UnsupervisedLearning/KMeansClustering_Grains.ipynb

{
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  {
   "cell_type": "code",
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   "source": [
    "#Requisite Scikit-Learn packages\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.manifold import TSNE\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "#Scipy packages\n",
    "from scipy.cluster.hierarchy import linkage, dendrogram, fcluster\n",
    "from scipy.stats import pearsonr\n",
    "\n",
    "#Visualisation and Computation packages\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": true
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   "source": [
    "grain_samples = np.array([[ 15.26,14.84,0.871 ,5.763 ,3.312 ,2.221 ,5.22  ],[ 14.88,14.57,0.8811,5.554 ,3.333 ,1.018 ,4.956 ],[ 14.29,14.09,0.905 ,5.291 ,3.337 ,2.699 ,4.825 ],[ 13.84,13.94,0.8955,5.324 ,3.379 ,2.259 ,4.805 ],[ 16.14,14.99,0.9034,5.658 ,3.562 ,1.355 ,5.175 ],[ 14.38,14.21,0.8951,5.386 ,3.312 ,2.462 ,4.956 ],[ 14.69,14.49,0.8799,5.563 ,3.259 ,3.586 ,5.219 ],[ 14.11,14.1 ,0.8911,5.42,3.302 ,2.7 ,5.    ],[ 16.63,15.46,0.8747,6.053 ,3.465 ,2.04,5.877 ],[ 16.44,15.25,0.888 ,5.884 ,3.505 ,1.969 ,5.533 ],[ 15.26,14.85,0.8696,5.714 ,3.242 ,4.543 ,5.314 ],[ 14.03,14.16,0.8796,5.438 ,3.201 ,1.717 ,5.001 ],[ 13.89,14.02,0.888 ,5.439 ,3.199 ,3.986 ,4.738 ],[ 13.78,14.06,0.8759,5.479 ,3.156 ,3.136 ,4.872 ],[ 13.74,14.05,0.8744,5.482 ,3.114 ,2.932 ,4.825 ],[ 14.59,14.28,0.8993,5.351 ,3.333 ,4.185 ,4.781 ],[ 13.99,13.83,0.9183,5.119 ,3.383 ,5.234 ,4.781 ],[ 15.69,14.75,0.9058,5.527 ,3.514 ,1.599 ,5.046 ],[ 14.7 ,14.21,0.9153,5.205 ,3.466 ,1.767 ,4.649 ],[ 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    "variety_numbers = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]\n",
    "varieties = ['Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Kama wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Rosa wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat','Canadian wheat']"
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  {
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    {
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4YHCffPJth+Q3sxbk334zp+45AAAAANDwxGyoyVlH7Jm3HLprvnjrzEx+9Lm6\n5wAAAABAQxOzoSallHz+1BEZ3Ldnzpk4OUtWra17EgAAAAA0LDEbatSvV7dcPXZUnli0Kh/7zvRU\nlftnAwAAAMCmiNlQs1ftNSAfeOP++f7UJ3L9pHl1zwEAAACAhiRmQwP4x7/YL0fts3Mu/t6MzH56\nad1zAAAAAKDhiNnQALo0lVw1ZlR26N4lZ397clatXV/3JAAAAABoKGI2NIjBfXvmyjNG5oGnluZz\nP7q/7jkAAAAA0FDEbGggxx60S/72dXvnv3//SH4y46m65wAAAABAwxCzocFc9OYDc+jufXPRjdPy\n5OKVdc8BAAAAgIYgZkOD6dG1S8aPPTxr17Xk3IlTsr6lqnsSAAAAANROzIYGtPfAHXPZOw7NXXMX\nZvzPZ9U9BwAAAABqJ2ZDgzr18D1yavPuufpns3LHnGfrngMAAAAAtRKzoYFd+o5Ds+eAXjlv4pQ8\nt3xN3XMAAAAAoDZiNjSw3j26ZvzYw/Ps8tW58IZpqSr3zwYAAACgcxKzocEdtke/fOjNB+W2++fn\nf37/SN1zAAAAAKAWYja0A3/7ur1z7IGD8pkf3Z/7nlhS9xwAAAAA2O7EbGgHSin54hkj03+Hbjl7\nwj1ZsWZd3ZMAAAAAYLsSs6Gd2Ll3j1z1rlGZu2B5PvW9GXXPAQAAAIDtSsyGduTo/Qbmn/5i31w3\naV6+N/WJuucAAAAAwHYjZkM7c94bD8jhe/bPR2+6N48+u6LuOQAAAACwXYjZ0M5069KUr4xpTinJ\nuImTs3Z9S92TAAAAAKDNidnQDg0d0CtfOG1Epj62KF/8ycy65wAAAABAmxOzoZ066bDdMvaIPfP1\nX83Jrx98pu45AAAAANCmxGxoxz751kNywODe+eB1U/PM0tV1zwEAAACANiNmQzu2Q/cuGT/28Cxd\ntTYfvG5KWlqquicBAAAAQJsQs6GdO3DXPvnEWw/Jb2YtyL//Zk7dcwAAAACgTYjZ0AH85Wv2zFsO\n3TVX3DozUx5bVPccAAAAANjmxGzoAEop+fypIzK4b8+cM2Fylq5aW/ckAAAAANimxGzoIPr16pav\njBmVxxetzMe+Mz1V5f7ZAAAAAHQcYjZ0IKOHDch5x++f7019ItffPa/uOQAAAACwzYjZ0MH807H7\n5ah9ds7FN8/I7KeX1T0HAAAAALYJMRs6mC5NJVeNGZUdunfJuAmTs2rt+ronAQAAAMAr1mYxu5Qy\ntJTyi1LK/aWUGaWUc1uPDyil/LSUMqv1351aj5dSytWllNmllGmllMM3+l7vbT1/VinlvW21GTqK\nwX175otnjMj9Ty7J5295oO5j3sLOAAAgAElEQVQ5AAAAAPCKteWV2euSnF9V1cFJjkzyz6WUQ5J8\nOMnPqqraP8nPWr9Okrck2b/1431JvpZsiN9JLk7ymiRHJLn4+QAObN5xBw3O37x27/zX7x7OT++b\nX/ccAAAAAHhF2ixmV1X1ZFVV97R+vjTJ/Ul2T3JKkv9uPe2/k7yj9fNTkvxPtcEdSfqXUnZLcmKS\nn1ZVtbCqqueS/DTJm9tqN3QkH3rLgRk+pG8uvGFqnly8su45AAAAAPCybZd7ZpdShiVpTnJnksFV\nVT2ZbAjeSXZpPW33JI9t9LR5rcc2d/yFP+N9pZRJpZRJzzzzzLZ+CdAu9ejaJePHNmfNupacO3FK\n1rdUdU8CAAAAgJelzWN2KaV3khuTnFdV1ZIXO3UTx6oXOf6nB6rq36qqGl1V1ehBgwa9vLHQAe0z\nqHcuO+XQ3DV3Ycb/fFbdcwAAAADgZWnTmF1K6ZYNIfv/qqq6qfXw/Nbbh6T136dbj89LMnSjp++R\n5IkXOQ5sodNetUfe2bx7rv7ZrNw559m65wAAAADAVmuzmF1KKUm+keT+qqq+tNFD30vy3tbP35vk\n5o2Ov6dscGSSxa23Ibk1yQmllJ1a3/jxhNZjwFa47B2HZs8BvXLetVPy3PI1dc8BAAAAgK3Slldm\nvzbJu5McV0qZ0vpxUpLPJ3lTKWVWkje1fp0kP0oyJ8nsJP+e5J+SpKqqhUkuS/KH1o9LW48BW6F3\nj64ZP/bwLFi2OhfdOC1V5f7ZAAAAALQfpSMGrdGjR1eTJk2qewY0pP/4zZx8+of359JThuc9Rw2r\new4AAAAAnVgp5e6qqkZvyblt/gaQQGP5m9funb84cFA+/cP7c98TL/aerAAAAADQOMRs6GSamkq+\neMbI9NuhW8ZNuCcr1qyrexIAAAAAvCQxGzqhgb175Kp3jcqcBctzyffuq3sOAAAAALwkMRs6qdfu\nNzD/+IZ9c+2kx/L9qU/UPQcAAAAAXpSYDZ3YB950QJr37J+P3nRvHlu4ou45AAAAALBZYjZ0Yt26\nNOXqMc1JScZNmJy161vqngQAAAAAmyRmQyc3dECvfP7UEZny2KJc+ZMH654DAAAAAJskZgM5ecRu\nGXvE0Pzrrx7Kb2Y9U/ccAAAAAPgzYjaQJPnkW4dn/1165wPXTs0zS1fXPQcAAAAA/oSYDSRJduje\nJePPas7SVWtz/vVT09JS1T0JAAAAAP5IzAb+6KBd++bjbz0kv37wmfzHb+fUPQcAAAAA/kjMBv7E\nX71mz5w4fHAu//HMTH1sUd1zAAAAACCJmA28QCklXzhtRHbp0yPjJkzO0lVr654EAAAAAGI28Of6\n9+qeq8c25/FFK/Px705PVbl/NgAAAAD1ErOBTRo9bEDOO37/3Dzlidxw97y65wAAAADQyYnZwGb9\n07H75ch9BuSTN8/IQ88sq3sOAAAAAJ2YmA1sVpemkqve1Zye3Zoy7tuTs3rd+ronAQAAANBJidnA\ni9q1X8988YyRue/JJfncjx6oew4AAAAAnZSYDbyk4w8enP/32mH5r989nNvum1/3HAAAAAA6ITEb\n2CIffstBGT6kby68YWqeXLyy7jkAAAAAdDJiNrBFenTtkvFjm7N6XUvOmzgl61uquicBAAAA0ImI\n2cAW22dQ71x6yqG5c+7CXPPz2XXPAQAAAKATEbOBrXLa4bvnHaOG5Cs/ezB3zV1Y9xwAAAAAOgkx\nG9gqpZR8+p2HZeiAXjlv4uQsWrGm7kkAAAAAdAJiNrDVevfomvFjm/PMstW56IZpqSr3zwYAAACg\nbYnZwMsyYo/+uejEg/KT++bnW3c8UvccAAAAADo4MRt42f72dXvnDQcMymU/vD/3P7mk7jkAAAAA\ndGBiNvCyNTWVXHnmyPTboVvGTZicFWvW1T0JAAAAgA5KzAZekYG9e+TLZ47KQ88sy6Xfv6/uOQAA\nAAB0UGI28Iq9bv+Bef8b9s3EPzyW7099ou45AAAAAHRAYjawTXzwTQekec/++ehN9+axhSvqngMA\nAABAByNmA9tEty5NuXpMc5Jk3ITJWbu+peZFAAAAAHQkYjawzQwd0CufO+2wTHlsUb700wfrngMA\nAABAByJmA9vUW0cMyZhXD82//uqh/HbWgrrnAAAAANBBiNnANnfx24Zn30G984HrpmTBstV1zwEA\nAACgAxCzgW1uh+5dcs1ZzVm8cm3Ov25qWlqquicBAAAA0M6J2UCbOGjXvvnEyQfnVw8+k2/8dm7d\ncwAAAABo58RsoM381ZF75cThg3P5rQ9k2rxFdc8BAAAAoB0Ts4E2U0rJF04bkUG9e2TchMlZumpt\n3ZMAAAAAaKfEbKBN9e/VPV8Z25zHFq7IJ747PVXl/tkAAAAAbD0xG2hzrx42IOe98YB8d8oTufGe\nx+ueAwAAAEA7JGYD28U/H7tfjtxnQD558/TMeWZZ3XMAAAAAaGfEbGC76NJUctW7mtOja1PGTZic\n1evW1z0JAAAAgHZEzAa2m1379cwVp4/MjCeW5PO3PFD3HAAAAADaETEb2K7eeMjg/PXRw/Kftz+c\nn90/v+45AAAAALQTYjaw3X3kpINyyG59c8H1U/PU4lV1zwEAAACgHRCzge2uR9cuGX9Wc1ava8m5\nEydnfUtV9yQAAAAAGpyYDdRi30G9c8nbh+fOuQvz1V/MrnsOAAAAAA1OzAZqc/qr9sgpo4bkqtse\nzB8eXlj3HAAAAAAamJgN1KaUkk+/49AMHdAr506YnEUr1tQ9CQAAAIAGJWYDterTs1uuHtOcp5eu\nzodunJaqcv9sAAAAAP6cmA3UbuTQ/rnozQfm1hnz8607H617DgAAAAANSMwGGsLfvW6fvP6AQbns\nB/flgaeW1D0HAAAAgAYjZgMNoamp5MozRqZvz245+9uTs3LN+ronAQAAANBAxGygYQzq0yNfftfI\nzH56WS79wYy65wAAAADQQMRsoKEcs/+gvP8N+2bCXY/lh9OerHsOAAAAAA1CzAYazvknHJBRQ/vn\nwzdNy2MLV9Q9BwAAAIAGIGYDDadbl6aMH9ucVMk5Eydn7fqWuicBAAAAUDMxG2hIQwf0ymdPPSyT\nH12UL//0wbrnAAAAAFAzMRtoWG8bOSTvGj00X/vVQ7l99oK65wAAAABQIzEbaGgXv/2Q7DNwx5x3\n7ZQsWLa67jkAAAAA1ETMBhpar+5dc81Zh2fxyrW54PqpaWmp6p4EAAAAQA3EbKDhHbxb33z85IPz\ny5nP5Ju3z617DgAAAAA1ELOBduHdR+6VEw4ZnC/8+IHcO29x3XMAAAAA2M7EbKBdKKXk8tNHZFDv\nHhk34Z4sW72u7kkAAAAAbEdiNtBu9O/VPVeNac6jC1fkE9+dXvccAAAAALYjMRtoV47Ye0DOPf6A\nfGfy47nx7nl1zwEAAABgOxGzgXbn7OP2y2v2HpBP3Dw9c55ZVvccAAAAALYDMRtod7o0lVw1ZlS6\nd23KuAmTs3rd+ronAQAAANDGxGygXdqt3w654vSRmfHEknzhlpl1zwEAAACgjYnZQLv1pkMG56+P\nHpZv3j43P7t/ft1zAAAAAGhDYjbQrn34LQfl4N365oLrp+apxavqngMAAABAGxGzgXatZ7cuueas\n5qxa25Lzrp2c9S1V3ZMAAAAAaANiNtDu7Tuody45ZXjumLMw//KL2XXPAQAAAKANiNlAh3DGq/bI\n20cOyVU/m5VJDy+sew4AAAAA25iYDXQIpZR85p2HZvf+O+TciVOyeMXauicBAAAAsA2J2UCH0adn\nt1w9tjnzl6zKh26clqpy/2wAAACAjkLMBjqUUUP758ITD8yPZzyV/7vz0brnAAAAALCNiNlAh/P3\nx+yT1x8wKJf94L7MfGpp3XMAAAAA2AbEbKDDaWoqufKMkenTs1vO/vY9Wblmfd2TAAAAAHiFxGyg\nQxrUp0e+dObIzHp6WS79wX11zwEAAADgFRKzgQ7r9QcMyj+8YZ9MuOvR/HDak3XPAQAAAOAVELOB\nDu2CEw7MyKH98+GbpuWxhSvqngMAAADAyyRmAx1aty5NGT+mOamScydOztr1LXVPAgAAAOBlELOB\nDm/PnXvlM6celnseXZSrbnuw7jkAAAAAvAxiNtApvH3kkJw5eo/8yy8fyu9mL6h7DgAAAABbScwG\nOo1PvX149hm4Y867dkqeXba67jkAAAAAbAUxG+g0enXvmvFjD8+ilWtzwfVT09JS1T0JAAAAgC0k\nZgOdyiFD+ubjJx+cX8x8Jt+8fW7dcwAAAADYQmI20Om8+8i9csIhg/OFHz+Qe+ctrnsOAAAAAFtA\nzAY6nVJKLj99RAb27pFxE+7JstXr6p4EAAAAwEsQs4FOqX+v7vnKmOY8unBFPvnd6XXPAQAAAOAl\niNlAp3XE3gNyzvH756bJj+eme+bVPQcAAACAFyFmA53auOP2zxF7D8jHvzs9cxcsr3sOAAAAAJsh\nZgOdWpemkq+MGZXuXZsybsI9Wb1ufd2TAAAAANiELY7ZpZSTSykXlVI++fxHWw4D2F5267dDLj9t\nRKY/viSX/3hm3XMAAAAA2IQtitmllH9N8q4k45KUJGck2asNdwFsVycM3zXvPWqvfOO3c/PzB+bX\nPQcAAACAF9jSK7OPrqrqPUmeq6rqkiRHJRnadrMAtr+PnHRwDt6tby64flrmL1lV9xwAAAAANrKl\nMXtl678rSilDkqxNsnfbTAKoR89uXTJ+bHNWrlmf8yZOyfqWqu5JAAAAALTa0pj9g1JK/yRXJLkn\nycNJJrbVKIC67LdL71zy9uH5/Zxn87Vfzq57DgAAAACtum7JSVVVXdb66Y2llB8k6VlV1eK2mwVQ\nnzNG75HfzF6QL982K0ftu3NetdeAuicBAAAAdHovemV2KeW41n9Pff4jyclJjm/9HKDDKaXkM+88\nNEP698w5E6Zk8Yq1dU8CAAAA6PRe6jYjb2j9922b+HhrG+4CqFXfnt0yfuzhmb9kVT5807RUlftn\nAwAAANTpRW8zUlXVxa2fXlpV1dyNHyuleANIoEMbNbR/LjjxwHz+lgfy7bsezV++Zq+6JwEAAAB0\nWlv6BpA3buLYDdtyCEAjet8x++SY/Qfm0u/fl5lPLa17DgAAAECn9VL3zD6olHJakn4b3ze7lPLX\nSXpul4UANWpqKrnyzJHp07Nrxk24JyvXrK97EgAAAECn9FJXZh+YDffG7p8/vV/24Un+vm2nATSG\nXfr0zJfOHJUH5y/LZT+8r+45AAAAAJ3SS90z++ZSyg+SfKiqqs9up00ADef1BwzKP7x+n3z913Ny\nzH4D85bDdqt7EgAAAECn8pL3zK6qan2SN22HLQAN7fwTDszIPfrlQzdOy7znVtQ9BwAAAKBT2dI3\ngPxdKeWaUsoxpZTDn/9o02UADaZ716aMH3t4Wqrk3IlTsm59S92TAAAAADqNLY3ZRycZnuTSJFe2\nfnyxrUYBNKo9d+6Vz7zz0Nz9yHO56rZZdc8BAAAA6DRe9J7Zz6uq6ti2HgLQXpwyavf8dtaCfPWX\ns3P0vjvn6P0G1j0JAAAAoMPboiuzSymDSynfKKXc0vr1If8fe3cenud91/n+c2tfLO+b5Ox74liO\n23ShG92TJgotpUDDOWeYGTgMc6YtZWmnwDmUMiyF0qHTMhczzDkzwJxDSlkKjZIm3QndaNM6lp19\nT2zJuy3Lsnbd5w/LjhfFsVPbtyS/XtelS9Lt55G/5g9i3vz8/RVF8TNndjSAmesjb1+di5e25v1/\ndV927R+pehwAAACAOe9k14z8WZK7k3RMff9IkvefiYEAZoOWhrp86tZ12Ts0lg/8TU/Ksqx6JAAA\nAIA57WRj9tKyLD+TZDJJyrIcTzJxxqYCmAVWdyzIr990db7y0Pb89288VfU4AAAAAHPaycbswaIo\nliQpk6Qoilcm6T9jUwHMEv/ihy7MW65ZkY9+/sFs2uJ/LQIAAACcKScbs38pyeeSXFoUxTeS/EWS\n956xqQBmiaIo8gc/1pml8xrz3tvWZ//IeNUjAQAAAMxJJxWzy7L8fpIfTvKqJP8myeqyLHvO5GAA\ns8Wi1oZ84ievy9O7BvMb/7Cp6nEAAAAA5qSTPZmdJC9PsjbJS5LcWhTFvzjRi4ui+O9FUWwvimLT\nEc9+syiKLUVR3Df1cdMRv/arRVE8VhTFw0VR3HDE8xunnj1WFMWHTmFegLPmFZcsyXvfeHn+7vtb\n8tn1m6seBwAAAGDOqTuZFxVF8T+TXJrkvjx38WOZg+tGns+fJfnjaV7zR2VZ/uExP/+aJO9OsjpJ\nR5IvFUVxxdQv/+ckb0myOcl3i6L4XFmWD5zM3ABn03vfeFm+9fiu/J+f3ZTrzl+Ui5e2Vj0SAAAA\nwJxxsiezr0/y6rIs/4+yLN879fG+E72hLMt7kuw+yZ//9iSfLstypCzLJ5M8loMnwV+e5LGyLJ8o\ny3I0yaenXgsw49TV1uQT774udbU1ee9t38/I+MQLvwkAAACAk3KyMXtTkpWn6fd8T1EUPVNrSBZN\nPVuV5NkjXrN56tnzPT9OURQ/VxTFvUVR3Ltjx47TNCrAqelY2JyPvaszm7bsyx/c9XDV4wAAAADM\nGScbs5cmeaAoiruLovjcoY8X8fv9SQ6uK7kuSV+Sj089L6Z5bXmC58c/LMs/Lcvy+rIsr1+2bNmL\nGA3g9Hjr6pX5Fz90Yf6frz+Zrz60vepxAAAAAOaEk9qZneQ3T8dvVpbltkNfF0Xx35J0T327Ocn5\nR7z0vCS9U18/33OAGevXbro633lyd375rzfk87/w2qyY31T1SAAAAACz2kmdzC7L8h+n+zjV36wo\nivYjvv3RHFxfkiSfS/Luoigai6K4OMnlSb6T5LtJLi+K4uKiKBpy8JLIF3MiHOCsaqqvzR//1LoM\njU7kF//qvkxMTvuPSgAAAAA4SSeM2UVRfH3q80BRFPuO+BgoimLfC7z3tiTfSnJlURSbi6L4mSR/\nUBTFxqIoepK8IckvJklZlvcn+UySB5LcleTflWU5UZbleJL3JLk7yYNJPjP1WoAZ77LlbfnNH7km\n33x8V/7LPz5e9TgAAAAAs1pRlnPvtOD1119f3nvvvVWPAZCyLPPe29bn85u25jP/5pV56YWLqx4J\nAAAAYMYoiuJ7ZVlefzKvPdkLIAF4EYqiyO++c006Fjblfbfdl/6hsapHAgAAAJiVxGyAM2x+U30+\n+e512bZvOL/6dz2Zi/8iBgAAAOBME7MBzoJ1FyzKL7/1yty5cWtu+86zVY8DAAAAMOuI2QBnyb95\n3SV57eVL85Hb788j2waqHgcAAABgVhGzAc6SmpoiH/+JtWlrqst7/vL7GR6bqHokAAAAgFlDzAY4\ni5a3NeXjP3FdHtm2P/+h+4GqxwEAAACYNcRsgLPsh69Ylp973SX5//75mXx+Y1/V4wAAAADMCmI2\nQAV+5a1XZu15C/Lv/7Ynm/ccqHocAAAAgBlPzAaoQENdTT5567pMlsn7P31fxicmqx4JAAAAYEYT\nswEqcuGS1vzOj16be5/ek//05UerHgcAAABgRhOzASr09utW5V0vPS9//NXH8s3Hd1Y9DgAAAMCM\nJWYDVOwjP7I6Fy9tzS/+1X3ZPTha9TgAAAAAM5KYDVCx1sa6fOrWddkzOJYP/PWGlGVZ9UgAAAAA\nM46YDTADrO5YkF+76ap8+aHt+R/feKrqcQAAAABmHDEbYIb46VddlDdfvSIf/fxD2bSlv+pxAAAA\nAGYUMRtghiiKIh97V2cWtzbkvbetz+DIeNUjAQAAAMwYYjbADLKotSGfePd1eXrXYH7jH+6vehwA\nAACAGUPMBphhXnnJkrznjZfnb7+/OX+/fkvV4wAAAADMCGI2wAz0vjdelpdftDi//tmNeWrnYNXj\nAAAAAFROzAaYgepqa/KJd1+XutqavPe29Rkdn6x6JAAAAIBKidkAM1THwub8wbs6s3FLf/7groeq\nHgcAAACgUmI2wAx2w+qV+d9eeWH+768/ma8+vL3qcQAAAAAqI2YDzHC/fvPVuWplW37lMxuyfd9w\n1eMAAAAAVELMBpjhmupr88c/tS6Do+P5xc/cl8nJsuqRAAAAAM46MRtgFrhseVt+85bV+cZju/In\n//h41eMAAAAAnHViNsAs8ZMvOz83d7bnP37xkXzv6T1VjwMAAABwVonZALNEURT5vXeuSfuCprzv\ntvXpHxqreiQAAACAs0bMBphF5jfV55O3rsvWfcP5tb/bmLK0PxsAAAA4N4jZALPMSy5YlF9+6xW5\nY2NfPv3dZ6seBwAAAOCsELMBZqGff92lec1lS/OR2+/Po9sGqh4HAAAA4IwTswFmoZqaIv/xJ9am\ntaEu7/nL9Rkem6h6JAAAAIAzSswGmKWWz2/Kx39ibR7eNpDfvuOBqscBAAAAOKPEbIBZ7PVXLs//\n/tqL8/9++5nctamv6nEAAAAAzhgxG2CW+8ANV6XzvAX54N/0ZMveoarHAQAAADgjxGyAWa6hriaf\nfPe6TEyW+YXb1md8YrLqkQAAAABOOzEbYA64aGlrfudH1+Tep/fkk19+tOpxAAAAAE47MRtgjnjH\nulV510vPy6e++li+9fiuqscBAAAAOK3EbIA55CM/sjoXL23N+/9qfXYPjlY9DgAAAMBpI2YDzCGt\njXX51K3rsmdwLB/8mw0py7LqkQAAAABOCzEbYI5Z3bEgv3rTVfnSg9vzZ998qupxAAAAAE4LMRtg\nDvqXr7oob756eX7vzoeyaUt/1eMAAAAA/MDEbIA5qCiK/MG71mZRa33ed9v6DI6MVz0SAAAAwA9E\nzAaYoxa3NuQTP7kuT+4azIc/d3/V4wAAAAD8QMRsgDnshy5dkve+4bL8zfc25+/Xb6l6HAAAAIAX\nTcwGmOPe96bL87KLFuXXP7sxT+0crHocAAAAgBdFzAaY4+pqa/KJd69LXW1N3vfp9Rkdn6x6JAAA\nAIBTJmYDnANWLWzO7/9YZ3o29+djdz9U9TgAAAAAp0zMBjhH3Hjtyvyvr7wg/+2fnsxXH95e9TgA\nAAAAp0TMBjiH/J83X5OrVrblVz6zIdv3DVc9DgAAAMBJE7MBziFN9bX51K3rMjg6nl/6zIZMTpZV\njwQAAABwUsRsgHPM5Sva8uFbVufrj+3Mf7nn8arHAQAAADgpYjbAOejdLzs/N69pz8e/8Ei+/8ye\nqscBAAAAeEFiNsA5qCiK/O4712Tl/Ka877b16R8aq3okAAAAgBMSswHOUQua6/PJW9elr384v/bZ\njSlL+7MBAACAmUvMBjiHvfTCRfmlt1yRO3r68lfffbbqcQAAAACel5gNcI77tz98aV592ZL85u33\n59FtA1WPAwAAADAtMRvgHFdTU+SPfuK6tDbU5b23rc/w2ETVIwEAAAAcR8wGIMvnN+UPf2JtHto6\nkN+548GqxwEAAAA4jpgNQJLkDVcuz8++5uL8z28/nbs2ba16HAAAAICjiNkAHPbBG6/KmlUL8u//\ntidb9g5VPQ4AAADAYWI2AIc11NXkU7euy/jEZN7/6fUZn5iseiQAAACAJGI2AMe4aGlrfudH1+S7\nT+3JJ7/yWNXjAAAAACQRswGYxjvWrcqPveS8/PFXHs23n9hV9TgAAAAAYjYA0/utt6/ORUta8/5P\n35c9g6NVjwMAAACc48RsAKbV2liXT966LrsHR/OBv9mQsiyrHgkAAAA4h4nZADyva1ctyIfedlW+\n9OD2/Pk3n6p6HAAAAOAcJmYDcEL/6tUX5U1XLc/v3vlQ7u/tr3ocAAAA4BwlZgNwQkVR5GM/vjaL\nWuvz3tvW58DoeNUjAQAAAOcgMRuAF7S4tSF/9JPX5cmdg/nwP9xf9TgAAADAOUjMBuCkvOrSpXnP\nGy7LX39vc/7hvi1VjwMAAACcY8RsAE7aL7zp8lx/4aL8+mc35eldg1WPAwAAAJxDxGwATlpdbU0+\n8e7rUlMk771tfUbHJ6seCQAAADhHiNkAnJLzFrXkD97VmZ7N/fnDLzxc9TgAAADAOULMBuCU3Xht\ne/6XV1yQP73niXzt4e1VjwMAAACcA8RsAF6U/6vrmly5oi2/8tcbsn1guOpxAAAAgDlOzAbgRWmq\nr82nfmpd9o+M55f+akMmJ8uqRwIAAADmMDEbgBftihVt+Y2u1fn6YzvzX+95oupxAAAAgDlMzAbg\nB3Lry8/PzWva8/EvPJz1z+ypehwAAABgjhKzAfiBFEWR333nmqyY35T33rY++4bHqh4JAAAAmIPE\nbAB+YAua6/PJW9elr384v/Z3G1OW9mcDAAAAp5eYDcBp8dILF+WX3nJFunv68pl7n616HAAAAGCO\nEbMBOG1+/ocvzasuXZIPf+7+PLZ9oOpxAAAAgDlEzAbgtKmtKfJHP3ldWhrq8p6/XJ/hsYmqRwIA\nAADmCDEbgNNqxfymfPzH1+ahrQP53TsfrHocAAAAYI4QswE47d5w1fL8zGsuzl986+ncff/WqscB\nAAAA5gAxG4Az4oM3Xpk1qxbkg3/Tk969Q1WPAwAAAMxyYjYAZ0RjXW0+deu6jE9M5v2fvi/jE5NV\njwQAAADMYmI2AGfMRUtb89s/em2+89TufOorj1U9DgAAADCLidkAnFE/uu68vPMlq/Kprzyabz+x\nq+pxAAAAgFlKzAbgjPsPb782Fy5pzfs/fV/2DI5WPQ4AAAAwC4nZAJxxrY11+dSt67JrcCQf+Jue\nlGVZ9UgAAADALCNmA3BWXLtqQT70tqvzpQe35S++9XTV4wAAAACzjJgNwFnzr199Ud541fL8zp0P\n5oHefVWPAwAAAMwiYjYAZ01RFPnYuzqzsLk+77nt+zkwOl71SAAAAMAsIWYDcFYtmdeYT7z7ujy5\nczC/+bn7qx4HAAAAmCXEbADOulddujT/7vWX5TP3bs4/3Lel6nEAAACAWUDMBqAS73/z5XnphYvy\n65/dlKd3DVY9DgAAABtxJN0AACAASURBVDDDidkAVKKutib/6d3XpaZI3nfb+oyOT1Y9EgAAADCD\nidkAVOa8RS35/R/rzIbN/fn4Fx6uehwAAABgBhOzAajU29a056decUH+6z1P5B8f2VH1OAAAAMAM\nJWYDULnf6LomV6yYl1/+zH3ZPjBc9TgAAADADCRmA1C5pvra/PFPvSQDw+P55c9syORkWfVIAAAA\nwAwjZgMwI1yxoi2/ccs1+adHd+ZP/+mJqscBAAAAZhgxG4AZ46defkHedu3K/OHdD2f9M3uqHgcA\nAACYQcRsAGaMoijy0Xd2ZsX8przv0+uzb3is6pEAAACAGULMBmBGWdBSn0/eel169w7n1z+7KWVp\nfzYAAAAgZgMwA730wsX5xTdfnts39Oav791c9TgAAADADCBmAzAj/dvXX5YfumRJPvy5+/PY9oGq\nxwEAAAAqJmYDMCPV1hT5xLuvS3NDbd7zl+szPDZR9UgAAABAhcRsAGasFfOb8oc/3pmHtg7k9+58\nsOpxAAAAgAqJ2QDMaG+8akV+5jUX58+/9XS+cP/WqscBAAAAKiJmAzDjffDGK3Ptqvn54N/2pK9/\nqOpxAAAAgAqI2QDMeI11tfnUrS/J2PhkfuHT92Visqx6JAAAAOAsE7MBmBUuXtqa//COa/OdJ3fn\nU195tOpxAAAAgLNMzAZg1njnS87LO9etyie//Gj++YldVY8DAAAAnEV1VQ8AAKfit95xbb7/zJ78\n3P+8Ny0NddnaP5yOhc35wA1X5h3rVlU9HgAAAHCGOJkNwKwyr7EuP/aS89I/NJ6+/uGUSbbsHcqv\n/t3G/P36LVWPBwAAAJwhYjYAs86nv/vscc+GxibysbsfrmAaAAAA4Gw4YzG7KIr/XhTF9qIoNh3x\nbHFRFF8siuLRqc+Lpp4XRVF8siiKx4qi6CmK4iVHvOenp17/aFEUP32m5gVg9ujdOzTt8y17h/Lo\ntoGzPA0AAABwNpzJk9l/luTGY559KMmXy7K8PMmXp75PkrcluXzq4+eS/ElyMH4n+XCSVyR5eZIP\nHwrgAJy7OhY2P++vveWP7skNf3RPPvXlR/PkzsGzOBUAAABwJp2xmF2W5T1Jdh/z+O1J/nzq6z9P\n8o4jnv9FedC3kywsiqI9yQ1JvliW5e6yLPck+WKOD+QAnGM+cMOVaa6vPepZc31tfuvt1+QjP7I6\n85vr8vEvPpI3/OHXcvMn/yl/8rXH8+zuAxVNCwAAAJwOdWf591tRlmVfkpRl2VcUxfKp56uSHLkA\ndfPUs+d7fpyiKH4uB09154ILLjjNYwMwk7xj3cH/FHzs7ofTu3coHQub84Ebrjz8/KdfdVH6+ody\nR09funv68vt3PZTfv+uhrD1/YW7pbM/Nne1pX/D8p7sBAACAmedsx+znU0zzrDzB8+MfluWfJvnT\nJLn++uunfQ0Ac8c71q06HK+n076gOT/72kvys6+9JM/uPpA7Nvbl9g29+e07Hsxv3/Fgrr9wUbo6\n23NTZ3uWtzWdxckBAACAF+Nsx+xtRVG0T53Kbk+yfer55iTnH/G685L0Tj1//THPv3YW5gRgDjl/\ncUt+/ocvzc//8KV5cudgujf0prunL795+wP5SPcDecXFi9PV2ZG3XbsyS+Y1Vj0uAAAAMI2iLM/c\nIeaiKC5K0l2W5bVT338sya6yLD9aFMWHkiwuy/KDRVHcnOQ9SW7KwcseP1mW5cunLoD8XpKXTP3I\n7yd5aVmWx+7iPsr1119f3nvvvWfkzwTA3PHotoHc3tOX7p7ePLFjMLU1RV516ZJ0dbbnhtUrs7Cl\noeoRAQAAYE4riuJ7ZVlef1KvPVMxuyiK23LwVPXSJNuSfDjJ3yf5TJILkjyT5MfLstxdFEWR5I9z\n8HLHA0n+VVmW9079nH+d5NemfuzvlGX5P17o9xazATgVZVnmwb6BdPccPLH9zO4Dqa8t8trLl6Wr\nsz1vuWZF2prqqx4TAAAA5pwZEbOrJGYD8GKVZZmNW/rT3dOXO3r6smXvUBrqavL6K5ala21H3nz1\n8rQ0zJQrJwAAAGB2E7PFbABOg8nJMuuf3Zvunt7c0dOX7QMjaaqvyZuuWpGuzva84arlaaqvrXpM\nAAAAmLXEbDEbgNNsYrLMd5/ane6e3nx+49bsGhxNa0Nt3nzNinR1duR1VyxNY52wDQAAAKdCzBaz\nATiDxicm8+0nDobtu+7fmr0HxtLWVJe3XrMyXWvb85rLlqa+tqbqMQEAAGDGE7PFbADOkrGJyXz9\nsZ3p3tCXLzywNQPD41nYUp8bV69MV2dHXnnJ4tQJ2wAAADAtMVvMBqACI+MTueeRnenu6c2XHtiW\nwdGJLJ3XkBuvPRi2X37R4tTUFFWPCQAAADOGmC1mA1Cx4bGJfPWh7enu6cuXH9qW4bHJrJjfmJvW\ntKersyMvuWBhikLYBgAA4NwmZovZAMwggyPj+fJD29O9oTdfe2RHRscns2phc27ubE9XZ3vWrFog\nbAMAAHBOErPFbABmqH3DY/nSA9ty+4be/NOjOzM+WebCJS25eerE9tXtbcI2AAAA5wwxW8wGYBbY\ne2A0d9+/Nd09ffnm47syMVnmkmWt6ersyC2d7bl8RVvVIwIAAMAZJWaL2QDMMrv2j+Tzm7amu6c3\n//zk7pRlcuWKtnR1tqdrbUcuXtpa9YgAAABw2onZYjYAs9j2fcO5c2Nfunv6cu/Te5Ikqzvm55a1\nHbl5TXvOX9xS8YQAAABweojZYjYAc0Tv3qHcubEvt/f0ZcOze5Mk152/MF2d7bm5sz3tC5ornhAA\nAABePDFbzAZgDnp294F09/Slu6c39/fuS5K87KJF6ersyNvWrMzytqaKJwQAAIBTI2aL2QDMcU/s\n2J87eg6uInl420BqiuQVFy9J19r2vO3a9ixubah6RAAAAHhBYraYDcA55JFtA+ne0Jvunr48sXMw\ntTVFXnXpktzS2ZEbVq/Mgpb6qkcEAACAaYnZYjYA56CyLPNA377Dq0ie3T2U+toir718Wbo62/OW\na1akrUnYBgAAYOYQs8VsAM5xZVmmZ3N/unt6c0dPX3r7h9NQV5PXX7Est6ztyJuuXp6WhrqqxwQA\nAOAcJ2aL2QBw2ORkmfXP7sntG/py58a+bB8YSXN9bd549fLc0tme11+5PE31tVWPCQAAwDlIzBaz\nAWBaE5NlvvvU7nT39ObzG7dm1+BoWhtq85ZrVqSrsyOvvWJpGuuEbQAAAM4OMVvMBoAXND4xmW8/\ncTBs33X/1uw9MJa2prrcsHplujrb8+rLlqa+tqbqMQEAAJjDxGwxGwBOydjEZL7+2M50b+jLF+7f\nmoGR8Sxqqc+N165MV2dHXnnJktTWFFWPCQAAwBwjZovZAPCiDY9N5J5HdqS7py9fenBbDoxOZOm8\nhrzt2vZ0dbbnZRctTo2wDQAAwGkgZovZAHBaDI1O5KsPb093T2++8tD2DI9NZsX8xty0pj23rO3I\nuvMXpiiEbQAAAF4cMVvMBoDTbnBkPF96cFu6e/ryjw/vyOjEZFYtbE5XZ3u6Ojty7ar5wjYAAACn\nRMwWswHgjNo3PJYv3r8t3T29+adHd2Z8ssyFS1oOh+2rVrYJ2wAAALwgMVvMBoCzZu+B0dx9/9Z0\n9/Tlm4/vysRkmUuXtaarsyO3rG3PZcvbqh4RAACAGUrMFrMBoBK79o/k85u2prunN//85O6UZXLV\nyrbDJ7YvWtpa9YgAAADMIGK2mA0Aldu+bzh3buxLd09f7n16T5Lk2lXz09XZkZvXtOf8xS0VTwgA\nAEDVxGwxGwBmlN69Q7mjpy/dPb3ZsLk/SXLd+QsPn9heuaCp4gkBAACogpgtZgPAjPXMrgPp3tib\n7g19eaBvX4oiedmFi9O1tj1vu7Y9y9oaqx4RAACAs0TMFrMBYFZ4Ysf+dE+d2H5k2/7UFMkrL1mS\nrs6O3Hjtyixubah6RAAAAM4gMVvMBoBZ55FtA+ne0Jvunr48sXMwtTVFXn3Z0nR1tueGa1ZmQUt9\n1SMCAABwmonZYjYAzFplWeaBvn2HT2w/u3so9bVFXnf5snStbc+br16RtiZhGwAAYC4Qs8VsAJgT\nyrJMz+b+3L6hN3ds7Etf/3Aa6mryhiuXpauzI2+6enlaGuqqHhMAAIAXScwWswFgzpmcLPP9Z/ak\nu6cvd2zsy46BkTTX1+aNVy/PLZ3tef2Vy9NUX1v1mAAAAJwCMVvMBoA5bWKyzHee3J3unt58ftPW\n7B4czbzGurzlmhXp6mzPay9floa6mqrHBAAA4AWI2WI2AJwzxicm860ndqV7Q1/uun9r+ofGMr+p\nLjesXpmutR151aVLUl8rbAMAAMxEYraYDQDnpNHxyXzjsZ25vac3X7x/WwZGxrOopT43XtueWzrb\n84pLlqS2pqh6TAAAAKaI2WI2AJzzhscmcs8jO9Ld05cvPbgtB0YnsnReY25aszJdnR25/sJFqRG2\nAQAAKiVmi9kAwBGGRifylYe2p7unN195aHtGxiezcn5TblrTnq617Vl3/sIUhbANAABwtonZYjYA\n8Dz2j4znyw9uy+0b+nLPIzsyOjGZVQub09XZnq7Ojly7ar6wDQAAcJaI2WI2AHAS+ofG8sUHtqW7\npzdff3RnxifLXLSkJTdPhe2rVrYJ2wAAAGeQmC1mAwCnaM/gaO6+f2u6e/ryzcd3ZrJMLls+7/CJ\n7cuWz6t6RAAAgDlHzBazAYAfwM79I/n8pq3p3tCb7zy1O2WZXLWyLbes7UhXZ3suXNJa9YgAAABz\ngpgtZgMAp8m2fcO5c2Nfunv68r2n9yRJ1qxakK7O9tzc2Z7zFrVUPCEAAMDsJWaL2QDAGbBl71Du\n6OlNd09fejb3J0nWXbAwXZ0duXlNe1YuaKp4QgAAgNlFzBazAYAz7Oldg+nuOXhi+8G+fSmK5GUX\nLk7X2va87dr2LGtrrHpEAACAGU/MFrMBgLPo8R37072hL909vXl0+/7UFMkrL1mSrs6O3Hjtyixu\nbah6RAAAgBlJzBazAYCKPLx1IN1Tq0ie3DmY2poir75sabo623PD6pVZ0Fxf9YgAAAAzhpgtZgMA\nFSvLMvf37ptaRdKbzXuG0lBbk9ddsTRdnR158zUrMq+xruoxAQAAKiVmi9kAwAxSlmU2bO5P94be\n3LGxL339w2msq8kbrlyerrXteeNVy9PSIGwDAADnHjFbzAYAZqjJyTLff2ZPbt/Qmzs3bc2OgZE0\n19fmTVcvT1dnR15/5bI01ddWPSYAAMBZIWaL2QDALDAxWeafn9yV7p6+3LVpa3YPjmZeY13ecs2K\ndHW257WXL0tDXU3VYwIAAJwxYraYDQDMMuMTk/nm47vS3dObuzZtzb7h8cxvqssNq1ema21HXnXp\nktTXCtsAAMDcImaL2QDALDY6PpmvP7Yj3Rv68oUHtmX/yHgWtdTnxmvbc0tne15xyZLU1hRVjwkA\nAPADE7PFbABgjhgem8g/PrIj3T19+dID2zI0NpGl8xpz05qVuWVtR156waLUCNsAAMAsJWaL2QDA\nHDQ0OpGvPLQ93T29+cpD2zMyPpmV85tyc2d7ujrbc935C1MUwjYAADB7iNliNgAwx+0fGc+XH9yW\n2zf05Z5HdmR0YjLnLWrOzZ3tuaWzI6s75gvbAADAjCdmi9kAwDmkf2gsX7h/a7p7+vKNx3ZmfLLM\nRUta0tXZka617blyRZuwDQAAzEhitpgNAJyj9gyO5q77t6a7pzffenxXJsvksuXz0tXZnq7Ojly2\nfF7VIwIAABwmZovZAADZMTCSuzb15faevnz3qd0py+SqlW25ZW1Hujrbc+GS1qpHBAAAznFitpgN\nAHCUrf3DuXNjX7p7evP9Z/YmSdasWpCuzvbc3Nme8xa1VDwhAABwLhKzxWwAgOe1ec+BqbDdl57N\n/UmSdRcszC2dHbm5sz0r5jdVPCEAAHCuELPFbACAk/L0rsF09xwM2w/27UtRJC+7aHFu6WzP29