Morten Hjorth-Jensen
2167 lines
426 KiB
Plaintext
2167 lines
426 KiB
Plaintext
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"# Decision trees, overarching aims\n",
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"\n",
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"\n",
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"We start here with the most basic algorithm, the so-called decision\n",
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"tree. With this basic algorithm we can in turn build more complex\n",
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"networks, spanning from homogeneous and heterogenous forests (bagging,\n",
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"random forests and more) to one of the most popular supervised\n",
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"algorithms nowadays, the extreme gradient boosting, or just\n",
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"XGBoost. But let us start with the simplest possible ingredient.\n",
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"\n",
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"Decision trees are supervised learning algorithms used for both,\n",
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"classification and regression tasks.\n",
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"\n",
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"\n",
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"The main idea of decision trees\n",
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"is to find those descriptive features which contain the most\n",
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"**information** regarding the target feature and then split the dataset\n",
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"along the values of these features such that the target feature values\n",
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"for the resulting underlying datasets are as pure as possible.\n",
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"\n",
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"The descriptive features which reproduce best the target/output features are normally said\n",
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"to be the most informative ones. The process of finding the **most\n",
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"informative** feature is done until we accomplish a stopping criteria\n",
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"where we then finally end up in so called **leaf nodes**. \n",
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"\n",
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"## Basics of a tree\n",
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"\n",
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"A decision tree is typically divided into a **root node**, the **interior nodes**,\n",
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"and the final **leaf nodes** or just **leaves**. These entities are then connected by so-called **branches**.\n",
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"\n",
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"The leaf nodes\n",
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"contain the predictions we will make for new query instances presented\n",
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"to our trained model. This is possible since the model has \n",
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"learned the underlying structure of the training data and hence can,\n",
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"given some assumptions, make predictions about the target feature value\n",
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"(class) of unseen query instances.\n",
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"\n",
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"\n",
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"## General Features\n",
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"\n",
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"The overarching approach to decision trees is a top-down approach.\n",
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"\n",
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"* A leaf provides the classification of a given instance.\n",
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"\n",
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"* A node specifies a test of some attribute of the instance.\n",
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"\n",
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"* A branch corresponds to a possible values of an attribute.\n",
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"\n",
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"* An instance is classified by starting at the root node of the tree, testing the attribute specified by this node, then moving down the tree branch corresponding to the value of the attribute in the given example.\n",
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"\n",
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"This process is then repeated for the subtree rooted at the new\n",
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"node.\n",
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"\n",
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"\n",
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"\n",
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"In simplified terms, the process of training a decision tree and\n",
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"predicting the target features of query instances is as follows:\n",
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"\n",
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"1. Present a dataset containing of a number of training instances characterized by a number of descriptive features and a target feature\n",
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"\n",
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"2. Train the decision tree model by continuously splitting the target feature along the values of the descriptive features using a measure of information gain during the training process\n",
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"\n",
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"3. Grow the tree until we accomplish a stopping criteria create leaf nodes which represent the *predictions* we want to make for new query instances\n",
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"\n",
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"4. Show query instances to the tree and run down the tree until we arrive at leaf nodes\n",
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"\n",
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"Then we are essentially done!"
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"text": [
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"2nd degree coefficients:\n",
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"zero power: 0.9984624951418368\n",
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"first power: 0.19520657797805885\n",
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"second power: -7.848309904755701e-05\n"
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]
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
},
|
||
{
|
||
"data": {
|
||
"image/png": 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ionRcSkqKOH78eNHLy0t0cXER+/btKx46dEgEIH7yySdSvsLRTHfu3Cnx+t9++63YqVMn0dXVVXR2dhZDQ0PFMWPGSKOszp07J44cOVIMDQ0VnZ2dRU9PT/GBBx4Qo6KipHP89ttv4oABA8SGDRtK79dHHnlE3Ldvn5SnpNFMoiiK+/btE/v06SNdv3PnzuKvv/5qkqe032Hh7zs6OrqUO09keZwBmIioGn3//fd46qmnsH//fnTt2tXaxSGqkxjMEBFZyA8//ICbN2+iTZs2kMlkOHToED766CN06NChxpdHIKpP2GeGiMhC3N3dsWHDBsybNw9ZWVlQqVQYN24c5s2bZ+2iEdVprJkhIiIim8ZJ84iIiMimMZghIiIim8ZghoiIiGxane8ArNfrcevWLbi7u3OyJyIiIhshiiIyMjIQEBBQ7qSTdT6YuXXrFoKCgqxdDCIiIqqE69evl7sYb50PZtzd3QEYboaHh4eVS0NERETmSE9PR1BQkPQ5XpY6H8wUNi15eHgwmCEiIrIx5nQRYQdgIiIismkMZoiIiMimMZghIiIim1bn+8yYS6fToaCgwNrFIBvm4OBQ7vBBIiKyvHofzIiiiMTERKSmplq7KGTjZDIZgoOD4eDgYO2iEBHVK/U+mCkMZPz8/ODi4sKJ9ahSCidnVKvVaNSoEd9HREQ1qF4HMzqdTgpkfHx8rF0csnG+vr64desWtFot7O3trV0cIqJ6o1438Bf2kXFxcbFySaguKGxe0ul0Vi4JEVH9Uq+DmUJsEiBL4PuIiMg6GMwQERGRTWMwU4f06tULU6dOtXYxiIiIahSDmXpqz549EASBQ9KJiMjm1evRTERERFQ5WelZ+Hnxz0g8m4gGTRpgzEdjrFYW1szYqKysLIwZMwZubm5QqVRYsmSJyf7vvvsOHTt2hLu7O5RKJUaNGoWkpCQAwJUrV9C7d28AgEKhgCAIGDduHABg+/bt6N69O7y8vODj44OBAwciISGhRl8bERHVfutfWI+A9wMQ/r9wyFbKoNForFYWBjM26o033kB0dDS2bNmCnTt3Ys+ePYiNjZX25+fn4/3338eJEyewdetWXL58WQpYgoKC8OOPPwIAzp8/D7VajU8++QSAIUh69dVXERMTgz///BMymQxDhw6FXq+v8ddIRES1l/a0VnrumeOJuLg4q5WFzUwWotFoEBsbi4iICCgUimq9VmZmJlatWoW1a9eib9++AIA1a9YgMDBQyjNhwgTpeUhICD799FM88MADyMzMhJubG7y9vQEAfn5+8PLykvI+/vjjJtdatWoV/Pz8cObMGbRu3boaXxUREdkSB6Fo6ZavmnyFdeHrrFYW1sxYgEajQVhYGPr27YuwsLBqr2pLSEhAfn4+unTpIqV5e3ujRYsW0vaxY8cwePBgNG7cGO7u7ujVqxcA4Nq1a+Wee9SoUQgJCYGHhweCg4PNOo6IiOoXmb4ohPjs98+q/Yt8mWWx2pXrkNjYWKjVagCAWq2u9qo2URTL3J+VlYV+/frBzc0N3333HWJiYrBlyxYAhuansjz22GNITk7GN998g8OHD+Pw4cNmHUdERPWLoCuaKNTP38+KJWEwYxERERFQqVQAgICAAISHh1fr9Zo2bQp7e3scOnRIStNoNPj3338BAOfOncPdu3excOFC9OjRAy1btpQ6/xYqaer95ORknD17Fu+88w4iIyNx3333WbVDFxER1V7GwYy9g3XXo2OfGQtQKBSIj49HXFwcwsPDq72qzc3NDc888wzeeOMN+Pj4wN/fH2+//TZkMkNs2qhRIzg4OGD58uWYOHEiTp8+jffff9/kHI0bN4YgCPjtt9/wyCOPwNnZGQqFAj4+Pvj666+hUqlw7do1zJgxo1pfCxFRfXRvP0uNRoM9e/YAANq3b4+EhASEhoaa/KyJPpmF5QoNDcXx48fLLA8Kio6T28mrtVzlYTBjIQqFApGRkTV2vY8++giZmZkYNGgQ3N3d8dprryEtLQ2AYfXmqKgovPXWW/j0008RHh6OxYsXY9CgQdLxDRs2xJw5czBjxgyMHz8eY8aMQVRUFDZs2ICXX34ZrVu3RosWLfDpp59K/W2IiKjqCvtZqtVqqFQq7N+/H126dMHt27cBADKZDHq9vthPlUqF+Pj4aglosrOysbHDRgRfCIYd7HAVV6GA4TpXcVVKM/7ZBE0AADpBh7S0NKv2mRHE8jpg2Lj09HR4enoiLS0NHh4eJvtyc3Nx+fJlBAcHw8nJyUolpLqC7yciMsfuXbvxdL+nIfuvp8eb09/Eh4s+NOvYdZvXIfIJy39x3rFyBxyfc6zUsXdd70Lxs+W/0Jf1+X0v1swQERHVEFEnwv1Nd2zAhqLERcD3+N68EwwHLr19CSHzQixarvysfDjCEMwkuici2Sm5aKcAQCz5Z54sDzs8d2BD+IZi56xJDGaIiIhqSNbpLOQcy6nSORKjEi0ezIi6okYa9aNqDJk/BCdOnAAAtGvXDpcuXUJISEiJP8eHj7dqExPAYIaIiKjG6HOLZlN3buEM9wh3s4+9+/Nd6LP0EAss3zvEOJjx9fdFcHCwNM8YAOl5aT+tjcEMERFRDdHnFwUzDR5rgNCPQs0+9lDoIeReygWqYXUZUWsUIFl3YFKlcJ4ZIiKiGmJcqyI4CGXkLE6QG/KL+uqtmSm8ji1hzQwREREAvajHxtMbcTzxeKl5cvNykZiYiIZeDRG6NxT2anukp6cDAFxcXJCXmwdHJ8diP7OzswEAfpl+aIRGAIA/r/2JT377BImJiVAqlXByLHsUZPfs7nCHO3RaXZn5Sn19+Xrc/u42Uk6k4Pq16wCA4A7BCHkxBLk5uVI+BjNEREQ2asfFHRj10yiz8o7cMBKD/hxUfsYy7L21F+tj1xs2bpaf/778++AOd2TmZEKj0VS40+3t72/j/DPnAQBOMARO6q1qZJzPwI8xP+JFvAgAyNfa3vI1bGYiIiICcO7uObPzNr7buErX0sq0iGkaU6Fj9IKhs4xMlFVqDcDss9klpt86eAv5OUUBjCbN9paxYc0MERERABFF/UZm9ZyF3k16m+zPyMjA2HFjkZKcAtd0Vyl9boO5SJGnlDkfi3Tq/55n+mdi3rh5mPLiFKQkp8CngQ+iVkfB3b3k0U0ZGRlI/DwRACCDrHJrABp1HP4Un2IKpkAOORq4NYBrbtHr8fb1rvi5rYzBDFWbqKgoTJ06FampqdV+rXHjxiE1NRVbt26t9msRUd1kPCF+mG8YejbpWSzPxd0XERcXB+9PvJH2q2EJmVcWvAKxgVjmfCz3ztlSuI5f/939zV7Xb63jWgCGmpnKzOti3Ml3/ILxkM2WAXmA9oIW493HS/ucnG1vBvNa08y0YMECCIKAqVOnSmmiKGL27NkICAiAs7MzevXqhfj4eOsVkqzuypUrEARBWgCtOq/zzDPPIDg4GM7OzggNDcWsWbOQn297bclEZB7jmhlBKLkTbOE6fHZGdQEDHhuAIUOGIDg4GJGRkSX+HDJkiEmewmCk8HzmBCeizFA+mVi5j27jYObBXg/C0ccw468+Vw+HOw5FGV0qdXqrqhU1MzExMfj666/Rtm1bk/RFixZh6dKliIqKQvPmzTFv3jz07dsX58+fL7UqjsgSzp07B71ej6+++gpNmzbF6dOn8dxzzyErKwuLFy+2dvGIqBoU1sw45znDOcoZFwsulpo361SW9LyiQ6wr7b8YRhAreT2jZiZBLqDxW41x+Z3L0GXpoBf10Oq1iA+Kh3cX22tmsnrNTGZmJp566il88803JpGpKIpYtmwZ3n77bQwbNgytW7fGmjVrkJ2dje+/N3MNizqsV69eeOmllzB16lQoFAr4+/vj66+/RlZWFsaPHw93d3eEhoZi27ZtAACdTmdS09CiRQt88skn0vlyc3MRFhaG559/Xkq7fPkyPD098c0335hVpqioKDRq1AguLi4YOnQokpOTi+X59ddfERERAScnJ4SEhGDOnDnQarXSfkEQ8MUXX2DAgAFwdnZGcHAwNm/eLO0vnG2yQ4cOEASh2Ireixcvhkqlgo+PD6ZMmYKCggJUxsMPP4zVq1ejX79+CAkJwaBBg/D666/jp59+qtT5iKj2K6yZGX5wOFw/csWNZTdKfeReKRrKLHOomY9S45qZi8cuYveW3Ui5kwLAsBL37t27odEUdd69Ny0323T4dcMpDRF2KQwFfxQgdncs+r3XD9PGT4PM1eqhQYVZvcRTpkzBo48+ioceesgk/fLly0hMTES/fv2kNEdHR/Ts2RMHDhwo9Xx5eXlIT083edRVa9asQYMGDXDkyBG89NJLmDRpEoYPH46uXbsiLi4O/fv3x+jRo5GdnQ29Xo/AwEBs2rQJZ86cwXvvvYe33noLmzZtAgA4OTlh/fr1WLNmDbZu3QqdTofRo0ejd+/eeO6558oty+HDhzFhwgRMnjwZx48fR+/evTFv3jyTPDt27MDTTz+Nl19+GWfOnMFXX32FqKgofPDBByb53n33XTz++OM4ceIEnn76aYwcORJnz54FABw5cgQAsHv3bqjVapPgIjo6GgkJCYiOjsaaNWsQFRWFqKgoaf/EiRPh5uZW5uPatWulvsa0tDR4e9veNxYiMk9hzUxQcpDZx5xyOIX0/Jr5nBGFomaiG+E3YDfMDtFB0Xh3+btoNLoR+s7ri0ajG2Hm9pmYuX2mSdq0rdOwfvd66fjlh5ab5HlnzTvSPplg9dCgwqzazLRhwwbExcUhJqb48LTEREOvbX9/f5N0f39/XL16tdRzLliwAHPmzKlawTp2BP67fo1RKoGjRyt0SLt27fDOO4Y34MyZM7Fw4UI0aNBACj7ee+89fPHFFzh58iQ6d+5scl+Cg4Nx4MABbNq0CU8++SQAoH379pg3bx6ee+45jBw5EgkJCWZ3qP3kk0/Qv39/zJgxAwDQvHlzHDhwANu3b5fyfPDBB5gxYwbGjh0LAAgJCcH777+P6dOnY9asWVK+4cOH49lnnwUAvP/++9i1axeWL1+OFStWwNfXFwDg4+MDpVJpUgaFQoHPPvsMcrkcLVu2xKOPPoo///xTuh9z587F66+/XubrCAgIKDE9ISEBy5cvx5IlS8y6H0RkewprZuT6ovn838W7SIZpLfOUyVPw+YrPoYUWF/MvolVcK0RGRlZ7+TRuGgTDdC0knzwfXPvpGjJ7ZQIAMpGJhYcXGnbeDylt2YlleN3ndeC/72vfnP4GV+5ckfLkIU86J4OZCrh+/TpeeeUV7Ny5E05OpfecvrcTliiKpXbMAgwf6q+++qq0nZ6ejqAg86NsAIZA5qYZMxhZmXEfI7lcDh8fH7Rp00ZKKwwEk5KSAABffvklVq5ciatXryInJwf5+flo3769yTlfe+01/Pzzz1i+fDm2bduGBg0amFWWs2fPYujQoSZpXbp0MQlmYmNjERMTY1ITo9PpkJubi+zsbLi4uEjH3Xseczr8hoWFQS4v+iOkUqlw6tQpadvPzw9+fn5mvR5jt27dwsMPP2wSZBFR3VNYMyPTF32Yn8M53MVdyGQy6PV6BAQE4JHXH8EHWz6AWq1GQEBA5YZJV0LWi1nY8dkOeGZ5wiPHA61utgIAOOc7m3W8ccdh41oeYw5yB3Rv1L3qha1hVgtmYmNjkZSUhIiICClNp9Ph77//xmeffYbz5w2zFCYmJkKlUkl5kpKSitXWGHN0dISjo2PVCnfPN/4aUYlr2tvbm2wLgmCSVhj06fV6bNq0CdOmTcOSJUvQpUsXuLu746OPPsLhw4dNzpGUlITz589DLpfjwoULePjhh80qi/GQxtLo9XrMmTMHw4YNK7avrIDW+LWUpaT7odcX9XibOHEivvvuuzLPcebMGTRq1EjavnXrFnr37o0uXbrg66+/LrcMRGS7SqqZWfntSogKsdiQ6vj4eLOHVFvKO8+8g+ju0Th86jC8UryAiYb0J5o+gT6D+iDhYgJCm4bC3c0wQCYjM8M07SiA44Zjvhz0JcQQsVieiIAI+LlW/EuftVktmImMjDT51gwA48ePR8uWLfHmm28iJCQESqUSu3btQocOHQAA+fn52Lt3Lz788MPqLVwFm3tswb59+9C1a1dMnjxZSktISCiWb8KECWjdujWee+45PPPMM4iMjESrVq3KPX+rVq1w6NAhk7R7t8PDw3H+/Hk0bdq0zHMdOnQIY8aMMdkufA84OBiGD+p0FV+bpKLNTDdv3kTv3r0RERGB1atXQyazvapXIjKfVDNjVIMxYOAAOPga/u4UDkAAioZU1yRBENCnZR/0adkHmScycRSGzyrnP5wRcjoEIQgxye8LX5O03Mu50MIw4OLB0Afh0vS/Mdgdaqb81clqwYy7uztat25tkubq6gofHx8pferUqZg/fz6aNWuGZs2aYf78+XBxccGoUeatnUFFmjZtirVr12LHjh0IDg7GunXrEBMTY/KP8/PPP8fBgwdx8uRJBAUFYdu2bXjqqadw+PBhKYgozcsvv4yuXbti0aJFGDJkCHbu3GnSxAQY+vAMHDgQQUFBGD58OGQyGU6ePIlTp06ZdBbevHkzOnbsiO7du2P9+vU4cuQIVq1aBcDQVOTs7Izt27cjMDAQTk5O8PT0NOseVKSZ6datW+jVqxcaNWqExYsX486dO9K+e/vqEFHdUFLNjGBXOxddlHsUlbHgbgEK7lZs5KbcRV5+JhtSq79qTp8+HVOnTsXkyZPRsWNH3Lx5Ezt37uQcM5UwceJEDBs2DCNGjECnTp2QnJxsUktz7tw5vPHGG1ixYoXUx+jzzz9Hamoq3n333XLP37lzZ6xcuRLLly9H+/btsXPnTqlzcqH+/fvjt99+w65du3D//fejc+fOWLp0KRo3Nl3jZM6cOdiwYQPatm2LNWvWYP369VLtkJ2dHT799FN89dVXCAgIwODBg6t6a0q0c+dOXLx4EX/99RcCAwOhUqmkBxHVTYU1M7YQzDgHO0P5jBIyJxkEe8Hsh8xJBtULKjgGVLE7Ri0jiOZ0drBh6enp8PT0RFpaGjw8PEz25ebm4vLlywgODi63zwbVDEEQsGXLFgwZMsTaRakwvp+ILEej0SA2NhYRERFSn5SS0ixp7p9zcWzpMbzyxytSWo/sHpA7195ajHvviUajwZ49ewAY5iMrTKvO+1Zdyvr8vletmAGYiIiokEajQVhYGNRqNVQqlbSMzb1plv5g9j7obRLIAEBaRhq8nWvn/FL33qf9+/ejS5cuuH37NgBDk/iBAwfQrVu3ar1vtUGtbmai2mPAgAGlTjQ3f/58axePiOqQ2NhYqNVqAIBarUZcXFyJaZbmdMu0RvVv/I1jp45Z/DqWcu892bx5sxTIAIbRwJs3b672+1YbsGaGzLJy5Urk5OSUuM+Ss+LW8VZPIjJDREQEVCpVsXlcSkqzJEFb1D/mK++v8Lfj33gp/CWLX8dS7r1Pw4cPx9KlS01qZoYPH45ly5bV+Jw4NY3BDJmlYcOG1i4CEdUTXl5eOL7rOE6dOIXWrVvDOd0wKdyx7cdw+vRpKU3noIPc1XL9WYyDmd7P98aK6StqdZNMSfPdnD17Fnv37gUA9OzZ02pz4tQ0BjNERFSrnHrsFFJ+T4EccpzFWZN9xmlydznabmsLz27mTc9QLqPpq0JbhNrEB/+9890oFIpiAyisMSdOTWOfGSIiqjXybuUh5fcUs/LqMnRI2pRksWsb18yg9g5gohKwZoaIiGqNpGNFwYlTEyc4dXBCiiYFbm5uyMzMhLfCG9pULTKjDQsrivkl97Or6HBkUS/C8VrR3CuCfe2cX4ZKxmCGiMha7t4F/v3X2qWwquT8NFzJNYy2yfjaDdhSNEt3ZshVTD/7AlLT0iATAL0IeHq4wz+3CV7EpwCAvCvXgAN3Tc6Znp6OsU8/jbvJyWjg44PvvvuuzHlK9AUijozJQ8C1ouVMcv89CxzgfFFmc3ICrNi5mMEMEZE1xMcDERFAXp61S2I1hxsCPccDef99Em3avQm+Rvu/tvsR+/4v7Z6jMtAkKQNYYdhK2r8T6PaRSQ4PAL8UbiQnAwMGlFmODLRGLpZL23ro4fLNXGCW5Zqw6rxmzawamLPPDFWbqKgoeHl51ci1xo0bZ5OzBlM9tmtXvQ5kAOCPZkWBDAA4aIvWgFv74Fr8Hv57icfphKKeutc9qv4xpr/ne/28J+ZBkDOQsSWsmSGbcuXKFQQHB+PYsWNo3759tV6rSZMmuHr1qknam2++iYULF1brdameMJ5T6dFHgRYtrFcWK9E57gdwGAAwqCAULnpDMJOqUMOhcwzGy5pBm61DTk4OHB0ckJefD2dnZ2gLjJqMFD7AiFeLnTs3Nxe3k5Lg7+dX/vIi1xoA/zM8XddjHaJbR2N28JOALtASL7N+aNDAqpdnMENUhrlz5+K5556Ttt3c3KxYGqpTjIOZsWOB4cOtVxYrEf98G/jHEMy8POEr2H9sDz30aBjYFF9+eKrU404cOQHN1xrDObwbAEveKJbHCUDjYqmllGNnCvC/k4bnguH3Ikx5EWjcw/wXQ1bFZiYb1atXL7z00kuYOnUqFAoF/P398fXXXyMrKwvjx4+Hu7s7QkNDsW3bNgCATqfDM888g+DgYDg7O6NFixb45JNPpPPl5uYiLCwMzz//vJR2+fJleHp64ptvvjGrTFFRUWjUqBFcXFwwdOhQJCcnF8vz66+/IiIiAk5OTggJCcGcOXOg1Wql/YIg4IsvvsCAAQPg7OyM4OBgbN68WdofHBwMAOjQoQMEQUCvXr1Mzr948WKoVCr4+PhgypQpKCgoMKvspXF3d4dSqZQeDGaILEdEUUAnCALEgv8CiXJWqrazN/oeris9n9nl0BeVQy/opfKQ7WAwY8PWrFmDBg0a4MiRI3jppZcwadIkDB8+HF27dkVcXBz69++P0aNHIzs7G3q9HoGBgdi0aRPOnDmD9957D2+99RY2bdoEAHBycsL69euxZs0abN26FTqdDqNHj0bv3r1NaiZKc/jwYUyYMAGTJ0/G8ePH0bt3b8ybN88kz44dO/D000/j5ZdfxpkzZ/DVV18hKioKH3zwgUm+d999F48//jhOnDiBp59+GiNHjsTZs4ZJso4cOQIA2L17N9RqNX766SfpuOjoaCQkJCA6Ohpr1qxBVFQUoqKipP0TJ04sdX2pwse1a9dMyvLhhx/Cx8cH7du3xwcffID8/Hzzf0FEZeHSHSbLlwgQIGrNC2bkdkaTwFggmIHe6KlML5WHbAebmUrQ8euOSMxMrNFrKt2UOPr80Qod065dO7zzzjsAgJkzZ2LhwoVo0KCBFHy89957+OKLL3Dy5El07twZc+bMkY4NDg7GgQMHsGnTJjz55JMAgPbt22PevHl47rnnMHLkSCQkJGDr1q1mleWTTz5B//79MWPGDABA8+bNceDAAWzfvl3K88EHH2DGjBkYO3YsACAkJATvv/8+pk+fjlmzZkn5hg8fjmeffRYA8P7772PXrl1Yvnw5VqxYAV9fw1gHHx8fKJVKkzIoFAp89tlnkMvlaNmyJR599FH8+eef0v2YO3cuXn/99TJfR0BA0dDMV155RZr++8iRI5g5cyYuX76MlStXmnVPiMxWi2oBjOdnAVChuVoqqrBmxjfNFwUzC+AgGvrMlDfHi3Ew43PWB8cGH4ODgwPy8/Nx584dwzl9faU0jUaDgN4BaPFeCwjy4ufOSMuQnrNmxjYxmClBYmYibmbctHYxytW2bVvpuVwuh4+PD9q0aSOl+fv7AwCSkgy98r/88kusXLkSV69eRU5ODvLz84t1on3ttdfw888/Y/ny5di2bRsamNmp6+zZsxg6dKhJWpcuXUyCmdjYWMTExJjUxOh0OuTm5iI7OxsuLi7Scfee5/jx4+WWISwsDHJ50R85lUqFU6eK2t39/Pzg5+dX0qElmjZtmvS8bdu2UCgUeOKJJ6TaGqK6RqPRICwsDGq1Gv7+/hAEAYmJiVCpVIiPj7d4QFNYMzNm7xg4xBWNZNLL9aUdAgCwd7aXnnukeSDtl6Lh2w4wnCcNRWkyyJC4LxHOrZzReIRpTxqNRoOXpryE1/Ca4doCa2ZsEYOZEijdlOVnqgXXtLe3N9kWBMEkrfCbhV6vx6ZNmzBt2jQsWbIEXbp0gbu7Oz766CMcPnzY5BxJSUk4f/485HI5Lly4gIcfftisspiz2rVer8ecOXMwbNiwYvvKG21gzrekku6HXl/0R3HixIn47rvvyjzHmTNn0KhRoxL3de7cGQBw8eJFBjNUdcb/ZmpJLUBsbCzUasMEdoUrLwOAWq1GXFycxdf3KayZ8Usz/ZKR3iW9zOMcfRyx97696Hm2Z4WuN2/jPMSlxZmkZaRnQNlRCez6r0yFHYBrye+EzMNgpgQVbe6xBfv27UPXrl0xefJkKS0hIaFYvgkTJqB169Z47rnn8MwzzyAyMhKtWrUq9/ytWrXCoUOHTNLu3Q4PD8f58+fRtGnTMs916NAhjBkzxmS7Q4cOAAAHB8O3Lp2u4g3lFW1mutexY8cAGGp8iOqiiIgIqFQqqNVqqRk3MTERAQEBCK+G2V0LvwTJ9UU1qlP8p+CfGf+UeZyLvQvmjJgDrwwvk2NL0v1cd7yy7RUAgCZHgzh1XLE8Kq+if9OFNTPOds7mvQiqFRjM1BNNmzbF2rVrsWPHDgQHB2PdunWIiYmRRgcBwOeff46DBw/i5MmTCAoKwrZt2/DUU0/h8OHDUhBRmpdffhldu3bFokWLMGTIEOzcudOkiQkw9OEZOHAggoKCMHz4cMhkMpw8eRKnTp0y6Sy8efNmdOzYEd27d8f69etx5MgRrFq1CoChqcjZ2Rnbt29HYGAgnJyc4Olp3oq5FWlmOnjwIA4dOoTevXvD09MTMTExmDZtGgYNGlRqzQ1RhdSimhm9Vo/sM9mw09vh6IajOHv2LO677z4AkJ7bXbVDAQpgr7Av52zmK6yZsdMXfRT9ffzvcpuzPJ088WqXV/FFzBfI1+Wb1KIUBkiFaekeRbU8DnoH2MuKl99eMKrRthMwvNVwtPVvWywf1V4MZuqJiRMn4vjx4xgxYgQEQcDIkSMxefJkaej2uXPn8MYbb2DVqlUICgoCYAhu2rVrh3fffRcffvhhmefv3LkzVq5ciVmzZmH27Nl46KGH8M477+D999+X8vTv3x+//fYb5s6di0WLFsHe3h4tW7aUOvsWmjNnDjZs2IDJkydDqVRi/fr1Uu2QnZ0dPv30U8ydOxfvvfceevTogT179ljwThk4Ojpi48aNmDNnDvLy8tC4cWM899xzmD59usWvRWRNok5EbIdYZJ3OktLkkONf/FvsucxJhvb72sOjY+nrHFXo2iXUzHj7ept17OJ+i7G43+Jy8939+S5ObzwNAFjQawG+n/l9sTy3f7iNs5sMIyYX91+MwOGcLM/WCKI5nR1sWHp6Ojw9PZGWllZsobHc3FxcvnwZwcHB5c8QSTVCEARs2bLFJpcm4PuJKuSjj4DC4PjHH4ES+pLVhKz4LMS0jjE7f5PZTdBkVhOLXPvVHa/i40MfY8U3K3DfzfsAAeil72WRcxdK3paMU48YBgI4t3CGSwuXYnnybuQhM86wCnfTT5si8CUGM7VBWZ/f92LNDBGRNVi4mcl4SHVFRh0Vzu0CAGJjEQ36NICjoyPy8vJw584d+Pr6okBdgPTthuYafYG+0tcqdm1RhEe2hyGQQfnzy5SmrPLInIumU8s5n4Oc8zllnkvmyOnXbBF/a2SWAQMGlDrR3Pz5861dPKJ6rXBIdd++fREWFgaNRmP2scaz3/589Wf0394f9tPt0X97f0T+Fom+f/TF60eKOs6n3k2t9LXu5XXOC5uXFM3wnVuQW+HzlffaPbt6wrmteZ15HRs5wmcgRyraItbMkFlWrlyJnJySv9F4e5vXxm2OOt7qSVTEgjUzxkOqKzqMWtQZTeUPPdRqNTZv3mwyRNsXvlKe82fOV/pa9/I/7A8HXdHgghu4Abs4uwqdr7zXLnOQIWNxBob3K3vtq/9t/h86D+1c4qR6VPsxmCGzNGzY0NpFIKJSGA+prvAwaqP56USICAgIwPDhw7Fs2TJpiLZXvheQYsjTvGlzqC5W8lr3EHRFgcNZ+7P41utb7AzfWaFzmPPaIzpGwFnlDLVaDZlMBr1eb1gL6r+AUqlUIjwynIGMDWMwQ0RkDRashVQoFIiPj0dcXJy0BIfZxTCqmRn6+FDM/WZusfNlx2XjwkMXAAAerh6Vvta9BG1R8OA4xxE7J+6s8PnMee3GeUJCQnDp0iWEhITgxIkTAICePXtWy3INVHMYzBARWZsFOgArFIrKNfcY1cw0atJI+lA3Pp+dd9FHhagTK3+texjXzIS1Cat0QGFOeYzzFM6vZTzPFtk2BjNERPWYcc1Mac0sxul5N/OQdiCtxHwA4BTiBEelo1nXNg5myltckqgsDGaIiKyhlswAbDyaSZCVEswYDZlO/iUZyb8kl3o+wU5Au7/awauHV7nXNm5mquywbCKAwQwRkdWkOAP/+gDIOg/cKFrLLD09HefOn0Ngw0DcuHkDLVu0lCYNu3ffvXnS09MRF2dYfyg8PNxksrHCY43Pl3EpA/YwTOd/M+smkm4kFSunCBFwBlD2FC2GvFoRKdtSygxmRFHE1XlXEbojVEpjMENVwWCGqk1UVBSmTp2K1NTUar/WuHHjkJqaiq1bt1b7tYgs4Yz+NiJeBXLtAfw7Hf+tGGDq5D0/y9pXUp7ia8kWyxuREIHFMCwLsPrEaqxetbrEQ1qPbI1u57pBJpY8PZlvui96x/c2XDYxASEIKeXiQPqBdFx574pJWpYuq+TMRGZgMEM25cqVKwgODsaxY8fQvn37arvOnj170Lt37xL3HTlyBPfff3+1XZvqh536C4ZAxohrriscC8zrb2IpXlle0nOdrPTV6E83Oo3TjU6Xuj/sWpgUzJy9cRZ90bfUvHnqPJPtPa32ICA9AD3R08xSE5liMENUgq5du0oTcRV69913sXv3bnTs2NFKpaK6RIeiviqPeHTEw+fHIGxlGGQ6603M3lHVEd6dSp4EMzcvF+vWrkNWVhZc3Vzx5JNPYuOGjcjOzgZgWHm7kItT8fWPjIkFRa/968iv8UOPH7AvbJ8FXgHVV1zOwEb16tULL730EqZOnQqFQgF/f398/fXXyMrKwvjx4+Hu7o7Q0FBpVWydTodnnnkGwcHBcHZ2RosWLfDJJ59I58vNzUVYWBief/55Ke3y5cvw9PTEN998Y1aZoqKi0KhRI7i4uGDo0KFITi7eSfDXX39FREQEnJycEBISgjlz5kCr1Ur7BUHAF198gQEDBsDZ2RnBwcHYvLlouvPCoZQdOnSAIAjo1auXyfkXL14MlUoFHx8fTJkyBQUFBWaV/V4ODg5QKpXSw8fHB7/88gsmTJgAwYqdNanuEI2CmQkNHkLnA52tGsgAwBN9n8DHD39c4uOLwV/g+srr2P3Gblz/5jq+ffJb3Fh1A1smbsGWiVsw7+l50nnsyvmebLweVI6joSOOp4dn9bwoqhdYM2PD1qxZg+nTp+PIkSPYuHEjJk2ahK1bt2Lo0KF466238PHHH2P06NG4du0a7O3tERgYiE2bNqFBgwY4cOAAnn/+eahUKjz55JNwcnLC+vXr0alTJzzyyCN47LHHMHr0aPTu3RvPPfdcuWU5fPgwJkyYgPnz52PYsGHYvn07Zs2aZZJnx44dePrpp/Hpp5+iR48eSEhIkIIn47zvvvsuFi5ciE8++QTr1q3DyJEj0bp1a9x33304cuQIHnjgAezevRthYWFwcCiaCj06OhoqlQrR0dG4ePEiRowYgfbt20vlnzhxIr777rsyX8eZM2fQqFGjYum//PIL7t69i3HjxpV7L4jMoTcKZgQI0OcZajYEOwE+j9X8+kCuYa7wG+FXZp5753NRKBTSCvf7t+9HAQxfHoyHe5fEOJjRygxfZvglgapCEOv4YjhlLSGem5uLy5cvIzg4GE5OTlL60Y5HkZ+YX6PldFA6oONR85svevXqBZ1Oh337DFWzOp0Onp6eGDZsGNauXQsASExMhEqlwsGDB9G5c+di55gyZQpu376N//3vf1LaRx99hEWLFmHkyJHYvHkzTp06hQYNGpRbnlGjRkGj0Ug1QQDwf//3f9i+fbvUAfjBBx/EgAEDMHPmTCnPd999h+nTp+PWrVsADH/QJk6ciC+++ELK07lzZ4SHh2PFihWl9pkZN24c9uzZg4SEBMjlcgDAk08+CZlMhg0bNgAAkpKSkJ6eXubraNKkCezsisf4jzzyCADgjz/+KPXY0t5PRCX5cG4/zBB3AQC2hL4F1ZxByLmYAztvO3RP7m7l0lXcoT8PIfehXADA5f6XMX77+FLz3vrmFv593tDjedGgRdgWvg2nJ51GmF9YjZSVbENZn9/3Ys1MCfIT85F/s2aDmcpo27at9Fwul8PHxwdt2rSR0vz9/QEYPsQB4Msvv8TKlStx9epV5OTkID8/v1gn2tdeew0///wzli9fjm3btpkVyADA2bNnMXToUJO0Ll26YPv27dJ2bGwsYmJi8MEHH0hpOp0Oubm5yM7OhouLi3Tcvec5fvx4uWUICwuTAhkAUKlUOHXqlLTt5+cHP7+yv3mW5MaNG9ixYwc2bdpU4WOJSmNaMyOTajMK9AXQaDQms+FqNBrExsYiNDQUCQkJiIiIMGu23NKO02g02LNnDwDDFyNLTOUvty/6t9fgSAPcSbgD39CiBSpFvYibu27i/Inz8DrrJaUXdjpmzQxVBYOZEjgoHcrPVAuuaW9vOhRCEASTtMI/Dnq9Hps2bcK0adOwZMkSdOnSBe7u7vjoo49w+PBhk3MkJSXh/PnzkMvluHDhAh5++GGzymJOBZ9er8ecOXMwbNiwYvvKq8kw5w9dSfdDry/qlFjZZqbVq1fDx8cHgwYNKrcMROYy7jMjCAJ0BYYP9ZTUFISFhSE+Pl4KPMLCwkwWSVSpVNL+0pR23P79+9GlSxfcvn0bgGGRxTNnzlQ5oJHbFQUz7hp3xDaLRfjZcPi1MHyBODHiBFL/lwo55MhAhpRXK/+vmQkMZqjyGMyUoCLNPbZi37596Nq1KyZPniylJSQUn4RiwoQJaN26NZ577jk888wziIyMRKtWrco9f6tWrXDo0CGTtHu3w8PDcf78eTRt2rTMcx06dAhjxowx2e