{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using SVM Seperating Plane Distance as a Feature\n",
    "\n",
    "Support Vector Machines (SVM) are one of my favorite machine learning algorithms. I have decided to make a set of blog posts to explore tricks for dealing with SVMs. Usually SVMs are employed as black box binary classifiers. In this post we are going to explore using the underlying SVMs representation to generate features to use as input for further calculation (for example as an input to other classifiers).\n",
    "\n",
    "<!-- TEASER_END -->\n",
    "\n",
    "\n",
    "## What is a Support Vector Machine (SVM)?\n",
    "\n",
    "Like many machine learning algorithms a support vector machine classifier may be viewed as a combination of some sort of non-linear feature transform followed by the application of a linear seperator. For example in the case of a neural network one may view all layers up to but excluding the output layer as a feature transform and the weights in the output layer as the coefficients of hyperplanes that seperate the target classes in the space of transformed features. \n",
    "\n",
    "In the case of neural networks the feature transform is learned from the data, can be carried out explicitly, and usually involves a dimensionality reduction. Support vector machines lie at the opposite end of this spectrum. For SVM's the feature transform is determined entirely a-priori instead of being learned, the feature transform is implicit and often infeasible to calculate explicitly, and most importantly the feature transform usually implies a drammatic <i> increase </i> in the number of features.\n",
    "\n",
    "Support vector machines can get away with this explosion of feature dimensionality because they utilize something called the kernel trick. The kernel trick is to learn a representation for your decision function whose coefficients represent weights for training examples which correspond to a seperating hyperplane in your high dimensional feature space. \n",
    "\n",
    "https://en.wikipedia.org/wiki/Kernel_method\n",
    "\n",
    "## Signed Orthogonal Distance as a Feature\n",
    "\n",
    "To apply an SVM classifier to a given data point we first determine the signed orthogonal distance of that point to our learned class separating hyperplane. To do this we take a dot product in the implicit feature space between the normal vector of the separating hyper plane (the normal vector of a plane is the vector perpendicular to the plane) and the test point. If the plane is zero-centered this dot product is equal to the orthogonal distance to the hyper plane multiplied by +1 for points on the side that the normal points towards side and -1 for points on the other. If the plane does not go through zero then this dot product is this distance plus some constant bias.\n",
    "\n",
    "Instead of simply taking the sign of this dot product as our classification it can often be helpful to treat the SVM as a feature extraction step and use the distance to the learned hyperplane as an additional feature which we can then apply other algorithms to. In particular we can pass this to simple probabilistic models such as GaussianNB to turn the results into a probability. This is especially useful when the metric we are trying to optimize (e.g. area under the ROC curve) differs from the hinge loss that is used to fit the SVM.   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import scipy\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "import sklearn\n",
    "from sklearn.datasets import load_digits\n",
    "from sklearn.svm import LinearSVC, SVC\n",
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n",
    "import sklearn.naive_bayes\n",
    "import sklearn.ensemble"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plt.rcParams.update(\n",
    "    {\n",
    "        \"font.size\":16,\n",
    "        \"image.cmap\":\"afmhot\",\n",
    "        \"image.interpolation\":\"nearest\",\n",
    "        \"figure.figsize\":(12, 5),\n",
    "    }\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Digits Example\n",
    "\n",
    "We go to a hand written digits dataset as an easy example. We use the built in sklearn digits data instead of MNIST to keep the examples fast to run. This dataset turns out to be too small to really explore this technique but it is still an interesting example.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "digits_ds = load_digits()\n",
    "\n",
    "input_features = digits_ds[\"data\"]\n",
    "labels = digits_ds[\"target\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "n_train = 1000\n",
    "\n",
    "train = input_features[:n_train]\n",
    "train_labels = labels[:n_train]\n",
    "\n",
    "test = input_features[n_train:]\n",
    "test_labels = labels[n_train:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We begin with the LinearSVC classifier. The LinearSVC classifier just finds a maximum margin separating hyperplane in the original feature space with no implicit feature transform involved. This means that the separating hyper-planes can be interpreted directly as projection vectors just like the principal vectors in Principal Component Analysis (PCA) or more directly the discriminant vectors in Linear Discriminant Analysis (LDA). We can access these vectors as the .coef_ attributes of the trained classifier and even get the dot products simply via the usual np.dot function.\n",
    "\n",
    "Since hyper-planes just have two sides to them we need to choose some way to adapt SVM to handle multi-class classification. The LinearSVC implementation in sklearn uses a \"one-vs-rest\" voting scheme building one classifier to distinguish each class from all examples of any other class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearSVC(C=1.0, class_weight=None, dual=True, fit_intercept=True,\n",
       "     intercept_scaling=1, loss='squared_hinge', max_iter=1000,\n",
       "     multi_class='ovr', penalty='l2', random_state=None, tol=0.0001,\n",
       "     verbose=0)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lsvc = LinearSVC(C=1.0)\n",
    "lsvc.fit(train, train_labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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VmvopRsSkiHhPRHwKuLLIAMzM+qKiekKknsk9lQQEEBFzgDuBfRuE8W/AElJvpdJ2GfBr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\nZmalcRIyM7PSOAmZmVlp/j/DvhPiNPIIyQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7b1eb432e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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NRla5NTOzTHc0fjSLkpMkzZO0RNJsSQfnvPZ0SXdLWiRpsaS/SPqqpLXyXO+a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\n3Jw0zMwst/8Prq6OCsqvP+AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7b1eb1e588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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GAvc1uUQXsJeklXPzQpuQFiw8VFdvJUnrR8QjuXpRd53a3M8mvDUJ1eaCmsXT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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7b1ea58400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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V2cysBE/o53NyMTMrwT2XfE4uZmYluOeSz8nFzKyELj/OlMuvOTYzK6HKl4Up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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7b1ea2dd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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718rRakvo28CStLAEuJnZUOCWUDmaJiFJq5I2Q/ocsKSkJXl7UsISkt4HvBoR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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7b1c7d0c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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zswI8oJ/PycXMrAC3XPI5uZiZFeCWSz7vRGlmVkBftH60i5JJkhZLWilpnqQj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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7b1e8c0f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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N8RnAryR9h9TNtSfweeD82jUuku4mTUt+hNTaORj4JHBdRExvFqeTi5lZAV3V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\nZqVzcjEzs9L9fzJuuGu4naFOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7b1c6d7160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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AgXz5F0lHAPsAX4iIJ/riHE4uZmZFtDDmctvjT3P74083qzaHxi2U3lo0S0TSV4DjgSMj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\nToqlDBXfz6XjdXhy6ZxLbT/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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7b1c70a3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9gIMj4qysbAYwFzge2CMrGwP8M/CZiPhltvsMSQH8RNKYiLivVW8ImugWi4iuiBhRY3Ni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\ndrBjqRHbtOzf6fhBPu+22Xm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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7b1c665160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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UcpG0KnAq8N0sKDOzfqmVy7nkcATwGumX/JrAo8BeEXFNRb0BVPRQRcQ1kvYE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\nLefkYmZmLefkYmZmLff/A4cdonDbd89XAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7b1c7d2d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(10):\n",
    "    plt.title(\"{} separator\".format(i))\n",
    "    plt.imshow(lsvc.coef_[i].reshape((8,8)), cmap=\"coolwarm\")\n",
    "    plt.colorbar()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is some clear correlation with the structure of the digits that they are supposed to be separating out for example the zero separator has high values in a zero shape and negative values in the hole area, the 2 separator has structures which would have high values for a diagonal slash going from right to left but low values for an opposite diagonal slash. It is difficult to see exactly why most of the separators work but if we look at the distribution of classification margins it is clear that they are doing a pretty good job. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#get the hyperplane distances for the SVC\n",
    "test_trans = np.dot(test, lsvc.coef_.transpose()) + lsvc.intercept_\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       ..., \n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.],\n",
       "       [ 0.,  0.,  0., ...,  0.,  0.,  0.]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#verify that this is the value used as the decision function\n",
    "test_trans - lsvc.decision_function(test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f7b1ea07630>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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HVY9AVzdiHa2ssWXlJeneB8YB/YEqi+n09PTyx2lpaaSlpflnKiIiIiJSjYyMDDIyMmr1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\nsWTJ/we2Sw8DGm55uAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7b1ea7f160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "\n",
    "hist_kwargs = dict(range=(-15, 8), bins=51, histtype=\"step\", normed=True, lw=3.0, alpha=0.8)\n",
    "\n",
    "for i in range(10):\n",
    "    label_mask = test_labels == i\n",
    "    h1 = ax.hist(test_trans[label_mask, i], color=\"r\", **hist_kwargs)\n",
    "    h2 = ax.hist(test_trans[np.logical_not(label_mask), i], color=\"b\", **hist_kwargs)\n",
    "\n",
    "h1[2][0].set_label(\"target digit\") \n",
    "h2[2][0].set_label(\"other digits\")\n",
    "plt.legend(loc=2)\n",
    "\n",
    "plt.xlabel(\"Signed Distance From Hyperplane\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f7b1c813e48>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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/0ahzDWAqcKqqTi0pyNIVsad7BC7pTtcJrNi/qn9zkQ9s2dR1BCtCO6vkqNXQ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7b1c8049b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "argidxs = np.argsort(test_labels)\n",
    "plt.imshow(test_trans[argidxs], aspect='auto', cmap=\"coolwarm\", vmax=5.0, vmin=-5)\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label(\"classification margin\")\n",
    "plt.xlabel(\"separator feature\")\n",
    "plt.ylabel(\"label sorted image number\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are a few oddballs in each category which end up on the wrong side of each hyperplane but each one-vs-rest classifier seems to do a pretty good job."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "74 misclassified test cases\n",
      "test error rate = 0.093\n"
     ]
    }
   ],
   "source": [
    "test_predictions = np.argmax(test_trans, axis=1)\n",
    "n_err = np.sum(test_labels != test_predictions)\n",
    "print(\"{} misclassified test cases\".format(n_err))\n",
    "print(\"test error rate = {:4.3f}\".format(n_err/len(test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The test error rate of the pure linear SVM isn't great but considering that this amounts to a single matrix multiplication and sorting of the output it is pretty good. Can we do any better by using the individual classifier margins as input features into a different classifier? Effectively treating the SVC as a dimensionality reducer? From the histograms above it is clear that in this 10 dimensional space our data looks somewhat similar to 10 different bumps each one centered on a vector with one positive mean and negative means in the other dimensions. Lets try Gaussian Naive Bayes and see what happens."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "63 misclassified test cases\n",
      "test error rate = 0.079\n"
     ]
    }
   ],
   "source": [
    "train_trans = lsvc.decision_function(train)\n",
    "\n",
    "gnb = sklearn.naive_bayes.GaussianNB().fit(train_trans, train_labels)\n",
    "\n",
    "gnb_pred = gnb.predict(test_trans)\n",
    "\n",
    "n_err_gnb = np.sum(test_labels != gnb_pred)\n",
    "print(\"{} misclassified test cases\".format(n_err_gnb))\n",
    "print(\"test error rate = {:4.3f}\".format(n_err_gnb/len(test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We do see an improvement over the LinearSVC by itself but Naive Bayes would have no trouble working in the full dimensional space. What error rate would GaussianNB achieve all on its own?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "165 misclassified test cases\n",
      "test error rate = 0.207\n"
     ]
    }
   ],
   "source": [
    "gnb_raw = sklearn.naive_bayes.GaussianNB().fit(train, train_labels)\n",
    "gnb_pred_raw = gnb_raw.predict(test)\n",
    "n_err_gnb_raw = np.sum(test_labels != gnb_pred_raw)\n",
    "print(\"{} misclassified test cases\".format(n_err_gnb_raw))\n",
    "print(\"test error rate = {:4.3f}\".format(n_err_gnb_raw/len(test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Without the LinearSVC acting as a dimensionality reduction layer the naive bayes has a test error of nearly 20% for this dataset. \n",
    "\n",
    "It is nice that naive bayes works well with the linear SVC as a dimensionality reducer but we know from experience that using a kernelized SVC on this data set can do better by itself. Lets see if we can get improved performance using the usual non-linear SVC implementation with the rbf kernel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,\n",
       "  decision_function_shape='ovo', degree=3, gamma=0.003, kernel='rbf',\n",
