FYS-STK4155/doc/Programs/ANN/Ann3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <p style=\"text-align: right;\"> Nicolas Dronchi </p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Day 23 Pre-Class assignment: Back propagation\n",
    "This pre-class assignment finishes out the videos from \"Neural Networks Demystified\" module.  Please watch the videos.  Again, you do not have to understand the equations but the math is included for completeness.\n",
    "\n",
    "If you are lost, I highly recommend reviewing the entire \"Neural Networks Demystified\" module which can be downloaded from github:\n",
    "\n",
    "    git clone https://github.com/stephencwelch/Neural-Networks-Demystified\n",
    "\n",
    "\n",
    "<img src=https://www.pyimagesearch.com/wp-content/uploads/2016/08/simple_neural_network_header.jpg width=400px>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Goals for this pre-class assignment:\n",
    "</p>\n",
    "1. Reviewing gradient descent\n",
    "1. Performing Back Propagation\n",
    "1. Training at network\n",
    "\n",
    "## Assignment instructions\n",
    "\n",
    "**This assignment is due by 11:59 p.m. the day before class** and should be uploaded into the appropriate \"Pre-class assignments\" dropbox folder in the Desire2Learn website.\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Gradient Decent\n",
    "\n",
    "&#9989; Do This -  watch the following video:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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hMKohVjvUpcYedL5+WWXA5LB5iwyGaiop6ROXlaOMqoX8CmRDIrFuhiWL8a6L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\nAAAAAAAAAAAAAAB//9k=\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"640\"\n",
       "            height=\"360\"\n",
       "            src=\"https://www.youtube.com/embed/5u0jaA3qAGk\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x1d9775b5eb8>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('5u0jaA3qAGk',width=640,height=360)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 1**: In simple terms, explain the \"Curse of Dimensionality\"?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to grid search/brute force solve for the best variables for all dimensions it would take N^D operations where D is the dimension. This can quickly reach amounts of time that aren't reasonably computable. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 2. Back Propagation:\n",
    "\n",
    "Now watch the following video:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"640\"\n",
       "            height=\"360\"\n",
       "            src=\"https://www.youtube.com/embed/GlcnxUlrtek\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x1d9775d8160>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo('GlcnxUlrtek',width=640,height=360)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 2**: The gradient decent algorithm in Neural Networks is often called  \"back propagation.\"  What is being passed back though the algorithm and causing the weights to be updated? "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The weights of how much they contribute to the error. The goal is to find out where the most error came from and then change that."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is a link to the entire code so far:\n",
    "\n",
    "https://raw.githubusercontent.com/stephencwelch/Neural-Networks-Demystified/master/partSix.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "&#9989; Do This -  Download and inspect the partSix.py file and run the following command:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.3 1. ]\n",
      " [0.5 0.2]\n",
      " [1.  0.4]]\n",
      "[[0.75]\n",
      " [0.82]\n",
      " [0.93]]\n"
     ]
    }
   ],
   "source": [
    "from partSix import *\n",
    "print(X)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "&#9989; Do This -  Create an instance of the Neural Network and apply forward function to estimate $\\hat{y}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.52155376],\n",
       "       [0.41215014],\n",
       "       [0.41576012]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# put your code here\n",
    "NN = Neural_Network()\n",
    "NN.forward(X)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 3**: How good is this initial estimation?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.24148593])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "NN.costFunction(X, y )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "pretty bad. The cost function gives an error of 0.241. It only guesses variables around 0.5."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "\n",
    "## 3. Training:\n",
    "\n",