7QoQMASH1kdLrSh5CWZu7cuXj99dfLzBMQEGCyLYoiVq9ejTFjxhQLloiqwrhmRibIkJ+Xb+g7Az3UajXi4uIQGRmJ2NhYaWRdYXBuvL80pR23efNmKZABDM3R5Z3LHPYqe2Q6ZsItzw0A4CQ64dT3pxA5x3BezU5NiQHLVd+rAFgzQ1XDYKaeaNq0KdauXYsdO3YgODgY69atQ0xMjMlCa59//jkOHjyIkydPIigoCNu2bcNTTz2Fw4cPm3S0LcnLL7+Mrl27YtGiRRgyZAh27txp0sQEAO+99x4GDhyIoKAgDB8+HDKZDCdPnsSpU6cwb17RSIjNmzejY8eO6N69O9avX48jR45g1apVAAxNRc7Ozti+fTsCAwPh5OQET0/zRkFUppnpr7/+wuXLl/HMM89U6Dii8hjXZQoA7OX20EILPfQICAhAeHg4ACAiIgIqlcqkhsV4f2lKO2748OFYunSpSc1Meecyh52bHaaNm4aPoz6WAhr/AH9ocjQAABlkECEiDWn4xe4XiKKICz0vIEGZ8N89YDBDlceh2fXExIkTMWzYMIwYMQKdOnVCcnKySS3NuXPn8MYbb2DFihUICgoCYAhuUlNT8e6775Z7/s6dO2PlypVYvnw52rdvj507d+Kdd94xydO/f3/89ttv2LVrF+6//3507twZS5cuRePGjU3yzZkzBxs2bEDbtm2xZs0arF+/XqodsrOzw6effoqvvvoKAQEBGDx4cFVvTZlWrVqFrl274r777qvW61D9oxeLmkBlkEEQDR/mfko/nD592mT16vj4eOzevRsXL17E7t27TfaXprTjgoODcfbsWWzZsgVbtmyxSBMTAMhlclxUXcTq3kUzCE/dORXei7zhvcgb2TmG+WhSfFPw7TvfYvW7q/HPg/9IeVkzQ1XB0UwcfVKrCIKALVu2SMM9bQnfT1QRs+f0xhzsAQBsaz4X7i/3QcHdAjiFOKFzQvHRh7VdSk4KlIuVePTQo3jlj1cAAPOHzseudoYRW9vnbYej1hEJ/gl4dtKzJsfayeyQ+FoifFxqfkg61V4czUREVMvpYVQzI8ik1asFuW3WUHg7eyNqSBTir8ZLae1928OuqeFjxk40/HRzcsOApgOkPHKZHP8X9n8MZKhKGMyQWQYMGCDNaXOvt956C2+99VYNl4jItpn0mREEaWi2rQYzADCqzSjc6nwL/64yzCEz7YFpUD2lAgDsGbMHANDUryn+eKr0+ZqIKoPBDJll5cqVyMnJKXGft3fJa7lURh1v9SSSCHn2mL5tOkJvh0In+ECXbhihpxMrPlKvNjEOxs6cOgMnjZPh37W++H4iS2EwQ2Zp2LChtYtAVKf4nWmF1scHFEs/c+kMWmpaWqRTrjUIdkXByvJPluPQhkOQQ471WA8A0Ira0g4lqjSOZiIisgK7rKKVpXXQoQAFSEEK1hesR1xcnBVLVjXGNS9N0RRNbzdFs9vNpLSsnCxrFIvqONbMACazxBJVFpvIqCIEfdGH/lrf9/Bd8iGz55CpzYyDmYH//WfM3dO9potE9UC9DmYcHBwgk8lw69Yt+Pr6wsHBgXMdUKWIoog7d+4UW1KCqFT6oun/H36kH2bP+g6XLl1CeHi4zTYxAYBrW9cy93uGmzfJJVFF1OtgRiaTITg4GGq1Wlq1maiyBEFAYGCgyWKXRKURdEVfnBoGBSA4ONhkRm5b5XqfK9rva4/0/cVXqLf3s4ffkxVf7JWoPPU6mAEMtTONGjWCVqut1Ho/RIXs7e0ZyJDZBH1Rl0Whjr1tvLp7wau7l7WLQfVIvQ9mgKLVptk8QETVKS0lDbtX78at67fgmOQlpcvs6m7ztkajQWxsLCIiImy6+YxqNwYzREQ1QK/X49e2vyLwZiB8YDrbba4210qlql4ajQZhYWFQq9VQqVSIj49nQEPVgkOziYhqQOqdVATeDCyWnmuXC5mYWvMFqgGxsbFQq9UAALVabdNDzql2Y80MEVENKMgvkJ5fUVzBJY8/0Bwi2qQfRUj7pVYsWfWJiIiASqWCWq22+SHnVLsxmCEiqgHagqKZb7MDs/Hqg37w+vxzQ4J73Zx7RaFQID4+HnFxcTY/5JxqNwYzREQ1oCCvqGbGwcUBXl5eRTvr8PxWCoUCkZGR1i4G1XHsM0NEVAMKCoqCGcgBcMZoIothMENEVAN0+UbzWN07C0QdrpkhqgkMZoiIqtn2r7fjaperRQmsmSGyKAYzRETV7M68O3DUOkrbOmfONk5kSQxmiIiqmUOmg/T8rO9ZuAxwMa2ZYTMTUZUwmCEiqmZ2esPA0TuudzDPfh4Gjhpo5RIR1S0MZoiIqpmscFFJe+D06dPF51thzQxRlVg1mPniiy/Qtm1beHh4wMPDA126dMG2bduk/aIoYvbs2QgICICzszN69eqF+Ph4K5aYiKji5HrDstiinVgUyLADMJHFWDWYCQwMxMKFC3H06FEcPXoUffr0weDBg6WAZdGiRVi6dCk+++wzxMTEQKlUom/fvsjIyLBmsYmIKkSuMwQzepneyiUhqpusGsw89thjeOSRR9C8eXM0b94cH3zwAdzc3HDo0CGIoohly5bh7bffxrBhw9C6dWusWbMG2dnZ+P77761ZbCIis2gLtNj+zXa45roCAHRyo1FM7ABMZDG1ps+MTqfDhg0bkJWVhS5duuDy5ctITExEv379pDyOjo7o2bMnDhw4UOp58vLykJ6ebvIgIrKGH6b9AKfnnaTtnIIcaDQaK5aIqG6yejBz6tQpuLm5wdHRERMnTsSWLVvQqlUrJCYmAgD8/f1N8vv7+0v7SrJgwQJ4enpKj6CgoGotPxFRafJi80y2z7icQVxcXPGMrJkhqhKrBzMtWrTA8ePHcejQIUyaNAljx47FmTNnpP3CPf/IRVEslmZs5syZSEtLkx7Xr1+vtrITEZXJqFVpaaOl2KzbjPDwcEMCOwATWYzVV812cHBA06ZNAQAdO3ZETEwMPvnkE7z55psAgMTERKhUKil/UlJSsdoaY46OjnB0dCx1PxFRTRG0RV+8xn04Dmv6ryk+LJuIqszqNTP3EkUReXl5CA4OhlKpxK5du6R9+fn52Lt3L7p27WrFEhIRmUfQFQUzPR7sYRrIsAMwkcVYtWbmrbfewoABAxAUFISMjAxs2LABe/bswfbt2yEIAqZOnYr58+ejWbNmaNasGebPnw8XFxeMGjXKmsUmIjKLcc2Mg5NDGTmJqCqsGszcvn0bo0ePhlqthqenJ9q2bYvt27ejb9++AIDp06cjJycHkydPhkajQadOnbBz5064u7tbs9hERCY0Gg1iY2MRGhqKhIQE6adYUFT7Yu9gb3oQa2aILEYQxbrdCy09PR2enp5IS0uDh4eHtYtDRHXMhrkbICwW4JLvUmyfS74L5KJhwrxWia3g5+9XtPP114ElSwzP9+0DunevieIS2YyKfH7Xuj4zRES2RPe5Dv4Z/nDPcy/2KAxkMh0zcfLkydJPwpoZoiqx+mgmIiJb5pRnmBRPJ+hw0/Nmsf358nz80eAPrOq4ynRH3a4UJ6pRDGaIiKqgcBHJZM9k9IjrgUuXLiEkJMTk56rwVRySTVSNGMwQEVVB4SKSolxEcHAwgoODAaDYz2LYAZjIYthnhoioCmR6w59Rk0UkiahGMZghIqqCwmYmvVxf+ZOwZoaoStjMRERUCbocHa6suQKnfEMHYL2sgsEMOwATWQxrZoiIKuHfWf/i+qSihWwrHMwQkcUwmCEiqgT1AbXJ9pmQMxU7ATsAE1kMgxkiokrwcvOSnr874l38Pux36xWGqJ5jnxkisl05OYDeOs07xoOXjjU5hqZ2IUBWlvknKCgoes6aGaIqYTBDRLbpySeBzZutdnkRiwFEADAMy5adPAW4uVmtPET1GYMZIrI9167VaCCzuCvwdQSgNWqYn/4/OVr+t3qBTqZDVUZmw9e3SuUjqu8YzBCR7cnPL3ru7w+0bl0sS4FWi/T0dHh4eMDezk7adnF2RnZOjpRekgKtFhqNBgAgb+COGT0OQCeYDqUukMml5zqZDu6uCiAyvGKvQxCAwYOBkJCKHUdEJhjMEJFt69sXWLfOJEmj0SAsLAxqtRqNlI2wIWgD8mLypP25yMVP7j/hw6sfFlszSaPR4L777sPt27cBAL6hvpiS8RIGHR0krYJ9r6beTTFjzHIgtJ+FXxwRmYOjmYjI9pQz4VxsbCzUasPQ6YDEAJNABgCc4IRHMx5FXFxciccWBjIAkJeUh6ExQ0sNZFKQghWtV6AfAxkiq2HNDBHVOREREVCpVFCr1QhQBACGFiMkIhFe8IITnOAkOCE83LRZSK/VI+RyCF5yfQmZWZkAAD+Zn7Q/1SEVt/JvQYQIAQLykIdoRTTWhK+psddGRMUxmCEi21bCsGaFQoH4+HjExcWhyfkmuD7FMFOv38t+cNztiIIzBXCydyrWxHT3x7u49vw1DMOwosS0oqeXOl3C0DVDcenSJYSEhODSpUsYFz6u2HmIqGYxmCEi21NGM5O2QAutVgtnJ2d069oNSeeSpH3N2jRD4v5EFKAAok5Evi7f5Nj0U+llXja9RzqCg4MRHBwMANJPIrIuBjNEVGf88cUf0L2ug3u2e4n7J/wxAUMTh6IVWgE6wPF9R8CoYufZvc/iKTwFAFjRbwUS/BOkfYmKRAzuOrhay09ElcNghohsm1Ezk/prNUKzQ0vNmuKeYrIgpEyUQS8Ubcv1RZ18zzY8i9ONT5scr3RTWqLERGRhDGaIyPaU0swkyy0aoHkl9ApgB4h6ETqdDjda3IB7T3e4HS6apbebfzcILgK0BVpkZGYg0DFQ2te2YVt4N/aW9rUJbIMXIl6otpdERJXHYIaI6g6j9ZLeyXkH+/7Zh27dukGtVkOVo0L8+ngkRCUg87xhpNK1968h+kC0lCcSkdLxi/osgkt7F2m+mruqu3B4yKGmXxERmYHBDBHZNqNmJn1BUZOR+pYamzdvluabUavViIuLg5AlQPbfFFvPJD6DY4OP4Xn18wCA5mguHX/u4jmIOrHY8ZGRRQEPEdUOnDSPiGxPKc1Mdkbfz/xV/hg+fDhUKhUAICAgAOHh4fDy9ZLy9EAPeJ/yRq///gtAgLSvVbtW0nw1xscTUe3DmhkiqjNkesP3M52gQ3x8vMl8M+Hh4VAoFCiYUICze89CzC19eLdrN1co71dCEIRixxNR7cNghohsm1EzkyAanutkOinwUCgUJk1Dfk/6wXuAN7Rp2pJPJxPgoHKA8N957z2eiGofBjNEZHtKaWYSdIYAxHj4dUns3O1g584/f0R1Bf81E5FN04siLp29iNOnT0OmNTQzGc8dUxaNRoPY2FhERESwCYnIhjGYISKblWrvjD9+74OANTfg9d9/gCGY0Wg0ZQYoGo1GGnatUqmkPjZEZHs4momIbM9/zUz7/Doi4G6jYrvvutxFXFxcmaeIjY0tNuyaiGwTa2aIyGYVCI7S8yuKK0h0TkSuLBe7nXfj1/Bfyzy2cNi1Wq3msGsiG8dghohsll4oWkspdXAqRrw3ApcuXcIr4a+U22RU0rBtIrJNDGaIyPb818xkHMwEBAYgODgYwcHBZp+Gw66J6gb2mSEim6VHUTAjs+efM6L6iv/6ichm6Y0qlxnMENVf/NdPRLZHFPGnMhwB116WkhjMENVf/NdPRDZHk5KBgrsfmKRpxZKXJyCiuo/BDBHZHPUtDZy0TtJ2iksK7IPtrVgiIrImjmYiIpuj0xYtV5DgexZzHBbgROQJK5aIiKyJNTNEZHP0RsFMru8tnDh1gvPEENVjDGaIyObotUWrZts5yhnIENVzDGaIyOYY18xAZt4K2URUd1UqmFm7di3y8vKKpefn52Pt2rVVLhQRUVmyruVLz0VBZ8WSEFFtUKlgZvz48UhLSyuWnpGRgfHjx1e5UEREpTk96TT0C/ylbT2DGaJ6r1LBjCiKEAShWPqNGzfg6elZ5UIREZXmzro7JtvpzretVBIiqi0qNDS7Q4cOEAQBgiAgMjISdnZFh+t0Oly+fBkPP/ywxQtJRFRIppNBhKED8Le9v4VP2Ekrl4iIrK1CwcyQIUMAAMePH0f//v3h5uYm7XNwcECTJk3w+OOPW7SAREQm/pvo97zqPNb1XIdXM9tatzxEZHUVCmZmzZoFAGjSpAlGjBgBJyenco4gIrIcURQh/jcsWycz9JXhkEwiqtTfgbFjxyI3NxcrV67EzJkzkZKSAgCIi4vDzZs3LVpAIqJCoq5ofpnCYEbOcIao3qvUcgYnT57EQw89BE9PT1y5cgXPPfccvL29sWXLFly9epXDs4moUr6J/QYf7PsAOdqcEvfbF9jjO3wHANDKDe1NMhQfjEBE9Uulgplp06Zh3LhxWLRoEdzd3aX0AQMGYNSoURYrHBHVL1GrozBq3yg4aB1K3C/Xy6XnhTUznmLJeYmo/qhUMHP06FF8/fXXxdIbNmyIxMTEKheKiOqnyT9MRsOUhmbltdcXYMAFYIxn82ouFRHVdpVqbHZyckJ6enqx9PPnz8PX17fKhSKi+sk3zby/HwXIx8gru/DHekAlupV/ABHVaZWqmRk8eDDmzp2LTZs2AQAEQcC1a9cwY8YMDs0mokrRi3rY6Qx/ki56X8TbmrehF/WQCTLoRT0ECNL8Mp28HfFbCgcbEJFBpYKZxYsX45FHHoGfnx9ycnLQs2dPJCYmokuXLvjggw8sXUYiqge0Wi1k/1UWyzxkOHT0EC5duoSQkBDp54kTJwAAfby8gN69rVhaIqpNKhXMeHh44J9//sFff/2FuLg46PV6hIeH46GHHrJ0+YionijIK5CeyxxlCA4ORnBwMAAU+4m4uKIDS1hahYjql0oFM4X69OmDPn36WKosRFSPaQu00nNRLpaRE4BYzn4iqlcqFcx8+umnJaYLggAnJyc0bdoUDz74IORyeYn5iIjudXzfcel5ucEMEZGRSgUzH3/8Me7cuYPs7GwoFAqIoojU1FS4uLjAzc0NSUlJCAkJQXR0NIKCgixdZiKqY76d9C1CvgyRtvUyvfkHs5mJqN6r1NDs+fPn4/7778eFCxeQnJyMlJQU/Pvvv+jUqRM++eQTXLt2DUqlEtOmTbN0eYmoDhJ3mNbEZDTIKOcA1twQUZFK1cy88847+PHHHxEaGiqlNW3aFIsXL8bjjz+OS5cuYdGiRRymTURmsROL/hSta74Oby5704qlISJbU6lgRq1WQ6vVFkvXarXSDMABAQHIyCjn2xUREQCZaKgk1gk6LD60GAqFwvyD2cxEVO9Vqpmpd+/eeOGFF3Ds2DEp7dixY5g0aZI0uunUqVNFwyhLsWDBAtx///1wd3eHn58fhgwZgvPnz5vkEUURs2fPRkBAAJydndGrVy/Ex8dXpthEVFv912okCqJ5gQybmYjISKWCmVWrVsHb2xsRERFwdHSEo6MjOnbsCG9vb6xatQoA4ObmhiVLlpR5nr1792LKlCk4dOgQdu3aBa1Wi379+iErK0vKs2jRIixduhSfffYZYmJioFQq0bdvX9b6ENUhMr3hT1GFOv4SEf2nws1MoigiLy8PP//8M65fv47z589DFEW0bNkSLVq0kPL1NmN2zu3bt5tsr169Gn5+foiNjcWDDz4IURSxbNkyvP322xg2bBgAYM2aNfD398f333+PF154oaLFJ6JaSNAbmor0QiWCGTYzEdV7lQpmmjVrhvj4eLRo0cIkgKmqtLQ0AIC3tzcA4PLly0hMTES/fv2kPI6OjujZsycOHDjAYIbIhiRvT8aVj68g7U4aXJxdkJ2TjYCBAWgxpwWgM+Qxu2aGzUxEZKTCwYxMJkOzZs2QnJyMZs2aWawgoiji1VdfRffu3dG6dWsAkDoT+/v7m+T19/fH1atXSzxPXl4e8vLypO2SVvcmopp3dsJZaNWG9ZdykQsZZEg8lghEALp8QzSjE3TQaDQV6wBMRPVepfrMLFq0CG+88QZOnz5tsYK8+OKLOHnyJH744Ydi+4R7qpFFUSyWVmjBggXw9PSUHpy0j6h2KEgsKDH975/+LuozI+gRZ7zukjnYzERU71UqmHn66adx5MgRtGvXDs7OzvD29jZ5VNRLL72EX375BdHR0QgMDJTSlUolgKIamkJJSUnFamsKzZw5E2lpadLj+vXrFS4PEVmWqBMhiIag4wzO4Gvha2lf1/Cu0mrZesGwaG35J2QzExEVqdQ8M8uWLbPIxUVRxEsvvYQtW7Zgz549xYZyBwcHQ6lUYteuXejQoQMAID8/H3v37sWHH35Y4jkLR1cRkXUdTzyOoRuH4krqFdhr7bETOwEA+Y3zkdkmE/jNkO/u1LtQQWXYkINNTERUYZUKZsaOHWuRi0+ZMgXff/89fv75Z7i7u0s1MJ6ennB2doYgCJg6dSrmz5+PZs2aoVmzZpg/fz5cXFwwatQoi5SBiKrHmuNrcCX1CgBAri9adFYn0+Gu+90Sj8n2yK74hdjMRFTvVSqYMZaTk4OCAtO2cA8PD7OO/eKLLwAAvXr1MklfvXo1xo0bBwCYPn06cnJyMHnyZGg0GnTq1Ak7d+6Eu7t7VYtORNUoR5sjPW/j00Z67u7iDqGXgP139iPoUlGfNq2LFk1mNDHv5GxmIiIjlQpmsrKy8Oabb2LTpk1ITk4utl+n05l1HtGMP0iCIGD27NmYPXt2RYtJRFakF/UISA6AMlWJST6TpPTOTTrj+eefB54HNBoNYmNjERERweYlIqq0SgUz06dPR3R0NFasWIExY8bg888/x82bN/HVV19h4cKFli4jEdmghgcaYv3y9cXStTCs66bRaBAWFga1Wg2VSoX4+PjKBTRsZiKq9yo1munXX3/FihUr8MQTT8DOzg49evTAO++8g/nz52P9+uJ/vIio/lEeV5aYnuqZCgCIjY2FWq0GYFi8tkJDstnMRERGKhXMpKSkSCOPPDw8kJKSAgDo3r07/v77b8uVjohsl1Fr86+Ov2It1mKVxyq0XdgWABAREQGVyjCKKSAgwLwh2UREJahUM1NISAiuXLmCxo0bo1WrVti0aRMeeOAB/Prrr/Dy8rJwEYnIFhWutwQArea1gk9TH/Ts2VNqSlIoFIiPj0dcXBzCw8Mr32eGzUxE9V6lgpnx48fjxIkT6NmzJ2bOnIlHH30Uy5cvh1arxdKlSy1dRiKyRUY1M926d0PLzi2LZVEoFIiMjKz4udnMRERGKhXMTJs2TXreu3dvnDt3DkePHkVoaCjatWtnscIRkQ0zWjNSbi8vPR8RURVVOJjR6/WIiorCTz/9hCtXrkAQBAQHB+OJJ55A27Ztq6OMRGSDBF1R84/MrlLd88y8EJuZiOq7Cv2FEUURgwYNwrPPPoubN2+iTZs2CAsLw9WrVzFu3DgMHTq0uspJRLVY0sYkHOl0BNHNo3Fi5Alo07XQa4uqZmRyCwczbGYiIiMVqpmJiorC33//jT///BO9e/c22ffXX39hyJAhWLt2LcaMGWPRQhJR7SWKIs5PPA9dqg4CBGguaHCmzRncUd9BC7QAAGRmZ1q5lERUl1Xo69IPP/yAt956q1ggAwB9+vTBjBkzOM8MUT0j6kToUk1n/T655yREXVHtyb8X/q2+ArCZiajeq1Awc/LkSTz88MOl7h8wYABOnDhR5UIRke0QtcWbfO4LvA9OcJK2W7VuZeGLspmJiIpUqJkpJSUF/v7+pe739/eHRqOpcqGIqPaLU8cZVsXOArzhbbIvY3UG7sf90rbCm+suEVH1qVAwo9PpYGdX+iFyuRxarbbKhSKi2m3diXUYs9XQN841xxW/4bdS82Y7ZMPOrVKzQJiHzUxE9V6F/sKIoohx48bB0dGxxP15eXkWKRQR1W5/Xy1atsROb/pn5GCzgxBEQ4Chk+twtNtR9Pfsb9kCsJmJiIxUKJgZO3ZsuXk4komo7hNFES1vtIR/mj+6ybtJ6ZoHNch/Nx83b9xEw8CG8HTzxMctP4ZcxknziKj6VCiYWb16dXWVg4hsSPBfwXh65dPF0hu6NcSUMVOgVquhUqkQHx8PhVc195dhMxNRvVeN03ISUV3ld8avxPTzuvNQq9UAALVajbi4uOopAJuZiMhINfbKI6K6ynhF7B+cf4AmR4MCzwIsWbYEqj4qqNVqBAQEIDw83IqlJKL6gsEMEVWc0SKSER9EwC/YDz179oRCoUB8fDzi4uIQHh4OhYJDsomo+jGYIaIKM66Z6dq9K1rf31raVigUiIyMrN4CGDczsc8MUb3HPjNEVGHGwYwgZzBBRNbFYIaIKsw4mJHZ8c8IEVkXm5nIZmg0GsTGxiIiIgIApOfG/TI0Gg327NkDAOjVq1el+2wYn6d9+/ZISEhAaGgoEhISil2zPjC+9wqFwmQ9JkFmhZoZNjMRkREGM2QTNBoNwsLCoFar4e/vD0EQkJiYWDSXiUIBjUaD++67D7dv3wYAKJVKnDlzpsKBx73nkclk0Ov10k/ja9YHxvdepVJh//79SLyViBCEAAAysjOsXEIiqu9YP0w2ITY2Vpq/5Pbt20hMTARgOpdJbGysFIAAQGJiYqXmObn3PHq93uRntc6fUgsZ33u1Wo3NmzcDRkuw/XvhXyuVjIjIgMEM2YSIiAioVCoAhhoXpVIJACZzmURERJis6q5UKis1z8m955HJZCY/69P8Kfl38tHapzXa+baDCiq082uHIZ2GwFV0lfK0DGtZ8wVjMxMRGWEzE9mEe+cvAVBsLhOFQoGzZ89i7969ACDNe1KZaxmfp127drh06RJCQkJw6dKlejN/yvWl15HwRgKgB5ZhmSExCbjV6xbaoZ2Uz1PhaZ0CEhH9h8EM2Yx75y8paS4ThUKBIUOGWORaxucJDg42+Vkf3F5322RyvJKkOaehkXOjmikQEVEpGMwQUYn0+YZIRrAT4Pukr8m+/df242LmRexotwNbHbbWfOHYzERERhjMUI0oHNpbkeHN+gI9rsy5As1hDdLS0uDpaWjOKHxub2+PgoICpKWlwcXFBdnZ2VI6gDL3labwmLLyGp83I8Mwksfd3R3Z2dnwC/dDi4UtYO9V9nVqs8LflWuBoV+M3lEP1WcqacRYbGws/kj6A1svbAUACGAwQUTWxWCGqp3x0N6KDG9O/jUZ1z64BgCQQYYMZBR7Xridi9xi6eXtK405eQvPaw9D0FJ4jbsxd+HQyAHN32pu1rVqG+Pf1ffy76GCCulZ6QgLC8P+/fvRrVs3qNVqOI12AkINxwisGSEiK+NoJqp2xkN7KzK8Oe9WXrWXrTrcOHHD2kWoNJPfle6/IenQS0OyC/fl5uZKx1ilZobNTERkhDUzVO0Kh1Ub18yYNbxZV/T0I3yE837nAQC3k25DqVRi27ZtGPDwACTeToRMkEEv6qFUKnHgwAEAQNcuXUvc5+XlVeLlUlNTpWNKy2ucR4AAEYYP1TAhDAvFhQAA/wb+957aZhj/rhxkDoAeECEiICAAw4cPx7Jlyww1M85OyIUhoGHNDBFZmyCKxl9x6p709HR4enoiLS0NHh4e1i5OnXf01lHsvrS7WHpOTg5u3rwJb29vpKSkoGHDhnB2di7zXMoNSjT5vAkA4O9Jf0M31BDd3Lx5Uzq+rPNW5pqFx5SV1/i8hTUVLdNbotv0bgAA9XA1rr58VcrvYu+C4a2GQ+WuKvPatYVGo0FcXBycxjqh4GYBRB8R7S+0l/rMxMXFYZl6GX5L+A0AcH3adQR6BNZsIf/8E3joIcPzt94CPvigZq9PRNWuIp/frJmp7zIygOhoQKstP285bhWkoMu5idAaV6nc6+o9P8sw4t8RmIiJAIA/k//E3wf+Ln4ec85bgWuWev5y8jS/2RzdYAhmDl49iOV/LjfJuvHvFdgfOr8CBbAeBYBIAAdyBAAyOEEPRXS0yb4Vd+5I+YVt2wB7n5ot5MmTRc9ZM0RU7zGYqc/0euD++4Hz5y1yunPBgHasRU4FAJDpi7p06YQyAqRaQC8rmpBFrpcX239Kcx54/PGaLFKVifgRgDeQfAd4fKTpvhEA7jM8F557Hmb2rSYiqhYMZuqzpCSLBTIAYNxe+fgZYPSJqp3PMbkomJn5jx7a41U7X3WS5RYFMwMuyNHrB8Pzlx4BrnsCepusPBD++3/xmfOMf9eCtRuq27a1cgGIyNoYzJBBq1bAuHFVOoWouwDkfQMAaNm2DwZ3fBjZ2dlYsmQJ0jMy4OHujtdeew0AiqW5uLiYnCs7Oxub599A4/+2O/QciYD2QytdNuNyuLu5AYKAjP+uP2XKFHz++edllqc8WYlOiFlqeH47TYYresN58zMWAdAjXwCyZ8+u8Hmri/H9EAQBoihKPwvvSfZCOewBaAQge5Zp2cW8NYAuHgAgvPsuILhb54W0bAk88oh1rk1EtQaDmfrMuO938+bAG29U7XQJu4DvDMGM0KUr0OcNHNi9G+/Nnm3IkJGBrt27QxTFYmn3Lk1wYPdu7Mlfj8JWq7NtWiHgjeLLF5jLpByZmUU7MjLgqFDgvf8mvyutPOU6lwUsjQEAxEOGD/877+1UQ61GgQAcrMx5LaQgtQDnx59H5gnDa8/JyUFoRjPDzsK3QeHPDODI195wgAMA4I6oLVZ2ccM/wPn/gpnJUwA32x3BRUS2j8EMWYxo1PhQOFzXeKiv8XDsktKMRURE4Fe3X4H/4o5mLZpVqWzG5ShccTsxMbHYkOPKrogtyIvakUIQgmc8nkH/tP6IOxWH7OvZ+LvF31ZdafvO/+7g7ta70rYAAQEIKP2AlKKnBfYFxcpuPAiSQ7OJyNoYzJDF6EVDLYRXphfCXw7Hvqv7AAAbxA3QueggT5fjdOPTpabda1jeMClAcveqWjNGeatuG++rzIrYgl3RB3pzNEfz9ObQzNdIo7EeOv0QFEust9K2Lq2oA7XcQw6ZkwyiKKKgoAByuRw6nU76aW9vLzU5FTgWIHJhZLF7YhK4cjkDIrIyBjP1mYVnUS38tv7g2QfhddoLOqMh2gIE6O/pSFpSWmnsfaq+1lFZq27fu6+iHIMc4djIEXnXSp61uKm6aaXPbQmivuh33fLblvB93LeM3EREtoXBDFlM4bd1l7yijqKOgY6QexQfqmw2AfB51AeubVyrWrxqJbOToeOJjkj9KxWirihw2D9pPxTJCsj1cqmTrVUYjziywCImbGYiotqEwUx9Vk01M4JYdK5mnzVDg8ENqnxuW2DvZQ/fYaY1HtlvZEORrICdzg4iRKs1yRjXzFiiCGxmIqLahAtNksUU9pmRiUVvqxOnTkCj0ZR6jEajwe7du6HRaKTnly9fltKqQ0nXtPS1Cs+rkxua2uSiHBcTLlbr6yrp+tK1jGKZkydPVvkes2aGiGoT1syQxRR+WzeeAfftd9/GtRXXEB8fX6wTqUajQVhYGNRqNfz9/SEIAhITE6XFKFUqVYnHVUVp17TktYyv8anyUym9VctW0Ol01fK6Srt+4bWMuya9O+tdHJ5zuEr3mDUzRFSbsGamPquBZiY99FCr1YiLiyuWPzY2Vlqo8fbt20hMTDQcozd88pZ2XFWUdk1LXsv4GloUrXkl+++fW3W8rtKuX3gt45oUEWKV7zFrZoioNmEwQxZT+G3duJlJB12Zc8moVIaVpJVKpTT/i0xmOL6yc76UpbRrWvJaxtcQZUUf+n/o/sBO7MQu7ILdADsc63kMumzLrzllfH3pdRnFrSLEKt9j1swQUW3CZqb6rJpqZoybmRZ9tAjhz5Q8d0tpc7+EhITg0qVLlZ7zpSzlzTdj6WucefsMcMuQbmf0z00sEJH2dxpStqcU6zRsyesXvq40fZq0/4P5HyDk/6rvHhMR1TQGM2QxhR2AjZuZIu6PgJfCq9RjSpv7JTg4uHoKWcY1q+Maq4+sRlZyFryzvKV9Xlle8Ev3AwA8vf5p7D692+LXl+w3/BizZwzG/rc4xFtn38LRdUdN9ldU4e8aYDMTEVkfgxmymJKamep9Q2YLYObTM02SBsUMwrTfpwEABL1gEhhUF8Fo2W69qLfYNV3tXeEod7TIuYiIKovBTH1WA81MxmsWlUWj0SA2NhYRERF1qtljZveZSMtLQ2JmopTW0LOh9DzEIwQdAzpW6Jw6rQ5Z2VlwdXGF3E5e5jYAZGVnwc/ZTzq+WYNmKGtZJnM5yB0wMWIiHO0YzBCRdTGYIYsRdSIWfrcQnS52ktIysjLgCc8yjytpKHFdCWjC/MLw68hfpW2NRoMpb0yRtl8NfxVNnzN/qYN779X+/fvRrVu3EreNh54nI1k6x8KeC9FoSCPLvEAiolqgvjcCUCEL1MzIT8pNAhkAOJ94vtzjShpKXFfFxsZCk1Y0Ud21K9cqfLzxvdq8eXOp28ZDz41dSLhQ2eITEdVKDGbqM+NmJkvINt383uN7hA8sf9hviUOJ66iIiAh4eHpI20GBQRU+3vheDR8+vNRtk+HuRv/UmzdvXqXXQERU27CZiSynaH44xA+Lx4crPzSruaikocR1lUKhwIIPF+DaREONjLOjc4WPv/delbUNGIaeKzYpkP51OgDA3dPdsi+KiMjKGMzUZxbuAGwczPj4+1QoKLl3uHRd5uputAJ4JQYV3XuvytuOjIxEwvYEpMMQzHCOOyKqa9jMRBYjao2CI3np+eo74xFeos7CTX2lMFl+QMZohojqFgYzZDlGNTOs8yuD8b+66p9ipvh1GMsQUR3Dj5z6zIxmpvLmf7l67ip2LdyFjMQMuKhd0AANDDtYM1Mq45qZf0/+C6fLTvDy8ir3uNTUVJw4fgLt2reDl5dXudvG9DlG0Qy/whBRHcNghkplzvwvu57chaanis+Tki/m11QxbY9RMCFfK0f82nizD7WDHeIRb/Z2Sbj8ABHVNfyOVp+VUzNjzvwv7jeKj4zJl+dD3oJVM6VxDLDujLn2/vZWvT4RkaWxZoZKVTiniVqtLnX+l8L5S9Kd0vGe13uACGQ5ZuHI8CM1XVyb4X6/O1SzVdi2YBty83Lh5OiEHj16wN6+9CCjoKAA+/btk/J37twZhw4dKnW7xPMJQIPBDeDcpGLDwYmIajsGM1Qqc+Z/kekNwYzWQYstB7bg0qVLdX6umKoSBAEtZrWA38t+FZpbJ0QTYpK/haZFmdtERPWFVZuZ/v77bzz22GMICAiAIAjYunWryX5RFDF79mwEBATA2dkZvXr1Qny8+f0LqBxmdAAunLOktA9HQTQcJ8pEBAcHl5mXTJV3b8vLX942EVF9YdVgJisrC+3atcNnn31W4v5FixZh6dKl+OyzzxATEwOlUom+ffsiIyOjhktKpSmsmdHLamqMMRERkSmrNjMNGDAAAwYMKHGfKIpYtmwZ3n77bQwbNgwAsGbNGvj7++P777/HCy+8UJNFrZuMamZECLh7+Y40tBdAicN+wx8Mh7ePt3ScVDMj1Mzkb3WR8fB3ACZD4Qv3hYaGIiEhodQh8kRE9Vmt7TNz+fJlJCYmol+/flKao6MjevbsiQMHDpQazOTl5SEvL0/aTk9Pr/ay2jod7BH3x2BkfR9vMrS3pGG/O+U7EXkuEr5NfaHRaKTJ2PJ1+dBoNPygrSDj4e/+/v4QBAGJiYlQqVTYv38/unXrBrVaDZlMBr1eX+oQeSKi+qzWDs1OTEwEAPj7+5uk+/v7S/tKsmDBAnh6ekqPoKCKrUpcH6WhHbJSfc3Kq9QpceqbUwAMNQhyvWEItg66EoduU9mMh7/fvn1bem+r1Wps3rxZ2qfX66V03mciIlO1NpgpdO8EX6Ioljnp18yZM5GWliY9rl+/Xt1FtF2iiIOBwNcdiuY9ueZ6DTHKGMQoY3DI9xBilDG43v46LnlekvIc1RzFi3+8iI0ZG006AJc0dJvKVjj8HQCUSiWUSiUAICAgAMOHD5f2yWQyKZ33mYjIVK1tZir8o15Y5V4oKSmpWG2NMUdHRzg6WndSMluRq8vDo08BbS7L0fmYIe33rr9jU7dNxfL2PtUb7/34HgDgyLUj+DHmRwDAMNHQn8nByYFNH5Vw7/B3ACbDqwv3hYSEcNg7EVEpam0wExwcDKVSiV27dqFDhw4AgPz8fOzduxcffvihlUtXN2jy06BxhtRUBAA6ma7EvAV2BdJzjxwPKDINH6iFx3q6eFZjSeu2wiHVhYyfG+8LDg6u8bIREdkCqwYzmZmZuHjxorR9+fJlHD9+HN7e3mjUqBGmTp2K+fPno1mzZmjWrBnmz58PFxcXjBo1yoqlrjsK+2HIdUXBzGs9XsPM8TOL5dX+qUXOxhwAwJi/x2DM32NM9vt7lF5bRkREVJ2sGswcPXoUvXv3lrZfffVVAMDYsWMRFRWF6dOnIycnB5MnT4ZGo0GnTp2wc+dOuLsXXw+IKk4v/hfMGNXMNG7QGAEBAcXyZrbPxFEcLfVcjg3ZtEdERNYhiKJYpycISU9Ph6enJ9LS0uDh4WHt4tQqV+P+wmOfTcWSNUtgrzes49NiZQs4DXMymeuk0M0VN3H799tITU2Fq6srsrKy4OXlBRd/FwRND4JrS1drvRSbZzzXjPH8MpxXhojqq4p8ftfaPjNU/XS5Ij744QMpkAGAu6l30T+sP9RqdbE5TVxGumDgvIElznviqmAgU1nGc83cO78M55UhIipfrR+aTdVHm6aHe25Rk10a0rA7dbc0t8m9c5oYz4nCeU8sx/i+3ju/DO8vEVH5GMzUYzpt0cilO27X8IrqFQyZMEQaCn/vnCbGc6Jw3hPLMb6v984vw/tLRFQ+NjPVY3qjUdipyhs4duRYsXlPjJs3OO9J9Sjpnpf2OyAiouLYAbgeO/W/35E83NDX5dJ9hzDhzAwrl4iIiMigIp/fbGaqx3Q6ozhW0FuvIERERFXAYKYOE0URt0/dxu51u5GSlALAMHJm9+7d0Gg0yEzPLMos1OkKOiIiqsPYZ6aOEkURsZGxyIzOhB3ssEe2B21j2uLBgQ9CrVbD398fHZ2VeB3LAAB6oeRlDIiIiGo71szUUfnqfGRGF9W8eOu9sWfxHmnI7+3bt5GRmSXt1+oLip2DiIjIFrBmpo7S5xXvAxP6TyjmesxFXm4eHB0d4V3gIu2T2zOuJSIi28Rgpo7S5xcPZoTrAnqgh2Ej/559duwATEREtolfx+uo22m3zc6b7ZANXcj5aiwNERFR9WHNTB2Vm5Nb6r7o16JxN/QukJ4O/PUnVNkavOI5vAZLR0REZDkMZuqovLy8Uve9NuI1eNzvAZw+Dcz4zpDYwqGGSkZERGRZbGaqgw5vO4zzY0pvNsrMzcTu3buRlpZWlCgINVAyIiIiy2PNTB104fkLCLwdWOr+R4c9iuN3j6N3gwb4qwbLRUREVB1YM1MHeSQXrWGhlWlN9sUhDsfvHgcA3Ll7tyaLRUREVC1YM1MH2ekNv9YshyxM9p2M6L3RGNR1ENRJajj4O0ApKJGYmAh/X1/gzh3DQWxmIiIiG8Vgpg6S6Q0VbineKTh+6jgUCgX2nduHuLg4hIeHAwDi4uJwv6Mj0KOHNYtKRERUZQxm6iA73X+/VgdAoVAAMPyMjIyU8kRGRgInT1qjeERERBbFPjN1jF6vl5qZRHk5K2GLRvvZzERERDaKNTN1ROK1RJyNOYsz8WcQhjAAZgQzREREdQCDmTrgny3/IHt4Nhx0DlIgAwB6WTnrLbFmhoiI6gA2M9UBFzZfgIOu+Ay+6b7pVigNERFRzWLNTB0gFhTVsPwd+DeS5cnIdszGtM+mWbFURERENYPBTB0gaouCGe9nvdG2XVv07NlTGslU+oFsZiIiItvHYKYuMJrkN+L+CHR5pIv1ykJERFTD2GemLtAVPZXby80/jjUzRERUBzCYqQuMambkDhUIZoiIiOoANjPZGE20Bpc/uozUxFS4OLsgOycbyktKaX+FamaIiIjqAAYzNubc8+eQdzEPMsiQi1zIIIMrXKX9Oboc80/GZiYiIqoD2MxkIw7dOITOKztDc11Tap7osGj8m/ZvDZaKiIjI+lgzYyM+3P8hDt88DLnO0Ix0ye8Spjw7RdqvF/TIt8/H2fZnK3cB1swQEZGNYjBjI1JzUwEAcr0hmNHb6eHq4QqdTge5XA7ogafbPI2WgS3NP6nItZuIiMj2MZixETq9DhAhrYjdIagD7r5518qlIiIisj72mbERelEPmb7o1yXYWaBZiB2AiYioDmAwYyN0og7N1c2lbYsEM0RERHUAm5lsRLffu2HgloHSts542l8iIqJ6jDUzNqLpyaYm2+ne6VU/KZuZiIioDmAwYyPsYS89X+exDm0/bmvF0hAREdUebGayEYVDsgHgo8sfwdvbu+onZc0MERHVAayZsRGCzhBs6GQ6ywQyREREdQSDGRtROPOvTsaOv0RERMbYzFRZ77wDXL9eY5cT8voAAHSCDhg71jInvXPH6AJsZiIiItvEYKayfv0VOHmy2i9z00WBbd4voundxgAAnUwLrF1r+QvJ5eXnISIiqoXYzFTL/ek7AE1v9JG28+1zLX8RFxdg6FDLn5eIiKgGsGamsn7+GcjPr/bLFEzbDVwt2v7JZz2Un0Wha5culruIUgl4eFjufERERDWIwUxlNWlSM9ex2yc9neg3ERkFGVg+aDWgUNTM9YmIiGo5NjPVcoK2qGPuG2++gdOnT0PBQIaIiEjCYKa20xY9bdu+LQMZIiKiezCYqe2Mghm5PUccERER3Yt9ZqxIo9EgNjYWERERACA9dxPdcOO3G7h04RKcbjpJ+eUODGaIiIjuxWDGSjQaDcLCwqBWq+Hv7w9BEJCYmIhAZSC+F7+H7rYOcsgRgADpmOy8bCuWmIiIqHZiMGMlsbGxUKvVAIDbt29L6fJEOXQovmRBimsKMpIz0AUWHJJNRERUBzCYqWGiKOJq2lX4NPWBb3Nf3LlzBw0aNAAA3L17F0oPpTSvzCn5Kexruw96fz0ONj+I3zr8ZsWSExER1U4MZmqQXtSj+7fdcfD6QTxy7BGMcRsDuBllcAcUWUWjlc4+cBab+2+Wtr29uFo2ERHRvRjM1KALyRdw8MZBtL3aFm/88ka5+XONli5wsXeBj4tPdRaPiIjIJjGYqUH5OsPyB4EpgeXm1Tpo4f6oO0Y1HQW5IMfI1iPh5uBW7nFERET1DYOZGqQX9QAAhwIHKS34g2D4DCxe4+LYyBEPeT1UY2UjIiKyVZw0rwbpRT0m/DkBr2x7RUpzbu6MgqACHEo6hIKgAul5pphpxZISERHZDtbM1KCCGwUYvW+0SdrdvLt4KOyhYvPNqFQqxMfHc/kCIiKicrBmpgbpU/Um23/iT/x2/TeT+WYSExMBAGq1GnFxcTVeRiIiIlvDYKYG6QuKgpmtQVvxbcC3GD5iOFQqFQBAqVRCqVQCAAICAhAeHm6VchIREdkSNjPVIF1B0cy+Ic1DcHrzaSgUCsTHxyMuLk4KXgqfs4mJiIiofDZRM7NixQoEBwfDyckJERER2Ldvn7WLVCmiVpSeuyncpGBFoVAgMjISCoXC5DkRERGVr9YHMxs3bsTUqVPx9ttv49ixY+jRowcGDBiAa9euWbtoFWbczAQugE1ERGQRtT6YWbp0KZ555hk8++yzuO+++7Bs2TIEBQXhiy++sHbRyiTqRaTsTsHFjy/iz7f+xO3Tt5H/fX7RfjuxjKOJiIjIXLW6z0x+fj5iY2MxY8YMk/R+/frhwIEDJR6Tl5eHvLw8aTs9Pb1ay1iaxLWJOD/+PABADjnOLjgLBxRNlqeF1irlIiIiqmtqdc3M3bt3odPp4O/vb5Lu7+8vDWG+14IFC+Dp6Sk9goKCaqKoxWQcyShz/xXfKzVTECIiojquVgczhQRBMNkWRbFYWqGZM2ciLS1Nely/fr0milhMamZqqfsmPzsZYj82MxEREVlCrQ5mGjRoALlcXqwWJikpqVhtTSFHR0d4eHiYPKzh36R/S0w/HXQaZwPPQqVQ1XCJiIiI6qZaHcw4ODggIiICu3btMknftWsXunbtaqVSmacgr6DEdHsHezza7FGMajOqhktERERUN9XqDsAA8Oqrr2L06NHo2LEjunTpgq+//hrXrl3DxIkTrV20sulKTu7UpBNeGPVCzZaFiIioDqv1wcyIESOQnJyMuXPnQq1Wo3Xr1vjjjz/QuHFjaxcNAKDRaBAbG4uIiAgoFAppW5tb8mglwa7kvj5ERERUOYIoinW6J2p6ejo8PT2RlpZm0f4zcd3jkHU6C+np6dCLeqTapSK0RSiSzyQDIuAsOMNOLB4ruvdzR8SOCIuVg4iIqC6qyOd3ra+Zqa0K0gugS9PBFa4AAHetO/Lj8+EOd0OGUkLENH1aDZWQiIiofmAwU0lHhCPw9PGEXC9HQ01Dk30ZThnQuGqglWtxxfcKAi4GwCXPBRkOGRg6a6iVSkxERFQ3MZippJWTVuLk7ZPwyPLAzx/9bLJvR7sd+HzA5wAAV3tX/Pvcvzh78ixXwiYiIqoGDGYqqXtQdzR0bwjHLMdi+xr5NMKApgNgL7fH2HZjEeAbgIDIACuUkoiIqO5jB+Aq0mXpsM9tn0laoxmNELIgxOLXIiIiqi8q8vldqyfNswUlDbXm8GsiIqKaw2CmihjMEBERWReDmaoq4Q7mFuTWfDmIiIjqKQYzVSQIAvTt9SZpN31vWqk0RERE9Q9HM1lAu23t8FSrp5CpyUSOXw52j9lt7SIRERHVGwxmLMBH6YMfEn5AXFwc55IhIiKqYQxmLEShUCAyMtLaxSAiIqp32GeGiIiIbBqDGSIiIrJpDGaIiIjIpjGYISIiIpvGYIaIiIhsGoMZIiIismkMZoiIiMimMZghIiIim8ZghoiIiGwagxkiIiKyaQxmiIiIyKYxmCEiIiKbVucXmhRFEQCQnp5u5ZIQERGRuQo/tws/x8tS54OZjIwMAEBQUJCVS0JEREQVlZGRAU9PzzLzCKI5IY8N0+v1uHXrFtzd3SEIgkXPnZ6ejqCgIFy/fh0eHh4WPTcV4X2uGbzPNYP3uWbwPteM6rzPoigiIyMDAQEBkMnK7hVT52tmZDIZAgMDq/UaHh4e/MdSA3ifawbvc83gfa4ZvM81o7ruc3k1MoXYAZiIiIhsGoMZIiIismkMZqrA0dERs2bNgqOjo7WLUqfxPtcM3ueawftcM3ifa0Ztuc91vgMwERER1W2smSEiIiKbxmCGiIiIbBqDGSIiIrJpDGaIiIjIpjGYqaQVK1YgODgYTk5OiIiIwL59+6xdJJs2e/ZsCIJg8lAqldJ+URQxe/ZsBAQEwNnZGb169UJ8fLwVS2wb/v77bzz22GMICAiAIAjYunWryX5z7mteXh5eeuklNGjQAK6urhg0aBBu3LhRg6+i9ivvPo8bN67Y+7tz584meXify7dgwQLcf//9cHd3h5+fH4YMGYLz58+b5OF7uurMuc+17T3NYKYSNm7ciKlTp+Ltt9/GsWPH0KNHDwwYMADXrl2zdtFsWlhYGNRqtfQ4deqUtG/RokVYunQpPvvsM8TExECpVKJv377S2ltUsqysLLRr1w6fffZZifvNua9Tp07Fli1bsGHDBvzzzz/IzMzEwIEDodPpaupl1Hrl3WcAePjhh03e33/88YfJft7n8u3duxdTpkzBoUOHsGvXLmi1WvTr1w9ZWVlSHr6nq86c+wzUsve0SBX2wAMPiBMnTjRJa9mypThjxgwrlcj2zZo1S2zXrl2J+/R6vahUKsWFCxdKabm5uaKnp6f45Zdf1lAJbR8AccuWLdK2Ofc1NTVVtLe3Fzds2CDluXnzpiiTycTt27fXWNltyb33WRRFcezYseLgwYNLPYb3uXKSkpJEAOLevXtFUeR7urrce59Fsfa9p1kzU0H5+fmIjY1Fv379TNL79euHAwcOWKlUdcOFCxcQEBCA4OBg/N///R8uXboEALh8+TISExNN7rmjoyN69uzJe14F5tzX2NhYFBQUmOQJCAhA69atee8raM+ePfDz80Pz5s3x3HPPISkpSdrH+1w5aWlpAABvb28AfE9Xl3vvc6Ha9J5mMFNBd+/ehU6ng7+/v0m6v78/EhMTrVQq29epUyesXbsWO3bswDfffIPExER07doVycnJ0n3lPbcsc+5rYmIiHBwcoFAoSs1D5RswYADWr1+Pv/76C0uWLEFMTAz69OmDvLw8ALzPlSGKIl599VV0794drVu3BsD3dHUo6T4Dte89XedXza4ugiCYbIuiWCyNzDdgwADpeZs2bdClSxeEhoZizZo1Uqcy3vPqUZn7yntfMSNGjJCet27dGh07dkTjxo3x+++/Y9iwYaUex/tcuhdffBEnT57EP//8U2wf39OWU9p9rm3vadbMVFCDBg0gl8uLRZZJSUnFvg1Q5bm6uqJNmza4cOGCNKqJ99yyzLmvSqUS+fn50Gg0peahilOpVGjcuDEuXLgAgPe5ol566SX88ssviI6ORmBgoJTO97RllXafS2Lt9zSDmQpycHBAREQEdu3aZZK+a9cudO3a1Uqlqnvy8vJw9uxZqFQqBAcHQ6lUmtzz/Px87N27l/e8Csy5rxEREbC3tzfJo1arcfr0ad77KkhOTsb169ehUqkA8D6bSxRFvPjii/jpp5/w119/ITg42GQ/39OWUd59LonV39MW71JcD2zYsEG0t7cXV61aJZ45c0acOnWq6OrqKl65csXaRbNZr732mrhnzx7x0qVL4qFDh8SBAweK7u7u0j1duHCh6OnpKf7000/iqVOnxJEjR4oqlUpMT0+3cslrt4yMDPHYsWPisWPHRADi0qVLxWPHjolXr14VRdG8+zpx4kQxMDBQ3L17txgXFyf26dNHbNeunajVaq31smqdsu5zRkaG+Nprr4kHDhwQL1++LEZHR4tdunQRGzZsyPtcQZMmTRI9PT3FPXv2iGq1WnpkZ2dLefierrry7nNtfE8zmKmkzz//XGzcuLHo4OAghoeHmwxZo4obMWKEqFKpRHt7ezEgIEAcNmyYGB8fL+3X6/XirFmzRKVSKTo6OooPPvigeOrUKSuW2DZER0eLAIo9xo4dK4qiefc1JydHfPHFF0Vvb2/R2dlZHDhwoHjt2jUrvJraq6z7nJ2dLfbr10/09fUV7e3txUaNGoljx44tdg95n8tX0j0GIK5evVrKw/d01ZV3n2vje1r4r+BERERENol9ZoiIiMimMZghIiIim8ZghoiIiGwagxkiIiKyaQxmiIiIyKYxmCEiIiKbxmCGiIiIbBqDGSIiIrJpDGaIyOrGjRsHQRAgCALs7e3h7++Pvn374ttvv4Verzf7PFFRUfDy8qq+ghJRrcRghohqhYcffhhqtRpXrlzBtm3b0Lt3b7zyyisYOHAgtFqttYtHRLUYgxkiqhUcHR2hVCrRsGFDhIeH46233sLPP/+Mbdu2ISoqCgCwdOlStGnTBq6urggKCsLkyZORmZkJANizZw/Gjx+PtLQ0qZZn9uzZAIDvvvsOHTt2hLu7O5RKJUaNGoWkpCQrvVIisjQGM0RUa/Xp0wft2rXDTz/9BACQyWT49NNPcfr0aaxZswZ//fUXpk+fDgDo2rUrli1bBg8PD6jVaqjVarz++usAgPz8fLz//vs4ceIEtm7disuXL2PcuHHWellEZGF21i4AEVFZWrZsiZMnTwIApk6dKqUHBwfj/fffx6RJk7BixQo4ODjA09MTgiBAqVSanGPChAnS85CQEHz66ad44IEHkJmZCTc3txp5HURUfVgzQ0S1miiKEAQBABAdHY2+ffuiYcOGcHd3x5gxY5CcnIysrKwyz3Hs2DEMHjwYjRs3hru7O3r16gUAuHbtWnUXn4hqAIMZIqrVzp49i+DgYFy9ehWPPPIIWrdujR9//BGxsbH4/PPPAQAFBQWlHp+VlYV+/frBzc0N3333HWJiYrBlyxYAhuYnIrJ9bGYiolrrr7/+wqlTpzBt2jQcPXoUWq0WS5YsgUxm+B62adMmk/wODg7Q6XQmaefOncPdu3excOFCBAUFAQCOHj1aMy+AiGoEa2aIqFbIy8tDYmIibt68ibi4OMyfPx+DBw/GwIEDMWbMGISGhkKr1WL58uW4dOkS1q1bhy+//NLkHE2aNEFmZib+/PNP3L17F9nZ2WjUqBEcHByk43755Re8//77VnqVRFQdGMwQUa2wfft2qFQqNGnSBA8//DCio6Px6aef4ueff4ZcLkf79u2xdOlSfPjhh2jdujXWr1+PBQsWmJyja9eumDhxIkaMGAFfX18sWrQIvr6+iIqKwubNm9GqVSssXLgQixcvttKrJKLqIIiiKFq7EERERESVxZoZIiIismkMZoiIiMimMZghIiIim8ZghoiIiGwagxkiIiKyaQxmiIiIyKYxmCEiIiKbxmCGiIiIbBqDGSIiIrJpDGaIiIjIpjGYISIiIpvGYIaIiIhs2v8DyvEeZ7c8L9wAAAAASUVORK5CYII=",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"%matplotlib inline\n",
