{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"name":"Εlbow method - Aξιολόγηση.ipynb","provenance":[{"file_id":"1d3kIo6D2AP7QNHWqIgeJmcbcCPqHaKCb","timestamp":1605013535615}],"collapsed_sections":["Nre7oxppyO07","SD9NpWgPyO1Y","PkznuNRa4-Hi"]},"kernelspec":{"name":"python3","display_name":"Python 3"}},"cells":[{"cell_type":"markdown","metadata":{"id":"5P5k9Vw1yO0x"},"source":["## Αξιολόγηση Συσταδοποίησης\n","\n","Θέλουμε να βρούμε έναν τρόπο να επιλέξουμε το βέλτιστο $k$ για το προηγούμενό μας πρόβλημα. Θέλουμε, δηλαδή, έναν τρόπο να αξιολογήσουμε την επίδοση του αλγορίθμου.\n","\n","Όπως ξέρουμε δεν υπάρχουν ετικέτες σε ένα πρόβλημα μη-επιβλεπόμενης μάθησης. Οι μετρικές που είδαμε στην επιβλεπόμενη μάθηση για την αξιολόγηση ενός αλγορίθμου (accuracy, confusion matrix, f1-score) χρειάζονται τις ετικέτες για να υπολογιστούν. Πώς μπορούμε, λοιπόν, να αξιολογήσουμε την επίδοση ενός αλγορίθμου συσταδοποίησης;\n","\n","Το πιο απλό μέτρο που μπορούμε να σκεφτούμε είναι να συγκρίνουμε για κάθε συστάδα τη διασπορά των παραδειγμάτων της συγκεκριμένης συστάδας.\n","\n","Για τη συστάδα $C$ το παραπάνω μπορεί να υπολογιστεί ως εξής:\n","\n","$$\n","I_C = \\sum_{i \\in C}{(x_i - \\bar{x}_C)^2}\n","$$\n","\n","όπου $x_i$ ένα παράδειγμα που ανήκει στη συστάδα $C$ με κέντρο $\\bar{x}_C$.\n","\n","Όσο πιο μικρό το μέτρο αυτό, τόσο μικρότερη διασπορά έχει η αντίστοιχη συστάδα, πράγμα επιθυμητό καθώς σημαίνει ότι είναι πιο \"συμπαγής\". Μετρικές σαν αυτή τις ονομάζουμε **inertia** (αδράνεια). Για να υπολογίσω τη συνολική αδράνεια, απλά προσθέτω τις διασπορές για όλα τα cluster.\n","\n","$$\n","Ι = \\sum_{C = 1}^k{I_C}\n","$$\n","\n","Πολλές φορές το σταθμίζουμε και με τη συνολική διασπορά στο σύνολο δεδομένων. Ας δούμε ένα αντίστοιχο παράδειγμα με το προηγούμενο, χρησιμοποιώντας την υλοποίηση του [KMeans](http://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html) από το scikit-klearn..."]},{"cell_type":"code","metadata":{"colab":{"base_uri":"https://localhost:8080/","height":282},"id":"5BvmrURqTHh-","executionInfo":{"status":"ok","timestamp":1636027191764,"user_tz":-120,"elapsed":36,"user":{"displayName":"Giorgos Siolas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjxnZOAObbc3X0z9X2rs1N_1geznqhrotkq3KF-p_M=s64","userId":"10127542075805046236"}},"outputId":"16253f53-6953-4e90-dbfe-fda77ac4d6bd"},"source":["# ΚΩΔΙΚΑΣ:\n","# --------------------------------------------\n","import numpy as np\n","import matplotlib.pyplot as plt\n","\n","\n","np.random.seed(55) # για να αναπαράγονται τα αποτελέσματα...\n","\n","p1 = np.random.rand(50,2) * 10 + 1 # 100 τυχαίοι αριθμοί από ομοιόμορφη κατανομή στο διάστημα [1,11), αποθηκευμένοι σε πίνακα διαστάσεων 50x2.\n","p2 = np.random.rand(50,2) * 10 + 12 # 100 τυχαίοι αριθμοί από ομοιόμορφη κατανομή στο διάστημα [12,22), αποθηκευμένοι σε πίνακα διαστάσεων 50x2.\n","\n","points = np.concatenate([p1, p2]) # ενώνουμε τους αριθμούς σε έναν ενιαίο πίνακα διαστάσεων 100x2\n"," # η πρώτη στήλη του πίνακα αντιστοιχεί στη συντεταγμένη x ενώ η δεύτερη στην y\n"," # δηλαδή η 30η γραμμή του πίνακα αντιπροσωπεύει τις 2 συντεταγμένες του 30ου παραδείγματος \n","\n","# ΣΧΕΔΙΑΣΗ:\n","# --------------------------------------------\n","\n","plt.scatter(points[:,0], points[:,1]) # για να σχεδιάσουμε τη γραφική παράσταση διακριτών σημείων χρησιμοποιούμε την scatter\n"," # τα 2 της ορίσματα είναι οι συντεταγμένες x και y όλων των σημείων"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":[""]},"metadata":{},"execution_count":1},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"code","metadata":{"id":"1zJWDlfByO0x","colab":{"base_uri":"https://localhost:8080/","height":282},"executionInfo":{"status":"ok","timestamp":1636027216262,"user_tz":-120,"elapsed":1605,"user":{"displayName":"Giorgos Siolas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjxnZOAObbc3X0z9X2rs1N_1geznqhrotkq3KF-p_M=s64","userId":"10127542075805046236"}},"outputId":"c94dac14-b4f6-431a-f29f-eded08330a82"},"source":["# ΚΩΔΙΚΑΣ:\n","# --------------------------------------------\n","\n","from sklearn.cluster import KMeans\n","\n","k = 5\n","km = KMeans(k, random_state=99)\n","km.fit(points)\n","\n","print(km.inertia_)\n","\n","# ΣΧΕΔΙΑΣΗ:\n","# --------------------------------------------\n","\n","plt.scatter(points[:,0], points[:,1], c=km.predict(points), lw=0, s=30)\n","plt.scatter(km.cluster_centers_[:,0], km.cluster_centers_[:,1], c=range(km.n_clusters), s=80)\n","axes_scaling = plt.axis('equal')"],"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["769.242668057399\n"]},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"WpeVa3CmyO0z"},"source":["Όσο μικρότερη η αδράνεια, τόσο καλύτερο clustering έχει γίνει. Προφανώς θέλουμε να **ελαχιστοποιήσουμε** το κριτήριο αυτό. Ας τρέξουμε λοιπόν τον $k$-means για $k$ από 1 μέχρι 100 να δούμε σε ποια τιμή ελαχιστοποιείται ο δείκτης αυτός."]