Morten Hjorth-Jensen
1772 lines
428 KiB
Plaintext
1772 lines
428 KiB
Plaintext
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"# Decision trees, overarching aims\n",
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"\n",
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"\n",
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"We start here with the most basic algorithm, the so-called decision\n",
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"tree. With this basic algorithm we can in turn build more complex\n",
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"networks, spanning from homogeneous and heterogenous forests (bagging,\n",
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"random forests and more) to one of the most popular supervised\n",
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"algorithms nowadays, the extreme gradient boosting, or just\n",
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"XGBoost. But let us start with the simplest possible ingredient.\n",
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"\n",
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"Decision trees are supervised learning algorithms used for both,\n",
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"classification and regression tasks.\n",
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"\n",
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"\n",
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"The main idea of decision trees\n",
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"is to find those descriptive features which contain the most\n",
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"**information** regarding the target feature and then split the dataset\n",
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"along the values of these features such that the target feature values\n",
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"for the resulting underlying datasets are as pure as possible.\n",
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"\n",
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"The descriptive features which reproduce best the target/output features are normally said\n",
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"to be the most informative ones. The process of finding the **most\n",
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"informative** feature is done until we accomplish a stopping criteria\n",
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"where we then finally end up in so called **leaf nodes**. \n",
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"\n",
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"## Basics of a tree\n",
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"\n",
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"A decision tree is typically divided into a **root node**, the **interior nodes**,\n",
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"and the final **leaf nodes** or just **leaves**. These entities are then connected by so-called **branches**.\n",
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"\n",
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"The leaf nodes\n",
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"contain the predictions we will make for new query instances presented\n",
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"to our trained model. This is possible since the model has \n",
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"learned the underlying structure of the training data and hence can,\n",
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"given some assumptions, make predictions about the target feature value\n",
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"(class) of unseen query instances.\n",
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"\n",
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"\n",
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"## General Features\n",
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"\n",
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"The overarching approach to decision trees is a top-down approach.\n",
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"\n",
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"* A leaf provides the classification of a given instance.\n",
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"\n",
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"* A node specifies a test of some attribute of the instance.\n",
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"\n",
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"* A branch corresponds to a possible values of an attribute.\n",
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"\n",
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"* An instance is classified by starting at the root node of the tree, testing the attribute specified by this node, then moving down the tree branch corresponding to the value of the attribute in the given example.\n",
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"\n",
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"This process is then repeated for the subtree rooted at the new\n",
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"node.\n",
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"\n",
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"\n",
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"\n",
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"In simplified terms, the process of training a decision tree and\n",
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"predicting the target features of query instances is as follows:\n",
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"\n",
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"1. Present a dataset containing of a number of training instances characterized by a number of descriptive features and a target feature\n",
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"\n",
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"2. Train the decision tree model by continuously splitting the target feature along the values of the descriptive features using a measure of information gain during the training process\n",
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"\n",
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"3. Grow the tree until we accomplish a stopping criteria create leaf nodes which represent the *predictions* we want to make for new query instances\n",
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"\n",
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"4. Show query instances to the tree and run down the tree until we arrive at leaf nodes\n",
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"\n",
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"Then we are essentially done!"
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"text": [
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"2nd degree coefficients:\n",
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"zero power: -0.22158725223474995\n",
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"first power: 0.24121476598003452\n",
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"second power: -0.0009532583857747255\n"
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]
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",
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"<Figure size 640x480 with 1 Axes>"
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"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_1_1.png"
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{
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_1_2.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"%matplotlib inline\n",
|
||
"\n",
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from sklearn.preprocessing import PolynomialFeatures\n",
|
||
"from sklearn.linear_model import LinearRegression\n",
|
||
"\n",
|
||
"steps=250\n",
|
||
"\n",
|
||
"distance=0\n",
|
||
"x=0\n",
|
||
"distance_list=[]\n",
|
||
"steps_list=[]\n",
|
||
"while x<steps:\n",
|
||
" distance+=np.random.randint(-1,2)\n",
|
||
" distance_list.append(distance)\n",
|
||
" x+=1\n",
|
||
" steps_list.append(x)\n",
|
||
"plt.plot(steps_list,distance_list, color='green', label=\"Random Walk Data\")\n",
|
||
"\n",
|
||
"steps_list=np.asarray(steps_list)\n",
|
||
"distance_list=np.asarray(distance_list)\n",
|
||
"\n",
|
||
"X=steps_list[:,np.newaxis]\n",
|
||
"\n",
|
||
"#Polynomial fits\n",
|
||
"\n",
|
||
"#Degree 2\n",
|
||
"poly_features=PolynomialFeatures(degree=2, include_bias=False)\n",
|
||
"X_poly=poly_features.fit_transform(X)\n",
|
||
"\n",
|
||
"lin_reg=LinearRegression()\n",
|
||
"poly_fit=lin_reg.fit(X_poly,distance_list)\n",
|
||
"b=lin_reg.coef_\n",
|
||
"c=lin_reg.intercept_\n",
|
||
"print (\"2nd degree coefficients:\")\n",
|
||
"print (\"zero power: \",c)\n",
|
||
"print (\"first power: \", b[0])\n",
|
||
"print (\"second power: \",b[1])\n",
|
||
"\n",
|
||
"z = np.arange(0, steps, .01)\n",
|
||
"z_mod=b[1]*z**2+b[0]*z+c\n",
|
||
"\n",
|
||
"fit_mod=b[1]*X**2+b[0]*X+c\n",
|
||
"plt.plot(z, z_mod, color='r', label=\"2nd Degree Fit\")\n",
|
||
"plt.title(\"Polynomial Regression\")\n",
|
||
"\n",
|
||
"plt.xlabel(\"Steps\")\n",
|
||
"plt.ylabel(\"Distance\")\n",
|
||
"\n",
|
||
"#Degree 10\n",
|
||
"poly_features10=PolynomialFeatures(degree=10, include_bias=False)\n",
|
||
"X_poly10=poly_features10.fit_transform(X)\n",
|
||
"\n",
|
||
"poly_fit10=lin_reg.fit(X_poly10,distance_list)\n",
|
||
"\n",
|
||
"y_plot=poly_fit10.predict(X_poly10)\n",
|
||
"plt.plot(X, y_plot, color='black', label=\"10th Degree Fit\")\n",
|
||
"\n",
|
||
"plt.legend()\n",
|
||
"plt.show()\n",
|
||
"\n",
|
||
"\n",
|
||
"#Decision Tree Regression\n",
|
||
"from sklearn.tree import DecisionTreeRegressor\n",
|
||
"regr_1=DecisionTreeRegressor(max_depth=2)\n",
|
||
"regr_2=DecisionTreeRegressor(max_depth=5)\n",
|
||
"regr_3=DecisionTreeRegressor(max_depth=7)\n",
|
||
"regr_1.fit(X, distance_list)\n",
|
||
"regr_2.fit(X, distance_list)\n",
|
||
"regr_3.fit(X, distance_list)\n",
|
||
"\n",
|
||
"X_test = np.arange(0.0, steps, 0.01)[:, np.newaxis]\n",
|
||
"y_1 = regr_1.predict(X_test)\n",
|
||
"y_2 = regr_2.predict(X_test)\n",
|
||
"y_3=regr_3.predict(X_test)\n",
|
||
"\n",
|
||
"# Plot the results\n",
|
||
"plt.figure()\n",
|
||
"plt.scatter(X, distance_list, s=2.5, c=\"black\", label=\"data\")\n",
|
||
"plt.plot(X_test, y_1, color=\"red\",\n",
|
||
" label=\"max_depth=2\", linewidth=2)\n",
|
||
"plt.plot(X_test, y_2, color=\"green\", label=\"max_depth=5\", linewidth=2)\n",
|
||
"plt.plot(X_test, y_3, color=\"m\", label=\"max_depth=7\", linewidth=2)\n",
|
||
"\n",
|
||
"plt.xlabel(\"Data\")\n",
|
||
"plt.ylabel(\"Darget\")\n",
|
||
"plt.title(\"Decision Tree Regression\")\n",
|
||
"plt.legend()\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Building a tree, regression\n",
|
||
"\n",
|
||
"There are mainly two steps\n",
|
||
"1. We split the predictor space (the set of possible values $x_1,x_2,\\dots, x_p$) into $J$ distinct and non-non-overlapping regions, $R_1,R_2,\\dots,R_J$. \n",
|
||
"\n",
|
||
"2. For every observation that falls into the region $R_j$ , we make the same prediction, which is simply the mean of the response values for the training observations in $R_j$.\n",
|
||
"\n",
|
||
"How do we construct the regions $R_1,\\dots,R_J$? In theory, the\n",
|
||
"regions could have any shape. However, we choose to divide the\n",
|
||
"predictor space into high-dimensional rectangles, or boxes, for\n",
|
||
"simplicity and for ease of interpretation of the resulting predictive\n",
|
||
"model. The goal is to find boxes $R_1,\\dots,R_J$ that minimize the\n",
|
||
"MSE, given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sum_{j=1}^J\\sum_{i\\in R_j}(y_i-\\overline{y}_{R_j})^2,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $\\overline{y}_{R_j}$ is the mean response for the training observations \n",
|
||
"within box $j$. \n",
|
||
"\n",
|
||
"\n",
|
||
"Unfortunately, it is computationally infeasible to consider every\n",
|
||
"possible partition of the feature space into $J$ boxes. The common\n",
|
||
"strategy is to take a top-down approach\n",
|
||
"\n",
|
||
"The approach is top-down because it begins at the top of the tree (all\n",
|
||
"observations belong to a single region) and then successively splits\n",
|
||
"the predictor space; each split is indicated via two new branches\n",
|
||
"further down on the tree. It is greedy because at each step of the\n",
|
||
"tree-building process, the best split is made at that particular step,\n",
|
||
"rather than looking ahead and picking a split that will lead to a\n",
|
||
"better tree in some future step.\n",
|
||
"\n",
|
||
"\n",
|
||
"### Making a tree\n",
|
||
"\n",
|
||
"In order to implement the recursive binary splitting we start by selecting\n",
|
||
"the predictor $x_j$ and a cutpoint $s$ that splits the predictor space into two regions $R_1$ and $R_2$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\left\\{X\\vert x_j < s\\right\\},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"and"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\left\\{X\\vert x_j \\geq s\\right\\},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"so that we obtain the lowest MSE, that is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sum_{i:x_i\\in R_j}(y_i-\\overline{y}_{R_1})^2+\\sum_{i:x_i\\in R_2}(y_i-\\overline{y}_{R_2})^2,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"which we want to minimize by considering all predictors\n",
|
||
"$x_1,x_2,\\dots,x_p$. We consider also all possible values of $s$ for\n",
|
||
"each predictor. These values could be determined by randomly assigned\n",
|
||
"numbers or by starting at the midpoint and then proceed till we find\n",
|
||
"an optimal value.\n",
|
||
"\n",
|
||
"For any $j$ and $s$, we define the pair of half-planes where\n",
|
||
"$\\overline{y}_{R_1}$ is the mean response for the training\n",
|
||
"observations in $R_1(j,s)$, and $\\overline{y}_{R_2}$ is the mean\n",
|
||
"response for the training observations in $R_2(j,s)$.\n",
|
||
"\n",
|
||
"Finding the values of $j$ and $s$ that minimize the above equation can be\n",
|
||
"done quite quickly, especially when the number of features $p$ is not\n",
|
||
"too large.\n",
|
||
"\n",
|
||
"Next, we repeat the process, looking\n",
|
||
"for the best predictor and best cutpoint in order to split the data\n",
|
||
"further so as to minimize the MSE within each of the resulting\n",
|
||
"regions. However, this time, instead of splitting the entire predictor\n",
|
||
"space, we split one of the two previously identified regions. We now\n",
|
||
"have three regions. Again, we look to split one of these three regions\n",
|
||
"further, so as to minimize the MSE. The process continues until a\n",
|
||
"stopping criterion is reached; for instance, we may continue until no\n",
|
||
"region contains more than five observations.\n",
|
||
"\n",
|
||
"\n",
|
||
"The above procedure is rather straightforward, but leads often to\n",
|
||
"overfitting and unnecessarily large and complicated trees. The basic\n",
|
||
"idea is to grow a large tree $T_0$ and then prune it back in order to\n",
|
||
"obtain a subtree. A smaller tree with fewer splits (fewer regions) can\n",
|
||
"lead to smaller variance and better interpretation at the cost of a\n",
|
||
"little more bias.\n",
|
||
"\n",
|
||
"The so-called Cost complexity pruning algorithm gives us a\n",
|
||
"way to do just this. Rather than considering every possible subtree,\n",
|
||
"we consider a sequence of trees indexed by a nonnegative tuning\n",
|
||
"parameter $\\alpha$.\n",
|
||
"\n",
|
||
"Read more at the following [Scikit-Learn link on pruning](https://scikit-learn.org/stable/auto_examples/tree/plot_cost_complexity_pruning.html#sphx-glr-auto-examples-tree-plot-cost-complexity-pruning-py).\n",
|
||
"\n",
|
||
"\n",
|
||
"For each value of $\\alpha$ there corresponds a subtree $T \\in T_0$ such that"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sum_{m=1}^{\\overline{T}}\\sum_{i:x_i\\in R_m}(y_i-\\overline{y}_{R_m})^2+\\alpha\\overline{T},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"is as small as possible. Here $\\overline{T}$ is \n",
|
||
"the number of terminal nodes of the tree $T$ , $R_m$ is the\n",
|
||
"rectangle (i.e. the subset of predictor space) corresponding to the $m$-th terminal node.\n",
|
||
"\n",
|
||
"The tuning parameter $\\alpha$ controls a trade-off between the subtree’s\n",
|
||
"complexity and its fit to the training data. When $\\alpha = 0$, then the\n",
|
||
"subtree $T$ will simply equal $T_0$, \n",
|
||
"because then the above equation just measures the\n",
|
||
"training error. \n",
|
||
"However, as $\\alpha$ increases, there is a price to pay for\n",
|
||
"having a tree with many terminal nodes. The above equation will\n",
|
||
"tend to be minimized for a smaller subtree. \n",
|
||
"\n",
|
||
"\n",
|
||
"It turns out that as we increase $\\alpha$ from zero\n",
|
||
"branches get pruned from the tree in a nested and predictable fashion,\n",
|
||
"so obtaining the whole sequence of subtrees as a function of $\\alpha$ is\n",
|
||
"easy. We can select a value of $\\alpha$ using a validation set or using\n",
|
||
"cross-validation. We then return to the full data set and obtain the\n",
|
||
"subtree corresponding to $\\alpha$. \n",
|
||
"\n",
|
||
"\n",
|
||
"### Schematic Regression Procedure\n",
|
||
"\n",
|
||
"Building a Regression Tree\n",
|
||
"\n",
|
||
"1. Use recursive binary splitting to grow a large tree on the training data, stopping only when each terminal node has fewer than some minimum number of observations.\n",
|
||
"\n",
|
||
"2. Apply cost complexity pruning to the large tree in order to obtain a sequence of best subtrees, as a function of $\\alpha$.\n",
|
||
"\n",
|
||
"3. Use for example $K$-fold cross-validation to choose $\\alpha$. Divide the training observations into $K$ folds. For each $k=1,2,\\dots,K$ we: \n",
|
||
"\n",
|
||
" * repeat steps 1 and 2 on all but the $k$-th fold of the training data. \n",
|
||
"\n",
|
||
" * Then we valuate the mean squared prediction error on the data in the left-out $k$-th fold, as a function of $\\alpha$.\n",
|
||
"\n",
|
||
" * Finally we average the results for each value of $\\alpha$, and pick $\\alpha$ to minimize the average error.\n",
|
||
"\n",
|
||
"\n",
|
||
"4. Return the subtree from Step 2 that corresponds to the chosen value of $\\alpha$. \n",
|
||
"\n",
|
||
"!eblock\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"## A Classification Tree\n",
|
||
"\n",
|
||
"A classification tree is very similar to a regression tree, except\n",
|
||
"that it is used to predict a qualitative response rather than a\n",
|
||
"quantitative one. Recall that for a regression tree, the predicted\n",
|
||
"response for an observation is given by the mean response of the\n",
|
||
"training observations that belong to the same terminal node. In\n",
|
||
"contrast, for a classification tree, we predict that each observation\n",
|
||
"belongs to the most commonly occurring class of training observations\n",
|
||
"in the region to which it belongs. In interpreting the results of a\n",
|
||
"classification tree, we are often interested not only in the class\n",
|
||
"prediction corresponding to a particular terminal node region, but\n",
|
||
"also in the class proportions among the training observations that\n",
|
||
"fall into that region. \n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"The task of growing a\n",
|
||
"classification tree is quite similar to the task of growing a\n",
|
||
"regression tree. Just as in the regression setting, we use recursive\n",
|
||
"binary splitting to grow a classification tree. However, in the\n",
|
||
"classification setting, the MSE cannot be used as a criterion for making\n",
|
||
"the binary splits. A natural alternative to MSE is the **classification\n",
|
||
"error rate**. Since we plan to assign an observation in a given region\n",
|
||
"to the most commonly occurring error rate class of training\n",
|
||
"observations in that region, the classification error rate is simply\n",
|
||
"the fraction of the training observations in that region that do not\n",
|
||
"belong to the most common class. \n",
|
||
"\n",
|
||
"When building a classification tree, either the Gini index or the\n",
|
||
"entropy are typically used to evaluate the quality of a particular\n",
|
||
"split, since these two approaches are more sensitive to node purity\n",
|
||
"than is the classification error rate. \n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"If our targets are the outcome of a classification process that takes\n",
|
||
"for example $k=1,2,\\dots,K$ values, the only thing we need to think of\n",
|
||
"is to set up the splitting criteria for each node.\n",
|
||
"\n",
|
||
"We define a PDF $p_{mk}$ that represents the number of observations of\n",
|
||
"a class $k$ in a region $R_m$ with $N_m$ observations. We represent\n",
|
||
"this likelihood function in terms of the proportion $I(y_i=k)$ of\n",
|
||
"observations of this class in the region $R_m$ as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"p_{mk} = \\frac{1}{N_m}\\sum_{x_i\\in R_m}I(y_i=k).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We let $p_{mk}$ represent the majority class of observations in region\n",
|
||
"$m$. The three most common ways of splitting a node are given by\n",
|
||
"\n",
|
||
"* Misclassification error"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"p_{mk} = \\frac{1}{N_m}\\sum_{x_i\\in R_m}I(y_i\\ne k) = 1-p_{mk}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* Gini index $g$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"g = \\sum_{k=1}^K p_{mk}(1-p_{mk}).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* Information entropy or just entropy $s$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"s = -\\sum_{k=1}^K p_{mk}\\log{p_{mk}}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Visualizing the Tree, Classification"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 2,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
" mean radius mean texture mean perimeter mean area mean smoothness \\\n",
|
||
"0 17.99 10.38 122.80 1001.0 0.11840 \n",
|
||
"1 20.57 17.77 132.90 1326.0 0.08474 \n",
|
||
"2 19.69 21.25 130.00 1203.0 0.10960 \n",
|
||
"3 11.42 20.38 77.58 386.1 0.14250 \n",
|
||
"4 20.29 14.34 135.10 1297.0 0.10030 \n",
|
||
".. ... ... ... ... ... \n",
|
||
"564 21.56 22.39 142.00 1479.0 0.11100 \n",
|
||
"565 20.13 28.25 131.20 1261.0 0.09780 \n",
|
||
"566 16.60 28.08 108.30 858.1 0.08455 \n",
|
||
"567 20.60 29.33 140.10 1265.0 0.11780 \n",
|
||
"568 7.76 24.54 47.92 181.0 0.05263 \n",
|
||
"\n",
|
||
" mean compactness mean concavity mean concave points mean symmetry \\\n",
|
||
"0 0.27760 0.30010 0.14710 0.2419 \n",
|
||
"1 0.07864 0.08690 0.07017 0.1812 \n",
|
||
"2 0.15990 0.19740 0.12790 0.2069 \n",
|
||
"3 0.28390 0.24140 0.10520 0.2597 \n",
|
||
"4 0.13280 0.19800 0.10430 0.1809 \n",
|
||
".. ... ... ... ... \n",
|
||
"564 0.11590 0.24390 0.13890 0.1726 \n",
|
||
"565 0.10340 0.14400 0.09791 0.1752 \n",
|
||
"566 0.10230 0.09251 0.05302 0.1590 \n",
|
||
"567 0.27700 0.35140 0.15200 0.2397 \n",
|
||
"568 0.04362 0.00000 0.00000 0.1587 \n",
|
||
"\n",
|
||
" mean fractal dimension ... worst radius worst texture \\\n",
|
||
"0 0.07871 ... 25.380 17.33 \n",
|
||
