PCA of stocks using Spark.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "source": [
    "## Analysis of stock prices using PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "import findspark\n",
    "findspark.init()\n",
    "from pyspark import SparkContext\n",
    "\n",
    "#sc.stop()\n",
    "sc = SparkContext(master=\"local[6]\",pyFiles=['lib/spark_PCA.py'])\n",
    "\n",
    "from pyspark.sql import *\n",
    "sqlContext = SQLContext(sc)\n",
    "\n",
    "%pylab inline\n",
    "import sys\n",
    "sys.path.append('./lib')\n",
    "\n",
    "import numpy as np\n",
    "from spark_PCA import computeCov"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13422"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# read the file in a dataframe.\n",
    "df=sqlContext.read.csv('SP500.csv',header='true',inferSchema='true')\n",
    "df.count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true,
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "columns=df.columns\n",
    "col=[c for c in columns if '_D' in c]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "source": [
    "Extract the tickers from the column names of `df`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(['AGN', 'EOG', 'WLP', 'CPB', 'YUM', 'JWN', 'FLS', 'TAP', 'BWA', 'AAPL'], 476)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tickers = map(lambda x: x[:x.index('_D')], col)\n",
    "tickers[:10],len(tickers)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "source": [
    "#### Create an RDD of numpy arrays\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "        0.        ,  0.        ,  0.        ,  0.        ,  0.        ,\n",
       "        0.        , -0.00830103,  0.        ,  0.        ,  0.        ])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def make_array(row):\n",
    "    arr = np.array([row['{}_D'.format(tickers[i])] for i in range(len(tickers))], dtype=np.float64)\n",
    "    return np.nan_to_num(arr)\n",
    "\n",
    "Rows = df.select(col).rdd.map(make_array).cache()\n",
    "Rows.first()[:20]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    },
    "scrolled": false
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'computeCov' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-1-54c2aa8903bb>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# Run ComputeCov to create the covariance matrix.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mOUT\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcomputeCov\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mRows\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      3\u001b[0m \u001b[0mOUT\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mkeys\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'computeCov' is not defined"
     ]
    }
   ],
   "source": [
    "# Run ComputeCov to create the covariance matrix.\n",
    "OUT=computeCov(Rows)\n",
    "OUT.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true,
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "from numpy import linalg as LA\n",
    "eigval,eigvec=LA.eigh(OUT['Cov'])\n",
    "eigval=eigval[-1::-1] # reverse order\n",
    "eigvec=eigvec[:,-1::-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "source": [
    "### Percentage-of-variance explained graph\n",
    "The percentage of variance explained as a function of the number of top eigen-vectors used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
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L0DN1IWWegxVV/PqF1dz54rt07diOn15+IpdPHuz9Bs65ZpdMUrhVUg7wNeB/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\nZW5S6Oo1BeecS5RxScGHzXb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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b9f6510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plotVarExplained(EV, k):\n",
    "    plot(([0] + list(cumsum(EV[:k])))/sum(EV))\n",
    "    title('Variance Explained for k Top Eigen-vectors Used')\n",
    "    ylabel('Fraction of Variance')\n",
    "    xlabel('Number of Eigen-vectors')\n",
    "    grid()\n",
    "plotVarExplained(eigval, 50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    },
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10bb16610>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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5hSc3MBwio0OOP3ot7YRJS1GW4w8MvuPN8Xt/8/K/I9R4SOowtblKggtsEmgaBHWX5zaO\n2IqH1zEfQX2fkiOwfM1W/G3Feu2bxtkOsrQ1TsOO66OmvSVLn3hg1SYt55VO9aSrg5Z7cdtY6ntz\nuPXxdUz96agaG8Lrk2oIz9u+RacGIPaN4G/m688t+JnOIYhAVhRAnH+2rR4OlOO3LUlbDfUseY27\no/47kYj3zGqUwAsFuAzavDUm62JcW9Q73ryjild94xa85Xt3au+9cY0/efXGvW7bBj1ZPs3rv30r\nTv/ObcFvatxNS/XQd3HYF65Pf/OUaHQjFdv1ty3XJxkh7HET6vd1D6/G6d+5reO4/r7biIV+zJ/f\n9TQmVEp446FzM9WRdxLnBmogkKUMBAIdGHEapU3acVtD2pakrYbS9OsZOX5HeG2lfHjcqqHWYNio\nCNzy0n3fIOc7c069/wdIzIRG9VgMwmmRJiVHnBYf4fib5M6Ztp5masF8htK0Gnv6OgHg7T/4m/Zb\nIHzPZvdWVVx4o+cgsHFHFTMmDuRqTyvQNxo/h0/89gF8+Jf3Z74uvztn9JjqnLV6GAFJq+duVU/w\nUw61EO/vaK0ecvz+wW2jNfzsb0+nWubn1VY2bBsLMlBm1fhVWmEawBX33sdqjQkT9S69FMON1VVn\nvK6aSfUoZNX4Fcxv0TR3zrQr0Qgfnv/+rA0sQ+QtX2e664UQVu8dM6jMRmld+9ALkZXEeKDvNP5m\nIO844TRWLhiHG4gsx2/pmarjulJi9eYRHPXlG/GKfWZpbfjPPz6EXy1ehQU7DePovWbGtjsvTfPJ\n3z2Aq/002FkpprIjMAZd4497741r/N7fsbprTLySfc9xBkCOI9aongY1/iAXU2xHjJkULMFGeVDN\nyPG7rsR//lFPJ16XEk5u7Tx6rPGUDd7fNCuGwIaVQJ/ZBP83r1+GOVOHcEzCGGw2+lrjz4u8GhI3\nUJUmToUr15k5jt/WsSUpp/zClYeJqnvdVq8j7kgReZrXLkA58qzG3bJPTdH2xbWjWnfxi7uexjUP\nPm8tEwf1Hao1XeMfSwi24iYFLqWG7tUTPtMPYxLfJWnCcafjztlcD/NA4/hT1PP4mq34xd3PNO3+\nraR6kiYOj44MlSwK9XN4wHMNfnEbvyPa9rH6uLtYA4Xgz4XcKRs4qocxuiYJySSvBXWeE5Rq8sni\nydGoNg1k5/grBtUD6IPLHJRjNYnzfvsAzvrJvfkbCc89kb4aW/6kOHDfj34Katz91p+XW+uxrbRC\njj+O6mFWjap9TXXnzEb1cFHLzc7qmdYd04a070OAUD2R9+39njqhAiBUtExsH6u3xfDbN4I/q1Kx\naUcVR3/lRtz15ItMXfk+FOfLHmj8RDDy/v60niSqx/tr04aWrd6CvzJucPZ2N94xs3P83rOpAC4p\nZayAsE1OtbqLE75+c+L91Ls0Of5Ry4oo7mm4OAubH39c+gabYA+Fjb0NsV5HTTTujmY07nLPm6To\n3PzYGqxYy2d35YRmo6kjsoxvm5KlfqqYEBvVs