1.1 Introduction - Machine Learning and Logistical Regression.ipynb

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    "# Introduction to Machine Learning"
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    "\n",
    "## What is Machine Learning?"
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    "Machine learning is the process of **extracting knowledge from data automatically**, usually with the goal of **making predictions on new, unseen data**. \n",
    "\n",
    "A classical example is a **spam filter**, for which the user keeps labeling incoming mails as either spam or not spam. A machine learning algorithm then \"learns\" a predictive model from data that distinguishes spam from normal emails, a model which can predict for new emails whether they are spam or not. "
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    "##### Two central concepts, Prediction and Generalization\n",
    "\n",
    "Firstly, central to machine learning is the concept of **automating decision making** from data **without the user specifying explicit rules** how this decision should be made."
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    "For the case of emails, the user doesn't provide a list of words or characteristics that make an email spam. Instead, the user provides examples of spam and non-spam emails that are labeled as such."
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    "The second central concept is **generalization**. The goal of a machine learning model is to predict on new, previously unseen data. In a real-world application, we are not interested in marking an already labeled email as spam or not. Instead, we want to make the user's life easier by automatically classifying new incoming mail."
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   "source": [
    "##### Concept of Machine learning\n",
    "<br>\n",
    "\n",
    "<img src=\"imgs/supervised_workflow.svg\" width=\"70%\">"
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    "##### Data representation\n",
    "\n",
    "The data presented to the algorithm is usually  as a **two-dimensional array (or matrix) of numbers**. Each data point (also known as a *sample* or *training instance*) that we want to either learn from or make a decision on is represented as a list of numbers, a so-called **feature vector**, and its containing features represent the properties of this point. \n",
    " For instance, we can represent an example dataset, consisting of **150 samples and 4 features, a 2-dimensional** array or matrix $\\mathbb{R}^{150 \\times 4}$ in the following format:\n",
    "\n",
    "\n",
    "$$\\mathbf{X} = \\begin{bmatrix}\n",
    "    x_{1}^{(1)} & x_{2}^{(1)} & x_{3}^{(1)} & \\dots  & x_{4}^{(1)} \\\\\n",
    "    x_{1}^{(2)} & x_{2}^{(2)} & x_{3}^{(2)} & \\dots  & x_{4}^{(2)} \\\\\n",
    "    \\vdots & \\vdots & \\vdots & \\ddots & \\vdots \\\\\n",
    "    x_{1}^{(150)} & x_{2}^{(150)} & x_{3}^{(150)} & \\dots  & x_{4}^{(150)}\n",
    "\\end{bmatrix}.\n",
    "$$\n",
    "\n",
    "(The superscript denotes the *i*th row, and the subscript denotes the *j*th feature, respectively."
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   "source": [
    "# Types of Machine Learning problems"
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    "### Supervised Learning: Classification and regression\n",
    "\n",
    "In **Supervised Learning**, we have a dataset consisting of both input features and a desired output.\n",
    "The task is to construct a model (or program) which is able to predict the desired output of an unseen object\n",
    "given the set of features.\n",
    "\n",
    "\n",
    "\n"
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    "Supervised learning is further broken down into two categories, **classification** and **regression**:"
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    "- **In classification, the label is discrete**, such as \"spam\" or \"no spam\". In other words, it provides a clear-cut distinction between categories. Furthermore, it is important to note that class labels are nominal, not ordinal variables. Nominal and ordinal variables are both subcategories of categorical variable. Ordinal variables imply an order, for example, T-shirt sizes \"XL > L > M > S\". On the contrary, nominal variables don't imply an order, for example, we (usually) can't assume \"orange > blue > green\".\n",
    "\n",
    "- **In regression, the label is continuous**, that is a float output. For example,\n",
    "in astronomy, the task of determining whether an object is a star, a galaxy, or a quasar is a\n",
    "classification problem: the label is from three distinct categories. On the other hand, we might\n",
    "wish to estimate the age of an object based on such observations: this would be a regression problem,\n",
    "because the label (age) is a continuous quantity.\n"
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    "\n",
    "In supervised learning, there is always a distinction between a **training set** for which the desired outcome is given, and a **test set** for which the desired outcome needs to be inferred. The learning model fits the predictive model to the training set, and we use the test set to evaluate its generalization performance."
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    "### Unsupervised Learning\n",
    "\n",
    "In **Unsupervised Learning** there is no desired output associated with the data.\n",
    "Instead, we are interested in extracting some form of knowledge or model from the given data.\n",
    "In a sense, you can think of unsupervised learning as a means of discovering labels from the data itself.\n",
    "Unsupervised learning is often harder to understand and to evaluate."
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   "source": [
    "# Logistical Regression"
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    "Logistic regression is used in classifying problems of machine learning."
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    "##### What's the relationship between linear regression and logistic regression?\n",
    "\n",
    "In linear regression, the outcome (dependent variable) is **continuous**. It can have any one of an infinite number of possible values. In logistic regression, the outcome (dependent variable) has only a limited number of possible values. (**discrete**) \n",
    "\n",
    "Suppose your problem was to not output the **temperature** (linear regression), but the **type of weather** that tomorrow might have (eg., sunny, cloudy, stormy, rainy etc). This problem will give an output belonging to a certain set of values predefined, hence it is basically classifying your output into categories. Classifying problems can be either binary (yes/no, o/1) or multiclass (like the problem described above). "
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    "##### Linear classifier and mutli-class classification\n",
    "\n",
    "In the field of machine learning, the goal of statistical classification is to use an object's characteristics to identify which class (or group) it belongs to. A **linear classifier** achieves this by making a classification decision **based on the value of a linear combination of the characteristics**. We usually use sigmoid function for binary classification but use softmax function in multi-class classification problem instead."
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    "##### Softmax, digits to distribution.\n",
    "<br>\n",
    "\n",
    "<img src =\"imgs/softmax.png\" width=\"70%\">"
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    "##### Encoding label with one-hot encoding\n",