a0\nZ+m8xqpHBAAA5jAxW8wGADhlj23fnzt6+nJ7T28e274/NUXyQ5cuSVdnR25cvTKLWhuqHhEAAJhj\nxGwxGwDgRSvLMg9vG0j3hoM7tp/adSB1NUVefdnSdHW2562rV2ZBc33VYwIAAHOAmC1mAwCcFmVZ\n5v7efbm9pzfdG/qyZe9QGmpr8rorlqarsyNvvmZF5jXWVT0mAAAwS4nZYjYAwGlXlmXue3Zvunv6\nckdPX7buG05jXU3ecOXydK1tz5uuWpHmhtqqxwQAAGYRMVvMBgA4oyYny3zvmT3p3tCbOzZuzc79\nI2mur82brl6ers6OvP7KZWmqF7YBAIATE7PFbACAs2Zissw/P7kr3T19uWvT1uweHM28xrq89ZoV\n6VrbntdctiwNdTVVjwkAAMxAYraYDQBQibGJyXzr8V3p7unNXZu2Zt/weBY01+eG1SvS1dmRV126\nJHW1wjYAAHCQmC1mAwBUbnR8Mv/06I509/Tliw9sy/6R8SxubciN165MV2d7XnHxktTWFFWPCQAA\nVEjMFrMBAGaU4bGJfO3hHenu6c2XH9yeobGJLGtrzE3XrkzX2o689IJFqRG2AQDgnCNmi9kAADPW\ngdHxfOWh7ene0JevPrw9I+OTaV/QlJvWtKersz3Xnb8wRSFsAwDAuUDMFrMBAGaF/SPj+dID29Ld\n05t/fGRHxibKnLeoOTd3tueWzo6s7pgvbAMAwBwmZovZAACzTv/QWL5w/9Z09/TlG4/tzPhkmYuX\ntqarsz1dnR25cmVb1SMCAACnmZgtZgMAzGp7Bkdz1/1bc/uG3nz7iV2ZLJPLl89LV2dHuta259Jl\n86oeEQAAOA3EbDEbAGDO2DEwks9v6kv3hr589+ndKcvk6vb56ZpaRXLBkpaqRwQAAF4kMVvMBgCY\nk7b2D+eOjX3p7unN+mf2Jkk6z1uQrs723NzZkVULmyueEAAAOBVitpgNADDnbd5zIHf09KW7py8b\nt/QnSV5ywcJ0dXbk5s72rJjfVPGEAADACxGzxWwAgHPKUzsHc8fGvty+oTcPbR1IUSQvu2hxbuls\nz9vWtGfpvMaqRwQAAKYhZovZAADnrMe27093T2+6e/ry2Pb9qSmSV126NF2d7bnx2pVZ2NJQ9YgA\nAMAUMVvMBgA455VlmYe3DaR7Q19u7+nN07sOpK6myGsuX5quzo68dfWKzG+qr3pMAAA4p4nZYjYA\nAEcoyzKbtuw7fGJ7y96hNNTW5HVXLMsta9vzpqtXZF5jXdVjAgDAOUfMFrMBAHgeZVlm/bN7072h\nL3du7MvWfcNprKvJG69anq7OjrzxquVpbqitekwAADgniNliNgAAJ2Fyssy9T+9Jd09v7ty4NTv3\nj6SloTZvunpFujrb88NXLEtTvbANAABnipgtZgMAcIomJsv88xO7cntPX+7a1Jc9B8bS1liXt1yz\nIl1r2/Oay5aloa6m6jEBAGBOEbPFbAAAfgBjE5P55uO70r2hN3ffvzX7hsezoLk+N65ema617fmh\nS5akrlbYBgCAH5SYLWYDAHCajIxP5OuP7sztG3rzxQe2ZXB0IktaG3LjtSvT1dmRl1+8OLU1RdVj\nAgDArCRmi9kAAJwBw2MT+drD23N7T1++8uD2DI1NZFlbY25e056uzva85IJFqRG2AQDgpInZYjYA\nAGfYgdHxfPnB7enu6c1XH96R0fHJtC9oOhi213Zk7XkLUhTCNgAAnIiYLWYDAHAWDQyP5UsPbkv3\nhr7c8+iOjE2UOX9xc25e05Guzvas7pgvbAMAwDTEbDEbAICK9B8Yy90PbE13T1++8djOTEyWuXhp\na7o623PL2o5csaKt6hEBAGDGELPFbAAAZoDdg6O5a9PWdPf05ttP7MpkmVyxYl66Og+e2L5k2byq\nRwQAgEqJ2WI2AAAzzPaB4YNhe0NfvvPU7iTJNe3z07W2PV1rOnLBkpaKJwQAgLNPzBazAQCYwfr6\nh3JHT1+6e/py37N7kyRrz1uQrs6O3NzZno6FzRVPCAAAZ4eYLWYDADBLPLv7QO7Y2Jfunt5s2rIv\nSfLSCxelq7M9N69pz/L5Tfn79VvysbsfTu/eoXQsbM4Hbrgy71i3quLJAQDgBydmi9kAAMxCT+0c\nTHdPb7p7+vLQ1oEURXLJktY8s+dAxiae+3t7c31tfu+dawRtAABmPTFbzAYAYJZ7bPtAbt/Ql//8\n1ccyPnn839nnNdbmfW+6PMvaGrNsXtPBz22NWdhcn5qaooKJAQDg1InZYjYAAHPExR+6I6fyN/a6\nmiJL5jVMRe7Gw5F72bzGLD3m2bzGuhSF8A0AQHVOJWbXnelhAACAF69jYXO27B067vmqhU35/Ptf\nlx0DI9kxMJKd+0cOf71jYCQ79o9k+8BI7u/dl12Do5mY5nR3U33Nc6H7yPB9TPReOq8xTfW1Z+OP\nCwAAz0vMBgCAGewDN1yZX/27jRkamzj8rLm+Nh+44arMb6rP/Kb6XLps3gl/xuRkmT0HRrPj2OB9\nKILvH8lTuwbz3ad2Z8+BsWl/RltT3fGnvduOiODzGrO8rTGLWxtSV1tzWv9nAAAAiZgNAAAz2qFL\nHj9298Pp3TuUjoXN+cANV57S5Y81NUWWzGvMknmNuWrliV87Oj6ZXYMj2Tkwmh37h4877b1j6rT3\njoGR7B8ZP+79RZEsaW04KnJPd+J76bzGLGypt+YEAICTZmc2AADwohwYHT8+eu8fPSp+75z6enRi\n8rj319cW00bvpfOOj9+tjc7hAADMRXZmAwAAZ1xLQ10uWFKXC5a0nPB1ZVlm39D4c2tOptnv3dc/\nnJ4t/dm1fyTTrPdOS0Ptc6H7+U57tzVm6byGNNbZ7w0AMBeJ2QAAwBlVFEUWtNRnQUt9Llt+4v3e\nE5Nldg+OHhW9j73c8rEd+/OtJ3alf2j6/d4LmutP6rT34taG1NZYcwIAMFuI2QAAwIxRW1Mcjs4v\nZGR8IruOWWty1MWWAyPZsHlvtu8bOeoCzUNqimRx6/GR+7kA3pDlbY1ZNq8p85vr7PcGAKiYmA0A\nAMxKjXW16VjYnI6FzS/42sGR8aP3eE+z6uTRbQPZuX8kYxPH7zlpqK05vMrkYPRumGbdSVOWtjWk\npcH/mQUAcCb4WxYAADDntTbWpbWxLhctbT3h68qyTP/Q2LSnvQ99vXnPgdz37J7sGhxNOc1+73mN\ndVk6r+EEJ74Pfl7S2piGupoz9CcGAJh7xGwAAIApRVFkYUtDFrY05PIVbSd87fjE5MH93tME70Mf\nD28dyNcHdmbf8Pi0P2NRS/1R0Xvpsae9p54vamlIjf3eAMA5TswGAAB4Eepqa7J8flOWz296wdcO\nj00cfZHl/pHsHBjNjv3Dh59975k92TEwkuGxyePeX1tTZEnrC5/2XtbWmLZG+70BgLlJzAYAADjD\nmuprc96ilpy3qOWEryvLMvtHxrPzyIstB4aPudxyNA/1HdzvPT55/J6Txrqa4yP3cfu9D35uqq89\nU39kAIDTTswGAACYIYqiSFtTfdqa6nPxC+z3npwss/eo/d7DU6e9nwvfz+w6kO89vSe7B0en/Rlt\njXXPXWx5ZPQ+Jn4vaW1IXa393gBAtcRsAACAWaimpsji1oYsbm3IlStPvN977NB+74Hn2e+9fyQP\n9u7LPQMjGRg5fr93USSLWxqOW2ky3bqThc319nsDAGeEmA0AADDH1dfWZMX8pqw4if3eQ6MH93tv\nP7zW5Pj4/eTOwezYP5LR8eP3e9fVFNMG76XzGrKsremo+N3aUGu/NwBw0sRsAAAADmtuqM35i1ty\n/uIX3u89MDJ+9Gnvw5dbHvy8bd9wNm3pz879I5lmvXea62uPCN2H4nfTMae9G7J0nv3eAICYDQAA\nwItQFEXmN9VnflN9Ll0274SvnZgss+fA6NEnvY9Zd/LEjsF858nd2XNgbNqfMb+p7ojI3ZRl8xqz\ntK1hmv3ejam15gQA5iQxGwAAgDOqdmr1yNJ5jS/42tHxyewaHDnuxPfO/c+F742b92bHwEgGRyeO\ne39NkSxuPea09/Ncbrmgud6aEwCYRSqJ2UVRPJVkIMlEkvGyLK8vimJxkr9KclGSp5L8RFmWe4qD\nf7P4T0luSnIgyb8sy/L7VcwNAADAmdVQV5P2Bc1pX9D8gq8dHBnPzv3Pf9r70InvHQMjGZ04fr93\nfW1xVNw+0eWWLQ3OggFA1ar8r/EbyrLcecT3H0ry5bIsP1oUxYemvv/3Sd6W5PKpj1ck+ZOpzwAA\nAJzDWhvr0tpYlwuXtJ7wdWVZZt/QeHbsHz7iYsvRo+L3lr3Due/Z/uwenH6/d0tD7fGRe97xEXzp\nvMY01NWcoT8xAJzbZtL/a/ntSV4/9fWfJ/laDsbstyf5i7IsyyTfLopiYVEU7WVZ9lUyJQAAALNK\nURRZ0FKfBS31uWx52wlfOzFZZvfg6HEnvI+83PLR7fvzzcd3pX9o+v3eC1vqpw3dx572XtTSYL83\nAJyCqmJ2meQLRVGUSf5rWZZ/mmTFoUBdlmVfURTLp167KsmzR7x389Szo2J2URQ/l+TnkuSCCy44\nw+MDAAAwF9XWFIdj8wsZGZ846oT3dOtO7nv24H7vobHp93svmXd85D54ueXRz+c31dnvDcA5r6qY\n/eqyLHungvUXi6J46ASvne6/1sf9o6+pIP6nSXL99ddP84/CAAAA4PRprKvNqoXNWbXw5PZ7T3fa\n+3AA3z+SR7YNZMfASMan2XPSUFcz/WnvI6L38qlfa26oPRN/XACoXCUxuyzL3qnP24ui+GySlyfZ\ndmh9SFEU7Um2T718c5Lzj3j7eUl6z+rAAAAA8AM4tN/7oqUn3u89OVmmf2js8EqT6VadbN5zIPc9\nuye7BkdTTnOUa15j3bRrTZbOa5h63pRlbY1ZMq8h9bX2ewMwe5z1mF0URWuSmrIsB6a+fmuS30ry\nuSQ/neSjU5//go1VswAAEU9JREFUYeotn0vynqIoPp2DFz/225cNAADAXFRTU2RRa0MWtTbkihUn\n3u89PjGZ3YOjBy+13D/Nae+BkTy4dV/ueXQkA8Pj0/6Mxa0NU2tNGqZZd9J0OIIvamlIjf3eAFSs\nipPZK5J8dmrXV12SvyzL8q6iKL6b5DNFUfxMkmeS/PjU6+9MclOSx5IcSPKvzv7IAAAAMLPU1dZk\n+fymLJ/f9IKvHR6bOG6tybEnvr/3zJ5s3zeSkfHJ495fW1MccbL7yNPex19uOa/xB9vv/ffrt+Rj\ndz+c3r1D6VjYnA/ccGXesW7Vi/55AMwdRTndv0ma5a6//vry3nvvrXoMAAAAmFXKssz+Q/u9j4je\nR11uefjZaCam2e/dVF/zXOh+nv3ehyJ4U/3R+73/fv2W/OrfbTzqwszm+tr83jvXCNoAc1RRFN8r\ny/L6k3ltVRdAAgAAADNMURRpa6pPW1N9Llk274SvnZwss3do7IjIPXzM5ZajeXrXgdz79J7sHhyd\n9me0NR293/urD28/KmQnydDYRD76+Ydy05r2NNTZ8Q1wLnMyGwAAADijxiYms2v/6OHovXNgdNpV\nJ0/uHDzhz2lpqM2C5vrDHwtb6rOwuSELWo5+tqB56nlzfRa01Ketsc7Ob4AZyslsAAAAYMaor63J\nygVNWbmgKcmC533dqz/6lWzZO3Tc8wXN9fnZ11yc/qGx7B0aS//QWPoPjOXJnYPpH9qbvQfGpt31\nfUhNkcxvrs/CQyG8pWEqeD8XwOcf9X3D4Sh+7CoUAKojZgMAAAAzwgduuHLandkf+ZHVL7gze3hs\n4mDkHhrL3gOHPo8e/2zq+2d2DR7+tWlWfx/WWFdz1InvBVMnvg+fAD/qVPhzkXx+c31qnQYHOK3E\nbAAAAGBGOBSsP3b3w+ndO5SOhc35wA1XntTlj031tWmqr82K+U2n9HtOTpbZPzqe/gPPRe+9Q6OH\nv953VAgfzZa9Q3mgtz/9Q2MZHJ044c9ua6o7bvXJ/MPrUY49FX5wXcrC5vq0NNSmKIRwgGOJ2QAA\nAMCM8Y51q04qXp8uNTVF5jfVZ35Tfc4/xfeOjk9m3/Ch2D16zKnwscMnvw+dEt/av+/wr42f4Dh4\nXU1x1OqTQye+j9sLfsxp8QXN9S7JBOY0MRsAAADgRWioq8nSeY1ZOq/xlN5XlmUOjE4cXHkydRJ8\n3zSrUA6dFt8+MJxHtg2kf2gsA8PjJ/zZLQ21B099tzRkQXPd4YswD8fxYy7IXNhy8JLMeQ0uyQRm\nPjEbAAAA4CwqiiKtjXVpbazLqoXNp/Te8YnJDAyPHw7eR+4FPxjGjzwVPpondu6fWp0yltEXuCTz\n8OnvaS7IPG4v+BHPXJIJnC1iNgAAAMAsUVdbk0WtDVnU2nDK7z10SebJXJDZf2A0z+wazN6hg3vD\nX+iSzJPaC35MJHdJJnCqxGwAAACAc8APcknmwMj44VUoe4/ZD95/xLqU/qGxbN5zIA/0HgzjB07i\nksyjVp8c/nr6veCHvndJJpybxGwAAAAAnldNTXF4pcj5i0/tvaPjk4dXnrzQBZn9Q2Pp7R86vCv8\nRJdk1tcWU4G77qgT30ftBT8ihB+5FqW+1iWZMFuJ2QAAAACcEQ11NVnW1phlbad+Sebg6MTR61CO\nWYVyMIgf/LVt+6YuyTwwloGRE1+S2dpQm4UtU+tQjj0B3nLM5ZjNzz1va6xzGhwqJmYDAAAAMKMU\nRZF5jXWZ9yIvydw3PP78e8GPuCCzf2gsj+/YfziSn+iSzNqaIvOb6qYN4c+dCj86hB967pJMOD3E\nbAAAAADmjLramixubcji1oYkraf03uGxiaMuyNx7xE7wg8F7NP1D4wd/7cBonto1eDiWlye4JLOp\nvuaF94Ifc0Hmwpb6tDW5JBOOJGYDAAAAQA5ekrlyQW1WLngRl2QeOg0+3QWZR5wS33tgLM/uPpBN\nU18PjT3/JZlFkbQ11h114nva9ShH7AU/9Lm53iWZzD1iNgAAAAD8AGpqioMnrlvqc0FaTum9I+MH\nd4Pvm2YVyt7Dz587Jb5lz9DhX5s4wSWZDbU1R1+IecT+70PfH4rkC45Zi+KSTGYqMRsAAAAAKtJY\nV5vlbbVZ3nZqp8EPXZJ5Mhdk7j0wlq37hvPQ1oHsG3rhSzLnNdY9d/nlob3gh0+FT3NB5tT381yS\nyRkmZgMAAADALHPkJZnnLTq19x66JPPw6pMjY/gR+8EPnRZ/bPv+w68ZnTjxJZlHnvA+/lT4EXvB\nW44+Ld5Y55JMXpiYzf/f3t3H+lmedQD/XrSn62kpa4TF8LINNYZo5kK3BqNM4swyJi6K2RZ8mYtz\n2YK6uYlBRzTEt/kPy5z/oQOCc2TGZYwIGmEGECcOGLRAZ8UYQbSQsQZaKJRRyuUffXp6euzLOdDT\n38M5n09y0uf3nOd+nutpkzvwzf27bgAAAACWkYM3yZy/7s7ze16aCbtn+oIftEHmgUD8yWdfyMPb\nn82O5/bk6eePvEnm9NSKI/cFnxWEHwjJV2Xd6pU5wSaZy4YwGwAAAAA4qqrK9KoVmV718jfJnBt4\nz+4LPvv8o08+N3N8tE0yT1o9d0PMWe1Rpuf0BZ8VhK+eOkFblFcZYTYAAAAAsKhmb5K5UPs3yfz/\nrVD2rwx/4aBe4due2j3z+WibZB68IeZh+oLPbZcyPZWVx2iTzBs2bcsVNz+Ux3bszmnrp3Pp+Wfl\nwg2nH5N7L0XCbAAAAABgtF7JJpm7vvPiTMj99BCAH6ov+M7de/LYjuez9fFnsnP3nuya5yaZ69fM\nXRW+as4K8AP9w9evWZW1q1bMrAa/YdO2XHb9gzMrz7ft2J3Lrn8wSQTahyHMBgAAAACWnKrKutVT\nWbd6asGbZO7Z+9JM+H3wqvAXsnP3gXYp+8//x7d2zXw+0iaZK4dNMl87PZX/eeq57Nl78Mrx3Xv2\n5oqbHxJmH4YwGwAAAABglqkVJ+TkE1+Tk098zYLGdXd279l7cDuUmVXhB/cF/6/tzx7yHo/t2H0s\nXmFJEmYDAAAAABwDVZU1q1ZmzaqVOfW100e8dtOjt2bbIYLr09Yfedxydmw6lQMAAAAAMG+Xnn9W\npqdWHHRuempFLj3/rAlVNH5WZgMAAAAAHGf7+2JfcfNDeWzH7py2fjqXnn+WftlHIMwGAAAAAJiA\nCzecLrxeAG1GAAAAAAAYPWE2AAAAAACjJ8wGAAAAAGD0hNkAAAAAAIyeMBsAAAAAgNETZgMAAAAA\nMHrCbAAAAAAARk+YDQAAAADA6AmzAQAAAAAYPWE2AAAAAACjJ8wGAAAAAGD0hNkAAAAAAIyeMBsA\nAAAAgNETZgMAAAAAMHrCbAAAAAAARk+YDQAAAADA6AmzAQAAAAAYPWE2AAAAAACjJ8wGAAAAAGD0\nhNkAAAAAAIyeMBsAAAAAgNETZgMAAAAAMHrCbAAAAAAARk+YDQAAAADA6AmzAQAAAAAYveruSddw\nzFXVt5P896TrmKBTkmyfdBEAx4k5D1hOzHnAcmLOA5aT5TznvbG7XzefC5dkmL3cVdU3unvjpOsA\nOB7MecByYs4DlhNzHrCcmPPmR5sRAAAAAABGT5gNAAAAAMDoCbOXpr+YdAEAx5E5D1hOzHnAcmLO\nA5YTc9486JkNAAAAAMDoWZkNAAAAAMDoCbMBAAAAABg9YfYSUlXXVNUTVbVl0rUALKaqen1V3VZV\nW6vqm1X18UnXBLCYqmp1Vd1dVfcP894fTLomgMVUVSuqalNV3TTpWgAWW1U9UlUPVtXmqvrGpOsZ\nMz2zl5CqOi/JriSf7+43TboegMVSVacmObW776uqdUnuTXJhd//bhEsDWBRVVUnWdveuqppK8rUk\nH+/ur0+4NIBFUVWXJNmY5KTufvek6wFYTFX1SJKN3b190rWMnZXZS0h335HkyUnXAbDYuvvx7r5v\nOH4mydYkp0+2KoDF0/vsGj5ODT9WpQBLUlWdkeSnklw16VoAGBdhNgCvalV1ZpINSe6abCUAi2v4\nyv3mJE8k+Wp3m/eApeqzSX47yUuTLgTgOOkkt1TVvVX1kUkXM2bCbABetarqxCRfTvKJ7n560vUA\nLKbu3tvdZyc5I8k5VaWtHLDkVNW7kzzR3fdOuhaA4+jc7n5Lkp9M8utDK2EOQZgNwKvS0DP2y0mu\n6+7rJ10PwPHS3TuS3J7kXRMuBWAxnJvkp4f+sX+d5Ceq6guTLQlgcXX3Y8OfTyT5SpJzJlvReAmz\nAXjVGTZCuzrJ1u7+zKTrAVhsVfW6qlo/HE8neUeSf59sVQDHXndf1t1ndPeZSX4uya3d/f4JlwWw\naKpqbVWt23+c5J1Jtky2qvESZi8hVfXFJP+a5Kyq+t+q+tCkawJYJOcm+aXsW6mzefi5YNJFASyi\nU5PcVlUPJLkn+3pm3zThmgAAeOW+O8nXqur+JHcn+bvu/ocJ1zRa1W0TdAAAAAAAxs3KbAAAAAAA\nRk+YDQAAAADA6AmzAQAAAAAYPWE2AAAAAACjJ8wGAAAAAGD0hNkAALBAVXV7VW08Ds/5jaraWlXX\nLWZdVXV2VV2w8AoX/Jzj8vcGAMDSJMwGAIDjqKpWLuDyX0tyQXf/4mLVMzg7yYLC7AW+BwAAvGLC\nbAAAlqSqOnNY1fy5qvpmVd1SVdPD72ZWCFfVKVX1yHD8y1V1Q1XdWFUPV9VHq+qSqtpUVV+vqu+a\n9Yj3V9WdVbWlqs4Zxq+tqmuq6p5hzM/Muu+XqurGJLccotZLhvtsqapPDOeuTPK9Sf62qn5zzvUr\nqurTVfVgVT1QVR87xD13zTp+b1VdOxy/b3jO/VV1R1WtSvKHSS6qqs1VddF836OqTh3usXm454/N\n89/mhKr6y6r64/lcDwAASWI1BQAAS9n3J/n57v5wVf1Nkvck+cJRxrwpyYYkq5P8Z5Lf6e4NVfWn\nST6Q5LPDdWu7+0er6rwk1wzjfjfJrd39K1W1PsndVfWPw/U/kuTN3f3k7IdV1VuTfDDJDyepJHdV\n1T9198VV9a4kb+/u7XNq/EiS70myobtfnBOyH83lSc7v7m1Vtb67X6iqy5Ns7O6PDjX9yXzeo6p+\nK8nN3f2pqlqRZM08nr8yyXVJtnT3pxZQNwAAy5yV2QAALGUPd/fm4fjeJGfOY8xt3f1Md387yc4k\nNw7nH5wz/otJ0t13JDlpCH3fmeSTVbU5ye3ZF4i/Ybj+q3OD7MHbknylu5/t7l1Jrk9ytBXO70hy\nZXe/ONRwqPsezr8kubaqPpxkxWGume973JPkg1X1+0l+qLufmcfz/zyCbAAAXgZhNgAAS9l3Zh3v\nzYFvJr6YA/8tvPoIY16a9fmlHPzNxp4zrrNvZfV7uvvs4ecN3b11+P2zh6mxjvwKhx0z9/lzzf79\nzDt298VJfi/J65NsrqqTD3P/o77HEOSfl2Rbkr+qqg/Mo/Y7k7y9qub+vQMAwBEJswEAWI4eSfLW\n4fi9L/MeFyVJVb0tyc7u3pnk5iQfq6oafrdhHve5I8mFVbWmqtYm+dkk/3yUMbckuXj/JoyHaTPy\nrar6gao6Ybhnhmu/r7vv6u7Lk2zPvlD7mSTrZo2d13tU1RuTPNHdn0tydZK3DOc/v7+P+CFcneTv\nk3zJJpIAACyEMBsAgOXo00l+taruTHLKy7zHU8P4K5N8aDj3R0mmkjxQVVuGz0fU3fcluTbJ3Unu\nSnJVd286yrCrkjw6POf+JL9wiGs+meSmJLcmeXzW+SuGjSO3ZF+Qfn+S25L84P4NIBfwHj+efau7\nN2VfP/I/G86/ec4z577zZ5Lcl32ruf0/CQAA81LdR/t2IgAAwPxU1UlJru7u9026FgAAlhZhNgAA\nAAAAo+crfQAAAAAAjJ4wGwAAAACA0RNmAwAAAAAwesJsAAAAAABGT5gNAAAAAMDoCbMBAAAAABi9\n/wMCBPWR3GRvdAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a1103f0d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Evaluating decent cluster option for KMeans\n",
    "ks = range(1, 6)\n",
    "inertias = []\n",
    "\n",
    "for k in ks:\n",
    "    model = KMeans(n_clusters = k)\n",
    "    model.fit(grain_samples)\n",
    "    inertias.append(model.inertia_)\n",
    "    \n",
    "# Plot of ks vs inertias\n",
    "plt.plot(ks, inertias, '-o')\n",
    "plt.xlabel('number of clusters, k')\n",
    "plt.ylabel('inertia')\n",
    "plt.title('KMeans Optimal Cluster')\n",
    "plt.xticks(ks)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "varieties  Canadian wheat  Kama wheat  Rosa wheat\n",
      "labels                                           \n",
      "0                       2          60          10\n",
      "1                       0           1          60\n",
      "2                      68           9           0\n"
     ]
    }
   ],
   "source": [
    "#Comparing present clusters to the grain varieties using cross-tabulation\n",
    "model = KMeans(n_clusters = 3)\n",
    "labels = model.fit_predict(grain_samples)\n",
    "df = pd.DataFrame({'labels': labels, 'varieties': varieties})\n",
    "\n",
    "# Creating crosstab using labels and varieties from the dataframe\n",
    "ct = pd.crosstab(df['labels'], df['varieties'])\n",
    "print(ct)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hierarchical clustering of the grain data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a115fce50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calculating the linkage\n",
    "mergings = linkage(grain_samples, method='complete')\n",
    "\n",
    "# Plotting the dendrogram using varieties as labels\n",
    "dendrogram(mergings, labels=varieties, leaf_rotation=90, leaf_font_size=5)\n",
    "plt.rcParams[\"figure.figsize\"] = (25,12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Extracting cluster labels for intermediate clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "varieties  Canadian wheat  Kama wheat  Rosa wheat\n",
      "labels                                           \n",
      "1                       0           0          47\n",
      "2                       0          52          23\n",
      "3                      13           1           0\n",
      "4                      57          17           0\n"
     ]
    }
   ],
   "source": [
    "labels = fcluster(mergings, 6, criterion='distance')\n",
    "\n",
    "# DataFrame with labels and varieties as columns\n",
    "df = pd.DataFrame({'labels': labels, 'varieties': varieties})\n",
    "\n",
    "# Creating a crosstab to count the number of times each grain variety coincides with each cluster label\n",
    "ct = pd.crosstab(df['labels'], df['varieties'])\n",
