afP+UrVMrwxIPYnuKVIeyRBvVoRxF+8S2OdDts0QT9PvRpu3z/VZ4AG+INqpL+xTH\nqjpsu3XZVqrahwa6/9U6QFqwYEEeWnfyySenKVOm9Lt5n3feeSu956mnnlrpubV5YtKkSTnS\nfO655zr+pbbBBhvkMoRLJ1PsuFOnTk1LlixJL7zwQieLkte94YYbpueff74W7RNB+rx581L8\ngt3JNHz48BQ/ENSlfeILds6cOZ0kyeuO9onttg7tE99pCxcuzNtLp2He8pa31KJ9YpsdM2ZM\nevHFF1P8yreuaeTIkSm+L/tLZbfJ8ePH556q2M9iKHgn06hRo/I1ui+//HIni5HXPW3atOwR\nx81Op4kTJ6YwqUP7RFnmz5+fl066xInm5MmTU13aJ7bdOpxjRa9z2EQbdTJFGWIfqtM51ty5\nczv+Q0O0T3znlj3HivOR2Ob6S7UOkL7zne/knebqq69OsUSKDffrX/96nsnuxBNP7K9+XidA\ngAABAgQIECBAgMCABWodIM2YMSN96EMfekNlbr311rTxxhun6dOnv+F5/yFAgAABAgQIECBA\ngEBZgVoHSLvsskuKpW+67LLL0n777bfKSRr6vs9jAgQIECBAgAABAgQIrK1AV0zzvbaV8n4C\nBAgQIECAAAECBAisi0Cte5BWVaHvfe97q3racwQIECBAgAABAgQIECgtoAepNKEMCBAgQIAA\nAQIECBBoioAAqSktqR4ECBAgQIAAAQIECJQWECCVJpQBAQIECBAgQIAAAQJNERAgNaUl1YMA\nAQIECBAgQIAAgdICAqTShDIgQIAAAQIECBAgQKApAgKkprSkehAgQIAAAQIECBAgUFpAgFSa\nUAYECBAgQIAAAQIECDRFQIDUlJZUDwIECBAgQIAAAQIESgsIkEoTyoAAAQIECBAgQIAAgaYI\nCJCa0pLqQYAAAQIECBAgQIBAaQEBUmlCGRAgQIAAAQIECBAg0BQBAVJTWlI9CBAgQIAAAQIE\nCBAoLSBAKk0oAwIECBAgQIAAAQIEmiIgQGpKS6oHAQIECBAgQIAAAQKlBQRIpQllQIAAAQIE\nCBAgQIBAUwQESE1pSfUgQIAAAQIECBAgQKC0gACpNKEMCBAgQIAAAQIECBBoioAAqSktqR4E\nCBAgQIAAAQIECJQWECCVJpQBAQIECBAgQIAAAQJNERAgNaUl1YMAAQIECBAgQIAAgdICAqTS\nhDIgQIAAAQIECBAgQKApAgKkprSkehAgQIAAAQIECBAgUFpAgFSaUAYECBAgQIAAAQIECDRF\nQIDUlJZUDwIECBAgQIAAAQIESgsIkEoTyoAAAQIECBAgQIAAgaYICJCa0pLqQYAAAQIECBAg\nQIBAaQEBUmlCGRAgQIAAAQIECBAg0BQBAVJTWlI9CBAgQIAAAQIECBAoLSBAKk0oAwIECBAg\nQIAAAQIEmiIgQGpKS6oHAQIECBAgQIAAAQKlBQRIpQllQIAAAQIECBAgQIBAUwQESE1pSfUg\nQIAAAQIECBAgQKC0gACpNKEMCBAgQIAAAQIECBBoioAAqSktqR4ECBAgQIAAAQIECJQWECCV\nJpQBAQIECBAgQIAAAQJNERAgNaUl1YMAAQIECBAgQIAAgdICAqTShDIgQIAAAQIECBAgQKAp\nAgKkprSkehAgQIAAAQIECBAgUFpAgFSaUAYECBAgQIAAAQIECDRFQIDUlJZUDwIECBAgQIAA\nAQIESgsIkEoTyoAAAQIECBAgQIAAgaYICJCa0pLqQYAAAQIECBAgQIBAaQEBUmlCGRAgQIAA\nAQIECBAg0BQBAVJTWlI9CBAgQIAAAQIECBAoLSBAKk0oAwIECBAgQIAAAQIEmiIgQGpKS6oH\nAQIECBAgQIAAAQKlBQRIpQllQIAAAQIECBAgQIBAUwQESE1pSfUgQIAAAQIECBAgQKC0gACp\nNKEMCBAgQIAAAQIECBBoioAAqSktqR4ECBAgQIAAAQIECJQWECCVJpQBAQIECBAgQIAAAQJN\nERAgNaUl1YMAAQIECBAgQIAAgdICAqTShDIgQIAAAQIECBAgQKApAgKkprSkehAgQIAAAQIE\nCBAgUFpAgFSaUAYECBAgQIAAAQIECDRFQIDUlJZUDwIECBAgQIAAAQIESgsIkEoTyoAAAQIE\nCBAgQIAAgaYICJCa0pLqQYAAAQIECBAgQIBAaYHhpXOQAQECBAgQIECAAAECBAZJ4LnnnkvL\nly8fpNxXzlYP0somniFAgAABAgQIECBAoIMC9913Xzr33HPT0Ucfnbbddtt08cUXt600epDa\nRm1FBAgQIECAAAECBAisSmDRokVp1qxZ6eqrr07XXHNNevLJJ/PbhgwZknbfffc0derUVX1s\nUJ4TIA0Kq0wJECBAgAABAgQIEFiTwDPPPJODoQiKbrjhhrRw4cL89g022CAdeeSR6dBDD00H\nH3xw2nzzzdP48ePTCy+8sKbsKntNgFQZpYwIECBAgAABAgQIEFidQFxHdPfdd+deogiK7rrr\nrtZbt9hiixwQHXLIIWnvvfdOI0eObL3W7gcCpHaLWx8BAgQIECBAgACBHhGIXqEbb7yxFRRF\nr1GkoUOHpr322itFQHTYYYfl64zqQiJAqktLKAcBAgQIECBAgACBBgg8/fTTbxg6F9cXRRo7\ndmw65phjck/RQQcdlCZOnFjL2gqQatksCkWAAAECBAgQIECgewSKoXM/+MEP3jB0bvr06Tkg\niuuJYujc8OH1Dz/qX8Lu2S6UlAABAgQIECBAgEBPCBSzzkVAFLPOPfXUU7nexdC5CIhiiSm6\nuy0JkLqtxZSXAAECBAgQIECAQAcE5syZ0xo69+Mf/7g169yYMWPy/YriWqI6D50bKJkAaaBS\n3keAAAECBAgQIECgxwTuv//+9P3vfz9PsnD77be3ar/ZZpvlyRUiKIqhcyNGjGi91u0PBEjd\n3oLKT4AAAQIECBAgQKAigSVLlqTZs2e3btj6q1/9KuccN2zdY4898rC5ww8/PG2//fYVrbF+\n2QiQ6tcmSkSAAAECBAgQIECgbQJz585NP/zhD1NcT3TdddelV155Ja87bth6xBFH5J6imI57\n8uTJbStTJ1ckQOqkvnUTIECAAAECBAgQ6IDAww8/nAOiuGHrT3/607Rs2bJcio033jgdd9xx\nKXqJYkru+fPnt17rQDE7skoBUkfYrZQAAQIECBAgQIBA+wSWLl2abrnlllZQ9Oijj7ZWvssu\nu7SuJ9ppp51az6+33no5QGo90SMPBEg90tCqSYAAAQIECBAg0FsCL730UvrRj36UryeKIXTx\n/0ijRo1KMWQuJliIv9OmTestmH5qK0DqB8jLBAgQIECAAAECBLpFIHqGYthcXE908803p9de\ney0XfcqUKel3f/d38yQL++23Xxo9enS3VKnt5RQgtZ3cCgkQIECAAAECBAhUIxAB0K233toK\niuLaoiLNmDEjB0TRU7TbbrulmIlO6l9AgNS/kXcQIECAAAECBAgQqI3AvHnz8mxz0UsUQ+de\nfPHFXLaRI0emd77znXno3KGHHpo22WST2pS5mwoiQOqm1lJWAgQIECBAgACBnhQohs7F8LkY\nOheTLkTacMMN0/vf//7cU3TAAQekmJpbKicgQCrn59MECBAgQIAAAQIEKhcoZp2LgOiaa65J\njzzySGsdO+64Y2vo3MyZMw2da8lU80CAVI2jXAgQIECgBwXuu+++fH+QXrl5Yg82sSoTaKtA\n3LD12muvTZdffnm66qqrUgylixTTbR944IE5KIpZ5zbddNO2lqvXViZA6rUWV18CBAgQqEzg\n1FNPzScxO++8c54qN05cXAhdGa+MCPSEQPzQEj1EERjddtttrZuyTp06NR199NH5u8Wsc+3d\nFARI7fW2NgIECBBokMARRxyRL46Ou9Dffffd6ZxzzknRm3TwwQfnk5q4HmDs2LENqrGqECBQ\nVmDBggVp1qxZraDoySefbGUZP7Ace+yx+ftj+vTphs61ZNr7QIDUXm9rI0CAAIEGCZx88sn5\nviLPPfdcnlEqfgWOmzJedtlleRk+fHh6+9vfnk92ImjabrvtGlR7VSFAYKACjz32WO4hiu+I\n2bNnp8WLF+ePxoQKRx55ZOs74i1veUu+aeuiRYvSCy+8MNDsva9iAQFSxaCyI0CAAIHeE5gw\nYUJ697vfnZdly5blYTIxXKY4GYoTojPPPDNPuRvD8CJY2nfffd2osfc2FTXuEYElS5bkmebi\neyCWvhMsbL311umggw7KQdHee++dRowY0SMq3VNNAVL3tJWSEiBAgEAXCAwdOjT3GkXP0Wmn\nnZaeeuqpfIIU9yq5/vrr09e+9rW8xEXXcXIUJ0qxxEmTRIBA9wo88cQTuQc5AqIbb7wxxVC6\nSLGvx72JiqG3W2yxRfdWskdKLkDqkYZWTQIECBDojMBGG22Ujj/++LzEr8o33XRTDphiKN6P\nf/zjvPz1X/912nzzzVvBkt6lzrSVtRJYG4Gilyh+/Ijl5z//eevjMcvcb//2b+eg6B3veIfe\n4pZMdzwQIHVHOyklAQIECDRAIO5yv//+++fljDPOSI8//ng+sYqTq/jF+eKLL85LvG+vvfbK\nvzrH1L477LBDA2qvCgS6XyBu1ho/blx33XV5ooWFCxfmShX7dvQGxz677bbbdn9le7gGAqQe\nbnxVJ0CAAIHOCmy22WbphBNOyEtctB29S3HyFcsNN9yQl7h2adq0aa1g6Td+4zfSxIkTO1tw\nayfQIwKvvPJK+slPftIKimKyhSJFr28EQ7HELSN7kwAAHL5JREFUfjl69OjiJX+7XECA1OUN\nqPgECBAg0AyBuE4hpgWP5bOf/Wz63//93/wrdREsXXrppSmWIUOGpF133bX13j322CONGjWq\nGQhqQaDDAjHJyp133tka/hr3JVq6dGku1frrr5+HzBVB0ZZbbtnh0lr9YAkIkAZLVr4ECBAg\nQKCEwCabbJJ+7/d+Ly+vvfZanhkvhvXEdUtxAnfHHXekc889N8U0wfHr9aGHHponhzC0pwS6\nj/akwK9+9avcexv7Vywvvvhiy2HGjBn5x4iYZCGGvcZQOqn5AgKk5rexGhIgQIBAlwsMGzYs\n7bnnnnn51Kc+lU/g4pqlYpKHq666KsUSKYbjRcAU1zrF3/i/RIDA6wJz587N1w/FMNaYWTIC\npCLFfYhicoXoyY19aMqUKcVL/vaQgACphxpbVQkQIECgGQJx36WjjjoqL1GjGI4XJ3px36VZ\ns2alb37zm3mJ16JHab/99ksxk9Y+++yT4rMSgV4SmD9/fr4nUfyoEMs999zTqn5cNxQTK8QU\n3DF0bvr06a3XPOhdAQFS77a9mhMgQIBAQwTiHkox090HPvCBFNdQ3HXXXTlgil/If/rTn+bp\nhy+66KJ8/dJb3/rWHCxFwBT3YRozZkxDFFSDwP8LxMxysd3H5Arxg0EMR41hqpGiNzbuURa9\nq/HDQVzDFzdqjUApru+LYEoiIECyDRAgQIAAgQYJxI1qd9ttt7ycdNJJKU4Wb7311nyiWJws\nxi/oX/7yl1O8d5dddsk9S9G7FMP4xo0b1yANVekFgbgha2zjs2fPztcS3X777enVV1/NVY+g\nZ6eddkpxb7EIiuI6Ij8K9MJWUa6OAqRyfj5NgAABAgRqLRAzb8Uv5bFEKoYbRbAUS/Q2xS/s\n559/fquHKXqWYomTycmTJ9e6fgrXewLz5s3LPURFQBSTlhQ9RKGx/fbb52AogiLDSntv+6ii\nxo0PkOLAUCbFr2uR6jCFanQBL1++PJWtUxmP+Gz8GhMpbDpdlqIcdWmfKE/McFMYxf87kWII\nQSx1aZ/wqENZwqQO7VN8rwwfPrwWLnVpn/CIFNNdF48Hc/8pu03G9lSUN76fO5li/QPd56Pe\nv/Vbv5WXKHOcbMb9l/oOR4oepgsuuCBXaZtttsnBUhE0xXC+/lJdtqkwie2pDu0TZlGOsttd\nf/b9vR5tU5fjd7EPhUmc36wuxSQKN998c95O4+99993Xen/UJ3qIYshoLBEUTZo0aXVZrfb5\nYna6OrRPFHKg+/NqK1TRC+Eb51hrap+KVrXGbIp9uF3H8MYHSMXOt0b1NbwYG0aksvmsYRUD\nfim+0GID7XRZCpP42+myFHh1KEfhEu3U6fJEGerUPtFOnTaJMtRlH4pyRKpTG9WlfcKl8InH\n65IGeiAvW+din498isfrUt4qPhNmsaxLneKms0cccUReoizRw3TLLbfki9njF/q4D8wll1yS\nl3h9ww03bPUuxZC8GM735pPKumzbRTnq0D5hV5QnHnc6rcu2UnWZi3aJshT77ZIlS9Ldd9+d\nt8EiKHryySdbq44T5biGKHqGiolHxo8f33p9XR/0Lcu65lHl5+qyrRTlKNqnyjquTV7FcWFd\nv+eKdQ20Ho0PkOIOyGVSRKrxS2YcMAaKWmZ9a/ps3OsiyhBjbTuZYuOM8bvRnV3Wt4p6xC8b\ndWmfKMuiRYvyUkXd1jWP2GbjgFOX9okv2DqUJbbdOPhGG3UyRfvE/hxj5OvgEhcn16EcsZ3E\nd25cM1NcP7Au7VT8EtzfZ8vWOfaxWFd8Jxc3kuxvnYP1enz3xIlj2ToV5YsT0FhOOeWU3BbR\noxRBUyxx8fsVV1yRl3h/bM9xr5jdd989X/B++OGHp+krZgKrqixFmdblb5jUpX0iiIzvnzhe\ndTLFfhbbS13a56mnnkrf//738zVEce1QDPkMpyJF8BMzzEUwHttkBORR/r6pirrUZZKGaJ+x\nY8fm75Qq6tXXaV0eh3VsszH5SydTtE+Upew5VnxvD+Q6y8YHSJ1sTOsmQIAAAQLdLhBBxsyZ\nM/PyR3/0R7k6jz76aO5Zit6lOKm9995784ntxRdfnF+PIU4777xz2nXXXfMkEHFSu/HGG3c7\nhfKXFJgzZ06+yXFcMxRL9BQ988wzrVwjOIhp6WNmuQi43/a2t6Xtttuu4z20rQJ60DMCAqSe\naWoVJUCAAAEC1QhsueWWKZa4oWak6KWJX/6LYCl6moqb2BZrjKF5ETBF4BTXjMR045tvvrmT\n3wKoYX/j3lwROMf1QrFtREAUvUV9U9yUNe7nFdtCEYRH74lEoNMCAqROt4D1EyBAgACBLheI\n4S/FJA7Tpk3Lw4Puv//+N/QWxAnytddem5eiujFcO06Oi2XHHXfMPQaRn9QdAjHk6eGHH04P\nPPBAvgFrBEWxvPjii2+oQFzrdsABB7R6FSNYjkA5hk09/fTTHb+M4Q2F9Z+eFxAg9fwmAIAA\nAQIECFQvMGXKlHTIIYfkpcg9ehBiWFX0KsR1TXEiHRfix9I3bbbZZnmq5rj5bUzZHMOsYvY8\ngVNfpfY+Xrx4cYqhlQ8++GAOhh566KH8+Je//OVK16dssskm+ZqhuDYtgqBYordQItAtAgKk\nbmkp5SRAgAABAl0usNFGG6VYDjvssFZN4kL0otcheiHiBDxOvq+55pq8tN644kFcxxSB0lZb\nbZWXeBzLpptuuk4z+PXN2+OUA52YMe4Xv/hFeuSRR1p/4/ETTzyxUi9PTDYTPUERxEYwGz2B\nERRFb5FEoJsFBEjd3HrKToAAAQIEulwghtnFDWlj6Zti2FUES8USJ+mx3HDDDXnp+96YmSqC\np+ilKJbohYoT9pgwIpZ4T6+nmIns+eefzz1BcV1Q3F8olscffzz/jSBoVTNIxkxycY1QBKMR\nDBVL9BTFxAoSgaYJCJCa1qLqQ4AAAQIEGiAQ1zLFEtet9E0vvfRS7tmIXo649iX+PvbYY/kk\nf9asWSmWN6eY4j8mBIj8il6s+BvDAGPyiMmTJ+clHr95Cuk351XH/8e02M8991wOfuLv3Llz\n07PPPpuv7YlhjbFEwBlL3KJjVSkmR4ihjBFgFr10xd/wkQj0koAAqZdaW10JECBAgECXCxS9\nGdGj8eYUw/WKXpH4G0FCXCMTw8YiSIhekzvuuOPNH3vD/+M6pwiUJkyYkO+XEoFDrLPv33hP\n3Ncogqn4WzyO/xf3oYseq+KmljEULe6VFcHdyy+/nIOUCFT6LjHZQdwDrO/feBwzBMZnis/2\n/RuPo0coXu8vRZ2iRy2CxBiiGMFhBEPR0xZ/o74SAQL/LyBAsiUQIECAAAECjRCI4XpxDUws\nkeJamAgeihv5RkAS990pelPivjx9e16KxxF0xDTVq+ttqQNWBF8RuE2dOjXXt28vWARDsRQ9\nZvGeuJ9VpBgSF++NukoECKxaQIC0ahfPEiBAgAABAg0TKK5VGuhNa6P3Zt68eXkpem7i//H8\nm3t6it6fCMYisIrrfYrHwRg9S/H88uXL8/VQRQ9TPB/Leuut1+qRKnqmir/jxo3LvVl9/0Yw\nKBEgMDgCAqTBcZUrAQIECBAg0OUCMZQuluiJKZMi0InerAiu5s+fXyYrnyVAoA0CQ9uwDqsg\nQIAAAQIECBAgQIBAVwgIkLqimRSSAAECBAgQIECAAIF2CAiQ2qFsHQQIECBAgAABAgQIdIWA\nAKkrmkkhCRAgQIAAAQIECBBoh4AAqR3K1kGAAAECBAgQIECAQFcICJC6opkUkgABAgQIECBA\ngACBdggIkNqhbB0ECBAgQIAAAQIECHSFgACpK5pJIQkQIECAAAECBAgQaIeAAKkdytZBgAAB\nAgQIECBAgEBXCAiQuqKZFJIAAQIECBAgQIAAgXYICJDaoWwdBAgQIECAAAECBAh0hYAAqSua\nSSEJECBAgAABAgQIEGiHgACpHcrWQYAAAQIECBAgQIBAVwgIkLqimRSSAAECBAgQIECAAIF2\nCAiQ2qFsHQQIECBAgAABAgQIdIWAAKkrmkkhCRAgQIAAAQIECBBoh4AAqR3K1kGAAAECBAgQ\nIECAQFcICJC6opkUkgABAgQIECBAgACBdggIkNqhbB0ECBAgQIAAAQIECHSFgACpK5pJIQkQ\nIECAAAECBAgQaIeAAKkdytZBgAABAgQIECBAgEBXCAiQuqKZFJIAAQIECBAgQIAAgXYICJDa\noWwdBAgQIECAAAECBAh0hYAAqSuaSSEJECBAgAABAgQIEGiHgACpHcrWQYAAAQIECBAgQIBA\nVwgIkLqimRSSAAECBAgQIECAAIF2CAiQ2qFsHQQIECBAgAABAgQIdIWAAKkrmkkhCRAgQIAA\nAQIECBBoh4AAqR3K1kGAAAECBAgQIECAQFcICJC6opkUkgABAgQIECBAgACBdggIkNqhbB0E\nCBAgQIAAAQIECHSFwJDlK1JXlHQdC/nss8+u4yf//2Pz589Pr732Who7dmwaMmRIqbzKfni9\n9dZL0VxLliwpm1Wpzy9btiy98sorafjw4Wn06NGl8qriw9E2L7/8chVZlcoj2mXRokXZJGw6\nmYYNG5ZGjRqVYvvtdIoyxDYT7dTpFCaxP7/66qsdLUqUIVxGjhyZ26mjhVmx8nHjxqV58+Z1\nuhh5/4n9KL5XyuxD4TphwoR+61P2+BD7e5R3gw02SLHPdTKNGDEilyHK1OkU38dxvBwzZkyn\ni5LbZuHChfk7qJOFie+cKMf666+foq06mYq2qcNxc8GCBWnp0qW1OceKdlm8eHEnmydvq3U6\nx4r9OI5XnQ4XinOssvtQfFdPnjy5/zaOAElavcCHP/zh5dttt93yFV8kq39Tj70yZ86cbPKx\nj32sx2q+5upecMEF2eWqq65a8xt77NWjjjpq+a677tpjtV5zde+///68rXzmM59Z8xt77NXP\nfe5z2eX222/vipr/xV/8RS7vgw8+2BXlbVchd9ppp+XHHHNMu1bXFeu58sor87Zy0UUXdUV5\n21XIP/zDP8wuzz//fLtWWfv1vPTSS9nkD/7gD2pf1nYW8Gtf+1p2+e53v9uW1Rpi138M6R0E\nCBAgQIAAAQIECPSIgACpRxpaNQkQIECAAAECBAgQ6F9AgNS/kXcQIECAAAECBAgQINAjAsM+\nuyL1SF3XqZpxYfnuu++eVlxD0fGLcNepAoPwoaFDh6YpU6akfffdN02fPn0Q1tCdWcaFg9tu\nu21629velsaPH9+dlRiEUofFXnvtlVZclzAIuXdnlnGR6EYbbZT22WeftMkmm3RnJQah1LEP\nzZgxI+2xxx61mACmvyrG5AyxXc+cObMWk230V952vT5p0qT0jne8I38ftmuddV9PTLIUx8v4\nLtxwww3rXty2lS/OsWL/2W233UpNzNK2ArdhRTGJRmwjsQ9tueWWbVhjd6wi9qHiHGsgk/CU\nrVXjZ7ErC+TzBAgQIECAAAECBAj0joAhdr3T1mpKgAABAgQIECBAgEA/AgKkfoC8TIAAAQIE\nCBAgQIBA7wh09m6WNXeOm6jNmjUr34Q0xg1vvvnmNS9x+4oXN7q85JJL0rHHHptvMtm+Nddz\nTXEj1LvvvjvdcccdaerUqenAAw9MMV6219MjjzySbrrppnydTexDcY2J9LrAN77xjTz+fptt\ntnn9yR58FN+1s2fPXqnmsR91+qaaKxXq1084PqxOJuWbMTs+vO7j+PC6Rd9HL774Yrr++uvz\nDUj33HPPfF1m39d7/fGtt96awuiQQw7pdYp8Lv7mG9/vuOOOabPNNhs0G9cgrYb20UcfTR/5\nyEfSVlttlU/uIlD627/927T33nuv5hO99fS//Mu/pMsuuyx9/etfTxtvvHFvVf5NtX3uuefS\nihu65YAoJvOIE7248/SXv/zlng4eY/6X2267LU/mcdddd+WL7r/whS+YwOLX28+Km92ls88+\nO6242Wj6zd/8zTdtVb313xtvvDH95V/+5UoXr3/1q19NcRF33ZLjw5pbxPHhdR/Hh9ct+j76\n4Q9/mM4666wUgdHChQvTfffdl/7u7/4uT3LU9329+viZZ55JJ5xwQp4g7O///u97lSHXO36Q\nP+yww/KxYPjw1/t1VtxkOD8/WDivr2mw1tCl+a64o3tacSfwdPLJJ6eYUWTFHXzTOeecky69\n9NL8/y6tVulix077j//4j2nFne5L59WUDL75zW/mIPG8887LVYov++OOOy4Hjx/96EebUs21\nqkf0pl133XXpP//zP/OvgkuWLMm9jf/zP/+Tfud3fmet8mrim5944on0la98pba9I+02//nP\nf57e+ta3pn/9139t96rXaX2OD6tmc3xY2cXxYWWTV199Nf3bv/1b/mGxOB7EPvXv//7vAqQV\nXNHjeOaZZ/b0uWbfrebxxx9PcQ5x4YUXpsmTJ/d9aVAfuwZpFbzPP/98uv/++9O73vWu1gZ6\n1FFHpSeffDL/yrGKj/TMU5///Odzd3iv/6LRt8FHjx6dPvShD7WeimFkO+ywQ95eWk/22IOY\nojS2kZjKOlL86jNu3Lg0d+7cHpNYubpLly7NB7/4dTC2lfgBptdTBEjbb799VzA4Pqy+mRwf\nVrZxfFjZJHoEPv7xj+cfoYtXJ06c6Pjwa4z4YTGOCwcddFDB09N/4/gQ5xTtDI4CXA/SKja7\np59+Oj/bd+hYNMzIkSPTs88+m3/pXMXHeuKp0047LV9j89hjj/VEfQdSyb7BUbw/goCf/exn\n6cQTTxzIxxv5ngiMiuDo4YcfTldeeWV66aWX0uGHH97I+q5NpaI3Ok6a3vOe96QYQialFAfA\nuGYvvl8eeOCBFGPL4wSqjveIcnxY/Rbr+LCyjePDyiajRo1K+++/f34hfnC45ZZb0n//93/n\nyxpWfndvPfPggw/mkRcXXHBBvs67t2q/6trGOUQMtY4h+nG5SwTTsV8V29CqP1X+WT1IqzB8\n6qmn8sH6zRfZRwO98MILq/hE7zwVExBIqxeIbuC49maLLbZI7373u1f/xh55Zc6cOTlQjMkI\nDjjggEG9oLIbSO+555707W9/O51++ul6jn7dYDHZQQQdca1GDGuO6/niOzh+YHjllVdq16yO\nD6tvEseH1dvEK44PK/v8zd/8Tb4WM3oI9ttvv5Xf0EPPLF68OI8uiO++adOm9VDN11zVhx56\nKP/wvN1226VPfvKT+YezuHZ3VRP7rDmntXtVD9IqvGLWpBgG8+YU3cLxy69EYFUC8+bNS3/+\n53+e4m9cr1bX2bdWVfbBem7KlCnpqquuSvELUIypjgvxY2KCXkwLFizIBnFdY7hI/y8QE5pE\nAD1p0qTcSx/PzpgxI1+gfO211+ahznWycnyoU2t0T1kcH1bdVueee26eqS2uP/rgBz+YvvWt\nb/XsRD5xDWb8uHrEEUesGqtHn40fneO6rOg5ihSTpcU5RUwSts8++wyaih6kVdDGLxkRDMUJ\nTd8UX3DFsKG+z3tMIH79/tjHPpYD6y996UsrzcbV60IxjfX73ve+PJTizVN19orNd77zndxL\ncvXVV6dPf/rTeQmL+JLvlskJBqOtYqx9/FoaQ5iLFLOHRhAZvTV1S44PdWuR+pfH8WHNbTRh\nwoQUM5LFeddg9wqsuSSdezUmOIlhhjFKqTg+xC0y4nr4+H9M992rafz48a3gqDCIwGiwjw8C\npEK7z99NN900X1R+7733tp6NjTQi2L7XJbVe9KCnBeKLLYKjmI//i1/8Ys/++tV3I4iT/lNO\nOaXvUymCgdiHenVSgugViXHT8bdYhg0blr9Tpk+f/garXvrPL3/5y9xbFDMVFSkOfDE8s47X\nIDk+FK3k70AEHB9WVop9Pq7BjImvirRo0aIcIC1fvrx4qqf+xoQ9Mbw47hdYHB+ixyR62OP/\nvTwiJQLEmA2yb7rzzjsH/XzcELu+4r9+HNFqzLkeF1DHxcIxA1dcMBf3KjE0ZhVgPf7UP/3T\nP+Uv9ve+9735AvOCI2Zt23LLLYv/9tTfd77znen8889Pca+fGC4QPzbE0Il4vleHqe6yyy4p\nlr4p7iUW4+57efKKCA7jou2Y9vfP/uzPUpwoxZT5cXJw8MEH9+WqxWPHh1o0Q9cUwvFh5aaK\nfT6uV4t9/k//9E9b+3zsW716r8k4X4iZTfum+JEoljc/3/c9vfB45syZ6T/+4z/yPaE233zz\ndMUVV+RzrcEeri9AWs3W9cd//MfpjDPOSEcffXTrBqCf+MQnVvNuT/eqQPwCVgwJiGtL+qb4\nJSjuGdWLKQ5+4RE9a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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x <- seq(0,5,0.1)\n",
    "f <- (x-2)^2 + 6\n",
    "log_f <- log(f)\n",
    "x_dat <- data.frame(x,f,log_f)\n",
    "require(tidyverse)\n",
    "x_dat <- gather(x_dat,\"func\",\"value\",f:log_f) #put this in long form\n",
    "#plot function and log transformation of function side by side. \n",
    "ggplot(x_dat,aes(x=x,y=value)) + geom_line() + facet_grid(.~func) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "awcBiaCQLc1z"
   },
   "source": [
    "Even though the log transformation is flatter than the original function, it still has a minimum at x = 2. \n",
    "\n",
    "In the sections on maximum likelihood estimation discussed in readings and lecture, the task is to find values of $\\beta_0$ and $\\beta_1$ that maximize the likelihood for simple linear regression. The likelihood function is calculated as: \n",
