FYS-STK4155/doc/LectureNotes/_build/jupyter_execute/chapter6.ipynb

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    "# Decision trees, overarching aims\n",
    "\n",
    "\n",
    "We start here with the most basic algorithm, the so-called decision\n",
    "tree. With this basic algorithm we can in turn build more complex\n",
    "networks, spanning from homogeneous and heterogenous forests (bagging,\n",
    "random forests and more) to one of the most popular supervised\n",
    "algorithms nowadays, the extreme gradient boosting, or just\n",
    "XGBoost. But let us start with the simplest possible ingredient.\n",
    "\n",
    "Decision trees are supervised learning algorithms used for both,\n",
    "classification and regression tasks.\n",
    "\n",
    "\n",
    "The main idea of decision trees\n",
    "is to find those descriptive features which contain the most\n",
    "**information** regarding the target feature and then split the dataset\n",
    "along the values of these features such that the target feature values\n",
    "for the resulting underlying datasets are as pure as possible.\n",
    "\n",
    "The descriptive features which reproduce best the target/output features are normally  said\n",
    "to be the most informative ones. The process of finding the **most\n",
    "informative** feature is done until we accomplish a stopping criteria\n",
    "where we then finally end up in so called **leaf nodes**. \n",
    "\n",
    "## Basics of a tree\n",
    "\n",
    "A decision tree is typically divided into a **root node**, the **interior nodes**,\n",
    "and the final **leaf nodes** or just **leaves**. These entities are then connected by so-called **branches**.\n",
    "\n",
    "The leaf nodes\n",
    "contain the predictions we will make for new query instances presented\n",
    "to our trained model. This is possible since the model has \n",
    "learned the underlying structure of the training data and hence can,\n",
    "given some assumptions, make predictions about the target feature value\n",
    "(class) of unseen query instances.\n",
    "\n",
    "\n",
    "## General Features\n",
    "\n",
    "The overarching approach to decision trees is a top-down approach.\n",
    "\n",
    "* A leaf provides the classification of a given instance.\n",
    "\n",
    "* A node specifies a test of some attribute of the instance.\n",
    "\n",
    "* A branch corresponds to a possible values of an attribute.\n",
    "\n",
    "* 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",
    "\n",
    "This process is then repeated for the subtree rooted at the new\n",
    "node.\n",
    "\n",
    "\n",
    "\n",
    "In simplified terms, the process of training a decision tree and\n",
    "predicting the target features of query instances is as follows:\n",
    "\n",
    "1. Present a dataset containing of a number of training instances characterized by a number of descriptive features and a target feature\n",
    "\n",
    "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",
    "\n",
    "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",
    "\n",
    "4. Show query instances to the tree and run down the tree until we arrive at leaf nodes\n",
    "\n",
    "Then we are essentially done!"
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      "2nd degree coefficients:\n",
      "zero power:  -1.4725246793626128\n",
      "first power:  -0.08935132374099551\n",
      "second power:  0.00034688149480437765\n"
     ]
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_1_1.png"
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_1_2.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "steps=250\n",
    "\n",
    "distance=0\n",
    "x=0\n",
    "distance_list=[]\n",
    "steps_list=[]\n",
    "while x<steps:\n",
    "    distance+=np.random.randint(-1,2)\n",
    "    distance_list.append(distance)\n",
    "    x+=1\n",
    "    steps_list.append(x)\n",
    "plt.plot(steps_list,distance_list, color='green', label=\"Random Walk Data\")\n",
    "\n",
    "steps_list=np.asarray(steps_list)\n",
    "distance_list=np.asarray(distance_list)\n",
    "\n",
    "X=steps_list[:,np.newaxis]\n",
    "\n",
    "#Polynomial fits\n",
    "\n",
    "#Degree 2\n",
    "poly_features=PolynomialFeatures(degree=2, include_bias=False)\n",
    "X_poly=poly_features.fit_transform(X)\n",
    "\n",
    "lin_reg=LinearRegression()\n",
    "poly_fit=lin_reg.fit(X_poly,distance_list)\n",
    "b=lin_reg.coef_\n",
    "c=lin_reg.intercept_\n",
    "print (\"2nd degree coefficients:\")\n",
    "print (\"zero power: \",c)\n",
    "print (\"first power: \", b[0])\n",
    "print (\"second power: \",b[1])\n",
    "\n",
    "z = np.arange(0, steps, .01)\n",
    "z_mod=b[1]*z**2+b[0]*z+c\n",
    "\n",
    "fit_mod=b[1]*X**2+b[0]*X+c\n",
    "plt.plot(z, z_mod, color='r', label=\"2nd Degree Fit\")\n",
    "plt.title(\"Polynomial Regression\")\n",
    "\n",
    "plt.xlabel(\"Steps\")\n",
    "plt.ylabel(\"Distance\")\n",
    "\n",
    "#Degree 10\n",
    "poly_features10=PolynomialFeatures(degree=10, include_bias=False)\n",
    "X_poly10=poly_features10.fit_transform(X)\n",
    "\n",
    "poly_fit10=lin_reg.fit(X_poly10,distance_list)\n",
    "\n",
    "y_plot=poly_fit10.predict(X_poly10)\n",
    "plt.plot(X, y_plot, color='black', label=\"10th Degree Fit\")\n",
    "\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "\n",
    "#Decision Tree Regression\n",
    "from sklearn.tree import DecisionTreeRegressor\n",
    "regr_1=DecisionTreeRegressor(max_depth=2)\n",
    "regr_2=DecisionTreeRegressor(max_depth=5)\n",
    "regr_3=DecisionTreeRegressor(max_depth=7)\n",
    "regr_1.fit(X, distance_list)\n",
    "regr_2.fit(X, distance_list)\n",
    "regr_3.fit(X, distance_list)\n",
    "\n",
    "X_test = np.arange(0.0, steps, 0.01)[:, np.newaxis]\n",
    "y_1 = regr_1.predict(X_test)\n",
    "y_2 = regr_2.predict(X_test)\n",
    "y_3=regr_3.predict(X_test)\n",
    "\n",
    "# Plot the results\n",
    "plt.figure()\n",
    "plt.scatter(X, distance_list, s=2.5, c=\"black\", label=\"data\")\n",
    "plt.plot(X_test, y_1, color=\"red\",\n",
    "         label=\"max_depth=2\", linewidth=2)\n",
    "plt.plot(X_test, y_2, color=\"green\", label=\"max_depth=5\", linewidth=2)\n",
    "plt.plot(X_test, y_3, color=\"m\", label=\"max_depth=7\", linewidth=2)\n",
    "\n",
    "plt.xlabel(\"Data\")\n",
    "plt.ylabel(\"Darget\")\n",
    "plt.title(\"Decision Tree Regression\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Building a tree, regression\n",
    "\n",
    "There are mainly two steps\n",
    "1. We split the predictor space (the set of possible values $x_1,x_2,\\dots, x_p$) into $J$ distinct and non-non-overlapping regions, $R_1,R_2,\\dots,R_J$.  \n",
    "\n",
    "2. For every observation that falls into the region $R_j$ , we make the same prediction, which is simply the mean of the response values for the training observations in $R_j$.\n",
    "\n",
    "How do we construct the regions $R_1,\\dots,R_J$?  In theory, the\n",
    "regions could have any shape. However, we choose to divide the\n",
    "predictor space into high-dimensional rectangles, or boxes, for\n",
    "simplicity and for ease of interpretation of the resulting predictive\n",
    "model. The goal is to find boxes $R_1,\\dots,R_J$ that minimize the\n",
    "MSE, given by"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\sum_{j=1}^J\\sum_{i\\in R_j}(y_i-\\overline{y}_{R_j})^2,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where $\\overline{y}_{R_j}$  is the mean response for the training observations \n",
    "within box $j$. \n",
    "\n",
    "\n",
    "Unfortunately, it is computationally infeasible to consider every\n",
    "possible partition of the feature space into $J$ boxes.  The common\n",
    "strategy is to take a top-down approach\n",
    "\n",
    "The approach is top-down because it begins at the top of the tree (all\n",
    "observations belong to a single region) and then successively splits\n",
    "the predictor space; each split is indicated via two new branches\n",
    "further down on the tree. It is greedy because at each step of the\n",
    "tree-building process, the best split is made at that particular step,\n",
    "rather than looking ahead and picking a split that will lead to a\n",
    "better tree in some future step.\n",
    "\n",
    "\n",
    "### Making a tree\n",
    "\n",
    "In order to implement the recursive binary splitting we start by selecting\n",
    "the predictor $x_j$ and a cutpoint $s$ that splits the predictor space into two regions $R_1$ and $R_2$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\left\\{X\\vert x_j < s\\right\\},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\left\\{X\\vert x_j \\geq s\\right\\},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "so that we obtain the lowest MSE, that is"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\sum_{i:x_i\\in R_j}(y_i-\\overline{y}_{R_1})^2+\\sum_{i:x_i\\in R_2}(y_i-\\overline{y}_{R_2})^2,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "which we want to minimize by considering all predictors\n",
    "$x_1,x_2,\\dots,x_p$.  We consider also all possible values of $s$ for\n",
    "each predictor. These values could be determined by randomly assigned\n",
    "numbers or by starting at the midpoint and then proceed till we find\n",
    "an optimal value.\n",
    "\n",
    "For any $j$ and $s$, we define the pair of half-planes where\n",
    "$\\overline{y}_{R_1}$ is the mean response for the training\n",
    "observations in $R_1(j,s)$, and $\\overline{y}_{R_2}$ is the mean\n",
    "response for the training observations in $R_2(j,s)$.\n",
    "\n",
    "Finding the values of $j$ and $s$ that minimize the above equation can be\n",
    "done quite quickly, especially when the number of features $p$ is not\n",
    "too large.\n",
    "\n",
    "Next, we repeat the process, looking\n",
    "for the best predictor and best cutpoint in order to split the data\n",
    "further so as to minimize the MSE within each of the resulting\n",
    "regions. However, this time, instead of splitting the entire predictor\n",
    "space, we split one of the two previously identified regions. We now\n",
    "have three regions. Again, we look to split one of these three regions\n",
    "further, so as to minimize the MSE. The process continues until a\n",
    "stopping criterion is reached; for instance, we may continue until no\n",
    "region contains more than five observations.\n",
    "\n",
    "\n",
    "The above procedure is rather straightforward, but leads often to\n",
    "overfitting and unnecessarily large and complicated trees. The basic\n",
    "idea is to grow a large tree $T_0$ and then prune it back in order to\n",
    "obtain a subtree. A smaller tree with fewer splits (fewer regions) can\n",
    "lead to smaller variance and better interpretation at the cost of a\n",
    "little more bias.\n",
    "\n",
    "The so-called Cost complexity pruning algorithm gives us a\n",
    "way to do just this. Rather than considering every possible subtree,\n",
    "we consider a sequence of trees indexed by a nonnegative tuning\n",
    "parameter $\\alpha$.\n",
    "\n",
    "Read more at the following [Scikit-Learn link on pruning](https://scikit-learn.org/stable/auto_examples/tree/plot_cost_complexity_pruning.html#sphx-glr-auto-examples-tree-plot-cost-complexity-pruning-py).\n",
    "\n",
    "\n",
    "For each value of $\\alpha$  there corresponds a subtree $T \\in T_0$ such that"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\sum_{m=1}^{\\overline{T}}\\sum_{i:x_i\\in R_m}(y_i-\\overline{y}_{R_m})^2+\\alpha\\overline{T},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "is as small as possible. Here $\\overline{T}$ is \n",
    "the number of terminal nodes of the tree $T$ , $R_m$ is the\n",
    "rectangle (i.e. the subset of predictor space)  corresponding to the $m$-th terminal node.\n",
    "\n",
    "The tuning parameter $\\alpha$ controls a trade-off between the subtree’s\n",
    "complexity and its fit to the training data. When $\\alpha = 0$, then the\n",
    "subtree $T$ will simply equal $T_0$, \n",
    "because then the above equation just measures the\n",
    "training error. \n",
    "However, as $\\alpha$ increases, there is a price to pay for\n",
    "having a tree with many terminal nodes. The above equation will\n",
    "tend to be minimized for a smaller subtree. \n",
    "\n",
    "\n",
    "It turns out that as we increase $\\alpha$ from zero\n",
    "branches get pruned from the tree in a nested and predictable fashion,\n",
    "so obtaining the whole sequence of subtrees as a function of $\\alpha$ is\n",
    "easy. We can select a value of $\\alpha$ using a validation set or using\n",
    "cross-validation. We then return to the full data set and obtain the\n",
    "subtree corresponding to $\\alpha$. \n",
    "\n",
    "\n",
    "### Schematic Regression Procedure\n",
    "\n",
    "Building a Regression Tree\n",
    "\n",
    "1. Use recursive binary splitting to grow a large tree on the training data, stopping only when each terminal node has fewer than some minimum number of observations.\n",
    "\n",
    "2. Apply cost complexity pruning to the large tree in order to obtain a sequence of best subtrees, as a function of $\\alpha$.\n",
    "\n",
    "3. Use for example $K$-fold cross-validation to choose $\\alpha$. Divide the training observations into $K$ folds. For each $k=1,2,\\dots,K$ we: \n",
    "\n",
    "  * repeat steps 1 and 2 on all but the $k$-th fold of the training data. \n",
    "\n",
    "  * Then we valuate the mean squared prediction error on the data in the left-out $k$-th fold, as a function of $\\alpha$.\n",
    "\n",
    "  * Finally  we average the results for each value of $\\alpha$, and pick $\\alpha$ to minimize the average error.\n",
    "\n",
    "\n",
    "4. Return the subtree from Step 2 that corresponds to the chosen value of $\\alpha$. \n",
    "\n",
    "!eblock\n",
    "\n",
    "\n",
    "\n",
    "## A Classification Tree\n",
    "\n",
    "A classification tree is very similar to a regression tree, except\n",
    "that it is used to predict a qualitative response rather than a\n",
    "quantitative one. Recall that for a regression tree, the predicted\n",
    "response for an observation is given by the mean response of the\n",
    "training observations that belong to the same terminal node. In\n",
    "contrast, for a classification tree, we predict that each observation\n",
    "belongs to the most commonly occurring class of training observations\n",
    "in the region to which it belongs. In interpreting the results of a\n",
    "classification tree, we are often interested not only in the class\n",
    "prediction corresponding to a particular terminal node region, but\n",
    "also in the class proportions among the training observations that\n",
    "fall into that region.  \n",
    "\n",
    "\n",
    "\n",
    "The task of growing a\n",
    "classification tree is quite similar to the task of growing a\n",
    "regression tree. Just as in the regression setting, we use recursive\n",
