Morten Hjorth-Jensen
1744 lines
421 KiB
Plaintext
1744 lines
421 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: -1.399819665759832\n",
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"first power: -0.04120453230477482\n",
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"second power: 0.0007267213049602343\n"
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]
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"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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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"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",
|
||
"Test set accuracy with Logistic Regression: 0.94\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"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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",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"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": {},
|
||
"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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ODjabTeswQkpyqBBCiFAIVQ41dcW2QYMG1a4aO5w4ccL5vCdTpkxh/Pjxzr+Li4tp3bo1OTk5lJYmsGsXtG8PaWmhidsMOnfuTF5eHi1atGDr1q1ahyOEENXs2wfduoHr8IlWK/z2W+1le0lJCa1ataJRo0ahD1Jjesuhhw8f5r///S8XX3wxjRs39m9llYQrBj3lUD0cdyGE/0J57uo1h5q6YtuiRQvy8vLcljuWtWzZ0uN69erV83iV+rPPErj//gQqK+0f3ptvQkaGujGbhaN5gdVqJSEhQeNohBCiuvXrqydkgMpKOHAAunSpe/1IaFKrtxy6c+dO7rrrLtavX6/ZtCvhikFPOVQPx10I4b9Qnrt6zaGmrtj26tWLVatWUVlZWa0d97p162jYsCEdO3b0a3v33Vf1IVZWwrhxMGIEhLs12vr16zl58iSxsbH06dMnvG8uhNAtKRt8l55ur1xVVlYti4qCDh20i0lv9JZDzzrrLMrLy4mKivLrfWsK5jxRKwYjicR9FpHJbDk0lOeuXnOoaUa+yMvLY+vWrZSXlzuXjRw5kgMHDvDpp586lx08eJCPPvqIyy+/3O9pCmpemaiogJ07gwo7IFdeeSXnnnsuV155ZfjfXAihW1I2+M5ms98xdOT7qCh4443wX6jUCyPkUIvFQnR0dNBX+oM5T9SKwUgicZ9FZDJbDg3luavXHGqIO7avvPIKRUVF/PnnnwD85z//ITc3F4B7772XxMREpkyZwjvvvMOePXuct9tHjhxJ//79ufnmm/njjz9o2rQpr776KhUVFQENbGGxVE/MergyIYQQIjAZGfY7hjt32styrRNyqJglh+7atYsHH3yQF154gfbt2/v9/mrQQwzhFon7LIQZhPrc1WMONUTF9rnnniM7O9v596effuq8gnzDDTeQmJjocb2oqCi+/PJLJk6cyEsvvcTx48fp27cv8+fPp1OnTn7H8dJL8MAD9qvMerkyIYQQInA2m/nLccmhQgghQkFvOdSiKDUbB4maSkpKSExMpLi4mJKSBM2vTNhsNvbt20daWprzqrveGCFGIcxGzrvQc80HWg/qYxSSQ/1nhBiFMBs570Iv1DnUEHds9SRcVyZyc2HHDnvnbD1dCRFCCCECFUwOVRSFiooKoqKi6uwzFqoc6k8MZhGJ+yyEGUTiuWuawaPMJDMT2rSB88+3/5uZqXVEQgghhLY2btxITEwMGzdurPV1ocyhvsZgJpG4z0KYQSSeu3LHVmdyc+H226uGz9ZyWiEhhBBCNXPnwokTkJ8PqamQnAyFhVV/Q63PtTl8mHmPPUabNm28vkWoc2ibNm2YN29erTGYTSTusxBmEInnrlRsdWbHjupzQkHVlAhSsTUmRVEoLy+nsuYHKzRjtVqJiYmJmKY5QujCQw8FtXoTYCxAdjbMn+/xNaHOoU2aNGHs2LHBb8hAInGfhTCDSDx3pWKrM3qd8Fj4r6KigoMHD1JaWlptbkihDzExMTRq1IimTZuGZPJyIYS6CoFvgOHvvEPy3XdD375urwl1Di0sLOSbb75h+PDhJCcnq7NRnYvEfRbCDCLx3JWKrc44JjweN06mRDCyiooKcnJyKCsrIzExkfj4+IjqvK9njsEUjhw5QlFREcePH6dVq1ZSuRVC5/YAo4D1QPKaNR4rtqHOoXv27GHUqFGsX78+Yn4oRuI+C2EGkXjuSsXWT+EYrbiuCY+3bNmCoihSSdKxgwcPUlZWRuvWrWnQoIHW4QgP4uPjSUxMZO/evRw8eJBmzZppHVLQpGwQZtYTKAbiAAYO9Pq6UObQnj17UlxcTFxcnN/rGlUk7rOITGbLoZF47krF1g/vvgv3329v4mS12q8KZ2SE5r1qmxKhUaNGoXlToQpFUSgtLSUxMVEqtTrXoEEDEhISKC0tJTU11fDJTMoGYWZRQALAmDEe79a6ClUOjYqKirj5iyNxn0VkMlsOjcRzVyq2frjvPlAU+/9ltGLhTXl5OeXl5cTHx2sdivBBo0aNKCoqory8nNjYWK3DEcK0HmA2KZwglQLySaGEZGZMLiTpZAGkpNhfVHD6/45RkR1/z5zJnuJiHomN5Zlp0zhDo33Ys2cPjzzyCM888wxnnKFVFOEVifsshBlE4rkrFVs/OCq1DjJasfDEMfqx9Nk0BsfnJKNWCxFa88jg9D1Xp2sugqFDfVg5M5NTxcUUKAqnTp0KRXg+OXXqFAUFBZrGEG6RuM9CmEEknrtSsfWDxVK9cqvVaMWzZ8+mpKSEhIQExo8fH/4AhE+M3qw1Upjpc5KyQehZUDk0Opp04Ju4OPsgF0EI5jxJT0/nm2++Cer9jSYS91lEJrPl0Eg8d6Vi64eXXoIHHtB+tOLZs2ezb98+0tLSTHHiCSHUIWWDf8IxGKCoElQOjT79c0WFOw9yngghPJGywT96zKFWrQMwkptugqwsWLHC/m+oBo4SQggRWpmZ0KYNnH++/d/MTK0jMr+gcmh0NBuBekeOsHHjxtAE6IONGzdSr149TWMIt0jcZyHMIJTnrl5zqFRs/WSz2fsD6eXKhBBCCP/k5sLtt9sHAYSqwQBzc7WNKxIEnENjYrABsy0WbBomYJvNxuzZszWNIdwicZ+FMINQnbt6zqHSFFkIIURE2bGjKiE7yGCAOhcdTQpwt6JA06aahZGSksLdd9+t2ftrIRL3WQgzCNW5q+ccKndshRCGtGXLFqZPn85rr72mdSjCYNLT7XORu9JqMEDho+hoioGlQPHhw5qFUVxczNKlSykuLtYshnCLxH0WwgxCde7qOYdKxVYIYTinTp3ihhtu4PHHH+euu+7is88+0zokYSA2G7z5pj0Rg7aDAQofRUezC7gM2LV9u2Zh7Nq1i8suu4xdu3ZpFkO4ReI+C2EGoTp39ZxDpSlyiOlxxDAhjO6f//wnGzZs4OmnnyYzM5M77riDwYMH07hxY61DEwaRkQEjRtibTnXoIOWzXjly6ICKaLoDfwJNO3fWLJ7u3bvz559/0lTD5tDhFon7LIQZhPLc1WsOlTu2IfTcc9VHDHvuOftokHroXC2EUf322288+eSTjBw5kkceeYQPP/yQoqIi7r33Xq1DEwYjgwHqm2sOXbkqmhigBZD/p3ZzT8fExNCiRQtiYmI0iyHcInGfhTCDUJ+7esyhUrENkVmzYOLE6iOGTZyov2GxhTCSiooKbr75Zmw2G3PnzgWgT58+PPfccyxatIjPP/9c4wiFEGqomUNPEkM2cCvQ88zdmuXQ7Oxsbr31VrKzs7UJQAORuM9CmEEknrvSFDkEcnNh8mTvzzuGxR4xIrCrHL1796ZVq1akpKQEHqQQBhQVFcVPP/3ktvyee+7hnnvu0SAifZGywZ10BzEeTzn0FNGcAH4HLBzVLIeeOHGC33//nRMnTvj/xgYVifssIpPZcqga567RcqhUbENgxw5QlNpfE8yw2HJXSgjhiZQN1WVmVs21Z7XaB7vIyNA6KlEXTzn0FNF0AtYCrWirWQ7t1KkTa9euDXh9I4rEfRaRyWw5NNhz14g5VJoih4CnYbBr0suw2EIIYUZ6nkBe1M5TDj3lch0+mlOSQ4UQIoSMmkOlYhsCNYfBtlph5Eh9DosthBBmVNsE8kLfPOXQtNbR/AI0BhTLr5rl0F9++YXGjRvzyy+/hP/NNRKJ+yyEGQRz7ho1h0rFNkQyMiAryz4KcnY2fPRR1d9ZWfq/lS+EHhw4cACLxYLFYmHZsmW1vvaee+7BYrFw7rnnotTVF0CYnp4nkBd1q5lDh/wlmubAFOA/HyVrlkObN2/OlClTaN68uTYBaCAS91kIMwjm3DVqDpU+tiFks1W/olzz70BdccUVFBQUkJKSYrr+AEK4atasGe3atWP37t2sW7eOESNGeHzdL7/8wuuvv47VauXll1/GYtFuOhAtSdlQxXHXb9w4+1VmaSljPNVyZkwMzYCJAOmJQW03mPOkWbNmTJw4Maj3N5pI3GcRmcyWQ4M5d42aQ6Vi64+5c+HECcjPh9RUSE6GwsKqv8Hjc4X1Ujl0EFLJJ6G97+t5e27DypXsKy0lLS1Nm+MgRBgNHDjQWbH15t5776WiooLbb7+dPn36hDE6fdmwYQP79u2TsuE0vU4gL/yTmwsciCYRWA/0KS6mURDbC+Y8KS0tZf369fTp04dGjYKJwjgicZ9FZDJbDg323DViDpWKrT8eeiig1ZJPP1RXWBiKrQozMdo47R6ce+65LFiwwGvFduHChaxatYrk5GSefvrpMEcn9E6tljJCG45ROWdXRnMeMAxYv2cPvc87T5N4duzYwbBhw1i/fj29e/fWJIZwi8R9FsIM1Dh3jZZDpY+tkR07Bh7m9BQCsP8ibNMGzj/f/m9mptYRBWTgwIEAHDp0iJ01Ri0oLS1l0qRJADz55JM0bdo07PEJIULDdVTOU0TTFdgBNK3fSrOYunbtyo4dO+jatatmMYRbJO6zEGYQieeu3LE1ujVroG9fraMQgTj7bNi/PzTbrqiovu3KSrj1Vnj00aqhRtXWvDn8/LPqm+3WrRuJiYkUFxezbt06OriMXPD444+Tl5dHjx49uOOOO1R/byGEdlxH5TxFNPWBDsDGvChaaxRT/fr1q5VBkSAS91kIM4jEc1cqtkZ3+m6WMKD9+2HfvvC/p8FYrVb69evHV199xQ8//MD1118PwJYtW3jppZcAeOWVV4gKVYXdINq2bUtBQYHWYRiSCVrsm5JjVE7HHdscYBZwS/SfmsWUk5PDrFmzmDhxIq1aaXfnOJwicZ+FMINwnbt6yqFSsTWyhg3lbq2RhXLqhJp3bF3fM5R3bENk4MCBfPXVV9X62d53332Ul5dz3XXXcV6I+tutXLmSYcOGOf+2Wq0kJCSQlpZGnz59GD16NCNGjAjbKMwvvvgiSUlJjB07Nizv58mRI0d4/vnnWb9+vXOgjSFDhrBy5UrNYqpLbUnX0YezstJeiXrzTZmOTS9cR+U8VRFNKbASuCO2VLOYSktLWblyZUS1EInEfRbCDNQ6d42UQ6Vi64/Zs+2jIhcUQEpK1QjGjr/B43OFsSkcPgQpFJDQzvf13J6Li4P776+KJzkkQ1KJcAlBs91qMjPdx2k36C/2c889F7BP61NWVsYXX3zBN998Q3x8PLNmzQr5+48ePZpLLrkERVEoLS1l27ZtfPbZZ7z77rsMHz6cjz76iKSkpJDH8eKLL9K2bVtNK7YHDx5k+vTpNGvWjD59+nDgwAHNYvFFbUnXtQ8n2P8dN84+CqTWV52FnWNUzvJpMZzxNmwGaNlSs3i6du3K5s2bNXt/LUTiPgthBmqcu0bLoVKx9UdGBiQk+L2aaqMinzxZvWIrRG2MOE67F/379ycqKoqTJ0+yZs0aHjo9Qvmjjz5KyzD8yO3duzc33HBDtWWzZ89m0qRJzJ49m9GjR/Pf//435HHoQYsWLcjJycF2+vsUHx+vcUTe1ZV0XftwOlRU2E8ZA58upmOzAekuP1dOndIsFiGEiBRGzKEyKrJO5ObCihWn5+vzxiofl/CTzQZDhxr+V3p8fDzdu3cHICMjg+zsbNLT03nwwQc1iykqKornn3+eQYMG8b///Y/Vq1c7nysuLmby5Ml06NCBevXqkZKSwujRo9m9e3e1bcyfPx+LxcI333zD9OnTadOmDfXq1aNHjx68//771V5rsVjIzs7mu+++w2KxOB9ZWVlusR08eJBGjRqRmJjIyJEj2a9i3+p69eo5K7V6V1vShao+nK6iouzXgYTOREfzK2ADft21y+1pn3KoCn799VdsNhu//vpraN9IRyJxn4Uwg2DPXSPmULljqwM+t08/3TdyPFCSlkbC+PFhjVMILQ0cOJBNmzY5K3L/+te/iI2N1TYo7BXt1atXs3TpUgYNGkRxcTHnnnsue/fu5ZZbbqFbt27k5eXx6quv0q9fP37++WfatGlTbRuTJ0/m6NGj3HXXXQDMmzeP0aNHc+LECWez4wULFvDggw/StGlT/vGPfzjXTXF0WQASEhI4fvw4PXr04KabbuKXX37hjTfeoKSkhK+++sr5uvLycoqLi33eR71Oo1TXgBWugw85uCZd1z6cri32DVJvjyzR0TQFbgWaNmxY7Sl/+3iNHz+ekpISEgJogdW0aVNuvfVW3Z4ToRCJ+ywiUzBlgx7Vde6aMocqok7FxcUKoBQXF6u+7ZwcRbFaFQWqHlFR9uUeOV50zjmqx6KmtLQ0BVDS0tK0DiXsjh8/rvzxxx/K8ePHtQ7FVN577z0FUADl8ssvV227tX1eK1asUABl1qxZXtdfv369AihXXXWVoiiKct999yn169dXNm3aVO11WVlZSqNGjZQxY8Y4l82bN08BlNatWytFRUXO5UVFRUrr1q2V5ORk5dixY87lbdq0UYYMGeIxjjZt2iiA8sEHH1RbftdddymAsnXrVrf98vVRm7i4OK8xhdLcuVVlp9Vq/9vb66KiqspWT6/LyVGUFStqKXddhDIfmJUqx+zll6vy38KFzsV+51CDiOQcKoQIPbPmULljqzG/26dHRdlfUFERlviE0IsGDRoA9qawL7zwgsbRVHFc2S0pKUFRFN577z0GDx5MWloaBw8edL4uLi6O/v37V7tz6nDnnXeSmJjo/DsxMZE77riDRx55hJUrV3LxxRf7FEvLli0ZNWpUtWXnn38+r776Kjt27KBTp04A9OzZk6+//trvfdULfwas8KWruc0md2l1Lzqao8AfQNejR4k7vTjcfbyOHj3KH3/8QdeuXYmLi6t7BROIxH0WwgyObt/OHx9/TNeGDYk7dgzy8yE1lUKS2fmPQmaRTz6pUAklt+ZTuD2V5LanB7E9/doM4Oox+RRYUmncLpnkA4XwgP05APLzsaWmYktOhu+r1nM8R2pq1cC4+fkBjVXkD0NUbMvKynjsscdYsGABhYWF9OjRg6eeeooLLrigznW/+eYbnn76aX799VdOnTpFx44duffee7nxxhvDEHnd6rrN78ZqlYqtiDgVFRVMnz4dgIkTJ9K+fXttA3JRUlIC2Cu4BQUFHDp0iK+++qpaE2FXVg995bt06eK2rGvXrgBu/XJr065dO7dlTZo0AeDQoUPOZcnJyQwfPtzn7eqNv5WZSK+4miKHxsSwDTgHWJ+TQ+/Ti/3OoUHatm0b55xzDuvXr6d37951r2ACkbjPQhheZibbbr3VXmYCrmduMjDD0zrPet5UwumHERiiYjt27Fg+/vhjHnjgAdLT05k/fz6XXHIJK1asYNCgQV7X+/zzz/nrX//KgAEDmD59OhaLhQ8//JCbbrqJgwcPajrwjIPf7dOjoigtL0cpL8dSWkqjRo3CGq8QWnjppZfYvHkzbdu2ZcqUKVqHU41jKP1OnTqhKAoAw4cPZ/LkyZrEU1JSgsVicSsbHLEBnDx5ksOHD/u8zeahnHM5AOGuzBidKXJodDRdgF+AdJeLRoH08SotLUVRFI/nSV26dOnCL7/8Qnp6emD7YUCRuM8iMgVTNuhKbi7cdltVmal1POEUkgbOKlq3bp1bH7fjx48r7du3VwYMGFDruhdccIHSsmVL5cSJE85l5eXlSvv27ZUePXr4HEM4+lT53D49Lk5JO93vTc99byK5f5D0sVXXokWLlJiYGMVisShff/216tsPto/toEGDFEBZvXq1UlFRoSQlJSnn+NgH3tHHdsaMGW7PPfPMMwqgfPnll85lbdu2rbWPbWxsrNt559iHefPmuS3z9VEbLfvY1tXvxxc5OYqyfLnvfTKN1sfWNDl04cKqTrQvv+z2tD99vIyQn4wQoxBmY5rzbvny6gMP6OhRfPp3RcT2sf3444+Jiori9ttvdy6rX78+GRkZPPLII+Tk5NCqVSuP65aUlJCcnEy9evWcy6Kjo3U5sp/PTeVkyh8RAZYuXcrdd99NYWGhs6nv1KlTddV8tqKigsmTJ7N69WouueQSBg4cCMD111/PnDlz+Pjjjxk5cqTbevn5+aQ6+p+c9tprr1XrZ1tcXMzrr79OUlISQ4YMcb4uPj7erzut3hi9jy0EN02zYyTIn3+Ghx/2fTRdIzJNDo2OZh/wCnDPwYOk1Xg6XM3N9+3bxyuvvMI999xDWlrNKMwpEvdZCENLTweLhX2KYi8zwa3MNCvdV2w3btxIx44d3YbePueccwDYtGmT16Q8dOhQZs6cydSpUxkzZgwWi4VFixbx888/8+GHH3p9z7KyMsrKypx/O35Yh5PXIbhPT/kT9HaE0LE1a9aQnZ1Nw4YNOeuss7j77rvJ0LDGsWHDBhYuXAjYmypt27aNzz77jOzsbC688EIWLVrkfO3TTz/NmjVrGDVqFKNGjaJ///7ExsaSnZ3Nl19+SZ8+fZg/f3617Tdt2pR+/fpx8803A/bpfvbu3cvcuXNp6DK1Sf/+/cnMzGTq1Kl06dIFq9XK5Zdf7veALsH2sX3llVcoKioC7FMHZWdn89RTTwH2SvPll18e8LZrqq0MC6Qy4zo1jKvaBqAyMtPk0OhoioCPgBuOHKnzR5paua/mdoqKivjoo4+44YYbIqaSF4n7LISh2Wzw6qsU3XmnvcxEKra6kZeXR4sWLdyWO5b9+eefXtedOnUqe/bs4emnn3b+6GrYsCGffPIJV155pdf1ZsyYweOPPx5k5IGrdU4+P+7Y+ju3nxB68cwzz/DMM89oHYbT4sWLWbx4MVarlfj4eGw2G0OGDGH06NFcdNFF1V6bmJjImjVreP755/nwww9ZsmQJ0dHR2Gw2Bg0axK233uq2/ZkzZ7Jq1SrmzJnDgQMH6NixI++99x7XXXddtdc9/fTTHD58mDlz5lBUVISiKOzZsyfsI5U+99xzZGdnO//Oyspi6tSpAIwZM0a1iq3aZVjN0ZRrCuVouloxTQ6NjqYbsBOgjjvGan1vPG+nGzt37gxkDwyrW7fI22chDO+mm+h2553sBLbQkYcZy3XDC+hxfkrVKMUFBeAYs8Dx/1qeKySZmY8UkkIB+difSz39/yKSSaKQu0cW0Lp3Ldts1AieeCJ0+x2SBs4qateunXLxxRe7Ld+1a5cCKC+88ILXdcvLy5VHH31Uufrqq5XFixcrCxcuVAYPHqzEx8cra9eu9breiRMnlOLiYucjJycnbH2q6pyTLyXFpz62Ws/tZ5p+CgGQPrbGouXn5ehju2LFClW2Z6bzLhRlWF3djnzZvtH62Jomhy5dWvVBPfGE15f58r3x5TyRHCpE5DHTeZe7pcRZeH3F8IjJobrvsNmgQYNqTZocTpw44Xzem3vuuYf//Oc/vP/++1x77bVcf/31fPPNN7Ro0YL777/f63r16tUjISGh2iNcapvGAvD5jm2d2xFCCB0LRRnmGE3ZE19G0zUi0+TQ6Gh+BzoBv9dyl1mt74237Xz99e906tSJ33//3b8NGtjvv0fePgthdLt2VDrLzN0cAyIjh+q+YtuiRQvy8vLcljuWtWzZ0uN6J0+eJDMzk0svvbTavJExMTFcfPHF/Pzzz5w8eTI0QQfB05em2jQWPvaxrXM7QgihY6EowxxTwziK0agomDULVqyArCxzdtUwTQ6NjiYRuAJIjPbei0qt74237Zx5ZiJXXHGFc6C3SJCYGHn7LITRtW9b4SwzGxALREYO1X3FtlevXmzfvt1t8Il169Y5n/fk0KFDnDp1ioqKCrfnysvLqays9PhcMHJz7R9ubm7g2/D0pal2BcTHim2d2xFCCB0LVRmWkWFPwI5EPGECDB1q3rLRNDk0OhobMAuwuQyoVpNa3xtv2+nb18asWbOwmfUL44HNFnn7LITRpbWodJaZjYmLmByq+4rtyJEjqaio4M0333QuKysrY968efTr1885muPevXvZunWr8zWpqakkJSXx73//u9pV5SNHjvCf//yHzp0719oEy1+ZmdCmDZx/vv3fzMzAt1XzS1PtCogfg0fVuh0hhObGjh2LoigMHTpU61B0KZgyrLZKks2mr0QcSqbJodHRHAd+B44fP17rttTKfZ62c/z4cX7//fc6YzCTSNxnIQyvstJZZvbsFzk5VPejIvfr14+rr76aKVOmkJ+fT4cOHXjnnXfIysoi0yXz3XTTTXz33XcoigJAVFQUEyZM4NFHH6V///7cdNNNVFRUkJmZSW5urnPqDjXUHGlTjWkjvE5j4ed0P+Ga208IIULBWxlW23QuMiJ8FdPk0OhotgB9gPUFBfSuY5tq5b6a29myZQt9+vRh/fr19O5dVxTmEIn7LIThVVRUlZkNjtK7Rnlo1hyq+4otwLvvvsvUqVNZsGABhYWF9OjRgy+++ILBgwfXut4//vEPzjjjDP71r3/x+OOPU1ZWRo8ePfj444/5+9//rlp8tQ1WoXql0mplCXCyUSNilyxReeNCCCNbsmQJJ0+eJDY2VutQ/ObPvKPekm5uLnz/Pdx2m32MRgjuQqNZ5gE3RQ6NjqYj8D3QMScHnnkG8vMhNdX+vOP/jmklanluycUXc7J/f2K9NMOuTceOHfn+++/p2LFjgHtrPJG4zyIymSqHVlZWlZk1+sebOoeGZKxlk6lraOqwTgvQqZP9DRITQ7Bx9ZhpyHR/OaaPOXbsmNahCB8cO3ZMpmfS2Ny5VWWo1Wr/2xtv5e2sWe7LXR/+zqjkLSajTfejB6rk0OnTa59nIpDHmDFh2f9ARHIOFUL4x2O+ys6uKuuuvtr5WrPnUN33sTWCsA7U5Ohjq/KgHWrKzQUPs0tEDMcIomoPrCJCw/E5Wf3ovy7U460ZqrdB+Lzd3Zs82X25g78jQfobkwhOnTk0Nxcef5w84CnAfYznAL3zDvz0k1+r5OXl8dRTT3kcaVotesuh4dhnIURgvOWrvH2VVWWmS4Fi9hwqv+RUEraBmhyZ39u3T2OOAUAOHrT/feyYtvFoISYmhpiYGI4cOaJ1KMIHpaWlzs9MhJ+/8456mobFaq09Ift7oVHmAQ+/WnPojh2gKBQAc4ACNd94zRq/Xl5QUMCcOXMoKFA1Cic95tBQ77MQInDe8lX2nsqqMrO83Pmc2XOoIfrYGkVYBmqyWvkCOH7yJA2++ILLLrssxG/ou5pXaMDe1Sk319j90/xlsVho1KgRRUVFJCYmqjpyqFDX8ePHKSkpISkpCYvFonU4Qfviiy84fvw4DRo00FXZUBtHknUtN2q7Ouy4uzdunD1RRkXBjBnw8MPu21i8GAYM8L/88TcmoQ6vOTQ9HSwWeiiKKndrvwCOAw2AywYO9GvdHj16hOzOpV5zaCj3WQg9MVMObduqguacbuHSpInzObPnUKnYGk1UFHcA+06dIu2OO8jVUds4T1doIESDaOlc06ZNOX78OHv37iUhIYFGjRoRFRVlisqT0SmKQkVFBaWlpZSUlFCvXj2aNm2qdViquOOOO9i3bx9paWm6Khtq4ynJul4d9jT4REaGfSCLnTvtidJmg8aN3bdx9dXqx1RjOlgRDjYbvPVW9RFNgnAHsA9Ia9iQ3L59g96eWiSHCqEtM+XQ5qlVhUleQRQVuZGRQ6ViG0ZqjA52ssK/6X7CydMVGojMuxxRUVG0atWKgwcPUlpaSlFRkdYhiRpiYmJISkqiadOmRPk5jZZQl6ckC7VPOVDz7p63bagdk9BIRgb/16gdd9yfwdvX3kj/1PpQUAApKfbnHf93jIrs5Tnlzjurtpmc7HcYW7Zs4frrr+e9996jS5cuKuxYFb3m0FDusxAieB7z1R/26X6uB65aVsK0NpGRQ6ViGya+zAlVV8U3MxPO3FzVMF4PfW9c1bxCA/bfDZH6gzAqKopmzZqRmppKeXk5lTrtFx2JrFYrMTExcgddR2om2UDmB1e7O4jMA64fmZlw223tUZSLOfdfGbz1VmsyplR/jS85dDTjsTdEDiyHxsXFMWDAAOLi4vxfuQ56zaGh3GchhDpq5qv9f1YSBwwAYoiNmBwqFdsw8OUHWl0VX8c2VlF1Z0kPfW9qclyhOess++AXDRtqHZH2LBaLIedEE0JLYZ0fXOiaI/8pSmtgDooSeA79O7E4KraB5NDWrVszZ84c1fatJj3m0FDvsxBCfXuzKjkH++BRb2CfxzYScqiMihwGdY0O5suw2I5tVNb4yPQ4SqfNBvXqaR2FEMLIPI3cKAM4RaaqHFoGZAFlAefQk1S/yOhvDi0rKyMrK4uyEM7Ho7ccGo59FkKoq42twqXEtI9NEAk5VCq2YeBtaG1Hqx5fhsWOjz+9nOp9AaVlkBDCjMI6P7jQtaoc+jtwBvB7wDm0ZsXW3xz6+++/c8YZZ/D777/7t6KBReI+C2F0zVIqnSXmPoojJodKxTYMav5AA3sS7t/f3nzKlzsTjilRq9+xVTh6NGRhCyGEpsI2P7jQNUcOtVo7AF8DHQLOoTUrtv7m0A4dOvD111/Twey3PVxE4j4LYXgVFThKzLGXJUdMDpWKbZhkZMDatdWTr6O5FNR9Z8KRuF3v2Fowf5MCIURks9lg6NDarzLn5torvwaZnUEEICMDfvghAat1OJAABJZDa1Zs/c2hCQkJDB8+nISEhAD3xHgicZ+FMLzKShKA4UCX9vUjJodKxTaMjhzx3lzK050J1y+a44p1pUvFNinR/E0KhBCitqSbmQlt2sD559v/zcwMf3wiPPbuPUBl5WzggHOZvznUtWIbyIjDBw4cYPbs2Rw4cKDuF5tEJO6zEIZXWckBYDaw6+CJiMmhUrENo7qaS7nemfD0RcvIgMFDrcQDjYDU1Oqdg8x0xUUI4b/4+HgaNWpEvKNDoQnUlnR9GTRImEd8fB4wHchzLvM3h3buHuuSQ6ufJ77k0Ly8PKZPn05eXp73F5lMJO6ziEymyqEVFThKzFfeOx4xOVQqtmHk62AotX3R6sdFsRUoAbZ+/71zHbNdcRFC+G/r1q2UlJSwdetWrUNRRV1J15dBg4R5jBjRi7lzS4iK6gUElkNj42OrcugffzjX8TWH9urVi5KSEnr16qX27ulWJO6ziEymyqGVlfTCXtY1o4VjkelzqFRsw8yXwVBq/aLV7KSLMa+4WCyWao+YmBiaNm1K9+7dGTt2LJ988gmnTp3SOsw6tW3bFovFotn7Hz9+nMcee4yOHTtSv359WrZsyS233MK+ffs0i0kItdSVdGVKoMgTdA51nVO8vBwwZg4VQohaVVQ4/+s68KzZc6hUbDVQ12AotX7RXIdWPv2lNfIVlzFjxjBmzBhGjx7NwIEDOXXqFO+++y4jR46kS5cu/Pjjj5rGZ7FYaNu2raYxeHPixAnOP/98nnzySY4cOcKVV15Jq1atmDdvHmeddRa7d+/WOkQhguJL9w2ZEihybNu2jUGDBnH06LbAc6hrxfbkScC/HOqIYdu2bQHvh9FE4j4LYXiVlWwDBgEHKHQuNnsOlYqtDtX6RXPN1qcrtka+4jJ//nzmz5/Pu+++y5IlS9iyZQs7duxg1KhR7Ny5k2HDhrFp0yatw9Slp556ih9++IEBAwawfft2PvjgA9atW8fzzz9PQUEBt9xyi9YhChEUX5KuTAkUOerVq0eHDh2oV69era+r9XvjoWLrTw71NQYzicR9FsLwKiupB3QAok4PmhcJOdSiKIqidRB6V1JSQmJiIsXFxWEd7j43137FuEMHly/hqFFM/OgjCoGY62/ntYVvAPb+QOPG2eu6ji+ull9Om83Gvn37SEtLI9dDey5H893avn633normZmZnHXWWWzYsCFksdbGYrHQpk0bsrKyPD7ftm1bsrOza92PUDh58iSpqakUFxezYcMGzjrrrGrP9+zZk82bN/Pzzz/Tp0+fsMYmtDNx4kQKCwtJTk5m1qxZWoejGo9loUa0ygdGpqscetVVTPz3v+059MY7eO3d1wDj5VAhhPpMlUP/+1+45BIAisdPZ+Pl0yIih8odWx3z1GR5V3YUi4FM4K33PncOcGG2Ky4Azz//PHFxcWzcuJHVq1e7PZ+Tk8M999xD+/btqV+/Po0bN+ayyy7je5dBtRxWrlyJxWJh7Nix5OXlMXbsWJo1a0aDBg3o3bs37777brXXz58/31n5zs7OrtYfeOjQoR7jnTt3Lj169KBBgwY0b96ccePGUVRUFPRx8GTNmjUUFxfTvn17t0otwMiRIwH4z3/+E5L3F/q0ePFiMjMzWbx4sdahqMqXuWyF+ZWXl1NQUED56b6xdfH0vdmdG1uVQxd85ncO9TcGM4jEfRaRyVQ5tLKScqAAaJgQOTlUKrYGkpsL6350/ciUagNcmO3HX2JiIhdffDEAK1asqPbc2rVr6dmzJ3PmzCEmJoZLL72UM888k2XLljF48GA++OADj9s8fPgw/fv353//+x9Dhw7lvPPO49dff2XMmDFMnz7d+boOHTowZswYAOLi4px9gceMGcNFF13ktt1JkyZx991306JFCy6++GIUReHNN9/kiiuuCMnd3F9++QWA3r17e3zesXzz5s2qv7cQQmjh119/JTU1lV9//TWg9XNzYc1PVU2RLQHk0GBjMKJI3GchDK+igl+BVODX/HytowkbqdgayI4dcIqqwaMsGGeQqEA5phfYsmWLc1lJSQl///vfKSkpYeHChWzdupVPPvmE//u//2Pt2rUkJCRw6623UlBQ4La9//znP3Tq1Ildu3bxwQcf8NVXX/H9998THx/Pk08+6WzyPGjQIObPnw9A06ZNnX2B58+fz8MPP+y23