    "\n",
    "One hot encoding transforms categorical features to a format that works better with classification and regression algorithms. \n",
    "\n",
    "Intuitively, one hot encoding will convert this ‘weather’ feature to four features, namely, ‘is_sunny’, ‘is_cloudy’, ‘is_stormy’, and ‘is_rainy’ which all are binary.\n",
    "\n",
    "|        | is_sunny | is_cloudy| is_stormy | is_rainy |\n",
    "|--------|----------|----------|-----------|-----------|\n",
    "| sunny  |     1    |     0    |     0     |     0     |\n",
    "| cloudy |     0    |     1    |     0     |     0     |\n",
    "| stormy |     0    |     0    |     1     |     0     |\n",
    "| rainy  |     0    |     0    |     0     |     1     |"
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   "source": [
    "##### Algorithm of Logistical regression "
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   "source": [
    "<img src =\"imgs/multi-class-logistic-regression.png\" width=\"80%\">"
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    "###### Logistical regression in matrix form"
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   "source": [
    "<img src =\"imgs/softmax-regression-vectorequation.png\" width=\"70%\">\n",
    "<img src =\"imgs/softmax-regression-scalarequation.png\" width=\"70%\">"
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   "source": [
    "# Poor Generalization - Overfitting"
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   "source": [
    "A statistical model describes random error or noise instead of the underlying relationship. (Error out of sample >> Error in sample)"
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    "##### Overfitting\n",
    "\n",
    "One of the most common tasks is to fit a \"model\" to a set of training data, so as to be able to make reliable predictions on general untrained data. In overfitting, a statistical model describes **random error or noise instead of the underlying relationship**. Overfitting occurs when a **model is excessively complex**, such as having too many parameters relative to the number of observations. A model that has been overfit has poor predictive performance, as it overreacts to minor fluctuations in the training data.\n",
    "\n",
    "##### Key factors of overfitting\n",
    "* data size ↓\n",
    "* stochastic noise ↑\n",
    "* deterministic noise ↑\n",
    "* hypothesis power ↑"
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   "source": [
    "##### Underfitting,  fitting well,  Overfitting\n",
    "<br>\n",
    "<img src =\"imgs/overfitting.png\">"
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    "This example demonstrates the problems of underfitting and overfitting and how we can use linear regression with polynomial features to approximate nonlinear functions. The plot shows the function that we want to approximate, which is a part of the cosine function. In addition, the samples from the real function and the approximations of different models are displayed. The models have polynomial features of different degrees. We can see that a linear function (polynomial with degree 1) is not sufficient to fit the training samples. This is called underfitting. A polynomial of degree 4 approximates the true function almost perfectly. However, for higher degrees the model will overfit the training data, i.e. it learns the noise of the training data. We evaluate quantitatively overfitting / underfitting by using cross-validation. We calculate the mean squared error (MSE) on the validation set, the higher, the less likely the model generalizes correctly from the training data. (http://scikit-learn.org/stable/auto_examples/model_selection/plot_underfitting_overfitting.html)"
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js09/9ln45BOXVEnkQmKJ82OJNB6KLGqEY5oX9RuOj/o33XQTd911FwDFihXL\nt+xff/1FamoqL730EmA02T700EN8++23+Tbb2mPgwIFUrVoVgK5du7JkyRIAZs6cyZ133sn9998P\nQEREBBERETat85tvvmHSpElZ5YcPH86QIUN4/fXXAQgJCWHYsGEopejUqRPBwcHs3r2bxo0bO2Sf\nhHAkR8QTZ8QSkHgCEk8s3DVRmT4d+vS5enqnTtC/P5w7B8WLF329XEHOTWznjbFEEhWRxVknBY4Q\nHR1tc9kDBw6QkJCQ9aXSWpOZmemwQABw3XXXZf0dGhqadfXg4MGDVKtWrVDrTEpKonLlylmvY2Ji\nOHz4cNbrsmXLZrt6Yr1dIdyNxBPbSTxxHXdMVFJSYMkS+Oqrq+cFB0O9erBhA7RuXfR1cwWJJbbz\nxlgiiYrwCDmbN4sXL8758+ezXiclJWX9HR0dTc2aNdm+fXuhtpXfugsSHR3Nli1bcp1X0IC4ChUq\nkJCQQI0aNQBjIF1UVJTN2xZC2EbiibBwx0Rl/XqoXx9Klcp9fosWsGaN7yQq7kxiifPJGBXhkRo2\nbMjChQs5ffo0SUlJjB07Nmtey5YtCQoKYsyYMVy8eJHLly+zbds2Nm3aZPO6ly9fzqFDhzh9+jTv\nvvuuzfXq06cPv/76Kz/88AOXL1/mxIkTWcGhfPny7Nu3L89le/bsyciRIzlx4gTJycm89dZbWf1S\nhRDOI/HEd7ljorJuHdxwQ97zmzeHtWuLrj7CdhJLHE8SFeFWbL0N34MPPkhcXBwxMTHcdddd2e5n\n7u/vz6JFi1i3bh2xsbGUK1eOxx57LNutBvNzxx130KVLF+rVq0eLFi245557bK5jbGwsCxYsYPTo\n0URERNCkSRO2bdsGwKBBg/j7778pU6ZM1qA763W98cYbNGjQgHr16tGwYUNatmzJyy+/nOe2fP6W\nhUIUQOKJxJOCeGKiYmlRcbd6ezOJJa6LJUo76ZNu3jLNKesWhaOUQt4T35DXe21O97gzEokn7kVi\niW/x5njy448waRL89JOLK2UlKgpWrYIqVXKfrzWULw8bN4IdQyTclsQT31GYWCItKkIIIYTwSe7W\nonL4MKSnX31bYmtKXWlVEcLbSaIihBBCCJ/kbomKpdtXQb1nZJyK8BWSqAghhBDCJ7ljotKsWcHl\npEVF+ApJVIQQQgjhk9ztHgIFDaS3aNYM/v4bMjKcXychXEkSFSGEEEL4LHdpUcnMNAbI29KiEh4O\nMTFg3rjhDgrAAAAgAElEQVRJCK8liYoQQgghfJI7df3avRsiIiAy0rbytWvDzp3OrZMQriaJihBC\nCCF8kjslKraOT7GIi5NERXg/SVSEEEII4ZPcKVHZsgUaNrS9fK1asGuX8+ojhDuQREUIKyNGjKBv\n376uroYQwsNJLPEM7pSobN8OderYXl4SFd/hy/FEEhXhNlatWkWrVq0oVaoUZcuW5eabb2bjxo1F\nXg/lbreBEULYRWKJsJW7JSp169pevlYtY1xLZqbz6iQknrhagKsrINyf1poNGzaQlJREo0aNiI6O\ndvg2UlNT6dSpExMmTKBr166kp6ezcuVKgoODHb4tIYTrXLhwgZUrV3L58mVatWpFWFiYQ9cvsUTY\nw10SlTNn4MSJ/J9In1N4OJQsCYcOQeXKTquaWzt69Cjr1q2jdOnStGrVyuEn8xJPXE9aVARpaWms\nWrWKtWvXcunSpWzztNYMHPgUbdp0o2/fCcTFNWbx4sUOr8Pu3btRStGtWzeUUgQHB9OuXTvq1q3L\nvn37uO222yhbtizlypWjT58+pKSkZC1bpUoVPvjgAxo0aEBYWBgPP/wwx44d46677iI8PJwOHTpw\n5swZABISEvDz82PixIlERUURFRXFmDFj8qzXmjVraNWqFaVLl6ZRo0YsX748a97XX39NtWrVCA8P\np1q1asyaNcvhx0UIT3Ps2DGWLVvGrlz6pJw+fZoGDW7k/vtfp1u3d4iLa8zhw4cdun2JJcIe7pKo\n7Nhh3MXLz86zMm/v/rV7926WLVvG0aNHr5q3Zs0aatSoT58+47jjjkHcfXc3Ll++7PDtSzxxMa21\nU36MVQt3ktt7kpiYqGNiauvw8Ca6RInrddOmrfW5c+ey5i9btkwXL15TQ6o2wvlKHR4eqTMzM7PK\nXLp0SY8aNVo3a9ZOd+7cU+/atcvuuqWkpOiyZcvq/v3768WLF+tTp05lzdu7d6/+/fffdUZGhj5+\n/Lhu3bq1fvbZZ7Pmx8bG6pYtW+rk5GSdmJioy5Urp5s0aaL/+ecfnZ6ertu2batHjhyptdY6Pj5e\nK6V0r169dFpamt66dauOjIzUS5cu1Vpr/eabb+q+fftqrbU+dOiQLlOmjP7ll1+01lr//vvvukyZ\nMvr48eP63LlzOjw8XO/Zs0drrfWRI0f0jh077N5vZ8nr+2dOd9r33lk/Ek/cS17vx5IlS3Tx4mV1\nyZK36JCQ8nro0NezzX/mmRd1cPBADZkatA4IGKbvu69vtjLJycm6X79HddOmt+knnnhOp6am2lU3\niSWO583x5PfftW7TpvDHxlEmTtS6f3/7l3v0Ua3HjnV4dYpUXp+vV155U4eElNclS96iixcvq3/9\n9dds86tUqadhrnluclEXL95Sf/PNN9nKrF+/Xt9++/26RYvb9eefj8927mILiSeOVZhYIi0qPu7J\nJ4dy+HBnUlI2cPbsNrZtK88777yfNT8+Ph64AShhTmnFuXNnSEtLyyrz9NMv8s47P7N+/XMsWNCQ\nG25oTWJiol31CAsLY9WqVfj5+fHII49Qrlw57rnnHpKTk6lWrRq33XYbAQEBlClThmeffTbb1QOA\nwYMHU7ZsWSpUqMDNN99M8+bNqV+/PoGBgXTp0oXNmzdnK//mm29SrFgx6taty4ABA3K94jBz5kw6\nduzI7bffDsBtt91G06ZNWbRoEQD+/v5s3bqVCxcuUL58ea6//nq79lkIb6K15v77e3Hu3DzOnFlO\nWtp2Pv98GmvXrs0qs3t3AhcvtgWM7hmXLrXlv/8SsuZfvHiRli3b8e23QWzY8CKTJx+hQ4culpNL\nm0gsEfZwlxaVbdvsG0hvUauWd96ieMOGDXzyySTS0rZx5sxyzp37ngce6E2m1YCcpKQEoK35KoiL\nF1uRkHAlnuzYsYNbb72TX39tx5o1T/Lii5/x3nt5t1LkRuKJ60mi4uN27tzLpUsdzVd+XLhwJ9u2\n7c2a36hRI7T+HbBM+4qoqGqEhoZmlZk06SvOn58L3InWQ0lPb89PP/1kd11q1arF5MmTOXDgANu2\nbSMxMZEhQ4aQnJxMjx49qFSpEqVKlaJPnz4cP34827Lly5fP+jskJOSq12fPns16rZSiUqVKWa9j\nYmJyTawSEhKYM2cOERERREREULp0aVavXk1SUhKhoaHMnj2bL774ggoVKtCpU6dcu7oI4StSUlJI\nSzsPtDanlMHPrwV7916JJzff3JTQ0MnAeSCDYsW+pFWrplnzN2zYwNGjivT0T4DbuXBhKn//vS3b\nyYctJJYIW7lLomLvQHqLuDjv7Pq1d+9e/P2bA2XNKTdz8WIGp06dyipTv35T/P0/BzSQRHDwDzRp\n0iRr/owZszh/fhDwGNCJ8+en8umnE+2ui8QT15JExcc1bVqfoKBpQCZwgdDQb2nevEHW/IYNGzJm\nzCiCghoRElKeChXeZfHiednWYQxes+4XeumaB7TVrFmTBx98kK1bt/LKK6