"1 0.05667 ... 24.990 23.41 \n",
|
||
"2 0.05999 ... 23.570 25.53 \n",
|
||
"3 0.09744 ... 14.910 26.50 \n",
|
||
"4 0.05883 ... 22.540 16.67 \n",
|
||
".. ... ... ... ... \n",
|
||
"564 0.05623 ... 25.450 26.40 \n",
|
||
"565 0.05533 ... 23.690 38.25 \n",
|
||
"566 0.05648 ... 18.980 34.12 \n",
|
||
"567 0.07016 ... 25.740 39.42 \n",
|
||
"568 0.05884 ... 9.456 30.37 \n",
|
||
"\n",
|
||
" worst perimeter worst area worst smoothness worst compactness \\\n",
|
||
"0 184.60 2019.0 0.16220 0.66560 \n",
|
||
"1 158.80 1956.0 0.12380 0.18660 \n",
|
||
"2 152.50 1709.0 0.14440 0.42450 \n",
|
||
"3 98.87 567.7 0.20980 0.86630 \n",
|
||
"4 152.20 1575.0 0.13740 0.20500 \n",
|
||
".. ... ... ... ... \n",
|
||
"564 166.10 2027.0 0.14100 0.21130 \n",
|
||
"565 155.00 1731.0 0.11660 0.19220 \n",
|
||
"566 126.70 1124.0 0.11390 0.30940 \n",
|
||
"567 184.60 1821.0 0.16500 0.86810 \n",
|
||
"568 59.16 268.6 0.08996 0.06444 \n",
|
||
"\n",
|
||
" worst concavity worst concave points worst symmetry \\\n",
|
||
"0 0.7119 0.2654 0.4601 \n",
|
||
"1 0.2416 0.1860 0.2750 \n",
|
||
"2 0.4504 0.2430 0.3613 \n",
|
||
"3 0.6869 0.2575 0.6638 \n",
|
||
"4 0.4000 0.1625 0.2364 \n",
|
||
".. ... ... ... \n",
|
||
"564 0.4107 0.2216 0.2060 \n",
|
||
"565 0.3215 0.1628 0.2572 \n",
|
||
"566 0.3403 0.1418 0.2218 \n",
|
||
"567 0.9387 0.2650 0.4087 \n",
|
||
"568 0.0000 0.0000 0.2871 \n",
|
||
"\n",
|
||
" worst fractal dimension \n",
|
||
"0 0.11890 \n",
|
||
"1 0.08902 \n",
|
||
"2 0.08758 \n",
|
||
"3 0.17300 \n",
|
||
"4 0.07678 \n",
|
||
".. ... \n",
|
||
"564 0.07115 \n",
|
||
"565 0.06637 \n",
|
||
"566 0.07820 \n",
|
||
"567 0.12400 \n",
|
||
"568 0.07039 \n",
|
||
"\n",
|
||
"[569 rows x 30 columns]\n",
|
||
" malignant benign\n",
|
||
"0 True False\n",
|
||
"1 True False\n",
|
||
"2 True False\n",
|
||
"3 True False\n",
|
||
"4 True False\n",
|
||
".. ... ...\n",
|
||
"564 True False\n",
|
||
"565 True False\n",
|
||
"566 True False\n",
|
||
"567 True False\n",
|
||
"568 False True\n",
|
||
"\n",
|
||
"[569 rows x 2 columns]\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0"
|
||
]
|
||
},
|
||
"execution_count": 2,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"import os\n",
|
||
"from sklearn.datasets import load_breast_cancer\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn.metrics import confusion_matrix\n",
|
||
"from sklearn.tree import export_graphviz\n",
|
||
"\n",
|
||
"from IPython.display import Image \n",
|
||
"from pydot import graph_from_dot_data\n",
|
||
"import pandas as pd\n",
|
||
"import numpy as np\n",
|
||
"\n",
|
||
"\n",
|
||
"cancer = load_breast_cancer()\n",
|
||
"X = pd.DataFrame(cancer.data, columns=cancer.feature_names)\n",
|
||
"print(X)\n",
|
||
"y = pd.Categorical.from_codes(cancer.target, cancer.target_names)\n",
|
||
"y = pd.get_dummies(y)\n",
|
||
"print(y)\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)\n",
|
||
"tree_clf = DecisionTreeClassifier(max_depth=5)\n",
|
||
"tree_clf.fit(X_train, y_train)\n",
|
||
"\n",
|
||
"export_graphviz(\n",
|
||
" tree_clf,\n",
|
||
" out_file=\"DataFiles/cancer.dot\",\n",
|
||
" feature_names=cancer.feature_names,\n",
|
||
" class_names=cancer.target_names,\n",
|
||
" rounded=True,\n",
|
||
" filled=True\n",
|
||
")\n",
|
||
"cmd = 'dot -Tpng DataFiles/cancer.dot -o DataFiles/cancer.png'\n",
|
||
"os.system(cmd)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0"
|
||
]
|
||
},
|
||
"execution_count": 3,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Common imports\n",
|
||
"import numpy as np\n",
|
||
"from sklearn.model_selection import train_test_split \n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.datasets import make_moons\n",
|
||
"from sklearn.tree import export_graphviz\n",
|
||
"from pydot import graph_from_dot_data\n",
|
||
"import pandas as pd\n",
|
||
"import os\n",
|
||
"\n",
|
||
"np.random.seed(42)\n",
|
||
"X, y = make_moons(n_samples=100, noise=0.25, random_state=53)\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(X,y,random_state=0)\n",
|
||
"tree_clf = DecisionTreeClassifier(max_depth=5)\n",
|
||
"tree_clf.fit(X_train, y_train)\n",
|
||
"\n",
|
||
"export_graphviz(\n",
|
||
" tree_clf,\n",
|
||
" out_file=\"DataFiles/moons.dot\",\n",
|
||
" rounded=True,\n",
|
||
" filled=True\n",
|
||
")\n",
|
||
"cmd = 'dot -Tpng DataFiles/moons.dot -o DataFiles/moons.png'\n",
|
||
"os.system(cmd)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Other ways of visualizing the trees\n",
|
||
"\n",
|
||
"**Scikit-Learn** has also another way to visualize the trees which is very useful, here with the Iris data."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"[Text(0.5, 0.9166666666666666, 'x[2] <= 2.45\\ngini = 0.667\\nsamples = 150\\nvalue = [50, 50, 50]'),\n",
|
||
" Text(0.4230769230769231, 0.75, 'gini = 0.0\\nsamples = 50\\nvalue = [50, 0, 0]'),\n",
|
||
" Text(0.5769230769230769, 0.75, 'x[3] <= 1.75\\ngini = 0.5\\nsamples = 100\\nvalue = [0, 50, 50]'),\n",
|
||
" Text(0.3076923076923077, 0.5833333333333334, 'x[2] <= 4.95\\ngini = 0.168\\nsamples = 54\\nvalue = [0, 49, 5]'),\n",
|
||
" Text(0.15384615384615385, 0.4166666666666667, 'x[3] <= 1.65\\ngini = 0.041\\nsamples = 48\\nvalue = [0, 47, 1]'),\n",
|
||
" Text(0.07692307692307693, 0.25, 'gini = 0.0\\nsamples = 47\\nvalue = [0, 47, 0]'),\n",
|
||
" Text(0.23076923076923078, 0.25, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 0, 1]'),\n",
|
||
" Text(0.46153846153846156, 0.4166666666666667, 'x[3] <= 1.55\\ngini = 0.444\\nsamples = 6\\nvalue = [0, 2, 4]'),\n",
|
||
" Text(0.38461538461538464, 0.25, 'gini = 0.0\\nsamples = 3\\nvalue = [0, 0, 3]'),\n",
|
||
" Text(0.5384615384615384, 0.25, 'x[2] <= 5.45\\ngini = 0.444\\nsamples = 3\\nvalue = [0, 2, 1]'),\n",
|
||
" Text(0.46153846153846156, 0.08333333333333333, 'gini = 0.0\\nsamples = 2\\nvalue = [0, 2, 0]'),\n",
|
||
" Text(0.6153846153846154, 0.08333333333333333, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 0, 1]'),\n",
|
||
" Text(0.8461538461538461, 0.5833333333333334, 'x[2] <= 4.85\\ngini = 0.043\\nsamples = 46\\nvalue = [0, 1, 45]'),\n",
|
||
" Text(0.7692307692307693, 0.4166666666666667, 'x[1] <= 3.1\\ngini = 0.444\\nsamples = 3\\nvalue = [0, 1, 2]'),\n",
|
||
" Text(0.6923076923076923, 0.25, 'gini = 0.0\\nsamples = 2\\nvalue = [0, 0, 2]'),\n",
|
||
" Text(0.8461538461538461, 0.25, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 1, 0]'),\n",
|
||
" Text(0.9230769230769231, 0.4166666666666667, 'gini = 0.0\\nsamples = 43\\nvalue = [0, 0, 43]')]"
|
||
]
|
||
},
|
||
"execution_count": 4,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
},
|
||
{
|
||
"data": {
|
||
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uXIX/Qbt48WLs2bMH2dnZ6Ny5M9vhEEIaQckAIUrC3t4ely5dQnZ2NvT09NgOp0HFxcWwsrLC4MGDkZCQwHY4hJBGUDcBIUrg+PHjOHbsGLZv367wiQAA6OnpITg4GEePHsWJEyeQl5eHqqoqtsMihLwHPRkgRMG9evUKPXv2hLW1NX755RelWeGPYRiMHTsW2dnZKC8vR0BAAJydndkOixBSDxrqS4iCW7t2LZ49e4YffvhBaRIBALh79y40NTXx+PFjaGtr4969e2yHRAh5D0oGCFFgWVlZ2LZtG/z9/dGtWze2w5GIrq4u7t+/jzdv3uD169e4ceMG2yERQt6DugkIUVACgQCffPIJiouLkZmZCS0tLbZDktibN2+wdetW+Pn5wcLCAtnZ2WyHRAipByUDhCiYly9fIjQ0FAYGBnBzc8PZs2cxbNgwtsNqlnv37kFdXR1dunRhOxRCSD0oGSBEwfz000+YOnUq2rRpg4kTJ2LPnj0KucAQIaTloKmFhCiYx48fg8Ph4M2bNzhy5IjC7EpICGm5aAAhIQrm0qVLYBgGlZWVWLp0Kezs7OR2bj6fj4KCArmdT9kYGhrCzMyM7TAIkTpKBghRMEZGRujYsSNOnjyJ/v37y+28fD4fVlZWKCsrk9s5lQ2Xy0V2djYlBKTFoTEDhBAAQHp6OmxsbLBv3z5YWVmxHY7Cyc7OhpOTE9LS0jBgwAC2wyFEqujJACFEhJWVFf2wI0TFUDJAVAL1hYuivm9CSF2UDJAWj/rC3yXLvu+UlBQEBgYiLCwM9+/fR1xcHPLz8zF//nzY2dnBx8cHALBp06b3llFRUQEdHZ1Gz/Xdd9/h8OHD+Oeff0SOv3HjBnbs2AEAOH36NO7evQtnZ2doampCXV0d27dvh7a2djOvlJCWg5IB0uIVFBSgrKyM+sL/X23fd0FBgVSSgaNHj+LRo0cwNzfH5cuXYWtri/Hjx8PMzAxmZmb49NNPUVRUhO+//x52dnbg8XiIiIh4p5yioiLEx8fj4sWLcHBwwNixYxs994YNG5Cfn//O13v27ImIiAhkZWXBwMAAQE0CVF1dDQMDA6VczZEQWaJkgKgM6guXDXt7eyxZsgRnzpzBwYMH8eeff4q8HxMTg+joaGzYsOG9Zbi4uKCqqgo8Hg9ubm4AapZjXrhwochxX3/9NQYNGiR2bNHR0fjmm28AQLjR044dO5CUlCRWskGIqqBFhwhphtpH3m+LiIhAbm6uRGX5+vpiyZIl75RZWloKZ2dnuLi4YP/+/U0NVWYYhkFhYSHU1dVRXV39zvvOzs5ITk5GSEjIe8twd3eHsbExdu/ejSNHjqCysrLZcZWXl+Phw4fo0aMHAAh3fGzfvj1evnzZ7PIJaUnoyQAhYsrOzsbatWthYWGBtLQ0nDx5UvgDv0+fPvj666+RmpqK6OhoPH78GBUVFWKXzefzIRAIsGPHDixbtgx5eXno3LkzACAhIQEzZszA2LFjMWPGDDg6Osri8pps+/btmDlzJkxMTLB69Wp88cUXwvd++ukn/PHHHygrK8PMmTPfW0bfvn3Rt29fVFVV4dSpUzhz5gzGjh1bb3dCXUFBQfj777+xePFirF+/HufOnYO2tjbs7Oxw+PBhTJkyRXish4cHysrK8PLlS+zatav5F05IC0LJACFiio6ORmBgIExMTDB+/HiR97p06YKlS5ciJCQEmZmZ73z22bNnWLlypcjXli1bhu7duwMA8vPzhT/8zczM8ODBA+HrBw8eCBcfUsQ9CpYuXSr8t42NDVJSUoSvp0yZIvIDuTEaGhqYMGGC2Md7enrC09NT+HratGnCf8+ePVvk2G3btoldLiGqhroJCBFT3fW53l6rq1WrVgAATU3NJj3iNjU1xYMHDwAAeXl5MDU1rfc9gUAgcdnypq+vj/T0dPD5/Hrfj4mJQbdu3eQcFSGkIfRkgBAxubi4wMvLC+bm5mjdurVEnzUyMmrwkXftqH4PDw9oaWnBzMwMQUFBGDFiBCZPngx3d3ckJiZi3LhxzboGeejXrx+ioqLqfc/Hx6feKYUREREYM2YMunbtKvZ5fH19UVpaCi6XK1JmSkoKVq1ahZ49e8LBwQHDhw+X9BIIUTmUDBAipvbt28Pc3BzPnz8XPoKOj48X+ZvH4wFAk34Avf1Dsu7j75iYmCZEzC62xlhwOBy0adMGFRUVwq8RQhpGyQAhYjIwMIC/vz/bYSgNtsZYDBs2DJ999hmePHkCb29v/PjjjzK4OkJaFhozQIiMxMTEICkpSapl9ujRAzweT/gY/tq1a3BycoKjoyOuXbsm1XM1F1tjLGqnELZt21YqUxQJUQX0ZICQOuLi4pCSkgIul4vNmzfj0KFDyMzMRGlpKUJCQrBhwwYUFxejqKgI1tbWePHiBe7fv499+/bBzs4OQ4cORW5uLhYtWiQs8/79+wgICACHw0H37t0xZswYrF27Fqamppg7dy569eoldny6urooLy9Hly5dAAAhISEIDw+HQCCAt7c3IiMjpV4nTcXWGIu7d+8iKSkJxcXFIv8PhJD3o2SAkDry8/PRu3dvTJo0Cdra2uBwONDS0kJOTo7wcbaDgwMsLS3h7OyMo0ePYsGCBSgqKkJ1dTU8PT1RUlKCFStWYODAgQCAsLAwtGrVClwuF9euXcOQIUPQtm1bzJo1SyQRaOzROFCzzbBAIICdnR2++OILlJSUQFdXFwBQUlIi49qRDFtjLPr374+pU6c2NWxCVBIlA4TUsWzZMmRlZcHb2xv+/v5ISEhAQkIC1qxZg9LSUgCAnp4etLW1oaenBwDQ0tJCZWUlBAIBqqur8fr1a+GjaqBmOqCzszOsra2FXzM1NcXu3buRlZWFOXPmiB0fh8OBuro6dHR0wDAMWrdujZKSEuG/FQmNsSBEeVAyQEgdUVFRuH37NgCgXbt2MDIyQkBAAFJTUxv97VVbWxv+/v64e/cuVq5cidTUVAA1S+36+fmhQ4cO0NXVxbBhw3DixAk8f/4cn3/+ufDzjT0az8nJwcaNGwEAn376KTgcDtzd3eHu7i7sJlBGMTExMDExwZgxY6RWpqurKy5fvoyMjAwANWMrNm3aBIZh4Ovri169er13aiIhqoiSAULqWLBggcjr2j742h+0dROC2ul+oaGhAAAdHR2RzXjqPgl4e0+BESNGSBybpaXlOyPj+/Tpw8poeUUfWxEZGQkHBwfh67fHVnz33XfvnZpIiCqiZIAQKantB1cFij624m1vj61oaGoiIaqIkgFCiMQUfWzF294eW2FqaorExEQANVMTJ06c2OSyCWkJKBkgpB4ODg5S/01/6NCh8Pb2hp2dHXr06IHPP/8cAwYMwIIFC+rt035bU46pXZdg8ODBwpH70qDIYysA4LvvvsOVK1fA4/EQGhr6ztiK+qYmEqLSGEJauLS0NAYAk5aWxjAMwyxYsIB5/vw5U1VVxTg6OjL5+fmMj48Pw+PxmMTERIZhGGbGjBkif4eHhzPJyclMeno6s3DhQobH4zF79+6VKI7ashiGYfr168fMnj2bSUpKEsb08uVL5sWLF8yCBQvq/XxTj0lOTmbCw8PfWx+NfV3a6taDMpFX/RDCBnoyQFTO9OnTcfjwYXz44YcYOXIkNDQ0UFVVBWNjY8TGxsLOzu69nw0KCkK3bt3A4XCQmZmJWbNmCd/z9fVFUVGR8PXEiRMxduzYestpynoB0jqGbao0toIQZUHJAFE5I0aMwO7du5GWloYtW7YgOjoa9vb2sLGxeafvWE2tZsXu2n7wqqoqeHh4QF9fv1kxNGW9AGkdQwghb6NkgKgcNTU1dO7cGQ8fPoSenh5sbW0RGRkJCwsLaGlpiRxrYmKCwMBAnD9/HjY2NvD29oa7uzvat2+Prl27YvHixcJja9cAaIy46wVs2rQJPj4+ws819RhZkvXYCnHWAmjK+Is1a9YgJycH+vr6WLVqFTp27PjOuZKSkrBmzRpcvHhRqtdHiCKiZICopLo/WIYMGYIhQ4aIvF/7Ay4oKAgA4OXlJXxv3759zTq3OOsFvHr1ClVVVc0+pjlcXV2xceNG6OnpYc6cOQgICEBISAhevHiBsWPHinSn1CYFERERsLS0hJ6eHqKjoyEQCGBrayvSndKYTp06wc7OrsFtiutqyn4Nmpqa0NHRgZaWFtq2bVvvucaMGaOUW0cT0hSUDBAiJ23atMHx48cbHJNQq3Xr1lixYkWzj6moqMCxY8cwcuRIiWIF2B9bIe5aAE0Zf+Hn5wcOh4Pjx48jJiYG/fr1o3UHiEqjZICojOzsbFbPXzu1Lz09Xa7nrd0kqPa84tYD22MrxF0LoCnjL2rXN2jfvj2ys7Np3QGi8igZIC2eoaEhuFwunJyc2A5FYXC5XBgaGjZ4DNtjK+pbC+D06dNo164dBgwYAKDp4y/Wr18PPp+PwsJChISEoEOHDu+cixBVwmEYhmE7CEJkjc/no6CggO0wFIahoeE7P/DS09NhY2ODtLQ04Q9bNjQ0KPH777+Hu7s72rRpI3Z5r169QnBwcKNdKo3Foij1Q4gs0JMBohLMzMzot71GKEqy1NDYCj8/P4nLE2dsRX2SkpLA5XIl/hwhyoieDBCi4m7duoWtW7diz549ePPmDfbt2wcrKyu2w1I42dnZcHJywsCBA7Fu3TqMHj1aZG8FQpQZJQOEqKhLly4hICAAR48ehbGxMZydnRESEoKysjK2Q1NYOjo6+M9//oOrV6+iT58+8Pb2xvTp06Gpqcl2aIQ0CyUDhKgQgUCAU6dOISAgAOfOnYO5uTm8vLwwa9Ys6Ojo0NiKRhgaGqJz5844e/YsAgICcOrUKZiZmcHT0xPz5s2jVR+J0qJkgBAV8Pr1axw4cABbtmzB9evX8fHHH2P58uWws7ODuro62+EprX/++QeBgYE4cOAAdHV1sWjRIixevBjGxsZsh0aIRCgZIKQFKykpwc6dO7Ft2zY8ePAA48ePh7e3N4YOHUr93VLE5/Oxbds27Ny5E9XV1Zg7dy48PT3Ro0cPtkMjRCyUDBDSAj1+/Bg7duxAWFgYysrK4OjoCC8vL1hbW7MdWotWWFiI8PBw7NixAwUFBZgyZQqWLVuGgQMHsh0aIQ2iZICQFuTmzZvYunUrfvzxR2hpacHV1RVLly5Fp06d2A5NpZSXl2Pv3r0IDAzEnTt3MGLECHh7e+OLL76gJzJEIVEyQEgLcPHiRQQEBODYsWMwNjbG0qVLwePxmr3VMmme6upqHDt2DJs3b0Zqaip69+4Nb29vzJgxg2YgEIWixnYAhJCmEQgEOHnyJIYNG4YhQ4bg+vXriIqKQm5uLnx8fCgRUADq6uqYMmUKLl26hOTkZHTq1AmzZs1C9+7dERwcjFevXrEdIiEAKBkgROm8fv0aMTEx6N27NyZMmIA3b97g6NGjyM7Oxvz586Gjo8N2iOQtHA4Hw4cPxy+//IKsrCwMHz4cy5Ytg5mZGVasWIGnT5+yHSJRcdRNQIiSePnypXBmQH5+PsaPH4/ly5fjk08+oX5oJcTn8xEcHIyoqChUVVVh7ty5+Pbbb2kGAmEFJQOEKLhHjx5hx44dCA8Pp5kBLVBRURHCw8Oxfft2PHv2DFOmTIG3tzfNQCByRckAIQrq5s2bCAwMxN69e6GtrQ1XV1d88803NDOghaqoqMDevXuxZcsW3LlzB8OHD4e3tzfGjBlDT36IzFEyQIiC+fvvvxEQEIDExES0b98eS5cuhaurKw0IVBH1zUBYtmwZHBwcaAYCkRkaQEiIAqidGfDpp5/C1tYW2dnZ2LlzJ3Jzc7F8+XJKBFRI3RkIKSkp6Ny5M2bPnk0zEIhMUTJACIvenhlQ+1vhjRs3MG/ePGhra7MdImEJh8PBZ599hp9//hn//PMPRowYITID4cmTJ2yHSFoQ6iYghAUvX75EVFQUgoODkZ+fjwkTJgj3DCDkffLy8oQzEN68eQNnZ2d8++23+M9//sN2aETJUTJAiBw9evQI27dvR3h4OMrLy+Hk5AQvLy/07NmT7dCIEnl7BsLkyZPh7e2NQYMGsR0aUVKUDBAiBzdv3sSWLVsQGxsLbW1t8Hg8fPPNNzA1NWU7NKLEamcgBAYG4vbt2/jss8+wfPlymoFAJEZjBgiRob///hv29vawsrLCL7/8gnXr1iEvLw8BAQGUCJBm09HRwYIFC5CdnY2ffvoJ5eXl+PLLL9GnTx/ExsbizZs3bIdIlAQlA4RImUAgwIkTJ4QzA3JychAdHY1///0X3t7e0NPTYztE0sKoq6tj8uTJuHjxIs6ePYsuXboIZyBs27YNJSUlbIdIFBwlA4RISWVlJfbs2YNevXrBzs4OAoEAiYmJuH79Or7++muaGUBkjsPhYNiwYTh58iSuXr0q3DrZzMwM3333Hc1AIO9FYwYIaabi4mLhzICHDx/Czs4O3t7e+OSTT9gOjZB3ZiDMmTMH3377LczNzdkOjSgQSgYIaaKHDx9i+/btiIiIQHl5OWbNmgUvLy9YWVmxHRoh7ygqKkJERAS2b9+Op0+fwt7eHt7e3vj444/ZDo0oAOomIEQM6enpePnyJQAgJycH8+fPx4cffoiIiAjweDzk5uZi165dlAgQhdW2bVv4+voiNzcXkZGRuHr1KgYPHizcWplhGDAMgz///BPV1dVsh0vkjJIBQhqRkpKCQYMGYcuWLZg0aZJwZsD69evB5/OxefNmdOzYke0wCRGLjo4OXFxckJ2djYSEBFRUVGDcuHHo06cPwsPDMXz4cPj5+bEdJpEz6iYgpAG5ubno27cvOBwOiouLYWlpCW9vb3z11Vc0IJC0CAzD4Pz58wgICMDJkyehp6eH4uJi7NmzB87OzmyHR+SEkgECPp+PgoICtsNQCIaGhjAzMxO+NjMzQ15eHjQ1NWFkZIS1a9di/vz5LEZIiGzk5ORg0qRJePDgAUpLSwEABQUFaNeunfAYulf8z9v3CmWnwXYAhF18Ph9WVlYoKytjOxSFwOVykZ2dLfwm9/X1RVZWFoyNjVFeXo5evXqxHCEhsmFoaIipU6cCqJkmW1ZWJrJbJt0rRL19r1B29GRAxaWnp8PGxgb79u1T+cFv2dnZcHJyQlpaGgYMGMB2OIQoFLpX/E9LvFfQkwECALCysmoxjZoQIjt0r2iZaDYBIYQQouIoGSDNkpKSgvHjx4PP5yM6OhoLFiyAnZ0drl69CgDw8fGBj49Pg2VUVFSIfb5NmzbBwcFB5GuPHz/GlClT4ObmhoiICACAs7MzXFxcwOPxUFlZKeFVEUKkTRHuFS9fvsTkyZPh4uKCb7/9FgDdK2pRMkAkcvToUYSFheH333/H999/DwAYP348zMzMMH/+fERFRWHt2rU4ceIEAIDH49VbTu1+7HPmzEFycrJY57548SI6dOjwztcvXLiAKVOmIDw8HMnJyXjz5g24XC7U1NRgYGAALS2tJl4tIaSpFPFe8eTJE1hbW2Pnzp14+vQpANC94v/RmAEiEXt7eyxZsgRnzpzBwYMH8eeff4q8X1VVhdDQUKxevfq9Zbi4uKCqqgo8Hg9ubm4Aanb6W7hwochxX3/9NQYNGgQAKC8vx/79+xESEoJTp06JHDd27FisWLEC6enpKCgoQGFhIX744QdwOBzs2LEDSUlJGDt2rDQunxAiJkW8V3Tq1An//PMPxo4dKzye7hU16MkAkQjDMCgsLIS6uvo7S5a+fv0aCxcuxJIlSxqcbuPu7g5jY2Ps3r0bR44cEevR3JUrV1BcXIylS5ciIyMDFy9eFL73wQcfYOvWrQgMDESrVq1gZGQEDocDAGjfvr1wGWFCiPwo4r3i559/xvTp03Hq1Ck8evQIhYWFdK/4f/RkgEhk+/btmDlzJkxMTLB69Wp88cUXwvd8fHxw69YthIeHY9SoUZg2bVq9ZfTt2xd9+/ZFVVUVTp06hTNnzmDs2LHC/v76fPrpp/j0008B1IwRGDx4MA4fPgxtbW2MGjUKbm5uqK6uhrOzM9TU1ODh4YGysjK8fPkSu3btkm4lEEIapYj3ik8++QSLFy/GX3/9hTdv3qBt27Z0r/h/lAwQiSxdulT4bxsbG6SkpAhfBwUFSVSWhoYGJkyYIHEM8fHxACByA9m7d6/IMdu2bZO4XEKI9CjqveLIkSMix9C9ogZ1E5Bm0dfXR3p6Ovh8fr3vx8TEoFu3bnKOihCiaOheodgoGSDN0q9fP0RFRSEsLKze901MTDB69GiJyvT19cWSJUvemWZ07949zJs3T2S60Pnz5+Hu7o7Fixfj0aNH4PP5mDhxIr7++mts3rxZ8gsihMiEPO8VpaWlwimD+/fvF359165dGDVqFICaVQR5PB6mTp2KyMhICa+m5aFkgEgsOzsbDg4OWL16NcaPHw+gZnc/AOjTpw+Cg4Ph6OiI8vJyPH78WKK5wXw+HwKBADt27EB1dTXy8vKE73Xr1u2dPr2QkBBoaWlBW1sbbdu2xa1bt2BnZ4fdu3fj2rVrzb9YQkiTsXWvSEhIwIwZM7Bz504cP34cAPDvv//i+fPnMDIyAlCzkmJERAQOHTqEtLQ0KV2x8qJkgEgsOjoagYGBWLlyJaqqqkTe69KlC5YuXYrBgwcjMzPznc8+e/YMPB5P5M/du3eF7+fn56Nz584AanYMfPDgQYOxpKWlYfPmzfjss88QFxeH/v37Y9++fRg5ciRGjBjR/IslhDQZW/eKBw8eCN9TV1eHQCDA1q1bRcYxAMDx48fx3//+V/i0QJVRMkAkVndvq7f3uWrVqhUAQFNTs0mreZmamgq/qfPy8mBqatrg8VZWVtDU1ES7du1QUlKCPXv2YP369Thz5gx++eUXic9PCJEetu4Vdd8TCAS4d+8enj17Bm9vb2RkZAjvDXZ2dvjjjz9w4MABic/f0tBsAiIxFxcXeHl5wdzcHK1bt5bos0ZGRg1OC6qdc+zh4QEtLS2YmZkhKCgII0aMgJmZGb777jtcuXIFAQEB8Pb2hqOjI9zc3PDq1SsEBQXhyZMnWLt2LWJjY9G1a9fmXCYhpJnYuldMnjwZ7u7uSExMxLhx49CjRw8cPHgQQM10wy+//BIpKSk4dOgQXr9+LfFYhZaItjBWcbXbkkqyFWdhYSGCg4Px/PlzjB49GhMnTpRxlPLRlLogRFXQveJ/WuK9gp4MEIkZGBjA39+f7TAIIQqO7hXKg8YMELmLiYlBUlKSVMvs0aMHeDweoqKihF+7evUqjI2NJRqhTAhRLLK4XwA1GyPVTkl89OgRlixZAnd3d5w/f17q51IG9GSAiCUuLg4pKSngcrnYvHkzDh06hMzMTJSWliIkJAQbNmxAcXExioqKYG1tjRcvXuD+/fvYt28f7OzsMHToUOTm5mLRokXCMu/fv4+AgABwOBx0794dY8aMwdq1a2Fqaoq5c+eiV69eYsenq6uL8vJydOnSBQDw5s0bREdHq+ymI4SwSdHvF0eOHMFHH32EO3fuAKhZEZHL5aK4uLjRQcstFSUDRCz5+fno3bs3Jk2aBG1tbXA4HGhpaSEnJ0c4LcjBwQGWlpZwdnbG0aNHsWDBAhQVFaG6uhqenp4oKSnBihUrMHDgQABAWFgYWrVqBS6Xi2vXrmHIkCFo27YtZs2aJfKN/ezZM6xcuVIknmXLlqF79+7C1+np6RAIBLCzs8MXX3yBwMBALF68GOvXr5d95RBCRCjy/eLJkyfIyMiAi4uLMBm4evUqgoODYWRkBG9vb5Xco4CSASKWZcuWISsrC97e3vD390dCQgISEhKwZs0alJaWAgD09PSgra0NPT09AICWlhYqKyshEAhQXV2N169fC3cIA2qm/Dg7O8Pa2lr4NVNTU+zevRtZWVmYM2eO2PFxOByoq6tDR0cHDMMgMzMTT548weXLlxEeHg4PDw8p1QQhpDGKfL84e/Ysnj59Cn9/f1y9ehW3bt2CqakpDAwM0KZNmyZNc2wJKBkgYomKisLt27cBAO3atYORkRECAgKQmpqK4cOHN/hZbW1t+Pv74+7du1i5ciVSU1MB1GxP6ufnhw4dOkBXVxfDhg3DiRMn8Pz5c3z++efCzzc2xSgnJwcbN24EULNjGYfDEU4jcnZ2Fu6DTgiRD0W+X0yfPh3Tp09Hbm4uIiIiYG5uDk9PTyxbtgxqamoqe7+gqYUqTh5TZBwcHIS7hymyljhdiBBpkdf3hzLcL1rivYJmExCZU/RvbEKI4qD7BTsoGSCEEEJUHCUDRGJ1txCWlqFDhwp3F3vftqRvqztP+MCBA3B0dMS8efOQnZ1d7/Fr1qyBg4MDeDweHj58iIqKCjg7OzfYv0gIaTpFuFe4urqif//+jZZb936iivcKSgaICFdXVxQWFqK6uhpOTk54+PAhfH194ebmJvwGrFX7jR4REYGUlBRkZGRg0aJFcHNzQ2xsrETn7dSpE+zs7BrclrSu2nnCtRITExETE4MtW7Zg69at9X5GU1MTOjo60NLSQtu2baGjowNnZ2eJ4iSE1FCWe0VkZCQsLCwaLPPt+4kq3itoNgERMX36dBw+fBgffvghRo4cCQ0NDVRVVcHY2BixsbGws7N772eDgoLQrVs3cDgcZGZmYtasWcL3fH19UVRUJHw9ceLEehcEqm9b0trXteqbJ+zl5YUlS5bAxMRE5Dx1+fn5gcPh4Pjx44iJiVHZUcOESIMy3CvEUd/9RBXvFZQMEBEjRozA7t27kZaWhi1btiA6Ohr29vawsbF5Z5MRNbWaB0u184arqqrg4eEBfX39Jp/f1NQUiYmJAGq2Ja1vY5P65gl/9NFH+Oijj3D79m28ePGi3rJr5yy3b9/+vV0JhBDxKMO9Qhz13U/Mzc0BqNa9gpIBIkJNTQ2dO3fGw4cPoaenB1tbW+FjNi0tLZFjTUxMEBgYiPPnz8PGxgbe3t5wd3dH+/bt0bVrVyxevFh4bO06AI2pb1vS06dPo127dsIpPPXNEz558iQSExNRVlYm7CbYtGmTSF/i+vXrwefzUVhYiJCQkGbVEyGqThnuFQCE257zeDyEhoYiOTm50fuJSt4rGKLS0tLSGABMWloaq3HMmDHjve9t2LCBKS4ulqi8kpISZt26dY0el5yczISHhzMMozh1QYgiUpTvj+beK5pyP2GYln+voAGERCG0adPmnUFHtfz8/NCmTRuJymvdujVWrFjR4DEVFRU4duwYOnbsKFHZhBD2NPde0ZT7iSrcK6ibgAAA6/1iPB4PQM3KXvI0e/Zs4XnZrgNClAHb3yd0r5ANSgZUnKGhIbhcLpycnNgORSFwuVwYGhqyHQYhCofuFaJa2r2C9iYg4PP5KCgoaPCYR48ewcvLC//++y/WrFmD0aNHyym6psvJycG3336LyspKbNmyRayFRwwNDYUDkwghosS5V0jqt99+g6+vL7Zt24Zhw4ZJrdzy8nJMnToVXbt2RWhoqMgOiNLQ0u4VlAyQRp07dw5Tp04Fl8vFsWPH0K9fP7ZDEtuzZ88wbdo0XLhwASEhIXB1dWU7JELI/ysuLoalpSWGDBmChIQEqZd/8uRJTJgwAfHx8ZgxY4bUy29JaAAheS+GYfDDDz9g1KhRsLa2RmpqqlIlAkDNdqanT5+Gq6sreDweXF1d8fr1a7bDIoSgZtrfq1evsGPHDpmUP378eNjb22Pp0qXvXX+E1KBkgNSrsrISLi4ucHd3x8KFC/Hbb7/ByMiI7bCaRFNTEyEhIdi1axdiYmIwcuRIPH78mO2wCFFpqampCAsLg7+/Pzp16iSz8+zYsQOvXr1qdHaRqqNuAvKOR48eYcqUKUhLS0NERATmzp3LdkhSc/HiRUyePBlqamo4evQoBg4cyHZIhKicqqoqDBo0CAzDIDU1FRoash3Lvm3bNnz77be4ePEiBg0aJNNzKStKBoiIS5cuwd7eHhwOBwkJCfj444/ZDknqHj58iClTpiAjIwNRUVHCKUOEEPkIDg6Gp6en3H44V1VVYeDAgeBwOLh8+bLMkw9lRN0ERGjPnj0YNmwYunbtiitXrrTIRAAAOnbsiJSUFDg6OmLOnDnw8PBAVVUV22ERohIePHiAlStXws3NTW6/pWtoaCAyMhKZmZkIDQ2VyzmVDT0ZIHjz5g2+/fZbhISEwMXFBSEhIdDW1mY7LJljGAbh4eH45ptvMGzYMBw8eLBFzRsmRBFNmTIFFy5cQE5ODvT09OR67kWLFmHv3r3Izs6W6TgFZUTJgIp79uwZpk+fjvPnz2PHjh3g8XhSn4+r6M6ePYtp06ahVatWOHbsGPr27ct2SIS0SLVT/Q4cOAAHBwe5n792KqOtrS1++uknuZ9fkVEyoMIyMzMxadIklJWV4ciRI1Jd8EPZ8Pl8TJo0CTdv3sSePXswffp0tkMipEUpLS2FtbU1LCwskJSUxNovHfHx8Zg5cyZOnDiB8ePHsxKDIqIxAyoqPj4etra2aNeuHdLS0lQ6EQBqtkM9f/48Jk6ciBkzZsDPzw/V1dVsh0VIi7Fu3To8fvwYYWFhrD59nDFjBkaPHg13d3eUlpayFoeioWRAxVRXV2P58uWYOXMmJk+ejPPnz6Nz585sh6UQuFwu9u/fjy1btmDz5s2ws7OjhUoIkYJr165h69atWLFiBbp3785qLBwOBz/88AMeP34Mf39/VmNRJNRNoEKKioowc+ZMnD59GgEBAfD09FS58QHi+vXXX+Hg4ABjY2McO3YMVlZWbIdEiFISCAQYNmwYnj9/jszMTIUZnLx+/XqsXbsW6enp6N27N9vhsI6SARVx/fp1TJo0Cc+fP8fBgwfx3//+l+2QFN6dO3cwadIk8Pl87Nu3D3Z2dmyHRIjSiY6OhouLC5KTkzF8+HC2wxGqrKxEv379YGBggD///BNqaqr9oFy1r15FHDt2DIMHD4aOjg5SU1MpERBTjx498Pfff+Pzzz/HxIkTsW7dOggEArbDIkRpPHv2DN7e3pgzZ45CJQIAoK2tjfDwcFy4cAG7d+9mOxzWUTLQggkEAqxZswb29vb44osv8Pfff7PeX6dsdHV1ceTIEaxduxarVq3CtGnTUFJSwnZYhCgFLy8vcDgcbNmyhe1Q6jV8+HDMmTMH3t7eePr0KdvhsIq6CVqokpISzJ49G4mJiVi3bh38/PxofEAzJSYmwsnJCV26dEFiYiIlVoQ0IDk5GSNHjkR0dDTmzZvHdjjv9ezZM1haWmL8+PH48ccf2Q6HNZQMtEB37tzBxIkTkZeXh/3792PChAlsh9Ri3LhxA5MmTUJBQQGNvSDkPSorK9G3b18YGRnh7NmzCt8fv2vXLsyfPx9nzpzBiBEj2A6HFYr9P0QklpSUhIEDB6KqqgqXL1+mREDKevbsicuXL2Pw4MEYM2YMAgMDQfk0IaICAgJw9+5dREREKHwiAABz587F0KFD4ebmhsrKSrbDYYXi/y8RsTAMg82bN+PLL7+Era0tLl26BEtLS7bDapH09fVx4sQJeHt7Y9myZXByckJZWRnbYRHCOldXV7i6umLDhg3w8vKCtbU12yGJRU1NDREREbh79y4CAgLYDocVlAwoserqasyZMwcXL17EV199BR8fH/j6+uL48ePQ19dnO7wWTV1dHRs3bsTBgwdx7NgxDB06FDk5OZgyZQry8/PZDo8QVly5cgU///wzDAwMYGJiwnY4ErG2toaXlxc2bNiAO3fusB2O3NGYASV25MgRTJs2Debm5njw4AFiYmIwbdo0tsNSOVlZWZg4cSJKS0tRWVmJ+fPnIygoiO2wCJE7AwMDFBUVQU1NDQMHDsSFCxeUopugVllZGaytrfGf//wHv/76q0oNulae/yUigmEYrFy5EmpqaigoKMD06dNhb2/PdlgqqW/fvuDxeGjdujVevXqFsLAwFBUVsR0WIXL34sULqKur4/vvv8e5c+eUKhEAapYk/+GHH3D69GkcPHiQ7XDkSrn+p4jQmTNnkJOTA4FAgLKyMjx+/BivX79mOyyV9fjxYxQXF4NhGFRWVsLPz4/tkAiRu3Xr1iE9PR3Lly+HlpYW2+E0yZdffokpU6Zg6dKluH//Pv766y+2Q5IL6iZQUmVlZVi3bh0mTZqEAQMGQFNTk+2QVB7DMLh9+zb279+PmTNn0gBOQpRUfn4+rKysMHDgQJw/fx5lZWVQV1dnOyyZomSAEEIIqcPDwwNnzpzBP//8AwB48uQJjI2NWY5KtjTYDkAW+Hw+CgoK2A5DIRgaGsLMzIztMFokVW5n1K7kg9oYO21s/PjxOHTokPB1fn4+JQPKhs/nw8rKiuZ9/z8ul4vs7Gy6cUuZqrczaleyR22MvTY2atQo5OTkwNXVFQcOHFCJAcEtLhkoKChAWVkZ9u3bp/J70GdnZ8PJyQkFBQV005YyVW5n1K7kg9oYu21MV1cXcXFx2Lt3LzQ0WtyPyne02Cu0srLCgAED2A6DtHDUzoisURtjlyokAgBNLSSEEEJUnmqkPGJKSUlBYGAgwsLCcP/+fcTFxSE/Px/z58+HnZ0dfHx8AACbNm16bxkVFRXQ0dFp9FzfffcdDh8+jH/++eed47ds2QI+n4+uXbvi22+/hbOzMzQ1NaGuro7t27dDW1u7eRdKWKMIbSw3Nxf29vb4+OOP8d///hdTpkyhNtYC1W1rjx8/xtatW/Hhhx8K25Y029ry5cvx9OlTlJeXIzY2VjjVubi4GB4eHsjLy8Pp06elcFX1U+WBlvVpyuBLlU4Gjh49ikePHsHc3ByXL1+Gra0txo8fDzMzM5iZmeHTTz9FUVERvv/+e9jZ2YHH4yEiIuKdcoqKihAfH4+LFy/CwcEBY8eObfTcGzZsqHcN+4yMDPz999/o3Lkz2rdvD6BmIE11dTUMDAyUdiEPVaWIbQwA2rRpg7KyMnTp0gUAtbGWoLG2tnnzZpG2Jc22tnnzZgCAl5cXSktLhXuj6OnpYffu3XBwcJDORdZD1Qda1qcpgy9VOhmwt7fHkiVLcObMGRw8eBB//vmnyPsxMTGIjo7Ghg0b3luGi4sLqqqqwOPx4ObmBgAQCARYuHChyHFff/01Bg0a1GhMN2/ehLm5OTZt2gRHR0dMnjwZP/zwAzgcDnbs2IGkpCSxvjmJYlDENtalSxecPXsWZWVlcHJyQkJCArWxFqCxtiaOpra1x48fw8/PD+Xl5WjVqlXzLkRCqjzQsj5NHXyp0skAwzAoLCyEuro6qqur33nf2dkZjo6OmDlzJj777LN6y3B3d0dcXBx2796NvLw8TJgwoVmrAZqamoLP5wMAWrdujdevX4PL5QIA2rdvj5cvXza5bCJ/itjGajdfqW1Xdb9GbUx5NdbWxNHUtmZiYoLdu3djy5YtuHz5Mj755JMmnb85ZDHQ0sfHp95ulIiICIwZMwZdu3YVuyxfX1+UlpaCy+WKlFlaWopFixZBU1MTw4cPh6OjozRCl5hKJwPbt2/HzJkzYWJigtWrV+OLL74QvvfTTz/hjz/+QFlZGWbOnPneMvr27Yu+ffuiqqoKp06dwpkzZzB27Nh6H7/VFRQUhL///huLFy/G+vXrce7cOWhra2PChAmIi4uDh4cHTExMoK+vDw8PD5SVleHly5fYtWuX1K6fyJ4itjF9fX3ExMSgvLwcM2bMAABqYy1AQ23t1q1bWLt2LW7cuIH//Oc/mDdvXr1lNKWtVVZWwsPDQ7gvh7u7Ow4fPgxtbW1h19eVK1ewfPlyYXeCIsrOzsbatWthYWGBtLQ0nDx5Erm5uQCAPn364Ouvv0Zqaiqio6Px+PFjVFRUiF02n8+HQCDAjh07sGzZMuTl5aFz584AgISEBMyYMQNjx47FjBkzKBlgw9KlS4X/trGxQUpKivD1lClTMGXKFLHL0tDQwIQJE8Q+3tPTE56ensLXdbceDg8PFzl227ZtYpdLFIuitrFhw4aJHEttTPk11NbMzc2xf/9+scuSpK1pa2sjLCxM5Gt121pjSauiiI6ORmBgIExMTDB+/HiR97p06YKlS5ciJCQEmZmZ73z22bNnWLlypcjXli1bhu7duwOoWcGw9oe/mZkZHjx4IHz94MED9O/fHwBY3f+AphbWoa+vj/T0dOFj+rfFxMSgW7duco6KtCTUxoi8UFuTTN1tet7esqd2HISmpiYqKyslLtvU1BQPHjwAAOTl5cHU1LTe9wQCgcRlSwslA3X069cPUVFRMDMzE067qWvNmjUQCATCR0fi8vX1xZIlS94ps7S0FM7OznBxcRHJ2nft2oVRo0YBAO7du4d58+bJdDQukZ/aNvb2b1K1TExMMHr0aInKfF/7AmramI2NDZKSkoRfq9u+3ncMUX7x8fHC+1ldERERyM3NxZo1a7BgwQKxylKFNubi4gIvLy/4+/ujdevWEn3WyMgIERERIn9qnwoAEP4feHh4gMPhwMzMDEFBQcjIyMDkyZMRHx8PNzc3jBs3TqrXJAlKBlDTV+Tg4IDVq1cLHw/V7SsKDg6Go6MjysvLm9VXVF1djby8POF7tX1FO3fuxPHjxwEA//77L54/fw4jIyMAQLdu3agPV8mx1b6Amilf06dPF75+u33VdwxRPtTGmq99+/YwNzfH8+fPMXv2bAA1CVXdv3k8HoYPH441a9ZIvEX5pk2bsG3bNuG4CU9PT/Tv3x+tW7dGTEwMwsPDMWvWLClekWRUesxALUXpKxIIBNi6dSuCgoKEjZEoP7ba1++//46ePXsKb/z1ta+3jyHKidpY8xkYGMDf35/tMFhDyQBk31eUmJgIoKavaOLEiSLvPXjwAL169YJAIMC9e/fw7NkzeHt7IyMjA7/88gu+/PLLplwSUSBsta/k5GSUlpbixo0baNWqFbp16/ZO+/rrr79Ejhk9ejTU1OiBobKhNiZ/MTExMDExwZgxY6RaLo/Hg76+PjZt2oRjx44hKSkJeXl5WLVqFT7++GOpnqsuSgbwv74ic