       "  max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
       "  tol=0.001, verbose=False)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svc = SVC(kernel=\"rbf\", gamma=0.003, decision_function_shape=\"ovo\")\n",
    "svc.fit(train, train_labels)\n",
    "svc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "35 misclassified test cases\n",
      "test error rate = 0.044\n"
     ]
    }
   ],
   "source": [
    "test_pred_nl = svc.predict(test)\n",
    "n_err_nl = np.sum(test_labels != test_pred_nl)\n",
    "print(\"{} misclassified test cases\".format(n_err_nl))\n",
    "print(\"test error rate = {:4.3f}\".format(n_err_nl/len(test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The SVC classifier by itself does a really good job here. One important thing to note here is that actually a good bit of the performance improvement of the SVC implementation over the LinearSVC implementation is due to the use of an one-vs-one multi-class voting scheme rather than from the use of the SVM algorithm itself. Looking at the classification margins we can see that we train classifiers for every pair of categories. This makes for very interesting decision function structure but the high correlation between the values makes GaussianNB behave poorly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f7b1eacfa58>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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b3jvRzX8IRkwpTjmcRf93QMeX8nyJzrEk5RosgWsgSn9QOf0oti5M1di4jI2N\nhUFIgaJRx+NWpNfZl6QdNaa1f2STlbzuA+9Kks44Apb4rqc/cNNo9dGHseDFWJmNnWNXMXWb7RV2\nCCpvSJu71l1IQ714/LpVevy6Vb/9+wdvDHODa2Z/Lellkv6Xu38nyC8JhNS7jpk9WtI7lOjhjUh6\nrLvfaGbvlXStu38D/u7P6sFt1ZWcNCTpGklPcHc3s6crKWH9IUkFST+SdEEbSZGLJb1H0rtbbbtJ\n0u+5+03zNaBYJBGJsAliodFNxA6qxuajrCS101MEBOV9NauwCAfMzjdYya9RYhsuQTfxHPcHlNoR\ndqRx5y4k6HcNTZMJDcwn77Kxj3m4ATnWeJ7Q8uGBv+tCH8uHGmb2Nkl/LunV7v6ZQ90eilSOspn9\njqSrJd0l6TNKSkRPo6lEUBo5yu77HqnuPqrkBPKyfdhVlJSvfiNpw7rD00cwylCSspBjS0MpMPWC\nJEfQ4ie0bwZZ4EjFR56P7HNlFhWs9rFrO4PKAoUxpnrR6GNR3Kmh1ci+UEofyeoXk2Mri0VYqdZu\nrsyu5/uy7NAxDuXkVuVZVHBrmUUdiRKBJDm97QDrwlSVcY5X9LG+p9SLfIXN8wFYjGUKqmSsiNn1\ndbZMS3wz+wpU7ViWSx9B31Fh1AtK51s5xNYFyodf0cfWtZVNtoZ3C7qBo2xmr1USxPwLd//IoW7P\n/iBtRPmvJX1TSTnorB7qKN8o6X91uF1dh35IvaBRU1rymsrPERkrmohIS1JDCrHiCrtWoxWvIqiq\n0W3IVaCOMqCmTDhz2rNQkqraZJt5LYaSYNDxpdhVZQ7DSI69Kxr5yjpzpiIgqzVSYDcRJDlMkqaa\n7F0NwCIQk1nGP282WN/vqLND0ICxQxYtyFKIWARjvB5OZnIA7p+lGvuuy/vZ2CzXmWO9M16D7LsF\nnVS92Bdd1sw2KAmmvsvdr2j9zAslfUDS1yV938zOmvHIcXdvWwyu25B2ND5G0nNbdIjZXtROSSxr\noEvQDKjJRp3NkLrIoYHLdUNHmUZwiSMoSc0orJi8wS9sDRZFjOqMl0oOElSLtQydI4rQV6AhlQIk\nqQYPBhQNg6oXQFWDXm9TRZAhqCVP5zl9txFMpKw32DpCD/QUGUh4aHi4sZmB+2ET3mrSA3qFHtAD\nz9tg6OwYm5cuq8R5nv5vGr/X+v9TWv/NxPTPdT3SrmRlSXMx/Q+TtGCyF2figfvTn0LXrmCRLFrb\nfmyKDWhSq5+HAAAgAElEQVRaDY9QL+g12ThUdVoCg3zZW29gPwBP0dHyVfs2mgEfY5GgZol1UHYJ\ni3xlaaVAgOixxyP7iRprO42wZiD/vNJkzstohSmIrOlnCV/bS4zmM5yDfHK4LxYb6ReSXSXWN6sG\n2LsdabJchL4iS1Yrx0PMXmyRXWdMScFgoKbYZP2/p8oW2pWF9Nv45imWDDdeZDk+q4YZ9YIeWFdC\nytRIjUl2dgs6Sb3YF13W3TdpVjKXu18i6ZKONeIQIe3o+qGkS83sizM+m57lL5X03Y626iBhdHd6\nB6YJs/MpqOObCZjkE8G8RSoyQds+9RsmwWXwC9i9sNw8TRakyX+wPQ65LNm+9IMt+1gWVVuaYzSZ\n2JiTb86+K5YcM3b9nDe2oQ/lWPQ/yrCxRovt5EFlPhrlo7cRUxlGpcj1sXdbybA1fHeJtSffx8bC\nMJS3y8G5UoNawaTASiFibW86O7BGMAJdhBzlOoxkRQ32brsF3VhwZCEi7Wh5h6T/UaIm8TklTvIf\nm9nfSTpd0plhmtc9yMGSl3SiUxYIVTSrAb5dlGWN2TPGNvMVI2Hl2CiiPkayrk/BKB90rDNQxSK3\nApa83p0+Ckp5kSRCKUkFmJVazLGIbAMWQLntfjYWVh/HNmiaYEULO5QiFkUkdIq7tzLHa80QLOoA\nywTXI/aucs6cna3jbCxvKDBOcCViEeKM2MHj3h1sbK4DQ6cP8p8niuy7Flay59+xla0La/rZujOw\n9XZk3y3ohmS+hwPSFhy5yczOU6Jf/DYlF3yvlvQDSee7e+DSaWFQ6E+/kFRrgZ016JxSxzrOpnfW\nKvC7wkJ1OCDbdzhLpPAKlOGAp+5cAeocQ45yJmbOXXYZLDMNvm80d72etlgaMxYW5b0OluF1e55t\n0EtgPlMeqnYMwXdLOdn9TRbRH/f0dIQBeKmWhZzgkrNfMNBktJdRY4mXNVgdbkps8Kyopy/wIUmj\nETsQ5yGtlsjhjVXYu6pCdhjV4F4ywDZEehPULIRNCg6FXkS5M0i9arv7jZKeaGYFScskjc4oI70g\n0deffiVpwg09JDVifzBeTv9dqbRdNkvLjSJz7ghWYHIbTbaDJaPxSQJyjm2YRVMi8H0zkOqAdX/h\nWBgrMD55vzOebByx9mdhlI86vvQgsTvD8qr7MmyuhAT9rntiJos4YEzdJsqydYdQFyRpNGZjmbef\nqXBkQfLfun7G2R1buRbZE760JN23i40FyvfGV7hdgl5EuTPAKeruXjaz2kJ3kiXGUc4YiyJSeTiq\nXUwxlE/vfO2eYqf5fI5u/qxzJm/ZiOwpdYEi9OLThGWao/6t8Pnpx0LjbKjqALmI9Dp5aZV91/E8\ncxwHC6w9DViIqAHl3qjztVQsIW53M70zNTIIVSlg2ymneVkVRmRzzJlaOsAOrFTneAlMEKOO9VAf\nlBcCoJXtJops3O8eYPzwZYPsu8aAmy9J1QF2G9Et6DnKnQGpzHe+pMslPVZSzsyqkn4i6S9bJacX\nHMrF9Ff01JGlzuBCRkiZPUmq7GHXydkcc5RpJT98nQUXqwas4JKFnGmS/Ecz86njSyW7eHtgMhwc\nyvT5lI5AEVIyDfcN/K442h44yldvLswo4jRCVgqkhyAaOKJoBH5+Bkp2dg161IuOIG1lvudLukrS\n7Up4ytskrZF0kaTvmtkL3f1zwVoZCCecnP6ETnWRaeU8ytul9IUqyICm1+cgQDn9G5D18uc8mz0e\nLmrNPsYttDosSV2GyX8xi8oWVx2N7Pu335XadgscaJUmu42g1IVSjkWaaMR3ogQjxEuYPU3mo/qw\npZiNZQcBgMkSW9QaQKNZkgrGaCD1LBtrsbF5Ww+s5VulyXzw4FGssvdl4NBXiNgaG0P2GS2WMlVm\nnGlcyKeyMC/QLbBW92JB2ojy5ZK+KunZ7g+GLMzsnZK+pKQ84YJzlLduSc/5Ou4IpsFJnU3KjaTR\nnVw2/SI+CZUC6nUYFYSTt3bLjUGfH/rU3ayyRT+TY45yYdOdyL5eTO+4+5HnoGdTZ4FSC3IN5kwV\njc3bIiwl34SOOKmEtz+gyg6Tnt6xrsADMY1oUoWVqAGVFzLs+nx8ir3b2gibt4N1puU7GbNchFLA\nsVyCle12s2rjKi+Hcm9wWtFDR6bWPVz+Hg4+0q5MR0l6/UwnWZLcvWlmH5b0+Y637CBgaDh9RCI0\nk4JW5qMR7pAR5UxgHlRu/Xpk77QAR4YKR8PBQIWm4ZVyfT0rChLdl17qiCbz0UhNBKN8oSW1aKEg\n+vx6k421HKwOVxaLrJErdHpLhoMFcCzUYEQ5gjrE/QU2b2n7S7AACkXIYCKVhxsZYvO2P2YHvizU\nyKbwbNiKo6HQU73oDNK+/Ts0d5nqlZJYSKtLQCKhU2W26uTjsI4vdazHiuknOlW9qLO9XFjqoMAW\nQd/JOM1Gk/+gioX1sw2xuZsl+VBeKlEF6a8yCa5MTFUg2EJegdXSaMLUUD/Lzh9qsKjgGIxw04pj\n1SaLOg7F6W/VqOoi1oCGRZ0mxPpyROxdFcuwUBAcy5NNWMUyw9pP4xc5IJk2kGEh4u3DjBK0PGJJ\nqZMl1pd1OK8yFUif6xL0kvk6g7Sj5W2SPmhmt7r79dMfmtlZkt4l6TUB2hYc5Ip+yQClF9BkB7bI\nUqoGyeCeKMNFBDr5NNLhu3ey59NTNOQEq8Y8Buz45likLFNhslEkYk1VIyYazHmJoFLAsDHZqJ0x\nc3y37WGHoN1LmRJBswYj7pCqMRKx/qHvi4Am51Ft2+XNbch+SuwQQddYejBYZmxdmxLj59cgHYEo\n1uysM9WL+3awPWV5H5Q5ZEumclD1YqHKw/WS+TqDOUevmc1WsihIus7M7lOSzLda0npJ2yX9uaSv\nhGpkKJz1qPQLw9XXsBP0+eewRTkfM0eciuHnovSrZjbDFrX1a5hzQflkr9/8SmT/8mezvsxlaJIP\n659VzmSsxqD+6USdXWvGa9O/gKO/eAV69qrA5b1p1isVdXohtNfNzHz7c16P7OvObjuGK+xQlsmn\n789zj2OHmhhW2qMR5WFnxWdolcajl7NDx2SDRU2X1LYj+wq8WXv0OhaVrYH+qUEK0boVbCyMV9nN\n0Qmr2f5cghVE791wLrLvFvQiyp3BfDOjKT3kiPzr1n/TuLv134IFoZquPgxmk1MaK0x8oQVQQqIB\nfSNahfC449mhQ/CKlSaU0UgZlTQj2efSfmRwAy5l7qRT0bND87E1yZwXDcCIKS0OA4vVUIQeawRU\nxQJXP4PUhdDg3xcWCqJSflTqEI6dHOJYs0p1VEGkDybb0TUwA99VTmwsdwtsoUbCuwxzOsrufsFB\nbMchAUlOGR5iiyZ1ZI1m4VJhB2beVVi9nH3ZagNmz8PIF92AmnCxqsEoIo3u1EHkqLLqCPTsbBVy\n+WAiZQRpMo1+dl3djFmkyZrMUaYlwSmdP9tkzyfJmlTRhCughNWYDl0VkTprVAeaSh1SHeiqpZ9b\nofsSr7HImsMXqsxaL6LcESzMVM4OgYigT0yxRX/9araohRSHl8IuJDwbntnvZAFinbqGSflQbmFo\ne1qUIp+FFcSAA1PYzPJ0HUrbUdgUK0mdhXzybOCNpbTsUcieqmRUYxbpqyo9ubPWZAe4ElTgCA06\nD+MsO0DTgwEFbT9VTCGVEXlfhq3qGAeWXaQykN2CnupFZ0Aq80WSHqeEl7xX2MXdP9HBdh0UkD1x\noD/sRKHJfzTUFHK6hC7XvYSxXvaDikCVGkJHR6D+LLwiboAr3wZMVqNRMqcRZWjfLDDHsZljfG/B\niDKVkxPcoLECSkDQcR8aeB5SHWg4Dyn4OgJlJkH7Q0eUaan30BHrbhvLabGYOcpmdrSkF0jaoL19\nVnf3l6Z9VtrKfI+R9F+S1qm9h+aSFpyjTBy8ajU0bxSZBwXlHNegPFw+Zp71GBTOp6ARXOJoSlIG\n2tOxU6qzSN9AlJ4ekSkxqT3BRFCnUnuwymEGO+6s/dkyUxzBhQ7gXZBR3WvgiFOpuv4se1dlh9IF\nECRZTZKKsKhGIQ/18yBoMiJt/7Jceh4upXWUodpLX45tKpR+NhizSnv9dVgxpVuwSDnKZvZsSf+p\nJEa4XdqLZI6ckLQz76OSJiU9W0lCX9gV4SCBKEfkcsxZowlrTRhlpWiAEzdtex7KEFMsH2btGcyy\n63mcMEXl8GDC12CGOadeCCfD1exjyXA0Qkwj0LQvGzSiHDNnjX5fWuKb8MklXhaZgDr5lSZz1Oh1\nO+X+0+TCgYgtbLj98FBGC5oMRuGqyfXBEtaDBTZP4gwbaxG0xzSiKGxxmFBYxBHld0v6vqQ/cncm\nBdQGaWfqSZJe4O5fO9Bf2E0YLKTfdI9dB6+OoOObg/JwtBpeDvDtIriA52CEmOKEFUzmaE+dic/n\noTwcpjpk2KJcdObclRvMIakofXtKK5ksEu1Lct0rSSuXQKm9mEntTTVZ31PnaDDDDnFYeQFqaleB\n5Fg/jP5zqgNULoA3NbS4TRbS4ajzRaP/oa//y+AQRyPKlMZSqrM9qAArBdIIdDnDkny7BouXo3y0\npDd0wkmW0jvKt4vqwcwBM7tI0h9JOl3SCkn3SvqCpPe6++QMuxFJfyvpWZL6JP1Y0uvc/ZeznpeX\ndEXrmSOSfiHpze7+g321ZbKcfrJ85xqm2fnkC5kgexU61lSLmCwMtQabXLRqYV+ObUAf/jxrzxue\nzyKyNFJGtW1jUAlPkvoANUKSKsailCTivuLf34OenYmgM0V1lyFWwY0idHu2/sFfIntKF6hH4SLW\nk1CvezBi19sUoZUIKg1IaYqh4gtcw+mhjFJlBsG6UwQKGZJUg5Vk+2JGvaDvagi+qyGHspQ9HGr8\nWtLyTj0s7Ux6q6S/MbOfuPu9B/g73yDpfklvaf3/UZIuk3SBpMfPsPuKEhL2qySNttrwPTM7zf0h\nFRw+Iempkt6oRNf51ZK+aWZnu/u85QBIqeYnXcAcXwpa3S4DT+gkOkITC0NTL17+XOi4w6hgDDU1\naZSPOi8VZ9ELmvxH+qf5IubY0eth2pfLyiyiPNHHIso0mp+FHOKIau1SxZQGVPkAhYgIt31/QNcd\no1nEEFRNhkbEKWhyHlW9IIcyXEkW0vloxHowZsEI2v5iZoFSLxaqrN2B402Srmz5rHcd6MNSzQx3\n/4aZXSDpDjO7XXtXdHB3Pz/l73yGu8+8S7/WzPZI+qSZXeDu3zezZylR2LjQ3a+VJDO7Tokj/CZJ\nl7Y+O03SiyRd7O6fan12raSNki5XwqmeE3Vwyv3Fr9gGdNojID8PjmfSdolxlLF+KA3CQdrIN29k\ni9QzTmd6cjSZj25YdEPPwrLOtGAKSRA76ubPomc7LcBBBz5M5huEcnUGeakU950275K0F0JftxNH\nPLTMIa14GTqiTNZMiUvW0uIwoXWmyfPpWAhYB0cSd3xx3QKsVtMlWLzUi3cpiSjfamZ3SJpNCSA+\na2rVi7cocVB3SBoXvjR6ELOc5Glcr0RN4/DW358pafO0k9z6uXEz+7ISKsalrY9/X0li4X/OsGuY\n2VWS3mxmsfvcCv/5KP3sPeUEFhWkJalpNMXhyhOBhSGC0e0Y9KPEF83zH8miBdS5oDxZuqHjgiOA\nQyzxDZ1QR7Y+8mno2aSAhSTVIX97ZOIBZF/sZ7dv5SyLKNOxhm8joL0b5M8D1Qvadlo4B+uTB/a+\nKEeZvqvQoJQy+r4I6JmG5vjQ70o505XAiiyhsIiT+RqSbuvUw9Lu+JdK+r+SXu0Od8J0uECJXMev\nWn8/WdIv29htlPQSM+t396KSJMO73X22J7VRUk7SsZJuneuXkrKa1/+cJeGc9Ri24ebgGkU5yuTE\n3YD7D41u00Xzi9ewH/iDJ9IM63AFOyQpA0Pu9Dqfgojzr7z239CzvQapBTDi0aywm50RKj8HOdZ0\nMG+98BL2+MDUi9hBOXN4qKFtJ8lkBwP0AEod69AIrSdPQM80lIqIvytUyYhh9dauwSKVh+t0Zem0\njnK/pM+GcJLN7HAlHOVvu/vPWx8vU0KzmI3p8PlSScWWXbt79mm7eYnFVSAPt3Q5441SJQi6kNAT\ncUjXi+ouUx3lI45gSURLop3IHovVQ+eIZrdTnm+cYQ5GIZNeJiu76jD0bKfUBRjxyE4yPVPvgznI\n0LGm1XaKTTaWq1BibSDHqvOUlb494zXWl4UsG8e4CASdh3AVpO2J4IGbgh48KIh8nlnYqou0kh91\nlPMwVyAHpQW7Bh2MKJvZOklXSnqSEgbA1ZIudff7UvzseiWiCxdIWinpPiVMgL9qBT27Gmkd5a8r\n4Qx/t5O/3MwGJH1RCX3iTzr57DTIAcoALW1LNJolTl/I0uQ/YEuvvaijTEHn+mSDOQvEcZQ4R5le\nh5dhMt94lTlf2Xx6xx2XpIa6wjjiQR1xKmkGdZetwjjTfRlmn4OHplyF7TlRIf1coWWC6XctNZnz\nRakXlFpAlRTwwQA6+rT9pQY7QEcg+a8B5dUqdVhwBE5zugXR6HmuETaRNRSsQxFlS05G35NUkvSS\n1sfvkfRdM3uku8/ZQWbWL+k7SsqMvk2Jk3ymkjyyY5XkmXWijedJutHdJ1t/nhczqb37QlpH+Uol\nyXaS9A21ieLSzEIzKyhRtjhS0nmzlCz2KIkaz8ayGf8+/f8N89jNq+l21ccv++2fT3nM+Trl9Avm\ntB0bozVWmLNDI8qhkyNCgrZ9+052+vdjwpZLpVxNuiHSCDflt5PoS3MTSxjODMJ64xDNMuOrWw5e\n59dhVBA67n40vQnqLt4rwUIvE0x5r3jewoWQJ1N2TwIaDXbQsUDdQZxbMA/t6Lqf/ETX/eSnsAUH\nCZ2LKL9Cia92vLvfLUlmdoukOyT9qRIfcS6cI+kYSb/n7le3PrvGzJZLeoOZFdrQZ/cH35d0tqSf\ntv4814Sx1r+lXlzTOsr/0/r/u5WcAtoh9S81s0jS5yU9RtKT3P1Xs0w2SvrdNj96kqR7Z4TqN0p6\ndpuOPllJlPrO+drxwpe/M22TddpJLNpBI750kaUIGfTNsdw2zFF+yplsDuENLvAGHdphoJEs4lhv\ne8LF7Nlw828YGzxLp1gy33j/amRfFXOsQ8vh0QSxJozok/ZQx4s6+aGpBfRA2Qfl4ei6ExpU3o6q\n5xDkIpjcDttCvyt9fm0e3ejTzz5Xp5/9YGGmD/7DP6JnhwTNAZkHz5R03bSTLEnufo+Z/Y8SgYX5\nHOXpzpstRj2m5IzTqQ34Qj2Y53Zhh54pKb2j/CeCtbHngiVh6c8o4ao83d2vb2P2JUkXm9m504VD\nzGxYycv69Ay7LyvhNz9f0r+27LKSXiDpm/MpXkiMXnjTr9jVy8knMMd6sC8sJ4tY00NoFec5sF/w\njetZdP6Jp0Nt3jzjvdKZQBflCDok9IqYJB2t/dXX0bN9kiW9KoaSYFOs8lwf3CiMUk3g1ebuRz8F\n2VezbB0plEeR/RBI0MtES9CzSaKgJJW8Y/UBOoISnFcUVCGGHlTqDTa3DAR36KGjCqkXWXjgC/2u\nBjJs3ekadE5C8WRJ/93m842SLtrHz16tJPL8PjN7pZIic2dJeq2kj8xH2yBw92va/bkTSKuj/MkO\n/s4PK+nYKySVzOysGf92v7s/oMRRvk7Sp83sTUoKjvxFy+b9M9r1CzP7DyXC0jklCYCvVHJFsE/e\nS38u/cJDI8oDBZhVC5MXIijgTkpY5+B1cj6GQviQj33Oacx+IGKcYxrNp3qmuJQvlrej1JH0z999\n4j6pXg8BVV1oQiWFgcltyL7c147BNTfGCyuRfaHBNtBSllFTaAS6kh9G9qUovUb5nhpzlOlNB3UE\nQ98EUR5uAxb4aGSYI4vHAnQeqfNLELg2TPB3RRNBuwadiyjPJ5ww7yLr7hUzO1cJi2Dj9MeS/snd\nX9OpBoYEvDTvCJ6ipJPe1vpvJi6TdLm7u5k9XUkJ6w8pIfz+SNIFLUd6Ji5WQip/t5IS1jcp4cLc\ntK+GlGvpJ9fWXWymH8nEAtSAlYhosmC1L/2rLlVZW6hUHY1YbxtlUb7Va1m5Ue7IwigljCjTDZEm\nWRH7JdvvQM9uwiqENPkvGt+B7K0Bs9sr7HYhW2XBkPEVpyN7WsI6ZOIo1jmG9nReZZrQsYYLD73O\np5XwMnDhpOsUb3/6g03Dw1IRM5QmA4MjtG8cs6C7BCkiytfeerd+8Ot7AjbB8koULlZJ+iMlyXyP\nlfROM2u4+ysD/M75hCeaSmgfN0j6Z3ffZ/QlbcGRT+zDxN39pWme5e5HpbQblfSy1n/z2VWUlK9+\nY5rnzgQ5Qa8YoY4sawuVk6M3KuS70mh1Fq4hVNpu7VLGUS43mGPdlw0bgeaJKbQsMiwsAKIv29ec\nhp5dqLMIKy04MhSxd1vqZyWsKxFTEDFnfZ83NpazMJYRNdhYHojTU2Uy8CYo9AHRIe2FVgqknGPa\nfgoacaf2tWb6uUg1o7Nwv6J7BF1jq+C7SlLVukvjOy3ScJTPP/kYnX/yMb/9+3u/+P12ZvMJLOyr\nFO7LJJ0n6dgZHOcfmtm4pP9rZh9x91v22VAGk3S8pMOUMA22SVot6ShJW1p/f5qk15nZ+W3y5B6C\ntKvwE7Q3M3OZpCEltAhGjFuAmIBKf4WRMO3YXxDnjjqCNKIMaanaU2TO0VCuEwm0cwNfUWJzKBsF\nrx3zgOYzXGRUh2yd9T2lXsRTrDw5dWQjSF2gVJM9g+uQPQXO5gfJlFV4lZ+DusKhk/moug2twJml\nUUro6FNHvArbT26a8B4BJUcp45jm7ESwgEgEdZcfhtiohKc8GyfpwQS6uXCKpNGZiYAt/FSJQ/sI\nSZ12lP9OSYLhGe5+4/SHZna6kuj2ZUoiyt9Swkh4znwPS8tRPrLd5y2tuo8qCacvOBC94FtvZdf5\na85hG24TLiS4QAkzR6DFzOi12jU/ZlHKlz8DqkDADZpGfOnzaRWoQkSvWNPbR1d/Dj3boG4xvdBs\nwCqHNOs7dNyo8vQ3IHtcXj1iia/E+aLUCOqYhgZNkqXX80SHeH+AtX9he0j7abSdql5QOhltT7cp\nIwVD5yrzfUnS+83sSHe/R5LM7Egl0m9v2sfPbpU0YmZHz5IRPltJGIlJGaXDFZLeNdNJliR3v8HM\nLpN0hbufambvV0LxnRcHxFF292vN7AOS/kHS7xzIsw4FiLM5vhteKTeYo0wLjnROUeXAMQUDuEtg\nsbQdW9iFRd3ZL+jLsC+AF02sksEW8T1lRhc4rD99VHZy0xb07Aw8NTXhdUQ2z24XvAF5oNARpwhN\nvcg0mXNH5O2KdZYYuTo/gexpoaAmdALovN1TYfNqZR/jt1MpP4o9VbYOri6kX2fprdpEiX3XvmHm\n5I9VGGd6FXxXw1VW7bVr0Dkd5Y9LepWkL5rZO1qfXS5pk6SPTRuZ2QZJdylxUq9offxJSa+T9DUz\ne68S1YszJb1d0s/cfVp+uJM4XtJcCS07lBQ6kaTfSNrnROlEMt9dkh7dged0NU46jemx0igrRedU\nXw4ceXhPRqPhFzxxPbLPZbYi+9DRAqotTDEckGqy7PefwX6gcxGM9o8vMufLC2wD9ZjFlA064mPO\nns91lNlkrHn6gweNUJabLLpNo3yhC3YMxLTIVFjQdYqq/4S8AejLhz2A9sN3RfuyFLPAV7egU5X5\n3L1oZk+Q9AFJn9KDJaxfN6sEtc34b/pnN5nZ2ZLepUR0YYWShL6PSnpvRxq4N+6R9HIlBfJm4xWt\nf1erLbv29bADcpRbhUMulnT/gTznUIHwrO69h1Evjj+CSSlRdFNlPp5YyOx/8QvGS73gmLBXoEZV\nL6BeKnUYshloD55fvv469OwOCty3ReiIb+j2NzY8gdlTRxlujKQoCOWB4kI7gYsuUYRW+aD8eV6Z\nj9qHm1uhSTj0+aH58F2DzkWU5e73K6lZMZ/NJrUpPufuv5b0wo41Zt+4XIm88M1KZOm2K1HdeJ4S\nzvQftuyeJOkn+3pYWtWLdlIbOSXh7eWS/izNc7oN5PooQ6UdILppk6DXarRrqJMfw9J/dXpdHVjG\nikp2cV1n1n4SpaRUhw7qdrYHdZRDtweCvis6FzOUww1oPkSL/WCAR5TD8mS7jcfKKymGS/jO4Eq1\nyFxZ+K7oGj5fZb6uRuAbvm6Fu/+7me1UkrT3ViX5oTVJP5P05BmltF8vaZ+DJ61HkdHeTMsJSV+Q\ndJW7fz/lc7oKJJnvvMexq5fJErwmK0BnpxFuUSb9IkmTsK4O5Sj/72eyam/jNfYLluUYB5pKC1He\nKI0oj9fYFfeaQvoXtvEpl6FnL4tZX5aajBqxpnEvsh/PMXm4B0qs4MiaArvtGG7uRvaVLOPJ5qfY\nzddQX/qNtJJhtJERse+6tbkG2Tu8mqIltUNzlCOomJIVO6gU62xdWJFP/77ooWC8yPq+ADnKE1X4\nXQuMwrVgOcrdxNE8yHD3b0v6tiX8kxWSdro/9BrH3VPxFtOqXlxAG7kQkI/TOyTUebzuBpb8d+5Z\nbFGmOpPkGo6Kww+wNUpjU1D+DBZd+O8fstP/H17AvgDdgOpZ5mBUII81D6Mp906mdx6/8xPmtF/8\nRPauKvDQQaPzlC7QHzHnZXNxGbI/+6cfRfZURaRZhoUXQDLFCNx0aTnwB878P+z5gakRgzHry21F\nRrdb71CVAh64R3LMGdxWDldCnHKUd06yNXD9CNtvtxVZ4KuYOx7Zdw267EbtYKBVpXmrpIvd/Ust\n53j7gTzzUFTm6xqQ6yNaCS+K4PU81drF9uGu1SpQYrIAb7GonqnBDZ1GcCmTj27QuP+hjvJwPr0D\nkC+wQ0HOmHMRwyhlVGWJi1FMS9Wyd7WswDZoi2FZ4Tzrf6vD7wudWfRsuElj+hk0b8DrdloCeijH\nxn6mHJbKQgMMI7n0N3e7K8zRrNXhgTUXroiSxNZASVqeYzdHXYNFSL1w96qZ1SV1LMs99Uwys2El\nlVJynRMAACAASURBVEw2KCkpPatt/u5ONepggfD/qPO1exerUGLGNkRatIN9V8iLhHOxyNYojB1b\noTIC3KDzgbmauP/h8yeq6Z3TbZthX0LvhZTNlXiRhtBJO5OQ9lK6l0mGNmuQtgMdccL5dng6p/z2\n/JnwxA1fLeWH0wM0mVeSVI/ZLWINHiorNTYWxqvpaVC5LLvFomtascrm+TC81RyvsL7M2sJUvehk\nMt8Cw39LukhJQZEDRtpkvnMkfVnSXPXmXInsx4IC8X3peDvs8LATi5bIJqC0JprMNzZOI7isQccc\nz67DXYx/VqyxRbaZC6sVSDf0+3el3xCPP5Fp5yapC+lBaSyhEUEFkd/sZM7OmSc/Atl7/xCy1y54\nw5hPP5ZpdLuy9th9G81AsQ6j23BahVaN2Lybtf+xIyyY0hdDXm3EHOVNe9JTR9YMs7bTPWLLLrbm\nr13C5u0Du1luxGiB1grsEizCiHILX5f092b2OSVO8xbNOlq7ezuRirZIG5e8Ug/q0t3i7t0lMHkQ\n0ID37ZvuZM7XGaewRBYaUQ6pqlGCEeLlS8PSUn5+HUv4esaj2aJZgDzW0Jissg16w4r0L+xb32CO\n13MeySZKXxYOHlgunSodTIComiQduZwlmu7+PJPb8yaMgkKFGAcFX2hxGOl7yDr/qjORPU3mwwlo\nMEK8fjm76W3AW0Sa2Ek5x9T5JZgqszV/7Qo2b0OugZK0vv+AKK6HDos3me/zrf8/t/XfNFwJacsF\njtppV9VHSHqBu9+Q9sELAaRsNHXWqmXmTMH9EPOCCUJrNIe+DSpO0AWfOUeUu2gB9UklXhKc6C5P\njTEOLi0CXW2yDY5qz1JQmSkqwVUeZf1JHeUIRr6adUC9gNJztSJbA+m8Cp1hQ+dVBJOgs1UmF5TL\nMft+mIwYW/pryokaWzOpv0b3iJBroMTneQ+HHBd28mFpl5p7RXfABQASJc7FbCI+76IjkD3l/01B\nSbZGwIgyjW7359l3HY5Y1O49b2ISX5GxU8dUNeyGngNlhSVpIMfsl8TpnbXL3rAKPbsIM/M3TzCK\n0qphRkWoONvQaVLQYMSiiPW3/yOyv2viMGR/WuFXyL4IKo7trDFK01DEDqyjoyzC2hxm7yoDryMK\nEeO3LcmxQ1A0zta1AehtrmUBaBXK6eXtbo8fiZ49UGB9v6Qv7K3dEnjoyDfCRduDYhGqXkiSu1/T\nyeel3cIvk/QWM/uOuzOxyC4G0SIuV9kiRW8pqbbwMkiBJskUm3exDYiW66bSduP1QWRPVTL68mzR\nXD+0z4qXD0FcYc7UfZXjkH1/zJxTUoGrCZ2LEWd9c8oI410OTrIr0Afy65D98jzkgRrTLc7X2IZ7\nSj9rz8D4NmR//1D6A/1IxJb+gSazXzfMbheoDvFvJhm9rT/H5hWVIiwPr0b2NzYeg+z7Yf8s6Uvv\n6N+1lR1YoywLjtRgXsfxA5uQ/UAZ6pnn2B7UNVi81IuOIq1H8QxJqyXdbWY/lvZSknd3/+OOtuwg\noAAkaKIsG3A33cYcjNNOCF29LT3WLmdt3zXO2r6T1aTQyatZZOfaW5me6ZNPYc5LqQHpBTC7fXWe\nddCOMvu+2ybTR4nvvJ9t/k8/lTkXpSaLIvZBR3ZpzBzZHVWWvLipyHigv7vlY8ieJuN4iUU1T83f\nmf7Zfew0Xx9mxV62jByO7KkCytHD7JC1ozJX7np73DvO7DdAbeHjBljuxY466/9N4+nH8oZlULd4\ngt3sbNnDDk1xlh2IR4vHIPtlCizVFAqLN5lPZnaypJdJOkHtldqemPZZaR3l31FCfh6XdHKbf1+Q\nhdNLlfSDiEZBj9lAE9Yg9QIqBJIlmVb9gzUOcDQ8yjBH+cKTmKM5kGGL/lQdJv9VmXOX72PRC3po\nOnbpjtS2G5awDYvqKI812HeNGuz52RwsbQujgseMQOdr+Hxkv0uM+rKhyKgXkwPpn7+1wSKytErj\n+BRUQIEiGVRXmFKs1g6xeZ4bY4e4QswOKnGGHfpOWXJ3atu7y8wxJXutJK0eYQfuap0Fa44YYWPz\nsOZ9yL5rsEipF2Z2lqRrlIhQHCfpZklLlcgb3y8pfYRA6SvzHYVauUBAqgVRwfQ772Ub9CnHsudn\nYbYDeTq9JitA9jpNRKQJXz+8nW0QF57IGlRusA23nKO8Wqrxyd7XLhCB/uW97FDwpOPZoYM6pvUs\nGwtU6SCGyXxjNeboH3XPV5H98gF2qszs3ILs+wvp3++KQRYxNVgc5oE1z0f2VPWCJKtJ0iDk/peg\nvF0zCwspwUTWPNQoLyr9WKbzhFbmK9fYurAUcprHoLpNrsBoMl2DxUu9eK+kL0h6iaSapJe6+41m\n9gRJ/yrpCvKwRV2Zj4CqUtDkfKo0kad1BYAtjVBSjnJIxY6Dgb5s2C9A+58qNVTq6ac9HfcUfVFY\neTjqKEewL8v1sPqqVqaqIwyEvmAVxuX3PHNG8FiACH1oojrQ9RyLEJdiduCmEXSiaU7XqDhiCwm9\n1aTvqgTWQKn79N5TY/FSLx4p6Y/1INshKyXayWZ2haS/knRW2octakeZHLZycKLncmyi04NfDToM\nJOqYoTJHcC7SQwGV5oEFwTCwPByUIjLY/xGUn5tqpn9hOegHNuCSMlVn0XPPsFMZjVhTVODtgnJQ\n2aHAnKlsFaoFxOkni8fsXTXyrO14XsGbL1pwBJe2pwfcOlReyLFcioGIjc1SQGErOgupo0zfVR2s\ngZJUbgTeVEJh8UaUc5Km3L1pZrslzZQPuk3SKeRhi9pRJjrKdOKWysy5c2cOAKwrgCIA1JGlCh80\nGk6jF5PFsBso1SeloKV269AZHM6nb//4JHtZVIKLyqsZrPwT2tlZAhVTrMh4rNkpphzhUGHFmunf\nl8F3lRlNz4WXpP4TH4/sQ2fGNOCaPAjXhXqGHSTKEbMfbzDaTi6bnppCZRTrYK+VpIE8W0foGjgE\naTVLcwtU7GuRcpSVcJA3tP58s6Q/MbOvtP5+iaSt5GGL2lEmkmllWHv+7tvYJnH6SYwDRSsFku9K\nD6F7JtiONdDHfgEVt//pD5hU0NNOZZGUGowi0sgXxT07GU927dL0Ds/Gm1iy2h+evAfZe5apRuSL\nLAFqIMPe1f01ljy3LM+0cHddzeQ9aaU9ypUh1fZoW5pVxgkuHnsJsvcISnZCx/eeXWxerRqGiaZN\ndvCIYSLr9iKjaiwtpI9YUxrLlt1s/1zF6PC6v8wOEfRdLWmwSrvdAsrjfxjhy5LOU8JHfq+kryoR\no2hIGpT0WvKwg+4om9mTJb1Z0klKshB3SPqRpHe5+60z7EYk/a2kZykpnfZjSa9z91/Oel5eCTH7\njySNSPqFpDe7+w/21RYSqaTJCFEMT9wwYk2juKTgCIm0S9JQf9jJOAyvHHMFdk3WgNEIGk1xKC3Y\nhJvQ4ctYVJN829IU21DGoeO7q8qiXkvzTApvMst2XMp1pIe4tQOMemGBI0LEUaZVAnNDTBaROl8G\nr74iSOE6fCnkZMPbCIOLeNbZwWPdINM0JxH0KgwWrFwSls63fBDKQEHszrIDdNdgkXKU3f1dM/58\ntZmdLekiJb7kN9z9W+R5hyKivEzSzyR9SImTvEHSX0j6sZmd6u7TOixfaf3bqySNSnqrpO+Z2Wnu\nvnnG8z4h6amS3ijpbkmvlvRNMzvb3W+eryGFOP1CVazCKlAwwy0POdCUvpAHDkCcZYeCQo5Nxh2j\n7LtSfpg7u1ajG3RohObVbgYV0PqHmGOXN0Yt6MsyRzOqMcc9yjHnYgBen9PKgtTZNBg1deh8GVDP\naTag0sHa7nIuaESZOr5bxthceVQB0oIMZk1D3D2avvIiVZmg2DHG1sDlA2xebRtn606RVmPtFixS\nR3k23P3nkn6+vz+f2lE2M5P0TCXh7OVKIsCbzOx8SXfMcl7nhLtfJemqWc++XtKvlXj8HzCzZ0l6\nnKQL3f3als11ShzhN0m6tPXZaZJeJOlid/9U67NrJW2UdLmkZ8/XlnIt/cJDebunn87E3it1mPAF\nfbsKiIJSPhm8YdWKJez5hSxblF/wPKb3amLXaoNx2OgFlbGiyXzHrEhPX3jW01iEuOzMmaIc4lrE\nNrg6zPwvQ+WCtUOMuxi/8KXIniYv5ifZWK73pb+eL/XBsQCT1fC8gvSzGJaqp7cLZF5JUrXGDlnV\nLHPEizVmf+SS9LQpepNCE8Q3rISbCsSGpWzerohZJb8eugtme58Y3NNrk6XaRcxsqaSvKZHTmFDC\n8fgHSZskvVxJpT7E+ZiF6VE4vZL9vqTN006yJLn7uJl9WQkV49IZdlVJ/znDrmFmV0l6s5nF7t4R\nLa9uo/qUYD5ZyHMllHRWEbadJtvRQw2NKI/DDWgNTV6kV9BQR3miGk4GitJG6Ia7mkZYA98WjFYY\nvcCgd1fJMapJwRmnnEyWTBNWXcwxR3ASziuFDbDieTVZY7kOuQpz1voi1j8jMVt4xuqwEhQA3SMm\ny+zlDsQsmELWQEmKM2wedgsWK0fZzPokvVPS8yWt096+rrf5bE6kNXy/pPWSzpF0vRLndBpXS/rz\ntL9wGi0PPyvpSEl/LWmzHow0nyTpl21+bKOkl5hZv7sXW3Z3u/vsUMRGJfIgx0q6VXOAJMTR8TY2\nwaIRq5exX1CBN180SkxAdZH7oQoR5RbuHGOL7AlLWfSCVoFySE2JYOSL8gVHgFLDbZvZhnLCMuZc\nFGtsM2/EMJESHrImayyiTBKgJKnwQKqLt9/Cl7Gxk5lgyZT5UnqqjC1lTv5g8R5k/8vB45B9fSDs\ndTgdm0M5qApSZOtOHjrWUzFz7tZ5+iToTRlWg4zm4CwdgMVS4Lsiyj+StJKJJHQPFi/14sNK8ta+\nrMSvPCCuUNpd51mS3ujuPzbbiyh1rxInmuInkk5v/fkOSU909+l7w2VKaBazMR15Xiqp2LJrtzNM\n26UnXe0D9ES84TDKh4McZSjrSCJr9FCAi59QHWWxDeW09aw8KY069sfMkcURYujc0Q2a4FEbmKoD\nLXJAr7frGVj9DIYd+yL2buswsXPLEak17iVJow1WZXLtEUypoQau88cybDnNwASuAXjiJsVSJE7z\nGcwxZwpr4efhu4rZ7QtdR4px+ohyFlIFh/rYGk7b3gfyjSSW3C5Jkxkow9EtWKQRZSVsgze6+993\n4mFpd7VBSQ/M8W8Fab/uN18saVjS0UoS8a42s3Pc/d79eNZ+gZRqpifiOzexheHU49miH8Mr6Fw2\n/UIyBXM8aWW+cRaEU7HJrrd/dDtb1C48kR026ZVsBvJ2aw5VO6B4/s5y+g33zs3sFPS7J7BDyhCs\naNJXY1G1Onw+5cnuhrJUh93zPWafh9QOqF0sUsIaSu01h5iTP7r0d5E9lUsrGnNMM3Ce7y6xd3Us\n1Byn/PwGPCRuKzMOOgHdP0en2LXjkctYEvEesAZKUq3JxnLXYPHqKFc0D5uAIu3Kd5ukJyuhWczG\n+ZJuob/Y3W9r/fF6M/uGpHskvUXSK5VEiduNzOmQxp4Z/98wj928DPyrPn75b/98yunn69TTz0/T\n9FTo7w87QKlzGhKUEwyT5zGWsP0QI5dhhyAa+aI8Xyq2X2+ktx/psr4MXcKaKiPQCl/UefQsc/Sz\ndeY8NkEyX5NW2utn3zVPS8PjXAT2rugBlI6FBqzSWMsw57HYYI77ZDX9AX0QFuyg1D8slxpwDZTm\n1+z+xfXX6qbrr53z3w8lOslRNrN1kq6U9CQlwdGrJV06Q6ks7XPeokTb+Ifufl7HGvhQfFLSCyV9\nuxMPS+sof1jSP5rZmKTPtD4bMbNLlMixveJAGuHuY2Z2pxJOsZRwjNuFF06SdG+Lnzxt92wzK8zi\nKZ+shJNy53y/96I/eedD/l7rYKLt+tUwCQpmcIfUUZ4oMmeBql4sgzkj+QxblB95OMtQphxouvZk\nm7DwQhMmNUFsWJK+f9YMMUetDm8jKk32/CaMau6pMZ4mLaO8up9FuLcMnb5voxmgtymHDbVjrM2N\nLfn0XNMafFcD2Slk36iHvSYerzNHn+qlHz7IblMMVm+ddFZApAkPBscMb0lt+5vxw/ZtNAMN6Civ\nGWEHPlrhc81Spg6Tm6c4zLHnbtBF5774t3//1Effi54dFB3iKLeS474nqSTpJa2P3yPpu2b2SHdP\nlfhiZkdLepukbR1p2Nx4h6SPmNm3JH1TbSi67v6JtA9Lteu4+8daX/AyJbJrUuKpNyW9z93/Le0v\nbAczWy3pRCVVVCTpS5IuNrNzpwuHmNmwEnm6T8/40S+32vT86Z9tcahfIOmb+1K8IA4PPeHe/Gvm\n3J1+Ck1MYe0h02UA6nvSqoVlSKuvwg36azcw5+i5ZzKlABpposSkoYhxU7aXWeRuCihNfPcmdkX5\ngscyx7EKOcdUR3l5gSW37XB2/VxtMsf98Ju+gOwtYmPfp9gV9HG59P1P2yJo/4vjXrxvo5kIPK92\n1BmFa7IOi8mA8uGStKRtOs7c2CmmYz1RT++ID+RY9H+8xObJVJXZZyCtZjzDDqCr8gtTHo7eZs6D\nVygRXjje3e+WJDO7RUl+2Z8qiTSnwYeV+HAnKqxuzelKeMqrlETAZ8OV1OBIhdSj0d3fYmYfURLp\nXSVpl6Rvu/tdaZ8hSWb2BUk3Kqm/PS7pBCVyb1VJf9cy+5Kk6yR92szepKTgyF+0/u39M9r0CzP7\nD0lXmllOSQLgK5W80Bftqy2kAh2N+JaKbCExY5tKPoaFC1AJa1jxCg53Gg2n7alUYRVFqDIxGLMN\nNwslSiKYLFiIYIEVcLtQhlGvSKztAxkWdcxCibIIqkNSzW5aHKY5Ckt804UH8pqMSIjBq5RMgTmO\nuSy8moJdQylNdN1pwAh0I2JUikoG8mpBnQCJqedQ2cgs1FGmgakowwYDbX858C1fMHSOevFMSddN\nO8mS5O73mNn/KBF72KejbGZ/KOnRSigR/9Wphs2BjyrxUV+upEbHQVG9kCS5+yZJ/3Qgv1BJKeoX\nSHq9Egm3+5SE9P96OpHP3d3Mnq6khPWHlCQM/kjSBe4+O6nwYiVXAO9WUsL6Jkm/5+437ashcZR+\nctENcfdOphYgsRNuuQr1ZMHCQOcWVbGgjnIdRu3uvo0lNFUezzas0SqLXiyF+qc0mY8WyaiBiPim\n37AyuPXzqHYru04eycJER2Njh163U6rG5G9YrjKthpeF8nmkUmATctMysC3Fx0ApHxgsi6B6DlVe\nIPNKkuIGOyT2x+y2pgId8aS6bzrQeUKBtfCh41tpsPZTGku3oIMR5ZMl/XebzzcqKRQ3L8xsREkg\n9M/dfdTCq3GcKOkid/9aJx5maWTJzKxdwtw0mpLG3J3d+R1imJlf88v0ziydiDQa8dPbWbTgUcew\nA9LSfPoo6FSdLbClGtsQaXRhdR/j/lHO8VduZny7J53CruGWZpj9pJjzOFVnYyefSR9lpfzwbuvL\notihZqLODqykLyXp279k1I4nnMzG/tKI9c9UM33/TMK+oYmaJ99+1b6NZsArjJeKoueSFEPHHR5q\ndh3/O8i+GLHkjqkG42RH4H3RNYcW+MjD2wV6G0HnLeHbH3/sUXLqMASAmfn4T7+Kf274sU/fq/1m\nVpH0/7n7W2d9/m5Jb3afP7pjZv8k6Th3P7/19+9JyoZK5jOzn0t6r7t/thPPS+vh3KN95Bib2V1K\n+MofP9BGHSzsmEw/ealzRw9Mt93KNrj1q5mmaRZcTY2X2QYxWWKncyLLJ0nr+8PKt932KxY1fcqp\nbEPMNVgp3xiWqs3DBDeyIVLc/ms2jp90Cns+pV40oQA6rgIJr/Np/zzhZBYRoomjSF+dykxAFG++\nGdmTaLgkGRXDD4zssWcj+9BVJolvR2kmVBEkC2XN8oHnbei+D4YuKDhiZucqkQN+9EH8tW+R9D4z\n+2mLCXFASLvD/pmktyrhCn9eScbiGknPk7RECUH7PEkfNbOau3/yQBt2MMA4ypAzBZ3B33k8TCLq\nSGHu9qCqFzg5D2a3V1cyxz1vLOHrFRcxR7MKN4kMTNoZhxHlcp1FykrA/qjB9JnwkvTy57KoYxPe\nscZN9m5Lzg4d5QYba6MVNnb++NlsslShM5g15iiTKHERjrMKrGA58AdvQ/arppjCx/YBVk2O8lJL\nDXYTd3yNHQzK0eHInhb/Ga+lHwtTVUg5KrO2jEK63QkrWd4IvTWl1MuFhB/ccLN+cMM+x+J8kr37\nSrz4qKR/lrTZzJYoScONJGVafy+5+wFxiNvg7Upy6W43s9vbtNGno9tpkJZ68beSjnT3vbgoZvZ5\nSZvc/fVm9q+STnH3g3ly2C+YmX/tRrbpsucz+3/7HJOredYzViP75YPpv2sZUimmKmxDjCO2+R83\nwlQpMlBs9zJ4B/K6S9h1/oqYRayLzq5MizDbnujV5mCi4+UfZ0k1l17CDgUrYki9gPJq9EqZJv/9\nzT8zusBr/pgpL6zMw7EG+oeopUhcF3ndv1yK7CloBNqp4DuMWPvL3oTsyxFbF8rOxn5s6ccylV2k\njmkfHDvkxlSScpR6AZKOjzv26K6hXoz97Bv455ac8ZR21IvvSIpnUyVaFAq5+4XztKOphJHQrk9c\n0us6VUFvxu/8vvbBgpivzbOR1iN6sZKkuXb4JyXizq+X9FklUeYFgUo93CmROspnnEV1KWF1OGBb\nrMKEphoV8ofZ5PQ0D/v+ec9hh444w5QLcg3mHI2LbUIUKDoC+/Ki565F9jnYl/kGixxN4mpsUEoB\n4nnPYf2Tz44x+yaj+UwAbd7QfZN74SXIPj/ODtCVYSaXRguUGJThqDbYIaucXYnsaUSZqIJQx5cG\nX6ifuSzPkucz8F01YCGirkHnqBdfkvR+MzvS3e+RJDM7UtI5kvZ14rugzWcfVOKWvFrSbzrVyGm4\ne7vfud9IO3qHJK2Y499WSr/NmBkXrp116ED0f2kUlHKah1iwAGcFk2WBUvl4hjKz78uwzZ9GlA9f\nwrLPaXviKrMfhIt+OcMiyjGQcGtCqcsVA+yWhvJezdkGF0M+dkXsSpny4ZcNdPqG8aHA/QNuDKqw\nmAztm8l+5shSHeJygemNVyIWkY2aUAYSluCmMpZUf54ciqPAhyYKqmeeg/5jBkasuwUd5FZ/XNKr\nJH3RzN7R+uxySZskfWzaqCX8cJekd7n7FZLk7nuVLTSzUSXJfD/oVANDIu3oukbSe83sVne/YfpD\nMztDiTTb91ofHSeJ6R8dQhRy4QY/jSh///tbkf1Tn8yioCFvguh3pfZlyDOlMlAf/jfmmF76Enaq\n6Y9ZVJPSBSivNp9N7/xS6sU/XcVUGi59CXu3dVighJakplxEOq8++VnWP6/6Q0Z3qEP5PCK9GLpv\n8v//+5B9DSZ8ZaEmdV/gZMHmS16L7CnoDQBZN+khKAPt4wyURYTPz9JqrIETWUOhU/Jw7l40sydI\n+oCkT+nBEtavm1EpWa3Pp//b52M70riDgLSr5KuUdMpPzexeSduVEKU3KCny8ZqW3aAS3eMFASJq\nTpPz6PCsFMNGmpoBHWUaIaagyXn0Wm18N7vOjzPM+aJRvnyGfd8mzRAH/Umvn8d3M5XIhjNHsAEV\nPmhRitDZ7WM7mRauQ54p1Y0mCB1TK+5gNJOowCKmjSo7QDfrYb8xVauh6xoFcaxpRJkWBKGOLy0m\nQ7FQHeVOql64+/1KqiDPZ7NJKSruEX5wNyBVMp8kWVI67hJJZ0k6TNIWJdXzPrmvUtHdCDPzL/wk\n/cLZgGtUFo5PqgRBKxetXZr++n/XJOOfTZZgdTK45pyxnnERY5j5X2nCIhYwSrlG9yP7Hcb46jSZ\nrwEOTSvzjENccTZ2cF8668udmTXInibzkb6UpIGIHYLolfLazOx6TPNjp9LfTE3W2DijEeglOUaB\nWtNgl5e7YzavphpwLEAJtGMatyL73QXGb6c3U6SICB0LExV2qKHu3ZohdkCvQ+WiQVD+/JH/j70z\nj7ezqs7/s8587pSbOSEDU0hCQgiQAIEwBBAQFKEqVhyhYq22tTgUiiOD2lpbtMWpDvy0oMWhVkEF\nlBnFMMgcmWQIQ4DMyZ3OvH5/vOfC5eYO7ze5m5zL5fl8+HBz7rr77LPPfvdee+1nPWvu9IZJ5tt4\nz4347ybst6Ih+t9IICWsy4q4KN8azna0gDi/1PGlV1Mr72I81oP3hzJcQN6ORs9pCWvafgZkY0v8\nyvHym5gm9TtWsKhgDTqDlAPtKbampUHGN40o//gWloj4lsMY7aWUZM4LjcLRuUOz83/yO1Y04pTl\n7LaDUlNSHv9QSaOC2SQ7FMz9wzeQvZfZ2LfCmxcDFCWJq2RsWf5mZE/nJrVvScVfZ3HpdkrDgQVE\naPtUrSaXYAnZjYIRrMw3phHunm4UgDi/1PGlPNznn2aRO98PXsmChY1XIUTmvEQ2TCijt2SPPrAG\n2ZePYElBZVhKtgQj3JSHm/T4G3oSbrYP3csivtXl7JBCqQU1GOULXYHz4ftZxLd6CNNXr6QgHQFE\n1kIHmTbeeT+yT2bYZ61AwfdahTm+CRgxSCwPKxBFD4kkWZDOeyrfRjnKmAoCbx1HL/XitcDwSCD2\nrmNmx0n6oKR5kvrfu7i77zmSHXslQB/2kMg1wXKpECF5xKE5ypR/ZjAK2jaBJdtR0Kgsbp+qjgTk\n89GxTATegLCqRuA1obWdJYKG7k9DrYET2W0EjfimYASawmDEuhA42kefcxIlpsl5oeOadI8YtZX2\nIMZ6RNnMpinKpduGKzSQGsdgiOUom9mJkq5UlNA3X9LVkpoUaeitljQqJD76I2yEhC0k02bATQJ2\nPZ2Mf+KmHGIKLidHQ9bMfK/5LGpnxpKOaDU5F9QKhEDjCcdy7t6DqUgOjISxm5TQYxk6csTHh9F8\n0rDAlYPiNqF1lFv2ZfXMvQivw6HTYJmwwYsK1FGuwiRi7CiDm7tild3sFGCVRnqAa0mGpUaMVWiJ\nEQAAIABJREFUVsd6tPZ7R2FmMyRdKmmg6numyEGLPSnjzvZPK1Kz+IiksqRPuftdZjZX0jWSror7\nho2EkNGU0DceVVhSu1SNv1BRDnFo6gW9/qcoldjnrcDr/GKa8WpTgBqxPQg576tV1jZNViukGeUo\nARVH6MZCD3F0fGjSUTHJkqyITFbosRGkjQjKvQnqLlNQjnI5yShZObHchZrBiDugXtCkVIoM1D8n\niYiSZLDOwWjFGI4of0PSIkXFUO6XtEMTNu4uNV/SZxQpBHnv37n7I2Z2niJH+sc70pGxjrY2tknQ\ngiYkEacY/KKMgV6rJWFUcOZ05qxh/hwUhangohfIPCh2mQrLmdOxBMVSpO0Yy8AR5elToPOCuZrM\nwSh5/KhpaBpLdSJTpUgUmEqGU/52mh06rBaW91oxyMmmziPoD82LoI4s3YGS8Dl5Da96HC7pw+5+\n6Ug0FtdDqEmqurub2TpFnI/b679bI2nU8ZOlsA4G1lEu0qgpW3hIBJr2HfPVGsixk6SObrhhwU2C\nbnA0EheaI07QyUQacHny6ijPP6bjQ7P5K7BsMUHoa9xEN6OZWBlWgYQxJUvD63wYUa7BQyWtOEod\ncdJ+ChbswAdiGFEeqxSDYdFIUZRXFj2K6n2MCOKuqg8rcoavl3SnpLPM7PeSKpI+JunJkerQK4nx\n+XDXR3SRamtlV8qTWhm/rTUTf9EvQf5ZBkZqqMxUaMD9DVNBxtIiXqnAmw644TYaaNS0DMeHHkJD\nInS0nTq++MGlJ0rKaaaOMqRGUPWfGgx5jPZD6GvYFqETyRsY35b0bkXU4B1G3CfjB5Lm1n/+rKKk\nvl4dqKqkd4xEZ15pdJUgJw6AHuTu+AOTjZo9jYnPZ5LxF/EtPYw7VyizhzGdYo7mVHaGwLj1+seR\n/RF7s+S/dIIdamihgKClheE8/t11bCwPg4mUKaABLUldNZbMRwugONAhlvhcWz5/CrJPpVh/Oqvx\nVUoqcJ6lYTR87ZW/QfbJDJQKhHJv1J4it+dByH5rhj0rVB4uCUpY91RaUduFCtxroc/eBDSgJaYl\nL4WvihgKPnYjys9KereZXacoh25jfwN3vyRuY7Gmo7t/rc/PfzSzRZJOkJSXdK27/ynuGzYSipVw\n2sIJyCGeuzB+hSxJKsNKfqSCWAlW/SuWaVXBsNq2dHE47Jg9kH3SNiN7qtQQGtQZJDj82MYaS6x/\nDqOmNGrH51pYhRWiZEFjU7Rq4eQ3vZ69QSekauTZoYlymik6IKcZF/mA31gZ8Pkp57gIVS8oqKNM\n18DKKI22j+Fkvm/W/7+bpIHKZbukkXWUt3mHqOb3t7fnbxsJjVSlkUqyUe4iAZdvY/ZUsSO0s0PL\nkzcacNJUwLlTYXs/TtSkCP2MU4eBzjXqHFGEpAVVoKIJpS44VDQRtKfJedSxNtofmkxJ10HgPIZe\nMukeQUHnZjkZ9tAUCmOJ9tcPu49kY2i2mJlJmq6BxZvZnWIDIAMoANQZpKoU655npXwXz2O6y2S7\nxSWm07TkdePwLiXp4T9tQPYrFrJFllaT48l8tDxsuMILo30sKbLwCpeOzxELoFIDHR/gkFDniJYh\n7r73HvgOoxvVN++H7LE8H7TPgmzHlDF6GM1LyafDKohkaAlre62E9WiCu68eyfbiFhyZqEhH+S+G\n+JuwdysBUAt4aqWRo4X7sLLIdNsi1ino5Bcay+/FOPZoyJO1behOQ4IuVlljizjWEA2YIHb8MZC/\nbcxxpMhCfnjosTz2aFZwJAWpKRTZZHzniI4NTXpNnPBWZJ/uZmNTyzDnrpJh+ueJKjs0VRPsUEM0\nryV2CJJYcmEGHoJogRLq+FI9dgrynDQSxjBHWZJkZvsoKjoyQRFP+UZ3X0XbiTu7vquI5/FVSQ9J\nYrtPg4Jo/3OOMuvLY4+xiPKkceGqt3X0QP4Z5CiHvlYzeIi48z4WLZhzFPtyUzX2uGytsu+WbhJk\n7aQbxB33Mfs9VoSVyNpSYSW1qeILBZ1ru61gcy0Bi9VsLscfHzo2lDaSvusmZO9l5qyl2tqYPS1W\nA6kj6aWMk91pLIE75KFvc4EdInrKULEjw/aIcRmmqZ2GeuOjFWOVemFmKUnfk3SaXp6S7mb2Q0mn\nu8dfLOOufEdJ+gd3/17chgnM7GpJx0n6nLt/ps/r7ZL+TdLJihIH/yDpI+7+QL+/z0r6nKR3SmqX\ndI+kc9x9yNLaJHKKlYVgpGnKVLbwpFNUIzM+WvNswU/A0qqUekEPKVR2ac/dYeTImBguvQ5vS7NF\nv6sK5w7YJKi80J67syINCWOflX6349LsANqVYGOZgdSLPXdvR/YpeOXLxyf++HcZHBsYdbQ5eyP7\nZAeLKDtN5ksz9R/Kga6kWPstSTaXuyE9gqwL47JsXiYT7LMSlSZJKlRZuXFaDrwZzuVGwVilXihS\nZ3ubokJ5l0l6XtI0Se+q/+7x+v9jIe4OvlHSC6ibMWFmp0naVxrwruWXioqb/K2kzZI+IekGM1vs\n7mv62F2iSIXj45KekPR3kq4xs2Xuft/I9DNsWeeODvYgVmtsYagEjuKGROhkvnUbYOnZXWHGdJp9\nVzRRExccCTgV8FjOHt1jSQ9xdHxKs9khqwITykj/gxcc2bQe2XsBVm/pYYcyg84UnTw+fR9kTyt8\n0qgpKWFNC4ikIUeZlrCmCJ0Y2SgYqxFlRQ7x59z9831eWy3p82aWlHSGAjjKF0v6GzO72n3k6oCZ\n2XhJF0k6S9L/9PvdyZIOkXSUu99cf22lIkf47PrfyMwWKwqvn+7u/11/7WZJqyRdIOmUwd4/ZPY/\nLSW/7vkO1v5Cqj8bv0N0XOiMCMkNlzj1YvXjm5B9einrf6bag+x7YFSTHspCcpSffAyO5ZKwY0mj\naqFB51pqCSz+U2ORvm7FHx/qLNBDRNcDmDo4qpHcZyDVqsFRTrFDYjkgb7enyg5khdDycOmwspGj\nFWM4oryLpFsH+d2tkj5JGouro3yRme0i6U9mdq2k/qu9u3ts77wPvijpPnf/kZn9T7/fnSRpTa+T\nXH+TrWZ2pSIqxln1l9+kiDP94z52VTO7XNI5ZpZ2H/gonkmGE7mhzsuM2UzFghbtIBHlLG0b6i43\nmurFnnMnIHvbVrt8SHQnmDh/cpSK20t8LLddSoZGo40l3XD32IuNT0JMK7jb2PgkAF2ARqfo2DQv\nZNQL0eh5CTpTaSgJBjnKazKMMx36oEK+3tY0O7Am4VygEWVaDCe07OJr2OlYI2m5ouJ4/XFo/fex\nEVf14kRF9IespHkDmLhAGLve5mGKwuP7DmKyUNIDA7y+SlHFlSZ375a0QNIT7t4/lLJKUkbSHEkP\nDvQGBZhgQIA3iWa2qPUUmf34fPz+bOpm49JTDLzoMFon5tXuMiWskH9LlXEp19l0ZE/pBYTPl0mx\n6146ltT5aq4xx3GdpiF7uoH2VBj3cpcpUHcZfrctNTbX1nr8uUYdr+4KjIDusieyT21dh+yrk2ci\ne4faubUki+C2FNiBe32W9Z+iUIs/lzcX2U1NdwkqfMAr2WnNbF2gz3mhxnIvGgVjmHrxA0mfNLNa\n/efnFHGU364omvxF0ljc2XuRpDsUOcsPDRahjQszSyuqnPIld//zIGYTFNEs+qN3dRkvqbtuN1BY\nqteOhrh2CiaNp84mrSAGWoYbIo2eN1qBj90msehIoyFkYQGK0GOJizTAAyupVCfxsdx1cmPNNTI+\neGyg6sLGiXsh+3FZ5qxtbWGqETQJt2zsYNBeYGk/9DkP/X0R0D2CHv75Gkgr24469VtJY5p6cZ6k\nPSSdX/+5F6aI5nsBaSzuSjBb0ofd/X7S+BA4R1HRki+MUHvBQSvnJeBJrq2JLWr3P8Ku+aYdEN+W\n0jqKMDKfhQVKQpewHp9l/PDrHpyM7N8271lkn4LXjsUai3zlA2qCTsiyyM71D7HS7W+dy8aSqlJQ\nqb2mFOMEN0Ha6PUPMt3lU+fT8YkvXUjl4Zohb/TnDw10WTk43rYX5GMbkwrsgjKNaTjXWh/8HbJv\ny7GDAS7BDQ6hd84+DTXdA4sA51Jh10BK7WhOskTQRsFYjSi7e0XSO8zs85KO0Es6yjeH1FG+WxE5\neodhZrMUqVe8T1LOzHJ6iR2VNbNxkjoURYkHqsLRGyHe1Of/s4ewG/R+6/Jvn//iz/sccKT2WbIi\n3oeIAZ4swCb0xAm0pCaQBAutugARWvWC2u82LewHTgTOsCbjSRMjad2h2VMb63oh9MZCn61ZU+Ch\nklZvayDVi12nscM/BaVkhS6vXps6C9lXmlgeSyXDHH2rhlOa4PKqYfrxYvsjuEfctnKlbrtt5Y52\nKQjGesGRulO8w1nCcR3lD0v6vpk96u6/38H33EMR1/ky9ROClvSPiiTe9lf04Y4d4O8XSHqqzk9W\n3e4UM8v14ykvVJTkNxi1Q6f99Wf6vTL4w0AjxKHnZ7EUTkc5AflhtLgKv4aDRRegY005x509kIfb\nHnaDDprkE3gedxXg5GG+wnZcVzdWoikdn5BXraElsjphoSOxvEV86KOVBfFcK7AoZQrK1SWg42ug\nsqBl2GelnGOK0HNzqEPiQcsO0UHLDnnx3xdf/J9B+0KAEzpHMcxstqTn3L1c/3lIuPtTcduO6yj/\nXFKbpJvNrEuRpnG/9/RdY7Z1t6ICJv1xo6RLJX1HkXN7haTTzezw3sIhZtamSA3jsj5/d6UiHsqp\n9b9XXSfvbZKuGYpPHbLgSHcJli1Os0X54T+xRJCD58W/tqMZynRsypWwjuAWUG1M4tfn19+4Ftmv\nOC3sYlWEUk2EXlCAvMvmFOPgXncDHcuwyYKFChvLMuSxTssyXuofbmPO0Ylv2ILsPQsiyilY+Ace\ncOlcOOrtdC4we/xcQXpB1+8Z9YLCa7CEeBLMtVOPRm2XqmG5shmYSFmBFCtKh2sU0Dk/FMxspqSv\nSHqdohDKtZLOcvenY/ztdhWFg3hCkaTw7ZKe1PCJXLEnfNzZcl2MN40Fd98q6eb+r1sUZlzdxym+\nQtJKSZeZ2dmKnPNz6+Zf6tPePWb2I0lfMbOMosH6kKTdFOkrD4piJdzDm8uwRYoqR0yfxUJrJZBB\nR4uTVOCNaY5GI2BkZ2KGSY5RLuK++7P8UDd2qKGSZvRg05KOX6gha4xn2lVjY7lo8UDsqsFRNfbd\nhkYzlMlaV2ac4z33YhJiW/NTkD35vjYUWQi3BXKUD1jK5G1MzyP7tLFS8qF5rC2LBxN8GgQJSKtp\nhvJzhfhzmRYcoVKsLRn2XdHIaT7NgiOtzg6gjYKRokuZWV7SDZJ6JL27/vLnJV1vZvu6+3CTJ3hR\nOEl/JemxPj+P2DVDXB3l00fqDYd6G/X5YO7uZvYGRSWsv6Yo+e9WSSvcvX/GyumKvrQLFZ1W7pV0\nvLvfO9QbknWHKjVQbeEk9Nk7O9hCkgT8iCp0lGnfafsVmHFchZGspLFFf