/g7+/Ptm3bOH36NDNm\nzLDrCmtOWmsOHjyY9frAgQNUrFjxqnLR0dH069ePkydPcvLkSU6dOkVqaipDhw4FoH379vz2228c\nOXKEWrVq8fDDDxe6TkJ4uvDwcEqXLgt8Z06J5/LlFdS1Ovt68cVn6dgxisDA8gQFRdKy5Vnef39U\n1nw/Pz+yx5JMtM68pngisUTkx50SlcK2qHj4eWiu6taty6VLK4H95pQfCAsLIyIiIqvMvHlfU6XK\ndxQrVp7AwOoMHTqI9u3bZ83381MoZR1PMuTcxAN5RKKSnJzM+vXrSU5OdnVVvM6nn75LnTr/EhIS\nTbFi0bRpE87zzz+Trcyjjw7i9Olj7NmziYMHd1G7du1s85966ilCQ+8B5uDvP5zQ0JV06dLFrnrs\n2rWLMWPGZA2sPXjwILNmzaJly5acPXuWEiVKEB4ezuHDh3n//fcLWFvBRo0aRVpaGtu3b2fKlCn0\n6NHjqjJ9+vRhwYIF/Pbbb2RmZnLhwgWWL19OYmIix44dY8GCBZw/f57AwEBKlChBQIDcRM8TSDxx\nDqUUCxfOIyLiGUqUqE5wcAPeeec1GjS4cuEjICCAOXOmcuRIAocO7WHp0gXZWmebNm1KTEwowcED\ngXmEhHSnVavmVLbjlkYSS4Q9rjVRcUQ8OXkSzp6FwtxQMyYGkpPh3LlCb94t1a1bl/fee5Pg4IaU\nKFGd0qWfYtGi77IlGtHR0ezatYn//vubkyePMnz4y9nW8eCD/QgN/Rql3ge+ITS0Ly+9NNiuekg8\ncT23T1RmzZpNTEwc7ds/RkxMHLNmzXZ1lbxKqVKl2LBhOdu2rWTPns0sWDCbwMDAq8qFhIQQFRWF\nv7//VfPee+8tRo9+iHbtZtOr11E2bVpNuXLl7KpHWFgYa9eupXnz5oSFhXHjjTdSv359PvzwQ4YP\nH87GjRspVaoUnTp14v7778+2bM4rJLZcMWndujXVq1enffv2DB06lNtuu+2qMpUqVeLHH3/k//7v\n/4iMjCQmJoYPPviAzMxMMjMz+fDDD4mKiqJs2bKsWLGCcePG2bXPouhJPHGupk2bcvjwXjZsWEhS\nUjxPP/1EruUiIiKIjIy86rsaGBjIqlW/8sgjZWjbdiZDhjTg55/n2HUVVGKJsMe1JCqOiieW1pTC\nXOz394fq1Y3nqXibp556jCNHEtiwYSGJif9xww03XFXGz8+PihUrUqJEiavmVa9enTVr/qBr1x10\n6PAD48e/weDBucekvEg8cT11Lc1U+a5YKX2t605OTiYmJo60tD+A+sAWQkLakJCwk8jISIfU05co\npa6pWdIbJCQkULVqVTIyMsxuJt4pr/fanO5xT42SeOJeJJb4TiwB744nK1fCq68av+3hyHgyfjxs\n2ABffWVfHSweeMD4yeXiu0eQeOI78aQwscStj0Z8fDxBQbEYQQCgPoGBMeadqIQoHF8PiL5K4olw\nNIkl3qEwb+M//xwEnsAR8aSw41MsvHWciq+ReJK7IktUCtOPMzY2lvT0eGCLOWULGRkJxNrz6FYh\ncnD0k2tF0ZN4ItyBxBLPd/q0MRDZ3jEmu3dXJy3tScDykOSthY4nhb01sUXVqrBvX+GXF+5B4knu\niiRRKWw/zsjISCZNGkdISBvCwxsTEtKGSZPGSTcNUWgxMTFcvnzZq5tWvZ3EE+EOJJZ4vlmzZvPA\nA73Yvn2f3WNMTpwIp3PnkxQrVgE/vz0EBz9f6HiyY0fhbk1sUaUKSMOwZ5N4kjenj1FxRD/O5ORk\n4uPjiY2NlZOKayD9QH2Ht/Ypl3jiHiSW+BZvjCfHjh0zY8laoDr2xpKBA6FFC7j33mQee0zTqFEo\nr7129YDughw/bgyGP3WqcIPpAfbvh9at4cCBwi3vahJPfIdbjlFxRL/wyMhImjVrJicVQvg4iSdC\nCEe4Ekuqm1PsiyXx8RAba8STe+8tx9at9icpcG13/LKIjoYjRyA9vfDrEMJdOT1RkX7hQghHkXgi\nhHCEK7FkjznFvliyf7+RqAC0bAn/+1/h6nGtA+kBAgKgYkXPbVERIj9OfwqMpV/4wIFtCAyMISMj\nQfqFu0hMTIwM1vIRMTExrq6Cwy1dCikpkTzxxHzGjh1FYKAfly+vk3jiAhJLfIs3xhPLucmAAYPI\nyJhIcLDtY9YuXYLDh8HyHNJq1eDiRTh40P6HNjoiUYEr41SqVy+wqNuReOI7ChNLiuw5KtIvXAjX\n8+Q+5bfeqilZEjIzISUlnYMHL3H0aDFKlvSjeXO46Sbo1Alq1HB1bYXwDZ4cTyznJ8uXn+Shh4qx\nZs05m89NDhyAG2+EQ4euTLvnHujdG7p1s68ut94Kr70G7drZt1xODz1ktOw8/PC1rUcIV8gvlji9\nRcUiMjJSEhQhRKH98Yf1qyAgCK2NLhjr1sGyZfDBB1CqFPTvDw8+COXLu6auQgjPEBkZQVAQREaG\n2ryMdbcvi5Yt4a+/7E9Utm+H2rXtWyY3VaoY9RLC2zg1USn/QXmKBxanfInyRIVFUT2iOnUi69Dw\nuobUKVcHPyW3YRNC2KbChxUIDw6nYlhFosKiiCsbR53IOjSLakaPHpXo0cNobVmzBiZNgrg46NgR\nXn752m79KYTwPpXGVCIiJIKSfhVJbFKZj9fUpm65utwQdQPhweH5LhsfbyQG1m68EYYOta8Ox44Z\n3cgqVLBvudxUqQILF177eoRwN07t+pWUmsTZ9LMcPXuUw6mH2X1iN9uObWNj0kZOnD/BTZVvomON\njtxd826iwqOcUg8hxBWe3FXj0JlDpFxMITE1kYMpB9l5fCdbj21l3eF1lAgqwa2xt9K5ZmfaV2tP\niaASnDkDX3wBH39sdAt75x3pFiaEI3lyPDlw+gAn0k6wYVciL78bT/cnt7P12FY2JW2iZpmatK/a\nns61OtOiUgv8/fyzLT9ihJFgjBp1Zdr58xAZCSdOQLFittXjzz+Nbl+rVl37Pq1aBS++aLTqCOFp\n8oslRTZGJacjZ4/wZ/yf/Lz7ZxbvXUztyNr0q9+PbnW6UbJYSafUSQhf58knFnnFE601u07sYsl/\nS1iwewFrD6/lzup30q9BPzpU60D6hQA+/dToFta3r3GSEZ7/BVMhhA28IZ7s3w9t2lx5YOLFSxfZ\nmLSRX/b+wk+7fuLI2SP0qteLBxs+SP3yxm3RH3wQbr7ZeJaKtWbNjAsjrVrZVo/PP4ctW2DChGvf\np8OHoUkT4zbFQngat0xUrGVczmDx3sVM/Wcqf+z/g971evN086epUUYufwrhSN5wYlGQk2knmb1t\nNl//8zVHzx5l8A2DGdh4IOkppRg2DH75BcaOhXvvdXKlhfBy3hBPDhwwEouDB3Mvu/vEbqb9M42p\n/0wltlQszzR/hrFP3ssbrwfQtm32sk89Zdx1a8gQ2+rxxBNGF9Wnn76GnTFlZkLx4kaLTqjtw22E\ncAsufeCjLQL9A+lcqzPfdfuOrY9vJTw4nFaTW9H7+97sPL7T1dUTQniQiJAIHm/2OGsHrWVu17ls\nOrKJ6p9W5/Ptb/Dep6eYOdMYt9Kzp/E0aCGE7/L3h8uX855fs0xN3mr7Fvuf2c8zzZ/hozUf8b9G\ntdmcOZ1LmZeylW3cGDZutH3bjhpID+DnZ9wu2Y5n3wrhEdwiUbEWFR7F27e9zX9P/0fdyLrcMuUW\nBv44kMTURFdXTQjhYZpFNWPmfTNZ9/A6DqUcosbYGqz1f5816y8SGQkNG8Ly5a6upRDCVQpKVCwC\n/AJ4oPYD/NFnFfw8gfkHJlJ3XF1+3v0zltaZJk1g0ybbtqu1456hYiF3/hLeyO0SFYuw4DBeufkV\n9gzeQ9nQstT7oh5vr3ib9Mvprq6aEMLDVC1dlUn3TGL1Q6tZdXAVjSdfT7snf2L8eOjRA0aPNrpO\nCCF8i62JisXhw4qKF9uwYsByxtw+hheXvEj76e3ZeXwntWsbLRrnzhW8nqQk4/d11xWq2rmKjZUW\nFeF93DZRSU5OZv369aSnpvNu+3fZ8PAG/jr0Fw3HN2TVAQfcIkMI4RMssSQ5OZlaZWvxY48f+bLT\nl7zw2wtMTLmPn/44zI8/QpcukJLi6toKIYqSvYnK33+fpkyZFI4fP85dNe5iy2Nb6FSzEzdNvom3\nV79JXN2L/PNPwetZvx6aNgVHPpBdWlSEN3LLRGXWrNnExMTRvv1jxMTEMWvWbKqUrsKCngsY2WYk\n3ed157lfnyMtI83VVRVCuLHcYglAu6rt2PL4FuqWq0vHBY145LPplL9O06qVXJEUwpfYk6jMmjWb\n7t1fZ9u2FVnxJNA/kGdaPMPfj/3N30f+Zn/7Jsxfu7nAda1fb9wlzJEkURHeyC3u+mUtOTmZmJg4\n0tL+AOoDWwgJaUNCws6sJ9ufOH+CJxY9wdajW/nm/m9oeF1Dx1ZeCC/lDXfpsZUtsQRgc9Jm+s3v\nR82ImjRJnMjY9yL44Qdo0cKx+yCEt/GGeHL2LJQvX3B3rSvxZAdQntziidaagZ/MZNbJ53i9/RBe\navXSVc9gsbj9dnjySejc2XH7tX49PPqo7eNkhHAXbn/XL2vx8fEEBcVinFgA1CcwMIZ4q8ucZULL\nMPuB2Qy7eRjtp7dn3PpxOCvhEkJ4JltiCUCjCo3Y8PAGKpeszJeqMc9//BedO8PPPxdxhYUQRc7W\nFpUr8aS8OeXqeKKU4omb+hDz60Z+/e9X7ph5B0fPHr1qXVrDhg2Ob1GJiTFutyyEN3G7RCU2Npb0\n9HhgizllCxkZCcTGxl5Vtnf93qx+aDUTN02k53c9OZduwwg2IYRPsCeWBAcE89EdH/HJHZ/w3oF7\n6DP2EwYO0kyZUoQVFkIUOVsTlSvx5Iw5Jfd4Uq8eHNgazc9dl9IiqgWNv2zM6gOrs5XZtw9CQqBC\nBUfswRWRkXD+vG2D+YXwFG6XqERGRjJp0jhCQtoQHt6YkJA2TJo0LltXDWs1y9Tkr4F/USygGDdO\nvpF9p/YVcY2FEO7I3lgCcE/cPawdtJZlp6bQ8t0HGT4qjbFji7DSQogiZWuiYoknfn6bCQ19Is94\nEhwMtWrBv9sDGNV2FBM7TaTL7C5M2HDl8fPOGJ8CxsD86GhpVRHexe3GqFgkJycTHx9PbGxsvicW\nFlprPlv3GW+vfJu5XecSFxpn1/JC+AJv6FNuL3tjCcC59HMMWjCIf4/s49S4H+l3Xwk6d/5X4okQ\nVrwhnmhtPCwxM9O2O3A1aZLBk0/uoVOnyDxjwaBBxjNVHn/ceL3nxB7unX0vt8bcyid3fsLgJ9Px\n8zvJm28GOzyetG8Pzz8Pd9zh0NUK4VT5xRK3TVQK67f/fqPrrK6kzb9M6N5apKfHM2nSOHr27F7k\ndRHC3XjDiUVR0VozcvlIxq4cx4nPphB8Zh9+fm9IPBHC5C3xxN8fLl6EgICCl61dG+bOzf9BjePG\nGU+onzTpyrQzF87QbV43jiYdY8vw9wn1/47MzDkOjyeDBsENN8AjjzhslUI4nU8lKsnJyUQ3qc7F\n+0vAhsGw6k5CQtpedacfIXyRt5xYFJXk5GSi7qxCRttgmPM9JNQkJKSuxBMh8J54EhxsPEMpOLjg\nZaOj4X//M37nZccOo0UjISF7K03ikUQqP1aNy9fFwczFcPZYrncivBYjR0J6Orz1lkNWJ0SR8Ki7\nfl2r+Ph4iqVUh0nroN5MuP1rAgIrX3WnHyGEKEh8fDyhe2vBvDnQrSvErSUzc5jEEyG8iL8/XLpk\nW9mUFAgLy7/M9ddDUBBXPfjx8MHDFFvaCXZ2gYdugtLFc70T4bWIiTESJCG8hdclKll35kg9AVNW\nQMXlnO+wg0qVK7m6akIID5MVT/ZHwoxfoOMjXLxes2JFnKurJoRwEFsH1GttPHeloERFKejUCRYs\nyD49NjaW9IuxsHww/O8FGNCSiyX/y/VOhIVVubIMphfexeMTleTkZNavX09ycjKQ404/QbdRbF48\ntW+oxTMrniHjcoaLayuEcGf5xpNzgwj+Np1SXUYzavFMZs1ycWWFEA5ha6Jy7hwUK2aUL0inTvDD\nDxlXxZPo6JcJCnqU8N1fEvjneYo9ojh46eA17sEVlStLi4rwLh6dqMyaNZuYmDjat3+MmJg4Zs2a\nDUDPnt1JSNjJ779P4MB/u1j37DouXLrAA3MfIP1yuotrLYRwR7bEk4Ob97Bx8FpK3P4uj0z+mN9+\nc3GlhRDXzNZEJTW14NYUi8OH57B581luu+21rHjy99+Qnh5BQsLn/P77BA7/sp8p90/hjhl3sPbQ\n2mvbCVOlSpCYaNv+COEJPHYwfXJyMjExcaSl/YHx5Okt+Q5Ky7icQfd53cnUmczpOocg/yCn1U0I\nd+Utg18dzd54cuDMAVqMv5WUJUNY9n9Pc8MNTquaEG7LW+JJuXKwdSuUL5/PQsCuXUZLye7d+Ze7\nEk/+A0phiSe9eh0iKiqEESOyl1+4eyEDfhzAwl4LaRZ17Q9YqVgR1q0zkhYhPIFXDqaPj48nKCgW\n46QCoH6+g9IC/QP59oFvAeg+r7t0AxNCZLE3nlQuWZm/Hv2D4rd9RLtXP2fv3iKqqBDC4RzdonIl\nnpQyp9QnIKAmc+cGMmDA1eU71uzIpM6TuHvW3WxM3GhHzXMnA+qFN/HYRCVrkCtbzClbyMhIyHdQ\nWpB/EHO6ziHjcgb95/fncqa0jQohChdPYkrFsPbxPwhs/R6tnpzC8eNFUFEhhMPZk6iEhxdc7ko8\n2W5OOUFa2r00bpxJXiGlU61OTLh7Ah2/6ci2Y9tsq3geZEC98CYem6hkG+Qa3piQkDZMmjSuwHuR\nB/kHMbfrXI6cPcLjCx/HFc9mEEK4l8LGk9hSsfzv8d8433IYrR6eS1paEVVYCOEwtiYqttyaGKzj\nyS2UKNGBgIDxlCnzBM89l3+X83vj7mXM7WO4Y8Yd7D1Z+GZaGVAvvInHjlGxSE5OJj4+ntjYWLse\nmJR6MZV209vROqY177V/z4k1FMJ9eEufcmcpbDzZnPgPLb/oQPPEafz51e3ZHvImhLfylnhStSos\nWQLVquW/3IwZ8Msvxm9bFDaeTNgwgdGrR7P6odVUDKto83IWn31mPHRy3Di7FxXCJbxyjIpFZGQk\nzZo1s/uprmHBYSzqtYifd//MmL/GOKl2QghPUth40qhiAxb1+57/XdeHR0asc1LthBDO4OgWFYvC\nxpNHmz7KI40f4Y4Zd3D6wmm7lgXp+iW8i8cnKteiTGgZfu3zKx+v+ZiZW2a6ujpCCA/WtkYrJnee\nzJS0e/hw6i5XV0cIYSNHj1FxhJdvepk2sW3oPKszaRn29SmVwfTCm/h0ogIQXTKaxb0X89xvz7Fs\n/zJXV0cI4cH6Nu/E663eZug/d/Lr6qOuro4QwgbOalG5FkopPrrjI6LCo+g/vz+ZOtPmZaVFRXgT\nn09UAOqUq8OcB+bQY16Pa77bhhDCt73R+SEeqNGXTt904r8D51xdHSFEAZzxwEdH8FN+fH3P1xw5\ne4SXlrxk83KlSoHWcNr+XmNCuB1JVEytY1vz8R0