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:  -5.030164788184997\n",
      "first power:  0.001268544905013411\n",
      "second power:  -5.234332597247826e-05\n"
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ENQYhfAQCgUAgENQYhPARCAQCgUBQYxDCRyAQCAQCQY1BCB+BQCAQCAQ1BiF8BAKBQCAQ1BiE8BEIBAKBQFBjEMJHIBAIBAJBjUEIH4FAIBAIBDUGIXwEAoFAIBDUGEJS+Hz44Yc0bdoUo9FI586d2bBhg7+bJBAIBAKBIAAIOeHz5Zdf8tBDD/HUU0+xfft2rrrqKgYMGMCJEyf83TSBQCAQCAR+JuSEz8yZM5k4cSJ33HEHrVu35u2336ZRo0Z89NFH/m4aFsnC2fyz7D+/399NEQiCioKSAvW9JEk26+5gLjFjkSwe1yUQCEKPkBI+xcXFbN26leuuu85m+3XXXcfGjRudHlNUVEROTo7NUlVkmjOp80YdLv7gYkrKSqqsHoEglFh/bD2xr8by+h+vA3D70tupPaM2J7NPunV8hjmDhm815Povr6+w7NbTW4l7NY6n1z5dqTYLBILAJaSEz/nz5ykrK6NOnTo22+vUqUNaWprTY1555RViY2PVpVGjRlXWvjhjnPo+szCzyuoRCEKJTac2UWopZcMJea7eb8d/I78kn+1p2906fs/ZPWSYM9hwvOK5fn+m/EmJpUStSyAQhB4hJXwUNBqNzbokSQ7bFKZOnUp2dra6nDzp3lOkN+i0OlX8ZJgzqqwegSCUUO4VV6/uHp9VmEWZpcyjugQCQegR5u8G+JKkpCR0Op2Ddefs2bMOViAFg8GAwWCojuYBkGBKIKswi0yzsPgIBO5gLUbKLGVkFWbZbHf3eAmJ7KJsEkwJbtUlEAhCk5Cy+ISHh9O5c2dWr15ts3316tVcccUVfmqVLUqnKzpWgcA9rMWIInqst7t7vDvHCOEjEIQ+IWXxAZgyZQpjx46lS5cudO/endmzZ3PixAnuuecefzcNgHhjPCA6VoHAXazFiCcixlk5d4VPYWkh5hIzJr3J0+YKBIIAJ+SEz80330x6ejovvPACqamptGvXjh9//JEmTZr4u2mAsPgIBJ6i3CulllJOZF+Ix+Wug4B1OXeFj3KcED4CQegRcsIHYNKkSUyaNMnfzXCKED4CgWdYC5dDGYfU995YfCqaW2cvkupH13e3mQKBIEgIqTk+wYAQPgKBZ1jfK4czDzvd7u7xnlh8xD0qEIQmQvhUM6rwKRSdqkBQEYWlhTaRlCtr8SnvGEmShPARCGoAQvhUM8LiIxC4j/3QVFVafApKCiguK/b4/AKBILgQwqeaUYSPiOMjEFSMvfiwtvi4E5DQ/hzlWVrt6xLCRyAITYTwqWaEO7tA4D7294l9AlHruD7OKLOUkV2U7fJ85dUl7lGBIDQRwqeaEUNdAoH7VHSfVOTSbi+MPBE+wiorEIQmQvhUM+pQV2EmFsni59YIBIGNJ15Y7uz3yOIjHBAEgpBECJ9qJt4kD3VZJAs5RTl+bo1AENj4WviUZ8URQ10CQc1ACJ9qxhhmJEIfAYiOVSCoCGUoq1ZELZvtyrq7wse6vCRJbtUl7k+BIDQRwscPiHk+AoF7KPdI84TmNtuVdXeFj1K+xFJCfkm+W2XF/SkQhCZC+PgB4dIuELiHIj5aJLSw2a6suyt8GsY0JFwXXu4x9nUJ4SMQhCZC+PgB4dIuELiHKkbiLwgfg85Ag+gGNvsrOj7RlFihpdW+rpyiHEotpZVovUAgCESE8PEDYqhLIHAPZxafBFMCiaZEm/2uUObtJJgS3BY+zeKbqdsqihMkEAiCDyF8/IAQPgKBeyj3SHJcMlqN3F3Fm+JtwkK4c7wnwqd2ZG1iDbHllhUIBMGLED5+QAgfgcA9lHskKSJJHSJ2R8TYHx9vjHdb+CSYEtSwE+IeFQhCDyF8/IDI0C4QVEyppVRNN2EtdrwRPp5YfDw5v0AgCD6E8PEDolMVCCrGen6N9fCWJxYZGyvOfxYjZ96URaVFqpu7ED4CQWgT5u8G1ESUTvVo5lFWHV4FyKb4LvW7oNFoSMtLY9eZXQ7HxRnjuKz+ZWg0mmptr0BQXeQW5fJnyp9YJAunc08DEB0eTZg2TBU7CUZbYSJJknpPlFpK+ffcv7Sr3Q6NRlOuFaegpIBNJzdRJpWpIkuDhlhjrEPZ9IJ08kvyaRzbuBq+BYFAUJUI4eMHFI+U3Wd3029+P3X7ohsXMaLNCC6ddSmpealOj/3i+i8Y02FMtbRTIKhubvr6JvVhQCExQr5flPvGWsSUWkrJK84j2hANwMsbXmb6r9OZO3wuYzuMde7V9d8Q87jvx/HN3m9s6oo3xaPVaEkw2sbauuKzKziVc4rTU04Ta4z1+ecWCATVhxA+fuCKRldwQ+sbOJJ5BIBTOac4X3Cevef2klmYqYqejnU7qsek5KRwruAce8/t9UeTBYJqYc/ZPQC0SmyFSW9Cg4Z7utwDwN2d7yazMJOb292MKcyEQWegqKyIDHOGKnz2nJOP33tuL3nFeWocHmcWH6WulgktiQyPBOC2Drep5ZWyJWUlHEg/AMCJ7BO0N7av2i9BIBBUKUL4+AFDmIElI5eo68+sfYYXN7xIhjlD7ZRjDDFsv3u7WuaF9S8w/dfpYs6BIKRRru+fx/xMclyyzb6rmlzFVU2uUtcTTAmk5qWSWZhJE5rYHG99LxnDjJj0Jgfho7x+M/IbOtTpYFOXtXXI2mVe3H8CQfAjJjcHANYdsvWcBFdlBIJQxFxixlxqBhyvf2c4uyecCR9rN3hlnyRJLu81wGbytLPzCwSC4EUInwBA6WQzCzOF8BHUWBTLik6jIzo8usLyzu4JZU6Os4cI6/L5JfmUWEqAC8LI1bmF8BEIQgshfAIAZ52sfWesuuJWEKlWIAhWFNESb4p3y3PRXYuPvfApKCkgNVeeRxeuCydCH1HuuW2Elbj/BIKgRwifAMC6k1U6f2HxEdQ0yht6coZ9LB/rgIfOrKcxhhg0yIJKcSxIMCU4FVnO7knrugQCQfAihE8AIOb4CASeCx/F5Vw5zjrgYYY5w8aVHUCr0api6VDGoXLrUnOBmTNJN6c7tFEgEAQvQvgEANad7PmC8zbb7MvkFOVQUlZSvQ0UCKoBj4WPCy8tgLziPNLy0hzOp7yvSPgoQ8tlUhnHs447tFEgEAQvQvgEAEonKyFxLPsY4Nghxxnj1PfWT7YCQajgrfBRLDv2ouRw5mGH86nCJ7N84WPSmzCFmWzKOqtDIBAEH0L4BACGMAORejmAmqsnUZ1Wp4of0fkKQhFV+Bgrb/GBC/eStaOAuxYfwGFYzFkdAoEg+BDCJ0BQOlnrSZf2iHk+glCmskNd9slHnd1LyntlnzNXdldlresSCATBixA+AYLSyRaXFdusW6N00qLzFYQiSg4t5SGgIiqy+Di7lxRrUnn3mf35lbIg3NkFglBACJ8AwdVkZmfbhPARhCK+nNzsrJyzc7sjfKwRzgUCQfAjhE+AYN/JlhdNVjx1CkIRVzGsXGEdkLCwtND3wsfFXCPhXCAQBDdC+AQI9p2ssPgIahqeWnyiDdFoNXIXlmnOVIfK7LE+n/0wmqcWH+t2CgQCz+nSpQuXXHIJ//77r9/aIIRPgGDdySrZpF2VER2vIBTxVPhoNVqbVC7K8fWj66tldBodMYYYdb0yQ131ourZtFMgEHiGJEns3r2bXbt2ERHhmCqmuhDCJ0CwfhKtKJqs6HgFoYZ1ugl3hY91WevUEi0SWqj744xxNikp3BlSVvdZ3ZMR+ghVUIn7TyDwjvT0dIqLZWeBevXq+a0dQvgECOXNQ7DfLjpeQahhPW/GOlhnRThL99IivoXDfnfXXe1LMCWI+08gqCQpKSkA1KpVi/DwcL+1QwifAMEd4SPc2QWhinJNxxhiCNOGuX2cU+GT4J7w0aAh1hhb4bmV98K5QCCoHKdPnwagQYMGfm2HED4BgrD4CGoyns7vUVDKpxekuyV8rIe24k3x6uTo8s6tvBf3n0BQORSLjxA+AsB5kDVXZUTHKwg1Kit8jmcfp0wqA6B5QnOH/Qp6nZ7o8Gi36rIXPsLiKhBUDkX41K9fv4KSVUvICJ9jx44xceJEmjZtislkonnz5kyfPl2dSBXoeGLxySzMxCJZqqVdAkF14GkMHwX73FumMBMNohs47Hd2jEfCxygsPgJBZQmUoS73B9MDnH379mGxWJg1axYtWrTgn3/+4c477yQ/P5833njD382rkPJijdhvt0gWcotyy52fIBAEE95afBQrjJKJPd4UX6GHZLwpnuPZxyusKzo8Gp1GR5lURrwpXggfgaCSBMpQV8gIn/79+9O/f391vVmzZuzfv5+PPvooKIRPpD6SMG0YpZZSlx2yMcxIhD6CgpICMswZQvgIQgZPM7MrKPfK4YzD6nq4LpxIfST5JfnlRkAvz5UdQKPREG+K53zBeTHHRyDwAWKoqxrIzs4mIcGzjtRfaDQat0zw9p3vqsOrOJB+oOobKAgaUnNT+e7f7yizlPm7KW5T2Tk+yvwe+3uoMkNd9mWF8BEIKocy1LUpaxPpBel+a0fICp/Dhw/z3nvvcc8995RbrqioiJycHJvFX9SJrANA7cjaLstYT7A8mH6QfvP7cdNXN1VL+wTBwQM/P8ANX93AysMr/d0Ut/E0M7tCnag6NuvKvaNsd3YvuXOfOSsr3NkFAu8pLi7m7NmzALy440XOFZzzW1sCfqjrueee4/nnny+3zJYtW+jSpYu6fvr0afr378+IESO44447yj32lVdeqfD81cWb173JumPruKrxVS7LOHvqPJp1tMrbJggejmYetXkNBry1+HSu15lnrn6GA+kHCNeFM6X7FABe7/M6Kw+v5Nqm1zoc82DXB9Fr9dxxafl9A8DLvV9m6f6l9G/RX52AnWHOwCJZynWFFwgEtqSmpspvdECE5/e6Lwl44TN58mRGjRpVbpnk5GT1/enTp+nVqxfdu3dn9uzZFZ5/6tSpTJkyRV3PycmhUaNGXre3MvRt3pe+zfuWW8Za+Cih+POK8ygpK0Gv01d5GwWBjyIigmlIxlvho9FoeKHXCw7bezXtRa+mvZwe0zKxJW/1f8ut8/do3IMejXsAwrlAIKgMyjAX0YCm4jl2VUnAC5+kpCSSkpLcKpuSkkKvXr3o3Lkzn3/+OVptxU9kBoMBg8FQ2WZWG86ED8jmd3dM94LQRxmKCaYhGW+FT3ViDDNiCjNhLjUL5wKBwEOUic1EQ1R4lF8f1EPGVnv69GmuueYaGjVqxBtvvMG5c+dIS0sjLS3N303zKdbzDKyf6IPp6V5QdZRZytS8V8F0TQSD8AERRFQg8BZr4ePv+zzgLT7usmrVKg4dOsShQ4do2LChzT5JkvzUKt/jquMVHbEAbJN9Bss1IUmS1wEMq5sEUwIpuSlB890KBIGCOtQV4//7PGSEz/jx4xk/fry/m1HlCOEjKI9gtALmFueq7ujejvtLksTx48c5cOAAx48fJysri8LCQgwGA3FxcTRu3JjWrVvTuHFjmyFiTxEWH4HAO4TFR+A11u7s1h246IgFEJzCR2mnMcyISW9y+7gzZ86wbNkyVqxYwR9//MG5cxW7x9aqVYvevXszZMgQhg0bRmRkpEdtFcJHIPAOIXwEXuNqcrPoiAUQ3MLHnc7QYrGwYsUKZs+ezU8//URZ2YUgjXq9npYtW9K0aVMSEhIwGo0UFRWRkZHBsWPH2LdvH+fOnWPx4sUsXryY6OhoRo8ezaOPPkqLFi3KqfUCIpaPQOAdx48fl9/Eeh6h3dcI4RNkCOEjKA/r6yCzMBNJkio1tFMduCN8SktLmT9/Pq+88goHDlyIVN6lSxeGDRtGnz596NSpU7kemoWFhfz999/8+OOPfP311xw6dIhZs2bx8ccfM2bMGF5++eUKcwiJDO0CgeeUlZVx8uRJeSXO80ClviZkvLpqCtbCxzrktzI5VFCzsbZEFJcVU1BS4MfWuEdFwufnn3+mXbt2TJgwgQMHDhAbG8ujjz7Kv//+y5YtW3j66afp1q1bhWEpjEYjPXr04OWXX+bAgQOsXbuWAQMGYLFYmDdvHq1atWLGjBk2ViR7xFCXQOA5qamplJaWotFpAmKoSwifIEO5YIrKijibf1bdroT8F9RsgnHSuyvhk5KSwsiRIxkwYAD79+8nISGB1157jZMnTzJjxgwuvvhir+vUaDT06tWLH3/8kT///JPu3buTn5/P448/zlVXXcWhQ4ecHieEj0DgOSdOnADAmGAErRA+Ag+JCo8iTCuPUCqeMCA6YoFMUAuf/8b9JUni/fffp3Xr1nz99dfodDoefvhhjh49yuOPP050dLRP67/88sv5448/+Oyzz4iJiWHTpk107tyZH374waGsED4Cgeco83v08XLQQiF8BB5hncXdGtERCyA4hY91DJ/z588zdOhQ7r//fnJzc+natSt///03M2fOJCYmpsraoNFomDBhArt376ZHjx7k5OQwfPhwXnjhBZs4YEL4CASeo05sjpNfhPAReIwQPgJXBKPwUdqYvT+bjh07snz5cgwGA++++y4bN26kY8eO1daWxo0bs3btWh588EEApk+fzp133klpaSkghI9A4A2K8CmNtr2P/IXw6gpCrIO8aTVaLJJFdMQC4MIfcjBdF+nmdPgdPln7CZJFolWrVixevLhaBY81er2et99+m1atWjF58mQ+/fRTcnJyWLBggeqNItzZBQL3Ueb4FEUVAf4XPsLiE4RYXzSNYxsD8nCBRbL4q0mCAEEROup1EeB/0EVFRWx+fzP8ApJFYty4cfz9999+Ez3W3HvvvSxZsgS9Xs/XX3/NyJEjiQ6T5xcVlhZiLjH7uYUCQXCgWHzKYuR5qUL4CDzG+qJpHt8cAAmJnKIcfzVJECAowqdFQgub9UDk/Pnz9O3blzN/nAENTH5uMnPmzCEqKsrfTVMZPnw433//PQaDge+//54H73kQrSR3m4H83QoEgYKSTgaAWAjXhWMKcz9Ce1UghE8QYi186kXXI1Ivh90XHXHNRpIk1cKjCOJAvSYOHz5Mt27d2LBhAxqjBm6FCXdN8HeznDJw4ECWLFlCWFgYCxYswPCLAaTA/W4FgkAiMzOTvLw8eSVW/v/yd1BVIXyCEGvhk2BMUOcdiI64ZpNXnEepRZ48GMgWH8Vz6vDhwyQnJ6O/Uw8t/G/+Lo9BgwYxb948NBoN5j/M8GdgfrcCQaChWHviEuNAHxj3uRA+QYiN8DElCE8TAXDh9zfoDDSIbmCzLVD4888/6dmzJ2lpabRv3561v62lOLEYCIwOsTxuueUWXnvtNXllJaz6eZV/GyQQBAHKxObEeolAYNznQvgEIdYXTrwpXggfAWAbATkQr4l169bRu3dvMjMz6datG+vXr8cQJ6eZ0Gl0RIf7NjBhVfDoo4/S6JpGIMFbj73FkSNH/N0kgSCgUSw+sXViASF8BF5i7c4eqH9ygurHmfAJFK+udevWMXDgQPLz8+nduzerV68mPj5ebXO8Kd7v4/7uoNFo6HFvD2gI5jwzI0eOpKioyN/NEggClmPHjgEQWUueiyqEj8ArHIa6jEL4CGyFTyDN+/rtt98YPHgwhYWFDBo0iOXLl6ueW+5kZg80akXXgpvAGG1k69atPProo/5ukkAQsBw+fBgAYy0jcCE1jT8RwicIcTXHR2Ror9k4s/jkFedRXFbstzb98ccfDBw4kIKCAvr3788333yD0WhU9wej8EkwJUAcXPPwNQC8//77fP311/5skkAQsCgJf3WJOgD1ocyfCOEThLic3CwytNdolGGtBFMCsYZYNMhDR/cuv5cfD/5oU3bP2T089PND3LfiPj7c8qHT8/177l9e3vAy+cX5AHyx8wu+3/e92+3566+/6N+/P/n5+fTp04dvv/1WFT0WycIbG9/g/b/eV9scLChtPZx0mK43dwVg4sSJYr6PIKRZfmA5c3bMKbfMTwd/4tNtn6rrFotFvS+kBDnnXSDc6yJlRRASZ4wjKjyKwtJC6kTWCahhDYH/sLae6LQ6GsQ04FTOKT7b8Rnf7vuWzCcuWASnrZ3G0v1L1fU+zfpwUeJFNud7Zt0zLPl