QULFrB582aWLVvGp59+yu+//06HDh1YtWqVW6XccTfYn0fNu8R79+4F7M3VPHEsz87OrvsgCyGEAbRr144lS5bQrl27gNbfsQPKcOlji+J3Dg02BiOKxH0WwvAqK2kHLAHapaRoHU3YRGsdgPBdejrsrXEtwiiDRAWqadOmABQWVo3o9vbbb5OXl8dDDz3E9ddfX+31Z599NlOnTmX8+PEsXLiQBx98sNrzVquVl19+mbi4OOeyvn37cvfddzNz5kxeffVV5s6d63ecTz75JJ06daoW9x133MGECRP4v//7P84//3znc653g33VuXPnan8fOXIEgIYNG3p8vWP/SktL/XofIYTQq6SkJK644oqA109Ph6243rH1P4cGG4MRReI+C2F4lZUkAVcAuPzmNTup2BqIzQb9B0WBS3dTow/LXRdHM17XuWK/+uorAK666iqP65x33nkAHqcK6tWrV7UKqMPo0aOZOXMmq1atCijOCy+80G1Zx44dAcjLy6u2fNCgQQwaNCig9xFCiEhVUFDAp59+ylVXXUVKAHcgbDY4b3g9+Mb+twXF7xwabAxGFIn7LIThVVRQAHwKXHXsGJFy5kpTZI3l5toHq/B10MNOnas+spSmiikGiarNwYMHAWjcuLFzmWOE4oEDB3psttu3b99q67pq06aNx/dxzFX7559/BhSnpybBjRo1AqCsrCygbdYmPj4egGPHjnl8/ujRo9ViEEIIo8vJyeHuu+8mJyfHuczfHHpm76o7tk0a+z/QoqcYzC4S91kIw6usJAe4G8gpKdE6mrCRO7YaysyE22+3Twxvtdrn3aszyUZV9bGtOe+emnJz7f2R0tO1vSO8ceNGALp27epcVllZCdhH/o2rpXlFzea7oWT148NYvXq1382dO3fuXK1vb+vWrQG8TgPhWO6tIi+EEEbTu3dvTp065fw7oBzqMo+t1er/wH41Y/BGLzlUDb7usxBCRyoq6A2cAoig34JSsdVIbm5VQgb7v+PGwYgRdSTBOipQaiTTgH4shEBxcTHLli0DYNiwYc7lNpuNbdu28fDDD/s9R6u3wZQcy1u2bBlgtL7buXMn77zzjl/rDBkypFrFtmfPngBe5/d1LO/Ro0eAUQohhH4FnENdKrZ4GLHeTDlUCBHBHIUjVLspZnbSFFkjO3ZU/86BjyMc1/LlzMy0X5Q5/3z7v475+fzh7ceCFvPDP/TQQxw9epS+ffsyYMAA5/ILLrgAgH//+99+b3PTpk3s2LHDbfn7778P4Nb3NSYmRvUr1WPHjkVRFL8eK1eurLaNgQMHkpiYyK5du9i0aZPbe3z88ccAXH755arGLoQQWtmxYwcjRoxgx44dgedQ14ptDb7kUNcYPNFTDlVLXfsshNChykp2ACOAHR665pmVVGw1kp7ufvPVp9EZo6K4FBgJXOpS2VMrmQb8Y0FFu3fv5pprriEzM5O4uDgya/y6GDduHKmpqTz77LO8+eabzqbJDqdOnWLZsmX89ttvbtuurKzk3nvvrdY3df369bzyyitYLBbuvPPOaq9v2bIlBw4coKioSL0dVEFsbCz33HMPAHfffbezTy3A7Nmz2bx5M0OGDPH7jrYwtksvvZSRI0dy6aWXah2KEKqLiooiISGBqKiowHNobGxVDj09nRz4nkNdY/BEDzlUbXXtsxBmYaocWlFBFJAAEXXuSlNkjdhs9uZJ48bZk15UlI8jHFutvOH4/6RJzsW1JVN/mlM5fizUbMEQqimFxo4dC9grnCUlJWzfvp2tW7eiKArp6eksWrSI7t27V1snKSmJJUuWcPnllzNu3DieeuopzjzzTJKTk9m/fz8bNmygqKiIf//735x55pnV1r3sssv45ZdfaN++PYMHD6a4uJjly5dTXl7Oo48+ytlnn13t9VdccQUvv/wyvXv35txzz6V+/fp06tSJiRMnhuaA+OHRRx/lm2++4fvvvyc9PZ3zzjuP7Oxs1q1bR0pKCm+//bbWIYowe+ONN+p+kRAG1a5dOz766CPn3wHl0NjYqhx6Ov+A7zm0Zgw1hTuHhkNd+yyEWZgqh56ex/YjgObNNQ4mfKRiq6GMDHt/oJ077UnPpwqo61WXigrnf9VKpgFXuAPk6GsaHR1NQkICLVu25KabbuLKK6/kiiuu8HqVqX///vz666+88MILLF26lO+++w6AFi1aMGTIEP72t78xfPhwt/WaNGnCDz/8wOTJk1m2bBklJSV07dqVBx54wFnJdjVjxgwURWHJkiV88MEHnDp1iiFDhuiiYlu/fn1WrFjBjBkzWLRoEZ999hmNGzdm7NixPPnkkx5HahZCCKOqqKjgxIkT1K9fn6ioqMByqGtTZJcR633NoTVjqCncOTQc6tpnIYQOVVRQAZwA6gORcuZKxVZjNpufCc+17ZVLBlYzmQb0Y8FPiodBO/zVvHlzZs6cycyZM/1ar2XLlixYsMCn18bFxfHyyy/z8ssve3zeMfWQJ0OHDlVlP2vToEEDnnjiCZ544omQvo8QRmGm0WhFdb/88gt9+vRh/fr19O7dGwggh7pWbE+edP7X1xzqKYaawpFDw8mXfRZC6ExlJb8AfYD1+/bh65lr9BwqFVuj8XLHFtRNpn7/WBBCCI3JaLTm1rZtWxYtWuScdzwgrhXbL76AbdsgNRWSk8koLOTqMfkUWFJp0gSSfs2HZ+zPUVgI+fm0tdlY9PLLdcZgphyqynEXQoRXZSVtgUVA29RUn1YxQw6Viq3RWK2cDewHmt9xBz9v317t6ZrJ1OhXXoQQvjv77LPZv38/zZs35+eff9Y6HJ/ULKMCLbMCnv5FGEbjxo0ZPXp0cBtZtaoqh375JTXPkoTTD68xAKMtFmjQwHi/+AKkynEXwgDMlEN7Haqwl1cACbWValXbMUMOlVGRjSYqiv3APmB/YWGtL1Vj+h8hhHHs37+fffv2sX//fq1D8UnNMmrs2MDLLDOORiuqO3z4MAsXLuTw4cOBbSA3F157rSqHBhIDsFBROHzbbcaew8cPQR93IQzCTDn08WmV9vIKOHz8eJ3bMksOlYqt0bg2Ra6l/6YZ59ILhqO/6/z587UORQiB5zLqnXcCL7MCnv5FGEZWVhY33nhjrWMb1EqFeVizgBuBLEUx3i++AAV93IUQqqsrh1qViqryyod5bM2SQ6ViazQ1v3VemOXKixDCnDyVUTX5U2Y5Bv9xXPszw2i0orpevXpx4sQJernMP+uX9HSwWIKLAfsoo70sFuP94gtQ0MddCKG6unKolcqq8qp9+zq3Z5YcKn1sjcbHofbj4803l54QwkfHj8Mzz0B+vnNgHMfgNzgGkdD4uT678nmYVBQglXzysb/O8f8ikmlMIb0X5MP3vm0/IzWVq55I5vDuQlKUfBIOpMIzKu+PD32VRGhYrVbq1asX+AZsNnjrLbj11sBjAOqBfTtG+8UXoKCPuxBCdZ6mKHNlpbKqvIr2rbpnhhHdDVGxLSsr47HHHmPBggUUFhbSo0cPnnrqKS644AKf1v/ggw948cUX2bx5MzExMXTt2pWnnnqK888/P8SRh4DrHVsvTZFdRzVzMOqVFyGEH44ds/97+DD84x/axlKHBGCGLy9827/tJp9+iCpmyaG7d+9mwoQJPPfcc7Rr1y6wjWRkwKOPwv799osUGRmQklJ18aKggB+zUvj035BCAfmkUEQyvdjEnbzBbmBC27Y8N2wYAUZgOKocdyGEqjxNUXbDDbBggf33f7Slgt0KTACeKyjwubwy+ojuhqjYjh07lo8//pgHHniA9PR05s+fzyWXXMKKFSsYNGhQretOnz6dJ554gpEjRzJ27FjKy8v57bff2LdvX5iiV1kdd2xrtrkHe1147Vro2zfEsQkhtJOba/9hLkQNZsmhlZWVlJWVUVlXG/a6OPJoo0Ywe3a1p3JzYUAbcH0HqxU2v/0zjH2DSqBMUYKPwUBUO+5CCFXVvMO6bJm9Ygv2O7aVQBnVyzOz033F9scff+T9999n1qxZTJgwAYCbbrqJM888k0mTJvH99997XfeHH37giSee4Pnnn+fBBx8MV8ihVUcfW09t7isr4ejREMYkhNCeCgPjCPMxUw7t0KEDS5cuDel7eMuhx07Z57/tACwdMSKi+vWE47gLITyrawo8xx3Wmje2LEqlvbxyvChC6H7wqI8//pioqChuv/1257L69euTkZHB2rVrycnJ8bruiy++SPPmzbn//vtRFIUjR46EI+TQquOOrVlGNRNC+Ck9XesIhA5JDvWPtxzaqn1s1YKTJ8MblBAiIvkzbWfNi3JRVLj84dv4PGag+4rtxo0b6dixIwk1Buw455xzANi0aZPXdb/99lv69u3LSy+9REpKCo0aNaJFixa88sortb5nWVkZJSUl1R66UUcfW0+jmv3zn/YvfKRO9SNERLDZ7KPGCeHCTDl0w4YNWCwWNmzYoMr2PPGWQ/fss1dsNwCW+fNDGoPehOO4CyGq83fazpoX5axU2ssrYMOuXaEOVzd03xQ5Ly+PFi1auC13LPvzzz89rldYWMjBgwdZs2YNy5cvZ9q0abRu3Zp58+Zx7733EhMTw7hx4zyuO2PGDB5//HH1dkJNUVE8CxwDGl5zjceXuLa5/+knmDzZfkJYrfaEnZGhXjh1NZEQQoTPs3feybFZs2gI9ku8PXu6DYxDSor9xY7/h+i5nT8XsiTTPvgOQOrpgXhueTCZTime1/vxJ1j97wIOnB6wJ4lCrh9eQI/zwxOzT881agRPPBGSzy8UzJRDW7duzVtvvUXr1q2D2s6zzz7LsWPHaNiwocfnPeXQFpWx5AKtgbf69Ak6Bgcj5FC1jrsQeldX2RBOtU3b6a1J8ptvVlWGo6iwl1dAaw85wLQUnWvXrp1y8cUXuy3ftWuXAigvvPCCx/X27t2rAAqgvP/++87lFRUVSteuXRWbzeb1PU+cOKEUFxc7Hzk5OQqgFBcXB70/QXv9dUWx36tVlLffrvWlOTmKYrVWvRwUJSrKvlwNc+dWbd9qtf/tkJaWpgBKWlqaOm8mhKjbF19UnexPPqlpKIGUPzk5imKxhK7MUkNxcbF+8oEPJIcGzvU7nMIB55fy2AVXqLJ9yaFCCG+CzaHP8LBzxfwPV4Qt7rqEOofqvilygwYNKCsrc1t+4sQJ5/Pe1gOIiYlh5MiRzuVWq5VrrrmG3Nxc9u7d63HdevXqkZCQUO2hG67tDOoYobC2qz3B8reJhBAiDFxPeItFuzgIbLL3HTvce1ioVWZFKjPl0MLCQj799FMKwzT6t2sOPYm9KXIh8OGevUHHYKQcGu7jLoQIPodaqaQQ+BT4Y2fkjCCr+4ptixYtyMvLc1vuWNayZUuP6zVu3Jj69evTpEkTomp0mk5NTQUwZiHtui8VFd5fR2gHkgplpVkIESDXWmEdI6iHQ0YGZGXBihX2f+vqBvHzz+7LZPC74Jgph+7Zs4e///3v7NmzJyzv55pDHRXbPcDYnZuCjsFIOTTcx10IYRdMDo2igj3A34HymAOhC1JntP/lU4devXqxfft2t8En1q1b53zeE6vVSq9evSgoKOBkjREMHX2KUhz9qIzEamUb8DuwzUvfKIdArvb4SkZfFkJ/tuXk2MsG0PyOrYPNBkOH1l3u5ObCww+7L//nP/Xb99AIzJRDe/TowaFDh+jRo0dQ29m2bRu///4727Ztq/V1rjm0nBh7DMChfv2CjsFIOVSt4y6E3vlaNoRToDnUSqW9vAKG9oucWRN0X7EdOXIkFRUVvPnmm85lZWVlzJs3j379+tGqVSsA9u7dy9atW6ute80111BRUcE777zjXHbixAnee+89unbt6vVKta5FRfEX4EzgL//6V50v9/dqj69CWWkWQgTmL489Zi8bQBd3bP3h6Q4WwNlnhz8WMzFTDo2OjqZx48ZERwc37uVf/vIXzjzzTP7yl7/U+VpHDv16uf09o4HGihJ0DEbKoWoddyH0zp+yQW88TfcTDTQGouvV0yqssNN9KdWvXz+uvvpqpkyZQn5+Ph06dOCdd94hKyuLTJcJnW666Sa+++47FJemeOPGjWPu3LncfffdbN++ndatW7NgwQKys7P5z3/+o8XuBK+O6X48cUzerDbXkSM7dNBnQhYiYunkjq2vHHewqiVmnd7BMhIz5dA9e/YwdepUnnzySc4444ywva89h1ogNpY9J08ydccOntyzJ+gYjJJDtTruQgjf1cyhVirZA0wFnszLI1LOXN1XbAHeffddpk6dyoIFCygsLKRHjx588cUXDB48uNb1GjRowPLly5k0aRJvv/02R48epVevXixdupQRI0aEKXqV6WyS5VBVmoUQQTLYHVvHHaxx4+x9DfV8B8tozJJDy8vLyc3Npby8POzvDUBsLOUnT5JbVqZaDEbIoZofdyFEndxyqKWScgVygfI6Bps1E4ui+HjbL4KVlJSQmJhIcXGx9iMkf/QRtlGj2AekJSaSW1SkbTxe2Gw29u3bR1paGrl6HOZRCBOyNWnCvsOHSQNyn38exo/XOiS/5ebq+w6WrvKBQejtmAWcn5o0gcOH7V/OHTtCFyCSQ4XQghnOO0cOPTvzDuIXvmFfuGmTfV57HQh1PjDEHVvhQsW7MEaYGF4IESCd3rGtq9wxwh0sEaFi7SMjc3owLcmhQohw8zmHLnK5S6vT3wOhIBVbo3FtinziBDzwAKSmQnIyFBZCfr79b6j6v4fnfl2ez6JvUykkmWQKue4v+XQ/v+71fN0+NUbgFEKEmQ772GZmVs3dabXam02pNaCdML9NmzYxcOBA1qxZ43U055CKjWUTMDAnhwnTNvHUU70i4rus+XEXQgB+5tCKCnt5BazZvp1e3buHL1ANScXWaL79tur/ZWXgw8jInnQHZlTb7umH2ow4V7AQRqWzeWxd5eZWJWSw/ztunH3wHLnbJXzRsmVLZsyYod2MBrGxtASert+A8U+2dJ5uZv8ua37chRD+59DKSlpi/63fsnnzMEaqLX398hG1y82FOXO0jsI/x47BTz9pHYUQkUdnd2w9TedTUWHvCySEL1JTU7nvvvtIdbQMCrfYWFKBe7CiKNVjMPN3WfPjLoTwP4dWVpIK3AcRde5KxdZIduzweYofXVmzRusIhIg8Ibhjm5trnxM7kDE1HFMRuJLpfIQ/SkpKWLZsGSVadXWJjaUE+Kb8BBZL9RjM/F3W/LirpG3btgwdOlTrMEQEC2sOraigBFgGlBw96v8bGpRUbI0kPV13d2F8MnCg1hEIEXlULisyM6FNGzj/fPu/LlOg+sQxFYFjmACZzkf4a+fOnVx00UXs1OrWaGwsO4GLT53i0X/siJjvcm3HfeXKlVgsFucjKiqK5ORkzjzzTMaMGcP//vc/wjn5xosvvsj8+fPD9n6ebNiwgQkTJtC7d2+Sk5NJTk6mb9++vPrqqzJlUgQLew6trGQncBGwMycniMiNRab78YGupirIzCTv1lupAKKAFtpG45UN7FMSNWxIbgRdKRJCS3kvvEDF+PH2suH11+0dcFSQm2tPxK7NoKKiICur9h/znkZvrG06HyOMMqurfGAQah2zkydPkp+fT2pqKrGOEYoDkJeXR0VFBVFRUbRo4Z5FvX4PzzuPk6tXkw+kHj1K/uGGIZuaSk/TjtR23FeuXMmwYcMYPXo0l1xyCYqiUFpayrZt2/jss8/Yu3cvw4cP56OPPiIpKSnksbZt25a2bduycuVKv55T07XXXss333zDX//6V/r06UNFRQVffPEFy5Yt48ILL+R///sfFiPepIgAdZUNgdIkhz50DSc//NBeXu3YQaxOmpTIdD+iuowMWowYAWvX2r/ZBQWQkuIcmXjz8gIWfZOCAjSjgEF/S+GcC0+PWux4Lbit5/dztb3un/+sGhU5OTmsh0eISNYiMbHqDxWbItfWt8dbUvY2eqO36XxkxGRRl9jYWGwq1CBr+8Fa6/cwNpZY7BduIXKmpvLluPfu3Zsbbrih2rLZs2czadIkZs+ezejRo/nvf/8byjB1495772X+/PnUr1/fueyee+7hhhtu4L333mPp0qVcdtllGkYovFGzMutKixy686xKzuB0eeXyXTQ9RdSpuLhYAZTi4mKtQ6lVTo6iWK2KYu+Ia39ERdmXh1Xr1koaKICSlpYW5jcXIoK99VbVyf/WW6pt1t+yJdSv15JR8oGeqHXMsrOzldtvv13Jzs5WKbLq6vweXnSRkg3K7aBkb94ckhgc0tLSdJNDazvuK1asUABl1qxZXtcfNGiQAiirVq1yLisqKlImTZqktG/fXomNjVWaNm2qXHvttcquXbuqrTtv3jwFUL7++mtl2rRpSuvWrZXY2File/fuyuLFi6u9ltO/O2o+9uzZoyiKorRp00YZMmSIsmXLFuWSSy5R4uPjlYSEBOXvf/+7kpeXF8QR8s3nn3+uAMqMGTNC/l5CX7TIoZ9wVVV59eOPods5P4U6h8odWxMJ5IqQN0E1CdTZNCNCRIwQTffj6Nszbpy9TKmrb48/ZVFuLnz4oXpllzCvY8eOsWHDBo4dOxaS7df5vY2N5RiwAThWx0BKRmhW76tgj3tGRgarV69m6dKlDBo0iOLiYs4991z27t3LLbfcQrdu3cjLy+PVV1+lX79+/Pzzz7Rp06baNiZPnszRo0e56667AJg3bx6jR4/mxIkTjB07FoAFCxbw4IMP0rRpU/7xj384101xtDID9u3bx9ChQ/nb3/7GrFmz+OWXX3jjjTcoKSnhq6++cr6uvLyc4uJin/exadOmdb7G0aS8WbNmPm9XmIMWOdRKRVV5VVam1q7onlRsDejNN9/kyJEjxMfHc/vttzuXO0ZMq9mG399m9UE3CZSKrRCaePO77zgCxAO3q9yHKyPDPl+eL30KfS2LXMuamsw8yqwITOfOnflJhenjAs6hsbF0Bn4Ce4c5L8zWrD7Y496jRw8Atm/fDsBjjz3G7t27+eGHH+jZs6fzdWPHjqV79+5MmzbNbQCogwcPsnnzZhJPd7e444476NGjB+PHj+eaa66hQYMG3HDDDTz66KM0a9bMrVm0w86dO/nggw8YNWqUc5nVauXVV19l27ZtdOrUCYA1a9YwbNgwn/dRqWO4miNHjjBr1iwSExO58sorfd6uCC9vZYMawp5Dqawqr05/ryOBVGwN6IknnnAOKuF64vl7RcgTvyeA9kQqtkJo4omlS+2DtgG3h+A89LVPoS9lUc2yxpXZR5kV2go4h7oOnHTypMdtq5JDTcYxQExJSQmKovDee+8xePBg0tLSOHjwoPN1cXFx9O/fv9qdU4c777zTWakFSExM5I477uCRRx5h5cqVXHzxxT7F0rJly2qVWoDzzz+fV199lR07djgrtj179uTrr7/2e189qaio4IYbbmDPnj0sWrSIxo0bq7JdoT5vZYNawplDe3WtgF9dFkQIqdiajD9XhDxRpTmzVGyF0F6Ad2zVakJZV1nkqawBeOEFGDkycisBwrvNmzfzl7/8hW+//dZ5F1BttX5vY2PZDPwF+PbXX+nRrp3b+mp2CdKLYI+7Y/7bhIQECgoKOHToEF999VW1JsKurB5+Q3Tp0sVtWdeuXQHYvXu3z7G08/CZNWnSBIBDhw45lyUnJzN8+HCft+tNZWUlt9xyC0uWLOHpp59m9OjRQW9T6JtucuhtlWz+9XR59ccf9Bg0KPBgDEQqtiYUyEiNjhMxPr7u5g91nrQyjL0Q2gvgApPaTShrK4u8NbWSSq3wJjU1lfHjx5OamhrS9/H6vY2NJRUYD6S+8w78/rtzVoCSXfkUkEr7ejCbfA6QShHJJFFIM/Lp+d9U+B7Iz6ewXiqHDkIq+SS0T62aWSA/Hxz7Vkcf3nAK9rhv3rwZgE6dOjmb7A4fPpzJkyerFqOvomq5c+XanPjkyZMcPnzY5+02b97cbVllZSW33nor7777LtOmTeORRx7xL1hhOLrKoZWVVeWVh++nWUnFVridiDfeCAsXem7+4NNJK3dshdCGaz8vPy8whbsJpRpdJ0Rkad68OVOmTNEugJ07aQ5MAfj3v+2P0xJOPwAe9LTus1X/TT798Elhod9hqi3Y456ZmQnApZdeSkpKCklJSZSUlPh1R3TLli1ufVP/+OMPoPpdWLXmh/3++++D6mPrqNTOmzePRx99lOnTp6sSl9Av3eXQioqq8ipE0xjpkVRsDayiAlasCK65g6cTceFC+zS5R49Wb/7g80krFVshtOfHeajVyMTBdp0QkeXIkSNs2rSJXr16ER8fH/T2/MqhubmwfDlHgE1AL+yDtIXcsWPw00/Qt2843s2jQI97RUUFkydPZvXq1VxyySUMHDgQgOuvv545c+bw8ccfM3LkSLf18vPz3e4Ov/baa9X62RYXF/P666+TlJTEkCFDnK+Lj4/3606rN8H0sVUUhdtuu4158+bxyCOP8OSTTwYdj9A3XebQysqq8urYMeLj4kIThM5IxdbA9u+H888PrrmDt/5AR4/C0KG+vdbtpJWKrRDa8/HOhdYjEwfSdUJEpu3bt3Peeeexfv16evfuHfT2/MqhO3bYYwDOA9YDwUfgozVrNK3Y+nLcN2zYwMKFCwEoLS1l27ZtfPbZZ2RnZ3PhhReyaNEi52uffvpp1qxZw6hRoxg1ahT9+/cnNjaW7OxsvvzyS/r06eM2KnLTpk3p168fN998M2Cf7mfv3r3MnTuXhg0bOl/Xv39/MjMzmTp1Kl26dMFqtXL55ZcT5+eP+mD62E6cOJG3336bnj170qVLF+dxcWjfvj0DBgwIaNtCf3SbQysqqsqr3bvp7aVPu9lIxdaAKiqq/x1Mcwd/pgjy9tr8fPvVKud7Sx9bIbTnwwUmGZlYGEnXrl3ZunWr2xyn/gooh6an22MAtgLBReCn03c6teLLcV+8eDGLFy/GarUSHx+PzWZjyJAhjB49mosuuqjaaxMTE1mzZg3PP/88H374IUuWLCE6OhqbzcagQYO49dZb3bY/c+ZMVq1axZw5czhw4AAdO3bkvffe47rrrqv2uqeffprDhw8zZ84cioqKUBSFPXv2+F2xDcbPP/8MwC+//MKNN97o9vyYMWOkYqt3x4/DM89U9Xv31A/+dH/5n59NZiKFpJJPPvbnUsnnIKlcck0ytnfd16ttm0E95/r/3Nyq8iopKRxHTRcsSl2TbwlKSkpITEykuLjYOWy9llJSbBw86JjUI9e5fMUK97usvsjMdG+j7+3KtetrrVZ7lz5FqXHF+6yzsG3aZJ92JC3NOSm5ECK0bElJ7CsutpcMH34IV19d6+tXrLDfsapJRib2Tm/5wAj0dswCzqGZmeCh0hUKNrDn0IYNyT16NCzvqUfz58/n5ptvZsWKFQwN5AeOEH6wNW7MvsLCGiWDCVgs8NZbuphQO9T5QO7YGlC0h08tmOYOvvZzy82Fdu3s/W+zsuCaa6rGqql2xVuaIguhPR/Ow1COTKzWlAdCOOTm5jJ79mzGjx+PLYgvVcA5NCOD3B49mD1lCuPPOANbu3ZVoyLvLqCAFJo0gaSTBZCSUnVnpcD+d1ExlOwsgNQUiorg68UF5JPiMnpyATdPTiH59ZlQXGx/z2Sfh5kKGbWOuxC6lpuri8Ha1JQLzAbGKwq2CJlQWyq2BtSlS0es1kT+/LMZoE6Twbr6udUcDXn8+OoDsIJLf1up2AqhiY5Nm5JYXEwz8KlLQKhGJlZ7ygMhwH6lf9myZR6bqvojmBxaEhfHsrw8bn3pJTg9jypUHxXZk8xMuP3R6jn0OQ+v630RDP04s6piqwNqHXchdG3HDjoCiWDPoSZQAiwDbgXjT6jtI6nYGtDy5csB+8WlcIwm6mk05BdesP9udq3cOq94Sx9bITSx/NZbwTEth48XmNQemTjcUx6IyNG1a1d+//33oLcTTA4NJAa/c2gtc61qQa3jLoSupaezvOZJaXBdAeeZG46RrHTA71trBw4cwGKxYLFYWLZsWa2vveeee7BYLJx77rluc3yJ4Nls9v5AwfxYzM219yuqrRust9GQH3qoKv9Wu+Itd2yF0IZrOetyHtZ1nqtRljjUNnq6EHqi2xyqs4qtlsaOHYuiKNK/VoSezQb33691FKFhtUbMaJB+37Ft1qwZ7dq1Y/fu3axbt44RI0Z4fN0vv/zC66+/jtVq5eWXX1Zt0myhHl+bC3rrh3f//faH2xVvqdgKoQ3Xk/R0mRvuZsH+jLQuhD9+++03LrvsMr744gvOPPNMzWNYt+7MiMihejjuQoTFBRfAiy/a//+Xv0CPHvyYlcLb/04m8XQ/+EF/S+Gcvjj7ztfsSw/BPVcYm8KUmfb3S8XeD98KTLm1gIR2dWyzxvZ/27ePy954gy8WLeLMAKevMpqAmiIPHDjQWbH15t5776WiooLbb7+dPn36BBygCA1/mgvW1Q/P7QKQzpKyEBGjxh3bn36C227zMshbiC7chqrfrhCNGzfmhhtuoHHjxprHcOJE49DlUJ3dsdXDcRciLFyvPg0dyk8jHqV/P3Btcxr1OWS9FLqclgz0TXcvLxICuCDd+M8/uUFRaOwyHoDZBTTdz+uvv86dd95JkyZNOHjwoNvzCxcu5MYbbyQ5OZnt27fTtGlTVYLVit6mKrj++us5ePAgTZs25b333gtoG96m+ahtugOf+yOddx621atluh8hwuz6Hj04+OuvNAVuum8pl7xyicc5agOdGswf4RoDINz0lg+MQG/HTPc5tHdvbBs3Sg4VIsyuHzKEg//3fzQFHvzb0/Rb8ojkUJXpcrqfgacnCz906BA7d+6kg0sbs9LSUiZNmgTAk08+afhKrR5999137Nu3j7S0tIC3EUhzQW8jJ7tN6yF3bIXQxHdZWThm5yx82Uqlh8uW4WoWXNdI60L469ixY2zdupXOnTvTsGHDgLcTTA51xGCzdcZqbRiaHKqzO7ZqHXch9O6733935tDWnxk/h0biuRtQDaRbt24kJiYCuDVHfvzxx8nLy6NHjx7ccccdwUcoQsLRNMrjwBV+yMyENm3sV67btLH/Xa1iK4OGCaGJCsV9XIMIGj9CmNDWrVvp06cPW7du1TyG0tKtocuhOqvY6uG4CxEWLr9ZKxT3KpLRcmgknrsBVWytViv9+vUD4IcffnAu37JlCy+99BIAr7zyClE6K5xFdRkZkJVlb1KRleX/gDLe+umeKJc7tkJozlL9PLRa4YcffDvPfRnpVYhw69y5M+vXr6dz5866iCFUObSsQl+/nfRw3IUIN8UEOTQSz92AayCO5siud2zvu+8+ysvLue666zjvvPOCj06EXDDTHXibwuD4cRkBWwitPfCgpdrdpDffhL59617P4x0kIXSgYcOG9O7dW9MmdTVjCEkOPamviq0ejrsQ4Tbyaqvhc2gknrsBV2zPPfdcwD6tT1lZGZ988gnffPMN8fHxzJo1S7UAhX45+um6ioqCBnFyx1YIrV18qdXvu0ne7iBpfdVZCIA///yTRx99lD///NMUMXjLofXjXCq2OujOo4fjLkS49Rtg/BwaieduwDWQ/v37ExUVxcmTJ1mzZg0PPfQQAI8++igtW7ZULUAROsE2lfDWT7d+Q6nYCqE5i8Xvu0ne7iDt3Kl6dEL47fDhwyxcuJDDhw/rIobQ5VB93bHVw3EXIixqTJln9BwaieduwDWQ+Ph4unfvDkBGRgbZ2dmkp6fz4IMPqhacCB21mkp47GMkg0cJoY0aSdlf3u4ghWMESCHqcuaZZ5KVlcWZZ56peQzr1p0ZnhyqA3o47kKEnQlyaCSeu0GVno5+tllZWQD861//IjY2NuigRGip3VTC7YqWRfrYCqG5AM5DtUZLF8LMQp5Do/TVFFmIiBRAxVZyqPaCqtg6+tkCXH755Vx88cVBByRCL+RNJXR2tVmIiBTgeRjsSK9ChMoff/xBt27d+OOPPzSNYdCgblRWVo9B1Ryqsxkl9HDchQg7E+TQSDx3o4NZuUGDBgDUq1ePF154QZWARN1uu+02iouLnXMJ+8vRVMKfieX9IhVbITRxW/fuFK9dSyIE1XKitonhc3PtF8fS0+UqtAivhIQERowYQUJCQlDbCSaHJiQkcMEFI8jMTKh2M1XVHKqziq1ax10Ivbtt8GCKlywxTQ6NxHM34IptRUUF06dPB2DixIm0b99erZhEHaZNmxbU+o6mEuPG2a8yq95UQiq2QmhiWr9+sHat/Y8QnIeZmVVNMK1Wezkid3RFuNhsNmbPnh30doLJoTabjbfemk3//iHMoTpriqzWcRdC76ZdfjksWWL/wwQ5NBLP3YA/tZdeeonNmzfTtm1bpkyZomZMbsrKypg8eTItW7akQYMG9OvXj6+//trv7VxwwQVYLBbuueeeEERpLCFtKiGDRwmhjSAHj3LwNNprsP0K9TJhfSQySw49ceIE27Zt48SJE5q8v2sM119/InQ5VGd3bPVw3IUIC9emjCbIoZF47gb0qS1evJjJkydjsVh46623Qj7x79ixY5k9ezbXX389//rXv4iKiuKSSy5h9erVPm/j008/Za3jToYAgptYvqZqJ5wMHiWENlyS8s/rLQFVIr2NmB5M33w9TVgficySQ//44w86d+6seR9bRwwhy6E6q9jq4bgLERYuSW7LNqvhc2hEnruKj7744gulTZs2SkJCggIogDJ16lRfVw/YunXrFECZNWuWc9nx48eV9u3bKwMGDPBpG8ePH1fatm2rPPHEEwqg3H333X7FUFxcrABKcXGxX+tFirlzFcVqVRSw/7vr7KuVtNPfkbTmzbUOT4jIcc899hMRlD78pFit9vPTVzk5Veey4xEVZV9e23OBbtOIjJYPzJRDS0tLlVWrVimlpaVBbUdvMdTMoTv6XVeVQ5s1U+19AqWH4y5EWLz6qjNR3cR8w+dQPZ67oc6hPt+xXbNmDdnZ2Zw6dYqzzjqLuXPn8sQTT6hdz3bz8ccfExUVxe233+5cVr9+fTIyMli7di05OTl1buPZZ5+lsrKSCRMmhDLUsLHZbFgsFmw6GLnFU9OKn9ZLH1shtJD29jwsgA1QsPjd1KmuK8rjx/s/jYHeJqyPNGbKofHx8QwaNIj4+PigthNMDlUrBgdPOXTtj/q6Y6v2PguhVy0ffsSZQyuxGj6HRuK563MN5JlnnkFRFI4ePcqGDRvICNOIIRs3bqRjx45uI3qdc845AGzatKnW9ffu3cs///lPZs6c6RzFWajH4wnn+/USIYSKXM/FytPFuz+VSG+Ty//0k73503PP2d9jwgTf+xXqbcL6SGOmHLp//35mzJjB/v37TRODpxx6StFXxVYPx12IcKisqBqnwgw5NBLPXd3XQPLy8mjRooXbcseyP//8s9b1H3roIc466yyuvfZan9+zrKyMkpKSag/hmacTrlofWxk8SoiwqTZuG/bz0J9KpKfJ5f/5T3j44aof34oC/szuJhPWa8tMOTQ/P5/Zs2eTn5+vyvb0EIOnHKpY9PXTTA/HXYhwiHI59RwVWyPn0Eg8d4OaxzYcjh8/Tr169dyW169f3/m8NytWrOCTTz5h3bp1fr3njBkzePzxx/0LNEJ5mjronL5W+EHryISIPK7XlCqxBlSJzMiAESPsV6g7dKi9GZSv2625TanUho+ZcmiPHj0oKChQfbtaxuAph547MAr+7/QLdHBxWA/HXYhwsNSo2Bo9h0biuauvy4IeNGjQgLKyMrfljqGrvTWNOnXqFPfddx833ngjffv29es9p0yZQnFxsfPhSx+kSFZz6qAOHXX/tRLCnFx+BGdmWgKehsR1tFe1mhKrOYKs8J3kUP2rmUM7d9VXU2QhItFj06ySQw1I9zWQFi1akJeX57bcsaxly5Ye13v33XfZtm0b48aNIysry/kAKC0tJSsri2PHjnlct169eiQkJFR7iLo5f1OHYFJrIYR/+vazqpIApSmxsZkph27dupW+ffuydetWVbantxicOVRn0/3o4bgLEW7duhs/h0biuav7GkivXr3Yvn27Wx8dR9OoXr16eVxv7969lJeXM3DgQM444wznA+wJ+4wzzuCrr74KaeyRoub8Wtt3yDy2QmhOxfmka95RCtPYgUIFZsqhDRs2pHfv3jRs2DCs7xvqGGrm0N+3ulRsddAUWQ/HXYiwcD3fVLxJo1UOjcRzV/d9bEeOHMlzzz3Hm2++6ZxqoKysjHnz5tGvXz9atWoF2JPwsWPH6Ny5MwDXXnutx4T9t7/9jUsuuYTbbruNfv36hW0/zMrTVAWrvvdeGOTm2vsbpKfLHR8hQsqHpOx6PkLt56bNJuesEZkph7Zu3Zo33ngjrO8Z6hg85dCvl3u/Y6tFDtXDcRci7Hy4OKz3HBqJ567uK7b9+vXj6quvZsqUKeTn59OhQwfeeecdsrKyyMzMdL7upptu4rvvvkM5fbWlc+fOzgRd0xlnnMFf//rXcIRvenVO91Otz19VArda7U0z5M6PECFSR1J2PR8dL1UUOTfNxkw59OTJk+Tn55OamkpsbGzY3z8UMXjKoeVepvvRKofq4bgLEXZ1XBw2Qg6NxHNX902Rwd7s6YEHHmDBggXcd999lJeX88UXXzB48GCtQ4t4vk5V4OmqtD+TXgsh/LM/v/aWE67no6JUXYOSc9N8zJJDf/vtN1q1asVvv/1mmhg851D3psha5lA9HHchwu3gYePn0Eg8d3V/xxbs0xLMmjWLWbNmeX3NypUrfdqWooP+KsFauHAhZWVlHqdwCDdPUxUMHmSB76q/To3hzoUQtZvZ5lyabvmGesDgIRYmv+X5qrGn89GVnJvmYpYc2qFDB/73v//Rwd/hRGsIJoeqFYODpxx64YgoXvqy+uu0zKFq77MQejW1+1W0XTOfesDYW6z8rcLYOTQSz11DVGxFdUOHDg3be/nSn8dtfq0ZVreKreOqtGtBEMhw50IIz3JzwbolhRGn/z6lWBk3zn5u1jx3PZ2PruTcFHqUkJDAiBEj6n5hHYLJof7GEFAOfTMKalRstcyhah13IfQsNxf2r2nDuNN//9MEOTQSz11DNEUW2qg5UqNLdyw31ebX8tAvQaYMESK0duwAqLqbpmBxXjWuqeb5aLVW9RGSc1PoVX5+Pi+99BL5+fmGiEGVHHr6DrmWOVQPx12IUNuxAyxU1VQrsRo+h0biuSsVW+FRUP15PCRlkClDhAil9HSIqpGUa7tq7Ho+ZmfD3r1ybgp9+/PPP5kyZQp//vmn7mMIKod6mcdWqxyqh+MuRKiZMYdG4rkrTZENaOXKlc7+QaFqlhxUf55aRmOVKUOECA2bDU51PMCy7VAPsFitdV41rnk+yrkp9KxXr14cPXo06O0Ek0N9jSGoHOqlYgva5FC1jrsQemazQbN+e1i2zjw5NBLPXanYGtANN9zAvn37SEtLIzdEw64F1Z9HxUmthRDuvPXbm5TzI/uANOCnHyy06KtVhELol+5zqGvF1gQDXgqhN95y6PTfP3fm0I3vW0m5WqsIRaCkBiI8Cqo/j1RshQiZWvvtufwIbpEm56Ewl+3btzN06FC2b9+u+xiCyqG13LHVgh6OuxBq8bXve0oz4+fQSDx3jf+piZAJuD+PS8W2/GRgc3nl5trf13VdT8uEiCR+9durpUuAEEYUExODzWYjJibGEDEEnENdKranyrXPoXo47kKowa8caoKbNJF47kpTZFGrgPrzuPygLipWaNPGfuXa16SemVlV8Fit9nXBfVk4O+f7MmWDEKHmV789EyRlIVydccYZLFy40FAxBJRDXSq2JaXa51A1jrvkUKEHkZZD9VBmhpvxPzWhOyVHq3+t/BkN0tvVtNtuC3B0SRX4M2WDEKHk6Lfnymu/PR/v2EpLCGEUp06d4vDhw5w6dcrUMRSWVFVsLWifQ4PdZ8mhQi8iLYfqocwMN6nYCtUdLqr6WjmKBW9zgdXk7WpazfEzfN1esIKaskEIlfnVb8+Hq83yg1MYyebNm2nSpAmbN282dQz5h9z72GqZQ4PZZ8mhQk/qzKGuJ4oJcqgeysxwk4qtUF3jJu5fq7pGg3Rc8YqP93w1reaFM59HlwxSbc1WhFCbL1d+fe63V8fVZvnBKYzmjDPO4JNPPuGMM84wdQypzfWVQ4PZZ8mhIpxUzaF1VGyNkEP1UGaGm1RsheoSEqtn0LpGg3S94tW/P9x4o/vVtLfeCnB0ySD51WxFiCD4c+XXZoOhQz2cA35cbZYfnMJokpOTueqqq0hOTjZ1DMlNXe/YKprn0GD2WXKoCBdVcqgrE+RQPZSZ4SYVW6E+l8IgMaH2K2KerngtXAhr11a/mhbw6JJBCmrKBiF8FJIrv3XcsZUfnMJoDh48yNy5czl48KC5Y3AZPKpRvPY5NJh9lhwqwiEkObSOiq0Rcqgeysxwk4qtUJ/LmR4To9SawLxd8Tp61P1qmk9X2EJAq0q1iBwhufJbR1KWH5zCaPbu3cttt93G3r17zR2DS8U2Orr2czIcOTTYfZYcKkJNcqhneigzw02m+zGgXD014PfEjyHSHVe8XAskvV3xggCnbBDCR2qdB7nnnQfffGP/w4cRHTMyYMQIe/Lv0EG+40LfevfujVJzFKQABJND1YqhVi4VW7dRn2oIRw5VY58lh4pQUi2Hjh4Nc+fa//Dht6zec2hYyiudkTu2Qn1+VGyNcMVLiFBT7Txwzeo+nodatYQQQnjhWrGtg+RQISSHiipSsRXq83HuLwdppiSESueB65VZP89DIfRu586dXHrppezUcHSWsMTgR8UWQp9D9XDchaiLKudBABVbPYvEc1eaIgv1BVAYeGqmlJtr7zeRni5XwkRkCLq5nsmSshCurFYr9erVw6rhdzssMfjRFNkhlDlUD8ddCF8EnUP9nMdW7yLx3JWKrQE9/vjjFBcXk5iYyLRp07QOx53rCRRg2/7MzKoR7qxWexMTuZMrRO0ez8qiGEgEpkVQIhORoV27dnz66adBbyeYHKpWDLXy846tJ2rm0LDssxA68PjGjabKoZF47lqUSOtVHICSkhISExMpLi4mISFB63Cw2Wzs27ePtLQ0fQ4k9fzz2CZMYB+Q1rgxuYcO+bV6bq59DrKagwBkZcmdWyFqY6tXj30nT5IG5J48CTExWodkOnrLB0ag1jGrrKykvLycmJiYoO5ABJND1YqhVkuXYrvsMnsOTUggt7jYr9XVzqFh2WchdMDWsCH7jh+359CdO6F9e61DCooez91Q51B97KUwlyD79hlh0mshdE8nSUwItWzatIn69euzadMmc8cQZKsntXOoHo67EGFngnEqIvHclV8+Qn1B/qAOdNLr3Fz7oAGuF+A9LRPqkmOsUyZIykK4atu2LQsWLKBt27bmjiHIpshq59CcnLb861/aHnczkxyqUya4OKyHMjPcjP+pCf0JsjAIZNj2zEx706vzz7f/m5npeZlQlxzjwITlh4xUbIXJNG7cmBtuuIHGjRubO4YgK7Zq59C//rUxDz54A//+t3bH3awkhwYmLDnUBBVbPZSZ4Wb8T03ojwqDR/kzbHtubtUgGWD/9/bb3ZeNGydXRNXk6bjLMa5bSH/IyHQ/wsQOHz7M4sWLOXz4sLljCGBU5JrUzaGHqaxczO23H5byXUWSQwMTtosBJqjY6qHMDDfjf2pCf1T6Qe3rpNee+hNVVko/3VCTvtD+kx8yQgQuKyuL6667jqysLHPHoMKoyKBmDs0CrqOyMkvKdxVJDvVfyHOoyab70UOZGW4y3Y9QX5gLA0d/Ik9TeNYcFbKuPkbCd56Ouxzj2tX2Q0ZG/Baidj179uTIkSPUr1/f3DGoVLH1Vd05tCdwBKu1vpTvKpIc6r+w5lATVGz1UGaGm/E/NaE/QRYG/vad8NSf6M03/e9jJPwTSD+uSBfooC61UauvkQxgIvQuKiqKuLg4osJc8Qt7DEE2RVY/h0YRFRXHm29GSfmuIsmh/gtrDvXzt6wec6geysxwk4qtUF8QFdtA+0546k/kTx8jERg5xv4bP169HzI1z5eaV7ID3Y4MYCL0aPfu3Vx99dXs3r3b3DEE8SM0FDn0vfd2c9FFVzNsmHbH3awkh/ovlDm0osLlST9+y+o1h+qhzAw3aYpsQEOGDOHgwYM0bdpU61A8C7CPrbe+EyNG+FZo2Wzur/O0TKhLjrFvMjOrvt8WC0yYAPffH/ix83S+9CKO7hTR1I+EHOx5J0S4VFRUUFJSQkW1X5/+CyaHqhVDrQKs2IYqh/btW8E774R4nyOY5FDfhCOHdq5Mpgd5NAWfK7Z6zqFhKa90Riq2BvTee+9pHULtAhwVWfofCrOqmfgUBV54wZ6UPb12xw57k6vavveezpd/0ooeFHGssh6Zmb5d/ZfzThhFeno6y5YtC3o7weRQtWKoVYAV21Cdy2HZZyFqEa4cOomeXEweAAves3LjvXXHpuccGonnrjRFjiBt27Zl6NChoX+jAJsih6LvhBB64Ovol/40Z/J0vlixv0klVp9HipTzTgidCfDisJzLwqzCnUMB7nvAKjnUgOSObZBWrlzJsGHDnH9brVYSEhJIS0ujT58+jB49mhEjRmAJ05ySL774IklJSYwdOzYs7+fJkZMnKTn9/7ziYiwWC0OGDGHlypW1rucYSGHcOHuBpfVACr5e9RPGFM7P15fRL/1tzlTzfAGwYP8RrGDx+Yqx3s47IbzZsGED55xzDj/++CO9e/c2bwyud2xPnYJnnoH8fEhNtS9z/D85GQoLnX/bgE3D8ln8bSqHSaYxhYwemo/t3drXq+u5DXv2cM68eX7vs+RQczNjDnWt2JZXWg2fQ/VQZoabVGxVMnr0aC655BIURaG0tJRt27bx2Wef8e677zJ8+HA++ugjkpKSQh7Hiy++SNu2bTWt2B48coTS0/+PiYrCn5b9GRn2QmjnTnuBpVXB4NqXw2q1F1oyqIN5hPvz9SXxBdKcyXG+rF0L11wDVqXqjq0/V4z1ct4JUZtWrVoxZ84cWrVqZe4YPv206v8nT8I//uHzqt1PP5y+Pf0IQitgDtDq2Wfh/fd9WkdyqLmZPYcCWK0Ww+dQPZSZYaeIOhUXFyuAUlxc7PbcihUrFECZNWuW23OnTp1Sxo8frwDKRRddpFo8w4YNU7p27aoMGzbM7bk2bdooQ4YM8bhebc+p6cS8eUpzUAAlLSlJiYuLC8v7qiUnR1GsVkWxtwGzP6Ki7MuF8Wn5+ebkKMqKFZ7fK9i45s5VlH40VLqCch5Ryty5qoYuTqstHwjP9HbMasuhmsvJURSLRUlz5FDXAkEPjx9/9GkXJIeal5lz6FkkKV1BGQbKvFePqRq7sAt1PpA+tiEUFRXF888/z6BBg/jf//7H6tWrnc8VFxczefJkOnToQL169UhJSWH06NFuQ3LPnz8fi8XCN998w/Tp02nTpg0rVqzgjz/+YNOmTdVea7FYyM7O5rvvvsNisTgfWVlZ1V63detWLr30Uho1akRiYiIjR45k//79qu13vXr1cDakCmAOPq352pdDGJOWn6/NBkOH1t4sKtBpDDIyICfqJH8Auy2VcndEmE5RURGff/45RUVFQW1n+/bt/PHHH2zfvl2zGLzasUN3ebMI+Pz0v6xZU+frJYeam5lz6IGYY/wBbAfG3mL8KlLIyysdMv6nZgAZp39hLl26FLBXas8991xeffVVLr30Ul5++WXuueceli9fTr9+/cjOznbbxuTJk3n//fe56667SEhIAKCwsJD58+c7X7NgwQKaNm1K586dWbBggfORkpLifM2+ffsYOnQorVu3ZtasWVx33XV8+umn3HTTTdXer7y8nIMHD/r8qCaIeWz1QAYCMDc9f77BzGmYmQkVFfYfxJWKRTfz6Amhlt27d3PllVdqPo9tSGNITw94yrxQ2Q1cefpfBg6s8/V6LmNF8PT8+QabQ8vLq/5+e76xf8uCPsrMsAvJfWCTCbQpssP69esVQLnqqqsURVGU++67T6lfv76yadOmaq/LyspSGjVqpIwZM8a5bN68eQqgtG7dWikqKlIURVHS0tIUQImKilKSk5OVY8eqmkvU1RQZUD744INqy++66y4FULZu3eq2X74+qvngg6pmVImJhmuKrCj2JilRUVVNWaRZp7mY7fN1NMFqRpQCKC2wStO/ENFbs1ojUOuYnTx5UsnPz1dOnjwZ1HYcOTQtLU2zGGo1d66umiKfBCUflJM33ujPLpiqjBXVme3zdeTQFGKd512M9ZThc2hYyis/hTqHyuBRYeC4w1pSUoKiKLz33nsMHjyYtLS0anc74+Li6N+/P1999ZXbNu68804SExOrLYuLi6OwsJCVK1dy8cUX+xRLy5YtGTVqVLVl559/Pq+++io7duygU6dOAPTs2ZOvv/7ar/10MvgdW9DvQABCHWb7fB1Nw1zv8+hlHj0h1BITE1OtBZJpY8jIgEcfhf37ISkJJk2CggJwvK/j/44RjEP53IwZxJSW2vf53Xf92gUzlbGiOrN9vp6aV/s6KrKe6aHMDDfdV2zLysp47LHHWLBgAYWFhfTo0YOnnnqKCy64oNb1Pv30Uz744AN++ukn9u/fT6tWrbjsssuYOnVqWEYndlVSYp/8JiEhgYKCAg4dOsRXX33l9ctm9VAx7NKli9uy6Gj7x+dPE4N27dq5LWvSpAkAhw4dci5LTk5m+PDhPm+3GpUqtlpPFWCzGbtAE7UL1eerxffW2TSslqkQRGQyQw51yMrKYvr06UyfPp22bduaOwZHR8G4OJgyJaBNqFIWvfkmWaWlTC8tZXpWll/7LDnU3MyZQ6v6t0dF+T4qsl7pocwMN91XbMeOHcvHH3/MAw88QHp6OvPnz+eSSy5hxYoVDBo0yOt6t99+Oy1btuSGG26gdevW/Prrr7zyyit8+eWXbNiwgQYNGoRtHzZv3gxAp06dUE4PCjF8+HAmT54cthgcolznx6vBERvAyZMnOXz4sM/bbd68edUfAU4u70qmChBGpNX31jFoxqO32v9W0M88ekJbZsihDmVlZezcuZOysrKwv7eeYvCFamVRTAxlwM7yct3vszA+rXPoI7dWLTNDDjVKeaWqkDRwVsm6devc+q8eP35cad++vTJgwIBa112xYoXbsnfeeUcBlLfeesuvOILtYzto0CAFUFavXq1UVFQoSUlJyjnnnOPTezv62M6YMcO5zNE/KCEhQQGUL7/80vlc27Zt/Z7ux7EP8+bNc1vm66OaJUuc/YNaNkrwqY9tTo6iLF9u/zdUQ8m7vocQNb8PwX4/9DDFRZrV3sc2zWoN35tGGCP1sTVCDtVCMH1sw6V5c3uMzZv7FmPIcmjXrvYNxMdLDhXVmDKHRsdU9W0XIRHR0/18/PHHREVFcfvttzuX1a9fn4yMDNauXUtOTo7XdYcOHeq27G9/+xsAW7ZsUT1WTyoqKpgwYQKrV6/mkksuYeDAgVitVq6//np+/PFHPv74Y4/r5efnuy177bXXKC4urrbs6NGjJCUlMWTIEOey+Ph4v+60euPoY+vrw9VXX1f19CsthVOnan+vzExo0wbOP9/+77/+pf5Q8jXfQ0aMjWw1vw9jxwb//dDHFBenW0jobFRVoQ2j59BIlZlp714L9n/rKo9CmkNjYgA4daJccqhwMm0OldRpeLpuirxx40Y6duzoHHzJ4ZxzzgFg06ZNtGrVyuftOeZqbdq0aa2vKysrq3bb3tFHtjYbNmxg4cKFAJSWlrJt2zY+++wzsrOzufDCC1m0aJHztU8//TRr1qxh1KhRjBo1iv79+xMbG0t2djZffvklffr0qTaNjyPmfv36cfPNN1NaWgrYK87PPfccDRs2dL6uf//+ZGZmMnXqVLp06YLVauXyyy8nLi6uzn1wFWgf29xceHmOlSOn/y6jjJNlCrt3Z/PUU08B9krz5Zdf7ny9o9kJ2P+dPdveBKVSpf6Cnt5j3Dj7wAdGb2Yi/Ofp+/DOO1XPB/r9cPTRUet7K0SwjJRDfbFp0yYGDx7M//3f/9GrVy9Vtqm3GBzlk6vayqOQ59CYGDYBg0+VUckmoJfk0AgnOdQ49FBmhpuuK7Z5eXm0aNHCbblj2Z9//unX9mbOnElUVBQjR46s9XUzZszg8ccf92vbixcvZvHixVitVuLj47HZbAwZMoTRo0dz0UUXVXttYmIia9as4fnnn+fDDz9kyZIlREdHY7PZGDRoELfeeqvb9mfOnMmqVauYM2cOx44do3nz5lx66aXOOXIdnn76aQ4fPsycOXMoKipCURT27Nnjd8U2UDt2wCmlqmJ7EvuPm5ycLKZOnQrAmDFjnBVbT1foKithwgR44QX71Tp/J9n2FJO3q4CSlCOPp+9DTYF8Pxx9dMaNU+d7G4jH4uM5UlJCfI0R1EVkMlIO9UWLFi2YPn26x33yx2OPPcaRI0eIj4/XLAZv/M1XIc+hMTG0AKYDE0h1tAmRHBrBTJ1DU1M5sm8f8adbKhhdqMsrXQpJA2eVtGvXTrn44ovdlu/atUsBlBdeeMHnbb333nsKoEyaNKnO1544cUIpLi52PnJycjTrH+ToY+upv5Me5eQoykWW/zn72Daikdc+Ejk5ivLBB4pisXjuU5GToygrVqjTtzaQfht660+kt3iMytP3oeYjmH49an1vA5Kaat+Btm01ePPIoLf+orWRHGo8VeVT2ukxLNK0zaGDBzs3XI/jkkOFuXNot272HYiL0+DNI0NE97Ft0KCBx5G8Tpw44XzeF6tWrSIjI4MRI0bw9NNP1/n6evXqkZCQUO0hfGOzwf0PVHVSsOD5ipujf8Y115x+3elVXK/Q2WwwdKj939xcWLHC/m8gMb35ZtXsCb5cBdRbn1y9xWNknr4PY8b49/2oa/uO723YOUYhN8Fc0iJ4ZsuhJSUlfPPNN6o1bdZjDI7yyZWmOTQmhhLgG6Ce5ZDbe3ijt5ylt3iMzNQ51HEr2iQ5VA9lZtiFpLqskuHDhytdunRxW/7NN98ogPL555/XuY1NmzYpSUlJytlnn62UlpYGFIeWV+iNdsdWURRF+frrqlGR4xq5Pe3pap/Vqiivveb5Ct3cuVWvt1rtfwfC16uAehiZT8/x1MZIV8RzchTlww/tdzzUbCFQ2/uF/Ng0aWL/grRvH8I3iWxGumNrthy6fv16BVDWr18f1HaMEENtoyKHNYdefLGy/nQ+/+/7yyWHhpjk0NrfL+THplMn+xckMTGEbxI+eigza4roO7a9evVi+/btblca1q1b53y+Nrt27eKiiy4iNTWVL7/8MqD+NHqUl5dHbm4ueXl5WofimcuVLouHb5i3PkF33w3LllVf7m3gp0Dv3PpyFVAXI/PpOB5vjHZFfNkyuPZa+x2PNm3sf/t6ldjfux/hOjZ5p06RC+TV1QFKRASz5dBu3bqxZ88eunXrFtR2gsmhasVQF9e7XzWFNYfGxNAN2AMMG9BecmgISQ71Lmw59ORJew4NzebDLlzlla6EpLqskh9++EGhxhx8J06cUDp06KD069fPuSw7O1vZsmVLtXXz8vKUdu3aKS1btlT27NkTVBx6u0Kv+zn4Vqxw3rFNa+TbHVtvV1GXL/f8ulDewNbb1V29xeOJEWJ0FUy8/t79COexSbNY7OdddLT6GxeKougvH9RGcqhnus+hSu0xhjWH/v3vVSv5WGjpLR/oLR5PjBCjK9Pm0CiZCz7UIvqObb9+/bj66quZMmUKkyZN4s033+T8888nKyuLZ5991vm6m266iS5dulRb96KLLmL37t3ccMMNrF69moULFzofNeddFSpznUPT0efPhaN/hqcuDDWvojqGf3cV6uHfA+mTG0p6i8cTo1wRdwg03kDufhjt2AjzMFsO3bt3L3fffTd79+7V5P31EkNYc2hMDHuBu4G9WVl+xaeXnKW3eDwxWp6QHGoMeiivwk3X0/0AvPvuu0ydOpUFCxZQWFhIjx49+OKLLxg8eHCt6/3yyy8A1ZK3w5AhQ7jgggtCEq/Ap073GRnQowf071/7nGVaDf8+YgQsWmSvow8YoH0CzMiwx7Rzp/34aB1PTUabfy7QeAOZOspox0aYi5ly6NGjR1m7di1Hjx4N+3vrKQYIYw6NieEosBY4Wlrqc3ySQ/1jtDwhOdQY9FJehVVI7gObjDSj8tPq1VVNkePja33p3Ln2JiWOpiXemqSEc/j3YAbaMNLAD2rz9bPUizFjqjdtGjOm7nUCbRIVrmMjTZFDT2/5wAj0dsx0n0MV32MMeQ695Zaqwu6333xaRXJoYCSHehe2HCpNkUMu1PnAoige2oqKakpKSkhMTKS4uFgXU//YbDb27dtHWloauYGMohRqa9diO/dc9gFp8fHk1nGVNzfXv6uoubn2q37p6epfdc3NtQ9MUPPKYFZW3e+VmVnVxMZqhZkzoXVr+3Pnnqu/K8Sh4O9nqZVgP+eadz8yMnx7T7WPTc1zwWa1sk9RSIuOJre8XJ03EdXoLR8Ygd6Ome5zKP7FGNIcescd9kIOYONGqGPAMcmhwZEcWvt7hjyHRkezr6KCNKuV3IoKdd5EVBPqfKDrPrbCoFz72PrAnznLQjUynmOEvu+/V6/fyMSJ9tECr7nGnpz1PsKhGjSdf84PgX7OYE/AWVn270tWlm8JGdQ/Nh7PBcd1Sj/PQSGMYPPmzbRo0YLNmzdHdAw1hTSHxsSwGWgBbP7jD68vkxyqDsmh3kkO9Z8ey6tQk4qtUJ9rH1sVGwSoOfWPK9fC7dpr3cuzQPuNuFIUz7H6O+S9CF5mJowe7b7cnz47ofrx4ev3wdu5IISZpaSkcPfdd5OSkhLRMQQqoBwaE0MK9sGjUrxM9yQ5NLJIDjUOI5dXgZKKrVCfD4NHBcLboAP/+lf1Zf4kupqFm6Me7hg90WqFf/6z7sLX08iTNdW8mmm0OevMoObn7WC1aj9Kpj/fB2/nghBm1qJFCx599FFatGgR0TEEKqAcGhNDC+BRoEViots2JYdGFtPnUJN1zjRyeRUoqdgK9YWoYust8c2eXVWJ9TfReSrcFAVuvdV+1bmyEiZPrns7NacT8MT1amao7j6L2nm7K/D++743hwoFf78P3qbwEMLMjhw5wtq1azly5EhExxCoQHLopt9jOIJ9VOQjxcVu60oOjSySQ43FyOVVoKRiK9QXor4JNhuMH+++vLLSfhU3kETnqXCzWuGtt6quPPuaMF37jTz7bPXDUPNqpszLpg1vyWzAAG3icfD3++BtXkYhzGz79u2ce+65bN++PaJjCFQgOfSzL2PZDpwLbPcwj63k0Mhi/hxqrlu2Ri6vAiUVWwP69ttv+e233/j222+1DsWzEN2xBbj/fu/9d/wt2Byj4c2cWb1wGz8+8ITp6DcycSLs3Qsffmh/ZGdXv5rpLTnIvGzq8NYc3Vsy03qgjvXr3ZfV9X3wNADHt8BvwLedO4cmUCE01KVLF3777Te6dOkS1HaCyaFqxaAVf3NomRJDF+zlSpfmzas9JznUvCI2h8bH23Noq1YhijS8jF5eBSQkkwiZjN7m4NO9zZur5rGNi1N9897mM/NnfrSa8+w9+2zVHH+BzrOm1n6I4Pgyh2I450Wui6fvG9i/k35zrNyvn+pxCjvJB/6TY+a/UM61608OnWiZVfXHRx9V24bkUHOK6ByakGBfuXNn1eMUdqHOB3LHVqgvRKMiO3gbKt7XK4memltNmVI1N1q4rkgGOuS98M7X5uj+jsgYypE3vfVZ6tvXzw25nmshbDUhhFZyc3OZOHGipnPP6iGGYPmTQ6+6JoZcYCKQu38/IDnUzCI6h0LVhkySQ81QXvnLHJ+c0JcwzP/lrVD1JdH50mQ5XAnTKHPWGUUo+l2FeuRN1ZrUue64SebgE8JVcXExn3/+OcUeBjGKpBjU4GsO7X9eDMXA50BxSQkgOdTMIjqHgukqtmYpr/wRrXUAwn+LFi3i2LFjNGzYkOuuu07rcNxpXCC4Di7h+reDoxB0Lbw9FYKOK8+h4uiflJ4uSVktvn62vvJ29XrECPU+M8fdjXHj7D8gAr67UVnJIuAY0PDgQXRYMggRlG7durFt27agtxNMDlUrBj1zzaFxR2LoBmwDaNYMkBxqZhGdQ4FF5eX2HFpcbIocGgnlVU1SsTWgSZMmsW/fPtLS0vRfsS0vh2eegfx8SE21L3P8PzkZCgtVf+7HrwpZ81k+B0jlK+C6v+TT/fyq9Wz5+ay9IpXPPoOm5HOQVC65JhnbuwG8X4Ax//gTzhg/JJmb/1rIOW3Cd4zC+lwY39uWmsraK6qObQnJjL28ENtzgW2zcn0+Eyvtz6WSTz6pFFUkUza9EOLV24cM4Oox+RRYUmncLpnkA4XwgJ/bj49nErAPSNuzxxRJWYhQ0H0O1VhmZlVl5GZLDG87nigvB9StSKgRo9Vqj0eaIgdP7c+2tjvAan5fMjLsleWdO6uaxAdiUnm5PYfu3y851KCkYivU98knVf8vL4d//COsb3/O6YfTt6cftb1mUYiDqsHt/T8L7/ubmZrHtjXwT09PqNyUCiDh9EMV5eUwdizMn6/WFoXQ3O+//86VV17JkiVL6NatW8TGEEo177CVKTH8DlwJLNm7F8ceB1uRCOZuazjuAkYytSqJoP4d4NqEuoWAEZm9vPLEHI3IhX7k5oa9IiuE8OCdd+Cnn7SOQgjVJCUlcfXVV5OUlBTRMYRSzTts5cSQBFwNJMXEVHttoP1bg+1zKXPYhp5afZfVGkjM18GnQjlIlRGZvbzyRCq2Ql07doRkJGQhRADWrNE6AiFUk5aWxowZM0hLS4voGEKp5kA85cSQBswA0ho2DHr7vo6660+MoN5dQKkYqS/YgcR8vRAS6kGqjMjs5ZUnUrEV6kpPlxFZhdCLgQO1jkAI1Rw/fpzNmzdz/PjxiI4hlGreYau0xnAc2AwcP3o06O2rcbc1VNMJRVrFKNhKvD/rB3oH2NcLIWpcMDHjTRmzl1eeSMVWqMtmg7fe0joKIcSYMQFO5CeEPm3ZsoWePXuyZcuWiI4h1FzvsM19J4YtQE/g2/V5zopCoJUite62qj2dkCoVIwOZNQtat7ZX4lu3hokT/dvXUFwE8PSd8vVCiCrN010rtia5QRMJ5VVNMniUUF9GBjz6KOzfD0lJMGkSFBRASor9ecf/HSO8hvi5zcsLWPRNCoUkk0whQzoX8N3WFBSgGQUM+lsK51zo+zZ//AlW/7uAA6RgBUYPL6DH+eHbH0/P7SpJ4c1MSKWAfFIoIpkkCrl7ZAGte2tz3EO1/e+2pPDl/9z31flZ9q19myW7C3hmrv37kEQhqRRwkBQmT4akk+p8x647/Z0oKoa3Z9q/K65x3jw5heTEqm36+ro645o8GUpK7KMky8BRwmQ6derEjz/+SKdOnSI6hnBwDsSzIpaGwI/Al18mcGUbuPFGWLAgsBGJ1Rx1V83BgsI1eq8ePPec/WeZg6LYl82e7dtnGYrBu7yNcu3r4FOqDFJV8wtgApFSXrmSiq0IDUcbobg4mDJFszByc+GsR8G1uJq5tfproj6HrJd8L5DPAVrmqjNioFrq5cJz89wL9XtfAHQQn1pyc+H8NtU/T1e+fJbrV8DMue7LR1xkbyoVSEw1v2PPrYCsefY4EtNhUo0fcck1fjgk4dvr6vTUU/aKbY1BXoQwg7i4OPpq3ApBDzGEU35hDKlAX6CQX5hY+Qyp7+QzkdPToFXms+vWVAoP2C/q+TLVmev0Zk2aQNKv+fCMttPU9aqXysNAimNaN5JpTCG9F+TD9+aZMq9kVz6H3k5lMi5T2Dku8p7+LIu2Q1KZ9206psFzrkc++RWplE2naho8P+IsKoaSZ+3fqSKSSaospOTWfAq3p2JLhE3D8ln8bSqHT38mo4fmY3u3+jZt+Pa6uqbMczJJs+RIK69AKrbC5Dxdha0pkKuyehtWXg/zCoZDXZ+nL5+l2tMP1HWl39epE9ScYkEIM8rLy+ONN95g3LhxtGjRImJjCKdjn/6XPOANYBzfcmHNufMc/JwMQdXpzVSQjH2ALDdve1poXAl42U9Xz9b+tNrT4CUBD9YSR/fTDycPUzj68zqfmGTKvEgrr0D62BpS8+bNSUtLo3nz5lqHonue+vPUFKo51dTgTz8mtfsc6VFdn6cvn6XaA4/40mfM14Ezgp1iQcoGYWYHDx5k7ty5HDx4MKjtBHOeqBWDIeTm0mbRDA4Cc4EI2GMR4ZoDaaf/NcOUeRFVXp0md2wN6Oeff9Y6BMPwdCfzhhtg4UL939n01uekNnq7k6y2mp+nY3wHRfHvs/Tn7mhurv2ubHq659fp6W65lA3CzLp3706uCqP5BHOeqBWDIezYgUVR6A5EyB6LCOdWMqxZY+hBGCOqvDrNoigmaUgeQiUlJSQmJlJcXExCgp4az+iXzWZj3759pKWl6eKkyq3RJzY3F9autVeIzj1Xf5XB3Fz7SIM1m8tmZekn1roqfKF+b8fnCaFrvuvPxYWa3zFhTpIP/CfHzH+6yKG5ufYhc+VnoohUP/5o6IqtHoU6H0hTZBERajbxXLYMrr0WrrlGn/PVqTJ0fQg4mkbPmqXtfH+un2ewzXe98Xf6h1DFIYSw++OPP+jRowd//PFHRMcQNqen7/sD6AFEwB4LUcUEU+ZFVHl1mjRFFhEnFEPVq82XAY7CfcfU9e6lKz0ePzVE0vQPQhhBo0aNGDp0KI0aNYroGMIqI4NG3bszdNo0Gp13HlgszinTFKqmXSshmRmTC6umTANNpoPzZ1q3QpI5tKuQVEsBCe1CP/Xd6t+T+eK9QlJOHzN8PX4hjitUz+38uZAlme77esuDyXRK0fG0gmVlcOmlhq/UQgSWV0jF1pDGjRvH4cOHady4MW+88YbW4RiOESosdfXbDKT/bTBqXgyoSW/HTw1qj54cDlI2CDNr1aoVL730UtDbCeY8USsGI2l1zjm89N//Ov/2NmXaNQFOmRYKCUB6f/ccmnQ6T2qRQ4fUMlUd6Ov4qaF+LkzyNA3heHQ7DaGzbMjL4w0TVGwjsbySiq0BLV261Nn3RvgvHBUWNe6mehvgSIs7znVNs6P3Cl8g9DQolK+kbBBmduLECXJzc7HZbNSvXz/g7QRznqgVg5HU3GfJof6THCo5VAuRWF5JH1sRcdSe7qWmzEz1+p966repRf/b2qbZMUKyClQkTKEkhFH88ccfpKena97HVusYwq3mPksO9Z/kUMmhWojE8kru2IqI5M90L/4Ix5VgLZrIerry+s9/wtln+3/8tBxNORC1TaFktH0RwsjS09NZsWIF6enpER1DuHnaZ8mh/pEc6vk5o+2L0URieSV3bEXECsUotuG4Ehzqq+Xe1LzyOmGC/8dPzSvxtXGM3hzKWTLCtS9CCDs9DISihxjCzds+Sw71j+TQ6iSHhl4klldSsRVCRZ6aG4XiSnC4m/c4khwE/kPG3+lzAhWOZBmufRFCVDlw4ACzZs3iwIEDER1DuIVznyWH1r4NyaHCH5FYXknFVogagrlSGc4rweGaN1WtJBeOK/HhSpZ6nWdYCDPbv38/M2bMYP/+/REdQ7j5u8+SQ6uTHOpOcmh4RGJ5JX1shXChxhQAoep7pAVf+zv50k8mHP2awjWVkxGnAhLC6Hr27Mnhw4cjPoZw82efJYdWJznUM8mh4RGJ5ZXcsRXiNDWvVIbrSnCo+XJV1der0eG4Eh+uZmxa9dESQgi9khzqTnKoZ5JDRahIxVaI06RpjLu6kpy/P2RC3a8pnMlSpjEQIry2bdvGgAED2LZtW0THEG6+7rPkUHeSQ72THBp6kVheSVNkAxo9ejSFhYUkJydrHYqpSNMYd3VNsB5Is6Xahv5XQzibsYV6X/wlZYMws/r169OtWzfq168f1HaCOU/UisFIfN1nyaHuJIfWTnJoaEVieWVRFEXROgi9KykpITExkeLiYhISErQOxxBsNhv79u0jLS2NXAMNc5eZ6Z6AIvUqomufH/Cc5HJz7U2nav6QycrSV7ISQi2SD/wnx8x/kkONT3KoEO5CnQ8M0RS5rKyMyZMn07JlSxo0aEC/fv34+uuvfVp33759jBo1iqSkJBISErjyyivZvXt3iCMWRmXWpjH+jlJZs8/PsmWe+ztJPxkh9M8sObS8vJy8vDzKy8s1eX+9xBBu/uyz5FA7yaFCDyKxvEIxgGuvvVaJjo5WJkyYoLzxxhvKgAEDlOjoaGXVqlW1rldaWqqkp6crqampysyZM5XZs2crrVq1Umw2m3Lw4EGf37+4uFgBlOLi4mB3JWKkpaUpgJKWlqZ1KGGVk6Moy5fb/9WLuXMVxWpVFLD/O3du7a/Pyal6veMRFVX7PuXkKMqKFZ5fo8djIkSgjJgPzJJD169frwDK+vXrg9qOEWLQUw4N53HXY76QHCqMSg9lZk2hzqG6r9iuW7dOAZRZs2Y5lx0/flxp3769MmDAgFrXnTlzpgIoP/74o3PZli1blKioKGXKlCk+x2DEHzJa01NSDhd/k184BJJgly+v/nrHY8UK/99fj8dEiGAYLR+YKYcWFRUpX3zxhVJUVBTUdowQg55yaLj2WY/5QnKoMDI9lJk1RXzFduLEiUpUVJTbAXjmmWcUQNm7d6/Xdfv27av07dvXbfmFF16otG/f3ucY9PZDplOnTkqjRo2UTp06aR2KV3pKyuEQSPILh0ASrFr7otdjYmZGKBuMTm/5oC6SQ90Z4TyRHKqPfCE5NLIYoWwwulDnA933sd24cSMdO3Z062B8zjnnALBp0yaP61VWVrJ582bOPvtst+fOOeccdu3aRWlpqcd1y8rKKCkpqfbQkyNHjlBaWsqRI0e0DkWc5ss0B/720VFDIHPSqdXnR29TP2hx/MNNygZRk5lyaEFBAXPmzKGgoCCo7QRznqgVg5GEY58lh7qTHBp+ZsuhkVhe6b5im5eXR4sWLdyWO5b9+eefHtc7fPgwZWVlAa07Y8YMEhMTnY9WrVoFGr6IEHUlP18nYFdbXQnWW6JSYwCQcE307gutjr8QWjNTDs3NzWX8+PGajhKshxjCLRz7LDnUneRQEaxILK90X7E9fvw49erVc1vumJPp+PHjXtcDAlp3ypQpFBcXOx85OTkBxS6MJZirkbUlP38nYFebtwRbV6Ky2TyP4ugrvYz2qPXxF0JLZsqhZ511FmVlZZx11lmqbM+oMYSbr/ssOdR9nySHCi1FYnml+4ptgwYNKCsrc1t+4sQJ5/Pe1gMCWrdevXokJCRUewhzU+NqpLfkp4fmRDUTbLgSVc1jMmKE9x8+oWrmpIfjL4RWJIeKcJAcKjlUCD3QfcW2RYsW5OXluS13LGvZsqXH9Ro3bky9evUCWldEFjUTlKcrtHpqTuQQzkTlOCbLlnn/4RPKZk56PP5ChIuZcuiOHTsYPnw4O3bsCOv76i2GcKtrnyWH2kkOFXoTieWV7iu2vXr1Yvv27W6DT6xbt875vCdWq5Xu3bvz888/uz23bt062rVrR6NGjVSPVxhPqBOUXpoTuQp3oqrth0+or3zr8fgLES5myqHR0dGkpKQQHR0d1vfVWwzhVtc+Sw61kxwq9CYSyyvdV2xHjhxJRUUFb775pnNZWVkZ8+bNo1+/fs5BKfbu3cvWrVvd1v3pp5+qJeZt27axfPlyrr766vDsgNC9cCQoNQaSUFO4E1VtP3zCceVbb8dfiHAxUw4944wzWLx4MWeccUbY31tPMYRbXfssOVRyqNCnSCyvdF+F79evH1dffTVTpkwhPz+fDh068M4775CVlUWmS1uLm266ie+++w5FUZzL7rrrLt566y0uvfRSJkyYQExMDLNnz6ZZs2Y89NBDWuyO0CFHgho3zp4MQpWgbDZ9XeHMyLD319m50/4DJJSxOX74uCZf1x8+tT1Xl9xce2JPT699H/R2/IUIBzPl0IqKCo4ePUpcXBxRjhpFBMYQbnXts+RQyaFCnyKxvCIks+Oq7Pjx48qECROU5s2bK/Xq1VP69u2r/O9//6v2miFDhiiedicnJ0cZOXKkkpCQoMTHxyuXXXaZsmPHDr/eX2+Tyxth4nYjxFhTTo590nWjTH6ek2OfPN4o8c6da59c3jHJ/Ny5vj1X1zYdE9hbrb6vZ1ZGPO+MRm/5wBdmyaHr169XAGX9+vVBbSeY80StGOqip3PZ132WHBpakkNDT0/nnRrCVV75I9Q51KIoLpdnhUclJSUkJiZSXFysi9Edv/jiC44fP06DBg247LLLtA7HI5vNxr59+0hLSzPd/Fm+Xt0MpczMqj41Vqv9arkRmgbl5nq/ul3bc9621aaN+1XqrKzIvapshLLB6PSWD4xArWNWWFjIN998w/Dhw0lOTg54O8GcJ2rFUBc95VC191lyaOAkh4aW2XJouMorf4Q6h0rF1gfyQ8Z/ekrKatJDMjRbMgr0R86KFfYRID0tHzpUtfCEqEbygf/kmPlPcmjoSA61kxwqtBDqfKD7waOE0AtvIw/+9FNo5o7zRg9zyqk1X14wUxTIFARCRJZDhw4xf/58Dh06FNExhJta+yw5tIrkUBEOkVheScVWCB95S4b9+4dm7jhvtE5Gas2XF+wUBTIFgRCRJTs7m5tvvpns7OyIjiHc1NpnyaF2kkNFuERieSVNkX2gt2ZU69ev5+TJk8TGxtKnTx+tw/HIjM2oPDVfqilczZkyM91HoAxHcy41m3Cp1QwqNxfWrgVFgXPPjeykbISywej0lg+MQK1jpigKFRUVREVFYbFYAt5OMOeJWjHURU85VK19lhwqOVTvzJZDw1Ve+SPUOVT30/0Id1deeaVuEp5Z+NJHpeaUBjWH14eq5kyhTgzhnGbAVW1NuPyNoa7pC3y1bFn1Plv//Cecfba2A5NoRcoGYWYWi4Xo6OB/tgRznqgVg5H4ss+SQ30jOVTfzJZDI7G8kqbIIuL50yzIdZLyH37QtjmTzWa/KhvqxOPaF0jNJlxqNIPy1BRr0qTwNmsTQoTHrl27uOKKK9i1a1dExxBude2z5NDaSQ4VWonE8koqtiKiBdJHxZEM+/bVR/8UtQah8KTmD5Zly9TdZ9cfOVlZ/jcF83T128Hf/kZCCCH8Izm0dpJDhQivyLo/LUQNwTYL0qo5k0Mop07w9oMlK8v+qG0uPX+mHrDZAj9unppiuQpXszYhROi1b9+ezz//POJjCLfa9llyqHeSQ4XWIrG8kju2IqKp0SwoXM2Zagp2RMS61PWDxdM+qzXao69qNsWqSaYuEMI8FEXh1KlTaDnmpR5iCLfa9llyqHeSQ4XWIrG8koqtiGhGHu4+1HPx+fuDxdOPhNtvt89RGEquTbFmzTLmZymEqNvGjRuJiYlh48aNER1DuNW2z5JDvZMcKrQWieWVVGxFxAu2j4pWQj0Xn78/WDz9SKistM9RGI6rzkOHwoQJxvwshRB1a9OmDfPmzaNNmzYRHUO41bXPkkM9kxwqtBaJ5ZXMY+sDvc1bqKf57bwxQoyB8LfvS6iFYy6+3Fzf+j/VNkdhuOYmjHRmPe/0RG/5wAj0dsyMcJ4YIcZASA6t/XWSQ7Vl1vNOT0KdD+SOrRA+CnffF1+E40q5r/2fHFena14BB3WbdwkhIlNhYSEfffQRhYWFER1DuKm1z5JD636d5FChpkgsr6RiK4QPQj3IRDC0GnjDk4wM7ecmFEKY0549exg1ahR79uyJ6BjCTY19lhzqG8mhQk2RWF7JdD8GtGXLFhRFwWKxaB1KxAh2SgOz8tSszDE3Yc3mXZF8nMJFygZhZj179qS4uJi4uLigthPMeaJWDEaixj5LDvVMcqi+/H97dx5U1Xn/cfxzBURQkEExomJQI1oNqbECajoak1pjtTqxuKTT1mS0mkysbY3Lz5k6aNUkWkc70Way1HFJ6sS4VSc6rWZptdbQWKy2BpdQtwiJS8JiABV4fn84UAmg3HOXc+4979cMk8m551y+5zs85+Nz71nCLUPdeLxiYhuC4uLi7C7BdRp71pvbP0G90/P/7H42oVtxbEA4i4iI8Ms1Wb6ME3/VEEr8sc9kaENkqPOEW4a68XjFqchAM4TyIw0CoTmnlTnp9C4Aoe/MmTN64oknbD8V2e4ags0f+0yG1keGIhjceLxiYgs0U6g+0iAQmjqtbMsWZ1wzBSD8VFVV6fLly6qqqnJ1DcHmr30mQ/+HDEUwuPF4xeN+msFpjypYuXKlSktLFR8fr1mzZtldTqO4ZXp4u9NjCb5+ShWCJxSODaHOaXkQCpzWs1AYJ2RoeCNDnSkUjg2hLtB5wMS2GZwWyqEQeKFQI3xz+/P/vo5n7tmDcRd4TsuDUOC0noXCOAmFGuEbMtR5GHeBx3NsAdjq009vnTr29WN87WllK1c23IZn7gHwtyNHjig6OlpHjhxxdQ3B5sZ99icyFHZx49hlYgugSWvX3jpd6pFHbv137dr6r3fpIo0fzzP3AARely5dtHLlSnWx8WssJ9QQbG7cZ38hQ2EnN45dJrYAGtWcuzZK3O0SQHAkJSXp2WefVVJSkqtrCDY37rM/kKGwmxvHLhNbAI1q6q6NjZ0exd0uAQRaSUmJdu/erZKSElfXEGxu3Gd/IENhNzeOXSa2ABrVs6d3p0fd6Zl7TV1jBADNVVBQoNGjR6ugoMDVNQSbG/fZH8hQ2M2NY5eJLYBG+ev0qLtdYwQAzZGenq7CwkKlp6e7uoZgc+M++wMZCru5cewysYUr8GmnNb6eHtXca4wA4G6ioqKUnJysqKgoV9cQbFFRUaquTtbf/hbFsdtLZCjs5MbjFRNbhD0+7fTNnU6PuhtvrjECgDs5d+6cpk6dqnPnzrm6hmBbvvycUlKm6pFHzpGhFpChsIsbj1eRdhcA7/Xv318pKSmuusuZVU192jliBHccDIbaa4xuD2YeYxA4HBsQziorK3X8+HFVVlb69D6+jBN/1RAqPv1U+r//q5R0XFIlGRpkZGhwhVuGuu14JTGxDUm7du2yu4SQcadPOwnlwKu9xmj69Ft95zEGgcWxAeGsV69eOnTokM/v48s48VcNoeL0acmYXpL+t89kaPCQocEVbhnqtuOVxMQWYY5PO+03ZcqtT/c/+eRW3wlkAAgNZKj9yFCg+bjGFmGNB587gy/XGAGAJB09elSJiYk6evSoq2sIpi5dpAULjkpKlHSUDLUJGQor3Ha8kvjGFi7Ap50AEPo6duyo+fPnq2PHjq6uIdieeaajqqrmq3//jsrMJEOBUOHG45XHGGPsLsLpSktL1bZtW5WUlCg+Pt7ucjRmzBhdvnxZSUlJjr0eoEuXLrp48aI6d+6sT7kvPRAUoXBsCHVOy4NQ4LSehcI4IUOB4AuFY0OoC3Qe8I1tCMrLy6sLPACoxbEB4aysrEz//Oc/9a1vfUtxcXGW38eXceKvGkKJG/cZ7hRuGerGscs1tgAAwPFOnz6tYcOG6fTp066uIdjcuM9AOHDj2OUbWwAA4Hh9+vTR6dOn1cXGizydUEOwuXGfgXDgxrHr+G9si4uLNW3aNCUlJal169YaNmyY8vLy7rpdTU2N1q9frzFjxiglJUWtW7fW/fffryVLlrjqQcUAAPcKpwxt1aqV7rvvPrVq1cqW3++UGoLNjfsMhAM3jl1HT2xramo0atQobdq0STNmzNDy5ct16dIlPfzww3f9Wr28vFxPPfWULl++rKefflq//e1vlZmZqZycHI0cOVLcMwsAEM7CLUMvXLigmTNn6sKFC0H/3U6qIdjcuM9AOHDj2HX0qchbt27V3//+d23ZskXZ2dmSpAkTJigtLU05OTnatGlTk9u2bNlSBw8e1ODBg+uW/fSnP1VqaqpycnL03nvv6Tvf+U7A9wEAADuEW4aWlZXpL3/5i55++umg/l6n1RBsbtxnIBy4cew6+hvbrVu36p577tG4cePqliUlJWnChAnauXOnrl+/3uS2LVu2rBfItR5//HFJUn5+vv8LBgDAIcItQ/v06aNjx46pT58+Qf/dTqoh2Ny4z0A4cOPYdfTE9siRI+rfv79atKhfZmZmpsrLy3Xq1Cmv3/Ozzz6TJLVv394vNQIA4ERkKADATRx9KnJRUZGGDBnSYHlycrIkqbCwUOnp6V695/LlyxUfH6+RI0c2uc7169frfZJdUlIi6dZDhZ2gpqam7r9OqenrQqFGINww7gKvtq+hcJ+GcMvQ48eP6wc/+IG2bdumvn37Wn4fX8aJv2q4GyeN5WDtM2A3J407f3Di2A10hgZtYltTU6MbN240a93o6Gh5PB5VVFQoOjq6weu1d/eqqKjwqobnn39e7777rl5++WUlJCQ0ud4LL7ygRYsWNViekpLi1e8LtKKiIrVt29buMu4oFGoEwg3jLvCuXr0a1B6Tof/T2CnSVvgyTvxVw904aSwHa58Buzlp3PmDE8duoDI0aBPb/fv3a9iwYc1aNz8/X71791ZMTEyj1wDVPmogJiam2b9/8+bN+tWvfqUpU6bomWeeueO68+fP16xZs+r+v7i4WPfee6/Onz8fVn/ogVZaWqqUlBRduHBB8fHxdpcTEuiZNfTNe/TMmpKSEnXt2lWJiYlB/b1kqPswRr1Hz6yhb96jZ9YEOkODNrHt3bu31q1b16x1a0+TSk5OVlFRUYPXa5d16tSpWe+3b98+/eQnP9GoUaP0yiuv3HX96OjoRj/lbtu2LX+8FsTHx9M3L9Eza+ib9+iZNV+/bjXQyFD3Yox6j55ZQ9+8R8+sCVSGBm1i27FjRz355JNebdOvXz8dOHBANTU19RqQm5ur2NhYpaWl3fU9cnNz9fjjj2vAgAF6++23FRnp6MuKAQBogAwFAODOHH1X5OzsbH3++efavn173bIrV65oy5Yt+v73v1/vE+GCggIVFBTU2z4/P1+jRo1Samqq3nnnHa9OuwIAIJSRoQAAN3H0R6/Z2dkaOHCgnnrqKX388cdq3769Xn75ZVVXVze4McWjjz4qSTp79qykWw8lHjFihL788kvNmTNHu3fvrrd+jx49NGjQoGbVER0drZycnEZPrULT6Jv36Jk19M179MyaUOobGRra6Jv36Jk19M179MyaQPfNYxz+zILaUP3jH/+oiooKZWRkaMWKFRowYEC99VJTUyX9L5TPnj2rbt26Nfm+kydP1vr16wNUNQAA9iNDAQBu4fiJLQAAAAAAd+Loa2wBAAAAALgbJrYAAAAAgJDGxBYAAAAAENJcPbG9fv265s2bp06dOikmJkZZWVnat29fs7a9ePGiJkyYoISEBMXHx2vs2LH673//G+CKncFq37Zv366JEyeqe/fuio2NVa9evfTcc8+puLg48EXbzJe/tdsNHz5cHo9HM2bMCECVzuNr3zZv3qxBgwapdevWSkhI0ODBg/X+++8HsGL7+dKzd999V8OGDVP79u2VkJCgzMxMvfHGGwGu2BmuXbumnJwcPfbYY0pMTJTH4/Hq5kjFxcWaNm2akpKS1Lp1aw0bNkx5eXmBK9gByFBryFDvkaHWkKHeI0OtcUyGGhebNGmSiYyMNLNnzzavvvqqGTRokImMjDQHDhy443ZlZWWmZ8+epkOHDmbZsmVm5cqVJiUlxXTp0sVcuXIlSNXbx2rf2rVrZ9LT082CBQvM66+/bmbOnGlatmxpevfubcrLy4NUvT2s9ux227ZtM61btzaSzLPPPhvAap3Dl77l5OQYj8djxo8fb1555RWzevVqM336dLNx48YgVG4fqz3buXOn8Xg8ZvDgwWb16tVmzZo1ZsiQIUaSWblyZZCqt8+ZM2eMJNO1a1fz8MMPG0lm3bp1zdq2urraDB482LRu3dosXLjQrFmzxvTp08fExcWZU6dOBbZwG5Gh1pCh3iNDrSFDvUeGWuOUDHXtxDY3N9dIMr/5zW/qllVUVJgePXqYQYMG3XHbZcuWGUnmH//4R92y/Px8ExERYebPnx+wmp3Al7598MEHDZZt2LDBSDKvv/66v0t1DF96dvv6qamp5te//rVrQtmXvh06dMh4PB5XhMntfOnZ8OHDTadOnUxlZWXdsps3b5oePXqYBx54IGA1O0VlZaUpKioyxhjz0UcfeRXKmzdvNpLMli1b6pZdunTJJCQkmCeeeCIQ5dqODLWGDPUeGWoNGeo9MtQ6p2Soaye2c+bMMREREaakpKTe8ueff95IMufPn29y24yMDJORkdFg+Xe/+13To0cPv9fqJL70rTGlpaVGkpk1a5Y/y3QUf/Rs0aJFpmvXrqa8vNw1oexL3yZOnGiSk5NNdXW1qampMWVlZYEu1xF86VlWVpbp27dvo8uzsrL8XquTeRvK48ePN/fcc4+prq6ut3zatGkmNja23j90wgUZag0Z6j0y1Boy1HtkqH/YmaGuvcb2yJEjSktLU3x8fL3lmZmZkqR//etfjW5XU1OjY8eONXi4fe22BQUFKisr83u9TmG1b0357LPPJEnt27f3S31O5GvPzp8/rxdffFHLli1TTExMoMp0HF/69t577ykjI0MvvfSSkpKSFBcXp+TkZK1ZsyaQJdvOl549/PDDOn78uBYsWKBPPvlEBQUFWrx4sQ4fPqy5c+cGsuyQd+TIEfXv318tWtSP1MzMTJWXl+vUqVM2VRY4ZKg1ZKj3yFBryFDvkaH28GeGRvq7uFBRVFSk5OTkBstrlxUWFja63RdffKHr16/fddtevXr5sVrnsNq3pixbtkwRERHKzs72S31O5GvPnnvuOT344IOaNGlSQOpzKqt9+/LLL3XlyhUdPHhQ77//vnJyctS1a1etW7dOP/vZzxQVFaXp06cHtHa7+PK3tmDBAp05c0ZLly7VkiVLJEmxsbHatm2bxo4dG5iCw0RRUZGGDBnSYPntfU9PTw92WQFFhlpDhnqPDLWGDPUeGWoPf2aoaye2FRUVio6ObrC8VatWda83tZ0kS9uGA6t9a8ymTZu0du1azZ07Vz179vRbjU7jS88++OADbdu2Tbm5uQGrz6ms9u3atWuSpKtXr+qtt97SxIkTJUnZ2dlKT0/XkiVLwjaUfflbi46OVlpamrKzszVu3DhVV1frtdde049+9CPt27dPAwcODFjdoc6fx8VQQYZaQ4Z6jwy1hgz1HhlqD38eF107sY2JidH169cbLK+srKx7vantJFnaNhxY7dvXHThwQFOmTNGIESO0dOlSv9boNFZ7VlVVpZkzZ+rHP/6xMjIyAlqjE/k6RqOioup9i9GiRQtNnDhROTk5On/+vLp27RqAqu3ly/icMWOGPvzwQ+Xl5dWdDjRhwgT17dtXP//5z135D8Pm8tdxMZSQodaQod4jQ60hQ71HhtrDnxnq2mtsk5OTVVRU1GB57bJOnTo1ul1iYqKio6MtbRsOrPbtdkePHtWYMWN0//33a+vWrYqMDO/PV6z2bOPGjTp58qSmT5+us2fP1v1IUllZmc6ePavy8vKA1W03X8Zoq1at1K5dO0VERNR7rUOHDpJunWoVjqz27MaNG1q7dq1GjRpV7xqXqKgojRw5UocPH9aNGzcCU3QY8MdxMdSQodaQod4jQ60hQ71HhtrDnxnq2oltv379dOrUKZWWltZbXvuJSr9+/RrdrkWLFkpPT9fhw4cbvJabm6vu3bsrLi7O7/U6hdW+1SooKNBjjz2mDh06aM+ePWrTpk2gSnUMqz07f/68bt68qYceekjdunWr+5FuBXa3bt20d+/egNZuJ1/GaL9+/XT58uUGQVJ7fUxSUpL/C3YAqz27evWqqqqqVF1d3eC1mzdvqqamptHXcEu/fv2Ul5enmpqaestzc3MVGxurtLQ0myoLHDLUGjLUe2SoNWSo98hQe/g1Q725fXM4+fDDDxs8q6qystLcd9999W7Lfe7cOZOfn19v2xdffNFIMh999FHdshMnTpiIiAgzb968wBdvI1/6VlRUZLp37246depkzpw5E6ySbWe1Z/n5+WbHjh0NfiSZ733ve2bHjh2msLAwqPsSTL78ra1atcpIMq+99lrdsoqKCtO9e3fTp0+fwBdvE6s9q6qqMgkJCSYtLc1cv369bnlZWZnp0qWL6d27d3B2wCHu9KiCwsJCk5+fb27cuFG37K233mrwDL7Lly+bhIQEM3HixGCUHHRkqDVkqPfIUGvIUO+Rof5hZ4a6dmJrzK3nJkVGRpo5c+aYV1991QwePNhERkaav/71r3XrDB061Hx9/l9aWmp69OhhOnToYJYvX25WrVplUlJSTKdOncylS5eCvRtBZ7Vv3/zmN40kM3fuXPPGG2/U+9m7d2+wdyOorPasMXLJM/iMsd638vJy07dvXxMVFWVmz55tXnrpJZORkWEiIiLMnj17gr0bQWW1Z0uWLDGSzIMPPmhWrVplVqxYYb7xjW8YSebNN98M9m7YYvXq1Wbx4sXmmWeeMZLMuHHjzOLFi83ixYtNcXGxMcaYyZMnG0n1JhZVVVVm4MCBpk2bNmbRokXmd7/7nenbt6+Ji4szJ06csGlvAo8MtYYM9R4Zag0Z6j0y1DonZKirJ7YVFRVm9uzZpmPHjiY6OtpkZGSYP/3pT/XWaepAeeHCBZOdnW3i4+NNmzZtzOjRo83p06eDVbqtrPZNUpM/Q4cODeIeBJ8vf2tf56ZQ9qVvn3/+uZk8ebJJTEw00dHRJisrq8G24ciXnv3hD38wmZmZJiEhwcTExJisrCyzdevWYJVuu3vvvbfJY1RtCDcWysYY88UXX5gpU6aYdu3amdjYWDN06NB630iGIzLUGjLUe2SoNWSo98hQ65yQoR5jjGn+icsAAAAAADiLa28eBQAAAAAID0xsAQAAAAAhjYktAAAAACCkMbEFAAAAAIQ0JrYAAAAAgJDGxBYAAAAAENKY2AIAAAAAQhoTWwAAAABASGNiCwAAAAAIaUxsAQAAAAAhjYktAAAAACCkMbEFAAAAAIQ0JrYAdPDgQXk8Hnk8Hr399tuNrpObm6s2bdrI4/Fozpw5Qa4QAABnIkMBZ/AYY4zdRQCw39ixY7Vr1y717t1b//nPfxQREVH32smTJ/XQQw/p6tWrmjx5statWyePx2NjtQAAOAcZCtiPb2wBSJJeeOEFRURE6MSJE3rzzTfrlhcWFmrEiBG6evWqRo8erd///vcEMgAAtyFDAfvxjS2AOlOnTtXatWvVrVs3nTx5Ul999ZWGDBmif//73/r2t7+tvXv3KiYmxu4yAQBwHDIUsBcTWwB1Ll68qJ49e6qiokKrVq3Sjh07tH//fqWnp2v//v1KSEiwu0QAAByJDAXsxanIAOp07txZM2fOlCT98pe/1P79+5Wamqo///nPjQbytWvXtHDhQo0ePVodO3aUx+PRk08+GdyiAQBwADIUsBcTWwD1zJw5Uy1a3Do0JCYmau/evUpOTm503StXrmjRokXKy8vTgAEDglkmAACOQ4YC9om0uwAAzlFVVaXp06erpqZGklReXn7H64GSk5P16aefqnPnzqqsrOTaIQCAa5GhgL34xhaAJMkYo6lTp+qdd95RUlKSunXrpsrKSuXk5DS5TXR0tDp37hzEKgEAcB4yFLAfE1sAkqS5c+dqw4YNatOmjXbv3q2lS5dKkjZs2KCPP/7Y5uoAAHAuMhSwHxNbAFqxYoVWrFihqKgobd++XRkZGZo0aZIeeOABVVdXa/78+XaXCACAI5GhgDMwsQVcbuPGjZo7d648Ho/Wr1+v4cOHS5I8Ho8WL14sSdq1a5cOHjxoZ5kAADgOGQo4BxNbwMX27NmjKVOmyBijlStX6oc//GG918eMGaOsrCxJ0rx58+woEQAARyJDAWdhYgu41KFDhzR+/HhVVVVp3rx5+sUvftHoerXXCR08eFA7d+4MYoUAADgTGQo4D4/7AVxq0KBB+uqrr+663qOPPipjTBAqAgAgNJChgPPwjS0AAAAAIKTxjS0An6xZs0bFxcWqqqqSJB07dkxLliyRJA0ZMkRDhgyxszwAAByLDAX8x2M4PwKAD1JTU3Xu3LlGX8vJydHChQuDWxAAACGCDAX8h4ktAAAAACCkcY0tAAAAACCkMbEFAAAAAIQ0JrYAAAAAgJDGxBYAAAAAENKY2AIAAAAAQhoTWwAAAABASGNiCwAAAAAIaUxsAQAAAAAhjYktAAAAACCkMbEFAAAAAIQ0JrYAAAAAgJD2/3GXkAA+XztFAAAAAElFTkSuQmCC",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"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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61ql9D0qMGTOGEnMSPoWELUHo5Pbbb8crr7yCZ599FrNmzVLcRphpVbNACoOmfEZWC6VjHT16FACwadMmxeRIAsePHwfAz05u2bIFDz/8MNatW4cNGzYAAPr06YP77rtP9f140ict6urqcNJJJ8Fg8L2TSHs+cyVhKszeiwfqu+++G0lJSVi6dCmeffZZxyz/FVdcgeeff97twyBBEIS/0Lqvaa0TRIwWapauiIgIicjUiydjkzAG9+nTB1deeSXS0tIcFt2FCxeiublZ8Rxq79nTz6Jnz56KY5gw9riz8gnjtjh/gxLCuD18+HB88803WLx4Md5++2288cYbAICMjAw89dRTGDt2rOZx9FBTUwPGGA4cOKBpDRX6BPDlde6++24kJyfjkksugclkcliVX3jhBdXvIRgQrl+170p4TlC7zongh4QtQegkNjYWCxcuRG5uLhYuXOhi/QOcA2hlZaXiMQ4dOiTZTg9KFlVh/7vuukuS1EGLvn37orCwEDabDT/99BP++9//4qWXXsLs2bORmJjocMHytk9aJCQkOGajfS1uO+Izl8NxHP75z3/in//8J44cOYLi4mK88847WLNmDcrKyvDTTz/pdssmCIIgnOgZm6qqqvDqq69iyJAh2Lx5M7p06eLY/9ChQ+12UdXD4cOHFccwYexxJ4aEMWjdunUYP368rnNmZWXhP//5DxobG7F161asW7cOr732Gq644gr88ssvjkRT3iL06dxzz8UPP/zgdvu2tjYsWrQIaWlp2LFjB1JSUhzrGGN4+umnPTp/eXk5CgsLPdqnPRmVBwwYAIPB4PBqkyO0m81mr89BBBYStgThATk5OXjuueewYsUKRZckweXpu+++A2NMIgAZY/juu+8k23lLRkYGOI7zyvXLYDBg6NChGDp0KEaOHInRo0fjk08+cQhbQaCJLZbtZdiwYdiwYQO+/fZbt7PMnp4/Li4OAwYMwO7du3HgwAEXNy2hDFF7P3OBpKQkTJw4ERMnTsThw4fx9ddfY/fu3ZJYXYIgCMIztMamv//+G4wxXHTRRRJRCwDFxcV+6V9bWxs2b96MzMxMxfPL42blDB8+HACwefNm3cJWIDY2FmPGjMGYMWOQkJCAhx9+GF988QXy8/M9Oo6c7t2749RTT8Xvv/+O2tpaRyUCNQ4fPoy6ujpceOGFElELAD/88IPHZXKEGFtPaI+wjY2NxbBhw7Blyxbs3btXkhmZMYYvvvgCXbt2xXnnnef1OYjAQsmjCMIDjEYjFi9ejNbWVsWba9++fTF27Fj8+uuvLvXfli9fjt9//x3jxo3THV+rRq9evXDttdeipKQES5YsUYxR2bp1K06cOAEA+PXXXxUtmkJbTEyMo61Hjx4A4FGCK3fMnj0bAJ+sSXDHEmhra5P0zZvz5+TkoLW1FfPnz5d8Fj/99BMKCwsRHx/vKH3kDd98843LZ9za2up4L+LPjyAIgtCH3rFJECAlJSUSl2eLxYL58+f7oac8999/P1paWiTnf/HFFxEdHY3rrrtOc9+rrroKffv2xXPPPeeY5BbT2toqqUG/efNmNDU1uWynNG63h9tvvx0nTpzAjBkzJC7HAnv27EF5eTkAPnFUbGwstm/f7ni+AHiXZj3ljuQIMbae/LWXvLw8AHB5Xli2bBn+/vtv3HjjjYoJu4jQgCy2BOEhV155Jc4//3zJACRm6dKlOP/88zFjxgysW7cOp512Gn799Vd88sknSE5OxtKlS33Sj9deew1//vkn5s2bh9WrV2PkyJFISEjA/v378cMPP6CsrAwVFRXo0qULvvjiC9xzzz3IzMzE4MGDkZSUhL///huffPIJYmJiHMITAMaNG4dnnnkGeXl5uOaaa9C1a1ekp6crul7r5fLLL8fdd9+NZ555BmazGVdffTVSUlJw4MABfPXVV7j77rsxd+5cr88/b948fPrpp1i9ejV+//13XHjhhaiqqsJ7772HtrY2rFixAt27d/e6/xMnTkRcXBxGjBiB9PR0tLa24osvvsBvv/2GSZMmudTDIwiCINyjd2xKS0vDNddcg/fffx/nnXceLrzwQlRWVmL9+vW48MIL8ddff3V4X9PS0nD8+HEMGTIEEyZMcNSxPXLkCF566SW3SZ2io6Oxdu1aXHbZZbjgggswbtw4nHnmmeA4Dnv37kVxcTGSkpIciZqeeuopbNy4EaNHj0b//v0RExOD7du346uvvsKAAQNw9dVX++R95efnY8uWLSgqKsKmTZtw0UUXoXfv3qisrMQff/yBrVu34u2330a/fv1gMBgwa9YsPPvsszjrrLMwYcIE1NfX4z//+Q/S09PRu3dvn/TJEz766CNH1YM9e/Y42gQxfsopp+C+++5zbJ+Tk4P33nsP77zzDvbs2YMLLrgAu3fvxgcffID+/fvjscce8/dbIHyJ3woLEUQIIa9jK2fTpk2OeoHyOraMMVZeXs5uueUWlpaWxiIiIlhaWhq75ZZbWHl5ue4+CLVWN27cqLrNiRMn2NNPP83OPfdc1rVrVxYbG8v69+/PJk6cyFatWuWoz/fbb7+xOXPmsLPPPpslJSWx6OhoNmDAAJaTk8N+/fVXl+M+/fTTzGw2s8jISAaAXXDBBY518mU5SnVsBd5//302duxYFh8fz6Kjo1m/fv3YzTffzH755Rfd51eqw8cYY8eOHWMPPfQQGzx4sKN27WWXXcaKi4tdttX6bJXqD7722mvsyiuvZOnp6SwmJoYlJSWxYcOGsaVLl0rq/hEEQQQKrXqhSvc1Afn9UKuOrdK9lzHt+74WnoxNDQ0N7K677mL9+vVj0dHRzGw2s0WLFrGWlhbFcUmrT1rvRelYwvZHjx5leXl5LDU1lUVHR7OzzjqLvf322y7H0Pq8LRYLmzNnDjObzSw6OprFxcWxU089lU2fPp199dVXju0+++wzNnXqVHbyySez7t27s27durHTTjuN3X///ay6ulqx7+7Qet/vvfceu+iii1hiYiKLjIxkJ510EhszZgx79tlnJedraWlhjz/+uKP/ffv2ZXfddRdraGhQPL7WdekLhOtX7U/peaWpqYk98sgjbODAgSwqKor16