|
||
"\n",
|
||
"import numpy as np\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from sklearn.preprocessing import PolynomialFeatures\n",
|
||
"from sklearn.linear_model import LinearRegression\n",
|
||
"\n",
|
||
"steps=250\n",
|
||
"\n",
|
||
"distance=0\n",
|
||
"x=0\n",
|
||
"distance_list=[]\n",
|
||
"steps_list=[]\n",
|
||
"while x<steps:\n",
|
||
" distance+=np.random.randint(-1,2)\n",
|
||
" distance_list.append(distance)\n",
|
||
" x+=1\n",
|
||
" steps_list.append(x)\n",
|
||
"plt.plot(steps_list,distance_list, color='green', label=\"Random Walk Data\")\n",
|
||
"\n",
|
||
"steps_list=np.asarray(steps_list)\n",
|
||
"distance_list=np.asarray(distance_list)\n",
|
||
"\n",
|
||
"X=steps_list[:,np.newaxis]\n",
|
||
"\n",
|
||
"#Polynomial fits\n",
|
||
"\n",
|
||
"#Degree 2\n",
|
||
"poly_features=PolynomialFeatures(degree=2, include_bias=False)\n",
|
||
"X_poly=poly_features.fit_transform(X)\n",
|
||
"\n",
|
||
"lin_reg=LinearRegression()\n",
|
||
"poly_fit=lin_reg.fit(X_poly,distance_list)\n",
|
||
"b=lin_reg.coef_\n",
|
||
"c=lin_reg.intercept_\n",
|
||
"print (\"2nd degree coefficients:\")\n",
|
||
"print (\"zero power: \",c)\n",
|
||
"print (\"first power: \", b[0])\n",
|
||
"print (\"second power: \",b[1])\n",
|
||
"\n",
|
||
"z = np.arange(0, steps, .01)\n",
|
||
"z_mod=b[1]*z**2+b[0]*z+c\n",
|
||
"\n",
|
||
"fit_mod=b[1]*X**2+b[0]*X+c\n",
|
||
"plt.plot(z, z_mod, color='r', label=\"2nd Degree Fit\")\n",
|
||
"plt.title(\"Polynomial Regression\")\n",
|
||
"\n",
|
||
"plt.xlabel(\"Steps\")\n",
|
||
"plt.ylabel(\"Distance\")\n",
|
||
"\n",
|
||
"#Degree 10\n",
|
||
"poly_features10=PolynomialFeatures(degree=10, include_bias=False)\n",
|
||
"X_poly10=poly_features10.fit_transform(X)\n",
|
||
"\n",
|
||
"poly_fit10=lin_reg.fit(X_poly10,distance_list)\n",
|
||
"\n",
|
||
"y_plot=poly_fit10.predict(X_poly10)\n",
|
||
"plt.plot(X, y_plot, color='black', label=\"10th Degree Fit\")\n",
|
||
"\n",
|
||
"plt.legend()\n",
|
||
"plt.show()\n",
|
||
"\n",
|
||
"\n",
|
||
"#Decision Tree Regression\n",
|
||
"from sklearn.tree import DecisionTreeRegressor\n",
|
||
"regr_1=DecisionTreeRegressor(max_depth=2)\n",
|
||
"regr_2=DecisionTreeRegressor(max_depth=5)\n",
|
||
"regr_3=DecisionTreeRegressor(max_depth=7)\n",
|
||
"regr_1.fit(X, distance_list)\n",
|
||
"regr_2.fit(X, distance_list)\n",
|
||
"regr_3.fit(X, distance_list)\n",
|
||
"\n",
|
||
"X_test = np.arange(0.0, steps, 0.01)[:, np.newaxis]\n",
|
||
"y_1 = regr_1.predict(X_test)\n",
|
||
"y_2 = regr_2.predict(X_test)\n",
|
||
"y_3=regr_3.predict(X_test)\n",
|
||
"\n",
|
||
"# Plot the results\n",
|
||
"plt.figure()\n",
|
||
"plt.scatter(X, distance_list, s=2.5, c=\"black\", label=\"data\")\n",
|
||
"plt.plot(X_test, y_1, color=\"red\",\n",
|
||
" label=\"max_depth=2\", linewidth=2)\n",
|
||
"plt.plot(X_test, y_2, color=\"green\", label=\"max_depth=5\", linewidth=2)\n",
|
||
"plt.plot(X_test, y_3, color=\"m\", label=\"max_depth=7\", linewidth=2)\n",
|
||
"\n",
|
||
"plt.xlabel(\"Data\")\n",
|
||
"plt.ylabel(\"Darget\")\n",
|
||
"plt.title(\"Decision Tree Regression\")\n",
|
||
"plt.legend()\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Building a tree, regression\n",
|
||
"\n",
|
||
"There are mainly two steps\n",
|
||
"1. We split the predictor space (the set of possible values $x_1,x_2,\\dots, x_p$) into $J$ distinct and non-non-overlapping regions, $R_1,R_2,\\dots,R_J$. \n",
|
||
"\n",
|
||
"2. For every observation that falls into the region $R_j$ , we make the same prediction, which is simply the mean of the response values for the training observations in $R_j$.\n",
|
||
"\n",
|
||
"How do we construct the regions $R_1,\\dots,R_J$? In theory, the\n",
|
||
"regions could have any shape. However, we choose to divide the\n",
|
||
"predictor space into high-dimensional rectangles, or boxes, for\n",
|
||
"simplicity and for ease of interpretation of the resulting predictive\n",
|
||
"model. The goal is to find boxes $R_1,\\dots,R_J$ that minimize the\n",
|
||
"MSE, given by"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sum_{j=1}^J\\sum_{i\\in R_j}(y_i-\\overline{y}_{R_j})^2,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $\\overline{y}_{R_j}$ is the mean response for the training observations \n",
|
||
"within box $j$. \n",
|
||
"\n",
|
||
"\n",
|
||
"Unfortunately, it is computationally infeasible to consider every\n",
|
||
"possible partition of the feature space into $J$ boxes. The common\n",
|
||
"strategy is to take a top-down approach\n",
|
||
"\n",
|
||
"The approach is top-down because it begins at the top of the tree (all\n",
|
||
"observations belong to a single region) and then successively splits\n",
|
||
"the predictor space; each split is indicated via two new branches\n",
|
||
"further down on the tree. It is greedy because at each step of the\n",
|
||
"tree-building process, the best split is made at that particular step,\n",
|
||
"rather than looking ahead and picking a split that will lead to a\n",
|
||
"better tree in some future step.\n",
|
||
"\n",
|
||
"\n",
|
||
"### Making a tree\n",
|
||
"\n",
|
||
"In order to implement the recursive binary splitting we start by selecting\n",
|
||
"the predictor $x_j$ and a cutpoint $s$ that splits the predictor space into two regions $R_1$ and $R_2$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\left\\{X\\vert x_j < s\\right\\},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"and"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\left\\{X\\vert x_j \\geq s\\right\\},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"so that we obtain the lowest MSE, that is"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sum_{i:x_i\\in R_j}(y_i-\\overline{y}_{R_1})^2+\\sum_{i:x_i\\in R_2}(y_i-\\overline{y}_{R_2})^2,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"which we want to minimize by considering all predictors\n",
|
||
"$x_1,x_2,\\dots,x_p$. We consider also all possible values of $s$ for\n",
|
||
"each predictor. These values could be determined by randomly assigned\n",
|
||
"numbers or by starting at the midpoint and then proceed till we find\n",
|
||
"an optimal value.\n",
|
||
"\n",
|
||
"For any $j$ and $s$, we define the pair of half-planes where\n",
|
||
"$\\overline{y}_{R_1}$ is the mean response for the training\n",
|
||
"observations in $R_1(j,s)$, and $\\overline{y}_{R_2}$ is the mean\n",
|
||
"response for the training observations in $R_2(j,s)$.\n",
|
||
"\n",
|
||
"Finding the values of $j$ and $s$ that minimize the above equation can be\n",
|
||
"done quite quickly, especially when the number of features $p$ is not\n",
|
||
"too large.\n",
|
||
"\n",
|
||
"Next, we repeat the process, looking\n",
|
||
"for the best predictor and best cutpoint in order to split the data\n",
|
||
"further so as to minimize the MSE within each of the resulting\n",
|
||
"regions. However, this time, instead of splitting the entire predictor\n",
|
||
"space, we split one of the two previously identified regions. We now\n",
|
||
"have three regions. Again, we look to split one of these three regions\n",
|
||
"further, so as to minimize the MSE. The process continues until a\n",
|
||
"stopping criterion is reached; for instance, we may continue until no\n",
|
||
"region contains more than five observations.\n",
|
||
"\n",
|
||
"\n",
|
||
"The above procedure is rather straightforward, but leads often to\n",
|
||
"overfitting and unnecessarily large and complicated trees. The basic\n",
|
||
"idea is to grow a large tree $T_0$ and then prune it back in order to\n",
|
||
"obtain a subtree. A smaller tree with fewer splits (fewer regions) can\n",
|
||
"lead to smaller variance and better interpretation at the cost of a\n",
|
||
"little more bias.\n",
|
||
"\n",
|
||
"The so-called Cost complexity pruning algorithm gives us a\n",
|
||
"way to do just this. Rather than considering every possible subtree,\n",
|
||
"we consider a sequence of trees indexed by a nonnegative tuning\n",
|
||
"parameter $\\alpha$.\n",
|
||
"\n",
|
||
"Read more at the following [Scikit-Learn link on pruning](https://scikit-learn.org/stable/auto_examples/tree/plot_cost_complexity_pruning.html#sphx-glr-auto-examples-tree-plot-cost-complexity-pruning-py).\n",
|
||
"\n",
|
||
"\n",
|
||
"For each value of $\\alpha$ there corresponds a subtree $T \\in T_0$ such that"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\sum_{m=1}^{\\overline{T}}\\sum_{i:x_i\\in R_m}(y_i-\\overline{y}_{R_m})^2+\\alpha\\overline{T},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"is as small as possible. Here $\\overline{T}$ is \n",
|
||
"the number of terminal nodes of the tree $T$ , $R_m$ is the\n",
|
||
"rectangle (i.e. the subset of predictor space) corresponding to the $m$-th terminal node.\n",
|
||
"\n",
|
||
"The tuning parameter $\\alpha$ controls a trade-off between the subtree’s\n",
|
||
"complexity and its fit to the training data. When $\\alpha = 0$, then the\n",
|
||
"subtree $T$ will simply equal $T_0$, \n",
|
||
"because then the above equation just measures the\n",
|
||
"training error. \n",
|
||
"However, as $\\alpha$ increases, there is a price to pay for\n",
|
||
"having a tree with many terminal nodes. The above equation will\n",
|
||
"tend to be minimized for a smaller subtree. \n",
|
||
"\n",
|
||
"\n",
|
||
"It turns out that as we increase $\\alpha$ from zero\n",
|
||
"branches get pruned from the tree in a nested and predictable fashion,\n",
|
||
"so obtaining the whole sequence of subtrees as a function of $\\alpha$ is\n",
|
||
"easy. We can select a value of $\\alpha$ using a validation set or using\n",
|
||
"cross-validation. We then return to the full data set and obtain the\n",
|
||
"subtree corresponding to $\\alpha$. \n",
|
||
"\n",
|
||
"\n",
|
||
"### Schematic Regression Procedure\n",
|
||
"\n",
|
||
"Building a Regression Tree\n",
|
||
"\n",
|
||
"1. Use recursive binary splitting to grow a large tree on the training data, stopping only when each terminal node has fewer than some minimum number of observations.\n",
|
||
"\n",
|
||
"2. Apply cost complexity pruning to the large tree in order to obtain a sequence of best subtrees, as a function of $\\alpha$.\n",
|
||
"\n",
|
||
"3. Use for example $K$-fold cross-validation to choose $\\alpha$. Divide the training observations into $K$ folds. For each $k=1,2,\\dots,K$ we: \n",
|
||
"\n",
|
||
" * repeat steps 1 and 2 on all but the $k$-th fold of the training data. \n",
|
||
"\n",
|
||
" * Then we valuate the mean squared prediction error on the data in the left-out $k$-th fold, as a function of $\\alpha$.\n",
|
||
"\n",
|
||
" * Finally we average the results for each value of $\\alpha$, and pick $\\alpha$ to minimize the average error.\n",
|
||
"\n",
|
||
"\n",
|
||
"4. Return the subtree from Step 2 that corresponds to the chosen value of $\\alpha$. \n",
|
||
"\n",
|
||
"!eblock\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"## A Classification Tree\n",
|
||
"\n",
|
||
"A classification tree is very similar to a regression tree, except\n",
|
||
"that it is used to predict a qualitative response rather than a\n",
|
||
"quantitative one. Recall that for a regression tree, the predicted\n",
|
||
"response for an observation is given by the mean response of the\n",
|
||
"training observations that belong to the same terminal node. In\n",
|
||
"contrast, for a classification tree, we predict that each observation\n",
|
||
"belongs to the most commonly occurring class of training observations\n",
|
||
"in the region to which it belongs. In interpreting the results of a\n",
|
||
"classification tree, we are often interested not only in the class\n",
|
||
"prediction corresponding to a particular terminal node region, but\n",
|
||
"also in the class proportions among the training observations that\n",
|
||
"fall into that region. \n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"The task of growing a\n",
|
||
"classification tree is quite similar to the task of growing a\n",
|
||
"regression tree. Just as in the regression setting, we use recursive\n",
|
||
"binary splitting to grow a classification tree. However, in the\n",
|
||
"classification setting, the MSE cannot be used as a criterion for making\n",
|
||
"the binary splits. A natural alternative to MSE is the **classification\n",
|
||
"error rate**. Since we plan to assign an observation in a given region\n",
|
||
"to the most commonly occurring error rate class of training\n",
|
||
"observations in that region, the classification error rate is simply\n",
|
||
"the fraction of the training observations in that region that do not\n",
|
||
"belong to the most common class. \n",
|
||
"\n",
|
||
"When building a classification tree, either the Gini index or the\n",
|
||
"entropy are typically used to evaluate the quality of a particular\n",
|
||
"split, since these two approaches are more sensitive to node purity\n",
|
||
"than is the classification error rate. \n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"If our targets are the outcome of a classification process that takes\n",
|
||
"for example $k=1,2,\\dots,K$ values, the only thing we need to think of\n",
|
||
"is to set up the splitting criteria for each node.\n",
|
||
"\n",
|
||
"We define a PDF $p_{mk}$ that represents the number of observations of\n",
|
||
"a class $k$ in a region $R_m$ with $N_m$ observations. We represent\n",
|
||
"this likelihood function in terms of the proportion $I(y_i=k)$ of\n",
|
||
"observations of this class in the region $R_m$ as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"p_{mk} = \\frac{1}{N_m}\\sum_{x_i\\in R_m}I(y_i=k).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"We let $p_{mk}$ represent the majority class of observations in region\n",
|
||
"$m$. The three most common ways of splitting a node are given by\n",
|
||
"\n",
|
||
"* Misclassification error"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"p_{mk} = \\frac{1}{N_m}\\sum_{x_i\\in R_m}I(y_i\\ne k) = 1-p_{mk}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* Gini index $g$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"g = \\sum_{k=1}^K p_{mk}(1-p_{mk}).\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"* Information entropy or just entropy $s$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"s = -\\sum_{k=1}^K p_{mk}\\log{p_{mk}}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Visualizing the Tree, Classification"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 2,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
" mean radius mean texture mean perimeter mean area mean smoothness \\\n",
|
||
"0 17.99 10.38 122.80 1001.0 0.11840 \n",
|
||
"1 20.57 17.77 132.90 1326.0 0.08474 \n",
|
||
"2 19.69 21.25 130.00 1203.0 0.10960 \n",
|
||
"3 11.42 20.38 77.58 386.1 0.14250 \n",
|
||
"4 20.29 14.34 135.10 1297.0 0.10030 \n",
|
||
".. ... ... ... ... ... \n",
|
||
"564 21.56 22.39 142.00 1479.0 0.11100 \n",
|
||
"565 20.13 28.25 131.20 1261.0 0.09780 \n",
|
||
"566 16.60 28.08 108.30 858.1 0.08455 \n",
|
||
"567 20.60 29.33 140.10 1265.0 0.11780 \n",
|
||
"568 7.76 24.54 47.92 181.0 0.05263 \n",
|
||
"\n",
|
||
" mean compactness mean concavity mean concave points mean symmetry \\\n",
|
||
"0 0.27760 0.30010 0.14710 0.2419 \n",
|
||
"1 0.07864 0.08690 0.07017 0.1812 \n",
|
||
"2 0.15990 0.19740 0.12790 0.2069 \n",
|
||
"3 0.28390 0.24140 0.10520 0.2597 \n",
|
||
"4 0.13280 0.19800 0.10430 0.1809 \n",
|
||
".. ... ... ... ... \n",
|
||
"564 0.11590 0.24390 0.13890 0.1726 \n",
|
||
"565 0.10340 0.14400 0.09791 0.1752 \n",
|
||
"566 0.10230 0.09251 0.05302 0.1590 \n",
|
||
"567 0.27700 0.35140 0.15200 0.2397 \n",
|
||
"568 0.04362 0.00000 0.00000 0.1587 \n",
|
||
"\n",
|
||
" mean fractal dimension ... worst radius worst texture \\\n",
|
||
"0 0.07871 ... 25.380 17.33 \n",
|
||
"1 0.05667 ... 24.990 23.41 \n",
|
||
"2 0.05999 ... 23.570 25.53 \n",
|
||
"3 0.09744 ... 14.910 26.50 \n",
|
||
"4 0.05883 ... 22.540 16.67 \n",
|
||
".. ... ... ... ... \n",
|
||
"564 0.05623 ... 25.450 26.40 \n",
|
||
"565 0.05533 ... 23.690 38.25 \n",
|
||
"566 0.05648 ... 18.980 34.12 \n",
|
||
"567 0.07016 ... 25.740 39.42 \n",
|
||
"568 0.05884 ... 9.456 30.37 \n",
|
||
"\n",
|
||
" worst perimeter worst area worst smoothness worst compactness \\\n",
|
||
"0 184.60 2019.0 0.16220 0.66560 \n",
|
||
"1 158.80 1956.0 0.12380 0.18660 \n",
|
||
"2 152.50 1709.0 0.14440 0.42450 \n",
|
||
"3 98.87 567.7 0.20980 0.86630 \n",
|
||
"4 152.20 1575.0 0.13740 0.20500 \n",
|
||
".. ... ... ... ... \n",
|
||
"564 166.10 2027.0 0.14100 0.21130 \n",
|
||
"565 155.00 1731.0 0.11660 0.19220 \n",
|
||
"566 126.70 1124.0 0.11390 0.30940 \n",
|
||
"567 184.60 1821.0 0.16500 0.86810 \n",
|
||
"568 59.16 268.6 0.08996 0.06444 \n",
|
||
"\n",
|
||
" worst concavity worst concave points worst symmetry \\\n",
|
||
"0 0.7119 0.2654 0.4601 \n",
|
||
"1 0.2416 0.1860 0.2750 \n",
|
||
"2 0.4504 0.2430 0.3613 \n",
|
||
"3 0.6869 0.2575 0.6638 \n",
|
||
"4 0.4000 0.1625 0.2364 \n",
|
||
".. ... ... ... \n",
|
||
"564 0.4107 0.2216 0.2060 \n",
|
||
"565 0.3215 0.1628 0.2572 \n",
|
||
"566 0.3403 0.1418 0.2218 \n",
|
||
"567 0.9387 0.2650 0.4087 \n",
|
||
"568 0.0000 0.0000 0.2871 \n",
|
||
"\n",
|
||
" worst fractal dimension \n",
|
||
"0 0.11890 \n",
|
||
"1 0.08902 \n",
|
||
"2 0.08758 \n",
|
||
"3 0.17300 \n",
|
||
"4 0.07678 \n",
|
||
".. ... \n",
|
||
"564 0.07115 \n",
|
||
"565 0.06637 \n",
|
||
"566 0.07820 \n",
|
||
"567 0.12400 \n",
|
||
"568 0.07039 \n",
|
||
"\n",
|
||
"[569 rows x 30 columns]\n",
|
||
" malignant benign\n",
|
||
"0 True False\n",
|
||
"1 True False\n",
|
||
"2 True False\n",
|
||
"3 True False\n",
|
||
"4 True False\n",
|
||
".. ... ...\n",
|
||
"564 True False\n",
|
||
"565 True False\n",
|
||
"566 True False\n",
|
||
"567 True False\n",
|
||
"568 False True\n",
|
||
"\n",
|
||
"[569 rows x 2 columns]\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0"
|
||
]
|
||
},
|
||
"execution_count": 2,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"import os\n",
|
||
"from sklearn.datasets import load_breast_cancer\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn.metrics import confusion_matrix\n",
|
||
"from sklearn.tree import export_graphviz\n",
|
||
"\n",
|
||
"from IPython.display import Image \n",
|
||
"from pydot import graph_from_dot_data\n",
|
||
"import pandas as pd\n",
|
||
"import numpy as np\n",
|
||
"\n",
|
||
"\n",
|
||
"cancer = load_breast_cancer()\n",
|
||
"X = pd.DataFrame(cancer.data, columns=cancer.feature_names)\n",
|
||
"print(X)\n",
|
||
"y = pd.Categorical.from_codes(cancer.target, cancer.target_names)\n",
|
||
"y = pd.get_dummies(y)\n",
|
||
"print(y)\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=1)\n",
|
||
"tree_clf = DecisionTreeClassifier(max_depth=5)\n",
|
||
"tree_clf.fit(X_train, y_train)\n",
|
||
"\n",
|
||
"export_graphviz(\n",
|
||
" tree_clf,\n",
|
||
" out_file=\"DataFiles/cancer.dot\",\n",
|
||
" feature_names=cancer.feature_names,\n",
|
||
" class_names=cancer.target_names,\n",
|
||
" rounded=True,\n",
|
||
" filled=True\n",
|
||
")\n",
|
||
"cmd = 'dot -Tpng DataFiles/cancer.dot -o DataFiles/cancer.png'\n",
|
||
"os.system(cmd)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 3,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0"
|
||
]
|
||
},
|
||
"execution_count": 3,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Common imports\n",
|
||
"import numpy as np\n",
|
||
"from sklearn.model_selection import train_test_split \n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.datasets import make_moons\n",
|
||
"from sklearn.tree import export_graphviz\n",
|
||
"from pydot import graph_from_dot_data\n",
|
||
"import pandas as pd\n",
|
||
"import os\n",
|
||
"\n",
|
||
"np.random.seed(42)\n",
|
||
"X, y = make_moons(n_samples=100, noise=0.25, random_state=53)\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(X,y,random_state=0)\n",
|
||
"tree_clf = DecisionTreeClassifier(max_depth=5)\n",
|
||
"tree_clf.fit(X_train, y_train)\n",
|
||
"\n",
|
||
"export_graphviz(\n",
|
||
" tree_clf,\n",
|
||
" out_file=\"DataFiles/moons.dot\",\n",
|
||
" rounded=True,\n",
|
||
" filled=True\n",
|
||
")\n",
|
||
"cmd = 'dot -Tpng DataFiles/moons.dot -o DataFiles/moons.png'\n",
|
||
"os.system(cmd)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Other ways of visualizing the trees\n",
|
||
"\n",
|
||
"**Scikit-Learn** has also another way to visualize the trees which is very useful, here with the Iris data."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 4,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"[Text(0.5, 0.9166666666666666, 'x[2] <= 2.45\\ngini = 0.667\\nsamples = 150\\nvalue = [50, 50, 50]'),\n",
|
||
" Text(0.4230769230769231, 0.75, 'gini = 0.0\\nsamples = 50\\nvalue = [50, 0, 0]'),\n",
|
||
" Text(0.46153846153846156, 0.8333333333333333, 'True '),\n",
|
||
" Text(0.5769230769230769, 0.75, 'x[3] <= 1.75\\ngini = 0.5\\nsamples = 100\\nvalue = [0, 50, 50]'),\n",
|
||
" Text(0.5384615384615384, 0.8333333333333333, ' False'),\n",
|
||
