meth_assignment_demo_final.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# COS 424 Homework 2 Demo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np \n",
    "from sklearn import tree\n",
    "from IPython.display import Image  \n",
    "from sklearn.externals.six import StringIO\n",
    "#import pydot\n",
    "import pandas\n",
    "import os\n",
    "# Enter your directory here\n",
    "os.chdir('/Users/brian_jo/Desktop/Project/COS424_2016/methylation_imputation')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data import: writing a parser\n",
    "\n",
    "One approach to importing the dataset can be to write a custom parser that reads in the data in your preferred format: (we will discuss an alternate approach later) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# utility functions to parse chromosome files\n",
    "\n",
    "# parse training file\n",
    "def parseTrainFile(filename='data/intersected_final_chr1_cutoff_20_train.bed'):\n",
    "    # open train file\n",
    "    flTestTissue = open(filename, 'r')\n",
    "    lines = flTestTissue.readlines()\n",
    "    flTestTissue.close()\n",
    "\n",
    "    # example of a line\n",
    "    # chr1\t10562\t10564\t+\t0.82051283\t0.962963\t0.9305556\t0.79591835\t0.9315069\t0.92941177\t0.975\t0.9569892\t0.8125\tnan\t0.8518519\t0.8518519\t0.95454544\t0.8684211\t0.9661017\t0.8630137\t0.8679245\t0.9230769\t0.8372093\t0.9326923\t0.9425287\t0.975\t0.93670887\t0.9491525\t0.9425287\tnan\tnan\t0.8695652\t0.87931037\t0.88235295\t0.92941177\t0.9705882\t0.90625\t0\n",
    "\n",
    "    # parse lines\n",
    "    lineIndex = 0\n",
    "    dLocPredVals = {}\n",
    "    for line in lines:\n",
    "\titems = line[:-1].split('\t')\n",
    "\tchrom = items[0]\n",
    "\tlocStart = int(items[1])\n",
    "\tlocEnd = int(items[2])\n",
    "\tsign = items[3]\n",
    "\tmethVals = [float(a) for a in items[4:]]\t\n",
    "\tx = np.all(np.isnan(methVals))\n",
    "\t#print x\n",
    "        locPair = (lineIndex, locStart, locEnd)\n",
    "\tdLocPredVals[locPair] = np.array(methVals) \n",
    "\tlineIndex +=1\n",
    "    return dLocPredVals;\n",
    "\n",
    "    \n",
    "# parse predictor file    \n",
    "def parsePartialFullFile(filename='data/intersected_final_chr1_cutoff_20_sample_partial.bed'):\n",
    "    # open partial file\n",
    "    flTestTissue = open(filename, 'r')\n",
    "    lines = flTestTissue.readlines()\n",
    "    flTestTissue.close()\n",
    "\n",
    "    # chr1\t100508463\t100508465\t+\t      nan\t0\n",
    "    # chr1\t546983\t           546985\t+\t0.8518519\t1\n",
    "    \n",
    "    # parse lines\n",
    "    lPairs = []\n",
    "    trainingIndices = []\n",
    "    testingIndices = []\n",
    "    lineIndex = 0\n",
    "    for line in lines:\n",
    "\t#print line\n",
    "\titems = line[:-1].split('\t')\n",
    "\tchrom = items[0]\n",
    "\tlocStart = int(items[1])\n",
    "\tlocEnd = int(items[2])\n",
    "\tstrand = items[3]\n",
    "\tmethValStr = items[4]\n",
    "\t#print items[4]\n",
    "\tif methValStr == 'nan':\n",
    "\t    methVal = -2.0;\n",
    "\t    testingIndices.append(lineIndex)\n",
    "\telse:\n",
    "\t    methVal = float(methValStr)\n",
    "\t    trainingIndices.append(lineIndex)\n",
    "\tlocPair = [lineIndex, locStart, locEnd,methVal]\n",
    "\tlPairs.append(locPair)\n",
    "\tlineIndex +=1;\n",
    "    lPairs = np.array(lPairs)\n",
    "    return lPairs,testingIndices, trainingIndices\n",
    "\t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of testing indices 372028\n",
      "Number of training indices 7523\n"
     ]
    }
   ],
   "source": [
    "# parse partial file\n",
    "lPairs,testingIndices, trainingIndices = parsePartialFullFile()\n",
    "print \"Number of testing indices \" + str(len(testingIndices))\n",
    "print \"Number of training indices \" + str(len(trainingIndices))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "379551\n",
      "379551\n"
     ]
    }
   ],
   "source": [
    "# parse training file\n",
    "dLocPredVals = parseTrainFile()\n",
    "print len(dLocPredVals.values())\n",
    "print len(testingIndices) + len(trainingIndices)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(379551, 34)\n",
      "[ 0.9148936   0.9268293   0.96153843  0.8867925   0.921875    0.88709676\n",
      "  0.89830506  0.9701493   0.94545454  0.8913044   0.93939394  0.8965517\n",
      "  0.9047619   0.6875      0.9189189   0.94871795  0.9230769   0.94285715\n",
      "  0.884058    0.93939394  0.87096775  0.9183673   0.8947368   0.82608694\n",
      "  0.84444445  0.68795432  0.60750366  0.8         0.72911892  0.94736844\n",
      "  0.9322034   0.8636364   0.9574468   0.        ]\n",
      "[  1.08400000e+03   5.34241000e+05   5.34243000e+05   6.88888900e-01]\n"
     ]
    }
   ],
   "source": [
    "# replace nan-entries of the traininig data arrays by averages\n",
    "allStacked = np.array(dLocPredVals.values())\n",
    "colMeans = np.nanmean(allStacked,axis=0)\n",
    "\n",
    "#http://stackoverflow.com/questions/18689235/numpy-array-replace-nan-values-with-average-of-columns\n",
    "#Find indicies that you need to replace\n",
    "inds = np.where(np.isnan(allStacked))\n",
    "#Place column means in the indices. Align the arrays using take\n",
    "allStacked[inds]=np.take(colMeans,inds[1])\n",
    "\n",
    "# lets see how the data loots line\n",
    "print allStacked.shape\n",
    "print allStacked[testingIndices[0],:]\n",
    "print lPairs[trainingIndices[0]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(7523, 34)\n",
      "(7523,)\n"
     ]
    }
   ],
   "source": [
    "# extract training indices\n",
    "X = np.take(allStacked,trainingIndices,axis=0)\n",
    "Y = np.take(lPairs,trainingIndices,axis=0)\n",
    "Y = Y[:,3] # take the leftmost column\n",
    "print X.shape\n",
    "print Y.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing out a simple method: Decision Tree?\n",
    "\n",
    "Will creating a decision tree be a good approach for this problem? In this approach, we train a regression decision tree as our model. This model splits the data into a tree and fits a linear repression model at each leaf. The main motivation is that this model can simultaneously select features and tune linear regression models at each leaf, i.e. can explain non-linear relationships between input and output variables. Finally, it provides an explanation of the model through a visual tree."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# train a regression decision tree classifier on the first 10 training entries\n",
    "# http://scikit-learn.org/stable/modules/generated/sklearn.tree.DecisionTreeRegressor.html\n",
    "\n",
    "clf = tree.DecisionTreeRegressor(max_depth=10)\n",
    "clf = clf.fit(X[0:1000], Y[0:1000])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# fit decision tree to all of data\n",
    "clf_all = clf.fit(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# draw decision tree - Keep in mind that you need to have pydot installed!\n",
    "from IPython.display import Image  \n",
    "dot_data = StringIO()  \n",
    "tree.export_graphviz(clf, out_file=dot_data)\n",
    "\n",
    "graph = pydot.graph_from_dot_data(dot_data.getvalue())  \n",
    "Image(graph.create_png())  \n",
    "#graph.write_pdf(\"dd.pdf\") "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(379551, 4)\n"
     ]
    }
   ],
   "source": [
    "# extract testing data\n",
    "# compare to existing values from the full file\n",
    "lPairs_all,_,_ = parsePartialFullFile('data/intersected_final_chr1_cutoff_20_sample_full.bed')\n",
    "print lPairs_all.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of indices for which values exist: 375934\n",
      "Number of testing indices: 372028\n",
      "Number of testing indices: 368411\n"
     ]
    }
   ],
   "source": [
    "# some of the methylation values are not known, so we take care to filter those out\n",
    "# extract indices where values exist\n",
    "values_exist = np.where(lPairs_all[:,3]!=-2.0)[0]\n",
    "# find the trsting indices for which values exist\n",
    "final_testing_indices = np.intersect1d(values_exist, testingIndices)\n",
    "print \"Number of indices for which values exist: \" + str(len(values_exist))\n",
    "print \"Number of testing indices: \" + str(len(testingIndices))\n",
    "print \"Number of testing indices: \" + str(len(final_testing_indices)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Known values shape: (368411,)\n",
      "Test feature vectors shape: (368411, 34)\n",
      "Predictions: \n",
      "[ 0.74566285  0.74566285  0.74566285 ...,  0.78181282  0.74566285\n",
      "  0.74566285]\n",
      "Ground Truth: \n",
      "[ 0.9137931   0.9318182   0.91752577 ...,  0.89772725  0.87341774\n",
      "  0.96103895]\n"
     ]
    }
   ],
   "source": [
    "# extract the known values for testing\n",
    "Y_test1 = np.take(lPairs_all,final_testing_indices,axis=0)[:,3]\n",
    "print \"Known values shape: \" + str(Y_test1.shape)\n",
    "\n",
    "# extract testing data features for prediction\n",
    "X_test1 = np.take(allStacked,final_testing_indices,axis=0)\n",
    "print \"Test feature vectors shape: \" + str(X_test1.shape)\n",
    "\n",
    "predictions = clf.predict(X_test1)\n",
    "\n",
    "# print predictions\n",
    "print \"Predictions: \"\n",
    "print predictions\n",
    "print \"Ground Truth: \"\n",
    "print Y_test1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                      y   R-squared:                       0.000\n",
      "Model:                            OLS   Adj. R-squared:                 -0.000\n",
      "Method:                 Least Squares   F-statistic:                    0.9086\n",
      "Date:                Thu, 03 Mar 2016   Prob (F-statistic):              0.340\n",
      "Time:                        18:18:16   Log-Likelihood:             4.8586e+05\n",
      "No. Observations:              368411   AIC:                        -9.717e+05\n",
      "Df Residuals:                  368409   BIC:                        -9.717e+05\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
      "------------------------------------------------------------------------------\n",
      "const          0.7421      0.001   1435.228      0.000         0.741     0.743\n",
      "x1             0.0006      0.001      0.953      0.340        -0.001     0.002\n",
      "==============================================================================\n",
      "Omnibus:                   444230.972   Durbin-Watson:                   2.004\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):         50802239.399\n",
      "Skew:                          -6.626   Prob(JB):                         0.00\n",
      "Kurtosis:                      58.981   Cond. No.                         9.79\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    },
    {
     "data": {
      "image/png": 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CzQOKUC0zZGVV2O9KVIP6HJiFGp2idt3V68pM2udkVOMcC7RHtcVyoz8NNZ+f\nDryGapsxVMNbSNOmLTjuuCO5//47iMfjdY7NXQ2Bl+POiR290NkmaNSojXiOEiJpaf3l4YcfXn9/\n6NA/SiLRU+AjgX9JIlEgX375pYiIvPLKK9Khwz7SunU3ufvuP0kymZTKykq56abbpGXLPaRLl/3l\niSeekAMOOFKKijrLaaedK1267CMpKQMFPpFo9AYpKmovJSUlG9D12WefSY8eB0tBQZFEo40F/iPw\npoRCDeS0086Sk07qL6FQvqgTwKESCuVJ8+ad5fHHH5dwOFXUqWKCrb5fEPhQEonuctttd8lLL42Q\n9u33ltatu8t99/15A8eIyZMnSyJRIDBc4C1bhd9sfDrDVt+7CxwmMFZgmK20HxcYI4nEIXLBBZes\nL+/551+QRKKllTVSQqFC01QeW8/3cPgGGTTosg34UFFRIUOG3CwtW+4uu+9+oPzpT3+ScDhXoIVp\nM7cJfCxwlKgzxd2iml+OXRtrdGaIeuyNFnWm6GEayLvWvv1NC/qb5dnPtJm/iTqvHGT/syQlJUPU\nY6+tQEf7HCJwvWkjOaKa1aniOTx85NN2DjOaH7Q25Is605wl8JqoZpht9BSKOlrcbf+zLe1YgUdN\nA8qwtqQJzBF4ytqetLqPsP8fC9xr7Y37+LGfwDGiGl2OqHbWxHjcQOB0gVEC3e1+rvX3PsaDFkZX\nN/td5Ms7RuABqy9T1DlEBEqsbScYHdkC3SUt7SQ5+uhTttbjvVOAeqKh1Tfs6HGxTZCZ2cAmAZ14\nIpFr5I9//OP6+02bthfPC08EbpGrr75O3n//fYnHG4tO0p9IIrG73HvvA3L99UMlkdhXYLxNTpkC\nVwpMkpSUkyQczhfPO1EkK6unfPjhh/Liiy/KY489JlOmTJHp06eb1+CzNlG+4Kv/X+bOv5uogHnL\nJpg/C7wr4XCBTbxJgWsEbvXlnSgZGY0lJSXP8n0siUQXeeCBh6vx5LrrbpRQ6EbL856oaciVUWlt\nShNYatf+LHCuL808icdz1pfXrVtvgRG++8+ImtS6+ybdv0n//udUo+PTTz+V3r0PldTUzsbPZ6xt\ndwtMEvWw6yDwiMCnoqasRgJvinoc9rC0twpc6qt/hJVzq7UnZunO86VZKCqUnhL1dpwnKjhOtvT5\nooLmY6MhKiooXhIVNgUCN/jK+8loi4p6GLrr/UQFQL5dby9wk6jgOdjufWXlvWB0L/LlP11UoB5o\n9FaKuvnKgvC7AAAgAElEQVQPsvulosK31Jenj6iAc/+dt2VDgfdFPUT3FV0QvWh1nyYqiCeKjudG\nAr+3frjfeLK36Fh83fqrm+hi5za739xXpxjf+tvvy0SFYKlEIqmb7X27K4BAoO2U2NHjYpvgzDMv\nkLS04wWmC7wt8XihfPHFF+vvFxd3FV3FOoF3hdx00y1y1ll/sInDPZyjpX37vaVJk3YCk33XbxUY\nYr9n2qToJpdKSU9vJx079pSMjAMkHj9P4vECGThwoKSm/sHSnCLwd195fxN1dx7tu/aQwED7/YTo\n6voqgYts8nHpPhR1r97N0icFPpDOnfevxpOhQ2+VSMQJgGGiLt9OCK8Rb7U9y649IjrRu3qmSmZm\nAxERGTHiZTt/9U/f/b+KanoZoiv/cZJIFMvrr7++nob77vuzJBLNRLWWDgJ/EHhbVEiJ0dNPVACc\nL6oNpAjc56tnnE2qtwqc7eNfIyu3o30nBO6Q6hrVdFHh0U9U4xsjKrDuEyi2Nru0HxjPC0QFVw/7\n5IouCKaJCpALRRcCC3x5DxbvfNYo0b2qQ0Q1xnPt+gmiE76Iamk/+fIfLaoBNba8g6zOXIE3BKaK\nChO3+EiKLlAO9pUxUVSguSMCjQVm+O5fZTyaa/9fMZrLRTWubgIHiAq9bPEsHpOs79zeYAOBP4o+\nB3+ytr1pac+2tiyVaDRVysvLt88EsB1AINB2SuzocbFNUFJSImefPUjy84ukZcuu8uabb1a7/9RT\nz0giUSTwmITDN0tWVkOZOXOmDBp0mYRCt/ge+hdl990PlFat9rAJzl2/UMClWyKhUIbE430EnpTU\n1GOkYcNmEo/3Fk9gfChZWY0lkTjJ/o+1ifRP9ikQNQ296qvjJtFzRCJwp02AJ4i3cX+TqHmqmagZ\ncY3oaniiwIuy1159q7X5559/luzsRhIO32gT1B42WT0p3iq8nagweULgHAmHMyQavULg75JItJe7\n7rpPRESysxuKmhYLbeK91/K/L+FwXPLzi6RJk3by+ONPiIge4F62bJmZ9WaLJ0RbiAr2tsart2wC\nL7c039oke42PLyNtQu0iKoAvExXG0wVWCawVFVadRTWhhqLnxZ4wHt9t5VxpfM8TPXfYSlTQe32v\nWs8loqbJk0UFx+viOVlcJHoO63Jrwz8EBhsf/2JpuhhvevnGw2hRYXOaqPY1SHRB8oSo1pkwPn0t\n6rThnEYaWP84x5Pdrc6zrbx0gWtFBXNzUeFyv9XZSlQ7c+37naX/yv6vENU0l4gK+FPF07RfFBWY\na0UFayvRcXeB/W5uZbmD7o+JCsx0gXslkdhTLr74qu3z8G8nUE8EWn3bBLS++d/Dm2++yfDhr5GT\nk8E111xK69atmTZtGj167M/q1eehrtcfEQ6H6dBhD2bMmE1p6TVEIr8g8ndisYNZt+5QEolnGDDg\nIIqLmzFy5DuMHz+eUCifdeuOAv5itS0nEmlKXl4BK1YcRUVFR2KxO6moWIs6HawBhEgki6qq64Fl\n6Kb/YEKhDCKRPwMRKiv7EYmsIZH4gObNmzFlyizgeeBoq2d/YB0pKT/y2mv/5qijjqrW5hkzZnD3\n3X/miSceRc9XPQTMIBT6ns6dhUaNClm4cBmLFy+kVasirr76Cj788GMWLFjK7ru3IRaLkZ2dzeDB\nFyFSYjx6GnV7b0QisYbTTuvBk08+wpw5c3j22Wd54onnmTt3hm2ix6msXOqjqBehUDYiH6FODCvR\nc1WvA60BIRRKJRxOo6pK3cyj0btp06YZJSWrWbZsJWvXliNSCbQAfkadFJoC0wmFmiKyAHVwiKOu\n6negj/G/0HNtJ6DODCWoM8NlqJv8vUB/1GHjRvQ4wsfoGazp6Dm7I+36cKO9CXreriN6NHQdOu/F\ngPOAR63dq1Bnj5jlB3WyWIO60U+0enJQp5I0ux9Cz5KVWJua2fhZZXUdgAYFWmVlpqHOHtcA36FO\nHdejRwjetXtR48NadCw1s744xNKCOnr0sDrSUAeUkOU9AT3W8IOldc4nMaCccDjB739/Mv/85xNb\nNYzcjkbgFLJzYkcvdLYbKioqpLy8XEpLS2uNJOHw448/yuGHHy3RaDvRPZdySU09U/r0OVYuuOBi\nueqqa+X777+X22+/QwYMGCxPPfX0+vIKCpqL7sGMEzXxfC0akWGwQHuJxxvI8cefKGef/Qfp3v0A\nCYe7iUZoaCVwvaSmNpUjjzxBLrvsann55Zdl0KDLpFu3fSUebymh0KUSChVLKJQusdggCYVOFc+s\nVmH1JgQukLS0A2S//fqsD6sloqG3SktLpby8XHr0OEgiketFNaEJEo8XyldffSVLliyRxo1bSzx+\nqsRil0giUSCjRo2SESNelni8gUQil0sicZSkpTWQaHSI5Z8okC2hUKYMHnyhVFVVyZQpUyQrq6GE\nQu1M+6gUmC2hUBPTaioE3pZoNEsuuGCg5OQ0MS2kv6hJLk/gM4FbpGHDNvLDDz/IlVcOkfPPv0ge\nfPBBSSQKJBIZLN5eVaao2TEpus+TME1KRPdKM0X3vvqIRu5YIKoJxkU1QBcJ4yFR82G6aASS35uW\nc6eoVn6Y5T9ZVOPqIKrlXWgaTAOjJ0/gYvt9qWkzWaYNufGwl6hTzuHiRe/4o6g2d5moya9A1LT3\ngLVtst3/TtT0l23tm2DXU0U1uhWiDhqH2/Xm4jl8FNj/y8VzfnGhtPqLmlXjopaA6aLmxxOtzT1t\nvCWt3jxRLXNvy3OawMuie5RZoscIvpN4vKFMnjx5mz/j2xPUEw2tvmFHj4ttjsrKSrnggkskEomJ\ni32XmVm4gRnSj/POu0jUW82ZZyZL8+adNlpPeXm5hEJh8cxKztkhbBPLQnvgoxIKxWwycN5hv9iE\nc4Ncd90N68tcsGCBxGIZogLPnQny759daZNaWNS01lt0Qi8WiEh2dmMZN26cPPPMc5KW5sxWUQmH\nU6SwsJWEQmEJhTIkFIpKTk5jycjIFd1/8hwt2rXrKdForngxCJ+UlJQ9bcIKGU0awzAczpYpU6bI\nccedLqHQfaJCfbavvJslN7eRhEJhKSxsISeffJpNps1FTVQu3ePWV00FIhKJpMhuu3WTSMTFRuwr\nnlnyNKvf75hwiE2s7n9T0T2vQyx/QuA6UaeTdKPhKPG8C//qyztEVAh/be13Z7/CVlZb8RxXWosX\n9zBsfexiNLYST3DkiTqBDBI1Tbq63P6UiAr93Sx/0pfmWFGnkaTVHbcy062e4b6074tnBoxaurh4\ne29rRYVtW/HiP8ZETcEuLmPU7rmxPFjUgzJm7XFn7nJEBV7C+ODOwf0i0F/+8pe/bLVnemcA9USg\nBZFCdjE88MDDDB/+JVVVLYE7gXJWr/4/Tj11QJ3hl4qLm5CaOh43ZkOhz2jatPZzZQ6xWIwWLTqg\nJjiAQ4jFMgiHTwLeBkag53cWIrIcDY10j6VtDMRJSxtPs2ZePQsXLqSiQoDbUVPOa1b+EkvRCTVz\nnYGa3I4EjgceACpYufIxDj30OAYOvJKysv7AwcAKksl5rFmTRzyeh8jfESlnxYp/smZNBRpiyaEd\nM2bMorLyHPTM0efATZSXT0PNqeXA/6Hhj+aQTN5Dnz7HsmjRMkTaGW0uLnaSeHwCd9xxCxUV5Tzy\nyH28+ur7qJk0Bz3f5NABPafVDlhGVdUifvwxRlXVDag5VoC7LG131Pz2vf1fg5rX1tn//6ImuiLU\nJHe+pbnL6gyjpsppwDDrlw4+WjqiYaAuAM62cr+zPosA1xofnkcjl0TRd+tWov2bAkwBfkIj0KVY\nGRVW13CjJ4m+WL6H1RtFz5SF0MgrWB98i8YdH4qaCfdDw1VdgZo1x/lo/ww13bZDz5GNR8+o5dn9\nBGr6bG1l/4SaOtug58iK0Sgha9CxdS7wMvrijjLUNKqmZJiBhu16Fw2Z9Tsrvw/wJc888wIBAmxr\n7OiFzjZHnz79RDfOc6qt4rOyTpARI0bUmmfVqlXSvn0Pycg4UDIyTpTs7Eby9ddfb7Kub7/9Vho0\nKJb09BaSkpIpl156pcTjDUTdwPvVsnre3VbLQyUUypfu3Q+UsrKy9eV99dVXEgo1luraxx6ibuTf\nizoI3GMr5OaiG/1dq6VPS+skKSn9RD3WPvLdu1MikaIaZe8lqulNEpgvKSlHSCiUIp4m6ZwJGtTI\n18vaIxKPN5QbbxwqicSeolpSgcBRkpraTfbcs/f69v3hD5eY9vGZrfLbiAa1nSPqrt5B1AHE1fGK\naSciaiLsJWrCKxY12zYUNRM2EdXI0u1eod1rYNpDpqhTzmJRZ4pTrMzHRF387xD1Rpwt6k3oAvam\nijpM1PQS9POhk6hW5f5/KGo69KdxDhVNRU187vxYA1E3/0ttTLwhqgWdaG043fo7V9SU586IvSGq\nQVVYm9ob/YfamDhc1KlDRM2dzUUdRZaJnhVLl+pHWO4