},{"cell_type":"code","metadata":{"id":"Z1nNY9rVyO00","colab":{"base_uri":"https://localhost:8080/","height":282},"executionInfo":{"status":"ok","timestamp":1636027311063,"user_tz":-120,"elapsed":24079,"user":{"displayName":"Giorgos Siolas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjxnZOAObbc3X0z9X2rs1N_1geznqhrotkq3KF-p_M=s64","userId":"10127542075805046236"}},"outputId":"ce64a5f2-a959-4a4b-f82c-b0e107679aac"},"source":["# ΚΩΔΙΚΑΣ:\n","# --------------------------------------------\n","\n","cluster_scores = []\n","for k in range(1, 101):\n"," km = KMeans(k, random_state=77)\n"," km.fit(points)\n"," cluster_scores.append(km.inertia_)\n","\n","# ΣΧΕΔΙΑΣΗ:\n","# --------------------------------------------\n","\n","plt.plot(range(1, 101), cluster_scores)"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["[]"]},"metadata":{},"execution_count":3},{"output_type":"display_data","data":{"image/png":"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\n","text/plain":["
"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"F_CRqirgyO02"},"source":["Παρατηρούμε ότι η αδράνεια μικραίνει όσο μεγαλώνει το $k$, και φτάνει στο 0 όταν $k=N$, όπου $N$ το πλήθος των παραδειγμάτων μας. Το να ορίσουμε μια συστάδα για κάθε δείγμα είναι τετριμμένη λύση, γιατί δεν μας βοηθάει να εξηγήσουμε τα δεδομένα και να εξάγουμε γνώση από αυτά, που είναι ο στόχος στην μη-επιβλεπόμενη μάθηση.\n","\n","Άρα δεν μπορεί να μας βοηθήσει το κριτήριο αυτό για τον υπολογισμό του βέλτιστου $k$.\n","\n","Ένα **εμπειρικό** κριτήριο που μπορεί να βοηθήσει είναι αυτό που αποκαλούμε [μέθοδο του \"αγκώνα\"](https://en.wikipedia.org/wiki/Elbow_method_(clustering)) (elbow). Κοιτάμε δηλαδή στη γραφική παράσταση της αδράνειας ή της διασποράς ως προς το $k$, σε ποιο σημείο σχηματίζει έναν \"αγκώνα\" η γραφική. Αυτό υπολογίζεται κοιτάζοντας και τη δεύτερη παράγωγο της αντίστοιχης γραφικής.\n","\n"]},{"cell_type":"code","metadata":{"id":"STb0jGmxyO04","colab":{"base_uri":"https://localhost:8080/","height":976},"executionInfo":{"status":"ok","timestamp":1636027334315,"user_tz":-120,"elapsed":863,"user":{"displayName":"Giorgos Siolas","photoUrl":"https://lh3.googleusercontent.com/a-/AOh14GjxnZOAObbc3X0z9X2rs1N_1geznqhrotkq3KF-p_M=s64","userId":"10127542075805046236"}},"outputId":"d9d06fa6-b703-4dae-dca8-cf7aad02bfc3"},"source":["# ΣΧΕΔΙΑΣΗ:\n","# --------------------------------------------\n","\n","plt.plot(range(2,8), cluster_scores[2:8])\n","plt.annotate(\"elbow\", xy=(3, cluster_scores[3]), xytext=(5, 4500),arrowprops=dict(arrowstyle=\"->\"))\n","plt.annotate(\"elbow\", xy=(5, cluster_scores[5]), xytext=(5, 4500),arrowprops=dict(arrowstyle=\"->\"))\n","plt.annotate(\"elbow\", xy=(6, cluster_scores[6]), xytext=(5, 4500),arrowprops=dict(arrowstyle=\"->\"))"],"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["Text(5, 4500, 'elbow')"]},"metadata":{},"execution_count":4},{"output_type":"display_data","data":{"image/png":"iVBORw0KGgoAAAANSUhEUgAAAX0AAAOuCAYAAADrTMf5AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nOzdd7ieVZ3v//fae6cXCKZIIKGEEhISBEMREAsqKI6OjqMiKqKMHnuZc45O1TnzO+MZ5xyxjDrqgKAwqGOvoKOj0VFKQEyFAJEQWggaEpJAQpL1+2M/gZ1kl6fd97rL+3VdXoRnt4WEDx++az33CjFGJEn10JN6AZKk/Bj6klQjhr4k1YihL0k1YuhLUo0Y+pJUI4a+VCEhhBhCODWE8IoQwu7U61HxGPqSVCOGvlRSIYT/CCHsCiHsDiFsDCGMGeRztjQ+vi2EcGjjtX9pvLY7hLAphPCUEMKHQgiPNj7+1cZ/MRwYQpgeQvAdnBVi6EslFEJ4C3AmcGCMsQfYDfxw308DPtP4+OPAtSGE6cBbgDc1Xu8B/hP4CDC28XXPbHy/v2r8b1vGfznKkaEvldNbgDHApsbs/iDgyH0/Kcb4Pxq/vAqYA7we2BVj/MKA14+OMW4DHm/8y2Qa8GPgpcB5wKos/0KUL0NfKqcA3Btj7Gn8L8QYDx/ha0Ya06wD3tn4vL8DDgNmA1d2ulgVh6EvldPngUNCCGcChBBODCG8bN9PCiF8uPHL1wBrgC8CvSGE1w54/bbGr38IzAfujzH+GugDRgEfz+yvQrkz9KUSijF+mv6QXtwY7ywBFu37acA7Gh8fA5wTY3wQ+CzwxcbrETi78fn/u/HHHzf+uBnYHn0Ub6UE/35KUn3Y9CWpRgx9SaoRQ1+SasTQl6Qa6Uu9AEnZCiH0ACcDG4GDYozXJV6SEjL0peo7EfgX+t98dQ79xzdVU453pOpbCKygv+T1hRBGJ16PEjL0pepbACylP/S3ApPSLkcpGfpS9S2kP/RH0f/ETEO/xgx9qfoWAst4sulPTrscpWToSxUWQpgB9AL34XhHGPpS1S0EljUemjYK2IJNv9YMfana9mziQn/TN/RrztCXqm3PJi482fQd79SYoS9V255NXOhv+o9g0681Q1+qqBBCHzCX/jdmQX/T34xNv9YMfam6jgbuizFuafx5H/2hb9OvMUNfqq6Bm7jQH/qbsOnXmqEvVdfAeT70j3c2YdOvNUNfqq7Bmv7D2PRrzdCXqmvgcU3ob/oPY9OvNUNfqqAQwmRgOrBmwMs2fRn6UkUdD6yIMe4a8Noo+m/PsunXmKEvVdNem7iNKxN7sOnXnqEvVdO+m7i9wE48p197hr5UTYNt4u4EtgM9IQTvya0pQ1+qmBBCoL/pDzyj3wc83njEso9iqDFDX6qeWcC2GONDA17b0/TBh67VmqEvVc++78SFRtNv/NqmX2OGvlQ9+27igk1fDYa+VD37buKCTV8Nhr5UPYONdwY2fY9t1pihL1VI4yjmkcCqfT7Ux97jHZt+TRn6UrUcB6yJMW7f5/V9xzs2/Zoy9KVqGWwTF/bfyLXp15ShL1XLYPN8sOmrwdCXqsWmr2EZ+lK1DHZcE2z6ajD0pYoIIUwFxgPrBvmwTV+AoS9VyQJgWeOhavsaeGTTpl9jhr5UHUNt4sLe4x2bfo0Z+lJ1DLWJC74jVw2GvlQdQ23iwv5N39CvKUNfqoAQQi8wH1g+xKfs2/QnNS5bUc0Y+lI1HAk8GGPcPMTHn2j6jUc0RMArE2vI0JeqYbhNXNi76YObubVl6EvVMNwmLux9ZBPczK0tQ1+qhuE2cWHvjVyw6deWoS9VQ6vjHZt+TRn6UsmFECYCM4Hbh/k0m74AQ1+qgvnArTHGncN8jk1fgKEvVcFIm7hg01eDoS+V30jzfLDpq8HQl8pvpJM7sP+RTZt+TRn6Uok1HqXQznjHpl9Thr5UbjOBXTHG9SN8nu/IFWDoS2XXTMsHm74aDH2p3JrZxIXBm76hX0OGvlRunTR9xzs1ZOhL5dbMyR3wyKYaDH2ppEIIo4BjgJVNfLpHNgUY+lKZHQusjTE+2sTnupErwNCXyqzZTVwY4simVybWj6EvlVezm7iwT9OPMe4AdgFjM1iXCszQl8qr2U1c2L/pg3P9WjL0pfJqZbyz70wfnOvXkqEvlVAIYQpwIHBXk19i0xdg6EtltQBYHmPc3eTn73tkE2z6tWToS+XUyiYuDD7esenXkKEvlVMr83wYfLxj068hQ18qp1ZO7oBNXw2GvlQyIYQe4Hhs+mqDoS+Vz+HAwzHGjS18jUc2BRj6Uhm1uokLHtlUg6EvlU+rm7hg