    "\n",
    "$$ \\prod_{i=1}^{n} p(y_i | x_i; \\beta_0, \\beta_1, \\sigma) =  \\prod_{i=1}^{n} \\frac{1} {{\\sigma \\sqrt {2\\pi } }} e^{{\\frac{ - ( {y_i - (\\beta_0 + \\beta_1x_i) })^2 }{2\\sigma^2} }} $$\n",
    "\n",
    "If we want to find those maximizing solutions, we need to take the derivative. I didn't talk about it above, but taking the derivative of a product of functions is kind of a pain, especially if there are a lot of factors like there are in the equation above (remember from the previous tutorial that $\\prod_{i=1}^{n}$ means you multiply that term for every value of $i$ from 1 to $n$). So to make this function easier to derive, we can take the log transformation! As stated above, the minimizing and maximizing values will stay the same after a log transformation, and using rule **2** from the logarithm rules we can make a long product into a long sum. Makes sense to take the natural log since that will also help simplify the exponential term ($e^{{\\frac{ - ( {y_i - (\\beta_0 + \\beta_1x_i) })^2 }{2\\sigma^2} }}$). \n",
    "\n",
    "$$\n",
    " \\ln{L}(\\beta_0, \\beta_1, \\sigma) = \\ln \\prod_{i=1}^{n} p(y_i | x_i; \\beta_0, \\beta_1, \\sigma)  \\\\\n",
    "   = \\sum_{i=1}^{n} \\ln  p(y_i | x_i; \\beta_0, \\beta_1, \\sigma)  \\\\\n",
    "   = \\sum_{i=1}^{n} \\ln (\\frac{1} {{\\sigma \\sqrt {2\\pi } }} e^{{\\frac{ - ( {y_i - (\\beta_0 + \\beta_1x_i) })^2 }{2\\sigma^2} }}) \\\\\n",
    "   = \\frac{-n}{2} \\ln{2\\pi} - n \\ln{\\sigma} - \\frac{1}{2\\sigma^2} \\sum_{i=1}^{n} (y_i - (\\beta_0 + \\beta_1x_i))^2\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LlmCsSvKPAA4"
   },
   "source": [
    "Taking the natural log of the likelihood made this a much nicer function for taking the derivative and finding maximum values. Try getting from the third line to the fourth line by hand using the logarithm rules described above and the tips on working with summations from the previous tutorial. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Bx05tUhQj8tT"
   },
   "source": [
    "---\n",
    "# Expected values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "zRn6mo1wj-5n"
   },
   "source": [