3PzJvcVvU/dviItLS1hX9GIESMwefJkuLu7IzExEePGjUOPHj1w8OBBADWLeHz55Zd4/vw5vvvuO1y5cgUBAQHw9vZu+oUSVrDVvmoXMqq9aZmbm7/TvmqTzdpjWsJNWhVRGxNPXFwcUlJSwOVysXnzZhw6dAiZmZkoLS1FSEgINmzYgOLiYhQVFcHa2hovXrzA/fv3sW/fPtjZ2WHo0KHIzc3FokWLhGXev38fAQEB4HA46N69O8aMGYO1a9fC1NQUc+fORa9evcSO78iRI/joo49w584dAMCkSZMwadIkZGRk4MKFC5QMyJq4fUUAMHz4cInLf3vRirrTvWJiYur9TO1527VrpzRTc0j92GxfQM3CRm+rPW9DxxDlQW1MPPn5+ejduzcmTZoEbW1tcDgcaGlpIScnR9iF4uDgAEtLSzg7O+Po0aNYsGABioqKUF1dDU9PT5SUlGDFihUYOHAgACAsLAytWrUCl8vFtWvXMGTIELRt2xazZs0SSQQa64558uQJMjIy4OLiIkwGACAwMBBHjx7Fzp07ZVo3lAyA+oqIbFH7IrJGbUw8y5YtQ1ZWFry9veHv74+EhAQkJCRgzZo1KC0tBVCzn4K2tjb09PQAAFpaWqisrIRAIEB1dTVev34tXLETqBkn4ezsDGtra+HXTE1NsXv3bmRlZWHOnDlixXb27Fk8ffoU/v7+uHr1Km7dugVzc3N4eXlhzpw58PPzk2lCQMmAFMij7+iXX37Bnj17wOFwMH/+fImnn5GWQRZtbffu3cjIyICuri6+//57qZVLlJO025hAIICbm5tw34K3F1WTp6ioKNy+fRtAzVNXIyMjBAQEIDU1tdEnJtra2vD398fdu3excuVKpKamAqhZwtnPzw8dOnSArq4uhg0bhhMnTuD58+f4/PPPhZ9vrDtm+vTpmD59OnJzcxEREQFzc3Ps3LkTGRkZKCkpgaura/MroAEqmwwoW9/RhQsXsGnTJnC5XAQHB1MyoEQUua09ffoUhw8fhqWlJYyNjWVVBUTGFLmNqampITIyEgAwf/58mVy/uN5eV6E2rtqxWHUTgtou3NDQUACAjo6OyIZidZ8EvL2644gRI5ocY9euXYXdMi4uLk0uR1IqmwwoW9+Rvb09nJycIBAIEBUVJYcaItKiyG3t3r170NPTw7Zt2+Dl5YW7d++KLJZClIMitzEAuHHjBtatWyey9oCyeXsMREujssmAsvUdBQQE4OzZswBqBuLExcVJqyqIjClyW+vYsSPatWsHoKbf+dWrV9K6bCJHitzGAKBnz544cOAAFi1ahPz8fJHleIliUNlkQNn6juzs7ODi4gKGYaQ+NoHIliK3NTMzM+jr68PT0xOvX79G3759m3/BRO4UuY09fPgQ69evh0AggJaWFjp27Nj8C24mBwcHqf+mP3ToUHh7e8POzu692xXXJc4xQMPrDvTt2xc8Hg+DBw8WzhZpMqaFSUtLYwAwaWlpMjvHjBkzZFa2NMmjLlSVvOpWEdsatSv5oDYm3rW/feyCBQuY58+fM1VVVYyjoyOTn5/P+Pj4MDwej0lMTGQY5n/XXPt3eHg4k5yczKSnpzMLFy5keDwes3fvXoliri3r/v37jLe3N8MwDOPl5cXw+fx3jhXnGIZhmMOHDzM7d+5kli9fLvL19PR0JjQ0lGEYhklOTmbCw8PfWx/iohVGmqCl9x0RxUFtjchaS2tj06dPx+HDh/HHH39g5MiR0NDQQFVVFYyNjREbG9vgZ4OCgmBoaIj27du/s3Szr68veDye8M+pU6fqLaO+5Zubckzt2LG6T2GAmnUH3N3dmzVIsT6UDBBCCGkxRowYgXPnzuHIkSOYMmUKYmNjYW9vDz8/P5SUlIgcW7saYu24iqqqKnh4eGDNmjXYunVrk87f0HbFkhxTd+zYH3/8gVu3bgEAvLy8cOzYMWzbtq1J8b2PyicDstgaeOjQocJdCBva+rMuHo8nPGbXrl3g8XgYN24cfH196z2+dt+C2r66iooKODs702qFCozttnbz5k3MmzcPX331FQIDAxsst257TEpKwuDBg6UbOJEJttsYALi6ugo3YKtPfe1Qmm1MTU0NnTt3RkVFBfT09GBra4uoqCgEBQVBS0tL5FgTExMEBgbizz//BFAzxdDd3R3ffvstQkJCRI7duHGjyBbFY8eOrff89W1XfPr0aaSnp0t0zPTp07Fz506sWrUKo0aNEq47sHDhQnh6eko0gFMsEnUqKIG6/SXK0HfEMO/vF/Lw8GBycnLee563+4qk1XdEGqeM/ZR1TZky5b3v1dce6/YrU7uSD2VuY+KOQ6jbDpvaxhSlPTZ0zRs2bGCKi4sb/Lw4x9SHxgyIQRn6jt7XL1RZWYl///0XFhYWElwxYYsytLVahw4dwqhRo+p9733tkbBPmdqYOBpqh8qoTZs2wicob/Pz80ObNm0a/Lw4x7ytoqICx44dk8oMjRY9tXDEiBHYvXs30tLSsGXLFkRHR8Pe3h42NjYi23AC7+870tfXb/L5G9r6s9b71qNOSEiAvb19k89N5EsZ2hoAHDhwAHl5ee/d/fJ97ZGwT1namDgaa4dNkZ2dLbWymqJ2al/dR/3yULsxVe15m1oPLToZqO07evjwobDvKDIyEhYWFu/tOzp//jxsbGyEfUft27dH165dsXjxYuGxGzduFOv89W39efr0abRr1w4DBgwAUP+aAgBw+PBhkSUuN23aJNJP9/fffyMoKAgvXryAiYkJJk2a1KQ6ItKhDG0tIyMDXl5emDBhAjw9PREUFCR2eyTsU4Y2BkC45TqPx0NoaCiSk5MbbYfNYWhoCC6XCycnp2aV05JwuVwYGhpK9BkOwzCMjOJhRXp6OmxsbJCWlibSQOWpoQUtvv/+e7i7u0v0OOjVq1cIDg7GihUrGjwuJSUFOTk5Ihkq23XRUilK3Ta3rYnbHuueR1GuvaVTlHpWhjbG5/NRUFDQ6HGqwtDQUJi8iatFPxlgS23fkZ2d3Tvv+fn5SVxe69atG00EavuORo4cKXH5RHk1t62Jc0xSUhK4XG6T4iPKTxnamJmZmcQ//IioFpsMsNl/pOx9R0R8bNexPNqasbEx3N3dqV2xhO36pjamGlpcMkD9R6Ka0ndEGqfq7YzalexRG6M2Jk8tbswAIP3+o5KSEkyePBkDBgzA5s2bpVYuUDOVa8qUKRg/fnyjCxM1RVP6joh4pNnOfvnlF6xcuRIhISGwtbWVSpm19u/fj6CgIOzdu1dkB7rmoHYlH9JqYwzDwM3NDQ8fPsShQ4ego6MjhehqVFVVYdasWeBwONi7dy80NKTzOya1MTmTeIUDFeTm5sbo6uoy+fn5Mik/ODiY4XA4zKVLl2RSPlFshYWFjLGxMTNt2jSZlP/mzRumf//+TP/+/Zk3b97I5BxEscXGxjIAmFOnTsmk/IsXLzIcDocJDg6WSflE9lrkkwFpunTpEoYMGYLt27eLTMeRpqqqKgwaNAgMwyA1NVVqmTVRDjweD3FxccjJyZHZ9q6XL1/G4MGDsW3bNnzzzTcyOQdRTEVFRbCwsMCIESNw8OBBmZ1n4cKFiI2NRXZ2Njp16iSz8xDZoGSgAVVVVfjoo4+goaGBS5cuQV1dXWbnSk1Nxccff4ygoCAsXbpUZuchiuXvv/+Gra0tduzYIbNks5a7uzt+/PFHulmrGFdXV8THxyMnJwcdOnSQ2XlevHgBS0tLDB06FEeOHJHZeYiMsPpcQsFt3bqVUVNTY65cuSKX8y1atIhp3bo1k5eXJ5fzEXa9fv2a6d27N/PRRx8xVVVVMj/fixcvGBMTkwb3JSAty19//cUAYEJDQ+Vyvri4OAYAc/LkSbmcj0gPPRl4Dz6fj549e2LevHnYvn27XM5ZXFwMS0tLDBkyBAkJCXI5J2FPYGAgli9fjsuXL8PGxkYu5zx48CAcHBxw8uRJjBs3Ti7nJOx48+YNbGxsoK2tjYsXL8r0yWYthmHwxRdf4NatW7h+/TpatWol83MSKWE5GVFYkyZNYjp27NikXaSaIz4+ngHAnDhxQq7nJfKVm5vLcLlcZsmSJXI9r0AgYEaPHs106dKFKS0tleu5iXwFBAQwampqct/N7/bt24y2tvY7u7ASxUbJQD0SExMZAMzhw4flfm6BQMB88cUXjJmZGfPq1Su5n5/Ih52dHSvJJsMwzJ07dxgdHR26WbdgtcnmN998w8r5/f39GQ0NDebq1ausnJ9IjroJ3vLq1Sv07NkTvXr1ws8//wwOhyP3GO7evYtevXphyZIlUl/XgLDv2LFjsLe3x+HDhzF16lRWYtiwYQPWrFmDjIwM9OrVi5UYiGwwDIOJEyciPT0d2dnZ0NXVlXsMlZWV6Nu3LwwNDXHu3DnhLopEgbGcjCgcLy8v5oMPPmDu3bvHahzr169nNDQ0mH/++YfVOIh0lZSUMJ06dWK+/PJLRiAQsBZHRUUFY2lpyXzyySdMdXU1a3EQ6Tt69CgDgPnpp59YjePMmTMMAGbnzp2sxkHEQ08G6sjKyoKNjQ3Wr18vk9UAJfH69Wv069cPbdu2xZ9//kmZdQvx7bffIjw8HNevX8eHH37Iaixnz57F8OHDsXPnTsyfP5/VWIh0lJSUoGfPnujbty9OnDjBypPNuubMmYMTJ07g5s2bMDIyYjUW0gi2sxFFUV1dzQwePJjp2bMnU1lZyXY4DMMwTEpKCgOAiYqKYjsUIgUZGRmMuro6s3HjRrZDEZozZw7Ttm1b5unTp2yHQqTAw8OD+eCDD5h///2X7VAYhmGYJ0+eMG3btmVmz57NdiikEZQM/L+IiAgGAHPu3Dm2QxHh7OzMtG3blnny5AnboZBmqKqqYj7++GPG2tqaef36NdvhCD19+pQxMDCgm3ULkJ6ezqipqTGbNm1iOxQRO3fuZAAwZ86cYTsU0gDqJkDNZkGWlpaYPHkydu3axXY4IgoKCmBhYYFx48Zh7969bIdDmigiIgJubm74888/MXToULbDEbFr1y7Mnz8fZ86cwYgRI9gOhzRBdXU1bG1tUVZWhvT0dGhqarIdkpBAIMCwYcNQUFCArKwsaGtrsx0SqQ/b2YgicHR0ZNq1a8cUFBSwHUq9du3axQBg/vjjD7ZDIU3w6NEjRk9Pj5k3bx7bodSrurqaGTp0KGNhYcFUVFSwHQ5pgrCwMAYAc/78ebZDqdfVq1cZDQ0Nxt/fn+1QyHuofDJw+vRpBgCzZ88etkN5r9qbtbm5Od2sldBXX33FGBoaKmyyyTAMc+3aNbpZK6naZHP+/Plsh9Kg5cuXM9ra2szt27fZDoXUQ6W7CSoqKtCnTx907NgRycnJrI+8bcj169fRr18/rFy5EqtWrWI7HCKm06dPY/To0YiJicGcOXPYDqdBvr6+2LZtG65du4YePXqwHQ4R08yZM/H777/j5s2bMDAwYDuc9yotLYW1tTXMzc3x66+/KvT9ViWxnY2wafXq1YympiZz48YNtkMRi6+vL6Otrc3cunWL7VCIGMrLy5kePXown332GatrCoirtLSU6dq1K/Pf//5XKeIlDPPrr78yAJgff/yR7VDEcvLkSQYAc+DAAbZDIW9R2ScDN2/eRJ8+fbBs2TKsX7+e7XDEUlZWhl69eqF79+747bffKLNWcKtXr8bGjRvxzz//wNLSku1wxPLLL79g3LhxOHDgAFq3bo3PP/8cOjo6bIdF6lFeXo7evXvDzMwMf/zxh9LcD6ZMmYK//voLOTk50NfXZzscUovtbIQNAoGAGTlyJNOtWzemrKyM7XAk8vPPPzMAmLi4OLZDIQ3IyclhtLS0mBUrVrAdisSmTp3KGBsbMxwOh9m/fz/b4ZD3WLlyJaOlpcXk5OSwHYpE8vLymNatWzMLFy5kOxRSh0oua7d//36cOXMGYWFh+OCDD9gORyJffvklpk6dCg8PD7x48YLtcEg9GIaBm5sbOnfuDD8/P7bDkciZM2eQlZWFly9fQkNDA48ePWI7JFKPnJwcbNq0CcuXL4eFhQXb4UikU6dOWL9+PcLDw3H58mW2wyH/T+W6CYqKimBhYYGRI0ciPj6e7XCa5OHDh7C0tISjoyPCw8PZDoe8JTY2FrNnz8avv/6K0aNHsx2ORF68eIG5c+fi2LFjAABHR0fs27eP3aCICIZhMHLkSOTl5eHatWtK2Y1TVVWFQYMGgWEYpKamQkNDg+2QVJ7KPRnw8fFBZWUltm3bxnYoTdaxY0ds2LABkZGRuHjxItvhkDoKCwvx7bffwsHBQekSAQDQ19fH0aNHcfToUejo6OD58+dsh0TeEhsbi5SUFISHhytlIgAAGhoaiIyMRFZWFkJCQtgOh0CFngy4uLjA1tYWX3/9NUJDQ7Fo0SK2Q2qW6upqfPzxx6iqqsK0adNgYWHB2na4BMjOzsb69evB5XJx6NAh5OTkoEOHDmyH1SwCgQAcDkdpBqa1dNu2bYOOjg5WrVqF//73v4iLi2M7pGZzd3dHTEwMtm/fjgcPHmD16tVsh6SyVCIZKC8vB5fLRadOnWBgYIAjR47gP//5D9thNVtMTAy+/vprdOvWDYMGDWoRNwdlFRoaCg8PD1RVVcHb2xtr1qxRuvEoRLENGDAA5eXlePjwIX766Sd8/vnnbIfUbBcvXsTEiROhr6+PiooK3L9/n+2QVJZKdBM8efIEAPDgwQPcvHkTa9euZTmi5isuLgaPx4O+vj7u3btH30Qse/jwIQQCAfT09BAQEIC///6b7ZBIC5OXl4ecnBxwOBy4uLigJfwe5+7ujvLycty6dQuPHj1qEdekrFRi1MbNmzcBAGpqavjmm29axAp+enp6uHz5MhYsWIBLly7h+vXrbIek0s6dOweBQAAul4vY2FiMHDmS1Xj4fD4KCgpYjYEthoaGMDMzYzsMqWIYRvj/OXLkSGzfvr1FdN/88ssv8PLyQmxsLN68eYPi4mJae4AlKpEMWFlZoX///ggLC8PgwYPZDkdq+vTpgwsXLsDPzw///vsv2+GotHHjxsHIyAj79u1Dq1atWI2Fz+fDysoKZWVlrMbBFi6Xi+zs7BaVEHA4HAwbNgwODg5wc3NjOxypMTY2xt69e/Hll18iKCgIurq6bIekslRizAAhqiQ9PR02NjbYt28frKys2A5HrrKzs+Hk5IS0tDQMGDCA7XAIURoq8WSAEFVkZWVFPxAJIWJpcjKgyn2S9ZGkn1KV664p/blUXy3ncbeiojZG35Piaqnfk01KBlS9T7I+4vZTqnrdSdqfS/Uln/7vlJQUBAYGIiwsDL/99hsuX76Mx48fY8OGDejduzd8fHwAAJs2bXpvGRUVFWItgvPxxx+jf//+6NKlC3x9fUXeEwgEmDBhAiZMmAAejwdnZ2doampCXV0d27dvh7a2dvMutB7Uxuh7UhItcUwK0MRkoKCgAGVlZSrZJ1mf2n7KgoKCRhuIKtedJPVUi+pLsvoS19GjR/Ho0SOYm5vj8uXLsLW1xfjx42FmZob58+dj/vz5yMjIwIkTJ9C7d2/weDxERES8U05RURHi4+Nx8eJFODg4YOzYsY2eW1dXF69fv0anTp3eeS80NBTjxo0TvuZyuaiuroaBgQG0tLSad9HvQW2MvifFJcvvSbY1a8wA9Uk2HdWdZKi+pMve3h5LlizBmTNncPDgQfz5558i71dVVSE0NLTBFeFcXFxQVVUFHo8nHOEuEAiwcOFCkeO+/vprDBo0SPj69OnT4HA4cHBwgJ2dHfT09AAA169fR3V1Nfr06YOcnBwAwA8//AAOh4MdO3YgKSlJrGSjqaiNSYbqq2VRuEWHah9Hvi0iIgK5ubkSleXr64slS5a8U2ZpaSmcnZ3h4uKC/fv3NzVUhUD1JTmqs5p564WFhVBXV0d1dbXIe69fv8bChQuxZMmSBn/7cXd3h7GxMXbv3o0jR46gsrJSrHPXzo9v27YtKioqhF///fffcffuXYSGhuLw4cMoKCgQHtu+fXu8fPlS0stkBbUvyVB9KQZWk4Hs7Gw4ODhg9erVGD9+PAAI//P79OmD4OBgODo6ory8HI8fPxa5cTSGz+dDIBBgx44dqK6uRl5envC9hIQEzJgxAzt37sTx48elek2yRPUlOaqz+m3fvh0zZ86Et7f3O7/9+/j44NatWwgPD8fhw4ffW0bfvn2xefNm/PDDD9DW1saZM2egpqaGiIgIkT91nwoUFRXByckJ8+bNg76+Ptq3b4/Dhw/j+PHj+OabbxAaGgp3d3dMmzYNhoaG8PDwgKurK44dO4YJEybIrD6aitqXZKi+FBerUwujo6MRGBgIExMTYcOo1aVLFyxduhQhISHIzMx857PPnj3DypUrRb62bNkydO/eHQCQn5+Pzp07AwDMzMzw4MED4esHDx6gf//+AAB1dXVpX5bMUH1JjuqsfkuXLhX+28bGBikpKcLXQUFBEpWloaEh9g/qtm3bvrMl8rRp00ReDx8+HMOHDwcAhd9dlNqXZKi+FBerTwbqrnf09tpHtau4aWpqiv34sS5TU1M8ePAAQM2a3qampvW+JxAIJC6bLVRfkqM6E4++vj7S09PB5/PrfT8mJgbdunWTc1SKj9qXZKi+FBerTwZcXFzg5eUFc3NztG7dWqLPGhkZ1Tu6uVZtX6eHhwe0tLRgZmaGoKAgjBgxApMnT4a7uzsSExNFRi4rOqovyVGdiadfv36IioqCj49PvdMHTUxMMHr0aInK9PX1RWlpKbhc7jtllpaWYtiwYdiwYQPGjBkDANi1axfi4uLwxx9/vPcYRUPtSzJUXwqMaYK0tDQGAJOWltaUjws9f/6cWblyJbNw4ULm2LFjzSqLTZLUR3PqTtnrqynX3ty2psx11tRrF/dzN27cYGbMmMGsWrWKGTduHMMwDDNjxgyGYRimd+/ezLZt25ivvvqKKSsrY1avXs1kZ2eLHcP9+/cZb29vhmEYxsvLi+Hz+SLvr1y5ktm0aRNz6tQphmEY5t69e8zmzZuF56/vGHHIu40pc/tiGKovSUnrZ58iYvXJgIGBAfz9/dkMQalQfUmO6uz92Oq//f3339GzZ0/h4DCBQICtW7ciKCgIs2fPrvcYRUXtSzJUX4pLqfYmiImJgYmJidQfGfJ4POjr62PTpk3YtWsXUlNTkZeXhz59+mDjxo1SPRdbZFF3rq6uuHz5MjIyMqRWpqKQdn0JBAK4ubmhvLwcrVq1Qnh4uFTKbQ5Gxv23iYmJAGr6bydOnCh8Lzk5GaWlpbhx4wZatWqFbt264dmzZ/D29kZGRgZ++eUX/PXXXyLHjB49GmpqCjcTulmk3cZu3ryJgIAAlJeXY8CAAfDy8pJKuYqC7mGyJfNkIC4uDikpKeByudi8eTMOHTqEzMxMlJaWIiQkBBs2bEBxcTGKiopgbW2NFy9e4P79+9i3bx/s7OwwdOhQ5ObmYtGiRcIy79+/j4CAAHA4HHTv3h1jxozB2rVrYWpqirlz56JXr15ix3fkyBF89NFHuHPnDgBg3rx5mDdvHjw9PeHs7Czt6pCIotddZGQkHBwcZHHpTaLI9aWmpobIyEgAwPz582Vy/ZJiq/92w4YNAP53czc3N8fBgwcBAI8fP8aXX36JL7/8UuQYRUkEFLmNWVhYYNeuXQCAqVOnyuT6JaXI9QUo3j2MTTJPBvLz89G7d29MmjQJ2tra4HA40NLSQk5OjvDxo4ODAywtLeHs7IyjR49iwYIFKCoqQnV1NTw9PVFSUoIVK1Zg4MCBAICwsDC0atUKXC4X165dw5AhQ9C2bVvMmjVLpCE09ijzyZMnyMjIgIuLizAZAIDKykr8+++/sLCwkHHtNEyR604RKXp93bhxA+vWrYORkZHsK0MM7du3h7m5OZ4/fy58PB8fHy/yN4/HAwDhVD9JvD1o0NPTU+R1fcl27XkbOoZNit7GAODQoUMYNWqUbCtCTMpQX6SGzJOBZcuWISsrC97e3vD390dCQgISEhKwZs0alJaWAgD09PSgra0tXJZUS0sLlZWVEAgEqK6uxuvXr4UrkQE1j1ydnZ1hbW0t/JqpqSl2796NrKwszJkzR6zYzp49i6dPn8Lf3x9Xr17FrVu3YG5ujoSEBNjb20uxFppGketOESl6ffXs2RMHDhzAokWLkJ+fLzL1iQ3Ufys5RW9jBw4cQF5eHry9vaV0xc2j6PVF/kfmyUBUVBRu374NAGjXrh2MjIwQEBCA1NTURn/b0NbWhr+/P+7evYuVK1ciNTUVQM0yqH5+fujQoQN0dXUxbNgwnDhxAs+fP8fnn38u/HxjjzKnT5+O6dOnIzc3FxERETA3NwcAHD58WCGWrFTkugOA7777DleuXAGPx0NoaCg0NNgdgqLI9fXw4UOsX78eAoEAWlpa6NixY/MvWIGowhgLQLHbWEZGBry8vDBhwgR4enpKvHiULChyfQGKdw9jVVOmIMhrekXdaUaKTF5TCyWhiHXHxtRCcbWU+pLkc/v372dcXFyYb775hqmoqGD27t3LeHp6Mq6urszr16+Z1atXM0uXLmXmzJnDBAQEMH5+foyjoyPDMAwzYcIEZvPmzYybmxtz7do1Zs+ePcypU6eY3NxcZuHChcyiRYuYoKAg4fRFT09P5urVq02qh3nz5kn92pv7maZoKW2M6oumFsrd2/2HRHxUd5JRxfpS9P5cRRtj0Vyq2Maag+pLvhQ6GSCEyI6i9+cq2hgLQloyuc3XkcX0jaFDhwp3oHrf1pVv4/F4wmN27doFHo+HcePGwdfXt97jr127BicnJzg6OuLatWuoqKiAs7Nzo31R0qQIdSfOMa6ursLNQAAgKSkJgwcPll7QYlKG+hIIBHB1dcXs2bPh5uYGQP71FRUVJdw06O3+3MbU9ud+8803wviBmv7c77//Hl5eXli7di2Sk5Oxbds23Lt3Dz169BAeV9ufW/dP3acCDx8+xMKFC8Hj8aCurq5wYyyUoY3dvHkT8+bNw1dffYXAwEAAqv09+fb9qT5vl8NWfbFBKsmAq6srCgsLUV1dDScnJzx8+BC+vr5wc3N7Z7vI2kYRERGBlJQUZGRkYNGiRXBzc0NsbKxE5+3UqRPs7Owa3Lqyrto1BWrNmzcPERERsLCweO8UppCQEISHhyMsLAwhISHQ0dGR6nQnZag7ces3MjJSZDrmmDFj0LVrV4niakxLqa/adQf27t2LN2/eAJBNfTVkwYIF2LJlCw4cOAADAwNERkbC29sbP//8M4YPH441a9bA0tISOjo6iImJAQCEhobCxMQEOjo62LBhA+Lj42FtbQ1nZ2eMGTMGXbp0wf79+xEYGIjVq1djxIgRCAoKwo8//ohPPvlE7Ng6duyIsLAwREREYMeOHSJPH2StpbSx2nUH4uLicPHiRQCq+z0JvHt/elt95cj7e5JNUukmmD59Og4fPowPP/wQI0eOhIaGBqqqqmBsbIzY2FjY2dm997NBQUHo1q0bOBwOMjMzMWvWLOF7vr6+KCoqEr6eOHEixo4d+04ZDS19WqupawqUlJRAV1dX+G9pU4a6E+cYeWlJ9aXMfeItuT+3JbUxQPbrDihDfYlDke5zbJDKk4ERI0bg3LlzOHLkCKZMmYLY2FjY29vDz8/vnR+gtSuJ1fZJVlVVwcPDA2vWrMHWrVubdP6Gtq6sVXdNgT/++AO3bt0CgEbXFGjdujVKSkrw8uVLiVdpE4cy1J04x8hLS6qv2j7x6upq5OfnNykeaWD7EW59j7PrI69uqJbUxg4cOIDc3FyRrhxpU4b6kmc5ykoqTwbU1NTQuXNnPHz4EHp6erC1tRU+ktHS0hI51sTEBIGBgTh//jxsbGzg7e0Nd3d3tG/fHl27dsXixYuFx4q7L0B9S5+ePn0a7dq1w4ABAwCIv6bApk2bRG5a7u7ucHd3h0AgkMlCHspQd+IcA8hnzm5LqS95rTvg6uqKjRs3Qk9PD3PmzEFAQABCQkLw4sULjB07VuS3NgcHB8THxyMiIgKWlpbQ09NDdHQ0BAIBbG1tRX5ra0x9j3CXLVuGvLy8d37bEncZ3beXjh0zZoyw+0KaWkobk9e6A8pQX8C796fk5ORG61SlNGU+oqLMtWxoHuqGDRuY4uJiicorKSlh1q1b1+hxycnJTHh4uPC1Iq4z0Jjm1p249Vv3PIo8p7kxylJfb3/u999/ZyIiIphff/2V2bVrF/PkyRPGy8uLWbVqFTN16lSRc9b+HR4eziQnJzNOTk7MqlWrmNWrVzOenp4i5/Dx8WFcXV2Ff3755Zd6r+PChQtMSEgIwzAMs2PHDubChQvvjfvgwYNMWFhYg9f29v/D26+pjdH3JMMoVn0pC8XY/aOJ2rRp884AlVp+fn5o06aNROW1bt0aK1asaPCYiooKHDt2TOFGN0uquXUnzjFJSUngcrlNjlGRKGt9KcsjXHk8zlZ0ytrG2EL1JV3Neo6bnZ0trTiapHYTlfT0dLmet3ZTl9rzNqUeVKHujI2N4e7u3qx6qkX11TTK8Ai3vsfZbHRDURuTDNVXC9OUxwn3799nuFwuA4D+/P8fLpfL3L9/n+pOSvVE9dW0+mIYxXiUycYjXIZp2rVTG6PvSVl/TyqDJqXWZmZmyM7ORkFBQVM+3iIZGhqKNeBE1etO3HqqRfUlWX0pitpHuPVNK/Pz82v08+IcI61HuNTG6HtSEsr6PdkYDsMwDNtBEEKkJz09HTY2NkhLSxN5zK4KVPnaCWkO2puAkBaqRfdvvocqXjMh0kDJACEtjKGhIbhcLpycnNgOhRVcLheGhoZsh0GIUqFuAkJaID6fL5U+3djYWGzfvh2xsbGwsrKSQmT/8+zZM0yZMgWjR49udEqvJFpqny4hskTJACGkXnw+H1ZWVpg/fz62b98uk3OEhYVh0aJF+Ouvv2BrayuTcxBCGkfJACGkXpMmTUJqaiqys7MlXsBLXNXV1RgyZAjKy8uRnp4OTU1NmZyHENIwpV6BkBAiG4mJiUhMTMT27dtllggAgLq6OiIjI3Hjxg1s27ZNZuchhDSMngwQQkS8evUKPXv2RO/evXHy5ElwOByZn9PDw0OYFKjK/vGEKBJKBgghIry8vBAWFobr16/jww8/lMs5S0pKYGVlhX79+uHEiRNySUAIIf9D3QSEEKGsrCwEBwdj1apVcksEAEBXVxc7duzAzz//jGPHjsntvISQGvRkgBACABAIBLC1tUVJSQkyMjLe2chI1hiGgZ2dHTIyMpCdnQ1dXV25np8QVUZPBgghAICoqChcunQJkZGRck8EAIDD4SAkJASFhYVYvXq13M9PiCqjJwOEEDx58gQWFhaYOnUqoqOjWY0lICAAvr6+uHLlCvr3789qLISoCkoGCCFwdHTEb7/9hpycHLRr147VWN68eYMBAwbggw8+wN9//w11dXVW4yFEFVA3ASEq7vfff0dcXBwCAwNZTwQAQFNTE5GRkUhNTUVkZCTb4RCiEujJACEqrKKiAn369EHHjh2RnJysUFP6FixYgIMHD+LmzZswMTFhOxxCWjR6MkCICtu0aRNyc3MRHh6uUIkAUBObtrY2PDw82A6FkBaPkgFCVNTNmzexceNGeHt7S31HQmkwMDDA1q1bER8fj99++43tcAhp0aibgBAVxDAMPv/8c9y/fx9Xr17FBx98wHZI9WIYBqNGjQKfz1foOAlRdvRkgBAVtH//fpw5cwY//PCDQv+A5XA4CA8PR15eHjZu3Mh2OIS0WPRkgBAVU1hYCEtLS4wcORLx8fFshyOWVatWYdOmTfjnn39gaWnJdjiEtDiUDBCiYlxdXREfH4+cnBx06NCB7XDEUlFRgV69eqFz5844c+aMwg12JETZUTcBISrkwoULiIqKwvfff680iQAA6OjoIDw8HCkpKYiNjWU7HEJaHHoyQIiKePPmDWxsbKCjo6O0K/t99dVXOH36NG7evAkDAwO2wyGkxaAnA4SoiODgYFy/fh0RERFKmQgAQFBQEN68eYPly5ezHQohLQo9GSCkhXv06BFev36Nnj17YsGCBdi2bRvbITVLeHg4Fi5ciPPnz6N79+5o3749jSEgpJkoGSCkBbtx4wZ69eqFUaNGITs7G9nZ2dDV1WU7rGYRCASwtbXFq1evcP/+fcTGxmLSpElsh0WIUqNuAkJasLt374JhGPz+++/o27cvLl26xHZIzVY7CyI7Oxtv3rzBnTt32A6JEKVHyQAhLVhubi4AQENDA5cuXQKXy2U3ICn44IMPkJWVBQ6Hg8rKSty6dYvtkAhRepQMENKCXb58GQAwefJk5OTkwNbWluWImu/DDz/EtWvXhBsYpaensxwRIcqPxgwQ0oIVFRXh6tWrGDZsGNuhyERGRgb09fXx4Ycfsh0KIUqNkgFCCCFExVE3ASGEEKLiNNgOgBBlxefzUVBQwHYYrDA0NISZmZnEn6M6k7zOCJEHSgYIaQI+nw8rKyuUlZWxHQoruFwusrOzJfrhRnUmeZ0RIi+UDBDSBAUFBSgrK8O+fftgZWXFdjhylZ2dDScnJxQUFEj0g43qTPI6I0ReKBkgpBmsrKwwYMAAqZTl4+ODTZs2vfP1iIgIjBkzBl27dhW7LF9fX5SWloLL5YqUWVpaikWLFkFTUxPDhw+Ho6OjNEKXiLTqTFXqixB5oAGEhLAgOzsbDg4OWL16NcaPHw/gfwsE9enTB8HBwXB0dER5eTkeP36MiooKscvm8/kQCATYsWMHqqurkZeXJ3wvISEBM2bMwM6dO3H8+HGpXpMsUX0RIlv0ZIAQFkRHRyMwMBAmJibCH261unTpgqVLlyIkJASZmZnvfPbZs2dYuXKlyNeWLVuG7t27AwDy8/PRuXNnAICZmRkePHggfP3gwQP0798fAJRq50KqL0Jki54MEMKCust7vL3UR6tWrQAAmpqaqKyslLhsU1NTPHjwAACQl5cHU1PTet8TCAQSl80Wqi9CZIueDBDCAhcXF3h5ecHc3BytW7eW6LNGRkaIiIh47/u1A9Q8PDygpaUFMzMzBAUFYcSIEZg8eTLc3d2RmJiIcePGNesa5InqixDZohUICWmC9PR02NjYIC0trUmD4QoLCxEcHIznz59j9OjRmDhxogyilI2mXntz6kyZ6wtofnshRNboyQAhLDAwMIC/vz/bYSgNqi9CZIvGDBCiRGJiYpCUlCS18m7evIl58+bhq6++QmBgoNTKVRTSri8AcHV1FQ4qJKSloCcDhMhYXFwcUlJSwOVysXnzZhw6dAiZmZkoLS1FSEgINmzYgOLiYhQVFcHa2hovXrzA/fv3sW/fPtjZ2WHo0KHIzc3FokWLhGXev38fAQEB4HA46N69O8aMGYO1a9fC1NQUc+fORa9evcSKzcLCArt27QIATJ06VSbXLylFri8AiIyMhIODgywunRDWUDJAiIzl5+ejd+/emDRpErS1tcHhcKClpYWcnBzhVDgHBwdYWlrC2dkZR48exYIFC1BUVITq6mp4enqipKQEK1aswMCBAwEAYWFhaNWqFbhcLq5du4YhQ4agbdu2mDVrlsgPtsam1dU6dOgQRo0aJduKEJMy1BchLQ0lA4TI2LJly5CVlQVvb2/4+/sjISEBCQkJWLNmDUpLSwEAenp60NbWhp6eHgBAS0sLlZWVEAgEqK6uxuvXr8HhcIRlCgQCODs7w9raWvg1U1NT7N69G1lZWZgzZ47Y8R04cAB5eXnw9vaW0hU3j6LXFyEtESUDhMhYVFQUbt++DQBo164djIyMEBAQgNTUVAwfPrzBz2pra8Pf3x93797FypUrkZqaCgBwd3eHn58fOnToAF1dXQwbNgwnTpzA8+fP8fnnnws/39i0uoyMDHh5eWHChAnw9PREUFBQ8y+4mRS5vgDgu+++w5UrV8Dj8RAaGgoNDbqNEuVHUwsJaQJ5TRVzcHBAfHy8zMpvCjamFopLEesLoKmFRPHRbAJCFJgi/mBTZFRfhDQNJQOEEEKIiqNkgBA5kcV0tKFDhwp30/P19cWSJUvg4+NT77HirinwdjlJSUkYPHiw1GNvDNv1Je4xb687wFZ9EdIclAwQIgWurq4oLCxEdXU1nJyc8PDhQ/j6+sLNze2drW9rf8hFREQgJSUFGRkZWLRoEdzc3BAbGyvReTt16gQ7O7sGt+GtVbumQFxcHC5evFhvefWVM2bMGHTt2lWiuBqjDPUlzjFAzboDFhYWwteyqC9CZI2GwRIiBdOnT8fhw4fx4YcfYuTIkdDQ0EBVVRWMjY0RGxsLOzu79342KCgI3bp1A4fDQWZmJmbNmiV8z9fXF0VFRcLXEydOxNixY98po6FteN/W0JoCkpTTHMpQX/KqC0IUAT0ZIEQKRowYgXPnzuHIkSOYMmUKYmNjYW9vDz8/P5SUlIgcq6ZW821XO2e+qqoKHh4eWLNmDbZu3dqk8ze0DW9dBw4cQG5uLtzc3JpVTnMpQ33Jqy4IUQT0ZIAQKVBTU0Pnzp3x8OFD6OnpwdbWVvj4WEtLS+RYExMTBAYG4vz587CxsYG3tzfc3d3Rvn17dO3aFYsXLxYeu3HjRrHOX982vKdPn0a7du2EU9nqW1Pg7WPqK0cWlKG+xDkGoHUHSAvBEEIklpaWxgBg0tLSWI1jxowZ731vw4YNTHFxcYOfF+eYt8/T1GtXhDpjo74YRjGunZCGUDcBIUqsTZs27wy4q+Xn54c2bdo0+HlxjklKSgKXy21yjIqE6ouQ+tHzLEKaITs7m9Xz83g8ADUr3MmKsbEx3N3dhedo7jWzWWds1BfAfjshpDGUDBDSBIaGhuByuXBycmI7FFZwuVwYGhpK9BmqM8nrjBB5ob0JCGkiPp+PgoICtsNghaGhYZMGF1KdyWZAJiHNRckAIYQQouJoACEhhBCi4igZIIQQQlQcJQOEEEKIiqNkgBBCCFFxlAwQQgghKo6SAUIIIUTFUTJACCGEqDhKBgghhBAVR8kAIYQQouIoGSCEEEJUHCUDhBBCiIqjZIAQQghRcZQMEEIIISqOkgFCCCFExVEyQAghhKg4SgYIIYQQFUfJACGEEKLiKBkghBBCVBwlA4QQQoiKo2SAEEIIUXGUDBBCCCEqjpIBQgghRMVRMkAIIYSoOEoGCCGEEBVHyQAhhBCi4v4PMP5Jj5JOjDoAAAAASUVORK5CYII=",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_24_1.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.datasets import load_iris\n",
|
||
"from sklearn import tree\n",
|
||
"X, y = load_iris(return_X_y=True)\n",
|
||
"tree_clf = tree.DecisionTreeClassifier()\n",
|
||
"tree_clf = tree_clf.fit(X, y)\n",
|
||
"# and then plot the tree\n",
|
||
"tree.plot_tree(tree_clf)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Alternatively, the tree can also be exported in textual format with the function exporttext.\n",
|
||
"This method doesn’t require the installation of external libraries and is more compact:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"|--- petal width (cm) <= 0.80\n",
|
||
"| |--- class: 0\n",
|
||
"|--- petal width (cm) > 0.80\n",
|
||
"| |--- petal width (cm) <= 1.75\n",
|
||
"| | |--- class: 1\n",
|
||
"| |--- petal width (cm) > 1.75\n",
|
||
"| | |--- class: 2\n",
|
||
"\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.datasets import load_iris\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.tree import export_text\n",
|
||
"iris = load_iris()\n",
|
||
"decision_tree = DecisionTreeClassifier(random_state=0, max_depth=2)\n",
|
||
"decision_tree = decision_tree.fit(iris.data, iris.target)\n",
|
||
"r = export_text(decision_tree, feature_names=iris['feature_names'])\n",
|
||
"print(r)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Algorithms for Setting up Decision Trees\n",
|
||
"\n",
|
||
"Two algorithms stand out in the set up of decision trees:\n",
|
||
"1. The CART (Classification And Regression Tree) algorithm for both classification and regression\n",
|
||
"\n",
|
||
"2. The ID3 algorithm based on the computation of the information gain for classification\n",
|
||
"\n",
|
||
"We discuss both algorithms with applications here. The popular library\n",
|
||
"**Scikit-Learn** uses the CART algorithm. For classification problems\n",
|
||
"you can use either the **gini** index or the **entropy** to split a tree\n",
|
||
"in two branches.\n",
|
||
"\n",
|
||
"### The CART algorithm for Classification\n",
|
||
"\n",
|
||
"For classification, the CART algorithm splits the data set in two subsets using a single feature $k$ and a threshold $t_k$.\n",
|
||
"This could be for example a threshold set by a number below a certain circumference of a malign tumor.\n",
|
||
"\n",
|
||
"How do we find these two quantities?\n",
|
||
"We search for the pair $(k,t_k)$ that produces the purest subset using for example the **gini** factor $G$.\n",
|
||
"The cost function it tries to minimize is then"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"C(k,t_k) = \\frac{m_{\\mathrm{left}}}{m}G_{\\mathrm{left}}+ \\frac{m_{\\mathrm{right}}}{m}G_{\\mathrm{right}},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $G_{\\mathrm{left/right}}$ measures the impurity of the left/right subset and $m_{\\mathrm{left/right}}$\n",
|
||
" is the number of instances in the left/right subset\n",
|
||
"\n",
|
||
"Once it has successfully split the training set in two, it splits the subsets using the same logic, then the subsubsets\n",
|
||
"and so on, recursively. It stops recursing once it reaches the maximum depth (defined by the\n",
|
||
"$max\\_depth$ hyperparameter), or if it cannot find a split that will reduce impurity. A few other\n",
|
||
"hyperparameters control additional stopping conditions such as the $min\\_samples\\_split$,\n",
|
||
"$min\\_samples\\_leaf$, $min\\_weight\\_fraction\\_leaf$, and $max\\_leaf\\_nodes$.\n",
|
||
"\n",
|
||
"\n",
|
||
"### The CART algorithm for Regression\n",
|
||
"\n",
|
||
"The CART algorithm for regression works is similar to the one for classification except that instead of trying to split the\n",
|
||
"training set in a way that minimizes say the **gini** or **entropy** impurity, it now tries to split the training set in a way that minimizes our well-known mean-squared error (MSE). The cost function is now"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"C(k,t_k) = \\frac{m_{\\mathrm{left}}}{m}\\mathrm{MSE}_{\\mathrm{left}}+ \\frac{m_{\\mathrm{right}}}{m}\\mathrm{MSE}_{\\mathrm{right}}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Here the MSE for a specific node is defined as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathrm{MSE}_{\\mathrm{node}}=\\frac{1}{m_\\mathrm{node}}\\sum_{i\\in \\mathrm{node}}(\\overline{y}_{\\mathrm{node}}-y_i)^2,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"with"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\overline{y}_{\\mathrm{node}}=\\frac{1}{m_\\mathrm{node}}\\sum_{i\\in \\mathrm{node}}y_i,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"the mean value of all observations in a specific node.\n",
|
||
"\n",
|
||
"Without any regularization, the regression task for decision trees, \n",
|
||
"just like for classification tasks, is prone to overfitting.\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"### Computing the Gini index\n",
|
||
"\n",
|
||
"The example we will look at is a classical one in many Machine\n",
|
||
"Learning applications. Based on various meteorological features, we\n",
|
||
"have several so-called attributes which decide whether we at the end\n",
|
||
"will do some outdoor activity like skiing, going for a bike ride etc\n",
|
||
"etc. The table here contains the feautures **outlook**, **temperature**,\n",
|
||
"**humidity** and **wind**. The target or output is whether we ride\n",
|
||
"(True=1) or whether we do something else that day (False=0). The\n",
|
||
"attributes for each feature are then sunny, overcast and rain for the\n",
|
||
"outlook, hot, cold and mild for temperature, high and normal for\n",
|
||
"humidity and weak and strong for wind.\n",
|
||
"\n",
|
||
"The table here summarizes the various attributes and\n",
|
||
"<table border=\"1\">\n",
|
||
"<thead>\n",
|
||
"<tr><th align=\"center\">Day</th> <th align=\"center\">Outlook </th> <th align=\"center\">Temperature</th> <th align=\"center\">Humidity</th> <th align=\"center\"> Wind </th> <th align=\"center\">Ride</th> </tr>\n",
|
||
"</thead>\n",
|
||
"<tbody>\n",
|
||