    "Please watch the following video:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/jpeg": 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amQ1ctpI3N/eGaWOK2YxRyQoJu9G7c1u8pVZWUOgjknGR2GMAZJ5ZNNu755U41ssMRWTc\nd6uysBEUBKv2ZMq5AO7aD3ucVBT6PdsYlXV4IpLbqUUhWNzJxY7W5h79Xuu2U3cUojcEExLkNuzW\nfpSk8tyhh1SO2tmi76MMVKyJMY0kV0PoqPPLBEykqV2jB74gi6vedZStSG9i5IZojIMqcMF3OkaP\nJsVmJICyIxwTgOMmsrXUQVXMkYR8BHLqFYnsCsThs+aslM1VrV6/BnHGjzseTw1xw42VZH3ZxtVn\nQHybh5ao2o24IBnhy0nBA4ic5cbuF28nx4u3mPLQG3StaPUIGjEqyxtEziNZFYFGkMvACBh2txe8\n9mrheQnOJYjgEnEicgvhE8+weOgsz0rAbyHcqcWLexwqcRNzHaWwq5yTtVj7CmrXv4BI8RnhEsaJ\nI8ZkQOkchkEbshOVRjFKATyPDbyGgs2aqK15L2FQS0sYChye/Xlw/vnLP4Pj8lW2Oo285YQTwzFA\nhcRSpIUEg3IWCk7QwBIz24oDbpVKrQClKUApSlAKUpQFaUpQGeHspP4Dfmt8hpD2UuPAf81vkNAY\nq1rv75b/AOc3/Lz1s1rXn3y3/wA5v+XnqMjNmlKVSioTX9Ft7xo+sKzdWuY7qHbJJGUnjTEcmY2G\n7G5uRyOdTdQfSCe6R4+rRhw06iYlFkKR8NTyVp4tuTy35bby71s8gMFh0YsYbMaetur2aksIJy1w\nuWkMpyZixPohLczyNW9JejNtfpsmDqRb3FtHJE5Voo7lFjl2LzUnaq43A421i0281RtPWWS1t/5x\nJbNu8rW0G3ikA8ReMV9CwfHk+TPLNrt/fRGMW1kLndFK0h4yoFkRQY4gWxncSe+/w45ZoDHcdE7K\nSOOJ0maOJo3jXrVyArxiQbgBJyLcRy3pjjOcDFsHRGxjVliSSMtEIS4mkZyqvxI93ELByjdm4Hyc\n614NW1ZnXdpionFiDnjqWMLQOZHUZwrCcxLg55bs+UYxrerbRnSSGKK39ojKhjMqOrANkbYy78gd\n23xZxQG1c9C9OkaR3hdjK07v/WLgBmuX4kpwJPT4YelKrjGKDobp/e5jkbZPb3KlridmE1sjRxNv\nL7uSscjOD2nnWLU9X1ON9sGndZHFuUdhIIhGsVtHJbsvFI44mmYrlcBQ3PmjZldCvppolNxbPazi\nKJpoyVeJJZFJeKOVT6NswMsAAdwxzyABGnoTpxgW2McpgVNgja5nK/f4bkMQX75+NbwtuPPvPHk5\nx2vQTTYp4p4YmiMTyS8NJH2PI8sU6s2Tuwk0QcKDjLHIPLGLSekl9IQZtOZU6pJcsITJJLvjmaFY\nUSVEBeUhXTJBCbi4jOAZ7V5rhNnV4xITxQwIGBiCVoiWLrtBmES8s8mPZ20bojdEbd9DtPmxxonm\nINud0088rk20L28ZZ3cs5MUsgYsSW3knJ51g/oHpnDMXBk4Z7VFzcgEeicuUngnivlew55g1tWlx\nqbHBhgUegd9LlAULJxj6FI542wynZjAKqNxDZGhFrGrPG7NpzwSdXvGSIGCf0eN4DZKXEyjMiNMG\nXsBj8LGM1Zqyp2rMmn9A9NhkSbhvLLFKZInlldjGOLxkjABAKLJhgSCxIySTUlD0et1jjiPFcRQW\n9upaVwTHbK6R5CELkrJIGwBuEhB5VHNqmriSQDT0eNpGWBi6R7AZnWNpfRm3pwOHIzAKQWZApIzW\nCPpDqhdkGks3DjjMhEqoeK8KOI0EhAkBkZlyrEKI+fM7RKsjSe06Cy0uOFw0ZlUBZRw+K7RMZTD3\n7qxO5kWBET0qlgO2qyaXG0iy5k3C4F1jeSplW2e1XvWyFXhv2LjmgznnmJttW1MSKs2mkxhLppZI\nZoixaEubdIUlkUNxQqAFmXnIM7QCRS+1bVUmZYdMSWETtGJGuViYwqkbCXbtPhM8gA/8PzxxFwot\nEldaHBNbR2k5mmjjRU3STSGZysTRb5JgQzyFWYlvKc9uK09P6JWkMTRZncO7ySE3Eq75GaBlkZI2\nCb06rAEIXvQhxje+6NGua0E3HSA7MqsI1uIl2Mrxh0LlzuDozspwCCuGAHMUh6R6s6u66QBEIrt0\nkac73eGGRoFW22cTv50WPBwSH3DswQNv+gOlZT+rE8LhCMGedgvBJaPAL9oYg57e9XyCtuy6K2kE\nYihEkcYFsFXiF8G0vZL+E7pMn7/NISM4wcYAAq+8ur4ORDCrqLiNVZlCK0DRRl2yZsrhzNzxnvVG\n053VS2v7swgPbyC5Xgu+I1ETRyXckbKno2OOLeIuyhjt4idudtTWM6xttpMZLd/OFcXIeMTybGN0\nUMjEZyGXYQuCAvEfHbytGh228PtcsHhkyZZT30APDyN2CMncR2FuZyaj5L7Ul4haBAi9cIIj3nbH\nCWtztjmLPmUbcKMuD2IalNMuZpHmEsXDCcHZyYc3gjeWPceUhR2I3ry77HarVEk9xFUtxrDo/Ds2\nF5SOCICSUyy8frEpOE5NI/I47AO929tbf82RcVJjxDIjTMpaaVgOOQXXazEFAQNq9ic9oGa3KVo2\nU1H+yT/5E37DVvmtDUf7JP8A5E37DVvmpvJvKVWqVWqUi+khjEExmBaEW1yZQpwxiCDiBTkYYrnn\nkeyK8+mi0Bo4usQSIZv5t2xtcSyShprOSG1jJilO0dXjZTzwxA7Tgn0TXZHSKR4ouPKsE7Rw5VeM\n4VSkW5jgbmwMny1z2gT3d2zpqGkx2saRWcyMZIp1e6Ch5YwqjkIZVXa5Hfdoxt55cIy2qzLhGW1W\nYY9A0uOM6IttcCCYdaZcXbQHDLyN4SQj7oVPD3A+PHPnBaa+kWRcWz3Rlt7u/PORy6TwRalI0SwM\n6i6RVS+RV5nLAt4QeutubrUhYSydWgXUADw4IpWuYcl1VW3usRY7SWI5dnaa0Ir25guI4E0zEM19\nODOgRVAaKKd7nYmSGkla6yz476MZ8MVpKskVJJUjT1iLS5USeYG7luZrMOkM3BZmuxLZQyTQrOFR\nTBxoyTksImAyRUdOejwj6tJxeHJHLE8PWLh4jCLpLUiVuLtI36fCucnasagkBu+nZ9ZvzccGLSSY\nlW2cSSyRqUWWIuQwQlBIkoaIqrHb4fNTWpJqt6saXE2jrFcKsqrFjjuFlvbOBQs0IKpmCZpGX8Iw\nnmFQtVKawvNDmkWMm6ka7mmRXZrtw79WtrWf0RWOyMwtaqw5A8iRyYiQttD0u+hhtTFcmGO0sLuK\nGS5nCJHML1YCAsxCzd9cBiO30PmwRNuxa6nqWYy+lpEplYSejIxhUCIGUlB3/eyTHK5J6uVxmRca\nem6jqS7OFo8IiMVpGs6yCAtGsJYZt2RWjiSRmjEZwUyWIwcVAb1h0IsYo1j9HfbzLm4lUu+61ZZG\nWNgm9TZWmMAAcAcuZzmPQ3TuFwOC3BJQmETziPMcHV1OA/bw+RPaeZJOTWE6rqgC50/c+Jw+x04Q\nZbmBInBZ9zKbdriTbyJMQXluFbmiX9/MkxuLFbaRUVoUM6uju3FBiaRAcbSiZcDGJRgciKAy/wBH\nrbqy2mJeCkwuF9HmEnGFybsOZg+8+jndjOOwYwMVBwfc00mOQOsUoUKdsPHmKLKT/aAxbfxQOQ77\naO3GeddNYNcvBGZ0iguCQZEidriJQJOapIyoW3RjGSowW7DjnGRXeotMIzbqkJlnHWCEO2PhS8Fm\ni4uQRMIgfTB/EAWrE4RbzVj+BHEzdZcRY9DdOgMZigKNFNHPGwmmLLJFAtsmGL5MfBVVKHvTjmCa\nt13oZp97LJNcxyPJIixuVubiPKRvDJGoEcgChZII5BjGG3MObNmXsp5GkuVdMJFKixNtZd6NbwyM\nctyfEjuNy8uWO1TW1WkkthIxUdio5u16D6ZEweKBo3BnIZJ5lObmIQSk9/32YgFGc4wPIKk9F0S2\ns93V1ddyRR4aWWQLHCCI0QSMQijceztzzzyqRqtUoFVqlKArSlKAUpSgFKUoAKqKpVaAzw9lJ/Ab\n81vkNIeyk/gP+a3yGgMVa1598t/85v8Al562a1rz75b/AOc3/Lz1GRmzSlKpRULrlvNI8XBuerhL\nhHlG1W40YRcxAt4OfNU1XLdNILF2tOvLIduo27WnDEpxeiM8Atwhy/D8LvfLQEHcaZfOkDx63DDb\n8KFI1WIlXm68kscwlklLktGpt9pJB4h5EgCt6y02/icLNqyXEzPemMvAkTKjQqqxpHCwUiJzG53h\njy8WTXMaq/R0vC1wblrlrSIbesSyulq2qxDDPG5jfbfGJioJJC5AIBqR6MpoLeh6fxRFJPfhysk0\naNMbfE4KzkPODEXwQGwQezlRhujdm02QtE51VYg09jKB1u5YPGsHK2VjcBJlcqzBlVTIObZIzXQX\nsdxNZunGghuXU+iJuaGM7+WAWDOAuFJ5ZOeQzgaHSN7VIbRLyOeSNZrdYXXYCZuFJh3CMu0Kqtkg\nYBYY80Uo0PaMGX73H3uZ8snWI+H3h8I8Xh+LsHPx1hyzPRDBUoqWfgr+SVXT7xWeWTUInRJbuXLq\nUEMMscgSHcjheHGDE25wT6FnlnNaEGnahLwzDrkexWs2dYbeF1eJbZYyiM5bas0oaXPMnkoOAa3r\nE6cLfVDCJOEJbo3yDer8Xh5nVFcjadvIYwKjVbSJki4onVY5LQRpM0m1ZBbyPCF2MVOI5ZgcEjJI\n8S1dcqwE72+XxZ09whFx1k3jpbxwMHtcQcAlSxa4ZynFDAcuTbe87M5q22SYSybJYZI2umaVSZGk\nhTqqKIU78hZOMI5DnACyNhckGuZ6JxaWs6vYxzF0t2FvDhgrxxNN6Isj4ySLgLiRuXEjyAWBPTaA\nEZZZl3b7mSOeUHGFc2ttGqpgDvOHHH28859gFKzljwUJJZ+ORo6ro17JcSzwX5tw6QRqnDMqoIlu\nN5CM20FpJon5Dn1cKSQ3LUGharsYfzu3EaHhh+AmFbMbcVU7N5