Notebooks/SVM/SVM.ipynb

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   "source": [
    "# Support Vector Machines\n",
    "### by [Richard W. Evans](https://sites.google.com/site/rickecon/), March 2019\n",
    "The code in this Jupyter notebook was written using Python 3.6. It uses data files ?. For the code to run properly, you will either need to have access to the internet or you should have the data file in the same folder as the Jupyter notebook file. Otherwise, you will have to change the respective lines of the code that read in the data to reflect the location of that data.\n",
    "\n",
    "This notebook follows some of the material in James, et al (2013, Ch. 9). Most of the sections in this notebook will build to the Support Vector Machines (SVM) binary classifier method. However, we will make reference to more general $K>2$ categorical dependent variable versions of SVM. We will cover:\n",
    "\n",
    "1. Maximal margin classifier\n",
    "2. Support vector classifier\n",
    "3. Support vector machines\n",
    "4. SVM ensemble for general categorical data\n",
    "\n",
    "SVM is generally thought of as the best binary classifier. People often loosely refer to the maximal margin classifier and the support vector classifier as support vector machines. However, this notebook will differentiate among these three methods. We will use the maximal margin classifier and support vector classifier as pedagogical steps to understanding the more general support vector machines."
   ]
  },
  {
   "attachments": {
    "Figure9_1.png": {
     "image/png": 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"
    },
    "Figure9_2.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Separating hyperplanes and maximal margin classifier\n",
    "Let $N$ observations $y_i$ indexed by $i=\\{1,2,...N\\}$ be classified into two categories $y_i\\in\\{-1,1\\}$. Note that this is different than the binary classification $\\{0,1\\}$ that we have used in previous binary classifiers. This distinction of using the set $\\{-1,1\\}$ is simply a normalization, but it provides some nice mathematical help for the maximal margin classifier (and SVM more generally). For now, assume that $y_i$ is predicted by two features $X_{1,i}$ and $X_{2,i}$.\n",
    "\n",
    "As a general definition, let the feature space $\\mathcal{S}^P$ have $P$ dimensions ($X_1, X_2,...X_P$). We can define a *hyperplane*, generally, as a $P-1$ dimensional affine subspace of $\\mathcal{S}^P$ defined by the following equation.\n",
    "\n",
    "$$ \\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + ...\\beta_P X_P = 0 $$\n",
    "\n",
    "In our example above with two feature variables $P=2$ ($X_1, X_2$), the feature space could be represented as a square with each data point being represented by a point $(X_{1,i},X_{2,i})$. A hyperplane through $\\mathcal{S}^2$ space is a line defined by,\n",
    "\n",
    "$$ \\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 = 0 $$\n",
    "\n",
    "which is a one-dimensional ($P-1$) object. Figure 9.1 from James, et at (2013) shows a hyperplane $1 + 2X_1 + 3X_2 = 0$ through $\\mathcal{S}^2$ space. The blue region is the set of points for which $1 + 2X_1 + 3X_2 > 0$ and the red region is the set of points for which $1 + 2X_1 + 3X_2 < 0$.\n",
    "\n",
    "![Figure9_1.png](attachment:Figure9_1.png)\n",
    "\n",
    "More generally, a hyperplane separates the $P$-dimensional feature space into two regions. In one region, $\\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + ...\\beta_P X_P > 0$, and in the other region $\\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + ...\\beta_P X_P < 0$.\n",
    "\n",
    "We call the feature data $(X_1, X_2, ... X_P)$ $separable$ if there exists a hyperplane $\\beta^P\\equiv\\{\\beta_0,\\beta_1,\\beta_2,...\\beta_P\\}$ perfectly classifies the binary data such that for all $y_i=1$, $\\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + ...\\beta_P X_P > 0$ and for all $y_i=-1$, $\\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + ...\\beta_P X_P < 0$. Figure 9.2 from James, et al (2013) shows a four *separating hyperplanes* that satisfy this condition.\n",
    "\n",
    "![Figure9_2.png](attachment:Figure9_2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A separating hyperplane has the following three properties.\n",
    "\n",
    "1. $\\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + ...\\beta_P X_P > 0$ for all $y_i = 1$\n",
    "2. $\\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + ...\\beta_P X_P < 0$ for all $y_i = -1$\n",
    "3. $y_i\\left(\\beta_0 + \\beta_1 X_1 + \\beta_2 X_2 + ...\\beta_P X_P\\right) = 0$\n",
    "\n",
    "That third condition will be important later on.\n",
    "\n",
    "A separating hyperplane classifies test observation $X_j=(X_{1,j},X_{2,j}, ... X_{P,j})$ based on the sign of $f(X_j) = \\beta_0 + \\beta_1 X_{1,j} + \\beta_2 X_{2,j} + ...\\beta_P X_{P,j}$. If $f(X_j)>0$, then $\\hat{y}_j=1$. \"If $f(X_j)<0$, then $\\hat{y}_j=-1$. We can also make use of the magnitude of $f(X_j)$. If $f(X_j)$ is far from zero, this means that $X_j$ is far from the hyperplane, and we can be confident about our class assignment for $X_j$. On the other hand, if $f(X_j)$ is close to zero, this means that $X_j$ is close to the hyperplane, and we are less certain about our class assignment for $X_j$."
   ]
  },
  {
   "attachments": {
    "Figure9_3.png": {
     "image/png": 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ulWxgJSoOAADADljgUOjyBDp1rE3FAQAAqho37QPo27utEwAAgFuh0LCYBQ6FLHBgE9Y4AABADcoNiyk3hHPqqEPFAQAAVqfcwIZ8/NiKigMAAFTy9defyTZ3Ty/lbUKCZHa0djL5Cxye7x8nO6rWpmZH6TbH4/H3t5+nf2OBA9Ucfdq6N/wb7Y2GG3H6je37p/cbZgLAaPg+NpYbfnz+cO272fjPeOLf8Mk2IUFmdbReMgvKDR8fvlzrqFqbNjv66+9/DH8wNbhZ9eeGdo4E6MGbl4ZyvuQBsLZb2LHPL5od6e/jR8usceifNQ7QvZzVqgdfBwE2cgsVh5XYMDLE6Wl06m5c/bmhikP/VBygY5m1hpGiA0Blyg2LKTdAuPpzQztHAtyQuRUKAGKZLQM3RcUBYK+WlQ8UHQCq8UjCxSxwgD6oOADsksIBwO6YLQO3RsUB4OaoVgDUocSwjAUO0A1PxwQAgLWYJM+l3AA9scYBAAAAiKfiAAAANMECB+iMigPTQm75vnt6iYpTHiQqjkGtnUxUnC4HFaXLk2NQayfTWpymkomK0+U7blCJTse/zwmYaDM3TvqlyslcKzf8/vbzcDg83z8+3z+mg6TbDC+VBxn/t3kyp/mk4xT2kh+nPEhUnC4HFRinGhUHJoy/b8qDNJJMVJwuB3UWbfNkDGptXX6MuxzUWbTNk2kqTlPJRMXp8mN8OvncPJnAOKfRFnd6+fc5ARNx8g9/s+XZS5OFiahkEsZZ1uQcPv1q5jz/Wpuzv9w2mcxj84OXly1CUoqKcxpt82Rai1OTigMs9P3T+61TWFHfo6NvfX96+x4dfRs/vV1+jDcZVKLT2HxyOipP5sfnD2/+/bDAYfTx4cu1CImXVlItmVWHNgavfwK5BUf3RHVvWJ/mjYbOFF6X6/IbPwA7ZfuGKMej+R0p9eeGno4JcHOUGwCgJ9dKNrA5d1UA7JKqAQB9sMChkHIDLVNxANirZUUHpQoAAOpQcQC4IcoNADTFAodCFjjQODuL9M/OkdC9zF0klRsAaIpyQ7mzc+jUkVZ/bmiNA8Du5ZQSlBsA1nA8sXUu3ByfOtpnjUP/rHGAm3K23kGhAWBVrjAvZoFDocsT6NQxqf7cUMWhfyoOAABrMOVbTLmhnI8fC6g4EE/FAQBgDWdTvq+//hySi8vGZWghbdKr2CbbVOvozTYLKg7P94+Hw+Hjw5dER5NthgZRbaolc9lAuYFl7OMAAAA78Ga5oabEtsGZOwoHdjQrmWvlht/ffk4mM87SZ720kmrJTEZTbqBZKg4AADDP5Zw5dhPfwmj5h0d1lJ9MotyQXjIwSLQpPDw2Wv7hsWlDa9xV0T93VQAAxLJh5GJ2cAhxehqdOvLVnxu+q9YTAAB0wCMJF1NuCOSksQvuqgAAgFx27KMFPnXshYoDAACwOgsc4AapOAAAwEJmy5mUG+A2qTgAAMASZssAaXaOBACAedQaZrHAAW6WigMAAOQySZ5LuQFumbsqAAAAgHjWODDh7unlcDh8//S+pzhNJRMVp6lkouI0lUxrcZpKJipOU8lExWkqmag4TSXTWpymkomK01QyUXHCkxn+kI6ZaBMSZ8Nk3mxw9/Ty4/OHN486W+DwfP84/OHjw5fLxuOriTZRQeokcxanMJnE4ZmaitNUMlFxmkqmMmscyDL+vtnk8PA4IdG6HFRUHIOqECckmkFViBMbrZGTExutkUE1dXL6HlQjJyc22s0OKvG25pcb0s5m+NuKSiZ2UIXRxsOj4oRo5FR3OajKVBzIUngFoPwCQmyckGhdDioqTuygohhU+OHhcUKidTmoqDg+xtU0MqimPsbj4Y2cnNho3z+9H0KlA15rc/o3OXEuj8rsaFabnEEl3tZZ53a4Zpu+cjvZJiRIus3ZXy5O5vTvoxJebDw8Kk6IqGhNDSpKm1ldc7RlS/eG3Xq80QAAVGPDSGhQ/bmhfRwAAADaclqyUaZhv9xVAQAARLLAodC1Ewi7o+IAAACEUW4ARioOAAAArbDAgZ6oOAAAADEscCh0eQKdOnbNzpEAAPC/7Ni3mHIDcMYaBwAAgO1Z4EB/VBwAAOBfrl2lv3t6uXt6SR+b2WYyh6iOKieTWODwfP842dFkm+f7x6g2bSaj3ECXVBwAAOBwyNixLzH9zp+9p1vmtGknmfGlyXJDeu6d0+a05dyXZnXUVDKwdyoOAACQ5fun9wteWkkLydQf9ceHLwteWklgjxY40Kujj3L3hn+/vNEAAAmmfIvZMLLc2Tl06lhJ/bmhNQ4AANw65Qa25fNGrzwdEwAAWMgCh1jOG51RcQAA4KZZ4LCYckMgJ40uuasCAAD+l4kfQBQVBwAAYDYLHIBJKg4AAPAvZsuZlBuAHCoOAABwOJgtA0SzcyQAADdNoWEuCxyATCoOAADctLunl+EP3z+9T7dJNIhqU7mjBcksKDc83z8eDoePD18WN6jZpmYy0D0VBybk/DbKjxMSpLU4TSUTFaepZKLiNJVMa3GaSiYqTlPJRMVpKpmoOE0l01qcppKJitNUMnPj3D29nLUfBzUGzOl0MpnLjvKTKXf2TuUkc2mYb8895HJ+fhbnzTY5Pc7N51pHp3HKkymsR8TGaSqZqDhNJRMVZ19lLPs4UEPU77+mdDmoUZej63JQhbo8J10OatTl6LocVKEuz8k4qGZHlzOpvtYmc06eP28vjBaSzJtFmQULHPJnRzktE21ip2GT5YaayaxqHNSCIlH7DGp7r/Su8I3++uvP119/ytMIjFMeJCqOQa2dTFScLj/GXQ4qKo5BrZ1MVJwuP8ZdDioqjkGtnUxUnMSgZs0pfn/7+fvbz/J8QoJExTGotZOJimNQb6pfBDi+2t+ld0Mp2hsNAEAJG0bC3tWfG9rHAQAAmKDcUG48h04at8M+DgAAAOs6LdlcK99Af1QcAACAFAscCikxcLNUHAAAgKuUG4DFVBwAAADWclmyUazhdtg5EgCAztmxbzELHAopN3DjrHEAAKBnduwD2Io1DgAA3LS7p5fhD98/vS9vExKkkY5yFjg83z8eDoePD1+uBRka1GzTVEdnLHDg1ljjAABAt6otahgn8NWs3WN+ueFwfYJdU/0c5vao3MANUnEAAKBPmbfQDxf5E5f6z1rOfWlWR00lM2m8yJ+42j+8lGiQ2Sazo5zDqyXz19//mAwCfTuqtHVv+F3rjQYAbo1N+xazYWS5s3Po1NGC+nNDaxwAAOiQcsNiyg1AFBUHAAB6o9xAU3z8uFmeVQEAAPyLBQ5RnDE4WOMAAEBnLHBYTLkBiKXiAABAz8yWAbai4gAAAFjgAMRTcQAAoCunM2SzZYANqTgAANCb1387HA53Ty+T7UPa3D295LRps6NrCxx+f/uZDvJ8//h8/zjZZjKZkDbVksnpCDioOJAj5zdWTpCoOOVBouIY1NrJRMUJHJSTs2oyUXEMau1kouL42UwHMaiQZIbGbx4y/mWizWSccVD5M/zyZM4OudZF/ojS5YbE1Hp86c02w7R8eCk9P0+3OX01J5lEg5Bk0qPOFFWwCIkTVUAxqLXj7LHUpeLAhPxfe5NBGkkmKk6XgzqLtnkyDQ4qKo1GTo5BrZ1MYJzTaJsn0+CgotJo5OT0PSgf46hkvn96HxKnxMeHL2d/GMXO08qjrTH5vBz1rDhRgyqME1JAiUomMM5ptM2TaWpQlb3bOgFuwvdP72v+8qujy0GNLr/EdKDLQRXq8mPc5aBGPsY3osuP8Tioyh/jnO7K22QOqk4yc4MkFjjkzKgn24QEieqoMM7Hhy/DZG9xraFBXQ5q1OWg9uVoN53uDb9FvNEAAJzxfAq4KfXnhu6qAAAAAOK5qwIAAG6RBQ7lxnPopMGbrHEAAICbo9xQ7to5BEYqDgAAAPMoN0AOFQcAALgtFjgUUm6ATCoOAAAAQDwVBwAAdul4PLrUvIAFDoUuT6BTB9eoOAAAsDNjreHrrz93Ty/pxndPLzltQoKUt1m7o1nlhuf7x+f7x3RHIW2qdRSVzCnlBkhQcQAAYE/GOfPXX38mG0/OzMc2+S0LO8pRIZl8ien3+FJOm5KOZiVT2EW6pWU1MIuKAwAAu/Tj84fJNt8/vQ/sMRGtWkclySy7n+Ljw5fJl3LahCjsKD+ZN1u6nwLmOvoh6d7wL6M3GgDogCnfYrZvKOfjx97Vnxta4wAAwF6Z77EhHz+YpOIAAMA+uIV+MQscwjl1kEPFAQCAHbCgfTHlBmAr77ZOAAAAZjNbpj6fOpjLGgcAAFrnforFLHAANqTiAADAzpgtA+yCigMAAPTJAgdgWyoOAADsidlyJuUGYHN2jgQAoHXXJsl3Ty+Hw+H7p/fXDhwaRLVJNGgzmYTn+8fhDx8fvqTbJBrktMnvaEfJAJlUHJiQ8yttd3GaSiYqTlPJRMVpKpmoODlfJasl01qcppKJitNUMlFxmkomKo6fzb0kcxpnclIdnszd08vZISHJLMsnncyPzx/ePCpngcPZvP35/vHa3HucnL/ZZny1xFmQnGQWvDo3n/JiREicppKJitNUMlFxmkqmMndVkCXkl+jmacRG63JQUXEMqppGBtXUO97loKLiGFQ1jQyqqXd8PDzw5OTMz/NXJZREu5z8Jw6/bHk5qMJkcsoNw6Sl8FL/+FKi3JAzO5pM5rLHWS/NaplIJrZsEaUw2mnZaMM0VopmUJtTcSBL4eWI8qsZsXFConU5qKg4BlUhTkg0g6oQJzZaIycnNlojg2rq5PQ9qNiT8/3T+8mAiTb5WaU7GssEOXEm/zIkmRyTE+/hf5NB3mxz+peZcdJ/