"<tr><td align=\"center\"> 1 </td> <td align=\"center\"> Sunny </td> <td align=\"center\"> Hot </td> <td align=\"center\"> High </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 0 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 2 </td> <td align=\"center\"> Sunny </td> <td align=\"center\"> Hot </td> <td align=\"center\"> High </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 3 </td> <td align=\"center\"> Overcast </td> <td align=\"center\"> Hot </td> <td align=\"center\"> High </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 4 </td> <td align=\"center\"> Rain </td> <td align=\"center\"> Mild </td> <td align=\"center\"> High </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 5 </td> <td align=\"center\"> Rain </td> <td align=\"center\"> Cool </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 6 </td> <td align=\"center\"> Rain </td> <td align=\"center\"> Cool </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 0 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 7 </td> <td align=\"center\"> Overcast </td> <td align=\"center\"> Cool </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 8 </td> <td align=\"center\"> Sunny </td> <td align=\"center\"> Mild </td> <td align=\"center\"> High </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 0 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 9 </td> <td align=\"center\"> Sunny </td> <td align=\"center\"> Cool </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 10 </td> <td align=\"center\"> Rain </td> <td align=\"center\"> Mild </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 11 </td> <td align=\"center\"> Sunny </td> <td align=\"center\"> Mild </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 12 </td> <td align=\"center\"> Overcast </td> <td align=\"center\"> Mild </td> <td align=\"center\"> High </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 13 </td> <td align=\"center\"> Overcast </td> <td align=\"center\"> Hot </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 14 </td> <td align=\"center\"> Rain </td> <td align=\"center\"> Mild </td> <td align=\"center\"> High </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 0 </td> </tr>\n",
|
||
"</tbody>\n",
|
||
"</table>\n",
|
||
"\n",
|
||
"### Simple Python Code to read in Data and perform Classification"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 6,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
" (0, 0)\t1.0\n",
|
||
" (0, 7)\t1.0\n",
|
||
" (0, 9)\t1.0\n",
|
||
" (0, 13)\t1.0\n",
|
||
" (1, 3)\t1.0\n",
|
||
" (1, 5)\t1.0\n",
|
||
" (1, 8)\t1.0\n",
|
||
" (1, 12)\t1.0\n",
|
||
" (2, 3)\t1.0\n",
|
||
" (2, 5)\t1.0\n",
|
||
" (2, 8)\t1.0\n",
|
||
" (2, 11)\t1.0\n",
|
||
" (3, 1)\t1.0\n",
|
||
" (3, 5)\t1.0\n",
|
||
" (3, 8)\t1.0\n",
|
||
" (3, 12)\t1.0\n",
|
||
" (4, 2)\t1.0\n",
|
||
" (4, 6)\t1.0\n",
|
||
" (4, 8)\t1.0\n",
|
||
" (4, 12)\t1.0\n",
|
||
" (5, 2)\t1.0\n",
|
||
" (5, 4)\t1.0\n",
|
||
" (5, 10)\t1.0\n",
|
||
" (5, 12)\t1.0\n",
|
||
" (6, 2)\t1.0\n",
|
||
" :\t:\n",
|
||
" (8, 12)\t1.0\n",
|
||
" (9, 3)\t1.0\n",
|
||
" (9, 4)\t1.0\n",
|
||
" (9, 10)\t1.0\n",
|
||
" (9, 12)\t1.0\n",
|
||
" (10, 2)\t1.0\n",
|
||
" (10, 6)\t1.0\n",
|
||
" (10, 10)\t1.0\n",
|
||
" (10, 12)\t1.0\n",
|
||
" (11, 3)\t1.0\n",
|
||
" (11, 6)\t1.0\n",
|
||
" (11, 10)\t1.0\n",
|
||
" (11, 11)\t1.0\n",
|
||
" (12, 1)\t1.0\n",
|
||
" (12, 6)\t1.0\n",
|
||
" (12, 8)\t1.0\n",
|
||
" (12, 11)\t1.0\n",
|
||
" (13, 1)\t1.0\n",
|
||
" (13, 5)\t1.0\n",
|
||
" (13, 10)\t1.0\n",
|
||
" (13, 12)\t1.0\n",
|
||
" (14, 2)\t1.0\n",
|
||
" (14, 6)\t1.0\n",
|
||
" (14, 8)\t1.0\n",
|
||
" (14, 11)\t1.0\n",
|
||
"Train set accuracy with Decision Tree: 0.73\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0"
|
||
]
|
||
},
|
||
"execution_count": 6,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Common imports\n",
|
||
"import numpy as np\n",
|
||
"import pandas as pd\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn.tree import export_graphviz\n",
|
||
"from sklearn.preprocessing import StandardScaler, OneHotEncoder\n",
|
||
"from sklearn.compose import ColumnTransformer\n",
|
||
"from IPython.display import Image \n",
|
||
"from pydot import graph_from_dot_data\n",
|
||
"import os\n",
|
||
"\n",
|
||
"# Where to save the figures and data files\n",
|
||
"PROJECT_ROOT_DIR = \"Results\"\n",
|
||
"FIGURE_ID = \"Results/FigureFiles\"\n",
|
||
"DATA_ID = \"DataFiles/\"\n",
|
||
"\n",
|
||
"if not os.path.exists(PROJECT_ROOT_DIR):\n",
|
||
" os.mkdir(PROJECT_ROOT_DIR)\n",
|
||
"\n",
|
||
"if not os.path.exists(FIGURE_ID):\n",
|
||
" os.makedirs(FIGURE_ID)\n",
|
||
"\n",
|
||
"if not os.path.exists(DATA_ID):\n",
|
||
" os.makedirs(DATA_ID)\n",
|
||
"\n",
|
||
"def image_path(fig_id):\n",
|
||
" return os.path.join(FIGURE_ID, fig_id)\n",
|
||
"\n",
|
||
"def data_path(dat_id):\n",
|
||
" return os.path.join(DATA_ID, dat_id)\n",
|
||
"\n",
|
||
"def save_fig(fig_id):\n",
|
||
" plt.savefig(image_path(fig_id) + \".png\", format='png')\n",
|
||
"\n",
|
||
"infile = open(data_path(\"rideclass.csv\"),'r')\n",
|
||
"\n",
|
||
"# Read the experimental data with Pandas\n",
|
||
"from IPython.display import display\n",
|
||
"ridedata = pd.read_csv(infile,names = ('Outlook','Temperature','Humidity','Wind','Ride'))\n",
|
||
"ridedata = pd.DataFrame(ridedata)\n",
|
||
"\n",
|
||
"# Features and targets\n",
|
||
"X = ridedata.loc[:, ridedata.columns != 'Ride'].values\n",
|
||
"y = ridedata.loc[:, ridedata.columns == 'Ride'].values\n",
|
||
"\n",
|
||
"# Create the encoder.\n",
|
||
"encoder = OneHotEncoder(handle_unknown=\"ignore\")\n",
|
||
"# Assume for simplicity all features are categorical.\n",
|
||
"encoder.fit(X) \n",
|
||
"# Apply the encoder.\n",
|
||
"X = encoder.transform(X)\n",
|
||
"print(X)\n",
|
||
"# Then do a Classification tree\n",
|
||
"tree_clf = DecisionTreeClassifier(max_depth=2)\n",
|
||
"tree_clf.fit(X, y)\n",
|
||
"print(\"Train set accuracy with Decision Tree: {:.2f}\".format(tree_clf.score(X,y)))\n",
|
||
"#transfer to a decision tree graph\n",
|
||
"export_graphviz(\n",
|
||
" tree_clf,\n",
|
||
" out_file=\"DataFiles/ride.dot\",\n",
|
||
" rounded=True,\n",
|
||
" filled=True\n",
|
||
")\n",
|
||
"cmd = 'dot -Tpng DataFiles/cancer.dot -o DataFiles/cancer.png'\n",
|
||
"os.system(cmd)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"The above functions (gini, entropy and misclassification error) are\n",
|
||
"important components of the so-called CART algorithm. We will discuss\n",
|
||
"this algorithm below after we have discussed the information gain\n",
|
||
"algorithm ID3.\n",
|
||
"\n",
|
||
"In the example here we have converted all our attributes into numerical values $0,1,2$ etc."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"X1 < 0.000 Gini=0.408\n",
|
||
"X1 < 0.000 Gini=0.408\n",
|
||
"X1 < 1.000 Gini=0.394\n",
|
||
"X1 < 2.000 Gini=0.394\n",
|
||
"X1 < 2.000 Gini=0.394\n",
|
||
"X1 < 2.000 Gini=0.394\n",
|
||
"X1 < 1.000 Gini=0.394\n",
|
||
"X1 < 0.000 Gini=0.408\n",
|
||
"X1 < 0.000 Gini=0.408\n",
|
||
"X1 < 2.000 Gini=0.394\n",
|
||
"X1 < 0.000 Gini=0.408\n",
|
||
"X1 < 1.000 Gini=0.394\n",
|
||
"X1 < 1.000 Gini=0.394\n",
|
||
"X1 < 2.000 Gini=0.394\n",
|
||
"X2 < 0.000 Gini=0.408\n",
|
||
"X2 < 0.000 Gini=0.408\n",
|
||
"X2 < 0.000 Gini=0.408\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X2 < 2.000 Gini=0.407\n",
|
||
"X2 < 2.000 Gini=0.407\n",
|
||
"X2 < 2.000 Gini=0.407\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X2 < 2.000 Gini=0.407\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X2 < 0.000 Gini=0.408\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"Split: [X3 < 1.000]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"# Split a dataset based on an attribute and an attribute value\n",
|
||
"def test_split(index, value, dataset):\n",
|
||
"\tleft, right = list(), list()\n",
|
||
"\tfor row in dataset:\n",
|
||
"\t\tif row[index] < value:\n",
|
||
"\t\t\tleft.append(row)\n",
|
||
"\t\telse:\n",
|
||
"\t\t\tright.append(row)\n",
|
||
"\treturn left, right\n",
|
||
" \n",
|
||
"# Calculate the Gini index for a split dataset\n",
|
||
"def gini_index(groups, classes):\n",
|
||
"\t# count all samples at split point\n",
|
||
"\tn_instances = float(sum([len(group) for group in groups]))\n",
|
||
"\t# sum weighted Gini index for each group\n",
|
||
"\tgini = 0.0\n",
|
||
"\tfor group in groups:\n",
|
||
"\t\tsize = float(len(group))\n",
|
||
"\t\t# avoid divide by zero\n",
|
||
"\t\tif size == 0:\n",
|
||
"\t\t\tcontinue\n",
|
||
"\t\tscore = 0.0\n",
|
||
"\t\t# score the group based on the score for each class\n",
|
||
"\t\tfor class_val in classes:\n",
|
||
"\t\t\tp = [row[-1] for row in group].count(class_val) / size\n",
|
||
"\t\t\tscore += p * p\n",
|
||
"\t\t# weight the group score by its relative size\n",
|
||
"\t\tgini += (1.0 - score) * (size / n_instances)\n",
|
||
"\treturn gini\n",
|
||
"\n",
|
||
"# Select the best split point for a dataset\n",
|
||
"def get_split(dataset):\n",
|
||
"\tclass_values = list(set(row[-1] for row in dataset))\n",
|
||
"\tb_index, b_value, b_score, b_groups = 999, 999, 999, None\n",
|
||
"\tfor index in range(len(dataset[0])-1):\n",
|
||
"\t\tfor row in dataset:\n",
|
||
"\t\t\tgroups = test_split(index, row[index], dataset)\n",
|
||
"\t\t\tgini = gini_index(groups, class_values)\n",
|
||
"\t\t\tprint('X%d < %.3f Gini=%.3f' % ((index+1), row[index], gini))\n",
|
||
"\t\t\tif gini < b_score:\n",
|
||
"\t\t\t\tb_index, b_value, b_score, b_groups = index, row[index], gini, groups\n",
|
||
"\treturn {'index':b_index, 'value':b_value, 'groups':b_groups}\n",
|
||
" \n",
|
||
"dataset = [[0,0,0,0,0],\n",
|
||
" [0,0,0,1,1],\n",
|
||
" [1,0,0,0,1],\n",
|
||
" [2,1,0,0,1],\n",
|
||
" [2,2,1,0,1],\n",
|
||
" [2,2,1,1,0],\n",
|
||
" [1,2,1,1,1],\n",
|
||
" [0,1,0,0,0],\n",
|
||
" [0,2,1,0,1],\n",
|
||
" [2,1,1,0,1],\n",
|
||
" [0,1,1,1,1],\n",
|
||
" [1,1,0,1,1],\n",
|
||
" [1,0,1,0,1],\n",
|
||
" [2,1,0,1,0]]\n",
|
||
"\n",
|
||
"split = get_split(dataset)\n",
|
||
"print('Split: [X%d < %.3f]' % ((split['index']+1), split['value']))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Entropy and the ID3 algorithm\n",
|
||
"\n",
|
||
"The ID3 algorithm learns decision trees by constructing\n",
|
||
"them in a top down way, beginning with the question **which attribute should be tested at the root of the tree**?\n",
|
||
"\n",
|
||
"1. Each instance attribute is evaluated using a statistical test to determine how well it alone classifies the training examples.\n",
|
||
"\n",
|
||
"2. The best attribute is selected and used as the test at the root node of the tree.\n",
|
||
"\n",
|
||
"3. A descendant of the root node is then created for each possible value of this attribute.\n",
|
||
"\n",
|
||
"4. Training examples are sorted to the appropriate descendant node.\n",
|
||
"\n",
|
||
"5. The entire process is then repeated using the training examples associated with each descendant node to select the best attribute to test at that point in the tree.\n",
|
||
"\n",
|
||
"6. This forms a greedy search for an acceptable decision tree, in which the algorithm never backtracks to reconsider earlier choices. \n",
|
||
"\n",
|
||
"The ID3 algorithm selects which attribute to test at each node in the\n",
|
||
"tree.\n",
|
||
"\n",
|
||
"We would like to select the attribute that is most useful for classifying\n",
|
||
"examples.\n",
|
||
"\n",
|
||
"What is a good quantitative measure of the worth of an attribute?\n",
|
||
"\n",
|
||
"Information gain measures how well a given attribute separates the\n",
|
||
"training examples according to their target classification.\n",
|
||
"\n",
|
||
"The ID3 algorithm uses this information gain measure to select among the candidate\n",
|
||
"attributes at each step while growing the tree.\n",
|
||
"\n",
|
||
"\n",
|
||
"### Cancer Data again now with Decision Trees and other Methods"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"(426, 30)\n",
|
||
"(143, 30)\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Test set accuracy with Logistic Regression: 0.94\n",
|
||
"Test set accuracy with SVM: 0.63\n",
|
||
"Test set accuracy with Decision Trees: 0.90\n",
|
||
"Test set accuracy Logistic Regression with scaled data: 0.96\n",
|
||
"Test set accuracy SVM with scaled data: 0.96\n",
|
||
"Test set accuracy with Decision Trees and scaled data: 0.89\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stderr",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:460: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
|
||
"STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
|
||
"\n",
|
||
"Increase the number of iterations (max_iter) or scale the data as shown in:\n",
|
||
" https://scikit-learn.org/stable/modules/preprocessing.html\n",
|
||
"Please also refer to the documentation for alternative solver options:\n",
|
||
" https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
|
||
" n_iter_i = _check_optimize_result(\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import numpy as np\n",
|
||
"from sklearn.model_selection import train_test_split \n",
|
||
"from sklearn.datasets import load_breast_cancer\n",
|
||
"from sklearn.svm import SVC\n",
|
||
"from sklearn.linear_model import LogisticRegression\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"\n",
|
||
"# Load the data\n",
|
||
"cancer = load_breast_cancer()\n",
|
||
"\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
|
||
"print(X_train.shape)\n",
|
||
"print(X_test.shape)\n",
|
||
"# Logistic Regression\n",
|
||
"logreg = LogisticRegression(solver='lbfgs')\n",
|
||
"logreg.fit(X_train, y_train)\n",
|
||
"print(\"Test set accuracy with Logistic Regression: {:.2f}\".format(logreg.score(X_test,y_test)))\n",
|
||
"# Support vector machine\n",
|
||
"svm = SVC(gamma='auto', C=100)\n",
|
||
"svm.fit(X_train, y_train)\n",
|
||
"print(\"Test set accuracy with SVM: {:.2f}\".format(svm.score(X_test,y_test)))\n",
|
||
"# Decision Trees\n",
|
||
"deep_tree_clf = DecisionTreeClassifier(max_depth=None)\n",
|
||
"deep_tree_clf.fit(X_train, y_train)\n",
|
||
"print(\"Test set accuracy with Decision Trees: {:.2f}\".format(deep_tree_clf.score(X_test,y_test)))\n",
|
||
"#now scale the data\n",
|
||
"from sklearn.preprocessing import StandardScaler\n",
|
||
"scaler = StandardScaler()\n",
|
||
"scaler.fit(X_train)\n",
|
||
"X_train_scaled = scaler.transform(X_train)\n",
|
||
"X_test_scaled = scaler.transform(X_test)\n",
|
||
"# Logistic Regression\n",
|
||
"logreg.fit(X_train_scaled, y_train)\n",
|
||
"print(\"Test set accuracy Logistic Regression with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
|
||
"# Support Vector Machine\n",
|
||
"svm.fit(X_train_scaled, y_train)\n",
|
||
"print(\"Test set accuracy SVM with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
|
||
"# Decision Trees\n",
|
||
"deep_tree_clf.fit(X_train_scaled, y_train)\n",
|
||
"print(\"Test set accuracy with Decision Trees and scaled data: {:.2f}\".format(deep_tree_clf.score(X_test_scaled,y_test)))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Another example, the moons again"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
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hZIyNPf744ygtLcU///nPFraO/IFFK5EDU6ZMwfPPP49jx47hX//6F6ZNm2Z3P0uhkpCQ4LAQSUpKAtAwyN9djmawKy0tBdBQ+B0/ftzpY1RXV1v/vWzZMqSmpuLVV1/Fzp07sXPnTgBAVFQUHn74YSxatAh6vd7tdjprqyOW2Y1jYmJa9HzusvytHAWs5e8ENPytGhetjl6fZbIucdkySRqNBlu2bMHixYuxevVqbNy4ERs3bgQApKenY9GiRS4HKhFRS1111VVNtiUnJwOA3YngLLfl5eW5VLTGxMRYZ3W/XNu2bfHNN9+411gAQ4YMQZs2bbB06VLs378fo0ePxuDBg9GjR48mGSuEwKpVq5CVlYWDBw+itLQUZrPZertlwp/GGr8nWq0WiYmJqKysbDLJ4OXvR2OhoaEYMGBAk+3XXXcdXn31Vezfv99p0WqZsf7o0aN218A9f/48zGYzfv75Z/Tt2xd33HEHXn75ZYwbNw533nknbrjhBgwePNjuxIgtVVVVhQMHDiAlJcU6ueTl6urqrG2+3Pr16/HPf/4Te/fuRXFxMUwmk/U2R38Hd0ydOtUnmbllyxasWrUKr7/+Otq2bev1xyfvYdFK5IBWq8WCBQtw9913Y8mSJbj33nvt7meZzffixYsQQtgtXC9cuACg6VliT1ied+XKlbj//vtdvp9Go8Fjjz2Gxx57DCdPnsSOHTuwZcsWrF+/HsuWLUN5eTleeeUVr7XTGcv74a+lXyIiIlBaWor8/Hy7V00tf6fL2+aJ1q1b4+WXX8ZLL72EH3/8ETt27MDHH3+M//73v5g2bRoiIiJwxx13ePw8RESOND75BsB69czZbZbipDnR0dF2t4eEhNgUkK6Kjo7GN998g4ULF+LTTz/F5s2bATQUwXPnzsXDDz9s3XfWrFl45ZVX0K5dO9x2221ITk62nnRdvHgxamtr7T6Ho9dt77U4ez/i4uLsrjBgOQFqObnsSFFREYCGGfSdqaysBNDQg+c///kPli5dijVr1liXkLv66qvx4osvYvjw4U4fxxXFxcUQQiAvL8/plU1LmwDgr3/9K/7whz8gISEBN954I9q2bWu9Gvzyyy87/DvIraqqCg888ACGDx+OBx98UO7mUDNYtBI5MWnSJDz//PM4fPiww/VFMzMzodFoUFtbi19++cVuMXTo0CEAQKdOnbzWtm7duuHjjz/GwYMHW/wYGRkZyMjIwO9+9zv8+9//xqhRo/D222/j73//uzWIfdmN9YorroBOp0NJSQmOHTvmUhdhT9rTqVMn7NmzB4cPH8bAgQOb3G75OyUlJdk9qGkpSZLQu3dv9O7dG7NmzbIuj7Ry5UoWrUREjWRkZCA7OxsmkwkHDhzAF198gb///e/4/e9/j9atW2Py5MnIz8/Hq6++ip49e+Kbb75BeHi49f7nz593qytpSxUWFsJsNjcpXC0nQB0V9BaWnPn0008xZswYl55z6NChGDp0KKqrq5GTk4NPP/0Ur732GkaPHm1dts4TljZdffXV+P7775vdv76+HkuWLEFKSgr279+PhIQE621CCLzwwgsetcdi//79+Pjjj13ePyMjo9krs/n5+cjLy0NeXp7D5Q0tV9r37dvHJepkxqKVyAmNRoOFCxfirrvuwnPPPYf09PQm+0RERGDQoEH4+uuv8X//9394+eWXbW6vrq7Gm2++CQC46aabvNa28ePH489//jNWr16N+fPnezyexdLFqbq6GsXFxdbHs5wtvbyLsbeEhYXhxhtvxGeffYbly5dj5cqVLt2npe256aabsGfPHrzyyiuYMWNGk9v//ve/W/fzJct77Y0uU0REgUqr1VpP+A0cOBBDhgzBJ598gsmTJ+OXX36BEAIjR460KVgBWIe9+FpdXR2+/fZbDBo0yO7zN1fk9O/fHwDwzTffuFy0WoSFhWHYsGEYNmwYYmJisGDBAmzdutXjojUyMhJdu3bFkSNHUFJS0uzwnYKCApSWlmLEiBE2BSsAfP/99147dvDFmNbIyEi7xwIAsGnTJpw/fx5TpkxBWFiYV8cMU8vYP61ARFYTJ05Ejx49cOrUKezatcvuPk8//TQA4LXXXsN7771n3V5eXo7f/e53uHjxIjIyMjBp0iSvtatv37648847UVhYiBtuuAH79u2zud1kMmH79u24++67rV1zDh8+jIceegh79uyxGX9ZW1uL559/HkDDeMvLv5wtk0vt2LHD5j7esnDhQoSGhuLNN9/EH//4R1RVVVlvq6urwwcffICvv/7aui0hIQGRkZHIz8/HkSNH3HqumTNnIioqCvv378cTTzwBo9EIADCbzXjhhRewadMmhIaG4qmnnvL4db377rtYsmQJTp48abO9sLDQWhz36dPH4+chIgokBw8etE4ieDnL1UvLiUvLSeTdu3fbdEM+c+YMnnnmGT+0tMH8+fNtug4fPXoUb7/9NqKjo20mwLJn7NixSEtLw9/+9jfs2LGjye11dXU2+bdz507rXBCXa/zeeGrWrFnWrrOXdwO2OHHihDXbEhMTERYWhr1799rkd3FxMR599FGvtAdoGNMqGlY9celn+/btzT5mXFwc3nzzTbs/lp5ff/3rX/Hmm2+iXbt2Xnst1DK80krUDEmSsHDhQtxxxx02EwtcbsyYMXjmmWewbNky3H333XjmmWeQlJSEI0eOoLKyEq1bt8batWu9FigWb731FoqLi/Hll1+iT58+SEtLQ3JyMqqqqnD8+HHrGc633noLAGA0GvHGG2/gjTfeQExMDDp06AAhBH755ReUlpZCp9PhH//4h81zjB8/HvPmzcP777+Pb775BmlpadBoNF6bFKFv3754++23MX36dCxduhQrVqxAly5dUF1djRMnTqCmpgarVq3C4MGDATT8PSZOnIi3334bffr0Qffu3a0TJDUXUikpKfjXv/6FiRMn4uWXX0Z2djYyMzNx6tQp5OfnQ6PR4JVXXkHPnj09fl0XL17EggULsGDBAqSmpiIlJQXV1dX4+eefYTQakZqaiiVLlnj8PEREgWTr1q146qmncO2116JLly6Ii4vDL7/8gk8++QRhYWF45JFHADR027z99tuxbt069O3bFyNGjMCFCxfw2Wef4frrr8cvv/zi87YmJyejpKQEvXv3xujRo1FaWoo1a9agpqYGK1eubHZuBL1ej48++gg333wzhg4dihEjRqB79+4AgNOnT2Pnzp2Ii4uzTnr017/+FV9++SWGDx+ODh06wGAwYO/evdi2bRsyMzMxfvx4r7yuhx56CN9++y2ys7Oxa9cujBw5EikpKbhw4QKOHj2KnJwcvPfee8jIyIBGo8HDDz+Mv/71r+jVqxduvfVWlJWVYcuWLUhPT0dKSopX2kTEopXIBRMmTEDv3r2xf/9+h/ssXboU1157Lf7+97/j+++/x4ULF5CcnIx7770Xf/zjH31yli4iIgKff/453n//fbzzzjv44YcfsHfvXsTHx6Nnz54YNmwYbr/9dutSNldccQVWrlyJL774Avv377cuAZOWlobJkyfjD3/4Q5OuRR07dsSnn36KP//5z9i3bx9Onz4NIQSGDRvmtddxzz33oE+fPli+fDm2bduGgwcPIioqCldeeSVuvfVWjBo1ymb/FStWIDIyEhs3bsSPP/7o8oQhAHDbbbfhhx9+wLJly/Cf//wH+/fvR0xMDMaPH4/Zs2fbHevaErfffjuMRiO2bt2KY8eO4cCBA2jVqhW6d++OCRMm4Pe//73fZk0mIlKLm266yTpJ4Pr161FRUYHU1FRMmjQJc+bMsVlaLSsrCxkZGVi3bh3+7//+D2lpaXjyySfx9NNP2yzB4ys6nQ5ffvklnn76aWRnZ6O0tBQ9evTA/Pnzcdttt7n0GP369cOPP/6IF198EZs3b8bXX38NvV6P1NRUjBs3DpMnT7buO3PmTERHRyMnJ8fa+yktLQ3PPvssHn/8ca9N9ihJErKysnDLLbdg5cqV+Oyzz1BRUYHExERcccUVWL58OUaOHGndf+nSpYiNjUVWVhZee+01JCUlYdKkSVi8eLG1CCfylCR80d+PiIiIiChAWZYDajwEhIh8g2NaiYiIiIiISLFUWbSWl5djzpw5uPHGG5GQkABJkuwuymxPVlYWJEmy+3P+/HnfNpyIiEhmzFAiIlIbVY5pLSwsxBtvvIFevXph3Lhx1uVE3LFq1Sp06dLFZhunsyYiokDHDCV/2759u0uzufbu3Rvjxo3zeXsCWVZWlktdlseNG8d1R0lVVFm0pqeno7i4GJIkoaCgoEWB2717d/Tt29cHrSMiIlIuZij52/bt211aY/O+++5TTdGq1LGsWVlZ+Oqrr5rdLyMjg0UrqYoqi1ZJkuRuAhERkSoxQ8nfFi1a5HIXdPKMK1e0idRIlWNavWHMmDHQarWIjY3FhAkTcPDgQbmbREREpArMUCIi8idVXmn1RJs2bTBv3jwMGDAAUVFROHDgAJYtW4YBAwZg165d6NWrl9371dbWora21vq72WxGUVER4uLieNaaiCiICSFQXl6OlJQUaDSBfS6YGUpERN7kcoYKlbt48aIAIBYuXNjixzhx4oSIiIgQt912m8N9Fi5cKADwhz/84Q9/+GP359dff21xDsmFGcof/vCHP/xRwk9zGRp0V1rtycjIwODBg/Htt9863Gfu3Ll48sknrb+XlpYiLS0Np07tRVRUhD+aSTLbsWMrvvlmO/73vzaoji6BJq4Y2hAN6o2A+dcUJEfUITW1Grff/jukp7eXu7mKceJELjZsWI0zZ8JwvjIEmnZnEd5Kj6l3TEVGuwxUVFTgpayXUF5aCfOFREQZ9ejQoRAjR45Bnz795W6+T73zzus4fToPx461hWh/EprwOvTq2hOTx06Wu2nkhoqyCvRP74/IyEi5myILZigRyYEZGhhczVAWrb8RQji9JK3X66HX65tsj4qKQFRUcB6oBJtWrcJgMIQiNFSPep0OGn0otKEaSBJgDtVDp5NgMJgQGdmKn4nLREa2gsGgg06nQ2hdKDT6UIQaQtEqshUioyIBDaAz6BBaY4RZp4MOehgMOkREhAf8+xgWpoder0NoqB5CHwqNHjCEGxreF1KdYO7mygwlIn9jhgaW5jI0sAffuOjEiRPYtWsXBgwYIHdTiIiIVIUZSkREvqbaK61btmxBZWUlysvLAQCHDx/GRx99BAC45ZZbEB4ejhkzZiA7Oxu5ublIT08HAIwcORJDhgxBz549rZNIvPDCC5AkCUuWLJHt9RAREfkLM5SIiNREtUXrzJkzcerUKevvH374IT788EMADWd9MzIyYDKZYDKZIISw7tejRw988MEHWL58Oaqrq5GYmIjrr78e8+fPR6dOnfz+OoiIiPyNGUpERGqi2qL15MmTze6TlZWFrKwsm20vvfSSbxpERESkEsxQIiJSE45pJSIiIiIiIsVi0UpERERERESKxaKViIiIiIiIFItFKxERERERESkWi1YiIiIiIiJSLBatREREREREpFgsWomIiIiIiEixWLQSERERERGRYrFoJSIiIiIiIsVi0UpERERERESKxaKViIiIiIiIFItFKxERERERESkWi1YiIiIiIiJSLBatREREREREpFghcjeAApcQJpSW5sBovACdLgnR0f0hSVq5m0VERKR4zFAioktYtJJPFBRswvHj82E0nrNu0+mSkZm5BPHxo2VsGRERkbIxQ4mIbLF7MHldQcEmHD78gE3YAoDReB6HDz+AgoJNMrWMiIhI2ZihRERNsWglrxLChOPH5wMQ9m4FAOTmLoAQJr+2i4iISOmYoURE9rFoJa9qGH9zzskeArW1Z1FamuO3NhEREakBM5SIyD4WreRVRuMFr+5HREQULJihRET2sWglr9Lpkry6HxERUbBghhIR2ceilbwqOro/dLpkAJKDPSTo9SmIju7vz2YREREpHjOUiMg+Fq3kVZKkRWbmEstvjW8FAHTs+CeuNechIUwoKdmN/PwNKCnZzUk5iIgCADPUP5ihROrDdVrJ6+LjR6Nbt5VN1pjT65PRseOfuMach7h+HxFR4GKG+hYzlEidWLSST8THj0Zc3KjfZkK8AJ0uCdHR/Xl22EOW9fsaL4dgWb+vW7eVDF0iIpVjhvoGM5RIvVi0ks9IkhYxMYPkbkbAaH79Pgm5uQsQFzeKBzZERCrHDPUuZiiRunFMKwW8QBm7wvX7iIjI35ihRKQEvNJKAS2Qxq5w/T4iIvInZigRKQWvtFLAsoxdaXxm1TJ2paBgk0wtaxm1rd9nOTtfVbUVUVHnIElmuZtEREQuYobKK1CucBN5C6+0UkAKxLErlvX7jMbzsP+6JOj1yYpYv6/x2fnu3YEOHVph2+5h+EUYZG4dERE5wwyVVyBd4SbyFl5ppYAUiGNX1LJ+n6Oz82FhlRgzYhM6JubJ1DIiInIFM1Q+gXaFm8hbWLRSQGrJ2BU1dMWxrN+n07Wx2a7XJytiqn5nZ+el344Rhnb6ERLYVZiISKmYofJo/go3kJu7QJHvLZGvsXswBSR3x66oqSuOktfva+7svCQBkWHVaBN10Y+tIiIidzBD5eHOFW4uh0TBhkUrBSR3xq6ocbFxpa7f5+rZ+fDQah+3hIiIWooZKg/OcEzkGLsHU0BydewKAHbF8SJXz85X1YX5uCVERNRSzFB5qG2GYyJ/YtFKAcuVsSuBONmEnCxn55se5DQQAiivDsP5sgT/NoyIiNzCDPW/5jK04Qp3iiJmOCbyN3YPpoDW3NgV97ri8Opgcyxn5xu6ikm4/Oy7+O2fX/3cC4Lny4iIFM+7GUrNcZahSprhmEgOLFop4Dkbu+JeV5wyL7YqcFnOzjeelKOqKgL/+WYofhEGhEfI2EAiInKZ9zKUXOEoQ/X6ZHTs+CfFjQ8m8hcWrRTU3Fts/Es/t069Lj87f+bMj9ix4zscOpSBsxV6aNLOyN08IiLyAvcylFyl5BmOieTCPnoU1NSy2LgaWc7Oh4ePRFlZMoTg1w0RUSBhhvqOJUMTE8cjJmYQ30MKejyKpKCn9MXGiYiIlIoZSkT+wO7BRGBXHCIiopZihhKRr7FoJfqNUhcbJyIiUjpmKBH5ErsHExERERERkWKxaCUiIiIiIiLFYtFKREREREREisWilYiIiIiIiBSLEzGRbIQwcaZBIiKiFmCGElEwYdFKsigo2ITjx+fDaDxn3abTJSMzc0lQr+nGgxAiImoOM9Q+ZihR4FJl9+Dy8nLMmTMHN954IxISEiBJEhYtWuTy/fPz8zF16lTEx8cjPDwcAwcOxLZt23zXYLJRULAJhw8/YBO2AGA0nsfhww+goGCTTC2TV0HBJuTk9MNPP92Oo0cfxk8/3Y6cnH5B+34QkW8wQ9WNGWofM5QosKmyaC0sLMQbb7yB2tpajBs3zq371tbWYsSIEdi2bRtWrFiBjRs3IikpCaNGjcJXX33lmwaTlRAmHD8+H4CwdysAIDd3AYQw+bVdcuNBCBH5CzNUvZih9jFDiQKfKrsHp6eno7i4GJIkoaCgAG+++abL933rrbdw8OBB7N69GwMHDgQADB8+HL169cKcOXOQk5Pjq2YT8Fu3nXNO9hCorT2L0tKcoFmkvPmDEAm5uQsQFzeK3ZyIyGPMUPVihjbFDCUKDqq80ipJEiRJatF9N2zYgM6dO1vDFgBCQkJwzz334LvvvkNeXp63mkl2GI0XvLpfIHDnIMQZIUwoKdmN/PwNKCnZHXRn2onINcxQ9WKGNsUMJQoOqrzS6omDBw/iuuuua7K9Z8+eAIBDhw4hNTW1ye21tbWora21/l5WVua7RgYwnS7Jq/sFAm8chHBSDiLyB2aovJihTTFDiYKDKq+0eqKwsBCxsbFNtlu2FRYW2r3f0qVLER0dbf1p166dT9sZqKKj+0OnSwbg6Cy/BL0+BdHR/f3ZLFl5ehDSkrE8PKNMRC3BDJUXM7QpZihRcAi6ohWA025Rjm6bO3cuSktLrT+//vqrr5oX0CRJi8zMJZbfGt8KAOjY8U9BNe7Ek4OQlkzKwRkWicgTzFD5MEObYoYSBYegK1rj4uLsngkuKioCALtnkAFAr9cjKirK5ifQ+epMYnz8aHTrthI6XRub7Xp9Mrp1Wxl0XXE8OQhxdywPZ1gkIk8wQ13HDPUPZihRcAi6Ma09evTAgQMHmmy3bOvevbu/m6RIvh7fER8/GnFxo7gI+G8sByGN33O9PhkdO/7J4XvuzlgezrBIRJ5ihrqGGepfzFCiwBd0Rev48ePx8MMPIycnB/37N3QVqa+vx+rVq9G/f3+kpKTI3EL5Wc4kNv5itpxJ9NaZXEnSBs2U/K5oyUGIO2N5uFQCEXmKGdo8Zqg8mKFEgU21ReuWLVtQWVmJ8vJyAMDhw4fx0UcfAQBuueUWhIeHY8aMGcjOzkZubi7S09MBANOnT8err76KiRMnYtmyZUhMTMRrr72GY8eOYevWrbK9HqUItDOJQphUdSba3YMQy1geo/E87P/NJOj1yYiO7o+LFz9x6TGDaakEomDFDPUNZqi8mKFEgUu1RevMmTNx6tQp6+8ffvghPvzwQwDAiRMnkJGRAZPJBJPJBCEufRHp9Xps27YNc+bMwaOPPoqqqir07t0bW7ZswdChQ/3+OvzF1eAJpDOJ3u6edeFCGMrKIhEeboS5PgwXz7WHJkQDUx1gLkpCJIoBVHvxFTTPMpan4ay+BNvQtR3Lw6USiMiCGeoeZmgDTzL01Cng5MnDqKsrRGhoHCIiukOSLk2tEh9vRlqa2SttdxUzlEg9VFu0njx5stl9srKykJWV1WR7UlISsrOzvd8ohXIneAJl4XJvd8/av387pk0bB6PxLof7aLV1ePLJuS1tcou5OpbHnTPKRBTYmKGuY4Ze4kmGDhw4Dkbj9Q73MRgEjhy56PfClRlKpA6qLVrJNe4GTyCcSfR296yCgk34/vvXYDROcrqfyRSKysqIFrXZU66M5XHnjDIRETFD7dwKX2VoTY2EggKN34tWgBlKpAZBt+RNMGnJ+mOBsHC5u1PYO+P8PWwqIqJAtkXGLWN5EhPHIyZmkN3g5FIJRESuYYY64rsMLS//iRlKRHbxSmsAa8nYmkA4k+jN7lmX3sM2ze4LAB077sbZs2sRGblUseHFpRKIiJrHDPV8P3cz9H//+wP0+vNeWxrIF5ihRPLgldYA1tLgUfuZRG92z2rJuCOT6SIOH75f0YuMu3JGmYgomDFDPd+vJRlqNJ5jhhJRE7zSGsA8CZ6WnElUytT43pwswZNxRz//PNtnyxoo5b0mIgpUzFBmKBEpB4vWAOZp8Liz3pm3p8b3hDe7ZzU/Psmx+vpilJTsRuvW17l9X2eU9F4TEQUqZigzlIiUg92DA5gleH77rfGtALwztsYyu2LjsT+W2RXl6OLjre5Zl95D1yaRaKykZHeL7ueIEt9rIqJAxAxlhhKRcvBKa4Bzdf2xlvL21Pje5M3JEuLi6qDTVcNoDHO4j05XjejoAk+a7JSS32siokDEDGWGEpEysGgNAr6c6a4lsyv6kzvds+yxnJWNixN4553OKC2NBwAIAUiNTrxHRxcgKelXm23efM1Kf6+JiAIRM9T7GWoPM5SInGHRGiQ8DR5HvDk1vtI0PiublPSrTaCK307WNi5eLUJCWnv1PQ/k95qISMmYoe5rLkObwwwlostxTCt5xJtT4ytNc2dlJanhRzgYqtOp04te7WIUyO81EVEwCuTv9eavbDrHDCWiy7FoJY80PzOgBL0+xaWp8ZXG1bOtNXW2HRY0mgR06/am12chDOT32hEhTCgp2Y38/A0oKdkNIUxyN4mIyGsC+Xvd1QzVaKJtftfpkpmhXsIMpUDC7sHkEedT4wOAQJs2U2RomedcPdu6+adBMF9IQNvYMkRGanHzzXMRH9/J6+3x5jIEalBf/y1ych7hsgREFLCYocCVV66EJGl9vmZqsGUol/ahQMMrreQxR1PjW5w6tRw5Of1UN5V8c2dlhQDKa8KQV5yAM+fa4fTpK1BWluzTwPPWMgRKFxd3Gkbji1yWgIgCXrBmqOXKZkzMIMTEDEJi4njExAxihnoBl/ahQMQrreQVltkVT59egVOnXmxyu+WLUk2h4OysrGUc69e5vSFasGi6J3w5k6U7hDD5pA2SZEZm5h5HzwouS0BEgSbYMlTOK5uBnqFc2ocCFYtW8qpz51Y7uEWdX5SO1uirqGqFHbndcbIkVZZ2+WomS1e50+1ICBOios4hLc0EbXEUzjWzyHxSUh70+ione3BZAiIKTMGSod5a57al1Jah7hS3XNqHAhWLVvIaNXxRVlSUo6qq0s17XY327T/Fjz+uxi+/7MHx421xoqYVpLgSaEOb7l1aWoz8/PNeaa+SREVFw2AIs3Y7anwW196VgIKCTTh/fi66d79o3a+8Jgzfnurr8HnCw137+3BZAiIKJIGeoVVV+2AyXYRWm4Dw8KtgNmsDMisdaWmGujsulUv7UKBi0Upeo+QvSrPZjJycHdi5cxtMpvoWPopAWVkmTp5JhGiXd6lTsGSGFFmOsvJo1NSUYfPmdV5qtbLodHrcfPM4lJW51u2osPBzu8Ecoa/GyE47ISp3AOjQ5FGqqlq52B4uS0BEgSPwM9TiZwC7vNEsVfFWhjbXVZxL+1CgYtFKXuONL0pfjPEwGmvxySdrsW/fIeTlxaKuruWPV4N6iIxTkHT10Gg1iGoVheL6EojYYlTqanHoaDJ0WufdX9VKrzciJORlXHVV81cCSkp2OxxTY13btugVCHFvk9svXEhFbW24ky7CEvT65IBaloCIKBgyNJh5K0Ob6ypumQDLaDzv4P7MUFInFq3kNZ5+UfpievaiokKsXZuF48eLcOJcLETSRUDrwTplOiMkrUCoLgQ3DrkB1159LVZvWI2jx4/BHFkJk+EkqusD8b+VQLVRj/xC1w5WSkp2O+3mJkkATPmoKf0OCOlu+0xCg+PH++HKK7+CkibvICLypaDI0KDl3Qx11lVcqRNgEXkqEI+uSSaefFG6M8bDVXV1Rrz//ps4fboYJ061geh4ApKuvqFgavGEvxLCw8Nxz/i7ceUVVwIAHpj8ADZv34zt33yFek09oA/AQBeACKtFuaHWqw9bb8y3+y1UWJgGnW42gNWKmryDiMhXgiNDg5SPMtRRV3GlToBF5AkWreRVLfmi9NX07GVlpaiqqkRNjQ5CVw9Ja0ZIqBYJcfFIS0lz/8UBCDOE4bprrkNCbIJ1m1arxa0jbkVmeib2H94Ps9ncosdWspNnTuJiYQHOVrRGeXkkIiLKGw5cmmi4EhATMwi//vpys48bokuEo9FRISEDcPXVj8m+LAERkb8EeoYGK19lqLOu4kpZ2ofIW1i0kte5+0XpnxkTJUCSoNFocON1N+LqHle38HEc65rZFV0zu3r9cZXgi51fYMt/P4cZGny18waMvnk9hECj0L10JSAmZpDTbm5CAFJIIgzR16Ci0vHyNnIvS0BE5G/BmqGBzNsZ6uq4VGYoBRKN3A2gwGT5okxMHI+YmEFOz+wpecZEair3l8744YfhqKuzneVXr0+2dkGzdHOzR1jyN/YRnvElIrKDGRq43M/QxpdkOS6VghOvtJLsOD27+pw/nw6NpjN+97vrUV9fYPdKgKWb27Fjc2EyXVqntaImDN+e7osb2w+Ro+lERAGFGao+7mQox6USNWDRSrLj9OzKlndai1M/x6H4XHuYazVAcQouhOlgNhvwyy9DkZgIJCbaH8cbHz8apaUd8e9//wVlZSbkFUfhnE4gLMLg51dBRBSYmKHK5mmGclwqUQMWrSQ7Ts+uXHmntRjWNRm1NeMAjGty+0svAQaDwJEjF5GWZj90JUmLsrJknD4dhnOVodCknfFpm4mIggkzVLm8laEcl0rEMa2kEJZuMDpdG5vtl4/xIP8rKtCgtsb52gY1NRIKCvhVQkQkF2aoMjFDibyHV1pJMdgNhoiIqGWYoUQUyFi0BgkhTKoIMnaDISIipWGGEhHJi0VrECgo2NRk9jmdLhmZmUvYZYiIiMgJZigRkfxYtAa4goJNv03OYDujoNF4HocPP8CxLgqTd1qLIidjW2LjzUhNM/mxRUREwYsZqi7MUKLAxaI1gAlhwvHj82F/CnwBQEJu7gLExY1SZDenYHNplkHHkzboDQLbj5xj6BIR+RgzVF2YoUSBjdOVBbCG8TfnnOwhUFt7FqWlOX5rEznmyiyDtTWS07PIRETkHcxQdWGGEgU2/s8NYEbjBa/uR8EnNt4MvcHeVYZLDAaB+Hj768sREakVM5Q8xQwl8h52Dw5gOl2SV/ej4JOaZsL2I+ew+cvvsOv73TDXaoBf26JtSgESEgyYNGk6EhPhcFF0IiK1YoaSp5ihRN7DojWARUf3h06XDKPxPOyPyZGg1ycjOrq/v5tGKpKaZkJ6p0IczjsBU40GqNAgKekcUlLCcdVVddBqfT+WSy3LTRBR4GCGkjcwQ4m8g0VrAJMkLTIzl/w286EE29BtGPfRseOf+MVFisblJohIDsxQCgTMUAoUHNMa4OLjR6Nbt5XQ6drYbNfrkzlVPymeZbmJxpOhWJabKCjYJFPLiCgYMENJzZihFEh4pTUIxMePRlzcKHYNIVXhchNEpATMUFIjZigFGhatQUKStIiJGSR3M8gJyyyDza0xFxskswyazUdcXm6Cn23P5Z3WOl0KIjbezLUNKWgxQ5WPGWrLnSWb+Nn2HDPU91i0EimEZZZBfuk1EKLYpf243ITn8k5rMaxrcrMHe9uPnAuazx8RqQsz1BaXbPIfZqh/sGglUpDUNBO/0H4jSa1d2o/LTXiuqEDjNGwBoLZGQlGBhp9PIlIsZuglXLLJf5ih/sGJmIhIkTSartDpkmGZpbMpCXp9CpebICIiasSyZBMzlAIFi1YiUiTLchO//db4VgBcboKIiMgeZigFGhatRKRY/lhuQggTSkp2Iz9/A0pKdkMIdt0hIiL1Y4ZSIOGYViJSNF8uN+HPRdeFMDV5DURERL7EDKVAwaKViBTPF8tNWBZdb7yGnWXRdW+dhbY8l71gb9VqIIBWXnkOIiIie5ihFAjYPZiIgk7zi64DubkLvNLNyRLsjdfLMxrPIzl5PRITT3v8HERERP7CDCU5qLJoraiowOOPP46UlBQYDAb07t0b77//frP3y8rKgiRJdn/Onz/vh5YTkRK4s+i6J1wJ9k6d9kCS5F3sPjbeDL3BXhsv0RsEYuPlbSd5BzOUiDzBDLXFDPUPVXYPnjBhAvbs2YNly5ahU6dOeO+99zB58mSYzWZMmTKl2fuvWrUKXbp0sdkWFxfnq+Z6xF4ffs70RuQZfy263lywSxIQFlaFlJRfccajZ/JMapoJ24+cQ1GB4/OYsfFmri8XIJihzFAiTzBDbTFD/UN1RevmzZvx5ZdfWkMWAIYPH45Tp05h9uzZuOuuu6DVOg+k7t27o2/fvv5orkf8OcCdKJj4a9F1VwO7VasKwBTm0XN5KjXNZBOoeae1NgFcVKCx+d3dAG78eI0x0P2DGcoMJfIUM7QpZqjvqa5o3bBhAyIiIjBx4kSb7dOmTcOUKVOQk5ODQYO8O9hcDv4c4E4UbCyLrhuN52G/25EEvT7Z49kJXQ3sysoIwKCcsMk7rcWwrsmorXG0KH1DV6ftR865FJLefjxqOWYoM5TIU8xQ55ihvqG6Ma0HDx5E165dERJiW2/37NnTentzxowZA61Wi9jYWEyYMMGl+9TW1qKsrMzmx1f8OcCdKBj5a9F1S7A3fY4GQgDV1eE4e7adR8/jbUUFGqfhCAC1NZLTs76+fDxfyTutxYG9oQ5/8k6rv1spM5QZSuQpZqhzzFDfZKjqrrQWFhaiQ4cOTbbHxsZab3ekTZs2mDdvHgYMGICoqCgcOHAAy5Ytw4ABA7Br1y706tXL4X2XLl2KxYsXe/4CXODOAHdvT2FOFCwsi6437j6o1yejY8c/eeUqjCXYG674SLA9iG74/eef+0EI1Z0/DDjBciabGQowQ4k8xwyly/kjQ1VXtAKAJDl+Q5zdNmrUKIwaNcr6+5AhQzB69Gj06NEDCxYswMaNGx3ed+7cuXjyySetv5eVlaFdO9+c2fHXAHeilpAkM+LizqF1azNKS3ejdetBqp3YxJeLrl/+HI6C/cSJAcjP5xpzrvD1eB53zmSruWgFmKHu7kfkTcxQ95+DGeq5QMhQ1RWtcXFxds8EFxUVAbh0tthVGRkZGDx4ML799lun++n1euj1erceu6X8NcCdyF0dk85g6LVbEBlZDgA4ePBL1U9s4otF1xtzFOwHD74KyDrnoToEy1VQf2CGur8fkbcwQ1uGGeqZQMlQ1RWtPXr0wJo1a1BfX28zJufAgQMAGmY1dJcQAhqNcroW+GuAO5E7OsTn4eYrv2my3dWJTcrLW6OkOAYaXShqwnT4+WAEKgtCUVVlQOGZdNSZLsDgyxcgM38Ee6AKpqugvsYMBZihJAdPM/T0aQ0KnFwpi483Iy0tcNcBZYa2XKBkqOqK1vHjx2PlypVYt24d7rrrLuv27OxspKSkoH9/90LoxIkT2LVrF0aOHOntprZY8334vTPAnchlwozrMvcDaFgXrdGNACTk5i5AXNwou5/LkpJYfPDBQphModZtn796+R5/gkZrxPV3LEa0rtrLjSciC2YoM5Rk4GGGnj6tQdeuCahxUngYDAJHjlwM6MKVgpvqitabb74ZN9xwA2bOnImysjJkZmZizZo1+Pzzz7F69Wrr+nIzZsxAdnY2cnNzkZ6eDgAYOXIkhgwZgp49e1onkXjhhRcgSRKWLFni7Gn9zh8D3IlcZcDPiDQ4KyadT2xSWRlhU7DaYzbpYKyJAFi0EvkMM5QZSv7naYYWFGicFqwAUFMjoaBAw6KVApbqilYAWL9+PebNm4cFCxagqKgIXbp0wZo1azBp0iTrPiaTCSaTCUJcOsPao0cPfPDBB1i+fDmqq6uRmJiI66+/HvPnz0enTp3keClO+WOAO5ErQlDq0n5G4wUIYbL5zArh3hg5kl9svBl6g2h2/EtsvGsHR95+PPIMM5QZSv7lSYY2dGNX5eF60GKG+oYq/xdERERgxYoVWLFihcN9srKykJWVZbPtpZde8nHLvI99+EkJ6hHt0n7V1SeQk9PP5sqGVpuA6Ojxvmoa+UBqmgnbj5zz2kyD3n488gwzlMi/PMlQnS4ZVVWvARjnm8aR1zFDfUOVRSsR+VcNOqG8JgwR+mo743EAQEJISAxOnVqOxhOfmEwXkZ6+xx/NJC9KTTN5NQC9/XjexjPZROQrnmSo0Xgev/yyBCxa1YUZ2pSnGcqilYiaJ2mw83hv3HzlNxCi8UQSl090Ym+mTqIGvl4nzhM8k01EPuNRhjJXqUGwZ2iLitZdu3Zh8ODBAIC1a9di4sSJTfbJycnBiBEjUFlZidmzZ+OFF15ocSOJSBlqjDqE6Y0220JCYpCaOuO3M8T22T+zTMHEk3Xi/HUV1F9nspmhRMGppRnKwpWYoS0sWq+99lrcdttt+OSTT7BgwQJMmDDBOuMgABw7dgxjxoxBZWUl7rvvPvzlL3/xWoPVyN6gekcTQbizL/mXks9w+Vor8YPd9eUAoL6+GPX1rk0yQcHLk3XiAu0qKDPUPczQwMAMZYZSyzFDPegevGzZMmzatAlHjx7F6tWrcd999wEAzp49i5tuugkFBQUYM2YM3nzzTUhBfJmloGBTkyn3dbpkZGYuaTLlvjv7kn95coZLqVw9gBDChHi8D8DRFVMJ+fnrnT5XdHQBdLpqGI1hDvfRaI3QGSpcaToFIaWP53EXM9Q1zNDAwAz1fYYaDALxHHNPDgRChra4aO3atSumTp2Kt956C4sXL8aUKVNQWVmJUaNG4dSpUxg8eDDWrl2LkJDgHTZbULDpt8XNmw6qP3z4AXTrttIapO7sS/7nyRkuJXLnACI26huEoLhh2I1dAnV1hQgNjUNdXRHsdWNKTPwVr7/eB9kfTYPU5iIMYTpMGDUBqW1SUVVVhaz1WagzXYChWgsYDV55jURKxgxtHjM0cDBDPcvQpKQzeP/9IWjbdhMkyX6hHB9v5hqtFNAcnyJyweLFixEWFoYTJ07g1VdfxdixY3HgwAH06NEDn376KcLCHJ8RCnRCmHD8+Hw4G1Sfm7sAQpjc2tfbbSwp2Y38/A0oKdnt9ccn5XLnAKLemO/SYyYmTvjtX/YfNy8vHdGxZxHT5gRiU0+iU/cK9OhTh269axDX9hTCowvceQlEqscMdYwZSkrm3wxt+P3aa/8frr7ajD596u3+sGClQOdR0ZqamopZs2YBAJ544gns2LEDGRkZ+PzzzxETE9Nk/7179+LJJ59Er169EBUVhYiICAwYMADvvvuuJ81QpIYxNeec7CFQW3sWpaU5bu3rLQUFm5CT0w8//XQ7jh59GD/9dDtycvqhoGCT156DAkOILtGl/eLiRqFbt5XQ6drYbNdqE3Hs2HCcOdPRF80jUi1mqGPMUAoUnmaoXp/MngJE8MKSN4899hhefPFFmM1mxMbG4osvvkBKSordfV944QVs27YNt99+O37/+9+joqICq1atwj333IPjx49j4cKFnjZHMYzGC17dz919nWE3KnKHIfoa1KM1tKLY4XgcvT7ZOuFJXNwom4lQCgtjsXPnO/5uNpEqMEPtY4ZSoPA0QzmZGFEDj4rW+vp6PPjggzCbG7okVFVVOe3ONGvWLGRlZcFguDRmbebMmejduzeef/55zJo1C61bt/akSYqh0yV5dT9393Wk+W5UEnJzFyAubhS/JAkAIElaFGASkvAPB+vLAR07/sn6eZEkLWJiBln3KCr6nx9bS6QezFDHmKEUKDzNUCJq0OLuwUII3H///fjss8+QkJCA9u3bo6amxumZ3kGDBtmELQCEhYVhzJgxqKurw7Fjx1raHMWJju4PnS4ZjkfeS9DrUxAd3d+tfT0lRzcqUo6801oc2BuK40fdO19VKV2NLYcGoqLG9oBap2O3JXKNZZ04Z7yxTpxaMEOdY4aSEjFDSS7MUA+utM6ZMwfZ2dmIiIjApk2bcPz4cUyZMgXZ2dl46qmn0K1bN5cf6+zZswCAhISEljZHcSRJi8zMJb91IZJge1a26Zk1d/b1hC+6XJE6uDLboTO/FKTi+JlUpFTr0CH9DCIiWmPq1L8jJETn8mNIkhmprS8iNqoeonofhEhvUVtIfQJlnThvYYY6xwwlpVFChnId4uDFDG1h0bp8+XIsX74coaGhWLduHfr164e+ffti2bJl+OmnnzB37lxs3LjRpcc6fPgw1q9fjwEDBqBjx8CaqCU+fjS6dVvZZN04vT4ZHTv+yebMmjv7esIXXa6CgeUMV3PT2yv5DJcrsx02R0CDvLx0GEJ1SEkJdyss27bNxejeuxAZ8dtarBd241TxC2iV+rRHbQpkrq4DqBaBsE6cNzBDXcMMDRzM0AaeZCjXIXYfMzSwuF20vvPOO5gzZw4kSUJWVhZuvPFGAIAkSViyZAnGjh2LTz75BLt27cK1117r9LHKysowceJEaDQa/POf/2zZK1C4+PjRLg+qd2fflrJ0ozIaz8P+mJxLEwLQJcF4hsubBxCxsSfRufN/m2w3Gc+j7MQTSI8ZggMlcV55rkDhzjqAgfS5C3TMUPcwQwMDM9QznPzLfczQwONW0bp582bMmDEDQgi89NJLmDJlis3tt912G/r374+cnBw8/fTT+Prrrx0+VnV1NW699Vb8/PPP+Oijj9CzZ8+WvQIVcGdQva8H4LvS5apDh0XsfmKHWs5wOTqz6OoYnBX/KkBml3qvHUAIYUL79g3ju5rOnNgwcck17fbg4MmbPH6uQOLOOoBq+FwSM7SlmKGBgRnaMpz8q2WYoYHH5aL1m2++wcSJE1FfX4+nn34ajz/+uN39nn/+eYwcORK7du3Cxo0bMXbs2Cb7GI1GjB8/Hl9//TXeffddu/uQ7zjrRpWQMBa5uQvZ/USlPB1zAwCZXerRo09dM3uZERGRh4sXP4bBkOz0oKy29ifo9VVOHksgQl+FlNYF+PV8Gyf7KRvHGpEzzNDAwQwNXErMUHcm/1LzrMPMUGqOy0XrwIEDUVlZ2ex+I0aMgBCOZ7eqr6/HnXfeiS+++AJvvfUWJk2a5GoTyIvsdaOqqyvEkSMPgd1P1MsbY26a07HDMYwY/jnCwqrw888N4+6cHZSZzYUuPW4rXY1X2+kLjkKVY42oOczQwMIMDUxKzNBAmvyLGUqe8GidVneZzWbcc8892LhxI1577TVMmzbNn09PjVzejUoIE3Jy+oHdT8iZjklnMLr37ibbnR2UaTSujVWtNBqa30lGjkI1MXEczpx5HTxQJV9jhioLM5Tc1ZIMDZTJv5ih5Cm/Fq1/+MMf8MEHH2DIkCGIjIzE6tWrbW4fNGgQOnTo4M8m0W+CpfsJtZwEgaFd9jX828HYVHsHZXp9T9TWhkOnq7Jzv4ZHrqgNw9nieB+13HOOJ8E4hzNn/uHgXjxQJe9ihioXM5Sa09IMDYTJv5ih5A1+LVr37t0LANixYwd27NjR5PZVq1YxcGVSW+ssbC9RQ/cTajlnsx2mxFxEZFi1k3vbPyiTJC1OnOiPzp3/CyEah3XDL9/92g8Cvu2S1VLOJ8Fo9t48UCWvYYYqFzOUAN9lqL/WIfYFZih5i1+L1u3bt/vz6chFBQWbkJu7wKV9ld79hFxjmd2wMWezHYa7OObU3kFZUVEGdu26Cb0uX6cVgFbfBq1Snsap7/cCqGhyPyVo/gpK83igSt7ADFUmZmjw8XeG+msdYl9ghpK3+LVoJeVx1GWjKeV3PwFsB/nX1OgBmAE4XhcuWLk2u6GtKhfHnDo6KDtzpiO+/7kT2vb8EbFR9bj+uolI7zQOFZVVAPa61RZ/8kZYtuRANTbeDL1BNLvGnLfWASQi9zFDg5McGeqPdYh9gRlK3sKiNYi53mVD+d1PAPuD/Hv1agWzeSBOX+wtX8MCxNmSBJRXhyHCUO1wbGpzB2VCaJBXnIDiOj1GhF2l6M+ThWdXRlp+oJqaZsL2I+fsrhdo4a11AInIfcxQcoc3MtTX6xD7AjOUvIVFaxBztctGaGgsrrjiL4rufuLobLdOV4n+/bfiYlk4foFensb5kS/PLApI+OroVRjde7fDsalKPyhrieYnwbDw/lij1DQTA5VIoZihgYcZ6n3MUPIWFq1BzNUuGx06LFZ02Do72y1JgBDAsEH/xYndN/m/cX7m6zOLuRfaYtOWCdY15izUMK6mpVyZBKNt2/+H/PyPVTfWiIhajhkaeJih3scMJW9h0RrEXO2yodcn+7glnmnubLckAZER5UhpfREXa9r4sWW+lXdaK0u3l9xfOgPmCHTqVIoxY26AwZCsinE1nnBlEoz27eepbqwREbUcM1TdmKH+wwwlb2DRGsQCYe0vwPWz3a30Nbjo2uR9zZIr7C5//mFdk5vtwrT9yDkftUODiopUJCSMg1YbHKHS3CQYahxrREQtxwxtOWYoM5QZSu5i0RrE1L72l4WrZ7sra12bua858ocdUFSgcfr8AFBbI6GoQMPxHF7EUCUiC2ZoyzBDgxczlDzBecyDnKXLhk5n2+VHr09Gt24rVTGWwHK223KQ0JgQQHlFJM4WJ3jl+dwJOyIiClzMUPcxQ4moJXillVS79peFs7Pd4rd/bt89HMJBIBMREbUUM5SIyPd4GosAXOqykZg4HjExg1QTthaOznYbja2QkzMSuSc6ydQyIiIKdMxQIiLf4pXWACGESbVneb2l8dnumho91q7djbNneW6GiIgcY4YyQ4lI2Vi0BoCCgk1NphHX6ZKRmblEFeNpvOnyQf6FhRcBfCtvg4hkIPfMnERqwgy9hBlKxAxVKhatKldQsOm3cSi20+0bjedx+PADqpkIgoi8QwkzcxKpBTOUiC7HDFUu9vlQMSFMOH58PuyvD9ewLTd3AYSQ5z+VECaUlOxGfv4GlJTslq0dgSg23gy9wd7f/RK9QSA23uynFpEz/vy/wJk5iVzDDA1ezFB1YYYSwCutqtYw7uSckz0EamvPorQ0x+/rYimlu1VxcSzy8yNQUhwBKUyDUL2E3CPR0NWFAmhZFw9L2DV3Fs6XYZeaZsL2I+fYfcXLfDGuzdn/BSKSDzO0ecxQZqg7mKHkSyxaVcxovODV/bxFKd2tzpwJxfLlS1BfH2qz/cvXL/27JV08lBJ2qWkmBqoX+eIgsbn/C61ajQfQyoNWE1FLMUOdY4aSO5ih5GssWlVMp0vy6n7e0Hx3Kwm5uQsQFzfK5zMzFhVpm4RtY5YuHu4GF8MusPjiINGV/wsJCV8CuK2FrfaNxhNQ5J/XoKzk0u/RMQIJbS599nk1gtSKGeocM5RcxQy9hBnqOyxaVSw6uj90umQYjedh/z+1BL0+GdHR/f3WJiV3tyJ5CGFCVNQ5pKWZoC2Owjm7n1X5+Oog0ZX/C6Gh5WjdOh9AunuN9hFXJqBojBNSkFoxQ0kNlL4cEzP0Emaob7FoVTFJ0iIzc8lvZ7ck2H5hNPyH6djxT379clNqdyuSR0HBJpw/Pxfdu1+0biuvCcO3p/rK2CpbvjpIdPUzrtdXu/yYvubKBBSNtfRKC5HcmKGkdEoZ2+wMM/QSZqhvceorlYuPH41u3VZCp2tjs12vT5Zlqn4ldrcieVi6C5lMF222R+irMbLTTojKHTK1zJavDhJd/YzX1oa59bhE5D3MUFIqS4Y2LggtXW4LCjbJ1DJbzFDyF15pDQDx8aMRFzdKEd1HlNjdivzPWXchSQKEAFD0CoS41+9ta8xXB4mu/F+oq4tAcXGiW4/bHCXMzEmkJsxQUholjW1uDjOU/IVFa4CQJK0ixrcosbsV+V9z3YUkCYApHzWl3wEh3f3XMDt8dZDoyv+FixdvgLc7vChlZk4iNWGGkpKoaWwzM5T8hUUreZ2lu1XjcRh6fTI6dvyTYsZhkO+42g2o3pgv+7eQLw8Sm/u/8L//5QI441H77eHMnETqxQwlNY1tZoaSv7BoJZ9QQner2FgTQkLqnE7Zzy4evuFqN6AQXSLqfdwWV/jyINH5/4W/e6H1RBRomKHBTW1jm5mh5A8sWmWk9GnMPSV3d6u2bevwhz/Mx4kTEThfHAEp9RxC9RJuGnoTumZ2BcAuHm6TBBBihNEYgqqqSqxY8ZyDHc3o2bMVQkMrG7oCNyIEIIUkwhB9DSoqqy49vM6IuqpwmEwCX331BXbs+NI3r8OhWxEZeQ6hoVWoqwtHeXkydu36HsD3Xn6ehtdlNNaitlYLoTEBGh74OdJ43bvG+P84ODFDfYsZKh81jm325YkWuf8vqF2gZCiLVpmoYRrzQNC6dREqK4tQI0VDanMKujANOnYtRY8edXI3TVVSElMQEhoCU70RIuM0Tp9pg/LycGicFFoVFUMwdOiWhgL1ssJV/Ja/Uel/hCRpER4WjqjoKJSXVUK0Lka1th5HjiUhslWtj1+VI87Xe6uoaI2amlYObzcYKhERUezic4WiqDoEosMJSKH10Gi0SE+Vb705VyagaMzXV1pcWfeO69wFH2aofzBD5aHWsc2uFJenT2tQ4KSAio83Iy1NnSdxmaG+xaJVBpZpzBufPbNMYy7HNPtEzlzZ6UpMuGk81v97A2qrjRBpZ1FcFgGYHQdPYX4blO8ejmFX5SAy/NLV1Kq6VohJfxYJbScAALRaLR668yGsWpuFE7+ehDm6DEZ9LQqrlDeNfVV5LLatexZmk87hPhqtESMm/xHhkUXNP6AkgMQKSFozQnUhGDl4BK675jovttg99iagyD+vQVnJpd+jYwQS2lwKNl+foXVl3TuucxdcmKEUDAJxbPPp0xp07ZqAGiff6QaDwJEjF1VZuDJDfUuVRWtFRQWeffZZrF27FkVFRejSpQueeeYZTJo0qdn75ufnY86cOfjss89QVVWFXr164bnnnsOIESP80HLlTGMe6N2qyLskScLAPgORkpSCt9a+jdKSUoiY8mbv90t1a5zYfRNSWhcgwlCL+PgrMPqWuYhoFWWzX3RkNH5/38NYv2U9cvZ9h3qDETAYffVyWqyuNtZpwQoAZpMOdTpAii117UElILxVGO6+bQp6dOnhhVZ6hhNQBD5mqHfawQwlX1PC2GZvKijQOC1YAaCmRkJBgUaVRSvADPUlVRatEyZMwJ49e7Bs2TJ06tQJ7733HiZPngyz2YwpU6Y4vF9tbS1GjBiBkpISrFixAomJiXj11VcxatQobN26FUOHDvV525UwjTm7VVFLpaemY/YDf8C6LetwvuC863eUUtCxSy/ccN0N0Grth21oSCjuHHMn0tum4+s9X6PepIQpmmyF1se7tF9CQjwSkqtd2jcmMgYTbp6AxDjvrjVH5Agz1DPMUPInjuckaqC6onXz5s348ssvrSELAMOHD8epU6cwe/Zs3HXXXQ4Pit966y0cPHgQu3fvxsCBA6337dWrF+bMmYOcnByft1/uaczZrYo8FRkRiakTp/rksSVJwoCrBmDAVQN88vieOrA3FB/+pfn9pt4xFT36cMwXKQ8z1DPMUCIieXh3RV4/2LBhAyIiIjBx4kSb7dOmTcPZs2edhuaGDRvQuXNna9gCQEhICO655x589913yMvL81m7LeScxrz5blVAbu4CCMFuDUREgYgZ2nLMUCIi+aiuaD148CC6du2KkBDbi8Q9e/a03u7svpb97N330KFDXmypfZZpzC2zvzUlQa9P8ck05u50qyIiosDDDG05ZigRkXxUV7QWFhYiNja2yXbLtsLCQp/ct7a2FmVlZTY/LWGZxvy33xrfCsB305jL3a2KiIjkxQxtOWYoEZF8VFe0Ag3j3lpymyf3Xbp0KaKjo60/7dq1a76hDlimMdfp2ths1+uTfToeRs5uVURELWFZ984ZX69zF2iYoS3DDCUitQmkDFXdRExxcXF2z+YWFTWsiWjvLLA37jt37lw8+eST1t/Lyso8Dl1/T2Nu6VZlNJ6H/TE5EvT6ZJ90qyIKBK4sHK6WL3+1sLfuXWO+XucukDBDW44ZSuSZ+HgzDAbR7Dqt8cxQrwmkDFVd0dqjRw+sWbMG9fX1NmNyDhw4AADo3r270/ta9rucK/fV6/XQ6/UtbbZd/p7G3NKtqmHmQwm2oevbblVEgSCQvvzVhOveeQ8z1LPnY4YStVxamhlHjlxEgZMMjY83q3aNVqUKlAxVXffg8ePHo6KiAuvWrbPZnp2djZSUFPTv7/gM5/jx43H06FGb2RHr6+uxevVq9O/fHykpKT5rt1LI1a2KKFCkppnQo0+dw59ACAYKXMxQzzBDiTyTlmZGnz71Dn9YsJIjqrvSevPNN+OGG27AzJkzUVZWhszMTKxZswaff/45Vq9ebV1fbsaMGcjOzkZubi7S09MBANOnT8err76KiRMnYtmyZUhMTMRrr72GY8eOYevWrXK+LL+So1sVERHJjxnqOWYoEZH/qa5oBYD169dj3rx5WLBgAYqKitClSxesWbMGkyZNsu5jMplgMpkgxKXuO3q9Htu2bcOcOXPw6KOPoqqqCr1798aWLVswdOhQOV6KbLzdrUoIEwOciEgFmKGeY4YSEfmXKovWiIgIrFixAitWrHC4T1ZWFrKysppsT0pKQnZ2tg9bF3wKCjbh+PH5NuvX6XTJyMxcwq5SREQKwwxVFmYoEVHzVFm0knIUFGz6bVIK25kUjcbzOHz4AY7xUai801pOJkREJDNmqDoxQ4n8j0UrtZgQJhw/Ph/2p/4XACTk5i5AXNwodnPykDcDMu+0FsO6Jje7bMv2I+cYukREPsIM9R9mKJH6sWj10IkTuYiMbCV3M2RRU7PPpjtTUwK1tWdx5Mg6GAxX+a1dFhUVZS26n9LOoHo7IIsKNE4fCwBqayQUFWgYuCqjtM8uUXOYocxQX1Nyhp48eRySpLqFPBTDZKr36uMp7bNLtli0eujDD7NgMOjkboYsEhJOoGvX5vfbufNDXLz4ve8bZEd9vUBhUQJEdDEkyQxIGmg0jr+QlHgGlUUmuUKJn12i5jBDm9+PGeoZJWSoxlKYakwQ0SUoKIxAq1bFWLPmLZ88X7Awm80oLIyEuVUFpJCGAtbZ59MZJX52yRaLVg8dPpyC0FDvLpiuFikp9S4F7tGj7XD2bKrvG2SHSTLDnHwWUkQVJA2QGJuATu07OdxfCeFG1BL87JIaMUOb348Zqn49uvTAV3t2oLSkDGhzASUl0Sg/3BYaOH+vyDmzEKiPLYbULg/QCBgMBvS/yvFa087ws6t8LFo9VNf+BKAPlbsZsjgNgfLqMEQYqiHZ+X8uBFBRE4bTYXUQHXP938CGVkAKMUGj0aDrFV1w74R7ER4WLlNbiIjocsxQZmgwSIpPwuNTH8Pba1fhzLkzMLcugSmyHCYWrR6TtCZIGiC+dRym3TkV7VLayd0k8hEWrR7S6MzQ6MxyN0M2O473wi3dv4UQsAldy9J+O473gqQTkOxONOEfIaGhuH7gcNw87OYWdxshIiLvY4YyQ4NFXOs4PDZtFj749APsO7wfJo0Z9ifhIndIGg0y0zvivjt+h8hWkXI3h3yIRauHRg6+HmGtwuRuhqzOiV5IkNYiFMXWbfVojYviTlxxZR9cIWPbAKBT+07omN5R5lYQEVFjzFBmaDDR6XS4Z8I96NmtJ85eOCt3cwJCbEws+vboC62WM2wHOhatHrrhuhsQGRXsZ3ZuhhDPoKb0O9Qb8xGiS4Qh+hp04RT95AWczc81F8/z/xupDzMUYIYGF0mS0KtrL/Tq2ssvz8cMdQ0zVPlYtJJXSJIWYTED5W4GuSA23gy9QTQ7Q15svPxd9jibn2vyTmvxwO3xcjeDiFqIGaoezNDAwwxVBxatRArn7YBMTTNh+5Fzqjjzytn8XFNUoEGdkRN6EBE1xgxlhjaHGaoOLFqJLqPEM6i+CMjUNFNQB1SwCtUp4+w/EQUmZigFMmaovFi0El1GqWdQGZDkDW+su8jPERH5DDOUAhkzVF4sWokaUWK4cSIF8obENjxDTES+xQylQMUMlReLViKFC9SJFFw5iCAiIvIEM5QoMLBoJVK4QJxIwdWDiNc/vOjHVhERUaBhhhIFBsenaIiIfMTVg4iyEn5FERERXY4ZSsGIn2YiUqzoGAG9QTjdRynr4cnJMmOnM3yfiIiCCzPUNcxQdWD3YCJSrIQ2ypyJUmkun7Ez/7zG7tn16BhhfR+V+n5xshQiIu9hhrqGGaoOLFqJSNGUOBOlElneownXJalywpFAnSyFiEhOzFDXMEOVj92DiYgChDsTjiiNmttORETqp+YcUnPbXcUrrUQUtAK9Kw0REZGvMEPJn1i0EimcZYKA5rp8+HKCgEAMpmDoSkNEFOyYob7BDCV/Y9FKpHCXTxDgiC8DzxfBpISDiEBcu4+IiGwxQ32DGUr+xqKVSAXknEjBF8Ek90EEEREFD2YokfqxaCUiWXBGQyIiopZhhlKwUe8UUkRERERERBTwWLQSEQUIyzgnZ3w9zqml1Nx2IiJSPzXnkJrb7ip2DyYirzh+1PbrxJ/jaQJxZsaWUPM4JzW3nYjIU8xQ+ak5h9TcdlexaCUir3js3nib3/011T2n3bclxzgnbx3wcIwWEQUrZqgyMEOVi0UrEfmEv6a6b+nMjEpYMiAQ8ICHiMj7mKHBgRnqOhatROSUK8HkSP555Q6bD4auNP7o8sW1+oiIHGOGqvd7nxmqLCxaicgpe8H038/1WD6/dbP3LStRbuACgd2VhmdviYjkxwxVJ2ao8rBoJaJmNQ6mxhNGkPLw7C0RkTIwQ9WHGao8yj6FQ0REREREREGNRSsREREREREpFotWIiIiIiIiUiwWrUTktugY4dX9PGGZmdEZTrtPRERKwQwlch9HghOR2xLauDbpgKv7eSIYpt1XMq7VR0TkHmYoWTBDXceilYjcprQv2UCedl/peMBDROQeZihZMENdx6KViNzGL1nla+lBUUsWU+cBDxGR65ihyscMVR4WrUTUIvySbZ4QJtSUfod6Yz5CdIkwRF8DSdL65blbclDExdSJiPyDGdo8ZihdjkUrEZEPVBRsQcHxRTAZz1m3aXXJiM9chIj4m/3SBncPiriYOhERKQEzlBpj0UpE5CWFxYXYd2gf9PU5SJb+CQCQLsuv+tpzOH/oIZwTD6ECfWRqpWOnf44DcHuz++3+fhfOlBX6vkEq0UrXSu4mEBEFjIqCLbhw+P8BsJ3V2GQ837C92+t+K1xJOVi0EhF5waGfD2H1xndRXVWFqQO3AHrbghVo+F0IINL4DtbtvggB52dk/a3kXHu4VLT+8C0Onz3h+wapRKgUJncTiIgCghAmFBxfhMYF62+3ApBQkLsIreJu9FtXYVIGFq1ERB4wm834YucX+HLnVtQZ65EaXYBIQ7XD/SUJiDRUIzmiEGeKEv3Y0uaZ61xbuttcp4HZyGW+LWrKfb+WIhFRMKgp/c6mS3BTAqbac6gp/Q5hMQP91i6SH4tWIqIWEkLg/U/fx54fv4ep3gRhDEWrUte6ikaVRCM0t6OPW+iekOIU1/Y70xahlSxaLfR6xycpiIjIdfXGfK/uR4GDRSsRUQuVV5TjcO5hmOrNEJXh0J5NRmyfAy7dNympGgZDno9b6J6zZ0OwbVvz+2Vm5iMlRVltl1N4eBTefVfuVhARqV+IzrUeSK7uR4GDRSsRUQuZxaX12URZNCIM9TAaEyBEa0hSscP7abWJuOWWPypuPM6hQ63wz382v9/NN4/HlVdW+r5BKmEyCcye/arczSAiUj1D9DXQ6pJhMp6H/XGtErT6NjBEX+PvppHMVFm0VlRU4Nlnn8XatWtRVFSELl264JlnnsGkSZOavW9WVhamTZtm97Zz586hTZs23m4uEQUVDcLCHkRNzQu//X556DZMvNS5858RH9/F7y1rTkiIBgaDQI2TKfsNBoFevdoiLc3scJ9gU1ZWLncT3MIMJSKlkiQt4jMX/TZ7sAR7GRrfcZHiTvoCDeu26g2i2XVaY+OZny2hyqJ1woQJ2LNnD5YtW4ZOnTrhvffew+TJk2E2mzFlyhSXHmPVqlXo0sX2oDEuLs4XzSWiIBMaOhAdOqzE8ePzYbxsQgm9PhkdO/4J8fGjZWydY2lpZhw5chEFThZTj483s2BVOWYoESlZRPzNQLfXm67Tqm+D+I7+W6fVXalpJmw/cg5FTjI0Nt7MNVpbSHVF6+bNm/Hll19aQxYAhg8fjlOnTmH27Nm46667oNU2f/ale/fu6Nu3r6+bS6Q6eae1/ML1gvj40YiLG4XS0hwYjReg0yUhOrq/Is8OXy4tjUVpIGOGEvkWM9Q7IuJvRqu4G1FT+h3qjfkI0SXCEH2N4jM0Nc3Ev6+PqK5o3bBhAyIiIjBx4kSb7dOmTcOUKVOQk5ODQYMGydQ6InXLO63FsK7JTru2hOoE3lh3EYltGgobBrBjkqRFTAy/j0g5mKFEvsMM9S5J0nJZG7JS3ZoFBw8eRNeuXRESYltv9+zZ03q7K8aMGQOtVovY2FhMmDCh2fvV1tairKzM5oco0BQVaJyGLQDUGSVMuzURo/u1weh+bTCsazLyTiv7zCcRNWCGEvkOM5TId1R3pbWwsBAdOnRosj02NtZ6uzNt2rTBvHnzMGDAAERFReHAgQNYtmwZBgwYgF27dqFXr15277d06VIsXrzY8xdAFGBqayQUFWgC7kyxK128WsX4rz1E3sAMJVKWYM7QQHvN5FuyFq3bt2/H8OHDXdp337596N27NwBAkhyfxXJ2GwCMGjUKo0aNsv4+ZMgQjB49Gj169MCCBQuwceNGu/ebO3cunnzySevvZWVlaNeunUttJyJ1caWLl94g8Ml3vFpE8mGGEpESuZqh24+cY+FKLpO1aO3cuTNWrlzp0r5paWkAGmYntHcmuKioCMCls8XuyMjIwODBg/Htt9863Eev10Ov17v92ETB4PhRx18lajyb6koXr9oaCcVF7NJF8mGGEgWGYM3QQLzCTL4ja9GanJyM+++/36379OjRA2vWrEF9fb3NmJwDBw4AaJjRsCWEENBoVDfEl0gRHrs33uFtPJtK5BvMUKLAwAwlap7qEmb8+PGoqKjAunXrbLZnZ2cjJSUF/fv3d/sxT5w4gV27dmHAgAHeaiYR/cZyNpWI5McMJVIXZihRA9VNxHTzzTfjhhtuwMyZM1FWVobMzEysWbMGn3/+OVavXm2zvtyMGTOQnZ2N3NxcpKenAwBGjhyJIUOGoGfPntZJJF544QVIkoQlS5bI9bKIiIh8jhlKRERqpLqiFQDWr1+PefPmYcGCBSgqKkKXLl2wZs0aTJo0yWY/k8kEk8kEIYR1W48ePfDBBx9g+fLlqK6uRmJiIq6//nrMnz8fnTp18vdLIVKU2Hgz9AbR7FgUIlIvZiiRbzBDiXxHEpenEbmsrKwM0dHROFR8CJFRkXI3h8hrLp+mfs/Xeix6orXHj7lpz3n06FPn8eP4y4G9oRjdr02z+72//X/YvOc5lJVUwHyuDWLqdcjMLMItt0zAVVe5382S1KmsrBytW3dCaWkpoqKi5G6OKjBDKVAxQ13PULW9LvKN8rJyXNn6ymYzVJVXWonId1LTTJzwgYiIqAWYoUS+wZHdRESNWLp4OaM3CLSO5YEJERHR5VzN0Nh4s59aRIGAV1qJiBpJTTNh+5FzTmdsjI03o1UMuzURERFdztUM5RVpcgeLViLyKbWeTXWli1dJmZ8aQ0REQSmQM5TIHSxaicghV2ZC1OkF3vioAAlt7IcTz6YSEVEwYoYSeQ+LViJyKJi7+Fw+AyQAXDyvRWnJpQOPqBgzwiINKDyTjsryKoRUGBBjqJSjqUREpEDMUOcZmtjm0hXkQH0fyHtYtBKRU8HYxSfvtBbDuia7sNZeIoA/AQA02jqMG/tnAEW+bh4REakEM9Q1eoPA9iPngu69Itdx9mAiokaKCjRuLw5vNoWitjbCRy0iIiJSh5ZkaG2N5PSKNBE/HURERERERKRYLFqJiIiIiIhIsVi0EhERERERkWKxaCUiIiIiIiLFYtFKREREREREisWilYiIiIiIiBSLRSsRUSOx8WboDcKt+2i0ddDrK3zUIiIiInVoSYbqDQKx8WYftYgCQYjcDSAiUprUNBO2Hzlns2bcxfNalJZcWncuKsaMsMhS/GvDv1BZXoWQCgMiDJVyNJeIiEgxXM3QxDaXitTYeDNS00x+bSepC4tWIiI7UtNMjQK0rsk+JWU1iNtzCqElFTCfawPU6/zXQCIiIoVyJUOJ3MHuwURERERERKRYLFqJiIiIiIhIsVi0EhERERERkWKxaCUiIiIiIiLFYtFKREREREREisWilYiIiIiIiBSLRSsREREREREpFotWIiIiIiIiUiwWrURERERERKRYLFqJiIiIiIhIsVi0EhERERERkWKxaCUiIiIiIiLFCpG7AUTkf3mntSgqcHzOKjbejNQ0kx9bREREpA7MUCL/Y9FKFGTyTmsxrGsyamskh/voDQLbj5xj6BIREV2GGUokD3YPJgoyRQUap2ELALU1ktOzyERERMGIGUokD/6PIiIiIiIiIsVi0UpERERERESKxaKViIiIiIiIFItFKxERERERESkWi1YiIiIiIiJSLBatREREREREpFgsWomCTGy8GXqDcLqP3iAQG2/2U4uIiIjUgRlKJI8QuRtARP6VmmbC9iPnnK4hFxtv5qLoREREjTBDieTBopUoCKWmmRioRERELcAMJfI/dg8mIiIiIiIixWLRSkRERERERIrFopWIiIiIiIgUi0UrERERERERKRaLViIiIiIiIlIsFq1ERERERESkWCxaiYiIiIiISLFUV7SWl5djzpw5uPHGG5GQkABJkrBo0SK3HiM/Px9Tp05FfHw8wsPDMXDgQGzbts03DSYiIlIIZigREamR6orWwsJCvPHGG6itrcW4cePcvn9tbS1GjBiBbdu2YcWKFdi4cSOSkpIwatQofPXVV95vMBERkUIwQ4mISI1C5G6Au9LT01FcXAxJklBQUIA333zTrfu/9dZbOHjwIHbv3o2BAwcCAIYPH45evXphzpw5yMnJ8UWziYiIZMcMJSIiNVLdlVZJkiBJUovvv2HDBnTu3NkatgAQEhKCe+65B9999x3y8vK80UwiIiLFYYYSEZEaqa5o9dTBgwfRs2fPJtst2w4dOuTvJhEREakCM5SIiOSguu7BniosLERsbGyT7ZZthYWFdu9XW1uL2tpa6++lpaUAgIqyCh+0kojUoKayBlGRUai4WAepXgu93gi9PhySFIKysnK5m0d+UvZbDgghZG6J7zFDiYjImypczFBZi9bt27dj+PDhLu27b98+9O7d2yvP66xrlKPbli5disWLFzfZ3j+9v1faRESB5HW5G0AyKC8vR3R0tN+ejxlKRESBorkMlbVo7dy5M1auXOnSvmlpaV55zri4OLtngouKigDA7hlkAJg7dy6efPJJ6+9msxlFRUWIi4vzaHyQnMrKytCuXTv8+uuviIqKkrs5QYfvv/z4N5BfIPwNhBAoLy9HSkqKX5+XGSqvQPjsqhnff/nxbyC/QPgbuJqhshatycnJuP/++/36nD169MCBAweabLds6969u9376fV66PV6m20xMTFeb58coqKiVPtBDwR8/+XHv4H81P438OcVVgtmqDKo/bOrdnz/5ce/gfzU/jdwJUODbiKm8ePH4+jRozbT8tfX12P16tXo37+/38+UExERqQUzlIiI5KDKiZi2bNmCyspKlJc3THRy+PBhfPTRRwCAW265BeHh4QCAGTNmIDs7G7m5uUhPTwcATJ8+Ha+++iomTpyIZcuWITExEa+99hqOHTuGrVu3yvOCiIiI/IQZSkREaqPKonXmzJk4deqU9fcPP/wQH374IQDgxIkTyMjIAACYTCaYTCab2aj0ej22bduGOXPm4NFHH0VVVRV69+6NLVu2YOjQoX59HXLT6/VYuHBhky5b5B98/+XHv4H8+DfwP2aod/CzKy++//Lj30B+wfQ3kEQwzNFPREREREREqhR0Y1qJiIiIiIhIPVi0EhERERERkWKxaCUiIiIiIiLFYtFKAIDy8nLMmTMHN954IxISEiBJEhYtWiR3swJSRUUFHn/8caSkpMBgMKB37954//335W5WUOHnXV7/+c9/MH36dHTp0gWtWrVCamoqxo4dix9++EHuphG1CL9T/IcZKj9+3uUVrBnKopUAAIWFhXjjjTdQW1uLcePGyd2cgDZhwgRkZ2dj4cKF2LJlC/r164fJkyfjvffek7tpQYOfd3n94x//wMmTJ/HYY49h8+bNWLFiBfLz8zFgwAD85z//kbt5RG7jd4r/MEPlx8+7vII1Qzl7MAGAdUkDSZJQUFCAhIQELFy4kGfOvGzz5s0YPXo03nvvPUyePNm6/cYbb8ShQ4dw+vRpaLVaGVsYHPh5l1d+fj4SExNttlVUVCAzMxPdu3fnep+kOvxO8Q9mqDLw8y6vYM1QXmklAA1fPJIkyd2MgLdhwwZERERg4sSJNtunTZuGs2fPIicnR6aWBRd+3uXVOGwBICIiAt26dcOvv/4qQ4uIPMPvFP9ghioDP+/yCtYMZdFK5EcHDx5E165dERISYrO9Z8+e1tuJglFpaSn27t2LK6+8Uu6mEJFCMUOJ7AuGDGXRSuRHhYWFiI2NbbLdsq2wsNDfTSJShN///veorKzEvHnz5G4KESkUM5TIvmDIUBatAWj79u3WrhvN/ezfv1/u5gYdZ11q2N2GgtH8+fPx7rvv4qWXXsLVV18td3MoyDFDlY0ZSmQrWDI0pPldSG06d+6MlStXurRvWlqaj1tDl4uLi7N7JrioqAgA7J5BJgpkixcvxnPPPYfnn38ejzzyiNzNIWKGKhgzlMhWMGUoi9YAlJycjPvvv1/uZpAdPXr0wJo1a1BfX28zJufAgQMAgO7du8vVNCK/W7x4MRYtWoRFixbhj3/8o9zNIQLADFUyZijRJcGWoeweTORH48ePR0VFBdatW2ezPTs7GykpKejfv79MLSPyryVLlmDRokV49tlnsXDhQrmbQ0QqwAwlahCMGcorrWS1ZcsWVFZWory8HABw+PBhfPTRRwCAW265BeHh4XI2LyDcfPPNuOGGGzBz5kyUlZUhMzMTa9asweeff47Vq1dzfTk/4uddPn/961+xYMECjBo1CqNHj8a3335rc/uAAQNkahlRy/E7xfeYocrBz7t8gjVDJWFZIZiCXkZGBk6dOmX3thMnTiAjI8O/DQpQFRUVmDdvHtauXYuioiJ06dIFc+fOxaRJk+RuWlDh510+w4YNw1dffeXwdsYSqRG/U/yDGaoM/LzLJ1gzlEUrERERERERKRbHtBIREREREZFisWglIiIiIiIixWLRSkRERERERIrFopWIiIiIiIgUi0UrERERERERKRaLViIiIiIiIlIsFq1ERERERESkWCxaiYiIiIiISLFYtBIREREREZFisWglIiIiIiIixWLRSkRERERERIrFopWImti1axckSYIkSfjwww/t7pOTk4OIiAhIkoQ5c+b4uYVERETKxAwl8j5JCCHkbgQRKc/YsWPxySefoEuXLjh48CC0Wq31tmPHjmHw4MEoKCjAfffdh1WrVkGSJBlbS0REpBzMUCLv4pVWIrJr2bJl0Gq1OHr0KFavXm3dfvbsWdx0000oKCjAmDFj8OabbzJsiYiILsMMJfIuXmklIofuv/9+vPXWW2jfvj2OHTuGyspKDBkyBAcOHMDgwYPxxRdfICwsTO5mEhERKQ4zlMh7WLQSkUN5eXm44oorUF1djZdeegkbNmzAjh070KNHD+zYsQMxMTFyN5GIiEiRmKFE3sPuwUTkUGpqKmbNmgUAeOKJJ7Bjxw5kZGTg888/txu2FRUVWLRoEcaMGYM2bdpAkiRMnTrVv40mIiJSAGYokfewaCUipx577DFoNA1fFbGxsfjiiy+QkpJid9+CggIsXrwYe/fuRd++ff3ZTCIiIsVhhhJ5R4jcDSAi5aqvr8eDDz4Is9kMAKiqqnI6/iY5ORlnzpxBamoqampqOFaHiIiCFjOUyHt4pZWI7BJC4P7778dnn32GhIQEtG/fHjU1NVi4cKHD++j1eqSmpvqxlURERMrDDCXyLhatRGTXnDlzkJ2djYiICGzatAnPP/88ACA7OxuHDx+WuXVERETKxQwl8i4WrUTUxPLly7F8+XKEhoZi3bp16NevHyZNmoSePXvCZDJh7ty5cjeRiIhIkZihRN7HopWIbLzzzjuYM2cOJElCVlYWbrzxRgCAJElYsmQJAOCTTz7Brl275GwmERGR4jBDiXyDRSsRWW3evBkzZsyAEAJ/+9vfMGXKFJvbb7vtNvTv3x8A8PTTT8vRRCIiIkVihhL5DotWIgIAfPPNN5g4cSLq6+vx9NNP4/HHH7e7n2Vczq5du7Bx40Y/tpCIiEiZmKFEvsUlb4gIADBw4EBUVlY2u9+IESMghPBDi4iIiNSBGUrkW7zSSkRERERERIrFK61E5FWvvPIKSkpKUF9fDwD46aef8NxzzwEAhgwZgiFDhsjZPCIiIsVihhLZJwn2USAiL8rIyMCpU6fs3rZw4UIsWrTIvw0iIiJSCWYokX0sWomIiIiIiEixOKaViIiIiIiIFItFKxERERERESkWi1YiIiIiIiJSLBatREREREREpFgsWomIiIiIiEixWLQSERERERGRYrFoJSIiIiIiIsVi0UpERERERESKxaKViIiIiIiIFItFKxERERERESkWi1YiIiIiIiJSrP8P4ghUm+uwyNwAAAAASUVORK5CYII=",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_42_0.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"from __future__ import division, print_function, unicode_literals\n",