Q1WQTUl1TnWh8iIg6wrjrA0THsb+NGaKB\nnDvb7waSm1u8NR7nnQYEGlqAHYGiokZEIt+jK+YfgMnAq1RUTK4znmBmZiaTJn3M8OFX8fe/n8zU\nqZPo0qW2185VR6dOnZgz5wcmT36fhQtn89BD9/Pcc4/RoMFZRCLvEwr53+IzAY2b1wJ4gMceu4PP\nPvuAyspKRowYwW233cbIkSOJRFajsftANYWfUU3hEHRF3gDVcCagcfam48URXExV1S9EozPQgLUT\n19cejc5AZAlefMDlaOSIi1AnkxZ06bKKvDx/viq8OI0uvt8KVLtpBPxEVdVarrvuai666DAyMweT\nni6ccEKcESNu5ZNP3iU1NRWA5s0boQ4OZaiDxiqgJ9AW1YDmUP2tR+NRrUiAVwmFJqDBiQ9HNdIn\ngHeMp8vQyBXvorEILwH2RLWoCsLho1HnhymWT9BYjA1Rjasxqr11R50gFqAao+NDEnWIqUS1boDV\neLEOF9i1QnTMudjgH6DOOEWoZnu41XmklbUG1e6KgHMszzLgRVTb7W3pf7C+qESDWOcYPQXWjp/R\nqWoyqnE7rS0FdeL4k/XXZZbOOXQI6uATs89nePP2BONLpv3G6p9oPPjJrv3b6HgB733ITWjefOMW\njgABtgZ29EJnmyKZTMq8efOkYcOWkpKyx/rVIuwjkUiWvPXWW5JMJqt9XD73u6qqqtqnpkNJZWXl\nBmX487rf8+bNk6ZN20pGxpESjR4pkCFpaSdIWlpDefTRxyWZTMrs2bOloKCZePHzukgo1MSih5xs\nq/qWpmX0FDhGotEsadSoWNLT+0p6+skSi2VbG08VKJT8/CI54IDDJC2tvWkDfSU1tY80bdpWjjrq\nBNH9nFMEGkkolCWpqadJOJwv0WgbycrqLVlZDSUtLVei0VME2ks43MTeG5ZldTQWyJdE4iyJxxvJ\nww8/sj66inu3WkVFhVRUVEhlZeX63ytWrJBGjYqtLSeaZlNkGkiBqHNCQkKhQ0XPVyUEeko43Fag\ngaSnHyIpKTmiezyF4t7N9fLLL8u8efOkSZM2kpbWV9QRJG7fCQmFYvLRRx/Z0YMM0Wgae9vvDqJH\nI9JFNbI29t1cQqFu4jmLdBHVslKMfycZH5qKalkFdq2BqHYYt2vuvWWpVk5ba1d3UQ06Jqphpdn9\nYksbF9W68u1eTHTPLtPK3N3oP9HakGHpjjGtKiF69OAwce9aUweRhKhTSMLq6ybe3mg3K2dv0f3F\nTF9Zmcandvbb0ZUvXpxJ1950CYcTMnXq1O312G8XUE80tPrmpml9U78wZswY+vc/lwULfiYUiiFS\ngdrzV+O5QLfHi0Beia5ek4TDqSSTSXTfJRXdW0jBG7/CwQf3pWfPLtx336OohhEhFAKRELriLSMU\nykBfF5OwvKXoXkOJrzwhEolQVNSamTOn2vUqq/dEdPU7FcgmEinh4osHEgqFKC4uZs2aNUQiER55\n5Bnmzv3R8gi6PxPBuU2rFrTaR0c5unJOWnvC6N7a74DB6L5Mb1S7iaDaz1Bf+jIrq8TKXmc0p63n\nj6Zxbc1ENY+ofVx+R0vYaC2x61VWbwn6GpJVdj9kNGSims8MS+f6JdVoj9t3uvE8HS/WYZrRm2J1\nx63vI3Y/ZuVV4GmP4iszhhdpP+n7n+qrqxQvNmKqpS3x8SPDygrbtTKr3x0tcGM0bPcy7FpqjWvl\nlifs41cqXvxFt7e1xldnqtElNWh+xPJUoq+wwe7F8GJLxvFc8lPsfsLHazf2KvH6PB0oJzs7g2XL\nFm/R29R3VgRu+zsndvRCZ6vDe+nl9aLeWt+LviCyl63+J4p6dx1uq1x3/wRbYRdb3lLRSBLpol5u\n3UT3dxaJF1G8j+i+yizRvZGE6L5PI9F9izJRj71CUXfvtyyNix7/s6hXYhfRiAp7Cnxuq+ZCgX9Z\nGf8USJdGjYrlpZdekpUrV4qISPv2PY22EtG9qDyjPUd0H2yNqBt8P6P1WGvrVFGNYrioF9qeovtW\nx4p63rnDuCLqIp4lutrva/S/YXQ9IKoxrhSN7NFdPA3rbWvTQONxtuih3FJR9/QGohpAhmj4pzK7\nnhCNrlFqbcmzPpludOeL7vGsEPVcLLAy7rI8b4tqCU9ZmfdbW9eI7gllC3xhY+A80T2ls0X3Cb8R\n3YN7R9QLsqfonqXj8XjLf7T1ZabR+7bVfY61y42p40U1r1KjJ9/ocZ6V14lqptNFx8fh4iLV655k\nqWhElA7Gh/FGx2Br02TRfcdWoscW7hbvpZxN7NoR1gczjeZs488LVtbtopqX86RsYu1YK7q3li9e\nfMZp9t/1/4OiWub5os9aupX9mN0fIe4tAv36nbSDZ4atC+qJhlbfsKPHxVbHyJEjJTW1kz1Yd0l1\n9+tBvv8X17j/vU2MMfHHZVRz3J5S3aHjPdGJdKzv2j/s4R4jas7xb5K3E4164VzKW9nk01jUdJVp\nk1Ce/Y/bxOQvo8hoyxNIk1tuuUV0g94fz2+Q1eV37V9kZTunC3f9Hl+6l0Qn4u9EHQXcWaYq0cm8\n0Np2sagg9tPVRFQwLxYVpNnixRRMWDkvik6sLk/S2pwn1WMBPi3V30BdZW28XVQoZ4kXkeIUUSeH\nI6wsv2v7IaJOJO6/Oz5wr7XHXV8uXlQO72iBRoGpEjUPRkQnfnd/oJV3i3338t27SvTMmvv/g6jA\nP0xUECREFwXNRYXIYKkeau1La9vhNXiVkOoxKdcaXc6s11BUQKaJF+y42NKmGO9cAOIc0XGeJ7qA\nWWv8WyK6CEqR6s4vV4i6638uKhD71uj/ppYvyz65Vqa731mgl2RmFuzoqWGrgnoi0OqPzlxPsXDh\nQtatW4CaTr7x3SlBHRrcOHQb2g7fot2bhpr5XJrvUBOXv6zJqLnna9+1L1HTUC7qXOGiNSxGnQTy\nUXPRNNTccw/wd9T54WPUrHO//f8UddL41spYirrqv2K/3+K22+5DzUCOrqSlLzRaXDu/QTfp82q0\nYZKldb/L7P7v0VeUNLZ8/2d8yLc6ZhgvQR1KVlmbv7E6nPv3Oh/fXHSNcss3EzVfibXTvQzUubi7\nl5r+iPbJ62g/HG7pFxgN91jedagjBPZ7Gt6brH+xNDlG56QavEnx8UV89DozbmYNHn9lZRUaDbPx\njgjE8BwmXPmVqOPOArQPq9AxMc/K+aZG+rYojx2vZli90/DMvo7GOHqMYwHa5xmoA8iNqHPMYrtW\nir4Q9BLU8WaJ5XFvm3ZvFD/IeOTGneNHyOp3/ejv/5XWlkzUBHkQ+hJR0OfhF2AOOTlZBAiwrbGj\nFzpbHY8++qhEImeJmny6iGoLZ4pqPY1FN7nPsVWpe3HhmeI5jCRsNX2uraJzxQtKe4yoc0bc0qWL\nBuTtbqvibFGNpZGoCWaQeC9UPF90w9+ly6ux0t1H9HUy7n8PUc3oAiuzSY30LcQ7xNvE0ibseqaV\nN8DadZhvNX+WqJNFhq3Qj7N8LprE70QPaBeI5yzRTlRzdNpAW9HAwoWiGsgAa5M7vF0gaibrY7Sc\nbbx3QYcLjXZ3kLlIVANxEUO6WrocUc0y13j8tq/9I0S1EPdizBzRA70uYG5HUW3MmTbPs3bkih4M\ndrwpNBobWdsy7V6OqLnRvTTzXPudIeqEcbrRf4LRdqHVlS6qtZ0t7tU0akJ1dD9nZbvD1oWiY/D3\nxrej7VqhqGaVJ95rcHoYHTmiFoF8qT4mjhc9KuG0SzcOX7L7x0l1zfUtKyPdaHcHpDNEn5H9xNOK\nC4yHre1znvFrb+v7FIHnRQMTZ4tzFtJ2ZlQLDl4fQKChBdgeaNWqFWlpX6Bd9Sl6MPY1dON8MZ5W\n9hF60Ho86hYdRQ/5PoGuVp/Bc244HBhiZbyLrlTfBQYCLxMO/4QekP0AdYdugsYTnIquoB+x9NPR\nFW2ZfZyGtwg9GFxh/xegWo6gLu2Lqe4qPw1dgfc3Wl8HnkO1jSOsbXHUhboEeM/4sL+1dQZ6AHuy\n8egWdBP/AdSdfSbq7h0mGo2QlTWfVq2cI8AiVEt8CXUp72L1JIFjjZ+DrY5SdMX/vPFsLfAPa8tB\nqFv8vsB1qEayyvjSwPLnWZtLUS3oHWu/AG+i2loJ7qWaeuRgNOpQE0U1oBXA3sb/YrTP21pZBcaX\n3dHDyo+hGtSz1hdzUI2rHNV85qMHjs+33+moy/1N6OHkPGvjaOA/dn0fK9vRPRIdTx8YbcuN3+NQ\nR6WGdm+o9eMZ1t/LUU3pBevnfkarG89LUS2tpeWL4TmXvGl1t0IPmrv5+C3j20HoGHkUzwHkX6gG\n94DRdTgav3IgqpUOx4tD2gV9kephwM3ogfH/WnlVQAlz5rixG2BnQn3zarHFxq6NJUuWcM45FzNh\nwhe0aNGCvLxM3n77E3QC+w7PE8yZbMrRSWwmOlmK3QfvTb0peN5iYt8hPC+0mK+s69EH+Us0AO4P\n6MT0i69usfLC9rvKyuuCmrEidq8K7/yO88hLRSeOFFTgzMV7E/Gr1o4/ooKwAi/ygzsPJVZW3NcW\n52nnPA4FeBA4DjU7jvXR4zwPw3heoc7bzrWpAs/b0d9WfPkrrA340juPT8ejSjxvQ3x5XJlFls+d\nn4tYW7qjwnQ2cCEwxmh13nguv3srswvMWwE0x/N0dULGeSg6/oHnaenyuTa2Nnrc2HDXQ3hejK2s\nD1yw5LDVl4WOHRdxpCVqBjwL9T79El0kzcLzNBQ8T80Uo8d5V1ZQ3Ss0bOma2++56GIrYrwKGX/O\nsHKfxvP0jBof1lH9OViH57XqvD7duHDPRbbVEQKWsMcerZg0aRL1BfXFyzHQ0HYyiAh9+hzHO+80\nZOHCkUyYcALvvfcO+qA3QFfgLdGDqp+jK98YqqHche4NhdHV+THoBBMBLrX0l6EP/FhUk4mhK//X\n0ZV0CzR6+S/oan0weiC1O95D/ySqCe2DCrDP0UPRRahQiKFaw2BUCL8HvIFqN7cDfzUazkf3is5H\nV/QZ6Ep4iKV5z8oJoxrE/UZLO3SPoz866d9laTLRfbkPUUF5OTqJNjMa70Qn6IjR/ikaRd5Nosdb\nulvtfxjVwD5FtcFeVt6+6NsDMlDNbhS66k+xtqejK/837NoDRvd+VvdwdJ9xL0v/M/AHVHsaYnWX\n2OdQVCP7HN0zSkE1hU9RTSTF+NASDeVUZPSvsPb+1/hyvvHqevvfE9VSxltb0tDQY0lUm+5jtBWi\nB9M/QxcIUVRzm44KjTHomHH9/KS1IQ0dTw+hmt0bqGA9GdXQMy1dAh2jV6Jj9//Q0GrNUA2qEA3d\ndZLRei/e8YoOVv7PqIb/Bqq5ZqNa9iuo1vYWuoeahR7hCKH7lZ8Bp6BCLo6Om8Osn7oYbZcCu6HP\nwltGZwWTJ3/FlClTCBBgW2IHW6J/O3755RdJSyuQ6p6JeaL7UXuIvmG6sVT3gttH1FNRRL0Xu4l6\nQa4WPVTaosbeREfxwgM1tr2F1qKHVf9uewWHS3UPvXWih34v8F1bIF4IrqTtcfQX3ZMaK7p35d8n\nelJ0T8t51z0sujflXgR6l+1x+EMUjRY9VhAVzwNyD9vLqPSlayHVA+OOFt0TSa/Byz6i+13zfdcu\nEd3netR3radU985bLJ7X23zR6O53++5/YbwIi+6hJUX3l07xpblR9P1e7v808fa7/P3ZSXR/6SDR\nfTK/h2CxeC9nXSp6UPkQ0f2j/UXfc3eXqDefCPzoo8eVs5ds6FF6huVzwZX7iY6jqPW9S3ei6B7f\nQN+17lLdQ/Zh8cJ6iai7/W7GOxeu6hHRfa1DRF3/fy/VXxL7nvXpI6J7e/6+Pk70SIQLw9VBqr8x\n/RXRce0P6Pyi9c+LUv3FoZVWfqFolP+1ot63UeP9QsvnH0P7CmTKkCFDdvR0sdVAsIe2VXEEukEz\nDbVV1EQBumybjLosDdhulG1nJBIJqqrK8LwKnclwAbpiXIWapFbb/Up0xZtu/+fbtXR0TyiEt5eD\nfa+w+5WoFtAO3SMZgO7/7Gb35+CN8yVW1mIftQt89Tq6EpbO3VvgSz+f6nSmoat2Zx49kOrmN5fO\nmcuc6TIVNSGtsP/u4Pj8GrSFakm3GB32C2ukdSZLjIYlvnx+2hOWt7a2OXOsnxcLqT5XzPX9diGo\nylETG/Z7Baph74X2ob/vVuLxcAGeqW0Yqqk4Oh1t7gD+Wvtfge5PxfD6Uix9uZW3GtVY3PhZ4ks3\nH69/HWI1/s/FM92Beg2moWZCZ7acZ7RVUPtYWWDlLrV63XvnBOVpmY8PJahGf4LxzY0D/3iYh/cs\nLcIz1y+z6+usvEXo+EpD+yGE1yfgjaEQOTk5BNi5sDPYTCPoJk1fdCabgAau+96XZhg6yq5HZwC3\nqVNJddhiY9fG4MFX8OyzYygpOZ14fBSpqRNZsWI1ahJ7GzU7rkH3JUaice8uQR/2R+z7CtSxIg19\nsHdDTVMj0P2Lqy3vOHRCcMLiUMsftnt9UXPbX9FJJQ1df3RBTYC5aOT2p1CTUSm6h5ZAzUQjUNPf\nWubkYCsAACAASURBVHSyGYxOLmPQCW4aai47Dd0/+xodEgNQ09aDeJE3eqNmvz+jE3sL1PT6HmpC\nBTX15QL34bnaZxiNH6Bu9MusHdfY/zfRCbIINdv9F3VzX2Y838Pa6iLHT7DyHkXNbs1QE1Y5au4q\nR/eYTrZ8+6HC+mFUgDvnl7+gcQjftXafgZrcJlv56db+zsbLF9Chfzy6Z3qv8fVa1Fx4M/oIXYSa\nUo+w63car36POhQtRE2536Am6M9QZ4yV6MSdZbyYbbwUdHyNM17no0LuBDQy/p2oULgGHSP/QCf+\na1Hh+KTdP9HKnG75+6NmwQjqgDPS+J9pfGmHmj87o0LkAtRB5Xs8J6JlqEPMEGvrrej4dgL1CrzI\n/1l4UU86oWbVf6ACOB+4GDVhdkfH6AyjId3SnG91jSMUCrNq1TwyMjKoD6gve2g7QwP2RTeCjrD/\n19n33b40A9En5yJ0pngbnaFrol4INBFh+PDhjBv3BW3bFlNevo6bbhpJZeV0VJClopNPjFCoitTU\nGGVlLoxPknBYSCajeJvs7lxRCvowJ/HCBoVRTayhXe+KF4apknC4CpEI+hZlt6oFL7yRK8sfggm8\nEFAJVHjkW5pFlq8jOlHOtDY5Z40oOqmtQ73b3Iq6HM95wHlPurcMu/Y5TS+M5ySRhk7a36F7ICfh\n7esMxwtv5MpzDghuveRe7+LCWjmHERduS/DCcrnQUc7RwjkwgPdm5Cie08i/Ue++SlQoOs8/wXOI\nqPDx0rUziue00B8VdBgv90Afl0o0MO/X6MJguZVTiuck5MJkOecHp6E5Bx//NecE45yRGhk9rn9n\nWPmplqcC7eN8VHivNf53Mfq/NFpcO/xORM5hyTmBOGcm/32/M8vpqOep40FXdBHxHp4zi6vH9ZfL\nX+kr0/HCWQCSPrrc73KaNy9i8uRJ5OW519bs+qgvAm1nMDk2xfPfBs9tyY8n0CXVPHT5f9n2IW3H\nIBQKcdZZZ/Hoow9yxRWXc/7551NQMJ9Y7FjgRuLxNIYPfxaRUpLJckpL1yJSjsg6RCqoqqpEpAyR\npH2LfdYhUmW/y/j007FEowlUe7gXOJpQaC5wAykpJ9G8eQuWLVtMMlmKSIXldZ/yamV55bu6qthz\nzwNRTWEenjbQAtVcvkPXMGeiw/BuvPeAvYRqVWejk95/gLfJzGzOtGnfkpVVSCRyGXAT8XgmH374\nIffddx+x2AXohPQGqsi3RyetI1DtbwiqBTyG886cMGEc5eXl9OhxEJHI4eh6KgV1/riYeDyPI488\nDD3cW4lzeS8qas+rr75MZmZfdGIXYAXRaArhsDOVueuHAieQnt6eYcNuRaSSq6++hpSUG43vx6Ja\niXPwGEZqapbReAaqATVBtYXTgQKi0XTUmcd54YGbcNVc6Jw7WqOPVAmeZpphvLgc1cCmot6gBWgU\n/8ZW9o2oh2UG6hyRhWrrBajmdSHqVLHCaF9j18tQwboUFWrOvR5ra1N0wTABFXiXW13pqGNGpfVX\nV7v2sY/3N6DCtAHqYNSd6tOYE2BjUW05zco4HNXWGhh9ztzeGj36UYC3AMuyfjjQV6/bAkjn1Vdf\nqVfCrD5hZ5DIJ6EzzgX2/0zUresSX5qb0BF3OToC30NtLqupDhk6dOj6P71796Z3797bhOjthZkz\nZ/Lggw8yduxYysrWMX/+AqqqKmjcuDHZ2dkkk0ni8ThLlixhzpw5VFVVkZ6eTrNmzVi8eDGLFumr\nVxo1akRlZSXLli1DRKioqKhRk9MMPMRisWrpQqEQkUiEysqall6qpamuJUdR7aMINY2urTVf3Yij\nE9g8PA1lY0hDhYN/ry+ODqG5wON2LcnOAacRbSlSUdNfFqrR/oynJTq0RLW0H1Chs7Ww4ZjZ/Gtb\nExFUsKWg5sylbLgbURNO69ocOG1c0+fl5TF16lQKCws3mmtnxqhRoxg1atT6/7feeivsHPLgN2Fn\naMA+6B6ZMzlej46ce3xp3gLuQG0ooJsh11I91hPUE5OjwxdffMF++x1MeXkM1Wo+Q00qGvVbzVVf\nog9xFO8w6Dvo6rPU0ixB96xSUcHSE91L6YwKGWcCOw1VgKfimXk6o/tc/dCV8lzgKHTfKYyakDqg\nWlVT1II8AhVCzjTUF9WaVhidGehK/VX7H0O7/12jNYkKpiao6acXeqxgrdF5ktE0C10556Mr8Det\nzZXoJD4N1SDmo0MnYe2ZaN8rUcGXj779+T94ob6OtPxzrAzHe2daPQXVJqfivY15DSpcPjUaVtun\nFbpGewnPTNcD3d97AzXJTbUyXLiyUlRrGmM0nmjtW+Xr04+Nlt1QTegVVJh1MLpboVrqCDxz3SFW\n/3/xzJg9jIYXrM/OQB+5lcbXd1ADSRdrgzPnHow+isVov7+G9yaCHkZ3mdX5Bt75uu+sDZ/jLVQ6\nWRtGoOMzhu4lrsYbn+noGJuF7iP+F9W4Zhndp6B7n5ONxiLL28v6tsKudTNeldr/g9G9y1JUs/zW\n+D3O6KtAn41v7aNm219+mUuTJvXjvWj1xeS4MyCK2kaK0adzMtXfGQ/eOz9AbRVz8d677sf293fd\nRliwYIF07Li3uQ/vZ67DqaJhfFzEfOd23Fo0PM9iUdfrU8R7z5QLSxQ11+kKy/e9uSu3szI/Fs81\nfB/xQmm5cEj9RMMj5VjZGaLu+c4d/FPRUE9LRUMjNbY0jcV7p1SaaEihvcULf5RjdItoeK9so3s/\nc6V+U/StAOfZvUtEgxCfJRpqKdvyOdf6hNWTKfBv0ajw+4u6xqeKF/29raUpFHUzT4q6bbu8mZZ+\nmpVdbnyOibrGV4keL3AhtGKiUebdEYfOotH1WwtcbfQOFXXrj4sXXildvPeVZYoeDYiJvvFARKO8\nNxcvSO8BAvcJ/CQasmo/UdfyH0TfKO2CPh9lbVop6uaeJnrcYR9Rt/2DrH+yxXsLdhPRceL6uK/V\nu5+vn8eKF5g4YXS79G68uPfLZYm+FUBEjzq4/j9O9EhIBx+v24keV+hs5R9hvHVlu7BbKaJHDA4S\nDd11rmhA4bfEG7+H271m4r2dfIHRtUiqHxG5UDQY9VwrO259/qZ44btcm1zItqgActBBfXf0NLHV\nQOC2v9VQiboXvYO6nL2ILn0H2gd0E6Enqj68j24ALNvulG4njBjxCi1bdmTKlB9ReT8f9fqLo4eI\nb0K9CvujK9cGqEZ0HrpqPwr1CMxANY5C++6E5824G7ry/BnV9jrb9RBqzd0f1ZQusfIm4DluDEK9\n76pQLz7wPNFaogeNnSZxB7ryjlndKXhvcW6FrroLrIws1KLcHe3em1EHkR6oFnUbGvmh3NpXgXdg\nFisnH11lg2plN1lZdxh/Mq2Oeaimdw/qHHIheoA4zehy2mVrK8sdFs9HQ0ldZt9R9AB7zPJhbWxn\n/FiBahkHoxppJrqPmGWfNPukoI/jSfa7yMpKNf6VoAepzzMe7GHlVxldzmrvNNxOxqdOqCkyhHoY\nzkMPcfe0dOuMx7ej2lVLtE/PQzVNtx/mFu+dUQ2lG3owP2p8b2r5zkXH3c3Gk/9Yvjxr17FG41RU\nA7zPeLkAHc/zrI4v0f2yq/CcZFoZryYaf1qhmmQZ/8/edYZXVWXt99xec9MTEgiQUEIREAGRDqLS\nHMGCvQz23sXRsfc61lHHhgUd1MEPC0hTZ5xR7FhAlA6h14T03Nz3+7HWzjkJQWVEg0zW89wnuefs\nvvfde6/2rvrrt5fW1VbbAsg9OAViHPMwxPLyPp2Pg2A75tdCOLNzIYYl52k/YhBOs7vOWxDz5zvB\nvJupmfY8NfVF5xdTcXExg8EUSgyrVL2dLqMAxBpQVlKceiMUh+uo3rSzaDvB1uj36/VmnqW3zfco\nzqMTKQCuXr2pnq236U+1rPNZ33n2U81/ouPZd3q7L6WEDknW222S1mlu9dtpRyUeTgEAvpPCSYYp\nMdbKKRxVCwqnVUAJ4zGBwhkax+yxjvq/1ZvzS5r/SR2TXK3fcFsrHXn+QAEiPtDxbIvezjMojrek\nhGKJEfizlj1H+zdM0wa03oEUbq0nJdZXOe1wPP1ZP/TOZgpHU6PzUkABh47rvB1GcejOpoRtKScw\nQ8ezjdazRMteTgnV0pI213G/vjNAumdRAJRTKVyziZdn2nM07fA5G7RfztAzIzRNks5/KWVNpFG4\nTVLC9vhpc5SkRLd+iuJU31n7cQFFQrBa8+9H26GelFA1f9b+ZrA+sHU2BbzZzEsrnesohatrQeGA\nSwh8pfnbUNb3a1r/I5S18U/NP99R/gTKuiikcL15lN+Js21naJk12p6rCESbervYY4RmDq2Zfg0q\nKiqC250OUSUeCLlFmwi9Tp+XJMjtfQKES7sJtqk19JmJ+hzUvM9BOL1kiP9NNmQJPAAxIY9B9A03\nQm60JmQJ9P94gzZEIdxHKuT2H9Lyumg6c6sP6nMPRMdXpe+NibSBkboZYoWYpmUZk3FTZ3WD+o2O\n7Vx9fiWE29oO0dvV7qLNNQ2emcjSWyA6MOgYHQox8TcAvhfB5qQMfmEEdkiYOfp9HIQr/E7zOush\nZE7HQjiis7SPPohP3XqIL+HbmncCRAJvrB6XQqz/2kA4k6Nhh82ZAOGML4ZwUU9DOO0UyLw27HcM\n9bEoE9h5jRnudzhsSKkAhFs0aRrmi8Keq42a5llth8GYbDgvEUce5zvjtuGcl6Ga9kSIwdGpEB1Y\nKkQlfzPE526rvotCrChvg+gHtzSoOwDhCN+CcL/FjYyDcdJ3Q9azExuzmfYW2teUgHrZ+P3Sjh07\nkJnZCpWVO2AfTjmwxX1PQw63Cajvm2V8eUz4euM/Yyy0amCHtAdsn5wgZGMk5IddDdtnx/jjmDQG\nrLcrRDz3oD43JudrHfUBsokMgoj15sL2GyPsDcL4bhG271YCO/vL+bUuL2RjPB1y+Jn4W0Edlzhk\nAzI+X1GIwUMfiIHFAk0ThIgyr4I4an+gbegGOQTOhYiiSmH7QHlho3aYfrohBgpnaT9nwfbHsiCb\nYwpsk/oE5GAziPsBLc8gixiz+1rYQMQWZE79WrYTTNfkM/5qbm1jQNMZkORMfZ8KEbW9BeBxfVau\nfXNBxL23QowmnnXU7YXtZ1jraKOJ4GAuHqVar1l75bBR8qscY2gOceOIXgkRH6+Ave5MvhKISNOv\n7ZulY2MAAYKwfS7N2jG+ZhX63KwP89yMpWljpT4zVqceyKWuDHIAmvmv0br8SEryoLh4G/YF2leM\nQpo5tL2MAoEAKivLIbqlLMiPKBfir5QPuZWeAfFHGgLR8TwB0WsFIOrGEOTHmQThvo6C/KDvh9xS\njUVkVwjaxWmQjf8vEH1JQtOnQg6kv0L8kwIQncfxWs4OyMZ/t6Y35tkhyM34bYi12D8hXISp41bI\nxjFQ/8a03lQIt3Y1bOfhPIgf158gy/U6CAf5EMR+yAs5XP8K4SLCEFSTw3UMTADNNyFeHxfq8zsh\nt31jreiD3O4vgeh4ukE2OWMOfgLEf21/bbPxgdpf+zkCYmEHbef1Ohdhzfugjl8f/f9wLfd2iF7U\n+Eu1g3Boo7Wdd0AOyoDW94SOWxaEa2mh4xmAcJB/heiORug7QlBhbtN2LdQ5eUzLvgc2Z218zI6G\nXJzudMztkTqu2ZAD+lGIX5c5UPppWUNgW6kO1vc3QOY9DBv0OFXzbde5vQ9ycCR07I7TdCZkT46W\nE4EcOPdqu/tC1ub+OjYnaT05EN1iUOf4Ysccd4ZcVvIhv4/TNF13LeNYHbdsredoyBp9WOtpAyCB\nkhInNFozNdOep6YWRf9ieu+991SenULb0q6ctgVXSwKP0Q5lv94h6z+SYtVXSNEhGcuvgwlMdaS7\nl6K7KnY8G676hoVa94MUnVG1vh/J+gCwD1MsBc33FRS90omUAKPm+VKKVdggCrCyeX6P6iUyKSCz\nXSiWkk69RQFFHxanWDbe4Hg/m6KLyaUNHFtN0Rc9q8+SCVytz5Y78p5EAb2t1fz7UfQrznHOoVjT\nhSl6JqMPLNM5uZKiUwpS9G6dKWC6LQjcommn6LiSYkWXRrFaNHV0og3q+1eKnnGNfj+Ools0bX6O\noucxVpQZOj6f6Vyd5kj7g47rmZTAnOb5Au1nB9YHgH5Jx8jM9fEUQGHz/gVH3fMpOijz7o8678Z6\n9u86dgZE+2ZH2ne0zQ9rfeMI3O14/3/atqt1fPJoW4CWONL1p+joghT9Z4C2NSMp+uZcCoBxBy3r\nFB0nP8Xi0kfRxznLfI62PjFEG7w5QdFtztU5D2nfwNra2qbeMvYIoVmH1ky/BtlOywZiyIiRAFv0\n5Yyn5USK8MEW3xG2fqTW8b9JZ8R/DfMaqYMRWZolYuCSGpbh/E591jCdaWvD5yaumBE7Nnxv+m7t\n4j1gc3KmzW7Y8a7MWDWs29RndI4GAsyMh8nrd+R11mFEsqZuI0Y1vnvOcfc7/jfta9gOZ3+8jvSN\njaNpg4ndtauxa1ius4xdzaVzrhtbV+b/RIN3zrzONUDU1zU1NheNtc/MjRP2qmF74rAhrRpby0bU\naqDMnLHqTFpnmc52Nva7c8JlmbXSEESgmZppz1JTX3R+MVVWVlJ8laIUq6oIJYz9TIo/U4bebl+m\ncE199d3tFA7gBdoh79vqrfcsvbFP1ffpFKvHoZr3On32mpYZ0PStKOFgZlEs8EyayRTLt4DesN+h\nWA2GKJaBqZSQIO9QuC/j95VHubmbNozV9NmUUDOdKf4/T+jzIIWL+SOFo0gi8AyBN7RtxnfrLG3j\nSZrmLQr3F6Pc8EfoOL1D4QyTKGF2ztE0Q7XNR+p4XKrjk0yxYjSc3kwdn6i2cQzFLyxHnx1L4bIi\nFC7xBa3/Bq27hdYxi+JPF9WxfJm2lapp5x+13r9TLPzStO5ZFOvQfIp1XietK4Vi5TiDwk0cS+F6\nQxTOZDrFgi+kdcQonNlrOhdhCmc2S/uVrO16VcfmDC2jK0VKMEPLDer7kzXvqZR10ZISQiaq7ZtG\n4ZqO1PFvSeFokwk8T1kXeZr3MYoVbrqmzaX41c2khODJ1HGLUjjHYTo25n0ahRMcoHNxKcUaM4Ui\nrRhKWRMHa54bNN0I7cNVOj5/0O+XUNboG9qODjqOv//9xhD2EQ7td68EbEA6N79vWrVqFdq0aQfS\nD1up7uRojAIcsJErzE3WAxutwSiyjb+RifDs5OIMsDBgK+OJ+sYJBhC4BrZFoLFANLdVg1tobtaG\nkzEGAmZenBwIYPt7wfGesK3uzK3aAP2am7QJt2LaYIB0qxz9MNyXk5MyxjVmPM24GUMAA+rcEIzX\njKdpl2mnC2I4EIAdadnS7yZ0Twi28YGxPo3DRg0hZM6MhZ/hQCpgW4uWwTZkMBylC7ZRhmmrGSfT\nd8CeI2PY4zS6sGADXsMxRmb+ne8NGLDRkSX0XdgxRgnHGBvEE1NOhT4rhW0MY8bSCZxs1pgJ3WLW\nk3NuTJgen2MunfUbDs38Pow+zrmezNow690Le76rYa8HY0B1FMQKEgAsFBcXIynJWIH+vmlfMQr5\n3XegAe0TB5ohknjttdcwb96nCIcDGDx4MMLhMPLz85GZmYlEIoHJkydj/vxvsGXLRqSlZaJXr/1x\n3HHHmQUKAJgw4Ty88MIXiMcDAGrg9W7C6acfgqSkGBKJGhQX78C//vUfLFuWh5qaThDf9s3Iz2+F\nZ599Cvfeex9WrixCq1Yt8MEHn6Kk5GCIefxSiHJ9JgAP/P5Dce+916Fjx44YM+YoVFfHICbU30MM\nJv4JoBRpaSnIycnCeeedi1NOOQV5eYXYsuVOiPHEarhcPXH33VfjxRdfx9dfd0YicQeAh+HxPIGL\nLz4RRUVFWLp0FQYO7Itx48bhpJNOwoYN2xCNBnDcccfj6adfREXFGxAjh7chFqHLYVlPITX1PvTs\n2RHbt5ehc+f2mDBhAmbNmoW77noI8fhR2k4C+AL77VeIeDwOUg69zZs3o6qqEh6PDx06tENhYUcs\nWPAd1q5dD7IG0WgyFi9eDLIlZBMvhmyuGwC44PV6kJubg1Wr1iGRiCM5OYZOnQqxZctmrFmzEbW1\nVYjHgXg8SdvQAmL4cQPErHwg5IA7B7IxPwYbTiwfNlzUiRCXjwWQEEKDALwG2aQHQ5ya39U007S8\nZRCr1KchBkNVkOjMIYhRSiEE/usc2GK8B2HH1SvW1WZBHPE/0L6fAnHsXgzbgGcjxFjnO9iHM2Af\n0kfrmiHEsGMrxEk+DIFxrYIYucyBGMqkQw7rOagfOcFcsPpBjDsm65iZA2+Q1lMFOWR7aT3mMATE\niOcjNKTt24sRi8V2ev57peYDbe+kfepAu/TSq/G3v01HefmxkB/jCgA5sKy16N27G/LyOmD69EUo\nL6+G3Hh7w+P5B3Jyghg//iikpaVi8eLFeOaZlyA/0vMhP9xJkBv30RC/IoP2sBqyoVwIsWB8VluS\nC7EEmw3Z8COQDQ4QBJH99G8GgCJYlg9kVPNthPgKzYf4Z+VBrMVSYYeFqYXgCC6AIJi8DvHrCkA2\n3lMhm007yCbq0f+/hWy+GyEbWVeIz9Z3kLAphjpoedkQlI6+kI39CchmaTimdIgJ/t8gFm/btb9h\nbWNrnQPA5kTNhjxEy31Ey/RBDpY3YPs9GU6nK8TdIBNy2CVDrDw/0bH/CmKaXql9K9P2GN+3Mojl\n33aIteM2Hfst2tbtOieHQ6xBX9H+AgKBOhtyQBpqBWA85DBzQ/wIh+k81ULm7Z9afluI1eC7EItJ\nU28ZBFVjM+SyY7AUi3SsBmi7vob421VB1rThfDZADpMoZN43QVwh1utYXKT/T4Gsq/U6PiaUj0fT\nL4Mg1VysczUNMu/LIGvOBPOshVwW2kMsHY3rSjYEoOifWm9DKgCwGjk5efjuuy+aObRm+lWpCaXQ\ne5a2b99OrzdMQZfYqjL9L2hbqxl8uX+pvmCm6hyuoFjnRQm0o+jS+hCYRNui61qKFV0vit7KWDt2\np23pRS3LR7H6IsXasJPqECJaxsWq9zAWiosp+pggAbfqMw6i6GBMudMp+pOWqreIUCwNr9O2plL0\nOTHNe7Qj78cUvUoXCrJEJ837ZwoeYGfNv07TL9H0WymWiV1pW0Wu0f610TIu0z6lUCwEL9B+JNNG\n0Hhen52tfY9SdF/GCnKxlml0jDECh+qYZ1EwBi/TMt+l6GJWarpvaVvVHab5X6fobdpRdEnX6vco\nRe/YloLEQopeL0/H0yCUHKVjY8o9XOs26CLfU3SRORQkmu4Ua8+BOjfX6Fz9SdNtpW1R2lL7OpD1\nLWAv134t0HE40DFHB1B0V+k6H8dqe4/XfGGKni1EWbN9CLzpKPtciu41h6LXPEzH4lbaa3iWI/0p\nOk5dtZ5TdPyTaCOVvKdleAmsdeR1frrr2HfQ8Ujho48+2tTbxB4j7CM6tH2Nmnpd7DFas2YNA4EM\n3YS+pBgBNPyBRfXH2I+iAH/V8f4cijLco+/mOt49qRtIW4oC3DzvS9lkzff7dIOpdTwbRTFUSKfA\nKH1MOTSdbeulG00SZZO90rHhkLJxJ1EOnTBlMzebchll4/9WN5woxYDC5F1HObAKKKbuqZqHlIM5\nohteCu3N20AteVkfOitOOTQW6t9xlAPyekeaQykbsHNcr3V8f1zHwnyvoBj1/F371t0xfsspG3Wt\nvh+obaqmHAxON4qztE0ZWn6MAutkDqb+lAPlIkeeYi3/FYoBCinuFGGKKXt3ymZ8DeVwPEzLDVAM\nIP6PYlzxDy3ftHspbUDlhKO+njo/vWiDW5Nilp+n/eukc2IOwgqd37840k+gbd7/d4qLx1Pa1k6s\nD1N1p86pudwltG/n6Pd81of3upFyGF9BG9CblAN4iKN/qY53zo+bcngad4stlLXbgueff35TbxN7\njLCPHGjNZvt7KbVo0QIFBW1hWVdA1to6AF/q24UQcYoXIhZZCRHttHWUYMCHcyFilYkQMdc8iHPy\nEghSxuuww8rlQEQ732q6uyAiskshoVMmQURVQyHiMgMRtEPTA6JX+x62g2s+RPT1KESX8j1ErEYI\nxFUlRGxm9BEhiAisGDbY77MQENolENHnERDR4kxtR0jTJUHEd5/Bdu7+D0Q8thIiLvoPRNS1TNsx\nQMeqFsAabYcBJAbEqfszHV9ovvaO9/kQI4J/6LsJEFFbR4gEpxXsn1kr2AEj82GDFp8B0UWequM3\nDRKBOQARnx0AEemZ+bUgItftEMQPo796FXZATUDm7FFN3wYiBr0bon96CyKWNPBo/9F+f6nv8hzt\nzoMdefsqLfcxiF4sS9t5HkRk/B+Ig3U72AE0gxARKTStc76h42n6kA977qsgetCzIXq/9yHgAFWO\nPlqQ+ZsCCYXUHyJ6/B6CTvM4BDy6DPWD3OdDxJY/6P9bUJ9egKyloPbfGM2k6PN0dO7cGc3UTL8m\nNfVFZ4/S+vXrOWzY4XS7Y7TDdfTQG2oWgQg7dz6QsVg2PZ5UinhuKYF5eqv30w71kUkDYlxYuD/H\njDmGbneK3p6T9Gab7rh1G3Pp07WMMEXcMpPAA/p9LkXEZsrYX/8GCXxCEQ91oZhgm/AnEW1PhCKy\nG0LhQu6iiAAfoXAXCynuCsa5PF3LyKJwfJ9QTKlDmmeNlhHWsoMUMOM1FFGXaWNa3djJzf4bivgw\niS5XTOsy4LWLCHSjOKqHKFxhoMH7/fRj+pZP4D8Uri5P2zGV4lh9FoULXkIRw2U4xjpCO5SKCb0S\ndpQZpYhDV1NM5sP6Pabv8nXcZmgdEdrhe7pr+nSK+8QCCgdcoP29Wd+HKFyfmaP/03ab0D3GjSJX\n5zVAO1SMKb8DRaQX0u/p2r6bdC6e0Hf9KKDb/9F5fVTHZTBl3XTTdGYMQrRDAKVRXBdWU8TXYW1L\nkqYz7UmiiFzXUEzvMyjrZglFlNkYRzawwZxcrX34m5ZzM4HWdLki3LRpU1NvEXuMsI9waPsaRfo7\ndwAAIABJREFUNfW6+FUoHo9z/vz5HD58JM3B5nJFec8999Wlqa6u5imnnKU/5ChFl7SMwEcE0njd\ndddx5cqVdel79RpMr/di3bAe0Q0hVTesXnS5zmNh4QGMxVqwRYv2vOKKK9i9e38GgyaGWVfdRDO1\nTfn6PJ8+XxI9nmQtrzNFR/U1RRTUgyIGGsNIJIeRSAZ9vrS6zciyYgyHM2hZYcoBuZDADXS7U+nx\npNCywvR60xkMprKwsDcnTJhAyzJxuMyBZOKvmQ2uIwUt/kyaQy0YTGNBQXeGwxns1+9QnnXWBQwG\nh1MOqmTdPHMpB5OJQ9aOtm7MxKUL6nhHaKP7mxhnoyjiy5gjnXkXYTic6mirjy5XmOFwC9qIK/Mp\nOiY/RfxrRIQmvp0pz0cRjWVSxGMjHG0M6bOPKH5nEcengBILLkfLuZKCcn82bZ/CCEX014Vy2TEX\nlg6UmGLZlAvUV1pOSNt1NOXic5Bjbszh59Nyjei4q6MvZlxb6pgvpqChZNWNk+07mKn/d6PtI1lE\nORD30zlv5xh7E0+wsYPMjGea9v8h/Z5KO26cOSQjfOWVV5piK/jVCM0H2l5JTb0umpReeeUVer0d\nKBzEV44f690877xL6tLt2LGDHk+A9XVjR1OcVWsJBJmZ2Zrr169vtB6/36kToW4A99V9T0rqqWk2\narkvOdK+TeAQAmvockUaLX/+/PmMRjvX23CSknrwk08+2a3x2LBhA/3+VNbX+4wk8H8Mh/O4ZMmS\nurR5eV0pepl/0g6pYj5tKbrCCOWGn0ZxJL7HkeZL3XRJ4RQvcbzbQNHpxel2+1hRUbHLNi9atEgP\nBdPmW1g/1E1CN9U3mZQ0mqmpubSdtp39HErR/+VRQt+Y589QLhntHM8WUg4j8/1Zij7RfK+h6Poq\nKfqt7vr84kbGoA0leKdTT+mhreck5SDKbtDeARS9mp/CFfWmcG/m/aMUjj2P9fVvXSkXJKfhUK2W\nU6r1+2jDWDX2Sej85DZ43o2iG5xI0cMlNE1b3nnnnbu1Fvd2wj5yoDXr0PYhEhPiHRDT62WONz8g\nLc3WWQQCxqnV6IVqITq5GID1cLsT+OqrecjKymq0nlAo5iifED2EcfQuQ03NegSDUYiuJQbRCxla\nps+WwettPARHUlISamo2wdbtlaGmZsNu+/2Ew2EkEpUQk3BA9FerALhQU7O9nsm1/L8coodbCxtV\nf5t+tta123a2dY7xMqDOad2U1bDPq+F2e+DzOeGe6lNGRgZE97len6RCdHtGh7VZ29YKicQqRCJR\nfbYDth6oGjK31fqpvxbkZ78ZoleCfi+Grcfyax7j8L4KNhTZRsh4lms/G45BpEFes8bK9W8lxMG5\nBKIDNM/W6HeznpxrDJA1ZJysnevJo31f6ahzDUS35oe4ojijGhjqBBlnQFwEKrV+MwYV2tcYRH+X\nBlkDJQC27fK30UzNtCepqS86TUo1NTXs3XswbcvBKwgcx5SUHG7YsKFe2rvuuo+hUD4t61q6XIPo\ncrUgcA1DoXa8+eY7frSe5557gaFQDi3rGgaD45iUlMNQqBuB6xgO9+bxx0/giy9OZijUgmJ9FqWY\n7Z+n/59GIMaHH35kl3Wceuo5DId7apm9eOKJZzCRSOz2mPz5zzczFOpAsUw8kEBnhkJdeNFFV9ZL\nN3fuXIZC6XS5rqBlddTb+bUUndNBFJHWCAJJtKwBtHVEJ1DMzWMULqk/gStpWTF6PGNp6w/HMRRq\nw3vvfeAn2zx48KEUkdu1FF1PEsWS8M8U8V8mQ6GhHDx4FN955x2GQhlab74jT3ttk9EFXUyB0zKi\nNxMc81oKx9aSwrWZ70kU/eY1ylEdpnWkUESPXWm7LRznGIP9aYtor6FwYskUse+1Oq5GdFugzw7Q\n8kIUUWaYwgkmaR0naxnGVSVNx/1S2rq/Aor+zdRZwMa5sSCFy+uiY3qNjpuBmeuk49yVIrY8Qvto\nwLJbMDU1j/F4fLfX4t5M2Ec4tH3NkU7n5n+Xampq8PDDD+PVV19FRUUlDjlkOCZOnIj09PSd0s6c\nORMffvgRsrOzYFkW1q1bj759D8TIkSN/sp5///vfmDNnLtLT03DqqadixowZ+PbbBejUqRDHHnss\nXC4XPvzwQ8yaNRuWJY6b8+Z9jAULFiASCePWW2/FuHHjdlk+SbzyyitYsGAhOnUq3An9ZHforbfe\nwieffIK1a9ciO7sFDjigJ8aOHbtTeV9//TWmTXsDgYAf4XAYq1atxubNm5CcnILKygoEg0HE43Gk\np2egS5fO+OijeVi06Dvk5raE1+tBWlo6PB43qqqq0aNHdxQVFWHjxo2oqqpCMBjCgAH9ccghh/ys\nNt94442YPXsOamvjGDBgIGbPnoVt27YjL68Vhg07GK1b5+GUU06B1+vF/Pnz8cYbb2LFiuUAgO3b\nt8PtdqNly1bo378fFixYgFmzZqOmphoHHdQP4XAI33zzDT76aB6qqqpQWVmBRIIIh8PIyMhA//79\nUF1djX/+818gCb/fj7Vr1yIer6lr33777QeSWLduHcrKylBVVQ2SCAT8IInq6hrsvE9a8Pm8qK1N\nwOfzoqqqColEol6/vV4f/H4fSktL/6u5FmpsD/jlW53X68XYsWPx4osv/iiX/XukfcWxenc70A4i\nQ6iE2BvvB+B52LKDpqb/+QOtmZrpf5Uau+80bwc/j/aVA213dWj/gCgP2kFwg1pBHGaaqZmaqZma\nhEQCUP+ZETA20/8WeX46ST0y8c2PhAC9PQzb27eZfmVavXo1BgwYiVWrvoftEBuHQeAPBtPRpUsh\nPv98HkiDjG5+6QYR3w9hsMMQRb0fYshQA8AHl4sA/EgkymBZAUSjMZSUbHKUYeJQueD1ujFq1CjM\nmPEuqqu3AwggFHIjKSkDGzasAulztNGAxRKioC+HOK2WO9pkYmvFYSPCGwR7r34qIU7TBo/P40hj\n0OMrHWWbSATSf8sKQcCGTRQAg6Af1DJMvS7Y8cZcsKMeGNxMwkbLL9P8BtndRDaocYy1eWaQ3E0U\nhLj+7+xDpbbDgh01wIwTYKPEG2R+k94J9Gvemb6VanlB2GvGGEtQ++Bsp6nPoNf7YSPnl0OMP8ph\nbyFxHQvzzKDbB7QNVRCcxkrYMdzMejBr1UQwSMBG169wlOvXdho0fmO446QogBpYVlz7Y9Kbtsdh\nY2KaE89EQjBzZubSRIIw0Rrk9xQMRrB1a5HDuKqZ9hbaXQ6tGgKJfgoETgCoHyWvmX4lIol+/Q7F\nqlXjIFZ3gyHh7NdDUDpyUFExDJ999h3IGASNoR0EzWEJBEzYAwGOzYGgf2yDANe6IOgHnyORWI1E\noj+ACSB9KCkZBkFy6AdBoVgOsfpqhZqaEZg2bRmqq3trWY+jvLwa69ffCHILBODW5FkIASn2QpAq\ntkFAgNMhyBg+yAb0IcS67FCIhVlLCNqEG8BUiKXZuZDNzQuxtHsYAhwcAXCnlv2EpsnUsqcB2Ary\nTIjl4BSt+xOIxdtJWvY7mu9IbcdILSMdgua+BcCxEADfbQBuhwgqrtB6purzi3TmQnV1S7qjIRaG\n70I2zhkQ9Im7NN9jEMDfkRB0j7DW5QPQG4JA0hKCirEWgnQSAbA/xFJ1obY1DAHY3QRBaolqGXn6\n91mt72ZtYxgCOpwM4HjIekmF3FfXQhA4ztV8IQjw8mQdmy90ro/VMUuDoNFsA/Cc1heBILxsgiDG\nJOn8zYUAW8cg0QW+hVgs9tU6Q5DtZisELcYcUg0PsycgFopHQYCiYxBQ5XR9Z+bKq23pBLGi/F7H\nOaBt2aTtDDnG+BBtSyqAtqioSEGPHn3RTL9/6gLZPY7X7/kArm665uxETWQj9OvTli1b6HKFafvu\ntKE4nRrhyi0Ui7oAxVemgILJZ95Po1jhvcH6fk7GN6uD4/t8/V6gFmbPUKzg3nGkmUyxpJtNGxPv\nA7UeM2kGsb4P1F20fbXMpz+B99WK7TrH8xUUa7l+FKu80Y53CYpvUybF4m4ZxeKwXYOyjeXcsY5n\ntRS/pEspQVFrKU7JlY40ExzjsYpi/ebEAdyh42y+t9e+jWrQRrC+P1eYwDbH94solqgdG7T7QAq6\nSLbW01XntgPFCu/+BnOVyvqAvMdQ0DqcfnABHWM3BQ3DWV+uvjfoH5v17wOONF9QrP5IsWScoe2/\nT/vqo/iaLdd5cZY/lOLHttnx7DLt54P6vQ9lnZn37+vcuyhYl7vyIZuu45dLQYbZSrFKdFPWa0Of\nwlwdhxmOZy/rGBbp9806V+b9t1pHD4oF5AhaVmpTbwl7lLCPWDnuLoe2AAKA97J+Xwa5Ev9SGgG5\n9i+GgA42RkMg18VvIaBu/1MUiURgWbWQ2ysgt8WFjhQLUV9E4oZgNxpaABG7tIDtjwUI0/0D7ICb\npqx0yG07pN8DWoahb/Tdt5BbMyA337Ww/ceS9L2hlZBbtBFhlumzVP3+Lezf1ULYvm0WZGmYWFdL\n9VkxxOfIiIw2QbgfQERsa3QcFjnyLoHc0jO1Ppf24zt9n9Dnpk0LHe+dbTPvN+s4pUBu+6ae5frX\nWXcy7DkjZDxzIX5dxodsB2RutkA4RT8kHtedEE5mLYCPYdNC7YNzLWyHhOtxtteIAI2PnPEL26jp\n47BxMb/XMp0heBZCOK9yiF1YmX5fAJmLNE2TDBl740dXAZkvT4O+L9Q+pjvSNawvClvUvCtaAAm9\nMwvAlfo9DTJu2yDry1hMbtZnLuz826jUsTF1O8WJCyHzu0b7VQOvt9mFd2+k3bVqGQCJNtgGtvCc\nsJFC/xtyQ35BwyEr5lMIB/idI00yBPX0MMivKR32zuUkvWzsm3TbbXfhuuvuBXkMBJh3I0TMsxKy\nCVfBsqpBmujNgARU9ELEXi4IQGsC4nA6HsC/IfcSL0TMkwUJBjkMIhYLQ3QH7SEbzpEQ/cJ0WNYg\nuFz/QW2tD8Bxmn4tXK4MJBKHQICPiyFitnKIeM0D2aiO0D6Etc4ibVNfyHKaDDtqcSvIhtcKEhft\nH5BDwA9780qHHB5J2ueZkM0nBeIM2wEisvs7ZPMaD4lV1gtyiHwHkaabO1MnSAyyl3W8MiGHT1eI\nuDKgY/EG7EOpDCLOHQABCjZx0Nppv57T/pyoY7lA2/GOztUYSKyyCER8WAkRLy6BTa21P/0hosnX\nYOsnx2ob5mjanhDR4WSds5Y6H3Ft81BInLgyyBznQQ5Tr/ZzPiQIZhZENH2Yjk21ljNW8/fT+fkc\n8tOdoWmOhNw9V8HWkZ0A+bmbQ8SIdj/R74foHE6D7eTsJBP8dCTkwjNH62ir4xaAiGXX6zjlQ9be\ncC1zG2z94hH6/1uQOe4DEUK9oO0douP0GmSdxiDzXIEpU57D+PHjG2nf75P2FSvH3e3A9wAugQjN\nnVf6xg6Xn0sHQQ7JEfrdiDCdnN95kMh71/9EWfv0gQYATz31FJ5//nlUV1ejY8eOWLNmDVatWoXM\nzEz07t0b8XgcCxcuxJYtW1BdXY3NmzejuroaLpcLaWlpSE9PR3p6Okhi0aJFiEaj6NSpEzZu3Iit\nW7eib9++iEajWLp0KQoLC9GlSxdMmjQJn3zyCSorK+HxeJCeno4uXbqgTZs2mDBhAt5//31MnTq1\nzk9n+/btKCoqgtfrRTAYxJQpU7Bhwwb1jWqJcDiMjRs3YsOGzSBbQA7lAQCOhWXJQUwSkUgEsVgM\npaWlKC6uhiyDCIBv4fHMRfv2LbBhwwZ4vV707dsXP/zwA5YsWYKaGvGXcrlcyM3NRVpaGjZvliWa\nnZ2NtLQ0LF68GBUVFfD5fFi/fj2qqqpgWRaysrLQvXt3LFmyBDt27IDf78eOHTtQVlaGRCKBaDSK\naDSKdevWwaw1l8sFkrAsC6GQIP+Xl5ejtrYWiYQXcugajmYdLKuyro+GvF4votEotm7d2mDGA5Bo\ny+MhB9O1AMrhcrl28uGSn/NYSADN6yEH0u6QC3L41kAOodofTw6XtqsnRF83EzY32hh5HO8tyGGR\nAzkkVjrSNfYbbmyr8gJ4BnIIXg25RJQ1km7P0t/+9jeceeaZv3o9vyXtKwfa7tLHP51kt+loAE86\nvp8E0dM56S+QUMDvQWJ5nLyLsppMBv1b0PXX38pgMIux2BCGQul84403697dcce9DAZbUZAk2tIO\nwtmNlhWl15tNy0qiZe3HUKgdhw07nNXV1STJZcuWMSurLZOS+jIYbM9oNJdt2uzHM864kLfddhcD\ngRyKPut4ij4qSJ8vjbHYYIbD6Zw9ezZJcubMmQyH0xmLDWEwmM0rr/wz582bR7c7SkGIaEGvN5mB\nQCot6wAKEoSgm4fD6bzkkssZDKYzFhvKYDCdt956BzMz2zAp6SAGgy3p9aaqbifToQvpTNGTBSmI\nE8m00eo7U3AtDXhwVPU/YT7++BM84IBBdLmyaUcKCNHnC9PvT3GkNcj9rWhZBnUjRtHd+bRuZ5SB\nMAWdvxUF3T2sbeqhaQMU3VgGbRT8HC23JUWP5dfnptxkfWbAlltr+gNoo8t3pw2QHNb2RTTv/o62\nmTwRCl6iQQ5pSdHPmfEz6dpQdK9RR3+z9JnRUfo0Xyf9bqI4GNDhmKM80w4T581EMkhm4zoyA1jc\nkXbUgQBtQGwDFm3Ai/200UxMfe01barjmRk/A1hcSBstpJX+n6x/QzovLWnix919991Nsgf8WoR9\nRIe2u3QnJNjRQZBrmfn8EjoKP32gPQIxfwtCrrk/oH5QKkO84YYb6j7vvfdeU6+TPUbz589nKJRD\nO3r0PIZCKayurmZZWRm93hAlwvJJFEOHBEXx/kfaUaRv1LzVDAYP4SOPCPTUkCFj6HLdqe9qKDBH\nl9LvH0vL8lNCcNzh2GRupEAPifI+KSmT8Xic0Wg6JYK2KNZDoTwmJ7eiBOI0xglBSsgWUiI1p1OM\nV8IMBFJoG7r8QMtKpst1j6NdeRSQWGPccYy2JUY7+vAWLfM2R75RtFH33ybwFS0rSI/nYN0I12ja\nz2lvziv12TdafjIFxT2dArpcrpvr55puraYxgSbjlEM8m7YhyBztf3faYL0vadsO0bZWa7kf6fuN\nlMPbhL+ZQTkMVtM2CkmmAPG+RNm4u+o8tNG612kfFlNCpyQ78n+l9WUSeJGy6Zs19pF+L6UYcAQp\nUFHDaBtq/EXzlur31zTPJIrRSBqda1YOnYEUA5NS1jeacX5e17+plHWd0I+Jxv6Kvi/V8fw/SnDQ\nGO1AqTMoh5vJeyYlkGmQEql7tY7ppfq+lsB4yjqrpUQ86EJ77dcQGE45/GL/FRTb3kLvvfdevb0S\n+8iBtrt+aH0hHe/V4PnQX9CGNRDliKFWsBFNDa2GiDUr9PMviIJjccPCbrzxxl/QlL2Xli1bBo/n\nAIguBwAORCLhwebNm2FZFtzuIGpqNkL0AkZhPRrATRAxUguICT0AeFFRcQi++050M4sXL0Uicbu+\n8wAYBeB7VFU9AFG2VzjyAgIQ84X+Pxjl5aUoKipCVVUVgIH6PA1u94EoKXkHohsCRKeUCdHPAKKz\n6QQRHVXD42mnbQXkvmIhkRjtaJcPYoIO7eMIiM6pBqLrAcRYw619N/lGQMRv+0H0UaNAJiEeb6lp\nczRtT4g+rlDbBm1rJuQuFYAYIGRAdFxh2Pc5M74miKQbIh7tAFEBA6KXrIb8fExQ0lGQn9QobesG\n2PpMaF29IPqfLtrv/SD6MEB+BsmQALCjAJwJkRwthYhxkyH6qQId2znaJpO/m45ZhY6Rc4311fp2\nQOZ1mbb/ENiGGodD3DCMYdAoiNhvFEQX1RvONSv5Wmi7wxA3h4aUrG0xPmNjYEvDxkJ0mKP0exii\n61oCCexpDF8Acf0oge3rNxLAgxDtRQeI/jgEWSsWbJHtXNjraw7qr6UxkPt1NUpLSxGNRhtp/95P\nQ4YMwZAhQ+q+33TTTU3XmD1Iu2uqMwRyeDX8/BL6DLJ7tYHsWMdCNO1Omgb5dbohK/BA1Dfr2uep\nS5cuqKmZB2FOAeBNBINeZGZmIjMzE7m5uRAl+ouwnY6fhWwcH0OU5P+CbJ4lCIdfQ69e3QEAPXt2\nh9f7rL4rhRgAdIcMt1kit0LuFSshPkZmI5+CtLRMtGrVCrFYCkSBDgDLUVv7ATIysiAMOCHGIJtg\nG6l+BZnGl+FyhZBIFMGWas+DZRFe79OadwdEuf8kRIFfAQGpOQBy2LxaV68ccM9ovjKIYcd2iL9e\ndwBz4XKVwuf7HnIwm6U0U/MuhK1/eh9yEBfp308hm2cLHeeZmm4h7IjgCW3rVsjmaCxKX4Yciv+C\nben5DGSjnKxjn6b5p+n7xRArxxQd/x06bsZ6dI7mawmZ7xzIgbwf5LBfBTnMlurYdoSowo2V31zY\nCP7J2n5zT3wD8pP0AXhTx9wNmeNiHd8n9K+JaPA0xHjiaYixyIdwrlnp2xTsLIRZpH+nQw5NY0Dk\n0zEykb6fhFwUjFBno5bbXZ8FYd+HJ+m4GafoFyGH3Xod0w6Q9fEs5PdSpWWk6nhM1nF9CvZv43kA\nHliWH5FIBM30+6ZkiD7rc/3ch/qx1P9bGgn5lS0B8Cd9drZ+DF0BMY36BrbXakNqak7+V6Unn3yG\nfn8SI5F8Jie34Icfflj3bsWKFezRYwAty+iKJDijZWXR7Q7T7Q7TsmJ0udLp8yXztNPOYW1tLUly\n48aN7Ny5N4PBXAJhWlYXAg8xFOrCCy+8jD17DlIxjZ9AgBkZrenzRRmJtGVaWkt+/vnnJMlPP/2U\nqam5jETy6fcn8eGHH+PixYsZDBp9SZDJyS0YiWTQ622p5XnociXz1Vdf5RtvvMlQKJWRSAFDoVQ+\n99zzLCw8gKFQS/r9yRw1ahw9nhQVIxndSor2M0wRH/pp65tSaEc99tDo3ywrxOnTp/MPfzhOffv8\nmjfItLQWTE5uQVtXF6T4UEVpWTFaltHTZFLEk0H93zyPONqX7HhuAqF6aet9MukM+CnvnXqeTM0b\nc5QTdHzPcrQvg7a+z8f6OqWMurmT515HmwL6cWt+T73xqK8b9NH2ZzOo9ybIqSnPpIvo+4CjvMZE\ni+kNxiiobQlpuz209ZZGF+qmrYczY2L0lc6+mXE0eU2QUdOPLEe/k1k/+Knzd2QCfZrgpSFOmTKl\nSfaAX4uwj4gcd9eqZSrkQDH2xydDZBZH7uF2/bekc7PvUklJCdavX4+8vLxGoXdIYs2aNYqOHsdz\nz72I4uIK9OvXE6NGCYp+JBJBVlYWJk16DnPnfgifj4jHgdraOI477kjMm/cZVq9ej8MOG4wTTji+\nDpW+qKgI99//MLZsKcbo0cPQo0cPtG7dGn6/HdesqqoKK1euRFZWVl38spqaGsybNw+hUAg9e/ZE\nRUUFVq9ejVgshuLiYhQVFeGll6YiEPDh9NNPRjgcrrOGrK2txdKlSzFlyqtYtGgFOnZsjb59+9RZ\nL65YsQLp6enIzc3F6tWrkZGRgaVLl6KoqAjffPMNXn31DZSUlCInJx2W5UNubgYefPAvaNGiBQDU\nWYkuX74chYWF6N69O0jixRdfxKuvvoGKinJ4vV6kpqbgxBPHo0ePHnjkkcewYMFi7L9/J2zdugWv\nv/4mNm7cAY/Hj3A4gaqqBMrKSmFZPmRlxbBt23ZUVRFt22Zh8uQXEY/H0b59e5SUlGDjxo144IEH\n8dlnixAIWAiFvCgq2ob09CQMHdoflmXhnXfmorIygS5d8rFp0xZs2rQdOTnpiMXS0K5dG5SUlGDF\nitUoLMxHUdF6fP3193C5KpFIEBs3bkY87obbnUAkEkJFRQKBQAhnnXUCzjzzDFiWhWOOOR5FRWvQ\ntm0eiosrEAq5UV1dg/Xr12PbtnLY/o0GMstAR8m8R6MuZGamY+nSFbChrgg73lhjv8kIhOMzMFdO\ni0oDEWYsIs07U3ZD60sj/jT1uWD7Ylbr/wn9UP/6YLu2GIgvA51WjvrQYdT/azFo0CA89dQTaN++\nMRX+75f+V60cv/qZz5qKmvaasxdRaWkp8/O70uf7I4G/MhTqxokTr6t7f8klExkK7U+JNxUjcDct\n6yaGw+mcP3/+TuWtXbuWqam5dLsvp3BveXzqqWd+tA2VlZV86qmnOHHiRF5wwQW85557uHz58npp\nZsyYwVAoi8C9tKwbGIlkcMGCBXXvE4kEhw8/nD5fJwIXMhAYwwEDDv3JeFQvv/x3er2ZFLSLK/T2\nfgt9vlNZULAfS0tLd5l31qxZDIUyKdGYr9fxOZfhcDrbtetOv/94An+l319IywpRrOjmUNBTDJfU\niWIMc4Le7k8g0IahUHq9ugYOPFjf/4VifJNEQd+4lrYFYRYlvlihpn2YwFnK3RhDlPs173Fabyfl\nVLIJPESJFRYicBOBuwlEOWjQEAaDUVrWGIpVYF8Cj9GyhtPmGP9C4FX9foXWa7jHdwk85uCw0h3j\nHWLjHFmQYmjxV4rFbCoFLaRAuStTxpW0LS5THf0yaCYpFO4tREHJuUPb6NP0R+rfy7X8bB2/AMVw\n5i8UwxQ/xVioE4G5BJ53zKFf6zOGTb0JpDMjI48bN2780fX3eyPsIxza7tI82Fp/QPRaHzVRWxqj\npl4Xew1NmTKFkchw2hBX6+jxBBiPx1lVVUWPx09gEwVS6gXHhnMXjz/+9J3Ku/32O+j1nuVI9xFz\ncjrssv6qqioecMAgBoMHU6zIMuhyDWE0msFvvvmmLl2vXgfrhinlWtbNPP308+veP/3005TD6Djd\ngI5hKNSOn3322Y/2v6Bgf92gTHsvoUBrJRiJHMxXXnlll3kPOugwChySyXs7gbMJnEyvt7tjTI+g\nmK9/4kh7g2606/V7Qg+K/rpZu7hjxw6SIuqtD8M0iLZ1HykwS6m62V6hf1MoFnqkWOz1om1d2NfR\ntg26MZu2daIcZKbs57XuQRSrxTAFQsxY8wUJHK3fr6dYLN5AcQe5SufiOK1vtLbzXaLd9vfzAAAg\nAElEQVTRQ8x8/qFjs8kxNr0oMF+nUawyG85Zex07068vabsc5FMOa5P+SYpIcCjF+vVCx7t/an8v\n0nkr1PkYTTns5jvSXks5+JK0v60ILKBYVIbo9Q7jgw8++KPr7/dG2EcOtN01CjkHwKMQy4CVEHOf\nc/Z0o5rpl1NlZSXIVNhShBjIBGpraxGPxyGS2SSI8jvFkTMNFRVVO5VXUVGJ2tpUx5NUtWpsnKZN\nm4bvv0+gomIWgPsBvI9E4kvs2HENrrrq5nrtdNZPptar/5JL/gQxbngZYj+0BCQ134/3v36/jKLf\nApnyo22vqGgsryDTk8mwx9SI4JzBKHdA9gajWrYghgXnQCxGPdi2bRsA1Dlz2zBalY7/ATEQIcSY\n4x7IfTIOsTYEBB3F78hrDCCg9Scc5TnrMX3KhjhEz4VYCBosA4Mub+CxTPSC+wB8AAFS/tTxMf1v\nzD7sL47/zZgYK0RL21wFMZJJYOdxdzfo19UQlfvHEMOkhn3yQFT9VQ3KStH6H4Sgm4QgBkVvQcbZ\nOYelWm8AYs0agR2FwI/aWv+Prp9m+v1REuxVuTdRU1909hpau3Ytk5KyaFmPEfiUgcDRHDNmfN37\nQw45gh7PMcoFFBB4TzmFNL755ps7lffVV18xFEqn+Pp8xFBoIC+5ZOIu63/iiScYCp3muPVW6e38\nTfbpc0hdugcffIThcFe9Qb/FYLAFZ82aRZKMx+O0LLdyDKack5mcnMmysrIf7f91191Mt7s7gf8o\n9xIjMImW9ShjsWyuW7dul3kfffRxhsOdKQC5b+sN/iYGAlmMRrPoct1P4FO63YO03HQCjytXYPzF\njiLwKYFHNP9a5TLcLC8vJyni1BYtCih+Y/+mgCK3o/iQvUHhxgoacDmtCTxL4DmtJ6r/T6dwWQ9r\nvUfp934U/6+TKVzUDJ3rVg04mKkULu4zCidrDDHO0+/G6MYJaj1A62mMG8ug+AzGKMDYH9B29j9G\n2/iAljuT4nhuHPDNnKXqsyRHv7Joc2X/0H7MpHB2BQTGaJlXUYxSXiXwIcVX7WJH+wZTxJGkgCLn\nEfib9tU40F9AWbO5FJ+80wkkMxhM5Xffffej6+/3RthHOLSfSwaZ43IAlzk+5vveQk29LvYq+uab\nb9i//wi2bduDZ5xxYb1DoLS0lIcffgxFDNOOQFdaViv26tV/l+W9//777NlzCAsKevKaa278UT3W\nokWL9ACcSXEOPpfAYIZCfXjXXffVpUskErz//ofYoUNvdu3an1OnTq1XTteufely3aob6QK6XCl8\n5513Gq0zkUhw6tSpvPHGm3jVVVdx0KCDGQxm0+vNZCzWgrm5nThgwMh6Is9dlfPgg4+wY8c+zM7u\nyOzsgrq2/fDDDxw69HC2bduDJ598Fh9++FFmZubR5Uqj15vKWCyXPl8ybWfsmG7OCQJ3My+vc726\nNm/ezP3260OPJ4MeT7pu4BmUQ9BPEWk+RkGAf5CWFaHHk8GkpFbMyWnPbt36cr/9+rFt2x70emO6\niRu0DosiOkymZaWwT5++TErK03fdKE7COwiUUByn2+vGP5Q2Ioex9BuhB8wtFJHh5F0cZKkUceBk\niqjQq+OQquUUUA5lo/8z+sZxenhEtX0GbSSFNvJLMkVH1o4iUq3Sdqfou8toO18n61ikaL0hinhx\nHYGnaFs6zqKIhw+kbdEY1QOvjz4bpmVFWVjYq5518b5C+B870Iz5/I0Q3MWGn72Fmnpd/O7otdf+\nwaysfIZCqRw79gSWlJTssbJnzpzJ3NyO9HgidLtTGImk88orr61zF/g5tGLFChYW9qLHE2AgEOWk\nSc/vMu15512m3N6fKFzP/gyFBnHo0DG7VeeepJde+juDwRg9ngDbt+/BJUuW7DJtdXU1x449Vjf5\nEAG3woTF6HIF2blzHy5atGiXebt1O4iWNZDAVbSsTHo8SXS7r2QgcCzz8gq5bds2kuTs2bOZlJSp\nrg5uulw+jhw5jklJ2XoABZmV1Zo33XQLQ6GWtKwJekCYA2fng2zEiCPpcvk0TZgeT5Q5OR0YCvWn\nZf2JlpVHIECXK0y/P5kpKbm8996/sFev/rTdFow7QhJdLvO/gfIyJvguPYzcjva49ZlxzzDpQhTj\nkMtoG3oYt4kr9JCOUC4OxiXAq/kyKVzeQQTCHDZs5O8aGeSnCP9jB5qhAT/zWVNRU6+LZvqVaMeO\nHT96KK1du5Z+fzJtmKlyihjpC0YiXfnuu+/+hq2tT7W1tXWGID+XNmzYwJqamp+dftq0aYxEDqRA\nNpFi4BGs++73n8D77qvPGe/YsYMVFRWsrKyse1ZcXFx3qQmHUynGEHSUW//jpPLy8jp80A8++ICR\nSCFtiKz19HrDdYeqoSuv/BM9ngscZb7M/fcfTFKsZE3bLr98It3u87S8cgIvsEuXvqyqqmLLlp0o\nhjsJijTgTj3YTnCU+5YeZG0oIk3zfATtuG+FFG46SBv6LM5IpBfffvvt3Zq/3xthHznQdtcopKF7\nPwA8tCca0kzN9GMUiUTgcu16uRYXF8PrTYMNMxWEoGaUwuVqg+3bt/8GrWycXC7XbqNKZGZmwuP5\n+ch00r+2sH/SeRB/LfG1qq4uwNat9hhYloVIJIJAIFDnR2hZFpKSkhCNRpFIJFBZuQN2ZKj6Y2+O\nAycFg0F4vd669rhcebB9xDLhdodQXl5eL8/mzdsRj7dzPGlXN1d+v7+ubVu3lqC2toOWFwTQEeXl\nlfD5fCgtrYLAelkQqLBCTdepXrmyZxejfrSrQog/HCCGH601nYEGc8Oy2jbp+mmmn08/9xdzEATH\nJgOiMzMmR1GIOVAz7cW0ZcsWTJo0CaWlZRgzZjQOOOCAn5Xvk08+wfTpMxCLJeGPf/wjkpOTfzpT\nE1FBQQGSk90oL78bicSpEOioVQCWgvwEBx305E+UIE7pr732Gr7++ht06NAeJ554Yt0h+sEHH2DO\nnLlIS0vFhAkTfvYBVVJSgnPOOQdFRWswcuQI/OlPAoRTWVmJZ555BuvXb8DgwYNw8MEHAxDn9cmT\nJ6OmJo5jjjkaiUQCr732D/h8Xpx00kkKcYad2jRgwABUVZ0DgXMKQA6gAIBrAHRAMPgURox4BS+9\n9BKmTn0dtbW1OOKIP2DMmDF44YUXUFxcgpEjR2DdunX4/PMvkJ/fFrW11WhIixZ9j2XLluHcc9/E\n2rVr0KdPH5x22ml17fr2229x1VVXYfHipSgrWwmJNjURbvfjaNUqF9OnT8fKlavwww/fY/bsOYjH\n4/B43IjH+0Duy2+ivDyK4cOH44cffkBlZRWSk2Pwev1wuV5CItEFQAYs6whs316Djh07oqZmMwRg\naB4ECmwR5CC/BxIHLRcCLlQL2a7O17p+gMBa1QC4A2LVORiCD3lpXZnl5TMwadJ2vPvuu2jdug2O\nPvoodOrkPCyb6fdGgyH6s3Worzu7DI2j3jcVNTXnvtfRpk2b2KJFAf3+k+lyXc1QKJPTp0//yXyv\nv/46Q6EsWtY19PtPYKtWHbl169bfoMX/PS1btoy9ew9lKJTKUCibwWCM7dvvz48//vhn5T/rrIsY\nDncncD3D4b488siTmEgk+NxzLzAUyqFl/ZmBwFFs3777jzpmGyorK1On8aEUa9Jsjh49jpWVlezR\noz+DwdG0rOsYCrXmQw89yqVLlzIWy6bXey7d7ssYCKQyEIjR7b6cXu/ZTEnJ4YoVK0jS0aZr6feP\no9ebQjFkkHpEn3Q4gasJJPPCCy/iSSedSY+nG8WvrBtdrpYMBNLo959Ay7qGHk8qfb5WjYoW8/I6\nc/bs2bzttrsZCLTVeobQstoyFsvm8uXL+eWXXyr02sm0ndnT6fHE2K/foRww4FCGQoMp1pERivP0\niQ4dWXuKlWEPfX86xRctRDHQOJ62w3MaBfl/pOq7jG5MnODlY3SRBsLrSk1vrBhNSJwc7Y/xFbyE\nNvRXOkUPFybwR1rWpQyH0zlv3rxftFb3NsI+InLcXaiT1qgfiW9vI52bfZdI4q233sKXX36J/Px8\nnHDCCXVcxNatW/HCCy+grKwMo0ePhs/nw/nnX4D33nND/OGzAWQhOflCXHXVORg3bhwKCwsxe/Zs\nfPTRR8jNzcXo0aNx7rnn4o033kIisT+AgwGE4PW+jzvvHI3LLtvZqPXtt9/Ghx9+iNWrV6Ndu3Y4\n9NBD0bdv353Sffjhh7jttttQW1uLNm3aYOnSpWjdujVuueWWOiiqhvTaa6/hgQcewNatW5GRkYHl\ny5cjHo9j+PDhGD9+PB566CHMnz8fiUQCycnJ6NatGwKBAJYvX46ioiKEw2Hk5+ejf//+AIRb9Xg8\nyMnJwcknn4y0tDQAwPTp03H44eORSJwNEVVuhmU9gKQkP4qLSyCgvi0AnIRgcCoeemgszjjjDADA\n119/jcmTJ+Orr75CWVkZtm3bjrVr16CkpAS1tdkQsN8g5KfTDsGgF1VVuUgkfoD8BB8BcCVSUpKw\nbVsXiOBjEQREtwaC+L8AAJGeHkHPnvtj1qz3ID/HOERUlgGJtu0CcBoEtHe6juJHEIT8SgB3Q7iP\njRDOpSNEHJcL4K+NzIAFy3IBIOzflhsi0jOgv86