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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# HW1 - Part 2\n",
"## CS-5891-01 Special Topics Deep Learning\n",
"## Ronald Picard\n",
"\n",
"In this noteboook we will walk through how to perform linear regression using gradient decent. The goal for this example is to predict what the a good market price should be for your home given previous data for the price based on size (square footage) and the number of bedrooms. The input data to our model will the size of a home and the number of bedrooms, and the output data of our model will be a good market price. Since this is a 3-D linear regression model, the equation of 3-D line (z = b + a * x + b * y) will be our model. \n",
"\n",
"To start we need import some needed classes."
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [],
"source": [
"import os\n",
"import numpy as np\n",
"import struct\n",
"from mpl_toolkits.mplot3d import Axes3D\n",
"import matplotlib.pyplot as pyplot\n",
"import csv\n",
"import time"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"First, we must change our path string to the path of our data file containing the features. (Please note that you must change this string to point to the housing_price_data.txt data file on your machine.) The data file is a csv-style matrix made up of 3 feature vectors (columns). Each entry in the first feature vector is the size of a particular house, each entry in the second feature vector is the number of bedrooms of the particular house, and each entry in the third feature vector is the price of that house. Each feature vector is of the same size, and there is a one-to-one correspondence between each indexed vector entry of the first, second, and third feature vectors in the feature matrix."
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [],
"source": [
"## path\n",
"path = 'C:/Users/computer/Desktop/git/deep-learning-jupyter-notebooks/1-linear-regression-using-gradient-descent/housing_price_data.txt'"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we retrieve the data from the data file as follows. This imports the feature data into a feature matrix from which we can extract each feature vector."
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [],
"source": [
"## retreive data \n",
"data = np.genfromtxt(path, delimiter=',', dtype=np.float64)\n",
"size_vector = data[:,0]\n",
"bedrooms_vector = data[:,1]\n",
"price_vector = data[:,2]\n",
"#print(size_vector)\n",
"#print(bedrooms_vector)\n",
"#print(price_vector)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we will normalize each of our feature vectors to (approximately) between -1 <= x <= 1. This will reduce the bias towards the larger feature and provide a more balanced model. We do this by using the using the formula: x(i) = (x(i) - Mean(x))/Std(x). The technique is known as feature scaling. (Please note that this means if we utilize our model later on, the input data must be normalized to produce an accurate prediction.)"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [],
"source": [
"## rectrieve size\n",
"m = np.size(price_vector)\n",
"\n",
"## find the mean\n",
"size_mean = np.mean(size_vector)\n",
"bedrooms_mean = np.mean(bedrooms_vector)\n",
"price_mean = np.mean(price_vector)\n",
"#print('size mean: ' + str(size_mean) + ', bedrooms mean: ' + str(bedrooms_mean) + ', price: ' + str(price_mean))\n",
"\n",
"## find the std\n",
"size_std = np.std(size_vector)\n",
"bedrooms_std = np.std(bedrooms_vector)\n",
"price_std = np.std(price_vector)\n",
"#print('size std: ' + str(size_std) + ', bedrooms std:' + str(bedrooms_std) + ', price std: ' + str(price_std))\n",
"\n",
"## normalize the data to between -1 <= x_j <= 1 using equation x_j^i = (x_j^i - u_j)/s_j \n",
"size_mean_vector = np.multiply(size_mean, np.ones(np.size(size_vector)))\n",
"#print(size_mean_vector)\n",
"normalized_size_vector = np.dot(1/size_std, size_vector-size_mean_vector)\n",
"#print(normalized_size_vector)\n",
"bedrooms_mean_vector = np.multiply(bedrooms_mean, np.ones(np.size(bedrooms_vector)))\n",
"#print(bedrooms_mean_vector)\n",
"normalized_bedrooms_vector = np.dot(1/bedrooms_std, bedrooms_vector - bedrooms_mean_vector)\n",
"#print(normalized_bedrooms_vector)\n",
"price_mean_vector = np.multiply(price_mean, np.ones(np.size(price_vector)))\n",
"#print(price_mean_vector)\n",
"normalized_price_vector = np.dot(1/price_std, price_vector - price_mean_vector)\n",
"#print(normalized_price_vector)\n",
"\n",
"\n",
"## create feature matrix\n",
"x = np.column_stack((np.ones(m), normalized_size_vector, normalized_bedrooms_vector))\n",
"#print(x[:,0])\n",
"#print(x[:,1])\n",
"#print(x[:,2])\n",
"\n",
"## re-assignment\n",
"y = normalized_price_vector\n",
"#print(y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we create our 3 X 1 parameter vector with values initialized to 1. The reason that our parameter vector contains only three values is because we are trying to perform a 3-D linear regression. This means we need to find the parameter values for the equation of a 3-D line h(x) = theta0 + theta1 * x theta2 * x (this is analagous to our z = d + a * x + b * y equation). (Please note that the initial value of 1 was chosen pesudo-arbitrarly. We could have just as easily chosen 0.5 and recieved (nearly) the same result for a linear regression model.)"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [],
"source": [
"## create parameter vector\n",
"theta = np.array([1, 1, 1])\n",
"#print(theta)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now that our model is set up and preprocessing is complete we need contruct our gradient descent algrorithm. This algorithm makes use of NumPy to perform linear alebra operations in a vectorized manner. The goal of our gradient decent algorithm is to minimize our cost function; which in this case is the least means squared. Calculating cost function gradient, multiplying it by the learning rate (step size), and subtracting this from the parameter vector iteratively will eventually lead us to the minima of our cost function and thus the ideal model parameters.\n",
"\n",
"There are three primary interative steps to our gradient decsent algorithm: \n",
"\n",
"1) Calculate the value of the cost function: j = (1/(2m)) * (X * Theta - Y)' * (X * Theta - Y). \n",
"\n",
"2) Calculate the value of the gradient of the cost function: dj_dTheta = (1/m) * (X' * X * Theta - X' * Y) \n",
"\n",
"3) Update the theta vector: Theta = Theta - alpha * dj_dTheta\n",
"\n",
"In the above steps: m = size of our feature vectors, Theta = parameter vector, Y = output profit feature vector, X = input feature matrix, j = cost function value, dj_dTheata = gradient vector with respect to the Theta vector, alpha = learning rate hyper-paramerter\n",
"\n",
"These steps repeat for the specified number of iterations. The final result of the Theta vector provides the values of theta0, theta1, and theta2 corresponding to our line equation.\n",
"\n",
"While our algorithm is running we will collect the cost function values and the corresponding interation # in two arrays that will allow us to plot the cost function value as a function of the number iterations; which will allow us see a plot of the learning curve for our gradient descent algorithm. "
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"elapsed time: 0.0019927024841308594 ms\n",
"final cost function value: 0.008769467118571728\n",
"interations: 100\n",
"Normalized Parameters: theta0: 2.6561398887836924e-05, theta1: 0.2583387777030867 , theta3: 0.7367893894351465\n"
]
}
],
"source": [
"# retrieve start time\n",
"start = time.time()\n",
"\n",
"## begin gradiant descent\n",
"alpha = 0.1\n",
"interations = 100\n",
"j_array = []\n",
"i_array = []\n",
"for i in range(interations):\n",
" \n",
" # calculate cost value\n",
" hx = np.dot(x, theta) # M X 3 times 3 X 1 = M X 1 \n",
" hx_minus_y = hx - y # M X 1 minus M X 1 = M X 1\n",
" hx_minus_y_transpose = np.transpose(hx_minus_y) # (M X 1)^T = 1 X M\n",
" j = np.dot(1/(2*m), np.dot(hx_minus_y_transpose, hx_minus_y)) # scalar * 1 X M times M X 1 = scalar\n",
" j_array.append(j)\n",
" i_array.append(i)\n",
"\n",
" # calculate gradient vector\n",