|
||
"\n",
|
||
"# Common imports\n",
|
||
"import numpy as np\n",
|
||
"import os\n",
|
||
"\n",
|
||
"# to make this notebook's output stable across runs\n",
|
||
"np.random.seed(42)\n",
|
||
"\n",
|
||
"# To plot pretty figures\n",
|
||
"import matplotlib\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from matplotlib.colors import ListedColormap\n",
|
||
"plt.rcParams['axes.labelsize'] = 14\n",
|
||
"plt.rcParams['xtick.labelsize'] = 12\n",
|
||
"plt.rcParams['ytick.labelsize'] = 12\n",
|
||
"\n",
|
||
"\n",
|
||
"from sklearn.svm import SVC\n",
|
||
"from sklearn import datasets\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.datasets import make_moons\n",
|
||
"from sklearn.tree import export_graphviz\n",
|
||
"\n",
|
||
"Xm, ym = make_moons(n_samples=100, noise=0.25, random_state=53)\n",
|
||
"\n",
|
||
"deep_tree_clf1 = DecisionTreeClassifier(random_state=42)\n",
|
||
"deep_tree_clf2 = DecisionTreeClassifier(min_samples_leaf=4, random_state=42)\n",
|
||
"deep_tree_clf1.fit(Xm, ym)\n",
|
||
"deep_tree_clf2.fit(Xm, ym)\n",
|
||
"\n",
|
||
"\n",
|
||
"def plot_decision_boundary(clf, X, y, axes=[0, 7.5, 0, 3], iris=True, legend=False, plot_training=True):\n",
|
||
" x1s = np.linspace(axes[0], axes[1], 100)\n",
|
||
" x2s = np.linspace(axes[2], axes[3], 100)\n",
|
||
" x1, x2 = np.meshgrid(x1s, x2s)\n",
|
||
" X_new = np.c_[x1.ravel(), x2.ravel()]\n",
|
||
" y_pred = clf.predict(X_new).reshape(x1.shape)\n",
|
||
" custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
|
||
" plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)\n",
|
||
" if not iris:\n",
|
||
" custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])\n",
|
||
" plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)\n",
|
||
" if plot_training:\n",
|
||
" plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\", label=\"Iris-Setosa\")\n",
|
||
" plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\", label=\"Iris-Versicolor\")\n",
|
||
" plt.plot(X[:, 0][y==2], X[:, 1][y==2], \"g^\", label=\"Iris-Virginica\")\n",
|
||
" plt.axis(axes)\n",
|
||
" if iris:\n",
|
||
" plt.xlabel(\"Petal length\", fontsize=14)\n",
|
||
" plt.ylabel(\"Petal width\", fontsize=14)\n",
|
||
" else:\n",
|
||
" plt.xlabel(r\"$x_1$\", fontsize=18)\n",
|
||
" plt.ylabel(r\"$x_2$\", fontsize=18, rotation=0)\n",
|
||
" if legend:\n",
|
||
" plt.legend(loc=\"lower right\", fontsize=14)\n",
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"plt.subplot(121)\n",
|
||
"plot_decision_boundary(deep_tree_clf1, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)\n",
|
||
"plt.title(\"No restrictions\", fontsize=16)\n",
|
||
"plt.subplot(122)\n",
|
||
"plot_decision_boundary(deep_tree_clf2, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)\n",
|
||
"plt.title(\"min_samples_leaf = {}\".format(deep_tree_clf2.min_samples_leaf), fontsize=14)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 10,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_43_0.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"np.random.seed(6)\n",
|
||
"Xs = np.random.rand(100, 2) - 0.5\n",
|
||
"ys = (Xs[:, 0] > 0).astype(np.float32) * 2\n",
|
||
"\n",
|
||
"angle = np.pi/4\n",
|
||
"rotation_matrix = np.array([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]])\n",
|
||
"Xsr = Xs.dot(rotation_matrix)\n",
|
||
"\n",
|
||
"tree_clf_s = DecisionTreeClassifier(random_state=42)\n",
|
||
"tree_clf_s.fit(Xs, ys)\n",
|
||
"tree_clf_sr = DecisionTreeClassifier(random_state=42)\n",
|
||
"tree_clf_sr.fit(Xsr, ys)\n",
|
||
"\n",
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"plt.subplot(121)\n",
|
||
"plot_decision_boundary(tree_clf_s, Xs, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
|
||
"plt.subplot(122)\n",
|
||
"plot_decision_boundary(tree_clf_sr, Xsr, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 11,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Quadratic training set + noise\n",
|
||
"np.random.seed(42)\n",
|
||
"m = 200\n",
|
||
"X = np.random.rand(m, 1)\n",
|
||
"y = 4 * (X - 0.5) ** 2\n",
|
||
"y = y + np.random.randn(m, 1) / 10"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 12,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/html": [
|
||
"<style>#sk-container-id-1 {color: black;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>DecisionTreeRegressor(max_depth=2, random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">DecisionTreeRegressor</label><div class=\"sk-toggleable__content\"><pre>DecisionTreeRegressor(max_depth=2, random_state=42)</pre></div></div></div></div></div>"
|
||
],
|
||
"text/plain": [
|
||
"DecisionTreeRegressor(max_depth=2, random_state=42)"
|
||
]
|
||
},
|
||
"execution_count": 12,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.tree import DecisionTreeRegressor\n",
|
||
"\n",
|
||
"tree_reg = DecisionTreeRegressor(max_depth=2, random_state=42)\n",
|
||
"tree_reg.fit(X, y)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 13,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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QQgi1hSuHmrpi27JlS49XlA8ePAjg8Uq0w8SJE3nggQec/5eWlnLKKafwyy/57NuXxGmnQXq6+jGbRefOndmzZw9t27Zl06ZNWocjhBBuCguhWzdwHT7RaoX1632X7WVlZbRv355mzZqFP0iN6S2HHjx4kK+++opLL73U52uHU6Ri0FMO1cNxF0IELpznrl5zqKkrtt27d+f333+vt9yx7Mwzz/T63ISEBBISEuot79cvCUVJwmqFWbMgK0u9eM3E0bzAarWSlJSkcTRCCOEuN9c9IQPU1MC+fdClS8PPj4bmtHrLodu2bePOO+8kNzdXsylXIhWDnnKoHo67ECJw4Tx39ZpDTV2xvfrqq7nzzjtZuXIl/fr1A+xTFSxYsIB+/frRrl27gLfpeBNramDcOBgyBCLdGi03N5cTJ04QHx9P7969I/viQghdk/LBP5mZ9qvLNTW1y2Ji4PTTtYtJb/SWQ88++2wqKyuJiYkJ+HVdhXKOqBWDkUTjPovoZaYcGs5zV6851BAV26+++oojR45w+PBhADZs2MD/+3//D4C//e1vNGnShKysLObNm8f27dvJyMgA4LbbbuONN95g+PDhPP/886SlpfHmm2+yefNmvvvuu5Djqq6GbdsiX7EdNmwYhYWFpKenU1BQENkXF0LompQP/rHZ7HcMx42zl+UxMfD225EvzyPBLDnUYrEQGxv615ZQzhG1YjCSaNxnEb3MlEPDee7qNYcaYkjHf/zjHwwfPpzbbrsNgI8++ojhw4czfPhwioqKAKiurqa6uto5GT3Ym0J9//33XHTRRdx9991cccUV7Nmzh6+++oqBAweGHJcerkwIIYQITlYW5OVBTo79t1m7lpglh27fvp0rr7yS7du3h/zawdJDDJEWjfsshBmE+9zVYw41xCW4vLy8BteZO3cuc+fOrbe8devWzJs3T7VYHLfd9XJlQgghRPBsNvOX45JDhRBChIPecqghKrZ6sn69vWP06afr640UQggh9C6UHHraaafx+eefhycwA8UQadG4z0KYQTSeu1KxDVB6un+jfamhoAC2brV30JZKtBBCCKMLJYcqikJ1dTUxMTF+jagZjhwaaAxmEI37LIQZROO5a4g+ttEoOxsyMmDwYPvv7GytIxJCCCG0s2bNGuLi4lizZk2D64YrhwYSg1lE4z4LYQbReO7KHVsdKiiA22+vHUJby6mFhBBCCNW8+CK0bQslJVBUBGlp9uWOv1NSvD6WERfHnH/8g4y4OJ8vEc4cmpGRwZw5c5wjR0eDaNxnIcwgGs9dqdjq0Nat7vNCgXZTCwl1KIpCZWUlNXXfWKEJq9VKXFxc1DTNEUI3nnkm6Ke2BEYDvPUWvPOO1yE4w5lDW7ZsyejRo0PbiMFE4z4LYQbReO5KxVaH9DrpsQhcdXU1+/fv5/Dhw1RWVmodjnARFxdHs2bNaNWqVVgmLxdCqKsE+A64WFFI8XELNpw5tKSkhO+++46LL76YlJSU0DdoANG4z0KYQTSeu1Kx1SG9TnosAlNdXU1+fj4VFRUkJyeTmJgYVR349coxmEJ5eTmHDh3i2LFjtG/fXiq3QujcDuA6IBdI8XELNpw5dMeOHVx33XXk5uZGzRfFaNxnIcwgGs9dqdgGqLAQcnPDP1JxVpb9YvS2bfWnRdi4cSOKokgFSef2799PRUUFp5xyCo0bN9Y6HFFHYmIiycnJ7Nq1i/3799O6dWutQ1KFlA/CrM4CSoGm0OAt2HDl0LPOOovS0lKaNm0a8HONKhr3WUQvM+XQaDx3pWIboG7dQFHszZxmzfLaxUcV3iY9btasWfheVKhCURQOHz5McnKyVGp1rHHjxiQlJXH48GHS0tJMkcikfBBmFQMkAVgsft2CDUcOjYmJISkpKejnG1E07rOIXmbKodF47krFNkCKYv8tIxULXyorK6msrCQxMVHrUEQDmjVrxqFDh6isrCQ+Pl7rcIQwtSd5kmO0pTkltKaYWx9NJSUZKC6G1NTaUZEd/3PysZwcdqxdy2PA1IULOfWGGzSJf8eOHTz22GNMnTqVU089VZMYIi0a91kIM4jGc1cqtiGQkYqFN47Rj6Xfpv453iMZsVqI8HuVBzl53xWAXkNh0CA/njhmDFVr11IMVGl4B6Kqqori4mKqqqo0iyHSonGfhTCDaDx3pWIbAq1GKp45cyZlZWUkJSXxwAMPRD4A4TczNG01O7O9R1I+CKMIKIfGxpKJfVRk0tNDet1QzpHMzEy+++67kF7faKJxn0X0MlMOjcZzVyq2AXJMIaDlSMUzZ86ksLCQ9PR0w590Qgh1Sfngv4IC+5yn4R4MUNQKOofGunxdCfHug5wjQghvpHzwnx5zqFXrAIxm/XrIyYG8vPAOHCWEECJ8srMhIwMGD7b/zs7WOqLoEHQOjY1lDZAArPnjj/AE54c1a9aQkJDAmjVrNIsh0qJxn4Uwg3Ceu3rNoVKxDVB6ur0/kF6uTAghhAhMQQHcfrv9ziHUDgZYUKBtXNEg6BwaF4cNmAnYNJyP0WazMXPmTGxR9CUgGvdZCDMI17mr5xwqTZGFEEJEla1baxOygwwGqHOxsaQC4wE0nI4jNTWV8ePHa/b6WojGfRbCDMJ17uo5h8odWyGEYW3cuJHJkyfzf//3f1qHIgwkM9Pe19OVVoMBCj/FxlIKfAmUlpZqFkZpaSlffvmlpjFEWjTusxBmEK5zV885VCq2QghDqqqqYtSoUUyZMoU777yTTz75ROuQhEHYbDBrlj0Rg7aDAQo/xcayHbgc2J6fr1kY27dv5/LLL2f79u2axRBp0bjPQphBuM5dPedQaYocZnocMUwIM3j++edZvXo1U6dOZfbs2fzjH/9g4MCBtGjRQuvQhAFkZcGQIfamU6efLuWzXjlyaK8jsXQHdgOtNHyzunfvzu7du2nVqpVmMURaNO6zEGYQznNXrzlU7tiG0Ysvuo8Y9uKL9tEg9dC5WggjW79+Pc888wzXXnstEydO5MMPP6SkpIS7775b69CEgdhsMhignrnm0GkvxhIHtAVK92sXU1xcHG3btiUuLk67ICIsGvdZCDMI97mrxxwqFdswmTEDHn7YfcSwhx/W37DYQhhNdXU1t956KzabjeyTJ1Lv3r156aWXWLhwIZ999pnGEQohQlU3h55Q4tgJjAFGj92tWQ7duXMnY8aMYefOndoEoIFo3GchzCAaz11pihwGBQXw6KPeH3cMiz1kSHBXOXr16kX79u1JTU0NPkghDComJoZVq1bVW37XXXdx1113aRCRvkj54E66gxiPpxxaRSzHgT+AFhzTLIceP36cP/74g+PHjwf+wgYVjfssopeZcqga567RcqhUbMNg61ZQFN/rhDIs9ueffx5cYEII05PyoVZ2du1ce1arfbCLrCytoxIN8ZRDq4jlDOAn4CbSNMuhZ5xxBj/99FPQzzeiaNxnEb3MlENDPXeNmEOlKXIYeBoGuy69DIsthBBmpOcJ5IVvnnJolct1+FiqJIcKIUQYGTWHSsU2DOoOg221wrXX6nNYbCGEMCNfE8gLffOUQ3v2juU3oAVwmB2a5dDffvuNFi1a8Ntvv0X+xTUSjfsshBmEcu4aNYdKxTZMsrIgL88+CvLOnfDRR7X/5+Xp/1a+EHqxb98+LBYLFouFr7/+2ue6d911FxaLhfPOOw+lof4AwtT0PIG8aFjdHHrnPbG0ASYCz01sqlkObdOmDRMnTqRNmzbaBKCBaNxnIcwglHPXqDlU+tiGkc3mfkW57v/BuvLKKykuLiY1NdVUfQGE8KR169Z07NiRP//8k5UrVzJkyBCP6/3222+89dZbWK1WXn/9dSwWS4Qj1QcpH+wcd/3GjbNfZZaWMsbjljPj4mgNPAzQpnFI2w3lHGndujUPP/xwSK9vNNG4zyJ6mSmHhnLuGjWHSsU2UC++CG3bQkkJFBVBWpp9uePvlJR6j5VtL6KYNFq2guYV3tfztQ3Xx1avWEHhoUOky9VTESUGDBjgrNh6c/fdd1NdXc3tt99O7969IxidvqxevZrCwkLS09O1DkVzep1AXgSmoAAObYolA8gFepeX0yyE7YVyjhw+fJjc3Fx69+5Ns2ahRGEc0bjPInqZKYeGeu4aMYdKxTZQzzwT8FOSTv6obu9e+5Bl0q5Z+GK0sdo9OO+885g/f77Xiu2CBQtYsWIFKSkpPPfccxGOTuiZWi1lhDYco3JeWRPLE8BFQO6+ffTSKJ6tW7dy0UUXkZubS69eWkURWdG4z0KYgRrnrtFyqPSxNTojDFEmtJOdDRkZMHiw/Xd2ttYRBWXAgAEAHDhwgG11Ri44fPgwjzzyCADPPPMMrVq1inh8Qgj1uY7KWUUsXYGtQHpsC81i6tq1K1u3bqVr166axRBp0bjPQphBNJ67csfW6EKZzE9o75xz7Hfew6G62n3bNTUwZgxMmlQ73Kja2rSBX39VfbPdunUjOTmZ0tJSVq5cyekuoxdMmTKFPXv20KNHD+644w7VX1sIoQ3XUTmriKURcDqw46B2/ecbNWrkVv5Eg2jcZyHMIBrPXanYGp0RhigT3u3dC4WFkX9Ng7FarfTr149vvvmGn3/+mZEjRwKwadMmXnvtNQBef/11YsJVYTeAQYMGkZeXp3UYhmSC1vqm5BiV03HHNh+YAdxhPaBZTPn5+cyYMYOHH36Y9u3baxZHJEXjPgthBpE6d/WUQ6Via3RGGKJMeBfOAcDq3rF1fc1w3rENkwEDBvDNN9+49bO9++67qaysZMSIEVx44YWqv+by5cu56KKLnP9brVaaNWtG27ZtOfvss7n22msZNmxYxCrUn376KWvXrmXy5MkReT1vpk2bxurVq8nNzWXHjh1kZGToulLtK+k6+nDW1NgrUbNmybAFeuE6KmdVdSyHgeXAHTHHNIvp8OHDLF++PKpah0TjPgthBmqdu0bKoVKxDdSTT9aOilxcDKmp9uWOvx0jGrs8VvZnMcWk0rIlND/hfT1f23D+/fbb9kn9wF6JkG9gxhaGZrtusrPrj9Vu0M/MeeedB9in9amoqGDp0qV89913JCYmMn369LC+9vXXX8/ll1+OoiiUl5ezdetWli5dyqJFi+jTpw9LlizBFoELTJ9++inz5s3TvGL72GOP0aJFC3r16sWhQ4c0jaUhvpKuax9OsP8eN84+CqRcL9QHx6icxZ/E0fUeWAeQnKxZPF27dmXdunWavb4WonGfhTADNc5do+VQqdgG6sEHISmwMY5VHRX5iy9qK7ZR3OxS+MmIY7V7ce655xITE8OJEyf44YcfePDBBwGYNGlS2Ifl79mzJ6NGjXJb9tJLLzF9+nQmTJjAZZddRm5uLrGx0VGkbt++nY4dOwJw5plnUl5ernFEnjWUdF37cDrIsAX6Y7OBrY/LuVVVpV0wQggRJYyYQ2VUZJ0oKICcHD8GOLbKWyYCZLPBoEGG/6aemJhI9+7dAcjKymLnzp1kZmZy//33axKPxWLh0Ucf5YYbbmDdunUsXrzY+VhFRQVTp06lW7duNGrUiObNm3PFFVewZs0at20sX74ci8XC3Llzef311+nUqRONGjUiMzOTV1991W3dDh06MG/ePOdrO36WL1/utl51dTUAu3fvpmnTpgwZMoQtW7aouu+OSq3e+Uq6UNuH05UMW6BTsbH8DtiA3z10sfA7h4bo999/x2az8fvvv4f3hXQkGvdZCDMI9dw1Yg6NjtsLOhdQ+/SYGB4AyoCke+6JYJRCaG/AgAGsXbvW2Z/z1VdfJT4+XtOYbr/9dj744AOWLl3KyJEjqaysZOjQofz444/cdNNN3HXXXZSWljJ79mwGDBjAf//7X8455xy3bbz++uvs3buXcePG0axZMxYtWsR9993HgQMHePrppwF45ZVXmDlzJitWrGD+/PnO53bp0sX595EjR1AUhe7du9OpUyc6duzIq6++yrBhw1i/fr2zL3BNTQ0HDx70ex9btGiBVYcX1RoasMJ18CEH16Tr2ofTtbW+wa8BmVNsLK2AMUCruDi3hwLt4/XAAw9QVlZGUoCtrwBatWrFmDFjompasWjcZxG9Qikf9Kahc9eUOVQRfiktLVUApbS0VNXt5ucritWqKFD7ExNjX+7RoEG1Kx49qmosakpPT1cAJT09XetQNHHs2DFlw4YNyrFjx7QOxVTef/99BVAA5YorrlBlm77eq5ycHAVQpk2b5vX5Bw4cUAClV69eiqIoyksvvaQAyldffeW2XmlpqdK+fXtl4MCB9bafmJio5Luc9BUVFUqfPn2UmJgYJS8vz7n8lltuUbwV2wMHDlQA5YUXXnBbPn36dAVQ/v3vfzuX7dixw3kc/fnZsWOH1/3v1q2bkpGR4fXxcJk9u7bstFrt/3tbLyamtmz1tF5+vqLk5Pgod12EKxeYXcjH7fffa3PfmDHOxQHnUIOI9hwqhAgvs+ZQuWOrsYDbp7v2qz3Z5FCIaNG4cWMAEhISePnllzWOxs5xVbesrAyA999/n8zMTM455xz279/vtu4ll1zCvHnzOHbsmHNfAEaOHOk2+FR8fDz3338/I0aM4IsvvuCuu+7yKxar1co9dVpyDB48GICtW7cyZMgQANq0acO3337r9z62Cefo3UEIZMAKf7qZ22xyl1b3YmM5AmwAuh47RtOTiyPdx+vIkSNs2LCBrl270rRp04afYALRuM9CmMGRI0fY8P/+H103bqRpUpJzcNqy7UVsezeNh4E0iiiqSSN3TAp/31JC84oiSEuzb6CoiKy0NP7+IJRtK6LZ6WmknEiBqSVQVLueragIW1oabDw5+G2R+zZIS6sdGDc/P6z7bIiKbXl5OZMmTeLDDz/k4MGDdO7cmQkTJnDDDTc0+NycnBymTp3Kb7/9xtGjR+nYsSNjxoxh/PjxupjzsqHb/PW4NgeUiq2IItXV1c7RgB9++GFOO+00bQM6yVGhdVRwN27cyLFjx0h1jGjuwf79+93mlHNtTuzQtWtXwD5Qk7/atWtHo0aN3Ja1bNkSgAMHauf+bNSoERdffLHf29WbQCsz0V5xNUUOjYtjM9AXyD14kF4nFwecQ0O0efNm+vbtS25uLr169Wr4CSYQjfsshBlsvuEG+i5dSi7geuYmAdM8PcHLBBPNT/4YgSEqttdccw2rVq3i+eefp1OnTixcuJAbb7yRmpoaRowY4fV53333HUOGDOHCCy/knXfeoWnTpnz++efce++9bN++vd7gLFoIuH16TAyHsbcPtJSW0kzDaQ+EiKTXXnuNdevW0aFDByZOnKh1OE5r164FoHPnzgAoikLXrl19li91K70Wi6XeOoqieH3Mm5iYGA4fPoyiKFgsFpo1a1Zve2C/SFBcXOz3dlNTU3VxIdAh0pUZozNFDo2NpQvwG5DZpIlzcTB9vLydI/7o0qULv/32G5mZmcHthwFF4z6L6BVK+aArq1bRZelSe5mpdSwRpPuK7b/+9S++/fZbZyIGuOiii9i5cycPP/ww119/vdcvXHPnziUuLo6lS5c6m89cfPHFbN68mblz5+qiYgsBzsgSE0MXoBBIP/dcCnbvjlCUQmhn0aJFPProo1gsFmbNmkUTly+2Wps1axYAl19+OQCdOnViz549DB482O8BlzZs2FBv2caNGwH3EYj9qeR26dKFwsJC0tPTKfAyRGx+fj6nnnqqX7EB7Nixgw4dOvi9fripOWBFQ4NnGJ1pcmhsLI2BHh4eCnRWM3/OEW8aN25Mjx6eojCvaNxnEb1CKR90ZcUKr2WmmelvmMs6PvnkExITExk+fLjb8ltvvZXdu3ezcuVKr8+Ni4sjPj7erS8bQPPmzes119Oa3zOy6HBkUiHC4csvv6RDhw4kJyczYsQIKisrmTRpEpdcconWoQH2O6DTp09n8eLF9OzZk+uuuw6Am266ieLiYmbMmOHxefv27au37P3333dLoCdOnODll18mJiaGK664wrk8MTERgJKSkpBid/Sx9fdHb31swV6ZycuzT/GSl+d7FFxPCgrg4YfhlFNg8GDIyLCPrms2psmhsbEUAhOBwsOH6z0cqVnNCgsLmThxIoWFheF9IR2Jxn0WwvAuuKC2zNQ6lgjS/R3b9evX06VLF2Jj3UN1XD1cv3495513nsfn3nHHHSxatIh77rmHxx57jCZNmvDFF1/wySefMG2ax9blThUVFVRUVDj/d/SjixSvdxECbA5o9rsRwrx++OEHdu7cSZMmTTj77LMZP348WYHWXlSydu1aFixYANj7K27bto0vvviCLVu20LdvX5YsWeK863Xvvffy7bffMmHCBJYvX85f/vIXkpKS2LVrF99//z2NGjUiJyfHbfudOnWiX79+3HHHHTRr1oyFCxeyatUqnnjiCTIyMpzr9evXj3/+85+MHz+eSy+9lLi4OAYPHkyaY5AGP4Xax3b+/Pns3LkTgOLiYk6cOMGzzz4L2Cs9/g525Q9fZViwfWddp4dx8DUAlZGZJofGxnII+AgYdfw46Q2srlbuq7udQ4cO8dFHHzFq1CjS0xuKwhyicZ+FMLw+fTjUvDkfHTrEKGiwzDQL3VdsDxw44NYUz6FFixbOx73p168fy5YtY/jw4bzxxhuAvQ/atGnTePDBB32+7rRp05gyZUoIkQfP55x8rndsXfrMBbwdIXRu6tSpTJ06VeswAFi8eDGLFy/GarWSmJhI27Zt6d27N9OmTWPYsGFuTTnj4uL48ssvefPNN5k/fz5PPfUUYB/YqW/fvtxyyy31tn/33XdTVlbG66+/zq5duzjllFN45ZVXuPfee93Wu/HGG8nNzeWDDz5g8eLF1NTUkJOTE3DFNlTZ2dn85z//cVv2xBNPAJCRkaFaxTYcZVjdEZVdhXM0Xa2YJofGxtIN2AZQ5w5yXWp9bjxvpxvbtm0LZg8Mq1u36NtnIcwgrXkm2w6tohqYwFQuH5nC+d1KoLgYHGN9OP52jFrs6TGXv0tI4YXHSkilmCLsj6Wd/PsQKTwypoTTmvnYfkEBvPlm+HY6LJMIqSgzM1MZOnRoveW7d+9ucH7JX3/9VUlLS1OuuOIK5YsvvlCWLVumTJo0SYmPj1eefvppn697/PhxpbS01PmTn58fkbkLG5yTb/hwJf3k3JLpbdoEv50wi/Y5+GQeW+PQ8r1yzGM7Z84c1bZplnMvXGXYsmXu2wx0+0abx9Y0OfTIkdo3avBgr6v587nx5xyRHCpEdDLLuZefryi/0ktRQDlBbNTkUN3fsW3ZsqXHK8oHDx4Eaq86ezJ+/Hhat27NJ5984ryjctFFF2G1Wpk8eTIjR470eCUb7PNkJiQkqLAHgWlwGgs/+9hGem4/IYRQU7jKME8jKoN9WbADUOmZaXJobCx/ANcAS0pL6eZlNbU+N9628+23f/D889ewZMkSunXzFoW5/PHHH1xzTXTtsxBGt3UrHOAII4APTi6Lhhyq+5GIunfvzsaNG6mqqnJb/vvvvwNw5plnen3u2rVr6d27d70RH/v06UNNTY1z1FE9cXxgXLlNY+G6Lz6aIje4HSGE0LFwlWGOEZUdRWlMDDz0EOzcac6uGqbJobGxJANXAr4muVPrc+NtO2eemcyVV15JchRNtZecHH37LITRZWZCMhauBBJP9jyNhhyq+4rt1VdfTXl5OR9//LHb8nnz5tGuXTv69evn9bnt2rXj119/pbq62m35Tz/9BIBN5csKBQX2ETpDGR3c0wfG7QqIn4NHNbgdIYTQsXCWYXVHVJ4xw7xlo2lyqNWKzWJhBmDzkQfV+tx4206fPjZmzJih+r7rmc0WffsshNHZbHBOuxhmAG2JiZ4cGpYGziq75JJLlJSUFGXWrFnKsmXLlLFjxyqAsmDBAuc6t912mxITE6Pk5eU5l7322msKoFx66aXKp59+qnzzzTfKo48+qsTGxioXX3xxQDE01CZ89uza/jhWq/3/UOTnK0pOjoe26rfcUtvHtnXr4LcTZmbpoxAs6WNrHGZ7r8x27gVbhuXn2/sCqV32Ga2PraKYJ4cejY1V1oNytGfPBl/P1+cmkHOk7naOHj2qrF+/Xjl69GiDzw2Fns7jSO2zEHqgp3MvVEfPOENZD0pZk2ZRk0MNUbE9fPiwcs899yht2rRR4uPjlR49eiiLFi1yW+eWW25RAGXHjh1uyz/++GPl/PPPV1q1aqU0bdpU6datm/LMM88o5eXlAcXg642I6CATt90WUMVWK2YqGIJhtsqSmZntvYqWc89X0lX7QqMrI1ZszZJDcxMSFEDJPf30gF67rlDOkdzcXHsMubkhxdAQPZ3HkdpnIfRAT+deqHJPOcV+7iYm1nvMrDnUoigNzBkjAPscfMnJyZSWlpKUlOT2WE4ODB5c/zk5OfYJ41U1diy5s2dzAoj/4AN6X3+9yi+gDpvNRmFhIenp6RSE0jbboI4fP86OHTs49dRTadSokdbhCB/M9l7l5uZy4sQJ4uPj6d27t9bh+C2QeUd9TeeyahX06+c+BEFMjL25VKBNpTzF5CsXCO/UyKHlTZvy+9GjdE9LI3HyZPvUEUVF4JjuyvG3Y1oJL4/l7trFiaZNie/Vi95/+1tA+1FeXs7vv/9O9+7dSUxMDOi5gdBTDo3UPguhB2bKoeWnncbvf/5J9xYtSHQZRNDMOVT3oyIbgacRwsI2UFNMDM7T7IwzwvACQk1y3Uj/zPYeGSkROwQy72jdeWhramDcOBgyBL7+2v5Y3bc0mJEgZR7wyPErh2Znk3j0KP3BXkm9886gX895hlgs8M47Ab2xiYmJ9O/fP+jXNqJo3GcRvcyUQxMVxV5muoxLYPYcqvvBo4wgogM1uQ7TWGdADz1xhKbjEMPKevJ9qjvoitAfx3tk9XMqLaEub0nW200qb9Ow/PST+3ZcBXqhMdCYRGgazKEFBTB2LHuAZ4E9ar2wogT8xu7Zs4dnn32WPXtUi8IjPeXQSO2zECJwvvLVnhMn7GWmS03V7DlUvsmppO4IYWG7KuE6GqSnT58OZGfD3r32v/futf8fbeLi4oiLi6O8vFzrUEQDDh8+7Hy/ROT5mnfUE2/TsCiK5yIxmLn1Ao1JhM5nDt26FRSFYuANoFjNFw7wjS0uLuaNN96guFjVKNzoLYdGYp+FEMHxla+Kq6rsZabF4nzM7DlUmiKryGaLwHDXVitLgWNA4//8h8v79AnzCwbGcZXGlaOJg26GAo8Ai8VCs2bNOHToEMnJyTRu3FjrkIQHx44do6ysjObNm2NxKfiNbOnSpRw7dozGjRtz+eWXax1OgwLtyuG4uzdunD1ROu7unXde/e1YrfDzzxBoMRnR7iXCyWsOzcwEi4UeiqLK3VpnDgUuD/CN7dGjR1jvXOoxh4Z7n4XQEzPlUFtMjL3MTEhwPmb2HCoVW6OJieEOoBBInz6dgoce0joiN76u0kRTxRagVatWHDt2jF27dpGUlESzZs2IiYkxTQXKqBRFobq6msOHD1NWVkZCQgKtWrXSOizV3HHHHboZdMYf3pKsa3lRdwCKrCz7F/1t204m75PretpOMNf+fMVUVqbOfosA2Gz2vrBjx9bv/BUEZw4FCnQ2wbvkUCG0ZaocerIwqSKGFTnRkUOlYhthgYz86ZFLU+QaHfS9qUvudNSKiYmhffv27N+/n8OHD3Po0CGtQxIu4uLiaN68Oa1atSLGtYm/iDhvSRa8D0Dh6e6er+2oGZPQQFYWGzt25Ppbsph20U2c17ktKZRAcTGkptrXcfztGBXZ02Pz5sHmzQDUpLYOuN/Qxo0bGTlyJO+//z5dunRRcw8BfebQcO+zECI03vLVxooKRgLPF1QxZHB05FCp2EZQQyOE+VPpXbe+tmH8gYMK2dn6GqnTcZVmzJjaZTq7IB5RMTExtG7dmrS0NCorK6nRab/oaGO1WomLi5O75zriKcn6Gr3RW5miZpeQiHQvEX77YtVp/J5/KZe/l4XVeoo9h06sfdyfHJq/cAVgr9juLY4JOIc2bdqU/v3707Rp0+B3xAc95tBw77MQInSe8lWjGvuoyI2wX7yPhhwq89j6KdR5lwoKICOj/lVYx7xQ/gyLXVAA89s/xhtMoxBIoBVVMcVBzS0Vbm3b2ti7t5A2bdLZs0f/TTmEMAs9zX8ZqojOEe4nmcc2OHrJobntr2I8n1EIWGmLJWa35FAhhJOZcmhlUgviDpewmU50PnlBD8ydQ2VU5Ajx1W/G32GxX30Vquu8ZXodqdN12gYhhAiGt9Ebo7FrQ7Sz59AKIA+oAILLoRXEO/+3oAScQysqKsjLy6OioiKk/WmInnJopPZZCKGuKqWKPOC4yzKz51Cp2EaIpy9oVis0berfsNgFBfDSS1CNe5Yz+wdUCBG9IjpHuNA1+8DIfwCnAn8AweXQEy4VW1ACzqF//PEHp556Kn/88Uewu2I40bjPQpjBxuoqTgU2UwVERw6Vim2E1P2CBvZEfO65kJvb8F2Jk9P4UeP2lincf7+5P6BCiOgWsTnCha7ZbPDaa6djtX4L2JNjMDn0hNsdWwLOoaeffjrffvstp0fRFeVo3GchzOB0ReFbYHBmo6jJoVKxjaCsLPjpJ/cEXFMDEybA88/7vivhuOPresfWAtx7b2RiF0IIrdhs9v5A3iogBQX2iq/Bu0OJBtx1VxI//3wxVmttv6xAc+iJOk2RA82hSUlJXHzxxVHVvzoa91kIM0hSFC4GWjWJi5ocKhXbCCsv99xkqk+f+nclXD9ojju+iqW2YpvYVO7WCiHMz1fSzc62Dyo0eLD9d3Z25OMTkbFv3z7mzJlJTc0+t+WB5NBKS23FNqlZ4Dl03759zJw5k3379jW8sklE4z4LYQb7qquZCeRX1ERNDpWKbYT5GgzF9a6Epw9aVhY8MsFKItAMaNm8kdt2zHTFRQgRnMTERJo1a0ZiYqLWoajCV9L1d9AgYQ579uxh/vzJWCx73JYHkkNHj4135tBWKYHn0D179jB58mT27NnjfSWTicZ9FtHLTDl0T3U1k4H/bqqOmhwqFdsI82cwFF8ftOQWMWwCyoBNr7zifI7ZrrgIIYKzadMmysrK2LRpk9ahhKyhpOvPoEHCPHr27Mnhw2W8807PoHNos5bxtTl07lznc/zNoT179qSsrIyePXuGYQ/1KRr3WUQvM+XQnopCGXAazYDoyKFSsdVAQ4Oh+Pyg1e2gizGvuFgsFrefuLg4WrVqRffu3Rk9ejQff/wxVVVVWofZIIvFQocOHTR7/YKCAm677TbatWtHo0aN6NSpE08++STHjx9v+MlC6FxDSVemA4pOIeXQeJdRkU+cAIyZQ4UQwieXQtB14Fmz51Cp2GrE12AoPj9orsMqV1cDxr7icsstt3DLLbdw4403MmDAAKqqqnjvvfe49tpr6dKlC7/88otmseXl5WGxWBik1SzWDdi+fTu9evVizpw5tGzZkmHDhlFdXc0zzzzD4MGDZc5BYXgNJV2ZDii6bN68mfPPP5/NmzcHn0M9VGwDyaGuMUSLaNxnIQyvpobNwPlAnstMtmbPoVKx1SGfHzTXbH2yYmvkKy5z585l7ty5vPfee3z22Wds3LiRrVu3ct1117Ft2zYuuugi1q5dq3WYunTbbbdRXFzMPffcw++//87ixYvZvHkzV199NT/99BNTp07VOkQhQuJP0pXpgKJHQkICp59+OgkJCT7X8/m58VCxDSSH+huDmUTjPgtheDU1JGCfHC2GOCA6cqhFURRF6yCMoKysjOTkZEpLSyM25H1Bgf2KsWNQDADefJOHx4+nBKjpeylPf/wv50AZ48bZ67qOD66WH06bzUZhYSHp6ekUeGjPZbFYAPD18RszZgzZ2dmcffbZrF69OmyxepOXl8epp57KwIEDWb58ucd1LBYLGRkZ5OXlRTS2VatW0bdvX9LS0ti1a5fbF459+/bRvn17EhMT2bdvH3FxcRGNTWjr4YcfpqSkhJSUFGbMmKF1OKrwWBZqRItcYAa6yaGvvcbD995LCVB97mU889FSQ+ZQIUR4mCaHHjsGTZoAcLz/IH6emhMVOVTu2OqYx6ZWMTEsArKBxb/87Dbao5muuAC89NJLNG3alDVr1vC///2v3uN5eXmMGzeODh06kJCQQGpqKtdeey3r1q2rt+7cuXOxWCxMnjyZLVu28Pe//52WLVvStGlTBgwYwL/+9S+39SdPnsypp54KwH/+8x+3/sCjR4+ut/3q6mqmT59Op06dSEhIoH379jz66KNhaw68dOlSAK644op6V9Fbt27NBRdcQElJCT/88ENYXl/o16JFi8jOzmbRokVah6KahuaxFdGhsrKS4uJiKisr/Vrf4+cmPt6ZQz/8+ceAc2igMZhBNO6ziF6myaE1NVQCxUBMI0vU5FCp2BpMSan7W+Y6yIXZvvwlJydz6aWXApCTk+P22P/+9z/OOussZs2aRWJiIldeeSWZmZksWbKEc889t976Dtu3b6dv376sWbOGv/71r5xzzjn89NNPXH755cx1GSGzZ8+e/P3vfwfsFUVHX+BbbrmF888/v952R44cydNPP43NZuOvf/0rhw8fZvr06WSF6QrDb7/9BkCvXr08Pu5Y7lhPCCGM7vfffyctLY3ff/896G0cLK9timxBCTiHqhGD0UTjPgtheNXV/A6kAb8fPap1NBEjFVuD2bu/dvAoC/ZmvEYZKCoYjukFNm7c6FxWVlbG8OHDOXbsGB999BHr16/no48+4scff+Sbb76hurqam266iRMn+0+5WrBgAcOGDWPLli0sWrSI//znP3z++edYrVbuuusu5zx9V111FS+++CIAnTt3dvYFnjt3LmPGjHHb5s6dO1m3bh3r169n2bJlfPHFF6xZs4aUlBTef/99tm/f7rb+5MmT640K3dDP5MmT3baxa9cuwN5czRPHcsd6QghhdB07duSzzz6jY8eOQW9j78H4essCyaFqxGA00bjPQhheTQ0dgc+AjiaYk9dfsVoHIALTuk39axFGGSgqGK1atQKgpKTEuezdd99l7969TJw4kWuvvdZt/Ysvvpg777yTV155haVLl3LNNde4PZ6YmMgrr7xCbGztR//yyy/n2muvZfHixcydO5eJEycGHOfrr7/uNu3PqaeeyqhRo3j99ddZsWIFp512mvOxnj17cssttwS0/brzB5aXlwPQ5GT/ibqaNm3qtp4QQhhd8+bNufLKK0PaRuv27ndsIbAcqkYMRhON+yyE4dXU0By4EiCKBn6Tiq3BtEiNcfvfDENz++IYXMox2BTAt99+C9jvqnpy/vnn88orr7Bq1ap6Fdu//vWvpKSk1HvOjTfeyOLFiz325W1IXFycxymBOnXqBOC8C+xw1VVXeY3dX56Oi6fHhRDCLIqLi1myZAnXXHMNqampQW2jZTvXL3hKwDlUjRiMJhr3WQjDq66mGFgCXFNZSbScuVKx1VhBgX0OvcxMPxOry5wEiU0VNm0yb6UWYP/+/QC0aNHCucwxAnG/fv38eq6rjIwMj+s67rbu3r074Bjbtm1LTExMveWJJ5t+hGMAqWbNmgFw5MgRj48fPdmfIjGKmp8IIcwtPz+f8ePH06dPH2cFK+Ac6jLdT2IT2Lg5sBzqKQazi8Z9FsLwamrIB8YDfU6ckIqtCL/sbLj9dvsAUFarfd69BscacqlAxcaGr1Ib8JeFMHHMYdu1a1fnsuqT8/cOHz7ca1NcaLji6yqUO5ze7pp68+mnn/Lpp58G9Jy6d3lPOeUU1qxZ43UaCMfyU045JaDXEUIIverVqxdVVVXO/4PKoS4V25gYJeD8VjcGb/SSQ9Xg7z4LIXSkuppeQBWAy80hs5OKrUYKCmoTMtSObjxkSANJsO4s8h62G2oyDerLQhiUlpby73//G4CLLrrIudxms7F582YmTZpEjx49Atrmzp07PS53DLLUrl27IKP139q1a5k3b15Az+nQoYNbxfass87is88+8zq/r2N5oMdHCCGMIOgc6lKxxcMFTTPlUCFEFHMUjuB2U8zsZFRkjWzd6v6ZAz9HZvTx4czOhowMGDwY59x8gfL2ZUGL+eEffPBBjhw5Qp8+fejfv79z+cUXXwwQ8F1PgG+++YZDhw7VW+6Yr2zAgAHOZfEnvwCpfaV68uTJKIoS0E/dUZEvu+wyAL744ot6TZ337dvHihUrSE5O9jg1kRBCGNHWrVsZMmQIW7duDT6HxtcfFdnBnxzqGoMnesqhamlon4UQOlRTw1ZgCLDVS7c1M5KKrUYyM+vffPVrZMaYGC4DrgUuO+MM52K1kmnQXxZU9Oeff3L99deTnZ1N06ZNya7z7WLcuHGkpqYydepU5syZU68Z8ZEjR3jvvfc8NtMtLy/ngQcecKus/utf/+Kjjz6iSZMmbqMVt2rViri4OLZv3+5s/qwXffv2ZcCAARQVFfHoo486l1dVVXHnnXdSWVnJ3XffTVxcnIZRCi1cdtllXHvttc6LH0KYRUxMDElJScTExASfQ+Pja3OoS1cNf3Ooawye6CGHqq2hfRbCTEyTQ6uriQGSIKrOXWmKrBGbzd48adw4e9Lze2RGq5W3HX8PG+Zc7CuZBtKcyvFloW4LhnBNJzR69GgAampqKCsrY8uWLWzatAlFUcjMzGThwoV0797d7TkpKSl88sknXHnlldx2221MmTKFM888k4SEBHbt2sXGjRs5cuQIa9asqTfP68iRI1myZAnLly+nX79+7Nmzh//+978oisKrr75Kenq6c934+HiGDh3KF198wVlnnUWvXr2Ij49nwIAB3HrrreE5IAGYM2cO/fv359VXX2XZsmV07dqVVatW8eeff9KvXz8ef/xxrUMUGnj77bcbXkkIA+rYsSMfffSR8/+gcmh8