3CY1iGjGw5UDGfT8OY5iRvGl5aDXlPzPt3buXAQMGkJeXR69evfjhhx8wmS4ELdt8ajOPrX5MXW8Y3bBSn706aRTbCICDGQfhImjUvhEnd59k4sSJrFmzBq1WPE8KQgtJkrhlyS3kFefRv0V/6kbVdVru1m9vJbMwk34t+tEwpiGnT5+msLCQsLAwzJFmyAgM4SPu0CBEp9WxdNRSvr/5e2KNsWJyswBwHDb6esTXTO0xFYCswiybFAupuak2x9qvA6TmpaqvZ/LPICFhLjWTXZhdbjuOHz/OddddR0ZGBpdffjlLly4lIiLCaX2NYxvz8rUvM/2a6Z58VL8yqOUgPhz4Idc2vRZ00H1ydyIiIvj111+ZNWuWv5snEPic/JJ88orlIIRn8s44LVNYWqhandPy0oAL83uSk5PJKs4ChPARVIJeTXsx6KJBgMgYLZBRPaT+8/rr1rAbL137EjqNPLZu7eHlThZ3ZVuGOcNmf3nX2dmzZ7nuuutISUmhTZs2/Pjjj05TUCjnuKTOJUy9air1o+u79RkDAb1Oz72X3cuNrW8EoDSulFdeeQWAxx9//EJ4foEgRHDn/reeY6qUUeb3tGjRIqDm8wnhEwII4SMA5xOFNRqN06FQ5X2z+GYO++zLuCt88vLyGDBgAAcOHKBJkyasWrWKxMREt9sabFjfd5MnT+bKK68kLy+PO++8E0mS/Nw6gcB3uHP/OyujCJ/mzZsH1D0vhE8IYN0Biw635uKqY7EXxmWWMrIKswDXqS0kSfJI+JSWljJy5Ei2bdtGrVq1WL16NQ0aNPC4rcGE9feq1Wr57LPPMBqNrF69ms8//9zPrRMIfIe3wkcd6mqaTEFJARAY97wQPiGAciEVlxVjLjVXUFoQqrgrfLKLspGQBbKrZKbWeb8qEj6SJDFp0iR++uknTCYTK1asoGXLll61NZiw/14vuugi/ve//wEwZcoUzp0757e2CQS+pLIWnzqN6wCg1WiJMcRUVTPdRgifECBSH4leqwfEcFdNxl3ho7xGhUep3hnlzfnJMGc4Hb9XePXVV/n444/RarUsXryYyy67rOK2Foae8AF4+OGH6dixI9nZ2Tz99NP+appA4FO8ET6SJKnCJ65+nPxqjKvQI7Q68H8LBJXG1TwOQc2hsLRQtfa5K3zijVZ53grLFz6uOr6FCxcybdo0AN555x2GDh3qVntDyeJTUFJAYWkhADqdjvfeew+Ajz/+mG3btvmtfQKBr/BG+Jw/f57c3Fw0Gg0RtWSvzkC534XwCRHEBOeajWKR0Wl0DqZk+5QmStnyon47CJ9Cx45v/fr1TJgwAZCHdiZPnuxxe63zzgUbMYYYNUik9ffXo0cPRo8ejSRJ3H///WLenSDosbH4ugiUa91nZBZmqtaehg0bki/JQVCF8BH4FCF8ajblJfu0twba5PQyOrcUWq/nl+SrcTlA7vj27dvH8OHDKS4u5sYbb2TGjBletTdQOkJv0Gq06ndrnwz29ddfJzIyko0bN7Jw4UJ/NE8g8BneWHwOHjwIBJ4rOwjhEzII4VOzsY/hY419pnZnOb3srxv7P/LDGYfV92fOnmHw4MFkZWXRvXt3vvjiC4+jFQdaR+gtrr6/Bg0a8NRTTwHw2GOPkZubW+1tEwh8hbWVx1VOSPs4Yf/++y8ArVu3Drj7XQifEEEIn5pNeR2Lqzk+5Qkf+/VTOafkN2Ww+a3NHD58mCZNmjikonCHotIi8ksCy/TtLeXddw8//DDNmzcnNTWV1157rbqbJhD4DG8sPtbCRx1eD4DM7CCET8igXFAiQ3vNpLLCJ7c4l5KyEofzKSju7/wM2fuyiYqKYtmyZdSqVcvjtipPhho0xBpjPT4+kChP+BiNRnUI8K233iItLc2hjEAQDHgjfPbu3QsIi4+gChEWn5qNR8LHypU8zhinlisvpQUAfwFbAA0sWLCA9u3bV6qt8ab4gHBtrQwV3XfDhw+na9euFBQU8NJLL1Vn0wQCn2E/56+otKjcMsVFxWrwwjZt2qh9jjInzt8Ed68jUHHlliyoGSiixR3hY+1RpdPqVPFTXqwejgA/yW+1fbQMGTLE67YG2tNfZbD3mLNHo9GoebxmzZrF0aNHq61tAoGvsB9JsJ8DCHb3QDpYLBZiY2OpW7duwN3zQviECCKOT83GHYtPTlEOJWUlDmWdWS2U93qtHtKBrwAJ6ACWKyzqHJ3KtDWYXdkV3LG09urVi759+1JSUsL06cGThV4gANs5ea4C5ZZaSskuyr5Q5r+g5a1bt0aj0QjhI6gaxFBXzaa8jsV6OCurMMsj4dPY0BgWAoUQ3iQc/XA9aCp3nVnHEQp2XLmz2/Pyyy8DMH/+fHbv3l3l7RIIfIVybWs1WhrFNgIc738l9x9AclwynJfft2nTxqZ8oNzzQviECEL41GzK61jCtGHEGmLVcm4LnzLIXpAtW3xioOWkliTGJDqU9WVbgw1377suXbpw0003IUmSSGUhCCqsLbRJEUk22+zLxBhiqBVZy8biY70/UO55IXxCBCF8ajYVDR9ZD4Xad0LOghhmmDNgNZzfdR7CgFFQp24dlwEPvWlroHSClcGT++5///sfWq2WpUuXsmXLlqpumkDgE6ydESoKeKqmwbESPmWWMtUiFCj3vBA+IYJyQeUV59m4JQtqBhWJCWX7yZyTlFhKbLbZ/3kXlhZi/ssMm/87+HqgfvkpLnzZ1mDCE+Fz8cUXM2bMGADh4SUIGpyFv3CY7Gw1fB0XHidbiZGHupS5PxA48/qE8AkRYg2xF/IGVTDfQBB6uCt8DmXI+XP0Wj0RetvEgco5fvrlJ1guH3fL5Fug7X/nMLoOeOhRW0MgM7uCp9/HtGnT0Gg0/PDDD+zatasqmyYQ+ARPAp4mmBLQZeqgDMIMYTRp0kTdFx0ejV6nr8aWu0YInxDB2i1ZDHfVLMosZepTVUXCR0k9kWBKUHN6Wae0OHr0KBPHTAQLhHcIZ9Kjk2zO4RPhE4IWn6zCLMosZRWWb9WqFSNHjgSE1UcQHDhLalye8DGnmAGIbxyPVqu1GSoLFEJS+BQVFdGxY0c0Gg07duzwd3OqDeHSXjOx9qhw1bko8WYOZcoWH2vRobw/m3GWoUOHkpmeCfWg0W2NSIxItDm3L4VPoJi9K4P1Z7D+Hcpj2rRpAHz99dfs27evKpolEPgMVdRYW3wLXQufrGNZAEQ1jnLYFyiEpPB5/PHHqV+/vr+bUe2ICc41E2uPijBtmNMy9kNdDsLHAlve38I///xDfK14GAVJsUkO5XxxjYWSO7tepycqXO7g3R1i7tChA8OGDUOSJDW4oUAQqHg61HX28FkA9A30DvsChZATPj/99BOrVq3ijTfe8HdTqh0hfGom7nQsyr7TuacdyiaYEmAtZO3MwmAwcN+b90GsvN3agmTT8VUiQnggdoSVwZv7TnFpX7BgAUeOHKmSdgkEvsB6Tp5L4WNV5uSBkwBIdSSbsoF0v4eU8Dlz5gx33nknX3zxBREREW4dU1RURE5Ojs0SrAjhE3jsTNvJ0EVD6TOvD+O/H09BSYHP6/BE+Dhb37B0A/wuv28xoQVfZX+llgnXhasWDeuOb93RdQxZNITtqdttzvvC+hd4Y6P80HEy+yRjvxvL1tNb1f2B6NpaWby577p06UL//v0pKytzmbn96bVP8+6f7/qkja748p8vuWf5PZRaSqu0HkHwsfvMboYuGsrqw6sB2/t/77m99JnXR11+PvQzAGHmMNLPyC5d5kR5ro/1UFmgEDLCR5Ikxo8fzz333EOXLl3cPu6VV14hNjZWXRo1alSFraxaRIb2wOPDLR+y7MAy1hxdw9ydc/nlyC8+r8Md4dMysaXteoK8vnHjRp575Dl541Wwp+4eDqQfsCnTMqElWo2WZvHNuCjxIkAe1ll+YDkfbPlAPef5gvNM/3U6j69+nMLSQubvms/8XfN5968Lf97ZRdlqpvdAmuxYGbx94HjqqacAmDt3LmfOnLHZdyrnFC9teIlHVj2CRbL4pqHO2rD2KWZtncWmk5uqrA5BcPLR3x+x7MAy0s2ykGmZ2JKmcU3RaXQUlBSw5ugadTlfIIdqtqT+d60mQpYlCwhMi4/zCQEBxHPPPcfzzz9fbpktW7awceNGcnJymDp1qkfnnzp1KlOmTFHXc3Jyglb8CItP4HHefN52veC8i5Le485k4SsbXcmv437ldO5pIsMjua75dRw/fpzhw4dTXFxM74G9mfDyBLRa+VkoQh/Bdc2vA2D56OWk5qbSOLYxjWMbs2HCBubtnMfH2z62+TzKewmJTHOmum5dRmlrVHgU4bpwH34L/sPb++7KK6+ka9eu/Pnnn3z44Yc2/ZzynZVaSskuzK4ykejsNxII4MI1MaHjBMZ3HE/XBl3RaDT8dedf7D+/36F8veh6/PXVX/JK3Qsx5cpLoOwvAl74TJ48mVGjRpVbJjk5mRdffJHNmzdjMBhs9nXp0oVbb72VuXPnOj3WYDA4HBOsiAztgYfyZximDaPUUlolotSdJyqNRkPP5J7qem5uLkOGDOHcuXN07NiRH776gcjISKfH1o+uT/3oC84CPRr3IDU3lY+3few0v5fyXrkOnZUJpE6wslSUod0VGo2GRx55hJEjR/LBBx/wxBNPqEP09t9ZVQgf68SS4mFJYI9yTfRp1oerm1ytbr+03qVcWu9Sp8fM3jFbflNXfskszAxId/aAFz5JSUkkJSVVWO7dd9/lxRdfVNdPnz5Nv379+PLLL+natWtVNjFgEO7sgYfyW7RIaMG+8/uq5Lfx9ImqrKyM0aNHs3v3burWrcvSpUtdih5XlJfYVHmvrDsrEwqu7AqVsbRef/31JCcnc+zYMebNm8c999zjcK4McwbNae6bxlph7X4v+gyBPd48pCjhY6IaR5FHntMUOYFAyMzxady4Me3atVOXiy6S5yI0b96chg0b+rl11YMY6go8rIWP9XpV1OFuxzJ16lSWL1+O0Wjkhx9+8Gpo11vhE0qu7AqVue/CwsJ4+OGHAZg5cyYWi8XhXFV1P1dHHYLgxdN+JTc3l/375SGwxKYXkhkL4SOoUoTwCTxU4RMfGMLn888/Z8aMGer7yy+/3Ks63RE+isjJNGciSYHr2lpZFEurt6libr/9duLi4jh48CDLli0DhPAR+B9P79W///4bi8VC48aNqVW3lnqOQLznQ1b4JCcnI0kSHTt29HdTqg0hfAKLotIi1X29eYI8VFEVedTc7Vg2bNjA3XffDcCzzz5b4dy58lDqKiorwlwiu61aexNad3hlUhm5xbketTWYqOx9FxUVpf4ub775psO5qkX4iHmBAitKykrUe9bdYenNm+Wsxt26dVPvifSC9IC850NW+NRErPMGVaULrMA9FJGjQUNyXDLgP4vPkSNHuOGGGygpKWHEiBFMnz69UnVGhUeh0+hs6nc11OWsTCB1gpXFFw8c999/P2FhYWzYsIEtW7bYDg9WUdJha6EqQmAIrLG+5pQckBXhTPicyD6hxogKpHteCJ8QQlHmFslCTlHwBmIMFay9GZIikmy2VUU9rjqWjIwMBgwYwPnz5+ncuTNz5sxR3da9RaPROPzhW1sNUnJTKCorcmhjKGVmV/CF8GnQoAG33HILAO+9957NH48Y6hJUN4oQjjPGodPqKiwvSZIqfLp27ap6Oh7OlJMiG3QGTGGmKmqt5wjhE0IYwgxE6mXvHNGR+R93ctxUFkmSyvWUKiwsZPjw4Rw4cIBGjRqxbNkyt6OaV4SD8LH6bEqHp1BTLD7KXCZvuP/++wH48ssvSTuTpm4XwkdQ3Xh6nx4/fpyzZ8+i1+vp1KmTepzSDySYEtBoNFXTWC8QwifEEC7tgYMz4ZNTlENJWYnP6sgtzqVMKlPrscZisTBhwgQ2bNhATEwMP/74I/Xq1fNZ3eUJHyUZqkJNED6lllLyivO8Ps9ll13G5ZdfTnFxMUd+uZC/SwgfQXXj6X2qWHs6duyIyWRySIocSDF8QAifkENMcA4crDsP63Fy6/gplUUxSRvDjJj0tqbkp59+msWLFxMWFsa3335Lu3btfFYvlC980vLSbMoq+5T2hlIcH1OYCYNODoJa2ftu8uTJAJz77RzIerbqhI/V0GRuca5PBbkguPFW+HTr1s3mOKUfCLQHHSF8QgwhfAIH684jTBtGrCHWZruv67Bm9uzZvPLKKwB88skn9O7d22d1KpQnfFy1MxQtPtbznSo7EXnEiBHUqlWLsqwy+C8rQHVYfKDqJlELgg9PA43+8ccfAGqwYHsLT6Dd70L4hBhC+AQO6p/8fxP9Khvvpdw6rDqWn376iUmTJgFyrrtx48b5rD5rrP/sLZKlXEuWEssnFIUP+G6I2Wg0MmHiBHnlv7RH1SV8RJ8hUPDkPs3Ozmbbtm0A9OzZ0+lxgXa/C+ETYogM7YGDfedRFaLUvo7Nmzdz0003UVZWxvjx43n22Wd9Vpc91p8npyin3BAKGeYM8kvyKbGU2BwbKvjytx1x2wjQAMeAs7KwrMykaVfY9xGizxAoeCJ8fvvtNywWCy1atFCzJDgIH2Ng3e9C+IQYwuITOFS38NmzZw+DBg2ioKCAfv36MWvWrCr1pLD+PEo7lLkuCsYwo1ym8EKZcF04EXrfeJYFCr78bU2JJrj4v5W/oLisWA2E6UuUtqq/kegzBP/hSdiJdevWAXDttdeq24TFR1CtiAztgYMypKUMg1Sl8AnPCadfv35kZGTQrVs3lixZQnh4uM/qcYYy/m8tfGpF1iI6PFot0yy+mUOZQHNt9QW+/G0zzBmgZBLZBRRVbRiE5vHNL9QrEOCZxUcRPr169VK32c8NEsJHUKUId/bAwcHiY6wi4ZMPq19YTUpKCm3btmXFihUeZ1v3BmcWH2vXfbBNzhqq83vAt79tZmEmJIOxrhGKgd2+v5+twyAo6VREnyFQcDeZcEZGBjt37gTgmmuuUbdbx5Rz5zzVjRA+IYYY6gocqmOo60zGGZgPmacyadKkCStXriQhoXo6GbeET7yj8AklV3YFn1t8NJDcO1nesNX397P1MFeD6AY22wQCdx9S1q9fjyRJtG7dmrp169rss/bsEnF8BFWKED6BQ1ULH7PZzE8v/gSpEBUfxapVq2jQoIFPzu0O1l5d1k+Iziw+meZMt58igxGfCx+gbd+2aMI0kAp/bfmr0ud1VkdVRhUXBC/uPqT88ssvgO0wl4L1fR5o97wQPiGG6MQCgzJLmerebS98fOHOrqSiOL/nPITDU//3FBdddFGlz+sJ1tGoz+SfkbcZbYWPMoxiLjWTkptic1wo4ctQBcq9W69WPep3rQ/AisUrKn1eZ3XYCB8xL1CAnOtRuY7Lu1clSWLFCvm67N+/v8N+IXwE1Yav8gYJKod1TBvlqclX86+Kioq44YYbWLVqFVqDFm6FLl26VOqc3mAdjfpIppxiwd7ikxyXrGZxt87bE2pUhcUnwZRAuwFytO0/f/6TnBzfJR52ZqET7uwCwCY0RXlDVHv37uX48eMYjUanAVKF8BFUG8oFVlxWjLnU7OfW1FyUP6/o8Gj0Oj3gmz/HoqIibrzxRn766Sc5J87EBGjin45Fp9Wp4kfJyWMvfBJNiWrnaV0m1Kgq4dO6c2tIgmJzMYsWLar0uZ3VIazEAmuU6yBCH6GGOnDG8uXLAXmYy1niY2XCv1ajJcYQUwUt9R4hfEKMSH0keq38Rys6Mv/hbHJgZf9giouLGTFiBCtWrMBoNLJ8+XLy6+c71FOd2CcjtBc+ccY4p2VCjaoSPgmmBOgsb581a5bPrLjWcziswxIIBO5ObFaEz+DBg53uV46PN8aj1QSW1Ais1ggqjUajES7tAYB9DB+w/XMsL8qxM0pKSrj55ptZtmwZRqORZcuW0f2q7qpVz9/C51zBOXVd2RZnjEOn1anr5wvO2xwTSiifqaCkgMLSwkqdy0H4XAJavZbt27ezdevWSrfVaR2I/kIg447wycjIYOPGjQAMGjTIaRn7uY2BRJi/G1BjOHMGioqgrMz5YrG43mddRkGjkRflvdW2IUfDOZED0qpVUPeMzf4d53bz+p8zybMUEh9di7cHvU9URByTVj3Av5kHISyMKVc9zg3tR0JYmOOi0104X5CQV5zHoIWDGNZqGFO6T/H6POYSMwMXDuRg+kGXZa5sfCWLb1zstPNQnqwtkoXcolyyi7IZvng4Z/PPqmXqR9dnxegV1IqspW4rLCzk5ptvZunSpRgMBn744QdWSau47d3bANBpdDZBA6sTe6+PeNOFpzt1bpN9mRB0Z48xxKDVaOWJoeZM6kXX8/gcC3cv5Km1T3Ey+yQgf5c5RTkQAbW61OLMpjPMnj3bJ/O5nAkfJedaoD2dC2Df+X3c9t1tPH310wxtNdTn55/842S+3/c9gPowVd59+uOPP2KxWGjfvj1NmjRxWkZ56As0V3YQwqf6uOoqOOj6D9OXfKK8mf+Yw76OwEJ17Ry8JIcZ/9im1IP/LS4wGsFg8O7VaISICIiMdH/R6Sr1ffx+4nd+O/4bKTkplRI+W05v4ddjv5Zb5qs9X/HmdW86FT4mvQlTmAlzqZnMwkxWHlrJ9rTtNsen5Kaw9uhabm53MwC5ubkMGzaMdevWYTQa+e677+jbty9DXhpCcVkxAJfWu9RvkZA71+vM6iOrATkmTJtabcgvzidMG0bn+p3VMj8d+gmQ01W0rd3WL22tSrQaLfHGeNLN6WSYM7wSPp9u/5RjWccAeci6VWIrcotyAYjqFsWZTWdYvHgxb7/9ttM5FZ5gnZJA+WOySBZyinJsJq0LAoMf9v3AltNbmLdzns+FT3FZMR9s+cBhe+d6nV0e8+WXXwIwfPhwl2U61e2EBk255/EXQvhUF8qfv053YdFqbdftF/v9Wq1sbVHG+SXJ9v1/r4czj5BbmEOj2IYkKsnh/it7Mus4BeZcwiwQZoGk8Fj0Fg25BVnqNr2kIdyisbUwWVNYKC/Z2VX7nSkYDLZCKDoaYmIgNtatV/Ppg0QXQmZ+eqWaoYiZDnU68Pmwzx32X/fFdeofn31mdoUEUwIpuSk2ZYa1GsazPZ/l8dWPs+boGnV7RkYGAwYM4K+//iIqKorly5fTs2dP8ovzVdHzx+1/cGm9Syv1uSrDy71f5tYOt1JcVkyjmEaqper0lNPqH+oLvV5gVLtRFJUV0TCmIbUja/utvVVJgimBdHO61y7tyu/+/oD3ubndzSRGJKrCuahBEU2bNuXo0aN8++23jBkzplJttRbmxjAjEfoICkoKyDBnCOETgKh9QhUMRyrefBo0bLlzCxqNBr1W7/IBJTMzk5UrVwIwatQol+e9rMFlpD6SamO9DhSE8Kkudu2qtqpe+H4c83bO47U+9/P4lY/b7Bs391rWHVtHpD6S/JJ8Xrr2cVomtGTkNyPVzq9BdH1OTTklC5/SUtuluFgesisqksWPp69mMxQUQH5+xYsi5pT6Mry76a//b7GQhfRqLJrYWEhI8GyJiFA7nYYxDZ2KjVqRtRyFj934drwp3kH4tEhowaX1LqVpXFNA7txOnTrFgAED+Oeff0hISODnn3/msssuU/eDbD3p3rC7X/NeaTQa2tVu57DdurPTaDQhaeWxp7Jz65TjLmtwGUkRSYBV7KeiTB4f/zjTp0/n888/96nwUV4V4aPkVxMEDlUpfJRzxhnjVCtteXz33XeUlJTQoUMH2rRpU27ZOlF1fNJGXyOETwiiWBmcxeWw/rPdeWanwx/wrjO7LtxcWi2Eh8tLdSNJslByJohycyEnR7Y4ufFalpWJrswiz+TPyZGXkyc9a4/RyIiocC7Tgj7pb1hyI9SqBbVrq699jukIy4eCk0fJynM+kddVmgfr1/179tNtdDdSUlKoV68eq1evpm3bC8IhlJN9BjOVnSRcnidgfkk+t4y9heeee461a9dy7NgxkpOTvW6rfRTtBFMCp3JOiVg+AYoyNFmVwsfdSciLFy8Gyrf2BDpC+IQg5XXAakbmhOYOwqd5fHN2ndmFudRMYWlhuTEcqhyNBkwmeUlKqtSpHv3pIf7vj3eILYS/Rq6msRQNmZmyBUl5LW8pLYXCQqILC2kPcPYs7P3WoZ73lDcf3U5/DbxhhLA5M6Hxclkc1arFpHNnaF8AcYbV1Ck6SLMMqK2JAv6zGByGxa8vpqSghNatW/Pjjz86/MGpHmMhOEk4mKmM8CkpKyGvOM/mPACxxlg0aJCQiKkdw7XXXsuaNWuYO3cu06dP97qt9n92wqU9sFEEqS8igzuc24kHqivOnDnDmjVrALj55pt93pbqQgifEEQ1uTsJQa9c5M3jL2RkVjq75LjkSnumBCIZRZkU6qFQD2caxNK4wWXuHyxJkJcHGRm89P2jrN32DXc3vYmRtXvBuXOyCPrv9dSRHRjSs0kya9BKEklm4FiavPzHzf8t/PQJ1wEvA7z7IMQ8Q4wedOlQQgk9Gzbku5tvJv733+HwYahXT17i4kI6y3kwU5kM7dZ/aLGGWPW9VqMlzhhHZmEmGeYMJkyYwJo1a5gzZw7PPPMMWq3nHljmErOD545waQ9slN8lrziP4rJiwnW+s8J70p/MnTsXi8VC165dadYseIdEhfAJQVx1YsVlxepTpZo8sjBT7XQTTYmV9kwJRKy/B487do1GnkwdHc2uBlrWZsGw/ldB10kORd/4+SHe+fMdpnZ7jPXbvyXr5CEW9JhJR10DVRxt3PYDpw/v5FJtA8LOniMxqxhDCTyWk8Pb/51nFDDn1CkMzz3n2B6jkb4JkfyuA0uDo7DnEWjUCBo2vPBat26lPeEEnlMZ8WA9z0Kntf3tEkwJqvC5/vrriYmJ4dixY6xfv95pcsiKUO53nUanRtQVwiewsf5dMs2ZPp07467wkSSJTz6RfYbvvPNOn9XvD4TwCUFcdWLWs/etJ9Lax/RQhE+oUCnh4+Q8rjoIZXt6cRaHwnI4Wxu01/aGOh3UMus3GJm2die3d+zHysMrSUlL4fLfL+WvTdsAaHsxXNK6Nobmt0Fqqu2SlSUPuZ0u5EqAk6dh80zHhuh0UL++rRgS4qjK8YXwcXZtJZgSOJx5mAxzBhEREYwaNYrZs2fz+eefeyV81KjNpnh1jpgQPoGNfR9WJcLHWL7wWb9+PQcPHiQqKiqoh7lACJ+QxFUnZt3hKV4jzoSPs2ODmeoWPhmFrr26rMucP3IeFsJfmduIjIzkubef47GUx3g3SseTj8xwrMBshrQ0Plz6DOv+WMCtCT0ZHtkZTp2Sl5Mn4fRpOdjlyZPysmmT8w+j08kCKDnZ+dKwoRywUuA2VSl8rMtMmDCB2bNn88033/D+++8TE+NZHqRy06mIDO0BR1FpEfkl+eq6r/tmdy0+s2fPBmD06NFERUX5tA3VjejZQpCKhI+9wBHCx7PzVCR8TmSfoNRS6rRsvCkeJNi+dDtFXxZBGTRu0phlS5cR1ySOx95+jAxzBpIkOXpsmUzQtCk7mkXwTRZc0qsPw69+2rZMWRmkpdmKIfv3KSlyuePH5WX9escP40oYNWlyQRjp9R59f6GOMrfOmwmongifrl27cvHFF7Nv3z6++uor7rjjjkrXFYr3fahgfz35Q/ikpaWxZMkSIPiHuUAIn5BEuYDzivMoKStRs4M7EziFpYWk5KY4bA+VDlCSpGoXPkoyToPOgCnMZFPGUGqAb+D4nuPyhotg6x9bSUpKUudfFZUVYS41E6F3Hp233HbodNCggbx07er8gyji6MQJOHbMcTl+XI6bVJ4w0mrlYbPmzeWlRYsL75s3l+dF1TCq2uKj/AFqNBomTJjAE088weeff+6x8LF3ZbepQ7izBxyuHmB9ff7yhM/7779PcXEx3bt390nKFH8jhE8IEmu44AKbWZipRspVh7qM8USFR6HT6CiTymwu/FBza80vyVetL+C9O2ippVTOm4TrDsL+u7OPs/Pbb79x39j74ARyeuA+kNg7kaT/3PUj9ZGEacMotZTK8zkqED5eu7Nbi6Pu3R33WyxybjlrIWQvjqyF0dq1jueoXdtWDFm/T0oKunxv7lAZ4aOKESfzLJydd+zYsUybNo2NGzeyf/9+WrVq5XZdwuITXNiL0aoSPq7c2fPz8/noo48AeOSRR3xat7+otPApLCzEaPRjvBeBAzqtjlhjLFmFWWSYMxyEj/KHnGBKULNqK9vtny6DHV89LWUVZqnvXYX0dzWfx2w289RTT/H2228jSRLEAjcBjSAxIlEtr/wmZ/PPkmHOoGFMQ6f1KL9Nlbmza7UX3OddCaOzZ+HIEdnV/tAh29fz5+X9Z8/CfxmcbYiJuSCGWraEVq0uLHFxVfOZqgHl98gqzKLMUubgnVUe5T11O3sYqVevHv3792fFihXMmTOHV155xeO6rIVzqD3whBIOTio+7psr6k/mzp1LRkYGzZo1Kzc3VzDhlfCxWCy89NJL/N///R9nzpzhwIEDNGvWjGeeeYbk5GQmTpzo63YKPCTBlKAKHwX7C9xa+CiuraH25Ocr4aMcF2OIIUzr/LZxJnz++OMPJk6cyP79+wEYO34sX9T9Aoyuj1GET0Vt8VscH61W9gqrWxeuuMJxf3a2LICciaJTp+TI2du3y4s9tWvbCiFlado04OcUWQuJrMIsG1FbEdZJQ+1xdU9OmDCBFStWMHfuXF588UV0bnrpVWTxcTq/TOA3/DnUVVxczIwZsqPFww8/7PY1Fuh4JXxefPFF5s6dy+uvv24z0al9+/a89dZbQvgEAAmmBI5kHnE6v8U+RQLIVgzF4mBdNtjxtfApT2zYWILy4fi84/T4tQcgP6F/8sknDBgwgIX/W0iZVAY4Dle5M9fC78KnImJj4dJL5cUesxmOHpVF0MGDcOAA7N8vL6mpFyxFGzbYHhcWBs2aOQqi1q0rHdnbV+h1eqLDo8ktziXDnOGZ8ClnuMHVPTlkyBASExNJTU1lzZo1XHfdde7V5URkqclQK5hfJqh+qlL4KMFqwXl/8vnnn3Ps2DHq1q3L7bff7rN6/Y1XwmfevHnMnj2b3r17c88996jbO3TowL59+3zWOIH3OOssyxM+9ttCTfhEhUeRV5xXpcJHp9URGx5L9qZs+AVOmE8AcMcdd/Daa6+RkOBoaSsvl5czrINQBqzwKQ+TCdq0kRd7cnJshdD+/fL6gQNyYlvl/bJltsfVqiWfr21b29fa1Z8FPsGUoAofT/DEq0shPDycm2++mQ8//JD58+e7L3yc1BUVHuXW/DJB9eOrPswZ2YXZSMjJoO0fwgoLC3nxxRcBmDp1KhERoXNNeCV8UlJSaNGihcN2i8VCSUlJpRslqDxC+Mgon6NFQgt2pO3w2pRfkfCRJIkff/yRgncL4L8MFUlNk/hh/g9cYTccFG+K91r4WAehjDXGOi0TtMTEQJcu8mKNxSK74FsLImU5flyOir1+vaP3WVKSa0FURUM5CaYEjmcf93gehjfCB2DMmDF8+OGHfPvtt3z00UdERkZ6VZe788sE1Y+zPszX547UR2IIM9jsmz17NqdOnaJhw4bcddddPqszEPBK+LRt25YNGzbQpEkTm+1ff/01nTp18knDBJXDWYZ2+w7PWuGHqvBRPr/SaZRYSigoKSAyvOI/CGvK+2PatGkTU6dOZb3yx2sEesL9j9/vIHrsz+EQ56eCSabWQyJajdajzxC0KK7zjRpBnz62+/LzYd8+2LMH9u6Vlz175OG08+fht9/kxZrExAtWp7ZtoX176NABEipvQVPz5Hl4/5Q33GA9adoiWWx+927dutGiRQsOHTrEd999x5gxYyqsq7zgmhXNLxNUP4qIrkrhY38tZGZm8vzzzwPw9NNPh5wDk1fCZ/r06YwdO5aUlBQsFgvffvst+/fvZ968eSxfvtzXbRR4QWUtPtlF2R57pgQiymduFNMIvVZPiaWEDHOG98LnP0EpSRJr167lpZdeYt26dQAYDAbq9q7L8fbHwQS1oms5PVd5wqci4Rnw83uqm8hI6NxZXqwpKJAFkbUY2rtXnluUni7PIbKfR9SggSyArJdWrTyaVO3Ng4NFspTrWaOIKQmJ7MJsm3lAGo2GMWPG8Nxzz/HFF1+4JXxciSwRyycwUS0+8S1s1n15bvtr4X//+x8ZGRm0bds2JOfseiV8hgwZwpdffsnLL7+MRqPh2Wef5dJLL2XZsmX07dvX120UeIGzDO32bqzO/oCtJ+h66pkSiNgHbTyTf4YMcwaNYht5dB7lzyAmLIbFixfzzjvvsHnzZgDCwsK47bbbmD59Oo//9bganLCiQIfOyqh/nC5SByh/kF7H8KkpREQ4n2BtNstDZIoY+ucf2L1bthClpMjLTz9dKK/XyxOo7QVR3bpOh8u8ydCeU5SDRbIAzn/XcF04kfpI8kvyyTBnOEyAVoTPL7/8QmpqKvXquU4uXGopJbsoW26rh9ZGgX+wHuoC55Y/b1H7E6trav/+/bz33nsAzJw5k7AQTF3j9Sfq168f/fr182VbBD7E/smzzFKmxqIpz+JTGc+UQMTag8Va+HjKyVMnYS189N5H5KbnAmA0Grnjjjt47LHHaNy4sVzPbteiRt1uFBYfv2EyQceO8mJNTo4sgnbtkpfdu+XXnJwL26xJSpIFUPv2cMklssBq08Yri0958ywUEkwJqvBpTnObfc2bN+eKK65g48aNLFq0iClTprisq7x4VKE2zB0qKL9H8wT5d3dm+avsuZXf3mKxcPfdd1NaWsrAgQPdnjAfbHglfLZs2YLFYqGrXUj8P//8E51OFxIhrYMd+04su8hq9r7JtcVHee+NZ0og4ixNh7ufKzs7myVLljB//nzW/boOJMgll3r16nH33Xdzzz33UKeObZbk8qw57pQRwsdPxMTIMYms52RJkpzWQxE+ynLggDx/aO1a26jV4eE82LQWzSJBf3oTxG2WxVEF3jDu/KYJpgRO5px0eV2MHTuWjRs38sUXX5QrfMqLRyWET2Ci/B51o+qWa/mrzLmVh7GPP/6Y9evXExERwQcffFDp8wcqXtnK7rvvPk6ePOmwPSUlhfvuu6/SjaoMK1asoGvXrphMJpKSkrjhhhv82h5/Yd+JKUM1UeFRhOvCbcq4eh8KHaCnwuf06dPMnj2bIUOGUKdOHSZOnCjP4ZGAZHj0rUc5fvw406dPdxA9Sj3O3rtbRgifAEKjkZOyDhkCTz0FX34J//4LeXnw99/w2Wfw4IPQs6csnIqLqbs/hTu3wfjZf8lRr6Oj5QnUY8fCzJmwbh1kZdlU467wsS5rz4gRI9Dr9ezYsYN//vnH5Xm89R4T+Ad7S72vfyPr6yElJYXHH38cgJdeeonk5GSf1BGIeGXx2bt3L5c6CU7WqVMn9u7dW+lGecuSJUu48847efnll7n22muRJIndu3f7rT3+xP4GKS9aKzj38AqFDtD6czvzuMnJyeH333/n119/Ze3atWzdutXm+NatWzN27Fg+LvmYo9JRhlw/BH05k11tvlMXT2Suvnfrfa4mmArhEwCYTI4Tqi0WOHqUP5f9H798+wbXZsbR/Wy4HIxRmWA9f/6F8k2bysNjnTphSMglKd/19QIV35OJiYkMGjSI77//ni+++ILXXnvNaTm3hI+L+WWC6sfGUm+Mr9Dy5ynW8z4nTZpETk4OXbt25f777/fJ+QMVr4SPwWDgzJkzNGvWzGZ7amqq3yZClZaW8uCDDzJjxgybWeieJO8LJexdYJ11eNYdbTBbfEotpRSVFjndZ31jR1miIAVWfbWKfz/7l21bt7Hnnz1YLBabY7p27cqQIUMYMmQI7du3R6PRMHPGTCioWHAoQkar0RJjiHFexup7t/+zU47PLc4luzDbIVaPED4BilYLzZtTOHwwT2e/wcVJdfl30l5ITcWybSva7TsupOk4dkyeTH30KCxZQk/gHHC21l+wfARcdpm8dO4sW5JwfU9KkvynqNFoGDt2LN9//z0LFizglVdeQat1NOhXxuJjXRdASVkJxWXF6HV61Yos8B2SJJGSkwLIlnq9Tl9lFp+jfxxl6dKl6PV6Pvnkk5BJTeEKr1RK3759mTp1Kj/88AOxsXLHnJWVxbRp0/zm1bVt2zZSUlLQarV06tSJtLQ0OnbsyBtvvEHbtm1dHldUVERR0YU/zZycnCprY0lJifokptFonC7l7atov/W+UkspbAULFj6Y9QG7z+yGbVBYq5C5xrmEhYWhC9PBv4AO/v3zX4oOF6HX6yk9WQqpsG/vPg7EH0Cv1xMeHq6+KotOp/N7Tp/U3FQ6zurI2fyzUAzkAbn/vWYD6cB56PF/PUhLkyMLrmWtzTmaNm9K7169ueaaa+jduzd169a12S9JUrlxVqyxjpHkyutCKeNsnoX1hNO41+IY2XYkX970pbpNCJ/AxsaqqNGwLHcrY/4Zw+c3fc4NzzwDQPG5NO55sRsJ/x6nUxp0Pg0Xp0PtcwXwzTfyAvJQW6tW0KULg2NS2V0EedkXkgqXWkq57OPLSDQl8sttvxDZJhJM8pSDX3/9lWuvvdahfe7EC3JmbZQkias+v4oSSwmbJm7i79N/03teb/KK84jQR/DTrT9xdZOrK/flCVQskoUen/Vg06lNQNXFWcswZ0AeLH53MSBHaG7Xrp1Pzh3IeCV83nzzTa6++mqaNGmiBizcsWMHderU4YsvvvBpA93lyJEjADz33HPMnDmT5ORk3nzzTXr27MmBAwfUdAH2vPLKK2qgpqqmuLiYZ/7r/KqTB5Y9oL7fxz7GfzreoczEhY6xGj6c9SEf8qHL82o0GgwGg40Ysl683afT6SgtLbVZysrKKC0tpaioiNzcXHJzc8nJyeHkuZOcTT0L+cjCxwVp/4VT1kRpkOpIUB95aQAf3vsh/Vv0d3lsbnGuy9xa9lxS9xIaxzbm2qaOfzoK7Wq3o2lcU65o5BjcUKfVMfiiwSw/IMfDWrbfNj2DcGcPbKz/mCRJYvWR1eQU5bD68GpuaC3PNzxMJp8nHIcrLxyXVKLn62ZTueZ8JGzZIi/Hj8uxiPbtYygwFCid8z603wCXXUZW26ZI/+5gfW0wl5jZcHoDtAG2whdffOFU+NhPZrWmPHf2zMJM/jj5BwDn8s/x67Ff1dQpBSUFrD26VggfH5JekK6KHoAhFw0BrMSpjzK0ZxRkwPeQk5FD+/btmTZtmk/OG+h4JXwaNGjArl27WLBgATt37sRkMjFhwgRuueWWcuc/eMNzzz1XoTBRvMwAnnrqKW688UZATrDWsGFDvv76a+6++26nx06dOtXGCyInJ4dGjTyL8eIuYWFh3HXXXUiS5HQBXO6raL+zfSsPraSwpJAejXtwNv8sB84foFFsI9omtaW0tJTi4mJKSkrURVlPz0snMy8Tg9aAUWNU95WWltp8HkmSKCwspLCwsEq+L28wmUzUrVeXOnXq0KBBA1q0bEHb1m1p1aoVF110EZHRkZRY5LQqAxcMZP3x9RU+PSn7jWFGTHpTuWVjDDEce/BYuZawqPAoDj9w2GWZpaOWcib/DPXerIe51Iy5xKzWKyw+gY3yu5RaSm3yKjmLp9U0rin/TJInIodpwxyHi86elSdRb9nCiV+WYNi+mzr5EuzYATt2kATsAMxhoF11NdfUL+H3GFgPfPPNN3zwwQcO+ZW8SYZqvy3DnOFQJliGxYMF5fuMNcSS+kiqev/72uJzavUpOAQGo4FFixZhMDgPpxBqeD0hJzIyslryd0yePJlRo0aVWyY5OZncXDm2Shur5IcGg4FmzZpx4sQJl8caDIZq+7ENBgOzZs2qlroALvm/S9h1ZhfPjHmGnw7+xIE/DzD6ytG82ufVco/7dNun3LHsDvq07MPy0RcicUuSpFpdiouLHRZn2z0pq2wvKytDr9cTFhbmsOj1eqKjo4mJiSE6OprVp1bz6Z5PGdJpCPPHzSc6OrrC4Te9ThbntSLlyMruCh93xYY7w3/lldFoNNSOrI1Wo1Wj+grhExyYwkwYdAaKyopsBIKzCOpJEUnlJwOtXRsGDoSBA9kyoh03fXUTN0R2YUmzJ2HLFjJ+W4lu2w5ii4A//6YP0BtoDhzNy+OHa6/llpEjZe+yTp3AaHSamV1B2ZZbnEtJWYl6nzhrv7IeZ4wjqzBLCB8fo3yfiRGJNg9bvgwyuW3bNnJXyP+bz7z0TLlTQkINr4XPgQMH+PXXXzl79qzD5NBnn3220g1TSEpKIikpqcJynTt3xmAwsH//fnr06AHIc2qOHTvmkFOspmD9dFBeh1fecdZoNBr0er3PrXqVYffa3ZAHTZo3ISbG+WRiVyidSEUh+v0hNrQaLfHGeNLN6WSaM6kfXV8WQW7ONRL4ByXZZ2peKhnmDHVIwvoacxYttyISTAmggX8j8uHGG+HGG1mzpzM3fzWSlhnwQ9OpHFrxBQ32nmJ0GrwELPjzT27580/5BHo9XHopN8afoTgKGnWxyHGKrAS49fyyzMJMakdeyG5v337lMzSPb87W1K0+G3oRyLga0vaVxSc/P59bRt8CZUAreOC+Byo8JpTwSvh8/PHH3HvvvSQlJVG3bl2bp1clhUV1ExMTwz333MP06dNp1KgRTZo0YcaMGYAc46ImYn2TePKHGUxeXZURJe5+Tn9ZWRJMCaSb0y8EoSx0DEIpCDyshU95Fh9Pridn12qGOQNJCweSYN/Ay3kpejV/nz5FvYxYeDeblVot5/v2JWnbNjmD/Z9/MhwYDvDNE1DvbejWTV66d0d32WU2Fhxr4ePK4tMioQVbU7cGRV8RTLi6RnzVNz/88MMc2H8AoiFseBhR4VGVOl+w4ZXwefHFF3nppZd44oknfN2eSjFjxgzCwsIYO3YsZrOZrl27snbtWuLja+afhHWGdk862xonfCqIW+JP4WNdv/JqHYRSEHhYT0AtV/g4mWBc0TmVSdMajcalGDmTmEvnzp3ZunUrXw0dyqSffpJd5zdv5otZ93HxoSw6n9WhTU2F776TF4DwcH5poOGX+iA1WgrDasmZ7J203z5/VDD0FcFEVQqfJUuW8PHHH6PRaJCul0hMSvS7d25141Xk5szMzIC0ouj1et544w3OnDlDTk4Oq1evrlHjlvbYDHV5KXyUidOBSrVafDz4o/IF7gShFAQeijXufMF5m5QxpRbZOaAyFp8SSwn5Jfk251HeK+sWycKNN8sOHvPnz5eHs5o1g9GjmTI4jMvvgn8PbpKz07/+Otxwg5x0tbiYzkeLeOIPaD3xCTkfWdu2cPfdNPx+LU0zAEkIn+qgqoTPyZMnufPOOwEYdfcoaFYz+xOvLD4jRoxg1apV3HPPPb5uj8CHWFs0rAP5VYTScZdJZeQV5xFtiK66RlaSUB/qsq5fuLIHB8rvdjzruJp1HeRgokkRSV5dTxH6CPRaPSWWEjLNmUSFR9lct+fyz9kkIL12yLVon9SyadMmjhw5QrNmzWziUcUnNoDk+vDffEgkCY4e5fXXhhL39x5GZtUn7shpNer0MGAYcDoK0tYsxByXxpr60CImGZCvUV9lDBdULHwyCzNVy5+7lJWVMXbsWDIzM7nssssYfu9wFn23qEYOm3slfFq0aMEzzzzD5s2bad++vcNk1wceqFkTpQIV5YJOL0j3qLO190yp6cJH/bOo5g5CWHyCE8UyeCjzkM32DHOG18JHmTR9Jv8MGeYMGsU2shmiPZJ1xKa8LkZH7969Wb16NQsXLuTpp58uPx7Vf1ahbX3b8WX9PZj7Pc6DLW6FjRvh9985uHQOTQ6eo34e1P/9MErCIsvCwaysDb83tlDQdQVRV/eRU3oIKkVFwqe4rJiCkgIiwyPdPueMGTNYv349kZGRLFy4kF9zfnVaR03AK+Eze/ZsoqKiWL9+PevXr7fZp9FohPAJEJQL+mTOSTV2jTsXub1nSpO4wPWKqxaLjwcecb5E9Tr7z9IjhE9woPw+hzJshY8ioJXf09Pf0Vr4WJ/PVV233norq1evZv78+Tz11FNuxaOyuSeSkmDoUBg6lEc67WP1nmVclgIjMuvRfE8qV5yEuLx8rsuD644Avw6F8HDo2lVO3HrNNbIrfQXZ6QWOuLrXI/QRhOvCKS4rJsOc4bbw2bJlixo897333qNFixZ8+8e3TuuoCXglfI4ePerrdgiqAPsOOFwXXn7cELtjFeETqJRaSskuyga8u3mt3dnLMxsHylCXED7BgSvhU9nf0dX14Kqu66+/nnvvvZf9+/ezbds2NPU1Fdbr6mEgw5xBoR42JMP2i3LJ6wSJ4XGcH7Seac9fTfsD2dx4vhbhaefkuUMbNsCLL8pu9JdffkEIXXEFRLpvpaipuJqaoNFoiDfG21j+KiIvL49bb72V0tJSRowYwfjx423qqO65i4GAGJANYZROTAktn2BKcHtMOBg8u6znNHgzDOVswqgzhPAReIL9fadQlcLHWV0xMTEMHToUgAULFrhVrytPR2d1xUUmQocOLO/TmNE3wW+/L4CDB+GTT2DMGGjYEEpK4I8/4OWX4brrIC5OFj9Tp8LKlZBn226BTHlWQU/75oceeoiDBw/SsGFDZs2apf4H1OT+xOsAhqdOnWLp0qWcOHGC4mLbJEkzZ86sdMMElcfV+LAnxway8FFM/dHh0Q7JPt3B3mzsKpaFED4CT3D1+ygTgL2dM1ae8HFWF8Ctt97Kl19+yaJFi7h8/OXlts9ZHfbnc1b2gljKhLZ9oUULmDhRnTDNr7/C+vXy64kTsGmTvLz6Kuh0chb6a66Rlx49IDpw5xRWF+Xd6570zUuWLOHTTz9Fo9Ewf/58m9AuNbk/8Ur4rFmzhqFDh9K0aVP2799Pu3btOHbsGJIkcemll1Z8AkG1EOrCp7I3rjKXKS0vjQxzBo1jG1dJPd4ihE9wUp7wsQlC6aF3nvX1YC4xYy41uyyrXCv9+vUjMTGRtLQ0Nm2wzfRdUR0KkiS5J3zsyyhu9M2awe23y9uOHbMVQseOwV9/ycvrr0NYmDw01ru3vHTrBjUkf5SCRbL4RPhYu64/+eST9OzZ02Z/Te5PvBrqmjp1Ko888gj//PMPRqORJUuWcPLkSXr27BmQ8X1qKpH6SPTaCx53nnS0vswJU1X44satqBMxl5gpLC2sdD3e4Er4CHf2wMaVJcc6/k2kPhJDmGd/6NaT3StKEaEMVYWHhzNy5EgAfl/+O1D+nA5naVzyS/JV5whrKhQ+zkhOhvHj4fPPZWvQsWMwd64sjJo2hdJS2ZPsf/+TLUDx8dCvnyyKtm6FsrKK6whycoty1TAIniaTVZAkiQkTJpCZmUmXLl147rnnHMqo/UkNdGf3Svj8+++/jBs3DpAzjpvNZqKionjhhRd47bXXfNpAgfdoNBqbi9obi08g5+CpDuGjfH6dRkd0ePWa4JXfLrsomzJLmdfeQILqxWXQuULPAom6Oq+1gLLOr2VfRuHWW28F4J/f/oFizy0+ynt75whFJFXKOtykCdx2G3z6KRw5Ii8ffwyjRslJWs1mWLUKnngCunSBWrXkXGUffgj798vDaSGG8j1G6CMwhhkd9rvTN8+ePZs1a9ZgMplYsGAB4eGOkd5rcn/ilfCJjIykqKgIgPr163P48GF13/nz533TMoFPsL6oxVCXI2on4iJRqfVTUXWHdbe27FhnwK6JHVUwEWOIsQnkp0Q3zjRnVurPxvqeVK7X2pG1iTXEOq1L4YorriA5OZnigmI4UP4TvvWfqmJ1sM7zl2hKdCjr076iaVO44w5YtAjS0mDXLnjrLRg8WJ77k5kJ334L990HF18MjRvDuHEwbx6kpFS+/gCgovu8ou/7xIkTPPbYYwC8/PLLXHTRRV7VE8p4JXy6devGH3/8AcCgQYN45JFHeOmll7j99tvp1q2bTxsoqBxC+JRPRUN6/uwc9Dq9amWyTlZaEzuqYEKr0dqIVuu0Dr62+CSYEmzO5SyFhEajUa0+7Cq/bkUUWSQLOUU5Nueyr0t5X2XD4hoNtG8PDz0Ey5ZBerrtMFh4OJw6JYueceNkL7LWreHBB+HHHyHftadmIFPRNVLe9y1JEnfddRe5ublcccUV3H///U7PUVxWbOPtW9PwSvjMnDmTrl27AvDcc8/Rt29fvvzyS5o0acKnn37q0wYKKocQPuVT0ef0t9hQ6j2Vc4rismK/tkXgPjZiJL7qhE+8Md7mXM3jm6tlrFGFzyEIK3Tt02IMM6rDWc7mljnrT6ptWFyvlwMiPv00rFsnW3+UYbDOnWWhtG8fvPsuDBoECQnyBOnXX4cdO4JmWKyiuXzl9Vlz5sxh5cqVGAwGPv30U3Q6ndNzKFY8DRobi2FNwSuvrmbNmqnvIyIi+PDDD33WIIFvCWnh44OIysEgfI5nH/cqCKXAf7iywlSFxUdJfmpfl3VQztatW2NsZKTwZCG71+2GHuXXU1BSQIY5g2bxzWzqCteF25Szb1e1EhEBffvKC0BGhiyIVq6UlxMnYO1aeXniCahTRy7br5/8WqdO9bbXTbwd6jp9+jQPP/wwAC+88AIXX3xxhXXEGePQaZ2Lo1DGK4tPs2bNSE9Pd9ielZVlI4oE/sfagyPkhI8vLT6FgSt84EJk3gST+0EoBf7DlfBJL0h32O/pOfNL8knNS1W3OaurqKzIwd09vKMsWtYvs00z5KoeZ2EUyrP4+L2vSEiQJz7Pni17i1lbfyIi4MwZmD8fxo6Vs9F36gRPPikLo//mrAYCFc0Dc/V9P/zww2RnZ3PZZZcxZcqUcuvwd7/mb7wSPseOHaPMiVthUVERKSEywSxUqKzFx1x6wZ070FADwVXCvdtti4+fwror7TucedhmXRDYWE8gbp4gDz+VSWWcyDkh7/fimo01xqJBFr1HMo8A8vVgfa7GsY3VYJ7213RRa/nPfeeWneWmHSpP+FjXFXDCxxqNBlq1gvvvh+XLZWuQYvnp1Ekus2MHvPaaPByWkCBPoH73XThwwK9N98bis2rVKr766iu0Wi2zZ88mLKz8wZyaLnw8GupaunSp+n7lypXExl4YGywrK2PNmjUkJyf7rHGCymPdAXvS2UYbotFqtGqk2XrR9aqieZWiWtzZzf51+VR+s8MZh23WBYGNIpR1Gh21ImphDDNSWFqo/o7eXE9ajZY4YxyZhZk2Qrik7EKMHcUqczb/LJnmTBrGNATkeFRFEUXQFDgKCxcu5KmnnnJaj30sH2sLhE1cMJOtO3thaSHmErPLBKh+xWCAXr3k5dVXZevPL7/IQ2KrVsnrK1bIC8jRpwcOlJeePcHo6FZeVbgrfPJL8ikuK0YqlZg8eTIAkydPpmPHjhXWofymNTGGD3gofIYPHw7IXgJKHB8FvV5PcnIyb775ps8aJ6g83lp8FM8UxZso1IWPS3f2Qv8G+XI21CUIfKytIUqE8NO5pyv9OyaYEsgszFTPE2+MV4WPQWfAFGYi3hjP2fyzNmJe+aPTXKJBOiqxYMECpk2b5nTY1JXFJ94YbzPHRxFIUeFRhGnDKLWUkmHOoIG+gVefrVqpUwduvVVeJEl2m1+1ShZCv/0Ghw7J1p933wWTSbYKKUKoSZMqbVpF/Zpi+ZOQyDRn8sk7n3Dw4EHq1q3LCy+84JM6Qh2PhrosFgsWi4XGjRtz9uxZdd1isVBUVMT+/fsZPHhwVbVV4AXKha1BQ6zRs9n7yrF/pvxp04mm5aWpMT78QXFZMdtTt1eZO3tqbirSfx4g/u4grJ/u/NkOgWfYDwP56ndUjisoKVDXnYksgK2pWzmbfxawEi+d4jEajfz777/s2LGj3Dr2pe9jW+o2TmSfcKjLOvK0kjHcup6gQqOBSy6Bxx6TrUDp6fDdd3DnndCggRxEcflymDRJjjzdtq1c9tdf5SSsPqaiPkex/AHs3r+bl156CYA33njDZhTGFcezjvPvuX/lOmpgZnbwco7P0aNHSUpKstmWlZXli/YIfIwaa8MUbxNUzZNjJy6dSLN3mpFblMvfp/+m3pv1mLRiks/b6i6DFg7i0tmXUibJ88wqY42x/kMqKi3ip4M/UX9mfab/Oh0IHOHjal0QmLgSPvb7vT2v9bqruh5Z9QiN32pMam6qeh0nJSQxZMgQQM7YXl4d83fNp/Pszmw5vcVlXfbHBKXwsSc6GoYPlydJnzwJO3fK2eV79ACtFvbuhTfekIfNEhPhppvgs88gNdUn1buTmkb5vp+f+jxms5lrrrmG0aNHV3jutUfXkvxOMrO3zbY5T03DK+Hz2muv8eWXX6rrI0aMICEhgQYNGrBz506fNU5QeTrW7Ui/5v144PIHPD727s53kxyXjFajJbsomyOZR9ieuh2AbanbfN1Ut9l6eisAdaPqck/neyrl3m09YTSzMFP9XMqrv4VP/xb96VyvMw1jGtI6qTU3t73ZL+0QeEbf5n3p3rA7d3W+C4A7L72TpnFNaRjTkIEtB9K2dluvzjux00SaxTejYUxD+jTrw6X1LqVnck96NO7BvV3uBeD2TrfTPL45eq2eorIi9p7ba3MdKzF9Fi5c6NRJZfjFw+lQpwMNYxqqy1WNr+LKxlfSrWE3eiX3YvLlk22OqbZYPtWNRgMdOsDUqbBhA5w/D4sXy2k2atWC3FxYskTORl+/Plx6qRxn6M8/weKdVdydPifBlACH4ffVvxMWFsYHH3zglren0q9F6CNoW6stN7a50as2BjtexfGZNWsW8+fPB2D16tX88ssv/Pzzz3z11Vc89thjrFq1yqeNFHhPuC6cn8f87NWxEzpNYEKnCbT+oDX7zu+