YTDJ7FdQPBzXV0rRzOZn0XVCDs\n1RYmMpkLraqxK9SjtgpSRiMCePj4/wAW3mO3eXTLo2cUDahMtwjAyXccVvxJQGc8MpLEyBdrKudu\n47Ac5JqYpQEbrNhLMcxzcIcGWMjMvfF3hdT6HIuBiJlyO+xK2CKv0e0mi4wllMoZ4uGWZidqWtvE\n5IbwC00cr7QSO+znLGt+lSiVnZWlKCqUVWqUoCtKUoBTNKCgKaj/AGWf/Im/Yat81o6j/ZZ/8ib9\nhq3jU3k3ilKVSmtecmU9nev8qVg4yenXxfhDx9nj8dNcs47iN7eUbop4ZoZFyRujlVUcZHZlWNQF\np0K0+JomSJwYTbsgaWR0zbRcCIlHJBxHyPl7aAnLW7ilTiRSJIgZk3owZdyMUddw5ZDAj2RWUuB2\nsBnPaQM4GT2+bnUaugWnVOovCstqTzim9EVvROL32e3D4PtCsWudGLO9NuZ42PVVmSDZI8YRZ4hD\nIMKcEmLvcnmATjtNATG9eXfDmcDmME9mB5TWGO9hZA4lj2HOG3qB3r8JhkntEne+zy7agbnoTZPB\naWuJVtrNouFBxXaPhxQXVusQ3kmMGO7cFkwx2JknaKyT9DLCRi0sckrHdlpJXc5aW4mDd8cZWS6u\nCPEOJ5lwB0DOBjJAz2ZIGeWeWe3lWC6voYl3SyxxruRcu6qN0jKiLzPMs7KoHjLDy1F6n0ZguzF1\nz0YW4lW3C8SIokycKVXZZCZSUCjPLsPlq2HojZKSQjljJbylmkZnL2shmh79ue0SHJHYaAmzKnp1\n/CPhDsXwvH4vH5KcePLDemVIDDcuVJVWAbnyO10PsMPLXLj7nmlbWQwOVdtx3Tysd4dpFfczE7g7\nOc/hGRt27NanSbS9GtBB1sSqsUjXdqsYlPA6tZ2tg7pwlzsWARLhs/fW8XggdurA9hBHlHPzVasq\nnkGUnyBgT2Z+SuC6NdKNCsoljtbmdbeK2jCW7LcvHbxRy3EhYIyFkk9F77cSdog8WM7UXRiwt7uK\nFXuUuZodSMcsMRXa945dp+sJEUhmhhVoYQxGyNiqjvqtA7KadEKh3VS5KoGYDcwVnIXPaQiM3sKT\n4q14dVtnxtuIGyquMSocoz8NWHPsL977PKoHVuk+mNcRWk0k3E6zwUVYrjhtMTJasjuq4ZAWdTk4\n5g9hBOtql1o1iEe4Bkgkh4kcrCW8hmBnjmLoF3iWXiCKTcBnvVx4hUXaV7PUmd9x1V1qEEWeJNGm\n2OWU7mAxFAVEzn/ChdMnxbhVYb6B3kjSaJ5IioljWRGeIuMoJFByhI5jPbXJaHpmluWjtxeJ1mXV\no5AZplzMTBBfB9zbg7iKNlb8mxyCTmXk6I2LOsjJKzLJHKCZ5SN0cxuMFd2CjTkyMvYzdvLlQpNR\nXEbAMsiMrKGVldSpVhlWBBwVI55q6KdG8F0bJdRtZT30ZKyKMHtVgQR4iOdcmfud6acgpKU6tHaR\noJXTgwpnKo6EMSwIXLE4AwMZNSC9DrATJcLHIksb3kkbJNInDe/DC5ZNjDBbexHkJyMYGAJ3iLnG\n5c5AxuGcnOBjynB9ysaXcRZlEsZZArMA65VXJCMefIEqwB8oNQt50N0+aXjSwmSTrMV3uaRiTPDD\nHBG5Oe+wkUfbnmme3NaT/c40kwdWMEnBMDWxXrEwzC1x1oxlg2dvG77zeLFAdXxV9Mvj/CH4Iy3u\nDtrAdRtxj0eHvnjjX0RO+eZd8SDnzZ15geMc65y1+57pqSGZo3knL3j8ZnIYG+3iUKq4RcJIVBAz\n5Sam5NFhcq0nEdlaB8mRlBa3VkQ7UwMEM2Vxg57KjvcR3uNmO/gaLjrNEYT2Sh1MZ77Z4YOPD732\nasOqW2SvWIdwaVCOKmQ8K7plIz2opBI8Q7a1otBhSMwq84hMXB4XGfaAZGkZwc7jIchdxJwqADHP\nNy6HAH4qh1kDzSq3EdtrzgBzsYlSAQCFIIB8VTMn1EkpBAIOQRkEcwQewgjtFUglV1V0YMjqGRgc\nhlYAqwPjBBFaekaalqgjjeVo0ighjSR9yxx28QiQIMDBIGSTkknyAAbNrAsa7UyF3O+Cc4MjtIwH\nkXcxwPEOVaN5V3m7D2UuPAf81vkNIeylx4D/AJrfIaEMVat9kNCwVmCSkttG4gGGVAdo5nvmUcvL\nW1SjI0a3Wx6Sb3mT+FV62PSTe8yfwrYpUFM1+tj0k3vMn8K0ruOOR0doXcxvxIy0EhMcmwx7l73k\n21mGf8RqVpQUyI4EWMdXGAMAdVbGMk4xs7Mkn26u2JndwTuyWz1d87mGGOdvaQBk+apWlKFMjCQQ\nAY2IXG0GCQgY5DGV5cqtKIeRhJHZjq7nlnJGNnl51Kiq0oK1vIvIwRwmw2Sw4EmGz2lht5589UKr\n+KbkAP7O/IL4I8HsHPHkqVpSi58SIjiRX4iwsrldhYW8gO3O7bkL2Z51dAFQBUidVGOSwSgcgAPw\nfIAPaqVpSiO3tI7in0knvMvzacU+kk95l+bUjVaCmRolPpJPeZfm04p9JJ7zL82pKlBTI3in0knv\nMvzarxT6ST3mX5tSNKCmR3FPpJPeZfm0Eh9JJ7zL82pGlBmR3FPpJPeZfm04p9JJ7zL82pKlBTI7\nin0knvMvzapxT6ST3mX5tSVKCmR3FPpJPeZfm04p9JJ7zL82pGlBTNG+ObSc4I9Am5FSp8B/E3MV\nIGtPV/7Pcf5Ev+21bZ7abwtpWlKVSmtdeEv5r/KlY6s1yORo3WGQRTNDMsUrLvWOQhQkhX8IK2Dj\nzVz/AEe0/U4XLXOoxXiGOzQI0CptaIAXc4MQUmSYd8Ae9Q9gIOAB0dK4uHRdXCrxtcBxGi5SG3i3\nzrd7wzPwzkOhjhIAAGMBTuqW1SO9lkgdJuqQwcY3UcvB23qNHtXbJGzPbqrAvuG1uYHjyAJ+lcQ+\nmamzWxXWYURhaiBVUNvdLGdJGBck3XFZjPtYkEW64xgvWeOxv4onSbVIp7gWN5ukZ+rEkvFsnCxD\nZCiMjgyYJTrBGSFGaDsaVA6/A0kqC3vxayb5AVMmd8rC22Dgs2GCrsOzszMPTHdathf5XN+pTejN\nhIw/DyCY1coQe9B74gE7ieXKs2dVhKrv3OgqySJWxuVWA5jcobBIIOM+Yke2ahZLa4WymSe+XiFy\netZEAij3oSpdfBOA43Y5bxyOOeuthfOF4GpRqu4Euq9Y3nq9vGD6MzYXfG77AefWCc5AJmsVYS/u\nXr+Cbn063k2F4ImKOsiExoSrpkqw5ciMn3a281zeiw3IZmur5Z7cbEQq0a75xPEF76JVK7ZVMRUk\n7+JgjxGW0VXEb8SQSE3N2VKvxAsZupuHGWx4SLhSv4JUrz25qp2YnDVdXZtGCMncUQtnO4quc4Az\nnGc4AHtCsZsYdxfhRlyix7iik8NW3KnMclDYOPKB5K2KVTBiFvHvEmxN4DgPtG4CQoZMNjPfGOPP\nl2DyVlpSgFVqlVFAVpSlAKUpQClKUApSlAZ4eylx4D/mt8hpD2UuPAf81vkNAY6UpQClKUApSlAK\nUpQCq1Sq0ApVKrQClKUApSlAVpSlAKUpQClKUBWlUqtAKUpQClKUBq6v/Z7j/Il/22rcNa2oxl4Z\nkUZZ4pFUZxlmQgDJ7OZqhuz+Jm/Rj+fU3mbzNmq1q9aP4mb3E+fVetH8TN+inz6WW0aXSoQdWn6y\nxS26rc9YYMylYdg4pDLzB2buznXG9BItDEzfzbNKkvVtKLbmnhDW23/syP0VVDBlBTYOZwVYcgB3\nF05fkYZSMMpVkQqytjII38xy/XWtHbqvg2u05BysMQ5jBB5N2gge4KqaFo8z06LopiMQcaY9XiVF\nEN1MyQtqDiJuG8REZW6MrYwOSElSAK67XILcXWnPdTBpgbkaeIrdldiYAzCSdnZQAFikBfavEjjb\ntVcTwtUxgWgxtZMcCLGxjlkxu8AnmR2GrEskBJNvI+c/fczBcggiMSysIwQSMLgY5eKll1keeXK9\nHOKhkkuWkaOw4uXlfhRDTLl7UzMgIwtoswPDJKGYN3pbfUn0btdHkt1h097gW0lleiJhkKUZ7USk\nR3Ch5JOdqQzAgheZPfZ7IWcYIIs1yu3aeBDldvg7Tu5YwMeTFXC1TORa4OGGRDEDhyS4yH7CSSfL\nmo3wMt5ZEN0yazzH12Gfh/1hBJHt4ax8KOeaR9r7wvDibwQWxDJyx2xtudGZ0CGVm4sL7DFIV4jn\ncskiPHgLlADjkvIcq7BwWwWgdiMkExocZGDjL8uRIqwQqBgW2AdoIEMWCE5oMb+weLyVlrM9UdIS\njWfg8vYgL4afZJ/N7rMsdwwlyO/HEeQbEGSSWZ4sBFUjvST4zWjIuiMrDMwU5Z9qXIOEQ8RpHCbs\nf1JyzE5zAefPB66SPcctbsxKlCWijJKHtXJfwT5KcIZ3dWO7Oc8KPOcBc539u0AewKVyLHSUlvvn\nv8iE6M2VnEWu7dXMcsccaOyBcbrmbigKcMHMuzcdoG2OEDIQYnNOs1gV1Ult8087FsZ3XEzzMAFA\nG0F8Dx4HPJySCkKFEDBRjCiNAo2nIwA+BggGsm9/xUn6K/SVVkefExHObbeXr+7DNSsPEf8AFS/o\nr9JTiP8AipP0V+fVszaM1Kw8R/xUn6K/PpxH/FSfor8+li0ZqqKwcR/xUn6K/PqvEf8AFSfoL9JS\nxaMwqtYOI/4qT9FfpKcR/wAVJ+gvz6WLRnpWDiP+Kk/RX59OI/4qT9Ffn0sWjPSsHEf8VJ+ivz6c\nR/xUn6K/PpYtGelYOI/4qT9Ffn04j/ipP0V+fSxaN6HspceA/wCY3yGrbUkrzBU8+TAA+4Carc+A\n/wCY3yGqUspSlAKUpQCsFnewzb+DLHLw5Hhk4bBtksZ2yRtt7HVgQR4iKz1yc+irFeRxJPcRx3s1\n5cypDILZRIEVu96uFPNndmJyWJyScUB1lK5bVdI4clmq3V+FmuWikHXrk5XqtzIBnfy7+NOypD+j\n0fqnUPh9z8+tOLST4/mgTNVrnbrQ1V4QLrUMPIVb+vXPMCKRh+H5VHuVln6OKVYLd6gjEEK3Xrlt\np8RwX5+xUaozGVtrh+L+ScpUHc6CirkXOoDmv/6+58bAH8PyGsn9H4/VOofD7n59ZvOi3nRM0qH/\nAKPx+qdQ+H3Pz6xpoKFmHWdQ5EAf1+58YB9PUlJJpccvRv4LROVWoOHo4oBDXeoMdznPXblcKWJR\ncB+e1SFz48Zq/wDo9H6p1D4fc/PrQJmlc1LooF1FGLrUNjQXDsOvXPNkktlQ53+R392tw9Ho/VOo\nfD7n59ROzTjVd5M0qD/o4u7PW9Q27cbOu3PhZJ3bt+ezAx5qv/o7H6p1D4fc/PqmSZpUN/R6P1Tq\nHw+5+fUZcaRi/t4Bd6hwns72WRevXHOSOewSJt27Iwsswx2Hd5hQqVnWVWoKXo4pxtu9QUhlJPXr\nk5UMCy835ZGRnxZq/wDo9H6p1D4fc/PoQmqVDf0ej9U6h8Pufn1X+j0fqnUPh9z8+gJilQ/9Ho/V\nOofD7n59X9D53l06xlkYvJJZ2zu7eE7tChZm85JJ9ugJWqN+8fLVao37x8tAXUqlVFAVpSlAKUpQ\nClKUBWlKUApSlAKUpQClKUApSlAKUpQClKUApSlAKUpQClKUBWsdz4D/AJjfIavqy58B/wAxvkNA\nWVTNKUBWlKUAqH1P+36f+be/7cVTFc42ow3F/aGF+IIZNQt5CAwCyxxwF1BYDcBuXvhkc+2gN3pK\ncC0f0t/aj31mgP6pTUtUT0s5Wwb8Xc2Mh8yx3tuzn9ANUtXWXYi+a9n8mVtZp6j4VufJOB+lHIv7\n63BWpqnZEfJcQ/rcL/7q26zLso54fbl4P0/wYb3wD7K/tCs1Yb3723tH3CDWeuS7T8Pk2u0+S+RW\nKHwpPZH7ArLWKLwpPZX9kVzxO1Dm/wDxZ1WxmWlKV2MkfJ/bYvNazfrmg/hUjUc/9tT/AEsv+9DU\njWIb+Z1xPt5ClKVs5CoiX+84fNYXP/mubT5tS9REn95xeewn/Vc238ajNw38mS5qtUNKpgVWlKAV\nDdBf7r07/Q2v+wlTNQ3QX+69O/0Np/sJQEzVG/ePlqtUb94+WgK0z/D2/J7NK4y66EtJcyz8aBUk\nvjeLGtqcxll00PIrcXAvM6cMT45dal705oDsJ50jVpHdURAWd3YKiKvhMzMcKB5TWjpet29zDFcQ\nPvimRXRgVIKsMjmGIz/CtPoR0d/m2F4eKsu94zlYuEvodtBb72Xe26Z+DxHfPfM55Vq9Ff7Fa/6e\nH/aWgJ7ry+Q/qob5fSn/AK9qtWrT2j26A2+vf4T+v+FUN9/g/Wf4Vr1R+z2x8ooDa663pf8Ar3at\nN6/pR/17dYKqew0BmF2/kH/Xt1TrUnm/69qsS9g9iq0BcLmQ+Mfq/hTjyemqxOwVBdKOmek6WB/O\nOpWVkSMqlxcRpKw/wQk73/4QaFSb2HRQTSH8Ly9o9is3Efyj/r2q8aH8pHofG5U6lKQCw3pYXzI3\nZ4OIdzDl5K37P+UT0Ok5/wA7iPnj0ay1CH9u3FZ148Ts9Fxl9kvJnqxlfl2dvl8xPk81XcV/IPd/\n+K87tfu19E5cbNdsAAe2RpIR4J8cyLy51KWX3UOjU3KLX9Hb/wDkbUftSDyVbRh4U1tT8jr2nYfg\njxfrIFV47el+T+NRNr0i0+cZgv7KYZXnFd28g7R6RzUnHIrDKsrDyqQR+qqczJxz6U/q/jRbjkDt\nPZVpB8lWp2D2B8lAZeseY+4f4VQXI58jy8x8mfJVtWr2t7P/ALRQGXrK+eqi4XIGe048X8ax1T8J\nfZ/caA2qUpQCrLnwH/Mb9k1fWO58B/zG/ZNAWUpSgK1SlKArXKroNna3tmlvbxxpJJeXDIFyomEF\ntEHRWyIyEjQd7jGPPXVVD6p/b9P/ADL39iGgL+mCk6fe47RbTOPZSNnH61qTjbIB8oB90Zqy9hEk\nUkZGQ8boR5QylT8tanRqYyWVm55l7W3YnzmJCf11124fJ+6/wZ3mTWB6Fn0ssDe0s8bH9QrcrU1k\nf1eY+SNm/RG791bQNZfZXN/Bzj/qvkveRjvfvUn5jfJWWrLgZRx/hb5KrEcqp8qj5K5fd4G/u8Py\nXVjj8N/+H5Ky1hT74/5qH9bj91c8XtQ5/wDrI6rY/wB3malBSuxkj5eV7F57W4/VNbfOqRqNuR/X\nbY/+Hu19syWjfIpqRrEN/P4R1xNkeXyxVaUrZyFQ1ycaraj02n6gf0LnTPpKmaiNQGNQsX8sF/F+\nmbSX/wCxUZvD2+D9iXpSlUwBVaoKUBSWNXUq6qynkVYBlI8hB5EVD9BB/wBl6aByAsbTkP8AISpq\noboL/denf6G1/wBhKAmao37x8tVqjfvHy0BWq1SuU6edGbrUGiNteNZlEdWkVmyBkMFRFXI34Mbu\nHU7GOMnGAOrJA5nAA5knkAB2kk9grl+i0imytirKRwYxkMCOSgHmPOKlej2mtDai3n2SbnuGZBuk\niSOeeWVLZOIMvFHHIsYyBkIOQHIRXRiNUs7dUVVURJhVUKoyPEByFASe4eUVQsMj26uFUPaPboCu\n4ef3DVrnl2HxeLz1fVH7Pc+WgGfMf1fxoSfJ+sVWvNen/wB1yxsXktbR4Lq8QlZGeULaWzdhEkgI\nM0o5+hxnljDMnKuWPjwwY683SO+j6NiaRNYeGrb/AHkj0HUL+G2hae4lit4I1y800ixRoPKzvgCv\nG+n38oazswyaXZy6iw5dZkYWtkp7Mgy4lm9pVU+Jq8l6Wa2dbn4k1+15LGcBzcqthaNjsgtkOziY\nb8AbiOTPnth26PQBwsc9zdXKgZO+34URxyZyYSsGQexcsR4jzNfP4/WBXUE1zWfPglz8j7vozqno\n6WtpUnJ8INavnetJ9yS5mLpp91fpRqqkNdXdnbsPvNivUogAT2shNw4PjDPggV5nJYPJ35N1KXJL\nPwm2s2ebM4QlvZyc16jddGVXaJbqaeZhlIFiiKkg+EsWByBwN8jYHlGapc9GZlj33F7FGuccMQOQ\nckbELJKrSyHs2qADnGDXifTEZVcr4dr0y/CPrsLQNDwU1hw1VWeS9Wpe+szyn+blAxu5gkFY7fAB\n9KzN4J9nFYzp0a8i9srZ5KE3ye7nOfar1qHo5esnemC3iGcKQ0UrIB2lQHWAdvI5OPSns17TRLpw\n3V7aBlON1xxS6SdvNDKitcEYHMkLz5McGqulYZ5rzX4/J0ei6I37fTieitv1iu48v/mg7SSsQGQd\n0kjfIOS1RdIYggRs4x28VkTPkUEZxXo8mg7ZCjadJcXAXLd7ay7FyME8JysAOcgYDHBwGxWG50WB\nMNdxSxA5AiWG6gjJwe93BQZnwDgZ5+Ja6rpFPv5Z+z/BFoWiN/b3/VFebcK8Em+887XS+e3ZIT6S\nERkA+dj2H2cVfb2sluwZWltz2AgO0mT4lZMc/YzXe2ukQS4WOXqyDB2CZXnK+IbH3CEezk+YGrl6\nPjJFpK8jZIaaVUeNcHmrSgAuQc8kzjHPbWv94xW3L98V7hdFaNJLJvya8EmpP/tXdRy1l0k1mE5h\n1jVIcfhG/vbYAeZUlHyVPad91bpVD3sPSC/l29i9YM2PIGe4D59s1uXfR548cSWK4LE7Iikibj6V\nIk38T2TnHmqkvR27kAMlpGqkAlUa3kl84Jkwq48272q0ulFt1vWvwzjPoDQnk0r4ODvxf1RX/U5E\ntZ/d96Zwc31KOVeWBNa2Eh9jvIUP6yan9P8A5T/SdMb7PT51I5tJZzxE4AGTwbnkeXiWo3oB9yS9\n1kg2entDAp2vfXTyQW4weeyVCWu25nlEGAIwSte+9Af5O+i2OJL8yatOMd7cd5ZIdozstVJMi8+y\nZ5B5hX6Wjzx8VWrS4v42/g+Y6Ww+hNEbjKsSXDDp1zlUYrklZx3Qj+UhrOpSCK36MfzhIG2ydRuL\nmNUbGe/eS2dIRjHhsBz7a996I6peXUSSX2nfzZKSMW7XkF4/MHO57cbVI5csntqVsbWKCNYYIo4Y\nkGEiiRY41HkVEACj2BWUeEvs1+nCLW135HwmlY+FiP8ApYaw1zk/dv0RtUpStnkFY7rwH/Mb9k1k\nrHdfe3/Mb9k0BZSqVWgFDShNAc30U6VLfz3MUaRPHAzbbiC5gmVkEjInFhV+JCzFZAMgg8F+zkDr\nya0kmqQwyLwGtpbmAcRgBNxYIZImi3AbtwyOWRlWAJwcaP3N5RJe6rIpcIzx4jlQK8W6e7lA5wRu\niOsiyBMOPRNwYl2qdubWKK/suFHHHxOvSScNFTfIyQ7nfaO+c+MnnQE9UJ0W1e0nXg2gkVIFVUDx\nuqmPC7TGz+EuGXz4YVN1xfQyO0hvLiKFZ+KTcB2IthHlJgZDIIQsrSMxyJJ1JPfbWIbvvVgwjLDn\nd2qa4eJiTaaOvu03RyL6ZHX3VIqlg+6KJvTRofdUGs1aei/2eJfSAx+9sY//AG1w+3x/fYw8sVd6\nfo1+TcNYoJUPeqfBA5eQcwO32KymtOxZckAuSFx3xBACnB845+WuMnUkalKpJG5WIffD50H6mb+N\nZaxt98Xzq4/WhH76xjfa+9euXydomWlUpXYyaN/yuLM+V5k92B3x/wCn+qt+o7WB31o/pLtP/Uim\nh+WQVI1iO1/u5HSfZjy+WKUqtbOYqP1O0d5rKRMYgnkaXJweE9rcR96MczxWh5eQHyVIVzn3QUu2\ntVFnJJHK0qoxRWccNgwYskTLKwztAERDZYcwMkR7DphK5VsOjoajujayraW6zhxMsSK/FfiSEqNu\n538bEAE558+fOpGqYap0KUpQhbNKqKXdlRFGWZiFUDyknkBUR0EOdL00jmDY2nZ2H0BKmRUP0F/u\nvTv9Da/7CUBM1Rv3j5arVD+8fLQFaVyPQvpDdX93dBgi29sGjwIhGzPI0b28jHrEp5wiQ7SI2G4F\nl75au6c6Nqd1LC1hddXVIZkb0eaIGR8bWKRKQ3eggE5Kk5HloDrV7RXMdHf7LD5owPc5fuqT0Cwk\nS14F2RKWe43K8j3IEEs8rRQPLMN04SB0jLMOezx1D9FLaOK0hjijSNFDhUjRURfRHzhVGBzyfboC\nVDDyihYZHPy1UUPaPb+SgG4ef3DWK9uo4o3llZY4o13vI5CoijtZmbkBVL+8it4nmmdY4o13O7di\ngexzJJwABzJIA5mvN73pha3LG5vetW1tA4aC3nsL+NEYNhLi4ZoNstwSRtQEhMjGW5j8zpXpJaDg\nPEUJYkvtjFNtvw2LizlPGhB1JpN7E2szD016YTTLJuhv7PTYwTI4tLri3UYHN5niQm2tSP8Au+Tt\ny3bQTGeUN0LgBJYruzslG1YHsb23edF5DjMYQLe2xz4YILDG4qMoentOkNhdSR3F5eW8CBhJaWVx\nKkDoRzW5u45SM3PjVDyj87cxt2t/Dq/NJ4n00HARJUZtQYeOQKcrZZ7EPOXtPecpP5J0l0hpGk4r\nxdJjJNc1GHdBOOcu+++8rP09E6ZeDDVhGLW/bb5uzhZNVsbocKKezt7NAoMzNBG8qY5JZrJySHGP\nRscx4A7HFn826XcEWljZ6bLwgBJOYLeeK3yA20dpuLkgg7c8s7nPMBvSrueS7d7W3Zo4Izsurpe0\nMOTWtoezjDseTsj7B3+eHo6tp9kojsbawspZ+GNqy20ckNpBzXj3GRkrkMFTIaRgeYAd18EMdKor\nWi9tXaX/ABT7Nvu+Mn7F1ia7WGvB+2WRw0vRfTLbEMFnxryRPwZZIZWXc3otzNCRwYAxbGBgc1RT\nyWsb9CrC2Vbi4luTODsRkuLl8PJ2Q2kEryEk45DvmOOZwOXYy9FtK0+D+zuZZGEam3kkt7u8nbcw\njQWzxqD4ZAG1I1BPeIpItsuhqoDc3F5cwzqrkFLlZobKEgFoonv45NwATv5mG5jnwVwi9lpE2rWL\nOnxu5Pgs5VHw53sXePWjCW2Mo8KfruzOOi6ANMOJc3dzGgJdLSTqsqKuOXW3SJRKw7doO1fK+A1Y\nYeit/d5NteQLa4724e1kikuOfPq5EzBYcf8AfFef4AIIeuti0K8ve/62DY5DQxXlmDJeDniS4FvJ\nDttSdpWMqCwGXGGCjJfXOptK9pbR2kjRhesXUUzp1YMFIjWGaFka8ZDuVC5CDDPyKLJt4mmXUZQk\n+UVGC8Um35+L2euHWrBz/qyXG7z90cW2g31u/VLW1tZ5Au9hDdPiIMCeLdtNCu1nPYC7O5yewMww\nvpk9kOsXlpdmUkRiXhJcHdIwVYbaGzkkKBjjvVBY4G4sRmu/OrR6bCEfT7+Mu7CNUWK8mvLgoXbB\ntppJJJW2sS7gYCknCjltaDfWZlE11dwdeYERwSMYBaq3emK2huVR2Y9jSlQzn0q4QefE07ScOLlP\nCerxSetJ805RS47VzZ7cLrE5Vq4kZcFll5VmeWTRQ3OP5x2QREjbZXS8GR+eB1rjhS3PHoS975S+\ncCraHZ3JaOytYEUFlkuog0MMZB79Y+rsnWJs8iAQqkHccjafYwW1MEIzLppyGlUkNf8AiKwMOcdp\n2gyjvn/BIXvms1DozpxaOCDTbZrqRcQpboLRljTC8WWe3CtBbJkZbn2gKGYhTNG6Yni40cDDhP8A\niPJQi9ZR59nPjbdfc9qW307WcorvadPw/eR5LF0Hto2VbeW+NzNiNQjJc3Fw4XkoWaNjgc2IBVF7\n5jtGTXp/3P8A7j8cWJ9ZYXjk7orIIBbRLgYF0VOLyXtyOUYzja+A57roR0OttKjYoWmuZARLcytI\n7lc5EMRldmitlPYm4k4yxZstXRp2D2BX9a6I6C/l46+ky/iT70qjy4vv8j8XpDrFj4yeHhScIb83\nb5/vMtTaoCqu1VACqFIVQOQAAGAAPFRHHPn4/Y8QrJVqfhez+4V9GfOjevlHuiikbl5jtq6rVA3L\nyHj/AHUBt0pSgFY7r72/5j/smslY7r72/wCY/wCyaAspVKrQCqOoIIIyCCCD4weRB81KHz0ByXQA\n23Fu0trVYEgJt+KL0XckvDuboOJVLs0REnEI3nOGxy2gDP0pvTDqWiADvZ57yBz5A1m7p7sscY/4\nqjfucXCy3urSI5dTKuNs8k0OOPdlWVZGYLIykEtETGVKAYZWUR3SfXOPcRPmJ10/UnRZIN797by2\nbXAlUZMTIvGjLnC8j2Dt3DOVA9KrkYdOnXV2mEEhiLn0ZmiAKPBzbiBQ7xq52CBiQCN3LArrqi7i\nRl1C3GTsltLoFcnbviltWQ47M7ZJef8ACuuBNx1kt6f5MTV1zJWtPS+QlX0k8o/TPF/+5W5WnaDE\n1wPTGKT9KMR8veq5R7L/AH92mMTKcXzXpfwblaVtGwlY4bB3cyfPyzy77zeSt2sMZ79xnxI2PZBH\n/trjJW0WcU3HmZqxTeFGf8RHuox+UCstYrnsB8jofdYA/qJrGP2L4U/Jp/B3jtMtVqlK7GSP6Rco\nN/4uW3lJ/wAMc8bv/wCUNUjWprMXEtrhB2tDKo9ko2D7uKy2cwkjjkHY6I49hlDfvrC7T5L5Oj7C\n5v4M1KUrZzFRXS+JnsrgJxN6qHXhNsY8N1fbuwcIQpDY5lSwHPFStY7u3SaN4pVDxyI0ciHsZHBV\nlPmIJozUJaskznvucXIkszhw4SaRQwlMgYNtk5Kyq0CAuQI2AOFB7GBrpqiOi0cIikaKNo2M88cu\n+WSeRpLeVrfLSyksw2xKRk8gRUvUWw1iu5sClKVTmKhugv8Adenf6G0/2EqXlkCKWIYgc8KrO3tI\ngJY+wKiOgh/7L03/AENp4sf9wniPZQE1VCflHyiq1Q+L2R8ooDluhOlXttNdG4HoMqQtGzXr3UvE\nWS4XY0fARIysHAUspO7aMkkFj1VcJ9ziyQXV7LndJHui3C6huDHE8mEsrhYolMc0ItQwBLf2yQ7m\nLMam+mWk3V0IuqTvbPGtw29bieIM5t5I4I2SI7WTjOrl2BK8EYB3cgOhXtrmej/3hR5HmHuTyj91\nSXR6zljtRFdNxGL3GQ0rzlYJJ5WhhaaTvpSkDRoWPM7O09tRHRi1jitxHGioizXQCqMAf1qfNASm\naxXd1FEjSyyJHFGrSSSOwVI0RSzu7HkqgAkk+SsoHmrybp50j/nKQ28JB0+B++YcxfToe3/FaRsO\nXidhu8FVLevQ9EnpOJqR8XwR4OkukcPQsF4s/Bb2+BIatrHX261K3CsrfMtvFIQuAoJN7dA+BJty\nVRvvanJ78kJGWUT3ciXMyskKENZ27gqxPiu50PMSkHvEPgA5PfnCcCNJtbyQsLa3FrGxGRDGDdyr\nkFiQOduhzj0zDPYo3V1C340jW0E11Ci463JDeXceARkWyBJQA7KQWI8FT4iykXSOqGPiNyjip8LT\nXltP5rpWlvScVzxG9Z7csorgs/3ZtbO6cnUGK5zp8bEN5L6RTgp57JGGD+MYY8AHiYNbtYbyQ2iQ\nwttwbq4MMbGBWAYQxMynF06kHI8BTuPMpnk7zULyDhW9peziRhiOJ0tZYYYUwpkcPDuEajAVQwy2\nByGSMkWvXmnW4G62uFBwqtDJHcXM0jEsWlWYq88jkktsAGSTgDl459U9OheqlKuD/NHnSdpwf/Ks\n/N7r/dio6O80u0tEitrK3WGeTd1eK2kmtVTGOJcSm2dSIk3Als5Ysqg5YVelgNPgeRdQ1BGJVppT\nKl1NczHbGve3ccpeVsIioOzvVFc9pHSiWHiT3dnvnlwZpbe4jdUjQsUhQXCx7YY1J8fNmdjzY1l0\nvplZXUy3Nzx7eOP+xxTW8pUblIe7kkiV41kZSVUFu9UnxuQPBj9W8aNrGwL43HWXszS0jTMPsTlS\n21K7fm8v/vcdDp0OpiQXctzbvOY2RY7i14gtombcIo5LaaNQ5whkcKdxQDwVUDGNXvb5g0lnBNp8\nbkgQXRVr+RCNkhjnhCm0VwcKXw5UNkqBvwnV7bUpDaWt1DJCoBvHhmRmYHwbRNpyGYYLntVSB2vl\nZfVLvgIkcKK08p4VtD4K5A5s+PAgRe+Y+QADJKg/lT6vaFN28NJ7FVqvLL0NR6e0+DqUrb3NLJej\n83ks9+WPVOl5LdWjgvLadtpkle2FyLSFyyicizaZWkbawRW5ZG5u9Ug7Nnrul2sHDhuYm2dkCyBr\nyaWVs84pCJJLmWRsktzZnJJ7TVNPtY7SFy8mT301zcSYUyPt7+Vz2KoVQAOxVVQOQrTtLBb5hdXc\nSvHtK2lvMgYRxPyaeSNxynkHiIyiELyLPng+pmjtauHOUd72O/Z8j0R6zyec4Jpb02rfJ3/hd5Ma\nXYybzdXWDdOu1VU7o7SEkN1aA45kkKXkwDIyjsVUVdK9A1IvAQG09GKTk4IvZEO17dfLaqQVc/hk\nFOwPuh7/AEmKSbqlmZ7QKA13LaXE0CRRuDtgSJG4fWJASc7SUU7uRKE7zRXdnEiW9wsyrshgtprS\nMyOx7yG3ga0aFUJO1RuUgAZJABNcn1R0qH9SDjLh9teeXqeiHTOFitLNSlsVcdlVe3d5m5PotuHS\nK0t+HdXDERJZyy2Odu0PNPJaMpW3QFdzHPaFALMqn0foroYsIdhd7i4cKbi6lbMs7qCBnI7yJckK\ng5KD4yWY4OiOhtaxGW42NfTiPrDIS0cYU5W1gZgCYEJbmQC7FmIGcDoK/Y6K6Khoq15JPEe170uC\nfvxPv+j9GngYVTk23tzbS7kWlj6U+6P40RuQ5HsH/XKrm7D7FE7B7Ar9g9xTePP7h/hVquOfPx/u\nFZKtT8L2f3CgAceUe6KqvhL7f7qEVRFG9eQ8fi9igNulKUArHdfe5PzH/ZNZKx3X3uT8x/2TQGOl\nKUBWqGq1SgIzo/ocdkJFiluJBK7SMJ5BJh3d5JGXvRgs8jE+1jFRvTKy6xJDb/j7TU4uXb6Jbogx\n5+ddLURqf9v0/wDMvf2IaqdOwbehXoubW2uB2T28M3vsav8A+6tbXu9lsJfSXYRvzZ4J4QPfGi9s\nCsujRw2yRWSzIzxxsyRlkEnBDkAiMHPDXcqZxjkKw9L+VnLJ6naG69q1njuG/wDLGa7Yf+okt+Xg\n8jMthL1qdlyPykB/9KQfTGtusE0BaSJwR3m8HylXXBA/4gh9qucHtMYqbSa3Ne+fpZsVhPKUf4kP\n/lYY/aNZqwXHJoz/AIivtMpHy4rlI1PZ4oz1juhlGx6U49kDIrJQ1MSOtFx4po6J0yinIB8R51Wr\nIFwqqe0AD3BV9WLbSsjGKj+jh/q8afiTJB8HkeEZ8+EFSFatjbmNp+Y2yTGVAPwQ6JuB8/EDn/io\n19SZ0TWo1yfv+TbpVKqa0cxSlKAh9GPDu9Qh9M8F4g8iXEQhYef0a0lb/wCpUzUNqXoV9ZS/gzLP\nZv8AnMouYS3mBt5VHnmqZqI3Pc+7/HwKUpVMCoboL/denf6G0/2EqZqH6C/3Xp3+htf9hKAmaH94\n+UUqjfvHy0Bwv3NJ42vdWSI7lieBFzHMjopkupVjUSXcwFv6IWUARHLv3gBWu7qiqBnAAycnAAyc\nYyfKcAe5XMdOYtYZrc6U0QAjuBIJSFXrDNbC2kkbeDwEj62SFEmWMYKEZKgdRXOaKPQ3Hkubwe5e\n3A/dW70aiuerMt3xdzSS7FlkjedYG5IsstudpfwjlScArzyDXn3TfV7rR9FupNKsLm+vOtXsVtFD\nFPecJ3vLr+szqCzyRoBnaMljtHLJI6YOE8WahHa2krdLPi3kkRulZw/8p37rJ09ToumyDr0qq19M\nOYtbdu+FvyI/rEy9uCCkbZ5F1NeDv91bUCnV3htWTCLIYVltmEfLMSuJGCMyjGVA2g5GDiuP6Ry3\nMcrvercJdzyO7teRyRTSSuxaSSQSqpzkknkPIMcqj8hFyckdpPaWYn9bEn9df3fofqtoGBoyw3U2\ns8SabzfBU9i9u9nz+l4MNKkpYsbrs3uPWR92VEiEX83tDIVCR8GWOaOJRhd2x1jyqr2DxkAcs5Et\npv3TdFih2rJcIyhiFlgffLKxyS0qgoZHckkkgcyTivClB5s3hHt8gA7FHmHP3SaxA7ju/BHgfvb2\n/F5vZr3S6rYEuw5Rk9iyajHvyv120u8/Pl0BoslSTW/J/mz6U6OaxZSh5VvrSeeXDTGOdG2hQdsS\ngncsSLkDIGe+Y82NVgY3EguWBCAEWqHlhGGDOw8Ukg7M8wmByLMK+ZpVDnaQCowWyAefaF+Qn2vL\nUhba7eWuOr3dxET4KrK5QdmSY2JXA5eLyCvHidWp4acoTUorZaat+t55czy4nV3a4TzfFbF4fjZk\ne/ai/WJDbj7zGR1g+KR+TLb+dcYZ/MVXnlsY9YvTGqpHgzy5EQPMKB4crj0iAj2SVHjrxzR/ui6j\naqFJhnjUknix4c7juYmSIrlyxJyQckntqX0z7pMbO8t3bSq8mBmJlkWONfBjCttOMkk9uSx8WAPF\nLQMfCerOLt5trPLwt8vFnnn0Nj4b2KSWyntfp+5HeNahEtI+qxTW8l1Kl1dybONbMyQmGfc3fTbp\npHBjUEsZMjBArX0u+u4JWniu7iJyDHGEmeSKOAMCqJFcAqA21WPejngeIVBQdMbO5nTg3YhEfZuZ\n7aSSRgV2gttJRQTkA98W83Pc1O82oqxEGSXIjIwQqjG+U47VUEeySo8dePB6NwsSc5YtYkW1qxaT\n1cqdb893iy4sW4Rw5QqVPWvervNPLn3HQv8AdG1F5Fhl6veW8Dq0yuhge4lXBWJ5YSV2K212AjwS\nFHMblrqZPuzW6x4ls54bh+9jKlbm33ntdihWUxoMscJk4wOZFeUIEij7dqIpJZj4hkszE9p7ST56\niFcyMZnBBYYRT/3cWcgHyOfCPtD8EVZ9T9BxaiouEtrcXkvB2u5eZ5n0Zo+LtjSXDL0WXPLu4H0x\n0S6SaRJGsVtqMEsjEyScWRYrmWVuckskUu1gxPixgDAGAAK9C6AaQZWXU5hgFWGnxsPAhcYa7ZT2\nSyryXxrGfEZHFfOf8n77nq65qHHuow+mWEiPOrDKXN0AJIbTBGGQd7JIPS7FPKTl9h1/PesWj4Wh\n6Q9GwZ69drKqf9u3Ot/kft9A9XcLAxf5qTcn9t1lxfwsix8+Udq+I+mHnq7vvIPdI/dVJOz21/aF\nX184fYFrE4PLxeIiityHI9g8n7jVW7D7FVXsHsUBTePP+if4Vajjnz8fj5eIVkq1PH7P8KAqGHlH\nu0Xw19v91CB5KoijevIePxexQG3SlKAVjuvvcn5j/smslY7v73J+Y/7JoDHSlKAUpSgK1x9lezy3\nVoZEkZ0utVhBkgktCYEZOFIqSqOIvDK98vJsZB7a6+ojVP7fp/5l7+xDQHOaRYpa6zOWubGNZnPA\ntXLve7ZI92IXkKmGNpzO+wcRTvIXaQa7S/txNDLE3gyxvGfYdSp/Ua4HpuwttUtpg6oGNvO6KQS5\njk4LyvbSRkXUxjEcacJ0kXGcNhRXotenGb+mfd7EXAj+jdy01naytyd7eFnHbhzGu8Z8zZHtVb0j\ngeSArHnduXABABz3uCCwyOecZHMDyYrF0W72OaH8Rd3UfsK8puIhjxARTxit7U498Mi4zlDy3bck\nDIBY8gMjx8qj+nGy4+h59Ihr4MovgyunKyxKr4yuRyJYYycYJ59mOXiq698An0pVv0WBP6gajujD\n95IvIEOG8HYSHAw2wEqAdpxtODtqVkXcCviII90YrljxqTRNHl/EwE1w/wAF9KxWrZRCe3aM+zjn\n+ustc07VnpTtWakCvxCT4PfAZbJ7R2DPmHu1t1o3ACyhseQk9uO1STjmox7IrerxaC0teGeUntd/\njI64m5iua6RadK15bzpsKIA78abhRo0bpwypUFgSGfIxg8uzJrpag+mUAaFXxkxyAciCcSd4QiMQ\nHkJKqOYPfHHkPox4pw5Z+R20OTWIlxteZOUrQ6PzB7aLwcqvDIVXUK0ZKFNr8wRtx7VSFdYu1Z55\nx1ZNcBmlKVTJF9KrdpLSQxgmWEpcwqO1pbaRbiNP+JownsOakLO4SaOOWM7o5UWRCPGjqGU+2CKy\nVDdF/QhPZn/9JMVi/wBNN6Nb4HpVV2h9m3NQ3tjyJqlKVTBZKzBSVXcwHJchc+bJ7Kiegv8Adem+\nL+o2n+wlTNQ3Qb+69O/0Nr/sJQE1VG/ePlpRv3j5aArSlc700i1I8FtNb0VRKpR+ELYs5iCS3DmQ\nSDYBIQqLIG3EMo5EAdFXOaL4En+rvv8An7qt3oxHc9XIu+LvMkuwTPC06wk94JZLU7C/hYKnkCvP\nINRXRi1SKGRE3lRd3/3yWWZv7dcjm8zMzdg7TQEhd28cqlJo45UPakqK6n2VcEGuG6Rfcd6L33Ob\nR7NHJyZLRWspM4PPdaMmT7Oa70AeSh8Xs/uNdsLSMXBethycXxTa9iNJ7T5+6T/yWNJnDdQ1C/si\nexJljvYPYIIjkI8vonZXmvSf+TH0htwzWU1hqCgcgsjWkx/+lONn/qV9m1Rjyr6PQ+ufS2jbMZy3\nfWlL1f1epzeBB7j85OkvQTWdJVjqGl31rGgLPM8DSQDHNmNzDui8p8KuSD7iWz2+fOB4h/15a/Uv\nNcf0s+5j0f1Xcb7SbOWRhgzpF1e45+MXFvskz7dfUaJ/tKncVpOCml/Y68ad7u85vR62M/OJuZx4\ngefnbyewPl9irZ3wMDtPZ5vKa+wulP8AJP0qYFtM1C7sHOCsdwqXtuPGQPAlGefMu3t+Px/pf/Jn\n6UWRZ4IbbVIwThrKcLKEHYTb3Oxs9vJC9ftYHW/QNKVa+pKW3WVUu57O5Z95zeFJHivIDzCslldy\nxHdFJJEfFsdl5eQgHB9utjX9Hu7GXg31rc2cgz3l1BJAzFT+CJVG4DkcjI5itCV8Dz+L2f4V6MfH\nw8T6otOMdjVPPu9kZkryZNN0vvO9jkZJkVgzBlCs23mqlkxyzg9niFdb0BvptavrbTLS2c3l24jj\nGQ8KeN5ZX5FYkQM7HHYhxk4FeX19xfyJ/uXjTNPOuXkeL/VIwLZHA322nEhk86vOQsh/wrGOR3Cv\nw+kenMXo/Bc4y+qWSTzz8c6S9eZy/kcKbqq5ZHtvQfovbaPYWun22dkCnfIeTzzMC01xJjlvdyW8\n2QByAqd2+c/q/eKN2r7J+Q1dX8qnOU5OUnbebfFn6aSSpFjg+Xxr2j/EPJV3PzfrH8ao/i9lf2hV\n1ZKWsTg8h2Hx/wDxRW5Dkf1fxqrdh9g1VfFQDf5j7hq1HHPmO09vL5avqkfj9k0BUMD2EVVPDX2D\n+6qFQe0CqRqN64A7D2e1QG3SlKAVju/vcn5j/smslY7v73J+Y/7JoDHSlKAUpSgFRGqf2/T/AMy9\n/YhqYrz+3S8tZbVbi4ja6e4n4KztcTo0csVrBJIZkU9XV7o5WNuQ44UY7AB1mvXLQtZuCAjXkcMu\nVBOydJYo9pPNT1hoOY8Wak65zV7LU7mLhnqCYkglVg1wSr288dwhxt5jdEvtE1t51T0un/p3PzK0\n2qQLtN7y+vY/FKtrdDzsyNav7JAtY/0hUsR4jzHZXOvaaobhLgdQBWCSEpuuMMHkikVidvIrscY/\nKHyVdqUuqpDIwFkCEJBjFzK4PlWMJ35HbitYkk2muC9FXwRIldLCASBY0jKysjBABnGChPn2Mp9u\ntyuc0uTUJU6zEbBorpYp4zuuhlHiTawBTIygU4POtvOqel0/9O5+ZWZu3ZjCi4xSf7mSVpy3L6V2\n9xu/H7VZ6g1XVAzNjT++xy33PaMjPgeTHuVfnVPJp/6dz8ysRVKjUFSok7gDKkqD3wGSMkZ5DH/F\nis1cppV/f3IuEjksJTBcywSPi6QLINsoRCY8SKiSRrvXIJU88g1JZ1T0un/p3PzKxGNSfB157/g2\n3kTNWTwrIpR1V1YYKuoZT5Mg9ozUTnVPS6f+nc/MpnVPS6f+nc/MroE6zN3RZQ9vEwVY+92tGgwq\nSISkiAeICQMParcrjrW7vor2SzEtgZZIzeC2/rHocckhUyF9vMNIkvL2fNUxnVPS6f8Ap3PzKzG0\nlZrEacm1sJmq1C51T0un/p3PzKZ1T0un/p3PzK0YJqobVPQLy2ueyOb+o3HZjLtvs5GPmm3xDz3n\nmqL6S6ze2UKzXEljDGZoo9wF1JlmbPD2rGcbgrDPn5ZJAO1q1nqVzBLAwsFEilQ6vc7kbtSRO85O\nrhWHnUUNQdPM6SlQifztgZ/m8nAyd1yMnHM428ufiqudV9Lp/wCnc/MoZJoVDdBv7r07/Q2v+wla\n2pX+o28ZllWy2BkUlOtuRvdUBIRCQoLDJ8Q51l6C3ML2NvFDJxeqwwWzvw3i3MlvEyuqyDPDeN43\nU88q4oCdNUb+Hy1WqH94+WgK1WqVBdM11MxwDTOEHFzbtOZJFRjAs8RkjUPGwKNHxNx5NtXC98wI\nAnq5vRfBl/1d/wD8/dVsdDEvhbsNQL8XeuziNAZdnVrcSlmte8wbrrJXHMIUzjsGjpnR+8teMsU9\nvNC8800ST9cMyiaV5WWW5lnl4hBfHJAOWcZJoCUq0sOXPx/uNauy9TwrSOQf+GukLe5cRRAfpVYt\n+wZhJYahHsAJbhJMpyByTqsrlzz8Q8RoDez7PuVa7jB/iP41pfzvaDw2MH+pjmtsez1mMYratb+G\nTAiuLeTPYEkjcn2NhoDJxPJj9f8ACrwGPi/UP3mryT6ZfaH/AOatwPSsfY5fuFAWhH8n6x/ChHlO\nPaY/vq9gPSt7uf3mg8xA9n//ACKA09S022uYjDcpBcQsMNFPDHNGw8hSQEGvKumH8m3orqO547KT\nT5mHKXTpjAo84tpA0I9pB2V7GWPp19z/AOatI8o3ex/8LXbC0jEwncJOPJ0RpM+WdG/kiLb6raTS\n6il7pMcwluLaWAw3MiRgskBZWZJI3cKGPed6WwM19TYwAPAAAAGAQAOQAGOQAptGPAb3f/7UAx2A\nr/1+bXTSdMxtJaeLLWpUgopbACO3cOX+HHm8VXBz4uftsPlJqoc+nX3P/mre3xhvY/8AgGvKUvJc\n+I9o8ansPsVdxCO0fq/g1Ygo9IfaOPlxTbjsUj28/JmgLzOMHs7D6b+FXrKP+iv8axgn0wHsj/8A\nFa91fwx8pbmCPlnDyRoceXvm7KA3w/s+5n5Ktjcc+eOZ7eXj89RX862x8DfP2f2eK4uO3x+gRkY8\n/ZV7Xsne8OwvX3HGQIYQvncTzIwHnANASwYHsINVj8NfYP7qjAl83MQQIPy1yWceyscDDPsOayQW\nV6JImae0CKx4qLaylnTHgpKbgCNs45lG9gUBMUpSgFYrz73J/lv+yay1ivPvcn+W/wCyaAspQUoB\nSlKAVpX2lQTywTyoWktiTE291A3FGwyqwWQB442AcEBkUjBANbtKAUpSgFa2rWEV1BLbzBjFMuyR\nUkkiZlOMrxImVlBxg4IyCR2GtmlAWwoEVUGcKoUbmLHAGBlmJLHznnV9UqtAKUpQHMy3uk6NK0W2\nGze+kFyyoqxrNIXt7RpMAgZG+HOByALHx1vf0o0/aG61HhmCAYffvMixBNm3cH4jqu3Gcmty/wBL\nt7jPHiWTKhDuzgoJEmCkZwRxI0b/AIa0YOiuno6SrbjiR42uZJmORKJ953Od8nFVW3tljgc8cqAt\nvOldnGtrJvaSO74hgkQAI6xDczBpSu7kchVyzDJUEAkYx020nx39spy6lWfDK0ah3Vh4ioOD4s8u\n3lW2ejdkYkgMOYY5GlWMyzlWleTil5QX9Gbi4fL7sMARgitefojp7o8fAKB1nX0OaZdq3K7ZlQb9\nqo3JimNpYBsZ50BsWdrZXU0epRgSShDEkwaRRiNpkKtESBxEMtwuWXcvEccsmpatbTbGK2iWGFds\na7iAWZySzF3ZnclndmZiWJJJJrZoBSlKA0db0m3vYxFcoZEDbwA8kZztZD30bA7SjupGcEOQcg1v\n1Sq0AFKUoDV1bT4rqFoJt/DfbuEcssDHawcYkhZWAyo5A86s0bSYLNGjt0KKz7yC7yEkKsajdIxI\nVY0RFXOFVFAAAArdpQFaof3j5arVG/ePloCtKUoCH6TyXadWa0LkideLEkaMZozyKGV1YW6jO4uR\nz24yM5qZqgqtARHTHpDBpdnNeXHgRKSqb44zI4VmCK8rBVOFY5JAwpqVhkDqrKQVZQykEEEMMggj\ntGDVl2yiOQuAUCOXVgCpUKSwIPIgjNcjpP3QIJNi3EE9s5jtmdWUnhNOtrvDbgvoaSXtom5cluNn\nACsQB19zcpEjSSyJFGvNpJHVEUZwCzsQBzIHPy1qTaXZXBEz21rOzIAsrQwykxtzG2QqcodxPI45\n1EX3SnTZ4mj62kfFjQkyQSFQkqWsqiRXTaN6XlsuCRlpwo77kNu0vrHT4YLNrlVFrZxHdK3g2sMb\nKs88oUJEpWCQ5baDw2x2HAGZujtn+BCYfNbSz2o9y3dRWObQCdvCvr+AK2SFlhn3jBGwteQytjOD\nkHPLtqYLDbuyNuN27IxjGc57MY8dRHRKO5WButCVXeZ3SOWZLgxREKEjE6uxmHItuYg5dgAFCigK\nPpl4D3l6jDyT2u79cE0ePcNY5odQQEiGzuMDPKaa3Zj5ArxSLn2WFT1RtlqokvLuzIQNbRWswKyh\n2dLnjjv4toMRVoG8bZDKeXZQGj1m6AG/TZSfHwZ7SVV9gySoW5eaqHUlHhw3cXl/qV0QPZeJWX9d\ndFWtqOoQWyh7iaKBC20PK6xqW2s20Fj27VY+wpPiNAc8nSbTSZF/nG3VouUqvPGjxHGcOj4KHHPB\n51mt9Yt5VV4WluUdQyPBb3FxG6nmCskaFCCOYOeddJmtO91S3hkihllVJJjiJSGO7vkjGSBhAXkR\nAWIBZ1UZJAoCNS6nJ7ywuCvp2NtCPZ2yTbx7aika37kg21pCAcBnunlYjHJuHHAPcLDsqeqN6Taq\nLK1kuW4REe0BZZTCrs7BEjVljctK7MFVQpLMwHjoDANNu28K7iQeSG2bd7G6WdgR/wAIoNBYvukv\n76RSu0w77eGPOQd4a3gSUNyx4eOZ9mpeByyqxG0sqsVyCVyAcEqSCRnGRypPv2Nw9pk2tsDkhN+D\nt3lRkLnGcc8UBHL0ftPw4jN5riWa5HLx7bh2GfPiti20q1jZWjtreNlyVZIIkZSRg7Sq5BIJ7PLW\nl0NivI7TbqEiyXAuLomRZRKrRtdStAN3DQLiNkXZt73aBzrbbWbQSrCbq34zMqrEJUMhZgWUCMHd\nzAJ7OwGgNizvYpgxikWQI7RsUO4B1OGXI5Eg8uXjFZq8+sNX0vRJLqBBOiLNmcym3URxrDLK0kNv\nHiWWJcKhlZCXMid++BWe8+6bZrkJb3TMLd7g8RBDGqpJMjbpSSCo4Ejb03DG0jOeQE/0d6Rx3s93\nAkbobRyhZ8YlAuLq1Lp5RxLOXmMjmBncHVZa8zw5MFlOxsMih3U7TgohBDMPECDnyGtHo3LHNALl\nLdLd7gs0oVVBkdHZOIZAqmZG2llcgblcHAzipOgOS6JXuqyzRdcjkSI2sZkDwxxqJRbWRZsjvhOb\ntr9Sng7IkIAyC/W0pQCsV597k/y3/ZNZaxXv3qT/AC3/AGTQFlUquaUApSlAKUpQClKUApSlAKUp\nQCq1Sq0ApVKrQClKUAqtUpQFaUpQClKUBUUqlKArSlKArVG/ePlpRv3j5aArSlKAUzSlAVrDPaQy\nFWkiidkbejPGjFGxt3IWGVbHLIrLQUBCydEtOMUsC2kUUUyCOVYN1vvRSGCkwFTtyq8h2gAdlYOk\nnRC1v8cVplC28lsoQx4CSxPC2S8ZaRdrn0NmKMVUlSVBHRUoDhNY+54ZknjS/ljSZZUERQiJFnN8\n8mFglj3MHvcrnvV6tENpxmuh6JWV1Ek5u5XcvcTdXiZg3AtBLIbeNmBIebY3fNk8gg/BqapQCrVi\nUMWCqGPIsFG4jyFu0jkPcq6lAVqL6TaFFqESxSvLGFaQhoWRWIlt5rWVDvRhtaG4lXsyMggggGpS\ngoAoAAA5ADA9gVHalosFxNDNIH3wlCArlUfhzR3EQkX8IJPDG47Oa+QkGSpQCrZY1YbWVWU9oYBh\n7hq6lAAMdnIeKo/pHppvLWW3EhhaQIUlUZaN45ElRwMjmHRT7VSFKA4ofc6gLszXVyQXncc1MqNN\nNeTgrM+44Et6zkEEM1vCSO8IMlZ9CrGOPhsskv8AWVu2d32u1wrOyueCECgb8bVAGFUYwK6SlAaU\nmkWrTGd4I3mOBvkHEKhSjDhh8iPvo4ydoGTGpPMCsi6fbiPgiCEQlWThCJBHtfw12AY2t4x462aU\nApSlAKUpQCsV596k/wAt/wBk1lrFe/epP8t/2TQGOlfBPdndKPUGgfBdR+0Kd2d0o9QaB8F1H7Qo\nD72qtfBHdndKPUGgfBdR+0Kd2d0o9QaB8F1H7QoD73pXwR3Z3Sj1BoHwXUftCndndKPUGgfBdR+0\nKA+96V8Ed2d0o9QaB8F1H7Qp3Z3Sj1BoHwXUftCgPvelfBHdn9KPUGgfBdR+0Kd2f0o9QaB8F1H7\nQoD73pXwR3Z/Sj1BoHwXUftCndn9KPUGgfBdR+0KA+96V8Ed2f0o9QaB8F1H7Qp3Z/Sj1BoHwXUf\ntCgPvelfBHdn9KPUGgfBdR+0Kd2f0o9QaB8F1H7QoD74pXwP3Z/Sj1BoHwXUftCq92f0o9QaB8F1\nH7QoD73pXwR3Z/Sj1BoHwXUftCndn9KPUGgfBdR+0KA+9xSvgjuz+lHqDQPguo/aFO7P6UeoNA+C\n6j9oUB98Ur4H7s/pR6g0D4LqP2hTuz+lHqDQPguo/aFAffFK+B+7Q6UeoNA+C6j9oU7tDpR6g0D4\nLqP2hQH3xVa+Bu7Q6UeoNA+C6j9oU7tDpT6g0D4LqP2hQH3zSvgbu0OlPqDQPguo/aNV7tDpT6g0\nD4LqP2jQH3zSvgbu0OlPqDQPguo/aNO7Q6U+oNA+C6j9o0B980FfA3dodKfUGgfBdR+0ad2h0p9Q\naB8F1H7RoD75pXwN3aHSn1BoHwXUftGndo9KfUGgfBdR+0aA++qV8C92j0p9QaB8F1H7Rp3aPSn1\nBoHwXUftGgPvqlfAvdo9KfUGgfBdR+0ad2j0p9QaB8F1H7RoD76pXwL3aPSn1BoHwXUftGndo9Kf\nUGgfBdR+0aA++qrXwJ3aPSn1BoHwXUftGndpdKfUGgfBdR+0aA+/KV8B92l0p9QaB8F1H7Rqvdpd\nKfUGgfBdR+0aA++6V8Cd2l0p9QaB8F1H7Rp3aXSn1BoHwXUftGgPvulfAndpdKfUGgfBdR+0ad2l\n0p9QaB8F1H7RoD77qtfAfdp9KfUGgfBdR+0ad2l0p9QaB8F1H7RoD78pXwH3afSn1BoHwXUftGnd\np9KfUGgfBdR+0aA+/KV8B92n0p9QaB8F1H7Rp3afSn1BoHwXUftGgPvylfAfdp9KfUGgfBdR+0ad\n2n0p9QdH/guo/aNAfflYr371J/lv+ya+CO7T6U+oNA+C6j9o1bL/AC0OlLKymw0DDAqcWuo5wRg4\n/wC0PPQHzVSlKAUpSgFKUoBSlKAUpSgFKUoBSlKAUpSgFKUoBSlKAUpSgFKUoBSlKAUpSgFKUoBS\nlKAUpSgFKUoBSlKAUpSgFKUoBSlKAUpSgFKUoBSlKAUpSgFKUoBSlKAUpSgFKUoBSlKAUpSgFKUo\nBSlKAUpSgFKUoBSlKAUpSgFKUoBSlKAUpSgFKUoBSlKAUpSgFKUoBSlKAUpSgFKUoBSlKAUpSgFK\nUoBSlKAUpSgFKUoBSlKAUpSgFKUoBSlKAUpSgFKUoBSlKAUpSgFKUoBSlKAUpSgFKUoBSlKAUpSg\nFKUoBSlKAUpSgFKUoBSlKAUpSgFKUoBSlKAUpSgFKUoBSlKAUpSgFKUoBSlKAUpSgFKUoBSlKAUp\nSgFKUoBSlKAUpSgFKUoD/9k=\n",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"640\"\n",
       "            height=\"360\"\n",
       "            src=\"https://www.youtube.com/embed/9KM9Td6RVgQ\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x1d9775b5da0>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo('9KM9Td6RVgQ',width=640,height=360)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "&#9989; Do This -  Now, create an instance of the ```trainer``` class from the partSix.py file. Call the objects ```train``` function by passing it the original ```X``` and ```y``` data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.000000\n",
      "         Iterations: 36\n",
      "         Function evaluations: 39\n",
      "         Gradient evaluations: 39\n"
     ]
    }
   ],
   "source": [
    "#Put your code here\n",
    "T = trainer(NN)\n",
    "T.train(X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.74998259]\n",
      " [0.82002105]\n",
      " [0.93000224]]\n",
      "[3.75622733e-10]\n",
      "[[0.75]\n",
      " [0.82]\n",
      " [0.93]]\n"
     ]
    }
   ],
   "source": [
    "print(NN.forward(X))\n",
    "print(NN.costFunction(X, y ))\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "&#9989; Do This -  If done correctly, the ```NN``` object should now be trained. Apply the forward function again to see the new estimation of $\\hat{y}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 4**: Hopefully this worked and the estimation is better than the previous one.  How close are these values to the original grades?  What shortcomings are there to testing using this approach?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These are very close values. I think some short comings is when there are local minimums in the data as well as when you have a low amount of data. I think it takes a large amount of data to train to be something useful and not just spit back out the same answers you trained it on."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "# Assignment wrap-up\n",
    "\n",
    "Please fill out the form that appears when you run the code below.  **You must completely fill this out in order to receive credit for the assignment!**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<iframe \n",
       "\tsrc=\"https://goo.gl/forms/SIRHykeawcq3Ip753\" \n",
       "\twidth=\"80%\" \n",
       "\theight=\"600px\" \n",
       "\tframeborder=\"0\" \n",
       "\tmarginheight=\"0\" \n",
       "\tmarginwidth=\"0\">\n",
       "\tLoading...\n",
       "</iframe>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import HTML\n",
    "HTML(\n",
    "\"\"\"\n",
    "<iframe \n",
    "\tsrc=\"https://goo.gl/forms/SIRHykeawcq3Ip753\" \n",
    "\twidth=\"80%\" \n",
    "\theight=\"600px\" \n",
    "\tframeborder=\"0\" \n",
    "\tmarginheight=\"0\" \n",
    "\tmarginwidth=\"0\">\n",
    "\tLoading...\n",
    "</iframe>\n",
    "\"\"\"\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---------\n",
    "### Congratulations, you're done with your pre-class assignment!\n",
    "\n",
    "Now, you just need to submit this assignment by uploading it to the course <a href=\"https://d2l.msu.edu/\">Desire2Learn</a> web page for today's dropbox (Don't forget to add your name in the first cell)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "&#169; Copyright 2017,  Michigan State University Board of Trustees"
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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