HW3-apm382.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# <p style=\"text-align: center;\">MIS 382N: Advanced Predictive Modeling</p>\n",
    "# <p style=\"text-align: center;\">Assignment 3</p>\n",
    "## <p style=\"text-align: center;\">Total points: 80 </p>\n",
    "## <p style=\"text-align: center;\">Due: Mon, October 24, by 11:59pm</p>\n",
    "\n",
    "\n",
    "Your homework should be written in a **Jupyter notebook**. Please submit **only one** ipynb file from each group, and include the names of all the group members. Also, please make sure your code runs and the graphics (and anything else) are displayed in your notebook before submitting."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question 1 - Stochastic Gradient Descent (10pts)\n",
    "\n",
    "1. Using stochastic gradient descent, derive the coefficent updates for all 4 coefficients of the model: $$ y = w_0 + w_1*x_1 + w_2*x_1^2 + w_3*x_2 $$ Hint: start from the cost function (Assume sum of squared error). If you write the math by hand, submit that as a separate file and make a reference to it in your notebook or include the image in your notebook.\n",
    "2. Write Python code for an SGD solution to the non-linear model $$ y = w_0 + w_1*x_1 + w_2*x_1^2 + w_3*x_2$$ Try to format similarly to scikit-learn's models. There should be a _fit_ function that takes parameters X, y, learning rate, and number of iterations, and a _predict_ function that takes an X value (optionally, an array of values). Use your new gradient descent regression to predict the data given in 'samples.csv', for 10 epochs, using learning rates: [.0001, .001, .01] . Plot MSE and the $w$ parameters as a function of epoch count."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question 2: Gradient Descent (5 pts)\n",
    "\n",
    "Suppose we are trying to use gradient descent to minimize a cost function y = f(w) as shown in the figure below. This function is linearly decreasing between A and B, constant between B and C, quadratic between C and D and constant between D and E. Assume that we have 10000 data points in our training set. If we choose the starting point between B and C, will we be able to find the local minima? Explain your answer. If your answer is \"Yes\", can you give a bound on the number of iterations required to get to the local minima?\n",
    "\n",
    "<img src=\"sgd.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question 3: Multi-layer Perceptron regressor (15 points)\n",
    "\n",
    "In this question, you will explore the application of Multi-layer Perceptron (MLP) regression using sklearn package in Python. We will use the same dataset used in HW2 Q5: Hitters.csv [here](https://rdrr.io/cran/ISLR/man/Hitters.html). \n",
    "\n",
    "Following code will load and split the data into training and test set using [train_test_split](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.train_test_split.html) with **random state 42** and **test_size = 0.33**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Owner\\Anaconda2\\lib\\site-packages\\sklearn\\cross_validation.py:44: DeprecationWarning: This module was deprecated in version 0.18 in favor of the model_selection module into which all the refactored classes and functions are moved. Also note that the interface of the new CV iterators are different from that of this module. This module will be removed in 0.20.\n",
      "  \"This module will be removed in 0.20.\", DeprecationWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(263, 16)\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.model_selection import (train_test_split,KFold)\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.neural_network import MLPRegressor\n",
    "from sklearn.cross_validation import KFold\n",
    "from sklearn.cross_validation import cross_val_score\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.metrics import fbeta_score, make_scorer\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "data = pd.read_csv('C:\\\\Users\\\\Owner\\\\Desktop\\\\Python\\\\AdvPredModeling\\\\hitters.csv')\n",
    "label_name = 'Salary'\n",
    "y = data[label_name]\n",
    "X = data.drop(label_name,axis=1)\n",
    "print X.shape\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X,y,test_size = 0.33, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One more thing to use in this problem is [StandardScaler](http://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.StandardScaler.html). Instead of fitting a model on original data, use StandardScaler to make each feature centered ([Example](http://scikit-learn.org/stable/auto_examples/applications/plot_prediction_latency.html#sphx-glr-auto-examples-applications-plot-prediction-latency-py)). Whenever you have training and test data, fit a scaler on training data and use this scaler on test data. Here, scale only features (independent variables), not target variable y."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "prepare MSE scoring variable, MLP's for diff hidden layer sizes and train/test data by scaling them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#first we scale our x variables\n",
    "X_scaler = StandardScaler()\n",
    "X_train = X_scaler.fit_transform(X_train)\n",
    "X_test = X_scaler.transform(X_test)\n",
    "MLPA = MLPRegressor(activation = 'tanh', hidden_layer_sizes = (2,), solver ='sgd', learning_rate = 'constant', random_state = 42, batch_size = 40, \n",
    "                  learning_rate_init = 0.001)\n",
    "MLPB = MLPRegressor(activation = 'tanh', hidden_layer_sizes = (15,), solver ='sgd', learning_rate = 'constant', random_state = 42, batch_size = 40, \n",
    "                  learning_rate_init = 0.001)\n",
    "mse = make_scorer(mean_squared_error)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1) Use [sklearn.neural_nework.MLPRegressor](http://scikit-learn.org/stable/modules/generated/sklearn.neural_network.MLPRegressor.html#sklearn.neural_network.MLPRegressor) to do a 5-fold cross validation using sklearn's [KFold](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.KFold.html#sklearn.model_selection.KFold). The cross validation must be performed on the **training data**. Use following parameter settings for MLPRegressor:\n",
    "\n",
    "    activation = 'tanh', solver = 'sgd', learning_rate='constant', random_state=42,\n",
    "    batch_size=40, learning_rate_init = 0.001\n",
    "    \n",
    "Now, consider two different settings for the number of hidden units:\n",
    "    \n",
    "   (a) *hidden_layer_sizes = (2,)* (b) *hidden_layer_sizes = (15,)*\n",
    "    \n",
    "   Report the average Root Mean Squared Error (RMSE) value based on your 5-fold cross validation for each model: (a) and (b) (6pts)\n",
    "   \n",
    "   \n",
    "2) Now, using the same parameters used in part 1), train MLPRegressor models on whole training data and report RMSE score for both Train and Test set (Again, use StandardScaler). Which model works better, (a) or (b)? Briefly analyze the result in terms of the number of hidden units. (5pts)\n",
    "\n",
    "\n",
    "3) MLPRegressor has a built-in attribute *loss\\_curve\\_* which returns the loss at each iteration. For example, if your model is named as *my_model* you can call it as *my\\_model.loss\\_curve\\_* ([example](http://scikit-learn.org/stable/auto_examples/neural_networks/plot_mlp_training_curves.html#sphx-glr-auto-examples-neural-networks-plot-mlp-training-curves-py)). Plot two curves for model (a) and (b) in one figure, where *X-axis* is iteration number and *Y-axis* is squared root of *loss\\_curve\\_* value. (4pts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rmse A: [ 307.50792543  546.87974159  439.93924147  420.0741545   334.53974802]\n",
      "AVG RMSE A: 409.788162201\n",
      "rmse B: [ 286.84504868  416.45656003  312.06216944  299.24343233  239.73039363]\n",
      "AVG RMSE B: 310.867520821\n"
     ]
    }
   ],
   "source": [
    "#A\n",
    "score = cross_val_score(MLPA, X_train, y_train, cv = 5, scoring = mse)\n",
    "print 'rmse A:', np.sqrt(score)\n",
    "M = sum(np.sqrt(score))\n",
    "print \"AVG RMSE A:\", M/5\n",
    "\n",
    "#B\n",
    "score = cross_val_score(MLPB, X_train, y_train, cv = 5, scoring = mse)\n",
    "print 'rmse B:', np.sqrt(score)\n",
    "M = sum(np.sqrt(score))\n",
    "print \"AVG RMSE B:\", M/5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that the model with the higher hidden layer size has the MSE decrease which makes sense itnuitively as more complex models generally decrease MSE but can start to overfit at some point"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we see that for both models the RMSE goes down when the the hidden layer sizes increase, meaning that model B is better and of course the RMSE increases when going from the training to the test data.\n",
    "However, the avg RMSE from part 1 and model B was lower than the RMSE for any of the models trained on the entire dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " RMSE on training data for part A: 364.368091219\n",
      "RMSE on training data for part B: 300.095370331\n",
      "RMSE on test data for part A: 486.722986238\n",
      "RMSE on test data for part B: 412.637972754\n"
     ]
    }
   ],
   "source": [
    "#getting training RMSe\n",
    "trainmodelA = MLPA.fit(X_train, y_train)\n",
    "trainmodelB = MLPB.fit(X_train, y_train)\n",
    "pred_Ya = trainmodelA.predict(X_train)\n",
    "pred_Yb = trainmodelB.predict(X_train)\n",
    "scoreA = mean_squared_error(y_train, pred_Ya)\n",
    "scoreB = mean_squared_error(y_train, pred_Yb)\n",
    "print 'RMSE on training data for part A:', np.sqrt(scoreA)\n",
    "print 'RMSE on training data for part B:', np.sqrt(scoreB)\n",
    "\n",
    "#getting testing RMSE\n",
    "testmodelA = MLPA.fit(X_train, y_train)\n",
    "testmodelB = MLPB.fit(X_train, y_train)\n",
    "pred_Ya = trainmodelA.predict(X_test)\n",
    "pred_Yb = trainmodelB.predict(X_test)\n",
    "scoreA = mean_squared_error(y_test, pred_Ya)\n",
    "scoreB = mean_squared_error(y_test, pred_Yb)\n",
    "print 'RMSE on test data for part A:', np.sqrt(scoreA)\n",
    "print 'RMSE on test data for part B:', np.sqrt(scoreB)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgAAAAGUCAYAAABDZ5oyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAghhBBFkCQAQgghRBH0/zkX8jd76nR4AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd574208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn\n",
    "\n",
    "Acurve = np.sqrt(testmodelA.loss_curve_)\n",
    "Bcurve = np.sqrt(testmodelB.loss_curve_)\n",
    "\n",
    "plt.figure(figsize=(8,6))\n",
    "\n",
    "plt.plot(Acurve, color='blue', label = 'A: hidden layer size (2,)')\n",
    "plt.plot(Bcurve, color='teal', label = 'B: hidden layer size (12,)')\n",
    "plt.ylabel('Square Root Loss', fontsize = 14)\n",
    "plt.xlabel('Number of Iterations', fontsize = 14)\n",
    "plt.title('Loss Curves for different hidden layer sizes by iteration', fontsize = 18)\n",
    "plt.legend(loc='upper right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question 4 - Bayesian Classifiers (10 pts)\n",
    "\n",
    "Download the Smarket dataset from Canvas. This contains about four years worth of daily prices for one stock. The goal is to predict whether or not the stock price will go up or down, and the features are the stock prices of the last five days.  \n",
    "The code below loads the dataset and all necessary sklearn modules (not that you can't use more if you feel like it). Look up any module on the scikit-learn website for a full description.\n",
    "\n",
    "1. The last 50 points will be the test dataset. For training, use the 1000 points prior to these 50 test points.\n",
    "2. Train Linear Discriminant Analysis, Quadratic Discriminant Analysis, and (Gaussian) Naive Bayes. Extract the probability of the stock price going up for each row in the test set.\n",
    "3. Plot the receiver operating characteristic (ROC) curve of each model, using the extracted probabilities and the true values for the test set. (3 pts)\n",
    "4. Report the area under the ROC curve (AUC) for each model. (2 pts)\n",
    "6. Justify the performance of each model, relative to the others. (1 pts)\n",
    "7. Repeat steps 1-6, only using the prior 100 points for training. Explain the changes in model performance. (4 pts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Prep"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import roc_curve, roc_auc_score\n",
    "from sklearn.naive_bayes import GaussianNB\n",
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis as LDA\n",
    "from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis as QDA\n",
    "data = pd.read_csv('C:\\\\Users\\\\Owner\\\\Desktop\\\\Python\\\\Datasets\\\\Smarket.csv', usecols=['Lag1','Lag2','Lag3','Lag4','Lag5','Direction'])\n",
    "newdata = pd.get_dummies(data)\n",
    "df = res.drop('Direction_Down', 1)\n",
    "train = df.ix[199:1199]\n",
    "test = df.ix[1200:]\n",
    "train_X = train[[0,1,2,3,4]] \n",
    "train_X = train_X.values\n",
    "train_y = train[[5]]\n",
    "train_y = train_y.values\n",
    "test_X = test[[0,1,2,3,4]]\n",
    "test_X = test_X.values\n",
    "test_y = test[[5]]\n",
    "test_y = test_y.values\n",
    "NB = GaussianNB()\n",
    "LD = LDA(solver='lsqr',shrinkage = 'auto')\n",
    "QD = QDA()\n",
    "Roc = roc_curve\n",
    "Roc_score = roc_auc_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we created a function to return the extracted probabilites for each type of model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 327,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def BayesianClassifier(modeltype, train_X, train_y, test_X):\n",
    "    \n",
    "    '''takes bayesian models of Linear/Quadratic Discriminant Analysis, Gaussian Naiive Bayes\n",
    "    and return an array of predicted probabilities as an array\n",
    "    \n",
    "        Note: data must be in an array   '''\n",
    "    \n",
    "    fitted_model = modeltype.fit(train_X, train_y)\n",
    "    predicted_y = modeltype.predict(test_X)\n",
    "    predicted_probabilities = modeltype.predict_proba(test_X)\n",
    "    return predicted_probabilities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "predictedprobsQD = BayesianClassifier(QD, train_X, train_y, test_X)\n",
    "predictedprobsNB = BayesianClassifier(NB, train_X, train_y, test_X)\n",
    "predictedprobsLD = BayesianClassifier(LD, train_X, train_y, test_X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "define function to return Roc parameters and AUC score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 300,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def RocCurve(predprobs, actual_y):\n",
    "    '''predicted probabilities should be in form of an array\n",
    "    \n",
    "    function returns the fpr, tpr, threshold and the AUC of the ROC Curve as the score1'''\n",
    "    \n",
    "    pos_probs = []\n",
    "    for i in predprobs:\n",
    "        pos_probs.append(i[1])\n",
    "    fpr, tpr, threshold = roc_curve(actual_y, pos_probs)\n",
    "    score = roc_auc_score(actual_y, pos_probs, average = 'weighted')\n",
    "    return fpr, tpr, threshold, score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Call function to get returned values as useable values for graphing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 301,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "QDfpr = RocCurve(predictedprobsQD, test_y)[0]\n",
    "QDtpr = RocCurve(predictedprobsQD, test_y)[1]\n",
    "QDthresh = RocCurve(predictedprobsQD, test_y)[2]\n",
    "QDAUCscore = RocCurve(predictedprobsQD, test_y)[3]\n",
    "NBfpr = RocCurve(predictedprobsNB, test_y)[0]\n",
    "NBtpr = RocCurve(predictedprobsNB, test_y)[1]\n",
    "NBthresh = RocCurve(predictedprobsNB, test_y)[2]\n",
    "NBAUCscore = RocCurve(predictedprobsNB, test_y)[3]\n",
    "LDfpr = RocCurve(predictedprobsLD, test_y)[0]\n",
    "LDtpr = RocCurve(predictedprobsLD, test_y)[1]\n",
    "LDthresh = RocCurve(predictedprobsLD, test_y)[2]\n",
    "LDAUCscore = RocCurve(predictedprobsLD, test_y)[3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now simply graph the different classifiers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 322,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAf4AAAF5CAYAAAB+2khFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nDJ9SlF4IzZEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xec739b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "lw = 2\n",
    "plt.plot(QDfpr, QDtpr, color='darkorange',\n",
    "         lw=lw, label='Quadratic Discriminant Analysis (AUC score = %0.2f)' % QDAUCscore)\n",
    "plt.plot(NBfpr, NBtpr, color='blue',\n",
    "         lw=lw, label='Gaussian Naiive Bayes (AUC score = %0.2f)' % NBAUCscore)\n",
    "plt.plot(LDfpr, LDtpr, color='teal',\n",
    "         lw=lw, linestyle = ':', label='Linear Discriminant Analysis (AUC score = %0.2f)' % LDAUCscore)\n",
    "\n",
    "plt.plot([0, 1], [0, 1], color='black', lw=lw, linestyle='--')\n",
    "plt.xlim([0.0, 1.0])\n",
    "plt.ylim([0.0, 1.05])\n",
    "plt.xlabel('False Positive Rate (1-Specificity)', fontsize=15)\n",
    "plt.ylabel('True Positive Rate (Sensitivity)', fontsize = 15)\n",
    "plt.title('Receiver operating characteristic', fontsize = 20)\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that Quadratic Discriminant Analysis model did the best with the highest AUC score and you see visually that the curve is the closest to the upper left corner. That corner is ideal because there you have the highest sensitivity (correct predictions) and the least false predictions (1-Specificity) or the false positive rate\n",
    "\n",
    "NB and LDA only did marginally better than 0.5 which is not good, as this indicates you could do almost as well by random chance of flipping a coin and guessing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## part 6\n",
    "### now we'll run the same things as before, except now we use only 100 training data points rather than 1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 330,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "newtrain = train.ix[1099:]\n",
    "train_X100 = newtrain[[0,1,2,3,4]] \n",
    "train_X100 = train_X100.values\n",
    "train_y100 = newtrain[[5]]\n",
    "train_y100 = train_y100.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 332,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "predictedprobsQD = BayesianClassifier(QD, train_X100, train_y100, test_X)\n",
    "predictedprobsNB = BayesianClassifier(NB, train_X100, train_y100, test_X)\n",
    "predictedprobsLD = BayesianClassifier(LD, train_X100, train_y100, test_X)\n",
    "\n",
    "QDfpr = RocCurve(predictedprobsQD, test_y)[0]\n",
    "QDtpr = RocCurve(predictedprobsQD, test_y)[1]\n",
    "QDthresh = RocCurve(predictedprobsQD, test_y)[2]\n",
    "QDAUCscore = RocCurve(predictedprobsQD, test_y)[3]\n",
    "NBfpr = RocCurve(predictedprobsNB, test_y)[0]\n",
    "NBtpr = RocCurve(predictedprobsNB, test_y)[1]\n",
    "NBthresh = RocCurve(predictedprobsNB, test_y)[2]\n",
    "NBAUCscore = RocCurve(predictedprobsNB, test_y)[3]\n",
    "LDfpr = RocCurve(predictedprobsLD, test_y)[0]\n",
    "LDtpr = RocCurve(predictedprobsLD, test_y)[1]\n",
    "LDthresh = RocCurve(predictedprobsLD, test_y)[2]\n",
    "LDAUCscore = RocCurve(predictedprobsLD, test_y)[3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 333,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAf4AAAF5CAYAAAB+2khFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\neUQEfkEQBEGYR/4DSkbYZ04kiJUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xdb28f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "lw = 2\n",
    "plt.plot(QDfpr, QDtpr, color='darkorange',\n",
    "         lw=lw, label='Quadratic Discriminant Analysis (AUC score = %0.2f)' % QDAUCscore)\n",
    "plt.plot(NBfpr, NBtpr, color='blue',\n",
    "         lw=lw, label='Gaussian Naiive Bayes (AUC score = %0.2f)' % NBAUCscore)\n",
    "plt.plot(LDfpr, LDtpr, color='teal',\n",
    "         lw=lw, linestyle = ':', label='Linear Discriminant Analysis (AUC score = %0.2f)' % LDAUCscore)\n",
    "\n",
    "plt.plot([0, 1], [0, 1], color='black', lw=lw, linestyle='--')\n",
    "plt.xlim([0.0, 1.0])\n",
    "plt.ylim([0.0, 1.05])\n",
    "plt.xlabel('False Positive Rate (1-Specificity)', fontsize=15)\n",
    "plt.ylabel('True Positive Rate (Sensitivity)', fontsize = 15)\n",
    "plt.title('Receiver operating characteristic', fontsize = 20)\n",
    "plt.legend(loc=\"lower right\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that when we only have the last 100 data points none of our models do better than random chance (.5), and LDA even did worse at .42 than just not having a model at all"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Question 5 - Logistic Regression (15pts)\n",
    "\n",
    "In this question we will be predicting mile per gallon (mpg) for Auto data set. ('Auto.csv' in Canvas)\n",
    "1. Convert mpg to a binary variable mpg01 which is 1 if had an mpg is greater than median mpg and zero otherwise\n",
    "2. Split the data into training and test. Use 42 as random seed and use 1/3rd of the data for testing. Our y variable is mpg01 and X matrix includes all the other variables except mpg01.\n",
    "3. Train a logistic regression with almost no regularization (pass l2 (ridge) to penalty and 1,000,000 to the C parameter which is the inverse of regularization strength lambda. This essentially does l2 regularization but applies very little weight to the penalty term) and report the [confusion matrix](http://scikit-learn.org/stable/modules/generated/sklearn.metrics.confusion_matrix.html) on the test data. Also report the accuracy for the \"mpg01 = 0\" class, the \"mpg01 = 1\" class, and the average per-class accuracy on the test data. Average per-class accuracy is described in this [post](http://rasbt.github.io/mlxtend/user_guide/evaluate/scoring/). You can use your confusion matrix to calculate this.\n",
    "4. Repeat step 3 except use l2 penalty with Cs of [0.001,0.01, 0.1, 1, 10 ,100, 1000]. You will want to use k-fold cross validation to select the best parameter. To evaluate which parameter is best, maximize the average per-class accuracy. To help with this task, check out [GridSearchCV](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.GridSearchCV.html#sklearn.model_selection.GridSearchCV) and how to make your own [custom scorer](http://scikit-learn.org/stable/modules/model_evaluation.html).\n",
    "5. Repeat question 4 except use l1 instead of l2 as the penalty type, use Cs of  [0.001, 0.01, ..., 1000]\n",
    "6. Which model produces the best average per-class accuracy? Why do you think this is the case? How do the models handle the different classes, and why is this so?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Following code will load and clean the dataset and load some useful functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n",
      "(392, 8)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mpg</th>\n",
       "      <th>cylinders</th>\n",
       "      <th>displacement</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>weight</th>\n",
       "      <th>acceleration</th>\n",
       "      <th>year</th>\n",
       "      <th>origin</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>18.0</td>\n",
       "      <td>8</td>\n",
       "      <td>307.0</td>\n",
       "      <td>130.0</td>\n",
       "      <td>3504</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>15.0</td>\n",
       "      <td>8</td>\n",
       "      <td>350.0</td>\n",
       "      <td>165.0</td>\n",
       "      <td>3693</td>\n",
       "      <td>11.5</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>18.0</td>\n",