" Text(0.3076923076923077, 0.5833333333333334, 'x[2] <= 4.95\\ngini = 0.168\\nsamples = 54\\nvalue = [0, 49, 5]'),\n",
|
||
" Text(0.15384615384615385, 0.4166666666666667, 'x[3] <= 1.65\\ngini = 0.041\\nsamples = 48\\nvalue = [0, 47, 1]'),\n",
|
||
" Text(0.07692307692307693, 0.25, 'gini = 0.0\\nsamples = 47\\nvalue = [0, 47, 0]'),\n",
|
||
" Text(0.23076923076923078, 0.25, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 0, 1]'),\n",
|
||
" Text(0.46153846153846156, 0.4166666666666667, 'x[3] <= 1.55\\ngini = 0.444\\nsamples = 6\\nvalue = [0, 2, 4]'),\n",
|
||
" Text(0.38461538461538464, 0.25, 'gini = 0.0\\nsamples = 3\\nvalue = [0, 0, 3]'),\n",
|
||
" Text(0.5384615384615384, 0.25, 'x[2] <= 5.45\\ngini = 0.444\\nsamples = 3\\nvalue = [0, 2, 1]'),\n",
|
||
" Text(0.46153846153846156, 0.08333333333333333, 'gini = 0.0\\nsamples = 2\\nvalue = [0, 2, 0]'),\n",
|
||
" Text(0.6153846153846154, 0.08333333333333333, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 0, 1]'),\n",
|
||
" Text(0.8461538461538461, 0.5833333333333334, 'x[2] <= 4.85\\ngini = 0.043\\nsamples = 46\\nvalue = [0, 1, 45]'),\n",
|
||
" Text(0.7692307692307693, 0.4166666666666667, 'x[1] <= 3.1\\ngini = 0.444\\nsamples = 3\\nvalue = [0, 1, 2]'),\n",
|
||
" Text(0.6923076923076923, 0.25, 'gini = 0.0\\nsamples = 2\\nvalue = [0, 0, 2]'),\n",
|
||
" Text(0.8461538461538461, 0.25, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 1, 0]'),\n",
|
||
" Text(0.9230769230769231, 0.4166666666666667, 'gini = 0.0\\nsamples = 43\\nvalue = [0, 0, 43]')]"
|
||
]
|
||
},
|
||
"execution_count": 4,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
},
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 640x480 with 1 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.datasets import load_iris\n",
|
||
"from sklearn import tree\n",
|
||
"X, y = load_iris(return_X_y=True)\n",
|
||
"tree_clf = tree.DecisionTreeClassifier()\n",
|
||
"tree_clf = tree_clf.fit(X, y)\n",
|
||
"# and then plot the tree\n",
|
||
"tree.plot_tree(tree_clf)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Alternatively, the tree can also be exported in textual format with the function exporttext.\n",
|
||
"This method doesn’t require the installation of external libraries and is more compact:"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 5,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"|--- petal width (cm) <= 0.80\n",
|
||
"| |--- class: 0\n",
|
||
"|--- petal width (cm) > 0.80\n",
|
||
"| |--- petal width (cm) <= 1.75\n",
|
||
"| | |--- class: 1\n",
|
||
"| |--- petal width (cm) > 1.75\n",
|
||
"| | |--- class: 2\n",
|
||
"\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.datasets import load_iris\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.tree import export_text\n",
|
||
"iris = load_iris()\n",
|
||
"decision_tree = DecisionTreeClassifier(random_state=0, max_depth=2)\n",
|
||
"decision_tree = decision_tree.fit(iris.data, iris.target)\n",
|
||
"r = export_text(decision_tree, feature_names=iris['feature_names'])\n",
|
||
"print(r)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Algorithms for Setting up Decision Trees\n",
|
||
"\n",
|
||
"Two algorithms stand out in the set up of decision trees:\n",
|
||
"1. The CART (Classification And Regression Tree) algorithm for both classification and regression\n",
|
||
"\n",
|
||
"2. The ID3 algorithm based on the computation of the information gain for classification\n",
|
||
"\n",
|
||
"We discuss both algorithms with applications here. The popular library\n",
|
||
"**Scikit-Learn** uses the CART algorithm. For classification problems\n",
|
||
"you can use either the **gini** index or the **entropy** to split a tree\n",
|
||
"in two branches.\n",
|
||
"\n",
|
||
"### The CART algorithm for Classification\n",
|
||
"\n",
|
||
"For classification, the CART algorithm splits the data set in two subsets using a single feature $k$ and a threshold $t_k$.\n",
|
||
"This could be for example a threshold set by a number below a certain circumference of a malign tumor.\n",
|
||
"\n",
|
||
"How do we find these two quantities?\n",
|
||
"We search for the pair $(k,t_k)$ that produces the purest subset using for example the **gini** factor $G$.\n",
|
||
"The cost function it tries to minimize is then"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"C(k,t_k) = \\frac{m_{\\mathrm{left}}}{m}G_{\\mathrm{left}}+ \\frac{m_{\\mathrm{right}}}{m}G_{\\mathrm{right}},\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"where $G_{\\mathrm{left/right}}$ measures the impurity of the left/right subset and $m_{\\mathrm{left/right}}$\n",
|
||
" is the number of instances in the left/right subset\n",
|
||
"\n",
|
||
"Once it has successfully split the training set in two, it splits the subsets using the same logic, then the subsubsets\n",
|
||
"and so on, recursively. It stops recursing once it reaches the maximum depth (defined by the\n",
|
||
"$max\\_depth$ hyperparameter), or if it cannot find a split that will reduce impurity. A few other\n",
|
||
"hyperparameters control additional stopping conditions such as the $min\\_samples\\_split$,\n",
|
||
"$min\\_samples\\_leaf$, $min\\_weight\\_fraction\\_leaf$, and $max\\_leaf\\_nodes$.\n",
|
||
"\n",
|
||
"\n",
|
||
"### The CART algorithm for Regression\n",
|
||
"\n",
|
||
"The CART algorithm for regression works is similar to the one for classification except that instead of trying to split the\n",
|
||
"training set in a way that minimizes say the **gini** or **entropy** impurity, it now tries to split the training set in a way that minimizes our well-known mean-squared error (MSE). The cost function is now"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"C(k,t_k) = \\frac{m_{\\mathrm{left}}}{m}\\mathrm{MSE}_{\\mathrm{left}}+ \\frac{m_{\\mathrm{right}}}{m}\\mathrm{MSE}_{\\mathrm{right}}.\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"Here the MSE for a specific node is defined as"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\mathrm{MSE}_{\\mathrm{node}}=\\frac{1}{m_\\mathrm{node}}\\sum_{i\\in \\mathrm{node}}(\\overline{y}_{\\mathrm{node}}-y_i)^2,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"with"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"$$\n",
|
||
"\\overline{y}_{\\mathrm{node}}=\\frac{1}{m_\\mathrm{node}}\\sum_{i\\in \\mathrm{node}}y_i,\n",
|
||
"$$"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"the mean value of all observations in a specific node.\n",
|
||
"\n",
|
||
"Without any regularization, the regression task for decision trees, \n",
|
||
"just like for classification tasks, is prone to overfitting.\n",
|
||
"\n",
|
||
"\n",
|
||
"\n",
|
||
"### Computing the Gini index\n",
|
||
"\n",
|
||
"The example we will look at is a classical one in many Machine\n",
|
||
"Learning applications. Based on various meteorological features, we\n",
|
||
"have several so-called attributes which decide whether we at the end\n",
|
||
"will do some outdoor activity like skiing, going for a bike ride etc\n",
|
||
"etc. The table here contains the feautures **outlook**, **temperature**,\n",
|
||
"**humidity** and **wind**. The target or output is whether we ride\n",
|
||
"(True=1) or whether we do something else that day (False=0). The\n",
|
||
"attributes for each feature are then sunny, overcast and rain for the\n",
|
||
"outlook, hot, cold and mild for temperature, high and normal for\n",
|
||
"humidity and weak and strong for wind.\n",
|
||
"\n",
|
||
"The table here summarizes the various attributes and\n",
|
||
"<table border=\"1\">\n",
|
||
"<thead>\n",
|
||
"<tr><th align=\"center\">Day</th> <th align=\"center\">Outlook </th> <th align=\"center\">Temperature</th> <th align=\"center\">Humidity</th> <th align=\"center\"> Wind </th> <th align=\"center\">Ride</th> </tr>\n",
|
||
"</thead>\n",
|
||
"<tbody>\n",
|
||
"<tr><td align=\"center\"> 1 </td> <td align=\"center\"> Sunny </td> <td align=\"center\"> Hot </td> <td align=\"center\"> High </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 0 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 2 </td> <td align=\"center\"> Sunny </td> <td align=\"center\"> Hot </td> <td align=\"center\"> High </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 3 </td> <td align=\"center\"> Overcast </td> <td align=\"center\"> Hot </td> <td align=\"center\"> High </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 4 </td> <td align=\"center\"> Rain </td> <td align=\"center\"> Mild </td> <td align=\"center\"> High </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 5 </td> <td align=\"center\"> Rain </td> <td align=\"center\"> Cool </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 6 </td> <td align=\"center\"> Rain </td> <td align=\"center\"> Cool </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 0 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 7 </td> <td align=\"center\"> Overcast </td> <td align=\"center\"> Cool </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 8 </td> <td align=\"center\"> Sunny </td> <td align=\"center\"> Mild </td> <td align=\"center\"> High </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 0 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 9 </td> <td align=\"center\"> Sunny </td> <td align=\"center\"> Cool </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 10 </td> <td align=\"center\"> Rain </td> <td align=\"center\"> Mild </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 11 </td> <td align=\"center\"> Sunny </td> <td align=\"center\"> Mild </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 12 </td> <td align=\"center\"> Overcast </td> <td align=\"center\"> Mild </td> <td align=\"center\"> High </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 13 </td> <td align=\"center\"> Overcast </td> <td align=\"center\"> Hot </td> <td align=\"center\"> Normal </td> <td align=\"center\"> Weak </td> <td align=\"center\"> 1 </td> </tr>\n",
|
||
"<tr><td align=\"center\"> 14 </td> <td align=\"center\"> Rain </td> <td align=\"center\"> Mild </td> <td align=\"center\"> High </td> <td align=\"center\"> Strong </td> <td align=\"center\"> 0 </td> </tr>\n",
|
||
"</tbody>\n",
|
||
"</table>\n",
|
||
"\n",
|
||
"### Simple Python Code to read in Data and perform Classification"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 6,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
" (0, 0)\t1.0\n",
|
||
" (0, 7)\t1.0\n",
|
||
" (0, 9)\t1.0\n",
|
||
" (0, 13)\t1.0\n",
|
||
" (1, 3)\t1.0\n",
|
||
" (1, 5)\t1.0\n",
|
||
" (1, 8)\t1.0\n",
|
||
" (1, 12)\t1.0\n",
|
||
" (2, 3)\t1.0\n",
|
||
" (2, 5)\t1.0\n",
|
||
" (2, 8)\t1.0\n",
|
||
" (2, 11)\t1.0\n",
|
||
" (3, 1)\t1.0\n",
|
||
" (3, 5)\t1.0\n",
|
||
" (3, 8)\t1.0\n",
|
||
" (3, 12)\t1.0\n",
|
||
" (4, 2)\t1.0\n",
|
||
" (4, 6)\t1.0\n",
|
||
" (4, 8)\t1.0\n",
|
||
" (4, 12)\t1.0\n",
|
||
" (5, 2)\t1.0\n",
|
||
" (5, 4)\t1.0\n",
|
||
" (5, 10)\t1.0\n",
|
||
" (5, 12)\t1.0\n",
|
||
" (6, 2)\t1.0\n",
|
||
" :\t:\n",
|
||
" (8, 12)\t1.0\n",
|
||
" (9, 3)\t1.0\n",
|
||
" (9, 4)\t1.0\n",
|
||
" (9, 10)\t1.0\n",
|
||
" (9, 12)\t1.0\n",
|
||
" (10, 2)\t1.0\n",
|
||
" (10, 6)\t1.0\n",
|
||
" (10, 10)\t1.0\n",
|
||
" (10, 12)\t1.0\n",
|
||
" (11, 3)\t1.0\n",
|
||
" (11, 6)\t1.0\n",
|
||
" (11, 10)\t1.0\n",
|
||
" (11, 11)\t1.0\n",
|
||
" (12, 1)\t1.0\n",
|
||
" (12, 6)\t1.0\n",
|
||
" (12, 8)\t1.0\n",
|
||
" (12, 11)\t1.0\n",
|
||
" (13, 1)\t1.0\n",
|
||
" (13, 5)\t1.0\n",
|
||
" (13, 10)\t1.0\n",
|
||
" (13, 12)\t1.0\n",
|
||
" (14, 2)\t1.0\n",
|
||
" (14, 6)\t1.0\n",
|
||
" (14, 8)\t1.0\n",
|
||
" (14, 11)\t1.0\n",
|
||
"Train set accuracy with Decision Tree: 0.73\n"
|
||
]
|
||
},
|
||
{
|
||
"data": {
|
||
"text/plain": [
|
||
"0"
|
||
]
|
||
},
|
||
"execution_count": 6,
|
||
"metadata": {},
|
||
"output_type": "execute_result"
|
||
}
|
||
],
|
||
"source": [
|
||
"# Common imports\n",
|
||
"import numpy as np\n",
|
||
"import pandas as pd\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.model_selection import train_test_split\n",
|
||
"from sklearn.tree import export_graphviz\n",
|
||
"from sklearn.preprocessing import StandardScaler, OneHotEncoder\n",
|
||
"from sklearn.compose import ColumnTransformer\n",
|
||
"from IPython.display import Image \n",
|
||
"from pydot import graph_from_dot_data\n",
|
||
"import os\n",
|
||
"\n",
|
||
"# Where to save the figures and data files\n",
|
||
"PROJECT_ROOT_DIR = \"Results\"\n",
|
||
"FIGURE_ID = \"Results/FigureFiles\"\n",
|
||
"DATA_ID = \"DataFiles/\"\n",
|
||
"\n",
|
||
"if not os.path.exists(PROJECT_ROOT_DIR):\n",
|
||
" os.mkdir(PROJECT_ROOT_DIR)\n",
|
||
"\n",
|
||
"if not os.path.exists(FIGURE_ID):\n",
|
||
" os.makedirs(FIGURE_ID)\n",
|
||
"\n",
|
||
"if not os.path.exists(DATA_ID):\n",
|
||
" os.makedirs(DATA_ID)\n",
|
||
"\n",
|
||
"def image_path(fig_id):\n",
|
||
" return os.path.join(FIGURE_ID, fig_id)\n",
|
||
"\n",
|
||
"def data_path(dat_id):\n",
|
||
" return os.path.join(DATA_ID, dat_id)\n",
|
||
"\n",
|
||
"def save_fig(fig_id):\n",
|
||
" plt.savefig(image_path(fig_id) + \".png\", format='png')\n",
|
||
"\n",
|
||
"infile = open(data_path(\"rideclass.csv\"),'r')\n",
|
||
"\n",
|
||
"# Read the experimental data with Pandas\n",
|
||
"from IPython.display import display\n",
|
||
"ridedata = pd.read_csv(infile,names = ('Outlook','Temperature','Humidity','Wind','Ride'))\n",
|
||
"ridedata = pd.DataFrame(ridedata)\n",
|
||
"\n",
|
||
"# Features and targets\n",
|
||
"X = ridedata.loc[:, ridedata.columns != 'Ride'].values\n",
|
||
"y = ridedata.loc[:, ridedata.columns == 'Ride'].values\n",
|
||
"\n",
|
||
"# Create the encoder.\n",
|
||
"encoder = OneHotEncoder(handle_unknown=\"ignore\")\n",
|
||
"# Assume for simplicity all features are categorical.\n",
|
||
"encoder.fit(X) \n",
|
||
"# Apply the encoder.\n",
|
||
"X = encoder.transform(X)\n",
|
||
"print(X)\n",
|
||
"# Then do a Classification tree\n",
|
||
"tree_clf = DecisionTreeClassifier(max_depth=2)\n",
|
||
"tree_clf.fit(X, y)\n",
|
||
"print(\"Train set accuracy with Decision Tree: {:.2f}\".format(tree_clf.score(X,y)))\n",
|
||
"#transfer to a decision tree graph\n",
|
||
"export_graphviz(\n",
|
||
" tree_clf,\n",
|
||
" out_file=\"DataFiles/ride.dot\",\n",
|
||
" rounded=True,\n",
|
||
" filled=True\n",
|
||
")\n",
|
||
"cmd = 'dot -Tpng DataFiles/cancer.dot -o DataFiles/cancer.png'\n",
|
||
"os.system(cmd)"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"The above functions (gini, entropy and misclassification error) are\n",
|
||
"important components of the so-called CART algorithm. We will discuss\n",
|
||
"this algorithm below after we have discussed the information gain\n",
|
||
"algorithm ID3.\n",
|
||
"\n",
|
||
"In the example here we have converted all our attributes into numerical values $0,1,2$ etc."
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 7,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"X1 < 0.000 Gini=0.408\n",
|
||
"X1 < 0.000 Gini=0.408\n",
|
||
"X1 < 1.000 Gini=0.394\n",
|
||
"X1 < 2.000 Gini=0.394\n",
|
||
"X1 < 2.000 Gini=0.394\n",
|
||
"X1 < 2.000 Gini=0.394\n",
|
||
"X1 < 1.000 Gini=0.394\n",
|
||
"X1 < 0.000 Gini=0.408\n",
|
||
"X1 < 0.000 Gini=0.408\n",
|
||
"X1 < 2.000 Gini=0.394\n",
|
||
"X1 < 0.000 Gini=0.408\n",
|
||
"X1 < 1.000 Gini=0.394\n",
|
||
"X1 < 1.000 Gini=0.394\n",
|
||
"X1 < 2.000 Gini=0.394\n",
|
||
"X2 < 0.000 Gini=0.408\n",
|
||
"X2 < 0.000 Gini=0.408\n",
|
||
"X2 < 0.000 Gini=0.408\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X2 < 2.000 Gini=0.407\n",
|
||
"X2 < 2.000 Gini=0.407\n",
|
||
"X2 < 2.000 Gini=0.407\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X2 < 2.000 Gini=0.407\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X2 < 0.000 Gini=0.408\n",
|
||
"X2 < 1.000 Gini=0.407\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X3 < 1.000 Gini=0.367\n",
|
||
"X3 < 0.000 Gini=0.408\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"X4 < 0.000 Gini=0.408\n",
|
||
"X4 < 1.000 Gini=0.405\n",
|
||
"Split: [X3 < 1.000]\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"# Split a dataset based on an attribute and an attribute value\n",
|
||
"def test_split(index, value, dataset):\n",
|
||
"\tleft, right = list(), list()\n",
|
||
"\tfor row in dataset:\n",
|
||
"\t\tif row[index] < value:\n",
|
||
"\t\t\tleft.append(row)\n",
|
||
"\t\telse:\n",
|
||
"\t\t\tright.append(row)\n",
|
||
"\treturn left, right\n",
|
||
" \n",
|
||
"# Calculate the Gini index for a split dataset\n",
|
||
"def gini_index(groups, classes):\n",
|
||
"\t# count all samples at split point\n",
|
||
"\tn_instances = float(sum([len(group) for group in groups]))\n",
|
||
"\t# sum weighted Gini index for each group\n",
|
||
"\tgini = 0.0\n",
|
||
"\tfor group in groups:\n",
|
||
"\t\tsize = float(len(group))\n",
|
||
"\t\t# avoid divide by zero\n",
|
||
"\t\tif size == 0:\n",
|
||
"\t\t\tcontinue\n",
|
||
"\t\tscore = 0.0\n",
|
||
"\t\t# score the group based on the score for each class\n",
|
||
"\t\tfor class_val in classes:\n",
|
||
"\t\t\tp = [row[-1] for row in group].count(class_val) / size\n",
|
||
"\t\t\tscore += p * p\n",
|
||
"\t\t# weight the group score by its relative size\n",
|
||
"\t\tgini += (1.0 - score) * (size / n_instances)\n",
|
||
"\treturn gini\n",
|
||
"\n",
|
||
"# Select the best split point for a dataset\n",
|
||
"def get_split(dataset):\n",
|
||
"\tclass_values = list(set(row[-1] for row in dataset))\n",
|
||
"\tb_index, b_value, b_score, b_groups = 999, 999, 999, None\n",
|
||
"\tfor index in range(len(dataset[0])-1):\n",
|
||
"\t\tfor row in dataset:\n",
|
||
"\t\t\tgroups = test_split(index, row[index], dataset)\n",
|
||
"\t\t\tgini = gini_index(groups, class_values)\n",
|
||
"\t\t\tprint('X%d < %.3f Gini=%.3f' % ((index+1), row[index], gini))\n",
|
||
"\t\t\tif gini < b_score:\n",
|
||
"\t\t\t\tb_index, b_value, b_score, b_groups = index, row[index], gini, groups\n",
|
||
"\treturn {'index':b_index, 'value':b_value, 'groups':b_groups}\n",
|
||
" \n",
|
||
"dataset = [[0,0,0,0,0],\n",
|
||
" [0,0,0,1,1],\n",
|
||
" [1,0,0,0,1],\n",
|
||
" [2,1,0,0,1],\n",
|
||
" [2,2,1,0,1],\n",
|
||
" [2,2,1,1,0],\n",
|
||
" [1,2,1,1,1],\n",
|
||
" [0,1,0,0,0],\n",
|
||
" [0,2,1,0,1],\n",
|
||
" [2,1,1,0,1],\n",
|
||
" [0,1,1,1,1],\n",
|
||
" [1,1,0,1,1],\n",
|
||
" [1,0,1,0,1],\n",
|
||
" [2,1,0,1,0]]\n",
|
||
"\n",
|
||
"split = get_split(dataset)\n",
|
||
"print('Split: [X%d < %.3f]' % ((split['index']+1), split['value']))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Entropy and the ID3 algorithm\n",
|
||
"\n",
|
||
"The ID3 algorithm learns decision trees by constructing\n",
|
||
"them in a top down way, beginning with the question **which attribute should be tested at the root of the tree**?\n",
|
||
"\n",
|
||
"1. Each instance attribute is evaluated using a statistical test to determine how well it alone classifies the training examples.\n",
|
||
"\n",
|
||
"2. The best attribute is selected and used as the test at the root node of the tree.\n",
|
||
"\n",
|
||
"3. A descendant of the root node is then created for each possible value of this attribute.\n",
|
||
"\n",
|
||
"4. Training examples are sorted to the appropriate descendant node.\n",
|
||
"\n",
|
||
"5. The entire process is then repeated using the training examples associated with each descendant node to select the best attribute to test at that point in the tree.\n",
|
||
"\n",
|
||
"6. This forms a greedy search for an acceptable decision tree, in which the algorithm never backtracks to reconsider earlier choices. \n",
|
||
"\n",
|
||
"The ID3 algorithm selects which attribute to test at each node in the\n",
|
||
"tree.\n",
|
||
"\n",
|
||
"We would like to select the attribute that is most useful for classifying\n",
|
||
"examples.\n",
|
||
"\n",
|
||
"What is a good quantitative measure of the worth of an attribute?\n",
|
||
"\n",
|
||
"Information gain measures how well a given attribute separates the\n",
|
||
"training examples according to their target classification.\n",
|
||
"\n",
|
||
"The ID3 algorithm uses this information gain measure to select among the candidate\n",
|
||
"attributes at each step while growing the tree.\n",
|
||
"\n",
|
||
"\n",
|
||
"### Cancer Data again now with Decision Trees and other Methods"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 8,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"(426, 30)\n",
|
||
"(143, 30)\n",
|
||
"Test set accuracy with Logistic Regression: 0.95\n",
|
||
"Test set accuracy with SVM: 0.63\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"Test set accuracy with Decision Trees: 0.90\n"
|
||
]
|
||
},
|
||
{
|
||
"name": "stdout",
|
||
"output_type": "stream",
|
||
"text": [
|
||
"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:465: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
|
||
"STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
|
||
"\n",
|
||
"Increase the number of iterations (max_iter) or scale the data as shown in:\n",
|
||
" https://scikit-learn.org/stable/modules/preprocessing.html\n",
|
||
"Please also refer to the documentation for alternative solver options:\n",
|
||
" https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
|
||
" n_iter_i = _check_optimize_result(\n"
|
||
]
|
||
}
|
||
],
|
||
"source": [
|
||
"import matplotlib.pyplot as plt\n",
|
||
"import numpy as np\n",
|
||
"from sklearn.model_selection import train_test_split \n",
|
||
"from sklearn.datasets import load_breast_cancer\n",
|
||
"from sklearn.svm import SVC\n",
|
||
"from sklearn.linear_model import LogisticRegression\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"\n",
|
||
"# Load the data\n",
|
||
"cancer = load_breast_cancer()\n",
|
||
"\n",
|
||
"X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
|
||
"print(X_train.shape)\n",
|
||
"print(X_test.shape)\n",
|
||
"# Logistic Regression\n",
|
||
"logreg = LogisticRegression(solver='lbfgs')\n",
|
||
"logreg.fit(X_train, y_train)\n",
|
||
"print(\"Test set accuracy with Logistic Regression: {:.2f}\".format(logreg.score(X_test,y_test)))\n",
|
||
"# Support vector machine\n",
|
||
"svm = SVC(gamma='auto', C=100)\n",
|
||
"svm.fit(X_train, y_train)\n",
|
||
"print(\"Test set accuracy with SVM: {:.2f}\".format(svm.score(X_test,y_test)))\n",
|
||
"# Decision Trees\n",
|
||
"deep_tree_clf = DecisionTreeClassifier(max_depth=None)\n",
|
||
"deep_tree_clf.fit(X_train, y_train)\n",
|
||
"print(\"Test set accuracy with Decision Trees: {:.2f}\".format(deep_tree_clf.score(X_test,y_test)))\n",
|
||
"#now scale the data\n",
|
||
"from sklearn.preprocessing import StandardScaler\n",
|
||
"scaler = StandardScaler()\n",
|
||
"scaler.fit(X_train)\n",
|
||
"X_train_scaled = scaler.transform(X_train)\n",
|
||
"X_test_scaled = scaler.transform(X_test)\n",
|
||
"# Logistic Regression\n",
|
||
"logreg.fit(X_train_scaled, y_train)\n",