gniEA4yDoeFMh/m2NievSYYv6DMzVmRBvoBII\nuHEujP+fjJ2pxwMRr1ZAIKlWQfbj3hAUvis13V2QQKe1+txAeP1bx9ZQDMLRpQNYCxlDL4Rj8+r3\nQgi4cVcAz6J//1fx739Px75C/6vQV7NhKykA8WScuYu0TUFNe835DeiKK65lONyJlnUNw+GDePjh\nxzKRSHDz5s3MyWnHQOAEut1X0O9Po88X1RtqC4rl36EUNIk0ut0XMRhM5fjxxzMYbE3LuobB4EBa\nVlRv9pfTNqseSSCHhxwyaqf2XHPNjQyF2lOCH44gcAWDwWzee+99nDZtGr/77jsmEgm++eab2paT\nKAFID1DuIY8+XzKffPLJurSG7r77br0ZX0yBSUrT27UBBg7rbfpofdaWYh6eQbFQ66Dfr1QuKVXz\nX0yf7wRmZbXlxo0bOWfOHAYC6RRYqMvqOAtJf5WOWyYlZlkqgc6cOHEiE4kE586dy0AgTds4njaY\nr7GSG6R1V1P86dzKwYQo0FqXabtv0DrHUEzbc3R8+mi/T9Q8Z1PMyFtqfREKPNMfKNzUi7RjfBkO\na53mvZqCrnGM1hmiHb+t4aelvgvThs3KJnCKPjuXwKm0gYtDBIboOJigpR9SfLhytL6rKTBTQYrP\n3Zna/jGOMgI6DiN0rUQ1TxYljlprytqMEThYxziVYuyRRTHqEGMOGbveBCZqGzJ1bM7S+oP6Ocox\n7y0p6/4w2utomNabTPHhe48dOx74W/7sf3XCPsKh7S41FtN9d+O8/5rU1OviV6UtW7boIWWggyoZ\nDhfw008/5S233Eqvd4JjQ3pDf5A+SlBHY6nWnXJg3a6bRSvdqD6jbLBOR9nZulkECDxEjydYz9Kw\nuLiYXm9Y8x1O2+n2I92osmhZMR588OHMzm6vm8b7uqka67e1NIjylpXKoUNHs6qqiiTp82WxPhTU\nWbq5nqQb0zTHu9MpkEVhipOyce79ijbMUhbFGVfyeL1n8/rrb2SvXsMITHGUdZSOzaeOvIMp0EoD\nCUQYCORw4MAR7NTpQIpTssmbSxF/Oce8F8X36Wwtt5biz2VEZPmUDX8MJUCpR8eFlEMwn4LvOJFy\nYCQom/loymG5TMuZqmmfpWzecyjWeofrmBkn4gAlmnfDQ2yV/p1E8d+6gHL4DqccNksoB+fjjjxX\n0za570A7EnW2lnES5dDYoulPpVwcTP77NX03iqtFmCJyTHZ8dxP4WuvZSMFmPIj2epuv7btK+/+N\njncBbaf8NZTfwr2Oum+mWDaa79O1zTlav7HwTFAO60soB2R3Dht2WFNtA78KYR850HbXyrEWIucw\n1AbCwzfTb0DFxcXweJIgUD0A4Ifb3RLbt2/Hli3bUVNT4EhdABGjJGBPmUv/7wzgcYhSfBWAByBh\n6IohohVnGSEIzNCNSCTiqK62DQVKSkrg8UQgy6IAtsSiHUQstQ7kiXj//W+xbVsJRN26DRLD1Vi/\nZUNESoeAXId//asS9933AAAgHq/Wchu2xyCgO9+1g4jUYhCoImp/TBoTwNHOU1NTgM2bt6O0tEzb\nYcigujvzdtS2FwK4BZWVK/HZZyGsXr26QTtqsfOY5wA4DyLgqIDMy1JIzLINkKhJf4DE8doAEaOZ\n9ni0rA3ax+3aHhOsswtE/PZ/EMOHDZBgp0/p9/0hIrbH9d0T2oYFqE9vQsSDZiw9ECML0+8abcd2\n2EFYAYkRl6dtv1DTr4aI7v4Iid8bhQ1RtQN2EFRA1kRPHddNmnYVRHz6DURs6YPMSRQiFtyg9TjX\nWzUkEOd6iMr/asi8GLu3Fvq/CeZq6nZGrCiACKAmQsSexhrS0v9DEPHxUnTu7Ax420y/VxoBWW0v\n6meVPttbqKkvOr8qxeNxtmnThW73rRR0g+eYnNyCW7Zs4dy5cxkK5VJgjlbR4zmULpe5aZ5PETu9\noTfZCyiiIzpuoG69OccoHE4RBb3BABJ3Y+fOPeu1p7a2lu3adafLdbbezN+lcBbH0fYB+jeBjmzZ\nsh2Fe5mtdfxd+3CNtvElTf80jzzyFJJkly4HUjijVRSQXSO+OozC3QzVdx/ru7P1Fn+W9refcgjr\nKIglMQq3sZLAJwwEWnLmzJm8/fZ7GAodQOFS52pfYtqHtfosicKZpCoHQAJ/Z8uWnen1HlxXpvQl\nSoGMco75R/qsH4GFFA7mMcccfKrcwftax0Qdnyma/1WKX90TFHSLVNpxwOZqO4/RMgZQOJpptDns\n/+POHNmj2pbvKWgdEyncXj/tx0At70yK2PocChfch8KtfaPjdKuWdw4FosqU/yWFa4tSJALrKSDE\nbbXeHyii5wcp3KUBCx7SoJ1GTNiZAi82h8K5zdIxPlX7+WfaYudntLxXtN4rtA89td4FFG4uTBGN\nrqZwsucT2Kp1nqHlCySccNpZBDycPXt2U2wBvxphH+HQ/hvKgMRdHwO5Lu1N1NTr4lenlStXsm/f\n4QyFUtmpU29++eWXde8mTXqeWVn5TErK4qmnns1zzrmIfr8RawUIxOjxhOjzxfSHuVk3jGkEwszP\n784zzjiDlmX0QEdTnFgX0eWKNAoZtXr1avbrdyj9/ig9nhR6vUm6UWylHJSX0eXK56233sFgMI02\nMkMKbURzg6ZeQ7d7JG+++TaSItJs335/3dAjtMOURAmE2aZNZ9pBF700ARwty/Q3SjuAZiGBN3Wz\nFmSKRx99jKQczDfddDtbterCli07Mzu7rYp2TUBIU34S5TBNEIgzEDiel146kRMmnEe/P4W21Zwz\nKKcZywA9HhMkMkwgQK/3MIroNUHR80Xp8ZigoM78JmCm02LPQDfdRtExpetzv6aL6Wc8dz7IDK6k\n0XeZgJZJmjePctCYYJk5tK0CjU42g3JweCgiwgpKSJZhFEgqUvS2pk0mqKmB1DIBUG+g6LuO1Tn6\nWssu0jL+qfWM0jwGxspZVswxP8ay0cyFqdfgQprxD2s/MrVvYYperYI2ar+zzX4tI4uZma1/k9/6\nb0nYRw60n2vV0gnAdxB4ajrymUH4Yg+3678lnZtmMrRhwwY89dTT2LGjDOPG/QEHHngg1q1bh2OO\nOQkff/wF/P58uN1r8M47r+Oggw6qy/fyy1Nw+unnwetth5qaJXjkkfsxYcKpP1lfZWUlBg4cgc8/\n/wGkH5a1DX379sJ7772NJUuWoG/fYSgtjQHYAsuqQUZGGjZt2gYyFZZViT59OuH9999uNHipk9au\nXYvLL78CS5euxJAh/XHLLbfA7/dj1qxZmD37XWRlpePss89GMBjE4Ycfi3ffnYfq6gAsayv8fuDl\nlydh7NgjUFNTg6effhqLFy9Hnz49MX78+LqApg1p69at6N//UBQVlYOsQUFBOo444lBUV8dx1FFj\n0bt3bwBiifrSSy/hiy++Rn5+HqqqqrBu3UYMGtQf3bp1w7PPPoctW7Zg1qz3sXr1dng8Mfj9xTjy\nyDHo06cnTjvtNLjdjbt3fvDBB3jrrRlITk5CYWFHnHzyWXC726Ks7HtkZaXhsMOG4IYbbkD//q9g\nzZorG+QeCZ9vIaqrN8PjyUc8/j1sZP0cAOvg82WD/H/2vjvMiip5++3bN8fJiWGGnGHIQ5AoWUEU\nFDNGFGFdXTO65pzz6oeCAVSMawBZAxJEEURABYEhZ5AlzwAT7vv9UXWm7wjuurv6G0TqefqZuX3P\nOX3O6b5VXVVvVe1HVlYEp5wyALt27cIrr7yJsjI/xIQbABCEZXkA7ABpUIgeSEb7rdomDEFSlkPY\nRLmeN8jEXIh5MEm/3wcxG5rzcf1/XcJ4u+DEkmVBkI/Ua5dDKg94IGbNMoi51wUxQxdDTKPrdOyw\nnt8CB83ohryjGxOrrXtTru3LEAj48N13X6Ju3UQz8++fjhaU4y9dwFgIpnY6Di/JD1c3ojroqBJo\nFRUVmDdvHkpKStCuXTtEIpHK7xYvXoy5c+ciEAigYcOG2L59O8LhMF58cSK++eZ7RCI+7N5dopD2\nziCT4HZPQe/ex2HmzC+xf/+piMfLYduvY9SoC3HSSSehXbt22LdvH7777jvk5uaivLwcN954I7Zt\n24YOHTqgV69esCwLSUlJyMnJwdKlS7Fz507k5ubi+++/x+TJk5Gbm4tBgwahuLgYX3/9NVq1aoXs\n7Gx4vV60b98e77zzDqZMmYLMzEyMHfsydu8GyP1ISQmgR4/OWLJkFbZu/RGBgA89ehyHxx9/pEpA\n94YNG/D444/joYeeQDzeEhLzPw4NG9ZCYWErTJjwHuLx8+B2r0U0+iVGj74I9erVw4IFCxAIBNC0\naVPMmjUbS5euR2pqBPPnL8DatQdApsLt3ozzzz8ZZ545BMXFxfjiiy+watUqBAIB5ObmYvjw4cjN\nzcVZZ52D99+fgtJSAjgDQA5s+zG0aFEXKSkpWLBgEXbsOAAp5r4LwiD7wOP5B8hiVFScCzIC4EnY\ntoVQyIu9e22QjQB8A5erHE2bNkCvXsdjwYIF+Oc/d6GkpAx79vwTP/5YDMk2txTAOrhcFuJxG8LM\nUwFcDfHXJVIHAJ0hvjQTdGyE2AUAPoTU6d0LYewROL5AA8sv1O9mwinz4oL4oVboGjvr8QTEn+mF\nwNwbQkIISnSeRtgc0HkYgWRpnz0Jc/fAEYiACBlChGgUwOkQf+F5EMH3JMQXlgJgLpzK2CV6bpfO\nwQUJCSjTsTpB/HgTIYLbpev0QLwqmQBeQZs2jfHJJ58c0UkG/hs6WgTa0UbVqrb/mnTw4EF26dKP\noVBDRqOdmZ6eX5nY9oorrtdqzG3UVOJjMHgcLStVzSPt9bwxuTRSs0oHOoi0XIrZL4tATXq9rZmU\nVIOBQDJjsZ70elO0bX01aYUpPowIvd4cWlaILpfJRh7S69aiQMgFgh0Od6NlRen11mYk0oKBgDGL\ntVfTUG0Kou5aOmbF43RMH4H69PlSuG7dOpKS7Nhpl67rj1B8ODE9341ifmutayzQPmZePl3TCxST\nmwkEfpmCHAwxEGhExxQXoRSzrEEgyvT0/IT9G6lmsem6lzUTzFetdR5mzYU6jxvpmP5epJh+a2g/\nA2lvpf0iFL9NUA9zv6M6vjGdXU1gNQ81LbbSeT5HCR/or+tspc+GMTmX0fF1hXSuUTrow9q6vqA+\nA8kUROazFLNhTd3nMMWfN50OzD9N71VdXZ/JaN9G/2+TsL67KX5csxf16ZgJW+icQronfoq/bwQF\nrWjWPJZOpev8hGuYe9+YYhI3pm+vXqMnxQR5jvZtS8d82U3v0zBK4uQQi4qKqpM9/OqEo8Tk+Etp\nCCQy8eeOI4Wq+7n41ejhhx9hINCfBnbscj3ILl36c/bs2QwE8ik+KuNjSKb4RPYoI/gHpbZThAI8\nSCZQpO1X6OcG+uM+keLDIMUf01X/z6M48ON6XEZh+I/qD91A2rfoj35gwji3UmK2SPGFpFMSxsbo\nwNHT6VReJsXXY8AF85XhCAihZ8+BJMlwuAaFQTeglD0x4QlpyrDW6LkfdE6mavQTFADJd8rEDJR/\nOkXYG/h3ia4tSxlYVzq1t0opTDWVEjZxBYH79LuaFPh5LQrzf1/P76UIgA66/v56X8yap2mfJJ1z\nPTrgjX0UIfyB7nWMwAEC32j7Oyiw9jU8VJCZeyAle+SaWXQg7DUo/qDE2mY9dM+/oeNnS6GANyoo\n/tQu+n09vdcnUZ4JM+69el/PpPMydbEe5jn6E0VQDdDvb9HPN+sYBZRnzbQ/j/IsDqcANGKU5MK2\n7seZlJcTs46pet8yKALKhLiYUJIyXc9pdASpCfP4p14rnfIsxBL2YzOdODYvCwt7VjOH+HUJR4lA\n+6Ww/YF6XAgJ4T9Lj+cgNotj9CvT0qWrsH9/bxjYcTzeDytWrMSqVasgGRFMNd6uENPJXoipqCvE\nBLRZzzeERFcYqHVd/dwKYtrpDScd54kAtuv/JRAYtIG7D4RAsNtDzEJttV0mBCfUP2GcgRBfCiDZ\nHmpBTDnNIPBpQH4/gYQVRyCwaEBg3AFd04lYuVKS0xQXl0B8Id0hpiRAzEEGOp6v5xpBfCzb9HN/\nCEy+GcRnY0xaxq9jLC0eXcNWXd96OCBej/ZvCfGzDIJUP/4YAlFPhZjl1ib0CUMytOTp9S8GcBMk\nc8d3EJh7W92ThgBWJ/QNQe7lSm1j6bxa6XfX6RhmzYDcHwOPN/szGFJp2tajQudbD1LOcCXEo7AY\nYsJrpf2yda2rIWziJMj9KYeTK3Id5Jkx0PgTICa8AjihBdsA9IXzHPXXcXZpv9WQMI6QjrFDxzTt\nT4Q8Kysh97QpJETAD6kC3gGShe8riNn0BgBDdV9awcGtddDr7dC594OYHi2ImVs70U8AACAASURB\nVBS6d80hz9823UOzH1m6njIAQaxYUYRjdOTRLxVo50GCSryQIKYhejTVc8foV6bCwpYIBidBmDrh\n8YxDmzat0KJFC5CzIIwAAF6DMKIIhKF9CGFEmRBmPRPCeL7U9l9CmO5MiFCcBHHIxwH8DUCGXtMG\nMA4iFMsB/D+IoHhX236g4/0Acay/DBE2cUjMk4n3WQSJ3bEhMfgm/qk7hNlOg6RcehXyOAHAZB3r\nQgDPoFMnAVtEoyGdy3sQpgwAY2FZEQBrAMzXczNQFXDwHIQxfarjXg/gM0isUxGAa7XPmRAG1wTA\nFxD/0PNwYtpmQPwyRRC38ekAToUw6FX6fSOIgEDC/Viq1y/W8c+FMNG1ED/SNgCzIILgOe27Wfeh\npe51KZyXjQ1w4vgA4Cndx8E6r1cB3AYRMH+GCNQ9EN/a5xDmfKrei1YQwXyrrvFDHXMxgK8hgvaA\nrmkHhOHbEGGcAeAFmGdUYtzSdT+vBrAMIhhf1vmXafsdEIFWABE0WwA8COAVyLM8VtuW6n7EdZ5L\nAHybcJ2VEGG9D0AfyIvUaZA4tKUQIWcEz9v6NxniU5sAB6Dyhn63Uu/DaTrvUjjpw8y1AeBgJQDo\nGP2+aSmqOg5deu5IoerW3H81qqio4HnnXUqvN8ZgMIdNmrTj1q1bSZJPPPE3ut0mPVOIQIB+fw26\n3SFaVpCWlUnxMXjo+Ld8akrx0xRhdCDPAbpcKaxbt4CxWKbC3vuoycn4kcI0vgm3O0y321RWjrBq\n6iLjyzKmuyRKLNV2va5XTTd+WpafTnVid8IcTSHGJDZv3oE7d+7k+vXrFdLeQftLgtpAII1Llizh\nkCGn/mSNBtZuKh+nJOxFEh0/S1TPpdC2Y6xXrxl9vtSEMRIrJQcoptWg7r3x55n9jCbsearOJ6Bt\natCBvKdQMqCcoOdMKEKGfjZ9QxQ/UBYPb1Y0fqAkOmEQZm0mxMGs28D9jS/MPD8G7p6SsMZ0VoX/\nm7UZ/6sJZTDPRSBhDkt0bs/oeS+r+lnDCYdX12r+N9WlE8c2PrSUynvuwPLNGsy8AwnrS/STmXtl\nwiDM+t10wiHMOOa5SU8YN1vHqUcgyKSkjMrf4tFCOEpMjv8pPQngIzga21Qcvkbaf0r9IIKxCGJL\n+TlqB3lF/zm/XXU/F786bd26lWvWrDmkuOXu3bu5aNEiLl68mHv27OGKFSu4c+dOlpSUsKioiPv2\n7eOGDRv41Vdfcdy4cZwyZQrnzJnDf/zjH1y6dCljsQwKWGA5gS/p92fzyy+/5Ouvv85QqAtNXJj4\ng9ycNm0aV61axdWrV3Pjxo3cv38/r7rqOvr9TSmBrn+j2x3mo48+ytWrV/OZZ55hINCX4gsS/4Tb\n7eO6des4adIkLca5lOKreI9+fxJnzpzJr7/+mtOmTeP06dOrrPuyy0ZT/FoHKD6QuQQiXLx4ceWe\nrFmzhmPHjuX06dNZVFTEOXPm8LPPPuM777xDv78Wxad1kMAier0xLl++nIsWLeK8efP4/fffc//+\n/ayoqODatWu5fv16zpgxg6+99hrffvtt9uo1kJZ1j65lD4H7Wbt2cwYCLSnB3Uso8Xw2b7vtNt5/\n//1855139AXhdgKv0rLq0bJaUfw8TzMYTOWIESPodl+g+1BEYCrD4Uzm5NSj230RDy/IlhB4ieKv\nq0Hxl31LCSJO1nvmoqQku0MZtwFoZFFeVuZTQDEtKQHQMyg+wTRK0P1CArsJTKYDMPoTJfA4lxJ0\nH6P4srIIWMr4p1DSi6VTfIuFFKE5lBJv6NF9mqtriCgzbU0BZKRTQCvDKf4/N+Ul5jEK+CVIiYsL\n6DqeIXA5xQ8HFVB30/GJFujcBlN8qOdq26coqdiCOqebKMH+b9ARbHfr81uke3UNgdoMh9OOuurV\n+IMKNAsiTB7R4+RfYUwb4vSpBbGjLETVynyJ7aZB7C9Dfmas6n4ufhe0e/duut3BKkwyHD6dL730\nEidMmMBwODGf40Hatpf79+8/ZJx4PM6HH36cLVp0YceOfatUhd62bRtTU3Np27cReI/BYFdeeOEo\nklLNOBbrUOX60WhTLly48LDzLSoqYpMmBZS38/k02U0sq+bP9kmkadOmMRrtmHC9OIPBGly1atXP\n9nnrrbfYsWMXtm3bmc888wwHDjyTwPMJY0xmnTqtGYkMTDhXRrc7WFnxmSSXL1/OPn1OYZMmHXnZ\nZX9h//4nMjm5JuvWbcq5c+fypptupmXdkDDGcqam5vFwgszlCtEB3pCW1ZmW1Uc/L1BhE1DG7aUI\nfzIQyGG3bn0oLwQZ+vd2SmaRxLyK61SgpFLAP5IbMiUliz5fPkVLOo4CgImr4KnLpKSaOrehKoSO\nV0GTRwEhpatAOEUFVOK6BqnAqanzyqcAcJ6iCFCjeWXrkUwJ2G5K0bbqUrK/tKCTUHhFwvh3UzSu\nlfq5XNvl0UFo9vjJnLJ07DkJ5x7Q+bSjbfsPqbz9eyf8QQUaIIKnt/4fhDhv/hfqCNH0DF2vx0/p\nCogTYDyOCbT/ieLxOFNTc+kk993IYLAGv/76a27atInRaCYFGbeIPt/Z7NVr0H91ndWrV/PUU4ez\nY8d+vOOOe1leXk6S3LRpEwOBxBRS8xgMphyWSfzwww+MRNJpWddQEHExSlqj6+h2J/PAgQP/dh57\n9+5lZmZtulz3ElhEj+cKNm3a/hCt19BDDz1KlyuZgkp8kJbViL17D2AwmEfRRj9nMNiE9977AJOS\nsmlZT+tenccuXfr97DzOO+9SBoPtCTzEQKAvu3Xrz3nz5jEYTKdoNfN5OEHWqVNv+v39KajU4RSU\n5iN0zKm3qLC5mRICEaFoQ4LkDIfTuGHDBt3zIRRk4Lk6XmM6iNG79fM9yuxbE4jQsk7UOmd1KGnT\nFlEQjdkMBGrwvffe4/jx4xkKdaCjkd+h+9ePokU+QKlnFqSD5NyoQqy1zvk9FV4tKemvHqJA7lNV\n8NWnoGdNGMo03Y9OdMygSXRg/PtU0AV+cq49BQkZowjZtASB95mOk01BkX5F0VIzKAmwc5mcnH1M\nQztKaASAeRDvKSBZRj/9H8ccCseLDgBn41AzZg2IF9+CCLQ/jMnxt6IvvviCsVgWo9Fm9PmSePfd\nD1R+t2jRIhYW9mJubhOeffYI7t2791e//oQJrzAQSGY02pzBYArfeefvh2137rmX0LLuSGDwJnZr\nMP3+DC5fvvwXXW/VqlXs0WMgc3Mbc9CgM7ht27afbev3RymxZ0Yb2kHb9vOZZ/4f69dvwzp1WvKR\nRx5nPB7n4sWL2bFjH+bmNuEZZ1zI3bt3H3bMLVu2aMqxPTTaXCjUgHPmzOHHH398WEFGkjNnzmQ4\n3FTnslOFkYlr+4ECOU+jCHnT9066XFFGo80ZDqdV5h2cNOkNBgKJMVoRSlhBugqyfAJhulypWkao\nWaXwse2zWKtWU/r9mXS7U+nzZTA/vxknTJhIUny+Z5xxAf3+DLrdtVTgZFF8T0UJc2upAiafIpDv\np2hkubRtHy+44GKdj0mfVayfPZRYu2Id+waK5tVM1z9F/z6gAq8RnXRXpsRNLh2faRIlY38SHT9g\nPh3/mkmxZXySAdp2JsPhNM6ePfsXPXO/J8JRItDc/75JFRoFwW3P0c/LIVCn/4V+yUY+CtHaCAfP\ne1i69dZbK//v3r07unfv/r/N7iiljh07YsOGIhQVFSErK6tKgc0WLVpgzpyPf9Prn3XWGejXrw/e\nf/99PPfcJNx11xPYsGETRo26tErqqb17S0AmZsLPhiAJ30ZZWR20aHEcQqEwHnnkVpxzzjkAgP37\n9+O6627BzJlzUbduHh599C7Url0b06a9V2UOn332Gc4+eyR27NgHv9+F7OwcdO3aAaWl+yEoUROG\nEINl+XDyySfhkksuBiApvq66agw+++xL1KqVi9deG4u8vLyfXW9JSQnc7hBKSw2c3g3bTkeHDoWH\ntI1GayEnJwsTJ16OtLRUuFzpOpckCGIwCYJMNJURUlC1WkANFBZ2QDxegXXrDmDo0OEoKSlFRYWl\nKbUsCApyHgRVOAKCgrQBdERqaip2796K0tIYBGWYhIqKuigu/hypqckIBiNo1aopHnvsHqxYsQI9\negzCvn0lOO+8objzzhuxdOlSPPjg09i4cQuWL98GKRJbAsGQ2XDSS/0A4CUImvQAKioqMG7cJAg6\ndwDEAHQtxBNRAeASAN/r/CdB2JcbkiLrPAga8nUIYrMxxPBzd0K7XRBkY0jn8YPuVwSCNN0CCQew\nIShLALDg9/uRlpaBoUMH4rbbbkY0Gv3Z+/x7oenTp2P69OnVPY1qp7n6d4H+dcPBsv631AFVTY43\n4FBgyCoITn01BCO8FRII9FOq7hedI47i8Thfe+01XnTRaN5++53cs2cPt23bxhtvvJkjRvyJkydP\nrra5LVy4kMFgGsU3NYXBYHPed99DVdo899xzdLuzKUHQc1WTuFGPNAoAog+BMC+9dCTLy8vZt+/J\n9PuHEPiEtv1XZmXVOURzWrRoEV2uGMXv8wkFcJBGy2qmWVKCFLPaZQRasmbN+lXMTCeccCo9ntYE\nBtOyejE9vSanTp3Kyy67gldffT1XrlxZ5Xrl5eVs3Lgt3e6r6CABqx4+X46u6VUCf6fPl89nnnmW\nqak1aVmPEVhCj+fPTE6uSdtuQDHhjaLbHaXf34RiHptBvz+PLpefToHTqLb9hOJnS6NooPfpOodR\nCojW1PbtVJv5gKIRmyS9mRR/1Sd0u69hVlYdTTg9nsBk+nwN2aZNJ/p8MYpJ7xTVhjpRMuM/qJrQ\nGDoIzgiBiRTzd45qVnUoZr5xdJIshyjVAD6hAFKOowA+0inI0ywKoONNHedOXU86xcz6CSUYPkzg\nfP18MauiQkOU5AIfU0yb2ZTg8XcI1KDHU5t//evtv90PohoJR4mG9p/SAwBuhASY9AbwDoC7/scx\n3RATZi1IUMjPgUIMjccxk+Mvpptuuo3BYBMCj9DnO4t16zZnZmZtejyXEHiIwWAtPv30sz/bPx6P\n86233uLVV1/Hp556qrL45n9L8XicEydO5NVXX8c+ffoT+CvFh/MwgeFMS8uvbLt+/Xr1UfWjZNSI\nMRBIYSyWpYywiOJbaUKgFy2rDk844VQNaTAmKzIS6cn33nuPpFTBbt++E/PzjVmslI5QaUHJYPGQ\nMsIQxUfzMAOB2nzssSdJkpMnT6aALnIofqeOBEJ0uYIE7qDLdS2j0UyuWLGCJSUlfOyxx3jNNdfz\n5ZdfPqwgkzWYMIi+FESfoD+bNOnIiy++hMnJ2fT7k5mTU5uZmXXocvUm8CgtqxV79OjPk04awkgk\nl2lpdejxBCh+pwuVISfTMZ/GKYJuhDJxk5HlQe1zpjL8DAqQ4w4VKDfo/8na5hm63QWUTB5mHV/Q\ngdXfqOO46aTYmkZ5IXFTEIPtda2m/4cqXBLBGLdQhGC7hHMHKUL2K/07lCJ4zfevUoTvTRRTZRfK\ni8kUiuCr0HYz9R7fQRGKfRPG2KPzdFME6RMEOjEtrdb/9PwfqYQ/qEBzQewTb+pxMX6dhJb9IUJy\nBURDA8S+cMlh2o7HMYH2i6i8vJxut59Ouqk4vd769HgSS4osYGpqzZ8d4/rrb2Yo1ITAnQwE+rJj\nx14sKyv7r+d00UWjGQq1JnAn3e58yltzG8pb9O20rMxKwTFmzF9p25crA+tCARncwWCwPsU3Yxho\nZ8obeTu6XEm65n2Va45EOnPKlCk844xzVHDcRNFY/Co4DKM3IQhUhjwgYZ++ZyyWxfHjX2QgYKDy\nZ1De4pvo9XtSNJgyulxjOHLkn9myZWcGAoN4eEFWR/v1pWgTOcpcB+maXlEB0ljXfyedqtBGQO2h\nZQXp9x9P4E56PHVUKAylCPwk3SMj4CsomlF/vV6iQJpNSZ1GiiAcqPO6O6HNCxTtridF0zsz4btp\nOrd2up+zKQJlI0XgmH07VffsAjrpw0jx1yVRQgjMuWsoGngrOqm69tGpTB6laJiJKcXG6xxMSZ+/\nUISziXMzqboG0vE9TtTrmDG269wH67yTCKQwI6POf/3sH8mEP6BAc+PICqI+HFX3c3FE0cGDB+ly\neWjg2wDp9bagbY9O+OFuYDicdtj+xcXFdLsDBLbSQJ7D4QJ+8skn/9V8Nm3apHXDdtMICdF0uiYw\nq2UMBGKMx+P885+vVib+HiUWqaJyzpbloQiENEoNK1I0vQh79OjLYLAHgVfo9V7CunVbcOfOncrM\n3ktYexOKoJhIKQRaI2GvblGGa9puo98fZWpqTUohUANY8FbZHzGDfULgEfbs2S+hf+Ixg6J1mH4H\nlXmupyNc2ynTPo0i0AwT/idFEO9MaJtMSdRLysuLi2JavJQiAI+jBL+/QhHCqbpvN+hh5rWcAmen\n9n+QIiyqhisILF+AHE681niKoBxL0YIWa5sknX9Gwr6RYjYco3N/SPslU4LNa+l4d1G0vY8pLw7n\n6r3qSgkPyNe19KCYSp8k8DSdWmat6OTiJAWAYhIBvMKqeTd3UQT8KL1GO4ogjFOE//kEUnjRRSP+\nl5/kEUv4Awo0QPIe5Vf3JP4FVfdz8ZtQSUkJhw+/lCkpNVmrVnO+//77/7bPypUr2aFDL7rdSbSs\nfGVEzzEUSlW/xyQCC2hZ3en1prBHj4HctGlTlTHWrFmjxT6Nn6ExQ6HOfOedd/jCCy+xRo1GTEnJ\nZVZWA9p2lLadzEaNWrJBgzaVn0Mhk03E+GGSKEG7xm9Ug5Z1egLTKaFte1hRUcHZs2fTtk12iyjF\njPQkgXK6XF41WdZjVWGRwx49BvCWW+5g8+aFDIWyGYvlMBbL1XksSGgrMUq2naZ7ElKGfgtF0IWV\n8S2gZfWibSdRNEMjiH7UPhUJY3ZThnw4QXYaRdgs0rmYfiUU01ZZQtsBlKDlbDpZWlLooPKSdT/S\n6WTxyKIIsUSknl8Z9wiKVmWKYtagJN5Np8SbzaeYTodTAowjOr6pGPApReNqQokxI0Vg2An3Nynh\nmiY7icnW4aMk+P2rzieTpvCpkxnEZCcxz4nJ4mHmYrLMGFi9QSyacWJ0njOTveSdhD2dRAe92IXy\nkpSmY7dg1WwryRRBWUQRpH1psq489thjv9VPvdoIf1CBNguSOG0agPf1eO9f9vi/pep+Ln4TOvvs\ni+n3n0QJGP0Hg8EMzp8//2fb79+/nzk59ehyPUBgLS3rPrpcUbZt250LFy7kzJkz2bRpR1pWEiVO\naDnd7jFs2LB1ldisk08+i2L+WkkRiPKDf/bZZxkM1iQwSxnB1ZSs708oI3tYP99GJ2P5PEoQ7MXK\ndL6hZT3BcDhdGcxbep1hzM9vSpJ84omnKVrYQoogaqTM53haVoyzZ89mWloeBaq9Sq9Xh17vWWzT\npjODwVyKWWopBZiQpn9/oFPypReFuRdQwBpfKtNsq8yyJcUM10j7D6RoFysob/dhin9mFatC5xOP\nSRTI+YW69kEUDeBP2m+8nh+ue/BqAnO9Uveyo7b5SK/dh2KWjOm9WUkxj0V0TSsomk2EAnBoRtFo\nalK03gjFvPmyritH11xLx+yqcx5AEWKm0sDxei1TxSFF72l73b8v9BqNKILhUp1/d4pJt1DbzdF9\nT6b4whZTTJl1KJpiA/3efNeMTqb9QXoPVlGAK2Zf/q5t/qprqqNzX0DRDuvQSX1VT69t9vc5Otn3\n79JzDyXMMaxrTCMQ5ubNm3/z3/3/JeEPKtC66dE94ehWfdM5hKr7ufhNKBLJoGOOIm37Gt55550/\n237+/PmMRJpVYarRaHN+/fXXlW2mTp3KaDQxQ0KcgUAW165dW9nG54vQceiTwJ/o9Tbk8cefQAns\n3UBh/sZc+DnFvJTIzGsrQzK+jTMJtGc4nMq2bXvw7LPPo2gPbZQRDmZWVj2SZKtW3SmCzoz1hjKV\nBnS5RvGuu+5iUVERa9VqpkynH4G1FFNggCJYTd95yhRrUZh5mjKuMmW8sxLaPq15I0cknPunMrti\nPZ+sY12szPdwguwSigA0n8soGs25yiizlFE2JXC6MluTLmoORWAZDSON4k8yY63Xvonm4+06x9UJ\n566naJzGPJmpfRvr/I3gTNQye1LMbtR5Jpozm2qfrpRUVfdTBOHshP5PUgROUsK4xbqGmQnt/kan\nXBEpLxmtKGbfMKXemvnuMzr+vSAdkyspZXIe0f/Pp7wsNNLxHqQIrxoUjaw2RRs2uR4TS+h0p2is\niffQpMm6mWKezSEQ5H333ffb/eCrgXCUCLRfmm0/AOBKSBrqRgBmQ6pXT4ekGD9GvyGFQlFIxnwh\nj2fdv4yFiUajKC/fDon9AYASlJX9WKVPNBpFRcUmOPE2O1FRsQ/hcLiyTSBQ9brAWlhWMVJSYrDt\ndZDyGsWQ7OmAPCbbIdnZAYmw2AGJdYKOFYZtb8PUqe9i3rxpqFOnFtxuG5LZfR2ACxGLSWmc1NQY\nJIs+EvrHAXSH1yvrqVevHu6883qEQm0hmdHzAKyD2+2Cba+tMnfJtH4TgNqQuKMxkKz2rLJOl2sd\nunQpRDC45Sf9A5DYqGch2fL7QaoQLENViumYYUgJGsMrNkMwVE9CMuYvhWURwF8g2eQP6D7MgZSM\n2QQnFi74k71YCyl/su4n5+yfnFuBqqVZ9ukcdgAYBintAjjlfuKQKgGl+jnxGciGVEToDfnZ14JE\n0hz6nEjcGOGU8PFB3PCJ7dYkXMf08+gR18+GEvslXo86ThTOfYxCWNt6SImcIki1q9aQ+Dcbkom/\nDFJ6CJAUsVshz/M+PWcqXffUsUw1bRdyc3NxjH6/9Dqk3sIlED/aY9U7nZ+l6n7R+U3olVdeZTCY\nTeAW+nxnsWbNhv8yl1w8Hufpp5/PUKiQwB0MhQo5bNh5VeKoKioq2KvXIAVP3M5QqDkvv/yaKuOM\nG/cC3e4MfTsdQstKZWFhD65du5YpKTXo8YygAA5qU1ILHUcnZdLtdKpEX6Vv0UkECti2bbdK0+aW\nLVuYkZFPj+dCWtZNDATSOWXKFJISp2bbYQpC7c80PhOPZyDz8hpx165dJMXH2KhRG/r9pxC4jcFg\nPu+4426mpubS47lYtRQx6QUCdZiT04C23YeCuMujbefQtiO0rOvodo9kUlI2Fy9ezLp1m9PnG0bL\nuoViWgtSzIt/+clbvDlupWisebr+RhQTWG/9Lke1m0ICtzMQaMn+/U/W1Fd/0bZ1tG9n1Wjq6+f6\nupen6/1IooAVYhRTo5mjreduoqP1tdUx6qkW0oxiivuzjtmSoq3dTtHOwhRN7laKKdaY8YbR8W1d\nRTGRBin+pSgl7dbFdNCFvoS96EHRPoMUTfMSHcun/19Dx+Q3hk6l8cTvQgQuophBU3TNJ+m1bqAA\nSpLo5LRMnFOMTlxeX4qvM0wxg99O8anla58meq4FRWM8Q+9rPQJhWlagMo3b0UI4SjS0Xwq5/w5S\nCAmQ16x5cCrfHUmk9+boo88//xyTJ09FamoSLrroIiQlJf3L9vF4HBMnTsS33y7G4sXf45tvlsPj\n8WLMmNEYOfJSAEB5eTnGjx+PoqJVaN++DYYMGYKKigo88MAjmDZtDurWrYn+/XvgxRcnYOfOHRg4\n8ASMHj0aXq8XmzdvxvjxL6C4uATRaBgzZsxCRUUFzjhjGMrLy/HWW+/Atm00atQAM2bMwtq1a5GR\nkYnTThuCMWPGwO12ktRs27YNzz8/Dvv2FePkk09C27ZtK79btmwZLrtsFJYvL0JWVibatm2HunVr\nH7IHxcXFGDt2LLZs+RHHH98dvXv3rpzjnj17QVYAsNGt23Ho2bMnxo4di48//hRerxcDBvRDq1at\n8Pbbf4fP58X555+HGjVqYM+ePXjuueewbds/0aRJQ8yfvwCPP/7IIXt99tnD8eWXX+DgwTIMHDgA\nbdu2xdSpH2PWrBmwLBvRaAixWCoKC9sgFkvGt98uQmZmFnr27I5hw4ZhwYIFePvtv8OygGXLlmLl\nyjUIhfzo2LEzwuEgXnvtTaxduw4ulwW324LfH0BaWgp27twLrzeIXbu2wev1Y8iQk3DppZfirrvu\nwaefTkNx8R5UVABer41ateogJSUJxcUHkZeXg+XL12H58jWw7VLUqlUDpaXEqlVbQB6AZQGRSBDl\n5eUIh/3w+XzYvn0XDh48CDIIr5fweoEDBw6