X5LMrExykikUe426MFqibFQzjZWiGdTmjnaO6d6waZA3GgDgFtgwErim/tzQGgcAAOiEcgPQFBUHAACAfzkej9cKN8BcKg4AANADCxzKjedQ0QFCqDgAAACoMkA8FQcAANg9CxwKKTfAGlQcAABg35Qbwjl1EELFAQCAVpxt2nf39JJuf/f0ktNmst+QNtU6ymwz6fn+sbzN8/1jTptqySwLYoEDrETFAQCA7V0+IGCYVCem1vkz83TLkDbVOrpsc222/Pvbz0SQYeKdnqJPthlfmmxT2FF+MguCXJ5ACxwgiooDAAAbc4V5sWXlhnAfH77U7A7YCxUHAABa9P3T+/G/yxrUbNNUMoN0FWB4tbBNSJBtk7HAAVZ19BPVveGfUW80ANAmU77FbBhZyGePW1N/bmiNAwAAmzHlW0y5AWifigMAAIBiDcRTcQAAYBsWOCxmgUOI09Pl1MEa3m2dwC6d/RN/+s9T4iUAAEbKDbTApw5WZY3DPJdPij6c/L5MvAQAACEscAD2whqHhc7WNYz/7l+udzgePRAEAOD/sMBhMeUGYEescZjhzbLCqbO/9+8+AMCbfGsCuAUqDrNd/kZM/I4cXnJvBQDAma+//qQb3D293D29VGvTSEfpNvkLHJ7vH5/vH9Md5TSo2aaRjoBAKg57clxk66wBAM4Nk+qvv/68vr6mFzgkpt+Fs/ezNoXRojpKtJlVbphMZmiT3zL9Uk6basmEdASEsI/Dnry+vtavIIy/8L5/er9tkGbjNJVMVJymkmkkTlPJhMdpKpmoOE0lExWnqWQaidNUMuFxmkomKs7cIGftT5P5/ul9zjw/kczcfC4bj4Oqn8ylcSL98eFLyaT67NiPD1+utRw7umwTNatfkExOnMJ8EmnkB2ktTlPJRMVpKpl24tSk4hCj2s2HCzqyzGEli79V7MLd00vhlx52ocuPcZeDGvnZvBFdfozHQQ0f45xPckibOh1lDqqko7kbRk5OSHJmLCFtqnUU2OaaLhdHnC5U2dE8NlOXg9qZV+aYe9JaOM/lCYwrHguDRMUpDxIVx6DWTiYqTpeDiorT5ckxqLWTiYrT5aCi4nR5cgxqcTL53+R/f/tZnszvbz+j4pQHaS1OlyfHoNZOJipO+aDqT049uHGeycdVvNl+25PcQg4AACzmiZhAiPpzQ3dVzPP6750U0qWH098KfhMAALCYcgOwX55VMdvpcpScxqsmAwAATLK1GWzCGoeF0qUEhQYAAMpZ4FBIoQG2ZY0DAAC0SLkhluoD1KfiAAAAdEiJATan4gAAAM2xwKHQ5Ql06qA++zgAAFDb3dPL8Ifvn96n2yQaRLWplkx+Rz8+f3jz1WHO/Hz/eDgcPj58SSQz2WZokNOmsKPWkgFqssYBAIBVHP+tJMg4S5/10qw21ZKJNc7SZ720UkdNJXOwwAGaoeIAAEC80ynf5fRvuMifXjJw2nLuSwvaNJLMYWqBwyhxJT/nIv/QJr9l+qWmklFugHYc/fh1b/g31xvN3r157Sjzq1viulNmBABmMeUrYQeHQj5+cE39uaGKQ/9UHNi7yXWqOXfMLjscgGVM+RZTbijkswcJKg7EU3Fgv2bdE3tZOCg8HNZw+bH02aM/pnyLKTeUOzuHTh2cUnEgnooDO7VgC67TmVvh4RCrZKkO7ItyQwkVh3IqDpBQf25o50igRYU7ftffMBwSMrfT97mFG6fcEM6pg82pOAD9GCZsi6dt5nusYdbnyoeQvbPAYTHlhlivr69OHbRAxQFojkkX3VjwYfb5Z7+UG2iBWgM0RcUB6IrbMWiHjxOQyQIHoFcqDgDQFqUK+mC2nEm5AejYu60TAACgK19//TkcDndPL4mHsIyVtZA21TpKtInqKMfz/ePhcPj48CXdoGabRpIBWmONAxOitk8PjFMeJCqOQa2dTGuaOjl+NtNBNh9U+I9Al++4QdWJUx4kM87kNfnwQbVwJ13hoK4tcPj97efkseMMfPIv53q+f8yMMza7lkxUPiFBWotTHiQqjkHVidNOMjWpOJClhd/oY5zyaCFxuhzUWbRGkmlEa+/4abStDj+L08jHuLVBxery5BhU+OFncWr+bA6b9g0X8M8u45+VCd5scyYRZ3JpQzrIm3EWJHMarSSZSzmX8S/bDFOR5/vH4aV0kMk2OXHGl64lk9NRus2sQU0qnK3FzqjLo4XESZeNKicTGOc02laHn8VpZFCVqThQQ+HSwTZ1OahR36NbpstzYlC70+XoCgflnLTpcgjj31z+YVacywY5bco7SrcZSwmzklm8g8PHhy+TE+9lNYvLV3M6erPN6V+WJ5PfZlWbJ7CGRNmoAwa1uaM9abo3/DLzRrMjG15V7uBbPo0o/Bj7KEL3bBgJ1Fd/bmiNAwAAABBPxQFoTsnV3ZwVrQCwLQscgBuh4gDwL0oVBPJxAq5RbgBuh4oD0KJls7VZu5GF9AgAVHY8sXUuwAQVB6BRc0sAZ+1nHa7cQFN8IKFjFjgUUmWAfVFxANqVP+96s2Xm4WZ3rKRwqQ7QH+UG4NaoOABNm9wJMt2g5FUo5wPGzbp7epl8RmzOQ2RzgjTVUcgDnp/vHycbRLWplkydjoDWHJVUu1f/masAnMqcgShP0I3xM5/4VIe0qdZRSDKZCxzGSfXHhy/XkplsExJkVkc1k/nr738Mf/D9FuaqPze0xgEA1pWzmka5gV1obce++j846XVzNTM5JCfn9XOolsxYbgB2wRqH/lnjANCU0yUPCg3sy2mhwVeLWezgUOjyBDp1sED9uaGKQ/9UHACAcmdTPl8t8ik3lPPxgxDuqgAAoDmN3EbBbfLxg/1ScQAAgLVY4FDI/RSwayoOAACkmPItptwA3DgVBwAAZjBbpqazz5uPH+zLu60TAACgXW6hX8wCh1jOG+yRigMAAG9zP8Viyg2BnDTYL3dVAAAAAPGscQAAIMtwqfnu6eVwOHz/9D7RMqTNfjtKLHB4vn88HA4fH75cCzLZIKrN0KCpZNJBgD2yxgEAgGlnK9uH2fWbEi/NatNOR1HJjJP8kJaJNvkdFSYzvhSSTGzaQAuscWBCTkW/Wpzxd3lInEYGFRWnqWSi4nT5jhvU2sm0FqepZKLidPmOG1TC119/Lv8yEfP7p/dvTr9PB3WtTU5HY5ycIDnJXOtoWTLpHRyuTarPLvLnXO2/bHO6bKFk9p6fzNjRm23GlzKTSQRJp5EjahlFSJwuBxUVp6lkouK09o7XZI0DWfKvD6xx+EoaGVTsyWkkK+94NQYVfnh4nNhojZycWAYVfnig19fXcWnDaf1icnJ+2WY8PD/Omw3OTs6yZM6iFQY5jfPj84c3G4yn8ePDl0Sl4FqDMyFthgbpOx1KOpo1qJyOQhQuo2hzFUbUoJo6OVHRmhpUlDazukbFgSyF10bKL/XExgmJ1uWgouLEpmFQk9G2Ojw8Tki0LgcVFcfHeDJOl4OKEjWoRk5ObLTCOFGT7SFObLStDj+L0+WgokQNqpGTExutkUE19TGu7OhhM90blvZ5owEAVuWJmEDj6s8NrXEAAIBSyg0Al1QcAAAAgHgqDgAAUMQCB4A3eTomAAAsp9xQbjyHThp0xhoHAABgM6clm2vlG2CnVBwAAGAhCxwAEtxVAQDAv9w9vQx/+P7pfbrNZIOabVroKMfz/ePwh48PX8rbhATZPBmLGqBv1jgAADDbOEu/qRzOetx2gcM4k9/QmMOyZC5PoLUh0BkVBwCA23U8cfj3NfycK/mJNvmHp1tOtqnW0Zs9Lig3DBf5E8sBMtuctpz7Umwy40uTbXJSUm6A/hz9YHdv+HXojQYAzpzNmX1bmMUODoUscID66s8NrXEAAIB5lBsKKTfAjVBxAAC4RXbsW0y5ASCTigMAAGbL1GOBA9wOFQcAgJtjgcNiFjiEc+qgYyoOAAC3xRXmxZQbAGZRcQAAAOo5LdAo1kDf3m2dAAAA9VjgsJgFDoGcNLgR1jgAANyKnHLD3dNLOsjd00tOm8lkQtrUTGbS8/1jnTbP9485bfaVDNAlFQcAAP5lmHgXTtFzgoS0yc+zPJnJBQ7DpDo9tY5qc9py1Y4m24wvFSYD9ErFAQDgRu19Zfv3T+/rdOR+ims+Pnw5+wPAqaN/KLs3/I5c/EaP9f6SX+ohQZqN01QyjcRpKpmoOE0lExWnqWTC4zSVTCNxmkomKk5TyUTFWTWZcfKc/93Az2ai4jBeui+ZcocEaS1OU8lExWkqmfA4TSXTSJymkgmJUzg3XMAaB1go5IZPIJyfTUh7/bfK/Y4/m7v7IbXAgb7l3BoDy73Su/I3+uuvP+VphARpLc7XX3/6OzldDioqTlPJRMXp8h03qLWTaS1OU8lExenyHd/joCa/Qv/+9vP3t5/lyYQEaS1OU8lExenyHTeotZNpJ079IoC7KvpXf+UMAEAfLHAAeuKuCgAAaIJyA0AhFQcAADin3ABQTsUBAAAAiPdu6wQAAKAtFjiUW/AcVqA/1jgAAACRrpVsgFuj4gAAcCvunl7unl5KGsS2qdbRrGSuzZZ/f/uZDvJ8//h8/1jYJiRIfps1OlJuAEYqDgAAN2Fy1j2rZaJN/uHVOspPJl1uSEy/J2fmmW1CouUfHtVR/tCAm6LiAADAbN8/vV/wUv2OYpP5+PBlwUuxHTWVzPjS+AcLHIBTR1u5dG/4d98bDQC3w2//ZWwYWejyBDp10JT6vx08qwIAoB+uMC+m3AAQzl0VAAB9Un2gJgscgEsqagZMOwAAIABJREFUDgAAnVBiWMwCh0LKDcCbVBwAAHpgygdAa1QcAAC4aRY4hHPqgIGKAwDA7lngsJhyQzinDhipOAAA7JtyAwBt8nRMAABulAUOUZwx4E0qDgAAOzbOmb/++nM4HH58/nBt7nf39DL84fun99ei5bdJNMhp00JHs8oNz/ePh8Ph48OXRDKTbYYGUW2qJVPYEXDL3FUBALB7Q7nhUPFS8ziTn/VSyx3lGGfps15aSbVkcjqqP3xgF1QcmHD39BLy6zwwTlPJtBanqWQMKhGnqWQMqkKcppIxqEScppKZFefH5w/X4ox/Hi7yp5cMvNnmzWQSca69dBonJ5lr0cY4yw4fLLuf4vJK/vP9Y/5F/qHNmy3P4uRHu4wTmEyio7OXcuIsFhWktThNJdNanKaS6W9QNak4kKXwy1PUJYghTmy0rQ5fKU4jWRnUZByDmoy21eErxWkkK4OajLPrQf34/OGyUnAWrWSKflosmIxz2WY8POd+ikRHZydnWTILyg0fH77k3H0wOdVPlAnSbXKSGeIUJnMaLTNIzqAWOx1UVLStDj+L09qgnJzww8/iNDKoylQcyJLzBWW9w1fS5aCidHlyDCr88DZ1OahRl++4QRUe/nqipNO1jYNq8y0rVLiLQZubIBhU+OFtSi9U2bsu3/E2s7rm2PgvJ8oNVXxvNADAwfMpgBtWf25ojQMAAAAQT8UBAIBbYYEDQE0qDgAA3ATlBoDKVBwAAACAeCoOAAD0zwKHEMfj8dqZBLik4gAA0IO7p5d22rTW0WS5Ief59pNtQoI0m4xaA7CAigMAwO4NE+/09LtamwY7Shsm1enp92SbkCDNJqPWACyj4gAAQM9+fP7w5t+7nwJgbSoOAAC79/3T+/G/m7ep3FFaTrnh48OX8b/XTLYJCdJmMn/9/Y9EG4CEo+Ju94ZVcN5oANg1v9CXsWFkocsT6NTBftX/VfKuWk8AACzgFvrFlBsKKTcAhdxVAQDQLuUGAPZLxQEAgA5Z4FDIAgegnIoDAECjLHBYTLkhnFMHLKDiAADQIleY2ZBqFxBCxQEAgK5Y4BDOqQOWUXEAAGiOBQ6LKTeEcLqAECoOAACt+/rrz93TS7rN3dNLTpvJvqI6Kk8mqqMcz/ePkw2i2uwlmdcT6TgA16g4AAC05dpV+sTUOr+UkG6Z06ZaMgs6unbqfn/7mehimHgX1gLyD0+3bCoZgEIqDgAATRuvMH//9P5am8RLK2khmbOOlpUbZvn48GXBSytpKhmANx2tkure8Nt38Rs9XD0o/+oQEme8lBESp5FBRcXp8uQY1NrJRMXpclBRcbo8OQa1djLH4/Hrrz+Hw+HH5w+H4l/i5fk09U4l4szawWG8tl84OR/ilM/wQ+IY1NrJRMXpclBRcbo8Oe0MqnBuuIA1DmQpvEMy5AbLcI0MysmpxqDCD19JI4NycqoxqEtDuWHQzsWhqHdqpXd82w0jC+9NaPPWBoMKP3wlUYNycsIPX0mbWV2j4kCWwssRUasrhzix0bY6PDxObLSmTo5BTUbb6vCzOF0OKkojWXnHJ+M0MqhhacOheLbc1KDGwxt5xwdRdx8UxolNw6Amo211+Fmc1gbVyMmJjdbIoJp6xytzV0X/6q+cAQCoyRMxAXK4qwIAAGZQbgBolooDAAAAEE/FAQCAvbLAAaBlKg4AAOyScgNA41QcAADgdl0r3ACUe7d1AgAAN+3u6WX4Q+K5j0Ob9IMhQ9pU7qgkmfwFDsOz6xPPkxsfbj/ZJv1QupA2lTsCWJU1DgAA+zDO0me9NKtNSLT8jhYnM7fcECURLaej/GQKo80dtWUOwEpUHAAAtpdeMjDZpvDwrZKJTftN6YUAc1sm2hQeXjmZ4/H419//OBwOw38BVnK0s073hqK1NxoA6IMNI8udnUOnDm5E/bmhNQ4AAHBD3EMBVGPnSACA2k6nfC4vz2KBQ6HLE+jUAeuxxgEAoCpXmBdTbgjn1AGrUnEAAKhHuYEN+fgBlak4AACwAxY4FHI/BVCfigMAQCWmfIspNwDskYoDAMA2zJbZkI8fUIGKAwBADW6hX8wCh3BOHVCHp2MCAKwucT/F3dPL8Ifvn95fOzy/TUiQpjr68fnDm68OJ/D5/vFwOHx8+HItyNCgQptqHR3KRq3WANRkjQMAwO6NE/iOe7w0zqtv09zhv76+KjcAlak4MC3kK0XU95Km4tw9vTg5qwZpLU5TyUTFaSqZqDh+NtcO0lqcppJ5M056w8jhIv/Zpf43k0ksB7j20mmcNzt6M85lm8t8JpN5M8jZ0obJZNILHBIX+UdDmzdbni0ESEebjFMzmdOWiWRyglwTUs2JKgk1FaepZKLiPN8/OjmrBmkwTjVHlc7uDd9yFr/ROYse6wRpLU5TybQWp6lkouI0lUxUnKaSiYrTVDKtxWkqmag4TSVzLc5ZxWHyl/IuBrU4yKw413Zw+P3tZ8l0+pB380K1OE0lExWnqWSi4jSVTFSc0xmsk9NyMiFxCueGC1jjAABAixLlhsqZALDQK70rf6O//vpTnkZIkNbiNJVMa3GaSiYqTlPJRMVpKpmoOE0l01qcppKJitNUMtfizP11vItBLQiSHyfx3fX3t5/lybQWp6lkouI0lUxUnKaSiYrz+9tPJ2fVIO3EqV8EcFdF/+qvnAEAKOSJmADh3FUBAMCtU24A6IOKAwAADVFuAOiGigMAAAAQT8UBAIBWWOAA0BMVBwCAFd09vZS3uXt6iWrTcjILyg3P94/jA+oTbdINctpkdtROMgAtUHEAAFjLMKlOz71z2py2nPvSfpOZlD97T7fMaTPZYwvJHE9MHg5QgYoDAMDuff/0fu89Xpsk//7289ohHx++xOZQon4yTQ0f4E1HN8V1r/4zVwEA5rKDQ6GzE+i8AZfqzw2tcQAAYGPKDYXcRgG0ScUBAIAtKTcA9Ord1gkAAOze6ZzZPJnKLks2PoRAI6xxAABgMxY4FFJuAFqm4gAAUORsyueO+nzKDQB9U3EAAIhktkw1FjgAjVNxAABYzoqGxSxwCOfUAa1RcQAAWMgVZgBIUHEAAFjR3dPL3dNLSYOabap1lLPA4fn+8fn+Md1RSJtqHa2ajGoX0CAVBwCAJXIWOEzOzGe1TLQpPLxyMrPup0hMvydn5pltQqJtmMzr66tyA9AmFQcAgNky76f4/ul9ZsCclok2hYfXTybfx4cvC16a1abBZDKjqTUAjTv6R6p7w1eixW/0cJmi/KtDYJymkmknTlPJxMZpKpmoOE0lExWnqWTaidNUMrFxmkomKk5+kGsVh10PqkIyh8Phx+cPb76a/11luLZfWEoICdJmnKaSiYrTVDJRcZpKpp04TSUTG6eFZArnhgtY40CW/HWYaxx+Fic22laHh8eJjdbUyTGoyWhbHX4Wp8tBRWkkK+/4ZJzF0c6+vfUxqDejFR4eVW6IEhWtME5sGgY1GW2rw8/itDaoRk5ObLRGBtXUO16ZigNZCi9rxK6ujNLIoJycagwq/PCVNDIoJ6eaDgZ1OVvuYFCXGhlU7F0SUQqzMqhqDCpxuJMTfvhK2szqGndV9K/+yhkA6N54V4XfsPlmbRgJQLj6c8N31XoCAOiGSfJcyg0AN8hdFQAAAEA8FQcAANZlgQPAbVJxAAAAAOKpOAAAsCILHABulmdV9M+zKgBgJXdPL4fkcx+HBlFt0g+YbDOZa+WG399+Dn9IPOZtfOb8ZJuQIIUd1UwGYJn6c0NrHAAAlhgn5+MfqvU466WVtJDMODmvJtHjSskcT6wRH2BVKg4AAEuMF/kTV/uHl9LLAXLaZHaUc3jNZBL3UwwX8HMu4yfa5B+ebtlsMqoMwN65q6J/7qoAAOqzfUO5s3Po1AGF3FUBAABY4AD0QMUBAIBgFjgUujyBTh2wR++2TgAAoFHjrM9kbxblBgAG1jgAALzBmna2YoED0A0VBwCAc8oNi1ngUEi5AeiJigMAwP+h3AAAIVQcAACIYYFDIQscgM6oOAAA/K/TKd/XX38OySnf3dPL3dNLOuBkg6g2NTt6s83ccsPz/eNkMpNtnu8fc9qUd5SZTEhHI+UGYO9UHAAA/uWy3DD8903jrDsxRR9eSs/hQ9pU6+is5WLDxDs9/Z5skz/DL+woP5nyjgB6ouIAALDE90/vz/5wy9xPEeL0dDl1QAeO/i3r3vANwBsNAGluoV9MuQFgF+rPDVUc+lf4qRrWTJZfvQmJMy7gDInT5aCi4nR5cgxqvThdfoy7HFRUnL4H9ePzh+EPy351tjmoteNkVhyGuwk+PnwpSWa8JaGpOIVBouIY1NrJRMXp8mPc5aCi4rQzqPoVB3dVkKXwXs3Cw1fS5aCidHlyDCr88DZ1OahRl++4QYUfXtmscsOh010MCgfV5jkxqPDD2+Rnc73DV9JmVteoOJCl8NpI1A2uQ5zYaFsdfhanPJqTkxltq8PP4hjUZLStDj+L42czEafLQRUucDiLttXhZ3FWfafy76cYL8oVXuIbDi+/bhkV5zTaVoefxTGoyWhbHX4Wp7VB+dkMP/wsTiODqsxdFf2zjwMA5DidPPu9mckODgA7Un9u+K5aTwAALTNJnku5AYA0d1UAAAAA8VQcAACYzQIHACapOAAAMI9yAwA5VBwAAN5w9/Qy+ZTKwDaNJBOS7eFweL5/nHx+W06Dmm3aSQagGyoOAABXJWbX40s5bSa7yG9Z2FGOdMvxGaJnxgUOOTPqoU1+y7kvLWjTSDIAPVFxAAC46vun95Mv5bSplszacu6niH1WfCJaTkdNJTM6Ho/XziRAT45ut+te/WeuAgC9soNDodMT6KQBldWfG1rjAABAFuWGQmcn0DIHoHvvtk4AAGAtZ/sRVLv1oEvKDQDM5a6K/rmrAoBbM7lFotLDAioOhS5PoFMHVOauCgCAIrFPbWCg3BDOqQNugYoDANCPqAdAQixbNgC3ScUBAOjE3CKCokMmCxwKuZ8CuFkqDgBAD5aVDxQdJik3hHPqgNuh4gAAAGtxPwVwyzwdEwDYvZKlCndPL28+umKImX6qRUibMfnJNtU6Gttcmy3//vYzkcnhcHi+fzwcDh8fvqQb5LRJNIhqUzMZCxyAm2KNAwDAVYlaxvhSTptqyQRKlxvGWfqlxEsLFHbUVDIAt0bFYYnj/5XTuE5iAMACx7f8+PzhkFwOML6U0yZhaJPfsrCjHDktE1fy0xf5T9vktyzsqJFkLHAAbo2Kw2yX5YPuawohl02irr00Fefu6aW/k9PloKLiNJVMVJwu33GDWjuZ1uKst/vjUHRI+P7p/eXk/CyfN9tcxrkMchonM0h5MmODxIaRHx++TM6u32zzfP94uhBgWZDD/11NsDiZyziLg5zelHHZ5vVEIn7UEomm4jSVTFScs4/xtslExTGotZNpME41Kg7zjL99L3959Fp0GL6pFH6ZCwnSWpzYb9uNDOos2ubJNBWnqWSi4nT5Me5yUGfRNk+mqTitPWyiqUEtTmaN51OM35ILvy4Ph5d/546Kcxpt82SaitNUMlFxYj8wrQ2qs3f8NNrmybQWpyYVhxlOyw2nf9990