       "      <td>8</td>\n",
       "      <td>318.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>3436</td>\n",
       "      <td>11.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>16.0</td>\n",
       "      <td>8</td>\n",
       "      <td>304.0</td>\n",
       "      <td>150.0</td>\n",
       "      <td>3433</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>17.0</td>\n",
       "      <td>8</td>\n",
       "      <td>302.0</td>\n",
       "      <td>140.0</td>\n",
       "      <td>3449</td>\n",
       "      <td>10.5</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mpg  cylinders  displacement  horsepower  weight  acceleration  year  \\\n",
       "0  18.0          8         307.0       130.0    3504          12.0    70   \n",
       "1  15.0          8         350.0       165.0    3693          11.5    70   \n",
       "2  18.0          8         318.0       150.0    3436          11.0    70   \n",
       "3  16.0          8         304.0       150.0    3433          12.0    70   \n",
       "4  17.0          8         302.0       140.0    3449          10.5    70   \n",
       "\n",
       "   origin  \n",
       "0       1  \n",
       "1       1  \n",
       "2       1  \n",
       "3       1  \n",
       "4       1  "
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "from pandas_ml import ConfusionMatrix\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn\n",
    "from sklearn import model_selection\n",
    "from sklearn.linear_model import LogisticRegression, LogisticRegressionCV\n",
    "from sklearn.metrics import mean_squared_error, confusion_matrix\n",
    "from sklearn.grid_search import GridSearchCV\n",
    "from sklearn.model_selection import (train_test_split,KFold)\n",
    "%pylab inline\n",
    "\n",
    "Auto = pd.read_csv('C:\\\\Users\\\\Owner\\\\Desktop\\\\Python\\\\Datasets\\\\Auto.csv', na_values='?').drop('name',axis = 1).dropna()\n",
    "print Auto.shape\n",
    "Auto.head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here I'm just creating the new mpg01 column"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "Autonew = Auto\n",
    "median = Autonew['mpg'].median()\n",
    "mask = Autonew['mpg']  > median\n",
    "mpg01 = []\n",
    "for i in mask:\n",
    "    if i == False:\n",
    "        mpg01.append(0)\n",
    "    else:\n",
    "        mpg01.append(1)\n",
    "mpg01 = pd.Series(mpg01)\n",
    "Autonew['mpg01'] = mpg01.values\n",
    "Autonew = Autonew.drop('mpg', 1) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "now we'll split the data into training and test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "label_name = 'mpg01'\n",
    "y = Autonew[label_name]\n",
    "X = Autonew.drop(label_name,axis=1)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X,y,test_size = 0.33, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "X_train = X_train.values\n",
    "X_test = X_test.values\n",
    "y_train = y_train.values\n",
    "y_test = y_test.values\n",
    "\n",
    "LOGIT = LogisticRegression(penalty = 'l2', C = 1000000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: for this type of confusion matrix you need a little setup\n",
    "\n",
    "-first install the module by running -pip install pandas_ml\n",
    "\n",
    "for more info about what's included see: https://github.com/pandas-ml/pandas-ml/\n",
    "\n",
    "Also note that mpg01 = 1 class represents high mileage (above median) \n",
    "and mpg01 = 0  is the low mileage class (below median)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted   0   1  __all__\n",
      "Actual                    \n",
      "0          55  15       70\n",
      "1           2  58       60\n",
      "__all__    57  73      130\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAf0AAAHWCAYAAAB9p1B9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n+pIkdYShL0lSRxj6kiR1hKEvSVJH/H8mbCgJE9+GngAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xdc31630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "population: 130\n",
      "P: 60\n",
      "N: 70\n",
      "PositiveTest: 73\n",
      "NegativeTest: 57\n",
      "TP: 58\n",
      "TN: 55\n",
      "FP: 15\n",
      "FN: 2\n",
      "TPR: 0.966666666667\n",
      "TNR: 0.785714285714\n",
      "PPV: 0.794520547945\n",
      "NPV: 0.964912280702\n",
      "FPR: 0.214285714286\n",
      "FDR: 0.205479452055\n",
      "FNR: 0.0333333333333\n",
      "ACC: 0.869230769231\n",
      "F1_score: 0.872180451128\n",
      "MCC: 0.755898667076\n",
      "informedness: 0.752380952381\n",
      "markedness: 0.759432828647\n",
      "prevalence: 0.461538461538\n",
      "LRP: 4.51111111111\n",
      "LRN: 0.0424242424242\n",
      "DOR: 106.333333333\n",
      "FOR: 0.0350877192982\n"
     ]
    }
   ],
   "source": [
    "def LogReg(modelwparams, X_train, X_test, y_train, y_test):\n",
    "    \n",
    "    '''You need to pass this function the LogReg model with the parameters you choose,\n",
    "    as well as all your data (train/test X's and Y)\n",
    "    \n",
    "    make sure your X and y's are arrays'''\n",
    "    \n",
    "    LOG = modelwparams\n",
    "    logit_fit_model = LOG.fit(X_train, y_train)\n",
    "    pred_y = logit_fit_model.predict(X_test)\n",
    "    \n",
    "    cm = ConfusionMatrix(y_test, pred_y)\n",
    "    print cm\n",
    "    cm.plot()\n",
    "    plt.show()\n",
    "    cm.print_stats()\n",
    "\n",
    "LogReg(LOGIT, X_train, X_test, y_train, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "TPR = True Positive Rate\n",
    "\n",
    "TNR = True Negative Rate\n",
    "\n",
    "ACC = Average per class Accuracy\n",
    "\n",
    "so we see from the stats that the accuracy for\n",
    "\n",
    "mpg01 = 0 class --> 78.57%\n",
    "\n",
    "mpg-1 = 1 class --> 96.67%\n",
    "\n",
    "avg per class acuuracy --> 86.92%"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted   0   1  __all__\n",
      "Actual                    \n",
      "0          54  16       70\n",
      "1           0  60       60\n",
      "__all__    54  76      130\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAf0AAAHbCAYAAADBOUOjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nUkcY+pIkdYShL0lSR/x/832HR3HqLQEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe241550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "population: 130\n",
      "P: 60\n",
      "N: 70\n",
      "PositiveTest: 76\n",
      "NegativeTest: 54\n",
      "TP: 60\n",
      "TN: 54\n",
      "FP: 16\n",
      "FN: 0\n",
      "TPR: 1.0\n",
      "TNR: 0.771428571429\n",
      "PPV: 0.789473684211\n",
      "NPV: 1.0\n",
      "FPR: 0.228571428571\n",
      "FDR: 0.210526315789\n",
      "FNR: 0.0\n",
      "ACC: 0.876923076923\n",
      "F1_score: 0.882352941176\n",
      "MCC: 0.780398972572\n",
      "informedness: 0.771428571429\n",
      "markedness: 0.789473684211\n",
      "prevalence: 0.461538461538\n",
      "LRP: 4.375\n",
      "LRN: 0.0\n",
      "DOR: inf\n",
      "FOR: 0.0\n"
     ]
    }
   ],
   "source": [
    "Cs = [0.001,0.01, 0.1, 1, 10 ,100, 1000]\n",
    "LOGITCV = LogisticRegressionCV(Cs = Cs, cv = 5)\n",
    "LogReg(LOGITCV, X_train, X_test, y_train, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "TPR = True Positive Rate\n",
    "\n",
    "TNR = True Negative Rate\n",
    "\n",
    "ACC = Average per class Accuracy\n",
    "\n",
    "so we see from the stats that the accuracy for\n",
    "\n",
    "mpg01 = 0 class --> 77.14%\n",
    "\n",
    "mpg-1 = 1 class --> 100%\n",
    "\n",
    "avg per class accuracy --> 87.69%\n",
    "\n",
    "We see that the avg per class slightly improved from part 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted   0   1  __all__\n",
      "Actual                    \n",
      "0          56  14       70\n",
      "1           1  59       60\n",
      "__all__    57  73      130\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAf0AAAHWCAYAAAB9p1B9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n7CugAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xdc316a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "population: 130\n",
      "P: 60\n",
      "N: 70\n",
      "PositiveTest: 73\n",
      "NegativeTest: 57\n",
      "TP: 59\n",
      "TN: 56\n",
      "FP: 14\n",
      "FN: 1\n",
      "TPR: 0.983333333333\n",
      "TNR: 0.8\n",
      "PPV: 0.808219178082\n",
      "NPV: 0.982456140351\n",
      "FPR: 0.2\n",
      "FDR: 0.191780821918\n",
      "FNR: 0.0166666666667\n",
      "ACC: 0.884615384615\n",
      "F1_score: 0.887218045113\n",
      "MCC: 0.786995764139\n",
      "informedness: 0.783333333333\n",
      "markedness: 0.790675318433\n",
      "prevalence: 0.461538461538\n",
      "LRP: 4.91666666667\n",
      "LRN: 0.0208333333333\n",
      "DOR: 236.0\n",
      "FOR: 0.0175438596491\n",
      "Predicted   0   1  __all__\n",
      "Actual                    \n",
      "0          56  14       70\n",
      "1           0  60       60\n",
      "__all__    56  74      130\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAf0AAAHbCAYAAADBOUOjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAHkNJREFUeJzt3Xm4ZHV95/F3dTdrQwRkecQFdJQvqAi0OIS2oQFFBKEj\nLsEgu4AoKIyBGdAQ0UFlEkXhQSACQRDDICpqJ0ZA2SGasBhZzBeIijOQIDItW7M1XfPHOVcv9+nu\nur+m69Y5fd6v56mH2s6vfvde4FOf3zl1qtfv95EkSSu/aaOegCRJmhqGviRJHWHoS5LUEYa+JEkd\nYehLktQRhr4kSR0xY9QTkCRJg0XE8cA8YBXgTOA64KvAYuCOzDxy0Bg2fUmSGi4i5gLbZ+ZsYCfg\nFcCpwMczcy4wLSL+ZNA4hr4kSc23G3BHRHwH+B7w98CszLy+fvwfgbcOGsTlfUmSmm99qna/J/Aq\nquAfX9wfA140aBBDX5KkAr1ebyjnr+/3+71lPPww8PPMXATcHRFPAS8b9/jawO8GvYbL+5IkNd8N\nwNsBImJjYCbwo3pfP8DuwPVL2fb3en7hjiRJkzeipk9EnALsAvSAE4BfAedSHc3/c+CwzFzm3Ax9\nSZIKTJs2bSjBuXjx4mWG/orgPn1Jkgr0ekPP5qFxn74kSR1h05ckqYBNX5IkNZ5NX5KkAjZ9SZLU\neDZ9tU5EbAL8O/Azqs+rTgeeAP48M2+KiDcC/yMz/3SE03xBImIr4FtUZ9h6V2b+unD7TwH3ZOZF\nw5hfqYjYA9guMz+5hMf2At6SmcdM/cykcm1u+oa+2mphZs4auxER76X6isnNMvMWoLWBX5sHXJWZ\nhy/PxksK1xF7E7Dukh7IzPnA/KmdjrT8DH1p9NYHHoDffwXlGZm5ZUScDzwKbAm8HPg3YJ/MXBgR\nhwCHU53Naj3glMz8m4g4EPgAsCbwCPAccGlmnlOP/3HgxZn55+MnEBHbAafV2z0DHJeZV0fEDsBf\nAWvU95+YmZfXr7M31XdhvwZ4GjgQ2Ar4MNVXZa4B/BB4T2buVb/OgWO3I2IO8AWqXXV94HOZeVn9\nc9+emacWvv4BmXnXhJ/rQODd9fabAr8GvgwcVW/3xfp11gTOqu9bj+oLQPalCvsj6p/nEeDe+vc7\nk2ol40LgPcB7gZvrv93Z9d/naKoVgqeW/qeXNFnu01dbrRkRt0bEbRHxK+CLwOfGPT7+jFmzgLcB\nWwAbA++NiJlUwbN7Zr4ReB/w1+O2eS0wNzPfQhVwhwJERK++ftb4yUTEDOAy4KTMfAPVm4kvRcR6\nwKXARzJza+Ag4KJ6FwXAjsCRmbklcBNwbGb+HXA2cElm7r+En2f87ZOAL2Tmm+qfZ5cJ8yp9/eNY\nsjnAgZn5GmAjqjdOuwDvAE6un7M7sCAzZ2fm5lQBflRm/vO4n+fEcb/fHevfL0C/Dvb3AZ+OiN3r\ncd9t4Ktper3eUC5TwdBXWy3MzFmZuU1mbgrsDFwyLszG+0FmLqq/nep2YL3MfALYC9gzIj4NfIKq\neY75Wf0cqJaeN4qILam+0/oXmXnvhNfYEliUmT8AyMxbM3MrYDuqfes31/ffRfXFGTvV292Smf9R\nX7+VqiGX+Abw5Yi4CHgj8PEJj6+o1/+XzHygvv5L4Ir6+r8Dq0XEmpn5LeCCiDgqIr5Uv8ZaSxlv\n/O/39zLzDuDTVN8VfuwSfs+SXgBDXyuFzPwnIIH/uoSHnxx3vQ/0IuKlwE+pvp/6euAvJmzz+Lix\nF1M11Q8Ah9TXJ1rEhDYeEa+j+m9s4lv46VS7FJY4tyWMPfH+VcfN7StUbziuoHpDcntErD3uuSvi\n9aFa+h/v2YlPiIgPAedRHVT5deDiZYz3+FLuB3g98J/A9st4jjQyNn1p6j3vv5CI2IxqX/Jtk9x+\nW+A3mfmZzLySqvWPLd8vyXlU+79nUS3jT5RAPyLeUo8zC/gR8BNgs4jYtr7/dcAOwDWTnCfAQ8Dr\nI2LVejfCXmMPRMSNwKzMvBD4IPAinn/A3I9XwOsPMvY7extwfmaeD9xTz3N6/dgi/vBGY6ki4l3A\nXOANwG4RMW8FzlPqPENfbbV6vU//1oi4jWqZ+7BJLAePtfHLgfsjIiPiFuBlVOH66iVtlJkPUe2j\nvjgzn1vC488A7wJOqudzJrB3Zv6W6gC1MyLiZ8BFwEGFy9ZXANdSvbG4luqjimP+O9U+8Fuo3mSc\nNP7jfZn58Ap4/YmWdnzB54EjIuJW4ErgFv7w+/wRMC8iTlvaoBHxMqrf2/71vA8EvlJ/d7jUGG1u\n+n61rjQJEbE+VWvfMTPvH/V8JI3OzJkzhxKcTzzxxNCT36YvDRARhwJ3AqcZ+JLazKYvSVKBtdZa\nayjB+fjjj9v0JUnSiuEZ+SRJKuBpeFeQdddd130NDXLTTTcxe/bsUU9D48yf7ynqm2Sbbbbhttsm\n+ylRTZU5c+a0N5WHrFGhr2bZYostRj0FqdFmzpw5+Ela6dj0JUnqiDaHvgfySZLUETZ9SZIK2PQl\nSVLj2fQlSSpg05ckSY1n05ckqUCbm76hL0lSgTaHvsv7kiR1hE1fkqQCNn1JktR4Nn1Jkgq0uekb\n+pIkFWhz6Lu8L0lSR9j0JUkqYNOXJEmNZ9OXJKnAqJp+RNwCPFLf/GVmfqC+f1/gqMycPWgMQ1+S\npIaLiNUAMnOXCfdvAxwy2XEMfUmSCoyo6W8FzIyIy4HpwCeAe4CTgaOBcyYziKEvSVKBEYX+QuCv\nM/O8iHgNcDlwJ/Ax4GlgUpPyQD5JkprvbuDrAJl5D7AJsDlwFnAxsEVEnDpoEENfkqQCvV5vKJcB\nDgG+ABARGwMJbFbv438fcFdmfmzQIC7vS5LUfOcB50fE9cBi4JDM7JcOYuhLklRgFPv0M/NZYL+l\nPHYfMPDjeuDyviRJnWHTlySpQJtPw2voS5JUoM2h7/K+JEkdYdOXJKmATV+SJDWeTV+SpAI2fUmS\n1Hg2fUmSCrS56Rv6kiQVaHPou7wvSVJH2PQlSSpg05ckSY1n05ckqYBNX5IkNZ5NX5KkAm1u+oa+\nJEkF2hz6Lu9LktQRNn1JkgrY9CVJUuPZ9CVJKmDTlyRJjWfTlySpQJubvqEvSVKBNoe+y/uSJHWE\nTV+SpAI2fUmS1Hg2fUmSCtj0JUlS49n0JUkq0Oamb+hLklSgzaHv8r4kSR1h05ckqYBNX5IkNZ5N\nX5KkAjZ9SZLUeDZ9SZIKjLLpR8SGwM3AW4E1gLOBZ4G7M/PQQdvb9CVJKtDr9YZyGSQiZlCF/ML6\nrk8CJ2XmjsDqEfGOQWMY+pIktcPngbOAB+rbtwLrR0QPWJuq8S+ToS9JUoFRNP2IOAj4TWZeCfTq\ny73A6cCdwIbANYPmbuhLktR8BwO7RsTVwFbAhcAFwJsz87XA14BTBw3igXySJBUYxYF8mTl37HpE\nXAUcAXwHeKy++wFg9qBxDH1JktrpUOCSiHgWeAY4bNAGhr4kSQVGfXKezNylvno3MKdkW0NfkqQC\now79F8ID+SRJ6gibviRJBWz6kiSp8Wz6kiQVsOlLkqTGs+lLklSgzU3f0JckqUCbQ9/lfUmSOsKm\nL0lSAZu+JElqPJu+JEkFbPqSJKnxbPqSJBVoc9M39CVJKtDm0Hd5X5KkjrDpS5JUwKYvSZIaz6Yv\nSVKBNjd9Q1+SpAJtDn2X9yVJ6gibviRJBWz6kiSp8Wz6kiQVsOlLkqTGs+lLklSgzU1/qKEfET3g\nTGAr4Cng0Mz8xTBfU5KkYWpz6A97ef+dwGqZORs4ATh1yK8nSZKWYtihPwf4AUBm/gTYdsivJ0nS\nUPV6vaFcpsKwQ/+PgEfG3V4UER48KEnSCAz7QL5HgbXH3Z6WmYuX9uSbbrqJLbbYYshTUokFCxaM\negpSo82ZM2fUU9A4N9xww9Bfo8379Icd+jcCewLfjIg/Bm5f1pNnz5495OmoxIIFC1h33XVHPQ2N\nM3/+/FFPQePMmTNnSkJGWlGGHfqXAbtGxI317YOH/HqSJA2VTX8pMrMPfGiYryFJ0lRqc+h7UJ0k\nSR3hGfkkSSpg05ckSY1n05ckqcAom35EbAjcDLwVWBM4HVgEPA0ckJkPLWt7m74kSS0QETOAs4GF\nQA/4EnBkZu5C9Wm54weNYehLklRghKfh/TxwFvAA0Af2ycyx89/MAJ4cNIChL0lSgVGEfkQcBPwm\nM6+kavlk5oP1Y7OBI4EvDpq7+/QlSWq+g4HFEbErsDVwYUTMA3am+hbbPTLz4UGDGPqSJBUYxYF8\nmTl37HpEXA18EHgbcDiwU2b+bjLjuLwvSVK79KlK+2nAWsBlEXFVRHxy0IY2fUmSCoz65Dz10foA\nLy7d1qYvSVJH2PQlSSow6qb/Qhj6kiQVaHPou7wvSVJH2PQlSSpg05ckSY1n05ckqYBNX5IkNZ5N\nX5KkAm1u+oa+JEkF2hz6Lu9LktQRNn1JkgrY9CVJUuPZ9CVJKmDTlyRJjWfTlySpQJubvqEvSVKB\nNoe+y/uSJHWETV+SpAI2fUmS1Hg2fUmSCtj0JUlS49n0JUkq0Oamb+hLklSgzaHv8r4kSR1h05ck\nqYBNX5IkNZ5NX5KkAjZ9SZLUeDZ9SZIKtLnpG/qSJBVoc+i7vC9JUkfY9CVJKmDTlyRJjWfTlySp\ngE1fkiQ1nk1fkqQCbW76hr4kSQVGEfoRMQ04BwhgMXAE8FB93zrAdOCAzPzlssZxeV+SpObbC+hn\n5hzgROCzwF8BF2XmTvV9mw8axNCXJKlAr9cbymVZMvO7wOH1zU2ABcBs4OURcSWwL3DNoLkb+pIk\ntUBmLo6IrwKnA38HvBJ4ODN3Bf4PcPygMQx9SZIKjKLpj8nMg4DNgHOp2v78+qH5wBsHbW/oS5JU\nYBShHxH7RcRYk38KeA64DnhHfd+OwJ2D5u7R+5IkNd+3gfMj4lqq7P4o8K/AeRFxBPAI1X79ZTL0\nJUkqMIqP7GXmQmCfJTz0tpJxXN6XJKkjbPqSJBVo8xn5bPqSJHWETV+SpAJtbvqGviRJBdoc+i7v\nS5LUETZ9SZIK2PQlSVLj2fQlSSpg05ckSY1n05ckqUCbm76hL0lSgTaHvsv7kiR1hE1fkqQCNn1J\nktR4Nn1JkgrY9CVJUuPZ9CVJKtDmpm/oS5JUoM2h7/K+JEkdYdOXJKmATV+SJDWeTV+SpAI2fUmS\n1Hg2fUmSCrS56Rv6kiQVaHPou7wvSVJHLLXpR8RioF/fnPi2pp+Z04c2K0mSGqrNTX+poZ+ZrgJI\nkrQSGbhPPyI2BN4PrEXV+KcDr8zMA4Y8N0mSGqfNTX8ybf7bwNbAfsBMYB6weJiTkiRJK95kQn/9\nzDwQmE/1BmAn4HXDnJQkSU3V6/WGcpkKkwn9BfU/E9gqMx8BVhnelCRJaq42h/5kPqd/VURcChwL\nXBERs4CnhjstSZK0og1s+pn5CeD4zLwP+DOqxr/3sCcmSVITrdRNPyIOqP/55vquh4FdgQuHOC9J\nkrSCTWZ5f+dx11cBdgCuw9CXJHXQKD6yFxHTgHOAoPoE3RHA08BX69t3ZOaRg8YZGPqZefCEF14P\nuKR8ypIkaTntRXU23DkRMRf4LNW5cz6emddHxFkR8SeZ+d1lDbI8Z917HNh0ObaTJKn1RrFPvw7z\nw+ubm1B9sm5WZl5f3/ePwFsHzX0y+/Sv5vnn4H8V8P1B20mStDIa1Rn5MnNxRHwVeCfwXqrj68Y8\nBrxo0BiT2ad/0rjrfeC3mXnX5Kc5eQsWLBj8JE0p/ybN0ubTf66M+v0+O+yww6inoQn6/f7gJ7VU\nZh5Unx7/X4A1xj20NvC7QdtPJvTfk5kfGX9HRFxQn6VPkqROGdGBfPsBL8vMU6jOlfMccHNEzM3M\na4HdgasGjbOsr9Y9l2opf9uIGH/a3VWYxBKCJElaYb4NnB8R11Jl90eBfwPOjYhVgJ8D3xw0yLKa\n/slUB+ydRrXEP/bWZlE9uCRJnTOKpp+ZC4F9lvDQTiXjLPXo/cz8VWZeA8wBtqyXD+4FdsPT8EqS\n1DqT+cje14GX1Ncfq7f52tBmJElSg63Up+EFNsnMeQCZ+SjwFxHx0+FOS5KkZmrzp2gm0/T7EbHl\n2I2I2Bx4dnhTkiRJwzCZpn8scGVE/N/69gbAfsObkiRJzbVSN/3M/CHwCuBDwPeAB6hO9ydJklpk\nMqfhfSXwQeBgYB3gM8C8Ic9LkqRGanPTX9bJefam+uq+WcBlVEv652Tmp6dobpIkaQVaVtP/FnAp\nsH1m3gsQEYunZFaSJDXUStn0gTcABwE3RMSvgIsHPF+SpJVem0N/WWfkuyMzjwVeCnyO6lR/G0XE\nP0TEHlM0P0mStIIMbO6Z+RzwXeC7EbEBsD/Vm4DvD3lukiQ1TpubftFyfWY+BJxaXyRJUou4j16S\npAJtbvqTOQ2vJElaCdj0JUkq0Oamb+hLklSgzaHv8r4kSR1h05ckqYBNX5IkNZ5NX5KkAm1u+oa+\nJEkF2hz6Lu9LktQRNn1JkgrY9CVJUuPZ9CVJKmDTlyRJjWfTlySpQJubvqEvSVKBNoe+y/uSJHWE\nTV+SpAI2fUmS1Hg2fUmSCtj0JUlS49n0JUkq0Oamb+hLklSgzaHv8r4kSR1h05ckqcAomn5EzAD+\nFtgUWBX4TGbOrx/bFzgqM2cPGsemL0lS8+0H/DYzdwR2B84AiIhtgEMmO4hNX5KkAiPap/8N4NL6\n+jTg2YhYDzgZOBo4ZzKDGPqSJDVcZi4EiIi1qcL/ROA84GPA08Ck3om4vC9JUoFerzeUyyAR8XLg\nKuAC4F7g1cBZwMXAFhFx6qAxbPqSJBUY0YF8GwGXA0dm5tX13VvWj20CXJyZHxs0jqEvSVLznQCs\nA5wYEX8J9IHdM/PpkkEMfUmSCoyi6WfmMcAxS3nsPmDgx/XAffqSJHWGTV+SpAKehleSJDWeTV+S\npAJtbvqGviRJBdoc+i7vS5LUETZ9SZIK2PQlSVLj2fQlSSpg05ckSY1n05ckqUCbm76hL0lSgTaH\nvsv7kiR1hE1fkqQCNn1JktR4Nn1JkgrY9CVJUuPZ9CVJKtDmpm/oS5JUoM2h7/K+JEkdYdOXJKmA\nTV+SJDWeTV+SpAI2fUmS1Hg2fUmSCrS56Rv6kiQVaHPou7wvSVJH2PQlSSpg05ckSY1n05ckqYBN\nX5IkNZ5NX5KkAm1u+oa+JEkF2hz6Lu9LktQRNn1JkgrY9CVJUuPZ9CVJKtDmpm/oS5LUEhGxHXBK\nZu4cEVsDZwHPAndn5qGDtnd5X5KkAr1ebyiXQSLiOOAcYLX6rr8ETsrMHYHVI+Idg8Yw9CVJKjCq\n0AfuBfYed/s2YP2I6AFrUzX+ZTL0JUlqgcy8DFg07q57gNOBO4ENgWsGjWHoS5JUYIRNf6LTgDdn\n5muBrwGnDtrA0JckqZ0eBh6rrz8ArDNoA4/elySpQIM+sncYcElEPAs8U99eJkNfkqQCowz9zLwP\nmF1fvxGYU7K9y/uSJHWETV+SpAINWt4vZtOXJKkjhh76EbFdRFw97NeRJGkqNOgje8WGurxfnzJw\nf+DxYb6OJEkabNhNf+IpAyVJarU2N/2hhv4SThkoSVKrtTn0PXpfapF+vz/qKWgC/ybN0uYj66fC\nVIW+fwVpBfB/aM3S7/f9m3RQm//mU/WRPd8KS5I0YkNv+uNPGShJUtvZ9CVJUuN5IJ8kSQXa3PQN\nfUmSCrQ59F3elySpI2z6kiQVsOlLkqTGs+lLklTApi9JkhrPpi9JUoE2N31DX5KkAm0OfZf3JUnq\nCJu+JEkFbPqSJKnxbPqSJBWw6UuSpMaz6UuSVKDNTd/QlySpQJtD3+V9SZI6wqYvSVIBm74kSWo8\nm74kSQVs+pIkqfFs+pIkFWhz0zf0JUkq0ObQd3lfkqSOsOlLklRglE0/IrYDTsnMnSNia+B0YBHw\nNHBAZj60rO1t+pIktUBEHAecA6xW3/Ul4MjM3AW4DDh+0BiGviRJBXq93lAuk3AvsPe42/tk5u31\n9RnAk4MGMPQlSWqBzLyMail/7PaDABExGzgS+OKgMdynL0lSgSYdvR8R+wAnAHtk5sODnm/oS5JU\noCmhHxH7AYcDO2Xm7yazjcv7kiS1TERMA04D1gIui4irIuKTg7az6UuSVGCUTT8z7wNm1zdfXLq9\nTV+SpI6w6UuSVKAp+/SXh01fkqSOsOlLklSgzU3f0JckqUCbQ9/lfUmSOsKmL0lSAZu+JElqPJu+\nJEkFbPqSJKnxbPqSJBVoc9M39CVJKtDm0Hd5X5KkjrDpS5JUwKYvSZIaz6YvSVIBm74kSWo8m74k\nSQXa3PQNfUmSCrQ59F3elySpI2z6kiQVsOlLkqTGs+lLklTApi9JkhrPpi9JUoE2N31DX5KkAm0O\nfZf3JUnqCJu+JEkFbPqSJKnxbPqSJBVoc9M39CVJKtDm0Hd5X5KkjrDpS5JUwKYvSZIaz6YvSVIB\nm74kSWo8m74kSQXa3PQNfUmSCowq9CPieGAesApwZmaeXzqGy/uSJDVcRMwFts/M2cBOwMuXZxyb\nviRJBUbU9HcD7oiI7wBrA8ctzyCGviRJzbc+8ApgT+BVwPeAzUsHcXlfkqQCvV5vKJcBHgYuz8xF\nmXk38FRErF86d0NfkqTmuwF4O0BEbAysSfVGoIjL+5IkFRjFPv3M/IeI2CEi/hnoAR/OzH7pOL1+\nv3ibYWrUZKSmafPng1dG/X7fv0kD9fv9of5RHnzwwaFk1UYbbTT0f5lc3pckqSNc3pckqUCbV3ds\n+pIkdYRNX5KkAjZ9SZLUeDZ9SZIKtLnpG/qSJBVoc+i7vC9JUkfY9CVJKmDTlyRJjWfTlySpgE1f\nkiQ1nk1fkqQCbW76hr4kSQXaHPou70uS1BE2fUmSCtj0JUlS49n0JUkq0Oam37TQb+9vUpoC/X5/\n1FPQBP5N1CZNC31JkhrNpi9JUke0OfQ9kE+SpI6w6UuSVMCmL0mSGs+mL0lSAZu+JElqPJu+JEkF\n2tz0Df2Oioge8Hqgn5l3jHo+ktQWbQ59l/c7qA787wH/DTglIs4Y8ZSkRoqIo0c9B2lFMvS76TDg\nwcw8BHgPMCsivjziOUmNEhFrAR+OiM+Oei5qll6vN5TLVDD0u+kuoB8RL83Mp4CdqILf/7lJf/Am\n4CFg04g4b9STkVYEQ7+bfg48AWwXERtk5jNUjX/N0U5LapS7gTOBA4HVI+IrI56PGsKmr1bJzIeB\nrwB7ALtFxCbAbOC1EbH6SCcnNURm3g98JzOfBY4GVomIi0c8LekF6fm1kN0VEZsB+wJbAmsAx2Xm\nnaOdldRMEbEB8D+BT2Xmf4x6PhqdRYsWDSU4Z8yYMfS6b+h3XETMANYBepn50KjnIzVZREzLzMWj\nnodG67nnnhtKcE6fPt3QlySpSdoc+p6cR5KkAm0+OY+hL0lSw9UnVTsT2Ap4Cjg0M39ROo5H70uS\nVGBEH9l7J7BaZs4GTgBOXZ65G/qSJDXfHOAHAJn5E2Db5RnE0JckqcCImv4fAY+Mu70oIooz3H36\n0gpWn+zobmDsnAerAvcDB2fmA8sx3oHA3Mw8JCL+nmpf3n8u5bknAVdm5o0F4y/OTAuANHmjOJLv\nUWDtcbeX6+Ojhr40HPdn5qyxG/X3GpwBvOuFDJqZew54ylzgqsJh/dyu1Hw3AnsC34yIPwZuX55B\nDH1palwHzIuIXwI/oToCdwdgd+AYquZwC3BkZj4TEfsDn6Bazvs18BhAvf1c4EHgy1T7+Z4BTgZW\no9rPd25E7E11hO9ZwHrAQuCjmfnTeiXiImBmPRdJzXcZsGtEjK3iHbw8g7ikJw1ZRKwC7APcQNWq\nv5+ZWwAbUn3N8fb1qsBDwLER8RLgf1EF+vY8f0lvrJV/BJiZmZsDuwInAhcDNwMfqE+nfAHVqZW3\nBT4I/O962zOAv61fc9K7ASSNTmb2M/NDmfnm+nL38oxj05eG46URcStVg1+VqlEfD+zGH9r1zsCr\ngR/Xn8FdBbiV6suPbszM3wJExEXALvU2Y/sS5wJ/A5CZD1J9fwIRAdCLiJlUXw17fj02wJoRsR7V\nVym/r77v68C5K/IHl9Rchr40HM/bpz+mDuUn65vTgW9k5jH1Y2tSBf9b6sfGLBp3fazpPzth3P9C\ntRtgzHTgyQnHFWycmf8vIhZTr/JlZr++LakDXN6XhmMyR/deA+wdERvUbfxsqq9wvQHYLiJeUn8k\nZ58ljHsd8KcAEbFhPdaqVG8QZmTmo8A9EfH++jm71tsA/BDYv77/3VTHAkjqAENfGo6lHRH/+/sz\n82fAp6iOtr+dKtBPyczfUO2z/xHwY57/2dyx7c8EFkbEvwJXAEdl5hNUJ+84uz669/3AofVzPkP9\nJqEe+90R8VPg7VQfBZLUAX7LniRJHWHTlySpIwx9SZI6wtCXJKkjDH1JkjrC0JckqSMMfUmSOsLQ\nlySpIwx9SZI64v8DRlmHqliYGVQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc79e4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "population: 130\n",
      "P: 60\n",
      "N: 70\n",
      "PositiveTest: 74\n",
      "NegativeTest: 56\n",
      "TP: 60\n",
      "TN: 56\n",
      "FP: 14\n",
      "FN: 0\n",
      "TPR: 1.0\n",
      "TNR: 0.8\n",
      "PPV: 0.810810810811\n",
      "NPV: 1.0\n",
      "FPR: 0.2\n",
      "FDR: 0.189189189189\n",
      "FNR: 0.0\n",
      "ACC: 0.892307692308\n",
      "F1_score: 0.89552238806\n",
      "MCC: 0.805387266257\n",
      "informedness: 0.8\n",
      "markedness: 0.810810810811\n",
      "prevalence: 0.461538461538\n",
      "LRP: 5.0\n",
      "LRN: 0.0\n",
      "DOR: inf\n",
      "FOR: 0.0\n"
     ]
    }
   ],
   "source": [
    "Cs = [0.001,0.01, 0.1, 1, 10 ,100, 1000]\n",
    "#need to use liblinear solver because lbfgs only supports l2 penalty\n",
    "LOGITCV2 = LogisticRegressionCV(Cs = Cs, penalty = 'l1', solver ='liblinear', cv = 5)\n",
    "LogReg(LOGITCV2, X_train, X_test, y_train, y_test)\n",
    "\n",
    "#here is #5 again but with stratifiedkfold method (its the default cv mehtod for logisticregressionCV)\n",
    "LOGITCV3 = LogisticRegressionCV(Cs = Cs, penalty = 'l1', solver ='liblinear')\n",
    "LogReg(LOGITCV3, X_train, X_test, y_train, y_test)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "TPR = True Positive Rate\n",
    "\n",
    "TNR = True Negative Rate\n",
    "\n",
    "ACC = Average per class Accuracy\n",
    "\n",
    "so we see from the stats that the accuracy for\n",
    "\n",
    "mpg01 = 0 class --> 80%\n",
    "\n",
    "mpg-1 = 1 class --> 98.3333%\n",
    "\n",
    "avg per class accuracy --> 88.46%\n",
    "\n",
    "We see that the avg per class slightly improved from parts 3 & 4 \n",
    "\n",
    "and with stratified K fold we even get to an avg per class accuracy of 89.23%"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6\n",
    "\n",
    "the last model does the best. It seems that they are predicting on the high mileage side by which I mean they are making more predictions for the mpg01 = 1 class and so pretty much all the false negatives are dropping out.\n",
    "\n",
    "The best accuracy we get is by running LogisticRegression CV with stratified K fold cross validation, l1 penalty and liblinear solver. The stratified K fold increases accuracy over normal cross validation by itself because it creates folds with equal numbers of both classes. The difference between the 2 regularization penalties l2 and l1 is so small it's hard to generalize as this is a small sample size but in this example l1 penalty slightly outperformed l2 in avg per class accuracy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Question 6: House Prices (kaggle competition) (25 pts)\n",
    "\n",
    "In this problem, we are going to explore a kaggle competition: [House Prices](https://www.kaggle.com/c/house-prices-advanced-regression-techniques). Your goal is to obtain the best score you can in this competition. This is an ongoing competition, and you have the opportunity to win the prize money! \n",
    "\n",
    "The first step is to make a Kaggle account. Then find the House Prices competition and read the competition details and the description of the dataset. You may find this [article](https://ww2.amstat.org/publications/jse/v19n3/decock.pdf) useful.\n",
    "\n",
    "Your work should meet the following requirements:\n",
    "\n",
    "1. Data Preprocessing. \n",
    " * Conduct some data preprocessing. (Hint: see if there is any skewed features and consider applying suitable transformation techniques to make them more \"normal\").\n",
    " * Impute the missing values (if any).\n",
    "2. Predictive Models. \n",
    " * You have to create at least three models: simple linear regression, Lasso and Ridge regression and multilayer perceptron. You may consider creating an ensemble of these models as well (optional). For Lasso and Ridge regression, optimize the alphas using cross validation. You may try other predictive models to get better scores (optional).\n",