    "binary splitting to grow a classification tree. However, in the\n",
    "classification setting, the MSE cannot be used as a criterion for making\n",
    "the binary splits.  A natural alternative to MSE is the **classification\n",
    "error rate**. Since we plan to assign an observation in a given region\n",
    "to the most commonly occurring error rate class of training\n",
    "observations in that region, the classification error rate is simply\n",
    "the fraction of the training observations in that region that do not\n",
    "belong to the most common class. \n",
    "\n",
    "When building a classification tree, either the Gini index or the\n",
    "entropy are typically used to evaluate the quality of a particular\n",
    "split, since these two approaches are more sensitive to node purity\n",
    "than is the classification error rate. \n",
    "\n",
    "\n",
    "\n",
    "If our targets are the outcome of a classification process that takes\n",
    "for example $k=1,2,\\dots,K$ values, the only thing we need to think of\n",
    "is to set up the splitting criteria for each node.\n",
    "\n",
    "We define a PDF $p_{mk}$ that represents the number of observations of\n",
    "a class $k$ in a region $R_m$ with $N_m$ observations. We represent\n",
    "this likelihood function in terms of the proportion $I(y_i=k)$ of\n",
    "observations of this class in the region $R_m$ as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "p_{mk} = \\frac{1}{N_m}\\sum_{x_i\\in R_m}I(y_i=k).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We let $p_{mk}$ represent the majority class of observations in region\n",
    "$m$. The three most common ways of splitting a node are given by\n",
    "\n",
    "* Misclassification error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "p_{mk} = \\frac{1}{N_m}\\sum_{x_i\\in R_m}I(y_i\\ne k) = 1-p_{mk}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Gini index $g$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "g = \\sum_{k=1}^K p_{mk}(1-p_{mk}).\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Information entropy or just entropy $s$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "s = -\\sum_{k=1}^K p_{mk}\\log{p_{mk}}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing the Tree, Classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "     mean radius  mean texture  mean perimeter  mean area  mean smoothness  \\\n",
      "0          17.99         10.38          122.80     1001.0          0.11840   \n",
      "1          20.57         17.77          132.90     1326.0          0.08474   \n",
      "2          19.69         21.25          130.00     1203.0          0.10960   \n",
      "3          11.42         20.38           77.58      386.1          0.14250   \n",
      "4          20.29         14.34          135.10     1297.0          0.10030   \n",
      "..           ...           ...             ...        ...              ...   \n",
      "564        21.56         22.39          142.00     1479.0          0.11100   \n",
      "565        20.13         28.25          131.20     1261.0          0.09780   \n",
      "566        16.60         28.08          108.30      858.1          0.08455   \n",
      "567        20.60         29.33          140.10     1265.0          0.11780   \n",
      "568         7.76         24.54           47.92      181.0          0.05263   \n",
      "\n",
      "     mean compactness  mean concavity  mean concave points  mean symmetry  \\\n",
      "0             0.27760         0.30010              0.14710         0.2419   \n",
      "1             0.07864         0.08690              0.07017         0.1812   \n",
      "2             0.15990         0.19740              0.12790         0.2069   \n",
      "3             0.28390         0.24140              0.10520         0.2597   \n",
      "4             0.13280         0.19800              0.10430         0.1809   \n",
      "..                ...             ...                  ...            ...   \n",
      "564           0.11590         0.24390              0.13890         0.1726   \n",
      "565           0.10340         0.14400              0.09791         0.1752   \n",
      "566           0.10230         0.09251              0.05302         0.1590   \n",
      "567           0.27700         0.35140              0.15200         0.2397   \n",
      "568           0.04362         0.00000              0.00000         0.1587   \n",
      "\n",
      "     mean fractal dimension  ...  worst radius  worst texture  \\\n",
      "0                   0.07871  ...        25.380          17.33   \n",
      "1                   0.05667  ...        24.990          23.41   \n",
      "2                   0.05999  ...        23.570          25.53   \n",
      "3                   0.09744  ...        14.910          26.50   \n",
      "4                   0.05883  ...        22.540          16.67   \n",
      "..                      ...  ...           ...            ...   \n",
      "564                 0.05623  ...        25.450          26.40   \n",
      "565                 0.05533  ...        23.690          38.25   \n",
      "566                 0.05648  ...        18.980          34.12   \n",
      "567                 0.07016  ...        25.740          39.42   \n",
      "568                 0.05884  ...         9.456          30.37   \n",
      "\n",
      "     worst perimeter  worst area  worst smoothness  worst compactness  \\\n",
      "0             184.60      2019.0           0.16220            0.66560   \n",
      "1             158.80      1956.0           0.12380            0.18660   \n",
      "2             152.50      1709.0           0.14440            0.42450   \n",
      "3              98.87       567.7           0.20980            0.86630   \n",
      "4             152.20      1575.0           0.13740            0.20500   \n",
      "..               ...         ...               ...                ...   \n",
      "564           166.10      2027.0           0.14100            0.21130   \n",
      "565           155.00      1731.0           0.11660            0.19220   \n",
      "566           126.70      1124.0           0.11390            0.30940   \n",
      "567           184.60      1821.0           0.16500            0.86810   \n",
      "568            59.16       268.6           0.08996            0.06444   \n",
      "\n",
      "     worst concavity  worst concave points  worst symmetry  \\\n",
      "0             0.7119                0.2654          0.4601   \n",
      "1             0.2416                0.1860          0.2750   \n",
      "2             0.4504                0.2430          0.3613   \n",
      "3             0.6869                0.2575          0.6638   \n",
      "4             0.4000                0.1625          0.2364   \n",
      "..               ...                   ...             ...   \n",
      "564           0.4107                0.2216          0.2060   \n",
      "565           0.3215                0.1628          0.2572   \n",
      "566           0.3403                0.1418          0.2218   \n",
      "567           0.9387                0.2650          0.4087   \n",
      "568           0.0000                0.0000          0.2871   \n",
      "\n",
      "     worst fractal dimension  \n",
      "0                    0.11890  \n",
      "1                    0.08902  \n",
      "2                    0.08758  \n",
      "3                    0.17300  \n",
      "4                    0.07678  \n",
      "..                       ...  \n",
      "564                  0.07115  \n",
      "565                  0.06637  \n",
      "566                  0.07820  \n",
      "567                  0.12400  \n",
      "568                  0.07039  \n",
      "\n",
      "[569 rows x 30 columns]\n",
      "     malignant  benign\n",
      "0         True   False\n",
      "1         True   False\n",
      "2         True   False\n",
      "3         True   False\n",
      "4         True   False\n",
      "..         ...     ...\n",
      "564       True   False\n",
      "565       True   False\n",
      "566       True   False\n",
      "567       True   False\n",
      "568      False    True\n",
      "\n",
      "[569 rows x 2 columns]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import os\n",
    "from sklearn.datasets import load_breast_cancer\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import confusion_matrix\n",
    "from sklearn.tree import export_graphviz\n",
    "\n",
    "from IPython.display import Image \n",
    "from pydot import graph_from_dot_data\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "\n",
    "cancer = load_breast_cancer()\n",
    "X = pd.DataFrame(cancer.data, columns=cancer.feature_names)\n",
    "print(X)\n",
    "y = pd.Categorical.from_codes(cancer.target, cancer.target_names)\n",
    "y = pd.get_dummies(y)\n",
    "print(y)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)\n",
    "tree_clf = DecisionTreeClassifier(max_depth=5)\n",
    "tree_clf.fit(X_train, y_train)\n",
    "\n",
    "export_graphviz(\n",
    "    tree_clf,\n",
    "    out_file=\"DataFiles/cancer.dot\",\n",
    "    feature_names=cancer.feature_names,\n",
    "    class_names=cancer.target_names,\n",
    "    rounded=True,\n",
    "    filled=True\n",
    ")\n",
    "cmd = 'dot -Tpng DataFiles/cancer.dot -o DataFiles/cancer.png'\n",
    "os.system(cmd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Common imports\n",
    "import numpy as np\n",
    "from sklearn.model_selection import  train_test_split \n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.datasets import make_moons\n",
    "from sklearn.tree import export_graphviz\n",
    "from pydot import graph_from_dot_data\n",
    "import pandas as pd\n",
    "import os\n",
    "\n",
    "np.random.seed(42)\n",
    "X, y = make_moons(n_samples=100, noise=0.25, random_state=53)\n",
    "X_train, X_test, y_train, y_test = train_test_split(X,y,random_state=0)\n",
    "tree_clf = DecisionTreeClassifier(max_depth=5)\n",
    "tree_clf.fit(X_train, y_train)\n",
    "\n",
    "export_graphviz(\n",
    "    tree_clf,\n",
    "    out_file=\"DataFiles/moons.dot\",\n",
    "    rounded=True,\n",
    "    filled=True\n",
    ")\n",
    "cmd = 'dot -Tpng DataFiles/moons.dot -o DataFiles/moons.png'\n",
    "os.system(cmd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Other ways of visualizing the trees\n",
    "\n",
    "**Scikit-Learn** has also another way to visualize the trees which is very useful, here with the Iris data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0.5, 0.9166666666666666, 'x[2] <= 2.45\\ngini = 0.667\\nsamples = 150\\nvalue = [50, 50, 50]'),\n",
       " Text(0.4230769230769231, 0.75, 'gini = 0.0\\nsamples = 50\\nvalue = [50, 0, 0]'),\n",
       " Text(0.5769230769230769, 0.75, 'x[3] <= 1.75\\ngini = 0.5\\nsamples = 100\\nvalue = [0, 50, 50]'),\n",
       " Text(0.3076923076923077, 0.5833333333333334, 'x[2] <= 4.95\\ngini = 0.168\\nsamples = 54\\nvalue = [0, 49, 5]'),\n",
       " Text(0.15384615384615385, 0.4166666666666667, 'x[3] <= 1.65\\ngini = 0.041\\nsamples = 48\\nvalue = [0, 47, 1]'),\n",
       " Text(0.07692307692307693, 0.25, 'gini = 0.0\\nsamples = 47\\nvalue = [0, 47, 0]'),\n",
       " Text(0.23076923076923078, 0.25, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 0, 1]'),\n",
       " Text(0.46153846153846156, 0.4166666666666667, 'x[3] <= 1.55\\ngini = 0.444\\nsamples = 6\\nvalue = [0, 2, 4]'),\n",
       " Text(0.38461538461538464, 0.25, 'gini = 0.0\\nsamples = 3\\nvalue = [0, 0, 3]'),\n",
       " Text(0.5384615384615384, 0.25, 'x[2] <= 5.45\\ngini = 0.444\\nsamples = 3\\nvalue = [0, 2, 1]'),\n",
       " Text(0.46153846153846156, 0.08333333333333333, 'gini = 0.0\\nsamples = 2\\nvalue = [0, 2, 0]'),\n",
       " Text(0.6153846153846154, 0.08333333333333333, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 0, 1]'),\n",
       " Text(0.8461538461538461, 0.5833333333333334, 'x[2] <= 4.85\\ngini = 0.043\\nsamples = 46\\nvalue = [0, 1, 45]'),\n",
       " Text(0.7692307692307693, 0.4166666666666667, 'x[1] <= 3.1\\ngini = 0.444\\nsamples = 3\\nvalue = [0, 1, 2]'),\n",
       " Text(0.6923076923076923, 0.25, 'gini = 0.0\\nsamples = 2\\nvalue = [0, 0, 2]'),\n",
       " Text(0.8461538461538461, 0.25, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 1, 0]'),\n",
       " Text(0.9230769230769231, 0.4166666666666667, 'gini = 0.0\\nsamples = 43\\nvalue = [0, 0, 43]')]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_24_1.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn import tree\n",
    "X, y = load_iris(return_X_y=True)\n",
    "tree_clf = tree.DecisionTreeClassifier()\n",
    "tree_clf = tree_clf.fit(X, y)\n",
    "# and then plot the tree\n",
    "tree.plot_tree(tree_clf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively, the tree can also be exported in textual format with the function exporttext.\n",
    "This method doesn’t require the installation of external libraries and is more compact:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "|--- petal width (cm) <= 0.80\n",
      "|   |--- class: 0\n",
      "|--- petal width (cm) >  0.80\n",
      "|   |--- petal width (cm) <= 1.75\n",
      "|   |   |--- class: 1\n",
      "|   |--- petal width (cm) >  1.75\n",
      "|   |   |--- class: 2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.tree import export_text\n",
    "iris = load_iris()\n",
    "decision_tree = DecisionTreeClassifier(random_state=0, max_depth=2)\n",
    "decision_tree = decision_tree.fit(iris.data, iris.target)\n",
    "r = export_text(decision_tree, feature_names=iris['feature_names'])\n",
    "print(r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithms for Setting up Decision Trees\n",
    "\n",
    "Two algorithms stand out in the set up of decision trees:\n",
    "1. The CART (Classification And Regression Tree) algorithm for both classification and regression\n",
    "\n",
    "2. The ID3 algorithm based on the computation of the information gain for classification\n",
    "\n",
    "We discuss both algorithms with applications here. The popular library\n",
    "**Scikit-Learn** uses the CART algorithm. For classification problems\n",
    "you can use either the **gini** index or the **entropy** to split a tree\n",
    "in two branches.\n",
    "\n",
    "### The CART algorithm for Classification\n",
    "\n",
    "For classification, the CART algorithm splits the data set in two subsets using a single feature $k$ and a threshold $t_k$.\n",
    "This could be for example a threshold set by a number below a certain circumference of a malign tumor.\n",
    "\n",
    "How do we find these two quantities?\n",
    "We search for the pair $(k,t_k)$ that produces the purest subset using for example the **gini** factor $G$.\n",
    "The cost function it tries to minimize is then"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "C(k,t_k) = \\frac{m_{\\mathrm{left}}}{m}G_{\\mathrm{left}}+ \\frac{m_{\\mathrm{right}}}{m}G_{\\mathrm{right}},\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "where $G_{\\mathrm{left/right}}$ measures the impurity of the left/right subset  and $m_{\\mathrm{left/right}}$\n",