YE35a9NBWrys0kga+ADjRf/c+4+AKrxs8mqjn6V5hsKCtfO2LV6RPqoCjZPAADWVrgoQKHq1BoLHABoQf25oadj7oxlFAAQ7nh0DQYA4rmrIkyFeyuUGwDgTSWLFIbtIf2SHVjgAEAgaxwivb6+rvp9Zdkve1+hACCH+xCVGwCIZY3DDMOv25wJvEk+AFS2bJnD5fMvu3/oNQBUo+KwROKLiOdWAMBW5hYdEu1vsO5ggQMA4dxVMc9438S1J1O82QYAqOP7p/eZz6348fnD4def9B2Rx+Px668/icLE0NdkgwptCoPMKjeMj4K/9iy9yQbhbap1lGiTEwTg1ljjMFtOpd/VAABo2XAzxfDf19fXxC/uH58/XJuNjxP4wmdzstg4yQegTSoOS7z+22SbaikBAIPhAv73T+8vr+R///T+x+cPp3s3nC5aTPzifvMmizF+YlnBmExOwiVtSoIsu58icSV/eCl9qT+kTc5qgmrJ/PX3PzJTArgdnj7dPztvA8DocnZ9+SsyfV9kZ79Sbd9Q7vQcOm9Ay+rPDa1xAABuSE59If1VzD5NnPJ5AEhQcQAAbkvmlkxzb7LYIwscAFiVigMAwNtupO7AYj4AAGkqDgDA7s2d+M26ht9r3cECh0Jz78cBuEEqDgDAXh3/bcGxcyeHnW3uoNwAQAXvtk4AAGCJ8kn+sqLDtX49HOqmWOAAkMMaBwCAGTq4ycICh0LKDQCZVBwAgP1Jz+rvnl7unl7SEXIaJNrk1x0mOypPZlabyXLD8/1jOsjz/WNUm3SDwGTqdATAGRUHAGD3Tif/+TP8wlrA3dPL119/Escej8ecjqKSKTl8NEyqC6fo+YenW062qdbRaUsLHADyqTgAADuTXuDw/dP7OmkMHX399Scx4fzx+cOPzx9ie5z70lk+b/79gjnzx4cvC16KVa2j0x7PzpVyA0DC0b+S3bORFQA9afkKc7oU0kKednAIcXoanTpgR+rPDa1xYELOTaG7i9NUMlFxmkomKk5TycTGaSqZduI0lUxUnKaSiY3TVDKNDOr19TVxn8WsTSXXODmLyw1RWxg0FackyOuJpgZ1yLs3pGYyBrVqnKaSiYrTVDKxcdpJpiYVB7IUfukJ+c4UGCckWpeDiopjUJNxuhxUFINaL04HH+PLOXN6J4W5aYQManJzh8xkyp3GKV/dUPg1dzw8Kk6IqGiNDCp/Q4r8aFsdfhany0FF8bO5XpwuP8aVqTiQpfCe2Gq31M7SyKBiT04jWXnHqzGo8MPD48RGa+TkxCrJ6vX1tc1BFT5Bs81BFW6aMB4eFSdEVLSmBhXFoMIPD48TEs3PZoU0YrWZ1TX2ceiffRwA6MbZRH0Xv91a2NzB9g0AHOzjAACQaS+z5cL1DuWUGwDYyrutEwAAmGGn8+TX19dEZeF4zF126ikJAOyINQ4AwG7seo4dvtghp70FDgBsSMUBAKCemjdZKDcAsC13VQAAezI88TH9NIfJNuNjIyfbFHZ0rc0w579WEbjc2etaR6e3Y+QkM2l46Fp6I/SQNuPT3SbbVEtmX9u/A+yCNQ4AwP6MJYNZL63U0eJk0msNLusRd08v1w657OhaOeP3t5+JTgc5D3tPtIl9VnxhR/nJ7OsR9wC7oOIAAOxP4kp+zkX+/IUAOR2VJPP6+vr1159rr57dZPFmtKFB4dKGMzlX+xNtCg9vsCMAlsndGJn9qv/M1VOXl1xivxIBQDfSOzic/io/a3n5W94ODiHynyECsAv154b+Ge3fVhWHyUWtSg8AcCmn7nDZJlGPeLMNaZ5CCnRJxYF49T9V+TfQKjoAwKXCooOKQ6HJJSQAO1V/bmgfB4LN2q8rdnMvAOhDyRM0lRsKBT6dFAAVByItqCAoOgDAm9J1h0uJSoRyAwCbUHFge4oOAHDN3LoDJdIbZAAw17utE6AfCgcAlLNj35teX18Xr/Z3GjMpNwCEs8YBAGiFW+gTli12MGcGYEMqDjTB+ggAOHN8y9ZJdcsCB4A1uKsCAGhC5nR6KFInnq88VrGrtVmjo5Diwtmc+fn+cfjDx4cv1w7JbxMSpJ1kfn/7eTgc/vr7H8PfKDcAhLDGgRgWKQBQYu4V5hZ+74w5hCezi7UM40z+xnMAIEHFAQDYn8SSgcRLZ23SLSfbjC9NtinsaJnLks1wkT9xqT+zzWnLxUFC2uTnmW45LG2wwAEg3NE/qd0brpOs/UaXX94J/6YFwF64hf5S4TIHJ3AWT0gBbkSdueEp+zgwIecG1OHVCgtcM5OpHKepZKLiNJVMVJzyqpaTUyeZqDhNJRMVp6lkouL8+Pzh7O/nfhPq8uR8/fUnJ0i6MJGzhUGO2DhNJTPEGR4+uuwreLODKo9TGCQqTpcnx6CqxWkqmag45T+bNbmrgibscYFDC7cQr6fL0RUOyjnZiy4HNepydMPUerEuz0nmoK6VG9q8Sj9+4W5z84XCk9bmoAoVDso52YvGfzYLGdTmVBzI0khFIOpO15A4UeekqUGdRds8mQYHFZWGQa0Xp8tBnUXb6vCzOFHRztY4zJ34tTmoCu9UTrkhf1OGtJA44+EhcRoZ1Fm0rQ4/i2NQk9G2OvwsTiMfYz+b6x1+FqeRQVVmH4f+1bxXZ9mFpkbKGQDUdzZt9rUk374WOADQgvr7OFjjAABsxvR4GeUGAHZBxYFIC1YrWOAAwOFweH19NVvOpNwAwF6oOBBsVgVBuQEAtQYA6JWKA/G+f3o/WUrIaQPADZrcEuju6SWnTXlHbSaTWODwfP84uYF5zg7nOUHqdFQzGQDWoOLAWoaawllZ4c2/BIDBMKkunKLnBAlpM77UQjL5s/d0y5w2kz1GdTTZJmrUAKzk3dYJ0D/1BQDCtfDL5fun90MJoFoyZ08SHQ23pVSeVLfweLaPD1+UEgBa5umY/av/BBQAIJwNIwEo5OmYAAAAQA/cVQEA0DoLHAqdnkAnDaAaaxwAAJqm3ADATqk4AADQs7OSzbUKDgDhVBwAANplgUOhyxPo1AFUo+IAANAo5QYAds3OkQDAusZps3kylVngALAtaxwAgBWdTvncPz+LBQ7hnDqAylQcAIC1nM2Zv/76c/f0kmh/9/SSbhDbplpH5aPO8Xz/+Hz/WNgmJEh+m1U7UuEC2JyKAwBQw9dffzJb5ky/E23yD4/qqDCZN1vOXeAwOTPPbBMSLf/w9TpyPwVAC1QcAIBVnE35fnz+kHng90/vS9rkHJ4vp6PwZBbcT/Hx4ctk2Jw2IdHyOypMJr8j5QaATRz9+9u94VuLNxpoQc713tjpIltxhbmEHRzKnZ1Dpw7gsMXc0BoHpoXcXBp1k2pIkKg4BrV2MlFxuhxUVJxqJye/o6FlSWJdvuMGtXYy7cSJLTfk30lRIU7OvgxrJFNyK0pOMpsMatU4XQ4qKk6XJ8eg1k4mKk7UoGpScWBC/p2uk0EaSSYqTpeDOou2eTIGtXacah/jktpBhUMScRp5p86ibZ7MZJxZCxz2Mqg6cdYoN5R/PQ2JMx4eEic/SLrc0Mhcoql36iza5sk0FSf23LY2qM7e8dNomyfT1KAqU3GAhfpe+N336BjVeaPL55OzIvT96d3p6Cxo53Cy50LsLg/XvP5bhb4OtQbF5rp8oyv/bFbW5aD2xT4O/bOPA7ChqGv7O51p3yY7OCxm+wYAVmUfBwB4Q1TlgvrMljMpNwDQHxUHANYSWyZQdAAA2BcVBwBgLa7PZ7LAAYAuvds6AQCgKybJAMBAxQEAqGG8LyaxD2h+m/RmopNtqiWTEyRngcPwLLT0puuTbcYHqoW02VEyAGzFXRUAwP4k9vWotuXH2FFJj7Pup0g8g73+49lbSGZfD6UHuEEqDgBADcNF/vTahJw2py3nvrRSR4XJ5Etcyc+5yD+0SbfMaVMtmZCOANjQ0c2W3av/zFWAQfil5tjJG2zOhpEA1FR/bmiNAwDABpQbAOienSMBANif05KNMg1Am6xxAGAtboKAayxwKHTtBALQFBUHAPZB/YJuKDcAcCNUHABYkTIBEM4CB4C9UHEAYF0hRQeVC7phgUM4pw6gWZ6O2T9PxwQasfhhmcoNDRqnzX6/zKXiUOjyBDp1AJk8HROAbn3/9H5u7WDBIVTw5pw5p6JUrU3NjmYlc63c8Pvbz8lknu8fCxvUbLNSR8oNAPtijUP/rHEA2nc5Z1NoaNbZlG/4/TK+g4k3rlqb+h1lJjNZbvj48OVaMuPE+1qbyQY126zXkYoDQIn6c8N31XoCgGvUF/bCjn2nvn96PxQUfIDrUG4A2B1rHPpnjQMAUUz5FrN9QyGfPYBy9nEAABplyreYcgMAt8ldFUyIWi/aVJymkomK01QyUXGaSqa1OE0lExWnqWSi4jSVTFScr7/+tJNMa3Gikhm2MEjscVAzTgvJvL6+joWbnI02V02m2ThNJdNanKaSiYrTVDJRcZpKJipOU8lUZo0DWRY/0y7k8PA4IdG6HFRUHIOqECckmkFViBMbbcOTc3mVvoNBrRHnMtqCBQ45D3HIERUnJNp4eGGckHLDqJFT3dQ7FRWnkTRio/U9qEZOTmw0g9qcigNZCq/VRG2pFbs1l0GtF8egqmlkUE29410OKirO4sPfnDPvfVCrKswq6vpV7HWwwmjj4YvjvL6+vr6+NjWoqDgGVU0jg2rqHS//2Qw5fKVoBrU5O0f2z86RABSyg8NidnAAoB12jgQAWme2nEm5AYAbp+IAAMxgtgwAZFJxAACIZ4EDAKg4AAATvv768/XXn2Hfvmtt7p5eJh/3kPM8iJwgUW3W62huuWFy4/Hn+8eoNukGrSUDwK6pOAAAWRLT7/xSQrplTptqyeR3VPhkzWHiXVgLyD883bKpZADYOxUHACBL4omP9R9RWS2ZnI7O2qx3P0XiiWj1H5bWVDIAtMnTMfvn6ZgAUI3tGwBolqdjAgAAAD1QcQAAiGGBAwCcerd1AgAAcDiclGzUaAD6YI0DAEAACxwKnZ7AaycTgH1RcQAAKKXcAACXVBwAANiYRQ0AXVJxAAAoYoFDocsT6NQB9EHFAQA4HA6H4/HoOvMCyg0AcI1nVQAA/zttPh6Pl1Plu6eXw+Hw/dP7RITJNkODnDaFHdVPJu35/vFwOHx8+JJukNMm0SC2o5rJ/PX3P85eUqwB6IY1DgBw6zKXNiRm1zkT73w50VpI5u7p5cfnD2++NM6Zx3l1iES02I5yrJSMcgNAT1QcAOCm5d9Jkbjan14IkN8mJFr+4YUdTZYbDlMLAU7b5Lec+9KsNiHR8g+/XOAAQE/eWDlJZ4avkt5oAN50VnHw+yKfHRwK2TASoLL6c0NrHADgdtkqcjHlhnDW1giDAAAgAElEQVROHUB/7BzJhJy9tfLjhARpLU5TyUTFaSqZqDhNJdNanKaSiYrTVDJRcWKTWXyFuamT01Qyh7ydF/PjhARpLU5TyUTFaSqZRuI0lUx4nKaSiYrTVDJRcZpKpp04NVnjQA2xm3g1ostBjbocXZeDKtTlOelyUKO+R7cjay9wqL8NZAXjoN4c3d4XOHT5lnGpyzc6/bO5d10Oal9UHJiQv7fWZJBGkomK0+WgzqJtnkyDg4pKo5GTY1BrJxMY5zRaSDIlt9A3OKioNHKipcsN+dtAJkRdvApJJirOePj4h9cTlZMJjHMabfNkGhxUVBqNnJy+B+VjvF4yTQ2qMjtH9s/OkQCcsWNfCTs4ALBTdo4EAGiXcgMA5FNxAIBbZ7acSbkBAGZRcQCAm3M6QzZbBgBW4umYAHCLxkJDzlMhJ9uEBGk8mWsLHH5/+3ktwiHvSWYhbap1FJUMALfAGgcAgAnpcoOnrwHAmzyron+eVdGC8ULZmaiHugGUuHt6mfznaLLN8A/dZJsddXTaJl1xSF/Jf75/nLzUH9JmKHxUSCaqIwAqqz83VHHon4rDtq7VGk6pOwC0zIaRAPRBxYF4Kg4byik3jNQdANqk4gBAH+rPDe3jAGuZVW5Y0B6ACpQbAGAxFQdYhfIBQAeUG0Icj8drZxKAvqk4QEPUKQDoiVoDwI1TcYB4CgcAHbDAoZBaAwAqDtAW1QqAFig3AEA5FQcAAIJZ4ADAQcUBAPqWs3Jqss3d00tUm10kk7/A4fn+8fn+Md3RZIOcNpkdNZLM8Xj8/e3n728/x7+xNgTgNqk4AECHhh37hkl1eu6d0+a05dyXZnXUQjKzyg1nf7g0vJSen+e0yewo5/AKyZzWGgC4ZSoOAECp75/ed9/jpY8PX87+UK3HWS+t5FqPlyUbCxwAbtbR74DuDb/4vdE1Fe7+2MLXaGDXTPkWs2FkubNz6NQBtKP+3NAaBwDoinIDG7JhJACnVByYkLP5VuU45UGi4kQN6lTJAoemBtXlO9XUyelyUFFxDGrtZKLitPYxDlngkLN9Y+U45UEWxzk7dX0M6jKIQVWIUx4kKo5BrZ1MVByDaoSKA1kKv8nFfsEtjxYSJ3H4JrdFRJ2c02ibJ9PgoKLSMKj14nQ5qLNoCekFDjsd1KqHj2Lvpyj8Rhj7Bbc82rI4l+WGsz/UTGa9OKfRNk+mwUFFpdHIyel7UD7G6yXT1KAqU3Gghi43JlhjUO2cqHYyCdTloAp1eU66HNQoPbqd3k/R91u2TP1tICuov9FmTQZ1I7o8J342d2dfg7JzZP/sHLmVBZfdfO0GSuy04tACG0YCcAvsHAn9mFs+UG4ASig3LKbcAAArscahf9Y4bCtnpYNaA1DOIwkXU3EA4EbUnxuqOPRPxaEF1+oOag1AFBWHZZQbALgdKg7EU3EAuAWnM+fL51Mk6puTDWq2qdzRj88f3nx1OIHDZuDpDbpC2lTrqGYyADTIPg4AwHKvr6+X5YYcOS0TbQoPr59MvsRDyHIeKZf/DLOcloUdVUsGAAYqDgDQg7NawyD/1q2clok2hYdvkkx6gcMocSU/55Fy+QsBcloWdlQtGQAYuKuif+6qAIBLdnAA4Na4qwIAYHXKDQBQgYoDAHBblBsAoA4VBwAAACCeigMAcEMscACAat5tnQAAQCXKDeVOz6HzBkCaNQ4AAGS5VrIBgDepOAAAN8ECh0LKDQDMpeIAAPRPuQEA6rOPAwDs1d3Ty+Fw+P7pfbpBzTZ76SjH8/3j8IePD1/SbSYb1GyzUkeXJRvFGgAmWeMAAPtwPHE4mVePf9hQ/Rxm9XhtgcPvbz9Lchgn5+MfNlQ5B+UGAHKoOADADlzOmccL+Ikr+cNL6Uv9OW0yO8o5vJFkBolL/eOriTbjS5NtCju67HHWS+XJ2MEBgGWOStTdG74leKMBdu1syudf9Xx2cCjkfgqAbtSfG1rjAACtc4V5MeUGANiQnSOZMLlB1x7jNJVMVJymkomKE7X9m0HtJU5TyUTFKQ8yzJm//vpzOBx+fP5wKJst+xhfk7OrYn6cwiDtxBk+fsOGF3/9/Y9D2cevkUE1mExUnC4/xl0OKipOU8lExWkqmag4rX2Ma7LGgSyFW4JF7SgWuzOZQa0Xp4V97C4ZVPjh4XFConU5qNFQd9g8jVjrveMbLnAo3McxahvI2O0kf3/7WV5uODRzcmKjNTWoKAYVfnh4nJBofjYrpBGrzayuUXEgS+GFo/LrV7FxQqJ1OaioOAY1GafLQUUxqFNnc+Yfnz+UTPkaGVRsnGuHzy03xF4yKowWlUx5nNPTNaxxKE+mkZMTG82gmk0jNlrfg2rk5MRGM6jN2Tmyf3aOBNgvG0YuZgeHKMejr4sAnbBzJADwLzaMXEy5IZCTBsBiKg4A0CKPJAQA9k7FAQD26u7pZXLbxZx9GUPaVEtmsqPMBQ45O29Ntnm+f8xpU95Ra8kAQA4VBwBo0dn0+HKBwzjrTky/h5fS8/OQNvmlhPJk0j3OKjekp9aTbXI2eA/paFYya3cEAPlUHACgaa+vr2/eTzE+oyH2CRTki9rgHQB6ZfPh/nlWBQA3woaRAJDgWRUAAEsoNwBAa1QcAAAAgHgqDgDA7lngAAANUnEAAPZNuQEA2qTiAAAAAMR7t3UCAADLWeBQ6PQEOmkAxLLGAQAAAIin4gAA7JUFDoXOTuC18wkAy6g4AECL7p5e7p5eqrVpJJlZQRLlhuf7x+f7x3ScnAY127SQjEoNALFUHIBdGqYcb/5v69QgUuIjPb6U02ayi/yWhR3lKIw2Oese2+S3TL+U06ZaMvmHW9EAwNpUHICdCblGCo04/tu1Bt8/vZ98KadNiBY6Gv34/OHNv399ff348CUwmUS08aWcNtWSyXT5qbPAAYBwR79dujd8pfBG04dZpYTYKRCEO5vy+Yc6n+0byqk4ANyg+nNDaxyA3Zi7csFKB4A3KTcAUIeKA7APy8oHig40yy30i1ngUEi5AYBq3m2dAK0bJ2wlC9RDgjQbp6lkouI0lUwjcZpKJipOU8mEx2kqmbM4C6Z87Q+qTpxr5Ybf336WZHI42VWxcOeFkDhNJRMep6lkouI0lUwjcZpKJipOU8mEx2kqmUbiNJVMYJyatlzj8F//8Z+n/5tsVjM3mNT3xfPWRleST2tjYW17fMfzrzDvcXQ0rtoCh5xHe+xXl4PiRvT9s8nmtqk4vFlBuFZW+O9//s/wP3WHTQzXnQqvYkVt4BeSTFScLgd1Fm3zZAxq7ThdfozbH1TJ/RQ3/jFOLHAov9ozRGgkTtTFq8lkMssNsYMKidPIO3UWbfNkmorTVDJRcar9bNaM42ezQjKtxalpg2dVjFWD//7n/+T8/VmDa69yjWdV0IHC67oeWkE73EJfwg4OIcbT6LwB3Jr6c8Nt9nF4s2ow/OW4kEFlAQAYKTdEccYAqKb2XRX/9R//mS4lDDdQHE6WPABAHyxwWEy5AQD2qNFnVYy7NljpAEB/vv76M9km5+EUIW1yHhhRuaPJviZN7rues913zubtIW1qJgMANW35rIo0Kx0AILGJyfhSTptqyaxh7gKH2O3WE9FyNnivnwwAtKPdisNB0QGAvowz5B+fPxzyLuMn2owv5bSZ7CIqmcKO8h/tkbifIucif/5234k2ORu8108GANqxzbMqZt0rMW4kaUfJZTyrgj6UXEH1rArYLzs4AECU+nPDjdc4jE+mSLDSASih3AD7pdwAALu2QcVh3BVy/JucooOlDXDjFA7g1ig3AMDebbPGYaggzF22oOgAzKVOAQAAW1m4j4PnVu6IfRzoyazdHJQbYL8scACAcPXnhu+q9QRQbigiTNYd1BoAAGBzKg7A/iTqDmoN0AELHAqdnkAnDYANqTgAe6W4AF1SbgCAbizfOdLjKgFgsZxNSSbb3D295LSplkxIRzme7x8LG0S1eb5/bCqZw/WSDQDUt82zKgDglg0T7/T0e7LN+NJkm8KO8pMp7yhngcMwr05MvycbRLUZX2onmZzKBQBUU1RxWG+ZgwUUAHBr3E8BAJ0pXeOgNAAAp47/lmgz7EKS3otkss340mSbwo7ykynvKMfHhy/jf5c1iGozvtROMn/9/Y/Tv1SsAWBbx2W/ioZCw3//83/GP8Sm9V//8Z/hMW9W/WeuAtwszwhYzAKHQpcn0KkD4Ez9ueHyNQ5DRWD4r5UOAGDHvsWUGwCgSwE7R/73P/9nXOxQ7r/+4z/VL5qSsxF65ThNJdPOoKLidHlyDKpOnKaSaWdQUXG6PDlRyeQ8MCIzTlPJ5MdJLHCI2kuytZNTHiQqzibveDpOU8kYVCJOeZCoOAZVJ047ydS0sOJwectDedFBraFlhd8IY7+1NzIHaG1QTk5mtK0OP4tjUJPRtjr8LE5+tGtX6Z2cSYULHGK/4Dbydbnw8LNyQ/mgQuLkPNqjWjKBcU6jbXX4WRyDmoy21eFncRr5GPvZXO/wsziNDKqyyKdjDkWHuVWD4RC1hsYVbvRVvk9Yg7oc1KjL0XX5Me5yUIU2GVS1W+i7fMsKpTdc3EphVrMO38vtPDkbbe6XQYUfvpIuB1XIz+bu7GtQC3eOTMjfSzJdZbBzZBQ7RwKszaZ9i9nBIYQtSwHIUX9uGF9xOEwVHTKXM6g4RFFxAFiVcsNiyg1RxjPp1AGQ0EnF4XCl6JC/qMHTMQOpOACsR7mhhIoDANS0p6djpp09NTO9U8PwtIuVMgGAynIewZDToGab+h1dKzf8/vYzHSRnp+7MNtU6qpMMALRmrYrD4aTocK3WMBQa1BoA6Mbr62vOExzyn/WQaDO+lNOmWjKZHaXLDTlT60Sb/MOjOmohGQBo0MKKw+ReDIWLGtosQxwLbJ07AKsb1ihWe5zE2FH9Hme9tJLETt2xm3jndFRt2/B97U8OAAv3cbi2z0L3j59YXDsIuVWmpHLhnliANXhGwAK2bwCATdTfx+FdVKDJWkPmIyoaN7w3doQGYOAXwVzKDQBwO5avcTjk1RHOnkBx6Gulwy6+HnlWBQDtUHEAgK3s5umYswoNlwd2U3TYxdejHaUKQN+UGwBgQz08HTO9K+TZUzMBAACALoWtcZi1bKGblQ67YI0DAC2wwAEAtrXLNQ6Tj7p885CDlQ4AcDOUGwDgBhVVHBbUGk6PPSg6AADkOR6PJc/JBoD6llccyu+JUHQAgFtggUOh01qDogMAO/Ju2+7HosNZ/eLybwCgBXdPL4fD4fun9yVthgY5bQo7aiGZWeWG5/vHw+Hw8eFLoqOQNkODnDaNJAMAexT/rIoF/vuf//Nf//GfFjsAsBfjLH3WSyt11FQyIcYZ+LI2OYeHJDO+tGoyFjUAsF8LKw7hCxBO77BQegCgcYmr/emFAKdt8lumX2oqmTPL7qfIudSfaJN/eFRHhckkWl6eQLeiALAjC5+OuZLTWoO7KqJ4OiZAOf+WLmD7hnIqDgAE2uXTMQOpMgDQGg8IYCvKDQDsXVsVh4OiAwAtUWtYzAKHcE4dALvT1l0Vg+HeCqWHKIUrZ3L2J68WJ2dD9WrJtBanqWSi4nT5jhvU2smEx/nx+cP4Nwv+LW1zUBXe8ZyKQ86DHnKExIl6YETsoP76+x/j3yz4+LU5qEbidHlyDGrtZKLidDmoqDhdnpz/z97dHceNa4Gi7j7lGDyv91bdCDxx2O+eEKwErAg8CdghWO9WHFYeVhK6D9ybu09LDYLEIgiC31e7dmnc4OIC+xeLINhOp45+VcVAraFBhYuQx65hHqWRTlVbSb5mHM94NToVvnl4nNhojRycSQvuiLlY7J0pooR3qoVTRFGd8oyHb74SnQrffCXemwk6tbkWKw40qPBsWPlJudg4IdG67FRUnNg0dGoy2labh8cJiRaVzOXUhkHJkK+RQ13nZTz3eorCEz7l568u48RGW+xyasOGacRGy7m1R4U0VorWSKeaehnrVIU4IdG8N6ul0UinKmvxqorT6fT//T//r5kOUayvDjCXFftKWMGh3NUxdOgACOGqCgBgx5Qbwjl0AOxXo3McCGSOA8AsJjgsptwAAC2rPzZ8V21PALBHV9/Kk/d6yLmPQ2ybppJJyFmpO79NSJAdJQMAe+SqCgD4n1tn6a+0cJuPMYdGknm91uZgpRMpLazUHbXAOwD0SsUBAG66NVpOnOrPuR1JSJvxoaaSSchZqTt/Ne9Em6gdTbbJWeA9ttcAsC/WceifdRwAZrmc5uDDM5MVHACgfdZxAICNGSTPpdwAALzJVRUAAABAPBUHAGA5ExwAgFtUHACAhZQbAIAEFQcAAAAgnooDALCECQ4AQJqKAwAwm3JDiPP5fOtIAkAHVBwA4H/uHp8nG0S1qZZMnR3leLp/KG/zdP8Q1aZaMq//Ua0BgCNQcQCA/xgG1YVD9PzN0y0n24wPTbYp3NHrPd4aKv/++jOx+TDwTo/Pc9pctpz7UGwy40OTba4aqDUAcBAqDgAw2/eP77dO4X85tJBMfR++fd46hf/lUJiMAgQAvTq73rJ7w+8YTzQAIazgUOj1AXToAKij/tjQHAcADsqJ5QWUG8I5dAB07N3WCQBAVQoNbMjLD4BDMceBaSHrk4cEaS1OU8m0FqepZKLiNJVMVJymkomKkx8kPfxrqlNRcUqCrDHBIWeVxzpBKsSZdT3FXjpVP0ivcZpKJipOU8lExWkqmag4TSXTWpymkgmMU42KAxPy1zBfO0hrcZpKprU4TSUTFaepZKLiNJVMVJx0kPwzzE11KipOSZD1yg2FP55CgrQWp6lkouI0lUxrcZpKJipOU8lExWkqmag4TSXTWpymkgmMU5OKAwDH5RJ6qrFg5Ghfv5XhOLw3WcULvSt/or/8+lOeRkiQ1uJ8+fXHwVk1SGtxmkomKk5TyUTFufXenPsl2FSnouIsC7Ler4jfX382EmTtOHMP3S46tSDIcZ7xTYK0FqepZKLiNJVMVBzvzbWDtBOnfhHA3TH75+6YACdnmAu4P0WIq8Po6AFQn7tjAkANxntsyMsPgINwd0wA+jdU9L/8+nM6nX58+utWs2FJxe8f3ydCVWvTyI7yJzgMFwB/+PY5kcxkm5AgbSajygDAAZnjAEDnLssNg/TYL+dWDok2hZsv2FFhMnNbvilnvbH8NckKo1VLZnyoMBkA6JWKAwCHkJjacCU9ZWCyTeHmC3ZUmEyiZf4Eh/RJ/vw2IdHyd1SYzPhQtWQAYF+sHNk/K0cCB2fFvmUsGAkAnbFyJACsyGgZAKAaK0cCcAhqDbOY4AAAlFNxAKBzBslzKTcAACFcVQEAAADEU3EAAP7HBAcAIIqKAwDwH8oNAEAgFQcAAAAgnooDAHA6meAAAERzrwoADuHu8Xn44/vH9+VtEg1y2lRLZtaOEp7uH06n04dvn0vaDA2i2jSYzGXJRpkGAE7mOADAAolRes4APjaHkD3++PTXm/9+OXIeR+CvJR5aSQvJjDt6un+4NUMEAI5MxQGAQxhO8qfnJuS0uWw596HYZMaHJttM7iin3HBKnupPzzi4bJNumdOmnWTGh3L2CAAHdDbrr3vDWRdPNAC3WMGh0OsD6NAB0KD6Y0PrOADAoSk3FFJuYCuXFxCZaAO0yRyH/pnjAHTPin2LKTeUU3GgsvRKJUoPQEL9saF1HJhw9/gcsiZZYJymkmktTlPJ6FQiTlPJ6FSFOE0lExInZHXGp/uH1uLM3eR1ueH3159779SqybQWp6lkJuNEtQlJpnKcppLRqQpxmkqmv07VpOJAlsKfp1Ertw9xYqNttflKcRrJSqcm4+jUZLR8V0O+Ro7tVZxGsrrafPEEh+HnTtSPnsI4sWnMipaY3bDfTk1GK9/cwVm2+axdtDBAOuwzlR+ntU45OOGbX8VppFOVqTiQJWfp9fU2X0mXnYrS5cHRqfDNVzIrq9dDvjY7FSXwGW/neorCSeBtziHXqcTmbfau0NrP+IIBRvmYxMs4fPOVeG8meMY3Zx2H/lnHAeiYS+gXa6fisFNee9S0uHywr5EJsDbrOABALkO+xZQbwjl0rGdfM6gBLqk4ALBLV2PmL7/+TA75chZBmGyTs/JiyI5qJpMjak27He0o3UaJAQAmqTgAsHtffv05TQ2tc1ZwzF/lMdEmakeTbcaH5iazYILD5JJX+aP3dMv8tbUmkynfUWYyLy8vqg80y/wIYFsqDgDsz60x86GMy0AWrrU5+P31Z0BOB6PWAABpVo7sn5Ujgf5cDZt9xOWzggPsy+a3nAB6YuVIAGAtyg0AQE0qDgDsm9FyJuUGAKAyFQcA9spV9ED3XBMB7Nq7rRMAgNkUGuYywQGOScEC2JY5DgDQOeUGAGATKg4AANAu8xSA/VJxAICemeAAh6VUAWxOxQEAAJq2oHag3AC0QMUBgB7cPT7fPT4XtgkJkt+mwo4yJzg83T+kd/R0/1CnTbUdnYJ6DdXMqiAoNwCNUHEAYPcmR+aZbUKi5W8etaNbbWaVG3KG1ok2hZvHRsvfPLPlrSMJlX349nmylJDTBqAaFQcAdu/7x/ft7DE2mZwdVet+YhhTf4RTLZm///3ndLt8A/UNNYXXr3O1BqBBZwtHdW/4keSJBjgUC0YWen0AHToA9q7+2NAcBwDojXIDANACFQcAgP+LCQ4AEOLd1gkAwBsuh3wGe7OY4FBIuQEAoqg4MGFYAr18WbKQOON67CFxuuxUVJwuD45OrRcn/GX849Nf5XFa61SdZ3yy3DDcnaFwebnxFg8hccrXuovtVAvJRMWJfaai4jSVTFScLp9xnVovTpcv4y47FRWntU7V5KoKsuTfVW6NzVfSZaeidHlwdCp88zZ12alRYe+iBtWxCrNau1PLJjg03qlNjJ3qu3ebbL4SnQrfvE3em+ttvpI2s7pFxYEshafmou7cNsSJjbbV5ivFaSQrnZqMo1MJhRMcGjm2V3HqZDU5wSHqrMgQJzbaVptfxRnuhTlafD1FU51q7ZlycMI3v4qjU5PRttr8Kk5rnXJwwje/itNIpypzd8z+uTsmsCMuoS9hBYdCXn4A9M3dMQGAJZQbwjl0AFDIypEAtOLWGeacRRMn2+Ss4JjfploymTtKlBsmV5nKWc4qZ6mqwB01kgwAUMgcBwCaMDmhPbFoYv3VIqslk7OjRJvYxaUS0eqvYrVqMi8vLyY4AEA5FQcA9iFxtj9nXcacFRzzV3mskEz+jm6ttfny8pJzAj9/OatEm6gdbZvMy39Nbg4A5LByZP+sHAm0z4p9i1m+AQDIZOVIADBaBgDogYoDAOyVCQ4AQMtUHADY3uUI2WgZAKAP7o4JQBMUGuYywQEAaJw5DgCwP8oNAED7VBwAAACAeCoOALAzJjgAALug4gAAe6LcAADshZUjAdjS3ePz8Mf3j+8XtwkJssdkJj3dPwx/fPj2edU21XYUlQyHMr4kXvMiAViVigMA7IYJDoUuD6CDdgSJWsNlA3UHgJW4qgKALQ0n8NOn8SfbhARpP5kF5YZhHJUeTYW0qbajqGQ4gslyw4KWAMxyVuDv3vAL1RMNsHcmOBS6OoCOW98WFBFUqYDu1R8bmuMAADug3FDo1gGEkZkOAOFUHAAA6Mri2oGiA0AsFQemjeulbx6ktTh3j8/9HZwuOxUVp6lkouLUTOb8X2vn09/LOHCCQ9SAqqk4k0FeH8A3D92+OrXHOE/3D00dnBCtdaqpOE0lExWnqWSi4ngZrx2kwTjVqDgwYfihXPhzOSRIa3FihyKNdOoq2ubJNBWnqWSi4tRMJmdOu/fmm8LLDeU/VpqKsyBIotyw3061H2fcfO2Ds8nPcc9448lExWkqmag41d6be4zTVDKBcWpScQBgdVdjZlfUU5PXWyPGdRkt0AhN8d5kVe5V0T/3qgA2lzmnndcsGFnIa++ACs/+GXQBHXOvCgB6Y8i3mHIDALBrKg4AVPV6tDy5xkHOSpCZbSbTayeZnGxz1vrKbNPIjtZORrEGAGpScQBgRZOX0OcvrJhok795umVTyfz49Neb/z6OmXPW+sof4RfWAqJ2tGoyyg0AUJmKAwBrib2e4vvH9wseWsnayeRcT1F/ra/Ejupf+t5UMgDAm6wc2T8rRwJbuRo2+yDKZwUHKFGyeKSKFdAxK0cC0Am3JFxMuQG2otwAEEvFAYAajJaBahQOABqh4gAADTHBAUIsKDqoUwCEU3EAYHVGy5mUGyDQrAqCcgPAGqwc2T8rRwLshYoDhJtcRVKtATiO+mNDFYf+qTgA7IJyA6znzbqDWgNwNCoOxFNxAGifcgMAsDZ3xwQAAAB68G7rBADo2d3j8+l0+v7xfbpBTptEg6g2lXc0trk1weH315+JvZz+O1E8PTN8ss0423yyTeGO8pMp3xEA0AJzHABYyziuXjtazo7ykymMNrfX6XJDYtG78aGcNiEKd5SfTGw0AGArKg4ArCU9EWBuy0Sbws1bTiZxJn98KKdNyY5mJVO4i2XRzv+VGR8AqMPKkf2zciQc3K1T7vmDXtZjwchyl8fQcQOABPeqIJ6KAxxWzvR+dYdtqTgUujqAjhsAJLhXBQAxMlcTiF1qgVmUGwq5jAIAGqfiANChWXUERYdNKDeEc+gAoDUqDky4e3wOGY0ExmkqmXbiNJVMbJymktlFpxbEL0lpWLGvtSPcTpyoZJ7uH0LuzhAYZ9tkLks2v7/+nLyTaGY+IUFai9NUMu3EaSqZ2DhNJaNTq8ZpKpmoOE0lExunnWRqUnEgS+HP5agzqEOc2GhbbR4eJzZaUwdHpyajpf9lPePdAb78+hO466aeqShX0RZPcCj8nRH1M2WIExttlqtyQ2AaG3YqcPOrOK11qpGDExutkU61+YyHpNFlp6J4b64Xp8uXcWUqDmQpXFuuzaXpGulU7MFpJCvPeDWBWc0dYK93CX0jz9R6z6XqT8AAACAASURBVHjJ9RT5N5hcY/OVFGb197//RGUSyDOV2NzBCd98JToVvvlKvDcTdGpz7lXRP/eqgOMoPC0/a4ztHgGLWcGh0OsD6NABQA73qgBgB9wjYDHlhkLKDQCwI++2TgCAnRmHfMPyDT8+/XVryDfOuUjMnoht0/iOZpUbxqs0E5MnhzaTDWq2qbCjYeGGNi+mAAAumeMAwBJDueHyjw3Vv8FnC7cUjVrrK0T9HIa6gwkOANAyFQcAZhjP0v/49NfwR+Js//BQenmInDaZO8rZfMNk5l5PMZzkT5zqz1nrazJIZpvMHeVsXpjMeLj+/vcf5QYAaJyVI/tn5Ug4jrVXjnQJfQkrOAAA27JyJAB0SLkBADggFQeAfsy6veVcJjgsptwAAByTigMAWa6Gx0bLAACkqTgAdGXxNIdV50ccmQkOAMBhvds6AQC2l1luMEieS7kBADgycxwAejN3toLZDQAArMHdMfvn7phwWDk3y1RuWI8JDgBAU9wdE4Aw6WrC94/vC8sNd4/Pk0WNnKpHTpCoNtWSmSw3PN0/TCYz2ebp/iGnTfmOWksGANgFcxz6Z44DsIbLUfetysXYJlHaCGlTbUf5yfz49Nebjw6fxuOg+sO3z7d2NNnmcmQ+2aZkR7OSWXtHAMBi5jgAsA/jeLuF6zLq55DeY7rcEGUck7cwOG8hBwCgNeY49M8cB4DKrOBQzpcXAISr//Xq7pgAEEm5odCtAwgA7I6rKgAgjHJDLNUHANg1FQcAoBVKDADQExUHAIhhgkOh1wfQoQOAXbNyZP8KVwcZbvNWvg58SJycG9fVj9NUMlFxmkomKk6XL+MuOxUVp3Iyt8oNv7/+HP4ovJvDcNvIkCCtxRmDLK44NHhwym/e0WCnouI0lUxUnKaSiYrjZZyI01QyUXGaSiYqTlPJRMUpCeLumDRq/OW9yeZt6rJToy571+XLOLxT5wslkTfU5jMVZfzJ0pOhU4XlhtYUZtVmpwqNneq7dz3xMn6t70713bue7KtTKg5kKTxVWH4a9jJObLStNr+KUx7NwcmMttXmV3Ha7NTiKkNTL+NNnqnE9RTDiYjyU4WDwjixaQRGK7meotlObbj5VZzyaCFxxs1D4jTSqatoW21+FUenJqNttflVnEZext6b621+FaeRTlXmqor+uaU5kMMl9ItZvqGclx8AVOCqCgCa8OXXn8nLE+4en8vbhARpLZkcT/cP6VmRkw2i2lTb0a02yg0A0CsVBwBunqVPDK3Hh3LaTMppWbijlZKZXDDyTflXYCZa5lx5G7KjWckU7uKk3AAAHVFxADi6xBnmxCoG40M5bUIU7ig/mdhohRLXauZceRt7qWfhjvZ13SkAUM46Dv2zjgOQZk77YlZwCHF5GB06AFhP/bHhu2p7AqBByg2LKTdEccQAoFeuqgA4LuUGAADWo+IAALOZ4AAAMEnFAYD/MFrOpNwAAJBDxQGA08loGQCAaCoOAMc1VBleXl6UG/KZ4AAAkEnFAeDQjJMBAFiJigMA5DLBAQAg37utEwCgtrvH5+GP7x/fl7cJCVK4ozrJ5Jcbnu4fTqfTh2+fb+1oaBDVpoUdRSUDAPTEHAcAlhgH5+Mf1fY466H6xnF1tR3V3+OshwCAw1JxADic4QR+esrAZcv0QzltqiVTuKNEm/wJDjkn8Ic2+S3TD+W0qZZMyI4AgD6cXXraveFXsicaYDHLNwAAHag/NrSOAwCwrsuSjTINAByHqyoAIMUEh0K3DiAA0D0VBwC4SbkBAGAxFQemhSwCf/f4HBWnPEhUHJ1aO5nW4jSVTFScLp/x1joVch+Hp/uHqDjlQfLjTE5w2GOn6sTZ6TM+GUSnVk2mtThNJRMVp8tnXKfWTqbBONWoODBh+MFd+LM7dihSHk2nMqNtnkxTcZpKJipOly/jwE79+PTXmw/NmuAw/DJo5HdGVDKZcV6XG64OXUg+lTtVJ07sC6a1TnX2jF9G2zyZpuI0lUxUHO/NtZMJjHMZbfNkWotTk4oDLJRzN7796rt3h3K+sHUulfT96nVrSfYr536u+9VlpziIvt+bbM7dMfvn7phwZO4RsJgVHApNTnAAACqrPzY0xwGgW1dDvsv/zLn0YLJNznIJITvKTCZwR+lyw+RsxpzpjiFtci5SrZlM4lHlBgA4IBUHgD4lzjDnLJcw2WZ8aLJN4Y7yk6mwo1PGJZQ511iGtMm58rZyMmOD41zFAwAkqDgAsETHyyWELBhZU2tX3rqeAgAYWMehf9ZxgAMy5FvM8g0hrg6jowcALbCOAwDxjPfYkJcfABzWu60TACCYS+gXM8EhluMGAAen4gDQFddTLKbcEMhBAwBOrqoA6JuBHwAAWzHHAQBMcIDlXt82tbX7pwCwFfeq6J97VcChXI6cvfHzqTjAXK8LDa8pPQA0xb0qAIhhqJxPuQHmyik35DcDoFcqDgBdefmvrRPZDeUGmGtWHUHRAeDIVBwAenP3+Hz3+DzZJiRIVJt2kpn0dP8wOYLKbFNtR3WS4SAWvBK8eAAOS8UBoCs5I+qhTX7L9EM5baolM3fzxRMcEiOonMHV0Ca/ZfqhFpKBNC8egGNScQDoyveP7+tEGx/KaVMtmVlulRt+f/05uW1iPbzYpfJydtRCMhyEwgEAs7hXRf/cqwLgTVZwgLlKKg4qVgCbc68KAKhBuQEqMz8C4IDebZ0AANSm3FDu8hg6bgehZADAXOY4AADz3CrZAABcUnEA4FhMcAAAqMPKkf0rXB1kuJ9c+YLzTcVpKpmoOE0lExWnqWRai9NUMlFx6iSTX3EY5pAXLncXEqSpOOfzebidx9///jP8y+KvmHY6FRinqWSi4sReT9FUpxpJJipOU8m0FqepZKLiNJVMVJymkomK004yVo6kUTn3ul9v8/A4IdG67FRUHJ2qECck2gE7NbfcECUqWmGc8jQuD+BQdyj/1bJ5p2LjhERrs1NRGjk4sdF0qtk0YqP13alGDk5sNJ3anIoDWQpPOZafsYyNExKty05FxYntVJRuOnU+n8dRXyOdauplnNh81vUUsXfyi4pWGCf89oQhJ0la61SIRjrV1Mt43LyRgxMbralOJTzdP+SPVfbSqVka6VRTL2PvzQppxGozq1tcVdG/+jNngPVcjZm9tWexgkOh1wfQoTuakhNr+/qJ3Jn0E+epgeOoPzZUceifigP0JKfiMLkawnjdwWSb9HSDkDbVkskpN4w/yhO/v3MuoZxsU21HscmMCzcMfLMc07KigzHtVjKfL08QHIR1HAC4KeeWhNWWVBgfymlTLZlbwmc3JH7EV7vmM+fK29hkhoUbODhD0x3J/wTY12XhwI6oOADs1Zuj5ZxFEIY2+S3TD+W0qZZMiJwBVaJN/uZRO6qWzOUcBxMcyKdIsYm5RQRFB2ANrqron6sqoA8uoV/M8g3lLCDCa6brt2xx+cDzBX1zVQUAb1BuWEy5AVYyOTT98O2z4evumOkAxHq3dQI7lr6g2m9ZgJblLIpx8mH+Xy8vL2bM8ZqCAgBpKg6zZf5I9csMiGKCw2KZn9jpCI72wHGAvTBPAWiHisM8lz9eE7+9xmZ+qgKFlBsAANgpFYclJn/ujw3O57OiA8Amyic4nNR3AAAKqDjMsOBCifHCV4Blrj5GDIAzzfrsdVQBANag4lBD1DQHxQs4OAPjlVh5BwBgDSoOe2LGBByTkfBcyz4q1R0AAGKpONQQ+Pt1QShFCujJ3ePz8Mf3j++XNQhvU21HiTaXDQo/9M7n8++vPxP3/BsXgb/VZrJBeJsKOwIAWOD/bJ3Angyj/Vm/ZY32gV6Ng/zxj8b9/vozs+Xf//6zi0/vsVLgTnjAJdVDoB0qDksMd6CYbGCCLrCSxHSA4aFEg6g240NNJXPrw/nl5eXNn+Dp+xwnPuoTP+iHh9K/+EPajA9VSAY4CB8FQCw3bpxtd+ufK3wAB5EoNyTa5Mxf8xEK7M6y2U8qDtC3+mNDcxxme/mvnGZ1UgIg061P5vQn9i4usgC4tKB2oNwAhDPHoX/mOABHkDPB4VbL9CSIdLSejH3vu5twKPkzHZQb4Ajqjw1VHPqn4gAcQX7F4XXjnKrEZMy9u+xylx2Ew5osOqg1wHGoOBBPxQHo3qxyw5vtcwoTmcH3KPOAALv2uvSg1gBHo+JAvMJX1eVd7kvSGOKEBGktTlPJRMVpKpmoOE0l01qcppKZG2duueHWVlfth5/mf//7TyJIzkfr+BO/8Jf9ECckyOs4cysOu+hUH3GaSiYqTlPJRMVpKpmoOE0l01qcppKJitNUMlFxmkomKk5JECtH0qdxFNGTLjs16rJ3XXaqkGMy6ffXn4vvoLmGZYvPp20+wWGNTu1dl8dk7FTfvetJl50q1OUx8d7cnX11