2Os1hZf/1SCXwhxihDiMSHEciHEecx5IYS40D+/\nVAhxGDk3TQhxuRDiUSHEI0KIlzfzAWx4ct02rFy3DaO1Oj77hwexcUc2f+EbH1mN5zaN4JJbV0TO\n5Q6cYa6j3HJQLnGJn6Txe3+5DuVKiZO/+ZdMgjhvGmGdnsqm1pUdr2tSd844wWIToFtHa3hyXfpd\n10ZrbtM0fvp9bJNJXESzVSCoiT2nH380oVgDVI8WuZtcnutLSYLvzB/ejRONIK3gnjEcf16o97p5\npIYDP3ctFq98kX1HEjL4FuZps/zv738WX7n6kUiZ7dV6W3IcJQp+IUQJwHcAnApgfwBnCCH2N4qd\nCmBv/7/3A7iInPsfANdIKRcCOBjAIxgHnPD1m3H812/GH+5/Dpfd8RR+e2+2zZBV9OXB86dFzuXe\nbJ3z4/f/UiMmLcbdKalfU+OuuSgwB2ea5XA7Nf4d2nuJEfwWr560PK9yqzU1flvKiHg/fv/ezCoN\n0LXkOBrN9s5svHL69rWG6kmj8ZspxoEGvXqYERJundiYwXjJMxuxZbSGb9+03EKbEo0/sory/qpv\nuGLtNvzfHU9pZZSS0alUz5EAlkspV0gpxwD8AsDpRpnTAVwmPdwJYJoQYo4QYiqAVwC4BACklGNS\nysaSqmREXqGlKJ4JzMbn+TX+6IWqc6YVcEA2427kWqPuNIIxL8dPB2UWOoG6nwYat9Tbbra6amtj\nyrEvNMEfHk9KEsd9A84dUFrq9GwKFgFvfL8f374SC867Ept2eDt4mZ+X1pNF8DcysVONP43myhnL\nG9F4eXfn+PGRhGgwFj/mXRnag2wGc7qiMwP3to9F07CPF9II/rkAqBl+lX8sTZndAawF8EMhxH1C\niB8IISY20N7MyMNfPrtxB5at3upfHz2fd2kc56Y5mkHwhwKB79lhfpx0bUhCXsFAb5UlSdu+n74m\noGe0fO+kCnNQV23RsClvqybAat3Vvq+N6olb9an35aTg+L1zlnqMb3XZHSsBABu2e4Lf7Id0hZCm\nfVzbsmLMklLDBi5q2XUl6q5k0y8kgbtnowq0qlJtsiKlZN+RGzI90QlIafyG8btWd+G6Eo+v3oLt\nY57XW6dq/I2gDOAwABdJKQ8FsA1AxEYAAEKI9wshFgshFq9dm2+3Jg553umdT6wP/s13rLxUT/SY\nYDX++HsFHHKCxm/rrHoDrM0NkNePnyLv5KF5O8W6c/Ln0mpTga2l5moi06rx+4W4FRPH8celbLDZ\nJ6JBQcZ549l02oWpMMjQatTbJKonzTYD3PusS4mLb3kC77jkb5l3amM1cf/gzY+txY9y7BMd5Foi\nqTH4MR8ej9hN/L9V4/hozcW3/rwcr/7mX7DkGS+yu1M1/mcBzCe/5/nH0pRZBWCVlFLFOl8ObyKI\nQEr5PSnlIinlolmzZqVpezrkeKlJLmp53c/iUjbY3BY5bSAMMPE0irVbRo3zfGe01ZeEpmj8TRD8\nsZG7NuEZEXJ8HWoCHqvLWO08eh1zz+ADWQK4DLuB7d1Ejhs/zdPUzpElZXNDXj0Z3Tm54LW6K4MV\n3potvL87EE4aP759JZ7f5GVO5VY2VJCe/8eHE9tUdyVrY6NJbnlHieRcPeakPlpzcfdKj0ZWnkpN\n2pcnE9II/rsB7C2E2F0IMQDgrQCuMMpcAeBdvnfPywBsklI+L6V8AcAzQoh9/XInAUj+Ek1ERMFN\nQfzRjmPj9vKAE7pKY9Q6XkIwFz3/xSsfwRFfugGbR6rBsYB3bNJqJe+OUXRQ5p08grxDSIjctWj8\nHF/LQU/ZEB7Ps7UinZgV6MRkCj/O4AnYtcjwPoY2WU8b5ZzunaQBnWzSUD2csZwqUnF1rN82hvVb\nR/G5Kx7Cuy65y7uWKZ61r53z03ux8DPXhO1RGr9DNf7oda4b2mdsAVxmvxyp1oNxoVb5HUn1SClr\nAD4A4Fp4Hjm/klI+JIQ4Swhxll/sKgArACwH8H0AZ5MqPgjgp0KIpQAOAfDlJrY/EdxLXfLMRty5\nYj1TOnoNmykzZ1viUjZkonqI8Upt9kE3+gg6I/PspiDjpsGtozV84/plgcBvhsafm+pRgl9KXHKr\nfdlum5zM12eb+DSqR+P4s/vx18lkpRBn5LPRVEmTtHk6Ld8ex/FvG63Fjg0TY2Sy4fr3xu26G7WN\n6kmD9VtHg7arLUlZOjNjX7vmoRe03+rdhXtY8HVK2B0plHDnNH7V5HYad1Pl6pFSXgVPuNNjF5N/\nSwDnWK69H8CiBtrYELg+QNPKctCMZJzgz23cjR4LvFfGeONuXICKgGBT7ep+/Lpo37TDnmpY4ZvX\nL8Mltz6JedMm4B+PmJ+bpqFXNcrxbzM2ijc/gZUnNwrWXQnGUSuor2rk6hlJonq4e7rRiZe2L0r1\nWILPEvztzXeqCX57k2Ppr//49RJc/eAL+NsnT8LsKUMxtUTvaX7iz//xYVx625P42j8chJP33wVT\nhyussTztKnTrSA2jw8b2pOyKPHrs3MuX4Hf3pXPpjlI9NuOuJFQPX4f5DUdr9eCadVs9WqsjNf5u\nR6NeLLxnTM62cFSP4vgtAyjOq0gInYcMzoNffgLQKCGvjqjoUoJJLcub48efjy6y3ds8ateazd98\nOdW+sbSRuyk06rom+OkqwqR6LG3PSvUkbIOovnQc1fPQc952kzvG0lFc9LnMe/78rqcBAB+7fCnO\n+P6dAHiNn15ntpq+59GaG7HlcG+O06B/tXhV6kBEMw5ASr5OKcOykfetKV8hRqth/1rvp3HoVONu\nV8NcVqdx7U3KlJnbq4c17vpePWM2jp+jery/AmC3VHQtnQ7QNTQbAm8G//q8++XSUZl28ogYHm2C\nP63Gn5LPVs9Yrel8bh4//mAPAlIRnfjSGneTczbpv5M0fnUszrgb7DOQ0gc+Lh//zMlh/vmHn/cm\nFE7jr0uZGIXuXVuP9F/W+SGvPclYqQW744G3mUhp96CzudOOEq8xpfF3bMqGbobylc2CeoKxqRka\n/6IvejsPBRq/xY8/3p1ThFoJOR8ad80zUcTtA6zkPRVaWQYV7fxp6SJT2NmEnzmwslA9HNT1Y/V6\nOj/+mMfhjOs61RM17nLfIZpaQT//0HObIhqxQnzKBv03vY26LG3Ua1w+flrHTv4mJFw22DjBR8+N\n1HTBX3d5o2teDVr1UW6VaEt/Em7Ekk7BGK3VgyG53s/fU1A9LcD2lEtWCk571kA1JP/j/+H+ZxO9\nX2i9KlufErJ2qideo+Hy+VPjblKf4sYIDVwBdKGdd1Cl1WqiUaWWghGNn68/sgK3Uj2hxq9x/HmM\nuwlUj+nVU61bBFjCO1u6ahN+Q1KR2ILdzINm3iQu4jftZx6ruRgoe2LE5tkCAHOmefYCjjqLYwF1\n2s3VxtgX/vQwm+44ryCtB4I/VKy83/aVv53jt2j8hOpRidsKqqcF2D6aXfBTr5mkFLt1V+KaB1/A\nv/3ifnw7JsWuVzZ6TC0nKdVDByI3KGj7BHNNoHG6MnXCNwoz7S9Nqfy7e5/F0lXpsm7k8erJG1Vq\n29UqrcYfUD31bPn4ueZxVE+ScZdNr2HxFKF47IXNuP7h1ZBSavXGtsvUThlnhrTCaKzmYigQ/Po5\n+h53nToBAO/OGXcvLW+SQfX86PaV+P39z8VekwVqZcspC9w4jOP4bU0YrbkRZbRT/fi7GltzUT3e\nV6s4TiLHX5cyCKFfvXlEK7d2y6g2eOOErLa3bMI1dKMItZymnYcm8UqSt6ynkbE/L9X4z/3NUrzh\n2/FeUQq06tSCP6WgNo/aKRmjPmNltOC8K/GVqx8hVI/ux59kE2EVA07jr9mpnmrd7jWiP0v0/t//\n65N432WLceMjaxL3v1V9JM64G2cf4lCtuxjy3aTiqKlJfnpiluPXuCb7uZGaqwWM2ZBXkKp7mb75\nVMBTSJBcPVLiqfXbEl1hR2t1bDNkUiMBdHnR81svbh1JFvzm9no0gMP8JgvOu1L77brECETKvrht\nDEd86Qa8/xV7ROqlUPe9ley7OVLzNmdwHJEoEELB7x377b2r8Ot7VgXlklxPaV3Vuovv3vREIEDi\nIoDTgN7bxvFLKTFWdzFY9oWHQdnYjbv6cbvGb14X/lu16X9vWRFshO2lbPCOD5Qdq+CPo0Q4qoc+\nP8fxc+/YNKrHfcrtVd02wRXl3EyBqCJjHuOgxsxY3cUEf5cp7prTDpqDGx9ZHdyTG4+xUcbk1GjV\nTeWckF/j15/dJb/5CT58z1ICr/zazQCAlV89zXqP0ZqLbaOmxj/+gr/3Nf7RZMHPZSssOcLbWi0F\nVcJ51mzwA1du8AOsuPsA4aRB8ZM7n8bHf7PUr5Nrr/eX+vGruv/9V0u0+yVz/GGBX979DL55w7LA\nXz7w6mnGDlyWhvz49pXY99PXBKslc4KwGneNw7Z9bOMyUapVVqUkWI1/qOwkapi0fzz03CY8+sJm\ndqVEOX6zTTWXFyxZuN/JQ2XtHXDCT31H85Fo0bSeXOoaj+rhBb+UEsOVEnaZMhS8k3UMJ193o+nD\nzfYAUeOuDY3GjKjLKX9vy9nFveff3bfKeo/Rah3bDJnkuhLVuouLbn7CqsA0G70v+EeSl1WcJ0nJ\n95hJGnzu5CJUAAAgAElEQVR1KQO+hutv9FCcxm+Cau229np+/P4OXoxwrluWqBSu9Dr81659NMh/\nQs8B+d056VW2yeOKJR5Hq/YGTsvJm9/FtnewLYcKENIOZccJnnG0GnrYDFVKdo0fupAAgNMuvBWn\nXPBXjWpTiDP81yy2mLj59rSD5uDle+wU/B4oGZMU89pCGkevmL5LU+u1QV0zVncxVHH8eqP3E8Kj\nDlX59cwWhHHKVV37XvVU6UMa9+qRWj1SSpY+ksH/dHzkl0uiB33sqLqRvlqXEj+58yn81zWP4gd/\nfTJX27Oi9wV/Do3fVRo/Q/WYcF1JXCrDwnxEZ/QYp/Gb9ZsIArjI9ZyAXPLMRrzr0rti66+7Hjf5\nnZueiGzHyFEWWaAbd/kywnBHjfLP/L3N92LTlMzL6TdQ11RKIpiYdlTDPVBjBX+gDTITM0f1xAl+\nC9UTJ8DmTBnCvrtMDutwZWJq76BdMZOhKpPkfqvKjdVcDFYsGj8kBARKQkBKT6tVewno97ffx0yY\nl0bjzxtZr75RwNsHnL+F47do/HHg3MvrrgwU1Dzu53nQ84J/ixGpGjcgwt8IqR7DGGjCldSzJjzO\ndQc2V09MSNlJ/30zrvOpIroyoO1VrpeNJEGzCXjOndPE85t24MIbH08cbErLvO/pDYF2D0TtIybH\nb/XCiQj+lH78jMZfKTkBFbNjrB58u8FYjl9qf7l70raPxayaqnUL1RPjduk4AnvMmqiV1bbvZG4X\nfmf9uD5Bp5vsafZJZdzlPFscx7ND1V2JDZZ9ZzWDuzFy6CsYqdYTvazStN2GjdurWLNlRDPqAvoY\n0domk6JkouDcy6kTRilt5FyD6H3jrqHxxxnjFDzePuyw4XH+Wn97WD4YitbL8M3mdxYibOMTa7fh\nibXbInXTjT6EaEzwSxkOPJPSCd0S7YPto79agtufWI8TF+6MA+ZO1esm/1aC+k3fvR2AZwD7ytWP\n4O6V3haX5vJawfZYpkC3bcRiXm+6BwKhFxPga/x+kaFKKRA0l9z6JKp1F2e9ck+tnfECNjwZT/W4\nFrdd/Te9lQCw16xJYR11qXH88ROSPfqVc0VVeG5jSAVSGnDQ6s7ptdRzUghjVyLtSkn1pDXu5vXq\nUTm83vGy3bx2EcqOkxu2lcDMSYNBVK4Jm8ZPgzLHAz2v8fOdUYfVuOt32PBafrWgtPYkjt8Uapww\nSDPjB+0gfvycVv72o3ZLVVfgw24IhLVbRnHhjY+z2uporY4rlz4fPMOdK9ZH6QxmsqL431tWRIqm\n3ZQ9kqAsbVpmzbsmqn3tIN4xQ5VQ4//Cnx7GV69+lNTL1w+EE2h6qsem8dsFohACe+08SSubpPHX\ngglJP07LqnZGcszU6jj6q3+OtK3myiCAK/oM0nc59t77esawq+pSYyhKzekTddL+CN7zJCtBcSvU\nwBZCNH9binOuGroSM6E8epQXmbqfmRG01eh5wW8iFdUjQ68eLZiKubZad8NEaYn3jl5r1ulYSH/d\n3dQ/hpAq+eKVD2M90TL22nkSFi2YntAiry6b2+avFq/CN65fhrv9/YcpvnHdMpzzs3ux+KkN/v0f\nwdevW6aV4TR+G9LQShRmOZvxOC5Xj9KQ6RvfMVYP3kccxx/46nN9QnnPUONuzHNV/e34TJjCif4U\nApg1eTD47XH8tK2MoLIYbtPkedpiOkkowV93MVhyrO0V8OjIupRBpKoJ+p7i7A9pOf40q9+4uUE9\nmyojwY99V/IZeaSUePkeOwUTIoXS+M3Mp6o/J9n8moW+E/ychwoXyej4Xj06x8/U5/LunGmSR9WY\nUP00hinasdW9l63eii/86WFyPJ32EMfxB+1khOrzm0b89obH7n9mg1aGnktyi129ZSTYezUNzPqs\nAtqozsz9AoTvaXigpFE9g2XHyinXDeHAnbMFcHHlbRyyDY7v0fW7s48O6qC58dmVrWVyZfMEGcfM\nbJ3qfJVq/Ga9ABlH0ckjaKtrHzem+20ar540Gr8eC6OfM3l4V9oj4G05lkqOYFfvqu5dpgxqx9VK\ny6b4NRt9J/jp4FCIcNuK6hGCjYil0DT+GM2Fu97c2Nsrw7dbMpOKEEKzEZhzWirB74aeCVncNlX/\npLeIu1/NjQ8m+8gvl+B/bnw8Q4Sv/psKhLhVGufOqQzkkwbLngD1hfRgnMbvV8MJBC5vkClsJw+G\n5rWqm86PX/ca89o8c9JgUH9Srp7ATz1mFRQcMw5ywlDVaRP8rtSpHtN/XeFff3ovnvYN/tE6wn+n\n9eNPRfWQf5v91kxdbouAt1E91boXfFlihPi2MUX1DEauAdJnRW0UPSn44wQM13E4zw9HCDgOb1Sl\nqNZdLW93UKcbbYt5fdXQ9J78ymtTdVq6mTelgMqko0kJtuOZcGXI+doDtaL1qGceJMtZL9I5fKaI\nh0bCo/3l8bWpqR4qmEqOsAZIxQl+xfGrVzjJF8ZKQA2VS4neQrzNKHqNqanuTDS+Wg6qR33a0KvL\nTczOyaWSsJU1v0MkzYCL4FurPmBWQ6keV3qCXwjPfdbEHX6qA3POpG17ev12/CBmFzaFNMoDF/2u\nYLqcui5fp+vy726s5qIkeNpmu9+3pg9XtOOqfxQcfwOI+/Cc4I/4jhONn+M/KbSNKBLsAeaxmpEX\nRgh73EC17uILf3oYm0eqmpCgnYsKeol0fGEaqoeDbUl67uVLsecnvc3azGdJigB2hEidWZG2tWy0\nRc/HY78uDODyrp+oBL8v5DzjbnxgGL8K5BUEipfuGnpA2Yy7sUqALyBU25XGr15FnDBPs+eu2RfM\nZId1KYPntBl3VVoH4XvHbRurY7hSivVcsaWTGKo42Jwi/YrXdv03v4te+G+zOZuZWAO2DlIP5fPH\n6i5KjsMqXmrltHDOFJx7yr74p2N2BxCutguOvwHEyQ7O+yNq3AUR/OFx7uPXiIGWnk6TbbFaT86l\no3Dnihdxya1P4oLrH9c8ShyLxm+es4EGocTl0zGhbkWTbm3aUQ0ijjkvlqSJxRH58vabgv89P7w7\n+HdU4w//rdw5S4Hg9/zR1eAcLJdScPzR9nIue+ZksGBm6PlRtWbn1H/r9AS0ttddidGaiwncvpI+\nbJNVmr0ATLdoao8ZKNlSNnhCteQrNNtGa5g4WI4VbrYkfXHPZSLum9O2KZjDxNyeVEr7xKzuVSEP\nNVZzUXL4FbdSKiolgbOP3wvzpntZS5VDQKHxN4A4TYnT+LnIXc94pndEm8avjtPTSemcvWvd2EmK\nQ7Xuam5mwqLxIxPV4wt+C8fPeaRwHZSG42/aUY1o20n87JJVm/DYC1uSmgxA1wzLJb0b3/5EmCEx\njtbgOH6AUD0VewAXpXpWbx7BU+u3Bee4VOCmxk8nq1qdT/sb148Vx1/2g0hqdRkbRQvoLphJ9zH7\nrzmZuVIGwmrQT9nAbRUp4FGmdSmxdbSGSYPlWOEWHYve36EGBD+30qQ0ZDLHb5s8woN0rHkav2Cf\nU/UNdU5dF2r8RQBXbsRSPSk0UWXclTKdO6fLaH9xATQKNUs63jisWLcVu80YDuprVOOnmQetXj3M\nO+OW69Rdb8P2asTVLckHe6zm4nNXPJTQYr9NpK0cZ6xgvl7Oj1+9J0X1KI1/qFKCK/nnV7LElRJH\nfflG7ZzJhwOh4P/5+16GWZMHcM2DL4TPQiZzve1RDVoh0PhLiupxUXNdDJRsfHuooKQx7pp2CtMw\nW3fD+A91z69ftwx/f/g8zPFz78vAuOtTPb7GH9cr7VRPesFvmzz0esN/m+Mksr2jtORSkuF7psqH\nR7nxxl0lf9RYdZzw+wHZI4Hzog81/qg29rHLl0Y8cgI3tASvnppro3qS22Vb4sfhtuXr8fO7nvHr\n0wVwyQk/p0Q61zBXhoPNRmtwWi+tes9ZE/GRV+2jJZ/auH0sIriS9q/NAvouy469G5vv/CmSLkJp\n/OobTDQ0fsXbctsLxqUv5j6pEpIHzpuKvXaerH23mpvWnTM8oC6nHH/dlSiX+GBCV+ubKTR+45Nv\nY7x6lLCqEH77gVWbtNY6IjT6bxurY3ggnuO3bb1JnQhetd9s6/VAdHXFavyacTe2Oi3WRa8jPE4n\nj2qMxq+gJgXl8lkNgv5yhh1nRG8K/ph3xwmxR57frHHVyrhrUj3cfDJWCwctl+yKIsLx19zEJHBx\ncKUEVXbLJVPjT1GHRehQcL7T9JJJQxXMnzFBO79he5TqSRN1mRaacTdG4zcf7dzLl+LTv38AC867\nMpiI1PNNIhq/I0JNlvYZ9e9we8t07VV0mfomjiH4bdTM5pFq4GWi89K6cbdel14UrSWYir4vjto0\nYR6LpBKWIBp/+CzU7dP1jbsqy+02n+qJW4hGNH7F8Q+EGv93336YvQJ4GTApOArzwPOvCwIekxWk\nmD13/X+XTY7fovErBILfUW302pzWxtUoelLwx2U1tGm1G3eENEUYuSsSqZ6aGwpvepZ3pzOvzU71\nUEiZ4M6ZMYDLBt4gHj7MQElgl6l6JOKG7WOR72DLmZ8HOtUT7cbmLkoUP7nzaa89vhBX2tbEgdCr\nxxEi0PjphKX6DzfZx0EFcCmBT2VC1ZKd8/HVW3DQ+dfhzRffHjmnPm2JaPy1ugzeRZw3010rX8SC\n867Ekmc24v/uWMmvUPyDazaP4N6nN7CbhyiBSleadBc6KVV0ubdyTkP12HI1qZz/QDy1BwA7DKrN\npnCs9O0ySaMkjuNX358K+Zrr+fHHzSeqvGNo/OO18XpPcvxZjbsAsGFbNeAm6670Obr4JTKgp124\n+bG1uP+ZjThk/rSQ/iFluVw9qtwPzzwi8blMSEOrNwV/WqonKX85x3FTwTtQdrCLEYK+cftY6tTJ\neWD68UfOS6Ak4mM6VHuUMFdGSsXRKsFPPVpU/1FzYdpxWnNNwW8ad6MVKVpq2eqtkXPqeuFrlnXX\n0/grZUX16PVx/V4lJeNyOqk+caRvv3jLovna+WrdxdeuewyALohXbw7Thki/fSrL7dbRuufVE9Mv\nza6mxpz6NuqZ42AGm9n6nVrlJ9nCqPcOhUQ4wZp9sCRE7HMqelJdVy00/sYRN2vaknlRjd+VZAeu\nBKrHTKn7Rn8wpaF6anUv8u/1B++KExbubG2zDbEcP2Pc5fp3Go2fo3roNQMlJ6Lxv7itGtX4m0n1\naBx/9MGCTcNjbqmqUBOb0pbrrqeqKl6Z0hxqkohLy8yhavhpO5qGyBt3TZsILUGfuOQIn+N3Q43f\nqMu2UQ1gMe7WXU17Nw3W1zz4Av7ob6JTdhzc8rHjscuUIazeQjV+z7irJqZtozVMHCjFG3cjGr9P\n9WQw7prvzabshQF8CYLfsjLXPMuMPuhYUjYohFSP91f1q/HS+HtT8Me8O1sn2Lg9dOGqu94OXCrw\nJKyXoXqYfDsAH8RjCgnlmpk3aMPk8SnXLRHyhwp0uUzblERXJAUkDZQdDA+UMWUoXEA+tX4bnlq/\nXbummcZd+l04qifwYIl5NlVH1eCqq3WpcfyU5lCUTVaqR/W7cIkfnqvWpZapVMHkqnWDpE7x1V3X\n0/gdlSJZb1fcu2cndglt34ToBvHh75Ij8JKdJmLBzGGs3sRQPf7EtKPqafyxxt0mePWYGj+3wTsQ\nUo9J408y7fLaFgpqU7u3+fGH5/WVn2pjofE3gDjqwpbkiQp+1/U2kDA3W+cFfDTc/vJ7VuF9ly1O\nbFfV1yTybr7gKaZU49eNu+YA4/qhK+O1YoB/Z1c9ELojDvgTiqLKAOBq4q6oQIXHk+u2Rc5nwaPE\n35+nepIFsxrMY4bGr9JwsFRPhONP115F9QiG6tkyUsWty9dFrhkZi9H4ySMrjb9WD6ke87HjNH5u\nUqgbHmem4Kd9S1E9UydUtHcl/XY6QgTHJyUFcDGu1QCC7R2T4PoTDIWN6hmtpaN6pORX+xJgjbve\nbyedV4//V+2elndfjazoScEfS/XYNH7WuKsLDqsfv3Fc7SMLxLt4ejla8m++YK4gricbu3PGXUcI\nXPeRV+D771pE2mTPPKiQlBFRacazDbrHBB2AJ3z95tiySaDfMYsfP0XAqxqCv1b3aDJFL9Bd3EKv\nHu93Wo2/VtdXZ/TT2PrkSEqbSNmnUuouNe7q7VLCcOJAVHPmBb+uqIwaZegbVz7s5ZITSZbnCIGS\nCNMgJGn8NqpnkFmtcvD2U9CP2ShG9dxJw89Gh9qMuwCsfvwKZUPjHzVWkq1Gbwr+HMZdk+pRu1vp\nHD8n+POnElbZORuhemj77nlqAznHaMIC2Gf2ZMycFG4CYQtHp0iKuFWa8ZwpCYK/iV49FHk1/pqh\ntSt/9KrrQgAYGlCCn9H4E+o3c7GraE4ONiqCCuS6q2eCpNpkyXE8jT+G41erh4mDUX8O7v51Y1ew\nEbMPME4FFX/loeDK0KtHCbaJg/Ecf6ORu9zWho1q/DbjLs3OGTHuOiH9s7ufnuPk/WeT87rGr751\nQfU0gDhBbNNe6X6gmnFXC+CKXlerR33x6QRB+1Q0LbNnH8gbpm1zM/NbEdFkOI8Sj+pJ5viHB0o4\nbu+Z+PCr9o6cV0bQJI2/mRw/Be/O6f2NezSzLyiO33OTDW0i1FahJsFgYrHMZZMNAVurR6k3BZtg\nojnwzRTewhC8dV8BUasvU8lQGv8kRvBzNFDd1furSTtRilEJ/nLJie47YHi3TBxI8OM34w8Cjj+d\nqOLyJNkUjiByO6HquAAu285ZnnHX+/dB86bikc+fgtcdvGtw3vTjHymonvyQUuKJtVtTaXkmXiAe\nDMq4q9LJ0uMmFE+fBqoT//6cY7y2KONuzq/gaRz8vSWj8ZuJvVQdicZd18WkwTL+75+PwrQJlcj5\nQONPpHpao/FzXj2hYE6vBNAJxHFEEDR06W1PBscDwZ9g3FXXUnc9LZUSucyu8YfHzbbqGr+naVfr\n9sjdgOphNf56ZIVSN1aC26