    "3. Evaluation: submit your model to kaggle submission site and report the public score.\n",
    "\n",
    "Briefly describe your work on each of these steps. Explain (very briefly) what approaches you tried, what worked and what did not work. Mention your team's kaggle name and include a screen shot of your public submission score. Finally, try your best to win this competition!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n",
      "(1460, 81)\n",
      "(1459, 80)\n",
      "   Id  MSSubClass MSZoning  LotFrontage  LotArea Street Alley LotShape  \\\n",
      "0   1          60       RL         65.0     8450   Pave   NaN      Reg   \n",
      "1   2          20       RL         80.0     9600   Pave   NaN      Reg   \n",
      "2   3          60       RL         68.0    11250   Pave   NaN      IR1   \n",
      "3   4          70       RL         60.0     9550   Pave   NaN      IR1   \n",
      "4   5          60       RL         84.0    14260   Pave   NaN      IR1   \n",
      "\n",
      "  LandContour Utilities    ...     PoolArea PoolQC Fence MiscFeature MiscVal  \\\n",
      "0         Lvl    AllPub    ...            0    NaN   NaN         NaN       0   \n",
      "1         Lvl    AllPub    ...            0    NaN   NaN         NaN       0   \n",
      "2         Lvl    AllPub    ...            0    NaN   NaN         NaN       0   \n",
      "3         Lvl    AllPub    ...            0    NaN   NaN         NaN       0   \n",
      "4         Lvl    AllPub    ...            0    NaN   NaN         NaN       0   \n",
      "\n",
      "  MoSold YrSold  SaleType  SaleCondition  SalePrice  \n",
      "0      2   2008        WD         Normal     208500  \n",
      "1      5   2007        WD         Normal     181500  \n",
      "2      9   2008        WD         Normal     223500  \n",
      "3      2   2006        WD        Abnorml     140000  \n",
      "4     12   2008        WD         Normal     250000  \n",
      "\n",
      "[5 rows x 81 columns]\n",
      "     Id  MSSubClass MSZoning  LotFrontage  LotArea Street Alley LotShape  \\\n",
      "0  1461          20       RH         80.0    11622   Pave   NaN      Reg   \n",
      "1  1462          20       RL         81.0    14267   Pave   NaN      IR1   \n",
      "2  1463          60       RL         74.0    13830   Pave   NaN      IR1   \n",
      "3  1464          60       RL         78.0     9978   Pave   NaN      IR1   \n",
      "4  1465         120       RL         43.0     5005   Pave   NaN      IR1   \n",
      "\n",
      "  LandContour Utilities      ...       ScreenPorch PoolArea PoolQC  Fence  \\\n",
      "0         Lvl    AllPub      ...               120        0    NaN  MnPrv   \n",
      "1         Lvl    AllPub      ...                 0        0    NaN    NaN   \n",
      "2         Lvl    AllPub      ...                 0        0    NaN  MnPrv   \n",
      "3         Lvl    AllPub      ...                 0        0    NaN    NaN   \n",
      "4         HLS    AllPub      ...               144        0    NaN    NaN   \n",
      "\n",
      "  MiscFeature MiscVal MoSold  YrSold  SaleType  SaleCondition  \n",
      "0         NaN       0      6    2010        WD         Normal  \n",
      "1        Gar2   12500      6    2010        WD         Normal  \n",
      "2         NaN       0      3    2010        WD         Normal  \n",
      "3         NaN       0      6    2010        WD         Normal  \n",
      "4         NaN       0      1    2010        WD         Normal  \n",
      "\n",
      "[5 rows x 80 columns]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: pylab import has clobbered these variables: ['plt', 'sqrt', 'test']\n",
      "`%matplotlib` prevents importing * from pylab and numpy\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.cross_validation import train_test_split\n",
    "import statsmodels.api as sm\n",
    "from patsy import dmatrices\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from math import sqrt\n",
    "import seaborn\n",
    "import matplotlib as plt\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "%pylab inline\n",
    "df = pd.read_csv(\"C:\\\\Users\\\\Owner\\\\Desktop\\\\Python\\\\Datasets\\\\AmesHousingtrain.csv\")\n",
    "kaggletestypred = pd.read_csv(\"C:\\\\Users\\\\Owner\\\\Desktop\\\\Python\\\\Datasets\\\\AmesHousingtest.csv\")\n",
    "\n",
    "print df.shape\n",
    "print kaggletestypred.shape\n",
    "print df.head()\n",
    "print kaggletestypred.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1 Preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABdoAAAWSCAYAAAAAeVc/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzs3Xm8XdP9//HXzTwTQVHEFB+pyCQJEWKeSlFqbrWq/ZpK\ntWiLqpo6mJW0qPmLokW/lBqLEDJIYkjKBxXzFGMic3Lv74/P2jn7nnvOvTc5+ydR7+fjkUfuPXef\nddbee+01fPba69Q1NDQgIiIiIiIiIiIiIiJLp82yzoCIiIiIiIiIiIiIyBeZAu0iIiIiIiIiIiIi\nIjVQoF1EREREREREREREpAYKtIuIiIiIiIiIiIiI1ECBdhERERERERERERGRGijQLiIiIiIiIiIi\nIiJSg3bLOgPSOmY20927V3j9GuAud78991o9cIO7H5J+bwu8Czzp7nuY2arAVcBaQHtgmrvvbmZ1\nwEXAdkADMAfYz91fayZfTT4/97dhwLnAqsCG6TOPBfYHhrj7MVXS3BNwd38h9xlbA5+kTa5290ur\n5am1zGxrYL67P9nCdhWPfZVtG+U9vdYWeAe40t1PbuH9XwVGAV8D6oB/ACe6+8LWfP7SyPbPzHoD\n/3D3TdLrWwJ/APoAHYBPgRuXNj+tPY7N5CdfnmYDE4Fj3X1u7r2PAWe7+73p932BQ93968183mnA\nTHe/oMrfHwPmA+sSx2BlYLa7Wwv7sRewvrufb2ZnAtPd/Q9mdihwN3A+MCKlCXCcuz/a7MFppZbq\ngPTa4jyl39unbUa5+69yaf0L+K27P2Bm2wM/Ah4BNnT3o3PbvQFs7O4zquRpEfAMsAnwAfBNdx9b\n434OANZw93+m379LlJE3ievnGXf/npmdDjzq7v+qkqfspvNMoDuN68XewPPACynNBmAYsD5wDTAY\nODkrP7XmqSxvU4HeKT/vAv9uIU/7AT/P7cuR7v5cM8erSdk3s2nApunXh1LaqwOLgOnp928TdUE9\n8C3gIODgdOymA4e7+wQzewRYjWhLGoCzgP8DPnD3nma2PvBc2o82Kc/fc/f/VDomrWVm2wKzgMOB\n3Ym24x1gBaIue8Tdj07l+Tbg/ZS/V9x913RcfpheB7jX3U82s4eB4919UoXP3B04I+1HO+Bid/9z\nSusIoFt6fSZwVnbdtXJ/Fn+umb1K1Bn1Kc9HAQ8S5XWTCu+t2q5XSsvdx6a663Si3C0ETnf321qb\n37LPX1yPpzb3/4BXiHI73d13MrMTgG8CXwE+Jurbc9z9/3LpdAZuAnYBXk7b7eLus1N99zJxzhuA\nvdz99Qp5GQhMzm27EPjR51UPVXnvIuA/ad9fAu4BVnT3Y8vKYSfg4XydWyW9PdOP8939n6nsPAys\nku9zNVeWK21jZt8iyvc76f/sPLYF3gO2J+rSrD5qdA4qHKOPgfPc/eyyNj+r19oAnxHt90vN5LE3\nsIW7/yX9/l1gCFGPdM9t912a6XeWb2NmKxP9r/bAj4HHiGsn8yt3P69aWim9k9z9t+nnC4AD3X31\n5t5Ti3wfy8y+DlxA5P2fxPX0i7SPU4FrKtUX6b1NjpWZdSXK9E5EfdoAXObuV+W2WYnqbcYbwKru\nPjy3/Y1E+3NE+j3fHnQExgE/cPf63Ht2Ieqm7sBcwIk+6ZutOD7/AFZw961yr/0v8Fd3vzP3WtYv\nWFyWgVWA77j7cenY/pqo0+em/J7g7m+38PltKbV904BN3f2jKtuuClwIbEaVOvHzYGZfA+4A+hPt\n54XE8Xg3/Vucp7L6PasXDnL3D8qurSbjpKXM2wHEeKkbUZd/QrRhn9sxStf1q7l+9HsA7v6V9Pt5\nwJvuflENn7F4nJ3rU80l+jIPAqe6+6e57Vs1jqw29jGzzYCLiWuwA3CLu59R1q6tDvQgrr92wCnu\nflcujfJr6GZ3P6cV+9ponJjrj64MXA6smPL0mLsfUa1P0dLnpLSr9U06pX2bnvbtb+5+upltTvSl\nGh2XFj6jSTubXludOIczge+Xt3FmdgpwIFGHLiL1qZv5nK2JOugbrdn31ijrfzQ5xxW2z855e+Df\nwHfz4/Pcds3GAiqUgeOA3xLtx8wa9qel2Ng3gL6tKae5NH8FdMrHdlJf5y/u/rVm3vcwcDzwVHN5\naub9FeN4zWzfKJ5SKS/lfcHWxlPM7PvAccR1XkfL5aRi3DArw8BYWln2q6VVYZsshlgPHO3u4yps\ndzgwy91vqJbW0tCM9i+OhiXYdhbQz8w6pt93JDq5mTOA+919oLtvDPwivb4/sLq7b+Lu/YmB7ycs\nhVQJ3Eo07n1Tnu4lOsct7c9ewMZlrx3v7oPTvyZBdjNbmrK8DbBFK7ZbkmNfKe87Ai8C+1Z7Uy7/\ntwO3u/uGxM2J7sBvluDzK6XdtoVNGsp/NrPViEBae+BoolPwOrFvS5ufLO2lyc9XyJUnd9+UxuUp\ncwRwgZl1MLNuwNlEIKoWRxEdveOBrYjOUdfUma3K3f/u7udX+NP3gey9x7n7IOBE4E815jOvpTqg\nkp2JAfj+Za/fRDR6mQbggPQ6Za9XlMr3LOBkYvBcD/yumW1bayBQfhPl5lRPDMqCW+5+mlcOaM9K\n2w4kBg+rVagXAV7OpTk4DVg+BI4hBh5F5mlx3oAngF8S9crrrcjTK8BIdx9ABLX/3Iq8lWtI+fso\nS5somxfkfv8GEZzYlAgQfp1oLz4AdqBU1hqI4FKWx9vzn5G8kDsHfynbx6W1HTCcuBGyM7AG8LuU\nj42BP+a2/RdR113h7rvmXr8g1+a0dIO0AzEI3C3txyDiZlTmMmArd+8MrAccbWYbLeW+1QPb5I7p\nWOJ4Nrn+Ul3bXLveJK00SDgH+EYaKOwB/N7MBi1lfinL2+hcuc0GxHsD17r7Bu4+lKhf1ixL4zhi\n4PtSGiwcBixIf/vM3TfM7UeTIHtyANFxfzydp5Mpq4fSjYkl1aprvopZxGD20ZSf8n5CVg6/BvRP\ng5Hm7EVcg+X5WZJ+TCWHEUHP7dPv2XkcQAwWF5TVR+XnoPwYNWnnk6xeGwhcD5zSQr7WJW705VW8\nHqq8Vm2bHYBn3X1Td388vf5Vd+9C9InOakVa5fVGtWu0KFl/aXsiILQLsC1xk+AraZvvpZ9bOhbl\nf78S+Chdo0NS2ivlN/AIGg8pbzNSHgYBPcxsndxbOhKB+7wX0vv7E3XlPtkfzKwfMfnjO+7+tbTd\njcA6ZWk0Oa5m1pO4yb+KmZXXLeVmlZdld5/oEWQfQNzAOChdk0OBm4kb4s3mgVLQEVo+/n8nbgg3\nVydWVGSZcvd/Ezejf5ny9AkR5Fw/n6fcZ5bXC9mNwfy+VxonLZFUFq4hylhHIth+Ca0/Ru1r+fyc\nMaRxpJmtQASCu+fK+RZEPy773FrPTdanGkhcI/OJAHFerePI64i6fhDQjxh7ZW5O191lRIB/MDHB\n4+qyNMqvocXByxaOQfl1kf3+B+D8XB/uktw2lfoUrdWkb0LcqJ0DHEq0W7ummw/XUuG4LOU5zc7h\n9UCjG7YpoP91YGC6jhb3qVsYH9XaxldyQTPnuFx2zjchbnwdUWW7JW17DgDGE/3EJpbg+Dc7Lnb3\nu3wJguzJX2g6Zq40Pl6qPDWjWhyvOUtaPlqMp5jZWkQ/Z4tUVjcHnl3Cz8lbkSplv0YnpHJ8EnBF\n+R/NrK27X+4FB9lBM9q/kMzsUmL20BuUBprl7gF2IxrcA4nKIJvFsTpwX7ahu0/Jvf5O7vXFszPK\nZsrsA+zu7oemP+9oZicRjflP3f0eonN1rbuPz6V3e3p/lmZvooPQhxj8TiYGvXsAO6WZJq8Qd+8f\nSMHfW9LntCNmlP4pHYujLWa8nUvMpJhAzOZckO6IX0cEh9oRA9l5RCWy0MwOJgJmPYnOZHsiiHaw\nu08H6szs/nR8xhIV4R7EzI4NiIrhdWI22tbAyHQ3eh93n5aO/0XAkWa2eQqMZHfqbyEqknNSx28D\n4BgzO4wYfP8EeNPMjkyf8RYxc/RWIvD7AtHh2Djl+9fufleaebA30flsYzHb8v9SXtsTHaTFM3gq\nOIoIFPV29+tTfn9GVLTfN7PvAWe6+yXpbwuJGbWvE3e0VyBu5J3v7qem/HQ2s4dqyE+18tST6ACs\nRyk4+QtiADcDuCbNypkDfJT+/g5wCDFroQMw38y6uPtZKc03gBtSGr8hgrD7Eo3ILcTA/hsWs9MH\nEbPDDk+dsduAt4ng3mvuPiJl+XSLmbZbAHcBndO2AE+m7UmfP4TofHUlZhN8z92npzvM44GR6f3f\nJQIRGwM3ufvpKYn2xIDD04yaoUQdcJiZeTpOawOzzWw/okN5IFGufmNmLxA3FPYhZlwcYmb907Hr\nTFwLbmYTgL7EzKXViQbsgLQPjco3MdDKroXTaHxTZxoxs7YH8FuLmW4vEoG1HkTd8BPiDv6G6XxM\nAzYCOpjZCGLGA+lzGrHGM4Ly9UFXM9vQ3V8kgg8f5PI0ysy6p/3tkF6fSdQ5X0/n+BRidnd3M3uR\nqFfPADrVkKesjqqjVFevQAQ5puTqwT5m9ixRz43J583M3k6fPdDMXiaClNXyVq4u5a83MRPycWBP\n4GMzG0UEsU9J6ZxElKsPiMDThsQMq3vN7LfAAOBGM5tPzHK4u9rnJT2I2XvZQPrqdDzaEIPztsRg\nfzIx028sEWg5jZjxdCARCPgB0dGfDpxJXA9vp3SPBQ43swVEPb+Apm1Beb6aSMf7cqL9OTbl7WMA\nd19AtAeZz9z96fS3z8zseeCrZvYn4sbTtsQ5Piydy05EEKE/MWOsU9nxqjrYytX9KxPX5hxgUQou\nvU0EmdczsxWJIOVw4B4ze5S4CXg88JssUOrur5rZb9Lr37bGs5x7AU+5+7qpvPwv0CVlpdpM8UbH\n1cy2I8p51r94ODsmqR39DxFM2DAdE1K+8se3s5ntTdRrh7n7fimt8lle+xL12k7p5sgKwJxU3z1D\n9JmmWczenUX0EwYQbexOxHmYSwT2FhFt8ZJc802OXdl2K6TPzeqgQ4F2qb39cfr8e9J1eDDRvr9L\n9F2y638P4joitTcQbfMQM9spHZ8xZfn6IxFc6EyavVf291OBLYGrzOxOon+Z1RN15G54m9lQSrMh\nuxPX6GHpGK1mZjsT9UcdsFE6Jt3M7BjgTprWBx+ldKuVr9+mdCYRdegnxI3sLqmt+7u7/zyXJqn/\nUamvl/19APB7olwNoTQhI7vuvkJudruZPUdcS22Jwe+eqf7rYmZzibbtSaLvcwXRf/iAqJ9uMrPb\nibquV3rtUHd/M+1zpdevSZ8/iJhpfRjRn+lqZncDBuyart1903H9vpndS5zni4A1zewmok/Tg+hb\ndiBmIt5J1E9jiYDSDcBQdz/QzHYkZpR3AP5jZl2I/sV9wKvAOum4P0o8kQBRH71B9NmfNLOz3H0U\nMYFhTTOblfbnZ+l4PknURRNSPh4GRhM3CWYC95nZ74nyfxDRj/k60aesI8r7x2b2kKeZgsSTV3ek\nc3EgjW+Q72IxM7EbcZ3Vpb7NQVk9k9raj4g6dArwKzNbD3gN+A7wOzO7iOiLPUH0bZ+0CJptSFxb\nU3Kfubicm9kdRH+tE3HtvELUPW+Y2USi3H3g7juamaVj2y2lcZq7n2dmhwCXEjdPO5nZxkQfcnG6\n7n5l+rzD0rH+mAiKzPV4gmZlIoC6VsraT9z9CaINfYHo521H1JOkc7R+qp/WTumtlvZ5HFEOB5jZ\nYKKM/C21MyOAg8zsXeJG77QlyNNxHk8hn0/MJD8bwN0bSDdNLfrlFxPX40Jgf3e/18yuTnlvR9Sr\nw4n+Tcd0jM/w0hMorc3PWZTqh2PSuWsHfC+1mxsBR6XrfkPgMzP7KdHmb0y0JVkdcTnRf+6Sjucs\noh9RPs6vS/u80GJc9pKZbeLuz5nZ2US7f1zav6MojSP3J8pl9qTJW8Rsd8zsSqK//2rK03vps2YA\nF6c6syuNJxCQ8vGCmS1Mx6YrUWd1NbMHaFxnzSXatEkW4/XexPhmbjp3O6X3vUvUB++kcwgRB9g2\n1asNxFhgajp3m5nZ5LTtme7+11TmLkj5+YAYQ71nZpum9zYAD5TvS9qf2Wb2FDEefzX9fwNRx69P\nXMeHAHtbBCB7pnZwVaItfol4MuerxDm+Py5bPiDq6sXnkKjXfpzOwfZEvdSTKI/ZNhOBW8xsD6IN\nqSfGi68TbezLxE3P9czsr8T4sC0xTroja89T//ZYot0bRzz90ZD6shcTT3/OBvbMt4fpmFQ6x43a\nJaLe+RPRLs0g2uWriZuyPYkydSFRv55FlIUV0zG+wt0vLj8XqY7tSkxG+yXRxuf7ud3SsdrW4snI\n/Yi2Kb/fWf3ahai/K8bGrPFTN/sCvyLqj0/dfRuLmxy/T/uzCPizu48ys4/MbKiXZl3vR7qB3FLf\nKqkar7Om8Y3/STG7anE8zOzclMd6YkZ6/kYZ1vz4YjF3n5r6e79I5+A6oCH1l8cRT3MfTZzr2ek9\ns4k2MetHXZb2/T/Ekxuf5j/D4gm1C9O+jSGu53c8PX3j6Ymv1AfdPaX1hKen4MrSqnjNl202mriG\ns/7400R79Bcz60F6wsfi6brLiP7VQmDf1E5VLGPN0Yz2LxiLwWQfj1ni36XyjOwGYobFgRZ3yfoT\nF0VmFHC1mT1kZiebWfYo663AHmY2yczOs3jMOp9m+WdkenvMuNgduNxiANuPaByacwmxTEVXoqHp\nTnTi7iQ6ANu7ez+iEjqTGJRuQHRqBxAX3JPp7vJEouLYN90Faw8cmfus9z1mX15GDLxfSz9fmO7A\njiFmaWyetruF1OknLvyH0l3avxEdrN8TM6qfIToxLxOdginErOvB6aLsSARi7iIqz/KZVx+4+5BU\nEZ5KXLhDSTOcPR6TmkYEKv+a8nU6MfN2EjFgfcjdN0/H7rzUgYFo7PZ2922JTsteHjORtiM6qc3Z\nmOj85M/hU0TH+XWiAd8SFgcE6lJ+fgr80t27EY8t/jyXn7Y15Ke58nQ6MCmd91OIRu0goqzMI8rW\nU0SDPJRooP6HuC6GEoOn84jgS36W6Xses9luIzra3yI6Kdmj2DsTQap3gfYWj7ECvOjuw4hHi3uX\npfkoMQjblSjX2SPRuxIBxGx27MXpWA0lAon52XOz0+tXp/dk+/I/ZtbDYomd9kRDP4loCIcRHfnV\niVlduxGN43lEkPL3xE2ijYh64J50HD9I2zycjvMaRPm/NTvuxCAgWzJjXTPL10n58t2Z6EScRXQa\n3k3bHESUh+zGwgVEwL4NUcdtSwxQziQ6kMOIwfbNxPV2S7re/prS2z/VYZNSx6mSrD4AeMIi8LkR\nsLHFzaCrgDEed8B3AVa3COR0I5bM6UcEEc4kOh/XEB38BUTnrJY8XUY8PteZuIb+RsyOeCvV1QcR\n5aiB6ACMMrNL0rF7MJe3PxGzZfZuIW/N2YCop/9InKN9iMDULOJaW53oEG5IdLpmEwPhk9PPU4jB\nQlvgttRpLGfpuPyHKKvZI9ZHAeemczCUFChPn3W2x9JN/YnrZAQxU+EX7v4KMfsye+8kYjAw2mLp\ngDOI2eUD02dtTumRx5tzQcif5M7ZjhXy3ZXU/rj7Y0Qd/5qZ3WRmB1njmdH5tL5NzJLK2uS27r4Z\n0Y78Or12JDE7aGPi+hxS9tn/MrPJFgGpSgYR1/uxxPWSBXnOIcpRX6JzOY8Inj4NbOaxZM/GNK1r\nnyLKYiVZX+B9YIdUpx9A4xlneVvljsVJ6fPeKdsmOyY3pX3fm+hfHEkEds40sw3y2xP1x++A3XJt\nzv5Eu0uql7LHwrOO/xUpnxsQ5ets4km3N4gA0JCU9krpunqeaPt6ENfgxTVe8w0pL38m6rkrKM1O\nPIjSzZqFRD3gafsHiTbxIaJ/cDlRHx5M9J/+RPQf+hFlvw2lJY3+mYISWf0HsfTVMKJftY3FTa7F\n3D3rfx2UC1pvlerE14g+Trv0+5XEQGlTIrA5PHeM3iJmBGbHqA8xcWEWUc7bEOd3ksUNwp8Q7QHE\nIL1S+foF0XcbnBuoD0j/zyYCTlOI9ipT3tdrFIh392dSfrOnEuYS9cMbFoHz3xL9NVLd8FTq8/Qk\nBvy7Ev01iJsnG6Q8rZLyPYFoNy909wvTa9ekOumm3L5Vex1ieaHhRJ/rTqIPtYho93/m7i/lyvwn\nRFmaT5zHHxP92lFEGXycaMc2I8pF+5TfZ4l6+JvEjfVeRLBj+3QeJqbPhxh4/q+7dyLasGyCAcQS\nXqsQfb0PiYkxWT0zO40BNif6Bm0oleWhaZvViH7nqkSfYDOiz/Jhro7/dvqsoUAPd/8qscxd5sB0\nDG+m8RN6AGum/dmDuBazyQSPmtltFk8vdiP6TFl91RfYzt0PJoJnn6Q662miXdqXCJwMScesc0qj\n0kzqQ1OfbihxboYQNzyuIJbYG0TpSZdDiTFGt3SMz0z13Z4p7f7pc94sT9fMeqY+xC+JdmEE0e/J\nXEzMYN2M6O9eCeDuc4g+7wBiQscruff0Jc7rWsR5bkPUS68RZekrRAD6pLT9nsQNs0PS8fxkCfOU\nLVXUl5h0UsndwMqpXP2O3A1a4gb0MHdfgbjBfmLabmXg4KU4Rr8HFljcyD6QqL/vTfs3hAi4rk0s\nm9WFqLdHEXXAOUSweB4xyeLnRL1/NnFj4wOqj/MB8FhW6VkiqLkRUYavTNdFPXEddSTK31VE33AQ\ncS43Jm50nUGMCb6SytozxA3n24h+zvhUB71IxBUmEed6CIDFBKNF7v4Bqc4i6pU+wJS0/TpE4Pkd\nImh9H3Hdjk5pb0bUU3XEDZyBxJM42U3cO4gJI2+m9x+eAnnDiGBt1h/+mpm1S/nYJ5X/ayjN6L+a\nWDqi0hN62c3jXik/ZxDjlDfdvQ9xI+t2ixuj26TjuHfK03VEW7xGev0vaR9eSp//InE9/7rsM/cA\nnkuxgmuI67wf6Rq2uKnekRindiTKxwxi3DeIGIMYqT0i+gl/T593FHGDfctUNvYnZh7nywbEOX4i\nnYfHiEl+jVQ6xxXapTriHG9JtL3rEO3CdKJtHJ7S7kq05x8QfZVbgR+m87n4PCQHpGP5OLChma2S\n+9viGEdqh/ukfsygbL/Tdlk9OIsYPxxSJTYGpf7sqcBOqZxkS7j8D3FzqH/a9xvT64vbFIubjB96\nafnLZvtWtByvK49v/G96vWIcL8UI+6d41Y7AuRYrAuS1NL7IO4Moc7sQ9RVEf+bS9BmPE33/aWZ2\ntcUNucz1RP06kBh/nJZPOO3vFcSTwEOIdn46sLaZvWBmo8xsZNr8EnffzOOp3C5mtltZWs1d83l7\nEHVypr27D0v9sLwb02cOJOrfd1ooY1Up0P7FsxVp4Oju7xCPvTfhcXdrHeLiv5tcxeXu9xN3Zv9M\ndCAmmVkvd3+LqIROIirhB600I6q52X23pnRfJgavfVu5L8OBcWZ2HzGg6k/pccIXgAstZjl1JALP\nBxIV5T5p24VERxaioXklV7ldRwTlMnek/ydS4THTZC0zu89i5soJuby0JSpC3P0+YobDUCLwNJjo\nzO9OdDbLlzLZnVhXdV7Kw15lAZhbACxm0K1HzJKeTAycs8qxQ0rn5ylfWxONKcSg6hfpPY+kbddO\nf3vAS3cP2xAzhZ8hBulrWCzvs7TeJQZGEHf3srX/sop9DjFQaEd0NgAW/n/Kz5akxsfdHyYa9NuJ\nzuI/iABGf6Jxz+5evpzOyZ5E0OSnxLWQDybdkvt5ETH7/FSiMdidKL9Ppd9HkO6SEkHZiUSjslKV\nNLMycKHF7K9rKDVifYmy92A6rz+ntNQMxKAaorF41t0/SPsyjbhrvyXxGP/TxODn5fS3AcDb7j6f\nKNP1RJDiQqKz+gBxR3kEMZhbh2hQs/wdQDQ+axJ10Mj0nvHufh0R/H6WxtdX/hjOJ4JRGxED933S\ntTCBuG5WI84TlAYWvyeuBYjA1prEjI9NiGth8VMAOVlwZHDKVyVZfTCH6MT0Jcrum0S92Bb4mcXs\nmb6k5QyIWU17pfc+Ryng/Q4VHh1fyjxlddTs1LnvRXS2vk0MTJzojM8gOpADPdbSnZfqdohz0ZMo\nO881k7dqjxJmr0/z0hrvb6Z8bUlc24vc/bOU74uJTuBC4GaL2XVtiDqtTXq9nsrtSLZ0zPrEzc3s\nfD8BnGpmJwJrp3ILcS48/fxvYlBP2s91quzPx8R5/BsxqJ1mZt9JefpX+swLvPFjo/mlYyrNfMq3\nP7j7D4k2YBwx+/uq3LbZ47cjicHij9OxI5fGRErnaSQxmCQd/2fKPjtb7mU4lT1AeooltevZ7Lt6\nos36YfqMT4njdjTpRl8N2gNXpvbzr1TvB4zOHddKT1X0AfY0s/HETKf57v5pCn5uSXTEVwLGm1n2\nPRkLiRvog4i24BsWjxPvRilwfSDRjs8mghdjiRucFxJBoduJeu9ion55INW/UJpROIeoz58mOtrN\nrbfdmmuelJ8fEjczdyUCGBD14iDi/BxKBBm7Ee3o/URduSlRrx9EXO/VrvOn0r5vAbzrpckJmQNS\nmzU57V+1myr56zc7j2sT7UN9KuO7ETPWnkv5WqlCOpn7PWYuNRAD75UpLR2zAXGtZMtfdaB15Qui\nTpid9vMhYoCcH+SV9/WqrqWaky0d04nog15gMZt7J6JfN5sIhnQl+gZbEedqnseEiQeIAXhWnz5A\nqb4aTurXE+V3RAuvQ9zYgygf73os8bGA6Jt9L/0tK/MQZTY/0eN14vp/myjzW3p8v8q9RLn7FzGZ\n4La0bReiz/c14OW0v2dT6m/Oo7S0wETiBkO27F8f4PqUx3nE4Dx7wjZ7Cujl9DlGPJF0EnH9D6LU\n351J1AfvEwHDn6b+02q5YzmVeIrqIFK/NAUh1nb38e7+PDErdMPcscjGMC+mPMwlrpXp7r4PEaB6\nhMbuBFZIdcQFRCB7MtHfXZj2GaLO/aPHjOtLqPwk+XHpZudYoo+zKtG3edTdX7d4ivkRMxtH9FP+\nkPrYTxDjo7XTfi9KeV0n9QnL0+1D9PUeSXXqIko3hCCePrw07cedxJMm2RMkU9Nx+VM6ppcSgerV\niHrhKuIX90gpAAAgAElEQVT8NwANqV74JzEbNL+M1HFEsON3NeSpa/kBNLNLzezpdIzWBV5Nx+g0\n4iZP5tXcOPFJYhzyFunpiaXJD9Hm75rOw43ERJXOxFN4Y4jz+XeAVHYXEH2zy4g+doe0/RgiOHUF\nUZf3bW6cn5PVy9unY3pwyt92RB9sc+La+YgYF77mcfPw30R5+SZRTsem9/Ug+kT3E+fzuOzYpeM3\nOP19ZAqin0OMA6FUZ81O+zY/bf9q7jjekY7jKErX7Vbp93nufk8aK06kdL18TLTVtxDX5irEWPgV\n4nq7j/jOrtOJOqQfpTb8FGKMuQLxHQ3ZZIosaJnZKrWD9xLfS/W1dAzqzexr7n4c0ZY+l45pu5TP\nMUTf9TWgq8fNj8+IG0Hzib7F0+mYZG30jenYDSfaoMUxDHefRfTxnyf6O6sSZeRtIoC+hrvfmsrm\nIqItmZU+bwhRR/QhguCWft6e6C9MyJWNdVNe5nusRABNYyQ/beYcZ8cwa5faEv2SrO+2MhETusPd\n56ayfFs6X3VEORhPXHe3U2oT8g4kxo0NaZv80nr5GMdOxOoKk4hxUrbfUKoHuxLlZkMqxMbKPA5c\nZ2Y/oFQGdwAuT3nB3bMlGG+htMTZ4skdSYt9q+bidTSNb6xkZt2qxPFWTttnMcL3iXZraNlHtjS+\nyOdtdtq///WYMAHxpP6E9Pd6d98l7b8T/aJfWcwOX8Fj2T1oGpMj5fsVL924vYEoz4OJPtt0SuPJ\n7cxsbOqzZU8D5VW85nN/Py+VjR8QN/Iy+RhFJBRPqazhaZUFd5+f6svmylhVCrT/d7uTCEr9pfwP\n7v6Ju9/s8VjlU6QLwN0XuPt97v4zYtZOFlTKB2TKHzPJ/62OaLCn0Pxdsux9FxNrrw0mOgJZ2n8n\nZol0JpZpWN1j1uBIYlbUtUSgp/yzq5mX/l9E9SWTLgH+4HHH7AiqPE5Daa3BOqLyGAZ8nIJ15RXW\ngcAOZvYKcZxXIhq4zKz0fxsicPZCCqAMcvd+qbLagDgX44jA41dpXDnsk3vPurkg1KzcNgcTjd6g\nNPjMvlytmn8Txz5/DocQjcVaxGDuMzPbhMbrk/UiOq9dPWZvvEacL2hcTpY0P1OpXp4qBQsb0r95\nxHm6mphZsBtxLB+zmBF5LHEszyc6avk85I9flmZ96gT9B3g6dSDfImaDnk0E29cmZjv8muhsNJfm\nTzxm5v6S0iC1jvjyvGzNwQHe+EtOsrJcn/s5y1952b6TKG8TKJVZiFkQbxCDnW8QQZpdiIFzN2JQ\n/TDRMasjglXbkx6Pd/fJpY9YnIc6ml5f+f1tT+lauDxtt1e6rt8hBrjXEtfMx8RyG1n5GJU+5xKi\nvphNXKNLu85m/ri1A/BYhmAlYlb4LsTgpjsxU3bFtG3+Ed7y41/rUmwV66hUV5+V/v4s0eHeL+Xl\nWosZ0ovzZrHEz+7ErKaPUx1ZLW8fEuc+rxulNbzz+1ffTDoQZewdYvbaPsSMrnakNdrTZzV3jUME\nj7K26Aai/ZlHLEWTzRwoz1P+eqiaP3d/x92vJQIDn1Aa6C2tuWXtD+4+1WNW7U7k1haGxTMu/kZ0\nWPNrqrambSpv25pr66D0paCZhcRg6mdEUPTrROd7NlG2tyFmMkHlunYI0X5laWV9x/z5/AkR8Ouf\ntu/QQh4zU2kcsH6J6GSvQumJn8xcYIbHF4LeSGnN7/Kb1/uT6j13n2XxyO8+xCzlbC3fnYkBc0/i\nXGb9iw9TOtn60p+5+w/T7JtdiS9j70/M9lzSPnS1YwcsroO6EV+u9Rhxrj6lVC/em9v8GuJG8rmk\npWuoXn6yG+FNypjFWsLHA9t6zJq6p1LeWnAXpUf8zwT+5THb6dyyzyvPX0v1y12UBt9LUr7y6Va6\nrlrb1yuXLdmQ3RwbTvSHpgM9U59nNDF5oJL8lxHOzeWr2g3P5lTqBywi2u0NzexkSmX+x8TMy50p\nlb/sM+vKfr+F6NOuQrp+iL5pn7Tt/e6erVU/x93/p0o+ss/Zj+hL/tRiibTeNH8jJ/tS57HEgPpw\nSv3d6ZSexKgnAjxXEGUhO5ZHEMHgocTNuDpikkAvM3sl5WEtmn7vTD4PpODwTIunf/YnjivE2GYN\nYkbg9FRHvArcnX6eDHzd3ReXgVw70aTetljeajuiDzmQCMi9SfT7s7z8KG2zKtF+/c3j+z66Ezdz\nnLihNJYoV/eY2Y8rpJuV82rtR13aPhtPrJ0CLRD1dAdSnZzydB3RV/wJ0fZ/n5h8kF2bT5CWsUq+\nmvL0D6LOWdo8zSKCkJtlG5Udo5uJGbqdiTo7X0/nv9D4bWISynlE+Xl1afJDtJ0HEeX8/4gAei+i\nb52tzz6vLJ3fEoGl03Ljtq8Rfd8biPFDi21ouqG8CXE86oj6OxtH9vX4ss7ORJBxYdnb64jxy0pE\nMHRw7n3Hu/vlRF9ioMXTiOWTJbLJCFt7LDEEzddl2XhgXtquUp2f72MvKvvbZ+5+rcdkl2z5lLeI\nMvcc8XTHL1Mep5SNoXalZaM9nmIe6u7ZDd6FxDW9Sy7vfyXG4iuZWU93/z0xfuwAjMndxJuX+z+r\nE7P9PSjlb2+PyRDQtMx94O6/Jvokza09nz+udUTZupn4wu4N3f2a9Pq1Zef4zPS++bm0ytvLJTnH\nC4nlgwd73JSotF02Tmyg8phxcfoWs7/7EMHTV4h6OF9v58eXdcTNkWz/NnT3a/L1a9r+aeKarBgb\ny7j7UUSwdi1gosUXfVfb9k1i8s42RJubTaBch9b3rarG68rkJ82Wx/Eq3ahoaazQmm3qadwXL49j\n4O5PpevgQEpjn6X6bHdvcPfRqewfQ0wyG0U8vZD1vcuPY0vX/Anpbzt73Gyvui/N5L1iGWtpBxVo\n/+LITvpo4pHkNmmWxrbNbHs1cLq7T83/0cy2tfRotcUaxOsDr5vZICs9ftKGuDP5anrbuxbaEHe/\n8/Y1szqLNY3WJe5qjSIez8nupNWZ2Tet8WM/TxB38d4mLqTszuRMYP0UtDiHeLxoTTNbm1he4Sri\nQst/AYYTy3Ssl37/DhXWkiszk8adwB6UlifIP+qdzRLBYo3TFYm7sJ2JRwePJAK3PYkGIlsftQdR\n8a3l7uu5+7rEzMHy5WPwmPH0AnHX/dvp/QOJDuBHRMD6ViIg285L63HdRwSLyb2nkhWIY1dv8ZRC\nfuZbXYWfRxFBh5XM7NsWj9KdRdylv4YINL9J3MVfk1JD+VLa35Y+Z0nzcymNyxOpPK1KdHKzY7YN\nUV7yHYcHicFelsenibvivdL+7EIMWHamFSzW0u9BLDPSi+iob2PxpSDfIDobn6V9XKdCEuXljhSc\n65yOxb+JdUmHZp9nscZ8az1GLGXTkehszSDKzrPE+pkdiX3PZgQeQcyK+irxSPhaxCOHHxLHZQPi\npsgjxIz+7ItJRhPBSiy+rb1btQyla6Et6VogBj+fAbun63oRMbi4khhsTKNxED17uiO7RuuIa3QR\nZcdyCS0ua1aahf1hGlyvSZT1W4hrvdH2FdLJ/tbk/C5t3rK62uKxz7ZEp28+UcY/IY7X4Nz2axMz\nRm6nFDDM57s8b6OJ5cK6weLHDp9pLjBAlK++QNv0vn2JdmImUV4GEvXVCimv2fIK+acyKl3jEPXl\ny+k967r7K+7+B2Jg3r/C9tXk97OOWEO/bQq6ZEG6nxGDz3Ys3TnLl52u1vhLKgeR1inMuRr4t1dY\nh7KC0aTHetNgo3/zm1c8Jk8Qj6MOItqdx1L7vQKNg9jPEcGs0en384mnpHqnz1+HaGOy2f6vUgrE\n52cXrUBpCZhDaNw+V+XxhcDtiKBlpgtlgzSLZTB6EOW8A1FPvFohyUcpzdrPZvPuQJTr3kSAbB3i\nOjmKuObrs/4FEShuoNS3qjOzPpQ69rNSuf8WS37NT6PpscuXo41Sfuam/MwibmBl1/kISuetG1GH\ntqH0CHhdyktdM/kpLys9UjozLWYftyYgUZ7OVrl8rUDp5voAoGO67joQQcKW0ipPN5t9Wq18ZfVO\nc2mWq9bXa5VUFtsSbepUon1sl87f5imvo4k6snPqZ+/QTJ6eoBRA+Dalm15jqrxeri73/yLihvkP\niUBNb2JCy1lEme+e/vUmjsNqxPX9eCrXjxH9ln6Urp/ZRB97W2CEma1vsc5rdm005wCijzyNmME2\nkgiCP0YE1VbJjR+y9g2iP/AqMTs76+8+BZxsjZfj60Jjq7n7I8SM4V5EHX8A0bfJ+uGb0bgfvi9A\nCpCtSeObDicRZTeblX0uMZO20SxpYp3orI+5tpWWr6ozs6NT3XsUTYOdKxATdeblys8kImC+a1YP\nE+1nA9H/yvY/fx2sRjzFcQkR7N24QroQ9clIM1sh5Td/Q/h+0nrR6XhkSzlk9XTW78pkgeAelK7N\ntXN56k/jQEYHIpD8KTEbsJY8nUCM+bIlnNoQN2gbiDLxatruDKpfd32Im3cXEuUxmyW5pPl5Iu3L\nU6mM9SbGc33S394jrps2aQzcjriZ9Rgxnh+UXl+XGJ+MJm5etK0yzq9Ln92OCKq+nq6Rh4j2pXsa\nt/VM7ffuRBC2CzHZpXcqnxulPJwA/MBiOSfMbL80noHSOvef0DpZXVZH83XWAzTuP4wm+inZvmWT\nW7Jzt5B4cqiTma1L3By4N/1f7+43EePlwURdtYrFMh6YWTuLGemfEksVZU/MZpNUGjGzlS1mv0Pc\nvPo68IKZ/ZCoo7KnaOpTeusRdeXqxIzwjag+Hqor+z+zOIaR6qHse9IgrhtP6W9EWm/f4iZL9i9z\nH3HDq13alzVS2XoI+FYWg0llIzvHrelT51Vrr8rTeYB4oiI7b2tQenoi++6n9imv36TUB83SOYi4\nEbVe+rcmESNZi6buI76HpGvZfi+uX4njtDkR8G4SG8szs/XcfYK7n0b0C9dM+3N4Ou7Z+umZm4kn\nLv7jpe83bE3fqtl4HU3jG9M9vuepPI63HtFGZXVKVtdsRdMltpZ0fFEtz5jZ6mmMkRlEzHifAXxk\n8b1FEDG5R8vSeYEo89mTFQcS39GQXxZyYNqOlF7W9y5X8Zpfwv2KhOJp4zfMbM+UVod0rKuVsWbV\nOgNPPj/Zoyp3WHx52FTionqimW3fIgKU5TYlHn1bQAzSrnD3iRZfUvXnNIiFuDizGX8nEY+0vE9p\nvevM62nb7sDhHo/4v2+xZvX5qSB2Ix6J+4Ro7KcSF/o/KM3CuJFoRG4G7rJYN+5VolKeRMy6OzHl\neya5GQKpM3ko8WU72ZehZksQVLv7elfafg/irtmv0+8fEbNZ10nbtSG+yDKbVTqTWC7mSqIBPJsI\nOt9PzGQ40WLJm78T66fnO9Z3El982qFCvg4mAnujzOyq9Dk3EoOUvxEB03VpHFw4C7jI4nGaNsRj\ndHvQ1I3EMX2GOH/5O3oN5T+7+7sWAf8/ELODsjXVJhB3eXsSs013JBrMrME5lHiEaQ4xc+Sz8rSX\nMj/l5ameaCz+SSyrcXVKaxYx+FhcEXt8geTpxLG9N23zMFEeVyQCKAem/aiUh8wuxCDxsJTOBCKI\n350osy/l0n+e6Bi+lXt/luY1RNlZhdKXoUKUo5+5+64WX8TyB4sAdRsi+PXvKvkqP1YT0jXyVHrt\nTI8vNVmZGAw9m/LYhehgP03MTKtPHexsSQ1LeX0+7Vc7otOSfeHLacTx3zDtZ9a5KN9fKD0Zk80w\ng+gMjiKO+1eJc/IJ0SDXEV+09nT63PeIAOzpxLXQhZjd9jGxJuMkqn+5Z3le8j93AIZaPGq2KlFm\nJxOd93bEY3lZYLv8vV2JR2rriOPVNXUCHiYClUubp0wn4pHBXunv7xKz93oR56M3cQPpO7k0Tk15\n340YpB/gsZ5cln6jvHl8adSlRJClnqjff9BcvlL5eo5Ybuk7xPk4lSgbKxN16dXE9XUacW08Sjzy\nWindDVN+2hDtQLY+5EFmdiARjHmL0iPgLR03iEDDXy2+dGwRadYyUf5XIm5CPEDckFiFpm1BtXSr\nfXYdsdTQZUQZmkXjgMQ6RP3+XCprDUQ9Wu1z/kR8ifNU4vp7Kve3amVlI4svcc63r9emz16ZuD6f\nJtrqqcSTR+ul/7/paUkLd3/GzH5O1M8diXK2rcfSDhCD2VvToPPuXB7+SKzDfwilerC1/kIEAP6T\n8vprIlCW78SuT/RDNiLalbnEl7S1yR+TVI/9gzj+h6SXD6C0NFOnVN5WIGb5HkPUg9sQS9QtIIJZ\nm6Y2pQtgHmteT0r52iMdxyzI2Npr/nyaHrtORD3zlXQcshm62xBtf0+i3/EWMYjPApGnps+aQZT3\n7pTW+7yKCPYNoWl5acj/7+7Ppnr2+bTf1drB8nS2zF23nxDnA+KGzHUWMwvvJo7nVKL+nkss/1Je\n9htyv6+XS3cepfqoWvl6lrhRMpko7x9X2s8yp1O5r9ecOiLAkf18occXlP+eKF8fpvzOA7q4+2Qz\nezwdm0+Ivno2A7c8T8cS1/sJpC+Xa+H15s5pA3FsxgLbW6yZmv39dmJQfXbKZ3ajaSRRF+xL3BB4\nOr32j1y65xDBkA6Untz8mOgnzKxyzHoSS7Zcl/ptWZ/kXeK6mkPUS7OIYP7PKK2rfhtxg+Aji++d\ngTjGPybaltWIcjCNeNozqyvOtljyrY4Iiq9K6TuNgFimxszmpABBA/G9FU8RbfoPKS1V8zdiWZhT\nc+992uJLZb9tZnsRfYPXiKDYJKKeOpVSUGEi0U8/n7ipmc3Yzc7JvcARqa53oj6GCI7eDLxoZguJ\na+dwoh84OvWxP6N0g2tbYsLHZKKd+y5xHTZK193ftviSzvHEJJ4XKE1y+jEx/niGCEqNJspI5j3i\nuv8RpSUt7iLaq+zG5ZoAqU5pIK79zGtEOdudqOcXEE8rj17SPHl88edhwCUWwfaFRP/lBKKP9Acz\nO5KoH8pnRmdWJZYkmJM+b+xSHqNziMkq9+XSnki0D+un/Z5BXDf1RL2+NVEPrU6UlWlEn+CHRLuU\n1fPX0nScf4OZzUuf+SARsMTdn0/17mlE3/rKdExuJ8Y4fyTG4pOIcjsVeMvd/5KCUhMsZg6vTgQH\nPyLapz09vjSzymFs5Fhi3NCNGD++nurztkRZycr92UT5HpbK7O+IQGSX9Pvpabts+/VTvrL6/UZ3\nf8TMjieWfJmcjtmR7r7AzL5FlI0V0mdfRFw73yfGi/XEmL2S1Ylrp01679uUljqaSdQ3KwL3peNy\nHHH99SJuUK5L6YuPy9uhfFu3WD6GkY5dD6JP9wMiGP1bIr5wKdF3uZwoL93IBTDd/QGLG2unEeOA\nw4Fv58rG/Wm/5hM3Nt6olJ8WtLZdOpsoh6sS5+09oh48O7WP1xJPBnQnAurPlqWzH6WnFjN3EO1t\noy+5zO33k6mcziQC1Pn6tQMRiP7AS0+lVXOulW4iP5T6SVOJ8e6zZjaf6Lf9MW3zV6K9Wvy9IK3s\nW7UUr/s1TeMb0DSO92d3n0jMvt+cUl1zYoqf5CczNje+aI38eW5PLMuyOtFGTScm70EsYXeZRZD6\nFcrKSSrzhxNPYM0izs1XiWtvBaJOf5m4gfopcU29Q+MbB1lazV3zrRnPlTuE+M7JM4hrZd9mytj0\n6slAXUPDkl5fIl8uFkHxRe6+KFVgf/RYMuRLw8yOIDqHI73sW6NFROS/Uwo4bAbsXHbTWEREqrB4\nyul4d680+WWZMbOuHktqtSUCV1d54+XMvvR5Wt7yUwSLL+Xe1N2PbXFjERGpmWa0i7RsbWIWWjbD\nqsk3cv+3c/fLiLvpIiLyJeHuJy/rPIiISGF+bWY7EDOi719OAsjLW56Wt/yIiMgXjGa0i4iIiIiI\niIiIiIjUQF+GKiIiIiIiIiIiIiJSAwXaRURERERERERERERqoEC7iIiIiIiIiIiIiEgNFGgXERER\nEREREREREamBAu0iIiIiIiIiIiIiIjVQoF1EREREREREREREpAbtlnUGvkzq6uoaikrrueeeY5NN\nNqk5nTFjxhSQGxg4cCBPP/10zem0bdu2gNyETTbZhOeee67mdIrM08Ybb8zUqVMLS69WReZn/vz5\nhaTz31yW6urqCshN6NevH1OmTKk5nfbt2xeQG9hoo4144YUXCkmrqLJU1Hkr0vKWp+UtP1BsnhYt\nWlRIOkXVS0XVAQMGDOCZZ54pJK2OHTsWkk7fvn15/vnnC0lr7ty5haSzvJ03KO7cFdXGFdWWQHHX\nW5HluyhF5WnBggUF5AY23XRTJk6cWEhaRfUDijxvCxcuLCSdwYMHM2nSpELSKqquLOqaq6+vLyA3\n0L9/f5599tlC0lre2twiFZmnIspSkWO4oq63IstSQ0MxYZMi66VOnToVkk6RY6Yi+ktFHqOi+m9D\nhw5lwoQJhaTVpUuXQtIpcnxSRF9g0KBBTJ48uYDcQLt2xYSFi6wD2rQpZk54kf3cYcOGtXpAoBnt\nX1D9+vVb1llopKgKrEjLY546d+68rLPQyPKWH1g+z5vy1DKVpdZZ3vK0vOUHlKfWWN7yA6oDWmt5\ny9Pylh9Qnlqja9euyzoLTSxvxwh0nFpjecsPLJ/nbXnLk9rc1lke87S8nbvl8Rh169ZtWWehieXt\nOC1vdRIsf8cIll2eFGgXEREREREREREREamBAu0iIiIiIiIiIiIiIjVQoF1EREREREREREREpAYK\ntIuIiIiIiIiIiIiI1ECBdhERERERERERERGRGijQLiIiIiIiIiIiIiJSAwXaRURERERERERERERq\noEC7iIiIiIiIiIiIiEgNFGgXEREREREREREREamBAu0iIiIiIiIiIiIiIjVQoF1ERERERERERERE\npAYKtIuIiIiIiIiIiIiI1ECB9iVkZjOrvH6Nme39eedHRERERERERERERJYtBdqXXMOyzoCIiIiI\niIiIiIiILD/aLesMfJGZ2aXA9sAbwIJlnB0RERERERERERERWQY0o30ppWVi+rh7X+C7wBbLOEsi\nIiIiIiIiIiIisgzUNTRoJZQlYWYz3L2HmV0IPOPu16bXbwNudPfbq713ypQpDf369fuccioiIiIi\nIiIiIiIiS2P8+PEMGzasrrXba+mYz9Emm2xSWFoNDQ3U1bX6PFc1ZsyYAnIDW2yxBU888UTN6bRt\n27aA3ITNNtuMcePG1ZxOkXkaMmQITz31VGHp1arI/MyfP7+QdP6by1IR12xm2LBhjB8/vuZ02rdv\nX0BuYNCgQUyePLmQtIoqS0WdtyItb3la3vIDxeZp0aJFhaRTVL1UVB0wfPhwnnzyyULS6tixYyHp\nDB48mEmTJhWS1ty5cwtJZ3k7b1DcuSuqjSuqLYHirrciy3dRisrTggXFrDQ5cuRIRo8eXUhaRfUD\nijxvCxcuLCSdrbbaiscee6yQtIqqK4u65urr6wvIDWy++eaMHTu2kLSKqgNGjBhR2Bi1KEXmqYiy\nVOQYrqjrrciyVNRk0CLrpU6dOhWSTpFjpiL6S0Ueo6L6b9tuuy0PP/xwIWl16dKlkHSKHJ8U0RfY\ncsstefzxxwvIDbRrV0xYuMg6oE2bYhZfKbKfuyS0dMySy0Zbo4H9zayNma0ObLsM8yQiIiIiIiIi\nIiIiy4gC7UuuAcDd7wBeBqYC1wK1T5kSERERERERERERkS8cLR2zhNy9R+7nY5ZlXkRERERERERE\nRERk2dOMdhERERERERERERGRGijQLiIiIiIiIiIiIiJSAwXaRURERERERERERERqoEC7iIiIiIiI\niIiIiEgNFGgXEREREREREREREamBAu0iIiIiIiIiIiIiIjVQoF1EREREREREREREpAYKtIuIiIiI\niIiIiIiI1ECBdhERERERERERERGRGijQLiIiIiIiIiIiIiJSAwXaRURERERERERERERqoEC7iIiI\niIiIiIiIiEgNFGgXEREREREREREREalBu2WdgS+TMWPGLHfpjRgxooCcQENDQyFpzZ49u4DclPTv\n37/mNN56660CclKy4oor1pzG22+/XUBOQlHHvEePHoWkA9ClS5ea05g5c2YBOSmZP39+zWk0NDQU\nkJOSuXPn1pxGEfuVmTVrViHpFFmWOnfuXHMaRZ+3Tp061ZxG165dC8hJ6NWrVyHpdOvWrZB0AHr3\n7l1IOm3aFDefYIMNNqg5jeuvv76AnMDw4cML61MMHTq0kHSguHp3wYIFhaQDxbRxRV5vRamvr1/u\n0nrvvfcKSafItIrq4wwfPpxp06bVnE6fPn0KyE0oon2D4sYnw4cPZ9y4cYWkNXjw4ELSgeLa8Pbt\n2xeSTlFpvf/++wXkJHz66aeFpLPKKqsUkg4UV76LSgdgpZVWKiSdGTNmFJLOokWLCkmnrq6ukHSK\nTKvIPBXVFyxyPFBUWu3aFRPOKyqdjh07FpJO0Wktb4pqT4pKZ3m83oqIB/3/SKu1NKNdRERERERE\nRERERKQGCrSLiIiIiIiIiIiIiNRAgXYRERERERERERERkRoo0C4iIiIiIiIiIiIiUgMF2kVERERE\nREREREREaqBAu4iIiIiIiIiIiIhIDRRoFxERERERERERERGpgQLtIiIiIiIiIiIiIiI1UKBdRERE\nRERERERERKQGCrSLiIiIiIiIiIiIiNRAgXYRERERERERERERkRoo0C4iIiIiIiIiIiIiUgMF2kVE\nREREREREREREatDu8/gQM6sHbnD3Q9LvbYF3gSfdfQ8zWxW4ClgLaA9Mc/fdzawOuAjYDmgA5gD7\nuftrzXzWNcBd7n57hb8NA84FVgVmAxOBY4H9gSHufkxR+ywiIiIiIiIiIiIiXw6fS6AdmAX0M7OO\n7j4P2BF4I/f3M4D73f0SADPrl17fH1jd3TdJr6+R0lpiKZh/KxGoH59e2xvonjZpWJp0RURERERE\nREREROTL7fMKtAPcA+wG3A4cCPwF2Cr9bXXgvmxDd5+Se/2d3OtvZz+b2Ux3755+3gfY3d0PTX/e\n0dXDnOcAACAASURBVMxOIoLoP3X3e4CjgWuzIHtK7/b0fnLp7g78kphZ/yFwsLtPN7ORwMVEQL4B\nGJnSvyX93w440t3HLOXxEREREREREREREZEvoM9rjfYG4GbgQDPrCPQHxuX+Pgq42sweMrOTzWz1\n9PqtwB5mNsnMzjOzgWVpln9Gpre7DwV2By43sw5AP2KpmJY85u6bu/umRBD9Z+n1E4Cj3H0wcYNg\nLnAQcG96bQDwdCvSFxEREREREREREZH/Ip/bl6GmWerrELPZ7wbqcn+7H1gX+DOwETDJzHq5+1vA\nhsBJQD3woJltm95WR3W3pnRfBv4D9F2CrK5lZveZ2bNEcH3j9PoY4EIzOwbo6e6LgAnAoWb2K6C/\nuy/VsjYiIiIiIiIiIiIi8sVV19Dw/39pcjOb4e49zOxU4stHtwFWBo539z0qbH8XcLW731H2+vHA\n2u7+4yzN9PrBwPbu/v30ZaiPuPt16W+PAj8CvgXg7qdV+LzvApu6+7Fm9jBwnrvfbWZbA6e5+3Zp\nu42J5W+OAnZy9xfNbLX02o+A8939hmrHYfbs2Q1dunRp/YETERERERERERERkc/dlClT6NevX3OT\nvRv5vNZozzJ0NfCxu09NQWwA0iz1se4+x8y6A+sDr5vZIOBdd3/HzNoQS85ky7O8a7G4+kvAN4EZ\nuc/b18yuB9YjZso7sTzNODP7h7tPSJ/7TeDxsrz2ALK14L+by+N67j4VmGpmQ4GNzGwu8Ka7X2Vm\nnYDBQNVA+9NPF7eyzBZbbMETTzxRczojRowoIDfQ0NBAXV2ry11Vs2fPLiA3oXPnzsyZM6fmdN56\n660CchM22GADXn755ZrTefvtt1veqBVGjhzJ6NGjC0mrR48ehaQzcODAQq6VmTNnFpCbsNVWW/HY\nY4/VnE6RNzaLOndt2hTzYNOWW27J44+XV6dLp6iy1L9/f5599tma0ynyvA0YMIBnnnmm5nS6du1a\nQG6Kq5MAunXrVkg6q622Gu+++24haRVVvldddVXef//9mtO5/vrrC8gNnHDCCZx33nmFpDV06NBC\n0tl666159NFHC0lrwYIFhaSzww478OCDD9acTlHXG8Dw4cN58skna06niD4XwOabb87YsWMLSauo\n63avvfbi73//eyFpFdWvPOigg7jppptqTqdPnz4F5Cau2wkTJhSS1pgxxXy91HHHHcdFF11USFqD\nBw8uJJ0i+7ndu3cvJJ1BgwYxefLkmtMpok0C2Hnnnbnvvvta3rAVVllllULSGTx4MJMmTSokrc6d\nOxeSTt++fXn++ecLSWvGjBktb9SCzTbbjHHjxrW84efovz1P7du3LySdIsv3okWLak6jyPakqP5b\nUbEugLZt2xaSzvJWvovMT1F9ymHDhjF+/PiWN2yFoiYo9+vXjylTprS8YcE+r0B7A0BaCubSCn/f\nFLjUzBYQy9lc4e4TzWxn4M9pjXWA8UTAHGI5mbuB94GngPwI//W0bXfgcHefD7xvZgcA55vZKsRS\nNKOBf5bl5XTgb2b2EfAvYrkbgOPSDYF6YEp634HAiSnfM4FDluioiIiIiIiIiIiIiMgX3ucSaM+W\neCl77VHg0fTzeUCTqVnufh9Q8Ra7u98G3Fbh9UObycc4YGSFP12X/uHudwJ3VnjvsRXed336JyIi\nIiIiIiIiIiJfUp/bl6GKiIiIiIiIiIiIiPw3UqBdRERERERERERERKQGCrSLiIiIiIiIiIiIiNRA\ngXYRERERERERERERkRoo0C4iIiIiIiIiIiIiUgMF2kVEREREREREREREaqBAu4iIiIiIiIiIiIhI\nDRRoFxERERERERERERGpgQLtIiIiIiIiIiIiIiI1UKBdRERERERERERERKQGCrSLiIiIiIiIiIiI\niNRAgXYRERERERERERERkRoo0C4iIiIiIiIiIiIiUgMF2kVEREREREREREREatBuWWfgy6Rt27bL\nXXqzZ88uICfFpdWlS5cCchIaGhoKSe/EE08sIDfhnHPO4Yorrqg5nXXXXbeA3MDIkSOZOnVqIWkN\nHz68kHSK8vHHHy936XXo0KGAnJQUcc1Nnz69gJzAlltuybRp0wpJa+7cuYWk079/f8aNG1dzOn36\n9CkgNyVFlKWijvUGG2zAlClTCklr4sSJhaRz5plnMmrUqELSmjlzZiHpXHTRRfzmN7+pOZ3ddtut\ngNyEAQMGFJJOXV1dIekUmdbDDz9cSDo77LBDIWmNGDGigNyUFFEH9OrVq4CchKLO24wZMwpJp8i0\n1l577ULSAVhjjTVqTmP8+PEF5ASGDh1aWFpF9t+KSuv+++8vJJ2RI0fy6KOPFpJWz549C0ln0KBB\njBkzpuZ0+vbtW0BuQrt2xYQERo8eXUg6gwcPLiytWbNmFZLOKaecwu23315IWkOGDCkknU8++aSQ\ndIrqK2222Wa88cYbhaRVRH2bWbRoUSHpfPbZZ4WkA8WNU9u3b19IOnPmzCkknVdeeaWQdLbYYgte\nfPHFQtIys0LSAaivry8knYaGhkLSKapsF2nhwoWFpHPHHXcUkk6/fv0KTau1NKNdRERERERERERE\nRKQGCrSLiIiIiIiIiIiIiNRAgXYRERERERERERERkRoo0C4iIiIiIiIiIiIiUgMF2kVERERERERE\nREREaqBAu4iIiIiIiIiIiIhIDRRoFxERERERERERERGpgQLtIiIiIiIiIiIiIiI1UKBdRERERERE\nRERERKQGCrSLiIiIiIiIiIiIiNRAgXYRERERERERERERkRoo0C4iIiIiIiIiIiIiUgMF2kVERERE\nREREREREatDu8/gQM5vp7t1bue2egLv7C+n3a4CtgU/SJle7+6UF5GlrYL67P1lrWiIiIiIiIiIi\nIiLy5fW5BNqBhiXYdi/gH8ALudeOd/c7qr3BzNq4e/0S5mkb4DNAgXYRERERERERERERWWqfV6C9\nCTPrDVwNrAy8DxwKrAXsAYw0s1OAfdLmTZa4MbOZwOXA9sDRZtYZOBdoC0wAjnT3BWY2DbgO+Aax\nv/sC84AjgIVmdjBwDNAT+CXQHvgQONjdp5vZysBNwOrAWGBHYLC7f5Tee2x6zzjgKHdfkpsKIiIi\nIiIiIiIiIvIFtyzXaL8EuMbdBxCB7EvSMi53Aie6+2B3n5a2PcfMJpvZJDPbOL3WFXjS3f8fe3ce\nJlV5rX//bobGZmhRnJAgipoFIggygwxxCEYRTKKiIGpMYjSImhMxXi8xYtCYKBoVOUT04IADqMcj\noEYTUQFBkckB0BUjDjgjyjxDvX/U5ti/Pg3d+Cyhke/nurjcteupe6+urq7aterxqVaSZku6W9Lp\nWV51SReVONbn7t5a0t8kXe7u72fbf82OM03SVHfvkI0bJ+mK7LZXS5rk7s0lPar8hwEysyaS+kjq\n5O5HS9osqV/wfQQAAAAAAAAAqOR22ox2SR0l/TjbHiPpL9sYO8jdHyu1b6OkLftM0kJ3fye7fK+k\nX0u6Lbu8ZdmZ2SWOWVpDM3tY+Znr1SVtafIfo/xyNnL3Z8zsq2z/cZKOljTTzAok7SHps238DAAA\nAAAAAACA76CCXO7bX+nEzJa7e3GpfZ9Lqu/um8ysmqSP3X2/7MtPJ25prJe+XFammbVQfkZ8t+zy\nscov43JatnRM62ypl9aSbnT3Y83sakkr3P3m7DbPSxrm7k9mX5R6dTZurqRTs1nwMrMlkg6X1Der\nf3BF74fVq1fnatasuZ33HgAAAAAAAABgRxo6dKiuuuqqgoqO31Ez2ssqaLqksyTdL+lsSVOz/Ssk\nFZcxfluZLqmRmTV294WS+kt6oZzblz5OsaSPs+1zS+yfpvwSMTeY2Q8l1c32T5L0uJndkq3lvpek\nOu7+wdYO+MYbb5RTUsW1b99eM2bMSM5p0aJFQDVSUVGR1qxZk5wT+UFELpdTQUGF/xa2atCgQQHV\n5N1www264ooryh9YjkMOOSSgGumiiy7SyJEjQ7I6duwYktOyZUu9+uqryTkffLDVP8Xt1qtXL02Y\nMCE5p7CwMKCavBNPPFFPP/10cs7ixYsDqpH69++vMWPGhGStXbs2JOeXv/yl7rzzzuScww8/PKCa\nvO7du+uFF15Izlm6dGl6MZJOPfVUPf744yFZs2fPDsnJTmRCslasWBGSc8stt+iyyy5Lzjn55JMD\nqpFOOOEE/fOf/wzJqlGjRkhO165dNWXKlJCsZ555JiTnuuuu0+DBFZ4PsVWdO3cOqCbvpJNO0lNP\nPZWcU69evYBq4s4nJcndQ3LOOecc3XfffSFZBx10UEhO1HP3/Pnz04uRNGDAAI0YMSIkq02bNiE5\nkY+lf/zjHyE5V111lYYOHRqStddee4XkXHzxxbr99tuTc5o2bRpQjXTcccdp0qRJIVlR73Uvu+wy\n3XLLLSFZq1atCskZPHiwrrvuupCsiL+5Hj16hL1WRp0rnXbaaXr00UdDsg488MCQnE6dOmn69Okh\nWRG9Din2b6569erJGZHnbwsXLgzJOe+883TPPfeEZJlZSE7Hjh310ksvhWRFTHaOfGxHiawp6m8k\n8jxge+yoRnuRmX2gfHM8J+lm5b+A9B4zu1zSYuW/DFWSxkq608wGSjotG1+W/93v7uvM7GeSHjWz\nLV+GekfpcaVMzMb3ymoZkl3+UtJzkg7Oxl0j6UEzO1vSS5I+VX4m/Jdm9ntJ/zCzKpLWSxogKa67\nBwAAAAAAAACo9HZIo93dt3ac48oYO11SsxK7zt9KZnGpy88rv2Z66XGNS2zPlnRstv22pKNKDZ9Y\nxqGWSToxW+Kmg6S27r4hy3hE0iNl1QcAAAAAAAAA2D3szC9D3VUcJOnhbNb6Okm/3Mn1AAAAAAAA\nAAAqERrt5XD3f6uMmfIAAAAAAAAAAEhSlZ1dAAAAAAAAAAAAuzIa7QAAAAAAAAAAJKDRDgAAAAAA\nAABAAhrtAAAAAAAAAAAkoNEOAAAAAAAAAEACGu0AAAAAAAAAACSg0Q4AAAAAAAAAQAIa7QAAAAAA\nAAAAJKDRDgAAAAAAAABAAhrtAAAAAAAAAAAkoNEOAAAAAAAAAECCaju7gN1J1apVK13eRx99FFCJ\ndNhhh4VkDRo0KKCa2Lwbb7wxoJK8G264ISTvySefDKgmr1GjRiE569atC8mJyqpXr15AJd9eXoQ6\ndeokZ2zevDmgkryo++jTTz8NyZFinidXrlwZUEls3gEHHBBQSWxWZaypbt26ITmS1LBhw+SM6tWr\nB1QSm1UZazrwwANDcqKyVq1aFVBJbF7NmjUDKslbs2ZNSM6ee+4ZkhOZVdke3xHPI9FZBQUFITmR\nWQcffHBITmTW0qVLQ3IkKZfLJWcUFxcHVBKb1aBBg5CcyKwNGzaE5EjSIYccEpLz5ZdfVqqcvffe\nOyRHinlvIknVqsW1qaKyatSoEZITmbVp06aQnIjnJOm7/xwQlVVYWBiSU6VKzLzpyPOAqJ5n5PNS\nZFZFMaMdAAAAAAAAAIAENNoBAAAAAAAAAEhAox0AAAAAAAAAgAQ02gEAAAAAAAAASECjHQAAAAAA\nAACABDTaAQAAAAAAAABIQKMdAAAAAAAAAIAENNoBAAAAAAAAAEhAox0AAAAAAAAAgAQ02gEAAAAA\nAAAASECjHQAAAAAAAACABDTaAQAAAAAAAABIQKMdAAAAAAAAAIAENNoBAAAAAAAAAEiwSzfazWzF\ndoztbWZNSu2ramafm9mf4qsDAAAAAAAAAOwOdulGu6Tcdow9VVKzUvtOkPQvSadv7UZmtqvfRwAA\nAAAAAACAb1G1nV1ANDNrJGm0pH0kfS7pZ5IaSuolqauZDZb0U3d/V9JZkm6RdJGZdXD3l7OMdyWN\nk3S8pBvMbJakEVnmakm/dPd/mVlPSb+XVF3SEkn93H3xjvtpAQAAAAAAAAA723dxtvZwSXe7+1GS\nHpQ03N1fkjRB0iB3P9rd3zWzGpKOkzRR0kOS+pbK+cLd27j7w5JGSbrY3dtKGiRpZDZmqrt3cPfW\nyjfmf/et/3QAAAAAAAAAgEqlIJfbntVXKhczW+7uxaX2LZZ0gLtvMrNqkj529/3M7G5JE939sWzc\nTyWd6u79zayepLmSGrl7LpvR3tXdF5lZLUmLJb0lqSA7THV3P9LMjpR0k6T6ys9qf9fdT9pavWvW\nrMkVFRWF3gcAAAAAAAAAgFgjRozQgAEDCsofmfedWzpGFV+3/SxJnc1sofIN9L0lHStpUnb9quy/\nVSR95e5Hl5ExXNIwd3/SzLpJunpbB5w/f34FSytfmzZtNGvWrOScunXrBlQjHXbYYfr3v/+dnDNq\n1KiAavJuuOEGXXHFFck5N954Y0A1eblcTgUFFf773Konn3wyoBrppJNO0lNPPRWSVa9evZCc9u3b\na8aMGck5GzduDKgmr3Pnzpo2bVpYXoSompYtWxZQTexj6dNPPw3JOf/88zV69OjknP322y+gmrye\nPXvqiSeeSM7ZZ599AqqROnTooJdffjkka/bs2SE5AwYM0IgRI0Ky1q5dG5Lz29/+VjfddFNyTuvW\nrQOqkbp3764XXnghJKtGjRohOR07dtRLL70UkjVnzpyQnKjHUuRzwOmnn65HHnkkOWffffcNqCb2\nsRT1etK7d2+NHz8+JCvquTLqNXfJkiUB1Ui9evXShAkTQrIOOOCAkJx27drplVdeCcly95Cc/v37\na8yYMSFZS5cuDckZOHCghg8fnpzToUOHgGqktm3baubMmSFZ7733XkhO1POkJG3YsCEkp2/fvnrw\nwQdDsiLeC5511ll66KGHAqqR9t5775CcHj166JlnngnJ2muvvUJyIp+X1q9fH5JzzDHH6MUXXwzJ\n2rRpU3JGt27dNHny5IBq4u6jE044Qf/85z9DsqLOc7t27aopU6aEZBUWFiZnRL6Hi3hOkuL6OJJC\nep1S7PvK7bGrLx1T1iNiuvJNdEk6W9LUbHuFpGJJMrNiSV0kNXT3xu5+iKQB+r/Lx8jdV0h618xO\n27LPzFpkm8WSPs62z037UQAAAAAAAAAAu6JdfUZ7kZl9oHzDPSfpZkkDJd1jZpcrv+TLz7KxYyXd\naWYDJT0uaZK7l5zyOkH5Lz4t1P+dFd9P0t/M7PfK32djJb0u6RpJj5rZl5Kek3Rw/I8IAAAAAAAA\nAKjMdulGu7tvrf7jyhg7XVKzbWR9JWn/7GLjUte9L+lHZdxmgvINegAAAAAAAADAbmpXXzoGAAAA\nAAAAAICdikY7AAAAAAAAAAAJaLQDAAAAAAAAAJCARjsAAAAAAAAAAAlotAMAAAAAAAAAkIBGOwAA\nAAAAAAAACWi0AwAAAAAAAACQgEY7AAAAAAAAAAAJaLQDAAAAAAAAAJCARjsAAAAAAAAAAAlotAMA\nAAAAAAAAkIBGOwAAAAAAAAAACWi0AwAAAAAAAACQoNrOLgA718cffxySc9hhh4VkHXLIIQHVxOY9\n+eSTAZXE5p188skBlUi5XC4sa968eSE5klS7du3kjOuvvz6gkrzOnTtr5MiRyTlVq1YNqCavc+fO\nGjVqVHJO/fr1A6qRTjrpJE2ZMiUkq3HjxiE5krRx48bkjO9973sBlcTmPfvsswGVSB06dNCLL74Y\nkrVgwYKQHEmaPXt2SE6tWrVCciTpvffeS84oKChIL0RS9+7dNWfOnJCsrl27huRIUvXq1UNypk6d\nGpIzYMCAkKyzzz47oJqvFRUVJWcUFxcHVBKbdffdd4fk9O7dW4899lhIVps2bUJyOnfuHPI3d+ih\nhwZUk1etWszbuP333z8kJzLr0UcfDcmRpDfeeCMkp7CwMCRHkj777LPkjBEjRgRUIt1zzz1hWWvW\nrAnJOf3008MeA1G/t759++rvf/97SFaXLl1CclasWBGS89FHH4Xk9OjRI+zvrWfPniE5Utxr3OLF\ni0NypPx78AibNm2qVDmR73WjsmrWrBmSE5m1bNmykJxVq1aF5ESeU1apEjOXO+p1acCAAaFZFcWM\ndgAAAAAAAAAAEtBoBwAAAAAAAAAgAY12AAAAAAAAAAAS0GgHAAAAAAAAACABjXYAAAAAAAAAABLQ\naAcAAAAAAAAAIAGNdgAAAAAAAAAAEtBoBwAAAAAAAAAgAY12AAAAAAAAAAAS0GgHAAAAAAAAACAB\njXYAAAAAAAAAABLQaAcAAAAAAAAAIAGNdgAAAAAAAAAAElTbkQczswaSRkg6QlKBpCckDXL3jd/i\nMVe4ex0zayTpCXdvnu0/RtJNkoqzobe5+8jU46RXDAAAAAAAAADYlezoGe2PSXrM3b8v6fuS6kj6\nU0qgmVUtZ0iu9LaZHSDpAUkXuHtTSZ0l/dzMeieUkit/CAAAAAAAAADgu2aHzWg3s2MlrXH3+yTJ\n3XNm9htJ75pZV0k/c/c3s7HPS/qtpLckDZfUTFJ1SUPcfaKZnSvpJ5JqS6piZj0ljZdUNxt3lbtP\n2EY5v5Z0t7u/ltXypZldIWmopPFmdrekie7+WFbPllnxtbbzOAAAAAAAAACA77gdOaO9maTZJXe4\n+wpJH0h6UlIf6X9nmx/g7nMkDZY0yd07SDpW0jAzK8pu3krST9z9B5LWSDrV3dtk427a3lokzZLU\ndCvjt8xWX7udxwEAAAAAAAAAfMdVli9DfUHST7PtMyQ9mm3/UNKVZjY3G1Mo6aDsun+6+7Jsu4qk\n683sNUnPSjrQzPb7Fuos2EHHAQAAAAAAAADsIgpyuR2ztLiZHSfpD+7ercS+YknvSGoo6WlJAyX9\nTdKv3H2emc2U1Nfd3y6Vda6k1u5+SYnLJ0rq5+6bzexdSd3c/QMzW+7uxdmXoU509xZmNlTSZne/\nukTmsZKudPcfmtmdkp5x90fNrED5JW/2qMhxtnUfrFmzJldUVLStIQAAAAAAAACAneyII47QggUL\nCio6foet0e7uk8zsejM7293vz77EdJjya6WvNbOHJV0hqdjd52U3e0bSJco34GVmLd391TLi95T0\nedb8/oGkRiWuKyhje4Skl83sMXd/zczqSbo2O74kvSepjfIz63srvx779hynTPPnzy9vSIW1adNG\ns2bNSs5ZvXp1QDVS165dNWXKlOScyPvooosu0siRI5NzGjVqVP6gCjrppJP01FNPJeecfPLJAdVI\nuVxOBQUVfr7Ypnnz5pU/qAKaNWsW8ji4/vrrA6rJu//++3X22Wcn51StWt53N1fcvffeq3PPPTc5\np379+gHVSH/+85915ZVXhmQ1btw4JOeCCy7QqFGjknPatWsXUE1ey5Yt9eqrZb2MbZ9nn302oBrp\n8ssv17Bhw0KyFixYEJIzevRonX/++SFZtWrVCskZPny4Bg4cmJxzyCGHBFQj/cd//IduvvnmkKyu\nXbuG5ESdl0gKe0yOHTtWZ555ZnJOxPP/Fj179tQTTzyRnHPggQcGVCMdffTRmjNnTkjWrbfeGpIT\n9fom5R+XEQYOHKjhw4cn5xx66KEB1cSdT0r5864IjRo10vvvvx+SNWLEiJCcG264QVdccUX5Ayug\nsLAwJOfaa6/V73//++ScDz/8MKAa6Z577tF5550XkrVmzZqQnHHjxqlPnz4hWVG/tzFjxqh///4h\nWV26dEnOiDrHlaTly5eH5ESeU/bs2TMkp0mTJnrrrbdCshYvXhyS06VLF02dOjUka8OGDckZxx57\nrJ577rmAauJE1lRcvM25sBUWeZ67bNmy8geV47jjjtOkSZMCqom7j9q2bauZM2eGZEWdBy5YsEBH\nHHFESNb22NFLx/xY0hlm9i/lv+h0jfLrsEv5pnYfSeNKjL9WUnUze93M5kn641ZyH5DUNlvS5WxJ\nb5a4Lld6290/zcaNMrO3JH0o6VZ3fzEbd6ekbtmSNR0krdrO4wAAAAAAAAAAdhM7bEa7JLn7R5J6\nbeW6z5Vfg73kvrWSLixj7L2S7i1xeYmkTlvJLc7++76kFiX2vyipvSSZ2YWS/j8ze9rdl2W1dCwR\nc2VFjwMAAAAAAAAA2L3s0EZ7ZeXuf1N+bXgAAAAAAAAAALbLjl46BgAAAAAAAACA7xQa7QAAAAAA\nAAAAJKDRDgAAAAAAAABAAhrtAAAAAAAAAAAkoNEOAAAAAAAAAEACGu0AAAAAAAAAACSg0Q4AAAAA\nAAAAQAIa7QAAAAAAAAAAJKDRDgAAAAAAAABAAhrtAAAAAAAAAAAkoNEOAAAAAAAAAEACGu0AAAAA\nAAAAACSg0Q4AAAAAAAAAQIJqO7uA3cn69esrXV5xcXFAJXFZHTt2DKgkNm/dunUBlXytXr16yRnz\n5s0LqCQ268gjjwzJyeVyIVmrVq0KqOZro0aNSs6YPn16QCVf69+/f3JGo0aNAirJ+/nPfx6Ss3Ll\nypAcSWrbtm1yxvLlywMqic3r3bt3QCWxWaeddlpIjiT94Q9/CMnZuHFjSI4kXXrppckZn3zySUAl\neRGPbUlas2ZNSE5k1uDBg0NyorI2bdoUUMnXvve97yVnLFq0KKAS6eijj9ZHH30UknXttdeG5ERm\nLVmyJCRHkrp06ZKcEXlusueee4bkRL7mRmX17ds3JCcya8OGDSE5UszrrpkFVJJ32223heQsXbo0\nJEeSbrzxxpCcyPOAa665JiTn888/D8lp0aJFSE61anEtoe7du4fkRL0uNWnSJCyrsLAwJCdSQUFB\npcopKioKyZGkmjVrhuQsW7YsJCcyq1atWpUqZ/Xq1SE5kVnjxo0LyYnOqihmtAMAAAAAAAAAkIBG\nOwAAAAAAAAAACWi0AwAAAAAAAACQgEY7AAAAAAAAAAAJaLQDAAAAAAAAAJCARjsAAAAAAAAAAAlo\ntAMAAAAAAAAAkIBGOwAAAAAAAAAACWi0AwAAAAAAAACQgEY7AAAAAAAAAAAJaLQDAAAAAAAAAJCA\nRjsAAAAAAAAAAAlotAMAAAAAAAAAkKDat30AM2sgaYSkIyQVSHpC0iB33/gtHnOFu9cxs0aSSVld\nNAAAIABJREFUnnD35tn+dpJulLSfpNWSZku6xN3XJh7vakkr3P3mxNIBAAAAAAAAALuYHTGj/TFJ\nj7n79yV9X1IdSX9KCTSzquUMyZXeNrP9JT2sfJO/qbu3lvR0Vg8AAAAAAAAAAN/Itzqj3cyOlbTG\n3e+TJHfPmdlvJL1rZl0l/czd38zGPi/pt5LekjRcUjNJ1SUNcfeJZnaupJ9Iqi2pipn1lDReUt1s\n3FXuPmEb5fxa0j3u/sqWHe7+WHbsvSSNltRY0ipJF7j7vGym+kHZ/oaSbnX34dltBks6R9Jnkj6U\nNCvt3gIAAAAAAAAA7Iq+7RntzZRfnuV/ufsKSR9IelJSH0kyswMkHeDucyQNljTJ3TtIOlbSMDMr\nym7eStJP3P0HktZIOtXd22TjbiqnliNL11LCNZLmuPtR2fHHlLjOJJ0gqb2kq82sqpm1lnSGpBaS\nTpbUtpxjAwAAAAAAAAC+o3bml6G+IOmn2fYZkh7Ntn8o6Uozm5uNKVR+Vrkk/dPdl2XbVSRdb2av\nSXpW0oFmtt83rOUYZc11d39e0t5mVju77kl33+juS5Sfvb5/Nv5/3H1d9sHBtmbSAwAAAAAAAAC+\nwwpyuVz5o74hMztO0h/cvVuJfcWS3lF+KZanJQ2U9DdJv8qWa5kpqa+7v10q61xJrd39khKXT5TU\nz903m9m7krq5+wdmttzdi7MvQ53o7i3M7I+Scu5+dRl1zpb0U3d/L7v8vvKz8X+rEl9yamavS+op\n6ceS9nL3Idn+myR9VN6Xoa5evTpXs2bNit+BAAAAAAAAAIAd7o033lDz5s0LKjr+W12j3d0nmdn1\nZna2u9+ffYnpMEl3u/taM3tY0hWSit19XnazZyRdonwDXmbW0t1fLSN+T0mfZ032H0hqVOK6gjK2\nb5c0w8yecPeZWfaPJU2TNFXS2ZKuNbPukr5w95VmVvqYW7KmSLrbzK5Xfsb9Kcp/WLBNr75a1o/x\nzXTq1EnTp09Pzolq/Lds2TL054sQVdO6desCqslr3769ZsyYkZxTu3bt8gdVQLNmzTR//vyQrCOP\nPDIkJ5fLqaCgws9hW7Vq1aqAavJq1qyp1atXJ+dE/M1ucfzxx+vZZ59NzmnUqFH5gyrg8MMP19tv\nv13+wApYuXJlSE6rVq00d+7c5JwVK1YEVJPXtWtXTZkyJTmnfv36AdXE/t6qV68eknPwwQfrvffe\nC8nauHFjSM5hhx2mf//738k5n3zySUA1UpcuXTR16tSQrCiRNdWtWzckp3nz5nrjjTeSczZt2hRQ\nTV7UucmiRYsCqpFOOeUUTZw4MSSrZcuWITkNGzYM+/mWLFkSkhP1e4s6N+ncubOmTZsWkhX19xZ5\nTrlhw4aQnMj3J1E1tW3bVjNnzkzOKeN96jdSXFys5cuXh2QtXbo0JOeggw7SBx98EJIVdR7QuHFj\nLVy4MCTr888/T87o0KGDXn755YBqpGrVYlpCbdq00axZMV9bt2zZsvIHVcBxxx2nSZMmhWQVFhaG\n5ESeL0U8vn/wgx/o+eefD6hGKioqKn9QBUQ+vqNedyMfS7Vq1UrOiLyPovpd3bp10+TJk0Oy9t57\n75CcqPcC22tHLB3zY0lnmNm/lP+i0zXKr4Mu5ZeL6SNpXInx10qqbmavm9k8SX/cSu4DktpmS8ec\nLenNEtflSm+7++eSzpR0k5m9aWbzlV+mZrnya7S3zrL+pPyXnJZlS9ZcSQ9Lel35teZf2cp4AAAA\nAAAAAMB33Lc6o12S3P0jSb22ct3nys8IL7lvraQLyxh7r6R7S1xeIqnTVnKLs/++r/wXlm7ZP0NS\n1zJuslb5DwRK51xT6nLJrD8p35QHAAAAAAAAAOzGduaXoQIAAAAAAAAAsMuj0Q4AAAAAAAAAQAIa\n7QAAAAAAAAAAJKDRDgAAAAAAAABAAhrtAAAAAAAAAAAkoNEOAAAAAAAAAEACGu0AAAAAAAAAACSg\n0Q4AAAAAAAAAQAIa7QAAAAAAAAAAJKDRDgAAAAAAAABAAhrtAAAAAAAAAAAkoNEOAAAAAAAAAEAC\nGu0AAAAAAAAAACSotrML2J1UrVq10uWtWLEioJK4rK+++iqgkryWLVvqgw8+SM6pV69eQDVf27hx\nY3LG9ddfH1CJdP/994dlrVq1KiQnKqtWrVoBleTlcrmQvD59+gRUk3f88cfrrrvuSs5p3bp1QDXS\noEGD9Pjjj4dk1a5dOySnVatWevnll5NzOnToEFDN1+rUqZOc8dprrwVUIh1++OFhWVE5Q4cO1X/9\n13+FZEU9f1922WV64oknknPatWsXUE1e1DlFgwYNQnIk6aCDDgrJmTx5ckhO8+bNNXfu3OScyPO3\nli1bav78+ck5TZo0Cagm78ADDwzJGTZsWEjOrbfeGpbVtGnTkJyWLVuGvJ506tQpoJq8iNcSKe41\nNzJrwYIFITktW7bUJ598EpIVdZ7btm1bvf/++8k5UeeUCxcuVMuWLUOyunfvHpIzevRoDRkyJCQr\n6v3A8OHD9de//jUk66ijjkrO6NChg+bNmxdQjVSjRo2QnDZt2ujNN98MyTrttNNCcqS4592ZM2eG\n5Ej595YR6tatW6ly1q5dG5IjVb77KDJr3bp1ITmbN28Oydljjz1CciKzbr311pCcu+66KzSropjR\nDgAAAAAAAABAAhrtAAAAAAAAAAAkoNEOAAAAAAAAAEACGu0AAAAAAAAAACSg0Q4AAAAAAAAAQAIa\n7QAAAAAAAAAAJKDRDgAAAAAAAABAAhrtAAAAAAAAAAAkoNEOAAAAAAAAAEACGu0AAAAAAAAAACSg\n0Q4AAAAAAAAAQAIa7QAAAAAAAAAAJKDRDgAAAAAAAABAAhrtAAAAAAAAAAAkqPSNdjObamYnlrh8\nupk9FZA7xswWmtlcM1tgZoMrcJtTzey32fZQM7sk2/6Zme2XWhMAAAAAAAAAYNdTbWcXUAEXSnrE\nzJ6TVCjpOkk/TAk0s6rZ5qXuPtHMakhyM7vH3T/a2u3c/fGtXHW+pDmSPk+pCwAAAAAAAACw66n0\njXZ3n29mEyRdKamWpHvd/T0zO0fSAEnVJU1394slyczukNRKUpGkce5+bbZ/kaT7lW/S/ymL3zKj\nv5akzZJWlxjbzN2Xm1l7Sde6+wlm9nNJR7r7b7bUZ2ZnSGopaayZrZHUzt03flv3BwAAAAAAAACg\ncqn0S8dk/iipr6QTJd1gZs0k/VhSR3c/WlJ1MzszG/s7d2+nfPP7h2bWpETOZ+7e2t3/O7t8s5nN\nlfS+pPvc/atsf67U8XNb2Za7PyzpVUlnuPvRNNkBAAAAAAAAYPdSkMuV7ilXTmZ2jaQV7j7MzC6V\ndLmkxZIKJO0h6X53v87MBii/lEs1SfUlXejuj2Wz1Nu5+ydZ3hhJj7j7BDOrJekFSRe5+6wyZrQP\ndfcfZjPam7n7f5jZUEmL3f02M5sqaYC7v76tn2H16tW5mjVrxt85AAAAAAAAAIAwv/jFL3TXXXcV\nVHR8pV86poTN2T8p31wf7e5XlxxgZodJukRSG3dfkTXT9ygxZFVZwe6+yswmSzpG0ixJG/X1bP89\nyrrNN/HGG29ERal9+/aaMWNGcs769esDqpG6dOmiqVOnJud89dVX5Q+qoF69emnChAnJOfXq1Quo\nJq9z586aNm1acs7IkSMDqpHuv/9+nX322SFZo0aNCsmpWbOmVq9enZxTq1atgGrycrmcCgoq/Ly6\nVX369AmoJm/s2LE688wzyx9YjtatWwdUIw0aNEg33nhjSFbt2rVDci666KKQv5UOHToEVJPXqlUr\nzZ07NznnnXfeCahGOu200/Too4+GZL322mshOUOHDtVVV10VkhX1/H3ZZZfplltuSc5p165dQDVS\np06dNH369JCsBg0ahOQ0atRI77//fkjW5MmTQ3LOOecc3Xfffck5VatWLX9QBfXr108PPPBAck6T\nJk3KH1QBrVu31uzZs0OyIu5rSbr11lt16aWXhmQ1bdo0JOfCCy/U3/72t+ScTp06BVQjtWjRQq+/\nvs35PRW25557huREPgcsWLAgJOdHP/qR/v73v4dkrVpV5tvI7Rb1unvFFVcEVCMtXLhQjRs3Dsnq\n3r17SM7o0aN1/vnnh2RFvR8YPny4Bg4cGJJ11FFHJWdkTZ+AaqQaNWqE5PTv319jxowJyTrttNNC\ncoqKirRmzZqQrJkzZ4bkdO3aVVOmTAnJqlOnTnJG1HsTSVq7dm1ITseOHfXSSy+FZBUWFobkRJ4v\nrVu3Ljkj8r1A1HluVI9Sku68886QnLvuuku/+MUvQrK2x66ydExpz0o6w8zqSZKZ7W1mDSUVS1ou\naaWZ1ZfUo5ycguz21SW1k/TvbP+7krZ0n35agXpWZMcGAAAAAAAAAOxmdslGu7vPk3SNpGfN7DVJ\nz0jaz93nSHoz+3ePpBdL3KysNXJuNrM5yq+xPtPdn8j2XyNppJnNkFSRj5vulnSXmc0xs13p/xIA\nAAAAAAAAACTaZZrC7n5NqctjJY0tY9w5W7n9QaUu99/GsSZL+n4Z+/+rxPZVJbYfkfTINsoHAAAA\nAAAAAHxH7ZIz2gEAAAAAAAAAqCxotAMAAAAAAAAAkIBGOwAAAAAAAAAACWi0AwAAAAAAAACQgEY7\nAAAAAAAAAAAJaLQDAAAAAAAAAJCARjsAAAAAAAAAAAlotAMAAAAAAAAAkIBGOwAAAAAAAAAACWi0\nAwAAAAAAAACQgEY7AAAAAAAAAAAJaLQDAAAAAAAAAJCARjsAAAAAAAAAAAmq7ewCdicFBQWVLi+X\nywVUEpdVWFgYUMm3l1dZVK1atdJlTZ8+PSTn+OOPD8nq06dPQDWxeePGjQuoJG/s2LEheb169Qqo\nJq9BgwYhObVq1QrJkaQDDzwwOaNKldjPpCPy1q9fH1BJbNbee+8dkhOZVbNmzZCcqKxPP/00oJLY\nrKj7qFGjRvrqq69Csr788suQnKisxo0bB1TytTp16iRnbNy4MaCS2Kzq1auH5ERmRdzXkVmV8fdW\nGWv64osvQnIis+rWrRuSI0k1atRIzmjevHlAJbFZ++67b0hOZFZRUVFIjiTVq1cvJKdatZgWTFTO\nunXrQnIis6L+bhs2bBiWVdn6JpK0efPmSpVTGVXG17jK9nuLvI+ingMqY79rezCjHQAAAAAAAACA\nBDTaAQAAAAAAAABIQKMdAAAAAAAAAIAENNoBAAAAAAAAAEhAox0AAAAAAAAAgAQ02gEAAAAAAAAA\nSECjHQAAAAAAAACABDTaAQAAAAAAAABIQKMdAAAAAAAAAIAENNoBAAAAAAAAAEhAox0AAAAAAAAA\ngAQ02gEAAAAAAAAASECjHQAAAAAAAACABDTaAQAAAAAAAABIUG6j3cymmtmJJS6fbmZPpR7YzMaY\n2UIzm5v965aauZ3HH2pml5S4XN3MlpjZH7dxm+PM7H+2ct0iMyv+NmoFAAAAAAAAAFReFZnRfqGk\nm82s0MxqS7pO0q9TDmpmVbPNy9y9laRBkkamZAboIWm+pD7ljMtt534AAAAAAAAAwHdYtfIGuPt8\nM5sg6UpJtSTd6+7vmdk5kgZIqi5purtfLElmdoekVpKKJI1z92uz/Ysk3S/ph5L+VOowL0k6cMsF\nM2sjaVh2vM8lnefui81sqqRXJHXN8s+VNFhSM0kPuvs12e2vkNRf+eb3KHe/Pdv/B0n9JH0m6WNJ\ni0vUcJakmyX9xszauPus7DYnS7pJ0kpJ00vUuI+kByXVlzRNUkF59yUAAAAAAAAA4Lunomu0/1FS\nX0knSrrBzJpJ+rGkju5+tKTqZnZmNvZ37t5OUktJPzSzJiVyPnP31u7+36XyfyTpcUkys0JJt0r6\nibu3lfSApGtLjF2d7R+d3eYCSS0kXWBmxWbWTvmmeWtJnST92syamVnbrObmknpKarcl0MyKJHWT\n9JSkh7Kfdcv+v0k60d3bqMSHAZKukfScuzfPblfyOgAAAAAAAADAbqIgl6vYiidmdo2kFe4+zMwu\nlXS58jPCCyTtIel+d7/OzAZIOl/52fL1JV3o7o9lM9rbufsnWd4Y5RvhG5VvUrd39wVmdpSkyZIW\nZtlVJC1y957ZjPb/cPeZZnaC8kvPnJzlvah80/1ESTVLzKS/TtKHkmpKKiqx/1ZJ77j7bWbWR/lm\n+s/MbF9Js9y9kZm1lvQXdz8+u82PJfV395+Y2RuSfuTuH2bXLZV0kLsv39p9uHr16lzNmjUrdH8D\nAAAAAAAAAHaOX/3qV7rjjjsqvIpJuUvHlLA5+yflG+Cj3f3qkgPM7DBJl0hq4+4rsmb6HiWGrCqV\n+Rt3n5A17kdL6pBlv+buW/ty1HUl6llXYn9uKz9PQXZdTltf3uUsSe3NbEtzf5/sy1lXbuM2ZR1n\nm+bNm1fBqPK1a9dOr7zySnLO2rVrA6qRunbtqilTpiTnrF69OqCavBNPPFFPP/10ck6dOnUCqsnr\n3Lmzpk2blpwzatSogGqke++9V+eee25IVv/+/UNyjj/+eD377LPJOXfddVdANXljx47VmWeeWf7A\ncowbNy6gmrxcLqeCgvQVqx544IGAaqS+ffvqwQcfDMmqVatWSE7v3r01fvz45JyDDz44vZjMUUcd\npddeey05Z/78+QHVxP7ePvvss5Cc3/zmN/rrX/8akhX1WLrgggtCnnf32WefgGqkn/zkJ3rsscdC\nsho3bhyS07JlS7366qshWS+88EJIzmWXXaZbbrklOSfqPpKkXr16acKECck5+++/f0A1Uvv27TVj\nxoyQrEceeSQkZ9iwYbr88stDslq1ahWS069fv5DXy6ZNmwZUIx199NGaM2dOSNaee+4ZknPooYfq\nnXfeCcmaPn16+YMqoH///hozZkxIVt26dUNyTjnlFE2cODE5J+o8d/z48erdu3dIVpMmTcofVAF/\n+ctf9Lvf/S4kq6ioKCRnyJAhGjJkSEhWxHnleeedp3vuuSc5R5I2btwYkvOLX/wi7HHZo0ePkJyG\nDRtq0aJFIVkLFy4MyenWrZsmT54cklW7du3kjNatW2v27NkB1Ujr168PyenYsaNeeumlkKwqVSq6\niMe2RZ4vbdiwITnjmGOO0YsvvhhQjbR58+byB1VAVE9QiutR3HHHHfrVr34VkrU9vumj7llJZ5hZ\nPUkys73NrKGkYknLJa00s/rKf8Foudz9VklFZvYDSQskNciWepGZVTezI7ajtqmSfmxmNbIvb+2d\n7Zsq6dRsf7Hyy8fIzPZUvsHfwN0bu/shyn9Y0Der5TAza2RmBco35LeYovx67zKzUySlP8sBAAAA\nAAAAAHY536jR7u7zlF+j/Fkze03SM5L2c/c5kt7M/t0jqeRHLKXXqCl9+TpJV7j7ekmnS7o5y56j\nr9dT39Y6N7mstpnKr7M+S/kvLx3h7vOz/f8j6XVJEyVt+Tjqp5L+4e4lP8YZr3yDfr2kiyQ9rfyX\nsH5cYszVko43s9clnVTqOgAAAAAAAADAbqLCS8e4+zWlLo+VNLaMceds5fYHbWucuz8s6eFse66k\nLmVkdC2xPUnSpK1cN0zSsDJuf63+3y9W3WJ0qXFfSDogu/hU9q901heSTiix66IycgEAAAAAAAAA\n33ExCxYBAAAAAAAAALCbotEOAAAAAAAAAEACGu0AAAAAAAAAACSg0Q4AAAAAAAAAQAIa7QAAAAAA\nAAAAJKDRDgAAAAAAAABAAhrtAAAAAAAAAAAkoNEOAAAAAAAAAEACGu0AAAAAAAAAACSg0Q4AAAAA\nAAAAQAIa7QAAAAAAAAAAJKDRDgAAAAAAAABAAhrtAAAAAAAAAAAkqLazC9idVK9evdLlrV+/PqCS\nvCpV0j+3Wbx4cUAlsXmbN28OqORry5YtS86oX79+QCWxWY0aNQrJicpq3bp1QCWxeb169Qqo5GsP\nPPBAcka/fv0CKpH69u0bljV8+PCQHElatGhRcsYhhxwSUMnXCgoKkjPq1KkTUEls1ttvvx2SI0nL\nly8PyVm9enVIjhTzehL5e1u3bl1ITsRrd3TWkiVLQnKispo2bRpQyddq1KiRnBF5/haVddBBB4Xk\nRGZt3LgxJCcq69NPPw2oJDYrl8uF5EjS0qVLQ3K++uqrkJzIrJUrV4bkSNKHH36YnNGjR4+ASmKz\nIt/H1axZMyQn8vEdpaioqFLl7LHHHiE5krTvvvuG5KxatSokJzKratWqITmRWRF9hcicyMdS1N9u\nZfy9RYnuL0aIOMeVpMLCwpCc6KyKYkY7AAAAAAAAAAAJaLQDAAAAAAAAAJCARjsAAAAAAAAAAAlo\ntAMAAAAAAAAAkIBGOwAAAAAAAAAACWi0AwAAAAAAAACQgEY7AAAAAAAAAAAJaLQDAAAAAAAAAJCA\nRjsAAAAAAAAAAAlotAMAAAAAAAAAkIBGOwAAAAAAAAAACWi0AwAAAAAAAACQgEY7AAAAAAAAAAAJ\ndkij3cw2m9l9JS5XNbPFZjbhG2Q9Z2YnlNp3qZmN+AZZVc3sczP70/beFgAAAAAAAAAAacfNaF8l\n6Ugzq5FdPkHSom+Y9aCks0rtOzPbXyFmtuXnPkHSvySdXoGxAAAAAAAAAAD8H9V24LGeknSypMeU\nb5Q/JKmLJJlZW0m3SqohaY2kn7n722Z2hKS7JVVX/kOBn0r6b0nXmVk1d99oZo0k1Xf3aWbWTdIQ\nSV9IOlLSLHfvnx3jXUnjJB0v6QZJD2d13CLpIjPr4O4vlzXWzGZJGiFpH0mrJf3S3f9lZj0l/T6r\nb4mkfu6++Fu59wAAAAAAAAAAldKOmq2dkzRW0lnZrPYWkmaUuP5NSce4e2tJV0u6Ptt/oaRb3P1o\nSW0kfejuX2W3/VE25kzlm+ZbtJR0iaQjJB1qZp1KXPeFu7dx94ezOo6TNFH5pn/fUjX/71hJoyRd\n7O5tJQ2SNDIbM9XdO2R1j5P0u+2+ZwAAAAAAAAAAu7QdtiyKu8+TdLDys8iflFRQ4uq6kh41szck\n/VX5JrkkvSRpsJkNknSwu6/L9o9VvsGu7L8Plch6xd0/cfecpFezY24xrsR2T0nPZ5n/I+lUMyso\nPdbMaknqJOkRM5sr6Q5J+2djGprZM2b2uqTLS9QNAAAAAAAAANhNFORyuW/9IGa23N2Lzewq5Web\nd1d+GZbfunsvM7tb0mx3vz1bCuZ5d2+c3fYQ5ZviAyVd4O4vZM3vd5Sf1f6QuzfJxnbbkpldHi5p\nprvfly0H09rdv8yue1RSZ+WXqimQtK+k3u4+qeRYM6sj6S13b1DGz/W8pGHu/mR27Kvd/dit3Q9r\n1qzJFRUVJd2XAAAAAAAAAIBv18CBAzV8+PCC8kfm7ag12rcUNFrSV+4+P2tMb7GnpI+y7Z9t2Wlm\nh7j7u5KGm9lByi8584K7rzKzF7K8krPZK8TMipVfH76Bu2/M9p2r/PIxk0qOdfcVZvaumZ3m7o9m\nY1u4++uSiiV9nA09t7zjvvXWW9tb6la1atVKc+fOTc5ZtWpVQDXSMcccoxdffDE559133w2oJq9/\n//4aM2ZMck69evUCqsk76aST9NRTTyXnTJkyJaAa6c9//rOuvPLKkKyf//znITmHH3643n777eSc\nxx9/PKCavEGDBunGG29MzmnQ4P98XveN9e3bVw8+WOHvgN6qfv36BVQj5XI5FRRU+LVnm4YPHx6S\nc/HFF+v2229PzunatWtANXktWrTQ66+/npzz/vvvB1QjnXLKKZo4cWJI1pw5c0Jyrr76al1zzTUh\nWdWqxZzmDB48WNddd11yTuPGjQOqkc466yw99NB2n/6UqVmzZiE5UY9tSXrkkUdCcoYOHaqrrroq\nOeeYY44JqCavR48eeuaZZ5JzatasGVCN1KVLF02dOjUkK+K8VJIuueQS3XbbbSFZe+65Z0jOueee\nq3vvvTc5Z9999w2oJu58UpL233//8gdVQOvWrTV79uyQrGnTpoXkRD6WqlevHpJz0UUXaeTIkeUP\nLEfUZLlf//rX+s///M+QrMWLY76qLPI8IOp+GjJkiIYMGRKS1bRp0+SMPn36aNy4ceUPrIA99tgj\nJKd3794aP358SJaZheQ0adIkrAfzxRdfhORE9U0kaf369ckZxx57rJ577rmAauIeS506ddL06dND\nsgoLC0Ny2rRpo1mzZoVkbdq0KTmjffv2mjFjRvkDd6DImu6///6QnOHDh2vgwIEhWdtjR67RLnf/\nyN3L6nrcIOnPZja7VE1nmNm8bMmWZpLuK3HdQ8o33rf1TjO3le1TJU3a0mTPTJDU08wKS42VpH6S\nfm5mr5rZPEm9sv3XKL/kzUxJfAkqAAAAAAAAAOyGdsiMdncvLmPfZEmTs+2XJZX82PIP2f6/SPrL\nVjLHS6q6tczs8iUlthuX2L5P/2/TXtmXrG6Z0tG41HXv6+svXy25f4LyDXoAAAAAAAAAwG5qh30Z\nKgAAAAAAAAAA30U02gEAAAAAAAAASECjHQAAAAAAAACABDTaAQAAAAAAAABIQKMdAAAAAAAAAIAE\nNNoBAAAAAAAAAEhAox0AAAAAAAAAgAQ02gEAAAAAAAAASECjHQAAAAAAAACABDTaAQAAAAAAAABI\nQKMdAAAAAAAAAIAENNoBAAAAAAAAAEhAox0AAAAAAAAAgAQ02gEAAAAAAAAASFBtZxewO1m/fn2l\nyysuLg6oJC5r7dq1AZXE5n366acBlcTmNW7cOKCS2KyVK1eG5ERl1a5dO6CS2LxatWoFVBKbN3z4\n8IBKYrMGDhwYknPxxReHZM2ZMyegmq9t2rQpOeOUU04JqCQ2a/z48SE5krRo0aKQnMjXuCVLliRn\nnHHGGQGV5LVp0yYkZ/Xq1SE5kpTL5UJyDj300JCcqKzbb789oJK8Hj16hORddtllAdXkRZ2fNm/e\nPCQnMmuPPfYIyZGk73//+8kZe+21V0AleVHnbxs3bgzJkaQaNWqE5Bx11FEhOZFZ8+bjmpvKAAAg\nAElEQVTNC8mRpM2bNydn7LfffgGV5O27774hOYWFhSE5ktSgQYOQnOXLl4fkSHHnFFHvd6NyIt+f\nVK1aNSQn6nwiMqsy1lTZRPZNorLq168fkiNJGzZsCMmpUqVyzXeOPA+Iyoo8X4rMqqjK9RsGAAAA\nAAAAAGAXQ6MdAAAAAAAAAIAENNoBAAAAAAAAAEhAox0AAAAAAAAAgAQ02gEAAAAAAAAASECjHQAA\nAAAAAACABDTaAQAAAAAAAABIQKMdAAAAAAAAAIAENNoBAAAAAAAAAEhAox0AAAAAAAAAgAQ02gEA\nAAAAAAAASECjHQAAAAAAAACABDTaAQAAAAAAAABIUG1HHcjMNkl6Tfnm/kZJF7v7y4mZR0k60N3/\nnl0+V9KNkj6UVCDptf+fvTuPk6o88/7/bRYRBET0ISwqyDKXuLBDg8g+Ju4QIibRSBxGnWGMiQuD\nJk70UceoDKKJ8hg3krgkJrjx01FJZBcRhAZExSu44YLI4sIO3VC/P+oQKtjQLfcV1s/79eLFqVN3\nfc9V1d1Vp66++y53v9DMbpA0xd0n7iSrgaQHJR0lqbqk99z9TDNrKmmhpLeyzJykLpJaSPqNpA6S\nfubuo1LuCwAAAAAAAABg37TbGu2S1rp7B0kys29KulVS78TMdpI6SXq+YN9j7v7jwkHufn0lsm6U\n9Gd3vyur8YSC697eWvtWZrZS0mWSBuxK4QAAAAAAAACA/cPubLQXFWwfKukzSTKzhpL+KKlOVs9Q\nd59uZqsl3SPpdElLJF0raYTyM84vlzRe+eb4wWbWXdIt5RxH2TF+I+kZd3/SzN6T9DtJZ2XHG+Tu\nf5XUKMuUJLn76zuofev1KyStMLMzv+bjAAAAAAAAAADYj+zONdprmlmJmS2UdJ+km7L950l6IZsx\n3lbSvGz/IZJedPcTJK3JxveTNFDSTe5eKuk6SX909w7uPja73Xez45RkS8mUZ5m7d5T0a0nDsn2j\nJY0xswlm9jMza1QwvkVB5l2pDwQAAAAAAAAAYP+xO2e0rytYOqarpIclnSDpVUkPmll1SePcfX42\nfqO7/znbXiBpg7tvMbMFkpru5DhfWTqmHE9l/8+R9G1Jcvc/m9kxkk5VfhZ9ScHyMV9ZOgYAAAAA\nAAAAAEkqyuVyu+VAZrbK3esWXF4q6QR3X5EtH3OGpB9Jut3dHykcb2bXS1q99QNHt16XzVjvuLWx\nvv3lgmNtv3RMR3f/zMw6Svofd+9bTr3PSBojqSS7bZsd3K+/q21n1q1bl6tVq1ZFwwAAAAAAAAAA\ne9B1112nG2+88StLiu/IHlmj3cyOVX7ZmpVmdrSkj9z9QTM7WFIHSY+onHXRy8laLanuTsZVmpn1\nkfSKu683szqSWkj6YPvaK6hnpxYsWJBQ4d8rLi7WzJkzk3Nq1qwZUI3Upk0bvfbaa8k5Efdpq4sv\nvlj3339/ck7VqlUDqskbMmSIxowZk5xTVlYWUI10ySWX6L777gvJ6ty5c0hO+/btNXfu3OScV155\nJaCavKFDh+qee+5JzmncuHFANXn9+/fXuHHjknM+/PDDgGqkH/3oR7r77rtDsi677LKQnFwup6Ki\nSr8e7lBJSUlANXlR39/t27cPqCbWRRddFJLzwAMPhGXVrRtyiqBRo0bpyiuvTM4ZOnRoQDVSq1at\ntGjRopCsdevWheS0bdtW8+fPr3hgJUT8jEjShRdeqN/+9rfJOU888UR6MZlnnnlGZ511VnLO5Zdf\nHlCN1K9fP02YMCEkq0qVmBUp+/Tpo0mTJoVkHXzwwSE53bp104wZM5JzDjvssIBqpGOPPVZvvfVW\nSFbUOeUJJ5yg119/veKBlbBy5cqQnF69emnKlCkhWVH37dJLL9Xo0aOTcxo0aBBQjTRo0CCNHTu2\n4oGV8OWXX4bkXHTRRXrggQdCslatWhWSc+WVV2rUqArn1VXK4Ycfnpzxwx/+UL/73e8CqompR5LO\nPPNMPfvssyFZLVq0CMlp3bq1Fi5cGJK1YsWKkJwePXpo2rRpIVmlpaXJGX379tXEiRMDqpG++OKL\nkJyBAwfqySefDMlq1KhRxYMqIeo8QIo5X4rqB0px5wHdu3fX9OnTQ7LGjx9f8aBKuPHGG3XdddeF\nZH0du7PRfrCZlWhbU3qwu+fMrLek/zSzUuUb5xdk1+9sqv3W6yZJuibLvaUS43eW21HS3VkdVSTd\n5+5zzKxpebcxs29Imq38h7huMbOfSDrO3dfspA4AAAAAAAAAwH5mtzXa3b36DvY/JOmhcvbXLdi+\nobzr3P1zSV22u+lXfrXr7kMKtpsXbM+R1DfbHilpZDm3XSzpK8vGuPunko4q7z4BAAAAAAAAAA4c\nMX/jCQAAAAAAAADAAYpGOwAAAAAAAAAACWi0AwAAAAAAAACQgEY7AAAAAAAAAAAJaLQDAAAAAAAA\nAJCARjsAAAAAAAAAAAlotAMAAAAAAAAAkIBGOwAAAAAAAAAACWi0AwAAAAAAAACQgEY7AAAAAAAA\nAAAJaLQDAAAAAAAAAJCARjsAAAAAAAAAAAlotAMAAAAAAAAAkKDani4Ae1Yul9urslq1ahVQSWze\nmjVrAirZpkGDBskZRx55ZEAleV26dAnJWbVqVUiOJK1evTo5o2vXrgGVxOZVqRL7u81mzZolZxxz\nzDHphWR69uwZklNSUhKSE5XVoUOHgErycrlcSN5HH30UUI3UpEkTffzxxyFZAwcODMmJzCoqKgrJ\nkaRTTjklOaOsrCygktisyNe4qKzWrVuH5ERlDR48OKCSf1ze3uKII47Y67I2btwYkiNJ1atXT874\n8ssvAyqJzYq4X1tt2rQpJKd27dohOZFZJ5xwQkhOVFbkz9txxx0XkrNhw4aQHElq3759SM7mzZtD\nciTp5JNPDsmJeJ8jxb0frFWrVkiOJB1++OEhOcuXLw/Jad26dVhW5ONUs2bNkJy1a9eG5EQ9d++N\n5wGoWOTzZFTWGWecEZITnVVZzGgHAAAAAAAAACABjXYAAAAAAAAAABLQaAcAAAAAAAAAIAGNdgAA\nAAAAAAAAEtBoBwAAAAAAAAAgAY12AAAAAAAAAAAS0GgHAAAAAAAAACABjXYAAAAAAAAAABLQaAcA\nAAAAAAAAIAGNdgAAAAAAAAAAEtBoBwAAAAAAAAAgAY12AAAAAAAAAAAS0GgHAAAAAAAAACABjXYA\nAAAAAAAAABJU210HMrPNkuYr39wvk/Qjd38lMbOtpMbu/nx2+YeS/kfSR5KKJM139wvN7AZJU9x9\n4k6yGkh6UNJRkqpLes/dzzSzppIWSnory8xJ6iLpXElXZzdfLWmouy9IuT8AAAAAAAAAgH3Pbmu0\nS1rr7h0kycy+KelWSb0TM9tJ6iTp+YJ9j7n7jwsHufv1lci6UdKf3f2urMYTCq57e2vtW5nZu5J6\nuvuXZnaqpPsldd2F+wAAAAAAAAAA2IftzkZ7UcH2oZI+kyQzayjpj5LqZPUMdffpZrZa0j2STpe0\nRNK1kkYoP+P8cknjlW+OH2xm3SXdUs5xlB3jN5Kecfcnzew9Sb+TdFZ2vEHu/ldJjbJMSZK7v76D\n2rdeXzgb/xVJTSr3MAAAAAAAAAAA9ie7c432mmZWYmYLJd0n6aZs/3mSXshmjLeVNC/bf4ikF939\nBElrsvH9JA2UdJO7l0q6TtIf3b2Du4/Nbvfd7Dgl2VIy5Vnm7h0l/VrSsGzfaEljzGyCmf3MzBoV\njG9RkHlXOXkX6e9n1QMAAAAAAAAADhBFuVxutxzIzFa5e91su6ukB9z9BDProfza6I9IGufu87Mx\n6929ZrZ9g6QN7n6LmRVJWunu9bNGesetS8Vsf7ng2NvPaD/J3T8xsy6S/tvdv5mNqyfpVOVn0Z8i\n6QRJtbPbttnB/eoj6W5JJ7v75zt7DNatW5erVavW13zkAAAAAAAAAAC708yZM1VcXPyVlU52ZHcu\nHfM37v6KmR1hZke4+zQz6ynpDEm/NbPb3f0RSaUFN9kiaWN225yZpda9Mft/swoeA3f/QtJjkh4z\ns2ck9ZRUsqMQM2uj/Oz8UytqskvSggVxn5VaXFysmTNnJuccfPDBAdVIbdu21fz585NzPv+8woex\n0nr37q3Jkycn56xZsya9mMyZZ56pZ599NjnnyCOPDKhGateunebNm1fxwEpYtWpVSE7Pnj01derU\n5Jw6deoEVJPXvn17zZ07NzmnSpW4PyKK+pkrKqr068VOtWnTRq+99lpI1ubNm0Nyor5uHTp0qHhQ\nJeVyuZDH/KOPPgqoRmrSpIk+/vjjkKyI70dJOv300/Xcc8+FZEV9f5922ml6/vn0P1xr1qxZejGS\nWrdurYULF4ZkffbZZyE53bt31/Tp00OyqlWLOT2NOlf64IMPAqrJGzRokMaOHVvxwArUr18/oBqp\nX79+mjBhQkhWgwYNQnJOPPHEsHPmjRs3VjyoEjp16qTZs2cn50S9vkV9b0tS9erVQ3I6dOigkpId\nvm36WqImgnXs2FFz5swJyYp6P9CrVy9NmTIlOeeII44IqEY6/vjj9cYbb4RkbdiwISQn8usW9TPX\npUsXzZo1KyRr9erVyRmRz91REwG7deumGTNmhGSVlpZWPKgSot5XSnGPU9TriSStWLEiOePUU0/V\nCy+8EFBN3GMU+XWLeo2L/P6O6AlEngdEnStFft1q1KgRkhP5OH0du3PpmL+92zWzY7NjrzSzo5Vf\nyuVBSQ9I6rD9+J1krZZUN6I4M+tjZltn0NeR1ELS1ndW5a37frSkJyRd4O7vRNQAAAAAAAAAANj3\n7M4Z7QebWYm2Na0HZ7PTe0v6TzMrVb5xfkF2/c6mMmy9bpKka7LcWyoxfme5HSXdndVRRdJ97j7H\nzJru4DY/l1Rf0v/LlrMpdfcuO6kBAAAAAAAAALAf2m2Ndncv92823P0hSQ+Vs79uwfYN5V2XLdey\nfXP7d+VkDSnYbl6wPUdS32x7pKSR5dx2saSvrM/u7hdLuri8+wQAAAAAAAAAOHDszqVjAAAAAAAA\nAADY79BoBwAAAAAAAAAgAY12AAAAAAAAAAAS0GgHAAAAAAAAACABjXYAAAAAAAAAABLQaAcAAAAA\nAAAAIAGNdgAAAAAAAAAAEtBoBwAAAAAAAAAgAY12AAAAAAAAAAAS0GgHAAAAAAAAACABjXYAAAAA\nAAAAABLQaAcAAAAAAAAAIAGNdgAAAAAAAAAAElTb0wVgzzrkkEP2qqz33nsvoJJtvvjii+SMhg0b\nBlSyzRFHHJGc8eKLLwZUIrVr1y4sq3///iE5ktSoUaPkjPnz5wdUkte+fXu98847yTmbNm0KqCav\nbdu2euONN5Jz6tSpE1CN1KZNGy1evDgk66yzzgrJkfJfu1QfffRRQCWxeUceeWRAJVIulwvLuvrq\nq0NyTj/9dE2dOjUkq379+iE5p512mhYsWJCcU69evYBq8iJe3yRpy5YtITmRWVHP38XFxSFZF154\nYXoxBSJeL99+++2ASvIiXnMlafz48SE5J554Yti5Sa9evUJyJKlKlfT5SVFft+Li4rBz5iZNmoTk\nSNLatWtDcl5//fWQnI4dO2rWrFkhWa1btw7JkfKvvalKSkoCKpGOP/74sKzS0tKQnI4dO4a9DtSo\nUSMkp0uXLlq0aFFIVsuWLUNyateuHZKzdOnSkBxJWrZsWUjON77xjZAcSTrooINCcjZs2BCSE5l1\n2GGH7VU51arFtRej+lSR57lR92/9+vUhORs3bgzJiXouicyaN29eSE5xcXFIz2RrVmUxox0AAAAA\nAAAAgAQ02gEAAAAAAAAASECjHQAAAAAAAACABDTaAQAAAAAAAABIQKMdAAAAAAAAAIAENNoBAAAA\nAAAAAEhAox0AAAAAAAAAgAQ02gEAAAAAAAAASECjHQAAAAAAAACABDTaAQAAAAAAAABIQKMdAAAA\nAAAAAIAENNoBAAAAAAAAAEhAox0AAAAAAAAAgATV9tSBzWyzpPnKN/vLJP3I3V9JzGwrqbG7P59d\nvl7SancfVTDmPUkd3f2zneSYpMckbZF0jqTzJH1f0ubs37+5+6tmNllSQ0nrJeUk/be7P5lyHwAA\nAAAAAAAA+5Y91miXtNbdO0iSmX1T0q2SeidmtpPUSdLzOxmTq0TOAElj3f0XZtZV0umS2rl7mZnV\nl3RQQdb33X1uStEAAAAAAAAAgH3Xnmy0FxVsHyrpM0kys4aS/iipjvL1DXX36Wa2WtI9yje9l0i6\nVtIISUdJulzSeEk3SjrYzLpLumVnxzWzpso35F+SdJKkjyT1l9Q3yyszs36S7pa0wt3LJKmcmfAs\nvwMAAAAAAAAAB7A92SSuaWYlZrZQ0n2Sbsr2nyfphWy2e1tJ87L9h0h60d1PkLQmG99P0kBJN7l7\nqaTrJP3R3Tu4+9hK1NBS0l1Z5peSvpMtO/NrSXe4ez9Jf5Z0tJm9ZWajzazndhmPmNnc7L4ctmsP\nBQAAAAAAAABgX7UnG+3rsoZ4a0mnSXo42/+qpH8xs+sktXH3tdn+je7+52x7gaQp7r4l2266g2Ps\naJmYrfvfc/cF2fYcSc22H5gdv4OkSyQtl/SYmQ0uGHKeu7fP7svnO7m/AAAAAAAAAID9UFEuV5kl\ny+OZ2Sp3r1tweamkE9x9RbZ8zBmSfiTpdnd/pHD89h9yuvU6M/uh8h90+uNs/6WSGrr7zwuOs1xS\nA0lHS3rG3dtk+6+SdIi731jeh6gW3P47kga7e38zmyTpKncvqcx9XrduXa5WrVpf96ECAAAAAAAA\nAOxGY8aM0ZAhQ4oqHpm3V6zRbmbHKj+7fqWZHS3pI3d/0MwOVn42+SP6+zXdd5S1WlLdgv1TlV/a\n5TZ3X2NmAyXNd/ecmf1dDTtiZv8kaYu7v53taidpcaXu4XYWLFhQ8aBKKi4u1syZM5NzDj/88IBq\npJYtW+rtt9+ueGAFXn/99YBq8gYMGKCnn346Oadhw4YB1eR17dpVr7zySnLOSy+9FFCNNGzYMI0c\nOTIkq3///iE5rVq10qJFi5Jz5s+fH1BN3jnnnKPHH388OWfTpk0B1eSdd955+v3vf5+cU6dOnYBq\npLPOOkvPPPNMWNbe5OOPPw7LatKkSUjekUceGVCNlMvlVFRU6XOGnbr66qtDcm699VZdc801IVn1\n69cPyRk+fLhGjBiRnNOjR4+AaqRu3bppxowZIVllZWUhOT169NC0adNCshYuXBiSc8kll+i+++5L\nzrnwwgvTi8kcdNBBIa8FEedcknTcccfpzTffDMkaP358SM4VV1yhO+64IySrV69eITkdOnRQSUml\n5tXs1F//+teAaqTvfe97euyxx0KymjRpEpIT+RwQ9X5g6NChuueee0KyWrduHZLTu3dvTZ48OTnn\nww8/TC9G0gUXXKCHH3644oGVUFpaGpIzZMgQjRkzJiSrRo0aITnnn3++Hn300ZCsli1bJmdE9QIk\naenSpSE5/fv317hx40KyvvGNb4TkRL33luLOl04++eSw9/LVq1dPzoj8XqpWLaa92LFjR82ZMyck\na8uWLSE5nTt31quvvhqStX79+uSMnj17aurUqQHVSLVr1w7JiTpXkqR58+ZVPKgSIl9Pvo492Wg/\n2MxKtK3ZPThrgPeW9J9mVqp84/yC7PqdTb3fet0kSddkube4+1gzu1vSS2a2RdIySReVc7udqS3p\nLjM7VFKZpLeVX0amsrcHAAAAAAAAAOzH9lij3d3L/fWbuz8k6aFy9tct2L6hvOuyNdK7bHfd/ZLu\nLydvsaQ2BZdvLy8/Wxam+w5q7VvefgAAAAAAAADAgWNPfhgqAAAAAAAAAAD7PBrtAAAAAAAAAAAk\noNEOAAAAAAAAAEACGu0AAAAAAAAAACSg0Q4AAAAAAAAAQAIa7QAAAAAAAAAAJKDRDgAAAAAAAABA\nAhrtAAAAAAAAAAAkoNEOAAAAAAAAAEACGu0AAAAAAAAAACSg0Q4AAAAAAAAAQAIa7QAAAAAAAAAA\nJKDRDgAAAAAAAABAAhrtAAAAAAAAAAAkqLanC8CeVbt27b0qa86cOQGV5A0YMCAkr2HDhgHV5HXt\n2jWkpjfffDOgmtisc845JyRHkqpXr56cMX/+/IBK8s4555yQvPr16wdUs82nn36anLFo0aKASqSz\nzjpLJSUlIVnjxo0LyXnggQd00UUXJecMHDgwoJq8Jk2ahHwvXX311QHVxGbddtttITm33nprWFbz\n5s1DcoYPH6577703Oee73/1uQDV5jRs3DslZvnx5SI4k1axZMyRn4cKFITlRWb/61a8CKskbNmxY\nSN7JJ58cUE3eqlWrQnI2bdoUkhOZVVRUFJITlRV5ThmVdeihh4bkRGZt3LgxJCcya8aMGSE5vXv3\nDsmqWrVqQDV5n3zySUjOsmXLQnKkuPcn69evD8k5//zz9fLLL4dkrVu3LjmjuLhYr732WkA1UllZ\nWUiOJC1ZsiQkp1WrViE5klS3bt2QnBUrVoTkSNKWLVtCcr744ou9KmfDhg0hOR07dtRHH30UktWo\nUaOQHEnK5XIhOVHP31E5paWlITmRWc8//3xIzpAhQ0KzKosZ7QAAAAAAAAAAJKDRDgAAAAAAAABA\nAhrtAAAAAAAAAAAkoNEOAAAAAAAAAEACGu0AAAAAAAAAACSg0Q4AAAAAAAAAQAIa7QAAAAAAAAAA\nJKDRDgAAAAAAAABAAhrtAAAAAAAAAAAkoNEOAAAAAAAAAEACGu0AAAAAAAAAACSg0Q4AAAAAAAAA\nQAIa7QAAAAAAAAAAJKj2jwo2s/qSJkjKSWokabOk5dnlLu5ett34wySd6+73VpBbVdIKdz/MzFpI\nWiDpLeV/abBa0oXu/k5i7X0krXX3WdnlYyX9WtKhkg6SNNndLzWzfpKekPSupCJJS939tJRjAwAA\nAAAAAAD2Lf+wRru7fyapvSSZ2XWS1rj7qJ3c5HBJ/y5pp432TK5g+y1375Ad5z8kXSPp4l0qepu+\nklZImpVdvlvSre7+Qnac4wvGTnT3gYnHAwAAAAAAAADso/5hjfbtFBVeMLPhki5QvmF+r7uPlnSL\npH8ysxJJL2SXn1Z+Fnk1Sde6+/9WkF1X0ufZMU6QNCa7bRVJAyRVzTLnSiqW9IqkRyVdL+kISd+X\n9IWkiySVmdkPJV0qqaGkJVsP4u5v7Oi+AQAAAAAAAAAOLLur0f43ZtZF+YZ2R+WXYZllZpOVn4ne\nomB2elVJ/d19jZn9H0nTJZXXaLesOb91WZfibP9/SPofdx9rZtWVb4gfJemfJJ3j7m5mcyWtd/fu\nZjZQ0jXufq6ZPSBpubv/KjvAHZKmmtlLkv4i6Tfuvio7Tp/s+JL0mLuPiHmkAAAAAAAAAAD7gj3x\nYagnS3rC3Te5+xrlZ5j3KGdcFUm3mdl8SX+WdGS27vv23nL3Du7eQtJwbVt65mVJPzez/5R0tLtv\nyva/7e6ebb+p/DryUn6t92blFezuD0pqLelxSf0kvWxmW39JMTE7fgea7AAAAAAAAABw4CnK5XIV\nj0pkZtdLWu3uo8zsSkm13P2/s+t+IekD5WeKjy2Y0f6vknpLGuzuOTP7UPnZ6p8qP9u8fvZhqIW3\nqS3pY3c/NLvcXNKZki6T9C+SPtlu/MPZ5f+vMMvMblLBjPZy7s9CSedKaiDp0squ0b5u3bpcrVq1\nvs5DBwAAAAAAAADYzQYNGqSxY8dWetnw3b50jKRpkn5tZv8jqbqk/so3rVdLqlMw7lBJy7Im+ymS\nmhRcV7SD7R6S3pYkMzvG3d+V9CszO0ZSG+Ub7ZV5cFYrv967sqxvSXrR3TebWWNJ9ZRfs71BJbL+\nZsGCBV9n+E4VFxdr5syZyTlNmzYNqEZq2LChli5dmpwzevTogGrybrrpJv385z9PzmnYsGFANXmX\nXnppyH2cM2dOQDXSmDFjNGTIkJCs6667LiSnWbNmev/995NzHnzwwfRiMlHfS/Xrl/dHObvmiiuu\n0B133JGcs2rVqooHVcL111+vG264ISTrww8/DMl54IEHdNFFFyXnDBwY93nXp59+up577rnknKlT\npwZUI91666265pprQrJuu+22kJxcLqeiopiPP2nevHlIzjvvvKMWLVok50ycODGgmvxr9+LFi0Oy\nli9fHpLTqVMnzZ49OyTr0UcfDcm54447dMUVVyTnNGnSpOJBlTRs2DCNHDkyOefkk08OqEbq2rWr\nXnnllZCsKVOmhORcffXVYc8n3/zmN0Ny2rdvr7lz5ybnfPnllwHVSL1799bkyZNDsqLOTdq0aaPX\nXnstJCvqufLyyy/XnXfeGZK1fv36kJyf/vSnuuWWW5JzqlatGlCNNHz4cI0YEfNH2cuWLQvJGTly\npIYNGxaSFfV1Gz16tC699NKQrHbt2iVnXHzxxbr//vsDqpHKyspCcoYOHap77rknJKtXr14hOccd\nd5zefPPNkKwVK1aE5PTs2TPsPD7i+/tb3/qWxo8fH1CNtGHDhpCc/v37a9y4cSFZjRo1Csnp0qWL\nZs2aFZJVWlqanNG9e3dNnz49oBqpWrWYtnBUj1JSyLmyJI0dO1aDBg0Kyfo6dnuj3d1fNbM/SJqt\n/Iehjt764aJmNidbKuZ/JY2S9Gx2eZakvxbEFE7D3/oBqlUkbZB0cbb/PDP7vqRSSR8r/4Gn/2e7\n2+5oOv84SWPN7NvKfxjqaZJ+aWbrs9v8xN1XmtkuPQYAAAAAAAAAgP3Hbmm0u/sN210eKekrv6Jw\n9+9tt6vrDiLrZ+PfkXTIDo55s6Sbt9u9SlKHgjGDC7bf2XpdtoZ7m4LblTvVx90naNsa7wAAAAAA\nAACAA9Ce+DBUAAAAAAAAAAD2GzTaAQAAAAAAAABIQKMdAAAAAAAAAIAENNoBAAAAAAAAAEhAox0A\nAAAAAAAAgAQ02gEAAAAAAAAASECjHQAAAAAAAACABDTaAQAAAAAAAABIQKMdAOJSdJYAACAASURB\nVAAAAAAAAIAENNoBAAAAAAAAAEhAox0AAAAAAAAAgAQ02gEAAAAAAAAASECjHQAAAAAAAACABDTa\nAQAAAAAAAABIUG1PF3Ag2bx5816XV6VK3O9aIrJWr14dUElsXr169QIq2WbDhg3JGYccckhAJbFZ\nZWVlITlRWYcffnhAJbF5tWrVCqhkm4iv3bp16wIqyatWLeYlpW7duiE5UVlFRUUBlcTm1a9fP6CS\n2KzmzZuH5ERmvfvuuyE5UVl722uuFHtuEpW1YsWKkJyoLDMLqGSb2rVrJ2fkcrmASmKzIl9PorIi\nX3cjsj744IOASvK+/PLLkJzI54Dly5eH5Hz66achOZFZkT9zEV+7Fi1aBFSSd9hhh4XkRH7dIh/v\nvU3UfYvKqVGjRkhOZFZpaWlITmTW3ni+tLfZG89N9kZRX/+onKj38JEi339Hv5evDGa0AwAAAAAA\nAACQgEY7AAAAAAAAAAAJaLQDAAAAAAAAAJCARjsAAAAAAAAAAAlotAMAAAAAAAAAkIBGOwAAAAAA\nAAAACWi0AwAAAAAAAACQgEY7AAAAAAAAAAAJaLQDAAAAAAAAAJCARjsAAAAAAAAAAAlotAMAAAAA\nAAAAkIBGOwAAAAAAAAAACWi0AwAAAAAAAACQoNqeLmBXmNmDks6U9Km7t9nJuF6SNrn7jOzy9ZIu\nlrQsG/KCu//MzCZJusrdS8rJOFPSjcr/UqKapF+6+/07yoq5hwAAAAAAAACAfcU+2WiX9BtJd0l6\nqIJxvSWtkTSjYN8odx9VmYOY2UGS7pXUyd0/MbPqkprtShYAAAAAAAAAYP+0Tzba3f0lM2tauM/M\nfizp3ySVSnpT0k8l/bukMjM7X9Jl2dCinWWb2Wrlm+v9JP1YUlVJn2fHLZW0qGD4TrMAAAAAAAAA\nAPu/fbLRvgNXS2rm7qVmVtfdV5nZryWt3jrr3Mz+WdIVWeNdkq52979sl3OIpBnuPiy7zTOSFpvZ\nBEnPSvqDu+eysRVlAQAAAAAAAAD2c0W5XK7iUXuhbEb7M1vXaDez5yStlfS0pKfdfW22jnpho/3v\nLhdk/W2NdjPbJKlGQTNdZna8pH+WNFjSfHcfsqOsnVm3bl2uVq1aKXcbAAAAAAAAAPAPdu655+pP\nf/pTpVc02Z9mtJ8hqaeksyVda2Yn7GLOhsImuyS5+xuS3jCzRyS9K2nIrgTPmzdvF0v6qpNOOkkv\nv/xyck7Lli0DqpEaNGigZcuWVTywAr/4xS8Cqsm78847dfnllyfnHHXUUQHV5F111VW6/fbbk3Pe\nf//99GIk3XXXXbrssssqHlgJP/nJT0JyWrZsqbfffjs559lnnw2oJu/yyy/XnXfemZwT+Yu2Sy65\nRPfdd19yzvLlywOqka699lrdfPPNIVkrV64MyRk1apSuvPLK5JxTTjkloJq80047Tc8//3xyzoIF\nCwKqkYYPH64RI0aEZN17770hOe+8845atGgRkvXuu++G5ORyORUVpa8W98EHHwRUk39d+vDDD0Oy\nlixZEpJTXFysmTNnhmTdfffdITkPP/ywLrjgguSc7t27B1ST9+///u/69a9/nZzTtm3bgGqkbt26\nacaMGRUPrIQXXnghJOeGG27Q9ddfH5J13nnnheSYmdw9Oeett94KqEbq37+/xo0bF5JVu3btkJx+\n/fppwoQJIVkvvvhiSM4tt9yin/70pyFZUZPTbr31Vl1zzTXJOVGvkxdffLHuv//+kKyo7+/bb79d\nV111VUjWhg0bQnJGjx6tSy+9NCQr4vk76n2AJFWrFtMSGjJkiMaMGROS1bFjx5Cctm3bav78+SFZ\nn332WUhOnz59NGnSpJCsTZs2JWd861vf0vjx4wOqkdavXx+SM2DAAD399NMhWY0bNw7J6dKli2bN\nmhWSFfG81LNnT02dOjWgGqlGjRohOZHvBSJ6ZpL0pz/9Seeee25I1tdRZbcfMU5R9k9mViTpaHef\nIukaSXUl1Za0Otv+urnKcg8xs14F17WXtDilaAAAAAAAAADA/mWfnNFuZr+X1FvS4Wb2gaSbJA02\ns0OzIb/M1mh/RtLjZna28h+GuqOpCLkdbBdJGp6t9b5e+aVpfhh3TwAAAAAAAAAA+7p9stHu7uX9\nHehX/ubN3RdJKvzbrOk7yOtbsF23YHuN8kvSlHebGypbLwAAAAAAAABg/7UvLx0DAAAAAAAAAMAe\nR6MdAAAAAAAAAIAENNoBAAAAAAAAAEhAox0AAAAAAAAAgAQ02gEAAAAAAAAASECjHQAAAAAAAACA\nBDTaAQAAAAAAAABIQKMdAAAAAAAAAIAENNoBAAAAAAAAAEhAox0AAAAAAAAAgAQ02gEAAAAAAAAA\nSECjHQAAAAAAAACABDTaAQAAAAAAAABIUG1PF3AgKSoq2uvyHnrooYBKpGHDhoVknXHGGQHVxOZV\nr149oJJtOnbsmJwR+b10zDHHhOR88sknITktW7YMyerSpUtANbF5S5cuDahkmyOOOCI5o06dOgGV\n5DVv3jwk59xzzw3JkaShQ4cmZ5SVlQVUsk2zZs2SM+rVq5deSKZHjx4hOd/97ndDciRp4sSJITlV\nqsTNJ/jggw+SM44++uiASqRcLheWNWHChJAcSVq7dm1IzpIlS0JyorJOPfXUgEpi85YvXx5QSV61\najFvBzZs2BCSE5n1X//1XyE5Y8eODcmKeN2WpP79++uFF14IyYp8zY16zl20aFFITmTW2WefHZIj\nSccdd1xyRpMmTQIqyYs6f6tVq1ZIjiR16NAhJKdmzZohOZLUr1+/kJyoxynqPCDy/UnUc8DKlStD\nciKzIt8z1a5dOyRn/fr1ITlRPyeR592HHHJISE5paWlITnTW3qRq1ap7XVanTp1CcqKzKosZ7QAA\nAAAAAAAAJKDRDgAAAAAAAABAAhrtAAAAAAAAAAAkoNEOAAAAAAAAAEACGu0AAAAAAAAAACSg0Q4A\nAAAAAAAAQAIa7QAAAAAAAAAAJKDRDgAAAAAAAABAAhrtAAAAAAAAAAAkoNEOAAAAAAAAAEACGu0A\nAAAAAAAAACSg0Q4AAAAAAAAAQAIa7QAAAAAAAAAAJKDRDgAAAAAAAABAgmp7uoDKMLMjJT0k6RuS\ntki6391/9TVuP0nSVe5eYmbvS/oyy8lJ+g9Jn0h61t1PLOe2RZLulNQ3G79e0rnuvri8LHd/Zdfu\nJQAAAAAAAABgX7RPNNollUm60t3nmVltSXPM7M/u/tYuZG2R1NvdP9+6w8yaKt8o/ztmVlXSIEmN\ntjbhzayxpLU7ygIAAAAAAAAAHFj2iUa7uy+VtDTbXmNmCyU1MbN7JM2U1EfSoZL+1d2nm9nBkn4j\nqY0kl3RwQVyRdrJkjpn9UNJASbWzceO2Hjs7/pLKZgEAAAAAAAAA9n/7RKO9kJk1k9RO+Qa7JFV1\n92IzO03S/5V0iqShkta6+/FmdqKkku1iJprZFkkb3L1bOYdpL+lEd//SzJpIesnMTpY0UdIj7j7v\na2QBAAAAAAAAAPZjRbncV1ZM2Wtly8ZMlnSTu4/L1l7/mbvPMLMGkl5y938ys6ck/dLdJ2e3my3p\nkmyN9vckdShn6Zhn3L1NNqO9p7v/a8H11ZVfo72fpCGSBrn7pPKydmbdunW5WrVqpT8QAAAAAAAA\nAIB/mBEjRmj48OFFlR2/z8xoN7Nqkh6X9LC7jyu4amP2/2bt+P5s/4BU9ACtLbzg7qWSxksab2af\nShogaVIls/5m/vz5lR1aoW7dumnGjBnJOdOnTw+oRho2bJhGjhyZnNO2bduAavJOOeUU/eUvf0nO\nqV69ekA1eb1799bkyZOTc0pKtv8jjV1z5ZVXatSoUSFZnTt3Dsnp0aOHpk2blpxTtWrVgGryTjrp\nJL388svJOUuXLq14UCUNHDhQTz75ZHLOxo0bKx5UCd///vf1hz/8ISSrU6dOITmtWrXSokWLknPK\nysoCqslr3bq1Fi5cmJzzxRdfBFQT91oiSY0bNw7Jadq0qRYvXhySVaVKzOpuRx11lD788MPknKOP\nPjqgGimXy6moqNKnHzs1YcKEkJy+fftq4sSJIVk333xzSM6ECRPUr1+/5JwHH3wwoJq8Zs2a6f33\n30/OWb58eXoxyr92v/rqqyFZjz/+eEjObbfdpquvvjok69133w3JGTt2rAYNGpScc8QRRwRUI91z\nzz0aOnRoSNa5554bktOnTx9NmjSp4oGVMHr06JCcxx9/XOecc05I1tlnnx2SM3jwYD300EPJOU2a\nNAmoRurXr1/Y60DUee7555+vRx99NCSrZs2aITlR592SFDHx7tRTT9ULL7wQUE3c1+3CCy/Ub3/7\n25CsqPOlyHOTOnXqhOREvu6uX78+OaNnz56aOnVqQDVx7yuj+jhSzM+bJHXv3j2sd7Z58+bkjMiv\nW9Rj1KlTJ82ePTskK+rndvjw4RoxYkRI1texL60vPkbSm+7+y0qMnSrpfEkysxOUX6t9l5hZezNr\nlG1XybLe39U8AAAAAAAAAMD+ZZ+Y0W5m3ZVvnC8ws7mScpKuzf4vzz2SfmNmb0haKKnw1ypfd62c\nBpLuN7ODssuzJG2dZrHvrLsDAAAAAAAAAPiH2Cca7e4+XVJ560A8XzBmpaTm2fYGSd/fQVbzcvYt\nVjbr3d1/J+l3BdeNV37ZmEplAQAAAAAAAAAOLPvS0jEAAAAAAAAAAOx1aLQDAAAAAAAAAJCARjsA\nAAAAAAAAAAlotAMAAAAAAAAAkIBGOwAAAAAAAAAACWi0AwAAAAAAAACQgEY7AAAAAAAAAAAJaLQD\nAAAAAAAAAJCARjsAAAAAAAAAAAlotAMAAAAAAAAAkIBGOwAAAAAAAAAACWi0AwAAAAAAAACQgEY7\nAAAAAAAAAAAJqu3pAg4kNWrU2OvyOnfuHFBJXFZRUVFAJdtEPEbVq1cPqGSbiJp69uwZUEls1vr1\n60NyojRp0mSvy6tVq1ZAJds0b948OaNKlbjftx5//PEhOevWrQvJicpas2ZNQCXbfPbZZ8kZW7Zs\nCagkr6ysLCRn+fLlITlNmzYNy9q8eXNIzlFHHaUlS5Yk50yYMCGgmtisfv36heTkcrmwrKeeeiok\nR5Iuu+yy5IzPP/88oJK8Zs2aheRFPgdEZX37298OyYnMqlq1akiOJA0fPjw5I+q5TZLOOuuskJzI\n9ydRWT/4wQ9CciKzGjduHJIjSccee2xyRuT3dr169UJyGjVqFJIjSe3btw/JKS0tDcmRpBYtWoTk\nbNq0KSTn8MMPD8mpU6dOSI4ktWrVKiRn48aNITmRos4pI7OieidROZHPS1FZe2NNBx10UEhOzZo1\nQ3L2Rn369NkrsyqLGe0AAAAAAAAAACSg0Q4AAAAAAAAAQAIa7QAAAAAAAAAAJKDRDgAAAAAAAABA\nAhrtAAAAAAAAAAAkoNEOAAAAAAAAAEACGu0AAAAAAAAAACSg0Q4AAAAAAAAAQAIa7QAAAAAAAAAA\nJKDRDgAAAAAAAABAAhrtAAAAAAAAAAAkoNEOAAAAAAAAAEACGu0AAAAAAAAAACSolnJjM1vt7nWi\nijGzAZJukFRdUpmkG9z9iV3MairpWXc/0cx6SRon6V1JRZKWu/s3zezfJK1190d2klNT0v2S2mS3\n/VzSqe6+zsw2S5qf7c9JGuDuH+xKvQAAAAAAAACAfVNSo1355nIIM2sraYSkf3b3D8ysmaQXzexd\nd58bUN9Udz+78Ep3v7cSGT+RtNTdf5DV2UpSaXbdWnfvsIu1AQAAAAAAAAD2A6mN9q/IZpKPkXS4\npOWS/kXSEklvu3tzM6snaYWk3u7+kplNkTRE0lWSfrF1Rri7v29mv8j2/8DMJkm6yt1LzOxwSbPd\n/ZjseA9LqpWV8CN3f6Wc0orKqfV6SavdfVSWP1NSH0mHSvpXd58uqZGk97fext0X7SwTAAAAAAAA\nAHBg+Ues0X6XpN+4eztJv5d0l7tvkfSWmbWW1F3SHEk9zOwgSUe6+zuSjs/2F5ot6bgdHGfrbPVl\nys+C7yTpe9nxy9PDzEqyfz/dwZiq7l4s6QpJ/zfbN0bSNWY23cxuMrOWBeNrZnlzzWyXlrgBAAAA\nAAAAAOzbwme0S+om6dvZ9sOSbsu2X5LUS9Ixkm6RdImkqZJeTTxedUn3mlk7SZsltdrBuK8sHVOO\nJ7P/50hqKknuPt/MjpH0TUmnSJplZt3c3SWtY+kYAAAAAAAAADiwFeVyu77Mupmtcve62+1bJqmR\nu282s2qSlrh7AzM7WdJQ5ZdiOVXSZEn/K+kLdx9tZg9JmuTuvynIGiKpq7tfYmZ/kfRTd59tZk0k\nTcuWorle0iHuPtzMqkpa7+4HZUvKPOPubbIPQ71q+0Z7OUvHFC5N86q7Ny/nPt8l6V13v+Prfhjs\n+vXrczVr1qzscAAAAAAAAADAHvDqq6+qc+fOlV46PHVGe3kHelnS9yU9IukHkqZl+2cpP8P9HXff\nZGbzJP2bpDOy62+X9Cczm+jui7MPQ/2xpHOy69+X1En55WQGFRzvUEkfZtuDJVVNvE9bFUmSmZ0k\n6U13/yJb6uY4SRN3JXDhwoVBpUkdOnRQSUlJcs7q1asDqpF69eqlKVOmJOcUFcUte9+zZ09NnTo1\nOad69eoB1eR169ZNM2bMSM6JqqlTp06aPXt2SNb69etDcnr06KFp06ZVPLACRx99dEA1eU2bNtXi\nxYuTcz7//POAavLatWunefPmJedUqRKzglibNm302muvhWSl/AK4UNu2bTV//vzknDVr1gRUk9e9\ne3dNnz49OWfLli0B1cT9vElS1C+SI5+XNm/eHJJTXFysmTNnJuesXbs2oBqpb9++mjhxl05FvqJf\nv34hOblcLuw1/KmnngrJGTBggJ5++unknKZNmwZUk9e+fXvNnTs3OWfTpk0B1cR9b0txz91du3bV\nK6+U93FLX1/VqjFvCzp37qxXX039I1xp+fLlAdVIp59+up577rmQrHr16oXknHTSSXr55ZdDspYt\nWxaSE/UcIEmNGzcOyenSpYtmzZqVnBP1vd2xY0fNmbP96q27Juo84LjjjtObb74ZklVaWhqSE3VO\nKcU8f0c9J0lxrydR57iStHHjxpCcyPOlWrVqVTyoEiJf4yK+vyPfC0T9vO3vX7eI5+/I54Co8/fI\n93BR55SRj9PXkdpor2lmHyjflM5JGiXpMkm/NbNh2vZhqMqa6x9I2tplnCbpe+6+ILt+vpldLekZ\nM6uh/NItfdz97Wz8SOUb8RcrPxN+q/8n6QkzGyzpBUm7+i52+6/k1sstJN1jZlJ+Tfv/dfendnAb\nAAAAAAAAAMABJqnR7u47un2506PcvVfB9h8k/WG765+W9LQkmdkvJP23mX3L3cuyNdHbFgy/LrvN\n29vt/2m2f7GkNtn2FElfmW7t7jcUbPct2F4pqXm2/bDyM/HLuz91y9sPAAAAAAAAADhw/CM+DDWE\nu/9sT9cAAAAAAAAAAEBFYhbnBQAAAAAAAADgAEWjHQAAAAAAAACABDTaAQAAAAAAAABIQKMdAAAA\nAAAAAIAENNoBAAAAAAAAAEhAox0AAAAAAAAAgAQ02gEAAAAAAAAASECjHQAAAAAAAACABDTaAQAA\nAAAAAABIQKMdAAAAAAAAAIAENNoBAAAAAAAAAEhAox0AAAAAAAAAgAQ02gEAAAAAAAAASFBtTxdw\nINmwYcNel1daWhpQSVzWpEmTAirJ69mzp8aPH5+c07hx44Bq8rp166aSkpLknGnTpgVUIz322GMa\nOXJkSNa1114bkiNJ9erVS86YMmVKQCV5gwcPDsn77LPPAqrJa9eunSZPnpycs3LlyvRiJLVp00Zj\nx44NyWrRokVITtu2bTV37tzknNatWwdUs021aukvvfPnzw+oROrRo4cWLlwYkhWV06lTJz366KMh\nWStWrAjJKS4u1t13352cs2TJkoBqpL59++rmm28OyXrqqadCciKzvv3tb4fk5HK5kKzI1xNJWr16\ndXLGwQcfHFBJXlFRUUjOrbfeGpLz1FNP6bbbbgvJMrOQnM6dO+uJJ55Izol6Tjr99NP15JNPhmR9\n5zvfCcmRpC+//DIk58orrwzJGTBgQFjW2WefHZLTpUsX/f73v0/OOf744wOqkTp27Bjy3kSSXn/9\n9ZCcX/7yl7r33ntDsnK5XEjOr371Kz344IMhWRHnlZ07d9bs2bMDqon7ue3evXvYe9SePXuG5Ehx\nr5dlZWUhOZFZEecTkTmrVq0KyZGkZcuWheQ0a9YsJCfS2rVr96qcOnXqhORIceeUUa/dU6dO1VVX\nXRWWVVnMaAcAAAAAAAAAIAGNdgAAAAAAAAAAEtBoBwAAAAAAAAAgAY12AAAAAAAAAAAS0GgHAAAA\nAAAAACABjXYAAAAAAAAAABLQaAcAAAAAAAAAIAGNdgAAAAAAAAAAEtBoBwAAAAAAAAAgAY12AAAA\nAAAAAAAS0GgHAAAAAAAAACABjXYAAAAAAAAAABLQaAcAAAAAAAAAIEG1PV3A9sysgaQ7JBVL+lzS\nJkkj3H3cduOaSnrW3U/cbv8Nkqa4+8QKjtNOUomkU939z4F3AQAAAAAAAABwANkbZ7Q/LWmyu7d0\n986SvifpyMIBZlY128xtf2N3v76iJnvme/r/2bvzMLnKMu/j3yYJITsCAoJsifCwZl8IhAQIKiAg\nsiiLBhzDDIogjgsIyqZOUFEBw4iCYiIqDBJQkMUBQ8IWgmSBgNyyKYgvO4GQQDb6/aNOoKdN0h3P\nPUMC3891cXHq1HN+dVd1ddWpu588BbcCh69oQCmlqd1VS5IkSZIkSZLekVarGe2llD2BhRFx0bJ9\nEfEEcEEp5SjgIKA7jT8QHL2CjEuAa4D5wKci4qPV/lHAFyNi/2roocBewG2llLUjYlE1S/5G4C5g\nILBvKWVb4ExgbeAR4JMRsaCU8jVgP6ALcEdEHJv4UEiSJEmSJEmS1hCr24z2HWgs57IiA4CDImKP\ndmTdBAwtpXSpLn8M+BVAKWUX4NGIeAyYDHyoxXHvA8ZXS9IsAL4KjI6IwcA9wBeqcT+IiGER0Rfo\nWkppmSFJkiRJkiRJeodYrWa0t1ZKGQ+MoLFO+wXAf0fES+05NiKWllJuAPYvpVxJo5n+perqw4HL\nqu3LgTHAVdXlv0bE3dX2zsD2wO3VMjKdgDur60aXUr4EdAXeBcwBfvdP3VFJkiRJkiRJ0hqrqbn5\nH5Y5f8tUS8ecFhG7t9i3Ho2Z5KcDgyPihGr/FsA11YzylhmXVPsnlVL2AD4LXAj8W0QcUkpZC/gb\nsBhYSmNW/3rAe4ANWmaWUvYDDo+II1vdRmfgr8DAiPh7KeV0oDkizlrZ/VuwYEFz165d/5mHRpIk\nSZIkSZL0f2TkyJFMnTq13d/huVrNaI+IP5RSvllK+beI+FG1uzvL+dLTSlt3dArwU+AY3pzBvhcw\nOyL2WTaoas5/hMaXo7bMnAaML6X0iYhHSildgU2BZ6qani+ldAcOAa5o6/7NmjWrrSHttssuu3DH\nHXfUzlmwYEFCNbDXXntx00031c6ZPHlyQjUN3/zmNzn11FNr52yyySYJ1TQcd9xxXHDBBbVzbr31\n1oRq4LLLLuOwww5Lycp4rAF22mkn7rvvvto5M2fOTKimYcyYMUycOLF2zgsvvJBQTcOJJ57Iueee\nWzvn+eefT6gGvv71r/O1r30tJatPnz4pOUcffTQ/+9nPaudst9129YupDBs2jLvuuqt2zuzZsxOq\ngX/913/lxz/+cUrWn/70p5Sc73//+3z+859PyXruuedScn7+85/ziU98onbO3//+94Rq4Oabb2b0\n6NEpWccff3xKzoEHHsjVV1+dkvWRj3wkJae5uZmmpvrfaz9lypSEahqqE/XaOeuss05CNTB06FCm\nT5+ekjVu3LiUnKuuuirtOVBKSck5++yzOfnkk2vnZL0mXXzxxYwdOzYl6+CDD07J2Weffbj++utT\nso477riUnEcffZTevXunZB1wwAEpOeeeey4nnnhi7ZwddtghoRo45phjuOiii9oe2A5z5sxJyTnv\nvPP43Oc+l5KVNanw/PPP54QTTkjJyjiv/PSnP80Pf/jDhGrgpZfatWBAm04++WTOPvvslKyRI0em\n5GT1TABef/31lJwRI0Zw2223pWS9/PLLtTP23XdfrrvuuoRqcuoBOOyww7jsssvaHtgOW265ZUrO\nzjvvzLRp01KyXnvttdoZu+++O7fcckv9YoAePXqk5AwaNIh77rknJSvrs+DUqVPTXk9WxWrVaK8c\nCJxbSvky8CyNLzU9icYSLa1tU0p5nEZzvBn4PC2a8hHxeinlWuAoGsvDABzGm8vELDMJOJZGo73l\n8c+VUo4GflXNYm8GvhoRD5VSLgbuB/4fkPMJRZIkSZIkSZK0xlntGu0R8TSNNdSXZ0KLcX8FOi9n\nzJWt8o4Hjm9x+V+Wc5vXANdUF/u2uu4WYOhyjvkakDN9U5IkSZIkSZK0xlrrrS5AkiRJkiRJkqQ1\nmY12SZIkSZIkSZJqsNEuSZIkSZIkSVINNtolSZIkSZIkSarBRrskSZIkSZIkSTXYaJckSZIkSZIk\nqQYb7ZIkSZIkSZIk1WCjXZIkSZIkSZKkGmy0S5IkSZIkSZJUg412SZIkSZIkSZJqsNEuSZIkSZIk\nSVINNtolSZIkSZIkSarBRrskSZIkSZIkSTXYaJckSZIkSZIkqYaOb3UB7yRNTU2rXV63bt0SKsnL\n2nXXXRMqyc2bP39+QiVv2nDDDWtnfPzjH0+oJDdr6dKlKTlZWR06dEioJDevd+/eCZXk5m233XYJ\nlTSMGDEiJWf8+PEpOUcffTRXXnll7ZwxY8YkVNMwbNgwHn/88do5Rx99dP1ikrPOP//8lByATTfd\nNCWnlJKSAznvJ3vvvXdCJQ0/+clPUnJefPHFlByALbbYIiVnypQpKTlZKkErsgAAIABJREFUWaNG\njUqopKG5uTkl7+GHH06opmH99ddPyTnjjDNScjKzFi9enJIDcMghh9TOWG+99RIqaTjllFNScubO\nnZuSA7DRRhul5EyaNCklJzPr0UcfTckBGDlyZO2MzPPcjM8mAHvssUdKTmbWggULUnIAdt5555Sc\nrJ7Auuuum5KzzTbbpOQADBkyJCWnS5cuKTmZWQsXLkzJAejYMacN17Nnz9Uqp3Pnzik5AO9+97tT\ncjJfK7OysnpwWTmZ5wFZWZmfvzOz2ssZ7ZIkSZIkSZIk1WCjXZIkSZIkSZKkGmy0S5IkSZIkSZJU\ng412SZIkSZIkSZJqsNEuSZIkSZIkSVINNtolSZIkSZIkSarBRrskSZIkSZIkSTXYaJckSZIkSZIk\nqQYb7ZIkSZIkSZIk1WCjXZIkSZIkSZKkGmy0S5IkSZIkSZJUg412SZIkSZIkSZJqsNEuSZIkSZIk\nSVINHbOCSilLgdk0mvdLgM9GxLSamf2ATSLi+uryUcB3gL8BTcDsiDh6JcePAr4YEftXxw6KiBNK\nKacDxwDPAOsAkyPiuDZq+TAQEfFgdXky8IWImFHnPkqSJEmSJEmS1mxpjXZgfkQMBCilfAA4G9i9\nZmZ/YDBwfYt9l0XECauQ0byC/d+LiO8BlFJuLaWMiogpK8k5ELgWeHAVbluSJEmSJEmS9DaX2Whv\narHdC3gBoJSyMXA50KO6vU9HxO2llHnAD4F9gb8DpwLfBjYDTgRuBM4C1iml7AqMW87tUN3GG7PL\nSynrA3+MiK3aU28pZR0as9pfrC6PBf4V6AQ8DHwCGAAcAIwspZwKHFJlfLSU8sPq/n4qIm5v60GS\nJEmSJEmSJL29ZK7R3qWUMqOU8ifgx8DXq/1HADdUs937AbOq/d2AmyJiR+CVavxo4CDg6xGxGDgN\nuDwiBkbEFdVxH6tuZ0a1HMzyrGgWe0ufL6XMAJ6ksSTMvdX+KyNiaEQMoDF7/VMRcSfwW+BLVS2P\nVmM7RMQw4PPAGe24TUmSJEmSJEnS20xTc3N7etJtK6W8HBE9q+2dgYsjYsdSym7AT4BLgd9ExOxq\nzKsR0aXaPhN4LSLGlVKagOcjYr2W66pX4/7H5Ra33XpG+90R0btao/0LEXHActZonxcR3yuldACu\nBH4ZEf9VHfN1YF0afwy4MSI+U0q5BLgmIia1uM1TIuLOUsqGwG0Rsc3KHqMFCxY0d+3atd4DLUmS\nJEmSJEn6X3XxxRczduzYf1hdZUUyl455Q0RMK6VsUErZICJuLaWMBD4E/KyU8t2IuBRY3OKQ14GF\n1bHNpZRVrWsJb87OX2cVa11aSrkBGAn8F3AJcEBEzKma86NWcvjC6v9LacdjOXv27FUpbaWGDx/O\nnXfemZZXV1Y9L774YkI1Dfvuuy/XXXdd7Zz58+cnVNNw6KGHcsUVV7Q9sA1dunRJqAb2228/rr32\n2pSs9773vSk5/fv3Z9asWW0PbMP999+fUE3DkUceyS9+8YvaOT169EiopuGAAw7gt7/9be2czp07\nJ1QDH/zgB7nxxhtTssaPH5+Sc80117D//vvXzhkzZkxCNQ1ZrwEf/vCHE6qBtddem0WLFqVknX/+\n+Sk5X/ziFznnnHNSsrp3756Sc+yxx3LhhRfWztl7770TqoEtt9ySv/zlLylZWe+7AwYMYObMmSlZ\n8+bNS8kZOXIkU6dOrZ0zatTKTgVXTXNzM01N7T5PX6GHH344oRro06cPjzzySErWK6+8kpLTr1+/\ntHPmxYsXtz2oHQYPHswf//jH2jnrrbdeQjXQu3dvHn300bYHtsPcuXNTcgYOHMiMGTNSstZaK+cf\nXWedUwJpj/dBBx3EpEmTaud06NAhoZrG+cRvfvOblKysCXwHHnggV199dUrWggULUnKOOOIIfvnL\nX6ZkZbwHHH744fzqV79KqAY23HDDlJzRo0dz8803p2RlvVZmnpssXLiw7UHtsPPOOzNt2rSUrCVL\nltTOGDFiBLfddltCNXmPUeZzqWfPnik5Q4YM4e67707JypBZz8svv5ySk/lze+yxx1Jyxo4dy8UX\nX5yStSoyl4554x2jlLJtlf18KWVz4JmI+AlwMTCw9fiVZM0D2vOb8RiNL00FOHRV6q1m0O9KYz12\ngO7AU6WUTsCRLca3VUv9d0xJkiRJkiRJ0honc0b7OtWa58sazmOq2em7A18qpSym0az+RHX9yv7k\nvey6ycDJVe64lYz/LvBfpZRjgN+1s94TSylH0vjS03tpfDErwNeA6cAzwF00vsQV4DLgolLK8TSa\n+a3rz/kTviRJkiRJkiRpjZLWaI+ITivYPxGYuJz9PVtsn7m86yLiRWBoq0MnLCcraHzR6jKnVfun\nAFOq7QnLjq1u70yWIyJ+BPxoOfvvAHZosWvPFtc9D/ReXp4kSZIkSZIk6e0tc+kYSZIkSZIkSZLe\ncWy0S5IkSZIkSZJUg412SZIkSZIkSZJqsNEuSZIkSZIkSVINNtolSZIkSZIkSarBRrskSZIkSZIk\nSTXYaJckSZIkSZIkqQYb7ZIkSZIkSZIk1WCjXZIkSZIkSZKkGmy0S5IkSZIkSZJUg412SZIkSZIk\nSZJqsNEuSZIkSZIkSVINNtolSZIkSZIkSaqh41tdwDtJhw4dVru8119/PaGShqamptoZ66+/fkIl\nuXldu3ZNqORN7373u2tn9OzZM6GShk022SQl54knnkjJ6d+/f0rWtttum1BNbt6SJUsSKnnTRhtt\nVDtj0aJFCZU0ZP2unHjiiSk52VlZ1ltvvdoZDz/8cEIlsP3226dljRgxIiUnM6u5uTklB6Bfv361\nM5599tmESmDLLbdMy8o8D8h6PVlnnXVScrKysn5HMvPe9773JVTS+B3Jypo5c2ZKDuT97i5dujQl\nJysr61ypd+/eaVndu3dPyYG8n9vixYtTcjKzMs7fM7PWXXfdhEoaevfunZLz6quvpuRA3ueTjM+n\ny2y99dYpOVmP06abbpqS06VLl5QcyPuMmvn5JCtrdawpS9a5YOfOnVNyMrMyz3OzshYuXJiSk/Va\nkvHZNDurR48eKTkAffv2TctqL2e0S5IkSZIkSZJUg412SZIkSZIkSZJqsNEuSZIkSZIkSVINNtol\nSZIkSZIkSarBRrskSZIkSZIkSTXYaJckSZIkSZIkqQYb7ZIkSZIkSZIk1WCjXZIkSZIkSZKkGmy0\nS5IkSZIkSZJUg412SZIkSZIkSZJqsNEuSZIkSZIkSVINNtolSZIkSZIkSarBRrskSZIkSZIkSTV0\nrBtQSlkKzKbRtF8CfDYiptXM7AdsEhHXV5ePAgZHxPEtxkwGvhARM1aS88aYUsohwFnA/6v+/xvg\nUaAD8DRwREQ8two1nQ7Mi4jv1bmvkiRJkiRJkqQ1W8aM9vkRMTAi+gOnAGcnZPYH9m21r7lm5qeA\nsRExuro8taq7H/BH4Lh/oiZJkiRJkiRJ0jtc7RntQFOL7V7ACwCllI2By4Ee1e18OiJuL6XMA35I\no2n9d+BU4NvAZsCJwI00ZpyvU0rZFRi3nNv5H0op/wkMBroAv46IM1td/zVgBPCTUspvgeuW5ZVS\nmqoan6ouDwHOAzoDrwKfBP6ygpp2qGbNbwacFxE/aNcjJkmSJEmSJEl628iY0d6llDKjlPIn4MfA\n16v9RwA3RMRAoB8wq9rfDbgpInYEXqnGjwYOAr4eEYuB04DLqxnnV1THfay6nRmllJnAoBY1nBIR\nQ6vb2b2UsmPLAiPi6zRmrR8RESdVu3crpcwA/lrd/k+r/X8CRkTEIOB0YNxKairA+4FhwOmllA7/\nzAMoSZIkSZIkSVpzZcxoX1A10yml7Az8HNgRuJvGDPJOwG8iYnY1fmFE/L7avg94LSJeL6XcB2yx\nktu5LCJOWHahmkm+zGGllGOq+7MxsD0wZzkZLWfFT42IA6qsLwHfAT4NrAtMLKVsTWO5mpU9Rr+L\niCXA86WUp4GNaMzSlyRJkiRJkiS9QzQ1N9db+ryU8nJE9Gxx+Slgx4h4rlo+5kPAZ4HvRsSlLce3\n/kLRZddVX346aFljvfXlat9k4As0lqr57+r6l0splwCTI2Jiqy9Dbbk9qtpe1mjflsaSMztWx98T\nEeNLKVtUWb2XU1Pr2u8DPhQRj6/osVqwYEFz165daz3ekiRJkiRJkqT/XdOnT2fo0KErXM68tdQ1\n2quG9Vo0ZnhvDvwtIn5SSlkHGAhcykrWWm9x3Tyg50rGtdSTxhI080opGwH7AJNXfsj/rBvYDXik\n2u4FPFltf7LFmFWpabnmzFneJPt/ztChQ5k+fXrtnNdffz2hGth5552ZNm1a7ZympnY/d9s0bNgw\n7rrrrto5r776akI1Dbvvvju33HJL7ZyePWs9Fd8wcOBAZsyYkZL15JNPtj2oHfbff3+uueaa2jmb\nbLJJQjUNgwYN4p577qmds2TJkoRqGrKe34sWLUqoBnbbbTduvfXWlKysmkaPHs3NN9+ckpUlq6b3\nvOc9CdXA9ttvzwMPPJCS9fLLL6fkZL2fANSdTLDM8OHDufPOO2vndOyYcdoFQ4YM4e67707JyjoP\nyHpNgrxzgaxzpfXXXz+hmoY+ffrwyCOPtD2wDe973/sSqmn8jmQ93jNnzkzJ6d+/P7NmzWp7YDss\nXLgwJSfr+f3aa68lVAOjRo1iypQpKVndu3dPyck6V4K816XM18qsn13W+dK6666bUA3stNNO3Hff\nfSlZWZ+Zsl67Ie/9JPO5lPE4jRw5kqlTpyZUA126dEnJebufm2S9n2T+7DJk1rPWWhkrU8OIESO4\n7bbbUrI6deqUkrO6PZcyf249evRIyRkwYEDaueDixYtTcjLfT1ZFxie+daq1zpe9i42JiOZSyu7A\nl0opi2k0qT9RXb+yT73LrpsMnFzljlvZ2Ii4t5Qyi8ba6k8At7Ues4LbHVHlrwXMBcZW+78NTCil\nfBX4XYvxrWtqnZfzaV6SJEmSJEmStEap3WiPiOX+iSgiJgITl7O/Z4vtM5d3XUS8CAxtdeiEVmP3\nbLH9SZaj1ZiW21OAd63gmGk0vuR0mdNWUlPL4/qu6DpJkiRJkiRJ0ttXzr/tkCRJkiRJkiTpHcpG\nuyRJkiRJkiRJNdholyRJkiRJkiSpBhvtkiRJkiRJkiTVYKNdkiRJkiRJkqQabLRLkiRJkiRJklSD\njXZJkiRJkiRJkmqw0S5JkiRJkiRJUg022iVJkiRJkiRJqsFGuyRJkiRJkiRJNdholyRJkiRJkiSp\nBhvtkiRJkiRJkiTVYKNdkiRJkiRJkqQabLRLkiRJkiRJklRDx7e6gHeSpUuXrnZ5Tz/9dEIlDU89\n9VTtjJdffjmhkoZhw4YREbVzevXqlVDNm1566aXaGZdccklCJTBhwgTOO++8lKxvfOMbKTkA/fv3\nr51xzjnnJFTSMGjQICZOnFg7p1OnTgnVNAwbNowrrriids7mm2+eUA3stttuzJw5MyVrp512SskB\nWGut+n9P3mCDDRIqedOGG25YO+PGG29MqAS23377tKxFixal5Oy8885MmTIlJWvBggUpOcOHD+eG\nG26onfPaa68lVANDhgzh17/+dUrWRz7ykZQcgObm5pScs88+OyXnqquuYty4cbVzzjjjjPrFtPDK\nK6/Uzsh6vc3MGjBgQEpOc3NzWtaVV16ZkgPw5JNP1s6YM2dOQiUwatSotNfJvn37puQMGjSIJ554\nIiXrqquuSsmZMGEC48ePT8kaPnx4Ss5uu+3G/fffXzsn67k0fvx4fvSjH6VkZZxzAQwdOpRLL700\nJatbt24pOUOGDGHSpEkpWTvuuGNKTtbv29y5c1NyhgwZwvTp01OyRo8enZIDeZ/ln3nmmZScTJ07\nd16tcl599dWUHIAlS5ak5GR+/s6S1RfMylm8eHFKTmZW1nv3xIkTU7PayxntkiRJkiRJkiTVYKNd\nkiRJkiRJkqQabLRLkiRJkiRJklSDjXZJkiRJkiRJkmqw0S5JkiRJkiRJUg022iVJkiRJkiRJqsFG\nuyRJkiRJkiRJNdholyRJkiRJkiSpBhvtkiRJkiRJkiTVYKNdkiRJkiRJkqQabLRLkiRJkiRJklSD\njXZJkiRJkiRJkmqw0S5JkiRJkiRJUg0d3+oCVlUpZSkwG2gCmoEDI+LxlYx/DBgUES+UUuZFRI9S\nyhbAn4AHafyx4RXgkxHx0EpytgB2iYhfVZePAgZHxPFZ902SJEmSJEmStOZZ4xrtwPyIGLgK45tX\nsP3wspxSyr8CpwJHryRnK+AI4FcryJMkSZIkSZIkvQOtiY32ptY7Ws8uL6VcA3wnIqYub/xycnoC\nL1THbgH8HOhaXffZiJgGjAO2LaXMACYAc4FNSynXA72BqyPipLp3TpIkSZIkSZK0ZlkTG+1dqmZ3\nE/BoRBxc7V/V2eV9qpyeQBdgWLX/aWCviFhUSnkfjRnsQ4CTgS9ExAHwRnO/H9AfWAxEKeX8iHiy\nxn2TJEmSJEmSJK1h1sRG+4JVXDpmRVouHXMocBGwD7A2ML6U0h9YCmy9koybI+KVKuMBYAvARrsk\nSZIkSZIkvYM0NTevWcuMl1JejoierfYdCQyPiM9Wl/8b+HpETG31ZagvR0TPanmYayKibzV+HeC5\niOheSjkd6BYRXy6ldABejYi1Symj+McZ7YMi4oTqcsvlapZrwYIFzV27dl3R1ZIkSZIkSZKk1cCY\nMWOYOHHiipYl/wdr4oz25d25vwCfLqU0Ae8Fhrbj2JbbuwGPVNu9gCeq7TFAh2p7HtDjn6j3DbNn\nz65z+P8wfPhw7rzzzto5Tz/9dEI1cOCBB3L11VfXznn55ZcTqmmofhlq5/Tq1SuhmoYPf/jD/OY3\nv6mdM2nSpIRqYMKECRx11FEpWd/4xjdScjbbbDOeeOKJtge24ZxzzkmopuG8887jc5/7XO2cTp06\nJVTTcM455/DFL36xds7mm2+eUA2ccMIJnH/++SlZO+20U0rOHnvsweTJk2vnbLDBBgnVNOy0007c\nd999tXNuuummhGrg85//PN///vdTshYtWpSSc9JJJ/Gtb30rJWvBggUpOWeeeSann3567ZzXXnst\noRr41re+xUkn5XwtzEc+8pGUnJ133plp06alZGX9/K+66qqU+3fGGWfUL6bSr1+/lPPBrIky/fv3\nZ9asWSlZAwYMSMlpbm6mqandn2VW6sorr0zJOeigg1LOvebMmZNQDZx22mmcddZZKVl9+/ZNycn6\nLACN390Mmee5w4cPT8k59thjufDCC2vnZD2Xxo8fz2c/+9mUrLXWWisl5/zzz+eEE05IyerWrVtK\nzrhx4/jKV76SkrXjjjvWzjjyyCP5xS9+kVANzJ07NyXnuOOO44ILLkjJGj16dErOtttuy4MPPpiS\n9cwzz6TkjBw5kqlTVzg3c5V07ty5dsawYcO46667EqqBV199NSVn991355ZbbknJ6tKlS0pO5uOU\n8fkk63Mu5L1ODh06lOnTp6dkjR8/PiVn4sSJjBkzJiVrVayJjfZ/+GQREbeXUv4C3A/8CbhnBeNb\nbveu1mhfC1gIjK32/ydwZSllDHADML/afy/weillJvAz4MW26pIkSZIkSZIkvf2tcY321svGtNj/\n8RXs79362Ij4K7DcP9tExMM0vuR0ma9U+5cArf+0OrHFcQe0o3xJkiRJkiRJ0ttMzr/vkiRJkiRJ\nkiTpHcpGuyRJkiRJkiRJNdholyRJkiRJkiSpBhvtkiRJkiRJkiTVYKNdkiRJkiRJkqQabLRLkiRJ\nkiRJklSDjXZJkiRJkiRJkmqw0S5JkiRJkiRJUg022iVJkiRJkiRJqsFGuyRJkiRJkiRJNdholyRJ\nkiRJkiSpBhvtkiRJkiRJkiTVYKNdkiRJkiRJkqQabLRLkiRJkiRJklRDx7e6AL21FixYsFplbb75\n5gmV5OZ16tQpoZI3bbDBBrUzBg8enFBJbtbzzz+fkrPZZpulZG233XYJ1eTm9ejRI6GSNw0YMKB2\nxpIlSxIqaejVq1dKzjrrrJOSk5W1cOHChEpy80aNGpVQSW5WU1NTSg7ABz7wgZScrl27puQAHHHE\nEbUzvvrVryZU0vDoo4+m5HTo0CElJzOrlJKSk5W1ePHihEpy85YuXZpQSUPWa9yVV16ZkpOZdfDB\nB6fkNDc3p2RddNFFCdU0bLLJJik5W221VUpOZtY222yTkpOZ1aVLl5ScrKyhQ4cmVJKblfla2a9f\nv5Sc7t27p+QA9O/fPyWnW7duKTlZ592Z7ydZn3Vef/31lJzMrM6dO6fkZGbNmzdvtcrJ/AzXsWNO\nq3J1fC5lfT7Jymlubk7JycwaOHBgSk52Vns5o12SJEmSJEmSpBpstEuSJEmSJEmSVIONdkmSJEmS\nJEmSarDRLkmSJEmSJElSDTbaJUmSJEmSJEmqwUa7JEmSJEmSJEk12GiXJEmSJEmSJKkGG+2SJEmS\nJEmSJNVgo12SJEmSJEmSpBpstEuSJEmSJEmSVIONdkmSJEmSJEmSarDRLkmSJEmSJElSDTbaJUmS\nJEmSJEmqoeNbXUB7lVLmRUSPFpePAgZHxPErOeaNMaWUDYBrgU7A54CfAy8Dr9P4g8PXIuK3bdTw\nlYgYV21vAVwbETvVvGuSJEmSJEmSpDXYmjSjvbmd+1Y0Zi/g3ogYFBG3Vft3j4gBwKHA+e3IOuWf\nuH1JkiRJkiRJ0tvYGjOjfWVKKfsBX6UxW/154MiIeLbF9f2AbwFdSimDgV2AJt78Q0Mv4IUW468C\n3gusA5wXEReXUsZVx88A7q9ur2Mp5cdV3t+AD0fEwv/VOytJkiRJkiRJWq2sSTPau5ZSZlT/zQTO\nbHHdrRGxc0QMAi4HTmp5YETMBk4DLouIgRHxWnXVH0op9wGTaTTOl/lkRAwBhgCfK6W8KyK+Aiyo\njv9ENW5r4AcRsSPwEnBw8n2WJEmSJEmSJK3mmpqb14zVT0opL0dEzxaXjwIGRcQJpZQdge8C76Ex\nq/2xiNi31Zg3tqvjHwMGRsSLpZTewM3ADhGxoJRyBnBgdVNbAB+MiOkta6jWaP99RJTq8peBjhHx\nHyu6DwsWLGju2rVr5sMiSZIkSZIkSUp27rnncuKJJza1d/zbYukY4AfAORHxu1LKKOD0dh7XBBAR\nj5ZSnga2L6V0A/YEhkXEwlLKZBpLyLwxvoWWy8QsbTFuuWbPnt3Osto2fPhw7rzzzto5jz32WEI1\ncMQRR/DLX/6yds4mm2ySUE3D7rvvzi233FI7p1OnTvWLqey6667cfvvttXNmzJiRUA0cf/zx/OAH\nP0jJ2m233VJy+vfvz6xZs2rnTJs2LaGahmOPPZYLL7ywdk6PHj3aHtRORx55JL/4xS9q5yxZsiSh\nGjjqqKOYMGFCStY222yTkpP1Opn5GjB48GD++Mc/1s5Za62cf5A2cODAtNeTpqZ2n3us1IABA5g5\nc2ZKVtYft0spRETtnK9+9attD2qHK664gkMPPTQl68tf/nJKzpAhQ7j77rtTsq688sqUnLPPPpuT\nTz65ds4hhxySUE1D1mvA0qVLE6qBYcOGcdddd6VkPfnkkyk5Bx10EJMmTUrJOvjgnH9s2tzcnPIa\nd9FFFyVUA2PHjuXiiy9OyRoyZEhKTr9+/dI+61x77bUpOaeeeirf/OY3U7Le+973puRknS9lveeO\nGTOGiRMnpmQtXrw4JedTn/oUP/nJT1KyunfvnpLzsY99jMsvvzwlq1u3brUz9ttvv7TfkxdeeKHt\nQe2Q+VwaPHhwSs7222/PAw88kJI1b968lJzM992Mmvbaay9uuummhGpgnXVW2g5rtxEjRnDbbbel\nZHXo0CElJ+tzJeR8jst8HmXJrCnrsT7xxBM599xzU7JWxZq0dMzKziZ6An+vto9a1eBSyobAlsBf\naazX/mLVZN8W2LnF0EWllJa/qTlnOJIkSZIkSZKkNdaa1Ghf2Ro3ZwK/LqXcDTy7knGt8yZX673f\nDJxUfYHqDUCnUsr9wH8ALf+U8mPgvlLKz9tRkyRJkiRJkiTpHWCNWTqm5frs1eUJwIRq+7fAb5dz\nTMsxb2xXl3uv4HYWAfuu4LqvAF9psatvi+u+2867IkmSJEmSJEl6G1mTZrRLkiRJkiRJkrTasdEu\nSZIkSZIkSVINNtolSZIkSZIkSarBRrskSZIkSZIkSTXYaJckSZIkSZIkqQYb7ZIkSZIkSZIk1WCj\nXZIkSZIkSZKkGmy0S5IkSZIkSZJUg412SZIkSZIkSZJqsNEuSZIkSZIkSVINNtolSZIkSZIkSarB\nRrskSZIkSZIkSTXYaJckSZIkSZIkqQYb7ZIkSZIkSZIk1dDxrS7gnWTx4sWrXd7WW2+dUEle1vTp\n0xMqadh99925//77a+dsttlmCdW86fnnn6+d0adPn4RKcrPmz5+fkpOVtcsuuyRUkpu3ZMmShEre\ntN1229XOeOqppxIqaXj3u9+dkvOud70rJScr66WXXkqo5E1Lly6tnfHwww8nVAIDBw7kz3/+c0rW\nxhtvnJIDeY/5448/npJTSuHBBx+snbPBBhskVJOb9eyzz6bkZGY999xzKTlZWeutt15CJbl5Tzzx\nREIlDa+99lpKzpw5c1JyDjrooLSsiy66KCUnK+uYY45JqATGjh2bljVhwoSUnH79+jF79uyUrClT\npqTknHrqqWlZJ5xwQkoOwPrrr187I/PzSb9+/VJyMs8p3/ve96bkdOrUKSUH8s5zO3TokJLTo0eP\nlJyOHfNaQhtuuGFKzup2HgDQpUuXlByAtdbKme+a9fzOylm4cGFKTmZW5s+tubk5JSfrvCsrp3v3\n7ik5kPd6kvm5MjOrvZzRLkmSJEmSJElSDTbaJUmSJEmSJEmqwUa7JEmSJEmSJEk12GiXJEmSJEmS\nJKkGG+2SJEmSJEmSJNVgo12SJEmSJEmSpBpstEuSJEmSJEmSVINGVmfgAAAgAElEQVSNdkmSJEmS\nJEmSarDRLkmSJEmSJElSDTbaJUmSJEmSJEmqwUa7JEmSJEmSJEk12GiXJEmSJEmSJKmGju0ZVEpZ\nCsym0ZhfAnw2Iqa190ZKKacD8yLie/9Ulf+kUkp/YAawd0T8vtq3BXBtROy0CjndgO8AHwDmAs3A\nhRHxk/yqJUmSJEmSJElrkvbOaJ8fEQMjoj9wCnB2xo2XUjpk5KzEYcCtwOGt9jevYs7FwAsR8b6I\nGAzsDazXetD/wf2RJEmSJEmSJK1m2jWjHWhqsd0LeGHZhVLKF4GPAmsDV0XEmdX+U4ExwNPA34A/\nVvsnA7OAXYFflVImAT8F1geeBT4ZEX+rZp4vb/8lwKvAAODdwKeq2xkOTIuIf2lR66HAXsBtpZS1\nI2JRtb9TKeVSYCAwpzp+FPCpiPhoVeco4AvAicCQiHijWR8Rz9OY4b5s3NeBF4ECbNvOx1SSJEmS\nJEmS9DbQ3hntXUopM0opfwJ+TKOxTCnl/cDWETGURuN7cCllRCllII3me1/gQ8CQVnmdImJoRHwf\n+AFwSTVb/pfVZVayH2DdiBgO/DvwW+C7EbE90LeU0reqbRfg0Yh4DJhc1bFMAcZXx8wDPgPcBAwt\npXSpxnwMuAzYgcayOSszADg+ImyyS5IkSZIkSdI7THsb7QuqpWO2A/YBfl7t/wDw/lLKDBproRdg\na2A3GrPbF0bEPBrN8JYub7E9HPhVtf1zGjPdV7Yf4Jrq//cBT0XEA9Xl+4Etq+3DaTTKl93eES2O\nf7zFGvOXAiMiYilwA7B/tQTMh4DftH4gSimnlFJmllL+1mL39Ih4vPVYSZIkSZIkSdLbX1Nzc9vL\nlZdSXo6Ini0uPwXsCJwMRERc1Gr854B3RcQZ1eXvAk9GxPeqpWO+EBEzquueAd4TEUtLKR2Bv0fE\nhqWUZ4GNl7P/EuCaiJhULS9zTUQsm8V+CY0m/NU0lqtZDCyl8QeF9YD3ABsAt0TEVtUxe9D4cteD\nl20DFwL/FhGHlFL6ADdGxPuW95gsW2ImIg5o63GcP39+c7du3dp8vCVJkiRJkiRJb53LLruMww47\nrKntkQ2rvEZ7KWVbGo3r54EbgbNKKb+MiPmllE1oNLenApeUUsbRWLt9fxrN6+W5g8bs80uBj9P4\n8lKA21ewf4W1tTAamB0R+7So+xLgI1XOFqWUYRFxF42Z7rdVw6bQWBf+GKrZ8BHxSCnlj6WUbwCn\nRcTrpZR1VnC7K3XPPfes6iErNHLkSKZOnVo7p0uXLm0PaochQ4Zw9913186ZPn16QjUNxx13HBdc\ncEHtnM022yyhmoYDDjiA3/629T/wWHUdO7b3V3fl9t13X6677rqUrF69eqXk7Lrrrtx+++21c3r0\n6JFQTUPfvn259957a+csWbIkoZqGgQMHMmPGjNo5Tz31VEI1uc+l3r17p+Rsu+22PPjgg7VzXnrp\npYRqGoYNG8Zdd91VO+exxx5LqAYOO+wwLrvssrYHtsPGG2+ckrP77rtzyy23pGRl/ew+/OEP85vf\n/MM/cltlN9xwQ0I18MMf/pBPf/rTKVn7779/Sk7ma8CkSZNSci6++GLGjh1bO+eUU05JqKahd+/e\nPProo7VznnjiiYRqYNSoUUyZMiUlKyvntNNO46yzzkrJ2mSTTVJyxo4dy8UXX1w755hjjkmoBpqb\nm2lqWuWPIss1YcKElJwxY8YwceLElKxLL700Jef3v/89H/jAB1KyTjjhhJSc/fbbj2uvvbZ2Ttbn\nk379+jF7dlurpLZP1jnlBz/4QW688caUrE6dOqXk7LnnnvzhD39IyerQoUPtjMzX7ldffTUlZ++9\n9047z+natWtKTlbPBFa/vgnAggULamdkPpeyPuuOHj2am2++OSUr6+e2yy67cMcdd6RkLV68uHZG\n5s+te/fuKTmDBg1K63k+9NBDKTmZn3VXRXuXjlmnWqN9Jo3lXMZERHNE/DeN9dPvLKXcC1wBdI+I\nmcB/AfcCvwNadk9bT6E/AfhkKWUWcCTwuTb2tz6+eTnbhwFXtRo3iUbjHuBB4LhSygPAusAPASLi\ndeBaYO/q/8uMpTET/uFSynQaf2D4EpIkSZIkSZKkd7x2TYuNiBX+KTgifsD//KLSZfv/A/iP5ezf\ns9Xlx2nMQG89bkX7/6XF9l9pfOFq6+v+YSpURFzDm2u7b7/8ewMRcTxwfKt9rwDHrmD8FBoz4SVJ\nkiRJkiRJ70DtndEuSZIkSZIkSZKWw0a7JEmSJEmSJEk12GiXJEmSJEmSJKkGG+2SJEmSJEmSJNVg\no12SJEmSJEmSpBpstEuSJEmSJEmSVIONdkmSJEmSJEmSarDRLkmSJEmSJElSDTbaJUmSJEmSJEmq\nwUa7JEmSJEmSJEk12GiXJEmSJEmSJKkGG+2SJEmSJEmSJNVgo12SJEmSJEmSpBpstEuSJEmSJEmS\nVEPHt7qAd5JOnTqtdnm33357QiUwZMiQlKzhw4cnVPOmwYMH185oampKqORNG2+8ce2MjTbaKKGS\nhh122CEl55VXXknJAVh33XVrZ3Tv3j2hkjf16tWrdsaSJUsSKnlTRk3Nzc0JlTRkPS8zH6eMrNXx\ntXvTTTdNqCQ3K+P5uMx6662XkrN06dKUHMh5TfnoRz+aUEluVufOnVNyIOe1G+Dggw9OycnKmjt3\nbkIluXmZ73FZWX379k3JyczaaqutUnKgca5b14QJExIqyc066qijUnLGjBmTlnXBBRek5AAceOCB\nKTnbbLNNSk52VoYuXbqk5Gy44YYpOZlZa62VN69w/fXXT8np2DGnBbPBBhuk5GSeK22yySYpOdnv\nu29XWefeWTkLFy5MyYG8c5P58+en5AC89tprKTlZny2zXt8yH6OsrEGDBqXkZGe1lzPaJUmSJEmS\nJEmqwUa7JEmSJEmSJEk12GiXJEmSJEmSJKkGG+2SJEmSJEmSJNVgo12SJEmSJEmSpBpstEuSJEmS\nJEmSVIONdkmSJEmSJEmSarDRLkmSJEmSJElSDTbaJUmSJEmSJEmqwUa7JEmSJEmSJEk12GiXJEmS\nJEmSJKkGG+2SJEmSJEmSJNVgo12SJEmSJEmSpBo6ZoSUUuZFRI9qe1/ge8D7gX2B+RFxaSnlKODG\niHhqJTlHAYMj4viMuqrMq4GNImJ4i32XANdExKRVyNkbOBPoAbwGBPCliPhbVq2SJEmSJEmSpDVP\nSqMdaAYopYwGzgU+EBFPAD9qMeZoYA6wwkZ7y6wMpZRewEBgXilly4j4yz+ZsyNwPrBfRPy52rcf\nsCXwt1ZjO0TE0jp1S5IkSZIkSZLWHFmN9qZSym40Guv7LGtol1JOB14B/gIMBi4tpbwKDAf60mjK\nd6MxQ3x0lbVpKeV6oDdwdUScVGW9n8aM8rWBR4BPRsSCUspjwARg/+r+HLqsGQ4cBPwWeBo4HBjX\noub3l1K+QmOG+r9HxHWllDuBf4mIP1W3ORn4AnAi8M0WuUTEtcu2q3GzgF2BXwHf/ycfR0mSJEmS\nJEnSGiZrjfbOwFXAgRHxUKvrmiPiSuCPwBERMRB4HbgMOD4i+gN70Wi2A/QDDqXRiP9YKWXTUsr6\nwFeB0RExGLgH+PcWt/FMRAwCLgS+1GL/4cAvq9s6vFVdW0TEEGA/4EellLWrcR8DKKVsDGwcETOA\nHYAZbTwGnSJiaETYZJckSZIkSZKkd5CsRvti4A5gbBvjmqr/F+DvVRObiHilxXIrN1eXFwL3A1sA\nOwPbA7eXUmYCY4DNW+ReVf3/nmo8pZSNgK0j4o6q+b+4lLJ9i2P+q7rth2nMkN8WuAI4pLr+o8Cv\nW9+BUsp6pZSZpZQopbRs9l/exn2XJEmSJEmSJL0NNTU3118SvZTyMrAh8AcaXzI6rtp/OjAvIr63\nbBmWiJhRrXl+YUSMaJVzFDAoIk6oLl8DfAfoCRweEUcu57Yfq455oZQyCPhOROxZSjkeOAt4kUaD\nvwfww4j4WvVlqLdExIQqYwrw2Yi4r5RyC3A8jdnx/xYRc0opE4DJEfGzFrf7BaBbRJzV8r6t7HFa\nsGBBc9euXdv9uEqSJEmSJEmS/u899NBDbL311k1tj2xIW6M9Il4rpXwImFpKeSoiLmk1Zh6NhjlA\nABuXUgZFxD2llO7AqyvJnwaML6X0iYhHSildgU2Xs0xNS4cBH4yI6QCllC2Bm4CvVdcfWkqZSGMt\n+K2qmqAxM/3LQM+ImFPt+w4wqZQyLSIerPatcsd89uzZq3rICg0fPpw777yzds5dd92VUA2ceOKJ\nnHvuubVzhg8fnlBNw7Bhw1LuX1NTu3+f2jR06FCmT59eO2ejjTZKqAa22GIL/vrXv6ZkvfLKKyk5\nO+ywA/fff3/tnO7duydU05D1OC1ZsiShmoY+ffrwyCOP1M6ZO3duQjUwaNAg7rnnnpSszp07p+Ts\nuOOOzJkzp+2BbVi0aFFCNQ0DBw5kxoy2ViJr2/z58xOqgd12241bb701JatXr14pOX379uXee+9N\nyXr22WdTckaPHs3NN99cO2ettXL+IeEee+zB5MmTU7Kyft922WUX7rjjjpSsl156KSVnn3324frr\nr6+dk/WeC3mvARkTZSD3tfuJJ55IyTnwwAO5+uqrU7K22mqrlJx+/fqlnMdnfRYYM2YMEydOTMk6\n6qijUnKam5vTzpkvuOCClJzPfOYz/Od//mdK1l577ZWSs8022/DnP/+57YH/RzLryTo3GTBgADNn\nzkzJynrfzXoNAOjYsX4LJuvzEsDSpUvbHtQOmedvWZ9PRo4cydSpU1OyunTpkpIzZMgQ7r777pSs\nTp061c7o378/s2bNSqgGFi5cmJKT1ceBvNelPffckz/84Q8pWRk/t8zPcFnnlJm/b+95z3tScrbe\nemseemhlbeP/HVlLxzQDRMSLwD7AV0sp+y3bX/kZcGEpZUZ1u4fRaJ7PAn5PY533FeU+BxwN/KqU\nMpvGMjWl5ZiWSilbAJsva7JXGX8B5pZShlTHPA5MB35HY+b6sk7KlTTWab+8xbFzgM8BE0spfyql\n3EpjqZlfrqgGSZIkSZIkSdI7Q8qM9ojo2WL7b0Cf6uK1LfZPAia1OOyPQOvpyxOq/5Ydc0CL7VuA\nocu57d4ttu8B9qwubracsYOrzRX+CTEingHWXs7+64HlTouKiD2Xt1+SJEmSJEmS9PaXNaNdkiRJ\nkiRJkqR3JBvtkiRJkiRJkiTVYKNdkiRJkiRJkqQabLRLkiRJkiRJklSDjXZJkiRJkiRJkmqw0S5J\nkiRJkiRJUg022iVJkiRJkiRJqsFGuyRJkiRJkiRJNdholyRJkiRJkiSpBhvtkiRJkiRJkiTVYKNd\nkiRJkiRJkqQabLRLkiRJkiRJklSDjXZJkiRJkiRJkmqw0S5JkiRJkiRJUg0d3+oC3kmWLFmy2uUN\nHDgwoZK8rN///vcJlTQMGzYsJW/LLbesX0xl6NChRETtnF//+tcJ1cC3v/1tLrjggpSsI444IiUH\nYPHixbUzHnjggYRKGrbYYouUvOeeey6hmoY+ffpwxx131M558cUXE6qBQYMGcfvtt6dk9evXLyUH\n4Pnnn6+d0b1794RK3tTc3Fw7Y86cOQmVwG677ZaWtXDhwpScvn378oc//CEl6+mnn07JGT16NDfd\ndFPtnIceeiihGthjjz3SXrs//vGPp+QAPPPMMyk5//7v/56S8+ijj3LcccfVzpk0aVJCNW9aa636\n81wy3ieXef3111NyrrrqqpScAw88MC1rm222Scnp168f1157be2cKVOmJFQDY8aM4dJLL03Jynot\nyczK+L0F+MxnPpOWdfbZZ6fknHTSSSnP7z59+iRU0/gduffee1Oyss69BwwYwDXXXJOS1alTp5Sc\nfv36cd1116VkbbXVVrUzdthhB+67776EamDevHkpOX379uWuu+5Kydpxxx1TciDvOZD1XpmZlfU5\nLitn0aJFKTkAc+fOTcnp2rVrSg7kPZcyPgtm5nTr1i0lJzNr3LhxKTk//elPU7PayxntkiRJkiRJ\nkiTVYKNdkiRJkiRJkqQabLRLkiRJkiRJklSDjXZJkiRJkiRJkmqw0S5JkiRJkiRJUg022iVJkiRJ\nkiRJqsFGu/T/2bvzeLvme//jr0MizSgSMZQOqHzNiSERNSRCb7Q/RSu9ghqquIipVdTVGlqKUjWl\nqFSpKq4x5baGmocgMQb14Za2FInWFDJKzu+PvdLue24iJ12fxsHr+Xh42Hvt73qvz1nnnL3X/pxv\nvluSJEmSJEmSarDRLkmSJEmSJElSDTbaJUmSJEmSJEmqwUa7JEmSJEmSJEk12GiXJEmSJEmSJKkG\nG+2SJEmSJEmSJNVgo12SJEmSJEmSpBo6tWdQKaUPcCvQCqwIzAFere4Pjoh324xfBvj3iDi/ur8a\nMAl4GugCPADsHRFzM76IUsoNwNIRsXnTtkuAKyPi14uQ8wXgOKAHMKOq91sR8dJC9lsS+GtELPNP\nlC9JkiRJkiRJ+gBr14z2iHgtItaPiA2Ac4HT591v22Sv9AX2a7Pt6Wr/9YBVgR3rFD5P1dRfF+hX\nSlm5Rs4A4HRgl4hYq6r1cuBT8xm7ZJtNLTT+6CBJkiRJkiRJ+ohp14z2Nlqa75RSjgB2o9FoPj8i\nxgAnAf1LKQ8DNwI/mzc+IuaUUiYAK1X7fx34AtAL+AxwCo0Z5bsA04AvRMRbpZRvAHsDs4HHI2L3\nKnIkcC3wJrAzcGpTeduUUo6p8g6JiJuqY+8SEc9Wx78bGA0cCXw/Iv6nqda/z4avxk0ANgN+Wc2i\n/xXQFbh+kc+iJEmSJEmSJOlDodYa7aWUwTSa2xsCnwVGl1LWBr4NRDXj/T+r4S3VPl2BQcBNTVFr\nAV8ENqbRaP9bNaP8YeCr1ZjDgQERMRA4sGnfnWk0vC+vbjdbOSI2ArYDLiildK7G7VTVshKwTEQ8\nDqxdHe+9LBERgyPiLOBs4McRMQCYspD9JEmSJEmSJEkfUi2trYu24kkp5VhgakScXkr5JtAtIk6o\nHvsB8GfgFhrro29QbW9eo3014NqI2LN67OvABhExurr/IrB+RLxaStkHWD0ijiil3Ay8DowDrouI\naaWUFYG7I+Iz1b6P0lgb/plqjfabIuKX1WP3APsCbwPXR8SAqv6eEXF8KeUxYFRE/L6U0g+4GegO\nnBMRZ1Uz2o+IiPFV3mtA34horZav+UNE9Hmvc/fOO++0du/efZHOtyRJkiRJkiRp8dprr7248MIL\nWxY+suGfWTrmn/V0RGxQSlkWGF9K2SYibqwem9k0rrXp/tymGkcAQ4Htgf8spawLjAL6llKeozFj\nvheNWe3HN2XN0wK0RsSfSylTSylr0pjZvkf1+BM0Zub/PiJeBdYvpRxJY9mZed5prjMi5uW364Q/\n/PDCJsy33+abb87dd99dO2dR/9CyIFtssQV33XVX7Zw777wzoZqG7373u3z/+9+vnfPpT3+6fjGV\n3XbbjUsuuaR2zqRJkxKqgR/+8IccccQRKVm77LJLSs7AgQN59NFHa+e8/PLLCdU0fP7zn+e3v/1t\n7Zy//vWvCdU0ZP0svf766wnVwMEHH8xZZ52VkjVgwICUnKFDh6Y8p/To0WPhg9ppww035KGHHqqd\n8+CDDyZUA/vvvz/nnntuStbMmTMXPqgdDj30UM4444yUrMmTJ6fknHTSSRx11FG1c5599tmEauCq\nq65i5MiRKVlf/epXFz6oHXbYYQeuu+66lKxvfvObKTnPPfccq666au2ca665JqGahqzXuNmzZydU\nA4MGDWLChAkpWeecc05KzsUXX8wee+yx8IHt0L9//5Sco48+mhNPPLF2TtZ17s0338y//du/pWTt\nsMMOKTkHHHAAP/nJT1KyRo8enZLT2tpKS0u73xe/p5NPPjkl58gjj+SUU06pnbPaaqslVAMjR47k\nqquuSsl66qmnUnKOOeYYvve976Vkde7cOSXnqKOO4qSTTkrJWmWVVWpnjBo1issvvzyhGpg6dWpK\nzj777MMFF1yQkrXOOuuk5GyyySaMHz8+JWuJJWotBvF3G2+8MQ888EBK1rRp02pnbLnlltx+++0J\n1cCsWbNSckaMGMFNN9208IHt0K1bt5ScrP4b5PTgsvpvAFmTgbPe5wKMGTMmJefCCy9kr732Ssla\nFHWfLe4GvlRK6VJK6UGjCX43MBXo2WZsC0BE/BU4CvhP2qmU0gJ8IiLuoLGWel8as81HAVtFxKoR\nsQqNpWeau31fqfbvD6wMzHuHe0VVw1IR8XS17VTgu9XYed7rt3J8KWWn6vau7f1aJEmSJEmSJEkf\nLrUa7RExAbgMmAjcB4yJiCcjYgrwUCnlsWo5GWiaXR4RVwHLVGu8tzW/P+90Bn5VLe8ykUZTfDlg\nhYj4+zTx6oNMp5dS1q9y/lJKmUhjuZl9IuLdauhVNGa+X9G076PAN6vj/L5aKmY1Gmu6z6+uQ4Bv\nVMvV9FvwWZIkSZIkSZIkfZgt8tIxEXF8m/unAafNZ9yoNps2aPP4utXNB9ts/2TT7Z81PbTZfMr5\n1HyOO7C6uft8xs8b8zKN5n3b7f8N/PcC9tmizf0/AEOaNh2zoONJkiRJkiRJkj68chaakiRJkiRJ\nkiTpI8pGuyRJkiRJkiRJNdholyRJkiRJkiSpBhvtkiRJkiRJkiTVYKNdkiRJkiRJkqQabLRLkiRJ\nkiRJklSDjXZJkiRJkiRJkmqw0S5JkiRJkiRJUg022iVJkiRJkiRJqsFGuyRJkiRJkiRJNdholyRJ\nkiRJkiSpBhvtkiRJkiRJkiTVYKNdkiRJkiRJkqQabLRLkiRJkiRJklRDp/e7gI+SLl26dLi8zp07\nJ1TS0LNnz9oZyyyzTEIluXlvvPFGQiW5eUsttVRCJblZs2fPTsnJynrnnXcSKsnN6927d0IluXlv\nv/12QiUNWc8nTzzxRErO0KFDU7LWWWedhGr+IeOcr7nmmgmV5GaNHz8+JQdg+vTpKTmtra0pOVlZ\n2223XUIluVkf//jHU3IyszraeXruuecSKmkYOHBgSl6/fv0SqmmYMWNGSs4mm2ySkpOZ1bVr15Qc\ngJVXXrl2xsEHH5xQSW5W//79U3IAtt5665Sck08+OSUnM+vb3/52Ss6RRx6ZknXHHXfUL6aS9XzS\nvXv3lJzMrMz33xnvdQFmzpzZoXKyvq7MrE6d8tpUWVmZ73XnzJmTkvPSSy91qJw+ffqk5ADMnTs3\nJacj/izNmjUrJSfrfU7Wuc7M6ojPS4vCGe2SJEmSJEmSJNVgo12SJEmSJEmSpBpstEuSJEmSJEmS\nVIONdkmSJEmSJEmSarDRLkmSJEmSJElSDTbaJUmSJEmSJEmqwUa7JEmSJEmSJEk12GiXJEmSJEmS\nJKkGG+2SJEmSJEmSJNVgo12SJEmSJEmSpBpstEuSJEmSJEmSVIONdkmSJEmSJEmSarDRLkmSJEmS\nJElSDZ3e7wLmKaXMAR4DWoBWYAegH7BbRByadIzngQ0j4rWMPEmSJEmSJEmSOkyjHXgnIjZos+3P\nwENtB5ZSloyIOf/EMVr/qcokSZIkSZIkSVqAjtRob2m7oZQyFPhWRHyxlHIssBqwKvCnUspuwMnA\nUKALMCYiLqj2+R4wFfgMcFtEHND2GKWUa4GVgY8BZ0bE2Gr7NsCJNJbV+WtEfK6U0g04G1gb6Awc\nFxHXl1LWAn5ebVsC2DEi/pB6ViRJkiRJkiRJHVpHWqO9aynl4VLKI6WUq5u2N89CXxMYHhG7Al8H\n3oiIjYHBwL6llE9V4wYBo6vxnymlfHk+x/taRAyqxh5SSlmmlLIs8FPgSxGxPvCVauzRwK0RMQQY\nDpxWSukK7AecUc3E3wh4sfZZkCRJkiRJkiR9oLS0tnaM1VRKKW9FRK8224YCh0XEdtWM9rkR8f3q\nsSuBdYHp1fBewH8As4HjI2JYNe5rwLoR8c3mNdpLKcfRWAce4FPACGA5YKeI2K1NHRNozJqft1xN\nb2AbYAMaTfiLgWsj4n/e62ucNm1aa7du3RbhrEiSJEmSJEmSFrdDDjmEM8888/+swrIgHWnpmPZ4\np+l2C3BQRNzSPKBqzrf960HrfMYMBzaOiJmllNtpLCEzL3d+doyIZ9tsi1LK/cC2wG9KKftGxB0L\nKv6JJ55Y0EOLbPDgwTz44IO1czp37pxQDay//vo88sgjtXPuvffehGoaDjzwQM4555zaOZl/jDro\noIM4++yza+dMnjw5oRo44YQT+M53vpOStf3226fkDBo0iAkTJtTO+dOf/pRQTcPIkSO56qqraud0\n6dIloZqGL37xi1x//fW1c158Mecf4uy///6ce+65KVlz585NyRk9ejRjxoypnbPOOuskVNMwdOhQ\n7rzzzto5Wc9Lw4YN44477kjJGj9+fErOUUcdxUknnZSS9eabb6bknHzyyXz729+unbPWWmslVAO7\n7747v/jFL1Ky1lhjjZScrOsSgF/96lcpOWeccQaHHnpo7ZwtttgioZqGL3/5y1xzzTW1c/r165dQ\nDWy++ebcfffdKVlPPvlkSs5+++3Heeedl5LVtWvXlJw99tiDiy++uHZO3759E6qBbbfdlhtuuCEl\nq3///mk5zzzzTErWtddem5Jz5JFHcsopp6RkZbwGQOP1u6Wl3e/VFyjrtTvrugRg4sSJKTmHHXYY\nP/rRj1Kysq69s95XAvTs2bN2RtZzEuSdo1GjRnH55ZenZK222mopOVnvKwFmz56dkvPZz36W++67\nLyXr+eefr52x6667cumllyZUA3369EnJ+fznP89vf/vblKzevXun5GyyySZp73VmzZpVOyPzuTtr\nMnDm79svf/nLlJwzzzyTQw45JCVrUXSkpWMW9YrjJuCAUkongFLK6tVyLgCDSymfKqUsAewEtH0H\nsTTwetVkXwMYUm2/H9h83hI0pZRlmo518LydSykDq/+vEo6XIv8AACAASURBVBHPR8TZwDhgvUX8\nGiRJkiRJkiRJH3AdaUb7ok7PGwt8Gni4lNICTOEfS8FMBM7hHx+Gel2bY9wI7FdKeRIIYDxARPy1\nlLIvcG1T5gjgBOCMUsrjNP448RywHfDv1YeyzgZepvEhqpIkSZIkSZKkj5AO02hvuz57te1O4M7q\n9vFtHmulsT760c3bSykAb0bEdvPJW7Xp7hcWUMdNNGawN2+bQeODT9uOPQXI+feIkiRJkiRJkqQP\npI60dIwkSZIkSZIkSR84HWZGe5bmWfCSJEmSJEmSJP2rOaNdkiRJkiRJkqQabLRLkiRJkiRJklSD\njXZJkiRJkiRJkmqw0S5JkiRJkiRJUg022iVJkiRJkiRJqsFGuyRJkiRJkiRJNdholyRJkiRJkiSp\nBhvtkiRJkiRJkiTVYKNdkiRJkiRJkqQabLRLkiRJkiRJklSDjXZJkiRJkiRJkmro9H4X8FEyd+7c\nDpc3ZcqUhErystZcc82ESnLzevXqlVDJPwwZMqR2xpgxYxIqaXjxxRdTckopKTlZWTvttFNCJQ0j\nR47kiCOOqJ2z7rrrJlTT8MUvfpGxY8fWzhkxYkRCNQ2tra0pOcstt1xKTlbWsssum1BJbt7DDz+c\nUEnDCy+8kJKz5JJLpuRkZq222mopOVlZK620UkIluVkd8fu29tprp+RkZWWeo6y83r17J1SSm/XE\nE0+k5GRmDR48OCUHoKWlpXbGJz7xiYRK8rM6mo723A1wxx13pORkZQ0bNqx2BjSu3bKyRo0alZID\nMHHixJScTp1y2h0HHnggDzzwQErW0KFDU3Jmz57doXIA3n777ZSc1VdfPSUnMyvzNS6rL7Teeut1\nqJxp06al5