+1aOPbzWJJPhZYEhxs6\nyeCmmf8kOUySNmyE1cZqzPmqJdlcy0E5PLpBNyXZBr15Mys+k6uwMsc9yfjtN6fY2NMD7prnoM7x\nnmwfLDksSQ1BJcQqa5mjT3WdbTM7VJIIdHF31he65hdh4ui4bFg1mUKDFS6KixHMK/hrRcHHue7+\nhCSZ2f2SHpX0AUWR5gGxI0XhCNz9+31+/t5ItNmLcKV7INy33b3dfbOkM+v/DfW3RUUnlY+H6R3n\n1VJOFq1WVy7RxJf4ziMMXOBDBC04QqkXKej4lpwt+j3dO6SOOCxo8iK9RiTRoITYWFacUTW6OmHk\nKDBpugw36DTMzq84vJ6H41NNQO1fcKikVAQDJZElqVAIe73N5zI7cFPVi1o3c+4syeYCdawdFEwJ\nXfyEtl+B0napJCzBDW8jGgUjuF6eJGllr5MsSe7+pJn9XlEBuEEdZe1AUbjthZldL+lD7v7QAL+b\nK+mb7h6bPzToqm1m75H0K3ffUP95SPSeFEYTCEeZoho4J6illTkkG7vi24eunBe65DJ1fEtQWmji\nJBble8FmIPs0XDMK1LlLxndIijAKR532RhvLngodS2hvzBmcNJmNz0Zn1I4suAGgnGMaUZ48mUVk\nN6SYtCClEYV27tJ774PstYkVWLEWRr3wYvzbjqm5DajtXIr1JQ9vXjYUGBWR0mqStdHKUR4xR3mh\noly1/lgl6a3D/O12F4XbAaxQlFc3EFolHUkaG2qV/56kZZI21H8eCi5p1DnKRN0BS6DBRZY6p3vs\nxjaVp16I3/7cmVSoHpnjz0o3LCoOTzf0/eex/j+8lvFwF01jCV/FCvu87dn4n5crjrCxPGA+G8tH\n1rGx3Hcqu94uVWFkCt5eUJrMgXuz9v+8kfHnF08eNg/nRZRrbC5QGs6SeeyzPriOOcr7TYmd5C5J\n6oERdML9l6SVM5kW8eJpdyD7Da1x8+sjtPfEf1amr2clFcY3wwNcB+MEP50cSB9gcLRAddV8ienD\nNwpGUPViqMJuwy3KO6so3GCby56SEEdtKEd5d0Vl/3p/ftWhFDCZj6IElSAef5KduI9bFt92Sw+L\nVqegqlOxzMadRpRzMHJEI8r3/Zl9V+/enx2Wt8B1Y3yOXeGSxTMHi5PQsbz30cYay/Yce67oQaIM\nx2flKtb+GQc9guy31OIfPJogf7unyg7zdz/KovPvXcRygLY6mwttMOGLHtCX3fNlZK8MW5dnJv7I\n2gf444L3I/stBTYXchl2oBwPk2qpBOfmHDuUvYZXHmZ2hqQz6v90Sd8ys/7VxPKS9lEkUBEbg65M\n7r56oJ/HKnBlPniQo/bt7WzRNOg8EtBkvkYDjYLOmAr1TD1sIYVkImxZZ4LQY5n0sFegNLEzdIns\nWdOZ84jnGlh3klDpgGLGFHiAhuXMa7AYDv1ucfRu0jRkXoMqFrU0c07JeNIDIgVOyIZrIC3qVIW5\nBY2CONSL22+7VXfcdutwZkMVgBsua3S7i8JB1KQXExGs3797sUHSNyR9kTQ8Or/9EQJZCGnBkUKJ\n2WdgWedCIVxFM1pwpAR9F0pjoYtyZ4VtEFRHuYuZq2bQsYaLeGeZ8YiJnFyZaKuKqzqEHksqtddV\nCTeWkjQz99zwRn3gzsqlZ8rs+r8t018Sf3CUjEnPUdC5UE2w7YsWHOksQ0eTVnsrsQ+MdI4leZLd\nXiTK8fuTggc+entLk9s7k+y5pW4+5Uw3CuI4ygcevFwHHrz8xX9/4+KLBjJbpYin3B8LJP1pmLfY\n7qJwBHXVi+9LkpndIOmDAyXzbQ/GuKNMrGGiBhxZ6jxms+xRL0EeK0HoiDLdgDIgWU3ijniOBfNV\nTDJpoRrlt8NNizh3VC+VVjkMPZY0yhdyLCWp6Cw5jz5bPRkWdSwn4jsYVSh5SZGH6m0lIG0n8Wg+\nTfii7dfGTUT2FA4TTasg4S6XYvzz1hxz2mmEmD63IW/VGgkjmMx3haQvmdlu7v6kJJnZbpKWSzp7\nmL/d7qJw2wt3Z6T1YTCmHWW0yWHJtLCbiuPswvigmz/XmGb2NNmuDIeGcgtp/6nzSEET0MpASoko\nZEjcMS3BJZLKq9Er3O4ylNSCC0NbBkbW6O0LjLgTUHk4Ms+2B7hkNIwoU3m4MhwfQeqIAfk2iUeU\na8CxpmOPtfOhek4VOtYVmJhKNcQbBSOYzPdtSX8r6Rdm9un6axdIWi3pW71G9dLRj0s6z90/F/Vh\n+4vC7SjqGs7zFNXheBmIUtuYdpRDVuajnONiGRZGAKVnJSmdjO+RdBapRBYyVx5W5qNoSrDr554a\ni0yNb2H9b6r2zycYGqUEizS1Zti1IIkS5xJsg+iBRRfGt8KxrLGxLBrLth+XZWNJby9oght9ViiH\ne6vHl9WiB+gcnJfjmpljlyuzubA1w+ZCC6Rk4TLHBh3xNljFMsWuaxJVsEdAWgq9JctAneOQa6DE\nqy42CmjS4mBw924zO1rSlxUpnPWWsP6Iu/fdcK3Pf31xurajKNz2wszaJf1KkXJbb7+kl1MDXnOU\n44A4s6ETO+gV69p1UBN0D9IX9lnLMMLaA/nbtFAATdqhV6ZPrGHjc/CksBzlQpVtiJ1AdWRiDka9\nYN8fe5q1f/AUGrVj5l1lNpZbS8xhmNrEZK/o+CyHyfkkeZFGiLsr7Lt69Gm2CB64MFxxFUnqhrkO\ndHz2fCG+NJ8kpRNrmH0L0xZWKr47kJoBI7hVNvbUPg1LZG8twcTO3OikaoxkgSZ3f0YRfWIom9XS\nthvwK1EUrh++IGmipCMk3SLpLyRtUVTa+hBJbyeNjWlHGV1rQseXRpTpFeuWTTARBHARQzv5Wejr\nVOA0pQlc9PM+tZqVCU7uA/kFMEJPuZTNqfjOUQZWVyvCynxrnmWRmtT+jBuZgFeyTWn2eenYU5rP\nmmfZXLMlcO6DjZRG4SiP9emnYWn4vdnYG9Rvz4JbOElqhhJlpaeYo4yRoDKc8edCZfpbYNvwNiLN\n5hp9DvNwbjYl2S1lo2AEqRejDccr4kWvrP/7GXf/o6Qbzewbkv5B0rCF9HoxVGW+60Gn3N2PAfaj\nDpgSDOcnbX/2bixpR2ocjlUicHTeAid2HHgAG3ucDU+5lzgBLf4mlISV5BLGDjUHL2FjSStk0etw\nKg9H26fcyyX7w6ignoX24UCf84P2b4XvEPY5wfbwgJ7ZZzGy96YWZF/NsMRXQr0IDVwiG2649NaO\n9qdRMJIR5VGG6YqqAVbNrKCoGl8vfibpctLYUKt2Qi9fieZJmibpSUkvSJqqiIz9nKSHyZs2CkjU\nl4qxUeerCpMLKhWYYR0wuTBgXuErAkpd6IFnjkqCtU8XN+p8kegLva6mY0klwSoJeN0Ow/Mhx1KS\nSrD9ApxrVTg+5BBKk9vgxRFeRxI1dqhJO4xYw0NTFvL5rQId0yKLWCcSkPJVit//FNZuR+ZKQfpf\nFQdTIPdfo7SE9diNKD+vl3SaVyuiW9xY//cc2thQBUdW9P5sZqdI+g9Jh7j7bX1eP1jSj+q/G3Wg\nDyNBBTqmTaCssCRt2cwW5RQ4FdBxoVJ4oRVBaHJeNsE2rHUbICkb8MMlrtRAF33EvYTfLb2upmPp\ne0DVCHjoCDqWktozLAFt0xYWFUxX2ckjm4zf/+ZUWNWLp59nc6E8jY19QWxdKNbgAbrK9O1mblyH\n7C0DtYKTG5A9UeHwaZSKyJ6rngpbeNqzbN0pVNh322H0BrcxMIYjyr9TlMj3C0WSdJ+ty9lVJL1X\nkdxdbMSdjRdK+nRfJ1mS3P02MztP0ufqHRpVqAaMhFag5igt8vHoA88g+9oRs+LbopalYuPc2Eni\nUdA0dJRvvPJuZH/6UubsGJwLhSrkcINNi3JqM8aidjf84i5kfwYcS7pBhxxLSUpBzvcNV7C5duZ+\nsCAL4KtTx5ceOq79GZsL792POcoOZRp7oDNFqRrPXjNsNbSXodTFnq0a1LFMZePP/do+f4Pa7obJ\nc9kUG8seKM1H9a5orkajYAxHlM+XtEv95y8pSuz7S0lNipzkvyeNxX0y9pI02PF3rbYjlN0IKAN5\nOLrop+GD3lVgC8nSw/ZE9rVa/Ac9JE1D4sl8KXgFmkttRfZd1WZk/873L0X2Cb8f2VNnswknpsSP\nOtK+dNXYWL79zAORvQ9bBOrloNxCmrBGJcQ2lRnn+C3vHajy6+AopB9F9t21+AcPqqOch9qz7/0g\nmwvJGnOssylGXWiBJaDzCTYXZr7rzcheaea4V5vYXEuU4iesbYb7IXV8m2GEmB5YqS5yTqMzmW+s\nwt0fk/RY/eeypI/V/9suxHWUn5D0AUlXDfC7DyjiLY865NLhykAXgASXxKkXmzaxB70ENrkMXNSo\nlE9TFvLP4Pm/s8I2iGyCOYOPPMY2xENnM/1TmjeyqcCirKl8/O+3x9l1by7JxvLPj7Ox7Ny9HdnT\nssVbCsw5yjYz7uKEdPyS0ZK05jlGF6jtxZ6VNsWXq9tsLJmMloZ/8FFmv2wmK+9ND03re9jnnZzH\n0kXIvLqFzZ3keLbu1DrjK6y0zmSFz7bCEtPUkV3bxb6rbDNzxPNQs7tREM7DaWyYWVpSxt23kVUy\ns2ZJJVIRMK6jfL6kH5jZA5J+qpeS+d4qab6kd8Z9w0YCifpSXi2Ve6M6kJ1b2abSChzxzhJc1Jhv\noe4iHcuwV6bZDHPuNqxjkmb5bZ/VIdFh0NFPMWdtfU/8qG8zHBvqHG3awMampcachc4Ec6xbs+zz\n0kPK1Kbnkf3GDSwKOq77BWRfyMRXmhgP+dVdFebk0+equcZujjoSzHHMpyDfvoepduz62OPIHmP9\nRmRuyfi3mh1ldnPUU2Y3pp1Fxgme0Mwca/rcWm53ZN8oGMPUi+8oyid+xwC/+y9JJUWayrEQy1F2\n98vNbL0ih/ncegfKku5QVF3lurhv2EggPGI64VJQs7NMo7LNzBksAPF/QkmReEnnZijeTiNBLWnm\nrFEe7rh25gCUgYa1JBxRppiUj++QUMoRVY2gY1lMsg2OJkbS7PmJOebcdcJDUEsrmzudOVbVsZSI\nf8rtLLGxb4ZUh/YJzNGkajK0cBG9zqfFZDKTJgxv1Bcw+mJZqLZTjn8wwLrFUBe5FR7Qi5A/PxGs\ngZI0JcEOoI2CMZzMd5Skfxzkd1co4i3HRuxdzd2vlXStmSUkTZK03h0Wq28wkBLWtIAIlTrqKrIN\nfa857KqpBqSRaJJjaHm4NEykCK1c8LpDGVczFf+GJ7KHUhM5WEY5A6gmNUh7oWO54uCwzg4FdY6o\nhFhXlR0Mjj4YVp+BoIdEAnrAfdPhbDvJlWExFkgpa0mzQ0pLgkXca0uORPaVNJs7PTl2m5Irxe8/\nPVCGRgomUqahPvyo1VFusO/pFcQURflzA2GdIkZEbGxPZb4mSXlF9cNGtaNMSjXzohesL7kMG8pn\nYOn5bDL+ht4NtWdTcK+liiBlh9qw8BRNJc2e38T6sygPebhJFlmjzlqhFt8ByEFt2JZU6bx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x5p+3xuhgsz0JLUVKZp7XqY0DSPmYfeWHBxGPjdrl0HT7mDprpsC17pDRZdggfijZthVUdnY0OT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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7b1ea7fb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_trans_nl = svc.decision_function(train)\n",
    "test_trans_nl = svc.decision_function(test)\n",
    "\n",
    "plt.imshow(test_trans_nl[argidxs], aspect='auto', cmap=\"coolwarm\")\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label(\"classification margin\")\n",
    "plt.xlabel(\"separator feature\")\n",
    "plt.ylabel(\"label sorted image number\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "122 misclassified test cases\n",
      "test error rate = 0.153\n"
     ]
    }
   ],
   "source": [
    "gnb_nl = sklearn.naive_bayes.GaussianNB().fit(train_trans_nl, train_labels)\n",
    "gnb_pred_nl = gnb_nl.predict(test_trans_nl)\n",
    "\n",
    "n_err_gnb_nl = np.sum(test_labels != gnb_pred_nl)\n",
    "print(\"{} misclassified test cases\".format(n_err_gnb_nl))\n",
    "print(\"test error rate = {:4.3f}\".format(n_err_gnb_nl/len(test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Instead of getting an improvement in our test error rate we get a worse error rate. However this is mostly due to the fact that naive bayes doesn't work well in cases where the features are sharing a lot of information and this is cleary the case here. There is an option in the SVC object to collapse the decision function down to the same shape we would get from an one-vs-rest voting scheme but this still uses the underlying one-vs-one fit classifiers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f7b1e877438>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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MBf4fboBVXX6aexxga2BxUwfbpMA1N0hgBLBgU44T8UfvWU+EluCdSVvYzLgu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\nhWsIIYQQQugI/w9JI5wKgVrfwwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7b1c80beb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "svc.decision_function_shape = \"ovr\"\n",
    "\n",
    "train_trans_nl = svc.decision_function(train)\n",
    "test_trans_nl = svc.decision_function(test)\n",
    "\n",
    "plt.imshow(test_trans_nl[argidxs], aspect='auto', cmap=\"coolwarm\")\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label(\"classification margin\")\n",
    "plt.xlabel(\"separator feature\")\n",
    "plt.ylabel(\"label sorted image number\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The structure once we collapse back down to an one-vs-rest sort of scheme still has the ear marks of the one-vs-one scheme. The separators built to distinguish eights from other categories had a fair amount of trouble whereas every separator was able to cleanly separate the zeros. There is no obvious correlation between the values of the collapsed separators and so Naive Bayes might have a chance again. However another trouble with GaussianNB is that it doesn't handle complex distributions very well. The distribution of any one of our separators might look somewhat gaussian by itself but their joint distribution certainly does not."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f7b1c6432b0>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bftptg11ONxUFk/jrw39P2R2PJk2ahEfV8vzfT3L9O3KYcUUGOQUOfDk2RlU6\nGD/dQ+1kNy6nomZcFhVjNWvWrEl27CExbBE8GQa+bIO6PUEO7QxStyfIge0BmhoiRMLx17B2qhtS\n+JeSzWajqnwUOtCJ0+7A7fKANggHNH09FuE+hb0/ynXXXEWmz00sFkt25CHz+/3s3LaeygoXXa1R\nAqEYoXCMSMzEtCxsNk12rh1PpmbTmkbmz31TsiOLNKS1GvTtP1FK3aiUekEp5VdK9SilNiql5o3M\n1bxqwH/uKaVKgM8CVxLvE9sJrAR+rLVuHp54QogzmTJxNv98/J/keEqx2U6/I1t3R4CKUWPoamum\nrq6O2traEU557pRSeDJcTLnQi9bg7zYxDJNwUNPvN8nOtXPFzVk8+3A3jUeiFJW5aWxsTHbsIcnM\n9EHMIBSCynI7LrdBJKKJhi16Ok2aGyJUjnVhWVBaeua2eamgqmoMHnWE1oO7ceVkkJntAxTR/gBR\nfx8el5tQ0MLp8KT0yOSqVSvIzwsz5fIMjhwK0VgXYdrFGWgd790ZDln09UZpbbLYtq6b33zv6mRH\nFmloas7ohP0spdRHgV8APwe+RXxAdAYw4s25B9ondhzwIpBDfPvZw8S7EvwP8F6l1BVa60PDllII\n8TrXXHUTT/733yjLLiYaiWDYbP9SzJqmRVtTiPG1Uzje3k9XV1cS0w5df38/ew6s4x2f8VFYYgel\nMGMaW4EiM8d2qv2SZuy0EIf39uHLyCZjYkayYw9JWckY9h3dT2Wtk+4OE9OMYXcYuD1QWu2kqy3G\nvi0B+no0Uyan5uK1l1WWTmTzphW867/G4O8J0dsbJBKO4cl3UDSpDMuyWPTnNcy+4JMpO20CYO2a\nhYRimrFT3Vx2XRZP/qmNur0hJs/xkp1no6/HZNu6fg7vDlFUWILL5Up2ZJGGdnTXJ+TnnNob4CfA\nZ7XWv3jNXUsT8gSDNNA/b78P9AAXaq2Pvnzw1MUsOXX/WxKeTghxWlprWlpa6Gwx6T7WiGE5cboV\nLpcLX5YPM6ZorPdTkFtFfl4e9a2RlP3luH37dpzeMAXFOcRiEbLzbNhsCmUAGiwL0IqKMS42reji\nZH+An34ztTY6gPiKfZsjjMOleGllPxUTM/DkuNCGoicQo3lviPx8g5xCOzvXmdx4+8XJjnxOunqa\n6Ww2OFEfwOW16GwJok0bfSpKc0MLoZDJrk09XDYpM9lRh8yyLFpaThCJaXLybGTnGXzg08Uc3B1k\n39YA/X3M1I3dAAAgAElEQVQWHo9i4jQPJZUONixyn3ZakBDnKoFzYj8ImMDvEvUDz8VAi9j5wMde\nW8ACaK2PKaXuBn6d4FxCiDPQWvPAA39k2bPruWjyTazfuIaWozbsLhPDHiAU6sLrzmHc2MmUl5XT\nH+rDVIGUXRwTDAaJRmK4PA4iEZNAn0WGzwaWBhQoMAyFtqCrPcqEmikUFRUlO/ag1dXV0dR+AH/A\nzqGDFjNu9OFwvlzQuDDLPLTV9dHTEebEkRixFG3+DxAIBDh2Yh8fvOtq7vnyP6gY7WDijAJcHk0w\nEOTogRD7Nkcx8LFy9XO8+93vSXbkIVFK0dsbZFSph4a6CHlFduwOxcQZXibOiH/yalmaSNhiwwt9\ndLb34nQ6k5xapKMEdie4DNgPvFMp9TWgCjgK/ERrPeK14ECLWCfgP8N9/lP3CyFGwMaNG1n6zFou\nmnwdNpuduqP7cWg3Od4SLNPE6zEJRLopKCjEQrPvyGZuvO3alB2JLSwsBMtJw8Eg46dn0tPdR1+P\nidtrw+GMvzFHwhbb1vYR7ld84H0fS3Liodm/fz8tHZ3MvGM0EX+YRfe3ctGCbAoqnESCGg20d2ie\nfaiHcWOq2LR1JW+74+3Jjj0koVAI0wrz3MIVmP5sdqzuZuML+1CAoQyssANPhguv18P6F3bS19dH\nZmbqjcgqpaiqmUx7fz27N/Uz7cIM4kvULJR6eT97RTSmOLAjgs0Wn89dWVmZ1Nwi/SRwJLb01O1e\n4u1VjwB3AL9UStn+bYrBsBtoEbsduEsp9ZzW+pWeuSo+UekTp+4XQoyAfzz5DNXFk7Hb4y2k5l96\nE8+vfIJQpJ+SvDFkOH1Eu8PsPbCTmNHDxBkVvO1tb01y6qEbP348XmcJq585xpjJPrJzMgkEQoQC\nMfr98dX6Lcej7NkUZtbsmUyfPj3JiYdm2/aXCJlQMiGbrHyDfSsVf763ld5Gjd3uJBqJkVttI6Mi\nG4fLQU9vas5xBmhubmbTSxsoKvTQ06Pp8VtkZNWQ4cvFikUwdS9ZWhHw++kLx1i8eDG3356aGzss\nWHALP/jFE1x4hZuFD3dw1a3ZOL0KrU9t5GHCc09203ZCMWFKCa2trVLEioRLYHMaA8gE3qu1fvrU\nsVVKqRriRe15WcR+C3gG2KeUehRoIr6w6w5gLHDT8MQTQrxWf38/h/Yf4fLpr05B92XkcNM172Df\nwW0cOLIWLEU4EsToi3DPD+7mqquuSunV3W63m/fc+RF+9tsv8IuvHWX2ldnUjHPjy3GhtObw7iBr\n/tlHeXkpkydcSHV1dbIjD0lXTzuZxZkEgyahw/0cXBqmIm8m2dX5WFEDZWj8gW4O7t2Pu7KPsim+\nZEceEq0193z3c8yc4GL1iyEC5FI7+zKycwtfWcAVCvhprd+Pp8/Apbp46MGHU7aIve666/jiVz3E\nVBjDZvH7e5spH+Mkr8hOX4/FwV1BCku85ObmUFJRmJL9jcX5T3P2kdjWbYdp23b4bKd1ALXAsn87\nvgS4TilVrLVuGVLIIRjQbzat9fNKqZuB7wBfARTxXby2ADdrrZcMX0QhxMsikQg2mwND/eviD687\ng1nTLmfG5IsJhgP0B/x0Rg9y7bWpu1PXyxoaGlj90naCrqnsa+ll/wNN2HUHTrciGrawGwZZXg+T\nxo/jve/6eMquZPd6MjEjJvtf7KDu2U7KPFPwR110hQMYDhvYYljaoNA5ieN7d3PbdZOSHXlI9u7d\nSziwj3feVszC5a2MnX0lWTk5hKNRoqaJTSkcTg+l4y6gcd8msrRm//7tKbk7mdaaBx+6n+x8ixcW\n93HDO3O56LosTh6L0NdjkpFtZ/rlPpY+1k1Xa5Bst8nYsWOTHVukoYGMxBbOqKVwxqttGPf+6bSl\n3R7gokTlOlcDHp7RWj8PPK+U8gK5QJfWOjBsyYQQr+Pz+bDZIRDqx+t+fRspm81OpjeLjq4WyqtK\nk5AwsVpbW/nSd76LZ9J0KhweNvzzCWwZeWAzMGx2nLUZeHMchDsjlJVNY/ToxPVCHGkXzr6Ch/72\nO5z+Hip9tXjwEbE0/bFWerr7MHBhquipTdCzaWpsT3bkIVm//kUunuWkuxcyikej7XaOdXZhYWCz\nu1DaAjOEy2aQOaqG/kOdBPvChMNh3G53suMPyv79+1n90mMseFs+zz7Sw+ZVfXS1m9SMd+PLddDc\nEGHRgx3UTs4kJ0+TES3C6x3xVpviDcAawEjsAD0F/D/gOuDJ1xy/AWgcyVFYGHif2FuBZ7XWsVOF\nqxSvQiSB3W5nwfXz2LBsH5PHzj7tOVprWrqOcOfHPzzC6RLvqYUL0aWVHKk7wuZF/6Bgxmx8lTWY\ngSjhjh4CJ4/TtqOO2W+7nLpoB8uWL+PaBak5+lxfX8eMMQrD6SYYLKA/EKW5q5FRvnFUlBejLYNw\nROMPddDSe4DHHn2Cb3/37pRbzR6NhnA7DTbsiODILaQfcGbm4/bmomw20GBGI0QDfgKWxm/G0KZ1\nxg09zmfLVz5LUY2ffdtbmfembCZc4Obw7hB7t/QTi2oKy1zc9qEiOlti9LQr2vd1EI1GZUqBSLhE\nLezSWv9TKbUK+J1SqpD4wq63AdcA70/IkwzCQEdinwI6lFKPAA9rrTcOYyYhxH9w8y03sWr5l6hr\n2Ed/wE9TSyNaWxTkFVFbPYXGlsNUji1kxowZyY56TkKhEEtfXItjwjR2Lvk7JRddhSsvn8gJP05b\nBtkZpWTXlNGXVc7mP65g+vUzeeL5RSy4ZkFKfuy8asUTvOP2XH77QBD6oLWngZr8C3E7MghFg4TD\nYWIxC4dhpyrvAva3LmfZsmXceOONyY4/KDXV41jxnMn2vWEcPh8OZxaezIJXXzMFdqcLpQxsho1A\n1MSlVMq9pgCbt62lYmY3GosJM7MpKnGSW+jCMjUQ33HOjCksU1FVU0hnXZjOzk6Ki4uTHV2kGSux\nu47fCtwD3E38k/n9wJ1a60cT+iwDMNCuyhcDjwBvB9YrpQ4opb6ilKoermBCiNMrLCzk2hvms3j1\nY+zYvhMCPuzhfOoPneTPT/ySFv9BvvClz6XkyNVrdXZ2gsvN3o0b8RZXY8/wEWvtJytzFE6nCzPU\nhxnuJ7uwkoLqmRxde4Qde/bQ1NSU7OiD1tDQgNfdQ3aWAiy6/e1ku8qwKyftPa0Eg2HshhePMwtD\nuQhF+8lxl/PY3x5PdvRBu+zyy9lfl0mn38QK+XG4swCINxHTp77SGHY7pmVimhpvaT67du1Kau6h\naGiop6TKhcNpYFmgDIXTacfltuN0OcjJc2F3GLjcDiwr3l4sFYt1kQK0GvztTD9K6z6t9V1a6xKt\ntVtrPSMZBSwMfGHXRmCjUurTxOc9vIf4Aq9vKqXWAg9prR8YvphCiJetX7+ep/++hPe8+VME+oM0\nnWwhGo1RUlbElcXzqWvaxvPPLebt73hbsqOeE7vdTiwSoeVIPTk1FxDrDuAxMmg9uolQqBV7bgY6\nZmIejeB2FBCLGXQc66C3t5fS0tSaDxwIBMjI0ES1prI6Rv3hNkaVTKKrrwuvIw+Hzc3LtY3dcMW/\nR7N+7WaCwSAejye5FzAIPp+PqdMXsL3lWSItDeRVzsKydHzDin87t6+tAa8nh6zSnPgfNSmktbUV\n04oQ6fdQUOzg6IEQJZXxXs1KqfjraSgsUxMNmxgxJ05bDvn5+ckNLtLSBXnVg37M02c/JekG1XdH\nax0DFgGLlFJZwFuBbxLffkyKWCGGmdaah/74NyZUXYwvMxtfZjbFxaP+5Zzs7Ct56vFnuOnmG1Oy\nQfzLCgoKyPW4iQWDYNgwe3to6dlB9sVjKBg9GeWwo4BIj5/u7QfpO9ZGrlHFkSNHmDBhQrLjD0pm\nZiYnTgYwLYMJ45wsXRygx99HhrMQhy1eoGodf/0ty8LUUTLcuTT3avbs2cPs2aefH32+umLufBbt\n2k/D9n10HtlGTvVMLG0Dy0JbMbTW9Hc00tt4mIKiCnSkK+U262hqamL8pAr2bW1i+lwfy59sZfol\nmXgzX/sJiaa7I0YkDB0nnVw9780p/wmKOD9t6Tya7AjDYkjNI5VSVcC7T93KgOZEhhJiqGKxGNu2\nbWPZyoU0nqzHZrMzdeJsrpp/A2PGjEl2vHN24MABejtCTJwy6oznuJwevLYC1q9fz4IFC0YwXWIZ\nhsHb3nQLTz27BG2Z9DTvpfjmC3AW5RKNhSEaRhkKw+Mk7+LJhHrbiR4KE+hPvXWnpaWlNDZZ1B+1\nqCx3YBGiP9xNlrsUS5soZaC1hWnGsIihMIhaYbzuDNa8sDblitji4mLMvj7cWR4I9tG0dTGegnIc\n3iy0Mgm0HcOKBCmsmoi/pYHO9nrKy8uTHXtQ2traiFkBCCn2bgxROdbDk/e3ceOdeeQVOdGWpul4\niK7WKHW73FTnTeO6a29IdmyRphK4Y9d5ZcBFrFIqm/gKtPcQ3zs3CPwD+BSwdFjSCTEIgUCAn/z8\nHvzRvcy8tIB5d1QQi1rs37WJH/96OfMveQe33/62lJ5z1tbWhtuRddbzPM5smppGtNPJsFhwzTWU\n5WTScnArjlIP9jwfhjaw270oFFqbmFaMUF8nuROr8R/djd2Rehs7WJaFco7i+RVHmTFFU1iaQW9z\nM2XGFKJmOD4MqxSGsuGwuwlHAnSHTlA7fhInT6TeGMLkyZPpbDyIr7oce7QYtxtC0W5CPZ1E+ntx\nZWaTUVqLy5NFW9sOjFw3v/3j/Xzvm99JdvSz6u3t5ff3/ZgTxzfT3tjIe+8qZdWyfrZv8WPYFb/4\nciPFFQ7cGTasmEHjIcXcC2/li5//Vsq1EBOpw0rTInZAC7uUUo8T36XrN0CEeI+wUVrrd2utF792\nK1ohkuV3v/8ZjtzD3PmxqUyYOor+QA+tbY3kjopy/dvzWbPlr7zwwspkxzwnTqcTS0fPel7MjOBJ\ng1+Idrudb339qwRb6/BUF+Aw3Bg63oZJaw0YELOwAgHsLhv2UR6ys7OTHXvQ7HY7Y2pr2X/Cx5PP\nwqjSWvzRVpr9B1E2A5vLheFwYhkWoUiA/mgXHf1HqS6vxeVKrRZbAMeOHaO02KS7sYnm+o3ECBAO\nt+DvOYJRacOqiNBtHqZu+yJ0NuTPrmXFhjXn/aK9UCjEj3/0DUaXHeTeu2dw67WT2LHRj8OdQchR\nwInoKFopYfs2O11NmUwcO51J4y7nO9/+gfSHFcNLD+GWAgY6ZDGB+NzXv2itG4cxjxBD0tjYyMGj\nG/nYl6bR3tbGnt37wLThsMfnE0Zj7eSW+XngwZ8xd+68+J7lKWjixIkEYl1EomGcjtPPEdRa0xNs\nYsbM949suGHypje9Cd9n7sIM9xMOdON0+zCwY1kxoiE/sf5efI5cgpEenBku8vLykh150JRS3Hrj\ndby0dx/hcJj6ji6c5Xl0B1ro7+0h11OO0+7FJEZPrAm/v5mSnBp6gx1cc9n8ZMcftN7eXuy2CKNs\n3TQbLk4cfoG82ROoHH8FofZeov19GA7InT2GUE8vfS3dRKJRdu7cSUlJSbLjn9Hq1S9QnNfAm26Y\niFKKWVNL+fHn9+OYPZbyW0ZRmxvv/xoLWhxeeZgH/7CN993+QZkHK4Zduk4nGNBvcq31FK3191Ol\ngFVKlSulHldKdSulepRSTyilKpKdSwyf9RvWMmmWl67OTnZs34PPXURBbhnZvjyyfXkU5JZSU1VN\nY/M+nnjiiWTHHbKsrCyunH8p+49sPTUS+ar+gJ+d+1/i6SUP0dnbQmdnJ7FYLElJE6e3txeH5cXW\np9H9ffR3NOJvO0qw8yRGOEamMw+0gcJB6+HjWFZqfjB02aWXkmn00d8bQhdlkHPpRBy5meSOGU2v\nu4MWfYQuWxPesmIqJ19KzLIImu1ceeWVyY4+aPv370cHQvzPx7JxmiZZpVlYxw7R/dwTBLcsJ3Dy\nMEaBE2UorN4Qfc0dREIh+vv7kx39P1q96ikWzCtBKYVlaX7xl72UXncpzoJCOptMmo9HaDoeof5I\nlNzJk5hw/cXsO7CUp59OvVZpIrVorQZ9SwWpORz1HyilPMBKYBzx+bvvBsYCK07dJ9JQd08bOXlu\n9u09QLa3CJfz9R+lOx0uysoKePhPj2CaZhJSJsb7/997yS0z2L5vDf7+bixtsWnHah5/5kH27NyP\nDnupKbqAX/7gQT76of/i4MGDyY58Tpqbm7Hhov9AMy5fNr6sfDJcOXid2ThsTixlol0QauuCLosf\n3vuT1xX4qaCiooLRlflYThNXTSFFUytxjHfSFzpJSVUtNVMupKx2Jln55YTMXo737uKmWxfg8/mS\nHX3QVixfxIzJDtq7TUwVoya3i7csUHzlK6P46peLueOKMFl7NoEZofT2S1B2A39TB6NGnXlBY7JF\no1E6Ok5QU5UDwI5dLbQbXqIeF1dclMMlF+RQPcpLZaGHmjIPs6aVMfnqaYTtimVLHiEUCiX5CkQ6\nS9PZBEPrTnCe+whQDYzTWtcDKKV2AYeAjwI/TV40MVwyPFmcONmJ02uSk3fmuWXRoB0dtbNjxw4u\nuOCCEUyYOF6vl29+++ssWvQMzy5cwuGDR/B3RKkqnEpFVQU1NdWvLBBpaW/k7q/+H/f84JtUVVUl\nNfdQ1dfX4w/6yc6poX3DbornX4DT50FbOl6sak24o4eulw5g9oU5tOc4Bw4cSLk2W263m1DYjTND\n4fRZuDLslF8znY7dRzm2dSu2NgeGshMI9mHl2XBVZ1PfkBIfjr3OkcPbueEaJ48s7OWC6S4++pF8\nysZmoQwDreGCOT5uvCXMvd/ZQ8P+TAqvm8mJ+5ef110YjFPZT63BY8ueNsL5hWRnKZyO+HhRTpaD\nptYQza1henpP4nI7iGZlk5XRy9atW7n00kuTfBUiXaXKyOpgpd1ILHALsOHlAhZAa30UWEt8qzSR\nhi666DK2re/AZpx5kUt3Z5CuFjvFudWcOHFiBNMlntfr5e1vfxv33PtN8vPzeevN7+Oqa+YzceKE\nf1nhXFxQTqF3LH/7y2NJTHtuuru7CRkhfIWjcPd4OPHEi3TuOkywtYNgczvtG/bQ8uwWVAAizigZ\njiJeXLMu2bGHpL+/n1GVdtyuMB2Nxzm5ZT8ddQ2EXWF6VRt9GT04pmWSc+U4bA4XTS2tyY48JH1B\nP22dFhleG++/M5tRZW5QRvyPEgUoKBzl4pN3FeLYvg1XQTaO/AwOHDiQ7OhnZLPZqBk9lZ27411B\nwhETE/B64sVDZ3eUTdu66OkJUV3uoLpCkZUR5mRrD/sPHKO1NTVfSyGSKR1HYicTb/317/YQ35xB\npKHRo0fjNsrYs+0wc+e/ft/xWMzixWUnqCm+AjNmpc1CiqefXkggEGDX0WXYDCc53grshgNLW3jc\nGZSPqqG6fBzrNy2ko6MjJXcDOnToEKrASWfgGFU1l5AXi9J98Dj+PUdRSpHhKcBb4OOE3oERdGLq\nMN1dPcmOPWjRaBR/bxMZ2RF6th8jGAaVl41rYjHZZQU4MzMINbTRs/UInS/uxmztw1CpNw5hmibY\nPGza2cvY0Q7Ky+1gM4BTQ5ivUTU2g4kVnWw/cJyMyiIWL1nM1KlTkxN8AObNv5Xnn7uHKZOKqCzJ\nJHaol0hFJv6+GAcP+5k03onToXC6PNgMg6xMG13ZIcb5Yqxcvohbb701pVsAivNXCs6wGpCzvgMq\npRxKqVuVUjUjESgB8oCu0xzvBHJHOIsYIUopPv3fX+alZf2s+Gc97a19AFiW5ujhDhb+tQ7dNZEJ\no2fRF2lj7NixSU58bqLRKL/6zU9YtOR3TL6ihzk39FM2cz/1gb+ycvPD7Ni+ky1bNvPYogfYc3Ar\nbkdWyo70RCIRbF4n7qvKOXpsPf3d7eSXjKZ89AUUFNUSjvbSYRwnY04FOhojHO0jNz8n2bEHxbIs\nfvWrHzJrksXHP5BN774WYn0GRtBH9ECU9oUH6Fi6B09+FuW3X4LVHyEznM2R/Qfx+/3Jjj8ohmFQ\nUVnFieYYE8Y5MRRo0zpt8aYMxbgxDkKN7QBs3r1jpOMOypw5c8grvpLfPLCPiWPz8HS00toc5tjx\nIGWjDGKhMKG+COFQkHAkTHNdG7V5MW6+tpAMTyuHDx9O9iWINJWuC7vOOhKrtY4qpR4Drgfqz3Z+\nqrr77rtf+XrevHnMmzcvaVnE0EydOpWr593K4V0neHZfExGrEcvU5GZUMLrkVipra2k4eZiy6kJq\na2uTHfec3Hf/L+kIr+fOT44m0GPS3dNJXoGDq68bR/uMfpY+cYDC2JUU5oxl7769KLc/ZduKeTwe\nbC4HtkwX+e+fiX9rA217D2NFTGzZbryXlVE8ZRyND72AGYxwsuU42dmptdhpyZLnMQMvceftJfzq\n4UZ8lVPxTZ+B8mbhcLtAa/yNJznx5FZ8M4rInz6eWPdJ8jxVLF2yjLfcfluyL2HAlFJcfOFcdu3Z\nTE+3hc2AaDiK5XZg2OOfkLw8aGRGLcIhC8Ntx7+zkX7P+b1rl2EYfOSj/8PChRX85k9PkGvY2bN8\nOw05mWSE+9FmfKtkr09RVJuJWX+MW26wk1dQytVXZLFm9ZKU+QO7s7OTFS+8wL66QxiGjWnjxnPl\n3LlkZZ19M5Z0tmrVKlatWpXsGK8zp6By0I9JhV2sBjqd4AhQNJxBEqiL04+4nmmEFvjXIlakrk9/\n9i6+9L/foNx2BZVlY7HbHNgMG6ZlcrRxPx2hI3z7a19L6Y/sjh07xr7Da/jg56fQ1trCpvpthAIW\nLpXDiSY//X0RKsbD4U1bsXE5OfYa6lpXpWzrqenTp2Ms/hud6/ZTcttF5FwxFn3JGAzDDigsK0bP\npjqCx9qxlEVhfhErlq7h9ttvT4nX2bIsVi5/nI+/r5K/PX6CE4HRlF98AVHDSSRsEYsE0Erh9OWS\nP24OHS+to+TKOYTy2yktrOaZp5/nzbfdmlJ/pFx84XweePAnrF0f4qabssBmYoWj8RFZW/w6tNb0\ntgTZvM/CKHVh8zgJ9vYlOfnZGYbBm9/8Vm688U1s2LCBdR/+CKEeL0UzZpFVkg9a03uimUMv7GFm\naQCn04fL5aG8zMfmPQ3Jjn9WWmueevppHlr0D5yjK/CVl6I1bN30Ij+8/z7GlpZRUV1NdWkZV8/7\n/+ydd5hcV3n/P+e26WV3dmf7rnrv1UXuso0dN3AMpgbyI0AghCQkBEICmJIQSAKEJJDQa4BgjE1x\nlatkC3XJ6qu2vc3szk6f287vj5WwMC4rWfLs2PN5nnl2NPfOud+zmp373ve+5/teXnHtgl8qz06C\n3XHHHeUTcxpbR6b+Z+tsmGwQ+zngo0KIh6WUI+dT0DlgHxN1sc9mAbD/ZdZS5WWmubmZz37+k3zj\na99m6857CXomakCzxSSLls7lr975cdraKtsy+LHHN7BwdQBNU/F6vYyOJeneb7Bz4xDCDOMzImiG\nRio7gJXfQn1oOjX+Vh595HHmz59fbvlnzJVXXknh/UliC1vo+/7j+DsacXImdjaPa9oIFwQqbqqE\nYgui4UZSiTydnZ3MmTOn3PJflN7eXrzGOA3xBjbvtgg2zULTVYomeD06ihBIwHXAUurIBBtwEmlU\nvxevx09mOEehUCAQCJR7KpPm8ccfJh4SHO9y2by5yIVXhHFKFooAcXJ5v1l02PxUnr6Cn2J/Ei3i\nR6mglsKGYXDfgw9TM30+8fYYNVHB2FgCkMyMa9TOXUnfwTC9Q0lqa0/gDQYw9Ppyy35Rfn3fvXz7\noXuZdfvNeE52GRsbG6NnsBdz9Xw2PLWDRXUhDgya/OyODaxfuZY/fec70bTK+b97RVIh5QFnymQ/\nVVcykck8LoTYzEQL2tPLhKWU8o/Otbiz5B7g80KIaSddCRBCTAMuBj5UPllVXi6ampr4+499hOHh\nYY4fn6iAaW9vn9Kdfs6EweEu5lwQBinZu/cAj96dZuRIlBn1lxCOTXSrKplFtHALmXyanrFdzGxd\nzFObtvCn7313mdWfOT+/+x4U2092bz+aqjO+6xiBBc345zfimjbZp3sodg8SKEQoKDDQ38/06e0k\nEomKCGJLpRJ+n0pXzzh4wvg8Hop5G9SJ9rqIiQX7AK4Lgfp2MoPH0NN5DMOL61bWQsUnnnicXdt/\nzjWX1fA/3x/lP78ySmrc4dJrYnili2NZjI85bNmc40e/NMk1TqPm0tkM/fBJwqun7qKuZ9PT08NT\nO/Ywd9lscrksbc0aC0Iarjtx6lQUQW10EY88voGVi202PNLFqnVvKrPqF6ZYLPKdn/2UGa+97rcB\nbCaTZtvTe/C2NhIK+PHHaul+dDPXve9duKtXsOHeDfD1r/P+97ynzOpf3bxC13VNOohdB1jACDDz\n5ON0ptLv52vA+4C7hRD/cPK1TwJdwP+UTVWVl514PE48XilVMJNH1z2UijbZbJYH7jzGYKef5dOu\nwtC9J5egCjRfAMfUUaQfRREkUn34hiuvVs00Tb73o58Sbl9M8sBGQms6aLv9CtSQDyEEQghqVs0i\nu7eXof/bhtcKMZYewZE2uq6XW/6kqK2tZThhTVgyuZJwAMZHc+iNBpZto2s6SHAdCSgomk4pnSVi\nBsjmx5k5u+N3bNWmMq7r8ou7v8XlF8W576Fu6ustjnbX8NXv2dzz0BCzZ05Y5B3tgbSvAc+Nq2ip\nDTLwxFP4Y1GMCgrWt23bhlHbTMCnEAlFOdGTZNE8FUV5JiPm8RqowTjbdg2yc1+Q9//NhWVU/OL8\n5je/IakJxo52YpomwUCAQqmEVl+LJzAR1PriMca9BiPHThCfNYM5113FQz+4k9f13UhLS0uZZ/Aq\nZipFaeeQybadnf4ijxnnW+hkkVLmmcgcHwa+C3wPOApcdXJblSoVzbLFF3Jw9xgD/Un2bSnQGJmN\nR/ciAIlE4uK4LrgqYW8cv17LaGaQYPD5m0BMVQ4ePEgiV6KUSmC0RWi8dS2eeBQt4EX1GwhNRQiF\n6PcSaK8AACAASURBVMKZ1F27hKI3j21ZZIojFdPsIBaL0dq+nIGBDKmRQfx+h4BiopglJA6KAooK\njgsSl8LYCMW+BLVKI92D+7n5dTeUewqTZt++fcSiGS66oIODR/O0zjYI17RRv/gPGHCms9Vdwr6W\naxA3307s1hswIgHGth6ksG8EVFi7pHIalGRyOQxfANOS+LwaiTGXTVvG6OrJkM2auK7EdSSpnMJP\n7h7nmte8DZ9v6jaV7Ozs5AMf/hB7E4N0Dg/Sk8+wt7eLfZ2HGUuO/k6XPDUWJZ+asLlTNQ3v7Gls\nePSRckmvwqvYnaASkVL2AreVW0eVKueDCy+8kJ/c9TXSmeMoTohwsB7HtScykyhIoFiwcWyBooKu\nekEKZs+bMteakyadTjOYGCaf6qXuxkX4YlGeubkO6BKpg50rEl06g8SG3eTH04Sj/opqx3rDjW/k\nK1/+a6K+MXLjoyxd3MK+Q2mKdomsJ4Bm+HEcSSmVJbl7O3W0cax3P9fe9iYuvHBqZ+9OJ5FI0Nqs\nkUmnEB6BqmuonhDeYJiW+DpSPUcY7TqAHvEhXRc3axGsbSPSMIPk8T1cc/U15Z7CpInX1aFjc/ho\nhli9oGmaweCAzc59OXQlB4CUKs5Qltba6dxyyy1lVvz89PT08PY/fx8D0kKvqyE0dwbmUILC0S4K\nx7rJbt3DkN9L+5qV1CyaC5aDcloNbDBeT9dAfxlnUOVcZWKFEJcBz3VFkpJS1p6bo0yeSQexQgg/\n8MfAZUzUx44yMZFvSSkL50delSpVno3X6+XP3v1R3vO+tyEdBaRECAUhFKQDxaKNU9Lx6F4sp4jr\n2igqXHNN5QQApzh+/DiF1BDCB77pcfg9c3+BkBLFqyMdMOpDpI4nyGSm/ir205k9ezY19Ss59tB9\nGKM70Xw+GmtDuP05+gayWLaCdCTpo3txRzOkPCcwDJV58+dUlCuBYRgMD2cYSxylodmgu7uEGtSw\nUjkUzYOGF7/SgEgLjEAY/8w4ek2Qnk0P4RYsSqVSuacwadauXcuHPn4HTWuWUtOo0HM8jSYls2bo\n5PIuxYIkMZSh++ARlt14IzU1U9fG/Kvf+Dp9jknH62+i5/GnyOw+QOZAJ94Fs4muWoTi92H2DpLo\nGSTx43vw2S511z7zfeNYFh7j+bspVjn/nOPMqgTeD2w77TX7XB5gskwqiBVCNAKPAnOYqC0dBGYA\ntwLvF0JcLqUcOl8iq1Sp8rssXLiQN9z6Dj73ya8yYicxqEO6Do4NQuqoioGUEkVoWE6JQFRnzZo1\n5ZZ9xuzYsQPHyqCGI+BKpHQRzw5khUBVVUyKOLaNR/Ux2F95X0fHThxk7Q0xpAO//vEjEGjCiLWj\neoI4ZoFs31FkKUcg2kSxkKUmUsev7rmfm266qSKsxAAWLFjAP37qCB94px9VEahehVTPPtTUbkLD\nFmHFYDzvZTwfQAsEsPN5dMPPeO8J9NoAv3zwXpYtW1buaUyKgYEBGhtc3LFujiT8uNkEo4MpDhVs\ngkGd5rYQRnqAtYstnnzipzz00NtYv359uWX/Hul0ml8/+jDRi1cQ7GhBlExSO56m9tbrUAM+rGIJ\ngUCvr8XOFyn1DFI82sPxLTvoWLGEYF2MzJETXHD91M00vyo49zWxB6WUW875qGfImVhs1QCXSCk3\nnXpRCHERcCfwz8Dbz7m6KlWqPC8Xr7sYzfhvssUkVkmgqz4MRTn5XSWRgHRd0qUBLrx8VUVZMJ1i\ndHQUIQRGOELuQD+h+a0IyXNkZKGYSGEnsyAEuqfyKqUsq0hTg8FQr4mp+JH5Eo7ZjyJUBGB4/Pg7\nZmCm0kSydZTsLEePHMM0TTweT7nlT4rx8XF03UNiVGLmHMySw00XKqxe2Uy8sQEhVIYTBTb9Zowt\neyWZRD+WncO0c0Sb29m+Z1e5pzBpHnviAV7/jnl8/5uPc3iXTWzmYurmLyJa5yc7lmLweCcRmeeD\nfxrhRI/D3334j1nz8N4p1ywgkUgwbhZpmTUNIQR6KIgn0oBbKKJ4PSiqijmSJLdhC0oBwo3TUBe2\n07V/mKNb/5eaplpaFY21a9eWeypVzh1T5qp5svehrgM+cnoACyClfBL4e+APzrWwKlWqvDCGYRCO\nBqmrjdOX3oXl5CeWdUkX13WR0iFROIKjp5g+o/LqYQHaWttwSoJwWxOZ3V2YwxkcXBzXwpEWjrRx\nXBvbsUk9eRhrNE/QiDFj5rRySz9jZs1awMigxb13lvD5W6mpm4OmedF8ITR/GAWD0uAYtivJ22MI\nPcbgSKKi7LUGBwdZf8Ucdu1zySRNrrnQy/orGojVhsBxEBIa6wK89g9auHRZHp+iYllZgotbMHNF\nSsXKKScYSfbjDxj0dJVYetlK6ptrCXlzuLkR2uIm198yg9XXruM/fqCybm2Atcty/OKeu8ot+/fQ\ndR3HcVF0DSuXp5TLEbtgBYrtUDhygvyBI6Tv3EAoOoPYoguJzJhLePZcPHXN1C+9lJHOEdpiDRjV\ncoLyIs/i8cL8QAhhCyESQogfCCHKYsA+2SA2CDxfVXbvye1VqlR5GdE0jbmz5uMP6wRCXnqz2xnI\n7SFtdZMsHeFQ8kGKWj/rL72JyBTL7kyWG2+6EZmXlPpGiba30f3Nh8h1DoBQJjKUQsFK5xi6ewup\n3xxB5l2C/lrWXXJRuaWfMW+47c089UAWy4rgmDau10N82ZU0rria+NIriS24GE+sGSs1iqsrWLaJ\nFAqmaZZb+qTRNA1FUclk0kyf4WHZkiCqFkLRdKSQWFYO08xim1kuviBIQBvAb9QDAnNonLZYQ7mn\nMGm8Hj+/2XgCb/1MgjVhli40uHi1xkWrNObO0gkGFGrjYYy6WTy5zeSClR4ef/QuHMcpt/Tfobm5\nmYjHS6a7H7dkovi8qIaBEgygN9bjDI8R7VhIYOZsFF3DtExy42nG+4fwZYvc+IZ3cGwgSWdnZ7mn\n8upGijN/PDfjwL8A7wSuYMLCdD3wpBCi7uWZzDNM9p7bIeCtwH3Pse0twMFzpqhKlSqToqOjA9Xr\ncuUlN3Gi9zAHDu0mmx9n1BrG4zFYd/HlrFp0CbsPb2T5yiXllntWrF69GkWFwrEkkfWzCBtt9H9v\nE3rUh6e5FrdkUuhOYo1kcJMWUlGJ1YeZO3duuaWfMfPmzSOfCqEoPoLtc4nOWIJdylPMJpGOjUAh\nGJ+OdF0SR7fi8/sJBIMTzRL8lWGfNnv2bD7/2T4Gkyluf20IyzQI1oRRVBXLLCAMFU7W9wa8GvPm\ne9i8y0vmWB92sUhrx5n3fy8Xq5Zfyo8/cSfhtnkUCy7h0O/njFwXmqc18dBTndx+vYqul8hms0Qi\nkTIofm5UVeXNN97Mfz32IMHX34ibL1LMZHAFaH4fTs8IgTXLwbRQdQPh0XGLJRwBWemwa98+aiON\n3PfAQxXRfOSVypqGM0+UPvwcr0kpdwGn1/U8IYR4AtjCxGKvj5+VwLNkskHsvwDfFUI0AD9komNX\nI3A7ExH4W8+PvCpVqjwfXq+Xa6+7isfu3c2KhRezdP5aCsUcQgj83iBCCMbGE9hquqJsmE7n0KFD\ntMwM0n88z9ijncTWLGDGH1xNfiBBYXgEJ21jlHzURWZRihQY7t5Dy/RaFi+unM5OpxBCUCqqKAEv\noba55Eb7AIHhC6OoGq5rY+fT+GobEcdUculBnPp6gsHKuREWiUTIFFRijSrZtEug/mRNZTGHMFRU\nn4FQlYnmDqZNwAdKwIvMuQhVYSSbKvcUJs2FF15IekzSOj9EIVfEdeXJFeLP3Ke1LEkw4mX/qIvj\n+NBUY0qWh/z5n72fX23YQN+GJ/BEI+SOnMC3cC52OoOi6IBA2hYi4AfpInM5hHAp5VLIaB0nBofw\n5ytvseUriS1DPS+6z9jeQ4ztO3TGY0spdwohDgOTWj0shHgb8CspZfI5ttUCN0gpvzuZsSYVxEop\nv3/SYuuTwNdP2zQEvEdK+cPJjFOlSpVzy22vv5U9u/eyY//jtDTMxKN7CQWjSCT9gyc4MbKLD330\nAxXT0enZdHV10TojSldPP3XBZZg7R+ndcwAHB0XoBLVGQv654DUINgYY6z/M0hULKsoj9hRSSrL5\nLLHpyylmRtB9EQxf+DTngYmAtpQZxVfXjHmiGwWrYjqTnaImFibrqJzokcTrJWYxh+LV0EJ+QCJd\nCQIUn8FIVsUu5VGCGkpRY3x0rNzyJ43P52PRgqUMjCsUS5KBIZumBo1iSeK4EiHB6xHgmriOgyta\nqYlNm5ILML1eL//6qU/zZx/6a/Z2n4CaMERDSNvBzuZwCkV0vxddk7iZPIpwCEyLUSPz2PYwWbfE\nvs5OpJQV46TximMS7gQ1C+dSs/CZu1gnfvKL86XmW8CFwO8FscD0k9vPXRALIKX8HyHE14G5POMT\ne0hK6U52jCpVqpxbCoUCplXg3gd/SqngABKhQlNbE1etv5KPf/rDLFiwoNwyXxLjyRJCqFj+HprX\n1lE3fTmarpEfy9K3Z5Dx/iPEZ69DIjF0L9dd/5pySz4ruru7cYXEdW1Uw4/hCz7rhD9xFjICETRf\nCBQPxZxVHrEvgbr6ekQhwPani6xYLrBKWQJ1jUjbQbrPWKgND+XoGlAxPVlUw4vMSlrqKqcmFuDW\nm2/gnk1Ps6+rn/2HivgDCuGwgqIqSBeKeZdDO3uZP03y6KYx/vBNr5tyQV4ikeCzX/oCnclhnMYY\n/kKGfC7H+D0b8M6bifQoOMU8Ho/AHMxCoUisvQa7aKMKwYxZIYaPHCSTH+fYsWPMnPnsrvVVXhbO\nY9tZIcQqJmLDn0z2LS+wLcAZeM5O1if2Y8DXpZT9wIFnbWsC/kRK+cnJHrRKlSovna6uLq6+/DXk\nky5twRX4IxEsp8Rovo9k3wCPPfIYf/uRD5Zb5kuiubmZoV6TcJPK0tvn4w8HcUvOhOVUoJZwa5TB\ng4P07dpOMDQHv8dTkfWwMBEsqH4fxdQgMe9anm/dreNYuJaJqwrMgsvY2NiUNsp/NqtWXMLP7n0C\ny4hx/8NjrL/Ch5b2Y/hDKKqOEIJczuKuXyZJZvzo03RkwcZMpFm9YlW55Z8R16y/ih/deTcqDrGm\nIJ3HLWZO0wmFFKSEbCZHKXmUtHAZGLamXM1oJpPhI5/5FIUZLYTb6tnzwEPUXHspcvd+fKuXUjh4\nBHMswfiWJ/AuXUWgxo+3JY6iCOxUDrQC+bQgKAfRQxOdv6pBbJk4R80OhBDfA44CO4E0sAL4MNAD\nfPkF3rfs5L6nuFEIsehZu/mYKFOd9CrAyWZiP87Eoq7ncihoPrm9GsRWqfIy4bout9xwK0qmlnm1\ni3BcG5BoupfmcJhIqYmurh289Y1vY8NjD1VUV6fTaWpqQmqC2Vd0oLgmiilQNe9E3aSY8MFtnt/C\nyIE9jB/vZOnS+USj0XLLPiuCwSDhcITx1DBWIYMW9PDshIXjlDDz4zi5NIph4DG8FAqFigpir7ri\nWn7682+iqBk2HzToS+dYt7yflgY/QvNx7FiRJ57KcCLlI7K6mfDSafTe/zh2tlBR9b8A8Xiclrog\nx3c9hBWdgx6OcegoKK5JKTVMrr+T5oYsfeMa82aFePrpp2lqaiq37N9y34MPMBoNUNvewr1f+xbq\n4jmoHS04W3fhCol/9RK0gI7naCfZnj14I0tRlBBSgpPNI2pKHHj4Sd781lbu/2UfIyMj5Z7Sq5dz\nl4ndx0Sg+QHAz0Tzq58Cn5BSjr7A+27mmUVfEvjo8+yXBP7fZMVMNoh9oRC+Bqgc874qrwqklBQK\nBXRdr7iawcnwwAMPMNyTZk5oHS423pAHzVA59afqtTwU5Wx2bd/F9u3bWb16dXkFnyX5fB5vVCPc\nGMQxixAUKLp2agE7UlEwFJWWpQ3s3P80f/kX35lyt2MnS2trKxGPzphrkTi0mfr5F6F7gghFQUqJ\n61hI2yJ1eAfBcDPFXDdCdSuu/re5uZk/etOf84nPfgw1GOGoVk+yK4S6ewQ7lyYnQnjmzqZ90UwU\nQ0XRFGTexU4XKu5iTErJYKKT9TdI+o7t49hulUJBoghJW5vDqtdovPZ1M+jqKvK1zx9n/XX5ckv+\nLa7rcveDDxC6eCXb9z5NKV+gcf4spBB4F88nt3EbUtdwR5IYHTHsosWRJx5CcxQ8Hj8hrYAyX+fm\nm7zMmWHwmLCmVIBe5eyQUn4W+OxZvPWLwLeZOEkdA17HRDb3dErAkJRy0iH38waxQojLgStPe+nd\nQogbnrWbj4lGB/sme8AqVc4nqVSKBx54kF/c/xDZfAHpuixZOJ9bbriO5cuXV2yA82y++fXvUKO3\nIxSBL+L7vZO7pus018+gN7OPf//Sl/ne9ydVIz/lcF2XcF0AQ/WiGB7yuWG8Moame397ae3aForH\nxlUKPLnpSa6++uryij4LTNPkX7/474wXLVTNRaguw7sfIdQ0C290wie1ND5Crv8YgUAzAlBcQbQ+\nUnFBLMBrb/lDurt6+btP3IF/Thv+S9ah+Dy4JZOQpqN4NaTjIFSBOZbBHsghUGloqKyaWNM0GRzq\npy4BAycUSgUHw/DgSoX0uIPM6ezanWPJIh+mZU4pz99sNkvGLJFPJTHqa1E0FRQFx7LxtjWS3bgF\nJRwicOVFBBsCGD4NM1MgvacTsXcvr7s9zup1LWCajJzop1TwMG/evHJP69XLOSonOOvDSznOhMcs\nQojpwICU8iV/4F8oE3sZE924YCL1+47n2McE9gN//lKFVKnyUunv7+ejd3wGy19H68r1BCM1OI7D\nYNcRPv2l/+Hmqy7mbW99yysikO3rGcCjhNF9+vNmp3TNg88TYtvurS+zunOH3+9HWAKkij8cxbJL\nFPNjFAsSRdGQrovEARe8/jDf/tGPePs73k5HR0e5pZ8R3/ru99h9Yhg1LFj6moUc35TC1zgDN5sm\nMzYCuBieEM2zViNtlYE9j1IqJKmpn11u6WeFEALd8ELRpdA9Sv/9T+HkLFTDg+s4GDV+wova8TbW\nk3xyH7oTwO/1sXDhwnJLPyP6+/vpOZ4gnVJYvDjKa28IYhgqvX0mm7fleXyzoH+whCJcaqMqTKF1\n0qqqUiwUSKTHCba3IIUg29WLUhMhs3UPvsXzUGrCKB4P2a4hamo0In6FGZe346yp58lHN7PiAgfh\nSo4dTLFq5Wupq3vZvfCrnOI8Luw6U6SUXedqrOcNYqWUdwB3AAghXOACKeWWc3XgKlXOJbZt88l/\n/ByelnnMnDn/t6+rqkrLjLnEW6dzz8O/ZFpHO5dddlkZlZ4bNEPFxkIzXrgiyFVsStIhn89XjCH+\n6cTjcXTHQ240i7++Fk33EIzUYxdLuI4NikDTDfp+cxjDE6FgZrn/vgd517vfWW7pkyadTvPgoxvx\nxKcRmxshvrAVOycYOTqIWttKyNuOzxtCURWK40n69j2JPZ7C1uXE76ACKZVK/PqBDRjBCBYqaqGW\n6NxZeGM1oEJxZJjk43uwi9vxqPWoHg+Bxgi9vb20tZWlu+VZ8e1vfoegz+Gdb65heptAUXK4UqG5\nPsCKZfX89OdJtu+B/r4RFk9vBDF1Ig2/30+tP8DBE92krRJaRwvZQ8fwL19AqbuPyC3XYA+MoNbV\nIF2TQKBEY5MxsRwxEGLUH6FzxwCN9T42btb40r//Sbmn9OqmzB8tIYQDXCil3HIypnwhRVJKOaly\n18n6xFZWIVKVVx27du1itCRZcloAezq6YdC+eA0/ueseLr300orPxl5x1aV8c+9dNDMdXMl4IUHR\nyiIQBDxRgt4aMsVRHL1IQ1sLpmlWZBArhGDRrCU8+tQjxGY2I20X13JRFA1FeMB1SR4ZJnkgg6tJ\n3JLLru1Pl1v2GbFr1y6MaAP5XJJISwghBNMunoM/1kffrqOkBjtJFgVmZhwFEyOgEii1kMgdp1Id\nDhOJBDYqprSIL1pHMNaBW3Qo9CQQuoJ0VSJNSxjv3IMvFGeo9wizbljMfQ89wJ+8Y9JrPsqKlJK7\nfvZt3nF7gMsv9BCrMwAoFBxSY3mGkjn++M0xhr8wwLGjgnjApaZm6mQqHcchmxonmxqkad0qfG3N\nDN39IPmd+9Ea6ibq0jUFN5NDiTfQ09/P+FiOWEzH51ehLs5DD+ynlM9z63XvqZYSlJvyXx99Eug9\n7fk5UTRpn9hTCCHiwO85p0spu8+FoCpVzobHNj5JtOWFrVtqG1rYvedJ+vr6aG1tfZmUnR9uu+0P\n+dK//hcnRvbhhMYJthlEO0IgJSMH+xgYFmTH8zStjVITqJ2SBuqT5Y1vvJ0f33onO3+4k4417dRO\nb0KoCma+xPDhIXp/k0Q3mxgz92MUBZlsptySz4h8Po9i+DDzGVzHASGQjkV8ThMNc5opjOWxTQsp\nC/g0hSOP9DA8ksVy8tTGpk7QcyYoisJQfx/hxha8dXUU0iN4gzV4A/UoqopQFBRNQxUG/dvvw9ZN\nio7Jlqd3Uin5vHvvvZdIKMkN17cRCOg4jkQREAmrRMMq4bDFkRMpLrkwSHLEJF5b5MTxA8DUqOne\nunUroq2RgJ1l9MGNRC9eSf31l9Pz3TuRqoqTK6D4vNiJUTQpcVWDRN4h2SMR0sLqdSgdlCye1sw7\n/1/l3Bl5pSLKXxN7x2nPP3Guxp2sT6wCfBp4N/B8/jVTr1delVcN6WwOj6/+BfcRQqB5fBQKhZdJ\n1flj5syZeIIq4zWHWHbjEmrr61GEBkji8+oY7O7l8GN9+KKt3HLlayvaoWF8fJxCNkdibwkrlcFV\nehAKOEWJh2ZCgQWM6IfBCWFYLu7kfbKnBKFQCKeYxR+o49iRzdTNacSWDh5totmBPxrEKpQoZPJg\nCVInUmSLaRSp01Khq73r6+sZGe4iNnsxYWWcUCtIZ5jR1BCFkoFUgkhV4igO+HSC7U2MnhjCDE4v\nt/RJIaXkl/d8n2WLvASDGpquUiqYgE3JskEIfDr4dJv6Gi+65vJHb1nOXfc+TDL5ZmKxWLmnwM8f\nuI/6ZYtYu3wB2x97gtQvH4FQADtXQKgKbr6AUFWQErN3EL2hDs/0tomOa5aF2TuECAUZHh7hDBab\nVzlPrGk+88TNhvOg41wz2UzsXwDvA/6ZiWD2M4ALvPnkz7OxW6hS5ZwRr4vR2zv+gvu4rouZzxCJ\nRF4mVeePjRs3EpsdpOmSWvRah57uI2QH87jSQfOptK1uYmnrHPZ9/yg3/9st5Zb7kvjIRz6G5ong\nRn0ke7rxKAE01YsQgrTTx6BzEE9bM4H6GeRT+6iPvfDFzFRj+fLlOF/9BtTXMnq8QHY4TaShjmIx\ny/C+IQZ2DiItBelaWMUC6f4MmvBjUSAaqSzf1FNs27YNj15i1gwvml8hkwNHukSiCiHpMJwYo2R7\nkY6NWzKJrphL8uGnUezKCIYGBgYo5vuI+AEpsYolNExCIQXDMBCA60pM02XbzlEc22btqoX0Dhzj\nqac2ccMNN5V7Chzr6aZj3QrqDIPxTIZEIUdmcJhsTz9KOIjMF9HaGnELRfSmelSvByWXxesB4ZYw\nB3tpvXYlib1dfOzTn+ZLn/98uaf0qmZLX++L7/QycbKB1vPhMuFisENKuenFxppsEPsOJmoYvshE\nEHuXlHKHEOLTwANA+yTHqVLlvHDlZZfwyOf+HTlvyfPWuw71HGfu9Hbi8fjLrO7c86Of/S+tKxqZ\nubyVR765GX+dl+a19eh+jXyyyKGHjuIPewnU+hkfH684a6JTZLNZerv6UP0h7HQWnydKqKYdwwgi\ncSnkEpAzkMN5ZL0fG5uGxsqaq9/v5+brrua/f3QPqm8ah35xjFmXS45sOAyFGDXxZejREFY+T1Gm\n8dSPk06eQAiTvScqrx+9aZr8+IdfZPkChe7+PLGmIM0NGsGQB8eVjI452KZLsqjgeuO4+SLpLcdw\nCxZ1wcpoZJHL5aiJKgwPQ2qsQE1EEI1qqKoAJBIQCoSCKt19Fn4DLFvS1OChNzlcbvnAxKJYx3bQ\nvQrLlyylu6ebTdt2I/xejFkd5HftJ+D3IVQVNRTAi0k4MmGTlnx8J7NXNDHnwgb66hV+8b17+Yvj\n72X69MrIpFc573yCiZrY5/riOvW6FEI8BfzBSXuu52SyQewMYJuU0hFC2Ez4wyKltIQQX2Si1dgn\nJi2/SpVzzLx585jdGqdz92+YvXTt753U85k0/fu38K6/eWW4wfUP9RNa42fXrw6w+i2LibYHKBZK\nSCmJz6phzqUddD7YQ7q7j0OHDk25dpaTZceOHWieIMVilob4EtqnXY6iKLjy5OLWOkGpME5v10YK\nQ70IJCtXLyu37DPm9je8nqf37WPHth8Rru1g6zd3UNswn8Y5q1EUBcd08YVieL0OJW8SIRSc1AjD\nyRFM08Tj8ZR7CpNm69atxGMperoKuOPdLLi8BdXQTzawUAgGFOJ1Kr/ZlmVwJIsRb6S0fxDTzDB7\ndmVYikUiEdIZyfx5ER7dmOUtt4YRAgS/e8Fx7ESJw0dK3HhtHZu39lIoOnh9UyO7vnrREjY88ji5\nXJ7xRBIEZLbvxQ4H0AaHUXSN1J33YrQ1E5jbgRLVSe1LYnX30zSvlobFzYAkHveQWdLI17/2FT7z\nj58r97RetUyxy9z5wD3AV5no9jUENACvB94F/BHQCvw38I9MVAI8J5N1HRgHTq0M6QdOb06uAbWT\n116lyrlHCMFH/uaDxNUCTz/2Kwa6jlLIZcmMJenctZnDG3/J+97+JpYuXVpuqeeEoD9A395BmpfX\n0bywDl/QSyDsJxDy4wv68Aa9LLplFoohSSaT5ZZ71pimie1aeLQALa0XIQS4OKCC0BSEJvAEIsSb\nlqC6KkI4rFu3rtyyzxhVVfmnT38KOzXC+Im9aFqAupaVSFNFlnQ0/KjoaLoXb6QeX7QRRQlSyOQq\nrt752NEDqMoIQb9g+cwxug/1kB3PcXj3cTbdt4OH79nK3q2HUPM9pA9sxNcxHU8whpK2WbBgncBc\nLAAAIABJREFUQbnlT4p4PE5dwzwiYZ2nD5jcc9846XET13VxXRfbcti5J8s/fSnB628KcuFKnW07\njvObHQVWrCh/d71isUhXdzd7t+0g21RL8OqLGHVMrNoQWmsj2rQWAhetRGuoxzVL6IM9BEb7aIzB\n8jesoGVpO0LTKGVzaKpKvCnKgQObXxHrESoWeRaP88d/At+QUn5BStkjpTRP/vxX4BvAZ6SUP2Wi\nhPUFa2smm4ndCSwAfg3cD9whhCgANhP1sTvOciJVqpwzwuEw//SpT7B9+3Z+ce8D9G7dhccwuHLt\nKq7+yz+mubm53BLPGZeuvZx//d5TrH3PYgrZIsVCCdVQEMqEX3o+m0coCk2L4gwk+sst96zp6OjA\nsfPUNawC10YqOkJTJ7JZApASFEGwpgWlW2VaY0tFWonBhEuBLxCiWDSpjc/DEB6K2RSuVUIIgap5\n0T0BVN2H6vXh9bWilGTFtWIF6DyS5KLVPubO9fDXn97Npod9WKofo64BvT7OYDaPMzaMUEqURgbQ\nAyE8wl9RC4TecPt7uONjG7jlWh/5vMNnvpBgWpuOz6fQ3WuRHHXoaNV4w80Bjpxw2X9wgLmLLmbG\njBnlls6X//ur9AU01rzlNo4NDzGybQ85yyL21tfimBalo92Y3QPIQgE3kyMjw9S1BKlb2IomXDAd\ntICP0niGuoZGxrNZmhs8DA4OVksKykWZ3QmexYXAPz3Pth3Ax08+3wa8YP3fZIPYLzJRUsDJwVcA\nPzj57y7gzyY5TpUq5xVd17ngggu44IILyi3lvHL99dfzxR9+jmwqix7U8Nd4EKcFM67rMto1TigW\nYCwzWkalL41Zs2bh8/owvGFcaSMcC01X4dQtWSEQQiJdG8MbZGx8qLyCXwI9PT2ohoIivVilLJlU\nD5rhxxOoATnRXreUSyHFGKruxdBDHN57AMdxUNXKMYeZNn0uP+gtsP5SlW//n0Vt+yxGRRH/kgvQ\nwrUoAjyGJDc2Rn58JkP7jiJzRTyqj0QiUW75k2bZsmWsu+xdfPVbH+edbwnypteFGEk6JEYdvB5o\niKu89bYQ2Rwc6iyw76Dk3/7jQ2Wvb+7r6+OJvbuZ/9bbUFQFVcKGXz2E99pLEJqGdbSb4oEjeGZP\no+b2G7H6BvGEffQfOsbYj7Yw97KZhFpi4Ep0XcdMF/Hn09Q1NJZ9bq9qptb13zhwFc9tgLD+5HaY\nsHNNv9BAk2128OBpzweFEGuAmYAfOCCltCYzTpUqVc4N4XCY1oZ2Ro6M0rAgRjFn4p5cuS0UMHMW\ndtrF4/cw3DM1FoqcDUII6upqsewcil9HKAKrkENRtYmJSolrWyiGgqNYJHOjJBKJimxvKaUknUoh\nvH5KZgZ/tBnDG/ptwC5dF6eYxynlMYtp7GIWM+Wye/duVqxYUWb1k2fNmjUkRjU2by8wKucznnWo\nX7WScOszrhKOI1G1GNm8TWT5ahK/vhuPZlRUsA5w/fU38OUv/QOPbSqw76CJlAKvF6a16cydYZAc\nczneXeLeh3NIaqfE5/aJJzfhmzUN5eTv2kmMEZwzA/xe7KEkpUPHidy0HhwHaTsofh+u5eBftQh1\nKMbhDXtY+/ZL8Hq95MfzdD2ylXeub+OJzYKmCrWEe0UwtYLYbwIfEUKEmKiJHWYi43ob8B6eydKu\nBfa+0EAvGsQKIQzgx8AXpJSPw0Q/MODI2aqvUqXKSyMWiyFNgWLrDO4dQ/PreMNepIRiqohrOrTM\naGSge4Tx1Atbj011Gpvr2H+4jzpnPv5gDNWr41o20nURikAPeCkW0+StBHpjhK6urikRDJwpPp8P\nVA2jsRlzNINVTCOtEiBQDR+KqqF6vAhXYhbS5Mb7qXPreeDXD1ZUEOvxeFhz4U3c89BPWHtDjPHu\nIVqbGn+73XUkliVxhYriDSPzWYymZjIHD1XcHZadO7fTFAddV/jAn9TQ0qRTMl2KJYlpSoSAh5/I\nc+S4STqdwHXdspeHDI8m8USfsSFMJ0dxgz58fj/pjdvwLZk7YRF20hVDrYkgR0cp9Q4TiIWwglG6\nNx/B79EoPH2Iv3rzUgp5lzUX3FhRCxBfaUyxHPgpi60PAO89+VwAOSYC2FPbf8VE/Pm8vOhfi5TS\nZCK9W3mFV1WqvEIRQpAby3P8qWEaZi0gGp+OJmrR1Rixlpk0zlnA4PFxurcOIFUX266sBgCn09ba\nTr40RLo4QCGXQuKieDRUn45iaFhWkb6urQQuagJxMhisQA4dOoTq9eHPDdJYk8Udf4z2+iSNNSmU\nUh9WbgynUMCRNqMjB1Bt8CkBjh05Xm7pZ8wHP/jXJDM6g4MOIlyD40psy6VUcilZIFWNfM4BzYs0\nLTyNLWgBvaLs8VzXZdPGX9DRqvPW14f5l6+k+MYPUxzoNElnHLp7Lb7z4zQPPp5nzXIvxbzNN7/+\nzbLX/Yb9Qcx8/rf/tmwLs1CkmM1hDgyj1McQHgMl4EcJ+BG6hohGQRH4iin8dSHGtu5juXaCT793\nLorQOHA0zg03vLaMs6oylRZ2SSldKeXfA23A5cAbgcuANinlP5xMlCKl3CKl3P9CY002MN0EVNYl\ncJUqr2AsyyKdsxFWMwfvO4RrSgI1UQLRCJrHINUzRueGEaysgaafcXfpKcWqlStxdZORsV2kSl2k\n0n3kcknyuVFGk8fp7tmEMy1PaGUHbrrA3LlzX3zQKcjBgwepDdvcdq3gY38znasu1RgZ3I5wh5nR\n7hLQhxgbOUDvkUdxbQtNePB6DfQK/P9VVRVXanT1OxQKLqatYNngOGDbkvSYSb7gghCoPh+oCv5g\nZbVOzmazZNIjdLR7mNamc92VPlQF7r43y1e+leaRjQUuWOnj8x+rZ8kCD36vxv13buDAgQNl1X3B\n6tUUj3YhpSSXyzFimxSOdVPqH0IJ+FEjwYnAVQiErqP4vAivF6tgM5ZTUT0GqnBJ9qT46S9c+hLL\n+NCH/4lQKFTWeb3qmUJB7G8lSZmSUj4hpfzJyZ+pMx1jst9+HwR+LoTIAj8HBnjWFKWU7pkevEqV\nKmfH7t27iTZOo3nlKtKDXWz/zn789TqaVyOfyKMQZMbSKxg8dBBDeNG0ygt0TjGcSAIKRGwK8QHS\nvSdQi16ka2OrRaLXtRFesYSe/91MvS9ccXWTpxgc6OXqi1SWL/JiGD4uuTjE/HlF9jzdQ1fPUQK6\nRJSy1DRcjpMvMJToIWENcclVf1pu6WeElJJ//8r/EK2NU8i7FEYSeJImmqYiXYntgouCoum4ZhHh\n8VDs6yGkaliWVTGWYkIIXMelWBSMJGzaW3SuuNiPpiogJjp22Y7EtiAaUaiNevBYfn59z6/LaiU2\nd+5cZkRj9O7cw4lSDtlUh7Mpjdk/iHQccNyJk78Q4LpIJM5YCiUawrQdElmLfLekPrSY//vud6ZE\nC90qIMpcEyuEuJSJLlzZk89fkFPlqy/GZM9sT5/8+aWTj9873hmMVaVKlZdIIpGgqX022USB9sVL\naVu0mPTICK5t45kWwF8TRQjo3nOURcsWl1vuS+L+Bx6lPjSfVK4XM5Mlsn4GQtMRuoa3OYqbK9B/\n904yu/tZNH9FxXWwArBtm2z6BIvmKiAEjlNCUTXqYz6uutz/23q2rTtGuOuBURwLNEswogxy4403\nllX7mdLZ2Un3YBJdUUknh1D9fsaPHiM8bzHCq6OoKsJ1cU2TUiqJY5Uwh/qJdHSQTqcrJigKBoOk\nM3ncksvxHov1l/hxpaBoTuR7hABVUXAcly07TK64oJljh0bZvmVnWXULIfi7v/gr3vFn7+VgapjQ\nmqX4OprJH+tB6DqlY914prchNBVp2djJFLJkojfFsbr6sPqG0HSD4cw4d/3iHq69aj1tbW1lnVMV\nWN3aesbveeDcSniUiTv6W04+f76wWpzcNqlsxGQDz0++wAGrVKnyMmMYBgGfB1+wjoGjQzRMryfa\nePriGJfhniSGq7FsWeV1sDpFb28v2ZxFsVRA5jWyxQT5nhSqVwdVQVoOrulgZwuolp9QXTOdnZ0V\n16FsdHSUUMAh5JeompdSYRxN8yGU3/2Kbm/zo8l+kikbXXoQmkOxWCQQqJxb7Vu2bSfQ0EGxuInc\nSD/BxmmUervJ+nwEp89BqBrSdSmNJ7DzGca3PokWrSWfzWIYRrnlT5rBwUG8HhVN9/LEbwqsv8QH\nEgxN+e1p2rIlW3YVGBz08OYbWjl4IInhesstnUAgwHgmgy/gp7RrP6XuPjwLZlPs6iF9/xOEr1mH\nYhhIKVEjIbSGGDgO1nCSUv8QvpY4rTdczYbRfn75qY9z6+VX8ZY3vqniLi5fSWzt6TtvYwsh7gOu\nAT4tpfzY8+x2BXCqVuZKzlFMOVmLrU+ci4NVqVLl3LBo0SKK3/geS1ZczLGuE/Tt7cEI66iGgmtL\niimTeE09etBg+fLl5ZZ71iSTSaRjU3KKoLrULJqLf3YcNTqxeKs0NEZ2Ty+y6FDIJEE3GBkZqbgg\nVgjBeDqN0qqABEXXyWcG8fpr0XQfEoGULlYxRy49iEdpR1Ai6gvR2dlZMdlJgFwuj+7xUTLzSFXi\neAUU82R2bSe9extatAbJhJ2YGgjiae3ASo2iSllRdZU7duzg5utbOXQYHtzwNP/17QxrlnkwPALX\nkdiupPOIxWObbN5w7RIkUDRLzJ05rdzSeeqpp3AaYzStXkiwLsaJXzxILhLAM6sdezhBfvtevPNn\n4ZnVgeLzYidGKR46Tn7LbjzT25HSJd7aQtgXwGlv5SePbyQcCnNzhd01eEVxntKQQog3Akte7AhS\nysdOe/7ouTp+tQSgSpUKJB6Ps3rpQg7u28GcZRcwvWM6iUQCyzLRNI3Y7Dp6Du1hweL5Fe3NaBgG\nqfQoriGov3wJ8WUrQUpsqwi4+FsbibUvYeTx7bBLcHTvHjTtbeWWfcbU1tYynLBIZyU1ERNNjeK4\nUMglQEqEUHAdm8OHs2C3IG0br/QQjoQrznmiob6O7O4jOFYKLRjEE29EZgpYIyNg2ZT6etHq6/G1\nz8A/czZOocDwPT+hff68cks/IwqFLDVRnQ//1WVs3HyC+x5OsX13gbZmDb9foX/QplQEx9bRdcH+\nzjQFU+emW8sf6P3s3l9jui5dd96LauhYmRwlXeBfugCJwH/RCqyuPlI/ux9cF+HzYjTH0Zvi2Klx\n1EiE+77wdWpjDWiqgipc/uW//oOrrriCYDBY7um9OjkPQawQogb4N+AvgP99kX0fPoOhpZTyqsns\nOOkg9qRf7HXAXCa6KDz7gJ+avL4qVaq8VN777j/hg3/7UR762Q9IlwqUSmlUVSUeayUSCBL32Lz/\nw893Z6cyCIVCFAo59KYYNaeCGCHQjN+10apZtYDc4T6GevumRNvOM0VVVZrbl7J9936uuFjHtU08\nWgChBnEcCyHBtAU7d7oEPNPID+/EQ4yxfJLG08pIKoF16y7mc1/4Ah6fJD9uogzniLUsxj+zCUXV\ncKwS6ZHjpPo6KXl96LW1ICWr16wut/Qzoqamju5Om66eNIZm8efvi3HpWi/DIy5SCupqNDwewYaN\nWf73rgMMDwdYdsFNrF5d3nlu376d+zY+jueCpYRnX4DUNZKPbcY8cAQUBcXno7jvMEZbM8GrLkKL\nhsF1yTyyGTs5hiYNQq0d1CyahSoFTfEGiuNjdG96hL/867/lv778xYpZnPdK4jwt7PpnYI+U8sdC\niBcMYplwwzpdxVygETgBDAENwDQmjAMOTVbApIJYIUQzsPHkASTP+OaeLqgaxFap8jLS29tL79Ah\nevs68Tf5qF9Si1AEiRPHOLYvy9+858PU1NSUW+ZLwrZtJA6BOc2o6kQNXnFohHzPINJ00CJ+gjPa\n0YN+jIYwSr5Use4E66+8mne957v49AJrVo7iOAU6OyX7Oy0yWZvhhEk+E4bC0zSbzTg4jKSG8HrL\nX0N5JtTW1lIfLnEgbxHwNtMyex2qL4hjmTiWhaobRJvm4vHVMHD4SeRciVA1Yg2VFayvXr2ae+76\nT3bteorbbvQzvc1L36BDS6OGpp08iUrJqqVe7r4vAb75/OPnP1PWAK+7u5vPfPU/ib/mMkRHC+nU\nGF2/fAjPrA4Cl63FHhlFCfgQfi/moeNk7nsMz8xplA4dpTQ4gqYYRBcuwxdtRNF0kJDP5wnWxGha\nuY5jXf+fvfuOk+uq7z7+ObfNnb6zvTdJK6vYklaW5CZZtmzcMKYTTDEQQkKoCZDy5MkTekgIkEBC\nCJAEAqEZEnDvXc2qXnWtyu5qe5vd6XPbef4Y2cjgspK1Gq2Z9+s1L2l3Zud+r72aOXPuOb/fYW7/\nxf9w6++9rWjnWHJ2CCGuAN5JYSnBy5JSrj/lZ19PoUjApVLKrad8fw2F5gYvVEDgBc10JvbLwBiw\nDuij0ApsDHgf8DYKC3pLSkrOkdHRUf7s059gINvHRW+fhxnzkc85eI6koi1A8KYA3/3ZN2loaOB1\nN7+u2HHPmOu66JqG0CA3HSf+aBfqpENEKUcRKnlvlKHNh/AvaUT4VKJl4Tk3qHvW+vXrSaV8PPJo\njMc3jyDRKa+ajxmoIafoqAEb3R7Dzozh4BAXo/i8APfddx/vf//7ix1/xpLJJNWVfjzHpKZxKYmB\nQ5jKAEEtiSIgldOxzAsI1i4kFK4nfugAZiQ8pzZ1QaE19IqVN/Dtb36KT/xRA34f9PTZ7OiyCAUV\nDF2QznhIdG64toZ7Hg8SCASKmvmOe+/FXNrBgvpq9p7oZWTT0wSWdmAsmg+KQAmYWD0DkEiixiLo\n9TUkH3oSYRiYHW0YaRV/cyuuZZPqG8AXDpGOyMISAk/SsmQVd933IG96w+tL3bvOtbM4EyuE0IFv\nAV+WUp5J99bPAX996gAWQEq5VQjxaeDzwK9m8kQzbXawFvgKMHjya09K2XNyF9rPga/P8HlKSkrO\ngrvvvYuDvQdov7YeNeTDUwL4K+oI1TaghWPE4xnq11XyjX//JyzLKnbcM2YYBkEjTG50ktE7nqQy\nWUFz2VLKow2URWupibXTHlmG3D1K4sAxLl1zcdEHAmcqHA6jCQXVaGRyyk+44mIUrZFM2kBHIxzw\nEatuIFS/gB7fMSpFDTVqIw/e81Cxo58WRVEYHBpEU3woXj8XN3fxR2/X+NRHG/jERxr4yO9HWL9o\nP5mjd2GoQez+QfJTk3TMm3vLRNauuxrTVLCyFtmUpLk6zNJ5McqCfhSpUl5msqqzmc5lVYyN9hQ1\nq23bPLJlE/VLF1FTU0t2cAQrnsBcOA+hCIQEoWkYzXUI08TL5tFbGtDqqom++XrMpkbC8xejVZWj\nVcRQK2NYuTyZiUmk5+GlMjQ0NeMZIY4cKXWtP9eEPP3bS/hzCstKv3iGcRZQmAh9IaPA/Jk+0Uxn\nYiuAISmlJ4RIA6deo3wE+PBMD1hSUvLK/fv3v4tZpaOHAwSqatF8v56lMoJ+/LEyJo71M+71sGPH\nDi699NIipj1zZWVlSM8l2zVMvb+NUFUZiijs1HfSGTzXRSiCKl8Tk33HKC+PFDvyKxKImExOb6O5\n/SIi/goCWgB/xEBK8FyXVDaPJwXhWDOpkRQRoriOW+zYp8Xn8zE2nsDQLC5fNs311zTgORaebaPo\nBhVVIa59TZBoeIjb79gJjo3n01m8aFGxo5+2eDxOOu1gqGFUIZlKWDzdlWB41EZRBE31BorSz3j8\nt8upnWvZbBZPVdBPXsnw5Sy0uio8ywJReH0RqoqU4CbTJ7upmQRWLkVm8ni5PErAAARqwMTLgloe\nwRocY3pwmLqKSnymiaob5PP5Ip5pyYuZOHyAycMHX/IxQogm4P8Avw+YQgiTXy8x9QkhokDyZRpg\nHQf+ELj3Be77QwrrZGdkpv9q+oFnm1YfpbB84NmP/6uB3EwPWFJS8sq4rsvASD/Vl8XwxyqfN4B9\nlqIqROpq0SsHOHjo4JwdxObzeWyfhzYh8Cs+7HyK3EQeL55FcRQUoeJJByufIabE+NFPf8SXvvSl\nOVuPsrKinDEngd9XTyxYhqb9en2vqquUmQaqopPNVZOcPIjqKpRXzq1d+7ZtIzCIhqZZe0kEgYdi\n+ECCl8s+16zi4hXlPLX5OGPpKDgZNm7cSFtbW7Hjn5atm58mlwmwa28G2/G455ExWpo0Otp8RCIq\n+w5aPPxkCsuWTE+3FbUjmWma4Lg4loVmGChCwQyHwHHx7AxAocGB66HoGsLnKwxkgwGk6yECPqzp\nOIGGFgAUnw9nOoFi+mA6yeLlhUYk+dTUnCoJ96oxg+UEFQsWUbHg1x8Wj97zglf02wEf8EN+PXh9\n9gifAj4JrAC6XuJQnwH+Wwixl8LV/Gc3dr0ZuAB4x8unLZjpcoJHKayHBfg34JNCiAeEEHdTWNvw\n85kesKSk5JVJp9M4noOdAyP44pfONZ+G0HwcOnT4HKY7u6anp9HKTVRPQXckueMjMJQh5IUJqWX4\npR8zZxKVZQTsKFOj0xw/frzYsc+YlR1BCJ2oP4aq/fYGNQGEwj5CeoSsSJNwJ6msnlsDAr/fT3w6\nywXzFHSRxXO9QhkxXDRDQTdVFBUUIVl5kaS8pQFFaPT09BQ7+mmRUvL4g0/QFruMv/vmEP/x00FU\nTWLbHpu2p/nVfdPU1wre/oYQB4/kEckQP/vp7UXLaxgGl63oZPhA4fWiorYGe3QC3WcghEAJ+VHD\nIWQ+jzB0lKCJMHTs0Qm0SAj/kvlkRnrx8nmkZePZNshC57LGhgY0TWdssI+mmgqam5uLdp6/s+QZ\n3F7YLgqNC64C1p9yE8APTv79JdeLSCl/AlwHTAN/CfzLyT+ngOuklD+d6WnNdBD7f08eBCnlvwIf\nAwJAHfD3wCdmesCSkpJXRkpJrDzG5LEUnvfiV2xcx2XySAZVm7sbKAKBAKGAHxFQEIqHllEIuiHI\neXjZPMLyMDUD0wgSViMoeZX777+/2LHPSDqdJp2cwrE8dL3w0vxC7yNCEagCbGHhSJcdm3eRy82d\ni2GKopDOCMrCKlYujuvm0A0XM6xgBMAIKJgRA0+m8OlZ/H6DQF0LBw689GXO841lWTi2w4KGJUwn\nbG7YEGD5UoPJaRefKfD74Uf/O80Xvj7OdZdHsXKj3Pnzu4p6qf0NN95EYvc+stMJFq3qxJucxo0n\n8FwH6Xq42SxeJoti+hCqiptK4wyPo1aVowYDaK1VTO/bgZASXVUJ+P2YhoGu6aSm45x4ZiPv+r23\nzNkrJXOZOIPbC5FSJqSUT/zm7eTdvVLKJ6WUmZfLI6V8SEp5OeCnUGrLL6W8Qkr58Omc10w7do0D\n46d8/Q3gG6dzoJKSkrMjHA7T0tDGjsMHGHpmgIbO3+5LLj3J6IFRvKRBU9Pp98w+X9TW1rKoeT6P\n7H+MTDJDhVaDoRg8N7wTAhQBnkdaJihTKrnjF3fwwQ9+sKi5z8TQ0BCOC37dIT41RE1VCxJwXEk+\n65LPSqSUKIpgenoQ18lRo84nPZ7j2LFjLF68uNinMGOmX2Ei7qEoeTxvAmQMVQkgFAU7nyeTSiI1\nB9sfZHqkHzXUzPDI+Ms/8XnEMAxy+SwPHf4Bt90a4shxiyUX+PjzD5dRXaUhJQwNO/zw50me3Jih\nrMzg2IEeuru7Wbp0aVEyL1iwgI/+3jv5xk9+SGBpB23LlnLwoacIrL0YL5XBy2RB05HJadBUUo9u\nIXDxUjTDgLxFYFkH7s7DxLc/RqRpAYrqg3SW6ekxMt1TfPwD76Wzs7Mo5/a77uLmhtP+mRdasPoS\nXnr+9sV+qLB2dvR0f+5Zp72S/GTN2AZgQEo5+HKPLykpObsUReGdb3kXe7/wabofHMSxXOpXNKL7\nCm+MTs5hZN8Q3fcN0FrXweqL5/abhp3MIaVG3B6nzmwprJ2U8uTLpUQoYGMxLSZp1FvpO9Zf7Mhn\nJJPJEJ9WqYm6TI4dIhKuRGCSmCpcllUVFV3RSaXiTI/1orqF5QZ23ppTXbsymQx1NSbHT0ziiDAd\nnWFS8RzxoQRWzkVRIRBVIWCw65BLpCnKyOEx0iJa7Oin5YEH7iWZO0Z9c5LJacllqwLcct3JblWy\nMNPVUGvwkffHkHKKzZtyTIxNMD09XdTcG66+mrbWVu64714ee/BJrHQSa3AYrb4Go7kBoWvYg6Pk\nj/aiVsZwUxnsdAYzECASCxF78w3kRsYZ2rQD79goAanyrj/5KFevXz/n61bPZdt7B2b1+aWURSnQ\nfTodu95NYTFu8ynf66NQ6+uHs5DtjAghejgl40kSeIOU8o5zn6ik5Oy7+aab+c8ffp8BSzKxT6F3\n43aijUEURSE5mAE3SkvLpbRFFJYtW1bsuGesq6uLweEkS9Zcw94HfkVf7ggRYqCB0EDxFBzbYYxh\nKowaImYZiTP/UF9U/f39KJqPrJumRrE4fOgJ8DURKKtHD4Rw7SyJ8R6SI8fRbUk1DUzKUUI5k5qa\nmmLHn7FMJkM0HCbkU7nnsRyNF1gkJjyUSIhwXRChCPKZPP/zgz4GRjUqO6MMPH0IvXHurP09cuQI\njzzwbW6+oZah/lEmJl1uvDoIwHTCZSrp4XkSvymoKNe45soAT26aJu/6mJqaKnJ6aG9vp6aiErWh\nmtXv/hDJ470c/smvyIyMo9VWY17QXhjMDo+TP3wMmc7iLV9EzYL5CAS2lPgMjQvnt/O1z3yexsa5\nezXoVWN2OnYV3Uw7dn2YQi3Yhyhs5Hp2J9nbge8LIaJSyn+ZtZSnRwL3AZ/+je/PuI1ZScn5LhAI\n8F/f+R5veec76D+RQw9FmDg0ged5aGqEylgl1WqO//Opv5qzHawA7rr7fsqr55Oxx3GEZMA8zrDa\nQygcQhEKruviCRfFUlASdWQDaVraW4od+4wkkykCwRCJdIYjIyMIfwwjlCQ9tQ85KRGKii9aiRZu\nJdl9gGZ7PqP0I3xyTg1iA4EAU1PjXHelj7t2q3zms8NcfX0DHUuDKDnBQG+GJzenGVKtrJa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4dwMEQ8nSFYXkblhYuY3NeNUV2JVATSdsjJNB6yMFAN+tFqKlF7CuuwhRDgN/FVxABwbQcPiSZB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\ngQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7b1e94b9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(\n",
    "    test_trans_nl[:, 5], \n",
    "    test_trans[:, 8], \n",
    "    c=test_labels, \n",
    "    cmap=\"viridis\",\n",
    "    s=100,\n",
    "    alpha=0.6\n",
    ")\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label(\"digit\")\n",
    "plt.xlabel(\"5th separator votes\")\n",
    "plt.ylabel(\"8th separator votes\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "38 misclassified test cases\n",
      "test error rate = 0.048\n"
     ]
    }
   ],
   "source": [
    "gnb_nl = sklearn.naive_bayes.GaussianNB().fit(train_trans_nl, train_labels)\n",
    "gnb_pred_nl = gnb_nl.predict(test_trans_nl)\n",
    "\n",
    "n_err_gnb_nl = np.sum(test_labels != gnb_pred_nl)\n",
    "print(\"{} misclassified test cases\".format(n_err_gnb_nl))\n",
    "print(\"test error rate = {:4.3f}\".format(n_err_gnb_nl/len(test)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Despite this difficulty switching the decision function shape option from \"ovo\" to \"ovr\" allows the GaussianNB to behave tolerably well although we did lose a bit of accuracy given this particular setup. However we now have a natural way to evaluate probabilities which are often nicer to deal with than distances. However as is common for Naive Bayes these probabilities tend to be unrealistically skewed towards 0 and 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f7b19953c50>"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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w3TEdMf52yZXeEBG/lTQOeFDSAyy/A0dExPY57/VMk+bbSAvk1ste7wEsqAW82XXPSbqa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\nQ6+ZmZmZVd7/A88AAmFjfgoyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7b1991a358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gnb_nl_probs = gnb_nl.predict_proba(test_trans_nl)\n",
    "\n",
    "plt.imshow(gnb_nl_probs[argidxs], aspect='auto', cmap=\"afmhot\")\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label(\"GNB probability\")\n",