vRXD0K6p6VkhMEqql+6Wn84XUTSa6e/3zDSyNtsQWXmV49933m1dib\nbD2pYMYbAPZ+N5rSnRMWBcuVoR2Dc+dUFJgjvL5Eo49Nqmekpq8kW42eEvyX3fEUTvrvWzTKw4RN\nEFAPhnoQgGGmZdavrZSEljRNwfbt1HGllanNSfJq/NKiiai2chw//euVS9YyJFmV/N3h8yLn1fOY\nvvwmWiX4S8zMmcarx4zopMLPEYLVMsdqJtXD160mEZpSgX4POmHbuHwabFirS6txt1wSnkso5fiN\nutTqwabxD5mC39WdFszEc5T+Uz7plZII7CXqUpPrnjRYDqiPUw/cJdIW237AJtUzfeIAppN9a8Nn\nYTT+BKonCa6Ump2HHldjw9Q9So6ICHdz7wr6N0gFkmEzpEbQU4Jf7f/65Lrt1jKmxv/dtx+Gs165\nJ57duENz0VPunLS4KUMqJYeleih04673g0aENkb18K6kQBg8Q6F+a3n7U/jxA6HWNmWogvceu7t2\nTgmb/XedgrnTJliX8s0M4NLvz9xQArcsW4tnN+6wXmdmHaUavwDvO640b26jHQr1DrRVhI3qSWH7\nMDV+wWj8GsdvcefkNP7RapjVU6Hu6gqB6cdPJyWl8ZcdJ3CNDTR+oT/38GAJF739cHzvnYdj58lR\nRSEL1cN5w23NoPGrd0LvufPkwUi5mivx5aseZetwpYxsiAR4zxxq/N4xaqA2c/UoFBp/DoRbEurH\nqWAwX+zMSYOYP2MCqnUZBKzU3HRePWVHsMZdmyANohDLDiYPlrF2y2jqnDocaK6QyDn/GSjCPDF6\nHWkEvyloKNRENnvKEG4770TsO3syW0erjLtmWmbAe653X3oXvvXn5dbrzIhk2k+EEKxBMQi0STDu\nKmFX1uoMz9Or0kyIY3VXu4h+gYrjEI4/3p1z0mD0mXZU6xHBWnf1lOEmHVXlNP6yCCYodaky7ipM\nGixj6nAFJ780qu0DwO/ue1Zz9VVjmvsWXI6m7cz2jjbbknon1E6TKf2zK8m+wvq5kiOCHP3q+ek7\nDvz4jQsLjj8HbIOQzrTmi3UEMH+6l+Z41QZPO3R9qqcUoXr0eiu++5p5X5vPdJDJzxGYO30CVm3Y\nDte1G/2S4Eq7xul1SP2Yug3tbKbbng2UTTE76wRDaFi9VzJq/IPldN0zjuOnuPCMQ3EKETgm1VNy\nnPAdCf7+ptudbZyqJtHMofpKKyxr4/gpzLZyHH/NlcEkGOmTY8qrhuf4TXdJ07hrgtP4K753ERA+\nn7n3LHd/E++85G/Bv+PcOdl894xXz2MvRFNeACH9Zcurn4TA6Mtx/I4I3ovqAvQZzJQNCh3l1SOE\nOEUI8ZgQYrkQ4jzmvBBCXOifXyqEOMw4XxJC3CeE+FOzGs7BNlvSARwR/I7A5CE9HW9delkvhYhP\nyxwKfv1+1LOA6uTqegFg3vRhrNqwoyGqBzEcv2TqDTZ/0Dj+ZD9+eq15PQAMG4PZNniyaPxPfuW1\nOHDu1OSC4AW/+Z0P220aTnnpLphBXFlN+qQkQl5WCD6+IuLVw7x/IehGKWEdVqqnluxPXq27sRz/\nmE85Wt05a3UMlJyIERfwFJXI9pUJKcO1OApH+fGLIC6Evhfa1uEUGjX9LnEBXNx3//U9Xspy6lX1\nm3tXsfcJNH7ymFlW3xKeddcR/FhTk7DqR4Ocxm9c1zEpG4QQJQDfAXAqgP0BnCGE2N8odiqAvf3/\n3g/gIuP8vwF4pOHWJiCtTzUFNT4FWpzraX+U6vn45UvxSz8PvkK5JNgEW9SzgE4cqj8LAcybPgGr\nNuzwN31J93wmPKHNn5OSo3psHH/yvWgHNTV+ldXSLHvMXjtpx7MYd1U6XxMXvOWQyDGO6jGzsF56\n5hEYKDuaV5KpXTkObwCnMI2XXJ/z7EP+vx0RGFTpREKvUrz4Z04zh5X+PLYc8iVHBAFWqq9HNX6P\nzuF4cU5JqCd4e2kpG4hXDxBuIwiEWy8CwPBAKVXiQEq3qCZwFAzXujtXvIh/f/U+2mb2AHD6IbtG\nyqrVgXrOfWZPyqSEKY1fQESUhLJG9XjH4oy7Ckn7UjcLaUTOkQCWSylXSCnHAPwCwOlGmdMBXCY9\n3AlgmhBiDgAIIeYBOA3AD5rYbhZpNH4TNG+2EgRKGFOvnhsfXYM7VqzXrh3w3dfMAaJp/ORc6OIm\nMG/6BGwdrWFHtd6gcTeO6jGNu95fOvhcmZLqEfy/AW9AU9i0mczGXea1cDQap/mZQWfqmacPhxq/\nyfFTJcAq+A03Tm6cKo8wBbWipPMTR9FNYKJqw7bq5U0/ejWpKmHz/655TDNsj1TrmDBQCoS0CVMA\nJVE9o5rGrwS/CNqqLvW2XvSOp6F5AD2nVGjctRvaKXaZMoQPnbR3ZFKYMlSJrKiocfdV++2M359z\nTCaqZ/WmEdRdZcDWzzmO7s4JpDTudorGD2AuAKrqrvKPpS1zAYBzAbR8KlNjw+yvcRo/9cFVHV2l\nbPD8+P26XTdiJCqXBKq1qDvnBhIFTM+ockIAU4jm2RjHbzsXjQ/gcsE3heoxBT+zsgCyu3Nyb2XP\nWVHfbc7IZ95Ltf+UA0KO38zUqr45YKddwp2S7FSPl5LXv68TulAmTfA7Me6J4X3tVE+JCn7S18/+\n6b3BvzePVDFUKVnzQpmCy6N67G2lE6t6Z4q39toqg3odovGnAaVE4jZb5wS/LVdRyYlmy6R2mjlT\nJ2B4IH4/YBO/XPwMLr3tST8thcHxi3AiDAQ/ea5w60W9zk4S/LkhhHgdgDVSyntSlH2/EGKxEGLx\n2rVrc91PCTBTk4vL80E7REj1qJQN4cCu1aPJnxwhcM1DL2ibjJvg3DmFMLnfpCezw6at8xy/91fn\n+NNq/DFUj6HJqc5sauJpInc/eOJeuPMTJ0XuqXDk7jNwxpF6bngucjei8ftVzZ8xjIvfcTiA6LKa\navzmrb/ydwd61xjpc7lXVyYavyNCG1KSUInT+E3qSt+AxwmoHvrOH3zW2wbxoec24aoHXsDsyUNW\njdZUPupuQs4rzbgb+vEDYUS6V2+40klrrKcavww0/ui1XNZYNfmYK6pKKUodVsnkzQU3poVA9P15\nfvyK4/eOpaN6OkfwPwuAjrR5/rE0ZY4B8AYhxEp4FNGJQoifcDeRUn5PSrlISrlo1qxZKZuvQwlp\nc5DEdTiO46c7cAWTiSsjxkmVIfLye3jjEW0TQNxNoXs65Dbuwt5RpIxq5kFmSEr1uHaN/3UHzQkG\ns6lhUpgCS3X4KNWTrPEPD5SD3P621zLP98IK78dQPTGRrqq8mV6AKgFm29VGJFXSR+hf7V5OSMQI\neFtTesf556H3N6G0ZEqfqHrpderdDjCODCrlxNkn7GkVbPTw5MGyp/Gn5PgrBsfv7UoX9nX1LrkJ\n+qOv3icykXMaP6e8cRsEqeczW15ynMgSUu0iRz3r0tggTNipHr0vDZQczfYD6GN0qOKkzgLQKNII\n/rsB7C2E2F0IMQDgrQCuMMpcAeBdvnfPywBsklI+L6X8hJRynpRygX/dn6WU72jmA1CE+dWNHCxx\nHD/Jmx0IflcGE4KSiTXXDYTJxe84DLd+/ATMnBQN9jCzH1KZqmtBdg06C+qui6N2nxEJYpKQkXqD\nTmd49XDLy8mDZXz7bYcFUblxVE/EuGvRZtJ49dBLbILfPM4Zd9988R3Wa0ybDr23jeN3HBFEagPh\nJMZNvN5+zdk1/hIzOSmaiNIn9BlUWWU/4fcm8K6bO21CDNUTHp8yoYJ6jMcYYKF6lHG3FrZUEKqH\nG4cfPGlvvP4g3fCqhPxhX7ge5//xYQC8xs9tqqSez2y6twrTj9WCYDPq8RapMoLPvV43wnOOCCUh\ngm+h7iuECJRQ1c4508JU5nOmTmD3B24FEgW/lLIG4AMAroXnmfMrKeVDQoizhBBn+cWuArACwHIA\n3wdwdovaG4sgv3pNf3lJXj3qowVh+G642XpA9ZABPmvyEOZNH8b1H3lFpL49Ihx0eF3A8UMf5LRD\ncvN+SgwAACAASURBVF4rcajVJSYMlDR/cQC+m6he1pqygRvghmZCqzdlx/CgyfH79zOpnhTGXSrQ\nBMvyRwUop/HHXeNYBX88x192nEDLVB4hNq0zHOyha6GesoGpn0idEif4qduho5dVk2rULZPSLsJq\n3KXvZ6jiRFI2mODcOQOqx3UhAw+2cHzZvlPFGJ9KyL9IEieWHIEpQ2V85nWh0I3X+KP2G7M/qUm8\nnpHqMUtQhSE45vCOAoPlkmf3ML4vAMyaPDhuHH8qM7uU8ip4wp0eu5j8WwI4J6GOmwHcnLmFGZCX\n6lEDjqN6pPQj9Oig87/j9IkDGCw7GoWx24xhPOBzq16bwuvCMHY71fPGQ+fiT0ufww2PrEnzyHj0\nhS3YlWgN9F7WyF3Du4Qb4GHkKaPxG/Wavtmhsc+u8U8f9jbtMHlaeh+bgmyOTc64a4LTps1Bphl3\n/WPThitByu5yKYzUVoKPMzCWiLATRONPYvRozqGyIzCKcFI135P2PCURTKrmu6BZPR3Bpzkw21Z2\nnCC/vw20zyshRvczUIJXIOT4bUJ1wFil2IK1lp7/Gu0Y9+7Llshlj+PXj1EPrSRvLgouFYp5WUmE\n7pxCE/wOthsN+eu5J+Depzfg8ntWaRvZtBI9FbmrxobJ3WY37qqVgHesyhgBFUzD5uQh/TeX3dPU\nEMwOmdXLhxtPXGAY58fvSj4fv7qUCjAFcwCbVAsXKAbowmLnyUP46t8dFPsstvdgPleFCMxvvuVg\n9hp6iW1wc+6ct3zsBNz1Sc/YXCk5qLmu5q7L7VWgVovqeSYNehw/fctcsg06Uap3qmi0p1/crr0/\n+spLJEeOmbCuRtyN4zYHMSd2ulLgwEXIBrYTsjoRRLs1V6UK5op8kMvLw7SbM+4GGn/Eq8eJ9CdF\nq7iS3xnNhsh4Za7zIndVMF3YmMGKE3mW+TOGcfohc4P3Ph7oKcGvNFdT409y51QdU3fnRJCWOZrm\nIfxw1EXt06ftF/E31vfs9e9pGHfTbJEYD8EKkqgfv4XqidP4A0For9eELQ/Juq2jWhluMOtUDw/O\ngyKubUIYXjA2usNBxLg7dUIFO/tZR8uOiHh32YSPup9AqPHT/Poc1VNyBN5+1G4AQu1ZKRZfu/Yx\nva2azSU8XjHeqdrlTV1jFfzaRKIEv10Iqcnvk69dGN6bbF2prqRUqlXjN8YnRwlx39W22uJQdqJa\nufLqkhmpHrMiIaKrCWrcpSvqwXKUlqVt7BiOv5tgM+7GBnA5YZh+jfho0+ycETqCVKc4utlTBvHe\n4/aIFfwBDI3fFmGbFra+atYrmOM24645EOiAShoctuAUinIpOhABXUDbbmMej9t60Suf7v3SYD6u\niJeiQ0Y2SInUY3D8k3zBT3fy4lB2BD5/+gFY8tmTgz7L+a+bzxBHw42RXFKmU4FZ3ykv3QWHzJ+G\nSYNlbNpRTdjQSKLsCLz/FXuG7VcBXGTSECLsBzaO36R6LrvjKfzj/+rGee5SzrBuKnG0beZ3pxp/\nYP/KwfFT5TG4nyOClSjtIoPlqMavoBTN8UBPCf6A489A9ThCaJ1Fzc6OE2bnTKPxq85tDlSuc5oD\n0GaETetTbKcujN8qqEjT+G0pG/zBarikcfWaCAR/jEBWNhTbtUB6qofSG1ydZnvjBl4o+KNllFfP\n9gTB7wjdkL5gJy//vLkReeQ6//5ThyvBt7Jli7S9J3M1Q91AzYhiCiEELn7n4fj9Ocdg7vQJXppy\nxhfe1gbvPNH4g9