    "The expected value $E(X)$, sometimes referred to as the expectation, is the most probable value of $X$ given the probability distribution from which it was drawn. In the case of a normally distributed variable (which is what's relevant for this class), the expected value of $X$ is $\\mu$, the center of the normal distribution, and expected value can be estimated from your data as the average of the observed values, $\\bar{x}$.\n",
    "\n",
    "Here, we'll review a few tips for working with expected values in equations. This will be helpful for the homework.  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fYw3BbP5gvlw"
   },
   "source": [
    "**Tip 1:** The expected value of a constant is that constant.\n",
    "\n",
    "$$E(c) = c$$\n",
    "\n",
    "**Tip 2:** The expected value of a sum is equal to the added expected values of the terms being added.\n",
    "\n",
    "$$E(X+Y) = E(X) + E(Y)$$\n",
    "\n",
    "**Tip 3:** You can pull coefficients out of the expected value. \n",
    "\n",
    "$$E(cX) = cE(X)$$\n",
    "\n",
    "**Tip 4:** The expected value of a random variable squared is the same as the squared expected value of that variable, plus its variance. \n",
    "\n",
    "$$E(X^2) = Var(X) + E(X)^2$$\n",
    "\n",
    "**Tip 5:** The expected value of the product of two random variables is the covariance of those variables plus the product of their expected values. \n",
    "\n",
    "$$E(XY) = Cov(X,Y) + E(X)E(Y)$$\n",
    "\n",
    "\n",
    "Here's one worked example to get you comfortable manipulating equations with expected values:\n",
    "\n",
    "$$\n",
    " E((X + cY)^2) =  E(X^2 + 2cXY + c^2Y^2) \\\\\n",
    "   = E(X^2) + E(2cXY) + E(c^2Y^2)  \\\\\n",
    "   = E(X^2) + 2cE(XY) + c^2E(Y^2) \\\\\n",
    "   = Var(X) + E(X)^2 + 2c(Cov(X,Y) + E(X)E(Y)) + c^2(Var(Y) + E(Y)^2) \\\\\n",
    "   = Var(X) + E(X)^2 + 2c Cov(X,Y) + 2cE(X)E(Y) + c^2Var(Y) + c^2E(Y)^2\n",
    "$$\n",
    "\n",
    "The first line expands the function using the Foil method. The second line separates the terms using **Tip 2**. The third line pulls out coefficients using **Tip 3**, and the fourth line applies **Tips 4 and 5**.\n",
    "\n",
    "That's all the math tools we've got for you today, folks! Fear not, the next tutorial will be more practical. We'll focus on fitting linear models in R. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XbWLxNERlLwg"
   },
   "source": [
    "*Notebook authored by Patience Stevens and edited by Amy Sentis and Fiona Horner.*"
   ]
  }
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