AD06dMnJSfzGq5z585pWRmWWmqplJw5c+ak5GRmvfvuuyk52Vnt5Yx2SZIkSZIkSZJq\nsNEuSZIkSZIkSVINNtolSZIkSZIkSarBRrskSZIkSZIkSTXYaJckSZIkSZIkqQYb7ZIkSZIkSZIk\n1WCjXZIkSZIkSZKkGmy0S5IkSZIkSZJUg412SZIkSZIkSZJqsNEuSZIkSZIkSVINNtolSZIkSZIk\nSarBRrskSZIkSZIkSTXYaJckSZIkSZIkqYZOi+MgpZTlgB8DGwOvA7OAH0bEuMVx/KY61gKuBdaL\niJnVthuASyLiijZjhwLjgOeAJYHJwC4R8ddSyh7ARhFxUClleyAi4unF+bVIkiRJkiRJkjqGxTWj\n/Trgjoj4TEQMAkYBK7dnx1LKkllFRMRTwNXAd6rsHYBO82myzzvmXRGxQUQMACYCo5uGtVb/3wFY\nO6tGSZIkSZIkSdIHy798RnspZTgwMyIumLctIl4AxpRSPgVcAnSrHjowIu6vZpN/n8bs9wKsUUq5\nlkZz/mPAmRExtsr/OnBENfZxYEZEHFxKWRY4D/hElf2NiLivyn24lHIVcBLw/6qcY4HVgFWBPwE/\nBVqqx1qAnsArbb62TYDtgC1KKUcDO0bE8wmnTZIkSZIkSZL0AbE4ZrSvDTy8gMcmA1tHxEY0Zrmf\n3fTY+sBBEbFGdf9r1Wz4QcAhpZRlSikr0pidPhjYFFijaf8zgdMjYmNgJDAWICKmA4cDdwG/iojn\nmvZZExgeEbtW9zcvpTxMo/G+FXBhc/ERMR74NXB4NfPdJrskSZIkSZIkfcQsljXam5VSzgE2A2YC\nn6Mxs30AMAdYvWnogxHx56b7h1ZLvUBjZvvqwIo0lqR5s8q+silja2DNajY6QI9SSreImBYRN5RS\nXgfObVPeryNiVtP9uyJiuyr7cOBUYP9/+ouXJEmSJEmSJH3otLS2ti58VA3V0jHHRMSwpm19gIeA\ni4DuEXFEtS769IhYqlo65rCmJve8pWQ+FxEzSym3A8cCywBfiog9q3EHAatXS8dMAVaKiNkLqOt5\nYMOIeK26fywwNSJObzpmcw1rAFdFxDrVh6FuWB3n58D1EXHNws7FtGnTWrt167awYZIkSZIkSZKk\n99Ho0aMZM2ZMy8JHNvzLZ7RHxG2llBNLKf8REedXm3vQ+DDRXsCL1bbdgQV98OnSwOtVk30NYEi1\nfQLw41LK0sA7wI401mkHuBk4BDgNoJQyICIeW8Tym0/k5sAf5jNmavV1LNTjjz++8EHtNGTIEO6/\n//7aOW+++WZCNTBixAhuuumm2jmdOuX9SG611VbceuuttXN69WrXt7ddBg0axIQJE2rnjBkzJqEa\nuOiii9hzzz1Tss4666yUnF69evHWW2/Vzhk4cGBCNQ3PPfccq666au2cddddN6GahnHjxrH99tvX\nzhkxYkRCNXDAAQfwk5/8JCWrX79+KTlf+cpXuPLKK2vnrLXWWgnVNKy99to8+eSTtXMefnhBK7It\nmt12241LLrkkJevll19OyTniiCP44Q9/mJK1zDLLpOTss88+XHDBBQsfuBAZzyOQ9/oG0Lt375Sc\nDTfckIceeiglK+vnO+v7ttxyyyVU07D99tszbty42jlZP0vrrrsukyZNSsk6//zzFz6oHc455xwO\nPPDAlKzBgwen5Oy+++784he/qJ0zYMCAhGoaOY89tqhva+ava9euKTn9+/fnmWeeScnKes80cuRI\nrrrqqpSsrGuToUOHcuedd9bOGTZsWP1igNbWVlpa2t07eE+jRo1KybnsssvYeeedU7Ky3ltecskl\n7LbbbilZQ4cOrZ2x9957M3bs2IRq8mTWNHLkyJSc3r1788Ybb6RkPfHEEyk5m222Gffcc09K1tJL\nL107I/M6YNq0aSk5G2+8MQ888EBK1pJLLqjFuGg22mgjJk6cmJI1e/Z85wIvkk022YTx48cnVEPa\na0BWjxJIe386ZswYRo8enZK1KBbX0jE7AGeUUo4AXqXRFD8CeBS4upSyO3BjtX1+bgT2K6U8CQQw\nHiAiXiql/AB4EHgNeBqY1zk+hMayNI/RaODfBRzQlNmeqfybVWu0LwG8Aew9nzGXAxdUs+lHuk67\nJEmSJEmSJH20LJZGe0RMBhb0Z+nmqR1HVePvBP7+p/5q3fQvLGD/yyJibLX0zLXAddU+f6PxAasL\nqmnVNvePb3P/ThpL08xv34uBi6vb99H4wFdJkiRJkiRJ0kfQEu93AQmOK6U8AkwCnouI+v8eV5Ik\nSZIkSZKkdlpcS8f8y0TE4e93DZIkSZIkSZKkj64Pw4x2SZIkSZIkSZLeNzbaJUmSJEmSJEmqwUa7\nJEmSJEmSJEk12GiXJEmSJEmSJKkGG+2SJEmSJEmSJNVgo12SJEmSJEmSpBpstEuSJEmSJEmSVION\ndkmSJEmSJEmSarDRLkmSJEmSJElSDTbaJUmSJEmSJEmqwUa7JEmSJEmSJEk12GiXJEmSJEmSJKmG\nTu93AR8lc+bM6XB5/fr1S6gkL+uuu+5KqKRhq622YtKkSbVzVlpppYRqGgYNGsQf//jH2jnTp0+v\nX0xy1htvvJGS06tXr5SsYcOG1S8mOS/z9w1gjTXWqJ3x6quvJlSSm7XUUkul5AC8+eabtTNmzJiR\nUElu3uzZsxMqyc2aMmVKSk5m1uTJk1NyAJ5++unaGd26dUuopOGVV15JyVlxxRVTcgC6du2akvPE\nE0+k5GRlbbnllgmV/ENra2vtjI54HbDEEnnzd7KyOtpzZdbv7YABA9KylltuuZQcgHfeeScl56mn\nnkrJyczq3r17Ss7QoUOZOHFi7ZxRo0YlVJObdfnll6fkXHbZZWlZyy+/fEoOwC233JKSM3To0JSc\nLB3xufu1115Lyendu3da1ty5c1NyMrP+9re/daicTp3y2otZr9+dO3dOyYGOd22SlZP1+gZ55/vF\nF19MycnOai9ntEuSJEmSJEmSVIONdkmSJEmSJEmSarDRLkmSJEmSJElSDTbaJUmSJEmSJEmqwUa7\nJEmSJEmSJEk12GiXJEmSJEmSJKkGG+2SJEmSJEmSJNVgo12SJEmSJEmSpBpstEuSJEmSJEmSVION\ndkmSJEmSJEmSarDRLkmSJEmSJElSDTbaJUmSJEmSJEmqwUa7JEmSJEmSJEk1dFqcByulLAf8GNgY\neB2YBfwwIsYtzjqa6vk88D2gKzATuC0iDn8/apEkSZIkSZIkfTAt7hnt1wF3RMRnImIQMApYuT07\nllKWzCyklLIOcDawS0SsA2wE/M8i7J9ajyRJkiRJkiTpg2mxzWgvpQwHZkbEBfO2RcQLwJhSyqeA\nS4Bu1UMHRsT9pZShwPdpzH4vwBqllGtpNOc/BpwZEWOr/K8DR1RjHwdmRMTBpZRlgfOAT1TZh0bE\neOBw4ISIeLaqpRU4v8raFvgO0Bn4G7BrRLxaSjkWWA1YFfhTKeVE4OfVuCWAHSPiD6knTpIkSZIk\nSZLUoS3OGe1rAw8v4LHJwNYRsRGNWe5nNz22PnBQRKxR3f9aNRt+EHBIKWWZUsqKNBrjg4FNgTWa\n9j8TOD0iNgZGAj+rtq8DPLSAeu6OiCERsSFwBY0G/jxrAsMjYldgP+CMiNiAxoz4F9/zDEiSJEmS\nJEmSPnQW6xrtzUop5wCb0Vgb/XM0ZrYPAOYAqzcNfTAi/tx0/9BSyg7V7ZWrsSvSWJLmzSr7yqaM\nrYE1Sykt1f0epZTuCynvE6WU/6pyOwPPNz3264iYVd0eDxxdSlkZuDYi2r30jCRJkiRJkiTpw6Gl\ntbV1sRyoWjrmmIgY1rStD41Z5RcB3SPiiGrt8+kRsVS1dMxhEbFdNX7eUjKfi4iZpZTbgWOBZYAv\nRcSe1biDgNWrpWOmACtFxOw29VxMozn/8/nUejtwWkT8d3XMYyNieLV0zNSIOL1p7CrAtsBBwL4R\ncceCzsE777zT2r37wnr8kiRJkiRJkqT30/bbb8+4ceNaFj6yYbHNaI+I20opJ5ZS/iMizq829wBa\ngV78Y9mV3YEFfdDo0sDrVZN9DWBItX0C8ONSytLAO8CONNZpB7gZOAQ4DaCUMiAiHqvuX11KuSci\nni2lLAHsU9XWC3ip2n+PBX1NpZRVIuJ54OxSyieB9YA7FjT+0UcfXdBDi2zTTTfl3nvvrZ3TtWvX\nhGpggw024OGHF7QyUPvdddddCdU0HHrooZxxxhm1c1ZaaaWEahq+8pWvcOWVV9bOueqqqxKqgSuu\nuIKddtopJevUU09NyfnkJz/Jn//854UPXIjjjjuufjGVCy+8kL322qt2Tr9+/RKqaTjllFM48sgj\na+d069Zt4YPa4dhjj+X4449Pycr6ndt7770ZO3Zs7Zz1118/oZqGDTfckIceWtCqZe332GOPJVQD\ne+21FxdeeGFK1lNPPZWSc9ppp/Gtb30rJStrMsGPfvQjDjvssNo5G2ywQUI1sOuuu3LppZemZGX9\nfK+11lppPwPnn3/+wge1w5lnnskhhxxSO2fLLbdMqKZhhx124Lrrrqud8/GPfzyhGhg8eDAPPvhg\nStYvf/nLlJyzzjqLgw8+OCVrwIABKTlf//rX+dnPfrbwgQux8sorJ1QDI0aM4KabbkrJWm655VJy\n1l9/fR555JGUrOuvvz4l55hjjuF73/teSlbWZKnDDjuMH/3oR7VzJk6cmFANXHbZZey8884pWZdf\nfnlKTmtrKy0t7e5nvKfll18+JeeVV15hhRVWSMk64YQTamdkXeMCLLFEzmrCmdeUw4YNS8lZddVV\nee6551KyXnwxZ5XgLbbYIq3nMXfu3NoZw4YN44477qhfDNCpU057cbPNNuOee+5Jycp6r5vV7wJ4\n++23a2dk/hxlvb5lvc8F0l67x40bx/bbb5+StSgW99IxOwBnlFKOAF6l0RQ/AniURtN7d+DGavv8\n3AjsV0p5EggaS7cQES+VUn4APAi8BjwNvFntcwiNZWkeo9HAvws4ICImlVIOBS4rpXSl0fC/odrn\neOCqUsprwG3ApxdQz7+XUnYDZgMvAycu4vmQJEmSJEmSJH3ALdZGe0RMBhb0J/PmKSdHVePvBO5s\n2n8W8IUF7H9ZRIytlp65Friu2udvND5gdX71/Ab4zXy2/xr49Xy2H9/m/inAKQuoR5IkSZIkSZL0\nEZDz74Q6huNKKY8Ak4DnImLc+12QJEmSJEmSJOnDb3EvHfMvExGHv981SJIkSZIkSZI+ej5MM9ol\nSZIkSZIkSVrsbLRLkiRJkiRJklSDjXZJkiRJkiRJkmqw0S5JkiRJkiRJUg022iVJkiRJkiRJqsFG\nuyRJkiRJkiRJNdholyRJkiRJkiSpBhvtkiRJkiRJkiTVYKNdkiRJkiRJkqQabLRLkiRJkiRJklSD\njXZJkiRJkiRJkmqw0S5JkiRJkiRJUg2d3u8C9P7q2rVrh8p65513EirJzZs9e3ZCJbl5Sy21VEIl\nuVnvvvtuSk5WVvfu3RMqyc3L/H3LymttbU2oJDfrrbfeSsnJypozZ05CJbl5Xbp0SagkN2v69Okp\nOdlZWWbMmFE7o6O95kLua1xWVkd7Xpo2bVpCJbl5LS0tCZXkZmW+7mZl9ejRIyUnK6tz584JleRm\nLbFE3ryrrKyOeJ462utup055b+OzspZffvmUnMysyZMnp+RkZ3Uks2bN6nBZHe19pdqnI/4sZT53\nZ70nzLruysqZO3duSk5mVkd8jVsUzmiXJEmSJEmSJKkGG+2SJEmSJEmSJNVgo12SJEmSJEmSpBps\ntEuSJEmSJEmSVIONdkmSJEmSJEmSarDRLkmSJEmSJElSDTbaJUmSJEmSJEmqwUa7JEmSJEmSJEk1\n2GiXJEmSJEmSJKkGG+2SJEmSJEmSJNVgo12SJEmSJEmSpBpstEuSJEmSJEmSVIONdkmSJEmSJEmS\naui0uA5USlkO+DGwMfA6MAv4YUSMW1w1zKem64DlI2KT96sGSZIkSZIkSdIH2+Kc0X4dcEdEfCYi\nBgGjgJXbs2MpZcnsYkopSwMbAL1KKZ9eXMeVJEmSJEmSJH24LJYZ7aWU4cDMiLhg3raIeAEYU0r5\nFHAJ0K166MCIuL+UMhT4Po3Z7wVYo5RyLY3m/MeAMyNibJX/deCIauzjwIyIOLiUsixwHvCJKvsb\nEXFfdfvLwK+BycDOwElV1s+BGcD6wD2llGOAs4G1gc7AcRFx/YLqzjljkiRJkiRJkqQPisU1o31t\n4OEFPDYZ2DoiNqIxy/3spsfWBw6KiDWq+1+rZsMPAg4ppSxTSlkR+A4wGNgUWKNp/zOB0yNiY2Ak\nMLbpsZ2BXwGXV7ebrRQRQyLiW8DRwK0RMQQYDpxWSum6kLolSZIkSZIkSR8RLa2trf/yg5RSDgI+\nHRGHVffPATYDZgKfA8YAA4A5wOoR0aOa0X5MRGzVlHMcsEN191PACGBFYIeI+FrTsVavZrRPBv4C\ntFT79KXRiO8BPBARq1T7PATsFhFPVTPab4uIS6rHJgBdqtoAegPbAC8D5wADm+t+r/PwzjvvtHbv\n3n2Rzp0kSZIkSZIkafHacccdufrqq1sWPrJhcX0Y6pPAjvPuRMSBpZQ+wEPAN4CXI2K3ak306U37\nvTPvRtV4Hw5sHBEzSym301hCBv7RSG+rpRo/u3ljKWUvoHcp5blqTE8as9q/2/a4lR0j4tk2GccC\nr0TEevOpe74effTRhQ1pt0033ZR77723dk6fPn0SqoE111yT3//+97VzrrnmmoRqGo4++mhOPPHE\n2jmrrLJKQjUNu+yyC7/61a9q5/z2t79NqAYuueQSdtttt5Ss448/PiVn1VVX5bnnnqud8+Mf/zih\nmoazzz6bgw46qHZO3759E6ppOO644zjuuOPS8urKrKdXr14pOd/85jc5/fTTa+dsttlmCdU0DB48\nmAcffLB2zrPPPrvwQe2w6667cumll6Zk3XfffQsf1A5jxoxh9OjRKVlZsmraaqutFj6oHb785S+n\nvV6uttpqKTkDBgzgscceS8n62c9+lpJz1llncfDBB9fOGTJkSEI1DVnXAauvvnpCNTBo0CAmTJiQ\nkpX1M3nSSSdx1FFHpWQNHDgwJWennXbiiiuuqJ3Tr1+/hGpg+PDh3HbbbSlZWdcmmc8Bv/nNb1Jy\njjrqKE466aSUrJ49e6bkHHjggZxzzjm1cx544IGEanLfC9xyyy0pOa+88gorrLBCStbkyZNTclpb\nW2lpaXeP5T1dcMEFCx+0EHvvvTdjx45d+MB2ePfdd1Ny9ttvP84777yUrOHDh6fk9O/fn2eeeSYl\n65VXXknJ2WKLLbjrrrtSsubOnVs7Y9iwYdxxxx31iyGnHsh9jct67s68XpoxY0btjM0335y77747\noRr42Mc+tvBB7ZB5jk4++eSUnKuvvpodd9xx4QOTLZalYyLiNqBLKeU/mjb3AFqBXjRmhwPsDizo\nA0iXBl6vmuxrAPPe9UwAtiilLF1K6URTQx+4GThk3p1SyoDq5s7AiIhYtZrVvhH/d/mYeW4C/v4u\nrZQy74p96XbWLUmSJEmSJEn6EFtca7RDY8mXYaWUP5RS7gd+TuMDTM8F9iylPAL05//OJp/nRqBz\nKeVJ4AfAeICIeKm6/yBwN/A88Ga1zyHARqWUx0opTwD/UX2I6Scj4u9TCiPij8AbpZRBNJr/zU6o\njvt4KWUS8L1q+0/aWbckSZIkSZIk6UNscS0dQ0RMZsGzxgc03T6qGn8ncGfT/rOALyxg/8siYmy1\nhMu1wHXVPn+j8UGlbX1iPvVtVN2c0Gb7DGC/+Yz/n/nVLUmSJEmSJEn6aFmcM9r/lY6rZpZPAp6L\niHHvd0GSJEmSJEmSpI+GxTaj/V8pIg5/v2uQJEmSJEmSJH00fVhmtEuSJEmSJEmS9L6w0S5JkiRJ\nkiRJUg022iVJkiRJkiRJqsFGuyRJkiRJkiRJNdholyRJkiRJkiSpBhvtkiRJkiRJkiTVYKNdkiRJ\nkiRJkqQabLRLkiRJkiRJklSDjXZJkiRJkiRJkmqw0S5JkiRJkiRJUg022iVJkiRJkiRJqsFGuyRJ\nkiRJkiRJNXR6vwv4KOnSpUuHy3vrrbcSKsnL2mijjRIqyc177bXXEir5h5aWltoZm2++eUIluVlT\npkxJyVl11VVTsgYMGJBQTW5ep065T7mf/vSna2d07dq1fiGVNddcMyVnxowZKTkAffv2rZ0xderU\nhEpy8z7zmc8kVJKbNW3atJQcgIEDB6bktLa2puRAznNAt27dEirJzZo1a1ZKTmZW1nNJVlbG63Z2\n3vTp0xMqyc1aZ511UnIys7p3756Sk5W15JJLJlSSm5V5bZKVtcoqq6TkZGbNnDkzJQegZ8+etTOG\nDh2aUEluVmZNJ5xwQlpWlgsuuCAlZ5999qmdsffee6fkANx2220pOQCllLSsjqYjXsMttdRSKTl9\n+vRJycnqBwDMnTu3Q+VkZmVdV2blZL6+ZWUNHjw4JSc7q72c0S5JkiRJkiRJUg022iVJkiRJkiRJ\nqsFGuyRJkiRJkiRJNdholyRJkiRJkiSpBhvtkiRJkiRJkiTVYKNdkiRJkiRJkqQabLRLkiRJkiRJ\nklSDjXZJkiRJkiRJkmqw0S5JkiRJkiRJUg022iVJkiRJkiRJqsFGuyRJkiRJkiRJNdholyRJkiRJ\nkiSphk6ZYaWU04E/RsRZ1f0bgT9HxL7V/dOAFyPijBrH+DlwfURcU0q5A1gBmAEsBfwO+G5EvPlP\n5B4LTI2I09ts3xg4E+hSHeOKiPheKWUP4FTgRaAFeCwi9vxnvy5JkiRJkiRJ0gdT9oz2e4HPApRS\nWoBlgbWbHv8scF/i8VqBnSNiILAeMAsYl5gPcDGwd0SsD6wD/FfTY5dHxAYRsb5NdkmSJEmSJEn6\naEqd0U6jif7j6vbawBPACqWUpYHpwBrAI6WUU4FtgLnAiRHxXwDvsf0cYCvgBWB2m2O2AETEu6WU\nI4BnSynrRsSkUsquwMFAZ+AB4ICIaC2lbAOcCCwJvBoRn2sOLKXsA+wA7Aj0AyZXx2gFnm57bEmS\nJEmSJEnSR1fqjPaIeBmYXUpZmX/MXn8A2ATYCJgEfBFYLyLWBT4HnFpKWb6U8uUFbP8SsHpErAns\nUeUu6PhzgceBNUopawA7AZ+NiA1oNO93LaUsC/wU+FI1E/4rTREtpZTRwBeA7SNiBnAGEKWUq0sp\n+5ZSujSN36mU8nD13x51zp0kSZIkSZIk6YPpX/FhqPcBm9JoiI8H7m+6fy+wGXAZQERMAe4ABr/H\n9i2atr8M3LaQ48+bZb4VsAEwoZTyCDAcWBUYAtwZEX+uMt9o2nd3GjPqR0bEu9Xj3wc2BG4GdgZ+\n2zR+3tIxG0TExe05OZIkSZIkSZKkD5eW1tbW1MBSyv40lojZFBgE9AauBN4Efk6j4f14RFxUjf8F\njXXPF7R9KxofNDpv+9XApdWHod4OHBYRD1ePLQk8A2wPDANWjIij29S3LTAqIr7aZvuxwGeAgcAX\nI+KP8/nalgReBVYDtgM2jIiD23tupk+f3tq1a9f2DpckSZIkSZIkvQ9OOeUUjjzyyHYvHZ69Rjs0\nZrR/C/hDtab566WU3sBawD401kvft2qk9wU2r8a3Z/vywJbApU3HawEopXQCfgD8OSKeKKXMAa4r\npZwREa+WUpYBetKYYT+mlPKpiPhTKWWZiHi9ynoEOBf4dSllRES8XEr5QkT8pnq8P/Au0DwLvt2e\nfPLJf2a3+dpoo42YOHFi7Zw5c+YkVAMbb7wxDzzwQO2cN974p07tfI0YMYKbbrqpds5rr72WUE3D\nzjvvzGWXXVY7Z+rUqQnVwL777stPf/rTlKz11lsvJWfIkCHcf//9tXOeeOKJhGoa9t57b8aOHVs7\np1OnvKfcPffck4suuqh2TtYf/3baaSeuuOKKlKwZM2ak5Oyxxx5cfHH9f2y08sorJ1TTsNVWW3Hr\nrbfWzunRo0dCNXnP3QCPP/54Ss4+++zDBRdckJKVNZkg67nyk5/8ZEI1sM0223DjjTemZPXt2zcl\nZ9CgQUyYMCElK+P6BmD//ffn3HPPrZ3Tu3fvhGoayK35IgAAIABJREFUsq4DVlpppYRqYIsttuCu\nu+5KyXrhhRdScnbddVcuvfTShQ9sh6WXXjolZ9ttt+WGG26ondOzZ8+EamDo0KHceeedKVnLLrts\nSs7aa6+d9l5n0qRJKTmjRo3i8ssvT8maOXNmSk7Wtcns2W0/tuyfk3WNm+nDXtM+++xTO6O1tZWW\nlpyPi7vttoUtGNA+W265JbfffntKVtZrXP/+/XnmmWdSst56662UnKw+DsBSSy1VO2O99dZLu4af\nMmVKSs7WW2/N7373u5SsrNfdzPdMGc/fm222Gffcc09CNXkya7r33ntTco488khOOeWUlKxF8a9Y\nOmYSjUb5+Dbb3oiI1yLiWhrrqD8G/A44PCKmLGT7/wBPAhfRaOQ3+2Up5dHqGF1pzGYnIn4PfAe4\nuZTyGI2lX1aIiL8C+wLXVkvK/K+rr4iY94eCG0opfYDdSilPl1IeBi4Gdqn+gCBJkiRJkiRJUv6M\n9uoDSXu32fa1NvePBI6cz74L2n7QAo615UJquZLGsjVtt98E3NRm2/FNt2+m0ZiHxrrs88u+mEbj\nXZIkSZIkSZL0EfavmNEuSZIkSZIkSdJHho12SZIkSZIkSZJqsNEuSZIkSZIkSVINNtolSZIkSZIk\nSarBRrskSZIkSZIkSTXYaJckSZIkSZIkqQYb7ZIkSZIkSZIk1WCjXZIkSZIkSZKkGmy0S5IkSZIk\nSZJUg412SZIkSZIkSZJqsNEuSZIkSZIkSVINNtolSZIkSZIkSarBRrskSZIkSZIkSTXYaJckSZIk\nSZIkqYZO73cBHyXvvvtuh8traWlJqCTP1KlTO1xenz59EirJzfvLX/6SUEnDW2+9lZLTqVPe00lG\nVpcuXRIqyc2bOXNmQiX/kPEc8LGPfSyhktys7t27p+QA9O3bt3ZGt27dEirJzXvllVcSKsnNynyN\ny8rKfB7IeF7qiN+3nj17puQAzJo1KyXnzTffTMnJyurfv39CJf+w3HLL1c7o2rVrQiW5WW+88UZK\nTmbWnDlzUnIAXnvttdoZmddK06dPT8nJPEdZWZnvB7KyMp8rM16bZs+enVBJriWWyJvDl5WV9boE\nedcmt912W4fKGT58eEpOa2trWtaTTz6ZkgN537eO+Fw5ZcqUDpXTEZ8DMvtdWVlZPYGsnIz3y/P0\n6NEjJacj/iwt0jEX+xElSZIkSZIkSfoQsdEuSZIkSZIkSVINNtolSZIkSZIkSarBRrskSZIkSZIk\nSTXYaJckSZIkSZIkqQYb7ZIkSZIkSZIk1WCjXZIkSZIkSZKkGmy0S5IkSZIkSZJUg412SZIkSZIk\nSZJqsNEuSZIkSZIkSVINNtolSZIkSZIkSarBRrskSZIkSZIkSTXYaJckSZIkSZIkqYZOmWGllJWA\nMcBaQAtwA3B4RLybeIxjgX2AKTTqPzoirk/InRoRPeezvT9wPtAbWAq4OyL2K6UMBcYBz9H4Wl+N\niH+rW4ckSZIkSZIk6YMle0b7NcA1EdEf6A/0BH6QfAyA0yNiA+DfgQvbu1MpZcn3eLh1AdvPAn4U\nEetHxNrA2U2P3RURG1SP2WSXJEmSJEmSpI+gtBntpZThwPSI+AVARLSWUr4BPF9KeR4YASwNfBy4\nNCK+V+23K3Aw0Bl4ADig2ncqcCawLTAN2D4iXm0+ZkQ8XUp5t5SyLNCdRtO9L/Aq8LWIeLGU8nNg\nBrA+cE81I/5sYCNgLnB8RFwLtJRSTpjP8VYA/tJ0zCebSmhJOXmSJEmSJEmSpA+szBntawMPNW+I\niKnAn2g09AcBXwIGAF8ppWxQSlkD2An4bDVDfS6wa7V7d+C+iBgI3E1juZj/pZSyMTAnIv5Ko3n+\n82r8r/jfM89XioghEfEt4LvAGxGxXjX2toUc7wzg9lLKf5dSDi2lLN2Uu3kp5eHqv6MW8XxJkiRJ\nkiRJkj4EUtdoX4AWGsuy3BIRbwCUUq4GNgPmABsCE0opLcDHgFeq/WZFxG+q2w8BWzdlfrOU8lVg\nKo3lYwA2odHIB7gEOKVp/JVNt7em0dwHICLerG7OnN/xIuKiUsqNwDbADsC+pZQB1bi7ImK79p4I\nSZIkSZIkSdKHT0tr64KWJl80pZStgGMiYmjTtl40Piz0O8CQiNiz2n488FcaM9g/HhFHzyfvrYjo\nVd3eEfh/EbFXtfTL1Ig4vc34KcCKETGnlNIJeCkilquWjrk+Iq6pxk0ARkXEH9pzvPnUNQnYHegF\nHLYojfZp06a1duvWrb3DJUmSJEmSJEnvg1NPPZXDDz+83UuHp81oj4hbSyknlVK+GhG/rD549DTg\n58B0YOtSSm9gJo2Z4V+rtl9XSjkjIl4tpSwD9IiIF1j09c/vA3YGfgl8lcbyL/NzCzAa+CZAKaV3\nNdN+vscrpYwAbo2Id0spKwB9aKzZ3msR6+Pxxx9f1F0WaMiQIdx///21c1pacpaZ33jjjXnggQdq\n57zwwgsJ1TSMHDmSq666qnZOz549E6ppGDFiBDfddFPtnEmTJiVUA9/61rc47bTTUrKGDRuWkrPR\nRhsxceLE2jm///3vE6pp2G233bjkkktq58ycOTOhmoa9996bsWPH1s7p169fQjWw/fbbM27cuJSs\nJZd8r8+tbr9tt92WG264oXZO3759E6pp2GSTTRg/fnztnClTpiRUk/t9e+mll1Jy9t9/f84999yU\nrC5duqTk7LXXXlx4Ybs/e32BllgiZ8W+Pffck4suuigla/XVV0/J2XTTTbn33ntTsu6+e0GXcIvm\n29/+NieffHLtnEGDBiVU07DVVltx66231s7p1WuRL0Pna9CgQUyYMCEl68EHH0zJGT16NGPGjEnJ\nyrqG23333fnFL35RO2e55ZZLqAa22WYbbrzxxpSsj3/84yk56623Xtp7nYz3FAD77LMPF1xwQUpW\n1s/SqFGjuPzyy2vnvP322wnV5F1PQt5rXNZrLsCsWbNScvbbbz/OO++8lKxSSu2MLbfckttvvz2h\nGhg+fHhKTmtra1pv4cknn1z4oHZYa621eOqpp1Kypk6dmpKT1TeBnJq23nprfve73yVUk/ccMHz4\ncG677baFD2yHHj16pOQMHjw47Ton4/uWdT0Jee91Bw4cyKOPPpqSdcstt6TkHH744Zx66qkpWYsi\nc412aCzd8u+llGeAp2l8qOh/Vo89CFwDPApcGREPR8Tvacx2v7mU8hhwM7BiNX5Rp9ofDHytlPIo\njXXeD1lAzolAn1LKpFLKI8CwhRzv34AnqrG/Bb4VETkdDkmSJEmSJEnSB17qGu0R8Rfg/yylUv3V\n9sWI+PJ89rmS/72G+rztvZpuXw3/n707j7/rruvE//pmbdI9LLYwiNNSPiiltE3SpGmbNC1LBURE\ncUBQlvm5zDgyKszoQ0cRxnFBRmUAdWSkgoAssgkDlNqmTXeS7mwfoVSldDrdSJfsy50/7u2vISZN\n0vOuTdLn8/HII9977rmv8z7nnnuW9z3f883HJj+/eRfT/qckZ+9k+Ot2eLw2yWv2YnpvSPKGnYx/\ncZKLd1YLAAAAAACPHdVXtAMAAAAAwGNK6RXtu9J7f2+S9/5LTAsAAAAAAP4luaIdAAAAAAAG0GgH\nAAAAAIABNNoBAAAAAGAAjXYAAAAAABhAox0AAAAAAAbQaAcAAAAAgAE02gEAAAAAYACNdgAAAAAA\nGECjHQAAAAAABtBoBwAAAACAATTaAQAAAABgAI12AAAAAAAYYMajXcBjyWg02ufypqamCiqp86Qn\nPWmfy5sxo/ZjcuSRRw7OeNGLXlRQSW3Wt7/97ZKcJLnnnnsGZ/zYj/1YQSW1eXfeeWdBJQ96/vOf\nPzhj7dq1BZWMtdZKciq3lccee+zgjDvuuKOgkgdt3rx5cMb3fM/3FFRSm3XccceV5CTJsmXLSnIq\nlvUD5s+fPzjjrrvuKqhk7Hu/93tLcjZu3FiSU5m1dOnSkpyqrDlz5hRU8qB58+YNzti0aVNBJWPb\ntm0ryTn77LNLciqzquYtSRYsWDA4o/I4YO7cuSU5a9asKcmpzDr++ONLciqzKs8HKo5NKve5VcfM\nd999d0lOkpx55pklOVu2bCnJSZKzzjqrLKvCk5/85JKcL3/5yyU5lVnPfOYzS3JGo1FZ1urVq0ty\nkrrtyVFHHbVP5VSeM1X1qSrPBaqyDj/88H0qZ188F3jJS15SklOdtadc0Q4AAAAAAANotAMAAAAA\nwAAa7QAAAAAAMIBGOwAAAAAADKDRDgAAAAAAA2i0AwAAAADAABrtAAAAAAAwgEY7AAAAAAAMoNEO\nAAAAAAADaLQDAAAAAMAAGu0AAAAAADCARjsAAAAAAAyg0Q4AAAAAAAPM2NsXtNa2Jrk+yVSSUZIP\n9d7f+jBybk4yv/d+996+dg+yn5rkM733Z7XWliX5VJJvJpmd5MO997cUTGNFkjf03q8ZmgUAAAAA\nwP5rrxvtSdb23k8umPaoIGNP81f23l/cWpub5LrW2t/23q/bXUBrbXrvfesjVyIAAAAAAPu7h9No\nn9rZwMkV6u9N8kOT3Jf13v++tXZwknckWZBkW5I3994/sX1Oa+2Xk7w24+b4X/Te3z5pin8kyZOT\nTE/yX3vvH22tnZzkD5McnOTOJK/pvf/f1tr8JH8xyTh/ZzX23te11q5O8rTW2leT/Omkrs0ZX51+\nUWvt1UlemuSQjG+ts7y19itJXplka5LP9d5/bRL54621P01yeJJ/23u/bO8WJQAAAAAA+7uHc4/2\nOa21a1pr107+f9l2z93ee5+f5M+SvHEy7DeSrOm9n9B7PzHJhduHTRrnr06yMMmpSX66tfbsJOck\n+Xbv/aTe+wlJPt9am5Fx0/5He+8Lk5yb5HcmUe9J8vO995N2UvPUZFqPS7IoyZeT/HySbZPsn0jy\n3tbarMn4JyV5ae99eWvtnIy/PFg4yd7+NjnTe++LkvxSkt/aw+UHAAAAAMABZGo02rs7uLTW7u29\nH7aT4TcnWdJ7/z+ttVOS/Hbv/XmttdVJ/k3v/aYdxv9mxleTvyrJvN77b02GvyXJ7UnOm/z7cJL/\n3Xu/tLX2zCSXJ7kp4+b5tCS3Jnl5kut77983yXhWkg/03k/Y7h7tN2V8Rf2f997f3Vr7eJL/0Xu/\naPKaizNuvs9PsrT3/m8nw9+W5Ku997/Yof4VSX6t935Fa+2JSS7tvT/9oZbdunXrRnPnzn3I5QsA\nAAAAwKPr61//eo477rid3t1lZx7OrWMeysbJ/1uHZvfevz652v0FSf5ra+2CJJ9M8qXe+2nbj9ta\nO3w3cSt77y/ezTjbL7S1e1jmXs3v9ddfv4exu3fqqafmiiuuGJwzbdrD+aWGf27RokW56qqrBuds\n3Vp3S/wlS5bk8ssvH5wzY0bdx+SUU07JF7/4xcE5hx32z77relie8Yxn5Gtf+1pJ1re//e2SnLPP\nPjsXXHDB4JwlS5YUVDM2Z86crF+/fnDOnXfeWVDN2FOe8pR861vfGpyzdu2ebu4eWuW6tLdfAO/K\n93//9+erX/3q4Jw77rijoJqxpUuXZuXKlYNzZs2atfuR9sDixYtz5ZVXlmRVbZd+4Ad+IF/5yldK\nsjZv3lyS8+xnP7tkH37XXXcVVJOcddZZufDCC3c/4r+gypoOOuigkpyq44A5c+YUVDN20kkn5dpr\nrx2cs2nTpoJq6o7fkuTww3d3OL5nKvcn27ZtK8mp2i5VHQdU7UsqVdY0c+bMkpyq86Wk7nxg4cKF\nWbVq1eCc4447rqCa5IgjjsiaNWtKsu6+++6SnGOOOSbf/OY3S7K2bNlSkvP0pz89f//3f1+SVaGy\nnqplVHn89sxnPrMkZzQaZWpqj3tjD2n16tUlOfPnz8/VV19dkjV79uzBGccff3y+9KUvFVRTd860\nfPnyrFixoiSr6pzptNNOy2WX1dwpuuJ9W7BgQdk6WdWDqzymnDdvXknOcccdl69//eslWXvj4XRZ\n93ZLdX7GV4onSVprR+yQc0mSl7TWDprcz/1HklzSWjs6yfre+weTvC3JyUl6kie01hZPsma01n6g\n935PkjWttQc6a6/ag7ouyfi+62mtPT3JUyb5O6v/ta21OZNxj9xFXs0WHAAAAACA/crDabQftMM9\n2h+4R/quLkH87STzWms3ttauTXLm9uP33q9N8pdJViW5IuNbu1yf5FlJvjh5zW9mfCuazUl+LMnv\nt9auS3Jtxvd1T5LXJfmT1to1D1HL9v4kyfTW2g1J/jrJqyf536X3fl6Sv02yepL9hl3Mb80lmAAA\nAAAA7Ff2+nfgeu87/V2+3vsx2/18dZKzJj+vTfKa3Yz/x0n+eIfnv5DkCzt53Q1Jlu1k+DVJTtxu\n0K9Ohl+c5OKdjL8x4+b8jsPfm+S9Owx7a777j6Cm937Wdj/fleSYAAAAAADwmFNzg24AAAAAAHiM\n0mgHAAAAAIABNNoBAAAAAGAAjXYAAAAAABhAox0AAAAAAAbQaAcAAAAAgAE02gEAAAAAYACNdgAA\nAAAAGECjHQAAAAAABtBoBwAAAACAATTaAQAAAABgAI12AAAAAAAYQKMdAAAAAAAG0GgHAAAAAIAB\nZjzaBTyWHHTQQftc3mg0KqhkbObMmYMz7r///oJKHrR+/frBGbNnzy6o5EGbNm0anHHHHXcUVJI8\n4xnPKMuaNWtWSU5V1qpVqwoqGVu6dGlJXuXn7SlPeUq++c1vDs6ZPn16QTVjd955Z0lO5XKqqGnu\n3LkFldTmbdiwoaCSsS1btpTkVL3/lVlbt24tyUmSu+++e3DGoYceWlBJbVblMqr6rFStk0mybdu2\nwRkbN24sqKQ2r+JY4gFV83f77beX5DzjGc8oy6o8hrvvvvsGZ8yZM6egkvqsKlU1VXxuHzBtWs11\nZZs3by7Jqcr60pe+VFBJcvrpp5dlVb1vxxxzTG655ZaSrCpPf/rTc9ttt5VkVe0r77333pKcyuOA\niu1kkqxevbokpzJrwYIFJTmj0agsq+p8t+q8ovKcqSqr8ryy6ry5okdVmVO1n0zqjuFvvfXWkpzj\njjuuNGtPuaIdAAAAAAAG0GgHAAAAAIABNNoBAAAAAGAAjXYAAAAAABhAox0AAAAAAAbQaAcAAAAA\ngAE02gEAAAAAYACNdgAAAAAAGECjHQAAAAAABtBoBwAAAACAATTaAQAAAABgAI12AAAAAAAYQKMd\nAAAAAAAGmPFoF5AkrbXZSVYmmZVxTX/Te39za21xkj9OMnvy3Id77295GPkrkhydZEOS+5K8rvf+\n9YE1L0vyxt77Dw3JAQAAAABg/7ZPXNHee9+YZHnv/aQkJyb5wdbaoiR/meT/mww/PslHBkzmFb33\nE5O8L8nb9vRFrbWHWkajAfUAAAAAAHAA2CeuaE+S3vu6yY+zM65rW5InJPm/k+dHSb6WJK21pUne\nnnGje5RkaZIFSX4ryZ0ZN+VX995/crtJTE3+X5nkP05yzk7yB0mmJ1mV5N/13je31m5O8uEkz0ny\n1tba1Un+bFLPliQvm2Qd2lr76C6mBwAAAADAY8A+cUV7Mr5yvLV2bZLbkpzfe1+V8W1jemvtY621\nn5ncYiZJ3pjk3/feT05yRpL1k+EnJnl9kh9IcmxrbclOJvXiJDdOss5N8rLe+7OTzEzy77Yb787e\n+4Le+0eSfCDJOyZXxC9J8n/2YnoAAAAAABzApkajfevuJ621w5J8Msl/6L1/pbX2r5M8L8krkmzr\nvZ/VWvuVJD+ScQP84733b0/umf5rvffnT3L+JMmlvfcPTu7RflTGDfl/SPILSR6X5H/03s+cjH9W\nxs37H5tc0b609/6t1tohSb7Se//eHerc5fR2NW/r168fzZkzp2Q5AQAAAADwyLj44ouzbNmyqd2P\nObbP3DrmAb33eyeN8XMybnDfnOR/ttb+V5I7WmtH9t5/v7X2mSQvTHJZa+15k5dv3C5qa757/n6i\n937tAw9aa4/Lg7eT2Zm1e1DuQ03vn/na1762B5F75qSTTsq11167+xF3o+qLlpNPPjnXXHPN4Jzv\nfOc7BdWMnX322bngggsG58yePXv3I+2h008/PZdeeungnKr37Ywzzsgll1xSklWlqqbKLxGXLl2a\nlStXDs6prGnZsmW5+OKLB+dMnz69oJq6dTvZ99bvyi9IFyxYkNWrVw/O2bBhQ0E1te/btm3bSnKq\nPm9JsnXr1pKc5cuXZ8WKFYNzDjnkkIJqkoULF2bVqlUlWVXLaPHixbnyyitLsrZs2VKSU7V+z5hR\nd7hctZw2bdpUUE3t561KZU1Vx3CLFi3KVVddNThn2rSaXyau3AZUqaypan9S9b4lddvKJUuW5PLL\nLx+cU7WMDvTjgCqVNc2dO3dwRtXxZFK3bld+3qr2u/Pnz8/VV19dkrVgwYKSnNFolKmpPe7XPaSK\nbe6Bvi5VnVdWHudu3rx5cEZlH6fq2OS0007LZZddVpJVdS5Q1TPZW/vErWNaa49vrR0++XlOkucm\n+Vpr7QXbjfb0jO+Pvqa1dkzv/cu997dmfG/1Z+zBZHbcmvUkT22tHTN5/JNJLtrxRb33+5Pc0lr7\n4Ul9syY1AgAAAADAvtFoT3J0khWtteuSXJXkvN77Z5P8ZGvta621a5K8N+Or0kdJfrG1dmNr7fok\nm5J8bieZo138nCTpvW9M8tokfzPJ2Zrkf+5i/J9M8vrJeJcl+Z7dTA8AAAAAgMeIfeLWMb33G5Oc\nvJPhr9jF+K/fyeCLJ//+2Ti997N2kbNiF9M9ZofHNyU5e4fR/mFX0wMAAAAA4LFjX7miHQAAAAAA\n9ksa7QAAAAAAMIBGOwAAAAAADKDRDgAAAAAAA2i0AwAAAADAABrtAAAAAAAwgEY7AAAAAAAMoNEO\nAAAAAAADaLQDAAAAAMAAGu0AAAAAADCARjsAAAAAAAyg0Q4AAAAAAANotAMAAAAAwAAa7QAAAAAA\nMMCMR7uAx5INGzbsc3kzZtStAlu3bh2cMXPmzIJKavMq5qs6r7KmzZs3l+RMTU2V5CTJli1bBmcc\nccQRBZU86NBDDx2csW3btoJKHnTIIYcMzrjnnnsKKhnbtGlTWVaVivV77dq1BZU86M477xycceSR\nRxZUMla13V2zZk1JTpKsX7++LKtKxfpdOV9VWZXb7qr9yX333VeSkyT33nvv4IzDDjusoJIHVezj\n9kWzZ8/e57Iq16WKrMrj3HXr1pXkHH744SU5Sd38fec73ynJSeqW06233lqSs2TJktx8882Dc044\n4YSCasaq1oG77rqrJCepP2auUFXTrFmz9qmc22+/vSQnqdvmHnXUUSU5Sd3+ZNWqVSU5lVkLFy4c\nnDEajUpykmTFihUlOUndce60aXXXFled61bVVHUMX3kuUJW1rx2/7S1XtAMAAAAAwAAa7QAAAAAA\nMIBGOwAAAAAADKDRDgAAAAAAA2i0AwAAAADAABrtAAAAAAAwgEY7AAAAAAAMoNEOAAAAAAADaLQD\nAAAAAMAAGu0AAAAAADCARjsAAAAAAAyg0Q4AAAAAAAPMeCTDW2u/nuQVSbZO/v1s733VIznNndTw\npiQ/neT2jOf313vvny7Iva/3fujQHAAAAAAA9m+P2BXtrbXFSV6Q5MTe+7OTPCfJt/bgddMfgXL+\nsPd+cpIfT/KePX3RbmoZDa4KAAAAAID93iN5RfvRSe7svW9Jkt773UnSWluY5I+THJxkQ5Kzk/xY\nkpcmOSTj5v/y1tobM26Mz0ryid77myevf2WS1yeZmeSqJP++9z5qrd2X5O1JXpRkXZIf7r3fsX1B\nvfevtda2tNYeP5n+e5I8LskdSV7be7+ltXbupK6Tklw6uSL+HUkWJNmW5M29908kmWqt/fZDTQ8A\nAAAAgAPfI3mP9i8k+d7W2tdaa+9qrS1trc1M8qEkv9B7PzHjq9w3TMY/KclLe+/LW2vPTXJc7/2U\nyfAFrbXTW2vPSPJvkiyZXKG+LckrJ68/OMnlk9xLMr5dzHdprS1KsrX3fmfGzfNzJ+N/cPL4AU/u\nvS/uvb8xyW8kWdN7P2Ey7oV7Oj0AAAAAAA58j9gV7b33ta21k5OckeSsjBvsv5Pk1t77NZNx7k+S\n1lqSnN97v2fy8ucleW5r7ZokUxk3tY9L8uwk85Osaq1NJTkoyW2T12zqvX928vPVGTfxH/DLrbVX\nJbkv46vkk+TUJD8y+fmvkvz+duN/dLufn5Nxc/+B+Xqgxo0PMT0AAAAAAB4jpkajf5lbjbfWfjTJ\nzyeZ2Xs/Y4fnXp1kfu/99ZPHb0vSe+/v3mG8/5Dk6N77r+8k/97e+2HbTeuFvffXTW79cl/v/Q93\nGP/2SdbW1tqMjL8AeOLk1jGf7r1/fDLeqiQv773ftCfTe6hlsG7dutHcuXMfekEBAAAAAPCo+sxn\nPpMXvehFU3s6/iN2RXtr7elJtvXevzEZdGKSryQ5p7W2oPe+urV2SJL1O3n5eUne0lr74OTK+Ccl\n2ZzkgiSfbK39ce/9jtbakUkO6b1/K+Mr3/fG5UlekeT9SV6V8e1fdub8jL8g+OXJfB3Re1/zMKaX\n66+/fm9fskunnnpqrrjiisE5M2bUrAILFy7MqlWrBuesX7+z1eHhWbp0aVauXDk4p/LLqGXLluXi\niy8enLN169aCapKzzjorF1544e5H3ANTU3v9kdip5cuXZ8WKFYNzjjjiiIJqxk466aRce+21g3O2\nbdtWUM3Y/Pnzc/XVVw/Oueeee3Y/0h6oXJeqVNW0adOmgmrGzjnnnHz+858fnHPkkUcWVJMsWrQo\nV111VUnWmjVrSnKe//zn57zzzivJqlJV05w5cwqqqdu/JXXb7jPOOCOXXLKrQ6m9c99995XkvOAF\nL8hnP/vZ3Y+4G4cddlhBNWOnn356Lr300sE5VfuTynVp9uzZJTmV26Wqdek5z3lO/u7v/m5wzsyZ\nMwuqqTueTJLDDz+8JOfEE0/MddddV5L1ne8k+zRvAAAgAElEQVR8pySn6pgySW699daSnFe+8pX5\nwAc+MDjnhBNOKKgmedaznpUbb7yxJOuuu+4qyTnzzDNz0UUXlWRVqaxp3rx5gzNOOOGE3HDDDQXV\nJLfffntJTtV2MkmOOuqokpzjjz8+X/rSl0qyNmzYsPuR9sCCBQuyevXqkqyFCxcOzhiNRmXHglXb\n28rP27RpNXfLrjxeqqip6ngyqVtGS5YsyeWXX16Sdffdd5fkvOhFL8pnPvOZkqy98Uj+MdRDkryj\ntXZ4ki1JvpHkZ5Kcm+SdrbU5Gf8R0X92y5Xe+/mT+7FfMbmtzH1JXtV7/2pr7b8k+UJrbVqSTRk3\nwb+VZG+7oa9Pcu7kj67ekeS1k+E75vy3JO9qrd04mY83J/nkw5geAAAAAAAHoEfyHu3XJDltJ0/d\nnfH90bf33sm/7V//jnz3Hyh9YPhH8933UH9g+GHb/fyxJB+b/PzmXdT3T0nO3snw1+3weG2S1+zp\n9AAAAAAAeGyp+R0BAAAAAAB4jNJoBwAAAACAATTaAQAAAABgAI12AAAAAAAYQKMdAAAAAAAG0GgH\nAAAAAIABNNoBAAAAAGAAjXYAAAAAABhAox0AAAAAAAbQaAcAAAAAgAE02gEAAAAAYACNdgAAAAAA\nGECjHQAAAAAABtBoBwAAAACAAWY82gU8lmzYsGGfy5s9e3ZBJWObN28enPHNb36zoJKxpUuXluQ9\n+clPLqjmQZs2bRqcMX369IJKas2ZM2efytoXP2/VKtalgw46qKCS2qzbbrutJCdJ1qxZMzjj8Y9/\nfEElD5o7d+7gjBkz6nbfVVmVn5GqrNFoVJKTJOvXrx+cMW1a3fUNGzduLMmp3J9UHAckyb333luS\nU5VVeayU1Lx3lTVVrZcVn5HqrH1tH1f1uU2SLVu2lORU1lSVVXF8U501b968kpyqrHXr1hVUUpu1\nLx6bVK5L27ZtK8m5/fbb96mcymOTqqw77rijJKcyq+L4/QFbt24tyVmxYsU+lbN8+fKSnNFoVJa1\ncuXKkpwkmZqaKsmpOjapyqncdld9TirPBSrnb0+5oh0AAAAAAAbQaAcAAAAAgAE02gEAAAAAYACN\ndgAAAAAAGECjHQAAAAAABtBoBwAAAACAATTaAQAAAABgAI12AAAAAAAYQKMdAAAAAAAG0GgHAAAA\nAIABNNoBAAAAAGAAjXYAAAAAABhAox0AAAAAAAaY8WgXsCdaa1uTXJ9kZpKvJHl1733Dw8i5r/d+\n6HaPfzHJ7yZ5Yu/9vqp6AQAAAAB47Nhfrmhf23s/uff+rCSbk/zcw8wZ7fD45Um+mOSlOxu5tTb9\nYU4HAAAAAIDHiP3iivYdXJLkWUnSWvvlJK/NuIH+F733tz/U8O211o5JcnCS/5TkvyR572T4qzNu\nvB+S8RcRy1trb0zy40lmJflE7/3Nk3E/keRfJTkoydt77//rEZpnAAAAAAD2UfvLFe1TSdJam5Hk\nB5Pc2Fo7OcmrkyxMcmqSn26tPXtXw7fPmXh5kr9OcmmSp7fWnrDdcycleWnvfXlr7blJjuu9nzIZ\nvqC1dvpkvNf23hdOpvUfW2tHls85AAAAAAD7tP2l0T6ntXZNxrd5+Yckf5Hk9IyvLt/Qe1+b5GNJ\nlu5k+MeTnLGTzFck+XDvfTQZ52XbPXd+7/2eyc/PS/LcyfSvSdKSHDd57hdba9cluTLjK9uPCwAA\nAAAAjylTo9GOty3f97TW7u29H7bDsNcnmdd7/63J47ckuT3jq9Yf33t/0/bDe+/vfCCntXZ8ktVJ\nbp3EzUpyc+/9jMmtY+b33l8/ef3bkvTe+7t3mP6yJP81yXN77xtbayuSvKn3vnJX83H//fePDjnk\nkIFLAwAAAACAR9LnP//5nHPOOVO7H3Nsf7lH+85m6JIk57bWfi/J9CQ/kuRVGV+lf25r7Xe3G/7K\nHXJ+IuOm+O8/ENZau6m19pSdTOe8JG9prX2w9762tfakjP8g6+FJvjNpsj8jyeLdzcSqVav2YFb3\nzPLly7NixYrBObNnzy6oJlmyZEkuv/zywTl///d/X1DN2Gte85r85V/+5eCcJz/5ycOLmXjuc5+b\n888/f3DO9Ok1f6f3rLPOyoUXXliSNXfu3JKcxYsX58orrxycU/kl4qmnnporrriiLK9CVU1Vy6lq\nG5Akt912W0nOS1/60nz84x8fnPP4xz++oJqxpUuXZuXKXX4fu8cOPvjggmqS+fPn5+qrry7JuuWW