tWLTZ8+nR06dKhD+kj4D44xyrNNEARBEARBEEr069cPABxWQIIgghOKsSUIgiAIgiAIgiBCGhK2BEEQBEEQBEEQREhDyaMIgiAIgiAIn/DNN984yqxpMXTo0HZlqyeAwsJCXe7REydO9FnJO4IIZkjYEgRBEARBED7hm2++0VWbNCcnJ2SEbbDG1hYWFuLbb791u12/fv1I2BKdAkoeRRAEQRAEQRAEQYQ0FGNLEARBEARBEARBhDTkiqwDm82GgwcPonv37uA4LtDdIQiCIAIEYwwNDQ3o3bs3DAaaG9YDjaEEQRAE0PFjKAlbHRw8eBB9+vQJdDcIgiCIIGH//v0wmUyB7kZIQGMoQRAEIaajxlAStjro3r07AP5LiIuLA267DVi1il85eDCwaxf/+osvwC6+GPL56DYYcPjrX9Dr3JP812mCIAjC59TX16NPnz6OcYFwj8sYqsGBA8DppwPi7B8GA/DLL8BJNIQSBEGENB09hpKw1YHgOhUXF8cPymJXqoQE5+sDB1SOYMO+nZWIG3tqh/WRIAiC8B/kUqsflzFUg//9TypqAcBmAyorgVNpCCUIgggLOmoMpQAhb2htdb4WzzikpUEpxXQbjEjNHNTh3SIIgiCIUMZs5i20YoxGYBANoQRBEIQbSNh6g5qwjY8HN3WqZFMbOGzOWYa0DIrFIgiCCHosFmDNGtTeuxh7pj6MyvWlge5Rp8JkApYv58UswP9ftoxvJwiCIEIDiwXYuJH/70/IFdkbWlqcr8XCtqkJyMx0xt8COLr0PWTNnOzHzhEEQRBesXIlMGMGACDB/sdWL8KuUTkYvKkwcP3qZOTmAtnZwO7dvKWWRC1BEEToUFAA5OXxYSQGAz9ZmZvrn3OTxdYb1Cy2zc2A1SrZtKe5h586RRAEQXiNxcKPxDI4AOaSIrLc+hmTCRgzhkQtQRBEKCEMpTYbv2yzAfn5/rPckrD1BjVh29TkImzR1uafPhEEQRDeU1bmmrXIDgeg4bNN/u0PQRAEQYQYZWVOUStgtfIeOP6AhK03aAlb+bdJwpYgCCL4MZtVVzEA3S/N9F9fCIIgCCIECXQCQBK23uCBKzIJW4IgiBDAZAL+7/9cmhmAslE5SB2f4f8+EQRBEEQIEegEgCRsvUGcPKprV+drckUmCIIIXcaOdWmyJveixFEEQRAEoZPcXKC8nM+KXF7uv8RRAGVF9g7BYhsZCcTEONvJFZlQgDGG1tZW2OTXBhEwDAYDIiMjO6xAOBGiKNyvI2IiA9ARgiAIgghdTKbAJP8jYesNgrCNipII22Mbt6LbYJPytkSnw2q14vDhw2hoaEArXQdBR2RkJLp3746ePXvCKPjMEJ0buceNWhvhUywWPuGI2UxZkAmCIAjvIWHrDSKL7a9Lv8Pp9uZuH74FBj6DpgOy2HZKrFYr9u/fj+bmZsTHx6Nbt24wGo1kIQwCGGOwWq04duwYamtr0djYiD59+pC4JZTv1yRsO5RA1jskCIIgwgsStt5gF7ZWGHDKVy9LVrnIFhK2nZLDhw+jubkZffv2RWxsbKC7QyjQrVs3xMfHY9++fTh8+DBSU1MD3SUi0CjdrymEoMNQq3eYnU2WW4IgCMJzKHmUN9iTR1ltHIxQrnvogIRtp4MxhoaGBsTHx5OoDXJiY2MRFxeHhoYGMJUapkQnglyR/Uqg6x0SBEEQ4QUJW2+wW2wNXWNhdbXRSiFh2+lobW1Fa2srunXrFuiuEDro3r274zsjOjnkiuxXAl3vkCAIgggvSNh6g/0BOKJbLEpyVkA84exi8yFh2+kQsh9TzGZoIHxPlLWaIGHrXwJd75AgCIIIL4Je2B47dgwLFizApZdeih49eoDjOBQWFurev7a2Fnl5eUhOTkbXrl0xduxYbN++vX2dEiWPyirMRcOdCx2ruLQ06bYkbDstlCgqNKDviXCgJGJDfMIjKMdQEYGsd0gQBEGEF0EvbA8fPoxHH30Uv//+O8466yyP9rXZbLjiiivw9ttv49Zbb8XTTz+NqqoqjBkzBmVlZd53yh5ji0i+vmH8gCTxSaXbkrAlCIIIDcLQYhuUY6gMkwkYM4YstQRBEET7CPqsyGlpaaioqECvXr3www8/ICMjQ/e+a9euRUlJCf79739j0qRJAIBrr70WgwcPxoIFC/D222971ylxHVsAiBB9jILoFSBhSxAEERqEobANyjGUIAiCIDqAoLfYRkdHo1evXl7tu3btWqSmpuIf//iHoy05ORnXXnstPv74YzQ3N3t+UKsVELKn2i22EMdSkrAlCIIITcLQFTnoxlCCIAiC6CCCXti2hx9//BHnnHMODLK0i8OGDcOJEyewa9cuxf2am5tRX18v+XMgzpxKwpYgCCJ8UKtj20lLQXXIGEoQBEEQHURYC9uKigqkyZM5AY62gwcPKu73xBNPID4+3vHXp08f50p3wlZeMoSELUF0CL///jseeeQRLF26NNBdIUIViwXVazaiZI0FFgvU79chbrX1lg4ZQwmCIIiwwWLhk/9ZLIHuCU9YC9vGxkZER0e7tMfExDjWKzF//nzU1dU5/vbv3+9Yd2hLuXND4SFIq6wLCVuC8DltbW246aabsHDhQsyaNQsfffRRoLtEhBoFBWB905E8ZRyGT0nHwr4F2LldJZ42xONsvaUjxtBgewgiCIIgvKOgAEhPB8aN4/8XFAS6R2EubGNjYxVjgJqamhzrlYiOjkZcXJzkDwBKZq5CyiXOrJLsm2/4bzFCIweX3IJLEES7efLJJ7F9+3Y8/vjjGDBgAGbOnImjR48GultEqGCxgOXlgWP2mtOwYSnLx9bPapzbiO/rndRi6+sxdNWq4HsIIgiCIDzHYgHy8pzDo80G5OcHftIyrIWtkA1SjtDWu3dvj443/J3bYIAz1ooDwPLygdpa9Z3IYksQPuWXX37BokWLMGnSJNx///1Ys2YNamtrcdtttwW6a0SoUFYGTiZWI2BFDxxxNghZ74FOa7H19Rh6++3B9xBEEARBeE5Zmeucr9UK7N4dmP4IhLWwHTp0KLZv3w6b7JPfunUrunTpgsGDB3t0PCWHY85mBaqq1HciYUsQPsNqteKWW26ByWTCypUrAQDnnnsunnnmGbz99tv45JNPAtxDIiQwm8FkCZHaYEQDujsbxC64nVTY+noMlefgCoaHIIIgCMJzzGZANozCaAQGDQpMfwTCRthWVFTgjz/+QKvI9XfSpEmorKzEBx984Gg7fPgw/v3vf2PChAmKsUNaKD3aMIMROOkk9Z1I2BKEzzAajSgtLcVff/2F+Ph4R/utt94KxhiuvPLKAPaOCBlMJnAvvCBp+j9uGUZcEONsEI8PncAV2R9jKMdJl4PhIYggCILwHJMJWL7cmWbIaASWLePbA4lGcGjw8Morr6C2ttaRgXHdunWw2P2XbrvtNsTHx2P+/PkoKirCnj170K9fPwD8oDxixAjccsst+O2339CzZ0+89tprsFqtWLhwocf9KJ28BJf8+x7HMuMM4JYvA7RqBJKwJQiCCD7+8Q/eN9bOgn25MC3cAnxrbwgjV+RgGUNfegmYO5f/OIPlIYggCILwjtxcIDub97wZNCg47uchIWyfeeYZ7N2717H8wQcfOGaQb7rpJonlRozRaMSGDRtwzz334KWXXkJjYyMyMjJQWFiIk08+2eN+jFh4BWAXts1nZSB6/Qf8t/j55+o7kbAlCIIIPo4flyyaTJAK2DAStsEyhk6dCkycGFwPQQRBEIT3mEzBdS8PCWFbXl7udpvCwkIUFha6tCcmJmLlypWOeLx2UVfneBl97pnOb7IDyv1YLHxgttkcXBcMQRBEWCATtgCk9+swckUOmjEU/nsIojGUIAii8xE2MbZ+QSRskZDgfO1jYRuMdaEIIhBUVlaC4zhwHIfPtTwjwMfZchyHUaNGgcmz1BCEHCVhG6YW284GjaEEQRCdk5Cw2AYNfhC2anWhsrNp1pnofKSmpmLAgAH4+++/sXXrVmRnZytut3PnTvzrX/+CwWDAyy+/DE6epYYg5Liz2JKw9T0rVwJNTXwlgZQUIDERqKlxLgPa65qagAkTgIwM1VPQGEoQBNF5IWHrCWrCNkLjY/RQ2GrVhaJBmeiMZGZmOoStGrfddhusVivy8vJw7rnn+rF3RMgiF7aMqbsik7D1DXfd1f5jLFoE5OQACm7TAI2hBEEQnRlyRfYEP1hsg7UuFBGiWCzAxo38/xBl1KhRAKAqbN98800UFxcjMTERjz/+uD+7RoQycmFrs6m7Iod4jG3YUVQElJYqrqIxlCAIovNCwtYT/CBsg7UuFBGChEmgWWZmJgDgyJEj2L17t2RdQ0MD5s2bBwBYtGgRevbs6ff+ESGKXNi2tpLFNpTYtEmxmcZQgiCIzgu5IntCcbHj5eGKFjgeoX2cPCoY60IRHcB55wGHDnXMsa1W6bFtNmD6dODBB7Wv1/bQqxfwww8+P+zpp5+O+Ph41NXVYevWrRgkMr0sXLgQFRUVGDJkCGbOnOnzcxNhjFzYtrVRjG0oYZ/wUoLGUIIgiM4JCVtP+PZbx8se+ZNRXLICWYW52jG2ra1enSrY6kIRHcChQ8CBA/4/Z4hhMBgwfPhw/Pe//8WWLVtw4403AgB+//13vPTSSwCAV155BcaOEuxEeKJksSVX5NAgJ0czgRRAYyhBEERnhIStlxjAMLIoHxWzs5HW1fd1bIlOQK9eHXdsucVWfM6OtNh2EJmZmfjvf/8ribO9/fbb0draihtuuAFZWVkddm4iTCGLrd+Zi+eQjCakoBpVSEY9EvHEvTVIaKkGkpP5jartr4WsyMLy008DtbV8GJBK4iiCIAiic0PCth1EwIrKTbuRdlma+kYkbAk1OsBtV0JBAV/nwmp1Bprl5nbsOTsIIYHUzp070dzcjPXr1+PLL79Et27dsGTJkgD3jghJjh2TLstjbEnY+pw3kAsgTtI25VJgzBg9O7/BC1sq5UUQBEGoQMK2HbTBiNTMQYCxSWMjErZEgAijQLMRI0bAaDSipaUFmzZtwl32siEPPvggevfuHeDeESGJksVWLGApeZTP4Ti+qpKAR9mKIyP5/16G9xAEQRC+xWLhS6yZzcHziElZkb3ECgM25yxDWobJp3VsCcKnmEy8OSRY7jhe0q1bN5x55pkAgNzcXOzduxdmsxl33HFHgHtGhCrV3/wiWS69423n/ZrjpPd1irH1CS+91I5sxcL3QWMqQRBEwAnWwhtksfWE555DTVMsDjYnoccVI5GVYR+RfZwVmSAIVzIzM7Fjxw6Ul5cDAF588UVEid1FCUInFaUW9Nr7P0nbOR88gJaTT0UUwIsocTFUstj6hKlTgYkTvXQiIYstQRBEUGCxAHl5zjlfm42PfMvODrwdhYStJ+TmIjEuDonydhK2BNHhjBo1Cq+++ioAYMKECbjssssC3CMiVDlUXAZ5ZgQjbGipb+QXIiKk93UStj7D62zFgsXWauX9mSnWliAIIiCUlbk6Mlmt/KRloIUtuSL7AhK2BNHhxMbGAgCio6Px/PPPB7g3RCjTK8sMJmuzwoCIGJGfrPi+Tq7IgUew2AI0rhIEQQQQs1nq1AR4mDOhAyFh6wtI2BJEh2K1WvHII48AAO655x4MHDgwsB0iQpq0DBOOJaVL2n664n5ERtqtgGSxDT7EMc80rhIEQQQMkwlYvrwdORM6EBK2vkAjeZS14Rh+eXgNKkotfuwQQYQXL730En766Sf069cP8+fPD3R3iDCge1p3yfLZD1zuFLAUYxs0WCzAxo1Ak1VksaU4W4IgiICSmwuUl/P35/Ly4KkmScLWF2hYbI3HGnDGoilIHdYH28bcg5I1FlhI4xKEbt555x3ce++94DgOK1asQJcuXQLdJSIcaG6WLre1OS2BcldkErYB4ZlnnFk3vy52CtsDe8liSxAEEWiCsfAGCVtfoOWKbMcAYNi3z2D4lHQs7FsQNGmxCSIY+fTTT9GvXz/Ex8fjhhtuQGtrKx588EFcdNFFge4aEWJUlFrw43MbXb1mlISt2GJLMbYBZckS4J57nB99qyjX5XlntdIYShAE4QcEr5lQMcqRsPUFOoStY1PYsJTl49E8stwShBqbNm3C3r170dbWhrPPPhsrV67Eo48+GuhuESFG8bQCpAxLx9l3jUPKsHQUTxOpIbmwbW11WmzJFTmgWCzAvfdK21rhtNgaWBvy80PnQYsgCCIUCdZatVqQsPUFGjG2ipvDiv623di9u4P6QxAhzuLFi8EYw/Hjx7F9+3bkBkvwBhEyVJRaMKooD0bwJj8jbBhZlO+03JIrctBSVsZX9BHTJrLYRqLVUVqCIAiC8D1qtWqDfUKRhK0vkOe8BlxKSYhpgxF7DIOCIi02QRBEOHKouMwhagUiYEXlJrsaUrLYkityUKBUSkJssY1AW9CUliAIgghHtGrVBjMkbH0Bx7mMws1dE9Gm8vH+H7cMDy83BVWwNUEQRDjRK8vs0tYGI1Iz7WpIy2JL5X4CiryUhMEAmNKdFtsYQ2vQlJYgCIIIR4K5Vq0WJGx9hSzONiY5HtXb9qIxtZ/Lpgv25QZNWmyCIIhwJC1DqnqsMGBzzjK+va3NdSpaHGNrNFKMbYARl5LYuxcYe4nTYvvVZ600hhIEQXQgwVyrVgvPgkMJdYxGaW09o5F/gDpjIFBZLtk02C8KgiCIcKPuqX8ha55dDcmttQBlRQ5CTCb+z2IBDlRG4CR7e2oSlfshCILoaHJzgexs3v140KDQ0C9ksfUV8gRS9tn+yr+PuW4bCmnFCIIgwogeCaLMB0rCVp4VmVyRgwIhK+faT5wWW8kkMkEQBNFhBGOtWi1I2PoKeckfoxEVpRYk79nqsinLC4G0YgRBEOHE4cPO101NrutbW52WWXJFDgrEWTnFWZGrDpLFliAIgnCFhK2vUBC2h4rLFD9gzhYCacUIgiDCiepq52sFi+3BDzY7FxobyWIbBIizcoqzIh/cSxZbgiCIYMFi4fMhBIPNjmJsfYVc2BoM6JVlhhUcjLLiP8xgABfsacWIdsPkhRiJoIS+p85B7X82gSUvReKgJCAlxWV9788LnQs7dwJFRc5lirENCEJWTrnF9qRUstgSBEH4C4uFn2g0m11dkgsKnJ41BgOfcCqQyf3IYusr5DG29uRRJTkrYAUnWcU9/3zoOKsTHmOwuzBaycoTEgjfk0GhHjURPiT8WYrEB2YBU6YA48a536GkxPmafssBQZyVU2yxTU4giy1BEIQ/EPIcjBvH/xenCRKHiwD8//wAR1vSk5yvUHBFBoCswlxUbduH+sHnOtdNmeLHjhH+JjIyEpGRkTh2TCFxGBF0NDQ0OL4zIoywWKBqi/fUSk/CNmAIZX9yckWTx21ksSUIguho3AlXcbiIgDXA0ZYkbH2FgiuyQFqGCXFD+jvXyTM6Wiw4snQNfnl4DSpKg8BBnWgXHMehe/fuqKurQ2NjY6C7Q2jQ2NiI+vp6dO/eHRzHud+BCB3++AM++0bJFTmgmEzAgMHaWZGDKcaLIAgiHHAnXIVwETFGI18aKFBQjK2vULHYOoiKcr5uaXG+LigAmz4DSWBIAmBbxKE4ZwWyCqn6fCjTs2dPNDY2Yt++fYiLi0P37t1hNBpJPAUBjDFYrVY0NDSgvr4e0dHR6NmzZ6C7RXiKxYIj60pQUQEkTRjF1w0Xk57evuOPHg189x3/miy2gSdC3WIbbDFeBEEQoYBW7CwgzXMgIBauQrhIfj4/TBqNwLJlgY22JGHrKzQstgAAsZujIGwtFrAZM8CJHOYMYBhZlI+K2dmuD2pEyGA0GtGnTx8cPnwYDQ0NqK2tDXSXCBmRkZFISEhAz549YZT/fongpqAANncTgklJHh+29v/uQUJKF+CKK4A9e0jYBhORyhZbNVe57GxKZUEQBKGGnglBPcI1N5e/3+7ezQveQN93Q0LYNjc34+GHH8bq1atRU1ODIUOG4LHHHsPFF1/sdt8vv/wSjz/+OH7++We0tbVh8ODBuO2223DzzTf7tpMKyaMkKFlsy8rAKcR6RcCKyk27SdiGOEajEampqUhJSUFrayts5M4YNBgMBkRGRpIFPRSxTwga3E0Iikr6NJ+VgcO9h+Ck/9izXpxzDrB9u8uhE555BOjShV/Yt8+5IsSFbUiMoe5QsdhqucoF+gGLIAgioFgsfCLEI0eAmhqgqgpISUENErH7gRosQRWqkALYgPrpVajZlYLEfomSbXMBTM6pQjWXgh4DEpFYWQPMrXJWF6iqgiklBabERKDEuZ+wDikpQKLomHFxHfqWQ0LYTps2DWvXrsXcuXNhNptRWFiIyy+/HBs3bsT555+vut8nn3yCiRMnYuTIkXjkkUfAcRzWrFmDqVOn4vDhw7jjjjt810lPXJGF2WazGYzjXMRtG4xIzaRyQOECx3GIEn//BEF4j94JwaYmx7roUwfipLwbAUHYimvaihFELSC9h4f4pFRIjKHuULHYunOVIwiC6JQUFAAzZigmS0wE8ITSPk8rHyrO/hcSsCBn69atDABbsmSJo62xsZENHDiQjRw5UnPfiy++mPXu3Zs1NTU52lpbW9nAgQPZkCFDdPehrq6OAWB1dXXqG511FmP85cP/jRsnXT93rnNdSYmzfcUKyX42gH2Xs1J33wiCIDoV+/czG8dJ77cAa4WRHdy237ndb78510+bxtjPP7vs4/In5uOPne2PP+5o1jUeBBEhM4a64403nN/H0qWSVStXMmY08quMRn6ZIAii07J/P2MK42Qw/NUBHTqGBn1W5LVr18JoNCIvL8/RFhMTg9zcXGzevBn79+9X3be+vh6JiYmIjo52tEVERKBnz56IjY31bUe9TR41bZpks5ahwylxFEEQhBomE7hFiyRNDMDmnGXS8A2RxRYxMU7XKL2I7+Eh7IocMmOoO1QstoCzJNDGjfx/ShxFEESnpqzM87J2YULQC9sff/wRgwcPRpzMJ3vYsGEAgB07dqjuO2bMGPz666946KGHsHv3bvz1119YtGgRfvjhB8ybN8+3HfUkxlY8KMsG6OhIG1Bairq5D+PPuUup/A9BEIQcWWxo42X/cJ0QlAvbpCTATUx18TRR5fkwcUUOmTHUHRpZkQE+nnbMGGdcLZX/IQii02I2ux3vwpWgj7GtqKhAWlqaS7vQdvDgQdV9H3roIezZswePP/44HnvsMQBAly5d8P777+Oqq65S3a+5uRnNosQj9fX17jvqTVZkwLUe365dYMOGIR5APADbi7PbVf6notSCQ8Vl6JVlpmRUBEGEFmolferqJJt16aaQ1Vp0D0d0NH+PjoqStsuQJKAKE4ttyIyh7tCw2MrxZfkfd+UwCIIggg6TCXjlFWD27ED3xO8EvbBtbGyUuEEJxMTEONarER0djcGDB2PSpEn4xz/+AavViuXLl+Omm27CF198gREjRiju98QTT2DhwoWeddRbV2T5AF1XB/EciwEMo4ryvCr/U5yzApmr8pEGBisMKM5ZTm7OBEGEBlo1vmXCVmKdVWqLiQFKS8Gam6E1hy1JQCWenAxhYRsyY6g73FhsBXxZ/ofq4xIEEbLcdJND2P6KU7AaU3HDRdUYMi7ZmaW4uhpITua3F15rrKtBIp66vwbJqEYV+HUp9te1SEQCajB7UjX6nqNxzO7dgUcf7bC3HfTCNjY2VjLzK9Bkf2jRivO59dZbsWXLFmzfvh0G+0PKtddei9NPPx1z5szB1q1bFfebP38+7rzzTsdyfX09+vTpo91RXwlbpUPD5nH5n4pSCzJX5TtKYhhho/q4BEGEBu5qfHsjbIuLNUUtIMtIHyYW25AZQ92h02Lrq/I/VB+XIIhQ5sDeNpxkf12OAXgK8/HMRqD8De/vYTs2Ak9prDcagdueB6B1/Pr6DhW2QR9jm5aWhoqKCpd2oa13796K+7W0tKCgoABXXHGFY0AGgMjISFx22WX44Ycf0CIWmCKio6MRFxcn+XOLPMZW7oqsFmOr0gcxVhg8Lv9zqLhMUucRcFojCIIggho3JX1QWytdoUfYZmVBK5VGG4zSBFRhEmMbMmOoO3RabIXyP2K8Kf+jJZAJgiCCnT1lzvukFfx41t57mNL9VcBoBJYtC/zEX9AL26FDh2LXrl0uMTrCTPHQoUMV9zty5Aja2tpgVZhpb21thc1mU1znNXILrXyGXG+MrQwGoCRnucdW1l5ZZpeHOKqPSxBESGCv8S3HcQ/TY7EV34NjYoCMDHA5OS73RQYO+669G9XbyqWhGmHiihwyYyjcJHzSabE1mXiXYWFI9vZhy1cCmSAIIhAMSHfen9vsDrrtvYcp3V+XLAmujPRBL2wnTZrkiOsRaG5uxhtvvIHhw4c73Jv27duHP/74w7FNSkoKEhIS8OGHH0pmlY8dO4Z169bhlFNO8Wm5gmNbf5Ess08/5QN0BLx0RW68fJJXcbFpGSY0xjnLW9igUA6DIAgiGDGZwL30kqRJUtLHnbC1WHDs8++dy8eP8/8LC8Ft24a6Oxbgr+mLcWTpGnD796Hve0tc741h4oocKmNoQQGQng6MG8f/Fw+fAHRbbAHflP/xlUAmCIIIBL1TnPfJNkR4fA9Tm2iU31/vvluakT7QBH2M7fDhwzF58mTMnz8fVVVVGDRoEIqKilBeXo4C0cg3depUfPvtt2B29zWj0Yi7774bDz74IEaMGIGpU6fCarWioKAAFosFb775ps/6WLm+FCl10sySHACWlwdOCMjRWe5HTpeu3qfr7pISB9RXAQCaM8dR4iiCIEKHG24AbrvNsdiUdTGyHssG1qwB5LGdYmFbUADb9BnoJrLNsrvvAZeQwI/IGRmIz8hAvLvzh4krciiMobriWT3Iigzw+7X3QSs3l+/D7t28lSNYHtwIgiDcIpoAvGCcEeVF0nuYVsZ3d4nzfHF/7SiCXtgCwKpVq/DQQw9h9erVqKmpwZAhQ7B+/XqMHj1ac78HHngA/fv3x4svvoiFCxeiubkZQ4YMwdq1a3HNNdf4rH/1G4qRqtDO2WzOjBVeuiLjxAnvOyaKUYtN7OL9cQiCIDoYl9JkMqtc7GEL0LevYtH5poOHEWOxoGbVOiQ8MMvFFYkDA8vLd0406kEkbBu37kTs4sVAVRXgi3hRPxPsY6iuhE9ii+2OHYDwfaTYPZOE10L2Ta11TU3AhAlARobbvgXzAxxBEISAi1AVeRql9o6QJHRSE64WC1BSAsyY4Rxq25M4LyDl0hjhlrq6OgaA1dXVKa4/tG4bs/HXgOTPZjAwtn8/v9GHHzrXPfGEc+ctW1z2k/yNHet9xwcMcB5nwgTvj+MJ+/ezo4+/xv6++SF2aN02/5yTIIiQ5ruclawNBsYA1gYD+y5nJWMWi/a9UXyvtf+53XbjRt19+t+EhxWPUcd7RauOB4Qr7sbQ/fsZMxikH7XR6Bw+GWOMLVig+3rQ/ZeT44+37zH79zP29dey908QBKHCypXOe6jBwC+z339XvNep3W+XLHFt93L4VO8Tcz8etJegj7ENBVLHZ6BslDQpCQMHbvly5xSFl67IvrLY+oWCAtj69EHiA7PQf/UipEwYhl2Z0/zbB4IgQoqKUgtGFeXBCN5kJ5Qmq/zfft3H4Ox/WjCD/qwZFaUWnLVuke7zE+3DbTyrxdIx5SGKioDSUt8ftx24jTUmCIIQoRbKccgi8noSebyoecjce6961I2nSafU+qSYGNDHkLD1EYM3FaJq3TbsyVmAo4uXgtu/T+qQ7m0dW18JW4UMoz7FYgGbPl1yQXEAzCVFqFwfXA8OBEEED4eKyxyiViACVhzZ+pfPzsE4A7jl+rNm8H3y88RgJ0cz4VNZWcdN1G7a1DHH9YJAPgwSBBGaqAnV/eWipIciYauU8d1g0Ba1nibOC2S5NBK2PiR1fAb6Fz6CHvNnul4BajG27urY+krYqhWe8hVlZYoWEw5Aw2fB8+BAEERwoVaarOfQ9gfkMICfaNy316PUuL2yzLC6tQETvsZkUsmuaTZ33ORsZmbHHNcLqHYuQRCeolaarG/vNmmDHSUPmSefVD7GmjXeZZYPZLk0Erb+wkcW24pSC358biMqSnVM4frTYmt2fTgF+AfL7pcGz4MDQRDBRVqGCc1dEh3LNnDYnLMMKacmqe901VWoWbwUx/qdpnlsbsQI5YlGHX0qyVlB4jZYMJmAFSt8Oo4xAMjJ0ZVAyl9Q7VyCIDxFLZQjtafTYrv/UITE80PuIXPPPcrHmDzZu6RPgSyXFhJZkcMCkbBt3P4bYi0W/hv2QNgWTyvAqKI8pMEGKwwozlmuv4RPRwtbkwncxInARx85mhiAslE5GDw+eB4cCIIIPmJ6dAVO1AAAmsdeyt/XduxQ3+GSS5A4ayZQ/AlQ/pv6dqdpC18tsgpzUTE7G0c/3Yze0UeQiBqguhro3r1j4j0JbXJzUTEkG0fWb8ZJMaLvIzmZX19djZqoZFQ2J6JXdA0SWqTrkJyM739JwKi3+azZv+I0bM0qRDAVwRMeBvPzeUst1c4lCEIPiqXJSpwW2zUfRGDeR9KyPfKM774ubxaocmkkbP3E/xauw7n217Hf/ResT19wK1fwD0la2IWtWoKVitnZfGkMJfydPOrssyXC1pqUjMGbCv3bB4IgQprYHnxpssoDbYpl1AAA8fYqtDEx2gcTe8p4QVqGCWkZk6WN9fUkbAMAX57CBJttsrM8xXz5evW6ixYLcEE6cBx3IAbNaEWU1yUsOhKqnUsQhDfIhWrVwTbYC57BCqOusj2+Lm8WiHJp5IrsBypKLRi6TvogJNRVxKFD2ju3tgKtrTiyrkQxwUrlJo3gG3+6IgMuwUER0ZEqGxIEQWhjKW9TX5mQwP93J2yjo33WHyJwuEuqpCfpkhC/2gp+XIpCS9DGr6rGGhMEQejkwD6nK3Kb3Y4ZrPc8X0LC1g+oZdjkbFbghx/cH+C113D6oikuzVYYkJqpEXwjFpr+ELaiYtAA/G8xJggibOjTSyNMw08WWyI4UEuqtHmz9nrxA5yQf6oF/DURhRYYDBS/ShBEeGLq5ZwctoIPdu0MMfvkiuwHhAybSuKWrV7tPj3J3Lkq27gRjgG22KrmDicIgnBDSg8Niy0J206FkFRJPqRcdx3vGZ6d7bpe7QFOELaRaKW5V4IgwpbkROcY2oaIThOzTxZbP+DMsOmKWG7aREt6xlsjmLYrsuREZLElCCIEEO4bbT5wRSZhGxYISZXkGYMFl2PAfQZOoRSu2BWZsfB3yyMIopMieibPyY3QLNtjsfAZksOhZjZZbP1EVmEuShK6Y9SLri7FAnWPvoSD1lT06gUkffsB8O67AHiRqyRL22DUdkUmiy1BEKGKVsZ4wWL755/axyBhGzbk5vK5FqfIhlDB5Vgp6ZLFwgtas9lp9W2xOV2RO4NbHkEQnRTR5HBSshHby/jXcoutu8R7oQZZbP1I/xtHKVptBRJP7YXTH5mMpJmTcWBHlaNdTZJuu+FFZ0ZkiwU1i5diz9SHUbm+lG8LtLAliy1BEHpQuj+pWGwZANx2G2CxgG3YoH1cSh4VVowapV3nVZx0qaAASE8Hxo3j/3/+Of/AJnZFllt1w8lqQRBEJ0dksX3sqQjHvbCgwLmJnsR7oQYJWz/CuySvhKod025dqCi1IO2PrxU3EUvFUU9eyb9YuhSsTx8kPjAL/VcvQsqEYdiVOU0qNLXc+nyF3BWZLLYEQXiLyj2LA8BWrQLWrXOfn4AstmGF4JKs5XIMqD+sZWcDg07lXZHjolskVgm5EBY//BEEQYQcojG0lfEOunLhqifxXqhBwtbPZBXmonLbfjR3T3RdGckPuIeKy1S/GMmDXF0db7WYNUvSzgEwlxTB2ixy5fOHsCVXZIIgfIXGPYsDgMpK97kISNiGHbm5QHk5b1lVixnTeliL6spfE1xri2NdOFotCILo5LS5ZkUGpMJVCNEQE+ohGiRsA0BahgnR/fu4rrALWz6Lsgpil73aWqCsTNFqwQFgLc6BOyAWW3JFJgjCWzRibBkAXHEFuJVSDxiXOw4J27DEXZ1XzYc14Zqw2RxjVjhaLQiC6ORYXevYAq7hG3q8YEIJEraBIi7Otc0ubFVdljkOuPJK53JtLWA2K1otGAAuUpQbjCy2BEGEEqJ7lly8cjk5QEYGkJsLw/79fH6BnAU4+uwb0mOQsO2UaD6sia8J++RJOFotCILo5IjGUMY569jKhaseL5hQgrIiBwoNYQvwLssVs7NR/856pDXsQty5g4Hx44EPPwQ+/hgA0PD+5+g+dCi4c84Btm937MsAlI3KweA/1jmPTRZbgiBCCdE9q+7+p1DVGIdeOIT466/gRa2AyYTE+TORCAA7d0qPQcmjOi1KWZIBSMbZA3tacNKpMQ4hnJ/PD2PhYLUgCKKTIxpDFz8dgevOk90LRZhM4XO/I2EbKNwIW4C33KZlzJS0/blmJ062v+5e+ApY0avgzjpLsg3r2h2DNxUCPXo4G7VKZ/gKstgSBNFeFOrYJppTkDhtmvt95UKWLLadGqWHtX2VUehrf3326S14YgUvglWFMEEQRCgiMjb1SInAmDGB64o/IVfkQKFD2MqpKLXA/L00VSPHGNiOHZI2Q+NxXlSKLaaBcEUmiy1BEN4inoyL0DkHS8KW0MBiAf73k/OaiGAtkiRR7mJ3CYIgQgbxc7/RqL5dmEHCNlB4IWzVsiW7JI+y2YBjx6jcD0EQoYG7OrZ6ha1cyJKwJUSUlQEtcI6zkWilJFEEQYQn4mdyvWNoGEDCNlAoCVs3D2F8tmTXB0BFu2htrdTiQRZbgiBCCfE9y82knwOy2BIamM1AK5zXRBRaKEkUQRDhiTeTw2EACdtAoSRsDx/W3IXPlrxCliGUAzd4sOvGcmHrjxhbstgSBOErvBmU5cKWkkeFPRYLn81TT81ZkwnION8pbGMNLZQkiiCI8IRckQm/IouLBQA2KhMoKHDdVkRWYS4abn/QscwtfQ1ITnbdsKZGelF7aLGtKLXgl4fX4MjSNfqr1JPFliAIX+FNjC25IncqCgqA9HRg3Dj+v5vhEwBw8ulO6/8XG1o7rLSFJ4KbIAjC55ArMuE3LBawwkKXZg4MLC/f7UgYP1AkZOPjFUVrzZY/pQ0eCNvinJVIHdYXZyyagqRZU8D69tX3xEBZkQmC8BXeuCKTsO00WCxAXp5zmLHZIEkEpYromkhNbFE8bnsFqTeCmyAIwqeQKzLhN8rKFCJleTibjkwW4gu0tVVRtMbfJy0TpFfYVpRaMGpVHgyiyF2O6RPcLq7IAFltCYLwDm8GZXkSKhK2YUtZmevcqa5EUOJrokUqbH0hSL0W3ARBEL6EXJEJv2E2gyllAQXADDoyWYgf8traFEWrQZ5SSqewPVRcBqNCOipdglvJQkvCliAITxDuGd64IsuhGNuwxWwGDLInGF2JoMTWf5Gw9ZUg9VpwEwRB+BJyRSb8hskEbsUK2GTilnEGcMt1ZLIQD8wqwtYFncmjemWZoeRArEtwk8WWIIj2ItxHfOFGRRbbsMVkApYvdxoijEboSwQlviZE46KvBKnXgpsgCMKXdFKLbeeR8MFGbi4M2dk4sn4zDu86gp6Dk5A0fqS+9Iw6XJFd0GmxTcswYe9ZE5C+c52jjXGcPsGtZLG12TrVD4ogCC8QT/IpCVu9MbZySNiGNbm5QHY2Lz4HDdKZ3VjFFVkQpOJhzBtBKgju/Hz+UtYtuAmCIHxJJ42x7TzvNBgxmZA0czKSPN1Ph8XWBk7qjuxB8qj0y88ARMKW+/prYMwY9zuSKzJBEO1FuFf5YlCuqlIurUaEDSaTh6JRRdj6UpB6JbgJgiB8iZeuyBYL78FiNofmvYtckUMRHRbb5syxkmVbqwflfmQJNZCSom8/JVdkyoxMEIQaFguOLF2D5prjjqaWg9UoWWPBsVrPY2zlyX5sg0+mlLSEFPHEsCxEJzcXKC/nsyKXl/PL3mZJNpn4+eBQfDAkCCJ0kN+jhOVjtZ67IodDRncStqGIjuRRsdXSUbjtWKP+C1QubJUEqxJksSUIQi8rVoD16YOkWVMQXX/Y0Rz1y48YPiUdO9/5zbmtDmFrsQALZ0jvewZmA6OUtIQYjazIgFSQhsNDHkEQ4Yv8HjVtmnP5rVWeWWzDJaM7CdtQRIcrMtu1S7oL2vBonkXfBeqtsCWLLUEQerBYwPLyVMueGWHDSGx2NuiIsS0rAwayMpd2jlLSEmLcCFuBcHnIIwgiPFG6RxUVOZeN8CycJ1wyupOwDUV0uCLLHxg5AP1tZfouULLYEgTRkWjU8haQ5AjQMSibzcBfnBlW2bDGKCUtIUal3I+ccHnIIwgiPFG6R4mJgGeuyOGS0Z2SR4Uiahbbrl2B48eV9wGwlxug7wKVD/Z6ra5qWZEJgiDEmM1gcJ2AEyNJgKdD2JpMwIIVJsycsRxLWT4iYIXNYISBUtISYsQW208/BXbt4vNIJCYCNTV8wrGUFAy0AM+hCpVIQS0SkYAapKIKZ/0nBSiBYzsMGgSMGkXXGEEQfkUpk7sYIzxzRQ6XjO4hIWybm5vx8MMPY/Xq1aipqcGQIUPw2GOP4eKLL9a1/3vvvYcXXngBP/30EyIjI3Haaafhsccew7hx4zq45x2EmsXWjbBd8FqqvgvUl67IZLElCEKOyQTuvPOAH35Q3eQ3nIYz8Cu/oDN5FJ+NNhelm7MxCLuRPJJS0gI0hkooLna+3rBBdbO+AO5QWvG0QhvHAStW8BcgQRCEH1ASojfdBKxezYvdSA8ttkB4ZHQPCVfkadOm4bnnnsONN96IF198EUajEZdffjm+//57t/s+8sgjuP7669GnTx8899xzeOyxxzBkyBAcOHDADz3vIOTJowRB2bWr5m7TbtKZGdmXrshksSUIQgk32dabEe1c8KCOrckEjJxsQvLkMaE5KncANIbasViApUt9f1zGKACXIAi/I8/knpXlXBfhYYytQKhndA96i+22bdvw7rvvYsmSJbj77rsBAFOnTsUZZ5yBefPmoaSkRHXfLVu24NFHH8Wzzz6LO+5QnHsNTdRckbt00d5Pby1bstgSBOEjKkotOLKuBGlpQNIEkcumhncJAKSgyrnQiYrL+xoaQ0WUuSYX8xlCAG6oPg0SBBGUuKsrK9TylieTMnjoihwuBL3Fdu3atTAajcjLy3O0xcTEIDc3F5s3b8b+/ftV933hhRfQq1cvzJkzB4wxHDt2zB9d7ni0XJG18FbYUowtQRBeUHLjK0gd1gdnLJqCpFlTwPr2ddZMIWHrF2gMFWE2827DHUEoZlkhCCKo8aTkmDyZlKfJo8KFoBe2P/74IwYPHoy4uDhJ+7BhwwAAO3bsUN33q6++QkZGBl566SUkJyeje/fuSEtLwyuvvKJ5zubmZtTX10v+ggqxxba5Wdqu8QDYcPt83g3LnbuUBxZbSWFoyopMEISdilILRrx9m2SQ4RgDy7O7bLoRttEQ3YcqKzumk50AGkNFmEx8LKyvxS3HeZ1lRTKGEgRB2PG05Jg8q7GnyaPChaB/pxUVFUhLS3NpF9oOHjyouF9NTQ0OHz6MTZs24euvv8aCBQvQt29fvPHGG7jtttsQGRmJ/Px8xX2feOIJLFy40HdvwteIL9DGRml7VJSqZbb7OyuBdwDMnq2d6EKnsC0ocP7oDAag6iQrkuQbkcWWIDolh4rL4HrnBjib3WXTjbCVMGgQJefxEhpDZQjZUTZv5q/D6mogOdmZFdm+XFsH1P9Vjb8bkvHu54mIRw1SUY3zr07GsAwAJSXA+vX8Me+7z6trUz6GLl9OlzhBEDxaJcfUXJKXL3feU7yNsQ11gv6dNjY2Ijo62qU9JibGsV4JwWXqyJEjePfddzFlyhQAwKRJk3DmmWfiscceUx2U58+fjzvvvNOxXF9fjz59+rTrffgU8QXa1CRtj44GTpzQ3p8x/srPzlb+degQtkozSQf220jYEgQBAOiVZYYNrm5BzGAEN2iQZ8JWSM6jds8iVKExVAGTCZg8WXOTBADHLMCF6YB4FDN+ApS/BJjO2uAUtvbP0hPUrDF0iRMEASiX83EX8ZCd7XSUFAvbA4eMOClOZacwI+iFbWxsLJrF7rZ2muyCLjY2VnU/AIiMjMSkSZMc7QaDAVOmTMGCBQuwb98+9O3b12Xf6OhoxQeBoEHsiiy32Ortt82mPu2jI8ZWaSZJ4vYgQK7IBNEpScswoTr9HCTv3e5oYxwHbrndZdMTYQtQch4voTHUezQtJmIxK55g9sWx6RIniE6PyQS8+aQFH99bgn5sN1JRhcwJKTCtk9bcBuB43fQX8AyrQhVSYMI+x7H2lR7CSYMHBuid+JegF7ZpaWmKZQUqKioAAL1791bcr0ePHoiJiUFCQgKMsqDpFPuFUFNTozgoBz3uLLYilCwmAPhpILVpHx0WW6WZJAMUrLNksSWITkvyKcnAXucyt2MHMGQIf0/xVAxQch6voDHUezQtJvvaJ2y9scYQBNGJKCjA9ffOwPViA9FH9j8VBgG4U6F9xM1moKlzhPMEffKooUOHYteuXS7JJ7Zu3epYr4TBYMDQoUNRXV2NFplQE2KKkpOTfd9hfyC22MqFbVSUZFPLmZcryU3eEV9tWliHsBV8+YXnHaMR6J1KFluCIETIs+gK91xPrbUGg9fJeTo7NIZ6j9I457gM22mx1Tw2QRCdG4sFmDHDZ8/QXCeqtR30wnbSpEmwWq1Yvny5o625uRlvvPEGhg8f7ojb2bdvH/744w/JvlOmTIHVakVRUZGjrampCW+99RZOO+001ZnqoEcreZTMYtv32pGo3LYf+yaL5nDy87VnbXQmj5IXho7vRhZbgiBEyIWtkNjOA2G7J2cBsHdvp5hp7ghoDG0f8nHOcRm2U9hqHpsgiM5NWZnvDUNCrEOYE/SuyMOHD8fkyZMxf/58VFVVYdCgQSgqKkJ5eTkKRAWdpk6dim+//RZMdCHk5+dj5cqVmD17Nnbt2oW+ffti9erV2Lt3L9atWxeIt+MbtCy28rimLl2QlmEC7pwM/Ps5vs1d7JMHdWyFwtCq25HFliA6L+0Utm0wImb2dDJjtQMaQ9uPZJwT8IGwVT02QRCdG7PZ98fsJLEOQS9sAWDVqlV46KGHsHr1atTU1GDIkCFYv349Ro8erblfbGwsvv76a8ybNw+vv/46jh8/jqFDh+LTTz9Fdna2n3rfAXhgsUXXrvx/sYtya6v28eWJRjTq2Lrdjiy2BNF5kQtb4d6jQ9i2wYjNOcuQlUFP/e2FxtAOwEfCliAIwgWTCbjlFuCNN3xzvE4UzhMSwjYmJgZLlizBkiVLVLf55ptvFNtTUlJQWFjYMR0LFFrJo2QxtujShf8vtvLaHy4tFt7bwWyWXes6XZFdIIstQRBiFCy2FaUWNC9ZhX4au+279m5E3j2HRK2PoDG0AxAJ28baJijnliYIgvCSUaOcwnbiRKB/fyA5GTVIxJG/apDCVSNugD3PgVCPG0D939WoRjJ6DEhEYiKApCRg5MhOIWqBEBG2hAwPsiIrCtuWFvXC8Ix5L2zJYksQhIDN5mKZ3XHPmxiy4Qm3yR36TjgLIFFLBDGF78Zgmv315o1N2FNAMbIEQfgQsXflxIlATo76s7uIOPtfZyXok0cRCnCcM5WiO1dkQdiKLLkn6loVC8NbLHDGwInRK07JYksQhMCJEy5NZ+kQtQBcPU8IIoiwWIAZtzrH2hg0dZaEowRB+AuxkSkyEhYL1J/dCQckbEMVwQIrFqJKrshCjK3IYnusplW1MLyLtVZYqQclYUsWW4LonMjdkAFwevcVe5gQRJBRVga0MSNawF+nMWjqLAlHCYLwF2KLbVQUyspcH6npvuMKCdtQJULBi1ynK3L36BYYZN+8I1lae4St0nZksSWIsKFyfSnKZj2HyvWl7jdWELa67wZK9zeCCBLMZt4NsAl8nG0MmjpLwlGCINqBxcKX99JlZRUL28hIx31HDN13XCFhG6p4KmxFltzYiFb1wvBksSUIQoG/M65FyoRhMC+9CykThmFX5jTtHRSErc2gU7CSxZYIYkwmPrZNLGw7ScJRgiC8pKAASE8Hxo3j/4uqrSkjEraH6yId9x3FZ3fCAQnbUEXpwU9J2NbVuW7f2qpeGF5J2OoVp2SxJYiwpHJ9Kfr/8G+HKzEHwFxSpGm53Tn/XZc2o80ZOlE/7VZg4ULFfY/8VduO3hJE+9BjVcnNBXr05oVtekoTJY4iCEIVb+Jjd2xzPo/fOC0SBfYEdYrP7qLz6LYIhykeC9vKykpwHAeO4/D5559rbnvrrbeC4ziMGjVKUvSd8AEqFtsD3+ySNLFRmfy0kCwrMsDP8owZ46bUD0AWW4Lo5NRvKHaJj+UANHy2SXH7ilILzvzsac1jxq14XjWNbMKtN6J4mrvpbILwPZ5YVSK68sLW2Ep1bAmCUMfT+FiLBfjvp06LbROLcghhxWd3eGERDlM8FrapqakYMGAAAGDr1q2q2+3cuRP/+te/YDAY8PLLL4PjdKcNIfSgYLFtqDyBtN+/krRxYGB5+UBlpbNR7LcvZ98+1zaqY0sQnZq4y7Nc4mMZgO6XZipuf6i4DAatiFohs7uoFqgYI2wYWZSPitJOPO1M+B2PrSrC9dvkKmzJckIQhICn8bFlZUAEnM/qrYhUFcIWC7BmDTBjBmVMBrx0Rc7M5B9mtITtbbfdBqvViunTp+Pcc8/1rneEOgoW2wZLreIXytmswJ49zl+VmrAtKOCnemRs20x1bAmiM5M6PgPNXXs4lhmAslE5SB2fobh9rywzbFo5kCMjAY7Dpttd3ZUFImBF5SZK90j4D4+zjoqFrWgSlywnBEGI8TQ+1mwGomTCVkkIC/eaKVNc7UidNWOyV8J21KhRANSF7Ztvvoni4mIkJibi8ccf9753hDoKwrbbgFRYFR4mmcH+axCsvEruxhYLP92jwFdra/TN+pDFliDClpj0Xo7XtrgEDN5UqLptWoYJe8/5h/rBoqJQUWrBiLdvU92kDUakZlK6R8J/eJx1VBC2jDkmjKnWJEEQSriLjxVjMgEXjXY+q9sMkS5CWH6vkdNZMyZ7VVNBsNgeOXIEu3fvxiDRJ9fQ0IB58+YBABYtWoSePXv6oJuECwquyHH9k1CcswKjimbAaHcDZJwB3HL7ryEqCmhuVrbYlpWpitCeqMLu3Toyr5HFliBCnsr1pajfUIy4y7OkFlnRhJgR7n/X/S8eBGxXWRkVhUPFZUhTcVe2woDNOcuQlUHpHgn/IVhV8vP54cxt1lGxK/3cuYDJhKa/gCW2KlQhBbVIRAJqkGKtQvMjKcAAAFVVQEoKv4/wOjERqKmRrmtqAiZMADKUvSIIgghOLBb+kdpsdr13mEz6sxifMrAV+I5//ekXUeglc6hU8jAR6MwZk70Stqeffjri4+NRV1eHrVu3SoTtwoULUVFRgSFDhmDmzJk+6yghQyV5VFZhLipmZ+Pop5vRqxeQNH6k88oWxLBc2FosqNn8BxIARefBeiRIZn0qSi04sq4EaWlA0oRR/PEZUxbGZLEliJBhV+Y0mEuKkAqALQV2jcpxWmbFnh4KMYUu1NSor4uKQq8sM6zgHJNwAjbOgMOfbEGWipszQXQkublAdjbvwjdokJsHw6oq5+ulSwEAgwDcqbStN+7IixYBOTlAYaEXOxME4W8KCpxWVIOBnyjzOmO66Fm9Vx9XY5bgYSIWt0Yj8M47wMiRnVPUAl66IhsMBgwfPhwAsGXLFkf777//jpdeegkA8Morr8AoOJMTvket3A94N8DTH5mMpJmTpVe2kityQQFsffoi8YFZqhFxYyd0cxymeFoBUof1xRmLpiBp1hSwvn35X7KagCWLLUGEBJXrS2EuKVIv6SO+b7S0uJ+00hK2kZFIyzChJGeFJHyCcQYYVixXjd0lCH+glnVUgsUC7NzZ8Z0pKgJK1ctqEQQRHPg8DEFshFJ45leL2508ufOKWqAddWyVEkjdfvvtaG1txQ033ICsrKz2945QR8li29CgvU9UFP9f+LFYLGAzZmhnLwVwzlm8i3FFqQWjiqTbc8yedXnvXuWdyWJLEEFP5fpSNNz3mHZJH3lsvlKsvpjaWvV19ntRVmEuqrbtw68L1uDI0jXg9u1tx/Q2QXhGuzIXl5X5vD+qbFIuq0UQRHAgZCb2KPmcO8RjrPD8LsOTuN3OgleuyIAzgdTOnTvR3NyM9evX48svv0S3bt2wZMkSn3WQUObEr3+ji7zxgQf4+By1K1vuilxWBk6P8LT/UtVi4jibVX2QJ4stQQQ1EvdjSMMRJCV95EK2uRmIjlY/sBtXZIG0DBPSMiZ72GuCaB/tdhk0mzusby5kKpfVIggi8IjvJXLalcDJjcVWwJO43c6A1xbbESNGwGg0oqWlBZs2bcJdd90FAHjwwQfRu3dvn3WQcKVyfSliG6pcVzCm7fcgd0U2m8G0SnII2JNC9coyK9p2beBQ2RCrvC9ZbAkiaFFyPxZwKemjJGy10ClsCcLf+MRl0GQCVq504+/kA3JyKIEUQQQpWpmJ253ASaewJaR4bbHt1q0bzjzzTOzYsQO5ubnYu3cvzGYz7rjjDl/2j1CgfkMxUtVWCn4PSr8kuSuyyQRu9izg1Vddt+U4pyi1WgGLBTFfrENLRCyi2xolmxrAkDzpAuX+kMWWIIIWrXsJ69LVmTiKMffCtrQUWLeOzxSbmAir5QBUsyzQIE0EEK16tR49hObmgsvOxvf3rce2t3ahEskwALj+omoMGZfszHZcXQ0kJ6O2Dtj5RTU+254MG4BUVKMSyahFIhJRgxuE/Z5+mnflT0igxFEEEcSoZSZ+/nlg0qT2WVKbGlrgyLtOY6ZuvBa2AB9nu2PHDpSXlwMAXnzxRUTRTHyHE3d5FthS5QzGmn4PSlmRzzzT8bLiohsRM+58JA5K4re9+mp+xc6dYH36IFGjT6pxumSxJYigReteYmgT3Sfa2lw3EAvbadP4JDciNFMH0jhBBBC1bKJeuQyaTDj/zZno96R2JuWCAiDvQf6cHMdbiJcskw6Rz2wEyt8ATK+/zgtbeVFdgiCCCrV7SXtFbUEBMLikFUK2otffjMI/89vV1U5Du+6aQpwtAEyYMAGXXXZZuztEuCd1fAbKRuW4SkmDQdvvQRC2bW3O0bSy0rE6be71SJw/k0+p1quXo5198YUeh2VlyGJLEEFL6vgMtEW5ROvztLQ4a1MruR0LbaWlLqLWLSRsiQCilk20PQ+iWpmU5e6KjPHnl8/7OhLNCB1Tqg1PEETQ0BH3EuF+EQnn5HLerAjvsyt3MtplsY2N5eMqo6Oj8fzzz/ukQ4Q+Bm8qROX62Tix9lMk9IpG4rmD3BeuEj9Mtrbyy4cOOdtSRU6JolJNXotagIQtQQQaC193uuaH3UhBFeIGpvBmpVF8DerIHnHAoRPK+zY1AV27KmdAFoRtcbHnfSJhSwQYj+rVthMld0XBcisWtw6rMQlbgggqLBb+d2w2u94rfH0vEe4XgrBtRQSsNs7zUIlOitfC1mq14pFHHgEA3HPPPRg4cKCv+kToJHV8BuBJvUexj75d2Db+vgeOtE/yEdYD5NlUnSvIFZkgAsbKlWAzZiAJQJJ8HccBK1ZIQxPk6BG23pR2o3ghIgjwRTZRrQdeATV3xSeeAObP5/WrxNJDwpYgggY9GdR9mZlYuF9E2fhxtxWR7cuu3Mnw2hX5pZdewk8//YR+/fph/vz5vuwT0VGIHyZbWrBt0tOI/eYzRxMbNpz/BQNuhS0DgBkzHO7Q1tQ05Q3JYksQgWH9erAZM9Q9LoQs6lrZjRvtieK0hG1GBi9+1U6j1EgWWyIMKCgA0tOBceP4/8LwKUfNXfGee1RqUAobKsW2EwThN0pLgRkz2plB3UOE+4VgsW1BVLvdmzsTXlls33nnHdx7773gOA4rVqxAly4qMVpEcCF6mDy0bS/Oe/9eyWoODCwvH1x2tmrSioOX3oKY0cPQ4+bxfFbljz8GqqoQcVih/BBAFluCCATTpoEVFbkPI7BalUWrgB5hC/D3luPH+Syu8+YBiYmoLa9BzaFmxJ/eBz3mTZfuS8KWCHHUSgZlZys/gKq5KypaeshiSxABR7DUqsXCd6TQzM0F2h5tBfYB3XtEelZju5OjW9h++umnmD17NmpqalBfXw8AeOihh3DRRRd1WOcIHyOy2B7etAu9FDbhbPZfbEqK4iF6r1wEnHSSsyEtDaiqUh+AyWJLEP6ltFSfqAX4B2ith2c9wpYxoKGBf92/P+9bCSDB/ofSUtd9SdgSIY43JYPU3BVd3Jkj7I9mNhv/++LalemCIAgPcVef1h9uwRGMt9gaoyl0xxN0uyJv2rQJe/fuRVtbG84++2ysXLkSjz76aEf2jfA1ImGbfI5J0UWQGey/WDVXZNkD6dFqNzPKZLElCP9SXKxP1HIc8K9/tV/YNjU5XSbj4ly3i1CYP6UYWyLEEeLgxHjzwKvoziwef2lymCD8jlp9WnfFR3yKMO7SeOkRuoXt4sWLwRjD8ePHsX37duSSXTz0EInS1NN6wmaU/lgYZwC33P6LVRO20dGOlxWlFiQc/FX7nDQoE4R/ycpSnLSyAqgbKkr09PjjQE6O5qGq9jXxL7SErWCtBYDu3V23UxqUyWJLhDi+KPOh5s7c3CYaf8kdmSD8jtLElcEAbNnimjhKCYuFj51vVyyukNiRxkuPoOrfnQnxA2Z1NYxW/kdzrN8ZOLJ0Dbh9e52/WB3C9lBxGQzKqWGckMWWIPxLRgY4mcC0gUNJzkrE3zvL2RgTo50RGcC0KY28Bak9wlbJYksDNREG5OaqJH/SiZo784kWErYEEUiUJq6WL+dzJbpDb1I5twjjM1lsPYKEbWdC/ONYtMjx0nDayUiaOVk61aySPEp8jF5ZZtjcOT2SxZYg/I99Asoal4A/71iKym37kFWYC8TGOrdpanIrbKNZI/LzgeoDJGwJQo4QG+tt7Uo1d+bYbiRsCSLQeDNxpeaF4ZXlloStV5Cw7UyUlTlff/6542XshvdRPE02paRksY2MlIzCaRkmlJ97jfY5yWJLEP6FMaC2FgBgHDQAJz83E2kZ9qdusbBtbHQrbGPRCKsVqChXKAkkCFt7MkEAyjG2SoMyDdREiOMLq4yaO3NMFxK2BBEMmEzAmDH6J660ksp5jOApRRPBHkHCtrNgsQBff624igMwsigfFaWiKSUlYStyQxYYkDtO+7xksSUI/3LihDOZU0KCdF1MjPO1TmFrNAK9e5LFliAEfGmVUbQKGUnYEkQo4qukcrDZnDcYmgj2CBK2nQWxtVaBCFhRuUk0paQkbJUeRrt21T4vWWwJwr/YrbUAXIWth67IXbgmLFsG9IwjYUsQAj61ykDBKkTCliBCEl8klQMgHZtJ2HqE7jq2RIhjNmuuboMRqZmiKSWlGFsFiy26ddM+L1lsCcK/6BW2Oiy2i+5vREIugLdchW3j1yWIjVgs9QRROh5lRSbCDMEqIx7efFrbkoQtQQQOiwUoKeFnqqqqgJQUIDERqKlxLgOq63IBTM6pQjWXgh4DEpFYWQPMde5X/1cVqpGCHgMTkQiVY4rH6hMn/Pv+QxwStp0FkwlYuRKYPt1llRUGbM5ZhqwM0ZSSTldkstgSRJChJWw9dEVOiFavYxv77efAt59LG++7D0hKkmbZoDq2RJghWGXy83nd6bVVRg0StgQRGAoKFJ+TPSXO/ufpOkV++AGYNg0oLGxnrzoHIeGK3NzcjHvvvRe9e/dGbGwshg8fji+++MLj41x88cXgOA633nprB/QyBMjNBfbvB5YuBe64AzX3LsavC9agattePmOqGL3Cliy2BBFc+NAVufHL74E1a4DKSn3nZsw12FBJ2B4/ru94hE+gMdT3tLfUjyYkbAnC/1gswIwZge6FMkVFqFxf2v7auJ2AkLDYTps2DWvXrsXcuXNhNptRWFiIyy+/HBs3bsT555+v6xgffPABNm/e3ME9DQFMJmDmTABAov1PEYqxJYjQRCRsa+sYEsTrPE0e9d1/ge/+69n5hWBDwXz15psum7AHHgSXmupjNUCoQWNox2Ay+c5KK5QOMpsBk3gyiIQtQfiHsrKgfmZ9csImvIAMGAy8xwgNn8oEvcV227ZtePfdd/HEE09gyZIlyMvLw9dff4309HTMmzdP1zGamppw11134d577+3g3oYRemNsFYSt5LZAFluC8Cu7X97geB337CPSUl4exth6hTjY0GIBs0+kieHAwPK8Le5HeAKNocGPvHTQ7j2iiWUhwzlBEB2Lm1w0gYQB+B6ZANpZG7cTEPTCdu3atTAajcjLy3O0xcTEIDc3F5s3b8b+/fvdHuPpp5+GzWbD3Xff3ZFdDS90uiIfKqt3aePEC0E8+0UQ4UZFqQUDtr7jWDaASUt5iS22OlyRldD8RRsM0mDDsjJwKvcAztaONLKEbmgMDW6USgdt2kquyAThd0wmNEydHeheuMAAFCIHPyDD0daeLOzhTtC7Iv/4448YPHgw4uKkodbDhg0DAOzYsQN9+vRR3X/fvn148skn8frrryNWbK0gtNHpily5owK9tI5DFluC8BuHisuQJpOeQimvtAwTLzyjovhkUF5abDkAVnA48H+Po28fANXVQHIyb6UdOVLqm2k2g3GcorhlBiM4n6WRJdSgMTS4USod1MZI2BJEINjbfwzOwKsAgE9xKf7AqahCMv55RyJOTq5xjneA87WQFbm6GjVRyXjqKSAZ1ahCMmqRiB6oQU/7MgCkoBrVSEb+vYnoH+/mmM3NqDrvCky/KgPoqCzsYUbQC9uKigqkpaW5tAttBw8e1Nz/rrvuwtlnn43rrrtO9zmbm5vRLNRoBFBf72qVDHt0uiKnjDtT+zhksSUIv9ErywwbpK44LqW8YmPdClv5MeQYwXB08Ej0nTtGu0MmE7gVK2CbMQMG0b2AcQZwy32ZRpZQg8bQ4EapdJCNMzpdI0jYEoTfSEt2uv5/gWy8iLkwGoHb7gSgY7hKBP+bFmdMv+MO4O5nXLe99FKg/xj3x0xFB2dhDzOC3hW5sbER0QqCKsbuUtfY2Ki678aNG/H+++/jhRde8OicTzzxBOLj4x1/WrPZYQvH8X9iFL6HtBHpLm1M7IxMFluC8BtpGSbUnuScbGqDEZtzlvHWWgHB6qbhilx/72L8NX2xqtuxi1jWIjcXhn37cGTpGvx5x1IcWboG3L69lPnCT9AYGtwIpYMEJymjETh/NFlsCSIQJMU7hW0bIrwSkfKM6XPmuNqKPLW4dmgW9jAj6C22sbGxkplfgaamJsd6Jdra2nD77bfj5ptvRkZGhuI2asyfPx933nmnY7m+vr5zDsxGozRxhVJWZBlV46ch5fxT+HqWAFlsCcLP9DgpFjjAG3yqN/+FLPnkkxBn29iompgmYXAqEv75T6D1T6CoSLJOse61O0wmJM2cjCQP3gfhG2gMDX5yc4EhQ4DvvwfOPx84tcgIfGtfScKWIPyHaLL39jsicN+d3llG5RnTfWFx9WUW9nAm6IVtWloaDhw44NJeUVEBAOjdu7fifqtWrcKff/6JZcuWoby8XLKuoaEB5eXlSElJQZcuXVz2jY6OVpzh7nTIha2OzyRp/SqUHbkJjtxyZLElCP9y5AgAgOvRQ9GjwmGx1YqxFX7rhYXA7NnAp5+ipikaB2MGoccVIz0TtURAoTE0+CkocCaQMhiAn8YacbqwkoQtQfgP0TPv4NMjdbkf6yE3F8jO5hM+DRpEArUjCXphO3ToUGzcuBH19fWS5Bdbt251rFdi3759aG1tRWZmpsu6VatWYdWqVfjwww8xceLEjuh2eCBPIKXwoFJRaoE4essIGwZsFtWtZIxP+1hSAhw5gtryGtTvrkK3c09Gj6kT6NdNEL7m8GH+f8+eyusFi+2xYzheuAaKlagbGpyvMzKAjAztutdE0EJjaHCjlBX5i6/Vha2k3i0NnwThW8TGnAj3Ekn8ewS0f5tkcfUPQS9sJ02ahGeeeQbLly93lBpobm7GG2+8geHDhzvcm/bt24cTJ07glFNOAQBcd911igP21VdfjcsvvxwzZszA8OHD/fY+QhJ5UICCKzKfhVWKUZy67bvv+FHb7pKcYP/DBwB7YDa4lSsoWIAgfEVrK1BXx79OUnH8FRW/6/rpvxU3Yf83C1xkJP02wwAaQ4MbpazIrSpZkeWW3eXL6SdKED7FA2Er/j0KKWkYo99moAl6YTt8+HBMnjwZ8+fPR1VVFQYNGoSioiKUl5ejoKDAsd3UqVPx7bffgtkF1CmnnOIYoOX079+fZpn1oMNi2yvLDCsMEjErWV69WvXwHBhYXh647GyaxiIIX3D0qONlo7ELXKInS0v5cgJu4H+b+fTbDANoDA1ulLIiM4WsyEqW3fx83r2RfqIE4SNE4TlH6iJU80LIf4/idDL02wwsQZ8VGeDdnubOnYvVq1fj9ttvR2trK9avX4/Ro0cHumvhjQ5hm5ZhQknOcrSB37YNRuzOzNF9Cs5moyrTBOEj/pe/3PE6+vuvUTytQLpBcbHuY3E2qgAfLtAYGrwoZUW+5DJXi62SZddKP1GC8CnbSpwW2/xbI1FQoLyd0u9RDP02AwfHGKWtdUd9fT3i4+NRV1fnUuQ+rElJkVp35swBVMo+VJRaULlpN1IzByHtj43A1Km6TsEMBnB799K0FkG0k4pSC1KGpUu8J9pgRPW2cme5n9JSYNgwXcdjBiO4veX025TRaceDdtCZPzO9MbEWiyixzIoFwKOP8is+/xy45BJYLEB6uvRh2mjkS3/QT5Qg2o/FAiztuxiPswcAAFfiY2wwXqn4G1P6PYqh36Y6HT0ehITFlggMrTUNkmX24otQm75KyzBh6Nwx/AO0ODZXo0wEA8AtX06/fILwAYeKy6Tx7QAiYEXlJtG0cUYGkKPsUSHek3EGcMupAjxBtIeCAv7hd9w4/r+a9Qfgf2pjxth/ckZXi62SZdebkiEEQShTVgYYmbSOrZrlVf57NBiccbb02wwsQR9jSwSGyvWlSGlrkrRxgL6YWOHXDQDiUhATJ6L2pFOR8OoT/GYXXUTR9QThI3plmWEDBwOcTjhtMCI1U1YFXijhU1QEvPqqo7n2qeWoOJGAXr2ApPEjaVQmiHbQrphYBWELUMkQguhIzGZgE5wxtm2IgNHI/9aUkP8eAfptBgMkbAlF6jcUI1Wh3RETq/WrFVtsDx1yvr7ySiRMnAjYhS0iI33RVYIgwHtN/DZmJk77ZikAwAYOm3OWKdeczcgA+vWTCNsep6Whx/jxfuotQYQ3WjGxHglbcZZWUMkQgugoTCZgwmVtwH/4ZZsh0q3lVf57pN9m4CFhSygSd3kW2FLeSiuGGQzg1KavBMQWW7GwTUmRpk8XZZ8jCEIDUS1o1NSg/q8qVCMFCecNQtKEUY7R9LS8LMAubBvufARZz2p4RCQkSJdpookgfIZStmMt648EFYstQRC+QS32/azTncL27TURSLkmMP0jvIeELaFI6vgM7BqVA3NJkUPcMnD6YmLFFluhpibA50MXPzzLZqIJglCgoACYMUNSTyDO/ofXATabA7fCXg9aNFkUPyhZ+7hyIUvCliB8hhCDl5/Pa1OP4u5EwvaXn6xIGE6WIILwFZr1oEXPpSm9SSKFIpQ8ilBl8KZCVK3bhj05C3B08VJw+/fpi4nl5HZeO1deCaxa5VzWsNhaLEDJGguq12zkF8Bnff3l4TU4snSNo80vWCyoWbwUe6Y+jMr1pf47L0FYLC6iVg7H+JqzsFiAlhbniqgoz85FwpYgfEpuLp8ZdeNG/r/ulBIiYfv4o1a3iaeUsFj484qHSqU2fxHIcxOEgFrsu+O6FD+XRpCwDUXoWyM0SR2fAYxXz2ysxNG/a9BDaQVjwKxZzmUVi21BAVA9fT7uxZPgANg4A3aPvBmDSlYhzZ4YR2Kl6kgKCmCbPh2JABIBsNWLsGtUDgZvKuzY8xIEwPtK6ajI5qg52w5he7isBj2zPO0gQRBaeBMTW9NgRKL9tRFWzxJPQdkiBWhYqToYTQsZQfgRt7Hv4udSnZO9ekt6Ef6BLLaEz6n9vUJ9pdXqdFVWsNhaLMDCGRbcZxe1AGBgNphLiiTZXiVWqo7CYgGbPl3yI+EAmEuKyHJL+AezWd0DQgQz2IP32iFsE3OvRvE0D81CBEH4nKrDToutEXyMrVrZETlqFqkZMzSsVB2IWwsZQfgRIfZdjCT2XSxsdVhsPSnpRfgHEraEz0k47ST1lUaj84FbdAMR3JRKSoCBrMxlN6VHe4eVqqMoK1M+L4CGzzZ13HmJzomFd70vWWNxPvSZTMB992nuxse+24P3PBC2FaXSJ0sjbBhZlO/SThCEf0lJcxW27hJPicdQJYuU3PFDr1BuL1oWMoLwNe5c3t3Wg/ZA2NKkTXBCwpbwOT1OVklaYzDwdxDBvcNusRXPeF13HbAbZpddlZwxHVaqjsJsVj4vgO6XZnbceYnOR0EBWN90JE8Zh+FT0rGwb4Fz5veii5zbXXIJsHgxGkeMcTRxLzzv9OvzQNgeKnadQIqAFZWb6ImTIAJJYk+psHWXeEo+hsqdPIxG5baOHD4F3FrICMJH6LWeasa+exBjS5M2wQkJW8L3yEaxY1P+CaxZA+zdy99BBGHb1uYy48UYcICTjt42gxH7z7hM0iaxUnUUJhO4U0+VnRcoG5XDxx4ThC+wWMDy8sAx/kdghA1LWT4ezbNbbpuanNtmZgLz5yP2luudbd27O197IGx7ZZlhlQ0BbTAiNZOeOAkioIgeqO+5w6qZeEppDAVcLVIrVmhYqToQtxYygvABnlpPTSZgzBiF69CDGFuatAlOKHkU4XtkU8PdrpsATJzobBAG7dZWxRkvJvOZMvzyM/pWVQFj/uM8xf3z/ZN9ooc0DVZTRiYljiJ8S1kZONmPIAJW9Lftxu7dJpgaG50rYmPtG4hu3eKB2ANhm5ZhQnHOcowsykcErGiDEZtzliErg544CSKgiLIiDx5oBTR+kspjKPDOO0ByMv+QLTy8Z2fz1iRxmz/IzQ3cuYnOgdukUHrxwBW5XSW9iA6DhC3he+RTWPIHbJHFVqmIfRdDMyC+QfXs6Trt1rWrz7qriVhUAIhNjvfPeYnOg9kMxhkcFluAt5zuMQziZ34tCsJWPJMsdp0SC1sdGR2zCnNRMTsblZt2IzVzEIlagggGRMIWVqvmpkpjqNEIjBzp+oDtTYZmXxHIcxPhj9rvwGPrqYfJo2jSJvggV2TC98iDeeTCVmSxVXJT+tdzJ6TbNzdLH9gB1VJBPkcmbF2mBAmivZhM4O6+S9L0f9wyPLzcxA+SHWSxFUjLMGHo3DFII1FLEMGBB8KWXH0Jwoe/Ay/q2Kq6NRMBgSy2hO+RW2yjo6XLws3C/kDuMuPFjgNznZtX7G1Bmrw0kEKpoA6BhC3hD8aPB5YscSwu2JfrHCSVhK2axVb82sNyPwRBBAkeCFtA3WpE9TWJzoRPrKde1LElggsStoTvcWexlWVFBmRuSn8cl2x+UVYzXs5rwThxo7+ErThxD0DClvALkgG5gy22BEEEGR4KW8DV1begwJlMx2DgrVn+SEtBEIGk3S7vHroiE8EHuSITvsddjK3MYiunco/UFTmSNeON5TIhS67IRDghnwwSI74GY2L4/3pibEnYEkRoIha2Xox1VF+TILyEhG3IQ8KW8D3yh3S5K7KCxVbMgV1Si20UWhDBZDG25IpMhBNMqWKyHbLYEkTnwguLrRiqr0kQXkLCNuShb43wPe202PbpIRW20WhGNNfKF5EVEAvb0lJg3TrUNMegsjkRyScnIWnCKMBkQuX6UtRvKEbc5Vme1561Wl2TVpGwJToCLauM2B3ek6zIJGwJIjRpp7D1NkOsUkwuxekSnQphPDUYXJ9liZCAhC3he/TG2DLmLP4lIrmr1BW5i6EZU69rAd4WNQpCYNo0oKgIAJBo/wMANptD5YCRSP2rBKkA2FJg16gcz2rQyuNrARK2ClSUWnCouAy9ssyUWddbtDwQyGJLEJ2Ldgpbb+prKsXkAhSn6w9o8iCIEMZTstaGLPTNEb5Hr8UW4G8iMmGL41KL7VuvN6PnEZmwbW3lLbV2USuHYwypf5VAkNgcAHNJESrXz9ZvuZW7IQMkbGV8f/O/MOrNWUgDgxUGFOcsR1YhPfloYrHgyLoS1PywGymoQtx5JwNduqhv70lWZBK2BBH6tFPYAp5liFWKyc3Lc74W/ufn88ck8eU7KMmXd3TYZAAJ25CHvjnC9+iNsQX4h3L5epmw7RnXAhxSKPdTXKzdDYXlhs82kbD1ERWlFox6cxYMdh9xI2wYWZSPitnZZLlVY+VKsBkzkAQgSWh73c0+3lpsqVQBQYQmPhC2gP4MsUoxuUpDnRCnS8LWN6gl+aLJA206dDKAhG3IQw7khO/x1GIr54TUFRnNza6xrm1tQFaWZjfk6XgYgO6XZmruI4GErSaHisscolYgAlZUbqIMJYpYLGAzZrhMuLjFW4stDcwEEZqIf7vtELZ6EWJyxSiFGOqJ0yX0Q0m+PKfDM34L4ymNnyELCVvC9+iNsQVcYwstFhz/eou0rbnZdbvWViAjA+jZU7ELjOPQFtXVuQygbFSOZwmkSNhq0ivL7DJ50AYjUjPpyUeRsjLPRS3g1mLb+NOf+GPuUhxZusbp7RAVpV1CSAGLBdi4kUqCEETAaafF1tPfshCTK5zWaOSX5W3u4nQJz1CaUKDJA206YjJA8nsRjC1eeDzRGBockLAlfI/8Ti2f+VKz2BYUwNanL7p++m/p9l9/7WqxFYSuMMoaDGg8b5RjNff++4g81Tk6tJnSPUscBZCwdUNahglN3ZIdyzZw2JyzjNyQ1TC7TgTowk0d29jN3+CUF2chadYUsF9/5Rs9jK8tKADS04Fx4/j/BQXedJQgCJ/QDmHr7W85NxcoL+cfzMvL+WWlNsJ3KE0o0OSBNt26+XYyQP57OV7vnSsyjaHBAwlbwvfILUXyZSWLrd1NU+7aCgBs9Wrg6FFpoyCIm5v5/127IvbiC5zr4+MlVt7ILrI4Xj2QsHVLbK94x+vmzLGUOEqD4gc+073tH3OXoj53LrB4MbBnD98YGekc0aurFfcTfmlWD27tHe7aRRCEZ3gpbNv7WzaZgDFjpMJKqY3wHTR5oJ+CAmDECNcyVvLJAL2WU6XfS0MN/2zZxukXtjSGBhckbAnf4672l5LFtqwMHFO2Z3GMuT7IC6JVsORGR0utVC0tUvdlbwQpCVv3iL7r2PiYAHYkuKkotWDUqnyJK7LW4+opL85C3OsvAg88AFRW8o2trXx5K8DtiGk4Vo/iafqmjCnOiyCCDC+FLf2WQxOaPHCPXDwC/OPH5s3SyQBPLKdKv5dI8M+N5ZYI3VZX+t0FFxQdTfged8JWyWJrNoOBA6dkseU4cPJyKMJ+gsU2KoqEbSAQW+NVJiYIPtFWGqTXjlFlW02KioDZs936XXGA7gzVQpyXfBac4rwIIkCIhe3PP/OeG1VVQEoK3ya8TkwEamocy2fXAc+hCpVIQS0SkYAapKIKZ/0nBShR30/rmAD4mu4TJvB5LQgiAKhl7hYX0fA0y7TS2BcB3tjSikjdGappDA0uSNgSvsdd0holi63JBO62W4GXX3Y93PjxriWBhP0Ei61c2MoTTnkhSI8eaEQPeSMJWykhLGwrSi04VFyGXlnmDo8L7pVlhhUGGEXitg1GRGjabVXYtAm48Ua3mwkZqt29NyHOKz+fn2WmOC+CCDAffuh8vXkz/6eDBAB3KK142gd9WrQIyMkBCgt179JhtUaJoMCf368e8ahlOVXqn3zsA5zCtg0Rustb0RgaXJArMuF7vLHYAsCwYY6X9QPPcraffrp68ijBYhsdLRW/LS3SfTwUpAUFwPo5X7iuIGErRSxsQ+izKbnhZaQO64uz7xqHlGHput12vSUtw4RfL73bsWwDh9LrnvPuYJmZLoktlKYUPMlQTXFeBBEkWCzAww8HuhfKFBUBpaW6NqVkOuGNv79fPYm2vMkyLYx9a9bwjzNiYeuJ1ZXG0OCBhC3he7yx2AJAba3jZdwlzgzHquV+AHWLbTtckS0WYOEMC27CateVgpAmeELQYltRasGId+Y4EpUZYePddks7NtPDkNvHOF4fnz4XI1d6MfLl5PDugLJSBNxpp7mIW08zVFOcF0EEAWVlwX0v3bTJ7SaUTCe8CdT36048eptl2mQCJk8GVqxwxti2IcJjqyuNocEBuSITvsdbi61I2CI11flabn0FXF2RfZg8qqwMGMjKFDM0k7CVEYLClo93lfZVr9tuuxAFA3U/ubfbkjwN109H9zMH8AvNzcAVVzhj3OSlCAYNAjdrFnDrrY4mylBNECGI2czfV4P1fpqZ6XYTT11CidAikN+vCRaYqkqA348oxonnpqTgH48m4ujfNUhmVYirTAEWQ1d8eW58PAT/p9MHNiGDhtCQhIQt4Xu8tdjW1Dhfi4WtmsXWanUGRkRFSV2R2xFjazYDf3Fm2BjnKm49rG0W9oSgsO2VZXZp88Rt12uOHXO+7trV7bXU/eUngaQk5ZXy4vGxsdix4SCGipqKpxWQuCWIUMNk4k1HM2YE3z1V8BhxAyXTCW8C9v0WFADTp7vdLNH+1x5i//oFuzKnYfCmwnYeifA39JRO+B53g7Eei60wkwbwIlUpxlbcJrfYyvfxQNiaTMCCFSZ8Pj0bl0FWe9SdNbqzIf48gu0hTAW5VdYKAzbnLENWByeQkqRv7NqVnxSIinK9tgViNMonya7DEw1WnLnhSUmb3qzIBEEEGbm5fDrWzZuBI3bLVHU1kJzMrxdeC9anjlz32GPAiRNAr166E0dRMp3wJiDfr8XCT/b4CQ6AuaQIletnI3U8ZQMPJYJe2DY3N+Phhx/G6tWrUVNTgyFDhuCxxx7DxRdfrLnfBx98gPfeew+lpaU4dOgQ+vTpg/Hjx+Ohhx5CQkKCfzrfWRFbYZXQEWMrttg2/7ob0VEy0dTWJnULlsfYykv1eJjYKDcXaCgZDLwuE7YhlCDJL4Ro8igx9Q88iazHfGfZrFxfihNr1iEhLQaJ5w4CRo3iR3yxsO3Wjf8fHe2dsJV5RRyvaUIXWTkhv7hXE0EPjaEhihD41w58krX21Vd5YSsuQaQDQZvv3s1b8kjUhhcd+f0qXrcBiD3nADR8tomEbYgR9MJ22rRpWLt2LebOnQuz2YzCwkJcfvnl2LhxI84//3zV/fLy8tC7d2/cdNNN6Nu3L37++We88sor2LBhA7Zv347Y2Fg/votOhtxtWI4Oi23ps99BuJVEb98MBv4mI9lPy2IrFhGAV6Kru5Hq2LolBF2R5SQma8e6ekLZiJswaOtb0muV43jXQrnFFtCOs/XgQTI2PQXWza7lhDrcvZoIemgM7ZwUFDgT/BgMvIXNq0ytwkS0uwlrBUwmErThTEd8v6rXbQBizxmA7pe6jykngougFrbbtm3Du+++iyVLluDuu/lSGVOnTsUZZ5yBefPmoaSkRHXftWvXYsyYMZK2c889Fzk5OXjrrbcwXYefPuEl7oStgsW2otSChJ93IRYA4zic8+EDkl1conZbW10ttuIYW3E8IwDYbKgoteDIuhKkpQFJE0a5vyPLrb724xAiwkDY1u2vQzxkltZ+iXx86ygd14mdyvWlrqIW4D+X/Hzgn/90tukRth7QrV8KinOWY2RRPiJgRRuM/nGvJoIaGkNDF0+treLtAeWstdnZXggRYSK6tZXq0hIS5NdDe68PtWzL/HVrAu6+G1iyxLdvQgUGoGxUDgaTtTbkCGphu3btWhiNRuTl5TnaYmJikJubi/vvvx/79+9Hnz59FPeVD8gAcPXVVyMnJwe///57R3WZAPDToo8xRLTsksRGbLFta8PmG17GiHdudwoCxuDWVtXWpm2xlQlbVluL1GF9kCYsz+bArVihPYUtFrZGIx9MQsJWShgI24Jn6zDigxsxcs/brqJUsLbqMHXUbyhGqtpKqxU4dMi57GNhi5gYZBXmomJ2Nio37UZq5iAStQSNoSGKp9ZW+fZ33unDrLX2ieiWE61IT/eBBZgIC+TX3M03A6tXt+/6cJttecwYp7C9/HLg/PN9Hl9eW16DmkPN6DLpChK1IUpQC9sff/wRgwcPRlxcnKR92LBhAIAdO3aoDspKHLI/WPbs2VNzu+bmZjSLrIH19fW6z9HZqSi14PTPnpG0uSSxEVlsa34/hOFiUQveOuvieixHyWKr4YrMyY7HMQaWlw9OawpbLGy7dgXq60nYygnBGFuLBRB/4/3xF0bu+Vj5ehOsrTpMHXGXZ4EtVblujUapp4IQY+tDYQvwibEoppYQoDE09NC2Wunb/rnnfJi11j4R3dbU5gh0aJcFmAh5lK65oiLnem+vD7fZlsXPdWPH8hZcH5Ng/yNCl6BO8VpRUYG0tDSXdqHt4MGDHh3vqaeegtFoxKRJkzS3e+KJJxAfH+/482Tg7+wcKi6TxPkBziQ2DkQW29rV6xQvQg6ApkySx9i6EbZKcDb7VKAacmELBE68WSw4snQNducuRt3ch4HS0sD0Q4670k5BSFmZdLkf9mhPoljdXCd2UsdnwGZQmCvkOD5lpNiiLVxPYvf59qCVaIrotNAYGnpoWa3kWCzAmjWu29tsvNVWCNNvV9Za+3gdCWmIkc7bYlBhsQAbN/L/Ce9RukbleHN9CNmWVa9bpTwVBCEjqIVtY2MjohUe/GLsD3GNSjGQKrz99tsoKCjAXXfdBbMQhKLC/PnzUVdX5/jbv3+/Zx3vxPTKMsMqu6xckths3ep42X/X54rHYQCOvLEOLXE9lE8kz4ocHa0dY6t0DoPGFLbFghaLyHW0Sxf+fyCEbUEBbH36ImnWFAx6/QHEv7gIbNgwYNo0//dFTgiW+zEPlH6HTYiVVyuW4oGpw2hUkMivvML7ZHmaPMoTKJEPoQCNoaGHYLUSo3QLKigA0tOBu+5yPYbRCMyZA5SX80KuvLwdbsN2T5NItAGiO6We22IwCUnh8xo3jv9fUBDoHoUuSteoHG89BHJzNa5bEraEDoJa2MbGxkrcmQSampoc6/VQXFyM3NxcZGdn4/HHH3e7fXR0NOLi4iR/hD7SMkwoyVmONnuUrJDExuEeabGArV6teQwGgMvJQfK08YgacpryRlartiuyG2HLOAO45SpT2AUFYH3TEVXGx5G1woja43ZLnL+FrcUCNmMGDDLpxQFgRUWBt9zKXJErSi348bmNqCgNgicZFUxJ0of5eNS5TMY4EKytekwdNpty4jT7ANxcedTZVlPD//exKzJBiKExNPRwa7WCqyuoGPH2JhMfligk9vFKZIo8rKIMVtU+yQkmIanm3h0MgltOME0GqCG/Rg0GvjKVTzwEIL1uxdQeJGFLuCeohW1aWhoqKipc2oW23r17uz3Gzp07ceWVV+KMM87A2rVrERGh4CpI+JSswlxUbyvHjuc3onpbuTRxVFmZptunpe9IcNu2OQvBa5UYEM/euSv3I4Pb9afyFLbFApaXB445nxgiYEXVIX5A97uwLSsDp2IJ5QBg0ya/dse1E85vs353JVKGpePsu8YhZVg6iqcF6ZT4iROSxdPwByLsju+NqelozBCVQPn3v6XXid33r/bexdgz9WFUrhdNLCgICABAUxOKpxUg6qf/OZrYgAH8kx4JW6IDoTE0NNG0WkHdFZTjgCefdN2+XSJT9H3/9WebLgtwsAlJT9y7A0kwTQa4IzcXeOIJ/pqz2YD33+eX9XoIeCrgCwqAlxY7n+s++56ELaFMUAvboUOHYteuXS6JJ7baXVmHDh2quf9ff/2FSy+9FCkpKdiwYQO6CQlbiA4nLcOEoXPHuCayMZvBNOIy0/ZtRYWQu9hiAduyRf0kYvHqaYytkA1PTlkZONkIyEFww4L/ha3ZrOomywAgM8A11kTfZffDexzx1UbY+KRhwWi51bo2zjgDsZdc4FxOSHC+LigA+vYFpkxBwtMPoP/qRUiZMAy7Mqfx61WEbd2uSmQWTVdMXqZ6PXlQwxYAuSITitAYGrqoWa0AdVdQxoD77pOKhXaLTJHF1pTaqtonMcEmJPW6dweSYJsMcIfFwl9rwry7zQbMn89/pu6uD08FvPDZdIFz7H7ypa5B+9kQgSWohe2kSZNgtVqxfPlyR1tzczPeeOMNDB8+3JGQYt++ffjjjz8k+x46dAiXXHIJDAYDPv/8cySrCRnCv5hM4FasUE0MZYTNmWjKjXXXxWIrjiVzJ2ztrngumM1gnPRnwQA0wW4R87ewNZnAzZzp0iy4ayMjwOnoRcJW/l25JA0LFmQWWzHHmiKlEySCWLVYgBkzXOKIOQDmkiLecqsibI/tOqCcIM1mVa/57KlVjCy2hAI0hoYngiuokriVC8h2i0xxeT53NertBJuQ1OPeHWiCbTLAHd721xsBL5yrq0jY1tu6Bu1nQwSWoPYpGj58OCZPnoz58+ejqqoKgwYNQlFREcrLy1EgmuKZOnUqvv32WzDRQ+ell16Kv//+G/PmzcP333+P77//3rEuNTUVF198sV/fCyEiNxeGIUPAhg1zEUOSRFN2a6WquNWy2LpLHqXmNmoygbv5JmDVKkfTIaQipU80sB+BSR41ahTwr39JmrjkZKe7diDRyCDhkjQsWNAQtjF9e0onSITM22VlqsmxOAANn21C6hBRFdtu3RzXYPfe3RSvY2YwgktMVO6IpxZbX2VXJsIKGkPDl9xcYMgQYMQI7bI+bkuouEM8yaYVGiTCZOJdou+7jz9vMAjJ3Fy+/Mzu3fqsiv6m3d+Tn/G2v25r1Wqcq6vN+czXZOgatJ8NEViCWtgCwKpVq/DQQw9h9erVqKmpwZAhQ7B+/XqMHj1ac7+dO3cCAJ5++mmXdRdccAENyoEmIwPcypWwzZgBg/1hygoDNucsQ5bgvmwy8dtMn+6weEkEglaMrdWqfX41iy2A/durIC5OEd+lFV16GtwLW4sFR9aVoKICSJowynf1RJVEuKfCp6NQcStngPS7DCY0hG33d1YC1mudDcJnr5EFlgHofmmm9HuKj3cI27ikaNSlDEJ8lXN62ZG87IsvlA/qqcXWV7G6RNhBY2j4kpHBWyLz8/khT0lACtZKrW008cJiW1DgFLUGg3LcrxoWCy9+zGbfi08hoVYw0u7vyc+YTMDNN0vr1950k/v+eiOIhc+m23TnM99DT3UL2s+GCDCMcEtdXR0DwOrq6gLdlfBj/352eOka9suCNezgtv2q2xxdvJT9nbOAncgcxxhvO2P10+9wvGYrVvDbGo3ONq2/n35SPNXBbfuZTbatDWDNp5zJL0dEKPdx2TLJflZw7Osrnmab5rzHSv/5Gjv82nuM7Vd5f+54+WXX/vfs6d2xfM3o0Yqfb1tScqB7ps6qVdrXBsc5X69a5dzvootctrUB7M9ROfz6n392rjvtNOfrO+5gbOhQ/rowGNnhpWuc18LNNyv3ITHR/fsQbV9VuN7nHxOhDI0HnkOfWceyfz9jGzdqDzHibfbvZ+zrr3UOSdde67zXlJfr6ovBIL2dGY36zrVypXNfg4GxJUsYe+89/s/b4TPU0PNdBgPbtkmHSk+/Z+FRzWjkl/XQOPoS58lqatrVfwGPfguET+jo8SDoLbZEmGMyIWnmZCS52SZx/kwkAqgaMBxCmpyuK19wbiO4YkZFAXpqM8osthYLsK/Egtj1a4TUVQ44AK3HWxAFKFtsLRaw/HyJq6kBDGM+nedsex1gszlwK1Z4XlBQybqs0yWsw1Gx2Bojg8SiLKegAGz6dO3YbbHLsdgKe9JJLpu2nHIGBm8q5BfE31N8vPN1U5PDu8AQH4ekmZOd69QsrR5abHtMuxLFG5dLM5ATBNEp0GOJFLYpKHDGOBoMvCVMc0jSabEVLK3V1Z67mgr7y2Mv77nHuZ7jAG+Gz1AjmK3KAu8sseCjeSXIwxEkoAYpqEIVUgArYJtTBZybAiQm8mXtqqqAlBR+R/vr3MREXHNXDep3V6H7oBQkVgKYa99OY7+Y/WXOTtTUSJM7eoHHvwUiJCBhS4QMFaUWpO5xlleR1HZtaOD/eyFsCwqALTMK8C+WByNsivGQEXF2Oa0kbFWSXMnbhEy4XHa2Y+SqKOXdl03Nu5HQbL+RDxrEx9UKo5uSK3KwCFu1GFuVeNSAYq8JrClqAf4JSui/EGMLALW1LptGdxXFtoq/J/GAKxK2LrX3VISt1QZoTQ1UlFokEzCOLNSzs33nAk8QRFihlrhHNCS5okPYigUCx0lvoYD3sZdiGFPua0e6LhOuHH2mAFPmzcD1avUaPrD/uSHB/uc1AwcqznTovR68+i0QIUFQZ0UmCDGHisukYlbMrbd6VhfULkIsFmDhDAuWsRmOUjVKwic6TlRORS7aNEryyOFszrSBxdMKkDqsL85YxJePwYsvAg88AEyZwpeVEZK7KFls3cUQ+wuN0k1Bh0ZNYAcGA5/9WEAsVhWErWS9PMZWQEvYqiR9Mhyp1qwDfKi4zKUtaLNQEwQRFKgl7nnxRWmbpMaom+RRcoEg3GKFNBBCjK3e2Est5Fl3Q6nua1hgsSBx3gz15zB/Isx0iNIpe3I9hFoWakI/JGyJkKFXlhmqcs5+k2utbdB3MLtYLCsDBjINwWyn7q9q54L8bmgygcvKknZHrZsGfuq6otSCUUUaA4T4ph2CrshBabE1m8EUpi2s4LDv/xYDa9YAe/cCl13mXKlksY2KcgpX8Xo1YdvY6MzSrdNiywGadYD534L09h20WagJgggK1MTjc8859YFcHPy+W9tiqyQQGAOmT+eHB5sNuPde96JTXpJHCbHlN9TqvoYFeiaH/YlIiXp6PQRbSSrCd5CwJUKGtAwTfho8WX0DqxURrerZjiXYRYjZDPzFqWe8FYgTZbRV9JeS3Q2/v/gRF8nKwPGZcE0mHCoug9HdrKdw0w5mV+RQErYmE7j590marDCgJGcF+r42H5g8mX+6UqpjCziFbUKC09Kqx2JbX++0sHfrJu2ThoeBlgU2LcOEkpzlaLM7LLfBiM05y8gNmSAIVUwm4M47XdttNn6oURIHX36rbbFVEggGA+8lKgwDekVnbi5QXs5bi59+Wjq8GAzSLMFkcQsAZnNweWmJlKin10Mo1DYmvIOELRFS9H72HnVrKDj38ZMCTU2oKLWges1G3H+//DiuSI6rJGxlA37WyltcY2zvmOuIB+mVZYbbirjCTVtssRUsfowFpqaunGAa5AQs/Pdassbi+iAlssZWj5yAqm17XRMuicWmksVWLGzVLLZxcc7XR444X8sttj//rPo23FlgswpzUb2tHDue34jqbeWUOIogCLfMmeN62xaGGiVx0MLULbZCPONTT0kFwp13ei86TSZgzBg+cdS+fbwjjeBMIw6nJItbxyJxRxcwmYB58wLWJwmymY7//c91E3fXg3gipbycEkeFC5Q8iggpUsdnYNeoHJhLiqTC0WBA3ez7EP/yYl3ids9zHyB9+81IA8MQ2fwO69od3HGpS7MkoZQOYYv6etdtYp1xumkZJlQOGIHUv7cod5DjnDdtsbDt1s0Zr2m1ug9K6mwUFIDNyEMys6EHDJjJLceIFbnOAUskRJPHngkoWTijFRJC2WzO7zQhwWmB1WOxVRO2Fgvw8ceKb8MKA76ctAyXurHApmWYyEpLEIRuTCbemqpWL1VeY9TKRTpne0XCVp5R9skn+bq6gpB47jnPapWq9XWyipNWqNV9DSU0swVffDE/kwHwmZYuuIBPhZ2czLcJr4Xsxr5eBwBJScDIkY4v22Lh3d3lPPGE/mzhRPhAwpYIOQZvKkTl+tk4sfZTJPSKRuK5g4CRI5FgMmHX/w64il4F+m93pu0zymynBsaLFkHMtsGIhrTBSKz4nd/AW2Erm+1OTY8F/uZf1859GAm7twPr1/MN8+Y5RxK5sK2sdJ5TnLEyEKhZjQPhimyxgOXlgWN8n4ywYSnLx8C8bGRnm/jBS/wdqH12ChbbyjUbkSq8p5gYZYut+Hvq0oU/fmururAtc00AJfAoHsLY2TR9TBCE78nN5TXJ7t282BQe7JXE4iWXRgCf2ne0j3NKLsvz5/NWL+FY/hCdau+D8B632YLFE7ijRvFfvM7jdlT2arWM2hkZvj0PERqQsCVCktTxGcB417vW4E2FaBx9ELHFX3h/cHu5oNZTzsBv+S8jNXMQ0h74J9BeYSuIIIsFWLcO1h+2wwjAFtsFCc8vBL76yilsxRk0xAOJWBgFQ5xtMLhDC5SVgZP1JwJW9Lftxu7dCsJWLb5VbLFtaUH52VcjfcdHjib23Xfg+vThF9QsttHRvABubZWWnxJ/f2bl2G4G4DPuCswglzqCIDoINUuVIBY3b+bnJ/tvjXQKW/v9UyueUTimP0QnlfrxPW6/W/k4p4OOrhcruKW310OACA/Ij5EIO6pr22nFtFvmohK6YejcMbyrp9jlV4+wbWhw3aa1lb/D9+kDzJoFY0MdAIBrPMGXdhEnFhKy6ALKMbZK5wwEwSRszWYwg2um4D2GQc4BTmxh1WGxbSyzIH3HRxIPAA4A27+fX2htdVqnlYStHPF3bDIBK1dKVjMAq5CDvBUZ9KBGEERA+Pxz4Lrr+MpzS553TR6lN75ViJftiHsZlfrpGNx+tx4KW39kr6ZEUIQYstgSYUVFqQWmnzd4tI8VBhd3ZADSm7b4Tr9/P468/Tmq/zyC5JOTkDRhlKvIrKtzPV5NDV8DQQYHYFRRHqou/S9ShEY1YSsWRsFQy1atD4FwRTaZwC1fLvmM/49bhoeXm5wDnB5XZNH33rrvAGIVNpG4ure08PvoEbby5FGCWWP9etTtOoTdg6/AheNJ1BIEERjkQkQpeZSu+NbSUmDdOv4+KMRNVlUBKfwoV/9XFaqRgqSeQEKzvV1hO8dr0bqa6BTsfhpYgipUIQW1tkT8Nb0G9SVViBuovp/jmE1NwIQJ5KuqgNvv1kNhq8e67wvILZ0QIGFLhBWHisuQ5uE+NcvXomfeP1xXiF1VRcKWnXkmkgAkCcuzOXCnnCLdV8kVWRxrKcMIG6p/q3YKW7HFVzyQdOnifE0WW1duuUUibBfs/SdMfUTr9bgii9ojkxPAyuASsy1JJuaBsK070op4eaPJBMyciXgAqRZn6C0NzARB+Bu5EGmFclZkTSExbRpQVKR5njj7nzckAnhCacXrHhxk0SIgJwcoLPSyF+GL5nfrobD1lZuwHrdzcSko8TLRuSBXZCKs6JVlhlV/0R8AQM8095Y7sbB1KePDGNjvv0sblVyRxaJUhhUGJGWd7mxQsthGRwMRGjUFS0tRN/dh/JW7GDWLlwJLl/J1EjqyYn0Ak0dVlFrw43MbUVEqen+yz8SUKk3YpcsVWfS9x/bsDqtRuh0DB+7MM50NwkAvH/Crq10O3f2lx3i3cwXItY4giEAjd0Vtg/qYo+hqXFrqVtQGDUVFfH9FKJa5CVO03quqG7mHwtYXbsJ6x0YaQwmAhC0RZqRlmFCSs8IzcXv0qHK7miuyAi5nU7LYRkYCl17q0mwDh5Kc5eh1wcnORiVhGxMjFbZiN+CrrwYbNgzxLy7CwNcfQOIDs4BZs/ggqb59O+4O7w9ha7HwAn3xYmDuXGDxYvxxxj+QOqwvzr5rHFKGpTvFolzsixM3ARKLw9FjUcqDutiS29iICBt/zMYeaTi6eCm4/fuk082CWBa7jP/9t7PurQgDgJFF+VIxDv/EIREEQbhDLkSsnHNi7/efWt3fk4qLO65zHcGmTY6XnUkYLVnCPxp4/F5FwvbIsWhdkwDtqRerd2ykMZQQIGFLhB1Zhbmo2rYPvy5Yg+aMTPc71NQot6u4IivhIuPUsiKLXJaPj5+CP+9Yispt+5BVmMufT7AiKrkiq1lsS0vBPvpIXcoz1nF3+I6O8y0o4EffKVOABx4AXnwReOABnPLrhzDYP3UjbBhVNAO/Fpa6lFTCiRPSZZHF9va7IpUHdfGExuHDDpEemzEEPebP5J/8xNfG3r3AmjVo3CyqEL9FpT4x+EzNlZt2S9q04pAIgiD8iViIPPaUc8x59uk2x/1S1dqXleXXvrabTP4ZoTMJo2ee4SsKCvPPNhv/3mXGa2VEwvaf/xetWxjrSSSmdE3pHRtpDCUESNgSYUlahgmnPzIZ1qQUt9vufeMr5RU6LbYMHLj0dGmjWh1b0aDQ9ZF7cPJzM/msywJCcig1i624DJAgbIuL3dunO+oO35ExthYLMGOGLuuvEQyn3jIcm2cWSldoWGyb7UlRXB5gxKJVqBkMAAkJztfia2PUKGDKFMSWOmf+2fLlqn1tgxGpmdIAI71ZRgmCIPyBIEQQ4bTYRqIVNht/W1a1bGZk6C4DE3BychwJpDqLMLJYgHvvdW232YARI3RYbkXPMI0s2rFveycB1KzlesdGGkMJAUoeRYQ1jYePQz2ylafPzvXKK3QKW27Ro8D77/OWOwEdwlZx8O/Wjbcg63FFFoRtVpY0mZESHXWH70hX5LIyj45jAMOwd++UNsottiJh2wKngJVkaTQandkuDh1y7puY6HytlnjKDgcofidWGLA5ZxmyMqTT1rqyjBIEQfiZiiOR6GF/HQn+/smY1NqXn88nGzKZ7CuFcSE1FZgzx5mZuLoaSE4GANT/XY1qJCMpCUhosbcrbOd47at1L7zAZ0iOjpYkjuostVCVBLyAy3ephOgZphnOZ5j2ZDpWs5YL/dAzNtIYSgiQsCXCmthUlxy0LhhcHYl59Loid+vmGtup5oqsR9gCvAvs4sWoQSLi6htgBPi7tVKMbUYGuJ49+X2UMBg67g7fkRZbs9njXVzKNmm4Iouzfbo8wERH89Ze8ftTs9iqwAF8Aq9Dh1DTFI2DMYPQ44qRLqJWgMoVEAQRbPQ6yTnmREA5E79E1DQ2OicQTz0VmD9fcZ/2ZEX2BJdsuh9+yAvb5mZehHP89GNnEUZKAl6MW4GqImzbMwngriSQ3rGRxlACIGFLhDldUru73UbV2qk3eVRrq6uwVcqKrMdiK2TSbWsDHngAIhsh2F9/gVPLity3L3D4MBiAv6cvhqn4LUT/+Su/7scfgSFD1PvfHjoyxtZkAq67Dnj3Xf3dkdck1nBFthkiAZvKA0xUlOu+HlhsAYAZjODGjwdMJiQCku9SDZOJBmOCIIKHpF5SV2SDQWqxBWSiRpw0TzwZGAAKCpyWQIOBF665saLK5EKpNjudQRjJBbwctwJV9AzTZohWH0M9QI+1XO/YSGMoQTG2RHgjE6RMQcIe75qsvG97hK03rsilpepWV9jdW//809kgPqddsHExMRi4Yj6izzzVuS5Rj6Tyko7OinzOOc7X118P3HEHsHgxau9djOpREyS2dhs4bL96kXR/DVfkVe9GqWdpVJh0qK1lmuvFMM4AbnkYTvcTBNG5EE2m5ue2Ye9eYMUKZ7oHgwF48knRrS5IhK2ae2sTJxK28slL6EtyFOqIk4M9/bSHpXhEzzDrv4jWlenYXQklX5QEIggBstgS4Y1MkHIrVwBxcfh90b9x6s//BgB0O+5abxSAflfklhbfuCLrKJMgkeUKwtaRVTlWe/D2lsr1pTixZh3iT0lD65DzEH/4GGKUNvSVsBWX0LnxRuCKKwAACULbnDnASy8BAGpeXI2Mi88BPnzAuY+GK3LKSZFIGaVyXnGMs524J+aj+GBPZwZrGY1ZF2Pfef9Az8FJSBo/kkZlgiBCH1G97wGmVsDuGnr0KJ+EyGbj/ycm2sVNkAhbNffWBmusc8xqbPR7H8Wu0YDMTdqPCJbNMWP4OWPdVmrRM0yv9Gj0Gqi9uaLVXEEEdwZrOeEfSNgS4Y1ckKamoiJ1KAb/PMX9vv622OookyB2m66qsGL3GgvMKEOyIF6VhK1c3HnJrsxpMJcUOc7vNmGVL3Dnup3stLYn9Y9zLfej4Yqs6k5cWqr4mRnA+Bq0s7ORptCX2CsuxMn3zlQ+JkEQRCgiErbC/dNiAe67TyWBVJAIWzX31q49nFOxFX834o8//CcsxSLPHtoLxrQFnz/wyH3X3Zgswl1SqHb1gyBUIFdkIryRC9KICBwqLoNRLWGUmPYIW6XgFXfCNiODLz+gAgPAnXmmY/mzSSsxYkpfJE8ZByZkZBYeQrqIckH7wGJbub5UImoBN6K2Iyy2MQq2YfFn2Nzs+j1oWGwlD2xiNCznjhq0SqK4Rw/XNoIgiFBGIa+DZmmcIBG2au6tXZKck76XZDXqrsPaXuQiTymzdEjUzPVA2HaWEkpEcEEWWyK8UShs1ivLDCs49+K2Pa7IatsJg0JEhPIxCwuB2bOBTz8FoqNRg0Qc/bsGPbs3I/76K4BPPgF+/hkAMBWrHLs5RKYwDexjV+T6DcVIbfdRvMDdICoXtnKLrUaMraqw1bCcO2rQbvnZdSUJW4Igwg3xfbK0FFi8GOf+VYX7kAIGIAVVqEIK6pGIof+pAbZ94dy+HVnzXbIZe4Gie+t259gYxZoc3XRb5qadaJXZAdpXLseveCBsO0sJJSK4IGFLhDcKFtu0DBOKc1Ygs2iGeqkfoH0WW7XthEFByfookJHhKBrvkk13wwb35wF8LmzjLhoGLG33YTzHE4ut0gSDN67IguW8qEjSLKlBu50stgRBdALEY87GjcDGjYgD8ITStk/Llu+6C4iL89jHVm9cph5c3FtFY2MsnONDRwtLd2V2QkbweSBsO0sJJSK4IGFLhDcKFlsAyCrMReU1ZyL1yuHq+/pa2DY1OQcFHXVQFYlw85MVBm0fx9imnpXm2Q4arsjiBFQ9pk7QHuXa6Yrc+N/vEJuQACQlAaNG6XNFBiSWc8UatErfn9xaTBAEEcpYLMDixd7vz5jHplBP4zI9RkXYdrSwlIs8cdkkTwWfL6zZXp9DLGx1lL1zlxTKH++F6FyQsCXCGwWLrUDqsHTtffW6IusVts3NHSZsHYmchNhaX2dFFmJ428nf501G//+tdSagemAWuJUr1afj2+mKHPvNZ8A3n/ELHAcMHepc6W5QtlvOFWvQlpS4bM6yL+WzbgcqAwhBEIQvKStrf74ED02hWnGZPhE+ognSroZGn9Rh1Ytc5AGeZwH2pTXbq3MIY3JUlDP0yQ1qSaH88V6IzgcljyLCGxWLLQC34vLo3gb144jRG2NrtbZf2Ir7L8IxvAjC18fJo2q+2dHuY1SuL5WIWsBemzcvTz1rhocW2yO/Vqh3gDHgxx+dy1oWWy0sFrAVK1yaOTCwvFDJAEIQBOEGs1m3eFHFQ1Oo4LLbjkNoI5r0LXi5UVcdVl8g