    " is the number of instances in the left/right subset\n",
    "\n",
    "Once it has successfully split the training set in two, it splits the subsets using the same logic, then the subsubsets\n",
    "and so on, recursively. It stops recursing once it reaches the maximum depth (defined by the\n",
    "$max\\_depth$ hyperparameter), or if it cannot find a split that will reduce impurity. A few other\n",
    "hyperparameters control additional stopping conditions such as the $min\\_samples\\_split$,\n",
    "$min\\_samples\\_leaf$, $min\\_weight\\_fraction\\_leaf$, and $max\\_leaf\\_nodes$.\n",
    "\n",
    "\n",
    "### The CART algorithm for Regression\n",
    "\n",
    "The CART algorithm for regression works is similar to the one for classification except that instead of trying to split the\n",
    "training set in a way that minimizes say the **gini** or **entropy** impurity, it now tries to split the training set in a way that minimizes our well-known mean-squared error (MSE). The cost function is now"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "C(k,t_k) = \\frac{m_{\\mathrm{left}}}{m}\\mathrm{MSE}_{\\mathrm{left}}+ \\frac{m_{\\mathrm{right}}}{m}\\mathrm{MSE}_{\\mathrm{right}}.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here the MSE for a specific node is defined as"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\mathrm{MSE}_{\\mathrm{node}}=\\frac{1}{m_\\mathrm{node}}\\sum_{i\\in \\mathrm{node}}(\\overline{y}_{\\mathrm{node}}-y_i)^2,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "with"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\overline{y}_{\\mathrm{node}}=\\frac{1}{m_\\mathrm{node}}\\sum_{i\\in \\mathrm{node}}y_i,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "the mean value of all observations in a specific node.\n",
    "\n",
    "Without any regularization, the regression task for decision trees, \n",
    "just like for classification tasks, is  prone to overfitting.\n",
    "\n",
    "\n",
    "\n",
    "### Computing the Gini index\n",
    "\n",
    "The example we will look at is a classical one in many Machine\n",
    "Learning applications. Based on various meteorological features, we\n",
    "have several so-called attributes which decide whether we at the end\n",
    "will do some outdoor activity like skiing, going for a bike ride etc\n",
    "etc.  The table here contains the feautures **outlook**, **temperature**,\n",
    "**humidity** and **wind**.  The target or output is whether we ride\n",
    "(True=1) or whether we do something else that day (False=0). The\n",
    "attributes for each feature are then sunny, overcast and rain for the\n",
    "outlook, hot, cold and mild for temperature, high and normal for\n",
    "humidity and weak and strong for wind.\n",
    "\n",
    "The table here summarizes the various attributes and\n",
    "<table border=\"1\">\n",
    "<thead>\n",
    "<tr><th align=\"center\">Day</th> <th align=\"center\">Outlook </th> <th align=\"center\">Temperature</th> <th align=\"center\">Humidity</th> <th align=\"center\"> Wind </th> <th align=\"center\">Ride</th> </tr>\n",
    "</thead>\n",
    "<tbody>\n",
    "<tr><td align=\"center\">   1      </td> <td align=\"center\">   Sunny       </td> <td align=\"center\">   Hot            </td> <td align=\"center\">   High        </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   0       </td> </tr>\n",
    "<tr><td align=\"center\">   2      </td> <td align=\"center\">   Sunny       </td> <td align=\"center\">   Hot            </td> <td align=\"center\">   High        </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   3      </td> <td align=\"center\">   Overcast    </td> <td align=\"center\">   Hot            </td> <td align=\"center\">   High        </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   4      </td> <td align=\"center\">   Rain        </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   High        </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   5      </td> <td align=\"center\">   Rain        </td> <td align=\"center\">   Cool           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   6      </td> <td align=\"center\">   Rain        </td> <td align=\"center\">   Cool           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   0       </td> </tr>\n",
    "<tr><td align=\"center\">   7      </td> <td align=\"center\">   Overcast    </td> <td align=\"center\">   Cool           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   8      </td> <td align=\"center\">   Sunny       </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   High        </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   0       </td> </tr>\n",
    "<tr><td align=\"center\">   9      </td> <td align=\"center\">   Sunny       </td> <td align=\"center\">   Cool           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   10     </td> <td align=\"center\">   Rain        </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   11     </td> <td align=\"center\">   Sunny       </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   12     </td> <td align=\"center\">   Overcast    </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   High        </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   13     </td> <td align=\"center\">   Overcast    </td> <td align=\"center\">   Hot            </td> <td align=\"center\">   Normal      </td> <td align=\"center\">   Weak      </td> <td align=\"center\">   1       </td> </tr>\n",
    "<tr><td align=\"center\">   14     </td> <td align=\"center\">   Rain        </td> <td align=\"center\">   Mild           </td> <td align=\"center\">   High        </td> <td align=\"center\">   Strong    </td> <td align=\"center\">   0       </td> </tr>\n",
    "</tbody>\n",
    "</table>\n",
    "\n",
    "### Simple Python Code to read in Data and perform Classification"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  (0, 0)\t1.0\n",
      "  (0, 7)\t1.0\n",
      "  (0, 9)\t1.0\n",
      "  (0, 13)\t1.0\n",
      "  (1, 3)\t1.0\n",
      "  (1, 5)\t1.0\n",
      "  (1, 8)\t1.0\n",
      "  (1, 12)\t1.0\n",
      "  (2, 3)\t1.0\n",
      "  (2, 5)\t1.0\n",
      "  (2, 8)\t1.0\n",
      "  (2, 11)\t1.0\n",
      "  (3, 1)\t1.0\n",
      "  (3, 5)\t1.0\n",
      "  (3, 8)\t1.0\n",
      "  (3, 12)\t1.0\n",
      "  (4, 2)\t1.0\n",
      "  (4, 6)\t1.0\n",
      "  (4, 8)\t1.0\n",
      "  (4, 12)\t1.0\n",
      "  (5, 2)\t1.0\n",
      "  (5, 4)\t1.0\n",
      "  (5, 10)\t1.0\n",
      "  (5, 12)\t1.0\n",
      "  (6, 2)\t1.0\n",
      "  :\t:\n",
      "  (8, 12)\t1.0\n",
      "  (9, 3)\t1.0\n",
      "  (9, 4)\t1.0\n",
      "  (9, 10)\t1.0\n",
      "  (9, 12)\t1.0\n",
      "  (10, 2)\t1.0\n",
      "  (10, 6)\t1.0\n",
      "  (10, 10)\t1.0\n",
      "  (10, 12)\t1.0\n",
      "  (11, 3)\t1.0\n",
      "  (11, 6)\t1.0\n",
      "  (11, 10)\t1.0\n",
      "  (11, 11)\t1.0\n",
      "  (12, 1)\t1.0\n",
      "  (12, 6)\t1.0\n",
      "  (12, 8)\t1.0\n",
      "  (12, 11)\t1.0\n",
      "  (13, 1)\t1.0\n",
      "  (13, 5)\t1.0\n",
      "  (13, 10)\t1.0\n",
      "  (13, 12)\t1.0\n",
      "  (14, 2)\t1.0\n",
      "  (14, 6)\t1.0\n",
      "  (14, 8)\t1.0\n",
      "  (14, 11)\t1.0\n",
      "Train set accuracy with Decision Tree: 0.73\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Common imports\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.tree import export_graphviz\n",
    "from sklearn.preprocessing import StandardScaler, OneHotEncoder\n",
    "from sklearn.compose import ColumnTransformer\n",
    "from IPython.display import Image \n",
    "from pydot import graph_from_dot_data\n",
    "import os\n",
    "\n",
    "# Where to save the figures and data files\n",
    "PROJECT_ROOT_DIR = \"Results\"\n",
    "FIGURE_ID = \"Results/FigureFiles\"\n",
    "DATA_ID = \"DataFiles/\"\n",
    "\n",
    "if not os.path.exists(PROJECT_ROOT_DIR):\n",
    "    os.mkdir(PROJECT_ROOT_DIR)\n",
    "\n",
    "if not os.path.exists(FIGURE_ID):\n",
    "    os.makedirs(FIGURE_ID)\n",
    "\n",
    "if not os.path.exists(DATA_ID):\n",
    "    os.makedirs(DATA_ID)\n",
    "\n",
    "def image_path(fig_id):\n",
    "    return os.path.join(FIGURE_ID, fig_id)\n",
    "\n",
    "def data_path(dat_id):\n",
    "    return os.path.join(DATA_ID, dat_id)\n",
    "\n",
    "def save_fig(fig_id):\n",
    "    plt.savefig(image_path(fig_id) + \".png\", format='png')\n",
    "\n",
    "infile = open(data_path(\"rideclass.csv\"),'r')\n",
    "\n",
    "# Read the experimental data with Pandas\n",
    "from IPython.display import display\n",
    "ridedata = pd.read_csv(infile,names = ('Outlook','Temperature','Humidity','Wind','Ride'))\n",
    "ridedata = pd.DataFrame(ridedata)\n",
    "\n",
    "# Features and targets\n",
    "X = ridedata.loc[:, ridedata.columns != 'Ride'].values\n",
    "y = ridedata.loc[:, ridedata.columns == 'Ride'].values\n",
    "\n",
    "# Create the encoder.\n",
    "encoder = OneHotEncoder(handle_unknown=\"ignore\")\n",
    "# Assume for simplicity all features are categorical.\n",
    "encoder.fit(X)    \n",
    "# Apply the encoder.\n",
    "X = encoder.transform(X)\n",
    "print(X)\n",
    "# Then do a Classification tree\n",
    "tree_clf = DecisionTreeClassifier(max_depth=2)\n",
    "tree_clf.fit(X, y)\n",
    "print(\"Train set accuracy with Decision Tree: {:.2f}\".format(tree_clf.score(X,y)))\n",
    "#transfer to a decision tree graph\n",
    "export_graphviz(\n",
    "    tree_clf,\n",
    "    out_file=\"DataFiles/ride.dot\",\n",
    "    rounded=True,\n",
    "    filled=True\n",
    ")\n",
    "cmd = 'dot -Tpng DataFiles/cancer.dot -o DataFiles/cancer.png'\n",
    "os.system(cmd)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above functions (gini, entropy and misclassification error) are\n",
    "important components of the so-called CART algorithm. We will discuss\n",
    "this algorithm below after we have discussed the information gain\n",
    "algorithm ID3.\n",
    "\n",
    "In the example here we have converted all our attributes into numerical values $0,1,2$ etc."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X1 < 0.000 Gini=0.408\n",
      "X1 < 0.000 Gini=0.408\n",
      "X1 < 1.000 Gini=0.394\n",
      "X1 < 2.000 Gini=0.394\n",
      "X1 < 2.000 Gini=0.394\n",
      "X1 < 2.000 Gini=0.394\n",
      "X1 < 1.000 Gini=0.394\n",
      "X1 < 0.000 Gini=0.408\n",
      "X1 < 0.000 Gini=0.408\n",
      "X1 < 2.000 Gini=0.394\n",
      "X1 < 0.000 Gini=0.408\n",
      "X1 < 1.000 Gini=0.394\n",
      "X1 < 1.000 Gini=0.394\n",
      "X1 < 2.000 Gini=0.394\n",
      "X2 < 0.000 Gini=0.408\n",
      "X2 < 0.000 Gini=0.408\n",
      "X2 < 0.000 Gini=0.408\n",
      "X2 < 1.000 Gini=0.407\n",
      "X2 < 2.000 Gini=0.407\n",
      "X2 < 2.000 Gini=0.407\n",
      "X2 < 2.000 Gini=0.407\n",
      "X2 < 1.000 Gini=0.407\n",
      "X2 < 2.000 Gini=0.407\n",
      "X2 < 1.000 Gini=0.407\n",
      "X2 < 1.000 Gini=0.407\n",
      "X2 < 1.000 Gini=0.407\n",
      "X2 < 0.000 Gini=0.408\n",
      "X2 < 1.000 Gini=0.407\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 0.000 Gini=0.408\n",
      "X3 < 1.000 Gini=0.367\n",
      "X3 < 0.000 Gini=0.408\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 1.000 Gini=0.405\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 1.000 Gini=0.405\n",
      "X4 < 1.000 Gini=0.405\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 1.000 Gini=0.405\n",
      "X4 < 1.000 Gini=0.405\n",
      "X4 < 0.000 Gini=0.408\n",
      "X4 < 1.000 Gini=0.405\n",
      "Split: [X3 < 1.000]\n"
     ]
    }
   ],
   "source": [
    "# Split a dataset based on an attribute and an attribute value\n",
    "def test_split(index, value, dataset):\n",
    "\tleft, right = list(), list()\n",
    "\tfor row in dataset:\n",
    "\t\tif row[index] < value:\n",
    "\t\t\tleft.append(row)\n",
    "\t\telse:\n",
    "\t\t\tright.append(row)\n",
    "\treturn left, right\n",
    " \n",
    "# Calculate the Gini index for a split dataset\n",
    "def gini_index(groups, classes):\n",
    "\t# count all samples at split point\n",
    "\tn_instances = float(sum([len(group) for group in groups]))\n",
    "\t# sum weighted Gini index for each group\n",
    "\tgini = 0.0\n",
    "\tfor group in groups:\n",
    "\t\tsize = float(len(group))\n",
    "\t\t# avoid divide by zero\n",
    "\t\tif size == 0:\n",
    "\t\t\tcontinue\n",
    "\t\tscore = 0.0\n",
    "\t\t# score the group based on the score for each class\n",
    "\t\tfor class_val in classes:\n",
    "\t\t\tp = [row[-1] for row in group].count(class_val) / size\n",
    "\t\t\tscore += p * p\n",
    "\t\t# weight the group score by its relative size\n",
    "\t\tgini += (1.0 - score) * (size / n_instances)\n",
    "\treturn gini\n",
    "\n",
    "# Select the best split point for a dataset\n",
    "def get_split(dataset):\n",
    "\tclass_values = list(set(row[-1] for row in dataset))\n",
    "\tb_index, b_value, b_score, b_groups = 999, 999, 999, None\n",
    "\tfor index in range(len(dataset[0])-1):\n",
    "\t\tfor row in dataset:\n",
    "\t\t\tgroups = test_split(index, row[index], dataset)\n",
    "\t\t\tgini = gini_index(groups, class_values)\n",
    "\t\t\tprint('X%d < %.3f Gini=%.3f' % ((index+1), row[index], gini))\n",
    "\t\t\tif gini < b_score:\n",
    "\t\t\t\tb_index, b_value, b_score, b_groups = index, row[index], gini, groups\n",
    "\treturn {'index':b_index, 'value':b_value, 'groups':b_groups}\n",
    " \n",
    "dataset = [[0,0,0,0,0],\n",
    "            [0,0,0,1,1],\n",
    "            [1,0,0,0,1],\n",
    "            [2,1,0,0,1],\n",
    "            [2,2,1,0,1],\n",
    "            [2,2,1,1,0],\n",
    "            [1,2,1,1,1],\n",
    "            [0,1,0,0,0],\n",
    "            [0,2,1,0,1],\n",
    "            [2,1,1,0,1],\n",
    "            [0,1,1,1,1],\n",
    "            [1,1,0,1,1],\n",
    "            [1,0,1,0,1],\n",
    "            [2,1,0,1,0]]\n",
    "\n",
    "split = get_split(dataset)\n",
    "print('Split: [X%d < %.3f]' % ((split['index']+1), split['value']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Entropy and the ID3 algorithm\n",
    "\n",
    "The ID3 algorithm  learns decision trees by constructing\n",
    "them in a top down way, beginning with the question **which attribute should be tested at the root of the tree**?\n",
    "\n",
    "1. Each instance attribute is evaluated using a statistical test to determine how well it alone classifies the training examples.\n",
    "\n",
    "2. The best attribute is selected and used as the test at the root node of the tree.\n",
    "\n",
    "3. A descendant of the root node is then created for each possible value of this attribute.\n",
    "\n",
    "4. Training examples are sorted to the appropriate descendant node.\n",
    "\n",
    "5. The entire process is then repeated using the training examples associated with each descendant node to select the best attribute to test at that point in the tree.\n",
    "\n",
    "6. This forms a greedy search for an acceptable decision tree, in which the algorithm never backtracks to reconsider earlier choices. \n",
    "\n",
    "The ID3 algorithm selects which attribute to test at each node in the\n",