SsWBLIXnLQs3v4pTHi0kTpeduoq2eTINdioqjdfRlo1dG+9UhTi3Dtrvrz/TG14Nql+PsYcTCMP/p28/lH7uLuOUK4zzOpll5YYGOxWVhk6tF2fcPPxlvG2cy2ibJ9Ngp6LSaOTg9N0pL+P1kmmqU5W5qqJ/1nGAxl0O+b78+pMeb+dcBJHZZnJgP9lm8x3NvZ7i6f7h1tUE4yav22Tu9DJOzqTHyR3ltCnf0eYTHACAalxVAXBcX379OeVd6ZBok795uuVkm/GhyTaFO3q9x2WGwfnVRMSX/0q0uZKePXE+n3PmOubsaLJNzjzYdBDlBgBgVSoOAFtatgpAYkZA1IUS+TnU3+Ng2YKRIdKLO/z97z/p9SajFM6DVW4AANbmqor+uaoCmmXIt9iG5YbMTAYtP6FefgBwNK6qAIA9KVlUsinKDQBAOBUHgG04w7xYOxMcMnfdftHBaw8AWIOKA8AGlBv6081kBwCAKO+2TgAAZmhwgsOlIY1bSTa1sE4jaQAAHTPHAaA2ExwWa7zcMDLfAQDgpOIAsLnWRstE2fviDgAAhVQcANiHvUxwuGSyAwBwZCoOAFtqebTclD2WG0bqDgDAMVk5EqC2W4PPu8fn0+n0/eP7xLbV2lTeUWabhKf7h9Pp9OHb55I2IUFutZm7qGRiR2OQ319/hiQMALAGcxwA2pIzuk60Kdx8wY4Kk8nx49Nfb/77OD4fBtVpOW1CoqU3n7u4w+tol23+/vefkmQAAFal4gDQlvSUgck2hZsv2FFhMnNbvinnBH7+Sf7CaJObz7rIYu1kAADWc97FFbCUaOr27wBz7XoFh0npFRze7KO7qwIAy9QfG5rjAEC7+i43nBYtKvm6vYUnAYA2qTgAwMbmLu7QTcEFAOibe1UAxEiskli4SMFhdT/B4dLcO1lcubVC5LC0ZHpbAICVWMehf9ZxgLVl3pFB3WGWQ5UbrmQu7jA0G26Qmfb3v/8c4bgBAGnWcaBFIfe3u3t8jopTHiQqjk6tnUxUnMBOvY6z4E6TvR6c8iBRcZ7uH0LuChl1a8m5cfIXd8gpN1w126pTt4K0Fqc8SFQcnVo7mag4OlUnTnmQqDg6tXYyUXF0qhEqDkwYfv0XjgFihyLl0XQqM9rmyTTYqcKY4/C+kYPT7Mu4ZIJD7C+D8miL40wu7pBZbnidxoadSkTbavOrOI0cnL47FRKnkU5dRds8mQY7FZVGIwen7055Ga+XTFOdqkzFgRq6nEzeZadGXfYuvFNRw/UNtflE//j015v/njkD8MO3z6HpbCkx2WFWuWHQ7A+Unp6yKF0ek7FTffeuJ112qlCXx8R7k1VZx6F/1nGAlSyuOLQ5zm/HkVdwSLg8LAvKDQM/vADgyOqPDVUc+qfiAGsonODwZtFhjJkoSQxtJhvUbBO7o1vlhmGMnRgwDyfwJxtEtam2o6s2+atF3qLoAACHVX9s6O6YAPtz9/i8+USJy4UwN0+m/vUCT/cPmwzdX15emr04AgB25/W3qtJ8LOs4AGzg/JZh/YKc0XuiTf7m6ZaTbcaHJtvk72jxBIecHwdDm3TLnDaTewxM5u9///n733+uXieTwQGAtOGmD28W8fd4P4iWuaqif66qgDUUXlVxa3HE04HfrZZvuJKuv5Rw9gaAI8svKPT3jVl/bGiOAwA0Z725DP39eAKAfLPmL5jsUE7FAaAhzudfOewBOWzHAWA9CyoIig6FVBwAWnHYQaZyw5sO3n0AiKV2sAkVB4ANvLxl66RojtcJAGxOqaKEigNAbT8+/eWmAyMTHOayEAMAsBcqDgBL5NyEcpKig3JDZaoVAByTeQpbUXEAqOrqvpgmO7CAwgEA1KRgsZiKA8BCIdMcBmPd4e7xOd3y7vE5p83kHkPaFCYza4LD5Df90/1DTpt0g6Z2lNkmnzoFAFCZigPAcguKDonrBc7n849PfxXWAoaH0kFC2owPFSaTYxh4J4bf+aP3dMucNpN7jNpRus3c8oFyAwBQn4oDQJHvH9/n1B1+fPpr+N9papGCq8sumjX2etlcj9gVHOoPp1sYwOfn0EK2AMABna3O1b3hZ70nGip482T+VQXh8s2YXsGh47etBSNjJeZKqDUAwKn4QsVuvk/rjw1VHPqn4gDbej26vno/HrDuoOIAAFRWUnRQcVjMVRUA65r8TH95eUkv7tDZzSyUGwAADkLFAaC2N4fc6fF2N0UH5QYAYBOL5yl0M8FhEyoOAKvLHE4fbbIDi3klAAC7oOIA0JaO6w4mOBQ6/9fWiQDALi2YrWCCQyErR/avcHWQYe39ZXe/azZOU8lExWkqmag4TSVTHudyoPjl15+cOOmxZWaQtGoHJ6fcMCzpVP7V3lSc2GT+/vef8V+WfbA32KlG4owrijk4jScTFaepZKLiNJVMVBzvzb0kExWnQjL5S0h++Pa5s5exlSNp1Jv3/Ku2eXickGhddioqjk69aZi88OXXny+//uRvknj0x6e/Nu9UbJxB4f2rCjcPjxMb7ffXny2kERutkWc8ViOdauoZHzdv5ODERtOp9dKI1UinmnrGD/je/PDt8+SgfWjT5cu4MhUHshSe/yw/fRobJyRal52KiqNTgXHSF1n8+PRXyRz7ap2adT1FYfk/avZj7CzKqGjjHIdlZyfa7JRnPHzz8Dgh0cbNGzk4sdF0qtk0YqP13alGDk5stEScoaZwVX24+pfddapBrqroX/2ZM3BAOdcmTLZZfGHCYHybZyZTmO2sNj8+/ZXI+en+If3dmTOHMKRNtR2dZvb69VPvUx0AmMtVFQCNOl+4eijnmoL86w4SLYeLMtIZ5idTmPb40GSbyXLDKW9+YKJN4eax0fI3z2yp3AAA7JSKA8C09OSCnGsT8q9fmGyZXgbi1vB+mUQy40PpNulywyzpiZElm8dGW3sGpnIDALAXrqron6sqoFCzZ5gzL7LYljtiFmr25QcA7I6rKgDIlV5U8s0LQCpTbiik3AAA7JqKA0BK+0O+ZusOyg0AAAen4gAwQ7Oj5XRim092IESzLz8AgDepOADctK+BelOTHUxwCOfQAQC7827rBAAa1f71FG8akrw14K+zXJByQxRHDADYNRUHgA4F1h3GIEa/AADM4qoKgDfsdILDldjFHTLbm+AAAMBAxQFg2n5Hy7GLO+xrYQsAALZ13u/PaDLVuWwb+jOOrr/8+nM6nb5/fJ9ofPf4nG4zNIhqsyyZdL3g6lNiDHK11WWz1ztaMMHh6f5h+OPDt8/pNokGOW3yd9RIMgAAseqPDc1xALjpcoLAWA54LfHQSpYls2C+w+toY5vxofGPW+WG319/3trpLOMofdZDK2kqGQCANqk4ALztanCemFaQnnFw2SbdMqdNeTKzFnf4/vH96/ZDm3FHOQknDCf5c071J9rkb55u2VQyAAB756qK/rmqAnhT/kUWOetoWjASAKBxrqoAoJL8iywm6wvKDQAAvKbiAHBok3WHsVmtjAAA6ISKAwCpgsKtO2iO/2iCAwAAb1JxAOB0yp7skPnvyg0AALzbOgEAGjJUCtKLSo4ym5FweQyVaQCAzqg4MOHu8Xn4o+QGeCFBmo3TVDJRcZpKppE4TSUTHucqyKy6w2uLR85P9w/DH4W3jRzihARpLU5TyTQSp6lkwuM0lUxUnKaSiYrTVDKNxGkqmfA4TSUTFaepZKLiNJVMO3FqclUFLDSO97rUd+8YpZ/onZ5yH7+M27egprOj3lGiyyd67FTfvaNvXT7R3pus64XelT/RX379KU/jy68/UXHKg0TF0am1k4mKU96pYfNEkJz4Y5u148wNMhmn5Gvl99efk8lctrnVfjLOVZA322+SzK32v7/+nPWNfKtTc4UEiYrTZaei4nR5cHRq7WSi4nTZqag4XR4cnVo7mag45Z2qXwQ4v+zzFBb5hnNonmhYbPL6hZwLHKq1WRwkZFGGq4+anLl/IW2q7Sg8mb///Wf8Rx/UAMCq6o8NreMAHJQV+y5ZA3JzXoQAQH+s4wAwYZgIkJgyMNmgZpuoHS3wesw8nORPL24U0qbajkKSOZ/Pw9SGcYKDcgMA0CVXVfTPVRXw2utT+t4jhdMcHMB8Xn4AwCZcVQGwAeO9U/ZBcP1FIeUGAOA4XFUBHI4x82K3Dp0x82IOHQDQMRUH4FicYV5MuQEAgFlUHABgG4o1AEDfrOMAHIgJDouZ4BDLcQMAjkDFATgK5QZa4FUHAByHqyoAmGCCAwAAC6g4AAc1jpbvHp/TLe8en6PaTGbVTjJjkES54en+4en+IR0ns01IkPId1UwGAKB7Kg7AEV2VGwprAfmbp1s2lcxktHFEnRha54/wC2sBUTuqlgwAwBGoOACHs+xagO8f3y94aCXVkvnx6a83//3l5eXDt8/D3+MfryUeWqDajnI0lQwAQJvOrsLt3jAj2hMNzGX5BgCAntQfG5rjAAAAAMRTcQDgDSY4AABQSMUBAAAAiKfiAMA1ExwAACin4gDA/0W5AQCAECoOTLh7fL57fG4qTnmQqDg6tXYyUXG6fBm31qmn+4fyIFFxnu4fouIs2Op8oSTO62Rai9NUMjqViFMeJCqOTtWJ01QyOpWIUx4kKo5O1YnTTjI1qTiQpXBAEjv4LI8WEqfLTl1F2zyZBjsVlUaznVo2wWH48iv/CgyJE/tzZ2601wcw6uBcRttq86s4OjUZbavNr+K09t4MidNIp66ibbX5VRydmoy21eZXcRp5GXtvrrf5VZxGOlWZigM1fP/4fusU4nXZqVGXvSvs1BGOSR/XU3z49nnrFFbUZe8KO+WY7MXYqb571xPvzdf67lTfvevJvjp13tfvSBYYhhCeaI5pOIefKBaMJ/kn26QrDiFtKu/odZu5FYehxJ7+2ptsM9bpJ9sU7qhCMq8PoM9eAKAd9ceG5jgA3Yq6cmEyWs6O8pMpjLa418vKDafk1L7YWX+FO1o7GeUGAIArKg5AP65W7Mu5DmJok99y7kOz2oREW9brBddT5EzCzJn1N7TJb1m4oxyx0QAADstVFf1zVQXHcTls9pqfpY8VHDZkggMA0D5XVQAsdGvMzCTlhkLKDQAAb1JxAHqg3AAAAK1RcQA4NBMcCpngAABwi4oDsHuGfIspN4Rz6AAARioOwL4pN7AtrzcAgFtUHAAOygSHcA4dAMCld1snALCcCQ6LKTcEctAAAN5kjgPQDwM/AABohzkOwF5N3hHz7vF5+OP7x/d12lTbUaJNTpCcCQ5P9w/DHx++fb4VZ2gz2aBCm2o7OmX0GgCAgTkOwF5dzWjYcILDOMjfhajrKcbB+fjHoRyz1wAAs6g4AD14c7Q8nORPnOqPapPePDaZyT3mB0kbzuEnzuSPD022SU8HCGmTM+MgKpn8PQIAHNzZZc/dG85neqKBkwUjAQAOrP7Y0BwHAAAAIJ6KA8BRmOAAAEBNKg4Ah6DcAABAZSoOAAAAQDwVB4D+meAAAEB977ZOgNbdPT6fIu60FxJnCBIVp5FORcVpKpmoOF0+4/U7lS43PN0/nIrv9TgEiYpTfuPJ8DjjMVxQo2m2U+VBouLo1HpxuuxUVJymkomK0+Uz3mWnouI0lUxUnKaSiYrT2su4JnMcyDKOkTbZfCWNdCr24DSSlWe8msKsxu+/phRmFdWpMc6tks2yaNvG8YxXo1OJzZs6ON6bCToVvnl4nJBo3psV0ojVZla3qDiQpfBkbPm55dg4IdG67FRUnDqdunt8nhxvXzZIxJkMcvf4nO5UfjJDnMJkxv98M85lm1uj5d9ff56mauST32dP9w+TtfacL8WrNq+jjTuqmcybcRZXH6JORxTGiT0r0lmnhjhddipKVKcaOTix0XRq7TS67FQU78314nT5Mq7s7CLe7g2/jz3RdGZWKSFRLAhpU21Hc5NJlxtOeYPzW20uR++TbUp2NCuZ8B29PoY+TgGAnao/NjTHAdilcbwdO59imfo5tNDrqFMiIVbKQbkBAKCEOQ79M8eBvfMaXsb9KcpdHUOHDgDYNXMcAP7nfD6PQ76Q1fsgn5ccAEAhFQeADpngUMj1FAAA5VQcgEY5w7yYckM4hw4AYAEVB6BFzjCzIdUuAIAQKg4AXTHBIZxDBwCwjIoD0BwTHBZTbgAAoB0qDkDrjJbZkJcfAMBi77ZOAOD/4hL6xUxwiOKIAQCEMMcBaMg4Zv7y68+XX39OybHf3ePz3eNzOuBkm5AgLSQzt9zwdP/wdP+Q2NFkg6g21XaU2QYAgCgqDkC7hqLDm8ZRd2KIPjl6n9WycEfVksmRP+pOtBwfymkTklLhjtQaAAAqU3EA2vX94/vJh3LalOxoVjKFu1gcbe4Ehw/fPmcmk2g5PpTTpmRHs5Ip3AUAAIHOrlbt3jAU8USzC5cjZy/afFZwAABgUv2xoZUjgYYYIS+g3AAAQJtcVQGwY8oNAAA0S8UBAAAAiKfiALBXJjgAANAyFQeAXVJuAACgcSoOAAAAQDz3qmDC3ePz8Mf3j++3DdJsnKaSaSROU8lExWkqmagJDk/3KMzpuwAAIABJREFUD8MfH759XpxMs3HSQcZjeOugtdmpwjhNJRMVp6lkouI0lUx4nKaSaSROU8lExWkqmag4TSUTHqepZBqJ01QygXFqMscBFhrHjVCZ6ynSxi/jhFvHEFjP+N7MeZMC1Xhvsq4Xelf+RH/59ac8jZAgrcX58utPfwenkU4NaaSTmUz1MsKtlpN7aTCZyc/z319//v76MxFkaDC0udXysk06zvh3SZCcOIkgr5N53X7cUf734OROM4XEyTkI1ZJpLU5TyUTFaSqZqDhdvoy77FRUnKaSiYrTVDJRcbp8GXfZqfI49YsA5xfnxHo3nMrzRLMvk5ceXM4xmWyTuH4hpE21HZ0yJjjkTLcLaXN5JmSyTbVkcoL8/e8/l//u4xEAOIj6Y0NXVQAtGobciYH3+NBkm/RyCTltMneUs3lUMgk51/UNbdItJ9uMD022KdzR6z3OeuiqzVW5AQCA9Zjj0D9zHGiQl+UyVnAo9PoAOnRz3brKd0dLWAHAYdX/Ea7i0D9DO5pyOeTzspxFuaGcikOJnBXF1B0AoGUqDsRTcaAdV+M9L8tZVBwKKTeUmLWAuboDALTJOg7AgbhDYT7lhkLKDSXcLw0AWEbFAajEkG8x5QY2tKDcoEIBAAxUHIBtGC2zIS+/TItrB4oOAMBJxQGowwUUi5ngEM6hAwCoQ8UBWJ3rKRZTbmC/THMAAFQcgA3cPT6Xt7l7fM5p018yk3JGeiFtnu4fctq0kMzLhcl9AQAQQsUBWNfrs/Rffv05TQ2th0cTbcaHJtsU7mhWMrE7ujXB4ffXn4mh9fBQenwe0mZ8qKlkCOSoAgCFVByAqqLOMH//+P7qDyr78O3z1R8AAHDpbH5p94bTpJ5otnJ1ot5LMZMVHNhc+RwH1SgAaEr9saE5DkA9RsuZlBtogXoBAFDo3dYJAJ0zSIZjUrAAAMxxAGiLCQ4AAPRBxQGgIcoNNMU8BQCghIoDABBMqQIAOKk4ALTDBAcatKB2oNwAAAxUHJhw9/h89/jcVJymkmmnU1Fxujw4XXbq6f6h/OaFsXGaSqadTkXF2fDgzKogzGrc5TOuU3XilAeJitPlwdGpOnGaSqadTkXF6fLgRCVTk4oDWQoHSLEj6kbG5611ysHJjLbV5ldxXkdbNsGh8Fsn9pdBC78zzudza51q5+CUbJ5ZR1g2u8HLOHzzqzitdSokjvdmIo5OTUbbavOrOK11ynszfPOrOI10qjIVB7J8//h+w83b1GWnRiW9yxmZT7bJmU0wt82tTmUGSR+TwoTzyw1Xte03B3g59e+hQWJ8mBkkqk3gjv7+9590y10rvGChZPMP3z4nNk8/Ohl5aVIBm6+ky04VGjvVd+822XwlOhW+eZu8N9fbfCVtZnXL2eXB3RtGMp5o6pgc3ke1uRy6T7aplsziILMqDsMft75sJhtEtZksfGySzFBu8IkHAPBa/bGhOQ5ApNipH4lo40M5baols8yC6ynSp5pLklmwo82TOZ/Pfc9rgGEKz76m0QLAyRyHIzDHAVrm/hTlXh9DR48+pEsM+5pVC0AL6o8NVRz6p+IALVNxKKTcQJcypzMoOgAwi6sqgP05X9g6l51Rbiik3ECX8q+ecJ0FAI1TcQCKqDIsptwAvDa3iKDoAEDLVBwA2CUTHOjPsvKBogMAzVJxAJYzwWExExwKKTcAALRPxQFYyJAPIFDJVAXTHABok4oDQG0mOIRz6AAAGqTiACxhgsNiyg3hHDoAgDa92zoBYH/S5Ya7x+fT6fT94/tbmw8NctokGkS1qZbMuKOEcV70h2+f020SDXLaVNvResm8vLycz2e1BgCAlpnjAETKGVeHRBsfymlTLZlJPz799ea/zx05J67Zjr2cO2dHWyWj3AAA0DgVB2Ce9ASH9ESAyzb5LdMP5bSplkx688lyw3AOPz1l4LLl3Ieu2kTtqIVkAABokCmp/RvGh55oolxVHLy08lnBAUgonBOkJAfApPpjQ3McgHkMj5dRbgAA4GisHAksZKicT7kBmPTh2+fYpU+AvXj93jdriW6oOACzGScDNMXgBHbqVp0x525QsAvWceifdRxgWyY4APkWTHMwJoE9yn+ze48TyDoOAADHZWgBRzCrtuh6K3ZNxQFgRSY4AHPNKjqoUMDuLKggKDqwX9ZxYMLd4/PpdPr+8X0LcYYgUXG67FRUnC4PTv1O3So3/P768+n+oXCcEHWFZ0ic8ZeQTq0dp8uDo1Ov5awimbOLpjoVFcd7czJIVBydWjVOiKY65b05GSQqTiMvv0zmOJBlHPhtsvlKuuxUlETvJjt+9/ic06Ykh2U7utU4M5l0s6jXQ85JjMs2b7bPD5JuORnn6f4hp01mMrM2KdzjfnV5cHQqsfmbPys/fPu8yc/NqE61+ZQV8jIO33wlm3dqcYTEht6bCZs/42toM6tbVBzIUnhyuPzc8mWc2GhbbR4eJzbarTjDuLqkHpET5OrRN5MZG0wmk54oMTeZnB0N0tdTvDlayK8CJEYjs4IkBi2TcS5/oAxxCpMZ/2WIc76Q2Py1qJFY7Iiukaxi09CpyWghmw/1hcv/zY3TWqc84+GbX8XRqcloW22+Eu/NyWhbbX4Vp5FOVeZeFf1zrwoCTV7mkHMdREibyZLEJsmMDRLXU0wO8k/JL5LJNiFBZu1opWQuj6FPMAA6UHhqel/jTNrkXhVA0yanmeTMQwlpMz7UTjI5E0zSvxVy6t+TbUKC5O9opWSuSjZzpzkAQH/2NZceBuY49M8cB6jM/SkKvT6ADh2783pg4OQkUF4y8ElCofpjQ/eqAIik3AAHd2tEEbVQOQDsiIoD8IZx2GycTGUmOLBfmWcvy2+OCwB7YR0H4NrlkM/187OY4BDOoWMvZk2WdjE2sIBiJXuk4jDDucDWuUMuL1c25OXHcSg6wAEpGXBAKg4zONUGJJjgUMj1FOzXsvKBogMA3VNxmOfl5eXyF/BLtg1zhnyGfIspN4Rz6NgLhQMg3+JpDuZHsFMqDsB/KDcAVKZaAUDfVByWMAzjsO4en+8en0PaVNtRhWQyJzjkDC0m2zzdP0S1qbajBcn4mAWgVwtmK5jgwH6pOACn08wJDonh9+TofWyT3zL90ObJzCo3pMfeOW0uW859aKUdxSbjSjQAujergqDcwK6pOCzkNzF9S7+8v398v+ChWOOO6u+xBYkfH9V+l4w7itqjz1UAjuPDt8+TX6A5baBxZz/vujecgPVEk2AFh8UsGAkUrsVgOAGc/u9PEh8LrKf+2PBdtT0Be2G0nEm5AQAIocpAr1QcdubWCAcAAACaouKwJ8oNrM3J+XwmOAAAQJp1HII1uGhCgylBB1QcgNHipRzMowagpvpjQ/eqAJhNuQEAACapOADMo9wAXFk2VcEEBwC6p+LAtLvH50aCtBanqWRai9NUMlFxopIpvJdebJymkomK01QyrcVpKpmoOC0kM7d8MNm+hU6Fx3m6f+jmGQ+P01QyUXGaSiYqTlPJRMXx3lw7SINxqlFxYMIwxCocaIUEaS1OU8m0FqepZKLiDJuXT3AYvifKvy1C4jSVTFScppJpLU5TyUTFaSeZ/KJDZrmhhU4Fxhk37+YZD4zTVDJRcZpKJipOU8lExfHe3EsygXFqcq8K4D9yBuRDm+8f35fEGRsk4rSZzI9Pf73Z4OXlZfjoT48iJr8e8oMUtsn5oqqWDPTkw7fP6feX9wIAh2KOAxOGYVh6UFcnSGtxmkomMM5ltFsSw/jLh1ZNZtxRTjKxB+e1/AH86b/jjfJywK04s8reJclcnhLJTOZ8YVk+OUKC9BqnqWSi4jSVzGWc4X/jP17+Z/1kWohzeTQ2T6a1OE0lExWnqWSi4jSVTFQc7829JBMYpyZ3xwzW4K0oG0yJNuVPGajQpsEdJSY4nEKnHtSZVjCWCaolc1Vl8KEEAFBZ/bGhikOwBof3DaYEu+P+FOVUHAAAtlV/bOiqCgBWd6tkAwBAx1QcACaY4BDOoQMAOAL3qoBDuBwzG+xRmQkOAMCRXa6lva91H8tZxyFYg4smNJgS9ak4LGaCQ6HXB9ChAwCOoMH7JVs5cvcaHN43mBKVWbFvMeWGcioOAMABZd6wvHLdQcVh9xoc3jeYEjUZ75VQcSjk5QcAHE1mrWFUs+jgXhW79/Ly4vc09EG5oZByAwDApLkVin1RcYCeGfItptwAAMBcy8oHHRcd3KsCDuHLrz+Tbe4en4c/vn98n24z2aBmmwo7yjF8TyQmxY1fJCFtqu2oJJmXlxdLlgIAx9Fx4WAxcxygW+vdknAcpW9ozGGNZOZOcKj/7dLC99mYQ04yyg0AAAek4gB9uhoz//j012nqNP7waM6p/kSbnCAhbcaHwpNZcD1Fzno/Q5t0y5w2k3uslsz4UKLNy39NpgQAcGQtnE9ag3tV9M+9Ko7JCg6LWcEBAIAFCqsGFW5a4V4VwCqMljMpNwAAQBQVB+if0TIAAFCfigPAf5jgAAAAgdwdE/pkkDyXcgMAAMQyxwEAAAC2VGHZyE2oOACY4AAAAPFUHJhw9/h89/jcVJymkmknTlPJxMZZO5n8csPT/UPIrZKjgrQWp6lk2onTVDKxcZpKRqcScZpKpp04TSUTG6epZHRq1ThNJRMVp6lk5sZZe55CVKdqUnEgS+GoL2TQOMaJjbbV5uFxJqPl7Ghsc6txTh0hs01OMulnfO6OFh/q4cM9/fme8wUwNLj8/1tt8nf0Zvu5yaTb5CSTEy1fYZxG0lgpWlMHR6cmo221+VWc1jrVyMGJjdZIp9p8xkPS6LJTUbw314tTbXg/q1Sxr6KDigNZvn98v+HmK2mkU3UOTk6x5vLRdFYhdY38ZNINJpMZG7zZqZDrKXI+9/NH+PnRTm99P81KJvH1NplM1A+U1wrPD0SdXmjzcspGDk4snQrffCVRnXJwwjdfiU6Fb74S782E+p2qsEmbh/qWs6uUuzcMqDzRB5cedc9tExKkkWRyKg6J4f1Vm8kGUW2q7Sinzd///nPyIQMA8F/tXIhxpf7YUMWhfyoOcIsFIwtdHUDHDQBgNFl3qD9bQcWBeCoO8CblhnIqDgAAaa/rDhteFqHiQDwVB3iTikOh1wfQoQMAaFn9saGVI4EjUm4opNwAAMCkd1snACw3jvoM9mZRbgAAgArMcYC9ujVshrWZ4AAAQA4VB9gl5YbFTHAopNwAAEAmFQfYH+WGxZQbAACgGhUH2D2jZaoxwQEAgHwqDrAzb56lv3t8vnt8Tm842SYkSMvJ3Jrg8Pvrz3SQp/uH1zdSXqNNtR1FJaPcAABAgooD7MmbZ5gnR92n0ymnTX7LRJtqyYwPFSYzmBxap9sUbr73ZAAA4E0qDrB73z++D2kTEi1/R4XJjA9lJrN4gsPow7fPCx6a1SYkWv6OCpMxwQEAgLSzn4zdGwZanugOuIR+MQtGAgBA/bGhOQ6wD8oNAADAvqg4AJ0zwQEAADah4gC7ZLScSbkBAAC2ouIA+3A5QjZaBgAA2vdu6wSAXAoNc5ngAAAAGzLHAeiTcgMAAGxLxQEAAACI56oKJtw9Pp9Op+8f37cQZwjSWpymkomKs/dnfKUJDk/3D6fT6cO3z+VBouIUBomKE9upqDhNJRMVp8tnXKfWi9Ply7jLTkXF0am1k4mK0+XLuMtORcVprVM1qTiQ5e7xuWToOI4be1KtUzlD98lkcobul0FuPeObJJNuU1jUyPkCGNtMxgkJkhNnbPB0//C6cbVk2pTTu/168xmftXlgMlF06s3NA5NpxNipwoPTpi6fcZ16c/PAZBrhvZnePDCZKPt6plxVQZbCQV35CfPLOLHRttr8Ks5ktMQI/PKhOgcnM5koidrHm3usv4LDrG+j4RtivUr5gmTKhXTqKtpWm1/FKY/m4GRG22rzqzg6NRmtfPOQON6biTg6NRltq82v4rTWKe/N8M2v4jTSqcrOFlHr3jD68kTvV/60gsk2OXWNkB1tmMyCcsNknThnAltmm8lviEaSOZ/Pv7/+nAwCAMCO1B8bqjj0T8WBQ3GLikKXB9BBAwDoSf2xoasqgH4oNxS6dQABAGABFQegE8oNAADQFBUHAE4nExwAAIim4gDNMfBbwASHQq8PoEMHAEChd1snAPyHQsNiyg0AANAgcxygRaoP1GSCAwAAa1BxgCYoMSxmgkM4hw4AgBAqDrC9yTPMd4/P6QiTDWq2qbmjyTZP9w+TOwppU21H4cmodgEAsBIVB2jdMKhODK0nG9RsU3lHPz799eajQ8lmGFSnh98hbartqEIyJjgAABDFypGwMZfQL/P943vXU4Rz6AAACHT2+7J7w6jME90m5YYSKg4hLg+jQwcA0LH6Y0NzHIBdUm6I4ogBALAS6zjAZkxwWEy5AQAA2qfiAK0wWgYAAHqi4gDsjAkOAACwCyoO0ASj5UzKDQAAsBdWjoTNGCQDAAAdM8cB2A0THAAAYEdUHJh29/jcSJDW4tw9Pvd3cLrs1Ol0erp/aCRIa3GaSiYqztP9Q38Hp8tORcVpKpmoOE0lExWny5dxl52KitNUMlFxmkomKo6X8dpBGoxTjYoDE4bxXuGoLyRIa3FiR9SJaDklgLFNeZyrP9ZLJifIZZxlExyGb9Dho/nWB/TkB3dmkJw4V/+/OJl0nPzfDelk8jUVJ/YbvZFOXUXbPJmm4jSVTFScppKJijNu3tnBuYy2eTJNxWkqmag4TSUTFafX96ZnvBEqDrCl/LJFyeg9sE1gMrNKNrfKDb+//kx85uZ8HFcb4ubsKD+Zwl4D1Pfh2+erP4AWeG+yqrPrn7s3DNU80W0aR93fP75Pt0k0yGmTv6OmkhkbJCoO6W/HYfidaDOOzyfbVNtRhWQAADig+mNDFYf+qTiwdxaMDOGjAADg4Or/IHR3TKBpyg3lbh1DAABYlXUcAHqm3AAAwFZUHIB2meBQSLkBAIANqTgAjVJuAACAXVNxAOjT65KNYg0AADVZORJWdDnkM9ibxQSHcA4dAACVmeMAa3EJPRvy8gMAYHMqDkBzTHAo5HoKAABa4KoKWMUw5Pvy68/pdPrx6a9bze4en4c/vn98n26TaJDTJn9HmyeTX254un84nU4fvn1OJDPZZmiQ06bajsqT+f315+l0+vvffxJtAABgbeY4QLzLcsOg/AzzOEqf9dBKWkhmHJyPfyTaxO5x7R3lmJWMCQ4AAGxCxQHWkpjaMBpO8qenDFy2nPvQgjbVkimc4DCe5E+c7U9PBLhsk9+ycEc5CqNdTW1QbgAAYCtnP0a7NwzhPNHVuIR+Mcs3RHGTFAAAXqs/NrSOA6zLeI9NeOEBALA5V1VAJLckXMwEh0AOGgAALVBxgDCup1hMuQEAAPqj4gBhDI8BAABGKg6wFgWITCY4AABAl6wcCfEMlQEAAFQcIJJaw1wmOAAAQK9cVcGEu8fnu8fnzuI0lUxUnKaSyYwzWW54un94un8oT6bBOE0l006cppKJitNUMlFxmkomNk5TybQTp6lkouI0lUxUnKaSiY3TVDLtxGkqmag4TSUTG6edZGpScSBL4RA0ZAQbGCck2uTmw5A73SxnWD4Z5/LRW83mJrM4Tv6O0m0uP09vfbBOfuYODdJxrtrkxCkMMjSLSqbwWyfqSyv2y0+n1oujU5NxuuxUlKhONXJwYqPp1NppdNmpKN6b68Xp8mVcmYoDWb5/fL/h5ivRqQpxEn58+uvNf8+8nmLBt+OHb58zW+5IYafaPCaNdCr24DSSlWe8Gp1KbN7UwfHeTNCp8M3D44RE896skEasNrO65exi6e4NE9c90Zu4e3yeHLqHtBnmC0y2qZbMZJCc5Rue7h/Sn6dDrWGyzeSHckibppIBAIDX6o8NVRz6p+JAgywYCQAAldUfG7pXBVCbckOhywPooAEA0CzrOADs2K3yDQAAbE7FAajKBIdCSgwAAOyFigNQj3JDOIcOAIBmqTgA7IYJDgAA7IiVI2Eei/YtZoJDodcH0KEDAKBl5jjADM4wL6bcAAAAR6PiAAt9+fXn7vE53ebu8TmnTUiQ8h3VTCbH0/3DZIOcNtV2tGoyJjgAALA7Kg6Q63LI9+XXn+GPxNA6f4RfWAuI2tF6ySyY4DAMvBND9PGhyTbpcX5Om8wd5Wy+LBnlBgAA9kjFAbJcDfl+fPpr+OP7x/d1EkjsqFoOOXt8/dCtcsPvrz9Lcvjw7fPVH2tL7KhaDgAAsCNnJ8q6N4z3PNGFrobNjmc+KziU8/IDAKBc/bGhe1XANAtGLqbcEM6hg61cXvFkZhMA5DDHoX/mOBRyCX0JFYcQ3sWwofTyK0oPAOxI/V+VKg79M1YppOKwmHIDsHc568Ke1B0A2In6Y0MrR0KKcsNiyg3A3mWWG2a1BIBDUXGAGYyWAQ5ibhFB0QEAXlNxAOKZ4ADs2rLygaIDAFxRcYCUcYT88vJitJxJuQEAADipOMAktQaAQymZqmCaAwBccq+K/hWuR3r3+Hw6nb5/fF+YRkicIUgjcXKCTPZ6DJJolnPoQuKEBMmc4DD8KE+s7n71q/3NlpNBruIkguQk8+Hb58Qe5ybzZuOcIMsarx0n5zDWj9NUMlFxmkomKk5rL+MQrXWqqThNJRMVp6lkouJ4GSfiNJVMVJymkomK01QyUXFKgrhXBY26HIvW37xBOT2K7XUi2hrJpNvfenRWuaHQGCQR7eqhwv3m72hxm7kt5zYO37xNXXZq1GXvunwZd9mpQjmf2/ulU+Gbt6nvTvXdu57sq1MqDmQpnFNQPkXiMk55tPI4OdvOij/ZONHg8qFbzeZ2Nt2+8CnIr8sOLd9sP/5jItrVQ/kt57aZtXmiU/nRljUO3/wqTnm0kDhdduoq2labX8XRqcloW21+FaeRl3HO53a1ZALjXEbbavOrODo1GW2rza/iNPIy9t5cb/OrOI10qjJXVfSv/swZjsmCkUAfCs8d7euHIACH4qoKAAAAoAfvtk4A6IEJDoUuD6CDBgBAH8xxAEopNwAAAK+pOABs7FbJBtgdizgAwCUVB6CICQ6FlBugNaoGABBFxQFYTrkB6NKyooNSBQBcsXIk/G/YbJxMZa9LNl6EsFPKDQDwmjkOHJ057YuZ4FBIuQFaNquCoNwAAG86+4HbvWFU44l+060h393j8/Cf3z++v7Xt0GayQc02NXd0q9zw++vP4Y/E7++n+4fANtV2FJ6MigPswvjmvUW5AYC9qD82dFUFLDEOzu8enxPj88rJdLzH18YxwNP9w+Y/9ycHJK8pN8BejJ8wV+/0zT95AKB95jj0zxyHW9JDvslSwuS0gpwgUW2qJTPs6Menv958dDiAk2f7T3llgsk21Xa0RjJXLz/vUAAA1lZ/bKji0D8Vhzc5w1zCCg7lVBwAAKis/tjQypHAPMoN4Rw6AAC6pOLAEZngsJhyQziHDgCAXlk5ksNRbqAFXnUAAHTPHAcglwkOAABAPhUHjs5oOZNyAwAAMIuKA4dmtAwAALASFQdgmgkOAADAXCoOTLt7fA4JEhWnMMLLy8uXX3++/PqTHi1P7mjoUbpZTrY5R6ZyMlct55Ybnu4fxv+/Jf1oZpyn+4fJOGOQdJw6yczaY7U4szJfO5moODq1djJRcbrsVFScLg+OTq2dTFScLjsVFafLg6NTaycTFSeqUzWpODBhGHwWjvNDag3hySTiTO4oc/Q+2TI8mVvNZiUz2TLhcmR+6wMxvySRaDn+42QpId0yNpkcOXusFif2S1SnVo1zGW3zZHRq7ThdvoxzPrerJRMY5zLa5sno1NpxvDfXTiYwzmW0zZNpqlOVqTjAEt8/vt86hf9ZI5kxZrPXU3z49vnqjw21kMMy+808octOjfruHaMun+imPrfDddkpXuvyifbeZFXnzYcNrG0YMXqiWabZigMAADBL/bGhOQ7ATcoNAADAYioOwNuUGwAAgBLvtk4AoE9jyUaNBgCAYzLHAXiDCQ6FLg/grYMJAAB9U3EArik3AAAA5VQcAIKZ1AAAACcVB+CKCQ6FXh9Ahw4AgGOyciR9smjfMsoNAABAFHMc6JA57WzFBAcAABipONAb5YbFTHAI59ABAHBkKg50RbmBDXn5AQDAJRUH4HQywaGY6ykAAOCKigP9MORbTLkBAAAIp+JAJ5QbaIqXHwAAqDjA0ZngEOLycDl0AABwOp3ebZ0ABDDBYTHlhkAOGgAAXDLHgQ4Z+AEAAGxOxYHdc0vCxUxwAAAA1qPiwO5dDY+NljMpNwAAAKtScQAAAADinZ3P7J6LDgAAABjULAKY4wAAAADEM8cB+jTMbfEGZxe8XNkRL1f2xSuWHfFy7ZI5DgAAAEA8FQcAAAAgnooDAAAAEE/FAQAAAIin4gAAAADEU3EAAAAA4qk4AAAAAPFUHAAAAIB4Kg4AAABAPBUHAAAAIJ6KAwAAABBPxQEAAACIp+IAAAAAxFNxAAAAAOKpOAAAAADxVBygWy8vL1unAAAAHNfZmAQAAAAIZ44DAAAAEE/FAQAAAIin4gAAAADEU3EAAAAA4qk4AAAAAPFUHAAAAIB4Kg4AAABAPBUHAAAAIJ6KAwAAABBPxQEAAACIp+IAAAAAxFNxAAAAAOKpOAAAAADxVBwAAACAeCoOAAAAQDwVBwAAACCeigMAAAAQT8UBAAAAiKfiAAAAAMRTcQAAAADiqTgAAAAA8VQcAAAAgHgqDgAAAEC8d1snAGzgfD6/vLxsnQWcTqfT+Xwe//ayZC98irILlx+wJ5+xtM3LtVe+L+Fwhg907302d/XbYuTFSeN8itI+H7DsyK2X68krtgvmOACwgfHnxeWPieEfnT0GKOEDlh1JvFzpg3Uc4EDO57NPcJpy9cPX72Aa51OU9r05frv8T69hGuTl2jEVBzgEv5IBSvgUZV/eLOCq6tKaxEVqXq7dUHEAoLbJXxjPLrSyAAAELElEQVSGdgAAHbCOAxyCS+MASvgUZRe8OIHWqDgAAEAPTERnX7xij0DFAQAA+ufGruzFrQVQ2SMVBwAA6JwLLmjf1atUuaEPKg4AANCty1GcIRxQmYoDAAD0SbmBHblao/d8PnvRdkDFAXZj1nxIH9AAcGQmqLNrLy8vig59UHEAAICumNoANELFAXbDLwY68+aJC2ubARSyzj974f4pR/B/tk4AgMOZ/G3hxwfAMsoNQFNUHAAAoCvKDeydOY/dUHEAYAPDr+Gr3xNmVwKUMEhjX8YfA2/+Hjj5SdAF6zgAsI1xGeqrf9wqH4BupEsPPmlpx/Bj4PTWi9YLtQ8qDgBs5nKmgx8WAHBAY9Hh8l+2SoZwbnAKAAAAxLOOAwAAABBPxQEAAACIp+IAAAAAxFNxAAAAAOKpOAAAAADxVBwAAACAeCoOAAAAQDwVBwAAACCeigMAAAD/f3t3kJswDEVRlEosJJGy/xUhtTtJB0gVhTQ15JmAfc4QYsnjq28b8hQHAAAAIE9xAAAAAPIUBwAAACBPcQAAAADyFAcAAAAgT3EAAAAA8hQHAAAAIE9xAAAAAPIUBwAAACBPcQAAAADyFAcAAAAgT3EAAAAA8hQHAAAAIE9xAAAAAPIUBwAAACBPcQAAAADyFAcAAAAgT3EAAAAA8hQHAAAAIE9xAAAAAPIUBwAAACBPcQAAAADyFAcAAAAgT3EAAAAA8hQHAAAAIO+49wYAAMKmYfz3m9PX5wMLF1cBAIs+5nneew8AAFXcFoSSZHC1SmUAgMcoDgBAyy7zQXk7OK/SGgBgC/c4AAC9KDltcZAbACBEcQAAWnZvOJAbACBFcQAA+EVuAIAIxQEAaNxlQVg/WDENo9wAACmKAwDA4SA3AECa4gAA9GVxzEFuAIA4xQEAaN96TSh8wwIAuIviAAB0zeMUAFCJ4gAAdGHx/ki5AQDqURwAgE7JDQBQleIAAPRIbgCA2hQHAKAXV31BbgCAqhQHAAAAIE9xAAA6snh/JABQg+IAAHREZQCAp1EcAIBeTMN4+vo05gAAz6E4AABdqBcXZAsAWKQ4AADtW3kLc0svmIZRbgCAvygOAEDjbnPDxncxz6HhfEZj6+YAoF3HvTcAAFDRynTDw4QGAChhxgEAaNZKbnB/JADUpjgAAG2qMd0AAJRTHACAZpXnBmMOABCnOAAADSq51tH4AwBUpTgAAK3xigQAvALFAQBoyl3nI9wfCQD1KA4AQDvcFgkAr0NxAAAasT03GHMAgCDFAQB4e9Mw/sQC1QAAXsRx7w0AADxipSyUDDv8tfzyd6czAGALxQEAeEsbc4CaAAC1OVUBAAAA5CkOAAAAQJ7iAAAAAOQpDgAAAECe4gAAAADkKQ4AAABA3sc8z3vvAQDgnUzDuPKvdzcB4ExxAAAAAPK+AQk2dtanqU1gAAAAAElFTkSuQmCC"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The *maximal margin classifier* is a linear boundary classifier based on a separating hyperplane. As can be seen in Figure 9.2 above, if the data are separable, then, in general, an infinite number of separating hyperplanes exist. The maximal margin classifier is defined by the separating hyperplane with the maximum distance from the closest observation.\n",
    "\n",
    "Define the margin $M$ as the minimum distance from the hyperplane to the closest observation. The maximal margin classifier is defined by the maximal margin hyperplane for which the margin $M$ is largest.\n",
    "\n",
    "$$ \\max_{\\beta_1,\\beta_2,...\\beta_P, M}\\quad M $$\n",
    "$$ \\text{s.t}\\quad \\sum_{j=1}^P\\beta^2_j = 1 $$\n",
    "$$ \\text{and}\\quad y_i\\left(\\beta_0 + \\beta_1 X_{1,i} + \\beta_2 X_{2,i} + ...\\beta_P X_{P,i}\\right) \\geq M \\quad\\forall i=1,...N $$\n",
    "\n",
    "The problem above is a linear programming problem and is very computationally efficient to solve. The constraint $\\sum_{j=1}^P\\beta^2_j = 1$ is necessary to make the inner product in the third line $y_i\\left(\\beta_0 + \\beta_1 X_{1,i} + \\beta_2 X_{2,i} + ...\\beta_P X_{P,i}\\right)$ the perpendicular distance from an observation $X_i$ to the hyperplane.\n",
    "\n",
    "Figure 9.3 from James, et al (2013) shows the maximal margin classifier for the data in Figure 9.2.\n",
    "\n",