f0/GbjiSlJrm6OkIID/btY29Sp9z1NBvdi/Np\ncht0IdyZO3b9sggOCGZ+j/ks2L2Az9d9btMySsmdv4T3kETFSq96vXi48cN0/rYz5zPOu7o6QggP\npZRizbCJ+BdPoeXrL7u6OkKIfLhj1y9rESERLOq9iFErRvHL3l9sWiYmRrp/Ce8giUoOw24eRlzZ\nOLv7hAohhLXggCA2vPgdO/mRvh995erqCCHy4M4tKhZVS1dlXrd59PuhH9uPbS+wvLSoCG/h1ETl\nyBFnrt05lFJ81ekrklKTeOOPN1xdHSGEB4spF8GCnj8z88gwPl/4p6urI4TIhbu3qFjcVPkmPuzw\nIZ1mdeL4+eP5lpUWFeEtnJqo1K4NTz8Nhw45cyuOFxwQzPfdv2falmnM2T7H1dURQniwDk1qMqL+\nTJ5e0YN1e/a7ujpCiBw8oUXFom+DvnSr042uc7uScTkjz3LSoiK8hVMTlR07ICgI6teHxx6D+Hhn\nbs2xyhUvx489fuTJRU+yOWmzq6sjhPBgr/duR7vgV2n7ZWdOnUt1dXWEEFY8pUXF4u22b1M8sDhD\nfhmSZxl5lorwFk5NVK67Dj74AHbtgogIaNIEBg6EvXuduVXHaXhdQ8bdNY57Z99L8rlkV1dHCOHB\nFg4fTKnzN9B89INorV1dHSGEyZNaVAD8/fz55v5vWBa/jIkbJ+ZaRrp+CW9RJIPpIyPh//4P9uyB\n6Gho0QL69oWdO4ti69ema52u9K7Xm+7zunMp85KrqyOE8FABAYq1w8eRcPIw/SaOdnV1hBAmWxIV\nreHsWShRomjqVJDw4HDmd5/PsGXDWHNozVXzK1SAEyfg4kUXVE4IByrSu35FRMCbb8J//8H118Mt\nt0D37rB1a1HWwn6j2owiyD/IrgcuCSFETlHlg5nb9Tu+2TuWKSttu82oEMK5bElUzp83urIHBBRN\nnQeMkpcAACAASURBVGxRq2wtvur8FV3nduXI2ex3L/L3h4oVPW+MsBA5ueT2xCVLwquvwr590LQp\ndOgAXbrAxo2uqE3BLM2s83fNZ/a22a6ujhDCg3W+NYrB183mkUX92XlEBtcL4Wq2JCru0u0rp861\nOjOw0UC6z+t+1eB6GacivIFLn6NSogS8+KLRwnLrrXDPPdCxI6y5uhXT5SJCIpjXdR5PLX6KHck7\nXF0dIYQH++jZm6lz6hVu/uwB0jLSXF0dIXyaLYmKuwykz83w1sMJDQzllaWvZJsud/4S3sAtHvgY\nGgrPPGMkLJ06Gd3BOnSAlStdXbPsGlVoxHvt3uO+2feRcjHF1dURQngopeDP0c9w4XAN7vr8KVdX\nRwif5sktKgB+yo8ZXWbw3b/fMXf73KzpMqBeeAO3SFQsgoON2xjv2WMkKwMGGC0tS5caA9ncwYBG\nA7gl5hYG/TRI7twjhCi0UqUUix//ipX7/+KdXya7ujpC+CxPb1EBKBNahnld5/HEoifYfWI3IF2/\nhHdwq0TFIijIuI3xzp3G7yefhFatYPFi90hYPr3zU/ac3MPn6z93dVWEEB7sphtK8Eq1eQxf8RIb\nDm5xdXWE8EkBAZ7domLRpGIT3mrzFg/MeYDzGeel65fwCm6ZqFgEBBi3Md6+3XjC/Ysvwg03wI8/\nujZhKRZQjHld5zFy+UjWHV7nuooIITzeyMG1aXTsI9pPfEC6lArhArZ2/XLnFhWLR5o8Qv3y9Xlq\n0VPS9Ut4BbdOVCz8/aFHD9iyBV55BUaMgIYNYe5cyMx0TZ2qRVRj/N3j6T6vO6fSTrmmEkIIj6cU\n/PZBHy7tbUPH8Y9Il1Ihipi/P1wq4DFpKSnu36ICoJRi/N3jWXNoDStSpnLwoOvOk4RwBI9IVCz8\n/OC++4zbGP/f/xlPva9bF2bOLDjIOMN9199Hp5qdeOinh+TkQghRaKVKwc9Pfcyavf/y7u+5P2la\nCOEc3tSiAlAiqARzus7h1T9fIDRmB0ePurpGQhSeRyUqFkpduY3xxx/D+PHGAySnTIGMjIKXd6T3\n27/PwTMHGbtubNFuWAjhVVrfGMIzFefw+p/D2HRYxqsIUVS8YTB9TnXL1WX0baNJu7sbu/efd3V1\nhCg0j0xULJQybmO8YgVMnAgzZkDNmjBhAly8WDR1CA4IZk7XOby14i02JrrpEyuFEB7hvZdqERf/\nMR0mduNs+llXV0cIn+DptyfOy0ONHiLyckNGrn/G1VURotA8OlGxUOrKbYxnzoT586F6dRg7FtKK\n4FlqVUtXZeydY+nxXQ9SL6Y6f4NCCK/k5we/j+nN+d0t6Tp5sKurI4RP8MYWFTDGq3T2+4ItZ5bz\n7bZvXV0dIQrFKxIVazfeaNzG+Pvv4fffoVo1+PBDOHfOudvtXrc7bWLb8PjCx2W8ihCi0MqXh5m9\nx/L7rr/44n8zXF0dIbyet7aoANSqEsatx79l8OLB7Du1z9XVEcJuXpeoWDRrZtzGePFiYyxL1arw\nzjvGVRFn+fiOj9l8ZDPT/pnmvI0IIbxel44l6BkwmyGLnmXPib2uro4QXs3bBtNbq1IFzu5pzGs3\nv0aPeT1Iv5zu6ioJYRevTVQsGjQwbmO8bBls22a0sIwYAaeccEfh0MBQvr3/W15Y8kLWk2GFEKIw\nJr7VgHI7h9N+fE85uRDCiWzt+uWJLSpVqsD+/fB086cpV7wcw/8Y7uoqCWEXr09ULOrUMcavrF5t\nfGmrV4fXXoMTJxy7nXrl6/Fm6zfp9V0vObkQQhRacDAseespEvdcx2NzXnN1dYTwWt7eopKQAFor\nptwzhelbprN031JXV0sIm/lMomJRsyZ8/TWsXw/Hjhmvhw7FofcZf6LZE0SFRzFs6TDHrVQI4XPi\n4hTvt5rC9L+/YeG/S1xdHSG8kje3qISGQsmSkJQEkcUjmXrvVPrP70/yuWRXV00Im/hcomJRtSp8\n+SVs3gznzxvPYRkyBBITr33dSikmdZ7ErG2zWPKfnFwIIQrv6UFlufHYVLp/+6CcXAjhBLa2qJQo\nUTT1cTRL9y+AdlXb0ateLwb+NFBu/CM8gs8mKhaVK8NnnxnjV/z8jCfdP/GE0VR6LcqGluXre/+f\nvfuOiuLs4gD8W/qKgiCLioUiKnbRqFFjBbvGHsVeYjf62aIxYmLsvUWs2AV7wVijotjFEntFwS5o\nlCILbLnfHxNRpC2wMFvucw4nZnZ25u6ye3nvzFvWo+++vngb/1Y7wTLGjI5EAuxd4AWTW93Reg03\nLhjTNk0Klfh44e6EPnJz+1yoAMC0xtPwIvYFVlxeIV5QjGnI6AuVT5ycgAULgHv3hNu71aoBP/4I\nhIVl/5jebt7wqejDVy4YYzliZwfsHj4NVx++wJxgblwwpk2ZFSpqNaBQCOPG9JGrK/D4i5mJLUwt\nENAhAL7BvrgTdUe8wBjTABcqX3F0BGbNAh48EIqXWrWA3r2B+/ezd7zpXtPxLPoZVl9drd1AGWNG\nxbuRBX4sGADfE5NxJ/Ku2OEwZjAyK1QSEgArK+Hupj76suvXJ2UdymKm10x029UNicpEcQJjTANc\nqKSjUCHgjz+AR4+EGcK++w7w8RG6iGWFhakFtnTYgl9P/Ir7b7NZ7TDGGIAlv5VFsXvT0WxVd55V\nkDEtyaxQkcsBqTTv4tG2r7t+ffJjtR/haueKSSd4VkGmu7hQyUTBgoCvr3DbtGpVwNsb6NBBGISv\nqXKycpjaaCq67+bGBWMs+8zNgaMzByDyYUkM3u4rdjiMGQRDL1TSuqMCCBP/rG6zGoG3AnnKYqaz\nuFDRUIECwPjxwpiVevWA1q2BNm2Aixc1e/6g6oPgVMAJvwX/lruBMsYMWunSEsyrvwabrm/GkfvB\nYofDmN4z9EKleHFhCYbENHp4OeRzwLq269BnXx/8K/8374NjLBNcqGSRtTUwapRQsDRvDnTuDDRr\nBpw5k/HzJBIJ1ny/Bhuub8DpiNN5EyxjzCAN7+eA2pH+6LSlN97L34sdDmN6TZNCxcoq7+LRNjMz\noFgx4OnTtB9vUqoJOpXrhMF/DeaJf5jO4UIlm6ysgGHDhDEsnToBvXoBjRoBwcFAet9zR2tHrG6z\nGj339ER0QnTeBswYMxgSCbBvfnPgXlu0XzOUGxeM5YCh31EB0h+n8slM75m4E3UHm25syrugGNMA\nFyo5ZGEBDBggzArWpw8waJAw8P7IkbQLllZlWqFl6ZYYfmh4nsfKGDMcdnbAzkFzcDbsOpafDRA7\nHMb0liazful7ofL1FMVfszKzQkDHAIw5OgZP3mdQ0TCWx7hQ0RJzc2Ea47t3geHDgdGjhamNg4JS\nFyzzms5D6ItQbLu1TZxgGWMGoZmXFD3ybcaow6MQ8SGdfh2MsQwZwx2V9AbUf6ly4cqYUHcCeu7p\nCZU6kxUwGcsjXKhomampMI3xzZvC4PvJkwFPT2DnTmHRKADIZ54Pmztsxk+HfsLzmOfiBswY02sr\nf68G2aPR8F7WixsXjGWDMRQqmXX9+mRU7VGwMLXAnLNzcj8oxjTAhUouMTEBOnYUpjGeOhWYMweo\nXBkIDBQS4jdO32BErRHovbc31KQWO1zGmJ6ysAD+/n0cwiPU+HnvArHDYUYio4a9vjGWQiUsLPP9\nTCQm2NBuAxZeWIgrL6/kfmCMZYILlVwmkXyexnjePODPP4Hy5YENG4AxtSYgQZmAxRcWix0mY0yP\nlfMwxfTqm7A4dC4uPb0udjjMwKnVwLffih2F9hj6rF8AULo08PBh+pP9fKmEbQksar4IPfb0QLwi\nPveDYywDXKjkEYlEmM74zBlg+XJg/XqgQjkztEzciBmnZ+BWZBaXvGeMsS+MG+iMqpHz0HJNdyQo\nE8QOhxmwHTuExr2hMIY7KnZ2QrH16pVm+3er1A1Vi1TF+L/H525gjGUi00JFIpEMl0gkdnkRjDGQ\nSIDGjYVpjDduBEL2loLqyGw0X9Ud0XFprMbEmJbowngozie5RyIBjszpifiIcujmP1HscJiBUqmA\nKVOAfuPviB2K1vKJmZnhz/oFAGXLCjOUasqvpR/23d+HI4+O5F5QjGVCkzsqRQCESiSS7RKJpLlE\nIpHkdlDG4tM0xodm9IXyrRuK9fLFwoVAPN9pZVqmVCvReUdnscMAOJ/kqkKFJAjovgL7Hm3HzqvH\nxQ6HGaBt2wCp0xP8+qiB2KEAWsonxnBHBch6oWIntcP6duvRL6gf3sW/y73AmFELuJnx9PqZFipE\nNAlAaQD+APoAeCiRSGZIJJJS2giQAbVqSXBz+ipIa27Gnmun4OYmDL6PjRU7MmYoZp6eifwW+cUO\ng/NJHmjXtBA6ma9Fz5198W88r1rPtEelAqZMVSGpVS+Mryt+lyBt5RMuVNLX2LUxulboikF/DeKF\nZZnWPY1+ipGHR2a4j0ZjVEj4dL7+70cJwA7ATolEwvPXaYnMWob1HVYjolov7DkUjWvXgFKlhBnD\nPnwQOzqmb6KiohAaGir890Uo/gz9E+vbrhc7LACcT/LCpt+bwuZlOzRZPIQbFyzHPuWT5ctjkPTN\nXDjYmWF07dFihwVAO/nE1BRQKtN/3BAG0wPZK1QAYLrXdDx49wAbr2/UflDMqHzZNlGTGr339sbo\nbzPOJZqMURkhkUiuAJgD4CyASkQ0BEB1AB21ETgTtCrTCi3dW8IvfDgCA4HTp4FHjwB3d8DXF3jH\nd16ZBgIDt8HZ2QNNmgxGSfeyaLuhLZY0X4JiNsXEDo3zSR6xsACOjZ+N669vYPZBXrWeZd+nfOLt\nPRw/zTiNyFKzsaH9BphIxJ+LR1v5hO+oZMzKzAqbO2zG2L/H8qr1LNu+bJs4O3ugp18vKNVK/Fz3\n5wyfp0mmcQDQgYiaEdEOIlIAABGpAbTOeejsS/OazsOlF5ew7dY2lC0rTGN88SLw+rUwveD48UBk\npNhRMl0VFRWF/v2HQi4PRnT0FSTUa4LIa+/QuHBjsUP7hPNJHqlUTopJ5Tdj0plRuP86QuxwmB76\nMp/ExJ8EOoyBYr8C0iSdabVrJZ8YS6Hi5ga8eAEkZmPenk+r1vfaywvLsqz7um0it1mFgKcBWFh/\nIUxNMp5CUJMxKpOJKM2/ckR0N5sxs3RYW1hjc/uUq9aXKgWsXi0sHhkbC3h4AKNHaz7NIDMe4eHh\nsLBwAVAZKH0AKH0R+U56IDw8XOTIBJxP8tZvA6uhQsxoNF7amxsXLMtS5JMm44HXnpA+KmNw+SSz\nQsVQZv0yNwecnYWeGtkxqvYomJuY86r1LMtS5BKzBKDjb7AKKQH6N/OuyeLfu2Wp1ChWAz/V/Al9\n9vZJsWq9szPg5wfcvCksuFWhAjB8OPDsmYjBMp3i4uKCpKRwIN9J4PsBwJ7foPz4HC4uLiJHxsQg\nkQAnpo7Du3/V6O/Pq9azrEnOJ6UCAY+9wIFhUCgiDC6fGMsdFQAoUyZ73b+AlKvWX311VbuBMYOW\nnEvwHPCaCLx1Ba7HapRLuFDRUb/U+wXxivg0V60vVgxYtAi4exfIlw+oUgUYOBB4wl1HjZ5MJsOa\nNctg0r4pLO6pII0cC39/P8hkMrFDYyIpZG+KLZ02YmPYHBy98Y/Y4TA9IpPJMG3BfKDtaFgddoZU\n0tYg84kxFSrZHafySQnbEljcfDG67+7Oq9YzjQltEz/A7SBQYR3w1xis9V+uUS7hQkVHmZmYYXOH\nzZhxZgZuvrmZ5j6FCwvTGD94ADg6At98A/TtCzx8mMfBMp3ysWwsytcui2DfPYiIuAcfny5ih8RE\n1tHLBR3yLUD7zd0RlyAXOxymJ4gIK1/uRzlVF4RsWGCw+USTQsUQZv0Ccl6oAIBPJR9UK1oNP/+d\n8SBoxr5UqHgTmHacinn1pkFKDdCunWa5hAsVHeZm54a5Teai2+5uSFAmpLufgwMwbRoQFga4ugJ1\n6gDduwN3xF84mOWxh+8eYuKJidj+w3bUqVXH4K58suzbOrEHrD9WRJM54q9/wfTDguB1CPv3EfaP\nmo0aNWoYbD7hOypZt6zlMux/sB8HHx7M+cGYwSMiDNw/CHUKdsSYdsNQvrwEVzXsPciFio7rXaU3\nPBw88MuxXzLdt2BBYPJkoWCpVAlo1Ajo3Bm4fj0PAmWiU6gU6L67O35r8BvKycqJHQ7TMWZmEgSP\nWYFLMXuxIOiI2OEwHffo30eYdHI8euXfglLOlmKHk6uMsVDJ6fJKBa0KYmO7jfgx6EdEfuSpSFnG\nlp/fgOcJd7H1x1kAgG+/FWa01QQXKjpOIpFgZeuV2Hl3J46GHdXoOTY2wIQJwOPHwoehRQugbVvg\n8uVcDpaJasqpKZBZyzCsxjCxQ2E6qoKbHaZW34Cfz/TDgxdRYofDdJRCpUDHLT1ges4X88dXFDuc\nXGcss34BQjdxtRp4+zbnx2rg0gC9q/RG/6D+vLAsS1fYv2GYcGIc6rwKgJOj0IeyVi0uVAyKvdQe\n69uuR999ffE2XvPsYm0NjBkj3GFp0gRo314oWs6dy8VgmShOR5yG/zV/rP1+LSQSidjhMB020acR\nqpr2QIP5P0Kt5sYFS21qyFS8fGyHqa1+gp2d2NHkPmO6oyKRAJUra6+nxZRGU/Aq9hVWXF6hnQMy\ng6JUK9FzT094RP6Kro0qJ2+vVQu4cEGzY3Choie83LzQrWI3/Bj0Y4ZXLqKiohAaGoqoqM9XS6VS\nYRrjR4+Adu2Abt0ALy/g1Km8iJzltg8JH9BzT0+sbrMahfMXFjscpgeCfacimp6j24JVGe6XVj5h\nhu3s07NYdn41rP9eh2HDjOOihzEVKgBQrZqwLps2WJhaYEuHLZh8cjLuRmW8dA3nE+MzLWQa8lsU\nQMT2EWjR4vP20qWBuDhhMfPMcKGiR6Y1noaI6AisupJ24yIwcBucnT3QpMlgODt7IDBwW4rHLS2B\nQYOEWcF69AB+/BGoXx84ejTn/VWZOIgIQw4MQavSrdC6DC/szjRTIJ8F9vTYgu1vJ2HXqbQbF5nl\nE2Z4PiR8QI/dPWAbshrzpxSBhYXYEeUNY5r1CxAKFU0HMmuirENZzGg8Az67fJCoTHvZe84nxufs\n07NYcXkFxrith11BE7i5fX5MIgFq1tSs+5ckt/oVSiQS4j6L2nfv7T185/8d/Gr6oVHFRsmzsERF\nRcHZ2QNyeTCAygBuQCpthIiIe+nO1KJUAtu2AdOnC+NaJk0CWrUSPkBMP2y8vhGzz87G5QGXEfch\nDuHh4XBxcUn3dy6RSEBEevcb5nySOwasWIWNd/wQ1HY5qlV2z1E+YfqNiNB9d3e8emKH+B2LsHTp\nP3B1TT+XAIaTTx4+FLpFp7Viu0olrOiuUhnO38Zbt4COHbUz+9cnRISO2zuisGVhdLX7EWvWlMee\nPVKYmAC2tipERnZDUtKv4HxiHKITolF1ZVUsbr4Y59Z54enTWCxebJri9/3774BCIbRBM8olfEdF\nz1z7+zpi9srhs7MPSrqVTb4qER4eDgsLFwhJAAAqw9TUCQcPHkz3NquZmTCN8c2bwliWX38FqlcH\ndu8WBtsx3Rb2bxjGHB2DwI6B2LsziK9WsSxrZGODpCgztJw3DyVLemSQT4rCxMQB17TVX4TpnE03\nNuHay+u4Nmsqrl9vhqZNjSeXZHRHJSFBuJtiKEUKAHh4AM+fAzEx2jumRCJBc0VLrDi9Do0G3EZg\n4B7Mn78Xz54Bv/76EArFYnA+MQ6fenq0cG+Bj1flmDPnDoKCpqTKJ8WKAZGaTBhHRLnyIxyaaVNk\nZCRJpfYE/EP4oQOhWQ+SSu0pMjLyi8euk9CRazYBUipQwJOkUnsKCNia6fFVKqK9e4mqVyeqWJFo\n61YipTIPXhjLsuevnlP5heVp+rHpafzuryd/Lr723/cy1773ufXD+UT7kj830hDCqOIE943p5JOt\nBNgR4K5xLmH65cLDC1RwRkFqN+gUmZpu1iiXEBlOPgkPJypRIu335u1bInv7zN9DfVOrFlFIiPaO\nFxkZSVZWFQguRwljihKsT6TIJ1ZWpQmIJeAO5xMDtyRkCbnOc6UrN66QlZU7Aco088nmzUTdugnP\nySiX8B0VPfL5KmcVYP9qoPwpoHRBhIeHQyaTwd/fD1JpI+TPXwnA7wAuIDb2KuTyYPTvPzTTAWwm\nJsI0xqGhwor3ixYBFSsCmzYJ3cSYbggM3AaXvu54cO05praZh5UrV6e6m2Zu7ozw8HDxgmQ6Lzmf\nyOsBezYBbcdDkr9+inxiZdUAQD8AJwE81DiXMP2xKWALas+ri/hDJbB3ZQWYm6+BseWSjO6oGNpA\n+k88PbU3oB4AHj0Kh0KxAQhvAlzrC7SbCzPzksn5ZO3aqbC09ARQEMAlcD4xTAs2LMSIv0Yiys8K\ndWo0gkr1AwDT/x5NmU/y5QM+fsz8mFyo6BEXFxckJYUDuAHI7YHdv0Pe9AmkjkIW9fHpgoiIe/jz\nz7EoUMAD2f1jI5F8nsZ46VJgzRrhVrG/P5CUlAsvjGksKioKff4YAGX5AlDufIQE+UlMnz738+cC\nAHADCkUEXFxcxAuU6bwU+SS8IXCtI+KbvUNBO2cAQj7Zt28brK1Lw9garsYiKioK/Tb/CIr5Dkmn\nrwP4gISEizC2XJJZoWJIA+k/0faA+l27yoPoI4AbwMnfAelzJFR5kPzZ8fHpgqCgZbC0nAHA/b9n\ncT4xJC9ev8DY8+OA4AmIe3wHiYn7oFC0ABD+3x4p84m1NRAfn/lxuVDRI1/eNbGxqQZp5Di0L9ke\no0JGQU3q5H1atmwJpTICOf1jI5EA3t7CNMZr1wJbtwJlygDLlwv9dlneu3r/KhStE4C9AUC8DEBl\nWFi4YuLEMZ8/F9JG8Pf340GKLENf5xOri1tg6xiHDnM34tM4Y09PT6jVz2BsDVdjERgaCFV5FbBv\nBwAJgFKwsioMS8sGRpVLjPGOijYLlZs3gY0brfHnn++FfJK/Fiz/egppUzM8VTxN3s/T0xMmJgEA\n3v23hfOJIfn56M8wjc8PhE7/b0tDAO6wsKiRZj7Jl0+zQoX7lOuhyMhIunTpEkVGRpJCpaDv1n5H\nM0/PTLFPQMBWkkrtycZG8zEqmjh/nqhlS6JixYgWLSKKj9fKYZkGVGoVNV7bmMyaWaXZh/zLz0V6\nYCB9ypn2fPm5uff6CZn9IqORcy8mP55buYSJ61XsK3Kc40jmZewJSEiRT+7cuZNpLiEynHzy9i2R\nnV3ar/HCBaIaNTJ8G/RSQgKRVKqdv+FNmxItWSL8+8t8svXmVnJf4k4xCTHJ+wYEbCUrq1Ikkbwn\nS8sqnE8MxIEHB6jYvGJkZVfwi/ZJFJmZzU43n1y5QuTpKfw7o1zCDQsD8PTDU3Kc60hnn55NsV2T\nhmt2Xb5M1K4dUZEiRHPmEMXGav0U7Ctzz86l2mtq08Ytm7PdcDSUhgXLPX4nd5LJKDc6fPJD8rbc\nzCUs76nUKvLe6E2+J3ypU6cbZGISZNT55P17IhubtF9jcDBR/foavyV6pWpVoosXM98vI4cPE5Uu\nTZSUlPbjA4IGUPdd3UmtVidvi4yMpL59X1CPHnyl0xC8iHlBReYVoZDwkOQLWwUK1CbgHS1dui/d\n5927R1SmjPDvjHIJr6NiIILuB+GnQz/h2qBrsJfa59l5b9wQ5sAODgZGjgSGDwdsbfPs9EbjwvML\n+D7we4QOCIVzQWdERUVlumZKWgxl3QOWu1r7DcOJi1EIm7UNRYvq3ceFZWJ6yHQcDjuM1XWD8V0d\nMxw9+g4q1WOjzSexsUDRosJK2V87dAhYvBg4fDgPA8wj/fsLSxIMHZq956tUQNWqwNSpQLt2ae8T\nr4hHjdU1MKb2GPTz7Je8/d9/hdXJL18GXF2zd34mPqVaCe+N3vBy9YJvA18Awti3RYvicPWqEw4d\nskz3uc+eAXXqCP/ldVSMwPdlv0cHjw7ou68v8rJBV7mysGjkqVPAvXtAqVLAb78B79/nWQgG7738\nPbru7IpVbVbBuaAw0Fkmk6FGjRoG33eciWPnwPmwcX2IBmNW8Ix/BiYkIgRLLy1FQIdAjPzJDBMm\nANWqFTLqfJLZOiqGOEYFABo2BI4fz/7zN20C7OyE2ULTk888H7Z32o7xx8bjduTt5O329kKBNH16\n+s9luu+PU3/AzMQME+tNTN4mkcgQEOCKsWPTL1IAzceocKFiQGY3mY1Xsa+w+OLiPD93uXJC0rpw\nQVhIyt0dmDgRePs2z0MxKESEfkH90M6jHdp5pHPJijEtszKzwslh2xHuNhl9J/KibIYi6mMUuu/u\njnVt1+HsoeJ49Uq4E27sjHHWLwBo2lQoVBSKrD9XoQD++AOYNi3zxTArOFbAHO856LyjMz4mfZ6P\ndtQoYNcu4NWrrJ+fie/Y42Pwv+aPLR22wNREmIJYqQS6dBF+vLwyfj4XKkbIwtQC2zptw4zTM3Dh\n+QVRYnB3F6YxvnJFuKtStiwwdizw+rUo4eiNqKgohIaGpppPfuGFhXgR8wJzmswRKTJmrDxkpfFn\nqyXYqvoBa7dEix0Oy4K08oma1Oixpwe6VeyG2rIWGDMGWLkSMDcXMVAdYYyzfgFA4cJCL4gL2Wgu\nbNwodNmqX1+z/ftU7YMaxWpgyIEhyb0+7O2FBu3q1Vk/P8s7aeWTl7Ev0WtPL2xstxGF8xcGIAyf\nHztWyCma3CmzshKWvEjvu/cJFyoGxtXOFavbrEaXnV3wLv5d5k/IJS4uwjTG168LH8Ty5YERI4S7\nLSylwMBtcHb2QJMmg+Hs7IHAwG0AgHPPzmH22dnY3nk7LEwtRI6SGaOBtX3QrrI3hhzuj+vXeYyQ\nPkgvn0wPmQ65Qo7pXtMxbpzQXad2bZGD1RGmpoBaLTS0vmbIhQoANG+e9fE3CoVwJ2XKFM2fI5FI\n4NfSD1dfXYX/Nf/k7cOGCQVzdu7qsNyXVj5RqpXw2eWDwd8MhpebcNvk+HGgVi3g7FkgMFD4l6bN\nowAAIABJREFUTmVGIhG+W3J5JjumN8o+pz/gWXpENfbIWGqxuQWp1CqxQyEioleviMaMEaaAHDSI\n6MkTsSPSDZGRkSSV2qeabvhOxB0qsaAE7b+/X6vng4HM0sPyjlwhJ5eZ1ahQy0X07p3Y0bCMpJdP\ndl7dSUXnFaUXMS/oxAmiEiWIoqNzfj5DyicmJkRKZerXOGeO8LfLUIWEEFWrlrXnrF5N5O2dvfPd\nibxDDnMc6Nqra8nb6tcn2r49e8djuSe9fPLTvp+o6aam9PadipYuFT4/pUsTBQYSqbLY5JTJiN68\nyTiX8B0VAzXDawZik2Ix4/QMAOl3LcorRYoA8+YB9+8Lt3urVwf69QMePRIlHJ0RHh4OCwsXfLny\nt5lFSfTd3xfdKnVD6zKtRYyOMWG8yvFBOxD/zXQ0+/E8Xr0SN5ew9KWVT0ztimLQkUHY1H4TCpo6\nYcAAwM8PsLERMVAdlF73L0O/o/Ltt0BYGPDmjWb7JyQIY1P++CN75ysnK4clzZeg0/ZO+JDwAVFR\nUWjW7BEWLUrK3gFZrkkrn8DDFtvvbkeL+M0o52GCs2eBWbOAu3eBrl0BkyxWFfnyAR8/ZrwPFyoG\nytzUHNs6bcPyy8vxy5qJaXYFEINMBsyYATx8CJQsKSTJnj2FGcOMkYuLC5KSwvHlyt/yWvdgbmmO\naY2niRgZY5+52bkhsOtaXC/dCSU8/HUil7DUUuUT0yuIb3Ufg6oOgpebF3x9gZo1gdZ8/SMVU1Ok\nOcOdIc/6BQjjCby8gKNHNdt/2TJhVfucdBv0qeSDFu4t4P2nN0o6l8Xs2d1x7tw7zJ17KPsHZVqX\nKp/Y/wW5dwQKh+xAwBoZjh4Vunk1aaJZV6+0WFtnPqCeCxUD5lTACX6N/TDr/izILbYgOvoK5PJg\n9O8/VPSrofb2wO+/C1dyPDyEAXldugA3b4oaVp6TyWTw9/eDVNoINjbVYFGxLmzq58POrjthZmIm\ndniMJavjUAvqa/FQtT+M6NiLOpNL2Gdf5xPTFnVRtUwVTG02FWfOCI2KpUvFjlI3ZXRHxVBn/fqk\neXPg4MHM9/vwAZg9W7jYmFMTqk3AtQfXkVC9J2JiLgIwwS+/hHM+0SFf5pMC9lUh6doBDrdmolHp\nejh/XlhDJ6c0mfmLCxUD56RwgtUVJ6DLJMBMDqAyzM2dER4eLnZoAITFIX/9FXj8GPjmG2G6xPbt\nhVnDjIWPTxdERNzDun2TYNPTCvt77U+eRYMxXREeHg7rUFdAbQF4TYSu5RIm+JRPxmxohxKNi+L4\n8GOQx5ugb19hgpNChcSOUDcZa9cvQFis8ciRzCe7mTNHuBtXvnzOz/ny2UtYH/QAau0ASh0FUBhq\ndRc8eBCR84MzrfHx6YLw8Lv4droT7BWd0NF5HBYuzP4dlK9xocLg4uICXIgH/nUAWg8BcB0KRYSw\nXYfkzw+MGycULI0aCTPStGqVvWkT9ZHUVorJdyZjauOpqFOiTqrHxR5jxJiLiwsUiRHAzklA+Z1A\nxc1ITFTpXC5hwHPlcyx9uBT7u+9HQauCmDBB6Gb7aWE+ziepGXOhIpMJq9TPmpX+PnfvAqtWZW2m\nr4y4uLhA+e9LYOd0oH1PwO4gJJLbuHevtHZOwLQm4HEArjx7hcYf18BvmSTFujk5zSXW1jxGxejJ\nZDKs9V8Oq6OXYFJsG8zr1oG/vx9kMplO/rGSSoVpjMPCgDZthMFZTZoAISFiR5Z7iAh99/XFt8W/\nxaDqg1I9nt50o4zlpeRuAGgP678sgBYDUdDjT1haCquZ62I+MUZv49+iw/YO8Gvph4qOFXHkCLBv\nH7BkifA455O0GXOhAggXCgMC0r6rkpgI+PgIXb5KlNDO+ZLzSeRYWF2ygMTne/QfrMSOHbYAOJ/o\niuAnwfj92CwUOLAHa1fmSzFYXhu5RKNFH9ObDiynP+DpRHVKZGQk7Tm5hxxmO1Dwk2AKCNhKUqk9\n2dpWI6nUngICtoodYpoSE4nWrCFycyNq0IDo2DEitVrsqLRr2qlpVHN1TZIr5KkeS296wMjIyGyd\nCwY0nSgTR2RkJF26dImWn1lBBSa5UOPWUbRp0za9yCeGLkmZRA3XN6Txf48nIqKoKCInJ6Ljx4XH\nOZ+kn08KFyZ6+TL1a2zdmmjfvmy9PXpn7FiiYcNSbx89mqh9+9z52xsZGUkXL16kLoFdqENgZ7Kz\nV9OSJUGcT3TA438fk2x2YbL1PEYXL6Z8TFu5pGdPog0bMs4l3LAwMsfCjpFstowsi9hq7Y9VXlAo\niDZuJCpblqh2baKDBw2jYNl7dy8Vm1+MXsS8SPPxS5cuka1ttf9+T8KPjY0nXbp0KVvnM6SGBRPf\nuCMTyPZ/9cnEfIVe5RNDNezAMGq1pRUpVUpSq4k6dEi5Bgjnk/TziZMT0bNnqV+jtzfR0aPZenv0\nzps3RPb2REuXCn9zP34k+v13ouLFid6+zd1zyxVyqrW6FlUb+RuZmc3gfCKy2MRYquRXicr2WkxT\np6Z+XFu5ZNAgouXLM84l3PXLyHi5eaGXay8oOiUCFq7/bdX9QbFmZsI0xrdvAyNHAj//LEyzuW+f\nsKKwProVeQsD9g/A7i674VTAKc190pq+WBfHGDHjNNN7Gsq5EdTNTuHLufZ1PZ8YolVXVuHEkxMI\n6BgAUxNTrFoldKGdPv3zPpxP0mfMs3594ugInDoF7NoFeHoCZcsCd+4Ap0/n/iQMVmZW2N1lN8Id\nVkDpXhicT8SjJjV67ekFh8SaML/2E8aPT72PtnKJJmNU+AqoEXrz5g2ZtrMk+DQgSJR6ecVCpSLa\nvZvI05OocmWibdvSXlVYV72Je0Oui1xp8/XNme77qZuejY1njm+Dw4CugDLdEPY8jCTDLAk1F/IV\nUJEcf3ycCs8tTA/ePiAiohs3iBwciO7dS70v55O084mLC1FYWOrXWK0aUWhott4evaVWEwUFEZ07\nl/fnPnzzCGGcHaHIfs4nIpl4bCJ9u6ouFS2eQGfPpr+fNnLJpElEf/yRcS7hhoWR2rhlM5n0NSOL\n1jK97gOqVhPt309UsyZRuXJEmzcLt6x1mVwhp9prapPvCV+Nn/NpXEBOk7UhNSyY7li0YQlhrDnB\nfTtZWLTW23yij+5F3SPHuY4U/CSYiIji4og8PIR+3+nhfJI6n5QqRfTgQerXWK4c0a1b2Xp7WDbV\nHzKLMKoQ5S9aUa/bJ/po/bX15LbYjX4cEUkDBmS+f05zyYwZRBMmZJxLJCR8abVOIpFQbh2baceD\nZw/gvdUbI2qMwNiGY8UOJ0eIgL//BqZOBV6/BiZOBHr0EFbd1SVEhB57ekCpViKwYyBMJHnb+1Ii\nkYCIJJnvqVs4n+i+v278BZ+9vWEWcAInt1VBlSpiR2T43sa/RW3/2phQdwL6V+sPIqB3b0AiATZs\nyP3zG1I+KVtW6Ers4ZFyX1dX4PhxwM0tDwM0cu/eAcW6ToNz80Ac8TkAFycXsUMyCiERIei0vRP8\nap7E8C7lceeOsDh3blq8WOiiunRp+rmEx6gYsTIlyuB4v+OYd3keDj08JHY4OSKRCItFhoQAa9YA\nmzcDZcoAK1cKUyvqikknJuHx+8dY33Z9nhcpjOWm1pVbY1X7P2HW83s07/wCT56IHZFhkyvkaLu1\nLTqW64j+1foDEPLdP/8ICzuyrDH26Yl1SaFCQNtCv8JOUQMjTo2ASp3GL4Zp1b2399B5R2dsar8F\nc38uj5kzc79IAYQxKrzgI8tQ6UKlsafLHvTe2xvXXl0TO5wck0iABg2EK2BbtgB79wLu7sDSpcIf\nnJzI6bzuq66swvY72xHUNQhSc/7LxwyPTyUfjGkwBKa9WsG7ZSxevxY7It2Vk3yiJjV67ukJZ1tn\nzPCaAQC4dAmYPFkYCJ0vn7ajNXzpFSoJCcYzmF6X9O8nQcKOVZAr5Bh5eCT4jnrGcpJP3sS9Qcst\nLTHbezYiTjSBmZlwZzYv8Mr0TCO1S9TG8lbL0SawDZ68N5zLoHXqAIcOAXv2CIVLqVLAggUazDCR\nhpwubLT//n5MDp6Mg90OQmYty3oAjOmJ8XXHo3XVbyHp2hHezZLw/r3YEemenOQTIsLoI6MRFR+F\ndW3XwURigtevgU6dhJXDS/PC3tnCd1R0i7c3EPPeAr+U2omQiBDMPjtb7JB0Vk7ySWxiLFoFtEKv\nKr3QungfTJoELFuGFAs75iZe8JFlybJLy6j0ktL0Ju6N2KHkin/+IercWVjYa+ZMouhozZ6X04WN\nzj49Sw5zHOji84uZ75zLYECDX5nuUqgU1C6wHZWd6EO1vlVRTIzYEemOnOaTmadnUiW/SvRe/p6I\niBISiOrUIfrtt1wMOh2GlE/Smt1LqSSSSAxjzS59NGsWUZ8+RM+jn5PzQmdae3Wt2CHpnJzkk0Rl\nInlv9KaBQQNJrVaTjw/RqFF5EPQXjhwR1irKKJfwHRWWbGiNoehasStabmmJmMQYscPRuipVgO3b\ngRMngBs3hDssU6Yg0yu+4eHhsLBwQXbmdb8deRvtt7XHpvabULNYzRy+Asb0g5mJGQI6BsDR/Tk+\nfjcKLVtRtu5kGqKc5JO119Zi5ZWVONzjMApaFQQRMGwYULiw0O2LZV9ad1Q+dfuS6N10AYahXz+h\n+7ZUWQyHexzGL8d/wf77+8UOS6dkN5+o1Cr03tsbBSwKwK+VH4KCJLh0CZg2LZcD/gqPUWFZNqXh\nFNRwqoHvA7+HXJHDQR06qnx5ICAAOHsWCA8XxrD8+ivw9m3a+2d3YaOwf8PQbHMzLGy2EM3dmydv\nz+lYF8b0gdRciiCfIJiWOoXY6lPw/fc5HydmCLKbT3bc3oFJJybhcPfDyQvEzpsHnD+vxMiRV/Du\nHeeTnEirUOFuX+KSyYBWrYD16wEPBw8E+QShf1B/BD8JFjs0nZGdfEJEGHpgKF7HvUZAxwDERJti\n6FDA3x/4+DFv2yfc9Ytli0qtou67ulPLLS0pUZkodji57vFjooEDiezticaNI3r9OvU+WV3Y6Fn0\nM3Jd5EorQlekeRxb22qizA8PA+qqwfTDm7g3VHZpWao2bB55eRF9/Ch2ROLLaj458OAAOc51pH9e\n/ZO8bccOInv7j2RlVZHziRbySd26RCEhKbc9fUpUrFi23x6mBWfPEpUuLSzyTEQU/CSYZHNkdOHZ\nBXED0yFZySdqtZrGHBlDNVfXpJiEGFKribp2JRo2TJz2yb17RGXKZJxLuGHB0pSkTKK2gW2pw7YO\nlKRMEjucPPH0KdHw4UR2dkQjRxK9eJHycU0XNnoZ85LKLi1Lc87MSfX8nPRN1wZDalgw/fH0w1Ny\nWehCNYcto0aNhEUJjZ2m+eRY2DFymONA555+Xib87FmiQoVUZGnZgPOJlvJJ/fpEwcEpt92/LywE\nycSjVhNVqUJ08ODnbX/d/4sc5zrSlZdXxAtMx2iaT3xP+FIlv0r0Lv4dEREtWUJUtSpRRIQ47ZNn\nz4SLARnlEu76xdJkbmqObZ22IVGZiO67u0OpVoodUq4rUUKYxvj2bWHGi4oVhf7fT58Kj8tkMtSo\nUQMyWfqzdr2Oe43GGxujZ+WeGFd3XIrHctI3nTF9VsK2BE70PoHXpWYjocJKtGgBxBjeMLgs0SSf\nnHhyAl13dcWuH3ahdonaAIBbt4D27YHJkx/CyioWnE+0I70xKtz1S1wSCfDzz8DMmZ+3tSrTCita\nrUDLLS3xz+t/xAtOh2iST6acnIJdd3fhWK9jsJfa4+xZYUzKrl3AmzfitE94emKWI5Zmltj5w07E\nJsWi++7uUKgUYoeUJ4oWFaYxvncPsLEBPD2BH38UVk/NyOu41/Da6IXvXb9HU2nTVH08s9s3nTFD\n4GrnihO9T+C523SY1FgJLy9hBWqWtuAnwfhh+w+YWmkqyuUrBwCIiABatAAWLgR8fOw5n2gRj1HR\nXT/8ALx4IYwr/aR9ufZY1nIZmm9uzsVKJogIf5z6AwE3AjC/8nxI4iV48EB4X9etA9zcxGuf8BgV\nphVyhZxabWlFbQPbUoIiIUvP1fR2pC57+5bI15eoUCGiXr2EPpVfe/rhKZVeUpo6Le2cYR/PrPZN\n1zYYUFcNpp8evXtEzgudyWviIipfXrj1rwlDyCWaOvTwENlMtSGLMgWSc8mff+4jd3eixYs/78f5\nRHv5pFmzlN2LiISuYPXrZ/fdYdq0YgVRq1apt++6s4sc5zpmecyKseQTtVpNE/6eQMVnFCcrh4Jk\na1uNLC2rk739R/L3T7mvGPlErSYyMck4l3DDgmkkUZlIHbd1pGabmtHHJM1Gw4o9cFzb3r8nmjqV\nSCYTBp/dvClsf/TuEbkucqUpR6do1MdTzARpSA0Lpr/C34eT+xJ3ajFjBpUoqabbtzPe39BySUb2\n3N1DDrMdyKJUgS9yyW2SSB7QpEmxqfbnfKKdfNKyJdH+/Sm3HTwoFDBMfHI5UdGiwnpoX/vr/l8k\nmyOjk09OanQsY8knKrWKRhwcQZWXVSYr+4Jf5JNEMjf/X5o5Q4x8kj8/FypMSxQqBfXa04tqr6md\nPBArPbowcDy3xMQQzZ4tLBzZyOcayWY50fLQ5XTp0iWyta323+sVfmxsPOnSpUtih5zMkBoWTL+9\niHlBFf0qUouFo0nmqKJTp9Lez5BzyddWX1lNReYVoQ1/b0iVSywt/XQqlxAZVj5p04Zo796U23bt\nImrXLttvD9Oy+fOJWrdO+7FjYcdINkdGe+7uyfAYxpJPkpRJ1GN3D6rrX5eOnz2u020TR8eMcwmP\nUWEaMzMxw7q261C3RF3UW1cPz2Oep7uvIQ8cL1BAGNy3/uRJhHo0g3L/YhyYMhjv3rlzn3HGNORU\nwAkhfUIQY3MRlX/rjY4/JGHz5tT7GXIu+YSIMOP0DMw4PQOn+pxCiyot/ssld//b4zUkkkmcS3KR\nmRmPUdF1w4YB9+8DBw6kfszLzQsHux/EkANDsObqmnSPYQz55GPSR7Td2hYfEj7gaM+jcC1aGXFx\nQwAk/beHbrVN8uXL+HEuVFiWmEhMMLfpXPT37I/a/rVx9dXV5Me+XMjQ0AeOb7y+Eb3/6oKgnlvx\n8lgntGgBDBxoB3f3W7CwmAAbm2qQShvB398vw1k4GDNmdlI7HO15FPntY+E2uTl++eM9fH0Btfpz\nPsmfP79B5xKFSoGB+wdi++3tONPvDMoUKgOZTIYZMzZAIpHC0nIBpNIKWLuWc0lu4sH0us/SEliy\nBBg5UpiR7WvfOH2DkD4hmHVmFiYenwg1qZMfM5Z88jL2Jeqtq4ei+YtiT5c9OHEkHxo2dEDdul6w\nsiqnk22TzAoV7qrBsm3XnV0kmyOjfff2pdnnU5OBWfo2oE2lVpHvCV9yXeRKtyNTdqxPTCRavZqo\nZEklVa8eTbt3vye1WqRA0wED6qrBDIdSpaRRh0dR6UUeVL3JI6pe/TlZWTkn55Phw0cYXC4hInov\nf0/eG72p1ZZWFJMQk7z90iWiIkWI5s2L0enXZEj5pEsXosDAlNuWLCEaOjTbbw/LJe3aCeNF0xMZ\nF0l1/OvQDzt+oPik+FTtE0PNJ9deXaMSC0rQjJAZFBampu+/J3J3Jzp2THhcV19TjRoZ5xJuWLAc\nufj8IhWdW5TMvKQEybVUfT4z+mLo24C26IRoare1HX2z/Bs6dPpQul/2pCSi9euF1Vbr1CE6dIh0\npmAxpIYFMzzLQ5eTwywHMik9mgB5inxy584dg8klRES33twi9yXuNGDXADp34Vzy6zpwgMjBIfV4\nCV1kSPmkWzeizZtTbps9m2jMmGy/PSyXPHkiTGpz+nT6+8gVcuq2qxtVXlaZLB1tU41JuXPnDh05\ncpVmzYqh/v2JmjYlatBAWOx5+PBzZGVVRK/ySeDNQCo0qxBN2z2DfH1jqVAhounTiRKyNlGrKBo0\n4EKFadnXxcfBkINkMtCa0KUdwfKDRgO19G1A292ou1Tuz3LktdCbrKztNEpgSiVRQABR+fLCFYN9\n+8QvWAypYcEMw9f5ZMXhFSQZa0aoO4sgUWWaT/QtlxAR7by9kxzmONDg5UOSCywrK3vq3v0aFSki\nrDyvDwwpn/TsSbRhQ8ptv/9ONGlStt8elosOHRLuOj55knL7l/lErVbTyK0jhXziejx5IHm+fH3p\nu+/ek62tUKCuWCHM8Hb0KJGvbyyZmJwgIEEv8kmSMonGHR1HsmkyMi9RkUxNb5KJSQgtWrQ/8yfr\niBYtMs4lPEaFZUlg4DY4O3ugSZPBcHb2QGDgNjy98xxqfxUQawkMqgY4BWba51OfBrRtvL4R9dbV\nw4CKA3Bu4lUkfDyJ6OgrkMuD0b//0FQLO35iagr4+AA3bwLjxwO//SYsHrlzp9AHnzFjl1Y+QbgJ\naJUp4BEA+LQB8r3Ax49j4eDgmuYx9CmXJCgT8NPBnzDu73HY0mILNozeBrk8GNHRV5CQ8BABAaY4\nePAd6tQRO1LjY2oKKJUpt/EYFd3VvDnwyy9AmzZAZKSw7et8snXrdpT7UAG0ywTo0BVo+BsgiYZc\nPhnt25vixQtgyxZg0CBhIdUmTYA2be6iQIGxACz/O1NlmJmV0cl88iz6GRpuaIjLzy7jw9x6UDy7\nBpWqItRqW/zyS+902ya6xto6kx3Sq2By+gO+Ampw0rpyaWVV8L9tswmwJ5QvSRgH6jC/IylVyiwd\nS9euWnyQf6Ceu3uSx58edOP1jRxPP6xWEwUFCXdXKlQQ7rYo03+LcgUM6Aoo02+Z5hMTO4K3jDDK\nhCq0WUPu7kTnz2t2HF3LJURCVy/PFZ7UYVsHei9/n2Y+KVCgts5MGaoJQ8on/fsTrVqVctvIkUQL\nFmT77WG5TK0mmjxZWF9ly5YPaeYTK6tCBGwl5N9N6FWH0Kco/bFkZrrHTJ1P3pOJyTm6fz8qD19Z\n5nbc3kGOcx1p5ulZNHRYOEkkr3V2+uHM9OqVcS7hOypMY2lduTQ1dYSJSQkAPwO4B9zZiXwBZfDE\n/DEabmiIx+8fp3ksmUwGf38/SKWNdHIWiuOPj6PyisqwNrdG6IBQVCpcKcczmUkkwtWfixeB+fOB\nP/8EypcHNmwAFIpceiGM6ahM84n6PnDsAKyOlkBU3YlwHzEcbTt/xNixwpXuT3Q9l6jUKsw/Nx8N\nNzTEkG+GYGfnnShoVRDOzi6Ij68F4NNl/BtQKu8bzOxD+oZn/dI/EgkwZQqwdSswdqwVFIoD+DKf\nKJXzkJh4E0AXIM4b2LQAFhFqLIibjbXX1n4qWlP4Op9YWbmjeXN7dOnigLi4vHx1aXsvf48eu3tg\n4vGJ2NtlH+KPjkfwiWKwtGwMfZ3JjGf9YlqT8RXQlFczX795TfPPzadCswvR7DOzKUmZlO4xdWkW\niqiPUdR3b18qvqA4HX54ONXjmsxkpim1muj4caKGDYlcXYWreYmJOYk+czCgK6BMv2Ulnzx4+oB6\n7u5JJee7UP1+B8ndnejIkdTH06VcQiTMwlNjVQ2qv64+hf0blrw9MpKofXuiEiXek6Vlfa3kEzEY\nUj4ZMoTozz9TbuvZU5gYhem+x48jycKiBwGR/+WOd2RmNpUsLeulyicn754kzxWe5LXBix68fZDm\n8VKOdRHuuH3/fd73gvhErVZTwI0AKjqvKP108CeKS/xIvr5EFSsK+USbbZO8Nnp0xrmEGxYsS9L6\nMmT0BQn7N4yabWpGlfwq0fHHx0WMPGMKlYJWXl5JhecWppGHRqaYKvRrudEgOn1amHWkRAnhj6Vc\nrrVDp2BIDQum/7KaT448OkJui92ozuKOVLzSY+rcmSg8XMQXkI538e9o5KGRJJsjozVX1pBKrSIi\n4eLEunXCSszjxgkz8uhigaUpQ8onw4cTLV6cclunTkTbtmX77WF5LCv5RKFSJF9M9T3hS7GJsRke\nOzFRuKgoxixwt97coiYbm1Dl5ZXp/DOh/+vixUTlyhG9efN5P33NJb6+XKgwLUvry5DRF0StVtPO\n2zvJbbEbtQloQ7fe3MrLcDOkVqvpwIMDVNGvIjVY14CuvLwiajwXLxK1aSP0uV2wgOjjR+0e35Aa\nFswwZDWfxCfF09RTU6nQ7EJU57dxVNDpLf38M9H793kZddrkCjktPL+QZHNkNHj/YHoT97kVceUK\nUf36RNWrC/82BIaUT9Iaj9KqlTCukOmPrOaTiA8R1G1XN3Ka70RrrqxJt/cHEdG7d0RubkQ7d+ZK\n6Km8iHlBg/cPJtkcGS06vyg5toMH057xTF/NnMmFCtMRCYoEmnd2HjnOdaQfdvxA119fFy0WlVpF\nf93/i2qurknll5Wn3Xd2k1rsuYO/cPUqUceORIULE82aRRST/g2eLDGkhgUzbi9jXtLAoIFUcKY9\nVRk9keyKRdLvvxN9+JD3sXxM+khLLiwhp/lOqS7GhIUJXYiKFCFavly8riO5wZDyyejRRHPnptzW\nuDHR339n++1heuTCswvUaH0jclvsRv5X/SlRmXY/7AsXhDuiz57lXizPop/RiIMjyG6WHY0+PJre\nxb9Lfuz2bWENmTNncu/8eW3x4oxzCQ+mZ3nG0swSY+qMQdiIMFQvWh3NNzeH90ZvBN0PglKtzPwA\nWhCTGIPloctRfll5/HriV4ypPQY3h9xE+3LtIZFI8iQGTXyaxvjYMeCff4BSpYCpU4EPH8SOjDHd\nULRAUaxssxLXBl9BrYZvoRpWBptj+qNkrWsYMwaIiMj9GMI/hGPCsQlwXuSME+EnENQ1CEE+Qajg\nWAF37wJ9+gA1awIuLsCDB8DgwcKgbaZ7eDC9catVvBZO9D6BdW3XYeutrXBZ5II/Tv2BV7GvUu5X\nCxgxAujZM/XnJSeICGefnkXXnV1ReXllmJmY4c6wO5jfbD7spfYAgLg4oGNHYPZsoG5d7Z1bbJkN\nppcQpZ71QBskEgnl1rGZboiKikJ4eDhcXFyyNcNOkioJO27vwLLQZXj8/jG6VeqGzuXGQfX9AAAO\noklEQVQ7o1bxWjCRaK+GlivkOP7kOAJvBeLAgwPwcvPCiJojUN+5vk4VJxm5fx+YMQM4cAAYMgT4\n3/+AQoWyfhyJRAIi0o8X/QXOJ4Ytp7kEAN7Gv8XKyyuxInQ1EqNtEXeuJ2rZtseIHqXQqhVgYaGd\nWN/EvcH+B/ux+cZm3Iq8hZ6Ve2J4zeEoZV8KSUnAwYPAsmXC+klDhwqNmoIFtXNuXWNI+eSXX4AC\nBYCJEz9v8/QE/P2BatXyOECWI9rIJ7cib2HpxaXYfmc7vi3+LXpU6oGWpVvCTmoHlQpo3Bho3RoY\nNy77cRIR7r69i913d2Pj9Y0wkZhg8DeD0bdqX9ha2X61L9C7t1BQr1uX/XPqosBAoFu39HMJFyos\nWwIDt6F//6GwsBCm7PX394OPT5dsH+/BuwfYdH0T9tzbg6j4KDQr1Qz1StZD3ZJ1UaZQGZiZmGl8\nLLlCjhtvbuD009M4FXEKp8JPoVrRauhYriN8KvnAIZ+DxsfSRsLTprAwYNYsYPduYMAAYPRowNFR\n8+cbUsOCGQZt5xI1qRESEYL1Vzdjz+39UMY4QPXIG7Wd6qFno2/RqWkx2Nho/hV4F/8OoS9DcTri\nNE6En8DdqLtoUqoJfCr6oFXpViClJU6dAvbsEe6ClisnLCDXuTNgaZnyWLqWT3LKkPLJpEnC78vX\n9/M2Dw/h91quXB4HyLJN2/kkXhGPPXf3YOvtrcltiYYuDVHaoj5+6lQdZ4/bavz5ICJEREfg/LPz\nOP30NI6GHUWSKglty7ZFj8o9ULNYzXQvnq5bB8ybB1y6JCyQaEi5ZN8+oF07LlSYFkVFRcHZ2QNy\neTCEOctvQCpthIiIe1r5woT9G4Zjj4/hzLMzOBN+Bq/iXsGlgAsKWxaGq8wVxe2Lw8rMChamFkhQ\nJkCukOPNxzd4GfsSj/59hBexL1C2UFl8V/I71CtZD95u3iiUL+u3Hz4lPDOzYkhKisDixfMwaNCA\nHL8+bYiIAObMEa5E9OkjXNUpWjTz5xlSw4Lpv9zOJWpS49KLS9h3/SSC/jmNh/GXoVAnQfrRHU7W\nJVHWqQRcitqgqEwKc1MTyJVyxCXF4VXcK7yIeYF7b+9BrpTDs4gn6pWsh3ol68PNrD4e3bPEpUvA\nuXPA+fNApUrC1dWuXYVuXmkJDNyGfv0Gw9S0MFSqN1i7dkWOGlC6wJDyyW+/Cety/P77523OzsCp\nU+n/Tpluye18Eq+IR/CTYIREhODMszO4/Ow61PG2qFDEEWWKlIaLgwusza1hZWYFFakgV8gRnRiN\nl7Ev8TT6Ke6+vQsbSxvULFYT9UrWQ2PXxqhSuEqmPTvu3we++w44eRKoUEG32ybZ8fffQNOmXKgw\nLQoNDUWTJoMRHX0leZuNTTUcO7YSNWrU0Np5Pn0ZydwGCdavYCErDMr/Fu18WqN0OXckqZJgZWYF\nqbkUjtaOcCrgBNeCrnC3d4e5qXmOzv054Y0HMBtACQAPsGLFYp1KCC9fAnPnCotGdusGjB8PlCiR\n/v6G1LBg+i+vcgkg5JPevQdAYW4GONSCxNYGTmXLIV4pQYxcjvz5CQWkUthYWaOApChsJEUhlZeB\nSVxxfHgvwatXwIsXQP78whX2mjWBOnWEBoS9fcbnjoqKQrFipaBQmAFwBfAE5uYKvHjxWK+vhhpS\nPvnjD2Hh3alTP29zdBS68BUunMcBsmzJ63zSs9cAqPKvAgodh2nBLejctx3KlC8NuVIOU4kppOZS\n2FrawqmAE4rZFEM5h3Kwk9pl6TyJiUDt2sDAgcIYN31pm2TF2bPAd99xocK0KLevWqQ8xy4AHQHk\n3rnSEhoaCi+v/oiNfZHi3JaWDfDs2QOda1y8eQMsWACsWSMMtvvlF8DVNfV+htSwYPovL3LJp/OU\nLFkGCQkSACdTncvGRoZnz4TvUVQUkJAg/JibA1ZWgK2tcMeyWLHsjTc5evQomjVrD+B88rmB2jhy\nZA+aNm2qtdeZ1wwpn0yfDnz8KIwF/KRAAaE4tbHJ4wBZtoiTT84CKAfgPqTSOlo/17hxwMOHQhdE\niUT/2iaa+OcfwNMz/Vyiecd/xv4jk8ng7++H/v0bwdzcGQpFBPz9/bT6BQkPD4eFhQvkcmsALhC+\njABQGebmzggPD8/VL6SLiwuSkiIgXP38fG4LC5dcP3d2FC4szAQybhywaBFQo4bQFWXiRKBMGbGj\nYyxteZFLACGfmJoWBmCNL7/PJibFER4ejho1ZHB3B9zdtXrarzilODegQV9Nlmd41i/9J04++TRA\npSwkEu22D44eFbp3//OPUKQA+tc20URms37x9MQsW3x8uiAi4h6OHVuJiIh7Wu9rLXwZwwF8BBAO\n4QokANyAQhEBlyx2Go6KikJoaCiioqI02l8mk2Hx4nkAHqQ4t1L5NMvnzksODsC0acCjR8KUxnXr\nAt27A3fuiB0ZY2nL7VwCCPlEpXoD4Am+/D6r1c9zPZcAgKenJywsolKc28LiLTw9PbN0bpZ7vi5U\nFArhv+Y560XM8ph4+SQGSUmdtZZPXr8Wxp9u3Cj8Xf9EX9smGcmsUOEF2pjOCgjYSlKpPVlZuRAg\nJam0Ikml9hQQsDVbx7G1rZbl569YsYosLQtSgQJVs3VusUVHC6u+OjoSdepkWAu0MZYVAQFbydw8\nPwH5CChFFha2eZpLPj3X2rqyXuaStBhSPpk/n+h///v8/9HRRPnz5+jtYQbs63xibl6WbGzkdPZs\n1o6RVj5RqYi8vYl8fdN/rr63Tb6kUGScS3iMCtNpn6bgy58/P+Li4rI8FZ82+qwawjSAHz8CK1cC\nY8YYTp9yxrIqKioK165dAyDc5eBckjOGNEZl8WJh+vclS4T/j4wUZljKwo0zZmS+zicXL8owdChw\n9WrKuyDpPTe9fOLnJ8Px48CJE4BZBgM0DCmfZJRLeIwK02kymSxHX8DPY12yP8YlpzHoAmtrYc2V\nMWPEjoQx8chksmwPXudcYti+7vrF41NYZr7OJ61bAyEhwqr1Bw4AJhkMrkgvn6xeHY21a2W4eDHj\nIuXT+Y0hn/AYFWbQPo91ydkYF8aYceNcYti4UGHaMH06EBcH/PyzsJp8etLKJ4mJ9li40A1BQUCR\nInkQrJ7gQoUZtE+zgEiljWBjUw1SaaNcmQWEMWbYOJcYNi5UmDaYmwsrrR85IhQt6fk6n1hajoRU\nuh+rV5ugSpW8i1cf8BgVZhQMqS9nThhSn3LGxMC55DNDyif+/sLCc2vXCv9/7pzQVfb8eRECZHrv\n1Sugfn2gXz9hIeb0uoFFRUVh16538PUtg1WrTNC+fd7GqSt4jAozesbSl5Mxlrs4lxgmvqPCtKlo\nUeD4caBrVyA4GFi/HnBySrlPXBywdKkMy5fLsHUr4OUlSqg6jwsVxhhjjBk1MzMuVJh2lSwpDK6f\nMUOYQc7LC2jWDFCrgfv3gW3bgIYNgStXhH1Z2rhQYYwxxphR4zsqLDeYmQGTJwODBgGHDwurzVtZ\nAWXLAnv3AjVqiB2h7uNChTHGGGNGjQsVlpsKFwZ69xZ+WNbwrF+MMcYYM2pcqDCmm7hQYYwxxphR\n40KFMd3EhQpjjDHGjBoXKozpJi5UGGOMMWbUTE0BpfLz/3Ohwphu4EKFMcYYY0aN76gwppu4UGGM\nMcaYUeNChTHdxIUKY4wxxowaFyqM6SYuVBhjjDFm1L4uVBISuFBhTBdwocIYY4wxo8Z3VBjTTVyo\nMMYYY8yopVWoWFmJFw9jTMCFCmOMMcaMGt9RYUw3caHCGGOMMaPGhQpjuokLFcYYY4wZNS5UGNNN\nXKgwxhhjzKhxocKYbuJChTHGGGNGjQsVxnQTFyqMMcYYM2pcqDCmm7hQYYwxxphR40KFMd3EhQpj\njDHGjNqXhQoRr0zPmK7gQoUxxhhjRu3LQiUxETA3B0y4hcSY6PhryBhjjDGj9mWhwt2+GNMdXKgw\nxhhjzKhxocKYbuJChTHGGGNGjQsVxnQTFyqMMcYYM2pfFio8kJ4x3cGFCmOMMcaMGt9RYUw3caHC\nGGOMMaNmZsaFCmO6iAsVxhhjjBk1vqPCmG7iQoUxxhhjRo0LFcZ0ExcqjDHGGDNqXKgwppu4UGGM\nMcaYUZNIhB+1WihUrKzEjogxBnChwhhjjDGWfFeF76gwpju4UGGMMcaY0eNChTHdw4UKY4wxxoye\nqSmgVHKhwpgu4UKFMcYYY0aP76gwpnu4UGGMMcaY0eNChTHdw4UKY4wxxoyeqSmwYwewdStQtqzY\n0TDGAEBCRLlzYImEcuvYjLHskUgkICKJ2HFkFecTxnSPoeWTokWBggWBNWuAunVFCIwxI5VRLuFC\nhTEjYmgNC8aYeAwtn1y+DFSsyGuoMJbXuFBhjAEwvIYFY0w8nE8YY9qQUS7hMSqMMcYYY4wxncOF\nCmOMMcYYY0zncKHCGGOMMcYY0zlcqDDGGGP/b+cOcaQIoyiM3ksGAhlQOBwWPWoUG2EJbALHSsCy\nAwwKRcIOWAQC8Y/BkNAIUpN6lTonadt5onOTL9XdAIwjVAAAgHGECgAAMI5QAQAAxhEqAADAOEIF\nAAAYR6gAAADjCBUAAGAcoQIAAIwjVAAAgHGECgAAMI5QAQAAxhEqAADAOEIFAAAYR6gAAADjXN3n\nm7e9z7cHTsSeAFuxJ3AMXWvtfQMAAMAffPULAAAYR6gAAADjCBUAAGAcoQIAAIwjVAAAgHGECn/V\n9qbtt7aP2l63/d721d53AcdjT4Ct2JNz8ffEXNT2XZInv18/1lrvdz4JOCh7AmzFnpyHUOGitg+T\nfE3yM8nt8mEB/pM9AbZiT87DV7/4l+dJniZ5luTxzrcAx2ZPgK3Yk5PwRIWL2n5K8iHJyyQv1lpv\ndz4JOCh7AmzFnpzH1d4HMFPbN0l+rbU+tn2Q5Evb12utzzufBhyMPQG2Yk/OxRMVAABgHL9RAQAA\nxhEqAADAOEIFAAAYR6gAAADjCBUAAGAcoQIAAIwjVAAAgHGECgAAMM4dEGDnOZHNB3kAAAAASUVO\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1b672a52b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(__doc__)\n",
    "\n",
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.model_selection import cross_val_score\n",
    "\n",
    "np.random.seed(0)\n",
    "\n",
    "n_samples = 30\n",
    "degrees = [1, 4, 15]\n",
    "\n",
    "true_fun = lambda X: np.cos(1.5 * np.pi * X)\n",
    "X = np.sort(np.random.rand(n_samples))\n",
    "y = true_fun(X) + np.random.randn(n_samples) * 0.1\n",
    "\n",
    "plt.figure(figsize=(14, 5))\n",
    "for i in range(len(degrees)):\n",
    "    ax = plt.subplot(1, len(degrees), i + 1)\n",
    "    plt.setp(ax, xticks=(), yticks=())\n",
    "\n",
    "    polynomial_features = PolynomialFeatures(degree=degrees[i],\n",
    "                                             include_bias=False)\n",
    "    linear_regression = LinearRegression()\n",
    "    pipeline = Pipeline([(\"polynomial_features\", polynomial_features),\n",
    "                         (\"linear_regression\", linear_regression)])\n",
    "    pipeline.fit(X[:, np.newaxis], y)\n",
    "\n",
    "    # Evaluate the models using crossvalidation\n",
    "    scores = cross_val_score(pipeline, X[:, np.newaxis], y,\n",
    "                             scoring=\"neg_mean_squared_error\", cv=10)\n",
    "\n",
    "    X_test = np.linspace(0, 1, 100)\n",
    "    plt.plot(X_test, pipeline.predict(X_test[:, np.newaxis]), label=\"Model\")\n",
    "    plt.plot(X_test, true_fun(X_test), label=\"True function\")\n",
    "    plt.scatter(X, y, label=\"Samples\")\n",
    "    plt.xlabel(\"x\")\n",
    "    plt.ylabel(\"y\")\n",
    "    plt.xlim((0, 1))\n",
    "    plt.ylim((-2, 2))\n",
    "    plt.legend(loc=\"best\")\n",
    "    plt.title(\"Degree {}\\nMSE = {:.2e}(+/- {:.2e})\".format(\n",
    "        degrees[i], -scores.mean(), scores.std()))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Model Selection - Measuring Performance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "**Hyperparameter optimization or model selection** is the problem of choosing a set of hyperparameters for a learning algorithm, usually with the goal of optimizing a measure of the algorithm's performance on an independent data set. \n",