ivLwCgAcejwvxeBzl5aVwtDMAcMG2faioAEQbq9Dz\nFgAvYrEQiov3ory8XPsYjTSeMIYNYTtl2s9854doVuUQjSyeMHZIr7X/ML8OC1X5t0/7V8DRGBPb\nWHr9cuTkZGP16tXweo+uMpCanefXCMH6XdCCf/P5SKHqftGpVjpw4AA3bdrEsrIylpaW8rvvvuPg\nwabU/BgK/LoGH3jgYZaWlnLTpk3cs2cPN27cyA0bNvDAgQM888wLVWubRI9nNPPzG3PVqlXct28f\nSdGGNm/ezH379nHTpk3cuXMn//nPf/7snOLxODdt2sSlS5eyvLycxcXF3LBhA9esWcP58+f/y76H\nW9v27dv/baZzszYTL2e0wYqKikotdf/+/Vy9ejXnz5/P4uLiw45TVlbGTZs2sbQ0MfjaObZt2/az\nSWoT++7fv5+bN28+JBnyzp07uWPHjsrPZm/Ly8u5fft27t69m6effh4Dge6V9yMvrzF37drF5s0L\n6fMNIzCJgcAQdunSj/F4nPF4vLIvKRrwrFmzqnxOTa1J276OwDgGAgVs0aKQfn8rSjmXUQTS6fd3\nZteufThz5ky+//77ijZtS0FA/pnBYBojkXQKyOYlClAjl5JdJYfRaAY3bdrEzMw6dLtHUIAxx6kG\nVJ+iXb5E4ATm5NRngwYtVdMaSfGdNdO2AQr0/jkKKOU01azqUyD6N9BBVD5O0UBzCEygoFgjlMoB\nLVUbvIICxjG1/lIomuck1fwMCjRLr5dMAfs8Tp8vmR988MFRl5iYPHo0BljlawAAIABJREFUtF9K\nFRCHiDnKE/7f8y/6/V9TdT8X1UbPPz9eS8KYYokG7uzRH20aTVJXtzvKUCiFbncKnfIcEXo8Qbpc\nPjrZ10mXqy3d7hA9niB79hxArzdE247QKY7opW2H2KvXoEMEQ3FxMZs2bUdTLNO2Yzp+KIFxeHjy\nyaf/Sybxwgsv0esNa6oqP93uEE8++UyWlpYe0nbKlCkMhVLo96czGs1kkyZtaFku2nYSXS4P/f4o\nhww5nbbtp5Oh3cdbb721yjjTp09nNJpxWEHmcoUJeOhyhdiuXfcqQokkZ8+erZk90unxhOl2B+n3\npzEnpx6XLFnC0tJSnnLK2fR4wvR6I+zX7xQ+9NBj9HpD9PvT6POl0OMJ0+Uy92Z3wvVbMBbLoQNp\nf5BAGYPBGlywYAG7du1PrzdKjyfE5OQ8vf8Cje/bdwD9/gjF5DaSToFSU6TUT6dorLlHBkZvE9iR\nMI9uygQNLD9MKQMT0s8enXtzOsCLYj0fpiBSzfhmji46iYJNcdBkiqnwoir3S66TTscUaK5nMoiY\neV5BB8bvpRNmENDr5dABrpTp9cxYbkp8YpxiYpVxatVq+otfxH4vhD+YQPu9UHU/F9VC3333HX2+\nNDoFM8N0AkYNSosUOHSG/jC/0HNTKP6Se5X5eOgEKpPiW3hbxzN5BmtRMmn0pGRtOEifbyhHjbqq\nyrzOPPMCypt7qbbrQPF7xClv1n0JbCNQi2PHjj3s2pYsWcJgMIOCLBxMQcCVMBDoy1tvvatK261b\ntzIUSqODuPuQ4js5j5KdYh8Fcp6jjG+ytvuCQJDfffcdScnMfzhBNmLEn+h2t6FoKjsJlNO2L+Sp\npw6vnENJSYmm5vqAEm+WQWCZjvEs8/Ob8Pbb72Yg0Efv1QF6vd3UV2mu+zDFD7mH4sN5JGEe2RRh\nEKegFWsRmMZQKJ9Dh55Nn+8sZcx7dJ736+chyqSv0vOdKIKyjBJonKzPz1qKH8qUsnlL98tLp1IA\nKejNFyjaVJAC/y+jFBkN67NSSBF8ps8BnYOpyj2aIkz+SRFa43Qu9XQOpq7ZX7Tfh/p5NkWgbaX4\nurIo6amOpzzv3yRc8xqKtlebElNWTNHy0vUaDekI3Apd67v63LTQftfofdihbS7igAFDf90fcTUT\njgm0I5Kq+7n4Tembb75h06YdGItls2fPQdyyZQtJ8qWXXqLHc4r+KJfqD5wUweRhVWjyKRTndyKz\nNrFeNoE0ulzNKUCKK7XtLorZ5kyKYLhcmcLEhDE+YcuW3UiSb7zxJnNyGtCyUihwa9PmZQpQgQS2\nKFMjgdt50kmnVBYY3bFjB7dv386XX36ZI0eOZDg8mBJb9SElhmksgRPodqcyFMrggAEns6SkRLWq\nzqy6tgasGjpgmFyIYl57gyJwC/joo4/+pK85MhkON2P9+u0oIIT7dO3/j8DNTEnJ4fr160lK0mO/\nP4ti3r2P8oZvximly+Vmw4YFup+kCLEetKxzEtqVUbSHcoqprQ6Bf1CAGR5WFSyX07bbsnXrLszP\nb0EJnTD3vj1FcOfofcugA3xITBV1C+XFgxRBnJjTkBTh1J7ycjOVIlBzKYHlCw/zPBXo/v6dIpxu\n0PmfQHkpCVMEytKEPvdTYu3m6TyHJXx362Gu0YQiEJtQXsZOpQTB30cRYB9QAsADlGcuMX3Xcjop\nxdpQgD7/oDzfTSnhJabStam99lBC/8VMTa1VXWzgNyEcE2hHJFX3c/Gb0datW7Xw5osE1tHtvobN\nmhUyHo9zxowZ9HrzldHtomhgyyiCLJ1OjNU+ZY4hStYGUt5aA5Q3aZNxYgBdru5aE+tObXe39juO\nosn9hWIGEmHpct3IIUPO4eeff06/P5MiyEx6I2q7cygaAim+mFYU5t2ZgUCEodDJDIcHMTU1l8nJ\nNRgKncxA4ESd01AdL40iJEx+wx8IdGROTgMuXLhQ52xyV67QNTWlI3w/oJicTqG8gWfqmg4nyMxx\nGd3uIAcMGEpBH6ZQApszCRTS5RrMcDidX3zxBQsKOikzPEuZZi7FhFtK0Via0e0epvN6QNdzHAVt\nZ/JKfkJBBMaVGYcp8VqdtJ8pzHqALldzHn98P95zzwN0uVIozP8ARVNpqfszV+eaQtG8ztb1mxed\nETrPPZSiq5kUYSXMW54ngzJMZtVsL4v0u236eYfOMUrRmjZSNGQT5Lyajmnzae1TTnlhyadokkna\nvli/v0P7GI1tEx0tMKBruUrX8a5euw7lxS6o6x6csN7XKRpYgKLNXar3wMQnDqH44oKU38UYiuZo\nTJNPsFWrrtXNEn5VwjGBdkRSdT8Xvxm9++67jEYTcwPG6fMlc+vWrYzH41oIM5MCjzZZ1A0EO6gM\nUcrYC9NPojjBM5Sx1KIIGCcY2e0eSY8nxmi0Py0rjSKEKijaWU398TelbbdnTk49btiwgdddN4ai\nSZBiEsunvAU3U4ZRlyIMjH+lNgOBTLpcN1de17Ja07L+mvD5Wtq2gc0bc2IZRUC8Qck6ks6zzjpL\n12MyXZg0R4bBnq7rnp7ASA8VYCkpuQnXqSDQhsOGncmNGzcyEEijvNHfRXmjN0xyPPPymjIQ6Jdw\n7j0CUXo8ufT7W1JMfYYpfqL78Y62P48iVHrpnBvStpvp/WtC0WZ9FC0kXe9dTXbu3Ju7du2i1xum\naGe1KWa0LFZN8vuMMmlSBGwTivbRTufRQPeuBx3B1Uev9bKeW0AJmjYpwobrMxCkk16rHh3QRkjH\nb67n+lCeQS/FPGhekOrq3nyk98ei5NGsS9EWg7qeJIqpM5sidGIUjdFUuM7UtZjg7XLKS0s7yrPd\nm/JSFaZktzHps7rR8THfm7Bnl1Gyu+zX8RsT6ECfL5lLliypbpbwqxKOEoH2SwOrj1E1UzQaRTy+\nAYLHAYAfUVFxAKFQCJZl4cUXn8H06a/jiisKcPfdN+Ptt1/CmDEd0KtXJ0hQaRtIXPwdSE5Ohm3v\nB3AhgJkARgJoB+AgJKBXqLy8HXr37ouXX74U0ahPx3ABeA1APzRtmoNrrhmAd9+9GR9++Bbeffdd\nrFy5HE4O61xIyOJ6SHDrpwDGARgFyxqIwsIgxo4dg+bNWyAedwpdki6QiZ8L0aJFc1jWQZ0DIDDq\nlpBg5XdAVuAf//gMEk3yka4tDz6fB7Z9EMBFAH6EwLjNGDYSybCx559/AoHAYPj9F8Pv74wWLTx4\n+eUXkJOTg65duwPoCCkG2RYO0rkNdu7chQMH2iSca4tg0INZs97Eaae1gNvdGc5Pri0kkHoppIjm\nfZCA5WQAXwIowmuv3YI33hiPUaN6YOTI0+Dx+AGcAWARgBEIBvNwxRUjsHPnTrjdSTrmDZDA4hiq\nBiavhANJD+s46xCNrkTNmimQoOJTIZWbroRA2TsD+AJSVP4ggBaQGr/TIDixyZDnMRtSBKMFgGcA\n5EAKcXyme7EFUlB0BKT0oQsS2tpTx7lb17wJQDokgPlaSOhrA51LM0ht4TqQbHtj9BmIQfI8XASB\n8Rfr/SXkOQjqeJ9DioDmQ4qhng6B9tfT82/oeGmQwPdXdT/X6bgfw7LSMGBACjZuLELjxv+qwtUx\nOka/DlX3i85vRuXl5ezSpR+DweMJ3MpQqBFvuOGWw7adO3cuCwt7sU6dVjzxxKEMBOpSctMdpM83\nnKeeOpz167eky3W/agymrtRx+ha7j8BWBoOt+eyzAtYYOvRcer3nUTLDr2EwWJcffPABSXLOnDkM\nhdLo919Av3+AvnkPoZhq0un15rNu3aZ0u6/Vt+bFDAazOXfuXJLkLbfcyWCwJ8VcuoO2XZtud+fK\nz8FgF95774PMz29K8X+VE/hWtQijvdSgA8E2oulFZmU1ZOfOfWnbZ1J8SYczKSbR5Ypw3LgXKvfw\n22+/5VNPPcVJkyZVQVM+8cTTDAbbU3xkDSlw77cJDGTbtl3o92dTUjp9Q+BCZmc3YOfOfZmdXZ+2\nnUYxAZbR7b6STi2vYXSCrhvouKIl1alTwGXLljEejzMvrxEt63G9Z7MYDKZxzZo1LCsrY2ZmLYrG\n1YPiq4rqvlxDCSwOUjS8y1RLCVLMon30WikU7W8bxQQXoGj4eynmx1SK76yCYrY0Jj9TrqYhgXt0\nL4IUU+ST2uYCihZ1KgWVGaUAQFZp3wspJmwTWB3T87kUrdHA94frnNpTfJlhii+ygpI82SB7r6ZA\n8xvptbN0XwsommQPiuaXTNE0R+qYJgn3CRQN35g0zyRwCiORzEMQrUcL4SjR0I42qu7n4jel0tJS\nPvvss7zhhhv597///bBtVqxYoUi/FwjMZSDQnxkZdWhZAlnu1Kk3d+/ezVWrVrFRo7Z0udz0eCK0\nrCDF7NiPAjxws3XrDpw+fTpJcvfu3Tz++EF0uTz0eoO8994HK6/ZunU3ilnKCIhzlEHbBNxs1aoT\nN23axIYN29Cy3PT5Ihw//sXK/mVlZRw+/BK6XF4KVDpPmY2bbrePgwadxqeffppiSq1DB2JuQgdu\npCSfvVIZ2lqKqfISjhgxmlu2bOHhBZlXGdZzBBbStkP/NsaooqKCf/rT1bRtrwqCOsoMI7TtkOaA\nPE6Zsiki+iSBeXS729Pl8tPl8jApKY+WdWPCXK7X9nOV2Uco/qA76fNF+fTTT3PWrFmsV6+AlmUz\nFsvkBx98wClTpnDcuHEcPXo0LasLRdhPoQgqmwIu8bJr1z6sUaM+xaTZhI7/6qAyd5OBP0Ax/6Xp\nPQjoOEYgupTpn6pjZVDMprMpJrmg3hdLn6MVCdfJ13MuXR+0vTFBTtJnpyHlxWowBSTyJEWgbqaY\nZ7vpfC3dX5fO06PnjFA04Q7btN2ZdHyWIb3WPJ13AQXt+ibFzDqXYtKuRTF9ZhHI5VNPPfMr/JKP\nPMIxgXZEUnU/F9VOjz32GH2+xKS62/TH/w9a1h1MTc3ljz/+WNl+4MDT6PH0p7xBm+KWZQSeoG03\nZShUl5dffm1l+9LS0kOYfm5uEyaWhBE/3J8oQIjnOXjw2bz++lsYCtViMHgWA4GavPXWuw+Zezic\nSSfcoIRAPfbs2Z/BYB4DAeMfu4riK7mPEmOUWD4mTiCLPl8hw+G+rFmzIQ8nyA4ePKj+ttPo+LsE\nWVhSUvKL9vm+++5XoWF8Yo8qEzUQ/c10wCPm2gfocnm4Z88etmvXmyJ4zHeTWDWR8QUUbaYlgUL6\n/acwEsngwoULefDgQZaXl3PgwGEMh1swFDqHHk8yLetEiqApoAA/wvR4OjEQSOW0adN4xRVX0imN\n8gXFN9SZIpAHqSC4lhJecbE+Dxcogz9RhUA/FQonUfxKiejBuRS/lAl0DrAqwtb4ThupMIlQhGti\nkuxyOrFgieEjQ+i8NF1DASsdpINkPJvit4tQhFfBT+57PV2HSbb9LUXz26/ffZvQ1iQivoyCbqyg\nCNcLWFDQ7b/7YR7hhGMC7Yik6n4uqp2ktMupCT/OpcqA5HM4PJgTJkwgaQp4mqrNx1PQX6bfbfqD\n3slAIPtfOsEvvHA0/f6TKW/ERRRT0UsE1jEUKuA999xHvz+NDnJuM/3+5Cr11+LxOOVN+0DCHM6g\nZYUpEH8jnE0+Q1LQm5kUwUllTjHed19iFWTnSCRpE6VoFvuVkUd+cRaIiy8ezarZ/L+jCIvEa3ag\ngBIMU99Kt9vH8vJy3n77PQwGu1BiqTZSkJi3JPQdrMdZCf3HsrCwF0nyww8/ZDjcImG/FlA0qOZ0\nqlN/TdFsPmBeXhM+8MADtKymeq3+lJeCAQnjv6lCoS4dQR3Xcwsp2Tc6677H9Lg6Yc5TKQCM2pR4\nxZaUOLEDFOGYTNHSzPy+0ftZkHC93XrOTafuXJyC8JxAMWUm6/O1L+EekiKsfNomi/I8H6DEymWz\n6ssFtc16ilBNBNCMouSQTKdocKRkIenLjh37/oe/yN8H4ZhAOyKpup+LaqcdO3YwO7suPZ6RFFNN\nDTrQezIc7s9XX32VpKR/korWbymzyKBAyW+ivOlK7FYs1oWffvpplevs2bOHn376Kd966y2+/fbb\n7Nt3MN1uP4PBZLZpcxzd7gA9niDPPfcCzpw5k7FY2yrMJBptxm+++abKmF5vOkUrWaUMK4lud/2f\nMKFMOppMBSV2qTuBp2lZnX7S9lBBZmjv3r3MyKhJEUJuulzpvPLKaw5pd/DgQc6YMYMfffQRX3zx\nRT7wwAP8/vvv+cILL9DrLaAEWFdQEH4ROlrXVzQFJ237bAJPMRQq4DXX3Mh9+/bx448/5kknnaYZ\nS/wUn02u3jNTN60rnXg1EljImjWlVty4ceMYCiXGuMVpWW5KaIM5V6GCYQL9/gi3bNlCjyeJonVc\nRNGCEoXoWr1uPp1io+UUs9t3FO2zBsUPaFG0tgBFY3pEBcQYHWMFBaJvspDUomjXp/1kfjbFtDeU\nkgCggGLG9VFeBp6i+M5ilBeedAoi1KAhXXReaFbRiW2cS9EEjXmzG6uGG7ypYz5OEXZputdX6rX9\nev1HKSbgxgTc/Oijj36FX+mRRzgm0I5Iqu7n4oigbdu28dprx/Dccy9hnz4DGAx2JPAK3e4rmZNT\nrzKv3+2330vbNtnfk+hAuFOUcU2hZOtP5bZt2yrHX7VqFTMzazMQaEeTrd7vT+N99z1Mkly7di2z\ns+syGu3IcLgpW7fuojXd3qO8bb/JpKTsyvyQhh5++BE6aZfaEgjT641RgAZxAn+nzxejz5dMl+sq\nAhNp202ZlZXHXyrIEmnHjh284Ya/8uyzL+aECRMP0c527drFxo3bMhwuoGWZANtWtKwo77jjXl56\n6RW07SBdrghtO5k+n/GZxQj46HJl0uMJ8ZRTTuM554zgiy++xA0bNjA3twGj0UKGQs2Yl9dQ684Z\nUEINAn5mZ9dgUlI6bbseJe7qAP3+M3juuZeSJBcvXsxAIJ2i5VTQ5bqHtWs3p9udTNHWKijaUYxA\nR7pcaRw58koNHq+tY75H8XWuVqFwvt77CAUY8Srl5eE4ihZ7hgqmKJ0g7RZ0zItROkUwm1A0sY6U\neLQKik8wXDlniS9LouOfq0mJKfNRtLAhFJPniXqulc69l87TFGG9QcczGt/zeu3OFAGYnyCkfHTC\nObwUf62fok1HKAIxpL8Jk+uxJQ3gJDU175CcnEcD4ZhAOyKpup+LI44qKir4yCOPs1+/UzlixOWV\n2UWWLFnCQCCTThDyAmVKaymmnBqUN+V2jEYzuWzZssoxe/YcRJfL+E7KKf6XGxkIpHHlypXs23cI\nbfu2yu/9/lN40UWXMD09ny6Xm1lZdSoRjon0448/0uOJ0vFDrabXm8S0tJp0udzMyKjFL7/8khs2\nbOCFF45i//6Jb/u/XJD9Uho9+ir6fBdShGmckiFlBIG1tO0o16xZw127dvHii0fR6x2ubQ6qYBhW\nua+BQFKlb+6kk86k2z1G2/UmUI+23UQZq8mhOZlAmJFIf7rdKXS5vLRtL/v2PYV79+6tnN+kSa8z\nGEymy+Vh48ZtOXHiRM136aOTs9AElO9iKFSP06ZN4wUXXELRmmw6/i4PgQJGo7n8859NWZk6KjxM\nLsdeFOTpExQzpAl8foNOTB31+WlA0Y7cKkDsBAFi8iS2o2hyXekAOkyOxnp0grkNaCNEEZRJdBID\nTKUIUreuO5dOXsl6FME7QPs01bmtpwj7E1Rg9dDvv9W/5vlbpd9voACH2hLI5OjRo3+9h+wIIRwT\naEckVfdz8buhyZMnMxb7qU/BVCe+n4mZEVyuR9ilS//Kvnl5zSgC0PR7gsCljMW68tNPP2WdOq0o\nJh/z/TMcNuwCkmLm/Dn65ptvGI02rzKnWKw9Z8+efUi/31KQGTr++JNZ1a84leJrJG27oBIB2qfP\nUIo2Y9p9TCeImQwGc7l69WqSZOPGHSg+qCcpAItyCuLw/IT+iamvdjAQqMkvvvjisHOMx+OVe3P3\n3Xer8NhAMYVWTXsWCp3L5557jqSEgVx55VV0oPgHCKxjLJbNDh26Usx1j2vfGZTgeDO/Byn+VfN5\nrwqURBDHKIr5zlQwv5aidZHio0sEET1Aqc12kwogx4cq4BGzhhsosP2fpuaqQQn6r0kRuqdQNLsI\nJVyF+jdK8VeSEnrQguJXu1Hv6zcUH2Ti2O0oPrpNFM1zEGvUyPv1H7ZqJhwlAu1YYPUflJo0aYLS\n0m8AfK9nPoQUT8iCVDnuBfN4xOM9sXq1E6Tbpk1LeDzPQepP7YMEoaairGwxGjVqhHbtWsLrfV6/\nL0Yw+Ao6dZLyeX6//2fnVKdOHa2iPUvPzEVZ2UrUr1+/sp9lyZFIhvX8J7RkyRJ8+umn2LZt28+2\n6dixJQKBlyBBxWUAnocEbs+HZa1Gw4YNAQCdOrVEIPAyJFC6HBJcnKejTIHHU46cnBwAQPv2LeHz\njQOwCkA3SHB3AYCPIVWsAQm0bq7fJcPjaY1NmzYddo6WZVXuTUpKCiSYvQaAJEhF6Re05VqUl3+E\neDyO/fv3w7ZtdOrUAaHQmwB2AfDCtp9DQUEr7NlzABKU/Srk/jYAsBxSBhGQ5+JtmCrXlvUcLCsM\nqd4NSLD7ZEgwdxtIQY4P4FTrzoFU/SaA3ZAg69aQCuBxSPB7BYD5es7c8ON1PvMBLNZzk7XtVO23\nE1JNOwYgExJIDf2bCQnwj0PuZT1IQHdzAAsh1akTn7+vdA31db6NAcxAIJB82HtxjI7Rr03V/aLz\nu6IJE16h3x9jKJTPaDSDDRu2ZCCQSbc7SNtuQQN48HpHcsiQcyr7bd++nS1adKTPl0EgQNtOpd8f\n4+uvv0lSfFOtWh3HQCCLPl8STztt+C+u8Dt16lSGQqkMhfIZDKbw3XffI/nramSXX34tA4FsxmLd\nGA6nHwJ4MXTgwAH263cKfb5UWpbJc5lKlyvISZNer2x38OBBDhgwlD6flK1p0KAVfb4oQ6F8xmJZ\n/Pzzzyvb7tq1i+3b91DTaj0KMq+CltWdlhVgKJSnqcke1HV+z0AgncuXL/+369q6dav6HL8gMEe1\nNZOf0EevtwYjkTbMz2/CzZs3Mx6Pc/Toq+n1RhgM1mC9egXcsGEDr776Ru1rzJFJ+ldyMHo8EZ51\n1vn0esMMhWoyN7cBzz33fNXAMimmxShtO4l+fya93hiTkmqqRmR8UqYUTIBixi2lAEZMWrZ0ismx\nJ8W0Waqa15UUjdbkgwzQ8buaFGcDE+b+me7jdDqB1yZwO6IanY9OWZpowthS3sjxK3oJ1ORtt931\nb+/F741wlGhoRxL1g+QBKgJw3WG+PwuS8+dbSK6bFodpU93Pxe+O9u7dy6KiIu7fv5/xeJxr167l\npk2bOGLE5fR4QvT5Uti8eSG7dx/AUCibwWAOO3fux2XLlnHNmjVcs2YNi4qKDgF4VFRUcO3atdy8\nefN/PKeSkhIWFRWxuNj4aJwjK+vwfXbs2MHTTjuPtWsXsHfvk3nBBRfR58umx5PJwYOHVgrUmTNn\nMhSqQ6e21ydMTs6uLER64onDWLt2AQcNOoNbtmxhPB7nxo0buW7dOi5btoyzZs2q4scylNguHo9X\n2dfDtV2zZg0vumgUPZ4Q/f5UNm/egUVFRVyxYgW/+uorpqfnMRDIot8f5csvT6zS98kn/8aGDduz\nadNOfO21SZwzZw7btz+e+fktmJlZjw6kvjbFNHi+mtY6Ukx6GUxOzmGtWgVs2rQd69dvzby8prz+\n+ptZUlLCUaP+ogmmjT/Ow/vvf4jff/89v/rqK86cOZOFhb2Yn9+cZ511Abt27U2PJ50uVyrFVxal\n15vGBg3aMDe3KXv0OJFt2nSk+M9MpYD3EgSRN0GQRVWImHp5pr5aQAVmNKGdm07cmU3HX5ekf706\nRoxOIH5Mx/foGDGK3+12ik8zlDCmCdp26qlFo7mHrcP3eyccJQLtSCm5bQNYBrFzbYTYNs4A8ENC\nm44AlkBsFP0A3Aqgw0/G0Xvzx6Bdu3Zh/vz5CIfDaNOmDR5//Gl8+OEM1KyZiUsuGY5du3YhKSkJ\nu3fvxvbt25GamopWrVohIyPjF42/e/du7Ny5E8cd1xcbNxJAJwB/AjANqalPoKhoEZKT/zvzSzwe\nx9dff409e/agoKAAgUAA4XAYgLA710+M4WlpizFx4kb4fD5YloXCwkL4fD5s3LgR3377Lf7yl5uw\nalUhSksvBHAPxJQ0AWIqPAcnn9wNb7/9OsaPH49LLnkWZWW5AFIB3ADbbogff9yC1q27YP36dqio\naAvb/gGZmR9hxowpqFevns6L2Lt3LyKRCCzLqjTd7dq1CwsXLkRmZiZs28b06dPx4YczQLowYsQZ\nGDx4MACgoqICX331FQ4cOICCggLMmzcPZWVlaNasGWrVqgXLsrB582bMmzcP2dnZyMrKQjAYxIcf\nfogtW7agS5cu+PLLrzBmzJPYv/8ZAHvgcp0Nl8uF8vKnADQEcDnE9JkHMcv5AWyDmOO8AJpCTKhF\nkLyIawD0APAneDzXIxLZiJ0764K8H8ASeL1X4LzzTsOyZetQXg5Eo25MnTodZB7ErPcdJA/ofXq9\nywA8COBhAAMBnA3J/fk0gCEAXoKYDT0AAhBz3nrIz/s2vW+36HyT9dxYiDnWtH8QwBzIe+/tEPYx\nRsfM0zkQwF8guSHvhZhHb9M9aAFgLoA+uvY1AP6m+7EJwDl6TNLzzQAUAngJHs9BlJYWH/aZ/j2T\nJXb8I0Ue/O6pI8QIbuh6PX6OkuE4HBKpmt9z/u9oyZIlTE3NZSzWlaFQA+bmNmIgUEhgEl0uqfcV\nCrUiEKRtCzrL7c5nOJxexQT272jixIl0TENOdvpQqCfff//9/2ru5eXl7NfvFIZC9en3d6CYLb1s\n0yYxY4Qctv0apXbXs7SsKAOBBoxEWrFRozZ87bXXGAymMRIxKLWbtF8/Oog7EniRXm8mSfKEEwZT\nAA+vUaoCpDMzsxbnzp1L286kIPu6U2KqMunzJfGllyZw6tSpjETBwFSfAAAgAElEQVTS6HYHmZlZ\nm1269KZt+2jbXrrdMUajPeh2p2m+xrY0QcfBYE1OnPgK9+/fzw4djmc43IThcEc68VlepqTU4LZt\n2zhy5Gjd59Z0uTJ44olDmZRUg4LOq5PQJ0wnvCKDElNGChIvlQ6cPUQJzr4vQat5igJrT6KAM16n\nmPqOp6AVvXRKwZAS85Wt7c/UMa+kZDZpqZrO9p+0H0wJBzBgjvj/b++846uo0v//uf3euSU9gXSQ\n3ntHAiJNRRA7YmFF7LoKVn7K17Kiq6vrupZVRBTrrmvHgmIQuyggICiEGoQAUgIJCUnu5/fHcyZz\nU4DoSnITz/v1yiv3zpw588y5M+eZ85znPI+SM4mSuNR08/cqmbIpbvNZFDOsh1aYLXM5wFOUGJlJ\ntKLpj6Fluuyu2qWTai/TBPkCZXSaQWs5iGlubK6uO5HWqKy63G3VfRKjriGWd91VM8pNYwdNZIQW\nLZwOeQ0zOQ/AP45QfhqsGehIGvq+qDd69syhzWZmoj6kOoTIJIRjKSanl9T3Yoqn2k1s1uy4Op2j\noqKCiYmZlEWzBsVlWx50n6/rb15kOnv2bPr9x9OKGDGb1RXZLbeQI0ZMoCRbZES5MwiE6XJNptMZ\nIPCF2rdLdVrfUMIyPR1x3N/o84mt0mYzlyaY+07jhAkTeN9996mO0PTUe151fO/Q4wnSMBIjOtLn\nacUK3EPxhJumOmbTlLlYdZTvsmPHASpayqm0XgruVnJuINCMPXr0U/N0Zq6zA+r4G9X3CkqElNtU\nB5tO8Qz8J8UbsIBikluryuepzn4zJSlqLC2vRVIUWTzF/b2cokxOVNcVmXjzDEp4qbtVpz8mYt9u\nilJaG7HNXDPWjFYUk1KKIkqheBSGKUk2AxTlV6H+UtS5SPGSNSgKJjKR7GO00vYMUGXyVTudQ0sZ\nXU95CThDyZxIKy/gbopyMjNgf66u7SaKkjPlPqTaZYVqr5YEmjMmJuM33ffRDJqIQnM2tACKX9OY\nQwFMhuS2qMHMmTMrP+fk5CAnJ+d/kStq2bhxPchR6psLYt6JTBfigaTtMMv4IF51QRQUbEA4HIa9\nul2vGrt27UJh4X4A10K8vUYCOB/AB0hJKceQIUN+k+zr1q1HUdEwiPkHkJ9TSe2ZjpKSvwIAhg8P\nq2szcUI81GwoKxsAm+0VWFbnBAAdADwEp/MXlJdfBTEzlQGYhZtuuhkAQFav04dwuBiHDh2CtJXp\nhTkSYpobDbs9CLu9NYDBat+5kPQmuyBmqssh72P9IMYDABgEMZuVoqKiAsuWrUZJyYmwUtaMhpji\nsgFMxE8/PQvygDovIKlNPABOVt/tat9HEI+7ewCMhaTQuR+S1qUZxHMPSq4MiCGjn6ov8rpdqv7N\nAJJVu34FSelyCoBrIObEb9X5NgO4Tx1jYv4eJ0FMnUshqWVCkMfzFADjIV6MIQAbANwKsWy1Vtc+\nVl3bDkh6m6mq7t6QdDHba5F7PWRKfQ3EQzRNbRsPy2o2GuLt+C6A6yFpkgapfXGq7k2Q37i/2n4e\nxMP3ZACnAXgNYp7soLY7AOxAONwMjZ3c3Fzk5uY2tBhNln6oanK8GbU7hnSB3FmtatkH/IFGaCec\ncCqdzpvVG+keOp0d6HZ3VG+dd6o30H6UNWVUb/CtCFzF1q271+kcpaWlKorFD+oN+mGKl5+PK1as\n+M2yP/WUGYA48u8uAq+yVatuleXeeust+nyplFHmixRz2huUqBkn0+dLoIQwonrjl6wBLleQN910\nEzt16sO2bbvz0UcfrawzPj6TYnaar9rGxwcffJDz58+nYbShZW77i2q/l+nzxSo59tAa/Ri0orlf\nTDG1pah9VPKmEmhOu91Du91Hm60HZc1WBSVlyfmU0VE/tmvXmTZbMmVNX5iyTiqGEsuxnFa8zQco\nqVISKOGiyigjzizKiOxTdf4v1PfxlPVzQ9Qo5DmKaTGdMpL6NyWwb0iNYmIoZk2/KrNeyXupOj6Z\n4kDxLiUSx1kUZxM/xfxoOnK8RRnZn0ErSodBYCGt0U+aOrZY/XnVvWaubUuhjH4TKSOk5ymjUNPj\n8HQl9zLKCHIEZYRdRhnNdlIyuVV7mcGNv6DldOJVbRyiLJw/REnymaLab45qoySaJsdBg05octFC\n0ERGaNGCEzIEyIa8ti+DLPqIJBOizKo7gkTS0PdFvSHpWHrQMFLpdoc4derVnDHjDvbuPZyDBo1g\nIBCvOuEAHY4kAm66XAls3vw4rl69us7neeaZZ+nxJFJMSWm020OcO/e53yRzXl5N13ub7WTabPH0\n+0+qdX7vjTfe4KBBJ3HAgFHs2LEnvd5EejzxHDlyPD/99FPGx6fR789UneZllR2WYSQyPz+/hgxv\nvGGGXxqoOr1b2bJlZ5LkTTfdRrc7SLe7Ga1M3wF26dKPl112Lf3+FgwEzqbXm0LDSGAweAoNYwgd\njhANI412u48Oh6E64BBlvijyhWAwAZ9a7hBUCqoNQ6F0FhQUsEuXvrQ87wLqmsy5IENtM+fHTFfy\nIGWeNJZWWh1xOW/Xrhs7d+6njnOr/7HqWJfqoFuo7WbOsS4U0/KnEW1gzjmZHodJapsZNupEiqk3\nXdVnegWa7fCAUkSPqXpOoZh3zUzWkUsDEtXv0kLJGa9kj6OZUkhkiqPpgSnHJUXIa7bPMIqiLKps\ne1FsQYpJMkxZaN1MXZvZPubcnimXKcPfCXxIw+jHadNu/U3PQLQCrdB+d0ZDPB3XQUZogNgfTBvE\nUwB+gdg1lkLclKrT0PdFvVJeXs6NGzdWSQdjcvDgQa5bt4579+7l+vXruWHDBubl5f0ml+OVK1dy\n9uzZfP7551lYWPirj1+2rKYiW75c1rOtXbuWb7zxBp9//nlu3rz5iPWEw2Hm5+dz69atlXEXS0tL\nuXDhQhpGepX6Y2JO4HvvvVejjjlz5tQI6utwuCtDU+3evZvXXXcDfb4RqjMso9d7Di+99Fp+9tln\nfPbZZ7l8+XLu2rWLL7/8Ml999VXu2bOHeXl53Lt3L1955RUGAoMo80ZzKKMf61yAgz/++CPz8vL4\nyCOP8Nlnn2VZWRlJcuPGjWoN2rmUUdlm1UH/l5JxYBFdriAzMlrRbr9AlfmEXm+WynX2LmW+5wMC\nt/Ciiy7jN998o15sNigZ/qU6dBclIHUnyvxjmKKAI+czX6eM/M6nOJBEziOuVUqkP2UE2IXWfOcv\nFGVpJot9kTKaOqjO+7Q6pkIpnaCqZwiBlZTA1LlKmZhKqYzivBJDGTGREiQ5SV1Dc0roqnWqc+5J\nKxURKU5CpjKLoRU6i5T5t2TK3OFqiiPIfZTR2qnq2i+LKL+WcXFpv/o5iGagFVpU0tD3hSaC3Nya\nimz9+t//PIWFhfR4ImNA7qLP15wrV66sUfbDDz+k39+OVhzCrxgIJFQJTDxq1BkU7zhT7o/Ytevx\ndZJl+fLlSoH8QkmZ0qbKuQBPjTV7Jrm5ucrs+Dkt01iXKu0XCnWlzxdLKwYnCcxgUlIGgbcrt9ls\nd/KSS67ik08+ScO4MKKsKFUZ3VxLCX1l7ruKVR0rZlECBIcpI6OqLw2isEYqhVA99NV4ipPOfspo\nrwWt9C57Isr1pZhrl1FMkKZTzWql0CIdQj6ijJYiZRhHUcT/jdgWpxTRDdWuLY7iuNOCVkizMiVD\np4iy91BGcKS8HLSjLP429y9nYmLWb7pXoxVohRaVNPR90ah5+eVXmJMzliNGTOAnn3xy2HIHDx7k\nDTfMYP/+o3j++VNZUFBQuW/37t0cMeLJGoososgR2bVrF//0pyvYv/8onnnmRA4fPp5DhpzCF154\n8YjHPfnk03S7Y+hwtKTNlsCEhAyeffbkGqO+cDjM886bQr+/NUOh8fT54nnCCSexf/9RnDbtFhYX\nF/Paa2+gx3NRZcfudN7EM864oMo1TplyFfv3H8Wrr55eQ0Fdd93NKinpKZQRQbbq4ONot/s5cOAY\n3n//Q1XmYebNe4F9+46gjB7+n2q3LRQz2AaKSe9kWnNIx1Hmt0rp8w1gKBSnOvsUAoPocMSxR48c\nTpw4iXZ75ILmj2iZ6FIpkfTN9CsP0+GIpd3ejWKSzaAsgD5BKRcPxbPwespIKqjq8av9GZSR1vWq\nbr+Spw0tU2qSKjdXKQnTlf5TWqPAwbTMqZEKdrpqDzNH2S5a0fETaC4alz+3OmcaZZRp0JrHM82o\noyieizGq7ZopWZPVdQ5Q8ptRRG4kMIeG0Yb33/9Q3W7oRgK0QotKGvq+aLTMm/cCDSOL4oDxFA0j\niV988UWtZUePnkCf71QCb9Hl+jOzstqzqKiIjz9u5tCK/HuahpHIb7755qgylJSUsE2b7nS7L6ck\nzwxSkjO+QsNowTlz5h722Ndff51er+ni/QzFeWUSk5OzuHv37iplw+EwFy9ezHnz5jEzsz1drqsJ\nvEWf7zQOHz6We/bsYfv2vRgM9mAo1J8ZGW0rk5GWlpayQ4fedLsvIfAWvd5z2L//8BqpZ77++mu+\n9NJLPOOMSfR4kun1tiPgpc12D4E3aBh9OG3aLSTJp59+hobRkjJquEd1uF0oEe3NaBoBiov+fyjO\nPV0IhOj1mnNWCZRR5SylsP5GMbMdp+pJo4xE/BSnodtpreHKUErFT4cjk5LTrCOt8FcPU3LmtaRk\nsj6D1rqtgarTz6KMgt5SisKcQxxCmSuLpwQhfp0SMd/MIN2bViqXOKW0UigOGi8r5dKa1tqyTuq8\nQ2nN5aUpWZ+lOH6Y81//R3Ei6qXOP1kpLQ+tSCBeSsqbN1T5AEXZ3qWu8RkCV6rtGQSSedZZ5x71\nXm5sQCu0qKSh74tGS7duQxhpsgL+xvPOm1Kj3K5du+h2hxiZWdrtfoI1FdkHEZ9ncfLky48qw+LF\nixkMdqO8kV+hOmervg4d+h/22AEDRqsO0Cz/OIFzGQicwhdeeKHWYz766CMGg31ojQBK6fHEcdu2\nbZVzcwsWLGBRUVHlMV9++SUDgY4Rx5TR50vl2rVrDyvb0qVLOXXqVHo8kaa/TfT740maEfgXROyb\nyR49+nDGjBnKlHoOrUXjpER/F4eKfv3MUYTp7XmXUixm2RWUEeI3FFPjyoh941Q9n1FGI0mUbM/m\n/o6sarb7mhI9v1wpkTjKGq9bKR6hVjuKQllBUVa3seoc1I+UEdxKiiK8Wf1/iOJ9Ojii7D7KvFsa\nZeQaUnK8TZkzm6QUT+S6wz9RTI7m9wKKEnuNotz+QmuU5qOVEZ0UhxTzfr6QltdpF4rSXcLExBZH\nvZcbG2giCk1H29dEEHlPh81wOEcte+jQJZWfDaM9ZA1SuEpddrvURRKbN2/G1q1bIc+RRUVFBcLh\nCvXNVq2O/Th0qASlpaW1SiOyRtbHyjrM6zhw4ADWrl2LgwcPHuEY2e52uzF06FAMHz4chmEc4Txy\n3JHaqlu3bujYsWO1LAFhmGumatbpQq9efXHnnXfC4XBAIuez1mPj4uKryC7bayvbQ/0/CFk/B0iU\neg8kpFkSZJ2VeeyOat8jz7EHsr7PbGMcplx5LdsiZYr8b5ap2RYih6E+2wA0h6x96xxRtvr5I7/v\nV+c4pP7HQZypTdkLIaHASqtdUxg1r+9oz4VG8/vR0C86jZaXXnqZhpFB8Xx7jIaRyK+++qrWsmlp\npqdb5J+XTmcabTYfbbb2FAeC5wn8k4aRyG+//ZaFhYXs1+8E+nwp9HoTOHr0BJaWlpIkf/zxRzZv\nfhxttliKV91dFDNPV/XnoceTwfj4NC5ZsqSGTG+++SZdriSKuehJAgHa7SOZktKCe/bs4QsvvESf\nL5aBQAsGg0mcOvVy9u17Iv3+FLpclxJ4jT7fWI4cOb6G+TCSQ4cOMTOzPWXt0muUea0A//nPx4/Y\nvlu3bmVsbHPa7XcR+A8NoydvvPH/kZSlEWLufYHAIzSMRH733XckySlTrqDMK/kp67peojg1dCBg\nsE2bPsozMkQxuf1FjTpmUbwBW1BGUZep9kxU/wepctMpETKaqeDCWZTEl2bmbYPidv+y2mcGLDaj\n4XdWn1tQ1qq9RnEUMWWKpzhVJFDWiv2bYm7sqo45TpUz3fD/qkZOl1IcPYbQCr1mUMyZ3Skm0Ntp\nmStDFA/NORHlb6VEcPFRTJemmdEMYGwGPfZSzIlx6vvTBGaqemZT5voC6tyZvP/+B+v0TDUm0ERG\naE3tVUP9NpraIInPP/8c27ZtQ8+ePdGiRYsq+1977TU8+ug8eL1u3HzzVejatSs+/vhjkEROTg5O\nOSWIRYuq19oTEkXiRUhs6RVwOgcjPT0VBw6UITs7DX/7250YPHgwLrnkajz77F6Uls4BcAAu1zAM\nHBiDyZMvwh13PIC8vCkgJwKYDuDfsNnGgDxP1b0aEpD2NSQnT8f27Rsq35SXLVuGjz/+GDfeOBNl\nZQMBBAF0gsfzINat+x4k0bZtdxw8uBCyNv8jAKdCcoX9AJfrQXTv3hvDhvXHzJm3wOORaBjhcBiL\nFi3C7t274Xa7UVJSgtTUVAwdehLKysZCRiqxAP4Dl8uLpUs/RceOHVFQUIDPPvsMoVAIxx9/PGbP\nno1169ahV69eeOONBcjPL0C7dukYP34sAoEAduzYge3bt+OFF95GWVkprr32Ypx33nkoLy9HQkI2\nCguHQSJnPAxZuZIOGWXshwTc/QFW4N3+kCDFH0HykuUA+ADyqN8ICeK7G0BXpKfb4HIF8fPPG+Fw\n2FFSUo5w2AZZ8vkVJLrHZABvQkZIher/15AoJHMgIVcPQow9pZARXzEk4sosAJcCuAsSrDgEibpx\nIoCHACRCRkb/gEQEuQ9AESTyR0dIlJN8WEtSt6rrKFDbOqu2eEqdb4/aXwggHhItZSUkSkgJJOfc\nPQAuBjAGwJ2QBB73QiKWfAfgIkhUHS9kBFuh6nMCyIDTuQEbN65BWloamhI6OHF00qBvOdGM5d3X\niqHQOBpGIt98883Dlt+5cyezszswGBxCu31djRFZINCBskbI9A6z9gWDOQwGExkKjWQw2I8dOvRm\nYWEhu3Y9nuJlt5cS2DaJMidjLno1vddWUeZYKtT3Cor3mWTJdruDlY4ed9wxi4aRSp+vDyW3lSWH\nxxPHHTt28IMPPmBMTPXAxy1ouvl7PBfzwQervnWXl5dz9OgJDAQ60uVqRyCZhnEKPZ4Y2mxdatTl\ncGTxxRdf5LfffstQKIWh0Mn0+7vS4zG9CUcQ8PPKK69kUlIWQ6ERdLmyaLM1YzA4ji5XHN3uWIZC\n42kYqbzjjllcunQpbba0au2QSpmbCrBqTMqJaqRinmsAZVSXSHHciJwrWqd+t/4UJ4tYVSagfpO7\nI+rNo7Xg+AYCF0TsM9354yiOFb1U2TaUwMKlEWV9tFzySVkyEKSMOm+k6XAh8o5Q+1IpgaINyqiq\nHcXjMka1wQ51/3RX92KcagOX+n2T1H12KWUkOI6Wk0uYMvrLVNsTCbyv5Ayocw1V5w6p6+tDmy2e\nr7322jF9VhsCNJERWlOjoe+LqMVaf3VAdShf1lh/FcmUKVfRZltfreMmX3rpJfr9fSM6q7dV52M6\nE+TTbo+lzWY6E4Tp8UzkjBkzedZZF9HpvJ7iRdeLMnFvdtaPqo6JBJaozs0M5FuhOqRlBBYzGExk\nRUUFN2zYQK83kbImawnFcWCnOuZz+v3xLC8v59q1a+nzJVHc4KlkjaHpyu7xTOZDD1V1w37xxRfp\n9/ejrAnLohWY+T3VKW6kpXwDtNli+OWXX7J58xYUk9tDBN5RHfVMiqPGnarDnUhZJBxPa8HzUtVx\nlhPYRq83ke+88w7t9kjFXq7a5SnV8ZrHkhKCKqTOYSqbcyjLBbap6zUdJ06lmCbNcpMojhvzKMpo\nYMTv+w9akekfpJgLzbb4QHX+0yPkmErxUGxN8WgkZS1aLEWB9qQ4XrSlvAj9mWKe/ivFLPmLOma1\nup4iylq4kdXulRyK9+GVEeeeRlHkbnUda2gp9WspTihfK5lPoihDc+3cx0oeJ+XFyDzXE+qazXNM\n4bnnXlQfj2y9giai0LRTyB+ELVu2AOgFCVILAH1w8OB+lJSU1CjbsiXw5JMPg4w0Sb6L3r1PxObN\nm3HoUH9YgYUHQ8w5A+B09oPP1x0xMTEgJ6j9NpSWDkZe3hb8/e/3ID39PTidz0JMQoNg3YI5sNnW\nIyYmBz7fOCQm+uH1TgLwXzgcE2Gz7UIodA38/vH497/nwW63Iz8/Hx7PcRAngZ4QU1JrBALHw+8f\ni1deeQ4OhwOtWrXCzJk3w+frgZiYYXA6B8PligPwPuz2u+D1zsfpp59eo73kOrdBAuDGqD0jVVDn\nTkr+AQAIu52YPv1WbNsWCwly/B7ExFcGCaLbAhKMGBATWB+ImetEiKmsm9q3D0AzeDyt4Pf7kZER\nC+BsSKDcSRBz2A0AsiD5xf4DMZ29CbEYDa1sdzEBOyFBi68FcCXEOWRxtXKDITnJBkNyldkh5rqu\nAP6ivg+CmAbbA2ij6hmn7oMTIlpuGMRM+Iz6PbpDTJilkGDA50DMklshzh5PQUykmyDmSNPJpR2A\nAMSBxa/aybxXhkCCBb0GMamaDFXtE1a/yz51zOUQc2eO+n5ItUtPWMGoB0FMmcfVcq5IR6ThyMur\nLXOVRvP709AvOlFBWVkZFy9ezA8++KAyVNX3339Pw0hRb76kzfZPtmjRqcpxKSnVHT1IGdEdpM83\nltOm3cpFixbRMDIp5q4wHY6ZbNOmB99++22+//77/Omnn3jBBZfS45lEWbC7hz5fbz722BMkJRv1\nNddcS5frOIpDwU4C5bTbL+aYMafzww8/5LJly7h+/XqOH38mu3cfzKuvns6vv/6aCxYsqJIBe9eu\nXfT7EylhkkhgPr3eWN59993csGFDjXZZu3YtP/jgA27atImPPPIYhw4dx7PPnsx169bVKJubm6uu\n00wDs1Sd41kmJ2dzxIhRFHf4sRS39/nKocUcAR9SI46etNzZt6kRwHcR7Xs6ZX3ZU2qkUkLgIXq9\nIW7cuJGrV6+m3R6gjOYmqdHOTWrkMYNiLhuiZJmovh+iuLt3p5jNwpRRbAqtnGETVbm9lPVp/1Sj\npbGUUd1AymhwmzqmPSVs1njKejQz3uF0yojvoLr2ARRnjTJ1bWZOtlhWXRJwimqf6ZQR4N9VWdPs\n/DJlxH2QYmZsVXmvSAbuYer/EMoo7iDFQedUiqkyjjIKeyzinH9X8rVWn+MpIbzClJxxGeq8nSjm\nzHLKurusiOsbzI4de/+OT2t0gCYyQmtqNPR90eAUFxezT5+hDAQ6MRQazOTkbObl5ZEk58yZS48n\nQI8nlhkZbblmzRqSZEZGTUVWVlbGM8+8gE6nj06nwZNPPpMlJSUkyfvvf4gul0G3O4Zt2/aojCdp\nxiQsLCxk27bdKaYfJx2OWM6caSVFrKio4EUXXUabzSDgpM3mY8+ex/OXX34hSX7xxRcMBpMZE3MC\n/f6WPP308w8b3XzBggUMBpPodksUDp+vA4PBHmzXrif37Nlz1Pbat28fr7vuJo4ZcxbvvvveKrEu\n//rXB+l0+lSkfC/d7limpLTg8uXLefnl11IWQZtttoQ2W5zqHA8ohdKcNltk/rBSylqwjRHbLqHD\n4WNCQgYNw4wC0pqG0ZsZGW25detWvvba63Q4zMjwBgEfbTYzUHBQdfarKJFDQrSi25sBjA0CDrrd\nifR6U2gtLDaD+3ojtrlUHclKVj8tb0en+k39lDmyFKVMzlD7XaoOM7RWiKIIzej9kfETp1IUuEMd\nZ8riphXNw6zHr2R0Rsj5NUX5n6+OMT0dMymLpAcouV+NOOeLEdc2TJU16w5QzK5hinek2d5mUGa3\n+p7DkSNP/w1PZnQDrdCikoa+L445e/fu5T33zOKf/zyd77//fo39f/nLLHq942jOP9ntszh48Gj+\n3//dwWnTbmRubi537NjBcDjMQKCmIqtOYWEh9+3bV+X8AweOoMPho83mZJ8+AxgKJdPp9NHt9vOM\nM87i4MHDVOcUpEzKf0OfL7lSgZocOHCAP//8c41IHpmZHSI6omL6/T04c+ZMPv3005Xu7JGUl5dz\n3Lhz1PycOW/3J1511bTKa3j55Zc5b9487tixgyRZVFTEe++9lwkJmXQ6zyMwj4YxguPGSRSItWvX\nMju7I93uGLrdfj788COcPXs2586dyy1btnDx4sX0+VIo82RLaBj9GB+fTputZ2Vn6HLFMRhMpiwj\n+J5u97kMhZLpcLSizKu9SMNI5AUXXMhAIF4ddybNEZ3dfgOHDx/LZ555hs899xynTZvOLl16qgzk\nGymu+15K+pocykiiI8Uh4nrVSf9dKRw3geMJnEu3O4lz585lQUEBr776ughFEqSMqsy5JFOZOCmj\nKXObUyk0c8HzAqVYTBd4u1JIKeq/mZ5lJGUe9GUlW7JSIlkRxznMzlXV7yJgU9vbK9kctKLum2G5\nBtCKXuKK+MugjLIXUeYBg7TidJZQrAQudb44imPIVxSnkBmU+UA/ZRnEfNrtqXzuuXm/7qFtBEAr\ntKikoe+LY0phYSGzszvQ4zmPwF9oGJl89NEnqpQ5//ypBB6JUFLf0W6Po9M5lcAdqhM+uiI7HGed\ndRFdrosoE/Wd1cOeTDGHtVKdWjPV4YYp4YRyGBMzrNbo97XhdHoppjWqjv1Kut2J9Psn0TCa85FH\nHqtxTI8eQ1k1OslLHD78NO7YsYMZGW0ZCIxiIDCecXGpXLVqFTt37keXaxDFvGSaBIvpdsewoKCA\nbdr0oM32YGUb2mwhGsZgBgJnMhBI4pIlS/jGG2+wffu+zMrqzBkz7uDMmXfQ4ehNGZ2V0uM5nWee\nOYm9ew9jamo7pqW1o883mMAs2mzdGBOTwfT01pT1TTGUYL/PRVzDxwTi6PONp80WR5vtdIozR1pE\nh9tDdfQTVB1eBgLJtNlilBJqrTr7zqpTHkagP/v0Gc558xkwsycAABu+SURBVOapDn8bxQliilIS\nLSgekRWUkVQn9bu2pIxKxynFMIrirGMqkkco5r4ptAIBn6Su5X3KiMhcA2Z6LbZS21Mj6j+JEhKr\nPUWBDlfX0Uoddx3F7BpDManG0wqPdRpFURVSnFC8qv7uqu08tByHTEeSM9X2TNWenSmm4svUPZVO\nMwalw9GbU6deW/cHppEArdCikoa+L44pEjk9MqTP9wyFUqqUefzxJ2gYA9QDXUGH4xLabJGRxH+b\nIjNJT+9AcXvuRpkTcdNKalmoOrZIz7NCAi7a7bFctmxZnc7RpcsA2u33q+N/pihIMxVIHt3uAPfv\n31/lmCuuuJ5e71mUeaGD9PlG8/bb7+KVV15Hl+sKWsrxPvboMZiBwEDKyKJ/hKxl9HoTuGnTJtps\nDlqebrMoc0em4nuG3bvXjL4/duy5lIXdZn257NRpIElJwSML182QYQfociWo3yqXonTuoyg1M13K\nOaqTv4QyP2TWu0p11I9T5r9Mb1DpfD2eZhSPRSfFNBdHKzhxKYEsulyJaknBCRHXuUkdE+m2v45W\n8s7NtDwje1E8E/tQRlbNKe7311M8PIdT5tzOjahrt1IcYVr54frSSra5NaL+vpQlAj0o3qkJlJem\neyPqe4Iy6mxPUYC9KMtCzP3zKCNDc7nAAsp86F3qHAWUl4PWlPs2MoTbl+rc41T9O1Q7vsL27fv9\n+gcnykETUWjay7ERUVRUhIqK1IgtaSgtLapSZsqUizFhQie43enw+ZojIeFDkCtq1GU+tia7du3C\nypUrUVxcjF9++QUrV65EUVFRjeMyMzMgC5y7QTzkDIhHHCALmpsD+Azi3QeIR106bLZJmDTpUoTD\nYRwJknjoobuQkvIofL40OJ2t4XaHILlf9wFoCacziN27d1c57t57/w99+xbC620Oj6c5hg0L4Oab\np2HNmvUoK+tTWS4c7o0dO3YrOftDFhnfBOBjeDwXolevXsjIyEBMTBKAz9VR+RCvOXPdaW9s27at\nisx5eXlISAjA7f4EZt/gcCxGdnY6AAm75XQmQjz8AMCAzRZERUUcZJHyWogHYJKSLQ7iHdkXsrA3\nDeINuRLisVcOWfzcB+ItWALxCvwFpaUlkAXBUL9PSO0DxCvRQFnZiSgtfRfi2Tca4pH5HKRL+AhW\nOKpPIZ6AYQApapsZfsoDIBniMbgX4qmYqursDUks/yGAvwK4FeLxOFQdb4fk6jVlo6oLqi4/gCUQ\nD8j96vtOJUMpgFUQj8ZidZxfbf/E/FUAzIfch2+rdsuD5W2aAvEUHQvgAXXMK7D69VxVfoW61iQA\nmbDZPkJ2dgY0mvqgoV90jikrVqyg02lOdK+hy3UqJ0yYVGvZnTsjzSrWn883lFdffQNJcc649daZ\n9PslRYbb3Zxebxzd7hCDwXZ0uUIMBhOZnt6er776Kknyhx9+YChkZgfOUP//pd54F9GK4J6l3v79\nlNFVBe32OL7zzjscMGAEQ6Fm7Np1EFetWlUpc3FxMY8/fjQNI5WGkcZu3Qbw/vvvV3W2Vm/IVzAl\npUWlAwpJLlq0iMcd141udywTE4/j5MmXsqCggAkJ6bRCMF1BYB99vpN58cVXqrmtZwksps3WgX5/\nOqdOvaZy5Dd//nwaRiJDofEqg3UmgXwCpbTbz+FZZ8lapKKiIg4cOIJOZ5w6T5AuVzYDgROZlJTF\n7777jldeeR1PPHGcClF1N4GfKObCkJLvcYqHYSLFjBdPMcs9RTGrvUbLQaGNalNDjXYSKE4QGRQT\nnzmPlabKjKDMtd2szvtX1Y77KabRBIoZcgqtjNQBSjDeU2iaMa1ULj9SQpr5KaMoMxt2mjp3iLIm\nzksxR/poZcK+XF2jmbgzjmLOM9O2TKaMhgMR9RmUMF3mWrgYVf44ta8DrflaMytBH1WvTx3jppU5\nwKCYRptT5sp20EztY6XlGaCObavqS6EsKpeM2MuXLz8mz3dDgiYyQmtqNPR9cUyZPn0GPZ5uFHNf\nJu32eN57772V3oEmtSmy1NTWjItL42WXXVvpyXfffX+j19uDwA8UV/JW6qE2F1S/rR7mj+jzpVSm\nk9m5cyfj47MopsdVFLOYQ3UKF1PMZu9RJv8nqm37aDpKOBx3EthCm+1xxsenc/HixVy1ahWnT7+V\nHs9pFHNbOT2eiXQ4QrRcub8k4OXcuXNZXl5Okly/fr1y3TfNV/cROJ0uV4gy7/ElxTW7DwEvTzvt\nPJaUlHDJkiXs2nUQk5NbcsKESdywYQPfe+89fv7556yoqGB+fj6ffvpp3nfffezRYyBFOXsp5tMU\nPvaYzONNm3aLctJoRXHt/4EOR0deeOHF3Lx5MzMy2iqTZz+KU0QHWlHqN9Ph+DODwXTGx2cyEGhG\nny+WoVAaY2NTmZXVni1btqcVvcKMlL+YltIyPQifoSQETadlunuBomBMxRlHmasaRvHEHEVx0zfv\nk/mqTJKq36YUQHN1j4ylzJeakTseo7Ug+luKg4xH7Tdl/UR9N5N6blDfr6f1ouJQ54xT17JGlTVz\nt/WieFOGKU4aXdRvuoNWnMv3KfO2E9T3dIpJ8X2KAvxcHdNPfQ9RXsCOpyy63kKJkxlDUaymJ+R6\nVc6MYTmcHTp0q8envn6AVmhRSUPfF8eUFi26RnTuTxAI0eVqT78/gfPnz2dtiuzAgQPs2nUAA4Gu\nDIUGMjW1VWXSy+7dh6oH3iw/l1WjIpAyWiigzXYrZ8y4rVIWl8ugKCmzk0qiFXUiMpXHp6rT6qk6\nkuSIfTtptyfQ52tFw8ik39+cVTNFz48ov5cy35VKny+LffoM5YEDBzh79mx6PKNora9qTpl7SaRE\ntjDr+oY2W1yt7bp8+XLGxjZnKDSUfn8bdu/en4aRyJiYE2kYafR6kyjOA8mUuaFYjhx5MkmyV6+h\nqkOPdOZ4l716ncBXXnmFgcAIta2zqiOGVZ12ltLvT60SsWXhwoUMBJIYDHanpbiOr/a7mKNGU/FU\nULwpq2enttMaJbWiKJMsJXNkMlHzdwyptnNTHEJOo7yURNYZSytdDSkvEWZGZz/lhStS1jSa6x/l\n+ABltBagjIjMRKDzKC9DkccmUDw1ze/LaYVb+xPlReXSiP1mVuyL1PerCdwfsf87dd0BVbeX1hwi\naTmgBCnu++b221SbXEOfL/UYPuUNA5qIQtNzaI2IUCgEYCPEtj8DwFKUlf2AoqJdGDNmdJWy5mM4\na9b9WLMmEwcOfIfCwk9RUHAeLr98OgCgvLwEwPqIo9ZDgt8WqO+LIfMdCXC7NyIuLqayZGZma0h0\nCkDmLw4A+AZAa8icRQXkGXkNMgdzIiQKxH7IHAkAXI9w+EwcPPgTiovXoaioM2S+JayOfRUS+HYN\ngP8HiVKxBQcP5uH775vhttvuQigUQlnZMgA3Q+Y71gH4SR2/LuLaNsLlctbarhMnXoq9e+9CYeFC\nFBUtx9Kly1Fc/Dr27fsAxcUrceiQE8C/IIFsFwBYjIULc1FUVIT8/K2QqBYbI2rMQ1xcDMrLyyFz\nWIDMgT0KYAqsuR0AeAMHD4bx+uuvq9+kHOPGnY0DB17E/v3fAXgaMjf5Q8Q5lql2WQlgoTrH26rt\nP4HMtUGdpzlkrmk1ZJ7uXUgA4PPUb/QoJCivOZc4QX13qb8yyJzoL6rOBZA5Myuljnwuh8y3lat2\nj5T1F8icVyGA2yBzhu9CglqvA/BPVefzqvwWdew36jrfjmiv1wEcr45bDvmtzfIAsAEy//iJOl8I\nVe/xDZA533sg83NhSGBkqPbYBYmIskq1zSa1by2AMwHMQWpqLDSa+qChX3SOKQsXLqRhJNJmO4MS\nyeHoXounnXY+JQWGWeZztmkjkQ4uu+wy9UZ+LWUORTL4ut3xNAwzk/DZ9HjOZXp6myoLlb/77jvG\nxaUyJqYffb5U5uSMpGEkMBTqS5stRJcrU719Z1PmXFrT5WrGnj0H0+/vSuB22mzNKCM4U7ZnKHNB\n7SmjrVTKGqoE9Zb/XkTZ/3Do0FNZWlpKhyOGlpmUlHmqeIoJ63xKNAo/n3jiiZoNRDIUakYrzuNe\nymjGalMxg7asss3vz+K6deuYktKaMpJMUaOOa+h0Bvntt98q02wa7fZ7Kea5ZIqX4RhVX1uK6fhS\n3n333STJ7du3q/iU5rkOqOsfqa6nixrR/DuiTDPKCLkjrTnD7up8swiMrnafNKcsMk6gNU/lpngk\nmsslOlHMo+mUEVecqj9AGbFlUEzSL6vztVL/DXXuBCVrgDK6DFLmulLUd3NER4pXp4tW9mm/Olcs\nJe5nopKjtWo3Myjz7epcXSjm0FvVPfMsxfQYR5mbM9fCTVNyfEixLnRQ15lJmdMcTBmhmZnXO6o2\nOVsdt5OAnVu2bPn9H+4GBk1khNbUaOj74pizfHlk+KDIDjaBxcXFNco/8MBDNIwc1TGW0+2ezPPP\nn0qSfPXVV+nztVUP8zQCF7N9+17My8vjokWL+O677/K2227nAw88UGvUjb1791bOf5HSGS9atIjr\n1q3jkiVL+I9//IN9+w5nRkZnjhp1Et98802Gw2G+8sorvPXWGezTJ4cu11UUM9Qh2mwjKO7pXxN4\nU3VkcyjOGIMJnEcxD5XT6z2b119/M0myX78TabOZwXaLKO7WM+nxpLF9+/bs3bvPEdfAHX/8GDoc\nM5QcO1XHPE/Vt5ZebzI9nhjKomASeIcxMSksKSnhKaecTZfraoq57jY6nWmcNWtWZd3r1q3jmDFn\nsGPHAXS7Ywi8q67BnN/6jn5/F/73v/8lKRFaQqFk1emS4iqfpNolWWULD1Dmg0gJuxVPMQHKYubk\n5OZKAWykzEfF04pOkqvadRxlDm0HxcznpeXy/hWthdAhOp1mFJBeqvOPVedqRlFkTooDyS0UxR1D\nmed7j+Jw4VbK41alaAIUs6fpTv+MUkTxFAX7DoFr1DVkUIIRf0tRhnfRUvQdKG78her+yKK45h9S\nSshci2dGIXGqc5gOU3PUvua0FpGbL01fUZTYJRSnlHEE/k2fL/G3P7xRDLRCi0oa+r44ptjtNRVZ\nKNS9cg6tNsrLy3nmmRfQ7Q7R601k377DKiN/hMNh/ulPV9LnS2Yo1IVJSVlcvXp1vV3Pzp072a5d\nTwYCbWgYmezTZyjT0lrRMNLodgd41lmT6PXG0DDSGROTwlatutLvP45+f4vKOTRSHEPS0lqrlDax\ndDji6XL5effd99VJjvz8fLZp050+XzO63QFOmjSZiYmZNIx0ejxBPv74k3zppVfo88UqWZrx008/\nJUnu2LGDXbr0p8+XQrc7yIsvvvKwGQw++eQTxsSk0OdLJeCl15tFrzeJU6ZcdZg5tG602fx0u5vR\nMDI5ZMgY7tq1iy1bmgudTS/CZjTnydq06cpt27axdevuSillq47aXBgtXpCBQDOlaOKVcvKqffGq\nc5e4j5069WNFRQVvv/1uer3xDIW6qRQ6ZrJMKxxXINCFbncM7XafqiO+cp8lixlCy1yM3ZKAn05n\nkIaREHEtx9HyuExSSsev/rJpjQY9qqzpiWk60Pgj/nvVtZoeoH5aXpKG+p5EK+yW2QZOdR5RwA5H\nkB9//PH/dtNHKWgiCq2pJXRTv03T4qabgHvvrbqNBLZv344tW7agVatWiIuLO2IdO3fuxKFDh5Ca\nmlojhfz69euxd+9etGvXDoZhHKaGY0NZWRl++OEHuN1utG3bFuFwGFu3bkVcXBxCoRCKi4tRUFCA\ntLQ0OBwO/PDDD7DZbOjQoYOKei+UlJRg9erV8Hq98Pl8iIuLQ0xMzBHOXJVwOIz8/HwEg0HExcWh\nrKwMW7duRWJiIgIBWcMVKYvb7a5y7M8//wyfz4eEhIQjnqe0tBQ///wzgsEgNm3ahLi4OLRs2bJG\nub1792Lt2rVITk7G3r17K9vHbreDJJYvX46CggJkZGSgoKAADocDmZmZyMzMrGyX3NxcrFmzBllZ\nWdiyZQsOHDiAtLQ0dOjQAZ06dUJeXh5WrlyJffv2Yffu3RgwYEBlXdu3b0fbtm0xaNCgSpny8/Ox\nfft2tGnTBiUlJfj888+xdetWpKeno0ePHti+fTuys7Phdrvx6aefYtOmTejevTtiY2OxcOFCBINB\njBkzBjt37sRXX30FADh48CDS0tIwcuRIlJaWYs2aNVi7di1yc3ORmpqKxMRE/PTTT8jKysIpp5yC\nUCiEuXPnwuVy4YQTTsD69esxf/58bNmyBX379kWLFi2wevVqFBYWom3btvj222+Rn5+PmJgYNGvW\nDO3atcP+/fuxYsUKFBQUoFu3bmjTpg3i4+OxadMmbN++HcnJyaioqMC2bduQkpKCoUOHori4GAMH\nDlTz2E2PppLgM1ouYBQkha2ZT+LeWso8DFkBWgzgQkj+iOo0KYX2xRfAgAHW9w4dgFWrGk4ejUbT\nNGkqCi0avBwdAB6BKLUOkHAJ7auVGQMJO9AawCUAHqtPARuCcNhSZt98IyMyrcw0Go3m8NTux1y/\n9EFVP9+XAJwK8TM2GQtgrvr8FYBYSOyaAjRR7HZRYhqNRqOpG9EwQktD1YUk+Wrb0cqkH2O5NBqN\nRtOIiIYRWl3HIdXtu7UeN3PmzMrPOTk5yMnJ+U1CaTQaTVMlNzcXubm5DS3G7040TAL2AzATMocG\nSMiHMKo6hjwOCX/9kvq+BsAQ1DQ5NimnEI1Go6kPtFPI78cSiLNHNiS3xVmwYiqZvAngfPW5HyR2\nUpOdP9NoNBrNrycaTI7lAK4E8D7E43E2xCFkqtr/BCQo3RiI80gRgIvqX0yNRqPRRDONfohZDW1y\n1Gg0ml+JNjlqNBqNRhNFaIWm0Wg0miaBVmgajUajaRJohabRaDSaJoFWaBqNRqNpEmiFptFoNJom\ngVZoGo1Go2kSaIWm0Wg0miaBVmgajUajaRJohabRaDSaJoFWaBqNRqNpEmiFptFoNJomgVZoGo1G\no2kSaIWm0Wg0miaBVmgajUajaRJohabRaDSaJoFWaBqNRqNpEmiFptFoNJomgVZoGo1Go2kSaIWm\n0Wg0miaBVmgajUajaRJohabRaDSaJkE0KLR4AAsA/ATgAwCxtZTJAPAxgFUAVgK4ut6k02g0Gk2j\nIBoU2k0QhdYGwEfqe3XKAPwZQEcA/QBcAaB9fQlYX+Tm5ja0CP8TjVn+xiw7oOVvaBq7/E2FaFBo\nYwHMVZ/nAhhXS5ntAJapzwcArAaQeuxFq18a+0PRmOVvzLIDWv6GprHL31SIBoWWAqBAfS5Q349E\nNoDuAL46hjJpNBqNppHhrKfzLADQrJbtt1b7TvV3OAIA/gPgGshITaPRaDQaAICtoQUAsAZADsSs\n2Bzi/NGulnIuAG8DeBfAQ4epax2A435/ETUajaZJkwegVUML0RS4D8CN6vNNAGbVUsYG4FkAD9aX\nUBqNRqPR/FriAXyImm77qQDeUZ8HAQhDHEOWqr9R9SumRqPRaDQajUaj0WiOSGNclD0KMm+4Fpap\ntToPq/3LIR6d0cTR5J8Ikft7AJ8B6FJ/otWJurQ/APQGUA7gtPoQ6ldQF/lzIFaMlQBy60WqunM0\n+RMBvAexxqwEcGG9SXZ0noZ4Yq84QplofnaPJn+0P7tNnvsA3KA+34ja59+aAeimPgcA/IiGW5Tt\ngDiuZEOcXJbVIssYAPPV574Avqwv4epAXeTvDyBGfR6Fxie/WW4hxAlpQn0JVwfqIn8s5OUtXX1P\nrC/h6kBd5J8J4B71ORHAL6g/b+yjMRiipA6nEKL52QWOLn80P7t1IhrWof0vNLZF2X0gD/RGSPST\nlwCcWq1M5DV9BemgjrY2r76oi/xfANinPn8Fq2ONBuoiPwBcBVkesrPeJKsbdZH/XACvAshX33fV\nl3B1oC7ybwMQUp9DEIVWXk/yHY3FAPYcYX80P7vA0eWP5me3TjR2hdbYFmWnAdgS8T1fbTtamWi5\nseoifyR/gvXGGg3Utf1PBfCY+n6kdZH1TV3kbw0xxX8MYAmASfUjWp2oi/xPQkLc/Qwxf11TP6L9\nLkTzs/tribZnt05Ey1D+SDSlRdl17Ryrrw+Mlk7118gxFMBkAAOPkSy/hbrI/xBk+Qghv0M0rNU0\nqYv8LgA9AJwAwIC8dX8JmddpaOoi/y0Qi0oOZE3pAgBdAew/dmL9rkTrs/triMZnt040BoV24hH2\nFUCUnbkoe8dhyrkgZph5AF7/XaX7dWyFOKmYZMAyDR2uTLraFg3URX5AJpOfhNjhj2TiqG/qIn9P\niCkMkDmc0RDz2JvHXLqjUxf5t0DMjAfV3ycQhRANCq0u8g8AcLf6nAdgA4C2kNFmtBPNz25didZn\n9w9BY1uU7YQ8pNkA3Di6U0g/RNfEbF3kz4TMk/SrV8nqRl3kj2QOosvLsS7yt4Os63RARmgrAHSo\nPxGPSF3k/xuA29XnFIjCi68n+epCNurmFBJtz65JNg4vfzQ/u38IGuOi7NEQT8t1AG5W26aqP5NH\n1P7lEPNRNHE0+Z+CTOSbbf11fQt4FOrS/ibRptCAusk/DeLpuAINv0ylOkeTPxHAW5B7fwXEySVa\neBEyt3cIMhKejMb17B5N/mh/djUajUaj0Wg0Go1Go9FoNBqNRqPRaDQajUaj0Wg0Go1Go9FoNBqN\nRqPRaDSa+iAFwAuQxb1LAHyO2gNaH0uyUXNha2dYa39+AbBeff6gjnVmATgn4vuFAP7xvwip0Wg0\nmujFBolreEnEtkwAV9ZS9liGhMvGkfNpHW4xt+MIx+RAFiObXACt0DR/QBp7tH2Npq4MA1AK4F8R\n2zZDIjsAMqp5E8BHkIC4cZC4n8shirCzKjcTwPURdayEKMZsSGqif6lt7wPwqjI9VT3LAFz+K2TO\nhYRs+wYSVHsOquZnMwP2zoLkuloK4Fq1LRXAu5AoOvf+inNqNI0WrdA0fxQ6AvjuKGW6QxTGUAB3\nAPgWEtj3Fkg8UKBm9PTI760gCrITgL2wlM8cAFfASjRbVwgJrN0bEuPwcNwIyXXVHZItwKbOdSZE\nEZ+FI6f50WiaBFqhaf4oVFdEj0BGTJHx6hZAFBEgqTOeU58/BpAAIHiUc2yApK8HRBlmQzIAxwD4\nVG1/ruZhR+TlOpSpLWXJR5ARXCmAH5QsGk2TRis0zR+FVagaLPZKSM6wpIhtRdWOqS0XWjmqPjfe\niM+lEZ8rUPtc3K/NrxYpU+S57ZCI9YejuixHmoPTaJoEWqFp/igshCifSyO2+Y9QfjGAiepzDoCd\nkBHPRliKsQeAFkc57z7IqM9MljjxCGWPxkbIfBwAjIWYI6Hkihw91qY0oylRqUZzTNAKTfNHYhyA\nIRC3+K8APAPgBrWvesbzmbCcOf4C8RwEJFFsPMTx4wpIKhSTw82vXQTgnxCnjdrK1ZUnlfzLIDmr\nzMzryyGjsGUQp5Dasrc3xszJGo1Go9FoNBqNRqPRaDQajUaj0Wg0Go1Go9FoNBqNRqPRaDQajUaj\n0Wg0Go1Go9FoNBqNRqPRaCL5/2PXok5pmnr2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117772a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# fit a linear regression line\n",
    "# http://stackoverflow.com/questions/19068862/how-to-overplot-a-line-on-a-scatter-plot-in-python\n",
    "import statsmodels.api as sm\n",
    "xs = Y_test1\n",
    "ys = predictions\n",
    "results = sm.OLS(ys,sm.add_constant(xs)).fit()\n",
    "\n",
    "print results.summary()\n",
    "\n",
    "plt.scatter(xs,ys)\n",
    "\n",
    "#X_plot = np.linspace(0,1,100)\n",
    "plt.plot(xs, xs*results.params[0] + results.params[1])\n",
    "plt.xlabel('Ground Truth')\n",
    "plt.ylabel('Predictions')\n",
    "plt.title('Plot of Ground Truth Methylation values vs Predictions ( Training Data)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0363286795224\n",
      "sqrt: 0.1906008382\n"