    "tree.\n",
    "\n",
    "We would like to select the attribute that is most useful for classifying\n",
    "examples.\n",
    "\n",
    "What is a good quantitative measure of the worth of an attribute?\n",
    "\n",
    "Information gain measures how well a given attribute separates the\n",
    "training examples according to their target classification.\n",
    "\n",
    "The ID3 algorithm uses this information gain measure to select among the candidate\n",
    "attributes at each step while growing the tree.\n",
    "\n",
    "\n",
    "### Cancer Data again now with Decision Trees and other Methods"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(426, 30)\n",
      "(143, 30)\n",
      "Test set accuracy with Logistic Regression: 0.94\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test set accuracy with SVM: 0.63\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "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": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_42_0.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from __future__ import division, print_function, unicode_literals\n",
    "\n",
    "# Common imports\n",
    "import numpy as np\n",
    "import os\n",
    "\n",
    "# to make this notebook's output stable across runs\n",
    "np.random.seed(42)\n",
    "\n",
    "# To plot pretty figures\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.colors import ListedColormap\n",
    "plt.rcParams['axes.labelsize'] = 14\n",
    "plt.rcParams['xtick.labelsize'] = 12\n",
    "plt.rcParams['ytick.labelsize'] = 12\n",
    "\n",
    "\n",
    "from sklearn.svm import SVC\n",
    "from sklearn import datasets\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.datasets import make_moons\n",
    "from sklearn.tree import export_graphviz\n",
    "\n",
    "Xm, ym = make_moons(n_samples=100, noise=0.25, random_state=53)\n",
    "\n",
    "deep_tree_clf1 = DecisionTreeClassifier(random_state=42)\n",
    "deep_tree_clf2 = DecisionTreeClassifier(min_samples_leaf=4, random_state=42)\n",
    "deep_tree_clf1.fit(Xm, ym)\n",
    "deep_tree_clf2.fit(Xm, ym)\n",
    "\n",
    "\n",
    "def plot_decision_boundary(clf, X, y, axes=[0, 7.5, 0, 3], iris=True, legend=False, plot_training=True):\n",
    "    x1s = np.linspace(axes[0], axes[1], 100)\n",
    "    x2s = np.linspace(axes[2], axes[3], 100)\n",
    "    x1, x2 = np.meshgrid(x1s, x2s)\n",
    "    X_new = np.c_[x1.ravel(), x2.ravel()]\n",
    "    y_pred = clf.predict(X_new).reshape(x1.shape)\n",
    "    custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
    "    plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)\n",
    "    if not iris:\n",
    "        custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])\n",
    "        plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)\n",
    "    if plot_training:\n",
    "        plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\", label=\"Iris-Setosa\")\n",
    "        plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\", label=\"Iris-Versicolor\")\n",
    "        plt.plot(X[:, 0][y==2], X[:, 1][y==2], \"g^\", label=\"Iris-Virginica\")\n",
    "        plt.axis(axes)\n",
    "    if iris:\n",
    "        plt.xlabel(\"Petal length\", fontsize=14)\n",
    "        plt.ylabel(\"Petal width\", fontsize=14)\n",
    "    else:\n",
    "        plt.xlabel(r\"$x_1$\", fontsize=18)\n",
    "        plt.ylabel(r\"$x_2$\", fontsize=18, rotation=0)\n",
    "    if legend:\n",
    "        plt.legend(loc=\"lower right\", fontsize=14)\n",
    "plt.figure(figsize=(11, 4))\n",
    "plt.subplot(121)\n",
    "plot_decision_boundary(deep_tree_clf1, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)\n",
    "plt.title(\"No restrictions\", fontsize=16)\n",
    "plt.subplot(122)\n",
    "plot_decision_boundary(deep_tree_clf2, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)\n",
    "plt.title(\"min_samples_leaf = {}\".format(deep_tree_clf2.min_samples_leaf), fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_43_0.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(6)\n",
    "Xs = np.random.rand(100, 2) - 0.5\n",
    "ys = (Xs[:, 0] > 0).astype(np.float32) * 2\n",
    "\n",
    "angle = np.pi/4\n",
    "rotation_matrix = np.array([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]])\n",
    "Xsr = Xs.dot(rotation_matrix)\n",
    "\n",
    "tree_clf_s = DecisionTreeClassifier(random_state=42)\n",
    "tree_clf_s.fit(Xs, ys)\n",
    "tree_clf_sr = DecisionTreeClassifier(random_state=42)\n",
    "tree_clf_sr.fit(Xsr, ys)\n",
    "\n",
    "plt.figure(figsize=(11, 4))\n",
    "plt.subplot(121)\n",
    "plot_decision_boundary(tree_clf_s, Xs, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
    "plt.subplot(122)\n",
    "plot_decision_boundary(tree_clf_sr, Xsr, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [],
   "source": [
    "# Quadratic training set + noise\n",
    "np.random.seed(42)\n",
    "m = 200\n",
    "X = np.random.rand(m, 1)\n",
    "y = 4 * (X - 0.5) ** 2\n",
    "y = y + np.random.randn(m, 1) / 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>DecisionTreeRegressor(max_depth=2, random_state=42)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">DecisionTreeRegressor</label><div class=\"sk-toggleable__content\"><pre>DecisionTreeRegressor(max_depth=2, random_state=42)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "DecisionTreeRegressor(max_depth=2, random_state=42)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "tree_reg = DecisionTreeRegressor(max_depth=2, random_state=42)\n",
    "tree_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_46_0.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.tree import DecisionTreeRegressor\n",
    "\n",
    "tree_reg1 = DecisionTreeRegressor(random_state=42, max_depth=2)\n",
    "tree_reg2 = DecisionTreeRegressor(random_state=42, max_depth=3)\n",
    "tree_reg1.fit(X, y)\n",
    "tree_reg2.fit(X, y)\n",
    "\n",
    "def plot_regression_predictions(tree_reg, X, y, axes=[0, 1, -0.2, 1], ylabel=\"$y$\"):\n",
    "    x1 = np.linspace(axes[0], axes[1], 500).reshape(-1, 1)\n",
    "    y_pred = tree_reg.predict(x1)\n",
    "    plt.axis(axes)\n",
    "    plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "    if ylabel:\n",
    "        plt.ylabel(ylabel, fontsize=18, rotation=0)\n",
    "    plt.plot(X, y, \"b.\")\n",
    "    plt.plot(x1, y_pred, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "\n",
    "plt.figure(figsize=(11, 4))\n",
    "plt.subplot(121)\n",
    "plot_regression_predictions(tree_reg1, X, y)\n",
    "for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
    "    plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
    "plt.text(0.21, 0.65, \"Depth=0\", fontsize=15)\n",
    "plt.text(0.01, 0.2, \"Depth=1\", fontsize=13)\n",
    "plt.text(0.65, 0.8, \"Depth=1\", fontsize=13)\n",
    "plt.legend(loc=\"upper center\", fontsize=18)\n",
    "plt.title(\"max_depth=2\", fontsize=14)\n",
    "\n",
    "plt.subplot(122)\n",
    "plot_regression_predictions(tree_reg2, X, y, ylabel=None)\n",
    "for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
    "    plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
    "for split in (0.0458, 0.1298, 0.2873, 0.9040):\n",
    "    plt.plot([split, split], [-0.2, 1], \"k:\", linewidth=1)\n",
    "plt.text(0.3, 0.5, \"Depth=2\", fontsize=13)\n",
    "plt.title(\"max_depth=3\", fontsize=14)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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2NDTY5yxlzZo1WLp0KX7++WdUVlbKcrS13gc15syZQ/2SCa9CwpYgdHL//ffj3//+N55//nnk5uaq7iMUuhDyYJUIVQGrq6t1v67auU6cOAGAb0X02WefaR576tQpAEC3bt2wZcsWzJ07F1988QU++OADAHxxrHnz5mHs2LG656M1Jy0Egdi5c2e3XkMvzfmfC3lAUkJC+Mui1FC/+uqr6N69O1asWIFnnnkGzzzzDCIiInDLLbfgpZdeouqhBEEEDMrcUEC8rjnbJogYZ6hdM4VzKIvu6SE2NhZbtmzB7NmzsXbtWnz++ecAeKE8a9YsTJs2zb7vfffdh3//+9/o0qUL/vGPfyA1NRXh4eEA+MJEdXV1qq+h9Tc7u/6r/S8SExNhMDjWXBVsjyu7Ltjt//73v073E+z24MGD8e2332LBggVYtWqVveDSgAED8MILL2DEiBFOz6OHyspKMMZw+PBhzJ071+WcAOCll17Cww8/jKSkJFx55ZUwmUyIjIwEALzyyiua70MgILznWu9VTU2N5mecCA5I2BKETiIjIzFnzhxMmTIF8+fPx5gxYxz2EQzosWPHVM8hjKsZWi3Umo0Lx7/22mu45557dJ2nf//++Oijj9DQ0ICffvoJX3zxBV599VWMGzcOnTp1wtChQ5s1Jy0EI6G2Au4NfPE/VxIaGopHHnkEjzzyCI4cOYLvv/8eb731Ft5++20cPXoU69ev9/jcBEEQbZmuXbuioKAAVqsVO3fuxFdffYVXX30V06dPR3x8PMaPH4+ysjK8/vrr6N+/P7Zs2SKLzjl69KhTUeYtKioqYLPZHMStYGNcCSLBBq1duxajR4/W9ZrDhg3DsGHDcObMGWzbtg1r167Ff/7zH1x77bXYuXNns1vrCXMaMGCAajVoJY2NjZg3bx46deqEHTt2ICkpyb6NMYbnn3/erdf/7rvv7AWd9HDBBRfg+uuvd+s1pAhRY8XFxRgwYIBsW2VlJY4fP44hQ4Z4fH7C/5CwJQg3uOuuu7Bo0SK8/vrrOP/88x22C2FeP/zwAxhjMgHIGENhYaFsP08Rqh1v2bJFt7AVEMKpLrnkEvTo0QN33nkn1q1bZxe2QtVnq9XqsgK0HqKionDeeedhz549KC4udhmO7O7r9+rVCxERESgqKsLp06cdwpGFCofeqsLYqVMnjB8/HuPGjUOvXr2wYcMGnDlzxr5iTRAEQbiP0WjEBRdcgAsuuACDBw/GZZddhk8//RTjx4/H33//DcYYrrjiCodrvGBXfU1DQwO2bt3qIHz02nWp3dYrbAUiIyMxfPhwDB8+HHFxcXj66aexYcOGZgvb6Oho9O7dG7t370ZVVRXi4uKc7n/8+HFUV1fj8ssvl4laAPjxxx/tLaX08t1337m1KJGdnd0sYTts2DAsWLAAX331FW699VbZtq+++sq+DxG8UB9bgnADo9GI+fPno66uDv/6178ctqelpWHEiBH29j5S3nzzTfz+++8YOXKk7vxaLQYOHIhBgwZh1apVeP/99x2222w2Wcn6oqIih/5ygLjSLBVlCQkJAACLxdKsOUqZPn06rFarrJeiwNmzZ+0hWp68flhYGMaPH4/jx49jwYIFsm0bNmzAF198gR49erjlkZZSV1eHb7/9Fowx2fipU6dQW1uL0NBQrywAEARBtDV27dql2r9VaZvS09MBAJs3b5aFPFssFq+1vdHDU089JQtT/vPPP/Hmm28iNjYW1113ndNjr7vuOqSlpWHRokWq/c8bGhrwf//3f/bnhYWFsj6+Amp2uzncd999OH36NCZPniwLORbYv3+/vU99cnIyIiMj8fPPP+P06dP2fSorK3Hvvfe6/dpz5swB4wvZ6vppbv/byy+/HN27d8fKlSuxY8cO+3htbS3mzZuHkJAQTJgwoVmvQfgX8tgShJvccMMNGDx4sGahjCVLluDSSy/F5MmTsXbtWpx33nn4448/8OmnnyIpKQlLlizxyjxWrVqFESNG4NZbb8Urr7yCAQMGICIiAgcPHsSWLVtQXl6Os2fPAuBzev7zn/9g+PDh6NGjB2JiYvDHH3/g888/R4cOHXDXXXfZzzty5Eh8+OGHGDt2LK655hpERESgX79+uPbaaz2e6913343vv/8eq1evhtlsxj/+8Q/ExMTg4MGDWL9+PfLz8+2rsJ68vtDH8JlnnsHmzZsxaNAgex/bdu3a4a233lLNjdLDmTNn7MZw0KBBSEtLw8mTJ7Fu3TocPXoUM2fO1F1IiyAIghDZsGEDHnroIQwdOhS9evVCYmIi/v77b3z66aeIjIy0RySlpqbipptuwkcffYSLL74Yl19+OY4dO4Z169Zh5MiR+Pvvv30+19TUVFRVVeGCCy7Atddei+rqaqxatQpnz57FsmXLEB0d7fT48PBwfPjhh7j66qsxbNgwXH755ejbty8A4ODBgygsLERiYqK9UNNLL72Er7/+GiNGjED37t0RERGBn3/+Gd988w169OiBG264wSt/V25uLrZu3YqCggJs2rQJV1xxBTp16oRjx47hzz//xLZt27By5Up07doVBoMB06ZNw0svvYTzzz8fY8aMQU1NDb744gukp6ejU6dOXpmTO0iFaGlpqcPYiy++aK+DERISguXLlyMrKwuZmZkYP348YmJisGbNGuzfvx/PPPOMx0U1iQChpcswE0QwoGz3o+SHH36wl59X9rFljLGSkhI2ceJElpqaykJCQlhqaiqbOHEiKykp0T0Hoe2M0IJBjRMnTrAnn3yS9e3bl0VGRrKoqChmNpvZbbfdxtasWWPfb+vWrSw3N5f17duXxcXFscjISGY2m9l9993n0HqooaGBPfrooywtLY2FhITISuwL/xdnJffV2gkwxrcCWL58ObvkkktY+/btWbt27ZjZbGZTp06VzcHZ6zOm3seWMb4H7X333cfS09NZaGgo69ChA7v55pvtLY+kOPvfCu0HNm7cyBjjew8+99xz7Morr2Qmk4mFhYWxlJQUNmzYMPbee+9p/h8IgiBaEmdtVdTazwgor3nO2v2oXdsZc92mTYs//viDzZgxg1144YUsMTGRhYeHs+7du7MJEyawP/74Q7ZvbW0te+ihh1jXrl1ZeHg4M5vNbN68eay+vl7VLjibk7O/Re1cwv4VFRVs0qRJLDk5mYWHh7OLL75Ytc+ss/+3xWJhM2bMYGazmYWHh7OYmBjWu3dvNmnSJPbNN9/Y9/vyyy/ZnXfeyc4991wWHR3NoqKi2HnnnceefPJJr/axFXj//ffZFVdcweLj41loaCjr3LkzGz58OHvppZdk/e7r6+vZs88+a59/Wloae/DBB1ltba3q+Z19Lr0BVNoCSX/U7Py2bdvYVVddxWJjY1lkZCS7+OKLHfogE8EJx5givo4gCIIgCIIgCACwt0ESQnIJgghMKMeWIAiCIAiCIAiCCGpI2BIEQRAEQRAEQRBBDRWPIgiCIAiCILyC3t6kze1JSgArVqzQFR59/fXXe63lHUEEMiRsCYIgCIIgCK+gtzdpc3uStiSBmlu7YsUKWWs/Lbp27UrClmgTUPEogiAIgiAIgiAIIqihHFuCIAiCIAiCIAgiqKFQZJ3YbDYcOXIE0dHR4DjO39MhCIIg/ABjDLW1tejUqRMMBlob1gvZUIIgCMLXNpSErU6OHDmCLl26+HsaBEEQRABw6NAhmEwmf08jaCAbShAEQQj4yoaSsNVJdHQ0AP6NiPniC2DKFH5Dz57AX3/xj599FuyJJ6Bci26EAce/3YWOAzq33IQJgiAIr1NTU4MuXbrYbQKhD5kNjYnR3O/wYaBPH0Ba/cNgAHbtAjqTCSUIgghqfG1DSdjqRAidiomJQUxoqLghLk58XF6ucbQNB389hpgRvX02P4IgCKLloHBa95DZUCfC9qef5KIWAGw24NgxoDeZUIIgiFaBr2woJQh5QkOD+Fi64hAXB6byRjXCiJShPVpgYgRBEAQRvJjNvIdWitEI9CATShAEQbiAhK0naAnbiAhwzz4r29UGDluylyI1g3KxCIIgAh6LBVi9GliyBJXzl2DX06tRWmTx96zaDCYTkJfHi1mA/710KT9OEARBBA8WC7BxI/+7paBQZE+orxcfS4Xt2bPA+PHA44/bh05Ovh+ZeTktODmCIAjCI/LzgUmT7E/jm35s8zgUZi9D5gq6lrcEOTlAVhawdy/vqSVRSxAEEVzk5/PliGw2PgonL4+/tvsa8th6gpbHtq4OsFplu8aktG+hSREEQRAeY7EAkyerbjKAYXBBLnluWxCTCRg+nEQtQRBEsGGxiKIW4H/n5raM55aErSdoCduzZx2ELRobW2ZOBEEQhOcUFztWLZIQAiuObdrbghMiCIIgiOCjuFgUtQJWKx+F42tI2HqCM2GrfCdJ2BIEQQQ+ZjPgpEojFQEkCIIgCNf4swggCVtPcCMUmYQtQRBEEGAyAa+8orqJigASBEEQhD78WQSQhK0nOCseRcKWIAgiOBk/XnW4/H+bqHAUQRAEQegkJwcoKeGrIpeUtEzhKICqInsGhSITbsIYQ0NDA2zKzwfhFwwGA0JDQ33WIJwIUjSu1yn9Ulp4IgRBEAQR3JhMLV8AkIStJ2gI25rf9qN+Zyk6aO1LtDmsViuOHz+O2tpaNNBnIaAIDQ1FdHQ0OnToAKMQL0O0bZQRN67GCa9hsfAFR8xmqoRMEARBeAYJW0+QCpTvvrM/jNn7C2yTbpDvSx7bNovVasWhQ4dQV1eH2NhYREVFwWg0kpfQzzDGYLVacfLkSVRVVeHMmTPo0qULiVtC+3pNwtan+KvfIUEQBNG6IGHrCRJhy557DlKZYoCiXQQJ2zbL8ePHUVdXh7S0NERGRvp7OoSCqKgoxMbG4uDBgzh+/DhSUijctM2jdb2mFAKfodXvMCuLPLcEQRCEe1DxKE+QFI/inPQ9BEDCto3CGENtbS1iY2NJ1AYwkZGRiImJQW1tLZir7zLR+qFQ5BbHn/0OCYIgiNYFCVtPkHpsXYWVkrBtkzQ0NKChoQFRUVH+ngrhgujoaPv7RbRxKBS5xfFnv0OCIAiidUHC1hMkN8DcCy/AJglGdvD5kLBtkwjVjylvM/AR3iOqWE2QsG15/NnvkCAIgmhdBLywra2txaOPPoorr7wSSUlJ4DgOc+bM0X18WVkZJkyYgA4dOqBdu3YYPHgwvvnmm+ZNSurZufNOGL5ab39qTUmV70vCtk1DhaICH3qPCDtaAjaIFz0C0oYq8Fe/Q4IgCKJ1EfDCtqKiAnl5eairq8P111/v1rF1dXW4/PLL8c0332Dx4sX45JNPkJKSgquuugrff/+955OS5NgiNBTo1Mn+NATUx5YgCCIoaYUe24C0oSqYTMDw4eSpJQiCIDwn4Ksip6eno7KyEhzH4fjx41i+fLnuY/Pz87Fr1y5s3rwZgwcPBgCMGDEC559/Ph599FFs27bNs0lJPbZhYUCI5N8oFb0ACVuCIIhgoRUK24C0oQRBEAThAwLeY8txnMehgh9//DHOPfdcu0EGgJCQENxxxx3Yvn07Dh8+7NmkpMI2NFRMDgJI2BIEQQQrrTAUOSBtKEEQBEH4gIAXts1h165d6N+/v8O4MPb7779rHltXV4eamhrZjx2psA0JIWFLEATRGmiFHtvm4DMbShAEQRA+oFUL24qKCiQkJDiMC2MVFRWaxy5YsACxsbH2ny5duogbBWEbEgJwnFzYKluGkLAlCJ+xe/duzJkzB0uWLPH3VIggpbTIgl8WbURpkYWErQKf2VCCIAiiVWCx8IX/LBZ/z4SnVQtbwHnFU2fbZs2aherqavvPoUOHAACHDwOnyk8JJ+DfSWctXUjYEoRPaGxsxB133IG5c+di2rRp+Pjjj/09JSLI2D72BaQMTMOFD41E8sB07Hz+c/Ud26iwBXxjQwPpJoggCILwjPx8ID0dGDmS/52f7+8ZtXJhm5iYqLqifOLECQBQXYkWCA8PR0xMjOwHABae9zbaHdrD79TQAKSlAatXa09C6cElCMIrLFy4ED///DPmz5+P7t274+6777Z/twnCFaVFFmR8+CgMTd3HjbDhvA2vijtIiwIGcY5tc/CFDe3TJ7BuggiCIAj3sViAKVNE82izAbm5/l+0bNXCtl+/fti5c6fDuDDWt29ft8+5GPdCtkbNGPDww9oHkMeWILzOrl27MG/ePNx8882YNWsWVq9ejcrKStx7773+nhoRJBwtLIbS32iUtmsLCxMft1GPrS9sKOPXEQLmJoggCIJwn+JixzVfqxXYu9c/8xFo1cL2hhtuwJ9//ilrSdDY2Ih3330XgwYNQidJ/1m9qP7DnK3mk7AlCK9itVoxceJEmEwm5De5fAYMGICXXnoJK1euxCeffOLnGRLBQMdMs8OYVXqFDw+XbGibwtYXNlRKINwEEQRBEO5jNgMGhSgyGoEePfwzH4GgELZffPEFPvzwQ6xduxYA8Mcff+DDDz/Ehx9+iNOnTwMAcnJyEBISggMHDtiPu+uuu9CnTx+MHTsWK1euxIYNG3DLLbdgz549eO655zyaC1MbVL6zUkjYEoRXMRqNKCoqwr59++zhjQBwzz33gDGG6667zo+zI4KF1AyT7LkVBvx12SRxQCpsgzwUOZBsqJRAuAkiCIIg3MdkAvLyxDJDRiOwdCk/7k9CXO/if+6++26Zsf3ggw/wwQcfAAD279+Prl27wmq1wmq1gjFReoaHh+Obb77Bo48+invvvRenT5/GBRdcgC+++ALDhg3zaC4H0QX9cEgcMBiAf/8bmDZN/QAStgRBEAFPxfsb0LvhCPBDHj/QikKRA8mGGgz8OkGg3AQRBEEQnpGTA2Rl8ZE3PXoExvWcY1IrRmhSU1OD2NhYVHTphoRD+2GNbA9jwVvA4MFAUhIQEaF+YKdOfBlIok1x9uxZ7N+/H926dUOE1meDCAjovWrDSKv6/vYb8MsvQHY2/7xHDzFO9v33gVtuASDagurqalnEAOEc4f/2xx/VOHYsJmBuggiCIIiWw9c2NCg8toFEyMkqAIAxNQUYO5YfdOaVbYbH1mLhk7PNZroBIAiC8CkNDfLrdSsKRQ4kOncGevdumdciG0oQBNG2CIoc24Ciupr/HRcnjvmgj20g9oYiCH9w7NgxcBwHjuOwfv16p/vec8894DgOQ4YMAQWjEE5Rfj4aG+Uhx60oFLktQjaUIAii7UEeW3cRVu6lwpbj+B+1G2kPhK1Wb6isLFp1JtoeKSkp6N69O/7++29s27YNWVlZqvv9+uuveOONN2AwGPDaa6+B45TNXAhCQn29/Hljo/x6TcLWN7z4IpCaClRWAmVlQHIyPy48jo93vi0xERgyxKkxJBtKEATRNiFh6ylSYQsAISF8KJsSD4Sts95QZJSJtsjQoUPtwlaLe++9F1arFVOmTMGAAQNacHZEUHLqlPy5s1BkErbeY9685p+D44Bly/jKJSqQDSUIgmibUCiypyiFrVY4sgfCNlB7QxFBisUCbNzI/w5ShgwZAgCawvbdd99FYWEh4uPj8eyzz7bk1IhgRSlsnYUiU45tYMEY74LVuKaRDSUIgmibkLD1FB8K20DtDUUEIa0k0Wzo0KEAgIqKCuwVKtU2UVtbi0cffRQAMG/ePHTo0KHF50cEIeSxDW4EF6wKZEMJgiDaJhSK7CE1JznIilRrCVubjf9RLh+7IBB7QxE+4OKLgaNHfXNuq1V+bpsNmDQJePJJ5wXPmkPHjsCPP3r9tH369LGXh9+2bRt6SFwvc+fORWlpKfr374+pU6d6/bWJVoqax5ZybIMHFy5YsqEEQRBtDxK2HhKd9xIK63ojc0VTjk+Ik39lY6P8JkknJhMZ41bP0aMt3+fYV0LahxgMBgwaNAhfffUVtm7dittvvx0A8Oeff+LVV18FALz22msw+kqwE60PNY8thSIHBxynywVLNpQgCKJtQcLWQzgAgwtyUTo9C6kZJtctfzwQtkQboGNH351b6bGVvqYvPbY+YujQofjqq69kebb33nsvGhoacNttt+Gyyy7z2WsTrRDy2PqFp/E0ziAVcahECsoxcWYS4mMBlJcDSUliVWThOZq2ffcd8Msv/PMNG/j0CoIgCIKQQMK2GYTAimOb9uoTtgShhg/CdmXk5/NFVqxWMdFMo5JooCMUkPr1119RV1eHdevWYcOGDYiKisLzzz/v59kRQcfJk/LnyhxbErY+YTEeAiSJPBddBQwfruPAKVNEYUt59ARBEIQKJGybQSOMSBnalONDwpYIRFpRotkll1wCo9GI+vp6bNq0CQ899BAA4Mknn0Tnzp39PDsi6HBVFZmKR/kctyoVh4aKj9Va6xEEQRAtisXCt1czmwPn9pKqInuIFQZsyV7Ke2sB1zm2BOEvTCbeJRIoVx0PiYqKQr9+/QAAOTk5OHDgAMxmMx544AE/z4wIRva+8bXs+V9LN2p7bCnH1msIdRTdrlQstbFkUwmCIPxKoDbdII+tm1Te/zQOxfZFwrWDkZkhscjksSUInzN06FDs2LEDJSUlAIDFixcjjPLXCTcpLbKg+7ZVsrFzNr+Nk+l3IUoYoFBkn7BrF3DsmAcBJOSxJQiCCAgsFj47RFjztdn4rLesLP/7UMhj6ybxcx9CnzljRU+tAAlbgvA5Qp4tAIwZMwZXX321H2dDBCtHC4thAJONGWHDGcsJcYBCkX1C584eBpCQx5YgCCIgKC52DGRy0lq8RSFh6y1I2BKEz4mMjAQAhIeH4+WXX/bzbIhgpWOmGTZwsjEbOLRLjhIHpMKWQpH9D3lsCYIgAgKzWUwrEXCrZoIPIWHrLUjYEoRPsVqtmDNnDgDgkUcewTnnnOPfCRFBS2qGCYf7XCkbK7n4ZrRPjBAHKBQ5sCCPLUEQREBgMgF5eaL0cbtmgg8hYestnBSPOvD0chxbV9SCkyGI1serr76K3377DV27dsWsWbP8PR0iyOkywix73v3GC+UCloRtQGCxABs3AtWnyWNLEAQRKOTkACUl/PW5pCRwOkmSsPUWTjy26e+/gOQxA7H7/LH4ZdFGlBZZWnBiBBH8rFq1CjNnzgTHccjLy0O7du38PSUi2Kmrkz9vbJR7AinH1u+8+KJYdfPZF0Rhe/wYeWwJgiD8TSA23SBh6y2chSID4AD0+u1DXPjQSCQPTEfhhACpi00QAcpnn32Grl27IjY2FrfddhsaGhrw5JNPYtSoUf6eGhFElBZZ1BcU1YStlseWcmxbnBdeAB55RPzXNzAxKure3IaAaS1BEATRmhGiZixB4pMjYestXAhbAPZSJUbYMLgglzy3BOGETZs24cCBA2hsbMSFF16I5cuX41//+pe/p0UEEYUT8pE8MF19QVEpbBsatPvYkse2RbFYgJkz5WMNED22BtaI3NzgudEiCIIIRgK1V60zSNh6Cyc5tqq7w4pjmwKgLjZBBCjz588HYwynTp3Czz//jJxASeAggoLSIguGFEyBEbzLz2FBkUKRA5biYoDJuzGhEaKNDUVDwLSWIAiCaI1o9aoN9AVFErbeQofHVkojjEgZGgB1sQmCIFohRwuL7aJWQLagqOaxpVDkgECtlYTUYxuCxoBpLUEQBNEaCeRetc4gYestVIStVePfa4UBW7KXIjUjgLKtCYIgWhEdM81QOP3kC4rksQ1YlK0kDAbgwotFj2041xAwrSUIgiBaI4Hcq9YZJGy9hYqwPf7JJpQPvd5h/MS7XyBzBYVVEgRB+IrUDBNOxYvKhwHyBUXKsQ1opK0kDhwA7nlA9Ng+O6chYFpLEARBtEYCuVetM0jYegsVYZtykQlJVw1wGE/qGd8SMyIIgmjTRPXpan/ccG4f+YIiVUUOeIRWEgCwa4/osY2LonY/BEEQviZQe9U6g4Stt1ArHmUwoPjzYsfxNWt8Px+CIIi2TnS0/WGYrV6+zZXHlkKRAwKhKudT/xI9tmho8N+ECIIg2hCB2KvWGSRsvYWKx/bob8dwzpa3HcbZ888HflkxgiCIYCcqSnxcWyvfdvas/Lkyx5ZCkf2OtCqntCpydQV5bAmCIAhHSNh6CxVhW150QPUfzNlsgV9WjCAIItiRilOlsFV4bCt/+Rv1Bw6JAydOiI9J2PoFaVVOaVXkyjLy2BIEQQQKFgsfrhwIPjsStt5CRdh2uOQcWME5jDPOEPhlxQivwJTNGImAg96jVoxUvJ46hcqZ84HVq3nrqxC28bu3IuzAfnHg8svFx5Rj6xekVTmlHtuEGPLYEgRBtBTOhKuQLjJyJP87P7/l5yeFhK23UMmxTR2Yhs3ZyxzELXf31OAJVic8wtB0N2YlT0/AI7xHBmVdeyL4UYrX558Axo0D0tKAmhrnx0oXPOh77BekVTmlHtuYSPLYEgRBtATOhKs0XQTgf+fm+tdzS3dy3kLFYwujEZkrclC2/SBKr7xTHL/sspabF+EXQkNDERoaipMnT/p7KoQLamtr7e8X0bo4e+iY+gbGgDNn9J+IhK3fEKpyvvyqZPG4kTy2BEEQvsaVcJWmiwhYrf7NtiRh6y3UhG2TByg1w4TUfwwUx1UqOh5bV4TiaYtwbF2Rr2ZItCAcxyE6OhrV1dU4484NNNGinDlzBjU1NYiOjgbHOaYNEMENO1runRNRKLJfMZmAiwY5r4ocSDleBEEQrQFXwlWaLiJgNPo321KlRw3hERoeWzvSIib18rYT+wbeiu5F7yMFAFsC/DUkGz03rfDJNImWo0OHDjhz5gwOHjyImJgYREdHw2g0koDyM4wxWK1W1NbWoqamBuHh4ejQoYO/p0V4wLF1Raj5vBAx12QiZXSGw3ZjVITnJ+c4MRyZPLb+J0TbY5ufL3oVDAY+fDkY+i0SBEH4E4uFF69ms3qGpCBcpeJWKlyFdJHcXN5MGo3A0qX+zbYkYestnHhsAQDSMEeJsD22rgjdi963Z+FyAMybC3Bs3XTVGzUieDAajejSpQuOHz+O2tpaVFVV+XtKhITQ0FDExcWhQ4cOMKp9f4mA5q+hE2DeXOB0QTAskjdxDFAp4+fIyZuzEXX5JUBiIm/RL7yQ30DC1v+EqntstULlsrKolAVBEIQWehYE9QjXnBz+ert3Ly94/X3dDQphe/LkSTz55JNYvXo1Tpw4gV69euGxxx7Drbfe6vLYjRs3Yv78+fj1119x+vRpdO/eHZMmTcL06dO9ezOrUjxKj8e25vNCpCgO4wDUfrmJhG0rwGg0IiUlBcnJyWhoaICNQhoDAoPBgNDQUPKeBynH1hXBvLnA9YJgU/Eo1j4aB6+dgvTVL/HjF10E/Pyzw3mjJt4CXHMN/6SiQtwQ5MI2KGyoKzQ8ts5C5fx9g0UQBOF3ioqAtWuBiAggPh6orETNvjLsfTMZjwBIRhnKbMn4aVI8bvqrEnF1ZUByMn9sWRlykpNx00NAzd4yRPdIRnx9PDC/EigT9zOVlcGUnAzs5s8v3WZ/3PTaOHRIfZ5eIiiE7Y033oiioiIsXLgQPXv2xMqVKzF+/HjYbDbcdtttmsdt2LABWVlZuOyyy7Bs2TK0b98en376KWbMmIF9+/Zh8eLF3pukK4+tVNhKVptjrskEWyL3JjAA0VcN9d7cCL/DcRzCpJ8BgiA8RveC4NmzAABDdHukr3wO+GARH15crpF7m5QkPpZe04N8QSoobKgrNDy2rkLlCIIg2iwTJgAFBQ7DMQAWqO3/vPpp4pp+ggIW4Hz22WcMAFu5cqVsfNSoUaxTp06ssbFR89jbb7+dhYeHs5MnT8rGr7zyShYTE+PWPKqrqxkAVl1drb7DjBmM8bdM/I/BIN/+v/+J2+bPl206FZMiO3bPkGy35kYQBNGWOLp2O7NJr7cAswHs6Nrt8h2Tk/ntXbvyzxMT5ddp5c/+/eKx1dXi+KhRkmEXtiDACBob6or9+8X3Y9w42ablyxkzGvlNRiP/nCAIok2zfbtze+enn2ref+czGxrwVZE//vhjREVFYezYsbLxiRMn4siRI9i2bZvmsaGhoQgLC0NkZKRsPC4uDhERzSgqoobSY6t87qR4VLt+8qXlnoVvenNmBEEQrYqU0RloDBWv4QxA8ZBsx/SNJo8thOu9EBqlhZbHNohDkYPGhrpCw2MLiC2BNm7kf1PhKIIg2jyFhf6egV8IeGG7a9cu9O7dGyGKHNb+/fvbt2sxdepU1NfX47777sORI0dQVVWFd955Bx9//DEeffRR705UmWPrTNgqWxUon+/bh8r5S7D/zqep/Q9BEIQKoSFiAoe1Q7J6JXmlsJUKVxUKp78nPmklochBY0Nd4aQqMsDn0w4fLubVUvsfgiDaNJmZ/p6BXwj4HNuKigp0797dYTwhIcG+XYtBgwbh22+/xdixY/H6668D4Iv5LFiwAA899JDT162rq0NdU+ERAKipqXE+UaWQVTZ20qiKDMBB2LKePREPIB4Ae2des9r/lBZZcLSwGB0zzUjNoEoaBEEEF6otfRoaAEl/6BCOOR7ImHitDQ/nf5865fS1BhfkonR6Fn+tbCUe26Cxoa5w4rFV4s32P67aYRAEQQQkGRlAQgJw4oS/Z9KiBLywBeC0cqmzbT/99BNuuOEGDBo0CEuXLkX79u3x7bff4sknn8TZs2fx1FNPaR67YMECzJ07V/8kmxGKrDTSnOKxp+1/CifkY0jBFKTCBisMKMzOQ+YKitEiCCI42DvoNpyzfZVjS5/qavmOgmdWikRUISKCVyg//eT09UJgxbFNe3lhK12cDGJhCwSJDXWFC4+tgDfb/1B/XIIggpnjUenocOIEGsDhKTyL0bfH49I+lXwBRSGCSXgsVC1W2yZ5XIl4PPd4JZJQjjLw25KbHlchHo9OqsQ50U7Ob7EA//mPz/7mgBe2iYmJqivKJ5pWIIRVZzWmT5+OlJQUfPzxx/a2BCNGjIDBYMCcOXNw++23q65kA8CsWbPw4IMP2p/X1NSgS5cu2hP1orBV4kn7n9IiC4YUTIERvHU3wib3RhAEQQQwx9YV4Zztq9Rb+vRWXPfVhK10LCKCd7u5oBFGpAxtqnnQSoRt0NhQV+j02Hqr/Q/1xyUIIpixWIATBxvRAUA9IvEcZuHF9/g6BM25hu3YCDynsc1oBJ6aDcDZ+WtqfCpsAz7Htl+/fti9ezcaFSu0O3fuBAD07dtX89gdO3ZgwIABDr32MjIyYLPZsHv3bs1jw8PDERMTI/txijLHVhmK7CzHVil0FXjS/udoYbFd1Nqn2OSNIAiCCHRqPi+E0pcoLPKhqkq+oaHBUXwqha3Z7PT1GmHEluyl4sIfx4nX8SDOsQ0aG+oKnR5bof2PFE/a/zgTyARBEIFOcTEQAv5aaQV/DffGNUztGgvwY0uX+n/hL+CF7Q033ICTJ0/io48+ko0XFBSgU6dOGDRokOaxnTp1wo8//gir4oZny5YtAACTN//7Sg9tQ4O8aoUbObZSNKt9uqBjphk2xW2hzBtBEAQRwMRckwll5qx9kU8ZigzIQ4+VzyMieGu7fLnDYTYAGzMeRvn2EsdUDcF6B7HHNmhsKFwUfJIKWyc202TiQ4YFk2w0enaz5S2BTBAE4Q/MZsAI/trd2BSg641rmNo19uGHgQMHAiRVwydNhLzMqFGjWHx8PMvLy2Pffvstmzx5MgPA3n33Xfs+d911FzMajaykpMQ+9uqrrzIA7Oqrr2b/+9//2FdffcVmzpzJQkJC2BVXXOHWHFz14Nt30U2O/Zo4Tmyo9/ff4vitt8oPTknR7PfUkNTRrXlK2Z05WXauH7KpuR9BEMHDmfYJsj619h7fa9Y4Xi8rKmTHli9ZLW676SZxw6FDjC1ZwqonPcD+fGAJO7L9kPYEwsP5488/3z4UbH1sGQsOG7p8Od/+XWgDr9qLVmhWO2CAy9c7dIixjRv5355C/XEJgghmqpO6MwawY0hy+xp26BBj336rfQ319BrraxsaFMK2traW3Xfffaxjx44sLCyM9e/fn61atUq2T3Z2NgPA9u/fLxv/6KOP2KWXXso6dOjA2rdvz/r06cPmzZvn0HDeFc7eiCPbDzGrVjNio5F/1y0W9ZssxhhLSNAUtiwpya15ynj3Xfm5CIIggol+/ezXL2tkO35s+3bGxoxxvFYePmw/bM8l/2Q2yTYb4JkqadeOP0e/fvahYBS2gW5DDx0SRa3SdMqIiOA39u/v1ms3B28IZIIgCL+QlsYYwM4mdHS4hjkTrroWGj3E1zaUY4yp9EkglNTU1CA2NhbV1dUOuUK/LNqICx8aqX3wxo3AeecBKSn88zFjgE8/FbfHxAC1terHtm8PnDzp2aTffRf45z/F5/RWEwQRoKi2JjvvPEDI4wwJAW6/HSgoUD/Bvn1ARQWOzXsDyWvfdMjPZQYDuAMH3IpJtbWPguH0KTQmdUTI3KeBykrUHDqE2DfeULUFhDbObOjGjcBIFRO6cSPfm9ZO+/bA6dNAx47A0/z7gbIyIDmZ3y48Fqpvam0DgMREYMgQ/yeEEQRBeAHV1mQmE3D4MP/70CH7vs4qvhcVAYMGySWD0ehZ0Sm1OTmzBd4g4KsiBwMdM82wgoPRISMMYkC7p1WRT5/mP11OWjJo4g8ha7EAmzejcm8FDp9NROKYIVSFmSAIp2i2JpNeGxsbtUUtgLO3TkB4USFSNLZzNptbpXELJ+Tj0tN839uQ8qPAtGl6/xzCTYR8VmmxJodcsPx83h4CwFEvvR8cByxbFiCJYXKofy5BEHrRFKpCoT1JHSBnFd/Xr+e3KeWDJ5Xl/dUuLeCLRwUDqRkmbM5eBqvSRyAtEeasKrIzYcuYY1EUvbS0sM3PB9LSgHHjEP/ENPSdNw4pA9NQOCG/ZedBEETQoNmarMjitPqtkvAixyrKUpjBoLtqBj+nyU7PR3gPlwWfLBZg8mTvvzBj/B2darUq/5GfD6Sn817s9HT+OUEQhBpaQtVigWhDJcX3tCq+b9kiP48Ud4tOOZ2TjyFh6yUyV+SgbPtB/D57NSrnLwFWr5aXCNPy2NpsrituCqvU7tKSwla48VC8pgFMvEklCIJQ4LQ1mRvC1qmoBQcuL0/3cjM/J0rdaElycvhQt40b+d+ylf3iYt/ZswDr4ePPG0KCIIIPp63JBH0hEbZaFd8ZUxe1nrTx8We7NApF9iKpGSakZoxV3yhtByQVts68tQKnTwMJCe5PqCWFrZMbD+EmlUKSCYJQIrQmM0iEpL012XP6ha0aDMChu+cj7fF/umWVnaaXED7DZNJ4m8xmPmzYFzYtwHr4OLshpJBkgiCUOE3lUAlFFiJkcnP5a4sQITNkiON5DAZg61Ygw72Oo/rSS3wEeWxbCo4TvbaeCFsJpUUW/LJoo2svaEsKW+HGQwXqn0sQhBapGSbsHXKnbGxL9lJ+IUzr+titGypnzsexYRoLiU3UtYtH2n9mua0INNNLCP9gMvG5sJ7UmnAC4zxwRfgY6p9LEIQ7OE3laPLY1rMQWY9wtQgZtfPk5bkval3OyceQx7YlCQkB6utxxnIcVUUW5zduUiTCtvDOPAx5527HIitqqMUU+AqTCXj0UeC55+RTAIct2UuRSd5agiA06HlXJrBZLAxlv6ZphSJffDHiF84Cnn8e+P4DzfNGdIz3eE6ZK3JQOj0LJz7bgk7hFXwx3cpK/s7gP//x+LyEh+TkAFlZqFi3BeV7KpCSDMSjEigvB5KSAAA1f5ejnCUh4Zx4h23C48rFbyH+WDEAoCf7E4/BjEAqHaXlTQkg7U0QRIDRdHnE3r38Ipj9etFkQ3fuDsHIkfIiTmoRMprn8eacfAwJ25YiPx/s9GlwACKPWxA+MA2F2cuQ+fwY18c2CdvSIguGvjPVHrJnL7IyPUs9zFePaPYm11zjIGzLP/oBmTde2rLzIAiiVWBraFQNKzoZEosoAIiIcH4CaW0DD1BNL6mpIWHrJ/LXmzBl+lh5lc1ZTdvygSlPQnWbgMUC/P7498gCL2zLkGyvBhpIwtFfN4QEQQQvakKVNTaCA2AF7zqVVkDWuq5opoR4aU6+hkKRWwKLBWyyvMKmUFTp6PYDro8/fRqwWFD38uuyPDRAUmRFjZYWtioe4pR+Ws03CIIgnMMa1D22J2xx/ANXwjY83LsTIvyGs6JKegsuFRcD9Qi1Pw9DfaDVjrJjMvE9fEnUEgThETYbuKaUxEaJHzNQr3negjy2LUFxsf3DJSUEVlS//i46ujr+k0+AUaPQVWWT0/xVZb9cX6NW3dkfvXQJgmgVGKzqi3OxXWL5Bz722BKBg7MWFR066Cu49OOPQHeIn4kw1FP+KkEQrRPJPbngsQVaf84+eWxbArMZTKPoxblfvur6+H//W3WYAfi/axdqVxsOAI9ti+b5EgTRerDZwGlcP2LTSNi2NdSKKgHArbcCP/3kuuCSxQI89hhQLxG2oWjAwoXkFSUIohUiqVFhbfJjtoWcfRK2LYHJBG7ZMriSeNLtTEc1Tg5A3BUXa+/Q0sKWPLYEQXgLZ/294+L43yRs2wxCUSWlgLXZeMG6cKHzCpyCx7dBEYp8sRMTShAEEbRIbOglmSHqPcKbsFggq5oczFAockuRkwNDdDQwbpzmLnWXXo6/L89Fx45AYn0pMGMGAN4zqyZzrTA4b6NDHluCIIIVZ9cvYdt33zk/BwnbVkVODqBmRq1WviVFSYm84JLFwgtas1n0+NbbxM9EpKG+VYfkEQTRhpF2FTAYNf1M+flijQJp1eRghYRtSzJkCBjHqebbAkDkOSb0mcNX4PxjxDSc1zSu5bv9c+Q09BHCkC0WVKzdjPI9FUg6NxGJY4YEhrAljy1BEK5QS9XQavUDAJMmARUVYC+/4jy2hYpHtTqGDOFvvqTmRgg7llbgVLtZy8sD6ieHQajBOPfJBplXVyqEW3OoHkEQbQCJx/ab70MweqSjcNUqvBdoleLdgUKRWxIhJFmryXxCAgC+rU+v75ao7iKViX0mDOQfLF8O1qULEqeNQ6/F05A4bRxYWhqfeNSSqIUOkseWIAhPcCZsGQMeewwcXCyckce21SGEJDsLO3Z2s3bHRDEU+fprxAKL+flAejowciT/Oz+/Jf4agiAIHyGxoQ1NfkxlxXitonzBXDWZhG1Lk5MDw8GDOHPJMMdtobzBPVpYrPnGyCRxdXVTK6EpDl4LjjGwDRu8MGE3oFBkgiC8hTNhCwA2m+taBCRsWyU5OXzYsVbOmLObtegEyWeiqXOA3nZBBEEQQYOseJRYFVkqXNWK8gV71WQStv7AZELkwPMdx5uEbcdMM6w6ikehqopvJaThtdAKefYZVDyKIAhv4SqVwmgE98Lz2hEwAAnbVoyzPq9Ob9bCHIVta/RaEATRxpHck0v72EqFq54ImGCDhK2/iIlxHGsStqkZJmzOXqYubq+6SnxcVcW3EtJ4Ca0WQz6DPLYEQXiC2nVCstrssNVg4K3vww/DcPAgKpasxp4HlqBiyWr5fiRs2yROb9akn4mmxZPW6LUgCKKNI7WhHH8xVBOuriJggg0qHuUvnAhbAMhckYPS6Vk48dkWdD67F3ERdcC11/LtLb78EgBw4pufUTcOSL3tNmDlStmpGMeBu+QSvnt9S0EeW4IgPEEt7FgydvaqG7B/0Hh0Cq9AfI9EYPBg0TKbTEicOhaJws53S85BxaPaLDk5fE6ttEoyAJmd/e3HeiT0FYVwbi5vxlqD14IgiDaOxIb+48YQbLxHcS2UIC28F+yQsPUXLoQtwHtuUzPGyvd54QX7w4QdG2EbmIZ9GbfgHMWpuPXrgbfekgtbxtSrj3oL8tgSBOEJaotiEqPcLiXGXjHeLchj26ZRvVmTfCb+9VQ9Pp4tVglVFcIEQRDBiMSuto8JwfDh/ptKS0LC1l/oELYOWCxgM2fKApQNYOhWtNpx3/Bwe/6QHasVCPHhW07tfgiC8AQ1j600x9bT6xYJW0JB1ekwxDU9DkO9Q3sLErQEQbQKpHbVaNTer5VBObb+whNhW1ysWhDKoJZlW1XlWHzFVZXR5kLtfgiC8AQXHlsStoS3OHZCtLOh4G0kFYoiCKLVIbWrvnRqBRgkbP2FmrB1dRNmNqsWhLKpFZnyh7Aljy1BEJ7gIsfW5aKfFiRsCQVJJvEzEQY+qokKRREE0erwxuJwEELC1l+oCdvaWufHmEzgli2TCVkG4ND5ox33VRO2rtpnNBfy2BIE4Qm+8thS8ahWj8XCV/PU23M2IUUubKlQFEEQrRIKRSZalC++cBhiDz0M5Oc7Py4nB4bP1tmfnr7pTqSP7u+4XzM9tqVFFux6ejXfPkPvHQN5bAmC8ARf5di2oVXqtkh+PpCeDowcyf92ZT4ByLz/D0xv8Fl7C3cFN0EQhFehUGSixbBYwB5/3GGYAwObkuvaEkqWltsnRqjeFJ7885DHwrZwQj5SBqah77xxSJw2DiwtTd8dA1VFJgjCE1x5bD0NRSZaLRYLMGWKaGKEIlAuhaQkPL1HWr2Dp9YbgtQjwU0QBOFNKBSZaDE0ikABAGfTUcVC+gFtaFAVrO1W5aN2z2H5oA5hW1pkwZCCybKCVBzTKbipjy1BEJ7gKse2DRllQh/FxY7rprqKQEnzrhWdA7whSD0W3ARBEN6EQpGJFkOjCBQAMIOOKhbSm7zGRtWbQgMYoioOyAd1CNujhcUwqlRZ1iW4yWNLEIQnqC2KeSMUmWi1mM2AQXEHo6sIlNT7LxG23hKkHgtugiAIb0KhyESLIRSBUohbxhnA5emoYiE1zBrCFoBjrWQdxaM6ZpphVamyrEtwk8eWIAhP8JXHlq4/rRaTCcjLEx0RuotAST22EpvoLUHqseAmCILwJm3UY9t2JHygkZMDQ1YWKtZtwfG/KtChZyISRw/WV5pRRygywFdMlklUHR7b1AwTfst6CP3Xvyg5D6dPcJPHliAIT6AcW8IDcnKArCxefPboobOysUYosiBIpSbLE0EqCO7cXP5jTVWXCYLwC200naft/KWBiMmExKljkejucTo8tgxAXVQiIk5WyPfVQf8HRwESYcvNf1Zf2UiqikwQhCf4yGNbfaASsR5OiQgOTCY3RaOGsPWmIPVIcBMEQXiTZoQiWyx8FIvZHHzXLwpFDkZ0eGwbzL0R0V7xQdbb7kdRUAOxOm8NqY8tQRDuYLGgYslqVGzZIxv+ZdFGVP55VBzwUNhGvzIPhROoJC0hQbowrEjPyckBSkr4qshCGyBPqySbTMDw4cF3U0gQRHChvEYJzyuOeRaKHOxV3UnYBiM6ikeF1VaCHTsmG/v0I9c5tgAcha2aYFWDPLYEQeglPx+sSxoSp41D4o9fyTZd+NBIxM6+XxzQKWxLi+TqwwCGwQW5DuNEG8ZJVWRALkiD/QaPIIjWjfIaNWGC+Pzeae57bFtDVXcStsGInlDko0cdSkAVLDii78PpqbAljy1BEHqwWMAmTwanUoFdQNpyTG+O7dHCYoexEFhxbBOVpCWacCFsBVrDDR5BEK0XtWtUQYH43MDcT+dpDVXdSdgGIzpCkdWaCZnYAX0fTvLYEgThS5z08lZFp1Hmq7rLzVojjEgZSiVpiSY02v0oaQ03eARBtF7UrlFSQuB+KHJrqOpOxaOCEWce2/btgVOnVA8r5zrq+3Aqjb1erytVRSYIQg9ms2PVdmfoFLapGSYUZudhcEEuQmBFI4zYkr0UmRmU6Eg0IfXY7tkDzJ8PlJUByclAfDxQWQmUleGC8GQ8BiAJZShDMqoQjwRU4qJ3yoDNyfzxZWXAuecCY8ZQMi1BEC2KWiV3KUa4H4rcGqq6B4WwPXnyJJ588kmsXr0aJ06cQK9evfDYY4/h1ltv1XX8J598gkWLFuGXX36B1WpF165dMWPGDEyZMsXHM/cRBgPAcbw3VOmxdSJs75wRp+/D6c1QZPLYEgShxGQCd/vtwH//q7mLTPi6UTwqc0UOSqdn4dimvUgZ2oNELciGyli9Wnz822/8jwrxABaobXhTZWz6dGDZMn3dAwiCILyAmgi94w7gnXd4sRvGNcKe0eNG8ahgr+oeFKHIN954IwoKCjB79mx88cUXyMjIwPjx47Fy5UqXxy5cuBA33ngj+vbti9WrV+PTTz/FtGnTUO8kBCkoEG70GhvlgrJ9e81DBnY5qrlNhjdDkcljSxCEGuef73RzMSThJW72sU3NMOGC+4cjlUQtALKhdiwW4IEHvH9exvhkN0rAJQiiBVFWcs/MFLcZ4X6OrUAwV3UPeI/t559/jq+//horV67E+PHjAQAjRozAgQMH8Mgjj2DcuHEwaqxE/PTTT3jiiSewYMECPProo/bxyy+/vEXm7lNCQ0VvrdRj266d5iHVv1uQoOfc5LElCMJLlBZZULF2M1JTgcQxQ0RLqRFZItAOZ8Qnbai5vLchGyqhuNh3Nslm410cwXgnSBBEwOKqp6zQy1tZTMrAPO9jG8wEvMf2448/RlRUFMaOHSsbnzhxIo4cOYJt27ZpHvvvf/8b4eHhuPfee309zZZH+JCqhSJrEGdO0nduyrElCMILFE7IR8rALug7bxwSp40DS0sTe6a4ELZJKBeftCGj7G3Ihkowm/k0Hl9gMARXhRWCIAIed1qOKYtJeVI8qjUQ8MJ2165d6N27N0IUNzb9+/e3b9fihx9+QO/evfHRRx/h3HPPhdFohMlkwmOPPeYyjKqurg41NTWyn4BCCM1zw2Mbtulb4OmngaIi5+d202MrNIOuraaqyARB8JQWWTCkYLLMyHCMgU1p6pniQtiGQ3IdqqryyRzbAmRDJZhMfC6sL8RtXp7H3lrBhlIkM0EQAu62HFNWNPakeFRrIOD/0oqKCnTv3t1hPCEhwb5di8OHD6O8vBz33Xcf5s2bh/POOw/ffPMNFi5ciEOHDuG/TgqXLFiwAHPnzm3+H+ArtDy2ToRt+3WrgXUA5s0DsrOBFSvUd3RD2Obni1+8V2DFDOUO5LEliDbJ0cJipKr0qeVsTT1TXAhbKeyOf4I7e5aK83gA2VAFQmWULVuAigq+CnJ5OZCUJFZFbnpeVQ38+nU5Pv85CVWIRzwqcdsV5eg/Mon//D77LH/O4cM9/mxKbajBwOtj+pgTBOGs5ZhWSLK0mJTUY/v1xhCMutHHEw4QAl7YAgDnZHXV2TabzYba2lqsWrXKXv1xxIgROHXqFF555RXMnTsXPTRCh2bNmoUHH3zQ/rympgZdunTx8C/wAdLiUYKwNRqB8HB9xxcU8JUcMzIct+kUtsrVJA4UikwQBE/HTDNscAwLYgYjuB493BK2HHhPL5eVRTmMHkA2VIHJBChCs9U4aQFGvgCZZXtxI1DyFmBKOC0KWw89wFoeGfqYEwSh1s7HVU/ZnBygf39g0CAghInC9rX/GNF7Ztu4rgS8sE1MTFRdUT5x4gQAcdVZ69ijR48iKytLNn711VfjlVdewc8//6xplMPDwxGuVyT6AyEUWeqxDQnRL2wBYNMmfcJWQ5wqV5NkYQ8CFIpMEG2S1AwT9g66DT22iZV3GThweU1N8dwQtoDE09sWLLMXIRvqOU49JpmSv+3sWe+fnz7mBNGmMZmAdxda8MnMzYhjFUhAJcYPL4PpbXnPbSRL+monJ4PbF49HWSWuwWf2c0XbKtvMdSXghW2/fv2watUqNDY2ynKEdu7cCQDo27ev5rH9+/fH0aOOLW5Yk9gyGAI+xVgbNY+tirCV9YJUMnSo+rhOj61yNclAHluCICT0uL4fIKlNxL2xRIyzdFPY2j29hFuQDfUcpx4To1HsTuChsPXEI0MQRBshPx/jZ07GeKmD6JumHydc3PQj5R3ciaof64DhrT/PIeCt0g033ICTJ0/io48+ko0XFBSgU6dOGDRokOaxN910EwDgiy++kI1//vnnMBgMyFDzVgYLasWjQkKAsDDZbjVJ3WFVk7bZ2ereWkC3sBXi+YViayEceWwJgpBw8qT8eUyM9jYnME7i6SXcgmyo5yhtnNEILJV+DCMi+N8eCluX5ycIom1isQCTJ3vtHtoAhoTHnFSeakUEvMf26quvxqhRo3D33XejpqYGPXr0wKpVq/Dll1/i3Xfftfffy8nJQUFBAfbt24f09HQAfDuDpUuXYtq0aTh+/DjOO+88bNiwAa+//jqmTZtm3y8oUSsepeKxje3fDaULvseJz7bgvLm38BK3Vy/twlGAW8WjhDoce/cCGUttwHuKHchjSxBtF6V4lRa6cyfH9v33deVEEo6QDW0eUhvXo4dCdEZEALW1Hgtbl+cnCKJt4oue220kzyHghS0ArFmzBk888QSefvppnDhxAr169ZIVswAAq9UKq9VqD5ECgNDQUHz99dd4/PHHMX/+fJw4cQLdunXDwoULZUUtghItj60yp6ldO6RmmJCaMRZYGA7U1Tl4dR1ws4+t0Bwab1O7H4IgJHhB2DKjEdzgwV6cVNuDbGjzsNs4Jc302Lo8P0EQbROh57Y376HbSJ5DUAjbqKgoLF68GIsXL9bcZ8WKFVih4oVMSEjAG2+8gTfeeMOHM/QDUo9tQ4M4phS27duLj8PCeGEr7K9FXZ38uYs+tk73I48tQbRdlMJWeu1xImyF2gA2gxEGis1sNmRDfYSXhC1BEIQMkwlYuBCYOdM75zMY2kyeQ1AIW0IFabNlwcOqkmMr62srraTchMXCRzyYzZLPuxuhyDLURCx5bAmi7aLmsbVYULF2M+KrqjSLPNR16Iza/7yLpMEUm0kEME3C1nr6LEot9FElCMKL3HijKGwzMoAbbrD32K5EPCr2VSKZK0dM9yR+H8m2E39XIglN23r0AAYPbjMXKBK2wYogUgFxtVgjFNnhmCbhqtkY3lNhSx5bgiCkKIVtYSHY9OlIdHFYRFwkIsYO99WsCMIrlNdGIAkAV3cW6WkMecs4e9FvgiCIZiGNcOrTB5g1C4CTe/cm4pt+2ioBXxWZ0EDqsT1zRhxzJmwFb25Dg2ZjeIsFbufYOt2PPLYE0XZRCFv23nva7cekSBfuCCIAsViA3SW8x9YABiNrEG0oQRBEc5HeizfZRKf37gQAErbBi/TGz0m7H1mOrSQU2VljeK+GIpPHliDaLgphq0vUAiRsiYCnuBg4iwj78wicFW0oQRBEc5F6bJvu7Z3euxMAKBQ5eAlReevcCEV22hjem6HI5LEliFZDaRGfH5uaCiSOGeI6Z0fpsYVOcat2fSOIAMJsBn5RCNvTxpi2UHSUIAgPUa1ro4VU2Dbdvzu9dycAkMc2ePFE2EpCkZ02hiePLUEQCv7vn28gZWAX9J03DonTxoGlpfHJPk6wVdfInnMq1y3VpS/y2BIBjskE9LlYFLbtDWfbStFRgiA8ID8fSE8HRo7kf7swnzJhW3uWt4lO790JACRsgxe1Gz8VYVt5VNKGQFEVOScHKCkBNm7kf9uTzz3NsSWPLUG0SkqLLBjy7t0yg8ExBjZFO7mnMHs5uJO18kFJH9vSK+9E9QOzwSUlORxbd5YWxAj/YrHwttFZ7lr33qKw3bLxLBWOIghCFU9yY7/4RLwXf+2NULsQ1rx3h77rVmvHbWF77NgxcBwHjuOwfv16p/vec8894DgOQ4YMkTV9J7yAlsf2hx9kQ7HzHkbhhKZvgyBsGxvtgtNkAoYPV6z2kMeWIAgJRwuLVY0FZ1NP7iktsmDI27lOw45TH/knYhfNAWJjHbaF/VokXrcIooXR7VmJEIVtxzjqZUsQhDru5sZaLMC/XxY9tnUIkwlhtXt3tz3CrRS3hW1KSgq6d+8OANi2bZvmfr/++iveeOMNGAwGvPbaa+A43WVDCD2oeWytVrDXX5cNGcAwuCAXpUUWeWEpaey+EmWLDupjSxBtmo6ZZqgtUTGDenLP0cJiGFWPkNB0PWowRjhs4gDxukUQLYhbnhWJsLW33ZOcp617TgiC4BFyY6U4y40tLgaMTLxPb0CophC2WIDVq4HJk6laMuBhKPLQoUMBOBe29957L6xWKyZNmoQBAwZ4NjtCGzWPbV2dqockBFYc27RXLoa1hO0ddwBVVbKhQyXUx5Yg2jKpGSaUnjdKNsY4DlyeenJPx0wzrK7MSygfWlW954jqZvt1iyBaELc8KxrCljwnBEFIcTc31mwGwjm5sFUTwsK1Ztw4Rz9SW62W7JGwHTJkCABtYfvuu++isLAQ8fHxePbZZz2fHaGNmrCNiQFT8Yw3woiUoT3kwlYZbgwARUVg//2vw/ChnSf0rfqQx5YgWi2dh5tlz7kNG6CVVJiaYcLOax5zer5jlWFYOqkIiTihut1+3SKIFsQtz4qKsKU+kwRBqOEsN1aJyQRMmyTep1u5UAchrLzWKGmr1ZI96qkgeGwrKiqwd+9e9JD852pra/Hoo48CAObNm4cOHTp4YZqEA2qhyFFR4JYtg23yZBiaBKUVBmzJXorMDJPrUOTCQlWPbwJOYO9eHVXXyGNLEMGPhW/pU1rKt/RJzWj64isXw+LjnZ7mgnszgc+1tx8oDcNQfK16zbGBE69bBNGCCJ6V3FzepDn1rEiF7TvvAJ9/jrraZDxiA5JRhjIkowrxiLNWwjajDBiQzO9bVgYkJ/PfocpK8blyW2IiMERHWy2CIAIKrbY+JpP+r/OISxuAZfzjp+aFIV4hhNWiSwTacrVkj4Rtnz59EBsbi+rqamzbtk0mbOfOnYvS0lL0798fU6dO9dpECQVaxaNycmDIykLFui04ehRIuHaweHPoJBT52LoiNH65A51VXqoW0bJVH81eluSxJYjgJj8ftkmTkQiGRAC2eRwKs5chc0WOo7A966JYTmWl081pPcKwCZkOvW0ZgIq3PkXmhNEe/AEE0XxycoCsLD6Mr0cPJzeHv/4qPn73XQDAOQAWqu27punHXTgOWLbMuXuHIIiAIT9f9KQaDPxCmUdfX8l9enyyozNLq6ftqlXA4MFtU9QCHoYiGwwGDBo0CACwdetW+/iff/6JV199FQDw2muvwSgEkxPeR6vdDwCYTEicOhZ95owVvS3KYyQ3qX8NnYDkMQPR+et3VF/K1DPK/gUpnJCPlIFp6r0sqSoyQQQvFgvY5MkwSDrLyorPKYVtXZ3z87kQth27hCJ3eQbeRrb9FRkALjsbSSRqCT+j2jFAilCxxdcwRrHMBBEkeDUVQeqAUrnn18rbHTu27YpaoBl9bNUKSN17771oaGjAbbfdhssuu6z5syO0UfPYquXNSlEJRT62rgjmzQXO23Ik8yHGpUUWDCmQ3/jKellSH1uCCE4sFlS/mAdO5ftqL+LkrrBVFKFzICwMOTnA5YdW4Ocl21E1+2Vw27cDK1a4NXWC8JRmVS4uLvb6fDRpq1VgCCKIENa63Gnr4xSpzZXev0twJ2+3reBRKDIgFpD69ddfUVdXh3Xr1mHDhg2IiorC888/77UJEuoc+Hwn0pWDa9fy3lOtT7ZKKHLN54VIcfViTd/So4XFSIXjja+9lyV5bAki+GgKP45V+W4DkiJO33jXYysYapMJME3NAJChc8IE0XyaHS5oNvNhwi2xeNtWq8AQRJAgvZ4o8fjr68JjK+BO3m5bwGOP7SWXXAKj0Yj6+nps2rQJDz30EADgySefROfOapmahLcoLbKgy2+fqW+cMkV7+VklFDnm6ks1bmclNHlitXpZ2gCUl5wkjy1BBBsWC9ikSbIoDClCEafUDJPXQ5G1VqAJwtd4JVzQZAKWLVPtROBVOK7tVoEhiCDAWXXiZhVx0ilsCTkee2yjoqLQr18/7NixAzk5OThw4ADMZjMeeOABb86PUIH3nGpgs0GzhLFKKHLKZeeqn8dg4EUpY7xgtViQun8zquLSEVd1QL4rgA4Tx+Bs+wREKM9DHluCCFyKi52mIVS88wUy78jin7gSthYLHzWyZw+QnIy6zT8i3Nlrk6Em/ISzXrVu3YDm5IDLysI3z2zBhqV70QHlOI4k3HADMLBrOZCUJFY+Lueff/8D8NOX5TiGJFQjHrGoRDLKUY4k3Cgc9913wC+/8K+xYQPfEJcgiIBEqzrxyy8DN9/s+ZpU9fF6xApPyF7qxmNhC/B5tjt27EBJSQkAYPHixQijVXif0zHTDCsA1dJcBoN2zINaVeSjR+1Dtd36ovGW2xA/oAdfUq17d36/sjIgLQ1gDHEac+IAhJ9S6UdJHluCCFzMZoeqxFKSzokRnzgTtvn5wKRJss1ORS1AHlvCb2hVE/UoXNBkwuVvjMW5T7quopyfD0z5io9yUotifvFTPk/OVDtZFLZJSR5MiiCIlkLretIcUZufD5S+1IAnm55/8U0Yrr622VNtE3gcigyIebYAMGbMGFx99dXNnhDhmtQMEzZnL3cMC+Y4PlFI65ukVhX52DH7UPRNVyF+4SyxpJrQpf7gQV0CVfXmmDy2BBG4mEzgLrlEe/uZM+JjpYdWeG6xOIhaXagVwCOIFkCrmmhzon1dVVFWhiuqmVR7kRlpRwm1FB+CIAIGb19PhGtFCMRQ5BcXh1JhdJ00684iMjISABAeHo6XX37ZKxMi9JG5Igel07NQs2odUmv/QsyAnsDo0c6/SSqhyFKPLVIUZaTcbNek6vkhYUsQ/sXC950u31OBjuGViKsrA849Fxgzhr9edO0KSNq2yZAKWy2PrSfVYcPC+IU4gvATunvVegmtcEUpdq8xCVuCCCgsFv47bDarXyu8eT0RrhWhEmF71hbqfqpEG8VjYWu1WjFnzhwAwCOPPIJzzjnHW3MidJKaYUJqxlT9B6iEIldv+1OM4VeGBroQtlIhywDUR8Yi/Ey1YicKRSYIv5GfDzZpMhLBkKjcNm0asHy5vECFkrNnxcdawtZsdn9elC9EBADeqCbq6oZXQC1cUQiKstkUXh4StgQRMOitoO6t6sTCtSLMJtpcmyGUCqPrxONQ5FdffRW//fYbunbtilmzZnlzToSvUIQiF96Zh9hFs+1DbMb9/DdYwImwZQD2D7gZ9V35BQ0OQHiHGMcdyWNLEP6hqAhs0iRwzuqeT5kC1NRob9fjsTWZ+Jx8JzjMgPJriVZAfj6Qns7XdkpPl5tPJWrhinl5wIEDKj0opba3sdFX0ycIwgVFRcDkyc2soO4mwrUijBMXnR99Moy8tTrxyGO7atUqzJw5ExzHIS8vD+3atfP2vAhfILmZrNx9FEPfmSbbzIGBTckFl5Ulz7GVcOqqG1CW0h/tbr4W3UdnAOPGASX7+I1Hjji+JnlsCaLlyc9vErUusNmA6mrt7XqELQB07Cg+njQJ6N4dlYhHWTnQoWciEu+7Xe4ZJmFLBDlaLYME86mGVriiw/7ksSUIvyN4apW3sR5VUHeTnBzg1NcNwPv88xtuoSgnvegWtp999hmmT5+OyspK1DSt8D/11FMYNWqUzyZHeBmJx7b6dwviVXbhbJJvrIrHtv0dN6Hb7beLA6mSxkNqBpg8tgTRsjT1ptWVwWowOBeZeoVtba34+KWXgJgYxAPiNeahCSRsiVaFpy2D1MIVHcKZpYXVSNgSRIvjqjdtS4QFtw+jPraeoDsUedOmTThw4AAaGxtx4YUXYvny5fjXv/7ly7kR3kbyxYjtnuBYVRkAM0i+sWqhyIob0v2FLuIxyGNLEC2Li960MqSxkWroFbbScOaoKMfzKCsgk5EmghwhD06KJze8quHM5LElCL+iVezNYGh+BXXdSG0u2Uzd6Ba28+fPB2MMp06dws8//4wctcxpIrCRiNL4LtGo6tRXtplxBnB5km+s2g1vuNidsrTIgvSf1zh/TfLYEkTL0tSbVgkDUHaVJNpizBg+3slJ8ajqMh3FowDRYxsVpZrC4GCUyWNLBDneaPGhFc5cc4qELUH4E7WFK4OBbyCgR/5YLHzufLNycSnKySOa1ceWCDIUVZETknjjaeMMqHj9PXAHD8i/sS6E7dHCYhicFaYByGNLEC2NyQQuM1M2xAAUD8lG8lsvioNCux0nwvaNRWfEgjh6hG10tPqJlB5bMtJEKyAnhy/65FD8SSda4cwV1SRsCcKfaBV7y8hwfaw7ReWc0kChyJ5AwrYtIf1irFsH659/AgBsKR2ROG2c41KzmudFckPaMdMMq6uPEHlsCaLlkfSkPnjT/Shbux09N60AmnqPAxBb+TgRthE4w1eAPGB1vMEmYUu0cYTcWE/7VmqFMyd0IGFLEP7Gk4UrrSgMjzy3JGw9goRtW+KHH8THX34JY9ONqfHoERROUFlScuGxTc0w4bdrXbR6Io8tQbQ8VVX2h2lv/Qspo5uWmaXCVsifdSJsI3EGVivw95/1jhsFYcuYKGxjVFp+AY5GmYw0EeR4wyujFc4cm0DCliACAZMJGD5c/8KVs6JybiONkqLFYN2QsG0rWCzAkiWqmzgAQwqmoLRIsaTkQtgCwIUv3O64jxTy2BJEyyMIW4NBXswpNFQMQdYpbI1G4JwuToTt6dPi95w8tkQbwJteGVWvEBWPIoigxFtF5QCQx9ZDSNi2FYqLnW42woZjmxRLSjqqIqN9e+evSx5bgmh5BGEbFycKWYB/LHhtdYQiR+Isli4FOic5EbbSVj8kbIk2gFe9MlDxCpGwJYigxBtF5eyQsPUI3X1siSDHbOZvajWEphUGpAxVLCmp5dgqPLaqrT2kkMeWIFoeqbBVEhnJe1l1eGyvvfwMInMAHHYUtvX7ShC2ZIl80UyrdRBVRSZaEYJXRmrevNrbkoQtQfgPiwXYvBmoqAAqK4GyMiA5GYiPlz8HVLflJCfjpoeAmr1liO6RjPj6eGC+eFxVtWRbVyfnFEJAOA44fLiFegwFPyRs2womE7BsGTB5soO4tYHD5uw8ZGYovjQ6QpHJY0sQAQZjzoVtRAT/W08oMmvaR1kRGUDYwf3AtGnywY8/5pMNlVU2qI8t0YoQvDK5ubzubJZXRg0StgThH/LzVe+T3SWu6cfdbaowBqSl8ffw1GrVJUERinzy5Encf//96NSpEyIiInDBBRfgvffec/s8Tz75JDiOQ9++fV3v3BrJyQEOHgRWrwbmz0fNpAew54ElOLb9IDJXqHxZ9AjbsDDHm1Yp5LEliJbl9GmgsZF/rOWxBXSFIp/+429ULFnNXzf0MmWKY7Kh8hohzI9oEciGep/mtvpxCglbgmh5LBaviFqfwBjYlFxsXm1pXm/cNkBQeGxvvPFGFBUVYeHChejZsydWrlyJ8ePHw2az4bbbbtN1jh07duDFF19EiqQNRpvEZALGjgUAxDT9aKInx5bjeK9tdbX6OQLxAkEQrRlJReQztjBEKre74bFtd7QE7aaNAwMHTnMvBTYbn2wocV+d3l2CdpJd2Lp14NQ8u4RPIBvqG0wm73lphdZBZjNgki4EkbAliJahuDig71k5mxWPj9uLQoMJeXlkPrUIeI/t559/jq+//hr/+c9/kJubixEjRmDZsmUYNWoUHnnkEVh1XPQbGxsxceJE5ObmolevXi0w61aCnhxbAKc4eTiy7LJAHluCaFF+mib2HQn/br1jKy/BY3vmDG/EnQhbAQ5uGHuDQZZseGxdESJPlivOBzA1zy7hdciGBj7K1kGFmyWLyhTdQBAtg1CLJkBphBF70aN5vXHbAAEvbD/++GNERUVhbJOXUWDixIk4cuQItm3b5vIcCxcuxIkTJ/Dss8/6apqtEx2hyBYLUF4l3092WQjg1S+CaG2UFllwwadz7c8NYBhckCtv5SXtZVtfr0vYSnH6jeY4PvlQ4saq+bxQ1dvLCZ5dwqeQDQ1s1FoHvfU2hSITRItjMqFyzmJ/z0IVKwzIxVIcBm9bm1OFvbUT8KHIu3btQu/evRGiyNHq37+/ffuQIUM0j//jjz/wzDPPYM2aNYhyVcGXkKMUthznMFZcDPSAE8NLHluCaDGOFhYjFfLvXAisOLZpL1KF4nBCKDLA5+O6eePMAbACOHz3fKT1b6roWF4O9OwJjB7tEJsZc00m2BI4iFtmMIDzWhlZQguyoYGNWuugBkbCliD8we/9x+NS3AcA+A198F/cjmSU4/pJSThngMTeJSXxBwiP48VtlWFJeO45IAnlKEMSqhCPOFQiuek5AKSgHDffnSS3oWrnBFCBRFw4bTAOMdG2erUKeysj4IVtRUUFunfv7jCekJBg366FzWbDXXfdhRtvvBHXXHONW69bV1eHOqFPI4Camhq3jm8VKIVteLhDmIbZDJQjCV1wRP0c5LEliBajY6YZNnAwSPyqjTDKW3lJPbbSHrQSGByFqBQjgBM9ByNt6nCXc0oZnYG/hmTDvLnAfk4GDpzCs0v4BrKhgY1a6yDGGcXQCBK2BNFidE8TQ///Rg88j1kwGoFxswHoNFfx4L/XQtV05fdb4KJbgLThrs+XCGB2qA+rsLcyAj4UGQA4JzHvzrYtWrQIxcXFeOWVV9x+zQULFiA2Ntb+06VLF7fPEfQoc2xV8mtNJsDUVV5QinJsCcI/pGaYUDLgJvtzKwzYkr1U9NYCcmGrITa4MWNQOX+JZtixat9rJ/TctAJla7djf/ZsnJi/BNyhg1T5ogUhGxq4CK2DhHVkoxG4azJ5bAnCH3RKFoVtI0I8FpHSqulbtzreTrvrcfVpFfZWRsAL28TERNUV5RMnTgAQV52VHDx4EE8//TRmz56NsLAwVFVVoaqqCo2NjbDZbKiqqsIZoSqoCrNmzUJ1dbX959ChQ975g4IJpcdWWRG5iSTuuP3xGdM54D74QNxIHluCaFG6Xy5656qWvOfYyksaiqzhsUVcHOJnTQW3fLnDJqHvdaqy77ULUkZnoNuKOUiYNZWWmlsQsqGBT04OsGULsGgR/3vkKBK2BOEXJDUnLhsR0iwRaTIBw4cDGRmOi1eeiGXhfGQ+nRPwocj9+vXDqlWr0NjYKMsR2rlzJwBo9tP7+++/cebMGcyYMQMzZsxw2B4fH48ZM2ZorkSHh4cjXMVD2aZQC0VWofHQEfsHKdzyN4pW/oUMYSN5bAmiZZGImMShKhVsdYQi27/rOTlAVhawbh1qfvoLpdE9ETN+NDLdFLWE/yAbGvjk54sFpAwGYP1UI64QNpKwJYiWQ1KFPLlzqO7wY1cIpnTvXt5TS+LUdwS8sL3hhhuwbNkyfPTRRxg3bpx9vKCgAJ06dcKgQYNUj7vggguwceNGh/H7778f1dXVeOutt2CiT5ZzdAjb0iILUhvFPCoDGC76+ClxB8FjW1QErF2LyroIVBwHkqLPIvb2MfxSFkEQ3uO4GEGBDh0ct0s8tmcWLnbscwvw1ZIFTCZg6lTXfa+JgIRsaGCjVhX5329oC1tZv1v69xOEd5G21wpxLZGk30fA+XfTm32vCW0CXtheffXVGDVqFO6++27U1NSgR48eWLVqFb788ku8++67MDaJr5ycHBQUFGDfvn1IT09HXFwchg8f7nC+uLg4NDY2qm4jFCiTAlRCkfkqrHKM0qqsNhuQnQ28/TYAPqk+vmkTWzwPXHY2sGKFt2ZMEIQ07DQx0XH7nj32h5EbP1c9BXv7bXCXXUaJPK0AsqGBjWpVZJt6KLLSs5uXR19RgvAqbghb6fdRKFXAGH03/U3A59gCwJo1a/DPf/4TTz/9NK666ips27YNq1atwu23327fx2q1wmq1glFOp/fQ4bHtmGmGVfExaoTkuOPH7aJWCQeAFRTw3lyCILxCg6UUAGCLbOe4GGWxAJ+ri1kpHAA2hTrAtxbIhgYuQlVkGQZHYavm2c2lryhBeBdJju3Js9rCVvl9ZEwMUKTvpn8JCmEbFRWFxYsXo7S0FHV1dfj1119x6623yvZZsWIFGGPo2rWr03N999132LVrlw9n24rQIWxTM0zYnJ1nF7ONMOLnm+aLO5SVOX0JDgA2bWrmRAmCAIDCCfkIKdkHAODOnEbhhHz5DsXFus/F2agDfGuBbGjgolYV+Z4ZjsJWzbNrpa8oQXiVTz4SPbZvvRuK/Hz1/dS+j1Lou+k/gkLYEn5CKWwlPQmlZK7IQfn2Eux4eSPKt5dg4MvjxY1qoZASGAAMHdq8eRIEgdIiC4YUTLH3iuUADC7IRWmRZNlYSATSATNQB3iCaC4WC9+iw5n3RtnK4+oxEk9Rk7BV8+y62zKEIAhtLBbghQWisG1AiKbnVTXSQgJ9N/0HCVtCk/KiEtlztmMHMGGC6r6pGSZccP9wvgWI9NseGysmHyhgAJ9jSwWkCKLZHC0slue3AwiBFcc2SZaNTSZApYUPIO8/zTgDuDzqAE8QzSE/H0hPB0aO5H9reX8ARSsPo6PHVs2z60nLEIIg1CkuBgxM3sdWy/Oq/D4aDOKtLn03/QsJW0KV0iILOpTIc19158RKheyJE2LiQffuqJw5H2dj+UqtXGQkFY4iCC+hle+eMlSxbJyTAxw6BCxZIhs+NW4ifp+9GhVLVoM7eIAqXxBEM2hWTqyKsAUcPbv0FSUI72E2A+GcmGPbiBCnnlfp9/HAAeDgQfpuBgIkbAlVjhYWQ83PqisnVuqxPXpUfHzppYhfOAsR6Z28MEOCIKSkZpiw/dZF9uc2cNiSvZSPolDS1MJHSpQpAX3mjEXi1LG01EwQzaRZObFSYSut0gqFZ5cgCK9hMgEPzRC/b1Yu1KXnVfp9pO9mYBDw7X4I/8B7fwBFli0fPuwqJ1bqsZUK2+Rk/rdQQl1SfY4gCBc09YJGRASqqoGavWWIGnAuEu4cY7ekgxfdArx3PwCgbngWMle4sWxM1XAJwmsIOXhScas7707DY0sQhHfQ6gd91RWNwCv84/seDEEseV6DDvLYEqrw1Y6XyzL2dOfESj221dXiY6H1SGgo/7uxkW6mCUIP2dnAwIHAvHnAE08g7vknkLZmMRKemAbWJU1M3pMsFkUmx7g+r7TS+cmTXp40QbRdmpUTKxG2hw9aqW0IQXgRp7nvkgiJ2ETy/QUj9K4RmmSuyEHp9CzUrFqHjjiK2PHX6iv0pFEsCgsWAN27y5teW62qTbAtFuDgZgvMKEbSEH5JrbTIgoq1m5GaCiSOGdJy8R4W/nXL91Qg6dzEln1tgigq0uwFDQAcGNiUKeCysoD6enGDsoetGtHRYrVzErYE4VVycoCsLD78uEcPN8yGRNiu+9SKaet4kexO3p6aR0rLS9US+PO1CUJAK/c9K6vpcymNJFS5NyUCH3rXCKekZpiQmjHV9Y4SSn8pRaraBsb4K4hUHDc2Olw88vOB3ZNewgt4GBwAG2fA3sH/RI/NbyO1qXYrm8aBW77M9xn6+fmwTZqMRDAIjYvYdA7cshZ4bYIAgMJCl7twNht/9yyE+wP6hG1UFHD8OADgzKFyRHo6R4IgVBFy79zhaLkRHZseG2F1vPl2QX6+ePNuMPCiGHAcaykTpjYfMp+EP3CW+24yQZ7TLkQXuoAWbQILCkUmvE75tv3aG61WuVdJkWdrsQBzJ1vsohYADMwG8+YCGCQNSXgvld4Skx5isYBNnix7XQDgWAu8NkEIZGa63IUZDLxLyE2P7ckqcf+Iwq9ROMFJPxKCIFqEAxbRY2sEn2Ort/CUlkdq8mQPKzQ3k2ZVhyYIL+OyH7RU2Orw2LrT0otoGUjYEl4naYiT6hhGIxAjyf1ruogITew3bwbOYY4VmVUrNNv0lpj0kOJicBo5wD5/baJNUlpkwS+LNqK0SHLXl5GhHd6Pptz3vDx+qdgNYVtaZEH7qiP25xyAwQW58tcmCKLFSe/uKGxdFZ6S2lA1j5TSlOmu0NxMmlUdmiDcRPgeaC2cuMx9d0PY0qJNYELClvA6qRdrxGIYDPwVJDpaHGtokK143XorsBdmh0PV5CUz6C0x6SFms+rrtshrE22OLeNfRcrANFz40EgkD0wXvafSu9JOnYD581F9133247hx48S4PjeErVpLrxBYcWwT3XEShD/p2FkubF0VnlLaUOU6mNGoPtYSJsylh4wgvIRe76nTftBu5NjSok1gQsKW8D4KK3Ym41Jg9Wq+g3VOjixv4cjBRtmKF2PAYU5uvRlnQPGQbPkYAC5Pb4lJDzGZwF1/vcMw4wy+f22iTVFaZMEl782wh70bYRO9p0JxJwA491xg1izEzpwujkkFrBvClm/pJf+uNsKIlKF0x0kQfkVyQz1qhNXx5luC0mskrIEpPVLLlnlYobmZNKs6NEHoxF3vqWbPWTdybGnRJjAhYUt4H8XScOSQAcDYseIVRGK0S4obHFa8lCFT3KuL0fP/3pKPjRjRMtUn+vSRPbWFhYM7eIAqXxBexan39MwZcTCyqbyTdCVZaojdELZ8S688NDZ1q26EEVuylyI1g+44CcKvSKoiJydanYpANa8RY8CqVXKPlFMvlY/x52sTbQOveU/dCEWmRZvAhKoiE95HuYSlvMGWrIJ169Ko2sQe0p70ycnyiw3QcmXYpaICgCHESFctwut0zHQMv7d7T9WErXQlWRo6JRW2Oio6Ci29jm3ai5ShPZBJopYg/I9E2MJq1d4PotdIaUMHD3Y0VZ5UaPYW/nxtovWj9T1w23vqZvEoj1t6ET6DPLaE91Em8yiFreRikdqhQXXFS0Z9vfyGHXAUur5CIWwdlgQJwgsovaQy76mPPLbS177g/uHkqSWIQMENYUteI4Lw4vfAgz62mmHNhF8gjy3hfZQe2/Bw+XPFTbnqitckcZcTR+uRoGgLpGwT5DNI2BJ+oHx7ieg9dcdjK32sU9gSBBFguCFsAW2vEfXXJNoSXvGeetDHlggsSNgS3seVx1blptxZmNJTj9ZhiLEet0sHW0rYnj0rf07ClmgBZN5TH3tsCYIIMNwUtoCjDc3PF4vpGAy8N4tyW4nWTrND3t0MRSYCDwpFJryPqxxbrZvyJpRV7EJZHWY9rBCyFIpMtGakN7PSz2BEBP9bT44tCVuCCE6kwtYDW0f9NQnCQ0jYBj0kbAnvo/TYKkORtW7Kmyj+S14WOQz1MNoUObYUiky0ZqSfb/LYEkTbwgOPrRTqr0kQHkLCNuihd43wPm4Uj1JbjTan1cmeh6MOEYYGQGqopTf+Fguwdi1qftyDciQj7uIeSBwzBDCZUFpkQcXazUhNhX3MLZTCFuB7KSj/RoJoDsq70IYG0TsrDYd3pyoyCVuCCE6aKWw9rRCrlpNLebpEm0JqTynHNighYUt4Hw9ybKWYEk7LnkdydXh2dj0wWzIoCOL8fGASX2kqpukHbwJsOofiwXeix+a3kQreA8ymc+CWLXMv0UhN2Nps8huPNk5pkQVHC4vRMdNMlXU9Rfk9kC74qHlsDQb+e8YYeWwJorXRTGErVIjNzeUP11MhVi0nF6A83ZaAFg8CCPLYBj30rhG+x02PLU6dkj29d0odokcrhG1DA28NJk2CGhxjMG8uAKcYY1NywWVl6bceJGydUjghH0MLJiMVDFYYUJidh8wVdOfjFAsfRVC+pwIdwysRF34WuOIK+T6uQpEBfoGovp48tgTR2mimsAXcqxCrlpM7ZYr4WPidm8ufk8SX96AiX57hs8UAErZBD71rhO9xM8dWKWyjw+sd92to4K9qTlALFuZsTYlGzRW2BEqLLBhSMAWGJo+4ETYMLshF6fQs8txqkZ8PNmkSEgEkSsfnzZPvp0fYhoTwQlbLY0thVAQRnHCcGJHhobAF9FeIVcvJVTNzVjfNJ+EcrSJftHjgHJ8uBpCwDXqoeBThe9z12J6WhyKjrk5+wy4cZzY7fVmmNmbQkWgkhYStJkcLi2GE/H8RAiuObaIKJapYLGCTJ6suuDig12Or3Jc8tgTROhDsZDOErV6EnFwpBoPjmJ48XUI/VOTLfXxe8VtqT0nYBiUkbAnf406ObVMhKBl1deoeW5MJuOoq1Zdk4FDZqY98jOPA5blINFJCwlaTjplm2BQyrRFGpAylOx9ViovBMbXlFhX0emwBNFafxP47n8aJ+UuAEyfE7W4KW4sF2LiRWoIQREAghCN7KGzd+T4LObnCSxqN/HPlmKs8XcI91BYUaPHAOb5YDJB9V6TOFjejnsiGBgYkbAnfowxF1vLY5ucDaWnAnDmy3Y99v9vRYyvc+PfqZR86e/7F9sfcIw8jYaw8b5H76Sf341VI2GqSmmHCX5feJRvbkr2UwpC1MJtVowhUccNjazx6GN3emYeEJ6aBLV8ubndD2ObnA+npwMiR/O/8fN2HEgThC5ohbD35PufkACUl/I15SQn/XG2M8B5qCwq0eOCcqCjvLgYovyt7//QsFJlsaOBAwpbwPXo8thYLMHkyn1OkIGn/Npz4vVQ+KAjiOrE1UMStN4nbIyIcvbwdO7o3b5tNdn7ZOAEA6DV1hOw5FY7SJn+9CSVI17Vv8eJ1qJo5H7j/fuC778QNtbX2h40N/A2vrECa9CQ6ha3PQ7sIgnAfD4Vtc77PJhMwfLhcWKmNEd6DFg/0k58PXHKJYxsr5WKAXs+p2nflp+3uC1uyoYEFCVvC9+jJsS0uVhW1AP8hrd55UD4oiFapJzc6WnysrBYLuC9Ipf1Dm3Oe1oxy6ZRQxWIB5k62oCsOyMa1PLjmvJmIe/4JYPFiYOtWccP119uXgm31KvnpEn58+lNdc6M8L4IIQDwUtvR9Dj5o8cA1SvEI8LcfW7bIFwPc8ZyqfVdCmHjfuOoDfcKWvnOBBWVGE75HT1Vks1msAqmAAYg7J1E+2NjI7yv1qEZFiY+9IWzVwpA9OU9rRtmzmFCluBg4hxU7FI5y+7/HmL1sJhfVHqit1Nz1wv89jdKibJeh4UKel3IVnPK8CMKPCMK2rAyYP198nJwsfxwfD1RW2p9fWA0sQhmOIRlViEccKpGCMpz/RTKwWfs4Z+dEfDyQmAgMGULqi/ALWpW7pU003K0yrWb7QiAuGD/0WCgyx7v+yJMNDSxI2BK+R4/H1mQCXnsNuOceh8OrU3oiPj3G8bxWq7bHVq3gFAlb7xPEwra0yIKjhcXomGn2eV6w2Qzs48xgTC5mGTwQt01LwaHxMUCp9m5G2HBs016Xf5uQ55Wby5+a8rwIIgA4eZL/XVUFPPGE7sPiADygtuH55k8JHAcsW+ZWvKzP+o0Sfqcl31s94tGZ51RtfkrbB8iFbZ0tRFd7K7KhgQXFERK+R29V5Ouusz+s632+/XFctwTH4lHCsVKPrTIUWXmMm4K06L631TeQsBUJUmFbmL0cKQPTcOFDI5E8MB2FE3xb6cFkAmbndZaFHtsMRnCeWD7BmrvI/7HCoLtCNeV5EUQAUVSknQrjT4SIEZ3Jg1RQp/XS0u+tnkJbnlSZFmzf6tX87YxU2DJDiG6vK9nQwIGELeF79FZFrqoSDxlysbifmvcV4Mek4tWLocilRRZc9PFT6htJ2IoEobAtLbJg6NtTYGiSmUbYMLggF6VFvq30kHP7WfsFt773+TAcKHG/oJnBIFpz6QKR0ejQemn7+Ffc8kRTnhdBBAiFhf6egTY6kwepoE7rxV/vrSvx6GmVaZMJGDuWD0YIg3jf+PJrIW7ZQ7KhgQGFIhO+R6/HViJsER/PC+LGRnXvKyBuE/Bi8aijhcVIhcb+JGxFglDY8u+tPJc7BFZdYbvNQpIMFNbdxFs/J5WLT107Fu17moCkJDHHbfBg0WpKF4jat4fhu++Aiy6yDw2eq97jmSCIACcz098z0EZn8qC7YaFE8ODP99ZkAkylRUDeWr77BSDLBc+prMTY7DKUc8lITATidpYB813klDc9zklOxpnOB4HD/FD2VccAdPftH0R4HRK2hO/Rk2ML8Bcdgbg4XtieOuXcY6sVitzMHNuOmWZYYYBRTdySsBUJQmHbMdPskNvaCKPusF2PEXLmAKB9e/63E2HbfuI44KabNLfLFohCQpD/0wWQLmDbzu0Fw7I8iokiiGAjIwPIzgYKCvw9Ezkcpzt5kArqtF78+t5efjnw7bdOd4lp+vEESad4sB49wLmZU074HxK2hO/xxGMbFyceV1ennWMrjHMc0K6duK2ZObapGSbsvOI+9NvwiuNGErYiQdjuJzXDhArT+Ui0/AqAL+C0JXspMn1cQEpWvlGHsLWvRmshWSCyGkIwd8phmbA1MBtYbi44rZKQBEEELitWANOnA599JqbzlJfzERzSx4Inylfbvv4a2LWL3755M99IVAdUUKf14rf3tqjIpaj1JhxjYFPIhgYbQSFsT548iSeffBKrV6/GiRMn0KtXLzz22GO49dZbnR63Zs0afPDBBygqKsLhw4eRkpKCoUOHYs6cOTCbzS00e0ImZAFdObaIi0NjSDhCAFhPVMK4f7/jeRsbRY9tWJg8l9cL7X76TbsMIGHrnCD02AJA4sBzgCZha03uiMwV3luRLS2yoPq/a9Gpdg9iLj4XGDOGN4pSYSvkgyvzz6VERmpvA2Tfq0ZmxDms2GEXjmL/CJANDVoyMvgfD/FK1do77hCFbYcObh2ak8O3Wtm7l/fm0WWo9eDL91bzc+uH3HPORjY02AgKYXvjjTeiqKgICxcuRM+ePbFy5UqMHz8eNpsNt912m+Zxzz33HDp27IgnnngC3bt3x6FDhzB//nxcdNFF2Lp1K/r06dOCf0UbRil+dHhsv9oeh0GWSsQCMJ46CbZ8uWNbFKnHNjxc7v2iPrYtQ5AKW+niSgjn2DvZUwqzl2Ho21OQKgy8Cd7rsmwZ0F2Sq+Nlj60xPAT7ODOsTB4+z4xGcBT71+YhG9r2yM8XC/wYDLyHzaOISq2FaJ2YTKQJWiu+eG+dfm79kHvODGRDg42AF7aff/45vv76a7shBoARI0bgwIEDeOSRRzBu3DgYhRJoCtauXYtkITG8iZEjR6Jr1654+eWXsXz5cp/Pn+A9WLKiPCqGsrTIgpDPt6IpIAobXv0do1Bj301VPklzbMPC5CJBJce2/LdSHPtgN1JTgcQxOhrNk7B1TbD+L6RhvHUNMAKAxYLKt9ei9qc9iO6RjPgBPYAhOj4nTYjVlhUwxltq6fVGj7B15bGVXPdCwkMwe5kJUyfnYQnLRQissBmMMFDsX5uHbGjw4o7HVbovoF611qOISslC9NFDDdhdSj1pCR61z2dzogS0qi3bP7cXX+zV+buCcQZweWRDg42AF7Yff/wxoqKiMHbsWNn4xIkTcdttt2Hbtm0YMmSI6rFKgwwAnTp1gslkwqFDh3wyX8KR5IHpKMzOE8M9pR7bxkYUZi/H0LcnywTBQsxUF7NSpFWRw8P55b2QEM1Kyol3ZNmFM5vOuS4KIBW2RqPYwTtYxZwvCNL/xd59HIQ12FNVDfg1exkufXsK4gHES3fkON7bqsPVwVdb1sBmA6Th9N7w2AqfRwAICWkKDctB0ZYs9MBeJA2m2D+CbGiw4o7HVbnvgw96sWqtZBFwdFYDfmLN9AATrQK1zyfQvCgBl9WWpfdk6em86gWan1MueVyJeJSVAx16JiJx9GCyoUFIwAvbXbt2oXfv3ggJkU+1f//+9u1aRlmNv//+GwcOHMD111/vdL+6ujrUSSru1tTUONmbkFJaZJHd4Nv7hE7P4j23kvfy1OFKDPnY0ctlABwq1zqg9NgKvwVhq/DYSl9DV1EA6UW0fXtA+AwEqZjzCVJxFSRYLMBv287YhW0oGjD07SnqnzXGdLs61Kot2zEY5FW7hRxbbwnbJo+byQSYxpoAkDEmeMiGBh8uPVcu9l20yItVayUL0QbW6HI+ROtH7TM3ZYr4WPjt7mfEZbVlaZ2Kvn2BWbOa9Xeo4bC4TQQdAV/StKKiAgkJCQ7jwlhFRYXuczU2NiInJwdRUVF44IEHnO67YMECxMbG2n+6dOni3sTbMEcLHYvYCH1CAcgMZf32X2CEeo4jB2hsaUKaYysVtoB6jq3y/DYXjeaVwlbAH8LWYkHFktX48/4lqJy/BFi9OjA63QehyC8uBiJx2v48BA3OL4RWF5+TJlIzTDhh6q++MS9PLmKFz1NzikdJ891CAn6NkvATZEODD2eeKyWbNzvua7PxXlshwrxZVWsl9joUok3VeVkMKCwWYOPGwDCdwYza59Nm0/+Z1UKotqz5uVXrLEAQCgJe2AIA56RAjbNtUhhjyMnJQWFhId5++22XRnbWrFmorq62/1DYlX6EHrBSZH1C//c/+3j84T80z8MMRlReMFz7haRVkQWBIPzW6n2rOL+zJezav4+JT6SthFpazOXnw9YlDYnTxqHX4mmIf2IaMG4ckJbGxwP5kyAUtmYz0E4ibENhVetWLOKGqyOxd4rj4B138PFY3m73Q8KW0AnZ0OBC8FxJUbsM5ecDTWnTDvvOmAGUlPBCrqSkGWHD0kJ7EK85ei6LgSQk8/P56NWRI/nf/jadwYza59Ng0PeZdUVOjpPPLQlbQgcBL2wTExNVV5RPnDgBAKor0UoYY5g0aRLeffddrFixAtddd53LY8LDwxETEyP7IfSRmmHC5uw8NPIledAII7ZkL+XDkC0W4KmnXJ/EwCftJ4y+VHsfVx5btd63TTBwTosCbLvlRUQX/Mf+/OQJMaSuRcWcxQI2eTIMar5rIUzWn3cNiv9FaZEFvyzaiNKiALiT0cBkAs7relo2VpV4jvrOHOeeq0MSemlHuDEsLbUPVRxqev3mFI8iYUvogGxo8OHScwXHcFABg0Hc12QChg/nf3ssMiUe2whDg+Z8lASSkNQK7Q4Ewa0kkBYDtFB+Pg0G4LnnXH9m3Tm/8LmVIRG2JxkJW0KdgBe2/fr1w+7du9GoKDO/c+dOAEDfvn2dHi8Y5LfeegvLly/HHXfc4bO5EiKZK3JQvr0EO17eiPLtJWLhqOJiXpBpcCS2Fx9me+AAv1TnbJX/7FnRUgmeWp2hyNzbBZpL2KVFFgz84BHZWPtKiZVpSWFbXAzOyf/L7/Fgihzb5IHpuPChkXzBsAmBuySe1E4ubOMr9gHgQ9/LBv9D3PDgg/LPicUCrF6NyvlL8Of9S1CxRBESfvas44udPQvk54P9+9/i6917O///cSZsnW0DHIpHEYQaZEODE6eeK6iHgwK8gFPu2yyRKbm2vLuiUZcHONCEpDuh3f4kkBYDXJGTAyxYwK/92mzAzJn8uN4oAU8E/OcfiML29RXtA/r/Q/gRFuB8/vnnDAB77733ZONXXXUV69SpE2tsbNQ81mazsZycHMZxHMvLy2vWPKqrqxkAVl1d3azztHkOHWKM4xjj5a3Djw1gR9dut+9rg/a+7I03xMcjRvDH9O7NP4+OZiwqSvvY//1Pc4o/v/St9nEAYz/+2AL/qCYOHWI2J/8vZjTy/1N/8eabmnNrgJEd2e7HuTmhoWNn1Tk3xiUw9vXX4tiTT4oHLV+u+tm1cRy/jTHGzj/f8bxXXaX6HjbAyKqnPqL93rpiwABx30sv9cn/iXAk2GwB2dDWiZYpVZqEQ4cYMxiaYTaeeUY88NNPdR3yrYYJ3bjR7T/TKzT7f9ACBMMcpTRnvsuXi8caDKL5dPV6Y7i19hd7Ev8K6P8PoY2vbUHAe2yvvvpqjBo1CnfffTeWLVuGjRs3YsqUKfjyyy/x/PPP2/vv5eTkICQkBAcOHLAfe9999yE/Px8TJ05Ev379sHXrVvvPL7/84q8/qW1jMvHtUzTyujgAtV9u4p8UF4NzVj5K2j7F3RxbNc9aEx0Hd3MYs0lr3bakx9ZkArdokfo2d8NkfYGT/4WsYFiAwWpPqo7Xh8c49kMG+GXlyZNVow2ECtuwWNRDkU+cUPW6h8CK2sPNqBQr9cBp9CElCLKhrROTCXjoIcdxpSey2d5KaXs+F3UrBPTmCLcUekK7/U2weJUFPJ2vp9784mIgkoke21NoH9D/H8J/BEX82po1a/DEE0/g6aefxokTJ9CrVy+sWrUKt956q30fq9UKq9UKJrmBXLt2LQDgzTffxJtvvik7Z3p6OkpKSlpk/oQCvuEmqv79DmKfe1zWHoUBiL5qKP/EbAbjOO1QXGn7FLUcW2dFUdQESBOpSY0OY+XdBiJl/zb+SUsXTLrpJkCtAun33wOZmS07FyVO/heygmEBhtGqnn/NJcXLKxULedouQujtFbaFz1VUFHCySTwbjaptgBphRJS5k2d/AEA5toRuyIa2TmbM4Fv7OGvr47KFiiuk15ZGR9uohskELFwIPPYY/7qBICSbbjuwdy//tweSqAW88D61MJ7O12WvWievF82dsrfKOIX2Af3/IfxHwHtsASAqKgqLFy9GaWkp6urq8Ouvv8oMMgCsWLECjDF07drVPlZSUgLGmOoPGWQ/YzIhbuEsFA/JtvtkGYDiIdlIGZ1h34dbtgw2LYEq9awpc2wBp0LEmcd2592vO4ylXCFp46Il5ppa8ux6erV3iydpifDkZO+9hqc46WNrLxgWaDAGQ536+x++6xfg88/FAeF/bzY7XSixV9gW9lcUyuGuvVb23AoDtmQvRay5Ge8h5dgSOiEb2jrR44lstrfSA49tfr4oag0GXuTqrcrsy+JJmkWJAoBg8CpLEeYr9czbbMD69c6P89SbbzIBObeKHtvTXFRA/38I/xEUwpZovfTctAJla7dj7/SXUbZ2O3puWiHfIScHhoMHUbFkNfY8sAQnx91l33Rwm1hl1i5onfUFlaIhFkuLLOizYbHD+MlaiZhVE7b5+WBNLXn6zhuHlIFpKJyQjx3rLNhw0xIcnvQ0UFSkb25KtES4ztVzn+LEY2svGBZo7NunuejBAWDPPCMOCB5bkwmYNk31GMYZxArbwucqMlL8TJ49y1vzJv6+ax7Kth/g/z+uCkQ5Q/L+nzmp74aTIIjWhasiU1r76BaQbnps1UJNH3tMn1BVK55UVMR7pT01n8GEnvcykOjfX34LoKdRQ3ME/OB+YgrRy3ntvfL/CYYq1IR70DI/4XdSRmeIXlo1TCYkTh2LRAC4c7M4/NEr4j5qHltnKMSixQIc3GxB5LrVSFXJ6z117CSihCdKMdfUkkeaD2wAw9CCyUABs68esfx54LKzgRUr9M1RY652AlzYBiT5+XyurBM46d8kXQC5+GL1/fcWA92780+E9yo8nO9DW1/Pj0naFHSf8Q+gf5MVb4awPXu0EkKn24hN36JwQn7gLiYQBOEzhNY+evfJzxfFp8HACw1NkaDTY2ux8GGm5eWehZqqCWJlWQNPzGewoee99DsWC759ZjM+WFqBXABxqEQyylCGZMAK2GaUAQOSgfh4oLISKCsTI8zKypCTnIwb/xWPE39XIomVIeZYMjAf4n4ax+HXX+1T6KDobOAJbn0PiKCBhC0RPFgsYO++a89VlPZ2PVVZj/aAR8I2Px/YOjkfb7ApMMKmmg/Zrouk16PSamu05FH2nuUAsIICcNOnAxm8kC8tsqBi7WZ0jqhAPJou5OeeC4wZI1o3rVBkErbu4aQAlBRmMIjiVtoLuapK/QBpSLjwXkVE8D81NQ7CVtZY3kNhW1pkQceTYm9SDsDgglyUTs8KzPBvgiACAq3iPVlZGoJKh7CVCgSO43+kl1lPcy+Vl+qCAkBiPu1/T3ExHxQT8IKwNZCfDzZ5MkYyhpFa+6xp+nFCfNOPx9xxB3DmjIMS1ft5cPt7QAQNFIpMBA9Oerq2+/hd3rrqFQpNAsRiAeZOtthFLeAoagGARceJT5TW12x2VrtZBgcAm/iqz4UT8pEyMA19541D/BPTgCeeABYv5kNe09LEJnZaHlsn+a0tRiDMQS8uCkABAAMH7sUXxQHpooKWsBX2sdnExQbBYws4F7ZOQued9QE+Wljs8DkN5CrUBEEEBnqr2QohmhU1zkORlQJBuMRKQ03Vah8qUcu9VKPJfAIIrr6vrYKmxWHNgp4tiUrcszufh2CrQk3oh4QtETw0VUlWgwN466r3qtQkFouLgXNYsV3UavHD67+JT5RXQ5MJnCK81Qaoil0GAEOHorTIgiEFkx28uuKOjP97LBYKRfYWGgWgGsFhER7A/plLwB06CEycKG7U8timpDjuIxXBSmF7UswN0uuxHVyQq1mErGOmGVbF5TuQq1ATBBEYREWpj0svS1KBMH2Gc4+tlqd11Srg4Yf5bS++6FpoKHMvtUTu0KamCZ62jSGagY7F4RZFokTd/TwEWksqwnuQsCWCB5MJh8aqNO4TsNnA9PZWbBIhZjOwjzO72Bm4BpJKuWpi7tJLZU+rFy5FaUwv2RgD+BzbjAwcLSyG0ZWf12aTt5BRQsLWPYQeyhKsMOBubhlily9Ct4VT+X3U+tgCcmGrFn6sFLaCN1bpsW3XTnzsRNg688CmZpiwOTsPjeDvAhthDNwq1ARBBAzSNTYpwiVKKRDqmXOPrZZA6NqVL/ok6CA9wlNaPOnAAT6nVkqT+QRAHje/4KI7QIsjUaLufh6CrQo1oR8StkRQEfrwDGgGv3KcahixKmfPAhYLwjdvxJQp8k1qclPmWVUTcwqDH58eg0595Bkk3IUX2itfdMw0u/ARg79b6NFD7rGVLquTsNWktMiCXxZtdPR45uTYDXNDl+7YvvoAZh/MkafpSMWmtzy2wl1jZKRoSQHgq680/wZXHtjMFTko316CHS9vRPn2EiocRRCES1x5qpQCoQGuc2wffNBRIJw86ZnwlLbkWbEC2L4dePll/re0cBR53HyLarVglcVhv2EwyJToTz857uLq8xBsVagJfVDxKCKoSM0woTB7OYYWTJKvynAc8NxzYDNn6sv/+PVXsC5pSALDLMX6jpo4toETxa0OYWuvhislMlL2d/w1JBs9NxdozzEvj79oS88TFSWKpEDIbw2EOSjYPvYFXPzhTKSCwQoDCrPzRNFntdpdCKFdOmLwWJXl2ZAQsfN8czy2grBljK/wCMgXJiwW4IUXVP8GBqDwmoUY4cIDm5phIi8tQRC6ETxVubn85VDpqRIEo2DmnAlbZdGohx8GZszgz2WxyM8DeCY8MzLkxaL0/h2E5zitFjxhAjBpEv+4Wzfg0Ud5+1ZeDiQl8ePCY6G6sbe3JSYCgwfb32yLBZg50/HvWLDAvWrhROuAhC0RdGSuyEHp9CzUrFqH1Nq/EDOgJzB6NJ/rmpAANmmSa89tUZF9H1f5tY0wYh3G4Hr8jx/QI2wbGviKfcoxCT2zugNN3Ytq75iK6K4dAKGH6mWXiZZEKWyPHVN/TX8QYB7b0iILMj58VPbeyqoFS98DabVPJWFh/P+9yRtbWmRB3O97EQnwwjc2VtxX8NhK3yehKrJARVMFY6mwdZKvxAGIH6XeXoggCKI55OTw1V/37uWFpvTGXikYmSEEdhMpsTlqRaNefpkXtmrn8YXwdPZ3EJ7hslqwdAG3a1dg6lTd5/VV9Wq1MGRAfUGEaP2QsCWCEt5TpXJBzckBV14OzJrlldcpL/gMeyP7Y8SPbwPP/48f9NRjKwggiwXYvBln1q6H4MONHj8GuPJKUdhKzyc1JBSK7JSjhcVIVYwJuaoOwtZZBe3wcLuw3Xz767hk5T1iP+LGRnDffSfu68pjC4iLHNL3T8hXUhG3VAiKIAhf4sxTlZMD9O8P/N//AVe3CwUEUyu5fjrLaRTO62vhSa1+vI/L91Vp53Tg636xyigDgMLS2zKUY0u0OnZ+W+a1cyWNuxyDx5oQGy/5quj12CqFbUMDf4VPSwPGjUPkj5vtm9i1o/kmfYIYklb4oBxb3XTMdCwEJhOJ0pxZVx5bAI01p2SiFmjqR7x7tzjgKsdWirQkqZCvpCjGYYWBCkERBOE38vOBSy7hc2cn361ePEpvjqs0Z9bbc6RWP97H5fvqprBtierVVAiKkEIeW6JVUVpkwXlfv+LWMbL8WSWCV88gF7bH1hXh9Oq1iO2VioQ7x6h7bJWhyKdPA5Mnq3roODCwKbngYmMc28MoQ5EFAiG/NRDmIEEpBgWRmCmM6w1FbjLYtpNnVC+SMimqx2MrIF2YAESXxpYtqNxbgSN1iUi4drA4X4IgiBZEKUTqmHqOrctQY4sFWLsW2LOHr0kg5E2WlQHJyaiqBmr2liG6RzLiu8q3ARAfxztuq9lXhr1vJmMy4hGHSiTbyrBvUjKq/gLi6nScQ8jTHDKE1I8Cl++rm8JWj2ffG1BYOiFAwpZoVfChqO71WTt068NIf0+liE9oqOhNkwjbivtmI9my0y5u2BPTwF1/vfxYtVDkM2ec9oDjbFZRSNfWihsoFNljql5ficxp48QBvaHITduMBitscAxtYZCIWzc8tmcaDIhUDppMwNixiAdwygL8WQxYLWSYCYJoedypiqwpJvLzxQJDGsQ1/XhCDIAFahued/NEHMdHzVA5XBlORaKbwtZbYcJ6ws6F8eJi+XOibUGhyESromOmGVb9TX8AAOnpGl8D6UVbImwTJaIWaApN/eQT+bH19er9Z530gGMGIxAXxz/xJBTZYkHl/CU4eNP9qJw5H1iyBFi92rcd6/0obDVb+khI7B4rH9Abitz03httVpxIu0C2iQHgBgwQB7Q8tvv2OZw24v++QeEE9Zg5Cq0jCMLfKENRG6EeiizgEGpssbgUtQEDYw5xsaptblopzv5WzRByN4WtN8KE9dpGsqEEQMKWaGWkZpiwOXuZe+K2pkZ9XEPYquHQYkjqcRWw2cSSkQoYZwCXtxRISOAHzpwRw3z1hCK//jpYly6If2Ia0tYsRvzzTwDTpgHjxvE5vb66wreEsLVYeIG+ZAkwfz5w//34+8IbkTIwDRc+NBLJA9M1xaLD4oLE43CqIUz7Bkbw5tbVoUM3URxX3/M4uO3bgTvvFPdVq4pcVwd8+63DaTkAQwqmOIjxlshDIgiCcIVSiNgM4gJg6aEG19ckwV0WLEia67YlYSSU+xg50s1bBIlNPdkQrmsRoDn9YvXaRrKhhAAJW6LVkbkiB2XbD+L32atx8rYprg9QE6GAPFTVhbBlSk+smliur+eXQJs4Peof2PPAElQsWQ3u4AH+ai8VroLX1lUossUCds892lJeZVXaa/g6x1ZSbAvTpgFPPAEsXozuOz6250UbYcOQgkn4fUWR4/GnT8ufSzy2Kz8I1b6BERY16uvFHrTh4Yh97Vm+h4D0s1FfDxQV4VTeO+LY4cOaf5IRNhzbtFc25iwPiSAIoiWRCpEN34ke22/WN9qvl5rePrNjAb+Apikuti0JI4tFXu6DMf55kYoJdUByP5JXEK57EUBPETG1z5Re20g2lBAgYUu0SlIzTOgzZywaurlO5Kj4fqf6Bp0eWwaAu/JK+aCasG1okBmFdlmX4dxFU5E4dax4tVcTtq5CkYuLXfunfXWF96XHVml9nWAE0HviIEfPrZNewvVNuWOqNzCCcGUMOH6cfyyEiQPyz8aiRWADB6L9lx/bh9jbb2vO1QqDQysfvRVGCYIgWgJBiEhTNkLRAJuNvyxrejZNJuDiIOnBzXH2uNi2JIw2b3Y0q4wBgwbp8NxK7mHOoqnIohcWAbS85XptI9lQQoCKRxGtmpq95Yh3sU/CoV/VN+gUttw11wA9ewLr10te2LWwVc1PcSVspdsFYWs2y4sZqeGrK7wvhW1xsS5RK2AAw+CCXPmg0mMrE7ai19WhSqPUI3v0KP87XvJJkm7fudPhf8+B9+IrQ9Rt4LA5O8+h6rHLSpQEQRB+4O9Dofbe4KHgr5+MiZdmQdRkZUmuV9Jr5d13A126iJWJy8uBpCS+KvK+ckSfkyRWRW7aBkB8HO/hNq39tmwBtm7lt3/yCTBmDADqhQqIwV2y91KJ5B6mDuI9THMqHWt5y4V56LGNZEMJARK2RKsm5txUl/toCkK9ocihoY5FNbwhbOfMAfr1Q93ve0TzIS1+JIQBm0zgrroK+PJL9flJVqW9ji+FrdnMz90NcRsCRWi0k1BkabVPhxsY6Xsj/I1aHlsNOMb43OCKCtT89BdKo3siZvxozVY+1K6AIIhAo5tZvE0MgXolfgdRU1XF/+Y44N//VrWfcfC8KrK7yCrqvvqoKGxjYuz7tCVhNGSItml1KVA1hG1zFgFctQTSaxvJhhIACVuilRPfo4PsuZpnU9Pbqbd4VEODo7DVyts9dUr9/AL794uP33sPeO89SPdiTz0tzlX6muedZxe2x4aNRTRXi3bfNQndJUt8187Alzm2JhPw9NPA3Lm6D2mEUS5unYQiW7lQgGncwKi1AtLy2GrADEZwgwcDJhNiwLeocIXJRMaYIIjAoVO6PBTZYJB7bAEVUSMI29hYl/UpfE1+vugNNBiAomsjcZGwUdGSr60II5OJ73Ik9ZIKuBSoEmHbwIVr21A30OMt12sbyYYSlGNLtG4URrUx/RyHLreNBg3vW3OErValZangVQpbi0Xb69oEJ5299DUlgi3luYfQ7ubR4rZ27Zyes1k489h6w5t77bXi42HD+KrIDzwAzJ+PUzfeIXsvbeCwJXup/HgnocjTHgjTrtKosuhwxhrmdLsUe5VrsrAEQQQzIaL/Y9CARhw4wIsiafuWBx5QHCMIW2mUix9QC3H9cJ2kk7hy4RP6ihy1BnJygAMHgIcfFm9vdAlUibB9cl64rkrHrlooeaMlEEEIkLAlWjcKQRp6wxhw27ej+oHZqDPyBi7UptJvFtAfilxfr1/YSvvTKsWRu20SNIQtQkOBSOfG21NKiyz48/4lqL7/ab4S8DGNvxPwjjdXuqKekQHMmgUsWgTMmoX2H70DbtUq++ZT2dOQuUJhXZ2EIscmhmrfwBw86DAU8dUnYnEqFY9tY0oq9k2aL69yTRAEEcxIikclRDXYQ0NLSnhRZLMBL74oKfjDWMAIW7UQ11PMN7ZRL0qR58++uSYT8MILvMDV3YpHImzjO4a7XATQ20KpOS2BCEIKhSITrRu1MnkZGTh7DIh52UWIqy88ts6ErZttEqpPWPH7agvMKEaScCMBOApbpbjzkMIJ+RhaMMleSIQtnof2zg6wWmU3RR7hKidZYlGjE1W2OwlF1gwntljEHCwJ9h6007OQqjKXkAvPxznLZqmfkyAIIhiRXsOl10/wa4zKIlJXXXYGnYX9/Cxs1UJc67kICKE+Jw6fwa8bm3JvW8A7qAyL/uc/gXfeEZ/n5flH0LkVvuvKJktwVRSqWfMgCA3IY0u0bpSCtCmsqubzQtctcpojbLW8lc5CkU0mYPlyp1Nikllvf+kHXDIuDUnjRoK99764U2ioPPzYC6vSpUUWDCmYJLtg6Gox1FykHtuICMft0v9hnYrn3YnHVlN0O/Gc23vQqonihATN4wiCIIISqe2T2Dmtgj8Hfq0SB/wsbNVCXG+dKC76Pv3oGd19WJuLmsgrKAjCvrluCNu21EKJCBzIY0u0btQ8tgBirskEW+JCnDUnFFkLZx5bQKxesW4d8NdfQFISKhGPsnKgQ89EJMZZgfHjAQCjsMF+mCz31gehyEcLi+2eWt3o/Z84w5URdVfYKkO21XDiObf3oA2vdNxIwpYgiNYGx/ELwo2NwJEjfDHCykoM2FeGx5AMBiAZZShDMmoQjz5f/Cke28yIHVk1Yw89eQ4FobZEAm/y28IZv3DqypPoDdREnpLmtMxpMdwQttRCifAHJGyJ1o2GxzZldAb+GpIN8+YCbXHbHI+tFlJhq+aBBHirNnWq/Wl80w8A4PvvXb+GD4Rtx0wdvXKVtLTHVuqNFfAkFFnwnE+aJBuW9aDdc8rxOBK2BEG0NvLzRftmsQDTpgHgq7wvUNv/TcnjDz7gj/cgvlYZttucMF1ZiKvENkZCtA++FpVqIk9JUIg+N4RtW2qhRAQOFIpMtG40PLYA0HPTClhTOmkf6wth6ywUWQ8hOtaifJBjm5phQl27eNc7StEQtsoCVE5xNxRZ0Zjv1M69qJy/hO8na7HoC0UG+DuoQ4eAJUtQM+kB7HlgCY5tPygWp1J77/zc1oIgCMKrWCzA5MnNO8eUKW7H12rlZnolTFdD2PpaVKqFRWdne1YJuKUKTqm+jhvCFnBdFMqfxbOI1gl5bInWjYbH1v40PgY4dkT9WL2hyJ56bFtK2Hqj8mNDAyLOVrt3jMr/ZNMdSzD4v9NkBai47GxgxQr1c7gbiqwQ0+1L/0b7J3gPAzgOGDdO3OiqF22T51y1B+1HHznszubMBSeUDCUIggh2iosdFgvdxmZz2xXqLDez2d4+yQJpe+6MV/qw6kWtT+4zz7jXN9ebnmyPXsdNYQtoF4Vqqb+FaFuQi4Fo3Tjx2AJwemE+WSnx7rVUjq0rlPNXIyTE68Wjjn3+o/t9aRUis7TIgsH/neZQgIoVFGh7bt312JaUaM+HMeB9RZEtT7BYwB55xGGYAwObEgzVPwiCIHRgNvMLgs3BYHDbFSqE7UrxmkdVsug76fYzLdZeRvBMAvI+ue70zfWpJ1vv63ggbN1+DYJoBiRsidaNC4+tM69d+/fyxb6lzfDYyta7/RGK3ExhWzghH0nXD3H/QIWwPVpYrHrB4QBg0yb1c7gyotL3r64O2LPH+ZyYosiWJxQXg9PwYnA2KvlIEEQrwWQCli3zWNzawKHwn3luu0LVwna95lGV2MYo4xndorI56O3l6iost6WqDDt9HS8JW6qYTPgKCkUmWjfN8NhyAAYX5PJ9S10JW0V/P4ED4x5BQvhJRL+9hB/wRyhyM3Js+TY/kz1bAVOI/Y6ZZtjguJrGAHBDh6qfw12PbXq68zlxnChuXYUia2E2g3GcqrhlBiO4gK/+QRAEoRMhfnbLFqCigh+rrATKy4GkJP550+NKxOO5xyuRhHL8hZ74DKNx9F0TSp5xXzyqhe16BaltlNoXH6G3l6uesFynVYYtFmDzZv49qqwEysqA5GQgPl7+HFB/LNnvgvBkPAYgqanadRXikYBKXPROGfDTT+KLnzjh8f+FKiYTvoKELdG6aYbHFgBCYMWxTXuR2t2zUOT0e/4BrF8vDkgNqS+FrZRmeGz5Nj+e5ViV/XIYyeecY3+emmFCRZcLkHhoh32MAXyObUaG+kmkq8NqwjYkRBSrdXWisVaD44BrrgE++4x/7qnH1mQCt2wZbJMnwyARt4wzgMujko8EQbQyTCZg7FiXu+3YCDynHGxGbqxWbmaz8Hb9CRfoyRfWK341qwyvz3eo4t8c4qGj4jUADBvGe/Q9iOOmismEr6BQZKJ10wyPLQA0wsj3LfU0FDkxUVtA+SLH1mjkBVxoqDjnZhjvjplmWN1r8mOn4sf9DmOJPeSVlbnoaO3CUYDrhQCOE8fr6mTvQ935Gfj/9u48Oooy3xv4tzqBgMSEgAQIzTphmwDiEjHKpg5ERkYuzs0ZtleWRsGFCHoNIo7AVTFeObgMiuxEo/HAhbggOoDAwIssGdF3wIUJAglhCySEECBA0s/7R9OdXqq7q6uru6u7v59zcrSrqypPPwF++dXvWU5ljm84d948IC2t4bXaii0AmEwwlJaiYvEaHJqxGBWL10AqLeHKF0QUtQI6N1Yr9g9Ig5DYKukTX4bluqwynKnBytVqCeHXxFhvKyYTqcGKLUU2bxVbD8llPQzYPX6JZd/Sjf9y/z08DEVGixbyCVRsrLrtYbxVbK1JtCRZFpCqqfEteFuHMx0+jOrfynEZyfjt939Ct5+/sJ2idD/bln1ktlKqrnZ8Lbf3rD1vFVvA8jOsrXVJbOO6d0bbR7OAv+dZDgjh+HNSW7G1MhrRcmoWWvp3FyKiiBAWVbggVmzLyixJa24uMGuW+z7xdViuQyV7mwYrV/vDz+WqA1KVp6gWFoltTU0NXnrpJaxZswaVlZXo0aMHXnjhBYwaNcrrteXl5cjJycGGDRtw+fJl3HrrrXj11VfxwAMPBKHlFHLeKrZuqnZnBmXB/OZCS1Irdx9n9gmYvaQk+QRK7aILShNbwBLAa2qAEydwfuZ8VJwDklGOhN8lWyLmPfe4TvJ57DFbkJTb5uZy5gjcdPY4sH+/16Ym/76V60H7xbMAS79ZJxXJUTJ023r82jXHxDU21vJgwaqy0rGy7m9iSxQmGEMpWAI2N1YrjRo1TF8pKQEWL3Y/B9Vu3un5uGTHGOpp7mpSEvZtOo9dn5XjDJIhAdh9bzla9EhGiy5JSDpzHpjecJ2xvBz/GNUdYz/9E0rNRt8eCFhXrg5Vcqu7kjxFu7BIbB955BEUFRUhNzcX3bp1wyeffILRo0fDbDZjzJgxbq+7evUqHnjgAVRVVeGdd95BcnIy3nvvPTz44IPYsmULBg0aFMRPQSGhsmLb+s8DgHS7qOItsZVZoMncpAkMjRuHLrG1tunCBST9z2wkOZ8rSQ3zY8rKHJJad27q0Qm4Vu3xHJv6eqCsDBVffoezhyrQqntLtDx/3vW8K1eAZs3k76G0Yms91zlxdU5s7Z/W+zMUmSiMMIZSMPlbhbNWOrt2DUBivHJlQ5w7fhx48klFlyXd+FLqrhtfNrtufLnRH8AxPIlD/7Uc8c+YHD63x/4wGoFp04B33/WhdRoxGHRYkqdop/vEduPGjdi8ebMtEAPAfffdh5KSEjz//PP4y1/+ghg38w5XrFiBgwcP4rvvvkNGRobt2ltvvRU5OTnYu3dv0D4HhYjKii2SnEKYt8RWZkiTVFuLf987Ad3+z92u56tNbL3NsbUmtkVFwKVLns+1zo/JzLRETSVPfKurlbd9/XqI+fPRErAN15UdxuwpsVVSsbX+DK9e9V6xtV9cihVbigKMoRROlKwOrFpZCOejKiAB6LHwceCZTACWZFFRf9x5Z8P/Z2UBt93WsGq1tbIss4q1w/97Os/5vaQky/ohGRlMakl3dJ/YFhYWIj4+HllOK/JNnDgRY8aMwd69e3HPPfJ7bBYWFqJ79+62gAwAsbGxGDduHF588UWcOHEC7dq1C2j7KcTUzrG1T4jk7uNMLrEF0PW7PFTd0Q7Nnd8MdMV2505l97POj+naVdn5bdpYApwCYv58lyRWdm6up+2I/KnYxsY6PKC4/v2PuHLTLQ3Dq61bVxBFMMZQChdKVwdWTekD3FAym21zVhX3h31MHjECGDs2IE0LaCWdSCO6XxX54MGD6NmzJ2KdfqHv06eP7X1P11rPk7v2p59+cnvt1atXUV1d7fBFYUjtqsgaVGwBSyJX+5Pr6sAuSyAqpTSxHTBA8S0vrPkah+d8iLpEBQOtbrlFcVKueC1lTwt4eNvHFvA8FDk21tZnjU6fQMKR/9fw/sCBlsfhRBGMMZTChbfVgcvKLCvoqlyEt2E+qp4ZDLY5q4pXS7bfT9b5dxeNrFhh2Sb+/vst/2XoJL3SfWJbUVGBFs7VM8B2rMJD1cWfa19//XUkJibavtq3b+9r00kP1O5j62tieyP6OD8LFgASGrkmbqK0FJgwwfM95ShNbNPTgfHjPZ97Q+Li/0HqytmIvWD31HfkSFzp/wf5+7tLMJ0ofi6uNLH1tnhUXZ1jhTc2FigqgnC3FZOfWxUQhQPGUAoXnrbG0SSxMhot60roObldutRWDlW8fZJ9xVbm76u/3FWOGTpJj3Q/FBkAJA//CHl6z59rZ82ahWeffdb2urq6moE5HKmt2NonVHL3ceN6XDwaXa2BBEtid/SO/0Tnv/+vy3kSAJGXB+mppyxJqFLe5tjaJ76rVwNPPQV89RXO18ahsgJIvnQENxcs9/59Pv8cTRctAv7vFsfjPiS20v33A1u3ej9RyVDk2Fj3n93+Z2g/r7hRI2DnTs+VYz+3KiAKB4yhFAz+DlV1t10QoOEQZeuyzbt3N0xHUTC39HzjVqisAFrhLBK6WN6rOnYeK984izOwXJeMsziHVsiZn4QkKJyvCgALFwLnzll+z7B74C3XH7m5lj62vg8g4BVbT5Vjhk7SG90nti1btpR9Klx54y+y3NNkLa6Ni4tDnNp5kKQfKiu25tvvgGGZ3SoNChPbxp3a4cyCj3Dxm124+cF70aVZDXC/a2IL3Biqu2uXb4mtL6siA5Z7p6c3rOi4bRugJLE1m4GqKvn7K/17ofSX2CtXHFZPbhN3Hs2v3tgK4cQJyzkGg+W3Jrko6i6xjY0FBgzwvO8utyqgCMcYSsGg1aJPctsFbdumcWJlNFoWWfKB3KrIP2wDnnvD9dzMDGDwYB9uvns38OWXlg85e7blwfqNhQ5N5eV45LlklF9LwqlfzuOH58vxdyRjE4AxD5Sj9/3JwA8/2G61b0ctUpppm3D6us8uUSjpPrHt3bs3CgoKUFdX5zBH6MCBAwCAXr16ebzWep49JddShFBZsTUIM8SUKZCsj4QVJraIjUXr4eloPfxGslpWBiFJkGQWrBAApHvvVXZfW8O8tMPbSr9KF4mym+fjoHFjxRVbKJ1T99lnEIsWOaye7OLaNaBDh4btiex5SmzT0yGNH2+pjjvfk1sVUBRgDKVA03rRJ+ftgvSaWGnWLvtY+YZrpmxNqrsDGGz/xrc3vuzc+fhtmCItw93LTJqtJu2uks7QSXqk+zm2I0eORE1NDdatW+dwPC8vDykpKejXr5/Ha3/99VeHLQnq6uqQn5+Pfv36ISUlJWDtJp1QO8cWgGS/SoNcQhkf73rMObE0GiEtWwaz05A9AUAaP963ai1gmRvkqWrrLbE1GoHlXiq2kmSJYh07yt9faRWmpkbRaWLRImULTbmbE+tpKDIArF4Nad8+XJgxB79Nno/z8xcDa9YAJSUa7iNBpE+MoRRoihc5UsmaWFmfS+slsdKkXWVlwD/+oVmbDBBYLKbgvx8v03QOrMkEHDtmqZ4fO8bQSfql+4rtsGHDMGTIEDzxxBOorq5GamoqCgoK8M033yA/P9+2/57JZEJeXh5+++03dLzxC/mkSZPw3nvvISsrC7m5uUhOTsb777+PQ4cOYcuWLZ6+LUUKtXNsAYiYGEjWR69yiW2zZq7Jm1zSaTLBkJmJig27UfX9Ydxy81Ukjn7I96TWKibGcfVfe0r2ZrWO9dqwAfj3vx3nDt3RDRg+3BKZ5VY89WGOLS5eVHSaT8t4yI0/s3s4ceHnMiRaX9j/LNLTkZie3vAeUZRgDKVAC0ZFVW6Ish743S7rhFkNxaIenc2HcfiwUXF7lMyPdq6kE+mR7hNbAFi/fj1mz56Nl19+GZWVlejRowcKCgowatQo2zn19fWor6+HsBvyGRcXh2+//RY5OTmYNm0aLl++jL59++Lrr7/GoEGDQvFRKNh83MfWDAkGCJgNMTDYP3qVS2xvusn1mLtqqtGIllOz3A+19UVsrOPqv/aUJLY32oOpUwHIzx0CYEnc5e6vtGLrYSiytZ8BeJ4D60zmt6XT+0rQ5sb/3/zua45tJSLGUAqoYA1V1Wti5Ve7rFsQabi/bh1icNSQqvjBglbzo4n0QBJC77tV60N1dTUSExNx4cIFJCQkhLo5pNShQ0CPHg2vd+8G7r674fUnnzhsZl6a9SyaZv0JrTKcHr3++CNw220Ot77epTsaHTnk+P369wd27tTwA8hISHBfDX3wQeDrr7X5PmfP2hawsNm4EThyBHj6ae/Xt28PHD/ucrjy9gcg/fnPSJr9pOVAfLyyYcsyEfdUURla39XBliQ7eOstYPp07/cl8gFjgTrst8hXVqascunv6sla0Us7sGIF8NhjmiS39TBgqrRU8RzbsjLLrCPnavuxY/p8iEDhL9CxICwqtkSq+Vix7dC3JZA12Pt9AMQ6J7Vy99faihWeh/hqWaWUq9g2bqy8YuumnS3u6Qn0sVsx2S6pLRvxBOJ7tEfza3ZbIwBAy5ZARoZLpD29sxht3e2Yy4otEVHQKKlc6qU6qJd2AHDcgujwYeXbBN34//NIwplyIDa5Jc6mZmBOhvIhyNzKhyINE1uKbN7m2DovHuUuMZVJbGWHz9ovXqS1sjLLU11PtEzm5ObSajHHNi4O2L5d9q12n38A6U/LANMsRd+izYCuDsOaHQT6IQMRESnmbvXkPn0szzeDVTnVehVnf9rRUDH2fQsiQD5Bz/DhM+h1xWkitXS/KjKRX3ys2PqS2MoRRUUOG6xrqrjY+1AlLRNbg8F1HnGjRpa9d5Wor5c/fvWqZUN6GRIExOMyKx+70TbdiIOZz9leO/QOE1siIt1wVx28+27g/vstQ2JXrAhdO7RaxVmJFSssn9efz+0uQfdlNWS9rjhNpBYTW4psPlZsL5xwM9dTYWIrARB5eUBRkcIG+sC6yIQnWg+/dR6OXFkJ8cEH/t2zpsZjgi6ZffsNo8/SaQ3X2r/BochEREFRVmbZCsZTUmWtDjrzJzFTQ64dwaxSapGQAtol6NatfNassSw7kpnp2/VEesLEliKbcyLoXMXbtMnh5c0L52DnBJlHpwoTW+BGcqW0qukLoxFYtsxzchvoxPbUKd+255HTtq3HzyAMPv6G0a6dyz7BAHD+2AU1rSMiIh8orT46VwflwmowKqehrlJqlZBqmaD//e/AqFHAX/4CdOgAPP984B8wEAUCE1uKbJ4qtmVlEK/nOp4OICNvCk4VOf2LLhOBhZsUTwDAvff63lYlTCagtBRYswbn5y/GtXinjXoCndj+7ncQ3qrG3iQnu03QhWSAtNS33zDOfL0fkkwFuPmcbPmHFEREpAlfq4/W6uC2bcCePaGrnNq349ixwC4c5VzN1ioh1SpBd/4ZCgEsWBC8oeFEWmJiS5HN0xzb4mJIMosOxaIeZ3Y5PTp1vk/TppCWL3OpFAoA0vjxQHq6H4324sYiE0mzpqJxq+aO79XWavqtqs9cdnhd9Lc9kJa5fm6fxMW5JOiHZixGxeI1kEpLfP4No3rjTtlHDBLcPKQgIiJNqKk+Go3A4MGWMBnKyqm1HYD3YdRqyVWztawYa5Ggy/0MgeANDSfSEldXocjmqWLbtSuEJLlU++oQg9b3Oj06db5PUhJgMsGQmYmKDbtR9f1h3HLzVSSOfiiwSa2Tq6cqYL/8lfjwQ0gDB2ry+PlUURnanDvqcOy2wr/i1KxjaFtaivMrC5E0J9v3G1sX7LIm6ACSPF7gWcIfB0Asll+l2vqQom06V8IgItKav6vqWne6UbL/bSAEctsfT6sve/rcvu6vq2SbJU/kfoZW3PqHwg0rthTZPFVsjUaX6mM9DNg9folrIuR8nxYtbPdoOTULv1s2C4kL5wY1qT2zoQiNa6sdjkkAxOOPa/KI9fTOYpdk0VbNNhqRNPE/1N1Y6T64CrUeno6jd/yn7G62sg8piIhIE1pUH62V02AnT1ot4uSOt2q23Oe2r/AGa66r9WcoN+eZW/9QuGFiS5HN26rIJhMMpaWoWLwGP81Zg/J9JRiwWuZxrVzFNsTcDsE1mzVZfcOyR6wjh0RR7XxejRNbAOjyz7Wonjbbob1uH1IQEZFmgjlfVUuB3vbH17m0oZzrajIBJSXAf/0Xt/6h8MahyBTZvO1jC9iqri19uY8OElt3Q3CFwQBJg0esbdONONl9MFIObbcd2zf6LdxjTRR1lNgCQOK7rwI5U1GxYTdOnwZaPJSBAUxqiYgCzt/hsKHg7zBqb6yV0ClTLAmzt0TR21zXzMzA9rHRCLz5JvDMM6EbGk7kL1ZsKbJ5q9iqvM/lusZuTgye1sPTUXzPeIchuAISpKVLNYtGKSPvdnh9z3K7R/E6S2wB2B5SpM3NYqWWiEhnlOx3GyzB2PbHl2q2u31+geBsg2QVqqHhRFpgYkuRTUnFVomCAoeXTTf+ry62kum2azXKv9yHo+PnoHL+YkjHS7UdB5aQ4PjaPpnVY2JLRES6pHS/22AKxjBqpYki57oS+Y+JLUU2LSq2ZWUQzz3ncEhPW8m0Hp6OzqvnosWsqdo/YnVObO0fDHhIbA8bB9kqyS6LOjGxJSKKKoFeqMkfoaxQOlewOdeVyD9MbCmyaVGxLS522RIIcLPfbaRJTHR8bbeC9E7TareXpR7fjvIv9+HwU2/h7KovHd9kYktEFFUCvVBTOHJXwbbOdQ3HBbmIQo2LR1Fkc05s3U1g8cSX/W4jjXPF9oZTRWW458MpHi9tPTwdrYenA2fPOr7BxJaIKKoEeqGmcONpj1trZTYcF+QiCjVWbCmyOSeyktwGOV74st9tpHGT2J7eWYwYl82A7NiPL3MesszElogoqgRjoaZw4q6CvXatPoZnE4UrJrYU2dRUaOUo3e820rhJbNsM6Ip6D/98mDvYjatq7LSCtPNrIiKKeOG6320guFsB+dln9bOwFlE4YmJLkU2rxBaIzq1k3CS2bdON+G78UtTB8vi9zumfEoMwQ1hXBnFOZFmxJSKKStxKxsK5gm1PTwtrEYUbJrYU2dQMPaYGTomtfaAdsNqEs/uOYe2T2zAGBXAmWVcGcY7cTGyJiCiKyO3fa61gL1zoen60L6xFpBYTW4psTGz9s369w8t5HVY4DJFqm25ExqzB2CPd4zI0WVhXBnH+GTCxJSKiKOFp/16jEcjKkt+ZMFoX1iLyBxNbIpJXVgbx1FMOhxaLKfjvx8scnjobjcCcZUZMlRqGJpsNMZDcrQzCObZERBQFlOzfy4W1iLTD7X6ISF5xMSSnZRtjUY/O5sM4fNjoEHRNJiAz04Si3ZlIxWG0ykh1G5VPfX8yeuYoExFR1PK0f69rDLUcT3UTPsvKLPfr2pVJL5E7rNgSkbyuXSGcxkfVIQZHDamyQ6SMRiAjy4hWWYM9Rt3kuzpi5wQu+UhERJFNbvVjd8OMPS2s5Wk4MxE1YGJLUYWrDPrAaIS0dCnMBuvKxzF4QlqCl5cafXpafKrIsdNjYEZG3hSX40REpE9yix+Rd1oMM1YynJmILJjYUmRzeqzpvPgReWEywVByDGfXbEPRmmOYU2ryee/B0zuLXY7Foh5ndnHJRyIivWO10D/+7t/raTgzETmShBAi1I0IB9XV1UhMTMSFCxeQ4GZvT9KZsjKIjh0d5onWIQa/MxzDrhLfqo6k3qmiMiTf1RExcPw5nN13jHNtKewwFqjDfgtPZWWWZNY+sYqJsSRojKHBwZ8BRZJAxwJWbClyeVz8KERtikJt0434bnzDisl1iMHu8UuY1BIR6RyrhaHHVZOJlOOqyBS5bix+5Fyxdbf4EQXOgNUmnHoqE2d2HUbre1MxgEktEZHuWRc/cq4WMoYGl5JVk4mIFVuKZBotfkTaaJtuRN/pg1mpJSIKE6wW6oenVZOJyIIVW4psJhMMmZk4u/swDiMVczKY1BIRESnFaiERhQsmthT5jEa0yjKiVajbQUREFIaMRia0RKR/HIpMREREREREYY2JLREREREREYU13Se2NTU1mD59OlJSUtCkSRP07dsXn376qaJr169fj9GjRyM1NRVNmzZFp06dMHbsWBQXFwe41URERKHHGEpERNFC93NsH3nkERQVFSE3NxfdunXDJ598gtGjR8NsNmPMmDEer33jjTfQpk0bzJ49G126dMHx48cxf/583H777dizZw/S0tKC9CmIiIiCjzGUiIiihSSEEKFuhDsbN27EQw89ZAvEVkOHDsVPP/2E0tJSxFjXoJdRXl6O5ORkh2MnT55Ep06d8Oijj2L58uWK21JdXY3ExERcuHABCQkJvn8YIiIKe+EUCxhDiYhITwIdC3Q9FLmwsBDx8fHIyspyOD5x4kScPHkSe/fu9Xi9c0AGgJSUFBiNRhw/flzTthIREekJYygREUUTXSe2Bw8eRM+ePREb6zhiuk+fPrb3fXXkyBGUlJRwCBUREUU0xlAiIoomup5jW1FRgS5durgcb9Gihe19X9TV1cFkMiE+Ph4zZszweO7Vq1dx9epV2+sLFy4AsJTQiYgoOlljgI5n8dgwhhIRkZ4EOoYGLbHdvn077rvvPkXn/vDDD+jbty8AQJIkt+d5es+ZEAImkwk7d+7EunXr0L59e4/nv/7665g3b57LcW/XERFR5KuoqEBiYmLQvh9jKBERRYpAxdCgJbbdu3fHsmXLFJ3boUMHAEDLli1lnyhXVlYCaHjq7I0QApMnT0Z+fj7y8vIwYsQIr9fMmjULzz77rO11VVUVOnbsiNLS0qD+MhPOqqur0b59exw/fpyLhfiA/eY79pk67DffXbhwAR06dFAcf7TCGBp9+PdTHfab79hn6rDffBfoGBq0xLZt27aYPHmyT9f07t0bBQUFqKurc5gjdODAAQBAr169vN7DGpBXrVqFFStWYNy4cYq+d1xcHOLi4lyOJyYm8g+vjxISEthnKrDffMc+U4f95juDIbhLVDCGRi/+/VSH/eY79pk67DffBSqG6nrxqJEjR6Kmpgbr1q1zOJ6Xl4eUlBT069fP4/VCCDz22GNYtWoVlixZgokTJwayuURERLrBGEpERNFE14tHDRs2DEOGDMETTzyB6upqpKamoqCgAN988w3y8/Md9t8zmUzIy8vDb7/9ho4dOwIAsrOzsWLFCkyaNAm9e/fGnj17bOfHxcXhtttuC/pnIiIiCgbGUCIiiia6TmwBYP369Zg9ezZefvllVFZWokePHigoKMCoUaMczquvr0d9fb3DKltffvklAGDlypVYuXKlw/kdO3bEsWPHFLcjLi4Oc+bMkR1aRfLYZ+qw33zHPlOH/ea7cOszxtDwxT5Th/3mO/aZOuw33wW6zyQRDnsWEBEREREREbmh6zm2RERERERERN4wsSUiIiIiIqKwxsSWiIiIiIiIwlrUJ7Y1NTWYPn06UlJS0KRJE/Tt2xeffvqpomvLy8sxYcIE3HLLLbjpppuQkZGBb7/9NsAtDj21fbZ+/XqMHj0aqampaNq0KTp16oSxY8eiuLg4CK0OPX/+rNl76aWXIEmSoj0ow52/ffb5559j0KBBSEhIQLNmzZCWloalS5cGsMX64E+/bdu2DUOGDEFycjLi4+PRp08fvPvuu6ivrw9wq0Pr4sWLyMnJwdChQ9GqVStIkoS5c+cqvp7xgDFUKcZQdRhDfccYqg5jqO90E0NFlBsyZIho3ry5+OCDD8TWrVvF5MmTBQDx8ccfe7yutrZW9OrVSxiNRpGfny82bdokRowYIWJjY8X27duD1PrQUNtnd911l3j44YfFypUrxfbt28VHH30kevbsKeLj48XBgweD1PrQUdtv9n744QcRFxcnWrduLdLS0gLYWn3wp89ef/11YTAYxJNPPim+/vprsWXLFrFo0SLxt7/9LQgtDy21/bZ582ZhMBjE4MGDxWeffSY2b94spk2bJgCI7OzsILU+NI4ePSoSExPFwIEDbf01Z84cRdcyHjCG+oIxVB3GUN8xhqrDGOo7vcTQqE5sv/rqKwFAfPLJJw7HhwwZIlJSUkRdXZ3ba9977z0BQHz33Xe2Y9evXxe///3vxV133RWwNoeaP3125swZl2MnTpwQjRo1EiaTSfO26ok//WZ1/fp10bdvX5GdnS0GDRoU8UHZnz775z//KQwGg3jjjTcC3Uzd8affxo4dK+Li4kRNTY3D8aFDh4qEhISAtFcvzGazMJvNQgghzp4961NQZjxgDFWKMVQdxlDfMYaqwxiqjl5iaFQPRS4sLER8fDyysrIcjk+cOBEnT57E3r17PV7bvXt3ZGRk2I7FxsZi3Lhx2LdvH06cOBGwdoeSP32WnJzsciwlJQVGoxHHjx/XvK164k+/WeXm5qKyshKvvfZaoJqpK/702aJFixAXF4dp06YFupm640+/NWrUCI0bN0bTpk0djjdv3hxNmjQJSHv1QpIkSJKk6lrGA8ZQpRhD1WEM9R1jqDqMoeroJYZGdWJ78OBB9OzZE7GxsQ7H+/TpY3vf07XW8+Su/emnnzRsqX7402dyjhw5gpKSEqSlpWnWRj3yt99+/vlnvPrqq1i8eDHi4+MD1k498afPduzYgZ49e2LdunXo3r07YmJiYDQa8cILL+DatWsBbXeo+dNvU6dOxbVr15CdnY2TJ0+iqqoKH330EQoLC5GTkxPQdoczxgPGUKUYQ9VhDPUdY6g6jKHBp2U8iOrEtqKiAi1atHA5bj1WUVERkGvDmZafu66uDiaTCfHx8ZgxY4ZmbdQjf/rNbDZj0qRJeOSRR/DHP/4xYG3UG3/67MSJEyguLkZ2djays7OxZcsWTJgwAQsWLMDEiRMD1mY98Kff+vXrh61bt6KwsBDt2rVDUlISJk6ciNdeew3PPfdcwNoc7hgPHDGGuscYqg5jqO8YQ9VhDA0+Lf9djPV+SmTzVDb3VlL359pwpsXnFkLAZDJh586dWLduHdq3b69V83RLbb8tXLgQxcXF+OKLLwLRLF1T22dmsxkXL15EQUEBRo0aBQC47777cOnSJbz99tuYN28eUlNTNW+vXqjtt++//x4jR45Ev379sGTJEjRr1gxbt27FSy+9hNraWvz1r38NRHMjAuOBb+/5e204YwxVhzHUd4yh6jCGBp9W8SCqE9uWLVvKPgWorKwEANmnB1pcG860+NxCCEyePBn5+fnIy8vDiBEjNG+n3qjtt9LSUrz88svIzc1F48aNUVVVBcDypN5sNqOqqgpxcXEu8zkigb9/P0+fPo3MzEyH48OGDcPbb7+N/fv3R2xQ9qffnnrqKbRu3RqFhYWIiYkBYPllxmAwYO7cuRg7diy6dOkSmIaHMcYDR4yh7jGGqsMY6jvGUHUYQ4NPy3gQ1UORe/fujV9++QV1dXUOxw8cOAAAHvc46927t+08X68NZ/70GdAQkFetWoXly5dj3LhxAWurnqjttyNHjuDKlSt45plnkJSUZPvatWsXfvnlFyQlJWHWrFkBb38o+PNnTW6uBmD58wcABkPk/tPnT7/9+OOPuOOOO2wB2So9PR1msxm//PKL9g2OAIwHjKFKMYaqwxjqO8ZQdRhDg0/TeODTGsoRZuPGjQKA+PTTTx2OP/jgg16X9H7//fcFALFnzx7bsevXr4u0tDTRr1+/gLU51PzpM7PZLEwmk5AkSSxdujTQTdUVtf12/vx5sW3bNpevW2+9VXTq1Els27ZNFBcXB+MjBJ0/f9aWLFkiu+dcdna2MBgM4tixYwFpsx7402+dO3cWvXr1cjnnxRdfFADEjz/+GJA2642vWxUwHjCGKsUYqg5jqO8YQ9VhDPVfKGNoVCe2Qlj2pUpKShJLly4VW7duFY899pgAIPLz823nTJo0ScTExDj8Ra6trRVpaWmiffv24uOPPxabN28WI0eOjJrN5dX02dNPPy0AiEmTJondu3c7fO3fvz8UHyWo1PabnGjYg08I9X127do1cfvtt4vExETxzjvviM2bN4uZM2eKmJgY8fTTT4fiowSV2n579913BQAxbNgw8dlnn4lNmzaJmTNnitjYWPGHP/whFB8lqDZu3CjWrl0rVq5cKQCIrKwssXbtWrF27Vpx6dIlIQTjgTPGUN8xhqrDGOo7xlB1GEPV0UMMjfrE9uLFiyI7O1u0adNGNG7cWPTp00cUFBQ4nDN+/HgBQBw9etTh+OnTp8Wjjz4qWrRoIZo0aSLuvvtusXnz5iC2PjTU9lnHjh0FANmvjh07BvdDhIA/f9acRUtQ9qfPKioqxJQpU0Tr1q1Fo0aNRLdu3cSbb74p6uvrg/gJQsOfflu3bp3o37+/uOWWW0SzZs1EWlqaeOWVV1w2nI9Env6NsvYT44EjxlDfMYaqwxjqO8ZQdRhD1dFDDJWEuDFgnoiIiIiIiCgMRe7sbyIiIiIiIooKTGyJiIiIiIgorDGxJSIiIiIiorDGxJaIiIiIiIjCGhNbIiIiIiIiCmtMbImIiIiIiCisMbElIiIiIiKisMbEloiIiIiIiMIaE1siIiIiIiIKa0xsiYiIiIiIKKwxsSUiIiIiIqKwxsSWiLBr1y5IkgRJkrB27VrZc/bu3Yv4+HhIkoScnJwgt5CIiEifGEOJ9EESQohQN4KIQm/EiBH44osv0KNHDxw8eBAxMTG29w4dOoT+/fvj3LlzGD9+PFatWgVJkkLYWiIiIv1gDCUKPVZsiQgAkJubi5iYGPz666/Iz8+3HT958iQyMzNx7tw5DB8+HMuXL2dAJiIissMYShR6rNgSkc3kyZOxYsUKdO7cGYcOHcKlS5cwcOBAHDhwAP3798emTZvQtGnTUDeTiIhIdxhDiUKLiS0R2Zw4cQJdu3bFlStX8NZbb6GwsBA7duxA7969sWPHDjRv3jzUTSQiItIlxlCi0OJQZCKyadeuHbKzswEAM2bMwI4dO9CpUyd88803sgG5pqYGc+fOxfDhw9GmTRtIkoQJEyYEt9FEREQ6wBhKFFpMbInIwTPPPAODwfJPQ4sWLbBp0yakpKTInnvu3DnMmzcP+/fvx5133hnMZhIREekOYyhR6MSGugFEpB91dXV4/PHHYTabAQCXL1/2OB+obdu2KCsrQ7t27VBbW8u5Q0REFLUYQ4lCixVbIgIACCEwefJkbNiwAa1atULnzp1RW1uLOXPmuL0mLi4O7dq1C2IriYiI9IcxlCj0mNgSEQAgJycHeXl5iI+Px1dffYXXXnsNAJCXl4eff/45xK0jIiLSL8ZQotBjYktEWLBgARYsWIBGjRph3bp1SE9Px6hRo9CnTx/U19dj1qxZoW4iERGRLjGGEukDE1uiKPfhhx8iJycHkiRh9erVGDp0KABAkiS88sorAIAvvvgCu3btCmUziYiIdIcxlEg/mNgSRbGNGzfCZDJBCIGFCxdizJgxDu8//PDD6NevHwBg5syZoWgiERGRLjGGEukLE1uiKLV7925kZWWhrq4OM2fOxPTp02XPs84T2rVrFz7//PMgtpCIiEifGEOJ9Ifb/RBFqYyMDFy6dMnreQ888ACEEEFoERERUXhgDCXSH1ZsiYiIiIiIKKyxYktEflm0aBGqqqpQV1cHAPjXv/6FV199FQAwcOBADBw4MJTNIyIi0i3GUCLtSILjI4jID506dUJJSYnse3PmzMHcuXOD2yAiIqIwwRhKpB0mtkRERERERBTWOMeWiIiIiIiIwhoTWyIiIiIiIgprTGyJiIiIiIgorDGxJSIiIiIiorDGxJaIiIiIiIjCGhNbIiIiIiIiCmtMbImIiIiIiCisMbElIiIiIiKisMbEloiIiIiIiMIaE1siIiIiIiIKa0xsiYiIiIiIKKz9fwN+SUYm67SfAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1100x400 with 2 Axes>"
      ]
     },
     "metadata": {
      "filenames": {
       "image/png": "/Users/mhjensen/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter6_47_0.png"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tree_reg1 = DecisionTreeRegressor(random_state=42)\n",
    "tree_reg2 = DecisionTreeRegressor(random_state=42, min_samples_leaf=10)\n",
    "tree_reg1.fit(X, y)\n",
    "tree_reg2.fit(X, y)\n",
    "\n",
    "x1 = np.linspace(0, 1, 500).reshape(-1, 1)\n",
    "y_pred1 = tree_reg1.predict(x1)\n",
    "y_pred2 = tree_reg2.predict(x1)\n",
    "\n",
    "plt.figure(figsize=(11, 4))\n",
    "\n",
    "plt.subplot(121)\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(x1, y_pred1, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "plt.axis([0, 1, -0.2, 1.1])\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.ylabel(\"$y$\", fontsize=18, rotation=0)\n",
    "plt.legend(loc=\"upper center\", fontsize=18)\n",
    "plt.title(\"No restrictions\", fontsize=14)\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.plot(x1, y_pred2, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
    "plt.axis([0, 1, -0.2, 1.1])\n",
    "plt.xlabel(\"$x_1$\", fontsize=18)\n",
    "plt.title(\"min_samples_leaf={}\".format(tree_reg2.min_samples_leaf), fontsize=14)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pros and cons of trees, pros\n",
    "\n",
    "* White box, easy to interpret model. Some people believe that decision trees more closely mirror human decision-making than do the regression and classification approaches discussed earlier (think of support vector machines)\n",
    "\n",
    "* Trees are very easy to explain to people. In fact, they are even easier to explain than linear regression!\n",
    "\n",
    "* No feature normalization needed\n",
    "\n",
    "* Tree models can handle both continuous and categorical data (Classification and Regression Trees)\n",
    "\n",
    "* Can model nonlinear relationships\n",
    "\n",
    "* Can model interactions between the different descriptive features\n",
    "\n",
    "* Trees can be displayed graphically, and are easily interpreted even by a non-expert (especially if they are small)\n",
    "\n",
    "### Disadvantages\n",
    "\n",
    "* Unfortunately, trees generally do not have the same level of predictive accuracy as some of the other regression and classification approaches\n",
    "\n",
    "* If continuous features are used the tree may become quite large and hence less interpretable\n",
    "\n",
    "* Decision trees are prone to overfit the training data and hence do not well generalize the data if no stopping criteria or improvements like pruning, boosting or bagging are implemented\n",
    "\n",
    "* Small changes in the data may lead to a completely different tree. This issue can be addressed by using ensemble methods like bagging, boosting or random forests\n",
    "\n",
    "* Unbalanced datasets where some target feature values occur much more frequently than others may lead to biased trees since the frequently occurring feature values are preferred over the less frequently occurring ones. \n",
    "\n",
    "* If the number of features is relatively large (high dimensional) and the number of instances is relatively low, the tree might overfit the data\n",
    "\n",
    "* Features with many levels may be preferred over features with less levels since for them it is *more easy* to split the dataset such that the sub datasets only contain pure target feature values. This issue can be addressed by preferring for instance the information gain ratio as splitting criteria over information gain\n",
    "\n",
    "However, by aggregating many decision trees, using methods like\n",
    "bagging, random forests, and boosting, the predictive performance of\n",
    "trees can be substantially improved."
   ]
  }
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