VtOInaVlqcYnbXky/G3guIUrpAOLlwXj1RjZ968fn3STHkuPgYPldPdBJKEvyd\n5MffNajnoHpo1F3dDfluZaBzpWRD+xUmGnlYJgyY6W0ZwQ/Tq8dcOiJoQxo4Dk8dcDnCvb/hMdcS\nmu8YbbBx5BynHkTuMu1Xm3CULVSPxvFHzkbLALpA4ameqDbGgRrduSLlgOP3BP/wQMkaROSQ97b/\nrlMiZdQrN90yFUqW/qRANUza1gjHXw/7tCPsz04Pz502AWu2jEbcb00FyqxLTQxbR2p4z4/uAqC/\n07RUDwduIjZtb/QeUa8eJ9I3atTwndBGvS3Gb/Bpmc2MAIA3kdsFv9M5Sdq6CaqDZ/Hjd4j2rRnC\nnDCAi/P3Vhg2ttgzNX5W8BNtQP3W61fLTs+9cy9mizmzvjQIeGchghiEax56ATc8vJop6/3lvB3o\nQH7TodEduegguvCMQ/Fff39gcG7+jOHgHNf/da8eu4Cm0PPoM+Vj7kFBBytXpuwIXPXAC7hlmRdZ\nPnGwzGv8DjXuCnbXK1onvb/ZRhvVY1McTI6fUj0lsrqNtJnUMXf6BEiJyCY2pi99xMjvTzp3rngR\nDz67GYDux8/tlAakE/wc+EnXu9d/nLyvfrwUdQ6uEgM25+psg/kKOQpN5foCdBkwWHask2+50Pjz\nQU2sUarH/phTJ1TCmZm4bSqjlJRMgixG41ffMs1GDubS0FxeUm37jYfOxWsPnJNQX8qVASm2+NOv\nCnYb2sK4kJl0k2n8A+x7AVAD6RsO3hVvOWK34JzaCIQaQG3PYnss87hO9UTLc3yvrd3cqkhBURkX\n3vg4AM++w3P81JDuHTvv1IX4+CmhIfTNi+bhkPnT8L7j9gjbpQVLeH9s/UnfH4He29BqyYYqQkRz\nygR1kMPzfPfgp1/Ud7KLaPwGN6/eDzV+0yRt5qSkQDn+uYxrsg2feu1+kWPq+d+8aD5WfvW0sK1M\nf6MGbNW0uLEUuOUaU4gjonVTQ7pO9ZRivcoKr54cCI27+suLE/zlUpiqlqai9YSzdyya0yX8t3K3\nCzS0FImoBIQ2yE0tzDQ0Ja0+HcFzxtFyekU7GJe8sI0eeI4/vkGK2+cE7DB5X4kcv//X5Jaj7pzx\nq4S4WAEKQakQTuM32jFxsMS6PHoTCKkUwFmv3BP/enxoCJ05aRC/P+cYzJseCjqOAqiUeE64JPhn\njvjx16Tmx2/1aCJ1qLiQVRHBH6/xq+9EczJR466N4qATSEodBgDwT8furgl3IH41Z96exiqod2jf\n0w44aeHOfiOj51iqh9H4d5o0gGnDFXAoO+Mn+NPlSe0ShJG76TV+IFyau6QjKKOvKzmqJ/zKKsBG\nCWnb0pxCCF1LS9obN0nQOiKd5DdrMfdRZdtA6CHtfjGw5bsBwpQWnkbE3Tf8dxDqX3JQrdfJcf0a\nTXDEtswvH2Nci5tszXQIwwP88KGG67SGcLNd1AZQEgJ1JhI1+LdGw+ltrJIIXNtkq84pzPJXgmu2\nhO63NM8M114g/A5UoXAEUPMfJlWgnVHnnKlDeOU+6XN32e5RZjh+ILQHqnNpnGoihlwneozSanRR\neO4pC60KlzOOVE9PCX6lmUcjd3lh/KET9wr+XRLC5/i93wHHz1A9mnHXH/xqpZB2z85yDD1hGlaT\nDE5ptSSzc8b1MaUlcsZOJf9sl4c2gOi5YUKNqclk2nAFJSGwftuY4a3i/R0oO9g2RrVIQ+AQm0Ia\n2stqXBP2JG1AdOUx2cLdU+0yqT3aZuykXao/VSxurzbjrimMa3Wdx7Yad8m3mjhYxoRKSaNsOOUp\nyvF7v02qRyVDi+vHX/uHg3Dw/Gn4l//TE/l+7vX745QD4qlOvU0WH3nLe1RKYtJmSFNpGnXjHE1E\np+CQPkCpnqkTKlpdFGcevQCvOyj9szaCnhL86iOaM2okMrDsYOn5J2vcouMI1KW+LHaE2qHK7sev\nNHx17zSC3zMGhb9N3tXk15NkWVqOP8syWj1xsDcoo/HbtCNb5C6ga/xaPYygpIKfq18hpKPSPaPV\nwOkIrS4TZuCNbWORIxbMwLLV3j6vSc2hGmqZEfycNwqQgeqhfvyO/dnNyXTm5AE882Jo3B2sRCNf\nTUGuvpOWvlyEipMtcAnwOHmvHfrxOFdsDrZFRdmiFKhxy3nWqf79pw8ei12mDuFLV/KbCJo2O0BX\nQtLSN/vuMhn7YnKqso2ipzh+9REVhaE0NFNbcYTAYLmkDxhHRKke39jyl8fXRq5XUJ4O6t6pqB4I\nTTMxKQR1Kj3VE89Ncu1OguluGJeywYQqymlf6pjN0KgJfl9sRt6PcRltY5pnjEvqFrhhMiJbp6H4\njUU+9dr98NGT982l8dP3qt4/l1XSLOsY/ZiC+tQ7lnfOtdPMPDtYLkXeiE3jH61SqifkrdO4Sprt\nS5vDP2wTX952bzVuI55ipJ49Zk1kM/EqcLl6zPigTkNPCf6X7zkTQDholLZg5v5gBxJH9Tge1RMX\nLj+oNH6fXrIZd2kOH0foHdzU0szUCsnG3XQCPSkfPIVr8LK0DWnTSHPLZ2o75aqhx9Jq/DRuIJXG\nH1OIbrZuglJ+Q5USy/Hvs8tkTdtLag9VFDSNnwhLPiiNp3oiHH9dd1iwZ+fUf0cFf3SCsnH8NMBN\nIAyUyppFFcju6mnNAFpy2P5fDTh+/bjuZJCg6CC6sisT424Hyv3eEvw/ePciTPEFLA0QGijpwpgd\nSL7Gb1I9HOjxIYPqsWn8550auvKZ6XHNkPWA44/R+N94yK4448jd/Pr4dkbbnUHjh70N6ScahqIg\nNgNu83EuItVc7pu3t9VpQ6zGH/POqXfXUKUUuKZq1ytN3+HbaoLSRXoqDe9vpcT73uvunGQ1Ztyw\nVnc1jj+vxj9QDo27qo+bk4xa/W4j7sFCIBXHT8tTZKV6bEqJbQIdNaiekOKk/dD/a7mnENF2U+eF\n8fLUyYKeEvxAqHVQDcXUGri+X/Y5fjpI4sLbFdQgUJqDTfBXDM8TXeO3ZLeMEUKOI7Crv1OV6zZf\nqwipBse/X3guKaJYxJSjqxk2clfTtDwkafy0zjSLkbgVS2DcZUYGHcBDZScwVHPXKy0xaZKcSCYP\n2q90jt/eTvMeZrurZt4cK8ev/1b7/yqlZJD0a6XsmBPoYLmEgZKDTTvCPaeFyKbxm+3jMnXGX88f\nLzu83h4IfuO+celGTHDKxtbRWsjxd6DK33OCX3WcoUop0N4jHL9F4NRdGXTa9Bq/yk/ie/VYQuxN\nDUJz47P4qYc8MdeGcNVAOcTpFh9hWm86hF4lXpvtwoW/0jJhKe3J8n45CsMUGJwhzWtXdLMNDpw2\nF9Slnpeph7raDVVKkd3WvPrU++LbasLcvUyBap62iT/4NzltCs5qjebjT5eWGQj7tTo8WHaCd6LO\ncXVNHCxpHliU4+d2Sktqh7kaToI182WJN5LbqB7d604/aYpx7pWO1V0tMLTT0HOCv0wEv0KU42co\nCCHwxyXP4zUX/CUokya83fTisXVUektzIxbzmtA4Ggq0aBvCZ6X96ktv8tIj7M2keUhSuGgbVZ3s\nRiwpJxCuWGCIRRjtSCOAOW8Vs90RYU3KpdH46buvGIKCy02kQDn+wUqJ9eoxV2lZqB4KyvFzGqVN\n449QPa5B9US0dPV99fpNg/ogQ/VwGjz3POFeAckfx+zr2TV+/h5lR7Bcjc2rJykNCAVVEs45YU98\n7DX74ri9ZoZ+/IXG33qoDzhYdoKZ2cahU5QcoWVPjA12IRUMRfhnEYkmBAAznxS3I5T5DKHw4AR/\n6BlENX5HAFf/23G4/Kyj2Ws4vPGQXfFPx+zO7tfK5eNPmzWUA9WIdS8WPXQeCMdpxEfaMhHYhKQJ\nzitLoWwIbgqanmGo4rDGXXOVltQezjMI0P34bf3VvCd3P9O4a2KuHzkcFXym4I9SPVw/MPMSCRH6\n8acz7uq/s3L8scF5zLcIBb/3m0uel9Rqj+P3Sk0ZquCcE/byMq0qqqcDNf6e8uMHQtpksFIK1mRR\nzwBGgzKFrxOXCz38ty17ogkzaINyiFGOXx33/mHjykONn25uLbDfnGg2SHWO4sC5U/H0i9txwVsP\nBQD8avEzwUBQgjgIjmI08Sx4zUtnY8bEAU0gslQPY9w1v43Nn5xzq+NAhcPkoQo2kzz5cZG7dABX\nSo7Gz5ttS+uRZXNXdAMBxKds4N6TV94U/HquHhM7Tx7EirXbou6MfrskPMFGNe8JMYLf1Pi9VZhX\njlMsTDTq1WNTSipMkjYg9MaLy+AanAsmB3vuLq4tnejO2XOCP+T4iXHXDzcP/Znt1yk4QmD2FN53\nV3PnTNBIVn71NKxcty3IShncj9QRXZHoA4XnwsOJwZUk0jZG8pmn/vjBY7Xf1NZgUj1Z/Pg5/O87\nFwEAfnHX00H7k9wUbTy5leM36pw6oaIZGoPrSftNDZVLUaFABX9JiFiqB/ofK2xCg068SQFcNtdO\nwI/cJfnmTdj62KB/3HW9DVc8qscfWwO6JxtFROOHwDkn7oUd1TredtRukfJxzwWki4vRrrdq/JaU\nDSpy19KngBQUqeX4gfOmYvJQGR88ce/4CtqAnqN6Ao6fCGTHERqXyw4kRvCrLfdMxHH8HBbMnMik\nbaUaP6/RVhh+nbahzGgUWXz1TVCNTBKqwbsfaXsOjV+B0lj8dwj/rc5Gk9iZdYZ103O3fOx4azvU\nuzP3SC7FRO5S464QvGGWtoX+zQqXUA5cFZo7p6DH9cIqLXOSUTdC9ZS93zXXu5YqOPvN8aJL739m\nY6S+KNXj0R+fP/2A1FHtFFmVDNv75jZiAYD7nt7gXRe8T9XvaeK4+DbQb0F1+ylDFTxw/mvwsj12\nSmr2uKMHNX7lfkYCTpRRy3c2YDV+RqucbRH8tKjJESt8522H6aHrkXaGlUSzT3p/BwJtO3q9I8Jn\ndV2d6rEhacVJVx5myoY4l8EsoKtmrh7a/lDj18vYVgCOQfXEuW06jgBcGWyLqBCn8dMNeRwhWH7e\npHjy0GIACaBLo/Fr2qleVuXq4dpxxILpVs8xKvgGSg6GB8LI3WP2nIn/vWUFm1DMpL+yPn3eiVIh\njuPn3sGP73iKvS834dg8xtL5knUWelDwe3+HyqXQrdARPGdHwGmVsyxh2mk0/tMSki3R20VTEiiN\n3641mhy/gk0bf+muU/Dq/XeObdPCXSZjwkAJy9dsDSR/ELlL/fgbMO4q0PQKVHxwFIb5TOYjUg8a\nM4voHZ84UYskVSg7AmPwOH4KLimdgqnxcxusRA3z0XrSIIyctvjxW4S9bovxvHroZuKqqyx6yXT8\n6l9ejvddttirw7gJ7ZMXnnEo9pw1CXc8sR6AZ5D+/Okvxc6To4qRSX9lnfga7Vs2/3tuIxYK22ZI\nadCE4TDu6EHB73XYoYqjeYrQDsFpmqbdyXGE1bAUJ7TTQk+sxRt3Vd2scU8IjeOnxzlc+aHjEtt0\nyZlH4I9LnsMHf36fpnGa7U0aFHErC2pn4W0XjMZv8XoyUXL0we0IYM5UfmMPJSAjHL96XkZMfPTk\nffDx3zwQtGGYi9wNInbtE0gaUO8SbuVi25Se9u1KyQmoHpvyYKN66Orv+H139ssj+Puuly9g281R\nPVnQoMJvVXzKDp+yQcFGH3KIdG9yzw6047LoWY7fNLq+bPeQZ+O55WRf/zTn8sDcmcjk+G1UT7ix\ntIw1XGdBsLuW/zsw7mr3zn8TGkUaaMW0bu0z8MLTvH+4p6xOi8R+w6CfGH78SuNnRsZbjtgN33nb\nYUE5JRxn+FGu9J42w3RacFTPmw8Pt7m0afz03xVHBFSP1TXZMkFxSk8o+O3PFDXuZkOjY8tu3I1P\n4BeZMNiJkr+2GzX+nhP81Kvnsn8+En932FxMGizj4ncejlft52kuPGeq/1Yf85HPnxIpmzZJWVrY\nqB5u9yvaBjVZUW+TRttmUgIVYyIAkpfjcWM3sEUYOcy5aF91m6jh3aiTmUyS2kFz+FNw2Ui167QU\n0AJX/9tx+PVZLydt0wVpGjn2s/cehf956yHaMWrcNQ3GQJTS4Y5Xyk6Qllkd3n/XKZg9ZRD/8Zp9\ntedN8uOniHsk0205qyCnxU3bVxpkdecM72soXxnuKbJe0AHoOaqHRu4e/pIZOPwlM8hZXRujMPdt\nVh2WZtscKDuaga9ZiKZs8P7G5eoRROOvp6B60iLk3fUwe1t0bVaEm9nTe4XgNmJxhMAfzjkmeE/m\nIA2EpGncTaHxmyXCXDs81GtQbdhvzhSs3xruVGUK6TQc99F7zWTuE3qXBJMJ1fI1rx5+Eig7Dqp1\nqa2EJg2W8bdPvipSPm4D+6Askp/JdFtupDvmoVF3stjlkoL71vnfMNXK2ZAVeQ347UTPCX4auRs9\np5ehMH2SOc15eKCErSNREm+g5OCoPWZEjqeF2cFV87io2aB9Igy/p0K5WVRP4MevJhdtVRFfRxqO\nHxBsPbT9NNHZwfOnhceNZ5zjJ6t733F7pBb8wbs1XpjadvCZDTsi13jtj0bBatsgGpN1c9w5o/1A\n326RCv7w3wMlgZ/7cRO2HE42YzYndINJIqbdu7VR8F/wlkPweotTRdmJbh0JeBPhS3YaxrH+5BuX\nZ8oGOjbS7IvRCeg5wa9cKIfYBFreX044jtV0zw+uzGDZwXamQyz70qnZG0oQFfyKhlCZMRmqh9Aa\n1KvH1D7u/MRJmQZfcC/Dq4cudBpZVYQDS6+HbhYCUgbgYywoJg9VgjQZDz+3OXI9B5vXzfH7evu7\nLmF81AFdIAd1MXw7Z7/IAy+9uF535P6Wm1Ce3moQt0xQcRugxIk2tVG7QlZHR6o0ZBX8bzx0rvUc\nx/E7ArjwjENw4sLZkfJZBb96zm4x7vac4L/nKS8g4/DdpkfOxWlh5j69tMxuM4bx9IvbtZzkzYRN\nsMW5c9JgJZoHyKxrl6l8LIINNqpHcxltYFkhLYZY8/5AOImZxWIFOg0Ai9P4Le/2JTtNxOTBMv5h\n0TzussCQzKXmpm3lcvXnARVY2mqIeU8KB82bil2nTsCKdVutZczjqTT+lO3V609xkQV5OH4TB86d\nigee3eS1hRwvOwLLv/xa+4XMrdUhU6sfrdnjdToVPSf4VZj+ogVR6iXOKyFC9ZAyvz37aDy1fhvO\nvXxp0z16OEQ5/mgZLy+Nr403k+pRgt8w7mpUTyMcv0sMsaxbbbTuqB9/+PutR8zXzqVtG+XyLz1z\nEbaNhoP3gf98jfW6fWd7Uasn7BvGRHDbJ6r4AC6GIAsqJYdMgPyzmc98xQe8VByv/9atpAxfv2MZ\nE5U4jT9Brf3Smw7Ap373YGybrXXTNuR0lab46fuOwrM+bZfW8A9kW6ltH6u3RCFsJXpO8P/pg8di\n62iNj7yzaDcAJ/jDf8+cNIiZkwYxWC6Nq+tWXKZIR8DC8TfWQCWMVY1coqlGNP6kjW442sTm1SME\n8NW/P0g7l7ZldKctbqlvw767TMaSz50c8V4J768Evze06G5UeWDz6qFohOoRlrpZbZsxxnN4+1Ev\nCQV/QlkTtC9nTdDGYcpQBVPm+N+KrpgSWpY0jg6YOwUPPuvRijsanNzbgZ5z55w/Y9iendL/m9e4\nO1B2mu7KyUFp8PEcP6F6mujVE2r8es4SM/VzHFTY/iAT1RymliBt1dof/tu2QgvoKEYCpdUw4wzn\nSeCE/gdO2AtASPsojX9rg4Kf+vHbtXb+xKAm+PlrQwO6cW2JsZEltJWtv4HumCaNcxZo1SVp/PZ5\nDwDwpw8ehx+95wgAvsbfePPGFT2n8cchbgBFOf5omYEyn+Gv2ajX9ahZ3qsnFHLNStLmXa9rdUF0\nsBstY8PZx++FSsmJ0DCAzvFzbqGaf7o6ZkZVx3yDtLIii7tlGnz05H3w3uN2x1Tfe6ZpGn8pfE+2\n9257BKox2zl+sHWrJG0cshgwGxkvL9lpOLlQBjhM37IhTbNVsFpcTq5ORc9p/HEIPibzVauGIz/X\nYQfLfN6UZkPlhIn346fG3SZSPYY2rZK01TP48U8YKOFDJ+3NcrRB5G7wPx18kjaT47ffO7XGH8QE\npCqeCCEEpg2HEbxK8G9pUPBXiBuira026o1q/FmD7uLcOZPJHnJN6pI6jtp9Br725oNzXs0jzdjY\ny9+5ztxsnkINBW4jnm5BXwn+pCUzV5ZiwLJvZ7MR7FHq2IUT9eNvKtVjiWSlk0tjXj3e3zRCzOaF\n1UyNv1XfU1E9zeH449tqOz5Qjnob2WDWwdEsud5Uztf7d4fNxZQh+/7RFP/+6n2wIMXqgD6i7Z19\n7DX74qfvPQqHkrgRG7gkfUmG705BKsEvhDhFCPGYEGK5EOI85rwQQlzon18qhDjMPz5fCHGTEOJh\nIcRDQoh/a/YDZEEcx2+CFfxkM4o8uOpDx+FbZxyaWC7Q+GPdOXk//kZXJOb1oR2hOasKGiBDq+EC\no9QH43ZHsyGt33icx1QzMMXX+Bv16ik7YaCblae3UT3a/grx94nznDLRSqqHi+dIwodO2hs3f+yE\nxHLcatJEpeTgmL1mopTCo4gm6es2r57EpxNClAB8B8CpAPYHcIYQYn+j2KkA9vb/ez+Ai/zjNQAf\nlVLuD+BlAM5hrh03ZMmYyH3IRqme/XedgtcfvGtiOXOPUiWkZk4axD8dszsAXXA2U+OPaNfKndNi\ngM2KM47YDSct3Bnve8UewfPtu8tktqzN8Bgn3NM+flJOnkZhpnvOC6cBjZ/uSWHb/i+JRtLLZn9X\nWa9QPvLNSP1tIkuV/IrHp0H935zG3y1Io/EfCWC5lHKFlHIMwC8AnG6UOR3AZdLDnQCmCSHmSCmf\nl1LeCwBSyi0AHgFgD69rMSqWXC8cuI43c9IgpllC35uJkOPXt8WjzRYi3C/gmD3DzKMN5zM3qR61\nqmgS1TN1uIJLzjwCMycNYnigjJ+97yhc8u4j2LKBG6PFnZO9JmXbwg1XUhXPDNsGPXmQZIi2Uj2p\nNP7slFcWMiPvxNoKwc8sJu33T9HuuOjmTkeals8F8Az5vQpR4Z1YRgixAMChAP6WtZHNQjlmWz0T\n3ED48Kv3wU/++ahmNyuCKMfPt3vnKUO49eMn4LxTFwbHGhVkNo6/rm1C0rxBefSeMwNPGEDX5tVt\nstAQaVsWl/m0GVBtPG7vaAK2NNhn9iRSl/c3KQjLBNX4k7jnVKvgoK7kssE1GV9vHqonLbioUvsp\nIAAAD0lJREFUcBvSTDxcHV1C8Y+PcVcIMQnAbwB8WEq52VLm/UKIxUKIxWvXrm1JO7htBBXOPn5P\nTUvjvvukwbJ1H95mwubVIyAi4eLzpg9rG7k0TvWYv6N2hFbgkjOPwGkHztH2wBUWbTRNDp4kZDH0\n58XS80+2rmaS8Ot/ORrXfFjfPMcehGWhepitNKPX+nWneBFnn7AngDB6OQ2yvl+6AU2zoa2YE8qa\nGXPpMTaSvss8+dOQVM8CoA7Z8/xjqcoIISrwhP5PpZS/td1ESvk9AN8DgEWLFrVEysTlvjn3lIX4\n0El7Y+FnrvHKjIPf5qVnLtL84xVsfvy2XC0UTef4AztC9JP8yyv3aOheFEcsmIEjjDQbdqqncY4/\nLiq6WUjrlcJh6nBFWwkBdiFq33wkvXGXq+HH/3QkZk8J3RpPXDg7SIaXHvnebyu+i8gg+VkZ8ZqF\nqJSc2GRw3YI0gv9uAHsLIXaHJ8zfCuBtRpkrAHxACPELAEcB2CSlfF54b/oSAI9IKb/RxHbnQrCb\nlHXJLNh/twq2VAFWjT+NN1KDa7ioB43S+PVy2QVAfthWIRzSfrbxmNibDftkbysf/ttq3I253yv3\nmZWyZXbkHUbt5vg54+7U4QrOf8NLtWOXvHsRpg1XcNOjrWEpWoVEwS+lrAkhPgDgWgAlAJdKKR8S\nQpzln78YwFUAXgtgOYDtAN7jX34MgHcCeEAIcb9/7JNSyqua+xjpoBKO2QZQmlS344HAq6dkCv7k\na5uv8Uc5/vEC3WCFIu4RsyZpG48JvlGoFmb16qFIonpahbzvtxXjr9kcPwCctJ+nvCnB3yUUf7qU\nDb6gvso4djH5twRwDnPdrcgfvNd0cLtJUdBv3U6BEPHqCTbwTr628SRtvHG31Rw/B2XPMB8pTltP\n+/SlDIb+TkFWP36KJONuq75u1tervnkrVmR6yu74sllXHMrbb8pQd7h4dkcrm4Qg74zVp5lo/G2U\nCGoXqGl+MjDqx501ECcrzOvjOP5Ww9zmUKEZxt2k/DediIY0fsvna/UGInm9ehrtx2xbMkxDWQX/\nmUcvwGClhDOY/FSdiL4S/BVmc3Ib2ikPPn7KQhw0b2rgCsjt5mRrnmg4SZv+e/eZEwEAZ71yz8Yq\nzgE3EPz68fiUDek+XOAqm6tl7UEa25QNSQFcrUJeb5dWe/UkGd7LGY1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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b9f6110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(eigvec[:, 0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "source": [
    "### Performing K-NN on sectors.\n",
    "1. Project the daily change sequences of all stocks on the top $d$ eigenvectors to get a vector in $R^d$.\n",
    "2. Find the $k$ closest neighbors to the unknown stock, and find the plurality label (the plurality label is the one that appears the largest number of times amond the $k$ neighbors. As there are more than 2 labels, it is possible that the plurality label is not the majority.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    },
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "476\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Ticker</th>\n",
       "      <th>Name</th>\n",
       "      <th>Sector</th>\n",
       "      <th>SECTOR_ID</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>APC</td>\n",
       "      <td>Anadarko Petroleum|Anadarko Petroleum Corp</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>APA</td>\n",