zSY7orw7OIlnIKswCYPvd26kbVbdS59NqtMSb4tXYKPafz9/Cp0FMA/6+62+/1C3wnrpRddk4caO6PqbDGMZ0GFPp845oO4IRbW0TQRvCDGyYsEFdv6H1DdzQ+gau/vxqNpzYQGZhphqFOcGUwIABA4iPjyc1NZVff/2V3r1725zv4qSL2XmP6wfYtePWOmwLKYtPecTHw803y4vFIidOXbFCjhS9ZQts3y4vL70kzyMaPBiGDoU+fWSXejdwp8+JN8TDf3+zkyZNok2bNm6dW5nLOLHTRN4d8K5bx4QiXll8UlNTadSoEQDLly9n5MiRXHfddTz++ONs2bLFpw0U+B9ngdP81cFlF2YjIc+/8ZWHk6vPV2optfnDEAiCCVcBD60ztrsa7qpMXTUGrRYuuwyeew7++kvOLTZ3LowYIQ+XnTkjJ18dNkweEhsyRE7AWs6QmLnETFGZHHagvD4na3MWnAFTtIlnn33W7Sb7+0EuUPBK+MTHx3Py5EkAfv75Z/r06QPIeUKcmU4FwY2zDjTTnOmXCc5K/daTKyuLK+GjWJbAMQu2QBDoWF/XaliG/yazKsNd33zzDWaz2fkJvKyrxlKnjjwE9tVX8pDYqlVyHKEmTaCwUJ4gfddd8pDY5ZfDiy/K84esUmko31+YNoyo8Cin1eTl5fHP4n8A6DGmB4mJiU7LOcMX0e5DAa+Ezw033MDo0aPp27cv6enpDBgwAIAdO3bQokULnzZQ4H+cCQMJiezC7GpvS1U8sVi7tFsLHyXKbqwhVg0KJxAEC64sPgBXXnkljRs3Jjc3l+XLl/u0LgFyAtW+fWV3+KNHZYHz4ouy4AF5WOyZZ6BjR9lT7P77YdUqMrPSgPIjtM+YMYOCzAKIh+b9mnvULGHxkfFK+Lz11ltMnjyZNm3asHr1aqKiZGWamprKpEn+8/YRVA3KU6J1B6qsVzdVceNau+Iq5y+1lKpuvDU1yJcguLERPnbxqLRareoF5IvhrqB2Z69qlAnSTz0lT3o+fVoe8hoyRA6MeOIEvP8+9OvHxW2v5quvYPxunZyE1Y6UlBRmzJghr/SB7FLPHj6F8JHx6jFWr9fz6KOPOmx/6KGHKtseQQDizCIC8k3UHM+eOCpLVVp87IWdCBooCGasr+vc4lybbQBjxozh1Vdf5ccffyQjI4OEhKqLgC6wol49uOMOeSkogDVrYOlSWLaMsDNnGLEXRuxNhYW1ZZf566+X3evr1WP69OmYzWZadmzJwTYHPf6+hfCRcVv4LF26lAEDBqDX621SVzhj6NChlW6YIHBQnhIzCkPT4qOcS4lSrSCEjyCYsbbCOBM+bdu25ZJLLmHnzp18/fXX3H333V7XFbLu7FVNRIRs+RkyBCwWfpj/DLs/eZmxR6NocioPVq+Wl0mTOHDJJczZvRuAO5+8k8f3PS6Ej5e4LXyGDx9OWloatWvXVlNXOEOj0YgJziGGK4uIPzo5NceMD3NWKZ8vJTdF9agAOJQphI8geKnI4gPyJOedO3eyYMECnwgfYfGpBFotB5rH8UxvONDheua1e0aOIP3dd7B5M9N37qQMGAJMmv5/FNSFvy9PlSdHuxHDx9pLtabn/HN7jo/FYqF27drqe1eLED2hh9KppeWlqSH3IfQsPoqFR0G1+NTQsO6C4Ka8yc0Kt9xyCxqNhg0bNnD8+HGf1CXwHpvfqWVLePxx2LSJnatWsfi/Mv/Taoncf4Tp62HZjFPQrBlMmQK//w7l/P9ae6nW9HmLHk9utlgsfPbZZwwePJh27drRvn17hg0bxrx589T8RoLQQunUjmQesdkeasLH/vMp68LiIwhGlOv2fMF5l/GoGjZsyDXXXAPIkZwrW1dOUY5NtniBZygWbfvf6Zn33gPg5ptv5pJz58ie9S7fXQwFYcCxY/DWW3DVVbKr/F13wU8/QXGxzTmUvjPGEFPjvVQ9Ej6SJDF06FDuuOMOUlJSaN++PW3btuXYsWOMHz+e66+/vqraKfAjyk1YWFposz3UhI/951PWhfARBCPKdWs9fOssHpUS02fBggVeP7xan9fasiDwDGf92+bNm1m2bBlarZbnn38eEhIwTbybG0ZBrcchb9E8GDMG4uLg7FnZY2zgQKhdW44rtGwZFBWJ+T1WeCR85syZw2+//caaNWvYvn07ixYtYvHixezcuZNffvmFtWvXMm/evKpqq8BPuLpRQk34uKKmm4UFwUmMIQadRmez7uxJ/8YbbyQ8PJw9e/awa9cur+rSaXXEGuTM4GK4y3uc9W9PP/00AOPGjaNVq1aAnIooKjyKgnA4c90V8MUXsuhZtQruvVf2HMvOlrcPHQq1a9PovmkM2Qd1w+Kq/XMFGh4Jn0WLFjFt2jR69erlsO/aa6/lySef9FkIdEHgEGu4kMjTmlARPhVN9BNPSIJgRKPR2Ih2V9dxXFycmrFdycHoDWKeT+Wx79/Wr1/PmjVr0Ov1DqkpHGIn6fVy0MQPP4RTp+Skqg88IA9/5eTQYOk6li6GXx7dLVuIvv9ejihdA/FI+OzatYv+/fu73D9gwACRnT0E0Wl1xBpjHbaHjPCpwKIjhI8gWLEW9eVdx8pw16JFi7x2UBHCp/Io353yu7344osATJw4keTkZJuy5X7fWi306AHvvAMnT8Lvv7N9VE9OxkBkYRksWCDHB6pVC0aPlj3HfJC6JFjwSPhkZGRQp04dl/vr1KlDppNok4Lgx7rTVDKiV3cHJ0nSBXd2Hw4/KWZjBfuM70L4CIIV62u3vOt44MCBxMXFkZKSwm+//VapukQsH++xfrDbvHkzv/zyC2FhYTzxxBMOZd0WmlotXHklP9x9DU0egtdnDIeHH4ZGjSAvDxYtghtukEXQqFGwZIkcWDGE8Uj4lJWVERbmeja4TqejtLS00o0SBB7WnWbzeDlac3V3cAUlBRSXFTu0xxdYn69FQguX+wSCYMJd4WMwGLjpppsA74e7hMWncpSUldjEW1KsPWPHjnWw9ihlwP3vO9OciaSFrE6tYeZMOH4cNm+GRx6RE6nm58OXX8JNN8kiaORIWQSFoCXII582SZIYP348BoPzrNhFRUVOtwuCH3th8MfJP8gwZyBJkstker5GucH1Wj2R+kifnjvBlKDm5mqR0ILfT/yu7qvpwb4EwYuN8KkgHtWYMWP45JNP+Oabb/jggw8wGo1e1SWEj3dYP0ge/fcoK1asQKvVMnXqVKflPf2+HTKzazTQtau8zJghJ079+mv45hvZRf7rr+UlOlpOmTFqlDyHSK/3+jMGCh5ZfMaNG0ft2rWJjY11utSuXZvbbrutqtoq8CPOLD7FZcUUlFSfSdTaDOxrseXs8wGYwkyY9Caf1iUQVBfuWnwArrrqKho1akROTg4rVqzwui4hfLwj0ywLnzhjHK++8ioAo0aNomXLlk7Lezq0WO78SI1Gzhw/YwYcOSKLoMceg8aNITdX9g4bNAjq1oW774Z168oNlhjoeGTx+fzzz6uqHYIAx/ppsVFsI/RaPSWWEjLMGUSG+9b64oqqjEPhSvgIV3ZBMGN9XVd0LWu1Wm655RZef/11FixYwI033uhRXSJDe+VQvreorCiWLFkCwLRp01yW99ji427/qdFAly7y8uqr8nDYokXw1Veyy/zs2fJSr548HDZqlGw1qibLvy/wOHKzoGZi3WkmmhL98nRXlcLHejgrOS4ZrUZbZXUJBNWFu15dCop314oVKzx2VBEWn8qhfG8Fa2Ur+o033kjbtm1dlvdUaHrVf2q1cMUV8N57kJICv/wCEyfKwRJTU2Wvse7d5bQZU6fCzp1y7rAAJ6SEz4EDBxg2bBhJSUnExMRw5ZVXsm7dOn83KySwf3IMNeFjfc6kiCS1UxHCRxDMeDLUBdChQwfat29PcXEx33zzjVd1CeHjHRnmDEiHjC3y9/fUU0+VW77KLD6uCAuD3r3hk0/gzBk5IvTo0RAZKc8JevVV6NgR2raFF16AAwe8q6caCCnhM2jQIEpLS1m7di1bt26lY8eODB48mLS0NH83Leix70D9KXyqYvjJ1ecTwkcQzHgqfMA2hYU3dQl3du/IMGfA74Ak/5d16tSp3PKe9MGSJKlziHzSp4WHw+DBcjygs2flYbDrrweDAf79F6ZPh1atoHNneOMN2VoUQISM8Dl//jyHDh3iySefpEOHDrRs2ZJXX32VgoIC9uzZ4+/mBT2uhEF1dnJqAr8qyJZu/fnijHEXhI/IzC4IYrwRPrfccgsgRw0+ceKEx3UJi493HDl6BP6L/6ukqSgPT77v3OJcyiR5MrLPvVQjImDECPj2W9kSNGcO9O8POh1s2yZPkm7UCK69Fj79FLKyfFu/F4SM8ElMTKR169bMmzeP/Px8SktLmTVrFnXq1KFz587+bl7QYzPUZQzdoa44Yxw6rU5YfAQhgTfCp3HjxvTs2ROQIzl7WleGOQOLZPGglcHDP2f/4UjmkXLL7Dm7h4W7F7L4n8Wcyz8HQG5RLt/s/YaFuxfaLIv/WczZ/LMArFuwDizQ9NKmdOvWrcK2WH/fFSWXVfpOY5ixar1UY2Nh3Dg5O3xampw+o0cPed7PunVwxx1Qp44cMHHfvqprRwWETG56jUbD6tWrGTZsGNHR0Wi1WurUqcPPP/9MXFycy+OKiops4g/l5ORUQ2uDj6SIJACiw6MxhBn84sFRlcJH+XyuXgWCYES5fjVoPHrSv/XWW1m/fj0LFixwGjXYGcoQtEWykFuU6zTNTTCTW5TL5R9fTpwxjpQpKU5DauQX59P1k67kl+QD0K95P34e8zNP/vIkH/79odPzXtv0WhYPWMze1XsB6D/BdVooa5R+sMRSQkFJQbnetX7JzJ6UJCdMvfdeeQ7QokXy0NiePXKKjLfeqr622BHwFp/nnnsOjUZT7vL3338jSRKTJk2idu3abNiwgb/++othw4YxePBgUlNTXZ7/lVdesYlF1KhRo2r8dMFDq8RWPNL9Ed647g3AP2btqrx5r2h0Bfd0vocXe8nRUh/s+iBjO4zl1g63+rwugaC6SIxI5Plrnuf1vq979KR/0003ER4ezu7du93O2G4MM2IKk+sIxeGulNwUzKVmUvNSXcYvS81LVUUPwMGMgwAcyJAn+rar3Y7eTXvTu2lvLm9wuVwm/SDvv/8+ZcVlUB8uu/Iyt9oToY8gXBcOVPx9+0X4WJOcLHt97d4te369/74cLdpPBLzFZ/LkyYwaNarcMsnJyaxdu5bly5eTmZlJTEwMAB9++CGrV69m7ty5PPnkk06PnTp1KlOmTFHXc3JyhPhxgkajUUUPhJ7wCdOG8dHgj9T1zvU7M+/6eT6vRyCobp7t+WzFheyIj49n4MCBfP/99yxYsIAOHTq4dVyCKYGU3BQyzBk0jW/qcb2BjHVf5yp+mX1/qKwrr6/1eY2BLQcCcDjjMC3ea0F6djoffPCBfMCVslh1B41GtuKdyT9DhjmDRrGu/7f8LnwUNBro0EFe/EjAC5+kpCSSkioebij4L6maVmtrxNJqtVgsrsebDQaDyxQcAteEmvARCAS2jBkzhu+//55FixbxyiuvOPStzrAWPqGGvfBxJjSUMvWj63M69zRZhVmUWcqc9l3K+4K/CihIL0CfqKekdYlH/VuCKUEVPu60XfSdMgE/1OUu3bt3Jz4+nnHjxrFz504OHDjAY489xtGjRxk0aJC/mxdyCOEjEIQ2gwYNIjY2lpMnT7Jhwwa3jgllzy574VNeGevo71mFWU77rlhjLJQBm+T18KvCQeuZ15W737dav/BSBUJI+CQlJfHzzz+Tl5fHtddeS5cuXfj999/54YcfuOSSS/zdvJCjuju44rJidexcpJEQCKoeo9Gopq1wN2N7KMfy8UT41ImqQ3R4NABn88+SUyQ7zVgLH61GS+ThSMiC+MR4CtoVOJSpCI+Fj3hoBEJI+AB06dKFlStXkp6eTk5ODps2bWLAgAH+blZIUt0dnBJ8S4OGWENoeYsIBIGKEszwm2++sfF+dYWw+PwXZNUq5Ie1+3ucMU59L0kSJb+VADBw9ECkMNkl3ZMHO3e/b6X/FA+NMiElfATVh3LD5RXnUVxWXOX1KTe2EmdHIBBUPT179qRBgwZkZWWxbNmyCsvXFOHj6oHPOjqy8l0cyjgEQIwhhjDthWm1a9eupfhUMeihzaA2gOypZQwzut0mdx9AMwqFxccaIXwEXhFrjEWDHMdCudmrEmGqFQiqH51Ox2233QbA559/XmH5UM7Q7pbFx0pgKNYVRfjY910zZsyQ33SC1LJUp2UqQgx1eYcQPgKv0Gq0qtm2Ojo5ceMKBP5h/PjxAPz888+kVJBzKZQtPtZWlYqGuqwtPoczD6vbFHbu3MnKlSvRaDXQ3XkZd3BXaIr+0xYhfAReU52dnLhxBQL/cNFFF9GjRw8sFgvz5pUf2yqUhY8nc3wSTAmqB5UzUaNYe1r0aAHx3gsfYfHxDiF8BF4jhI9AUDO4/fbbAfjss8/KzQslhI+jxedo5lF1G8Dx48dZvHgxAD1H97Qp42kCUSF8vEMIH4HXVGcnp5iZfZ5ZWCAQVMiIESOIjIzk0KFD/PHHHy7LCeHjKHxKLLLnlmIBevvttykrK6N37960vaStbZkqsPiYS8wUlhZ6df5QRQgfgddUp0u7eGIRCPxHVFQUN998MyBbfVwRqnF8LJLFxonDmdCQJOmC27iVO7tCvCmezMxMPv74YwAef/xxhwe5qhA+ym+h0+jU2EI1HSF8BF4jhroEgpqDMtz11VdfkZub67SMcn8WlhZiLjFXW9uqmuzCbCQuDPE5E3b5Jfk2lhv7virBlMBHH31Efn4+l1xyCX379nVaxhOU8vkl+S7DiqixhUzxTjPK10SE8BF4TXW6rgrhIxD4lyuuuIKLLrqI/Px8vv76a6dlosKj0GnkOFuhNNylfBYlhIez+GVKmXBdOBH6CIe+KlobzTvvvAPAY489hkajqbTwcSesiOg7HRHCR+A1wuIjENQcNBqNavX59NNPXZYJxXk+1slHXQkN6z7KmajZuWonZ8+epXHjxowcOVIta42n/ZtWo1XjBbkz70ggI4SPwGuE8BEIaha33XYbOp2OjRs3smfPHqdlQlH4KENbiRGJLuOX2fdRNukhLLB87nIApkyZgl6vtymr4E3/VpHlXfSdjgjhI/AaIXwEgppFvXr1GDp0KACzZs1yWiYUhY8zb62KhI9NX7UfTh45SXx8PBMnTlQ32+fO8qZ/q+j7Fn2nI0L4CLymujo4i2QhqzALEEn2BAJ/c/fddwPwxRdfUFBQ4LBfCB95vynMhEFnAAn4XS5z7733EhUVpR4TrgsnKvzCujfhOtwWPkYhfBSE8BF4TXV1cNYeFSKOj0DgX/r27UtycjJZWVlOJzmHoku7tXhw1e9Zu7KD1Xyn40AKGAwGHnjgAYdzW/dpwuJTPQjhI/Aa5UbKKszCIlmqrB7lxo3UR2IIM1RZPQKBoGK0Wi133nkn4Hy4q6ZYfOyFnTOBkWBKUK09EyZMoE6dOg7nVsqHacNsrD/uUtH3rQZ/FdZyFSF8BF6j3EgSEtmF2VVWj3hiEQgCi9tvv52wsDA2bdrE7t27bfaFYoZ2b4a6AAznDXAI0MCjjz7q9NzWc4K8ibNTkYVN9J+OCOEj8JpwXTiR+kigajs5ceMKBIFF3bp1GTZsGOBo9Ql1i48rYZdR6NhPnV11FoCYTjE0b97c6bmdTob2ADHU5TlC+AgqRXV0cuLGFQgCD+tJzvn5+er2UBc+7lp8jh07RsqmFACaD3EueqzLe9u/CXd2zwnzdwMEwU2CKYGTOSfL7eSOZh7llyO/MK7jOMJ14eWe7+/Tf7P8wHKbDNBbU7eqdQkEgsCgd+/eNGvWjCNHjrB48WLVTTvYhM+fp/7kRPYJRrQdQZmljDk75tCjcQ9aJbVSy1jPk8krzgMufL4T2Sf4YucX7Du/D7jw+WfOnIlkkaAZNGndxGX9wuJT/QjhI6gU7nRyj65+lG///ZYEUwI3trmx3PONXjKagxkHne6rF1XP+4YKBAKfotVqufvuu3niiSd4//33uf3224MycvPIb0ZyIvsERxsc5WD6Qe5Ydgd9mvVh9djVahlr8ZBfnG+zbeqaqSzcvVAtWy+qHufPn+eTTz6RN1xZft+l7PO2fyvv+y4pKyGnKMemnEAIH0ElcaeTO5l9EoBTOacqPN/JHLns+I7j1flDIMfEuL/r/ZVpqkAg8DETJ05k+