    "![Figure9_3.png](attachment:Figure9_3.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some properties are notable about the maximal margin classifier, which will have an analogue with the support vector classifier of the next section and with the more general support vector machines. Note that the maximal margin hyperplane is defined by a relatively small number of observations. In the example above, the maximal margin hyperplane is defined by three observations. Adding more data with larger margins will not change the maximal margin classifier. The observations that define the maximal margin hyperplane are called the support vector."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# See example at \n",
    "# http://scikit-learn.org/stable/auto_examples/svm/plot_separating_hyperplane.html\n",
    "import numpy as np\n",
    "from sklearn import svm\n",
    "from sklearn.datasets import make_blobs\n",
    "\n",
    "from pylab import rcParams\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sb\n",
    "%matplotlib inline\n",
    "rcParams['figure.figsize'] = 10, 8\n",
    "sb.set_style('whitegrid')\n",
    "\n",
    "# we create 40 separable points\n",
    "X, y = make_blobs(n_samples=40, centers=2, random_state=6)\n",
    "X1 = X[:, 0]\n",
    "X2 = X[:, 1]\n",
    "\n",
    "# Fit the model using support vector classifier method\n",
    "# with high penalty for error terms (C=1000)\n",
    "clf = svm.SVC(kernel='linear', C=1000)\n",
    "clf.fit(X, y)\n",
    "\n",
    "# Generate the scatterplot of the data\n",
    "plt.scatter(X1, X2, c=y, s=30, cmap=plt.cm.Paired)\n",
    "\n",
    "# Get the limits of X1 and X2\n",
    "ax = plt.gca()\n",
    "X1_lims = ax.get_xlim()\n",
    "X2_lims = ax.get_ylim()\n",
    "\n",
    "# create grid to evaluate model\n",
    "X1_vec = np.linspace(X1_lims[0], X1_lims[1], 30)\n",
    "X2_vec = np.linspace(X2_lims[0], X2_lims[1], 30)\n",
    "X2_mat, X1_mat = np.meshgrid(X2_vec, X1_vec)\n",
    "X1X2 = np.vstack([X1_mat.ravel(), X2_mat.ravel()]).T\n",
    "y_hat = clf.decision_function(X1X2).reshape(X1_mat.shape)\n",
    "\n",
    "# plot decision boundary and margins\n",
    "ax.contour(X1_mat, X2_mat, y_hat, colors='k', levels=[-1, 0, 1], alpha=0.5,\n",
    "           linestyles=['--', '-', '--'])\n",
    "# plot support vectors\n",
    "ax.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1], s=100,\n",
    "           linewidth=1, facecolors='yellow')\n",
    "# print(clf.support_vectors_)"
   ]
  },
  {
   "attachments": {
    "Figure9_6.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Support vector classifiers\n",
    "Most often, the data are not separable and cannot be perfectly classified by a single hyperplane. In these cases, the maximal margin classifier doesn not exist. The support vector classifier uses a *soft margin* such that the hyperplane does not perfectly predict the dependent variable. Intuitively, the support vector classifier maximizes the same margin $M$ but allows for positive errors for some observations (misclassification) subject to a \"misclassification budget\" $C$.\n",
    "\n",
    "$$ \\max_{\\beta_0,\\beta_1,\\beta_2,...\\beta_P, \\epsilon_1, \\epsilon_2, \\epsilon_N ,M}\\quad M $$\n",
    "$$ \\text{s.t}\\quad \\sum_{j=1}^P\\beta^2_j = 1 $$\n",
    "$$ \\text{and}\\quad y_i\\left(\\beta_0 + \\beta_1 X_{1,i} + \\beta_2 X_{2,i} + ...\\beta_P X_{P,i}\\right) \\geq M(1-\\epsilon_i) \\quad\\forall i=1,...N $$\n",
    "$$ \\epsilon_i \\geq 0, \\quad \\sum_{i=1}^N \\epsilon_i \\leq C $$\n",
    "\n",
    "Some key properties of the support vector classifier.\n",
    "* The errors $\\epsilon_i$ are called slack parameters, because they represent the Lagrangian multiplier of an occasionally binding constraint. $\\epsilon_i=0$ when the constraint binds. $\\epsilon_i>0$ when the constraint does not bind.\n",
    "* If $y_i$ is on the wrong side of the margin $M$, then the error for that observation must be greater than one $\\epsilon_i>1$\n",
    "* If $y_i$ is between on margin and the hyperplane, but on the correct side of the hyperplane, then $\\epsilon_i\\in(0,1)$\n",
    "* If $y_i$ is on the correct side of the hyperplane and outside of the margin, then $\\epsilon_i=0$.\n",
    "* $C$ is a tuning parameter that acts as an error budget. No more than $C$ observations can be on the wrong side of the hyperplane (misclassified). $C$ is generally chosen through cross validation.\n",
    "* Observations that lie directly on the margin, or on the wrong side of the hyperplane are support vectors.\n",
    "\n",
    "Figure 9.6 from James, et al (2013) shows two support vector classifiers. Identify the $\\epsilon_i$ for each observation.\n",
    "\n",
    "![Figure9_6.png](attachment:Figure9_6.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "from sklearn.svm import LinearSVC\n",
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "iris = datasets.load_iris()\n",
    "X = iris['data'][:, (2, 3)]  # petal length and petal width\n",
    "X1 = X[:, 0]\n",
    "X2 = X[:, 1]\n",
    "y = (iris['target'] == 2).astype(np.float64)  # 1=Iris-Virginica, 0=not Iris-Virginica\n",
    "\n",
    "plt.scatter(X1, X2, c=y, s=30, cmap=plt.cm.Paired)\n",
    "\n",
    "# C in this function is slightly different from C in the above theory. C here is like the alpha\n",
    "# in the lasso. It is a penalty on violations. Low C gives the fewest violations and the\n",
    "# widest street. High C gives the most violations and the narrowest street.\n",
    "svclf = Pipeline([('scaler', StandardScaler()), ('linear_svc', LinearSVC(loss='hinge', C=1000)),])\n",
    "# svclf = LinearSVC(loss='hinge', C=1)\n",
    "svclf.fit(X, y)\n",
    "\n",
    "# Get the limits of X1 and X2\n",
    "ax = plt.gca()\n",
    "X1_lims = ax.get_xlim()\n",
    "X2_lims = ax.get_ylim()\n",
    "\n",
    "# create grid to evaluate model\n",
    "X1_vec = np.linspace(X1_lims[0], X1_lims[1], 30)\n",
    "X2_vec = np.linspace(X2_lims[0], X2_lims[1], 30)\n",
    "X2_mat, X1_mat = np.meshgrid(X2_vec, X1_vec)\n",
    "X1X2 = np.vstack([X1_mat.ravel(), X2_mat.ravel()]).T\n",
    "y_hat = svclf.decision_function(X1X2).reshape(X1_mat.shape)\n",
    "\n",
    "# plot decision boundary and margins\n",
    "ax.contour(X1_mat, X2_mat, y_hat, colors='k', levels=[-1, 0, 1], alpha=0.5,\n",
    "           linestyles=['--', '-', '--'])\n",
    "# plot support vectors\n",
    "# ax.scatter(svclf.support_vectors_[:, 0], svclf.support_vectors_[:, 1], s=100,\n",
    "#            linewidth=1, facecolors='yellow')\n",
    "# print(clf.support_vectors_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Support Vector Machines (SVM)\n",
    "The Support Vector Classifier of the last section is nice in that it allows for errors in the classification close to the boundary. But the linear boundary is a liability. The simplest way to expand the support vector classifier to include a nonlinear boundary is to include polynomial terms and cross product variables in the feature set. For example, instead of the simple feature set $(X_1,X_2,...X_P)$ of $P$ features, we could expand it to $2P$ features by adding squared terms for each of the features $(X^2_1,X^2_2,...X^2_P)$. The optimization problem would become the following:\n",
    "\n",
    "$$ \\max_{\\beta_0, \\beta_{1,1},\\beta_{1,2},...\\beta_{P,1}, \\beta_{P,2}, \\epsilon_1, \\epsilon_2, \\epsilon_N ,M}\\quad M $$\n",
    "$$ \\text{s.t}\\quad \\sum_{j=1}^P\\sum_{k=1}^2\\beta^2_{j,k} = 1 $$\n",
    "$$ \\text{and}\\quad y_i\\left(\\beta_0 + \\sum_{j=1}^P\\beta_{j,1} X_{j,i} + \\sum_{j=1}^P\\beta_{j,2} X^2_{j,i}\\right) \\geq M(1-\\epsilon_i) \\quad\\forall i=1,...N $$\n",
    "$$ \\epsilon_i \\geq 0, \\quad \\sum_{i=1}^N \\epsilon_i \\leq C $$\n",
    "\n",
    "To explain the solution, think about the support vector classifier from the previous section. We estimated $P+1+N+1$ paramters $\\beta_0,\\beta_1,...\\beta_P,\\epsilon_1,...\\epsilon_N, M$. However, some of the $\\epsilon_i$ were 0. The only observations for which $\\epsilon_i$ was positive were the observations in the support vector. And what mattered was the distance of those observations to the hyperplane.\n",
    "\n",
    "It can be shown that the linear Support Vector Classifier from the previous section can be equivalently stated as the following,\n",
    "\n",
    "$$ f(x) = \\beta_0 + \\sum_{i=1}^N\\alpha_i\\langle x, x_i\\rangle $$\n",
    "\n",
    "where $\\langle x, x_i\\rangle$ represents the inner product of $x$ and another set of features for observation $i$. The inner product is related to distance. Similarly the weights $\\alpha_i$ are only positive for observations in the support vector. To estimate the parameters $\\beta_0,\\alpha_1,...\\alpha_N$, one needs all the ${n \\choose 2}$ inner products. The notation ${n \\choose 2}$ is read \"n choose 2\" and signifies all the possible pairs that exist $N(N-1)/2$ among $N$ objects in a set."
   ]
  },
  {
   "attachments": {
    "Figure9_9.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the set of observations in the support vector as $\\mathcal{S}$. Because only observations in the support vector will have positive weights $\\alpha_i>0$, we can restate the more general linear version of the support vector classifier with inner products as the following.\n",
    "\n",
    "$$ f(x) = \\beta_0 + \\sum_{i\\in\\mathcal{S}}\\alpha_i\\langle x, x_i\\rangle $$\n",
    "\n",
    "The inner product $\\langle x, x_i\\rangle$ is a single specification of a more general object called a *kernel*. A *kernel* is a function that measures the similarity or distance of two observations. The inner product is one possible kernel. We could write the support vector classifier as a more general classifier that is a function measures of data similarity that are the general *kernel* $K(x, x_i)$.\n",
    "\n",
    "$$ f(x) = \\beta_0 + \\sum_{i\\in\\mathcal{S}}\\alpha_i K(x, x_i) $$\n",
    "\n",
    "When the kernel is the inner product, the model is the support vector classifier. When the kernel is more general, the classifier is a **support vector machine**.\n",
    "\n",
    "One possible kernel, beyond the inner product kernel, is the polynomial kernel of polynomial degree $d$. An SVM with a polynomial kernel of degree $d=3$ is shown on the left side of Figure 9.9 from James, et al (2013). Note how this kernel allows for two borders, each of which is nonlinear.\n",
    "\n",
    "$$ K(x_i, x_{i'}) = \\left(1 + \\sum_{j=1}^p x_{j,i} x_{j,i'}\\right)^d $$\n",
    "\n",
    "![Figure9_9.png](attachment:Figure9_9.png)\n",
    "\n",