    "\n",
    "# Printing ct\n",
    "print(ct)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# T-SNE Visualization of dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RyiTTNDX8rhEK5hd+8iSYH9Lr97xn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TIwQrPR5K6b7+GGK27mrf/3el5w9HPSjtdRofh02OIKqF3ZKkAXnkrI9KYda0YKmdnE3E7QuGnU\nTK51an2SSiq/goGPQ/IAkCP2HE6Y9V+PuBi9KSEEyO/WkbWl8bAdhyRJkiRJ2qDvfuIchldXaDaa\na8eqw1W+8p7v0Khv5HTqNBFCkVB8JqH0HAvQKQtzTlrTq7u4ZqQMmYWEvnemGWuDYu1PsOrdkNxL\n6yT3CAyfRVz90bSjSV1nEVqSJEmSJG3QXy75G0kzGTOeNBPuufW+FBJppgr53QgLfwl9b4HSS2DW\n+wgLf07ILko7Wltx8DRgZNToCFTOJyaDaUSSUmM7DkmSJEmStEELtp7Hvf+6f8x4o95kzsJZKSTS\nTBayCwl9x6YdY/M0bms/HnKQ3A+Zvq7GkdLkSWhJkiRJkrRBh7/vUIo9xfXG8sUc+zx/L+YsnJ1S\nKmkKyO9B+9JbAtltup1GSpVFaEmSJEmStEFPe3E/R33yVZT6SvTMKpMv5XnS8/bifd95e9rRpEkt\n9L0dQnHUaBl6jyGEUiqZJqMYI7HyE5KlB5Pc92SS5W8i1m9+eGs07yVWf09s3NmhlBqvEGNMO8Na\n/f39ccmSJWnHkCRJkiRJo1QrVe7+x73M23IO87acm3YcaUqI9euJA5+G+nWQWdAqQJdfSggh7WiT\nRjL4VRg8DaisGQkQyoQF5xByO2302RgbxFUfgJGftQr+sQbFpxHmnmqhvwtCCFfHGPs367UWoSVJ\nkiRJkiR1W4xV4v1PgTg8aiYDpReQmfu5jT6fDH4RBr/M+hdAFqF8KJk5H5/ouBrl4RShbcchSZIk\nSZIkqfuadwHtToUnULt2088Pf5f1C9AAVaj8mBib48+nCWMRWpIkSZIkSVL3ZRZBrLefyy3e9PPJ\n4AYm6oBF6MnEIrQkSZIkSZKkrguZ2VB6ETC6f3OJ0PuWTS9Q2Ie2J6lzOxNCYQISaqJYhJYkSZIk\nSZKUijDnY1A+FCgCBcgshDknEYpP3fSzs98PoRfIrxnJAmXC7I91LrAekVzaASRJkiRJkqaSGGsw\n8kti/XpC7lFQehEh05d2rLViMgShSAiWfTT5hVAgzPkYcfYHW+01MvMIYfPOzYbcTrDwQuLQt6D+\nV8jtQuh9PSH36M6G1sPmn0aSJEmSJEmbKSYriMteDskDEIeJlGHgZFhwFiG3Q7rZqn8grv7Imsve\ncsTySwmz308IxVRzSZsjhCJkH/7XashuTZj9gQ4kaonVK4lDX259XxX6Cb3HEnLbd2y/6cp2HJIk\nSZIkSZspDpwMzXsgDq8ZqUBcRVz13+nmqt9AXPFmaN5O60K2KlR+RFz5X6nmkqayZPh84opjoPYH\naN4BlfOJyw4lNm5LO9qUYxFakiRJkiRpc41cBDRGDUaoX0dMhts90RVx6KtAbdRoFaoXE5tL04gk\nTWkxNmHgf4DKOqPN1icgBk9NK9aUZRFakiRJkiRps2U3PLWZfWw7onErkIwdD0Vo3t31ONKU1/w3\nxGqbiQRqV3U9zlRnEVqSJEmSJGlzlQ8BCqMGs1B4CiGU0kjUkn8CbQvksQpe0iY9fJm5tFrbtJtb\n1NUo04FFaEmSJEmSpM0U+o6H3C4QeoA8hF7IbEmYc2K6uXqPgTFF8DL0vJKQmZtKJmkqC5k+KB0E\njL4ssUzoOyaNSFNaLu0AkiRJkiRJU0XI9MKCc6D2R2jcBNnFUHwmIaRbYgm57WH+WcSBk6B+NYS5\n0Pt6Qs+RqeaSprIw5xPEWIfqJRDyQAJ9xxFKz0872pQTYoxpZ1irv78/LlmyJO0YkiRJkiRJklIU\nYwLVy4i130NmIaF8KCG7VTpZkuXQfABy26fbdmeSCSFcHWPs35zXehJakiRJkiRJ0qQRY524/Cho\nXAdxGCgQB78I875AKO7f9TwhMx8y87u+73RiT2hJkiRJkiRNajFWiNU/EuvXM5k+1a/OiMPnQuOv\nawrQADVghLjyXa32GJpyPAktSZIkSZKkzRKb9xIrP4bmfYTiM6B4ACFkO7pnMnweDJwAZIEEMgth\n3tcIuR06uq9SNHI+xEqbiQTq10Fh765H0vhYhJYkSZIkSdImxerviSuOBZpAjThyHuR2gflnEEKh\nM3vWb4DVHwFGHhps3klc/lpY9BtC8EP+01LIb2Ai2cicJjO/UyVJkiRJkrRRMTaJK98FVGi1RqDV\nKqF+I3H4B53bd/jMh/Z7aBTiANSXdGxfpSuUDwfKbSZmQe7xXc+j8bMILUmSJEmSpI1r3MjYYjDA\nCFTO79y+yQNA0mYiQLKyc/sqXaUXQPlgoAQUIfRCmE2Y92VPv09RtuOQJEmSJEnSJuSBDVwI2KFW\nHACh+Gxi9Q+0TmCvI9Yh/6SO7at0hRAIc04k9h4NtT9CmAelZxNCKe1oeoQsQkuSJEmSJGnjco+F\nML/VgmNdoUzoeVXn9i0fAsNnQOM2HuoLXYa+NxKyCzq3ryaFkNsJcjulHUMTwCK0JEmSJEmSNiqE\nAPO+RFz+GqAOsdmaKB4EpRd1cN8iLDiLOHwOjPwcMrMJPa8mFPfr2J6SJp5FaEmSJEmSJG1SyO8C\nW/wOqpdCsgzy+xDyO3d+31CGniOgsCfUbwAyxJjYG1iaQixCS5IkSZIkabOEUIDSQV3dM8Yqcfkb\noXEtxAghC5lFMP97hOyirmaR9Mj4lpEkSZIkSZImrTh4GtSvgVgBRiAOQfMu4qr3px1N0mayCC1J\nkiRJkmaUlUtXce1l13Pf7UvTjqLNUfkRUB012IDaH4ixkkYiSQ+T7TgkSZIkSdKMkCQJpx3/TX7+\njUsoFPPUq3X2PGB3Pnz2uyj3ltKOpw2JtY3MNSF0L4qkR8aT0JIkSZIkaUY4/7SL+MW3fkN9pM7Q\nqmFqI3WuvfRvnPrWr6cdTRtTeh5tz1HmdiVk+roeR9LDZxFakiRJkiTNCOd+7kKqw+u3daiN1Lns\nrD9QG9nIaVulKvS9CzJbAOU1IyUIswhzTkwz1owSY41YuYBk5TtIVn+C2Lgl7UgPS4yR2LyfmAym\nHWXGsh2HJEmSJEmaEQZXDbUdjzFSrdQolApdTqTNEbILYNHPoXIhsX4NZHck9PwHITMv7WgzQoxV\n4rL/hMatwDCQJQ6fTZzzSTLlF6Udb5Ni9YrWJZbJMiAhFvcjzDmJkJmbdrQZxZPQkiRJkiRpRtjz\nWY8nZMY2EF647Xz65vamkEibK4QyoedlZOb8D5m+oy1Ad1EcPgca/6BVgAZoAiOw+kPEOJJisk2L\njX8SV74ZkntoXW5Zh+rlxBVvTDvajGMRWpIkSZIkzQhvOOkIemaVyeWzAGSyGYo9Rd75lWMIwdvt\npLZGLgTaFZszUP9rt9M8LHHoO20utqxD/WZi/e+pZJqpbMchSZIkSZJmhO123pqvXXcy55z8E274\nw99ZvOu2vPzdL2aHPR6VdjRp8gobuvwxgdDT1SgPW/NftE5ujxKy0LwH8rt0PdJMZRFakiRJkiTN\nGIu2W8BbTn5d2jGkKSP0vIpY/yPEyqiJuZB7fDqhNlfhyVD7M61WHOuINcg/LpVIM5XtOCRJkiRJ\nkiS1V3wWlF8DFIFeCL2QWUiY//VJ38Ym9PwnZPqA7DqjZSgfSshulVasGcmT0JIkSZIkSZLaCiEQ\nZr+H2HsE1JZAZi4UnkoIk7+sGDLzYMF5xMH/g+plrdYiPUe2itPqqsn/1SJJkiRJkiQpVSG7FZRf\nlHaMhy1ktyLMOTHtGDOe7TgkSZIkSZIkSR3jSWhJkiRJkqRJJsYG1P4IcRAK+xAy89OOJEmPmEVo\nSZIkSZKkSSTWbyKueD3EkTUDDWLf28n0vSndYNI0EZPlMHIRxGEo7E/IPzbtSNOeRWhJkiRJktQV\ntWqdS753Ob//8VXMXTSbF73lIHbpf0zasSaVGJvEFUdDsmz9icHTiIUnEgr7pBNMmibiyKXElcev\n+bcGcCqx5+WEWR8ihJBmtGnNIrQkSZIkSeq42kiNd+z7Ie78+z2MDFUJmcClZ/2et3zudbzwjc9N\nO97kUf9z63TmGCPE4TMtQkvjEJNh4qp3AiPrjDagcg4UD4Ti09KKNu15MaEkSZIkSeq4X3z7N9x5\nU6sADRCTSHW4xpfe8W2GByopp5tE4hDQ7jRmhGR1t9NI00vtD7T9/ooVYuXHXY8zk1iEliRJkiRJ\nHXf5j65kZLg6Zjybz3LDFTenkGiSyvdDrI8dD2VC+eDu55GmlbiRuaRrKWYii9CSJEmSJKnjZs3r\nbTsek0jP7HKX00xeIdMHsz8ElHiobNMDuV2h9KIUk0nTQOFpENsUm0MPofyS7ueZQSxCS5IkSZKk\njjvk2OdT7CmuNxYCzJrfx65P3imlVJNTpudwwoIzofwKKB5EmPNxwvzvEkIh7WjTXkxWkAycQvLA\nYSQr3kys/jHtSJpAIdMHcz5N602eAq3SaAlKL4TCM9INN82FGDd2DH0TD4fwcuAE4HHAk2OMS9aZ\nez9wNNAEjosx/mJT6/X398clS5Zs6mWSJEmSJGkKOuvTP+Y7J5xNrpAjxkjP7B4+/av/x/a7bpt2\ntNTEGKH6K+LQ6RBXQ/G5hN7XETKz044248RkOfGBQyBZCdTWjJZh1vvJ9L4yzWiaYLF5L4z8vHUJ\naHF/Qn6PzXuufgNx4BRoXA/ZxYS+txOKM7d4HUK4OsbYv1mvHWcR+nG0GqZ8BXjPg0XoEMJuwJnA\nk4FtgF8Dj40xNje2nkVoSZIkSZKmt9XLBvjb726ib14vu++7K5nMzP6QdjJwCgx9C3jwcsYCZLcg\nLLigdWpTXZMMfHbN70Vt/YnQQ9jiSkIopZJrJolrWmWEMPn+XIj164jLjgBGeKi3dAnmnEim/MIU\nk6Xn4RShx/U7GmO8Mcb49zZTLwF+EGOsxhj/BdxCqyAtSZIkSZJmsNkLZvH0l+zDE/bfbcYXoGOy\nHIa+wUMFaIAaNB8gVs5JK9bMVb2MMQVoADLQ8PLMTorNB0hWvJV43+7E+x5PsvwNxOa/0461njjw\naVrfq+se6B2BgU8ynkO+M0Wn/rTfFrhznX+/a82YJEmSJEmSAGrXQsi3mRiB6m+6nUaZhe3HYx3C\nvO5mmUFibBCXHw7VS4EG0ITa74nLXkaMI2nHe0j9+vbjycpWKx1t1CaL0CGEX4cQ/tbmx8aujAxt\nxtq+JRBCeFMIYUkIYcnSpUs3N7ckSZIkSdLUll1Iq8vpaBnIbt3tNDNe6D0KKI8azUF+N0JucRqR\nZobqZZAsp1WAflAT4hCMXJRWqrEyizYwkYPQ09UoU9Emi9AxxgNjjLu3+XH+Rh67C1j3u3M74J4N\nrP/VGGN/jLF/0aIN/WZKkiRJkiRNM7ndIbM1kB01USD0vCaNRB0XY4Nk4BSS+55Ecu8uJA/8B7F2\nTdqxAAjFfWHWu4AyhD6gBPndCXO/mHa06a35L4jVseNxmNi4tft5NqT3WMa+SVGCnv8ktP1Eg9bV\nqXYcFwCvDCEUQwg7ADsDV3VoL0mSJEmSpCknhECY/y3I7QqUIPRCmAVzTiTkd0s7XkfE1R+BoW9C\nHAAiNP5GXP46Yv0faUcDINP7WsIWfyDM+xph4U/ILDibkF2QdqzpLbczhOLY8dBDyO3S/TwbkOl5\nCcw6fs33aRkoQs/LCbPenXa0KSE3nodDCIcBnwcWAReGEP4SYzwoxnh9COFs4AZaZ+nfGmNsjj+u\nJEmSJEnS9BGyWxEWnkds3NEqzOZ2JoRC2rE2KDbvJw5/G6p/gtyjCb1HEfKP27xnk+VQuQAYfeq1\nShz6MmHuZyc67iMSMr1QeFLaMWaOwr6Q2QqadwD1NYM5CHOh9Lw0k42R6T2K2HMEJEshM58QRp+M\n1oaEyXR7Y39/f1yyZEnaMSRJkiRJkjRKbNxFXHYYxGFaxcIMUCTMO5VQfOamn69dS1zxeoiDYyez\nO5NZdOFER9YaMVaIg5+H4XOBJpSeR5j1bkJmftrRAIjJKuLASTDyc4gJlA4kzPoAIbuByyI1KYQQ\nro4x9m/Oa8d1ElqSJEmSJEkzQxw8ZU0bjQcvU0yACnHVh2HRZYQQNr5AbjHEepuJDEzT9iOTQYyR\nuPx1UL+BtafQK+cRa1fAwp8T2rXC6LKQmUOYcyLMOTHtKOqQTvWEliRJkiRJ0nRS+z0PFaDXkayA\n5DoBwDcAAB1rSURBVP5NPh4y86F8CFAaNVMk9B0zEQnVTv1qaPyd9dugNCBZ3jp5LHWBRWhJkiRJ\nkiRtWpizgYmkdVnb5iwx+6PQ+4Y1a2Ugtzth/umE3E4TFlOj1G+Edle1xWFi7W/dz6MZyXYckiRJ\nkiRJ2rSeo2DwfyBW1hksQPEAQqZvs5YIIUeYdRzMOq4zGTVWbjGEHMTRF0KWIffoNBJpBvIktCRJ\nkiRJkjYp9Lwcyq8EihBmtf5Z6G/18tXkVdgPMvOA7DqDAUKeUD4krVSaYTwJLUmSJEmSpE0KIRBm\nv5/YdwzUb4bsNoTc9mnH0iaEkIX5PyCuej/UrgAi5HcnzDmJkJmddjzNEBahJUmSJEmStNlCZj4U\nn9qx9WOsEQe/CJWzWy0kis8izHovIbtVx/ac7kJ2C8L8bxDjCMQmIbN5PbyliWIRWpIkSZIkSZNG\nXPlWqF4JrOlhPPIzYu0KWPgLQmZWqtmmuhBKENJOoZnIntCSJEmSJEmaFGL9Zqj+kbUFaACakAwR\nK+c88nVjg2TodJKlzye5/1kkqz9FTFaPO+9EiM1lxOrviY1b0o6yUbF+PXHom8TKj4nJUNpxNMV4\nElqSJEmSJEmTQ+MmCFmIoycqUP/LI142rnwnVC8DRloDw2cQq7+GhT9pnQ5OQYyROHASDH8PQhFi\nnZjfhTDvq4TMvFQytRNjQlz1bhi5GGgCeQgfg/nfJuSfMLF7NZdB7XIg12rDkumb0PWVHk9CS5Ik\nSZIkaXLIbk+bCjRQgOxOj2jJWP/H+gVoAGqQ3A+VCx/RmhNi5Mcw/INWljgAjED9euLKd6eXqZ2R\nn0D1Elq/fnVgGOIgccWxxJhM2DbJ0PeJS59FXHUCcfWHifc/gzhy6YStr3RZhJYkSZIkSdLkkN8T\nso8C8uuPhzyh5/BHtmb9Oto2Qo4VYu2qR7bmBIhD3wYqo0YbULuKmKxIIVF7cfiHEEfnBOIgNG6c\nmD0at8LASbTasAxDHAIqxJXHT5q2KRofi9CSJEmSJEmaFEIIhPmnQ/EAWl1ks5DbjTD/e4TsFo9s\n0eyWENqVwAqQXTyOtOOUrNrARBaSga5G2bjGBsYDxA3NPTyx8pMN7JOB6sUTsofSZU9oSZIkSZIk\nTRohM5cw7wvEWINYJ2R6x7dg4amQmQfNCrBO+4iQI/S8bHxrj0fxmVD5IWOKr5leyG6XSqS2Sv8B\n9RsZe2q7APndJ2aPOEKr3/RoCcRqm3FNNZ6EliRJkiRJ01ZMlhNHLiHW/kKM7XoNa7IKoTD+AjQQ\nQpYw/3utVh8UgCJktyPM+wYhu9W413/EufreCpm5azJBq0xXIsz+BKHtye10hJ7DoPBECD1rRooQ\nyoS5pxBCdmL2KB0ItLsgMmkV6zskGb6AZOmzSe59HMnS5xFHftmxvWY6T0JLkiRJkqRpKRk4FYa+\nCqEAJJBZBPO+RchNolOm6oqQ3Zqw4CxicxlQhczWhNCmT3RXM20BC39KHPoe1K6E3GJCz+sI+V1T\nzTVaCHmY902oXUGsXUnILIDSiwnZBRO3Sf5JUD4YRn625lR0AArQdywhu/XE7bOOZPhcWH0Cay+s\nbN5GXPkemHvymqK4JlKYTO8C9vf3xyVLlqQdQ5IkSZIkTXFx5FLiqneMulAtA9nHkFl0YWq5pqLY\nvJc48CmoXgrkoHwYoe+dhEzPJp+VNleMsXUp48jPIBQI5UMJ+cd3bL/k/n0huX/sRHZHMosu6ti+\n00kI4eoYY//mvNaT0JIkSZIkadqJw2eMKkADJNC8i9i4hZDbKZVcU01MhojLXgrJctb27B0+k1i/\nDuafmfppYk0fIQQoPoVQfErH94qx0b4ADdC8s+P7z0STp8GMJEmSJEnSRElWtR8PWUgGu5tlCouV\n89f8eq17aVwNGjdB/dq0YknjEkIOMgvbT3ao/cdMZxFakiRJkiRNP6XnAcU2ExHyj+t2mqmrcT0w\n+kQ5ECM0/t71ONKE6T0OKI8aLEHfu9JIM+1ZhJYkSZIkSdNO6Hk1ZLcBSmtGMq2fzzqBENoVp9VW\ndice+jVcRwiQfXS300gTJtP7Spj9wdaFpQCZrWH2J8iUD0432DRlT2hJkiRJkjTthEwfLDiPWDkX\nqr+B7CJCz2sI+d3SjjalhJ7DiEOnQawCcc1oDrLbQuHJaUaTxi3T8wroeQUxJoTgWd1OsggtSZIk\nSZKmpZDpIfQeAb1HpB1lygqZubDgLOKqD0P9z0AGigcS5nzUSwk1bViA7jyL0JIkSZIkSdqgkHsM\nYcH3ibEGZFqXum1AjCPQuBnCfEJuu+6FlDSpWYSWJEmSJEma5GKsQfVSaN4F+T0gv0/XTyKHUNjo\nfDJ0Jgx+CshArBPzuxPmnUbIzO9OQEmTlkVoSZIkSZKkSSw27iQufxXEIYg1CHnI7QLzTyeENpcG\npiBWr4CBk4DKQ4P1a4kr3kpYcGZquTR1xeY90LgdcjsSslumHUfjZMMTSZIkSZKkSSyuei8kD7SK\n0NQhDkP9BuLgl9OOtlYc+ibrFaABaED9b8TGnWlE0hQVY41kxduISw8irnwbcelzSFa+hxgbaUfT\nOFiEliRJkiRJmqRisgrq1wHJqJkqVM5NI1J7yf3tx0MekuXdzaIpLQ58GqqXAVWIA0ANRn5JHDwt\n7WgaB4vQkiRJkiRJk9bo4vPmznVZcT+gTc/o2ITczl2Po6kpxgjDPwSqo2ZGYPh7aUTSBLEILUmS\nJEmSNEmFzDzI7QSMvoQwD6UXphGprdB7FGRms14hOpRh1rsJmZ7UcmmqSYCR9lNxqKtJNLEsQkuS\nJEmSJE1iYc5nIMwCymsGeiD7KELf21LNta6QmU9Y+FPofS3kHguFfQlzv0im98i0o2kKCSELud3a\nT+af2N0wmlAhxph2hrX6+/vjkiVL0o4hSZIkSZI0qcRkEEZ+SmzcQSjsCcVnE0I+7VgzRmzeTRw4\nBWq/hzAbeo4i9LycEEafUNd4xdq1xBWvhVgFmkAeQoEw/0xCfteJ2ydZDdVfQxyBwv6E3HYTtvZM\nEUK4OsbYv1mvtQgtSZIkSZIktReb9xMfeOGaS/LW9OEOZSgfTmb2B1LNNl3Fxu3EoW9A4ybI7UHo\nff2EFolj9XLiirfRanOTABH6jiEziT5dMBU8nCJ0rtNhJEmSJEmSpKkqDp8OcZj1LoKMFRg+k9j3\nZkJmfmrZpquQexRhzsc6snZMhokr3w5U1p8Y/CqxsC+hsFdH9p3p7AktSZIkSZIkbUjtKqA+djwU\noH5z1+NonGqX074kWiVWzut2mhnDIrQkSZIkSZK0IdlH07aEFmuQ3abbaTResQ60a08cgVqXw8wc\nFqElSZIkSZKkDQi9RwGFUaMFKOxNyG2fRiSNR3FfiI02E2VC6YVdjzNTWISWJEmSJEmSNiDkH0eY\ndypktgSKQB6KBxDmnpZ2ND0CITMXZn+E1u9lDgitiyZLB0HhGSmnm768mFCSJEmSJEnTQqzfALWr\nIbsIis8mhNEnmB+ZUHwWLPotJPdD6CVk+iZkXaUj0/MyYqGfWLkA4hChdCDk+wkhbPYaMUaIK4Ai\nIdPbubDThEVoSZIkSZIkTWkxNokr3wHVy4AIIQcUYP53CfmdJ2SPEAJkt5yQtZS+kHs0YdZxj+jZ\nWFtCXPUBaN4DRGJxP8Kck1qnrNWW7TgkSZIkSZI0pcXhc6D6W2AEqEIcgriSuPKtrROr0gSJjTuJ\nK46G5m20LjKsQ/Vy4vKj/FrbCIvQkiRJkiRJmtoqZwGVUYMRmveuKRZKEyMOf6/NxYZ1aN4KjRtS\nyTQVWISWJEmSJEnSFFdvPxwybQqG0jg0/kn7r7csNO/udpopwyK0JEmSJEmSprbSoUBp7Hjog9xj\nxr18jE2SodNJlj6X5P59SVadQGwuG/e6moIKTwKKY8djHXKP63qcqcIitCRJkiRJkqa00PtqyD8W\nQs+akSKEHsLczxHC+MtfcdV/wcDJ0LwdkvuhcjZx2WHEZHDca2tqCT2vhMwsILvOaAlKzyPkFqcV\na9LLpR1AkiRJkiRJGo8QSjD/B1D9DbH2R8hsSSgfSsguHPfasXE7jPwSqK4z2oBkFbFyLqH3yHHv\noakjZObAgnOJg6fAyKWQ6YXyEYTe16YdbVKzCC1JkiRJkqQpL4QclA4klA6c2IXrf6NVQquOmqhA\n7SqwCD3jhOxWhDknwZy0k0wdtuOQJEmSJEmSNiS7DYTYZiIPuUd3O400JVmEliRJkiRJkjYkv1er\nED26oUDIEcqvTCWSNNVYhJYkSZIkSZI2IIRAmPcdKOwD5IEiZBcT5n2dkNsu7XjSlGBPaEmSJEmS\nJHVcbNxGHPgs1K6EzBzoOYrQ8ypCCGlH26SQXUiYfzoxWQVxBDJbTInc0mRhEVqSJEmSJEkdFZv/\nJi57KcQhIIHmKhj4FLH5L8LsD6Ydb7OFzBy8jU56+GzHIUmSJEmSpI6KQ1+HWAGSdUYrMHwmMVmR\nVixpo2LjVpKBz5Ks+gixejkxJpt+SG15ElqSJEmSJEmdVbsGaIwdD0Vo3AqF/q5HkjYmGf4RrP4o\nra/bBnHkfCg8DeaeRgie6324/BWTJEmSJElSZ+V2oG0ZKtYgu03X40gbE5MBWH0CMMLaN0/iMFSv\ngOrFKSabuixCS5IkSZIkqaNC7xuAwqjRIhSeSrAIrcmmdgWEfJuJYeLIhV2PMx1YhJYkSZIkSVJH\nhfzjCPNOg8w2QB4oQOn5hLn/l3Y0TVFJ5UKSpQeR3PsEkgcOI1avmLjFQ3FDExBKE7fPDGJPaEmS\nJEmSpBkm1pYQB78Mzbug8CRC75sJucUd3TMU94NFl0JcAaGHYDFPj1AyfBas/h9a7TKAxvXEFcfA\nvK8Sik8d/waFpwGhzUSJUH7Z+NefgTwJLUmSJEmSNIMklZ8Tlx8Ftd9C859QOZe47CXExm0d3zuE\nQMjMtwCtRyzGBAZOZm0Beq0R4uBnJmSPEAqEeV+G0Nv6QRko/v/27jbG0rI+A/j1P2d2dmdnl+0C\nC6KAYIMfVAilW6MtUo3U1/rammhtJdUqWF9C1BqNJjW0tbapNqnaqlSD1VK1NVTqa6tWbH2pYAUF\nkQIWRSEg8s7uzuzM3P0wA12W2QXZeeZhz/n9kpM5c9/nPHN9uOfJmWufvZ9k+iUpN9G8X1wJDQAA\nADAmFgu8M3L3Am8+advSbvvL1GbbY/AA1+5I2m3Lz81duWI/piZ/KdnylWTmS4s/c+2JqeFhK3b8\ncaOEBgAAABgXC9cnC3csN5Hs/Maqx4GfWa1f3Je53X7PuRW+yWUN1idTT1vRY44r23EAAAAAjIva\nmGRh+bnBwasaBe6PqmEy/dKkpnabWZfacHovmbh3SmgAAACAMVGD6WTdU5Os3W1iKjV9ai+Z4GdV\n06cl07+/9I8qw2SwJTngjNS6X+s7GntgOw4AAACAMVKbzkhrO5KZf09qMmlzyfSpybqn9x0N7pOq\nSm04NW36pUlmkqxLVfUdi71QQgMAAACMkaqp1OZ3ps3fsLhH9PChi1dIw36mapBk9205eCBSQgMA\nAACMoRoenAztAw10z57QAAAAAAB0RgkNAAAAAEBnlNAAAAAAAHRGCQ0AAAAAQGfcmBAAAAAAGCtt\n7upk7pJkcFiy5rhUVd+RRpoSGgAAAAAYC63Np93yxmTHZ5KaSNKS4RHJ5rNSw4P6jjeybMcBAAAA\nAKyo1nambf9kFm5+bRZufWva3BV9R0qStG1nJzs+l2QmaXckbVsyd2XaLa/rO9pIcyU0AAAAALBi\nWptNu/GFyc7Lk2xLMkzb9pG0TW/NYOrX+w237UNJtu82OJfMfiNt4ZbUYFMfqUaeK6EBAAAAgBXT\ntn082fk/WSygk2Q+yY7k1jentR09Jsvilc/LGiRt93KalaKEBgAAAGDktPkb0nZ+J23htr6jjJ8d\nn8o9rzZOkkEye9Fqp7m7tU/MsptDDLckg0NXPc64sB0HAAAAACOjtZm0m1+fzHwhqcmk7Uxb/6LU\nxtelqvqONx4GG/YwsZAMplY1yu5qw6vSZr6YLNySZEeSNUkmUpveZn10SAkNAAAAwMhot/5JMvPF\nJLNJm10c3PbhtOHhqekX9JptXNT6F6TNfu2e21vUpmTiUf2EujPC8ODk4E+nbfvHZOf5yfChqfW/\nlZo4stdco04JDQAAAMBIaG022X5OkpndZrYn2/42UUKvjsmTkqnfSbadlWQiqUqyNrX5zFT1vztw\nDTamNrw4yYv7jjI2lNAAAAAAjIa2PcnC8nMLN61qlHFWVakDXpc2/dvJ7PnJYFMy+dhUrek7Gj1R\nQgMAAAAwGuqAZHBIsvDj3SeSNVt7iTTOavigZOoZfcfgAaD/698BAAAAGFutzaft+EwWbnp5Fm56\nddrMeWmt3a9jVVVq01uSrEty503mhkmtT238gxVKDPysXAkNAAAAQC9aa2k3vyqZ/cpdN7FrM+cl\n65+XOuDN9+uYtfZXk4M+nHb7e5O5q5LJ41LTL3fjOeiREhoAAACAfsx+PZn96l0F9KLtybaPpq1/\nYWri6Pt12FpzXGrzu1cmI7DPbMcBAAAAQC/azJeTtm35yZn/XN0wQGeU0AAAAAD0Y3BAkjXLTAyT\nwcbVTgN0RAkNAAAAQC9q6llJhstMJFl78mrHATqihAYAAACgFzV8cLLpL5Jan9SGpccBqc1npgYb\n+o4HrBA3JgQAAACgN4OpJ6Wte1wye36SiWRya6om+44FrCAlNAAAAAC9qppK1p7UdwygI7bjAAAA\nAACgM0poAAAAAAA6o4QGAAAAAKAzSmgAAAAAADqjhAYAAAAAoDMTfQcAAAAAgP1B23lpsvOiZPig\nZPLEVKnW4L7wmwIAAAAAe9HazrSbX5XMfHVxoIZJbUwOPDs1cXi/4WA/YDsOAAAAANiLdseHlgro\nHYuPdkeycH3azaf3HQ32C66EBgAAAIC92f7RLBbQu1pI5r6XNn9DanhwH6n2WZv/adq29yc7zkuG\nW1LTv5dae2LfsRhBSmgAAAAA2Js2u4eJSrKnuQe2tnBj2k+fkSzckmRnMn952uy30ja+JoPpU/qO\nx4ixHQcAAAAA7M3U05NM3nN8eGgyOGzV4+xJay2tzd+3197xgWTh1iQ7dxndntz2jrSFbZ3kY3wp\noQEAAABgL2r61GR4eFLrl0bWJrU+tentqapesyVJa7NZuPWP0647Pu26R2ThhmenzV609zfN/EeW\nvYq7hsnc5Z3kZHzZjgMAAAAA9qIGG5ODz012fDZt9vxkeHhq6jceMHtBt5tfm8x8KcnM4sDcd9Nu\nelFy0CdSE0ct/6bBIUkuXeZgO5PBgd0EZWwpoQEAAADYr83Pz+eCz16Yqy+7Jkc96siccPKxGQxW\ndgOAqslk6pmpqWeu6HH3VZu/9u4F9F0Ts2l3vD+16Y+WfV9NvyRt9r9y9xsuTiRrHpWaOKKjtIwr\nJTQAAAAA+62brr8lp5/45tx03c3ZObMzaybX5EFHH5J3nHdGNvzcdN/xujf3g6Qmk7ZbCZ35ZO57\ne3xbrX1M2sY3Jrf/WZLB4hXQa45NbX5Xp3EZT/aEBgAAAGC/9VcvPzPXXfWTbL9tR+Zm57P99h25\n+rJr8r7Xf6jvaKtj4uhlCugkmUgmjt3rWwfTL0gd8vXUgR9MbflsBgednbIVBx3YpxK6qp5XVZdU\n1UJVbd1l/Kiq2l5VFy493rPvUQEAAADg/y0sLORr/3JB5ufm7zY+NzuXL330Kz2lWl01PDRZ99Qk\n63abWJuafvG9v7/WpdYcmxo+pJuAkH3fjuPiJM9N8t5l5q5srR2/j8cHAAAAgD1qrS07vjC//Pgo\nqk1/mjY8Itn290m7PZk8IbXxTamJw/uOBkn2sYRurV2aJFW1MmkAAAAA4D4aDAY54YnH5r+/8J0s\nzC/cNT6cGOaXn7l1L+8cLVUTqY2vTja+uu8osKwu94Q+uqq+VVXnVdXjOvw5AAAAAIyp0997ag44\naGPWbVjcjmJqw7oc9ODNOe0dp/ScDLjTvV4JXVWfT/KgZabe1Fr7xB7edm2SI1trP62qX0zyz1X1\nyNbarcsc/2VJXpYkRx555H1PDgAAAMDYO/ShW/J3V74r533sa/nhpVfnYccdlZN+8zGZXDfZdzRg\nyb2W0K21k3/Wg7bWZpLMLD3/ZlVdmeThSS5Y5rXvS/K+JNm6dev4bNYDAAAAwIqYml6Xp/zuE/qO\nAexBJ9txVNWWqhouPX9YkmOSfL+LnwUAAAAAwAPXPpXQVfWcqvpRkscm+VRVfW5p6qQk366qi5L8\nU5LTWms37ltUAAAAAAD2N/e6HcfetNbOSXLOMuMfT/LxfTk2AAAAAAD7v0624wAAAAAAgEQJDQAA\nAABAh5TQAAAAAAB0RgkNAAAAAEBnlNAAAAAAAHRGCQ0AAAAAQGeU0AAAAAAAdEYJDQAAAABAZ5TQ\nAAAAAAB0RgkNAAAAAEBnlNAAAAAAAHRGCQ0AAAAAQGeU0AAAAAAAdEYJDQAAAABAZ5TQAAAAAAB0\nRgkNAAAAAEBnlNAAAAAAAHRGCQ0AAAAAQGeU0AAAAAAAdEYJDQAAAABAZ5TQAAAAAAB0RgkNAAAA\nAEBnqrXWd4a7VNVPkvyg7xyMnIOT3NB3CFhl1j3jxppn3FjzjBtrnnFk3TNurPn9z0Nba1vuywsf\nUCU0dKGqLmitbe07B6wm655xY80zbqx5xo01zziy7hk31vxosx0HAAAAAACdUUIDAAAAANAZJTTj\n4H19B4AeWPeMG2uecWPNM26secaRdc+4seZHmD2hAQAAAADojCuhAQAAAADojBKakVVVz6uqS6pq\noaq27jJ+VFVtr6oLlx7v6TMnrJQ9rfmluTdW1RVVdVlVPbmvjNClqnpLVf14l/P70/rOBF2oqqcs\nnc+vqKo39J0HulZVV1XVd5bO7Rf0nQdWWlV9oKqur6qLdxk7sKr+raouX/q6uc+MsNL2sO59nh9h\nSmhG2cVJnpvky8vMXdlaO37pcdoq54KuLLvmq+oRSZ6f5JFJnpLkr6tquPrxYFX85S7n90/3HQZW\n2tL5+91JnprkEUlesHSeh1H3hKVz+9Z7fynsd87K4uf0Xb0hyRdaa8ck+cLS9zBKzso9133i8/zI\nUkIzslprl7bWLus7B6yWvaz5ZyX5SGttprX2v0muSPLo1U0HwAp5dJIrWmvfb63NJvlIFs/zAOyn\nWmtfTnLjbsPPSvLBpecfTPLsVQ0FHdvDumeEKaEZV0dX1beq6ryqelzfYaBjD0ly9S7f/2hpDEbR\nK6vq20v/vc9/W2UUOaczjlqSf62qb1bVy/oOA6vk0NbatUmy9PWQnvPAavF5fkQpodmvVdXnq+ri\nZR57uyLo2iRHttZ+IclrkpxdVQesTmLYN/dzzdcyY62rjNCle/kd+JskP5/k+Cye69/ea1johnM6\n4+hXWmsnZHEbmldU1Ul9BwKgEz7Pj7CJvgPAvmitnXw/3jOTZGbp+Ter6sokD0/iJic84N2fNZ/F\nq+SO2OX7w5NcszKJYHXd19+BqjozySc7jgN9cE5n7LTWrln6en1VnZPFbWmWu+8LjJLrquqw1tq1\nVXVYkuv7DgRda61dd+dzn+dHjyuhGTtVteXOm7JV1cOSHJPk+/2mgk6dm+T5VbW2qo7O4pr/Rs+Z\nYMUt/YF2p+dk8WadMGrOT3JMVR1dVZNZvPHsuT1ngs5U1XRVbbzzeZInxfmd8XBuklOWnp+S5BM9\nZoFV4fP8aHMlNCOrqp6T5J1JtiT5VFVd2Fp7cpKTkpxRVXNJ5pOc1lqzGT77vT2t+dbaJVX1sSTf\nTTKX5BWttfk+s0JH/ryqjs/i1gRXJTm13ziw8lprc1X1yiSfSzJM8oHW2iU9x4IuHZrknKpKFv9+\nPbu19tl+I8HKqqp/SPL4JAdX1Y+S/GGStyX5WFW9JMkPkzyvv4Sw8vaw7h/v8/zoqtZsIQcAAAAA\nQDdsxwEAAAAAQGeU0AAAAAAAdEYJDQAAAABAZ5TQAAAAAAB0RgkNAAAAAEBnlNAAAAAAAHRGCQ0A\nAAAAQGeU0AAAAAAAdOb/AMruoYoY3YDLAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a115f4b90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "model = TSNE(learning_rate = 200) #Instantiating a TSNE with learning rate of 200\n",
    "tsne_features = model.fit_transform(grain_samples)\n",
    "\n",
    "xs = tsne_features[:,0] #0th feature\n",
    "ys = tsne_features[:,1] #1st feature\n",
    "\n",
    "# Scatter plot, coloring by variety_numbers\n",
    "plt.scatter(xs, ys, c= variety_numbers)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Correlation between width and length of the grain samples data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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nG3jWM/NuSy9qk9vRAGUgYAYAAIASebdLeJ7+YKZ3KD99Zts/29H78vuHqCRJPBRFNPxO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\nSdJpt3Lv9s2lr5FY1clsAAAAAGA4HcwN2N3qLH2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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a115e1a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computed correlation value = 0.994340931012\n"
     ]
    }
   ],
   "source": [
    "# Assign the 0th column of grains: width\n",
    "width = grain_samples[:, 0] #width of grain samples\n",
    "\n",
    "# Assign the 1st column of grains: length\n",
    "length = grain_samples[:, 1] #length of grain samples\n",
    "\n",
    "# Scatter plot width vs length\n",
    "plt.scatter(width, length)\n",
    "plt.axis('equal')\n",
    "plt.show()\n",
    "\n",
    "# Calculating the Pearson correlation\n",
    "correlation, pvalue = pearsonr(width, length)\n",
    "print(\"Computed correlation value = %s\" % correlation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using PCA to decorrelate the grain measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qBHjIsuP1X/qT347/+Hj/0X/PcQUAgAgVzQBrsTDOah6rhHpqSm4bq8er5CYJ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\n55N8oe1aGJyPJnlLrfWtSX4lyY2W66HHSikbSf5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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a115f45d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computed correlation = -4.25484023037e-17\n"
     ]
    }
   ],
   "source": [
    "model = PCA() #PCA Instance\n",
    "\n",
    "pca_features = model.fit_transform(grain_samples)\n",
    "\n",
    "xs = pca_features[:,0] \n",
    "ys = pca_features[:,1]\n",
    "\n",
    "# Scatter plot xs vs ys\n",
    "plt.scatter(xs, ys)\n",
    "plt.axis('equal')\n",
    "plt.show()\n",
    "\n",
    "# Calculating the Pearson correlation of xs and ys\n",
    "correlation, pvalue = pearsonr(xs, ys)\n",
    "print(\"Computed correlation = %s\" % correlation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Using PCA to compute the first principal component from the grain measurement dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Computed mean of the grain sample = \n",
      " [ 14.84752381  14.55928571   0.87099857   5.62853333   3.25860476\n",
      "   3.70020095   5.40807143]\n"
     ]
    },
    {
     "data": {
      "image/png": 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uX0i1Uk6RpFop58rlCwPZMD7LLmmAUbDBDAAAAEy0k2wDH/fMSbelezXM7WiAcSBgBgAA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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1a12e6c390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatter plot of the untransformed points\n",
    "plt.scatter(grain_samples[:,0], grain_samples[:,1])\n",
    "\n",
    "model = PCA() \n",
    "model.fit(grain_samples)\n",
    "\n",
    "# Get the mean of the grain samples: mean\n",
    "mean = model.mean_\n",
    "print (\"Computed mean of the grain sample = \\n {}\".format(mean))\n",
    "\n",
    "first_pc = model.components_[0,:] #Extracting the first principal component\n",
    "\n",
    "# Plot first_pc as an arrow, starting at mean\n",
    "plt.arrow(mean[0], mean[1], first_pc[0], first_pc[1], color='red', width=0.01)\n",
    "\n",
    "plt.axis('equal') #Keeping axes on the same scale\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}