01eDoS+VTztNf7Bz+jb9GjL0pfJp9eQOuJGrBkNfKpEQwjjgMOC2Fr/UI5sCDH2pbOYBq2OM+wb4SGz6Agx9qWza2cQFm74aDH2pXNrZxAWbvhoMfalcWt7EbbyDlxjjrn0+5JWJNWToS+XS7hn9fVs+jX2Bx4FxXViXSsLQl0oihDAD6AXua/FLBxvt7OFcv2YMfak8FgLLYoyxxa8bbBN3D+f6NWPoS+XRzU3cPWz6NWPoS+XRzeOae9j0a8bQl8qjnccvwPBN39CvGUNfKoEQQh8wF1jRxpcP1/Qd79SMoS+Vw9HAfTHGLW187aBHNhts+jVj6Evl0O4mLriRqwEMfakc2t3EBTdyNYChL5WDTV9dYehL5dDuyR2w6WsAQ18quBDCZGA6sKbNb2HT1xMMfan4jgdWDPKUzGbZ9PUEQ18qvk42cWH4I5s2/Zox9KXi62QTF3xHrgYw9KXi62QTF3xHrgYw9KUCa9xqtYDOxjs2fT3B0JeKbRawLcb4UAffY6SmP9ErE+vD0JeKrdNNXBim6ccYdwI7gPEd/gyVhKEvFVunm7gwfNMHRzy1YuhLxdbpJi4MP9MHN3NrxdCXiq0b453hzumDTb9WDH2poEIIY4AjgVUdfquRxjs2/Rox9KXiOg5YE2Pc3uH3GWm8Y9OvEUNfKq5ubOKCTV8DGPpScXVjng82fQ1g6EvFZdNX1xn6UnF147gm2PQ1gKEvFVAIYSr975Jd14VvN9KRTZt+jRj6UjEtAJbFGGMXvpfvyNUTDH2pmLq1iQu+I1cDGPpSMXVrExds+hrA0JeKqVubuNDcRq5NvyYMfalgQgi9wHxgeZe+ZTNHNm36NWHoS8VzJPBgjHFzl76fRzb1BENfKp5ubuKCRzY1gKEvFU83N3GhufGOVybWhKEvFU83N3FhhPFOjHEX8BgwoYs/UwVl6EvFk8V4Z7imD871a8PQlwokhDARmAnc3sVvO9JGLjjXrw1DXyqW+cCtMcaRQroVNn09wdCXiqXbm7hg09cAhr5ULN2e58PIRzbBpl8bhr5ULFk0/WbGOzb9mjD0pYJonJPv9nFNaG68Y9OvCUNfKo6ZwK4Y4/ouf99mN3Jt+jVg6EvFkcVoB5rfyLXp14ChLxVHFpu4YNPXAIa+VBw2fWXO0JeKI4tNXPDIpgYw9KUCCCGMAo4BVmbw7T2yqScY+lIxHAusjTE+msH39simnmDoS8WQ1SYu2PQ1gKEvFUNWm7hg09cAhr5UDFlt4oJNXwMY+lIxZDLeaTzaoZmmvwWYEEIwEyrOv8FSYiGEKcCBwF0ZfPseIMYYdw/3SY0rEx/FKxMrz9CX0lsALB8pmNvUzGhnD+f6NWDoS+ml3sTdw7l+DRj6Unqpj2vuYdOvAUNfSq8oTd+HrtWAoS8l1Dgts4BiNH0fulYDhr6U1uHAwzHGjRl9/1abvqFfcYa+lFaWox1ovek73qk4Q19KK8tNXGjuscp72PRrwNCX0sq66XtkU3sx9KW0snzmDnhkU/sw9KVEQgjjgMOA2zL8MTZ97cXQl9KZB6yOMTbbxNth09deDH0pnaw3ccGmr30Y+lI6WW/igk1f+zD0pXSy3sSF1o5s2vRrwNCX0inaeMemXwOGvpRACGEG0Avcl/GPanW8Y9OvOENfSmMhsCzGGDP+Oa00/a3AeK9MrDb/5kpp5LGJCy00/cbNXVuBiZmuSEkZ+lIaeczzobWmDz5eufIMfSmNwjX9BjdzK87Ql3IWQugDjgNW5PDjWjmyCR7brDxDX8rf0cB9McYtOfysVsc7Nv2KM/Sl/OU12oHWxzs2/Yoz9KX85bWJCzZ97cPQl/Jn01cyhr6UvzyeubOHTV97MfSlHIUQJgPTgTU5/UibvvZi6Ev5Oh5YEWPcldPPs+lrL4a+lK88N3Gh9XP6PnSt4gx9KV95buJCe+Mdm36FGfpSvvLcxIX2xjs2/Qoz9KWchBAC/U0/7/GOTV9PMPSl/MwCtsUYH8rxZ9r0tRdDX8pP3pu4YNPXPgx9KT95b+KCRza1D0Nfyk+qpt9K6G8FxoYQejNajxIz9KX8pGj6LY13Gnf2bsG5fmUZ+lIOQghjgDnAqpx/dKvjHfBRDJVm6Ev5OA5YE2PcnvPPbXUjF5zrV5qhL+UjxWgHbPrah6Ev5SPFJi7Y9LUPQ1/Kh01fhWDoS/nI+5k7e7R6ZBNs+pVm6EsZCyFMBcYD6xL8+HbHOzb9ijL0pewtAJY1zsDnrd3xjk2/ogx9KXupNnHBpq99GPpS9lJt4oJNX/sw9KXspdrEBZu+9mHoSxlqPLhsPrA80RJs+tqLoS9l60jgwRjj5kQ/3yOb2ouhL2Ur5SYutDfe8c1ZFWboS9lKuYkL7Y13bPoVZuhL2bLpq1AMfSlbNn0VSkjzJkGp+kIIE4EHgckxxlaDt1treBwYH2Nsuu2HEAL9/6IYk2rdyo5NX8rOfODWhIEf6B/v7Grl6xqPi3DEU1GGvpSd1KOdXmB3jHF3G1/rG7QqytCXslPGTdw9fINWRRn6UnZSN/12NnH3sOlXlKEvZaAxT0/5zB2w6WsQhr6UjZnArhjj+oRrsOlrP4a+lI3Uox2w6WsQhr6UjdSbuGDT1yAMfSkbRWn67Ya+Tb+iDH0pG6k3caGz8Y6PYqgoQ1/qshDCKOAYYGXipXQy3vEduRVl6EvddyywNsb4aOJ12PS1H0Nf6r4ibOKCTV+DMPSl7ivCJi7Y9DUIQ1/qPpu+CsvQl7rPpq/CMvSlLgohTAGmAHclXgp0dk7fN2dVlKEvddcCYHmbz7Dvtk7HOzb9CjL0pe4qymgHOhvvPAqMarznQBVi6EvdVZRNXOig6XtlYnUZ+lJ3VaXpg3P9SjL0pS4JIfTQH/qlb/oNzvUryNCXuudw4OEY48bUC2mw6Ws/hr7UPUUa7UBnRzbBpl9Jhr7UPUXaxIXOxzu+QauCDH2pe4rY9DsZ73h6p4IMfal7inBxykA2fe3H0Je6IIQwDjgMuC31Wgaw6Ws/hr7UHfOA1THGTkK222z62o+hL3VH0TZxwSObGoShL3VH0TZxwSObGoShL3VHEZt+N8Y7Nv2KMfSl7ihq0+90I9emXzGGvtShEMIM+gP2vtRr2YdNX/sx9KXOLQSWNR5HXCQ2fe3H0Jc6V8TRDtj0NQhDX+pcETdxwaavQRj6UueK2vQ7PbL5GNAbQhjdpfWoAAx9qQMhhD7gOGBF6rUMoqPxjlcmVpOhL3XmaOC+GOOW1AsZRKfjHfBRDJVj6EudKepoBzrfyAWbfuUY+lJnirqJCzZ9DcLQlzpj01epGPpSZ4p2ccpANn3tx9CX2hRCmAxMB9akXssQutH0fYNWxRj6UvuOB1bEGHelXsgQOj2nD75Bq3IMfal9Rd7Ehe6Nd2z6FWLoS+0r8iYudG8j16ZfIYa+1D6bvkrH0JfaEEII9Df9Ioe+TV/7MfSl9swCtsUYN6ReyDBs+tqPoS+1p+ijHbDpaxCGvtSeom/iQneObNr0K8bQl9pThqbfjfGOTb9iDH2pPWVo+t16R66hXyGGvtSiEMIYYA6wKvVaRtCtpu94p0IMfal1xwFrYozbUy9kBN1o+tvpP6E6pgvrUQEY+lLryjDagS40/caViW7mVoihL7Wu8Ju4jTeP9QLdeBicm7kVYuhLrStD0+8DdjWaeqds+hVi6EutK/LFKXt0YxN3D5t+hRj6UgtCCFOB8cC61GsZQTc2cfew6VeIoS+1ZgGwrEtjkyzZ9DUoQ19qTeE3cRts+hqUoS+1pgybuGDT1xAMfak1Nn2VmqEvNSmE0AvMA5anXksTuvGEzT1s+hVi6EvNOxLYEGPclHohTejmeMemXyGGvtS8sox2oLvjHZt+hRj6UvPKsokL3W/6hn5FGPpS8+rc9B3vVIShLzXPpq/SM/SlJoQQJgKHALenXkuTPLKpQRn6UnPmA7fGGLsVpFnzyKYGZehLzSnTaAe6/47cSY1n9KvkDH2pOWXaxIUujnca10JGwCsTK8DQl5pT56YPzvUrw9CXRtAYa5Th4pSBurmRC871K8PQl0Y2k/6rB9enXkgLbPoalKEvjaxsox2w6WsIhr40srJt4kJ3j2yCTb8yDH1pZGVs+t0e79j0K8LQl0ZWxqbf7fGOTb8iDH1pGCGEUcAxwMrUa2mRTV+DMvSl4R0LrI0xbku9kBZl0fQN/Qow9KXhlXG0Ax7Z1BAMfWl4ZdzEBY9sagiGvjQ8m34/m35FGPrS8Mra9Lt9Tt+mXxGGvjSEEMIUYApwV+KltMMjmxqUoS8NbQGwPMa4O/VC2uCRTQ3K0JeGVtbRDtj0NQRDXxpaWTdxwaavIRj60tBs+k/yysSKMPSlQYQQeugPfZs+EGPcAewCxnbreyoNQ18a3OHAwzHGjakX0qZuH9kE5/qVYOhLgyvzaAe6P94B5/qVYOhLgyvzJi50fyMXbPqVYOhLg7Pp78+mXwGGvjQ4m/7+fLxyBRj60j5CCOOAw4DbUq+lA1k0fcc7FWDoS/ubB6xuHFMsqyyavuOdCjD0pf2VfbQDHtnUEAx9aX9l38QFN3I1BENf2l9Vmr5HNrUfQ1/an01/cDb9CjD0pQFCCDPob8n3pV5Lh2z6GpShL+1tIbAsxhhTL6RDNn0NytCX9laF0Q7Y9DUEQ1/aWxU2ccGmryEY+tLeqtT0Paev/Rj6UkMIoQ84DliRei1d4DtyNShDX3rS0cB9McYtqRfSBVmNd7wyseQMfelJVRntQAZNP8b4OLADGNfN76t8GfrSk6qyiQvZNH1wxFN6hr70JJv+yNzMLTlDX3pSJZp+CKGH/n+2d2fw7W36JWfoS0AIYTIwHbgz9Vq6oA/YmdG7im36JWfoS/2OB1bEGHelXkgXZDXaAZt+6Rn6Ur9KjHYastrEBZt+6Rn6Uj83cZtj0y85Q1/qZ9Nvjk2/5Ax91V7jHaYLqE7o2/Q1JENfglnAthjjhtQL6RKbvoZk6EvVGu1ANk/Y3MOmX3KGvlStTVzIdrxj0y85Q1+qXtPPerxj0y8xQ1+y6bfiEWz6pWboq9ZCCGOAOcCq1GvpIpu+hmToq+6OA9bEGLenXkgXeWRTQzL0VXdVG+2ARzY1DENfdVe1TVzI9sjmFrwysdQMfdVdFZt+ZuOdGONO4DFgfBbfX9kz9FV3C6le6Gc53gHn+qVm6Ku2QghT6W+s61Kvpcuy3MgF5/qlZuirzhYAyzK6YSolm76GZOirzqq4iQs2fQ3D0FedVXETF2z6GoahrzqrctPPMvRt+iVm6KuWQgi9wDxgeeq1ZCDr8Y5Nv8QMfdXVkcCGGOOm1AvJQNbjHZt+iRn6qquqjnYgn41cm35JGfqqq6pu4kI+G7k2/ZIy9FVXNv322fRLzNBXXdn02+dGbokZ+qqdEMJE4BDg9tRryYhHNjUkQ191NB+4tfHEyCryyKaGZOirjqo82gGPbGoYhr7qqMqbuGDT1zAMfdWRTb8zNv0SM/RVK41r/qp4ccpAWTf9LcBEr0wsJ0NfdTMT2BVjXJ96IRnKtOnHGHcBjwITsvoZyo6hr7qp+mgHsm/64Fy/tAx91U3VN3Eh+3P64Fy/tAx91U0dmn7WG7ngoxhKy9BX3dSl6ecx3rHpl5Chr9oIIYwCjgFWpl5Lxmz6GpKhrzo5FlgbY9yWeiEZs+lrSIa+6qQOox2w6WsYhr7qpA6buOCRTQ3D0Fed1KXpe2RTQzL0VSd1afp5jHds+iVl6KsWQghTgCnAXYmXkoc8xjs2/ZIy9FUXC4DlMcbdqReSA5u+hmToqy7qMtoBm76GYeirLuqyiQs2fQ3D0Fdd2PS7y6ZfUoa+Ki+E0EN/6Nel6edxZNOmX1KGvurgcODhGOPG1AvJSV7vyLXpl5Chrzqo02gH8hnvbAEmNP4rSiXi3zDVQZ02cSGHpt84+roNr0wsHUNfdWDTz4YPXSshQ191YNPPho9XLiFDX5UWQhgHHAbclnotObLpa0iGvqpuHrA6xrgj9ULysGdjNafHTXhss4QMfVWdo53seGyzhAx9VZ2buNmx6ZeQoa+qs+lnx6ZfQoa+qs6mnx2bfgkZ+qqsEMIM+kPwvtRryZFNX8My9FVlC4FlMcaYeiE5sulrWIa+qqxuox2w6WsEhr6qrG6buJDPY5X38M1ZJWToq8rq2PTzHu/Y9EvG0FclhRD6gOOAFanXkrO8xzs2/ZIx9FVVRwP3xRi3pF5Izmz6Gpahr6qq0/WIA9n0NSxDX1W1kPrN88GmrxEY+qqqOm7iQr5NfyswPoTQm9PPUxcY+qqqOh7XhByPbDYe37wVmJjHz1N3GPqqnBDCZGA6cGfqtSSQ53gHfINW6Rj6qqLjgRUxxl2pF5JAnuMd8FEMpWPoq4rqOtoBm75GYOiriuq6iQs2fY3A0FcV2fTzY9MvGUNflRJCCNT3jVlg09cIDH1VzSxgW4xxQ+qFJJLnUzbBpl86hr6qps6jHUgz3rHpl4ihr6qp8yYupBnv2PRLxNBX1dj0bfoahqGvqrHp2/Q1DENflRFCGAPMAValXktCNn0Ny9BXlRwHrIkxbk+9kIRs+hqWoa8qqftoB9Ic2bTpl4ihryqp+yYu5D/e8c1ZJWPoq0ps+vmPd3xzVskY+qoSm75NXyMw9FUJIYSpwATg7tRrSSzvpr8VGOuVieVh6KsqFgBLY4wx9UISy7XpN/7/3oIjntIw9FUVjnb65d30wbl+qRj6qgo3cfvlfWQTPLZZKoa+qsKm3y/vjVzwDVqlYuir9BqbiPOA5anXUgCpxjs2/ZIw9FUFRwIbYoybUi+kAGz6GpahrypwtPMkm76GZeirCtzEfZJNX8My9FUFNv0n2fQ1LENfVWDTf1KKI5s2/RIx9FVqIYSJwCHA7anXUhApxjs2/RIx9FV284FbY4x5t9uiSjHe8aFrJWLoq+wc7ewtVdN3vFMShr7Kzk3cvdn0NSxDX2Vn09+bTV/DMvRVWiGEgE1/XzZ9DcvQV5kdDOwC1qdeSIHY9DUsQ19lthAvTtmXj1bWsAx9lZmjnf2lGO88CowOIfTl/HPVBkNfZeYm7v5yb/qN/9LyXbklYeirzGz6+xtF/jN9MPRLw9BXKYUQRgHHACtTr6VgUmzkgnP90jD0VVbHAmtjjNtSL6RgUsz0waZfGoa+ysrRzj4a71tIcXoHbPqlYeirrNzE3V8PsDvGuDvBz7bpl4Shr7Ky6e8v1WgHbPqlYeirrGz6+0u1iQs+iqE0DH2VTghhCjAFuCvxUoomddN3vFMChr7KaAGwPNHsushs+hqRoa8ycrQzOJu+RmToq4zcxB1cyqbvRm5JGPoqI5v+4FKd0QePbJaGoa9SCSH0AMdj0x9M6vGOTb8EDH2VzWHAphjjxtQLKaDUG7k2/RIw9FU2C3G0MxSbvkZk6Kts3MQdmk1fIzL0VTZu4g7Npq8RGfoqG5v+0FI2/ceAUY17DlRghr5KI4Qwjv6N3NtSr6WgkjX9xpWJvkGrBAx9lck8YHWMcUfqhRRUynP64Fy/FAx9lYmjneGlHO+Ac/1SMPRVJm7iDi/lRi740LVSMPRVJjb94RWh6TveKThDX2Vi0x+eTV8jMvRVCiGEGfQ32ftSr6XAbPoakaGvslgILGscDdTgUjd9N3JLwNBXWTjaGZlHNjUiQ19l4SbuyIow3rHpF5yhr7Kw6Y8s9XjHpl8Chr4KL4TQBxwHrEi9loKz6WtEhr7K4GjgvhjjltQLKTibvkZk6KsMHO00x6avERn6KgM3cZtj09eIDH2VgU2/OamPbNr0S8DQVxnY9JuTerzjYxhKwNBXoYUQJgPTgTtTr6UEUo93fAxDCRj6KrrjgRUxxl2pF1ICqZv+dqA3hDA64Ro0AkNfRedop3lJm75XJpaDoa+icxO3eambPriZW3iGvorOpt+81DN98Nhm4Rn6KqwQQqC/6Rv6zbHpa0SGvopsFrAtxrgh9UJKIvU5fbDpF56hryJztNOaIox3bPoFZ+iryNzEbU0Rxjs2/YIz9FVkNv3W2PQ1IkNfRWbTb41NXyMy9FVIIYQxwBxgVeq1lIhNXyMy9FVUxwFrYozbUy+kRGz6GpGhr6JytNO6IhzZtOkXnKGvonITt3VFGO/4eOWCM/RVVDb91hVhvOMD1wrO0FdR2fRbZ9PXiAx9FU4IYSowAbg79VpKxqavERn6KqIFwNLG89nVvCI0fTdyC87QVxE52mlPEZq+RzYLztBXEbmJ257kRzb3vK+i8eY6FZChryKy6benCOMdsO0XmqGvQgkh9ALzgOWp11JCRRjvgHP9QjP0VTRHAhtijJtSL6SEbPoakaGvonG00z6bvkZk6Kto3MRtn01fIzL0VTQ2/TY0LpHvpRihb9MvMENfRWPTb08fsKsgb2iz6ReYoa/CCCFMBA4Bbk+9lhJKfkZ/AJt+gRn6KpL5wK0xxqKEV5kUZRMXfOhaoRn6KhJHO+0ryiYu+NC1QjP0VSRu4rbPpq+mGPoqEpt++2z6aoqhr0JoHDm06bevSE3fjdwCM/RVFAcDu4D1qRdSUkVq+h7ZLDBDX0WxEC9O6YRHNtUUQ19F4WinM0Ua79j0C8zQV1G4iduZIo13bPoFZuirKGz6nSlc029szqtgDH0lF0IYBRwDrEy9lhIrTNOPMe4AdgNemVhAhr6K4FhgbYxxW+qFlFiRmj441y8sQ19F4Ginc4Vp+g3O9QvK0FcRuInbuSId2QQfxVBYhr6KwFApQu4AACAASURBVKbfuaKNd3wUQ0EZ+ioCm37nijbesekXlKGvpEIIU4ApwF2Jl1J2Nn01xdBXaguA5THG3akXUnJFa/pu5BaUoa/UHO10R9Gavkc2C8rQV2pu4naHTV9NMfSVmk2/O2z6aoqhr2RCCD3A8dj0u6Fo5/Rt+gVl6Culw4BNMcaNqRdSAUUb79j0C8rQV0oLcbTTLUUb79j0C8rQV0pu4naPTV9NMfSVkpu43WPTV1MMfaVk0+8em76aYugriRDCOPo3cm9LvZaKsOmrKYa+UpkHrG7csqTOFe3I5iPAZK9MLB5DX6k42umuQo13YoyP0/9fHmNTr0V7M/SVipu43VW08Q74eOVCMvSVik2/uwrV9Bt8vHIBGfpKxabfXUVs+m7mFpChr9yFEGbQH1L3pV5LhRSx6Xtss4AMfaWwEFgWY4ypF1IhNn01xdBXCo52uq9oRzbBpl9Ihr5ScBO3+4o43rHpF5ChrxRs+t1XxPGOTb+ADH3lKoTQBxwHrEi9loqx6asphr7ydhRwX4xxS+qFVIxNX00x9JU3L07Jhk1fTTH0lTc3cbNh01dTDH3lzU3cbNj01RRDX3mz6WejqOf0Df2CMfSVmxDCZGA6cGfqtVRQEcc7PnCtgAx95el4YEWMcVfqhVRQEcc7Nv0CMvSVJ0c72bHpqymGvvLkJm52itr0J3llYrEY+sqTTT87hWv6McadwA5gXOq16EmGvnLRaHsLMPSzUsSmDx7bLBxDX3mZBWyLMW5IvZCKKuKRTfANWoVj6CsvjnayVbjxToNNv2AMfeXFTdxsFXW8Y9MvGENfebHpZ8umr6YY+sqLTT9bNn01xdBX5kIIY4A5wKrUa6miEEIP/f8sF/Gdzjb9gjH0lYe5wJoY4/bUC6moPmBnjDGmXsggfBRDwRj6yoMXp2SrqMc1wUcxFI6hrzy4iZutom7igk2/cAx95cFN3GwVdRMXbPqFY+grDzb9bBW56buRWzCGvjIVQpgKTADuTr2WCity0/fIZsEY+sraAmBpQU+WVIVNX00z9JU1RzvZs+mraYa+suYmbvZs+mqaoa+s2fSzV+Rz+jb9gjH0lZkQQi8wD1ieei0VV/TxzkSvTCwOQ19ZOhLYEGPclHohFVfY8U6McRewHRifei3qZ+grS4528lHkpg/O9QvF0FeW3MTNR2GbfoNz/QIx9JUlm34+bPpqmqGvLNn081GGpm/oF4Shr0yEECYChwC3p15LDRT5yCb40LVCMfSVlfnArTHGIodRVRR9vGPTLxBDX1lxtJOfoo93bPoFYugrK27i5qfoTd+N3AIx9JUVm35+it70PbJZIIa+uq7xlnubfn5s+mqaoa8sHAzsAtanXkhN2PTVNENfWViIF6fkqQxHNm36BWHoKwuOdvJV9PGOTb9ADH1lwU3cfBV9vGPTLxBDX1mw6efLpq+mGfrqqhDCKOAYYGXqtdSITV9NM/TVbccCa2OM21IvpEZs+mqaoa9uc7STv6I3/S30X5lo3hSAfxPUbW7i5q/QTb9xZeKjwITUa5Ghr+6z6eev6Of0wYeuFYahr26z6eev6OMd8PHKhWHoq2tCCFOAKcBdiZdSN4Ue7zTY9AvC0Fc3LQCWxxh3p15IzZSh6XtssyAMfXWTo500ytD0PbZZEIa+uslN3DRs+mqaoa9usumnYdNX0wx9dUXjjTfHY9NPoSxHNm36BWDoq1sOAzbFGDemXkgNlWG8Y9MvCENf3bIQRzuplGG8Y9MvCENf3eImbjo2fTXN0Fe3uImbjk1fTTP01S02/XTK0vQN/QIw9NWxEMI4+jdyb0u9lpoqS9N3vFMAhr66YR6wOsa4I/VCaqoMRzZt+gVh6KsbHO2kVYbxjk2/IAx9dYObuGmVYbxj0y8IQ1/dYNNPqwxNfwsw3isT0/NvgLrBpp9W4Zt+43HbW4GJqddSd4a+OhJCmEF/07wv9VpqrAxNH3yDViEY+urUQmBZjDGmXkiNFb7pN/gGrQIw9NUpRzvp2fTVNENfnXITN70ynNMHm34hGPrqlE0/vbKMd2z6BWDoq20hhD7gOGBF6rXUXFnGOzb9AjD01YmjgPtijFtSL6TmbPpqmqGvTnhxSmJ73uwUY9yVei1NsOkXgKGvTriJm15ZWj74KIZCMPTVCTdx0yvLPB986FohGPrqhE0/vbIc1wSbfiEY+mpLCGEyMB24M/Vaaq5M4x2bfgEY+mrX8cCKkmwgVlnZxjs2/cQMfbXL0U4xlKnpe2SzAAx9tctN3GKw6aslhr7aZdMvBpu+WmLoq2UhhEB/0zf007PpqyWGvtoxC9gWY9yQeiEq1ZHNrcC4EEJv6oXUmaGvdjjaKY7SjHcaF+1swSsTkzL01Q43cYujTOMdcK6fnKGvdtj0i6M0Tb/BuX5ihr7aYdMvDpu+WmLoqyUhhDHAHGBV6rUIsOmrRYa+WjUXWBNj3J56IQLK2fQN/YQMfbXKi1OKpYxN3/FOQoa+WuUmbrGU6Zw+2PSTM/TVKjdxi6Vs4x2bfmKGvlpl0y+WMo53bPoJGfpqWghhKjABuDv1WvSEsjV9j2wmZuirFQuApY2306sYbPpqiaGvVjjaKR6bvlpi6KsVbuIWj01fLTH01QqbfvGU8cimTT8hQ19NaTwDfR6wPPVatJeyjXds+okZ+mrWkcCGGOOm1AvRXso23rHpJ2boq1mOdorJpq+WGPpqlpu4xVS2pr8NGBtC6Eu9kLoy9NUsm34xlarpN97j8QhemZiMoa9m2fSLqWxNH3zoWlKGvkYUQpgAHALcnnot2k/ZjmyCD11LytBXM+YDt8YYyxYudVCq8U6DTT8hQ1/N8OKU4irjeMemn5Chr2a4iVtcZWz6HttMyNBXM9zELa4yNn3foJWQoa9hhRACNv0is+mrJYa+RnIwsAtYn3ohGpRNXy0x9DWShXhxSpHZ9NUSQ18jcbRTbGU8p2/TT8jQ10jcxC22Mo53bPoJGfoaiU2/2Mo43rHpJ2Toa0ghhFHAMcDK1GvRkGz6aomhr+EcC6yNMW5LvRANqaxN39BPxNDXcBztFF9Zm77jnUQMfQ3HTdzis+mrJYa+hmPTL74yHtm06Sdk6Gs4Nv3iK+N451FgtFcmpmHoa1AhhCnAFOCuxEvR8Eo33hlwZaJtPwFDX0NZACyPMe5OvRANq4xNHzy2mYyhr6E42imH0jX9Bpt+Ioa+huImbjnY9NUSQ19DsemXg01fLTH0tZ8QQg9wPDb9MijjkU2w6Sdj6GswhwGbYowbUy9EIyrreMemn4ihr8EsxNFOWZR1vGPTT8TQ12DcxC2Bxv3FNn21xNDXYNzELYceYHdJ30th00/E0NdgbPrlUNaWDz50LRlDX3sJIYyjfyP3ttRr0YjKOs8HH7qWjKGvfc0DVscYd6ReiEZk01fLDH3ty9FOeZT1jD7Y9JMx9LUvN3HLo+zjHZt+Aoa+9mXTL4+yj3ds+gkY+tqXTb88bPpqmaGvJ4QQZtDfHu9LvRY1xaavlhn6GmghsLRxs5GKr8xN/zGgL4QwKvVC6sbQ10COdsqltE3fKxPTMfQ1kJu45VLmI5vgXD8JQ18D2fTLpczjHbDpJ2HoC4AQQh9wHLAi9VrUtNKOdxps+gkY+trjKOC+GOOW1AtR06rQ9A39nBn62sOLU8qnCk3f8U7ODH3t4SZu+dj01TJDX3u4iVs+Nn21zNDXHjb98in7kU2bfgKGvgghTAamA3emXotaUvbxjk0/AUNfAMcDK2KMu1IvRC2pwnjHpp8zQ1/gaKesyt70fXNWAoa+wE3csrLpq2WGvsCmX1Y2fbXM0K+5EEKgv+kb+uVj01fLQpEfnT516tR4+OGHp15Gpe3YsYNbb72VhQsXpl6KWrR+/Xp27NjBrFmzUi+lLdu3b2f16tUsWLAg9VIq56abbnooxjhtsI/15b2YVhx++OEsWbIk9TIq7Xvf+x6f/OQnufbaa1MvRS36yEc+wkMPPcRHPvKR1Etpy4YNG5g3b57/jGcghLB2qI853qm5ZcuW2fJL6vHHH6evr9C9bViTJk3ikUceSb2M2jH0a27p0qX+53VJ7dy5k1Gjynvb4JgxY9i9ezfbt29PvZRaMfRrzqZfXmVv+iEE234Chn6Nbd++nTvvvJPjjjsu9VLUhrI3fYDJkycb+jkz9Gvs1ltv5cgjj2TMmDGpl6I2lL3pQ/9cf/PmzamXUSuGfo0tXbrU0U6J2fTVDkO/xtzELbedO3eWvulPnjzZpp+zSob+47t28w8/WMW9Dz+aeimF5iZuuVVlvGPTz1clQ//ejY9y9Q13c+FlN/Dwth2pl1NYNv1yq8p4x6afr0qG/uFTJ/C51y3i7t9v4+IrlvDY4z4mfl8PPfQQW7duZfbs2amXojbZ9NWOSoY+wDPmPIVLXvU0brp7I++6+jfs2l3cZwylsGe00/+8NZWRTV/tqGzoA5y38GD+9sXz+NHK9XzwO8sp8sPl8uZop/xs+mpHpUMf4KIzjuAtzzqSK6+7m0/95x2pl1MYbuKWn01f7ah86AO8/5y5vOzEQ/i/P1rNV5esS72cQrDpl18Vjmza9PNX7t8xTerpCfzjnyzkoS3b+YtvLGPaxDE8Z+701MtKZteuXaxcuZLjjz8+9VLUgSqMd2z6+atF0wcY3dfDZ177dI47eBJvu+pmbln3cOolJbNmzRqmTZvGAQcckHop6kAVxjs2/fzVJvQBJo7p47I3nMzUSaN54+U38ruHtqZeUhKOdqrBpq921Cr0AaZPGssX33gqAK+/7Ho2PFK/Z3m7iVsNVWn6hn6+ahf6AEdMncBlbziZhx7ZwUWX38CW7WW+W7p1Nv1qqErTd7yTr1qGPsDTZh3Ipy84iVX3P8Jbr7yJHTt3p15Sbmz61WDTVztqG/oAz5k7nQ+/fAG/uP0hPvD1pbV489bWrVu59957Ofroo1MvRR2qQtMfM2YMIQSvTMzRiKEfQrgshPBgCGH5gNf+KYRwawhhaQjhmyGEAwd87C9CCHeEEG4LIZwz4PVzG6/dEUL4QPf/UtrzykWz+PPnH8M3fnMv/3jNbamXk7kVK1Ywd+7c0oeFqnFOH9zMzVszTf9y4Nx9XvsxcHyMcSGwGvgLgBDCPODVwPzG13w6hNAbQugFPgW8EJgHnN/43EJ4x3OP4oJTZ/MvP7+Ty//rd6mXkykvTqmOKox3wGObeRuxJsQYF4cQDt/ntR8N+NPrgFc0fv1S4Msxxu3A70IIdwCnND52R4xxDUAI4cuNz13Z0eq7JITA/3rp8Wx4ZDt/972VTJs0lvMWHpx6WZlwE7c6qjDeAZt+3rox038j8MPGrw8BBj7n4J7Ga0O9Xhi9PYFPnH8iT589hfd+5RauW/P71EvKhJu41WHTVzs6Cv0Qwl8BO4GrurMcCCG8OYSwJISwZMOGDd36tk0ZO6qXf71wEbOfMp4/++ISbn2gWu0jxmjTrxCbvtrRduiHEN4AvBi4ID557OVeYNaATzu08dpQr+8nxvi5GOOiGOOiadOmtbu8th04fjRXvPEUxo/u5Q2X3ch9Fbpy8f7776e3t5cZM2akXoq6wKavdrQV+iGEc4H/CbwkxrhtwIe+A7w6hDAmhHAEcDRwA3AjcHQI4YgQwmj6N3u/09nSs3PIgeO44o2nsHX7zkpdubhnE9eLU6rBpq92NHNk82rg18CxIYR7QghvAv4ZmAT8OIRwSwjhXwBijCuAr9K/QXsN8PYY464Y407gHcC1wCrgq43PLay5T53M516/iLW/38affbEaVy462qmWqhzZtOnnq5nTO+cP8vKlw3z+/wb+9yCv/wD4QUurS+wZc57CR191Au+8+je8+8u/4dMXPJ3envK25GXLlvHc5z439TLUJVUZ79j081Xrd+Q248ULZ/I3583j2hXr+dB3VpT6Xbs2/eqIMVaq6Rv6+Sn/75gcvPHMI1i/+TE+u3gNTz1gLG9/zlGpl9Syxx9/nNWrVzNvXmHeE6cO7Nq1i97e3krsz/jQtXwZ+k16/7lzWb/5Mf7p2tuYPmkMf7po1shfVCC33XYbhx12GOPHj0+9FHVBVTZxwaaft2r8rslBT0/gI684gd9v3cEHvrGMqZPG8Jxjy3PloqOdaqnKPB9s+nlzpt+CPVcuzn3qJN525c38tkRXLvpO3Gqx6atdhn6LJo7p4wsXPXnl4l0luXLRpl8tVdnEBZt+3gz9NkyfNJYrLjqFCLz+shtKceWiTb9aqjbesennx9Bv05HTJnLphYvY8Mh23nj5jWwt8JWLGzduZOPGjRx++OGpl6Iuqdp4x6afH0O/AyfOnsKnLjiRlfdv5q1X3czju4p55eLy5cs5/vjj6enxb3dVVKnp75npl/k9MGViCnTouXNn8OGXLWDx6g28v6BXLnpxSvVUqemPHj2a3t5er0zMSTV+1yT2ypNn8cDmx/joj1czY/JY3n/u3NRL2oubuNVTpaYPT871x44dm3oplWfT75J3PvcoXnPqbD7zszu54ld3pV7OXtzErZ4qNX1wrp+n6vyuSSyEwN83rlz80HdXMG3SGF60IP2Vi7t372b58uU2/YqpatNX9mz6XdTbE/jk+Sdy0uwpvOcrt3B9Aa5cXLt2LQcccABTpkxJvRR1UZXO6YNNP0+GfpeNHdXLpRcuYtaUcVz8xSXc9kDa38hu4lZT1cY7Nv38GPoZGHjl4oWX3ZD0ykU3caupauMdH8WQH0M/I4dOGc/lFz155eKmbY8nWYebuNVUxabveCcfhn6Gjjt4Mp99/dOTXrlo068mm77aZehn7PQ5U/l/rzyBG+76A+/58i3s2p3fm7ceffRR1q5dy7HHHpvbz1Q+bPpql6Gfgz86YSZ/8+J5XLPiAf7uu/ldubhy5UqOOeYYRo8encvPU36q1vTdyM1PdapCwb2pceXi5xavYcbkfK5cdLRTXR7ZVLuq87umBD5w7lwebFy5OGPyWF7x9EMz/Xlu4lZXFcc7Nv18ON7J0Z4rF888airv//pSfnbbg5n+PJt+dVVtvGPTz4+hn7P+KxdP4tgZk3jbVdleuWjTry6bvtpl6CcwaewoLr/oZA6akN2Vi+vXr+fxxx9n5syZXf/eSs+mr3YZ+olMnzyWK954Crtj5MIv3MBDW7r7LPE9LT+E0NXvq2Kw6atdhn5Cc6ZN5NI3nMz6zY91/cpFn7lTbTZ9tcvQT+yk2VP45/NPYvm9m7p65aKbuNVWxSObXpmYD0O/AJ43bwb/0OUrF93ErbaqjXdGjRrFqFGjeOyxx1IvpfKq87um5F59ymwe2PwYH/uP23nq5LH8zw6uXNy5cyerVq1i/vz5XVyhiqRq4x14cq4/bty41EupNJt+gbz77KM5/5RZfPpnd/LFX9/V9ve54447mDlzJhMnTuza2lQsVWv64EPX8lKt3zUl9+SVizv44HdWMH3SGM49vvUrF93Erb6qNn03c7Nn0y+Yvt4ePnn+iZw460De9eVbuOF3f2j5e7iJW302fbXL0C+gcaN7ufTCkzl0yjguvuJGVq9vrf24iVt9Nn21y9AvqCkTRnPFRacwZlT/lYv3b2r+ykWbfvVVsen7Bq18jBj6IYTLQggPhhCWD3jtoBDCj0MItzf+OKXxegghfCKEcEcIYWkI4aQBX3Nh4/NvDyFcmM1fTrXMOmg8l190Mo88tpM3XHYjmx4d+crFzZs38+CDDzJnzpwcVqhUqnZOH3yDVl6aafqXA+fu89oHgJ/EGI8GftL4c4AXAkc3/vdm4DPQ/y8J4IPAqcApwAf3/ItCw5s/8wA+97qns+ahLU1dubh8+XLmz59Pb29vTitUClUd79j0szdi6McYFwP77ia+FLii8esrgD8e8PoXY7/rgANDCAcD5wA/jjH+Ica4Efgx+/+LREM4/aip/L9XPo0bfvcH3vfV4a9cdLRTD1Uc79j089HuTH9GjPH+xq8fAGY0fn0IsG7A593TeG2o19Wkl5wwk78+7zh+sOwB/v57K/d71+4111zDunXr3MStCZu+2tXxRm7sT5+uPTAjhPDmEMKSEMKSDRs2dOvbVsLFzzySi888gst/dRf/8vM1e33spz/9KZ///OdZunQp8+bN44ILLmDt2rWJVqqs2fTVrnZDf31jbEPjj3uugLoXmDXg8w5tvDbU6/uJMX4uxrgoxrho2rRpbS6vuv7yRcfxkhNm8o/X3Mo3br7niddf/OIX8/3vf59ly5ZxzTXXsH79eg49NNvrGJWOTV/tajf0vwPsOYFzIfDtAa+/vnGK5zRgU2MMdC3wghDClMYG7gsar6lFPT2Bf/rThZw+5yn8z68t5eer+/9r6PTTT+fOO+8E4Oqrr+bKK690M7fCbPpqVzNHNq8Gfg0cG0K4J4TwJuD/AM8PIdwOPK/x5wA/ANYAdwCfB94GEGP8A/D3wI2N//2vxmtqw5i+Xj77uqdz9IxJvPXKm1h2zyb6+vo44YQT2Lx5M1/60pd46lOfmnqZylAVj2za9PMx4u+aGOP5Q3zo7EE+NwJvH+L7XAZc1tLqNKRJY0dxxUUn87JP/4qLLr+Br7/1dF7zmtcwZ84czj57v781qpgqjnd8DEM+fEduiU2fPJYvvukUdu6OXHjZDfzJBW/gssv892odVHG842MY8mHol9ycaRO59MKTeWDzY7zp8hvZtG3kd+2q/Gz6apehXwFPP6z/ysUV923mnI8t5he3e9S16qrY9CdNmsSWLVu8MjFjhn5FPG/eDL7xttOZMKaX1116Ax/89nIe3TH8IxtUXlVs+n19fYwePZpt27alXkqlGfoVsvDQA/n+u57JG884git+vZbzPvELbln3cOplKQNVbPrgXD8Phn7FjB3Vy9/+0Tz+7eJTeezxXfzJZ37FR3+8msd37U69NHVRFY9sgsc282DoV9TpR03lh+85i5c+bSaf+MntvPzTv+KOB21QVVHF8Q74Bq08GPoVdsC4UXz0lU/jMxecxD0bt3HeJ37JZb/8HbuHeUqnyqHK4x2bfrYM/Rp44YKDufa9Z3HmUVP5X99byQX/ej33Ptz8TVwqHpu+2mXo18T0SWP51wsX8Y9/soCl9zzMuZcs5us33ePxuJKy6atdhn6NhBB41cmz+eG7z2LuwZP483//LW+98mZ+v2V76qWpRTZ9tcvQr6HZTxnPl9/8DP7ihXP56a0Pcs7HfsFPVq1PvSy1wKavdhn6NdXbE3jLs+bw7XecwdSJo3nTFUv4wNeXsmX7ztRLUxNs+mqXoV9zxx08mW+/4wze+uw5fHXJOl748cXc8Dufel10ntNXuwx9Maavl/efO5evvuUZBAKv+tyv+fAPVrF9p49xKKIYI7t27arkJTk+dC17hr6esOjwg/jhu5/J+afM5rOL1/CST/4XK+/zH8Ci2dPyQwipl9J1PoYhe4a+9jJhTB//8LIFfOENJ/OHbTt46ad+yad/dge7fENXYVR1Exds+nkw9DWo58ydzrXvOYvnz5vBR665jVd+9tes/f3W1MsS1d3EBZt+Hgx9DemgCaP51GtO4mOvehqr1z/CCz/+C/7t+rt9Q1diVW76buRmz9DXsEII/PGJh3Dte87ixNkH8pffXMYbL7+RBzc/lnpptVXlpu+RzewZ+mrKzAPH8aU3nsrfvWQ+v17ze17wscV8f+n9qZdVS1U9rgk2/TwY+mpaT0/gwtMP5/vveiaHHTSet//bzbzny7/xXt6cVXm8M3HiRK9MzJihr5bNmTaRr7/1dN77vGP47tL7Oedji/nl7Q+lXlZtVHm809vby7hx49i61UMDWTH01Za+3h7e/byj+WbjXt7XXno9H/rOCu/lzUGVmz4418+aoa+O7LmX96IzDufyX93FeZ/8Bb/1Xt5MVbnpg3P9rBn66tjYUb188I/mc9XFp/Lojl283Ht5M2XTVycMfXXNGUdN5Rrv5c2cTV+dMPTVVd7Lm70qH9kEm37WDH1lYt97eV97qffydkvVxzs2/WwZ+srMnnt5/8/LF/Dbdf338n7jZu/l7VTVxzs+dC1bhr4yFULg1ac8eS/v+77afy/vH7buSL200qpD03e8kx1DX7nYcy/vBxr38r7gksXey9smm746YegrN709gf/mvbwds+mrE4a+cue9vJ2petN3IzdbHYV+COG9IYQVIYTlIYSrQwhjQwhHhBCuDyHcEUL4SghhdONzxzT+/I7Gxw/vxl+AymnQe3l/6L28zah60/fIZrbaDv0QwiHAu4BFMcbjgV7g1cA/ApfEGI8CNgJvanzJm4CNjdcvaXyeam7PvbyvPnk2n/35Gl76z97LO5Kqn9O36Wer0/FOHzAuhNAHjAfuB54LfK3x8SuAP278+qWNP6fx8bNDFW92VssmjOnjwy9fwGVvWMRDW7yXdyRVH+/Y9LPVdujHGO8F/i9wN/1hvwm4CXg4xrhnZ+4e4JDGrw8B1jW+dmfj85/S7s9X9Tx37gx+9N4n7+V9lffyDqrq4x2bfrY6Ge9Mob+9HwHMBCYA53a6oBDCm0MIS0IISzZs2NDpt1PJDLyX9zbv5R2UTV+d6GS88zzgdzHGDTHGx4FvAGcABzbGPQCHAvc2fn0vMAug8fEDgN/v+01jjJ+LMS6KMS6aNm1aB8tTWXkv7/Bs+upEJ6F/N3BaCGF8YzZ/NrAS+E/gFY3PuRD4duPX32n8OY2P/zRa3zSMPffyfuiP5vGrO3/POR9bzA+WeS9v1Zv+xIkT2bp1K7t3+2juLHQy07+e/g3Zm4Flje/1OeD9wPtCCHfQP7O/tPEllwJPabz+PuADHaxbNdHTE3jDGUfw/Xc9k9kHjedtVzXu5X20vvfyVr3p9/T0MH78eK9MzEhHv3NijB8EPrjPy2uAUwb53MeAP+3k56m+jpo+ka+99XQ+9Z938Mmf3sH1v/sD//SKEzjz6KmpyZVotQAAFZlJREFUl5a7qh/ZhCfn+pMmTUq9lMrxHbkqjVG9PbznecfwzbedzvjRT97Lu21HvR7jUPXxDjjXz5Khr9LZ917eF378F1y/Zr8zAZVV9fEO+NC1LBn6KqU99/Je/WenESO86nPX8cFvL2drDR7eVpem77HNbBj6KrVnzHkK17ynv/V/8bq1nPvxxfzqzodSLytTNn11wtBX6Y0f3ccH/2g+X3nzM+gNgdd8/nr++lvLKvvIZpu+OmHoqzJOOeIgfvjus7j4zCO46vq7OeeSxfzy9uq1/jo0fTdys2Poq1LGje7lr188j6/9t2cwpq+H1156PX/xjaU88lh1zvXX6cimus/QVyU9/bCD+MG7n8lbzjqSr9y4jnMuWczPV1fjWU51Ge/Y9LNh6Kuyxo7q5S9edBxff+vpjB/Tx4WX3cD7v7aUzSVv/XUY79j0s2Poq/JOnD2F773zTN767Dn8+03reMFHF/Oftz6Yellts+mrE4a+amHsqP7rGb/5tjOYPK6Piy6/kT//6m/ZtK18rd+mr04Y+qqVE2YdyHffeSbveM5RfOuWe3n+JT/nP1auT72sltj01QlDX7Uzpq+X/37OsXzrbWdw0ITRXPzFJbz3K7fw8LYdqZfWFJu+OmHoq7YWHHoA33nHmbz77KP57m/v43kfXcy1Kx5IvawR2fTVCUNftTa6r4f3Pv8Yvv2OM5g+aQxv+dJNvOvq3/CHrcVt/XU5p2/oZ8PQl4D5Mw/g2+84g/c9/xh+uPx+XnDJzwt7S1cdxjs+hiE7hr7UMKq3h3edfTTfeceZPPWAsbztqpt5+1U389CW7amXtpc6jHcmTJjAtm3bvDIxA4a+tI/jDp7MN992Bv/jnGP58cr1vOCSxXz3t/dRlCud69D0e3p6mDBhAlu2bEm9lMox9KVBjOrt4e3POYrvvetMZk0Zxzuv/g1vvfJmNjySvvXXoemDm7lZMfSlYRwzYxJff+vpvP/cufz0tgd5/iU/59u33Ju09deh6YPHNrNi6Esj6Ovt4a3PnsMP3nUmhz9lAu/+8i28+Us38eDmx5Ksx6avThj6UpOOmt7f+v/yRXNZvHoDz79kMd+4+Z7cW38djmyCTT8rhr7Ugt6ewJvPmsMP3v1Mjpo+kfd99bdcfMUSHtiUX+uvy3jHpp8NQ19qw5xpE/nqW57B37x4Hv9150M8/5Kf8+9L1uXS+usy3rHpZ8PQl9rU2xN405lH8MN3n8VxT53M//jaUi66/Ebue/jRTH+uTV+dMPSlDh0xdQJffvNpfOiP5nH9mj9wziWL+cqNd2fW+m366oShL3VBT0/gDWccwTXveSbzD5nM+7++jNdfdgP3ZtD6bfrqhKEvddFhT5nAv118Gn//0vnctHYjL/joz7nq+rVdbf02fXXC0Je6rKcn8LpnHM617zmLE2YdyF99czmvvfR61v1hW1e+f12ObNr0s2HoSxmZddB4rrr4VP7hZQu45e6HOedji/nSr+9i9+72W//u3bvZvXs3PT3V/0fXxytno/q/c6SEQgi85tTZXPves3j6YVP4m2+v4DX/eh1rf7+1re+3Z7QTQujySovHxytnw9CXcnDolPF88Y2n8H9evoAV927m3I/9gsv/63ctt/66bOKCTT8rhr6UkxACrz6lv/WfcsRBfOi7K3n1567jroeab/112cQFm35WDH0pZzMPHMflF53MP71iIase2My5H1/Mv/5iDbtGaP0xxlo1fTdys9FR6IcQDgwhfC2EcGsIYVUI4RkhhINCCD8OIdze+OOUxueGEMInQgh3hBCWhhBO6s5fglQ+IQT+dNEsfvzeZ3H6nKn8f99fxSs/+2vu3DD4pSE7d+7kqKOOYuPGjYwaNYpVq1Zx3nnn5bzqfHlkMxudNv2PA9fEGOcCJwCrgA8AP4kxHg38pPHnAC8Ejm78783AZzr82VLpPfWAsVx64SI++soTuH39I7zo47/gc4vv3K/19/X1ceqpp/KFL3yBvr4+/vZv/5ZnPetZiVadjwkTJvDoo4+ya9eu1EuplNDum0ZCCAcAtwBHxgHfJIRwG/DsGOP9IYSDgZ/FGI8NIXy28eur9/28oX7GokWL4pIlS9pan1Q2D25+jL/85nL+Y9V6Tpx9IP/0ioUcNX3SEx9ftmwZZ599Nj09PfT09HDHHXcwfvz4hCvO3gEHHMDdd9/NAQcckHoppRJCuCnGuGiwj3XS9I8ANgBfCCH8JoTwryGECcCMAUH+ADCj8etDgHUDvv6exmuSgOmTx/L51z+dj7/6afzuoa286BO/5DM/u5Odu/ovB1+wYAELFy5kw4YN/NVf/VXlAx+c62ehk9DvA04CPhNjPBHYypOjHAAa/wXQ0n9KhBDeHEJYEkJYsmHDhg6WJ5VPCIGXPu0QfvTes3jusdP5x2tu5U8+8ytWr++fbf/5n/85EydO5OKLL0680nw41+++TkL/HuCeGOP1jT//Gv3/EljfGOvQ+OODjY/fC8wa8PWHNl7bS4zxczHGRTHGRdOmTetgeVJ5TZ80ls+89iT++TUnsm7jo7z4E7/kn396O897wTls2rSJMWPGpF5iLmz63dd26McYHwDWhRCObbx0NrAS+A5wYeO1C4FvN379HeD1jVM8pwGbhpvnS3UXQuDFC2fyo/eexfPnzeD//mg1L/v0f7Hq/vqEoE2/+zo98PtO4KoQwmhgDXAR/f8i+WoI4U3AWuCVjc/9AfAi4A5gW+NzJY1g6sQxfOqCkzhv2f38zbeW86JP/IJnHzON1z3jMJ51zHR6e6r7SAabfvd1FPoxxluAwXaIzx7kcyPw9k5+nlRnL1pwMKcd+RQu/6/fcfWN63jj5Us45MBxXHDabF65aBZTJ1Zv5GPT7z7fkSuVyEETRvO+FxzLrz7wXD71mpOYfdB4PnLNbZz+4Z/y7i//hiV3/SGXe3rzYtPvvnq8n1uqmFG9PZy38GDOW3gwt69/hKuuv5uv33QP377lPuY+dRKvPe0w/vjEQ5g4ptz/iPvQte6z6Usld/SMSXzoJfO5/q/O5sMvX0BPCPz1t5Zz2j/8hL/51nJue6C84xEfutZ95a4Bkp4wfnQf558ym1efPIvfrHuYK69by1eWrONL163llMMP4rXPOIxz5z+V0X3l6XqTJk3irrvuSr2MSjH0pYoJIXDS7CmcNHsKf33ePP59yTquuv5u3nX1b5g6cTSvOnkW558ym0OnFP8dvTb97jP0pQo7aMJo3vKsOfzZM49k8e0buPK6u/nMz+7kMz+7k+fOnc5rTzuMs46eRk9Bj326kdt9hr5UAz09gWcfO51nHzudex9+lKuvv5sv33g3/7HqQWYfNJ4LTp3Nny6axUETRqde6l48stl95RnuSeqKQw4cx38/51h+9YGz+cT5J/LUA8by4R/eymkf/gnv+8ot3Hz3xsIc+7Tpd59NX6qp0X09vOSEmbzkhJnc9sAjXHX9Wr5x87184zf3Mu/gybzuGYfx0qfNZPzodDFh0+++tp+nnwefpy/la8v2nXzrN/dy5XVrufWBR5g0po8/efqhvPa02Xs92z8vDzzwAE972tN44IEHcv/ZZTbc8/QNfUn7iTFy09qNXHndWn6w7AF27NrNaUcexOtOO5wXzJ/BqN58JsNbt25l+vTpbN3a/OXxMvQldeD3W7bz1SX3cNX1a7ln46NMmzSG80+exfmnzubgA8Zl+rNjjIwaNYrHHnusNhfCd4OhL6lju3ZHFq/ewJeuW8t/3vYgAXjecTN47WmHceZRUzM79nnggQdy1113ceCBB2by/atouND3X52SmtLbE3jO3Ok8Z+501v3/7d17bJX1Hcfx97cXWkopYCnQnmMLzomDsdIzYmV1F/GCOhBbt6kTEvePWzSLi2HukizZJW7JlhiXLNuy6BaHOqfSukicbnPsolnroIdrkU2RQg9gy/0il16++6OPBqfiBuc5T3uezytpOOXy6+cXks95zvf8zjn73+DRl3bw23/u5A9drzO9soxbG+v47LwkE8uye+zzzRM8Kv3s0JFNEfm/nX9eGV+75mL+8Y0F/PjmuUwuL+HeZ7bQ+P3nWf7EetbvPJi1n6U3XcsuXemLyFkrKSpkydwES+Ym2LL7MA+3d9OWzvDk2h7mJCaw7NI6FtfXMHZM4Vn/DL0VQ3bpSl9EsuJD1RXc2zyHjm9ewfeWzObkwCD3rNxA4/f/xHef7uLVvqP/13r33XcfHR0db13pX3fddXR1dYWUPj50pS8iWTW+tJhl86ez9NI6/rn9ACvau1nRvp1fvvgaTRdWsrSxjitnvf+xz5qaGu644w6mT59OOp1m8+bNXHTRRTnaRf7S6R0RCV3fkZM8vmYnj3bsIHPwOFMrSrjlklpuuaSWqRWl7/pv3J2mpiYKCwsZGBjgxhtvZPny5TlOPjrpyKaIjAiDQ87ql3tZ0d7N3/7dR4EZV88aPvb5sQ9UYvb2Y58dHR0sWLAAdyeTyTBp0qSIko8uOrIpIiNCYYFx5aypXDlrKt37jvFoxw4eX7OT32/awwVV47i1sY7PpJJMKCsGoLGxkZkzZ1JeXq7CzxJd6YtIpE70D/LMxt2saO8mveMgpcUFLKlPsPTSOuYkJ9Df3w9AcXFxxElHD413RGRU2JQ5xCMd3TyV3sXx/kHqz5/I0sZaFtfXUFp89sc+40alLyKjyuET/bSu7WFFezev9h1jfGkRiz5STUsqyby6Se+Y/cvbqfRFZFRyd9q37eeJYO5/vH+Q888bS/PcBM2pJDMmj4s64oik0heRUe/YyQGe27yH1s4ML766F3doqJ1ISyrJojnVTBphH/UYJZW+iOSVPYdO8Lt1GVo7M2x9/QjFhcblM6fQkkpy+cVVlBTFe/6v0heRvOTudO0+TFtnhqfW7WLv0ZNMGFvM4vpqmhuSpGonxnL+r9IXkbw3MDjEC6/spS2d4bnNezjRP8T0yjKaG5I0NySorSyLOmLOqPRFJFaOnOjn2U3D8//21/bhDvPqJtGSSvLpOdVvvfgrX6n0RSS2MgeP81Q6Q1s6wyu9RxlTWMCVs6bQ3JDkkxdVMaYo/95sWKUvIrHn7mzKHGZlZw9Pr9/FvmOnmFRWzPX1NTSnktQnJ+TN/F+lLyJymv7BIf7+7z5Wdmb4Y9frnBoY4oKqcbQ0JLihIUFy0uie/6v0RUTew+ET/fx+425WdmZ46bX9ADTOOI+WVIJr51RTUTr65v+hlr6ZFQJrgIy7LzKzGcBjQCWwFljm7qfMrAT4NfBRYB9wk7tvP9PaKn0RyaWd+994a/6/be8xSooKuGrWVFpSCT7+war3/eCXkSLs0r8bmAdUBKX/ONDq7o+Z2c+B9e7+MzO7A/iIu3/JzG4Gmt39pjOtrdIXkSi4O+t2HqQtneHp9bs48EY/k8vHsLi+hhtTSWbXVIzo+X9opW9mSeAh4F7gbmAx0AdMc/cBM5sPfNvdF5rZc8Htf5hZEbAHqPIzBFDpi0jUTg0M