    "\n",
    "In effect, learning algorithms learn parameters that model/reconstruct their inputs well, while hyperparameter optimization is to **ensure the model does not overfit its data by tuning**, e.g., regularization.\n",
    "\n",
    "https://en.wikipedia.org/wiki/Hyperparameter_optimization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "##### Training set, validation set, testing set\n",
    "\n",
    "<img src =\"imgs/training-validation-testing.jpeg\" width=\"60%\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "##### K-fold cross-validation\n",
    "\n",
    "Data (labeled) is precious, and this approach lets us only use ~ (k-1)/k of our data for training. On the other hand, we will only ever try to apply our model 1/k-1 of our data for testing.\n",
    "A common way to use more of the data to build a model, but also get a more robust estimate of the generalization performance, is cross-validation.\n",
    "In cross-validation, the data is split repeatedly into a training and non-overlapping test-sets, with a separate model built for every pair. The test-set scores are then aggregated for a more robust estimate.\n",
    "\n",
    "The data is first split into k (often 5 or 10) equal-sized folds, and then for each iteration, one of the k folds is used as test data, and the rest as training data:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "##### Steps for K-fold cross-validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "1. Split the dataset into K **equal** partitions (or \"folds\").\n",
    "2. Use fold 1 as the **testing set** and the union of the other folds as the **training set**.\n",
    "3. Calculate **testing accuracy**.\n",
    "4. Repeat steps 2 and 3 K times, using a **different fold** as the testing set each time.\n",
    "5. Use the **average testing accuracy** as the estimate of out-of-sample accuracy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Diagram of **5-fold cross-validation:**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<img src =\"imgs/07_cross_validation_diagram.png\" width=\"50%\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Minimize loss function (Optimization)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "##### Loss function\n",
    "A loss function or cost function is a function that maps an event or values (prediction) onto a real number intuitively representing some \"cost\" associated with the event. It's a way of measuring how well your classification or regression algorithm is working. \n",
    "\n",
    "<img src =\"imgs/Costfunction.png\" width=\"25%\" align=left><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "##### (Batch) gradient descent\n",
    "\n",
    "Gradient descent is a first-order iterative optimization algorithm. To find a local minimum of a function using gradient descent, one takes steps proportional to the negative of the gradient (or of the approximate gradient) of the function at the current point."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "##### Graident descent\n",
    "\n",
    "<img src =\"imgs/gradientdescent00.png\" width=\"50%\" align=left><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "##### Stochastic gradient descnet\n",
    "Batch gradient descent performs **redundant computations for large datasets**, as it recomputes gradients for similar examples before each parameter update. SGD does away with this redundancy by performing one update at a time. It is therefore usually much faster and can also be used to learn online. \n",
    "\n",
    "Stochastic gradient descent (often shortened in SGD), also known as **incremental gradient descent**, is a stochastic approximation of the gradient descent optimization method for minimizing an objective function that is written as a sum of differentiable functions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<img src =\"imgs/gradientdescent3.png\" width=\"50%\" align=left><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "##### Momentum\n",
    "\n",
    "SGD has trouble **navigating ravines**, i.e. areas where the surface curves much more steeply in one dimension than in another, which are common around local optima. In these scenarios, SGD oscillates across the slopes of the ravine while only making hesitant progress along the bottom towards the local optimum as in Image 2.\n",
    "\n",
    "Momentum is a method that helps accelerate SGD in the relevant direction and dampens oscillations as can be seen in Image 3. It does this by adding a fraction γγ of the update vector of the past time step to the current update vector:\n",
    "\n",
    "http://sebastianruder.com/optimizing-gradient-descent/index.html#momentum"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<img src =\"imgs/Momentum1.png\" width=\"20%\" align=left><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<img src =\"imgs/Momentum2.png\" width=\"70%\" align=left><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "##### Learning rate decay\n",
    "\n",
    "In training highly complex model, it is usually helpful to anneal the learning rate over time. Good intuition to have in mind is that with a high learning rate, the system contains too much kinetic energy and the parameter vector bounces around chaotically, unable to settle down into deeper, but narrower parts of the loss function. **Knowing when to decay the learning rate can be tricky**: Decay it slowly and you’ll be wasting computation bouncing around chaotically with little improvement for a long time. But decay it too aggressively and the system will cool too quickly, unable to reach the best position it can.\n",
    "\n",
    "http://cs231n.github.io/neural-networks-3/#anneal"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "Problems with the learning rate. On the left, slow convergence, and oscillation on the right."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<img src =\"imgs/learningrate1.png\" align=left><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<img src =\"imgs/learningrate2.png\" align=left><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Regularization\n",
    "\n",
    "Regularization, in mathematics and statistics and particularly in the fields of machine learning and inverse problems, refers to a process of introducing additional information in order to solve an ill-posed problem or to prevent overfitting. \n",
    "\n",
    "Add a **penalty term(regularization term)** on the complexity of cost function for constraining model complexity.\n",
    "\n",
    "<img src =\"imgs/regularization.png\" width=\"35%\" align=left>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "* Ridge Regression = L2 Regularization (Regularization)\n",
    "* Lazzo Regression = L1 Regularization (Regularization + variable selection)\n",
    "\n",
    "<img src =\"imgs/lassoridge.png\" width=\"70%\" align=left><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Early Stopping\n",
    "\n",
    "Up to a point, this improves the learner's performance on data outside of the training set. Past that point, however, improving the learner's fit to the training data comes at the expense of increased generalization error. Early stopping rules provide guidance as to how many iterations can be run before the learner begins to over-fit. \n",
    "\n",
    "https://en.wikipedia.org/wiki/Early_stopping"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "<img src =\"imgs/early-stopping.png\" width=\"60%\" align=left><br>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reference\n",
    "\n",
    "not finished"
   ]
  }
 ],
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