" x_transpose_x = np.dot(np.transpose(x), x) # 3 X M times M X 3 = 3 X 3\n",
" x_transpose_x_theta = np.dot(x_transpose_x, theta) # scalar * 3 X 1 = 3 X 1 \n",
" x_transpose_y = np.dot(np.transpose(x), y) # 3 X M times M X 1 = 3 X 1\n",
" dj_dtheta = np.dot(1/m, x_transpose_x_theta - x_transpose_y) # 3 X 1 minus 3 X 1 = 3 X 1\n",
"\n",
" # update theta vector\n",
" theta = theta - np.dot(alpha, dj_dtheta) # 3 X 1 - scalar * 3 X 1 = 3 X 1\n",
"\n",
" #input(\"Press Enter to continue...\")\n",
"\n",
"# retrieve end time\n",
"end = time.time()\n",
"\n",
"# logger data\n",
"print('elapsed time: ' + str(end-start) + ' ms')\n",
"print('final cost function value: ' + str(j))\n",
"print('interations: ' + str(interations))\n",
"print('Normalized Parameters: theta0: ' + str(theta[0]) + ', theta1: ' + str(theta[1]), ', theta3: ' + str(theta[2]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As printed above, the parameters after 100 iterations came out to (approximatly) the following as shown above:\n",
"\n",
"1) theta0 = 2.6561398887530704e-05\n",
"\n",
"2) theta1 = 0.8795566151371863\n",
"\n",
"3) theta2 = -0.04796939659432394\n",
"\n",
"Therefore, our 3-D line equation becomes: \n",
"\n",
"Price = 2.6561398887530704e-05 + 0.8795566151371863 * Size -0.04796939659432394 * Bedrooms \n",
"\n",
"Finally we will plot the results. \n",
"\n",
"1) The first plot is normalized line solution of the gradient decent algorithm. \n",
"\n",
"2) The second plot is denormalized line solution of the gradient decent algorithm. \n",
"\n",
"3) The third plot is the learning curve that relates the cost function value to the number of iterations of the algorithm. As seen by this plot, the cost function converges rapidly in about 20 iterations at a 0.1 leraning rate. "
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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MR5J0kwgLmWxlcpXJFnzkGGvOVvZfkAk0kEjl7clkHLiuVqtFp9MpRKzVapNknMSEQ5J0kwiC1+tV0ggQHLHKy2SSjJb4hltvODKW90kmYyGEkkvOzc0NioyThJzEeESSdJNQ4PV6lTQChCZbGWrSjQXxfCcSGdvtdpqamoKKLeSoXKfTJck4iXGFJOl+wSFPctlsNjo6OigrK4uKmEaSXhgtyPsppx5kyGN4vV4cDkfQd+TUhDpVkSTjJMYKSdL9gkJ+NXe73cp/u7q6qKioiOr78RDoaJNupHHU/1VDPm6Px4PT6fT7TD2BJ0fHSTJOYrSRJN0vGALJVh0pxkKIkiRNyHZG4UhUTcZCCI4dO6akLEKpKZKKiiTiRZJ0vyBQa2zliSg1AcWaLhjPkW48CCRjm82mPIjUZJws/EhipEiS7hmOUGQbWMQAPgKJJXI900g3HCJFxnLBh9PpTJJxElEjSbpnKMIVNIRDrIQ4EQl0NBGJjCF04YfdbsdgMJCenp4k4y8wkqR7hkEmW6fTyf79+1m6dGlEso0X6sg4Fp3umU7UkeRtJ0+eJDs7O+j3kMk3WfjxxUCSdM8QBBY0aDQaXC5Xwm7ceNMLEwGJeDDI50sm1MCxQhV+REpTTJRzmUQwkqQ7wRFLQcNoQk26RqORwcFBMjMzycjICNlpIAkUIlUj2iq8wO8kCz8mLpKkOwGhnsRRv+KP9Q1nt9vZu3cvWq2WrKws2tvbsVgseL1eUlJSyMjIICMjg8zMTCWPOREQqFI4HdsdjozVhR8nTpxgxowZfqmJZOHH+EWSdCcQAjW2MPZkK4Sgt7eXuro6HA4HS5YsISMjA6fTqURxQggcDgcWiwWLxUJraytWqxWv14vdbqe+vl4h5PFKxqebdMMhFBmbzWZ0Ol2y8GOCIEm6EwByVGuz2TAYDEEa27Hah56eHhoaGsjIyGDmzJk0NzeTlZUVJDWTJInU1FRSU1P92oQLIdizZw85OTlYLBb6+/sVMk5NTQ2KjBMxARgNEjXZ5/V6E3pM0RZ+qN3ekoUfY48k6Y5jqDW2Q0NDNDU1sWDBgjEn266uLhobG8nOzuass84iPT0du90e10SaRqOhsLDQr4GhbFxjsVgwm8309fVhtVoRQpCWlqaQsRwZhzJLH02Mh/TCaCIWMpYhT8TKOfokGY8ekqQ7DhGqoEGn0yllu2MBr9fLyZMnaWpqIi8vj0WLFvl18A1UL4xkvyRJUjr4BpKxzWZT0hS9vb1BZKzX65V0y+mKjKPF6SLdcBiu8OPAgQMsXrw4WfgxykiS7jhCpIIGjUajKBRi3WYskzcej4fOzk6am5spLCxkyZIlIdt8x+MyFiskSSI9PZ309HSKioqU5XJu2GKxMDAwgMViYd++fQBBkXFaWlrMZHymRbqxQp2+0uk+p4hIhR9JMo4eSdIdB4jUoUGG3AAyFsgFDNFMVMmTLx9++CGTJk1i2bJlGAyGsOsHGt6MJaFoNBqFjOVJvPnz5+P1ev0i4+7ubmw2G/A5GcuytrS0tDEnhLF8U0kEhlNUhCPjcPK2LyqSpHsaEU2HBhnxRLrRkK7b7aatrY329nYAli5d6pdGCIfRTC+MFjQajRLhqqEm46GhIU6ePIndbgdQiFsdGScy0h3tFMh4qPCLVmssn9fe3l6ysrLIyMjwk7Z9URQVSdI9DfB6vQwMDKDX69Hr9VFdaLEa0gz3HbfbTXNzM52dnZSWlrJ8+XIOHDgQNSmoSXe83yRqMi4uLlaWe71erFarHxnLkbHT6aSpqUmJjFNTU0d8nIkg80Q+IEaKcGTc19dHenr6F7bwI0m6Y4TAgobW1laKi4v9JFWREM8FF4p0nU4nzc3NdHd3U1ZWxsqVK5VIODBlMNz+jIcoayTQaDRkZmaSmZnpt9xms3H06FFSU1MxmUx0dHRgt9uVtIY6Mo6FjBORXkjUBGIiJyY9Ho8S4arxRen4kSTdBCNcQYOsRkgk1KTrcDhoamqit7eXiooKVq5cGdJ4JRbSPVMhSRJ6vZ7Jkyf7Lfd4PEpkHIqM5ag4IyODlJSUkK/bo01kE5F03W53yJRXuMgYou/4IQc12dnZCdn30UCSdBOEcB0a5AsqXjVCLNBoNNhsNlpaWhgYGKCyslIpFw2FMyF6HS2EuvHlcuesrCy/5TIZm81mBgYGaGtrw+Fw+KU1MjIyEvJ7J4ocPR5PwioF5Ug3FkSjNQZ47bXXOHjwIHfeeeeo7GsikCTdUcZwHRpkaLXahJKuzWbDZDJhMpmorq5m9uzZCckbgy9yMRqNZGRkRFQ8TBTE+uCJRMaykmJgYACbzca+ffvQarVBkbFcaRgrJiLpjmbEH3hvmUwmcnJyRmXbiUKSdEcJ0XZokJEo0rVYLDQ0NGCxWEhLS6Oqqor8/Pyovhur9lYIQUNDAx0dHWRnZ2Oz2XC5XOj1er+SXnmWeqJgtCantFot2dnZyqvuwMAAy5Ytw+12K5FxX18fLS0tOJ1OtFqtX2QcDRlPxPRCImEymcjNzT3duxERE+dOGKeQq6bMZjNZWVnDkq0MrVYbNFkQ7XihbkKz2UxDQwM2m42qqioKCws5fvx4QppNysoHi8WCRqNhxYoVeDweZb9cLhdmsxmLxcLJkycxm814PB5SUlJwOBx0dnZOOOex0YROp/MjYxlut1uJjNVkrNPpQpIxTMxIN5EwmUxUVlae7t2IiCTpxgl1QYPZbKalpYUFCxZE/f14Il25QEJ9MwwODlJfX4/b7VaiWnXeOJZ0wXDry2R78uRJysrKyMjIYOrUqUqUL0Ov15OXl0deXp6yTAiB0+nkk08+weVy0dbWpthAqqvIMjMz46oiG02crsoxnU5HTk5O0Ouxy+VSIuOenh6amppwuVzodDp0Oh1ut5uBgYFRTe8kinQTPWeQjHTPQIQqaNDr9XERaDzFDvLNYDQaqa+vB6CqqsqP4NTrx0q6oW4Kl8tFc3MzXV1dlJeXs2LFCrRarVJQEQ0kSSIlJQWdTkd5eblCarLZjRwZy/4K4F+4kJmZOSpa2Vj2d7xAr9eHJePOzk76+vqCyFidL5Y9KmJBItMWiTy3g4ODSdI9UxCpQ4NWqw0SeQ+HeCPd/v5+2tra0Gg0VFdXR5w0iHWMwPRCINmGkpmNFGqzm0B/hcAqMpvNFqQIkNukjyYmioJDr9eTnp6uvOXIUKd3urq6sFgsuN1uv1z7cGScqEg3HuVCLBgcHExOpE1kRNuhYSSpgmj3o6+vD6PRiNfrZdasWUEz5aEQS7EDfB7pulwumpqa6O7uHnWyVXu5DrcvoarIAuVZg4ODmM1m9u3b5xfdZWZmxhzdyZgoxjQQOiINld4BX2GMnDMOJOPAyDiRpBtpu5pPP8UbQ5ouECaTKeRb33hCknRDINYODSNJFQy3Hz09PTQ2NpKWlkZubi4zZsyIinDlMWIhXa/XS3t7O7W1tWELKEaKkWqBA+VZVquVhoYGZs+erRCK+lU7FKFMJCXFcIglDWAwGDAYDEG5dnVk3NnZicViwWazodfrsVqto3ruwhVGaN99F8OWLejefRfL22/jXbo0ru0nc7oTDOoLUHahiqbMMJ6oKBJRq43Ds7KyWLBgAenp6Rw5ciQmctdoNFGlPeTS4Pb2doqKihJCtomEECLsJJQ6upMJRVZSqMlYraQYz34GgRhp7lWSJAwGA/n5+X7SwsbGRgwGA2lpaSHPXaCxfLRkHJhe0L77Loa77kL33nt4J0/GvnUr3nnz4j4ej8cT9xvOWCFJuvhrbJ1OJ0ePHmXp0qUJfcUMRbpCCDo7O2lqaiI3N5ezzz6btLQ05fNYI1e5LDIcZFOXnp4eKisrmTZtGnq9PqabOJ7uEaNJPsP9RuGiO3UPN3XboLS0NHQ6nfL56VZSDIdETnilpqYGkbGsQpEj4/b2dqxWa0gyDtUZ2uPxoNVo0P797z6yff99hWxd3/seqK73WDFRcvFfaNINVdAgdyJIdE5PTbper5eOjg5aWlrIz88PaxweaxojXArD6XTS2NhIX1+fXxqhpaUlJlKPNj8b6junE5IUvoebzWajp6cHi8VCY2Oj4jomKylG4jo2UewiITyZyyqUlJSUoHOnfpCpO0Mr/e/S09G++y7Vjz5K+r59PrK9+25cGzeOiGzV+yDv43jGF5J0I5mGj4QUYiEgmRBbWlpobW2lqKiIpUuXRtRZjlR3qybbUD4MsfpByBNvE9HpKRTkThU5OTk4HA5mzpwJ+FtADg4O+hndBFbehasgS9SDRo4wE7HdWCbSIj3I7DYbnjffJPv++8n45BPsBQUc/+EP6fv2t0nPzyfDZCLD7R5xsYzdbic9PT3u748VvlCkG4psR4ssYu3S0NraisViwel0cs4550SVh4on0pVt8pqamsKSrXr9WKRv8TygxkOkGyvCWUCqvRX6+/tDVpDJZJyobgmJinRHRb0gBLq//Y38LVvQffAB3pISOm+5BXNNDSWVleSdarkUKsUzXDPSUDAajePaXUzGF4J0Y+nQEC9kQhyuS0NLSwudnZ1MmTKFjIwMqqurox4j1kjX4/HQ19dHf38/U6dOZebMmRGPO1aJmby+JEkMDAwokc5wY4x30o32jSXQW0GGuoKsu7sbs9mMy+XC4XBQW1vrR8YjJbZEFRuMKFcsBNq//c2Xs/3wQ7xTpmC/915cGzbQ09lJZkaGnz471mak4ch4IigX4Awn3UgFDcMh1lylXI4ZKj2gLjIoLS1VKro6Ozuj3j5Er+11OBw0NDTQ29tLSkoKy5Yti+pY4mk22dnZSVtbG5mZmbhcLux2u59xixwhypH8mUS64RCqgszlcnHo0CEKCgqwWCx0dHQoagAl53nqfEUb2cE4814QAu2uXT6y/egjP7LlVAuo4bYrp3gCm5GGI2Pw9b87ePAgra2tSJKkSAWNRiNXX301hw8fRpIkfv/73zNr1iwuvfRSmpqamDp1Kn/605/Iy8tDCMGmTZv461//Snp6Ok8++SSLFy8GYPv27fzqV78C4Kc//SkbN24EYN++fXzve9/DZrOxZs0aHnjgASRJor+/n4KCgjeAqUATsE4IMSAfyxlHuuqChoGBATo6Opg7d25MN5EctcaiSQz16q9WB4xGkYFGo4moRrDb7TQ2NjIwMMC0adMoLS2lqakp6mOPNtIVQnDy5ElMJhPp6eksPaWplMdRu2ipNbMGgwGbzUZ3dze5ubmjEulNFAgh0Gq1IdUADodDUQPIr9mBkZ3sSRH4WyZSvRD1byME2nfe8elsZbK97z4f2Qbkm+NNW4QjY7lysbW1lV27dnHo0CFWrlwJQElJCd/61rd49tlncTqdWK1W7rzzTr72ta+xefNmtmzZwpYtW9i6dSuvvPIKtbW11NbWsnv3bq677jp2795Nf38/d9xxBx9//DGSJLFkyRLWrl1LXl4e1113Hf/zP//DihUrWLNmDa+++iqrV69my5YtAG8JIbZIkrQZ2AzcLO/zGUO6oQoa5Ogz1qhF/l4spKvT6RTSdTgcNDY20t/fP2yRQSxRVbhIN5BsZe9cefY4WgyXvpD1ww0NDeTl5ZGbm8u0adMwGAw4nU7lWMK5aDmdTj799FPcbrff7HZaWpryuh2OXMYSidDpRlIDyGmZcK/ZcppCVlKoX7GdTmdCzpXH4xmezE+Rbcpdd6HdvRtvaSn2++/HtX59ENnKiPW+Gg7yZObq1asZHBxk4cKF/OQnP6Gvr4+lS5fywgsvAJ9LB3fu3MmuXbsA2LhxI6tWrWLr1q3s3LmTDRs2IEkSK1aswGg00tnZya5duzj//POVB+X555/Pq6++yqpVqxgcHFQIfsOGDTz//POsXr2anTt3Amw/tYvbgV2cSaQry748Hk9QhwZZ/hUrZNKNBVqtFqvVSkdHB0ajkalTpzJr1qyIN0SsEXWgusBut9PQ0IDJZPIjW/X6o2F4I4Sgu7ubhoYGcnJyWLx4MampqRw4cMBPvTBc2sBgMJCSksLkyZOVWeZAcunq6sJutyuRjZyeGInR93hAPNK6cJGd/BZhMpkYHBzk6NGjyuSd+uElNz2NF2G/KwTat9/2ke2ePVGRrYxEWkaqzW5kRdD3v/9I+tQaAAAgAElEQVR9Dh48yJIlS3jggQfo6uqipKQE8EXC3d3dALS3t1NeXq5sq6ysjPb29ojLy8rKgpYDdHV1IYToBBBCdEqS9HkdOxOYdKPp0BAPeULsKgGr1UpfXx9dXV3MnDmTOXPmRD0REyvper3eILINN16spBuYXpDLkOvr68nJyWHRokV+7dlHQ70QjlzUHguBygA1sSTKfnC0yX20thmopLBarVRXV2MwGMJ68Y7UcUx1EP5kW1aG/b/+C9cVVwxLtjLClQGPBkwmk0KobrebTz75hIceeojly5ezadMm+bU/JEJdx+Gu70jLo8GEI91YOjTE250hWrJWG4dnZWWRn58f1MwwEmLdP7fbTU9PDwMDA1RVVQ1L7vHqeoUQ9Pb2Ul9fT2ZmZlBlnIxEToqFa4ET6BMwNDSEzWbj0KFDfpFeLJNRoZCI9EIiVQaRlBShTG4MBkMQGYclQyHQvvWWj2z37vWR7X//N67LL4+abGUkMtJVqxfKysooKytj+fLlAFxyySVs2bKFSZMm0dnZSUlJCZ2dnYqZUllZGa2trcq22tramDJlCmVlZUo6Ql6+atUqysrKaGtrC1ofYNKkSUiSVHIqyi0ButX7OeFI1+Px4HK5ourQEO9FPhzpDg0NUV9fj9PpZPr06eTn59PW1pYwT12bzUZDQwNGozFmNUKska7NZmPPnj2kp6dz1llnRRSbx6N2GClRBzpo2Ww2amtrmTFjhpKiCOXJK0eHobr0BiIRD5KxrhyTodfryc3N9ZNSyaW8karHXC4X5qEhsj/8kNQtW9B+/PGIyFY9dqLKqtWkO3nyZMrLyzl+/DizZs3irbfeYu7cucydO5ft27ezefNmtm/fzre+9S0A1q5dy29+8xtqamrYvXs3OTk5lJSUcOGFF3LLLbcwMOATH7z++uvcdddd5Ofnk5WVxUcffcTy5ct56qmnuP7665Vt3XvvvRuBLcBGYKd6Pycc6cr97hOJcKRrMpmor6/H6/UG9R6Lp/3OcKQrO2gNDQ0xffp0Kisrqauri6nqLVo1Qn9/P8ePH8flcrF06VIyMjKG/V6sul75O6NNauE0n4H5T7mSTKvVRrSBHM/phUDEo15Ql/IGKinsdjvmoSFcL75I5n/8BxlHjmAvLqbpppuwrltHRl4eGR4PaePQ/jJQp/vQQw9x+eWX43Q6qaqq4oknnsDr9bJu3Tq2bdtGRUUFf/7znwFYs2YNf/3rX6muriY9PZ0nnngCgPz8fH72s5+xbNkyAH7+858r5+zRRx9VJGOrV69m9erVAGzevJl77733fEmSrgJagO+o93PCkW48iEdzqybDgYEBGhoakCSJqqqqkAJsnU6nRFfRIhzpymRrNpupqqpi3rx5ShQaa+Q6HPr7+6mrqyMlJYWZM2fS1tYWFeHK2x/PmttwlWRyLzJZ0tbY2Oj3yi3/JqP5KjyeSDccJCDz3XfJv+suqvbtw1tRgf3BB3HU1JDh8cCpc3by5Em/yU51WieaN4lEYXBw0M/Y6Oyzz+bjjz8OWu+tt94KWiZJEg8//HDI7V555ZVceeWVQcuXLl3K4cOHg5YXFBQghPhauP0840k3Hs2tTqdTJiQaGhrQ6/XMmDEjYolhvN0j1CRqtVqpr6/HYrEwffp0hWwDj2U0MDAwQF1dHXq9nrlz55KZmRkXqU/EMuBQNpBq96yTJ09itVrZv38/Xq83iFjikbQlsrvuiElOCLSvv+7L2X7yCZ7ycmr/8z+ZfPPNYDCgATIg6GEsT3ZaLBaMRiPt7e0hi2Nk5UmyP5oPE450Y73A9Hq90jcqGgghMJvNSuPEOXPmBEVKoTASI3OZbK1Wq9LJdzTUCKFgNBqpq6tDq9Uye/Zsv4mqeHLAE5F0Q0H9yu1yucjKyqKiogIhhEIsodoGqZUUkcyKxmU3igCy9VZUYH/oIYYuvpjupiYmD9PkMtxkp7o4pre31693m9PppL29XTlvo6nZdblcCTH/GW1MONKNFdEqEWQtamNjozJZc9ZZZ0U9Tjyk6/F4lIqx6dOnU1BQMKyuN17SNZlMSj545syZIaP2WCfG1CQdLZmOO+IZBpIkhW0bJKco+vr6aG5uVspP1RN36j5u4+bYhUD72ms+st2/H29lJfaHHsL13e+CwYDHYhlRWiVccYzZbObYsWNKRaPZbA7y4ZXLoGMdfzw+yMNhwpFuvNVl4SBfAE1NTeTk5LBw4ULcbjeNjY2jOo4aFouF+vp6jEYjhYWFUet644kSPR4Pn3zyCUKIYRtZxmN4I0v4Ojo6lBxqenp6xOMZ740koyHIcBItWRVgNpv9VAGyy1hXV9fpazMvBNpXXyVly5bPyfY3v/GRrWoiMVGpEI1GQ2pqql9RQaApuvyGGeg2Fu05GzcPtgiYcKQLsZGPTqcL6Vfg9Xrp7OykubmZ/Px8P+G/7IQfC6KJdM1mM/X19TgcDiWyTVQZ59DQEHV1dTgcDhYsWBBVriue9EV3dze1tbUUFRUpxRRWqzXs6/dopxfG200WrlNFe3s7RqNRMUkPLOmVI+OEVN0Fku3Uqdgefhh3TY0f2cpIlJY2VGGEOq0T5MN7yvoxnAxQPm+pqanY7fYJkVqACUq6sSCwFFhuvtjS0hLWODyeSrZAxYMagWSbn5+vRD3yzTdakDXELpeL6upqbDZb1C2poyVEudNFa2sr+fn5LF++XPG+kAlDXVGmfv12u93Y7Xbsdruf1+x4wminAuSS9KysLCorK5XlaknbwMAAbW1tOByOkCW9ceU+YyRbGeOh/XokGaBcNi7n2F988UWef/55nE4n9913H/Pnz+eaa64hJycHrVaLTqfj448/pr+/f0wcxi699FLefPPNWkI4jMEXgHRlAvV4PLS1tdHW1sakSZNYtmxZ2ImPeEg31Ku52Wymrq4Ol8tFVVWV35McRleNIBO7umBD3q9oSSSaooGTJ0/S2NhIQUEBFRUVymRI4NtEuEmW48ePk5qaisvlUozcAcX0JpYihkRhLHS6n32m4eBBHVlZBr761UzUhYxyFZnsRdHQ0HDqekxFr89i8uQ0srIyQ1YJnhoM7Suv+Mj2wAEf2T7yCO5LL41ItjLGlV1kANTdOuQc+4IFC1izZg2/+tWvKC4u5u2338bpdPLOO+/4EfaWLVvGxGHsa1/7Gm+88caMUA5jMEFJN5ZXVDmibG1tpaSkhOXLlw/7tI230kqGOtpUE2AgRoN05fyw3W5XUhZqyCmDkdxEag+G3NxcpYdbU1NTzOkI2QtAvZ9y9CIXMbS3t+NwOJQiBvWk1ERtn65+C3j3XS133GHA6wWvV+L553U8+KBdaRMWWEUmBNx6q4HHHjPgdoNWK1ixwsimTYdJS7Ny+PBh3/lJTyf//ffJuu8+tIcO+cj20Udxr1sXFdnKGMv0wmjB5XJRUVHB+vXrAXjmmWeC1hkrhzFV2XCQwxhMUNKNBi6Xi5aWFtra2khLS4uKbEcKj8fDgQMHhiVbGfGSruzMJcvMIikfRiIzE0LQ19dHXV1dSA+G0ZKMqaOXSZMmKcvVEZ+6BXhqaqqfOXoiJtJGO9JTb/Phh/VkZgp8SkRBQ4PE++9r+frXPdjt8MADet57T0dxseCmm5wcPy7x6KMG5EvF45F4//08enpW8sADHzBt6lTEzp3kPPAA6ceOYZ0yhZabb8b8rW+RnpNDptmsaGWjwXhIL8QKo9Hol0aTJIkLLrgASZL413/9V37wgx+MmcOYPEYohzGYoKQb6dXP6XTS3NxMd3c35eXlLFiwgM7OzoQSrjxpZbfbmT9/vt8kSiTE2ggSfDfv4cOHlQKKcJpe9RjxkO7AwAC1tbWkpqaG9WBItOY2nG+A3W7HbDZjNpsZHBzEaDTy8ccfB0m1oiWZsYCadC0WifR0ofoM7Hbfb/iLX6Tw6qtasrIE3d0arrkmlVmzPIT6CXt7ofsvzRRtvh7twYN4p03D9uijeC69lElAVggjeb1e73eOQhndeL3ehNwvHo8nYb9JYGHE+++/z5QpU+ju7ub8889n9uzZYb87lg5jMEFJNxTk5ou9vb1UVlYqxuFmszkue0cYPrc3ODhIfX09Ho+H6dOnY7PZYqqI0el0UROibHojF1DMnz8/IaY3Ho+Hjz/+GK1Wq1SqRbPtaC+6kRK1eoKlqKgIu93OiRMnmDdvnl9pr7pbhTpFEY37WKJzuv/4j25eeEFHQYHAbgeDAc46y0esb7yhpaBAoNFAaqqgr0/CaJQIdcoko4mZv/sNUtUQtsce86URTpGlDsJK2mR5VqCRvPzQimXyNRa43e7weegRwmg0+t17suNXcXExF198MXv27BkzhzF5jFAOYzBBSVd9Q6i7JkydOjWo0+1IPXVDPfEHBwepq6vD6/VSXV2t/NgjNSUPBbV3blVVFTabjby8vFE3vVFLzM4666yobrrxYngDoXWzag2o7MsrT9wFGqQHTtwl0trx3/7NhU7ny+2WlMD11zuoqBAI4SNgt9v3X5sNWls1OBw+LlVfxnoczNXXkv0f38By4yaFbIeDwWAI2TJIbSTf399PX18fra2tynkKlP3Fg0SmFwYHB5Umr/KDJCsrC4vFwuuvv87Pf/5z1q5dOyYOY/IYhHAYgwlKuuDT0jY2NjI4OBiya4KMeEk3VMse2WVMCMH06dODotpY2/xEyunKzSUDvXM7Ojpi9siNROwWi4W6ujqcTmfCJGanC+E0oGqpltFo9JNqZWZm4nA4yMjIGHXDGzkYSEmB6693cf31/ooPSYLrr3dyzz2+V/CODgmtVjClRFBi6KGuQUehp5P8FCvnXyhYf3cpvcbVURNuOAQaybvdbgoLC8nOzvaTtLW2toY0ko92gjPRBuby/djV1cXFF1+sjHnZZZfxjW98g2XLlo2Jw9i6dev4yU9+UksIhzGYoKTb29vLsWPHqKqqGrbpZLyTVervySW0QMSqrljHChWFqvurhXqYxDpGuNJheSLOYrFQXV0dpHqIBoGkG81r+Xgg6nDuY7JBemtrKyaTSTG8Ub96x9vDLdqURU2Nm/Jywd69Gh5/XM8kfT+6Q81IVgsF+jJuWN9Dzf0LQadjcHAQzWDipF3RGslH29V4rFr1VFVVcfDgwaB1CgoKxsRh7NQYM8Lt64Qk3cLCQpYvXz4q2tNw0Ol0DAwMcOzYMSRJGraEFmInRPW+OZ1OGhsb6evrY2qE/mojbcGjTldMnz6doqKioHFi0fWeKYY38LlB+uDgIGlpaRQXF4fs4RZoeBPYZj4UYukc8eWVLs7rfZFaUxb7TNWkpXpxVs0CXRGV3y0BnUfZ5unQ0wYayUNwBVlfX19QBZnNZvPr+DKaMJlMCclDJwITknQlSRr1H00No9FIX18fZrOZOXPmRP1jxpPKEEJw4sQJenp6QuakAxGr6Y1M0mpSj9TqR9YoRztJdyaRroxoe7iF8uSVzVsCJ+6ikqF5vehefBHDli1ojxzhrqkruap8B63eWXi9Eld+38WKFR7V6olrvx6PMfpwRvLyNeh0OhX7x8BGmvHCZDJFrRo63ZiwpBsroiGSgYEB6uvr0Wq1FBYWUlhYGNPTM5ZI1+Vy0dTUhMVi8VNbDIdYZWZy3f+JEyeYOnUqM2fOjHge5Mg4mn2R1zWbzdTW1uJ2u8nMzCQrK2tctFKPF/Ea3gRO3KmjPXVfv6AJKa8X3Qsv+Mj26FE8M2Zg+93vyL7kEv4otJw8aScjQxDIKeO5ckyGOpXT2trKwoULkSRpWCP5WB3HkqQ7ziAbjId7kqrJVrY9bGpqSojpjdvtpqmpia6uLqWMVi20Hg7RphfcbjctLS10dHRQXFwcE6lHG0k7nU66u7uVyT69Xh/yNVz9Ci43vhwtjCdSjzRx99lnn2EwGPwnpDQayvbsoWzbNlJqa31k+/jjuP/lX+AU0eiAsrLQ52sikK4a6ofZcEbyFouF1tZWrFarkldXq00CH+gOhyNhcrTRgiRJ84CyLwTpyqY3gaQrd0/Q6XTMmjXLb8IgXtObcN9xu900NzfT2dlJRUWFQoJtbW0x3TzDEbvH46G1tZX29nZKS0uZOnUqKSkpUW8/mpSB0+mkvr6e3t5eMjIyWLRoEV6vF5fLFfI1XI78urq66O/vx+v10tvb60fGox0Vy4cQzyZHO+cod+stKCjwkYzXi27nTvR33YXu2DEcVVXU/eIXtK5ciVeSSDt61O/cpKamhtyf8ZReiAbRTLKGcxyTy8QDjeSNRiMfffQRGo2Grq4upRu3x+Nh6dKllJaW8tJLL9HY2EhNTQ39/f0sXryY//3f/8VgMOBwONiwYQP79u2joKCAZ555hqlTpwJw1113sW3bNrRaLQ8++CAXXnghAK+++iqbNm3C4/Fw9dVXy/IwvzHq6uqeAdYDLiGEkCTpfHxKhqsnJOmO1FO3v7+f+vp69Hp9UPcEGVqtFqfTGdM4oQhRHXGWl5ezcuVKvygiVm+EcJGo2j1N7THR0tIyoom3wGNpbGxU8s+TJk2iq6trWPWIOqLp6OjA4/FQWFjoR8Y2m80vzyf/xarr9HrhpZe0vP22DkmC1avdnH++Jy7yHU0IIdAAur/8BcPWrWg/+wzPrFnYtm3D/e1vM0mrZRKRCSbQh2JctwAaRajz6oFG8i0tLRw7dgyTycSGDRvo7u7mqquuwuVyMWfOHAYHBwG4+eab+fGPf0xNTQ3XXnst27Zt47rrrmPbtm3k5eVRV1fHjh07uPnmm3nmmWc4evQoO3bs4MiRI3R0dPD1r3+dEydOAPDDH/6QN954g7KyMpYtW8batWuZO3eu3xiSJA0AVwH/A3iAHwG3ANYJSboQu6eu2+3263kWjmwDvxML1EQtXxBynXYg2aq/E4toPJDYhRB0dHTQ1NREcXEx55xzjl9EH2sOOBSpq4+loqKCFStWKFFGPKmCwKoyGeo8X1dXl1Ltp/ZaGC4qfu89La+8olOKDZ5/Xk9BgWDJkugfPKM+u+7xkPf66xT93/+L/vhxH9n+/ve4L75YSSPICEcw6nPT3d2N2WzGarWi1+sVXXG0FXenA4kqiJk2bRo/+MEP+Mtf/sLrr78OQFNTE1dddRW33nor999/P0II3n77bZ5++mnAZ3Zz++23c91117Fz505uv/12AC655BL+z//5Pwgh2LlzJzU1NaSkpDBt2jSqq6vZs2cP4JONVlVVAVBTU8POnTuZM2eO3xj4zG5uB3576t8ewApMmrCkGy2EELjdbo4cOUJWVlbUPc/iTS84nU6amppoa2ujtLSUFStWRCTUeLS9LpcLIYRi+1dQUBDWqlJeP1qoH2aB0XPgg2O0K9LC5fnUXgvqqFi2gHQ6nUpRytGjGvLyhFIvkJkpOHZMc3pI1+NB9/zzGLZuZcaxY7hnzMD2xBO4L7ooiGyHQ6hz09zcjEajIS0tLWjiLpyB/OlCIjW6JpPJb0Lzxhtv5O6772ZoaAiAvr4+cnNzlftQbVCjNrWRz3FfXx/t7e2sWLFC2ab6O4EmOLt37w4aA2gDSoUQ8oX3MvBV4OwJS7rDRbpCCCWN4HK5mDJlivJ0igaRTMlDQc5TdnR0MG3atGHJVkY8pDs4OMhHH31ETk4OixcvVjpehFs/ngq2zs5OGhsbKSwsDIqeZYyFTne4qHhgYACHw8HBgwdPybjK6erKx2DQYDAYsNkM5OX5xjOb4cgRDV6vxMyZHuKoB1Hg8YBGEyZn7PGge+45Xxrh+HE8s2dz/I47yL36atIjvF3FCiEEKSkpitJGhtfrVaJi9cSdbHajJuREEWEgYqnUjBXqarSXXnqJ4uJilixZovgmRDKoidXUJtS9FOGaFqc+l4QQv5Uk6d+BhglLuuEg2xHW19eTlpbGvHnz6O/vj5kcom2p7vV6aWtro7W1ldzcXIqKimIi91hIVz4uSZJYvHhxVLO1sZCuEAKHw8Gnn35Kfn6+4psbDqdTcytHJampqZhMJhYuXIgQgrIyO//93xoaG724XGby8qxkZ7ezb18G//u/lZhMqeh0WjIzdfznfzqZMiV4/yNFuoODcOONKbz3no7UVMFPfuLkO985dZ2EIFvbk0/ivugieg8fJn8EOtRQCJfT1Wg0ISvJwpndBLaYT8RvmuhIV34DeP/993nhhRf461//it1uZ3BwkB/96EcYjUaF+NUGNbLZTVlZGW63G5PJRH5+flgTHCDk8sLCQr8xgDKgA+DURNpSIcSDwIMTlnRDVVGpyXb+/PlkZGQAvhJB+bUrWgyXXpBb1jQ3NzNp0iTOOeccnE4ntbW1MY0TDenKKguDwcC0adMYGhqKWh4TLenKVo4Oh4Pq6mrFE3Q0tq1GIolakiSmTEnj9tuhoUGDJMH06RnodHk8/7yb7m4t2dlDgIOTJ7X89