|
||
"print(\"Test set accuracy Logistic Regression with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
|
||
"# Support Vector Machine\n",
|
||
"svm.fit(X_train_scaled, y_train)\n",
|
||
"print(\"Test set accuracy SVM with scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
|
||
"# Decision Trees\n",
|
||
"deep_tree_clf.fit(X_train_scaled, y_train)\n",
|
||
"print(\"Test set accuracy with Decision Trees and scaled data: {:.2f}\".format(deep_tree_clf.score(X_test_scaled,y_test)))"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"### Another example, the moons again"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 9,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
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",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"from __future__ import division, print_function, unicode_literals\n",
|
||
"\n",
|
||
"# Common imports\n",
|
||
"import numpy as np\n",
|
||
"import os\n",
|
||
"\n",
|
||
"# to make this notebook's output stable across runs\n",
|
||
"np.random.seed(42)\n",
|
||
"\n",
|
||
"# To plot pretty figures\n",
|
||
"import matplotlib\n",
|
||
"import matplotlib.pyplot as plt\n",
|
||
"from matplotlib.colors import ListedColormap\n",
|
||
"plt.rcParams['axes.labelsize'] = 14\n",
|
||
"plt.rcParams['xtick.labelsize'] = 12\n",
|
||
"plt.rcParams['ytick.labelsize'] = 12\n",
|
||
"\n",
|
||
"\n",
|
||
"from sklearn.svm import SVC\n",
|
||
"from sklearn import datasets\n",
|
||
"from sklearn.tree import DecisionTreeClassifier\n",
|
||
"from sklearn.datasets import make_moons\n",
|
||
"from sklearn.tree import export_graphviz\n",
|
||
"\n",
|
||
"Xm, ym = make_moons(n_samples=100, noise=0.25, random_state=53)\n",
|
||
"\n",
|
||
"deep_tree_clf1 = DecisionTreeClassifier(random_state=42)\n",
|
||
"deep_tree_clf2 = DecisionTreeClassifier(min_samples_leaf=4, random_state=42)\n",
|
||
"deep_tree_clf1.fit(Xm, ym)\n",
|
||
"deep_tree_clf2.fit(Xm, ym)\n",
|
||
"\n",
|
||
"\n",
|
||
"def plot_decision_boundary(clf, X, y, axes=[0, 7.5, 0, 3], iris=True, legend=False, plot_training=True):\n",
|
||
" x1s = np.linspace(axes[0], axes[1], 100)\n",
|
||
" x2s = np.linspace(axes[2], axes[3], 100)\n",
|
||
" x1, x2 = np.meshgrid(x1s, x2s)\n",
|
||
" X_new = np.c_[x1.ravel(), x2.ravel()]\n",
|
||
" y_pred = clf.predict(X_new).reshape(x1.shape)\n",
|
||
" custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n",
|
||
" plt.contourf(x1, x2, y_pred, alpha=0.3, cmap=custom_cmap)\n",
|
||
" if not iris:\n",
|
||
" custom_cmap2 = ListedColormap(['#7d7d58','#4c4c7f','#507d50'])\n",
|
||
" plt.contour(x1, x2, y_pred, cmap=custom_cmap2, alpha=0.8)\n",
|
||
" if plot_training:\n",
|
||
" plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\", label=\"Iris-Setosa\")\n",
|
||
" plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\", label=\"Iris-Versicolor\")\n",
|
||
" plt.plot(X[:, 0][y==2], X[:, 1][y==2], \"g^\", label=\"Iris-Virginica\")\n",
|
||
" plt.axis(axes)\n",
|
||
" if iris:\n",
|
||
" plt.xlabel(\"Petal length\", fontsize=14)\n",
|
||
" plt.ylabel(\"Petal width\", fontsize=14)\n",
|
||
" else:\n",
|
||
" plt.xlabel(r\"$x_1$\", fontsize=18)\n",
|
||
" plt.ylabel(r\"$x_2$\", fontsize=18, rotation=0)\n",
|
||
" if legend:\n",
|
||
" plt.legend(loc=\"lower right\", fontsize=14)\n",
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"plt.subplot(121)\n",
|
||
"plot_decision_boundary(deep_tree_clf1, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)\n",
|
||
"plt.title(\"No restrictions\", fontsize=16)\n",
|
||
"plt.subplot(122)\n",
|
||
"plot_decision_boundary(deep_tree_clf2, Xm, ym, axes=[-1.5, 2.5, -1, 1.5], iris=False)\n",
|
||
"plt.title(\"min_samples_leaf = {}\".format(deep_tree_clf2.min_samples_leaf), fontsize=14)\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 10,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"np.random.seed(6)\n",
|
||
"Xs = np.random.rand(100, 2) - 0.5\n",
|
||
"ys = (Xs[:, 0] > 0).astype(np.float32) * 2\n",
|
||
"\n",
|
||
"angle = np.pi/4\n",
|
||
"rotation_matrix = np.array([[np.cos(angle), -np.sin(angle)], [np.sin(angle), np.cos(angle)]])\n",
|
||
"Xsr = Xs.dot(rotation_matrix)\n",
|
||
"\n",
|
||
"tree_clf_s = DecisionTreeClassifier(random_state=42)\n",
|
||
"tree_clf_s.fit(Xs, ys)\n",
|
||
"tree_clf_sr = DecisionTreeClassifier(random_state=42)\n",
|
||
"tree_clf_sr.fit(Xsr, ys)\n",
|
||
"\n",
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"plt.subplot(121)\n",
|
||
"plot_decision_boundary(tree_clf_s, Xs, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
|
||
"plt.subplot(122)\n",
|
||
"plot_decision_boundary(tree_clf_sr, Xsr, ys, axes=[-0.7, 0.7, -0.7, 0.7], iris=False)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 11,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [],
|
||
"source": [
|
||
"# Quadratic training set + noise\n",
|
||
"np.random.seed(42)\n",
|
||
"m = 200\n",
|
||
"X = np.random.rand(m, 1)\n",
|
||
"y = 4 * (X - 0.5) ** 2\n",
|
||
"y = y + np.random.randn(m, 1) / 10"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 12,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"text/html": [
|
||
"<style>#sk-container-id-1 {\n",
|
||
" /* Definition of color scheme common for light and dark mode */\n",
|
||
" --sklearn-color-text: #000;\n",
|
||
" --sklearn-color-text-muted: #666;\n",
|
||
" --sklearn-color-line: gray;\n",
|
||
" /* Definition of color scheme for unfitted estimators */\n",
|
||
" --sklearn-color-unfitted-level-0: #fff5e6;\n",
|
||
" --sklearn-color-unfitted-level-1: #f6e4d2;\n",
|
||
" --sklearn-color-unfitted-level-2: #ffe0b3;\n",
|
||
" --sklearn-color-unfitted-level-3: chocolate;\n",
|
||
" /* Definition of color scheme for fitted estimators */\n",
|
||
" --sklearn-color-fitted-level-0: #f0f8ff;\n",
|
||
" --sklearn-color-fitted-level-1: #d4ebff;\n",
|
||
" --sklearn-color-fitted-level-2: #b3dbfd;\n",
|
||
" --sklearn-color-fitted-level-3: cornflowerblue;\n",
|
||
"\n",
|
||
" /* Specific color for light theme */\n",
|
||
" --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
|
||
" --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
|
||
" --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
|
||
" --sklearn-color-icon: #696969;\n",
|
||
"\n",
|
||
" @media (prefers-color-scheme: dark) {\n",
|
||
" /* Redefinition of color scheme for dark theme */\n",
|
||
" --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
|
||
" --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
|
||
" --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
|
||
" --sklearn-color-icon: #878787;\n",
|
||
" }\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 {\n",
|
||
" color: var(--sklearn-color-text);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 pre {\n",
|
||
" padding: 0;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 input.sk-hidden--visually {\n",
|
||
" border: 0;\n",
|
||
" clip: rect(1px 1px 1px 1px);\n",
|
||
" clip: rect(1px, 1px, 1px, 1px);\n",
|
||
" height: 1px;\n",
|
||
" margin: -1px;\n",
|
||
" overflow: hidden;\n",
|
||
" padding: 0;\n",
|
||
" position: absolute;\n",
|
||
" width: 1px;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-dashed-wrapped {\n",
|
||
" border: 1px dashed var(--sklearn-color-line);\n",
|
||
" margin: 0 0.4em 0.5em 0.4em;\n",
|
||
" box-sizing: border-box;\n",
|
||
" padding-bottom: 0.4em;\n",
|
||
" background-color: var(--sklearn-color-background);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-container {\n",
|
||
" /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
|
||
" but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
|
||
" so we also need the `!important` here to be able to override the\n",
|
||
" default hidden behavior on the sphinx rendered scikit-learn.org.\n",
|
||
" See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
|
||
" display: inline-block !important;\n",
|
||
" position: relative;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-text-repr-fallback {\n",
|
||
" display: none;\n",
|
||
"}\n",
|
||
"\n",
|
||
"div.sk-parallel-item,\n",
|
||
"div.sk-serial,\n",
|
||
"div.sk-item {\n",
|
||
" /* draw centered vertical line to link estimators */\n",
|
||
" background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
|
||
" background-size: 2px 100%;\n",
|
||
" background-repeat: no-repeat;\n",
|
||
" background-position: center center;\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Parallel-specific style estimator block */\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-parallel-item::after {\n",
|
||
" content: \"\";\n",
|
||
" width: 100%;\n",
|
||
" border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
|
||
" flex-grow: 1;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-parallel {\n",
|
||
" display: flex;\n",
|
||
" align-items: stretch;\n",
|
||
" justify-content: center;\n",
|
||
" background-color: var(--sklearn-color-background);\n",
|
||
" position: relative;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-parallel-item {\n",
|
||
" display: flex;\n",
|
||
" flex-direction: column;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
|
||
" align-self: flex-end;\n",
|
||
" width: 50%;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
|
||
" align-self: flex-start;\n",
|
||
" width: 50%;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
|
||
" width: 0;\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Serial-specific style estimator block */\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-serial {\n",
|
||
" display: flex;\n",
|
||
" flex-direction: column;\n",
|
||
" align-items: center;\n",
|
||
" background-color: var(--sklearn-color-background);\n",
|
||
" padding-right: 1em;\n",
|
||
" padding-left: 1em;\n",
|
||
"}\n",
|
||
"\n",
|
||
"\n",
|
||
"/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
|
||
"clickable and can be expanded/collapsed.\n",
|
||
"- Pipeline and ColumnTransformer use this feature and define the default style\n",
|
||
"- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
|
||
"*/\n",
|
||
"\n",
|
||
"/* Pipeline and ColumnTransformer style (default) */\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-toggleable {\n",
|
||
" /* Default theme specific background. It is overwritten whether we have a\n",
|
||
" specific estimator or a Pipeline/ColumnTransformer */\n",
|
||
" background-color: var(--sklearn-color-background);\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Toggleable label */\n",
|
||
"#sk-container-id-1 label.sk-toggleable__label {\n",
|
||
" cursor: pointer;\n",
|
||
" display: flex;\n",
|
||
" width: 100%;\n",
|
||
" margin-bottom: 0;\n",
|
||
" padding: 0.5em;\n",
|
||
" box-sizing: border-box;\n",
|
||
" text-align: center;\n",
|
||
" align-items: start;\n",
|
||
" justify-content: space-between;\n",
|
||
" gap: 0.5em;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 label.sk-toggleable__label .caption {\n",
|
||
" font-size: 0.6rem;\n",
|
||
" font-weight: lighter;\n",
|
||
" color: var(--sklearn-color-text-muted);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
|
||
" /* Arrow on the left of the label */\n",
|
||
" content: \"▸\";\n",
|
||
" float: left;\n",
|
||
" margin-right: 0.25em;\n",
|
||
" color: var(--sklearn-color-icon);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
|
||
" color: var(--sklearn-color-text);\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Toggleable content - dropdown */\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-toggleable__content {\n",
|
||
" max-height: 0;\n",
|
||
" max-width: 0;\n",
|
||
" overflow: hidden;\n",
|
||
" text-align: left;\n",
|
||
" /* unfitted */\n",
|
||
" background-color: var(--sklearn-color-unfitted-level-0);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
|
||
" /* fitted */\n",
|
||
" background-color: var(--sklearn-color-fitted-level-0);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-toggleable__content pre {\n",
|
||
" margin: 0.2em;\n",
|
||
" border-radius: 0.25em;\n",
|
||
" color: var(--sklearn-color-text);\n",
|
||
" /* unfitted */\n",
|
||
" background-color: var(--sklearn-color-unfitted-level-0);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
|
||
" /* unfitted */\n",
|
||
" background-color: var(--sklearn-color-fitted-level-0);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
|
||
" /* Expand drop-down */\n",
|
||
" max-height: 200px;\n",
|
||
" max-width: 100%;\n",
|
||
" overflow: auto;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
|
||
" content: \"▾\";\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Pipeline/ColumnTransformer-specific style */\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
|
||
" color: var(--sklearn-color-text);\n",
|
||
" background-color: var(--sklearn-color-unfitted-level-2);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
|
||
" background-color: var(--sklearn-color-fitted-level-2);\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Estimator-specific style */\n",
|
||
"\n",
|
||
"/* Colorize estimator box */\n",
|
||
"#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
|
||
" /* unfitted */\n",
|
||
" background-color: var(--sklearn-color-unfitted-level-2);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
|
||
" /* fitted */\n",
|
||
" background-color: var(--sklearn-color-fitted-level-2);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
|
||
"#sk-container-id-1 div.sk-label label {\n",
|
||
" /* The background is the default theme color */\n",
|
||
" color: var(--sklearn-color-text-on-default-background);\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* On hover, darken the color of the background */\n",
|
||
"#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
|
||
" color: var(--sklearn-color-text);\n",
|
||
" background-color: var(--sklearn-color-unfitted-level-2);\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Label box, darken color on hover, fitted */\n",
|
||
"#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
|
||
" color: var(--sklearn-color-text);\n",
|
||
" background-color: var(--sklearn-color-fitted-level-2);\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Estimator label */\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-label label {\n",
|
||
" font-family: monospace;\n",
|
||
" font-weight: bold;\n",
|
||
" display: inline-block;\n",
|
||
" line-height: 1.2em;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-label-container {\n",
|
||
" text-align: center;\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Estimator-specific */\n",
|
||
"#sk-container-id-1 div.sk-estimator {\n",
|
||
" font-family: monospace;\n",
|
||
" border: 1px dotted var(--sklearn-color-border-box);\n",
|
||
" border-radius: 0.25em;\n",
|
||
" box-sizing: border-box;\n",
|
||
" margin-bottom: 0.5em;\n",
|
||
" /* unfitted */\n",
|
||
" background-color: var(--sklearn-color-unfitted-level-0);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-estimator.fitted {\n",
|
||
" /* fitted */\n",
|
||
" background-color: var(--sklearn-color-fitted-level-0);\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* on hover */\n",
|
||
"#sk-container-id-1 div.sk-estimator:hover {\n",
|
||
" /* unfitted */\n",
|
||
" background-color: var(--sklearn-color-unfitted-level-2);\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
|
||
" /* fitted */\n",
|
||
" background-color: var(--sklearn-color-fitted-level-2);\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
|
||
"\n",
|
||
"/* Common style for \"i\" and \"?\" */\n",
|
||
"\n",
|
||
".sk-estimator-doc-link,\n",
|
||
"a:link.sk-estimator-doc-link,\n",
|
||
"a:visited.sk-estimator-doc-link {\n",
|
||
" float: right;\n",
|
||
" font-size: smaller;\n",
|
||
" line-height: 1em;\n",
|
||
" font-family: monospace;\n",
|
||
" background-color: var(--sklearn-color-background);\n",
|
||
" border-radius: 1em;\n",
|
||
" height: 1em;\n",
|
||
" width: 1em;\n",
|
||
" text-decoration: none !important;\n",
|
||
" margin-left: 0.5em;\n",
|
||
" text-align: center;\n",
|
||
" /* unfitted */\n",
|
||
" border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
|
||
" color: var(--sklearn-color-unfitted-level-1);\n",
|
||
"}\n",
|
||
"\n",
|
||
".sk-estimator-doc-link.fitted,\n",
|
||
"a:link.sk-estimator-doc-link.fitted,\n",
|
||
"a:visited.sk-estimator-doc-link.fitted {\n",
|
||
" /* fitted */\n",
|
||
" border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
|
||
" color: var(--sklearn-color-fitted-level-1);\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* On hover */\n",
|
||
"div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
|
||
".sk-estimator-doc-link:hover,\n",
|
||
"div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
|
||
".sk-estimator-doc-link:hover {\n",
|
||
" /* unfitted */\n",
|
||
" background-color: var(--sklearn-color-unfitted-level-3);\n",
|
||
" color: var(--sklearn-color-background);\n",
|
||
" text-decoration: none;\n",
|
||
"}\n",
|
||
"\n",
|
||
"div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
|
||
".sk-estimator-doc-link.fitted:hover,\n",
|
||
"div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
|
||
".sk-estimator-doc-link.fitted:hover {\n",
|
||
" /* fitted */\n",
|
||
" background-color: var(--sklearn-color-fitted-level-3);\n",
|
||
" color: var(--sklearn-color-background);\n",
|
||
" text-decoration: none;\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* Span, style for the box shown on hovering the info icon */\n",
|
||
".sk-estimator-doc-link span {\n",
|
||
" display: none;\n",
|
||
" z-index: 9999;\n",
|
||
" position: relative;\n",
|
||
" font-weight: normal;\n",
|
||
" right: .2ex;\n",
|
||
" padding: .5ex;\n",
|
||
" margin: .5ex;\n",
|
||
" width: min-content;\n",
|
||
" min-width: 20ex;\n",
|
||
" max-width: 50ex;\n",
|
||
" color: var(--sklearn-color-text);\n",
|
||
" box-shadow: 2pt 2pt 4pt #999;\n",
|
||
" /* unfitted */\n",
|
||
" background: var(--sklearn-color-unfitted-level-0);\n",
|
||
" border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
|
||
"}\n",
|
||
"\n",
|
||
".sk-estimator-doc-link.fitted span {\n",
|
||
" /* fitted */\n",
|
||
" background: var(--sklearn-color-fitted-level-0);\n",
|
||
" border: var(--sklearn-color-fitted-level-3);\n",
|
||
"}\n",
|
||
"\n",
|
||
".sk-estimator-doc-link:hover span {\n",
|
||
" display: block;\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* \"?\"-specific style due to the `<a>` HTML tag */\n",
|
||
"\n",
|
||
"#sk-container-id-1 a.estimator_doc_link {\n",
|
||
" float: right;\n",
|
||
" font-size: 1rem;\n",
|
||
" line-height: 1em;\n",
|
||
" font-family: monospace;\n",
|
||
" background-color: var(--sklearn-color-background);\n",
|
||
" border-radius: 1rem;\n",
|
||
" height: 1rem;\n",
|
||
" width: 1rem;\n",
|
||
" text-decoration: none;\n",
|
||
" /* unfitted */\n",
|
||
" color: var(--sklearn-color-unfitted-level-1);\n",
|
||
" border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 a.estimator_doc_link.fitted {\n",
|
||
" /* fitted */\n",
|
||
" border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
|
||
" color: var(--sklearn-color-fitted-level-1);\n",
|
||
"}\n",
|
||
"\n",
|
||
"/* On hover */\n",
|
||
"#sk-container-id-1 a.estimator_doc_link:hover {\n",
|
||
" /* unfitted */\n",
|
||
" background-color: var(--sklearn-color-unfitted-level-3);\n",
|
||
" color: var(--sklearn-color-background);\n",
|
||
" text-decoration: none;\n",
|
||
"}\n",
|
||
"\n",
|
||
"#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
|
||
" /* fitted */\n",
|
||
" background-color: var(--sklearn-color-fitted-level-3);\n",
|
||
"}\n",
|
||
"</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 fitted 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 fitted sk-toggleable__label-arrow\"><div><div>DecisionTreeRegressor</div></div><div><a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.6/modules/generated/sklearn.tree.DecisionTreeRegressor.html\">?<span>Documentation for DecisionTreeRegressor</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\"><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": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"from sklearn.tree import DecisionTreeRegressor\n",
|
||
"\n",
|
||
"tree_reg1 = DecisionTreeRegressor(random_state=42, max_depth=2)\n",
|
||
"tree_reg2 = DecisionTreeRegressor(random_state=42, max_depth=3)\n",
|
||
"tree_reg1.fit(X, y)\n",
|
||
"tree_reg2.fit(X, y)\n",
|
||
"\n",
|
||
"def plot_regression_predictions(tree_reg, X, y, axes=[0, 1, -0.2, 1], ylabel=\"$y$\"):\n",
|
||
" x1 = np.linspace(axes[0], axes[1], 500).reshape(-1, 1)\n",
|
||
" y_pred = tree_reg.predict(x1)\n",
|
||
" plt.axis(axes)\n",
|
||
" plt.xlabel(\"$x_1$\", fontsize=18)\n",
|
||
" if ylabel:\n",
|
||
" plt.ylabel(ylabel, fontsize=18, rotation=0)\n",
|
||
" plt.plot(X, y, \"b.\")\n",
|
||
" plt.plot(x1, y_pred, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
|
||
"\n",
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"plt.subplot(121)\n",
|
||
"plot_regression_predictions(tree_reg1, X, y)\n",
|
||
"for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
|
||
" plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
|
||
"plt.text(0.21, 0.65, \"Depth=0\", fontsize=15)\n",
|
||
"plt.text(0.01, 0.2, \"Depth=1\", fontsize=13)\n",
|
||
"plt.text(0.65, 0.8, \"Depth=1\", fontsize=13)\n",
|
||
"plt.legend(loc=\"upper center\", fontsize=18)\n",
|
||
"plt.title(\"max_depth=2\", fontsize=14)\n",
|
||
"\n",
|
||
"plt.subplot(122)\n",
|
||
"plot_regression_predictions(tree_reg2, X, y, ylabel=None)\n",
|
||
"for split, style in ((0.1973, \"k-\"), (0.0917, \"k--\"), (0.7718, \"k--\")):\n",
|
||
" plt.plot([split, split], [-0.2, 1], style, linewidth=2)\n",
|
||
"for split in (0.0458, 0.1298, 0.2873, 0.9040):\n",
|
||
" plt.plot([split, split], [-0.2, 1], \"k:\", linewidth=1)\n",
|
||
"plt.text(0.3, 0.5, \"Depth=2\", fontsize=13)\n",
|
||
"plt.title(\"max_depth=3\", fontsize=14)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "code",
|
||
"execution_count": 14,
|
||
"metadata": {
|
||
"collapsed": false,
|
||
"editable": true
|
||
},
|
||
"outputs": [
|
||
{
|
||
"data": {
|
||