    "plt.xlabel(\"separator feature\")\n",
    "plt.ylabel(\"label sorted image number\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we use something with more flexibility like a random forest classifier we fully recover the classifying power that the SVM gave us and a small apparent improvement in the meaningfullness of our probabilities (since nearly all the probabilities in the mid range are mis-classifications. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "35 misclassified test cases\n",
      "test error rate = 0.044\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f7b1967cc18>"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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VFXuCtOX9g8pDbBERkj4NnEbq3DYAuA0YXh3wZkaTttlPBAYB9wMjegp4zczM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\nZmZmZlZ6/w/zHErS5zT7kQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7b19bbbc88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rfc_nl = sklearn.ensemble.RandomForestClassifier()\n",
    "rfc_nl.fit(train_trans_nl, train_labels)\n",
    "rfc_nl_pred = rfc_nl.predict(test_trans_nl)\n",
    "rfc_nl_probs = rfc_nl.predict_proba(test_trans_nl)\n",
    "\n",
    "n_err_rfc_nl = np.sum(test_labels != rfc_nl_pred)\n",
    "print(\"{} misclassified test cases\".format(n_err_rfc_nl))\n",
    "print(\"test error rate = {:4.3f}\".format(n_err_rfc_nl/len(test)))\n",
    "\n",
    "plt.imshow(rfc_nl_probs[argidxs], aspect='auto', cmap=\"afmhot\")\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label(\"RandomForest probability\")\n",
    "plt.xlabel(\"separator feature\")\n",
    "plt.ylabel(\"label sorted image number\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also since the RandomForestClassifier is much more robust to features with correlated information we can try to use the full ovo decision function space. In this case though it results in significantly worse classification even if we do a little hand tweaking of the forest parameters.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "165 misclassified test cases\n",
      "test error rate = 0.207\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f7b18cb1128>"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jm9J8pbiW0ia9ewPrANMk3UZYhaOemVn2iumSxTjSFqPVyg6gIBeWHUABYu2I\nMqjsAAoS44psrWZbV90bZQfgqie/FdnKdCRwqaSXgD+Z2XxJfYDPAMcCX8hysrRJ78cJK7LNJazB\n3KiS09BjHOl11bFN2QEU4PmyAyhIrKOHMY70enLoXKKiI72SnmbxvHJ1QonDfEm1hTL6AK8DlwEb\npT132hXZUhcJV0mMI72eyLsyxTgxJWYxJr3OuYRVM+kFrqegwVT/G+VcSR4tO4ACvKvsAAqydtkB\nFCTGOQCx1onGuJCDK1hFR3rNbGRR516mk94YVyOKsbVSj5ZdqYBLdi07gvwdHOlMthhbe0GcI72x\nfq9irFVephOQ3lDRpLdIy/TPXIxJr6uOIddXshS+rUd9RTZXshjvoDjXI5EkvZI+BJwC7Eyo550D\nTAJOM7MHs5wr7YpsuZG0u6TrJT0n6S1JT0u6TNIHGvYbIOlXkl6U9Lqkf0j6YJPzrShpnKRZkuZJ\nulXSkN57Rs4555xzXWbBguwfXUbStsDtwC7ANcC45POuwBRJH8lyvjJGegcCdwE/BV4kdDk6AbhN\n0ofM7Olkv2uSxw4jTJ4+EZgkaSszq7/jfQGwJ3AMMA04HLhO0vZmFuOiV84555xz7cXRsuz7hF68\nu5nZa7WNklYFJiSP7572ZKmWIS6apM0Id6WONrNzJA0H/gTsYmY3JvusRkhqx5vZqGTbVsC9wEgz\nuzjZ1geYCjxqZvu2uaYvQ1wRsS5DHONt2E3KDsBlEmOf3lh/Bn0iWzVMoouWIZ6yZ/bjtv97V8Rf\nI+l1YISZ/bnJY58GLjKzVdOeL3V5g4J9JJ0t6TeSNkq27yxpafOS2mIXtd/rfYBZtYQXIFkJ7mpg\neN1x+xDyvMvr9ptP6Oe2h6RYJ/I655xzzrUWQXkDnVuXZRq5TVXeIGkN4G/AdsBrwCrAecAM4OuE\npPWILBeWtByhufAg4AeESfq19ZUH03xpuanACEn9zWxest80M3uryX59CW/6H8kSl3Ou52KdGRtj\na69Y+Yioc4nuTGKzuh04UdKEhvKGlYHjgClZTpb2b9Q4YANgR+BOFr+LPoGwFFxWtwO1AuQnCPUa\ntYYKAwmlDI1qI8JrELrtDCTM4mu138AexOW6TKwJR4ylKK5aVik7AOdccaq7OEW9E4HJwAxJ1wDP\nAesCexG6tA7NcrK0Se9w4Bgzuy2pma03k5AQZ/VlYDXgvYRJaBMk7WhmsbZZdD0Ua3K4T9kBFCDW\nmaOvlx3GA+qJAAAgAElEQVRAQWJs27ha2QEUxGv1XGYRjPSa2R2Stge+C+xBGMycTQ9blqVNelcB\nnm3xWD8gc9GzmT2WfHmnpGuB6cDxwKGE0ds1mhxWG7mdU/d5wzb7zW7y2EIv1n3dH1i5Y9SuDDEu\nuAFwbdkBFCDWSUSx/gzGKNbvlZdtdKc5hPZSXSnHpFfS+sC5wCcIOd8EYFRdx61Ox38AGEtoPbYy\nYcD0p2Z2XofjVgceM7PPLkX4C6VNeh8jtISY0OSxnYFMmXYjM3tV0pMs+ps5Ffhkk10HAzOTet7a\nfvtK6tdQ17sFYYDwyXbXXWtpgnbOLSHWUfm+ZQfgUov1e+VJb3dag8VH6KaXFEdTOSW9klYijKy+\nCYxINp8BTJS0pZm92eH4jwLXJ+c4CHgV2JQOFVaSlgdeBvYjNDJYammT3p8BP5H0KvC7ZNsASQcS\n+uIevDRBSFoH2BwYn2y6ChgpaYiZ3ZTssxowDLik7tCrCe8cPlc7Nim/2B+4zszavk7E2DJq3bID\nKECM3yeAF29N3VqwMjb6r/8rO4RCdO1IzlKaW3YALrUY5zbE+ia5a+Q30nswoenAZmY2DUDSg4T5\nWIcQRoCbkiTgIuAfDaO1N3S6qJn9R9ILwPyeh94QT9o+vZJ+QKi9VfJhwALgLDP7TuoLSn8C7iGU\n/80F3g+MAtYGtjOzJ5P/pJuB9YHRhL85JwAfBLYys2frzvd7wij0aMLkt0MJBc47mNn9beIov0Gx\nW6Z1Q4/svMmXIXbOLeO6oc+tJLPrdsh+3B63LRG/pAnAimY2pGH7ZMDMbJc2cewK/AMYYma3Zo5H\nOhPY1Mw+nfXYZlJ3GDKz4yX9nFB2sDZhyPkfZvZUxmveRhiJ/TbhTtTThCHvH9QmsZmZSfoUcDZh\n5bZ+wK3A0PqENzGSMMx+GjAAuB/Yo13C65xzzjkXtfxWZNsC+EuT7VOBTrW2Oyaf+0u6jdC1aw6h\nRe1xTVrONpoOfFHSncCVhO4Ni40YmdkFHc6xUFesyFYGSRbjLN8YJ3HEegt2XuddKsdsbNkhFGIF\nnVJ2CIWIsf411l7RMRpQdgAFmEkXjfRes2324/a+s9lI79vA/5jZiQ3bTyMkri1fSpLB0kMIjQXO\nIwxyfpQwUHmtmX2mw/PolLmbmTV2FWsp7eIUzTok1CwAXq1vGlwVMSZTMT4nVyXfLTuAQvyHOJPe\nGOtEXXX436uCpejTO/nB15j8YKHp23KEkdnxtmhU5MZkktr3Jb2/rptXMxvnGUzaN8XT6bDUm6Sn\nCPW9v1zaoHrL5mUHUIAYJwZsVHYABbm97AAKsEOkNb3blx1AQWKcoNduhKbKvHtDNUwqO4CMhn5o\nVYZ+aNWF/x77++ea7daujWyzBcLqvZx8buz+9X+E1Xi3JnQIa8rMZnQ4fyZpk95vEFbFeAX4I/AC\noVHAZ4DVCd0ddgJ+IekdM7swzyCLEmtXgNhkLRp35bkt0nIpn6BXHf667lwiv+4NUwl1vY0GAw+n\nOHapSdoE+BjwHsK6Ebeb2T+znidt0rsZcFeT5sCnSvojsK6Z7S1pPHAkcGHWQMrgI73VsF7ZARTk\nnrIDKMCukSaHsY70xlhXvmbZARQkxpHeGFeZ66qR3vyS3quAcZIGmdl0AEmDCJPURnc49u+E1GQP\n4K912/ckVBDc2e5gSf0IA6sjgPra3fmSLgIOM7O30z6R5VLu92XgVy0e+xXwpeTrKwgtyJxzzjnn\nXFkWLMj+0dwvCWWuV0raR9I+hG4OM4DzaztJ2lDSfySdVNtmZrOB7wPfkHSGpN0kHQ+cDFyYogPY\n2YQc8xTCAmarJp/HEBLhcVn+S9KO9K4KvKvFY2uxaFWNueTYRLhofhusGry8oTomenmDc851h5xG\nes1sXtJv9xzgYhYtQ3xU3Qq5sGgdBzUcf6qkuYR1FI4mtB07Ezg9xeW/AIw1s+/VbXsKOCN5XT4K\nOCLtc0mb9N4AfE/SI2Z2d21jsrTcGSwa0d+U0LHDOeecc86VJb8+vZjZM4TVb9vtM4PFSxDqHzuX\nNiu3tbEicEeLx24nY+fFtEnvYYSs/g5JM4F/ERao2JCwCtq3kv1WISwmUQle01sN3r2hOrx7Q7V4\n94bqiLGmN0aR1vSWaQJh1d3G7g8k2ydmOVmWZYhXAA4EtgPeTRienkKoyajc76MvQ+xc/mJd7MbL\nG5xzaXXN4hSXbJr9uC8/0RXx10gaAownTIK7gtA9bB3Cyr57Eeaczart36lGeJleka3sGJyLTayv\nJ570OufS6oakUZLZ+PdlP27EP7si/pqGFdnq/8CoyTY6rc7mKzY655xzzsUmjvKGA/M8WeqkV9Lu\nwDcJLcn6NTxsZpb9LYVzzjnnnMtfBEmvmV2U5/lSJb2S9gKuJhQSbw5cC/QnNCaeAdyUZ1DOuap6\no+wA3DIu1tuX/yk7gALE+L3qqu9TBElv3tL+zJ1M6MpwFGES6Ulmdo+kzYDrCCtuVI53b6gGX5Gt\nOnbVKp13qqBYuzf4imzVUbnZ4in4imyut6VNejcHvgssIBQNLw9gZo9LGkNIii8vIsAixdiup3/Z\nARTggbIDKEiMb1AmXhrjW0l49xfiXMqmq0alchLj6zrE+bxiHdDoGj7Su4S0Se8CYL6ZmaQXCa0Q\na82CZwGVrOeN8QU/xueUqfN0hcwtO4AibLll2REUYq6v31gZMd4yj1WMb/y7iie9S0j7+vAYIbGd\nCNwFjJJ0CyHHOpqwJnPlvFR2AM7F5gOXlR1BIeZV70bWMivGko1YRfnGv5vkuCJbLNImvb8FNku+\nPoUwoe2Z5N/zgS/mHFeveFfZARQgxvKGWN+cRDnKcf+ny46gEDG+VkCcP4Ox3hmK8XsV4+9V25UR\nelsEI72SLgBOM7NpTR7bCDjFzL6W9nypkl4z+2nd13dL+hCwJ7ASMMHMHk57QVesGEc5YnyxhzhL\nUdikkpVOHcX4ewVeClAlMSbzsf5edQ2rftILjAR+ASyR9BLeN30VyDfpbWRmzwC/7Mmx3STWEUTn\nSrPyuLIjKMQ8zi47BOecyyaCkd5Eq6U+1wXezHKiTEmvwlqc72bJxSk6rnfcjWKcZx7jqGisM3zj\nbFnWNatX5spbllWHtyyrDm9ZVrCKJr2S9gP2q9s0VlLjOOVKwBDg7iznTrs4xZqEPr37tTmm7XrH\n3cjnY1dD5d5NLcMmWqs35NWmSJN551zEKpr0EjqEDUm+NmBr4O2Gfd4GbgVOyHLitCO9vwZ2AX5C\nyBVzHVCUdC2wO3C6mX23bvsA4GxgOCGrvw04ysweajh+ReB04EvAAOA+4Dgza7tS3HvzfBKuMGuX\nHUBB7io7gAIcGGlyuE3ZARQkxpHed5cdQEFiHOmN0c1lB1Avx6RX0vrAucAnABEaGowys6dTHNss\nEAM+bGZLtOI3sx8BP0qOnQbsa2b3L0X4C6VNencBjjSzC/O4aD1JBwBb0rxm4xpCxn8YoTf3icAk\nSVuZ2ay6/S4gTKw7hlDsfDhwnaTtm/2H1vgIYjX496k6fuMjva5kfgfPuUROLcskrUSo3HgTGJFs\nPgOYKGlLM0tTV3sBcH7Dtsc7HWRmG2eJtZO0Se9s4IU8LwwgaQ3gh8Ao4PcNjw0HdgB2MbMbk21T\nCEnt6OQYJG0FHACMNLOLk203AlOBU4F9847bOeecc66r5TfSezAwCNis1jpM0oPAE8AhhBHgTmaZ\n2R2dd1tckgsONLPfJP/eCLgU+CBwHSH3ez3t+dImvecB35B0rVmuQzlnAg+Y2WWSft/w2DDCf9KN\ntQ1mNlfS1YRyh1HJ5n0I5RaX1+03X9KlwHGSVjCzpneGYmzXM6DsAAoQ4/KbEGnLMiaWHYBbxq1W\ndgAFiXEhhxj79EbaFWoYMKW+V66ZTU8WKRtOuqS3p04Crqj79w+B9QmjxiOAMYS7/Kmk7dP7Q0nr\nAQ9LmgDMWXIXOyXtRQEkfRz4MqG0oZktgIeabJ8KjJDU38zmAYOBaWb2VpP9+gKbAI80u8AmWQKu\niBi7N8TYZQNi7d6wW9khFMK7N1SHd2+oDu/eULD8Rnq3AP7SZPtU4LMpz/FNSaMJC5pNISwqkaYE\n+n3AA7CwzGIv4CtmdoWkRwgT2fJNeiXtRairXRF4f5NdjLBSWyqSViA0Gx5nZk+22G0gzZsRz04+\nr0F4zR7Ikkl4/X4D08blnHPOOReF/BanaJdnrZHi+PGEOVqzgI2AYwn1wJ+ov5vfQj8W9eL9L0Le\n+n/Jvx8jY1fTtHf4fwjcSUh8H21VLpDBcYQn8r2lPM9SmVnmxQsS4+2iljMRXdeZUXYABfnn6TEW\nQ8G7T4qvyCZ1cV/FxPedircHe9dIMdI7eZoxeXqxYZjZV+v+eYukqwh38k8Ddu5w+HTg48ANhFKK\nu83s1eSxtYFXWxzXVNpX8g2BI8zswSwnb0bSBoQuDAcB/ST1I7S/AFhR0urAa4R3Fc3eQdRGbufU\nfd6wzX6zmzwGLL6s40rJh+s+repfqi7G8oZY28vtF2FyCHHOAWj2xyAGMdb0xvBW8hUyZl29yBZ0\nnoK180bho2bs5Ka7tcvHmo0At4/L7HVJfwUOTLH7/wJnJwtWbA18s+6xHYCHs1w77c/cveT3puy9\nhDKJS1iU7EIokTiWUJvxYUKtyCebHD8YmJnU85Lst6+kfg11vVsQSlxblU943YNzOYvhj5irthhr\nX133GsDibx47Nq3tRTm26Z1KyKkaDSZj0pmVmf0oWY1te+DHtS5diVWBC7OcT2maMUj6CHARcIiZ\n3ZLlAk3OtRohW280mVD38SvCsnKfBP4EDK0tMpEc+xRwiZnVWpZtTRg0+6qZjU+29QEeBB43s6Yt\nyyTF2VDUOZe7fJvWdA/vP+xc/sys9F8sSfbvE7Mf1/d7S8Yv6UhgHKFl2fRk2yBCn93RZpape0OS\nyz0IPGVmu2SPsufSDsz8hdAJ5kZJb7BkFykzs42WPGxJZjYXWKJwOXnxnVGX4F5FmOF3STLj7xUW\nLTc3ru5890m6DDhXUl/C5LdDCT3lDmgXS4ytbWK8XRnjDHOI83nFemv59WNL/xtWiHXLDqAAfTvv\nUkkx3kWJsRxqStkB1ElR3ZDWLwlzuq6UdHKy7VTCNI6FC05I2pAwMDnGzE5Pth1NaJY1ibDewyDg\naGAdOuRodecVoW3aToQGLWPMbIaknYEnGhYrayvt79H1NF8xLU9Wfw0zM0mfIixD/FPCxLdbCSO/\nzzYcO5KwOshphLzvfmCPTsvWxVgjFeNzctUR62pYq4yLc6T3+bPjTOZdNfhqm8XKq7zBzOZJ2hU4\nB7iYRcsQH1VXakqyvfZR8xhhkbDPAKsT0pSbgQPN7O5O104WMfsbsB1hvtcqhLUjZgBfJ8zbOiLt\nc0lV3hAjL29wzqUV6+uklzc4l79uKW94PXX32kVWObs74q+R9Cvg/wGfI3QR+zfwUTO7R9JI4Fgz\na1Zv3FSMd0xSi7G9V4y3zGMV4/cqxpKh4OyyAyhEvN+v+MTYP6R/2QEUoJtWZMtxIluZhgPHmNlt\nyXytejOBDbKcrGXSK+krwF/N7OXk67YaZtRVQoxJb4wrssVYpwxt2opUWIyrHALsoGPLDqEQMa40\nF2v3hlifV2zSLDHWW3Ks6S3TKkBjSWtNfcvbVNqN9F5IeE18mc4tIYxQ51EpMdYfxjhy43Vf1RHj\n7xTAG3Zd2SEUYmXtUXYIuYv19mWMd4ZiHOl1uXsM2J1QQ9xoZ0IXiNTavT5sDDxX93V03lt2AC4V\nX5yiOmL9Xu0XYXIIcXbbiPE5QZyTlGN8g9JVI71xlDf8DPiJpFeB3yXbBkg6EDgcODjLyVr+zJnZ\njGZfO9fbYhzhAB/lqJJ3lx1AQWJc4rubairzFGsrNlecGJJeMztf0nuBsYQ2aQD/ABYAZ5nZb7Oc\nL8Y3Ws5VQoz117G+oDzXeZdKWqXsAAqwetkBFOTNsgNwlbNgftkR5MPMjpf0c8KiZWsTym7/YWaZ\nqx9j/RvlnHO58VG26vAJX84FVZ/Iliw4dibwOzO7k7Bi71LxpNd1vVgTjhhbEMUqxlH5WK1QdgAF\n8dcLl1XVyxvM7N+SDgH+nNc5l+mkd2bZARQgxjZsMdYdQpyJVKzdG168a1jZIRRi9Y9eXXYIuXul\n7AAKEuPchvXKDiBykZQ33At8CLgxj5Mt00lvjO+cny87ALdMi3USER+5quwICjE3W4vLSoixy0Gs\non296BJVH+lNHA38XtIMwtoRS1W0sUwnvd6yrBrWLjuAgsQ4gh1vy7L4kkOI8/u1btkBFCTGZD7G\nBKSrWpZVvKY3cQVhfuqVwDuSXiSsDVFjZrZR2pO1W5FtYoagzMx2y7C/c6nFersyRjGWbAAMKjuA\ngsS48EuMZQDO9UQkI73Xs3iSu1TavdFaruFC7ye8iZ4OvACsQ/hb8BxhxYzKifEF37kyxbjgBsDd\nS3dHrWsp0hFs51wcSa+ZjczzfO0Wpxha+1rSvsCPgB3M7Pa67dsBlyWPOeecc865LhDJRLZcpS2p\nOQ04uT7hBTCz2yWNAU4n1FtUitf0VkOMDfQBniw7gAJsXnYABTkk0hHRGGt61yw7gILEuDiF1/S6\nNCR9CDgF2BlYA5gDTAJOM7MHs5wr7c/cpsCLLR77F7BJlot2ixjLG2J8EYlVjN1DYpycB3C33V12\nCIVYQR8pO4TcxdrX27ms8pzIJml94FzgE4CACcAoM3s643mOB74H3GxmO6XYf1vgBsL7vqsITarW\nBYYBn5K0k1n6F2il6f4g6RHgMTPbt8ljVwKbmdkH0l60G0iKs0jPOZe7peyS07W8pte5/JlZ6b9Y\nkuzhz2c/bvBlS8YvaSXCmMabwHeSzWcAKwFbmlmqGxGS3gvcD7wOPJEy6Z0ArAbsZmav1W1flZB4\nv2pmu6e5PqQfGBwL/FbSQ8AfWDSR7bOEO5pfSntB55xzzjlXrBxreg8mNC7YzMymAUh6EHgCOIQw\nApzGz4BLCHljn5THbA+MqE94AczsNUlnAhelPA+QMuk1s0slvURIfk8grPT4DnAnsIeZXZ/lot0i\nxvrDGFtGxdqn9+GyAyhAjDWiADtEOiIa4/cr1ppeVw2Tyg6gTo7dG4YBU2oJL4CZTZd0CzCcFEmv\npC8CHwa+QLZlhTvdZst0Gy51CaiZTQAmSFqOsNrtS2ZW6YYYMSaIzpUpxjpliHfBgxiXjV6h7AAK\n4otTuKxyrOndAvhLk+1TCXf825I0APghcKyZvZKxrOp24ERJExrKG1YGjgOmZDlZT37m+hPqOPoA\nlU56Y5zIFiP/PlXHXWUHUJB3bEbZIRRCSr2QUWXMLDuAgsQ4SOOTDouV40jvQELHhEazCd0UOjmb\nMC/s4h5c+0RgMjBD0jWEtSHWBfYi5KNDs5wsddIraW/gVGCrZNO2wD2SfgVMNLPfZblwN4jxXeZ6\nZQdQgFhXZItxVHTDsgMoyrjBZUdQiBhHsD2Rqo4Y/15lGnYsWJqk966X4O6Xi4tB0hDgy4TShszM\n7A5J2wPfBfYgJOCzKbJlWbI4xR8Jy8EdB5xV9/A04KtAqqRX0s40L3t5xcwG1u03gPDuYDhhZPk2\n4Cgze6jhfCsS+gR/CRgA3AccZ2Y3dYqlkn3WOohxNCDOdCPO9l4Dyg6gIDuMfqPsEAoR42tgrOUN\n75QdQAFi/V51izQT2bZZI3zU/PLxprvNofmIbqsR4Hq/AH4NzJK0OqHd2fLAcsm/3zSztqmLmT1A\nijKKNNIOdp4C/MbM/lvS8iye9D4EHJrxugZ8i8XvhjYOfF1DGDg6jDDYdyIwSdJWZjarbr8LgD2B\nYwgJ+OHAdZK2T/6jWoqxni1GXt5QHd00yuE6i7EVm7dhcy7IsaZ3KqGut9FgOs/J/gChb8A3mzw2\nGzgK+HH9xqS12dNmlvt7vbRJ7weA0cnXjf+Nc+jZhNlHzeyOZg9IGg7sAOxiZjcm26YQktrRwKhk\n21bAAcDIWq2IpBsJ36BTgSX6CjvnnHPOxS7Hmt6rgHGSBpnZdABJg4AdWZQbtjK0ybYfAcsRBin/\n2eTxJwg54B3JtURoTXay2dJNsFgu5X5zCR0bmhlE69XaWun0VnwYMKuW8AKY2VzgakK5Q80+hDv6\nl9ftNx+4FNhDkt89cc4559wyZ8H87B8t/BKYDlwpaR9J+xC6OcwAzq/tJGlDSf+RdFJtm5nd2PhB\nuHv/qpnd1HDnfuGpGv69HKEueKk7EqZNev8BnJDU2dZYUk97OPD3Hlz7t8l/zkuSfitpg7rHtiCU\nTTSaCmwoqX/y78HANDN7q8l+fYmzZM0555xzrq0FC7J/NGNm84BdgceBi4HxhBHa3ZLHalT30Ukp\ntVVpyxu+Qxhmfgz4GyHY4wm9zVcnWxnBq4QJajcQRpA/nJz/VkkfNrOXCMXR05ocOzv5vAYwj/Zt\nNEged84555xzPWRmzwCf67DPDFKstGZmu+QVV1ZpV2SbLmkbwopsewDzgZ2Aa4HvthiebnWu+wgd\nFmpuknQTIan+FmHSXK94b29dqBfF2AYrxrY2EGf3hhhXOYR422AdGuGkr+3LDqAgMbbYjHHBjW56\nXc9xIlsZlksWQ4NFiXT9toWyLJSWZUW2Z4CD0u6fhZndK+lx4GPJpnbtMWqP1z43aw1a2292k8cW\n8q4A1RBrs/kY3VN2AC6T27x7g3PRynEiWxluabLt9ibbjAy5bNo+vROBQ81siS5fkjYDfmFmu6a9\naApTgU822T4YmFlXQzIV2FdSv4a63i0IE9yezDEm55xzzrlKqHDSO7aoE6fNjocCq7V4bFVg56UJ\nQtJHgfezqAvDVcBISUNqi0xIWo3Q1eGSukOvJvznfI5QWI2kPsD+wHVF9HjrdjHeAot1wYOXyg6g\nAK1eJKouxrKh4C9lB5C7Vm2Gqi7WlSlj002vFWkWp+hGZlZ60gutZ9q9D3g97Ukk1Wb93Uso6dmG\nMCnuaeC8ZLerCH3uL5E0mvD7fkLy2LiFAZndJ+ky4FxJfQmT3w4ltFE7oFMsXtNbDf0771JJMf4R\ni7X+OlZ3D9uv7BByF+vPYIyvgzEO0nRT2WTFa3oL0fJnTtKBwIHJPw04X9JrDbutBHyQsDxxWlOB\nLwBHEn6Pnwf+AIwxs9kAZmaSPkXo8vBToB9wKzDUzJ5tON9I4AzgNMKg4P3AHmZ2f6dAuumH07kY\n+CqH1fKRq+P7q/iA1/Q6B1S6vGExkgYCnwI2IOSD9czMUjdAUKtlKCV9lZBQQihfqI3M1nubsATd\nmWb2QtqLdgNJFuM75xifU9tFuSssxpnLMY7cQLzdG96w8WWHkLuVNaLsEAoR4+tgjH+v5gJmVvo7\nL0l2zUezH7f3Xd0Rf42k3YE/Aiu32MXMrGObtIXnS7P2uqRJwDebTWSrKknxDXE451wGaV7/q8a7\nN7iydUPSKMmu2ib7cfvc0x3x10h6iNCJ6zDg0aWdq9VxYCaplV2d0BosmqTXOeeccy5WkdT0DgKO\nMrMH8zhZx6TXzP4taWPinCPlnHPOORedSGp67yXH+alpS/D+AewOTMzrwt0gxtWjYqz7WrvsAArS\nTSv35GXLsgNwmQyJsBSgtPVNCxZj/80Vyg6gAJPKDqBOJEnvt4ELJT1uZrct7cnSJr3nEdqHLU9o\n7PgcDS3MzKxyzRC8VqMaKveDtQybUnYALhOv6XXOdbm7CR3Cbpb0Bkt2+zQz2yjtydImvTckn78N\nHNVin9Sz55xzzjnnXHGqujhFg/8BDieUOTzKUt7QTpv0Hth5F+ecc8451w0imcg2EjgtSy/edlIl\nvWZ2UR4Xc84555xzxcuzplfS+sC5wCcAAROAUWb2dIfjNgR+DGxNmKLzBmGRsjPN7O8pLr0AuHEp\nQl9Mpl7yCsVSg4GBhL5pD1uFi8J8GeJqiLGBOcCTZQdQgFiXgI110Y0ZB8ZX/xrjBGWIc5JyjH+v\nZpYdQJ28yhskrUSYo/cmUFv95QxgoqQtzezNNoevArwIfAd4BlgN+DrwV0mfNrO/dLj8FcCeZFv5\nt6VUi1MASPpv4HRgrbrN/wJOMrNf5xFMb/LFKZxzy7oKj1m05BPZXNm6YXEHSXZxD0b2vvLUkvFL\nOhI4G9jMzKYl2wYBTwDHmtm5GWPrA0wD7jWz4R32HQ6cQ0h6rwXmNO5jZqk7i6UawJD0JeD85KKX\nAM8D6wJfAs6XNM/Mfp/2os4555xzrjg51vQOA6bUEl4AM5su6RZgOKHsITUzmy/pVdIN9v85+XxQ\n8rHwNIQyCyNDI4W0d+1GA781s8ZFzS+SNB44DvCk1znnnHOuC+RY07sFoV1to6nAZ9OcICmPXQ54\nF3AIsCnwrRSH5tp6O23S+35C4tvMJTT/z3DOOeeccyXIMekdSJOyAsLcrjVSnuMs4Ojk69eAL5jZ\n5E4HmdkNnfbJIm3S+xqwfovH1k8ed84555xzXaDL+vSeQ6gIWBf4CvB7SZ8xs7+lOVjSQGAHFjVS\nuM3MZmcNIm3S+3fge8kycDfVBbEDYXJbmrYTzjnnnHOuF6QZ6X3sbXi8c2uQOTQf0W01ArwEM5sF\nzEr++TdJkwiT4zomvZJOJ4wS9yXU8QK8LelsMzs5zfVrstT0bg9MlvQsYRnidQmjvE/SuvShq21Y\ndgAFiLG10oCyAyhIjMtgx/g7BfG2zdsowk4HZ0X6zbpqXtkRuDRuLjuAOmkmsm3aN3zU/PWNprtN\nJdT1NhoMPNyT2IC7gCM77SRpFHAi8GsWb6TwZeBESS+a2Y/TXjTt4hTPS9oa+BowhJDdTycsT3yh\nmVXy1zHGvocxJr0vlR1AQWL8+YtVJV/gUojxee29d9kRFOMXl5cdQf5i7esdoauAcZIGmdl0WNiy\nbEd6MOiZTGobAvwzxe7fAH5kZkfVbXsMuEHS68ChhMUv0l07xj6NaUiyGJuYx5hIbVR2AAW5vewA\nCln8A0oAACAASURBVBDj7xSEe2oxeqXsAAoQ68/gq2UHUIB3yg6gADfTPX16f/Ku7Mcd/lLTPr39\ngfsIi1PUyglOBVYGtqoNfCarrz0FjDGz05NtpxAGSm9h0SjtfwO7AgeY2RUdnsdbwN5mNqHJY58A\nrjGzfmmfX9o+ve8C+pvZzLpthwAfBK4zs2vSXtA5F8Q4Ku+qJcY3yTGu8hWrFcoOIHJ5dW8ws3mS\ndiVMRruYRcsQH9Vwp191HzX3EMoYPg+sTkh87wc+bmZTUlz+ZUKuuUTSSyi5eDnLc0k10ivpKuAZ\nMzs0+ffJwFhCAfMA4ItmdlmWC5fNV2Rzzrn4xHr30leaq45uGek9twcTYka90h3x10j6CfBVQhnD\n783sP5KWBz4H/AK4yMyOSH2+lEnvLOBbZvbH5N/PAr8xs5Mk/RjYzsy2y/50yuPlDdURa3nD3WUH\nUIBNyg6gILGWN/yr7AAKsGXZARTEyxuqoZvKG364evbjvv1qd8RfI2lVQoeHHYH5hHZlAwmrsN0M\n7GVmr6c9X9o7rAOBF5IAPkioybgoeewvhJ5rlRPj7PkYPVV2AC61e8oOwC3z/ukjvc4BuS5OURoz\ne03STsCnWNRIYTahkcLfLeOtneVS7vcyixan2BWYZWZPJP9eIcN5FpK0l6QbJL0m6VVJd0gaWvf4\nAEm/kvSipNcl/SNJuBvPs6KkcZJmSZon6VZJQ7LG45xzzjkXiwXzs390IwuuMbPjzOzryee/ZU14\nIX2yOgEYI+lwQoPg+mWHNwdmZLloMgnuL8CdwL6EtZuvYPF2mNcAuwOHAZ8mJNeTJDV2ObkAOAg4\nifBO4DngOkmx3uVyzjnnnGtrwYLsH7FLW9O7DqEp8PaERHV/M3speewO4G4z+2aqC0obAY8Ax5nZ\neS32GQ78CdjFzG5Mtq0GTAPGm9moZNtWwL3ASDO7ONnWh9BI+VEz27dNHHHeA3POuWWYT2RzZeuG\nmlhJ9r0Vsx934tvlxy9pAZD6F9nM+qTdN+3iFC8An2zx8CeAt9JekDAqOx/43zb7DCOUUNxYF8Nc\nSVcDw4FRyeZ9CHO3Lq/bb76kS4HjJK1gZi1r5X0iWzXEOpHN+/RWR6wT2WLs0zss0uRwl7IDcKlM\nKjuAOt1arpDCqSxKekVYGG0l4GrC/LJ1gb0JfYN/neXES90q1MzmZjxkR8IcsgOS1mcbEVZ3O8fM\nfpbsswXwUJNjpwIjJPVPesMNBqaZWWPSPZXwd2oTwqhyUz6RrRpmdt7FdQmfyFYtMfaKfsReLDuE\nQkhrlR1C7mL8+esmVS1XMLMxta8lnUQood2jviewpJWB68jYmruMn7n1ko+zgBMIk/M/B/xEUp+k\n5GEgoZSh0ezk8xqEFTQHEnoFt9pvYI5xu5J4s3nnihHn71YPlqFypYjz5697VDXpbXAIcFjDIhiY\n2RuSzgbOA85Ie7Iykt7lgFWAr5jZlcm2yZI2JiTBTet8nXPOOefcMuVdtK4w6wusmeVkmVuN5aC2\nZFzjknL/B6yTTJqbQxjNbVQbuZ1T97ndfrObPOacc845F7UFPfjoQncBYxs7d0l6DzCG0FwhtTJG\neqcCnVZvm0rziXODgZl1w9xTgX0l9Wuo692CMKfryXYXWTddvK5k/TvvUkkx1irHemM51ols8zrv\nUj3n9GDt1QqI8e/V2mUHUIAHyg6gTpcmsVkdAUwEnpI0hTCRbR1CN7F5wBeznKyMpPfPhJl4exDa\nktXsCTxjZi9IugoYKWmImd0EC1uWDSO0Tqu5GhhLqAken+zXB9gfuK5d5waAGF8avXtDdTxfdgAF\naGyiHYtYk94Yuzfs9+0YF+yFD5QdQAFiXIa4m8SQ9JrZvZI2Ab5NSHQ/RFiP4WxCA4SX2x3fqGWf\nXknfzRaXnZb6otL1hCXSTyJMZNufkAiPNLPxCg0JbyasAjea8Np8AvBBYCsze7buXL8nLGIxmjD5\n7VBgL2AHM7u/TQxxNnN0zrllmPfpdWUru88thBzn+B4c9wO6I/6itEt6s7xJsCzNgSWtAnyfsBLb\nGoTuYd83s8vq9hlAyOT3BfoBtwLfNrOHGs61ImHm3hcJg7f3A6NrI8RtYojzldE555ZhnvS6snVD\n0ijJRvfguLPojviLkmpFthhJshjrD2Msb4ixDAW8prdKYu0nGmPLqBdv3LXsEAqx+k4Tyw4hdzGW\nQz1KdySNkuyYHhx3Nt0Rfz1JXwUOADYkDILWMzN7X9pzxfpanspLZQfgUsm6+okrj/9OudINub7s\nCAoxl67KQ3Lhr+3FyrOmV9L6wLmEVXhF6MA1ysye7nDcR4FvADsB7yH8mbgJOMnMpqe47smEuVsP\nAfcBb/f8WWRIepM622GEwNcExpjZDEk7A0+Y2aylCcQ555xzzuUjr6RX0kqEFZbfBEYkm88AJkra\n0szebHP45wmdt84lJK7rAd8F7pK02BytFg4CfmRmRy3Nc6hJlfRKWgP4G6HV2GuExSXOIywN93VC\nP9wj8gjIOeecc84tnRxHeg8GBgGbmdk0AEkPAk8QVkw7t82xZ5rZYjcBJd1KaDzwdUKv3XbWJHTq\nykXakd5xwAbAjoRGwPWloxOAY/MKqDdtXnYABYixpjfWlmV3lx1AATYpO4CCxNqy7F9lB1CAYZFO\n+Nql7ABcKpPKDqBOjknvMGBKLeEFMLPpkm4BhtMm6W1MeJNtMyW9SCh36OQGYCtCr96lljbpHQ4c\nY2a3JX1w680kJMSV82jZAbhUnio7AJfaPWUH4JZ5/4x0crZ3b3BZ5Zj0bgH8pcn2qYQuXJlI+gBh\nbZKHU+w+CviTpJcJFQdLrLRrZqmfatqkdxWgVd1FP6hmhX2MM81jHOmNVZSrYblKibMzyhllB1CI\nGFemXK3sAAoQ46JD/7+9ew+To6zyOP79EUJIIhAweAE2RoiIAck+66OACISIBpAs6ALKCgmwCIKo\nsCAIwhIuioJycbm7yl0XBVGIkkhMuIggLCqECCIxCUTkmgAxFy7J2T/e6tDp6Z7pmXRXdZ05n+fp\nZ2aqq6tOT89Un37r1HmBjYBFdZYvJLWdbVo2cHoZ6UTTD5p4yOPZ1ysb3G/04vq0Zlf8M2kCiOl1\n7tsFmNXsDjtJJL3l4LW84XdFB9AGHkuGwG95g8cZ2SbolKJDaIvtig4gNKWTkt4OnZHtYtLManua\nWTPTJ55BSmxbotmk9xLgIkkvAz/Mlg2TdAhwNKnIOYTQC/26X2DoCB4/JIcQkmaS3qezWw8WUX9E\nt9EIcF2SvgkcBkw0s6Z6C5rZ5Ga334ym3nfN7ApJm5N6pZ2RLb6d9Ds9x8yub2VQeYnTyyG0VvxP\nhaJ5HL2GNDTmzX1FB+BcM0nvO7JbRYPrMmaT6nprjaa5ulwkfY3U9OBoM/thT+u3S9ODTWb2VUmX\nksocNgZeBG43s9JeZxQjbeXwetEBtInHU+YeS4bA58xlXg0sOoA2ebjoANrA62vVKVpY3nALcK6k\nkZUJJSSNJHX06nG2Y0lfAs4ETjKzS3u7c0nrAHsA76X+jGxnNr2t/jwNscf6Q4+nK73W9EbLsvLw\n+AEFfLYsG110AG2ypOgAQlNm0hnT+Eqyg/vwuKvoGr+kIaTZ0JYBp2aLzwCGAmPMbGm23ghSw6XJ\nZnZWtuwzwPXAVN6sFKh4xcwe7eF5bAL8htQn2HizccKq5NXMaruKNdSbGdkGABOBHUi91f4G/Ba4\n1sxWNLudTuJxCjmPI1JeT5l7fK2eKDqA0Csep4HtpAuJWmlJyiFc2djpRYedolUjvWa2VNI44Hzg\nGt6chvjYSsKbUdWtYnz2dffsVu1OYFwPuz8XeJ40G/CTpGs6nwcOJc329vHePJemRnolvQuYBmwJ\nLACeBd4ObEbq7LC7mc3vzY6LFiO95bFJ0QG0icc+0R7/p8DnBxTwOdLr9cxQKIdOGuk9sA+Pu47O\niL9C0pPA8cCNpEPxB83swey+rwPbmNnezW5vrSbXu4jUUu8jZjbCzD5oZiOAnYANSFMShxBCCCGE\nDrCyD7cO9Fbg79kEFEtYvYvEDGBsbzbWbHnDOOAoM/tt9UIzu0fSyaSkuHQ8jrR5VNorJfuh3xQd\nQOj3vB4vPF5/E7PMtVeHJrG9tYA0exvAHFafM+JDwPLebKzZpPcfND4T9hwlLbv0eCrWY3mD19OV\nHi9k83oRkVceyxu8Xkw5zmGCuGvRAbTBzKIDqOIk6Z1Jque9CbgcuFjSP5MaO43PljWt2aT3OuDz\nwG117juCVNhcOh4vZPN4lbnH5BBK+kmxB/OKDqBNPE4BCz4v+vJafz1/6g5Fh9By79v93qJDcM1J\n0nsKaRIMzOxSSWuTLmAbApxD144Q3Wp4IZukQ6t+XAc4GXiZlG1XLmTbF1gPONvMLuvV0yhYXMhW\nHnEhW3l4HWXzKkZ6y8Nrv3JvOulCtn378Lgb6Yz426W7kd7/qbNsM+rPynExUKqkN4TQeh4/dIHP\nMyheeX2tIukNveVkpLchSYOAz5vZhc0+pruk991rHlJn8/oGHUIIwRePs5dFIt9eHpJeScOBF62q\nLEHSYOAo4DhS1cGaJ71l67sb/PJ4sAefH7q8jrKF8vD4fxVCX5Q16c1GcM8hTUAxBHhZ0teymt4D\nSRNWvB14AJjUm203PSObRx7foD0e8L2OBnj8+wshtIfX42Bon7ImvcB/AV8ktSb7Pany4EJJo4Ev\nAI8Dh5vZrb3dcG+mIf44cCTwXmDd2vvNbPMmtzMT2KXB3VPNbM9svWHAt4G9gcHAvaQp7x6p2d4g\n4Czgs8Aw0vzQJ5rZ3T3F8lIzAYfCvVB0AG3i8QPKvKIDaJO39bxKKXmchvjJogNokyl9mV6rw+1/\nXdER+FbipPfTwCVmdnRlQdZc4X+A24EJZtant9Cmkl5JewK3krLurYCppCHnHYH5QI8JZpUjSbO7\nVfsw8B3g51XLpgAjSFn9S6TuETMljTGz6m5jPwD2IE1TNxc4GpgmaXsze7i7QIb1Iuiy8JhIvbPo\nANrEY8s8r502vI7K1x6IPfDaveFzDhPEDYoOwLkSJ73/BNxcs+ynpKT3vL4mvND8SO+ppA4Nx5LO\nspxiZr+XtCUwjfr9e+sysy6dmiQdQcrXbsh+3hvYAdjVzO7Klt1HSmpPAI7Jlo0BDgAONrNrsmV3\nAbNJvdv26S4Wj31SQwit5/HDpFdeXyuPk/Q8UXQAzpU46R0ILK5ZVvn5+TXZcLNJ71akGouVgFUe\nZ2aPS5pMSop/3JcAsqvw9gVuMbNKxcEE4OlKwpvt6xVJt5LKHY7JFv8r6Rj346r1Vkj6X+BESQPN\nrGEplMeDo8cm+lHLVh5eS1GGFx1Am3icyMHr8WK0w4P7YzHy1FYlTnoBNpVUXTY7oGr5atWpZtb0\n7OPNJr0rgRVmZpKeJ5Ud3J/d9zSwRbM7rONTwFuAq6uWbQ08Umfd2cBBkoaY2VLSrKdzzax27uXZ\npDOSo4BHG+3Y4/+bx6TDa41eKA+P/1fg84O/19dqxpJeX7PT8U7WhKJDcK3kSe+NDZb/rM6yAXWW\n1dVs0vtnUmI7A/g/4BhJ95AGCo5jza5fmUiaGGhq1bKNSKUMtRZmXzck5awbAYu6WW+j7nbssf7Q\n45uYx9N64HN65dFFBxB6JWZkK49xDhPEnYoOoA1mFh1AlRInvYe0a8PNJr3XA1tm359GuqBtQfbz\nCuDf+7JzSe8EPgqcb2a5vz4ep4H1qOnzFqFw9xUdQOj3vB4vqnrzuyG5ne22I7QyqZK0GXABsBsg\nUh54jJk91cRjvwF8ILttRNV1WPWY2dWN7ltTTSW9ZnZx1fcPSno/sDuphHS6mf2pj/s/iPTLq33y\ni0ijubU2qrq/8nVEN+strHOfax4bL3usO/TK499fKBe/xwuvhRuh02XXXs0ElpHyNoCvAzMkbWtm\ny3rYxNHAH0hdwCa2LdAm9Ok9yswWkFpHrKmJwENmNqtm+WzgY3XWHw08mdXzVtbbR9K6NXW9W5PO\n9MfFoSGE0IDfBDGUgccPyZ30P9XCkd7DgZHAlmY2F0DSLOAvwBGkEeCGzGz97DFb0MsZ1FqtsL85\nSR8gJbHH1Ln7FuBgSTtVJpmQtD6pq0N1t8JbgdOB/YBrs/UGAPsD07rr3ACpJYU3UdNbHh5rer3W\nU3rt0+uxptdrXfk4bVx0CC0XNb3t1cKkdwJwXyXhBTCzedm1XXvTQ9LbSRomvZIq7cmaYWbW2wR6\nEqm7zA/r3HcLqTzwOkknkCanOCm779yqnf5R0g3ABZLWIV38dhTpE8kBPQXgsabX4yfn6N5QHt3O\nBlNiXpNejx+S/db0zik6hJZLA3+hXVqY9G5N/a4Js0ktZ0ujuxzpDJpPentF0trAZ4DbzKxLoVLW\nGu0TpGmILyZNe/xbYKyZ/a1m9YNJtSVnkiZZewgYb2YP9RRHjPSWQ4z0lofXUTavPI70ej3bMM5h\ngrhr0QG0gdOR3u46ZdW7/qpjNUx6zWxyu3ZqZm/Qw3T22UQVh2W37tZ7lTQF8fEtCzB0FK/N5j3y\neKYBOqtOr5U8jmDH8SKEpMQty9rG63tUCB3PY8LhNTn0yuOZoYFFB9AmkcyH3mom6V1M1/l+6+iu\no1a9EeCO1a+TXo81vR55rdHzKJoqhaLF8aI8ovdwezWT9A7NbhXP1F9tNqmut9ZooK8tawvRr5Pe\n9YsOoA08jrTVa8TsgccL9IYXHUCbeBwRBZ/HiyFFBxCad8P7io7AtRaWN9wCnCtppJnNA5A0EtgR\nOKF1u2k/efyk1QxJFheylUO3xd8l5rGJtNcPKB5LUSAuZCsTj+UNQ3tepXSmAGZW+HCvJNumD497\nhK7xSxoC/JE0OcWp2eIzSC/hmMrcCZJGkE62TDazs6oevzOwMfBO4LukBgV3kPZ1Ux/C7LN+PdIb\nysHrH6nHDyihXLwm86Ec4hjYXq0a6TWzpZLGAeeTZtCtTEN8bNVkYWTLK7dqpwM7VzZHai17VPbz\ngBaF2ZR+PdJbdAwhhBBCf+Ux/5DUMSO9fTmb/RidMVLdLl4H0Zrisf7wpaIDaAOvvV9LVf3fpGFF\nBxD6Pa9vai5H5X+9c8/rhNBCXo8PTVna8yql4/HCFI+JvFdxujIUzeNxHXxeeM1Hdys6gja4u+gA\nVok+vV3166TX40HE4wvqcUQefLb38jrSG8l8eWxSdABt4vF48Y+vnFZ0CK5F0ttVv67p9djaxuOb\ns8vTevgdkQrl4fFDssfjOsArRQfQBmYPFR1Cy0ljOqImVpJt3ofH/ZWo6XXL45P3mPR6fRPzmPR6\nHZX3+Fp55bHEC3y+X8Hviw7AtRjp7crn/1GTPJ4G85j0eu3T61H06S2X6NNbHh779E7QIUWH4Fok\nvV316/KGomMIIYQQ+iuP+UcntSzbrA+PW0CUN7jVl3qXTuex7svryM3DRQfQBl5fK68lNh47o3h9\nrTyebTh3qNvcqiPESG9X/Trp9XgQiY4U5eHxzdnra+WVx3IoryU2HssbpkexfFtF0ttVvEeFEFrG\nYyIPfi+O8shjcuhVvFbtFUlvV5H0hhBaJpLDULSBRQfQJpEght6KpLerSHpDKIjHU8teDyhek3mP\nJV6RHIaQRNLbldf3qBBCAbyW6HlMDr2Kkd7y8PpadYpIeruKpDeE0DJR0xuK5jE59Cpeq5C3SHpD\nx4uEozw8tswDvwdKjyPzXkcPPSaI7yo6AOdipLcrr8fy4MjgogNoE4/JvNcDitfyBo8j815fK49J\n7/yiA3CulUmvpM2AC4DdAAHTgWPM7KkmHjsIOAv4LDAM+CNwopnd3cIQm+L1PSqEUACPSRT4/IDi\n1ZKiAwihQ7Qq6ZU0GJgJLAMOyhZ/HZghaVszW9bDJn4A7AEcD8wFjgamSdrezHKdpymmIQ4dz+sn\ns0ikysPr36BH8X9VHmYvFx1Cy0kbdMQ0vpJs3T48bjldpyGW9GXg28CWZjY3WzYS+AvwFTO7oJs4\nxgB/AA42s2uyZQOA2cBjZrZPH8Lss36d9G6Vw36WAENz2E+FxzZYm+S0n5dI513y8liO+8pLnrNh\nLQbWy2lfXk+ZP53TfpYDfXkD7ostctqPV4uADXPa1wY57SdPP6Nr0lgESdaX49Zr1E16pwODzGyn\nmuV3pNVt127iOBX4GjDMzJZXLZ8MnAisb2a5Ve/06wGMPOadX0y+tVgv5LivvOSVcDxPvqNEHl+r\nPD905ZlIeZXX/9YS8ruo5tGc9pO3vC46zPP/6uUnDup5pZLRqGuLDmGVFv7PbU3K52vNBvbt4bGj\ngbnVCW/VY9cBRpHjv22/TnrzGNV7Paf9VHisqRye036W5Lgvct5XXkbluK+ngH/KcX8ePZfTft4A\n1s9pX3n+DeYpr8GTucC7c9rXuA5KED1qYdK7EekkQK2F9HxioLvHVu7PTb9OevM4tbecfEd6vbaM\nysNi8jvdCz7bRT2R476WAK/mtK+8Era85XW2YTn5jfR6PQbm9Tf4Evl1VZhz17ic9pQf7Tyj6BBW\niZZlXfXrpDevg6PHOts8/TXHfeVR8uJZ3ol8T5cMt4rHUpS8xXFwzeT5N5jXcbCTEkSH5tO3VsjP\n1lnWqNS70Shu7WPrXe5RGeFdWOe+tum3SW8nFJqHEEIIIbSamY1s4eZmk+p6a40G/tTEY/eRtG5N\nXe/WpM/CeZ4gZK08dxZCCCGEEErlFmD7rE0ZsKpl2Y7Az3t47K2kC9b2q3rsAGB/YFqenRugH7cs\nCyGEEEII3ZM0hDSL2jLg1GzxGaSOrGPMbGm23ghSReJkMzur6vE/Aj4OnEC6VvIoYE9gBzN7KK/n\nATHSG0IIIYQQGsiS2nHA48A1wLXAHOCjlYQ3o6pbtYOBK4EzgSnApsD4vBNeiKS3LSRtJulGSS9J\nelnSTZKiu1IHkrSvpJslPSlpqaTHJH1D0luKji10T9JUSSslnVF0LKE+SXtKulPS4uxYeL+ksUXH\nFVYnaUdJ0yQ9K+kVSQ9KOqTouELnMLMFZrafmQ0zsw3M7N/M7Mmadeab2QAzO7Nm+atmdryZbWJm\nQ8xsBzO7O99nkETS22JVc1RvSZqj+kDgPaQ5qgcXGVuo6zhSG9GvArsDlwBHAr8qMqjQPUkHANsC\nUZ/VoSQdQWpo/wCwD6mJ/U/w2U68tCS9H7iddGH7YcAngfuB72evYQhu9NvuDW10ODCS1eeonkWa\no/oIoOEc1aEQe5nZi1U/3yVpEXCVpLFmdkdBcYUGJG0InAccA/yo4HBCHZLeBZwPHGdm/1111+0F\nhRQaO4A0ALaXmVW6AP5a0hhgInB5YZGF0GIx0tt6E4D7KgkvgJnNA+4B9i4qqFBfTcJb8QCpJmnT\nnMMJzfkW8LCZ3VB0IKGh/wBWEAlTGQwEXqtKeCteJnKE4Ez8Qbfe1sAjdZbPJvW0C51vLOm0eW7z\ngYfmSPoIqWToC0XHErq1I/AYcICkJyS9Lukvko4qOrDQxVWAJH1X0jslbSDpc6QLl84rNrQQWivK\nG1pvTeaoDgWTtClwOnC7mf2+6HjCmyQNBC4DzjWzXBuah17bJLudA5xEamO0H3CRpAE1JQ+hQGY2\nW9KuwM3A0dni14DPm9lPiosshNaLpDeEjKShpEbbrwGHFhxO6OpEYF3gG0UHEnq0FvAWYKKZVZrX\n3yHp3aQkOJLeDiFpFHATMIt0TcpyUine5ZKWm1nUzQc3IultvTWZozoURNK6pP6BI4GdzezpYiMK\n1bKWfyeTakXXzV6vSi/IQZI2ABab2cqiYgyreREYBUyvWf4rYLykt5vZs/mHFeo4m/RB/1/N7I1s\n2UxJw4ELiYtFgyNR09t6azJHdSiApLVJIx3/AuxhZvE6dZ7NgUHAdaQPj4tIJUMGfCX7fpvCogu1\nZhcdQGjaNqQLQ9+oWX4/8FZJbysgphDaIpLe1luTOapDziQJ+CHp4rW9zeyBYiMKDfwB2DW7ja26\niTQ70Fgg6nw7x83Z1/E1y/cAFsQob0d5Btg2+/BfbXtSqcPC/EMKoT2ivKH1vke6svznkqrnqJ4P\nXFFYVKGRS0hN888Clknaruq+BWb2t2LCCtXM7BXgrtrl6TML84ua3SfUZ2a/lHQHqS50Y9KFbPsD\nu5GmJA2d4yLgx8AUSZcAy0g1vZ8GzqszAhxCacksJjRqNUmbkRqzf4w0EjUdOLZ2yr5QPElzgREN\n7j7dzGKK2w4maQVwlpmdVnQsYXXZVN5nkz5UbkhqYXZ29FfuPJLGky4U3Zp0segcUo/lKyyShOBI\nJL0hhBBCCMG9qOkNIYQQQgjuRdIbQgghhBDci6Q3hBBCCCG4F0lvCCGEEEJwL5LeEEIIIYTgXiS9\nIYQQQgjBvUh6QwghhBCCe5H0hhD6BUmTJB2S4/4k6QJJT0taIemnbdjHLpJiYo4QQmhCTE4RQugX\nJM0EBpjZzjntbz/gBuBY4F5goZk90eJ9nAb8FzDQzFa2ctshhODN2kUHEEIIfSFpHTN7rYNjGA2Y\nmV3YzhBqvrZmo9JAM3u9ldsMIYSiRXlDCGEVSe+RdLOkZyUtkzRf0g2S1qpaZ7ikyyQtkLRc0qOS\nPleznUmSVkraKdveYkkvSLpI0ro1606W9KCklyU9L+nXkrarWWeXbHuflHSFpOeAZ7L7tpB0jaS/\nSloqaY6kSyQNq3r8TGAXYMdsOyslzai6/0OSpmdx/iP7/oM1MVwl6SlJ20u6R9JS4FsNfo9zgdOy\n71dm5Q0Ts58HS/pWFu+r2deTJanq8YMknSdpVhbT3yXdIum9VetURnkBXq/sJ7tvbPbzaqPakg7O\nlo+ojlXStZIOyV7LV4E9m401hBDKIkZ6QwjVfgm8CByRfd2UlACtBayUtB5wDzCIlHDNA8YDl2aj\nnhfXbO9a4MfAxcCHSIngEODQqnU2BS4AngSGAgcCd0r6gJnNrtned4HbsnUqyfMmwN9IZQQLjjrM\n9QAABUBJREFUgXcDJwO/AHbM1jkSuD57HoeTRkZfAZC0LXAHMBuYmK1/UhbDdmY2K1tmwAbAj4Bv\nZ+ssa/B73Af4MjAJ2C7b3xxJA4BfAVsBZwCPANuTfpcbAl/JHj8IWA/4OvB0dt9RwL2StjKz54Dv\nAZtlv8sPA9XlDZbdajVaviswBpgMPAfM60WsIYRQDmYWt7jFLW4AbyUlTnt1s86pwFJg85rlV5CS\npbWynydl27q4Zr2TgdeBUQ22vxYwAHgMOL9q+S7Z9m5s4nkMICW7K4AxVctnAnfVWf9GUrK8XtWy\n9UhJ/41Vy67Mttnw91Oz3TOBFTXLDsq2sWOd38tyYHg3v5fBpET9y1XLT8u2t1bN+rtky3euWT4p\nWz6iatlc4B/Axq2INW5xi1vcOvUW5Q0hBADM7EXgr8A3JR0maVSd1cYDvwPmSxpQuZFGBIeT6lhX\nbRL4Sc3j/5eUlH6oskDSbpJmSHoBeIOUFL8HeC9d/ax2gaSB2Sn3R7OSg9eBu7O7622j1k7AFDNb\nvCrw9P0tpOSx2uukEeS+Gg/MB+6r+f3dDqxDGkkFQNL+ku6TtIj0e1lCGglv5jn11n1m9nxfYw0h\nhDKI8oYQQrXdSKe4vwEMz2pTzzWzy7L73wZsQUr+ahlptLjasw1+3hRA0r+QksjbSKfp/04aXfw+\nb5YvVPt7nWXfBL4AnE7qkrCYdNr/5gbbqLVRg+0+QzqNX+15M1uTljdvA0bSw+9P0gTSB4QrSa/H\nC6SR7tto7jn1Vr3n31SsIYRQFpH0hhBWMbN5wMGwqtb1aOASSXPNbBrplP+zwJeo3zHgzzU/vx14\ntOZnSDW4AP9GSqo+ZVUttyRtCCyqF2KdZZ8Grjazs6sev16d9RpZCLyjzvJ31IlhTXs8VkbT96P+\n729e9vXTwF/M7D8qd0ham5SgN2N5tv11apY3SlTrPa9mYw0hhFKIpDeEUJeZPSzpOOAwYBtgGjCV\nlAg/ZWYv9LAJAfuTLhKrOIA0kvu77OfB2c9vPkgaB4wgJVyrhdRgP0NIp/+rHVpn/Vepn/TdCewp\naaiZLcliWA+YAMyos/6amAp8ClhiZo93s1695zSRVBpS7dXs62BS+UPF/OzrNsD0quV7tSHWEEIo\nhUh6QwgASHo/cCFpQoUnSAnWIaSR2Erydz4pkf2NpPNJI7tDSVf472Rm+9Rsdk9J55BqfrcjXfl/\ntZnNye6fSupycLWkK0n1qqcAC+qF2CD0qcAkSY9kcX8K2KHOen8CjpS0PzAHWJwlc2cCnwBmSKq0\nIDuRlEie2WCffXU9aSR9hqTvAA+RRmNHkZLsvc1sefac9pZ0HjAF+CDpw0btyPOfsq/HS7qNdOHc\ng2b2jKQ7gZMkvUi6yPBAUmeLVscaQgilEElvCKHiGdII4bGkmtjlwCzgE2b2BwAze0XSh0nJ6wmk\n2tyXSMnvTTXbM1KidTzweeA14HKqWl2Z2a8kfQn4T1Ky+gipa8ApdB2pbTTS+8Xs61nZ118AnwHu\nr1nvW8CWpFZfbyGN8I4zs1mSxpLag11FSq7vJXU+mFWzjd6WN6y2vpm9IWk88FXgc6QkdAkpCZ9C\n+h3B6u3IDgceII3S3lyzzSnAJaSWbKdmsVdGgz8LXEr6ILMc+AGpg8X36sTY5Xn1ItYQQiiFmIY4\nhNBykiaRkqz3mFltmUIIIYSQu2hZFkIIIYQQ3IukN4QQQgghuBflDSGEEEIIwb0Y6Q0hhBBCCO5F\n0htCCCGEENyLpDeEEEIIIbgXSW8IIYQQQnAvkt4QQgghhODe/wN5Y/FtSDgNrgAAAABJRU5ErkJg\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7b18d041d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "svc.decision_function_shape = \"ovo\"\n",
    "\n",
    "train_trans_nl_ovo = svc.decision_function(train)\n",
    "test_trans_nl_ovo = svc.decision_function(test)\n",
    "\n",
    "rfc_nl = sklearn.ensemble.RandomForestClassifier(n_estimators=100, max_features=21, max_depth=10)\n",
    "rfc_nl.fit(train_trans_nl_ovo, train_labels)\n",
    "rfc_nl_pred = rfc_nl.predict(test_trans_nl_ovo)\n",
    "rfc_nl_probs = rfc_nl.predict_proba(test_trans_nl_ovo)\n",
    "\n",
    "n_err_rfc_nl = np.sum(test_labels != rfc_nl_pred)\n",
    "print(\"{} misclassified test cases\".format(n_err_rfc_nl))\n",
    "print(\"test error rate = {:4.3f}\".format(n_err_rfc_nl/len(test)))\n",
    "\n",
    "plt.imshow(rfc_nl_probs[argidxs], aspect='auto', cmap=\"afmhot\")\n",
    "cbar = plt.colorbar()\n",
    "cbar.set_label(\"RandomForest probability\")\n",
    "plt.xlabel(\"separator feature\")\n",
    "plt.ylabel(\"label sorted image number\")\n",
    "\n"
   ]
  },
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   "metadata": {},
   "source": [
    "## Thoughts\n",
    "\n",
    "I have used this trick a number of times in kaggle competitions to get a significant boost in my leaderboard score. Mostly this is not due to the improvement of the predictions themselves but the ease of making tweaks to the output values to optimize the competition metric. Since SVM works in a kernel space it is very hard to optimize for metrics other than the hinge loss. This often drives the choice of a reasonable means of classifying the data but it doesn't easily admit a probability estimate. Using the classification margin as a classification confidence allows us to select appropriate scaling and clippings to maximize the desired metric (e.g. area under the ROC curve) on a held out validation set. This is of course no different in principle from using a stacked classifier as we have done in this post. \n",
    "\n",
    "Gaining access to the hyper-plane distance ourselves is particularly useful in cases with very imbalanced classes where it is not at all unusual for the most likely classification for every point to be one class or the other. An additional line of defense in this case is altering the class weights or building a stratified k-fold. But even when applying these other techniques it is often best to also set a best classification threshold by hand."
   ]
  }
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  "nikola": {
   "author": "Tim Anderton",
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   "date": "2017-2-4",
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   "slug": "SVMFeatureExtractors",
   "tags": "SVM",
   "title": "Using SVMs as Feature Extractors",
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