fG0OdWkJ5G8OrRtDXZHOoZHQ0D4LYSamyaEn57H9CCA5WeNgIkfu2GooKwvy8iAnx/7brz44rlddXO4iBn31ug5HhdvxMuGeTmjevHnMmzePRYsWsWLFCmJiYrj55pv5+OOP2bBhA+ecc47H5w0YMIDff/+dBx98kMaNG7Ns2TK++eYbysrKuPzyy1m8eLHbgFMOp59+Oj/99BM9evTg66+/5pdffuHcc8/liy++YMyYMfXWnz17NjfddBMHDhxg4cKFZGdn85///Ef14xCMzMxM1qxZw+jRoykuLuaTTz7BYrEwadIkcnJyaNSokdYhCiGEaqqrqzly5IizBU1QOdS1KbJLNw5/c2jdGOqKdA6NhIb2WQihQ9XVVANHgGg6c+WOrcZstgATnmvmdbkkHPQdYA+ysuwDcGzbZk/q4UjIasyz2q5dO1588UVefPHFgJ7XpUsXv/vnpqWl8d5773l93Nd+jB492nlHOlzat2/PnDlzwvoaQhiNmUakFbV+++03evfuTW5uLr169QKCyKGuFdsTJ5x/+ptDPcVQVyRyaCT5s89CCJ2pqeE3oDeQW1ZGIGeukXOoVGyNxssdW1A3mQb8ZUEIIXRARqQ1rw4dOrBw4ULnvONBca3YbtoEU6dCURGkpZGVksLfHyyhbFsRzU5PI2UfcJ/9MVJSoKSEDiUlLHzmmQZjMFMOVeW4CyEiq6aGDsBCoENSkt9PM3oOlYqt0VitnAPsBdq88w6/Pv2028N1k6mRr7oIIQJ3zjnnsHfvXtq0acOvv/6qdTgNqltGhVJmBT0FjDCEFi1acOONN4a2kQ8/rM2h69bx67p1bg83P/njNQbgRrBfQZ47N7RYDEKV4y6EQZglh3apqqYNJ8urxo393pbRc6j0sTWamBj2AoXA3gaG71Zj+h8hhLHs3buXwsJC9u7dq3UoDapbRo0eHVqZZcYRaUWtgwcPsmDBAg4ePBjcBgoK4P77a3NoMDEAC4CD8+bBqlXBxWEwIR93IQzELDn00iE1teVVZaVf2zNDDpWKrdG4NkX20b/TjHPphWL06NEe54MVQmjDUxk1b15oZZZag+gJfcrLy+Omm24iLy8vuA1s3eozb/oVA3DTyd/88ENI2zKKkI+7EEJ1DeVQi1JdW175OY+tGXKoVGyNpu4nzgszXHURQpiXpzKqrkDLLDOOSCtq9ezZk+PHj9OzZ8/gNpCZCRZLaDEAx0/+ZsCAkLZlFCEfdyGE6hrKoVZqasur1q392qYZcqj0sTUaPydZNuNcekIIPzgGlTtyxG1gHMfgN87/QdPHzs4rYSZF7MP+WBpFFJHGIVJoTglpFLGfNHp+BXzq/+tlFRVxzYNpHDwAqUoRSfvSYKqK+5OfH7a3TvhmtVpJSEgIfgM2G7zzDniY2s3vGIAEgFtugT59go/FQEI+7kII1Xn6nu/KSk1teeVn3QGMP6q7ISq25eXlTJo0iQ8//JCDBw/SuXNnJkyYwA033ODX8z/77DNmzpzJmjVrqK6upkOHDtx7773cfvvtYY48DFzv2PpoUvX11+4PW63Gu+oihAhQdjY4+gUdOgSPP65pOL40B+73Z8XpgW875eSPsDNLDv3zzz956KGHePHFF+nYsWNwG8nKgkmT7OdJ8+bwyCNQXAypqbUXL4qL+SUvlY8/gTSKKSKVUlJ4g3+wE3goMZEXn3ySICMwHFWOuxBCVZ6mKBs1CubPt1d24yzV/KnAQ8CLhw8HVF4ZeVR3Q1Rsr7nmGlatWsXzzz9Pp06dWLhwITfeeCM1NTWMGDHC53Off/55Hn/8ce644w4mTpxIXFwcmzZt4oTL/HWG4sdVF0e7+7r13iFDwhSTEEJ7BQUwdqzWUQgdMksOrampoaKigpqG2rA3xJFHmzaFiRPrPVxQAP0zwPVVrFZ4s9FD1Bw9QsXJWKKFasddCKGqundXv/7aXrEF+x3bGrCXVyF2wTAURee+/PJLBVAWLlzotvySSy5R2rVrp1RVVXl97q+//qpYrVblhRdeCDmO0tJSBVBKS0tD3lZIcnOVdFAAJb1pU4+rLFumKPZqrftPTk7kwkxPT7fHmJ4euRcVIpqdPPGd5YOnQkB+Qv4pPXl8Nc8FfpIcWl9D+clbDj3RLMX+R6dOmscohAgPvZ17+fn2Mik/v+H1rNba8up8/lv7z8MPRyZYP4Q7F+h+8KhPPvmExMREhg8f7rb81ltvZffu3axcudLrc//5z3+SkJDA3XffHe4wI8ePO7ZmGNVMCBEgFQbGEeYjOTRw3nKotVG8/R+jtvgSQhhKINN21h1MKoZql3/872NrdLqv2K5fv54uXboQG+vearpHjx7Ox73573//S5cuXfj4448544wziImJwWazMWHChAabUVVUVFBWVub2owt+9LH1NKrZ/X51ZhNCGJbNBm++qXUUQmfMlENXr16NxWJh9erVIW/LF285VImLZzVgycsLewx6EqnjLoSoFei0nXUvyFmpsZdXwOqionCHqxu672N74MABj4MVtGjRwvm4N4WFhRQXF3PPPffwzDPP0LVrV77//nuef/558vPzef/9970+d9q0aUyZMiX0HVBbTAzTgaNAk3PO8bqao939q6/CSy/Biy/CzJn2ZJ2VpW5IBQX2K0WZmcbtbC6EKdx8M9P/8Q97+dC6Ndx7r8eBcUhNta8fxsc2FaUw55US5+A7YB+I56oxqZzW2/PzfslLZc4nKSRR+zwLMOLiYnoMDiFONfe1oMBQFxDMlENPOeUU3nnnHU455ZSQtjN9+nSOHj1KkyZNvK7jKYeOI55TgHcSE0OOwZXec6hax10II/CnfIgEX9N2eion6g0mRbW9vAIOFUTRcIphaeCsoszMTGXo0KH1lu/evVsBlGnTpnl9blxcnAIoixYtclt+3333KYCydetWr889fvy4Ulpa6vzJz8/XR/+gTZtq28zffLPPVeu2twdFiYlpuJ1+IGbPrn0Nq9X+v6Lor4+CEFGhvLz2ZP/LXzQNJdjy55dfFMViCW+5FQo99RX1h+TQ4NX9DP9BF0UBpbpZkmqvITlUCOFJqDn0r/zb+cQplqeiJofqvilyy5YtPV5RPnjwIFB71dnbcwGG1BkO+NJLLwXw2awmISGBpKQktx9dcG1n0MAIhb6u9qgh0GYSQogwcz3hNe5vG+xE7zt21O9loWa5FW3MlENLSkpYsmQJJSUlIW/LH3Vz6AniKQGWHDumSgxGyaGRPu5CiNBzqJUae3kFHFYqoiaH6r5i2717dzZu3EhVVZXb8t9//x2AM8880+tzHX2I6lJOfmuy1h0dwghcO4BXV3tfj/APIhXuirMQIkCuNUIdlG9ZWZCXBzk59t8NdYPIzgZPU6vK4HfBM1MO3bFjB3//+9/ZsWNHRF6vbg49QTw7gOFVlarEYJQcGunjLoSwCyWHxlDNDuDvQAllUZNDtf/m04Crr76a8vJyPv74Y7fl8+bNo127dvTr18/rc//+978D8NVXX7kt/9e//oXVaqVPnz7qBxxuViubgT+AzYcO+Vw12Ks9/pLRl4XQmZqa2vLh6FGtowHs5c2gQQ2XO97m31a73Io2ZsqhPXr04MCBA14r3P7avHkzf/zxB5s3b/a5Xt0cWkUcPYADQI9u3UKKAYyTQ9U67kIYgb/lQ6QEm0Ot1DjLq6yr2kZPDg1LA2eVXXLJJUpKSooya9YsZdmyZcrYsWMVQFmwYIFzndtuu02JiYlR8vLynMtOnDih9OrVS0lOTlZeffVV5dtvv1UeffRRJSYmRrnrrrsCikE3/ap27aqdp7JxY7+ekp9vn8M2HO3rZ8+2t/l3tP2X/kFCaOjgwdryISFB62gC4m3u0A8/1Doyd7rJBQGQHOou0PzkyKHH+g+q/WAePapKLJJDhdAXo557dXPoVSyp/UeFucjVEvV9bAGWLFnCTTfdxJNPPsnQoUNZuXIlixYtYuTIkc51qqurqa6udjaRAoiLi+Pbb7/lhhtuYOrUqfztb3/jk08+4fnnn+fVV1/VYldC58d0P3X5e7UnGIE2kxBChJGO+tgGytvdq/79tYnHTMySQ3fs2MGoUaMi3iTWkUMbNbM3RR4F7NiyRZVtGyGHanXchRD+8zTdj7O8aqCFp5nofrofgMTERF599VWfiXTu3LnMnTu33vIWLVrw1ltv8dZbb4UxwgjS4STLNps0ExRCF/y82KVH9aYqkCbIqjFLDq2srKSgoIDKykptAoiPpxIoACqPHVNts3rPoZofdyFEg+rm0FhrDZU1J8srA383CJQhKrbChQ4rtkIInWhgpHS9c8wdum2bvZ+hnr/si8jr1KkTy5cv1y6A+Hg6AcsB2rfXLo4I0/y4CyH84ppDu/9RTcu7TpZXbdpoHFnkSMXWaFQehVLvE8MLIQJgkKuyvsodvd+9ElEsPr727xMnAMmhQojI8yuH7na50K2DWRIiRSq2RuN6x7aqCqZOhaIiSEuDlBQoKan9H3w+9vuyIhZ+n0YJKaRQwoi/FNF9cMPP8+uxI0fs/zcwJZEQQkUGuGObnV07d6fVam86pcd+hUJ/1q5dy4ABA/jhhx/o2bNn5AOIj2ctMAD44bffyF12alR8ljU/7kIIJ79zaHV1bXm1ezc9IxqldqRiazQLFtT+XVUFjz8e9Ka6A9NcF3x/8kdNe/faz0IzZnsh9EbnFVvHdASOMGtq7P2BhgyRu12iYe3atWPatGm0a9dOmwDi42mHPW/GnmgeNZ9lzY+7EAIIMIfW1DjLq3YpKRGOVDvRc2/aDAoK4J57tI4icOPG2WMXQoSXa1NkHY6KvHVr/bp3dbW9P5AQDUlLS+Oee+4hzdFCKNLi40kD7gGOlTSLms+y5sddCAEEmENrapzlVZpUbIUubd1qmD50bsya7YXQmzDfsS0osE9LEux1Km9T+px+euixCfMrKyvj66+/pqysTJsA4uMpA74GWiSVRM1nWfPjrqJBgwbRoUMHrcMQUSqiObS62llelVVUBPeCBiQVWyPJzNTlXZgGmTXbC6E3YbzwlZ0NGRkweLD9d3Z24NtwTEfgGCpApvQRgdi2bRtDhw5lm1YXSuPj2QYMBUrLd0TNZ7mh4758+XIsFovzJyYmhubNm9OlSxdGjBjBkiVLqI7geBuffvopkydPjtjrebJlyxaefPJJzj33XFJTU2nWrBk9e/bkueee44hjDBIRVSKeQ2tqnOXVtv37Q4jcWKSPrZHYbPDOO6waM4ZqwDAT/5g12wuhNzU1rAJ7+fDXv6q22WD7xnoaudHXlD4ywqzw5cwzzyQ/Pz/kJrGrVq2iurqaGB/T53n8LMbHcyaQD6TZbPS6NDqmp/L3uF9//fVcfvnlKIpCeXk5W7duZenSpSxatIg+ffqwZMkSbBE4SJ9++inz5s3TtHL77rvv8s9//pMrrriCESNGEB8fT05ODpMmTeLDDz/k559/pnHjxprFJ7zzp3wIlCY5tLq6trw65RTV9kXvpGJrNFlZtB0yBH76CQ4csI9KXFwMqanOUYrXLStm4XepKEBrijn/6lT6/jXFfV2o9zzVHlu2DH77zf5/aqoMHCVEpCgKbR1/N22q2mZ99evxlpR9jdzoaUofGS1ZNCQ+Pl6VilHbtm19Pu71sxgfTzxgA2friGiYnsrf496zZ09GjRrltuyll15i+vTpTJgwgcsuu4zc3FxiY83/1fPaa69lwoQJNG/e3LnsjjvuIDMzk+eee453332X8ePHaxeg8Kqh8iEYWuTQFTfUcB4nyyvXqcrMThF+KS0tVQCltLRU61B8ys9XFKtVUexZ1/4TE2NfHjE336ykgwIo6a1bR/CFhYhyW7fWnvgjR6q22UDLlXCvryWj5AK9UeO47dy5U7n99tuVnTt3qhiZO5+fxeefV3aCcjsoO2fNClsMiqIo6enp9hyanh7W1/FHQ8c9JydHAZRp06Z53cYNN9ygAMqCBQucy44fP64899xzSteuXZWEhAQlOTlZufzyy5XVq1d73P6cOXOU1157TcnMzFQSEhKU008/XXnllVfc1s3IyFA4+f3D9ScnJ0dRFEUZOHCgkpGRoeTn5yvDhw9XmjdvrjRp0kT561//qmzevDnII+S/3377TQGUcePGhf21hH5okUPvsbxWW1699lr4di5A4c6h0sfWZNQadTSkDu5RNBG0ELri2sdWxfMw0L6xgZRDBQXw4YcyWrJo2NGjR1m9ejVHjx4N22v4/OzGx3MUWA0cLS/3uZ1QB4nREzWO++233w7A0qVLAaisrGTo0KFMmTKF/v378/LLLzNhwgQ2btzIgAED+PXXX+tt4/XXX+f5559n1KhRTJs2jZSUFO677z6efPJJ5zqvvPIKF1xwAQDz5893/nTp0sW5zpEjRxg4cCDx8fFMnTqV8ePHs3z5coYNG+bWF7impob9+/f7/VPjx+B9hYWFADLCdJTRIodalOra8qqyMtRdMAzztwcxoVmzZlFeXk5iYqIzWTg4Rkxz/YAHOnZTyE0CpWIrhDZqapgFlAOJW7dye0PrB8BXv566/C2HXMuaumTMOVFX586dWbVqVcjbCTqH/hFPZ2AV1Ha/8cBszerVOO5nnXUWYB9UCeyV1OXLl/PVV18xdOhQ53p33nknZ555Jg899BDLly9328aWLVvYuHGjs1n0+PHjOf/885k6dSpZWVlkZGRw1VVX8emnn7JixYp6zaId9u/fz8MPP8wjjzziXJaamsojjzzCd999x5AhQwDYtWsXp556qt/7uGPHDp8jLldXV/P0008TGxvLyJEj/d6uiCxf5UMoIp1DYy01dFZOllft26uxC4YgFVsDevrppyksLCQ9Pb3eSee4KjRunP3qTqAjNQbbwd2Na8XWiNMTCWFUisLTQCGQvm6dqhVb8L8/oT/lUN2yxpWZR5gV2gs6h7r2UztxwuO2VcmhJpSUlATgnDLo/fffJzMzk3POOYf9dUZsveSSS5g3bx7Hjh1zG2Bp5MiRbn194+Pjuf/++xkxYgRffPEFd911l1+xWK1W7rnnHrdlgwcPBmDr1q3Oim2bNm349ttv/d7HNm3a+Hz8nnvu4eeff+bZZ5/ljDPO8Hu7IrJ8lQ+himQOve7qavh/LguihFRsTSiQq0J1BdPBvR65YyuENlSax1aN0YkbKoc8lTUAL78M114b3ZUA4dm6dev4y1/+wvfff0+PHj3C9jpeP7vx8awD/gJ8/+efeIpAlRyqM2ocd0eF1lHB3bhxI8eOHSPVx53v/fv3097lTpNrc2KHrl27ArB9+3a/Y2nXrh2NGjVyW9ayZUsADhw44FzWqFEjLr74Yr+368ukSZN48803GTNmDI899pgq2xT6pYsc+n4N6/7fyfJq1y6P5ZUZScXWpAIdqdFxEiYmNtz8ocET1ohz7QphBiq0kFCzGaWvcshbUyup1Apv0tLSeOCBByLSP9HjZzc+njTgASDt55/hvvsgLQ1SUjiUV0LZtiJOa53GBCCVIopI4xAptKCEXvOL4Ed73GXbiygmjRanpZBCCRQV2bcDtX875jqN4Pyv3qhx3NeuXQvYmzUDKIpC165defXVV70+p26l1+Lhu4Vysszz9Jg3vqZxUVzK0OrqaoqLi/3ebmpqqsdtT548meeee46bb76Zt99+O6BYhfHoJofW1NSWVy1aBBeAAUnFVtQ7CW+6CRYs8Nz8wa8TVu7YCqGNEO/YRrIZZajdJkT0adOmDRMnTtQugBUraANMBPj+e/vPSc1P/gBM8/Tcd2v/TDr545e9e+2JV8NOumoc91mzZgFw+eWXA9CpUyf27NnD4MGDsfr5nWHDhg31lm3cuBGAjh07OpepVXHMz88PuY/tlClTmDJlCqNGjWLOnDl+76swJl3l0Orq2vLqZIuEaCAVWwOrrraPuhhKUwdPJ+GCBfZpco8ccW/+4PcJKwW3ENpwvWMb4Je7hkYnDkeFM5RuEyL6lJeXs3btWnr27EliYmLI2wsohxYUwP/9H+XAWqAnEHoEftK4k24ox11RFGbMmMHixYvp2bMn1113HQA33XQTDz/8MDNmzODRRx+t97x9+/bRunVrt2Xvv/8+kyZNcvazPXHiBC+//DIxMTFcccUVzvUcMZaUlJCSkhJQvK5C7WP79NNPM3nyZEaOHMncuXOlUmtyusuhNTW15VVFReTKK41JxdbA9u6FwYNDa+rgrT/QkSMwaJB/69Y7YaXwFkIbQd6x1XJ04kC7TYjotWXLFi644AJyc3Pp1atXyNsLKIdu3WqPAbgAyAVCj8BPGnfS9fe4r127lgULFgD2yvC2bdv44osv2LJlC3379mXJkiXOprr33nsv3377LRMmTGD58uX85S9/ISkpiV27dvH999/TqFEjcnJy3LbfqVMn+vXrxx133EGzZs1YuHAhq1at4oknniAjI8O5Xr9+/fjnP//J+PHjufTSS4mLi2Pw4MEBN6UOpY/tG2+8wVNPPcUpp5zCJZdcwqJFi9web926NZdccklQ2xb6o8scWl1dW17t2RO58kpjUrE1oLpdbkJp6hDI9EDe1i0qsl+pcr62650iGRVZiMgJ4nyT0YmFUXTt2pVNmza5VWKCEVQOzcwEi4WuisImILQIAqTx3Ff+HvfFixezePFirFYriYmJtG3blt69ezNt2jSGDRvm1v80Li6OL7/8kjfffJP58+fz1FNPAfaBnfr27cstt9xSb/t33303ZWVlvP766+zatYtTTjmFV155hXvvvddtvRtvvJHc3Fw++OADFi9eTE1NDTk5ORGdO9YxPdKuXbsYPXp0vccHDhwoFVu9chQQR47A1Km1/d5TUqCkfp/4koQ0fp2ewsOUkHaybz1AGkXsJ42/XZ+C7T0vfem9bFOVx776iq5gL69UaOFiGIrwS2lpqQIopaWlWoeitGqVrgAKpCv2b7L2n5yc4LY3e7aixMTYtxETY//fn3WtVkWxWGr/dj7vvvuUdFAAJT01NbighBCB+/XX2nOvaVO/nrJsmeJWjjh+Xn5ZUfLzwxuuEekpFxiJno5b0Dl09uzapBfmH+d5DL6TchTIyclRAGXOnDlahyLMbvZs93PPLD8Wi27KkXDnArlja0CxHt61UC7oBtLPbcgQWLgQDh6EO++svUHkdsVbmiILoY0gmiKHa3RiNaY7EMJVQUEBM2fO5IEHHnCbzzRQQefQrCwKevRg5pQpPHDmmdhOnIDU1NpRkbcX0+y0VFKSgeJi52OUlDj/P1QKe9cVUxKfytzPUmhOCWkUU0QqVmDimGKScpfDmjX212zVStOBo0C94y6ErhUUwNixWkehqgJgJvCAomCLkgm1pWJrQF26dMJqTWb3bvvACmo0F/Snn1vdEZHrtnp0dgOSiq0Q2lAUOgHJQGs/B00Jx+jEak53IIRDWVkZX3/9NWPGjAlpO6Hk0LKmTfl6xw7GTJ8OJ+dQBfdRkb3JzobbJ9WeF54uQw0ZCYOUMbUVWx3kU7WOuxC6tnWrew7VOh4VlAFfA2NA8776kSIVWwNatmwZYL+4FKnRRD2NiFyX84q3zNEmhDZqaljm+Pvvf/f7aWqOThzJ6Q5EdOnatSt//PFHyNsJJYcGG0NAOdTHPKtaUOu4C6FrJ/vRLzPR2DBdAeeZq3Ff/UgJ+FLgvn37sFgsWCwWvv76a5/r3nXXXVgsFs477zy3Sa+FOmw2+8jFoX4Jzcmx//bF04jIUHsx2e2Kt+sVZnnfhYgc1/PN5Tz05zxXozwB36OnC6Enus2hOqvYam3QoEEoiuJxECYhVGOzwZtvah1FeFitUTMSZMB3bFu3bk3Hjh35888/WblyJUOGDPG43m+//cZbb72F1Wrl9ddfV23CbKGeQJoLeuuH52m+Wz00nRIiKrmeoCfL3Eg3Cw5kpHUhArF+/Xouv/xyli5dyplnnql5DCtXnhkVOVQPx12IiLj5ZvjHP+x/d+oEo0ezblkxC79LpYQUUihhxMXF9Bical/HS1/6UB4r+7OYqbPtr+fog7+fVB59FJqfCGyb66uruXzRIpYuXMiZQU5dZTRBNUUeMGCAs2Lrzd133011dTW33347vXv3DjpAER6BNhf01g+vTx8PG9dZUhYiatS5Y7tqlX0sDI+DvIXpwm04+uwKAdCiRQtGjRpFixYtNI/h+PEW4cuhrndsddDqSQ/HXYiIcL3y1L49qy6eSL/H7cMkO7yYA3lzwpfTkoDMc+uXFc2DuCDdYvduRjVrRguX8QDMzqIE0Ub4rbfe4h//+ActW7Zk//799R5fsGABN910EykpKWzZsoVWrVqpEqyWysrKSE5OprS0lKSkJE1jGTlyJPv376dVq1a8//77QW0jJ8c+Mb2n5YMGeX+eX32SnngC27PPUgikt2pFQXFxUDEKIQL03/8ycuBA9gOxbbvw730bPDZ/bOg8V0MkxwCIJD3lAiPR03HTfQ594AFsL79sz6GpqRQUFQUVoxAiQGVljExOZj/QJKkNn5fvkRyqsnDngqDv2AIcOHCAbdu2cbpLG7PDhw/zyCOPAPDMM8+YolKrN//5z38oLCwkPT096G0E21zQ0+jJ9ab1kDu2QmhDUfgPUAgk7cn3OOpqpJoF+zPSuhCBOHr0KJs2baJz5840adIk6O2EkkMdMdhsnbFam4Qnh+qsj61ax10I3aupcebQVmUlhs+h0XjuBlUD6datG8nJyQD1miNPmTKFPXv20KNHD+64447QIxRh4WgW5cifwTYXzM6GjAz7leuMDPv/MniUEBpxu7Rcf1yDKBo/QpjQpk2b6N27N5s2bdI8hsOHN4Uvh+qsKbIejrsQEeGSQz2deUbLodF47gZVsbVarfTr1w+An3/+2bl806ZNvPbaawC8/vrrxOjsqqNwl5UFeXn2JhV5eYEPKOOtn27pYbljK4QmfHwJtlrh55/9O8/9HelViEjq3Lkzubm5dO7cWRcxhCuHlh3R13cnPRx3ISLCx8VhI+bQaDx3g66BOJoju96xvfvuu6msrGTEiBFceOGFoUcnwi6U6Q68TetxsERGwBZCEy4nZKNG7neTZs3yMlBNHR7vIAmhA02aNKFXr16aNqmrG0NYcmipviq2ejjuQkSEywkZF2f8HBqN527QFdvzzjsPsE/rU1FRwccff8x3331HYmIi06dPVy1AoV+OfrquYmKgRSu5YyuEJlzu2MbFBX43ydsdJK2vOgsBsHv3biZNmsTu3btNEYO3HJqSqq+myHo47kJEhEvFNibG+Dk0Gs/doGsg5557LjExMZw4cYIffviBBx98EIBJkyaFNKiRiJxQm0p466ebnCIVWyE0Uef2T6B3k7zdQdq2TZ3whAjFwYMHWbBgAQcPHtRFDOHLofq6Y6uH4y5ERJgsh0bjuRt0DSQxMZHu3bsDkJWVxc6dO8nMzOT+++9XLTgRPmo1lfDYx0gGjxJCGyGeb97uIEViBEghGnLmmWeSl5fHmWeeqXkMK1eeGZkcqgN6OO5CRIRrrdQSeLc6veXQaDx3Qyo9Hf1s8/LyAHj11VeJj48POSgRXmo3lah3RSuIwkAIoYIQk7Jao6ULYWZhz6E6GxVZiKgR4vkmOVR7IVVsHf1sAa644gouvfTSkAMS4Rf2phI6u9osRNTwNJN8gEId6VWIcNmwYQPdunVjw4YNmsZw/vndqKlxj0HVHKqzGSX0cNyFiAiT5dBoPHdjQ3ly48aNAUhISODll19WJSDRsLFjx1JaWuqcSzhQjqYSgU4s7zep2AqhDUVhLFAKJJ9zTtCb8TUxfEGB/eJYZqZchRaRlZSUxJAhQ0hKSgppO6Hk0KSkJC65ZAjZ2UluN3dUzaE6q9iqddyF0L2amtocetppQW9GLzk0Gs/doCu21dXVTJ48GYCHH36Y00L4AIjAPPXUUyE939FUYtw4+1Vm1ZtKSMVWCG3U1OAsHS6+WPXNZ2fXNsG0Wu3liNzRFZFis9mYOXNmyNsJJYfabDbeeWcm554bxhyqs6bIah13IXTPNYf26KH65iOdQ6Px3A26BvLaa6+xbt06OnTowMSJE9WMqZ7y8nLuu+8+2rVrR6NGjejZsycffPBBwNuZNGkSFoslqjpRexPWphIyeJQQ2nA930K8wFR3xNdQ+xXqZcL6aGSWHHr8+HE2b97M8ePHNXl91xhGjjwevhyqszu2ejjuQkSEa1NGE+TQaDx3g3rXFi1axKOPPorFYmHWrFlhn/j3mmuuYd68eTz11FN89dVX9OnThxtvvJGFCxf6vY21a9fy4osv0rp16zBGaiyhTCxfl9sJJ4NHCaENl6S8/U9L0JVIT6Omh9I3X08T1kcjs+TQDRs20LlzZ8372DpiCFsO1VnFVg/HXYiIcElye4qshs+hUXnuKn5aunSpkpGRoSQlJSmAAihPPPGEv08P2pdffqkAysKFC92WX3LJJUq7du2UqqqqBrdRWVmp9OzZU7nnnnuUgQMHKt26dQs4jtLSUgVQSktLA36u2c2erShWq6KA/fcPI99Q0k9+RtJTUrQOT4jo8f/+n/1EBOVBZihWq/38DER+fu357PiJiVGUX37xvDw/P7jtNfQ8vTJaLjBTDj18+LCyYsUK5fDhw0FvI1ThiKFuDl1x8yxd5VA9HHchImLDBmeiepfRhs+hejx3w51D/b5j+8MPP7Bz506qqqo4++yzmT17Nk8//bT6Ne06PvnkExITExk+fLjb8ltvvZXdu3ezcuXKBrfx/PPPc/DgQZ577rlwhRlRNpsNi8WCTQcjt3hqWrFgofSxFUILB4prsAEW4G2eDWoaEm9XlfPy4IEHAp/GQG8T1kcbM+XQxMREzj//fBITE0PaTig5VK0YHDzl0Lnz9dXHVu19FkKv9u6uzaEP8qHhc2g0nrt+10CmTp2KoigcOXKE1atXkxWhEUPWr19Ply5diI11H+eqx8lO3evXr/f5/A0bNvDss8/yf//3f1H1xkaKpxOuyv/rJUIIFe3ZU/9LcKCVSE8TzFutcP318OKL9vP9oYf871eotwnro42ZcujevXuZNm0ae/fuNU0MnnJopaKvpsh6OO5CRMKuvNqT0ZFNjZxDo/Hc1X0N5MCBA7Ro0aLecseyAwcOeH1uTU0Nt912G9dccw1/+9vfAnrdiooKysrK3H5EfZ5OOIv0sRVCE23T6s/BF2gl0tME844GUGD/HcjsbjJhvbbMlEOLioqYOXMmRUVFIW9LLzF4yqFY9PXVTA/HXYhIyGjvmkPt32WNnEOj8dzVV+npha+Kkq/HZs6cydatW3nllVcCfs1p06aRnJzs/Gnfvn3A24gGnk64UTfLqMhCaKFli9rzTSH4SqTrqOkLF9Y/jQO9gq2nCeujkVlyaI8ePSguLnbebdaC2jF4yqGjx+irKbIejrsQkdA61f3isNFzaDSeu0HPYxspLVu29HhF+eDBgwAer0QD7Nq1iyeffJLnn3+e+Ph4Dh06BEBVVRU1NTUcOnSIhIQEGjdu7PH5EydO5IEHHnD+X1ZWJpVbL7KyYMgQ+0l6+ulg+9YK87SOSogo5NKmMbEpbNoU/J1RxwTzBQX2O0quzSWDaUrsa8J6ET6SQ/WvXg79IQbe0ToqIaKQSw20USP4favkUKPR/R3b7t27s3HjRqqqqtyW//777wBe59P7888/OXbsGPfeey8pKSnOnx9++IGNGzeSkpLic/7dhIQEkpKS3H6Eb87yIMS5v4QQQXJJyrFxFlWSoDQlNjYz5dBNmzbRp08fNm3aFPK29BiD8/TV2XQ/ejjuQkSES+0zJkadPKdlDo3Gc1f3d2yvvvpq3nnnHT7++GOuv/565/J58+bRrl07+vXr5/F5PXv2JCcnp97y++67j9LSUubMmaOLUYXNIDu7dlRHqxWWjZY+tkJoou4oNCqpd0dJik7DMFMObdKkCb169aJJkyYRfd1wx1A3h359h76aIuvhuAsRESbLodF47uq+YnvppZdyySWX8I9//IOysjJOP/10Fi1axL///W8WLFhAzMlLIFlZWcybN4/t27eTkZFB8+bNGTRoUL3tNW/enKqqKo+PicB5mqoge473O7YFBfZRIDMz5cuxEKoL8Euw6/kIvs9NaQZlTGbKoaeccgpvv/12xF83nDF4yqH/fMv7HVstcqgejrsQEeFasfVjIFS959BoPHcN0WZ0yZIl3HTTTTz55JMMHTqUlStXsmjRIkaOHOlcp7q6murqahQdXN2MJg1O9+PyfmRnQ0YGDB5s/52dHaEghYgWAVxtdj0fTznF/iPnpjmZJYeeOHGCgoICTpw4YZoYPE73U+O5YqtVDtXDcRciIkyWQ6Px3LUoes5iOlJWVkZycjKlpaWa97e12WwUFhaSnp5OQSCzRodBQYH9JHYtC260fMB/lRspBNKTkyk4dMjjejEx9tHd5C6QECp5911sWVkUAm2TmrO7tMTjap7OR1dybnqnp1xgJGoct9WrV9O7d29yc3Pp1atX0LGEkkPVisHB07n4N+u/+a3mUnsObdaMgrIyTXOo2vsshG7973/YLriAQqBd00QKyw97XM0oOVSP5264c6gh7tgKdwsWLHA2I9Oap07xY8bWb77h6ap0oMOdCyF8W/GfGhYA/wZ6lY3xetXY0/noSs5NoUenn346//73vzk90OFE6wglh6oVg4OnHHrXvfXv2GqZQ9XeZyH06ssvanPoFUcuM3wOjcZzV+7Y+ilar9L725+noMClU/xPH2G77jq5YytEBBUUwLOnzOItZRwAt5HNezG3eTzHjHK1WY+iNReEKlqPW1A5dMsybH/5i27u2AoRDQoK4OZTlrNMuQiA53mUSTHPSw5VmdyxFZoJpD+PzQaDBp08iT1M9yNThggRXlu34tY/UsHi9apx3fPRaq0dJ0POTaFXRUVFvPbaaxQVFRkiBlVy6MlzWsscqofjLkS4bd0KKLU11Rqshs+h0XjuSsVWeORppMZx4+zLG+QhKYN9uPO8PMjJsf/OylIzYiGiW2YmxFrck7KvSeBdz8edO2HXLjk3hb7t3r2biRMnsnv3bt3HEFIO9TKPrVY5VA/HXYhwM2MOjcZzV/fT/Yj6li9fTkVFBQkJCWGbcsFXf54Gr0L5GCJdpgwRIjxsNhg5QmH5+1AB7GVzg1eN656Pcm4KPevZsydHjhwJeTuh5FB/Ywgph3qp2II2OVSt4y6Entls8MB9NSx/2Z5Dd7DL8Dk0Gs9dqdga0KhRo8I+KnJmpv3Ga93+PH71P/fQFFkIoR5v/fbOO7cG2/vYR0VOfouvs6ZqFqMQeqX7HOpasZVhUIRQnbccOvSvNdhetufQdomfkq2TO6/Cf1IDER6F1J9HKrZChI3PfnsuX4LlNBRms2XLFgYNGsSWLVt0H0NIOdTHHVst6OG4C6EWf3Ooxeq99aFRROO5K199hFdB9+dx+UZdXeVnn6I6Cgrsr+v6XE/LhIgmDfbbc7095KNLgBBGFBcXh81mIy4uzhAxBJ1DXSq21dXa51A9HHch1BBQDjWBaDx3pSmy8Cmo/jwuX6iPHFXIyLBfufY3qWdn1xY8Vqv9uVB/WSQ75/s7ZYMQ4dRgvz1ptihM7NRTT9V8/vZAYwgqh7pUbI8fR/McqsZxlxwq9KDBHGqyiq0eysxIkzu2QnXFB9w/VoGMBuntatrYsUGOLqmCQKZsECKcHP32XLn12wsiKUtLCGEUVVVVHDx4kKqqKlPHsLe4tmJrQdE8h4a6z5JDhV5EWw7VQ5kZaVKxFaor3FP7sXLcu/U2F1hd3q6m1b0R5e/2QhXSlA1CqKzBfnsB3rGVL5zCSNatW0fLli1Zt26dqWPYWVC/j62WOTSUfZYcKvSkwRwaYMVW7zlUD2VmpEnFVqguvX39j1VDo0E6rnglJnq+mla3u6Dfo0uGyFezFSHU5s+VX5/99gJIyvKFUxjNqaeeyscff8ypp55q6hgyTtVXDg1lnyWHikhSNYc2ME6FEXKoHsrMSJOKrVBdapp7YdDQaJCuV7zOPRduuqn+1bR33glydMkQNdhsRQiVBHLl12aDQYM8nAMB3LGVL5zCaFJSUrjmmmtISUkxdQxt0l3v2Cqa59BQ9llyqIgUVXJoABeHjZBD9VBmRppUbIX6XLJYk8a+R4P0dMVrwQL46Sf3q2lBjy4ZopCmbBDCT6pd+Q3garN84RRGs3//fmbPns3+/fvNHYPL4FGNErTPoaHss+RQEQlhyaENMEIO1UOZGWlSsRXqcznTY2IUnwnM2xWvI0fqX03zeoUtzLSqVIvoodqV3wDu2MoXTmE0u3btYuzYsezatcvcMbhUbK1W3+dkJHJoqPssOVSEm2o5NICKrRFyqB7KzEiT6X4MqEBPDfg9qXsJywfHFS/XskRvV7wgyCkbhPCTaudBTQ3O0mHOnAZXz8qCIUPsyf/00+UzLvStV69eKCpMaRVKDlUrBp9cKrYNXayKRA5VY58lh4pwCksOfeaZBlfXew6NSHmlM3LHVqgvgIqtEa54CRFuqp0Hrlndz/NQq5YQQggvXCu2DZAcKoTkUFFLKrZCfQ307atLmikJodJ54HplNsDzUAi927ZtG5dddhnbNBydJSIxBFCxhfDnUD0cdyEaosp5EETFVs+i8dyVpshCfUEUBp6aKRUU2PtNZGbKlTARHUJurmeypCyEK6vVSkJCAlYNP9sRiSGApsgO4cyhejjuQvgj5Bzqer6Z4PMejeeuVGwNaMqUKZSWlpKcnMxTTz2ldTj1uZ5AQbbtz86uHeHOarU3MZE7uUI0QFGYApQCyQsX8tTQoVpHJIRqOnbsyJIlS0LeTig5VK0YfArwjq0naubQiOyzEHpQU1ObQ7/8kqfGjdM6opBE47lrUaKtV3GQysrKSE5OprS0lKSkJE1jsdlsFBYWkp6ers+BpHJzsZ1zDoVAetOmFJSXB/T0ggL7HGR1BwHIy5M7t0L49MQT2J591n7utWpFQXGx1hGZjp5ygZGocdxqamqorKwkLi4upDsQoeRQtWLw6cgRbImJ9vM4IYGC48cDerraOTQi+yyEHsyejW3sWPu5l5JCwcGDWkcUEj2eu+HOofrYS2EuIfbtM8Kk10LoklynFCa2du1aGjVqxNq1a80dQ4itntTOoXo47kJERADT/RhBNJ67UrEV6gvxqlCwk14XFNgHDXC9AO9pmVCXHGMdMVlSFsJVhw4dmD9/Ph06dDB3DCE2RVY7h+bnd+DVV7U97mYmOVRHTJZD9VBmRppUbIX6QqzYBjNse3a2venV4MH239nZnpcJdckxDk7YvsjIHVthYi1atGDUqFG0aNHC3DGEWLFVO4dedVUL7r9/FJ98ot1xNyvJocEJWw41WcVWD2VmpEnFVqhPhcGjAhm2vaCgdpAMsP++/fb6y8aNkyuiavJ03OUYNyysX2RMlpSFcHXw4EEWLVrEQQ37vUUkBt3l0IPU1Czi9tsPSvmuIsmhwZEc6j89lJmRJhVboT6V5s/0d9JrT/2Jamqkn264SV/owIX9i4zMYytMLC8vjxEjRpCXl2fuGHSXQ/OAEdTU5En5riLJoYELew41WcVWD2VmpMl0P0J9ER55zdGfyNMUnnVHhWyoj5Hwn6fjLsfYN19fZFQZ8dtkSVkIV2eddRbl5eU0atQoqmNQW8M59CygHKu1kZTvKpIcGriI5lATXBw2Y3nVELljK9SnQsU2kP4TnvoTzZoVeB8jEZhg+nFFu2AHdfHF7VwJoY+tDGAi9C4mJoamTZsSo8I8r0aOwR/q5tAYYmKaMmtWjJTvKpIcGriw59AQLg7rMYcapbxSk1RshfpCrNgG03/CU3+iQPoYieDIMQ7cAw+o90Wm7rmyfl1wSVkGMBFG8OeffzJ8+HD+/PNP88fguFsUxMUqtXPo++//ydChw7noIu2Ou1lJDg1cOHPoyp/NlUP1UGZGmjRFNqCBAweyf/9+WrVqpXUonoXQfMNb/4khQxouuGy2+ut4WibUJcfYP9nZtZ9tiwUeegjuvTf4Y+fpXPn+e4WBwH6g1dlnB70df885ISKpurqasrIyqqurQ9pOKDlUrRjCJRw5tE+faubN0+8+G53kUP9EIod+8v9qanNot25Bb0cvOVTv5VU4SMXWgN5//32tQ/AthBEdw95/QggN1E18igIvv2xPyp7W3brV3uTK12fe07liUWpwlA6fnfOMX7HJOSeMIjMzk6+//jrk7YSSQ9WKIVzCcT7rfZ+F+UUqhyqK4syh3/V4wK/Y9JxDo/HclabIUWTQoEGRmaQ5hKbI4eg/IYTW/B39MpDmTJ7OFSu1LzL1eatffX3knBNCh4JsiiznszAjLXLoP/9PcqgRyR3bEC1fvpyLLrrI+b/VaqVZs2a0bduWs88+m2uvvZZhw4ZFrOP2p59+ytq1a5k8eXJEXs8jq5XDJ//ce/w4FouFjIwMv4YbdwymMG6cvdDSejAFf6/8CeOJ5Hvrz+iXgTZnqnuuAFio/RJcVWPx64qx3s45IbxZvXo1ffv25ZdffqFXr17REUNNDUydav+7qAjS0tz/TkmBkhLn/zZg7UVFLPo+jYOk0IISbhxUhO0938/z9djqw4fpO306vyxdSq9LLw0ofMmh5mXGHOpasa2qsRo+h+qhzIw4RfiltLRUAZTS0lK35Tk5OQqgXH/99cr8+fOV9957T3nzzTeV+++/X8nMzFQApU+fPkp+fn5E4rzlllsUb2/rwIEDlYyMjPAHsWuXAiiAkmC1KikpKQG/bn6+ouTk2H9rZfZsRbFaFQXsv2fP1i4WoS4t3tvZsxUlJsb+mjEx9V9z2TL7Y3V/cnJ8bzc/X1E+/FBRLBZFeZM7nE/sbV0d0Pmjh3POCLzlAuGbGsetqKhIeeutt5SioiIVI9NnDOknc2i6p0Ihwj9FoLx18ncghaXkUPMyaw6dxNPOJ15hXWr4HKqHMrOucOdQi6KEMD9EFCkrKyM5OZnS0lKSkpKcyx13bKdNm8aECRPcnqMoCtOnT2fChAn06NGD3NxcYmNDv0k+ePBg9u3bR+vWrVm2bJnbY6NHj2bevHl4elsHDRpEXl5e+CdqLiykjc3GPiC9cWOad+xIeXm5oSaILiiwN2Ope3UwL08fV+FE8LR8bwsK7E2nTj+9/muFGld2NlSNvYPFytvsA6wd+vD7jl/UDF/gPRcI3/R03HzlUF1YtQpb374UAumAjmYP8btQkhxqXmbOoQVjp/AfZTL7gDhbD9bm/6Zm+ILw5wLpYxtGFouFRx99lBtuuIF169axePFi52MVFRVMnTqVbt260ahRI5o3b84VV1zBmjVr3LaxfPlyLBYLc+fO5fXXX6dTp07k5OSwYcMGVq9e7bZuhw4dmDdvnvO1HT/Lly93W6+goIDrrruOlJQUmjZtypAhQ9iyZYt6O2611rZxN+h1E3/7cwjj0fK9tdlg0CDfzaKCncYgKwuuHlbDFmADUHJ0p0pRC6EPhw4d4vPPP+fQoUMhbWfLli1s2LAhqLynVgw+rVgRvm0H4RDw+cnf/haWkkPNy8w5dExWbQ7df3y3SlFrJyLllc5IxTYCbr/9dgCWLl0KQGVlJUOHDmXKlCn079+fl19+mQkTJrBx40YGDBjAr7/+Wm8br7/+Os8//zyjRo0iOTkZgNLSUp588knnOq+88goXXHABAPPnz3f+dOnSxbnOkSNHGDhwIPHx8UydOpXx48ezfPlyhg0b5jYceE1NDfv37/f7p8a1lAtxHls9kMEAzEvP720ocxpmZ8Pnn9ZeSDp2XPXwhNDUn3/+ybBhwzSfxzbsMZzM43rxJzDs5G9/C0s9l7MiNHp+b0PNoXNm136XPW6CHKqHMjPiwtLA2YQa6mM7bdo0r889cOCAAii9evVSFEVRXnrpJQVQvvrqq3qv0b59e2XgwIH1tp+YmOjsp5uenq4ASlxcnBITE6Pk5eU512+ojy2gvPDCC27Lp0+frgDKv//9b+eyHTt2OPvJ+vOzY8eO2g3u21fbP6hRI6Vbt26R6dursob6cwjjMtt7m59/sp8TtznPvVha66qvj1lIH9vgqHHcTpw4oRQVFSknTpwIKRZHDk1PT9cshoakN2mimz62J072rz0RRB9bM5WzopbZ3ltHDn2Wx5w5NIFWhs+hkSqvAhHuHCqjIkeAow15WVkZYJ9DLzMzk3POOYf9+/e7rXvJJZcwb948jh07RuPGjZ3LR44cia1Oe4rExERKSkr44osvuOuuu/yKxWq1cs8997gtGzx4MABbt25lyJAhALRp04Zvv/3W731s06aN64v4/Tw9y8qyj6bnrT+HMC6zvbeOpmGuoyKDPubRE0ItcXFxpKamRkcMKSlw9Cg0awYTJ9qXFReD47UdfztGMA7XY8uWEffbb6QC/Pe/Ad1NNls5K2qZ7b115FDXUZEVjJ9D9VBmRpohKrbl5eVMmjSJDz/8kIMHD9K5c2cmTJjADTfc4PN5S5Ys4aOPPmLVqlUUFhbSunVrBgwYwOTJk8nMzIxQ9LUVWkcFd+PGjRw7dsznh23//v20b9/e+b9rc2KHuLg4ALZv3+53LO3ataNRo0Zuy1q2bAnAgQMHnMsaNWrExRdf7Pd23ahUsdXDNAE2m7ELNeFduN5bLT63jqZh1jodn/TQNExoz+g51CEvL4/JkyczefLkyMzJrocYkpJqK7YBUqUsuvVW8n77jcnA5IoKOgT4dMmh5mX2HGrB+DlUD2VmpBmiYnvNNdewatUqnn/+eTp16sTChQu58cYbqampYcSIEV6f98ILL9CmTRsef/xxOnbsSH5+PlOnTqVXr178/PPPdOvWLSLxr127FoDOnTsD9tGSu3btyquvvur1OXUrvRbHZO0ulJMDM3l6zBtf8+k6tgdQXV1NcXGx39tNTU2t3bZrxTbIwaOys2vnI7Na7QMCBNJXQggtaPW5dQyaYR2r4Lhpm5QkXyiFndFzqENFRQXbtm2joqIioq+rtxj8oVpZFBdHBbANqDh6VOUohXCndQ49NLbGmUMTEy2Gz6FGKa9UFZYGzir68ssvFUBZuHCh2/JLLrlEadeunVJVVeX1ufv27au3rLCwUImLi1OysrICiiOUPrbXX3+92z706NFDSU1NVaqrqxt8Xcf2x40b51zm6B+UkpKiAMrrr7/ufGz06NE++9h66uvq6E/71FNP1Vvm749bH9vSUmcfhbZxCUqnTg33sc3Pt89Blp9f29fBtZtPTEzoc4O5voYQnj4PoXxGwvW5DUT5NaNq+7e3bh25F44iRutjq/ccqoVQ+thGiiPGVq3S/SpDwpZD77zTuZG9X/4qOVQ4mTGHlo19oDaHpqZG7oWjSLhzge47Q37yySckJiYyfPhwt+W33noru3fvZuXKlV6fm5aWVm9Zu3btsNls5Ofnqx5rXcrJeWwXL15Mz549ue666wC46aabKC4uZsaMGR6ft2/fvnrL3n//fQoK3GezKy8vJyYmhiuuuMK5LDExEYCSkpKQYnf0sfX3x62Prcsd5MpK2LIFysu9v1Z2tn3uscGD7b9ffVX9oeTrvkZ2dvDbEsbn6fMQ6mdED9NbNG0cXAsJYV5GzqHRzHFzdP/+hsujsObQk12eAK6+vFJyqADMm0ObJUoONTrdN0Vev349Xbp0ITbWPdQePXo4Hz/vvPP83t6ff/7Jzp07ueqqq3yuV1FR4Xbr3tFP1pu1a9eyYMECwF7h3LZtG1988QVbtmyhb9++LFmyxNlU99577+Xbb79lwoQJLF++nL/85S8kJSWxa9cuvv/+exo1akROTo7b9jt16kS/fv244447KD9ZS6ysrOSJJ54gIyPDuV6/fv345z//yfjx47n00kuJi4tj8ODBHr+g+BJKH9vCPVYcDZaOUgUUc+DACR5++FmSk6F58+bOwa4KCmqbnYD998yZ9iYodSfZDravg6fXGDfOPvCB0ZuZiMB5+jycnJErpM+Io4+OWp/boLi+eABdFIR5GSWH+mPt2rVceOGF/Pe//6Vnz54hb0+vMRQU2MducvBVHoU9h8bFsRa4EDhN2QCcKzk0ykVNDjUBPZSZkab7iu2BAwfo2LFjveUtWrRwPu6vqqoqsrKySExM5P777/e57rRp05gyZYrf2168eDGLFy/GarWSmJhI27Zt6d27N9OmTWPYsGFufVvj4uL48ssvefPNN5k/fz5PPfUUYL8S3rdvX2655ZZ627/77rspKyvj9ddf58iRI7Rq1YrBgwfz9NNPu6134403kpubywcffMDixYupqakhJycn4IptKLb9aeXIyb+PUg0UAfDii08AkJGR4azYerpCV1MDDz0EL79sv1oX6CTbdfm6CihJOfp4+8zVFehnxNFHZ9w4dT63QVEUngTKgcS7747gCwu9MkoO9Ufbtm2ZPHkybdu2DWk7Tz75JOXl5c4WTlrE4MvWrfWXeSuPwp5D4+JoC0wGlpDUYDzC/EydQ2tqanOoCQZ2iUR5pTthaeCsoszMTGXo0KH1lu/evbvBvq2uampqlJtvvlmJiYlRPv300wbXP378uFJaWur8yc/P16R/kKOP7Zw5cyL6uqHI33bc2UehFfE++0n88ouiWCye+1Tk5ytKTo46fWuD6behtz65eovHqDx9HqxW9fr2qPW5Dcp119XugMv81kI9euor6o9oz6FGlJ+vKJB+cgyLdG1z6JNPOjc8hK8khwpz59Dx42t3YNUqDQIwv6jvY9uyZUuPV5QPHjwI1F519kVRFMaMGcOCBQuYO3cuw4YNa/A5CQkJJCUluf0I/9jauzeB9HbVLTsbzj3XfeBk13VtNhg0yP67oABycuy/A47n5FVAx01zf64C6q1Prt7iMTJPn4dZswL/jPjavuNzG3GuJ5NJ5pMWoTFTDi0rK+O7775TpVmznmOw2exTyTpomkPj4igDvgNiLKU+46kbm55ylt7iMTJT51DXW88myKF6KDMjLizVZRWNHTtWSUxMVCorK92WL1q0SAGUH374wefza2pqlNtuu02xWCzKu+++G3QcWl2lN+IdW6Wy0nnHtl1svMerbp6u+Fks9qvPdc2eXbuu1Wr/Pxj+XgXUw8h8eo7HFyNdEc/PV5QPP1SUxYtr4w33leKwH5+//732Q2KEN8GAjHbH1kw5NDc3VwGU3NzcoLcRqkjF0NCoyBHLoS+8oOSezOffPT5DcmiYSQ5t+DXDenzGjav9kKxZE6YXiRw9lJl1Rf0d26uvvpry8nI+/vhjt+Xz5s2jXbt29OvXz+tzFUVh7NixzJkzh7fffptbb7013OFGxJ49eygoKGDPnj1ah+KZy1Uui9XzVTdPfTQUBT780H2Zt4Gfgr1z689VQD2MzKfneLwx2hXxr7+GG26A66+vjdffz0gwdz8icnxqatgDFAB7ApiHWpiXmXJot27d2LFjR8jz54aSQ9WKwV8JCRrn0Lg4ugE7gPM7t5EcGkaSQ32LeA4NYPwBvYp0eaULYakuq+ySSy5RUlJSlFmzZinLli1Txo4dqwDKggULnOvcdtttSkxMjJLn0q/srrvuUgDltttuU3766Se3n9WrVwcUg56u0ut+Dr6amtp5wOLjPa6Sn1+/X5Cnq6jLltVfB+xXBMNFb1d39RaPJ0aI0VUo8QZz9yNix+eqq2rPvbZtVd64UBR95QJ/SQ51p/scqjQcY8Ry6Ouv1z5p/ny/nqK3fKC3eDwxQoyuTJtDs7Jqc2hamsobF4oid2wBWLJkCTfddBNPPvkkQ4cOZeXKlSxatIiRI0c616murqa6uhrFpbPJF198AcC7775L//793X6uvvrqiO9H1HCdZsS1848Lmw0efLD+8rpXUR3Dv7sK9/DvwfTJDSe9xeOJUa6IOwQbb7B3PyJ2fEw2VYFQh1ly6K5duxg/fjy7du2K+GvrKQaIYA6Ni2MXMB7YtXev37HpKWfpLR5PJIeG5/UCZrIp8/RSXkWSISq2iYmJvPrqq+zZs4eKigp+++03brjhBrd15s6di6IodOjQwbksLy8PRVE8/uTl5UV2J0Q9997bcMLVKiENGQILF9qbdeXlgdajvmdl2ePIydFHPHVpcQEiFMHGG2xyjdjx8XIhSUQ3s+TQI0eO8NNPP3HkyJGGVzZxDA4RyaFxcRwBfoKA9llyaGAkh4bn9QJmsovDeiqvIsUQFVthTv4m3EgnJEc/juuvt/cf+fpr/58byujNDdF0pMAGGOGKuCtHvK6Jsqam4fc62OQaseNjsqQshKsuXbqwevVqunTpEtUxOEQkh8bF0QVYDXRp1cqvp0gODZzkUP9eT3JoYPRUXkWKVGyFpvxNuHUTUriSXygDbXga2GDVKpg50/7b7PR+RbyuIUPcb3AqSsPvdSjJNRzHp955IHdshYgqYc+hcXG1f1dWNhiP5NDgSQ71TXKo8IdUbIXmAr2KGo6R8RyF248/qtdvZOxY6NvX3g+qb18YPTr0OPVOz1fE6/rxx/o5zJ/3OpTkqubx8XgemOxqsxCu1q1bR9u2bVm3bl1Ux1BXWHNoXBzrgLbAOh/99CSHqkNyqG8RzaEm6GOrx/Iq3KRiKwxFzel/HFwLtxtuqF+WBdtvpG6BP29e/avO4Wx2JbzLzoYbb6y/3N8+O+H68uHv58HbeXD8mMuHzgRJWQhXqampjB8/ntTU1KiOIRQB59C4OFKxDx6VGh/vcRXJodHHrDn0aLm5Lg4bvbwKhlRsRXg4MpvKzTr8HXgg2MLNEa5rM5n77284Lk/9Rjz54Yfav402Z51Z1H3PHaxWbfs0BfJ58HYeHD1irqQshKu2bdsyadIk2rZtG9UxhCLQHLq/NI62wCSgbePG9bYnOTT6mDmHlpeZK4cavbwKhlRshaEkJnpe3rRp7d+hFm6KAosWwUMP2R978cWGt1O334i3BD1ggP13OO48C/94es8BPvhAuz5NgX4evA3A0aSx9A8S5lVeXs5PP/1EeXl5VMcQikBz6Ihb4ijHPiqyp32WHBp9zJxDE5uaq2Jr9PIqGFKxFYbi7dx0jGSuVuHWoYN9wArH1Wd/kqZrv5GdO+GWW9wfv+UW6NPH/rfR5qwzE2/vef/+2sQDgX8evA3A0SjOXElZCFdbtmzhvPPOY8uWLVEdQygCzaHHlXi2AOcBW4qK6j1Pcmj0MXMObZJgrhxq9PIqGLFaByAC9/3331NVVUVsbPS9fY4C1bUAc+3T4atw89Y85oEH4OWX7es5Crfy8sC3A/bHHI/PnQvjx9ubTg0YUJuQ/dkPEZqCAvtnITOz/vvlSGjjxrm/51oO1pGbW39ZQ5+HrCz7qJTbttnXs9mA9xW+B6qA2H/9K0zRCqGNLl26sH79ejp27BjSdkLJoWrFoJVAc2gl9ul+1gMdk5I8blNyqPlEbQ5dWlObQz/8MEzRRo7Ry6ugKMIvpaWlCqCUlpZqHYohpFssCqCkx8aqvu3ZsxUlJkZRwP579uzax/LzFcVqtT/m+ImJsS/3tB3HuhaLojz0UO16gWwnHPshguf6vlqt3o9rfr6i5OSo+54Gw9NnDRRl+vQgNjZwYO0Gjh1TO1ShSC4Ilhy3wKSnp9tzaHq66tsOJIf2ZlXtP+PH19uO5FDzieoceuWVtRvYu1f1WEX4c4E0RRbhEabBo8D3UPH+zpHmacCLl18OfDvh2g8RnECaogcyKmM4R9701l/J9e6E31zPN39GYhHCQAoKCnj44Ycp0LAjpR5iCFUgObTGGkcB8DBQUFLiXE9yqDlFfQ513ZAJcqgZyqtAGf9dE1HJV4HqT7Lzpz9GJJKmkeasM4Jw9LsK98ib3vorBdWkzmRz8AnhqrS0lM8//5zS0tKojkEN/ubQf30bRynwOVB69KhzHcmh5iQ51FwVW7OUV4GIvk6aJrBw4UKOHj1KkyZNGDFihNbh6Javm8X+9s9x7e+jNl99WERw1O535e3q9ZAh6r1nqvZXqqlhIXAUaLJ4MSNGjVInSCF0oFu3bmzevDnk7YSSQ9WKwQgUBYiLoxuwGdyGVJYcak6SQ11y6JIljBg7Vp0gNRJN5ZWDRVHC0FbUhMrKykhOTqa0tJQkLwMoRIrNZqOwsJD09HTdNi+wxcRQWFNDusVCwbPP2hcWFUFamvvfKSlQUqLqY//7I4UvF5aQShHFpHH1VdA3o/7zftmZxqefQiuK2E8afxuRwvnd1I3F22O/7ExjzqcpJFNCa4oYcFUafftE7hiZ4jEv66n5vm77tYTP3y2iCPtjadj/vvW+FM5IVXd/Skjh4J8lpCpFJJ0W5HF45x1seXkUAult2lCwZw9CXXrKBUaip+NmiByqYYzZ2bWVkVMtefypnGp/4Prr7XO6uKxXtzIRqebArjFarfaKjTRFVoea72tOjv1OraflgwaFFGY9BQV1BoIKxpAh2L75xp5D27WjoLBQzRAF4c8FcsdWhIdrx5vHH4/oS59/8sfpU8/r9T3547QwTAH589qf4jVOERg139fTgQc8PfBK8Nv0JuXkj2r27rV/Q5Fve8Ik/vjjD4YNG8Znn31Gt27dojaGcKp7h61CieMPYBjw2YEDuO6xx1FlA3idYO+2RuIuYDQL5X2tK5KjV6vSOsBk9/rMXl55YvwG5EJ/Vq3SOgIhBDQ8caQQBtK8eXOGDx9O8+bNozqGcPI03U9zYDjQ3MP6wfRxDbXPpcxhG35q9V1WaxAxfwefCnmQKk+jUBmY2csrT6RiK9S3YoXWEQghQL7tCVNJT09n2rRppKenR3UM4VR3IJ5K4kgHpgHpQcz7W1cgo+76GyOodxcwnKP3RqtQBxHz90KIKoNUmaxia/byyhOp2Ar1XXCB1hEIISB8bb6E0MCxY8dYt24dx44di+oYwsnTdD/HgHWgyj6rcbc1XFMJhXv0Xr0JtRIfyPODvQPs74UQNS6YOJ9oImYvrzyRiq1QX58+0KSJ1lEIIdSeOFIIDW3cuJGzzjqLjRs3RnUM4eZ6h+2PLXFsBM4Cfiksc1YUgq0UqXW3Ve2phFSrGBlEdjaccoq9Et++PTz8cGD7Go6LAJ4+U/5eCFGtebrJpsyLhvKqLhk8SoRHSgocPQrNmsHEifZlxcWQmur+t2O01zA+9ssq+N8nxewjlVJSuKhnCYVr7f9bgBEXF9NjsP/b/CUvlU8+gVYUs59ULht5ctRdNfchwG3syi3mjY/tj6VRTBGpHCKFR8aUcFozbY57uB4r+7OY52bX39cUSmrfSx/bOFQK775gf/8PkUJzSmhNMbc+mkpKsjqfsduuLqFvh2JK4lN54QVIdYmzBSVMHFNMUsfabZbEpzLxBfso2Y59skLteoF8ViZOhEOHoE0bGThKmMoZZ5zBL7/8whlnnBHVMUSCcyCemjhSgF+Aw9tiyciAm26C+fODG5FYzalZ1JxKyFfFyGzXBgsKYOxY93GSXnwRZs70770Mx+Bd3ka59nfwKdUGqTLZHdtoKa9cScVWhFdSUm3FVgMFBdB/ErgWVW+vdV/nxRzIm+N/gdwXaKfGsPIqshbAi5/UL9SfeArQQXxq+veHMH2258f8eS/X5MCDL9Rf3mtocNMPePqMzf7cfhfBZrMn3Lpf4pLqfHFIAfr4sZ5fnn3WXrF1tNMTwiSaNm1Knz59oj6GSCrYbaUNVvpQww72Mrbm/2g+r4QZJ6c+owbKxhRRsiWNlA7+TXWWlZbG3x+Esm1FNDs9jZQTKTA1MtPBeXus9/YiJpCGQu20bmWk0POrEvhUB9PbqfhY+YoiHlHcp7A7RArNa0pq38tk79s4vh1m1Lg8jxLSqouomJwGHQOPqyQhjW3TcX6mDtWksH1MCWU/FmE7LY2froQfPi1i38n3ZPQVJdhedN+mLS2N/9yQwr8Wljin+rvqCmrX8/ez4jq9T3V1QOeKHkVbeQVSsRUm5+kqbF3BXJUN56TzwVB1gnID8+e9VHv6gYau9Ps7dYKaUywIYUZ79uzh7bffZty4cbRt2zZqY4ik8lezKaKGWcA48nmLOz2vOD2w7TbH8yjLWknCPkBWPQHulxF0Bp73tUID++x1GrwgmyOn4OXYv2v/5XF6RA/8nerRbyaYMi/ayiuQPraG1KZNG9LT02nTpo3Woeiep/48del9fB1/+zKp3edIr847z3vXF3/eS7UHHvGnz5i/A2eoMcWClA/CrPbv38/s2bPZv39/SNsJ5RxRKwZDKCjgjJfGcgCYDUTBHgtBGyD95G+jd7SOqvLqJLlja0C//vqr1iEYhqc7maNGwYIFxriz6a3fiTd6u5McDjYbvPNO7XvqEMh7Gcjd0YIC+13ZzEzP6+ntbrmUD8KsunfvToEKXzJDOUfUisEQtm7Foih0B6Jkj4XArXQweEfrqCqvTrIoimv3ceFNWVkZycnJlJaWkpSUpHU4umez2SgsLCQ9PV0XJ1VBnT6xjv+bNoXycu+VFi0VFNhHG6zbZNbRd1MPGqr0hfu1He/hkSPhab4byIWFup8xYU6SC4Ijxy0wusihBQX2oXPla6KIVnr70mUC4c4F0hRZRIW6TTxtNti+Hc49V79z1qk2fL2KXJtFaz3nn+M97dMn9Oa7ngQ6/YMazYiFEN5t2LCBHj16sGHDhqiOIWJONo/ZAPQAomCPhahlteq7SZ8foqq8OkmaIouoFI7h6tXW0CBHkb5bWvfupaLUXsjX4/ELVTRN/yCEETRr1oxBgwbRrFmzqI4horKyaNa9O4OeeopmF1wALVpASQllfxYzdXbqyVGE7VOUlZHCtEdLaH5CB1PFgTPGEsfIvSen6Hv0UWh+wj7N2r6KFNokRCbmX/JSefcT+7RurbFPD4eWxy/M299UlMKcV2qnsHPs61VjUjmtt/ZTB3pdD6BlS+jf3/DJPurKK6Qpst/01Ixq3LhxHDx4kBYtWvD2229rGos3umhG5UNOjv1Oo6flwUz5Ei7Z2fX7bmZlBd73NlSemkV7orfjFwojNAX3xAjlg5HpKRcYiZ6OmxHOEcmh6pAcqh3JocKTcOcCuWNrQF9++aUz4YngqD3liydq3FH1NMiRFneb/Zk2Se+jSwdKb4NC+UvKB2FWx48fp6CgAJvNRqNGjYLeTijniFoxGImnfZYcGhjJoZJDtRCN5ZX0sRVRSe0pX+pSs/9p3b6bWvS99TSljdVau8woCStQ0TKFkhBGsGHDBjIzMzXvY6t1DJHmaZ8lhwZGcqjkUC1EY3klFVsRtcJV4AY66FCg/Jk3VW2evsTMmgU7dwZ+/Pydl1cvfA0KZbR9EcLIMjMzycnJITMzM6pjiDRv+yw51H+SQyWHaiEayyup2IqoFo6RbMN9NTjcV8q98fQlJtDjF8mRlMOdMLUeFVqIaKOHgVD0EEOk+dpnyaH+kxzqTnJo+EVjeSUVWyFUFomrwZFu3uNIcBD8l5hwX4V3Fe6EGcl9EULY7du3jxkzZrBv376ojiHSIr3PkkO9b0NyqAhENJZXUrEVoo5Qr1JG6mpwpOZNVSvBRapfUyQSph7nGBbC7Pbu3cu0adPYu3dvVMcQaYHus+RQd5JD65McGhnRWF7JqMhCuFBrCgBPIzEaUSCjRzY0gmUkRtGEyMw/G6l9EULUOuusszh48GDUxxBpgeyz5FB3kkM9kxwaGdFYXskdWyFOUvsqZaSuBoeTv1dV/bkiHamr8JFoxqZVHy0hhNAryaH1SQ71THKoCBep2ApxkjSNqc+fBBfIl5lI9GuKVMKUaQyEiKzNmzfTv39/Nm/eHNUxRJq/+yw5tD7Jod5JDg2/aCyvpCmyAd14442UlJSQkpKidSimIk1j6vNngvVAmy3ZbJEZfTISzdgisS+BkvJBmFWjRo3o1q0bjRo1Cmk7oZwjasVgJP7us+TQ+iSH+iY5NLyisbyyKIqiaB2EEZSVlZGcnExpaSlJSUlah6N7NpuNwsJC0tPTKTDQMHfZ2fUTULReRXTt7wPeE1xBgb3pVN0vM3l5+ktYQoRKckFw5LgFRnKo8UkOFaK+cOcCQzRFLi8v57777qNdu3Y0atSInj178sEHH/j13KKiIkaPHk2rVq1o0qQJ/fv35/vvvw9zxMKozNo0JtBRKuv29/n6a+99naSvjBD6ZpYcWllZyZ49e6isrNTk9fUSQ6QFss+SQ+0khwo9iMbyCsUALrnkEqV58+bKW2+9pSxbtkwZM2aMAijvv/++z+cdP35cOfPMMxWbzaYsWLBA+eabb5Rhw4YpsbGxyvLlywOKobS0VAGU0tLSUHYlaqSnpyuAkp6ernUoEZefryjLltl/68Hs2YpitSoK2H/Pnu17/fz82vUdPzExDe9Pfr6i5OTUX09vx0OIUBgxF5glh+bm5iqAkpubG/Q2QhWpGPSUQyN93PWWMySHCqPSQ5lZV7hzqO4rtl9++aUCKAsXLnRbfskllyjt2rVTqqqqvD73jTfeUADlxx9/dC6rrKxUunbtqvTt2zegOIz4ZUZLekrKkRRoAgy3YBLssmXu6zt+cnICf329HQ8hQmW0XGCmHHro0CFl6dKlyqFDh4LeRqgiFYOecmgkj7vecobkUGFkeigz6wp3DtV9U+RPPvmExMREhg8f7rb81ltvZffu3axcudLnc8844wz69+/vXBYbG8uoUaP45ZdfKCwsDFvc4dS5c2eSkpLo3Lmz1qEIF5GY1DxQwYxSqdZQ/3o8HtFAygfhykw5NDk5mcsuu4zk5OSQthPKOaJWDEYSqX3WY86QHBp9zJRDo7G80n3Fdv369XTp0oXYWPcBnHv06OF83NdzHet5eu4ff/zh9bkVFRWUlZW5/ehFeXk5hw8fpry8XOtQhIuGEmCgfXTUEEyCVau/j96mftDi+GtBygfhykw5tLi4mDfeeIPi4uKQthPKOaJWDEYSqX2WHOpOcqg2zJRDo7G80n3F9sCBA7Ro0aLecseyAwcOhOW506ZNIzk52fnTvn37QEMXUcZXAvRn8vVw8CfBekpWagwAEolJ3v2l1fEXQmtmyqEFBQU88MADmo4SrIcYIi1S+yw51J3kUBGqaCyvdF+xBbBYLEE9FspzJ06cSGlpqfMnPz+/4UCFoYV6NdJbAgRtmxP5SrC+kpXN5n0UR3/oZaRHac4lop1ZcujZZ59NRUUFZ599dsjbMnIMkebvPksOlRwq9CUayyvdV2xbtmzp8arwwYMHATxeTVbjuQkJCSQlJbn9CPNS62qkpwSoh+ZEnhJsJJJV3eMxZIj3Lz7hauakh+MvhFYkh4pIkBwqOVQIPdB9xbZ79+5s3LiRqqoqt+W///47AGeeeabP5zrWC/S5InqonZzqJkA9NSdyFalk5TgeX3/t/YtPOJs56fX4CxEJZsqhW7du5eKLL2br1q0RfV29xRBpDe2z5NBakkOFnkRjeaX7iu3VV19NeXk5H3/8sdvyefPm0a5dO/r16+fzuZs2bXIb9bGqqooFCxbQr18/2rVrF7a4hXGEOznppTlRXZFMVr6++IT7qrdej78QkWCmHBobG0tqamq9gbCiLYZIa2ifJYfWkhwq9CQayyvdz2OrKPb59lJSUpRZs2Ypy5YtU8aOHasAyoIFC5zr3HbbbUpMTIySl5fnXHb8+HGlW7duSvv27ZX3339f+fbbb5Wrr75as8nl1aKn+e28MUKMDsFOph7M63iafF1Ls2fb99Wxz+GaI8/XvH5qzvnnix6PfzgY6dwzIj3lAn9JDnVnhHPECDE6SA6VHGomRjr3jCjcucAQVfglS5bw+OOP8+STT3Lw4EE6d+7MokWLuOGGG5zrVFdXU11djaIozmUJCQl8//33PPLII9x9990cPXqUnj178tVXXzFw4EAtdkXokONq5Lhx9qvM4boaabPp7wpnVpa9z862bfarzOGKz3Fl2/WqvuuVbV+P+aOgwH7XIDPT+z7o8fgLEQlmyaHV1dUcOXKEpk2bEuO4fRSFMURaQ/ssOVRyqNCnaCyvDHHHVg/kanNgjBBjXUa7Gpmfb79Sa5R4fV3ZDuWq9+zZtXcLrNbwXTE3CiOee0aip1xgJGoct9zcXAVQcnNzQ4ollHNErRgaoqfz2N99lhwaXpJDI0NP516oIlVeBSLcOdSiKC6XZ4VXZWVlJCcnU1paqvnojkuXLuXYsWM0btyYyy+/XNNYvLHZbBQWFpKenm66+bP8ubIZbtnZtX1qrFb71fJg5smLtIIC71e2fT3ma3sZGfWvVOflRe+VZSOUD0amp1xgJGoct5KSEr777jsuvvhiUlJSgo4llHNErRgaoqccqvY+Sw4NnuTQ8DNTDo1UeRWIcOdQqdj6Sb7MBEZPSVlNekiGZktEoXzJycmxjwLpafmgQaqEJ4QbyQXBkeMWGMmh4SM5tJbkUBFp4c4Fuh8VWQi98Dby4KpV4Zk7zhu9zCmnxpx5oU5RINMQCBE9Dhw4wNy5cz3OrRtNMUSaWvssOdSd5FARbtFYXknFVgg/eUuG554bnrnjvNFDIlJjzjw1piiQaQiEiB47d+7k1ltvZefOnVEdQ6Sptc+SQ2tJDhWREI3llTRF9pOemlHl5uZy4sQJ4uPj6d27t6axeGPGZlSemi/VFanmTNnZ9UegjFRzLrWacanZBKqgAH76yT7JwXnnRXdSNkL5YGR6ygVGosZxUxSF6upqYmJisFgsQccSyjmiVgwN0VMOVWufJYfaSQ7VNzPl0EiVV4EIdw41xHQ/wt2wYcN0k/DMwt+h7l2nNKg7vD7UNmcKd1KI1BQDnvhqxhVIHA1NXxCIr7+uvXJtscCDD8K990ZncpbyQZiVxWIhNjb0ry2hnCNqxWAk/uyz5FD/SQ7VNzPl0Ggsr6Qpsoh6gTQJysqyX1XNyYGff9a2OZPNZr8qG+7EU7cfkFrNuNRqAlW3OZaiwIsvRq5ZmxAiMrZv386VV17J9u3bozqGSGtonyWH+iY5VGglGssrqdiKqBZMHxVHMuzTRx99U9QYgMIbT19Y1OyT4/olJy8vuKZgnq5+Q3D9jYQQQvhPcqhvkkOFiKzouj8tRB2hNgnSsjkThHfqBG9fWIYM8b3fgU49YLOFdtw8NcdyiFSzNiFE+J122ml8/vnnUR9DpPnaZ8mh3kkOFVqLxvJK7tiKqKZGk6BINWeqS40REX1paEoET/utxkiPgXJc/a77PoJMWyCEmSiKQlVVFVqOeamHGCLN1z5LDvVOcqjQWjSWV1KxFVHNyEPdh3suvkC/sHj6knD77fY5CsMtKwt27oSHHjLmeymEaNiaNWuIi4tjzZo1UR1DpPnaZ8mh3kkOFVqLxvJKKrYi6qnRR0UL4Z6LL9AvLJ6+JNTU2OcojNRV5xkzjPleCiEalpGRwZw5c8jIyIjqGCKtoX2WHOqZ5FChtWgsr2QeWz/pae5CPc1v540RYgxGoH1fwi0Sc/EVFPjX/8nXHIWRmptQmPfc0ws95QIj0dNxM8I5YoQYgyE51Pd6kkO1Z9ZzTy/CnQvkjq0QftKi70tDInGl3N/+T7766ajZvEsIEZ1KSkr46KOPKCkpieoYIk2tfZYc2vB6kkOFmqKxvJKKrRB+CPcgE6HQauANT7KytJ+bUAhhTjt27OC6665jx44dUR1DpKmxz5JD/SM5VKgpGssrme7HgDZu3IiiKFgsFq1DiRqhTmlgVp6alTnmJqzbvCuaj1MkSfkgzOqss86itLSUpk2bhrSdUM4RtWIwEjX2WXKoZ5JD9cdMOfT/t3f/sVXV9x/HX7c/uGXUAlV+tUWKKUMo7RgOGAnB4QbIQiC4kNFBlNI6dWoFl4HMH8UIETeCzrEfMH6ss1ISUoo4kFAHhI0hywQRkJkOsEIbN36sQNEKt/18/+BLtVLK/Xl+3PN8JCeGc89p3+edfs7Lz73n3OPF8xUTWxe65ZZb7C7Bc9p7zpvX30Ht6Pl/dj+b0Ms4PyBeJSYmRuWerEjGSLRqcJNoHDMZej0y1JniKUO9eL7iUmQgCG5+pEEsBHNZmZMu7wLgfidOnFBBQYHtlyLbXYPVonHMZGhbZCis4MXzFRNbIEhufaRBLNzosrING5xxzxSA+BMIBHT69GkFAgFP12C1aB0zGfoFMhRW8OL5isf9BMlJjypYtmyZLly4oLS0ND355JO21nIjfF16fOvosQRfvaQK1nLD+cHNnJQFbuKkvrlhjJCh8Y0MdS43nB/cLNZZwMQ2SE4KZTcEnhtqRGS+/Py/r+KZe/Zh7MWWk7LATZzUNzeMETfUiMiQoc7E2IstnmMLwHanTl29fOzL5/hrl5UtW3b99jxzD0C0HThwQH6/XwcOHPB0DVbz4jFHGxkKO3hx7DKxBdCh1auvXjJ1zz1X/7t69RevZWVJ06bxzD0AsZeVlaVly5Ypy8aPsZxQg9W8eMzRRIbCLl4cu0xsAdxQsN/cyLddAoi1Hj166NFHH1WPHj08XYPVvHjM0UKGwk5eHLtMbAHc0I2+ufGrl0jxbZcAYu38+fPasmWLzp8/7+karObFY44WMhR28uLYZWIL4IYGDAj+EqmbPXOvvXuMACBYx44d06RJk3Ts2DFP12A1Lx5ztJChsJMXxy4TWwA3FK1LpDq6xwgAgpGXl6f6+nrl5eV5ugarefGYo4UMhZ28OHaZ2MITeKczfJFeIhXMPUYAcDPJycnq06ePkpOTPV2D1ZKTk9Xc3Ed/+1sy5+0wkKGwixfPV0xsEfd4pzNyN7tEqiPB3mMEAB2pra1VcXGxamtrPV2D1X7xi1r17Vuse+6pJUPDRIbCDl48XyXZXQBCN2zYMPXt29dT33IWrhu90zlhAt84aJVr9xh9OZh5lEHscH5AvGpqatKRI0fU1NQU0c+JZIxEqwa3OHVKeuqpJklHJDWRoTYgQ60VTxnqtfOVxMTWlTZv3mx3Ca7R0TudhLI1rt1j9NBDV3vPowxii/MD4tXAgQO1d+/eiH9OJGMkWjW4RU2NZMxASV8cMxlqLTLUWvGUoV47X0lMbBHneKfTGYqKrr7D/+9/X+09gQwAzkeGOgMZCgSHe2wR13jwuXNEco8RABw8eFDp6ek6ePCgp2uwUlaW9OyzByWlSzpIhtqIDEWovHa+kvjEFh7AO50A4H69e/fWggUL1Lt3b0/XYLVHHumtQGCBhg3rrREjyFDALbx4vvIZY4zdRbjBhQsX1LVrV50/f15paWm21jJ58mSdPn1aPXr0cOy9AFlZWaqrq1NmZqZO8Z30gGXccH5wMydlgZs4qW9uGCNkKGAPN5wf3CzWWcAnti60f//+1sADgC/j/IB4dfHiRb377ru66667dMstt4T9cyIZI9GqwU28eMzwrnjKUC+OXe6xBQAAjldTU6OxY8eqpqbG0zVYzYvHDMQDL45dPrEFAACON3jwYNXU1CjLxps8nVCD1bx4zEA88OLYdfwnto2NjZozZ44yMjKUkpKioUOHav369UHtu3HjRhUUFCgnJ0edO3dWdna2ZsyY4al3LgAA3hVPGZqSkqKcnBylpKTY8vudUoPVvHjMQDzw4th1/MT2vvvuU1lZmUpLS/XWW29p+PDhKigo0Lp1626670svvaRPP/1UTz/9tLZt26ZFixbpwIEDGjZsmI4cOWJB9QAA2CeeMvTkyZMqKSnRyZMnLf/dTqrBal48ZiAeeHHsOvpS5K1bt6q6ulrr1q1TQUGBJGns2LGqra3Vz372M/3whz9U4rUHlLbjzTffVM+ePdusu+eee5Sdna2XX35Zq1atimn9AADYJd4y9OLFi9q1a5cefvhhS3+v02qwmhePGYgHXhy7jv7EtqqqSqmpqZo2bVqb9YWFhaqvr9e+ffs63P+rgSxJGRkZysrK8tS7FwAA74m3DB08eLDef/99DR482PLf7aQarObFYwbigRfHrqMntocPH9agQYOUlNT2g+X8/PzW10N1/Phx1dbWKjc3Nyo1AgDgRGQoAMBLHH0p8tmzZ3XHHXdctz49Pb319VAEAgEVFRUpNTVVc+fO7XDbzz//XJ9//nnrv8+fPy/p6oOF7dbS0tL6XyfU0x431AjEI8ZebF3rqTHG5kpuLt4y9MiRI/rBD36gysrKiCbWkYyRaNVwM04ax1YdM+AEThp7kXLi2I15hhqL7Ny500gKajlw4IAxxpgBAwaYe++997qfVV9fbySZF198Mejf39LSYu6//36TmJhoNm3adNPtS0tLg66XhYWFhcVby7Fjx4LOn2ggQ1lYWFhY4mWJVYZa9ontwIED9Yc//CGobW+//XZJ0q233truO8rnzp2T9MW7zjdjjFFxcbHKy8tVVlamKVOm3HSfBQsW6Mknn2z9d0NDg/r166ePP/5YXbt2Der3et2FCxfUt29fnTx5UmlpaXaX4xr0LXT0LDz0LXTnz5/X7bffHnT+RAsZ6j2Mz/DQt9DRs/DQt9DFOkMtm9j26dNHxcXFIe2Tl5eniooKBQKBNvcIHTp0SJI0ZMiQm/6Ma4G8du1arV69WjNnzgzqd/v9fvn9/uvWd+3alT/eEKWlpdGzMNC30NGz8NC30CUkWPsVFWSodzE+w0PfQkfPwkPfQherDHX0l0dNnTpVjY2NqqysbLO+rKxMGRkZGjlyZIf7G2P04IMPau3atVqxYoUKCwtjWS4AAI5BhgIAvMTRXx41ceJEjRs3To888oguXLignJwcVVRUaNu2bSovL2/z/L2ioiKVlZXp2LFj6tevnySppKREq1ev1uzZs5WXl6d33nmndXu/369vfvOblh8TAABWIEMBAF7i6ImtJG3cuFFPP/20nnvuOZ07d0533nmnKioqNH369DbbNTc3q7m5uc23bL355puSpDVr1mjNmjVttu/Xr58++uijoOvw+/0qLS1t99IqtI+ehYe+hY6ehYe+hc5tPSND3YuehYe+hY6ehYe+hS7WPfMZ44JnFgAAAAAAcAOOvscWAAAAAICbYWILAAAAAHA1JrYAAAAAAFfz/MS2sbFRc+bMUUZGhlJSUjR06FCtX78+qH3/+9//atasWbrtttv0ta99TaNGjdJf/vKXGFdsv3B7tnHjRhUUFCgnJ0edO3dWdna2ZsyYoZqaGguqtl8kf2tf9swzz8jn8wX1DEq3i7Rnb7zxhu6++26lpaWpS5cuys3N1cqVK2NYsTNE0redO3dq3Lhx6tmzp1JTU5Wfn69XX31Vzc3NMa7aXhcvXtS8efM0fvx49ejRQz6fTwsXLgx6f/KADA0WGRoeMjR0ZGh4yNDQOSZDjceNGzfOdOvWzfz+9783O3bsMMXFxUaSef311zvcr6mpyQwZMsRkZWWZ8vJys337djNlyhSTlJRkdu3aZVH19gi3ZyNGjDCTJ082a9asMbt27TKvvfaaGTRokElNTTWHDx+2qHr7hNu3Lztw4IDx+/2mV69eJjc3N4bVOkMkPXvxxRdNQkKC+clPfmLeeust8/bbb5vly5ebX//61xZUbq9w+1ZdXW0SEhLMd77zHbNp0yZTXV1tHn/8cSPJlJSUWFS9PU6cOGG6du1qxowZ09qv0tLSoPYlD8jQUJCh4SFDQ0eGhocMDZ1TMtTTE9stW7YYSWbdunVt1o8bN85kZGSYQCBww31/85vfGEnm73//e+u6K1eumMGDB5sRI0bErGa7RdKz//znP9etq6urM8nJyaaoqCjqtTpJJH275sqVK2bo0KGmpKTE3H333XEfypH07J///KdJSEgwL730UqzLdJxI+jZjxgzj9/tNY2Njm/Xjx483aWlpManXKVpaWkxLS4sxxpjTp0+HFMrkARkaLDI0PGRo6MjQ8JCh4XFKhnr6UuSqqiqlpqZq2rRpbdYXFhaqvr5e+/bt63DfgQMHatSoUa3rkpKSNHPmTP3jH/9QXV1dzOq2UyQ969mz53XrMjIylJWVpZMnT0a9VieJpG/XLFmyROfOndPixYtjVaajRNKz5cuXy+/36/HHH491mY4TSd+Sk5PVqVMnde7cuc36bt26KSUlJSb1OoXP55PP5wtrX/KADA0WGRoeMjR0ZGh4yNDwOCVDPT2xPXz4sAYNGqSkpKQ26/Pz81tf72jfa9u1t++RI0eiWKlzRNKz9hw/fly1tbXKzc2NWo1OFGnfPvjgAy1atEi/+93vlJqaGrM6nSSSnu3evVuDBg1SZWWlBg4cqMTERGVlZempp57S5cuXY1q33SLp28MPP6zLly+rpKRE9fX1amho0GuvvaaqqirNmzcvpnW7GXlAhgaLDA0PGRo6MjQ8ZKj1opkHnp7Ynj17Vunp6detv7bu7NmzMdnXzaJ53IFAQEVFRUpNTdXcuXOjVqMTRdK3lpYWzZ49W/fdd5++//3vx6xGp4mkZ3V1daqpqVFJSYlKSkr09ttva9asWVq6dKkKCwtjVrMTRNK3kSNHaseOHaqqqlJmZqa6d++uwsJCLV68WD/96U9jVrPbkQdtkaE3RoaGhwwNHRkaHjLUetE8LybdfJP41tHH5jf7SD2Sfd0sGsdtjFFRUZH++te/qrKyUn379o1WeY4Vbt+WLVummpoabd68ORZlOVq4PWtpadHFixdVUVGh6dOnS5LGjh2rS5cu6ZVXXtHzzz+vnJycqNfrFOH27d1339XUqVM1cuRIrVixQl26dNGOHTv0zDPPqKmpSc8++2wsyo0L5EFor0W6r5uRoeEhQ0NHhoaHDLVetPLA0xPbW2+9td13Ac6dOydJ7b57EI193Swax22MUXFxscrLy1VWVqYpU6ZEvU6nCbdvH3/8sZ577jktWbJEnTp1UkNDg6Sr79S3tLSooaFBfr//uvs54kGk4/OTTz7RhAkT2qyfOHGiXnnlFe3fvz9uQzmSvj366KPq1auXqqqqlJiYKOnq/8wkJCRo4cKFmjFjhu64447YFO5i5EFbZOiNkaHhIUNDR4aGhwy1XjTzwNOXIufl5eno0aMKBAJt1h86dEiSOnzGWV5eXut2oe7rZpH0TPoikNeuXatVq1Zp5syZMavVScLt2/Hjx/XZZ5/piSeeUPfu3VuXPXv26OjRo+revbsWLFgQ8/rtEMnfWnv3akhX//4kKSEhfk99kfTtvffe01133dUayNcMHz5cLS0tOnr0aPQLjgPkARkaLDI0PGRo6MjQ8JCh1otqHoT0HcpxZuvWrUaSWb9+fZv19957702/0vu3v/2tkWTeeeed1nVXrlwxubm5ZuTIkTGr2W6R9KylpcUUFRUZn89nVq5cGetSHSXcvv3vf/8zO3fuvG75xje+YbKzs83OnTtNTU2NFYdguUj+1lasWNHuM+dKSkpMQkKC+eijj2JSsxNE0rf+/fubIUOGXLfNz3/+cyPJvPfeezGp2WlCfVQBeUCGBosMDQ8ZGjoyNDxkaOTszFBPT2yNufpcqu7du5uVK1eaHTt2mAcffNBIMuXl5a3bzJ492yQmJrYZyE1NTSY3N9f07dvXvP7666a6utpMnTrVMw+XD6dnjz32mJFkZs+ebfbu3dtm2b9/vx2HYqlw+9YeLzyDz5jwe3b58mUzbNgw07VrV/OrX/3KVFdXm/nz55vExETz2GOP2XEolgq3b6+++qqRZCZOnGg2bdpktm/fbubPn2+SkpLM9773PTsOxVJbt241GzZsMGvWrDGSzLRp08yGDRvMhg0bzKVLl4wx5MFXkaGhI0PDQ4aGjgwNDxkaHidkqOcnthcvXjQlJSWmd+/eplOnTiY/P99UVFS02eaBBx4wksyJEyfarP/kk0/M/fffb9LT001KSor59re/baqrqy2s3h7h9qxfv35GUrtLv379rD0IG0Tyt/ZVXgnlSHp29uxZ89BDD5levXqZ5ORk8/Wvf9388pe/NM3NzRYegT0i6VtlZaUZPXq0ue2220yXLl1Mbm6ueeGFF6574Hw86ugcda1P5EFbZGjoyNDwkKGhI0PDQ4aGxwkZ6jPm/y+YBwAAAADAheL37m8AAAAAgCcwsQUAAAAAuBoTWwAAAACAqzGxBQAAAAC4GhNbAAAAAICrMbEFAAAAALgaE1sAAAAAgKsxsQUAAAAAuBoTWwAAAACAqzGxBQAAAAC4GhNbAAAAAICrMbEFoD179sjn88nn82nDhg3tbrNv3z6lpqbK5/Np3rx5FlcIAIAzkaGAM/iMMcbuIgDYb8qUKdq8ebPuvPNOHT58WImJia2vffjhhxo9erTOnDmjBx54QGvXrpXP57OxWgAAnIMMBezHJ7YAJElLlixRYmKi/vWvf6m8vLx1fX19vSZMmKAzZ85o0qRJWrVqFYEMAMCXkKGA/fjEFkCr4uJirV69Wv3799eHH36oS5cuacyYMTp06JBGjx6t7du3q3PnznaXCQCA45ChgL2Y2AJoVVdXpwEDBuizzz7Tyy+/rKqqKu3evVt5eXnavXu3unXrZneJAAA4EhkK2ItLkQG0yszMVElJiSRp7ty52r17t7Kzs7Vt27Z2A7mxsVELFy7UpEmT1Lt3b/l8Ps2aNcvaogEAcAAyFLAXE1sAbTzxxBNKSLh6akhPT9f27duVkZHR7rZnzpzR888/r/379+tb3/qWlWUCAOA4ZChgnyS7CwDgHIFAQD/+8Y/V0tIiSfr00087vB+oT58+OnXqlDIzM9XU1MS9QwAAzyJDAXvxiS0ASZIxRsXFxfrzn/+sHj16qH///mpqalJpaekN9/H7/crMzLSwSgAAnIcMBezHxBaAJGnevHkqKytTamqqtmzZosWLF0uSysrK9MEHH9hcHQAAzkWGAvZjYgtAS5cu1dKlS5WcnKzKykoNHz5c06dPV35+vpqbm7VgwQK7SwQAwJHIUMAZmNgCHvenP/1J8+bNk8/n0x//+EeNHz9ekuTz+fTCCy9IkjZv3qw9e/bYWSYAAI5DhgLOwcQW8LCtW7eqqKhIxhgtW7ZMP/rRj9q8PnnyZI0cOVKSNH/+fDtKBADAkchQwFmY2AIetXfvXk2bNk2BQEDz58/XnDlz2t3u2n1Ce/bs0RtvvGFhhQAAOBMZCjgPj/sBPGrUqFG6dOnSTbf77ne/K2OMBRUBAOAOZCjgPHxiCwAAAABwNT6xBRCR5cuXq6GhQYFAQJL0/vvva9GiRZKkMWPGaMyYMXaWBwCAY5GhQPT4DNdHAIhAdna2amtr232ttLRUCxcutLYgAABcggwFooeJLQAAAADA1bjHFgAAAADgakxsAQAAAACuxsQWAAAAAOBqTGwBAAAAAK7GxBYAAAAA4GpMbAEAAAAArsbEFgAAAADgakxsAQAAAACuxsQWAAAAAOBqTGwBAAAAAK7GxBYAAAAA4Gr/B+kAIs6lEDwoAAAAAElFTkSuQmCC",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_46_0.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.tree import DecisionTreeRegressor\n",
|
||
"\n",
|
||
"tree_reg1 = DecisionTreeRegressor(random_state=42, max_depth=2)\n",
|
||
"tree_reg2 = DecisionTreeRegressor(random_state=42, max_depth=3)\n",
|
||
"tree_reg1.fit(X, y)\n",
|
||
"tree_reg2.fit(X, y)\n",
|
||
"\n",
|
||
"def plot_regression_predictions(tree_reg, X, y, axes=[0, 1, -0.2, 1], ylabel=\"$y$\"):\n",
|
||
" x1 = np.linspace(axes[0], axes[1], 500).reshape(-1, 1)\n",
|
||
" y_pred = tree_reg.predict(x1)\n",
|
||
" plt.axis(axes)\n",
|
||
" plt.xlabel(\"$x_1$\", fontsize=18)\n",
|
||
" if ylabel:\n",
|
||
" plt.ylabel(ylabel, fontsize=18, rotation=0)\n",
|
||
" plt.plot(X, y, \"b.\")\n",
|
||
" plt.plot(x1, y_pred, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
|
||
"\n",
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"plt.subplot(121)\n",
|
||
"plot_regression_predictions(tree_reg1, X, y)\n",
|
||
"for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
|
||
" plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
|
||
"plt.text(0.21, 0.65, \"Depth=0\", fontsize=15)\n",
|
||
"plt.text(0.01, 0.2, \"Depth=1\", fontsize=13)\n",
|
||
"plt.text(0.65, 0.8, \"Depth=1\", fontsize=13)\n",
|
||
"plt.legend(loc=\"upper center\", fontsize=18)\n",
|
||
"plt.title(\"max_depth=2\", fontsize=14)\n",
|
||
"\n",
|
||
"plt.subplot(122)\n",
|
||
"plot_regression_predictions(tree_reg2, X, y, ylabel=None)\n",
|
||
"for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
|
||
" plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
|
||
"for split in (0.0458, 0.1298, 0.2873, 0.9040):\n",
|
||
" plt.plot([split, split], [-0.2, 1], \"k:\", linewidth=1)\n",
|
||
"plt.text(0.3, 0.5, \"Depth=2\", fontsize=13)\n",
|
||
"plt.title(\"max_depth=3\", fontsize=14)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 14,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {
|
||
"filenames": {
|
||
"image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_47_0.png"
|
||
}
|
||
},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"tree_reg1 = DecisionTreeRegressor(random_state=42)\n",
|
||
"tree_reg2 = DecisionTreeRegressor(random_state=42, min_samples_leaf=10)\n",
|
||
"tree_reg1.fit(X, y)\n",
|
||
"tree_reg2.fit(X, y)\n",
|
||
"\n",
|
||
"x1 = np.linspace(0, 1, 500).reshape(-1, 1)\n",
|
||
"y_pred1 = tree_reg1.predict(x1)\n",
|
||
"y_pred2 = tree_reg2.predict(x1)\n",
|
||
"\n",
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"\n",
|
||
"plt.subplot(121)\n",
|
||
"plt.plot(X, y, \"b.\")\n",
|
||
"plt.plot(x1, y_pred1, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
|
||
"plt.axis([0, 1, -0.2, 1.1])\n",
|
||
"plt.xlabel(\"$x_1$\", fontsize=18)\n",
|
||
"plt.ylabel(\"$y$\", fontsize=18, rotation=0)\n",
|
||
"plt.legend(loc=\"upper center\", fontsize=18)\n",
|
||
"plt.title(\"No restrictions\", fontsize=14)\n",
|
||
"\n",
|
||
"plt.subplot(122)\n",
|
||
"plt.plot(X, y, \"b.\")\n",
|
||
"plt.plot(x1, y_pred2, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
|
||
"plt.axis([0, 1, -0.2, 1.1])\n",
|
||
"plt.xlabel(\"$x_1$\", fontsize=18)\n",
|
||
"plt.title(\"min_samples_leaf={}\".format(tree_reg2.min_samples_leaf), fontsize=14)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Pros and cons of trees, pros\n",
|
||
"\n",
|
||
"* White box, easy to interpret model. Some people believe that decision trees more closely mirror human decision-making than do the regression and classification approaches discussed earlier (think of support vector machines)\n",
|
||
"\n",
|
||
"* Trees are very easy to explain to people. In fact, they are even easier to explain than linear regression!\n",
|
||
"\n",
|
||
"* No feature normalization needed\n",
|
||
"\n",
|
||
"* Tree models can handle both continuous and categorical data (Classification and Regression Trees)\n",
|
||
"\n",
|
||
"* Can model nonlinear relationships\n",
|
||
"\n",
|
||
"* Can model interactions between the different descriptive features\n",
|
||
"\n",
|
||
"* Trees can be displayed graphically, and are easily interpreted even by a non-expert (especially if they are small)\n",
|
||
"\n",
|
||
"### Disadvantages\n",
|
||
"\n",
|
||
"* Unfortunately, trees generally do not have the same level of predictive accuracy as some of the other regression and classification approaches\n",
|
||
"\n",
|
||
"* If continuous features are used the tree may become quite large and hence less interpretable\n",
|
||
"\n",
|
||
"* Decision trees are prone to overfit the training data and hence do not well generalize the data if no stopping criteria or improvements like pruning, boosting or bagging are implemented\n",
|
||
"\n",
|
||
"* Small changes in the data may lead to a completely different tree. This issue can be addressed by using ensemble methods like bagging, boosting or random forests\n",
|
||
"\n",
|
||
"* Unbalanced datasets where some target feature values occur much more frequently than others may lead to biased trees since the frequently occurring feature values are preferred over the less frequently occurring ones. \n",
|
||
"\n",
|
||
"* If the number of features is relatively large (high dimensional) and the number of instances is relatively low, the tree might overfit the data\n",
|
||
"\n",
|
||
"* Features with many levels may be preferred over features with less levels since for them it is *more easy* to split the dataset such that the sub datasets only contain pure target feature values. This issue can be addressed by preferring for instance the information gain ratio as splitting criteria over information gain\n",
|
||
"\n",
|
||
"However, by aggregating many decision trees, using methods like\n",
|
||
"bagging, random forests, and boosting, the predictive performance of\n",
|
||
"trees can be substantially improved."
|
||
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|
||
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|
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