"image/png": 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2NDTY5yxlzZo1WLp0KX7++WdUVlbKcrS13gc15syZQ/2SCa9CwpYgdHL//ffj3//+N55//nnk5uaq7iMUuhDyYJUIVQGrq6t1v67auU6cOAGAb0X02WefaR576tQpAEC3bt2wZcsWzJ07F1988QU++OADAHxxrHnz5mHs2LG656M1Jy0Egdi5c2e3XkMvzfmfC3lAUkJC+Mui1FC/+uqr6N69O1asWIFnnnkGzzzzDCIiInDLLbfgpZdeouqhBEEEDMrcUEC8rjnbJogYZ6hdM4VzKIvu6SE2NhZbtmzB7NmzsXbtWnz++ecAeKE8a9YsTJs2zb7vfffdh3//+9/o0qUL/vGPfyA1NRXh4eEA+MJEdXV1qq+h9Tc7u/6r/S8SExNhMDjWXBVsjyu7Ltjt//73v073E+z24MGD8e2332LBggVYtWqVveDSgAED8MILL2DEiBFOz6OHyspKMMZw+PBhzJ071+WcAOCll17Cww8/jKSkJFx55ZUwmUyIjIwEALzyyiua70MgILznWu9VTU2N5mecCA5I2BKETiIjIzFnzhxMmTIF8+fPx5gxYxz2EQzosWPHVM8hjKsZWi3Umo0Lx7/22mu45557dJ2nf//++Oijj9DQ0ICffvoJX3zxBV599VWMGzcOnTp1wtChQ5s1Jy0EI6G2Au4NfPE/VxIaGopHHnkEjzzyCI4cOYLvv/8eb731Ft5++20cPXoU69ev9/jcBEEQbZmuXbuioKAAVqsVO3fuxFdffYVXX30V06dPR3x8PMaPH4+ysjK8/vrr6N+/P7Zs2SKLzjl69KhTUeYtKioqYLPZHMStYGNcCSLBBq1duxajR4/W9ZrDhg3DsGHDcObMGWzbtg1r167Ff/7zH1x77bXYuXNns1vrCXMaMGCAajVoJY2NjZg3bx46deqEHTt2ICkpyb6NMYbnn3/erdf/7rvv7AWd9HDBBRfg+uuvd+s1pAhRY8XFxRgwYIBsW2VlJY4fP44hQ4Z4fH7C/5CwJQg3uOuuu7Bo0SK8/vrrOP/88x22C2FeP/zwAxhjMgHIGENhYaFsP08Rqh1v2bJFt7AVEMKpLrnkEvTo0QN33nkn1q1bZxe2QtVnq9XqsgK0HqKionDeeedhz549KC4udhmO7O7r9+rVCxERESgqKsLp06cdwpGFCofeqsLYqVMnjB8/HuPGjUOvXr2wYcMGnDlzxr5iTRAEQbiP0WjEBRdcgAsuuACDBw/GZZddhk8//RTjx4/H33//DcYYrrjiCodrvGBXfU1DQwO2bt3qIHz02nWp3dYrbAUiIyMxfPhwDB8+HHFxcXj66aexYcOGZgvb6Oho9O7dG7t370ZVVRXi4uKc7n/8+HFUV1fj8ssvl4laAPjxxx/tLaX08t1337m1KJGdnd0sYTts2DAsWLAAX331FW699VbZtq+++sq+DxG8UB9bgnADo9GI+fPno66uDv/6178ctqelpWHEiBH29j5S3nzzTfz+++8YOXKk7vxaLQYOHIhBgwZh1apVeP/99x2222w2Wcn6oqIih/5ygLjSLBVlCQkJAACLxdKsOUqZPn06rFarrJeiwNmzZ+0hWp68flhYGMaPH4/jx49jwYIFsm0bNmzAF198gR49erjlkZZSV1eHb7/9Fowx2fipU6dQW1uL0NBQrywAEARBtDV27dql2r9VaZvS09MBAJs3b5aFPFssFq+1vdHDU089JQtT/vPPP/Hmm28iNjYW1113ndNjr7vuOqSlpWHRokWq/c8bGhrwf//3f/bnhYWFsj6+Amp2uzncd999OH36NCZPniwLORbYv3+/vU99cnIyIiMj8fPPP+P06dP2fSorK3Hvvfe6/dpz5swB4wvZ6vppbv/byy+/HN27d8fKlSuxY8cO+3htbS3mzZuHkJAQTJgwoVmvQfgX8tgShJvccMMNGDx4sGahjCVLluDSSy/F5MmTsXbtWpx33nn4448/8OmnnyIpKQlLlizxyjxWrVqFESNG4NZbb8Urr7yCAQMGICIiAgcPHsSWLVtQXl6Os2fPAuBzev7zn/9g+PDh6NGjB2JiYvDHH3/g888/R4cOHXDXXXfZzzty5Eh8+OGHGDt2LK655hpERESgX79+uPbaaz2e6913343vv/8eq1evhtlsxj/+8Q/ExMTg4MGDWL9+PfLz8+2rsJ68vtDH8JlnnsHmzZsxaNAgex/bdu3a4a233lLNjdLDmTNn7MZw0KBBSEtLw8mTJ7Fu3TocPXoUM2fO1F1IiyAIghDZsGEDHnroIQwdOhS9evVCYmIi/v77b3z66aeIjIy0RySlpqbipptuwkcffYSLL74Yl19+OY4dO4Z169Zh5MiR+Pvvv30+19TUVFRVVeGCCy7Atddei+rqaqxatQpnz57FsmXLEB0d7fT48PBwfPjhh7j66qsxbNgwXH755ejbty8A4ODBgygsLERiYqK9UNNLL72Er7/+GiNGjED37t0RERGBn3/+Gd988w169OiBG264wSt/V25uLrZu3YqCggJs2rQJV1xxBTp16oRjx47hzz//xLZt27By5Up07doVBoMB06ZNw0svvYTzzz8fY8aMQU1NDb744gukp6ejU6dOXpmTO0iFaGlpqcPYiy++aK+DERISguXLlyMrKwuZmZkYP348YmJisGbNGuzfvx/PPPOMx0U1iQChpcswE0QwoGz3o+SHH36wl59X9rFljLGSkhI2ceJElpqaykJCQlhqaiqbOHEiKykp0T0Hoe2M0IJBjRMnTrAnn3yS9e3bl0VGRrKoqChmNpvZbbfdxtasWWPfb+vWrSw3N5f17duXxcXFscjISGY2m9l9993n0HqooaGBPfrooywtLY2FhITISuwL/xdnJffV2gkwxrcCWL58ObvkkktY+/btWbt27ZjZbGZTp06VzcHZ6zOm3seWMb4H7X333cfS09NZaGgo69ChA7v55pvtLY+kOPvfCu0HNm7cyBjjew8+99xz7Morr2Qmk4mFhYWxlJQUNmzYMPbee+9p/h8IgiBaEmdtVdTazwgor3nO2v2oXdsZc92mTYs//viDzZgxg1144YUsMTGRhYeHs+7du7MJEyawP/74Q7ZvbW0te+ihh1jXrl1ZeHg4M5vNbN68eay+vl7VLjibk7O/Re1cwv4VFRVs0qRJLDk5mYWHh7OLL75Ytc+ss/+3xWJhM2bMYGazmYWHh7OYmBjWu3dvNmnSJPbNN9/Y9/vyyy/ZnXfeyc4991wWHR3NoqKi2HnnnceefPJJr/axFXj//ffZFVdcweLj41loaCjr3LkzGz58OHvppZdk/e7r6+vZs88+a59/Wloae/DBB1ltba3q+Z19Lr0BVNoCSX/U7Py2bdvYVVddxWJjY1lkZCS7+OKLHfogE8EJx5givo4gCIIgCIIgCACwt0ESQnIJgghMKMeWIAiCIAiCIAiCCGpI2BIEQRAEQRAEQRBBDRWPIgiCIAiCILyC3t6kze1JSgArVqzQFR59/fXXe63lHUEEMiRsCYIgCIIgCK+gtzdpc3uStiSBmlu7YsUKWWs/Lbp27UrClmgTUPEogiAIgiAIgiAIIqihHFuCIAiCIAiCIAgiqKFQZJ3YbDYcOXIE0dHR4DjO39MhCIIg/ABjDLW1tejUqRMMBlob1gvZUIIgCMLXNpSErU6OHDmCLl26+HsaBEEQRABw6NAhmEwmf08jaCAbShAEQQj4yoaSsNVJdHQ0AP6NiPniC2DKFH5Dz57AX3/xj599FuyJJ6Bci26EAce/3YWOAzq33IQJgiAIr1NTU4MuXbrYbQKhD5kNjYnR3O/wYaBPH0Ba/cNgAHbtAjqTCSUIgghqfG1DSdjqRAidiomJQUxoqLghLk58XF6ucbQNB389hpgRvX02P4IgCKLloHBa95DZUCfC9qef5KIWAGw24NgxoDeZUIIgiFaBr2woJQh5QkOD+Fi64hAXB6byRjXCiJShPVpgYgRBEAQRvJjNvIdWitEI9CATShAEQbiAhK0naAnbiAhwzz4r29UGDluylyI1g3KxCIIgAh6LBVi9GliyBJXzl2DX06tRWmTx96zaDCYTkJfHi1mA/710KT9OEARBBA8WC7BxI/+7paBQZE+orxcfS4Xt2bPA+PHA44/bh05Ovh+ZeTktODmCIAjCI/LzgUmT7E/jm35s8zgUZi9D5gq6lrcEOTlAVhawdy/vqSVRSxAEEVzk5/PliGw2PgonL4+/tvsa8th6gpbHtq4OsFplu8aktG+hSREEQRAeY7EAkyerbjKAYXBBLnluWxCTCRg+nEQtQRBEsGGxiKIW4H/n5raM55aErSdoCduzZx2ELRobW2ZOBEEQhOcUFztWLZIQAiuObdrbghMiCIIgiOCjuFgUtQJWKx+F42tI2HqCM2GrfCdJ2BIEQQQ+ZjPgpEojFQEkCIIgCNf4swggCVtPcCMUmYQtQRBEEGAyAa+8orqJigASBEEQhD78WQSQhK0nOCseRcKWIAgiOBk/XnW4/H+bqHAUQRAEQegkJwcoKeGrIpeUtEzhKICqInsGhSITbsIYQ0NDA2zKzwfhFwwGA0JDQ33WIJwIUjSu1yn9Ulp4IgRBEAQR3JhMLV8AkIStJ2gI25rf9qN+Zyk6aO1LtDmsViuOHz+O2tpaNNBnIaAIDQ1FdHQ0OnToAKMQL0O0bZQRN67GCa9hsfAFR8xmqoRMEARBeAYJW0+QCpTvvrM/jNn7C2yTbpDvSx7bNovVasWhQ4dQV1eH2NhYREVFwWg0kpfQzzDGYLVacfLkSVRVVeHMmTPo0qULiVtC+3pNwtan+KvfIUEQBNG6IGHrCRJhy557DlKZYoCiXQQJ2zbL8ePHUVdXh7S0NERGRvp7OoSCqKgoxMbG4uDBgzh+/DhSUijctM2jdb2mFAKfodXvMCuLPLcEQRCEe1DxKE+QFI/inPQ9BEDCto3CGENtbS1iY2NJ1AYwkZGRiImJQW1tLZir7zLR+qFQ5BbHn/0OCYIgiNYFCVtPkHpsXYWVkrBtkzQ0NKChoQFRUVH+ngrhgujoaPv7RbRxKBS5xfFnv0OCIAiidUHC1hMkN8DcCy/AJglGdvD5kLBtkwjVjylvM/AR3iOqWE2QsG15/NnvkCAIgmhdBLywra2txaOPPoorr7wSSUlJ4DgOc+bM0X18WVkZJkyYgA4dOqBdu3YYPHgwvvnmm+ZNSurZufNOGL5ab39qTUmV70vCtk1DhaICH3qPCDtaAjaIFz0C0oYq8Fe/Q4IgCKJ1EfDCtqKiAnl5eairq8P111/v1rF1dXW4/PLL8c0332Dx4sX45JNPkJKSgquuugrff/+955OS5NgiNBTo1Mn+NATUx5YgCCIoaYUe24C0oSqYTMDw4eSpJQiCIDwn4Ksip6eno7KyEhzH4fjx41i+fLnuY/Pz87Fr1y5s3rwZgwcPBgCMGDEC559/Ph599FFs27bNs0lJPbZhYUCI5N8oFb0ACVuCIIhgoRUK24C0oQRBEAThAwLeY8txnMehgh9//DHOPfdcu0EGgJCQENxxxx3Yvn07Dh8+7NmkpMI2NFRMDgJI2BIEQQQrrTAUOSBtKEEQBEH4gIAXts1h165d6N+/v8O4MPb7779rHltXV4eamhrZjx2psA0JIWFLEATRGmiFHtvm4DMbShAEQRA+oFUL24qKCiQkJDiMC2MVFRWaxy5YsACxsbH2ny5duogbBWEbEgJwnFzYKluGkLAlCJ+xe/duzJkzB0uWLPH3VIggpbTIgl8WbURpkYWErQKf2VCCIAiiVWCx8IX/LBZ/z4SnVQtbwHnFU2fbZs2aherqavvPoUOHAACHDwOnyk8JJ+DfSWctXUjYEoRPaGxsxB133IG5c+di2rRp+Pjjj/09JSLI2D72BaQMTMOFD41E8sB07Hz+c/Ud26iwBXxjQwPpJoggCILwjPx8ID0dGDmS/52f7+8ZtXJhm5iYqLqifOLECQBQXYkWCA8PR0xMjOwHABae9zbaHdrD79TQAKSlAatXa09C6cElCMIrLFy4ED///DPmz5+P7t274+6777Z/twnCFaVFFmR8+CgMTd3HjbDhvA2vijtIiwIGcY5tc/CFDe3TJ7BuggiCIAj3sViAKVNE82izAbm5/l+0bNXCtl+/fti5c6fDuDDWt29ft8+5GPdCtkbNGPDww9oHkMeWILzOrl27MG/ePNx8882YNWsWVq9ejcrKStx7773+nhoRJBwtLIbS32iUtmsLCxMft1GPrS9sKOPXEQLmJoggCIJwn+JixzVfqxXYu9c/8xFo1cL2hhtuwJ9//ilrSdDY2Ih3330XgwYNQidJ/1m9qP7DnK3mk7AlCK9itVoxceJEmEwm5De5fAYMGICXXnoJK1euxCeffOLnGRLBQMdMs8OYVXqFDw+XbGibwtYXNlRKINwEEQRBEO5jNgMGhSgyGoEePfwzH4GgELZffPEFPvzwQ6xduxYA8Mcff+DDDz/Ehx9+iNOnTwMAcnJyEBISggMHDtiPu+uuu9CnTx+MHTsWK1euxIYNG3DLLbdgz549eO655zyaC1MbVL6zUkjYEoRXMRqNKCoqwr59++zhjQBwzz33gDGG6667zo+zI4KF1AyT7LkVBvx12SRxQCpsgzwUOZBsqJRAuAkiCIIg3MdkAvLyxDJDRiOwdCk/7k9CXO/if+6++26Zsf3ggw/wwQcfAAD279+Prl27wmq1wmq1gjFReoaHh+Obb77Bo48+invvvRenT5/GBRdcgC+++ALDhg3zaC4H0QX9cEgcMBiAf/8bmDZN/QAStgRBEAFPxfsb0LvhCPBDHj/QikKRA8mGGgz8OkGg3AQRBEEQnpGTA2Rl8ZE3PXoExvWcY1IrRmhSU1OD2NhYVHTphoRD+2GNbA9jwVvA4MFAUhIQEaF+YKdOfBlIok1x9uxZ7N+/H926dUOE1meDCAjovWrDSKv6/vYb8MsvQHY2/7xHDzFO9v33gVtuASDagurqalnEAOEc4f/2xx/VOHYsJmBuggiCIIiWw9c2NCg8toFEyMkqAIAxNQUYO5YfdOaVbYbH1mLhk7PNZroBIAiC8CkNDfLrdSsKRQ4kOncGevdumdciG0oQBNG2CIoc24Ciupr/HRcnjvmgj20g9oYiCH9w7NgxcBwHjuOwfv16p/vec8894DgOQ4YMAQWjEE5Rfj4aG+Uhx60oFLktQjaUIAii7UEeW3cRVu6lwpbj+B+1G2kPhK1Wb6isLFp1JtoeKSkp6N69O/7++29s27YNWVlZqvv9+uuveOONN2AwGPDaa6+B45TNXAhCQn29/Hljo/x6TcLWN7z4IpCaClRWAmVlQHIyPy48jo93vi0xERgyxKkxJBtKEATRNiFh6ylSYQsAISF8KJsSD4Sts95QZJSJtsjQoUPtwlaLe++9F1arFVOmTMGAAQNacHZEUHLqlPy5s1BkErbeY9685p+D44Bly/jKJSqQDSUIgmibUCiypyiFrVY4sgfCNlB7QxFBisUCbNzI/w5ShgwZAgCawvbdd99FYWEh4uPj8eyzz7bk1IhgRSlsnYUiU45tYMEY74LVuKaRDSUIgmibkLD1FB8K20DtDUUEIa0k0Wzo0KEAgIqKCuwVKtU2UVtbi0cffRQAMG/ePHTo0KHF50cEIeSxDW4EF6wKZEMJgiDaJhSK7CE1JznIilRrCVubjf9RLh+7IBB7QxE+4OKLgaNHfXNuq1V+bpsNmDQJePJJ5wXPmkPHjsCPP3r9tH369LGXh9+2bRt6SFwvc+fORWlpKfr374+pU6d6/bWJVoqax5ZybIMHFy5YsqEEQRBtDxK2HhKd9xIK63ojc0VTjk+Ik39lY6P8JkknJhMZ41bP0aMt3+fYV0LahxgMBgwaNAhfffUVtm7dittvvx0A8Oeff+LVV18FALz22msw+kqwE60PNY8thSIHBxynywVLNpQgCKJtQcLWQzgAgwtyUTo9C6kZJtctfzwQtkQboGNH351b6bGVvqYvPbY+YujQofjqq69kebb33nsvGhoacNttt+Gyyy7z2WsTrRDy2PqFp/E0ziAVcahECsoxcWYS4mMBlJcDSUliVWThOZq2ffcd8Msv/PMNG/j0CoIgCIKQQMK2GYTAimOb9uoTtgShhg/CdmXk5/NFVqxWMdFMo5JooCMUkPr1119RV1eHdevWYcOGDYiKisLzzz/v59kRQcfJk/LnyhxbErY+YTEeAiSJPBddBQwfruPAKVNEYUt59ARBEIQKJGybQSOMSBnalONDwpYIRFpRotkll1wCo9GI+vp6bNq0CQ899BAA4Mknn0Tnzp39PDsi6HBVFZmKR/kctyoVh4aKj9Va6xEEQRAtisXCt1czmwPn9pKqInuIFQZsyV7Ke2sB1zm2BOEvTCbeJRIoVx0PiYqKQr9+/QAAOTk5OHDgAMxmMx544AE/z4wIRva+8bXs+V9LN2p7bCnH1msIdRTdrlQstbFkUwmCIPxKoDbdII+tm1Te/zQOxfZFwrWDkZkhscjksSUInzN06FDs2LEDJSUlAIDFixcjjPLXCTcpLbKg+7ZVsrFzNr+Nk+l3IUoYoFBkn7BrF3DsmAcBJOSxJQiCCAgsFj47RFjztdn4rLesLP/7UMhj6ybxcx9CnzljRU+tAAlbgvA5Qp4tAIwZMwZXX321H2dDBCtHC4thAJONGWHDGcsJcYBCkX1C584eBpCQx5YgCCIgKC52DGRy0lq8RSFh6y1I2BKEz4mMjAQAhIeH4+WXX/bzbIhgpWOmGTZwsjEbOLRLjhIHpMKWQpH9D3lsCYIgAgKzWUwrEXCrZoIPIWHrLUjYEoRPsVqtmDNnDgDgkUcewTnnnOPfCRFBS2qGCYf7XCkbK7n4ZrRPjBAHKBQ5sCCPLUEQREBgMgF5eaL0cbtmgg8hYestnBSPOvD0chxbV9SCkyGI1serr76K3377DV27dsWsWbP8PR0iyOkywix73v3GC+UCloRtQGCxABs3AtWnyWNLEAQRKOTkACUl/PW5pCRwOkmSsPUWTjy26e+/gOQxA7H7/LH4ZdFGlBZZWnBiBBH8rFq1CjNnzgTHccjLy0O7du38PSUi2Kmrkz9vbJR7AinH1u+8+KJYdfPZF0Rhe/wYeWwJgiD8TSA23SBh6y2chSID4AD0+u1DXPjQSCQPTEfhhACpi00QAcpnn32Grl27IjY2FrfddhsaGhrw5JNPYtSoUf6eGhFElBZZ1BcU1YStlseWcmxbnBdeAB55RPzXNzAxKure3IaAaS1BEATRmhGiZixB4pMjYestXAhbAPZSJUbYMLgglzy3BOGETZs24cCBA2hsbMSFF16I5cuX41//+pe/p0UEEYUT8pE8MF19QVEpbBsatPvYkse2RbFYgJkz5WMNED22BtaI3NzgudEiCIIIRgK1V60zSNh6Cyc5tqq7w4pjmwKgLjZBBCjz588HYwynTp3Czz//jJxASeAggoLSIguGFEyBEbzLz2FBkUKRA5biYoDJuzGhEaKNDUVDwLSWIAiCaI1o9aoN9AVFErbeQofHVkojjEgZGgB1sQmCIFohRwuL7aJWQLagqOaxpVDkgECtlYTUYxuCxoBpLUEQBNEaCeRetc4gYestVIStVePfa4UBW7KXIjUjgLKtCYIgWhEdM81QOP3kC4rksQ1YlK0kDAbgwotFj2041xAwrSUIgiBaI4Hcq9YZJGy9hYqwPf7JJpQPvd5h/MS7XyBzBYVVEgRB+IrUDBNOxYvKhwHyBUXKsQ1opK0kDhwA7nlA9Ng+O6chYFpLEARBtEYCuVetM0jYegsVYZtykQlJVw1wGE/qGd8SMyIIgmjTRPXpan/ccG4f+YIiVUUOeIRWEgCwa4/osY2LonY/BEEQviZQe9U6g4Stt1ArHmUwoPjzYsfxNWt8Px+CIIi2TnS0/WGYrV6+zZXHlkKRAwKhKudT/xI9tmho8N+ECIIg2hCB2KvWGSRsvYWKx/bob8dwzpa3HcbZ888HflkxgiCIYCcqSnxcWyvfdvas/Lkyx5ZCkf2OtCqntCpydQV5bAmCIAhHSNh6CxVhW150QPUfzNlsgV9WjCAIItiRilOlsFV4bCt/+Rv1Bw6JAydOiI9J2PoFaVVOaVXkyjLy2BIEQQQKFgsfrhwIPjsStt5CRdh2uOQcWME5jDPOEPhlxQivwJTNGImAg96jVoxUvJ46hcqZ84HVq3nrqxC28bu3IuzAfnHg8svFx5Rj6xekVTmlHtuEGPLYEgRBtBTOhKuQLjJyJP87P7/l5yeFhK23UMmxTR2Yhs3ZyxzELXf31OAJVic8wtB0N2YlT0/AI7xHBmVdeyL4UYrX558Axo0D0tKAmhrnx0oXPOh77BekVTmlHtuYSPLYEgRBtATOhKs0XQTgf+fm+tdzS3dy3kLFYwujEZkrclC2/SBKr7xTHL/sspabF+EXQkNDERoaipMnT/p7KoQLamtr7e8X0bo4e+iY+gbGgDNn9J+IhK3fEKpyvvyqZPG4kTy2BEEQvsaVcJWmiwhYrf7NtiRh6y3UhG2TByg1w4TUfwwUx1UqOh5bV4TiaYtwbF2Rr2ZItCAcxyE6OhrV1dU4484NNNGinDlzBjU1NYiOjgbHOaYNEMENO1runRNRKLJfMZmAiwY5r4ocSDleBEEQrQFXwlWaLiJgNPo321KlRw3hERoeWzvSIib18rYT+wbeiu5F7yMFAFsC/DUkGz03rfDJNImWo0OHDjhz5gwOHjyImJgYREdHw2g0koDyM4wxWK1W1NbWoqamBuHh4ejQoYO/p0V4wLF1Raj5vBAx12QiZXSGw3ZjVITnJ+c4MRyZPLb+J0TbY5ufL3oVDAY+fDkY+i0SBEH4E4uFF69ms3qGpCBcpeJWKlyFdJHcXN5MGo3A0qX+zbYkYestnHhsAQDSMEeJsD22rgjdi963Z+FyAMybC3Bs3XTVGzUieDAajejSpQuOHz+O2tpaVFVV+XtKhITQ0FDExcWhQ4cOMKp9f4mA5q+hE2DeXOB0QTAskjdxDFAp4+fIyZuzEXX5JUBiIm/RL7yQ30DC1v+EqntstULlsrKolAVBEIQWehYE9QjXnBz+ert3Ly94/X3dDQphe/LkSTz55JNYvXo1Tpw4gV69euGxxx7Drbfe6vLYjRs3Yv78+fj1119x+vRpdO/eHZMmTcL06dO9ezOrUjxKj8e25vNCpCgO4wDUfrmJhG0rwGg0IiUlBcnJyWhoaICNQhoDAoPBgNDQUPKeBynH1hXBvLnA9YJgU/Eo1j4aB6+dgvTVL/HjF10E/Pyzw3mjJt4CXHMN/6SiQtwQ5MI2KGyoKzQ8ts5C5fx9g0UQBOF3ioqAtWuBiAggPh6orETNvjLsfTMZjwBIRhnKbMn4aVI8bvqrEnF1ZUByMn9sWRlykpNx00NAzd4yRPdIRnx9PDC/EigT9zOVlcGUnAzs5s8v3WZ/3PTaOHRIfZ5eIiiE7Y033oiioiIsXLgQPXv2xMqVKzF+/HjYbDbcdtttmsdt2LABWVlZuOyyy7Bs2TK0b98en376KWbMmIF9+/Zh8eLF3pukK4+tVNhKVptjrskEWyL3JjAA0VcN9d7cCL/DcRzCpJ8BgiA8RveC4NmzAABDdHukr3wO+GARH15crpF7m5QkPpZe04N8QSoobKgrNDy2rkLlCIIg2iwTJgAFBQ7DMQAWqO3/vPpp4pp+ggIW4Hz22WcMAFu5cqVsfNSoUaxTp06ssbFR89jbb7+dhYeHs5MnT8rGr7zyShYTE+PWPKqrqxkAVl1drb7DjBmM8bdM/I/BIN/+v/+J2+bPl206FZMiO3bPkGy35kYQBNGWOLp2O7NJr7cAswHs6Nrt8h2Tk/ntXbvyzxMT5ddp5c/+/eKx1dXi+KhRkmEXtiDACBob6or9+8X3Y9w42ablyxkzGvlNRiP/nCAIok2zfbtze+enn2ref+czGxrwVZE//vhjREVFYezYsbLxiRMn4siRI9i2bZvmsaGhoQgLC0NkZKRsPC4uDhERzSgqoobSY6t87qR4VLt+8qXlnoVvenNmBEEQrYqU0RloDBWv4QxA8ZBsx/SNJo8thOu9EBqlhZbHNohDkYPGhrpCw2MLiC2BNm7kf1PhKIIg2jyFhf6egV8IeGG7a9cu9O7dGyGKHNb+/fvbt2sxdepU1NfX47777sORI0dQVVWFd955Bx9//DEeffRR705UmWPrTNgqWxUon+/bh8r5S7D/zqep/Q9BEIQKoSFiAoe1Q7J6JXmlsJUKVxUKp78nPmklochBY0Nd4aQqMsDn0w4fLubVUvsfgiDaNJmZ/p6BXwj4HNuKigp0797dYTwhIcG+XYtBgwbh22+/xdixY/H6668D4Iv5LFiwAA899JDT162rq0NdU+ERAKipqXE+UaWQVTZ20qiKDMBB2LKePREPIB4Ae2des9r/lBZZcLSwGB0zzUjNoEoaBEEEF6otfRoaAEl/6BCOOR7ImHitDQ/nf5865fS1BhfkonR6Fn+tbCUe26Cxoa5w4rFV4s32P67aYRAEQQQkGRlAQgJw4oS/Z9KiBLywBeC0cqmzbT/99BNuuOEGDBo0CEuXLkX79u3x7bff4sknn8TZs2fx1FNPaR67YMECzJ07V/8kmxGKrDTSnOKxp+1/CifkY0jBFKTCBisMKMzOQ+YKitEiCCI42DvoNpyzfZVjS5/qavmOgmdWikRUISKCVyg//eT09UJgxbFNe3lhK12cDGJhCwSJDXWFC4+tgDfb/1B/XIIggpnjUenocOIEGsDhKTyL0bfH49I+lXwBRSGCSXgsVC1W2yZ5XIl4PPd4JZJQjjLw25KbHlchHo9OqsQ50U7Ob7EA//mPz/7mgBe2iYmJqivKJ5pWIIRVZzWmT5+OlJQUfPzxx/a2BCNGjIDBYMCcOXNw++23q65kA8CsWbPw4IMP2p/X1NSgS5cu2hP1orBV4kn7n9IiC4YUTIERvHU3wib3RhAEQQQwx9YV4Zztq9Rb+vRWXPfVhK10LCKCd7u5oBFGpAxtqnnQSoRt0NhQV+j02Hqr/Q/1xyUIIpixWIATBxvRAUA9IvEcZuHF9/g6BM25hu3YCDynsc1oBJ6aDcDZ+WtqfCpsAz7Htl+/fti9ezcaFSu0O3fuBAD07dtX89gdO3ZgwIABDr32MjIyYLPZsHv3bs1jw8PDERMTI/txijLHVhmK7CzHVil0FXjS/udoYbFd1Nqn2OSNIAiCCHRqPi+E0pcoLPKhqkq+oaHBUXwqha3Z7PT1GmHEluyl4sIfx4nX8SDOsQ0aG+oKnR5bof2PFE/a/zgTyARBEIFOcTEQAv5aaQV/DffGNUztGgvwY0uX+n/hL+CF7Q033ICTJ0/io48+ko0XFBSgU6dOGDRokOaxnTp1wo8//gir4oZny5YtAACTN//7Sg9tQ4O8aoUbObZSNKt9uqBjphk2xW2hzBtBEAQRwMRckwll5qx9kU8ZigzIQ4+VzyMieGu7fLnDYTYAGzMeRvn2EsdUDcF6B7HHNmhsKFwUfJIKWyc202TiQ4YFk2w0enaz5S2BTBAE4Q/MZsAI/trd2BSg641rmNo19uGHgQMHAiRVwydNhLzMqFGjWHx8PMvLy2Pffvstmzx5MgPA3n33Xfs+d911FzMajaykpMQ+9uqrrzIA7Oqrr2b/+9//2FdffcVmzpzJQkJC2BVXXOHWHFz14Nt30U2O/Zo4Tmyo9/ff4vitt8oPTknR7PfUkNTRrXlK2Z05WXauH7KpuR9BEMHDmfYJsj619h7fa9Y4Xi8rKmTHli9ZLW676SZxw6FDjC1ZwqonPcD+fGAJO7L9kPYEwsP5488/3z4UbH1sGQsOG7p8Od/+XWgDr9qLVmhWO2CAy9c7dIixjRv5355C/XEJgghmqpO6MwawY0hy+xp26BBj336rfQ319BrraxsaFMK2traW3Xfffaxjx44sLCyM9e/fn61atUq2T3Z2NgPA9u/fLxv/6KOP2KWXXso6dOjA2rdvz/r06cPmzZvn0HDeFc7eiCPbDzGrVjNio5F/1y0W9ZssxhhLSNAUtiwpya15ynj3Xfm5CIIggol+/ezXL2tkO35s+3bGxoxxvFYePmw/bM8l/2Q2yTYb4JkqadeOP0e/fvahYBS2gW5DDx0SRa3SdMqIiOA39u/v1ms3B28IZIIgCL+QlsYYwM4mdHS4hjkTrroWGj3E1zaUY4yp9EkglNTU1CA2NhbV1dUOuUK/LNqICx8aqX3wxo3AeecBKSn88zFjgE8/FbfHxAC1terHtm8PnDzp2aTffRf45z/F5/RWEwQRoKi2JjvvPEDI4wwJAW6/HSgoUD/Bvn1ARQWOzXsDyWvfdMjPZQYDuAMH3IpJtbWPguH0KTQmdUTI3KeBykrUHDqE2DfeULUFhDbObOjGjcBIFRO6cSPfm9ZO+/bA6dNAx47A0/z7gbIyIDmZ3y48Fqpvam0DgMREYMgQ/yeEEQRBeAHV1mQmE3D4MP/70CH7vs4qvhcVAYMGySWD0ehZ0Sm1OTmzBd4g4KsiBwMdM82wgoPRISMMYkC7p1WRT5/mP11OWjJo4g8ha7EAmzejcm8FDp9NROKYIVSFmSAIp2i2JpNeGxsbtUUtgLO3TkB4USFSNLZzNptbpXELJ+Tj0tN839uQ8qPAtGl6/xzCTYR8VmmxJodcsPx83h4CwFEvvR8cByxbFiCJYXKofy5BEHrRFKpCoT1JHSBnFd/Xr+e3KeWDJ5Xl/dUuLeCLRwUDqRkmbM5eBqvSRyAtEeasKrIzYcuYY1EUvbS0sM3PB9LSgHHjEP/ENPSdNw4pA9NQOCG/ZedBEETQoNmarMjitPqtkvAixyrKUpjBoLtqBj+nyU7PR3gPlwWfLBZg8mTvvzBj/B2darUq/5GfD6Sn817s9HT+OUEQhBpaQtVigWhDJcX3tCq+b9kiP48Ud4tOOZ2TjyFh6yUyV+SgbPtB/D57NSrnLwFWr5aXCNPy2NpsrituCqvU7tKSwla48VC8pgFMvEklCIJQ4LQ1mRvC1qmoBQcuL0/3cjM/J0rdaElycvhQt40b+d+ylf3iYt/ZswDr4ePPG0KCIIIPp63JBH0hEbZaFd8ZUxe1nrTx8We7NApF9iKpGSakZoxV3yhtByQVts68tQKnTwMJCe5PqCWFrZMbD+EmlUKSCYJQIrQmM0iEpL012XP6ha0aDMChu+cj7fF/umWVnaaXED7DZNJ4m8xmPmzYFzYtwHr4OLshpJBkgiCUOE3lUAlFFiJkcnP5a4sQITNkiON5DAZg61Ygw72Oo/rSS3wEeWxbCo4TvbaeCFsJpUUW/LJoo2svaEsKW+HGQwXqn0sQhBapGSbsHXKnbGxL9lJ+IUzr+titGypnzsexYRoLiU3UtYtH2n9mua0INNNLCP9gMvG5sJ7UmnAC4zxwRfgY6p9LEIQ7OE3laPLY1rMQWY9wtQgZtfPk5bkval3OyceQx7YlCQkB6utxxnIcVUUW5zduUiTCtvDOPAx5527HIitqqMUU+AqTCXj0UeC55+RTAIct2UuRSd5agiA06HlXJrBZLAxlv6ZphSJffDHiF84Cnn8e+P4DzfNGdIz3eE6ZK3JQOj0LJz7bgk7hFXwx3cpK/s7gP//x+LyEh+TkAFlZqFi3BeV7KpCSDMSjEigvB5KSAAA1f5ejnCUh4Zx4h23C48rFbyH+WDEAoCf7E4/BjEAqHaXlTQkg7U0QRIDRdHnE3r38Ipj9etFkQ3fuDsHIkfIiTmoRMprn8eacfAwJ25YiPx/s9GlwACKPWxA+MA2F2cuQ+fwY18c2CdvSIguGvjPVHrJnL7IyPUs9zFePaPYm11zjIGzLP/oBmTde2rLzIAiiVWBraFQNKzoZEosoAIiIcH4CaW0DD1BNL6mpIWHrJ/LXmzBl+lh5lc1ZTdvygSlPQnWbgMUC/P7498gCL2zLkGyvBhpIwtFfN4QEQQQvakKVNTaCA2AF7zqVVkDWuq5opoR4aU6+hkKRWwKLBWyyvMKmUFTp6PYDro8/fRqwWFD38uuyPDRAUmRFjZYWtioe4pR+Ws03CIIgnMMa1D22J2xx/ANXwjY83LsTIvyGs6JKegsuFRcD9Qi1Pw9DfaDVjrJjMvE9fEnUEgThETYbuKaUxEaJHzNQr3negjy2LUFxsf3DJSUEVlS//i46ujr+k0+AUaPQVWWT0/xVZb9cX6NW3dkfvXQJgmgVGKzqi3OxXWL5Bz722BKBg7MWFR066Cu49OOPQHeIn4kw1FP+KkEQrRPJPbngsQVaf84+eWxbArMZTKPoxblfvur6+H//W3WYAfi/axdqVxsOAI9ti+b5EgTRerDZwGlcP2LTSNi2NdSKKgHArbcCP/3kuuCSxQI89hhQLxG2oWjAwoXkFSUIohUiqVFhbfJjtoWcfRK2LYHJBG7ZMriSeNLtTEc1Tg5A3BUXa+/Q0sKWPLYEQXgLZ/294+L43yRs2wxCUSWlgLXZeMG6cKHzCpyCx7dBEYp8sRMTShAEEbRIbOglmSHqPcKbsFggq5oczFAockuRkwNDdDQwbpzmLnWXXo6/L89Fx45AYn0pMGMGAN4zqyZzrTA4b6NDHluCIIIVZ9cvYdt33zk/BwnbVkVODqBmRq1WviVFSYm84JLFwgtas1n0+NbbxM9EpKG+VYfkEQTRhpF2FTAYNf1M+flijQJp1eRghYRtSzJkCBjHqebbAkDkOSb0mcNX4PxjxDSc1zSu5bv9c+Q09BHCkC0WVKzdjPI9FUg6NxGJY4YEhrAljy1BEK5QS9XQavUDAJMmARUVYC+/4jy2hYpHtTqGDOFvvqTmRgg7llbgVLtZy8sD6ieHQajBOPfJBplXVyqEW3OoHkEQbQCJx/ab70MweqSjcNUqvBdoleLdgUKRWxIhJFmryXxCAgC+rU+v75ao7iKViX0mDOQfLF8O1qULEqeNQ6/F05A4bRxYWhqfeNSSqIUOkseWIAhPcCZsGQMeewwcXCyckce21SGEJDsLO3Z2s3bHRDEU+fprxAKL+flAejowciT/Oz+/Jf4agiAIHyGxoQ1NfkxlxXitonzBXDWZhG1Lk5MDw8GDOHPJMMdtobzBPVpYrPnGyCRxdXVTK6EpDl4LjjGwDRu8MGE3oFBkgiC8hTNhCwA2m+taBCRsWyU5OXzYsVbOmLObtegEyWeiqXOA3nZBBEEQQYOseJRYFVkqXNWK8gV71WQStv7AZELkwPMdx5uEbcdMM6w6ikehqopvJaThtdAKefYZVDyKIAhv4SqVwmgE98Lz2hEwAAnbVoyzPq9Ob9bCHIVta/RaEATRxpHck0v72EqFq54ImGCDhK2/iIlxHGsStqkZJmzOXqYubq+6SnxcVcW3EtJ4Ca0WQz6DPLYEQXiC2nVCstrssNVg4K3vww/DcPAgKpasxp4HlqBiyWr5fiRs2yROb9akn4mmxZPW6LUgCKKNI7WhHH8xVBOuriJggg0qHuUvnAhbAMhckYPS6Vk48dkWdD67F3ERdcC11/LtLb78EgBw4pufUTcOSL3tNmDlStmpGMeBu+QSvnt9S0EeW4IgPEEt7FgydvaqG7B/0Hh0Cq9AfI9EYPBg0TKbTEicOhaJws53S85BxaPaLDk5fE6ttEoyAJmd/e3HeiT0FYVwbi5vxlqD14IgiDaOxIb+48YQbLxHcS2UIC28F+yQsPUXLoQtwHtuUzPGyvd54QX7w4QdG2EbmIZ9GbfgHMWpuPXrgbfekgtbxtSrj3oL8tgSBOEJaotiEqPcLiXGXjHeLchj26ZRvVmTfCb+9VQ9Pp4tVglVFcIEQRDBiMSuto8JwfDh/ptKS0LC1l/oELYOWCxgM2fKApQNYOhWtNpx3/Bwe/6QHasVCPHhW07tfgiC8AQ1j600x9bT6xYJW0JB1ekwxDU9DkO9Q3sLErQEQbQKpHbVaNTer5VBObb+whNhW1ysWhDKoJZlW1XlWHzFVZXR5kLtfgiC8AQXHlsStoS3OHZCtLOh4G0kFYoiCKLVIbWrvnRqBRgkbP2FmrB1dRNmNqsWhLKpFZnyh7Aljy1BEJ7gIsfW5aKfFiRsCQVJJvEzEQY+qokKRREE0erwxuJwEELC1l+oCdvaWufHmEzgli2TCVkG4ND5ox33VRO2rtpnNBfy2BIE4Qm+8thS8ahWj8XCV/PU23M2IUUubKlQFEEQrRIKRSZalC++cBhiDz0M5Oc7Py4nB4bP1tmfnr7pTqSP7u+4XzM9tqVFFux6ejXfPkPvHQN5bAmC8ARf5di2oVXqtkh+PpCeDowcyf92ZT4ByLz/D0xv8Fl7C3cFN0EQhFehUGSixbBYwB5/3GGYAwObkuvaEkqWltsnRqjeFJ7885DHwrZwQj5SBqah77xxSJw2DiwtTd8dA1VFJgjCE1x5bD0NRSZaLRYLMGWKaGKEIlAuhaQkPL1HWr2Dp9YbgtQjwU0QBOFNKBSZaDE0ikABAGfTUcVC+gFtaFAVrO1W5aN2z2H5oA5hW1pkwZCCybKCVBzTKbipjy1BEJ7gKse2DRllQh/FxY7rprqKQEnzrhWdA7whSD0W3ARBEN6EQpGJFkOjCBQAMIOOKhbSm7zGRtWbQgMYoioOyAd1CNujhcUwqlRZ1iW4yWNLEIQnqC2KeSMUmWi1mM2AQXEHo6sIlNT7LxG23hKkHgtugiAIb0KhyESLIRSBUohbxhnA5emoYiE1zBrCFoBjrWQdxaM6ZpphVamyrEtwk8eWIAhP8JXHlq4/rRaTCcjLEx0RuotAST22EpvoLUHqseAmCILwJm3UY9t2JHygkZMDQ1YWKtZtwfG/KtChZyISRw/WV5pRRygywFdMlklUHR7b1AwTfst6CP3Xvyg5D6dPcJPHliAIT6AcW8IDcnKArCxefPboobOysUYosiBIpSbLE0EqCO7cXP5jTVWXCYLwC200naft/KWBiMmExKljkejucTo8tgxAXVQiIk5WyPfVQf8HRwESYcvNf1Zf2UiqikwQhCf4yGNbfaASsR5OiQgOTCY3RaOGsPWmIPVIcBMEQXiTZoQiWyx8FIvZHHzXLwpFDkZ0eGwbzL0R0V7xQdbb7kdRUAOxOm8NqY8tQRDuYLGgYslqVGzZIxv+ZdFGVP55VBzwUNhGvzIPhROoJC0hQbowrEjPyckBSkr4qshCGyBPqySbTMDw4cF3U0gQRHChvEYJzyuOeRaKHOxV3UnYBiM6ikeF1VaCHTsmG/v0I9c5tgAcha2aYFWDPLYEQeglPx+sSxoSp41D4o9fyTZd+NBIxM6+XxzQKWxLi+TqwwCGwQW5DuNEG8ZJVWRALkiD/QaPIIjWjfIaNWGC+Pzeae57bFtDVXcStsGInlDko0cdSkAVLDii78PpqbAljy1BEHqwWMAmTwanUoFdQNpyTG+O7dHCYoexEFhxbBOVpCWacCFsBVrDDR5BEK0XtWtUQYH43MDcT+dpDVXdSdgGIzpCkdWaCZnYAX0fTvLYEgThS5z08lZFp1Hmq7rLzVojjEgZSiVpiSY02v0oaQ03eARBtF7UrlFSQuB+KHJrqOpOxaOCEWce2/btgVOnVA8r5zrq+3Aqjb1erytVRSYIQg9ms2PVdmfoFLapGSYUZudhcEEuQmBFI4zYkr0UmRmU6Eg0IfXY7tkDzJ8PlJUByclAfDxQWQmUleGC8GQ8BiAJZShDMqoQjwRU4qJ3yoDNyfzxZWXAuecCY8ZQMi1BEC2KWiV3KUa4H4rcGqq6B4WwPXnyJJ588kmsXr0aJ06cQK9evfDYY4/h1ltv1XX8J598gkWLFuGXX36B1WpF165dMWPGDEyZMsXHM/cRBgPAcbw3VOmxdSJs75wRp+/D6c1QZPLYEgShxGQCd/vtwH//q7mLTPi6UTwqc0UOSqdn4dimvUgZ2oNELciGyli9Wnz822/8jwrxABaobXhTZWz6dGDZMn3dAwiCILyAmgi94w7gnXd4sRvGNcKe0eNG8ahgr+oeFKHIN954IwoKCjB79mx88cUXyMjIwPjx47Fy5UqXxy5cuBA33ngj+vbti9WrV+PTTz/FtGnTUO8kBCkoEG70GhvlgrJ9e81DBnY5qrlNhjdDkcljSxCEGuef73RzMSThJW72sU3NMOGC+4cjlUQtALKhdiwW4IEHvH9exvhkN0rAJQiiBVFWcs/MFLcZ4X6OrUAwV3UPeI/t559/jq+//horV67E+PHjAQAjRozAgQMH8Mgjj2DcuHEwaqxE/PTTT3jiiSewYMECPProo/bxyy+/vEXm7lNCQ0VvrdRj266d5iHVv1uQoOfc5LElCMJLlBZZULF2M1JTgcQxQ0RLqRFZItAOZ8Qnbai5vLchGyqhuNh3Nslm410cwXgnSBBEwOKqp6zQy1tZTMrAPO9jG8wEvMf2448/RlRUFMaOHSsbnzhxIo4cOYJt27ZpHvvvf/8b4eHhuPfee309zZZH+JCqhSJrEGdO0nduyrElCMILFE7IR8rALug7bxwSp40DS0sTe6a4ELZJKBeftCGj7G3Ihkowm/k0Hl9gMARXhRWCIAIed1qOKYtJeVI8qjUQ8MJ2165d6N27N0IUNzb9+/e3b9fihx9+QO/evfHRRx/h3HPPhdFohMlkwmOPPeYyjKqurg41NTWyn4BCCM1zw2Mbtulb4OmngaIi5+d202MrNIOuraaqyARB8JQWWTCkYLLMyHCMgU1p6pniQtiGQ3IdqqryyRzbAmRDJZhMfC6sL8RtXp7H3lrBhlIkM0EQAu62HFNWNPakeFRrIOD/0oqKCnTv3t1hPCEhwb5di8OHD6O8vBz33Xcf5s2bh/POOw/ffPMNFi5ciEOHDuG/TgqXLFiwAHPnzm3+H+ArtDy2ToRt+3WrgXUA5s0DsrOBFSvUd3RD2Obni1+8V2DFDOUO5LEliDbJ0cJipKr0qeVsTT1TXAhbKeyOf4I7e5aK83gA2VAFQmWULVuAigq+CnJ5OZCUJFZFbnpeVQ38+nU5Pv85CVWIRzwqcdsV5eg/Mon//D77LH/O4cM9/mxKbajBwOtj+pgTBOGs5ZhWSLK0mJTUY/v1xhCMutHHEw4QAl7YAgDnZHXV2TabzYba2lqsWrXKXv1xxIgROHXqFF555RXMnTsXPTRCh2bNmoUHH3zQ/rympgZdunTx8C/wAdLiUYKwNRqB8HB9xxcU8JUcMzIct+kUtsrVJA4UikwQBE/HTDNscAwLYgYjuB493BK2HHhPL5eVRTmMHkA2VIHJBChCs9U4aQFGvgCZZXtxI1DyFmBKOC0KWw89wFoeGfqYEwSh1s7HVU/ZnBygf39g0CAghInC9rX/GNF7Ztu4rgS8sE1MTFRdUT5x4gQAcdVZ69ijR48iKytLNn711VfjlVdewc8//6xplMPDwxGuVyT6AyEUWeqxDQnRL2wBYNMmfcJWQ5wqV5NkYQ8CFIpMEG2S1AwT9g66DT22iZV3GThweU1N8dwQtoDE09sWLLMXIRvqOU49JpmSv+3sWe+fnz7mBNGmMZmAdxda8MnMzYhjFUhAJcYPL4PpbXnPbSRL+monJ4PbF49HWSWuwWf2c0XbKtvMdSXghW2/fv2watUqNDY2ynKEdu7cCQDo27ev5rH9+/fH0aOOLW5Yk9gyGAI+xVgbNY+tirCV9YJUMnSo+rhOj61yNclAHluCICT0uL4fIKlNxL2xRIyzdFPY2j29hFuQDfUcpx4To1HsTuChsPXEI0MQRBshPx/jZ07GeKmD6JumHydc3PQj5R3ciaof64DhrT/PIeCt0g033ICTJ0/io48+ko0XFBSgU6dOGDRokOaxN910EwDgiy++kI1//vnnMBgMyFDzVgYLasWjQkKAsDDZbjVJ3WFVk7bZ2ereWkC3sBXi+YViayEceWwJgpBw8qT8eUyM9jYnME7i6SXcgmyo5yhtnNEILJV+DCMi+N8eCluX5ycIom1isQCTJ3vtHtoAhoTHnFSeakUEvMf26quvxqhRo3D33XejpqYGPXr0wKpVq/Dll1/i3Xfftfffy8nJQUFBAfbt24f09HQAfDuDpUuXYtq0aTh+/DjOO+88bNiwAa+//jqmTZtm3y8oUSsepeKxje3fDaULvseJz7bgvLm38BK3Vy/twlGAW8WjhDoce/cCGUttwHuKHchjSxBtF6V4lRa6cyfH9v33deVEEo6QDW0eUhvXo4dCdEZEALW1Hgtbl+cnCKJt4oue220kzyHghS0ArFmzBk888QSefvppnDhxAr169ZIVswAAq9UKq9VqD5ECgNDQUHz99dd4/PHHMX/+fJw4cQLdunXDwoULZUUtghItj60yp6ldO6RmmJCaMRZYGA7U1Tl4dR1ws4+t0Bwab1O7H4IgJHhB2DKjEdzgwV6cVNuDbGjzsNs4Jc302Lo8P0EQbROh57Y376HbSJ5DUAjbqKgoLF68GIsXL9bcZ8WKFVih4oVMSEjAG2+8gTfeeMOHM/QDUo9tQ4M4phS27duLj8PCeGEr7K9FXZ38uYs+tk73I48tQbRdlMJWeu1xImyF2gA2gxEGis1sNmRDfYSXhC1BEIQMkwlYuBCYOdM75zMY2kyeQ1AIW0IFabNlwcOqkmMr62srraTchMXCRzyYzZLPuxuhyDLURCx5bAmi7aLmsbVYULF2M+KrqjSLPNR16Iza/7yLpMEUm0kEME3C1nr6LEot9FElCMKL3HijKGwzMoAbbrD32K5EPCr2VSKZK0dM9yR+H8m2E39XIglN23r0AAYPbjMXKBK2wYogUgFxtVgjFNnhmCbhqtkY3lNhSx5bgiCkKIVtYSHY9OlIdHFYRFwkIsYO99WsCMIrlNdGIAkAV3cW6WkMecs4e9FvgiCIZiGNcOrTB5g1C4CTe/cm4pt+2ioBXxWZ0EDqsT1zRhxzJmwFb25Dg2ZjeIsFbufYOt2PPLYE0XZRCFv23nva7cekSBfuCCIAsViA3SW8x9YABiNrEG0oQRBEc5HeizfZRKf37gQAErbBi/TGz0m7H1mOrSQU2VljeK+GIpPHliDaLgphq0vUAiRsiYCnuBg4iwj78wicFW0oQRBEc5F6bJvu7Z3euxMAKBQ5eAlReevcCEV22hjem6HI5LEliFZDaRGfH5uaCiSOGeI6Z0fpsYVOcat2fSOIAMJsBn5RCNvTxpi2UHSUIAgPUa1ro4VU2Dbdvzu9dycAkMc2ePFE2EpCkZ02hiePLUEQCv7vn28gZWAX9J03DonTxoGlpfHJPk6wVdfInnMq1y3VpS/y2BIBjskE9LlYFLbtDWfbStFRgiA8ID8fSE8HRo7kf7swnzJhW3uWt4lO790JACRsgxe1Gz8VYVt5VNKGQFEVOScHKCkBNm7kf9uTzz3NsSWPLUG