\nW0pyfviHfzif+tSnSrKq1u+XvOQl+eQnPzk4p+p9q9qXJPvm/uT2228vyXn5y1+eD33oQ4NznvCE\nJ+x+pD109tln54ILLhicU3X8dvrpp+fSSy8tydqyZUtJzplnnpmLLrqoJGvGjJpTnarltHHjxoJq\n6tajJKm6CGjRokW56qqrSrLWrFlTkvP85z8/5513XknWtm3bSnJ+8Ad/MJ/73OcG58ybN6+gmtr3\nbfPmzSU5ldulTZs2leRU7uMq1qXnPOc5+bu/+7uCapJp02puclC5jKam9rif9ZCqeiZJ3blu5Wdu\n/fr1gzMq97nLly8vyRmNRmXrQMV5V5KcccYZueSSS0qy5syZMzhjwYIFWb16dUE1dcdKJ554Yq67\n7rqSrKp+wDnnnJPPf/7zJVl7Y3+5dcw/O1PuvV+b5C+TrEpyRZI/771fv4vhN+yQ8+NJPrFD5Ccy\nvm/7d02r935+kg8muaK1dkOSj2b8h1I/n2Rma+3LSX5nMi0AAAAAAB5j9osr2ne8bcx2w/84yR/v\nxfDDJv8/bSfPvXG7h+/b4bl3JHnHTkp4wUMWDgAAAADAAW9/uaIdAAAAAAD2SRrtAAAAAAAwgEY7\nAAAAAAAMoNEOAAAAAAADaLQDAAAAAMAAGu0AAAAAADCARjsAAAAAAAyg0Q4AAAAAAANotAMAAAAA\nwAAa7QAAAAAAMIBGOwAAAAAADKDRDgAAAAAAA2i0AwAAAADAABrtAAAAAAAwwIxHu4DHkrlz5+7T\neUNNnz59cEZrraCS2rzNmzcXVPKg2bNnD86ofO8PO+ywkpx77rmnJCdJ1q5dOzjjiCOOKKjkQbNm\nzRqcsWXLloJKHjRt2vDvSis+tw+oWEZJcvTRR5fkVGdVmTlz5uCMbdu2FVRSm3Wgv29PetKTBmdU\n7k+q9gOV24Cqmr7v+76vJKcqq3IZJTX73cptQMU2qTInSebMmVOSU7mcKtaDqvmqzKo45qrOqjzO\nrcqaMaPutLniGLVyu1SVVbkNqHrfKs67HnDooYeW5FRtl6rqmZqaKslJkkMOOaQkp/J4qer8ZDQa\nleRUZlWcC1bmrFy5siSnMmvp0qUlOaPRqCzryiuvLMnZunVrSU7l5239+vUlOfPmzSvJqc7aU65o\nBwAAAACAATTaAQAAAABgAI12AAAAAAAYQKMdAAAAAAAG0GgHAAAAAIABNNoBAAAAAGAAjXYAAAAA\nABhAox0AAAAAAAbQaAcAAAAAgAE02gEAAAAAYACNdgAAAAAAGECjHQAAAAAABtBoBwAAAACAAfbr\nRntrbVtr7X3bPZ7eWrujtfa3k8c/1Fr7z3uZ+Zuttd/ZYdizW2tf2c3rVrTWTt6baQEAAAAAsP/b\nrxvtSdYmOb61Nnvy+LlJvvXAk733T/fe37qXmX+d5N/sMOzlST74sKsEAAAAAOCANePRLqDAZ5O8\nMMnHk7wi40b5GUnSWnt1kgW9919orb0syW8m2ZLknt77ma21aUl+P8k5SbYmeXfv/V2ttbtbawt7\n76sm0/jxJM+bZP5JkgVJ5iT5m977m/+lZhQAAAAAgH3P/n5F+yjJh5K8YnJV+wlJrtrJOEnyG0me\n13s/KcmLJ8N+JslTk5zQez8xyQcmwz+UcdM+rbXFSe7qvd80ee7Xeu+nJHl2kjNba8fXzxYAAAAA\nAPuLqdFotPux9lGttXt774e11lYleVeSpyU5P8kbeu8vnlzRPr/3/vrJlehPS/KRJB/vvd/dWvub\nJH/ae79gh9x/leSy3vtTW2t/lOSfeu9/NHnu55L8dMa/DXBUkl/ovX+ktbZiMt1rdlXvunXrRnPn\nzq1eDAAAAAAAFPriF7+YU045ZWpPxz8Qbh2TJH+b5A+SnJnk8Tsboff+71trC5O8KMnVrbX5uwrr\nvd/SWru5tXZmkh9NsjhJWmvfl+QNGTfv722tnZvkoD0t8sYbb9zTUXdr0aJFueqqHS/ef/RU1bNt\n27aCasZOPfXUXHHFFYNzNm/eXFDN2NKlS7Ny5crBOVVf2CxYsCCrV68uybrnnntKcs4+++xccMEF\nux9xN4444oiCasbmz5+fq6++enDOli1bCqoZq/rMTZ8+vaCa2nWp6jNXtQ2oVFXTjBk1u++FCxdm\n1apVux9xD1R9cX/KKafki1/8YklWlaqaqtbt0047LZdddllJVtU2YPHixbnyyitLsqpU1VS1jJK6\nz1zV8dK+djyZ1NZUtZyqtt1V28klS5bk8ssvL8nasGFDSc5ZZ52VCy+8sCRr5syZJTlnnHFGLrnk\nkpKsqv1u1bpUtYwqj9+mTav5ZfmTTz4511yzy2vX9srWrVtLciqPlyq2S5XbyampPe4dPaTK4zfH\nS3tm06ZNgzOq+hNJ3bpUue1eunRpSc5oNCqbv4r3/0A+VkrqPm+P1nnl/n7rmAfW9PckeXPv/cu7\nGrG1dkzvfVXv/U1Jbk/yrzK++v1nW2vTJ+Mcud1LPpTkj5Lc1Hu/dTLssCT3J7mvtfY9SX6wdG4A\nAAAAANjv7O+N9lGS9N6/3Xt/527G/YPW2g2ttRuSXN57vyHJ/0ryrSQ3tNauzeS+7BMfTfIDST74\nwIDJa65L8tUk709y6Y61AAAAAADw2LJf3zqm937YToZdnOTiyc/vTfLeyc8/upNxt2Z8K5g37OS5\nu5LM3snw1+6ilrP2snwAAAAAAA4A+/sV7QAAAAAA8KjSaAcAAAAAgAE02gEAAAAAYACNdgAAAAAA\nGECjHQAAAAAABtBoBwAAAACAATTaAQAAAABgAI12AAAAAAAYQKMdAAAAAAAG0GgHAAAAAIABNNoB\nAAAAAGAAjXYAAAAAABhAox0AAAAAAAbQaAcAAAAAgAFmPNoFPJZs3rx5n8ubOXNmQSV1RqPRPpc3\na9asgkpq8+65556CSmqzDj744JKcqqyNGzcWVFKbt23btoJKHlS9TRlq69atJTnTptV9B1yZVaWi\npvXr1xdUUps1ffr0kpykbt2uWieTZMOGDWVZFarmrXIfV7UOrF27tiQnqXnfKvdvVSr3cVVZlZ+3\ndevWleTMnTu3JCep2XZXbkeqtpOV5wJVWZXnA1VZmzZtKsmpzqpQtS5VHpfef//9JTlTU1MlOUnd\n57eqpqrlXbk/ue+++0pyDj/88JKcJJk9e3ZJTuWxd9V7V3WeU5Vz0EEHleQkyZw5c0pyrrzyypKc\nyqzFixcPzhiNRiU5SfKNb3yjJCdJnvjEJ5bk3HLLLSU5Se1nd0/tex0IAAAAAADYj2i0AwAAAADA\nABrtAAAAAAAwgEY7AAAAAAAMoNEOAAAAAAADaLQDAAAAAMAAGu0AAAAAADCARjsAAAAAAAyg0Q4A\nAAAAAANotAMAAAAAwAAa7QAAAAAAMIBGOwAAAAAADDDj0S6gQmttW5L3995/avJ4epLbklzRe3/x\nQ7zuiUn+IslTksxMcnPv/UUPMf5Tk3ym9/6snTy3Iskbeu/XDJoZAAAAAAD2KwfKFe1rkxzfWps9\nefzcJN/ag9e9JckXeu8n9t6fmeRX9+A1o4dZIwAAAAAAB6AD4or2ic8meWGSjyd5RZK/TnJGkrTW\njkzyniTHZNyU/5ne+5eSHJ3kvAcCJsMyec0fJDknybYk/633/pHtJ9ZaOyjJuUlOSNKTHPRIzRgA\nAAAAAPuuA+WK9lGSDyV5xeSq9hOSXLXd829Ock3v/dlJfj3JX02GvyvJe1prF7TWfq21dnSStNZe\nmuSEyS1inpvkD1pr37PDNP9dkrWTK+HflGTBIzRvAAAAAADsww6URvsDV6N/X8ZXs//vJFPbPX16\nJs313vuKJPNaa4f03r+Q5F8neXeSZyS5prX2+Mn4fz0Z//YkFyVZuMMklyZ5/2ScG5Nc/0jMFwAA\nAAAA+7ap0Wj/v+V4a+3e3vthrbXfSPL6JGcmeXzGf5z0xa21a5K8tPf+D5Px/ynJD/Te798h59MZ\n32LmjCQ39N7/cjL8fUk+kuTGJJ/uvZ/QWvtEkrf33i+ajHN1kp9+qD+Gunbt2tHBBx9cN+MAAAAA\nAJS7+OKLs2zZsqndjzl2oNyj/YEZfk+S7/Tev9xaW7bd85ckeVWS326tnZnkjt77/a215Umu7L2v\nb60dmvE93P9pMv7PTBrsj8u48f7GJHO2y1yZ5JVJLmqtHZ/x7Woe0rXXXjtkHr/L6aefnksvvXRw\nzsyZMwuqSRYtWpSrrrpq9yPuxtatWwuqGVuyZEkuv/zywTnTptX94sfixYtz5ZVXDs5Zu3ZtQTXJ\n2WefnQsuuKAkq+pLpKpltG3btoJqxqrWpcqaDtRtQKUDuaaNGzcWVJMsXbo0K1euLMmaPn16Sc5p\np52Wyy67rCSrap9SuZwqVNYzZ86c3Y+0BxYuXJhVq1aVZFXt484888xcdNFFg3MqL5KoWk7r168v\nqKZ2Xar6vC1fvjwrVqwoyZo7d25JTtW2e8OGDQXVJMuWLcvFF19cklV1nHvGGWfkkksuKcmquhCs\ncv2uqqnqvZs1a1ZBNcmpp56aK664oiRr8+bNJTmV79vU1B73RR5S5fpdUVPVeUBSd0xZeV55+OGH\nl+QsWLAgq1evLsmq2u8eyOvSQQfV/NnCyvet6tik8rxy8eLFgzNGo1HZ9u0b3/hGSc6xxx6bm266\nqSTrlltuKcmpPF7aGwdKo32UJL33byd5506e/62M78V+fcZ/DPWnJsPnJ3lna21zxrfReXfv/eok\nV7fWFmd8O5htSf5T7/321tpTt8v80yTntta+nOSrSWq2BAAAAAAA7FcOiEZ77/2wnQy7OMnFk5+/\nk+RHdjLO25K8bReZv5LkV3YY9o+ZXLnee9+Q8f3gAQAAAAB4DDtg/hgqAAAAAAA8GjTaAQAAAABg\nAI12AAAAAAAYQKMdAAAAAAAG0GgHAAAAAIABNNoBAAAAAGAAjXYAAAAAABhAox0AAAAAAAbQaAcA\nAAAAgAE02gEAAAAAYACNdgAAAAAAGECjHQAAAAAABtBoBwAAAACAATTaAQAAAABgAI12AAAAAAAY\nYMajXcBjyYwZtYu7Im9qaqqgkvqsfUn1fFXkHXbYYQWV1GatW7euJCdJNm7cODjjoIMOKqjkQdOn\nTx+csWXLloJKHrRt27bSvH1F5XKqyNq6dWtBJQ+qWL8POeSQgkpqszZv3lySk9TtLyv3u7Nnzx6c\nUbEdecDcuXPLsqpU7S8PPfTQkpyqrDVr1hRU8qB77713cMa8efMKKhmrWt6V24CDDz64JGc0GpXk\nVNkXt91r164tyUnqlnfV+1+ZVXnMVbH9rjw2qdp2H+jvW9W5RcVxYKXHPe5x+1xW5TKq+qxMm1Z3\njWpVVtVnt6qeyuPuqqzKY5Oq7ck3vvGNfSrnaU97WknOaDQqy1q1alVJTlK7b9pTrmgHAAAAAIAB\nNNoBAAAAAGAAjXYAAAAAABhAox0AAAAAAAbQaAcAAAAAgAE02gEAAAAAYACNdgAAAAAAGECjHQAA\nAAAABtBoBwAAAACAATTaAQAAAABgAI12AAAAAAAYQKMdAAAAAAAGOCAb7a21S1pr52z3+GWttc/u\nZLzXtdZuaK1dP/n/h3aTe25r7aU7Gb6stfbpmuoBAAAAANifzHi0C3iE/FySj7bWLkwyK8l/S/K8\n7UdorT0lya8lObH3fn9rbW6SJwyY5mjAawEAAAAA2E8dkI323vuXW2t/m+RXkxyc5L1JRq21ryW5\nKsnJSX4+yb1J1k1esy7JPyZJa+3ZSf4syZwkNyV5Xe/9nu2nMbli/o+SrE1y2b/AbAEAAAAAsA86\nIG8dM/GWJD+R5Jwkb50Me1qSd/ben5Xk0iS3J7m5tfae1tqLtnvt+5L8p977iUm+lORN2we31mYn\n+fMkL+y9L0hy1CM6JwAAAAAA7LMO2Eb75Ar1Dyf5q9775sngf+y9r5o8v633fk6SH03Sk/xha+03\nW2uHJTm8937p5DXvTbJ0h/hnJPlm7/2bk8fvfyTnBQAAAACAfdfUaHTg3lq8tfamJPf13v+wtfbU\nJJ/uvZ+wi3HnJ3lPkjOS3Nh7f+pk+DFJPtJ7X9BaOzfJpzO+ncz/6L0vm4zzQ0l+uvf+4oeqZ926\ndaO5c+dWzR4AAAAAAI+A1atXZ8GCBVN7Ov4BeY/2h/D/L5jW2tFJjuq9XzsZdFLGV7zf21q7u7V2\nWu/9siQ/meTiHXK+luSprbV/3Xu/Ockr9mTiN9xww/A5mFi8eHGuvPLKwTnTptX8UsMpp5ySL37x\ni4NztmzZUlDN2JIlS3L55ZcPzpk+fXpBNWOLFi3KVVddNTin6n1buHBhVq1aVZK1bt26kpxly5bl\n4ot3/MjtvYMOOqigmrGq923jxo0F1YwtXbo0K1euHJwze/bsgmrqllFStx047bTTctllw/+Extat\nWwuqGat63w455JCCapKTTz4511xzTUnW5s2bdz/SHqhcl6pU1VS1P1mwYEFWr15dklWlsqapqT0+\njn1I8+fPz9VXXz04Z82aNQXVjJ199tm54IILBufMmzevoJrkpJNOyrXXXrv7EfdA1Tag6pgySaou\nKKraBsyYUXPqVbVuJ8natWtLcqr2b0ly8MEHl+RULqdt27aV5FQde1cdm1SdUybJzJkzS3IO5Pct\nqTkfOP3003PppZfufsQ9UHVMeeKJJ+a6664ryao6ZzqQz0+SmuOlqp5JklRdVFq5Lq1fv74k59RT\nT80VV1xRkvXEJz5xcMaxxx6bm266qaCa5GlPe1pJzmg0KjuGr9rePlrnTI+1Rvv2R9szk7xt0nDf\nkOSOJD83ee41Sf6stTYnyTeTvHb71/feN7bWfjbJZ1tra5NckqRmDwUAAAAAwH7lgG60997fvN3P\n/5jkhO0e/1OSs3fxuuuTnLqT4a/b7ufzknx/Zb0AAAAAAOx/Dtg/hgoAAAAAAP8SNNoBAAAAAGAA\njXYAAAAAABhAox0AAAAAAAbQaAcAAAAAgAE02gEAAAAAYACNdgAAAAAAGECjHQAAAAAABtBoBwAA\nAACAATTaAQAAAABgAI12AAAAAAAYQKMdAAAAAAAG0GgHAAAAAIABNNoBAAAAAGCAGY92AY8l06bV\nfq9RkTd37tyCSuqyPvGJTxRUMrZkyZJccMEFg3PmzZtXUM3YokWLsnr16sE573rXuwqqSb7yla/k\n1a9+dUnWhz/84ZKcpGaZv/3tby+oZGzRokV597vfPThn+vTpBdWMLV26NB/4wAcG58yaNaugmvEy\nev/731+SdeSRR5bknHbaaTnvvPMG57zwhS8sqOZBs2fPHpxx3XXXFVSSnHzyyWVZn/vc50pyPvrR\nj+Ztb3tbSdbU1FRJzkc+8pH89//+3wfnLFiwoKCacc6FF15YkrV8+fKSnCQZjUYlOb/8y79ckrNy\n5cr80i/90uCcn/qpnyqo5kE333zz4IxDDz20oJKxzZs3l+S8853vLMl53/veV5Z18sknl+QsWrQo\nV1xxxeCco446qqCaZP78+fn6179ellXl6KOPLsn53d/93ZKc97znPWXHzFWfuYULF5YcL23ZsqWg\nmmTx4sX5q7/6q5KsW265pSTnU5/6VN7ylreUZM2YUdPu+NjHPpbf+73fK8k65ZRTBmecfvrpueyy\nywqqqetRnHjiiTn//PNLsl7ykpeU5CR15/K33nprSU5S9/m97777SnLuvvvukpx77723JCdJbrvt\ntpKcyl5O1bl8xbby2GOPLdvmrlq1qiSnMmvhwoUlOaPRqDRrT7miHQAAAAAABtBoBwAAAACAATTa\nAQAAAABgAI12AAAAAAAYQKMdAAAAAAAG0GgHAAAAAIABNNoBAAAAAGAAjXYAAAAAABhAox0AAAAA\nAAbQaAcAAAAAgAE02gEAAAAAYACNdgAAAAAAGECjHQAAAAAABpjxaBewO621X0/yiiRbJ/9+tve+\nahfjnpvk0733jz9E3rlJliVZk2Rbkp/vvV+1k/F+Nsna3vv7h88FAAAAAAAHqn260d5aW5zkBUlO\n7L1vaa3NSzKrIPqNvfePt9aem+TPkzx7h+lO773/z4LpAAAAAABwgNunG+1Jjk5yZ+99S5L03u9O\nktbabyR5UZI5SS7vvf/cji9srZ2c5A+THJzkziSv6b3/3x1GW5nk2Mn4K5Jcl+S0JH/dWjssyX29\n9z9srR2b5M+SPCHJliQv673f3Fp7Y5Ifz7j5/4ne+5tL5x4AAAAAgH3evn6P9i8k+d7W2tdaa+9q\nrS2dDH9H731R7/2EJHNbay/c/kWttRlJ3pHkR3vvC5Ocm+R3dpL/4iQ3bvd4Zu/9lN77H+0w3gcm\n0zwxyZIk/2dyNfxxvfdTkpyUZEFr7fSB8wsAAAAAwH5majQaPdo1PKTW2lSSM5KcleRnkvxqkvuT\n/Ockc5McmXET/K0P3KM9SU9yeZKbkkxl/IXCrb33H9zhHu13JPnF3vtXJ1e0/2bv/ZLJdN+U5L6M\nby3zld779+5Q1x8k+dFJzlTGV87/bu/93F3Ny7p160Zz584tWCoAAAAAADxSpqamMhqNpvZ0/H39\n1jHpvY8yvsXLytbajUl+Nsmzkszvvd86aYgftMPLppL8v/buHjQKM4wD+BMjQolSFATpXPsWUSma\nxKGg2C6CQgQ/cCgZjoBDEAWrThEaB1GXhOgQGjI4+YGIIGjppEvxgw41hh66VexWKLYIrZAOl0Kw\niVHfBxrx94PA5Xjvn+eOJNz973jfiZVJrKUAAAPYSURBVGaz+fkcsV/PcWDqn3Osn+0BbYtWsf7t\nvHdi2sTExOsunVd3d3fcvXu3Oier+F+7dm3K/bt69WrCNC0DAwNx4sSJ6pwVK1YkTNPS398f586d\nq87JyIiImJycjDVr1qRkXbx4MSVn3bp18eDBg/kXzmN4eDhhmpaxsbHo6+urzmlvb0+YpmV0dDT2\n799fnbNkScaxFxEjIyNx4MCBlKzly5en5AwODsbx48erc7Zv3z7/ote0adOmuHPnP+dvv7GHDx8m\nTBPRaDRifHw8JevGjRspOZcvX449e/akZLW1vfbzoVe6dOlS7N27tzqns7MzYZqIo0ePxunTp1Oy\ntm7dmpLT1dUV9+7Nelb9Gzt8+HBKzu3bt2Pz5s3zL5xHb29vwjQtfX19MTY2Vp2zfv36hGnynk9G\nRJw9ezYl5/z582mP+YYNG1JyDh06FENDQ9U5q1atSpgmYt++fXHhwoWUrI0bN6bkrF69Oh49epSS\ndfLkyZSc8fHxaDQaKVnLli1LyRkeHo6DBw9W57x48SJhmtZriv7+/pSsJ0+epORcu3Ytenp6UrIW\nL86pO65cuRK7du1Kyeru7q7OOHbsWJw6dSphmohFi3I2OThy5EicOXMmJWvnzp0pOZn/l54+fZqS\ns2XLlrh161ZK1rNnz6ozduzYEdevX0+YJu/vbdu2bXHz5s2UrKwuJ/P50vPnz6szMn+POjo6UnI6\nOzvj/v37KVldXV0pOVNTU2mvB9/Egt46ppTySSnl4xlXfRYRP09f/q2UsjQids9y02ZErJw+TDVK\nKYtLKW/VJjabzT8i4pdSSs901pJSygcR8V1ENEopHdPXf1RKWfk2PwMAAAAAgHfXQv9E+9KIGCml\nfBitQ0gfR2v7mN8jYiIifo2ImW8rTUVENJvNv0spu2fctj0ihiJi8t81s3jVHjq9ETFaShmMiL+i\ndRjq96WUTyPih1JKRGubma+itR0NAAAAAADviQVdtDebzR8jYrbtXwamv15e35hx+ado7cU+55qX\nrv/ipe+/mXH5cUR8OcttRqJ16CoAAAAAAO+pBb11DAAAAAAALHSKdgAAAAAAqKBoBwAAAACACop2\nAAAAAACooGgHAAAAAIAKinYAAAAAAKigaAcAAAAAgAqKdgAAAAAAqKBoBwAAAACACop2AAAAAACo\noGgHAAAAAIAKinYAAAAAAKigaAcAAAAAgAqKdgAAAAAAqNA2NTX1f88AAAAAAADvLJ9oBwAAAACA\nCop2AAAAAACooGgHAAAAAIAKinYAAAAAAKigaAcAAAAAgAqKdgAAAAAAqPAPhDYj3ZzXA6QAAAAA\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x13c9aef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#try to see how variables are correlated but its hard to tell since we have so many features\n",
    "def plot_corr(df,size = 25):\n",
    "    '''Function plots a graphical correlation matrix for each pair of columns in the dataframe.\n",
    "\n",
    "    Input:\n",
    "        df: pandas DataFrame\n",
    "        size: vertical and horizontal size of the plot'''\n",
    "\n",
    "    corr = df.corr()\n",
    "    fig, ax = plt.subplots(figsize=(size, size))\n",
    "    ax.matshow(corr)\n",
    "    plt.xticks(range(len(corr.columns)), corr.columns);\n",
    "    plt.yticks(range(len(corr.columns)), corr.columns);\n",
    "    \n",
    "plot_corr(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZkAAAEDCAYAAADnWHnrAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nupyQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xdd06ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x9f630f0>"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEpCAYAAABoRGJ5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nM9JbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xdb4ee48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#to replicate the prof's benchmark we first just ran a regression with total sq ft and neighborhod in a regression\n",
    "#variables = SalesPrice = TotalBsmtSF + Neighborhood\n",
    "#before this though let's look at the scatterplots of these variables\n",
    "\n",
    "#as Square footage gets larger, so does price --> positive correlation\n",
    "SFPrice = plt.scatter(df['SalePrice'], df['TotalBsmtSF'])\n",
    "show(SFPrice)\n",
    "\n",
    "df['Neighborhood'].value_counts().plot(kind='bar')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "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>SalePrice</th>\n",
       "      <th>TotalBsmtSF</th>\n",
       "      <th>Neighborhood</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>208500</td>\n",
       "      <td>856</td>\n",
       "      <td>CollgCr</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>181500</td>\n",
       "      <td>1262</td>\n",
       "      <td>Veenker</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>223500</td>\n",
       "      <td>920</td>\n",
       "      <td>CollgCr</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>140000</td>\n",
       "      <td>756</td>\n",
       "      <td>Crawfor</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>250000</td>\n",
       "      <td>1145</td>\n",
       "      <td>NoRidge</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   SalePrice  TotalBsmtSF Neighborhood\n",
       "0     208500          856      CollgCr\n",
       "1     181500         1262      Veenker\n",
       "2     223500          920      CollgCr\n",
       "3     140000          756      Crawfor\n",
       "4     250000         1145      NoRidge"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfnew = df[['SalePrice'] + ['TotalBsmtSF'] + ['Neighborhood']]\n",
    "dfnew[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "475     132500\n",
      "1010    135000\n",
      "753     275500\n",
      "162     220000\n",
      "1185    104900\n",
      "1059    220000\n",
      "1277    197900\n",
      "1197    144000\n",
      "1097    170000\n",
      "120     180000\n",
      "1362    104900\n",
      "323     126175\n",
      "342      87500\n",
      "916      35311\n",
      "966     160000\n",
      "591     451950\n",
      "499     120000\n",
      "685     207500\n",
      "1000     82000\n",
      "1034    119750\n",
      "874      66500\n",
      "867     129000\n",
      "209     145000\n",
      "879     136500\n",
      "1064    154000\n",
      "723     135000\n",
      "826     109500\n",
      "863     132500\n",
      "1352    134900\n",
      "597     194201\n",
      "         ...  \n",
      "974     167500\n",
      "259      97000\n",
      "996     136500\n",
      "347     157500\n",
      "349     437154\n",
      "158     254900\n",
      "781     175900\n",
      "452     204000\n",
      "809     106000\n",
      "500     113000\n",
      "469     187000\n",
      "22      230000\n",
      "370     172400\n",
      "724     320000\n",
      "1148    116900\n",
      "761     100000\n",
      "1379    167500\n",
      "1140    139000\n",
      "408     280000\n",
      "1032    310000\n",
      "601     141000\n",
      "1015    227000\n",
      "152     190000\n",
      "1358    177500\n",
      "387     125000\n",
      "548     125000\n",
      "1407    112000\n",
      "552     255500\n",
      "251     235000\n",
      "104     169500\n",
      "Name: SalePrice, dtype: int64\n"
     ]
    },
    {
     "ename": "NotFittedError",
     "evalue": "This StandardScaler instance is not fitted yet. Call 'fit' with appropriate arguments before using this method.",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNotFittedError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-91-21ffeb6a55cd>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      8\u001b[0m \u001b[1;31m#scaler = StandardScaler()\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      9\u001b[0m \u001b[1;31m#X_train = scaler.fit_transform(train)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 10\u001b[1;33m \u001b[0mX_test\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mscaler\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtransform\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtest\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     11\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     12\u001b[0m \u001b[1;31m#######Fit MLR model on training data###############\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Users\\Owner\\Anaconda2\\lib\\site-packages\\sklearn\\preprocessing\\data.pyc\u001b[0m in \u001b[0;36mtransform\u001b[1;34m(self, X, y, copy)\u001b[0m\n\u001b[0;32m    639\u001b[0m             \u001b[0mThe\u001b[0m \u001b[0mdata\u001b[0m \u001b[0mused\u001b[0m \u001b[0mto\u001b[0m \u001b[0mscale\u001b[0m \u001b[0malong\u001b[0m \u001b[0mthe\u001b[0m \u001b[0mfeatures\u001b[0m \u001b[0maxis\u001b[0m\u001b[1;33m.\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    640\u001b[0m         \"\"\"\n\u001b[1;32m--> 641\u001b[1;33m         \u001b[0mcheck_is_fitted\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'scale_'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    642\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    643\u001b[0m         \u001b[0mcopy\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcopy\u001b[0m \u001b[1;32mif\u001b[0m \u001b[0mcopy\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mNone\u001b[0m \u001b[1;32melse\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mcopy\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Users\\Owner\\Anaconda2\\lib\\site-packages\\sklearn\\utils\\validation.pyc\u001b[0m in \u001b[0;36mcheck_is_fitted\u001b[1;34m(estimator, attributes, msg, all_or_any)\u001b[0m\n\u001b[0;32m    688\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mall_or_any\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mhasattr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mestimator\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mattr\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0mattr\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mattributes\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    689\u001b[0m         \u001b[1;31m# FIXME NotFittedError_ --> NotFittedError in 0.19\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 690\u001b[1;33m         \u001b[1;32mraise\u001b[0m \u001b[0m_NotFittedError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmsg\u001b[0m \u001b[1;33m%\u001b[0m \u001b[1;33m{\u001b[0m\u001b[1;34m'name'\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mtype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mestimator\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__name__\u001b[0m\u001b[1;33m}\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    691\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    692\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNotFittedError\u001b[0m: This StandardScaler instance is not fitted yet. Call 'fit' with appropriate arguments before using this method."
     ]
    }
   ],
   "source": [
    "#now that we know a little about our data let's finally run a MLR of these variables and see the results we get\n",
    "#Split data into training & test Sets\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "train, test = train_test_split(dfnew, test_size = 0.33)\n",
    "print train['SalePrice']\n",
    "#scaler = StandardScaler()\n",
    "#X_train = scaler.fit_transform(train)\n",
    "X_test = scaler.transform(test)\n",
    "\n",
    "#######Fit MLR model on training data###############\n",
    "#Step 1: setup design matrices\n",
    "y, X = dmatrices('SalePrice ~ TotalBsmtSF + Neighborhood', data=train, return_type='dataframe')\n",
    "#Step 2: Fit regression model\n",
    "model = sm.OLS(y, X)\n",
    "results = model.fit()\n",
    "print results.summary()\n",
    "\n",
    "##first Let's find the in-sample MSE and then we'll find the out of sample MSE and RMSE\n",
    "ypred = results.predict(X)\n",
    "MSE_insample = mean_squared_error(y, ypred)\n",
    "RMSE_insample = sqrt (MSE_insample)\n",
    "print 'Coefficients:'\n",
    "print results.params\n",
    "print \"The MSE on the training data is:\", MSE_insample\n",
    "print \"the RMSE on the training data is:\", RMSE_insample\n",
    "#Out of Sample Prediction\n",
    "y, X = dmatrices('SalePrice ~ TotalBsmtSF + Neighborhood', data=X_test, return_type='dataframe')\n",
    "ypred = results.predict(X)\n",
    "MSE_OOS = mean_squared_error(y, ypred)\n",
    "RMSE = sqrt(MSE_OOS)\n",
    "print \"The MSE on the test data is:\", MSE_OOS\n",
    "print \"The MSE goes up by\", MSE_OOS - MSE_insample, \"when you go from train to test data\"\n",
    "print \"The RMSE is:\", RMSE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        Id  MSSubClass MSZoning  LotFrontage  LotArea Street Alley LotShape  \\\n",
      "510    511          20       RL         75.0    14559   Pave   NaN      Reg   \n",
      "944    945          20       RL          NaN    14375   Pave   NaN      IR1   \n",
      "1075  1076          70       RL         75.0    13125   Pave   NaN      Reg   \n",
      "111    112          80       RL          NaN     7750   Pave   NaN      IR1   \n",
      "748    749          20       RL         59.0    10593   Pave   NaN      IR1   \n",
      "\n",
      "     LandContour Utilities    ...     PoolArea PoolQC Fence MiscFeature  \\\n",
      "510          Lvl    AllPub    ...            0    NaN   NaN        Shed   \n",
      "944          Lvl    NoSeWa    ...            0    NaN   NaN         NaN   \n",
      "1075         Lvl    AllPub    ...            0    NaN   NaN         NaN   \n",
      "111          Lvl    AllPub    ...            0    NaN   NaN         NaN   \n",
      "748          Lvl    AllPub    ...            0    NaN   NaN         NaN   \n",
      "\n",
      "     MiscVal MoSold YrSold  SaleType  SaleCondition  SalePrice  \n",
      "510     2000      6   2009        WD         Normal     164900  \n",
      "944        0      1   2009       COD        Abnorml     137500  \n",
      "1075       0      7   2007       CWD         Normal     219500  \n",
      "111        0      4   2010        WD         Normal     180000  \n",
      "748        0      3   2010        WD         Normal     260400  \n",
      "\n",
      "[5 rows x 81 columns]\n",
      "        Id  MSSubClass MSZoning  LotFrontage  LotArea Street Alley LotShape  \\\n",
      "720    721         120       RL          NaN     6563   Pave   NaN      IR1   \n",
      "1323  1324          30       RL         50.0     5330   Pave   NaN      Reg   \n",
      "143    144          20       RL         78.0    10335   Pave   NaN      IR1   \n",
      "733    734          20       RL         80.0    10000   Pave   NaN      Reg   \n",
      "596    597          70       RM         60.0     3600   Pave  Grvl      Reg   \n",
      "\n",
      "     LandContour Utilities    ...     PoolArea PoolQC Fence MiscFeature  \\\n",
      "720          Low    AllPub    ...            0    NaN   NaN         NaN   \n",
      "1323         HLS    AllPub    ...            0    NaN   NaN         NaN   \n",
      "143          Lvl    AllPub    ...            0    NaN   NaN         NaN   \n",
      "733          Lvl    AllPub    ...            0    NaN  GdWo        Shed   \n",
      "596          Lvl    AllPub    ...            0    NaN   NaN         NaN   \n",
      "\n",
      "     MiscVal MoSold YrSold  SaleType  SaleCondition  SalePrice  \n",
      "720        0     12   2006        WD         Normal     275000  \n",
      "1323       0     12   2009        WD         Normal      82500  \n",
      "143        0      6   2009        WD         Normal     204000  \n",
      "733      400      3   2009        WD         Normal     131400  \n",
      "596        0     10   2006        WD         Normal     114504  \n",
      "\n",
      "[5 rows x 81 columns]\n"
     ]
    }
   ],
   "source": [
    "print train.head()\n",
    "print test.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [Root]",
   "language": "python",
   "name": "Python [Root]"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}