8ZetvbSlMzy/pZdTg0N8cEo5zakEN8xNUDNxbNQR3yHMD1G5H7gHGB98XwkcdPeB4PseIBHcTgA7AYI7hEPB3997jhlEREIzpqiAq2dP4+rZ0zj0Rj+rNu6irTPDD5/dyo+e28r8Cyppbhie/5eXjPzPpTrrhGa2COh197Vm9qlsBTKz24HbAWpra7O1rIjIOZtQVsytjXXc2lhH975jtAXz/68+uYFv/W4TC2dPo7khwWUXTqZohM7/z3q8Y2Y/AJYBA0ApUAG0AQvReEdEYsLd6dxxgNbODKs27ObQ8X6qxpewpL6GllSSWTUVOc8U+pHN4Ep/efBE7hPAytOeyN3g7j81szuBOac9kdvi7p8707oqfREZTU4ODLL65V5aOzOs3tpL/6Bz8bTxNAfn/6dWlOYkR65L/wKGj2yeB6SBpe5+0sxKgRVAA7AfuNndt51pXZW+iIxWB46dYtWGXbSmM6R3HKTAoOnCybSkEiycPY2yMeHN//XiLBGRCG3rO8pT6Qyt6Qw9B45TNqaQa2ZPoyWVZP4HKiksyO7xT5W+iMgIMDTkrOk+QFu6h1UbdnPkxABTK0q4YW6CllSSmdPGv/8i/wOVvojICHOif5Dnt/TS2tnDX//Vx8CQM6u6gpZUguvn1jBl/NnP/1X6IiIj2L6jJ3l6/fD8f0PPIQoMrptTzU8+nzqr9cJ8cZaIiJyjyvISbmuawW1NM3il9yht6Z7QfpZKX0RkBLlwSjlfXXhxaOuPzJeMiYhIKFT6IiIxotIXEYkRlb6ISIyo9EVEYkSlLyISIyp9EZEYUemLiMTIiH4bBjPrA7rPYYnJxO/jGOO257jtF7TnuDiXPde5e9W7/cGILv1zZWZr3uv9J/JV3PYct/2C9hwXYe1Z4x0RkRhR6YuIxEi+l/4vog4QgbjtOW77Be05LkLZc17P9EVE5O3y/UpfREROk3elb2bnm9lqM+sys81mdlfUmcJmZqVm9pKZrQ/2/J2oM+WKmRWaWdrMVkWdJRfMbLuZbTSzdWYWi4+VM7OJZvakmb1sZlvMbH7UmcJkZjOD/983vw6b2Veytn6+jXfMrBqodvdOMxsPrAVucPeuiKOFxswMGOfuR82sGHgBuMvd2yOOFjozuxuYB1S4+6Ko84TNzLYD89w9NmfWzewh4O/u/oCZjQHK3P1g1LlywcwKgQzQ6O7n8pqlt+Tdlb6773b3zuD2EWALkIg2Vbh82NHg2+LgK7/uzd+FmSWBTwMPRJ1FwmFmE4BPAA8CuPupuBR+4Arg1WwVPuRh6Z/OzKYDDUBHtEnCF4w51gG9wB/dPe/3DNwP3AMMRR0khxz4g5mtNbPbow6TAzOAPuBXwRjvATMbF3WoHLoZ+E02F8zb0jezcmAl8BV3Pxx1nrC5+6C7zwWSwCVm9uGoM4XJzBYBve6+NuosOXaZu6eAa4E7zewTUQcKWRGQAn7m7g3AMeDr0UbKjWCUdT3wRDbXzcvSD+baK4FH3L016jy5FDz0XQ1cE3WWkDUB1wcz7seABWb2cLSRwufumeDXXqANuCTaRKHrAXpOe+T6JMN3AnFwLdDp7q9nc9G8K/3gSc0HgS3ufl/UeXLBzKrMbGJweyxwFfBytKnC5e7fcPeku09n+CHwn919acSxQmVm44LDCQQjjquBTdGmCpe77wF2mtnM4LeuAPL2UMZ/uYUsj3Zg+KFTvmkClgEbgxk3wDfd/ZkIM4WtGngoeKa/AHjc3WNxhDFmpgJtw9c1FAGPuvuz0UbKiS8DjwTjjm3AFyLOE7rgTv0q4ItZXzvfjmyKiMh7y7vxjoiIvDeVvohIjKj0RURiRKUvIhIjKn0RkRhR6YuIxIhKX0QkRlT6IiIx8h/RIf3y2dndfAAAAABJRU5ErkJggg==\n","text/plain":["
"]},"metadata":{"needs_background":"light"}}]},{"cell_type":"markdown","metadata":{"id":"Nre7oxppyO07"},"source":["Δηλαδή στη συγκεκριμένη περίπτωση θα ήταν $k=3$, $k=5$ ή $k=6$.\n","\n","Για να αποκτήσουμε μια πιο \"αντικειμενική\" εικόνα υπάρχουν 2 βασικοί τρόποι [αξιολόγησης αλγορίθμων συσταδοποίησης](https://en.wikipedia.org/wiki/Cluster_analysis#Evaluation_and_assessment): η *εξωτερική* (external) και η *εσωτερική* (internal).\n"]},{"cell_type":"markdown","metadata":{"id":"zveA4SlUyGIb"},"source":["### Εξωτερική Αξιολόγηση\n","\n","Η εξωτερική αξιολόγηση (Extrinsic evaluation) απαιτεί την εκτέλεση του αλγορίθμου σε ένα πρόβλημα επιβλεπόμενης μάθησης (που έχουμε τις ετικέτες δλδ ποιο δείγμα ανήκει σε ποια ομάδα) και την \"εξωτερική\" του αξιολόγηση με βάση αυτές. Δεν αποτελεί τυπική περίπτωση συσταδοποίησης και δεν θα την εξετάσουμε περισσότερο.\n"]},{"cell_type":"markdown","metadata":{"id":"UO23IBPxyrwW"},"source":["\n","### Εσωτερική Αξιολόγηση\n","Η Εσωτερική αξιολόγηση (Intrinsic Evaluation) απαιτεί την ανάλυση της δομής ή της ευστάθειας των παραγόμενων από τον αλγόριθμο συστάδων. Για να το πετύχουμε αυτό, χρησιμοποιούμε διάφορους δείκτες ή συντελεστές.\n","\n","\n","- [Dunn index](https://en.wikipedia.org/wiki/Dunn_index):\n","Ο αριθμητής του dunn index είναι ένα μέτρο της **μικρότερης απόστασης μεταξύ δυο συστάδων** (π.χ. απόσταση μεταξύ των κέντρων τους). \n","Στον παρονομαστή μπαίνει ένα μέτρο του **μεγέθους της μεγαλύτερης συστάδας** (π.χ. η απόσταση μεταξύ των 2 πιο απομακρυσμένων παραδειγμάτων που ανήκουν στη συστάδα αυτή).\n","\n","$$\n","DI= \\frac{ min \\left( δ \\left( C_i, C_j \\right) \\right)}{ max \\, Δ_p }\n","$$\n","\n","όπου $C_i, C_j$ είναι δυο τυχαία κέντρα συστάδων, $δ \\left( C_i, C_j \\right)$ είναι ένα μέτρο της απόστασής τους και $Δ_p$ είναι ένα μέτρο της \"διαμέτρου\" της συστάδας $p$, όπου $p \\in [0,k]$.\n","\n","- [Silhouette coefficient](https://en.wikipedia.org/wiki/Silhouette_(clustering)):\n","$$\n","s \\left( i \\right) = \\frac{b \\left( i \\right) -a \\left( i \\right) }{max \\left( a \\left( i \\right) , b \\left( i \\right) \\right)}\n","$$\n","\n","Έστω $i$ ένα σημείο (point) οποιασδήποτε συστάδας. \n","\n","Το $a(i)$ είναι η μέση απόσταση του $i$ από όλα τα υπόλοιπα σημεία της συστάδας στην οποία ανήκει. Όσο μικρότερο είναι το $a(i)$, τόσο περισσότερο ομοιάζει το $i$ στα υπόλοιπα δείγματα της συστάδας.\n","\n","To $b(i)$ είναι η μικρότερη μέση απόσταση του $i$ από όλα τα σημεία σε οποιαδήποτε άλλη συστάδα, στην οποία το $i$ δεν ανήκει. Η συστάδα με την μικρότερη μέση απόσταση από το $i$ θεωρείται \"γειτονική\" (η δεύτερη καλύτερη επιλογή ομαδοποίησης).\n","\n","Μικρό $a(i)$ σημαίνει ότι η συστάδα του $i$ είναι συμπαγής ενώ μεγάλο $b(i)$ σημαίνει ότι το $i$ έχει μεγάλη απόσταση από την κοντινότερη συστάδα.\n","\n","Το εύρος τιμών που μπορεί να πάρει το $s(i)$ είναι στο $[-1, 1]$. Όσο πιο μεγάλο, τόσο πιο ξεκάθαρες οι συστάδες μεταξύ τους. Για να είναι το $s(i) \\approx 1$, πρέπει το $b(i) >> a(i)$.\n","\n","Για να αξιολογήσουμε τον αλγόριθμό μας συνήθως παίρνουμε το μέσο όρο των $s(i)$ για όλα τα $i$.\n","\n"]}]}