0SkqLLBjy7t0yg8ExBjZFO7mnMHs5uJO18kFJH9vSK+9E9QOzwSUlORxbd5YWxAj/YrHwttFZ7lr33qKw3bLxLBWOIghCFU9yY7/4RLwXf+2NULsQ1rx3h77rVmvHbWF77NgxcBwHjuOwfv16p/vec8894DgOQ4YMkTV9J7yAlsf2hx9kQ7HzHkbhhKZvgyBsGxvtgtNkAoYPV6z2kMeWIAgJRwuLVY0FZ1NP7iktsmDI27lOw45TH/knYhfNAWJjHbaF/VokXrcIooXR7VmJEIVtxzjqZUsQhDru5sZaLMC/XxY9tnUIkwlhtXt3tz3CrRS3hW1KSgq6d+8OANi2bZvmfr/++iveeOMNGAwGvPbaa+A43WVDCD2oeWytVrDXX5cNGcAwuCAXpUUWeWEpaey+EmWLDupjSxBtmo6ZZqgtUTGDenLP0cJiGFWPkNB0PWowRjhs4gDxukUQLYhbnhWJsLW33ZOcp617TgiC4BFyY6U4y40tLgaMTLxPb0CophC2WIDVq4HJk6laMuBhKPLQoUMBOBe29957L6xWKyZNmoQBAwZ4NjtCGzWPbV2dqockBFYc27RXLoa1hO0ddwBVVbKhQyXUx5Yg2jKpGSaUnjdKNsY4DlyeenJPx0wzrK7MSygfWlW954jqZvt1iyBaELc8KxrCljwnBEFIcTc31mwGwjm5sFUTwsK1Ztw4Rz9SW62W7JGwHTJkCABtYfvuu++isLAQ8fHxePbZZz2fHaGNmrCNiQFT8Yw3woiUoT3kwlYZbgwARUVg//2vw/ChnSf0rfqQx5YgWi2dh5tlz7kNG6CVVJiaYcLOax5zer5jlWFYOqkIiTihut1+3SKIFsQtz4qKsKU+kwRBqOEsN1aJyQRMmyTep1u5UAchrLzWKGmr1ZI96qkgeGwrKiqwd+9e9JD852pra/Hoo48CAObNm4cOHTp4YZqEA2qhyFFR4JYtg23yZBiaBKUVBmzJXorMDJPrUOTCQlWPbwJOYO9eHVXXyGNLEMGPhW/pU1rKt/RJzWj64isXw+LjnZ7mgnszgc+1tx8oDcNQfK16zbGBE69bBNGCCJ6V3FzepDn1rEiF7TvvAJ9/jrraZDxiA5JRhjIkowrxiLNWwjajDBiQzO9bVgYkJ/PfocpK8blyW2IiMERHWy2CIAIKrbY+JpP+r/OISxuAZfzjp+aFIV4hhNWiSwTacrVkj4Rtnz59EBsbi+rqamzbtk0mbOfOnYvS0lL0798fU6dO9dpECQVaxaNycmDIykLFui04ehRIuHaweHPoJBT52LoiNH65A51VXqoW0bJVH81eluSxJYjgJj8ftkmTkQiGRAC2eRwKs5chc0WOo7A966JYTmWl081pPcKwCZkOvW0ZgIq3PkXmhNEe/AEE0XxycoCsLD6Mr0cPJzeHv/4qPn73XQDAOQAWqu27punHXTgOWLbMuXuHIIiAIT9f9KQaDPxCmUdfX8l9enyyozNLq6ftqlXA4MFtU9QCHoYiGwwGDBo0CACwdetW+/iff/6JV199FQDw2muvwSgEkxPeR6vdDwCYTEicOhZ95owVvS3KYyQ3qX8NnYDkMQPR+et3VF/K1DPK/gUpnJCPlIFp6r0sqSoyQQQvFgvY5MkwSDrLyorPKYVtXZ3z87kQth27hCJ3eQbeRrb9FRkALjsbSSRqCT+j2jFAilCxxdcwRrHMBBEkeDUVQeqAUrnn18rbHTu27YpaoBl9bNUKSN17771oaGjAbbfdhssuu6z5syO0UfPYquXNSlEJRT62rgjmzQXO23Ik8yHGpUUWDCmQ3/jKellSH1uCCE4sFlS/mAdO5ftqL+LkrrBVFKFzICwMOTnA5YdW4Ocl21E1+2Vw27cDK1a4NXWC8JRmVS4uLvb6fDRpq1VgCCKIENa63Gnr4xSpzZXev0twJ2+3reBRKDIgFpD69ddfUVdXh3Xr1mHDhg2IiorC888/77UJEuoc+Hwn0pWDa9fy3lOtT7ZKKHLN54VIcfViTd/So4XFSIXjja+9lyV5bAki+GgKP45V+W4DkiJO33jXYysYapMJME3NAJChc8IE0XyaHS5oNvNhwi2xeNtWq8AQRJAgvZ4o8fjr68JjK+BO3m5bwGOP7SWXXAKj0Yj6+nps2rQJDz30EADgySefROfOapmahLcoLbKgy2+fqW+cMkV7+VklFDnm6ks1bmclNHlitXpZ2gCUl5wkjy1BBBsWC9ikSbIoDClCEafUDJPXQ5G1VqAJwtd4JVzQZAKWLVPtROBVOK7tVoEhiCDAWXXiZhVx0ilsCTkee2yjoqLQr18/7NixAzk5OThw4ADMZjMeeOABb86PUIH3nGpgs0GzhLFKKHLKZeeqn8dg4EUpY7xgtViQun8zquLSEVd1QL4rgA4Tx+Bs+wREKM9DHluCCFyKi52mIVS88wUy78jin7gSthYLHzWyZw+QnIy6zT8i3Nlrk6Em/ISzXrVu3YDm5IDLysI3z2zBhqV70QHlOI4k3HADMLBrOZCUJFY+Lueff/8D8NOX5TiGJFQjHrGoRDLKUY4k3Cgc9913wC+/8K+xYQPfEJcgiIBEqzrxyy8DN9/s+ZpU9fF6xApPyF7qxmNhC/B5tjt27EBJSQkAYPHixQijVXif0zHTDCsA1dJcBoN2zINaVeSjR+1Dtd36ovGW2xA/oAdfUq17d36/sjIgLQ1gDHEac+IAhJ9S6UdJHluCCFzMZoeqxFKSzokRnzgTtvn5wKRJss1ORS1AHlvCb2hVE/UoXNBkwuVvjMW5T7quopyfD0z5io9yUotifvFTPk/OVDtZFLZJSR5MiiCIlkLretIcUZufD5S+1IAnm55/8U0Yrr622VNtE3gcigyIebYAMGbMGFx99dXNnhDhmtQMEzZnL3cMC+Y4PlFI65ukVhX52DH7UPRNVyF+4SyxpJrQpf7gQV0CVfXmmDy2BBG4mEzgLrlEe/uZM+JjpYdWeG6xOIhaXagVwCOIFkCrmmhzon1dVVFWhiuqmVR7kRlpRwm1FB+CIAIGb19PhGtFCMRQ5BcXh1JhdJ00684iMjISABAeHo6XX37ZKxMi9JG5Igel07NQs2odUmv/QsyAnsDo0c6/SSqhyFKPLVIUZaTcbNek6vkhYUsQ/sXC950u31OBjuGViKsrA849Fxgzhr9edO0KSNq2yZAKWy2PrSfVYcPC+IU4gvATunvVegmtcEUpdq8xCVuCCCgsFv47bDarXyu8eT0RrhWhEmF71hbqfqpEG8VjYWu1WjFnzhwAwCOPPIJzzjnHW3MidJKaYUJqxlT9B6iEIldv+1OM4VeGBroQtlIhywDUR8Yi/Ey1YicKRSYIv5GfDzZpMhLBkKjcNm0asHy5vECFkrNnxcdawtZsdn9elC9EBADeqCbq6oZXQC1cUQiKstkUXh4StgQRMOitoO6t6sTCtSLMJtpcmyGUCqPrxONQ5FdffRW//fYbunbtilmzZnlzToSvUIQiF96Zh9hFs+1DbMb9/DdYwImwZQD2D7gZ9V35BQ0OQHiHGMcdyWNLEP6hqAhs0iRwzuqeT5kC1NRob9fjsTWZ+Jx8JzjMgPJriVZAfj6Qns7XdkpPl5tPJWrhinl5wIEDKj0opba3sdFX0ycIwgVFRcDkyc2soO4mwrUijBMXnR99Moy8tTrxyGO7atUqzJw5ExzHIS8vD+3atfP2vAhfILmZrNx9FEPfmSbbzIGBTckFl5Ulz7GVcOqqG1CW0h/tbr4W3UdnAOPGASX7+I1Hjji+JnlsCaLlyc9vErUusNmA6mrt7XqELQB07Cg+njQJ6N4dlYhHWTnQoWciEu+7Xe4ZJmFLBDlaLYME86mGVriiw/7ksSUIvyN4apW3sR5VUHeTnBzg1NcNwPv88xtuoSgnvegWtp999hmmT5+OyspK1DSt8D/11FMYNWqUzyZHeBmJx7b6dwviVXbhbJJvrIrHtv0dN6Hb7beLA6mSxkNqBpg8tgTRsjT1ptWVwWowOBeZeoVtba34+KWXgJgYxAPiNeahCSRsiVaFpy2D1MIVHcKZpYXVSNgSRIvjqjdtS4QFtw+jPraeoDsUedOmTThw4AAaGxtx4YUXYvny5fjXv/7ly7kR3kbyxYjtnuBYVRkAM0i+sWqhyIob0v2FLuIxyGNLEC2Li960MqSxkWroFbbScOaoKMfzKCsgk5EmghwhD06KJze8quHM5LElCL+iVezNYGh+BXXdSG0u2Uzd6Ba28+fPB2MMp06dws8//4wctcxpIrCRiNL4LtGo6tRXtplxBnB5km+s2g1vuNidsrTIgvSf1zh/TfLYEkTL0tSbVgkDUHaVJNpizBg+3slJ8ajqMh3FowDRYxsVpZrC4GCUyWNLBDneaPGhFc5cc4qELUH4E7WFK4OBbyCgR/5YLHzufLNycSnKySOa1ceWCDIUVZETknjjaeMMqHj9PXAHD8i/sS6E7dHCYhicFaYByGNLEC2NyQQuM1M2xAAUD8lG8lsvioNCux0nwvaNRWfEgjh6hG10tPqJlB5bMtJEKyAnhy/65FD8SSda4cwV1SRsCcKfaBV7y8hwfaw7ReWc0kChyJ5AwrYtIf1irFsH659/AgBsKR2ROG2c41KzmudFckPaMdMMq6uPEHlsCaLlkfSkPnjT/Shbux09N60AmnqPAxBb+TgRthE4w1eAPGB1vMEmYUu0cYTcWE/7VmqFMyd0IGFLEP7Gk4UrrSgMjzy3JGw9goRtW+KHH8THX34JY9ONqfHoERROUFlScuGxTc0w4bdrXbR6Io8tQbQ8VVX2h2lv/Qspo5uWmaXCVsifdSJsI3EGVivw95/1jhsFYcuYKGxjVFp+AY5GmYw0EeR4wyujFc4cm0DCliACAZMJGD5c/8KVs6JybiONkqLFYN2QsG0rWCzAkiWqmzgAQwqmoLRIsaTkQtgCwIUv3O64jxTy2BJEyyMIW4NBXswpNFQMQdYpbI1G4JwuToTt6dPi95w8tkQbwJteGVWvEBWPIoigxFtF5QCQx9ZDSNi2FYqLnW42woZjmxRLSjqqIqN9e+evSx5bgmh5BGEbFycKWYB/LHhtdYQiR+Isli4FOic5EbbSVj8kbIk2gFe9MlDxCpGwJYigxBtF5eyQsPUI3X1siSDHbOZvajWEphUGpAxVLCmp5dgqPLaqrT2kkMeWIFoeqbBVEhnJe1l1eGyvvfwMInMAHHYUtvX7ShC2ZIl80UyrdRBVRSZaEYJXRmrevNrbkoQtQfgPiwXYvBmoqAAqK4GyMiA5GYiPlz8HVLflJCfjpoeAmr1liO6RjPj6eGC+eFxVtWRbVyfnFEJAOA44fLiFegwFPyRs2womE7BsGTB5soO4tYHD5uw8ZGYovjQ6QpHJY0sQAQZjzoVtRAT/W08oMmvaR1kRGUDYwf3AtGnywY8/5pMNlVU2qI8t0YoQvDK5ubzubJZXRg0StgThH/LzVe+T3SWu6cfdbaowBqSl8ffw1GrVJUERinzy5Encf//96NSpEyIiInDBBRfgvffec/s8Tz75JDiOQ9++fV3v3BrJyQEOHgRWrwbmz0fNpAew54ElOLb9IDJXqHxZ9AjbsDDHm1Yp5LEliJbl9GmgsZF/rOWxBXSFIp/+429ULFnNXzf0MmWKY7Kh8hohzI9oEciGep/mtvpxCglbgmh5LBaviFqfwBjYlFxsXm1pXm/cNkBQeGxvvPFGFBUVYeHChejZsydWrlyJ8ePHw2az4bbbbtN1jh07duDFF19EiqQNRpvEZALGjgUAxDT9aKInx5bjeK9tdbX6OQLxAkEQrRlJReQztjBEKre74bFtd7QE7aaNAwMHTnMvBTYbn2wocV+d3l2CdpJd2Lp14NQ8u4RPIBvqG0wm73lphdZBZjNgki4EkbAliJahuDig71k5mxWPj9uLQoMJeXlkPrUIeI/t559/jq+//hr/+c9/kJubixEjRmDZsmUYNWoUHnnkEVh1XPQbGxsxceJE5ObmolevXi0w61aCnhxbAKc4eTiy7LJAHluCaFF+mib2HQn/br1jKy/BY3vmDG/EnQhbAQ5uGHuDQZZseGxdESJPlivOBzA1zy7hdciGBj7K1kGFmyWLyhTdQBAtg1CLJkBphBF70aN5vXHbAAEvbD/++GNERUVhbJOXUWDixIk4cuQItm3b5vIcCxcuxIkTJ/Dss8/6apqtEx2hyBYLUF4l3092WQjg1S+CaG2UFllwwadz7c8NYBhckCtv5SXtZVtfr0vYSnH6jeY4PvlQ4saq+bxQ1dvLCZ5dwqeQDQ1s1FoHvfU2hSITRItjMqFyzmJ/z0IVKwzIxVIcBm9bm1OFvbUT8KHIu3btQu/evRGiyNHq37+/ffuQIUM0j//jjz/wzDPPYM2aNYhyVcGXkKMUthznMFZcDPSAE8NLHluCaDGOFhYjFfLvXAisOLZpL1KF4nBCKDLA5+O6eePMAbACOHz3fKT1b6roWF4O9OwJjB7tEJsZc00m2BI4iFtmMIDzWhlZQguyoYGNWuugBkbCliD8we/9x+NS3AcA+A198F/cjmSU4/pJSThngMTeJSXxBwiP48VtlWFJeO45IAnlKEMSqhCPOFQiuek5AKSgHDffnSS3oWrnBFCBRFw4bTAOMdG2erUKeysj4IVtRUUFunfv7jCekJBg366FzWbDXXfdhRtvvBHXXHONW69bV1eHOqFPI4Camhq3jm8VKIVteLhDmIbZDJQjCV1wRP0c5LEliBajY6YZNnAwSPyqjTDKW3lJPbbSHrQSGByFqBQjgBM9ByNt6nCXc0oZnYG/hmTDvLnAfk4GDpzCs0v4BrKhgY1a6yDGGcXQCBK2BNFidE8TQ///Rg88j1kwGoFxswHoNFfx4L/XQtV05fdb4KJbgLThrs+XCGB2qA+rsLcyAj4UGQA4JzHvzrYtWrQIxcXFeOWVV9x+zQULFiA2Ntb+06VLF7fPEfQoc2xV8mtNJsDUVV5QinJsCcI/pGaYUDLgJvtzKwzYkr1U9NYCcmGrITa4MWNQOX+JZtixat9rJ/TctAJla7djf/ZsnJi/BNyhg1T5ogUhGxq4CK2DhHVkoxG4azJ5bAnCH3RKFoVtI0I8FpHSqulbtzreTrvrcfVpFfZWRsAL28TERNUV5RMnTgAQV52VHDx4EE8//TRmz56NsLAwVFVVoaqqCo2NjbDZbKiqqsIZoSqoCrNmzUJ1dbX959ChQ975g4IJpcdWWRG5iSTuuP3xGdM54D74QNxIHluCaFG6Xy5656qWvOfYyksaiqzhsUVcHOJnTQW3fLnDJqHvdaqy77ULUkZnoNuKOUiYNZWWmlsQsqGBT04OsGULsGgR/3vkKBK2BOEXJDUnLhsR0iwRaTIBw4cDGRmOi1eeiGXhfGQ+nRPwocj9+vXDqlWr0NjYKMsR2rlzJwBo9tP7+++/cebMGcyYMQMzZsxw2B4fH48ZM2ZorkSHh4cjXMVD2aZQC0VWofHQEfsHKdzyN4pW/oUMYSN5bAmiZZGImMShKhVsdYQi27/rOTlAVhawbh1qfvoLpdE9ETN+NDLdFLWE/yAbGvjk54sFpAwGYP1UI64QNpKwJYiWQ1KFPLlzqO7wY1cIpnTvXt5TS+LUdwS8sL3hhhuwbNkyfPTRRxg3bpx9vKCgAJ06dcKgQYNUj7vggguwceNGh/H7778f1dXVeOutt2CiT5ZzdAjb0iILUhvFPCoDGC76+ClxB8FjW1QErF2LyroIVBwHkqLPIvb2MfxSFkEQ3uO4GEGBDh0ct0s8tmcWLnbscwvw1ZIFTCZg6lTXfa+JgIRsaGCjVhX5329oC1tZv1v69xOEd5G21wpxLZGk30fA+XfTm32vCW0CXtheffXVGDVqFO6++27U1NSgR48eWLVqFb788ku8++67MDaJr5ycHBQUFGDfvn1IT09HXFwchg8f7nC+uLg4NDY2qm4jFCiTAlRCkfkqrHKM0qqsNhuQnQ28/TYAPqk+vmkTWzwPXHY2sGKFt2ZMEIQ07DQx0XH7nj32h5EbP1c9BXv7bXCXXUaJPK0AsqGBjWpVZJt6KLLSs5uXR19RgvAqbghb6fdRKFXAGH03/U3A59gCwJo1a/DPf/4TTz/9NK666ips27YNq1atwu23327fx2q1wmq1glFOp/fQ4bHtmGmGVfExaoTkuOPH7aJWCQeAFRTw3lyCILxCg6UUAGCLbOe4GGWxAJ+ri1kpHAA2hTrAtxbIhgYuQlVkGQZHYavm2c2lryhBeBdJju3Js9rCVvl9ZEwMUKTvpn8JCmEbFRWFxYsXo7S0FHV1dfj1119x6623yvZZsWIFGGPo2rWr03N999132LVrlw9n24rQIWxTM0zYnJ1nF7ONMOLnm+aLO5SVOX0JDgA2bWrmRAmCAIDCCfkIKdkHAODOnEbhhHz5DsXFus/F2agDfGuBbGjgolYV+Z4ZjsJWzbNrpa8oQXiVTz4SPbZvvRuK/Hz1/dS+j1Lou+k/gkLYEn5CKWwlPQmlZK7IQfn2Eux4eSPKt5dg4MvjxY1qoZASGAAMHdq8eRIEgdIiC4YUTLH3iuUADC7IRWmRZNlYSATSATNQB3iCaC4WC9+iw5n3RtnK4+oxEk9Rk7BV8+y62zKEIAhtLBbghQWisG1AiKbnVTXSQgJ9N/0HCVtCk/KiEtlztmMHMGGC6r6pGSZccP9wvgWI9NseGysmHyhgAJ9jSwWkCKLZHC0slue3AwiBFcc2SZaNTSZApYUPIO8/zTgDuDzqAE8QzSE/H0hPB0aO5H9reX8ARSsPo6PHVs2z60nLEIIg1CkuBgxM3sdWy/Oq/D4aDOKtLn03/QsJW0KV0iILOpTIc19158RKheyJE2LiQffuqJw5H2dj+UqtXGQkFY4iCC+hle+eMlSxbJyTAxw6BCxZIhs+NW4ifp+9GhVLVoM7eIAqXxBEM2hWTqyKsAUcPbv0FSUI72E2A+GcmGPbiBCnnlfp9/HAAeDgQfpuBgIkbAlVjhYWQ83PqisnVuqxPXpUfHzppYhfOAsR6Z28MEOCIKSkZpiw/dZF9uc2cNiSvZSPolDS1MJHSpQpAX3mjEXi1LG01EwQzaRZObFSYSut0gqFZ5cgCK9hMgEPzRC/b1Yu1KXnVfp9pO9mYBDw7X4I/8B7fwBFli0fPuwqJ1bqsZUK2+Rk/rdQQl1SfY4gCBc09YJGRASqqoGavWWIGnAuEu4cY7ekgxfdArx3PwCgbngWMle4sWxM1XAJwmsIOXhScas7707DY0sQhHfQ6gd91RWNwCv84/seDEEseV6DDvLYEqrw1Y6XyzL2dOfESj221dXiY6H1SGgo/7uxkW6mCUIP2dnAwIHAvHnAE08g7vknkLZmMRKemAbWJU1M3pMsFkUmx7g+r7TS+cmTXp40QbRdmpUTKxG2hw9aqW0IQXgRp7nvkgiJ2ETy/QUj9K4RmmSuyEHp9CzUrFqHjjiK2PHX6iv0pFEsCgsWAN27y5teW62qTbAtFuDgZgvMKEbSEH5JrbTIgoq1m5GaCiSOGdJy8R4W/nXL91Qg6dzEln1tgigq0uwFDQAcGNiUKeCysoD6enGDsoetGtHRYrVzErYE4VVycoCsLD78uEcPN8yGRNiu+9SKaet4kexO3p6aR0rLS9US+PO1CUJAK/c9K6vpcymNJFS5NyUCH3rXCKekZpiQmjHV9Y4SSn8pRaraBsb4K4hUHDc2Olw88vOB3ZNewgt4GBwAG2fA3sH/RI/NbyO1qXYrm8aBW77M9xn6+fmwTZqMRDAIjYvYdA7cshZ4bYIAgMJCl7twNht/9yyE+wP6hG1UFHD8OADgzKFyRHo6R4IgVBFy79zhaLkRHZseG2F1vPl2QX6+ePNuMPCiGHAcaykTpjYfMp+EP3CW+24yQZ7TLkQXuoAWbQILCkUmvE75tv3aG61WuVdJkWdrsQBzJ1vsohYADMwG8+YCGCQNSXgvld4Skx5isYBNnix7XQDgWAu8NkEIZGa63IUZDLxLyE2P7ckqcf+Iwq9ROMFJPxKCIFqEAxbRY2sEn2Ort/CUlkdq8mQPKzQ3k2ZVhyYIL+OyH7RU2Orw2LrT0otoGUjYEl4naYiT6hhGIxAjyf1ruogITew3bwbOYY4VmVUrNNv0lpj0kOJicBo5wD5/baJNUlpkwS+LNqK0SHLXl5GhHd6Pptz3vDx+qdgNYVtaZEH7qiP25xyAwQW58tcmCKLFSe/uKGxdFZ6S2lA1j5TSlOmu0NxMmlUdmiDcRPgeaC2cuMx9d0PY0qJNYELClvA6qRdrxGIYDPwVJDpaHGtokK143XorsBdmh0PV5CUz6C0x6SFms+rrtshrE22OLeNfRcrANFz40EgkD0wXvafSu9JOnYD581F9133247hx48S4PjeErVpLrxBYcWwT3XEShD/p2FkubF0VnlLaUOU6mNGoPtYSJsylh4wgvIRe76nTftBu5NjSok1gQsKW8D4KK3Ym41Jg9Wq+g3VOjixv4cjBRtmKF2PAYU5uvRlnQPGQbPkYAC5Pb4lJDzGZwF1/vcMw4wy+f22iTVFaZMEl782wh70bYRO9p0JxJwA491xg1izEzpwujkkFrBvClm/pJf+uNsKIlKF0x0kQfkVyQz1qhNXx5luC0mskrIEpPVLLlnlYobmZNKs6NEHoxF3vqWbPWTdybGnRJjAhYUt4H8XScOSQAcDYseIVRGK0S4obHFa8lCFT3KuL0fP/3pKPjRjRMtUn+vSRPbWFhYM7eIAqXxBexan39MwZcTCyqbyTdCVZaojdELZ8S688NDZ1q26EEVuylyI1g+44CcKvSKoiJydanYpANa8RY8CqVXKPlFMvlY/x52sTbQOveU/dCEWmRZvAhKoiE95HuYSlvMGWrIJ169Ko2sQe0p70ycnyiw3QcmXYpaICgCHESFctwut0zHQMv7d7T9WErXQlWRo6JRW2Oio6Ci29jm3ai5ShPZBJopYg/I9E2MJq1d4PotdIaUMHD3Y0VZ5UaPYW/nxtovWj9T1w23vqZvEoj1t6ET6DPLaE91Em8yiFreRikdqhQXXFS0Z9vfyGHXAUur5CIWwdlgQJwgsovaQy76mPPLbS177g/uHkqSWIQMENYUteI4Lw4vfAgz62mmHNhF8gjy3hfZQe2/Bw+XPFTbnqitckcZcTR+uRoGgLpGwT5DNI2BJ+oHx7ieg9dcdjK32sU9gSBBFguCFsAW2vEfXXJNoSXvGeetDHlggsSNgS3seVx1blptxZmNJTj9ZhiLEet0sHW0rYnj0rf07ClmgBZN5TH3tsCYIIMNwUtoCjDc3PF4vpGAy8N4tyW4nWTrND3t0MRSYCDwpFJryPqxxbrZvyJpRV7EJZHWY9rBCyFIpMtGakN7PSz2BEBP9bT44tCVuCCE6kwtYDW0f9NQnCQ0jYBj0kbAnvo/TYKkORtW7Kmyj+S14WOQz1MNoUObYUiky0ZqSfb/LYEkTbwgOPrRTqr0kQHkLCNuihd43wPm4Uj1JbjTan1cmeh6MOEYYGQGqopTf+Fguwdi1qftyDciQj7uIeSBwzBDCZUFpkQcXazUhNhX3MLZTCFuB7KSj/RoJoDsq70IYG0TsrDYd3pyoyCVuCCE6aKWw9rRCrlpNLebpEm0JqTynHNighYUt4Hw9ybKWYEk7LnkdydXh2dj0wWzIoCOL8fGASX2kqpukHbwJsOofiwXeix+a3kQreA8ymc+CWLXMv0UhN2Nps8huPNk5pkQVHC4vRMdNMlXU9Rfk9kC74qHlsDQb+e8YYeWwJorXRTGErVIjNzeUP11MhVi0nF6A83ZaAFg8CCPLYBj30rhG+x02PLU6dkj29d0odokcrhG1DA28NJk2CGhxjMG8uAKcYY1NywWVl6bceJGydUjghH0MLJiMVDFYYUJidh8wVdOfjFAsfRVC+pwIdwysRF34WuOIK+T6uQpEBfoGovp48tgTR2mimsAXcqxCrlpM7ZYr4WPidm8ufk8SX96AiX57hs8UAErZBD71rhO9xM8dWKWyjw+sd92to4K9qTlALFuZsTYlGzRW2BEqLLBhSMAWGJo+4ETYMLshF6fQs8txqkZ8PNmkSEgEkSsfnzZPvp0fYhoTwQlbLY0thVAQRnHCcGJHhobAF9FeIVcvJVTNzVjfNJ+EcrSJftHjgHJ8uBpCwDXqoeBThe9z12J6WhyKjrk5+wy4cZzY7fVmmNmbQkWgkhYStJkcLi2GE/H8RAiuObaIKJapYLGCTJ6suuDig12Or3Jc8tgTROhDsZDOErV6EnFwpBoPjmJ48XUI/VOTLfXxe8VtqT0nYBiUkbAnf406ObVMhKBl1deoeW5MJuOoq1Zdk4FDZqY98jOPA5blINFJCwlaTjplm2BQyrRFGpAylOx9ViovBMbXlFhX0emwBNFafxP47n8aJ+UuAEyfE7W4KW4sF2LiRWoIQREAghCN7KGzd+T4LObnCSxqN/HPlmKs8XcI91BYUaPHAOb5YDJB9V6TOFjejnsiGBgYkbAnfowxF1vLY5ucDaWnAnDmy3Y99v9vRYyvc+PfqZR86e/7F9sfcIw8jYaw8b5H76Sf341VI2GqSmmHCX5feJRvbkr2UwpC1MJtVowhUccNjazx6GN3emYeEJ6aBLV8ubndD2ObnA+npwMiR/O/8fN2HEgThC5ohbD35PufkACUl/I15SQn/XG2M8B5qCwq0eOCcqCjvLgYovyt7//QsFJlsaOBAwpbwPXo8thYLMHkyn1OkIGn/Npz4vVQ+KAjiOrE1UMStN4nbIyIcvbwdO7o3b5tNdn7ZOAEA6DV1hOw5FY7SJn+9CSVI17Vv8eJ1qJo5H7j/fuC778QNtbX2h40N/A2vrECa9CQ6ha3PQ7sIgnAfD4Vtc77PJhMwfLhcWKmNEd6DFg/0k58PXHKJYxsr5WKAXs+p2nflp+3uC1uyoYEFCVvC9+jJsS0uVhW1AP8hrd55UD4oiFapJzc6WnysrBYLuC9Ipf1Dm3Oe1oxy6ZRQxWIB5k62oCsOyMa1PLjmvJmIe/4JYPFiYOtWccP119uXgm31KvnpEn58+lNdc6M8L4IIQDwUtvR9Dj5o8cA1SvEI8LcfW7bIFwPc8ZyqfVdCmHjfuOoDfcKWvnOBBWVGE75HT1Vks1msAqmAAYg7J1E+2NjI7yv1qEZFiY+9IWzVwpA9OU9rRtmzmFCluBg4hxU7FI5y+7/HmL1sJhfVHqit1Nz1wv89jdKibJeh4UKel3IVnPK8CMKPCMK2rAyYP198nJwsfxwfD1RW2p9fWA0sQhmOIRlViEccKpGCMpz/RTKwWfs4Z+dEfDyQmAgMGULqi/ALWpW7pU003K0yrWb7QiAuGD/0WCgyx7v+yJMNDSxI2BK+R4/H1mQCXnsNuOceh8OrU3oiPj3G8bxWq7bHVq3gFAlb7xPEwra0yIKjhcXomGn2eV6w2Qzs48xgTC5mGTwQt01LwaHxMUCp9m5G2HBs016Xf5uQ55Wby5+a8rwIIgA4eZL/XVUFPPGE7sPiADygtuH55k8JHAcsW+ZWvKzP+o0Sfqcl31s94tGZ51RtfkrbB8iFbZ0tRFd7K7KhgQXFERK+R29V5Ouusz+s632+/XFctwTH4lHCsVKPrTIUWXmMm4K06L631TeQsBUJUmFbmL0cKQPTcOFDI5E8MB2FE3xb6cFkAmbndZaFHtsMRnCeWD7BmrvI/7HCoLtCNeV5EUQAUVSknQrjT4SIEZ3Jg1RQp/XS0u+tnkJbnlSZFmzf6tX87YxU2DJDiG6vK9nQwIGELeF79FZFrqoSDxlysbifmvcV4Mek4tWLocilRRZc9PFT6htJ2IoEobAtLbJg6NtTYGiSmUbYMLggF6VFvq30kHP7WfsFt773+TAcKHG/oJnBIFpz6QKR0ejQemn7+Ffc8kRTnhdBBAiFhf6egTY6kwepoE7rxV/vrSvx6GmVaZMJGDuWD0YIg3jf+PJrIW7ZQ7KhgQGFIhO+R6/HViJsER/PC+LGRnXvKyBuE/Bi8aijhcVIhcb+JGxFglDY8u+tPJc7BFZdYbvNQpIMFNbdxFs/J5WLT107Fu17moCkJDHHbfBg0WpKF4jat4fhu++Aiy6yDw2eq97jmSCIACcz098z0EZn8qC7YaFE8ODP99ZkAkylRUDeWr77BSDLBc+prMTY7DKUc8lITATidpYB813klDc9zklOxpnOB4HD/FD2VccAdPftH0R4HRK2hO/Rk2ML8Bcdgbg4XtieOuXcY6sVitzMHNuOmWZYYYBRTdySsBUJQmHbMdPskNvaCKPusF2PEXLmAKB9e/63E2HbfuI44KabNLfLFohCQpD/0wWQLmDbzu0Fw7I8iokiiGAjIwPIzgYKCvw9Ezkcpzt5kArqtF78+t5efjnw7bdOd4lp+vEESad4sB49wLmZU074HxK2hO/xxGMbFyceV1ennWMrjHMc0K6duK2ZObapGSbsvOI+9NvwiuNGErYiQdjuJzXDhArT+Ui0/AqAL+C0JXspMn1cQEpWvlGHsLWvRmshWSCyGkIwd8phmbA1MBtYbi44rZKQBEEELitWANOnA599JqbzlJfzERzSx4Inylfbvv4a2LWL3755M99IVAdUUKf14rf3tqjIpaj1JhxjYFPIhgYbQSFsT548iSeffBKrV6/GiRMn0KtXLzz22GO49dZbnR63Zs0afPDBBygqKsLhw4eRkpKCoUOHYs6cOTCbzS00e0ImZAFdObaIi0NjSDhCAFhPVMK4f7/jeRsbRY9tWJg8l9cL7X76TbsMIGHrnCD02AJA4sBzgCZha03uiMwV3luRLS2yoPq/a9Gpdg9iLj4XGDOGN4pSYSvkgyvzz6VERmpvA2Tfq0ZmxDms2GEXjmL/CJANDVoyMvgfD/FK1do77hCFbYcObh2ak8O3Wtm7l/fm0WWo9eDL91bzc+uH3HPORjY02AgKYXvjjTeiqKgICxcuRM+ePbFy5UqMHz8eNpsNt912m+Zxzz33HDp27IgnnngC3bt3x6FDhzB//nxcdNFF2Lp1K/r06dOCf0UbRil+dHhsv9oeh0GWSsQCMJ46CbZ8uWNbFKnHNjxc7v2iPrYtQ5AKW+niSgjn2DvZUwqzl2Ho21OQKgy8Cd7rsmwZ0F2Sq+Nlj60xPAT7ODOsTB4+z4xGcBT71+YhG9r2yM8XC/wYDLyHzaOISq2FaJ2YTKQJWiu+eG+dfm79kHvODGRDg42AF7aff/45vv76a7shBoARI0bgwIEDeOSRRzBu3DgYhRJoCtauXYtkITG8iZEjR6Jr1654+eWXsXz5cp/Pn+A9WLKiPCqGsrTIgpDPt6IpIAobXv0do1Bj301VPklzbMPC5CJBJce2/LdSHPtgN1JTgcQxOhrNk7B1TbD+L6RhvHUNMAKAxYLKt9ei9qc9iO6RjPgBPYAhOj4nTYjVlhUwxltq6fVGj7B15bGVXPdCwkMwe5kJUyfnYQnLRQissBmMMFDsX5uHbGjw4o7HVbovoF611qOISslC9NFDDdhdSj1pCR61z2dzogS0qi3bP7cXX+zV+buCcQZweWRDg42AF7Yff/wxoqKiMHbsWNn4xIkTcdttt2Hbtm0YMmSI6rFKgwwAnTp1gslkwqFDh3wyX8KR5IHpKMzOE8M9pR7bxkYUZi/H0LcnywTBQsxUF7NSpFWRw8P55b2QEM1Kyol3ZNmFM5vOuS4KIBW2RqPYwTtYxZwvCNL/xd59HIQ12FNVDfg1exkufXsK4gHES3fkON7bqsPVwVdb1sBmA6Th9N7w2AqfRwAICWkKDctB0ZYs9MBeJA2m2D+CbGiw4o7HVbnvgw96sWqtZBFwdFYDfmLN9AATrQK1zyfQvCgBl9WWpfdk6em86gWan1MueVyJeJSVAx16JiJx9GCyoUFIwAvbXbt2oXfv3ggJkU+1f//+9u1aRlmNv//+GwcOHMD111/vdL+6ujrUSSru1tTUONmbkFJaZJHd4Nv7hE7P4j23kvfy1OFKDPnY0ctlABwq1zqg9NgKvwVhq/DYSl9DV1EA6UW0fXtA+AwEqZjzCVJxFSRYLMBv287YhW0oGjD07SnqnzXGdLs61Kot2zEY5FW7hRxbbwnbJo+byQSYxpoAkDEmeMiGBh8uPVcu9l20yItVayUL0QbW6HI+ROtH7TM3ZYr4WPjt7mfEZbVlaZ2Kvn2BWbOa9Xeo4bC4TQQdAV/StKKiAgkJCQ7jwlhFRYXuczU2NiInJwdRUVF44IEHnO67YMECxMbG2n+6dOni3sTbMEcLHYvYCH1CAcgMZf32X2CEeo4jB2hsaUKaYysVtoB6jq3y/DYXjeaVwlbAH8LWYkHFktX48/4lqJy/BFi9OjA63QehyC8uBiJx2v48BA3OL4RWF5+TJlIzTDhh6q++MS9PLmKFz1NzikdJ891CAn6NkvATZEODD2eeKyWbNzvua7PxXlshwrxZVWsl9joUok3VeVkMKCwWYOPGwDCdwYza59Nm0/+Z1UKotqz5uVXrLEAQCgJe2AIA56RAjbNtUhhjyMnJQWFhId5++22XRnbWrFmorq62/1DYlX6EHrBSZH1C//c/+3j84T80z8MMRlReMFz7haRVkQWBIPzW6n2rOL+zJezav4+JT6SthFpazOXnw9YlDYnTxqHX4mmIf2IaMG4ckJbGxwP5kyAUtmYz0E4ibENhVetWLOKGqyOxd4rj4B138PFY3m73Q8KW0AnZ0OBC8FxJUbsM5ecDTWnTDvvOmAGUlPBCrqSkGWHD0kJ7EK85ei6LgSQk8/P56NWRI/nf/jadwYza59Ng0PeZdUVOjpPPLQlbQgcBL2wTExNVV5RPnDgBAKor0UoYY5g0aRLeffddrFixAtddd53LY8LDwxETEyP7IfSRmmHC5uw8NPIledAII7ZkL+XDkC0W4KmnXJ/EwCftJ4y+VHsfVx5btd63TTBwTosCbLvlRUQX/Mf+/OQJMaSuRcWcxQI2eTIMar5rIUzWn3cNiv9FaZEFvyzaiNKiALiT0cBkAs7relo2VpV4jvrOHOeeq0MSemlHuDEsLbUPVRxqev3mFI8iYUvogGxo8OHScwXHcFABg0Hc12QChg/nf3ssMiUe2whDg+Z8lASSkNQK7Q4Ewa0kkBYDtFB+Pg0G4LnnXH9m3Tm/8LmVIRG2JxkJW0KdgBe2/fr1w+7du9GoKDO/c+dOAEDfvn2dHi8Y5LfeegvLly/HHXfc4bO5EiKZK3JQvr0EO17eiPLtJWLhqOJiXpBpcCS2Fx9me+AAv1TnbJX/7FnRUgmeWp2hyNzbBZpL2KVFFgz84BHZWPtKiZVpSWFbXAzOyf/L7/Fgihzb5IHpuPChkXzBsAmBuySe1E4ubOMr9gHgQ9/LBv9D3PDgg/LPicUCrF6NyvlL8Of9S1CxRBESfvas44udPQvk54P9+9/i6917O///cSZsnW0DHIpHEYQaZEODE6eeK6iHgwK8gFPu2yyRKbm2vLuiUZcHONCEpDuh3f4kkBYDXJGTAyxYwK/92mzAzJn8uN4oAU8E/OcfiML29RXtA/r/Q/gRFuB8/vnnDAB77733ZONXXXUV69SpE2tsbNQ81mazsZycHMZxHMvLy2vWPKqrqxkAVl1d3azztHkOHWKM4xjj5a3Djw1gR9dut+9rg/a+7I03xMcjRvDH9O7NP4+OZiwqSvvY//1Pc4o/v/St9nEAYz/+2AL/qCYOHWI2J/8vZjTy/1N/8eabmnNrgJEd2e7HuTmhoWNn1Tk3xiUw9vXX4tiTT4oHLV+u+tm1cRy/jTHGzj/f8bxXXaX6HjbAyKqnPqL93rpiwABx30sv9cn/iXAk2GwB2dDWiZYpVZqEQ4cYMxiaYTaeeUY88NNPdR3yrYYJ3bjR7T/TKzT7f9ACBMMcpTRnvsuXi8caDKL5dPV6Y7i19hd7Ev8K6P8PoY2vbUHAe2yvvvpqjBo1CnfffTeWLVuGjRs3YsqUKfjyyy/x/PPP2/vv5eTkICQkBAcOHLAfe9999yE/Px8TJ05Ev379sHXrVvvPL7/84q8/qW1jMvHtUzTyujgAtV9u4p8UF4NzVj5K2j7F3RxbNc9aEx0Hd3MYs0lr3bakx9ZkArdokfo2d8NkfYGT/4WsYFiAwWpPqo7Xh8c49kMG+GXlyZNVow2ECtuwWNRDkU+cUPW6h8CK2sPNqBQr9cBp9CElCLKhrROTCXjoIcdxpSey2d5KaXs+F3UrBPTmCLcUekK7/U2weJUFPJ2vp9784mIgkoke21NoH9D/H8J/BEX82po1a/DEE0/g6aefxokTJ9CrVy+sWrUKt956q30fq9UKq9UKJrmBXLt2LQDgzTffxJtvvik7Z3p6OkpKSlpk/oQCvuEmqv79DmKfe1zWHoUBiL5qKP/EbAbjOO1QXGn7FLUcW2dFUdQESBOpSY0OY+XdBiJl/zb+SUsXTLrpJkCtAun33wOZmS07FyVO/heygmEBhtGqnn/NJcXLKxULedouQujtFbaFz1VUFHCySTwbjaptgBphRJS5k2d/AEA5toRuyIa2TmbM4Fv7OGvr47KFiiuk15ZGR9uohskELFwIPPYY/7qBICSbbjuwdy//tweSqAW88D61MJ7O12WvWievF82dsrfKOIX2Af3/IfxHwHtsASAqKgqLFy9GaWkp6urq8Ouvv8oMMgCsWLECjDF07drVPlZSUgLGmOoPGWQ/YzIhbuEsFA/JtvtkGYDiIdlIGZ1h34dbtgw2LYEq9awpc2wBp0LEmcd2592vO4ylXCFp46Il5ppa8ux6erV3iydpifDkZO+9hqc46WNrLxgWaDAGQ536+x++6xfg88/FAeF/bzY7XSixV9gW9lcUyuGuvVb23AoDtmQvRay5Ge8h5dgSOiEb2jrR44lstrfSA49tfr4oag0GXuTqrcrsy+JJmkWJAoBg8CpLEeYr9czbbMD69c6P89SbbzIBObeKHtvTXFRA/38I/xEUwpZovfTctAJla7dj7/SXUbZ2O3puWiHfIScHhoMHUbFkNfY8sAQnx91l33Rwm1hl1i5onfUFlaIhFkuLLOizYbHD+MlaiZhVE7b5+WBNLXn6zhuHlIFpKJyQjx3rLNhw0xIcnvQ0UFSkb25KtES4ztVzn+LEY2svGBZo7NunuejBAWDPPCMOCB5bkwmYNk31GMYZxArbwucqMlL8TJ49y1vzJv6+ax7Kth/g/z+uCkQ5Q/L+nzmp74aTIIjWhasiU1r76BaQbnps1UJNH3tMn1BVK55UVMR7pT01n8GEnvcykOjfX34LoKdRQ3ME/OB+YgrRy3ntvfL/CYYq1IR70DI/4XdSRmeIXlo1TCYkTh2LRAC4c7M4/NEr4j5qHltnKMSixQIc3GxB5LrVSFXJ6z117CSihCdKMdfUkkeaD2wAw9CCyUABs68esfx54LKzgRUr9M1RY652AlzYBiT5+XyurBM46d8kXQC5+GL1/fcWA92780+E9yo8nO9DW1/Pj0naFHSf8Q+gf5MVb4awPXu0EkKn24hN36JwQn7gLiYQBOEzhNY+evfJzxfFp8HACw1NkaDTY2ux8GGm5eWehZqqCWJlWQNPzGewoee99DsWC759ZjM+WFqBXABxqEQyylCGZMAK2GaUAQOSgfh4oLISKCsTI8zKypCTnIwb/xWPE39XIomVIeZYMjAf4n4ax+HXX+1T6KDobOAJbn0PiKCBhC0RPFgsYO++a89VlPZ2PVVZj/aAR8I2Px/YOjkfb7ApMMKmmg/Zrouk16PSamu05FH2nuUAsIICcNOnAxm8kC8tsqBi7WZ0jqhAPJou5OeeC4wZI1o3rVBkErbu4aQAlBRmMIjiVtoLuapK/QBpSLjwXkVE8D81NQ7CVtZY3kNhW1pkQceTYm9SDsDgglyUTs8KzPBvgiACAq3iPVlZGoJKh7CVCgSO43+kl1lPcy+Vl+qCAkBiPu1/T3ExHxQT8IKwNZCfDzZ5MkYyhpFa+6xp+nFCfNOPx9xxB3DmjIMS1ft5cPt7QAQNFIpMBA9Oerq2+/hd3rrqFQpNAsRiAeZOtthFLeAoagGARceJT5TW12x2VrtZBgcAm/iqz4UT8pEyMA19541D/BPTgCeeABYv5kNe09LEJnZaHlsn+a0tRiDMQS8uCkABAAMH7sUXxQHpooKWsBX2sdnExQbBYws4F7ZOQued9QE+Wljs8DkN5CrUBEEEBnqr2QohmhU1zkORlQJBuMRKQ03Vah8qUcu9VKPJfAIIrr6vrYKmxWHNgp4tiUrcszufh2CrQk3oh4QtETw0VUlWgwN466r3qtQkFouLgXNYsV3UavHD67+JT5RXQ5MJnCK81Qaoil0GAEOHorTIgiEFkx28uuKOjP97LBYKRfYWGgWgGsFhER7A/plLwB06CEycKG7U8timpDjuIxXBSmF7UswN0uuxHVyQq1mErGOmGVbF5TuQq1ATBBEYREWpj0svS1KBMH2Gc4+tlqd11Srg4Yf5bS++6FpoKHMvtUTu0KamCZ62jSGagY7F4RZFokTd/TwEWksqwnuQsCWCB5MJh8aqNO4TsNnA9PZWbBIhZjOwjzO72Bm4BpJKuWpi7tJLZU+rFy5FaUwv2RgD+BzbjAwcLSyG0ZWf12aTt5BRQsLWPYQeyhKsMOBubhlily9Ct4VT+X3U+tgCcmGrFn6sFLaCN1bpsW3XTnzsRNg688CmZpiwOTsPjeDvAhthDNwq1ARBBAzSNTYpwiVKKRDqmXOPrZZA6NqVL/ok6CA9wlNaPOnAAT6nVkqT+QRAHje/4KI7QIsjUaLufh6CrQo1oR8StkRQEfrwDGgGv3KcahixKmfPAhYLwjdvxJQp8k1qclPmWVUTcwqDH58eg0595Bkk3IUX2itfdMw0u/ARg79b6NFD7rGVLquTsNWktMiCXxZtdPR45uTYDXNDl+7YvvoAZh/MkafpSMWmtzy2wl1jZKRoSQHgq680/wZXHtjMFTko316CHS9vRPn2EiocRRCES1x5qpQCoQGuc2wffNBRIJw86ZnwlLbkWbEC2L4dePll/re0cBR53HyLarVglcVhv2EwyJToTz857uLq8xBsVagJfVDxKCKoSM0woTB7OYYWTJKvynAc8NxzYDNn6sv/+PVXsC5pSALDLMX6jpo4toETxa0OYWuvhislMlL2d/w1JBs9NxdozzEvj79oS88TFSWKpEDIbw2EOSjYPvYFXPzhTKSCwQoDCrPzRNFntdpdCKFdOmLwWJXl2ZAQsfN8czy2grBljK/wCMgXJiwW4IUXVP8GBqDwmoUY4cIDm5phIi8tQRC6ETxVubn85VDpqRIEo2DmnAlbZdGohx8GZszgz2WxyM8DeCY8MzLkxaL0/h2E5zitFjxhAjBpEv+4Wzfg0Ud5+1ZeDiQl8ePCY6G6sbe3JSYCgwfb32yLBZg50/HvWLDAvWrhROuAhC0RdGSuyEHp9CzUrFqH1Nq/EDOgJzB6NJ/rmpAANmmSa89tUZF9H1f5tY0wYh3G4Hr8jx/QI2wbGviKfcoxCT2zugNN3Ytq75iK6K4dAKGH6mWXiZZEKWyPHVN/TX8QYB7b0iILMj58VPbeyqoFS98DabVPJWFh/P+9yRtbWmRB3O97EQnwwjc2VtxX8NhK3yehKrJARVMFY6mwdZKvxAGIH6XeXoggCKI55OTw1V/37uWFpvTGXikYmSEEdhMpsTlqRaNefpkXtmrn8YXwdPZ3EJ7hslqwdAG3a1dg6lTd5/VV9Wq1MGRAfUGEaP2QsCWCEt5TpXJBzckBV14OzJrlldcpL/gMeyP7Y8SPbwPP/48f9NRjKwggiwXYvBln1q6H4MONHj8GuPJKUdhKzyc1JBSK7JSjhcVIVYwJuaoOwtZZBe3wcLuw3Xz767hk5T1iP+LGRnDffSfu68pjC4iLHNL3T8hXUhG3VAiKIAhf4sxTlZMD9O8P/N//AVe3CwUEUyu5fjrLaRTO62vhSa1+vI/L91Vp53Tg636xyigDgMLS2zKUY0u0OnZ+W+a1cyWNuxyDx5oQGy/5quj12CqFbUMDf4VPSwPGjUPkj5vtm9i1o/kmfYIYklb4oBxb3XTMdCwEJhOJ0pxZVx5bAI01p2SiFmjqR7x7tzjgKsdWirQkqZCvpCjGYYWBCkERBOE38vOBSy7hc2cn361ePEpvjqs0Z9bbc6RWP97H5fvqprBtierVVAiKkEIeW6JVUVpkwXlfv+LWMbL8WSWCV88gF7bH1hXh9Oq1iO2VioQ7x6h7bJWhyKdPA5Mnq3roODCwKbngYmMc28MoQ5EFAiG/NRDmIEEpBgWRmCmM6w1FbjLYtpNnVC+SMimqx2MrIF2YAESXxpYtqNxbgSN1iUi4drA4X4IgiBZEKUTqmHqOrctQY4sFWLsW2LOHr0kg5E2WlQHJyaiqBmr2liG6RzLiu8q3ARAfxztuq9lXhr1vJmMy4hGHSiTbyrBvUjKq/gLi6nScQ8jTHDKE1I8Cl++rm8JWj2ffG1BYOiFAwpZoVfChqO71WTt068NIf0+liE9oqOhNkwjbivtmI9my0y5u2BPTwF1/vfxYtVDkM2ec9oDjbFZRSNfWihsoFNljql5ficxp48QBvaHITduMBitscAxtYZCIWzc8tmcaDIhUDppMwNixiAdwygL8WQxYLWSYCYJoedypiqwpJvLzxQJDGsQ1/XhCDIAFahued/NEHMdHzVA5XBlORaKbwtZbYcJ6ws6F8eJi+XOibUGhyESromOmGVb9TX8AAOnpGl8D6UVbImwTJaIWaApN/eQT+bH19er9Z530gGMGIxAXxz/xJBTZYkHl/CU4eNP9qJw5H1iyBFi92rcd6/0obDVb+khI7B4rH9Abitz03httVpxIu0C2iQHgBgwQB7Q8tvv2OZw24v++QeEE9Zg5Cq0jCMLfKENRG6EeiizgEGpssbgUtQEDYw5xsaptblopzv5WzRByN4WtN8KE9dpGsqEEQMKWaGWkZpiwOXuZe+K2pkZ9XEPYquHQYkjqcRWw2cSSkQoYZwCXtxRISOAHzpwRw3z1hCK//jpYly6If2Ia0tYsRvzzTwDTpgHjxvE5vb66wreEsLVYeIG+ZAkwfz5w//34+8IbkTIwDRc+NBLJA9M1xaLD4oLE43CqIUz7Bkbw5tbVoUM3URxX3/M4uO3bgTvvFPdVq4pcVwd8+63DaTkAQwqmOIjxlshDIgiCcIVSiNgM4gJg6aEG19ckwV0WLEia67YlYSSU+xg50s1bBIlNPdkQrmsRoDn9YvXaRrKhhAAJW6LVkbkiB2XbD+L32atx8rYprg9QE6GAPFTVhbBlSk+smliur+eXQJs4Peof2PPAElQsWQ3u4AH+ai8VroLX1lUossUCds892lJeZVXaa/g6x1ZSbAvTpgFPPAEsXozuOz6250UbYcOQgkn4fUWR4/GnT8ufSzy2Kz8I1b6BERY16uvFHrTh4Yh97Vm+h4D0s1FfDxQV4VTeO+LY4cOaf5IRNhzbtFc25iwPiSAIoiWRCpEN34ke22/WN9qvl5rePrNjAb+Apikuti0JI4tFXu6DMf55kYoJdUByP5JXEK57EUBPETG1z5Re20g2lBAgYUu0SlIzTOgzZywaurlO5Kj4fqf6Bp0eWwaAu/JK+aCasG1okBmFdlmX4dxFU5E4dax4tVcTtq5CkYuLXfunfXWF96XHVml9nWAE0HviIEfPrZNewvVNuWOqNzCCcGUMOH6cfyyEiQPyz8aiRWADB6L9lx/bh9jbb2vO1QqDQysfvRVGCYIgWgJBiEhTNkLRAJuNvyxrejZNJuDiIOnBzXH2uNi2JIw2b3Y0q4wBgwbp8NxK7mHOoqnIohcWAbS85XptI9lQQoCKRxGtmpq95Yh3sU/CoV/VN+gUttw11wA9ewLr10te2LWwVc1PcSVspdsFYWs2y4sZqeGrK7wvhW1xsS5RK2AAw+CCXPmg0mMrE7ai19WhSqPUI3v0KP87XvJJkm7fudPhf8+B9+IrQ9Rt4LA5O8+h6rHLSpQEQRB+4O9Dofbe4KHgr5+MiZdmQdRkZUmuV9Jr5d13A126iJWJy8uBpCS+KvK+ckSfkyRWRW7aBkB8HO/hNq39tmwBtm7lt3/yCTBmDADqhQqIwV2y91KJ5B6mDuI9THMqHWt5y4V56LGNZEMJARK2RKsm5txUl/toCkK9ocihoY5FNbwhbOfMAfr1Q93ve0TzIS1+JIQBm0zgrroK+PJL9flJVqW9ji+FrdnMz90NcRsCRWi0k1BkabVPhxsY6Xsj/I1aHlsNOMb43OCKCtT89BdKo3siZvxozVY+1K6AIIhAo5tZvE0MgXolfgdRU1XF/+Y44N//VrWfcfC8KrK7yCrqvvqoKGxjYuz7tCVhNGSItml1KVA1hG1zFgFctQTSaxvJhhIACVuilRPfo4PsuZpnU9Pbqbd4VEODo7DVyts9dUr9/AL794uP33sPeO89SPdiTz0tzlX6muedZxe2x4aNRTRXi3bfNQndJUt8187Alzm2JhPw9NPA3Lm6D2mEUS5unYQiW7lQgGncwKi1AtLy2GrADEZwgwcDJhNiwLeocIXJRMaYIIjAoVO6PBTZYJB7bAEVUSMI29hYl/UpfE1+vugNNBiAomsjcZGwUdGSr60II5OJ73Ik9ZIKuBSoEmHbwIVr21A30OMt12sbyYYSlGNLtG4URrUx/RyHLreNBg3vW3OErValZangVQpbi0Xb69oEJ5299DUlgi3luYfQ7ubR4rZ27Zyes1k489h6w5t77bXi42HD+KrIDzwAzJ+PUzfeIXsvbeCwJXup/HgnocjTHgjTrtKosuhwxhrmdLsUe5VrsrAEQQQzIaL/Y9CARhw4wIsiafuWBx5QHCMIW2mUix9QC3H9cJ2kk7hy4RP6ihy1BnJygAMHgIcfFm9vdAlUibB9cl64rkrHrlooeaMlEEEIkLAlWjcKQRp6wxhw27ej+oHZqDPyBi7UptJvFtAfilxfr1/YSvvTKsWRu20SNIQtQkOBSOfG21NKiyz48/4lqL7/ab4S8DGNvxPwjjdXuqKekQHMmgUsWgTMmoX2H70DbtUq++ZT2dOQuUJhXZ2EIscmhmrfwBw86DAU8dUnYnEqFY9tY0oq9k2aL69yTRAEEcxIikclRDXYQ0NLSnhRZLMBL74oKfjDWMAIW7UQ11PMN7ZRL0qR58++uSYT8MILvMDV3YpHImzjO4a7XATQ20KpOS2BCEIKhSITrRu1MnkZGTh7DIh52UWIqy88ts6ErZttEqpPWPH7agvMKEaScCMBOApbpbjzkMIJ+RhaMMleSIQtnof2zg6wWmU3RR7hKidZYlGjE1W2OwlF1gwntljEHCwJ9h6007OQqjKXkAvPxznLZqmfkyAIIhiRXsOl10/wa4zKIlJXXXYGnYX9/Cxs1UJc67kICKE+Jw6fwa8bm3JvW8A7qAyL/uc/gXfeEZ/n5flH0LkVvuvKJktwVRSqWfMgCA3IY0u0bpSCtCmsqubzQtctcpojbLW8lc5CkU0mYPlyp1Nikllvf+kHXDIuDUnjRoK99764U2ioPPzYC6vSpUUWDCmYJLtg6Gox1FykHtuICMft0v9hnYrn3YnHVlN0O/Gc23vQqonihATN4wiCIIISqe2T2Dmtgj8Hfq0SB/wsbNVCXG+dKC76Pv3oGd19WJuLmsgrKAjCvrluCNu21EKJCBzIY0u0btQ8tgBirskEW+JCnDUnFFkLZx5bQKxesW4d8NdfQFISKhGPsnKgQ89EJMZZgfHjAQCjsMF+mCz31gehyEcLi+2eWt3o/Z84w5URdVfYKkO21XDiObf3oA2vdNxIwpYgiNYGx/ELwo2NwJEjfDHCykoM2FeGx5AMBiAZZShDMmoQjz5f/Cke28yIHVk1Yw89eQ4FobZEAm/y28IZv3DqypPoDdREnpLmtMxpMdwQttRCifAHJGyJ1o2GxzZldAb+GpIN8+YCbXHbHI+tFlJhq+aBBHirNnWq/Wl80w8A4PvvXb+GD4Rtx0wdvXKVtLTHVuqNFfAkFFnwnE+aJBuW9aDdc8rxOBK2BEG0NvLzRftmsQDTpgHgq7wvUNv/TcnjDz7gj/cgvlYZttucMF1ZiKvENkZCtA++FpVqIk9JUIg+N4RtW2qhRAQOFIpMtG40PLYA0HPTClhTOmkf6wth6ywUWQ8hOtaifJBjm5phQl27eNc7StEQtsoCVE5xNxRZ0Zjv1M69qJy/hO8na7HoC0UG+DuoQ4eAJUtQM+kB7HlgCY5tPygWp1J77/zc1oIgCMKrWCzA5MnNO8eUKW7H12rlZnolTFdD2PpaVKqFRWdne1YJuKUKTqm+jhvCFnBdFMqfxbOI1gl5bInWjYbH1v40PgY4dkT9WL2hyJ56bFtK2Hqj8mNDAyLOVrt3jMr/ZNMdSzD4v9NkBai47GxgxQr1c7gbiqwQ0+1L/0b7J3gPAzgOGDdO3OiqF22T51y1B+1HHznszubMBSeUDCUIggh2iosdFgvdxmZz2xXqLDez2d4+yQJpe+6MV/qw6kWtT+4zz7jXN9ebnmyPXsdNYQtoF4Vqqb+FaFuQi4Fo3Tjx2AJwemE+WSnx7rVUjq0rlPNXIyTE68Wjjn3+o/t9aRUis7TIgsH/neZQgIoVFGh7bt312JaUaM+HMeB9RZEtT7BYwB55xGGYAwObEgzVPwiCIHRgNvMLgs3BYHDbFSqE7UrxmkdVsug76fYzLdZeRvBMAvI+ue70zfWpJ1vv63ggbN1+DYJoBiRsidaNC4+tM69d+/fyxb6lzfDYyta7/RGK3ExhWzghH0nXD3H/QIWwPVpYrHrB4QBg0yb1c7gyotL3r64O2LPH+ZyYosiWJxQXg9PwYnA2KvlIEEQrwWQCli3zWNzawKHwn3luu0LVwna95lGV2MYo4xndorI56O3l6iost6WqDDt9HS8JW6qYTPgKCkUmWjfN8NhyAAYX5PJ9S10JW0V/P4ED4x5BQvhJRL+9hB/wRyhyM3Js+TY/kz1bAVOI/Y6ZZtjguJrGAHBDh6qfw12PbXq68zlxnChuXYUia2E2g3GcqrhlBiO4gK/+QRAEoRMhfnbLFqCigh+rrATKy4GkJP550+NKxOO5xyuRhHL8hZ74DKNx9F0TSp5xXzyqhe16BaltlNoXH6G3l6uesFynVYYtFmDzZv49qqwEysqA5GQgPl7+HFB/LNnvgvBkPAYgqanadRXikYBKXPROGfDTT+KLnzjh8f+FKiYTvoKELdG6aYbHFgBCYMWxTXuR2t2zUOT0e/4BrF8vDkgNqS+FrZRmeGz5Nj+e5ViV/XIYyeecY3+emmFCRZcLkHhoh32MAXyObUaG+kmkq8NqwjYkRBSrdXWisVaD44BrrgE++4x/7qnH1mQCt2wZbJMnwyARt4wzgMujko8EQbQyTCZg7FiXu+3YCDynHGxGbqxWbmaz8Hb9CRfoyRfWK341qwyvz3eo4t8c4qGj4jUADBvGe/Q9iOOmismEr6BQZKJ10wyPLQA0wsj3LfU0FDkxUVtA+SLH1mjkBVxoqDjnZhjvjplmWN1r8mOn4sf9DmOJPeSVlbnoaO3CUYDrhQCOE8fr6mTvQ935Gfj/9u48Oooy3xv4tzqBgMSEgAQIzTphmwDiEjHKpg5ERkYuzs0ZtleWRsGFCHoNIo7AVTFeObgMiuxEo/HAhbggOoDAwIssGdF3wIUJAglhCySEECBA0s/7R9OdXqq7q6uru6u7v59zcrSrqypPPwF++dXvWU5ljm84d948IC2t4bXaii0AmEwwlJaiYvEaHJqxGBWL10AqLeHKF0QUtQI6N1Yr9g9Ig5DYKukTX4bluqwynKnBytVqCeHXxFhvKyYTqcGKLUU2bxVbD8llPQzYPX6JZd/Sjf9y/z08DEVGixbyCVRsrLrtYbxVbK1JtCRZFpCqqfEteFuHMx0+jOrfynEZyfjt939Ct5+/sJ2idD/bln1ktlKqrnZ8Lbf3rD1vFVvA8jOsrXVJbOO6d0bbR7OAv+dZDgjh+HNSW7G1MhrRcmoWWvp3FyKiiBAWVbggVmzLyixJa24uMGuW+z7xdViuQyV7mwYrV/vDz+WqA1KVp6gWFoltTU0NXnrpJaxZswaVlZXo0aMHXnjhBYwaNcrrteXl5cjJycGGDRtw+fJl3HrrrXj11VfxwAMPBKHlFHLeKrZuqnZnBmXB/OZCS1Irdx9n9gmYvaQk+QRK7aILShNbwBLAa2qAEydwfuZ8VJwDklGOhN8lWyLmPfe4TvJ57DFbkJTb5uZy5gjcdPY4sH+/16Ym/76V60H7xbMAS79ZJxXJUTJ023r82jXHxDU21vJgwaqy0rGy7m9iSxQmGEMpWAI2N1YrjRo1TF8pKQEWL3Y/B9Vu3un5uGTHGOpp7mpSEvZtOo9dn5XjDJIhAdh9bzla9EhGiy5JSDpzHpjecJ2xvBz/GNUdYz/9E0rNRt8eCFhXrg5Vcqu7kjxFu7BIbB955BEUFRUhNzcX3bp1wyeffILRo0fDbDZjzJgxbq+7evUqHnjgAVRVVeGdd95BcnIy3nvvPTz44IPYsmULBg0aFMRPQSGhsmLb+s8DgHS7qOItsZVZoMncpAkMjRuHLrG1tunCBST9z2wkOZ8rSQ3zY8rKHJJad27q0Qm4Vu3xHJv6eqCsDBVffoezhyrQqntLtDx/3vW8K1eAZs3k76G0Yms91zlxdU5s7Z/W+zMUmSiMMIZSMPlbhbNWOrt2DUBivHJlQ5w7fhx48klFlyXd+FLqrhtfNrtufLnRH8AxPIlD/7Uc8c+YHD63x/4wGoFp04B33/WhdRoxGHRYkqdop/vEduPGjdi8ebMtEAPAfffdh5KSEjz//PP4y1/+ghg38w5XrFiBgwcP4rvvvkNGRobt2ltvvRU5OTnYu3dv0D4HhYjKii2SnEKYt8RWZkiTVFuLf987Ad3+z92u56tNbL3NsbUmtkVFwKVLns+1zo/JzLRETSVPfKurlbd9/XqI+fPRErAN15UdxuwpsVVSsbX+DK9e9V6xtV9cihVbigKMoRROlKwOrFpZCOejKiAB6LHwceCZTACWZFFRf9x5Z8P/Z2UBt93WsGq1tbIss4q1w/97Os/5vaQky/ohGRlMakl3dJ/YFhYWIj4+HllOK/JNnDgRY8aMwd69e3HPPfJ7bBYWFqJ79+62gAwAsbGxGDduHF588UWcOHEC7dq1C2j7KcTUzrG1T4jk7uNMLrEF0PW7PFTd0Q7Nnd8MdMV2505l97POj+naVdn5bdpYApwCYv58lyRWdm6up+2I/KnYxsY6PKC4/v2PuHLTLQ3Dq61bVxBFMMZQChdKVwdWTekD3FAym21zVhX3h31MHjECGDs2IE0LaCWdSCO6XxX54MGD6NmzJ2KdfqHv06eP7X1P11rPk7v2p59+cnvt1atXUV1d7fBFYUjtqsgaVGwBSyJX+5Pr6sAuSyAqpTSxHTBA8S0vrPkah+d8iLpEBQOtbrlFcVKueC1lTwt4eNvHFvA8FDk21tZnjU6fQMKR/9fw/sCBlsfhRBGMMZTChbfVgcvKLCvoqlyEt2E+qp4ZDLY5q4pXS7bfT9b5dxeNrFhh2Sb+/vst/2XoJL3SfWJbUVGBFs7VM8B2rMJD1cWfa19//XUkJibavtq3b+9r00kP1O5j62tieyP6OD8LFgASGrkmbqK0FJgwwfM95ShNbNPTgfHjPZ97Q+Li/0HqytmIvWD31HfkSFzp/wf5+7tLMJ0ofi6uNLH1tnhUXZ1jhTc2FigqgnC3FZOfWxUQhQPGUAoXnrbG0SSxMhot60roObldutRWDlW8fZJ9xVbm76u/3FWOGTpJj3Q/FBkAJA//CHl6z59rZ82ahWeffdb2urq6moE5HKmt2NonVHL3ceN6XDwaXa2BBEtid/SO/0Tnv/+vy3kSAJGXB+mppyxJqFLe5tjaJ76rVwNPPQV89RXO18ahsgJIvnQENxcs9/59Pv8cTRctAv7vFsfjPiS20v33A1u3ej9RyVDk2Fj3n93+Z2g/r7hRI2DnTs+VYz+3KiAKB4yhFAz+DlV1t10QoOEQZeuyzbt3N0xHUTC39HzjVqisAFrhLBK6WN6rOnYeK984izOwXJeMsziHVsiZn4QkKJyvCgALFwLnzll+z7B74C3XH7m5lj62vg8g4BVbT5Vjhk7SG90nti1btpR9Klx54y+y3NNkLa6Ni4tDnNp5kKQfKiu25tvvgGGZ3SoNChPbxp3a4cyCj3Dxm124+cF70aVZDXC/a2IL3Biqu2uXb4mtL6siA5Z7p6c3rOi4bRugJLE1m4GqKvn7K/17ofSX2CtXHFZPbhN3Hs2v3tgK4cQJyzkGg+W3Jrko6i6xjY0FBgzwvO8utyqgCMcYSsGg1aJPctsFbdumcWJlNFoWWfKB3KrIP2wDnnvD9dzMDGDwYB9uvns38OWXlg85e7blwfqNhQ5N5eV45LlklF9LwqlfzuOH58vxdyRjE4AxD5Sj9/3JwA8/2G61b0ctUpppm3D6us8uUSjpPrHt3bs3CgoKUFdX5zBH6MCBAwCAXr16ebzWep49JddShFBZsTUIM8SUKZCsj4QVJraIjUXr4eloPfxGslpWBiFJkGQWrBAApHvvVXZfW8O8tMPbSr9KF4mym+fjoHFjxRVbKJ1T99lnEIsWOaye7OLaNaBDh4btiex5SmzT0yGNH2+pjjvfk1sVUBRgDKVA03rRJ+ftgvSaWGnWLvtY+YZrpmxNqrsDGGz/xrc3vuzc+fhtmCItw93LTJqtJu2uks7QSXqk+zm2I0eORE1NDdatW+dwPC8vDykpKejXr5/Ha3/99VeHLQnq6uqQn5+Pfv36ISUlJWDtJp1QO8cWgGS/SoNcQhkf73rMObE0GiEtWwaz05A9AUAaP963ai1gmRvkqWrrLbE1GoHlXiq2kmSJYh07yt9faRWmpkbRaWLRImULTbmbE+tpKDIArF4Nad8+XJgxB79Nno/z8xcDa9YAJSUa7iNBpE+MoRRoihc5UsmaWFmfS+slsdKkXWVlwD/+oVmbDBBYLKbgvx8v03QOrMkEHDtmqZ4fO8bQSfql+4rtsGHDMGTIEDzxxBOorq5GamoqCgoK8M033yA/P9+2/57JZEJeXh5+++03dLzxC/mkSZPw3nvvISsrC7m5uUhOTsb777+PQ4cOYcuWLZ6+LUUKtXNsAYiYGEjWR69yiW2zZq7Jm1zSaTLBkJmJig27UfX9Ydxy81Ukjn7I96TWKibGcfVfe0r2ZrWO9dqwAfj3vx3nDt3RDRg+3BKZ5VY89WGOLS5eVHSaT8t4yI0/s3s4ceHnMiRaX9j/LNLTkZie3vAeUZRgDKVAC0ZFVW6Ish743S7rhFkNxaIenc2HcfiwUXF7lMyPdq6kE+mR7hNbAFi/fj1mz56Nl19+GZWVlejRowcKCgowatQo2zn19fWor6+HsBvyGRcXh2+//RY5OTmYNm0aLl++jL59++Lrr7/GoEGDQvFRKNh83MfWDAkGCJgNMTDYP3qVS2xvusn1mLtqqtGIllOz3A+19UVsrOPqv/aUJLY32oOpUwHIzx0CYEnc5e6vtGLrYSiytZ8BeJ4D60zmt6XT+0rQ5sb/3/zua45tJSLGUAqoYA1V1Wti5Ve7rFsQabi/bh1icNSQqvjBglbzo4n0QBJC77tV60N1dTUSExNx4cIFJCQkhLo5pNShQ0CPHg2vd+8G7r674fUnnzhsZl6a9SyaZv0JrTKcHr3++CNw220Ot77epTsaHTnk+P369wd27tTwA8hISHBfDX3wQeDrr7X5PmfP2hawsNm4EThyBHj6ae/Xt28PHD/ucrjy9gcg/fnPSJr9pOVAfLyyYcsyEfdUURla39XBliQ7eOstYPp07/cl8gFjgTrst8hXVqascunv6sla0Us7sGIF8NhjmiS39TBgqrRU8RzbsjLLrCPnavuxY/p8iEDhL9CxICwqtkSq+Vix7dC3JZA12Pt9AMQ6J7Vy99faihWeh/hqWaWUq9g2bqy8YuumnS3u6Qn0sVsx2S6pLRvxBOJ7tEfza3ZbIwBAy5ZARoZLpD29sxht3e2Yy4otEVHQKKlc6qU6qJd2AHDcgujwYeXbBN34//NIwplyIDa5Jc6mZmBOhvIhyNzKhyINE1uKbN7m2DovHuUuMZVJbGWHz9ovXqS1sjLLU11PtEzm5ObSajHHNi4O2L5d9q12n38A6U/LANMsRd+izYCuDsOaHQT6IQMRESnmbvXkPn0szzeDVTnVehVnf9rRUDH2fQsiQD5Bz/DhM+h1xWkitXS/KjKRX3ys2PqS2MoRRUUOG6xrqrjY+1AlLRNbg8F1HnGjRpa9d5Wor5c/fvWqZUN6GRIExOMyKx+70TbdiIOZz9leO/QOE1siIt1wVx28+27g/vstQ2JXrAhdO7RaxVmJFSssn9efz+0uQfdlNWS9rjhNpBYTW4psPlZsL5xwM9dTYWIrARB5eUBRkcIG+sC6yIQnWg+/dR6OXFkJ8cEH/t2zpsZjgi6ZffsNo8/SaQ3X2r/BochEREFRVmbZCsZTUmWtDjrzJzFTQ64dwaxSapGQAtol6NatfNassSw7kpnp2/VEesLEliKbcyLoXMXbtMnh5c0L52DnBJlHpwoTW+BGcqW0qukLoxFYtsxzchvoxPbUKd+255HTtq3HzyAMPv6G0a6dyz7BAHD+2AU1rSMiIh8orT46VwflwmowKqehrlJqlZBqmaD//e/AqFHAX/4CdOgAPP984B8wEAUCE1uKbJ4qtmVlEK/nOp4OICNvCk4VOf2LLhOBhZsUTwDAvff63lYlTCagtBRYswbn5y/GtXinjXoCndj+7ncQ3qrG3iQnu03QhWSAtNS33zDOfL0fkkwFuPmcbPmHFEREpAlfq4/W6uC2bcCePaGrnNq349ixwC4c5VzN1ioh1SpBd/4ZCgEsWBC8oeFEWmJiS5HN0xzb4mJIMosOxaIeZ3Y5PTp1vk/TppCWL3OpFAoA0vjxQHq6H4324sYiE0mzpqJxq+aO79XWavqtqs9cdnhd9Lc9kJa5fm6fxMW5JOiHZixGxeI1kEpLfP4No3rjTtlHDBLcPKQgIiJNqKk+Go3A4MGWMBnKyqm1HYD3YdRqyVWztawYa5Ggy/0MgeANDSfSEldXocjmqWLbtSuEJLlU++oQg9b3Oj06db5PUhJgMsGQmYmKDbtR9f1h3HLzVSSOfiiwSa2Tq6cqYL/8lfjwQ0gDB2ry+PlUURnanDvqcOy2wr/i1KxjaFtaivMrC5E0J9v3G1sX7LIm6ACSPF7gWcIfB0Asll+l2vqQom06V8IgItKav6vqWne6UbL/bSAEctsfT6sve/rcvu6vq2SbJU/kfoZW3PqHwg0rthTZPFVsjUaX6mM9DNg9folrIuR8nxYtbPdoOTULv1s2C4kL5wY1qT2zoQiNa6sdjkkAxOOPa/KI9fTOYpdk0VbNNhqRNPE/1N1Y6T64CrUeno6jd/yn7G62sg8piIhIE1pUH62V02AnT1ot4uSOt2q23Oe2r/AGa66r9WcoN+eZW/9QuGFiS5HN26rIJhMMpaWoWLwGP81Zg/J9JRiwWuZxrVzFNsTcDsE1mzVZfcOyR6wjh0RR7XxejRNbAOjyz7Wonjbbob1uH1IQEZFmgjlfVUuB3vbH17m0oZzrajIBJSXAf/0Xt/6h8MahyBTZvO1jC9iqri19uY8OElt3Q3CFwQBJg0esbdONONl9MFIObbcd2zf6LdxjTRR1lNgCQOK7rwI5U1GxYTdOnwZaPJSBAUxqiYgCzt/hsKHg7zBqb6yV0ClTLAmzt0TR21zXzMzA9rHRCLz5JvDMM6EbGk7kL1ZsKbJ5q9iqvM/lusZuTgye1sPTUXzPeIchuAISpKVLNYtGKSPvdnh9z3K7R/E6S2wB2B5SpM3NYqWWiEhnlOx3GyzB2PbHl2q2u31+geBsg2QVqqHhRFpgYkuRTUnFVomCAoeXTTf+ry62kum2azXKv9yHo+PnoHL+YkjHS7UdB5aQ4PjaPpnVY2JLRES6pHS/22AKxjBqpYki57oS+Y+JLUU2LSq2ZWUQzz3ncEhPW8m0Hp6OzqvnosWsqdo/YnVObO0fDHhIbA8bB9kqyS6LOjGxJSKKKoFeqMkfoaxQOlewOdeVyD9MbCmyaVGxLS522RIIcLPfbaRJTHR8bbeC9E7TareXpR7fjvIv9+HwU2/h7KovHd9kYktEFFUCvVBTOHJXwbbOdQ3HBbmIQo2LR1Fkc05s3U1g8cSX/W4jjXPF9oZTRWW458MpHi9tPTwdrYenA2fPOr7BxJaIKKoEeqGmcONpj1trZTYcF+QiCjVWbCmyOSeyktwGOV74st9tpHGT2J7eWYwYl82A7NiPL3MesszElogoqgRjoaZw4q6CvXatPoZnE4UrJrYU2dRUaOUo3e820rhJbNsM6Ip6D/98mDvYjatq7LSCtPNrIiKKeOG6320guFsB+dln9bOwFlE4YmJLkU2rxBaIzq1k3CS2bdON+G78UtTB8vi9zumfEoMwQ1hXBnFOZFmxJSKKStxKxsK5gm1PTwtrEYUbJrYU2dQMPaYGTomtfaAdsNqEs/uOYe2T2zAGBXAmWVcGcY7cTGyJiCiKyO3fa61gL1zoen60L6xFpBYTW4psTGz9s369w8t5HVY4DJFqm25ExqzB2CPd4zI0WVhXBnH+GTCxJSKiKOFp/16jEcjKkt+ZMFoX1iLyBxNbIpJXVgbx1FMOhxaLKfjvx8scnjobjcCcZUZMlRqGJpsNMZDcrQzCObZERBQFlOzfy4W1iLTD7X6ISF5xMSSnZRtjUY/O5sM4fNjoEHRNJiAz04Si3ZlIxWG0ykh1G5VPfX8yeuYoExFR1PK0f69rDLUcT3UTPsvKLPfr2pVJL5E7rNgSkbyuXSGcxkfVIQZHDamyQ6SMRiAjy4hWWYM9Rt3kuzpi5wQu+UhERJFNbvVjd8OMPS2s5Wk4MxE1YGJLUYWrDPrAaIS0dCnMBuvKxzF4QlqCl5cafXpafKrIsdNjYEZG3hSX40REpE9yix+Rd1oMM1YynJmILJjYUmRzeqzpvPgReWEywVByDGfXbEPRmmOYU2ryee/B0zuLXY7Foh5ndnHJRyIivWO10D/+7t/raTgzETmShBAi1I0IB9XV1UhMTMSFCxeQ4GZvT9KZsjKIjh0d5onWIQa/MxzDrhLfqo6k3qmiMiTf1RExcPw5nN13jHNtKewwFqjDfgtPZWWWZNY+sYqJsSRojKHBwZ8BRZJAxwJWbClyeVz8KERtikJt0434bnzDisl1iMHu8UuY1BIR6RyrhaHHVZOJlOOqyBS5bix+5Fyxdbf4EQXOgNUmnHoqE2d2HUbre1MxgEktEZHuWRc/cq4WMoYGl5JVk4mIFVuKZBotfkTaaJtuRN/pg1mpJSIKE6wW6oenVZOJyIIVW4psJhMMmZk4u/swDiMVczKY1BIRESnFaiERhQsmthT5jEa0yjKiVajbQUREFIaMRia0RKR/HIpMREREREREYY2JLREREREREYU13Se2NTU1mD59OlJSUtCkSRP07dsXn376qaJr169fj9GjRyM1NRVNmzZFp06dMHbsWBQXFwe41URERKHHGEpERNFC93NsH3nkERQVFSE3NxfdunXDJ598gtGjR8NsNmPMmDEer33jjTfQpk0bzJ49G126dMHx48cxf/583H777dizZw/S0tKC9CmIiIiCjzGUiIiihSSEEKFuhDsbN27EQw89ZAvEVkOHDsVPP/2E0tJSxFjXoJdRXl6O5ORkh2MnT55Ep06d8Oijj2L58uWK21JdXY3ExERcuHABCQkJvn8YIiIKe+EUCxhDiYhITwIdC3Q9FLmwsBDx8fHIyspyOD5x4kScPHkSe/fu9Xi9c0AGgJSUFBiNRhw/flzTthIREekJYygREUUTXSe2Bw8eRM+ePREb6zhiuk+fPrb3fXXkyBGUlJRwCBUREUU0xlAiIoomup5jW1FRgS5durgcb9Gihe19X9TV1cFkMiE+Ph4zZszweO7Vq1dx9epV2+sLFy4AsJTQiYgoOlljgI5n8dgwhhIRkZ4EOoYGLbHdvn077rvvPkXn/vDDD+jbty8AQJIkt+d5es+ZEAImkwk7d+7EunXr0L59e4/nv/7665g3b57LcW/XERFR5KuoqEBiYmLQvh9jKBERRYpAxdCgJbbdu3fHsmXLFJ3boUMHAEDLli1lnyhXVlYCaHjq7I0QApMnT0Z+fj7y8vIwYsQIr9fMmjULzz77rO11VVUVOnbsiNLS0qD+MhPOqqur0b59exw/fpyLhfiA/eY79pk67DffXbhwAR06dFAcf7TCGBp9+PdTHfab79hn6rDffBfoGBq0xLZt27aYPHmyT9f07t0bBQUFqKurc5gjdODAAQBAr169vN7DGpBXrVqFFStWYNy4cYq+d1xcHOLi4lyOJyYm8g+vjxISEthnKrDffMc+U4f95juDIbhLVDCGRi/+/VSH/eY79pk67DffBSqG6nrxqJEjR6Kmpgbr1q1zOJ6Xl4eUlBT069fP4/VCCDz22GNYtWoVlixZgokTJwayuURERLrBGEpERNFE14tHDRs2DEOGDMETTzyB6upqpKamoqCgAN988w3y8/Md9t8zmUzIy8vDb7/9ho4dOwIAsrOzsWLFCkyaNAm9e/fGnj17bOfHxcXhtttuC/pnIiIiCgbGUCIiiia6TmwBYP369Zg9ezZefvllVFZWokePHigoKMCoUaMczquvr0d9fb3DKltffvklAGDlypVYuXKlw/kdO3bEsWPHFLcjLi4Oc+bMkR1aRfLYZ+qw33zHPlOH/ea7cOszxtDwxT5Th/3mO/aZOuw33wW6zyQRDnsWEBEREREREbmh6zm2RERERERERN4wsSUiIiIiIqKwxsSWiIiIiIiIwlrUJ7Y1NTWYPn06UlJS0KRJE/Tt2xeffvqpomvLy8sxYcIE3HLLLbjpppuQkZGBb7/9NsAtDj21fbZ+/XqMHj0aqampaNq0KTp16oSxY8eiuLg4CK0OPX/+rNl76aWXIEmSoj0ow52/ffb5559j0KBBSEhIQLNmzZCWloalS5cGsMX64E+/bdu2DUOGDEFycjLi4+PRp08fvPvuu6ivrw9wq0Pr4sWLyMnJwdChQ9GqVStIkoS5c+cqvp7xgDFUKcZQdRhDfccYqg5jqO90E0NFlBsyZIho3ry5+OCDD8TWrVvF5MmTBQDx8ccfe7yutrZW9OrVSxiNRpGfny82bdokRowYIWJjY8X27duD1PrQUNtnd911l3j44YfFypUrxfbt28VHH30kevbsKeLj48XBgweD1PrQUdtv9n744QcRFxcnWrduLdLS0gLYWn3wp89ef/11YTAYxJNPPim+/vprsWXLFrFo0SLxt7/9LQgtDy21/bZ582ZhMBjE4MGDxWeffSY2b94spk2bJgCI7OzsILU+NI4ePSoSExPFwIEDbf01Z84cRdcyHjCG+oIxVB3GUN8xhqrDGOo7vcTQqE5sv/rqKwFAfPLJJw7HhwwZIlJSUkRdXZ3ba9977z0BQHz33Xe2Y9evXxe///3vxV133RWwNoeaP3125swZl2MnTpwQjRo1EiaTSfO26ok//WZ1/fp10bdvX5GdnS0GDRoU8UHZnz775z//KQwGg3jjjTcC3Uzd8affxo4dK+Li4kRNTY3D8aFDh4qEhISAtFcvzGazMJvNQgghzp4961NQZjxgDFWKMVQdxlDfMYaqwxiqjl5iaFQPRS4sLER8fDyysrIcjk+cOBEnT57E3r17PV7bvXt3ZGRk2I7FxsZi3Lhx2LdvH06cOBGwdoeSP32WnJzsciwlJQVGoxHHjx/XvK164k+/WeXm5qKyshKvvfZaoJqpK/702aJFixAXF4dp06YFupm640+/NWrUCI0bN0bTpk0djjdv3hxNmjQJSHv1QpIkSJKk6lrGA8ZQpRhD1WEM9R1jqDqMoeroJYZGdWJ78OBB9OzZE7GxsQ7H+/TpY3vf07XW8+Su/emnnzRsqX7402dyjhw5gpKSEqSlpWnWRj3yt99+/vlnvPrqq1i8eDHi4+MD1k498afPduzYgZ49e2LdunXo3r07YmJiYDQa8cILL+DatWsBbXeo+dNvU6dOxbVr15CdnY2TJ0+iqqoKH330EQoLC5GTkxPQdoczxgPGUKUYQ9VhDPUdY6g6jKHBp2U8iOrEtqKiAi1atHA5bj1WUVERkGvDmZafu66uDiaTCfHx8ZgxY4ZmbdQjf/rNbDZj0qRJeOSRR/DHP/4xYG3UG3/67MSJEyguLkZ2djays7OxZcsWTJgwAQsWLMDEiRMD1mY98Kff+vXrh61bt6KwsBDt2rVDUlISJk6ciNdeew3PPfdcwNoc7hgPHDGGuscYqg5jqO8YQ9VhDA0+Lf9djPV+SmTzVDb3VlL359pwpsXnFkLAZDJh586dWLduHdq3b69V83RLbb8tXLgQxcXF+OKLLwLRLF1T22dmsxkXL15EQUEBRo0aBQC47777cOnSJbz99tuYN28eUlNTNW+vXqjtt++//x4jR45Ev379sGTJEjRr1gxbt27FSy+9hNraWvz1r38NRHMjAuOBb+/5e204YwxVhzHUd4yh6jCGBp9W8SCqE9uWLVvKPgWorKwEANmnB1pcG860+NxCCEyePBn5+fnIy8vDiBEjNG+n3qjtt9LSUrz88svIzc1F48aNUVVVBcDypN5sNqOqqgpxcXEu8zkigb9/P0+fPo3MzEyH48OGDcPbb7+N/fv3R2xQ9qffnnrqKbRu3RqFhYWIiYkBYPllxmAwYO7cuRg7diy6dOkSmIaHMcYDR4yh7jGGqsMY6jvGUHUYQ4NPy3gQ1UORe/fujV9++QV1dXUOxw8cOAAAHvc46927t+08X68NZ/70GdAQkFetWoXly5dj3LhxAWurnqjttyNHjuDKlSt45plnkJSUZPvatWsXfvnlFyQlJWHWrFkBb38o+PNnTW6uBmD58wcABkPk/tPnT7/9+OOPuOOOO2wB2So9PR1msxm//PKL9g2OAIwHjKFKMYaqwxjqO8ZQdRhDg0/TeODTGsoRZuPGjQKA+PTTTx2OP/jgg16X9H7//fcFALFnzx7bsevXr4u0tDTRr1+/gLU51PzpM7PZLEwmk5AkSSxdujTQTdUVtf12/vx5sW3bNpevW2+9VXTq1Els27ZNFBcXB+MjBJ0/f9aWLFkiu+dcdna2MBgM4tixYwFpsx7402+dO3cWvXr1cjnnxRdfFADEjz/+GJA2642vWxUwHjCGKsUYqg5jqO8YQ9VhDPVfKGNoVCe2Qlj2pUpKShJLly4VW7duFY899pgAIPLz823nTJo0ScTExDj8Ra6trRVpaWmiffv24uOPPxabN28WI0eOjJrN5dX02dNPPy0AiEmTJondu3c7fO3fvz8UHyWo1PabnGjYg08I9X127do1cfvtt4vExETxzjvviM2bN4uZM2eKmJgY8fTTT4fiowSV2n579913BQAxbNgw8dlnn4lNmzaJmTNnitjYWPGHP/whFB8lqDZu3CjWrl0rVq5cKQCIrKwssXbtWrF27Vpx6dIlIQTjgTPGUN8xhqrDGOo7xlB1GEPV0UMMjfrE9uLFiyI7O1u0adNGNG7cWPTp00cUFBQ4nDN+/HgBQBw9etTh+OnTp8Wjjz4qWrRoIZo0aSLuvvtusXnz5iC2PjTU9lnHjh0FANmvjh07BvdDhIA/f9acRUtQ9qfPKioqxJQpU0Tr1q1Fo0aNRLdu3cSbb74p6uvrg/gJQsOfflu3bp3o37+/uOWWW0SzZs1EWlqaeOWVV1w2nI9Env6NsvYT44EjxlDfMYaqwxjqO8ZQdRhD1dFDDJWEuDFgnoiIiIiIiCgMRe7sbyIiIiIiIooKTGyJiIiIiIgorDGxJSIiIiIiorDGxJaIiIiIiIjCGhNbIiIiIiIiCmtMbImIiIiIiCisMbElIiIiIiKisMbEloiIiIiIiMIaE1siIiIiIiIKa0xsiYiIiIiIKKwxsSUiIiIiIqKwxsSWiLBr1y5IkgRJkrB27VrZc/bu3Yv4+HhIkoScnJwgt5CIiEifGEOJ9EESQohQN4KIQm/EiBH44osv0KNHDxw8eBAxMTG29w4dOoT+/fvj3LlzGD9+PFatWgVJkkLYWiIiIv1gDCUKPVZsiQgAkJubi5iYGPz666/Iz8+3HT958iQyMzNx7tw5DB8+HMuXL2dAJiIissMYShR6rNgSkc3kyZOxYsUKdO7cGYcOHcKlS5cwcOBAHDhwAP3798emTZvQtGnTUDeTiIhIdxhDiUKLiS0R2Zw4cQJdu3bFlStX8NZbb6GwsBA7duxA7969sWPHDjRv3jzUTSQiItIlxlCi0OJQZCKyadeuHbKzswEAM2bMwI4dO9CpUyd88803sgG5pqYGc+fOxfDhw9GmTRtIkoQJEyYEt9FEREQ6wBhKFFpMbInIwTPPPAODwfJPQ4sWLbBp0yakpKTInnvu3DnMmzcP+/fvx5133hnMZhIREekOYyhR6MSGugFEpB91dXV4/PHHYTabAQCXL1/2OB+obdu2KCsrQ7t27VBbW8u5Q0REFLUYQ4lCixVbIgIACCEwefJkbNiwAa1atULnzp1RW1uLOXPmuL0mLi4O7dq1C2IriYiI9IcxlCj0mNgSEQAgJycHeXl5iI+Px1dffYXXXnsNAJCXl4eff/45xK0jIiLSL8ZQotBjYktEWLBgARYsWIBGjRph3bp1SE9Px6hRo9CnTx/U19dj1qxZoW4iERGRLjGGEukDE1uiKPfhhx8iJycHkiRh9erVGDp0KABAkiS88sorAIAvvvgCu3btCmUziYiIdIcxlEg/mNgSRbGNGzfCZDJBCIGFCxdizJgxDu8//PDD6NevHwBg5syZoWgiERGRLjGGEukLE1uiKLV7925kZWWhrq4OM2fOxPTp02XPs84T2rVrFz7//PMgtpCIiEifGEOJ9Ifb/RBFqYyMDFy6dMnreQ888ACEEEFoERERUXhgDCXSH1ZsiYiIiIiIKKyxYktEflm0aBGqqqpQV1cHAPjXv/6FV199FQAwcOBADBw4MJTNIyIi0i3GUCLtSILjI4jID506dUJJSYnse3PmzMHcuXOD2yAiIqIwwRhKpB0mtkRERERERBTWOMeWiIiIiIiIwhoTWyIiIiIiIgprTGyJiIiIiIgorDGxJSIiIiIiorDGxJaIiIiIiIjCGhNbIiIiIiIiCmtMbImIiIiIiCisMbElIiIiIiKisMbEloiIiIiIiMIaE1siIiIiIiIKa0xsiYiIiIiIKKz9fwN+SUYm67SfAAAAAElFTkSuQmCC",
|
||
"text/plain": [
|
||
"<Figure size 1100x400 with 2 Axes>"
|
||
]
|
||
},
|
||
"metadata": {},
|
||
"output_type": "display_data"
|
||
}
|
||
],
|
||
"source": [
|
||
"tree_reg1 = DecisionTreeRegressor(random_state=42)\n",
|
||
"tree_reg2 = DecisionTreeRegressor(random_state=42, min_samples_leaf=10)\n",
|
||
"tree_reg1.fit(X, y)\n",
|
||
"tree_reg2.fit(X, y)\n",
|
||
"\n",
|
||
"x1 = np.linspace(0, 1, 500).reshape(-1, 1)\n",
|
||
"y_pred1 = tree_reg1.predict(x1)\n",
|
||
"y_pred2 = tree_reg2.predict(x1)\n",
|
||
"\n",
|
||
"plt.figure(figsize=(11, 4))\n",
|
||
"\n",
|
||
"plt.subplot(121)\n",
|
||
"plt.plot(X, y, \"b.\")\n",
|
||
"plt.plot(x1, y_pred1, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
|
||
"plt.axis([0, 1, -0.2, 1.1])\n",
|
||
"plt.xlabel(\"$x_1$\", fontsize=18)\n",
|
||
"plt.ylabel(\"$y$\", fontsize=18, rotation=0)\n",
|
||
"plt.legend(loc=\"upper center\", fontsize=18)\n",
|
||
"plt.title(\"No restrictions\", fontsize=14)\n",
|
||
"\n",
|
||
"plt.subplot(122)\n",
|
||
"plt.plot(X, y, \"b.\")\n",
|
||
"plt.plot(x1, y_pred2, \"r.-\", linewidth=2, label=r\"$\\hat{y}$\")\n",
|
||
"plt.axis([0, 1, -0.2, 1.1])\n",
|
||
"plt.xlabel(\"$x_1$\", fontsize=18)\n",
|
||
"plt.title(\"min_samples_leaf={}\".format(tree_reg2.min_samples_leaf), fontsize=14)\n",
|
||
"\n",
|
||
"plt.show()"
|
||
]
|
||
},
|
||
{
|
||
"cell_type": "markdown",
|
||
"metadata": {},
|
||
"source": [
|
||
"## Pros and cons of trees, pros\n",
|
||
"\n",
|
||
"* White box, easy to interpret model. Some people believe that decision trees more closely mirror human decision-making than do the regression and classification approaches discussed earlier (think of support vector machines)\n",
|
||
"\n",
|
||
"* Trees are very easy to explain to people. In fact, they are even easier to explain than linear regression!\n",
|
||
"\n",
|
||
"* No feature normalization needed\n",
|
||
"\n",
|
||
"* Tree models can handle both continuous and categorical data (Classification and Regression Trees)\n",
|
||
"\n",
|
||
"* Can model nonlinear relationships\n",
|
||
"\n",
|
||
"* Can model interactions between the different descriptive features\n",
|
||
"\n",
|
||
"* Trees can be displayed graphically, and are easily interpreted even by a non-expert (especially if they are small)\n",
|
||
"\n",
|
||
"### Disadvantages\n",
|
||
"\n",
|
||
"* Unfortunately, trees generally do not have the same level of predictive accuracy as some of the other regression and classification approaches\n",
|
||
"\n",
|
||
"* If continuous features are used the tree may become quite large and hence less interpretable\n",
|
||
"\n",
|
||
"* Decision trees are prone to overfit the training data and hence do not well generalize the data if no stopping criteria or improvements like pruning, boosting or bagging are implemented\n",
|
||
"\n",
|
||
"* Small changes in the data may lead to a completely different tree. This issue can be addressed by using ensemble methods like bagging, boosting or random forests\n",
|
||
"\n",
|
||
"* Unbalanced datasets where some target feature values occur much more frequently than others may lead to biased trees since the frequently occurring feature values are preferred over the less frequently occurring ones. \n",
|
||
"\n",
|
||
"* If the number of features is relatively large (high dimensional) and the number of instances is relatively low, the tree might overfit the data\n",
|
||
"\n",
|
||
"* Features with many levels may be preferred over features with less levels since for them it is *more easy* to split the dataset such that the sub datasets only contain pure target feature values. This issue can be addressed by preferring for instance the information gain ratio as splitting criteria over information gain\n",
|
||
"\n",
|
||
"However, by aggregating many decision trees, using methods like\n",
|
||
"bagging, random forests, and boosting, the predictive performance of\n",
|
||
"trees can be substantially improved."
|
||
]
|
||
}
|
||
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|
||
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