       "      <td>Apache Corporation</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>60</th>\n",
       "      <td>BHI</td>\n",
       "      <td>Baker Hughes Inc</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>COG</td>\n",
       "      <td>Cabot Oil &amp; Gas</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>101</th>\n",
       "      <td>CHK</td>\n",
       "      <td>Chesapeake Energy</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>102</th>\n",
       "      <td>CVX</td>\n",
       "      <td>Chevron Corp.</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>107</th>\n",
       "      <td>XEC</td>\n",
       "      <td>Cimarex Energy</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>124</th>\n",
       "      <td>CXO</td>\n",
       "      <td>Concho Resources</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>125</th>\n",
       "      <td>COP</td>\n",
       "      <td>ConocoPhillips</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>DVN</td>\n",
       "      <td>Devon Energy</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>172</th>\n",
       "      <td>EOG</td>\n",
       "      <td>EOG Resources</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>173</th>\n",
       "      <td>EQT</td>\n",
       "      <td>EQT Corporation</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>185</th>\n",
       "      <td>XOM</td>\n",
       "      <td>Exxon Mobil Corp.</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>219</th>\n",
       "      <td>HAL</td>\n",
       "      <td>Halliburton Co.</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>227</th>\n",
       "      <td>HP</td>\n",
       "      <td>Helmerich &amp; Payne</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>230</th>\n",
       "      <td>HES</td>\n",
       "      <td>Hess Corporation</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>268</th>\n",
       "      <td>KMI</td>\n",
       "      <td>Kinder Morgan</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>292</th>\n",
       "      <td>MRO</td>\n",
       "      <td>Marathon Oil Corp.</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>293</th>\n",
       "      <td>MPC</td>\n",
       "      <td>Marathon Petroleum</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>322</th>\n",
       "      <td>MUR</td>\n",
       "      <td>Murphy Oil</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>325</th>\n",
       "      <td>NOV</td>\n",
       "      <td>National Oilwell Varco Inc.</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>330</th>\n",
       "      <td>NFX</td>\n",
       "      <td>Newfield Exploration Co</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>338</th>\n",
       "      <td>NBL</td>\n",
       "      <td>Noble Energy Inc</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>347</th>\n",
       "      <td>OXY</td>\n",
       "      <td>Occidental Petroleum</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>349</th>\n",
       "      <td>OKE</td>\n",
       "      <td>ONEOK</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>364</th>\n",
       "      <td>PSX</td>\n",
       "      <td>Phillips 66</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>366</th>\n",
       "      <td>PXD</td>\n",
       "      <td>Pioneer Natural Resources</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>386</th>\n",
       "      <td>RRC</td>\n",
       "      <td>Range Resources|Range Resources Corp.</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>405</th>\n",
       "      <td>SLB</td>\n",
       "      <td>Schlumberger Ltd.</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>433</th>\n",
       "      <td>FTI</td>\n",
       "      <td>TechnipFMC</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>435</th>\n",
       "      <td>TSO</td>\n",
       "      <td>Tesoro Petroleum Co.</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>446</th>\n",
       "      <td>RIG</td>\n",
       "      <td>Transocean</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>466</th>\n",
       "      <td>VLO</td>\n",
       "      <td>Valero Energy</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>491</th>\n",
       "      <td>WMB</td>\n",
       "      <td>Williams Cos.</td>\n",
       "      <td>Energy</td>\n",
       "      <td>EN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Ticker                                        Name  Sector SECTOR_ID\n",
       "41     APC  Anadarko Petroleum|Anadarko Petroleum Corp  Energy        EN\n",
       "45     APA                          Apache Corporation  Energy        EN\n",
       "60     BHI                            Baker Hughes Inc  Energy        EN\n",
       "83     COG                             Cabot Oil & Gas  Energy        EN\n",
       "101    CHK                           Chesapeake Energy  Energy        EN\n",
       "102    CVX                               Chevron Corp.  Energy        EN\n",
       "107    XEC                              Cimarex Energy  Energy        EN\n",
       "124    CXO                            Concho Resources  Energy        EN\n",
       "125    COP                              ConocoPhillips  Energy        EN\n",
       "145    DVN                                Devon Energy  Energy        EN\n",
       "172    EOG                               EOG Resources  Energy        EN\n",
       "173    EQT                             EQT Corporation  Energy        EN\n",
       "185    XOM                           Exxon Mobil Corp.  Energy        EN\n",
       "219    HAL                             Halliburton Co.  Energy        EN\n",
       "227     HP                           Helmerich & Payne  Energy        EN\n",
       "230    HES                            Hess Corporation  Energy        EN\n",
       "268    KMI                               Kinder Morgan  Energy        EN\n",
       "292    MRO                          Marathon Oil Corp.  Energy        EN\n",