     ]
    }
   ],
   "source": [
    "# compute mean squared error\n",
    "mean_sq_error = np.mean((Y_test1-predictions)**2)\n",
    "print mean_sq_error\n",
    "print \"sqrt: \" + str(np.sqrt(mean_sq_error))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  0.00157048],\n",
       "       [ 0.00157048,  1.        ]])"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(Y_test1,predictions)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, with RMSE = 0.191 and r = 0.002, this is not performing as well as we would like... Let's start over, shall we?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Alternate method for Data import: pandas\n",
    "\n",
    "### [pandas](http://pandas.pydata.org/) is a python package that is aimed at dealing with data inputs that are well-organized, such as the .bed files that we have.\n",
    "\n",
    "For more information about various useful functionalities of pandas, go here:\n",
    "\n",
    "http://pandas.pydata.org/pandas-docs/stable/index.html\n",
    "\n",
    "You will also find a lot of helpful questions and answers that have been discussed in StackOverflow (simply google your question, and most likely, the top search results will be StackOverflow discussion threads)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# read_csv() function needs the parameter sep to tell it what your separator is\n",
    "train_bed = pandas.read_csv('data/intersected_final_chr1_cutoff_20_train.bed', sep='\\t', header=None)\n",
    "sample_p_bed = pandas.read_csv('data/intersected_final_chr1_cutoff_20_sample_partial.bed', sep='\\t', header=None)\n",
    "sample_f_bed = pandas.read_csv('data/intersected_final_chr1_cutoff_20_sample_full.bed', sep='\\t', header=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "      <th>28</th>\n",
       "      <th>29</th>\n",
       "      <th>30</th>\n",
       "      <th>31</th>\n",
       "      <th>32</th>\n",
       "      <th>33</th>\n",
       "      <th>34</th>\n",
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       "      <td>0.941176</td>\n",
       "      <td>0.939024</td>\n",
       "      <td>0.949152</td>\n",
       "      <td>0.956989</td>\n",
       "      <td>0.933333</td>\n",
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       "      <td>0.916667</td>\n",
       "      <td>0.959459</td>\n",
       "      <td>0.974683</td>\n",
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       "    <tr>\n",
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       "      <td>0.930556</td>\n",
       "      <td>0.795918</td>\n",
       "      <td>0.931507</td>\n",
       "      <td>0.929412</td>\n",
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       "      <td>0.942529</td>\n",
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       "      <td>NaN</td>\n",
       "      <td>0.869565</td>\n",
       "      <td>0.879310</td>\n",
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       "      <td>0.970588</td>\n",
       "      <td>0.906250</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>chr1</td>\n",
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       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>chr1</td>\n",
       "      <td>10661</td>\n",
       "      <td>10663</td>\n",
       "      <td>+</td>\n",
       "      <td>0.765957</td>\n",
       "      <td>0.714286</td>\n",
       "      <td>0.647059</td>\n",
       "      <td>0.821429</td>\n",
       "      <td>0.851064</td>\n",
       "      <td>0.714286</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.934783</td>\n",
       "      <td>0.788462</td>\n",
       "      <td>0.658537</td>\n",
       "      <td>0.864865</td>\n",
       "      <td>0.521739</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>chr1</td>\n",
       "      <td>10669</td>\n",
       "      <td>10671</td>\n",
       "      <td>+</td>\n",
       "      <td>0.866667</td>\n",
       "      <td>0.892857</td>\n",
       "      <td>0.891304</td>\n",
       "      <td>0.944444</td>\n",
       "      <td>0.905660</td>\n",
       "      <td>0.762712</td>\n",
       "      <td>...</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.967742</td>\n",
       "      <td>0.949152</td>\n",
       "      <td>0.900000</td>\n",
       "      <td>0.931818</td>\n",
       "      <td>0.875000</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>chr1</td>\n",
       "      <td>10688</td>\n",
       "      <td>10690</td>\n",
       "      <td>+</td>\n",
       "      <td>0.897436</td>\n",
       "      <td>0.880952</td>\n",
       "      <td>0.867925</td>\n",
       "      <td>0.958333</td>\n",
       "      <td>0.900000</td>\n",
       "      <td>0.737500</td>\n",
       "      <td>...</td>\n",
       "      <td>0.964286</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>0.976744</td>\n",
       "      <td>0.888889</td>\n",
       "      <td>0.846154</td>\n",
       "      <td>0.936508</td>\n",
       "      <td>0.820513</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10 rows × 38 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     0      1      2  3         4         5         6         7         8   \\\n",
       "0  chr1  10468  10470  +  0.750000  0.681818  0.888889  0.518518  0.866667   \n",
       "1  chr1  10492  10494  +  0.882353  0.705882  0.918367  0.842105  0.935484   \n",
       "2  chr1  10496  10498  +  0.849315  0.843137  0.847458  0.883721  0.913043   \n",
       "3  chr1  10541  10543  +  0.868132  0.941176  0.939024  0.949152  0.956989   \n",
       "4  chr1  10562  10564  +  0.820513  0.962963  0.930556  0.795918  0.931507   \n",
       "5  chr1  10576  10578  +  0.661017  0.775510  0.887097  0.583333  0.880000   \n",
       "6  chr1  10578  10580  +  0.711864  0.804348  0.783333  0.676471  0.913043   \n",
       "7  chr1  10661  10663  +  0.765957  0.714286  0.647059  0.821429  0.851064   \n",
       "8  chr1  10669  10671  +  0.866667  0.892857  0.891304  0.944444  0.905660   \n",
       "9  chr1  10688  10690  +  0.897436  0.880952  0.867925  0.958333  0.900000   \n",
       "\n",
       "         9  ...        28  29  30        31        32        33        34  \\\n",
       "0  0.971429 ...  0.945946 NaN NaN  0.875000  0.949152  0.861111  0.760000   \n",
       "1  0.964286 ...  0.925532 NaN NaN  0.909091  0.942529  0.814815  0.757576   \n",
       "2  0.922222 ...  0.951456 NaN NaN  0.916667  0.947917  0.918033  0.894737   \n",
       "3  0.933333 ...  0.889908 NaN NaN  0.947368  0.684211  0.857143  0.916667   \n",
       "4  0.929412 ...  0.942529 NaN NaN  0.869565  0.879310  0.882353  0.929412   \n",
       "5  0.927536 ...  0.878378 NaN NaN  0.733333  0.945455  0.821429  0.742857   \n",
       "6  0.941176 ...  0.942857 NaN NaN  0.857143  0.814815  0.764706  0.805970   \n",
       "7  0.714286 ...       NaN NaN NaN       NaN  0.934783  0.788462  0.658537   \n",
       "8  0.762712 ...       NaN NaN NaN       NaN  0.967742  0.949152  0.900000   \n",
       "9  0.737500 ...  0.964286 NaN NaN       NaN  0.976744  0.888889  0.846154   \n",
       "\n",
       "         35        36  37  \n",
       "0       NaN  0.437500   0  \n",
       "1       NaN  0.660377   0  \n",
       "2  0.921569  0.852459   0  \n",
       "3  0.959459  0.974683   0  \n",
       "4  0.970588  0.906250   0  \n",
       "5  0.961538  0.777778   0  \n",
       "6  0.918367  0.750000   0  \n",
       "7  0.864865  0.521739   0  \n",
       "8  0.931818  0.875000   0  \n",
       "9  0.936508  0.820513   0  \n",
       "\n",
       "[10 rows x 38 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# head() function outputs the first n rows of your data\n",
    "train_bed.head(n = 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>chr1</td>\n",
       "      <td>10468</td>\n",
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       "      <td>0.913793</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>chr1</td>\n",
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       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>chr1</td>\n",
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       "      <td>10498</td>\n",
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       "      <th>3</th>\n",
       "      <td>chr1</td>\n",
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       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>chr1</td>\n",
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       "      <td>10564</td>\n",
       "      <td>+</td>\n",
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       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>chr1</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>chr1</td>\n",
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       "      <td>10580</td>\n",
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       "      <td>0.897436</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>chr1</td>\n",
       "      <td>10661</td>\n",
       "      <td>10663</td>\n",
       "      <td>+</td>\n",
       "      <td>0.862745</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>chr1</td>\n",
       "      <td>10669</td>\n",
       "      <td>10671</td>\n",
       "      <td>+</td>\n",
       "      <td>0.939394</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>chr1</td>\n",
       "      <td>10688</td>\n",
       "      <td>10690</td>\n",
       "      <td>+</td>\n",
       "      <td>0.965517</td>\n",
       "      <td>0</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      0      1      2  3         4  5\n",
       "0  chr1  10468  10470  +  0.913793  0\n",
       "1  chr1  10492  10494  +  0.931818  0\n",
       "2  chr1  10496  10498  +  0.917526  0\n",
       "3  chr1  10541  10543  +  0.933884  0\n",
       "4  chr1  10562  10564  +  0.936842  0\n",
       "5  chr1  10576  10578  +  0.951219  0\n",
       "6  chr1  10578  10580  +  0.897436  0\n",
       "7  chr1  10661  10663  +  0.862745  0\n",
       "8  chr1  10669  10671  +  0.939394  0\n",
       "9  chr1  10688  10690  +  0.965517  0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_f_bed.head(n = 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The format of these .bed files are discussed in the github repo readme, as well as the assignment PDF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7610\n",
      "(array([  1084,   1154,   1214, ..., 379252, 379258, 379368]),)\n"
     ]
    }
   ],
   "source": [
    "# You can refer to each *column* of the datatable by index:\n",
    "test_indeces = sample_p_bed[5]==1\n",
    "train_indeces = sample_p_bed[5]==0\n",
    "print(sum(test_indeces))\n",
    "print(np.where(test_indeces))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are 7610 positions (out of total 379551) where the last column entry is 1 (the positions that are observed in the 450K BeadChip).\n",
    "\n",
    "Now, let's try taking the mean of each row (mean methylation value across tissues at a location in chr1):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0         0.782426\n",
       "1         0.836918\n",
       "2         0.897671\n",
       "3         0.913804\n",
       "4         0.907181\n",
       "5         0.801933\n",
       "6         0.809198\n",
       "7         0.698955\n",
       "8         0.889537\n",
       "9         0.864452\n",
       "10        0.724535\n",
       "11        0.881583\n",
       "12        0.894980\n",
       "13        0.885859\n",
       "14        0.724211\n",
       "15        0.884685\n",
       "16        0.808047\n",
       "17        0.896089\n",
       "18        0.892571\n",
       "19        0.704055\n",
       "20        0.783236\n",
       "21        0.711146\n",
       "22        0.391053\n",
       "23        0.235756\n",
       "24        0.141029\n",
       "25        0.388317\n",
       "26        0.342627\n",
       "27        0.643686\n",
       "28        0.468989\n",
       "29        0.426951\n",
       "            ...   \n",
       "379521    0.814346\n",
       "379522    0.893050\n",
       "379523    0.889165\n",
       "379524    0.903788\n",
       "379525    0.750231\n",
       "379526    0.825168\n",
       "379527    0.830262\n",
       "379528    0.788398\n",
       "379529    0.864323\n",
       "379530    0.918622\n",
       "379531    0.730308\n",
       "379532    0.890458\n",
       "379533    0.812594\n",
       "379534    0.880824\n",
       "379535    0.825518\n",
       "379536    0.842819\n",
       "379537    0.848609\n",
       "379538    0.800425\n",
       "379539    0.886900\n",
       "379540    0.888341\n",
       "379541    0.904936\n",
       "379542    0.795856\n",
       "379543    0.771345\n",
       "379544    0.867522\n",
       "379545    0.913678\n",
       "379546    0.921191\n",
       "379547    0.902365\n",
       "379548    0.827983\n",
       "379549    0.740661\n",
       "379550    0.894867\n",
       "dtype: float64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# mean() function with axis = 1 takes row-wise averages.\n",
    "train_bed[list(range(4,37))].mean(axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see that the averages are all ratios (between 0 and 1)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Y6MMb/TPACGB9ZN71wMiY9A2eLiIiVVDNJ+qPBp4H9sGqvFYWjE+1HN7W1vbW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\nIiIiIiIiIiIi5fj/DhR875DZFBwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10aed4590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# the histogram of the data\n",
    "plt.hist(train_bed[list(range(4,37))].mean(axis=1).tolist(), 50)\n",
    "\n",
    "plt.xlabel('Mean methylation proportion')\n",
    "plt.ylabel('Frequency')\n",
    "plt.title('Distribution of mean methylation across 33 samples')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How good is the mean approximation?\n",
    "\n",
    "We can ask a very naive question: how good is the mean approximation for imputation? In this case, we just fill in the test files with the mean of 33 samples, and see how well the approximation performs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7523\n",
      "368411\n"
     ]
    }
   ],
   "source": [
    "# Let's take indices of the sample file that aren't nans for comparison:\n",
    "# By the way, learning the python list comprehension construction is totally worth it.\n",
    "# Check out http://www.secnetix.de/olli/Python/list_comprehensions.hawk if the following code confuses you.\n",
    "\n",
    "not_nans_in_full = ~np.isnan(sample_f_bed[4])\n",
    "test_indeces_nan_filtered = [test_indeces[x] and not_nans_in_full[x] for x in range(len(test_indeces))]\n",
    "\n",
    "print(sum(test_indeces_nan_filtered))\n",
    "\n",
    "train_indeces_nan_filtered = [train_indeces[x] and not_nans_in_full[x] for x in range(len(train_indeces))]\n",
    "\n",
    "print(sum(train_indeces_nan_filtered))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        ,  0.79374181],\n",
       "       [ 0.79374181,  1.        ]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Python list comprehension keeps coming up...\n",
    "row_means = train_bed[list(range(4,37))].mean(axis=1)\n",
    "test_indeces_nan_filtered_numeric = np.where(test_indeces_nan_filtered)[0]\n",
    "\n",
    "row_means_test = [row_means[x] for x in test_indeces_nan_filtered_numeric]\n",
    "partial_values_test = [sample_f_bed[4][x] for x in test_indeces_nan_filtered_numeric]\n",
    "\n",
    "np.corrcoef(row_means_test, partial_values_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Among test values (7523 of them, we are seeing r = 0.79 and r^2 = 0.63)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.157066842941\n"
     ]
    }
   ],
   "source": [
    "# http://stackoverflow.com/questions/17197492/root-mean-square-error-in-python\n",
    "def rmse(predictions, targets):\n",
    "    return np.sqrt(((predictions - targets) ** 2).mean())\n",
    "\n",
    "print(rmse(np.array(row_means_test), np.array(partial_values_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And RMSE = 0.16. Let's see how well this generalizes to the rest of the test set, using the same method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.          0.77229991]\n",
      " [ 0.77229991  1.        ]]\n",
      "0.11748933978\n"
     ]
    }
   ],
   "source": [
    "train_indeces_nan_filtered_numeric = np.where(train_indeces_nan_filtered)[0]\n",
    "\n",
    "row_means_test = [row_means[x] for x in train_indeces_nan_filtered_numeric]\n",
    "full_values_test = [sample_f_bed[4][x] for x in train_indeces_nan_filtered_numeric]\n",
    "\n",
    "print(np.corrcoef(row_means_test, full_values_test))\n",