1HIFnHVyPa2Zq2bN9uWQ4/Yc7X2G0XsegvASErZEeKNhsXVnsUuYNwPF0wqUjyPGjcXWMd/tC2HrzhW5A+rYFuesQMKiuzzbSWGWv35DsWImZc5mU0+T6M5iK/4Om5tR+9M+/X30VtiWlalmhOZslPKRIIgwwWQCVqzwWtxaYUDxTZ6ZQtWyGfvMmioaG5O6NHokLL2loIDPvKyVgVkQvlrCzh9Zht2ew0fCljImEx0FuSIT4U07LLaSuqVawlZDOB55rhBJq14AduzgBbBwHH8K23bE2FaUWjBqVb7n9WoV4k3jLs8CW+paJogZDODUpuM9tNgmnuzGvVyMjvggRcxmMI4DpyDemcGo/l4IgiBCDcF/dvNm4MgRoKYGqK521hAXXicmora8Bq8/VY1KJONvDMLm/2/v7uNjOvP+gX9OJjGCRISEMBSR1Jao9ifxVEG7VluWX/0SbO/dsq8o7WqtZ7fe2w1LlbLcd2tpo1lP3W6L6upqf60WLasEi7a79RCpiBBCJEIlIZnr/mNMMs9z5syZmTOTz/v1yktyZs7JNVck3/me7/WA/rj8jgGFiz1LHt3Ny/SKZWy0jC8+ImfOsNwhuS5XGS4uNk2ROXsWKC0F4uNNTzB/3qqV6Wfn5rHe+nj8J4C4e6tdV6AVYlGOhzeXAl/Hm37egNeVfK6YTL7CxJZCm6uKrU7neplCNOxb6jKxdZY4hoej9fRngO1vNxwLsort5f35SJCz568NcecOpOJiq3ckbUemolYXgfC6hqRXAJBycpy/c3G3UIVNYhvbuaXzRkkSkJjYcEtYacXWYIC0bh2Mzz6LMIvkVkhhkHK45CMRhRiDAcjMdPu043uBWctsDiqcH+tsXqbX1F5/wg13c4Y9WSzL6SrDn74NPPusKu1tBScrXv/Z5uurV4GJE00LLSrAFZPJVzgUmUKbq4ot4DbBrN+3VEnFNjbWlEw5SqBUnmNbT+XEtt2gJCjZiVAC7McUCYFwo/WQbenxx11PbjLfUdfrHd8hdrEqcsnwiah+uH/D47t2NWzJI0nu+9KVrCyEFRWhbO0WnJ6xFmVrt0AqOs+VL4io0fL5/Fg1WI788UNi665PPB2Sm5VlmhNcPzd4+L3MOBA2bjTtbayQ3Wth+CQVsGJLoc1VxRYwJUZOgpvVvqVbFSa2gPtKoyfkVmyVLh5VXAz8/e/A6dMo18fjRk0rCEMftC8+6lEzBWA/JPfHH+3n3rpbcdPdvr8uEtuE0WnAD22AYwdNB5o0aRgiHRHh/aIoBgNaP5eJ1t5dhYgoJARFFc6PFVvzVjZLlwLz5zvuEyVDcq2q2XtVWLnaGwcOmHYQUMhnlXlqtIIisa2pqcHvf/97bN68GeXl5ejVqxcWL16MYcOGuT334sWLmDFjBnbt2gWj0YihQ4di1apV6Nq1qx9aTgHnrmLrZJ7luQkL0HRqVsO+pUortoC6FVslQ5GPHUPFvCWoPFuKqG7xaNW5VcO+rpYRJTcXmDSp/ktH29xUPj8P0Wttx5rZkyIi7KPVzZv2T3T3xsKyYuuI5fE7d6zn9oaHN/wMAOD69YZ9bJUOQyYKQoyh5C8+nR+rBsvYePCgaZ9eGXNSK27AOoa6ma/63Z5SvLs7HgJAW5Ri9+PxaNe9Fdo2KUfMd6XAEtN5htJSHBwVj5U7uuEfYgAu6wye3QxISlKtaxQZODCw35/IRlAkthMnTsS2bdswffp0JCUlYcOGDXjyySexd+9ePPLII07Pu3XrFoYOHYobN27gpZdeQkREBFatWoXBgwfjxIkTaN2atZaQJ6di60CXWWOAFIvIomSOrTmABiKx/eijhmOHDiHm0CHE2D5XkkwrXmZlmW4tWyS1zkQPfgh4U3J/h9h8A6G4GOWb/o6KUyWIGpCCNrbPc7ewlRcVW0RE2Ce25sRX6cJRREGIMZT8yZsqnLnKmZTko6R4166Gz3fvNn3IEHPvQ64U2MxV/fTehwNpAN4DICQJ5UvXIdZmTK7LPjEYTHcSPvvMg9apZMIEr6q1RL6g+cT28OHDeO+997B8+XLMnj0bAPDMM8+gZ8+emDt3Lr7++mun565Zswb5+fk4fPgwUu/98j3xxBPo2bMn/vjHP2LJkiV+eQ0UQAortmhlU6tUULEVu3dDys1VdyiynDm2xcXASy+5v5YQDatU5OfL+/5Xrpja7m41SSGANWsgpk6tr/yKzQ6e523F1ma7H7uKbfPmDV9bJras2FIjwRhKwULu6sCKFRcDr7yi4gXVJQmB2P+cAoxvWDlKVp906NDw+YsvmmKfg1WrXa1o7dFjNTXAiBFMakmTNJ/Ybtu2DTqdDpMtJsc3bdoUWVlZeOmll3DhwgV07NjR6bmpqan1ARkAunfvjsceewxbtmxhUG4MFFZsrSp9jq5jyUlyJgEQk6dAGj3K/kFfVmzzPZhzY16lQu5wpi5dTNVTd4ltXR3E1KlWW/s4nNHqy4qtzVDkqr9/Dl3JNTQBAjsniciPGEMpGHiyOrBinsTGQLFYMll2n5SXN3w+b551oqsin1fTiVSg+VWRjx8/juTkZERHR1sdT0tLAwCcOHHC4XlGoxHffvst+vTpY/dYWloaCgoKcNPRnD+Y5iNVVlZafVCQUroqsuU8HEfXseSi6igZ6xw/7mCfV1nkJLZJSbIXRhIACt/8/6j8/Wvyvn+HDvKS8ro6eXvfuqrYCtGQQCsdirxvX/2Xkft2oUm16XdemLcqIApxjKEUDOSsDlxcbFpBt7hY4TfxIDYGjMXKUbJXTL5+veFz29FmKsnNBe67D3j0UdO/ubk++TZEXtN8YltSUoKEhAS74+Zjly5dcnje9evXUVNTo+jcV199FS1btqz/cHY3m4KAu4qts6HItsHPVWLrYh9cEaazvptqPv6XvyiLDHISW4PBNHdWRgCXAHR+/zVEr3/D+oGf/hQ1D/R2fH1nSaYlIeTtfusqsa2tbehbOYtH2Q5FrqgAFi1yeJoEQHi5VQFRMGAMpWDgblscVRIrD2JjwFisHCV7+yTzewy93v6mvAqcVY4V32Ag8iHND0WuqqqC3sGb2qb33lxXOXljbD6u5Nz58+dj5syZ9V9XVlYyMAcrL/exdXodJ4xouFskpDBIS1+FmDvXrnppGqY8GZKn46zczbE1J77mpSkPHgTKylBRWI7KgqtoGXETLf/6tvvvs3cv9E8/DXx/wvq43MQWgPToo8CePa6f5GoosnkYMuD8e9rOsbWs2JaWuhx2JgFeb1VApHWMoeQv3gxVdbVVkKrDlG1io9y5pRU3gMqCq4hKjEOrzq1QUViOPy+7iiswnRePq7iGOMxd0gqt4MF81eJiYM0a0+f9+llNoHXUJ0uXNiyJUf/azRXbVq18krS7qhxzSDJpjeYT28jISNRYvsG9p/reEMVIJ3enzMeVnKvX6x0GcwpCCiu2+yfmYtAGixUaZCa2VU/9Bwp7jUa7dkDrkf2B/HynQ3Ilo9HzyCB3VWTAdN3MTAAWKzquXAn8Vcb3qauzTiwtry/3d0POG9m7d03J6OXLKPv71yg/ehbxKEV0Yjxw61bD85xVxSXJ9DO8c8e+Ytupk+lxJ8mtACBxqwIKcYyh5A9qLPzkbKsg1RMri9goVwysV0U+vheY5WDnu+H9gSFDPGzP5s2m7fAKCoDp0622EMqKj8f/m2XaauiHH+Px/pxWuIZynEApBv7feKSlAigpAQDcjYzCP/aqPwdWyV67RIGi+cQ2ISEBFy9etDtecu8XuX379g7Pi42NhV6vr3+eJ+dSCFFYse2/cQpKpg5Hgpx9bC00bx+DHgusA6aA44WTRFgYJE8jgyeJrSODBsn7Pjqd4wUomjSRXbGF3Hl1b74J8eKLaA3A6eYhe/aY3jk5eqek15sS2zt3rCu2CQmmYWfPPmuX3AoAErcqoEaAMZR8Tc2KqqOtgrSYWKnapubNTYnt1avA//yP3cMx9z46ARhi+cDf7n3cE34uH+88mosNYVmqrijtqppOpDWan2Pbu3dvnDlzxm7xiby8vPrHHQkLC0NKSgqOHj1q91heXh66du2KqKgo1dtLGqOwYhuOOlw5YLFCg6PEtkUL+2O2iaXBAOntt2FbbxSQIOXkeB4ZvE1sU1NNe8+5EhZmilrt2jm+vtxKjGXF1QXx4ovyFpqaPNnxpB5ze2wrthERpsheVARs2YLyJWtRMGkJbszIhnT4MLBhg6z2EQUzxlDyNdmLHClkTqzM96W1kFip1qbiYuDyZVXaJAHIwWQkGItVnwOblQUUFpoW7yosVHkbJiIVaT6xzcjIQF1dHXJycuqP1dTUYP369ejbt2/9vJ2ioiKcOnXK7twjR45YBebTp09jz549yPRwGAoFKduE1PZrJ0laLXRoO9Di1qujxNZyj1QzR4lnVhbCLlxA+ZK1KMqYgetL1kK6UKQsMsjZx9adDRuAw4eB7GyUz1uCgklLUDlpBrBkCbBlC3D+vKltjl6fB3Ns4WTFVFuyZwSZh27bqNOZbk7UlVdaL9Rl/lncG3bWav5zSFw3Hy1XLmCllhoNxlDyNdmLHHlBi4mVKm2Su4e8TDoY0Q1nPbqxIHe1aYPBNMyalVrSMs0PRe7bty8yMzMxf/58lJaWolu3bti4cSMKCwuRa7Es3jPPPIOvvvoKwmLI4W9+8xusW7cOI0aMwOzZsxEREYGVK1eibdu2mDVrViBeDvmbuyHEDhLbWuhwcMJbGJRq8dfb0XWaNbM/5qyiajCg1fzn4PVC/N5WbM1SU4HUVLQCnLfJWWIrt2LrYiiy5fBsZ0O17YSF2b1Tys0FRl25gzgAuvJrELl/briW3L4gCmGMoeRr/hqq6miYcqB53Sa5e8jLVIcwnEU32TcW1JgbTaQlmq/YAsCmTZswffp0bN68GdOmTcPdu3exc+dOpKenuzwvKioKX375JdLT07F48WK8/PLLePDBB/HVV18hzrwiHYU2d4mtzVDk/Kn/jauHC60XjnJynbuSg2HM7hJPb6mV2Mrho4rthTHTcHvMr+q/lhwN6bYlSaaIa/EOorgYWPhsMdrgWsPTLDcZ8vXPgihIMIaSr3lSvfR6P1qVaKIdBgPwtoydCmQwQsJk5OCyziDrxgK38aFQFBTv/Jo2bYrly5dj+fLlTp/z5ZdfOjxuMBiwdetWH7WMNM/Dim3S06lAqoNo4OA64T+ctn+er5OpHTtcP+7rxLZJE/kVWyeJbcen001bLZjdm4tbFx6BwgkLECddQ3RXi20SkpOBkSPtonR+PpAonK86zYotkQljKPmDnOqlViqEWmkHgIbloHfuBM6csd8myPJzB1sGVf5wFSUtklH12Ej8qoUBC7vJqyJzGx8KRUGR2BIp5mHF1mli6uA6DhOqH3+U1SxFiouBhQtdP0fNZM52qLUkmcaYeTvHVq8HbObyAUBY7V1cqm2LxA0vybp8UhJQICXBKJwMPWHFlohIM5xVCHv1Mt3fVHubGk/boWhfXC/aYLXnr8EAPPecx9fJzQUm/+5egv66KUGXu92QFlebJvJWUAxFJlLM0zm2HiS2jojly02Rxhfy853uyVrPlxXbe9e+9I8f5J1fV+f4eGUl8PHHdoclAAM2TkbJEXnjoAwGIHudAR/j5/XHrHqHiS0RkWY4qxD26wc8+ihw332+C59y2qHWKs7u5OaaXqu3r9nbocRaXG2ayFtMbCm0eVixvXqqTNl17pEAiMk+mqSSlGSqmrri48S25Egx2p3e6911S0udPqSD0XqbJTeysoCBqzLqv7bqHQ5FJiLyCznzVR2tngz4f46nP1ZxdkbNea1qJOjmudFbtgDvvmuqWhMFMya2FNrcJYLffWf1Zev/GI79Ex3cPpWZ2AKAZPTRrV+DAVi3zvVr8mVi26QJLu/P9/6PRmKi04fqEGa9zZIMRZ+ddHj88nfOE2giIlKH3AqkbYXQUVj1R+U0kJVKNavFaiXon30GjB8PjBtn+vktX66BRbWIFGJiS6HNVUJaXAyxfbv10yHQf+MU++GwNte53a4znA0KFmE+vPWblQUUFQFbtqB8hoP5tj5MbOt0EWg3KAl18needaxjR4erQBoh4esJOUhwtHiXEyVHipHy6TKHj8WPTHN8k4KIiFThaQXScvXkQ4cCVzn15764ltVsNavFaiTojn5+c+f6d2g4kZqY2FJoc5XY5jteUTccdfbDYW2u0+yhn0CaMMEuuRVSGKQcH9/6NRiAzEy0mj7R/rEbN9T7PjYrod64dgeffGvA1xPWeZfc6vWmdxEXLgBr16Jy0gycnrEWVw4X2W+z5Mbl/fnQObnF4PQmBRERqUJJBdJgMC1wlJoa2Dme5nYAvqtQ2lazP/tM3dfsbYLu6Odnxu1/KBhxdRUKba4S26QkCEmCZLMgUy109sNhba/TqhWwYQOkqVNx468f49pNPWL+Tze0Htnff1F52za7Q+L530CKiPD+9nNxMcQLL1ilr61QgT9MLsaB81konTocupnTEP+PDz2/tnnBrnurQEYDiFbYTHMF2Vlya75J4UkVmIiI5PF2ZV3zTjdnz5rO8ffCRb7c9sdZNbuw0PTh7DXbrZjshpxtlpxx9POzxO1/KNiwYkuhzVViazBAWrcORos5q3UIw8EJb9knQrbXiY01/ZuaipYrFyBx3Xy0fi7Tr3sFiNmz7Q5LEOosXpWfD8km0kkAuhjP4uxZICHVgPihPZVdW+4+uDIkpJoryI45vElBRESqUGM4rLly6u/kSc2FnBxxt0+so9dsWeHt1AmYM8e3FVPbn58tbv9DwYaJLYU2d4s+ZWUhrKgIZWu34N/ZW1B6+Lzj4bCOKraBlJ9vV2k2U2XxqqQkCJvXLACcC+vWEOQ8WFDLioqJLQAM2pCF0sMXcPHnz8EIGTcpiIhINf6cr6omX2/74+l8WttEWwhgxQrfz3W1/PktX87tfyi4cSgyhTY5yZfBgNbPZaK1J9cJdGLrZBg1YFq8SvL2FqvBACknB2LSpPpUsQgd8fscQ0OQc3aL1x2VE1vAVLnFR2uB4v9C2c6DuHwZiB3RH4OY1BIR+Zw3w2EDxdth1O6Yq6FTppgSZneJorP5ruZK8vDhvutj889vyBDTCsmBGhpO5C1WbCm0Ka0qurlOebmzNZH9xMEwakDlxauysiA99FD9lwkp8dZ34jWU2Na7d5Oix4JMVmqJiDRGzn63/uKPbX88qWY72+cX8M82SGaBGhpOpAZWbCm0qZXYfvml1ZctF83G/qKWHq/iq6qsLIQNH46ynQdx7UwZ2iS3Vn/xKvNcYgBNjNXWjylNbNXckoiIiIKCLxdqUsofi1fJrWabE23L4chmnOtKJA8rthTaJC/3XAVMCzW99ZbVIc1sJXOvQnn/yud8s3hVZGTD51VV1o+5uGlgOdfVaLs1kBo/EyIiChq+XqjJG4GsUNpWsLOygPPngdmzOdeVSAkmthTanCyw5BFP9rsNNS4S2x+2HHV6WtiFhgW5biz8bx81joiIgoGvF2oKRrZ73JoXiDIYTIs4BeOCXESBxqHIFNqcbc7mCU/2uw01ThLbkiPF6Hx0q/PzLBfk2urieUREFPJ8vVBTsHFWwbZcICoYF+QiCjRWbCm0qVGx9WS/21DjJLG9vD8fYZDZt5xTS0TUqPljoaZg4qyCvXWrNoZnEwUrJrYU2tSo2ALy97sNNZaJbU1N/aftBiWhzsWfj/0TLTbda9LEFy0jIqIgEqz73fqCsxWQZ870/b61RKGMiS2FNjUqtmaNcSuZpk0dHk5INeDrCTmohen2u20vWy2sxcSWiIjArWTMbCvYlrS0sBZRsGFiS6FNrYptY9WsmdOHBm3IwtXDhfhy9Eq7xbWsFtZiYktERI2Us717zRXslSvtz2nsC2sRKcXElkKbmhXbRuiHj76z+tpqiDFMldv7/yvTbliy1cJa4VyjjoiIGh9nKx+bGQxAZqb9sOTGvLAWkTeY2FJoY8VWMdPKx9usjjnau9d2WHItdI1jYS0iIiIn5O7dy4W1iNTDUgqFNlZsFbu8Px8JNrNnzUOMbZPWQRuyUDJ1OK4cOIu2A7thkOXj/BkQEVEj42rvXtukNSvLtNXP2bOmSq3t48XFpuslJTHhJXKFFVsKbazYKuZo5WNXe/cmpBrQe/oQu6T3m8UfWX1tO5yZiIgo1Dha+djVEGNnC2u5G85MRA2Y2FJos6kWcpVB+dQYYlxypBg9P11hdczRcGYiItIuZwsgkXNqDDGWO5yZiEyY2FJo27vX6suFnXJ5t9MD5pWPT6zai6uHCz3eu/fy/nzoYF01t1oxmYiINI0VQ+W83bvX1XBmIrInCcEJcO5UVlaiZcuWuHHjBqKjowPdHJKruBiiUydIFv/Fa6FDYlghDpw3cJ6KH5QcKUZ82n1WyW0tdLh6uJCLS1FQYjzwHPsseBUXm5JZy+RKpzMlaYyhvsf+p1Dj63jAii2Frvx8q6QWMFULuxjP8m6nn3DFZCKi4MWKYWBxxWQiz3BVZApdSUkQYWGQjNbVwnNh3bg/nB+5XDGZiIg0y7wAkm3FkDHUf9ytmExEDVixpdBlMEDKyYExrKFa+Lz0Fn6fw2HI/uZsxWQiItIuVgy1wdmKyURkjRVbCm1ZWQgbPhxXD57FWXRDdn8mtURERHKxYkhEwYKJLYU+gwFxmQbEBbodREREQchgYEJLRNrHochEREREREQU1JjYEhERERERUVDTfGJbUVGByZMnIy4uDs2bN8fQoUNx7Ngxt+cZjUZs2LABo0aNQseOHdG8eXP07NkTixcvRnV1tR9aTkREFFiMoURE1FhIQths9KkhRqMRgwYNwjfffIM5c+agTZs2WLNmDS5cuIB//vOfSEpKcnrurVu3EBUVhX79+mHkyJGIj4/HwYMHsXHjRqSnp2PPnj2QJElWO7i5PBERAcEVDxhDiYhIS3wdDzS9eNS2bdvw9ddfY+vWrcjIyAAAjB07FsnJycjOzsa7777r9NwmTZrgwIEDGDBgQP2xZ599Fp07d0Z2djZ2796Nn/70pz5/DURERIHAGEpERI2Jpocib9u2DW3btsWYMWPqj8XFxWHs2LHYsWMHampqnJ7bpEkTq4Bs9tRTTwEATp48qX6DiYiINIIxlIiIGhNNJ7bHjx/Hww8/jLAw62ampaXh9u3bOHPmjMfXvHz5MgCgTZs2qrSRiIhIixhDiYioMdH0UOSSkhKkp6fbHU9ISAAAXLp0CSkpKR5d87XXXkN0dDSeeOIJp8+pqamxupN948YNAKZx4URE1HiZ44CGl6eoxxhKRERa4usY6rfE1mg04s6dO7Keq9frIUkSqqqqoNfr7R5v2rQpAKCqqsqjNixZsgRffPEF1qxZg5iYGKfPe/XVV7Fw4UK74x07dvTo+xERUWgqKytDy5Yt/fb9GEOJiChU+CqG+i2x3bdvH4YOHSrruSdPnkT37t0RGRnpcA6QeauByMhI2d///fffx+9+9ztkZWXh+eefd/nc+fPnY+bMmfVfV1RU4L777kNRUZFf38gEu8rKSnTs2BEXLlzgSpgysc+UYb95jn2mzI0bN9CpUyfExsb69fsyhjY+/B31HPtMGfab59hnyvg6hvotse3evTvWr18v67nmYVIJCQkoKSmxe9x8rH379rKu9/nnn+OZZ57BiBEj8Oabb7p9vl6vd3iXu2XLlvzPq0B0dDT7zUPsM2XYb55jnyljO2/V1xhDGy/+jnqOfaYM+81z7DNlfBVD/ZbYtmvXDhMnTvTonN69e2P//v0wGo1WHZCXl4dmzZohOTnZ7TXy8vLw1FNPoU+fPtiyZQvCwzU9rZiIiMgOYygREZFrml4VOSMjA1euXMH27dvrj127dg1bt27Fz3/+c6s7wgUFBSgoKLA6/+TJkxgxYgQ6d+6MnTt3ejTsioiIKJgxhhIRUWOi6VuvGRkZ6NevH37961/j+++/R5s2bbBmzRrU1dXZLUzx2GOPAQAKCwsBADdv3sTw4cNRXl6OOXPm4OOPP7Z6fmJiIvr37y+rHXq9HtnZ2Q6HVpFz7DfPsc+UYb95jn2mTDD1G2NocGO/eY59pgz7zXPsM2V83W+S0PieBeag+re//Q1VVVVITU3FihUr0KdPH6vnde7cGUBDUC4sLESXLl2cXnfChAnYsGGDj1pNREQUeIyhRETUWGg+sSUiIiIiIiJyRdNzbImIiIiIiIjcYWJLREREREREQY2JLREREREREQW1Rp3Y1tTUYN68eWjfvj0iIyPRt29ffP7557LOvXjxIsaOHYuYmBhER0dj9OjR+OGHH3zcYm1Q2m/bt2/HuHHj0LVrVzRr1gz3338/Zs2ahYqKCt83OsC8+b9madiwYZAkCS+88IIPWqk93vbb+++/j/79+6N58+aIiYnBgAEDsGfPHh+2OPC86bMvvvgCQ4cORZs2bRATE4O0tDRs3rzZxy3Whlu3biE7OxuPP/44YmNjIUmSR4sjVVRUYPLkyYiLi0Pz5s0xdOhQHDt2zHcN1gDGUGUYQz3HGKoMY6jnGEOV0UwMFY3Y+PHjRXh4uJg9e7Z46623RP/+/UV4eLjYv3+/y/Nu3rwpkpKSRHx8vFi2bJlYuXKl6NixozAYDOLatWt+an3gKO231q1bi5SUFPHyyy+LdevWiWnTpokmTZqI7t27i9u3b/up9YGhtM8sffDBB6J58+YCgJg6daoPW6sd3vRbdna2kCRJZGZmijfffFO88cYbYsqUKWLTpk1+aHngKO2zHTt2CEmSxIABA8Qbb7whVq9eLdLT0wUAsXLlSj+1PnDOnTsnAIhOnTqJIUOGCABi/fr1ss6tq6sTAwYMEM2bNxcLFiwQq1evFg888ICIiooSZ86c8W3DA4gxVBnGUM8xhirDGOo5xlBltBJDG21im5eXJwCI5cuX1x+rqqoSiYmJon///i7PXbZsmQAgDh8+XH/s5MmTQqfTifnz5/uszVrgTb/t3bvX7tjGjRsFALFu3Tq1m6oZ3vSZ5fM7d+4s/vCHPzSaoOxNvx08eFBIktQogoklb/ps2LBhon379qK6urr+2N27d0ViYqLo1auXz9qsFdXV1aKkpEQIIcSRI0c8Csrvv/++ACC2bt1af6y0tFTExMSIX/ziF75obsAxhirDGOo5xlBlGEM9xxiqnFZiaKNNbOfMmSN0Op24ceOG1fElS5YIAKKoqMjpuampqSI1NdXu+M9+9jORmJioelu1xJt+c6SyslIAEDNnzlSzmZqiRp8tXLhQdOrUSdy+fbvRBGVv+m3cuHEiISFB1NXVCaPRKG7evOnr5mqCN33Wt29f0aNHD4fH+/btq3pbtczToJyZmSnatm0r6urqrI5PnjxZNGvWzOqNTqhgDFWGMdRzjKHKMIZ6jjFUHYGMoY12ju3x48eRnJyM6Ohoq+NpaWkAgBMnTjg8z2g04ttvv7Xb3N58bkFBAW7evKl6e7VCab85c/nyZQBAmzZtVGmfFnnbZ0VFRVi6dCmWLVuGyMhIXzVTc7zpt927dyM1NRWvv/464uLiEBUVhYSEBKxevdqXTQ44b/psyJAh+Pe//42XX34ZZ8+eRUFBARYtWoSjR49i7ty5vmx20Dt+/DgefvhhhIVZh9S0tDTcvn0bZ86cCVDLfIcxVBnGUM8xhirDGOo5xtDAUDOGhqvduGBRUlKChIQEu+PmY5cuXXJ43vXr11FTU+P23Pvvv1/F1mqH0n5zZtmyZdDpdMjIyFClfVrkbZ/NmjULDz30EMaPH++T9mmV0n4rLy/HtWvXcODAAezZswfZ2dno1KkT1q9fjxdffBERERGYMmWKT9seKN78X3v55Zdx7tw5vPLKK1i8eDEAoFmzZvjggw8wevRo3zQ4RJSUlCA9Pd3uuGW/p6Sk+LtZPsUYqgxjqOcYQ5VhDPUcY2hgqBlDG21iW1VVBb1eb3e8adOm9Y87Ow+AonNDgdJ+c+Tdd99Fbm4u5s6di6SkJNXaqDXe9NnevXvxwQcfIC8vz2ft0yql/Xbr1i0AQFlZGd577z2MGzcOAJCRkYGUlBQsXrw4ZIOyN//X9Ho9kpOTkZGRgTFjxqCurg45OTn45S9/ic8//xz9+vXzWbuDnZp/F4MFY6gyjKGeYwxVhjHUc4yhgaHm38VGm9hGRkaipqbG7nh1dXX9487OA6Do3FCgtN9s7d+/H1lZWRg+fDheeeUVVduoNUr7rLa2FtOmTcOvfvUrpKam+rSNWuTt72hERIRVFSMsLAzjxo1DdnY2ioqK0KlTJx+0OrC8+f184YUXcOjQIRw7dqx+ONDYsWPRo0cP/Pa3v22UbwzlUuvvYjBhDFWGMdRzjKHKMIZ6jjE0MNSMoY12jm1CQgJKSkrsjpuPtW/f3uF5sbGx0Ov1is4NBUr7zdI333yDUaNGoWfPnti2bRvCw0P7/orSPtu0aRNOnz6NKVOmoLCwsP4DAG7evInCwkLcvn3bZ+0ONG9+R5s2bYrWrVtDp9NZPRYfHw/ANNQqFCntszt37iA3NxcjRoywmuMSERGBJ554AkePHsWdO3d80+gQoMbfxWDDGKoMY6jnGEOVYQz1HGNoYKgZQxttYtu7d2+cOXMGlZWVVsfNd1R69+7t8LywsDCkpKTg6NGjdo/l5eWha9euiIqKUr29WqG038wKCgrw+OOPIz4+Hp988glatGjhq6ZqhtI+Kyoqwt27dzFw4EB06dKl/gMwBewuXbpg165dPm17IHnzO9q7d29cvXrVLpCY58fExcWp32ANUNpnZWVlqK2tRV1dnd1jd+/ehdFodPgYmfTu3RvHjh2D0Wi0Op6Xl4dmzZohOTk5QC3zHcZQZRhDPccYqgxjqOcYQwND1RjqyfLNoeTQoUN2e1VVV1eLbt26WS3Lff78eXHy5Emrc5cuXSoAiCNHjtQfO3XqlNDpdGLevHm+b3wAedNvJSUlomvXrqJ9+/bi3Llz/mpywCnts5MnT4oPP/zQ7gOAePLJJ8WHH34oLl265NfX4k/e/F9btWqVACBycnLqj1VVVYmuXbuKBx54wPeNDxClfVZbWytiYmJEcnKyqKmpqT9+8+ZNYTAYRPfu3f3zAjTC1VYFly5dEidPnhR37typP/bee+/Z7cF39epVERMTI8aNG+ePJvsdY6gyjKGeYwxVhjHUc4yh6ghkDG20ia0Qpn2TwsPDxZw5c8Rbb70lBgwYIMLDw8VXX31V/5zBgwcL2/y/srJSJCYmivj4ePHaa6+JVatWiY4dO4r27duL0tJSf78Mv1Pabw8++KAAIObOnSs2b95s9bFr1y5/vwy/UtpnjqCR7MEnhPJ+u337tujRo4eIiIgQs2fPFq+//rpITU0VOp1OfPLJJ/5+GX6ltM8WL14sAIiHHnpIrFq1SqxYsUL85Cc/EQDEO++84++XERBvvPGGWLRokXj++ecFADFmzBixaNEisWjRIlFRUSGEEGLChAkCgFViUVtbK/r16ydatGghFi5cKP70pz+JHj16iKioKHHq1KkAvRrfYwxVhjHUc4yhyjCGeo4xVDktxNBGndhWVVWJ2bNni3bt2gm9Xi9SU1PFp59+avUcZ38oL1y4IDIyMkR0dLRo0aKFGDlypMjPz/dX0wNKab8BcPoxePBgP74C//Pm/5qtxhSUvem3K1euiAkTJojY2Fih1+tF37597c4NRd702V/+8heRlpYmYmJiRGRkpOjbt6/Ytm2bv5oecPfdd5/Tv1HmIOwoKAshxPXr10VWVpZo3bq1aNasmRg8eLBVRTIUMYYqwxjqOcZQZRhDPccYqpwWYqgkhBDyBy4TERERERERaUujXTyKiIiIiIiIQgMTWyIiIiIiIgpqTGyJiIiIiIgoqDGxJSIiIiIioqDGxJaIiIiIiIiCGhNbIiIiIiIiCmpMbImIiIiIiCioMbElIiIiIiKioMbEloiIiIiIiIIaE1siIiIiIiIKakxsiYiIiIiIKKgxsSUiIiIiIqKgxsSWiHDgwAFIkgRJkrBlyxaHz8nLy0OLFi0gSRLmzJnj5xYSERFpE2MokTZIQggR6EYQUeCNHj0aH330Ebp3745//etf0Ol09Y+dPn0aAwcORFlZGSZMmID169dDkqQAtpaIiEg7GEOJAo8VWyICALz66qvQ6XQ4deoU3nnnnfrjly5dwvDhw1FWVoaRI0fi7bffZkAmIiKywBhKFHis2BJRvUmTJiE3NxddunTB6dOn8eOPPyI9PR3fffcdHnnkEezatQuRkZGBbiYREZHmMIYSBRYTWyKqd/HiRSQlJaGqqgqrVq3Chx9+iH379iElJQX79u1DTExMoJtIRESkSYyhRIHFochEVK9Dhw6YNm0aAGDGjBnYt28fOnfujM8++8xhQL516xYWLFiAkSNHol27dpAkCRMnTvRvo4mIiDSAMZQosJjYEpGVadOmISzM9KchNjYWu3btQkJCgsPnXrt2DQsXLsSxY8fQp08ffzaTiIhIcxhDiQInPNANICLtqK2txZQpU2A0GgEAt2/fdjkfKCEhAcXFxejQoQOqq6s5d4iIiBotxlCiwGLFlogAAEIITJo0CTt37kRcXBy6dOmC6upqZGdnOz1Hr9ejQ4cOfmwlERGR9jCGEgUeE1siAgDMnTsXGzduRIsWLfDxxx/jlVdeAQBs3LgR33//fYBbR0REpF2MoUSBx8SWiLBixQqsWLECERER2L59O1JTUzF+/Hj06tULdXV1mD9/fqCbSEREpEmMoUTawMSWqJHbtGkT5s6dC0mSsGHDBgwbNgwAIEkSFi1aBAD46KOPcODAgUA2k4iISHMYQ4m0g4ktUSP2ySefICsrC0IIrFy5Ek8//bTV46NGjULfvn0BAPPmzQtEE4mIiDSJMZRIW5jYEjVSBw8eRGZmJmprazFv3jxMnz7d4fPM84QOHDiAHTt2+LGFRERE2sQYSqQ93O6HqJHq378/fvzxR7fPe+yxxyCE8EOLiIiIggNjKJH2sGJLREREREREQY0VWyLyyurVq1FRUYHa2loAwLfffovFixcDANLT05Genh7I5hEREWkWYyiReiTB8RFE5IXOnTvj/PnzDh/Lzs7GggUL/NsgIiKiIMEYSqQeJrZEREREREQU1DjHloiIiIiIiIIaE1siIiIiIiIKakxsiYiIiIiIKKgxsSUiIiIiIqKgxsSWiIiIiIiIghoTWyIiIiIiIgpqTGyJiIiIiIgoqDGxJSIiIiIioqDGxJaIiIiIiIiCGhNbIiIiIiIiCmpMbImIiIiIiCio/S/jUYBdj9eY1gAAAABJRU5ErkJggg==",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"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."
|
||
]
|
||
}
|
||
],
|
||
"metadata": {
|
||
"language_info": {
|
||
"codemirror_mode": {
|
||
"name": "ipython",
|
||
"version": 3
|
||
},
|
||
"file_extension": ".py",
|
||
"mimetype": "text/x-python",
|
||
"name": "python",
|
||
"nbconvert_exporter": "python",
|
||
"pygments_lexer": "ipython3",
|
||
"version": "3.9.15"
|
||
}
|
||
},
|
||
"nbformat": 4,
|
||
"nbformat_minor": 4
|
||
} |