    "Another popular kernel for the SVM is the radial kernel, sometimes also called the Gaussian kernel or the radial basis function (RBF) kernel. The right panel of Figure 9.9 shows a radial kernel SVM classifier fit to the data.\n",
    "\n",
    "$$ K(x_i, x_{i'}) = \\exp\\Bigl(-\\gamma\\sum_{j=1}^p\\left(x_{j,i} - x_{j,i'}\\right)^2\\Bigr) $$"
   ]
  },
  {
   "attachments": {
    "Figure9_10.png": {
     "image/png": 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"
    },
    "Figure9_11.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using kernels is a clever way to leverage the linearity of the support vector classifier methodology, but then use very rich functions to measure distance of each point from each other. The following four panels in two figures, 9.10 and 9.11 from James, et al (2013), compares the performance of radial kernel SVM's with different $\\gamma$ tuning parameters versus LDA and support vector classifier. SVM performs well.\n",
    "\n",
    "![Figure9_10.png](attachment:Figure9_10.png)\n",
    "\n",
    "![Figure9_11.png](attachment:Figure9_11.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# This example is taken from the scikit-learn documentation\n",
    "# http://scikit-learn.org/stable/auto_examples/svm/plot_iris.html\n",
    "import numpy as np\n",
    "from sklearn import svm, datasets\n",
    "\n",
    "\n",
    "def make_meshgrid(x, y, h=.02):\n",
    "    \"\"\"Create a mesh of points to plot in\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    x: data to base x-axis meshgrid on\n",
    "    y: data to base y-axis meshgrid on\n",
    "    h: stepsize for meshgrid, optional\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    xx, yy : ndarray\n",
    "    \"\"\"\n",
    "    x_min, x_max = x.min() - 1, x.max() + 1\n",
    "    y_min, y_max = y.min() - 1, y.max() + 1\n",
    "    xx, yy = np.meshgrid(np.arange(x_min, x_max, h),\n",
    "                         np.arange(y_min, y_max, h))\n",
    "    return xx, yy\n",
    "\n",
    "\n",
    "def plot_contours(ax, clf, xx, yy, **params):\n",
    "    \"\"\"Plot the decision boundaries for a classifier.\n",
    "\n",
    "    Parameters\n",
    "    ----------\n",
    "    ax: matplotlib axes object\n",
    "    clf: a classifier\n",
    "    xx: meshgrid ndarray\n",
    "    yy: meshgrid ndarray\n",
    "    params: dictionary of params to pass to contourf, optional\n",
    "    \"\"\"\n",
    "    Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])\n",
    "    Z = Z.reshape(xx.shape)\n",
    "    out = ax.contourf(xx, yy, Z, **params)\n",
    "    return out\n",
    "\n",
    "\n",
    "# import some data to play with\n",
    "iris = datasets.load_iris()\n",
    "# Take the first two features. We could avoid this by using a two-dim dataset\n",
    "X = iris.data[:, :2]\n",
    "y = iris.target\n",
    "\n",
    "# we create an instance of SVM and fit out data. We do not scale our\n",
    "# data since we want to plot the support vectors\n",
    "C = 1.0  # SVM regularization parameter\n",
    "models = (svm.SVC(kernel='linear', C=C),\n",
    "          svm.LinearSVC(C=C),\n",
    "          svm.SVC(kernel='rbf', gamma=0.5, C=C),\n",
    "          svm.SVC(kernel='poly', degree=3, C=C))\n",
    "models = (clf.fit(X, y) for clf in models)\n",
    "\n",
    "# title for the plots\n",
    "titles = ('SVC with linear kernel',\n",
    "          'LinearSVC (linear kernel)',\n",
    "          'SVC with RBF kernel',\n",
    "          'SVC with polynomial (degree 3) kernel')\n",
    "\n",
    "# Set-up 2x2 grid for plotting.\n",
    "fig, sub = plt.subplots(2, 2)\n",
    "plt.subplots_adjust(wspace=0.4, hspace=0.4)\n",
    "\n",
    "X0, X1 = X[:, 0], X[:, 1]\n",
    "xx, yy = make_meshgrid(X0, X1)\n",
    "\n",
    "for clf, title, ax in zip(models, titles, sub.flatten()):\n",
    "    plot_contours(ax, clf, xx, yy,\n",
    "                  cmap=plt.cm.coolwarm, alpha=0.8)\n",
    "    ax.scatter(X0, X1, c=y, cmap=plt.cm.coolwarm, s=20, edgecolors='k')\n",
    "    ax.set_xlim(xx.min(), xx.max())\n",
    "    ax.set_ylim(yy.min(), yy.max())\n",
    "    ax.set_xlabel('Sepal length')\n",
    "    ax.set_ylabel('Sepal width')\n",
    "    ax.set_xticks(())\n",
    "    ax.set_yticks(())\n",
    "    ax.set_title(title)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's compute some error rates and see how well each of the above models predicts flower type."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import classification_report\n",
    "\n",
    "X_train, X_test, y_train, y_test = \\\n",
    "    train_test_split(X, y, test_size=0.25, random_state=18)\n",
    "\n",
    "svc_lin1 = svm.SVC(kernel='linear', C=C)\n",
    "svc_lin1.fit(X_train, y_train)\n",
    "y_pred_lin1 = svc_lin1.predict(X_test)\n",
    "print(classification_report(y_test, y_pred_lin1))\n",
    "pred_wrong_lin1 = y_pred_lin1 != y_test\n",
    "MSE_lin1 = pred_wrong_lin1.mean()\n",
    "print('lin1 MSE for test set is', MSE_lin1)\n",
    "error0_lin1 = (((y_test == 0) * (pred_wrong_lin1)).sum() /\n",
    "               (y_test == 0).sum())\n",
    "print('j=0 error rate for lin1 is', error0_lin1)\n",
    "error1_lin1 = (((y_test == 1) * (pred_wrong_lin1)).sum() /\n",
    "               (y_test == 1).sum())\n",
    "print('j=1 error rate for lin1 is', error1_lin1)\n",
    "error2_lin1 = (((y_test == 2) * (pred_wrong_lin1)).sum() /\n",
    "               (y_test == 2).sum())\n",
    "print('j=2 error rate for lin1 is', error2_lin1)\n",
    "\n",
    "svc_lin2 = svm.LinearSVC(C=C)\n",
    "svc_lin2.fit(X_train, y_train)\n",
    "y_pred_lin2 = svc_lin2.predict(X_test)\n",
    "print(classification_report(y_test, y_pred_lin2))\n",
    "pred_wrong_lin2 = y_pred_lin2 != y_test\n",
    "MSE_lin2 = pred_wrong_lin2.mean()\n",
    "print('lin2 MSE for test set is', MSE_lin2)\n",
    "error0_lin2 = (((y_test == 0) * (pred_wrong_lin2)).sum() /\n",
    "               (y_test == 0).sum())\n",
    "print('j=0 error rate for lin2 is', error0_lin2)\n",
    "error1_lin2 = (((y_test == 1) * (pred_wrong_lin2)).sum() /\n",
    "               (y_test == 1).sum())\n",
    "print('j=1 error rate for lin2 is', error1_lin2)\n",
    "error2_lin2 = (((y_test == 2) * (pred_wrong_lin2)).sum() /\n",
    "               (y_test == 2).sum())\n",
    "print('j=2 error rate for lin2 is', error2_lin2)\n",
    "\n",
    "svc_rbf = svm.SVC(kernel='rbf', gamma=0.5, C=C)\n",
    "svc_rbf.fit(X_train, y_train)\n",
    "y_pred_rbf = svc_rbf.predict(X_test)\n",
    "print(classification_report(y_test, y_pred_rbf))\n",
    "pred_wrong_rbf = y_pred_rbf != y_test\n",
    "MSE_rbf = pred_wrong_rbf.mean()\n",
    "print('RBF MSE for test set is', MSE_rbf)\n",
    "error0_rbf = (((y_test == 0) * (pred_wrong_rbf)).sum() /\n",
    "               (y_test == 0).sum())\n",
    "print('j=0 error rate for rbf is', error0_rbf)\n",
    "error1_rbf = (((y_test == 1) * (pred_wrong_rbf)).sum() /\n",
    "               (y_test == 1).sum())\n",
    "print('j=1 error rate for rbf is', error1_rbf)\n",
    "error2_rbf = (((y_test == 2) * (pred_wrong_rbf)).sum() /\n",
    "               (y_test == 2).sum())\n",
    "print('j=2 error rate for rbf is', error2_rbf)\n",
    "\n",
    "svc_pol = svm.SVC(kernel='poly', degree=3, C=C)\n",
    "svc_pol.fit(X_train, y_train)\n",
    "y_pred_pol = svc_pol.predict(X_test)\n",
    "print(classification_report(y_test, y_pred_pol))\n",
    "pred_wrong_pol = y_pred_pol != y_test\n",
    "MSE_pol = pred_wrong_pol.mean()\n",
    "print('Pol MSE for test set is', MSE_pol)\n",
    "error0_pol = (((y_test == 0) * (pred_wrong_pol)).sum() /\n",
    "               (y_test == 0).sum())\n",
    "print('j=0 error rate for pol is', error0_pol)\n",
    "error1_pol = (((y_test == 1) * (pred_wrong_pol)).sum() /\n",
    "               (y_test == 1).sum())\n",
    "print('j=1 error rate for pol is', error1_pol)\n",
    "error2_pol = (((y_test == 2) * (pred_wrong_pol)).sum() /\n",
    "               (y_test == 2).sum())\n",
    "print('j=2 error rate for pol is', error2_pol)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Higher order SVM\n",
    "SVM can also be used to classify data with more than two categories $K>2$. This is an SVM ensemble method.\n",
    "\n",
    "The first approach is a *one-versus-one* or *all-pairs* ensemble. This approach estimates a binary SVM on all pairs of categories ${K \\choose 2}$ and then use a majority vote classification rule as the prediction rule.\n",
    "\n",
    "A second approach is a *one-versus-all* ensemble. In this method, one estimates $K$ binary SVM's where the dependent variable is one class versus the rest of the classes. Again, the prediction rule is a majority vote classification rule."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. When to use SVM versus Random Forest\n",
    "Cross-validation on test sets is the only sure way to compare the accuracy of two prediction models. However, the following are some \"rules of thumb\" that can hold in general.\n",
    "\n",
    "Random forest positives.\n",
    "* Random forests are usually better suited for $K>2$ categorical dependent variable problems.\n",
    "* Random forests are work well when the feature variables include a mixture of categorical and continuous features.\n",
    "* Random forests scale well with number of observations\n",
    "\n",
    "Random forest negatives.\n",
    "* Random forests do not scale well with number of features.\n",
    "\n",
    "SVM positives\n",
    "* SVM is often best for binary classification.\n",
    "* SVM scales well with the number of features.\n",
    "* SVM is not influenced by more predictable points.\n",
    "\n",
    "SVM negatives\n",
    "* SVM does not scale well for large $N>100,000$.\n",
    "* SVM can be heavily influenced by outliers and points within the margin (support vectors)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References\n",
    "* James, Gareth, Daniela Witten, Trevor Hastie, and Robert Tibshirani, [*An Introduction to Statistical Learning with Applications in R*](http://link.springer.com.proxy.uchicago.edu/book/10.1007%2F978-1-4614-7138-7), New York, Springer (2013).\n",
    "* Geron, Aurelien, *Hands-On Machine Learning with Scikit-Learn & TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems*, O'Reilly (2017)."
   ]
  }
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