    "print(rmse(np.array(row_means_test), np.array(full_values_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are seeing r = 0.772 (r^2 = 0.596), and RMSE = 0.117. This is not an excellent prediction (as you could probably guess), but let's see what happened with an informative graph:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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D2A8SFBugeRNttreyGCEUGiFC/I3x/fff47vvvsO3336LxYsX47333sdbb72P9evXAugK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\n7Ln8P/iRo9o4hGhjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116a8d350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "plt.scatter(full_values_test, row_means_test)\n",
    "\n",
    "plt.xlabel('Actual methylation values')\n",
    "plt.ylabel('Prediction by taking row means')\n",
    "plt.title('Performance of the simplest predictor (row means)')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This graph actually could have an interesting interpretation: at any given location with actual methylation values (slicing the graph vertically), there is a distribution of means across other tissues. Is this distribution roughly Gaussian? Or is it some other distribution? You can probe further to find out! You may come across interesting conclusions, but this is not in the scope of this assignment."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's try one other very simple approach - imputation by similarity\n",
    "\n",
    "There is another very naive hypothesis we can test: that the imputation values will roughly follow the pattern of the most similar tissue. The simplest way to implement this is to simply fill in all values with the methylation value of the closest tissue. (more sensible methods will take some weighted average among the 33 known tissues, *hint* *hint* ;) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sample 4 has r = \n",
      "0.378598417584\n",
      "Sample 5 has r = \n",
      "0.345252677334\n",
      "Sample 6 has r = \n",
      "0.361315960374\n",
      "Sample 7 has r = \n",
      "0.317478997909\n",
      "Sample 8 has r = \n",
      "0.747913758746\n",
      "Sample 9 has r = \n",
      "0.800082923738\n",
      "Sample 10 has r = \n",
      "0.819903104044\n",
      "Sample 11 has r = \n",
      "0.726106574721\n",
      "Sample 12 has r = \n",
      "0.622060560327\n",
      "Sample 13 has r = \n",
      "0.415857835124\n",
      "Sample 14 has r = \n",
      "0.489532506005\n",
      "Sample 15 has r = \n",
      "0.530428055146\n",
      "Sample 16 has r = \n",
      "0.49737091449\n",
      "Sample 17 has r = \n",
      "0.456762207392\n",
      "Sample 18 has r = \n",
      "0.42315902776\n",
      "Sample 19 has r = \n",
      "0.452502097166\n",
      "Sample 20 has r = \n",
      "0.472791940205\n",
      "Sample 21 has r = \n",
      "0.595136127269\n",
      "Sample 22 has r = \n",
      "0.468653133869\n",
      "Sample 23 has r = \n",
      "0.958137133375\n",
      "Sample 24 has r = \n",
      "0.903443669227\n",
      "Sample 25 has r = \n",
      "0.907276390419\n",
      "Sample 26 has r = \n",
      "0.901410887449\n",
      "Sample 27 has r = \n",
      "0.881939901448\n",
      "Sample 28 has r = \n",
      "0.870240568323\n",
      "Sample 29 has r = \n",
      "0.285251817427\n",
      "Sample 30 has r = \n",
      "0.746240943036\n",
      "Sample 31 has r = \n",
      "0.748603867482\n",
      "Sample 32 has r = \n",
      "0.561316455818\n",
      "Sample 33 has r = \n",
      "0.414797029478\n",
      "Sample 34 has r = \n",
      "0.465293045341\n",
      "Sample 35 has r = \n",
      "0.891189876985\n",
      "Sample 36 has r = \n",
      "0.425833780183\n"
     ]
    }
   ],
   "source": [
    "# we have partial_values_test defined from above:\n",
    "for i in range(4,37):\n",
    "    test_array = [train_bed[i][x] for x in test_indeces_nan_filtered_numeric]\n",
    "    test_array_mod = [test_array[x] for x in range(len(test_array)) if ~np.isnan(test_array[x])]\n",
    "    temp_partial_values_test = [partial_values_test[x] for x in range(len(partial_values_test)) if ~np.isnan(test_array[x])]\n",
    "    print(\"Sample \" + str(i) + \" has r = \")\n",
    "    print(np.corrcoef(test_array_mod, temp_partial_values_test)[0,1])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our test sample is very similar to sample 23 (r = 0.958!!). Let's fill in our predictions with values from sample 23 and see what happens:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.          0.92177299]\n",
      " [ 0.92177299  1.        ]]\n",
      "0.0670191751457\n"
     ]
    }
   ],
   "source": [
    "samp_23_test = [train_bed[23][x] for x in train_indeces_nan_filtered_numeric]\n",
    "full_values_test = [sample_f_bed[4][x] for x in train_indeces_nan_filtered_numeric]\n",
    "\n",
    "# Need to take out nans. However, in the real assignment, you must fill in the nans with some value for full imputation:\n",
    "samp_23_test_mod = [samp_23_test[x] for x in range(len(samp_23_test)) if ~np.isnan(samp_23_test[x])]\n",
    "full_values_test_mod = [full_values_test[x] for x in range(len(samp_23_test)) if ~np.isnan(samp_23_test[x])]\n",
    "\n",
    "print(np.corrcoef(samp_23_test_mod, full_values_test_mod))\n",
    "print(rmse(np.array(samp_23_test_mod), np.array(full_values_test_mod)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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8hR/snlIq+qiA8qN0N+0ji8rWLjaNxPkeSPkj2hK4174vpvwTz5kGkEXgoFD/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fkj1p6rsFdE5ZZ8RIWcJqlcj5VUNFYjKiJpEGUyKqJMW27sN1u7NSlt5DFKW8qhN985TayzXTuN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\ndFtK9dpXK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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10beaef50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "plt.scatter(full_values_test_mod, samp_23_test_mod)\n",
    "\n",
    "plt.xlabel('Actual methylation values')\n",
    "plt.ylabel('Prediction by taking values from the most similar sample')\n",
    "plt.title('Performance of the simplest predictor (row means)')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even using this simple approach to use existing information from the sample_partial file provides a much better result (r = 0.922, r^2 = 0.850, RMSE = 0.067). Therefore, you can guess that from your assignment, we are generally expecting a result that is better than this, although we will not necessarily grade on accuracy of your imputation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Incorporating genetic and epigenetic information\n",
    "\n",
    "As you might be aware, the genome is not a random sequence of A,T,C,G's. There are a lot of information that is buried in the genome (a lot of which we still don't have a good understanding), and using annotations from previous experiments can help in analyses of studies that involving genetic sequences.\n",
    "\n",
    "For this exercise, we will import [ENCODE](https://www.encodeproject.org/) annotations of the genome into the pipeline. ENCODE outlines the putative regulatory elements in the genome that have been identified by a set of experiments. Since DNA methylation is an epigenetic feature, this set of information may give us a better understanding of the distribution of likely methylation sites.\n",
    "\n",
    "First, I navigate to ENCODE portal in UCSC genome browser:\n",
    "\n",
    "https://genome.ucsc.edu/ENCODE/downloads.html\n",
    "\n",
    "And want to incorporate information from transcription factor binding sites (Txn Factor ChIP):\n",
    "\n",
    "http://hgdownload.cse.ucsc.edu/goldenPath/hg19/encodeDCC/wgEncodeRegTfbsClustered/\n",
    "\n",
    "Note: Refer to https://en.wikipedia.org/wiki/Transcription_factor for more information on transcription factors. In short, they are a set of proteins that bind to different regions in the genome to modulate gene expression, which leads to protein production."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Note: this code assumes that you downloaded the Transcription factor database from ENCODE under ./annotations/\n",
    "txn_factors = pandas.read_csv('annotations/wgEncodeRegTfbsClusteredV3.bed', sep='\\t', header=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>chr1</td>\n",
       "      <td>10073</td>\n",
       "      <td>10329</td>\n",
       "      <td>ZBTB33</td>\n",
       "      <td>354</td>\n",
       "      <td>2</td>\n",
       "      <td>204,246</td>\n",
       "      <td>354,138</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>chr1</td>\n",
       "      <td>10149</td>\n",
       "      <td>10413</td>\n",
       "      <td>CEBPB</td>\n",
       "      <td>201</td>\n",
       "      <td>1</td>\n",
       "      <td>343</td>\n",
       "      <td>201</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>chr1</td>\n",
       "      <td>16110</td>\n",
       "      <td>16390</td>\n",
       "      <td>CTCF</td>\n",
       "      <td>227</td>\n",
       "      <td>7</td>\n",
       "      <td>213,612,621,627,628,631,662</td>\n",
       "      <td>110,139,171,209,227,200,170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>chr1</td>\n",
       "      <td>29198</td>\n",
       "      <td>29688</td>\n",
       "      <td>TAF1</td>\n",
       "      <td>184</td>\n",
       "      <td>1</td>\n",
       "      <td>157</td>\n",
       "      <td>184</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>chr1</td>\n",
       "      <td>29275</td>\n",
       "      <td>29591</td>\n",
       "      <td>GABPA</td>\n",
       "      <td>198</td>\n",
       "      <td>1</td>\n",
       "      <td>180</td>\n",
       "      <td>198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>chr1</td>\n",
       "      <td>89795</td>\n",
       "      <td>90051</td>\n",
       "      <td>USF1</td>\n",
       "      <td>185</td>\n",
       "      <td>2</td>\n",
       "      <td>68,202</td>\n",
       "      <td>146,185</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>chr1</td>\n",
       "      <td>91156</td>\n",
       "      <td>91580</td>\n",
       "      <td>CTCF</td>\n",
       "      <td>223</td>\n",
       "      <td>9</td>\n",
       "      <td>9,640,645,657,663,669,672,675,685</td>\n",
       "      <td>183,223,138,115,115,145,141,144,220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>chr1</td>\n",
       "      <td>104859</td>\n",
       "      <td>105089</td>\n",
       "      <td>CTCF</td>\n",
       "      <td>106</td>\n",
       "      <td>2</td>\n",
       "      <td>48,49</td>\n",
       "      <td>87,106</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>chr1</td>\n",
       "      <td>138850</td>\n",
       "      <td>139274</td>\n",
       "      <td>CTCF</td>\n",
       "      <td>166</td>\n",
       "      <td>3</td>\n",
       "      <td>24,213,679</td>\n",
       "      <td>166,125,127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>chr1</td>\n",
       "      <td>235541</td>\n",
       "      <td>235877</td>\n",
       "      <td>SP1</td>\n",
       "      <td>120</td>\n",
       "      <td>1</td>\n",
       "      <td>196</td>\n",
       "      <td>120</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      0       1       2       3    4  5                                  6  \\\n",
       "0  chr1   10073   10329  ZBTB33  354  2                            204,246   \n",
       "1  chr1   10149   10413   CEBPB  201  1                                343   \n",
       "2  chr1   16110   16390    CTCF  227  7        213,612,621,627,628,631,662   \n",
       "3  chr1   29198   29688    TAF1  184  1                                157   \n",
       "4  chr1   29275   29591   GABPA  198  1                                180   \n",
       "5  chr1   89795   90051    USF1  185  2                             68,202   \n",
       "6  chr1   91156   91580    CTCF  223  9  9,640,645,657,663,669,672,675,685   \n",
       "7  chr1  104859  105089    CTCF  106  2                              48,49   \n",
       "8  chr1  138850  139274    CTCF  166  3                         24,213,679   \n",
       "9  chr1  235541  235877     SP1  120  1                                196   \n",
       "\n",
       "                                     7  \n",
       "0                              354,138  \n",
       "1                                  201  \n",
       "2          110,139,171,209,227,200,170  \n",
       "3                                  184  \n",
       "4                                  198  \n",
       "5                              146,185  \n",
       "6  183,223,138,115,115,145,141,144,220  \n",
       "7                               87,106  \n",
       "8                          166,125,127  \n",
       "9                                  120  "
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "txn_factors.head(n = 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see that this file is also in bed format. You don't have to pay too much attention columns after 4 (it outlines details of the experimental evidence of this transcription factor). You are familiar with columns 0, 1 and 2, and column 3 outlines which transcription factor binds to this location."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "set(['HSF1', 'SMARCC2', 'SMARCC1', 'POLR3G', 'MAFK', 'CCNT2', 'MAFF', 'ZNF143', 'BHLHE40', 'SIX5', 'HDAC6', 'BCLAF1', 'ZNF263', 'MYC', 'SETDB1', 'BRCA1', 'TRIM28', 'SP1', 'SP2', 'SP4', 'CREB1', 'ESRRA', 'NR2C2', 'GATA2', 'GATA3', 'GATA1', 'GTF2F1', 'RFX5', 'MAZ', 'RBBP5', 'FOXA1', 'RUNX3', 'ELK1', 'POU2F2', 'TCF12', 'CTBP2', 'MTA3', 'KDM5A', 'KDM5B', 'FOXP2', 'NFATC1', 'ZNF217', 'PRDM1', 'HMGN3', 'FAM48A', 'GTF3C2', 'TCF7L2', 'SMARCB1', 'SIRT6', 'CHD1', 'ZKSCAN1', 'CHD2', 'SAP30', 'RDBP', 'IKZF1', 'BACH1', 'EGR1', 'JUN', 'PPARGC1A', 'GTF2B', 'FOXA2', 'NFE2', 'KAP1', 'ZBTB33', 'ELK4', 'TCF3', 'FOS', 'ZNF274', 'PAX5', 'POLR2A', 'BRF2', 'STAT3', 'BRF1', 'ZEB1', 'TAF7', 'GRp20', 'TAF1', 'ESR1', 'TBP', 'HNF4G', 'HNF4A', 'MEF2C', 'MEF2A', 'CTCF', 'PHF8', 'HDAC1', 'HDAC2', 'YY1', 'BATF', 'HDAC8', 'RCOR1', 'FOXM1', 'SREBP1', 'CBX3', 'IRF3', 'SPI1', 'NANOG', 'STAT2', 'STAT1', 'SMC3', 'NR2F2', 'USF2', 'USF1', 'FOSL1', 'FOSL2', 'PML', 'ARID3A', 'TAL1', 'E2F6', 'BDP1', 'IRF1', 'MAX', 'EP300', 'RELA', 'TBL1XR1', 'IRF4', 'STAT5A', 'GABPA', 'NRF1', 'JUNB', 'BCL11A', 'JUND', 'WRNIP1', 'NFYB', 'NFYA', 'EZH2', 'ELF1', 'SRF', 'MYBL2', 'SMARCA4', 'TEAD4', 'CEBPB', 'CTCFL', 'TFAP2A', 'TFAP2C', 'UBTF', 'ZZZ3', 'ETS1', 'SUZ12', 'RPC155', 'SIN3A', 'NR3C1', 'ZBTB7A', 'RAD21', 'REST', 'RXRA', 'POU5F1', 'EBF1', 'PBX3', 'NFIC', 'THAP1', 'E2F4', 'E2F1', 'MXI1', 'CEBPD', 'SIN3AK20', 'MBD4', 'BCL3', 'ATF1', 'ATF3', 'ATF2'])\n",
      "161\n"
     ]
    }
   ],
   "source": [
    "# set() function takes the unique values from an array. There are 161 distinct TFs in this table.\n",
    "print(set(txn_factors[3]))\n",
    "print(len(set(txn_factors[3])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# How many rows from each factor?\n",
    "factor_dict = {}\n",
    "for item in txn_factors[3]:\n",
    "    if item not in factor_dict:\n",
    "        factor_dict[item] = 0\n",
    "    factor_dict[item] += 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CTCF : 162209\n",
      "CEBPB : 146873\n",
      "EP300 : 138836\n",
      "POLR2A : 134990\n",
      "FOS : 131528\n",
      "RAD21 : 119039\n",
      "JUND : 97411\n",
      "MYC : 96959\n",
      "FOXA1 : 89906\n",
      "MAX : 85949\n",
      "MAFK : 84087\n",
      "GATA2 : 73974\n",
      "STAT3 : 67977\n",
      "SPI1 : 67572\n",
      "RUNX3 : 66222\n"
     ]
    }
   ],
   "source": [
    "# sorted() function sorts entries in a dictionary by the metric you specify.\n",
    "sorted_factors = sorted(factor_dict, key=factor_dict.get, reverse=True)\n",
    "for i in range(15):\n",
    "    print(sorted_factors[i] + \" : \" + str(factor_dict[sorted_factors[i]]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Let's only take CTCF entries in chr1.\n",
    "# List comprehension comes to save the day again.\n",
    "rows_to_take = [txn_factors[0][x] == 'chr1' and txn_factors[3][x] == 'CTCF' for x in range(len(txn_factors[0]))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14627"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(txn_factors[1][np.where(rows_to_take)[0]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c48a550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# the histogram of the data\n",
    "plt.hist(txn_factors[1][np.where(rows_to_take)[0]].tolist(), 1000)\n",
    "\n",
    "plt.xlabel('Location in Chr 1')\n",
    "plt.ylabel('Frequency')\n",
    "plt.title('Distribution of CTCF element sites in Chr 1')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a big gaping hole in the middle of the chromosome. What is going on? If you have a little bit of background in biology, you may be able to guess right away.\n",
    "\n",
    "Let me give you a hint:\n",
    "\n",
    "https://en.wikipedia.org/wiki/Centromere"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}