vTp7Nixg99//52rrroqqISPRbKo/VJKTora/1j3VZIkORU+ihVI6d8GtBjAgBYDaFe7Hc8//zxms5lLOl7CTRNvYswlY1y2YVzHceQV5zG6/WivPkN537cS/wxQI04LhPARVBJ3YnYoN2RFHaG5xExhaSEA7/Z/l2hDtI9aKRAIqoLExETGjBnDJ598wnvvvWcjfHKLcykpK0Gv0/u5la7JKcpRQ3FkmDOc9lUFJQVqQlJnFh/l9dErHuXapteSn5/Pe++9B8C0qdMY2XNkuW2IM8bx1NVPef0Z7MOKaDUXpu4q/XKsIZYwrfi7VxCTmwWVwp2nO3eFj7Lf23gWAoGg+rn/ftkS++2333Ly5Ekby4K1xSEQse6T7IWPMs9Q2abX6onUR1542DNnYpEsDnNoPv30UzIyMmjWrBk33HBDlX+G8sKKKG0TMXxsEcJHUCkq8iiwTjehuHu6wj67sUAgCHw6dOhAz549KSsr4//+7//QaXXEGmKBwB/uciV8Si2lDpOYlX7JWmhkFWbZ7C8pKWHmzJmAHLcnLKzqrSzWaS/ciS0kEMJHUEkqsvhYp5tw1+Ij0lIIBMGFkoph1qxZmM3moJnn40r4wIVhInvxYB2/LCUnhaKyIkDutxYsWMDx48epXbs248ePr46PoNZt3VYFIXycI4SPoFK460oJF3LZuELcpAJBcDJ06FAaNWpEeno6ixcvDhrhY90n2Qsf+yF6h1QUwKGMQ4A8PG/SmXj55ZcB2dpjMpmqtvFWeBJNWiCEj6CSeCJ8KuoElScscZMKBMFFWFgY9913HwDvvvtu0KStsLfwWDtp2Asf63kySh91OPOwuv71119z8OBBEhISuOeee6q87dZUKHxEZnYbhPARVApfCh/xdCIQBC933HEHRqORHTt2UHqkFAgu4ePK4uPsgUwVPhmy8Ik3xPPSSy8B8PDDDxMdXb0eqcLi4xlC+AgqhfUNZx1tWcH+iaq8LO7iJhUIgpfExEQmTJgAwOFlsiAoL8xFIOCO8HFmNVGHujLloS7+hT179hAbG6t6uVUnQvh4hhA+gkqh3FAllhIKSgoc9lvfiBbJokYRdYa4SQWC4ObRRx9Fq9VycttJSAsCi4+Vp+mZ/DM2/ZPbc3wkSP0xFZBd+2NjY6u83fa4iqcmpg84RwgfQaWI0Eeg18oBypx1cq6eQJwhvLoEguCmWbNmjBgxQl75IwiEj1X77CPLlyd8lD7qRPYJOAA5x3OIiorioYcequIWO6cii4+I42OLED6CSlFRbh77JxB3hI94OhEIgpcnnnhCfvMPnDpRcZoaf2JvkbZG8fgqz+JjsVhgvbxt0qRJJCYmVmVzXSLc2T1DCB9BpSlP+NhvK8+lXdykAkHw06lTJy654hKQYN+yff5uTrmU2x8VVjzUxT7gNIQbw3nkkUeqrJ0VIeb4eIYQPoJK44nwERYfgSD0GX/feADObjjL+fPn/duYcvAk1Y6D8LEAa+X1Xrf0onbt2lXWzopw1gc7S6chkBHCR1Bp3BE+Oo3OZRkFMRFPIAgN+vTuA/VAKpHUhJ2BhnXWdaV/sn5fofD5BzgHGOHGiTdWT6Nd4KwPzi3KVYfvxLxJW4TwEVQad4RPk7gmLssAlJSVqB4VQvgIBMFNYkQi9JDfv/POO2RmBp5bu7nUrKabUPon6/cZ5gyKy4rJL5GzsVtPEI4Oi4Z1/61cAY3qNKqeRrvAWVgRpa81hZkw6asvinQwIISPoNK4cqWECzdfi4QWNuv2WGdxts7uLBAIgo94Uzy0BmpDdnY2b775pr+b5IDSF4Vpw2gc21jdbt1XKXOANGjUxKsAa75bA5lABNDV/w9r1mFFFKEmLOiuEcJHUGlcWXwkSVJvvhbx/3UmLjK0K8fGGmLRaXVOywgEguDAGGbEFG6CXvL6O++8E3BzfayHsBJNF7yxlL6qoKSA1Dw5Pk+cMU7tlwoLC3lvxn/Dd1cBBv8PJUXoIwjXhQOO3mjCld0RIXwElcaVK2VBSQHFZcVAxRYfMQlPIAgtEkwJcDFc3P5i8vLyeP311/3dJBus+xzrfic5LhmtRv5rVFJSWO9///33STmVAjFAFxz2+wNnYUVEn+oaIXwElaYiV0q9Vk/DmIaAa/dRcZMKBKFFgikBNHDrA7cCsmBIS0vzc6su4Er4JEUkqcPtSvZ1Zf+5c+f43//+B0BM/xiQY7cGxPC8/QOo6FNdI4SPoNK4E0MiMSLRaRlnZQUCQfCj3Msturaga9eumM1mXn31VT+36gLKQ5i98LFetxc+06dPJycnh06dOlG/R33AdhjMn7i0+IjM7A4EjfB56aWXuOKKK4iIiCAuLs5pmRMnTjBkyBAiIyNJSkrigQceoLi4uHobWgNxR/i4m8VdCB+BIDSwdnpQrCT/93//x8mTJ/3ZLBXrFDkuhU/mBeGzZ88eZs2aBcBbb71FYmSiui8QEENd7hM0wqe4uJgRI0Zw7733Ot1fVlbGoEGDyM/P5/fff2fx4sUsWbLEr9E0awruCB9rM2x5WdzFTSoQhAbW/UKfPn3o2bMnRUVFPPnkk35umYyroS5XFp9HHnkEi8XC9ddfT8+ePdUygdJnCeHjPkEjfJ5//nkefvhh2rdv73T/qlWr2Lt3L/Pnz6dTp0706dOHN998k48//picHNcZwQWVR7mx8kvy1cnM4LxjKSorwlxqdjiH4v3lb+8IgUDgG5R7ObMwE41Gw8yZM9FoNCxcuJA//vjDz61z/mAGsheU0l8piUvTd6azcuVK9Hq9Oklb8ZYKlD7LXvgId3bXhPm7Ab5i06ZNtGvXjvr166vb+vXrR1FREVu3bqVXr15OjysqKqKoqEhdFyLJc2KNsWjQICGRac4kxhDDtDXT+PX4r4DcQUSFRxGmDaPUUkqGOYMIfQQgdywvrH+B1UdWA+ImFQhCBeVe/m7fd6qAaNevHbt/3s2DDz7IX3/9hVbr+tlbkiRe/O1F9pzbo26LDo/m2Z7P0ii28gEDldAa9hafeGO8rZgphbWfybkpHnjgAVq0kD1UlbkzgdJn2cdTExYf14SM8ElLS6NOnTo22+Lj4wkPDy/Xk+CVV17h+eefr+rmhTRajZY4YxyZhZlkmDPYeHIjb//5trq/aVxT1d3ybP5ZMswZqpfXp9s+5eNtH18oG9+0upsvEAiqgGbxzQA4knmEI5lH5I3tIOL3CLZu3cqcOXO4/fbbXR7/7/l/efbXZx22142qy/+u/V+l22ctDBrGNCRMG0ZSRBImvUltOwAb4OyJs9SuXZunn35a3az0VU3jAqPPcjXUJeL4OOLXoa7nnnsOjUZT7vL333+7fT6NRuOwTZIkp9sVpk6dSnZ2troEysS7YMP6pjuTfwaAS+pcwqdDP+WR7o/YlLF2aVfKDmgxgEU3LmJoq6HV2WyBQFBF3ND6BhbesJB3+7/Lu/3fpU2tNhAFQ++S7/GpU6eWa2E/kyf3DfWi6vFu/3cZfNFgAM7mn/VJ++y9TtfetpaVY1YCcE+Xe5gzbA5TW01F94fssfXuu+/aONbceemdfD3ia57sERhzloQ7u/v41eIzefJkRo0aVW6Z5ORkt85Vt25d/vzzT5ttmZmZlJSUOFiCrDEYDBgMBrfqELgmwZTA4czDZJgz1Buuc73O3N7pdpsyYDsJWnnfr3k/RrUr/1oQCATBg16n55b2t6jrG09tZO+5vXQe3plty7dx4MAB/ve//zFjxgynxyt9Q7P4Ztzf9X60Gi3LDyx3Gf3dU6zd2QGuanKVui9CH8HYDmO56r6rKCuVHWdGjhxpc7xJb+KmNjf5pC2+QExudh+/Cp+kpCSSkpJ8cq7u3bvz0ksvkZqaSr169QB5wrPBYKBz584+qUPgGuubztUN50z4qJOahTlWIAhpFItETmkOb731FoMGDeLtt99mzJgxXHLJJQ7l7SfnKn2Eq5AYnlKRMJg1axYbN24kKiqKDz/8sNyRg0DAun81l5gpLC202S64QNB4dZ04cYIdO3Zw4sQJysrK2LFjBzt27CAvLw+A6667jjZt2jB27Fi2b9/OmjVrePTRR7nzzjuJiYnxc+tDH+ubTnmSshcz5Vl8xM0pEIQ21kPdAwcO5MYbb6S0tJSJEydSWlrqUN5+joqzoXJvKSkrIbc4Vz6/E6+slJQU1e3+pZdeonHjxg5lAg1nD586jY7o8Gh/NisgCRrh8+yzz9KpUyemT59OXl4enTp1olOnTuocIJ1Ox4oVKzAajVx55ZWMHDmS4cOH88Ybb/i55TUDm5uu0IXFxyiEj0BQU1H7iP/6h/fff5+4uDi2bt3qNHu7feThioKgeoJiTQLHdBMWi4Xbb7+dnJwcunbtyn333Vfp+qoD67AiaXlp6rZAt1T5g6ARPnPmzEGSJIflmmuuUcs0btyY5cuXU1BQQHp6Ou+9956Yv1NNWLtSuhIzzkzVQvgIBDUDe+FSt25dZs6cCcAzzzzDjh07bMrb9w2+FD7KOZylm3jvvfdYtWoVRqORzz77DJ3O/+ko3EEJKwKoXnSiX3VO0AgfQWDj0Ryf/574yixlZBVmOS0rEAhCC2fCZfz48QwbNoySkhJGjx6N2XwhuKkr4ZNbnEtJWUml2uKqj9q5cydPPPEEAG+++SZt2rSpVD3ViVajVR8ulYjTYu6kc4TwEfgEa1fKioSPMkaviB7r4wUCQWjiTPhoNBo++eQT6taty7///suDDz6o7rPvR2INFywa1kNV3uCsj8rKyuLGG2+kqKiIwYMHu0yPFMgo/ah9clWBLUL4CHyCN15dymt0eDR6nb66mioQCPyAq6GqpKQk5s2bh0aj4eOPP+bzzz+3Kaccp9Pq1Pk4lR3usj+3xWLhtttu4/DhwyQnJzN37tygnBvjLLmqwBEhfAQ+QbnBUnJTXLpRusolI8yxAkHoY23xtUgWm319+/blhRdeAODee+/lr7/+cpprylfzfOxj+Dz55JMsW7YMg8HAkiVLSEgITsHgkFzVGJyfo6oRwkfgE5Qb7nTuacC5G6UIsCUQ1FyUYRgJiZwix4jN06ZNY8iQIRQVFTFkyBDOp5wHbPsH5SGpsi7tqqu8MZ5Zs2apQRQ//fRTLr300kqd25/Y98Oib3WOED4Cn+DMumNvKrafnCiEj0BQczCEGdTkxM4sNlqtloULF9KpUyfOnj1LwecFkFc1Fh/l+NRNqUyaNAmAF154gVtvvbVS5/U3rqzsAluE8BH4BPvhKmfDV/aTE4XwEQhqFhUJl6ioKJYvX06DRg0gHZgLRTlFbh/vLhmFGbAHlr66FIvFwl133WWTgDRYEcLHPYTwEfiEcF04UeFR6rqzG06n1RFrjAXsJkGLcWiBoEbgjnCpX78+n3z9CUQD56DXNb04evSofLyTIKjesGPZDvgaLGUWxo0bx0cffRSUk5ntEcLHPYTwEfgMa5d0VzecO95fAoEgNHHXYhNdLxrGgy5Ox759++jWrRsbN26stMWnuLiYhx9+mL1z9gLQb2Q/Pv30U7Ta0PgrdBU0VmBLaPzagoDA2Vi8qzKZ5gtDXeLmFAhqBu4KlwxzBiRCu6nt6NixI2fPnuXqq69m65dbwYJXGdoPHDjANddcw9tvvy1v6AlPvf5U0ERmdgf7eGjiodI5QvgIfIaN8HExfGWTzNSJu6pAIAhd3B2qUvqGuvXr8ttvvzFq1CjKysr4afZPMAsObjmIJElu1ZmZmckzzzxD+/bt2bRpE7GxsUTfFg29IDEisXIfKMAQQ13uIYSPwGd4YvERQ10CQc3DXXd0674hOjqahQsXMmfOHCJjIuEMbHl1C5dddhmzZ8/m5MmTDseXlJSwYcMG7r//fho3bsyLL75IcXEx/fv3Z+u2reQ3z1fPH0rYfx77BKwCmTB/N0AQOrglfIxC+AgENRX7fH2usO8bNBoN48aNI6ljEoPvGoxmm4atW7dy9913A3LC08aNGxMWFkZ2djYHDhygpORCPq/27dszffp0brjhBrKLstUAiqGWKse6L401xBKmFX/xzhDfisBnCItP5SgrK7PprAWCYCY8PNxh0rBHc3xw7Bua1m8KAyGufxxPRDzB999/z19//UVaWhppaWk2ZePj4xk6dCijRo2iX79+qteWcu4IfQSGMIP3HzAAsZ4vKfpV1wjhI/AZngifdHO6ED7/IUkSaWlpZGVl+bspAoHP0Gq1NG3alPDwcHVbZYWPsp6ty+axxx/jiSeeIDs7m0OHDnHixAkAIiIiaNWqFU2aNHHqoh7K/Y4SViSvOC8kP5+vEMJH4DOchZa3R9l+MuckpZbS/2/vzsOauPY+gH8HCCEQDKhAgoKBehURBcEVrYituBSv2624tSq9tOJWtb1aXy3ita5XbWtRq1iBW2ld6lJtLa6AW1VEUCqIiiguIC6UfZHkvH9wMzWsAYEA+X2eJ0+ZmTMzZ45T8uXMciqsp4tUocfS0hLGxsYt4n0iRLcplUo8fvwY6enpsLW15c/p2gaf8peiVNNKpkROcQ7MjMwgkUjg5uYGNzc3jerWkoMPUHZcFHyqR8GH1JvavMcn5UUKgLK/UEQGooavXBOlUCj40NOmTct6woToNgsLCzx+/BilpaUQCAQANA8+VT3xKTQQwkRggvyX+XhR+KJON++29OBjbmSOtOw0ek1INeipLlJvanOpKz0vnZ/W5R4O1T09xsbGWq4JIfVLdYlLoVDw814NPtU9jl5dOHndlxiWH5m9pVEdF70Rv2oUfEi9efUXSVV/idF7Jiqny+GPtEyVndOqXuESRQkKSwsrLP8x4Ue4bXdDatb/hqhogODT0ofK4YMP/W6tEgUfUm/kZnIYC4zRuU3nKh+jtJXYqo3p1dWia2NVjxCiZWJDMf+7obLgsv739biafhUKpoDYUAwbiU2FMpq+C6gqLf2N8U6WTgAARwtHLdek6aLgQ+qNxEiCpFlJOO97vsoyYkMxEmcm4tiUYzj53kmEjg5tvAqSFkMul/819EAzd+/ePXAch/j4eABAVFQUOI5rkU/5cRxXbY/N84LnAIBNwzYhcWai2h9JKq/d41PUsu/xWTpwKRL8EzCp2yRtV6XJouBD6pWtxLbG18DbSGzg9YYX3rJ/C8YCurelOZo2bRo4jgPHcTAwMICtrS38/f2RlVW3v8Kbg4iICHAcV+F9MVKpFDY26j0TDx8+BMdxOH78eKPU7dV/D4FAACsrKwwZMgQ7d+6EUqms1bZCQ0NhZmbWMBVF9cFFdVPz0I5DK+3tAV5/hPaWfnOzgZ4BnCyd6PJ5NSj4EELqZNiwYUhPT8e9e/ewY8cOHDlyBDNnztR2tRrMgAEDYGBggKioKH5eUlISioqKkJOTgzt37vDzIyMjIRAI0L9//0ar36v/Hr/99hs8PT3x8ccfw9vbG6WlpY1Wj5pUFXxeKl4ipzhHrUxt1tdUSw8+pGYUfAhpQhhjyC/J18pH00EfVYRCIaRSKdq3bw8vLy/4+Pio9XAoFAp88MEHsLOzg0gkQufOnfH111+rbWPatGkYPXo01q9fD5lMhjZt2mDWrFlqb7DOzMzEyJEjIRKJYGdnh/Dw8Ap1SUtLw6hRoyAWi9GqVSuMHz8eT5484ZcHBgbCxcUFO3fuhK2tLcRiMfz9/aFQKLBu3TpIpVJYWlpi5cqVVR6vWCxGr1691IJPVFQUBgwYgAEDBlSY37t3b5iYmCAiIgIDBgyAmZkZ2rRpA29vb6SkpGjczoWFhXjnnXfQt29fvHhR9Ze96t+jXbt2cHV1xf/93//h559/xm+//YbQ0FC+3MaNG9GtWzeYmJjAxsYGM2fORF5eHl/v6dOnIzs7m+9BCgwMBADs2rULPXv2hKmpKaRSKSZNmoTMzEyNj0OlquDyZ9Gf/M/VPaau6bAXVaHgQ+g9PoQ0IQUvCyBeXfG+hsaQtzgPJoYmdVr37t27iIiI4N/XApS9xK59+/bYu3cv2rZtiwsXLuDDDz+ETCbD+PHj+XKRkZGQyWSIjIzEnTt34OPjAxcXF/j5+QEoC0cPHjzA6dOnYWhoiLlz56p94TLGMHr0aJiYmCA6OhqlpaWYOXMmfHx81MJISkoKfvvtN0RERCAlJQX/+Mc/kJqaik6dOiE6OhoXLlyAr68v3nrrLfTt27fS4/T09MRPP/2kVvdBgwZBqVQiMjIS//znP/n5kydPBgDk5+djwYIF6NatG/Lz8xEQEIAxY8YgPj6+wpAO5WVnZ8Pb2xtGRkY4deoUTExq9+8zePBgODs748CBA3zd9PT0sGnTJsjlcqSmpmLmzJlYuHAhtmzZAnd3d3z11VcICAhAcnIygLLABwAlJSVYsWIFOnfujMzMTMyfPx/Tpk3D0aNHa1WnqoKParqmMaaox4e8Lgo+hJA6+eWXXyAWi6FQKFBUVASgrDdBRSAQYPny5fy0nZ0dLly4gL1796oFH3NzcwQFBUFfXx8ODg545513cOrUKfj5+eHWrVv47bffcPHiRfTp0wcA8N1336FLly78+idPnsT169eRmprK32vz/fffo2vXroiJKRvFGygLYjt37oSpqSkcHR3h6emJ5ORkHD16FHp6eujcuTPWrl2LqKioKoPPoEGDsGrVKqSnp0MmkyE6Ohr/+te/oFQq+d6sBw8eIDU1FZ6engCAcePGqW3ju+++g6WlJRITE+Hk5FRl+z558gQ+Pj5444038OOPP6oN/VAbDg4OuH79Oj89b948/mc7OzusWLEC/v7+2LJlCwwNDSGRSMBxHKRSqdp2fH19+Z/t7e2xadMm9O7dG3l5eXw40oTqkfbyT2VpGkheJ/gwxlr8e3xIzSj4ENKEGAuMkbc4T2v7rg1PT09s3boVBQUF2LFjB27duoU5c+aolfn222+xY8cO3L9/H4WFhSgpKYGLi4tama5du0JfX5+flslkSEhIAFB2D42BgQF69uzJL3dwcFC7+TYpKQk2NjZqNxg7OjrCzMwMSUlJfPCRy+UwNTXly1hZWUFfX1+t18XKyqrayzf9+/eHoaEhoqKi4OzsjMLCQri6uoIxhpycHNy+fRu///47hEIh3N3dAZT1NH3++ee4ePEinj17xt9snJaWVm3wefvtt9GrVy/s3btXrX1qizGmdqNrZGQkVq1ahcTEROTk5KC0tBRFRUXIz8+vtkcpLi4OgYGBiI+Px4sXL9SOw9FR80ena+rxqSmQqB5Dr0vwKSwtRLGiWKP9kJaL7vEhpAnhOA4mhiZa+dT2KRATExN07NgR3bt3x6ZNm1BcXKzWw7N3717Mnz8fvr6+OH78OOLj4zF9+nSUlJSobefVy2OqNlB9qaruO6qubuW/2KuaX9l+qtt3ZYyNjdG7d29ERkYiMjISAwYMgL6+PgwMDODu7s7P79evH4yMjAAAI0eOxPPnzxEcHIxLly7h0qVLAFChHcp75513cPbsWSQmJlZbriZJSUmws7MDANy/fx8jRoyAk5MT9u/fj9jYWGzevBkA1O6rKi8/Px9eXl4Qi8XYtWsXYmJicPDgQY2Oo7yq7tFRPdFV0/t1VOvX5T0+qrBkoGcAE0HdLuuS5o96fAgh9WLZsmUYPnw4/P39YW1tjbNnz8Ld3V3tSa/a3NQLAF26dEFpaSmuXLmC3r17AwCSk5PV3nHj6OiItLQ0PHjwgO/1SUxMRHZ2ttolsfri6emJ3bt3IysrC4MGDeLne3h4ICoqCr///jumT58OAHj+/DmSkpKwbds2vPnmmwCAc+fOabSfNWvWQCwW46233kJUVFStelVUTp8+jYSEBMyfPx8AcOXKFZSWlmLDhg18T9fevXvV1jE0NFQbZgIAbt68iWfPnmHNmjV8G1+5cqXW9QFev8en/LAXtQnsr+6DHvfWXdTjQwipF4MGDULXrl2xatUqAEDHjh1x5coVHDt2DLdu3cLnn3+OmJiYWm2zc+fOGDZsGPz8/HDp0iXExsbin//8J0Sivwa2ffvtt9G9e3dMnjwZV69exeXLl/H+++/Dw8ND7RJZffH09MTt27cREREBDw8Pfr6Hhwd++eUX3Lt3j7+/x9zcHG3atMH27dtx584dnD59GgsWLNB4X+vXr8fkyZMxePBg3Lx5s9qyxcXFyMjIwKNHj3D16lWsWrUKo0aNgre3N95//30AwBtvvIHS0lJ88803uHv3Lr7//nt8++23atuRy+XIy8vDqVOn8OzZMxQUFMDW1haGhob8eocPH8aKFSs0Po5X1Rh8ahhKQrV+saK40mEvqkM3NhOAgg8hpB4tWLAAwcHBePDgAWbMmIGxY8fCx8cHffr0wfPnz+v0np+QkBDY2NjAw8MDY8eOxYcffghLS0t+OcdxOHToEMzNzTFw4EC8/fbbsLe3x549e+rz0Hj9+vWDUCgEALi5ufHze/XqBYVCAZFIxN+Iraenh927dyM2NhZOTk6YP38+/vOf/9Rqf19++SXGjx+PwYMH49atW1WWi4iIgEwmg1wux7BhwxAZGYlNmzbh559/5u8RcnFxwcaNG7F27Vo4OTkhPDwcq1evVtuOu7s7ZsyYAR8fH1hYWGDdunWwsLBAaGgo9u3bB0dHR6xZswbr16+v1XGovG6Pj4nABAI9QaXbqAkFHwIAHKvtyztauJycHEgkEmRnZ6NVq1barg5p4YqKipCamgo7Ozv+nhBCWoKqzu07L+7gb9/8DWJDMXIX5/LzpxyYgvCEcKwfsh6fuH9S7bal66V4kv8E12ZcQ3er7hrXacfVHfA74gfvTt44MvFI7Q+KNGmafn9Tjw8hhJBGo+ptySvJw0vFXzdU16Y3pq6PtNOj7ASg4EMIIaQRSYQS/mfVk1xA4wQfTe8jIi0bBR9CCCGNRl9Pnx+S4tXgounj7K+Wqe0j7ar9abIP0nJR8CGEENKoKuuxaZQenyK6uZlQ8CGEENLIygcXJVPWLvgYvealLgo+Oo2CDyGEkEZVPvjkFudCycremK0ay6s262uKgg8BKPgQQghpZOWDi+q/IgMRRAJRletVWL+Igg+pPQo+hBBCGlX5S1W1DSTU40NeBwUfQkiTce/ePXAch/j4eG1XpcmRy+X46quvtF2NelH+qazaPNEF1C34vFS8RF5Jntr6RDc1m+CzcuVKuLu7w9jYGGZmZhWWX7t2DRMnToSNjQ1EIhG6dOmCr7/+uvErSogOWL16NXr16gVTU1NYWlpi9OjRSE5ObpR9Dxo0CBzHgeM4CIVCtGvXDiNHjsSBAwcaZf8N6dVje/VTWlqKmJgYfPjhh3xZ1VAdzVH5S1W17YlRBaTaBJ9X3xn06ruEiO5pNsGnpKQE7777Lvz9/StdHhsbCwsLC+zatQs3btzAkiVLsHjxYgQFBTVyTQlp+aKjozFr1ixcvHgRJ06cQGlpKby8vJCfn98o+/fz80N6ejru3LmD/fv3w9HRERMmTFALBg2lpKSkQbevOrZXPwYGBrCwsICxsXGD7ruxVHWPT20vddXmPT6qfZgZmUFfT1/j9UjL02yCz/LlyzF//nx069at0uW+vr7YtGkTPDw8YG9vjylTpmD69Okt4q9AQpqaiIgITJs2DV27doWzszNCQkKQlpaG2NhYvoxcLseqVavg6+sLU1NT2NraYvv27WrbuXz5Mnr06AEjIyP07NkTcXFxGu3f2NgYUqkUNjY26Nu3L9auXYtt27YhODgYJ0+e5Ms9evQIPj4+/Cjpo0aNwr179/jlpaWlmDt3LszMzNCmTRssWrQIU6dOxejRo/kygwYNwuzZs7FgwQK0bdsWQ4YMAQAkJiZixIgREIvFsLKywnvvvYdnz57x6zHGsG7dOtjb20MkEsHZ2Rk//fSTxsf26kfVnqpLXXK5HAAwZswYcBzHTzcXVQYfDd+orFo/tyRXbdiL6tD9PUSl2QSfusjOzkbr1tWf5MXFxcjJyVH7EKI1jAH5+dr5vMZ4xdnZ2QBQ4f+3DRs28IFm5syZ8Pf3x82bNwEA+fn58Pb2RufOnREbG4vAwEB8+umnda7D1KlTYW5uzv+xU1BQAE9PT4jFYpw5cwbnzp2DWCzGsGHD+F6btWvXIjw8HCEhITh//jxycnIqvXwUFhYGAwMDnD9/Htu2bUN6ejo8PDzg4uKCK1euICIiAk+ePMH48eP5dZYuXYqQkBBs3boVN27cwPz58zFlyhRER0fX+RhVYmJiAJSNXJ+ens5PNxeq8HH50WWIVooQEBmgNr8mEqEEHDgA6pewjqcch8V/LCBaKeI/fXf0RYmihIIP4RlouwIN5ffff8fevXvx66+/Vltu9erVWL58eSPVipAaFBQAYrF29p2XB5iY1Ho1xhgWLFiAAQMGwMnJSW3ZiBEjMHPmTADAokWL8OWXXyIqKgoODg4IDw+HQqHAzp07YWxsjK5du+Lhw4dVXs6uiZ6eHjp16sT36OzevRt6enrYsWMHOK7sSzIkJARmZmaIioqCl5cXvvnmGyxevBhjxowBAAQFBeHo0aMVtt2xY0esW7eOnw4ICICrqytWrVrFz9u5cydsbGxw69YttGvXDhs3bsTp06fRr18/AIC9vT3OnTuHbdu2wcPDo8rj2LJlC3bs2MFPf/TRR9iwYYNaGQsLCwCAmZkZ3yPUnHS16IrWotZ4UfgCRaVFAAA9Tg/9bftrtL5q2Iusoiy8KHwBSxNLAMDh5MN4VvBMreylR5dw89lNCj6Ep9XgExgYWGPoiImJQc+ePWu13Rs3bmDUqFEICAjgu6WrsnjxYixYsICfzsnJgY2NTa32R4gumz17Nq5fv45z585VWNa9e3f+Z47jIJVKkZmZCQBISkqCs7Oz2n0rqpBQV4wxPuTExsbizp07MDU1VStTVFSElJQUZGdn48mTJ+jduze/TF9fH25ublAqlWrrlP8dFBsbi8jISIgrCamqbRcVFVX4/VNSUoIePXpUewyTJ0/GkiVL+OnKHuZo7sxF5ng4/yGeFjzl55kITNDGuI3G22gtas0HHxXVzwEDA/CB6wcYHDYYKVkpyCrMouBDeFoNPrNnz8aECROqLVPba9eJiYkYPHgw/Pz8sHTp0hrLC4VCCIXCWu2DkAZjbFzW86KtfdfSnDlzcPjwYZw5cwbt27evsFwgEKhNcxzHhwr2GpfWKqNQKHD79m306tULAKBUKuHm5obw8PAKZVU9Jqo6vaqyepmU6wlTKpUYOXIk1q5dW6GsTCbDH3/8AQD49ddf0a5dO7XlNf2+kUgk6NixY7VlWgKRQARbiW2d128tao2UrJRKg4+9uT1sJbawNLHky6huhKaR2YlWg0/btm3Rtm3betvejRs3MHjwYEydOhUrV66st+0S0mg4rk6XmxobYwxz5szBwYMHERUVBTs7u1pvw9HREd9//z0KCwshEpW9rffixYt1rlNYWBiysrIwbtw4AICrqyv27NkDS0tLtGrVqtJ1rKyscPnyZbz55psAysJTXFwcXFxcqt2Xq6sr9u/fD7lcDgODir9GHR0dIRQKkZaWVu1lrdchEAigUCgaZNvNgSYDnb5ahnp8iEqzubk5LS0N8fHxSEtLg0KhQHx8POLj45H3v7+Ob9y4AU9PTwwZMgQLFixARkYGMjIy8PTp0xq2TAiprVmzZmHXrl344YcfYGpqyv//VlhYqPE2Jk2aBD09PXzwwQdITEzE0aNHsX79eo3WLSgoQEZGBh4+fIhLly5h0aJFmDFjBvz9/eHp6Qmg7JJR27ZtMWrUKJw9exapqamIjo7Gxx9/jIcPHwIo67FavXo1fv75ZyQnJ+Pjjz9GVlZWhV6gyo7/xYsXmDhxIi5fvoy7d+/i+PHj8PX1hUKhgKmpKT799FPMnz8fYWFhSElJQVxcHDZv3oywsDCN26g6crkcp06dQkZGBrKyNH+su6Uo/xJEoIbg8793Bmn6kkTScjWb4BMQEIAePXpg2bJlyMvLQ48ePdCjRw9cuXIFALBv3z48ffoU4eHhkMlk/EfV7U0IqT9bt25FdnY2Bg0apPb/2549ezTehlgsxpEjR5CYmIgePXpgyZIllV46qkxwcDBkMhneeOMNjBkzBomJidizZw+2bNnClzE2NsaZM2dga2uLsWPHokuXLvD19UVhYSHfA7Ro0SJMnDgR77//Pvr16wexWIyhQ4fCyMio2v1bW1vj/PnzUCgUGDp0KJycnPDxxx9DIpFAT6/s1+qKFSsQEBCA1atXo0uXLhg6dCiOHDlSp96xymzYsAEnTpyAjY1NjfcNtUSVjdBeVfB59V4g6vEhHKvvC+3NXE5ODiQSCbKzs6vsHiekvhQVFSE1NRV2dnY1ftmShqdUKtGlSxeMHz8eK1as0HZ1mrWGPrc/P/05vjj7BWb3mo1vRnwDJVPC4N8GYGDI+CQDVmIrLI9ajsDoQHzk9hHiMuJw+dFl/DzhZ/y989/rvT5E+zT9/m6xj7MTQkhN7t+/j+PHj8PDwwPFxcUICgpCamoqJk2apO2qkRqUH/YiuygbDGV/x6suZ9E9PqQyzeZSFyGE1Dc9PT2EhoaiV69e6N+/PxISEnDy5El06dJF21UjNajq7c8mAhMY6htWKEPBh6hQjw8hRGfZ2Njg/Pnz2q4GqQNNxvtS/fy88Plfj7NT8NF51ONDCCGk2alN8EnNSv3rMpgRPdWl6yj4EEIIaXZU9/FoEnyyi8vGkjMWGENoQC+s1XUUfAghhDQ7qlDzZ9GfUDJltcGnqmmimyj4EEIIaXZUl6yUTImc4hx+lPZXw42ZkZnaOhR8CEDBhxBCSDMkNBDCRFA2vEtVT23p6+lDIpTw0xR8CEDBhxBCSDOlyePq1V36IrqJgg8hpEkJDAyscZBQUiY0NBRmZmbarobW1Dr40MjsBBR8CCF1cObMGYwcORLW1tbgOA6HDh2qUIYxhsDAQFhbW0MkEmHQoEG4ceOGWpmq1q2tqKgocBwHjuOgp6cHiUSCHj16YOHChUhPT3/t7WvTq8f26mfp0qXw8fHBrVu3+LK6FhorCz7lH1enHh9SHgUfQkit5efnw9nZGUFBQVWWWbduHTZu3IigoCDExMRAKpViyJAhyM3NbbB6JScn4/Hjx4iJicGiRYtw8uRJODk5ISEhocH2CZSFvNLS0gbdR3JyMtLT0/nPZ599BpFIBEtLywbdb1NGl7pIXVDwIYTU2vDhw/HFF19g7NixlS5njOGrr77CkiVLMHbsWDg5OSEsLAwFBQX44YcfAAByuRwAMGbMGHAcx0+rfP/995DL5ZBIJJgwYYJGgcnS0hJSqRSdOnXChAkTcP78eVhYWMDf31+tXEhICLp06QIjIyM4ODiojeoOABcuXICLiwuMjIzQs2dPHDp0CBzHIT4+HsBfvTDHjh1Dz549IRQKcfbsWTDGsG7dOtjb20MkEsHZ2Rk//fST2rYTExMxYsQIiMViWFlZ4b333sOzZ880PjbVRywWq13qCg0NxfLly3Ht2jW+Vyg0NLTG7TZnqt6drMKqR19/tQdI9e4fottoyApCmhDGGAoKCrSyb2NjY3AcVy/bSk1NRUZGBry8vPh5QqEQHh4euHDhAj766CPExMTA0tISISEhGDZsGPT19fmyKSkpOHToEH755RdkZWVh/PjxWLNmDVauXFmreohEIsyYMQPz589HZmYmLC0tERwcjGXLliEoKAg9evRAXFwc/Pz8YGJigqlTpyI3NxcjR47EiBEj8MMPP+D+/fuYN29epdtfuHAh1q9fD3t7e5iZmWHp0qU4cOAAtm7dir/97W84c+YMpkyZAgsLC3h4eCA9PR0eHh7w8/PDxo0bUVhYiEWLFmH8+PE4ffp0ndpaxcfHB3/88QciIiJw8uRJAIBEIqlhreZNbUiKSh5nLz9NPT4EoOBDSJNSUFAAsVislX3n5eXBxMSkXraVkZEBALCyslKbb2Vlhfv37wMALCwsAABmZmaQSqVq5ZRKJUJDQ2FqagoAeO+993Dq1KlaBx8AcHBwAADcu3cPlpaWWLFiBTZs2MD3VtnZ2SExMRHbtm3D1KlTER4eDo7jEBwcDCMjIzg6OuLRo0fw8/OrsO1///vfGDJkCICyy38bN27E6dOn0a9fPwCAvb09zp07h23btsHDwwNbt26Fq6srVq1axW9j586dsLGxwa1bt9CpU6cqj6N9+/Zq06p2VBGJRBCLxTAwMKjQni2VKsg8zHmIEkWJ2rzyZSpbRnQTBR9CSIMp34PEGNOoV0kul/OhBwBkMhkyMzPrVAfGGF+Xp0+f4sGDB/jggw/UgkxpaSnfO5KcnIzu3bvDyMiIX967d+9Kt92zZ0/+58TERBQVFfFBSKWkpAQ9evQAAMTGxiIyMrLScJuSklJt8Dl79qxam5ib02UbVZC58+IOAMBQ3xDGAuNKy5T/meguCj6ENCHGxsbIy8vT2r7ri6rHISMjAzKZjJ+fmZlZoReoMgKBQG2a4zgolco61SUpKQlAWZhSbSM4OBh9+vRRK6e61FZZOFOFp/Je7SFTbfvXX39Fu3bt1MoJhUK+zMiRI7F27doK23q1nSpjZ2en04+uV6Z88Gktal3h346CDymPgg8hTQjHcfV2uUmb7OzsIJVKceLECb63o6SkBNHR0Wpf+gKBAAqFosHqUVhYiO3bt2PgwIH8pbV27drh7t27mDx5cqXrODg4IDw8HMXFxXxguXLlSo37cnR0hFAoRFpaGjw8PCot4+rqiv3790Mul8PAoP5//RoaGjZoezY1qiCTW5KrNl1ZmaqWE91DT3URQmotLy8P8fHx/FNOqampiI+PR1paGoCyADdv3jysWrUKBw8exB9//IFp06bB2NgYkyZN4rcjl8tx6tQpZGRkICsr67XrlZmZiYyMDNy+fRu7d+9G//798ezZM2zdupUvExgYiNWrV+Prr7/GrVu3kJCQgJCQEGzcuBEAMGnSJCiVSnz44YdISkrCsWPHsH79ev64qmJqaopPP/0U8+fPR1hYGFJSUhAXF4fNmzcjLCwMADBr1iy8ePECEydOxOXLl3H37l0cP34cvr6+9RJY5HI5/2/x7NkzFBcXv/Y2m7LqnuAqX8ZAz4Af4oLoOEbUZGdnMwAsOztb21UhOqCwsJAlJiaywsJCbVelViIjIxmACp+pU6fyZZRKJVu2bBmTSqVMKBSygQMHsoSEBLXtHD58mHXs2JEZGBiwDh06MMYYW7ZsGXN2dlYr9+WXX/LLa6oPx3HM1NSUOTs7s3/9618sPT29Qvnw8HDm4uLCDA0Nmbm5ORs4cCA7cOAAv/z8+fOse/fuzNDQkLm5ubEffviBAWA3b95U219WVpbadpVKJfv6669Z586dmUAgYBYWFmzo0KEsOjqaL3Pr1i02ZswYZmZmxkQiEXNwcGDz5s1jSqWy2mMrvy/GGAsJCWESiYSfLioqYuPGjWNmZmYMAAsJCamyzRpaY5zbxaXFrE9wH2b0hRETrxKzoEtBFcqUlJYw9+/c2Qc/f9Bg9SBNg6bf3xxjVVy81lE5OTmQSCTIzs5Gq1attF0d0sIVFRUhNTUVdnZ2ajfTkqYlPDwc06dPR3Z2NkQikbar0yzQuU0am6bf33SPDyGElPPf//4X9vb2aNeuHa5du8a/a4dCDyHNHwUfQggpJyMjAwEBAfxTae+++26d3iFECGl6KPgQQkg5CxcuxMKFC7VdDUJIA6CnugghhBCiMyj4EEIIIURnUPAhpAmghytJS0PnNGmqKPgQokWqoRm0NSI7IQ2lpKRs0FDVUCCENBV0czMhWqSvrw8zMzN+AE5jY2ONBvEkpClTKpV4+vQpjI2NG2RoDkJeB52RhGiZakDPuo4+TkhTpKenB1tbWwrypMmh4EOIlnEcB5lMBktLS7x8+VLb1SGkXhgaGkJPj+6mIE0PBR9Cmgh9fX26H4IQQhoYxXFCCCGE6AwKPoQQQgjRGRR8CCGEEKIz6B6fclQv3crJydFyTQghhBCiKdX3dk0vz6TgU05ubi4AwMbGRss1IYQQQkht5ebmQiKRVLmcY/RecTVKpRKPHz+Gqalpvb5/IicnBzY2Nnjw4AFatWpVb9sl6qidGw+1deOgdm4c1M6NoyHbmTGG3NxcWFtbV/sqBerxKUdPTw/t27dvsO23atWK/qdqBNTOjYfaunFQOzcOaufG0VDtXF1Pjwrd3EwIIYQQnUHBhxBCCCE6g4JPIxEKhVi2bBmEQqG2q9KiUTs3HmrrxkHt3DionRtHU2hnurmZEEIIITqDenwIIYQQojMo+BBCCCFEZ1DwIYQQQojOoOBDCCGEEJ1BwaeRbNmyBXZ2djAyMoKbmxvOnj2r7So1a4GBgeA4Tu0jlUr55YwxBAYGwtraGiKRCIMGDcKNGze0WOPm4cyZMxg5ciSsra3BcRwOHTqktlyTdi0uLsacOXPQtm1bmJiY4O9//zsePnzYiEfR9NXUztOmTatwfvft21etDLVzzVavXo1evXrB1NQUlpaWGD16NJKTk9XK0Dn9+jRp56Z0TlPwaQR79uzBvHnzsGTJEsTFxeHNN9/E8OHDkZaWpu2qNWtdu3ZFeno6/0lISOCXrVu3Dhs3bkRQUBBiYmIglUoxZMgQfiw2Urn8/Hw4OzsjKCio0uWatOu8efNw8OBB7N69G+fOnUNeXh68vb2hUCga6zCavJraGQCGDRumdn4fPXpUbTm1c82io6Mxa9YsXLx4ESdOnEBpaSm8vLyQn5/Pl6Fz+vVp0s5AEzqnGWlwvXv3ZjNmzFCb5+DgwD777DMt1aj5W7ZsGXN2dq50mVKpZFKplK1Zs4afV1RUxCQSCfv2228bqYbNHwB28OBBflqTdv3zzz+ZQCBgu3fv5ss8evSI6enpsYiIiEare3NSvp0ZY2zq1Kls1KhRVa5D7Vw3mZmZDACLjo5mjNE53VDKtzNjTeucph6fBlZSUoLY2Fh4eXmpzffy8sKFCxe0VKuW4fbt27C2toadnR0mTJiAu3fvAgBSU1ORkZGh1uZCoRAeHh7U5q9Bk3aNjY3Fy5cv1cpYW1vDycmJ2r6WoqKiYGlpiU6dOsHPzw+ZmZn8MmrnusnOzgYAtG7dGgCd0w2lfDurNJVzmoJPA3v27BkUCgWsrKzU5ltZWSEjI0NLtWr++vTpg//+9784duwYgoODkZGRAXd3dzx//pxvV2rz+qVJu2ZkZMDQ0BDm5uZVliE1Gz58OMLDw3H69Gls2LABMTExGDx4MIqLiwFQO9cFYwwLFizAgAED4OTkBIDO6YZQWTsDTeucptHZGwnHcWrTjLEK84jmhg8fzv/crVs39OvXD2+88QbCwsL4G+aozRtGXdqV2r52fHx8+J+dnJzQs2dPdOjQAb/++ivGjh1b5XrUzlWbPXs2rl+/jnPnzlVYRud0/amqnZvSOU09Pg2sbdu20NfXr5BYMzMzK/yVQerOxMQE3bp1w+3bt/mnu6jN65cm7SqVSlFSUoKsrKwqy5Dak8lk6NChA27fvg2A2rm25syZg8OHDyMyMhLt27fn59M5Xb+qaufKaPOcpuDTwAwNDeHm5oYTJ06ozT9x4gTc3d21VKuWp7i4GElJSZDJZLCzs4NUKlVr85KSEkRHR1ObvwZN2tXNzQ0CgUCtTHp6Ov744w9q+9fw/PlzPHjwADKZDAC1s6YYY5g9ezYOHDiA06dPw87OTm05ndP1o6Z2roxWz+l6vVWaVGr37t1MIBCw7777jiUmJrJ58+YxExMTdu/ePW1Xrdn65JNPWFRUFLt79y67ePEi8/b2ZqampnybrlmzhkkkEnbgwAGWkJDAJk6cyGQyGcvJydFyzZu23NxcFhcXx+Li4hgAtnHjRhYXF8fu37/PGNOsXWfMmMHat2/PTp48ya5evcoGDx7MnJ2dWWlpqbYOq8mprp1zc3PZJ598wi5cuMBSU1NZZGQk69evH2vXrh21cy35+/sziUTCoqKiWHp6Ov8pKCjgy9A5/fpqauemdk5T8GkkmzdvZh06dGCGhobM1dVV7TE/Uns+Pj5MJpMxgUDArK2t2dixY9mNGzf45Uqlki1btoxJpVImFArZwIEDWUJCghZr3DxERkYyABU+U6dOZYxp1q6FhYVs9uzZrHXr1kwkEjFvb2+WlpamhaNpuqpr54KCAubl5cUsLCyYQCBgtra2bOrUqRXakNq5ZpW1MQAWEhLCl6Fz+vXV1M5N7Zzm/ldpQgghhJAWj+7xIYQQQojOoOBDCCGEEJ1BwYcQQgghOoOCDyGEEEJ0BgUfQgghhOgMCj6EEEII0RkUfAghhBCiMyj4EEIIIURnUPAhhDQLmZmZ+Oijj2BrawuhUAipVIqhQ4fi999/B1A2wvahQ4e0W0lCSJNnoO0KEEKIJsaNG4eXL18iLCwM9vb2ePLkCU6dOoUXL15ou2qEkGaEenwIIU3en3/+iXPnzmHt2rXw9PREhw4d0Lt3byxevBjvvPMO5HI5AGDMmDHgOI6fBoAjR47Azc0NRkZGsLe3x/Lly1FaWsov5zgOW7duxfDhwyESiWBnZ4d9+/bxy0tKSjB79mzIZDIYGRlBLpdj9erVjXXohJB6RsGHENLkicViiMViHDp0CMXFxRWWx8TEAABCQkKQnp7OTx87dgxTpkzB3LlzkZiYiG3btiE0NBQrV65UW//zzz/HuHHjcO3aNUyZMgUTJ05EUlISAGDTpk04fPgw9u7di+TkZOzatUstWBFCmhcapJQQ0izs378ffn5+KCwshKurKzw8PDBhwgR0794dQFnPzcGDBzF69Gh+nYEDB2L48OFYvHgxP2/Xrl1YuHAhHj9+zK83Y8YMbN26lS/Tt29fuLq6YsuWLZg7dy5u3LiBkydPguO4xjlYQkiDoR4fQkizMG7cODx+/BiHDx/G0KFDERUVBVdXV4SGhla5TmxsLP7973/zPUZisRh+fn5IT09HQUEBX65fv35q6/Xr14/v8Zk2bRri4+PRuXNnzJ07F8ePH2+Q4yOENA4KPoSQZsPIyAhDhgxBQEAALly4gGnTpmHZsmVVllcqlVi+fDni4+P5T0JCAm7fvg0jI6Nq96Xq3XF1dUVqaipWrFiBwsJCjB8/Hv/4xz/q9bgIIY2Hgg8hpNlydHREfn4+AEAgEEChUKgtd3V1RXJyMjp27Fjho6f316+/ixcvqq138eJFODg48NOtWrWCj48PgoODsWfPHuzfv5+eJiOkmaLH2QkhTd7z58/x7rvvwtfXF927d4epqSmuXLmCdevWYdSoUQAAuVyOU6dOoX///hAKhTA3N0dAQAC8vb1hY2ODd999F3p6erh+/ToSEhLwxRdf8Nvft28fevbsiQEDBiA8PByXL1/Gd999BwD48ssvIZPJ4OLiAj09Pezbtw9SqRRmZmbaaApCyOtihBDSxBUVFbHPPvuMubq6MolEwoyNjVnnzp3Z0qVLWUFBAWOMscOHD7OOHTsyAwMD1qFDB37diIgI5u7uzkQiEWvVqhXr3bs32759O78cANu8eTMbMmQIEwqFrEOHDuzHH3/kl2/fvp25uLgwExMT1qpVK/bWW2+xq1evNtqxE0LqFz3VRQjRaZU9DUYIabnoHh9CCCGE6AwKPoQQQgjRGXRzMyFEp9HVfkJ0C/X4EEIIIURnUPAhhBBCiM6g4EMIIYQQnUHBhxBCCCE6g4IPIYQQQnQGBR9CCCGE6AwKPoQQQgjRGRR8CCGEEKIzKPgQQgghRGf8P7uFChSCet8zAAAAAElFTkSuQmCC",
      "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"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test set accuracy with Logistic Regression: 0.94\n",
      "Test set accuracy with SVM: 0.63\n",
      "Test set accuracy with Decision Trees: 0.90\n",
      "Test set accuracy Logistic Regression with scaled data: 0.96\n",
      "Test set accuracy SVM with scaled data: 0.96\n",
      "Test set accuracy with Decision Trees and scaled data: 0.89\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:460: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
      "\n",
      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
      "Please also refer to the documentation for alternative solver options:\n",
      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
      "  n_iter_i = _check_optimize_result(\n"
     ]
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from sklearn.model_selection import  train_test_split \n",
    "from sklearn.datasets import load_breast_cancer\n",
    "from sklearn.svm import SVC\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "\n",
    "# Load the data\n",
    "cancer = load_breast_cancer()\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
    "print(X_train.shape)\n",
    "print(X_test.shape)\n",
    "# Logistic Regression\n",
    "logreg = LogisticRegression(solver='lbfgs')\n",
    "logreg.fit(X_train, y_train)\n",
    "print(\"Test set accuracy with Logistic Regression: {:.2f}\".format(logreg.score(X_test,y_test)))\n",
    "# Support vector machine\n",
    "svm = SVC(gamma='auto', C=100)\n",
    "svm.fit(X_train, y_train)\n",
    "print(\"Test set accuracy with SVM: {:.2f}\".format(svm.score(X_test,y_test)))\n",
    "# Decision Trees\n",
    "deep_tree_clf = DecisionTreeClassifier(max_depth=None)\n",
    "deep_tree_clf.fit(X_train, y_train)\n",
    "print(\"Test set accuracy with Decision Trees: {:.2f}\".format(deep_tree_clf.score(X_test,y_test)))\n",
    "#now scale the data\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler()\n",
    "scaler.fit(X_train)\n",
    "X_train_scaled = scaler.transform(X_train)\n",
    "X_test_scaled = scaler.transform(X_test)\n",
    "# Logistic Regression\n",
    "logreg.fit(X_train_scaled, y_train)\n",
    "print(\"Test set accuracy Logistic Regression with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
    "# Support Vector Machine\n",
    "svm.fit(X_train_scaled, y_train)\n",
    "print(\"Test set accuracy SVM with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
    "# Decision Trees\n",
    "deep_tree_clf.fit(X_train_scaled, y_train)\n",
    "print(\"Test set accuracy with Decision Trees and scaled data: {:.2f}\".format(deep_tree_clf.score(X_test_scaled,y_test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Another example, the moons again"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "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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",
      "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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