rdOvvc987AqATV+/vMU3ntPS26uwOXyWTFOq3SzovnPPrI9cQLPnDnYtm/H/a1v+cJhEuNcFutEWjizG3WL+Y6ODqxWK/v27fOLiuNuGXQKiSRdtcPYXXfdxV133QXArl27uPfee/nDH/7Ad77zHZ599llqamqCzG62b9/OypUrefbZZ/nHf/xHJEli7dq1XHbZZdxwww10dHRQW1vLOeecgxCC2tpaGhsbKS0tZceOHTz99NNIksRXv/pVZQyCzW7ukyTp24BpwpKuDCEEvb29NDQ0kJ6e7ke2MkZT/qUm28CJK4/HM6ra3sHBQWpra5EkSZn4GxgYwGQyRb394YhxaGhIeVDMmTOH9vb2qD1Px2sZcHo6zJ+vPmYd3d2pNDXpSU31RX+VlR5SUhxkZAiGhobo7OzEZrMzOJjKhx/m0N9voKrKzeWXaygo0HD0qIYjRzS8+aaOzEyBJIFBD+ZuK0e/ey9f7flFSLKVEUsZcLQYDfWCJPm3mHc6nRw9epT58+eHndQM9KGIZh8SnV4YrjBi69at1NTU8NOf/pRFixZx1VVXAXDVVVexfv16qquryc/PZ8eOHQDMmzePdevWMXfuXHQ6HQ8//LDy0PjNb37DhRdeiMfj4corr2TevHlBYwAFwDYASZLSgWIhRB9M4OIIuYWMTLYLFiwIabQNwc0po0GgXlUIQWdnJ01NTRQWFoacuIrHXCdUWa9c4eXxeJgxY4bf5Em8ZcCBsFqt1NbW4nQ6mTFjhhIpxEKK6nXHyk83Hng8cOyYFiF8HrVeLxw6pOWii7QUFxdTXFyM1QoPPmhg504tbW1eiorcHDrk5J13bBQVWXn55TJcLi0uF+j1EuU5gxh73Di8evqL8rA99RTutWvp6tFy4A0NOTmwbJlHmS9LRDeKREjG5G2Gm9R0OBzKpKbc1VhWXKgVJoH3RqLNbgJ9gwFWrVrFqlWrAJ8Jjqw+UCM1NVVxGwvErbfeyq233hq0fM2aNaxZsyZoecAYancxPdAgSdJq4MCEJd2Ojg56e3sjkq2MeO0dIbgZY6juwTKizQOroZZ0Wa1WpQOF/OSNtH602w9leCP7jwa2+YklZTARfBQArFZISxOce66Hw4d95Ftd7fGLhv/f/9PxyScajEYNublO+vpS6O9PxeHIxuHwmYgL3/9gt0vU2zORAL3eyxOZ1zI7dYjiAxq+//10XC6fXnjlSg+PP25Hqx0f6YVoEIkcJUkiNTWV1NRUv4m7cJ2f1V0qZK1xImAymaioqEjItkcDQgiTJEmPALcC701Y0i0rK1OqT4ZDvEY0LpeLDz/8kLy8vGEnlYC4LiqtVovdbufw4cOYzeaQRBg4RjyRrsvloqGhISrDm2i3r34bcDgcDA0NkZWVFTGiOR1EnZ4O2dm+3/Sf/smN3Q79/Rry8z/fj9paDbm5vrSB06nBapXIyvJFyW43aCSBHiceoUEAAh36FAkkDS0tcPXVOaSkeHC7naSnC3Q6De+9p+W557z8y79E35E5Fow16YZDOAvIQAN5uWw80EA+mlx6JBiNRs4666y4vz8WEEK8LEnS34HzJyzpxvIj6fX6qLWqQgi6u7tpaGjA4/FwzjnnJKym2+Fw0NXVhdlsZu7cucybNy8qo5VYDW+GhobYs2cPlZWVw7qYxeIcJkkSHo+H2tpauru7yczMVDpqyDeWbH4j60RPB+lqtbBhg4snntDT1ub796WXuvwMZCorvdTV6Zg2zcuBA1q8Xh/h6oQLAwKXMIAkITQ6hFcuWfX1O/N6wenUYTbrEQKGhiAlxYvB4OXw4R4qKpqx2WzU1tYq50Mt1+rqknC7YcoUEVPlXCLTC6MB9cSdEILU1FSKior8Oj93dHRgt9tH1PlZ7aU7niBJ0gJgFvA3fNVpJ4CeCUu6sSCa6E3dZjwnJ4dFixZx8ODBEdnNhYPaZjE/P5+cnBy/6qNIiDan6/V6aW1tpaWlBSBsRVwgoi14kLc/ODiolB273W7lXMs3VqBOVO4LZzabx7R6qrxcsHmzE5NJIiNDEJiR+s533NTVaWhu1lCQ78TYrWGO5TAZzj52S1/CLelxYUCrhdQ0n3LB4UBpGOlLIfj+JAkcDg1CaPjGN6ZwzjmT2LNnD8XFxZjNZkWu5XQKfv3rs9m9OxdJgvnzPezcaSM7OzrmTUSeONHt18N1fna73UpUfPLkScxmc1A1YkZGBunp6UGBSWBTynEEuQotG/g6cB6Q84Ug3UjRo6x+qK+vD2ozLhdIjNasq9phTI465X5U0WK4nK484dfY2MikSZNYsmQJR44cifpGGi7SDdx+ZmYmFRUVfkQd7sZyOp10dHTQ399Pc3MzVqtVmT2Xb6ysrKyEzXIbDFBUFPrYsrPhFz+3cvJ/XoGPH+YZ2wV8lPk1pLkLWJKXxrRpbtrbNUyb5iUtDXbu1GE0SrhcEjqdrwWPy+VLRcinb/Jkr+J/K0lSkPH3Pffo2Ls3BafTR5yHDgl+8IMhbrqpLijqC/X7eTyehJBuopzLIv2uOp1u2M7P3WsOhlgAACAASURBVN3dWK1W5fpKS0vj008/ZXBwkLy8POx2O//wD/+Aw+HA7XZzySWXcMcdd4y52c3ixYv505/+ZBBCHAWOSpK0ELhGCNEIE1i9MNL8mFrXm56eHrLNuDwxNlwuN3C/Al/RAr0L1DaL8XSbCEWK6kg9Ly9PUVe43e5RMbyRH051dXXk5uaybNkydDodPT09UW/bYDCQk5ODy+VixgxfN5NwZuByhCO/jo807xcRbje6P/2JjLvvJr+hAcuMGVz/y3LWLlyIw6Vh2jQ76spxl8unCHv1VR1ut6+PmV7vI9vKSi85Ob4Uw+LFkX/XPXt02O2fXycul5ampsksWJCmEI0cFQshFHtD+ZwkSoaWiEg3ngg6XDWifM10d3fz17/+lSNHjrBmzRpKSkqoqanhhhtuwOVyce6557J69Wruv//+MTW7ufbaawGukiTpd0IIN/A1fNHu7TCBSTceyGR1ynotqIgiECPR9xoMBuUVvLW1ldLS0pCv+CNp8SOjr6+Puro6MjIy/CJ1iG/iLTD/bTKZOHHiBCkpKSxcuFB5OAkhgrosxIpwZuByhCNraO12u9IQUR0BjghuN7pnniHlnnvQNDTgOessbE8/zaeVlUytqmJmBkDwudPr4bbbnNxwgxOrFf7+dx0nT0q88YaOtjYJq9UXOd966+cudaEelLNmedm1S+BwyB6zghkzvCHb4ag7MMgpG7PZzMGDBxUSjsX0OxwSnV4YDaivmUcffZSvfOUr7Nu3j97eXvr7+wFfkwCXy4UkSWNudrNx40Z++9vfXsTnZjdWYJUkSd8BPpuwpBuPvWNPTw9NTU2kpKREJFv1d+JxGnO73XR3d9Pc3MzkyZMj+jDE2zgTfGRYW1uLTqcLezzxeB3I61ssFkUvHMqVLR6SjWZ/wkU4ckNEdQTo8XhwuVy0tLSE1YgGQSbbu+9G09joI9s//hH3mjW+hOyRI1EdS1aW708uA77uOhf792uw2yXmz/cEdXoIxM03O3nrLR3Nzb7quZwcwT33OEKuG6qZ5t69e5k/f75yTlpbW0O2mI/F8Mbr9SYkvZOo9uvytaTRaJg0aRKFhYWcffbZ1NXV8cMf/lDp2j2WZjenmhKUAhp8T+0OIBfYDDgnLOlC9IQyMDDA0NAQra2tzJ07NyqXMYjd9EZ2vt+3b59SGjzcRFysxQ7gu4APHDiA2+0OKp4IRKzEqNFocDqdHDlyhKGhIWbMmBF1p+BEdwMOFQHa7XaOHDmCwWDw04impKT4kU56ejqSx+NPtgsXYt2xA8/q1X7ONfHKu3Q6WLYs+t8yKwv+/ncrH3+sxe2GJUs8QRN8wyFUaW+oqFhteKN+UwjM33o8npjSadEikcUR8Pl1rtVqOXDgAEajkYsvvpjPPvss7LqJNrsRQrglSZoE9AIbhBBNkiRpJjTpDgej0UhdXR1arZbc3FxmzpwZNeFC9JGuLDOrr6/H6/UyZ84cP/F4JMQS6cpt0+12O/PmzQtZPDESuN1uTp48SX9/P3Pnzh22vX0goll3tHOQcvXU5MmTFd22/PAbGhrCbDbT29lJ9gsvMO0PfyCtsxP7nDmYt21De9FF6EI8FBOhqQ23Pb3eV0QxmgjXYl6tmw0XFTudzog+0/EiUYbr4dIWubm5rFq1io8++mjMzW7a2toAOiRJOg+4FEgFtJIkPSmEeOeMJF2TyURdXR2SJCk9z44ePRqTrywMX2GmVj5kZWWxePFimpqaYrphoyFdp9NJQ0MDAwMDTJ8+Xbk4Rgter1eZ6MvLy6O0tDTqwhMZsRxzonW6StsXjYbJr77qi2ybmnAvXEjvr39N74oVmC0WzIcO4fF4SEtL88uLToQqu3gQTVTc29tLb2+vX0+ycFFxrEjERKi6BLinpwe9Xk9ubi42m40333yTm2++2c+IZizMbrZv3w4+s5ufAB8CrwPnALdKkjSxrR0DQ/vBwUHq6uoQQlBdXe332h2P/4JOp8Nms4X8rL+/n9raWtLS0vyUD/FMjEVqjyNLzKZNm8asWbOQJEmJqEd6E6jlX3Lu2Wg0xqRIiBXxphdi6nnmcqHbscM3QdbUhGfRIqxbt+L5xjdIkSRK/bbra48zNDSEyWSivb0do9HI0aNHyc7OVtQC47Ujw0gRGBW73W6mTJlCamqqEhW3tLQoLn3p6el+D6hozZESBbVGt7Ozk40bN+LxePB6vaxbt45vfvObzJ07d0zNbhYtWgQ+s5vvCiHuOLWrH55yGRuc0KQrY2hoiLq6OjweD9XV1SGF0qPlNGY0GqmtrUWv1zNv3rygV7hYxwn19JebS7a1tQVJzCD2vmqBUMu/1PIyeduJjPTUpNvdLbF/vwaPB84+2xvS29bhgEcf1bNrl46UFMFVV7m44AL/h5qyvy4X+j/+EcO99waRbTi2VrfHkTXFhw4doqqqSnkdb2lpUV7FMzIy/EgnmuKZiRQ5y7nXcFGxLO+T8+dOpzNk/nysHlBqL92zzjqL/fv3B61zGsxuABySJC2WJOkBoBE4CVQDiyY06ZrNZk6cOIHL5aK6ujqivVu8pCtHrXIUDTBr1qyQrkYwMjWC2jaypKQkrOoh1r5qasgPjZSUlCB5GcTXgicedHdLPPKIHrfbx4cffKDlX//VRXm5P0Ft367jjTd0lJb6qsAeeshASYmDBQs+30fJ7Ub/1FMY7rkHTXOzj2zvvhvPhRfG1Q5YCKFMOoUinaGhoZCa4nA93BJBuoki8kgP81Dm6HL+XI6KQ7UMSk9PT9j+qkl3HOJ8fCqGAnzlwDuAH05o0rVYLFRUVESV39Tr9Uq0Ei3k9MKBAwcUQf9w5YZarTbm3LHsZNbQ0BCxPY6MeMzD5bcBr9cbsSlnPNt2Op3U1dXR19cXJOAPLGqQI929e30Rbmmp72bs6ZF4/30tNTX+D8a9e7UUFQm0Wl/XhhMnNPz7v6dQU+Pie5dZSf3T/7J061ZST57Es3gx1nvvxXPBBfH1XlchnBlQKNKJ1MNNUU5MALMbiF1loOTPA9qmB0bFdrudPXv2YDAYRjUqHsclwAghPgi1fEKTbklJSdTRa6yRrmyzODAwwNlnnx21bEqn02G326NaV66Ks1qt9Pf3R+VkBrFF03a7XZFVzZw5c9gHVCzpBY/Hg8PhYO/evUybNo2qqirFbzWwqEEmYdl7we329/nWaHwGM4EoKBDU12vweAT792txOiEt1cvL/9OD/s7H2TTwS4Zmz8b70EOjQrYQWxQZqYebTMSdnZ1YLBb27NkT1GI+XnnWeCHdcFA/oHJzc3E6ncyfP3/YqDjWXPF4Jt1wmNCkGwuiJV273U59fT2Dg4NMnToVl8sVNeFC9J666tf89PR0Zs+eHfVNFE006nK5aGxspLe3F4PBwKJFi6K6waNJLwghaG9vp7m5GfCZ6UiShNPpDFvUIMu3enp6MBqNaLUH6Oqahs2mIyXFgMNh4Jxzgln3mmtc3HKLhsZGDTYbTE4ZoOrA23gtNt7JWcX3d8zjsaa5/OXeOXTfJDFpkqCmxsVll7kJ1a/TYoG0tKDGDkHHN9LIVO0l4HK5cDgcLFy4UJm0U+tn1dFfVlZWVN0YEkW6ibSLDBcVB/rxNjU1KeX3MhmHOy9Go5HS0tLAIcc1vlCkG+m1X5Zl9ff3U1VVxdy5cxFC0NTUFNM4w0Wh6vY48mv+nj17YrrYI42hln9VVFSwYsUK9u/fH3X0FinSVU/A5efnc84557B3795ho2O9Xq9MyhQVFVFXV8eXvzyXyko7u3a5sVotLFrUzcDAEJ9++rl8Kysri6oqAw//1xB/3nyY/8/el4c3Vabt31m77xtdoC3dW8rShYKjTpEBhFEUdQSX0ZFxcHABRPwsy/iJMgI6IAiogIioP4fRcf0ExXEURaWFslqg+743SbPvyfv7I76HkzRJkzRp2e7r6nVpSc55T3pyn+d9nvu5nw8uhCJfegqc6EjIxk2BRDgKJc8B1dV8WAavctDaSlBf74eqKh5eflnHTG7o7ubgr3/1R3U1F0IhsG6dDnPnOn44ejMdQP+2bCMgNtjTGEQiETONwbZox87h+4p0Ae9LuwaLnu358Q7QWtt8LsHBwYxTH1UQtLW14YEHHkB3dze4XC4WLVqEpUuXQiKRYP78+WhubkZKSgo++OADREREgBCCpUuX4uDBgwgMDMTbb7+NgoICAMC+ffuwbt06AMCaNWvw4IMPAgBOnDiBP/3pT9BoNJgzZw62bt0KDocz4BzffPNNBCGk3971Xtak687N4SjSpRFhX1+flSyLHt/dAoCj87CnQmRkZFgV/dwtjNmLdAkh6OzsRHNzMyP/oje6u9Mg7L1WLpejpqbGbgHOkzZjHo+H/Pwg5OcDQDCAqIHyraYmRP/f/yHln//Ekh4pmqL24nzczeDGRqO7mwuRCBCJKPFY/mYmEwcaDcHJkzw0NnKQkWFZ25Il/qip4SI01FKQW7XKD5mZZmRn2zf38SYGi5wdRX+0aMeeUUZz5gKBgPG+8JkRkJfgyXw0dlRsO6WC5oo//vhjHDlyBJ999hl2796NcePGYdOmTSgoKIBCoUBhYSFmzJiBt99+G9OnT0dZWRk2bNiADRs2YOPGjfjyyy9RV1eHuro6VFRUYPHixaioqIBEIsHatWtRWVkJDoeDwsJCzJ07FxEREVi8eDF27dqFKVOmYM6cOfjqq68we/ZsbNiwweoc33zzTRmAZ+xd22VNuu7AVqdrNBrR0tKC7u5uu7IsT2Ebhep0OjQ0NEAmkyE9PR3R0dEDviTujuBhn8OZ/IvCHUWCLUFT822dTmdXtUFJ1Bsz0hj5Fp+PpAMHINy0Cdy2NhgKCyHeuBF/zh2Hn4/2QyTqw0cfjYHZHADAfu6PyyUwmzkALDPRzpzhIizs14GSQkCvB86d4zokXW8SmSfHc2QERH2KxWIxFAoFjh8/zhgBsQ3ShyIn9Da82QLM/ly2bNmCRx55BCtWrEBsbCyam5uZSDUkJIQZtPrZZ5/h8OHDACxmNKWlpdi4cSM+++wzPPDAA+BwOIxGvaurC4cPH8aMGTOY+seMGTPw1VdfobS0FHK5HFOnTgUAPPDAA/j0008xe/bsAedYuXLl7bgSSdedG5mSCdtmcfTo0V4jWwpKiOycqrPxOOz3uAp6LVKpFLW1tfD397cr/2If390RPHS8j0QicfiwYK/F1S+V07+ZTgfBe+9ZyLa9HabiYqi3boVp+nQEcTjIApCVDWg0wPff+6Ovz2KraDJZHzMkxICEBAOSkvQABOByLQU5pdKSz6W8Eh09PPpZb1kwsjXFfn5+4HK5yMrKsjICYrf3elqc8ja86TBmC3br7q9GMwCA5uZmnDp1CiUlJejp6UF8fDwAS/G9t7cXgLXhDXDR2MbZ79nnYBvh2J4DgMOpBJc16boDmiM6evQoEhISXJ6kQN/rTiRHK9XJycmYMmXKoKTuLukajUY0NTVBKBQiJydn0F55d9ILhBCo1Wpm/ZmZmU6v3ZMUzIDX63QQvPsuhJs3W8h28mSot22D6aab7KoRAgKAGTNM6OgQQKu1kCkhHHC5QEaGAbNny3H77Z2oqZEyOtonn4zD2rXJUKk4IISL3/3OiBtusP+Z+yLS9eVYHUdWkLaNDGwjIBoVszXFvkpV+MphDLA/fl2pVOLOO+/Eli1bHOrpAfcNbxz93l1c8aTLbjgghKCkpMStETw0ShyMoM1mM9rb29Ha2gqz2WyVU3XlHK6QLlVWiEQixMXFITs726XjuzquiLYEE0JcXv9QrCMZst20CdyODgvZbt8O07Rpg0q/Fi82ICaG4IsvuJBI5JgzJxj33WeEJS3qD2Asc11arRbx8UokJNTh7FkgIECFcePUaGi4WLDzZRfVSAyldKQpZkv6bDXFgYGBzG7Qm5Gpr5zLAAvBsrtCDQYD7rzzTtx333244447AABxcXHo6upCfHw8urq6mNFYjoxtkpKSmFQB/X1paSmSkpKomY3V6+2dA0CvozVf1qQ72Bge9uj04uJiVFZWuv3EpYUxRzchm6xiY2MxZcoUHDt2zK2bdjDSZacq0tLSEBoaOqQx7LYQi8Woq6tDWFgY8zl5Mt7HlYcTh8OxkO3u3ZbItqMDppISqHfscIlsKYRC4N57jbjrLj3On6/GxIkTHZ7voowN+M1vLL9ny9hsRwfpdDrIZDKvjQ66VCYBczj2R6gbjUaoVCrGKevUqVNWw0Xpg8lVT15b+Cq9wPbSpf//5z//GTk5OVi+fDnzOmpsU1ZWNsDwZvv27ViwYAEqKioQFhaG+Ph4zJo1C6tWrUJ/v0V88PXXX2P9+vWIjIxESEgIysvLUVJSgnfeeQdPPPGE3XPAYnhjF5c16QIDIy322Jrw8HCrhgNKoO5GuvZG9tiex14By51z2CNRe/IvLpeLrq4ut7reHJGuQqFAbW3tr0qCfI8mMdAindlsZnLB7PNyOJyL5KDTwe/ttzH5pZfg39cH45Qp0L72GkylpV5panAHbBkbBa2MSyQSq4nQtpON3Y3afDFWx5tETg28hUIhZDIZxo8fz6SZ6NTejo4O6HQ6CASCAZMqBiN/X6YXgIvB108//YR3330X+fn5zEP4xRdfRFlZGe6++27s2bMHY8aMYfwW5syZg4MHDyI9PR2BgYHYu3cvACAyMhJ/+9vfUFxcDAB49tlnmfvk9ddfZyRjs2fPxuzZswFgwDkAbHC03suedCnYM8/sja0BPCNdexIw6jAWGBjotIDlKmxJly3/oh4M7EjBkxE87NdrtVrU19dDrVYjMzPT444e+rDr7u5GZGQk8zlQAiaEWLarKhX83nsP/lu2gNfVBem4cTC++SaIl8jWWxV3WhkXCoXIyspijm3PEFwoFA4gH0ck6Iucri9Mwdk7FRr12xsuStMTtKPMdriorRGQrwzMbR9m119/vcN74b///e+A33E4HOzYscPu6xcuXIiFCxcO+H1RURGqqqoG/D4qKsr2HBJH677sSZcKk+vq6uDv7++zmWeARatKI0N7DmNsuBOJ0LyxK/Iv+npP0gu0ANfX14e0tDTExsZ6FC1RMiWEIDU1lfEUVqvVTMtvaGgoQgQChH74Ifw2bwa3qwv6khLUrFwJRXExMjIzLaNzYfkb0h9Ptsy+hCPyYedG+/r6oFarrfwWQkJCmCm+vkgv+OKYrpCjPfexwYaLqlQqGAwGr69ZoVD4xHDd17jsSffChQtQq9UuVfEFAoHbZjR8Ph8qlQptbW0ujccBXC++UXC5XMjlchw/fhwBAQGDRs/uRrocDgd9fX1obGy0SlMAFt47fNhisejnB8yY4fi4NIowmUzMF8hWS2owGKDo6wP/7bcRsWsXhH19kObno+mpp9CTm4sxycnISUpicsGUvOn10IfJUIh4OGCvoYHtt8Ce4ku31hKJBCEhIW7ttBzBV+26nhxzsOGi3d3daG1tZeb5uTJe3hVIpdLLzncBuAJIl24DXYG7ka5Wq0VfXx8MBgPy8vJc9mCgeWBXbibq16rX6zFp0iSXntyuRrp0jFBzczOCg4PtWkUePcpBeTkXSUmWTq2PP+Zg3DjrnKXRCNTXAzodwejRJgQEcPDJJ3ycOcNDbKwZ99xjQlwcAK0WAXv3ImTTJnC7umC67jp0bN6MC3FxiIqORkqAZbT4yZMnYTabmTbX0NBQhISEMFEhzRFfbkTM9lugoKoWqVRq5Ssw1BHzvhgg6c3x6+wCZktLC/Lz85lJ0/YeTLZ5c1fqI5ej2Q1wBZCuO1ttV0mX7cMQFhaG4OBgt01vBlsTzauqVCrExcW5NZvKlUi3v78ftbW1CAoKQkpKCgDY/ZJWV3MQE0OgUFgMwzUaoK/vIunqdAQ7dnBx5gxgNvMRHc1DXBzBt9/yEBAAVFfzUF1F8EruTkTs2ABudzdM11+Pvi1bcC4mBmHh4SgeO3ZAdGfrTdvQ0ACj0chMJqA/9H22EbHRaASHw2F2LvT3lxoZc7lc+Pv7IzQ0lPk7sKNAR25sg8nYfGlM422wc9qDjZeXSCSMpniwvPkl7qXrEJc96bqDwUxv2ONxUlJSkJWVhe7ubocjexzBGenayr/y8vKY9kNvHF+lUqG2thaEECbv3NXV5fAaQkOB8nJAIuGCwyEQizkICPBjCO6774D/+z8eVCrLl+bsWYL+fi6CggAuxwyuXA6NrBqNhvdQcH06xDt2ojouBlwuMC4jgxljZAtHOlLqvSCVStHW1gadTgc/Pz+riNjPz4/J5Tc0NCA6Opr5PGjqgxrM0HONJGxzmY7sIJ3J2GyNb3xBur4y0Rms0GlvkCbbHJ2dN6evra6uRlNTE3N/LVy4EF988QViY2OZQtdIGN3QczjDZU+67mzJHBmZU2lWe3v7gNZgd8ew0/fYRtS0/bizs3NAp5qnhTE2qMeDXC4f4JvrLDIuLjbjww/58Pe3fJZjx5ohFgshEimhUvlj924/1NTwwOMBZrOl80sqBULN/QiRdsBoBBqFaZBufAVPtqeifIM/QkMD8ec/czF+vHufm73ROVTQr1AooFAo0N3dDZVKBb1eDx6Ph6SkJERHR4PP5zPXSaNidu6ZHn8k0hOuSsacydhsjW/MZjN0Oh04HM6QfHnZ8PWYdHfgzAZSqVSisrISR44cQX19Pb7++muEhYXho48+wuLFi5nX2prQDIfRDT2HM1z2pOsObMmQ7QtLnblst+CeKB5sDWmcyb9sX+8K2CRqMpnQ3NyM7u5uhx4Pzkg3NBS47joz/P0BHg+IjDShpiYcFy7U49NPI6DThcNsjoTBwAEHHAiMWvDNHPSJuOD4h8MYHQW+Px8f1sfi/PkI5OQIYDRysHs3B0FBBF9+ycO5c1wkJZmxcqURaWnuybvYgv7IyEg0NzdDo9EgOzsbQqEQcrkczc3NUKlUTBREo+Lg4GBGxz2SBbuhSMYcFanOnz8PPz8/hzI26j/rTlBiMpm8UuRjw9sGOjweD2FhYbj//vshk8mwYMECPPTQQ6ivrx+w9pEwuqHncIbLnnQ9sXckhKCnpweNjY1Mt5qjxL2rpuT2ztPb24uGhgZERkYOeg53XcaMRiPa29vR0tKCxMREp8Y9zkg3LAyIjSVQqwnCwswQibjIyAjB1Knj8c03fEyZYkJjgxk97QQcgx7+kIDHDYAgPADhaeHQ6bTIyzNDp0tBQgIXXK6lW4zPB/7+dwH4fIvZTEcHB089JcCePXq8/z4fP/7IRWwswbJlgxMx7S5sbm5GYmIiJk+ezFyrbVRII+KOjg4olUqYzWaGhOiPs4Idoy02mbxGxN6WSnE4HPB4PERHRzNkbOs/29vba9Xiy3YgcxTNerOQ5stjUsjlcqSnp4PL5SIzM3OA9/VIGN3QczjDZU+67oDP50OpVKKiogIhISEoKCiAv73xAjbvcZd09Xo9Ojs7ER4e7lLzhDsuYLQJRKFQQKVSDTpPDXBMupYIzIybbzbjyBEeRCIOxowhuOEGYjGPSdai/sMqzO46h48MN8PMD0BKdgjCxgSgocGA4GAt0tKMmDevCZ9/noTu7jCMGsUFny+AWi2ETMZBbq6FUKOiLMMo//d/BSgv5yEkhKC1lYO//EWI/ft1iHXgySSTyVBbW4uQkBAUFhY6rWrzeDy76gG6PacPQXbBjuaJBQIBM80jJiZmQERMP0dKnu6Qsa8NbwDH/rOOZGzsZgZ6/b5IL/gyZWHP7MYVjJTRDcVVQ7pSqRQ1NTVQq9UoKSlxWOCxhTukq1QqUVdXB7Vajbi4OGRmZrr0PlcjXUpAdMSPq3I5W9JlR3kAEB7Owdy5BJbpCwDUavBffRPzN+3EB6JpqB19E36fTyANCAEhUsTFdePll4MRGxuCgACAw4lAXp4JZWV8dHeboNfrER8vRn9/CEQigsBAPrhcPgwGAX76yaJ+4PGAwEBAJAJOnuTi5putHwpU3aHX65GTk+O0EWWwa6cRLjUnoV1mdGxOc3MzFAoFOBwO4uLiEBoaCrPZzBTsaARsm55wtWDnqwjSFSJ3JGOj18+WsRmNRuh0OmZ34K6MzR58bevoTDI2EkY3sY6iBxYue9Id7Kag43EIIcjKykJ1dbXLhAu4Rrps+VdmZiY0Gg10Op3L5xjMZFytVqOurg4Gg4ExEv/5Z7uDRu2Cki47t0m3vFafn1oN/ptvQrB5Mzh9feCVluK+VfdAOWkKOjtb0NdXjzFj0pCQEDfgc09J4eGNNwhqa/kQCHgYN06Ijz/mYMcOHhQKE0wmI0pKOvHDDzFQKAB/fx74fB4IEYAdqNOCY09PD9LS0hz6+A4FVBEQEBAArVYLo9GIvLw8hIaGQqFQQC6XM4oP6jVAI2J/f/8BnydbOUGPz84TD0ek6w4cqQXOnTuHoKAgj2Vs9jDcto5sjITRDT2HM1z2pOsI9sbjsCMVV+Fs/hc1+haLxYz8i2pH3Rn37ohUDAYDGhoa0N/fj4yMDKtto7vXYDKZrKr5Vl8clcpCtq+8Ak5fH0ylpTCsWgXTddehq6sLLWeOITExESUlk51+4cLDgcmTL36+8+cT5Oaa0NLCRWysAMXF8XjvPS5eeYUHrdYMvd6MUaP6weNV4cwZiym3VCpFfHy8Vd7WF6Dt1nFxcVbn8vf3t5Jx0TypQqGASCRiCnbsHPFgBTudTgehUOjVPLG35V30IREdHW3VRs+e3mtPxkbbnR0Rqy8jXblczuh077nnHhw+fBgikQhJSUlYu3btiBjd0HM4A2eQ6uLwWOsPEeyocrDxOD///DOuu+46t45v+x5b+VdCQoLVF0AsFqOvr89lv1vbc5jNZrS0tKCzsxMpKSlISEgYQMyuXgeVXJ04cYIZABgWFmb5sgAQ7NlzkWynTYNh1SqYr7sO/f39jN3jWDvNDZ6CEOD777k4doyLmBiCu+4ygRA5qqurmcGNarWasTpvCQAAIABJREFUmSxsT587FKjVatTU1IDP5yMjI2PQnL490DypXC5nCleAZVIDXWtISAgMBgPq6upgNBqRmZlpl5gGOLG5iJMnT2L8+PFejSJ/+eUXpKenD1qDYMvYKCE7cmMTiUSQyWRIS0vz2jopfvvb3+LYsWM+dTAbAhzeqJfkat0Fh2MZ/93c3MwMmHQ2HsdTuCL/AjzT9tLjU29eZ8d39Vg0b8vj8VBSUgKj0WiJ2rq7odmyBeHvvQehVAp5SQnk27ZBUFoKLpeL+jNnAADjxo1zKxXjCjgcoLTUjNJSM/R6Perr66HRaAZ4Z9CuLblcDplMZtUoQYktNDTU5byjyWRCU1MTJBLJgMGg7sJRnpQK+bu7u3Hu3DnodDqEhoYiOjoaWq2WKVjZpnnYKQpCCDOuHHCeJx6pjjRHMjZ7bmyA5fPq6enxSMbmDL5URvgSVwTpNjU1DfCcdQZ3JTxUYtbQ0ICoqKhBFQOeyMyMRiOTX3LVm9feddgWydh5W4Fej9h9+5C4ZQs4IhFMN90E5f/8D+S0K+7sWWi1WgQEBCAiIgL9/f0wGo0IDg726hecNqN0d3cjNTXVrtsZu2vLXqMEO+9K9amUiNntovRv19TUhKSkJBQXF/vEmYzL5TLm8u3t7YiPj0dycjKzXtreqtfr4e/vbxXBU3Nwdwp2I+Uy5gj23NgIIWhtbYVGo4FGo/FIxuYI3tb/DieuCNINCQlxOSp011O3v78fGo0GPT09mDRpkkveue7obqmRuMFgQEFBgctVetux7U6LZCoV+Lt2QUDJdvp0SxphyhTAbIayvR09PT1ITU1FfHy8ld61tbUVSqWSKb6wt8/uEjG1rmxoaEBcXByKi4vd+rKxGyXs5V3lcrmVzaK/vz/kcjmCg4MxadIkj1IJrkKn0zHFzvz8fGaHwOfzERQUhFGjRgG4GMGz9cRardbqwUHzpLY5YnpPGQwGGI1GJkd8qeeJaaGKgqZn6PXbytgoGTv7jlLS9bW1py9wRZAuW1c5GKi942Ckq1QqUVtbCwAIDg5GVlaWy62W7hjeUCNxOtXXVbBlYLYtr8wXR6m0kO3WrRay/d3vLGRbUmIhwF+NZmJjYzF58mSGAPl8/gBTEjYRt7e3M3lMWyJ2RKL08xQKhZg4caJXCVAoFCIqKoppFzUYDKitrYVcLkdMTAz0ej1Onz494MERHBw85O0pdRHr6OhAWloaYmJinBIBO4Jny4vsPTjYBTvaYScWi1FfX4+kpCQr1Qs7IvaUiH0VPdsbJuBIT23Pk5etnqB5faVSeVl66QJXCOm6g8EkYLbyr4iICJw+fdruyB5PzmE0GtHY2AiRSIT09HTmS2obuQ4GtiJhQCpBqQR/504IXn11ANkCF6NrOrrdFQK013hA++AVCgU6OzutOsBozs/Pzw8tLS1QKBTIzMz0qSsUbetua2tDSkoKcnNzrUjE2YODTWyu/g2kUilqa2sRGRlp9dDyBLYPDgAXc/AKBZqbmyGRSEAIQVRUFLhcLlQqFbPjcNbqDHhesBsqXFUvsB8wNCp25MZ2/PhxnDp1CgaDAVVVVcjOzh5SMe2rr77C0qVLYTKZ8PDDD6OsrMzjY7mCK4J0PWkFtgVb/sUmQ2fvcQR7MjOz2Yy2tja0t7fbzT27k5KgxZbW1lZERkYiNDTUctNRst26FRyxGKYZMyxkO3kygIvThLVaLTIzM4ccKdA+eDaR0oKSTCZDXV0d5HI5hEIhwsPDIZVKYTabvTbwkQ2qtqATN+wd31HHGlUidHV1QaFQ2PX6Ze+M9Ho96urqoNfrfVJspKARoVKphFqtZjyd6Xq7u7tRX1/PKAfY6+Xz+V4p2A0VQ9HpOnJjS01NhUAgQGNjI9avX4/q6mq89tprKPk1qHB3fY899hj+85//MDn/uXPnIjc316M1u4IrgnTdgS2B2sq/MjIyBtyAnhTGKNg+D7GxsSgpKXEoHbIlXb3e4ncrlwPx8QSpqQSEWIpkaWlp6Ozsx88/y6AVN6Lw2H5kfvI+BDIZtKWlMK1ZA86vBh0mkwktLS3o7e31WcMB+zr0ej06OjoQExODgoICcDgcK6csNlHQiNjTiQparZaRZeXl5bk9XJMWwNiVeNqxRbf67NZhStJjx461K+XzJuRyi5SOPkhoxGhPOUA/X9phRgt27NQPLdixndhoVKzT6UAIgdFo9Kolpi/agGNiYpCbm4vi4mK89tprQzrWsWPHkJ6ejrFjxwIAFixYgM8+++wa6Q4GT01vqMNYQkKC00KcpxIwaiQeHBxsNZXYHmwjXaMR+OorDrq7OfDzIzh9GsjPN0Ms5qC3V4CICD7OHPOHvPwCAqsuoE0XjkU33gDNEw+iLzXVErGVl4PL5UKj0SAuLg4FBQUeTyx2BdTLl8/nD0hb2GvFValUA4jNNsJ0tF6qZaada+xIaKiw17HV39+P6upqJhdLR9CwiY2mU4ZKxLQpRqlUIjc3d9DiKrV3DA4OHrA1p3liewU7qvSgk4+Tk5MZFQXgHSc2X3kveGtqhD2Tm4qKiiEf1xmuCNJ1B3w+HxKJBM3NzS7Jv+h73Il0VSoV1Go1mpqaBh1gSWFLuiIR0NXFQWKiJRoJDCTYu1eAvDyCcH8N9v6vCG0tHIwlEkSNyoDxut/j8IJo/H6OGdG4SPgBAQEYNWoUVCoVTp8+beW6xd6KDgU0NSOTyVyeLswmCgqq9ZTL5RCLxWhqaoLBYLDaOoeGhkImkzEKCF93rtFUgk6nw/jx460iaUfEZmu67qo2lS1vS05ORlZWlscE7qxgR5s6uru7IZVKweFwmIeWVqtl/iaO8sTuFOyMRqNPmhe8RbreNrNxBVcV6VJzEx6P55LDGIWrpMs2EqdVelcJwZZ0zWZLKsFkstzsajUHSqkJiScPovPLKki1vwc3IAaBRQXoFUTAyCXo7zczPg0ArKRLF49rZiLM7u5u1NXVeUzE7MJVcnIyMjMzh3TDsrWe7IhNo9FALpejt7cXVVVVIIQwpjRisZjxRPAmCCFob29He3s7xo4dO6iWmE1sOp3OitjUavUAD4egoCCr46nValRXV8Pf339QN7WhgBbsqD/I+PHjERYWZiURpC3stgVGTwp2l3qk68j8xpe4Ikh3sC86W/6VkpICtVrt1peUz+dDq9U6/Hej0YiWlhYrI/Hjx4+7NV2Vki69mcPDzYiI4KGnh4tAjgbizyqQ8H07+IbvIEudi5CwVEil4TCFmeFnArq7gYCAJlRVdTvtuGJXiRMTEwF4RsR07D31CvZVKyaHw4FQKGRaTidMmIDw8HC73WrspoOhbPVlMhlqamoQERHhkSrBz88PMTExA0bxUCK2lYRptVrGmJ3tD+wLKBQKVFdXIzw83CpPbE8iyFYN0AIjzcPTe8hZwY5KGdmTM7y1K5HL5Uj5debcUFBcXIy6ujo0NTUhMTER+/fvx/vvvz/0BTrBFUG6jmBP/iWVSiGTydw6jqNIl50XtjUSpyTqanGIy+Uy9noAIBRy8PsbZKha9wXU//oKJaoLaC+6HUcnvACFIAmms1xMSjVDLicQiw2YNKkTU6bwkZDgfseVO0Ts7+8PjUYDPp/vcurEU7DNy0ePHo309HTm2hx1q1Fis7fVH6xtmLYla7Vaj4pyziAQCAZIwnp7e5mcf2hoKLNDsdXmeiNSNJlMaGxshFQqRXZ29qDKFUfKFGoJKRKJmPQP9cigaxYIBFAqlaiurkZcXJxPJnZ4K9Ll8/nYvn07Zs2aBZPJhIULFyIvL2/Ix3V6Tp8efZhg+yVyJv8SCAQejd+xHfPT19eH+vp6h3lhd8akU4lSTU2Nxfycy0XSxx8jYu9e/FYqhWn2bBhW7UTqpAIkNXEgkRiRk8NBXZ0WgYH9uPFGAf761zgEB3tvG2dLxFRfLBaLERUVBbPZjAsXLsBkMjFGL97KEQOWiKympgbBwcEoKioa9OHF7lazt9W3bRu29W/o7OxEW1ubw1SCN6HT6VBbWwuTyYTCwkKr5gEaYdIcsa32mR1hugqxWIy6ujokJCSgqKjI42tjFxhtC3b0M25vb2ei4tjYWAQHBzPKD3YkPFQilsvlXhu/PmfOHMyZM8crx3IFVwTpUtjKv+zlGD2ZBMF+D9tI3FlbsCvnYXeSRUREYGpuLjg7dkC4fTt4Mhkk11+P+nvugS4/H6EhIQjt7UF8fCiiow0A6pCXF4Tk5LEYNUoIX9WSqMlPa2srRo8ejYyMDKvPlB0R9/T0MBGxp0Ss1+vR0NAAlUqFrKysIWuJ7W31aTGJkoRMJoNQKGQ6G9Vq9YBx394AO09MgwFbOIow2Z+xreSOLQljQ6/XM+Tu7S5ACnZeWygUQiQSISUlBXFxcUx6oqenh/FcYEfEdCfhaHQSPb49IvZ0asSlgCuGdOm8MFfkX56Qrk6nw5kzZ6yMxJ3BWaQ7wJRGLofgjTcg2LYNHKkUxt//HpqVK+E/aRLG4SJJSCQSxqchODgYMTF88PlS6PXekSrZgnZchYeHO4w27Y1SZ4/IcZWI2YSUmpqK7Oxsn0WbNNLt7e0Fh8NBSUkJkze29W9gR8TuGnizwdbcupsndjSunn7G7K0+tVc0Go0QiUTIyMhwaZrBUGA0GpmW9gkTJjCBiL+/v5UHNB0xr1Ao0NLSAqVSyahY2A8PZ97EFD09PV6LdIcbV4SfLiEENTU1SEpKcimH6o6nLpUMdXV1YeLEiS4bidfV1SE8PNwqmrFLtq+/DsH27QzZGlauBJk0yepY9pob2NGaXC5n8peU1Oi22RNoNBqGKDMyMryS22QTMc270tQEn89Hf38/oqOjMXbsWJ/6o7IVF6mpqYiLGzgFg4KSBF0vNTBnE3FQUNCgkqn6+noolUpkZ2f7PAdOH8wcDgcCgcCuq5k3xvBQ0DTbmDFjPGoWYRfs5HI5k06x1WvTh5RWq8XmzZvxzjvv4Pz584MGPyMIhx/EFUG6gIUcXbV7c4V0bVMVbW1tzAhmV9DY2IiAgADEx8cPJFuZzBLZUrK95RYYysoGkC3116WFuqSkJIdfcHYhif7Qij6biJ01aNBx7tQXgl308QU0Gg0uXLgAvV6P4OBgaDQaqxwx/dJ5i4Rpaogas3tyXOqHwDYwt2dMw+FwrDS38fHxPs0Tm81mxk86OzubSU/YFhjpA5qd16ZjeNxZn16vR01NDcxmM7Kzs132JXH1Wqhem0bGn3zyCY4dO4bu7m5MnToVf//73zFmzJhL2WXsGumy4Yx0bY3Ek5OTwePx3J440dLSAh6Ph4SEBGabxJHJLka2MhmMt95qIduJEwe8XyKRoL6+fkiTG2yLHHK5nJnIwCZigUBgNeLcGbl7A+xuMjrdg/1v9AtnGxGzVQjuEKbBYGC2v1lZWV6PNqmRjj1iS0xMREREhNdUCPZAh67GxsYiOTnZpb8du0lCLpczOdfB0ilsRcnYsWMZ9YgvodPpsHHjRhw9ehS33HIL+vv7cerUKWzdutXl4a8jgCufdA0Gg8v2jj///LNds3OxWMzkMNPS0qwKE+6SLi3QJCcnw1+rhfC118DfsWNQsmU3N2RkZHjdTMWWiCUSCZRKJfz8/DBq1ChEREQ4bb8dKmjL76hRozBmzBiXCMJTImYXAQdLJXgD7GgzIyMDPB6PWbO7VpiugD5MqMZ3qPeKo3QKXaufnx/a2trg5+eHzMxMr41wcoZTp05h6dKluOOOO/D0008Pyzm9hGuky8axY8cwceJEhlio1SGPx0NmZqbdm9edmWRmsxlarRYd584h9K23kPDhhxCoVJBNnw7NihXwnzJlAKmxW2mHOk7GFbBHnNsShFwuh8FgGEBqQ7nhqS+DQCBAenr6kCvpbO8Ge0TM5/Mt8rvwcJ/niQEwuVRnDxO2oxk7f+muHIwQwvglpKSkYNSoUT57mNB0SltbG8RiMYRCIfh8vlcfHvag0+mwYcMG/Pjjj9i5cyfGjRvn1eMPA6580qVO+q7g1KlTyMrKApfLRV1dHTQazaCeAT///DOmTp3q8Oa2ytv290P42msQvPYaOHI5jLfeCsWTT6I/Odkuqel0OkgkEqSmpvr0CwS47jjG9kGgP7bOYK5s841GI5qamtDf3++yL4OnIIRAJpMxqQT6YPOGm5kj0IkRRqMRWVlZLk0WYYMtB6MPD7bSg5IaXbNWq0V1dTUEAgEyMjJ8amAEWB6WFy5cQEhICNLT0xlVjqPil701u4sTJ05g2bJl+MMf/oAVK1ZcqoMnB8M10mXjzJkz4HK5UCgUA5onHKG8vNzueJkBZLtjBwSvv24h29tus6QRxo8fcDw6caClpYUpQtgagHszgmBHRwkJCRg9erRHkwUcRZe2UjDbbrLExESfPkzYqQR29OdozUMlYrbELS0tzauyLHvpFKPRCA6HA51Oh+TkZCQmJvp0q03z7r29vVaFOWevt1WnuOMaB1geKOvXr8fRo0exc+dOn3eG+RjXSBe4aCReX1+PxMREZGZmukw8lZWVyM/PZwjSqrtGLLZEtpRsb7/dQrb5+XaPxZ7ckJ6ebkW6KpUKMpmMuXEJIVZbfE9mk8nlctTW1iIwMBDp6elejY5sv2w0iqddSKmpqYiIiPDp1Fa5XI6amhqEhoYiLS3Npe35UIiYno+mLnw9kVYulzPRZlhYGBNlUl0uu/jljb8t1RRHR0cjJSXF46Iqe7dEVQi0kEvXy+VyERERgRMnTmD58uWYP38+li9ffrlGt2xc+aRrMpkcNj3YGombTCZERES4FZ2cPn2a0awynWRi8cXIVqEYlGw9mdzAbgulNy8tblCCcKQVpa5nNH3i65lS7G6ypKQkmEwmqy0ze83eqOazfWeH2r3mChEHBASgtbUVCoXC55pbwPK3b2hogEwmQ05OzoDzUVJjR5dsdQrb49fV81F/Bnvn8wbYhVyFQoHNmzfju+++g1KpxF133YWZM2fi1ltv9XnaZBhw9ZIu20icRpXNzc0QCASMuYsrqKqqwujRoxEcHAyzSATh9u0QvPGGhWznzbOQrYNkP9W/9vX1eWVyAyUz+qNSqRi5DyU0kUjETPj1tZeAbTeZPZWAbRFJoVAAwIB0iitRFVu/7MtCEpuIe3p6IJFIIBAIEB4e7rMcMYVIJGIGULqTmqFWmOydh+0UCXsObP39/aipqWFST8Ohf62oqMCKFStw77334u6778bZs2dx8uRJrFy58lqkeznAbDbDYDAw/69UKlFXVwdCCDIzM62e2u3t7TCZTEhOTnbp2IQQVFdXg4hEGPvZZwjdt89CtnfcAcMzzzgkW3eaG4YKah3Y1dWFvr4+cLlcBAYGIiwsDKGhoQgLC/NqJxIFfahFRUUhNTXVrejVNoqnsirbiJj9mVEjnJCQEI/1y+5ArVajpqYGQqEQGRkZEAgEDBFTYqO5S28QsU6nQ01NDQC4NYHaGWzN1mnjjJ+fH4KDg6FUKmEymZCXl+ezeW9saDQarFu3DidPnsSuXbuQlZXl83OOAK4e0tXpdEzbJbVztEV3dzdUKhXS0tKcHpMpkvX1gffqq/DbuRNclQp9paVovO8+ID/fqpLPJhza3BAeHs4M0vMlqGewn58fE9HbtgprNBqvtQrT2WQmk8mhzM4TsBsNKBFzuVwEBQVBo9HAaDQiJyfHp1OFAWvNraP7iILtg2BP6cG2PHR2DNqe7MgMx5ughcfGxkaEhIQwxEw71dydeuEqjh49iqeffhp//OMfsWTJEp/nw0cQVz7pGgwG1NbWore3l+mUcXSziEQiiMVih09YpkjW1wfBtm0QvPEGoFLBRCPbvDzmi2Zb9GL7zQ5H3o/mUelDZjAysu1QY7cK06jYWT7NWTeZL0DJqLm5mbk2tgcC/RmKGY0tXNHcurJuWyJmR8RsImbLslwpBA4VtIWXEDIgmrZtGaZWmGwFgicObGq1Gs8//zzOnj2LXbt2XcqdZN7ClU+6er2ekScN9iWh0wbsCa4JITD19FjIdudOC9neeaeFbJ1MCKVFHYlEgqioKEZUbksOtmNaPAWVnHV0dAyp28pRq7A9Pa5IJHK7m2woYHvqpqWlWUWKbA8Edl7btsDorp9AbW2tx5rbwWCPiNVqNQghGDVqFGJiYobchDLY+amMzx2Zm23LsCvjh9jnpNHtQw89hMcee2xYotuamhrMnz+f+f/GxkY8//zzWLZsmc/P/SuufNIlhECv17v0WpVKhbq6OkxkteESQmDu7QV/61YL2arVLpEtm/zsFXWMRqMVodEb1naL7w450CJLTEwMUlJSvH4T2zZGSKVSqFQqCAQCJCQkIDIyckA6xZug3XlyudylKQfs99kSGrvASCNi28+avbX3tubWEWjhKi4uDtHR0Va5bVt9qzeIWKvV4sKFC/Dz82Ny00MBe/wQ+7Oma+7o6EBGRgZefPFFnD9/Hrt27UJ6evqQzukpTCYTEhMTUVFR4XIdxwu48kkXsGyNXH3dL7/8gqKioota24YGBE6depFsy8pAcnIcHoNOj6AyNGqM4wrYuVaZTAatVmvlBhYWFmZ3i88ecZ6RkeETU2o22N1k9ItK1+wLGRg7EvOWMxclB0cPPR6Ph6ampmFrFzYYDMx04ezsbLvRtL1uQE+JmCpLOjo6kJmZ6dMZbPShJxKJsGzZMlRXVyMwMBCzZs3CrFmzcPvtt/vs3M7w9ddfY+3atfjpp5+G87QOb9zLXpfBBu1AGgx8Ph8Gg4EZmgcAnNRUGJ94Asa77nJKtoBFPF5XVwd/f39MmjTJ7QqzUChEdHQ0kw+l9nsymQxSqRStra3MFj8sLAyBgYEQi8VQKpXIyMjwuXmzs9lkwcHBzLRUtgyso6ODkYFRYggLCxvUb5aCztRydTyPq7A3m0yv16O/vx8tLS0MCSsUCjQ1NXm8+xgMVCve1NQ0aDrI0VRkSsRs03JnRExzxaGhoXa7Kb0NgUAAoVCInTt3gsfj4aeffkJcXBxOnz4NtVrt03M7w/79+3HPPfeM2PltcUVFuq7YO9Ii2Q8//ICEhARmNIorX3JPmhs8Bc3/UX9bgUAAHo/nszZhCtptRYs67pKfI/WBo7y20Whkxta7MpFjqGC3Q7ONtwdTegzF/Fuj0aC6utprW3v2tdi2C9MuNZPJxLiP+doXma7lyJEjKCsrw6JFi/DXv/7V5zl/V6DX65GQkIBz584Niw0lC1dHemEwpzH2TDIaWVL1AfUQoBV8NqF5u7nBFdAR51FRUUhJSQGfz7fbJkzHndB1uxpZ2oJOwvVF9xotetF10/wfj8eDUqnE6NGjXfaBHQoo+VHN7WBdT7am8O5O5zCbzWhtbUV3dzeysrKGZaaXTCbD+fPnERgYCH9//wHtwt7KEbOhUCjw7LPPorGxEbt37/bKaHRv4bPPPsOOHTvw9ddfD/epr27SHTC54ddBd2zYIzTAMutMrVYjPj5+WPrs1Wo1M24lMzNz0Ao6O7KUyWQDutPCwsKcai3NZjM6OjrQ3t4+LJNwAUsq4cKFC+Dz+QgJCYFKpWJcwYZSYHQEtnnLYJpbZ3BnOodMJkNNTQ3TNOLrB4qzFl5nEfFQiJgQgu+//x4rV67E4sWLsWjRoksiumVjwYIFmDVrFh566KHhPvXVSbqukK0j0EgzICCA6dpRq9Xg8/lWmlZvEQO7aJWenj6kgoe94pFQKGTWTNfNjqbd7SbzBHSMu0wms5tKsBdZujNuyB6o5jYuLs4n0bSt5E4mkzGddaNGjUJ0dLTXjGgcgV6jOy28rhCxM1cwhUKBNWvWoLW1Fbt27RpOVQCkUikefvhhVFVVgcPh4K233rI7SkutVmP06NFobGz0eTONHVwdpEudxoZCtiqVCvX19QDsT26guT8aEVNiYLfbuhMx2I4495UFIiU0WqyjGmI2MfhSH0qLSO5co21kKZPJGEMXdhrIHjFQza3BYHCoEvA26JDG0aNHIzIycoD/gauE5iqoEkKr1SInJ2fI12jrCkYd4+i6FQoFYmJiUF1djVWrVuHxxx/Hn//852GPbh988EHccMMNePjhh6HX66FWqy/FycBXB+lSS0FmJpkbZOvp5AZ2pENzxEajkSl4hYWFOSx49ff3M1ODh6NVmG1gnp6ejqCgIObhQWVJbL8Gb2hxlUolampqEBAQ4BVbSWrowo6IaRWfkplSqURnZyfS0tJc8koeKqhfAk0J2YvGna3bEz1ub28vGhoafD45gk3E7733Hvbv34+uri5cd911DPH5umWZDblcjgkTJqCxsfFSHkoJXC2k+/TTTzOSo8LCQoSEhAz6hxmsucETsFuEqaYVAOOH6ufnh46ODhBCvDbifLD1UE2xs24ytquWPS1uWFjYAAMaR6CpBKlUiqysLJ9u7+i6e3t70dbWxowft/Uh9kUTCb13PGmJ9mQ6h16vR3V1NQAgOzt7WCwQCSH49ttvsXr1aixduhQPPvggmpqacOLECcycOdOn2l9bnD59GosWLUJubi7OnDmDwsJCbN261effIQ9wdZBuTU0NysvLUVFRgZMnT0Kv12PcuHEoLCxEcXEx8vLymEjCbDajr68PTU1Nbjc3eAKTyQSZTIampibI5XIIBAL4+fn53AVMpVJZuWS5mxM1m80DJGAcDsehBMzTVMJQwM4V0w429hgcmmclhHhkJWkPVFccGmoxTvfmhA9H0zkIIZDL5UhPT8eoUaO8cr7BIJPJsGrVKvT29uKNN97A6NGjh+W8jlBZWYkpU6bgp59+QklJCZYuXYrQ0FC88MILI7ouO7g6SNcWWq0Wp0+fRnl5OY4fP45z584hMDAQycnJqKqqwhNPPIE777zT5/k+drMB9UflcrlMwYtGxOzCkSvmM87AjjS9PZvMngSMz+cjICAAcrkcQUFBXrMldAYawTc0NLhE8I4eIK4YwlOYTCY0NTVBIpEgOzvb57quFQbAAAAgAElEQVRiwFIQokWjwMBAqFQqn452Aiyf7X/+8x88++yzWL58OR544IFLQpnQ3d2NKVOmoLm5GQBw5MgRbNiwAQcOHBjZhQ3E1Um6ttBqtVi4cCGqq6tx3XXXoampCS0tLUhKSkJxcTEKCwtRVFSEiIgIr0VnMpkMtbW1LjUb2KuE07yfq3lWtocvW/zvS5hMJtTV1UEsFiMiIgJ6vZ5pLmCv25skTDW3AoEAmZmZHj+cqOSOPkBsJXdsvwZPVAJDASEEbW1t6OzsHNDC62igpTfasqVSKVauXAmJRII33njDLbP/4cANN9yAN998E1lZWXjuueegUqnw8ssvj/SybHGNdAHLTfzTTz/hN7/5DfOFob6pFRUVqKioQGVlJRQKBXJychgSnjBhgts+B+wR57Ym6u6u2TbPyp6bxm61pd1koaGhw2Lwze7uSkpKQlJSklWaga2YsK3g0wKju2tkW0v6ykvA1jhHqVTCYDCAx+MhOTkZ0dHRPkkFsUG1zO7MYRvqdA5CCA4dOoTnnnsOK1aswP333z+s0W1KSgoTsfP5fFRWVtp93enTpxnlwtixY7F3795haTxxE9dI1x0YDAb88ssvDBGfPXsWfD4fBQUFKCgoQFFRETIyMux+EVwdcT4U2Lba0tlYHA4HY8aMQWxsrNfNp21Bc8W0tdWVSNNR4cjVbTKdUkFz8L4mBHZaaMyYMfDz83PYJjxYd5qroEGASCTySvpisOkcAoEAYWFh0Gg0KCsrg1wux+uvv874awwnUlJSUFlZ6XOP5mHCNdIdCgghUCgUqKysREVFBY4dO4b6+nrExsYy0XBBQQEOHTqEhIQEZGdnezTi3F2wlReUFOhW2XZ778i5zF2wc5reyBU76gRkR/JCoZDZNQyX5latVqO6upqRutmLyB0ZwrNTKu585jKZDNXV1T5/qLAf2t9//z1efvllSKVSTJgwAQsWLMDMmTOHtdmB4hrpWnCNdB2ANjVUVFTg888/x+eff44xY8Zg7NixjGStoKDAI5d9V0C7yeiYbNvokO0vwRboUz0r3d67amXoLJXgbbDzrD09PVAoFPD390dUVBRDaL76XNktw1lZWW49VFw1hLclcDr1Vy6XIycnZ9jkTxKJBM888ww0Gg1efvlldHd3o7KyEuPHj8e0adOGZQ1spKamMvWURx55BIsWLRr2NXgR10jXV1CpVLj//vuxdu1a5OXl4cKFC6ioqMDx48dx8uRJmEwmjB8/HkVFRSgqKkJOTs6QPFu1Wi1qa2uZgZvuRH22ciS5XM4UXyiZ2dPhepJKGCrYAyjT0tKY3QZbMUG9GujabSfcugsaaVJzeG9Emo5SKvThBwCdnZ0+f5DZrunAgQN44YUXsGrVKixYsOCSaDTo7OxEQkICent7MWPGDGzbtg033njjSC/LU1wj3ZEA7UI6ceIEjh07hoqKClRXVyMsLIzRDhcVFTESMmegueK+vj6kp6d7za6PyqgomSmVSqZ6HxwczBCFu1Gfp7CnuXUER14N7m7vjUYj6uvroVKpkJ2dPSzNKlKpFPX19dBqtUzk601DeEcQi8V4+umnYTQasWPHjuG2O3QZzz33HIKDg7FixYqRXoqnuEa6lwoIIRCJREyR7tixY0w3HI2GCwoKEBYWBg6HA7PZjJ6eHrS0tCA+Pn5YcsUGgwGtra1ob29nSIsWjdhRpbdBW1s9baqwbclmtzY7SqnQc3prUoUrsNfC60h54IkhvD0QQvD555/jxRdfxOrVqzF//vxLIrqloNpj6jo3Y8YMPPvss7j55ptHemme4hrpXsowm82or69nSPjEiRNQq9VISkpCW1sb5s2bh8WLF/vUNJ1CrVajpqYGAoHAqoPNlszYky3stau6A41Gg5qaGvD5/CFpbu3BUUqFNhn4+fkhNzfX56OPAGuPhqysrEGv011DeEcQiUR46qmnwOFwsH379mGZAceGyWRidnRffPGF3dc0NjZi3rx5ACw7j3vvvRerV68ezmV6G9dI93JDWVkZvvzyS8ycORPd3d2oqqpixgPRiHjs2LFei3qpKkEsFrvkOUtzlexCnbs+DWyTb1/P72Kvu62tDW1tbYiKimIkVbQzjW0G761IkN2wkp6ePiSDGPYUZJlMxnQDstdO5YKEEHz66afYsGED/va3v+EPf/jDiES3mzdvRmVlJeRyuUPSvQJxjXQvNxw/fhyFhYUMadE84PHjx5lCXWNjIxITE1FQUMB01HmiC6aqhISEBCQlJXlM5Ow2W+p3QCMzW9XBcGtuAUtxrrq62m7DgclksuoEZHsn0x9PtM8ajQYXLlxAQEAAMjIyfDL40tY/uby8HO+99x4AICAgANu2bcPEiRNHhHDb29vx4IMPYvXq1di8ebPXSddkMg3LSHcPcI10r0SYzWa0tbWhvLwcx44dw/HjxxlXL1qomzBhgkOycJRK8CboCHp2m63RaASXy0VycjJiY2N97tHAnqrg7kh39trZDRGD5bbZLbzDNaqHnvfjjz/Gli1bcPPNN0MoFKKyshI333wzHnvssWFZAxt33XUXVq5cCYVCgX/84x8+iXS1Wi0+/vhjzJgxY1htJgfBNdK9WmA0GnHu3DnG5Of06dPgcDiYOHEi08iRmJiIjz/+GLm5uUMaX+MObM3ahUKhlTE5u9g1lPywLcRiMerq6pCYmOgVSZatN4Y9Ha5Op3O7hdcb6OnpwVNPPYWAgABs3bp1xJsMvvjiCxw8eBCvvfYaDh8+7BPSPXjwIJYvX4758+fjqaeeGhYDIhdxjXSvVhBCoFQqceLECaaR4/z58wwJFxYWYvLkyT41wqY2iFRza0uobC0rjSqpixZ7QoQ7KQg6OcJkMiErK8tnhTIqC6ROcX19fdDr9YiIiGAmcvjCy5cNs9mMjz76CP/4xz/w/PPP4/bbb78klAkrV67Eu+++Cz6fzzys7rjjDib14S7MZrPVPSAWi/HHP/4Ra9euRXFxMQghEIvFI/6w+RVXF+l+9dVXWLp0KUwmEx5++GGUlZWN9JIuCXz55Zf4f//v/+Gll14Ch8PBsWPHmIi4u7sb6enpTFpi0qRJCA4OHtKXl72td3e8OpVQsduD2ZX7sLAwu11p7KJVWlrasFXq2S28o0ePZqZEsL18vSX/YqO7uxvLly9HSEgItmzZMizj1j2BNyPdCxcuIDU1Ff7+/nj00UdRXV2NyZMno7m5GZ2dnVi/fj1+85vfeGHVQ8LVQ7omkwmZmZn4z3/+w1g2/vOf/0Rubu5IL+2ShslkQm1tLZMfPnXqFPR6PfLz8xkizs3NdWucDG0Z9paROc0Ps4td7K40gUCAxsZGBAUFIT093SdFK1uYTCbU19czznSOGiuoSsK2CYWtOnCntdlsNuODDz7AK6+8gnXr1mHu3LnDFt1qtVrceOON0Ol0MBqNuOuuu7B27Vqn7/GUdNnRrV6vx+LFi3H8+HHk5uZi3bp1CA4OxhtvvIGbbroJ4eHhOHToEAQCAZYtW+bx9XkJVw/pHj16FM899xwOHToEAFi/fj0Ay1bnGtyDVqvFqVOnrEzgg4ODmdxwUVHRgNE/bM2tr4pzbFB/idbWVsjlcgiFQqu0hC8HbtJ8sacPFmcPEfogsdfa3N3djaVLlyIyMhKvvPLKsI7LAS5qn4ODg2EwGHD99ddj69atmDJlilfPwybcc+fOQa1W49ChQ1izZg0WLVqE2NhY/PWvf0VSUhIA4JtvvsHTTz+Nl156CTNmzPDqWjyAw5vB96HAMKOjo8NqpEhSUhIqKipGcEWXL/z9/TF16lRmvDXNmR0/fhzl5eXYv38/WltbMWbMGEyaNAkdHR0ICgpCWVnZsG1zNRoNM3KpoKAAHA6HybGKRCI0NjZa2UfSrrShbO0NBgNqa2uh1+sxceJEj/PFfD4fkZGRVqSp1+uZaLizs5NpbW5vb4dGo4FUKsVbb72FF198Eb///e9HJHfL4XAYf2iDwQCDweCTdXC5XOh0Ojz11FM4cOAAoqKi8Nvf/hYA8OSTT2L9+vU4fPgwSktL8emnn2L37t3YvHkzpk+f7vW1eBNXHOnai9yd3RALFy7EF198gdjYWFRVVQGwuC/Nnz8fzc3NSElJwQcffICIiAgQQrB06VIcPHgQgYGBePvtt1FQUAAA2LdvH9atWwcAWLNmDR588EEfXN3IgsPhIDo6GrNnz8bs2bMBXCzilJWVYfTo0TAajbjllluQm5vLRMTjx4/3eiHLYDCgvr4eGo0G+fn5CAwMZP4tMDAQgYGBiI+PZ9ZIW2zb29uZ/LAnzRA9PT1obGxEamoq4uLivE42QqEQMTExjPSJtjY3NzfjzTffREtLC8LDw/HOO+8gLi4OxcXFXj2/qzCZTCgsLER9fT0ee+wxlJSUeOW4dIo3AJw5cwZvvvkm/P390dTUhE8++QRr1qzBsmXLkJOTg5tvvhlffPEFEhIScNttt+Hxxx/3yhp8jSuOdGnrLEV7e7tTQ+Y//elPePzxx/HAAw8wv9uwYQOmT5+OsrIybNiwARs2bMDGjRvx5Zdfoq6uDnV1daioqMDixYtRUVEBiUSCtWvXorKyEhwOB4WFhZg7d+6l6GbvdXC5XAgEAnz99ddIS0sDYInWqAn83r178csvv0AgEGDSpElMfjg9Pd2jaJNtMZmSkoLs7OxBiY9dgKNbUfact8bGRqhUKqdbe51Oh+rqavB4PBQWFg6L0xpgud6PPvoI27dvx/r16zFnzhwQQlBbWzssBkSOwOPxcPr0aUilUsybNw9VVVUYN26cx8ejqQQOh8M0PAgEAtTW1iItLQ16vR7z5s3D0aNH8dRTT+GDDz7Avffei9bWVqSlpY34wEx3cMXldI1GIzIzM/Hf//4XiYmJKC4uxvvvv4+8vDyH72lubsYtt9zCRLpZWVk4fPgw4uPj0dXVhdLSUtTU1OCRRx5BaWkp7rnnHqvX0Z+dO3cCwIDXXe2gU2zZJvANDQ2Ii4uzyg/HxsY6JVCtVsvMRfOFxSR7ay+TyaDT6RjrTIVCgYyMjGGbwgtYrA6XLFmC+Ph4bNq0aURJ1hnWrl2LoKAgrziC/etf/8JHH32E0tJS3HbbbTh//jzef/99PProoyguLkZ/fz+mTZuGhQsXYsmSJV5Yvc9w9eR0+Xw+tm/fjlmzZsFkMmHhwoVOCdceenp6mK1pfHw8ent7AdjPF3d0dDj8/TVYwOFwEBYWhunTpzP5NkIIOjo6UFFRgfLycuzYsYPxfaAm8JMmTUJgYCBMJhMuXLgAlUrlU48G2629SqXC+fPnwePxEBMTg7a2NjQ3N/t0Ci9gifree+89vP7669i4cSNmzZp1SehuKfr6+iAQCBAeHg6NRoNvvvkGzzzzzJCP+/LLL+PTTz/FkiVLcPLkSdx66604efIkvvnmGxw6dAjx8fFISkrCtm3bPJ45eCngiiNdAJgzZw7mzJnj9eM6yhe7m0e+BsvnQ42777zzTgCWPOH58+dRUVGBf//731i9ejVUKhW0Wi1mzpyJhx56aFg6jgghaG1tRVdXF7Kzs60iTPZ4oc7OTsaCkd1NNxSznPb2dixZsgSjR4/GDz/8gLCwMK9ckzfR1dWFBx98ECaTCWazGXfffTduueUWt45hzzNBKpXiueeew4wZMzB//nz88ssveOGFF7B8+XIsWrQIqampmD9/Pm644QZvXs6wY+QH2V+CiIuLQ1dXFwDLDUYF9o7yxba/r66uxltvvYWcnBzk5eVh69atACwFuhkzZiAjIwMzZsxAf38/AMuXfMmSJUhPT8f48eNx8uRJ5lj79u1DRkYGMjIysG/fPp9f+0iCx+MhPz8fDz/8MHbt2oV7770XkZGR+Nvf/ob09HT84x//wPXXX4/Zs2djzZo1+OSTT9De3m73oecplEolKisrYTAYUFxcPGBLTwtwSUlJyM3NRUlJCYqKijBq1CgYDAY0NjaivLwclZWVqKurQ09PDzQazaBrNJvNePvtt/GHP/wBy5cvx65du4aVcNva2jBt2rQB96w9jB8/HqdOncLZs2dRVVWFZ5991u3z8Xg8SCQS7Ny5E+fOnQMAtLS0oLy8nHnN6tWr8csvvyAuLg733nsvpk6dOizaa1/jisvpegLbnO7TTz+NqKgoppAmkUjw0ksv4cCBA9i+fTsOHjyIiooKLFmyBMeOHYNEIkFhYSFDluPHj8c777yDadOmQaFQoLCwEJ9++inefvttREZGMsft7+/Hxo0bcfDgQWzbto057tKlS5kCXVFRkVWB7sSJE1dFgQ6wpHPi4+OtCm6EEPT19VmZwHd2diI1NdXKBD40NNStaNNsNjPWljk5OUP2Ltbr9VZtzbZTLWgzB2AhvCeeeAJjx47FSy+9NCL+AV1dXejq6kJBQYHVPevNpiK27vbAgQNYvXo1JkyYAJVKhdGjR6OsrAzZ2dn49ttvMWnSJLzyyitoaWnBli1bvLaGYYTjm48Q4uzniseCBQvIqFGjCJ/PJ4mJieTNN98kIpGI3HTTTSQ9PZ3cdNNNRCwWE0IIMZvN5NFHHyVjx44l48aNI8ePH2eOs2fPHpKWlkbS0tLIW2+9ZXWOuXPnkq+//ppkZmaSzs5OQgghnZ2dJDMzkxBCyKJFi8j777/PvJ6+7v333yeLFi1ifm/7umuwwGQykZqaGrJv3z7y2GOPkSlTppCJEyeS++67j7zyyivkyJEjpL+/n6hUKrs/HR0d5NtvvyXnzp0jCoXC4euG8qNUKolIJCINDQ3k1KlT5PDhw2Ty5MnkuuuuIwkJCWTr1q1EpVKN9EfJgN6z3oDRaGT+WyKREKlUSjZu3Ej27NlDCCFEq9WSMWPGkMOHD5N33nmH3HbbbWTWrFnkxhtvJJWVlV5ZwwjAIa9ei3R9jObmZtx4442oqqrCmDFjIJVKmX+LiIhAf38/brnlFpSVleH6668HAEyfPh0bN27E4cOHodVqsWbNGgDACy+8gICAgMt5btSwQafT4fTp04z3MDWBLygoYCLiiIgIfPbZZxg/fjxycnKstL6+RmtrKx5//HEkJiaipKQEZ8+exblz53D48OER94dl37NDiboVCoWVx8SPP/6I559/Hs888wxeffVV3Hfffbj77rsBAP/+97+xd+9eHDhwAP39/Thz5gxKS0u9cTkjhatHvXApQalU4s4778SWLVuc3rz2Hny2BTqtVoudO3fCbDZj7969TL97U1MTFixYAIlEgoKCArz77rsQCoXQ6XR44IEHcOLECURFReFf//oXUlJSAFhao/fs2QMej4dXX30Vs2bN8vq1jzT8/PxQUlLCiPbJrybwdEDozp07UVNTg6KiInR2dkIkEqGwsBBRUVE+LYKazWbs2bMHe/fuxaZNm3DTTTddUkVXV+/ZwXD+/Hns3LkTv/vd73Drrbdi1apV6OzsxLJlyzB9+nS0tLTg2WefZUg3ODgY+fn5ACzByGVOuE5xrZDmIxgMBtx555247777cMcddwAYWoHOz88PM2fOxKZNm3D69Gl89dVXKC8vxzPPPIMnn3wSdXV1iIiIwJ49ewAAe/bsQUREBOrr6/Hkk08ykp7z589j//79OHfuHL766is8+uijMJlMw/a5jBQ4HA4iIiIwa9YslJSUYNSoUTh79ix2796N/Px8HDlyBPfddx+mTp2KP/3pT9i2bRvKy8uh0Wi8tobm5mbMnTsXdXV1+PHHHzF9+vRLinDt3bOegkr7Tp48CaVSiaysLJw6dQpcLhdmsxkLFy5EdnY27r//fqxduxYrV668rBochgRnuYdhz4JcITCbzeSPf/wjWbp0qdXvV6xYQdavX08IIWT9+vXk6aefJoQQ8sUXX5Cbb76ZmM1mcvToUVJcXEwIIUQsFpOUlBQikUiIRCIhKSkpRCwWE5VKRSZNmkTKy8tJVFQUMRgMhBBCfv75ZzJz5kxCCCEzZ84kP//8MyGEEIPBQKKioojZbCYvvvgiefHFF5k1sV93tcBsNhOz2Wz33/R6PTl16hR5/fXXycKFC0lBQQEpKioif/nLX8gbb7xBKisriVwudyufK5fLySuvvEImTJhAvvvuO4fnHkk4umc9hVKpJMuWLSNz584l+/btI4QQsnDhQvLCCy8QmUxGCCFELpeTQ4cOkdWrV5OKigqvnPcSgkNevUa6PsCRI0cIAJKfn08mTJhAJkyYQA4cODDkAt2bb75JJkyYQIKCgsj//M//kL6+PpKWlsa8trW1leTl5RFCCMnLyyNtbW3Mv40dO5b09fWRxx57jLz77rvM7xcuXEg+/PBDX38kly3MZjORy+Xku+++I+vXryd33HEHGTduHJk2bRpZsWIF2b9/P2loaCBKpdIu4VZVVZFp06aRJUuWEKVSOaxrf+ihh0hMTAxzTziDo3vWExw7doxkZ2eTLVu2kHnz5pF58+aREydOkNbWVjJt2jRy6NAhJlC4gnGNdK8k9Pf3k9LSUvLDDz8MIN1x48YRQgjJzc0dQLoikYg8+uijA0j33//+9/At/gqA2WwmHR0d5JNPPiHPPPMMuemmm8i4cePI7bffTl544QXy5Zdfks7OTrJp0yYyceJE8v33349IdPv999+TEydOuES6noKtTKB47bXXyCOPPEIIsezW1q1bR8rKyojRaCS7d+8mv/3tbxkVzxUMh7x6Lad7GSI8PBylpaUoLy+HVCqF0WgEYG3uw84HG41GyGQyREZGOswfm0wmTJo0ieksampqQklJCTIyMjB//nzo9XoAFlXA/PnzkZ6ejpKSEjQ3NzPHWr9+PdLT05GVlcX4GV+J4HA4SEhIwO23344NGzbgv//9L06fPo2///3vSExMxKeffoqpU6eivLwcP/30E2688f+3d64xVV1ZHP9vsTMktsHK0KolgXsxDJeXpr4gYy1I8IVQKZeINVHBFkYKltHRaui0RUkFRA0NUIOpNDRTWqRaaJVHS/EBqGAVRBB6B1Cgo2ABheIF9PKfD1zOgCJq5VH0/L5wzj77sQ4h62zW2mut+aNiu50/f/6w5tolKZ20yMzMxIkTJwAACoVCitibNGkSZs2ahUOHDuHTTz/Fm2++iXfeeUcKs38akZXuMEIS+fn5KCgoQGdn52PNdf36dem4WW+8u0qlgrOzM1JTUwH0RK+99tprAAAPDw8pgi01NVXyknt4eODLL79EZ2cnampqoNFoMGfOHMTExEClUknryQ66R8PAwADW1tbw9fXFvn37UFNTg5SUlBE9hjbSCCHQ0tICNzc37N+/HwkJCfjggw/Q2toKpVKJ9PR0AICDgwNMTU3R1tYGrVYLT0/PUZZ8lBlsGzwKW/Inhu7ubu7fv5/Lli2js7MzraysuG7dOnZ0dLCpqYm1tbWPNF9JSQlnzJhBOzs72tjYMCwsjCRZVVXF2bNn08LCgmq1mh0dHSRJrVZLtVpNCwsLzp49m1VVVdJc4eHhVCqVtLS05NGjR1lXV8cFCxYwJyeHbm5u7O7ulh10Twg1NTVDZl64cOEC4+PjmZeXJ7UlJSVx7969JHsCKry8vNjY2Mj09HS6urrS29ubNjY2TEhIGBIZxhCyTXekuXr1KpcvX86TJ0+SJNvb23nmzBlqtVqeP3+ee/bsoVarJdmjvEbTo+3l5cWzZ88yNzeXbm5usoPuCWKolO6uXbtoa2vLTZs20dHRkSkpKSTJL774gkuXLuXcuXO5ceNGqX9rayuvXbvG1NRUlpaWPvb6Y5D76lU5OGKYMDExQUtLC3Jzc2FpaSmVkxk/fjwmTpyI4OBgKXnHQEk8qA+MGG5bYG/VjJkzZ+LYsWP91u5Lrxz3ezbYGJmxjbe3NyorK1FaWgoAiI6OlnIZGxsb48aNGwgODsaqVasAAJGRkVCpVPDw8JAyyMn8H9mmO0wYGBjA398fubm52LRpE/Ly8iTlqlarkZGRgVOnTsHX1xfvv/8+8vPzJZst9SVLRkJp5efnIz09Hebm5vDx8cGPP/6IkJCQIXHQBQUFwc7ODjNmzMCsWbMAyJnWRpKVK1fC0dERlZWVMDU1lezyj0p0dLQUJHLu3Dns2LED6enp2LJlC1555RU4Ojriu+++Q2JiIry9vZGZmdnPPyBzF4Ntg0d4O/5EUlNTw23btlGhULC8vJwtLS10cXFheXk5Ozs7mZGRwYiICJqbm/PFF1+kVqulVqtlUlISi4qKBjySQ5JZWVn85ptveOvWrSGTtde8QJJqtZrJyckkyYCAAMbFxZEkY2NjpeNAycnJ9Pb2JklevHiR9vb27OjoYHV1NRUKBc3MzHj9+vV+a2zevLlfgMiWLVtIkkeOHOkXIDJnzhySPUeOFAoFm5qa2NzcTIVCwebm5iF757FIRkYGLS0taWFhIf0uh5udO3fSzMyMTk5O/Pzzz9nQ0EArKyvGx8eTJL/66iu+9957jIyMHBF5xgCyTXck0Wq1/OWXX6T7rq4uBgcHMzExkefOnaO7uzsbGhqk50VFRVyxYgWzs7N548YNvv3229y5cyeXL19ODw8PdnV13bNGa2srKyoq+j3T6XT3VdIPQ1+lOxQOuoGUrpxp7fG4c+cOlUolq6qq2NnZSXt7e5aVlQ37ut3d3bS0tGRaWprUlpubS2tra3Z2dkqyyUjINt2RpKurC1FRUQAALy8vXL58GfX19Vi5ciXKyspgZmYmlSgPDw/H6dOnERQUBFdXV+zevRspKSk4fPgwvL29kZqais8++wxvvfWWZHZoa2vDwYMH4eDgAAMDA9y8eRNGRkaPVVYcAJycnKREI0qlEoWFhff0MTQ0xMGDBwccHxoaitDQUOleCIGFCxdCCIGAgAD4+/vLpZAek8LCQkybNg1KpRIA4OPjg7S0tCHNezsQQghkZWXByckJHh4eAICzZ8/C2dlZOqs72tnRxgqy0h0GnnvuOfj4+CAzM3j/JCAAAAYVSURBVBPR0dHo6urCu+++C0dHR+zZswdOTk4gCX9/f5iamiIpKQmTJk1CR0cHysrKsGTJEiQnJ+P8+fNobGxEYGAggB4b6jPPPIO6ujrk5eXhpZdegk6nw9q1a+Hu7o7i4mJ4enpi9erVA9qDg4OD8dNPP8HPzw/u7u4wNjYe1kz8+fn5mDp1KhobG+Hq6gorK6v79qXsoHsoBvoInTlzZkTWNjc3R0BAAF5//XWYmJjg8uXLiImJkZXtIyI70oYBIQQcHBzw4YcfIi0tDRkZGdIO8tVXX8W8efMQHx+PxMREaDQaZGVl4dKlSzA0NERJSQnWr1+P2NhY5Ofno7S0FAEBAQAg7WRra2vx7LPPwtbWFuXl5VJ5c09PT3z77beoqKgA0JNGEOgJpoiLi8OxY8dQUFAAhUKBtLQ01NfX3yN7r/NsKOh1vr3wwgvw9PREYWHhY5dCqq+vh5GREdRqNaysrKBSqXDq1KmnxkE32h+hrVu3ori4GObm5sjKyhr0QyozMLLSHWGCgoIwffp0bNiwAaWlpZg/fz5ycnKwfft2AD2RYJ988gm+/vpr1NXVoaGhQSoD3rujqK2thaGhIaZMmYKTJ09ixYoVWLZsGdasWYPbt2/jwoUL/dYsLS1FREQEampqEBUVhePHjyMpKQnV1dX9+mk0GgQGBmLq1KlS6aLfS3t7u1S0sb29HdnZ2bC1te0XKXd3BF1SUhJI4vTp0zAyMsKUKVOwaNEiZGdno6WlBS0tLcjOzsYPP/yAxYsXo6KiAiUlJVCpVIiIiICLiws0Gg1cXFwQEREBAMjIyIBGo4FGo0FCQgLWr18PoOcURVhYmFTyJywsTFLUf2Tu93EaKYQQ+Pnnn7Ft27YRW/OJYzCD78janWXIHkfV3r176eXlRUdHxwGdRjt27OCuXbtIkkuWLOH3339PnU5HkrS1teWlS5ekvr2ONgcHBx44cIC//fYb165dS5VKRYVCwfj4eOp0Oh44cICenp78+OOPGRkZycDAQGmO1tZWxsbGcs2aNdy3bx+vXLnywPeoqqqivb097e3taW1tzfDwcJJ87ExrcXFxNDc3vyeY5Glx0N2+fZsKhYLV1dWSI+3ixYujLZbMvciOtLGCoaEhQkJCEBISAqAnsXRffv31V9TX12Pu3LloampCc3MzzMzMMG7cOFy5cgVdXV39/uXrLX5YWVmJpUuXYsKECZg8eTJCQ0OxatUq6HQ66HQ6tLW1ISwsDHZ2diCJN954A6mpqVCr1WhuboalpSWEECgoKEBRURGioqIGTaaiVCpRUlJyT7uxsTFycnLuaRdCIC4ubsC5/Pz84OfnBwAoLi6GiYkJfH19UVJSgpkzZyImJuapcdCNHz8esbGxWLRoEXQ6Hfz8/GBjYzPaYsk8Ag+qkSbzB0QIYQJAB8AYQDCAMJJNQohVADaTnCGEGEeyW9/fDMBZkiZCiAkA9gE4TPLQIGs4ATAAcJzknbueXQCwleTR4Xi/wRBCzAJwGsDfSJ4RQsQAaAUQTHJin34tJJ8XQhwBsJNknr49B8AWAAsA/JlkuL79XwBukdw9wq8k85Qh23THICSvk2wmqSG5gWST/lEdgBj9tRBC9LqVFwOo0l9PA9AN4D995xRC9PtbIHmMZE5fhSuEGKfvZwzg8Yy+v596APUke132qQBeBtAghJgCAPqfjX36960DYwrgv4O0y8gMK7LSfYIgeYJkov5aR7I3t6IxgEz9tRZAB3oUVd+x3X3v71bCeiYD2A8gi2TtUMr+sJC8BqBOCPFXfZMLgHIA6QDW6NvWAEjTX6cDWC16cABwk+RVAFkAFgohnhdCPA9gob5NRmZYkW26TzhCCEHyoz5NVQDOAfinEKKbZNJA40h268dSP48HgL8DqCT5j2EXfHCCAfxbCPEnANUAfNGzgUgRQqwDUAvAW9/3KICl6NnZ39L3BclmIcQOAEX6fttJNo/cK8g8rcg2XZkHIoT4CMBfACSSPDXa8sjIjGVk84LMoAghfAFsBDAdwMtCiHn3MT3IyMg8BPJOV+aB6B1TswDMR4/y9SN5bzibjIzMA/kffelKLEbbRTwAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# plot results\n",
"\n",
"# plot normalized linear regression\n",
"fig = pyplot.figure()\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"ax.scatter3D(normalized_size_vector, normalized_bedrooms_vector, normalized_price_vector, c='b', marker='o')\n",
"normalized_xmin = -3\n",
"normalized_xmax = 3\n",
"normalized_h_x_min = theta[0] + np.multiply(theta[1], normalized_xmin) + np.multiply(theta[2], normalized_xmin)\n",
"normalized_h_x_max = theta[0] + np.multiply(theta[1], normalized_xmax) + np.multiply(theta[2], normalized_xmax)\n",
"ax.plot3D([normalized_xmin, normalized_h_x_max], [normalized_xmin, normalized_h_x_max], [normalized_h_x_min, normalized_h_x_max], 'red')\n",
"ax.set_title('Normalized 3-D Linear Regression')\n",
"ax.set_xlabel('Size')\n",
"ax.set_ylabel('Bedrooms')\n",
"ax.set_zlabel('Price')\n",
"pyplot.show()\n",
"\n",
"# plot denormalized linear regression\n",
"xmin_size = np.dot(normalized_xmin, size_std) + size_mean\n",
"xmax_size = np.dot(normalized_xmax, size_std) + size_mean\n",
"xmin_bedrooms = np.dot(normalized_xmin, bedrooms_std) + bedrooms_mean\n",
"xmax_bedrooms = np.dot(normalized_xmax, bedrooms_std) + bedrooms_mean\n",
"h_x_min = np.dot(normalized_h_x_min, price_std) + price_mean\n",
"h_x_max = np.dot(normalized_h_x_max, price_std) + price_mean\n",
"fig2 = pyplot.figure()\n",
"ax2 = fig2.add_subplot(111, projection='3d')\n",
"ax2.scatter3D(size_vector, bedrooms_vector, price_vector, c='b', marker='o')\n",
"ax2.plot3D([xmin_size, xmax_size], [xmin_bedrooms, xmax_bedrooms], [h_x_min, h_x_max], 'red')\n",
"ax2.set_title('Denormalized 3-D Linear Regression')\n",
"ax2.set_xlabel('Size in ft^2')\n",
"ax2.set_ylabel('Bedrooms')\n",
"ax2.set_zlabel('Price')\n",
"pyplot.show()\n",
"\n",
"# plot learning curve\n",
"pyplot.figure()\n",
"pyplot.plot(i_array, j_array, 'red')\n",
"pyplot.title('Learning Curve')\n",
"pyplot.xlabel('Iterations')\n",
"pyplot.ylabel('Cost')\n",
"pyplot.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"I currently live in an apartment; however, for illustration we will test this model on my apartment as if it were a house. The features of my apartment are as follows:\n",
"\n",
"Size (ft^2): 925\n",
"Number of Bedrooms: 2\n",
"\n",
"Now we will use our model to predict a good market price given the features of my house. "
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Nomalized Good Market Price: $-1.2963059031963535\n",
"Good Market Price: $166000.26594221333\n"
]
}
],
"source": [
"# features\n",
"size_feature_value = 925\n",
"bedrooms_feature_value = 2\n",
"\n",
"# perform normalization of the features\n",
"normalized_size_feature_value = np.dot(1/size_std, size_feature_value - size_mean)\n",
"normalized_bedrooms_feature_value = np.dot(1/bedrooms_std, bedrooms_feature_value - bedrooms_mean)\n",
"\n",
"# normalized price\n",
"normalized_price = theta[0] + theta[1]*normalized_size_feature_value + theta[2]*normalized_bedrooms_feature_value\n",
"\n",
"# denormalize the price\n",
"price = np.dot(normalized_price, price_std) + price_mean\n",
"\n",
"print('Nomalized Good Market Price: $' + str(normalized_price))\n",
"print('Good Market Price: $' + str(price))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As illustrated, a good market price for my house based on this model is approximately $166000.27. This looks correct based on our denormalized linear regression plot shown above."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This concludes part 2."
]
}
],
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