       "293    MPC                          Marathon Petroleum  Energy        EN\n",
       "322    MUR                                  Murphy Oil  Energy        EN\n",
       "325    NOV                 National Oilwell Varco Inc.  Energy        EN\n",
       "330    NFX                     Newfield Exploration Co  Energy        EN\n",
       "338    NBL                            Noble Energy Inc  Energy        EN\n",
       "347    OXY                        Occidental Petroleum  Energy        EN\n",
       "349    OKE                                       ONEOK  Energy        EN\n",
       "364    PSX                                 Phillips 66  Energy        EN\n",
       "366    PXD                   Pioneer Natural Resources  Energy        EN\n",
       "386    RRC       Range Resources|Range Resources Corp.  Energy        EN\n",
       "405    SLB                           Schlumberger Ltd.  Energy        EN\n",
       "433    FTI                                  TechnipFMC  Energy        EN\n",
       "435    TSO                        Tesoro Petroleum Co.  Energy        EN\n",
       "446    RIG                                  Transocean  Energy        EN\n",
       "466    VLO                               Valero Energy  Energy        EN\n",
       "491    WMB                               Williams Cos.  Energy        EN"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pickle\n",
    "D=pickle.load(open('Tickers.pkl','rb'))\n",
    "TickerInfo=D['TickerInfo']\n",
    "TickerInfo.head()\n",
    "\n",
    "tickersToIgnore = ['NSC', 'ABC', 'ROK','MAS', 'APD']\n",
    "print len(tickers)    \n",
    "\n",
    "# list all companies in the Energy sector\n",
    "TickerInfo[TickerInfo['SECTOR_ID']=='EN']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true,
    "run_control": {
     "frozen": false,
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    }
   },
   "outputs": [],
   "source": [
    "def calc_sectors(tickers):\n",
    "    sectors = []\n",
    "    for t in tickers:\n",
    "        try: \n",
    "            sectors.append(TickerInfo[TickerInfo['Ticker'] == t]['SECTOR_ID'].item())\n",
    "        except:\n",
    "            sectors.append(t)\n",
    "    return sectors\n",
    "sectors = calc_sectors(tickers)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true,
    "run_control": {
     "frozen": false,
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    }
   },
   "outputs": [],
   "source": [
    "# Create a dictionary that maps each ticker to the corresponding basis vector\n",
    "Tick_rep={}\n",
    "for i in range(len(tickers)):\n",
    "    Tick_rep[tickers[i]]=eigvec[i,:] * eigval[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "476"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(sectors)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "source": [
    "`find_closest` takes a query ticker, d and k as input and returns a sorted list of tickers, their sectors, and their distance from the query ticker.\n",
    "\n",
    "For example:\n",
    "```python \n",
    "find_closest('HAL') \n",
    "```\n",
    "should return \n",
    "\n",
    "```\n",
    "[('HAL', 'EN', 0.0),\n",
    " ('SLB', 'EN', 0.0054474558470919412),\n",
    " ('APA', 'EN', 0.0095375619627422019),\n",
    " ('HP', 'EN', 0.0095667138343728166),\n",
    " ('BHI', 'EN', 0.01280991458941858),\n",
    " ('RDC', 'RDC', 0.012865326588403255),\n",
    " ('NBL', 'EN', 0.01654306862676054),\n",
    " ('APC', 'EN', 0.019824473381124783),\n",
    " ('COP', 'EN', 0.020783142716246431),\n",
    " ('ETR', 'UTIL', 0.021988972018102161),\n",
    " ('DO', 'DO', 0.022236500402408065)]\n",
    "```\n",
    "\n",
    "Similarly for bank of america:\n",
    "```python\n",
    "find_closest('BAC')\n",
    "```\n",
    "\n",
    "```\n",
    "[('BAC', 'FIN', 0.0),\n",
    " ('AIG', 'FIN', 0.1166233109896993),\n",
    " ('STI', 'FIN', 0.1390683030203888),\n",
    " ('FITB', 'FIN', 0.1479186255365789),\n",
    " ('C', 'FIN', 0.1710861632442088),\n",
    " ('KEY', 'FIN', 0.18822247596796085),\n",
    " ('RF', 'FIN', 0.19362473601644403),\n",
    " ('HBAN', 'FIN', 0.19807819614960992),\n",
    " ('WFC', 'FIN', 0.2322604278432217),\n",
    " ('PNC', 'FIN', 0.32297570683407145)]\n",
    " ```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "run_control": {
     "frozen": false,
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('BAC', 'FIN', 0.0),\n",
       " ('AIG', 'FIN', 0.1166233109896993),\n",
       " ('STI', 'FIN', 0.1390683030203888),\n",
       " ('FITB', 'FIN', 0.1479186255365789),\n",
       " ('C', 'FIN', 0.1710861632442088),\n",
       " ('KEY', 'FIN', 0.18822247596796085),\n",
       " ('RF', 'FIN', 0.19362473601644403),\n",
       " ('HBAN', 'FIN', 0.19807819614960992),\n",
       " ('WFC', 'FIN', 0.2322604278432217),\n",
       " ('PNC', 'FIN', 0.32297570683407145)]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d=20\n",
    "k=5\n",
    "T='HAL'\n",
    "\n",
    "l2squared = lambda x: (np.sum(np.square(x)))\n",
    "        \n",
    "def find_closest(T,d=10,k=10):\n",
    "\n",
    "    index = tickers.index(T)\n",
    "    \n",
    "    U_basis = np.mat([eigvec[:,i] for i in range(d)], dtype=float64).T\n",
    "    U_prime = np.mat([eigvec[:,i] for i in range(d)], dtype=float64)\n",
    "    U = Rows.map(lambda (r): np.dot(r, U_basis))\n",
    "\n",
    "    X = U.map(lambda r: np.matmul(r, U_prime))\\\n",
    "         .map(lambda r: np.square(r - r[:,index].item()))\\\n",
    "         .sum()\n",
    "\n",
    "    dist = []\n",
    "    for i in range(len(tickers)):\n",
    "        tick = tickers[i]\n",
    "        dist.append((tick, sectors[i], X[:,i].item()))\n",
    "    dist.sort(key=lambda (x,y,z): z)\n",
    "    return dist[:k]\n",
    "\n",
    "find_closest('BAC')"
   ]
  }
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